Finite Group Databasebeta

← #11887296

Subgroups — #11887296

Order 1152.

878 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#10595229C211yesmaximal, characteristic
2#10594553C211yesmaximal, characteristic, complemented
3#10592477C211yesmaximal, characteristic, complemented
4C3×D3×#102C211yesmaximal, characteristic, complemented
5C3×#4768C211yesmaximal, characteristic, complemented
6#10591459C211yesmaximal, characteristic, complemented
7#10591441C211yesmaximal, characteristic, complemented
8#10591425C211yesmaximal, characteristic, complemented
9#10590956C211yesmaximal, characteristic, complemented
10#10590848C211yesmaximal, characteristic, complemented
11#10590744C211yesmaximal, characteristic, complemented
12C8×#626C211yesmaximal, characteristic, complemented
13#10590618C211yesmaximal, characteristic, complemented
14#10590516C211yesmaximal, characteristic, complemented
15#10590469C211yesmaximal, characteristic, complemented
16#81652—31nomaximal
17#78759—31nomaximal
18C2×C3×D3×D4C2211yescharacteristic
19C2×#3796C2211yescharacteristic
20#64147C2211yescharacteristic
21C2×#3754C2211yescharacteristic
22C2×C8×C3⋊D3C2211yescharacteristic, complemented
23#64106C2211yescharacteristic, complemented
24C3×#936C2211yescharacteristic
25C2×C3×D3×C8C2211yescharacteristic
26C3×D3×C4⋊C4C2211yescharacteristic
27C3×#890C2211yescharacteristic, complemented
28#63977—21no—
29#63971—21no—
30#63969—21no—
31D3×#217—21no—
32C4×#626C2211yescharacteristic
33Dic3×D12C2211yescharacteristic
34#63857C2211yescharacteristic
35#63856C2211yescharacteristic
36#63850—21no—
37#63849C2211yescharacteristic, complemented
38#63848—21no—
39#63845—21no—
40#63844C2211yescharacteristic, complemented
41#63841—21no—
42C2×#3719C2211yescharacteristic, complemented
43C2×#3716C2211yescharacteristic
44C32×#102C2211yescharacteristic
45#63643C2211yescharacteristic, complemented
46#63635C2211yescharacteristic, complemented
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#816C2211yescharacteristic, complemented
51C3×C8×Dic3C2211yescharacteristic, complemented
52C3×#810C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54#63575C2211yescharacteristic, complemented
55#63573C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63565C2211yescharacteristic, complemented
58#63562C2211yescharacteristic
59#63557C2211yescharacteristic, complemented
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61#5806—31no—
62#5694—31no—
63#5676—31no—
64#5513—31no—
65C3×#488—31no—
66C2×C3×#102—31no—
67#5218—31no—
68#5116—31no—
69C8×#67—31no—
70#5066—31no—
71#5054—31no—
72#4971—31no—
73#4813—31no—
74#4808—31no—
75#4805—31no—
76#4804—31no—
77#4784—31no—
78#4783—31no—
79#4779—31no—
80#4778—31no—
81#4778—31no—
82#4778—61no—
83#4776—31no—
84#4772—31no—
85D3×#102D311yescharacteristic, complemented
86#4768D311yescharacteristic, complemented
87#4767—31no—
88#4766—31no—
89#4758—31no—
90C4×#204—31no—
91C8×D12—31no—
92C23×C3×D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95C2×C4×C3⋊D3C2311yescharacteristic
96C2×#634C2311yescharacteristic
97C2×C3×#67—21no—
98C3×D3×D4—22no—
99C3×D3×D4—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626D411yescharacteristic
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3796—22no—
109#3796—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3757—21no—
113#3754—41no—
114#3752—21no—
115C4⋊(C3⋊Dic3)—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C8×C3⋊D3—41no—
119C3×#217—21no—
120C3×#217—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
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⋊Dic3D411yescharacteristic
134#3722—21no—
135#3722D411yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141Dic32—21no—
142#3719—41no—
143#3716—22no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#239—31no—
147C2×#237—31no—
148C2×D3×D4C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×#125—31no—
151C3×#124—31no—
152C2×C3×C4⋊C4—31no—
153#953—61no—
154C2×#217—61no—
155#946—31no—
156C2×#216—31no—
157#939—61no—
158#938—31no—
159#938—31no—
160#938—61no—
161#936C2×D311yescharacteristic
162#935—61no—
163D4×Dic3—31no—
164C2×#214—31no—
165C2×#214—31no—
166C2×#214—31no—
167C2×#214—61no—
168#929—61no—
169C4×#67—31no—
170#926—61no—
171#924—31no—
172#924—31no—
173C2×Dic12—31no—
174C2×#204—31no—
175C2×D3×C8—31no—
176C2×D3×C8—31no—
177C2×D3×C8—61no—
178C2×D3×C8C2×D311yescharacteristic
179#898—61no—
180#898—61no—
181#897—31no—
182#897—31no—
183#897—31no—
184#897—61no—
185#894—61no—
186#892—31no—
187#892—31no—
188#892—61no—
189D3×C4⋊C4C2×D311yescharacteristic
190#890—61no—
191#890C2×D311yescharacteristic, complemented
192#889—61no—
193#887—31no—
194#884—61no—
195#883—61no—
196#882—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×Dic6—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×#102—21no—
204C3×#102—31no—
205C3×#102—31no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C4×C8—31no—
