Finite Group Databasebeta

← C22×#10576178 #72282620

Subgroups — C22×#10576178 #72282620

Order 2048.

Only the 472128 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 1189 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#60644C211yesmaximal, characteristic, complemented
2C22×#60469C212yesmaximal, complemented
3C23×#3068C212yesmaximal, complemented
4C22×#60182C212yesmaximal, complemented
5C22×#61109C218yesmaximal, complemented
6C22×#61107C2116yesmaximal, complemented
7C22×#61106C2116yesmaximal, complemented
8C22×#60387C212yesmaximal, complemented
9C22×#63090C212yesmaximal, complemented
10C2×#10576178C21192yesmaximal, direct product factor
11C23×#3019C211yesmaximal, characteristic, complemented
12C23×#3021C211yesmaximal, characteristic, complemented
13C23×#3585C212yesmaximal, complemented
14C22×#61110C218yesmaximal, complemented
15C23×#585C2212yescomplemented
16C23×#585C2211yescharacteristic, complemented
17C24×H(5,𝔽2)C2211yescharacteristic, complemented
18C2×#63090C221192yescomplemented
19C22×#3584C22116yescomplemented
20C22×#3586C2218yescomplemented
21C22×#3586C2218yescomplemented
22C22×#3585C22116yescomplemented
23C22×#3585C22116yescomplemented
24C22×#3585C221192yescomplemented
25C22×#3585C2218yescomplemented
26C22×#3585C2218yescomplemented
27C23×#577C2218yescomplemented
28C23×#576C2218yescomplemented
29C23×#575C2212yes—
30C23×#575C2212yescomplemented
31C23×#575C2212yescomplemented
32C23×#575C2212yescomplemented
33C23×#575C2212yescomplemented
34C24×AGL(1,ℤ/8)C2212yescomplemented
35C24×AGL(1,ℤ/8)C2212yescomplemented
36C23×#568C2212yescomplemented
37C23×#568C2212yescomplemented
38C22×#3449C2211yescharacteristic, complemented
39C23×#535C2211yescharacteristic, complemented
40#10576178C2214096yesdirect product factor
41C2×#61110C221768yescomplemented
42C2×#61109C221768yescomplemented
43C2×#61107C2211536yescomplemented
44C2×#61106C2211536yescomplemented
45C22×#3292C22132yescomplemented
46C22×#3291C22132yescomplemented
47C22×#3290C22164yescomplemented
48C22×#3289C22132yescomplemented
49C22×#3288C22132yescomplemented
50C22×#3288C22164yescomplemented
51C2×#60644C22196yescomplemented
52C22×#3155C2218yescomplemented
53C22×#3153C2214yescomplemented
54C22×#3154C2218yescomplemented
55C22×#3151C2214yescomplemented
56C23×#472C2218yescomplemented
57C2×#60469C221192yescomplemented
58C22×#3069C2218yescomplemented
59C22×#3069C2218yescomplemented
60C22×#3068C2218yescomplemented
61C22×#3068C2218yescomplemented
62C22×#3068C221192yescomplemented
63C22×#3068C22116yescomplemented
64C22×#3068C22116yescomplemented
65C22×#3067C22116yescomplemented
66C23×#471C2218yescomplemented
67C22×#3022C2218yescomplemented
68C23×#455C2214yescomplemented
69C2×#60387C221192yescomplemented
70C22×#3018C22116yescomplemented
71C22×#3021C22116yescomplemented
72C22×#3021C2218yescomplemented
73C22×#3021C22196yescomplemented
74C22×#3020C2218yescomplemented
75C22×#3019C22116yescomplemented
76C22×#3019C22196yescomplemented
77C22×#3019C2218yescomplemented
78C23×#454C2214yescomplemented
79C23×#453C2214yescomplemented
80C23×#453C2214yescomplemented
81C2×#60182C221192yescomplemented
82C22×#2957C22116yescomplemented
83C22×#2956C22116yescomplemented
84C22×#2955C22116yescomplemented
85C23×#430C2212yescomplemented
86C23×#413C2211yescharacteristic, complemented
87C23×#413C2212yescomplemented
88C23×#421C2212yescomplemented
89C23×#421C2212yescomplemented
90C24×#100C2211yescharacteristic, complemented
91C22×#2873C2211yescharacteristic, complemented
92C22×#585C2318yes—
93C22×#585C2318yescomplemented
94C22×#585C23196yescomplemented
95C22×#585C2318yescomplemented
96C22×#585C23148yescomplemented
97C23×2−1+4C2314yescomplemented
98C23×2−1+4C2312yescomplemented
99C23×H(5,𝔽2)C2314yes—
100C23×H(5,𝔽2)C2314yescomplemented
101C23×H(5,𝔽2)C2318yescomplemented
102C23×H(5,𝔽2)C23148yescomplemented
103C23×H(5,𝔽2)C2312yescomplemented
104C24×#41C2312yes—
105C24×#41C2312yes—
106C24×#41C2311yescharacteristic
107C24×#41C2312yes—
108C25×D4C2311yescharacteristic
109#63090C2312048yescomplemented
110C2×#3586C231384yescomplemented
111C2×#3586C231384yescomplemented
112C2×#3585C231768yescomplemented
113C2×#3585C231768yescomplemented
114C2×#3585C231384yescomplemented
115C2×#3585C231384yescomplemented
116C2×#3585C2312048yescomplemented
117C2×#3584C231768yescomplemented
118C22×#578C23132yescomplemented
119C22×#577C23164yescomplemented
120C22×#577C23132yescomplemented
121C22×#577C23132yescomplemented
122C22×#577C231384yescomplemented
123C22×#576C23164yescomplemented
124C22×#576C23132yescomplemented
125C22×#576C231384yescomplemented
126C22×#575D418yescomplemented
127C22×#575D418yescomplemented
128C22×#575D4196yescomplemented
129C22×#575C2318yes—
130C22×#575C2318yes—
131C22×#575C23196yes—
132C22×#575C2318yes—
133C22×#575C2318yes—
134C22×#575C23196yescomplemented
135C22×#575C2318yescomplemented
136C22×#575C2318yescomplemented
137C22×#575C23196yescomplemented
138C22×#575C23196yescomplemented
139C22×#575C2318yescomplemented
140C22×#575C2318yescomplemented
141C22×#575C23196yescomplemented
142C23×#137D414yescomplemented
143C23×#137D414yescomplemented
144C23×#137C2314yescomplemented
145C23×#137C2314yescomplemented
146C23×#137C2314yescomplemented
147C23×#137C2314yescomplemented
148C23×#137C2314yescomplemented
149C23×AGL(1,ℤ/8)D414yescomplemented
150C23×AGL(1,ℤ/8)D414yescomplemented
151C23×AGL(1,ℤ/8)C2318yes—
152C23×AGL(1,ℤ/8)C2318yescomplemented
153C23×AGL(1,ℤ/8)C2318yescomplemented
154C23×AGL(1,ℤ/8)C23196yescomplemented
155C23×AGL(1,ℤ/8)C2314yescomplemented
156C23×AGL(1,ℤ/8)C2314yescomplemented
157C23×AGL(1,ℤ/8)C2318yescomplemented
158C23×AGL(1,ℤ/8)C2318yescomplemented
159C23×AGL(1,ℤ/8)C23196yescomplemented
160C23×AGL(1,ℤ/8)C2314yescomplemented
161C23×AGL(1,ℤ/8)C2314yescomplemented
162C23×AGL(1,ℤ/8)C2314yescomplemented
163C23×#135C2318yes—
164C23×#135C2318yescomplemented
165C24×SD16C2314yescomplemented
166C24×D8C2314yescomplemented
167C22×#568C2318yescomplemented
168C22×#568C2318yescomplemented
169C22×#568C2318yescomplemented
170C22×#568C2318yescomplemented
171C22×#568C23196yescomplemented
172C22×#568C23196yescomplemented
173C23×#131C2318yescomplemented
174C23×#131C2318yescomplemented
175C24×M16C2312yes—
176C24×M16C2312yes—
177C24×M16C2312yes—
178C2×#3449C23148yescomplemented
179C22×#536C2314yescomplemented
180C22×#535C2318yescomplemented
181C22×#535C23148yescomplemented
