Finite Group Databasebeta

← C22×#62862 #72281007

Subgroups — C22×#62862 #72281007

Order 1024.

486493 conjugacy classes of subgroups.

The subgroup lattice has 1305 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#62862C21192yesmaximal, direct product factor
2C22×#3545C214yesmaximal, complemented
3C22×#3543C214yesmaximal, complemented
4C22×#3533C218yesmaximal, complemented
5C22×#3534C218yesmaximal, complemented
6C22×#3542C2116yesmaximal, complemented
7C22×#3532C218yesmaximal, complemented
8C22×#3491C212yesmaximal, complemented
9C22×#3485C212yesmaximal, complemented
10C22×#3490C214yesmaximal, complemented
11C22×#3484C214yesmaximal, complemented
12C23×#535C211yesmaximal, characteristic, complemented
13C23×#534C212yesmaximal, complemented
14C23×H(5,𝔽2)C2212yescomplemented
15C24×#41C2211yescharacteristic, complemented
16C25×D4C2211yescharacteristic, complemented
17C25×D4C2212yescomplemented
18#62862C2214096yesdirect product factor
19C2×#3491C221192yescomplemented
20C2×#3485C221192yescomplemented
21C2×#3490C221384yescomplemented
22C2×#3484C221384yescomplemented
23C2×#3545C221384yescomplemented
24C2×#3543C221384yescomplemented
25C2×#3533C221768yescomplemented
26C2×#3534C221768yescomplemented
27C2×#3542C2211536yescomplemented
28C2×#3532C221768yescomplemented
29C22×#559C2214yescomplemented
30C22×#555C2218yescomplemented
31C22×#553C22116yescomplemented
32C22×#552C22116yescomplemented
33C22×#551C22116yescomplemented
34C22×#551C22116yescomplemented
35C22×#551C2218yescomplemented
36C22×#551C22116yescomplemented
37C22×#550C2218yescomplemented
38C22×#547C22116yescomplemented
39C22×#546C22116yescomplemented
40C22×#546C22116yescomplemented
41C22×#546C22116yescomplemented
42C22×#546C22116yescomplemented
43C22×#546C22116yescomplemented
44C22×#546C22116yescomplemented
45C22×D42C22116yescomplemented
46C22×D42C22116yescomplemented
47C22×D42C2214yescomplemented
48C22×#563C2214yescomplemented
49C22×#562C22116yescomplemented
50C22×#562C2218yescomplemented
51C22×H(3,𝔽4)C2214yescomplemented
52C22×#560C2218yescomplemented
53C22×#560C22116yescomplemented
54C22×#560C2218yescomplemented
55C22×#536C2214yescomplemented
56C22×#542C22116yescomplemented
57C22×#540C22116yescomplemented
58C22×#540C22116yescomplemented
59C22×#537C2218yescomplemented
60C22×#535C2218yescomplemented
61C22×#535C2218yescomplemented
62C22×#535C2218yescomplemented
63C22×#535C22116yescomplemented
64C22×#535C22196yescomplemented
65C22×#539C2218yescomplemented
66C22×#539C2218yescomplemented
67C22×#538C22116yescomplemented
68C22×#538C22116yescomplemented
69C22×#538C22116yescomplemented
70C22×#538C2218yescomplemented
71C22×#543C2212yescomplemented
72C22×#534C2212yes—
73C22×#534C2218yescomplemented
74C22×#534C2218yescomplemented
75C22×#534C2214yescomplemented
76C22×#534C2218yescomplemented
77C22×#534C2218yescomplemented
78C22×#534C2218yescomplemented
79C22×#534C2214yescomplemented
80C22×#534C2218yescomplemented
81C22×#534C221192yescomplemented
82C23×#127C2212yescomplemented
83C22×#529C2218yescomplemented
84C23×#124C2212yescomplemented
85C22×#525C2218yescomplemented
86C22×#525C2214yescomplemented
87C22×#525C22116yescomplemented
88C23×#123C2214yescomplemented
89C23×#123C2214yescomplemented
90C23×#123C2214yescomplemented
91C23×#121C2218yescomplemented
92C23×#121C2214yescomplemented
93C23×#120C2214yescomplemented
94C23×#120C2214yescomplemented
95C23×#120C2214yescomplemented
96C23×#120C2218yescomplemented
97C22×#518C2214yescomplemented
98C22×#518C2212yescomplemented
99C23×#117C2211yescharacteristic, complemented
100C24×C22⋊C4C2212yescomplemented
101C27C2312yes—
102C27C2312yescomplemented
103C22×H(5,𝔽2)—432no—
104C22×H(5,𝔽2)C23196yescomplemented
105C23×#41—416no—
106C23×#41C2318yes—
107C23×#41C2314yes—
108C23×#41C2318yescomplemented
109C23×#41C23116yescomplemented
110C23×#41C23148yescomplemented
111C24×Q8C2311yescharacteristic, complemented
112C24×D4—416no—
113C24×D4—432no—
114C24×D4C2314yes—
115C24×D4C2312yes—
116C24×D4C2314yes—
117C24×D4C2312yes—
118C24×D4C2314yes—
119C24×D4C2312yes—
120C24×D4C2318yes—
121C24×D4C2318yes—
122C24×D4C2314yes—
123C24×D4C2318yes—
124C24×D4C23148yescomplemented
125C24×D4C2314yescomplemented
126C24×D4C2318yescomplemented
127C24×D4C2311yescharacteristic, complemented
128C24×D4C2318yescomplemented
129C24×D4C23116yescomplemented
130C24×D4C23196yescomplemented
131C25×C4C2311yescharacteristic
132C25×C4C2312yescomplemented
133C25×C4C2312yescomplemented
134C25×C4C2314yescomplemented
135#3545C2314096yescomplemented
136#3543C2314096yescomplemented
137#3542C23116384yescomplemented
138#3534C2318192yescomplemented
139#3533C2318192yescomplemented
140#3532C2318192yescomplemented
141C2×#563C231192yescomplemented
142C2×#562C231768yescomplemented
143C2×#562C231384yescomplemented
144C2×H(3,𝔽4)C231192yescomplemented
145C2×#560C231384yescomplemented
146C2×#560C231768yescomplemented
147C2×#560C231384yescomplemented
148#3491C2312048yescomplemented
149#3490C2314096yescomplemented
150#3485C2312048yescomplemented
151#3484C2314096yescomplemented
152C2×#559C231192yescomplemented
153C2×#555C231384yescomplemented
154C2×#553C231768yescomplemented
155C2×#552C231768yescomplemented
156C2×#551C231768yescomplemented
157C2×#551C231768yescomplemented
158C2×#551C231384yescomplemented
159C2×#551C231768yescomplemented
160C2×#550C231384yescomplemented
161C2×#547C231768yescomplemented
162C2×#546C231768yescomplemented
163C2×#546C231768yescomplemented
164C2×#546C231768yescomplemented
165C2×#546C231768yescomplemented
166C2×#546C231768yescomplemented
167C2×#546C231768yescomplemented
168C2×D42C231768yescomplemented
169C2×D42C231192yescomplemented
170C2×D42C231768yescomplemented
171C2×#543C23196yescomplemented
172C2×#542C231768yescomplemented
173C2×#540C231768yescomplemented
174C2×#540C231768yescomplemented
175C2×#539C231384yescomplemented
176C2×#539C231384yescomplemented
177C2×#538C231768yescomplemented
178C2×#538C231768yescomplemented
179C2×#538C231768yescomplemented
