Finite Group Databasebeta

← #10815966

Subgroups — #10815966

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#82926C211yesmaximal, characteristic
2#82918C211yesmaximal, characteristic, complemented
3C2×#5005C211yesmaximal, characteristic, complemented
4C2×#4824C211yesmaximal, characteristic, complemented
5#78631C211yesmaximal, characteristic, complemented
6C3×#1897C211yesmaximal, characteristic, complemented
7#71582C211yesmaximal, characteristic, complemented
8#70390C211yesmaximal, characteristic, complemented
9#70377C211yesmaximal, characteristic, complemented
10#70374C211yesmaximal, characteristic, complemented
11#69984C211yesmaximal, characteristic, complemented
12#68774C211yesmaximal, characteristic, complemented
13#68745C211yesmaximal, characteristic, complemented
14#68744C211yesmaximal, characteristic, complemented
15#68740C211yesmaximal, characteristic, complemented
16#22889—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C3×#525C2211yescharacteristic
19C2×C3×#117C2211yescharacteristic
20C2×#950C2211yescharacteristic
21C2×#950C2211yescharacteristic
22C2×#948C2211yescharacteristic, complemented
23C22×#208C2211yescharacteristic
24C2×#907C2211yescharacteristic
25C2×#907C2211yescharacteristic
26C2×C3×#104C2211yescharacteristic, complemented
27C2×C3×#104C2211yescharacteristic, complemented
28C3×#407C2211yescharacteristic
29#5234C2211yescharacteristic, complemented
30C2×#830C2211yescharacteristic
31C2×#830C2211yescharacteristic
32#5129C2211yescharacteristic
33#5129C2211yescharacteristic
34C2×#822C2211yescharacteristic, complemented
35C2×#822C2211yescharacteristic, complemented
36#5050C411yescharacteristic, complemented
37#5047C411yescharacteristic, complemented
38#5047C411yescharacteristic, complemented
39#5046C411yescharacteristic, complemented
40#5040C411yescharacteristic, complemented
41#5037C411yescharacteristic, complemented
42#5037C411yescharacteristic, complemented
43#5036C411yescharacteristic, complemented
44#5012—21no—
45#5011—21no—
46#5011—21no—
47D4×C3⋊C8—21no—
48#5005—24no—
49#5002C2211yescharacteristic
50#5002C2211yescharacteristic
51#4999C2211yescharacteristic, complemented
52#4997C2211yescharacteristic, complemented
53C2×#805C2211yescharacteristic
54C2×#805C2211yescharacteristic
55C2×#805C2211yescharacteristic
56C2×#805C2211yescharacteristic
57C2×#803C2211yescharacteristic, complemented
58C2×C4×C3⋊C8C2211yescharacteristic, complemented
59#4824—24no—
60#4727—21no—
61#4727—21no—
62#4726—21no—
63D3×C22⋊C8—21no—
64C3×#339C2211yescharacteristic, complemented
65C3×#339C2211yescharacteristic, complemented
66#4558C2211yescharacteristic, complemented
67#4558C2211yescharacteristic, complemented
68#4524C2211yescharacteristic, complemented
69#4524C2211yescharacteristic, 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#1897D311yescharacteristic, complemented
79#1876—31no—
80#1876—31no—
81#1866—31no—
82#1855—31no—
83#1765—31no—
84#1750—31no—
85C2×C3×#41C2311yescharacteristic
86C23×C3×C4C2311yescharacteristic
87C22×#67—21no—
88C2×#235—21no—
89C2×#235—21no—
90C2×#235—22no—
91C2×#235—22no—
92C2×#235—41no—
93C2×#235—41no—
94C2×#235C2×C411yescharacteristic
95C2×#235C2×C411yescharacteristic
96C2×#235C2311yescharacteristic
97C2×#235C2311yescharacteristic
98C22×D12C2×C411yescharacteristic
99C22×C4×D3—21no—
100C22×Dic6C2×C411yescharacteristic
101C2×C3×M16C2311yescharacteristic
102C2×C3×M16C2311yescharacteristic
103C3×#123—21no—
104C3×C22⋊Q8C2×C411yescharacteristic
105C3×C22⋊Q8C2×C411yescharacteristic
106C3×#121C2×C411yescharacteristic
107C3×#121C2×C411yescharacteristic
108C3×#120—21no—
109C3×C4×D4—21no—
110C3×C4×D4—21no—
111C3×#117—22no—