182C22×#535C2314yescomplemented
183C22×#532C2314yescomplemented
184C23×#127C2312yescomplemented
185C23×#124C2312yescomplemented
186C23×#117C2311yescharacteristic
187#61110C2318192yescomplemented
188#61109C2318192yescomplemented
189#61107C23116384yescomplemented
190#61106C23116384yescomplemented
191C2×#3292C2311536yescomplemented
192C2×#3291C2311536yescomplemented
193C2×#3290C2313072yescomplemented
194C2×#3289C2311536yescomplemented
195C2×#3288C2311536yescomplemented
196C2×#3288C2313072yescomplemented
197#60644C2311024yescomplemented
198C2×#3155C231384yescomplemented
199C2×#3154C231384yescomplemented
200C2×#3153C231192yescomplemented
201C2×#3151C231192yescomplemented
202C22×#497C2318yescomplemented
203C22×#496C2318yescomplemented
204C22×#496C23116yescomplemented
205C22×#495C23116yescomplemented
206C22×#493C2318yescomplemented
207C22×#492C2318yescomplemented
208#60469C2312048yescomplemented
209C2×#3069C231384yescomplemented
210C2×#3069C231384yescomplemented
211C2×#3068C231384yescomplemented
212C2×#3068C231384yescomplemented
213C2×#3068C231768yescomplemented
214C2×#3068C231768yescomplemented
215C2×#3068C2312048yescomplemented
216C2×#3067C231768yescomplemented
217C22×#473C23132yescomplemented
218C22×#472C23164yescomplemented
219C22×#472C23132yescomplemented
220C22×#472C231384yescomplemented
221C22×#471C23164yescomplemented
222C22×#471C23132yescomplemented
223C22×#471C23132yescomplemented
224C22×#471C231384yescomplemented
225#60387C2312048yescomplemented
226C2×#3022C231384yescomplemented
227C2×#3021C231384yescomplemented
228C2×#3021C231768yescomplemented
229C2×#3021C2311024yescomplemented
230C2×#3020C231384yescomplemented
231C2×#3019C231768yescomplemented
232C2×#3019C231384yescomplemented
233C2×#3019C2311024yescomplemented
234C2×#3018C231768yescomplemented
235C22×#456C23132yescomplemented
236C22×#454C23132yescomplemented
237C22×#454C23132yescomplemented
238C22×#454C231192yescomplemented
239C22×#455C23132yescomplemented
240C22×#455C23132yescomplemented
241C22×#455C231192yescomplemented
242C22×#453C23132yescomplemented
243C22×#453C23132yescomplemented
244C22×#453C231192yescomplemented
245C22×#453C23132yescomplemented
246C22×#453C231192yescomplemented
247#60182C2312048yescomplemented
248C2×#2957C231768yescomplemented
249C2×#2956C231768yescomplemented
250C2×#2955C231768yescomplemented
251C22×#444C23164yescomplemented
252C22×#443C23164yescomplemented
253C22×#430C2318yescomplemented
254C22×#430C2318yescomplemented
255C22×#430C23196yescomplemented
256C23×#108C2318yescomplemented
257C22×#421C2318yescomplemented
258C22×#421C2318yescomplemented
259C22×#421C2318yescomplemented
260C22×#421C2318yescomplemented
261C22×#421C23196yescomplemented
262C22×#421C23196yescomplemented
263C23×#104C2318yescomplemented
264C23×#104C2318yescomplemented
265C22×#413C2318yescomplemented
266C22×#413C2318yescomplemented
267C22×#413C2318yescomplemented
268C22×#413C23196yescomplemented
269C22×#413C23148yescomplemented
270C23×#101C2314yescomplemented
271C23×#101C2312yescomplemented
272C23×#100C2314yescomplemented
273C23×#100C2318yescomplemented
274C23×#100C2312yescomplemented
275C23×#100C23148yescomplemented
276C23×#100C2314yescomplemented
277C2×#2873C23148yescomplemented
278C22×#405C2318yescomplemented
279C22×C4×M16C2314yescomplemented
280C2×#585C241192yes—
281C2×#585C241192yescomplemented
282C2×#585C241512yescomplemented
283C2×#585C241192yescomplemented
284C2×#585C241256yescomplemented
285C22×2−1+4C24116yes—
286C22×2−1+4C24196yescomplemented
287C22×2−1+4C2418yescomplemented
288C22×2−1+4C24148yescomplemented
289C22×H(5,𝔽2)C24116yes—
290C22×H(5,𝔽2)C24116yes—
291C22×H(5,𝔽2)C24196yes—
292C22×H(5,𝔽2)C24196yescomplemented
293C22×H(5,𝔽2)C241192yescomplemented
294C22×H(5,𝔽2)C241256yescomplemented
295C22×H(5,𝔽2)C2418yescomplemented
296C22×H(5,𝔽2)C24148yescomplemented
297C23×#41C2×D414yes—
298C23×#41C2×D414yes—
299C23×#41C2×D414yes—
300C23×#41C2×D414yes—
301C23×#41C2×D414yes—
302C23×#41C2×D414yes—
303C23×#41C2×D4148yes—
304C23×#41C2×D4148yes—
305C23×#41C2414yes—
306C23×#41C2414yes—
307C23×#41C2414yes—
308C23×#41C2414yes—
309C23×#41C2414yes—
310C23×#41C24148yes—
311C23×#41C2414yes—
312C23×#41C24148yes—
313C23×#41C2414yes—
314C23×#41C2414yes—
315C23×#41C2414yes—
316C23×#41C24148yes—
317C23×#41C24124yes—
318C24×Q8C2×D412yes—
319C24×Q8C2×D412yes—
320C24×Q8C2412yes—
321C24×Q8C2411yescharacteristic
322C24×D4C2×D412yes—
323C24×D4C2×D412yes—
324C24×D4C2412yes—
325C24×D4C2414yes—
326C24×D4C2412yes—
327C24×D4C24124yes—
328C24×D4C2411yescharacteristic
329C25×C4C2411yescharacteristic
330#3586C2412048yescomplemented
331#3586C2412048yescomplemented
332#3585C2414096yescomplemented
333#3585C2414096yescomplemented
334#3585C2412048yescomplemented
335#3585C2412048yescomplemented
336#3584C2414096yescomplemented
337C2×#578C241768yescomplemented
338C2×#577C2411536yescomplemented
339C2×#577C241768yescomplemented
340C2×#577C241768yescomplemented
341C2×#577C2412048yescomplemented
342C2×#576C2411536yescomplemented
343C2×#576C241768yescomplemented
344C2×#576C2412048yescomplemented
345C2×#575C2×D41192yes—
346C2×#575C2×D41192yescomplemented
347C2×#575C2×D41384yescomplemented
348C2×#575C2×D41384yescomplemented
349C2×#575C2×D411536yescomplemented
350C2×#575C241192yes—
351C2×#575C241192yes—
352C2×#575C241512yes—
353C2×#575C241192yes—
354C2×#575C241192yes—
355C2×#575C241512yescomplemented
356C2×#575C241192yescomplemented
357C2×#575C241192yescomplemented
358C2×#575C241512yescomplemented
359C2×#575C241512yescomplemented
360C2×#575C241192yescomplemented
361C2×#575C241192yescomplemented
362C2×#575C241512yescomplemented
363C22×#137C2×D4116yes—
364C22×#137C2×D4116yes—
365C22×#137C2×D4116yescomplemented
366C22×#137C2×D4116yescomplemented
367C22×#137C2×D41192yescomplemented
368C22×#137C2×D41192yescomplemented
369C22×#137C24116yes—
370C22×#137C24116yes—
371C22×#137C24196yescomplemented
372C22×#137C24196yescomplemented
373C22×#137C24196yescomplemented
374C22×#137C24196yescomplemented
375C22×#137C24116yescomplemented
376C22×#137C24196yescomplemented
377C22×AGL(1,ℤ/8)C2×D4116yes—
378C22×AGL(1,ℤ/8)C2×D4116yes—
379C22×AGL(1,ℤ/8)C2×D4116yescomplemented
380C22×AGL(1,ℤ/8)C2×D4116yescomplemented
381C22×AGL(1,ℤ/8)C2×D41192yescomplemented
382C22×AGL(1,ℤ/8)C2×D41192yescomplemented
383C22×AGL(1,ℤ/8)C24132yes—
384C22×AGL(1,ℤ/8)C241192yes—
385C22×AGL(1,ℤ/8)C24116yes—
386C22×AGL(1,ℤ/8)C24116yes—
