Finite Group Databasebeta

← C2×#72235062 #72235083

Subgroups — C2×#72235062 #72235083

Order 2048.

At least 8523 conjugacy classes of subgroups; only the 2664 normal subgroups are shown.

The subgroup lattice has 767 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#184773C212yesmaximal, complemented
2C2×#106670C212yesmaximal, complemented
3C2×#188085C211yesmaximal, characteristic, complemented
4C2×#6342764C211yesmaximal, characteristic, complemented
5C2×#115697C212yesmaximal, complemented
6C2×#115173C212yesmaximal, complemented
7C2×#201819C212yesmaximal, complemented
8#72235062C2116yesmaximal, direct product factor
9C22×#36098C211yesmaximal, characteristic
10C2×#359507C212yesmaximal, complemented
11C23×#546C2211yescharacteristic
12C23×#525C2211yescharacteristic
13C24×#120C411yescharacteristic
14C25×C22⋊C4C2211yescharacteristic
15C2×#60064C2212yescomplemented
16C22×#2849C2211yescharacteristic
17C22×#2847C411yescharacteristic
18C22×#2846C411yescharacteristic
19C2×#36098C418yes—
20C2×#36098C2218yes—
21C22×#2539C411yescharacteristic
22C22×#2534C411yescharacteristic
23C22×#2411C2211yescharacteristic
24C22×#2404C2211yescharacteristic
25C22×#2412C411yescharacteristic
26C22×#2405C411yescharacteristic
27C22×#2342C2211yescharacteristic
28C22×C4×#120C411yescharacteristic
29C2×#20591C2212yescomplemented
30C2×#20579C2214yescomplemented
31#6342764C2218yescomplemented
32C2×#17392C2212yescomplemented
33C2×#17392C2212yescomplemented
34C22×#1462C2212yes—
35C22×#1462C2212yes—
36C22×#1462C2214yescomplemented
37#359507C22116yescomplemented
38C2×#10738C2214yescomplemented
39#201819C22116yescomplemented
40#188085C2218yescomplemented
41#184773C22116yescomplemented
42C2×#8114C2214yescomplemented
43#115697C22116yescomplemented
44#115173C22116yescomplemented
45#106670C22116yescomplemented
46C28C2×C411yescharacteristic
47C24×#41C2311yescharacteristic
48C25×D4C2×C411yescharacteristic
49C26×C4C2×C411yescharacteristic
50C26×C4C2311yescharacteristic
51C22×#546C2×C414yes—
52C22×#546D414yes—
53C22×#546D414yes—
54C22×#546C2314yes—
55C23×#124D411yescharacteristic
56C22×#525C2×C414yes—
57C22×#525D414yes—
58C22×#525D418yes—
59C22×#525D414yes—
60C22×#525C2314yes—
61C23×#123C2×C411yescharacteristic
62C23×#123C2×C411yescharacteristic
63C23×#123C2×C411yescharacteristic
64C23×#123D411yescharacteristic
65C23×#123C2311yescharacteristic
66C23×C22⋊Q8D411yescharacteristic
67C23×#121C2×C411yescharacteristic
68C23×#121D411yescharacteristic
69C23×#121D411yescharacteristic
70C23×#120C2×C411yescharacteristic
71C23×#120C2×C411yescharacteristic
72C23×#120C2×C418yes—
73C23×#120C2×C411yescharacteristic
74C23×#120C2×C411yescharacteristic
75C23×#120C2×C411yescharacteristic
76C23×#120C2×C411yescharacteristic
77C23×#120C2×C411yescharacteristic
