Finite Group Databasebeta

← #72312422

Subgroups — #72312422

Order 2048.

At least 10690 conjugacy classes of subgroups; only the 4094 normal subgroups are shown.

The subgroup lattice has 807 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72312407C212yesmaximal, complemented
2#72312402C211yesmaximal, characteristic, complemented
3#72312399C211yesmaximal, characteristic, complemented
4#72312393C214yesmaximal, complemented
5#72312391C212yesmaximal, complemented
6#72312386C212yesmaximal, complemented
7#72312054C218yesmaximal, complemented
8#72311196C218yesmaximal, complemented
9#72278409C212yesmaximal, complemented
10#72263640C211yesmaximal, characteristic, complemented
11C2×D4×B(4,𝔽2)C211yesmaximal, characteristic, complemented
12#72234425C218yesmaximal, complemented
13#72234135C211yesmaximal, characteristic, complemented
14D4×#2196C218yesmaximal, complemented
15#72233421C214yesmaximal, complemented
16C2×#499787C214yesmaximal, complemented
17#72232721C211yesmaximal, characteristic, complemented
18#72232066C211yesmaximal, characteristic, complemented
19#72231473C214yesmaximal, complemented
20C2×D4×H(5,𝔽2)C2211yescharacteristic, complemented
21C23×B(4,𝔽2)C2212yescomplemented
22#7699471C2214yescomplemented
23D43C2214yescomplemented
24#7696413C2214yescomplemented
25#7695992C2214yescomplemented
26#7682631C2212yescomplemented
27#7682069C2214yescomplemented
28#7666076C2212yescomplemented
29C2×#58990C2214yescomplemented
30#7631334C2211yescharacteristic
31#7631286C2211yescharacteristic
32C2×D4×#120C2211yescharacteristic
33C22×#2196C2218yescomplemented
34#6629386C2212yescomplemented
35#6629358C2212yescomplemented
36C2×#32926C2211yescharacteristic, complemented
37C2×#32898C2214yescomplemented
38C2×#32898C2212yescomplemented
39C2×#32888C2214yescomplemented
40#6591500C2218yescomplemented
41#6591460C2218yescomplemented
42D4×B(4,𝔽2)C2218yescomplemented
43D4×B(4,𝔽2)C2218yescomplemented
44D4×B(4,𝔽2)C2218yescomplemented
45D4×#453C2218yescomplemented
46#6487644C2212yescomplemented
47#6487485C2212yescomplemented
48#6470225C2214yescomplemented
49#6470019C2214yescomplemented
50C2×#25771C2211yescharacteristic, complemented
51C2×#24260C2211yescharacteristic, complemented
52C2×#24404C2212yescomplemented
53C2×#23900C2212yescomplemented
54#6385983C2211yescharacteristic, complemented
55#6385971C2211yescharacteristic, complemented
56C2×D4×#99C2211yescharacteristic, complemented
57C2×C4×B(4,𝔽2)C2211yescharacteristic, complemented
58#512142C2218yescomplemented
59#511908C2218yescomplemented
60#511771C2218yescomplemented
61#508192C2218yescomplemented
62#508086C2218yescomplemented
63#508062C2218yescomplemented
64#503566C2214yescomplemented
65#503194C2218yescomplemented
66#503182C2214yescomplemented
67#503182C2218yescomplemented
68#502790C2214yescomplemented
69#502778C2218yescomplemented
70#502766C2218yescomplemented
71#502766C2214yescomplemented
72#502701C22116yescomplemented
73#502661C22116yescomplemented
74#501156C22116yescomplemented
75#501156C22116yescomplemented
76#501156C22116yescomplemented
77#501084C22116yescomplemented
78#500942C2214yescomplemented
79#500769C2218yescomplemented
80#500757C2214yescomplemented
81#500757C2218yescomplemented
82#500499C2214yescomplemented
83#500487C2218yescomplemented
84#500475C2218yescomplemented
85#500475C2214yescomplemented
86#500397C2214yescomplemented
87#500218C2214yescomplemented
88#500218C2218yescomplemented
89#500049C2218yescomplemented
90#500049C2214yescomplemented
91#500049C22116yescomplemented
92#500009C22116yescomplemented
93#499843C22116yescomplemented
94#499787C2214yescomplemented
95#499787C22116yescomplemented
96#499787C2218yescomplemented
97#499787C2218yescomplemented
98#499787C2218yescomplemented
99#499787C2218yescomplemented
100#499787C22116yescomplemented
101#499787C22116yescomplemented
102#499281C2218yescomplemented
103C2×#13346C2218yescomplemented
104C2×#13343C2218yescomplemented
105#497490C2218yescomplemented
106#497478C2218yescomplemented
107D4×#353C2218yescomplemented
108D4×AΣL(1,𝔽16)C2218yescomplemented
109D4×AΣL(1,𝔽16)C2218yescomplemented
110D4×AΣL(1,𝔽16)C2218yescomplemented
111#496528C2212yescomplemented
112#496516C2212yescomplemented
113#496330C2212yescomplemented
114#496225C2214yescomplemented
115#496225C2214yescomplemented
116#496189C2214yescomplemented
117C4×#2196C2218yescomplemented
118#495599C2212yescomplemented
119#495588C2212yescomplemented
120C2×#13088C2214yescomplemented
121C2×#13086C2214yescomplemented