387C22×AGL(1,ℤ/8)C241192yescomplemented
388C22×AGL(1,ℤ/8)C241192yescomplemented
389C22×AGL(1,ℤ/8)C241512yescomplemented
390C22×AGL(1,ℤ/8)C24196yescomplemented
391C22×AGL(1,ℤ/8)C24196yescomplemented
392C22×AGL(1,ℤ/8)C241192yescomplemented
393C22×AGL(1,ℤ/8)C241192yescomplemented
394C22×AGL(1,ℤ/8)C241512yescomplemented
395C22×AGL(1,ℤ/8)C24196yescomplemented
396C22×AGL(1,ℤ/8)C24196yescomplemented
397C22×AGL(1,ℤ/8)C24116yescomplemented
398C22×AGL(1,ℤ/8)C24196yescomplemented
399C22×#135C2×D4132yescomplemented
400C22×#135C2×D41192yescomplemented
401C22×#135C24132yes—
402C22×#135C241192yes—
403C22×#135C241192yescomplemented
404C23×Q16C2×D418yescomplemented
405C23×Q16C2418yescomplemented
406C23×SD16C2×D418yescomplemented
407C23×SD16C2×D418yescomplemented
408C23×SD16C24116yes—
409C23×SD16C24196yescomplemented
410C23×SD16C2418yescomplemented
411C23×SD16C2418yescomplemented
412C23×D8C2×D418yescomplemented
413C23×D8C24116yes—
414C23×D8C24196yescomplemented
415C23×D8C2418yescomplemented
416C2×#568C241192yescomplemented
417C2×#568C241192yescomplemented
418C2×#568C241192yescomplemented
419C2×#568C241192yescomplemented
420C2×#568C241512yescomplemented
421C2×#568C241512yescomplemented
422C22×#131C24132yes—
423C22×#131C241192yescomplemented
424C22×#131C24132yescomplemented
425C22×#131C241192yescomplemented
426C23×M16C2×D414yes—
427C23×M16C2×D414yes—
428C23×M16C2×D414yes—
429C23×M16C2×D414yes—
430C23×M16C2×D4148yes—
431C23×M16C2414yes—
432C23×M16C2414yes—
433C23×M16C24148yes—
434C23×M16C2414yes—
435C23×M16C2414yes—
436C23×M16C2414yes—
437C23×M16C2414yes—
438C23×M16C24148yes—
439C23×M16C2414yes—
440C23×M16C2414yes—
441C23×M16C24148yes—
442C24×C8C2414yes—
443#3449C241256yescomplemented
444C2×#536C24196yescomplemented
445C2×#535C241192yescomplemented
446C2×#535C241256yescomplemented
447C2×#535C24196yescomplemented
448C2×#532C24196yescomplemented
449C22×C4⋊Q8C2414yescomplemented
450C22×#127C2418yes—
451C22×#127C24148yescomplemented
452C22×#127C2414yescomplemented
453C22×#124C2418yes—
454C22×#124C24148yescomplemented
455C22×#124C2418yescomplemented
456C22×#117C2414yes—
457C22×#117C24124yes—
458C23×C42C2412yes—
459#3292C2418192yescomplemented
460#3291C2418192yescomplemented
461#3290C24116384yescomplemented
462#3289C2418192yescomplemented
463#3288C2418192yescomplemented
464#3288C24116384yescomplemented
465#3155C2412048yescomplemented
466#3154C2412048yescomplemented
467#3153C2411024yescomplemented
468#3151C2411024yescomplemented
469C2×#497C241192yescomplemented
470C2×#496C241192yescomplemented
471C2×#496C241384yescomplemented
472C2×#495C241384yescomplemented
473C2×#493C241192yescomplemented
474C2×#492C241192yescomplemented
475#3069C2412048yescomplemented
476#3069C2412048yescomplemented
477#3068C2412048yescomplemented
478#3068C2412048yescomplemented
479#3068C2414096yescomplemented
480#3068C2414096yescomplemented
481#3067C2414096yescomplemented
482C2×#473C241768yescomplemented
483C2×#472C241768yescomplemented
484C2×#472C2411536yescomplemented
485C2×#472C2412048yescomplemented
486C2×#471C241768yescomplemented
487C2×#471C241768yescomplemented
488C2×#471C2411536yescomplemented
489C2×#471C2412048yescomplemented
490#3022C2412048yescomplemented
491#3021C2414096yescomplemented
492#3021C2412048yescomplemented
493#3020C2412048yescomplemented
494#3019C2414096yescomplemented
495#3019C2412048yescomplemented
496#3018C2414096yescomplemented
497C2×#456C241768yescomplemented
498C2×#454C241768yescomplemented
499C2×#454C241768yescomplemented
500C2×#454C2411024yescomplemented
501C2×#455C241768yescomplemented
502C2×#455C241768yescomplemented
503C2×#455C2411024yescomplemented
504C2×#453C241768yescomplemented
505C2×#453C241768yescomplemented
506C2×#453C241768yescomplemented
507C2×#453C2411024yescomplemented
508C2×#453C2411024yescomplemented
509#2957C2414096yescomplemented
510#2956C2414096yescomplemented
511#2955C2414096yescomplemented
512C2×#444C2411536yescomplemented
513C2×#443C2411536yescomplemented
514C2×#430C241192yescomplemented
515C2×#430C241192yescomplemented
516C2×#430C241512yescomplemented
517C22×#108C24132yescomplemented
518C22×#108C241192yescomplemented
519C2×#421C241192yescomplemented
520C2×#421C241192yescomplemented
521C2×#421C241192yescomplemented
522C2×#421C241192yescomplemented
523C2×#421C241512yescomplemented
524C2×#421C241512yescomplemented
525C22×#104C24132yes—
526C22×#104C241192yescomplemented
527C22×#104C24132yescomplemented
528C22×#104C241192yescomplemented
529C2×#413C241192yescomplemented
530C2×#413C241192yescomplemented
531C2×#413C241192yescomplemented
532C2×#413C241512yescomplemented
533C2×#413C241256yescomplemented
534C22×#101C24116yescomplemented
535C22×#101C2418yescomplemented
536C22×#101C24196yescomplemented
537C22×#101C24148yescomplemented
538C22×#100C24116yes—
539C22×#100C241192yescomplemented
540C22×#100C24196yescomplemented
541C22×#100C2418yescomplemented
542C22×#100C24116yescomplemented
543C22×#100C24196yescomplemented
544C22×#100C241256yescomplemented
545C22×#100C24148yescomplemented
546#2873C241256yescomplemented
547C2×#405C241192yescomplemented
548C2×C4×M16C24196yescomplemented
549C22×#97C2418yescomplemented
550C22×C4×C8C2418yescomplemented
551C26H(5,𝔽2)11yescharacteristic
552#585C251512yes—
553#585C251512yescomplemented
554#585C251512yescomplemented
555C2×2−1+4C251192yes—
556C2×2−1+4C251256yescomplemented
557C2×2−1+4C251128yescomplemented
558C2×2−1+4C25196yescomplemented
559C2×H(5,𝔽2)C251256yes—
560C2×H(5,𝔽2)C251192yes—
561C2×H(5,𝔽2)C251192yes—
562C2×H(5,𝔽2)C251512yescomplemented
563C2×H(5,𝔽2)C251256yescomplemented
564C2×H(5,𝔽2)C251128yescomplemented
565C2×H(5,𝔽2)C25196yescomplemented
566C22×#41C22×D418yes—
567C22×#41C22×D418yes—
568C22×#41C22×D4148yes—
569C22×#41C22×D4148yes—
570C22×#41C22×D418yes—
571C22×#41C22×D418yes—
572C22×#41C22×D418yes—
573C22×#41C22×D418yes—
574C22×#41C22×D4196yes—
575C22×#41C22×D4196yes—
576C22×#41C22×D4148yes—
577C22×#41C22×D4148yes—
578C22×#41C22×D4196yes—
579C22×#41C22×D4196yes—
580C22×#41C22×D4148yes—
581C22×#41C22×D4148yes—
582C22×#41C22×D4196yes—
583C22×#41C22×D4196yes—
584C22×#41C22×D41384yes—
585C22×#41C22×D41384yes—
586C22×#41C2518yes—
587C22×#41C25148yes—
588C22×#41C2518yes—
589C22×#41C25148yes—
590C22×#41C25148yes—
591C22×#41C251128yes—
592C22×#41C25148yes—
593C22×#41C25148yes—
594C22×#41C25148yes—
595C22×#41C251128yes—
596C22×#41C25148yes—
597C22×#41C25148yes—