78C23×#120D411yescharacteristic
79C23×C4×D4C2×C411yescharacteristic
80C23×C4×D4D411yescharacteristic
81C23×#117C2311yescharacteristic
82C24×C22⋊C4C2×C411yescharacteristic
83C24×C22⋊C4C2×C411yescharacteristic
84C24×C22⋊C4C2×C414yes—
85C24×C22⋊C4C2×C411yescharacteristic
86C24×C22⋊C4D411yescharacteristic
87C24×C22⋊C4C2314yes—
88C24×C22⋊C4C2311yescharacteristic
89C24×C22⋊C4C2311yescharacteristic
90#60064C2318yescomplemented
91C22×#407C2314yes—
92C22×#407C2314yes—
93C2×#2849C2×C414yes—
94C2×#2849C2314yes—
95C2×#2847C2×C418yes—
96C2×#2846C2×C418yes—
97C2×#2539C2×C418yes—
98C2×#2534C2×C418yes—
99C2×#2411C2×C414yes—
100C2×#2411C2314yes—
101C2×#2404C2×C414yes—
102C2×#2404D414yes—
103C2×#2404D414yes—
104C2×#2404D418yes—
105C2×#2404C2314yes—
106C2×#2412C2×C418yes—
107C2×#2405C2×C418yes—
108C2×#2342C2×C414yes—
109C2×#2342C2314yes—
110C2×C4×#120C2×C418yes—
111C22×#386C2×C411yescharacteristic
112C22×#386C2×C411yescharacteristic
113C22×#386C2×C411yescharacteristic
114C22×#385C2×C411yescharacteristic
115C22×#381C2×C411yescharacteristic
116C22×#381C2311yescharacteristic
117C22×#380C2×C411yescharacteristic
118C22×#379C2×C411yescharacteristic
119C22×#379C2×C411yescharacteristic
120C22×#379C2×C411yescharacteristic
121C22×C4×C22⋊C4C2×C411yescharacteristic
122#20591C2318yescomplemented
123#20579C23116yescomplemented
124#17392C2318yescomplemented
125#17392C2318yescomplemented
126C2×#1462D418yescomplemented
127C2×#1462C2318yes—
128C2×#1462C2318yes—
129C2×#1462C23116yescomplemented
130C22×#323D418yescomplemented
131#10738C23116yescomplemented
132#8114C23116yescomplemented
133C27C22⋊C411yescharacteristic
134C27C22×C411yescharacteristic
135C27C22×C411yescharacteristic
136C27C22×C414yes—
137C27C22×C411yescharacteristic
138C23×#41C22×C412yes—
139C23×#41C2×D412yes—
140C23×#41C2×D412yes—
141C23×#41C2×D412yes—
142C23×#41C2×D412yes—
143C23×#41C2×D412yes—
144C23×#41C2×D414yes—
145C23×#41C2×D414yes—
146C23×#41C2×D412yes—
147C23×#41C2412yes—
148C24×Q8C2×D411yescharacteristic
149C24×D4C22⋊C411yescharacteristic
150C24×D4C22⋊C414yes—
151C24×D4C22⋊C411yescharacteristic
152C24×D4C22⋊C411yescharacteristic
153C24×D4C22⋊C411yescharacteristic
154C24×D4C22⋊C411yescharacteristic
155C24×D4C22×C411yescharacteristic
156C24×D4C22×C411yescharacteristic
157C24×D4C22×C411yescharacteristic
158C24×D4C22×C414yes—
159C24×D4C2×D411yescharacteristic
160C25×C4C22⋊C411yescharacteristic
161C25×C4C22⋊C411yescharacteristic
162C25×C4C22×C411yescharacteristic
163C25×C4C22×C412yes—
164C25×C4C22×C411yescharacteristic
165C25×C4C22×C414yes—
166C25×C4C22×C411yescharacteristic
167C25×C4C2×D414yes—
168C25×C4C2×D414yes—
169C25×C4C2×D411yescharacteristic
170C25×C4C2×D411yescharacteristic
171C25×C4C2412yes—
172C25×C4C2411yescharacteristic
