Finite Group Databasebeta

← #72261840

Subgroups — #72261840

Order 2048.

Only the 4366 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 655 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#72261805C211yesmaximal, characteristic, complemented
2#72261795C212yesmaximal, complemented
3#72261759C212yesmaximal, complemented
4#72261739C214yesmaximal, complemented
5#72261720C218yesmaximal, complemented
6#72261708C214yesmaximal, complemented
7#72261340C212yesmaximal, complemented
8#72258084C211yesmaximal, characteristic, complemented
9#72237305C211yesmaximal, characteristic
10#72234208C214yesmaximal, complemented
11#72233779C212yesmaximal, complemented
12#10586931C418yescomplemented
13#10586796C414yescomplemented
14#10586748C2214yes—
15#10586740C2214yes—
16#10586493C414yescomplemented
17#10586422C2212yes—
18#10586422C2212yes—
19#10586186C2211yescharacteristic
20#10586186C2211yescharacteristic
21C22×#3549C2211yescharacteristic
22#7622469C2218yescomplemented
23#7622466C2214yescomplemented
24#6374204C2214yescomplemented
25#6374203C2212yescomplemented
26#6374186C2211yescharacteristic, complemented
27#6374186C2212yescomplemented
28#6371562C2211yescharacteristic, complemented
29#6371543C2214yescomplemented
30#6371444C2212yescomplemented
31#493621C22116yescomplemented
32#493621C22116yescomplemented
33#493620C2218yescomplemented
34C2×#12778C2218yescomplemented
35C2×#12778C2218yescomplemented
36#493605C2218yescomplemented
37#493465C2218yescomplemented
38#493463C2214yescomplemented
39#493396C2214yescomplemented
40#493396C2212yescomplemented
41#493372C2214yescomplemented
42#493365C2212yescomplemented
43#363976C2214yescomplemented
44#363958C2218yescomplemented
45#359562C2212yescomplemented
46#359562C2214yescomplemented
47#359513C2214yescomplemented
48#359470C2212yescomplemented
49#63076C2311yescharacteristic, complemented
50#63066D418yes—
51#63046C2×C4116yescomplemented
52#63045C2×C4116yes—
53#63045D418yes—
54#63040D418yes—
55#63028C2×C4116yescomplemented
56#63024C2×C4116yes—
57#63024D418yes—
58#62876C2×C418yes—
59#62876D418yes—
60#62874D4116yes—
61#62874C2318yes—
62#62862C2×C418yescomplemented
63#62855D414yes—
64#62855C2314yes—
65#62852D414yes—
66#62852C2314yes—
67#62836C2×C414yes—
68#62836D414yes—
69#62833C2×C412yes—
70#62833C2×C412yescomplemented
71#62832D418yes—
72#62832D412yes—
73#62824C2×C418yes—
74#62824C2×C412yes—
75#62824C2×C418yescomplemented
76#62824C2×C412yescomplemented
77#62824D412yes—
78#62822C2×C414yescomplemented
79#62815D412yes—
80#62815C2312yes—
81#62814D414yes—
82#62812D412yes—
83#62812C2312yes—
84#62811D412yes—
85#62811C2311yescharacteristic
86#62811C2312yes—
87#62811C2311yescharacteristic
88C2×#3484D414yes—
89#62759D418yes—