122C2×#13041C2218yescomplemented
123#493995C2212yescomplemented
124C2×#12687C2214yescomplemented
125C23×H(5,𝔽2)D411yescharacteristic, complemented
126C23×H(5,𝔽2)C2312yescomplemented
127C25×D4D411yescharacteristic, complemented
128D4×H(5,𝔽2)C2318yescomplemented
129C2×#3496D411yescharacteristic, complemented
130C2×#3496C2311yescharacteristic, complemented
131C2×#3484C2312yescomplemented
132C22×D42C2311yescharacteristic
133C22×D42C2314yescomplemented
134C23×#120C2312yes—
135C2×C4×H(5,𝔽2)C2311yescharacteristic, complemented
136C22×B(4,𝔽2)C2311yescharacteristic
137C22×B(4,𝔽2)C2318yes—
138C22×B(4,𝔽2)C2312yes—
139C22×B(4,𝔽2)C2312yescomplemented
140C22×B(4,𝔽2)C2312yescomplemented
141C22×B(4,𝔽2)C2318yescomplemented
142C22×B(4,𝔽2)C2318yescomplemented
143C22×B(4,𝔽2)C2312yescomplemented
144C22×#453C2318yescomplemented
145C23×#99C2312yescomplemented
146#59818C2314yescomplemented
147#59816C2314yescomplemented
148#59814C2318yescomplemented
149#59126C2318yescomplemented
150#59001C2312yescomplemented
151#59000C2314yescomplemented
152#59000C2312yescomplemented
153#58998C2312yescomplemented
154#58997C2312yescomplemented
155#58997C2314yescomplemented
156#58992C2314yes—
157#58992C2318yescomplemented
158#58990C2318yes—
159#58990C2314yes—
160#58990C2318yescomplemented
161#58990C2318yescomplemented
162#58990C2318yescomplemented
163#52103C2314yescomplemented
164C2×#2679C2314yescomplemented
165C2×#2669C2314yescomplemented
166C2×#2847D411yescharacteristic, complemented
167C2×#2846D412yescomplemented
168#36260D414yescomplemented
169#36260C2314yes—
170#36212D414yescomplemented
171#36212C2314yes—
172D4×#127D414yescomplemented
173D4×#127C2314yes—
174D4×#120D414yescomplemented
175D4×#120D414yescomplemented
176D4×#120D414yescomplemented
177D4×#120C2314yes—
178D4×#120C2314yes—
179D4×#120C2314yes—
180#35274D412yescomplemented
181#35250D412yescomplemented
182#35001D414yescomplemented
183#34980D414yescomplemented
184#34936C2312yes—
185#34736C2312yes—
186C2×#2433D411yescharacteristic, complemented
187C2×#2433C2314yes—
188C2×#2408C2311yescharacteristic
189C2×#2410D412yescomplemented
190C2×#2403C2312yes—
191C2×#2403C2314yes—
192#34171D411yescharacteristic, complemented
193C4×D42C2314yescomplemented
194C2×#2358C2314yescomplemented
195C2×D4×C22⋊C4D411yescharacteristic, complemented
196C2×C4×#120C2311yescharacteristic
197C4×#518D411yescharacteristic, complemented
198C2×#2196C2318yes—
199C2×#2196C23116yescomplemented
200C2×#2196C23116yescomplemented
201C2×#2196C23116yescomplemented
202C2×#2196C23116yescomplemented
203C22×#353C2318yescomplemented
204C22×AΣL(1,𝔽16)C2318yescomplemented
205C22×AΣL(1,𝔽16)C2318yescomplemented
206C22×AΣL(1,𝔽16)C2318yescomplemented
207#33020C2314yescomplemented
208#32990C2314yescomplemented
209#32975C2314yescomplemented
210#32969C2314yescomplemented
211#32926C2318yescomplemented
212#32926C2314yescomplemented
213#32920C2314yescomplemented
214#32898C2314yescomplemented
215#32898C23116yescomplemented
216#32898C23116yescomplemented
217#32898C2318yescomplemented
218#32888C23116yescomplemented
219#32888C2318yescomplemented
220#32888C2314yescomplemented
221#25899C2314yescomplemented
222#25870C2314yescomplemented
223#25771C2318yescomplemented
224#25771C2314yescomplemented
225#25739C2314yescomplemented
226#24412C23116yescomplemented
227#24404C23116yescomplemented
228#24404C23116yescomplemented
229#24260C2314yes—
230#24260C2314yescomplemented
231#24260C2318yescomplemented
232#24222C2318yescomplemented
233#24056C2318yescomplemented
234#24018C2318yescomplemented
235#23906C2318yescomplemented
236#23900C2318yes—
237#23900C2318yescomplemented
238#23900C2318yescomplemented
239D4×#100C2318yescomplemented
240D4×#99C2318yescomplemented
241D4×#99C2318yescomplemented
242C4×B(4,𝔽2)C2314yes—
243C4×B(4,𝔽2)C2318yescomplemented
244C4×B(4,𝔽2)C2314yescomplemented
245C4×#453C2318yescomplemented
246C2×#1889C2311yescharacteristic
247C2×#1889C2312yescomplemented
248C2×#1867C2311yescharacteristic, complemented
249#20726C2312yescomplemented
250#20722C2312yescomplemented
251C2×#1799C2311yescharacteristic, complemented
252C2×#1792C2318yescomplemented
253C2×#1790C2318yescomplemented
254C2×#1790C2311yescharacteristic, complemented
255C2×#1790C2312yescomplemented
256C2×#1783C2314yescomplemented
257C2×#1781C2314yescomplemented
258C2×#1781C2312yescomplemented
259C2×C4×#99C2311yescharacteristic, complemented
260#13461C2318yescomplemented
261#13422C23116yescomplemented
262#13422C2318yescomplemented
263#13422C2318yescomplemented
