Finite Group Databasebeta

← #11887815

Subgroups — #11887815

Order 1152.

828 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595402C211yesmaximal, characteristic
2#10595380C211yesmaximal, characteristic, complemented
3#10592884C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5186C211yesmaximal, characteristic, complemented
6#10591657C211yesmaximal, characteristic, complemented
7#10591585C211yesmaximal, characteristic, complemented
8#10591581C211yesmaximal, characteristic, complemented
9#10591558C211yesmaximal, characteristic, complemented
10D3×#835C211yesmaximal, characteristic, complemented
11#10591539C211yesmaximal, characteristic, complemented
12#10590821C211yesmaximal, characteristic, complemented
13#10590717C211yesmaximal, characteristic, complemented
14#10590690C211yesmaximal, characteristic, complemented
15#10590679C211yesmaximal, characteristic, complemented
16#80769—31nomaximal
17#80194—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21#64156C2211yescharacteristic
22Q8×C3⋊Dic3C2211yescharacteristic
23C2×#3755C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#946C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29#63909C2211yescharacteristic
30#63907—21no—
31#63906—21no—
32#63904—21no—
33C4×#625C2211yescharacteristic
34#63891—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63888—21no—
37#63878—21no—
38#63872C2211yescharacteristic
39#63862—21no—
40#63845—21no—
41#63843C2211yescharacteristic
42#63841C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63648C2211yescharacteristic
46#63641C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic
52C3×#816C2211yescharacteristic
53#63575C2211yescharacteristic
54#63574C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63553C2211yescharacteristic
61#5817—31no—
62#5642—31no—
63#5639—31no—
64#5633—31no—
65C3×#467—31no—
66C3×#451—31no—
67C2×#835—31no—
68#5188D311yescharacteristic, complemented
69#5187—31no—
70#5186D311yescharacteristic, complemented
71#5185—31no—
72#5185—31no—
73#5185—61no—
74Dic3×Q16—31no—
75#5113—31no—
76C8×#67—31no—
77#5048—31no—
78#5047—31no—
79#5045—31no—
80#4882—31no—
81#4877—31no—
82#4814—31no—
83#4807—31no—
84#4804—31no—
85D3×#103—31no—
86#4800—31no—
87#4800—31no—
88#4796—31no—
89#4790—31no—
90#4736—31no—
91#67⋊C8—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—41no—
97C2×C3×C4×D3—21no—
98C2×C3×C4×D3C2311yescharacteristic
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—21no—
101C2×C3×Dic6C2311yescharacteristic
102C2×#626—21no—
103C2×#626—21no—
104C2×#625D411yescharacteristic
105C2×#624—21no—
106C2×D3×Dic3—21no—
107#3799—22no—
108#3799—41no—
109C32×Q16—41no—
110C2×C32×C8C2311yescharacteristic
111#3755—41no—
112#3752—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4×C3⋊Dic3—21no—
117C4×C3⋊Dic3C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C3×#216—22no—
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×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C3×D3×C8—41no—
132#3724D411yescharacteristic
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3300—91noSylow
145C22×C3×Q8—31no—
146C2×#239—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×#235—31no—
149C2×C3×Q16—21no—
150C2×C3×Q16—31no—
151C2×C3×Q16C2×D311yescharacteristic
152C2×C3×Q16C2×D311yescharacteristic
153C22×C3×C8—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—31no—
