Finite Group Databasebeta

← #72340512

Subgroups — #72340512

Order 2048.

At least 8138 conjugacy classes of subgroups; only the 4030 normal subgroups are shown.

The subgroup lattice has 689 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72338880C212yesmaximal, complemented
2#72338641C212yesmaximal, complemented
3#72317502C2116yesmaximal, complemented
4#72316511C212yesmaximal, complemented
5#72263749C211yesmaximal, characteristic, complemented
6C2×#8698894C211yesmaximal, characteristic, complemented
7#72263633C211yesmaximal, characteristic, complemented
8#72252042C214yesmaximal, complemented
9#72251186C211yesmaximal, characteristic, complemented
10#72240271C211yesmaximal, characteristic, complemented
11#72236574C2116yesmaximal, complemented
12#72234133C212yesmaximal, complemented
13#72233448C214yesmaximal, complemented
14#72232721C211yesmaximal, characteristic, complemented
15#72231473C214yesmaximal, complemented
16#72216616C211yesmaximal, characteristic, complemented
17#72210575C214yesmaximal, complemented
18#10586472C2211yescharacteristic, complemented
19#8698894C22116yescomplemented
20C2×#52004C2212yescomplemented
21C2×#48088C2212yescomplemented
22C2×#45599C2211yescharacteristic, complemented
23C2×#59945C2211yescharacteristic, complemented
24C2×#58997C2211yescharacteristic, complemented
25C2×#58990C2212yescomplemented
26C2×#39361C2211yescharacteristic
27C2×#38904C2211yescharacteristic
28C2×#36702C2212yescomplemented
29C2×#52301C2211yescharacteristic, complemented
30C2×D4×#120C2211yescharacteristic
31#6596199C2218yescomplemented
32#6595772C2218yescomplemented
33#6595646C2218yescomplemented
34#6591514C2218yescomplemented
35D4×B(4,𝔽2)C2218yescomplemented
36#6573693C2218yescomplemented
37#6496264C2212yescomplemented
38#6491100C2212yes—
39#6490931C2212yescomplemented
40#6470225C2214yescomplemented
41#6470225C2214yescomplemented
42#6470019C2214yescomplemented
43#6454041C2212yescomplemented
44#6454041C2212yescomplemented
45#6453830C2212yescomplemented
46#6440460C2214yescomplemented
47C2×#23900C2214yescomplemented
48#6437445C2214yescomplemented
49#6385983C2211yescharacteristic, complemented
50#6385971C2211yescharacteristic, complemented
51#6385971C2211yescharacteristic, complemented
52#512142C2218yescomplemented
53#512119C2218yescomplemented
54#511771C2218yescomplemented
55#508249C2218yescomplemented
56#508193C2218yescomplemented
57#508138C2214yescomplemented
58#508095C22132yescomplemented
59#508087C2214yescomplemented
60#508087C2214yescomplemented
61#508087C2218yescomplemented
62#508086C2218yescomplemented
63#508086C2218yescomplemented
64#508062C2214yescomplemented
65#503444C2218yescomplemented
66#503182C2218yescomplemented
67#502969C2218yescomplemented
68#502962C2218yescomplemented
69#502798C2218yescomplemented
70#502780C2218yescomplemented
71#502709C22132yescomplemented
72#501156C22132yescomplemented
73#501097C22132yescomplemented
74#500757C22116yescomplemented
75#500507C22116yescomplemented
76#500489C22116yescomplemented
77#500405C22116yescomplemented
78#500218C22116yescomplemented
79#500177C22116yescomplemented
80#500057C22116yescomplemented
81#499832C22116yescomplemented
82#499787C22116yescomplemented
83#499282C22116yescomplemented
84#499137C22116yescomplemented
85#498927C22116yescomplemented
