Finite Group Databasebeta

← #10815939

Subgroups — #10815939

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×C3×#421C211yesmaximal, characteristic, complemented
2#84080C211yesmaximal, characteristic
3#84075C211yesmaximal, characteristic, complemented
4#83757C211yesmaximal, characteristic, complemented
5C2×#4823C211yesmaximal, characteristic, complemented
6#72001C211yesmaximal, characteristic, complemented
7#71591C211yesmaximal, characteristic, complemented
8#71582C211yesmaximal, characteristic, complemented
9#70390C211yesmaximal, characteristic, complemented
10#70377C211yesmaximal, characteristic, complemented
11#70376C211yesmaximal, characteristic, complemented
12#70373C211yesmaximal, characteristic, complemented
13#70372C211yesmaximal, characteristic, complemented
14#70369C211yesmaximal, characteristic, complemented
15#70367C211yesmaximal, characteristic, complemented
16#22887—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×C3×M16C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C2×#950C2211yescharacteristic
21C2×#950C2211yescharacteristic
22C2×#948C2211yescharacteristic
23C2×#948C2211yescharacteristic
24#5791C2211yescharacteristic
25C2×#907C2211yescharacteristic, complemented
26C3×#421—24no—
27C2×C3×#104C2211yescharacteristic
28C2×C3×#104C2211yescharacteristic
29C2×C3×#104C2211yescharacteristic
30C2×C3×#104C2211yescharacteristic
31#5239C411yescharacteristic, complemented
32#5239C411yescharacteristic, complemented
33#5238C411yescharacteristic, complemented
34#5238C411yescharacteristic, complemented
35#5234—21no—
36#5234—21no—
37#5234C2211yescharacteristic
38#5234C2211yescharacteristic
39#5233C2211yescharacteristic
40#5233C2211yescharacteristic
41#5228C411yescharacteristic, complemented
42#5227C411yescharacteristic, complemented
43#5218C411yescharacteristic, complemented
44#5217C411yescharacteristic, complemented
45#5207—21no—
46#5207C2211yescharacteristic
47C2×#830—21no—
48C2×#830C2211yescharacteristic
49C2×#830C2211yescharacteristic
50#5129C2211yescharacteristic, complemented
51#5128—21no—
52#5127—21no—
53C2×#822C2211yescharacteristic, complemented
54C2×#822C2211yescharacteristic, complemented
55#5122C2211yescharacteristic, complemented
56#5119C2211yescharacteristic, complemented
57#5111—21no—
58C8×#67—21no—
59C2×#805C2211yescharacteristic, complemented
60C2×#805C2211yescharacteristic, complemented
61C2×#803C2211yescharacteristic, complemented
62C2×C4×C3⋊C8C2211yescharacteristic, complemented
63#4823—24no—
64#4558C2211yescharacteristic, complemented
65#4558C2211yescharacteristic, complemented
66#4524C2211yescharacteristic, complemented
67#4524C2211yescharacteristic, complemented
68#4523C2211yescharacteristic, complemented
69#4523C2211yescharacteristic, complemented
70#3002—31no—
71C2×#444—31no—
72#2933—31no—
73C2×#421D311yescharacteristic, complemented
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#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
101C2×C3×M16—21no—
102C2×C3×M16—22no—
103C2×C3×M16—41no—
104C2×C3×M16C2311yescharacteristic
105C2×C3×M16C2311yescharacteristic
106C22×C3×C8—21no—
107C3×#117—22no—
108C3×#117—41no—
109C2×C3×C4⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C42C2311yescharacteristic
112C2×C3×C42C2311yescharacteristic
113#953—21no—
114#950—22no—
115#950—22no—
116#950—41no—
117#950—41no—
118#948—22no—
119#948—22no—
120#948—41no—
121#948—41no—
122C2×#216C2×C411yescharacteristic
123C2×#216C2×C411yescharacteristic
124C2×#215C2×C411yescharacteristic
125C2×#215C2×C411yescharacteristic
126C2×#214C2×C411yescharacteristic
127C2×#214C2×C411yescharacteristic
128C2×#213C2×C411yescharacteristic
129C2×#213C2×C411yescharacteristic
130#930C2×C411yescharacteristic
131#930C2×C411yescharacteristic
132#929—21no—
133C4×#67—21no—
134C4×#67—21no—
135#926C2311yescharacteristic
136#924C2×C411yescharacteristic
137#924C2×C411yescharacteristic
138C2×#208—21no—
139C2×#208—21no—
140C2×#208C2311yescharacteristic
141C2×#208C2311yescharacteristic
142C22×C3⋊C8—21no—
143C22×C3⋊C8—21no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148#907—22no—
149#907—41no—
