Finite Group Databasebeta

← #11887534

Subgroups — #11887534

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×Q8×#67C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic
3C2×#63662C211yesmaximal, characteristic, complemented
4C3×#5227C211yesmaximal, characteristic, complemented
5#10591634C211yesmaximal, characteristic, complemented
6#10591623C211yesmaximal, characteristic, complemented
7#10591583C211yesmaximal, characteristic, complemented
8#10591564C211yesmaximal, characteristic, complemented
9Dic3×#215C211yesmaximal, characteristic, complemented
10#10591549C211yesmaximal, characteristic, complemented
11D3×#835C211yesmaximal, characteristic, complemented
12#10591544C211yesmaximal, characteristic, complemented
13#10591179C211yesmaximal, characteristic, complemented
14#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
15#10591126C211yesmaximal, characteristic, complemented
16#83550—31nomaximal
17#80049—31nomaximal
18C22×C32×Q8C2211yescharacteristic
19C2×C3×D3×Q8C2211yescharacteristic
20C2×#3805—21no—
21C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C3×#946—21no—
24C3×#946C2211yescharacteristic
25C3×Q8×Dic3C2211yescharacteristic
26C3×#944—21no—
27C3×#944C2211yescharacteristic
28C2×C3×#215C2211yescharacteristic
29C2×C3×#215C2211yescharacteristic
30C3×#930C2211yescharacteristic
31C3×C4×#67—21no—
32C3×C4×#67C2211yescharacteristic
33C3×#924—21no—
34C3×#924C2211yescharacteristic
35#63962—21no—
36#63918C2211yescharacteristic
37#63908C2211yescharacteristic
38#63893—21no—
39Dic3×D12C2211yescharacteristic
40#63891—21no—
41D3×C4⋊Dic3C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63662C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#830C2211yescharacteristic
51#63574C2211yescharacteristic
52#63573C2211yescharacteristic
53#63573C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62Q8×#67D311yescharacteristic, complemented
63#5611—31no—
64#5555—31no—
65C3×#448—31no—
66#5227—31no—
67#5227D311yescharacteristic, complemented
68C2×#835—31no—
69C2×#835—31no—
70C2×#835—31no—
71C2×#835—61no—
72#5171—31no—
73#5170—31no—
74#5162—31no—
75Dic3×SD16—31no—
76#5083—31no—
77#5079—31no—
78#5048—31no—
79#5048—31no—
80#5043—31no—
81#5043—31no—
82#5041—31no—
83C4×#215—31no—
84#5020—31no—
85D4×C3⋊C8—31no—
86#4805—31no—
87D3×#103—31no—
88#4792—31no—
89#4791—31no—
90#67⋊C8—31no—
91#4721—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
99C22×C3⋊Dic3—21no—
100C2×C3×#67—21no—
101C2×C3×#67D411yescharacteristic
102C3×D3×Q8—22no—
103C3×D3×Q8—41no—
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3—21no—
106C2×C3×C4×D3C2311yescharacteristic
107C2×C3×Dic6—21no—
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#625—21no—
111#3805—44no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C4⋊(C3⋊Dic3)—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)—41no—
118C2×C3⋊(C3⋊C8)C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C3×#217—21no—
121C3×#217D411yescharacteristic
122C3×#215—22no—
123C3×#215—41no—
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4D411yescharacteristic
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4—21no—
133C3×Dic3⋊C4—21no—
134C3×Dic3⋊C4D411yescharacteristic
135C3×C4×Dic3—21no—
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139Dic3⋊Dic3—21no—
140Dic3⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3715—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×#237—61no—
153C2×C3×SD16—31no—
154C2×C3×SD16—31no—
155C3×C4⋊Q8—31no—
156C3×C4⋊Q8—61no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—31no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8—61no—
