Finite Group Databasebeta

← #10815965

Subgroups — #10815965

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
1C3×#2880C211yesmaximal, characteristic, complemented
2#84080C211yesmaximal, characteristic
3C2×#5236C211yesmaximal, characteristic, complemented
4C2×#5144C211yesmaximal, characteristic, complemented
5#78596C211yesmaximal, characteristic, complemented
6#72017C211yesmaximal, characteristic, complemented
7#72010C211yesmaximal, characteristic, complemented
8#72009C211yesmaximal, characteristic, complemented
9#70011C211yesmaximal, characteristic, complemented
10#70000C211yesmaximal, characteristic, complemented
11#69997C211yesmaximal, characteristic, complemented
12#69996C211yesmaximal, characteristic, complemented
13#69984C211yesmaximal, characteristic, complemented
14#69966C211yesmaximal, characteristic, complemented
15#69907C211yesmaximal, characteristic, complemented
16#22889—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C2×C3×#131C2211yescharacteristic
19C2×C3×#131C2211yescharacteristic
20C2×#950C2211yescharacteristic
21C2×#950C2211yescharacteristic
22#5791C2211yescharacteristic
23C2×#926C2211yescharacteristic
24C22×#208C2211yescharacteristic
25C2×#901C2211yescharacteristic, complemented
26C3×#408—21no—
27C3×#408—21no—
28C3×#408C2211yescharacteristic
29C3×#408C2211yescharacteristic
30C3×#407—21no—
31C3×#407C2211yescharacteristic
32C2×C3×C22⋊C8—21no—
33C2×C3×C22⋊C8C2211yescharacteristic
34#5239C411yescharacteristic, complemented
35#5239C411yescharacteristic, complemented
36#5238C411yescharacteristic, complemented
37#5238C411yescharacteristic, complemented
38#5236—24no—
39C2×#837C2211yescharacteristic
40C2×#837C2211yescharacteristic
41C2×#837C2211yescharacteristic
42C2×#837C2211yescharacteristic
43#5233C2211yescharacteristic
44#5233C2211yescharacteristic
45#5228C411yescharacteristic, complemented
46#5227C411yescharacteristic, complemented
47#5218C411yescharacteristic, complemented
48#5217C411yescharacteristic, complemented
49C2×#830C2211yescharacteristic
50#5144—24no—
51C2×#825C2211yescharacteristic, complemented
52C2×#825C2211yescharacteristic, complemented
53C2×#822C2211yescharacteristic, complemented
54C2×#822C2211yescharacteristic, complemented
55#5110C2211yescharacteristic, complemented
56#5102C2211yescharacteristic, complemented
57#5101C2211yescharacteristic, complemented
58C2×#815C2211yescharacteristic, complemented
59C2×C8×Dic3C2211yescharacteristic, complemented
60#4730—21no—
61#4729—21no—
62#4728—21no—
63#67⋊C8—21no—
64#4558C2211yescharacteristic, complemented
65#4558C2211yescharacteristic, complemented
66#4555C2211yescharacteristic, complemented
67#4555C2211yescharacteristic, complemented
68#4550C2211yescharacteristic, complemented
69#4550C2211yescharacteristic, complemented
70#3002—31no—
71C2×#443—31no—
72#2933—31no—
73C2×#421—31no—
74#2880D311yescharacteristic, complemented
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#1765—31no—
84#1750—31no—
85C2×C3×#41—21no—
86C2×C3×#41—21no—
87C2×C3×#41—22no—
88C2×C3×#41—22no—
89C2×C3×#41—41no—
90C2×C3×#41—41no—
91C2×C3×#41C2×C411yescharacteristic
92C2×C3×#41C2×C411yescharacteristic
93C2×C3×#41C2311yescharacteristic
94C2×C3×#41C2311yescharacteristic
95C22×C3×Q8C2×C411yescharacteristic
96C22×C3×D4—21no—
97C22×C3×D4C2×C411yescharacteristic
98C23×C3×C4—21no—
99C23×C3×C4C2311yescharacteristic
100C2×#235C2311yescharacteristic