90#62759C2314yes—
91C2×#3549C2×C414yescomplemented
92C2×#3549D418yes—
93C2×#3549C2314yes—
94C22×#555C2×C412yescomplemented
95C22×H(3,𝔽4)C2×C412yescomplemented
96C22×#535C2312yes—
97C2×#3444D412yes—
98C22×#532C2311yescharacteristic
99#60076C2311yescharacteristic, complemented
100#60070C2312yescomplemented
101#60070C2314yescomplemented
102#60064C2312yescomplemented
103#33358C23116yescomplemented
104#33358C2318yescomplemented
105C2×#2128C23116yescomplemented
106C2×#2126C2318yescomplemented
107#21009C2318yescomplemented
108#21009C2314yescomplemented
109C2×#1910C2318yescomplemented
110C2×#1910C2318yescomplemented
111#20947C2318yescomplemented
112#20947C2314yescomplemented
113C2×#1884C2314yescomplemented
114C2×#1884C2314yescomplemented
115#20710C2314yescomplemented
116#20710C2312yescomplemented
117#20584C2312yescomplemented
118#20584C2314yescomplemented
119#20360C2312yescomplemented
120C2×#585C2×D412yes—
121C2×#585C2×D411yescharacteristic
122C2×#585C2×D412yes—
123C2×#585C2411yescharacteristic
124C22×H(5,𝔽2)C2×D414yes—
125C23×#41C2×D411yescharacteristic
126C23×#41C2411yescharacteristic
127C24×D4C2×D412yes—
128C2×#568C2412yes—
129C2×#568C2412yes—
130#3551C22⋊C4132yescomplemented
131#3551C2×D4116yes—
132#3551C2×D418yes—
133#3551C2×D4116yes—
134#3550C2×D414yes—
135#3549C22⋊C4116yescomplemented
136#3549C22⋊C4116yescomplemented
137#3549C22⋊C4132yescomplemented
138#3549C2×D414yes—
139#3549C2×D418yes—
140#3549C2×D4116yes—
141#3549C2×D418yes—
142#3549C2×D418yes—
143#3549C2×D418yes—
144#3549C2×D4116yes—
145#3545C22⋊C4116yescomplemented
146#3545C22⋊C4132yescomplemented
147#3545C22⋊C4132yescomplemented
148#3545C22×C418yes—
149#3545C22×C4132yes—
150#3544C22⋊C4116yescomplemented
151#3544C22×C418yes—
152#3529C22⋊C4116yescomplemented
153#3529C2×D418yes—
154C2×H(3,𝔽4)C22⋊C4116yescomplemented
155C2×H(3,𝔽4)C22×C418yes—
156#3510C22⋊C414yes—
157#3510C22⋊C414yes—
158#3510C22⋊C4116yes—
159#3510C22×C4116yes—
160#3510C22×C414yes—
161#3510C2×D414yes—
162#3509C22⋊C414yes—
163#3509C22×C414yes—
164#3508C22⋊C414yes—
165#3508C22⋊C4116yes—
166#3508C2×D414yes—
167#3508C2×D4116yes—
168#3500C22⋊C414yes—
169#3500C22⋊C414yes—
170#3500C22⋊C4116yes—
171#3500C22×C4116yes—
172#3500C22×C414yes—
173#3500C2×D414yes—
174#3500C2×D4116yes—
175#3500C2×D414yes—
176#3500C2×D414yes—
177#3499C22⋊C414yes—
178#3499C22×C414yes—
179#3499C2×D414yes—
180#3498C22⋊C414yes—
181#3498C22⋊C4116yes—
182#3498C2×D414yes—
183#3498C2×D4116yes—
184#3498C2×D414yes—
185#3498C2×D4116yes—
186#3487C22⋊C414yes—
187#3487C22×C412yes—
188#3487C2×D412yes—
189#3487C2×D414yes—
190#3486C22⋊C414yes—
191#3486C22×C414yes—
192#3486C22×C412yes—
193#3486C22×C412yes—
194#3485C22⋊C414yes—
195#3485C22×C414yes—