180C2×#538C231384yescomplemented
181C2×#537C231384yescomplemented
182C2×#536C231192yescomplemented
183C2×#535C231384yescomplemented
184C2×#535C231384yescomplemented
185C2×#535C231384yescomplemented
186C2×#535C231768yescomplemented
187C2×#535C2311024yescomplemented
188C2×#534C23196yes—
189C2×#534C231384yescomplemented
190C2×#534C231384yescomplemented
191C2×#534C231192yescomplemented
192C2×#534C231384yescomplemented
193C2×#534C231384yescomplemented
194C2×#534C231384yescomplemented
195C2×#534C231384yescomplemented
196C2×#534C231192yescomplemented
197C2×#534C2312048yescomplemented
198C22×C4⋊Q8C2318yescomplemented
199C22×#127C2314yes—
200C22×#127C23196yescomplemented
201C22×#127C2318yescomplemented
202C22×#127C2314yescomplemented
203C22×#127C23116yescomplemented
204C2×#529C231384yescomplemented
205C22×#126C23116yescomplemented
206C22×#126C23116yescomplemented
207C22×#126C23116yescomplemented
208C22×#126C23116yescomplemented
209C22×#125C2318yescomplemented
210C22×#125C23116yescomplemented
211C22×#124C2314yes—
212C22×#124C2318yescomplemented
213C22×#124C2314yescomplemented
214C22×#124C2318yescomplemented
215C22×#124C23116yescomplemented
216C22×#124C23116yescomplemented
217C22×#124C2318yescomplemented
218C22×#124C23116yescomplemented
219C22×#124C23196yescomplemented
220C2×#525C231768yescomplemented
221C2×#525C231384yescomplemented
222C2×#525C231192yescomplemented
223C22×#123C2318yes—
224C22×#123C2318yes—
225C22×#123C23116yes—
226C22×#123C2318yes—
227C22×#123C2318yescomplemented
228C22×#123C2318yescomplemented
229C22×#123C2318yescomplemented
230C22×#123C2318yescomplemented
231C22×#123C2318yescomplemented
232C22×#123C23116yescomplemented
233C22×#123C2318yescomplemented
234C22×#123C23116yescomplemented
235C22×#123C23116yescomplemented
236C22×#123C23116yescomplemented
237C22×#123C23116yescomplemented
238C22×#123C2318yescomplemented
239C22×#123C23116yescomplemented
240C22×#123C23116yescomplemented
241C22×#123C231192yescomplemented
242C22×#123C231192yescomplemented
243C22×#123C231192yescomplemented
244C22×C22⋊Q8C23116yescomplemented
245C22×C22⋊Q8C2318yescomplemented
246C22×C22⋊Q8C23116yescomplemented
247C22×C22⋊Q8C23116yescomplemented
248C22×C22⋊Q8C2318yescomplemented
249C22×C22⋊Q8C23116yescomplemented
250C22×C22⋊Q8C23116yescomplemented
251C22×#121C23116yes—
252C22×#121C23116yes—
253C22×#121C2318yes—
254C22×#121C23116yes—
255C22×#121C2318yes—
256C22×#121C23116yescomplemented
257C22×#121C23116yescomplemented
258C22×#121C2318yescomplemented
259C22×#121C23116yescomplemented
260C22×#121C2318yescomplemented
261C22×#121C23116yescomplemented
262C22×#121C23116yescomplemented
263C22×#121C23116yescomplemented
264C22×#121C23116yescomplemented
265C22×#121C23116yescomplemented
266C22×#121C23116yescomplemented
267C22×#121C23116yescomplemented
268C22×#121C23116yescomplemented
269C22×#121C23116yescomplemented
270C22×#121C231384yescomplemented
271C22×#121C231192yescomplemented
272C22×#120C2318yes—
273C22×#120C2318yes—
274C22×#120C2318yes—
275C22×#120C2318yes—
276C22×#120C2318yes—
277C22×#120C23116yes—
278C22×#120C23116yes—
279C22×#120C231192yescomplemented
280C22×#120C2318yescomplemented
281C22×#120C2318yescomplemented
282C22×#120C2318yescomplemented
283C22×#120C2318yescomplemented
284C22×#120C23116yescomplemented
285C22×#120C2318yescomplemented
286C22×#120C23116yescomplemented
287C22×#120C2318yescomplemented
288C22×#120C23116yescomplemented
289C22×#120C2318yescomplemented
290C22×#120C231192yescomplemented
291C22×#120C231192yescomplemented
292C22×#120C231384yescomplemented
293C2×#518C231192yescomplemented
294C2×#518C23196yescomplemented
295C22×C4×Q8C2318yescomplemented
296C22×C4×D4C23116yes—
297C22×C4×D4C23116yescomplemented
298C22×C4×D4C23116yescomplemented
299C22×C4×D4C23116yescomplemented
300C22×C4×D4C23116yescomplemented
301C22×C4×D4C23116yescomplemented
302C22×C4×D4C23116yescomplemented
303C22×C4×D4C23116yescomplemented
304C22×C4×D4C2318yescomplemented
305C22×#117C2318yescomplemented
306C22×#117C2318yescomplemented
307C22×#117C2314yescomplemented
308C22×#117C23116yescomplemented
309C22×#117C23116yescomplemented
310C22×#117C23148yescomplemented
311C23×C4⋊C4C2312yescomplemented
312C23×C4⋊C4C2318yescomplemented
313C23×C4⋊C4C2318yescomplemented
314C23×C22⋊C4C2314yes—
315C23×C22⋊C4C2318yes—
316C23×C22⋊C4C2312yes—
317C23×C22⋊C4C2318yes—
318C23×C22⋊C4C23196yescomplemented
319C23×C22⋊C4C2314yescomplemented
320C23×C22⋊C4C2318yescomplemented
321C23×C22⋊C4C2318yescomplemented
322C23×C22⋊C4C2314yescomplemented
323C23×C22⋊C4C2318yescomplemented
324C23×C22⋊C4C2318yescomplemented
325C23×C22⋊C4C23116yescomplemented
326C23×C22⋊C4C2318yescomplemented
327C23×C42C2312yescomplemented
328C26—232no—
329C26—416no—
330C26—816no—
331C26—816no—
332C26C2412yes—
333C26C2412yes—
334C26C2412yes—
335C26C2414yes—
336C26C2414yes—
337C26C2414yes—
338C26C24148yes—
339C26C2414yes—
340C26C2418yes—
341C26C2411yescharacteristic
342C26C24148yescomplemented
343C2×H(5,𝔽2)—4768no—
344C2×H(5,𝔽2)C241512yescomplemented
345C22×#41—464no—
346C22×#41—4384no—
347C22×#41—464no—
348C22×#41—432no—
349C22×#41—864no—
350C22×#41C241192yes—
351C22×#41C24196yes—
352C22×#41C241192yescomplemented
353C22×#41C241384yescomplemented
354C22×#41C241256yescomplemented
355C23×Q8—48no—
356C23×Q8C2414yes—
357C23×Q8C2414yes—
358C23×Q8C2418yes—
359C23×Q8C24124yescomplemented
360C23×D4—264no—
361C23×D4—232no—
362C23×D4—416no—
363C23×D4—416no—
364C23×D4—432no—
365C23×D4—432no—
366C23×D4—4384no—
367C23×D4—432no—
368C23×D4—48no—
369C23×D4—464no—
370C23×D4—464no—
371C23×D4—4768no—
372C23×D4—432no—
373C23×D4—464no—
374C23×D4—832no—
375C23×D4—832no—
376C23×D4—864no—
377C23×D4C2418yes—
378C23×D4C2418yes—
379C23×D4C2418yes—
380C23×D4C24196yes—
381C23×D4C24148yes—
382C23×D4C2412yes—
383C23×D4C2412yes—
384C23×D4C2414yes—
385C23×D4C2414yes—
386C23×D4C2412yes—
387C23×D4C2412yes—
388C23×D4C2414yes—
389C23×D4C2418yes—
390C23×D4C24196yes—
391C23×D4C24116yes—
392C23×D4C24148yes—