161C3×#121—31no—
162C3×C4×Q8—31no—
163C3×C4×D4—31no—
164C3×C4×D4—61no—
165#946—21no—
166#946C2×D311yescharacteristic
167Q8×Dic3C2×D311yescharacteristic
168#944—21no—
169#944C2×D311yescharacteristic
170C2×#215—31no—
171C2×#215C2×D311yescharacteristic
172C2×#215C2×D311yescharacteristic
173#938—31no—
174#935—61no—
175D4×Dic3—31no—
176C2×#214—31no—
177#930—31no—
178#930C2×D311yescharacteristic
179C4×#67—21no—
180C4×#67C2×D311yescharacteristic
181C2×C4⋊Dic3—31no—
182C2×C4⋊Dic3—31no—
183C2×C4⋊Dic3—31no—
184C2×C4⋊Dic3—61no—
185#924—21no—
186#924C2×D311yescharacteristic
187C22×C3⋊C8—31no—
188C22×C3⋊C8—31no—
189C22×C3⋊C8—31no—
190C22×C3⋊C8—61no—
191C2×D3×C8—31no—
192#897—61no—
193D3×C4⋊C4—31no—
194#888—31no—
195#886—61no—
196#886—61no—
197#883—61no—
198#878—61no—
199C4×D12—31no—
200#869—31no—
201C3×#103—31no—
202C3×#103—31no—
203C3×C22⋊C8—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—31no—
213#835—31no—
214#835—31no—
215#835—61no—
216#835—61no—
217#835—61no—
218#835—61no—
219#835C2×D311yescharacteristic
220#835C2×D311yescharacteristic
221#832—31no—
222#830—31no—
223#830C2×D311yescharacteristic
224(C2×D3)⋊C8—31no—
225#817—31no—
226#817—31no—
227#816—31no—
228#816—31no—
229Dic3⋊C8—31no—
230C8×Dic3—31no—
231#810—31no—
232#809—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
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—42no—
257C3×#67—42no—
258C3×#67SD1614yescomplemented
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C3×D12—21no—
266C3×D12—21no—
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#625—42no—
275D3×Dic3—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—31no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—24no—
299C2×C3×Q8—22no—
300C2×C3×Q8—22no—
301C2×C3×Q8—21no—
302C2×C3×Q8—21no—
303C2×C3×Q8—31no—
304C2×C3×Q8—41no—
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—
316C2×C3×D4—31no—
317C2×C3×D4—61no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—21no—
321C22×C3×C4—31no—
322C22×C3×C4—41no—
323C22×C3×C4—61no—
324C22×C3×C4C22×D311yescharacteristic
325C22×C3×C4C22×D311yescharacteristic
326C2×#67—21no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67#6711yescharacteristic
330C22×Dic3—61no—
331C22×Dic3—61no—
332C22×Dic3—61no—
333C22×Dic3—61no—
334C22×Dic3—121no—
335D3×Q8—22no—
336D3×Q8—41no—
337#237—124no—
338#237—124no—
339C2×D12C22×D311yescharacteristic
340C2×C4×D3—21no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3C22×D311yescharacteristic
344C2×Dic6—21no—
345C2×Dic6—61no—
346C2×Dic6—61no—
347C2×Dic6C22×D311yescharacteristic
348C3×SD16—62no—
349C3×SD16—121no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C3×C4⋊C4—31no—
353C3×C4⋊C4—31no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C22⋊C4—31no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—61no—
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C42—31no—
366C3×C42—61no—
367#217—21no—
368#217—61no—
369#217—61no—
370#217#6711yescharacteristic
371#215—22no—
372#215—41no—
373#215—121no—
374#214—121no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4#6711yescharacteristic
380C4⋊Dic3—21no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—121no—
392C4⋊Dic3C22×D311yescharacteristic
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4#6711yescharacteristic
401C4×Dic3—21no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—31no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8—121no—
411C2×C3⋊C8—121no—
412C2×C3⋊C8—122no—
413C2×C3⋊C8C22×D311yescharacteristic
