Finite Group Databasebeta

← #11889422

Subgroups — #11889422

Order 1152.

826 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595379C211yesmaximal, characteristic
2#10595361C211yesmaximal, characteristic
3#10592885C211yesmaximal, characteristic, complemented
4C3×#5188C211yesmaximal, characteristic, complemented
5C3×#5182C211yesmaximal, characteristic, complemented
6#10591653C211yesmaximal, characteristic, complemented
7#10591613C211yesmaximal, characteristic, complemented
8#10591600C211yesmaximal, characteristic, complemented
9#10591562C211yesmaximal, characteristic, complemented
10#10591549C211yesmaximal, characteristic, complemented
11#10591541C211yesmaximal, characteristic, complemented
12#10590814C211yesmaximal, characteristic, complemented
13#10590727C211yesmaximal, characteristic
14#10590715C211yesmaximal, characteristic, complemented
15D3×#816C211yesmaximal, characteristic, complemented
16#80782—31nomaximal
17#80493—31nomaximal
18C2×Q8×C3⋊D3C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C2×C32×Q16C2211yescharacteristic
21#64155C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944C2211yescharacteristic
27C2×C3×#216C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C4×#626C2211yescharacteristic
30#63896—21no—
31#63890—21no—
32D3×C4⋊Dic3C2211yescharacteristic
33#63881—21no—
34#63877—21no—
35#63871C2211yescharacteristic
36#63869C2211yescharacteristic
37#63868—21no—
38#63865—21no—
39#63849C2211yescharacteristic
40#63846—21no—
41#63844C2211yescharacteristic
42#63840—21no—
43C2×#3712C2211yescharacteristic
44#63662C2211yescharacteristic
45#63647C2211yescharacteristic
46#63643C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#818C2211yescharacteristic
51C3×#816C2211yescharacteristic
52C3×Dic3⋊C8C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63566C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61#5727—31no—
62#5642—31no—
63#5632—31no—
64#5581—31no—
65C3×#467—31no—
66C3×#462—31no—
67#5189—31no—
68#5188D311yescharacteristic, complemented
69#5186—31no—
70#5186—31no—
71#5186—31no—
72#5186—61no—
73#5182D311yescharacteristic, complemented
74#5111—31no—
75C2×#816—31no—
76#5082—31no—
77#5050—31no—
78#5043—31no—
79#5030—31no—
80#4888—31no—
81#4877—31no—
82#4836—31no—
83#4829—31no—
84#4816—31no—
85#4814—31no—
86#4805—31no—
87#4802—31no—
88#4802—31no—
89D3×#103—31no—
90#4797—31no—
91#4789—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×C4×D3C2311yescharacteristic
101C2×C3×Dic6C2311yescharacteristic
102C2×#627—21no—
103C2×#626D411yescharacteristic
104C2×D3×Dic3—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—41no—
108C32×Q16—41no—
109C2×C32×C8C2311yescharacteristic
110#3756—22no—
111#3752—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113#3750—21no—
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#216—41no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3C2311yescharacteristic
120C3×C4⋊Dic3C2311yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3D411yescharacteristic
137#3722—21no—
138#3722—21no—
139#3722D411yescharacteristic
140(C2×D3)⋊Dic3D411yescharacteristic
141Dic32—21no—
142Dic32—21no—
143#3712—41no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C2×D3×Q8—31no—
147C2×D3×Q8—31no—
148C2×D3×Q8—61no—
149C22×Dic6—31no—
150C2×C3×Q16—21no—
151C2×C3×Q16—31no—
152C2×C3×Q16C2×D311yescharacteristic
153C2×C3×Q16C2×D311yescharacteristic
154C22×C3×C8—31no—