112C3×#117—41no—
113C3×#117C2311yescharacteristic
114C2×C3×C4⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C42C2311yescharacteristic
117C2×C3×C42C2311yescharacteristic
118#950—22no—
119#950—22no—
120#950—41no—
121#950—41no—
122#948—22no—
123#948—41no—
124C2×#216C2×C411yescharacteristic
125C2×#216C2×C411yescharacteristic
126C2×#215C2×C411yescharacteristic
127C2×#215C2×C411yescharacteristic
128C2×#214C2×C411yescharacteristic
129C2×#214C2×C411yescharacteristic
130C2×#213C2×C411yescharacteristic
131C2×#213C2×C411yescharacteristic
132C2×#208—21no—
133C2×#208—21no—
134C2×#208—22no—
135C2×#208—41no—
136C2×#208C2311yescharacteristic
137C2×#208C2311yescharacteristic
138C22×C3⋊C8—21no—
139C22×C3⋊C8—21no—
140C22×C3⋊C8C2311yescharacteristic
141C22×C3⋊C8C2311yescharacteristic
142C22×C3⋊C8C2311yescharacteristic
143C22×C3⋊C8C2311yescharacteristic
144#907—22no—
145#907—22no—
146#907—41no—
147#907—41no—
148C2×ΓL(1,𝔽25)—21no—
149C2×ΓL(1,𝔽25)—21no—
150C2×D3×C8—21no—
151C2×D3×C8—21no—
152C3×#104—22no—
153C3×#104—41no—
154C3×C22⋊C8—21no—
155C3×C22⋊C8—21no—
156#830—21no—
157#830—21no—
158#830C2×C411yescharacteristic
159#830C2×C411yescharacteristic
160#830C2×C411yescharacteristic
161#830C2×C411yescharacteristic
162#830D411yescharacteristic
163#830D411yescharacteristic
164#830D411yescharacteristic
165#830D411yescharacteristic
166#822—22no—
167#822—41no—
168(C2×D3)⋊C8—21no—
169(C2×D3)⋊C8—21no—
170(C2×D3)⋊C8—21no—
171(C2×D3)⋊C8—21no—
172#810C2×C411yescharacteristic
173#810C2×C411yescharacteristic
174#810C2×C411yescharacteristic
175#810C2×C411yescharacteristic
176#809C2×C411yescharacteristic
177#809C2×C411yescharacteristic
178#809C2×C411yescharacteristic
179#809C2×C411yescharacteristic
180#805—22no—
181#805—22no—
182#805—22no—
183#805D414yescomplemented
184C4⋊(C3⋊C8)—21no—
185C4⋊(C3⋊C8)—21no—
186#803—21no—
187#803—41no—
188C4×C3⋊C8—22no—
189C4×C3⋊C8—21no—
190C22×#41—31no—
191C2×#135—31no—
192C2×#135—31no—
193C2×#131—31no—
194C2×#131—31no—
195C2×#131—31no—
196C22×M16—31no—
197#525C2×D311yescharacteristic
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#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×#104C2×D311yescharacteristic, complemented
221C2×#104C2×D311yescharacteristic, complemented
222#416—31no—
223#416—31no—
224#408—31no—
225#408—31no—
226#408—31no—
227#408—61no—
228#408—61no—
229#407—61no—
230#407C2×D311yescharacteristic
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#339C2×D311yescharacteristic, complemented
240#339C2×D311yescharacteristic, complemented
241#336—31no—
242#336—31no—
243C24×C3#4111yescharacteristic
244C23×D3—21no—
245C3×#41—21no—
246C3×#41—21no—
247C3×#41—21no—
248C3×#41—21no—
249C2×C3×Q8C22×C411yescharacteristic
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4C22×C411yescharacteristic
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4C22×C411yescharacteristic
262C22×C3×C4C22×C411yescharacteristic
263C22×C3×C4C2×D411yescharacteristic
264C22×C3×C4C2×D411yescharacteristic
265C22×C3×C4#4111yescharacteristic
266C22×C3×C4C2411yescharacteristic
267C2×#67—21no—
268C2×#67—21no—
269C2×#67—21no—
270C2×#67—21no—
271C2×#67—42no—
272C2×#67—42no—
273C22×Dic3—21no—
274#235—21no—
275#235—21no—
276#235—21no—
277#235—21no—
278#235—21no—
279#235—21no—
280#235—22no—
281#235—22no—
282#235—41no—
283#235—41no—
284#235—42no—
285#235—42no—
286#235—42no—
287#235—42no—
288#235C2×D412yes—
289#235#4112yes—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—41no—
293C2×D12C22×C411yescharacteristic
294C2×D12C22×C411yescharacteristic
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—21no—
298C2×C4×D3—21no—
299C2×C4×D3—42no—
300C2×C4×D3—42no—
301C2×Dic6—22no—
