Finite Group Databasebeta

← #11887294

Subgroups — #11887294

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594005C211yesmaximal, characteristic
2#10593947C211yesmaximal, characteristic, complemented
3C8×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C3×#4697C211yesmaximal, characteristic, complemented
5C3×C4×#204C211yesmaximal, characteristic, complemented
6#10590961C211yesmaximal, characteristic, complemented
7#10590956C211yesmaximal, characteristic, complemented
8#10590943C211yesmaximal, characteristic, complemented
9#10590940C211yesmaximal, characteristic, complemented
10#10590855C211yesmaximal, characteristic, complemented
11#10590841C211yesmaximal, characteristic, complemented
12#10590686C211yesmaximal, characteristic, complemented
13#10590652C211yesmaximal, characteristic, complemented
14#10590270C211yesmaximal, characteristic, complemented
15#10590267C211yesmaximal, characteristic, complemented
16#81652—31nomaximal
17#79677—31nomaximal
18C2×#3802C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20C2×C8×C3⋊D3C2211yescharacteristic
21C2×C8×C3⋊D3C2211yescharacteristic, complemented
22C4×C4⋊(C3⋊D3)C2211yescharacteristic
23C2×C3×#204C2211yescharacteristic
24C3×#875C2211yescharacteristic
25C3×C4×D12C2211yescharacteristic
26C3×#870C2211yescharacteristic, complemented
27C3×C4×Dic6C2211yescharacteristic, complemented
28#63923—21no—
29D3×(C2×D3)⋊C4—21no—
30#63916C2211yescharacteristic
31#63906—21no—
32#63900C2211yescharacteristic
33#63897—21no—
34#63891—21no—
35#63871C2211yescharacteristic
36#63871C2211yescharacteristic
37#63871C2211yescharacteristic, complemented
38#63868—21no—
39#63849C2211yescharacteristic, complemented
40#63845—21no—
41#63836—21no—
42C2×#3718C2211yescharacteristic, complemented
43C2×#3715C2211yescharacteristic
44C32×C4×C8C2211yescharacteristic, complemented
45#63647C2211yescharacteristic
46#63647C2211yescharacteristic, complemented
47C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#816C2211yescharacteristic, complemented
54C3×#816C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic
60#63562C2211yescharacteristic
61#5694—31no—
62#5676—31no—
63#5581—31no—
64#5554—31no—
65C3×#488—31no—
66C3×C4×SD16—31no—
67#5173—31no—
68#5169—31no—
69#5066—31no—
70#5054—31no—
71#5028—31no—
72#5009—31no—
73#4866—31no—
74#4862—31no—
75#4813—31no—
76#4813—31no—
77#4808—31no—
78#4807—31no—
79#4805—31no—
80#4804—31no—
81#4779—31no—
82#4778—31no—
83#4776—31no—
84#4772—31no—
85D3×#102—31no—
86D3×#102—31no—
87#4697D311yescharacteristic, complemented
88C4×#204D311yescharacteristic, complemented
89C8×D12—31no—
90C8×D12—31no—
91C8×D12—61no—
92C22×D32—21no—
93C2×C4⋊(C3⋊D3)D411yescharacteristic
94C2×C4×C3⋊D3C2311yescharacteristic
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×C3×D12C2311yescharacteristic
97C2×C3×D12C2311yescharacteristic
98C2×C3×C4×D3—21no—
99C2×C3×Dic6C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#626—21no—
102C2×#626—21no—
103C2×#625—21no—
104C2×#624—21no—
105C2×D3×Dic3—21no—
106#3802—22no—
107#3802—41no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112C32×C42C2311yescharacteristic
113#3752D411yescharacteristic
114#3752D411yescharacteristic
115C4⋊(C3⋊Dic3)D411yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—41no—
119C8×C3⋊D3—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×C4×Dic3—21no—
131C3×#204—22no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142#3718—41no—
143#3715—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#237—31no—
147C2×D3×D4—31no—
148C2×D3×D4—31no—
149C2×C3×SD16—31no—
150C3×#125—31no—
151C3×#124—31no—
152C3×C4×Q8—31no—
153C3×C4×D4—31no—
154#946—31no—
155#946—31no—
156#946—31no—
157C2×#216—31no—
158C2×#216—31no—
159C2×#215—31no—
160#938—31no—
161C2×#214—31no—
162#930—61no—
163C2×(C2×D3)⋊C4—61no—
164C2×#204C2×D311yescharacteristic
165C2×D3×C8—31no—
166C2×D3×C8—31no—
167C2×D3×C8—31no—
168C2×D3×C8—31no—
169C2×D3×C8—61no—
170C2×D3×C8—61no—
171#898—61no—
172#897—31no—
173#897—31no—
174#897—31no—
175#895—31no—
176#894—61no—
177#894—61no—
178#892—31no—
179#892—31no—
180#892—61no—
181D3×C4⋊C4—31no—
182D3×C4⋊C4—31no—
183#890—61no—
184#889—61no—
185#886—61no—
186#884—61no—
187#883—61no—
188#882—61no—
189#882—61no—
190D3×C22⋊C4—61no—
191#876—61no—
192#875C2×D311yescharacteristic
193C4×D12—31no—
194C4×D12—31no—
195C4×D12—61no—
196C4×D12C2×D311yescharacteristic
197#872—61no—