264#13419C23116yescomplemented
265#13419C2318yescomplemented
266#13375C23116yescomplemented
267#13375C2318yescomplemented
268#13346C23116yescomplemented
269#13346C23116yescomplemented
270#13346C2318yescomplemented
271#13346C2318yescomplemented
272#13346C23116yescomplemented
273#13346C23116yescomplemented
274#13346C23116yescomplemented
275#13343C23116yescomplemented
276#13343C23116yescomplemented
277#13343C23116yescomplemented
278#13343C2318yescomplemented
279#13343C23116yescomplemented
280#13298C2314yescomplemented
281#13298C2314yescomplemented
282#13296C2314yescomplemented
283#13293C2314yescomplemented
284#13223C2314yescomplemented
285#13223C2314yescomplemented
286#13221C2314yescomplemented
287#13221C2318yescomplemented
288#13218C2318yescomplemented
289#13218C2314yescomplemented
290#13088C2314yescomplemented
291#13088C2318yescomplemented
292#13088C23116yescomplemented
293#13088C2314yescomplemented
294#13088C23116yescomplemented
295#13086C23116yescomplemented
296#13086C2314yescomplemented
297#13086C2314yescomplemented
298#13086C2318yescomplemented
299#13086C23116yescomplemented
300#13082C23116yescomplemented
301#13082C23116yescomplemented
302#13047C23116yescomplemented
303#13047C2318yescomplemented
304#13041C2318yes—
305#13041C23116yescomplemented
306#13041C23116yescomplemented
307#13041C2318yescomplemented
308#13041C23116yescomplemented
309#13041C23116yescomplemented
310#13041C23116yescomplemented
311#12964C2318yescomplemented
312#12958C23116yescomplemented
313#12958C2318yescomplemented
314#12958C2318yescomplemented
315#12856C2318yescomplemented
316#12852C2318yescomplemented
317#12852C2314yescomplemented
318#12797C2318yescomplemented
319#12793C2314yescomplemented
320#12793C2318yescomplemented
321#12793C2314yescomplemented
322#12759C2318yescomplemented
323#12759C23116yescomplemented
324#12693C2318yescomplemented
325#12687C2314yes—
326#12687C2318yescomplemented
327#12687C2318yescomplemented
328#12687C2318yescomplemented
329#12687C2318yescomplemented
330C4×#353C2318yescomplemented
331C4×AΣL(1,𝔽16)C2314yescomplemented
332C4×AΣL(1,𝔽16)C2314yescomplemented
333C4×AΣL(1,𝔽16)C2318yescomplemented
334C2×#1393C2318yescomplemented
335C2×#1390C2318yescomplemented
336C27C2×D412yescomplemented
337C22×H(5,𝔽2)C2411yescharacteristic
338C22×H(5,𝔽2)C2418yes—
339C22×H(5,𝔽2)C2412yes—
340C23×#41C2×D412yescomplemented
341C23×#41C2×D414yescomplemented
342C24×D4C2×D411yescharacteristic
343C24×D4C2×D411yescharacteristic
344C24×D4C2×D412yescomplemented
345C24×D4C2×D411yescharacteristic, complemented
346C24×D4C2×D414yescomplemented
347C24×D4C2×D414yescomplemented
348C24×D4C2×D414yescomplemented
349C24×D4C2×D414yescomplemented
350C24×D4C2412yes—
351C25×C4C2×D411yescharacteristic, complemented
352#3496C2414yes—
353#3484C2418yes—
354C2×#547C2×D414yescomplemented
355C2×D42C2×D414yes—
356C2×D42C2×D414yes—
357C2×D42C2×D414yes—
358C2×D42C2×D414yescomplemented
359C2×D42C2414yes—
360C2×D42C2418yes—
361C2×D42C2414yes—
362C2×#532C2×D412yescomplemented
363C22×#127C2×D411yescharacteristic
364C22×#127C2×D414yescomplemented
365C22×#127C2414yes—
366C22×#121C2×D411yescharacteristic
367C22×#121C2×D411yescharacteristic
368C22×#121C2×D412yes—
369C22×#121C2×D414yescomplemented
370C22×#120C2×D412yes—
371C22×#120C2×D412yes—
372C22×#120C2×D412yescomplemented
373C22×#120C2×D414yescomplemented
374C22×#120C2×D412yescomplemented
375C22×#120C2×D414yescomplemented
376C22×#120C2×D412yescomplemented
377C22×#120C2×D414yescomplemented
378C22×#120C2414yes—
379C22×#120C2411yescharacteristic
380C22×#120C2414yes—
381C22×#120C2412yes—
382C22×#120C2414yes—
383C4×H(5,𝔽2)C2414yes—
384C2×#518C2411yescharacteristic
385C22×C4×D4C2×D411yescharacteristic
386C22×C4×D4C2411yescharacteristic
387C23×C22⋊C4C2×D412yescomplemented
388C2×B(4,𝔽2)C2414yes—
389C2×B(4,𝔽2)C2412yes—
390C2×B(4,𝔽2)C2418yes—
391C2×B(4,𝔽2)C2418yes—
392C2×B(4,𝔽2)C2418yes—
393C2×B(4,𝔽2)C2412yes—
394C2×B(4,𝔽2)C24116yes—
395C2×B(4,𝔽2)C2418yes—
396C2×B(4,𝔽2)C2414yes—
397C2×#453C2418yes—
398C2×#453C24116yes—
399C22×#100C2418yes—
400C22×#99C2411yescharacteristic
401C22×#99C2418yes—
402C22×#99C2411yescharacteristic
403C22×#99C2412yes—
404C22×#99C2418yes—
405#2867C2×D414yescomplemented
406#2858C2×D414yescomplemented
407#2856C2×D418yescomplemented
408#2856C2×D418yescomplemented
409#2849C2×D418yescomplemented
410#2847C2×D414yescomplemented
411#2847C2×D414yescomplemented
412#2847C2×D414yescomplemented
413#2847C2×D414yescomplemented
414#2846C2×D418yescomplemented
415#2846C2×D418yescomplemented