101C3×#131—22no—
102C3×#131—22no—
103C3×#131—41no—
104C3×#131—41no—
105C2×C3×M16—21no—
106C2×C3×M16—21no—
107C2×C3×M16C2311yescharacteristic
108C2×C3×M16C2311yescharacteristic
109C22×C3×C8—21no—
110C22×C3×C8—21no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113#953—21no—
114C2×#217—21no—
115#950—22no—
116#950—22no—
117#950—41no—
118#950—41no—
119C2×#216C2×C411yescharacteristic
120C2×#216C2×C411yescharacteristic
121C2×#215C2×C411yescharacteristic
122C2×#215C2×C411yescharacteristic
123C2×#214C2×C411yescharacteristic
124C2×#214C2×C411yescharacteristic
125C2×#213C2×C411yescharacteristic
126C2×#213C2×C411yescharacteristic
127#930C2×C411yescharacteristic
128#930C2×C411yescharacteristic
129#929—21no—
130C4×#67—21no—
131C4×#67—21no—
132#926—22no—
133#926—41no—
134#926C2311yescharacteristic
135C2×C4⋊Dic3—21no—
136#924C2×C411yescharacteristic
137#924C2×C411yescharacteristic
138C2×C4×Dic3C2311yescharacteristic
139C2×C4×Dic3C2311yescharacteristic
140C2×#208—21no—
141C2×#208—22no—
142C2×#208—41no—
143C2×#208C2311yescharacteristic
144C2×#208C2311yescharacteristic
145C22×C3⋊C8—21no—
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148#901—22no—
149#901—41no—
150C2×ΓL(1,𝔽25)—21no—
151C2×D3×C8—21no—
152C3×C22⋊C8—21no—
153C3×C22⋊C8—21no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156C3×C22⋊C8—21no—
157C3×C22⋊C8—21no—
158C3×C22⋊C8D411yescharacteristic
159C3×C22⋊C8D411yescharacteristic
160C3×C22⋊C8D411yescharacteristic
161C3×C22⋊C8D411yescharacteristic
162#837—22no—
163#837—22no—
164#837—22no—
165#837D414yescomplemented
166#835C2×C411yescharacteristic
167#835C2×C411yescharacteristic
168#835C2×C411yescharacteristic
169#835C2×C411yescharacteristic
170#832C2×C411yescharacteristic
171#832C2×C411yescharacteristic
172#832C2×C411yescharacteristic
173#832C2×C411yescharacteristic
174#830C2×C411yescharacteristic
175#830C2×C411yescharacteristic
176#830C2×C411yescharacteristic
177#830C2×C411yescharacteristic
178#825—22no—
179#825—41no—
180#822—22no—
181#822—41no—
182(C2×D3)⋊C8—21no—
183(C2×D3)⋊C8—21no—
184#815—21no—
185#815—41no—
186Dic3⋊C8—21no—
187Dic3⋊C8—21no—
188C8×Dic3—21no—
189C8×Dic3—22no—
190C22×#41C2×D311yescharacteristic
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131C2×D311yescharacteristic
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×#104—31no—
222#416—31no—
223#416—31no—
224#408—21no—
225#408—21no—
226#408—31no—
227#408C2×D311yescharacteristic
228#408C2×D311yescharacteristic
229#407—21no—
230#407C2×D311yescharacteristic
231C2×C22⋊C8—21no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8C2×D311yescharacteristic
234#405—31no—
235C2×#97—31no—
236C2×C4×C8—31no—
237#341—31no—
238#341—31no—
239#339—31no—
240#339—31no—
241#336—31no—
242#336—31no—
243C24×C3—21no—
244C24×C3#4111yescharacteristic
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—22no—
248C3×#41—22no—
249C3×#41—21no—
250C3×#41—21no—
251C3×#41—21no—
252C3×#41—21no—
253C3×#41—42no—
254C3×#41—42no—
255C3×#41—41no—
256C3×#41—41no—
257C3×#41—42no—
258C3×#41—42no—
259C3×#41C2×D412yes—
260C3×#41#4112yes—
261C2×C3×Q8—21no—
262C2×C3×Q8—22no—
263C2×C3×Q8—41no—
264C2×C3×Q8C22×C411yescharacteristic
265C2×C3×Q8C22×C411yescharacteristic
266C2×C3×D4—21no—
267C2×C3×D4—22no—
268C2×C3×D4—21no—
269C2×C3×D4—21no—
270C2×C3×D4—21no—
271C2×C3×D4—21no—
272C2×C3×D4—41no—
273C2×C3×D4—42no—
274C2×C3×D4—42no—