173C22×#124C22⋊C414yes—
174C22×#124C2×D414yes—
175C2×#525C22⋊C4116yes—
176C2×#525C22⋊C4116yes—
177C2×#525C2×D4116yes—
178C2×#525C2×D4116yes—
179C22×#123C22⋊C412yes—
180C22×#123C22⋊C414yes—
181C22×#123C22⋊C412yes—
182C22×#123C22⋊C414yes—
183C22×#123C22⋊C414yes—
184C22×#123C22⋊C414yes—
185C22×#123C22×C414yes—
186C22×#123C22×C414yes—
187C22×#123C22×C414yes—
188C22×#123C22×C412yes—
189C22×#123C2×D412yes—
190C22×#123C2×D412yes—
191C22×#123C2×D414yes—
192C22×#123C2412yes—
193C22×C22⋊Q8C22⋊C414yes—
194C22×C22⋊Q8C2×D414yes—
195C22×#121C22⋊C414yes—
196C22×#121C22⋊C414yes—
197C22×#121C22⋊C414yes—
198C22×#121C22×C414yes—
199C22×#121C2×D414yes—
200C22×#121C2×D414yes—
201C22×#120C22⋊C414yes—
202C22×#120C22⋊C412yes—
203C22×#120C22⋊C414yes—
204C22×#120C22⋊C412yes—
205C22×#120C22⋊C412yes—
206C22×#120C22⋊C414yes—
207C22×#120C22⋊C412yes—
208C22×#120C22⋊C414yes—
209C22×#120C22⋊C414yes—
210C22×#120C22⋊C414yes—
211C22×#120C22⋊C414yes—
212C22×#120C22⋊C414yes—
213C22×#120C22×C414yes—
214C22×#120C22×C414yes—
215C22×#120C22×C414yes—
216C22×#120C22×C414yes—
217C22×#120C22×C414yes—
218C22×#120C22×C414yes—
219C22×#120C22×C414yes—
220C22×#120C2×D414yes—
221C22×C4×D4C22⋊C414yes—
222C22×C4×D4C22⋊C414yes—
223C22×C4×D4C22×C414yes—
224C22×C4×D4C2×D414yes—
225C22×#117C22×C412yes—
226C22×#117C2×D414yes—
227C22×#117C2×D414yes—
228C22×#117C2412yes—
229C23×C4⋊C4C22⋊C411yescharacteristic
230C23×C4⋊C4C22⋊C411yescharacteristic
231C23×C4⋊C4C2×D411yescharacteristic
232C23×C4⋊C4C2×D411yescharacteristic
233C23×C22⋊C4C22⋊C414yes—
234C23×C22⋊C4C22⋊C411yescharacteristic
235C23×C22⋊C4C22⋊C411yescharacteristic
236C23×C22⋊C4C22⋊C411yescharacteristic
237C23×C22⋊C4C22⋊C411yescharacteristic
238C23×C22⋊C4C22⋊C411yescharacteristic
239C23×C22⋊C4C22×C412yes—
240C23×C22⋊C4C22×C411yescharacteristic
241C23×C22⋊C4C22×C411yescharacteristic
242C23×C22⋊C4C22×C414yes—
243C23×C22⋊C4C22×C414yes—
244C23×C22⋊C4C22×C412yes—
245C23×C22⋊C4C22×C414yes—
246C23×C22⋊C4C22×C411yescharacteristic
247C23×C22⋊C4C22×C411yescharacteristic
248C23×C22⋊C4C22×C411yescharacteristic
249C23×C22⋊C4C2×D414yes—
250C23×C22⋊C4C2×D414yes—
251C23×C22⋊C4C2×D411yescharacteristic
252C23×C22⋊C4C2×D411yescharacteristic
253C23×C22⋊C4C2×D414yes—
254C23×C22⋊C4C2×D412yes—
255C23×C22⋊C4C2×D411yescharacteristic
256C23×C22⋊C4C2×D411yescharacteristic
257C23×C22⋊C4C2×D412yes—
258C23×C22⋊C4C2×D411yescharacteristic
259C23×C22⋊C4C2×D411yescharacteristic
260C23×C22⋊C4C2×D414yes—
261C23×C22⋊C4C2×D414yes—
262C23×C22⋊C4#4114yes—
263C23×C22⋊C4#4114yes—
264C23×C22⋊C4C2412yes—
265C23×C22⋊C4C2412yes—
266C23×C42C22⋊C411yescharacteristic
267C2×#407C2×D418yescomplemented
268C2×#407C2418yes—
269C2×#407C2418yes—
270C22×C22⋊C8C2×D418yescomplemented
271#2404C22⋊C4116yes—
272#2404C22⋊C4116yes—
273#2404C2×D4116yes—
