Finite Group Databasebeta

← #11889457

Subgroups — #11889457

Order 1152.

806 conjugacy classes of subgroups.

The subgroup lattice has 749 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5727C211yesmaximal, characteristic
2#10593920C211yesmaximal, characteristic
3#10592789C211yesmaximal, characteristic, complemented
4C3×#5082C211yesmaximal, characteristic, complemented
5#10591598C211yesmaximal, characteristic, complemented
6#10591596C211yesmaximal, characteristic, complemented
7#10591595C211yesmaximal, characteristic, complemented
8#10591595C211yesmaximal, characteristic, complemented
9#10591559C211yesmaximal, characteristic, complemented
10#10591557C211yesmaximal, characteristic, complemented
11#10591549C211yesmaximal, characteristic, complemented
12D3×#835C211yesmaximal, characteristic, complemented
13#10590383C211yesmaximal, characteristic, complemented
14#10590326C211yesmaximal, characteristic
15#10590286C211yesmaximal, characteristic, complemented
16#83552—31nomaximal
17#81749—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C32×C4⋊Q8C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C2×#3756C2211yescharacteristic
23C4×#634C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×#946C2211yescharacteristic
26C3×#896—21no—
27C3×#896—21no—
28C3×#893—21no—
29C3×#888—21no—
30C3×C4×D12C2211yescharacteristic
31C3×#870C2211yescharacteristic
32C3×C4×Dic6C2211yescharacteristic
33D3×C4⋊Dic3C2211yescharacteristic
34#63884—21no—
35#63878—21no—
36#63862—21no—
37#63857C2211yescharacteristic
38#63857C2211yescharacteristic
39#63846—21no—
40#63841C2211yescharacteristic
41C2×#3719C2211yescharacteristic
42C2×#3711C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51C3×#803C2211yescharacteristic
52#63576C2211yescharacteristic
53#63574C2211yescharacteristic
54#63573C2211yescharacteristic
55#63567C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×D4×Q8—31no—
62#5727D311yescharacteristic
63#5694—31no—
64#5541—31no—
65C3×#491—31no—
66#5228—31no—
67#5228—31no—
68#5225—31no—
69C2×#835—31no—
70#5090—31no—
71#5090—31no—
72#5090—61no—
73#5082D311yescharacteristic, complemented
74#5063—31no—
75#5052—31no—
76#5051—31no—
77#5045—31no—
78#5043—31no—
79#5030—31no—
80#5022—31no—
81#5011—31no—
82#4816—31no—
83#4815—31no—
84#4813—31no—
85#4809—31no—
86#4809—31no—
87#4805—31no—
88#4802—31no—
89D3×#103—31no—
90#4716—31no—
91#4706—31no—
92C2×C32×Q8C2311yescharacteristic
93C2×C32×Q8C2311yescharacteristic
94C2×#634C2311yescharacteristic
95C3×D3×Q8—22no—
96C3×D3×Q8—22no—
97C3×D3×Q8—41no—
98C3×D3×Q8—41no—
99C2×C3×D12D411yescharacteristic
100C2×C3×C4×D3—21no—
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6C2311yescharacteristic
107C2×D3×Dic3—21no—
108C32×C4⋊C4—21no—
109C32×C4⋊C4—21no—
110C32×C42C2311yescharacteristic
111#3756—41no—
112#3756—41no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115C4×C3⋊Dic3—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×(C2×D3)⋊C4—21no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3D411yescharacteristic
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⋊C4—21no—
131C3×C4×Dic3—21no—
132C2×C3×C3⋊C8C2311yescharacteristic
133C2×C3×C3⋊C8C2311yescharacteristic
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140Dic32—21no—
141#3719—22no—
142#3711—41no—
143D3×C3⋊C8—41no—
144#3312—91noSylow
145C22×C3×Q8—31no—
146C22×C3×Q8—31no—
147C2×D3×Q8C2×D311yescharacteristic
148C2×D3×Q8C2×D311yescharacteristic
149C3×C4⋊Q8—21no—
150C3×C4⋊Q8—61no—
151C3×C4⋊Q8C2×D311yescharacteristic
152C3×C4⋊Q8C2×D311yescharacteristic
