Finite Group Databasebeta

← #10815959

Subgroups — #10815959

Order 768.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#805C211yesmaximal, characteristic, complemented
2#78610C211yesmaximal, characteristic
3#78600C211yesmaximal, characteristic, complemented
4#78596C211yesmaximal, characteristic, complemented
5C2×#4700C211yesmaximal, characteristic, complemented
6C3×C4×C22⋊C8C211yesmaximal, characteristic, complemented
7#71532C211yesmaximal, characteristic, complemented
8#69954C211yesmaximal, characteristic, complemented
9#69795C211yesmaximal, characteristic, complemented
10#69793C211yesmaximal, characteristic, complemented
11#69789C211yesmaximal, characteristic, complemented
12#68695C211yesmaximal, characteristic, complemented
13#68695C211yesmaximal, characteristic, complemented
14#68694C211yesmaximal, characteristic, complemented
15#68646C211yesmaximal, characteristic, complemented
16#22888—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C22×C3×C42C2211yescharacteristic
19#5791C2211yescharacteristic
20C22×#208C2211yescharacteristic
21C2×#904C2211yescharacteristic
22C2×#904C2211yescharacteristic
23C2×#901C2211yescharacteristic
24C2×#901C2211yescharacteristic
25C2×#901C2211yescharacteristic, complemented
26C2×C3×C22⋊C8C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28C2×C3×C4×C8C2211yescharacteristic, complemented
29C2×C3×C4×C8C2211yescharacteristic, complemented
30#5207C2211yescharacteristic
31#5113C2211yescharacteristic
32#5113C2211yescharacteristic
33#5110C2211yescharacteristic
34#5110C2211yescharacteristic
35#5110C2211yescharacteristic, complemented
36C2×#819C2211yescharacteristic, complemented
37C2×#819C2211yescharacteristic, complemented
38#5102C2211yescharacteristic, complemented
39#5101C2211yescharacteristic, complemented
40C2×#805—24no—
41C2×#805C2211yescharacteristic
42C2×#805C2211yescharacteristic
43C2×#805C2211yescharacteristic
44C2×#805C2211yescharacteristic
45C2×#805C2211yescharacteristic, complemented
46C2×#805C2211yescharacteristic, complemented
47#4739C411yescharacteristic, complemented
48#4738C411yescharacteristic, complemented
49#4734C411yescharacteristic, complemented
50#4734C411yescharacteristic, complemented
51#4733C411yescharacteristic, complemented
52#4733C411yescharacteristic, complemented
53#4732C411yescharacteristic, complemented
54#4731C411yescharacteristic, complemented
55#4730—21no—
56#4729—21no—
57#4728—21no—
58#4727—21no—
59#4727—21no—
60#4726—21no—
61#67⋊C8—21no—
62D3×C22⋊C8—21no—
63#4700—24no—
64C3×#336C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66#4552C2211yescharacteristic, complemented
67#4552C2211yescharacteristic, complemented
68#4523C2211yescharacteristic, complemented
69#4523C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933—31no—
73C22×#104—31no—
74#2880—31no—
75#1974—31no—
76#1937—31no—
77#1929—31no—
78#1896—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1764—31no—
84C4×C22⋊C8D311yescharacteristic, complemented
85C23×C3×C4—21no—
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—41no—
93C2×#235—41no—
94C2×#235C2×C411yescharacteristic
95C2×#235C2×C411yescharacteristic
