Finite Group Databasebeta

← #10815971

Subgroups — #10815971

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#83793C211yesmaximal, characteristic, complemented
2C2×#4821C211yesmaximal, characteristic, complemented
3C2×#4824C211yesmaximal, characteristic, complemented
4#78833C211yesmaximal, characteristic
5#78555C211yesmaximal, characteristic, complemented
6C3×#1765C211yesmaximal, characteristic, complemented
7#72010C211yesmaximal, characteristic, complemented
8#70292C211yesmaximal, characteristic, complemented
9#69900C211yesmaximal, characteristic, complemented
10#69845C211yesmaximal, characteristic, complemented
11#69830C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68941C211yesmaximal, characteristic, complemented
14#68757C211yesmaximal, characteristic, complemented
15#68745C211yesmaximal, characteristic, complemented
16#22889—31nomaximal, Sylow
17C2×D3×#41C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic
19C2×#950C2211yescharacteristic
20C2×#948C2211yescharacteristic
21C2×#907C2211yescharacteristic, complemented
22C2×D3×M16C2211yescharacteristic
23C2×#904C2211yescharacteristic
24#5524C2211yescharacteristic
25C2×#872C2211yescharacteristic
26C2×C3×#104C2211yescharacteristic
27C3×#416C2211yescharacteristic
28C3×#405C2211yescharacteristic, complemented
29C2×C3×#97C2211yescharacteristic, complemented
30C2×#837C2211yescharacteristic
31C2×#825C2211yescharacteristic
32C2×#825C2211yescharacteristic, complemented
33#5129—21no—
34#5129C2211yescharacteristic
35#5126—21no—
36#5126C2211yescharacteristic
37C2×#822C2211yescharacteristic, complemented
38#5110—21no—
39#5110C2211yescharacteristic
40#5110C2211yescharacteristic, complemented
41C2×(C2×D3)⋊C8—21no—
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#819C2211yescharacteristic, complemented
45#5002C2211yescharacteristic
46#4999C2211yescharacteristic, complemented
47C2×#805C2211yescharacteristic
48C2×#805C2211yescharacteristic, complemented
49C2×C4×C3⋊C8C2211yescharacteristic, complemented
50#4824—24no—
51#4821—24no—
52#4810C411yescharacteristic, complemented
53#4809C411yescharacteristic, complemented
54#4808C411yescharacteristic, complemented
55#4806C411yescharacteristic, complemented
56#4783C411yescharacteristic, complemented
57#4781C411yescharacteristic, complemented
58#4776C411yescharacteristic, complemented
59#4773C411yescharacteristic, complemented
60#4706—21no—
61#4706—21no—
62#4688—21no—
63C8×D12—21no—
64C3×#341C2211yescharacteristic, complemented
65C3×#339C2211yescharacteristic, complemented
66#4558C2211yescharacteristic, complemented
67#4550C2211yescharacteristic, complemented
68#4550C2211yescharacteristic, complemented
69#4532C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933—31no—
73C2×#421—31no—
74#2880—31no—
75#1975—31no—
76#1937—31no—
77#1929—31no—
78#1897—31no—
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1765D311yescharacteristic, complemented
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
101C3×#131—22no—
102C3×#131—41no—
103C2×C3×M16—21no—
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C22×C3×C8—21no—
107C22×C3×C8C2311yescharacteristic
108C22×C3×C8C2311yescharacteristic
109C3×#117C2311yescharacteristic
110C2×C3×C42C2311yescharacteristic
111#950—22no—
112#950—22no—
113#948—22no—
114#948—41no—
115C2×#216C2×C411yescharacteristic
116C2×#215C2×C411yescharacteristic
117C2×#214C2×C411yescharacteristic
118C2×#213C2×C411yescharacteristic
119C2×(C2×D3)⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×C4×Dic3C2311yescharacteristic
122C2×#208—21no—
123C2×#208C2311yescharacteristic
124C2×#208C2311yescharacteristic
125C22×C3⋊C8—21no—
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128#907—22no—
129#907—41no—
130D3×M16—22no—
131D3×M16—41no—
132C2×Dic12C2×C411yescharacteristic
133#904—41no—
134#904—41no—
135C2×D24C2×C411yescharacteristic
136C2×#204C2×C411yescharacteristic
137C2×#204C2×C411yescharacteristic
138C2×ΓL(1,𝔽25)—21no—
139C2×ΓL(1,𝔽25)—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×#104D414yescomplemented
153C3×#103C2×C411yescharacteristic
154C3×#103C2×C411yescharacteristic
155C3×#102C2×C411yescharacteristic
156C3×#102C2×C411yescharacteristic
157C3×#97—21no—
158C3×#97—41no—
159C3×C4×C8—21no—
160#837—22no—
161#825—22no—
162#825—41no—
163#822—22no—
164(C2×D3)⋊C8—21no—
165(C2×D3)⋊C8—21no—
166(C2×D3)⋊C8—21no—
167(C2×D3)⋊C8—21no—
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—41no—
181#810C2×C411yescharacteristic
182#810C2×C411yescharacteristic
183#809C2×C411yescharacteristic
184#809C2×C411yescharacteristic
185#805—22no—
186#805—22no—
187C4⋊(C3⋊C8)—21no—
188C4⋊(C3⋊C8)—21no—
189C4×C3⋊C8—22no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131C2×D311yescharacteristic
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#443—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×#104C2×D311yescharacteristic
222#416—31no—
223#416C2×D311yescharacteristic
224#408—31no—
225#408—31no—
226#408—31no—
227#408—61no—
228#408—61no—
229#407—31no—
230#407—61no—
231C2×C22⋊C8—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—61no—
234#405C2×D311yescharacteristic, complemented
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×#41C2×D412yes—
248C3×#41#4112yes—
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—21no—
281#235—21no—
282#235—42no—
283#235—42no—
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—42no—
310C3×M16C2×D412yes—
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×C8—42no—
318C2×C3×C8C22×C411yescharacteristic
319C2×C3×C8C22×C411yescharacteristic
320C2×C3×C8C2×D411yescharacteristic
321C2×C3×C8C2×D411yescharacteristic
322C3×C4⋊C4C22×C411yescharacteristic
323C3×C4⋊C4C22×C411yescharacteristic
324C3×C22⋊C4—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42C2×D412yes—
328#216—22no—
329#215—22no—
330#214—22no—
331#213—22no—
332(C2×D3)⋊C4—21no—
333(C2×D3)⋊C4—21no—
334(C2×D3)⋊C4—21no—
