Finite Group Databasebeta

← #11887532

Subgroups — #11887532

Order 1152.

919 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic
3#10592926C211yesmaximal, characteristic, complemented
4C2×C3×#835C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591585C211yesmaximal, characteristic, complemented
7#10591584C211yesmaximal, characteristic, complemented
8#10591565C211yesmaximal, characteristic, complemented
9#10591549C211yesmaximal, characteristic, complemented
10D3×#835C211yesmaximal, characteristic, complemented
11#10591544C211yesmaximal, characteristic, complemented
12#10591536C211yesmaximal, characteristic, complemented
13#10591177C211yesmaximal, characteristic, complemented
14C3⋊C8×#67C211yesmaximal, characteristic, complemented
15#10591101C211yesmaximal, characteristic, complemented
16#83550—31nomaximal
17#78805—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3804—21no—
21C2×#3755C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23#64139C2211yescharacteristic
24C3×#946—21no—
25C3×#946C2211yescharacteristic
26C3×Q8×Dic3C2211yescharacteristic
27C3×#944—21no—
28C3×#944C2211yescharacteristic
29C3×C4×#67—21no—
30C3×C4×#67C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C3×#924—21no—
33C3×#924C2211yescharacteristic
34C22×C3×C3⋊C8C2211yescharacteristic
35#63966—21no—
36#63918C2211yescharacteristic
37#63909C2211yescharacteristic
38#63895—21no—
39#63894C2211yescharacteristic
40#63890—21no—
41D3×C4⋊Dic3C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63657C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#835C2211yescharacteristic
51#63574C2211yescharacteristic
52#63574C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63564C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62Q8×#67D311yescharacteristic, complemented
63#5555—31no—
64#5507—31no—
65C2×C3×#103—31no—
66#5227—31no—
67#5227—31no—
68#5227—31no—
69#5227—61no—
70C2×#835—31no—
71C2×#835D311yescharacteristic, complemented
72#5114—31no—
73C8×#67—31no—
74#5083—31no—
75#5079—31no—
76#5048—31no—
77#5048—31no—
78#5043—31no—
79#5043—31no—
80C4×#215—31no—
81#5020—31no—
82D4×C3⋊C8—31no—
83#4971—31no—
84#4818—31no—
85#4807—31no—
86#4806—31no—
87#4805—31no—
88D3×#103—31no—
89#4792—31no—
90#4791—31no—
91#4788—31no—
92C2×C32×Q8—21no—
93C2×C32×Q8—22no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2311yescharacteristic
96C2×C32×Q8C2311yescharacteristic
97C22×C32×C4—21no—
98C22×C32×C4C2311yescharacteristic
99C2×#638—21no—
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C3×D3×Q8—22no—
104C3×D3×Q8—41no—
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#626—21no—
111C2×#624—21no—
112#3804—44no—
113C2×D3×Dic3—21no—
114#3755—22no—
115#3755—41no—
116#3752—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4D411yescharacteristic
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3—21no—
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4⋊Dic3C2311yescharacteristic
129C3×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4D411yescharacteristic
134C3×C4×Dic3—21no—
135C3×C4×Dic3C2311yescharacteristic
136C2×C3×C3⋊C8—41no—
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141#3722—21no—
142#3722—21no—
143#3717—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—21no—
147C22×C3×Q8—31no—
148C22×C3×Q8C2×D311yescharacteristic
149C22×C3×Q8C2×D311yescharacteristic
150C2×D3×Q8C2×D311yescharacteristic
151C2×#237—61no—
152C2×#235—61no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4⋊Q8—61no—
156C3×C22⋊Q8—31no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C4×Q8—31no—
161C3×C4×D4—31no—
162C3×C4×D4—61no—
163C2×C3×C4⋊C4—31no—
164#946—21no—
165#946C2×D311yescharacteristic
166Q8×Dic3C2×D311yescharacteristic