416#2846C2×D418yescomplemented
417#2683C2414yes—
418#2679C2414yes—
419#2679C2418yes—
420#2669C2414yes—
421#2669C2418yes—
422#2669C2414yes—
423#2542C2×D412yescomplemented
424#2542C2412yes—
425#2541C2×D412yescomplemented
426#2541C2×D414yescomplemented
427#2541C2×D414yescomplemented
428#2541C2412yes—
429#2501C2×D414yescomplemented
430#2501C2×D418yescomplemented
431#2436C2×D414yescomplemented
432#2433C2×D418yescomplemented
433#2433C2×D418yescomplemented
434#2433C2×D418yescomplemented
435#2433C2×D414yescomplemented
436#2433C2×D414yescomplemented
437#2433C2×D414yescomplemented
438#2433C2414yes—
439#2433C2418yes—
440#2410C2×D418yescomplemented
441#2410C2×D418yescomplemented
442#2410C2×D418yescomplemented
443#2410C2×D418yescomplemented
444#2409C2×D412yescomplemented
445#2409C2412yes—
446#2408C2×D414yescomplemented
447#2408C2×D412yescomplemented
448#2408C2414yes—
449#2408C2412yes—
450#2405C2×D414yescomplemented
451#2403C2×D418yescomplemented
452#2403C2×D418yescomplemented
453#2403C2×D418yescomplemented
454#2403C2418yes—
455#2403C2414yes—
456#2403C2418yes—
457#2366C2414yes—
458#2358C2414yes—
459#2358C2418yes—
460#2358C2414yes—
461D4×C22⋊C4C2×D414yescomplemented
462D4×C22⋊C4C2×D414yescomplemented
463D4×C22⋊C4C2×D414yescomplemented
464D4×C22⋊C4C2×D414yescomplemented
465C4×#127C2×D414yescomplemented
466C4×#127C2414yes—
467C4×#120C2×D412yescomplemented
468C4×#120C2×D412yescomplemented
469C4×#120C2×D414yescomplemented
470C4×#120C2412yes—
471C4×#120C2412yes—
472C4×#120C2414yes—
473C2×#390C2×D414yescomplemented
474C2×#390C2414yes—
475C2×#386C2×D412yescomplemented
476C2×#386C2×D414yescomplemented
477C2×#386C2411yescharacteristic
478C2×#386C2414yes—
479C2×#385C2×D411yescharacteristic, complemented
480#2280C2×D412yescomplemented
481C2×#380C2×D411yescharacteristic, complemented
482C2×#379C2×D411yescharacteristic, complemented
483C2×#379C2×D412yescomplemented
484C2×#379C2×D412yescomplemented
485C2×#379C2×D414yescomplemented
486C42×D4C2×D414yescomplemented
487C42×D4C2×D414yescomplemented
488C4×#117C2×D412yescomplemented
489C2×C4×C22⋊C4C2×D414yescomplemented
490C2×C4×C22⋊C4C2×D411yescharacteristic, complemented
491C2×#353C2418yes—
492C2×#353C24116yes—
493C2×#353C2418yes—
494C2×AΣL(1,𝔽16)C2418yes—
495C2×AΣL(1,𝔽16)C2418yes—
496C2×AΣL(1,𝔽16)C2418yes—
497C2×AΣL(1,𝔽16)C24116yes—
498C2×AΣL(1,𝔽16)C24116yes—
499C2×AΣL(1,𝔽16)C24116yes—
500C2×AΣL(1,𝔽16)C2418yes—
501#1889C2418yes—
502#1889C2418yes—
503#1889C2412yes—
504#1889C2412yes—
505#1887C2418yes—
506#1867C2414yes—
507#1867C2418yes—
508#1856C2418yes—
509#1800C2414yes—
510#1799C2414yes—
511#1799C2414yes—
512#1792C24116yes—
513#1792C2418yes—
514#1790C24116yes—
515#1790C2418yes—
516#1790C2418yes—
517#1790C2414yes—
518#1783C2418yes—
519#1783C2414yes—
520#1781C2418yes—
521#1781C2418yes—
522#1781C2414yes—
523C4×#100C2414yes—
524C4×#99C2414yes—
525C4×#99C2414yes—
526#1393C2418yes—
527#1393C24116yes—
528#1393C2418yes—
529#1390C2418yes—
530#1390C2418yes—
531#1390C2418yes—
532#1390C24116yes—
533#1390C2418yes—
534C26C22×D411yescharacteristic
535C26C22×D412yes—
536C26C22×D414yes—
537C26C22×D412yes—
538C26C22×D412yes—
539C26C22×D414yes—
540C26C22×D414yescomplemented
541C2×H(5,𝔽2)C2514yes—
542C2×H(5,𝔽2)C2512yes—
543C23×Q8C22×D412yescomplemented
544C23×D4#12012yes—
545C23×D4#12014yes—
546C23×D4#12012yes—
547C23×D4#12011yescharacteristic
548C23×D4#12011yescharacteristic
549C23×D4#12014yes—
550C23×D4#12012yes—
551C23×D4#12011yescharacteristic
552C23×D4C22×D412yes—
553C23×D4C22×D414yes—
554C23×D4C22×D414yes—
555C23×D4C22×D412yes—
556C23×D4C22×D414yes—
557C23×D4C22×D414yes—
558C23×D4C22×D418yes—
559C23×D4C22×D414yes—
560C23×D4C22×D414yes—
561C23×D4C22×D414yes—
562C23×D4C22×D412yes—
563C23×D4C22×D418yescomplemented
564C23×D4C22×D412yescomplemented
565C23×D4C22×D414yescomplemented
566C23×D4C2511yescharacteristic
567C23×D4C2514yes—
568C24×C4C22×D411yescharacteristic
569C24×C4C22×D411yescharacteristic
570C24×C4C22×D412yes—
571C24×C4C22×D412yes—
572C24×C4C22×D412yes—
573C24×C4C22×D411yescharacteristic
574C24×C4C22×D414yescomplemented
575C24×C4C22×D414yescomplemented
576C2×C4⋊Q8C22×D412yescomplemented
577C2×#127#12014yes—
578C2×#127C22×D414yes—
579C2×#127C22×D414yes—
580C2×#127C22×D418yescomplemented
581C2×#127C22×D412yescomplemented
582C2×#127C22×D418yescomplemented
583C2×#127C2514yes—
584C2×#121#12014yes—
585C2×#121#12014yes—
586C2×#121#12018yes—
587C2×#121C22×D414yes—
588C2×#121C22×D414yes—
589C2×#121C22×D414yes—
590C2×#121C22×D418yes—
591C2×#121C22×D418yescomplemented