335(C2×D3)⋊C4—21no—
336(C2×D3)⋊C4—42no—
337C4⋊Dic3—21no—
338C4⋊Dic3—21no—
339Dic3⋊C4—42no—
340C4×Dic3—21no—
341C4×Dic3—21no—
342#208—21no—
343#208—21no—
344#208—21no—
345#208—21no—
346#208—42no—
347C2×C3⋊C8—21no—
348C2×C3⋊C8—21no—
349C2×C3⋊C8—21no—
350C2×C3⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—42no—
354C2×C3⋊C8C22×C411yescharacteristic
355C2×C3⋊C8C22×C411yescharacteristic
356C2×C3⋊C8C2×D411yescharacteristic
357C2×C3⋊C8C2×D411yescharacteristic
358Dic12—41no—
359D24—41no—
360#204—41no—
361#204—41no—
362ΓL(1,𝔽25)—42no—
363ΓL(1,𝔽25)—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—22no—
395#131—41no—
396#131—62no—
397#131—62no—
398#131—121no—
399#131—121no—
400C2×M16—21no—
401C2×M16—31no—
402C2×M16—31no—
403C2×M16—61no—
404C2×M16—61no—
405C2×M16—61no—
406C2×M16—62no—
407C2×M16—121no—
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—21no—
411C22×C8—31no—
412C22×C8—31no—
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—61no—
436C4⋊C8—61no—
437#104—62no—
438#104—62no—
439#104—62no—
440#104—62no—
441#104—121no—
442#104D1214yescomplemented
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—31no—
452C22⋊C8—31no—
453C22⋊C8—31no—
454C22⋊C8—31no—
455C22⋊C8—31no—
456C22⋊C8—31no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—61no—
460C22⋊C8—61no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8—61no—
464C22⋊C8—61no—
465C22⋊C8—61no—
466C22⋊C8—61no—
467#97—21no—
468#97—41no—
469C4×C8—21no—
470C4×C8—62no—
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×Q8C4×D412yes—
486C3×D4—22no—
487C3×D4—22no—
488C3×D4—21no—
489C3×D4C4×D412yes—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—22no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—22no—
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—42no—
505#67—42no—
506#67—41no—
507#67—41no—
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—21no—
524D12—42no—
525D12—42no—
526D12—81no—
527C4×D3—21no—
528C4×D3—21no—
529C4×D3—21no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—21no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—42no—
536C4×D3—42no—
537C4×D3—41no—
538C4×D3—41no—
539C4×D3—41no—
540C4×D3—41no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—21no—
545Dic6—42no—
546C3×C8—21no—
547C3×C8—21no—
548C3×C8—22no—
549C3×C8—21no—
550C3×C8—21no—
551C3×C8—41no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—41no—
557C3⋊C8—41no—
558C24—31no—
559C24—61no—
560#41—21no—
561#41—21no—
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—122no—
573#41—122no—
574#41—121no—
575#41—122no—
576#41—122no—
577#41—121no—
578#41C2×D1212yes—
579#41#23512yes—
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—42no—
633M16—61no—
634M16—61no—
635M16—61no—
636M16—61no—
637M16—122no—
638M16—122no—
639M16—122no—
640M16C2×D1212yes—
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—42no—
652C2×C8—61no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
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—
680C42C2×D1212yes—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—22no—
684C22×C3—41no—
685C22×C3—41no—
686C22×C3C2×C4×D411yescharacteristic
687C22×C3#54611yescharacteristic
688C22×C3#55111yescharacteristic
689C2×D3—21no—
690C2×D3—21no—
691C2×D3—21no—
692C2×D3—21no—
693C2×D3—21no—
694C2×D3—21no—
695C2×D3—41no—
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—22no—
705C3×C4—42no—
706C3×C4—41no—
707C3×C4—41no—
708C3×C4C2×C4×D411yescharacteristic
709C3×C4#51811yescharacteristic
710C3×C4D4211yescharacteristic
711C3×C4#54611yescharacteristic
712Dic3—21no—
713Dic3—21no—
714Dic3—41no—
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—61no—
732Q8—61no—
733Q8—61no—
734Q8—61no—
735Q8—122no—
736Q8C4×D1212yes—
737D4—22no—
738D4—22no—
739D4—21no—
740D4—61no—
741D4—61no—
742D4—61no—
743D4—61no—
744D4—122no—
745D4—122no—
746D4—122no—
747D4—122no—
748D4—121no—
749D4—121no—
750D4—121no—
751D4—121no—
752D4—241no—
753D4C4×D1212yes—
754C2×C4—21no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—31no—
761C2×C4—31no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—61no—
765C2×C4—61no—
766C2×C4—61no—
767C2×C4—61no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—122no—
777C2×C4—122no—
778C2×C4—122no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4—121no—
785C2×C4—121no—
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C22×D1211yescharacteristic
788C2×C4C2×#23511yescharacteristic
789C2×C4C2×D3×D411yescharacteristic
790C2×C4#100411yescharacteristic
791C2×C4#100911yescharacteristic
792C8—21no—
793C8—21no—
794C8—21no—
795C8—21no—
796C8—22no—
797C8—41no—
798C8—61no—
799C8—61no—
800C8—61no—
801C8—61no—
802C8—121no—
803C8—121no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—42no—
807C2×C3#235811yescharacteristic
808C2×C3#295511yescharacteristic
809C2×C3#295711yescharacteristic
810D3—41no—
811D3—41no—
812D3—81no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—22no—
817C22—41no—
818C22—41no—
819C22—61no—
820C22—61no—
821C22—61no—
822C22—61no—
823C22—61no—
824C22—61no—
825C22—121no—
826C22—121no—
827C22—121no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—241no—
832C22—241no—
833C22—244no—
834C22#552711yescharacteristic
835C22C4×D3×D411yescharacteristic
836C22#555411yescharacteristic
837C4—22no—
838C4—42no—
839C4—41no—
840C4—41no—
841C4—61no—
842C4—61no—
843C4—121no—
844C4—121no—
845C4—241no—
846C4C2×C4×D1211yescharacteristic
847C4#549011yescharacteristic
848C4#554511yescharacteristic
849C4D4×D1211yescharacteristic
850C3#2288911yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—42no—
854C2—121no—
855C2—121no—
856C2—241no—
857C2—241no—
858C2#7357711yescharacteristic
859C2#7989711yescharacteristic
860C2#7989911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1765C2
socleC22×C3C2×C4×D4
prime radical#78833C2
cosocleC22×C3×C4C24
hypercenter#1765D3
hypocenterC3#22889
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1765