393C23×D4C24196yes—
394C23×D4C24148yes—
395C23×D4C241192yes—
396C23×D4C24116yes—
397C23×D4C24116yes—
398C23×D4C241192yes—
399C23×D4C24196yes—
400C23×D4C2418yes—
401C23×D4C24116yes—
402C23×D4C2414yes—
403C23×D4C24116yes—
404C23×D4C24116yes—
405C23×D4C241192yes—
406C23×D4C241256yescomplemented
407C23×D4C24196yescomplemented
408C23×D4C241192yescomplemented
409C23×D4C24124yescomplemented
410C23×D4C241192yescomplemented
411C23×D4C241384yescomplemented
412C23×D4C241512yescomplemented
413C24×C4—216no—
414C24×C4—416no—
415C24×C4—416no—
416C24×C4—816no—
417C24×C4C2411yescharacteristic
418C24×C4C2411yescharacteristic
419C24×C4C2414yes—
420C24×C4C24124yes—
421C24×C4C2414yes—
422C24×C4C2412yes—
423C24×C4C2418yes—
424C24×C4C2418yes—
425C24×C4C2418yes—
426C24×C4C24116yes—
427C24×C4C2418yes—
428C24×C4C2414yes—
429C24×C4C2414yes—
430C24×C4C24116yes—
431C24×C4C2418yes—
432C24×C4C24148yescomplemented
433C24×C4C24148yescomplemented
434C24×C4C24196yescomplemented
435#563C2411024yescomplemented
436#562C2414096yescomplemented
437#562C2412048yescomplemented
438H(3,𝔽4)C2411024yescomplemented
439#560C2412048yescomplemented
440#560C2414096yescomplemented
441#560C2412048yescomplemented
442#559C2411024yescomplemented
443#555C2412048yescomplemented
444#553C2414096yescomplemented
445#552C2414096yescomplemented
446#551C2414096yescomplemented
447#551C2414096yescomplemented
448#551C2412048yescomplemented
449#551C2414096yescomplemented
450#550C2412048yescomplemented
451#547C2414096yescomplemented
452#546C2414096yescomplemented
453#546C2414096yescomplemented
454#546C2414096yescomplemented
455#546C2414096yescomplemented
456#546C2414096yescomplemented
457#546C2414096yescomplemented
458D42C2414096yescomplemented
459D42C2411024yescomplemented
460D42C2414096yescomplemented
461#543C241512yescomplemented
462#542C2414096yescomplemented
463#540C2414096yescomplemented
464#540C2414096yescomplemented
465#539C2412048yescomplemented
466#539C2412048yescomplemented
467#538C2414096yescomplemented
468#538C2414096yescomplemented
469#538C2414096yescomplemented
470#538C2412048yescomplemented
471#537C2412048yescomplemented
472#536C2411024yescomplemented
473#535C2412048yescomplemented
474#535C2412048yescomplemented
475#535C2412048yescomplemented
476#535C2414096yescomplemented
477#534C241512yes—
478#534C2412048yescomplemented
479#534C2412048yescomplemented
480#534C2411024yescomplemented
481#534C2412048yescomplemented
482#534C2412048yescomplemented
483#534C2412048yescomplemented
484#534C2412048yescomplemented
485#534C2411024yescomplemented
486C2×C4⋊Q8C241192yescomplemented
487C2×#127C24196yes—
488C2×#127C241192yescomplemented
489C2×#127C24196yescomplemented
490C2×#127C241384yescomplemented
491C2×#127C241512yescomplemented
492#529C2412048yescomplemented
493C2×#126C241384yescomplemented
494C2×#126C241384yescomplemented
495C2×#126C241384yescomplemented
496C2×#126C241384yescomplemented
497C2×#125C241192yescomplemented
498C2×#125C241384yescomplemented
499C2×#124C24196yes—
500C2×#124C241192yescomplemented
501C2×#124C24196yescomplemented
502C2×#124C241192yescomplemented
503C2×#124C241384yescomplemented
504C2×#124C241384yescomplemented
505C2×#124C241192yescomplemented
506C2×#124C241384yescomplemented
507C2×#124C241512yescomplemented
508#525C2414096yescomplemented
509#525C2412048yescomplemented
510#525C2411024yescomplemented
511C2×#123C241192yes—
512C2×#123C241384yes—
513C2×#123C241192yes—
514C2×#123C241192yes—
515C2×#123C241192yescomplemented
516C2×#123C241192yescomplemented
517C2×#123C241192yescomplemented
518C2×#123C241192yescomplemented
519C2×#123C241192yescomplemented
520C2×#123C241384yescomplemented
521C2×#123C241192yescomplemented
522C2×#123C241384yescomplemented
523C2×#123C241384yescomplemented
524C2×#123C241384yescomplemented
525C2×#123C241384yescomplemented
526C2×#123C241192yescomplemented
527C2×#123C241384yescomplemented
528C2×#123C241384yescomplemented
529C2×#123C2411024yescomplemented
530C2×#123C2411024yescomplemented
531C2×#123C2411024yescomplemented
532C2×C22⋊Q8C241384yescomplemented
533C2×C22⋊Q8C241192yescomplemented
534C2×C22⋊Q8C241384yescomplemented
535C2×C22⋊Q8C241384yescomplemented
536C2×C22⋊Q8C241192yescomplemented
537C2×C22⋊Q8C241384yescomplemented
538C2×C22⋊Q8C241384yescomplemented
539C2×#121C241384yes—
540C2×#121C241384yes—
541C2×#121C241192yes—
542C2×#121C241384yes—
543C2×#121C241192yes—
544C2×#121C241384yescomplemented
545C2×#121C241384yescomplemented
546C2×#121C241192yescomplemented
547C2×#121C241384yescomplemented
548C2×#121C241192yescomplemented
549C2×#121C241384yescomplemented
550C2×#121C241384yescomplemented
551C2×#121C241384yescomplemented
552C2×#121C241384yescomplemented
553C2×#121C241384yescomplemented
554C2×#121C241384yescomplemented
555C2×#121C241384yescomplemented
556C2×#121C241384yescomplemented
557C2×#121C241384yescomplemented
558C2×#121C2412048yescomplemented
559C2×#121C2411024yescomplemented
560C2×#120C241192yes—
561C2×#120C241192yes—
562C2×#120C241192yes—
563C2×#120C241192yes—
564C2×#120C241384yes—
565C2×#120C241192yes—
566C2×#120C241384yes—
567C2×#120C2411024yescomplemented
568C2×#120C241192yescomplemented
569C2×#120C241192yescomplemented
570C2×#120C241192yescomplemented
571C2×#120C241192yescomplemented
572C2×#120C241192yescomplemented
573C2×#120C241384yescomplemented
574C2×#120C241384yescomplemented
575C2×#120C241192yescomplemented
576C2×#120C241192yescomplemented
577C2×#120C241384yescomplemented
578C2×#120C2411024yescomplemented
579C2×#120C2411024yescomplemented
580C2×#120C2412048yescomplemented
581#518C2411024yescomplemented
582#518C241512yescomplemented
583C2×C4×Q8C241192yescomplemented
584C2×C4×D4C241384yes—
585C2×C4×D4C241384yescomplemented
586C2×C4×D4C241384yescomplemented
587C2×C4×D4C241384yescomplemented
588C2×C4×D4C241384yescomplemented
589C2×C4×D4C241384yescomplemented
590C2×C4×D4C241384yescomplemented
591C2×C4×D4C241384yescomplemented
592C2×C4×D4C241192yescomplemented
593C2×#117C241192yescomplemented