86#497484C22116yescomplemented
87#497307C22116yescomplemented
88D4×AΣL(1,𝔽16)C22116yescomplemented
89#496414C2212yescomplemented
90#496330C2212yescomplemented
91#496306C2212yescomplemented
92#496225C2214yescomplemented
93#496225C2214yescomplemented
94#496189C2214yescomplemented
95#493995C2212yescomplemented
96#493995C2212yescomplemented
97#493956C2212yescomplemented
98#493879C2214yescomplemented
99#493370C2214yescomplemented
100C2×#12687C2214yescomplemented
101C25×D4D411yescharacteristic, complemented
102#62983C2314yescomplemented
103D4×H(5,𝔽2)C2314yescomplemented
104#62773C2312yes—
105C2×#3484C2314yes—
106C22×#550D411yescharacteristic, complemented
107C22×D42C2312yes—
108C22×D42C2311yescharacteristic
109C22×#535C2312yes—
110C23×#121D411yescharacteristic, complemented
111C23×#120C2312yes—
112C22×B(4,𝔽2)C2318yescomplemented
113C2×#3019C2318yescomplemented
114#59945C2318yes—
115#58997C2318yes—
116#58990C23116yes—
117#52301C2318yes—
118C2×#2804C2311yescharacteristic
119C2×#2684C2312yes—
120C2×#2684C2311yescharacteristic
121C2×#2684C2311yescharacteristic
122C2×#2679C2311yescharacteristic
123C2×#2669C2312yes—
124C2×#2669C2312yes—
125#52004C23116yes—
126#48088C23116yes—
127#45599C2318yes—
128#39361D418yescomplemented
129#39361C2318yes—
130#38904D418yescomplemented
131#38904C2318yes—
132#36702C23116yes—
133C2×#2867D411yescharacteristic, complemented
134C2×#2847D411yescharacteristic, complemented
135C2×#2847D411yescharacteristic, complemented
136C2×#2846D412yescomplemented
137D4×#120D418yescomplemented
138D4×#120C2318yes—
139C2×#2548D411yescharacteristic, complemented
140C2×#2541C2311yescharacteristic
141C2×#2504D411yescharacteristic, complemented
142C2×#2487C2311yescharacteristic
143C2×#2431D412yescomplemented
144C2×#2433D411yescharacteristic, complemented
145C2×#2433C2312yes—
146C2×#2408C2311yescharacteristic
147C2×#2410D412yescomplemented
148C2×#2410D412yescomplemented
149C2×#2403C2312yes—
150C2×#2403C2312yes—
151C2×#2619D412yescomplemented
152C2×#2622D412yescomplemented
153C2×#2380C2312yes—
154C2×#2358C2312yes—
155C2×D4×C22⋊C4D411yescharacteristic, complemented
156C2×D4×C22⋊C4D411yescharacteristic, complemented
157C2×#2308C2312yes—
158C2×C4×#124C2311yescharacteristic
159C2×C4×#120C2311yescharacteristic
160C2×C4×#120C2311yescharacteristic
161C2×#2293D411yescharacteristic, complemented
162C2×#2196C23132yescomplemented
163C2×#2127C23116yescomplemented
164C22×AΣL(1,𝔽16)C23116yescomplemented
165#33020C2318yescomplemented
166#33020C2318yescomplemented
167#32990C2318yescomplemented
168#32976C2318yescomplemented
169#32926C2318yes—
170#32920C2318yescomplemented
171#32898C2318yescomplemented
172#32898C2318yescomplemented
173#32888C2318yescomplemented
174#25947C2314yes—
175#25918C2314yescomplemented
176#25900C2314yescomplemented
177#25853C2314yescomplemented
178#25771C2314yes—
179#25739C2314yescomplemented
180#24412C23116yescomplemented
181#24404C23116yescomplemented
182#24404C23116yescomplemented
183#24350C2314yescomplemented
184#24350C2314yescomplemented
185#24314C2314yescomplemented
186#24260C2314yescomplemented
187#24260C2314yescomplemented
188#24224C2314yescomplemented
189#24058C23116yescomplemented
190#24056C2318yes—
191#24056C2314yes—
192#24056C2314yes—
193#24018C2314yes—
194#23912C23116yescomplemented