211#835—31no—
212#832—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#830—31no—
216#821C2×D311yescharacteristic
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220#818—31no—
221#817—31no—
222#816—31no—
223#816—31no—
224#816—61no—
225#816C2×D311yescharacteristic, complemented
226Dic3⋊C8—31no—
227C8×Dic3C2×D311yescharacteristic, complemented
228#810—31no—
229#810C2×D311yescharacteristic, complemented
230#809—31no—
231#809C2×D311yescharacteristic
232#808—31no—
233#808—31no—
234#808—31no—
235#808—61no—
236#807—31no—
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3C2×D411yescharacteristic
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D411yescharacteristic
253C4×C3⋊D3—21no—
254C4×C3⋊D3—21no—
255#634—21no—
256#634—21no—
257C3×#67—42no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12#4112yes—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—22no—
272#626—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C3⋊(C3⋊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—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×D4—21no—
298C2×C3×D4—31no—
299C2×C3×D4—61no—
300C2×C3×D4—62no—
301C2×C3×D4—121no—
302C2×C3×D4C22×D311yescharacteristic
303C2×C3×D4C22×D311yescharacteristic
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C2×#67—21no—
307C2×#67—31no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—121no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314#239—62no—
315#239—121no—
316#237—62no—
317#237—121no—
318D3×D4—22no—
319D3×D4—41no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12C22×D311yescharacteristic
323C2×C4×D3—21no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3C22×D311yescharacteristic
330C2×Dic6—31no—
331C2×Dic6—31no—
332C2×Dic6—61no—
333C2×Dic6C22×D311yescharacteristic
334C2×C3×C8—21no—
335C2×C3×C8—31no—
336C2×C3×C8—31no—
337C2×C3×C8—121no—
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—21no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4C22×D311yescharacteristic
347C3×C4⋊C4C22×D311yescharacteristic
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351#217—21no—
352#217—21no—
353#217—31no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#216—121no—
361#214—62no—
362#214—121no—
363#214—121no—
364#214—122no—
365(C2×D3)⋊C4—31no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
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—121no—
376C4⋊Dic3—21no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—121no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—62no—
407D3×C8—41no—
408D3×C8—121no—
409D3×C8—121no—
410D3×C8—122no—
411C22×C32—41no—
412C22×C32—41no—
413C22×C32—41no—
414C22×C32C22×D411yescharacteristic
415C2×C3⋊D3—21no—
416C2×C3⋊D3—21no—
417C2×C3⋊D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—21no—
420C2×C3×D3—22no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C2×C3×D3—84no—
424C2×C3×D3#13512yes—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—21no—
429C3⋊Dic3—41no—
430C3⋊Dic3—41no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
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×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—91no—
457C4×D4—91no—
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—91no—
467#103—31no—
468#103—31no—
469#103—91no—
470#103—91no—
471#102—31no—
472#102—31no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102D3211yescharacteristic
477C22⋊C8—91no—
478C22⋊C8—91no—
479C4×C8—31no—
480C23×C3—21no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3—41no—
484C23×C3—61no—
485C23×C3—122no—
486C23×C3—122no—
487C23×C3—241no—
488C22×D3—21no—
489C22×D3—31no—
490C22×D3—31no—
491C22×D3—42no—
492C22×D3—42no—
493C22×D3—61no—
494C22×D3—81no—
495C22×D3D3×D411yescharacteristic
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—21no—
499C3×D4—21no—
500C3×D4—21no—
501C3×D4—21no—
502C3×D4—32no—
503C3×D4—41no—
504C3×D4—41no—
505C3×D4—61no—
506C3×D4—122no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—122no—
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—42no—
523#67—62no—
524#67—122no—
525#67—241no—
526#67—241no—
527#67—242no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—122no—
541C2×Dic3—241no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—62no—
547D12—122no—
548D12#23512yes—
549C4×D3—21no—
550C4×D3—21no—
551C4×D3—42no—
552C4×D3—61no—
553C4×D3—61no—
554C4×D3—61no—
555C4×D3—61no—
556C4×D3—121no—
557C4×D3—121no—
558C4×D3—122no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—61no—
563Dic6—61no—
564Dic6—61no—
565Dic6—61no—
566Dic6—121no—
567Dic6—121no—
568C3×C8—21no—
569C3×C8—21no—
570C3×C8—41no—
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—62no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C2×C32—81no—
579C2×C32#54611yescharacteristic
580C2×C32C2×#13511yescharacteristic
581C2×C32#57711yescharacteristic
582C3⋊D3—41no—
583C3×D3—22no—