157#947—31no—
158#947—31no—
159#947—61no—
160#947—61no—
161#946—61no—
162#946C2×D311yescharacteristic
163#946C2×D311yescharacteristic
164#946C2×D311yescharacteristic
165Q8×Dic3—31no—
166Q8×Dic3—31no—
167Q8×Dic3—31no—
168Q8×Dic3—61no—
169C2×#216C2×D311yescharacteristic
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—61no—
173#930—31no—
174#930—61no—
175C4×#67—31no—
176C4×#67—31no—
177C4×#67—61no—
178#926—31no—
179C2×C4⋊Dic3—31no—
180C22×C3⋊C8—31no—
181C2×D3×C8—31no—
182C2×D3×C8C2×D311yescharacteristic
183#898—61no—
184#896—61no—
185#895—31no—
186#893—61no—
187#892—31no—
188#892—61no—
189D3×C4⋊C4—31no—
190#890—31no—
191#890—31no—
192#890—61no—
193#889—61no—
194#887—31no—
195#886—61no—
196#885—61no—
197#884—61no—
198#883—61no—
199#879—61no—
200#877—61no—
201C3×#107—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—61no—
212#835C2×D311yescharacteristic
213#835C2×D311yescharacteristic
214#835C2×D311yescharacteristic
215#830—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8C2×D311yescharacteristic
223#818—31no—
224#818C2×D311yescharacteristic
225#816—31no—
226#816C2×D311yescharacteristic
227Dic3⋊C8—31no—
228Dic3⋊C8—31no—
229Dic3⋊C8—61no—
230C8×Dic3—31no—
231C8×Dic3—31no—
232#810—31no—
233#809—31no—
234#809—31no—
235#808—31no—
236#808—31no—
237#807—31no—
238C22×C3⋊D3—21no—
239C22×C3×D3C2×D411yescharacteristic
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⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—42no—
264C3×Dic6—21no—
265C3×Dic6—42no—
266C3×Dic6#4112yes—
267#626—42no—
268#626—42no—
269#625—22no—
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—91no—
285#452—91no—
286#451—31no—
287C4×Q16—91no—
288C8×D4—91no—
289#416—91no—
290C2×#103—91no—
291C2×C3×Q8—21no—
292C2×C3×Q8—21no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—121no—
297C2×C3×Q8C22×D311yescharacteristic
298C2×C3×Q8C22×D311yescharacteristic
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C22×C3×C4—31no—
302C22×C3×C4—31no—
303C22×C3×C4—61no—
304C2×#67—31no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C22×Dic3—61no—
309#239—62no—
310#239—121no—
311D3×Q8—22no—
312D3×Q8—41no—
313#235—62no—
314#235—121no—
315C2×D12—31no—
316C2×D12—31no—
317C2×D12—61no—
318C2×D12—61no—
319C2×D12—61no—
320C2×C4×D3—21no—
321C2×C4×D3—61no—
322C2×C4×D3—61no—
323C2×C4×D3—61no—
324C2×C4×D3C22×D311yescharacteristic
325C2×C4×D3C22×D311yescharacteristic
326C2×Dic6—21no—
327C2×Dic6C22×D311yescharacteristic
328C3×Q16—41no—
329C3×Q16—41no—
330C3×Q16—42no—
331C3×Q16—62no—
332C2×C3×C8—21no—
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—61no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347#217—31no—
348#217—31no—
349#217—61no—
350#216—22no—
351#215—121no—
352#215—121no—
353#215—122no—
354(C2×D3)⋊C4—21no—
355(C2×D3)⋊C4—21no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—31no—
358(C2×D3)⋊C4—31no—
359(C2×D3)⋊C4—61no—
360(C2×D3)⋊C4—61no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4—121no—
368C4⋊Dic3—31no—
369C4⋊Dic3—31no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3—121no—
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380C4⋊Dic3C22×D311yescharacteristic
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—31no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C4×Dic3—61no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—121no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406D3×C8—41no—