96C2×#235C2311yescharacteristic
97C2×#235C2311yescharacteristic
98C2×#235C2311yescharacteristic
99C22×D12C2×C411yescharacteristic
100C22×C4×D3—21no—
101C22×Dic6C2×C411yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C2×C3×C42—22no—
107C2×C3×C42—21no—
108C2×C3×C42—41no—
109C2×C3×C42C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111#953—21no—
112#930C2×C411yescharacteristic
113#930C2×C411yescharacteristic
114#929—21no—
115C4×#67—21no—
116C4×#67—21no—
117#926C2311yescharacteristic
118#924C2×C411yescharacteristic
119#924C2×C411yescharacteristic
120C2×#208—21no—
121C2×#208—22no—
122C2×#208—41no—
123C2×#208C2311yescharacteristic
124C2×#208C2311yescharacteristic
125C2×#208C2311yescharacteristic
126C2×#208C2311yescharacteristic
127C22×C3⋊C8—21no—
128C2×Dic12C2×C411yescharacteristic, complemented
129C2×Dic12C2×C411yescharacteristic, complemented
130#904—22no—
131#904—22no—
132#904—41no—
133#904—41no—
134C2×D24C2×C411yescharacteristic, complemented
135C2×D24C2×C411yescharacteristic, complemented
136C2×#204C2×C411yescharacteristic, complemented
137C2×#204C2×C411yescharacteristic, complemented
138C2×#204C2×C411yescharacteristic, complemented
139C2×#204C2×C411yescharacteristic, complemented
140#901—22no—
141#901—22no—
142#901—22no—
143#901—41no—
144#901—41no—
145#901—41no—
146C2×ΓL(1,𝔽25)—21no—
147C2×ΓL(1,𝔽25)—21no—
148C2×ΓL(1,𝔽25)—21no—
149C2×D3×C8—21no—
150C2×D3×C8—21no—
151C2×D3×C8—21no—
152C3×C22⋊C8C2×C411yescharacteristic
153C3×C22⋊C8C2×C411yescharacteristic
154C3×C22⋊C8C2×C411yescharacteristic
155C3×C22⋊C8C2×C411yescharacteristic
156C3×C22⋊C8D411yescharacteristic
157C3×C22⋊C8D411yescharacteristic
158C3×C22⋊C8D411yescharacteristic
159C3×C22⋊C8D411yescharacteristic
160C3×C4×C8—22no—
161C3×C4×C8—41no—
162#830—21no—
163#830—21no—
164#821C2×C411yescharacteristic, complemented
165#821C2×C411yescharacteristic, complemented
166#821C2×C411yescharacteristic, complemented
167#821C2×C411yescharacteristic, complemented
168(C2×D3)⋊C8—21no—
169(C2×D3)⋊C8—21no—
170(C2×D3)⋊C8—21no—
171(C2×D3)⋊C8—21no—
172(C2×D3)⋊C8—21no—
173(C2×D3)⋊C8—21no—
174#819—22no—
175#819—41no—
176#816C2×C411yescharacteristic, complemented
177#816C2×C411yescharacteristic, complemented
178#816C2×C411yescharacteristic, complemented
179#816C2×C411yescharacteristic, complemented
180#815—21no—
181Dic3⋊C8—21no—
182Dic3⋊C8—21no—
183C8×Dic3—21no—
184#805—22no—
185#805—22no—
186#805—22no—
187#805—22no—
188#805—41no—
189#805D414yescomplemented
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131—31no—
196C22×M16—31no—
197#525—31no—
198C22×C42C2×D311yescharacteristic
199#452—31no—
200#452—31no—
201#451—31no—
202#450—31no—
203#449—31no—
204#449—31no—
205#448—31no—
206#447—31no—
207#443—64no—
208#436—61no—
209#435—61no—
210#435—61no—
211C8×D4—61no—
212C2×#108—31no—
213C2×#108—31no—
214#424—31no—
215C2×#104—31no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104—64no—
222#416—31no—
223#416—31no—
224#408—31no—
225#408—31no—
226#408—31no—
227#408—61no—
228#408—61no—
229#407—31no—
230#407—61no—
231C2×C22⋊C8—61no—
232C2×C22⋊C8C2×D311yescharacteristic
233C2×C22⋊C8C2×D311yescharacteristic
234#405—31no—