598C22×#41C25148yes—
599C22×#41C25164yes—
600C22×#41C251128yes—
601C23×Q8C22×D414yes—
602C23×Q8C22×D414yes—
603C23×Q8C22×D414yes—
604C23×Q8C22×D414yes—
605C23×Q8C22×D414yes—
606C23×Q8C22×D414yes—
607C23×Q8C22×D4148yes—
608C23×Q8C22×D4148yes—
609C23×Q8C2514yes—
610C23×Q8C2512yes—
611C23×Q8C25112yes—
612C23×Q8C25124yes—
613C23×D4C22×D414yes—
614C23×D4C22×D414yes—
615C23×D4C22×D414yes—
616C23×D4C22×D414yes—
617C23×D4C22×D414yes—
618C23×D4C22×D414yes—
619C23×D4C22×D4148yes—
620C23×D4C22×D4148yes—
621C23×D4C2514yes—
622C23×D4C25124yes—
623C23×D4C25148yes—
624C23×D4C25164yes—
625C23×D4C2514yes—
626C23×D4C2512yes—
627C23×D4C25112yes—
628C23×D4C25124yes—
629C24×C4C22×D412yes—
630C24×C4C22×D412yes—
631C24×C4C22×D4124yes—
632C24×C4C22×D412yes—
633C24×C4C22×D412yes—
634C24×C4H(5,𝔽2)112yes—
635C24×C4H(5,𝔽2)12yes—
636C24×C4H(5,𝔽2)11yescharacteristic
637C24×C4C2511yescharacteristic
638C24×C4C2512yes—
639C24×C4C25112yes—
640#578C2512048yescomplemented
641#577C2514096yescomplemented
642#577C2512048yescomplemented
643#577C2512048yescomplemented
644#576C2514096yescomplemented
645#576C2512048yescomplemented
646#575C22×D411536yes—
647#575C22×D411536yescomplemented
648#575C22×D412048yescomplemented
649#575C22×D412048yescomplemented
650#575C251512yes—
651#575C251512yes—
652#575C251512yes—
653#575C251512yes—
654#575C251512yescomplemented
655#575C251512yescomplemented
656#575C251512yescomplemented
657#575C251512yescomplemented
658C2×#137C22×D41384yes—
659C2×#137C22×D41384yes—
660C2×#137C22×D41384yescomplemented
661C2×#137C22×D41384yescomplemented
662C2×#137C22×D411024yescomplemented
663C2×#137C22×D411024yescomplemented
664C2×#137C251192yes—
665C2×#137C251192yes—
666C2×#137C251256yescomplemented
667C2×#137C251256yescomplemented
668C2×#137C251256yescomplemented
669C2×#137C251256yescomplemented
670C2×#137C251256yescomplemented
671C2×#137C251192yescomplemented
672C2×AGL(1,ℤ/8)C22×D41384yes—
673C2×AGL(1,ℤ/8)C22×D41384yes—
674C2×AGL(1,ℤ/8)C22×D41384yescomplemented
675C2×AGL(1,ℤ/8)C22×D41384yescomplemented
676C2×AGL(1,ℤ/8)C22×D411024yescomplemented
677C2×AGL(1,ℤ/8)C22×D411024yescomplemented
678C2×AGL(1,ℤ/8)C251512yes—
679C2×AGL(1,ℤ/8)C251192yes—
680C2×AGL(1,ℤ/8)C251384yes—
681C2×AGL(1,ℤ/8)C251192yes—
682C2×AGL(1,ℤ/8)C251512yescomplemented
683C2×AGL(1,ℤ/8)C251512yescomplemented
684C2×AGL(1,ℤ/8)C251256yescomplemented
685C2×AGL(1,ℤ/8)C251256yescomplemented
686C2×AGL(1,ℤ/8)C251256yescomplemented
687C2×AGL(1,ℤ/8)C251512yescomplemented
688C2×AGL(1,ℤ/8)C251512yescomplemented
689C2×AGL(1,ℤ/8)C251256yescomplemented
690C2×AGL(1,ℤ/8)C251256yescomplemented
691C2×AGL(1,ℤ/8)C251192yescomplemented
692C2×#135C22×D41384yes—
693C2×#135C22×D41768yescomplemented
694C2×#135C22×D411536yescomplemented
695C2×#135C251384yes—
696C2×#135C251512yes—
697C2×#135C251512yescomplemented
698C22×Q16C22×D4132yes—
699C22×Q16C22×D41192yescomplemented
700C22×Q16C25196yescomplemented
701C22×SD16C22×D4132yes—
702C22×SD16C22×D4132yes—
703C22×SD16C22×D41192yescomplemented
704C22×SD16C22×D41192yescomplemented
705C22×SD16C251192yes—
706C22×SD16C251256yescomplemented
707C22×SD16C25196yescomplemented
708C22×SD16C25196yescomplemented
709C22×D8C22×D4132yes—
710C22×D8C22×D41192yescomplemented
711C22×D8C251192yes—
712C22×D8C251256yescomplemented
713C22×D8C25196yescomplemented
714#568C251512yescomplemented
715#568C251512yescomplemented
716#568C251512yescomplemented
717#568C251512yescomplemented
718C2×#131C251384yes—
719C2×#131C251512yescomplemented
720C2×#131C251512yescomplemented
721C2×#131C251384yescomplemented
722C22×M16C22×D418yes—
723C22×M16C22×D418yes—
724C22×M16C22×D418yes—
725C22×M16C22×D418yes—
726C22×M16C22×D4196yes—
727C22×M16C22×D4196yes—
728C22×M16C22×D4148yes—
729C22×M16C22×D4148yes—
730C22×M16C22×D4196yes—
731C22×M16C22×D4196yes—
732C22×M16C22×D41384yes—
733C22×M16C25148yes—
734C22×M16C25148yes—
735C22×M16C251128yes—
736C22×M16C2518yes—
737C22×M16C25148yes—
738C22×M16C2518yes—
739C22×M16C25148yes—
740C22×M16C25148yes—
741C22×M16C251128yes—
742C22×M16C25148yes—
743C22×M16C25148yes—
744C22×M16C25148yes—
745C22×M16C251128yes—
746C23×C8C22×D418yes—
747C23×C8C22×D418yes—
748C23×C8C22×D4148yes—
749C23×C8C2518yes—
750C23×C8C25148yes—
751#536C251256yescomplemented
752#535C251512yescomplemented
753#535C251256yescomplemented
754#532C251256yescomplemented
755C2×C4⋊Q8C25148yescomplemented
756C2×#127C25196yes—
757C2×#127C251128yescomplemented
758C2×#127C25148yescomplemented
759C2×#124C25196yes—
760C2×#124C251128yescomplemented
761C2×#124C25196yescomplemented
762C2×#117C25148yes—
763C2×#117C25164yes—
764C22×C42C2514yes—
765C22×C42C25124yes—
766#497C251512yescomplemented
767#496C251512yescomplemented
768#496C2511024yescomplemented
769#495C2511024yescomplemented
770#493C251512yescomplemented
771#492C251512yescomplemented
772#473C2512048yescomplemented
773#472C2514096yescomplemented
774#472C2512048yescomplemented
775#471C2514096yescomplemented
776#471C2512048yescomplemented
777#471C2512048yescomplemented
778#456C2512048yescomplemented
779#455C2512048yescomplemented
780#455C2512048yescomplemented
781#454C2512048yescomplemented
782#454C2512048yescomplemented
783#453C2512048yescomplemented
784#453C2512048yescomplemented
785#453C2512048yescomplemented
786#444C2514096yescomplemented
787#443C2514096yescomplemented
788#430C251512yescomplemented
789#430C251512yescomplemented
790C2×#108C251384yescomplemented
791C2×#108C251512yescomplemented
792#421C251512yescomplemented
793#421C251512yescomplemented
794#421C251512yescomplemented
795#421C251512yescomplemented
796C2×#104C251384yes—
797C2×#104C251512yescomplemented
798C2×#104C251384yescomplemented
799C2×#104C251512yescomplemented
800#413C251512yescomplemented
801#413C251512yescomplemented
802#413C251512yescomplemented
803C2×#101C25196yescomplemented
804C2×#101C251128yescomplemented
805C2×#101C251192yescomplemented
806C2×#101C251256yescomplemented
807C2×#100C251192yes—
808C2×#100C251256yescomplemented
809C2×#100C251512yescomplemented
810C2×#100C25196yescomplemented
811C2×#100C251128yescomplemented
812C2×#100C251192yescomplemented
813C2×#100C251256yescomplemented
814#405C251512yescomplemented
815C4×M16C251256yescomplemented
816C2×#97C25196yescomplemented
817C2×C4×C8C25196yescomplemented
818C25D42112yes—
819C25D4211yescharacteristic
820C25D4212yes—
821C25D4211yescharacteristic
822C25C2×H(5,𝔽2)112yes—
823C25C2×H(5,𝔽2)11yescharacteristic
