Finite Group Databasebeta

← #11869696

Subgroups — #11869696

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595023C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3#10592812C211yesmaximal, characteristic, complemented
4C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
5C3×#5106C211yesmaximal, characteristic, complemented
6#10591122C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590709C211yesmaximal, characteristic, complemented
9#10590708C211yesmaximal, characteristic, complemented
10#10590705C211yesmaximal, characteristic, complemented
11#10590704C211yesmaximal, characteristic, complemented
12#10590684C211yesmaximal, characteristic, complemented
13#10590679C211yesmaximal, characteristic, complemented
14#10590677C211yesmaximal, characteristic, complemented
15#10590674C211yesmaximal, characteristic, complemented
16#79185—31nomaximal
17#78591—31nomaximal
18C2×#3828C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C22×C3×C3⋊C8C2211yescharacteristic
25#63977—21no—
26D3×#217—21no—
27#63966—21no—
28#63955—21no—
29#63909C2211yescharacteristic
30#63909C2211yescharacteristic
31C4×#626—21no—
32C4×#626—21no—
33D3×C4⋊Dic3C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35C4×D3×Dic3—21no—
36#63857C2211yescharacteristic
37#63857C2211yescharacteristic
38#63855—21no—
39#63841C2211yescharacteristic
40#63841C2211yescharacteristic
41#63648C2211yescharacteristic, complemented
42#63648C2211yescharacteristic, complemented
43#63643C2211yescharacteristic, complemented
44#63643C2211yescharacteristic, complemented
45C3×(C2×D3)⋊C8C2211yescharacteristic
46C3×(C2×D3)⋊C8C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic
48C3×(C2×D3)⋊C8C2211yescharacteristic
49C3×#818C2211yescharacteristic, complemented
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53#63575C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#5791—31no—
62C2×#926—31no—
63#5524—31no—
64D3×#117—31no—
65C3×#427—31no—
66C2×C3×C22⋊C8—31no—
67#5113—31no—
68#5113—31no—
69#5113—31no—
70#5113—61no—
71C2×(C2×D3)⋊C8D311yescharacteristic, complemented
72#5106—31no—
73#5106D311yescharacteristic, complemented
74#5002—31no—
75#4998—31no—
76#4888—31no—
77#4885—31no—
78#4884—31no—
79#4882—31no—
80#4868—31no—
81#4866—31no—
82#4863—31no—
83#4862—31no—
84#4737—31no—
85#4737—31no—
86#4736—31no—
87#4735—31no—
88#4723—31no—
89#4723—31no—
90#4722—31no—
91#4721—31no—
92C23×C3×D3D411yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—22no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C22×C3×Dic3D411yescharacteristic
101C2×C3×C4×D3—22no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3D411yescharacteristic
104C2×C3×C4×D3D411yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×C4×D3C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×C32×C8—22no—
112C2×C32×C8C2311yescharacteristic
113C2×C32×C8C2311yescharacteristic
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4×Dic3—21no—
125C3×C4×Dic3—21no—
126C2×C3×C3⋊C8—22no—
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139Dic32—21no—
140Dic32—21no—
141#3091—91noSylow
142C23×C3×C4—31no—
143C2×#235—31no—
144C2×#235—31no—
145C2×#235—61no—
146C22×C4×D3C2×D311yescharacteristic
147C22×C3×C8—21no—
148C22×C3×C8—31no—
149C22×C3×C8C2×D311yescharacteristic
150C22×C3×C8C2×D311yescharacteristic
151C3×#117—31no—
152C3×#117—31no—
153#953—61no—
154C2×#217—61no—
155#930—31no—
156#930—31no—
157#929—61no—
158C4×#67—61no—
159C4×#67—61no—
160#926—31no—
161#926—31no—
162#926—31no—
163#926—31no—