155C3×C4⋊Q8—31no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C4×Q8—31no—
159#946—31no—
160#946—31no—
161#946—31no—
162#946—61no—
163#946C2×D311yescharacteristic
164#946C2×D311yescharacteristic
165Q8×Dic3C2×D311yescharacteristic
166#944C2×D311yescharacteristic
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—61no—
170C2×#216C2×D311yescharacteristic
171C4×#67—31no—
172C2×C4⋊Dic3—31no—
173C2×ΓL(1,𝔽25)—31no—
174C2×ΓL(1,𝔽25)—31no—
175C2×D3×C8C2×D311yescharacteristic
176#898—61no—
177#897—31no—
178#896—61no—
179#896—61no—
180#896—61no—
181#894—61no—
182#893—61no—
183#892—31no—
184#892—31no—
185D3×C4⋊C4—31no—
186#890—31no—
187#890—61no—
188#889—61no—
189#888—61no—
190#888—61no—
191#887—31no—
192#886—61no—
193#67⋊C4—61no—
194#878—61no—
195#877—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×#103—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(C2×D3)⋊C8—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220#818C2×D311yescharacteristic
221#817—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—31no—
226#816—31no—
227#816—61no—
228#816C2×D311yescharacteristic
229#815—31no—
230Dic3⋊C8C2×D311yescharacteristic
231#810—31no—
232#810—31no—
233#810—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237#803—31no—
238C22×C3⋊D3C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C32×Q8—21no—
243C32×Q8—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3C2×D411yescharacteristic
250C4×C3⋊D3—21no—
251C4×C3⋊D3—21no—
252C4×C3⋊D3—42no—
253#634—21no—
254#634—42no—
255#634#4112yes—
256C2×C3×Dic3—21no—
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×C4×D3—21no—
264C3×C4×D3—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267#627—42no—
268#626—22no—
269D3×Dic3—42no—
270D3×Dic3—42no—
271C32×C8—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—91no—
276D4×Q8—91no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
282#467—31no—
283#462—31no—
284#451—91no—
285#451—91no—
286#441—91no—
287#435—91no—
288#419—91no—
289C2×#103—91no—
290C2×C3×Q8—21no—
291C2×C3×Q8—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×Q8C22×D311yescharacteristic
295C2×C3×Q8C22×D311yescharacteristic
296C2×C3×Q8C22×D311yescharacteristic
297C22×C3×C4—31no—
298C2×#67—31no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301D3×Q8—62no—
302D3×Q8—62no—
303D3×Q8—62no—
304D3×Q8—122no—
305D3×Q8—121no—
306D3×Q8—121no—
307D3×Q8—121no—
308D3×Q8—122no—
309C2×D12—31no—
310C2×C4×D3—31no—
311C2×C4×D3—31no—
312C2×C4×D3—61no—
313C2×C4×D3—61no—
314C2×C4×D3—61no—
315C2×C4×D3—61no—
316C2×C4×D3—61no—
317C2×C4×D3—121no—
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6—31no—
320C2×Dic6—31no—
321C2×Dic6—61no—
322C2×Dic6—62no—
323C2×Dic6—61no—
324C2×Dic6—61no—
325C2×Dic6—61no—
326C2×Dic6—61no—
327C2×Dic6—121no—
328C2×Dic6—121no—
329C2×Dic6C22×D311yescharacteristic
330C3×Q16—41no—
331C3×Q16—41no—
332C3×Q16—42no—
333C3×Q16—121no—
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—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—61no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—61no—
352#217—31no—
353#216—41no—
354#216—62no—
355#216—62no—
356#216—122no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—31no—
360(C2×D3)⋊C4—31no—
361(C2×D3)⋊C4—31no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—121no—
369C4⋊Dic3—21no—
370C4⋊Dic3—31no—
371C4⋊Dic3—31no—
372C4⋊Dic3—31no—
373C4⋊Dic3—61no—
374C4⋊Dic3—61no—
375C4⋊Dic3—61no—
