Finite Group Databasebeta

← #10815946

Subgroups — #10815946

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
1#79075C211yesmaximal, characteristic, complemented
2C2×#4821C211yesmaximal, characteristic, complemented
3#78833C211yesmaximal, characteristic
4#78663C211yesmaximal, characteristic, complemented
5C2×#4717C211yesmaximal, characteristic, complemented
6C3×#1938C211yesmaximal, characteristic, complemented
7#70545C211yesmaximal, characteristic, complemented
8#70373C211yesmaximal, characteristic, complemented
9#70291C211yesmaximal, characteristic, complemented
10#70011C211yesmaximal, characteristic, complemented
11#69830C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68941C211yesmaximal, characteristic, complemented
14#68757C211yesmaximal, characteristic, complemented
15#68739C211yesmaximal, characteristic, complemented
16#22887—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×#950C2211yescharacteristic
19C2×#907C2211yescharacteristic
20C2×D3×M16C2211yescharacteristic
21C2×#904C2211yescharacteristic
22C2×#901C2211yescharacteristic
23C2×#901C2211yescharacteristic, complemented
24#5524C2211yescharacteristic
25C2×#872C2211yescharacteristic
26C3×#424C2211yescharacteristic, complemented
27C2×C3×#104C2211yescharacteristic
28C3×#416C2211yescharacteristic
29C3×#408C2211yescharacteristic
30C2×C3×#97C2211yescharacteristic, complemented
31C2×#837C2211yescharacteristic
32#5234C2211yescharacteristic
33C2×#825C2211yescharacteristic
34C2×#825C2211yescharacteristic, complemented
35#5129C2211yescharacteristic, complemented
36#5126C2211yescharacteristic
37C2×#822C2211yescharacteristic, complemented
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×#819C2211yescharacteristic, complemented
41#5002C2211yescharacteristic
42#4997C2211yescharacteristic, complemented
43C2×#805C2211yescharacteristic
44C2×#805C2211yescharacteristic, complemented
45C2×C4×C3⋊C8C2211yescharacteristic, complemented
46#4838—21no—
47#4836—21no—
48#4836—21no—
49#4834—21no—
50#4821—24no—
51#4810C411yescharacteristic, complemented
52#4809C411yescharacteristic, complemented
53#4808C411yescharacteristic, complemented
54#4806C411yescharacteristic, complemented
55#4783C411yescharacteristic, complemented
56#4781C411yescharacteristic, complemented
57#4776C411yescharacteristic, complemented
58#4773C411yescharacteristic, complemented
59#4727—21no—
60#4727—21no—
61#4726—21no—
62D3×C22⋊C8—21no—
63#4717—24no—
64C3×#341C2211yescharacteristic, complemented
65C3×#339C2211yescharacteristic, complemented
66#4558C2211yescharacteristic, complemented
67#4550C2211yescharacteristic, complemented
68#4550C2211yescharacteristic, complemented
69#4532C2211yescharacteristic, complemented
70#3002—31no—
71C2×#444—31no—
72#2933—31no—
73C2×#421—31no—
74#2880—31no—
75#1974—31no—
76#1938D311yescharacteristic, complemented
77#1929—31no—
78#1897—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1764—31no—
84#1750—31no—
85C2×C3×#41C2311yescharacteristic
86D3×#41—22no—
87D3×#41—22no—
88D3×#41—41no—
89D3×#41—41no—
90C2×#239C2×C411yescharacteristic
91C2×D3×Q8C2×C411yescharacteristic
92C2×#237—21no—
93C2×#237C2×C411yescharacteristic
94C2×D3×D4—21no—
95C2×D3×D4C2×C411yescharacteristic
96C2×#235—21no—
97C2×#235C2311yescharacteristic
98C2×#235C2311yescharacteristic
99C22×C4×D3—21no—
100C22×C4×D3C2311yescharacteristic
101C2×C3×M16C2311yescharacteristic
102C2×C3×M16C2311yescharacteristic
103C22×C3×C8C2311yescharacteristic
104C22×C3×C8C2311yescharacteristic
105C3×#117C2311yescharacteristic
106C2×C3×C42C2311yescharacteristic
107#950—41no—
108#950—41no—
109C2×#216C2×C411yescharacteristic
110C2×#215C2×C411yescharacteristic
111C2×#214C2×C411yescharacteristic
112C2×#213C2×C411yescharacteristic
113C2×(C2×D3)⋊C4—21no—
114C2×Dic3⋊C4—21no—
115C2×C4×Dic3C2311yescharacteristic
116C2×#208C2311yescharacteristic
117C2×#208C2311yescharacteristic
118C22×C3⋊C8C2311yescharacteristic
119C22×C3⋊C8C2311yescharacteristic
120#907—22no—
121#907—41no—
122D3×M16—22no—
123D3×M16—41no—