407D3×C8—121no—
408C22×C32C22×D411yescharacteristic
409C2×C3⋊D3—41no—
410C2×C3⋊D3—41no—
411C2×C3⋊D3—41no—
412C2×C3×D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3#13512yes—
418C32×C4—41no—
419C32×C4—41no—
420C32×C4C2×#4111yescharacteristic
421C32×C4H(5,𝔽2)11yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—22no—
427C3×Dic3—21no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C3×Dic3—41no—
431C2×#41—91no—
432C22×Q8—31no—
433C2×Q16—31no—
434C2×Q16D3211yescharacteristic
435C2×SD16—91no—
436C22×C8—31no—
437C22×C8—91no—
438#126—181no—
439#125—91no—
440#125—181no—
441#124—91no—
442#124—181no—
443#123—181no—
444C22⋊Q8—31no—
445C22⋊Q8—31no—
446C22⋊Q8—31no—
447C22⋊Q8—181no—
448#121—91no—
449#121—181no—
450C4×Q8—91no—
451C4×Q8—91no—
452C4×D4—91no—
453C4×D4—181no—
454#117—91no—
455#117—181no—
456C2×C4⋊C4—91no—
457#107—31no—
458#107—91no—
459#106—91no—
460C4⋊C8—91no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—91no—
466#103—91no—
467#103—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471C22⋊C8—31no—
472C22⋊C8—91no—
473C4×C8—91no—
474C23×C3—31no—
475C23×C3—31no—
476C22×D3—61no—
477C22×D3—61no—
478C22×D3—121no—
479C22×D3D3×D411yescharacteristic
480C22×D3D3×D411yescharacteristic
481C3×Q8—22no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—41no—
494C3×Q8—61no—
495C3×Q8—122no—
496C2×C3×C4—21no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—31no—
502C2×C3×C4—31no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—122no—
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—62no—
517#67—62no—
518#67—122no—
519#67—122no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—31no—
525C2×Dic3—31no—
526C2×Dic3—31no—
527C2×Dic3—31no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—61no—
532C2×Dic3—121no—
533C2×Dic3—122no—
534C2×Dic3D3×D411yescharacteristic
535C2×Dic3D3×D411yescharacteristic
536D12—61no—
537D12—61no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12—121no—
542D12—122no—
543D12—122no—
544C4×D3—21no—
545C4×D3—21no—
546C4×D3—21no—
547C4×D3—21no—
548C4×D3—42no—
549C4×D3—122no—
550C4×D3—122no—
551C4×D3—122no—
552Dic6—21no—
553Dic6—42no—
554Dic6#23712yes—
555C3×C8—21no—
556C3×C8—21no—
557C3×C8—41no—
558C3×C8—61no—
559C3×C8—61no—
560C3⋊C8—21no—
561C3⋊C8—21no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C2×C32#54611yescharacteristic
566C2×C32C2×#13511yescharacteristic
567C2×C32#57811yescharacteristic
568C3⋊D3—81no—
569C3×D3—22no—
570C3×D3—41no—
571#41—182no—
572#41—361no—
573C2×Q8—31no—
574C2×Q8—61no—
575C2×Q8—62no—
576C2×Q8—121no—
577C2×Q8C2×D3211yescharacteristic
578C2×Q8C2×D3211yescharacteristic
579C2×D4—91no—
580C2×D4—91no—
581C2×D4—181no—
582C2×D4—181no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—61no—
586C22×C4—181no—
587C22×C4—181no—
588Q16—41no—
589Q16—62no—
590SD16—361no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—121no—
595C2×C8—361no—
596C2×C8C2×D3211yescharacteristic
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—91no—
604C4⋊C4—91no—
605C4⋊C4—181no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C22⋊C4—61no—
611C22⋊C4—61no—
612C22⋊C4—61no—
613C22⋊C4—91no—
614C22⋊C4—91no—
615C22⋊C4—181no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—91no—
620C42—181no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3—61no—
