Finite Group Databasebeta

← #11887265

Subgroups — #11887265

Order 1152.

873 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#10594886C211yesmaximal, characteristic
2#10594849C211yesmaximal, characteristic, complemented
3#10592815C211yesmaximal, characteristic, complemented
4C2×C3×#821C211yesmaximal, characteristic, complemented
5C3×C8×#67C211yesmaximal, characteristic, complemented
6#10591172C211yesmaximal, characteristic, complemented
7#10591124C211yesmaximal, characteristic, complemented
8#10590969C211yesmaximal, characteristic, complemented
9#10590954C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590861C211yesmaximal, characteristic, complemented
12#10590834C211yesmaximal, characteristic, complemented
13#10590825C211yesmaximal, characteristic, complemented
14#10590767C211yesmaximal, characteristic, complemented
15#10590744C211yesmaximal, characteristic, complemented
16#79440—31nomaximal
17#78759—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic
21#64133C2211yescharacteristic
22#64133C2211yescharacteristic
23C2×#3746C2211yescharacteristic, complemented
24C3×C4×#67C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×D3×C8C2211yescharacteristic, complemented
27#63976—21no—
28D3×#217—21no—
29#63961—21no—
30#63955—21no—
31#63908C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63885—21no—
34#63884—21no—
35#63869C2211yescharacteristic, complemented
36#63860C2211yescharacteristic
37#63858—21no—
38#63857C2211yescharacteristic, complemented
39#63847—21no—
40#63844C2211yescharacteristic, complemented
41#63841C2211yescharacteristic, complemented
42C2×#3716C2211yescharacteristic
43C2×#3716C2211yescharacteristic
44#63645C2211yescharacteristic, complemented
45#63643C2211yescharacteristic, complemented
46#63643C2211yescharacteristic, complemented
47C3×#830C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic
52C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63567C2211yescharacteristic, complemented
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5806—31no—
62#5550—31no—
63#5541—31no—
64#5513—31no—
65C3×C8×D4—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5116—31no—
69#5116—31no—
70#5116—61no—
71#5114—31no—
72#5113—31no—
73C2×#821D311yescharacteristic, complemented
74C8×#67D311yescharacteristic, complemented
75#4971—31no—
76#4847—31no—
77#4845—31no—
78#4784—31no—
79#4783—31no—
80#4778—31no—
81#4772—31no—
82#4768—31no—
83#4767—31no—
84#4766—31no—
85#4758—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4721—31no—
90#4697—31no—
91C4×#204—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C2×C3×D12—22no—
99C2×C3×D12—21no—
100C2×C3×D12—41no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×#625—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114#3757—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3750—21no—
118#3750—21no—
119#3746—41no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D3×C8—41no—
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141Dic32—21no—
142#3716—22no—
143#3716—41no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—21no—
150C22×C3×C8—31no—
151C22×C3×C8C2×D311yescharacteristic
152C22×C3×C8C2×D311yescharacteristic
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#953—61no—
156C2×#217—61no—
157#939—61no—
158#938—31no—
159#937—61no—
160#936—31no—
161#935—61no—
162#935—61no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166#930—31no—
167#929—61no—
168C4×#67C2×D311yescharacteristic
169#926—31no—
170#926—61no—
171C2×C4⋊Dic3C2×D311yescharacteristic
172#924—31no—
173#924—31no—
174#924—31no—
175#924—31no—
176#924—31no—
177#924—61no—
178#924—61no—
179C2×Dic12—31no—
180C2×Dic12—31no—
181C2×Dic12—61no—
182C2×#204—31no—
183C2×#204—31no—
184C2×D3×C8C2×D311yescharacteristic, complemented
185#898—61no—
186#897—31no—
187#894—61no—
188#892—31no—
189#890—31no—
190#889—61no—
191#889—61no—
192#887—31no—
193#884—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#877—61no—
197#875—31no—
198C4×D12—31no—
199#870—31no—
200C4×Dic6—31no—
201C3×C4⋊C8—31no—
202C3×#102—31no—
203C3×#102—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—31no—
207C3×C22⋊C8—31no—
208C3×C4×C8—31no—
209#832—31no—
210#832—31no—
