Finite Group Databasebeta

← #11887814

Subgroups — #11887814

Order 1152.

846 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595362C211yesmaximal, characteristic
2#10595344C211yesmaximal, characteristic, complemented
3#10592885C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5185C211yesmaximal, characteristic, complemented
6#10591655C211yesmaximal, characteristic, complemented
7#10591614C211yesmaximal, characteristic, complemented
8#10591591C211yesmaximal, characteristic, complemented
9#10591559C211yesmaximal, characteristic, complemented
10#10591552C211yesmaximal, characteristic, complemented
11#10591537C211yesmaximal, characteristic, complemented
12#10590954C211yesmaximal, characteristic, complemented
13#10590814C211yesmaximal, characteristic, complemented
14#10590720C211yesmaximal, characteristic, complemented
15#10590650C211yesmaximal, characteristic, complemented
16#80769—31nomaximal
17#80616—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C2×C3×#215C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63916C2211yescharacteristic
30#63913—21no—
31#63912—21no—
32C4×#626C2211yescharacteristic
33#63900C2211yescharacteristic
34#63896—21no—
35#63881—21no—
36#63869C2211yescharacteristic
37#63859—21no—
38#63854—21no—
39#63847—21no—
40#63844C2211yescharacteristic
41#63841C2211yescharacteristic
42#63836—21no—
43C2×#3710C2211yescharacteristic
44#63662C2211yescharacteristic
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63576C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63563C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61#5677—31no—
62#5639—31no—
63#5633—31no—
64#5581—31no—
65C3×#467—31no—
66C3×#464—31no—
67#5188D311yescharacteristic, complemented
68#5186—31no—
69#5186—31no—
70#5186—61no—
71#5185D311yescharacteristic, complemented
72#5173—31no—
73#5171—31no—
74#5113—31no—
75C8×#67—31no—
76#5056—31no—
77#5047—31no—
78#5045—31no—
79C4×#216—31no—
80#4882—31no—
81#4877—31no—
82#4834—31no—
83#4829—31no—
84#4815—31no—
85#4807—31no—
86D3×#103—31no—
87D3×#103—31no—
88#4800—31no—
89#4790—31no—
90#4774—31no—
91#4772—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94Q8×C3⋊D3—22no—
95Q8×C3⋊D3—41no—
96C2×C4×C3⋊D3—21no—
97C2×C4×C3⋊D3C2311yescharacteristic
98C2×#634—21no—
99C2×#634C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3C2311yescharacteristic
102C2×#626—21no—
103C2×#626D411yescharacteristic
104C2×#625—21no—
105C2×#624—21no—
106C2×D3×Dic3—21no—
107#3795—22no—
108#3795—41no—
109C32×Q16—41no—
110C2×C32×C8C2311yescharacteristic
111#3756—22no—
112#3752—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C3×#215—41no—
117C3×(C2×D3)⋊C4—21no—
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×C4×Dic3—21no—
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724—21no—
133#3724—21no—
134#3724—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3710—41no—
144#3300—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—61no—
148C2×#237—31no—
149C2×#235—31no—
150C2×C3×Q16—21no—
151C2×C3×Q16C2×D311yescharacteristic
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×SD16—31no—
154C22×C3×C8—31no—
155C3×#124—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159#947C2×D311yescharacteristic
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164#946C2×D311yescharacteristic