196#3485C22×C412yes—
197#3485C2×D412yes—
198#3485C2×D414yes—
199#3484C22⋊C4116yes—
200#3484C22⋊C4116yes—
201#3484C22⋊C414yes—
202#3484C2×D412yes—
203#3484C2×D414yes—
204#3484C2×D412yes—
205#3484C2×D414yes—
206#3483C22⋊C4116yescomplemented
207#3483C2×D418yes—
208C2×#555C22⋊C4116yescomplemented
209C2×#555C22×C418yes—
210#3458C2×D414yes—
211#3455C22⋊C4116yes—
212#3449C2×D4116yes—
213#3449C2×D418yes—
214#3449C2×D412yes—
215#3449C2×D414yes—
216#3449C2×D414yes—
217#3449C2×D412yes—
218#3449C2×D412yes—
219#3449C2414yes—
220#3449C2412yes—
221C2×#535C22×C414yes—
222C2×#535C2×D414yes—
223C2×#535C2×D4116yes—
224C2×#535C2×D414yes—
225C2×#535C2×D414yes—
226C2×#535C2×D414yes—
227C2×#535C2414yes—
228#3444C22⋊C4116yes—
229#3444C22⋊C414yes—
230#3444C22⋊C414yes—
231#3444C22⋊C414yes—
232#3444C22⋊C414yes—
233C2×#533C2×D412yes—
234C2×#532C22×C412yes—
235C2×#532C2×D412yes—
236C2×#532C2×D418yes—
237C2×#532C2×D412yes—
238C2×#532C2×D412yes—
239C2×#532C2412yes—
240C22×C4⋊Q8C22×C411yescharacteristic
241C22×#127C2×D411yescharacteristic
242C22×#127C2×D414yes—
243C22×#124C22×C411yescharacteristic
244C22×#124C22×C414yes—
245C22×#124C2×D411yescharacteristic
246C2×#525C2×D414yes—
247C2×#525C2×D412yes—
248C2×#525C2×D414yes—
249C2×#525C2×D412yes—
250#3428C2×D414yes—
251#3428C2×D414yes—
252#3428C2×D412yes—
253#3428C2×D411yescharacteristic
254#3428C2×D412yes—
255#3428C2411yescharacteristic
256C2×#518C2×D414yes—
257C2×C4×#41C2×D412yes—
258C2×C4×#41C2×D412yes—
259C22×#117C2×D412yes—
260C23×C42C2×D411yescharacteristic
261C2×#410C2418yes—
262C2×#410C2414yes—
263C2×2−1+4C2×C22⋊C414yes—
264C2×2−1+4C2×C22⋊C412yes—
265C2×2−1+4C2×C22⋊C414yes—
266C2×2−1+4#12014yes—
267C2×2−1+4C23×C412yes—
268C2×2−1+4C22×D414yes—
269C2×H(5,𝔽2)C2×C22⋊C4116yes—
270C2×H(5,𝔽2)C2×C22⋊C414yes—
271C2×H(5,𝔽2)C2×C22⋊C414yes—
272C2×H(5,𝔽2)C2×C22⋊C412yes—
273C2×H(5,𝔽2)#120116yes—
274C2×H(5,𝔽2)#12014yes—
275C2×H(5,𝔽2)C22×D414yes—
276C2×H(5,𝔽2)C22×D414yes—
277C2×H(5,𝔽2)C22×D412yes—
278C22×#41C2×C22⋊C412yes—
279C22×#41#12018yes—
280C22×#41#12018yes—
281C22×#41C23×C411yescharacteristic
282C22×#41C22×D411yescharacteristic
283C22×#41C22×D412yes—
284C22×#41C22×D418yes—
285C22×#41C22×D411yescharacteristic
286C22×#41C22×D412yes—
287C22×#41C22×D414yes—
288C22×#41C22×D412yes—
289C22×#41C22×D412yes—
290C22×#41C22×D414yes—
291C22×#41C22×D412yes—
292C22×#41C2511yescharacteristic
293C23×Q8C2×C22⋊C411yescharacteristic
294C23×Q8C23×C411yescharacteristic
295C23×D4C2×C22⋊C414yes—
296C23×D4C2×C22⋊C414yes—
297C23×D4C2×C22⋊C411yescharacteristic
298C23×D4#12018yes—
299C23×D4C22×D411yescharacteristic
300C23×D4C22×D412yes—
301C23×D4C22×D414yes—
302C24×C4C22×D412yes—
303C24×C4C22×D411yescharacteristic
304#563C2×C22⋊C418yes—
305#563C2×C22⋊C4132yes—