594C2×#117C241192yescomplemented
595C2×#117C24196yescomplemented
596C2×#117C241384yescomplemented
597C2×#117C241384yescomplemented
598C2×#117C241256yescomplemented
599C22×C4⋊C4C24116yes—
600C22×C4⋊C4C2418yes—
601C22×C4⋊C4C24116yes—
602C22×C4⋊C4C24116yes—
603C22×C4⋊C4C24116yes—
604C22×C4⋊C4C24116yes—
605C22×C4⋊C4C2418yes—
606C22×C4⋊C4C2418yes—
607C22×C4⋊C4C2418yes—
608C22×C4⋊C4C24148yescomplemented
609C22×C4⋊C4C241192yescomplemented
610C22×C4⋊C4C241192yescomplemented
611C22×C22⋊C4C2418yes—
612C22×C22⋊C4C2418yes—
613C22×C22⋊C4C24196yes—
614C22×C22⋊C4C2418yes—
615C22×C22⋊C4C2418yes—
616C22×C22⋊C4C241192yes—
617C22×C22⋊C4C2418yes—
618C22×C22⋊C4C24116yes—
619C22×C22⋊C4C24148yes—
620C22×C22⋊C4C24116yes—
621C22×C22⋊C4C241192yes—
622C22×C22⋊C4C24116yes—
623C22×C22⋊C4C24116yes—
624C22×C22⋊C4C24116yes—
625C22×C22⋊C4C24116yes—
626C22×C22⋊C4C24116yes—
627C22×C22⋊C4C24116yes—
628C22×C22⋊C4C24116yes—
629C22×C22⋊C4C2418yes—
630C22×C22⋊C4C24116yes—
631C22×C22⋊C4C241512yescomplemented
632C22×C22⋊C4C24196yescomplemented
633C22×C22⋊C4C241192yescomplemented
634C22×C22⋊C4C241192yescomplemented
635C22×C22⋊C4C24196yescomplemented
636C22×C22⋊C4C241192yescomplemented
637C22×C22⋊C4C241192yescomplemented
638C22×C22⋊C4C241384yescomplemented
639C22×C22⋊C4C241192yescomplemented
640C22×C42C2414yes—
641C22×C42C2414yes—
642C22×C42C24116yes—
643C22×C42C2418yes—
644C22×C42C24148yescomplemented
645C25—216no—
646C25—216no—
647C25—216no—
648C25—232no—
649C25—232no—
650C25—232no—
651C25—2384no—
652C25—416no—
653C25—48no—
654C25—416no—
655C25—432no—
656C25—4192no—
657C25—416no—
658C25—432no—
659C25—432no—
660C25—432no—
661C25—464no—
662C25—416no—
663C25—432no—
664C25—8192no—
665C25—8192no—
666C25—8256no—
667C25—8256no—
668C25H(5,𝔽2)116yes—
669C25C2514yes—
670C25C2518yes—
671C25C2514yes—
672C25C2514yes—
673C25C2512yes—
674C25C2511yescharacteristic
675C25C25148yes—
676C25C25148yes—
677C25C25148yes—
678C25C25124yes—
679C25C25124yes—
680C25C25124yes—
681C25C251128yes—
682C25C25196yes—
683C25C25148yes—
684C25C25112yes—
685C25C251128yescomplemented
686H(5,𝔽2)—42048no—
687C2×#41—4768no—
688C2×#41—41024no—
689C2×#41—4768no—
690C2×#41—4384no—
691C2×#41—8768no—
692C2×#41C251512yes—
693C2×#41C251256yes—
694C2×#41C251512yescomplemented
695C2×#41C2511024yescomplemented
696C22×Q8—416no—
697C22×Q8—496no—
698C22×Q8—416no—
699C22×Q8—432no—
700C22×Q8C25196yes—
701C22×Q8C25148yes—
702C22×Q8C25148yes—
703C22×Q8C25164yescomplemented
704C22×D4—264no—
705C22×D4—264no—
706C22×D4—2768no—
707C22×D4—264no—
708C22×D4—2384no—
709C22×D4—48no—
710C22×D4—416no—
711C22×D4—48no—
712C22×D4—4192no—
713C22×D4—48no—
714C22×D4—416no—
715C22×D4—48no—
716C22×D4—4192no—
717C22×D4—4384no—
718C22×D4—4384no—
719C22×D4—464no—
720C22×D4—41024no—
721C22×D4—4384no—
722C22×D4—432no—
723C22×D4—416no—
724C22×D4—416no—
725C22×D4—496no—
726C22×D4—464no—
727C22×D4—464no—
728C22×D4—432no—
729C22×D4—464no—
730C22×D4—464no—
731C22×D4—464no—
732C22×D4—4768no—
733C22×D4—4768no—
734C22×D4—42048no—
735C22×D4—4384no—
736C22×D4—4768no—
737C22×D4—8384no—
738C22×D4—8384no—
739C22×D4—8768no—
740C22×D4C25196yes—
741C22×D4C25196yes—
742C22×D4C25196yes—
743C22×D4C251128yes—
744C22×D4C251256yes—
745C22×D4C251192yes—
746C22×D4C251192yes—
747C22×D4C25196yes—
748C22×D4C251192yes—
749C22×D4C251192yes—
750C22×D4C251192yes—
751C22×D4C25124yes—
752C22×D4C25124yes—
753C22×D4C25148yes—
754C22×D4C25148yes—
755C22×D4C25148yes—
756C22×D4C25196yes—
757C22×D4C25148yes—
758C22×D4C251256yes—
759C22×D4C251512yes—
760C22×D4C251192yes—
761C22×D4C25124yes—
762C22×D4C25124yes—
763C22×D4C251128yes—
764C22×D4C251256yes—
765C22×D4C251256yes—
766C22×D4C251128yes—
767C22×D4C251512yes—
768C22×D4C251512yes—
769C22×D4C251256yescomplemented
770C22×D4C25164yescomplemented
771C22×D4C251512yescomplemented
772C22×D4C251512yescomplemented
773C22×D4C2511024yescomplemented
774C23×C4—28no—
775C23×C4—28no—
776C23×C4—232no—
777C23×C4—2192no—
778C23×C4—232no—
779C23×C4—216no—
780C23×C4—432no—
781C23×C4—432no—
782C23×C4—4192no—
783C23×C4—4192no—
784C23×C4—432no—
785C23×C4—464no—
786C23×C4—416no—
787C23×C4—432no—
788C23×C4—416no—
789C23×C4—464no—
790C23×C4—432no—
791C23×C4—8192no—
792C23×C4C25148yes—
793C23×C4C25124yes—
794C23×C4C25148yes—
795C23×C4C25112yes—
796C23×C4C25164yes—
797C23×C4C25112yes—
798C23×C4C25116yes—
799C23×C4C2514yes—
800C23×C4C2518yes—
801C23×C4C2512yes—
802C23×C4C2518yes—
803C23×C4C2512yes—
804C23×C4C25196yes—
805C23×C4C25148yes—
806C23×C4C251192yes—
807C23×C4C25196yes—
808C23×C4C251192yes—
809C23×C4C25196yes—
810C23×C4C25196yes—
811C23×C4C25148yes—
812C23×C4C25196yes—
813C23×C4C251128yescomplemented
814C23×C4C251128yescomplemented
815C23×C4C251256yescomplemented
816C4⋊Q8C251512yescomplemented
817#127C251256yes—
818#127C251512yescomplemented
819#127C251256yescomplemented
820#127C2511024yescomplemented
821#126C2511024yescomplemented
822#126C2511024yescomplemented
823#126C2511024yescomplemented
824#126C2511024yescomplemented
825#125C251512yescomplemented
826#125C2511024yescomplemented
827#124C251256yes—
828#124C251512yescomplemented
829#124C251256yescomplemented
830#124C251512yescomplemented
831#124C2511024yescomplemented
832#124C2511024yescomplemented
833#124C251512yescomplemented
834#124C2511024yescomplemented
835#123C251512yes—
836#123C2511024yes—
837#123C251512yes—
838#123C251512yes—
839#123C251512yescomplemented
840#123C251512yescomplemented
841#123C251512yescomplemented
842#123C251512yescomplemented
843#123C251512yescomplemented
844#123C2511024yescomplemented
845#123C251512yescomplemented
846#123C2511024yescomplemented
847#123C2511024yescomplemented
848#123C2511024yescomplemented
849#123C2511024yescomplemented
850#123C251512yescomplemented
851#123C2511024yescomplemented
852#123C2511024yescomplemented
853C22⋊Q8C2511024yescomplemented
854C22⋊Q8C251512yescomplemented
855C22⋊Q8C2511024yescomplemented
856C22⋊Q8C2511024yescomplemented
857C22⋊Q8C251512yescomplemented
858C22⋊Q8C2511024yescomplemented