167#944—21no—
168#944C2×D311yescharacteristic
169C2×#215—31no—
170C2×#215—31no—
171C2×#215—31no—
172C2×#215—31no—
173C2×#215—31no—
174C2×#215—61no—
175C2×#215—61no—
176#930—31no—
177#930—31no—
178#930—31no—
179#930—61no—
180#929—61no—
181C4×#67—21no—
182C4×#67C2×D311yescharacteristic
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3C2×D311yescharacteristic
185#924—21no—
186#924C2×D311yescharacteristic
187C22×C3⋊C8—31no—
188C22×C3⋊C8C2×D311yescharacteristic
189C2×#204—31no—
190C2×D3×C8—31no—
191#897—61no—
192#896—61no—
193#895—31no—
194#894—61no—
195#893—31no—
196D3×C4⋊C4—31no—
197#888—31no—
198#886—61no—
199#886—61no—
200C4×D12—31no—
201#869—31no—
202C3×#103—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#103—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#830—31no—
222#830—61no—
223#821—31no—
224(C2×D3)⋊C8—31no—
225#817—31no—
226#816—31no—
227Dic3⋊C8—31no—
228C8×Dic3—31no—
229#810—31no—
230#810—31no—
231#809—31no—
232#808—31no—
233#808—31no—
234#808—31no—
235#808—31no—
236#808—31no—
237C4⋊(C3⋊C8)—31no—
238C4×C3⋊C8—31no—
239C23×C32C2×D411yescharacteristic
240C22×C3⋊D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C32×Q8—21no—
243C32×Q8—21no—
244C32×Q8—21no—
245C32×Q8—42no—
246C32×Q8#4112yescomplemented
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4—21no—
251C2×C32×C4—42no—
252C2×C32×C4C2×D411yescharacteristic
253C2×C32×C4C2411yescharacteristic
254#638—42no—
255C2×C3⋊Dic3—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—21no—
258C3×#67SD1614yescomplemented
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×C4×D3—42no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—42no—
273#627—42no—
274#626—42no—
275#624—42no—
276D3×Dic3—42no—
277C3⋊(C3⋊C8)—21no—
278C3⋊(C3⋊C8)—21no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281D4×Q8—31no—
282#547—91no—
283#487—91no—
284#483—91no—
285#483—91no—
286#475—91no—
287#465—91no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—31no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—22no—
299C2×C3×Q8—22no—
300C2×C3×Q8—21no—
301C2×C3×Q8—21no—
302C2×C3×Q8—31no—
303C2×C3×Q8—41no—
304C2×C3×Q8—42no—
305C2×C3×Q8—41no—
306C2×C3×Q8—41no—
307C2×C3×Q8—42no—
308C2×C3×Q8—61no—
309C2×C3×Q8—62no—
310C2×C3×Q8—121no—
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×Q8C22×D311yescharacteristic
313C2×C3×Q8C22×D311yescharacteristic
314C2×C3×Q8C22×D311yescharacteristic
315C2×C3×D4—31no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—31no—
320C22×C3×C4—41no—
321C22×C3×C4—61no—
322C22×C3×C4—61no—
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C2×#67—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—121no—
329C2×#67#6711yescharacteristic
330C22×Dic3—21no—
331C22×Dic3—61no—
332D3×Q8—22no—
333D3×Q8—41no—
334#237—124no—
335#235—124no—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—61no—
339C2×D12—61no—
340C2×C4×D3—21no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6—21no—
346C2×Dic6—61no—
347C2×Dic6—61no—
348C2×Dic6C22×D311yescharacteristic
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8—121no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4—61no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—21no—
369#217#6711yescharacteristic
370#215—62no—
371#215—62no—
372#215—122no—
373#215—121no—
374#215—121no—
375#215—121no—
376#215—122no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—121no—
385(C2×D3)⋊C4#6711yescharacteristic
386C4⋊Dic3—21no—
387C4⋊Dic3—21no—
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—21no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4#6711yescharacteristic
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—41no—