824C25C2×H(5,𝔽2)12yes—
8252−1+4C261256yes—
8262−1+4C261128yescomplemented
827H(5,𝔽2)C261256yes—
828H(5,𝔽2)C261256yes—
829H(5,𝔽2)C261128yescomplemented
830C2×#41C23×D4148yes—
831C2×#41C23×D4148yes—
832C2×#41C23×D4196yes—
833C2×#41C23×D4196yes—
834C2×#41C23×D41192yes—
835C2×#41C23×D41192yes—
836C2×#41C23×D4196yes—
837C2×#41C23×D4196yes—
838C2×#41C23×D4196yes—
839C2×#41C23×D4196yes—
840C2×#41C23×D41256yes—
841C2×#41C23×D41256yes—
842C2×#41C23×D41192yes—
843C2×#41C23×D41192yes—
844C2×#41C23×D41256yes—
845C2×#41C23×D41256yes—
846C2×#41C23×D41192yes—
847C2×#41C23×D41192yes—
848C2×#41C23×D41256yes—
849C2×#41C23×D41256yes—
850C2×#41C26148yes—
851C2×#41C26148yes—
852C2×#41C26164yes—
853C2×#41C26164yes—
854C2×#41C26164yes—
855C2×#41C26164yes—
856C2×#41C26164yes—
857C2×#41C26164yes—
858C2×#41C26164yes—
859C2×#41C26164yes—
860C2×#41C26164yes—
861C22×Q8C23×D418yes—
862C22×Q8C23×D418yes—
863C22×Q8C23×D4148yes—
864C22×Q8C23×D4148yes—
865C22×Q8C23×D4148yes—
866C22×Q8C23×D4148yes—
867C22×Q8C23×D4148yes—
868C22×Q8C23×D4148yes—
869C22×Q8C23×D41128yes—
870C22×Q8C23×D41128yes—
871C22×Q8C26112yes—
872C22×Q8C26116yes—
873C22×Q8C26124yes—
874C22×Q8C26132yes—
875C22×D4C23×D418yes—
876C22×D4C23×D418yes—
877C22×D4C23×D4148yes—
878C22×D4C23×D4148yes—
879C22×D4C23×D4148yes—
880C22×D4C23×D4148yes—
881C22×D4C23×D4148yes—
882C22×D4C23×D4148yes—
883C22×D4C23×D41128yes—
884C22×D4C23×D41128yes—
885C22×D4C26124yes—
886C22×D4C26124yes—
887C22×D4C26132yes—
888C22×D4C26112yes—
889C22×D4C26116yes—
890C22×D4C26132yes—
891C22×D4C26164yes—
892C23×C4D42124yes—
893C23×C4D42124yes—
894C23×C4D42124yes—
895C23×C4D42124yes—
896C23×C4D42112yes—
897C23×C4D42196yes—
898C23×C4D42124yes—
899C23×C4D4211yescharacteristic
900C23×C4D4212yes—
901C23×C4D4212yes—
902C23×C4D4212yes—
903C23×C4D4212yes—
904C23×C4D4211yescharacteristic
905C23×C4D4212yes—
906C23×C4C23×D412yes—
907C23×C4C23×D4112yes—
908C23×C4C23×D412yes—
909C23×C4C23×D4124yes—
910C23×C4C23×D4124yes—
911C23×C4C23×D412yes—
912C23×C4C23×D412yes—
913C23×C4C23×D412yes—
914C23×C4C23×D412yes—
915C23×C4C23×D4112yes—
916C23×C4C23×D4112yes—
917C23×C4C23×D4124yes—
918C23×C4C23×D4124yes—
919C23×C4C23×D4196yes—
920C23×C4C2×H(5,𝔽2)16yes—
921C23×C4C2×H(5,𝔽2)112yes—
922C23×C4C2×H(5,𝔽2)112yes—
923C23×C4C2×H(5,𝔽2)148yes—
924C23×C4C2×H(5,𝔽2)124yes—
925C23×C4C2×H(5,𝔽2)11yescharacteristic
926C23×C4C2×H(5,𝔽2)12yes—
927C23×C4C26112yes—
928C23×C4C26116yes—
929C23×C4C2611yescharacteristic
930C23×C4C2616yes—
931#137C23×D411024yes—
932#137C23×D411024yes—
933#137C23×D411024yescomplemented
934#137C23×D411024yescomplemented
935#137C261256yes—
936#137C261256yes—
937#137C261256yescomplemented
938AGL(1,ℤ/8)C23×D411024yes—
939AGL(1,ℤ/8)C23×D411024yes—
940AGL(1,ℤ/8)C23×D411024yescomplemented
941AGL(1,ℤ/8)C23×D411024yescomplemented
942AGL(1,ℤ/8)C261512yes—
943AGL(1,ℤ/8)C261256yes—
944AGL(1,ℤ/8)C261256yes—
945AGL(1,ℤ/8)C261256yescomplemented
946#135C23×D411536yes—
947#135C23×D412048yescomplemented
948#135C261512yes—
949C2×Q16C23×D41384yes—
950C2×Q16C23×D41512yescomplemented
951C2×Q16C261128yescomplemented
952C2×SD16C23×D41384yes—
953C2×SD16C23×D41384yes—
954C2×SD16C23×D41512yescomplemented
955C2×SD16C23×D41512yescomplemented
956C2×SD16C261256yes—
957C2×SD16C261128yescomplemented
958C2×SD16C261128yescomplemented
959C2×D8C23×D41384yes—
960C2×D8C23×D41512yescomplemented
961C2×D8C261256yes—
962C2×D8C261128yescomplemented
963#131C261512yes—
964#131C261512yescomplemented
965C2×M16C23×D4196yes—
966C2×M16C23×D4196yes—
967C2×M16C23×D4196yes—
968C2×M16C23×D4196yes—
969C2×M16C23×D41256yes—
970C2×M16C23×D41256yes—
971C2×M16C23×D41192yes—
972C2×M16C23×D41192yes—
973C2×M16C23×D41256yes—
974C2×M16C23×D41256yes—
975C2×M16C26164yes—
976C2×M16C26164yes—
977C2×M16C26148yes—
978C2×M16C26148yes—
979C2×M16C26164yes—
980C2×M16C26164yes—
981C2×M16C26164yes—
982C2×M16C26164yes—
983C2×M16C26164yes—
984C2×M16C26164yes—
985C22×C8C23×D4116yes—
986C22×C8C23×D4196yes—
987C22×C8C23×D4148yes—
988C22×C8C23×D4196yes—
989C22×C8C23×D41192yes—
990C22×C8C26148yes—
991C22×C8C26164yes—
992C4⋊Q8C26164yescomplemented
993#127C261128yes—
994#127C26164yescomplemented
995#124C261128yes—
996#124C261128yescomplemented
997#117C26164yes—
998C2×C42C26124yes—
999C2×C42C26132yes—
1000#108C261512yescomplemented
1001#104C261512yes—
1002#104C261512yescomplemented
1003#101C261128yescomplemented
1004#101C261256yescomplemented
1005#100C261256yes—
1006#100C261128yescomplemented
1007#100C261256yescomplemented
1008#97C261128yescomplemented
1009C4×C8C261128yescomplemented
1010C24C2×D42112yes—
1011C24C2×D42112yes—
1012C24C2×D42124yes—
1013C24C2×D4216yes—
1014C24C2×D42112yes—
1015C24C2×D42148yes—
1016C24C2×D4212yes—
1017C24C2×D4212yes—
1018C24C2×D4211yescharacteristic
1019C24C2×D4211yescharacteristic
1020C24C22×H(5,𝔽2)112yes—
1021C24C22×H(5,𝔽2)116yes—
1022C24C22×H(5,𝔽2)16yes—
1023C24C22×H(5,𝔽2)11yescharacteristic
1024#41C24×D4196yes—
1025#41C24×D4196yes—
1026#41C24×D41128yes—
1027#41C24×D41128yes—
1028#41C24×D41128yes—
1029#41C24×D41128yes—
1030#41C24×D41128yes—
1031#41C24×D41128yes—
1032#41C27132yes—
1033#41C27132yes—
1034C2×Q8C24×D4148yes—
1035C2×Q8C24×D4148yes—
1036C2×Q8C24×D4164yes—
1037C2×Q8C24×D4164yes—
1038C2×Q8C24×D4164yes—
1039C2×Q8C24×D4164yes—
1040C2×Q8C24×D4164yes—
1041C2×Q8C24×D4164yes—
1042C2×Q8C2718yes—
1043C2×Q8C27116yes—
1044C2×D4C24×D4148yes—
1045C2×D4C24×D4148yes—
1046C2×D4C24×D4164yes—
1047C2×D4C24×D4164yes—
1048C2×D4C24×D4164yes—
1049C2×D4C24×D4164yes—
1050C2×D4C24×D4164yes—
1051C2×D4C24×D4164yes—
1052C2×D4C27116yes—
1053C2×D4C27116yes—
1054C2×D4C2718yes—
1055C22×C4C2×D42112yes—
1056C22×C4C2×D42112yes—
1057C22×C4C2×D42112yes—
1058C22×C4C2×D42112yes—
1059C22×C4C2×D42112yes—
1060C22×C4C2×D42148yes—
1061C22×C4C2×D42112yes—
1062C22×C4C2×D42124yes—
1063C22×C4C2×D42124yes—
1064C22×C4C2×D42124yes—
1065C22×C4C2×D42124yes—
1066C22×C4C2×D42112yes—
1067C22×C4C2×D42112yes—
1068C22×C4C2×D42196yes—
1069C22×C4C2×D42196yes—
1070C22×C4C2×D42112yes—
1071C22×C4C2×D42124yes—
1072C22×C4C2×D4216yes—
1073C22×C4C2×D42124yes—
1074C22×C4C2×D42196yes—
1075C22×C4C2×D42196yes—
1076C22×C4C2×D42148yes—
1077C22×C4C2×D42196yes—
1078C22×C4C2×D4212yes—
1079C22×C4C2×D4212yes—
1080C22×C4C2×D4212yes—
1081C22×C4C24×D4112yes—
1082C22×C4C24×D416yes—
1083C22×C4C24×D4112yes—
1084C22×C4C24×D4124yes—
1085C22×C4C24×D4112yes—
1086C22×C4C24×D4112yes—
1087C22×C4C24×D4112yes—
1088C22×C4C24×D4112yes—
