Finite Group Databasebeta

← #11889368

Subgroups — #11889368

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
1C3×#5639C211yesmaximal, characteristic
2#10594915C211yesmaximal, characteristic
3#10592749C211yesmaximal, characteristic, complemented
4C3×#5052C211yesmaximal, characteristic, complemented
5#10591653C211yesmaximal, characteristic, complemented
6#10591625C211yesmaximal, characteristic, complemented
7#10591596C211yesmaximal, characteristic, complemented
8#10591541C211yesmaximal, characteristic, complemented
9#10591147C211yesmaximal, characteristic
10#10591107C211yesmaximal, characteristic, complemented
11#10591102C211yesmaximal, characteristic, complemented
12D3×#810C211yesmaximal, characteristic, complemented
13#10590562C211yesmaximal, characteristic, complemented
14#10590490C211yesmaximal, characteristic, complemented
15#10590426C211yesmaximal, characteristic, complemented
16#83603—31nomaximal
17#80915—31nomaximal
18C22×#634C2211yescharacteristic
19C2×D3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C3×Q8×Dic3C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C3×#926C2211yescharacteristic
28C3×#924C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#892—21no—
31C3×D3×C4⋊C4C2211yescharacteristic
32C3×#890C2211yescharacteristic
33C3×#889—21no—
34C3×#883—21no—
35C3×#879—21no—
36#63982—21no—
37#67⋊Dic3—21no—
38#63896—21no—
39#63866C2211yescharacteristic
40#63857C2211yescharacteristic
41#63844C2211yescharacteristic
42#63840—21no—
43C2×D3×C3⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic
46#63637C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#810C2211yescharacteristic
49C3×#808C2211yescharacteristic
50#63576C2211yescharacteristic
51#63574C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63567C2211yescharacteristic
54#63567C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×#552—31no—
62#5639D311yescharacteristic
63#5632—31no—
64D4×Dic6—31no—
65C3×#470—31no—
66#5186—31no—
67#5182—31no—
68#5127—31no—
69#5120—31no—
70#5069—31no—
71#5063—31no—
72#5052D311yescharacteristic, complemented
73#5051—31no—
74#5050—31no—
75#5050—31no—
76#5050—31no—
77#5050—61no—
78#5045—31no—
79#5031—31no—
80#5030—31no—
81#5011—31no—
82#5004—31no—
83#4996—31no—
84#4971—31no—
85C2×#810—31no—
86#4862—31no—
87#4857—31no—
88#4813—31no—
89D3×#103—31no—
90#4797—31no—
91#4789—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—22no—
96C2×#634—21no—
97C2×#634—41no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#627—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—41no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3756—22no—
112#3756—41no—
113C2×C3⋊(C3⋊C8)C2311yescharacteristic
114C2×C3⋊(C3⋊C8)C2311yescharacteristic
115C3×#217—21no—
116C3×#217—21no—
117C3×#217D411yescharacteristic
118C3×#216—41no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4D411yescharacteristic
131C3×C4×Dic3—21no—
132C3×C4×Dic3—21no—
133C3×C4×Dic3C2311yescharacteristic
134C3×#208—41no—
135C2×C3×C3⋊C8C2311yescharacteristic
136C2×C3×C3⋊C8C2311yescharacteristic
137#3724—21no—
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C2×D3×Q8—31no—
146C22×Dic6—31no—
147C22×Dic6—31no—
148C22×Dic6—31no—
149C22×Dic6—61no—
150C2×C3×Q16—31no—
151C2×C3×M16—31no—
152C3×#126—61no—
153C3×#125—31no—
154C3×#125—61no—
155C3×#123—61no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C4×Q8—31no—
162C3×C4×D4—31no—
163C3×#117—31no—
164C3×#117—61no—