376C4⋊Dic3—61no—
377C4⋊Dic3C22×D311yescharacteristic
378C4⋊Dic3C22×D311yescharacteristic
379C4⋊Dic3C22×D311yescharacteristic
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—31no—
385Dic3⋊C4—61no—
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—121no—
395C4×Dic3—21no—
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3C22×D311yescharacteristic
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406ΓL(1,𝔽25)—121no—
407ΓL(1,𝔽25)—121no—
408D3×C8—41no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—21no—
411C2×C3⋊D3—21no—
412C2×C3⋊D3—21no—
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3#13712yes—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—22no—
421C3⋊Dic3—21no—
422C3⋊Dic3—41no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×Q8—91no—
431C22×Q8—91no—
432C2×Q16—31no—
433C2×Q16—91no—
434C2×Q16D3211yescharacteristic
435C2×M16—91no—
436C22×C8—31no—
437C4⋊Q8—31no—
438C4⋊Q8—181no—
439#126—181no—
440#125—91no—
441#125—181no—
442#123—181no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—91no—
446C22⋊Q8—91no—
447C22⋊Q8—181no—
448C22⋊Q8—181no—
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—91no—
452C4×D4—181no—
453#117—91no—
454#117—181no—
455C2×C4⋊C4—91no—
456#107—31no—
457#106—91no—
458#106—91no—
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#103—91no—
470C22⋊C8—91no—
471C22⋊C8—91no—
472#97—91no—
473C23×C3—31no—
474C22×D3—31no—
475C22×D3—31no—
476C22×D3—61no—
477C22×D3D3×D411yescharacteristic
478C3×Q8—22no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—21no—
484C3×Q8—21no—
485C3×Q8—21no—
486C3×Q8—21no—
487C3×Q8—41no—
488C3×Q8—41no—
489C3×Q8—41no—
490C3×Q8—61no—
491C3×Q8—61no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—21no—
497C2×C3×C4—31no—
498C2×C3×C4—31no—
499C2×C3×C4—31no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—62no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—31no—
516C2×Dic3—31no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—122no—
525C2×Dic3—122no—
526C2×Dic3D3×D411yescharacteristic
527C2×Dic3D3×D411yescharacteristic
528C2×Dic3D3×D411yescharacteristic
529D12—62no—
530C4×D3—21no—
531C4×D3—21no—
532C4×D3—61no—
533C4×D3—61no—
534C4×D3—61no—
535C4×D3—61no—
536C4×D3—121no—
537C4×D3—121no—
538C4×D3—122no—
539C4×D3—122no—
540C4×D3—122no—
541C4×D3—124no—
542C4×D3—122no—
543Dic6—21no—
544Dic6—21no—
545Dic6—32no—
546Dic6—32no—
547Dic6—62no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553Dic6—122no—
554Dic6—122no—
555Dic6—124no—
556C3×C8—21no—
557C3×C8—21no—
558C3×C8—41no—
559C3×C8—61no—
560C3×C8—61no—
561C3⋊C8—21no—
562C3⋊C8—21no—
563C3⋊C8—61no—
564C3⋊C8—61no—
565C3⋊C8—121no—
566C2×C32#54611yescharacteristic
567C2×C32C2×#13711yescharacteristic
568C2×C32#57811yescharacteristic
569C3⋊D3—41no—
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—91no—
573C2×Q8—181no—
574C2×Q8—181no—
575C2×Q8—182no—
576C2×Q8—182no—
577C2×Q8—361no—
578C2×Q8—361no—
579C2×Q8C2×D3211yescharacteristic
580C2×Q8C2×D3211yescharacteristic
581C2×D4—91no—
582C22×C4—31no—
583C22×C4—91no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4—181no—
587Q16—41no—
588Q16—121no—
589Q16—182no—
590M16—361no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—121no—
595C2×C8C2×D3211yescharacteristic
596C4⋊C4—31no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—91no—
605C4⋊C4—91no—
606C4⋊C4—181no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4—181no—