592C2×#120#12018yes—
593C2×#120#12018yes—
594C2×#120C22×D414yes—
595C2×#120C22×D414yes—
596C2×#120C22×D411yescharacteristic
597C2×#120C22×D411yescharacteristic
598C2×#120C22×D414yes—
599C2×#120C22×D414yes—
600C2×#120C22×D414yes—
601C2×#120C22×D414yes—
602C2×#120C22×D418yes—
603C2×#120C22×D418yes—
604C2×#120C22×D418yes—
605C2×#120C22×D418yescomplemented
606C2×#120C22×D418yescomplemented
607C2×#120C2514yes—
608C2×#120C2514yes—
609C2×#120C2511yescharacteristic
610C2×#120C2511yescharacteristic
611#518C2512yes—
612C2×C4×D4#12014yes—
613C2×C4×D4C22×D412yes—
614C2×C4×D4C22×D412yes—
615C2×C4×D4C22×D414yes—
616C2×C4×D4C22×D412yes—
617C2×C4×D4C22×D414yescomplemented
618C2×C4×D4C2512yes—
619C22×C4⋊C4#12011yescharacteristic
620C22×C4⋊C4C22×D411yescharacteristic
621C22×C4⋊C4C22×D414yescomplemented
622C22×C22⋊C4#12012yes—
623C22×C22⋊C4#12012yes—
624C22×C22⋊C4#12012yes—
625C22×C22⋊C4C22×D414yes—
626C22×C22⋊C4C22×D411yescharacteristic
627C22×C22⋊C4C22×D414yes—
628C22×C22⋊C4C22×D412yes—
629C22×C22⋊C4C22×D411yescharacteristic
630C22×C22⋊C4C22×D411yescharacteristic
631C22×C22⋊C4C22×D411yescharacteristic
632C22×C22⋊C4C22×D414yescomplemented
633C22×C22⋊C4C22×D414yescomplemented
634C22×C42C22×D411yescharacteristic
635C22×C42C22×D414yescomplemented
636C22×C42C22×D414yescomplemented
637B(4,𝔽2)H(5,𝔽2)18yescomplemented
638C2×#100C2518yes—
639C2×#99C2514yes—
640C2×#99C2518yes—
641C2×#99C2512yes—
642C2×#99C2512yes—
643#390C22×D414yes—
644#390C22×D418yescomplemented
645#390C22×D418yescomplemented
646#390C22×D414yescomplemented
647#390C22×D414yescomplemented
648#390C2514yes—
649#386C22×D418yes—
650#386C22×D412yes—
651#386C22×D414yes—
652#386C22×D418yescomplemented
653#386C22×D418yescomplemented
654#386C2514yes—
655#386C2512yes—
656#385C22×D412yes—
657#385C22×D412yes—
658#385C22×D414yescomplemented
659#385C22×D414yescomplemented
660#384C22×D414yescomplemented
661#384C22×D414yescomplemented
662#380C22×D414yes—
663#380C22×D412yescomplemented
664#380C22×D412yescomplemented
665#379C22×D414yes—
666#379C22×D412yes—
667#379C22×D412yes—
668#379C22×D418yes—
669#379C22×D418yes—
670#379C22×D414yescomplemented
671#379C22×D414yescomplemented
672#379C22×D418yescomplemented
673C4×C4⋊C4C22×D412yescomplemented
674C4×C4⋊C4C22×D412yescomplemented
675C4×C22⋊C4C22×D412yes—
676C4×C22⋊C4C22×D412yes—
677C4×C22⋊C4C22×D414yes—
678C4×C22⋊C4C22×D414yescomplemented
679C4×C22⋊C4C22×D418yescomplemented
680C43C22×D414yescomplemented
681C25C2×#12014yes—
682C25C2×#12012yes—
683C25C2×#12012yes—
684C25C2×#12014yes—
685C25C2×#12012yes—
686C25C23×D411yescharacteristic
687C25C23×D414yes—
688C25C23×D414yes—
689C25C23×D411yescharacteristic
690C25C23×D414yes—
691C25C23×D414yes—
692C25C23×D411yescharacteristic
693C25C23×D411yescharacteristic
694H(5,𝔽2)C2×H(5,𝔽2)14yescomplemented
695C22×D4B(4,𝔽2)12yes—
696C22×D4B(4,𝔽2)11yescharacteristic
697C22×D4B(4,𝔽2)14yes—
698C22×D4B(4,𝔽2)11yescharacteristic
699C22×D4C2×#12014yes—
700C22×D4C2×#12014yes—
701C22×D4C2×#12018yes—
702C22×D4C2×#12018yes—
703C22×D4C2×#12014yes—
704C22×D4C2×#12014yes—
705C22×D4C2×#12014yes—
706C22×D4C2×#12014yes—
707C22×D4C2×#12018yes—
708C22×D4C23×D411yescharacteristic
709C22×D4C23×D414yes—
710C22×D4C23×D414yes—
711C22×D4C23×D411yescharacteristic
712C22×D4C23×D411yescharacteristic
713C22×D4C23×D414yes—
714C22×D4C23×D414yes—
715C22×D4C2611yescharacteristic
716C23×C4C2×#12011yescharacteristic
717C23×C4C2×#12014yes—
718C23×C4C2×#12012yes—
719C23×C4C2×#12011yescharacteristic
720C23×C4C2×#12011yescharacteristic
721C23×C4C2×#12012yes—
722C23×C4C2×#12012yes—
723C23×C4C2×#12011yescharacteristic
724C23×C4C23×D411yescharacteristic
725C23×C4C23×D414yes—
726C23×C4C23×D412yes—
727C23×C4C23×D412yes—
728C23×C4C23×D414yes—
729C23×C4C23×D412yes—
730#120C2×H(5,𝔽2)14yes—
731C2×C4⋊C4C2×#12014yes—
732C2×C4⋊C4C2×#12012yes—
733C2×C4⋊C4C23×D414yes—
734C2×C4⋊C4C23×D412yes—
735C2×C22⋊C4C2×#12018yes—
736C2×C22⋊C4C2×#12018yes—
737C2×C22⋊C4C2×#12018yes—
738C2×C22⋊C4C2×#12012yes—
739C2×C22⋊C4C2×#12012yes—
740C2×C22⋊C4C23×D411yescharacteristic
741C2×C22⋊C4C23×D414yes—
742C2×C22⋊C4C23×D414yes—
743C2×C22⋊C4C23×D411yescharacteristic
744C2×C22⋊C4C23×D412yes—
745C2×C22⋊C4C23×D414yes—
746C2×C22⋊C4C23×D412yes—
747C2×C22⋊C4C23×D412yes—
748C2×C42C2×#12012yes—
749C2×C42C23×D414yes—
750C2×C42C23×D412yes—
751C2×C42C23×D414yes—
752#99C2×H(5,𝔽2)14yescomplemented
753C24C2×B(4,𝔽2)12yes—
754C24C2×B(4,𝔽2)14yes—
755C24C2×B(4,𝔽2)12yes—
756C24C22×#12011yescharacteristic
757C24C22×#12014yes—
758C24C22×#12014yes—