584C3×D3—42no—
585C24—61no—
586#41—182no—
587#41—361no—
588C2×Q8—31no—
589C2×Q8—91no—
590C2×D4—31no—
591C2×D4—61no—
592C2×D4—62no—
593C2×D4—91no—
594C2×D4—121no—
595C2×D4—181no—
596C2×D4—181no—
597C2×D4C2×D3211yescharacteristic
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—91no—
601C22×C4—181no—
602C22×C4—181no—
603Q16—361no—
604SD16—182no—
605SD16—361no—
606C2×C8—31no—
607C2×C8—31no—
608C2×C8—91no—
609C2×C8—121no—
610C2×C8—361no—
611C2×C8C2×D3211yescharacteristic
612C4⋊C4—31no—
613C4⋊C4—31no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—61no—
617C4⋊C4—91no—
618C4⋊C4—91no—
619C4⋊C4—181no—
620C4⋊C4—181no—
621C4⋊C4—181no—
622C4⋊C4—181no—
623C4⋊C4C2×D3211yescharacteristic
624C22⋊C4—61no—
625C22⋊C4—61no—
626C22⋊C4—91no—
627C22⋊C4—91no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C22⋊C4—181no—
631C22⋊C4—181no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—181no—
636C42—181no—
637C22×C3—21no—
638C22×C3—32no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—62no—
648C22×C3—81no—
649C22×C3—81no—
650C22×C3—81no—
651C22×C3—121no—
652C22×C3—121no—
653C22×C3—244no—
654C22×C3C2×D3×D411yescharacteristic
655C22×C3C2×D3×D411yescharacteristic
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—22no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—62no—
662C2×D3—61no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—84no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3#91212yes—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—81no—
680C3×C4—121no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4C2×#23511yescharacteristic
684C3×C4#100411yescharacteristic
685C3×C4D3×#4111yescharacteristic
686C3×C4#100911yescharacteristic
687Dic3—21no—
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—61no—
694Dic3—61no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3—121no—
699Dic3—121no—
700Dic3—241no—
701Dic3—241no—
702C32#329611yescharacteristic, complemented, Sylow
703C23—21no—
704C23—31no—
705C23—61no—
706C23—91no—
707C23—122no—
708C23—122no—
709C23—241no—
710Q8—61no—
711Q8—61no—
712Q8—181no—
713Q8—181no—
714D4—21no—
715D4—21no—
716D4—32no—
717D4—61no—
718D4—122no—
719D4—182no—
720D4—362no—
721D4—721no—
722C2×C4—21no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—91no—
732C2×C4—122no—
733C2×C4—181no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—362no—
738C2×C4—721no—
739C2×C4C22×D3211yescharacteristic
740C8—21no—
741C8—61no—
742C8—61no—
743C8—181no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—62no—
748C2×C3—81no—
749C2×C3—81no—
750C2×C3—122no—
751C2×C3—161no—
752C2×C3#549011yescharacteristic
753C2×C3#567611yescharacteristic
754C2×C3C2×#91211yescharacteristic
755C2×C3#576211yescharacteristic
756C2×C3D3×#13511yescharacteristic
757C2×C3#577011yescharacteristic
758D3—22no—
759D3—42no—
760D3—122no—
761D3—121no—
762D3—121no—
763C22—32no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22—61no—
768C22—61no—
769C22—62no—
770C22—121no—
771C22—121no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—244no—
776C22D32×D411yescharacteristic
777C4—41no—
778C4—61no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—181no—
785C4—361no—
786C4—361no—
787C4D3×#23511yescharacteristic
788C4#6431411yescharacteristic
789C3—21no—
790C3#7875911yescharacteristic, complemented
791C3#8165211yescharacteristic, complemented
792C2—62no—
793C2—81no—
794C2—122no—
795C2—361no—
796C2#1059428011yescharacteristic
797C2D3×#91211yescharacteristic
798C2#1059475311yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595229C2
hypercenter#102D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594553C2semidirect
3. #10592477C2semidirect
4. C3×D3×#102C2semidirect
5. C3×#4768C2semidirect
6. #10591459C2semidirect
7. #10591441C2semidirect
8. #10591425C2semidirect
9. #10590956C2semidirect
10. #10590848C2semidirect
11. #10590744C2semidirect
12. C8×#626C2semidirect
13. #10590618C2semidirect
14. #10590516C2semidirect
15. #10590469C2semidirect
22. C2×C8×C3⋊D3C22semidirect
23. #64106C22semidirect
27. C3×#890C22semidirect
37. #63849C22semidirect
40. #63844C22semidirect
42. C2×#3719C22semidirect
45. #63643C22semidirect
46. #63635C22semidirect
50. C3×#816C22semidirect
51. C3×C8×Dic3C22semidirect
52. C3×#810C22semidirect
54. #63575C22semidirect
55. #63573C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63565C22semidirect
59. #63557C22semidirect
85. D3×#102D3semidirect
86. #4768D3semidirect
191. #890C2×D3semidirect
225. #816C2×D3semidirect
227. C8×Dic3C2×D3semidirect
229. #810C2×D3semidirect
702. C32#3296semidirect
790. C3#78759semidirect
791. C3#81652semidirect

Maximal subgroups

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

subgroupindex
#105952292
#105945532
#105924772
C3×D3×#1022
C3×#47682
#105914592
#105914412
#105914252
#105909562
#105908482
#105907442
C8×#6262
#105906182
#105905162
#105904692
#816523
#787593