302C2×Dic6—21no—
303C2×Dic6—41no—
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—
312C3×C4⋊C4—21no—
313C3×C4⋊C4—21no—
314C3×C4⋊C4—42no—
315C3×C4⋊C4C22×C411yescharacteristic
316C3×C4⋊C4C22×C411yescharacteristic
317C3×C22⋊C4—21no—
318C3×C22⋊C4—21no—
319C3×C22⋊C4—21no—
320C3×C22⋊C4—21no—
321C3×C22⋊C4—21no—
322C3×C22⋊C4—42no—
323C3×C42—21no—
324C3×C42—21no—
325C3×C42—21no—
326C3×C42—21no—
327C3×C42C2×D412yes—
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#208—21no—
337#208—21no—
338#208—21no—
339#208—42no—
340#208—42no—
341#208C2×D412yes—
342C2×C3⋊C8—21no—
343C2×C3⋊C8—21no—
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—42no—
353C2×C3⋊C8—42no—
354C2×C3⋊C8C22×C411yescharacteristic
355C2×C3⋊C8C22×C411yescharacteristic
356C2×C3⋊C8C22×C411yescharacteristic
357C2×C3⋊C8C22×C411yescharacteristic
358C2×C3⋊C8C2×D411yescharacteristic
359C2×C3⋊C8C2×D411yescharacteristic
360C2×C3⋊C8C2×D411yescharacteristic
361C2×C3⋊C8C2×D411yescharacteristic
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—62no—
371C2×#41—62no—
372C2×#41—61no—
373C2×#41—61no—
374C2×#41—121no—
375C2×#41—121no—
376C2×#41C22×D311yescharacteristic
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—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—31no—
413C22×C8—31no—
414C22×C8—61no—
415C22×C8—61no—
416C22×C8—61no—
417C22×C8—61no—
418#123—21no—
419C22⋊Q8C4×D311yescharacteristic
420C22⋊Q8C4×D311yescharacteristic
421#121C4×D311yescharacteristic
422#121C4×D311yescharacteristic
423#120—21no—
424C4×D4—21no—
425C4×D4—21no—
426#117—22no—
427#117—41no—
428#117C22×D311yescharacteristic
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—34no—
439#104—41no—
440#104—62no—
441#104—62no—
442#104—62no—
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—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—61no—
468#97—121no—
469C4×C8—61no—
470C4×C8—62no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—41no—
475C23×C3—41no—
476C23×C3C4×D411yescharacteristic
477C23×C3C4×D411yescharacteristic
478C23×C3C2×#4111yescharacteristic
479C22×D3—21no—
480C22×D3—21no—
481C22×D3—42no—
482C22×D3—42no—
483C22×D3—81no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×D4—21no—
487C3×D4—21no—
488C3×D4—42no—
489C3×D4—41no—
490C3×D4—41no—
491C3×D4—81no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—22no—
506C2×C3×C4—41no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4C4×D411yescharacteristic
514C2×C3×C4C4×D411yescharacteristic
515C2×C3×C4C23×C411yescharacteristic
516C2×C3×C4C22×D411yescharacteristic
517C2×C3×C4C22×D411yescharacteristic
518C2×C3×C4C2×#4111yescharacteristic
519C2×C3×C4H(5,𝔽2)11yescharacteristic
520C2×C3×C4H(5,𝔽2)11yescharacteristic
521#67—22no—
522#67—22no—
523#67—42no—
524#67—42no—
525#67—41no—
526#67—41no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—42no—
530D12—21no—
531D12—21no—
532D12—21no—
533D12—42no—
534D12C4×D412yes—
535C4×D3—22no—
536C4×D3—22no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—41no—
540C4×D3—41no—
541Dic6—21no—
542Dic6—21no—
543Dic6—21no—
544Dic6—42no—
545Dic6C4×D412yes—
546C3×C8—41no—
547C3×C8—41no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—21no—
551C3⋊C8—21no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—22no—
555C3⋊C8—21no—
556C3⋊C8—21no—
557C3⋊C8—41no—
558C24—61no—
559C24#23711yescharacteristic
560#41—21no—
561#41—21no—
562#41—21no—
563#41—21no—
564#41—32no—
565#41—32no—
566#41—62no—
567#41—62no—
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—62no—
583C2×Q8—61no—
584C2×Q8—121no—
585C2×Q8C2×C4×D311yescharacteristic
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—62no—
592C2×D4—61no—
593C2×D4—61no—
