Finite Group Databasebeta

← #11889257

Subgroups — #11889257

Order 1152.

883 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595078C211yesmaximal, characteristic
2#10594841C211yesmaximal, characteristic, complemented
3#10592812C211yesmaximal, characteristic, complemented
4C3×#5114C211yesmaximal, characteristic, complemented
5C3×#5111C211yesmaximal, characteristic, complemented
6#10591184C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic, complemented
8#10590942C211yesmaximal, characteristic, complemented
9#10590939C211yesmaximal, characteristic, complemented
10#10590895C211yesmaximal, characteristic, complemented
11#10590859C211yesmaximal, characteristic, complemented
12#10590849C211yesmaximal, characteristic, complemented
13#10590795C211yesmaximal, characteristic, complemented
14#10590759C211yesmaximal, characteristic, complemented
15#10590709C211yesmaximal, characteristic, complemented
16#80686—31nomaximal
17#79502—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C22×C32×C8C2211yescharacteristic, complemented
21#64135C2211yescharacteristic, complemented
22C3×#930C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C3×#924C2211yescharacteristic, complemented
25C2×C3×#204C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
27#63983—21no—
28#63959—21no—
29#63958—21no—
30#63956—21no—
31#63921—21no—
32#63918C2211yescharacteristic, complemented
33#63894C2211yescharacteristic
34#63862—21no—
35#63860C2211yescharacteristic
36#63857C2211yescharacteristic
37#63856C2211yescharacteristic
38#63853—21no—
39Dic3×Dic6C2211yescharacteristic, complemented
40#63841C2211yescharacteristic
41#63838—21no—
42C2×#3719C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47#63643C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×#816C2211yescharacteristic, complemented
53C3×#815C2211yescharacteristic, complemented
54C3×Dic3⋊C8C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5641—31no—
62#5612—31no—
63#5550—31no—
64#5542—31no—
65C3×#465—31no—
66C3×#435—31no—
67#5169—31no—
68#5166—31no—
69#5137—31no—
70#5131—31no—
71#5114D311yescharacteristic, complemented
72#5113—31no—
73#5113—31no—
74#5113—61no—
75#5111D311yescharacteristic, complemented
76#5047—31no—
77#5035—31no—
78#4870—31no—
79#4868—31no—
80#4845—31no—
81#4842—31no—
82#4817—31no—
83#4816—31no—
84#4770—31no—
85#4765—31no—
86#4737—31no—
87#4733—31no—
88#4731—31no—
89#4723—31no—
90#4714—31no—
91#4710—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95#3828—22no—
96#3828—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3—21no—
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#627—21no—
106C2×#626—21no—
107C2×#624—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8—41no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4D411yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×#204—41no—
129C3×ΓL(1,𝔽25)—41no—
130#3724—21no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134#3722—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#3719—41no—
143#3717—22no—
144#3311—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C2×C3×SD16—31no—
151C2×C3×M16—31no—
152C22×C3×C8—21no—
153C22×C3×C8C2×D311yescharacteristic, complemented
154C22×C3×C8C2×D311yescharacteristic, complemented
155C3×C22⋊Q8—31no—
156C3×#121—31no—
157C3×C4×D4—31no—
158#946—31no—
159Q8×Dic3—31no—
160C2×#216—31no—
161C2×#215—31no—
162#938—61no—
163#937—61no—
164#937—61no—
165#936—31no—
166#936—61no—
167#930C2×D311yescharacteristic
168C4×#67C2×D311yescharacteristic
169#926—31no—
170#926—31no—
171#926—31no—
172#926—61no—
173#924—31no—
174#924—31no—
175#924C2×D311yescharacteristic, complemented
176C2×Dic12—31no—
177C2×#204—31no—
178C2×#204C2×D311yescharacteristic
179C2×ΓL(1,𝔽25)C2×D311yescharacteristic
180#898—61no—
181#897—31no—
182#894—61no—
183#893—31no—
184#892—31no—
185#888—31no—
186#887—61no—
187#887—61no—
188#885—61no—
189#884—61no—
190#883—61no—
191D3×C22⋊C4—61no—
192D3×C22⋊C4—61no—
193#879—61no—
194#879—61no—
195#879—61no—
196#875—31no—
197C4×D12—31no—
198#869—31no—
199C4×Dic6—31no—
200C3×#106—31no—
201C3×C4⋊C8—31no—
202C3×#103—31no—
203C3×#102—31no—
204C3×C22⋊C8—31no—
205C3×C22⋊C8—31no—
206C3×#97—31no—
207#832—31no—
208#832—31no—
209#830C2×D311yescharacteristic, complemented
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821—61no—
219#821C2×D311yescharacteristic
220(C2×D3)⋊C8C2×D311yescharacteristic
221#818—31no—
222#817—31no—
223#817C2×D311yescharacteristic, complemented
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—61no—
230#816—61no—
231#816C2×D311yescharacteristic, complemented
