Finite Group Databasebeta

← #11887533

Subgroups — #11887533

Order 1152.

980 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#638C211yesmaximal, characteristic, complemented
2#10594928C211yesmaximal, characteristic
3C3×#5227C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591630C211yesmaximal, characteristic, complemented
6#10591592C211yesmaximal, characteristic, complemented
7#10591591C211yesmaximal, characteristic, complemented
8#10591571C211yesmaximal, characteristic, complemented
9#10591569C211yesmaximal, characteristic, complemented
10#10591553C211yesmaximal, characteristic, complemented
11#10591552C211yesmaximal, characteristic, complemented
12#10591538C211yesmaximal, characteristic, complemented
13#10591175C211yesmaximal, characteristic, complemented
14#10591148C211yesmaximal, characteristic, complemented
15#10591124C211yesmaximal, characteristic, complemented
16#80049—31nomaximal
17#78805—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×Q8×C3⋊D3C2211yescharacteristic
20C2×#3804—21no—
21#64155—21no—
22#64155C2211yescharacteristic
23Q8×C3⋊Dic3C2211yescharacteristic
24#64153—21no—
25#64153C2211yescharacteristic
26C4×#638—21no—
27C4×#638C2211yescharacteristic
28#64133—21no—
29#64133C2211yescharacteristic
30C2×C3×#215C2211yescharacteristic
31C2×C3×#215C2211yescharacteristic
32C3×#930C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C22×C3×C3⋊C8C2211yescharacteristic
35#63961—21no—
36#63919C2211yescharacteristic
37#63916C2211yescharacteristic
38#63900C2211yescharacteristic
39#63899—21no—
40#63898C2211yescharacteristic
41#63854—21no—
42C2×#3716C2211yescharacteristic
43C2×#3710C2211yescharacteristic
44C3×#835C2211yescharacteristic
45C3×#835C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63573C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54#63572C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63567C2211yescharacteristic
58#63563C2211yescharacteristic
59#63557C2211yescharacteristic
60#63553C2211yescharacteristic
61Q8×#67—31no—
62Q8×#67—31no—
63Q8×#67—61no—
64#5611—31no—
65#5507—31no—
66C3×#448—31no—
67C2×C3×#103—31no—
68#5227D311yescharacteristic, complemented
69C2×#835D311yescharacteristic, complemented
70#5171—31no—
71#5170—31no—
72#5162—31no—
73Dic3×SD16—31no—
74#5114—31no—
75C8×#67—31no—
76#5041—31no—
77#4971—31no—
78#4818—31no—
79#4807—31no—
80#4806—31no—
81#4805—31no—
82#4805—31no—
83D3×#103—31no—
84D3×#103—31no—
85#4792—31no—
86#4792—31no—
87#4791—31no—
88#4791—31no—
89#4788—31no—
90#67⋊C8—31no—
91#4721—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638D411yescharacteristic
100Q8×C3⋊D3—22no—
101Q8×C3⋊D3—41no—
102C2×C4×C3⋊D3—21no—
103C2×C4×C3⋊D3C2311yescharacteristic
104C2×#634—21no—
105C2×#634C2311yescharacteristic
106C2×C3×#67—21no—
107C22×C3×Dic3—21no—
108C2×C3×D12C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#624—21no—
112#3804—44no—
113C2×D3×Dic3—21no—
114#3757—21no—
115#3757D411yescharacteristic
116#3752—21no—
117#3752D411yescharacteristic
118C4⋊(C3⋊Dic3)—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120#3750—21no—
121#3750—21no—
122#3750—21no—
123#3750—21no—
124#3750D411yescharacteristic
125C4×C3⋊Dic3—21no—
126C4×C3⋊Dic3C2311yescharacteristic
127C3×#215—22no—
128C3×#215—41no—
129C3×(C2×D3)⋊C4—21no—
130C3×C4⋊Dic3—21no—