124C2×Dic12C2×C411yescharacteristic
125#904—22no—
126#904—22no—
127C2×D24C2×C411yescharacteristic
128C2×#204C2×C411yescharacteristic
129C2×#204C2×C411yescharacteristic
130#901—22no—
131#901—22no—
132#901—41no—
133#901—41no—
134C2×ΓL(1,𝔽25)—21no—
135C2×ΓL(1,𝔽25)—21no—
136C2×ΓL(1,𝔽25)—21no—
137C2×ΓL(1,𝔽25)—21no—
138C2×D3×C8—21no—
139C2×D3×C8—21no—
140C2×D3×C8—21no—
141C2×D3×C8—21no—
142#897C2×C411yescharacteristic
143#897C2×C411yescharacteristic
144#895C2×C411yescharacteristic
145#895C2×C411yescharacteristic
146#886—21no—
147#882—21no—
148C4×D12—21no—
149C4×D12—21no—
150#872—22no—
151#872—41no—
152C3×C4⋊C8—21no—
153C3×C4⋊C8—21no—
154C3×#104—22no—
155C3×#103C2×C411yescharacteristic
156C3×#103C2×C411yescharacteristic
157C3×#102C2×C411yescharacteristic
158C3×#102C2×C411yescharacteristic
159C3×C22⋊C8—21no—
160C3×C22⋊C8—21no—
161C3×#97—22no—
162#837—22no—
163#830—21no—
164#830—21no—
165#825—22no—
166#825—41no—
167#822—41no—
168(C2×D3)⋊C8—21no—
169(C2×D3)⋊C8—21no—
170(C2×D3)⋊C8—21no—
171(C2×D3)⋊C8—21no—
172(C2×D3)⋊C8C2×C411yescharacteristic
173(C2×D3)⋊C8C2×C411yescharacteristic
174(C2×D3)⋊C8C2×C411yescharacteristic
175(C2×D3)⋊C8C2×C411yescharacteristic
176(C2×D3)⋊C8D411yescharacteristic
177(C2×D3)⋊C8D411yescharacteristic
178(C2×D3)⋊C8D411yescharacteristic
179(C2×D3)⋊C8D411yescharacteristic
180#819—22no—
181#810C2×C411yescharacteristic
182#810C2×C411yescharacteristic
183#809C2×C411yescharacteristic
184#809C2×C411yescharacteristic
185#805—22no—
186#805D414yescomplemented
187#803—21no—
188C4×C3⋊C8—21no—
189C4×C3⋊C8—41no—
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×#117—31no—
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#424C2×D311yescharacteristic, complemented
215#421—64no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104—31no—
219C2×#104—31no—
220C2×#104—31no—
221C2×#104C2×D311yescharacteristic
222#416—31no—
223#416C2×D311yescharacteristic
224#408—31no—
225#408—31no—
226#408—61no—
227#408—61no—
228#408C2×D311yescharacteristic
229#407—31no—
230#407—61no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—61no—
234#405—31no—
235C2×#97C2×D311yescharacteristic, complemented
236C2×C4×C8—31no—
237#341—31no—
238#341C2×D311yescharacteristic, complemented
239#339—31no—
240#339C2×D311yescharacteristic, complemented
241#336—31no—
242#336—31no—
243C23×D3—21no—
244C23×D3#4111yescharacteristic
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C2×C3×Q8C22×C411yescharacteristic
250C2×C3×D4—21no—
251C2×C3×D4C22×C411yescharacteristic
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4C2411yescharacteristic
255C2×#67—21no—
256C2×#67—21no—
257C2×#67—21no—
258C2×#67—21no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3#4111yescharacteristic
262#239—22no—
263#239—41no—
264D3×Q8—22no—
265D3×Q8—41no—
266#237—22no—
267#237—41no—
268#237—42no—
269#237—42no—
270D3×D4—22no—
271D3×D4—41no—
272D3×D4—42no—
273D3×D4—42no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—21no—
278#235—21no—
279#235—21no—
280#235—42no—
281#235—42no—
282#235C2×D412yes—
283#235#4112yes—
284C2×D12—21no—
285C2×D12—21no—
286C2×D12—21no—
287C2×D12C22×C411yescharacteristic
288C2×D12C22×C411yescharacteristic
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—42no—
298C2×C4×D3—42no—
299C2×C4×D3C22×C411yescharacteristic
300C2×C4×D3C22×C411yescharacteristic
301C2×C4×D3C2×D411yescharacteristic
302C2×C4×D3C2×D411yescharacteristic
303C2×Dic6—21no—
304C2×Dic6C22×C411yescharacteristic
305C2×Dic6C22×C411yescharacteristic
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—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×C8C22×C411yescharacteristic
317C2×C3×C8C22×C411yescharacteristic
318C2×C3×C8C2×D411yescharacteristic
319C2×C3×C8C2×D411yescharacteristic
320C3×C4⋊C4C22×C411yescharacteristic
321C3×C4⋊C4C22×C411yescharacteristic
322C3×C22⋊C4—21no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42C2×D412yes—
326#216—41no—
327#215—41no—
328#214—41no—
329#213—41no—
330(C2×D3)⋊C4—21no—