274#2404C2×D4116yes—
275C2×#386C22⋊C414yes—
276C2×#386C22⋊C414yes—
277C2×#386C22⋊C412yes—
278C2×#386C22⋊C412yes—
279C2×#386C22⋊C414yes—
280C2×#386C22×C414yes—
281C2×#386C22×C414yes—
282C2×#386C22×C414yes—
283C2×#385C22×C414yes—
284C2×#381C22×C414yes—
285C2×#381C22×C412yes—
286C2×#381C2×D414yes—
287C2×#381C2×D414yes—
288C2×#381C2412yes—
289C2×#380C22×C414yes—
290C2×#379C22×C414yes—
291C2×#379C22×C414yes—
292C2×#379C22×C414yes—
293C2×C4×C22⋊C4C22×C414yes—
294C2×#323C2×D4132yescomplemented
295C26C2×C22⋊C411yescharacteristic
296C26C2×C22⋊C412yes—
297C26C2×C22⋊C412yes—
298C26C2×C22⋊C411yescharacteristic
299C26C2×C22⋊C411yescharacteristic
300C26C2×C22⋊C412yes—
301C26C2×C22⋊C412yes—
302C26C2×C22⋊C411yescharacteristic
303C26C2×C22⋊C411yescharacteristic
304C26C2×C22⋊C412yes—
305C26C2×C22⋊C414yes—
306C26C4×D414yes—
307C26C4×D414yes—
308C26C23×C412yes—
309C26C23×C411yescharacteristic
310C26C23×C412yes—
311C26C23×C412yes—
312C22×#41C2×C22⋊C414yes—
313C22×#41C2×C22⋊C414yes—
314C22×#41C2×C22⋊C414yes—
315C22×#41C2×C22⋊C414yes—
316C22×#41#12014yes—
317C22×#41#12014yes—
318C22×#41#12014yes—
319C22×#41#12014yes—
320C22×#41#12014yes—
321C22×#41#12014yes—
322C22×#41#12014yes—
323C22×#41#12014yes—
324C22×#41C22×D414yes—
325C22×#41C22×D414yes—
326C22×#41C22×D414yes—
327C22×#41C22×D414yes—
328C23×Q8C2×C22⋊C412yes—
329C23×Q8#12012yes—
330C23×Q8#12012yes—
331C23×Q8#12014yes—
332C23×Q8C22×D412yes—
333C23×D4C2×C22⋊C412yes—
334C23×D4C2×C22⋊C412yes—
335C23×D4C2×C22⋊C414yes—
336C23×D4C2×C22⋊C412yes—
337C23×D4C2×C22⋊C414yes—
338C23×D4C2×C22⋊C414yes—
339C23×D4C2×C22⋊C412yes—
340C23×D4C2×C22⋊C414yes—
341C23×D4C2×C22⋊C414yes—
342C23×D4C2×C22⋊C411yescharacteristic
343C23×D4C2×C22⋊C412yes—
344C23×D4C2×C22⋊C411yescharacteristic
345C23×D4C2×C22⋊C412yes—
346C23×D4C2×C22⋊C411yescharacteristic
347C23×D4C2×C22⋊C412yes—
348C23×D4C2×C22⋊C411yescharacteristic
349C23×D4C2×C22⋊C412yes—
350C23×D4C2×C22⋊C412yes—
351C23×D4C2×C22⋊C412yes—
352C23×D4#12012yes—
353C23×D4#12012yes—
354C23×D4#12014yes—
355C23×D4C23×C412yes—
356C23×D4C23×C412yes—
357C23×D4C23×C412yes—
358C23×D4C22×D412yes—
359C24×C4C2×C22⋊C412yes—
360C24×C4C2×C22⋊C418yes—
361C24×C4C2×C22⋊C411yescharacteristic
362C24×C4C2×C22⋊C411yescharacteristic
363C24×C4C2×C22⋊C411yescharacteristic
364C24×C4C2×C22⋊C412yes—
365C24×C4C2×C22⋊C411yescharacteristic
366C24×C4C2×C22⋊C412yes—
367C24×C4C2×C22⋊C412yes—
368C24×C4C2×C22⋊C411yescharacteristic
369C24×C4C2×C22⋊C411yescharacteristic
370C24×C4C2×C22⋊C411yescharacteristic
371C24×C4C2×C22⋊C414yes—
372C24×C4C2×C22⋊C412yes—
373C24×C4C2×C22⋊C412yes—
374C24×C4C2×C22⋊C414yes—
375C24×C4C2×C22⋊C412yes—
376C24×C4C4×D414yes—
377C24×C4C4×D414yes—
378C24×C4#12012yes—
379C24×C4#12012yes—
380C24×C4#12012yes—
381C24×C4#12012yes—
382C24×C4#12014yes—