150C2×ΓL(1,𝔽25)—21no—
151C2×D3×C8—21no—
152C3×#104—22no—
153C3×#104—22no—
154C3×#104—22no—
155C3×#104D414yescomplemented
156#835C2×C411yescharacteristic
157#835C2×C411yescharacteristic
158#835C2×C411yescharacteristic
159#835C2×C411yescharacteristic
160#832C2×C411yescharacteristic
161#832C2×C411yescharacteristic
162#832C2×C411yescharacteristic
163#832C2×C411yescharacteristic
164#830—21no—
165#830—21no—
166#830—21no—
167#830—21no—
168#830—21no—
169#830—21no—
170#830C2×C411yescharacteristic
171#830C2×C411yescharacteristic
172#830C2×C411yescharacteristic
173#830C2×C411yescharacteristic
174#830D411yescharacteristic
175#830D411yescharacteristic
176#830D411yescharacteristic
177#830D411yescharacteristic
178#822—22no—
179#822—41no—
180(C2×D3)⋊C8—21no—
181(C2×D3)⋊C8—21no—
182#815—21no—
183Dic3⋊C8—21no—
184Dic3⋊C8—21no—
185C8×Dic3—21no—
186#805—22no—
187#805—41no—
188#803—22no—
189C4×C3⋊C8—41no—
190C22×#41C2×D311yescharacteristic
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131—31no—
196C22×M16C2×D311yescharacteristic
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—24no—
216C2×#104—31no—
217C2×#104—31no—
218C2×#104C2×D311yescharacteristic
219C2×#104C2×D311yescharacteristic
220C2×#104C2×D311yescharacteristic
221C2×#104C2×D311yescharacteristic
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—31no—
232C2×C22⋊C8—31no—
233C2×C22⋊C8—61no—
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—21no—
287C22×C3×C4—21no—
288C22×C3×C4—42no—
289C22×C3×C4—42no—
290C22×C3×C4C22×C411yescharacteristic
291C22×C3×C4C22×C411yescharacteristic
292C22×C3×C4C2×D411yescharacteristic
293C22×C3×C4C2×D411yescharacteristic
294C22×C3×C4#4111yescharacteristic
295C22×C3×C4C2411yescharacteristic
296C2×#67—21no—
297C2×#67—21no—
298C2×#67—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—42no—
310C3×M16C2×D412yes—
311C2×C3×C8—21no—
312C2×C3×C8—21no—
313C2×C3×C8—42no—
314C3×C4⋊C4—42no—
315C3×C22⋊C4—42no—
316C3×C42—21no—
317C3×C42—21no—
318C3×C42—21no—
319C3×C42C2×D412yes—
320#217—21no—
321#217—21no—
322#217—21no—
323#216—22no—
324#216—41no—
325#215—22no—
326#215—41no—
327#214—22no—
328#214—41no—
329#213—22no—
330#213—41no—
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—42no—
343#208—42no—
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⋊C8—21no—
351C2×C3⋊C8—21no—
352C2×C3⋊C8—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—42no—
355C2×C3⋊C8—42no—
356C2×C3⋊C8C22×C411yescharacteristic
357C2×C3⋊C8C22×C411yescharacteristic
358C2×C3⋊C8C22×C411yescharacteristic
359C2×C3⋊C8C22×C411yescharacteristic
360C2×C3⋊C8C2×D411yescharacteristic
361C2×C3⋊C8C2×D411yescharacteristic
362C2×C3⋊C8C2×D411yescharacteristic
363C2×C3⋊C8C2×D411yescharacteristic
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—62no—
395#131—62no—
396#131—62no—
397#131—121no—
398#131—121no—
399#131—121no—
400C2×M16—21no—
401C2×M16—22no—
402C2×M16—31no—
403C2×M16—31no—
404C2×M16—41no—
405C2×M16—61no—
406C2×M16—61no—
407C2×M16—61no—
408C2×M16C22×D311yescharacteristic
409C2×M16C22×D311yescharacteristic
410C22×C8—21no—
411C22×C8—31no—
412C22×C8—31no—
413C22×C8—31no—
414C22×C8—31no—
415C22×C8—61no—
416C22×C8—61no—
417C22×C8—61no—
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—22no—
438#104—22no—
439#104—22no—
440#104—62no—
441#104—121no—
442#104#6714yescomplemented
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—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—61no—
468#97—62no—
469C4×C8—61no—
470C4×C8—121no—
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—22no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—22no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—22no—
515C2×C3×C4—42no—
516C2×C3×C4—42no—
517C2×C3×C4—42no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4C4×D411yescharacteristic
526C2×C3×C4C4×D411yescharacteristic
527C2×C3×C4C23×C411yescharacteristic
528C2×C3×C4C22×D411yescharacteristic
529C2×C3×C4C22×D411yescharacteristic
530C2×C3×C4C2×#4111yescharacteristic
531C2×C3×C4H(5,𝔽2)11yescharacteristic
532C2×C3×C4H(5,𝔽2)11yescharacteristic
533#67—42no—
534#67—41no—
535#67—41no—