331(C2×D3)⋊C4—21no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—42no—
335C4⋊Dic3—21no—
336C4⋊Dic3—21no—
337Dic3⋊C4—42no—
338C4×Dic3—21no—
339C4×Dic3—21no—
340#208—21no—
341#208—21no—
342#208—21no—
343#208C2×D412yes—
344C2×C3⋊C8—21no—
345C2×C3⋊C8—21no—
346C2×C3⋊C8—21no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8C22×C411yescharacteristic
351C2×C3⋊C8C22×C411yescharacteristic
352C2×C3⋊C8C2×D411yescharacteristic
353C2×C3⋊C8C2×D411yescharacteristic
354Dic12—22no—
355D24—22no—
356#204—22no—
357#204—22no—
358ΓL(1,𝔽25)—42no—
359ΓL(1,𝔽25)—42no—
360ΓL(1,𝔽25)—42no—
361ΓL(1,𝔽25)—42no—
362D3×C8—42no—
363D3×C8—42no—
364D3×C8—42no—
365D3×C8—42no—
366C2×#41—31no—
367C2×#41—31no—
368C2×#41—31no—
369C2×#41—31no—
370C2×#41—61no—
371C2×#41—61no—
372C2×#41—62no—
373C2×#41—62no—
374C2×#41—121no—
375C2×#41—121no—
376C2×#41C22×D311yescharacteristic
377C22×Q8—31no—
378C22×D4—31no—
379C22×D4—61no—
380C23×C4—31no—
381C23×C4—61no—
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—61no—
403C2×M16—61no—
404C2×M16—61no—
405C2×M16—61no—
406C2×M16—62no—
407C2×M16—121no—
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—31no—
411C22×C8—31no—
412C22×C8—61no—
413C22×C8—61no—
414C22×C8—61no—
415C22×C8—61no—
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—62no—
427#117—121no—
428#117C22×D311yescharacteristic
429C2×C4⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42—31no—
432C2×C42C22×D311yescharacteristic
433#108—62no—
434#108—121no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437#104—22no—
438#104—34no—
439#104—62no—
440#104—62no—
441#104—62no—
442#104—121no—
443#103—31no—
444#103—31no—
445#103C4×D311yescharacteristic
446#103C4×D311yescharacteristic
447#102—31no—
448#102—31no—
449#102C4×D311yescharacteristic
450#102C4×D311yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—31no—
460C22⋊C8—31no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8—61no—
466C22⋊C8—61no—
467#97—22no—
468#97—61no—
469C4×C8—61no—
470C4×C8—121no—
471C23×C3—21no—
472C23×C3C2×#4111yescharacteristic
473C22×D3—21no—
474C22×D3—21no—
475C22×D3—21no—
476C22×D3—21no—
477C22×D3—41no—
478C22×D3—41no—
479C22×D3—42no—
480C22×D3—42no—
481C22×D3—81no—
482C22×D3C4×D411yescharacteristic
483C22×D3C4×D411yescharacteristic
484C3×Q8—21no—
485C3×Q8—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—41no—
489C3×D4—41no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4C23×C411yescharacteristic
499C2×C3×C4C22×D411yescharacteristic
500C2×C3×C4C22×D411yescharacteristic
501C2×C3×C4C2×#4111yescharacteristic
502C2×C3×C4H(5,𝔽2)11yescharacteristic
503C2×C3×C4H(5,𝔽2)11yescharacteristic
504#67—22no—
505#67—22no—
506#67—42no—
507#67—42no—
508#67—41no—
509#67—41no—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—42no—
515C2×Dic3—41no—
516C2×Dic3—41no—
517C2×Dic3—41no—
518C2×Dic3C4×D411yescharacteristic
519C2×Dic3C4×D411yescharacteristic
520D12—21no—
521D12—21no—
522D12—21no—
523D12—42no—
524D12—42no—
525D12—81no—
526D12C4×D412yes—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—22no—
533C4×D3—21no—
534C4×D3—22no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—41no—
540C4×D3—41no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6C4×D412yes—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—21no—
549C3×C8—21no—
550C3×C8—41no—
551C3×C8—41no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—22no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—41no—
558C24—31no—
559C24—61no—
560#41—21no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—32no—
565#41—32no—
566#41—61no—
567#41—61no—
568#41—62no—
569#41—62no—
570#41—61no—
571#41—61no—
572#41—61no—
573#41—61no—
574#41—122no—
575#41—122no—
576#41—121no—
577#41—122no—
578#41—122no—
579#41—121no—
580C2×Q8—31no—
581C2×Q8—31no—
582C2×Q8—61no—
583C2×Q8—62no—
584C2×Q8—121no—
585C2×Q8C2×C4×D311yescharacteristic
586C2×D4—21no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—61no—
590C2×D4—61no—
591C2×D4—61no—
592C2×D4—61no—
593C2×D4—62no—
594C2×D4—61no—
595C2×D4—61no—
596C2×D4—61no—