195#23907C2314yes—
196#23906C2318yes—
197#23900C2314yes—
198#23900C2314yes—
199#23900C2318yes—
200#23900C23116yescomplemented
201D4×#100C2318yescomplemented
202D4×#99C2318yescomplemented
203D4×#99C2318yescomplemented
204C4×B(4,𝔽2)C2318yescomplemented
205C4×B(4,𝔽2)C2318yescomplemented
206C4×#455C2318yescomplemented
207C2×#1889C2318yescomplemented
208#20953C2318yescomplemented
209#20889C2318yescomplemented
210#20726C2312yes—
211#20722C2312yes—
212#20722C2312yes—
213#20609C2318yescomplemented
214C2×#1783C2314yes—
215C2×#1781C2314yes—
216C2×#1781C2314yes—
217#13463C23116yescomplemented
218#13424C23132yescomplemented
219#13424C23116yescomplemented
220#13424C23116yescomplemented
221#13422C23132yescomplemented
222#13422C23132yescomplemented
223#13419C23116yes—
224#13377C23116yescomplemented
225#13348C23132yescomplemented
226#13348C23116yescomplemented
227#13348C23116yescomplemented
228#13346C23132yescomplemented
229#13346C23132yescomplemented
230#13343C23116yes—
231#13295C2318yescomplemented
232#13292C2318yescomplemented
233#13223C2318yescomplemented
234#13223C2318yescomplemented
235#13221C2318yes—
236#13218C2318yes—
237#13088C23116yescomplemented
238#13088C23116yescomplemented
239#13086C23116yescomplemented
240#13086C23116yescomplemented
241#13082C23116yescomplemented
242#13082C23116yescomplemented
243#13049C23132yescomplemented
244#13041C23132yescomplemented
245#12966C23132yescomplemented
246#12958C23132yescomplemented
247#12856C2314yes—
248#12854C23116yescomplemented
249#12852C2318yes—
250#12852C2314yes—
251#12852C2314yes—
252#12798C2318yescomplemented
253#12793C2318yescomplemented
254#12793C2318yescomplemented
255#12759C23132yescomplemented
256#12696C23116yescomplemented
257#12694C2314yes—
258#12693C2318yes—
259#12687C2314yes—
260#12687C2318yes—
261#12687C2314yes—
262#12687C23116yescomplemented
263C4×#354C2318yescomplemented
264C4×AΣL(1,𝔽16)C2318yescomplemented
265C4×AΣL(1,𝔽16)C2318yescomplemented
266#12574C23116yescomplemented
267C27C2×D412yes—
268C22×H(5,𝔽2)C2414yes—
269C23×#41C2×D412yescomplemented
270C24×D4C2×D411yescharacteristic
271C24×D4C2×D411yescharacteristic
272C24×D4C2×D411yescharacteristic
273C24×D4C2×D418yes—
274C24×D4C2×D412yes—
275C24×D4C2×D412yescomplemented
276C24×D4C2412yes—
277C25×C4C2×D411yescharacteristic
278C25×C4C2×D411yescharacteristic, complemented
279#3501C2412yes—
280#3496C2412yes—
281#3484C2418yes—
282#3484C2414yes—
283C2×#550C2×D418yescomplemented
284C2×D42C2×D414yes—
285C2×D42C2×D414yes—
286C2×D42C2×D414yes—
287C2×D42C2418yes—
288C2×D42C2414yes—
289C2×#535C2×D418yescomplemented
290C2×#535C2418yes—
291C22×#127C2×D411yescharacteristic
292C22×#127C2×D411yescharacteristic, complemented
293C22×#127C2×D412yescomplemented
294C22×#127C2×D412yescomplemented
295C22×#127C2412yes—
296C22×#124C2×D412yescomplemented
297C22×#124C2411yescharacteristic
298C22×#121C2×D411yescharacteristic
299C22×#121C2×D411yescharacteristic
300C22×#121C2×D412yes—
301C22×#121C2×D412yescomplemented
302C22×#121C2×D418yescomplemented
303C22×#120C2×D412yes—
304C22×#120C2×D412yes—
305C22×#120C2×D418yes—
306C22×#120C2×D412yes—
307C22×#120C2×D412yes—
308C22×#120C2×D412yes—
309C22×#120C2×D412yescomplemented
310C22×#120C2418yes—
311C22×#120C2412yes—
312C22×#120C2411yescharacteristic