131C3×C4⋊Dic3C2311yescharacteristic
132C3×C4⋊Dic3C2311yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C2×C3×C3⋊C8—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139#3724—21no—
140#3724—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3716—41no—
144#3710—41no—
145#3298—91noSylow
146C22×C3×Q8—21no—
147C22×C3×Q8C2×D311yescharacteristic
148C22×C3×Q8C2×D311yescharacteristic
149C2×D3×Q8—31no—
150C2×D3×Q8—31no—
151C2×D3×Q8—61no—
152C2×#237—61no—
153C2×#235—61no—
154C2×C3×SD16—31no—
155C2×C3×SD16—31no—
156C22×C3×C8—31no—
157C3×#121—31no—
158C2×C3×C4⋊C4—31no—
159#946—31no—
160#946—31no—
161#946—61no—
162#946—61no—
163#946—61no—
164#946—62no—
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—61no—
168#944—31no—
169#944—31no—
170#944—61no—
171#944—61no—
172#944—61no—
173#944—62no—
174C2×#215C2×D311yescharacteristic
175C2×#215C2×D311yescharacteristic
176#938—31no—
177#935—61no—
178D4×Dic3—31no—
179C2×#214—31no—
180#930C2×D311yescharacteristic
181#929—61no—
182C4×#67—31no—
183C4×#67—31no—
184C4×#67—61no—
185C4×#67—61no—
186C4×#67—61no—
187C4×#67—62no—
188C2×C4⋊Dic3C2×D311yescharacteristic
189#924—31no—
190#924—31no—
191#924—61no—
192#924—61no—
193#924—61no—
194#924—62no—
195C22×C3⋊C8C2×D311yescharacteristic
196C2×#204—31no—
197C2×D3×C8—31no—
198C2×D3×C8—31no—
199#896—61no—
200#895—31no—
201#894—61no—
202#893—31no—
203D3×C4⋊C4—31no—
204D3×C4⋊C4—31no—
205#888—31no—
206#888—31no—
207#883—61no—
208#878—61no—
209C3×#103—31no—
210C3×#103—31no—
211C3×#103—31no—
212C3×#103—31no—
213C3×#103—31no—
214C3×#103—31no—
215C3×C22⋊C8—31no—
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#835C2×D311yescharacteristic
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#835C2×D311yescharacteristic
222#832—31no—
223#830C2×D311yescharacteristic
224#821—31no—
225(C2×D3)⋊C8—31no—
226(C2×D3)⋊C8—31no—
227#817—31no—
228#817—31no—
229#817—31no—
230#816—31no—
231#816—31no—
232#816—31no—
233Dic3⋊C8—31no—
234Dic3⋊C8—31no—
235C8×Dic3—31no—
236C8×Dic3—31no—
237#810—31no—
238#810—31no—
239#810—31no—
240#808—31no—
241#808—31no—
242#808—31no—
243C23×C32C2×D411yescharacteristic
244C22×C3⋊D3C2×D411yescharacteristic
245C22×C3×D3—21no—
246C32×Q8—21no—
247C32×Q8—21no—
248C32×Q8—21no—
249C32×Q8—42no—
250C32×Q8#4112yescomplemented
251C2×C32×C4—21no—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—42no—
256C2×C32×C4C2×D411yescharacteristic
257C2×C32×C4C2411yescharacteristic
258#638SD1614yescomplemented
259C2×C3⋊Dic3—21no—
260C2×C3⋊Dic3—21no—
261C2×C3⋊Dic3C2×D411yescharacteristic
262C2×C3⋊Dic3C2×D411yescharacteristic
263C2×C3⋊Dic3C2×D411yescharacteristic
264C4×C3⋊D3—21no—
265C4×C3⋊D3—21no—
266C4×C3⋊D3—42no—
267#634—21no—
268#634—21no—
269#634—42no—
270C3×#67—42no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—42no—
275C3×D12—21no—
276C3×D12—21no—
277#627—42no—
278#626—42no—
279#624—42no—
280D3×Dic3—42no—
281C3×C3⋊C8—21no—
282C3×C3⋊C8—21no—
283C3×C3⋊C8—21no—
284C3×C3⋊C8—21no—
285D4×Q8—91no—
286#547—91no—
287#487—91no—
288#483—91no—
289#483—91no—
290#475—91no—
291#465—91no—
292#465—91no—
293#461—91no—
294#448—31no—
295#448—91no—
296C4×SD16—91no—
297C8×D4—91no—
298C2×#103—31no—
299C2×#103—91no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—22no—
304C2×C3×Q8—22no—
305C2×C3×Q8—21no—
306C2×C3×Q8—21no—
307C2×C3×Q8—42no—
308C2×C3×Q8—41no—
309C2×C3×Q8—41no—