612C22⋊C4—61no—
613C22⋊C4—61no—
614C22⋊C4—91no—
615C22⋊C4—91no—
616C22⋊C4—181no—
617C22⋊C4—181no—
618C22⋊C4—181no—
619C42—31no—
620C42—61no—
621C42—181no—
622C42—181no—
623C22×C3—21no—
624C22×C3—32no—
625C22×C3—61no—
626C22×C3—61no—
627C22×C3C2×D3×D411yescharacteristic
628C22×C3C2×D3×D411yescharacteristic
629C2×D3—21no—
630C2×D3—21no—
631C2×D3—62no—
632C2×D3—61no—
633C2×D3—61no—
634C2×D3—61no—
635C2×D3—61no—
636C2×D3—61no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3#91812yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—42no—
644C3×C4—41no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—61no—
649C3×C4—61no—
650C3×C4—61no—
651C3×C4—81no—
652C3×C4—121no—
653C3×C4—121no—
654C3×C4—121no—
655C3×C4—121no—
656C3×C4#100411yescharacteristic
657C3×C4#100411yescharacteristic
658C3×C4D3×#4111yescharacteristic
659C3×C4D3×#4111yescharacteristic
660Dic3—21no—
661Dic3—21no—
662Dic3—21no—
663Dic3—41no—
664Dic3—41no—
665Dic3—41no—
666Dic3—41no—
667Dic3—62no—
668Dic3—61no—
669Dic3—62no—
670Dic3—61no—
671Dic3—122no—
672Dic3—121no—
673Dic3—121no—
674Dic3—121no—
675Dic3—241no—
676C32#331211yescharacteristic, complemented, Sylow
677C23—31no—
678C23—91no—
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—21no—
683Q8—61no—
684Q8—61no—
685Q8—92no—
686Q8—181no—
687Q8—362no—
688Q8—362no—
689D4—182no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—31no—
693C2×C4—31no—
694C2×C4—31no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—91no—
702C2×C4—181no—
703C2×C4—181no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—362no—
707C2×C4—362no—
708C2×C4—362no—
709C2×C4C22×D3211yescharacteristic
710C8—21no—
711C8—61no—
712C8—61no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—62no—
718C2×C3#561011yescharacteristic
719C2×C3#561211yescharacteristic
720C2×C3C2×#91811yescharacteristic
721C2×C3#576611yescharacteristic
722C2×C3#577111yescharacteristic
723C2×C3D3×#13711yescharacteristic
724D3—22no—
725D3—122no—
726D3—121no—
727D3—121no—
728C22—32no—
729C22—61no—
730C22—61no—
731C22—181no—
732C22—181no—
733C22—181no—
734C22D32×D411yescharacteristic
735C4—41no—
736C4—41no—
737C4—61no—
738C4—61no—
739C4—61no—
740C4—121no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—181no—
745C4—182no—
746C4—361no—
747C4#6431211yescharacteristic
748C4#6433011yescharacteristic
749C3—21no—
750C3#8049311yescharacteristic, complemented
751C3#8078211yescharacteristic, complemented
752C2—62no—
753C2—361no—
754C2D3×#91811yescharacteristic
755C2#1059476811yescharacteristic
756C2#1059529611yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
prime radicalC2×#626D4
hypercenterC2×Q16D32
hypocenterC32#3312
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
3. #10592885C2semidirect
4. C3×#5188C2semidirect
5. C3×#5182C2semidirect
6. #10591653C2semidirect
7. #10591613C2semidirect
8. #10591600C2semidirect
9. #10591562C2semidirect
10. #10591549C2semidirect
11. #10591541C2semidirect
12. #10590814C2semidirect
14. #10590715C2semidirect
15. D3×#816C2semidirect
68. #5188D3semidirect
73. #5182D3semidirect
676. C32#3312semidirect
750. C3#80493semidirect
751. C3#80782semidirect

Maximal subgroups

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

subgroupindex
#105953792
#105953612
#105928852
C3×#51882
C3×#51822
#105916532
#105916132
#105916002
#105915622
#105915492
#105915412
#105908142
#105907272
#105907152
D3×#8162
#807823
#804933