859C22⋊Q8C2511024yescomplemented
860#121C2511024yes—
861#121C2511024yes—
862#121C251512yes—
863#121C2511024yes—
864#121C251512yes—
865#121C2511024yescomplemented
866#121C2511024yescomplemented
867#121C251512yescomplemented
868#121C2511024yescomplemented
869#121C251512yescomplemented
870#121C2511024yescomplemented
871#121C2511024yescomplemented
872#121C2511024yescomplemented
873#121C2511024yescomplemented
874#121C2511024yescomplemented
875#121C2511024yescomplemented
876#121C2511024yescomplemented
877#121C2511024yescomplemented
878#121C2511024yescomplemented
879#120C251512yes—
880#120C251512yes—
881#120C251512yes—
882#120C251512yes—
883#120C2511024yes—
884#120C251512yes—
885#120C2511024yes—
886#120C251512yescomplemented
887#120C251512yescomplemented
888#120C251512yescomplemented
889#120C251512yescomplemented
890#120C251512yescomplemented
891#120C2511024yescomplemented
892#120C2511024yescomplemented
893#120C251512yescomplemented
894#120C251512yescomplemented
895#120C2511024yescomplemented
896C4×Q8C251512yescomplemented
897C4×D4C2511024yes—
898C4×D4C2511024yescomplemented
899C4×D4C2511024yescomplemented
900C4×D4C2511024yescomplemented
901C4×D4C2511024yescomplemented
902C4×D4C2511024yescomplemented
903C4×D4C2511024yescomplemented
904C4×D4C2511024yescomplemented
905C4×D4C251512yescomplemented
906#117C251512yescomplemented
907#117C251512yescomplemented
908#117C251256yescomplemented
909#117C2511024yescomplemented
910#117C2511024yescomplemented
911C2×C4⋊C4C251192yes—
912C2×C4⋊C4C25196yes—
913C2×C4⋊C4C251192yes—
914C2×C4⋊C4C251192yes—
915C2×C4⋊C4C251192yes—
916C2×C4⋊C4C251192yes—
917C2×C4⋊C4C25196yes—
918C2×C4⋊C4C25196yes—
919C2×C4⋊C4C25196yes—
920C2×C4⋊C4C251128yescomplemented
921C2×C4⋊C4C251512yescomplemented
922C2×C4⋊C4C251512yescomplemented
923C2×C22⋊C4C25196yes—
924C2×C22⋊C4C25196yes—
925C2×C22⋊C4C251256yes—
926C2×C22⋊C4C25196yes—
927C2×C22⋊C4C25196yes—
928C2×C22⋊C4C251512yes—
929C2×C22⋊C4C25196yes—
930C2×C22⋊C4C251192yes—
931C2×C22⋊C4C251128yes—
932C2×C22⋊C4C251192yes—
933C2×C22⋊C4C251512yes—
934C2×C22⋊C4C251192yes—
935C2×C22⋊C4C251192yes—
936C2×C22⋊C4C251192yes—
937C2×C22⋊C4C251192yes—
938C2×C22⋊C4C251192yes—
939C2×C22⋊C4C251192yes—
940C2×C22⋊C4C251192yes—
941C2×C22⋊C4C25196yes—
942C2×C22⋊C4C251192yes—
943C2×C22⋊C4C251256yescomplemented
944C2×C22⋊C4C251512yescomplemented
945C2×C22⋊C4C251512yescomplemented
946C2×C22⋊C4C251256yescomplemented
947C2×C22⋊C4C251512yescomplemented
948C2×C22⋊C4C251512yescomplemented
949C2×C22⋊C4C2511024yescomplemented
950C2×C22⋊C4C251512yescomplemented
951C2×C42C25148yes—
952C2×C42C251192yes—
953C2×C42C25196yes—
954C2×C42C25148yes—
955C2×C42C251128yescomplemented
956C24—216no—
957C24—28no—
958C24—216no—
959C24—296no—
960C24—216no—
961C24—232no—
962C24—296no—
963C24—216no—
964C24—232no—
965C24—232no—
966C24—264no—
967C24—232no—
968C24—296no—
969C24—2192no—
970C24—2192no—
971C24—2192no—
972C24—2512no—
973C24—496no—
974C24—464no—
975C24—448no—
976C24—496no—
977C24—4192no—
978C24—4256no—
979C24—496no—
980C24—4192no—
981C24—4192no—
982C24—4192no—
983C24—4384no—
984C24—496no—
985C24—4192no—
986C24—4128no—
987C24—4128no—
988C24—864no—
989C24—8128no—
990C24—8128no—
991C24—8128no—
992C24—8256no—
993C24—8256no—
994C24—81536no—
995C24—8256no—
996C24—81536no—
997C24—1664no—
998C24C2×H(5,𝔽2)116yes—
999C24C2×H(5,𝔽2)18yes—
1000C24C2×H(5,𝔽2)196yes—
1001C24C26124yes—
1002C24C26148yes—
1003C24C26124yes—
1004C24C26124yes—
1005C24C26112yes—
1006C24C2616yes—
1007C24C26164yes—
1008C24C26164yes—
1009C24C26164yes—
1010C24C26132yes—
1011C24C26132yes—
1012C24C26132yes—
1013C24C261128yes—
1014C24C26164yes—
1015C24C26116yes—
1016C24C2611yescharacteristic
1017#41—41024no—
1018#41—41024no—
1019#41—4512no—
1020#41—81024no—
1021C2×Q8—496no—
1022C2×Q8—4128no—
1023C2×Q8—496no—
1024C2×Q8—4192no—
1025C2×Q8C261128yes—
1026C2×Q8C26164yes—
1027C2×Q8C26164yes—
1028C2×D4—2384no—
1029C2×D4—2384no—
1030C2×D4—21024no—
1031C2×D4—2384no—
1032C2×D4—2512no—
1033C2×D4—448no—
1034C2×D4—496no—
1035C2×D4—448no—
1036C2×D4—4256no—
1037C2×D4—448no—
1038C2×D4—496no—
1039C2×D4—448no—
1040C2×D4—4256no—
1041C2×D4—4512no—
1042C2×D4—4512no—
1043C2×D4—4384no—
1044C2×D4—4512no—
1045C2×D4—4192no—
1046C2×D4—496no—
1047C2×D4—496no—
1048C2×D4—4128no—
1049C2×D4—4384no—
1050C2×D4—4384no—
1051C2×D4—4192no—
1052C2×D4—4384no—
1053C2×D4—4384no—
1054C2×D4—4384no—
1055C2×D4—41024no—
1056C2×D4—41024no—
1057C2×D4—4512no—
1058C2×D4—41024no—
1059C2×D4—8512no—
1060C2×D4—8512no—
1061C2×D4—81024no—
1062C2×D4C261128yes—
1063C2×D4C261128yes—
1064C2×D4C261128yes—
1065C2×D4C261256yes—
1066C2×D4C261256yes—
1067C2×D4C261128yes—
1068C2×D4C261256yes—
1069C2×D4C261256yes—
1070C2×D4C261256yes—
1071C2×D4C26132yes—
1072C2×D4C26132yes—
1073C2×D4C26164yes—
1074C2×D4C26164yes—
1075C2×D4C26164yes—
1076C2×D4C261128yes—
1077C2×D4C26164yes—
1078C2×D4C261256yes—
1079C2×D4C26132yes—
1080C2×D4C26132yes—
1081C22×C4—248no—
1082C22×C4—28no—
1083C22×C4—248no—
1084C22×C4—28no—
1085C22×C4—2192no—
1086C22×C4—2256no—
1087C22×C4—232no—
1088C22×C4—216no—
1089C22×C4—2192no—
1090C22×C4—296no—
1091C22×C4—264no—
1092C22×C4—232no—
1093C22×C4—4192no—
1094C22×C4—4192no—
1095C22×C4—4256no—
1096C22×C4—4256no—
1097C22×C4—4192no—
1098C22×C4—4384no—
1099C22×C4—496no—
1100C22×C4—4192no—
1101C22×C4—496no—
1102C22×C4—4384no—
1103C22×C4—4192no—
1104C22×C4—8256no—
1105C22×C4C26148yes—
1106C22×C4C26112yes—
1107C22×C4C26196yes—
1108C22×C4C26124yes—
1109C22×C4C26148yes—
1110C22×C4C26116yes—
1111C22×C4C26112yes—
1112C22×C4C26164yes—
1113C22×C4C26132yes—
1114C22×C4C26164yes—
1115C22×C4C26116yes—
1116C22×C4C26164yes—
1117C22×C4C261128yes—
1118C22×C4C261256yes—
1119C22×C4C261128yes—
1120C22×C4C261256yes—
1121C22×C4C261128yes—
1122C22×C4C261128yes—
1123C22×C4C26164yes—
1124C22×C4C261128yes—
1125C4⋊C4C261256yes—
1126C4⋊C4C261128yes—
1127C4⋊C4C261256yes—
1128C4⋊C4C261256yes—
1129C4⋊C4C261256yes—
1130C4⋊C4C261256yes—
1131C4⋊C4C261128yes—
1132C4⋊C4C261128yes—
1133C4⋊C4C261128yes—