153C3×#125—31no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C22⋊Q8—61no—
157C3×C22⋊Q8—61no—
158C3×C4×Q8—31no—
159C3×C4×D4—31no—
160C3×C4×D4—61no—
161#946C2×D311yescharacteristic
162#946C2×D311yescharacteristic
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—31no—
166C2×#216—31no—
167C2×#216—31no—
168C2×#216—61no—
169C2×#216—61no—
170#935—61no—
171#926—31no—
172C2×C4⋊Dic3—31no—
173#924—31no—
174#924—31no—
175C2×#208—31no—
176C22×C3⋊C8—31no—
177C2×Dic12—31no—
178C2×ΓL(1,𝔽25)—31no—
179C2×D3×C8—31no—
180#898—61no—
181#897—31no—
182#897—31no—
183#896—21no—
184#896—21no—
185#894—61no—
186#893—21no—
187#892—31no—
188#892—61no—
189D3×C4⋊C4—31no—
190#890—61no—
191#889—61no—
192#888—21no—
193#879—61no—
194#877—61no—
195C4×D12C2×D311yescharacteristic
196#870C2×D311yescharacteristic
197C4×Dic6—31no—
198C4×Dic6—31no—
199C4×Dic6—61no—
200C4×Dic6C2×D311yescharacteristic
201C3×#103—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#97—31no—
206#835—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#835—31no—
211#835—31no—
212#835—31no—
213#835—61no—
214#835—61no—
215#835C2×D311yescharacteristic
216#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#835C2×D311yescharacteristic
219#830—31no—
220#830—31no—
221(C2×D3)⋊C8—31no—
222(C2×D3)⋊C8—31no—
223#817—31no—
224#816—31no—
225#816—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#808—31no—
230#808—31no—
231#808—31no—
232#807—31no—
233#807—31no—
234C4⋊(C3⋊C8)—31no—
235C4⋊(C3⋊C8)—31no—
236C4⋊(C3⋊C8)—61no—
237#803C2×D311yescharacteristic
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×C4C2×D411yescharacteristic
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251#634—21no—
252#634—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×D12—22no—
260C3×C4×D3—21no—
261C3×C4×D3—21no—
262C3×C4×D3—21no—
263C3×C4×D3—21no—
264C3×C4×D3—42no—
265C3×C4×D3—42no—
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—31no—
278#485—91no—
279#483—91no—
280#479—91no—
281#470—91no—
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—21no—
292C2×C3×Q8—31no—
293C2×C3×Q8—61no—
294C2×C3×Q8—61no—
295C2×C3×Q8—62no—
296C2×C3×Q8—62no—
297C2×C3×Q8—121no—
298C2×C3×Q8—121no—
299C2×C3×Q8C22×D311yescharacteristic
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×Q8C22×D311yescharacteristic
303C2×C3×D4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—61no—
307C22×C3×C4—61no—
308C22×Dic3—61no—
309D3×Q8—22no—
310D3×Q8—22no—
311D3×Q8—41no—
312D3×Q8—41no—
313C2×D12#6711yescharacteristic
314C2×C4×D3—21no—
315C2×C4×D3—21no—
316C2×C4×D3—61no—
317C2×C4×D3C22×D311yescharacteristic
318C2×C4×D3C22×D311yescharacteristic
319C2×Dic6—21no—
320C2×Dic6—21no—
321C2×Dic6—31no—
322C2×Dic6—31no—
323C2×Dic6—61no—
324C2×Dic6C22×D311yescharacteristic
325C2×C3×C8—31no—
326C2×C3×C8—31no—
327C3×C4⋊C4—21no—
328C3×C4⋊C4—21no—
329C3×C4⋊C4—21no—
330C3×C4⋊C4—21no—
331C3×C4⋊C4—31no—
332C3×C4⋊C4—31no—
333C3×C4⋊C4—31no—
334C3×C4⋊C4—31no—
335C3×C4⋊C4—41no—
336C3×C4⋊C4—41no—
337C3×C4⋊C4—61no—
338C3×C4⋊C4—61no—
339C3×C4⋊C4—61no—
340C3×C4⋊C4—61no—
341C3×C4⋊C4—61no—
342C3×C22⋊C4—31no—
343C3×C22⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C42—21no—
347C3×C42—61no—
348C3×C42C22×D311yescharacteristic
349C3×C42C22×D311yescharacteristic
350#217—61no—
351#217—61no—
352#217—61no—
353#216—62no—
354#216—121no—
355#216—121no—
356#216—121no—
357#216—121no—
358#216—122no—
359#216—122no—
360(C2×D3)⋊C4—21no—
361(C2×D3)⋊C4—21no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4#6711yescharacteristic
366(C2×D3)⋊C4#6711yescharacteristic
367C4⋊Dic3—31no—
368C4⋊Dic3—31no—
