Finite Group Databasebeta

← #11889300

Subgroups — #11889300

Order 1152.

860 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#10595427C211yesmaximal, characteristic
2#10594581C211yesmaximal, characteristic, complemented
3#10592497C211yesmaximal, characteristic, complemented
4C3×#4815C211yesmaximal, characteristic, complemented
5C3×#4804C211yesmaximal, characteristic, complemented
6#10591632C211yesmaximal, characteristic, complemented
7#10591599C211yesmaximal, characteristic, complemented
8#10591598C211yesmaximal, characteristic, complemented
9#10590946C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590776C211yesmaximal, characteristic, complemented
12#10590723C211yesmaximal, characteristic, complemented
13#10590592C211yesmaximal, characteristic, complemented
14#10590461C211yesmaximal, characteristic, complemented
15#10590424C211yesmaximal, characteristic, complemented
16#81526—31nomaximal
17#78855—31nomaximal
18C2×C3×#239C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64156C2211yescharacteristic
21C2×#3756C2211yescharacteristic, complemented
22C2×#3744C2211yescharacteristic
23#64096C2211yescharacteristic, complemented
24C3×#946C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic, complemented
26C3×#892C2211yescharacteristic
27C3×#892C2211yescharacteristic, complemented
28#63922—21no—
29D3×(C2×D3)⋊C4—21no—
30#63919C2211yescharacteristic, complemented
31C4×#627—21no—
32#63915—21no—
33#63909C2211yescharacteristic
34C4×#625C2211yescharacteristic
35#63898C2211yescharacteristic
36#63886—21no—
37#63859—21no—
38#63859—21no—
39#63857C2211yescharacteristic
40#63857C2211yescharacteristic, complemented
41#63850—21no—
42C2×#3716C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63641C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#817C2211yescharacteristic, complemented
52C3×#809C2211yescharacteristic
53C3×#807C2211yescharacteristic, complemented
54#63574C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60#63555C2211yescharacteristic, complemented
61#5829—31no—
62#5630—31no—
63#5533—31no—
64#5533—31no—
65C3×#485—31no—
66C3×#416—31no—
67#5239—31no—
68#5114—31no—
69#5111—31no—
70#5052—31no—
71#5003—31no—
72#5001—31no—
73#4889—31no—
74#4885—31no—
75#4870—31no—
76#4864—31no—
77#4816—31no—
78#4815D311yescharacteristic, complemented
79#4808—31no—
80#4804D311yescharacteristic, complemented
81#4798—31no—
82#4798—31no—
83#4798—61no—
84#4794—31no—
85#4794—31no—
86#4776—31no—
87#4770—31no—
88#4761—31no—
89#4757—31no—
90#4731—31no—
91#4728—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C3×#239—22no—
97C3×#239—41no—
98C2×C3×D12—21no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×#627—21no—
104C2×#626—21no—
105C2×#626—21no—
106C2×#625D411yescharacteristic
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3756—41no—
113#3752—21no—
114#3752—21no—
115#3750—21no—
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119#3744—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×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133#3724D411yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136#3722—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141(C2×D3)⋊Dic3D411yescharacteristic
142#3716—22no—
143#3711—41no—
144#3311—91noSylow
145C2×C3×#41—31no—
146C2×#239C2×D311yescharacteristic
147C2×D3×D4—31no—
148C22×D12—31no—
149C22×C3×C8—31no—
150C3×C22⋊Q8—31no—
151C3×#117—31no—
152C3×#117—31no—
153#947—31no—
154#947—31no—
155#947—61no—
156#946C2×D311yescharacteristic
157C2×#216—31no—
158C2×#216—31no—
159C2×#216—61no—
160#939—61no—
161#937—61no—
162D4×Dic3—31no—
163C2×#214—31no—
164#930—31no—
165#929—61no—
166C4×#67—31no—
167C4×#67—31no—
168C2×(C2×D3)⋊C4—61no—
169#924—31no—
170#924—31no—
171C2×#208—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—61no—
176C2×ΓL(1,𝔽25)—31no—
177C2×D3×C8C2×D311yescharacteristic, complemented
178#897—31no—
179#897—31no—
180#895—31no—
181#895—61no—
182#894—61no—
183#893—31no—
184#892C2×D311yescharacteristic
185#892C2×D311yescharacteristic, complemented
186#888—31no—
187#888—31no—
188#887—31no—
189#887—31no—
190#887—61no—
191#885—61no—
192#885—61no—
193#882—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#879—61no—
197#876—61no—
198#876—61no—
199C4×Dic6—61no—
200C4×Dic6—61no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211#835C2×D311yescharacteristic, complemented
212#835C2×D311yescharacteristic, complemented
213#832—31no—
214#830—31no—
215#821—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8C2×D311yescharacteristic
220#817C2×D311yescharacteristic, complemented