759C24C22×#12011yescharacteristic
760C24C22×#12014yes—
761C24C22×#12011yescharacteristic
762C24#348412yescomplemented
763C24C24×D411yescharacteristic
764C24C24×D411yescharacteristic
765C2×D4#219618yescomplemented
766C2×D4C2×B(4,𝔽2)18yes—
767C2×D4C2×B(4,𝔽2)14yes—
768C2×D4C2×B(4,𝔽2)14yes—
769C2×D4C22×H(5,𝔽2)12yes—
770C2×D4H(7,𝔽2)12yes—
771C22×C4C2×B(4,𝔽2)11yescharacteristic
772C22×C4C2×B(4,𝔽2)12yes—
773C22×C4C2×B(4,𝔽2)11yescharacteristic
774C22×C4C22×#12011yescharacteristic
775C22×C4C22×#12014yes—
776C22×C4C22×#12012yes—
777C22×C4C22×#12012yes—
778C22×C4C22×#12012yes—
779C22×C4C22×#12012yes—
780C22×C4C24×D411yescharacteristic
781C22⋊C4#348412yescomplemented
782C23C2×#219618yescomplemented
783C23C22×B(4,𝔽2)14yes—
784C23C22×B(4,𝔽2)11yescharacteristic
785C23C22×B(4,𝔽2)14yes—
786C23C22×B(4,𝔽2)11yescharacteristic
787C23#6039912yes—
788C23C23×#12011yescharacteristic
789C23C2×#348411yescharacteristic
790C23#6284211yescharacteristic
791C23D4×H(5,𝔽2)12yes—
792D4C2×#2196116yescomplemented
793C2×C4C2×#219614yescomplemented
794C2×C4C22×B(4,𝔽2)12yes—
795C2×C4C22×B(4,𝔽2)12yes—
796C2×C4D4×H(5,𝔽2)12yes—
797C22C22×#219612yes—
798C22C22×#219618yes—
799C22#763128611yescharacteristic
800C22C23×B(4,𝔽2)11yescharacteristic
801C22C2×#6039911yescharacteristic
802C4C22×#219614yes—
803C2#7221661611yescharacteristic
804C2C23×#219611yescharacteristic
805C2#7223484011yescharacteristic
subgroupG/H
center, socleC22C23×B(4,𝔽2)
commutator, Frattini, cosocleC22×D4C26
LCSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×D4 ◁ C22×D42 ◁ G
LECSG ▷ C22×D4 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72312407C2semidirect
2. #72312402C2semidirect
3. #72312399C2semidirect
4. #72312393C2semidirect
5. #72312391C2semidirect
6. #72312386C2semidirect
7. #72312054C2semidirect
8. #72311196C2semidirect
9. #72278409C2semidirect
10. #72263640C2semidirect
11. C2×D4×B(4,𝔽2)C2semidirect
12. #72234425C2semidirect
13. #72234135C2semidirect
14. D4×#2196C2semidirect
15. #72233421C2semidirect
16. C2×#499787C2semidirect
17. #72232721C2semidirect
18. #72232066C2semidirect
19. #72231473C2semidirect
20. C2×D4×H(5,𝔽2)C22semidirect
21. C23×B(4,𝔽2)C22semidirect
22. #7699471C22semidirect
23. D43C22semidirect
24. #7696413C22semidirect
25. #7695992C22semidirect
26. #7682631C22semidirect
27. #7682069C22semidirect
28. #7666076C22semidirect
29. C2×#58990C22semidirect
33. C22×#2196C22semidirect
34. #6629386C22semidirect
35. #6629358C22semidirect
36. C2×#32926C22semidirect
37. C2×#32898C22semidirect
38. C2×#32898C22semidirect
39. C2×#32888C22semidirect
40. #6591500C22semidirect
41. #6591460C22semidirect
42. D4×B(4,𝔽2)C22semidirect
43. D4×B(4,𝔽2)C22semidirect
44. D4×B(4,𝔽2)C22semidirect
45. D4×#453C22semidirect
46. #6487644C22semidirect
47. #6487485C22semidirect
48. #6470225C22semidirect
49. #6470019C22semidirect
50. C2×#25771C22semidirect
51. C2×#24260C22semidirect
52. C2×#24404C22semidirect
53. C2×#23900C22semidirect
54. #6385983C22semidirect
55. #6385971C22semidirect
56. C2×D4×#99C22semidirect
57. C2×C4×B(4,𝔽2)C22semidirect
58. #512142C22semidirect
59. #511908C22semidirect
60. #511771C22semidirect
61. #508192C22semidirect
62. #508086C22semidirect
63. #508062C22semidirect
64. #503566C22semidirect
65. #503194C22semidirect
66. #503182C22semidirect
67. #503182C22semidirect
68. #502790C22semidirect
69. #502778C22semidirect
70. #502766C22semidirect
71. #502766C22semidirect
72. #502701C22semidirect
73. #502661C22semidirect
74. #501156C22semidirect
75. #501156C22semidirect
76. #501156C22semidirect
77. #501084C22semidirect
78. #500942C22semidirect
79. #500769C22semidirect
80. #500757C22semidirect
81. #500757C22semidirect
82. #500499C22semidirect
83. #500487C22semidirect
84. #500475C22semidirect
85. #500475C22semidirect
86. #500397C22semidirect
87. #500218C22semidirect
88. #500218C22semidirect
89. #500049C22semidirect
90. #500049C22semidirect
91. #500049C22semidirect
92. #500009C22semidirect
93. #499843C22semidirect
94. #499787C22semidirect
95. #499787C22semidirect
96. #499787C22semidirect
97. #499787C22semidirect
98. #499787C22semidirect
99. #499787C22semidirect
100. #499787C22semidirect
101. #499787C22semidirect
102. #499281C22semidirect
103. C2×#13346C22semidirect
104. C2×#13343C22semidirect
105. #497490C22semidirect
106. #497478C22semidirect
107. D4×#353C22semidirect
108. D4×AΣL(1,𝔽16)C22semidirect
109. D4×AΣL(1,𝔽16)C22semidirect
110. D4×AΣL(1,𝔽16)C22semidirect
111. #496528C22semidirect
112. #496516C22semidirect
113. #496330C22semidirect