597C2×D4—121no—
598C2×D4—122no—
599C2×D4—122no—
600C2×D4C2×C4×D311yescharacteristic
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—61no—
609C22×C4—61no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4—61no—
616C22×C4—61no—
617C22×C4—61no—
618C22×C4—122no—
619C22×C4—122no—
620C22×C4C23×D311yescharacteristic
621Q16—62no—
622Q16—121no—
623SD16—62no—
624SD16—62no—
625SD16—121no—
626SD16—121no—
627D8—62no—
628D8—121no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—21no—
633M16—32no—
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—31no—
648C2×C8—31no—
649C2×C8—31no—
650C2×C8—31no—
651C2×C8—61no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—122no—
658C2×C8—122no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8C2×C4×D311yescharacteristic
662C2×C8C2×C4×D311yescharacteristic
663C2×C8D3×D411yescharacteristic
664C2×C8D3×D411yescharacteristic
665C4⋊C4—61no—
666C4⋊C4—61no—
667C4⋊C4—122no—
668C4⋊C4C2×C4×D311yescharacteristic
669C4⋊C4C2×C4×D311yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—122no—
676C42—21no—
677C42—21no—
678C42—61no—
679C42—61no—
680C42D3×D412yes—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—41no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3C2×C4×D411yescharacteristic
687C22×C3#54611yescharacteristic
688C22×C3#55111yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—22no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—21no—
696C2×D3—41no—
697C2×D3—41no—
698C2×D3—41no—
699C2×D3—41no—
700C2×D3—41no—
701C2×D3—81no—
702C2×D3—81no—
703C2×D3—84no—
704C3×C4—42no—
705C3×C4—41no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4C2×C4×D411yescharacteristic
709C3×C4#51811yescharacteristic
710C3×C4D4211yescharacteristic
711C3×C4#54611yescharacteristic
712Dic3—22no—
713Dic3—21no—
714Dic3—21no—
715Dic3—41no—
716Dic3—81no—
717C23—21no—
718C23—31no—
719C23—31no—
720C23—61no—
721C23—61no—
722C23—61no—
723C23—61no—
724C23—121no—
725C23—121no—
726C23—122no—
727C23—122no—
728C23—241no—
729C23D3×#4111yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—32no—
733Q8—61no—
734Q8—61no—
735Q8—61no—
736Q8—122no—
737D4—21no—
738D4—21no—
739D4—32no—
740D4—41no—
741D4—41no—
742D4—62no—
743D4—62no—
744D4—61no—
745D4—61no—
746D4—61no—
747D4—122no—
748D4—122no—
749D4—122no—
750D4—122no—
751D4—121no—
752D4—121no—
753D4—241no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—31no—
759C2×C4—31no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—62no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—62no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—122no—
779C2×C4—122no—
780C2×C4—122no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4D3×#4111yescharacteristic
790C2×C4#100911yescharacteristic
791C2×C4#100911yescharacteristic
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—41no—
797C8—41no—
798C8—61no—
799C8—61no—
800C8—61no—
801C8—61no—
802C8—62no—
803C8—121no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—81no—
807C2×C3#235811yescharacteristic
808C2×C3#295511yescharacteristic
809C2×C3#295711yescharacteristic
810D3—41no—
811D3—41no—
812D3—42no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—62no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—241no—
832C22—241no—
833C22—244no—
834C22C4×D3×D411yescharacteristic
835C22#565411yescharacteristic
836C22#570511yescharacteristic
837C4—42no—
838C4—41no—
839C4—41no—
840C4—41no—
841C4—61no—
842C4—61no—
843C4—62no—
844C4—121no—
845C4—241no—
846C4#552111yescharacteristic
847C4C4×D3×D411yescharacteristic
848C4#560911yescharacteristic
849C4#567611yescharacteristic
850C3#2288711yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—81no—
854C2—121no—
855C2—121no—
856C2—122no—
857C2—241no—
858C2#7583611yescharacteristic
859C2#7989711yescharacteristic
860C2#7989911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1938C2
socleC22×C3C2×C4×D4
prime radical#78833C2
cosocleC22×C3×C4C24
hypercenter#1938D3
hypocenterC3#22887
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

