Finite Group Databasebeta

← #11887547

Subgroups — #11887547

Order 1152.

902 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×#5632C211yesmaximal, characteristic, complemented
2#10594906C211yesmaximal, characteristic
3#10592747C211yesmaximal, characteristic, complemented
4C3×#5043C211yesmaximal, characteristic, complemented
5#10591623C211yesmaximal, characteristic, complemented
6#10591584C211yesmaximal, characteristic, complemented
7#10591565C211yesmaximal, characteristic, complemented
8D3×#835C211yesmaximal, characteristic, complemented
9#10591174C211yesmaximal, characteristic, complemented
10#67⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
11C2×#63565C211yesmaximal, characteristic, complemented
12#10590577C211yesmaximal, characteristic, complemented
13#10590556C211yesmaximal, characteristic, complemented
14#10590458C211yesmaximal, characteristic, complemented
15#10590439C211yesmaximal, characteristic, complemented
16#83550—31nomaximal
17#81450—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C22×C3×Dic6C2211yescharacteristic
20C2×#3804—21no—
21C32×C22⋊Q8C2211yescharacteristic
22C2×#3755C2211yescharacteristic
23#64139C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C3×#944C2211yescharacteristic
26C3×C4×#67C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C3×#897C2211yescharacteristic
29C3×#896—21no—
30C3×#888—21no—
31C3×#887C2211yescharacteristic
32C3×#67⋊C4—21no—
33C3×#878—21no—
34#63966—21no—
35#63918C2211yescharacteristic
36#63909C2211yescharacteristic
37#63895—21no—
38#63894C2211yescharacteristic
39#63890—21no—
40D3×C4⋊Dic3C2211yescharacteristic
41C2×#3717C2211yescharacteristic
42C2×#3717C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic
44#63662C2211yescharacteristic
45#63636C2211yescharacteristic
46#63635C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#835C2211yescharacteristic
49C3×#830C2211yescharacteristic
50C3×#808C2211yescharacteristic
51C3×#808C2211yescharacteristic
52Dic3⋊(C3⋊C8)C2211yescharacteristic
53#63566C2211yescharacteristic
54#63566C2211yescharacteristic
55#63565C2211yescharacteristic
56#63565C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×D4×Q8—31no—
62#5632D311yescharacteristic, complemented
63#5555—31no—
64#5507—31no—
65C3×#483—31no—
66#5227—31no—
67#5227—31no—
68C2×#835—31no—
69C2×#835—31no—
70#5083—31no—
71#5079—31no—
72#5048—31no—
73#5048—31no—
74#5048—31no—
75#5048—61no—
76#5043—31no—
77#5043D311yescharacteristic, complemented
78C4×#215—31no—
79#5020—31no—
80D4×C3⋊C8—31no—
81C2×#810—31no—
82#4864—31no—
83#4862—31no—
84#4854—31no—
85#4852—31no—
86#4818—31no—
87#4806—31no—
88D3×#103—31no—
89#4792—31no—
90#4738—31no—
91#67⋊C8—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C22×C3×Dic3—21no—
98C22×C3×Dic3—21no—
99C3×D3×Q8—22no—
100C3×D3×Q8—41no—
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×#626—21no—
111C2×#624—21no—
112#3804—44no—
113C2×D3×Dic3—21no—
114C32×C4⋊C4—21no—
115C32×C4⋊C4C2311yescharacteristic
116C32×C22⋊C4—21no—
117#3755—41no—
118#3752—21no—
119C4⋊(C3⋊Dic3)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)—41no—
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C2×C3⋊(C3⋊C8)C2311yescharacteristic
123C3×#217D411yescharacteristic
124C3×(C2×D3)⋊C4—21no—
125C3×(C2×D3)⋊C4D411yescharacteristic
126C3×C4⋊Dic3—21no—
127C3×C4⋊Dic3—21no—
128C3×C4⋊Dic3C2311yescharacteristic
129C3×C4⋊Dic3C2311yescharacteristic
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⋊C8C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138Dic3⋊Dic3—21no—
139Dic3⋊Dic3—21no—
140#3722—21no—
141#3722—21no—
142#3717—22no—
143#3717—41no—
144D3×C3⋊C8—41no—