114. #496225C22semidirect
115. #496225C22semidirect
116. #496189C22semidirect
117. C4×#2196C22semidirect
118. #495599C22semidirect
119. #495588C22semidirect
120. C2×#13088C22semidirect
121. C2×#13086C22semidirect
122. C2×#13041C22semidirect
123. #493995C22semidirect
124. C2×#12687C22semidirect
125. C23×H(5,𝔽2)D4semidirect
126. C23×H(5,𝔽2)C23semidirect
127. C25×D4D4semidirect
128. D4×H(5,𝔽2)C23semidirect
129. C2×#3496D4semidirect
130. C2×#3496C23semidirect
131. C2×#3484C23semidirect
133. C22×D42C23semidirect
135. C2×C4×H(5,𝔽2)C23semidirect
139. C22×B(4,𝔽2)C23semidirect
140. C22×B(4,𝔽2)C23semidirect
141. C22×B(4,𝔽2)C23semidirect
142. C22×B(4,𝔽2)C23semidirect
143. C22×B(4,𝔽2)C23semidirect
144. C22×#453C23semidirect
145. C23×#99C23semidirect
146. #59818C23semidirect
147. #59816C23semidirect
148. #59814C23semidirect
149. #59126C23semidirect
150. #59001C23semidirect
151. #59000C23semidirect
152. #59000C23semidirect
153. #58998C23semidirect
154. #58997C23semidirect
155. #58997C23semidirect
157. #58992C23semidirect
160. #58990C23semidirect
161. #58990C23semidirect
162. #58990C23semidirect
163. #52103C23semidirect
164. C2×#2679C23semidirect
165. C2×#2669C23semidirect
166. C2×#2847D4semidirect
167. C2×#2846D4semidirect
168. #36260D4semidirect
170. #36212D4semidirect
172. D4×#127D4semidirect
174. D4×#120D4semidirect
175. D4×#120D4semidirect
176. D4×#120D4semidirect
180. #35274D4semidirect
181. #35250D4semidirect
182. #35001D4semidirect
183. #34980D4semidirect
186. C2×#2433D4semidirect
189. C2×#2410D4semidirect
192. #34171D4semidirect
193. C4×D42C23semidirect
194. C2×#2358C23semidirect
195. C2×D4×C22⋊C4D4semidirect
197. C4×#518D4semidirect
199. C2×#2196C23semidirect
200. C2×#2196C23semidirect
201. C2×#2196C23semidirect
202. C2×#2196C23semidirect
203. C22×#353C23semidirect
204. C22×AΣL(1,𝔽16)C23semidirect
205. C22×AΣL(1,𝔽16)C23semidirect
206. C22×AΣL(1,𝔽16)C23semidirect
207. #33020C23semidirect
208. #32990C23semidirect
209. #32975C23semidirect
210. #32969C23semidirect
211. #32926C23semidirect
212. #32926C23semidirect
213. #32920C23semidirect
214. #32898C23semidirect
215. #32898C23semidirect
216. #32898C23semidirect
217. #32898C23semidirect
218. #32888C23semidirect
219. #32888C23semidirect
220. #32888C23semidirect
221. #25899C23semidirect
222. #25870C23semidirect
223. #25771C23semidirect
224. #25771C23semidirect
225. #25739C23semidirect
226. #24412C23semidirect
227. #24404C23semidirect
228. #24404C23semidirect
230. #24260C23semidirect
231. #24260C23semidirect
232. #24222C23semidirect
233. #24056C23semidirect
234. #24018C23semidirect
235. #23906C23semidirect
237. #23900C23semidirect
238. #23900C23semidirect
239. D4×#100C23semidirect
240. D4×#99C23semidirect
241. D4×#99C23semidirect
243. C4×B(4,𝔽2)C23semidirect
244. C4×B(4,𝔽2)C23semidirect
245. C4×#453C23semidirect
247. C2×#1889C23semidirect
248. C2×#1867C23semidirect
249. #20726C23semidirect
250. #20722C23semidirect
251. C2×#1799C23semidirect
252. C2×#1792C23semidirect
253. C2×#1790C23semidirect
254. C2×#1790C23semidirect
255. C2×#1790C23semidirect
256. C2×#1783C23semidirect
257. C2×#1781C23semidirect
258. C2×#1781C23semidirect
259. C2×C4×#99C23semidirect
260. #13461C23semidirect
261. #13422C23semidirect
262. #13422C23semidirect
263. #13422C23semidirect
264. #13419C23semidirect
265. #13419C23semidirect
266. #13375C23semidirect
267. #13375C23semidirect
268. #13346C23semidirect
269. #13346C23semidirect
270. #13346C23semidirect
271. #13346C23semidirect
272. #13346C23semidirect
273. #13346C23semidirect
274. #13346C23semidirect
275. #13343C23semidirect
276. #13343C23semidirect
277. #13343C23semidirect
278. #13343C23semidirect
279. #13343C23semidirect
280. #13298C23semidirect
281. #13298C23semidirect
282. #13296C23semidirect
283. #13293C23semidirect
284. #13223C23semidirect
285. #13223C23semidirect
286. #13221C23semidirect
287. #13221C23semidirect
288. #13218C23semidirect
289. #13218C23semidirect
290. #13088C23semidirect
291. #13088C23semidirect
292. #13088C23semidirect
293. #13088C23semidirect
294. #13088C23semidirect
295. #13086C23semidirect
296. #13086C23semidirect
297. #13086C23semidirect
298. #13086C23semidirect
299. #13086C23semidirect
300. #13082C23semidirect
301. #13082C23semidirect
302. #13047C23semidirect
303. #13047C23semidirect
305. #13041C23semidirect
306. #13041C23semidirect
307. #13041C23semidirect
308. #13041C23semidirect
309. #13041C23semidirect
310. #13041C23semidirect
311. #12964C23semidirect
312. #12958C23semidirect