235C2×C4×C8C2×D311yescharacteristic, complemented
236C2×C4×C8C2×D311yescharacteristic, complemented
237#341—31no—
238#341—31no—
239#339—31no—
240#339—31no—
241#336C2×D311yescharacteristic, complemented
242#336C2×D311yescharacteristic, complemented
243C24×C3#4111yescharacteristic
244C23×D3—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—24no—
251C22×C3×C4—21no—
252C22×C3×C4—42no—
253C22×C3×C4—42no—
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C2×D411yescharacteristic
257C22×C3×C4C2×D411yescharacteristic
258C22×C3×C4#4111yescharacteristic
259C22×C3×C4C2411yescharacteristic
260C2×#67—21no—
261C2×#67—21no—
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—21no—
266C2×#67—21no—
267C2×#67—42no—
268C2×#67—42no—
269C22×Dic3—21no—
270#235—21no—
271#235—21no—
272#235—21no—
273#235—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—21no—
278#235—21no—
279#235—21no—
280#235—22no—
281#235—22no—
282#235—41no—
283#235—41no—
284#235—42no—
285#235—42no—
286#235—42no—
287#235—42no—
288#235C2×D412yes—
289#235#4112yes—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—41no—
293C2×D12C22×C411yescharacteristic
294C2×D12C22×C411yescharacteristic
295C2×D12C22×C411yescharacteristic
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C2×Dic6—22no—
304C2×Dic6—21no—
305C2×Dic6—41no—
306C2×Dic6C22×C411yescharacteristic
307C2×Dic6C22×C411yescharacteristic
308C2×Dic6C22×C411yescharacteristic
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8C22×C411yescharacteristic
318C2×C3×C8C22×C411yescharacteristic
319C2×C3×C8C22×C411yescharacteristic
320C2×C3×C8C22×C411yescharacteristic
321C2×C3×C8C2×D411yescharacteristic
322C2×C3×C8C2×D411yescharacteristic
323C2×C3×C8C2×D411yescharacteristic
324C2×C3×C8C2×D411yescharacteristic
325C3×C42—21no—
326C3×C42—21no—
327C3×C42—21no—
328C3×C42—42no—
329C3×C42C2×D412yes—
330#217—21no—
331#217—21no—
332#217—21no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—21no—
335C4⋊Dic3C22×C411yescharacteristic
336C4⋊Dic3C22×C411yescharacteristic
337Dic3⋊C4—21no—
338Dic3⋊C4—21no—
339C4×Dic3—21no—
340#208—21no—
341#208—21no—
342#208—21no—
343#208—21no—
344#208—21no—
345#208—21no—
346#208—21no—
347#208—42no—
348#208C2×D412yes—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—42no—
354Dic12—22no—
355Dic12—41no—
356D24—22no—
357D24—41no—
358#204—22no—
359#204—22no—
360#204—41no—
361#204—41no—
362ΓL(1,𝔽25)—42no—
363ΓL(1,𝔽25)—42no—
364ΓL(1,𝔽25)—42no—
365D3×C8—42no—
366D3×C8—42no—
367D3×C8—42no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—31no—
371C2×#41—31no—
372C2×#41—31no—
373C2×#41—62no—
374C2×#41—62no—
375C2×#41—61no—
376C2×#41—61no—
377C2×#41—121no—
378C2×#41—121no—
379C22×Q8—31no—
380C22×D4—31no—
381C22×D4—61no—
382C23×C4—21no—
383C23×C4—61no—
384C23×C4C22×D311yescharacteristic
385#135—62no—
386#135—62no—
387#135—121no—
388#135—121no—
389C2×Q16—31no—
390C2×Q16—31no—
391C2×SD16—31no—
392C2×SD16—31no—
393C2×SD16—31no—
394C2×SD16—31no—
395C2×D8—31no—
396C2×D8—31no—
397#131—62no—
398#131—62no—
399#131—62no—
400#131—121no—
401#131—121no—
402#131—121no—
403C2×M16—31no—
404C2×M16—31no—
405C2×M16—31no—
406C2×M16—31no—
407C2×M16—61no—
