Finite Group Databasebeta

← #11887545

Subgroups — #11887545

Order 1152.

892 conjugacy classes of subgroups.

The subgroup lattice has 785 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5632C211yesmaximal, characteristic, complemented
2#10594907C211yesmaximal, characteristic
3#10592742C211yesmaximal, characteristic, complemented
4C3×#5048C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591583C211yesmaximal, characteristic, complemented
7#10591564C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591171C211yesmaximal, characteristic, complemented
10C3⋊C8×#67C211yesmaximal, characteristic, complemented
11C2×#63566C211yesmaximal, characteristic, complemented
12#10590556C211yesmaximal, characteristic, complemented
13#10590501C211yesmaximal, characteristic, complemented
14#10590453C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#83550—31nomaximal
17#80689—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×#3805—21no—
21C32×C22⋊Q8C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C3×#944C2211yescharacteristic
24C2×C3×#215C2211yescharacteristic
25C3×#930C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C22×C3×C3⋊C8C2211yescharacteristic
28C3×#897C2211yescharacteristic
29C3×#896—21no—
30C3×#888—21no—
31C3×#887C2211yescharacteristic
32C3×#67⋊C4—21no—
33C3×#878—21no—
34#63962—21no—
35#63918C2211yescharacteristic
36#63908C2211yescharacteristic
37#63893—21no—
38Dic3×D12C2211yescharacteristic
39#63891—21no—
40D3×C4⋊Dic3C2211yescharacteristic
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63662C2211yescharacteristic
46#63657C2211yescharacteristic
47#63635C2211yescharacteristic
48#63635C2211yescharacteristic
49C3×#835C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#808C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62#5632D311yescharacteristic, complemented
63#5611—31no—
64#5555—31no—
65C3×#465—31no—
66#5227—31no—
67#5227—31no—
68C2×#835—31no—
69C2×#835—31no—
70#5170—31no—
71#5162—31no—
72C8×#67—31no—
73C2×#816—31no—
74#5083—31no—
75#5079—31no—
76#5048—31no—
77#5048D311yescharacteristic, complemented
78#5043—31no—
79#5043—31no—
80#5043—31no—
81#5043—61no—
82#5040—31no—
83C4×#215—31no—
84#5020—31no—
85D4×C3⋊C8—31no—
86#4862—31no—
87#4854—31no—
88D3×#103—31no—
89#4792—31no—
90#4778—31no—
91#4758—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×C3×#67—21no—
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C3×D3×Q8—22no—
99C3×D3×Q8—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6—22no—
104C2×C3×Dic6—21no—
105C2×C3×Dic6—21no—
106C2×C3×Dic6—41no—
107C2×C3×Dic6C2311yescharacteristic
108C2×C3×Dic6C2311yescharacteristic
109C2×#627—21no—
110C2×#625—21no—
111#3805—44no—
112C2×D3×Dic3—21no—
113C2×D3×Dic3—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117C4⋊(C3⋊Dic3)—21no—
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217D411yescharacteristic
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×Dic3⋊C4—21no—
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×Dic3⋊C4D411yescharacteristic
133C3×C4×Dic3—21no—
134C3×C4×Dic3C2311yescharacteristic
135C2×C3×C3⋊C8—41no—
136C2×C3×C3⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142#3715—22no—
143#3715—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C22×C3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#237—61no—
150C2×#237—61no—
151C22×Dic6C2×D311yescharacteristic
152C2×C3×SD16—31no—
153C22×C3×C8—31no—
154C3×C4⋊Q8—31no—
155C3×C4⋊Q8—61no—
156C3×C22⋊Q8—21no—
157C3×C22⋊Q8—31no—
158C3×C22⋊Q8—61no—
159C3×C22⋊Q8—61no—
160C3×C22⋊Q8C2×D311yescharacteristic
161C3×C22⋊Q8C2×D311yescharacteristic
162C3×#121—31no—
163C3×C4×Q8—31no—
164C3×C4×D4—31no—
165C3×C4×D4—61no—
166#944C2×D311yescharacteristic