369C4⋊Dic3—61no—
370C4⋊Dic3—61no—
371C4⋊Dic3—61no—
372C4⋊Dic3—61no—
373C4⋊Dic3#6711yescharacteristic
374C4⋊Dic3C22×D311yescharacteristic
375C4⋊Dic3C22×D311yescharacteristic
376C4⋊Dic3C22×D311yescharacteristic
377Dic3⋊C4—21no—
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—61no—
383Dic3⋊C4—61no—
384Dic3⋊C4—61no—
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387Dic3⋊C4—121no—
388C4×Dic3—21no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—121no—
394#208—121no—
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
404Dic12—62no—
405ΓL(1,𝔽25)—121no—
406D3×C8—121no—
407C22×C32C22×D411yescharacteristic
408C2×C3×D3—21no—
409C2×C3×D3—21no—
410C2×C3×D3—21no—
411C2×C3×D3—21no—
412C2×C3×D3—21no—
413C2×C3×D3#13712yes—
414C32×C4—21no—
415C32×C4—21no—
416C32×C4—41no—
417C32×C4—41no—
418C32×C4C2×#4111yescharacteristic
419C32×C4H(5,𝔽2)11yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3—41no—
422C3×Dic3—22no—
423C3×Dic3—21no—
424C3×Dic3—21no—
425C3×Dic3—41no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C22×Q8—31no—
429C22×Q8—31no—
430C2×Q16—91no—
431C2×Q16—91no—
432C2×Q16—91no—
433C2×M16—91no—
434C22×C8—91no—
435C4⋊Q8—61no—
436C4⋊Q8D3211yescharacteristic
437#126—181no—
438#125—31no—
439#125—181no—
440#123—181no—
441C22⋊Q8—31no—
442C22⋊Q8—31no—
443C22⋊Q8—61no—
444C22⋊Q8—61no—
445C22⋊Q8—91no—
446C22⋊Q8—91no—
447C4×Q8—31no—
448C4×Q8—91no—
449C4×D4—31no—
450C4×D4—61no—
451#117—91no—
452#117—181no—
453C2×C4⋊C4—91no—
454#107—91no—
455#106—91no—
456#106—91no—
457C4⋊C8—91no—
458#103—31no—
459#103—31no—
460#103—31no—
461#103—31no—
462#103—91no—
463#103—91no—
464#103—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468C22⋊C8—91no—
469C22⋊C8—91no—
470#97—31no—
471C23×C3—31no—
472C23×C3—31no—
473C22×D3C2×#6711yescharacteristic
474C22×D3C2×#6711yescharacteristic
475C3×Q8—21no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C3×Q8—32no—
484C3×Q8—41no—
485C3×Q8—41no—
486C3×Q8—41no—
487C3×Q8—41no—
488C3×Q8—61no—
489C3×Q8—122no—
490C3×Q8—122no—
491C3×D4—62no—
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—41no—
502C2×C3×C4—41no—
503C2×C3×C4—61no—
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—61no—
511C2×C3×C4—122no—
512C2×C3×C4—122no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C2×#6711yescharacteristic
516C2×C3×C4C2×#6711yescharacteristic
517C2×C3×C4C23×D311yescharacteristic
518C2×C3×C4C23×D311yescharacteristic
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—121no—
528C2×Dic3—121no—
529C2×Dic3—122no—
530C2×Dic3C2×#6711yescharacteristic
531C2×Dic3C2×#6711yescharacteristic
532D12—22no—
533C4×D3—21no—
534C4×D3—21no—
535C4×D3—21no—
536C4×D3—21no—
537C4×D3—42no—
538C4×D3—42no—
539C4×D3—122no—
540Dic6—21no—
541Dic6—42no—
542Dic6—42no—
543Dic6—62no—
544Dic6—61no—
545Dic6—61no—
546Dic6—61no—
547Dic6—61no—
548Dic6—121no—
549Dic6#23712yes—
550C3×C8—61no—
551C3×C8—61no—
552C3⋊C8—21no—
553C3⋊C8—21no—
554C3⋊C8—61no—
555C3⋊C8—61no—
556C3⋊C8—61no—
557C3⋊C8—61no—
558C3⋊C8—121no—
559C3⋊C8—121no—
560C2×C32#54611yescharacteristic
561C2×C32C2×#13711yescharacteristic
562C2×C32#57811yescharacteristic
563C3×D3—22no—
564C3×D3—41no—
565C2×Q8—31no—
566C2×Q8—61no—
567C2×Q8—61no—
568C2×Q8—62no—
569C2×Q8—62no—
570C2×Q8—91no—
571C2×Q8—121no—
572C2×Q8—121no—
573C2×Q8C2×D3211yescharacteristic
574C2×Q8C2×D3211yescharacteristic
575C2×D4—31no—
576C22×C4—31no—
577C22×C4—31no—
578C22×C4—61no—
579C22×C4—61no—
580C22×C4—181no—
581Q16—182no—
582Q16—361no—
583Q16—361no—
584M16—361no—
585C2×C8—31no—
586C2×C8—31no—
587C2×C8—91no—
588C2×C8—91no—