275C2×C3×D4C22×C411yescharacteristic
276C2×C3×D4C22×C411yescharacteristic
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—21no—
280C22×C3×C4—21no—
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—42no—
287C22×C3×C4—42no—
288C22×C3×C4C22×C411yescharacteristic
289C22×C3×C4C22×C411yescharacteristic
290C22×C3×C4C2×D411yescharacteristic
291C22×C3×C4C2×D411yescharacteristic
292C22×C3×C4#4111yescharacteristic
293C22×C3×C4C2411yescharacteristic
294C2×#67—21no—
295C2×#67—21no—
296C2×#67—21no—
297C22×Dic3—21no—
298C22×Dic3—21no—
299#235—21no—
300#235—21no—
301#235—21no—
302#235—21no—
303C2×D12C22×C411yescharacteristic
304C2×C4×D3—21no—
305C2×Dic6C22×C411yescharacteristic
306C3×M16—21no—
307C3×M16—21no—
308C3×M16—21no—
309C3×M16—21no—
310C3×M16—42no—
311C3×M16—42no—
312C2×C3×C8—21no—
313C2×C3×C8—21no—
314C2×C3×C8—21no—
315C2×C3×C8—21no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—42no—
319C2×C3×C8—42no—
320C2×C3×C8C2×D411yescharacteristic
321C2×C3×C8C2×D411yescharacteristic
322C2×C3×C8C2×D411yescharacteristic
323C2×C3×C8C2×D411yescharacteristic
324#217—21no—
325#217—21no—
326#217—21no—
327#217—42no—
328#216—22no—
329#216—41no—
330#215—22no—
331#215—41no—
332#214—22no—
333#214—41no—
334#213—22no—
335#213—41no—
336(C2×D3)⋊C4—21no—
337(C2×D3)⋊C4—21no—
338C4⋊Dic3—42no—
339C4⋊Dic3C22×C411yescharacteristic
340C4⋊Dic3C22×C411yescharacteristic
341Dic3⋊C4—21no—
342Dic3⋊C4—21no—
343C4×Dic3—21no—
344C4×Dic3—21no—
345C4×Dic3—21no—
346C4×Dic3—21no—
347C4×Dic3C2×D412yes—
348#208—21no—
349#208—21no—
350#208—21no—
351#208—42no—
352#208C2×D412yes—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—42no—
360C2×C3⋊C8C22×C411yescharacteristic
361C2×C3⋊C8C22×C411yescharacteristic
362C2×C3⋊C8C22×C411yescharacteristic
363C2×C3⋊C8C22×C411yescharacteristic
364ΓL(1,𝔽25)—42no—
365D3×C8—42no—
366C2×#41—21no—
367C2×#41—21no—
368C2×#41—22no—
369C2×#41—22no—
370C2×#41—31no—
371C2×#41—41no—
372C2×#41—41no—
373C2×#41C4×D311yescharacteristic
374C2×#41C4×D311yescharacteristic
375C2×#41C22×D311yescharacteristic
376C2×#41C22×D311yescharacteristic
377C22×Q8C4×D311yescharacteristic
378C22×D4—21no—
379C22×D4C4×D311yescharacteristic
380C23×C4—21no—
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—22no—
395#131—22no—
396#131—41no—
397#131—41no—
398#131—62no—
399#131—121no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—31no—
403C2×M16—31no—
404C2×M16—61no—
405C2×M16—61no—
406C2×M16—62no—
407C2×M16—121no—
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—21no—
411C22×C8—21no—
412C22×C8—31no—
413C22×C8—31no—
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—31no—
427#117—62no—
428#117—121no—
429C2×C4⋊C4—61no—
430C2×C22⋊C4—61no—
431C2×C42—31no—
432C2×C42—31no—
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—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C22⋊C8—21no—
456C22⋊C8—21no—
457C22⋊C8—31no—
458C22⋊C8—31no—
459C22⋊C8—31no—
460C22⋊C8—31no—
461C22⋊C8—61no—
462C22⋊C8—61no—
463C22⋊C8#6711yescharacteristic
464C22⋊C8#6711yescharacteristic
465C22⋊C8#6711yescharacteristic
466C22⋊C8#6711yescharacteristic
467#97—61no—
468#97—121no—
469C4×C8—62no—
470C4×C8—61no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—41no—
476C23×C3—41no—
477C23×C3—42no—
478C23×C3—42no—
479C23×C3—81no—
480C23×C3C4×D411yescharacteristic
481C23×C3C4×D411yescharacteristic
482C23×C3C2×#4111yescharacteristic