1134C22⋊C4C261128yes—
1135C22⋊C4C261128yes—
1136C22⋊C4C261128yes—
1137C22⋊C4C261128yes—
1138C22⋊C4C261128yes—
1139C22⋊C4C261256yes—
1140C22⋊C4C261256yes—
1141C22⋊C4C261256yes—
1142C22⋊C4C261256yes—
1143C22⋊C4C261256yes—
1144C22⋊C4C261256yes—
1145C22⋊C4C261256yes—
1146C22⋊C4C261256yes—
1147C22⋊C4C261256yes—
1148C22⋊C4C261128yes—
1149C22⋊C4C261256yes—
1150C42C26164yes—
1151C42C26164yes—
1152C42C261256yes—
1153C42C261128yes—
1154C23—248no—
1155C23—224no—
1156C23—264no—
1157C23—232no—
1158C23—248no—
1159C23—264no—
1160C23—248no—
1161C23—296no—
1162C23—264no—
1163C23—248no—
1164C23—296no—
1165C23—296no—
1166C23—2192no—
1167C23—296no—
1168C23—264no—
1169C23—2128no—
1170C23—2128no—
1171C23—2128no—
1172C23—464no—
1173C23—4192no—
1174C23—432no—
1175C23—464no—
1176C23—4128no—
1177C23—464no—
1178C23—4128no—
1179C23—4128no—
1180C23—4128no—
1181C23—4256no—
1182C23—464no—
1183C23—4128no—
1184C23—4384no—
1185C23—4384no—
1186C23—464no—
1187C23—464no—
1188C23—4128no—
1189C23—464no—
1190C23—8192no—
1191C23—8384no—
1192C23—8384no—
1193C23—8384no—
1194C23—81024no—
1195C23—8768no—
1196C23—81024no—
1197C23—16192no—
1198C23C22×H(5,𝔽2)148yes—
1199C23C22×H(5,𝔽2)124yes—
1200C23C22×H(5,𝔽2)164yes—
1201C23C22×H(5,𝔽2)14yes—
1202C23H(7,𝔽2)18yes—
1203C23C27116yes—
1204C23C27132yes—
1205C23C27116yes—
1206C23C27116yes—
1207C23C2718yes—
1208C23C2714yes—
1209C23C2713yes—
1210Q8—464no—
1211Q8—464no—
1212Q8—4128no—
1213D4—2256no—
1214D4—2256no—
1215D4—2256no—
1216D4—432no—
1217D4—464no—
1218D4—432no—
1219D4—432no—
1220D4—464no—
1221D4—432no—
1222D4—4256no—
1223D4—4128no—
1224D4—464no—
1225D4—464no—
1226D4—4256no—
1227D4—4256no—
1228D4—4128no—
1229D4—4256no—
1230D4—4256no—
1231D4—4256no—
1232C2×C4—232no—
1233C2×C4—224no—
1234C2×C4—232no—
1235C2×C4—224no—
1236C2×C4—2128no—
1237C2×C4—296no—
1238C2×C4—248no—
1239C2×C4—2128no—
1240C2×C4—264no—
1241C2×C4—2192no—
1242C2×C4—296no—
1243C2×C4—4128no—
1244C2×C4—4128no—
1245C2×C4—4128no—
1246C2×C4—4256no—
1247C2×C4—464no—
1248C2×C4—4128no—
1249C2×C4—464no—
1250C2×C4—4256no—
1251C2×C4—4128no—
1252C2×C4C27132yes—
1253C2×C4C2718yes—
1254C2×C4C27164yes—
1255C2×C4C27116yes—
1256C2×C4C27132yes—
1257C2×C4C2718yes—
1258C22—296no—
1259C22—248no—
1260C22—216no—
1261C22—28no—
1262C22—216no—
1263C22—216no—
1264C22—232no—
1265C22—216no—
1266C22—232no—
1267C22—232no—
1268C22—264no—
1269C22—232no—
1270C22—464no—
1271C22—4128no—
1272C22—4128no—
1273C22—496no—
1274C22—496no—
1275C22—4192no—
1276C22—496no—
1277C22—864no—
1278C22—8128no—
1279C22—8128no—
1280C22—8128no—
1281C22—8256no—
1282C22—1664no—
1283C22#62862116yesdirect product factor
1284C22C23×H(5,𝔽2)116yes—
1285C22C23×H(5,𝔽2)18yes—
1286C22C23×H(5,𝔽2)16yes—
1287C22C2×H(7,𝔽2)112yes—
1288C22C2811yescharacteristic
1289C4—28no—
1290C4—28no—
1291C4—232no—
1292C4—216no—
1293C4—264no—
1294C4—232no—
1295C2—216no—
1296C2—28no—
1297C2—416no—
1298C2—416no—
1299C2—432no—
1300C2—416no—
1301C2C2×#62862112yesdirect product factor
1302C2C24×H(5,𝔽2)11yescharacteristic
1303C2C22×H(7,𝔽2)12yes—
subgroupG/H
center, socleC24C26
commutator, Frattini, cosocleC22C28
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C24 ◁ G
LECSG ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#62862C2direct (N × H)
2. C22×#3545C2semidirect
3. C22×#3543C2semidirect
4. C22×#3533C2semidirect
5. C22×#3534C2semidirect
6. C22×#3542C2semidirect
7. C22×#3532C2semidirect
8. C22×#3491C2semidirect
9. C22×#3485C2semidirect
10. C22×#3490C2semidirect
11. C22×#3484C2semidirect
12. C23×#535C2semidirect
13. C23×#534C2semidirect
14. C23×H(5,𝔽2)C22semidirect
15. C24×#41C22semidirect
16. C25×D4C22semidirect
17. C25×D4C22semidirect
18. #62862C22direct (N × H)
19. C2×#3491C22semidirect
20. C2×#3485C22semidirect
21. C2×#3490C22semidirect
22. C2×#3484C22semidirect
23. C2×#3545C22semidirect
24. C2×#3543C22semidirect
25. C2×#3533C22semidirect
26. C2×#3534C22semidirect
27. C2×#3542C22semidirect
28. C2×#3532C22semidirect
29. C22×#559C22semidirect
30. C22×#555C22semidirect
31. C22×#553C22semidirect
32. C22×#552C22semidirect
33. C22×#551C22semidirect
34. C22×#551C22semidirect
35. C22×#551C22semidirect
36. C22×#551C22semidirect
37. C22×#550C22semidirect
38. C22×#547C22semidirect
39. C22×#546C22semidirect
40. C22×#546C22semidirect
41. C22×#546C22semidirect
42. C22×#546C22semidirect
43. C22×#546C22semidirect
44. C22×#546C22semidirect
45. C22×D42C22semidirect
46. C22×D42C22semidirect
47. C22×D42C22semidirect
48. C22×#563C22semidirect
49. C22×#562C22semidirect
50. C22×#562C22semidirect
51. C22×H(3,𝔽4)C22semidirect
52. C22×#560C22semidirect
53. C22×#560C22semidirect
54. C22×#560C22semidirect
55. C22×#536C22semidirect
56. C22×#542C22semidirect
57. C22×#540C22semidirect
58. C22×#540C22semidirect
59. C22×#537C22semidirect
60. C22×#535C22semidirect
61. C22×#535C22semidirect
62. C22×#535C22semidirect
63. C22×#535C22semidirect
64. C22×#535C22semidirect
65. C22×#539C22semidirect
66. C22×#539C22semidirect
67. C22×#538C22semidirect
68. C22×#538C22semidirect
69. C22×#538C22semidirect
70. C22×#538C22semidirect
71. C22×#543C22semidirect
73. C22×#534C22semidirect
74. C22×#534C22semidirect
75. C22×#534C22semidirect
76. C22×#534C22semidirect
77. C22×#534C22semidirect
78. C22×#534C22semidirect
79. C22×#534C22semidirect
80. C22×#534C22semidirect
81. C22×#534C22semidirect
82. C23×#127C22semidirect
83. C22×#529C22semidirect
84. C23×#124C22semidirect
85. C22×#525C22semidirect
86. C22×#525C22semidirect
87. C22×#525C22semidirect
88. C23×#123C22semidirect
89. C23×#123C22semidirect
90. C23×#123C22semidirect
91. C23×#121C22semidirect
92. C23×#121C22semidirect
93. C23×#120C22semidirect
94. C23×#120C22semidirect
95. C23×#120C22semidirect
96. C23×#120C22semidirect
97. C22×#518C22semidirect
98. C22×#518C22semidirect
99. C23×#117C22semidirect
100. C24×C22⋊C4C22semidirect
102. C27C23semidirect
104. C22×H(5,𝔽2)C23semidirect
108. C23×#41C23semidirect
109. C23×#41C23semidirect
110. C23×#41C23semidirect
111. C24×Q8C23semidirect
124. C24×D4C23semidirect
