Finite Group Databasebeta

← #11887289

Subgroups — #11887289

Order 1152.

872 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594003C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic, complemented
3#10592544C211yesmaximal, characteristic, complemented
4C3×#4847C211yesmaximal, characteristic, complemented
5C3×#4834C211yesmaximal, characteristic, complemented
6#10590969C211yesmaximal, characteristic, complemented
7#10590954C211yesmaximal, characteristic, complemented
8#10590946C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590852C211yesmaximal, characteristic, complemented
11#10590830C211yesmaximal, characteristic, complemented
12#10590705C211yesmaximal, characteristic, complemented
13#10590674C211yesmaximal, characteristic, complemented
14C4×#3716C211yesmaximal, characteristic, complemented
15#10590293C211yesmaximal, characteristic, complemented
16#81186—31nomaximal
17#79440—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×#3746C2211yescharacteristic, complemented
21C2×#3744C2211yescharacteristic
22#64084C2211yescharacteristic
23C4×#634C2211yescharacteristic, complemented
24C2×C3×D3×C8C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×C4×D12C2211yescharacteristic
27C3×C4×D12C2211yescharacteristic
28C3×#870C2211yescharacteristic, complemented
29#63922—21no—
30D3×(C2×D3)⋊C4—21no—
31#63909C2211yescharacteristic
32#63906—21no—
33#63890—21no—
34D3×C4⋊Dic3C2211yescharacteristic
35#63884—21no—
36#63878—21no—
37#63862—21no—
38#63857C2211yescharacteristic
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic, complemented
41#63846—21no—
42#63841C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×C4⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
51C3×#818C2211yescharacteristic, complemented
52C3×#817C2211yescharacteristic, complemented
53C3×C4×C3⋊C8C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5694—31no—
62#5554—31no—
63#5550—31no—
64#5541—31no—
65C3×#478—31no—
66C3×C8×D4—31no—
67#5116—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5068—31no—
72C4×#214—31no—
73#4887—31no—
74#4885—31no—
75#4864—31no—
76#4862—31no—
77#4847D311yescharacteristic, complemented
78#4845—31no—
79#4845—31no—
80#4845—61no—
81#4834D311yescharacteristic, complemented
82#4783—31no—
83#4776—31no—
84#4772—31no—
85D3×#102—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4721—31no—
90#4697—31no—
91C4×#204—31no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×D12D411yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×C4×D3C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#625—21no—
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×D12—22no—
107D3×D12—41no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116#3750—21no—
117C4×C3⋊Dic3—21no—
118#3746—41no—
119#3744—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132C3×D3×C8—41no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3716—22no—
144#3296—91noSylow
145C2×#237—31no—
146C2×D3×D4—31no—
147C2×#235—31no—
148C22×D12—31no—
149C22×C3×C8—31no—
150C22×C3×C8—31no—
151C3×#125—31no—
152C3×C4×D4—31no—
153C3×C4×D4—31no—
154#937—61no—
155#935—61no—
156C2×#214—31no—
157#930—31no—
158#930—61no—
159C2×(C2×D3)⋊C4—61no—
160#926—31no—
161C2×C4⋊Dic3—31no—
162#924—31no—
163#924—31no—
164#924—31no—
165C2×Dic12—31no—
166C2×Dic12—31no—
167C2×Dic12—61no—
168C2×#204—31no—
169C2×#204—31no—
170C2×#204—31no—
171C2×#204—61no—
172C2×D3×C8C2×D311yescharacteristic
173C2×D3×C8C2×D311yescharacteristic, complemented
174#898—61no—
175#897—31no—
176#897—31no—
177#897—31no—
178#895—31no—
179#894—61no—
180#894—61no—
181#892—31no—
182#892—61no—
183D3×C4⋊C4—31no—
184#890—61no—
185#889—61no—
186#886—61no—
187#884—61no—
188#882—61no—
189D3×C22⋊C4—61no—
190#879—61no—
191#877—61no—
192#875—31no—
193#875—31no—
194#875—61no—
195C4×D12C2×D311yescharacteristic
196C4×D12C2×D311yescharacteristic
197#870C2×D311yescharacteristic, complemented
198C4×Dic6—31no—
199C4×Dic6—31no—
200C4×Dic6—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—21no—
204C3×C4⋊C8C2×D311yescharacteristic, complemented
205C3×C4⋊C8C2×D311yescharacteristic, complemented
206C3×#102—31no—
207C3×#102—31no—