383C24×C4#12014yes—
384C24×C4C23×C412yes—
385C24×C4C23×C412yes—
386C24×C4C23×C412yes—
387C24×C4C23×C411yescharacteristic
388C24×C4C22×D418yes—
389C24×C4C22×D412yes—
390C24×C4C22×D412yes—
391C24×C4C22×D412yes—
392C24×C4C22×D411yescharacteristic
393C24×C4C22×D411yescharacteristic
394C24×C4C22×D411yescharacteristic
395C24×C4C22×D411yescharacteristic
396C24×C4C22×D412yes—
397C24×C4C22×D412yes—
398C24×C4C22×D412yes—
399C24×C4C22×D412yes—
400C24×C4C22×D412yes—
401C24×C4C2×#4112yes—
402C24×C4C2×#4112yes—
403C24×C4H(5,𝔽2)14yes—
404C24×C4H(5,𝔽2)14yes—
405C24×C4C2511yescharacteristic
406C2×#123C2×C22⋊C418yes—
407C2×#123C2×C22⋊C4116yes—
408C2×#123C2×C22⋊C418yes—
409C2×#120#99116yes—
410C2×#120C2×C22⋊C418yes—
411C2×#120C2×C22⋊C4116yes—
412C2×#120C2×C22⋊C418yes—
413C2×#120C2×C22⋊C418yes—
414C2×#120C2×C22⋊C418yes—
415C2×#120C2×C22⋊C4116yes—
416C2×#117C2×C22⋊C418yes—
417C2×#117C22×D418yes—
418C22×C4⋊C4C2×C22⋊C412yes—
419C22×C4⋊C4C2×C22⋊C412yes—
420C22×C4⋊C4C2×C22⋊C414yes—
421C22×C4⋊C4C2×C22⋊C414yes—
422C22×C4⋊C4C22×D412yes—
423C22×C4⋊C4C22×D412yes—
424C22×C22⋊C4C2×C22⋊C412yes—
425C22×C22⋊C4C2×C22⋊C418yes—
426C22×C22⋊C4C2×C22⋊C412yes—
427C22×C22⋊C4C2×C22⋊C412yes—
428C22×C22⋊C4C2×C22⋊C412yes—
429C22×C22⋊C4C2×C22⋊C412yes—
430C22×C22⋊C4C2×C22⋊C414yes—
431C22×C22⋊C4C2×C22⋊C414yes—
432C22×C22⋊C4C2×C22⋊C414yes—
433C22×C22⋊C4C2×C22⋊C414yes—
434C22×C22⋊C4C2×C22⋊C414yes—
435C22×C22⋊C4C2×C22⋊C412yes—
436C22×C22⋊C4C2×C22⋊C412yes—
437C22×C22⋊C4C2×C22⋊C412yes—
438C22×C22⋊C4C2×C22⋊C412yes—
439C22×C22⋊C4C2×C22⋊C412yes—
440C22×C22⋊C4C2×C22⋊C412yes—
441C22×C22⋊C4C2×C22⋊C412yes—
442C22×C22⋊C4C2×C22⋊C412yes—
443C22×C22⋊C4C2×C22⋊C412yes—
444C22×C22⋊C4C2×C22⋊C412yes—
445C22×C22⋊C4C4×D418yes—
446C22×C22⋊C4C4×D418yes—
447C22×C22⋊C4#12012yes—
448C22×C22⋊C4#12012yes—
449C22×C22⋊C4#12012yes—
450C22×C22⋊C4#12012yes—
451C22×C22⋊C4#12018yes—
452C22×C22⋊C4#12114yes—
453C22×C22⋊C4#12114yes—
454C22×C22⋊C4#12114yes—
455C22×C22⋊C4#12114yes—
456C22×C22⋊C4#12118yes—
457C22×C22⋊C4#12118yes—
458C22×C22⋊C4#12312yes—
459C22×C22⋊C4#12312yes—
460C22×C22⋊C4#12312yes—
461C22×C22⋊C4#12312yes—
462C22×C22⋊C4#12318yes—
463C22×C22⋊C4C23×C412yes—
464C22×C22⋊C4C23×C412yes—
465C22×C22⋊C4C23×C412yes—
466C22×C22⋊C4C23×C412yes—
467C22×C22⋊C4C23×C412yes—
468C22×C22⋊C4C22×D412yes—
469C22×C22⋊C4C22×D418yes—
470C22×C22⋊C4C22×D412yes—
471C22×C22⋊C4C22×D418yes—
472C22×C22⋊C4C22×D412yes—
473C22×C22⋊C4C22×D412yes—
474C22×C22⋊C4C22×D412yes—
475C22×C22⋊C4C22×D412yes—
476C22×C22⋊C4C2×#4118yes—
477C22×C42C2×C22⋊C414yes—
478C2×C22⋊C8C22×D4116yescomplemented
479#386C2×C22⋊C4116yes—
480#386C2×C22⋊C418yes—
481#386C2×C22⋊C418yes—
482#381C2×C22⋊C418yes—
483#381C22×D418yes—
484C25#37911yescharacteristic
485C25#37912yes—
486C25#37912yes—
487C25#37911yescharacteristic
488C25#37912yes—