165C2×C3×C4⋊C4—31no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic
168#944—31no—
169C2×#216—31no—
170C2×#216—31no—
171C2×#216—31no—
172C2×#216—31no—
173C2×#216—61no—
174C2×#216—61no—
175C2×#216C2×D311yescharacteristic
176D4×Dic3—61no—
177C4×#67C2×D311yescharacteristic
178#926C2×D311yescharacteristic
179#924—31no—
180#924C2×D311yescharacteristic
181C2×#208C2×D311yescharacteristic
182C22×C3⋊C8—31no—
183C2×D3×C8—31no—
184#897—31no—
185#896—61no—
186#892—21no—
187D3×C4⋊C4C2×D311yescharacteristic
188#890C2×D311yescharacteristic
189#889—21no—
190#888—61no—
191#888—61no—
192#887—31no—
193#883—21no—
194#67⋊C4—61no—
195#879—21no—
196#878—61no—
197#878—61no—
198#878—61no—
199#869—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×#103—31no—
203C3×#103—31no—
204#835—31no—
205#835—31no—
206#835C2×D311yescharacteristic
207#830—31no—
208#830—31no—
209#830—31no—
210#830—61no—
211(C2×D3)⋊C8—31no—
212#816—31no—
213#816—31no—
214#816—31no—
215#816—31no—
216#815—31no—
217Dic3⋊C8—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—31no—
222#810—31no—
223#810—31no—
224#810—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—61no—
229#810—61no—
230#810C2×D311yescharacteristic
231#808—31no—
232#808—31no—
233#808C2×D311yescharacteristic
234#807—31no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237#803—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3C2×D411yescharacteristic
240C32×Q8—21no—
241C32×Q8—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4C2×D411yescharacteristic
247C2×C32×C4C2411yescharacteristic
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—42no—
251#634—21no—
252#634—21no—
253#634—21no—
254#634—42no—
255#634#4112yes—
256C3×#67—22no—
257C2×C3×Dic3—21no—
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×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269#627—42no—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—31no—
276D4×Q8—91no—
277#491—91no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—31no—
282#467—91no—
283#462—91no—
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—31no—
292C2×C3×Q8C22×D311yescharacteristic
293C2×C3×Q8C22×D311yescharacteristic
294C2×C3×D4—31no—
295C22×C3×C4—21no—
296C22×C3×C4—31no—
297C22×C3×C4—61no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C2×#67#6711yescharacteristic
301C22×Dic3—61no—
302C22×Dic3—61no—
303C22×Dic3—61no—
304C22×Dic3—121no—
305D3×Q8—62no—
306D3×Q8—121no—
307C2×C4×D3—21no—
308C2×C4×D3—61no—
309C2×C4×D3C22×D311yescharacteristic
310C2×Dic6—31no—
311C2×Dic6—31no—
312C2×Dic6—31no—
313C2×Dic6—31no—
314C2×Dic6—61no—
315C2×Dic6—61no—
316C2×Dic6—62no—
317C2×Dic6—62no—
318C2×Dic6—62no—
319C2×Dic6—61no—
320C2×Dic6—61no—
321C2×Dic6—61no—
322C2×Dic6—61no—
323C2×Dic6—122no—
324C2×Dic6—121no—
325C2×Dic6—121no—
326C2×Dic6—121no—
327C2×Dic6—121no—
328C2×Dic6—122no—
329C2×Dic6C22×D311yescharacteristic
330C3×Q16—121no—
331C3×M16—121no—
332C2×C3×C8—31no—
333C2×C3×C8—31no—
334C3×C4⋊C4—21no—
335C3×C4⋊C4—21no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—31no—
338C3×C4⋊C4—31no—
339C3×C4⋊C4—31no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—41no—
342C3×C4⋊C4—61no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C22⋊C4—21no—
351C3×C22⋊C4—21no—
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—41no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C22⋊C4—61no—
358C3×C42—31no—
359C3×C42—61no—
360C3×C42—61no—
361#217—21no—
362#217—21no—
363#217—61no—
364#217#6711yescharacteristic