313C22×#120C2411yescharacteristic
314C4×H(5,𝔽2)C2414yes—
315C2×#518C2414yes—
316C22×C4×Q8C2×D411yescharacteristic, complemented
317C22×C4×D4C2×D411yescharacteristic
318C22×C4×D4C2411yescharacteristic
319C22×#117C2×D412yescomplemented
320C23×C4⋊C4C2×D411yescharacteristic, complemented
321C23×C22⋊C4C2×D412yes—
322C23×C22⋊C4C2×D412yescomplemented
323C23×C22⋊C4C2×D412yescomplemented
324C2×B(4,𝔽2)C2418yes—
325C2×B(4,𝔽2)C24116yes—
326C2×B(4,𝔽2)C2418yes—
327C2×#455C2418yes—
328C2×#453C24116yes—
329C22×#100C2418yes—
330C22×#99C2418yes—
331C22×#99C2418yes—
332#2867C2×D418yescomplemented
333#2847C2×D418yes—
334#2847C2×D418yescomplemented
335#2846C2×D4116yes—
336#2804C2414yes—
337#2684C2414yes—
338#2684C2418yes—
339#2684C2414yes—
340#2679C2414yes—
341#2669C2418yes—
342#2669C2418yes—
343#2622C2×D4116yescomplemented
344#2619C2×D4116yescomplemented
345#2548C2×D418yescomplemented
346#2541C2×D414yescomplemented
347#2541C2414yes—
348#2504C2×D418yescomplemented
349#2487C2×D414yescomplemented
350#2487C2414yes—
351#2433C2×D418yes—
352#2433C2×D418yescomplemented
353#2433C2418yes—
354#2431C2×D4116yescomplemented
355#2410C2×D4116yes—
356#2410C2×D4116yescomplemented
357#2408C2×D414yes—
358#2408C2414yes—
359#2403C2×D418yes—
360#2403C2×D418yescomplemented
361#2403C2418yes—
362#2403C2418yes—
363#2380C2418yes—
364#2358C2418yes—
365D4×C22⋊C4C2×D418yes—
366D4×C22⋊C4C2×D418yescomplemented
367#2308C2×D418yescomplemented
368#2308C2418yes—
369C4×#124C2×D414yescomplemented
370C4×#124C2414yes—
371C4×#120C2×D414yes—
372C4×#120C2×D414yescomplemented
373C4×#120C2414yes—
374C4×#120C2414yes—
375C2×#391C2×D411yescharacteristic, complemented
376#2293C2×D418yescomplemented
377C2×#390C2×D412yescomplemented
378C2×#390C2×D412yescomplemented
379C2×#390C2411yescharacteristic
380C2×#386C2×D412yes—
381C2×#386C2×D412yescomplemented
382C2×#386C2×D412yescomplemented
383C2×#386C2×D412yescomplemented
384C2×#386C2411yescharacteristic
385C2×#386C2411yescharacteristic
386C2×#386C2412yes—
387C2×#385C2×D411yescharacteristic
388C2×#385C2×D412yescomplemented
389C2×#385C2×D411yescharacteristic, complemented
390C2×#382C2×D411yescharacteristic, complemented
391C2×#380C2×D411yescharacteristic
392C2×#380C2×D411yescharacteristic, complemented
393C2×#379C2×D411yescharacteristic
394C2×#379C2×D412yes—
395C2×#379C2×D412yes—
396C2×#379C2×D412yescomplemented
397C2×#379C2×D411yescharacteristic, complemented
398C2×C4×C4⋊C4C2×D411yescharacteristic, complemented
399C2×C4×C22⋊C4C2×D411yescharacteristic
400C2×C4×C22⋊C4C2×D412yescomplemented
401C2×C4×C22⋊C4C2×D411yescharacteristic, complemented
402C2×C43C2×D411yescharacteristic, complemented
403C2×#354C24116yes—
404C2×#353C24132yes—
405C2×AΣL(1,𝔽16)C24116yes—
406C2×AΣL(1,𝔽16)C24132yes—
407C2×AΣL(1,𝔽16)C24116yes—
408#1889C2418yes—
409#1889C2418yes—
410#1889C24116yes—
411#1887C24116yes—
412#1885C2418yes—
413#1867C2418yes—
414#1867C2418yes—
415#1867C24116yes—
416#1856C2418yes—
417#1800C2414yes—
418#1799C2414yes—
419#1799C2414yes—
420#1792C2418yes—
421#1790C2418yes—
422#1790C24116yes—
423#1790C2418yes—
424#1783C2418yes—
425#1783C2414yes—
426#1781C2418yes—
427#1781C2418yes—
428#1781C2414yes—
429#1781C2414yes—
430C4×#100C2414yes—
431C4×#99C2414yes—
432C4×#99C2414yes—
433#1393C24116yes—
434#1390C24116yes—
435#1390C24132yes—
436#1390C24116yes—