536#67—81no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540D12—21no—
541D12—21no—
542C4×D3—41no—
543C4×D3—41no—
544Dic6—21no—
545Dic6—21no—
546C3×C8—22no—
547C3×C8—41no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—21no—
555C3⋊C8—21no—
556C3⋊C8—41no—
557C3⋊C8—41no—
558C24—21no—
559C24#23711yescharacteristic
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#41#23512yes—
579#41C2×#6712yes—
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—21no—
611C22×C4—21no—
612C22×C4—42no—
613C22×C4—42no—
614C22×C4—61no—
615C22×C4C2×C4×D311yescharacteristic
616C22×C4C2×C4×D311yescharacteristic
617C22×C4D3×D411yescharacteristic
618C22×C4D3×D411yescharacteristic
619C22×C4#23711yescharacteristic
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×#6712yes—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—31no—
644C2×C8—31no—
645C2×C8—31no—
646C2×C8—31no—
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—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—61no—
662C2×C8—122no—
663C2×C8—122no—
664C2×C8—122no—
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—
680C42C2×#6712yes—
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—42no—
708C3×C4—41no—
709C3×C4—81no—
710C3×C4C2×C4×D411yescharacteristic
711C3×C4#51811yescharacteristic
712C3×C4D4211yescharacteristic
713C3×C4#54611yescharacteristic
714Dic3—41no—
715Dic3—41no—
716Dic3—41no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—41no—
722C23—41no—
723C23—42no—
724C23—42no—
725C23—61no—
726C23—81no—
727C23#67⋊C411yescharacteristic
728C23#67⋊C411yescharacteristic
729C23C2×#23711yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—21no—
733Q8—42no—
734Q8—61no—
735Q8—61no—
736Q8C4×#6712yes—
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—
753D4C4×#6712yes—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4#67⋊C411yescharacteristic
785C2×C4#67⋊C411yescharacteristic
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×#23511yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4#100411yescharacteristic
791C2×C4C22×#6711yescharacteristic
792C8—22no—
793C8—41no—
794C8—61no—
795C8—61no—
796C8—61no—
797C8—61no—
798C8—61no—
799C8—61no—
800C8—61no—
801C8—61no—
802C8—121no—
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—
834C22C2×#67⋊C411yescharacteristic
835C22#549511yescharacteristic
836C22#580611yescharacteristic
837C4—21no—
838C4—21no—
839C4—22no—
840C4—42no—
841C4—41no—
842C4—81no—
843C4—121no—
844C4—121no—
845C4—121no—
846C4#548611yescharacteristic
847C4#549011yescharacteristic
848C4C2×C4×#6711yescharacteristic
849C4D4×#6711yescharacteristic
850C3#2288711yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—241no—
858C2#7898911yescharacteristic
859C2#7899011yescharacteristic
860C2#8209911yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC2×C3×#421C2
socleC22×C3C2×C4×D4
prime radical#84080C2
cosocleC22×C3×C4C24
hypercenterC2×#421D3
hypocenterC3#22887
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×C3×#421C2semidirect
3. #84075C2semidirect
4. #83757C2semidirect
5. C2×#4823C2semidirect
6. #72001C2semidirect
7. #71591C2semidirect
8. #71582C2semidirect
9. #70390C2semidirect
10. #70377C2semidirect
11. #70376C2semidirect
12. #70373C2semidirect
13. #70372C2semidirect
14. #70369C2semidirect
15. #70367C2semidirect
25. C2×#907C22semidirect
31. #5239C4semidirect
32. #5239C4semidirect
33. #5238C4semidirect
34. #5238C4semidirect
41. #5228C4semidirect
42. #5227C4semidirect
43. #5218C4semidirect
44. #5217C4semidirect
50. #5129C22semidirect
53. C2×#822C22semidirect
54. C2×#822C22semidirect
55. #5122C22semidirect
56. #5119C22semidirect
59. C2×#805C22semidirect
60. C2×#805C22semidirect
61. C2×#803C22semidirect
62. C2×C4×C3⋊C8C22semidirect
64. #4558C22semidirect
65. #4558C22semidirect
66. #4524C22semidirect
67. #4524C22semidirect
68. #4523C22semidirect
69. #4523C22semidirect
73. C2×#421D3semidirect
155. C3×#104D4semidirect
442. #104#67semidirect
850. C3#22887semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#4212
#840802
#840752
#837572
C2×#48232
#720012
#715912
#715822
#703902
#703772
#703762
#703732
#703722
#703692
#703672
#228873