489C25#38612yes—
490C25#38612yes—
491C25#38612yes—
492C25#38618yes—
493C25#38612yes—
494C25C2×#9918yes—
495C25C22×C22⋊C411yescharacteristic
496C25C22×C22⋊C414yes—
497C25C22×C22⋊C412yes—
498C25C22×C22⋊C412yes—
499C25C22×C22⋊C411yescharacteristic
500C25C22×C22⋊C411yescharacteristic
501C25C22×C22⋊C411yescharacteristic
502C25C22×C22⋊C411yescharacteristic
503C25C22×C22⋊C412yes—
504C25C22×C22⋊C414yes—
505C25C22×C22⋊C412yes—
506C25C22×C22⋊C412yes—
507C25C22×C22⋊C411yescharacteristic
508C25C2×C4×D412yes—
509C25C2×C4×D412yes—
510C25C2×C4×D418yes—
511C25#51812yes—
512C25#51812yes—
513C25C24×C411yescharacteristic
514C22×Q8#37914yes—
515C22×Q8#37914yes—
516C22×Q8C2×#12014yes—
517C22×Q8C2×#12014yes—
518C22×D4#37912yes—
519C22×D4#37914yes—
520C22×D4#37912yes—
521C22×D4#37912yes—
522C22×D4#37914yes—
523C22×D4#37912yes—
524C22×D4#37914yes—
525C22×D4#37914yes—
526C22×D4C2×#9918yes—
527C22×D4C22×C22⋊C412yes—
528C22×D4C22×C22⋊C414yes—
529C22×D4C22×C22⋊C412yes—
530C22×D4C22×C22⋊C412yes—
531C22×D4C22×C22⋊C412yes—
532C22×D4C22×C22⋊C414yes—
533C22×D4C2×#12014yes—
534C22×D4C2×#12014yes—
535C23×C4#37912yes—
536C23×C4#37911yescharacteristic
537C23×C4#37912yes—
538C23×C4#37914yes—
539C23×C4#37914yes—
540C23×C4#37911yescharacteristic
541C23×C4#37912yes—
542C23×C4#37914yes—
543C23×C4#37914yes—
544C23×C4#38612yes—
545C23×C4#38612yes—
546C23×C4#38612yes—
547C23×C4#38612yes—
548C23×C4#38618yes—
549C23×C4C22×C22⋊C414yes—
550C23×C4C22×C22⋊C412yes—
551C23×C4C22×C22⋊C412yes—
552C23×C4C22×C22⋊C412yes—
553C23×C4C22×C22⋊C412yes—
554C23×C4C22×C22⋊C412yes—
555C23×C4C22×C22⋊C414yes—
556C23×C4C22×C22⋊C412yes—
557C23×C4C22×C22⋊C412yes—
558C23×C4C22×C22⋊C412yes—
559C23×C4C22×C22⋊C411yescharacteristic
560C23×C4C22×C22⋊C411yescharacteristic
561C23×C4C22×C22⋊C412yes—
562C23×C4C2×C4×D418yes—
563C23×C4C2×C4×D412yes—
564C23×C4C2×C4×D412yes—
565C23×C4#51814yes—
566C23×C4C2×#12014yes—
567C23×C4C2×#12014yes—
568C23×C4C2×#12012yes—
569C23×C4C2×#12012yes—
570C23×C4C2×#12012yes—
571C23×C4C2×#12012yes—
572C23×C4C2×#12014yes—
573C23×C4C2×#12014yes—
574C23×C4C2×#12011yescharacteristic
575C23×C4C2×#12011yescharacteristic
576C23×C4C2×#12012yes—
577C23×C4C2×#12012yes—
578C23×C4C2×#12012yes—
579C23×C4C2×#12012yes—
580C23×C4C2×#12012yes—
581C23×C4C2×#12112yes—
582C23×C4C2×#12112yes—
583C23×C4C2×#12112yes—
584C23×C4C2×#12112yes—
585C23×C4C2×#12311yescharacteristic
586C23×C4C2×#12311yescharacteristic
587C23×C4C2×#12312yes—
588C23×C4#53412yes—
589C23×C4#53412yes—
590C23×C4#53414yes—
591C23×C4#53412yes—
592C23×C4#53412yes—
593C23×C4#53414yes—
594C23×C4D4214yes—
595C23×C4D4214yes—
596C23×C4D4214yes—
597C23×C4D4214yes—
598C23×C4D4214yes—
599C23×C4D4214yes—
600C23×C4D4214yes—
601C23×C4D4214yes—
602C23×C4#54614yes—
603C23×C4#54614yes—
604C23×C4#54614yes—