310C2×C3×Q8—42no—
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×D4—31no—
316C2×C3×D4—61no—
317C22×C3×C4—22no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—61no—
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C2×#67—21no—
325C2×#67—31no—
326C2×#67—31no—
327C2×#67—61no—
328C2×#67—61no—
329C22×Dic3—21no—
330C22×Dic3—61no—
331D3×Q8—62no—
332D3×Q8—62no—
333D3×Q8—122no—
334D3×Q8—121no—
335D3×Q8—121no—
336D3×Q8—122no—
337#237—124no—
338#235—124no—
339C2×D12—61no—
340C2×D12C22×D311yescharacteristic
341C2×C4×D3—31no—
342C2×C4×D3—31no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—62no—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—61no—
353C2×Dic6—61no—
354C2×Dic6—61no—
355C2×Dic6—61no—
356C2×Dic6—61no—
357C2×Dic6—62no—
358C3×SD16—62no—
359C3×SD16—121no—
360C2×C3×C8—31no—
361C2×C3×C8—31no—
362C2×C3×C8—31no—
363C2×C3×C8—31no—
364C2×C3×C8—121no—
365C3×C4⋊C4—31no—
366C3×C4⋊C4—31no—
367C3×C4⋊C4—31no—
368C3×C4⋊C4—61no—
369C3×C22⋊C4—61no—
370#217—31no—
371#217—31no—
372#217—61no—
373#217—61no—
374#217—61no—
375#217—62no—
376#217—61no—
377#217—61no—
378#215—22no—
379#215—41no—
380#214—121no—
381(C2×D3)⋊C4—21no—
382(C2×D3)⋊C4—31no—
383(C2×D3)⋊C4—31no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—62no—
390C4⋊Dic3—21no—
391C4⋊Dic3—31no—
392C4⋊Dic3—31no—
393C4⋊Dic3—61no—
394C4⋊Dic3—61no—
395C4⋊Dic3—61no—
396C4⋊Dic3—62no—
397C4⋊Dic3C22×D311yescharacteristic
398C4⋊Dic3C22×D311yescharacteristic
399C4⋊Dic3C22×D311yescharacteristic
400Dic3⋊C4—31no—
401Dic3⋊C4—31no—
402Dic3⋊C4—61no—
403Dic3⋊C4—61no—
404Dic3⋊C4—61no—
405Dic3⋊C4—61no—
406Dic3⋊C4—61no—
407Dic3⋊C4—61no—
408Dic3⋊C4—61no—
409Dic3⋊C4—61no—
410Dic3⋊C4—61no—
411Dic3⋊C4—61no—
412Dic3⋊C4—61no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—61no—
418Dic3⋊C4—61no—
419C4×Dic3—31no—
420C4×Dic3—31no—
421C4×Dic3—61no—
422C4×Dic3—61no—
423C4×Dic3—61no—
424C4×Dic3—62no—
425C2×C3⋊C8—41no—
426C2×C3⋊C8C22×D311yescharacteristic
427C2×C3⋊C8C22×D311yescharacteristic
428C2×C3⋊C8C22×D311yescharacteristic
429C2×C3⋊C8C22×D311yescharacteristic
430#204—121no—
431D3×C8—121no—
432D3×C8—121no—
433C22×C32—21no—
434C22×C32—21no—
435C22×C32C2×SD1612yes—
436C22×C32C22×D411yescharacteristic
437C2×C3⋊D3—21no—
438C2×C3⋊D3—21no—
439C2×C3⋊D3C2×SD1612yes—
440C2×C3×D3—41no—
441C2×C3×D3—41no—
442C2×C3×D3—41no—
443C32×C4—22no—
444C32×C4—21no—
445C32×C4—41no—
446C32×C4C2×#4111yescharacteristic
447C32×C4H(5,𝔽2)11yescharacteristic
448C3⋊Dic3—21no—
449C3⋊Dic3—21no—
450C3⋊Dic3—41no—
451C3⋊Dic3—41no—
452C3⋊Dic3C2×SD1612yes—
453C3×Dic3—41no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C2×#41—181no—
457C22×Q8—91no—
458C22×Q8D3211yescharacteristic
459C2×SD16—31no—
460C2×SD16—31no—
461C2×SD16—91no—
462C22×C8—31no—
463C22×C8—91no—
464C4⋊Q8—91no—
465C4⋊Q8—91no—
466C4⋊Q8—181no—
467#123—181no—
468#123—181no—
469C22⋊Q8—91no—
470C22⋊Q8—91no—
471C22⋊Q8—181no—
472C22⋊Q8—181no—
473C22⋊Q8—181no—
474#121—31no—
475#121—91no—
476C4×Q8—91no—
477C4×D4—91no—
478C4×D4—91no—
479C4×D4—181no—
480C2×C4⋊C4—31no—
481C2×C4⋊C4—91no—
482#106—91no—
483#106—91no—
484#106—91no—
485C4⋊C8—91no—
486#103—31no—
487#103—31no—
488#103—31no—
489#103—31no—
490#103—31no—
491#103—31no—
492#103—91no—
493#103—91no—
494#103—91no—
495#102—91no—
496C22⋊C8—31no—
497C22⋊C8—91no—
498C4×C8—91no—
499C23×C3—21no—