437C26C22×D412yes—
438C26C22×D412yes—
439C26C22×D411yescharacteristic
440C26C22×D411yescharacteristic
441C26C22×D412yes—
442C26C22×D418yes—
443C2×H(5,𝔽2)C2514yes—
444C22×#41C22×D418yes—
445C23×Q8C22×D411yescharacteristic
446C23×D4#12011yescharacteristic
447C23×D4#12011yescharacteristic
448C23×D4#12014yes—
449C23×D4#12012yes—
450C23×D4#12014yes—
451C23×D4#12012yes—
452C23×D4#12012yes—
453C23×D4#12011yescharacteristic
454C23×D4C22×D414yes—
455C23×D4C22×D414yes—
456C23×D4C22×D412yes—
457C23×D4C22×D412yes—
458C23×D4C22×D414yes—
459C23×D4C22×D414yes—
460C23×D4C22×D414yes—
461C23×D4C22×D418yes—
462C23×D4C22×D418yes—
463C23×D4C22×D412yes—
464C23×D4C22×D414yes—
465C23×D4C22×D412yes—
466C23×D4C2514yes—
467C23×D4C2511yescharacteristic
468C24×C4C22×D411yescharacteristic
469C24×C4C22×D411yescharacteristic
470C24×C4C22×D412yes—
471C24×C4C22×D414yes—
472C24×C4C22×D411yescharacteristic
473C24×C4C22×D414yes—
474C24×C4C22×D411yescharacteristic
475C24×C4C22×D412yes—
476C2×#127#12014yes—
477C2×#127C22×D418yes—
478C2×#127C22×D414yes—
479C2×#127C22×D414yes—
480C2×#127C22×D414yes—
481C2×#127C22×D418yes—
482C2×#127C2514yes—
483C2×#124C22×D418yes—
484C2×#124C22×D412yes—
485C2×#124C2512yes—
486C2×#121#12014yes—
487C2×#121#12014yes—
488C2×#121#12018yes—
489C2×#121C22×D418yes—
490C2×#121C22×D414yes—
491C2×#121C22×D414yes—
492C2×#121C22×D418yes—
493C2×#120#12018yes—
494C2×#120#12018yes—
495C2×#120C22×D418yes—
496C2×#120C22×D414yes—
497C2×#120C22×D418yes—
498C2×#120C22×D412yes—
499C2×#120C22×D412yes—
500C2×#120C22×D418yes—
501C2×#120C22×D418yes—
502C2×#120C22×D418yes—
503C2×#120C22×D418yes—
504C2×#120C2514yes—
505C2×#120C2512yes—
506C2×#120C2512yes—
507#518C2514yes—
508C2×C4×Q8C22×D414yes—
509C2×C4×D4#12014yes—
510C2×C4×D4C22×D412yes—
511C2×C4×D4C22×D412yes—
512C2×C4×D4C22×D414yes—
513C2×C4×D4C22×D412yes—
514C2×C4×D4C2512yes—
515C2×#117C22×D418yes—
516C22×C4⋊C4#12011yescharacteristic
517C22×C4⋊C4C22×D414yes—
518C22×C4⋊C4C22×D411yescharacteristic
519C22×C4⋊C4C22×D411yescharacteristic
520C22×C22⋊C4#12012yes—
521C22×C22⋊C4#12012yes—
522C22×C22⋊C4#12012yes—
523C22×C22⋊C4C22×D418yes—
524C22×C22⋊C4C22×D418yes—
525C22×C22⋊C4C22×D411yescharacteristic
526C22×C22⋊C4C22×D412yes—
527C22×C22⋊C4C22×D411yescharacteristic
528C22×C22⋊C4C22×D418yes—
529C22×C22⋊C4C22×D411yescharacteristic
530C22×C22⋊C4C22×D412yes—
531C22×C22⋊C4C22×D411yescharacteristic
532C22×C22⋊C4C22×D411yescharacteristic
533C22×C22⋊C4C22×D411yescharacteristic
534C22×C42C22×D411yescharacteristic
535C22×C42C22×D411yescharacteristic
536C22×C42C22×D412yes—
537C22×C42C22×D411yescharacteristic
538C2×#100C2518yes—
539C2×#99C2518yes—
540C2×#99C2518yes—
541#391C22×D414yes—
542#390C22×D418yes—
543#390C22×D412yes—
544#390C22×D418yes—
545#390C2512yes—
546#386C22×D412yes—
547#386C22×D414yes—
548#386C22×D418yes—
549#386C22×D418yes—
550#386C22×D418yes—
551#386C22×D418yes—
552#386C22×D412yes—
553#386C2512yes—
554#386C2514yes—
555#386C2512yes—
556#385C22×D414yes—
557#385C22×D418yes—
558#385C22×D414yes—
559#382C22×D414yes—
560#380C22×D414yes—
561#380C22×D414yes—
562#379C22×D418yes—
563#379C22×D418yes—
564#379C22×D414yes—
565#379C22×D418yes—
566#379C22×D414yes—
567C4×C4⋊C4C22×D414yes—
568C4×C22⋊C4C22×D414yes—
569C4×C22⋊C4C22×D414yes—
570C4×C22⋊C4C22×D418yes—
571C43C22×D414yes—
572C25C2×#12012yes—