145#3298—91noSylow
146C22×C3×Q8—31no—
147C22×C3×Q8—31no—
148C2×D3×Q8C2×D311yescharacteristic
149C2×#237—61no—
150C2×#235—61no—
151C22×Dic6C2×D311yescharacteristic
152C3×C4⋊Q8—31no—
153C3×C4⋊Q8—61no—
154C3×C22⋊Q8—21no—
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—
163C2×C3×C4⋊C4—31no—
164#944C2×D311yescharacteristic
165C2×#215—31no—
166C2×#215—31no—
167C2×#215—31no—
168C2×#215—31no—
169C2×#215—61no—
170#930—31no—
171#930—31no—
172#930—31no—
173#930—61no—
174#929—61no—
175C4×#67C2×D311yescharacteristic
176C2×C4⋊Dic3—31no—
177C2×C4⋊Dic3C2×D311yescharacteristic
178C22×C3⋊C8—31no—
179C22×C3⋊C8—31no—
180C22×C3⋊C8—31no—
181C22×C3⋊C8—61no—
182C2×#204—31no—
183C2×#204—31no—
184C2×D3×C8—31no—
185#897—61no—
186#897C2×D311yescharacteristic
187#896—21no—
188#896—61no—
189#895—31no—
190#894—61no—
191#893—31no—
192D3×C4⋊C4—31no—
193#888—21no—
194#888—31no—
195#887C2×D311yescharacteristic
196#886—61no—
197#886—61no—
198#67⋊C4—21no—
199#878—21no—
200C4×D12—31no—
201#869—31no—
202C3×#106—31no—
203C3×#106—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—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#835C2×D311yescharacteristic
217#835C2×D311yescharacteristic
218#830—31no—
219#830C2×D311yescharacteristic
220(C2×D3)⋊C8—31no—
221#816—31no—
222#816—31no—
223Dic3⋊C8—31no—
224C8×Dic3—31no—
225#810—31no—
226#810—31no—
227#810—31no—
228#810—31no—
229#809—31no—
230#809—31no—
231#809—61no—
232#808—31no—
233#808—31no—
234#808—61no—
235#808C2×D311yescharacteristic
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
250#638—42no—
251C2×C3⋊Dic3—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C3×#67SD1614yescomplemented
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—42no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
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#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—31no—
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—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—
308C22×C3×C4—21no—
309C22×C3×C4—31no—
310C22×C3×C4—61no—
311C22×C3×C4—61no—
312C22×C3×C4—61no—
313C22×C3×C4C22×D311yescharacteristic
314C22×C3×C4C22×D311yescharacteristic
315C2×#67—61no—
316C2×#67—61no—
317C2×#67—61no—
318C2×#67—121no—
319C2×#67#6711yescharacteristic
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—61no—
323D3×Q8—22no—
324D3×Q8—41no—
325#237—124no—
326#235—124no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×C4×D3—21no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3C22×D311yescharacteristic
336C2×Dic6—22no—
337C2×Dic6—21no—
338C2×Dic6—21no—
339C2×Dic6—41no—
340C2×Dic6—61no—
341C2×Dic6—61no—
342C2×Dic6C22×D311yescharacteristic
343C2×Dic6C22×D311yescharacteristic
344C2×C3×C8—31no—
345C2×C3×C8—31no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—21no—
349C3×C4⋊C4—31no—
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⋊C4—61no—
358C3×C4⋊C4C22×D311yescharacteristic
359C3×C4⋊C4C22×D311yescharacteristic
360C3×C22⋊C4—21no—
361C3×C22⋊C4—21no—
362C3×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—41no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217#6711yescharacteristic
369#215—62no—
370#215—121no—
371#215—121no—
372#215—121no—
373#215—122no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—121no—
382(C2×D3)⋊C4#6711yescharacteristic
383C4⋊Dic3—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—61no—
388C4⋊Dic3—61no—
389C4⋊Dic3—61no—
390C4⋊Dic3C22×D311yescharacteristic
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—21no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4#6711yescharacteristic