410C2×C3⋊C8—61no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—121no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415#204—121no—
416D3×C8—121no—
417C22×C32—21no—
418C22×C32—21no—
419C22×C32C2×SD1612yes—
420C22×C32C22×D411yescharacteristic
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3C2×SD1612yes—
427C32×C4—22no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4C2×#4111yescharacteristic
431C32×C4H(5,𝔽2)11yescharacteristic
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3C2×SD1612yes—
440C2×#41—181no—
441C22×Q8—31no—
442C22×Q8D3211yescharacteristic
443C2×SD16—91no—
444C2×SD16—91no—
445C2×SD16—91no—
446C22×C8—31no—
447C22×C8—91no—
448C4⋊Q8—31no—
449C4⋊Q8—61no—
450C4⋊Q8—91no—
451#123—181no—
452#123—181no—
453C22⋊Q8—31no—
454C22⋊Q8—31no—
455C22⋊Q8—61no—
456C22⋊Q8—61no—
457C22⋊Q8—181no—
458#121—91no—
459#121—91no—
460C4×Q8—31no—
461C4×D4—31no—
462C4×D4—61no—
463C4×D4—91no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—91no—
466#106—91no—
467#106—91no—
468#106—91no—
469C4⋊C8—91no—
470#103—31no—
471#103—31no—
472#103—31no—
473#103—31no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#103—91no—
479#102—91no—
480C22⋊C8—91no—
481C22⋊C8—91no—
482C4×C8—91no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—121no—
490C22×D3C2×#6711yescharacteristic
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—22no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—21no—
497C3×Q8—21no—
498C3×Q8—22no—
499C3×Q8—41no—
500C3×Q8—41no—
501C3×Q8—42no—
502C3×Q8—42no—
503C3×Q8—44no—
504C3×Q8—61no—
505C3×Q8—61no—
506C3×Q8—122no—
507C3×Q8#23512yescomplemented
508C3×Q8#23712yescomplemented
509C3×D4—34no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—31no—
521C2×C3×C4—31no—
522C2×C3×C4—31no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—41no—
527C2×C3×C4—42no—
528C2×C3×C4—42no—
529C2×C3×C4—44no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—122no—
537C2×C3×C4—122no—
538C2×C3×C4D3×D411yescharacteristic
539C2×C3×C4C2×#6711yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541C2×C3×C4C23×D311yescharacteristic
542#67—122no—
543#67—122no—
544#67—122no—
545#67—242no—
546#67#21514yescomplemented
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—42no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—121no—
555C2×Dic3—122no—
556C2×Dic3C2×#6711yescharacteristic
557C2×Dic3C2×#6711yescharacteristic
558C2×Dic3C2×#6711yescharacteristic
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—121no—
564D12—121no—
565D12—122no—
566C4×D3—21no—
567C4×D3—21no—
568C4×D3—42no—
569C4×D3—122no—
570C4×D3—122no—
571C4×D3—122no—
572Dic6—21no—
573Dic6—21no—
574Dic6—42no—
575Dic6—122no—
576Dic6—122no—
577C3×C8—61no—
578C3×C8—61no—
579C3⋊C8—21no—
580C3⋊C8—21no—
581C3⋊C8—61no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—61no—
585C3⋊C8—121no—
586C3⋊C8—121no—
587C2×C32—22no—
588C2×C32#54611yescharacteristic
589C2×C32C22×SD1611yescharacteristic
590C2×C32#57811yescharacteristic
591C3⋊D3—81no—
592C3×D3—22no—
593#41—364no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—31no—
597C2×Q8—41no—
598C2×Q8—61no—
599C2×Q8—62no—
600C2×Q8—121no—
601C2×Q8—181no—
602C2×Q8C2×D3211yescharacteristic
603C2×Q8C2×D3211yescharacteristic
604C2×D4—31no—
605C2×D4—91no—
606C2×D4—181no—
607C2×D4—181no—
608C22×C4—21no—
609C22×C4—31no—
610C22×C4—61no—
611C22×C4—61no—
612C22×C4—181no—
613C22×C4—181no—
614C22×C4C2×D3211yescharacteristic
615SD16—182no—
616SD16—361no—
617SD16—361no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C2×C8—91no—
622C2×C8—121no—
623C2×C8—361no—
624C4⋊C4—31no—
625C4⋊C4—31no—
626C4⋊C4—31no—
627C4⋊C4—31no—
628C4⋊C4—61no—
629C4⋊C4—61no—
630C4⋊C4—61no—
631C4⋊C4—61no—
632C4⋊C4—61no—