365#216—41no—
366#216—62no—
367#216—62no—
368#216—122no—
369#216—121no—
370#216—121no—
371#216—122no—
372(C2×D3)⋊C4—21no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4#6711yescharacteristic
375C4⋊Dic3—21no—
376C4⋊Dic3—21no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3C22×D311yescharacteristic
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—21no—
386Dic3⋊C4—21no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4#6711yescharacteristic
393C4×Dic3—21no—
394C4×Dic3—21no—
395C4×Dic3—61no—
396C4×Dic3—61no—
397C4×Dic3C22×D311yescharacteristic
398#208—41no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—121no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—21no—
414C2×C3×D3—21no—
415C2×C3×D3#13712yes—
416C32×C4—21no—
417C32×C4—41no—
418C32×C4—41no—
419C32×C4C2×#4111yescharacteristic
420C32×C4H(5,𝔽2)11yescharacteristic
421C3⋊Dic3—22no—
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×Q16—91no—
435C2×M16—31no—
436C22×C8—91no—
437C4⋊Q8—91no—
438C4⋊Q8—181no—
439#126—61no—
440#125—31no—
441#125—61no—
442#123—61no—
443C22⋊Q8—31no—
444C22⋊Q8—31no—
445C22⋊Q8—91no—
446C22⋊Q8—181no—
447C22⋊Q8—181no—
448C22⋊Q8D3211yescharacteristic
449C4×Q8—31no—
450C4×Q8—91no—
451C4×D4—31no—
452C4×D4—181no—
453#117—31no—
454#117—61no—
455C2×C4⋊C4—31no—
456#107—91no—
457#106—31no—
458#106—91no—
459C4⋊C8—91no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
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—21no—
474C23×C3—31no—
475C23×C3D3×D411yescharacteristic
476C23×C3C2×#6711yescharacteristic
477C22×D3C2×#6711yescharacteristic
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—41no—
483C3×Q8—41no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×D4—62no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
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—41no—
503C2×C3×C4—41no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—122no—
511C2×C3×C4D3×D411yescharacteristic
512C2×C3×C4C2×#6711yescharacteristic
513C2×C3×C4C23×D311yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515#67—22no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—122no—
527C2×Dic3—122no—
528C2×Dic3—122no—
529C2×Dic3—124no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—42no—
536C4×D3—122no—
537Dic6—21no—
538Dic6—21no—
539Dic6—32no—
540Dic6—32no—
541Dic6—62no—
542Dic6—61no—
543Dic6—61no—
544Dic6—62no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—61no—
549Dic6—121no—
550Dic6—121no—
551Dic6—122no—
552Dic6—122no—
553Dic6—122no—
554Dic6—122no—
555Dic6—124no—
556C3×C8—61no—
557C3×C8—61no—
558C3⋊C8—21no—
559C3⋊C8—21no—
560C3⋊C8—61no—
561C3⋊C8—61no—
562C3⋊C8—61no—
563C3⋊C8—61no—
564C3⋊C8—121no—
565C3⋊C8—121no—
566C2×C32—41no—
567C2×C32#54611yescharacteristic
568C2×C32C2×#13711yescharacteristic
569C2×C32#57811yescharacteristic
570C3×D3—22no—
571C2×Q8—31no—
572C2×Q8—91no—
573C2×Q8—91no—
574C2×Q8—182no—
575C2×Q8—181no—
576C2×Q8—182no—
577C2×Q8—181no—
578C2×Q8—361no—
579C2×Q8—361no—
580C2×Q8C2×D3211yescharacteristic
581C2×D4—31no—
582C22×C4—31no—
583C22×C4—61no—
584C22×C4—181no—
585C22×C4—181no—
586C22×C4C2×D3211yescharacteristic
587Q16—121no—
588Q16—182no—
589Q16—361no—
590M16—121no—
591C2×C8—31no—
592C2×C8—31no—
593C2×C8—91no—
594C2×C8—91no—
595C2×C8—361no—
596C4⋊C4—21no—
597C4⋊C4—31no—
598C4⋊C4—31no—
599C4⋊C4—31no—
600C4⋊C4—31no—
601C4⋊C4—61no—
602C4⋊C4—61no—
603C4⋊C4—61no—
604C4⋊C4—61no—
605C4⋊C4—61no—
606C4⋊C4—61no—
607C4⋊C4—181no—