1089C22×C4C24×D4132yes—
1090C22×C4C24×D4132yes—
1091C22×C4C24×D4124yes—
1092C22×C4C24×D4124yes—
1093C22×C4C24×D4132yes—
1094C22×C4C24×D4132yes—
1095C22×C4C24×D412yes—
1096C22×C4C22×H(5,𝔽2)124yes—
1097C22×C4C22×H(5,𝔽2)112yes—
1098C22×C4C22×H(5,𝔽2)132yes—
1099C22×C4C22×H(5,𝔽2)116yes—
1100C22×C4C22×H(5,𝔽2)13yes—
1101C22×C4C22×H(5,𝔽2)112yes—
1102C22×C4C22×H(5,𝔽2)16yes—
1103C22×C4C2713yes—
1104C22×C4C2714yes—
1105C22×C4C2718yes—
1106Q16C24×D41512yes—
1107SD16C24×D41512yes—
1108SD16C24×D41512yes—
1109D8C24×D41512yes—
1110M16C24×D41128yes—
1111M16C24×D41128yes—
1112M16C24×D41128yes—
1113M16C24×D41128yes—
1114M16C27132yes—
1115M16C27132yes—
1116C2×C8C24×D4196yes—
1117C2×C8C24×D41128yes—
1118C2×C8C24×D4196yes—
1119C2×C8C24×D41128yes—
1120C2×C8C27132yes—
1121C42C27116yes—
1122C23C22×D42112yes—
1123C23C22×D4213yes—
1124C23C22×D42112yes—
1125C23C22×D4216yes—
1126C23C22×D4216yes—
1127C23C22×D42124yes—
1128C23C22×D42116yes—
1129C23C22×D42132yes—
1130C23C22×D42112yes—
1131C23C22×D42116yes—
1132C23C22×D4211yescharacteristic
1133C23C23×H(5,𝔽2)13yes—
1134C23C23×H(5,𝔽2)14yes—
1135C23C23×H(5,𝔽2)18yes—
1136Q8C25×D4132yes—
1137Q8C25×D4132yes—
1138D4C25×D4132yes—
1139D4C25×D4132yes—
1140C2×C4C22×D42112yes—
1141C2×C4C22×D42112yes—
1142C2×C4C22×D4216yes—
1143C2×C4C22×D42112yes—
1144C2×C4C22×D42124yes—
1145C2×C4C22×D4216yes—
1146C2×C4C22×D42124yes—
1147C2×C4C22×D42124yes—
1148C2×C4C22×D42124yes—
1149C2×C4C22×D42124yes—
1150C2×C4C22×D42116yes—
1151C2×C4C22×D42132yes—
1152C2×C4C22×D42124yes—
1153C2×C4C22×D42124yes—
1154C2×C4C22×D42132yes—
1155C2×C4C22×D42132yes—
1156C2×C4C22×D42132yes—
1157C2×C4C22×D42116yes—
1158C2×C4C22×D42132yes—
1159C2×C4C22×D42112yes—
1160C2×C4C25×D416yes—
1161C2×C4C25×D418yes—
1162C2×C4C25×D416yes—
1163C2×C4C25×D418yes—
1164C2×C4C25×D418yes—
1165C2×C4C25×D418yes—
1166C2×C4C25×D418yes—
1167C2×C4C25×D418yes—
1168C2×C4C23×H(5,𝔽2)13yes—
1169C2×C4C23×H(5,𝔽2)14yes—
1170C2×C4C23×H(5,𝔽2)18yes—
1171C2×C4C2811yescharacteristic
1172C8C25×D4164yes—
1173C22#1057617814yesdirect product factor
1174C22C23×D4213yes—
1175C22C23×D4218yes—
1176C22C23×D4213yes—
1177C22C23×D4218yes—
1178C22C23×D4214yes—
1179C22C23×D4214yes—
1180C22C24×H(5,𝔽2)11yescharacteristic
1181C4C23×D4216yes—
1182C4C23×D4218yes—
1183C4C23×D4218yes—
1184C4C23×D4218yes—
1185C4C26×D412yes—
1186C2C24×D4211yescharacteristic
1187C2C2×#1057617816yesdirect product factor
subgroupG/H
center, socleC23C22×D42
commutator, Frattini, cosocleC2×C4C28
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C2×C4 ▷ C2 ▷ C1

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#60644C2semidirect
2. C22×#60469C2semidirect
3. C23×#3068C2semidirect
4. C22×#60182C2semidirect
5. C22×#61109C2semidirect
6. C22×#61107C2semidirect
7. C22×#61106C2semidirect
8. C22×#60387C2semidirect
9. C22×#63090C2semidirect
10. C2×#10576178C2direct (N × H)
11. C23×#3019C2semidirect
12. C23×#3021C2semidirect
13. C23×#3585C2semidirect
14. C22×#61110C2semidirect
15. C23×#585C22semidirect
16. C23×#585C22semidirect
17. C24×H(5,𝔽2)C22semidirect
18. C2×#63090C22semidirect
19. C22×#3584C22semidirect
20. C22×#3586C22semidirect
21. C22×#3586C22semidirect
22. C22×#3585C22semidirect
23. C22×#3585C22semidirect
24. C22×#3585C22semidirect
25. C22×#3585C22semidirect
26. C22×#3585C22semidirect
27. C23×#577C22semidirect
28. C23×#576C22semidirect
30. C23×#575C22semidirect
31. C23×#575C22semidirect
32. C23×#575C22semidirect
33. C23×#575C22semidirect
34. C24×AGL(1,ℤ/8)C22semidirect
35. C24×AGL(1,ℤ/8)C22semidirect
36. C23×#568C22semidirect
37. C23×#568C22semidirect
38. C22×#3449C22semidirect
39. C23×#535C22semidirect
40. #10576178C22direct (N × H)
41. C2×#61110C22semidirect
42. C2×#61109C22semidirect
43. C2×#61107C22semidirect
44. C2×#61106C22semidirect
45. C22×#3292C22semidirect
46. C22×#3291C22semidirect
47. C22×#3290C22semidirect
48. C22×#3289C22semidirect
49. C22×#3288C22semidirect
50. C22×#3288C22semidirect
51. C2×#60644C22semidirect
52. C22×#3155C22semidirect
53. C22×#3153C22semidirect
54. C22×#3154C22semidirect
55. C22×#3151C22semidirect
56. C23×#472C22semidirect
57. C2×#60469C22semidirect
58. C22×#3069C22semidirect
59. C22×#3069C22semidirect
60. C22×#3068C22semidirect
61. C22×#3068C22semidirect
62. C22×#3068C22semidirect
63. C22×#3068C22semidirect
64. C22×#3068C22semidirect
65. C22×#3067C22semidirect
66. C23×#471C22semidirect
67. C22×#3022C22semidirect
68. C23×#455C22semidirect
69. C2×#60387C22semidirect
70. C22×#3018C22semidirect
71. C22×#3021C22semidirect
72. C22×#3021C22semidirect
73. C22×#3021C22semidirect
74. C22×#3020C22semidirect
75. C22×#3019C22semidirect
76. C22×#3019C22semidirect
77. C22×#3019C22semidirect
78. C23×#454C22semidirect
79. C23×#453C22semidirect
80. C23×#453C22semidirect
81. C2×#60182C22semidirect
82. C22×#2957C22semidirect
83. C22×#2956C22semidirect
84. C22×#2955C22semidirect
85. C23×#430C22semidirect
86. C23×#413C22semidirect
87. C23×#413C22semidirect
88. C23×#421C22semidirect
89. C23×#421C22semidirect
90. C24×#100C22semidirect
91. C22×#2873C22semidirect
93. C22×#585C23semidirect
94. C22×#585C23semidirect
95. C22×#585C23semidirect
96. C22×#585C23semidirect
97. C23×2−1+4C23semidirect
98. C23×2−1+4C23semidirect
100. C23×H(5,𝔽2)C23semidirect
101. C23×H(5,𝔽2)C23semidirect
102. C23×H(5,𝔽2)C23semidirect
103. C23×H(5,𝔽2)C23semidirect
109. #63090C23semidirect
110. C2×#3586C23semidirect
111. C2×#3586C23semidirect
112. C2×#3585C23semidirect
113. C2×#3585C23semidirect
114. C2×#3585C23semidirect
115. C2×#3585C23semidirect
116. C2×#3585C23semidirect
117. C2×#3584C23semidirect
118. C22×#578C23semidirect
119. C22×#577C23semidirect
120. C22×#577C23semidirect
121. C22×#577C23semidirect
122. C22×#577C23semidirect
123. C22×#576C23semidirect
124. C22×#576C23semidirect
125. C22×#576C23semidirect
126. C22×#575D4semidirect
127. C22×#575D4semidirect
128. C22×#575D4semidirect
134. C22×#575C23semidirect
135. C22×#575C23semidirect
136. C22×#575C23semidirect
137. C22×#575C23semidirect
138. C22×#575C23semidirect
139. C22×#575C23semidirect
140. C22×#575C23semidirect
141. C22×#575C23semidirect
142. C23×#137D4semidirect
143. C23×#137D4semidirect
144. C23×#137C23semidirect
145. C23×#137C23semidirect
146. C23×#137C23semidirect
147. C23×#137C23semidirect
148. C23×#137C23semidirect
149. C23×AGL(1,ℤ/8)D4semidirect
150. C23×AGL(1,ℤ/8)D4semidirect
152. C23×AGL(1,ℤ/8)C23semidirect
153. C23×AGL(1,ℤ/8)C23semidirect
