Finite Group Databasebeta

← #10815944

Subgroups — #10815944

Order 768.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5005C211yesmaximal, characteristic, complemented
2#78610C211yesmaximal, characteristic
3#78600C211yesmaximal, characteristic, complemented
4#78596C211yesmaximal, characteristic, complemented
5C2×#4717C211yesmaximal, characteristic, complemented
6C3×#1750C211yesmaximal, characteristic, complemented
7#71591C211yesmaximal, characteristic, complemented
8#69954C211yesmaximal, characteristic, complemented
9#69843C211yesmaximal, characteristic, complemented
10#69795C211yesmaximal, characteristic, complemented
11#69789C211yesmaximal, characteristic, complemented
12#68695C211yesmaximal, characteristic, complemented
13#68695C211yesmaximal, characteristic, complemented
14#68694C211yesmaximal, characteristic, complemented
15#68646C211yesmaximal, characteristic, complemented
16#22887—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C2×C3×#117C2211yescharacteristic
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×#97C2211yescharacteristic, 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
40#5005—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#4717—24no—
64C3×#336C2211yescharacteristic, complemented
65C3×#336C2211yescharacteristic, complemented
66#4552C2211yescharacteristic, complemented
67#4552C2211yescharacteristic, complemented
68#4523C2211yescharacteristic, complemented
69#4523C2211yescharacteristic, complemented
70#3002—31no—
71C2×#444—31no—
72#2933—31no—
73C2×#421—31no—
74#2880—31no—
75#1974—31no—
76#1938—31no—
77#1929—31no—
78#1897—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1764—31no—
84#1750D311yescharacteristic, complemented
85C23×C3×C4C2311yescharacteristic
86C22×#67—21no—
87C2×#235—21no—
88C2×#235—21no—
89C2×#235—22no—
90C2×#235—22no—
91C2×#235—41no—
92C2×#235—41no—
93C2×#235C2×C411yescharacteristic
94C2×#235C2×C411yescharacteristic
95C2×#235C2311yescharacteristic
96C2×#235C2311yescharacteristic
97C2×#235C2311yescharacteristic
98C22×D12C2×C411yescharacteristic
99C22×C4×D3—21no—
100C22×Dic6C2×C411yescharacteristic
101C22×C3×C8C2311yescharacteristic
102C22×C3×C8C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×#117—22no—
106C3×#117—41no—
107C2×C3×C4⋊C4—21no—
108C2×C3×C22⋊C4—21no—
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
129C2×Dic12C2×C411yescharacteristic
130#904—22no—
131#904—22no—
132#904—41no—
133#904—41no—
134C2×D24C2×C411yescharacteristic
135C2×D24C2×C411yescharacteristic
136C2×#204C2×C411yescharacteristic
137C2×#204C2×C411yescharacteristic
138C2×#204C2×C411yescharacteristic
139C2×#204C2×C411yescharacteristic
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×#97—22no—
161C3×C4×C8—41no—
162#830—21no—
163#830—21no—
164#821C2×C411yescharacteristic
165#821C2×C411yescharacteristic
166#821C2×C411yescharacteristic
167#821C2×C411yescharacteristic
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
177#816C2×C411yescharacteristic
178#816C2×C411yescharacteristic
179#816C2×C411yescharacteristic
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—
198C2×#117C2×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#444—64no—
208#436—61no—
209#435—61no—
210#435—61no—
211C8×D4—61no—
212C2×#108—31no—
213C2×#108—31no—
214#424—31no—
215#421—64no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104—31no—
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×#97C2×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—21no—
251C22×C3×C4C22×C411yescharacteristic
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C2×D411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4#4111yescharacteristic