628C22×C3—61no—
629C22×C3—61no—
630C22×C3C2×D3×D411yescharacteristic
631C22×C3C2×D3×D411yescharacteristic
632C2×D3—21no—
633C2×D3—21no—
634C2×D3—21no—
635C2×D3—21no—
636C2×D3—21no—
637C2×D3—121no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—121no—
641C2×D3—121no—
642C2×D3—121no—
643C2×D3—241no—
644C2×D3—241no—
645C2×D3—241no—
646C2×D3#91912yes—
647C3×C4—21no—
648C3×C4—21no—
649C3×C4—42no—
650C3×C4—41no—
651C3×C4—41no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—61no—
655C3×C4—62no—
656C3×C4—61no—
657C3×C4—81no—
658C3×C4—121no—
659C3×C4—121no—
660C3×C4—121no—
661C3×C4C2×#23711yescharacteristic
662C3×C4#100411yescharacteristic
663C3×C4#100411yescharacteristic
664C3×C4D3×#4111yescharacteristic
665Dic3—22no—
666Dic3—21no—
667Dic3—21no—
668Dic3—41no—
669Dic3—41no—
670Dic3—41no—
671Dic3—61no—
672Dic3—61no—
673Dic3—61no—
674Dic3—61no—
675Dic3—121no—
676Dic3—121no—
677Dic3—121no—
678Dic3—121no—
679Dic3—241no—
680C32#330011yescharacteristic, complemented, Sylow
681C23—31no—
682C23—31no—
683C23—181no—
684Q8—21no—
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—32no—
689Q8—61no—
690Q8—122no—
691D4—182no—
692D4—181no—
693D4—181no—
694D4—362no—
695D4—362no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—31no—
699C2×C4—31no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—61no—
706C2×C4—61no—
707C2×C4—61no—
708C2×C4—91no—
709C2×C4—91no—
710C2×C4—122no—
711C2×C4—181no—
712C2×C4—362no—
713C2×C4—362no—
714C2×C4C22×D3211yescharacteristic
715C8—21no—
716C8—61no—
717C8—61no—
718C8—181no—
719C2×C3—21no—
720C2×C3—21no—
721C2×C3—21no—
722C2×C3—62no—
723C2×C3—121no—
724C2×C3#559111yescharacteristic
725C2×C3#561011yescharacteristic
726C2×C3C2×#91911yescharacteristic
727C2×C3#576611yescharacteristic
728C2×C3D3×#13511yescharacteristic
729C2×C3#577911yescharacteristic
730D3—22no—
731D3—41no—
732D3—241no—
733D3—241no—
734D3—481no—
735C22—32no—
736C22—61no—
737C22—61no—
738C22—61no—
739C22—61no—
740C22—61no—
741C22—361no—
742C22—361no—
743C22—361no—
744C22D32×D411yescharacteristic
745C4—41no—
746C4—41no—
747C4—61no—
748C4—61no—
749C4—62no—
750C4—121no—
751C4—121no—
752C4—121no—
753C4—181no—
754C4—181no—
755C4—361no—
756C4D3×#23711yescharacteristic
757C4#6433011yescharacteristic
758C3—21no—
759C3#8019411yescharacteristic, complemented
760C3#8076911yescharacteristic, complemented
761C2—62no—
762C2—121no—
763C2—721no—
764C2D3×#91911yescharacteristic
765C2#1059476611yescharacteristic
766C2#1059529011yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radical#10595402C2
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. #10595380C2semidirect
3. #10592884C2semidirect
4. C3×#5188C2semidirect
5. C3×#5186C2semidirect
6. #10591657C2semidirect
7. #10591585C2semidirect
8. #10591581C2semidirect
9. #10591558C2semidirect
10. D3×#835C2semidirect
11. #10591539C2semidirect
12. #10590821C2semidirect
13. #10590717C2semidirect
14. #10590690C2semidirect
15. #10590679C2semidirect
68. #5188D3semidirect
70. #5186D3semidirect
680. C32#3300semidirect
759. C3#80194semidirect
760. C3#80769semidirect

Maximal subgroups

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

subgroupindex
#105954022
#105953802
#105928842
C3×#51882
C3×#51862
#105916572
#105915852
#105915812
#105915582
D3×#8352
#105915392
#105908212
#105907172
#105906902
#105906792
#807693
#801943