408C2×M16—61no—
409C2×M16—61no—
410C2×M16—61no—
411C2×M16—62no—
412C2×M16—121no—
413C22×C8—61no—
414C22×C8—61no—
415C22×C8—61no—
416C22×C8—61no—
417C22×C8C22×D311yescharacteristic
418C22×C8C22×D311yescharacteristic
419C22×C8C22×D311yescharacteristic
420C22×C8C22×D311yescharacteristic
421#123—61no—
422C22⋊Q8—31no—
423C22⋊Q8—31no—
424#121—31no—
425#121—31no—
426#120—61no—
427C4×D4—61no—
428C4×D4—61no—
429#117—31no—
430C2×C42—22no—
431C2×C42—21no—
432C2×C42—41no—
433C2×C42C22×D311yescharacteristic
434C2×C42C22×D311yescharacteristic
435#108—62no—
436#108—121no—
437C4⋊C8—61no—
438C4⋊C8—61no—
439#104—34no—
440#104—62no—
441#104—62no—
442#104—62no—
443#104—62no—
444#104—121no—
445#103—31no—
446#103—31no—
447#103—31no—
448#103—31no—
449#102—31no—
450#102—31no—
451#102—31no—
452#102—31no—
453C22⋊C8—61no—
454C22⋊C8—61no—
455C22⋊C8—61no—
456C22⋊C8—61no—
457C22⋊C8—61no—
458C22⋊C8—61no—
459C22⋊C8—61no—
460C22⋊C8—61no—
461C22⋊C8C4×D311yescharacteristic
462C22⋊C8C4×D311yescharacteristic
463C22⋊C8C4×D311yescharacteristic
464C22⋊C8C4×D311yescharacteristic
465C22⋊C8D1211yescharacteristic
466C22⋊C8D1211yescharacteristic
467C22⋊C8D1211yescharacteristic
468C22⋊C8D1211yescharacteristic
469#97—61no—
470C4×C8—22no—
471C4×C8—41no—
472C4×C8—61no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—22no—
476C23×C3—41no—
477C23×C3C4×D411yescharacteristic
478C23×C3C4×D411yescharacteristic
479C23×C3C2×#4111yescharacteristic
480C22×D3—21no—
481C22×D3—21no—
482C22×D3—21no—
483C22×D3—42no—
484C22×D3—42no—
485C22×D3—81no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—48no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4C4×D411yescharacteristic
504C2×C3×C4C4×D411yescharacteristic
505C2×C3×C4C23×C411yescharacteristic
506C2×C3×C4C22×D411yescharacteristic
507C2×C3×C4C22×D411yescharacteristic
508C2×C3×C4C2×#4111yescharacteristic
509C2×C3×C4H(5,𝔽2)11yescharacteristic
510C2×C3×C4H(5,𝔽2)11yescharacteristic
511#67—22no—
512#67—22no—
513#67—42no—
514#67—42no—
515#67—41no—
516#67—41no—
517#67—41no—
518#67—41no—
519#67—42no—
520#67—81no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—42no—
527D12—21no—
528D12—21no—
529D12—21no—
530D12—21no—
531D12—21no—
532D12—42no—
533D12C4×D412yes—
534C4×D3—22no—
535C4×D3—22no—
536C4×D3—42no—
537C4×D3—42no—
538C4×D3—41no—
539C4×D3—41no—
540C4×D3—41no—
541C4×D3—41no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—21no—
546Dic6—21no—
547Dic6—42no—
548Dic6C4×D412yes—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3×C8—21no—
555C3×C8—21no—
556C3×C8—21no—
557C3⋊C8—22no—
558C3⋊C8—41no—
559C3⋊C8—41no—
560C3⋊C8—41no—
561C24—61no—
562C24#23511yescharacteristic
563#41—32no—
564#41—32no—
565#41—62no—
566#41—62no—
567#41—61no—
568#41—61no—
569#41—61no—
570#41—61no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—61no—
575#41—61no—
576#41—61no—
577#41—122no—
578#41—122no—
579#41—121no—
580#41—121no—
581#41—122no—
582#41—122no—
583C2×Q8—31no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—62no—
587C2×Q8—61no—
588C2×Q8—121no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4—61no—
600C2×D4—61no—
601C2×D4—121no—
602C2×D4—122no—
