Finite Group Databasebeta

← #11889448

Subgroups — #11889448

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic
2#10594942C211yesmaximal, characteristic
3#10592744C211yesmaximal, characteristic, complemented
4C3×#5052C211yesmaximal, characteristic, complemented
5#10591613C211yesmaximal, characteristic, complemented
6#10591594C211yesmaximal, characteristic, complemented
7#10591574C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591185C211yesmaximal, characteristic, complemented
10#10591147C211yesmaximal, characteristic
11#10591100C211yesmaximal, characteristic, complemented
12#10590543C211yesmaximal, characteristic, complemented
13#10590518C211yesmaximal, characteristic, complemented
14#10590477C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#80915—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C32×C22⋊Q8C2211yescharacteristic
21#64135C2211yescharacteristic
22C3×#944C2211yescharacteristic
23C2×C3×#216C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#896—21no—
29C3×#888—21no—
30C3×#887C2211yescharacteristic
31C3×#67⋊C4—21no—
32C3×#878—21no—
33#63969—21no—
34#63956—21no—
35D3×C4⋊Dic3C2211yescharacteristic
36#63878—21no—
37#63870—21no—
38#63869C2211yescharacteristic
39#63856C2211yescharacteristic
40Dic3×Dic6C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63657C2211yescharacteristic
47#63635C2211yescharacteristic
48#63634C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#810C2211yescharacteristic
51C3×#808C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60#63554C2211yescharacteristic
61C3×D4×Q8—31no—
62#5639—31no—
63#5632D311yescharacteristic
64#5541—31no—
65C3×#470—31no—
66#5228—31no—
67#5228—31no—
68#5225—31no—
69C2×#835—31no—
70#5186—31no—
71#5182—31no—
72#5127—31no—
73#5120—31no—
74#5090—31no—
75#5082—31no—
76#5052D311yescharacteristic, complemented
77#5051—31no—
78#5050—31no—
79#5045—31no—
80#5045—31no—
81#5045—61no—
82#5043—31no—
83#5030—31no—
84#5022—31no—
85#5011—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
94C2×C3×#67D411yescharacteristic
95C22×C3×Dic3—21no—
96C3×D3×Q8—22no—
97C3×D3×Q8—41no—
98C2×C3×C4×D3—21no—
99C2×C3×C4×D3C2311yescharacteristic
100C2×C3×Dic6—22no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6—41no—
104C2×C3×Dic6C2311yescharacteristic
105C2×C3×Dic6C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×D3×Dic3—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4C2311yescharacteristic
110C32×C22⋊C4—21no—
111#3757—21no—
112C4⋊(C3⋊Dic3)C2311yescharacteristic
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114C4×C3⋊Dic3—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#216—41no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4—21no—
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4D411yescharacteristic
129C3×C4×Dic3—21no—
130C3×C4×Dic3C2311yescharacteristic
131C3×#208—41no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134#3724—21no—
135#3724—21no—
136Dic3⋊Dic3—21no—
137Dic3⋊Dic3—21no—
138Dic3⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3718—22no—
142#3718—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C22×Dic6C2×D311yescharacteristic
149C2×C3×Q16—31no—
150C2×C3×M16—31no—
151C3×C4⋊Q8—31no—
152C3×C4⋊Q8—61no—
153C3×C22⋊Q8—21no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C22⋊Q8C2×D311yescharacteristic
159C3×C22⋊Q8C2×D311yescharacteristic
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163#946—31no—