306#563C2×C22⋊C4116yes—
307H(3,𝔽4)C2×C22⋊C418yes—
308H(3,𝔽4)C2×C22⋊C4116yes—
309H(3,𝔽4)C2×C22⋊C4132yes—
310H(3,𝔽4)C2×C22⋊C4116yes—
311Q82C2×C22⋊C418yes—
312#555C2×C22⋊C418yes—
313#555C2×C22⋊C4116yes—
314#555C2×C22⋊C4132yes—
315#555C2×C22⋊C4116yes—
316#555C2×C22⋊C4132yes—
317#555C2×C22⋊C4116yes—
318#536C2×C22⋊C414yes—
319#536C2×C22⋊C418yes—
320#536C2×C22⋊C414yes—
321#536C2×C22⋊C414yes—
322#536C2×C22⋊C418yes—
323#536C2×C22⋊C418yes—
324#536C2×C22⋊C4132yes—
325#536C2×C22⋊C418yes—
326#536#12018yes—
327#536#12014yes—
328#536#12018yes—
329#536#12018yes—
330#536C23×C414yes—
331#536C23×C418yes—
332#536C22×D418yes—
333#536C22×D414yes—
334#535C2×C22⋊C418yes—
335#535C2×C22⋊C414yes—
336#535C2×C22⋊C4116yes—
337#535C2×C22⋊C414yes—
338#535C2×C22⋊C4116yes—
339#535C2×C22⋊C414yes—
340#535C2×C22⋊C4132yes—
341#535C2×C22⋊C418yes—
342#535#120116yes—
343#535#12018yes—
344#535#12018yes—
345#535#12014yes—
346#535#120132yes—
347#535#12018yes—
348#535#12018yes—
349#535#120132yes—
350#535#12018yes—
351#535C22×D418yes—
352#535C22×D414yes—
353#535C22×D418yes—
354#535C22×D4116yes—
355#535C22×D4116yes—
356#535C22×D414yes—
357#534#12018yes—
358#534#12018yes—
359#534#12018yes—
360#533C2×C22⋊C414yes—
361#533C2×C22⋊C414yes—
362#533C2×C22⋊C4116yes—
363#532C2×C22⋊C414yes—
364#532C2×C22⋊C414yes—
365#532C2×C22⋊C4116yes—
366#532C2×C22⋊C418yes—
367#532C2×C22⋊C418yes—
368#532C2×C22⋊C4132yes—
369#532#12014yes—
370#532#12014yes—
371#532#12018yes—
372#532#12018yes—
373#532#12018yes—
374#532#120132yes—
375#532C22×D414yes—
376#532C22×D418yes—
377#532C22×D414yes—
378#532C22×D414yes—
379#532C22×D414yes—
380#532C22×D4116yes—
381C2×C4⋊Q8C2×C22⋊C412yes—
382C2×C4⋊Q8C2×C22⋊C418yes—
383C2×C4⋊Q8#12012yes—
384C2×C4⋊Q8C23×C412yes—
385C2×#127C2×C22⋊C412yes—
386C2×#127C2×C22⋊C418yes—
387C2×#127#12012yes—
388C2×#127#12018yes—
389C2×#127#12018yes—
390C2×#127#120132yes—
391C2×#127C22×D412yes—
392C2×#127C22×D418yes—
393C2×#124C2×C22⋊C412yes—
394C2×#124C2×C22⋊C418yes—
395C2×#124C2×C22⋊C412yes—
396C2×#124C2×C22⋊C418yes—
397C2×#124C2×C22⋊C4132yes—
398C2×#124#12012yes—
399C2×#124#12012yes—
400C2×#124#12018yes—
401C2×#124#12018yes—
402C2×#124C23×C412yes—
403C2×#124C23×C418yes—
404C2×#124C22×D412yes—
405#525C2×C22⋊C418yes—
406#525C2×C22⋊C414yes—
407#525C2×C22⋊C414yes—
408#525C2×C22⋊C418yes—
409#525C2×C22⋊C418yes—
410#525C2×C22⋊C414yes—
411#525C2×C22⋊C414yes—
412#525C2×C22⋊C418yes—
413#525#12014yes—
414#525#12018yes—
415#525#12014yes—
416C2×#123#12018yes—
417C2×#123#12014yes—
418C2×#120#12018yes—
419C2×#120#12014yes—
420#519C2×C22⋊C414yes—
421#519C2×C22⋊C412yes—
422#519C2×C22⋊C414yes—
423#519C23×C412yes—
424#518C2×C22⋊C4116yes—
425#518C2×C22⋊C414yes—
426#518C2×C22⋊C414yes—
427#518C2×C22⋊C412yes—