164#926—61no—
165#926—61no—
166#926—61no—
167#926C2×D311yescharacteristic
168#926C2×D311yescharacteristic
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171#924—31no—
172#924—31no—
173C2×C4×Dic3—61no—
174C22×C3⋊C8C2×D311yescharacteristic
175#897—31no—
176#897—31no—
177#895—31no—
178#895—31no—
179#892—31no—
180#892—31no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183#886—61no—
184#882—61no—
185D3×C22⋊C4—61no—
186#877—61no—
187C4×D12—61no—
188C4×D12—61no—
189#872—61no—
190C42×D3—61no—
191C3×#107—31no—
192C3×#107—31no—
193C3×#106—31no—
194C3×#106—31no—
195C3×C22⋊C8—31no—
196C3×C22⋊C8—31no—
197C3×C22⋊C8—31no—
198C3×C22⋊C8—31no—
199#821—31no—
200#821—31no—
201#821—31no—
202#821—31no—
203#821—31no—
204#821—31no—
205#821—61no—
206#821—61no—
207(C2×D3)⋊C8C2×D311yescharacteristic
208(C2×D3)⋊C8C2×D311yescharacteristic
209(C2×D3)⋊C8C2×D311yescharacteristic
210(C2×D3)⋊C8C2×D311yescharacteristic
211#818—31no—
212#818—31no—
213#818C2×D311yescharacteristic, complemented
214#818C2×D311yescharacteristic, complemented
215#817—31no—
216#817—31no—
217#817C2×D311yescharacteristic, complemented
218#817C2×D311yescharacteristic, complemented
219#816—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816—61no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—22no—
238C22×C3×D3—22no—
239C22×C3×D3—41no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×C32×C4C2×D411yescharacteristic
243C2×C32×C4#4112yes—
244C2×C32×C4#4112yes—
245C2×C32×C4C2411yescharacteristic
246#638—42no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4×C3⋊D3—42no—
253#634—21no—
254#634—21no—
255C2×C3×Dic3—22no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×C4×D3—22no—
263C3×C4×D3—22no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268#626—42no—
269#626—42no—
270D3×Dic3—42no—
271D3×Dic3—42no—
272C32×C8—21no—
273C32×C8—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#525—91no—
277C2×#117—91no—
278#485—91no—
279#485—91no—
280#484—91no—
281#483—91no—
282#482—91no—
283#482—91no—
284#481—91no—
285#480—91no—
286#427—31no—
287#427—91no—
288#416—91no—
289#416—91no—
290C2×C22⋊C8—31no—
291C24×C3—31no—
292C23×D3D1211yescharacteristic
293C22×C3×C4—21no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—62no—
300C22×C3×C4—62no—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—121no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3D1211yescharacteristic
311#235—64no—
312#235—62no—
313#235—62no—
314#235—62no—
315#235—62no—
316#235—122no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—61no—
320C2×D12—61no—
321C2×D12—61no—
322C2×C4×D3—22no—
323C2×C4×D3—22no—
324C2×C4×D3—61no—
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—121no—
329C2×C4×D3D1211yescharacteristic
330C2×C4×D3D1211yescharacteristic
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—31no—
334C2×Dic6—31no—
335C2×Dic6—61no—
336C2×C3×C8—22no—
337C2×C3×C8—22no—
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—42no—
343C2×C3×C8—62no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C42—61no—
355C3×C42—61no—
356#217—21no—
357#217—21no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—121no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
400C2×C3⋊C8—22no—
401C2×C3⋊C8C22×D311yescharacteristic
402C2×C3⋊C8C22×D311yescharacteristic
403C22×C32—21no—
404C22×C32—21no—
405C22×C32#12312yes—
406C22×C32C22×D411yescharacteristic
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3⋊D3—41no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—44no—