164Q8×Dic3—31no—
165#944C2×D311yescharacteristic
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—31no—
169C2×#216—31no—
170C2×#216C2×D311yescharacteristic
171#935—61no—
172C4×#67C2×D311yescharacteristic
173#926—31no—
174#926—31no—
175#926—61no—
176C2×C4⋊Dic3—31no—
177#924—31no—
178#924C2×D311yescharacteristic
179C2×#208C2×D311yescharacteristic
180C22×C3⋊C8—31no—
181C2×D3×C8—31no—
182#897C2×D311yescharacteristic
183#896—21no—
184#892—61no—
185D3×C4⋊C4—31no—
186#890—31no—
187#889—61no—
188#889—61no—
189#888—21no—
190#887C2×D311yescharacteristic
191#883—61no—
192#67⋊C4—21no—
193#879—61no—
194#879—61no—
195#878—21no—
196#877—61no—
197#870—31no—
198C4×Dic6—31no—
199C3×#106—31no—
200C3×#103—31no—
201C3×#103—31no—
202#835—31no—
203#835—31no—
204#835—31no—
205#835—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—61no—
213#835—61no—
214#835C2×D311yescharacteristic
215#830—31no—
216#830—31no—
217#830—31no—
218#830—61no—
219(C2×D3)⋊C8—31no—
220#816—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#815—31no—
225Dic3⋊C8—31no—
226#810—31no—
227#810—31no—
228#810C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—61no—
232#808C2×D311yescharacteristic
233#807—31no—
234#807—31no—
235#807—61no—
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—
250C3×#67—22no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—42no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×C4×D3—21no—
260C3×C4×D3—21no—
261C3×C4×D3—42no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264C3×Dic6—21no—
265C3×Dic6—21no—
266C3×Dic6—21no—
267C3×Dic6—42no—
268C3×Dic6—42no—
269C3×Dic6#4112yes—
270D3×Dic3—42no—
271C3⋊(C3⋊C8)—21no—
272C3⋊(C3⋊C8)—21no—
273C3×C3⋊C8—21no—
274C3×C3⋊C8—21no—
275#552—91no—
276D4×Q8—31no—
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×Q8—31no—
293C2×C3×Q8—31no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—61no—
297C2×C3×Q8—62no—
298C2×C3×Q8—121no—
299C2×C3×Q8—121no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4—61no—
307C22×C3×C4C22×D311yescharacteristic
308C22×C3×C4C22×D311yescharacteristic
309C2×#67#6711yescharacteristic
310C22×Dic3—21no—
311C22×Dic3—61no—
312D3×Q8—22no—
313D3×Q8—41no—
314C2×C4×D3—21no—
315C2×C4×D3—61no—
316C2×C4×D3C22×D311yescharacteristic
317C2×Dic6—22no—
318C2×Dic6—21no—
319C2×Dic6—21no—
320C2×Dic6—41no—
321C2×Dic6C22×D311yescharacteristic
322C2×Dic6C22×D311yescharacteristic
323C2×Dic6C22×D311yescharacteristic
324C3×Q16—121no—
325C3×M16—121no—
326C2×C3×C8—31no—
327C2×C3×C8—31no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—41no—
334C3×C4⋊C4—61no—
335C3×C4⋊C4—61no—
336C3×C4⋊C4—61no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4C22×D311yescharacteristic
340C3×C4⋊C4C22×D311yescharacteristic
341C3×C22⋊C4—21no—
342C3×C22⋊C4—21no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—31no—
345C3×C22⋊C4—41no—
346C3×C22⋊C4—61no—
347C3×C22⋊C4—61no—
348C3×C42—31no—
349C3×C42—61no—
350#217—21no—
351#217—61no—
352#217—61no—
353#217—61no—
354#217—121no—
355#217#6711yescharacteristic
356#216—41no—
357#216—62no—
358#216—62no—
359#216—121no—
360#216—121no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4#6711yescharacteristic
364C4⋊Dic3—21no—
365C4⋊Dic3—31no—
366C4⋊Dic3—31no—
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3—61no—
374C4⋊Dic3C22×D311yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—61no—