414C2×C3⋊C8C22×D311yescharacteristic
415D3×C8—121no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32C2×SD1612yes—
419C22×C32C22×D411yescharacteristic
420C2×C3×D3—21no—
421C2×C3×D3—21no—
422C2×C3×D3—41no—
423C2×C3×D3—41no—
424C2×C3×D3—41no—
425C2×C3×D3C2×SD1612yes—
426C32×C4—21no—
427C32×C4—22no—
428C32×C4—41no—
429C32×C4C2×#4111yescharacteristic
430C32×C4H(5,𝔽2)11yescharacteristic
431C3⋊Dic3—41no—
432C3⋊Dic3—41no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3C2×SD1612yes—
439C2×#41—181no—
440C22×Q8—31no—
441C22×Q8D3211yescharacteristic
442C2×SD16—31no—
443C2×SD16—31no—
444C2×SD16—91no—
445C22×C8—91no—
446C22×C8—91no—
447C4⋊Q8—31no—
448C4⋊Q8—61no—
449C4⋊Q8—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—31no—
454C22⋊Q8—61no—
455C22⋊Q8—61no—
456C22⋊Q8—181no—
457#121—31no—
458#121—91no—
459C4×Q8—31no—
460C4×D4—31no—
461C4×D4—61no—
462C4×D4—91no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—91no—
465#106—91no—
466#106—91no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8—91no—
481C4×C8—91no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3—61no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3C2×#6711yescharacteristic
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—22no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—21no—
496C3×Q8—22no—
497C3×Q8—41no—
498C3×Q8—41no—
499C3×Q8—42no—
500C3×Q8—42no—
501C3×Q8—44no—
502C3×Q8—61no—
503C3×Q8—61no—
504C3×Q8—122no—
505C3×Q8#23712yescomplemented
506C3×Q8#23712yescomplemented
507C3×D4—34no—
508C3×D4—61no—
509C3×D4—61no—
510C3×D4—122no—
511C2×C3×C4—22no—
512C2×C3×C4—22no—
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—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—31no—
524C2×C3×C4—31no—
525C2×C3×C4—31no—
526C2×C3×C4—41no—
527C2×C3×C4—41no—
528C2×C3×C4—42no—
529C2×C3×C4—42no—
530C2×C3×C4—44no—
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×C4D3×D411yescharacteristic
538C2×C3×C4C2×#6711yescharacteristic
539C2×C3×C4C23×D311yescharacteristic
540C2×C3×C4C23×D311yescharacteristic
541#67—42no—
542#67—122no—
543#67—122no—
544#67#21514yescomplemented
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—121no—
553C2×Dic3—121no—
554C2×Dic3—122no—
555C2×Dic3—122no—
556C2×Dic3—122no—
557C2×Dic3—122no—
558C2×Dic3—242no—
559C2×Dic3C2×#6711yescharacteristic
560C2×Dic3C2×#6711yescharacteristic
561C2×Dic3C2×#6711yescharacteristic
562D12—21no—
563D12—21no—
564C4×D3—21no—
565C4×D3—21no—
566C4×D3—42no—
567C4×D3—122no—
568C4×D3—122no—
569Dic6—21no—
570Dic6—21no—
571Dic6—42no—
572Dic6—122no—
573Dic6—122no—
574C3×C8—61no—
575C3×C8—61no—
576C3⋊C8—21no—
577C3⋊C8—21no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—61no—
581C3⋊C8—61no—
582C3⋊C8—121no—
583C3⋊C8—121no—
584C2×C32—22no—
585C2×C32#54611yescharacteristic
586C2×C32C22×SD1611yescharacteristic
587C2×C32#57811yescharacteristic
588C3×D3—22no—
589C3×D3—81no—
590#41—364no—
591C2×Q8—21no—
592C2×Q8—22no—
593C2×Q8—31no—
594C2×Q8—41no—
595C2×Q8—61no—
596C2×Q8—62no—
597C2×Q8—121no—
598C2×Q8—181no—
599C2×Q8C2×D3211yescharacteristic
600C2×Q8C2×D3211yescharacteristic
601C2×D4—31no—
602C2×D4—31no—
603C2×D4—61no—
604C2×D4—181no—
605C22×C4—21no—
606C22×C4—31no—
607C22×C4—61no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612SD16—62no—
613SD16—121no—
614SD16—361no—
615C2×C8—31no—
616C2×C8—31no—
617C2×C8—91no—
618C2×C8—91no—
619C2×C8—361no—
620C2×C8—361no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—61no—
628C4⋊C4—61no—
629C4⋊C4—91no—
630C4⋊C4—91no—
631C4⋊C4—181no—
632C4⋊C4—181no—
633C4⋊C4—181no—
634C22⋊C4—31no—
635C22⋊C4—31no—