198#870C2×D311yescharacteristic, complemented
199C4×Dic6C2×D311yescharacteristic, complemented
200C3×#106—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×C4×C8—21no—
208C3×C4×C8C2×D311yescharacteristic, complemented
209C3×C4×C8C2×D311yescharacteristic, complemented
210#835—31no—
211#832—31no—
212#832—31no—
213#832—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222(C2×D3)⋊C8—61no—
223#817C2×D311yescharacteristic, complemented
224#816C2×D311yescharacteristic, complemented
225#816C2×D311yescharacteristic, complemented
226#816C2×D311yescharacteristic, complemented
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—31no—
237C4⋊(C3⋊C8)—61no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4⋊(C3⋊D3)—22no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—81no—
266C3×Dic6—21no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—42no—
271#626—81no—
272#625—42no—
273#624—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—31no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—31no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C22×C3×C4—61no—
301C2×#67—61no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C22×Dic3—61no—
306#239—62no—
307#239—121no—
308#237—62no—
309#237—121no—
310D3×D4—62no—
311D3×D4—62no—
312D3×D4—121no—
313D3×D4—121no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12C22×D311yescharacteristic
320C2×D12C22×D311yescharacteristic
321C2×C4×D3—21no—
322C2×C4×D3—31no—
323C2×C4×D3—31no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×SD16—62no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—21no—
351C3×C42—61no—
352C3×C42C22×D311yescharacteristic
353C3×C42C22×D311yescharacteristic
354#217—61no—
355#216—121no—
356#216—121no—
357#215—121no—
358#214—121no—
359(C2×D3)⋊C4—21no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—31no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
365(C2×D3)⋊C4—31no—
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—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
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—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404#204—22no—
405D3×C8—121no—
406D3×C8—121no—
407D3×C8—121no—
408D3×C8—121no—
409D3×C8—122no—
410D3×C8—122no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—21no—
413C2×C3⋊D3—21no—
414C2×C3⋊D3—21no—
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3#13512yes—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—21no—
426C32×C4—21no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—31no—
441C2×SD16—91no—
442C22×C8—91no—
443C22×C8—91no—
444#126—181no—
445#125—31no—
446#125—181no—
447#124—31no—
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—31no—
457C4×D4—31no—
458C4×D4—91no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—91no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—31no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—91no—
478C22⋊C8—91no—
479C4×C8D3211yescharacteristic, complemented
480C23×C3—61no—
481C23×C3—61no—
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—31no—
485C22×D3—31no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×D4—32no—
501C3×D4—61no—
502C3×D4—61no—
503C3×D4—61no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—241no—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4D3×D411yescharacteristic
516C2×C3×C4D3×D411yescharacteristic
517C2×C3×C4D3×D411yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520#67—122no—
521#67—122no—
522#67—122no—
523#67—241no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—122no—
537D12—21no—
538D12—21no—
539D12—21no—
540D12—62no—
541D12—62no—
542D12—64no—
543D12—122no—
544D12—241no—
545D12#23512yes—
546C4×D3—61no—
547C4×D3—61no—
548C4×D3—61no—
549C4×D3—61no—
550C4×D3—61no—
551C4×D3—61no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—81no—
555C4×D3—121no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—121no—
559C4×D3—122no—
560C4×D3—122no—
561C4×D3—122no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566C3×C8—22no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—41no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C3⋊C8—121no—
578C2×C32#54611yescharacteristic
579C2×C32C2×#13511yescharacteristic
580C2×C32#57711yescharacteristic
581C3⋊D3—22no—
582C3⋊D3—41no—
583C3×D3—42no—
584C3×D3—81no—
585C24—181no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—91no—
593C2×D4—181no—
594C2×D4—181no—
595C2×D4—181no—