165Q8×Dic3C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—61no—
169C2×#215C2×D311yescharacteristic
170#938—31no—
171C4×#67—31no—
172#926—31no—
173C2×D3×C8—31no—
174C2×D3×C8—31no—
175C2×D3×C8C2×D311yescharacteristic
176#896—61no—
177#895—31no—
178#894—61no—
179#893—61no—
180#892—31no—
181#892—61no—
182D3×C4⋊C4—31no—
183D3×C4⋊C4—31no—
184#890—31no—
185#889—61no—
186#889—61no—
187#887—31no—
188#885—61no—
189#885—61no—
190#884—61no—
191#884—61no—
192#883—61no—
193#67⋊C4—61no—
194#879—61no—
195#878—61no—
196#876—61no—
197C4×D12—31no—
198#872—61no—
199#870—31no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×C4⋊C8—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#102—31no—
207#835—31no—
208#835—31no—
209#835—61no—
210#835C2×D311yescharacteristic
211#835C2×D311yescharacteristic
212#835C2×D311yescharacteristic
213#832—31no—
214#832—31no—
215#830—31no—
216#821—31no—
217#821C2×D311yescharacteristic
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222#818C2×D311yescharacteristic
223#817—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—31no—
228#816—61no—
229Dic3⋊C8C2×D311yescharacteristic
230C8×Dic3—31no—
231#810—31no—
232#810—31no—
233#809—31no—
234#808—31no—
235#807—31no—
236#807—31no—
237C4×C3⋊C8—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3C2×D411yescharacteristic
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4×C3⋊D3—21no—
252C4×C3⋊D3—21no—
253C4×C3⋊D3—42no—
254#634—21no—
255#634—42no—
256#634#4112yes—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267#626—22no—
268#626—42no—
269#625—42no—
270#624—42no—
271D3×Dic3—42no—
272C32×C8—21no—
273C3⋊(C3⋊C8)—21no—
274C3×C3⋊C8—21no—
275C3×C3⋊C8—21no—
276#552—91no—
277#548—91no—
278#488—91no—
279#485—91no—
280#480—91no—
281#479—91no—
282#467—31no—
283#465—91no—
284#464—31no—
285#452—91no—
286#451—91no—
287C4×Q16—91no—
288C8×D4—91no—
289#416—91no—
290C2×#103—91no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C2×C3×D4—31no—
298C22×C3×C4—31no—
299C2×#67—31no—
300C2×#67—61no—
301C2×#67—61no—
302C2×#67—61no—
303C22×Dic3—61no—
304D3×Q8—62no—
305D3×Q8—62no—
306D3×Q8—122no—
307D3×Q8—121no—
308D3×Q8—121no—
309D3×Q8—122no—
310#237—62no—
311#237—121no—
312#235—62no—
313#235—121no—
314C2×D12—31no—
315C2×D12—61no—
316C2×D12C22×D311yescharacteristic
317C2×C4×D3—31no—
318C2×C4×D3—31no—
319C2×C4×D3—61no—
320C2×C4×D3—61no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3—61no—
325C2×C4×D3—121no—
326C2×C4×D3C22×D311yescharacteristic
327C2×Dic6—31no—
328C2×Dic6—31no—
329C2×Dic6—61no—
330C2×Dic6—61no—
331C2×Dic6—61no—
332C2×Dic6—121no—
333C3×Q16—41no—
334C3×Q16—41no—
335C3×Q16—42no—
336C3×SD16—121no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—31no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C22⋊C4—61no—
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C42—31no—
354C3×C42—61no—
355#217—31no—
356#217—61no—
357#217—61no—
358#216—62no—
359#216—62no—
360#216—122no—
361#215—41no—
362(C2×D3)⋊C4—21no—
363(C2×D3)⋊C4—21no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—31no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—121no—
374C4⋊Dic3—21no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—31no—
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—
396C4×Dic3—21no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407D3×C8—41no—
408D3×C8—121no—
409D3×C8—121no—