636C22⋊C4—61no—
637C22⋊C4—61no—
638C22⋊C4—61no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C22×C3—22no—
644C22×C3—22no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—22no—
651C22×C3—32no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—121no—
655C22×C3—121no—
656C22×C3—121no—
657C22×C3D3×SD1612yes—
658C22×C3C2×#21512yes—
659C22×C3C2×D3×D411yescharacteristic
660C22×C3C22×#6711yescharacteristic
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3C2×#21512yes—
667C3×C4—22no—
668C3×C4—22no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—22no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—32no—
675C3×C4—42no—
676C3×C4—42no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—61no—
680C3×C4—61no—
681C3×C4—121no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4C2×#23711yescharacteristic
685C3×C4C2×#23711yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4#100411yescharacteristic
688Dic3—21no—
689Dic3—21no—
690Dic3—41no—
691Dic3—41no—
692Dic3—41no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3—241no—
699Dic3C2×#21512yes—
700C32#329811yescharacteristic, complemented, Sylow
701C23—31no—
702C23—61no—
703C23D3×#6711yescharacteristic
704Q8—21no—
705Q8—21no—
706Q8—21no—
707Q8—42no—
708Q8—61no—
709Q8—61no—
710Q8—122no—
711Q8—362no—
712Q8#380512yescomplemented
713D4—34no—
714D4—61no—
715D4—61no—
716D4—122no—
717D4—362no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—42no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—122no—
732C2×C4—181no—
733C2×C4—181no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4—362no—
737C2×C4D3×#6711yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—61no—
740C8—61no—
741C8—181no—
742C8—181no—
743C2×C3—24no—
744C2×C3—22no—
745C2×C3—22no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—62no—
750C2×C3—241no—
751C2×C3#559111yescharacteristic
752C2×C3C2×D3×SD1611yescharacteristic
753C2×C3#577911yescharacteristic
754C2×C3#580611yescharacteristic
755C2×C3C22×#21511yescharacteristic
756C2×C3#583811yescharacteristic
757D3—22no—
758D3—81no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22D3×#21512yes—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—22no—
771C4—32no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—121no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4—361no—
780C4C2×#380511yescharacteristic
781C4#6433011yescharacteristic
782C3—21no—
783C3#8004911yescharacteristic, complemented
784C3#8355011yescharacteristic, complemented
785C2—22no—
786C2—62no—
787C2—241no—
788C2C2×D3×#21511yescharacteristic
789C2#1059532811yescharacteristic
790C2#1059549411yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radical#10594907C2
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. C2×#63662C2semidirect
4. C3×#5227C2semidirect
5. #10591634C2semidirect
6. #10591623C2semidirect
7. #10591583C2semidirect
8. #10591564C2semidirect
9. Dic3×#215C2semidirect
10. #10591549C2semidirect
11. D3×#835C2semidirect
12. #10591544C2semidirect
13. #10591179C2semidirect
14. #67⋊(C3⋊C8)C2semidirect
15. #10591126C2semidirect
62. Q8×#67D3semidirect
67. #5227D3semidirect
246. C32×Q8#41semidirect
258. C3×#67SD16semidirect
505. C3×Q8#237semidirect
506. C3×Q8#237semidirect
544. #67#215semidirect
700. C32#3298semidirect
712. Q8#3805semidirect
783. C3#80049semidirect
784. 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
#105949072
C2×#636622
C3×#52272
#105916342
#105916232
#105915832
#105915642
Dic3×#2152
#105915492
D3×#8352
#105915442
#105911792
#67⋊(C3⋊C8)2
#105911262
#835503
#800493