208C3×C22⋊C8—31no—
209C3×C22⋊C8—31no—
210C3×C4×C8—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821C2×D311yescharacteristic
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic, complemented
222#818C2×D311yescharacteristic, complemented
223#817—31no—
224#817C2×D311yescharacteristic, complemented
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#810—31no—
232#810—31no—
233#810—31no—
234#809—31no—
235#809—31no—
236#808—31no—
237C4×C3⋊C8C2×D311yescharacteristic, complemented
238C22×C3⋊D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—22no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—81no—
270#626—42no—
271#626—81no—
272#625—42no—
273D3×Dic3—42no—
274D3×Dic3—42no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—31no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—31no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C22×C3×C4—31no—
299C22×C3×C4—31no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307#237—62no—
308#237—121no—
309D3×D4—62no—
310D3×D4—121no—
311#235—62no—
312#235—121no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12—62no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—121no—
320C2×D12D1211yescharacteristic
321C2×D12C22×D311yescharacteristic
322C2×C4×D3—21no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3C22×D311yescharacteristic
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×C3×C8—21no—
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8—121no—
339C2×C3×C8C22×D311yescharacteristic
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C22⋊C4—61no—
352C3×C42—21no—
353C3×C42C22×D311yescharacteristic
354C3×C42C22×D311yescharacteristic
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#214—62no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
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—121no—
372(C2×D3)⋊C4—121no—
373(C2×D3)⋊C4D1211yescharacteristic
374(C2×D3)⋊C4D1211yescharacteristic
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3D1211yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
387Dic3⋊C4—21no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—121no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
400C2×C3⋊C8C22×D311yescharacteristic
401C2×C3⋊C8C22×D311yescharacteristic
402Dic12—121no—
403Dic12—121no—
404Dic12—122no—
405#204—62no—
406#204—121no—
407#204—121no—
408#204—122no—
409D3×C8—41no—
410D3×C8—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—22no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3#13512yes—
424D32—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—31no—
444#126—181no—
445#125—31no—
446#125—181no—
447#124—91no—
448#123—181no—
449#123—181no—
450C22⋊Q8—91no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×D4—31no—
458C4×D4—31no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—31no—
464#106—31no—
465#106—91no—
466C4⋊C8D3211yescharacteristic, complemented
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—31no—
479C4×C8—31no—
480C23×C3—31no—
481C23×C3—31no—
482C23×C3—61no—
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3C2×D1211yescharacteristic
494C22×D3C2×D1211yescharacteristic
495C3×D4—32no—
496C3×D4—62no—
497C3×D4—61no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—241no—
511C2×C3×C4C2×D1211yescharacteristic
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—122no—
518#67—122no—
519#67—122no—
520#67—241no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—122no—
534C2×Dic3—122no—
535C2×Dic3C2×D1211yescharacteristic
536C2×Dic3C2×D1211yescharacteristic
537D12—22no—
538D12—21no—
539D12—61no—
540D12—61no—
541D12—61no—
542D12—61no—
543D12—121no—
544D12—121no—
545D12—122no—
546D12—241no—
547D12#23912yes—
548C4×D3—21no—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—21no—
552C4×D3—81no—
553C4×D3—122no—
554C4×D3—122no—
555Dic6—62no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32#54611yescharacteristic
578C2×C32C2×#13511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—81no—
581C3×D3—22no—
582C3×D3—42no—
583C3×D3—41no—
584C24—181no—
585#41—182no—
586#41—361no—
587C2×Q8—91no—
588C2×Q8—91no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—91no—