605C23×C4#54614yes—
606C23×C4#54614yes—
607C23×C4#54614yes—
608C23×C4#54614yes—
609C23×C4#54614yes—
610C23×C4C23×D412yes—
611C23×C4C23×D411yescharacteristic
612C23×C4C23×D411yescharacteristic
613C23×C4C23×D412yes—
614C23×C4C23×D412yes—
615C23×C4C22×#4112yes—
616C23×C4C2×H(5,𝔽2)14yes—
617#120C2×#99132yes—
618C2×C22⋊C4#38614yes—
619C2×C22⋊C4#38614yes—
620C2×C22⋊C4#38618yes—
621C2×C22⋊C4#38614yes—
622C2×C22⋊C4#38614yes—
623C2×C22⋊C4#38618yes—
624C2×C22⋊C4C2×#9918yes—
625C2×C22⋊C4C22×C22⋊C414yes—
626C2×C22⋊C4C22×C22⋊C414yes—
627C2×C22⋊C4C22×C22⋊C414yes—
628C2×C22⋊C4C22×C22⋊C414yes—
629C2×C22⋊C4C2×#12014yes—
630C2×C22⋊C4C2×#12014yes—
631C2×C22⋊C4C2×#12118yes—
632C2×C22⋊C4C2×#12118yes—
633C2×C22⋊C4C2×#12314yes—
634C2×C22⋊C4C2×#12314yes—
635C24#178114yes—
636C24#189118yescomplemented
637C24C2×#37911yescharacteristic
638C24C2×#37911yescharacteristic
639C24C2×#37912yes—
640C24C2×#37914yes—
641C24C2×#37911yescharacteristic
642C24C2×#37912yes—
643C24C2×#37911yescharacteristic
644C24C2×#38611yescharacteristic
645C24C2×#38612yes—
646C24C2×#38611yescharacteristic
647C24C2×#38614yes—
648C24C2×#38614yes—
649C24#230811yescharacteristic
650C24#230812yes—
651C24#230811yescharacteristic
652C24D4×C22⋊C412yes—
653C24D4×C22⋊C412yes—
654C24D4×C22⋊C412yes—
655C24D4×C22⋊C412yes—
656C24D4×C22⋊C412yes—
657C24D4×C22⋊C412yes—
658C24D4×C22⋊C412yes—
659C24D4×C22⋊C412yes—
660C24C22×#9918yes—
661C24C22×#9914yes—
662C24#288314yes—
663C24C23×C22⋊C411yescharacteristic
664C24C23×C22⋊C411yescharacteristic
665C24C23×C22⋊C411yescharacteristic
666C24C22×C4×D412yes—
667C24C2×#51812yes—
668C2×D4#178118yes—
669C2×D4C22×#9918yes—
670C22×C4#178114yes—
671C22×C4C2×#37912yes—
672C22×C4C2×#37914yes—
673C22×C4C2×#37912yes—
674C22×C4C2×#37912yes—
675C22×C4C2×#37912yes—
676C22×C4C2×#38614yes—
677C22×C4C2×#38614yes—
678C22×C4C2×#38611yescharacteristic
679C22×C4C2×#38611yescharacteristic
680C22×C4C2×#38612yes—
681C22×C4#230812yes—
682C22×C4#230812yes—
683C22×C4D4×C22⋊C414yes—
684C22×C4D4×C22⋊C414yes—
685C22×C4D4×C22⋊C414yes—
686C22×C4D4×C22⋊C414yes—
687C22×C4#240312yes—
688C22×C4#240314yes—
689C22×C4#240312yes—
690C22×C4#240312yes—
691C22×C4#240312yes—
692C22×C4#240314yes—
693C22×C4#240512yes—
694C22×C4#240514yes—
695C22×C4#240512yes—
696C22×C4#240512yes—
697C22×C4#240512yes—
698C22×C4#240514yes—
699C22×C4#241014yes—
700C22×C4#241014yes—
701C22×C4#241014yes—
702C22×C4#241014yes—
703C22×C4#241014yes—
704C22×C4#241014yes—
705C22×C4#241014yes—
706C22×C4#241014yes—
707C22×C4C22×#12012yes—
708C22×C4C22×#12012yes—
709C22×C4C22×#12011yescharacteristic
710C22×C4C22×#12112yes—
711C22×C4C22×#12311yescharacteristic
712C22×C4C2×#53412yes—
713C22×C4C2×#53412yes—
714C22×C4C2×D4214yes—
715C22×C4C2×D4214yes—
716C22×C4C2×#54614yes—
717C22×C4C2×#54614yes—