Complements

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

NH ≅ G/Ntype
1. #79075C2semidirect
2. C2×#4821C2semidirect
4. #78663C2semidirect
5. C2×#4717C2semidirect
6. C3×#1938C2semidirect
7. #70545C2semidirect
8. #70373C2semidirect
9. #70291C2semidirect
10. #70011C2semidirect
11. #69830C2semidirect
12. #68946C2semidirect
13. #68941C2semidirect
14. #68757C2semidirect
15. #68739C2semidirect
23. C2×#901C22semidirect
26. C3×#424C22semidirect
30. C2×C3×#97C22semidirect
34. C2×#825C22semidirect
35. #5129C22semidirect
37. C2×#822C22semidirect
40. C2×#819C22semidirect
42. #4997C22semidirect
44. C2×#805C22semidirect
45. C2×C4×C3⋊C8C22semidirect
51. #4810C4semidirect
52. #4809C4semidirect
53. #4808C4semidirect
54. #4806C4semidirect
55. #4783C4semidirect
56. #4781C4semidirect
57. #4776C4semidirect
58. #4773C4semidirect
64. C3×#341C22semidirect
65. C3×#339C22semidirect
66. #4558C22semidirect
67. #4550C22semidirect
68. #4550C22semidirect
69. #4532C22semidirect
76. #1938D3semidirect
186. #805D4semidirect
214. #424C2×D3semidirect
235. C2×#97C2×D3semidirect
238. #341C2×D3semidirect
240. #339C2×D3semidirect
850. C3#22887semidirect

Maximal subgroups

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

subgroupindex
#790752
C2×#48212
#788332
#786632
C2×#47172
C3×#19382
#705452
#703732
#702912
#700112
#698302
#689462
#689412
#687572
#687392
#228873