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—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
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×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—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—31no—
644C2×C8—31no—
645C2×C8—31no—
646C2×C8—31no—
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—61no—
658C2×C8—61no—
659C2×C8—61no—
660C2×C8—61no—
661C2×C8—122no—
662C2×C8—122no—
663C2×C8—122no—
664C2×C8—122no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—42no—
668C4⋊C4C2×C4×D311yescharacteristic
669C4⋊C4C2×C4×D311yescharacteristic
670C22⋊C4—21no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—42no—
676C42—21no—
677C42—21no—
678C42—21no—
679C42—21no—
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—41no—
690C22×C3—41no—
691C22×C3—41no—
692C22×C3—81no—
693C22×C3—81no—
694C22×C3C2×C4×D411yescharacteristic
695C22×C3#54611yescharacteristic
696C22×C3#55111yescharacteristic
697C2×D3—22no—
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—41no—
708C3×C4—41no—
709C3×C4—41no—
710C3×C4—81no—
711C3×C4C2×C4×D411yescharacteristic
712C3×C4#51811yescharacteristic
713C3×C4D4211yescharacteristic
714C3×C4#54611yescharacteristic
715Dic3—22no—
716Dic3—41no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—41no—
721C23—41no—
722C23—61no—
723C23—61no—
724C23—122no—
725C23—122no—
726C23—241no—
727C23#67⋊C411yescharacteristic
728C23#67⋊C411yescharacteristic
729C23C2×#23711yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—32no—
733Q8—61no—
734Q8—61no—
735Q8—61no—
736Q8—122no—
737D4—21no—
738D4—21no—
739D4—32no—
740D4—42no—
741D4—41no—
742D4—41no—
743D4—62no—
744D4—62no—
745D4—61no—
746D4—61no—
747D4—61no—
748D4—81no—
749D4—122no—
750D4—122no—
751D4—122no—
752D4—121no—
753D4—121no—
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—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—22no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—61no—
776C2×C4—62no—
777C2×C4—62no—
778C2×C4—61no—
779C2×C4—122no—
780C2×C4—122no—
781C2×C4—122no—
782C2×C4—121no—
783C2×C4—121no—
784C2×C4#67⋊C411yescharacteristic
785C2×C4#67⋊C411yescharacteristic
786C2×C4C22×C4×D311yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4#100411yescharacteristic
790C2×C4D3×#4111yescharacteristic
791C2×C4#100911yescharacteristic
792C8—41no—
793C8—41no—
794C8—61no—
795C8—61no—
796C8—61no—
797C8—61no—
798C8—61no—
799C8—61no—
800C8—62no—
801C8—61no—
802C8—61no—
803C8—121no—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—41no—
807C2×C3—41no—
808C2×C3—81no—
809C2×C3#235811yescharacteristic
810C2×C3#295511yescharacteristic
811C2×C3#295711yescharacteristic
812D3—42no—
813D3—81no—
814C22—21no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—62no—
826C22—81no—
827C22—81no—
828C22—121no—
829C22—121no—
830C22—121no—
831C22—121no—
832C22—121no—
833C22—244no—
834C22C2×#67⋊C411yescharacteristic
835C22#559111yescharacteristic
836C22#565811yescharacteristic
837C4—21no—
838C4—21no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—62no—
844C4—81no—
845C4—121no—
846C4C4×D3×D411yescharacteristic
847C4#554511yescharacteristic
848C4#560911yescharacteristic
849C4#561011yescharacteristic
850C3#2288911yescharacteristic, complemented, Sylow
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—81no—
856C2—122no—
857C2—241no—
858C2#7487911yescharacteristic
859C2#7898911yescharacteristic
860C2#7899011yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1897C2
socleC22×C3C2×C4×D4
prime radical#82926C2
cosocleC22×C3×C4C24
hypercenter#1897D3
hypocenterC3#22889
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1897