211#830C2×D311yescharacteristic
212#821—31no—
213#821—31no—
214#821C2×D311yescharacteristic
215#821C2×D311yescharacteristic
216#821C2×D311yescharacteristic
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8C2×D311yescharacteristic, complemented
219#818—31no—
220#818—31no—
221#818—61no—
222#817—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—31no—
230#816—61no—
231#816—61no—
232Dic3⋊C8C2×D311yescharacteristic, complemented
233C8×Dic3C2×D311yescharacteristic, complemented
234#810—31no—
235#810—31no—
236#808—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253#634—21no—
254#634—21no—
255#634—21no—
256#634—21no—
257C3×#67—22no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266C3×D12—21no—
267C3×D12—42no—
268C3×D12#4112yes—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271#625—42no—
272#625—81no—
273D3×Dic3—42no—
274D3×Dic3—81no—
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—91no—
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—31no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—62no—
300C2×C3×D4—61no—
301C2×C3×D4—121no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67D1211yescharacteristic
312C22×Dic3—21no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315#237—62no—
316#237—121no—
317#235—62no—
318#235—121no—
319C2×D12—22no—
320C2×D12—21no—
321C2×D12—41no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—61no—
325C2×C4×D3—61no—
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—41no—
338C2×C3×C8—41no—
339C2×C3×C8—42no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—31no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—31no—
351C3×C42—31no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—121no—
363#217—121no—
364#217D1211yescharacteristic
365#214—62no—
366#214—121no—
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)⋊C4D1211yescharacteristic
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—121no—
396Dic3⋊C4—121no—
397Dic3⋊C4D1211yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406Dic12—121no—
407Dic12—122no—
408#204—62no—
409#204—121no—
410D3×C8—41no—
411C22×C32—21no—
412C22×C32—21no—
413C22×C32#13512yes—
414C22×C32C22×D411yescharacteristic
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—84no—
425C32×C4—21no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—91no—
438C22×D4—31no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8D3211yescharacteristic
444#126—181no—
445#125—91no—
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—91no—
459#117—91no—
460#117—181no—
461C2×C4⋊C4—31no—
462C2×C22⋊C4—181no—
463#107—91no—
464#106—91no—
465#106—91no—
466C4⋊C8—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—31no—
479C4×C8—31no—
480C23×C3—21no—
481C23×C3—31no—
482C23×C3—61no—
483C23×C3—61no—
484C23×C3—122no—
485C23×C3—122no—
486C23×C3—241no—
487C23×C3C2×D1211yescharacteristic
488C23×C3D3×D411yescharacteristic
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—81no—
494C22×D3C2×D1211yescharacteristic
495C3×D4—32no—
496C3×D4—62no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—122no—
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—31no—
508C2×C3×C4—31no—
509C2×C3×C4—31no—
510C2×C3×C4—41no—
511C2×C3×C4—41no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—122no—
517C2×C3×C4C2×D1211yescharacteristic
518C2×C3×C4D3×D411yescharacteristic
519C2×C3×C4C23×D311yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521#67—22no—
522#67—122no—
523#67—122no—
524#67—241no—
525#67—241no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—42no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—241no—
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545C2×Dic3C2×D1211yescharacteristic
546D12—21no—
547D12—21no—
548D12—21no—
549D12—42no—
550D12#23512yes—
551C4×D3—21no—
552C4×D3—21no—
553C4×D3—122no—
554C4×D3—241no—
555Dic6—61no—
556Dic6—61no—
557Dic6—61no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—121no—
564Dic6—121no—
565Dic6—121no—
566Dic6—121no—
567C3×C8—22no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—41no—
573C3×C8—61no—
574C3×C8—61no—
575C3⋊C8—21no—
576C3⋊C8—21no—
577C2×C32—22no—
578C2×C32#54611yescharacteristic
579C2×C32C2×#13511yescharacteristic