573C25C2×#12012yes—
574C25C2×#12014yes—
575C25C2×#12014yes—
576C25C2×#12012yes—
577C25C23×D411yescharacteristic
578C25C23×D411yescharacteristic
579C25C23×D414yes—
580C25C23×D414yes—
581C25C23×D414yes—
582C25C23×D412yes—
583C25C23×D412yes—
584C22×Q8C23×D412yes—
585C22×D4B(4,𝔽2)11yescharacteristic
586C22×D4B(4,𝔽2)11yescharacteristic
587C22×D4B(4,𝔽2)12yes—
588C22×D4B(4,𝔽2)14yes—
589C22×D4C2×#12014yes—
590C22×D4C2×#12014yes—
591C22×D4C2×#12018yes—
592C22×D4C2×#12018yes—
593C22×D4C2×#12014yes—
594C22×D4C2×#12014yes—
595C22×D4C2×#12014yes—
596C22×D4C2×#12014yes—
597C22×D4C2×#12018yes—
598C22×D4C23×D414yes—
599C22×D4C23×D411yescharacteristic
600C22×D4C23×D414yes—
601C22×D4C23×D411yescharacteristic
602C22×D4C23×D411yescharacteristic
603C22×D4C23×D414yes—
604C22×D4C23×D414yes—
605C22×D4C2611yescharacteristic
606C23×C4C2×#12011yescharacteristic
607C23×C4C2×#12012yes—
608C23×C4C2×#12011yescharacteristic
609C23×C4C2×#12011yescharacteristic
610C23×C4C2×#12011yescharacteristic
611C23×C4C2×#12014yes—
612C23×C4C2×#12012yes—
613C23×C4C2×#12012yes—
614C23×C4C23×D411yescharacteristic
615C23×C4C23×D414yes—
616C23×C4C23×D412yes—
617C23×C4C23×D412yes—
618C23×C4C23×D412yes—
619C23×C4C23×D414yes—
620C23×C4C23×D412yes—
621C2×C4⋊C4C2×#12014yes—
622C2×C4⋊C4C2×#12012yes—
623C2×C4⋊C4C23×D412yes—
624C2×C4⋊C4C23×D412yes—
625C2×C22⋊C4C2×#12018yes—
626C2×C22⋊C4C2×#12018yes—
627C2×C22⋊C4C2×#12018yes—
628C2×C22⋊C4C2×#12012yes—
629C2×C22⋊C4C2×#12012yes—
630C2×C22⋊C4C23×D412yes—
631C2×C22⋊C4C23×D414yes—
632C2×C22⋊C4C23×D412yes—
633C2×C22⋊C4C23×D412yes—
634C2×C22⋊C4C23×D414yes—
635C2×C22⋊C4C23×D412yes—
636C2×C22⋊C4C23×D412yes—
637C2×C22⋊C4C23×D412yes—
638C2×C42C2×#12012yes—
639C2×C42C23×D412yes—
640C2×C42C23×D414yes—
641C2×C42C23×D412yes—
642C2×C42C23×D412yes—
643C24C2×B(4,𝔽2)12yes—
644C24C2×B(4,𝔽2)14yes—
645C24C2×B(4,𝔽2)12yes—
646C24C22×#12011yescharacteristic
647C24C22×#12014yes—
648C24C22×#12011yescharacteristic
649C24C22×#12014yes—
650C24C22×#12011yescharacteristic
651C24C22×#12014yes—
652C24C24×D411yescharacteristic
653C24C24×D411yescharacteristic
654C2×D4C2×B(4,𝔽2)14yes—
655C2×D4C2×B(4,𝔽2)14yes—
656C2×D4C2×B(4,𝔽2)18yes—
657C2×D4H(7,𝔽2)14yes—
658C22×C4C2×B(4,𝔽2)12yes—
659C22×C4C2×B(4,𝔽2)11yescharacteristic
660C22×C4C2×B(4,𝔽2)11yescharacteristic
661C22×C4C22×#12014yes—
662C22×C4C22×#12011yescharacteristic
663C22×C4C22×#12012yes—
664C22×C4C22×#12012yes—
665C22×C4C22×#12012yes—
666C22×C4C22×#12012yes—
667C22×C4C24×D411yescharacteristic
668C23C22×B(4,𝔽2)14yes—
669C23C22×B(4,𝔽2)14yes—
670C23C22×B(4,𝔽2)11yescharacteristic
671C23C22×B(4,𝔽2)11yescharacteristic
672C23C23×#12011yescharacteristic
673C23#6284212yes—
674C23#6285212yes—
675C2×C4#3355114yes—
676C2×C4C22×B(4,𝔽2)12yes—
677C2×C4C22×B(4,𝔽2)12yes—
678C2×C4#6284212yes—
679C22C2×#3355112yes—
680C22#762288012yes—
681C22#763066811yescharacteristic
682C22C23×B(4,𝔽2)11yescharacteristic
683C22#1057487311yescharacteristic
684C4C2×#3355114yes—
685C2C2×#762288011yescharacteristic
686C2C22×#3355111yescharacteristic
687C2#7225127811yescharacteristic
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. #72338880C2semidirect
2. #72338641C2semidirect
3. #72317502C2semidirect
4. #72316511C2semidirect
5. #72263749C2semidirect
6. C2×#8698894C2semidirect
7. #72263633C2semidirect