380Dic3⋊C4—61no—
381Dic3⋊C4—61no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4#6711yescharacteristic
387C4×Dic3—21no—
388C4×Dic3—61no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—121no—
393C4×Dic3C22×D311yescharacteristic
394#208—41no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—61no—
400C2×C3⋊C8—61no—
401C2×C3⋊C8—121no—
402C2×C3⋊C8C22×D311yescharacteristic
403C2×C3⋊C8C22×D311yescharacteristic
404D3×C8—121no—
405C22×C32—21no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32C22×D411yescharacteristic
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3#13712yes—
412C32×C4—21no—
413C32×C4—41no—
414C32×C4—41no—
415C32×C4C2×#4111yescharacteristic
416C32×C4H(5,𝔽2)11yescharacteristic
417C3⋊Dic3—41no—
418C3⋊Dic3—41no—
419C3×Dic3—22no—
420C3×Dic3—21no—
421C3×Dic3—21no—
422C3×Dic3—21no—
423C3×Dic3—41no—
424C3×Dic3—41no—
425C3×Dic3—41no—
426C22×Q8—31no—
427C22×Q8—31no—
428C2×Q16—31no—
429C2×Q16—91no—
430C2×Q16—91no—
431C2×M16—31no—
432C22×C8—91no—
433C4⋊Q8—31no—
434C4⋊Q8—61no—
435#126—181no—
436#125—91no—
437#125—181no—
438#123—181no—
439C22⋊Q8—31no—
440C22⋊Q8—31no—
441C22⋊Q8—61no—
442C22⋊Q8—61no—
443C22⋊Q8—91no—
444C22⋊Q8D3211yescharacteristic
445C4×Q8—31no—
446C4×Q8—91no—
447C4×D4—31no—
448C4×D4—61no—
449#117—91no—
450#117—181no—
451C2×C4⋊C4—91no—
452#107—91no—
453#106—31no—
454#106—91no—
455C4⋊C8—91no—
456#103—31no—
457#103—31no—
458#103—91no—
459#103—91no—
460#103—91no—
461#103—91no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466C22⋊C8—91no—
467C22⋊C8—91no—
468#97—91no—
469C23×C3—21no—
470C23×C3—31no—
471C23×C3D3×D411yescharacteristic
472C23×C3C2×#6711yescharacteristic
473C22×D3C2×#6711yescharacteristic
474C3×Q8—21no—
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—32no—
479C3×Q8—41no—
480C3×Q8—41no—
481C3×Q8—61no—
482C3×Q8—61no—
483C3×Q8—61no—
484C3×Q8—61no—
485C3×Q8—61no—
486C3×Q8—122no—
487C3×Q8—122no—
488C3×D4—62no—
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—21no—
498C2×C3×C4—21no—
499C2×C3×C4—31no—
500C2×C3×C4—31no—
501C2×C3×C4—31no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
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—122no—
513C2×C3×C4—122no—
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518#67—22no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—42no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—121no—
529C2×Dic3—121no—
530C2×Dic3—122no—
531C2×Dic3C2×#6711yescharacteristic
532C2×Dic3C2×#6711yescharacteristic
533C2×Dic3C2×#6711yescharacteristic
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—42no—
537C4×D3—122no—
538Dic6—21no—
539Dic6—21no—
540Dic6—21no—
541Dic6—21no—
542Dic6—21no—
543Dic6—42no—
544Dic6—42no—
545Dic6#23712yes—
546C3×C8—61no—
547C3×C8—61no—
548C3⋊C8—21no—
549C3⋊C8—21no—
550C3⋊C8—61no—
551C3⋊C8—61no—
552C3⋊C8—61no—
553C3⋊C8—61no—
554C3⋊C8—121no—
555C3⋊C8—121no—
556C2×C32—41no—
557C2×C32#54611yescharacteristic
558C2×C32C2×#13711yescharacteristic
559C2×C32#57811yescharacteristic
560C3×D3—22no—
561C2×Q8—31no—
562C2×Q8—31no—
563C2×Q8—31no—
564C2×Q8—61no—
565C2×Q8—62no—
566C2×Q8—61no—
567C2×Q8—62no—
568C2×Q8—121no—
569C2×Q8—121no—
570C2×Q8C2×D3211yescharacteristic
571C2×D4—31no—
572C22×C4—31no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—181no—
576C22×C4C2×D3211yescharacteristic
577Q16—121no—
578Q16—182no—
579Q16—361no—
580M16—121no—
581C2×C8—31no—
582C2×C8—31no—
583C2×C8—91no—