500C23×C3—61no—
501C23×C3D3×D411yescharacteristic
502C23×C3D3×D411yescharacteristic
503C22×D3—21no—
504C22×D3—31no—
505C22×D3—31no—
506C22×D3—61no—
507C3×Q8—22no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—21no—
512C3×Q8—21no—
513C3×Q8—21no—
514C3×Q8—22no—
515C3×Q8—41no—
516C3×Q8—41no—
517C3×Q8—42no—
518C3×Q8—42no—
519C3×Q8—44no—
520C3×Q8#23512yescomplemented
521C3×Q8#23712yescomplemented
522C3×D4—61no—
523C3×D4—61no—
524C3×D4—122no—
525C2×C3×C4—22no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—22no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—42no—
540C2×C3×C4—42no—
541C2×C3×C4—44no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—61no—
545C2×C3×C4—122no—
546C2×C3×C4D3×D411yescharacteristic
547C2×C3×C4D3×D411yescharacteristic
548C2×C3×C4C23×D311yescharacteristic
549C2×C3×C4C23×D311yescharacteristic
550#67—34no—
551#67—34no—
552#67—42no—
553#67—64no—
554#67—122no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—31no—
559C2×Dic3—31no—
560C2×Dic3—31no—
561C2×Dic3—31no—
562C2×Dic3—31no—
563C2×Dic3—31no—
564C2×Dic3—42no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—62no—
569C2×Dic3—62no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—61no—
574C2×Dic3—122no—
575D12—21no—
576D12—21no—
577D12—122no—
578C4×D3—61no—
579C4×D3—61no—
580C4×D3—61no—
581C4×D3—61no—
582C4×D3—121no—
583C4×D3—121no—
584C4×D3—122no—
585C4×D3—122no—
586C4×D3—122no—
587C4×D3—122no—
588C4×D3—122no—
589C4×D3—124no—
590Dic6—61no—
591Dic6—61no—
592Dic6—61no—
593Dic6—61no—
594Dic6—121no—
595Dic6—121no—
596Dic6—122no—
597Dic6—122no—
598Dic6—122no—
599Dic6—122no—
600Dic6—124no—
601C3×C8—61no—
602C3×C8—61no—
603C3×C8—61no—
604C3×C8—61no—
605C3⋊C8—21no—
606C3⋊C8—21no—
607C3⋊C8—21no—
608C3⋊C8—21no—
609C2×C32—22no—
610C2×C32#54611yescharacteristic
611C2×C32C22×SD1611yescharacteristic
612C2×C32#57811yescharacteristic
613C3⋊D3—22no—
614C3×D3—81no—
615#41—364no—
616C2×Q8—21no—
617C2×Q8—22no—
618C2×Q8—41no—
619C2×Q8—91no—
620C2×Q8—181no—
621C2×Q8—181no—
622C2×Q8—182no—
623C2×Q8—361no—
624C2×Q8C2×D3211yescharacteristic
625C2×Q8C2×D3211yescharacteristic
626C2×D4—31no—
627C2×D4—61no—
628C2×D4—91no—
629C2×D4—181no—
630C22×C4—21no—
631C22×C4—61no—
632C22×C4—91no—
633C22×C4—181no—
634C22×C4—181no—
635C22×C4—181no—
636C22×C4C2×D3211yescharacteristic
637SD16—62no—
638SD16—121no—
639SD16—361no—
640C2×C8—31no—
641C2×C8—31no—
642C2×C8—31no—
643C2×C8—31no—
644C2×C8—121no—
645C2×C8—361no—
646C4⋊C4—31no—
647C4⋊C4—31no—
648C4⋊C4—31no—
649C4⋊C4—61no—
650C4⋊C4—91no—
651C4⋊C4—91no—
652C4⋊C4—181no—
653C4⋊C4—181no—
654C4⋊C4—181no—
655C4⋊C4—181no—
656C4⋊C4—181no—
657C4⋊C4—181no—
658C4⋊C4—181no—
659C22⋊C4—61no—
660C22⋊C4—91no—
661C22⋊C4—91no—
662C22⋊C4—181no—
663C22⋊C4—181no—
664C22⋊C4—181no—
665C22⋊C4—181no—
666C42—91no—
667C42—181no—
668C22×C3—21no—
669C22×C3—21no—
670C22×C3—21no—
671C22×C3—21no—
672C22×C3—21no—
673C22×C3—22no—
674C22×C3—41no—
675C22×C3—41no—
676C22×C3—121no—
677C22×C3—121no—
678C22×C3—121no—
679C22×C3D3×SD1612yes—
680C22×C3D3×SD1612yes—
681C22×C3C2×D3×D411yescharacteristic
682C22×C3C2×D3×D411yescharacteristic
683C2×D3—32no—
684C2×D3—32no—
685C2×D3—41no—
686C2×D3—41no—
687C2×D3—41no—
688C2×D3—62no—
689C2×D3—61no—
690C2×D3—61no—
691C2×D3—61no—
692C2×D3—61no—
693C2×D3—121no—
694C2×D3—121no—
695C3×C4—24no—
696C3×C4—22no—