416C2×C3×D3#13512yes—
417C32×C4#12312yes—
418C32×C4C2×#4111yescharacteristic
419C32×C4C2×#4111yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C2×#41—91no—
430C23×C4—31no—
431C22×C8—31no—
432C22×C8D3211yescharacteristic
433#123—181no—
434C22⋊Q8—91no—
435C22⋊Q8—91no—
436#121—91no—
437#121—91no—
438#120—181no—
439C4×D4—181no—
440C4×D4—181no—
441#117—31no—
442#117—31no—
443#117—91no—
444#117—91no—
445#117—91no—
446#117—181no—
447#117—181no—
448C2×C4⋊C4—91no—
449C2×C4⋊C4—91no—
450C2×C22⋊C4—181no—
451C2×C42—181no—
452#107—31no—
453#107—31no—
454#107—91no—
455#107—91no—
456#106—31no—
457#106—31no—
458#106—91no—
459#106—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468C22⋊C8—31no—
469C22⋊C8—31no—
470C22⋊C8—31no—
471C22⋊C8—31no—
472C23×C3—21no—
473C23×C3—31no—
474C23×C3—31no—
475C23×C3—62no—
476C23×C3—62no—
477C23×C3—121no—
478C23×C3C2×D1211yescharacteristic
479C23×C3D3×D411yescharacteristic
480C22×D3—22no—
481C22×D3—22no—
482C22×D3—41no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—121no—
486C22×D3C2×D1211yescharacteristic
487C22×D3C2×D1211yescharacteristic
488C2×C3×C4—21no—
489C2×C3×C4—22no—
490C2×C3×C4—21no—
491C2×C3×C4—22no—
492C2×C3×C4—31no—
493C2×C3×C4—31no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4C2×D1211yescharacteristic
506C2×C3×C4#23512yes—
507C2×C3×C4D3×D411yescharacteristic
508C2×C3×C4#23712yes—
509C2×C3×C4#23712yes—
510C2×C3×C4#23912yes—
511C2×C3×C4C23×D311yescharacteristic
512C2×C3×C4C23×D311yescharacteristic
513#67—122no—
514#67—122no—
515#67—124no—
516#67—122no—
517#67—122no—
518C2×Dic3—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—122no—
533C2×Dic3—122no—
534C2×Dic3C2×D1211yescharacteristic
535C2×Dic3C2×D1211yescharacteristic
536D12—62no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—61no—
541D12—121no—
542D12—122no—
543D12—122no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—124no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—62no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—121no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—41no—
566C3×C8—41no—
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C2×C32—22no—
572C2×C32C2×#12311yescharacteristic
573C2×C32C2×#13511yescharacteristic
574C2×C32#57511yescharacteristic
575C3⋊D3—81no—
576C3×D3—22no—
577C3×D3—41no—
578C24—31no—
579#41—182no—
580#41—182no—
581C2×Q8—91no—
582C2×D4—91no—
583C2×D4—181no—
584C2×D4—181no—
585C2×D4—181no—
586C22×C4—31no—
587C22×C4—31no—
588C22×C4—31no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—62no—
592C22×C4—62no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4C2×D3211yescharacteristic
597C2×C8—22no—
598C2×C8—31no—
599C2×C8—31no—
600C2×C8—62no—
601C2×C8C2×D3211yescharacteristic
602C2×C8C2×D3211yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—31no—
607C4⋊C4—91no—
608C4⋊C4—91no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C22⋊C4—61no—
614C22⋊C4—61no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C42—61no—
623C42—61no—
624C42—181no—
625C42—181no—
626C42—181no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—22no—
633C22×C3—32no—
634C22×C3—41no—
635C22×C3—41no—
636C22×C3—61no—
637C22×C3—61no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—124no—
642C22×C3#88612yes—
643C22×C3#89412yes—
644C22×C3C22×D1211yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—21no—
647C2×D3—21no—
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—44no—
652C2×D3—122no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—241no—