589C2×C8—361no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—31no—
593C4⋊C4—31no—
594C4⋊C4—31no—
595C4⋊C4—31no—
596C4⋊C4—61no—
597C4⋊C4—61no—
598C4⋊C4—61no—
599C4⋊C4—61no—
600C4⋊C4—61no—
601C4⋊C4—91no—
602C4⋊C4—181no—
603C4⋊C4—181no—
604C4⋊C4—181no—
605C4⋊C4—181no—
606C22⋊C4—31no—
607C22⋊C4—31no—
608C22⋊C4—61no—
609C22⋊C4—61no—
610C22⋊C4—181no—
611C22⋊C4—181no—
612C22⋊C4—181no—
613C42—61no—
614C42—181no—
615C42—181no—
616C42C2×D3211yescharacteristic
617C22×C3—21no—
618C22×C3—32no—
619C22×C3—61no—
620C22×C3—61no—
621C22×C3—61no—
622C22×C3—61no—
623C22×C3—61no—
624C22×C3C2×D3×D411yescharacteristic
625C22×C3C22×#6711yescharacteristic
626C2×D3—21no—
627C2×D3—21no—
628C2×D3—21no—
629C2×D3—21no—
630C2×D3—21no—
631C2×D3#94212yes—
632C3×C4—22no—
633C3×C4—21no—
634C3×C4—21no—
635C3×C4—21no—
636C3×C4—21no—
637C3×C4—21no—
638C3×C4—21no—
639C3×C4—41no—
640C3×C4—41no—
641C3×C4—41no—
642C3×C4—41no—
643C3×C4—41no—
644C3×C4—61no—
645C3×C4—61no—
646C3×C4—62no—
647C3×C4—81no—
648C3×C4—81no—
649C3×C4—121no—
650C3×C4—121no—
651C3×C4—121no—
652C3×C4C2×#23711yescharacteristic
653C3×C4#100411yescharacteristic
654C3×C4D3×#4111yescharacteristic
655C3×C4#100911yescharacteristic
656Dic3—22no—
657Dic3—21no—
658Dic3—21no—
659Dic3—41no—
660Dic3—41no—
661Dic3—41no—
662Dic3—122no—
663Dic3—121no—
664Dic3—121no—
665Dic3—121no—
666Dic3—121no—
667Dic3—241no—
668C32#331211yescharacteristic, complemented, Sylow
669C23—31no—
670C23—31no—
671Q8—21no—
672Q8—21no—
673Q8—21no—
674Q8—21no—
675Q8—32no—
676Q8—61no—
677Q8—122no—
678Q8—122no—
679Q8—181no—
680Q8—181no—
681D4—62no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—31no—
685C2×C4—31no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—122no—
695C2×C4—122no—
696C2×C4—181no—
697C2×C4—181no—
698C2×C4—362no—
699C2×C4D3×#6711yescharacteristic
700C2×C4D3×#6711yescharacteristic
701C2×C4C22×D3211yescharacteristic
702C8—61no—
703C8—61no—
704C8—181no—
705C8—181no—
706C2×C3—21no—
707C2×C3—21no—
708C2×C3—21no—
709C2×C3—62no—
710C2×C3—121no—
711C2×C3#567611yescharacteristic
712C2×C3D3×#13711yescharacteristic
713C2×C3#577911yescharacteristic
714C2×C3#580611yescharacteristic
715C2×C3C2×#94211yescharacteristic
716C2×C3#583811yescharacteristic
717D3—22no—
718D3—41no—
719C22—32no—
720C22—61no—
721C22—61no—
722C22—61no—
723C22—61no—
724C22—61no—
725C22C2×D3×#6711yescharacteristic
726C4—21no—
727C4—21no—
728C4—41no—
729C4—41no—
730C4—61no—
731C4—61no—
732C4—62no—
733C4—121no—
734C4—121no—
735C4—121no—
736C4—361no—
737C4—361no—
738C4D3×#23711yescharacteristic
739C4#6431411yescharacteristic
740C3—21no—
741C3#8174911yescharacteristic, complemented
742C3#8355211yescharacteristic, complemented
743C2—62no—
744C2—121no—
745C2#1059522911yescharacteristic
746C2D3×#94211yescharacteristic
747C2#1059532811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×D12D4
hypercenterC4⋊Q8D32
hypocenterC32#3312
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10592789C2semidirect
4. C3×#5082C2semidirect
5. #10591598C2semidirect
6. #10591596C2semidirect
7. #10591595C2semidirect
8. #10591595C2semidirect
9. #10591559C2semidirect
10. #10591557C2semidirect
11. #10591549C2semidirect
12. D3×#835C2semidirect
13. #10590383C2semidirect
15. #10590286C2semidirect
73. #5082D3semidirect
668. C32#3312semidirect
741. C3#81749semidirect
742. C3#83552semidirect

Maximal subgroups

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

subgroupindex
C3×#57272
#105939202
#105927892
C3×#50822
#105915982
#105915962
#105915952
#105915592
#105915572
#105915492
D3×#8352
#105903832
#105903262
#105902862
#835523
#817493