313. #12958C23semidirect
314. #12958C23semidirect
315. #12856C23semidirect
316. #12852C23semidirect
317. #12852C23semidirect
318. #12797C23semidirect
319. #12793C23semidirect
320. #12793C23semidirect
321. #12793C23semidirect
322. #12759C23semidirect
323. #12759C23semidirect
324. #12693C23semidirect
326. #12687C23semidirect
327. #12687C23semidirect
328. #12687C23semidirect
329. #12687C23semidirect
330. C4×#353C23semidirect
331. C4×AΣL(1,𝔽16)C23semidirect
332. C4×AΣL(1,𝔽16)C23semidirect
333. C4×AΣL(1,𝔽16)C23semidirect
334. C2×#1393C23semidirect
335. C2×#1390C23semidirect
336. C27C2×D4semidirect
340. C23×#41C2×D4semidirect
341. C23×#41C2×D4semidirect
344. C24×D4C2×D4semidirect
345. C24×D4C2×D4semidirect
346. C24×D4C2×D4semidirect
347. C24×D4C2×D4semidirect
348. C24×D4C2×D4semidirect
349. C24×D4C2×D4semidirect
351. C25×C4C2×D4semidirect
354. C2×#547C2×D4semidirect
358. C2×D42C2×D4semidirect
362. C2×#532C2×D4semidirect
364. C22×#127C2×D4semidirect
369. C22×#121C2×D4semidirect
372. C22×#120C2×D4semidirect
373. C22×#120C2×D4semidirect
374. C22×#120C2×D4semidirect
375. C22×#120C2×D4semidirect
376. C22×#120C2×D4semidirect
377. C22×#120C2×D4semidirect
387. C23×C22⋊C4C2×D4semidirect
405. #2867C2×D4semidirect
406. #2858C2×D4semidirect
407. #2856C2×D4semidirect
408. #2856C2×D4semidirect
409. #2849C2×D4semidirect
410. #2847C2×D4semidirect
411. #2847C2×D4semidirect
412. #2847C2×D4semidirect
413. #2847C2×D4semidirect
414. #2846C2×D4semidirect
415. #2846C2×D4semidirect
416. #2846C2×D4semidirect
423. #2542C2×D4semidirect
425. #2541C2×D4semidirect
426. #2541C2×D4semidirect
427. #2541C2×D4semidirect
429. #2501C2×D4semidirect
430. #2501C2×D4semidirect
431. #2436C2×D4semidirect
432. #2433C2×D4semidirect
433. #2433C2×D4semidirect
434. #2433C2×D4semidirect
435. #2433C2×D4semidirect
436. #2433C2×D4semidirect
437. #2433C2×D4semidirect
440. #2410C2×D4semidirect
441. #2410C2×D4semidirect
442. #2410C2×D4semidirect
443. #2410C2×D4semidirect
444. #2409C2×D4semidirect
446. #2408C2×D4semidirect
447. #2408C2×D4semidirect
450. #2405C2×D4semidirect
451. #2403C2×D4semidirect
452. #2403C2×D4semidirect
453. #2403C2×D4semidirect
461. D4×C22⋊C4C2×D4semidirect
462. D4×C22⋊C4C2×D4semidirect
463. D4×C22⋊C4C2×D4semidirect
464. D4×C22⋊C4C2×D4semidirect
465. C4×#127C2×D4semidirect
467. C4×#120C2×D4semidirect
468. C4×#120C2×D4semidirect
469. C4×#120C2×D4semidirect
473. C2×#390C2×D4semidirect
475. C2×#386C2×D4semidirect
476. C2×#386C2×D4semidirect
479. C2×#385C2×D4semidirect
480. #2280C2×D4semidirect
481. C2×#380C2×D4semidirect
482. C2×#379C2×D4semidirect
483. C2×#379C2×D4semidirect
484. C2×#379C2×D4semidirect
485. C2×#379C2×D4semidirect
486. C42×D4C2×D4semidirect
487. C42×D4C2×D4semidirect
488. C4×#117C2×D4semidirect
489. C2×C4×C22⋊C4C2×D4semidirect
490. C2×C4×C22⋊C4C2×D4semidirect
540. C26C22×D4semidirect
543. C23×Q8C22×D4semidirect
563. C23×D4C22×D4semidirect
564. C23×D4C22×D4semidirect
565. C23×D4C22×D4semidirect
574. C24×C4C22×D4semidirect
575. C24×C4C22×D4semidirect
576. C2×C4⋊Q8C22×D4semidirect
580. C2×#127C22×D4semidirect
581. C2×#127C22×D4semidirect
582. C2×#127C22×D4semidirect
591. C2×#121C22×D4semidirect
605. C2×#120C22×D4semidirect
606. C2×#120C22×D4semidirect
617. C2×C4×D4C22×D4semidirect
621. C22×C4⋊C4C22×D4semidirect
632. C22×C22⋊C4C22×D4semidirect
633. C22×C22⋊C4C22×D4semidirect
635. C22×C42C22×D4semidirect
636. C22×C42C22×D4semidirect
637. B(4,𝔽2)H(5,𝔽2)semidirect
644. #390C22×D4semidirect
645. #390C22×D4semidirect
646. #390C22×D4semidirect
647. #390C22×D4semidirect
652. #386C22×D4semidirect
653. #386C22×D4semidirect
658. #385C22×D4semidirect
659. #385C22×D4semidirect
660. #384C22×D4semidirect
661. #384C22×D4semidirect
663. #380C22×D4semidirect
664. #380C22×D4semidirect
670. #379C22×D4semidirect
671. #379C22×D4semidirect
672. #379C22×D4semidirect
673. C4×C4⋊C4C22×D4semidirect
674. C4×C4⋊C4C22×D4semidirect
678. C4×C22⋊C4C22×D4semidirect
679. C4×C22⋊C4C22×D4semidirect
680. C43C22×D4semidirect
694. H(5,𝔽2)C2×H(5,𝔽2)semidirect
752. #99C2×H(5,𝔽2)semidirect
762. C24#3484semidirect
765. C2×D4#2196semidirect
781. C22⋊C4#3484semidirect
782. C23C2×#2196semidirect
792. D4C2×#2196semidirect
793. C2×C4C2×#2196semidirect

Maximal subgroups

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

subgroupindex
#723124072
#723124022
#723123992
#723123932
#723123912
#723123862
#723120542
#723111962
#722784092
#722636402
C2×D4×B(4,𝔽2)2
#722344252
#722341352
D4×#21962
#722334212
C2×#4997872
#722327212
#722320662
#722314732