256C22×C3×C4C2411yescharacteristic
257C2×#67—21no—
258C2×#67—21no—
259C2×#67—21no—
260C2×#67—21no—
261C2×#67—21no—
262C2×#67—21no—
263C2×#67—21no—
264C2×#67—42no—
265C2×#67—42no—
266C22×Dic3—21no—
267#235—21no—
268#235—21no—
269#235—21no—
270#235—21no—
271#235—21no—
272#235—21no—
273#235—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—22no—
278#235—22no—
279#235—41no—
280#235—41no—
281#235—42no—
282#235—42no—
283#235—42no—
284#235—42no—
285#235C2×D412yes—
286#235#4112yes—
287C2×D12—22no—
288C2×D12—21no—
289C2×D12—41no—
290C2×D12C22×C411yescharacteristic
291C2×D12C22×C411yescharacteristic
292C2×D12C22×C411yescharacteristic
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—42no—
299C2×C4×D3—42no—
300C2×Dic6—22no—
301C2×Dic6—21no—
302C2×Dic6—41no—
303C2×Dic6C22×C411yescharacteristic
304C2×Dic6C22×C411yescharacteristic
305C2×Dic6C22×C411yescharacteristic
306C2×C3×C8—21no—
307C2×C3×C8—21no—
308C2×C3×C8—21no—
309C2×C3×C8—21no—
310C2×C3×C8—21no—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8C22×C411yescharacteristic
315C2×C3×C8C22×C411yescharacteristic
316C2×C3×C8C22×C411yescharacteristic
317C2×C3×C8C22×C411yescharacteristic
318C2×C3×C8C2×D411yescharacteristic
319C2×C3×C8C2×D411yescharacteristic
320C2×C3×C8C2×D411yescharacteristic
321C2×C3×C8C2×D411yescharacteristic
322C3×C4⋊C4—42no—
323C3×C22⋊C4—42no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42C2×D412yes—
328#217—21no—
329#217—21no—
330#217—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—21no—
333C4⋊Dic3C22×C411yescharacteristic
334C4⋊Dic3C22×C411yescharacteristic
335Dic3⋊C4—21no—
336Dic3⋊C4—21no—
337C4×Dic3—21no—
338#208—21no—
339#208—21no—
340#208—21no—
341#208—21no—
342#208—21no—
343#208—21no—
344#208—21no—
345#208—42no—
346#208C2×D412yes—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—42no—
352Dic12—22no—
353Dic12—41no—
354D24—22no—
355D24—41no—
356#204—22no—
357#204—22no—
358#204—41no—
359#204—41no—
360ΓL(1,𝔽25)—42no—
361ΓL(1,𝔽25)—42no—
362ΓL(1,𝔽25)—42no—
363D3×C8—42no—
364D3×C8—42no—
365D3×C8—42no—
366C2×#41—31no—
367C2×#41—31no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—31no—
371C2×#41—62no—
372C2×#41—62no—
373C2×#41—61no—
374C2×#41—61no—
375C2×#41—121no—
376C2×#41—121no—
377C22×Q8—31no—
378C22×D4—31no—
379C22×D4—61no—
380C23×C4—61no—
381C23×C4C22×D311yescharacteristic
382#135—62no—
383#135—62no—
384#135—121no—
385#135—121no—
386C2×Q16—31no—
387C2×Q16—31no—
388C2×SD16—31no—
389C2×SD16—31no—
390C2×SD16—31no—
391C2×SD16—31no—
392C2×D8—31no—
393C2×D8—31no—
394#131—62no—
395#131—62no—
396#131—62no—
397#131—121no—
398#131—121no—
399#131—121no—
400C2×M16—31no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—31no—
404C2×M16—61no—
405C2×M16—61no—
406C2×M16—61no—
407C2×M16—61no—
408C2×M16—62no—
409C2×M16—121no—
410C22×C8—61no—
411C22×C8—61no—
412C22×C8—61no—
413C22×C8—61no—
414C22×C8C22×D311yescharacteristic
415C22×C8C22×D311yescharacteristic
416C22×C8C22×D311yescharacteristic
417C22×C8C22×D311yescharacteristic
418#123—61no—
419C22⋊Q8—31no—
420C22⋊Q8—31no—
421#121—31no—
422#121—31no—
423#120—61no—
424C4×D4—61no—
425C4×D4—61no—
426#117—22no—
427#117—31no—
428#117—41no—
429C2×C4⋊C4—21no—
430C2×C22⋊C4—21no—
431C2×C42C22×D311yescharacteristic
432C2×C42C22×D311yescharacteristic
433#108—62no—
434#108—121no—
435C4⋊C8—61no—
436C4⋊C8—61no—
437#104—34no—
438#104—62no—
439#104—62no—
440#104—62no—
441#104—62no—
442#104—121no—
443#103—31no—
444#103—31no—
445#103—31no—
446#103—31no—
447#102—31no—
448#102—31no—
449#102—31no—
450#102—31no—
451C22⋊C8—61no—
452C22⋊C8—61no—
453C22⋊C8—61no—
454C22⋊C8—61no—
455C22⋊C8—61no—
456C22⋊C8—61no—