Complements

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

NH ≅ G/Ntype
1. #83793C2semidirect
2. C2×#4821C2semidirect
3. C2×#4824C2semidirect
5. #78555C2semidirect
6. C3×#1765C2semidirect
7. #72010C2semidirect
8. #70292C2semidirect
9. #69900C2semidirect
10. #69845C2semidirect
11. #69830C2semidirect
12. #68946C2semidirect
13. #68941C2semidirect
14. #68757C2semidirect
15. #68745C2semidirect
21. C2×#907C22semidirect
28. C3×#405C22semidirect
29. C2×C3×#97C22semidirect
32. C2×#825C22semidirect
37. C2×#822C22semidirect
40. #5110C22semidirect
44. C2×#819C22semidirect
46. #4999C22semidirect
48. C2×#805C22semidirect
49. C2×C4×C3⋊C8C22semidirect
52. #4810C4semidirect
53. #4809C4semidirect
54. #4808C4semidirect
55. #4806C4semidirect
56. #4783C4semidirect
57. #4781C4semidirect
58. #4776C4semidirect
59. #4773C4semidirect
64. C3×#341C22semidirect
65. C3×#339C22semidirect
66. #4558C22semidirect
67. #4550C22semidirect
68. #4550C22semidirect
69. #4532C22semidirect
83. #1765D3semidirect
152. C3×#104D4semidirect
234. #405C2×D3semidirect
235. C2×#97C2×D3semidirect
238. #341C2×D3semidirect
240. #339C2×D3semidirect
442. #104D12semidirect
850. C3#22889semidirect

Maximal subgroups

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

subgroupindex
#837932
C2×#48212
C2×#48242
#788332
#785552
C3×#17652
#720102
#702922
#699002
#698452
#698302
#689462
#689412
#687572
#687452
#228893