125. C24×D4C23semidirect
126. C24×D4C23semidirect
127. C24×D4C23semidirect
128. C24×D4C23semidirect
129. C24×D4C23semidirect
130. C24×D4C23semidirect
132. C25×C4C23semidirect
133. C25×C4C23semidirect
134. C25×C4C23semidirect
135. #3545C23semidirect
136. #3543C23semidirect
137. #3542C23semidirect
138. #3534C23semidirect
139. #3533C23semidirect
140. #3532C23semidirect
141. C2×#563C23semidirect
142. C2×#562C23semidirect
143. C2×#562C23semidirect
144. C2×H(3,𝔽4)C23semidirect
145. C2×#560C23semidirect
146. C2×#560C23semidirect
147. C2×#560C23semidirect
148. #3491C23semidirect
149. #3490C23semidirect
150. #3485C23semidirect
151. #3484C23semidirect
152. C2×#559C23semidirect
153. C2×#555C23semidirect
154. C2×#553C23semidirect
155. C2×#552C23semidirect
156. C2×#551C23semidirect
157. C2×#551C23semidirect
158. C2×#551C23semidirect
159. C2×#551C23semidirect
160. C2×#550C23semidirect
161. C2×#547C23semidirect
162. C2×#546C23semidirect
163. C2×#546C23semidirect
164. C2×#546C23semidirect
165. C2×#546C23semidirect
166. C2×#546C23semidirect
167. C2×#546C23semidirect
168. C2×D42C23semidirect
169. C2×D42C23semidirect
170. C2×D42C23semidirect
171. C2×#543C23semidirect
172. C2×#542C23semidirect
173. C2×#540C23semidirect
174. C2×#540C23semidirect
175. C2×#539C23semidirect
176. C2×#539C23semidirect
177. C2×#538C23semidirect
178. C2×#538C23semidirect
179. C2×#538C23semidirect
180. C2×#538C23semidirect
181. C2×#537C23semidirect
182. C2×#536C23semidirect
183. C2×#535C23semidirect
184. C2×#535C23semidirect
185. C2×#535C23semidirect
186. C2×#535C23semidirect
187. C2×#535C23semidirect
189. C2×#534C23semidirect
190. C2×#534C23semidirect
191. C2×#534C23semidirect
192. C2×#534C23semidirect
193. C2×#534C23semidirect
194. C2×#534C23semidirect
195. C2×#534C23semidirect
196. C2×#534C23semidirect
197. C2×#534C23semidirect
198. C22×C4⋊Q8C23semidirect
200. C22×#127C23semidirect
201. C22×#127C23semidirect
202. C22×#127C23semidirect
203. C22×#127C23semidirect
204. C2×#529C23semidirect
205. C22×#126C23semidirect
206. C22×#126C23semidirect
207. C22×#126C23semidirect
208. C22×#126C23semidirect
209. C22×#125C23semidirect
210. C22×#125C23semidirect
212. C22×#124C23semidirect
213. C22×#124C23semidirect
214. C22×#124C23semidirect
215. C22×#124C23semidirect
216. C22×#124C23semidirect
217. C22×#124C23semidirect
218. C22×#124C23semidirect
219. C22×#124C23semidirect
220. C2×#525C23semidirect
221. C2×#525C23semidirect
222. C2×#525C23semidirect
227. C22×#123C23semidirect
228. C22×#123C23semidirect
229. C22×#123C23semidirect
230. C22×#123C23semidirect
231. C22×#123C23semidirect
232. C22×#123C23semidirect
233. C22×#123C23semidirect
234. C22×#123C23semidirect
235. C22×#123C23semidirect
236. C22×#123C23semidirect
237. C22×#123C23semidirect
238. C22×#123C23semidirect
239. C22×#123C23semidirect
240. C22×#123C23semidirect
241. C22×#123C23semidirect
242. C22×#123C23semidirect
243. C22×#123C23semidirect
244. C22×C22⋊Q8C23semidirect
245. C22×C22⋊Q8C23semidirect
246. C22×C22⋊Q8C23semidirect
247. C22×C22⋊Q8C23semidirect
248. C22×C22⋊Q8C23semidirect
249. C22×C22⋊Q8C23semidirect
250. C22×C22⋊Q8C23semidirect
256. C22×#121C23semidirect
257. C22×#121C23semidirect
258. C22×#121C23semidirect
259. C22×#121C23semidirect
260. C22×#121C23semidirect
261. C22×#121C23semidirect
262. C22×#121C23semidirect
263. C22×#121C23semidirect
264. C22×#121C23semidirect
265. C22×#121C23semidirect
266. C22×#121C23semidirect
267. C22×#121C23semidirect
268. C22×#121C23semidirect
269. C22×#121C23semidirect
270. C22×#121C23semidirect
271. C22×#121C23semidirect
279. C22×#120C23semidirect
280. C22×#120C23semidirect
281. C22×#120C23semidirect
282. C22×#120C23semidirect
283. C22×#120C23semidirect
284. C22×#120C23semidirect
285. C22×#120C23semidirect
286. C22×#120C23semidirect
287. C22×#120C23semidirect
288. C22×#120C23semidirect
289. C22×#120C23semidirect
290. C22×#120C23semidirect
291. C22×#120C23semidirect
292. C22×#120C23semidirect
293. C2×#518C23semidirect
294. C2×#518C23semidirect
295. C22×C4×Q8C23semidirect
297. C22×C4×D4C23semidirect
298. C22×C4×D4C23semidirect
299. C22×C4×D4C23semidirect
300. C22×C4×D4C23semidirect
301. C22×C4×D4C23semidirect
302. C22×C4×D4C23semidirect
303. C22×C4×D4C23semidirect
304. C22×C4×D4C23semidirect
305. C22×#117C23semidirect
306. C22×#117C23semidirect
307. C22×#117C23semidirect
308. C22×#117C23semidirect
309. C22×#117C23semidirect
310. C22×#117C23semidirect
311. C23×C4⋊C4C23semidirect
312. C23×C4⋊C4C23semidirect
313. C23×C4⋊C4C23semidirect
318. C23×C22⋊C4C23semidirect
319. C23×C22⋊C4C23semidirect
320. C23×C22⋊C4C23semidirect
321. C23×C22⋊C4C23semidirect
322. C23×C22⋊C4C23semidirect
323. C23×C22⋊C4C23semidirect
324. C23×C22⋊C4C23semidirect
325. C23×C22⋊C4C23semidirect
326. C23×C22⋊C4C23semidirect
327. C23×C42C23semidirect
342. C26C24semidirect
344. C2×H(5,𝔽2)C24semidirect
352. C22×#41C24semidirect
353. C22×#41C24semidirect
354. C22×#41C24semidirect
359. C23×Q8C24semidirect
406. C23×D4C24semidirect
407. C23×D4C24semidirect
408. C23×D4C24semidirect
409. C23×D4C24semidirect
410. C23×D4C24semidirect
411. C23×D4C24semidirect
412. C23×D4C24semidirect
432. C24×C4C24semidirect
433. C24×C4C24semidirect
434. C24×C4C24semidirect
435. #563C24semidirect
436. #562C24semidirect
437. #562C24semidirect
438. H(3,𝔽4)C24semidirect
439. #560C24semidirect
440. #560C24semidirect
441. #560C24semidirect
442. #559C24semidirect
443. #555C24semidirect
444. #553C24semidirect
445. #552C24semidirect
446. #551C24semidirect
447. #551C24semidirect
448. #551C24semidirect
449. #551C24semidirect
450. #550C24semidirect
451. #547C24semidirect
452. #546C24semidirect
453. #546C24semidirect
454. #546C24semidirect
455. #546C24semidirect
456. #546C24semidirect
457. #546C24semidirect
458. D42C24semidirect
459. D42C24semidirect
460. D42C24semidirect
461. #543C24semidirect
462. #542C24semidirect
463. #540C24semidirect
464. #540C24semidirect
465. #539C24semidirect
466. #539C24semidirect