410C22×C32C22×D411yescharacteristic
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3⋊D3#13512yes—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C32×C4—41no—
421C32×C4—41no—
422C32×C4C2×#4111yescharacteristic
423C32×C4H(5,𝔽2)11yescharacteristic
424C3⋊Dic3—22no—
425C3⋊Dic3—21no—
426C3⋊Dic3—41no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—41no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C2×#41—91no—
434C22×Q8—91no—
435C2×Q16—91no—
436C2×Q16D3211yescharacteristic
437C2×SD16—31no—
438C22×C8—31no—
439C22×C8—91no—
440#126—181no—
441#125—91no—
442#125—181no—
443#124—31no—
444#124—181no—
445#123—181no—
446C22⋊Q8—31no—
447C22⋊Q8—31no—
448C22⋊Q8—91no—
449C22⋊Q8—181no—
450#121—91no—
451#121—181no—
452C4×Q8—31no—
453C4×Q8—91no—
454C4×D4—91no—
455C4×D4—181no—
456#117—91no—
457#117—181no—
458C2×C4⋊C4—91no—
459#107—31no—
460#107—91no—
461#106—91no—
462C4⋊C8—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470#102—31no—
471#102—91no—
472#102—91no—
473C22⋊C8—91no—
474C22⋊C8—91no—
475C4×C8—91no—
476C23×C3—31no—
477C23×C3—61no—
478C22×D3—21no—
479C22×D3—31no—
480C22×D3—31no—
481C22×D3—61no—
482C22×D3D3×D411yescharacteristic
483C3×Q8—22no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—41no—
495C3×D4—61no—
496C3×D4—61no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—31no—
503C2×C3×C4—31no—
504C2×C3×C4—31no—
505C2×C3×C4—41no—
506C2×C3×C4—41no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4C23×D311yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514#67—62no—
515#67—122no—
516#67—122no—
517#67—122no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—31no—
522C2×Dic3—31no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3D3×D411yescharacteristic
532C2×Dic3D3×D411yescharacteristic
533C2×Dic3D3×D411yescharacteristic
534D12—21no—
535D12—21no—
536D12—62no—
537D12—122no—
538C4×D3—21no—
539C4×D3—21no—
540C4×D3—61no—
541C4×D3—61no—
542C4×D3—61no—
543C4×D3—61no—
544C4×D3—121no—
545C4×D3—121no—
546C4×D3—122no—
547C4×D3—122no—
548C4×D3—122no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—124no—
552Dic6—32no—
553Dic6—32no—
554Dic6—62no—
555Dic6—61no—
556Dic6—61no—
557Dic6—121no—
558Dic6—122no—
559Dic6—122no—
560Dic6—124no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—41no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C2×C32#54611yescharacteristic
572C2×C32C2×#13511yescharacteristic
573C2×C32#57811yescharacteristic
574C3⋊D3—22no—
575C3×D3—41no—
576C3×D3—81no—
577#41—182no—
578#41—361no—
579C2×Q8—91no—
580C2×Q8—181no—
581C2×Q8—182no—
582C2×Q8—361no—
583C2×Q8C2×D3211yescharacteristic
584C2×Q8C2×D3211yescharacteristic
585C2×D4—31no—
586C2×D4—91no—
587C2×D4—181no—
588C2×D4—181no—
589C22×C4—31no—
590C22×C4—91no—
591C22×C4—181no—
592C22×C4—181no—
593C22×C4—181no—
594Q16—41no—
595Q16—182no—
596SD16—121no—
597C2×C8—31no—
598C2×C8—31no—
599C2×C8—91no—
600C2×C8—121no—
601C2×C8—361no—
602C2×C8C2×D3211yescharacteristic
603C4⋊C4—31no—
604C4⋊C4—31no—
605C4⋊C4—31no—
606C4⋊C4—61no—
607C4⋊C4—61no—
608C4⋊C4—61no—
609C4⋊C4—91no—
610C4⋊C4—91no—
611C4⋊C4—181no—
612C4⋊C4—181no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—61no—
619C22⋊C4—61no—
620C22⋊C4—91no—
621C22⋊C4—91no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C42—31no—
626C42—61no—
627C42—181no—
628C42—181no—
629C22×C3—21no—
630C22×C3—61no—
631C22×C3—61no—