596C2×D4—182no—
597C2×D4—361no—
598C22×C4—61no—
599C22×C4—91no—
600C22×C4—91no—
601C22×C4—181no—
602C22×C4—181no—
603Q16—361no—
604SD16—62no—
605SD16—361no—
606C2×C8—91no—
607C2×C8—91no—
608C2×C8—361no—
609C2×C8—361no—
610C2×C8C2×D3211yescharacteristic
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—61no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—61no—
627C22⋊C4—91no—
628C22⋊C4—91no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—61no—
635C42—181no—
636C42C2×D3211yescharacteristic
637C22×C3—21no—
638C22×C3—62no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3C2×D3×D411yescharacteristic
645C22×C3C2×D3×D411yescharacteristic
646C2×D3—22no—
647C2×D3—32no—
648C2×D3—32no—
649C2×D3—41no—
650C2×D3—41no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—62no—
655C2×D3—61no—
656C2×D3—61no—
657C2×D3—61no—
658C2×D3—61no—
659C2×D3—62no—
660C2×D3—61no—
661C2×D3—61no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—244no—
671C2×D3—244no—
672C3×C4—22no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—41no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4C2×#23511yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689C3×C4#100911yescharacteristic
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—61no—
697Dic3—61no—
698Dic3—61no—
699Dic3—61no—
700Dic3—121no—
701Dic3—121no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—61no—
704C23—61no—
705C23—91no—
706C23—91no—
707C23—362no—
708C23—362no—
709C23—721no—
710Q8—61no—
711Q8—61no—
712Q8—61no—
713Q8—61no—
714D4—32no—
715D4—61no—
716D4—61no—
717D4—61no—
718D4—182no—
719D4—362no—
720D4—362no—
721D4—721no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—91no—
729C2×C4—91no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—241no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4#380211yescharacteristic
738C2×C4#380211yescharacteristic
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—21no—
742C8—181no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—122no—
748C2×C3—241no—
749C2×C3#555011yescharacteristic
750C2×C3#567611yescharacteristic
751C2×C3#576211yescharacteristic
752C2×C3D3×#13511yescharacteristic
753C2×C3D3×#13511yescharacteristic
754C2×C3#577011yescharacteristic
755D3—42no—
756D3—62no—
757D3—62no—
758D3—81no—
759D3—122no—
760D3—122no—
761D3—121no—
762D3—121no—
763C22—62no—
764C22—92no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—724no—
776C22C2×#380211yescharacteristic
777C4—21no—
778C4—21no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—181no—
786C4—181no—
787C4D3×#23511yescharacteristic
788C4#6430811yescharacteristic
789C3—21no—
790C3#7967711yescharacteristic, complemented
791C3#8165211yescharacteristic, complemented
792C2—122no—
793C2—182no—
794C2—241no—
795C2—361no—
796C2#1059400711yescharacteristic
797C2#1059468411yescharacteristic
798C2#1059468611yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radical#10594005C2
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. #10593947C2semidirect
3. C8×C4⋊(C3⋊D3)C2semidirect
4. C3×#4697C2semidirect
5. C3×C4×#204C2semidirect
6. #10590961C2semidirect
7. #10590956C2semidirect
8. #10590943C2semidirect
9. #10590940C2semidirect
10. #10590855C2semidirect
11. #10590841C2semidirect
12. #10590686C2semidirect
13. #10590652C2semidirect
14. #10590270C2semidirect
15. #10590267C2semidirect
21. C2×C8×C3⋊D3C22semidirect
26. C3×#870C22semidirect
27. C3×C4×Dic6C22semidirect
37. #63871C22semidirect
39. #63849C22semidirect
42. C2×#3718C22semidirect
44. C32×C4×C8C22semidirect
46. #63647C22semidirect
47. C4⋊(C3⋊(C3⋊C8))C22semidirect
51. C3×#817C22semidirect
52. C3×#816C22semidirect
53. C3×#816C22semidirect
54. C3×#816C22semidirect
55. #63576C22semidirect
56. #63574C22semidirect
57. #63565C22semidirect
87. #4697D3semidirect
88. C4×#204D3semidirect
198. #870C2×D3semidirect
199. C4×Dic6C2×D3semidirect
208. C3×C4×C8C2×D3semidirect
209. C3×C4×C8C2×D3semidirect
223. #817C2×D3semidirect
224. #816C2×D3semidirect
225. #816C2×D3semidirect
226. #816C2×D3semidirect
479. C4×C8D32semidirect
702. C32#3296semidirect
790. C3#79677semidirect
791. C3#81652semidirect

Maximal subgroups

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

subgroupindex
#105940052
#105939472
C8×C4⋊(C3⋊D3)2
C3×#46972
C3×C4×#2042
#105909612
#105909562
#105909432
#105909402
#105908552
#105908412
#105906862
#105906522
#105902702
#105902672
#816523
#796773