603C2×D4—122no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—24no—
610C22×C4—21no—
611C22×C4—42no—
612C22×C4—42no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—61no—
619C22×C4—122no—
620C22×C4—122no—
621C22×C4C2×C4×D311yescharacteristic
622C22×C4C2×C4×D311yescharacteristic
623C22×C4C2×D1211yescharacteristic
624C22×C4C2×D1211yescharacteristic
625C22×C4#23511yescharacteristic
626C22×C4C23×D311yescharacteristic
627Q16—62no—
628Q16—121no—
629SD16—62no—
630SD16—62no—
631SD16—121no—
632SD16—121no—
633D8—62no—
634D8—121no—
635M16—32no—
636M16—61no—
637M16—61no—
638M16—61no—
639M16—61no—
640M16—61no—
641M16—61no—
642M16—61no—
643M16—122no—
644M16—122no—
645M16—122no—
646M16—122no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8—122no—
662C2×C8—122no—
663C2×C8C2×C4×D311yescharacteristic
664C2×C8C2×C4×D311yescharacteristic
665C2×C8C2×C4×D311yescharacteristic
666C2×C8C2×C4×D311yescharacteristic
667C2×C8C2×D1211yescharacteristic
668C2×C8C2×D1211yescharacteristic
669C2×C8C2×D1211yescharacteristic
670C2×C8C2×D1211yescharacteristic
671C4⋊C4—31no—
672C4⋊C4—31no—
673C4⋊C4—61no—
674C4⋊C4—61no—
675C22⋊C4—61no—
676C22⋊C4—61no—
677C22⋊C4—61no—
678C22⋊C4—61no—
679C22⋊C4—61no—
680C42—21no—
681C42—21no—
682C42—21no—
683C42—42no—
684C42—61no—
685C42D3×D412yes—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—21no—
691C22×C3—21no—
692C22×C3—21no—
693C22×C3—42no—
694C22×C3—42no—
695C22×C3#44312yescomplemented
696C22×C3C2×C4×D411yescharacteristic
697C22×C3#54611yescharacteristic
698C22×C3#55111yescharacteristic
699C2×D3—22no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C2×D3—41no—
705C2×D3—41no—
706C2×D3—41no—
707C2×D3—41no—
708C2×D3—84no—
709C3×C4—24no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—42no—
713C3×C4C2×C4×D411yescharacteristic
714C3×C4#51811yescharacteristic
715C3×C4D4211yescharacteristic
716C3×C4#54611yescharacteristic
717Dic3—22no—
718Dic3—41no—
719Dic3—41no—
720Dic3—41no—
721Dic3—41no—
722C23—22no—
723C23—21no—
724C23—21no—
725C23—41no—
726C23—61no—
727C23—61no—
728C23—61no—
729C23—122no—
730C23—122no—
731C23—241no—
732C23C4×D1211yescharacteristic
733C23C4×D1211yescharacteristic
734C23C2×#23511yescharacteristic
735Q8—32no—
736Q8—61no—
737Q8—61no—
738Q8—61no—
739Q8—61no—
740Q8—61no—
741Q8—122no—
742D4—32no—
743D4—62no—
744D4—62no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—61no—
749D4—61no—
750D4—122no—
751D4—122no—
752D4—122no—
753D4—122no—
754D4—121no—
755D4—121no—
756D4—121no—
757D4—121no—
758D4—241no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—48no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—61no—
777C2×C4—62no—
778C2×C4—62no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—122no—
784C2×C4—122no—
785C2×C4—122no—
786C2×C4—121no—
787C2×C4—121no—
788C2×C4—121no—
789C2×C4—121no—
790C2×C4C4×D1211yescharacteristic
791C2×C4C4×D1211yescharacteristic
792C2×C4C22×C4×D311yescharacteristic
793C2×C4C22×D1211yescharacteristic
794C2×C4C2×D3×D411yescharacteristic
795C2×C4#100411yescharacteristic
796C2×C4D3×#4111yescharacteristic
797C2×C4#100911yescharacteristic
798C8—21no—
799C8—21no—
800C8—21no—
801C8—21no—