457C22⋊C8—61no—
458C22⋊C8—61no—
459C22⋊C8C4×D311yescharacteristic
460C22⋊C8C4×D311yescharacteristic
461C22⋊C8C4×D311yescharacteristic
462C22⋊C8C4×D311yescharacteristic
463C22⋊C8D1211yescharacteristic
464C22⋊C8D1211yescharacteristic
465C22⋊C8D1211yescharacteristic
466C22⋊C8D1211yescharacteristic
467#97—22no—
468#97—61no—
469C4×C8—41no—
470C4×C8—61no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—41no—
474C23×C3—41no—
475C23×C3C4×D411yescharacteristic
476C23×C3C4×D411yescharacteristic
477C23×C3C2×#4111yescharacteristic
478C22×D3—21no—
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—81no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—22no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4C4×D411yescharacteristic
501C2×C3×C4C4×D411yescharacteristic
502C2×C3×C4C23×C411yescharacteristic
503C2×C3×C4C22×D411yescharacteristic
504C2×C3×C4C22×D411yescharacteristic
505C2×C3×C4C2×#4111yescharacteristic
506C2×C3×C4H(5,𝔽2)11yescharacteristic
507C2×C3×C4H(5,𝔽2)11yescharacteristic
508#67—22no—
509#67—22no—
510#67—42no—
511#67—42no—
512#67—42no—
513#67—41no—
514#67—41no—
515#67—41no—
516#67—41no—
517#67—81no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—42no—
524D12—21no—
525D12—21no—
526D12—21no—
527D12—21no—
528D12—21no—
529D12—42no—
530D12C4×D412yes—
531C4×D3—22no—
532C4×D3—22no—
533C4×D3—42no—
534C4×D3—42no—
535C4×D3—41no—
536C4×D3—41no—
537C4×D3—41no—
538C4×D3—41no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6C4×D412yes—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—21no—
552C3×C8—21no—
553C3×C8—21no—
554C3⋊C8—22no—
555C3⋊C8—41no—
556C3⋊C8—41no—
557C3⋊C8—41no—
558C24—61no—
559C24#23511yescharacteristic
560#41—32no—
561#41—32no—
562#41—62no—
563#41—62no—
564#41—61no—
565#41—61no—
566#41—61no—
567#41—61no—
568#41—61no—
569#41—61no—
570#41—61no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—122no—
575#41—122no—
576#41—121no—
577#41—121no—
578#41—122no—
579#41—122no—
580C2×Q8—31no—
581C2×Q8—31no—
582C2×Q8—31no—
583C2×Q8—62no—
584C2×Q8—61no—
585C2×Q8—121no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—61no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—121no—
599C2×D4—122no—
600C2×D4—122no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—61no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—122no—
614C22×C4—122no—
615C22×C4C2×C4×D311yescharacteristic
616C22×C4C2×C4×D311yescharacteristic
617C22×C4C2×D1211yescharacteristic
618C22×C4C2×D1211yescharacteristic
619C22×C4#23511yescharacteristic
620C22×C4C23×D311yescharacteristic
621Q16—62no—
622Q16—121no—
623SD16—62no—
624SD16—62no—
625SD16—121no—
626SD16—121no—
627D8—62no—
628D8—121no—
629M16—32no—
630M16—61no—
631M16—61no—
632M16—61no—
633M16—61no—
634M16—61no—
635M16—61no—
636M16—61no—
637M16—122no—
638M16—122no—
639M16—122no—
640M16—122no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—21no—
645C2×C8—21no—
646C2×C8—21no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—61no—
650C2×C8—61no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—122no—
654C2×C8—122no—
655C2×C8—122no—
656C2×C8—122no—
657C2×C8C2×C4×D311yescharacteristic
658C2×C8C2×C4×D311yescharacteristic
659C2×C8C2×C4×D311yescharacteristic
660C2×C8C2×C4×D311yescharacteristic
661C2×C8C2×D1211yescharacteristic
662C2×C8C2×D1211yescharacteristic
663C2×C8C2×D1211yescharacteristic
664C2×C8C2×D1211yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—42no—
668C4⋊C4—61no—
669C4⋊C4—61no—
670C22⋊C4—42no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—61no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—61no—