221#816—31no—
222#815—31no—
223#815—31no—
224Dic3⋊C8—31no—
225Dic3⋊C8—31no—
226Dic3⋊C8—61no—
227#810—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#809C2×D311yescharacteristic
235#808—31no—
236#808—31no—
237#807C2×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—
245C32×Q8—21no—
246C32×Q8—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—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—21no—
263C3×D12—42no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270#627—42no—
271#626—42no—
272#626—81no—
273#625—41no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#556—91no—
280#546—91no—
281#489—91no—
282#485—31no—
283#482—91no—
284#476—91no—
285#470—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290#440—91no—
291#435—91no—
292#418—91no—
293#416—31no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—21no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—31no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C22×Dic3—61no—
311#239—22no—
312#239—41no—
313D3×D4—62no—
314D3×D4—121no—
315C2×D12—21no—
316C2×D12—31no—
317C2×D12—31no—
318C2×D12—61no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—121no—
323C2×D12C22×D311yescharacteristic
324C2×C4×D3—21no—
325C2×C4×D3—61no—
326C2×C4×D3C22×D311yescharacteristic
327C2×C4×D3C22×D311yescharacteristic
328C2×Dic6—31no—
329C2×Dic6—31no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—61no—
333C2×C3×C8—21no—
334C2×C3×C8—31no—
335C2×C3×C8—31no—
336C2×C3×C8—121no—
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4C22×D311yescharacteristic
345C3×C4⋊C4C22×D311yescharacteristic
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C42—61no—
350C3×C42—61no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#216—121no—
357#216—121no—
358#216—122no—
359#214—62no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—31no—
364(C2×D3)⋊C4—31no—
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—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—121no—
375(C2×D3)⋊C4—121no—
376C4⋊Dic3—61no—
377C4⋊Dic3—61no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—31no—
383Dic3⋊C4—31no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—121no—
391C4×Dic3—21no—
392C4×Dic3—21no—
393C4×Dic3—31no—
394C4×Dic3—31no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—121no—
399#208—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405#204—62no—
406#204—121no—
407#204—121no—
408#204—122no—
409ΓL(1,𝔽25)—121no—
410D3×C8—41no—
411C22×C32C22×D411yescharacteristic
412C2×C3⋊D3—41no—
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3×D3—22no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424D32—84no—
425C32×C4—41no—
426C32×C4—41no—
427C32×C4C2×#4111yescharacteristic
428C32×C4H(5,𝔽2)11yescharacteristic
429C3⋊Dic3—21no—
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C2×#41—31no—
438C22×D4—91no—
439C2×Q16—91no—
440C2×SD16—91no—
441C2×SD16—91no—
442C2×M16—91no—
443C22×C8—31no—
444C4⋊Q8—91no—
445#126—181no—
446#126—181no—
447#124—91no—
448#124—181no—
449#123—181no—
450C22⋊Q8—31no—
451C22⋊Q8—91no—
452C22⋊Q8—91no—
453#121—91no—
454#121—181no—
455#120—181no—
456C4×Q8—91no—
457C4×Q8—181no—
458C4×D4—91no—
459C4×D4—91no—
460#117—31no—
461#117—31no—
462C2×C22⋊C4—181no—
463#107—31no—
464#106—31no—
465#106—91no—
466C4⋊C8—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103D3211yescharacteristic, complemented
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477C22⋊C8—31no—
478C22⋊C8—91no—
479#97—91no—
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×D3D3×D411yescharacteristic
494C22×D3D3×D411yescharacteristic
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—21no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×D4—32no—
502C3×D4—61no—
503C3×D4—122no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—122no—
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—122no—
524#67—121no—
525#67—121no—
526#67—241no—
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—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—241no—
540C2×Dic3D3×D411yescharacteristic
541C2×Dic3D3×D411yescharacteristic
542D12—21no—
543D12—42no—
544D12—61no—
545D12—61no—
546D12—61no—
547D12—61no—
548D12—121no—
549D12—121no—
550D12—122no—
551D12—241no—
552D12#23512yes—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—241no—
559Dic6—62no—
560Dic6—61no—
561Dic6—61no—
562Dic6—61no—
563Dic6—61no—
564Dic6—121no—
565Dic6—122no—
566Dic6—122no—
567C3×C8—21no—
568C3×C8—21no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—121no—
577C2×C32#54611yescharacteristic
578C2×C32#57511yescharacteristic