154. C23×AGL(1,ℤ/8)C23semidirect
155. C23×AGL(1,ℤ/8)C23semidirect
156. C23×AGL(1,ℤ/8)C23semidirect
157. C23×AGL(1,ℤ/8)C23semidirect
158. C23×AGL(1,ℤ/8)C23semidirect
159. C23×AGL(1,ℤ/8)C23semidirect
160. C23×AGL(1,ℤ/8)C23semidirect
161. C23×AGL(1,ℤ/8)C23semidirect
162. C23×AGL(1,ℤ/8)C23semidirect
164. C23×#135C23semidirect
165. C24×SD16C23semidirect
166. C24×D8C23semidirect
167. C22×#568C23semidirect
168. C22×#568C23semidirect
169. C22×#568C23semidirect
170. C22×#568C23semidirect
171. C22×#568C23semidirect
172. C22×#568C23semidirect
173. C23×#131C23semidirect
174. C23×#131C23semidirect
178. C2×#3449C23semidirect
179. C22×#536C23semidirect
180. C22×#535C23semidirect
181. C22×#535C23semidirect
182. C22×#535C23semidirect
183. C22×#532C23semidirect
184. C23×#127C23semidirect
185. C23×#124C23semidirect
187. #61110C23semidirect
188. #61109C23semidirect
189. #61107C23semidirect
190. #61106C23semidirect
191. C2×#3292C23semidirect
192. C2×#3291C23semidirect
193. C2×#3290C23semidirect
194. C2×#3289C23semidirect
195. C2×#3288C23semidirect
196. C2×#3288C23semidirect
197. #60644C23semidirect
198. C2×#3155C23semidirect
199. C2×#3154C23semidirect
200. C2×#3153C23semidirect
201. C2×#3151C23semidirect
202. C22×#497C23semidirect
203. C22×#496C23semidirect
204. C22×#496C23semidirect
205. C22×#495C23semidirect
206. C22×#493C23semidirect
207. C22×#492C23semidirect
208. #60469C23semidirect
209. C2×#3069C23semidirect
210. C2×#3069C23semidirect
211. C2×#3068C23semidirect
212. C2×#3068C23semidirect
213. C2×#3068C23semidirect
214. C2×#3068C23semidirect
215. C2×#3068C23semidirect
216. C2×#3067C23semidirect
217. C22×#473C23semidirect
218. C22×#472C23semidirect
219. C22×#472C23semidirect
220. C22×#472C23semidirect
221. C22×#471C23semidirect
222. C22×#471C23semidirect
223. C22×#471C23semidirect
224. C22×#471C23semidirect
225. #60387C23semidirect
226. C2×#3022C23semidirect
227. C2×#3021C23semidirect
228. C2×#3021C23semidirect
229. C2×#3021C23semidirect
230. C2×#3020C23semidirect
231. C2×#3019C23semidirect
232. C2×#3019C23semidirect
233. C2×#3019C23semidirect
234. C2×#3018C23semidirect
235. C22×#456C23semidirect
236. C22×#454C23semidirect
237. C22×#454C23semidirect
238. C22×#454C23semidirect
239. C22×#455C23semidirect
240. C22×#455C23semidirect
241. C22×#455C23semidirect
242. C22×#453C23semidirect
243. C22×#453C23semidirect
244. C22×#453C23semidirect
245. C22×#453C23semidirect
246. C22×#453C23semidirect
247. #60182C23semidirect
248. C2×#2957C23semidirect
249. C2×#2956C23semidirect
250. C2×#2955C23semidirect
251. C22×#444C23semidirect
252. C22×#443C23semidirect
253. C22×#430C23semidirect
254. C22×#430C23semidirect
255. C22×#430C23semidirect
256. C23×#108C23semidirect
257. C22×#421C23semidirect
258. C22×#421C23semidirect
259. C22×#421C23semidirect
260. C22×#421C23semidirect
261. C22×#421C23semidirect
262. C22×#421C23semidirect
263. C23×#104C23semidirect
264. C23×#104C23semidirect
265. C22×#413C23semidirect
266. C22×#413C23semidirect
267. C22×#413C23semidirect
268. C22×#413C23semidirect
269. C22×#413C23semidirect
270. C23×#101C23semidirect
271. C23×#101C23semidirect
272. C23×#100C23semidirect
273. C23×#100C23semidirect
274. C23×#100C23semidirect
275. C23×#100C23semidirect
276. C23×#100C23semidirect
277. C2×#2873C23semidirect
278. C22×#405C23semidirect
279. C22×C4×M16C23semidirect
281. C2×#585C24semidirect
282. C2×#585C24semidirect
283. C2×#585C24semidirect
284. C2×#585C24semidirect
286. C22×2−1+4C24semidirect
287. C22×2−1+4C24semidirect
288. C22×2−1+4C24semidirect
292. C22×H(5,𝔽2)C24semidirect
293. C22×H(5,𝔽2)C24semidirect
294. C22×H(5,𝔽2)C24semidirect
295. C22×H(5,𝔽2)C24semidirect
296. C22×H(5,𝔽2)C24semidirect
330. #3586C24semidirect
331. #3586C24semidirect
332. #3585C24semidirect
333. #3585C24semidirect
334. #3585C24semidirect
335. #3585C24semidirect
336. #3584C24semidirect
337. C2×#578C24semidirect
338. C2×#577C24semidirect
339. C2×#577C24semidirect
340. C2×#577C24semidirect
341. C2×#577C24semidirect
342. C2×#576C24semidirect
343. C2×#576C24semidirect
344. C2×#576C24semidirect
346. C2×#575C2×D4semidirect
347. C2×#575C2×D4semidirect
348. C2×#575C2×D4semidirect
349. C2×#575C2×D4semidirect
355. C2×#575C24semidirect
356. C2×#575C24semidirect
357. C2×#575C24semidirect
358. C2×#575C24semidirect
359. C2×#575C24semidirect
360. C2×#575C24semidirect
361. C2×#575C24semidirect
362. C2×#575C24semidirect
365. C22×#137C2×D4semidirect
366. C22×#137C2×D4semidirect
367. C22×#137C2×D4semidirect
368. C22×#137C2×D4semidirect
371. C22×#137C24semidirect
372. C22×#137C24semidirect
373. C22×#137C24semidirect
374. C22×#137C24semidirect
375. C22×#137C24semidirect
376. C22×#137C24semidirect
379. C22×AGL(1,ℤ/8)C2×D4semidirect
380. C22×AGL(1,ℤ/8)C2×D4semidirect
381. C22×AGL(1,ℤ/8)C2×D4semidirect
382. C22×AGL(1,ℤ/8)C2×D4semidirect
387. C22×AGL(1,ℤ/8)C24semidirect
388. C22×AGL(1,ℤ/8)C24semidirect
389. C22×AGL(1,ℤ/8)C24semidirect
390. C22×AGL(1,ℤ/8)C24semidirect
391. C22×AGL(1,ℤ/8)C24semidirect
392. C22×AGL(1,ℤ/8)C24semidirect
393. C22×AGL(1,ℤ/8)C24semidirect
394. C22×AGL(1,ℤ/8)C24semidirect
395. C22×AGL(1,ℤ/8)C24semidirect
396. C22×AGL(1,ℤ/8)C24semidirect
397. C22×AGL(1,ℤ/8)C24semidirect
398. C22×AGL(1,ℤ/8)C24semidirect
399. C22×#135C2×D4semidirect
400. C22×#135C2×D4semidirect
403. C22×#135C24semidirect
404. C23×Q16C2×D4semidirect
405. C23×Q16C24semidirect
406. C23×SD16C2×D4semidirect
407. C23×SD16C2×D4semidirect
409. C23×SD16C24semidirect
410. C23×SD16C24semidirect
411. C23×SD16C24semidirect
412. C23×D8C2×D4semidirect
414. C23×D8C24semidirect
415. C23×D8C24semidirect
416. C2×#568C24semidirect
417. C2×#568C24semidirect
418. C2×#568C24semidirect
419. C2×#568C24semidirect
420. C2×#568C24semidirect
421. C2×#568C24semidirect
423. C22×#131C24semidirect
424. C22×#131C24semidirect
425. C22×#131C24semidirect
443. #3449C24semidirect
444. C2×#536C24semidirect
445. C2×#535C24semidirect
446. C2×#535C24semidirect
447. C2×#535C24semidirect
448. C2×#532C24semidirect
449. C22×C4⋊Q8C24semidirect
451. C22×#127C24semidirect
452. C22×#127C24semidirect
454. C22×#124C24semidirect
455. C22×#124C24semidirect
459. #3292C24semidirect
460. #3291C24semidirect
461. #3290C24semidirect
462. #3289C24semidirect
463. #3288C24semidirect
464. #3288C24semidirect
465. #3155C24semidirect
466. #3154C24semidirect
467. #3153C24semidirect
468. #3151C24semidirect
469. C2×#497C24semidirect