580C2×C32#57711yescharacteristic
581C3×D3—41no—
582C3×D3—42no—
583C3×D3—81no—
584C24—61no—
585#41—182no—
586#41—361no—
587C2×Q8—91no—
588C2×Q8—91no—
589C2×D4—31no—
590C2×D4—31no—
591C2×D4—31no—
592C2×D4—62no—
593C2×D4—61no—
594C2×D4—121no—
595C2×D4—181no—
596C2×D4—181no—
597C22×C4—31no—
598C22×C4—61no—
599C22×C4—181no—
600C22×C4—181no—
601C22×C4C2×D3211yescharacteristic
602Q16—361no—
603SD16—182no—
604SD16—361no—
605C2×C8—31no—
606C2×C8—31no—
607C2×C8—41no—
608C2×C8—121no—
609C2×C8C2×D3211yescharacteristic
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C22⋊C4—31no—
624C22⋊C4—31no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C42—31no—
634C42—181no—
635C42—181no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—62no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—244no—
654C22×C3#90412yes—
655C22×C3#91212yes—
656C22×C3C22×D1211yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C2×D3—21no—
659C2×D3—22no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—41no—
667C2×D3—84no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4C2×#23511yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4D3×#4111yescharacteristic
682Dic3—21no—
683Dic3—21no—
684Dic3—21no—
685Dic3—41no—
686Dic3—41no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697Dic3—241no—
698Dic3—241no—
699C32#329611yescharacteristic, complemented, Sylow
700C23—31no—
701C23—61no—
702C23—61no—
703C23—122no—
704C23—122no—
705C23—241no—
706C23D3×D1211yescharacteristic
707Q8—181no—
708Q8—181no—
709Q8—181no—
710Q8—181no—
711D4—32no—
712D4—62no—
713D4—61no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—362no—
718D4—721no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4—362no—
734C2×C4—721no—
735C2×C4D3×D1211yescharacteristic
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—21no—
739C8—61no—
740C8—61no—
741C2×C3—22no—
742C2×C3—22no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—42no—
747C2×C3—122no—
748C2×C3—121no—
749C2×C3—241no—
750C2×C3#549011yescharacteristic
751C2×C3#555411yescharacteristic
752C2×C3C2×#90411yescharacteristic
753C2×C3#575111yescharacteristic
754C2×C3C2×#91211yescharacteristic
755C2×C3#576211yescharacteristic
756D3—41no—
757D3—42no—
758D3—81no—
759C22—21no—
760C22—21no—
761C22—61no—
762C22—62no—
763C22—61no—
764C22—61no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—244no—
771C22#6380712yes—
772C22C2×D3×D1211yescharacteristic
773C4—21no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—361no—
780C4—361no—
781C4—361no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6433011yescharacteristic
785C3—21no—
786C3#7875911yescharacteristic, complemented
787C3#7944011yescharacteristic, complemented
788C2—22no—
789C2—121no—
790C2—122no—
791C2—241no—
792C2#1059467711yescharacteristic
793C2C2×#6380711yescharacteristic
794C2#1059507311yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC22×C8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. #10594849C2semidirect
3. #10592815C2semidirect
4. C2×C3×#821C2semidirect
5. C3×C8×#67C2semidirect
6. #10591172C2semidirect
7. #10591124C2semidirect
8. #10590969C2semidirect
9. #10590954C2semidirect
10. #10590863C2semidirect
11. #10590861C2semidirect
12. #10590834C2semidirect
13. #10590825C2semidirect
14. #10590767C2semidirect
15. #10590744C2semidirect
23. C2×#3746C22semidirect
26. C2×C3×D3×C8C22semidirect
35. #63869C22semidirect
38. #63857C22semidirect
40. #63844C22semidirect
41. #63841C22semidirect
44. #63645C22semidirect
45. #63643C22semidirect
46. #63643C22semidirect
52. C3×(C2×D3)⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63573C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
58. #63567C22semidirect
73. C2×#821D3semidirect
74. C8×#67D3semidirect
184. C2×D3×C8C2×D3semidirect
218. (C2×D3)⋊C8C2×D3semidirect
232. Dic3⋊C8C2×D3semidirect
233. C8×Dic3C2×D3semidirect
699. C32#3296semidirect
786. C3#78759semidirect
787. C3#79440semidirect

Maximal subgroups

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

subgroupindex
#105948862
#105948492
#105928152
C2×C3×#8212
C3×C8×#672
#105911722
#105911242
#105909692
#105909542
#105908632
#105908612
#105908342
#105908252
#105907672
#105907442
#794403
#787593