802C8—21no—
803C8—21no—
804C8—21no—
805C8—21no—
806C8—62no—
807C8—121no—
808C8—121no—
809C8—121no—
810C2×C3—21no—
811C2×C3—22no—
812C2×C3—21no—
813C2×C3—41no—
814C2×C3#235811yescharacteristic
815C2×C3C2×#44311yescharacteristic
816C2×C3#295611yescharacteristic
817D3—42no—
818D3—81no—
819D3—81no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—42no—
828C22—42no—
829C22—62no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22—121no—
835C22—121no—
836C22—121no—
837C22—121no—
838C22—244no—
839C22#470012yescomplemented
840C22C2×C4×D1211yescharacteristic
841C22#549011yescharacteristic
842C22#552711yescharacteristic
843C4—24no—
844C4—21no—
845C4—21no—
846C4—42no—
847C4—62no—
848C4—121no—
849C4—121no—
850C4—121no—
851C4—121no—
852C4C4×D3×D411yescharacteristic
853C4#554511yescharacteristic
854C4D4×D1211yescharacteristic
855C4#555411yescharacteristic
856C3#2288811yescharacteristic, complemented, Sylow
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—122no—
862C2—241no—
863C2—241no—
864C2#7357711yescharacteristic
865C2C2×#470011yescharacteristic
866C2#7854111yescharacteristic
subgroupG/H
centerC2×C4C22×D12
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×C4×C22⋊C8C2
socleC22×C3C2×C4×D4
prime radical#78610C2
cosocleC22×C3×C4C24
hypercenterC4×C22⋊C8D3
hypocenterC3#22888
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
1. C22×#805C2semidirect
3. #78600C2semidirect
4. #78596C2semidirect
5. C2×#4700C2semidirect
6. C3×C4×C22⋊C8C2semidirect
7. #71532C2semidirect
8. #69954C2semidirect
9. #69795C2semidirect
10. #69793C2semidirect
11. #69789C2semidirect
12. #68695C2semidirect
13. #68695C2semidirect
14. #68694C2semidirect
15. #68646C2semidirect
25. C2×#901C22semidirect
28. C2×C3×C4×C8C22semidirect
29. C2×C3×C4×C8C22semidirect
35. #5110C22semidirect
36. C2×#819C22semidirect
37. C2×#819C22semidirect
38. #5102C22semidirect
39. #5101C22semidirect
45. C2×#805C22semidirect
46. C2×#805C22semidirect
47. #4739C4semidirect
48. #4738C4semidirect
49. #4734C4semidirect
50. #4734C4semidirect
51. #4733C4semidirect
52. #4733C4semidirect
53. #4732C4semidirect
54. #4731C4semidirect
64. C3×#336C22semidirect
65. C3×#336C22semidirect
66. #4552C22semidirect
67. #4552C22semidirect
68. #4523C22semidirect
69. #4523C22semidirect
84. C4×C22⋊C8D3semidirect
128. C2×Dic12C2×C4semidirect
129. C2×Dic12C2×C4semidirect
134. C2×D24C2×C4semidirect
135. C2×D24C2×C4semidirect
136. C2×#204C2×C4semidirect
137. C2×#204C2×C4semidirect
138. C2×#204C2×C4semidirect
139. C2×#204C2×C4semidirect
164. #821C2×C4semidirect
165. #821C2×C4semidirect
166. #821C2×C4semidirect
167. #821C2×C4semidirect
176. #816C2×C4semidirect
177. #816C2×C4semidirect
178. #816C2×C4semidirect
179. #816C2×C4semidirect
189. #805D4semidirect
235. C2×C4×C8C2×D3semidirect
236. C2×C4×C8C2×D3semidirect
241. #336C2×D3semidirect
242. #336C2×D3semidirect
695. C22×C3#443semidirect
839. C22#4700semidirect
856. C3#22888semidirect

Maximal subgroups

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

subgroupindex
C22×#8052
#786102
#786002
#785962
C2×#47002
C3×C4×C22⋊C82
#715322
#699542
#697952
#697932
#697892
#686952
#686942
#686462
#228883