167C2×#215—31no—
168C2×#215—31no—
169C2×#215C2×D311yescharacteristic
170#938—31no—
171#935—61no—
172D4×Dic3—31no—
173C2×#214—31no—
174C2×#214—31no—
175#930—31no—
176#930C2×D311yescharacteristic
177C4×#67C2×D311yescharacteristic
178C2×C4⋊Dic3—31no—
179C2×C4⋊Dic3—31no—
180C2×C4⋊Dic3—31no—
181C2×C4⋊Dic3—61no—
182C22×C3⋊C8—31no—
183C22×C3⋊C8C2×D311yescharacteristic
184C2×D3×C8—31no—
185#897—61no—
186#897C2×D311yescharacteristic
187#896—21no—
188D3×C4⋊C4—31no—
189#888—21no—
190#888—31no—
191#887C2×D311yescharacteristic
192#886—61no—
193#886—61no—
194#883—61no—
195#67⋊C4—21no—
196#878—21no—
197#878—61no—
198C4×D12—31no—
199#869—31no—
200C3×#106—31no—
201C3×#103—31no—
202C3×#102—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—31no—
213#835—61no—
214#835—61no—
215#835C2×D311yescharacteristic
216#830—31no—
217#830—31no—
218#830—31no—
219#830—61no—
220(C2×D3)⋊C8—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225Dic3⋊C8—31no—
226C8×Dic3—31no—
227#810—31no—
228#810—31no—
229#809C2×D311yescharacteristic
230#808—31no—
231#808—31no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808—61no—
236#808C2×D311yescharacteristic
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—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—42no—
253C3×#67—42no—
254C3×#67SD1614yescomplemented
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—42no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—42no—
267C3×Dic6—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—42no—
271C3×Dic6—42no—
272C3×Dic6#4112yescomplemented
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—31no—
288#465—91no—
289#461—91no—
290#448—91no—
291#448—91no—
292C4×SD16—91no—
293C8×D4—91no—
294C2×#103—91no—
295C2×#103—91no—
296C2×C3×Q8—21no—
297C2×C3×Q8—31no—
298C2×C3×Q8—31no—
299C2×C3×Q8—61no—
300C2×C3×Q8—62no—
301C2×C3×Q8—61no—
302C2×C3×Q8—62no—
303C2×C3×Q8—121no—
304C2×C3×Q8—121no—
305C2×C3×Q8C22×D311yescharacteristic
306C2×C3×Q8C22×D311yescharacteristic
307C2×C3×D4—31no—
308C2×C3×D4—31no—
309C2×C3×D4—61no—
310C22×C3×C4—21no—
311C22×C3×C4—31no—
312C22×C3×C4—61no—
313C22×C3×C4—61no—
314C22×C3×C4C22×D311yescharacteristic
315C22×C3×C4C22×D311yescharacteristic
316C2×#67—21no—
317C2×#67—61no—
318C2×#67—61no—
319C2×#67#6711yescharacteristic
320C22×Dic3—21no—
321C22×Dic3—61no—
322C22×Dic3—61no—
323C22×Dic3—61no—
324C22×Dic3—61no—
325C22×Dic3—121no—
326D3×Q8—22no—
327D3×Q8—41no—
328#237—124no—
329#237—124no—
330C2×D12C22×D311yescharacteristic
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3C22×D311yescharacteristic
335C2×Dic6—22no—
336C2×Dic6—21no—
337C2×Dic6—21no—
338C2×Dic6—41no—
339C2×Dic6—61no—
340C2×Dic6—61no—
341C2×Dic6C22×D311yescharacteristic
342C2×Dic6C22×D311yescharacteristic
343C3×SD16—121no—
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C2×C3×C8—121no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—21no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—41no—
353C3×C4⋊C4—61no—
354C3×C4⋊C4—61no—
355C3×C4⋊C4—61no—
356C3×C4⋊C4—61no—
357C3×C4⋊C4C22×D311yescharacteristic
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C22⋊C4—21no—
360C3×C22⋊C4—21no—
361C3×C22⋊C4—31no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—61no—
369#217—61no—
370#217#6711yescharacteristic
371#215—41no—
372#215—62no—
373#215—121no—
374#214—62no—
375#214—121no—
376(C2×D3)⋊C4—21no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4#6711yescharacteristic
381C4⋊Dic3—21no—
382C4⋊Dic3—31no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—31no—
386C4⋊Dic3—61no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—121no—
393C4⋊Dic3C22×D311yescharacteristic
394Dic3⋊C4—21no—
395Dic3⋊C4—21no—