579C2×C32#57711yescharacteristic
580C3⋊D3—81no—
581C3×D3—41no—
582C3×D3—42no—
583C3×D3—41no—
584C24—181no—
585#41—62no—
586#41—121no—
587C2×Q8—91no—
588C2×Q8—181no—
589C2×Q8C2×D3211yescharacteristic
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—91no—
593C2×D4—91no—
594C2×D4—181no—
595C2×D4—182no—
596C2×D4—181no—
597C2×D4—361no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—61no—
601C22×C4—181no—
602Q16—361no—
603SD16—182no—
604SD16—361no—
605M16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—121no—
610C2×C8C2×D3211yescharacteristic
611C4⋊C4—31no—
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—91no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C4⋊C4C2×D3211yescharacteristic
621C22⋊C4—61no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—91no—
625C22⋊C4—91no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C42—61no—
633C42—61no—
634C42—91no—
635C42—181no—
636C22×C3—21no—
637C22×C3—62no—
638C22×C3—61no—
639C22×C3—61no—
640C22×C3—61no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3C2×D3×D411yescharacteristic
647C22×C3C2×D3×D411yescharacteristic
648C2×D3—21no—
649C2×D3—21no—
650C2×D3—22no—
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—21no—
654C2×D3—21no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3—244no—
667C2×D3—244no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—81no—
677C3×C4—81no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23511yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—61no—
691Dic3—61no—
692Dic3—61no—
693Dic3—61no—
694Dic3—121no—
695Dic3—121no—
696Dic3—122no—
697Dic3—121no—
698Dic3—121no—
699C32#331111yescharacteristic, complemented, Sylow
700C23—31no—
701C23—31no—
702C23—61no—
703C23—181no—
704C23—362no—
705C23—362no—
706C23—721no—
707Q8—21no—
708Q8—21no—
709Q8—181no—
710Q8—181no—
711Q8—362no—
712D4—32no—
713D4—61no—
714D4—122no—
715D4—181no—
716D4—181no—
717D4—362no—
718D4—361no—
719D4—721no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—91no—
732C2×C4—91no—
733C2×C4—122no—
734C2×C4—181no—
735C2×C4—721no—
736C2×C4C22×D3211yescharacteristic
737C8—21no—
738C8—61no—
739C8—61no—
740C8—181no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—21no—
744C2×C3—121no—
745C2×C3—122no—
746C2×C3—121no—
747C2×C3#549011yescharacteristic
748C2×C3#565411yescharacteristic
749C2×C3#576811yescharacteristic
750C2×C3#577011yescharacteristic
751C2×C3#577011yescharacteristic
752C2×C3#577711yescharacteristic
753D3—41no—
754D3—42no—
755D3—41no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—361no—
769C22—361no—
770C22—361no—
771C22—724no—
772C22D32×D411yescharacteristic
773C4—41no—
774C4—41no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—181no—
781C4—181no—
782C4—361no—
783C4D3×#23511yescharacteristic
784C4#6431411yescharacteristic
785C3—21no—
786C3#7885511yescharacteristic, complemented
787C3#8152611yescharacteristic, complemented
788C2—121no—
789C2—121no—
790C2—122no—
791C2—721no—
792C2#1059427211yescharacteristic
793C2#1059475711yescharacteristic
794C2#1059476311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
prime radical#10595427C2
hypercenter#103D32
hypocenterC32#3311
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #10594581C2semidirect
3. #10592497C2semidirect
4. C3×#4815C2semidirect
5. C3×#4804C2semidirect
6. #10591632C2semidirect
7. #10591599C2semidirect
8. #10591598C2semidirect
9. #10590946C2semidirect
10. #10590830C2semidirect
11. #10590776C2semidirect
12. #10590723C2semidirect
13. #10590592C2semidirect
14. #10590461C2semidirect
15. #10590424C2semidirect
21. C2×#3756C22semidirect
23. #64096C22semidirect
25. C2×C3×D3×C8C22semidirect
27. C3×#892C22semidirect
30. #63919C22semidirect
40. #63857C22semidirect
44. C32×#103C22semidirect
45. #63641C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#817C22semidirect
53. C3×#807C22semidirect
54. #63574C22semidirect
55. #63567C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. #63555C22semidirect
78. #4815D3semidirect
80. #4804D3semidirect
177. C2×D3×C8C2×D3semidirect
185. #892C2×D3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
211. #835C2×D3semidirect
212. #835C2×D3semidirect
220. #817C2×D3semidirect
237. #807C2×D3semidirect
470. #103D32semidirect
699. C32#3311semidirect
786. C3#78855semidirect
787. C3#81526semidirect

Maximal subgroups

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

subgroupindex
#105954272
#105945812
#105924972
C3×#48152
C3×#48042
#105916322
#105915992
#105915982
#105909462
#105908302
#105907762
#105907232
#105905922
#105904612
#105904242
#815263
#788553