8. #72252042C2semidirect
9. #72251186C2semidirect
10. #72240271C2semidirect
11. #72236574C2semidirect
12. #72234133C2semidirect
13. #72233448C2semidirect
14. #72232721C2semidirect
15. #72231473C2semidirect
16. #72216616C2semidirect
17. #72210575C2semidirect
18. #10586472C22semidirect
19. #8698894C22semidirect
20. C2×#52004C22semidirect
21. C2×#48088C22semidirect
22. C2×#45599C22semidirect
23. C2×#59945C22semidirect
24. C2×#58997C22semidirect
25. C2×#58990C22semidirect
28. C2×#36702C22semidirect
29. C2×#52301C22semidirect
31. #6596199C22semidirect
32. #6595772C22semidirect
33. #6595646C22semidirect
34. #6591514C22semidirect
35. D4×B(4,𝔽2)C22semidirect
36. #6573693C22semidirect
37. #6496264C22semidirect
39. #6490931C22semidirect
40. #6470225C22semidirect
41. #6470225C22semidirect
42. #6470019C22semidirect
43. #6454041C22semidirect
44. #6454041C22semidirect
45. #6453830C22semidirect
46. #6440460C22semidirect
47. C2×#23900C22semidirect
48. #6437445C22semidirect
49. #6385983C22semidirect
50. #6385971C22semidirect
51. #6385971C22semidirect
52. #512142C22semidirect
53. #512119C22semidirect
54. #511771C22semidirect
55. #508249C22semidirect
56. #508193C22semidirect
57. #508138C22semidirect
58. #508095C22semidirect
59. #508087C22semidirect
60. #508087C22semidirect
61. #508087C22semidirect
62. #508086C22semidirect
63. #508086C22semidirect
64. #508062C22semidirect
65. #503444C22semidirect
66. #503182C22semidirect
67. #502969C22semidirect
68. #502962C22semidirect
69. #502798C22semidirect
70. #502780C22semidirect
71. #502709C22semidirect
72. #501156C22semidirect
73. #501097C22semidirect
74. #500757C22semidirect
75. #500507C22semidirect
76. #500489C22semidirect
77. #500405C22semidirect
78. #500218C22semidirect
79. #500177C22semidirect
80. #500057C22semidirect
81. #499832C22semidirect
82. #499787C22semidirect
83. #499282C22semidirect
84. #499137C22semidirect
85. #498927C22semidirect
86. #497484C22semidirect
87. #497307C22semidirect
88. D4×AΣL(1,𝔽16)C22semidirect
89. #496414C22semidirect
90. #496330C22semidirect
91. #496306C22semidirect
92. #496225C22semidirect
93. #496225C22semidirect
94. #496189C22semidirect
95. #493995C22semidirect
96. #493995C22semidirect
97. #493956C22semidirect
98. #493879C22semidirect
99. #493370C22semidirect
100. C2×#12687C22semidirect
101. C25×D4D4semidirect
102. #62983C23semidirect
103. D4×H(5,𝔽2)C23semidirect
106. C22×#550D4semidirect
110. C23×#121D4semidirect
112. C22×B(4,𝔽2)C23semidirect
113. C2×#3019C23semidirect
128. #39361D4semidirect
130. #38904D4semidirect
133. C2×#2867D4semidirect
134. C2×#2847D4semidirect
135. C2×#2847D4semidirect
136. C2×#2846D4semidirect
137. D4×#120D4semidirect
139. C2×#2548D4semidirect
141. C2×#2504D4semidirect
143. C2×#2431D4semidirect
144. C2×#2433D4semidirect
147. C2×#2410D4semidirect
148. C2×#2410D4semidirect
151. C2×#2619D4semidirect
152. C2×#2622D4semidirect
155. C2×D4×C22⋊C4D4semidirect
156. C2×D4×C22⋊C4D4semidirect
161. C2×#2293D4semidirect
162. C2×#2196C23semidirect
163. C2×#2127C23semidirect
164. C22×AΣL(1,𝔽16)C23semidirect
165. #33020C23semidirect
166. #33020C23semidirect
167. #32990C23semidirect
168. #32976C23semidirect
170. #32920C23semidirect
171. #32898C23semidirect
172. #32898C23semidirect
173. #32888C23semidirect
175. #25918C23semidirect