Complements

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

NH ≅ G/Ntype
2. #82918C2semidirect
3. C2×#5005C2semidirect
4. C2×#4824C2semidirect
5. #78631C2semidirect
6. C3×#1897C2semidirect
7. #71582C2semidirect
8. #70390C2semidirect
9. #70377C2semidirect
10. #70374C2semidirect
11. #69984C2semidirect
12. #68774C2semidirect
13. #68745C2semidirect
14. #68744C2semidirect
15. #68740C2semidirect
22. C2×#948C22semidirect
26. C2×C3×#104C22semidirect
27. C2×C3×#104C22semidirect
29. #5234C22semidirect
34. C2×#822C22semidirect
35. C2×#822C22semidirect
36. #5050C4semidirect
37. #5047C4semidirect
38. #5047C4semidirect
39. #5046C4semidirect
40. #5040C4semidirect
41. #5037C4semidirect
42. #5037C4semidirect
43. #5036C4semidirect
51. #4999C22semidirect
52. #4997C22semidirect
57. C2×#803C22semidirect
58. C2×C4×C3⋊C8C22semidirect
64. C3×#339C22semidirect
65. C3×#339C22semidirect
66. #4558C22semidirect
67. #4558C22semidirect
68. #4524C22semidirect
69. #4524C22semidirect
78. #1897D3semidirect
183. #805D4semidirect
220. C2×#104C2×D3semidirect
221. C2×#104C2×D3semidirect
239. #339C2×D3semidirect
240. #339C2×D3semidirect
850. C3#22889semidirect

Maximal subgroups

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

subgroupindex
#829262
#829182
C2×#50052
C2×#48242
#786312
C3×#18972
#715822
#703902
#703772
#703742
#699842
#687742
#687452
#687442
#687402
#228893