718C22⋊C4C22×#9918yes—
719C23#1386712yes—
720C23#1386711yescharacteristic
721C23#1386712yes—
722C23#1386711yescharacteristic
723C23#1386711yescharacteristic
724C23#1386711yescharacteristic
725C23C2×#178112yes—
726C23C2×#178114yes—
727C23C2×#178112yes—
728C23#2058512yes—
729C23#2058512yes—
730C23C2×#189114yes—
731C23C2×#189118yescomplemented
732C23#2177814yes—
733C23D4×#9918yes—
734C23D4×#9918yes—
735C23C22×#37911yescharacteristic
736C23C22×#38611yescharacteristic
737C23C2×#230811yescharacteristic
738C23C2×D4×C22⋊C412yes—
739C23C2×D4×C22⋊C412yes—
740C23C23×#9912yes—
741C23C2×#288312yes—
742C2×C4#1386712yes—
743C2×C4#1386712yes—
744C2×C4#1386714yes—
745C2×C4C2×#178114yes—
746C2×C4C2×#240312yes—
747C2×C4C2×#241014yes—
748C2×C4C2×#240512yes—
749C22#35950712yes—
750C22#35950712yes—
751C22#35957912yes—
752C22#35957914yes—
753C22#35957912yes—
754C22#35959312yes—
755C22#35959312yes—
756C22C2×#1386711yescharacteristic
757C22C22×#178111yescharacteristic
758C22C2×#2058511yescharacteristic
759C22C22×#189112yes—
760C22C2×#2177812yes—
761C22C2×D4×#9914yes—
762C2C2×#35950711yescharacteristic
763C2#7223506214yesdirect product factor
764C2C2×#35957911yescharacteristic
765C2C2×#35959311yescharacteristic
subgroupG/H
center, socleC23#13867
commutatorC25C24×C4
Frattini, cosocleC24×C4C25
prime radicalC22×#36098C2
LCSG ▷ C25 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C25×C4 ◁ G
LECSG ▷ C24×C4 ▷ C22 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#184773C2semidirect
2. C2×#106670C2semidirect
3. C2×#188085C2semidirect
4. C2×#6342764C2semidirect
5. C2×#115697C2semidirect
6. C2×#115173C2semidirect
7. C2×#201819C2semidirect
8. #72235062C2direct (N × H)
10. C2×#359507C2semidirect
15. C2×#60064C22semidirect
29. C2×#20591C22semidirect
30. C2×#20579C22semidirect
31. #6342764C22semidirect
32. C2×#17392C22semidirect
33. C2×#17392C22semidirect
36. C22×#1462C22semidirect
37. #359507C22semidirect
38. C2×#10738C22semidirect
39. #201819C22semidirect
40. #188085C22semidirect
41. #184773C22semidirect
42. C2×#8114C22semidirect
43. #115697C22semidirect
44. #115173C22semidirect
45. #106670C22semidirect
90. #60064C23semidirect
122. #20591C23semidirect
123. #20579C23semidirect
124. #17392C23semidirect
125. #17392C23semidirect
126. C2×#1462D4semidirect
129. C2×#1462C23semidirect
130. C22×#323D4semidirect
131. #10738C23semidirect
132. #8114C23semidirect
267. C2×#407C2×D4semidirect
270. C22×C22⋊C8C2×D4semidirect
294. C2×#323C2×D4semidirect
478. C2×C22⋊C8C22×D4semidirect
636. C24#1891semidirect
731. C23C2×#1891semidirect
763. C2#72235062direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#1847732
C2×#1066702
C2×#1880852
C2×#63427642
C2×#1156972
C2×#1151732
C2×#2018192
#722350622
C22×#360982
C2×#3595072