483C22×D3—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—42no—
488C3×Q8C4×D412yes—
489C3×D4—22no—
490C3×D4—22no—
491C3×D4—21no—
492C3×D4—21no—
493C3×D4—21no—
494C3×D4—42no—
495C3×D4—42no—
496C3×D4—42no—
497C3×D4—41no—
498C3×D4—41no—
499C3×D4C4×D412yes—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—22no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—42no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4C4×D411yescharacteristic
520C2×C3×C4C4×D411yescharacteristic
521C2×C3×C4C23×C411yescharacteristic
522C2×C3×C4C22×D411yescharacteristic
523C2×C3×C4C22×D411yescharacteristic
524C2×C3×C4C2×#4111yescharacteristic
525C2×C3×C4H(5,𝔽2)11yescharacteristic
526C2×C3×C4H(5,𝔽2)11yescharacteristic
527#67—42no—
528#67—41no—
529#67—41no—
530#67—81no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—22no—
535C2×Dic3—41no—
536C2×Dic3—41no—
537C2×Dic3—41no—
538C2×Dic3—41no—
539C2×Dic3—41no—
540D12—21no—
541D12—21no—
542C4×D3—41no—
543C4×D3—41no—
544Dic6—21no—
545Dic6—21no—
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—21no—
555C3⋊C8—21no—
556C3⋊C8—22no—
557C3⋊C8—41no—
558C24—21no—
559C24#23511yescharacteristic
560#41—21no—
561#41—21no—
562#41—22no—
563#41—22no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—21no—
568#41—42no—
569#41—42no—
570#41—41no—
571#41—41no—
572#41—42no—
573#41—42no—
574#41—61no—
575#41—61no—
576#41—61no—
577#41—61no—
578#41D3×D412yes—
579#41#23712yes—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—31no—
583C2×Q8—41no—
584C2×Q8C2×C4×D311yescharacteristic
585C2×Q8C2×C4×D311yescharacteristic
586C2×D4—21no—
587C2×D4—22no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—31no—
593C2×D4—41no—
594C2×D4—42no—
595C2×D4—42no—
596C2×D4—61no—
597C2×D4—61no—
598C2×D4—61no—
599C2×D4C2×C4×D311yescharacteristic
600C2×D4C2×C4×D311yescharacteristic
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—42no—
611C22×C4—42no—
612C22×C4—61no—
613C22×C4—61no—
614C22×C4—61no—
615C22×C4C2×C4×D311yescharacteristic
616C22×C4C2×C4×D311yescharacteristic
617C22×C4#23511yescharacteristic
618C22×C4C2×#6711yescharacteristic
619C22×C4C2×#6711yescharacteristic
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—42no—
635M16—42no—
636M16—61no—
637M16—61no—
638M16—61no—
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—42no—
652C2×C8—42no—
653C2×C8—61no—
654C2×C8—61no—
655C2×C8—61no—
656C2×C8—61no—
657C2×C8—61no—
658C2×C8—61no—
659C2×C8—122no—
660C2×C8—122no—
661C2×C8C2×#6711yescharacteristic
662C2×C8C2×#6711yescharacteristic
663C2×C8C2×#6711yescharacteristic
664C2×C8C2×#6711yescharacteristic
665C4⋊C4—31no—
666C4⋊C4—31no—
667C4⋊C4—61no—
668C4⋊C4—61no—
669C4⋊C4—122no—
670C22⋊C4—61no—
671C22⋊C4—61no—
672C22⋊C4—61no—
673C22⋊C4—61no—
674C22⋊C4—61no—
675C22⋊C4—122no—
676C42—32no—
677C42—61no—
678C42—61no—
679C42—61no—
680C42—61no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—21no—
684C22×C3—21no—
685C22×C3—22no—
686C22×C3—21no—
687C22×C3—21no—
688C22×C3—21no—
689C22×C3—21no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—81no—
696C22×C3—81no—
697C22×C3—84no—
698C22×C3C2×C4×D411yescharacteristic
699C22×C3#54611yescharacteristic
700C22×C3#55111yescharacteristic
701C2×D3—41no—
702C2×D3—41no—
703C2×D3—41no—
704C3×C4—21no—
705C3×C4—21no—
706C3×C4—22no—
707C3×C4—41no—
708C3×C4C2×C4×D411yescharacteristic
709C3×C4#51811yescharacteristic
710C3×C4D4211yescharacteristic