632C22×C3—61no—
633C22×C3—121no—
634C22×C3—121no—
635C22×C3—121no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C2×D3×D411yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3—21no—
641C2×D3—32no—
642C2×D3—32no—
643C2×D3—41no—
644C2×D3—41no—
645C2×D3—41no—
646C2×D3—62no—
647C2×D3—61no—
648C2×D3—61no—
649C2×D3—61no—
650C2×D3—61no—
651C2×D3—121no—
652C2×D3—121no—
653C3×C4—21no—
654C3×C4—21no—
655C3×C4—42no—
656C3×C4—41no—
657C3×C4—41no—
658C3×C4—41no—
659C3×C4—41no—
660C3×C4—61no—
661C3×C4—61no—
662C3×C4—61no—
663C3×C4—81no—
664C3×C4—121no—
665C3×C4—121no—
666C3×C4—121no—
667C3×C4#100411yescharacteristic
668C3×C4#100411yescharacteristic
669C3×C4D3×#4111yescharacteristic
670C3×C4D3×#4111yescharacteristic
671Dic3—21no—
672Dic3—21no—
673Dic3—21no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—62no—
678Dic3—61no—
679Dic3—62no—
680Dic3—61no—
681Dic3—122no—
682Dic3—121no—
683Dic3—121no—
684Dic3—121no—
685Dic3—241no—
686C32#330011yescharacteristic, complemented, Sylow
687C23—31no—
688C23—61no—
689C23—91no—
690Q8—21no—
691Q8—21no—
692Q8—21no—
693Q8—21no—
694Q8—92no—
695Q8—181no—
696Q8—362no—
697D4—61no—
698D4—61no—
699D4—182no—
700D4—362no—
701D4—362no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—31no—
705C2×C4—31no—
706C2×C4—31no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—91no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—362no—
718C2×C4—362no—
719C2×C4—362no—
720C2×C4C22×D3211yescharacteristic
721C8—21no—
722C8—61no—
723C8—61no—
724C8—181no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—121no—
729C2×C3—241no—
730C2×C3#561011yescharacteristic
731C2×C3#561211yescharacteristic
732C2×C3#576611yescharacteristic
733C2×C3D3×#13511yescharacteristic
734C2×C3D3×#13511yescharacteristic
735C2×C3#577911yescharacteristic
736D3—41no—
737D3—62no—
738D3—62no—
739D3—81no—
740D3—122no—
741C22—61no—
742C22—61no—
743C22—61no—
744C22—92no—
745C22—121no—
746C22—121no—
747C22—121no—
748C22—181no—
749C22—181no—
750C22D32×D411yescharacteristic
751C4—41no—
752C4—41no—
753C4—61no—
754C4—61no—
755C4—61no—
756C4—121no—
757C4—121no—
758C4—121no—
759C4—181no—
760C4—182no—
761C4—361no—
762C4#6431211yescharacteristic
763C4#6433011yescharacteristic
764C3—21no—
765C3#8061611yescharacteristic, complemented
766C3#8076911yescharacteristic, complemented
767C2—121no—
768C2—182no—
769C2—241no—
770C2#1059476411yescharacteristic
771C2#1059476611yescharacteristic
772C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595362C2
hypercenterC2×Q16D32
hypocenterC32#3300
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #10595344C2semidirect
3. #10592885C2semidirect
4. C3×#5188C2semidirect
5. C3×#5185C2semidirect
6. #10591655C2semidirect
7. #10591614C2semidirect
8. #10591591C2semidirect
9. #10591559C2semidirect
10. #10591552C2semidirect
11. #10591537C2semidirect
12. #10590954C2semidirect
13. #10590814C2semidirect
14. #10590720C2semidirect
15. #10590650C2semidirect
67. #5188D3semidirect
71. #5185D3semidirect
686. C32#3300semidirect
765. C3#80616semidirect
766. C3#80769semidirect

Maximal subgroups

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

subgroupindex
#105953622
#105953442
#105928852
C3×#51882
C3×#51852
#105916552
#105916142
#105915912
#105915592
#105915522
#105915372
#105909542
#105908142
#105907202
#105906502
#807693
#806163