697C3×C4—21no—
698C3×C4—22no—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—41no—
703C3×C4—42no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—121no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4C2×#23511yescharacteristic
710C3×C4C2×#23711yescharacteristic
711C3×C4#100411yescharacteristic
712C3×C4#100411yescharacteristic
713Dic3—32no—
714Dic3—32no—
715Dic3—41no—
716Dic3—41no—
717Dic3—41no—
718Dic3—62no—
719Dic3—61no—
720Dic3—61no—
721Dic3—61no—
722Dic3—61no—
723Dic3—121no—
724Dic3—121no—
725Dic3—122no—
726Dic3—122no—
727Dic3—121no—
728Dic3—121no—
729Dic3—121no—
730Dic3—121no—
731C32#329811yescharacteristic, complemented, Sylow
732C23—61no—
733C23—91no—
734C23#381111yescharacteristic
735Q8—21no—
736Q8—21no—
737Q8—21no—
738Q8—42no—
739Q8—181no—
740Q8—181no—
741Q8—362no—
742Q8—362no—
743Q8#380412yescomplemented
744D4—61no—
745D4—61no—
746D4—94no—
747D4—122no—
748D4—362no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—42no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—91no—
758C2×C4—91no—
759C2×C4—91no—
760C2×C4—122no—
761C2×C4—181no—
762C2×C4—181no—
763C2×C4—181no—
764C2×C4—181no—
765C2×C4—362no—
766C2×C4—362no—
767C2×C4—362no—
768C2×C4#381111yescharacteristic
769C2×C4C22×D3211yescharacteristic
770C8—61no—
771C8—61no—
772C8—61no—
773C8—61no—
774C2×C3—22no—
775C2×C3—22no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3—42no—
780C2×C3—241no—
781C2×C3#549011yescharacteristic
782C2×C3#559111yescharacteristic
783C2×C3C2×D3×SD1611yescharacteristic
784C2×C3C2×D3×SD1611yescharacteristic
785C2×C3#576611yescharacteristic
786C2×C3#577911yescharacteristic
787D3—62no—
788D3—62no—
789D3—81no—
790D3—122no—
791C22—21no—
792C22—21no—
793C22—92no—
794C22—121no—
795C22—121no—
796C22—121no—
797C22—181no—
798C22—181no—
799C22#6394012yes—
800C22C2×#381111yescharacteristic
801C4—21no—
802C4—22no—
803C4—41no—
804C4—92no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—181no—
809C4—181no—
810C4—361no—
811C4—361no—
812C4C2×#380411yescharacteristic
813C4#6433011yescharacteristic
814C3—21no—
815C3#7880511yescharacteristic, complemented
816C3#8004911yescharacteristic, complemented
817C2—22no—
818C2—182no—
819C2—241no—
820C2C2×#6394011yescharacteristic
821C2#1059533711yescharacteristic
822C2#1059550011yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594928C2
hypercenterC22×Q8D32
hypocenterC32#3298
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. Q8×#638C2semidirect
3. C3×#5227C2semidirect
4. C2×C3×#835C2semidirect
5. #10591630C2semidirect
6. #10591592C2semidirect
7. #10591591C2semidirect
8. #10591571C2semidirect
9. #10591569C2semidirect
10. #10591553C2semidirect
11. #10591552C2semidirect
12. #10591538C2semidirect
13. #10591175C2semidirect
14. #10591148C2semidirect
15. #10591124C2semidirect
68. #5227D3semidirect
69. C2×#835D3semidirect
250. C32×Q8#41semidirect
258. #638SD16semidirect
520. C3×Q8#235semidirect
521. C3×Q8#237semidirect
731. C32#3298semidirect
743. Q8#3804semidirect
815. C3#78805semidirect
816. C3#80049semidirect

Maximal subgroups

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

subgroupindex
Q8×#6382
#105949282
C3×#52272
C2×C3×#8352
#105916302
#105915922
#105915912
#105915712
#105915692
#105915532
#105915522
#105915382
#105911752
#105911482
#105911242
#800493
#788053