633C4⋊C4—61no—
634C4⋊C4—91no—
635C4⋊C4—181no—
636C4⋊C4—181no—
637C22⋊C4—31no—
638C22⋊C4—31no—
639C22⋊C4—61no—
640C22⋊C4—61no—
641C22⋊C4—181no—
642C22⋊C4—181no—
643C22⋊C4—181no—
644C42—31no—
645C42—61no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—21no—
651C22×C3—22no—
652C22×C3—32no—
653C22×C3—41no—
654C22×C3—41no—
655C22×C3—61no—
656C22×C3—61no—
657C22×C3D3×SD1612yes—
658C22×C3C2×#21512yes—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—241no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3C2×#21512yes—
673C3×C4—21no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—32no—
680C3×C4—41no—
681C3×C4—42no—
682C3×C4—42no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—61no—
686C3×C4—61no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691C3×C4C2×#23511yescharacteristic
692C3×C4C2×#23711yescharacteristic
693C3×C4#100411yescharacteristic
694C3×C4#100411yescharacteristic
695Dic3—21no—
696Dic3—21no—
697Dic3—41no—
698Dic3—41no—
699Dic3—41no—
700Dic3—41no—
701Dic3—121no—
702Dic3—121no—
703Dic3—241no—
704Dic3C2×#21512yes—
705C32#329811yescharacteristic, complemented, Sylow
706C23—31no—
707C23—181no—
708C23D3×#6711yescharacteristic
709Q8—21no—
710Q8—21no—
711Q8—21no—
712Q8—42no—
713Q8—61no—
714Q8—61no—
715Q8—122no—
716Q8—362no—
717Q8#380412yescomplemented
718D4—34no—
719D4—181no—
720D4—181no—
721D4—362no—
722D4—362no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—31no—
728C2×C4—31no—
729C2×C4—31no—
730C2×C4—42no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—122no—
738C2×C4—122no—
739C2×C4—181no—
740C2×C4—362no—
741C2×C4—362no—
742C2×C4D3×#6711yescharacteristic
743C2×C4C22×D3211yescharacteristic
744C8—61no—
745C8—61no—
746C8—181no—
747C8—181no—
748C2×C3—22no—
749C2×C3—22no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—42no—
754C2×C3—62no—
755C2×C3#549011yescharacteristic
756C2×C3C2×D3×SD1611yescharacteristic
757C2×C3#576611yescharacteristic
758C2×C3#580611yescharacteristic
759C2×C3C22×#21511yescharacteristic
760C2×C3#583811yescharacteristic
761D3—22no—
762D3—241no—
763D3—241no—
764D3—481no—
765C22—21no—
766C22—21no—
767C22—32no—
768C22—61no—
769C22—61no—
770C22—361no—
771C22—361no—
772C22—361no—
773C22D3×#21512yes—
774C22C2×D3×#6711yescharacteristic
775C4—21no—
776C4—22no—
777C4—32no—
778C4—41no—
779C4—61no—
780C4—61no—
781C4—121no—
782C4—121no—
783C4—121no—
784C4—121no—
785C4—361no—
786C4C2×#380411yescharacteristic
787C4#6433011yescharacteristic
788C3—21no—
789C3#7880511yescharacteristic, complemented
790C3#8355011yescharacteristic, complemented
791C2—22no—
792C2—62no—
793C2—721no—
794C2C2×D3×#21511yescharacteristic
795C2#1059532711yescharacteristic
796C2#1059549311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594906C2
hypercenterC22×Q8D32
hypocenterC32#3298
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
1. C3×Q8×#67C2semidirect
3. #10592926C2semidirect
4. C2×C3×#835C2semidirect
5. #10591623C2semidirect
6. #10591585C2semidirect
7. #10591584C2semidirect
8. #10591565C2semidirect
9. #10591549C2semidirect
10. D3×#835C2semidirect
11. #10591544C2semidirect
12. #10591536C2semidirect
13. #10591177C2semidirect
14. C3⋊C8×#67C2semidirect
15. #10591101C2semidirect
62. Q8×#67D3semidirect
71. C2×#835D3semidirect
246. C32×Q8#41semidirect
258. C3×#67SD16semidirect
507. C3×Q8#235semidirect
508. C3×Q8#237semidirect
546. #67#215semidirect
705. C32#3298semidirect
717. Q8#3804semidirect
789. C3#78805semidirect
790. C3#83550semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×#672
#105949062
#105929262
C2×C3×#8352
#105916232
#105915852
#105915842
#105915652
#105915492
D3×#8352
#105915442
#105915362
#105911772
C3⋊C8×#672
#105911012
#835503
#788053