428#518C22×D414yes—
429#518C22×D412yes—
430C4×#41C2×C22⋊C414yes—
431C4×#41C2×C22⋊C414yes—
432C4×#41C2×C22⋊C4116yes—
433C4×#41C2×C22⋊C414yes—
434C4×#41C2×C22⋊C414yes—
435C4×#41C2×C22⋊C4116yes—
436C4×#41#12014yes—
437C4×#41#12014yes—
438C4×#41#120116yes—
439C2×#117C2×C22⋊C414yes—
440C2×#117#12014yes—
441C2×#117#120116yes—
442C2×#117C22×D414yes—
443C2×#117C22×D412yes—
444C2×#117C22×D414yes—
445C2×#117C22×D412yes—
446C2×#117C22×D414yes—
447C22×C42C2×C22⋊C411yescharacteristic
448C22×C42C2×C22⋊C411yescharacteristic
449C22×C42C2×C22⋊C412yes—
450C22×C42C2×C22⋊C414yes—
451C22×C42#12014yes—
452C22×C42C22×D412yes—
453C25C2×#12012yes—
454C25C2×#12011yescharacteristic
455C2×#41#379132yes—
456C2×#41#37918yes—
457C2×#41#37918yes—
458C2×#41C22×C22⋊C418yes—
459C2×#41C22×C22⋊C414yes—
460C2×#41C22×C22⋊C418yes—
461C2×#41C22×C22⋊C414yes—
462C2×#41C22×C22⋊C418yes—
463C2×#41C2×#12014yes—
464C2×#41C2×#12018yes—
465C2×#41C2×#12014yes—
466C2×#41C2×#120116yes—
467C2×#41C2×#12018yes—
468C2×#41C2×#12018yes—
469C2×#41C2×#12014yes—
470C2×#41C2×#12014yes—
471C2×#41C2×#12014yes—
472C2×#41C2×#12018yes—
473C2×#41C2×#12014yes—
474C2×#41C23×D414yes—
475C2×#41C23×D414yes—
476C22×Q8#37918yes—
477C22×Q8C22×C22⋊C412yes—
478C22×Q8C22×C22⋊C411yescharacteristic
479C22×Q8C22×C22⋊C412yes—
480C22×Q8C22×C22⋊C418yes—
481C22×Q8C2×#12014yes—
482C22×Q8C2×#12012yes—
483C22×Q8C2×#12012yes—
484C22×Q8C2×#12014yes—
485C22×Q8C24×C411yescharacteristic
486C22×D4#379132yes—
487C22×D4#37918yes—
488C22×D4C22×C22⋊C418yes—
489C22×D4C22×C22⋊C412yes—
490C22×D4C22×C22⋊C411yescharacteristic
491C22×D4C22×C22⋊C412yes—
492C22×D4C2×#12018yes—
493C22×D4C2×#12014yes—
494C22×D4C2×#12012yes—
495C22×D4C2×#12014yes—
496C22×D4C2×#12018yes—
497C22×D4C2×#12012yes—
498C22×D4C2×#12014yes—
499C22×D4C2×#12018yes—
500C22×D4C2×#12018yes—
501C22×D4C2×#120116yes—
502C22×D4C2×#12012yes—
503C22×D4C2×#12012yes—
504C22×D4C2×#12012yes—
505C22×D4C23×D411yescharacteristic
506C22×D4C23×D412yes—
507C23×C4C22×C22⋊C412yes—
508C23×C4C22×C22⋊C412yes—
509C23×C4C22×C22⋊C411yescharacteristic
510C23×C4C22×C22⋊C411yescharacteristic
511C23×C4C2×#12018yes—
512C23×C4C2×#12014yes—
513C23×C4C2×#12011yescharacteristic
514C23×C4C2×#12012yes—
515C23×C4C2×#12011yescharacteristic
516C23×C4C2×#12012yes—
517C23×C4C2×#12011yescharacteristic
518C23×C4C23×D412yes—
519C23×C4C23×D411yescharacteristic
520C4⋊Q8#37914yes—
521C4⋊Q8#37918yes—
522C4⋊Q8#37914yes—
523C4⋊Q8#379116yes—
524C4⋊Q8C22×C22⋊C414yes—
525C4⋊Q8C22×C22⋊C418yes—
526C4⋊Q8C22×C22⋊C414yes—
527C4⋊Q8C22×C22⋊C4116yes—
528#127#37914yes—
529#127#379116yes—
530#127#379132yes—
531#127#37914yes—
532#127#37918yes—
533#127C2×#12014yes—
534#127C2×#120116yes—
535#127C2×#120132yes—
536#127C2×#12018yes—