396Dic3⋊C4—21no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4#6711yescharacteristic
400C4×Dic3—21no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—31no—
406C2×C3⋊C8—41no—
407C2×C3⋊C8—61no—
408C2×C3⋊C8—61no—
409C2×C3⋊C8—121no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412D3×C8—121no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32C2×SD1612yes—
416C22×C32C22×D411yescharacteristic
417C2×C3×D3—21no—
418C2×C3×D3—21no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3C2×SD1612yes—
423C32×C4—21no—
424C32×C4—41no—
425C32×C4—41no—
426C32×C4C2×#4111yescharacteristic
427C32×C4H(5,𝔽2)11yescharacteristic
428C3⋊Dic3—41no—
429C3⋊Dic3—41no—
430C3×Dic3—22no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C3×Dic3C2×SD1612yes—
436C2×#41—181no—
437C22×Q8—31no—
438C22×Q8—31no—
439C2×SD16—31no—
440C2×SD16—91no—
441C2×SD16—91no—
442C22×C8—31no—
443C22×C8—91no—
444C4⋊Q8—31no—
445C4⋊Q8—61no—
446C4⋊Q8—91no—
447#123—181no—
448#123—181no—
449C22⋊Q8—31no—
450C22⋊Q8—61no—
451C22⋊Q8—61no—
452C22⋊Q8—181no—
453C22⋊Q8D3211yescharacteristic
454#121—31no—
455#121—91no—
456C4×Q8—31no—
457C4×D4—31no—
458C4×D4—61no—
459C4×D4—91no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462#106—31no—
463#106—91no—
464#106—91no—
465C4⋊C8—91no—
466#103—31no—
467#103—91no—
468#103—91no—
469#103—91no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#102—31no—
476C22⋊C8—91no—
477C22⋊C8—91no—
478C4×C8—91no—
479C23×C3—21no—
480C23×C3—31no—
481C23×C3—61no—
482C23×C3D3×D411yescharacteristic
483C23×C3C2×#6711yescharacteristic
484C22×D3—21no—
485C22×D3C2×#6711yescharacteristic
486C3×Q8—21no—
487C3×Q8—21no—
488C3×Q8—21no—
489C3×Q8—21no—
490C3×Q8—32no—
491C3×Q8—41no—
492C3×Q8—41no—
493C3×Q8—61no—
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—122no—
497C3×Q8—122no—
498C3×D4—34no—
499C3×D4—61no—
500C3×D4—61no—
501C3×D4—122no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—31no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—41no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—122no—
525C2×C3×C4—122no—
526C2×C3×C4D3×D411yescharacteristic
527C2×C3×C4C2×#6711yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—42no—
531#67—122no—
532#67—122no—
533#67#21514yescomplemented
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—42no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—121no—
543C2×Dic3—121no—
544C2×Dic3—122no—
545C2×Dic3—122no—
546C2×Dic3—122no—
547C2×Dic3—122no—
548C2×Dic3—242no—
549C2×Dic3C2×#6711yescharacteristic
550C2×Dic3C2×#6711yescharacteristic
551C2×Dic3C2×#6711yescharacteristic
552D12—21no—
553D12—21no—
554C4×D3—21no—
555C4×D3—21no—
556C4×D3—42no—
557C4×D3—122no—
558C4×D3—122no—
559Dic6—21no—
560Dic6—21no—
561Dic6—21no—
562Dic6—42no—
563Dic6—42no—
564Dic6—122no—
565Dic6—122no—
566Dic6#23712yescomplemented
567C3×C8—61no—
568C3×C8—61no—
569C3⋊C8—21no—
570C3⋊C8—21no—
571C3⋊C8—61no—
572C3⋊C8—61no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—121no—
576C3⋊C8—121no—
577C2×C32—22no—
578C2×C32#54611yescharacteristic
579C2×C32C22×SD1611yescharacteristic
580C2×C32#57811yescharacteristic
581C3×D3—22no—
582C3×D3—81no—
583#41—364no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×Q8—61no—
587C2×Q8—62no—
588C2×Q8—61no—
589C2×Q8—62no—
590C2×Q8—121no—
591C2×Q8—121no—
592C2×Q8—181no—
593C2×Q8C2×D3211yescharacteristic
594C2×D4—31no—
595C2×D4—31no—
596C2×D4—61no—
597C2×D4—181no—
598C22×C4—31no—
599C22×C4—61no—
600C22×C4—61no—
601C22×C4—181no—
602C22×C4—181no—
603C22×C4—181no—
604C22×C4C2×D3211yescharacteristic
605SD16—121no—
606SD16—182no—
607SD16—361no—
608C2×C8—31no—
609C2×C8—31no—
610C2×C8—91no—
611C2×C8—91no—
612C2×C8—121no—
613C2×C8—361no—
614C4⋊C4—21no—
615C4⋊C4—31no—
616C4⋊C4—31no—
617C4⋊C4—61no—