608C4⋊C4—181no—
609C4⋊C4—181no—
610C4⋊C4—181no—
611C4⋊C4C2×D3211yescharacteristic
612C22⋊C4—21no—
613C22⋊C4—31no—
614C22⋊C4—31no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—181no—
619C42—31no—
620C42—61no—
621C42—61no—
622C42—181no—
623C22×C3—22no—
624C22×C3—21no—
625C22×C3—21no—
626C22×C3—21no—
627C22×C3—21no—
628C22×C3—21no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—32no—
632C22×C3—41no—
633C22×C3—41no—
634C22×C3—61no—
635C22×C3—61no—
636C22×C3C2×D3×D411yescharacteristic
637C22×C3C22×#6711yescharacteristic
638C2×D3—21no—
639C2×D3—21no—
640C2×D3#95112yes—
641C3×C4—21no—
642C3×C4—21no—
643C3×C4—21no—
644C3×C4—21no—
645C3×C4—41no—
646C3×C4—41no—
647C3×C4—41no—
648C3×C4—41no—
649C3×C4—41no—
650C3×C4—61no—
651C3×C4—61no—
652C3×C4—61no—
653C3×C4—81no—
654C3×C4—81no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4—121no—
658C3×C4—121no—
659C3×C4#100411yescharacteristic
660C3×C4D3×#4111yescharacteristic
661C3×C4D3×#4111yescharacteristic
662C3×C4#100911yescharacteristic
663Dic3—21no—
664Dic3—21no—
665Dic3—21no—
666Dic3—41no—
667Dic3—41no—
668Dic3—41no—
669Dic3—41no—
670Dic3—62no—
671Dic3—62no—
672Dic3—122no—
673Dic3—122no—
674Dic3—121no—
675Dic3—121no—
676C32#331211yescharacteristic, complemented, Sylow
677C23—31no—
678C23D3×#6711yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—61no—
682Q8—61no—
683Q8—92no—
684Q8—181no—
685Q8—181no—
686Q8—181no—
687Q8—362no—
688Q8—362no—
689D4—62no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—31no—
695C2×C4—31no—
696C2×C4—31no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—122no—
704C2×C4—181no—
705C2×C4—181no—
706C2×C4—362no—
707C2×C4—362no—
708C2×C4D3×#6711yescharacteristic
709C2×C4C22×D3211yescharacteristic
710C8—61no—
711C8—61no—
712C8—181no—
713C8—181no—
714C2×C3—21no—
715C2×C3—21no—
716C2×C3—21no—
717C2×C3—42no—
718C2×C3—41no—
719C2×C3—41no—
720C2×C3—62no—
721C2×C3#561011yescharacteristic
722C2×C3D3×#13711yescharacteristic
723C2×C3#577911yescharacteristic
724C2×C3C2×#95111yescharacteristic
725C2×C3#582911yescharacteristic
726C2×C3#583811yescharacteristic
727D3—22no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—32no—
732C22—61no—
733C22—61no—
734C22C2×D3×#6711yescharacteristic
735C4—21no—
736C4—41no—
737C4—41no—
738C4—61no—
739C4—61no—
740C4—61no—
741C4—121no—
742C4—121no—
743C4—121no—
744C4—121no—
745C4—182no—
746C4—361no—
747C4#6431211yescharacteristic
748C4#6431411yescharacteristic
749C3—21no—
750C3#8091511yescharacteristic, complemented
751C3#8360311yescharacteristic, complemented
752C2—41no—
753C2—62no—
754C2#1059530511yescharacteristic
755C2#1059532811yescharacteristic
756C2D3×#95111yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#67D4
hypercenterC22⋊Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592749C2semidirect
4. C3×#5052C2semidirect
5. #10591653C2semidirect
6. #10591625C2semidirect
7. #10591596C2semidirect
8. #10591541C2semidirect
10. #10591107C2semidirect
11. #10591102C2semidirect
12. D3×#810C2semidirect
13. #10590562C2semidirect
14. #10590490C2semidirect
15. #10590426C2semidirect
72. #5052D3semidirect
676. C32#3312semidirect
750. C3#80915semidirect
751. C3#83603semidirect

Maximal subgroups

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

subgroupindex
C3×#56392
#105949152
#105927492
C3×#50522
#105916532
#105916252
#105915962
#105915412
#105911472
#105911072
#105911022
D3×#8102
#105905622
#105904902
#105904262
#836033
#809153