584C2×C8—91no—
585C2×C8—361no—
586C4⋊C4—21no—
587C4⋊C4—31no—
588C4⋊C4—31no—
589C4⋊C4—61no—
590C4⋊C4—61no—
591C4⋊C4—61no—
592C4⋊C4—61no—
593C4⋊C4—61no—
594C4⋊C4—91no—
595C4⋊C4—91no—
596C4⋊C4—181no—
597C4⋊C4—181no—
598C4⋊C4—181no—
599C4⋊C4—181no—
600C4⋊C4—181no—
601C4⋊C4C2×D3211yescharacteristic
602C22⋊C4—21no—
603C22⋊C4—31no—
604C22⋊C4—31no—
605C22⋊C4—61no—
606C22⋊C4—61no—
607C22⋊C4—181no—
608C22⋊C4—181no—
609C42—31no—
610C42—61no—
611C42—181no—
612C42—181no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—32no—
621C22×C3—41no—
622C22×C3—41no—
623C22×C3—41no—
624C22×C3—61no—
625C22×C3—61no—
626C22×C3C2×D3×D411yescharacteristic
627C22×C3C22×#6711yescharacteristic
628C2×D3—21no—
629C2×D3—21no—
630C2×D3#94212yes—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—41no—
638C3×C4—41no—
639C3×C4—41no—
640C3×C4—61no—
641C3×C4—61no—
642C3×C4—61no—
643C3×C4—62no—
644C3×C4—81no—
645C3×C4—81no—
646C3×C4—121no—
647C3×C4—121no—
648C3×C4—121no—
649C3×C4C2×#23711yescharacteristic
650C3×C4#100411yescharacteristic
651C3×C4#100411yescharacteristic
652C3×C4D3×#4111yescharacteristic
653Dic3—22no—
654Dic3—21no—
655Dic3—21no—
656Dic3—21no—
657Dic3—41no—
658Dic3—41no—
659Dic3—41no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—241no—
665Dic3—241no—
666C32#331211yescharacteristic, complemented, Sylow
667C23—31no—
668C23D3×#6711yescharacteristic
669Q8—21no—
670Q8—21no—
671Q8—32no—
672Q8—61no—
673Q8—61no—
674Q8—61no—
675Q8—61no—
676Q8—61no—
677Q8—122no—
678Q8—122no—
679D4—62no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—31no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—122no—
694C2×C4—122no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4—362no—
698C2×C4D3×#6711yescharacteristic
699C2×C4C22×D3211yescharacteristic
700C8—61no—
701C8—61no—
702C8—181no—
703C8—181no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3—21no—
707C2×C3—41no—
708C2×C3—41no—
709C2×C3—62no—
710C2×C3—81no—
711C2×C3#561011yescharacteristic
712C2×C3D3×#13711yescharacteristic
713C2×C3#577911yescharacteristic
714C2×C3#580611yescharacteristic
715C2×C3C2×#94211yescharacteristic
716C2×C3#583811yescharacteristic
717D3—22no—
718C22—21no—
719C22—21no—
720C22—21no—
721C22—32no—
722C22—61no—
723C22—61no—
724C22C2×D3×#6711yescharacteristic
725C4—21no—
726C4—41no—
727C4—41no—
728C4—61no—
729C4—62no—
730C4—61no—
731C4—61no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4—361no—
736C4—361no—
737C4D3×#23711yescharacteristic
738C4#6431311yescharacteristic
739C3—21no—
740C3#8091511yescharacteristic, complemented
741C3#8355211yescharacteristic, complemented
742C2—41no—
743C2—62no—
744C2#1059515011yescharacteristic
745C2D3×#94211yescharacteristic
746C2#1059546511yescharacteristic
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. #10592744C2semidirect
4. C3×#5052C2semidirect
5. #10591613C2semidirect
6. #10591594C2semidirect
7. #10591574C2semidirect
8. D3×#835C2semidirect
9. #10591185C2semidirect
11. #10591100C2semidirect
12. #10590543C2semidirect
13. #10590518C2semidirect
14. #10590477C2semidirect
15. #10590439C2semidirect
76. #5052D3semidirect
666. C32#3312semidirect
740. C3#80915semidirect
741. C3#83552semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
#105949422
#105927442
C3×#50522
#105916132
#105915942
#105915742
D3×#8352
#105911852
#105911472
#105911002
#105905432
#105905182
#105904772
#105904392
#835523
#809153