398C4×Dic3—21no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—31no—
403C2×C3⋊C8—31no—
404C2×C3⋊C8—61no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8—121no—
408C2×C3⋊C8—121no—
409C2×C3⋊C8—122no—
410C2×C3⋊C8C22×D311yescharacteristic
411C2×C3⋊C8C22×D311yescharacteristic
412#204—62no—
413#204—121no—
414D3×C8—121no—
415C22×C32—21no—
416C22×C32—21no—
417C22×C32C2×SD1612yes—
418C22×C32C22×D411yescharacteristic
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3C2×SD1612yes—
425C32×C4—21no—
426C32×C4—41no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3×Dic3—22no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—41no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3C2×SD1612yes—
438C2×#41—181no—
439C22×Q8—31no—
440C22×Q8—31no—
441C2×SD16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—91no—
445C22×C8—91no—
446C4⋊Q8—31no—
447C4⋊Q8—61no—
448C4⋊Q8—91no—
449#123—181no—
450#123—181no—
451C22⋊Q8—31no—
452C22⋊Q8—61no—
453C22⋊Q8—61no—
454C22⋊Q8—181no—
455C22⋊Q8D3211yescharacteristic
456#121—91no—
457#121—91no—
458C4×Q8—31no—
459C4×D4—31no—
460C4×D4—61no—
461C4×D4—91no—
462C2×C4⋊C4—31no—
463C2×C4⋊C4—91no—
464#106—31no—
465#106—31no—
466#106—91no—
467C4⋊C8—91no—
468#103—31no—
469#103—31no—
470#103—91no—
471#103—91no—
472#103—91no—
473#103—91no—
474#103—91no—
475#103—91no—
476#103—91no—
477#102—91no—
478C22⋊C8—31no—
479C22⋊C8—91no—
480C4×C8—91no—
481C23×C3—21no—
482C23×C3—31no—
483C23×C3D3×D411yescharacteristic
484C23×C3C2×#6711yescharacteristic
485C22×D3—61no—
486C22×D3—61no—
487C22×D3—121no—
488C22×D3C2×#6711yescharacteristic
489C3×Q8—21no—
490C3×Q8—21no—
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—32no—
494C3×Q8—41no—
495C3×Q8—41no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—122no—
500C3×Q8—122no—
501C3×D4—34no—
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—61no—
525C2×C3×C4—122no—
526C2×C3×C4—122no—
527C2×C3×C4—122no—
528C2×C3×C4D3×D411yescharacteristic
529C2×C3×C4C2×#6711yescharacteristic
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—122no—
533#67—122no—
534#67—122no—
535#67—242no—
536#67#21514yescomplemented
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—42no—
542C2×Dic3—42no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—121no—
546C2×Dic3—122no—
547C2×Dic3C2×#6711yescharacteristic
548C2×Dic3C2×#6711yescharacteristic
549C2×Dic3C2×#6711yescharacteristic
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—121no—
555D12—121no—
556D12—122no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—42no—
560C4×D3—122no—
561C4×D3—122no—
562C4×D3—122no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—42no—
567Dic6—42no—
568Dic6—122no—
569Dic6—122no—
570Dic6#23712yescomplemented
571C3×C8—61no—
572C3×C8—61no—
573C3⋊C8—21no—
574C3⋊C8—21no—
575C3⋊C8—62no—
576C3⋊C8—61no—
577C3⋊C8—61no—
578C3⋊C8—61no—
579C3⋊C8—61no—
580C3⋊C8—121no—
581C2×C32—22no—
582C2×C32#54611yescharacteristic
583C2×C32C22×SD1611yescharacteristic
584C2×C32#57811yescharacteristic
585C3⋊D3—81no—
586C3×D3—22no—
587#41—364no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—61no—
591C2×Q8—62no—
592C2×Q8—61no—
593C2×Q8—62no—
594C2×Q8—121no—
595C2×Q8—121no—
596C2×Q8—181no—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—31no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4—61no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4C2×D3211yescharacteristic
609SD16—182no—
610SD16—361no—
611SD16—361no—
612C2×C8—31no—
613C2×C8—31no—
614C2×C8—91no—
615C2×C8—91no—
616C2×C8—361no—
617C2×C8—361no—
618C4⋊C4—21no—
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—61no—
626C4⋊C4—61no—