618C4⋊C4—61no—
619C4⋊C4—61no—
620C4⋊C4—61no—
621C4⋊C4—91no—
622C4⋊C4—91no—
623C4⋊C4—181no—
624C4⋊C4—181no—
625C4⋊C4—181no—
626C4⋊C4C2×D3211yescharacteristic
627C22⋊C4—21no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C42—31no—
635C42—61no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—22no—
642C22×C3—32no—
643C22×C3—41no—
644C22×C3—41no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3D3×SD1612yes—
651C22×C3C2×#21512yes—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C22×#6711yescharacteristic
654C2×D3—21no—
655C2×D3—21no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3C2×#21512yes—
660C3×C4—21no—
661C3×C4—21no—
662C3×C4—21no—
663C3×C4—21no—
664C3×C4—32no—
665C3×C4—41no—
666C3×C4—41no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—61no—
671C3×C4—61no—
672C3×C4—62no—
673C3×C4—81no—
674C3×C4—81no—
675C3×C4—121no—
676C3×C4—121no—
677C3×C4C2×#23711yescharacteristic
678C3×C4#100411yescharacteristic
679C3×C4#100411yescharacteristic
680C3×C4D3×#4111yescharacteristic
681Dic3—22no—
682Dic3—21no—
683Dic3—21no—
684Dic3—41no—
685Dic3—41no—
686Dic3—121no—
687Dic3—121no—
688Dic3—121no—
689Dic3—121no—
690Dic3—241no—
691Dic3—241no—
692Dic3C2×#21512yes—
693C32#329811yescharacteristic, complemented, Sylow
694C23—31no—
695C23—61no—
696C23D3×#6711yescharacteristic
697Q8—21no—
698Q8—21no—
699Q8—32no—
700Q8—61no—
701Q8—61no—
702Q8—61no—
703Q8—122no—
704Q8—122no—
705Q8—362no—
706D4—34no—
707D4—61no—
708D4—61no—
709D4—122no—
710D4—362no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—31no—
716C2×C4—31no—
717C2×C4—31no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—122no—
724C2×C4—122no—
725C2×C4—181no—
726C2×C4—181no—
727C2×C4—362no—
728C2×C4—362no—
729C2×C4—362no—
730C2×C4D3×#6711yescharacteristic
731C2×C4C22×D3211yescharacteristic
732C8—61no—
733C8—61no—
734C8—181no—
735C8—181no—
736C2×C3—22no—
737C2×C3—22no—
738C2×C3—21no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—42no—
742C2×C3—62no—
743C2×C3—241no—
744C2×C3#561011yescharacteristic
745C2×C3C2×D3×SD1611yescharacteristic
746C2×C3#577111yescharacteristic
747C2×C3#580611yescharacteristic
748C2×C3C22×#21511yescharacteristic
749C2×C3#583811yescharacteristic
750D3—22no—
751D3—81no—
752C22—21no—
753C22—21no—
754C22—32no—
755C22—61no—
756C22—61no—
757C22—121no—
758C22—121no—
759C22—121no—
760C22D3×#21512yes—
761C22C2×D3×#6711yescharacteristic
762C4—21no—
763C4—32no—
764C4—41no—
765C4—41no—
766C4—61no—
767C4—62no—
768C4—61no—
769C4—121no—
770C4—121no—
771C4—361no—
772C4—361no—
773C4D3×#23711yescharacteristic
774C4#6431311yescharacteristic
775C3—21no—
776C3#8068911yescharacteristic, complemented
777C3#8355011yescharacteristic, complemented
778C2—22no—
779C2—62no—
780C2—241no—
781C2#1059515011yescharacteristic
782C2C2×D3×#21511yescharacteristic
783C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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×#5632C2semidirect
3. #10592742C2semidirect
4. C3×#5048C2semidirect
5. #10591623C2semidirect
6. #10591583C2semidirect
7. #10591564C2semidirect
8. D3×#835C2semidirect
9. #10591171C2semidirect
10. C3⋊C8×#67C2semidirect
11. C2×#63566C2semidirect
12. #10590556C2semidirect
13. #10590501C2semidirect
14. #10590453C2semidirect
15. #10590439C2semidirect
62. #5632D3semidirect
77. #5048D3semidirect
254. C3×#67SD16semidirect
272. C3×Dic6#41semidirect
533. #67#215semidirect
566. Dic6#237semidirect
693. C32#3298semidirect
776. C3#80689semidirect
777. C3#83550semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
#105949072
#105927422
C3×#50482
#105916232
#105915832
#105915642
D3×#8352
#105911712
C3⋊C8×#672
C2×#635662
#105905562
#105905012
#105904532
#105904392
#835503
#806893