537#127C2×#12014yes—
538#124#37914yes—
539#124#379116yes—
540#124#379132yes—
541#124#37918yes—
542#124#37914yes—
543#124#37914yes—
544#124#37914yes—
545#124#37918yes—
546#124#379116yes—
547#124C22×C22⋊C414yes—
548#124C22×C22⋊C4116yes—
549#124C22×C22⋊C4132yes—
550#124C22×C22⋊C418yes—
551#124C22×C22⋊C414yes—
552#124C2×#12014yes—
553#124C2×#12018yes—
554#124C2×#12014yes—
555#124C2×#120116yes—
556#123#37918yes—
557#123#379116yes—
558#123#37918yes—
559#120#37918yes—
560#120#37918yes—
561#120#379116yes—
562#117#379132yes—
563#117#37918yes—
564#117#37918yes—
565#117C22×C22⋊C418yes—
566#117C22×C22⋊C414yes—
567#117C22×C22⋊C418yes—
568#117C22×C22⋊C414yes—
569#117C2×#12018yes—
570#117C2×#12018yes—
571#117C2×#12018yes—
572#117C2×#12014yes—
573#117C2×#12014yes—
574C2×C22⋊C4C2×#12014yes—
575C2×C22⋊C4C2×#12018yes—
576C2×C42#379132yes—
577C2×C42#37918yes—
578C2×C42#37918yes—
579C2×C42C22×C22⋊C418yes—
580C2×C42C22×C22⋊C412yes—
581C2×C42C22×C22⋊C412yes—
582C2×C42C2×#12012yes—
583C2×C42C2×#12014yes—
584C2×C42C2×#12018yes—
585C2×C42C2×#12012yes—
586C2×C42C2×#12012yes—
587C2×C42C2×#12012yes—
588C24C2×#37911yescharacteristic
589C24C2×#37912yes—
590C24C2×#37911yescharacteristic
591C24#284618yes—
592C24#284614yes—
593C24C22×#12012yes—
594C24C22×#12011yescharacteristic
595C2×Q8C2×#37918yes—
596C2×Q8C2×#37914yes—
597C2×Q8C2×#37914yes—
598C2×Q8C2×#37914yes—
599C2×Q8C2×#37918yes—
600C2×Q8#284614yes—
601C2×Q8C23×C22⋊C414yes—
602C2×D4C2×#37918yes—
603C2×D4C2×#379116yes—
604C2×D4C2×#37914yes—
605C2×D4C2×#37918yes—
606C2×D4C2×#37914yes—
607C2×D4C2×#37914yes—
608C2×D4C2×#37918yes—
609C2×D4#284614yes—
610C2×D4#2846116yes—
611C2×D4#284618yes—
612C2×D4C22×#12014yes—
613C2×D4C22×#12018yes—
614C22×C4C2×#379116yes—
615C22×C4C2×#37918yes—
616C22×C4C2×#37911yescharacteristic
617C22×C4C2×#37912yes—
618C22×C4C2×#37911yescharacteristic
619C22×C4#284618yes—
620C22×C4#284618yes—
621C22×C4#284614yes—
622C22×C4C23×C22⋊C412yes—
623C22×C4C23×C22⋊C411yescharacteristic
624C22×C4C22×#12012yes—
625C22×C4C22×#12014yes—
626C22×C4C22×#12012yes—
627C22×C4C22×#12014yes—
628C22×C4C22×#12011yescharacteristic
629C22⋊C4C2×#37918yes—
630C42C2×#37912yes—
631C42C2×#37912yes—
632C42C2×#37912yes—
633C42C2×#37912yes—
634C42C2×#379116yes—
635C42C2×#379116yes—
636C42C2×#37918yes—
637C23#1467918yes—
638C23C22×#37911yescharacteristic
639C23C2×#284612yes—
640C23C2×#284614yes—
641C2×C4#1467918yes—
642C2×C4C22×#37914yes—
643C2×C4C22×#37912yes—
644C2×C4C2×#284611yescharacteristic
645C2×C4C2×#284611yescharacteristic
646C2×C4#6039912yes—
647C2×C4#6040112yes—
648C22C2×#1467911yescharacteristic
649C22#637073512yes—
650C4#662889611yescharacteristic
651C4#662889711yescharacteristic
652C4#662890012yes—