592C2×D4—181no—
593C2×D4—182no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—361no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—181no—
601C22×C4—181no—
602Q16—361no—
603SD16—182no—
604SD16—361no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—121no—
608C2×C8—121no—
609C2×C8C2×D3211yescharacteristic
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—61no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—181no—
634C42—181no—
635C42C2×D3211yescharacteristic
636C22×C3—21no—
637C22×C3—32no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—62no—
643C22×C3—61no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C22×D1211yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—21no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—244no—
666C2×D3—244no—
667C2×D3#90412yes—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4#100411yescharacteristic
682C3×C4C2×#23911yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—122no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699C32#329611yescharacteristic, complemented, Sylow
700C23—31no—
701C23—31no—
702C23—61no—
703C23—181no—
704C23—362no—
705C23—362no—
706C23—721no—
707Q8—181no—
708Q8—181no—
709Q8—181no—
710Q8—181no—
711D4—32no—
712D4—62no—
713D4—61no—
714D4—181no—
715D4—181no—
716D4—362no—
717D4—362no—
718D4—721no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—241no—
732C2×C4—362no—
733C2×C4—362no—
734C2×C4D3×D1211yescharacteristic
735C2×C4D3×D1211yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—21no—
739C8—61no—
740C8—61no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—62no—
745C2×C3—121no—
746C2×C3—122no—
747C2×C3#555411yescharacteristic
748C2×C3#563011yescharacteristic
749C2×C3C2×#90411yescharacteristic
750C2×C3#575111yescharacteristic
751C2×C3D3×#13511yescharacteristic
752C2×C3#577511yescharacteristic
753D3—22no—
754D3—42no—
755D3—41no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—32no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—62no—
764C22—61no—
765C22—61no—
766C22—121no—
767C22—121no—
768C22—361no—
769C22—361no—
770C22—361no—
771C22—724no—
772C22C2×D3×D1211yescharacteristic
773C4—21no—
774C4—21no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—361no—
781C4—361no—
782C4—361no—
783C4#6431411yescharacteristic
784C4D3×#23911yescharacteristic
785C3—21no—
786C3#7944011yescharacteristic, complemented
787C3#8118611yescharacteristic, complemented
788C2—62no—
789C2—121no—
790C2—122no—
791C2—721no—
792C2#1059462911yescharacteristic
793C2D3×#90411yescharacteristic
794C2#1059471311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
prime radical#10594003C2
hypercenterC4⋊C8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #10593920C2semidirect
3. #10592544C2semidirect
4. C3×#4847C2semidirect
5. C3×#4834C2semidirect
6. #10590969C2semidirect
7. #10590954C2semidirect
8. #10590946C2semidirect
9. D3×#821C2semidirect
10. #10590852C2semidirect
11. #10590830C2semidirect
12. #10590705C2semidirect
13. #10590674C2semidirect
14. C4×#3716C2semidirect
15. #10590293C2semidirect
20. C2×#3746C22semidirect
23. C4×#634C22semidirect
25. C2×C3×D3×C8C22semidirect
28. C3×#870C22semidirect
40. #63857C22semidirect
42. #63841C22semidirect
44. C32×C4⋊C8C22semidirect
46. #63643C22semidirect
50. C3×(C2×D3)⋊C8C22semidirect
51. C3×#818C22semidirect
52. C3×#817C22semidirect
53. C3×C4×C3⋊C8C22semidirect
54. #63573C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
57. #63567C22semidirect
77. #4847D3semidirect
81. #4834D3semidirect
173. C2×D3×C8C2×D3semidirect
197. #870C2×D3semidirect
204. C3×C4⋊C8C2×D3semidirect
205. C3×C4⋊C8C2×D3semidirect
221. (C2×D3)⋊C8C2×D3semidirect
222. #818C2×D3semidirect
224. #817C2×D3semidirect
237. C4×C3⋊C8C2×D3semidirect
466. C4⋊C8D32semidirect
699. C32#3296semidirect
786. C3#79440semidirect
787. C3#81186semidirect

Maximal subgroups

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

subgroupindex
#105940032
#105939202
#105925442
C3×#48472
C3×#48342
#105909692
#105909542
#105909462
D3×#8212
#105908522
#105908302
#105907052
#105906742
C4×#37162
#105902932
#811863
#794403