680C42D3×D412yes—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—21no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—81no—
690C22×C3—81no—
691C22×C3C2×C4×D411yescharacteristic
692C22×C3#54611yescharacteristic
693C22×C3#55111yescharacteristic
694C2×D3—22no—
695C2×D3—41no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—84no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—42no—
707C3×C4—81no—
708C3×C4C2×C4×D411yescharacteristic
709C3×C4#51811yescharacteristic
710C3×C4D4211yescharacteristic
711C3×C4#54611yescharacteristic
712Dic3—22no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717C23—21no—
718C23—21no—
719C23—41no—
720C23—41no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726C23—241no—
727C23C4×D1211yescharacteristic
728C23C4×D1211yescharacteristic
729C23C2×#23511yescharacteristic
730Q8—32no—
731Q8—61no—
732Q8—61no—
733Q8—61no—
734Q8—61no—
735Q8—61no—
736Q8—122no—
737D4—32no—
738D4—62no—
739D4—62no—
740D4—61no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—61no—
745D4—122no—
746D4—122no—
747D4—122no—
748D4—122no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—121no—
753D4—241no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—61no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—122no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4C4×D1211yescharacteristic
785C2×C4C4×D1211yescharacteristic
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C22×D1211yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4D3×#4111yescharacteristic
791C2×C4#100911yescharacteristic
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—21no—
797C8—21no—
798C8—21no—
799C8—21no—
800C8—62no—
801C8—121no—
802C8—121no—
803C8—121no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3#235811yescharacteristic
809C2×C3#295511yescharacteristic
810C2×C3#295711yescharacteristic
811D3—42no—
812D3—81no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—62no—
823C22—81no—
824C22—81no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22C2×C4×D1211yescharacteristic
835C22#549011yescharacteristic
836C22#552711yescharacteristic
837C4—21no—
838C4—21no—
839C4—42no—
840C4—62no—
841C4—81no—
842C4—121no—
843C4—121no—
844C4—121no—
845C4—121no—
846C4C4×D3×D411yescharacteristic
847C4#554511yescharacteristic
848C4D4×D1211yescharacteristic
849C4#555411yescharacteristic
850C3#2288711yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—122no—
856C2—241no—
857C2—241no—
858C2#7357711yescharacteristic
859C2#7857911yescharacteristic
860C2#7858011yescharacteristic
subgroupG/H
centerC2×C4C22×D12
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1750C2
socleC22×C3C2×C4×D4
prime radical#78610C2
cosocleC22×C3×C4C24
hypercenter#1750D3
hypocenterC3#22887
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #1750

Complements

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

NH ≅ G/Ntype
1. C2×#5005C2semidirect
3. #78600C2semidirect
4. #78596C2semidirect
5. C2×#4717C2semidirect
6. C3×#1750C2semidirect
7. #71591C2semidirect
8. #69954C2semidirect
9. #69843C2semidirect
10. #69795C2semidirect
11. #69789C2semidirect
12. #68695C2semidirect
13. #68695C2semidirect
14. #68694C2semidirect
15. #68646C2semidirect
25. C2×#901C22semidirect
28. C2×C3×#97C22semidirect
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. #1750D3semidirect
189. #805D4semidirect
235. C2×#97C2×D3semidirect
236. C2×C4×C8C2×D3semidirect
241. #336C2×D3semidirect
242. #336C2×D3semidirect
850. C3#22887semidirect

Maximal subgroups

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

subgroupindex
C2×#50052
#786102
#786002
#785962
C2×#47172
C3×#17502
#715912
#699542
#698432
#697952
#697892
#686952
#686942
#686462
#228873