470. C2×#496C24semidirect
471. C2×#496C24semidirect
472. C2×#495C24semidirect
473. C2×#493C24semidirect
474. C2×#492C24semidirect
475. #3069C24semidirect
476. #3069C24semidirect
477. #3068C24semidirect
478. #3068C24semidirect
479. #3068C24semidirect
480. #3068C24semidirect
481. #3067C24semidirect
482. C2×#473C24semidirect
483. C2×#472C24semidirect
484. C2×#472C24semidirect
485. C2×#472C24semidirect
486. C2×#471C24semidirect
487. C2×#471C24semidirect
488. C2×#471C24semidirect
489. C2×#471C24semidirect
490. #3022C24semidirect
491. #3021C24semidirect
492. #3021C24semidirect
493. #3020C24semidirect
494. #3019C24semidirect
495. #3019C24semidirect
496. #3018C24semidirect
497. C2×#456C24semidirect
498. C2×#454C24semidirect
499. C2×#454C24semidirect
500. C2×#454C24semidirect
501. C2×#455C24semidirect
502. C2×#455C24semidirect
503. C2×#455C24semidirect
504. C2×#453C24semidirect
505. C2×#453C24semidirect
506. C2×#453C24semidirect
507. C2×#453C24semidirect
508. C2×#453C24semidirect
509. #2957C24semidirect
510. #2956C24semidirect
511. #2955C24semidirect
512. C2×#444C24semidirect
513. C2×#443C24semidirect
514. C2×#430C24semidirect
515. C2×#430C24semidirect
516. C2×#430C24semidirect
517. C22×#108C24semidirect
518. C22×#108C24semidirect
519. C2×#421C24semidirect
520. C2×#421C24semidirect
521. C2×#421C24semidirect
522. C2×#421C24semidirect
523. C2×#421C24semidirect
524. C2×#421C24semidirect
526. C22×#104C24semidirect
527. C22×#104C24semidirect
528. C22×#104C24semidirect
529. C2×#413C24semidirect
530. C2×#413C24semidirect
531. C2×#413C24semidirect
532. C2×#413C24semidirect
533. C2×#413C24semidirect
534. C22×#101C24semidirect
535. C22×#101C24semidirect
536. C22×#101C24semidirect
537. C22×#101C24semidirect
539. C22×#100C24semidirect
540. C22×#100C24semidirect
541. C22×#100C24semidirect
542. C22×#100C24semidirect
543. C22×#100C24semidirect
544. C22×#100C24semidirect
545. C22×#100C24semidirect
546. #2873C24semidirect
547. C2×#405C24semidirect
548. C2×C4×M16C24semidirect
549. C22×#97C24semidirect
550. C22×C4×C8C24semidirect
553. #585C25semidirect
554. #585C25semidirect
556. C2×2−1+4C25semidirect
557. C2×2−1+4C25semidirect
558. C2×2−1+4C25semidirect
562. C2×H(5,𝔽2)C25semidirect
563. C2×H(5,𝔽2)C25semidirect
564. C2×H(5,𝔽2)C25semidirect
565. C2×H(5,𝔽2)C25semidirect
640. #578C25semidirect
641. #577C25semidirect
642. #577C25semidirect
643. #577C25semidirect
644. #576C25semidirect
645. #576C25semidirect
647. #575C22×D4semidirect
648. #575C22×D4semidirect
649. #575C22×D4semidirect
654. #575C25semidirect
655. #575C25semidirect
656. #575C25semidirect
657. #575C25semidirect
660. C2×#137C22×D4semidirect
661. C2×#137C22×D4semidirect
662. C2×#137C22×D4semidirect
663. C2×#137C22×D4semidirect
666. C2×#137C25semidirect
667. C2×#137C25semidirect
668. C2×#137C25semidirect
669. C2×#137C25semidirect
670. C2×#137C25semidirect
671. C2×#137C25semidirect
674. C2×AGL(1,ℤ/8)C22×D4semidirect
675. C2×AGL(1,ℤ/8)C22×D4semidirect
676. C2×AGL(1,ℤ/8)C22×D4semidirect
677. C2×AGL(1,ℤ/8)C22×D4semidirect
682. C2×AGL(1,ℤ/8)C25semidirect
683. C2×AGL(1,ℤ/8)C25semidirect
684. C2×AGL(1,ℤ/8)C25semidirect
685. C2×AGL(1,ℤ/8)C25semidirect
686. C2×AGL(1,ℤ/8)C25semidirect
687. C2×AGL(1,ℤ/8)C25semidirect
688. C2×AGL(1,ℤ/8)C25semidirect
689. C2×AGL(1,ℤ/8)C25semidirect
690. C2×AGL(1,ℤ/8)C25semidirect
691. C2×AGL(1,ℤ/8)C25semidirect
693. C2×#135C22×D4semidirect
694. C2×#135C22×D4semidirect
697. C2×#135C25semidirect
699. C22×Q16C22×D4semidirect
700. C22×Q16C25semidirect
703. C22×SD16C22×D4semidirect
704. C22×SD16C22×D4semidirect
706. C22×SD16C25semidirect
707. C22×SD16C25semidirect
708. C22×SD16C25semidirect
710. C22×D8C22×D4semidirect
712. C22×D8C25semidirect
713. C22×D8C25semidirect
714. #568C25semidirect
715. #568C25semidirect
716. #568C25semidirect
717. #568C25semidirect
719. C2×#131C25semidirect
720. C2×#131C25semidirect
721. C2×#131C25semidirect
751. #536C25semidirect
752. #535C25semidirect
753. #535C25semidirect
754. #532C25semidirect
755. C2×C4⋊Q8C25semidirect
757. C2×#127C25semidirect
758. C2×#127C25semidirect
760. C2×#124C25semidirect
761. C2×#124C25semidirect
766. #497C25semidirect
767. #496C25semidirect
768. #496C25semidirect
769. #495C25semidirect
770. #493C25semidirect
771. #492C25semidirect
772. #473C25semidirect
773. #472C25semidirect
774. #472C25semidirect
775. #471C25semidirect
776. #471C25semidirect
777. #471C25semidirect
778. #456C25semidirect
779. #455C25semidirect
780. #455C25semidirect
781. #454C25semidirect
782. #454C25semidirect
783. #453C25semidirect
784. #453C25semidirect
785. #453C25semidirect
786. #444C25semidirect
787. #443C25semidirect
788. #430C25semidirect
789. #430C25semidirect
790. C2×#108C25semidirect
791. C2×#108C25semidirect
792. #421C25semidirect
793. #421C25semidirect
794. #421C25semidirect
795. #421C25semidirect
797. C2×#104C25semidirect
798. C2×#104C25semidirect
799. C2×#104C25semidirect
800. #413C25semidirect
801. #413C25semidirect
802. #413C25semidirect
803. C2×#101C25semidirect
804. C2×#101C25semidirect
805. C2×#101C25semidirect
806. C2×#101C25semidirect
808. C2×#100C25semidirect
809. C2×#100C25semidirect
810. C2×#100C25semidirect
811. C2×#100C25semidirect
812. C2×#100C25semidirect
813. C2×#100C25semidirect
814. #405C25semidirect
815. C4×M16C25semidirect
816. C2×#97C25semidirect
817. C2×C4×C8C25semidirect
826. 2−1+4C26semidirect
829. H(5,𝔽2)C26semidirect
933. #137C23×D4semidirect
934. #137C23×D4semidirect
937. #137C26semidirect
940. AGL(1,ℤ/8)C23×D4semidirect
941. AGL(1,ℤ/8)C23×D4semidirect
945. AGL(1,ℤ/8)C26semidirect
947. #135C23×D4semidirect
950. C2×Q16C23×D4semidirect
951. C2×Q16C26semidirect
954. C2×SD16C23×D4semidirect
955. C2×SD16C23×D4semidirect
957. C2×SD16C26semidirect
958. C2×SD16C26semidirect
960. C2×D8C23×D4semidirect
962. C2×D8C26semidirect
964. #131C26semidirect
992. C4⋊Q8C26semidirect
994. #127C26semidirect
996. #124C26semidirect
1000. #108C26semidirect
1002. #104C26semidirect
1003. #101C26semidirect
1004. #101C26semidirect
1006. #100C26semidirect
1007. #100C26semidirect
1008. #97C26semidirect
1009. C4×C8C26semidirect
1173. C22#10576178direct (N × H)
1187. C2C2×#10576178direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#606442
C22×#604692
C23×#30682
C22×#601822
C22×#611092
C22×#611072
C22×#611062
C22×#603872
C22×#630902
C2×#105761782
C23×#30192
C23×#30212
C23×#35852
C22×#611102