627C4⋊C4—91no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—21no—
632C22⋊C4—31no—
633C22⋊C4—31no—
634C22⋊C4—61no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—31no—
639C42—61no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—22no—
646C22×C3—32no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—61no—
650C22×C3—61no—
651C22×C3D3×SD1612yes—
652C22×C3C2×#21512yes—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—21no—
656C2×D3—21no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—121no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—241no—
666C2×D3C2×#21512yes—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—32no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—61no—
678C3×C4—62no—
679C3×C4—61no—
680C3×C4—81no—
681C3×C4—81no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4C2×#23711yescharacteristic
686C3×C4#100411yescharacteristic
687C3×C4D3×#4111yescharacteristic
688C3×C4#100911yescharacteristic
689Dic3—22no—
690Dic3—21no—
691Dic3—21no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—121no—
696Dic3—121no—
697Dic3—241no—
698Dic3C2×#21512yes—
699C32#329811yescharacteristic, complemented, Sylow
700C23—31no—
701C23—181no—
702C23D3×#6711yescharacteristic
703Q8—21no—
704Q8—21no—
705Q8—32no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—122no—
710Q8—122no—
711Q8—362no—
712D4—34no—
713D4—181no—
714D4—181no—
715D4—362no—
716D4—362no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—31no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—122no—
731C2×C4—122no—
732C2×C4—122no—
733C2×C4—181no—
734C2×C4—362no—
735C2×C4—362no—
736C2×C4D3×#6711yescharacteristic
737C2×C4C22×D3211yescharacteristic
738C8—61no—
739C8—61no—
740C8—181no—
741C8—181no—
742C2×C3—22no—
743C2×C3—22no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—42no—
748C2×C3—62no—
749C2×C3#565411yescharacteristic
750C2×C3C2×D3×SD1611yescharacteristic
751C2×C3#577911yescharacteristic
752C2×C3#580611yescharacteristic
753C2×C3C22×#21511yescharacteristic
754C2×C3#583811yescharacteristic
755D3—22no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—21no—
760C22—21no—
761C22—32no—
762C22—61no—
763C22—61no—
764C22—361no—
765C22—361no—
766C22—361no—
767C22D3×#21512yes—
768C22C2×D3×#6711yescharacteristic
769C4—21no—
770C4—32no—
771C4—41no—
772C4—41no—
773C4—61no—
774C4—62no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—121no—
779C4—361no—
780C4D3×#23711yescharacteristic
781C4#6431411yescharacteristic
782C3—21no—
783C3#8145011yescharacteristic, complemented
784C3#8355011yescharacteristic, complemented
785C2—22no—
786C2—62no—
787C2—721no—
788C2#1059514811yescharacteristic
789C2C2×D3×#21511yescharacteristic
790C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊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×#5632C2semidirect
3. #10592747C2semidirect
4. C3×#5043C2semidirect
5. #10591623C2semidirect
6. #10591584C2semidirect
7. #10591565C2semidirect
8. D3×#835C2semidirect
9. #10591174C2semidirect
10. #67⋊(C3⋊C8)C2semidirect
11. C2×#63565C2semidirect
12. #10590577C2semidirect
13. #10590556C2semidirect
14. #10590458C2semidirect
15. #10590439C2semidirect
62. #5632D3semidirect
77. #5043D3semidirect
254. C3×#67SD16semidirect
272. C3×Dic6#41semidirect
536. #67#215semidirect
570. Dic6#237semidirect
699. C32#3298semidirect
783. C3#81450semidirect
784. C3#83550semidirect

Maximal subgroups

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

subgroupindex
C3×#56322
#105949062
#105927472
C3×#50432
#105916232
#105915842
#105915652
D3×#8352
#105911742
#67⋊(C3⋊C8)2
C2×#635652
#105905772
#105905562
#105904582
#105904392
#835503
#814503