176. #25900C23semidirect
177. #25853C23semidirect
179. #25739C23semidirect
180. #24412C23semidirect
181. #24404C23semidirect
182. #24404C23semidirect
183. #24350C23semidirect
184. #24350C23semidirect
185. #24314C23semidirect
186. #24260C23semidirect
187. #24260C23semidirect
188. #24224C23semidirect
189. #24058C23semidirect
194. #23912C23semidirect
200. #23900C23semidirect
201. D4×#100C23semidirect
202. D4×#99C23semidirect
203. D4×#99C23semidirect
204. C4×B(4,𝔽2)C23semidirect
205. C4×B(4,𝔽2)C23semidirect
206. C4×#455C23semidirect
207. C2×#1889C23semidirect
208. #20953C23semidirect
209. #20889C23semidirect
213. #20609C23semidirect
217. #13463C23semidirect
218. #13424C23semidirect
219. #13424C23semidirect
220. #13424C23semidirect
221. #13422C23semidirect
222. #13422C23semidirect
224. #13377C23semidirect
225. #13348C23semidirect
226. #13348C23semidirect
227. #13348C23semidirect
228. #13346C23semidirect
229. #13346C23semidirect
231. #13295C23semidirect
232. #13292C23semidirect
233. #13223C23semidirect
234. #13223C23semidirect
237. #13088C23semidirect
238. #13088C23semidirect
239. #13086C23semidirect
240. #13086C23semidirect
241. #13082C23semidirect
242. #13082C23semidirect
243. #13049C23semidirect
244. #13041C23semidirect
245. #12966C23semidirect
246. #12958C23semidirect
248. #12854C23semidirect
252. #12798C23semidirect
253. #12793C23semidirect
254. #12793C23semidirect
255. #12759C23semidirect
256. #12696C23semidirect
262. #12687C23semidirect
263. C4×#354C23semidirect
264. C4×AΣL(1,𝔽16)C23semidirect
265. C4×AΣL(1,𝔽16)C23semidirect
266. #12574C23semidirect
269. C23×#41C2×D4semidirect
275. C24×D4C2×D4semidirect
278. C25×C4C2×D4semidirect
283. C2×#550C2×D4semidirect
289. C2×#535C2×D4semidirect
292. C22×#127C2×D4semidirect
293. C22×#127C2×D4semidirect
294. C22×#127C2×D4semidirect
296. C22×#124C2×D4semidirect
301. C22×#121C2×D4semidirect
302. C22×#121C2×D4semidirect
309. C22×#120C2×D4semidirect
316. C22×C4×Q8C2×D4semidirect
319. C22×#117C2×D4semidirect
320. C23×C4⋊C4C2×D4semidirect
322. C23×C22⋊C4C2×D4semidirect
323. C23×C22⋊C4C2×D4semidirect
332. #2867C2×D4semidirect
334. #2847C2×D4semidirect
343. #2622C2×D4semidirect
344. #2619C2×D4semidirect
345. #2548C2×D4semidirect
346. #2541C2×D4semidirect
348. #2504C2×D4semidirect
349. #2487C2×D4semidirect
352. #2433C2×D4semidirect
354. #2431C2×D4semidirect
356. #2410C2×D4semidirect
360. #2403C2×D4semidirect
366. D4×C22⋊C4C2×D4semidirect
367. #2308C2×D4semidirect
369. C4×#124C2×D4semidirect
372. C4×#120C2×D4semidirect
375. C2×#391C2×D4semidirect
376. #2293C2×D4semidirect
377. C2×#390C2×D4semidirect
378. C2×#390C2×D4semidirect
381. C2×#386C2×D4semidirect
382. C2×#386C2×D4semidirect
383. C2×#386C2×D4semidirect
388. C2×#385C2×D4semidirect
389. C2×#385C2×D4semidirect
390. C2×#382C2×D4semidirect
392. C2×#380C2×D4semidirect
396. C2×#379C2×D4semidirect
397. C2×#379C2×D4semidirect
398. C2×C4×C4⋊C4C2×D4semidirect
400. C2×C4×C22⋊C4C2×D4semidirect
401. C2×C4×C22⋊C4C2×D4semidirect
402. C2×C43C2×D4semidirect

Maximal subgroups

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

subgroupindex
#723388802
#723386412
#723175022
#723165112
#722637492
C2×#86988942
#722636332
#722520422
#722511862
#722402712
#722365742
#722341332
#722334482
#722327212
#722314732
#722166162
#722105752