653C2#7224091111yescharacteristic
subgroupG/H
center, socleC2#72240911
commutatorC22×Q8C24×C4
Frattini, cosocleC22×#41C25
prime radical#72237305C2
LCSG ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2 ◁ C22×C4 ◁ #62811 ◁ G
LECSG ▷ C22×#41 ▷ C22 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #72261805C2semidirect
2. #72261795C2semidirect
3. #72261759C2semidirect
4. #72261739C2semidirect
5. #72261720C2semidirect
6. #72261708C2semidirect
7. #72261340C2semidirect
8. #72258084C2semidirect
10. #72234208C2semidirect
11. #72233779C2semidirect
12. #10586931C4semidirect
13. #10586796C4semidirect
16. #10586493C4semidirect
22. #7622469C22semidirect
23. #7622466C22semidirect
24. #6374204C22semidirect
25. #6374203C22semidirect
26. #6374186C22semidirect
27. #6374186C22semidirect
28. #6371562C22semidirect
29. #6371543C22semidirect
30. #6371444C22semidirect
31. #493621C22semidirect
32. #493621C22semidirect
33. #493620C22semidirect
34. C2×#12778C22semidirect
35. C2×#12778C22semidirect
36. #493605C22semidirect
37. #493465C22semidirect
38. #493463C22semidirect
39. #493396C22semidirect
40. #493396C22semidirect
41. #493372C22semidirect
42. #493365C22semidirect
43. #363976C22semidirect
44. #363958C22semidirect
45. #359562C22semidirect
46. #359562C22semidirect
47. #359513C22semidirect
48. #359470C22semidirect
49. #63076C23semidirect
51. #63046C2×C4semidirect
55. #63028C2×C4semidirect
62. #62862C2×C4semidirect
70. #62833C2×C4semidirect
75. #62824C2×C4semidirect
76. #62824C2×C4semidirect
78. #62822C2×C4semidirect
91. C2×#3549C2×C4semidirect
94. C22×#555C2×C4semidirect
95. C22×H(3,𝔽4)C2×C4semidirect
99. #60076C23semidirect
100. #60070C23semidirect
101. #60070C23semidirect
102. #60064C23semidirect
103. #33358C23semidirect
104. #33358C23semidirect
105. C2×#2128C23semidirect
106. C2×#2126C23semidirect
107. #21009C23semidirect
108. #21009C23semidirect
109. C2×#1910C23semidirect
110. C2×#1910C23semidirect
111. #20947C23semidirect
112. #20947C23semidirect
113. C2×#1884C23semidirect
114. C2×#1884C23semidirect
115. #20710C23semidirect
116. #20710C23semidirect
117. #20584C23semidirect
118. #20584C23semidirect
119. #20360C23semidirect
130. #3551C22⋊C4semidirect
135. #3549C22⋊C4semidirect
136. #3549C22⋊C4semidirect
137. #3549C22⋊C4semidirect
145. #3545C22⋊C4semidirect
146. #3545C22⋊C4semidirect
147. #3545C22⋊C4semidirect
150. #3544C22⋊C4semidirect
152. #3529C22⋊C4semidirect
154. C2×H(3,𝔽4)C22⋊C4semidirect
206. #3483C22⋊C4semidirect
208. C2×#555C22⋊C4semidirect

Maximal subgroups

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

subgroupindex
#722618052
#722617952
#722617592
#722617392
#722617202
#722617082
#722613402
#722580842
#722373052
#722342082
#722337792