711C3×C4#54611yescharacteristic
712Dic3—42no—
713Dic3—41no—
714Dic3—41no—
715Dic3—41no—
716Dic3—81no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—61no—
726C23—81no—
727C23C4×#6711yescharacteristic
728C23C4×#6711yescharacteristic
729C23C2×#23511yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734Q8—61no—
735Q8—61no—
736Q8#67⋊C412yes—
737D4—22no—
738D4—22no—
739D4—21no—
740D4—21no—
741D4—21no—
742D4—42no—
743D4—42no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—61no—
748D4—61no—
749D4—122no—
750D4—121no—
751D4—121no—
752D4—241no—
753D4#67⋊C412yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—62no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—121no—
778C2×C4—121no—
779C2×C4—121no—
780C2×C4—121no—
781C2×C4—121no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4C4×#6711yescharacteristic
785C2×C4C4×#6711yescharacteristic
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×#23711yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4#100411yescharacteristic
791C2×C4C22×#6711yescharacteristic
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—41no—
807C2×C3—41no—
808C2×C3—42no—
809C2×C3—81no—
810C2×C3#235811yescharacteristic
811C2×C3#295511yescharacteristic
812C2×C3#295711yescharacteristic
813D3—81no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—22no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—81no—
829C22—81no—
830C22—84no—
831C22—121no—
832C22—121no—
833C22—121no—
834C22#549011yescharacteristic
835C22#549511yescharacteristic
836C22C2×C4×#6711yescharacteristic
837C4—21no—
838C4—21no—
839C4—22no—
840C4—41no—
841C4—122no—
842C4—121no—
843C4—121no—
844C4—121no—
845C4—241no—
846C4C2×#67⋊C411yescharacteristic
847C4#548611yescharacteristic
848C4D4×#6711yescharacteristic
849C4#580611yescharacteristic
850C3#2288911yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—241no—
858C2#8209911yescharacteristic
859C2#8379211yescharacteristic
860C2#8381211yescharacteristic
subgroupG/H
centerC2×C4C22×#67
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#2880C2
socleC22×C3C2×C4×D4
prime radical#84080C2
cosocleC22×C3×C4C24
hypercenter#2880D3
hypocenterC3#22889
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
1. C3×#2880C2semidirect
3. C2×#5236C2semidirect
4. C2×#5144C2semidirect
5. #78596C2semidirect
6. #72017C2semidirect
7. #72010C2semidirect
8. #72009C2semidirect
9. #70011C2semidirect
10. #70000C2semidirect
11. #69997C2semidirect
12. #69996C2semidirect
13. #69984C2semidirect
14. #69966C2semidirect
15. #69907C2semidirect
25. C2×#901C22semidirect
34. #5239C4semidirect
35. #5239C4semidirect
36. #5238C4semidirect
37. #5238C4semidirect
45. #5228C4semidirect
46. #5227C4semidirect
47. #5218C4semidirect
48. #5217C4semidirect
51. C2×#825C22semidirect
52. C2×#825C22semidirect
53. C2×#822C22semidirect
54. C2×#822C22semidirect
55. #5110C22semidirect
56. #5102C22semidirect
57. #5101C22semidirect
58. C2×#815C22semidirect
59. C2×C8×Dic3C22semidirect
64. #4558C22semidirect
65. #4558C22semidirect
66. #4555C22semidirect
67. #4555C22semidirect
68. #4550C22semidirect
69. #4550C22semidirect
74. #2880D3semidirect
165. #837D4semidirect
850. C3#22889semidirect

Maximal subgroups

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

subgroupindex
C3×#28802
#840802
C2×#52362
C2×#51442
#785962
#720172
#720102
#720092
#700112
#700002
#699972
#699962
#699842
#699662
#699072
#228893