467. #538C24semidirect
468. #538C24semidirect
469. #538C24semidirect
470. #538C24semidirect
471. #537C24semidirect
472. #536C24semidirect
473. #535C24semidirect
474. #535C24semidirect
475. #535C24semidirect
476. #535C24semidirect
478. #534C24semidirect
479. #534C24semidirect
480. #534C24semidirect
481. #534C24semidirect
482. #534C24semidirect
483. #534C24semidirect
484. #534C24semidirect
485. #534C24semidirect
486. C2×C4⋊Q8C24semidirect
488. C2×#127C24semidirect
489. C2×#127C24semidirect
490. C2×#127C24semidirect
491. C2×#127C24semidirect
492. #529C24semidirect
493. C2×#126C24semidirect
494. C2×#126C24semidirect
495. C2×#126C24semidirect
496. C2×#126C24semidirect
497. C2×#125C24semidirect
498. C2×#125C24semidirect
500. C2×#124C24semidirect
501. C2×#124C24semidirect
502. C2×#124C24semidirect
503. C2×#124C24semidirect
504. C2×#124C24semidirect
505. C2×#124C24semidirect
506. C2×#124C24semidirect
507. C2×#124C24semidirect
508. #525C24semidirect
509. #525C24semidirect
510. #525C24semidirect
515. C2×#123C24semidirect
516. C2×#123C24semidirect
517. C2×#123C24semidirect
518. C2×#123C24semidirect
519. C2×#123C24semidirect
520. C2×#123C24semidirect
521. C2×#123C24semidirect
522. C2×#123C24semidirect
523. C2×#123C24semidirect
524. C2×#123C24semidirect
525. C2×#123C24semidirect
526. C2×#123C24semidirect
527. C2×#123C24semidirect
528. C2×#123C24semidirect
529. C2×#123C24semidirect
530. C2×#123C24semidirect
531. C2×#123C24semidirect
532. C2×C22⋊Q8C24semidirect
533. C2×C22⋊Q8C24semidirect
534. C2×C22⋊Q8C24semidirect
535. C2×C22⋊Q8C24semidirect
536. C2×C22⋊Q8C24semidirect
537. C2×C22⋊Q8C24semidirect
538. C2×C22⋊Q8C24semidirect
544. C2×#121C24semidirect
545. C2×#121C24semidirect
546. C2×#121C24semidirect
547. C2×#121C24semidirect
548. C2×#121C24semidirect
549. C2×#121C24semidirect
550. C2×#121C24semidirect
551. C2×#121C24semidirect
552. C2×#121C24semidirect
553. C2×#121C24semidirect
554. C2×#121C24semidirect
555. C2×#121C24semidirect
556. C2×#121C24semidirect
557. C2×#121C24semidirect
558. C2×#121C24semidirect
559. C2×#121C24semidirect
567. C2×#120C24semidirect
568. C2×#120C24semidirect
569. C2×#120C24semidirect
570. C2×#120C24semidirect
571. C2×#120C24semidirect
572. C2×#120C24semidirect
573. C2×#120C24semidirect
574. C2×#120C24semidirect
575. C2×#120C24semidirect
576. C2×#120C24semidirect
577. C2×#120C24semidirect
578. C2×#120C24semidirect
579. C2×#120C24semidirect
580. C2×#120C24semidirect
581. #518C24semidirect
582. #518C24semidirect
583. C2×C4×Q8C24semidirect
585. C2×C4×D4C24semidirect
586. C2×C4×D4C24semidirect
587. C2×C4×D4C24semidirect
588. C2×C4×D4C24semidirect
589. C2×C4×D4C24semidirect
590. C2×C4×D4C24semidirect
591. C2×C4×D4C24semidirect
592. C2×C4×D4C24semidirect
593. C2×#117C24semidirect
594. C2×#117C24semidirect
595. C2×#117C24semidirect
596. C2×#117C24semidirect
597. C2×#117C24semidirect
598. C2×#117C24semidirect
608. C22×C4⋊C4C24semidirect
609. C22×C4⋊C4C24semidirect
610. C22×C4⋊C4C24semidirect
631. C22×C22⋊C4C24semidirect
632. C22×C22⋊C4C24semidirect
633. C22×C22⋊C4C24semidirect
634. C22×C22⋊C4C24semidirect
635. C22×C22⋊C4C24semidirect
636. C22×C22⋊C4C24semidirect
637. C22×C22⋊C4C24semidirect
638. C22×C22⋊C4C24semidirect
639. C22×C22⋊C4C24semidirect
644. C22×C42C24semidirect
685. C25C25semidirect
694. C2×#41C25semidirect
695. C2×#41C25semidirect
703. C22×Q8C25semidirect
769. C22×D4C25semidirect
770. C22×D4C25semidirect
771. C22×D4C25semidirect
772. C22×D4C25semidirect
773. C22×D4C25semidirect
813. C23×C4C25semidirect
814. C23×C4C25semidirect
815. C23×C4C25semidirect
816. C4⋊Q8C25semidirect
818. #127C25semidirect
819. #127C25semidirect
820. #127C25semidirect
821. #126C25semidirect
822. #126C25semidirect
823. #126C25semidirect
824. #126C25semidirect
825. #125C25semidirect
826. #125C25semidirect
828. #124C25semidirect
829. #124C25semidirect
830. #124C25semidirect
831. #124C25semidirect
832. #124C25semidirect
833. #124C25semidirect
834. #124C25semidirect
839. #123C25semidirect
840. #123C25semidirect
841. #123C25semidirect
842. #123C25semidirect
843. #123C25semidirect
844. #123C25semidirect
845. #123C25semidirect
846. #123C25semidirect
847. #123C25semidirect
848. #123C25semidirect
849. #123C25semidirect
850. #123C25semidirect
851. #123C25semidirect
852. #123C25semidirect
853. C22⋊Q8C25semidirect
854. C22⋊Q8C25semidirect
855. C22⋊Q8C25semidirect
856. C22⋊Q8C25semidirect
857. C22⋊Q8C25semidirect
858. C22⋊Q8C25semidirect
859. C22⋊Q8C25semidirect
865. #121C25semidirect
866. #121C25semidirect
867. #121C25semidirect
868. #121C25semidirect
869. #121C25semidirect
870. #121C25semidirect
871. #121C25semidirect
872. #121C25semidirect
873. #121C25semidirect
874. #121C25semidirect
875. #121C25semidirect
876. #121C25semidirect
877. #121C25semidirect
878. #121C25semidirect
886. #120C25semidirect
887. #120C25semidirect
888. #120C25semidirect
889. #120C25semidirect
890. #120C25semidirect
891. #120C25semidirect
892. #120C25semidirect
893. #120C25semidirect
894. #120C25semidirect
895. #120C25semidirect
896. C4×Q8C25semidirect
898. C4×D4C25semidirect
899. C4×D4C25semidirect
900. C4×D4C25semidirect
901. C4×D4C25semidirect
902. C4×D4C25semidirect
903. C4×D4C25semidirect
904. C4×D4C25semidirect
905. C4×D4C25semidirect
906. #117C25semidirect
907. #117C25semidirect
908. #117C25semidirect
909. #117C25semidirect
910. #117C25semidirect
920. C2×C4⋊C4C25semidirect
921. C2×C4⋊C4C25semidirect
922. C2×C4⋊C4C25semidirect
943. C2×C22⋊C4C25semidirect
944. C2×C22⋊C4C25semidirect
945. C2×C22⋊C4C25semidirect
946. C2×C22⋊C4C25semidirect
947. C2×C22⋊C4C25semidirect
948. C2×C22⋊C4C25semidirect
949. C2×C22⋊C4C25semidirect
950. C2×C22⋊C4C25semidirect
955. C2×C42C25semidirect
1283. C22#62862direct (N × H)
1301. C2C2×#62862direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#628622
C22×#35452
C22×#35432
C22×#35332
C22×#35342
C22×#35422
C22×#35322
C22×#34912
C22×#34852
C22×#34902
C22×#34842
C23×#5352
C23×#5342