232#815C2×D311yescharacteristic, complemented
233Dic3⋊C8C2×D311yescharacteristic, complemented
234#810—31no—
235#809—31no—
236#808—31no—
237#807—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4×C3⋊D3—42no—
256#634—21no—
257#634—21no—
258C3×#67—41no—
259C3×#67—81no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×D12—21no—
267C3×D12—21no—
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#627—42no—
273#626—42no—
274#624—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—91no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—31no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—31no—
292#418—91no—
293#416—91no—
294C23×D3—61no—
295C23×D3—61no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C22×C3×C4—21no—
301C22×C3×C4—31no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—21no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309C2×#67D1211yescharacteristic
310D3×D4—62no—
311D3×D4—121no—
312#235—62no—
313#235—62no—
314#235—64no—
315#235—121no—
316#235—121no—
317#235—122no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—61no—
321C2×D12—62no—
322C2×D12—61no—
323C2×D12—121no—
324C2×D12C22×D311yescharacteristic
325C2×C4×D3—61no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—121no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6—31no—
332C2×Dic6—31no—
333C2×Dic6—61no—
334C2×Dic6—61no—
335C2×Dic6—61no—
336C2×Dic6C22×D311yescharacteristic
337C3×SD16—121no—
338C3×M16—121no—
339C2×C3×C8—21no—
340C2×C3×C8—21no—
341C2×C3×C8—31no—
342C2×C3×C8—31no—
343C2×C3×C8—41no—
344C2×C3×C8—41no—
345C2×C3×C8—42no—
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C2×C3×C8C22×D311yescharacteristic
349C2×C3×C8C22×D311yescharacteristic
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359#217—21no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—121no—
368#217D1211yescharacteristic
369#216—121no—
370#215—62no—
371(C2×D3)⋊C4—21no—
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—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4D1211yescharacteristic
380C4⋊Dic3—31no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—61no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3C22×D311yescharacteristic
390C4⋊Dic3C22×D311yescharacteristic
391Dic3⋊C4—21no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4D1211yescharacteristic
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3—121no—
405C4×Dic3C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408Dic12—121no—
409#204—41no—
410#204—62no—
411ΓL(1,𝔽25)—41no—
412C22×C32—21no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C22×D411yescharacteristic
416C2×C3⋊D3—22no—
417C2×C3⋊D3—41no—
418C2×C3⋊D3—41no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425D32—84no—
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—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C2×#41—91no—
439C22×D4—91no—
440C2×Q16—91no—
441C2×SD16—31no—
442C2×SD16—91no—
443C2×M16—31no—
444C22×C8D3211yescharacteristic, complemented
445C4⋊Q8—91no—
446#126—181no—
447#126—181no—
448#124—91no—
449#124—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454#121—31no—
455#121—181no—
456#120—181no—
457C4×Q8—91no—
458C4×Q8—181no—
459C4×D4—31no—
460C4×D4—91no—
461#117—91no—
462#117—91no—
463C2×C22⋊C4—181no—
464#107—91no—
465#106—31no—
466#106—91no—
467C4⋊C8—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#103—91no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—31no—
480#97—31no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—61no—
484C23×C3C2×D1211yescharacteristic
485C23×C3D3×D411yescharacteristic
486C22×D3—21no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3—122no—
491C22×D3—122no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3C2×D1211yescharacteristic
497C3×Q8—61no—
498C3×Q8—61no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—121no—
502C3×D4—241no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—41no—
524#67—81no—
525#67—122no—
526#67—122no—
527#67—122no—
528#67—124no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544D12—21no—
545D12—21no—
546D12—32no—
547D12—32no—
548D12—62no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—122no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3—124no—
558C4×D3—241no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—62no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—61no—
567Dic6—121no—
568Dic6—122no—
569Dic6—122no—
570C3×C8—21no—
571C3×C8—21no—
572C3×C8—21no—
573C3×C8—21no—
574C3×C8—41no—
575C3×C8—41no—
576C3×C8—61no—
577C3×C8—61no—
578C3⋊C8—21no—
579C3⋊C8—21no—
580C2×C32—41no—
581C2×C32#54611yescharacteristic