660C2×D3—241no—
661C2×D3#90412yes—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—22no—
665C3×C4—61no—
666C3×C4—61no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4#88612yes—
672C3×C4#89412yes—
673C3×C4C2×#23511yescharacteristic
674C3×C4C2×#23711yescharacteristic
675C3×C4C2×#23711yescharacteristic
676C3×C4C2×#23911yescharacteristic
677Dic3—21no—
678Dic3—21no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—122no—
684Dic3—121no—
685Dic3—121no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692C32#309111yescharacteristic, complemented, Sylow
693C23—31no—
694C23—31no—
695C23—62no—
696C23—62no—
697C23—121no—
698C23—181no—
699C23D3×D1211yescharacteristic
700Q8—181no—
701Q8—181no—
702D4—181no—
703D4—181no—
704D4—362no—
705D4—362no—
706D4—362no—
707C2×C4—31no—
708C2×C4—31no—
709C2×C4—62no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—181no—
721C2×C4—181no—
722C2×C4—181no—
723C2×C4—362no—
724C2×C4—362no—
725C2×C4—362no—
726C2×C4#379612yes—
727C2×C4D3×D1211yescharacteristic
728C2×C4#380412yes—
729C2×C4C22×D3211yescharacteristic
730C8—21no—
731C8—21no—
732C8—61no—
733C8—61no—
734C2×C3—22no—
735C2×C3—22no—
736C2×C3—21no—
737C2×C3—21no—
738C2×C3—21no—
739C2×C3—42no—
740C2×C3—62no—
741C2×C3—121no—
742C2×C3C2×#88611yescharacteristic
743C2×C3C2×#89411yescharacteristic
744C2×C3C2×#90411yescharacteristic
745C2×C3#574811yescharacteristic
746C2×C3D3×#13511yescharacteristic
747C2×C3#576811yescharacteristic
748D3—22no—
749D3—41no—
750D3—242no—
751D3—241no—
752D3—241no—
753C22—21no—
754C22—21no—
755C22—32no—
756C22—61no—
757C22—61no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—124no—
762C22—361no—
763C22—361no—
764C22—361no—
765C22#6389012yes—
766C22C2×D3×D1211yescharacteristic
767C4—61no—
768C4—61no—
769C4—121no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—361no—
774C4—361no—
775C4—361no—
776C4#6389012yes—
777C4C2×#379611yescharacteristic
778C4C2×#380411yescharacteristic
779C3—21no—
780C3#7859111yescharacteristic, complemented
781C3#7918511yescharacteristic, complemented
782C2—22no—
783C2—62no—
784C2—121no—
785C2—721no—
786C2D3×#90411yescharacteristic
787C2#1059467611yescharacteristic
788C2C2×#6389011yescharacteristic
subgroupG/H
centerC2×C4D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595023C2
hypercenterC22×C8D32
hypocenterC32#3091
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. #10592812C2semidirect
4. C2×C3×(C2×D3)⋊C8C2semidirect
5. C3×#5106C2semidirect
6. #10591122C2semidirect
7. #10591105C2semidirect
8. #10590709C2semidirect
9. #10590708C2semidirect
10. #10590705C2semidirect
11. #10590704C2semidirect
12. #10590684C2semidirect
13. #10590679C2semidirect
14. #10590677C2semidirect
15. #10590674C2semidirect
41. #63648C22semidirect
42. #63648C22semidirect
43. #63643C22semidirect
44. #63643C22semidirect
49. C3×#818C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×#817C22semidirect
53. #63575C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
71. C2×(C2×D3)⋊C8D3semidirect
73. #5106D3semidirect
213. #818C2×D3semidirect
214. #818C2×D3semidirect
217. #817C2×D3semidirect
218. #817C2×D3semidirect
692. C32#3091semidirect
780. C3#78591semidirect
781. C3#79185semidirect

Maximal subgroups

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

subgroupindex
#105950232
D3×#9262
#105928122
C2×C3×(C2×D3)⋊C82
C3×#51062
#105911222
#105911052
#105907092
#105907082
#105907052
#105907042
#105906842
#105906792
#105906772
#105906742
#791853
#785913