582C2×C32#57511yescharacteristic
583C2×C32#57711yescharacteristic
584C3⋊D3—42no—
585C3×D3—41no—
586C3×D3—81no—
587C24—181no—
588#41—182no—
589#41—361no—
590C2×Q8—31no—
591C2×Q8—91no—
592C2×Q8—181no—
593C2×D4—31no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—181no—
598C2×D4—182no—
599C2×D4—181no—
600C2×D4—361no—
601C22×C4—31no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4C2×D3211yescharacteristic
605Q16—361no—
606SD16—121no—
607SD16—182no—
608M16—121no—
609C2×C8—31no—
610C2×C8—31no—
611C2×C8—41no—
612C2×C8C2×D3211yescharacteristic
613C2×C8C2×D3211yescharacteristic
614C4⋊C4—31no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—91no—
619C4⋊C4—91no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4—181no—
624C22⋊C4—31no—
625C22⋊C4—31no—
626C22⋊C4—61no—
627C22⋊C4—61no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C42—31no—
636C42—181no—
637C42—181no—
638C42—181no—
639C22×C3—22no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C22×D1211yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3—244no—
673C2×D3—244no—
674C3×C4—22no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—61no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4#100411yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4D3×#4111yescharacteristic
689Dic3—21no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—122no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—121no—
701Dic3—121no—
702Dic3—241no—
703Dic3—241no—
704C32#331111yescharacteristic, complemented, Sylow
705C23—31no—
706C23—61no—
707C23—181no—
708C23—362no—
709C23—362no—
710C23—721no—
711C23D3×D1211yescharacteristic
712Q8—61no—
713Q8—61no—
714Q8—181no—
715Q8—181no—
716Q8—362no—
717D4—61no—
718D4—61no—
719D4—92no—
720D4—121no—
721D4—181no—
722D4—241no—
723D4—362no—
724D4—362no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—362no—
739C2×C4—721no—
740C2×C4D3×D1211yescharacteristic
741C2×C4C22×D3211yescharacteristic
742C8—21no—
743C8—21no—
744C8—61no—
745C8—61no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—42no—
750C2×C3—41no—
751C2×C3—41no—
752C2×C3—121no—
753C2×C3—241no—
754C2×C3#555411yescharacteristic
755C2×C3#561011yescharacteristic
756C2×C3#574811yescharacteristic
757C2×C3#575111yescharacteristic
758C2×C3#576211yescharacteristic
759C2×C3#576811yescharacteristic
760D3—41no—
761D3—81no—
762D3—122no—
763D3—122no—
764D3—242no—
765C22—21no—
766C22—21no—
767C22—21no—
768C22—61no—
769C22—61no—
770C22—61no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—182no—
775C22—361no—
776C22—361no—
777C22—724no—
778C22C2×D3×D1211yescharacteristic
779C4—21no—
780C4—61no—
781C4—61no—
782C4—61no—
783C4—121no—
784C4—121no—
785C4—121no—
786C4—361no—
787C4—361no—
788C4—361no—
789C4#6430611yescharacteristic
790C4#6433011yescharacteristic
791C3—21no—
792C3#7950211yescharacteristic, complemented
793C3#8068611yescharacteristic, complemented
794C2—41no—
795C2—121no—
796C2—241no—
797C2—362no—
798C2#1059467611yescharacteristic
799C2#1059467711yescharacteristic
800C2#1059507511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595078C2
hypercenterC22×C8D32
hypocenterC32#3311
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. #10594841C2semidirect
3. #10592812C2semidirect
4. C3×#5114C2semidirect
5. C3×#5111C2semidirect
6. #10591184C2semidirect
7. #10591093C2semidirect
8. #10590942C2semidirect
9. #10590939C2semidirect
10. #10590895C2semidirect
11. #10590859C2semidirect
12. #10590849C2semidirect
13. #10590795C2semidirect
14. #10590759C2semidirect
15. #10590709C2semidirect
20. C22×C32×C8C22semidirect
21. #64135C22semidirect
24. C3×#924C22semidirect
32. #63918C22semidirect
39. Dic3×Dic6C22semidirect
42. C2×#3719C22semidirect
46. #63643C22semidirect
47. #63643C22semidirect
48. C3×#830C22semidirect
51. C3×#817C22semidirect
52. C3×#816C22semidirect
53. C3×#815C22semidirect
54. C3×Dic3⋊C8C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
57. #63567C22semidirect
71. #5114D3semidirect
75. #5111D3semidirect
153. C22×C3×C8C2×D3semidirect
154. C22×C3×C8C2×D3semidirect
175. #924C2×D3semidirect
209. #830C2×D3semidirect
223. #817C2×D3semidirect
231. #816C2×D3semidirect
232. #815C2×D3semidirect
233. Dic3⋊C8C2×D3semidirect
444. C22×C8D32semidirect
704. C32#3311semidirect
792. C3#79502semidirect
793. C3#80686semidirect

Maximal subgroups

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

subgroupindex
#105950782
#105948412
#105928122
C3×#51142
C3×#51112
#105911842
#105910932
#105909422
#105909392
#105908952
#105908592
#105908492
#105907952
#105907592
#105907092
#806863
#795023