Finite Group Databasebeta

← #11878435

Subgroups — #11878435

Order 1152.

804 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5628C211yesmaximal, characteristic
2#10594855C211yesmaximal, characteristic
3#10592744C211yesmaximal, characteristic, complemented
4C3×#5050C211yesmaximal, characteristic, complemented
5#10591638C211yesmaximal, characteristic, complemented
6#10591635C211yesmaximal, characteristic, complemented
7#10591594C211yesmaximal, characteristic, complemented
8#10591594C211yesmaximal, characteristic, complemented
9#10591185C211yesmaximal, characteristic, complemented
10#10591145C211yesmaximal, characteristic
11#10591127C211yesmaximal, characteristic, complemented
12#10590521C211yesmaximal, characteristic, complemented
13#10590520C211yesmaximal, characteristic, complemented
14#10590519C211yesmaximal, characteristic, complemented
15#10590518C211yesmaximal, characteristic, complemented
16#83413—31nomaximal
17#80192—31nomaximal
18C2×C3×D3×Q8C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C32×C22⋊Q8C2211yescharacteristic
22#64135C2211yescharacteristic
23C3×#946C2211yescharacteristic
24C2×C3×#216C2211yescharacteristic
25C2×C3×#216C2211yescharacteristic
26C3×#924C2211yescharacteristic
27C3×#897C2211yescharacteristic
28C3×#894—21no—
29C3×#892C2211yescharacteristic
30C3×#888—21no—
31C3×#885—21no—
32C3×#883—21no—
33#63961—21no—
34#63961—21no—
35#63873—21no—
36#63863—21no—
37#63856C2211yescharacteristic
38#63856C2211yescharacteristic
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41C2×#3718C2211yescharacteristic
42C2×#3718C2211yescharacteristic
43C2×#3711C2211yescharacteristic
44C2×D3×C3⋊C8C2211yescharacteristic
45#63662C2211yescharacteristic
46#63662C2211yescharacteristic
47#63657C2211yescharacteristic
48#63635C2211yescharacteristic
49#63634C2211yescharacteristic
50C3×#830C2211yescharacteristic
51C3×#810C2211yescharacteristic
52C3×#810C2211yescharacteristic
53#63575C2211yescharacteristic
54#63573C2211yescharacteristic
55#63566C2211yescharacteristic
56#63566C2211yescharacteristic
57#63565C2211yescharacteristic
58#63565C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
60(C2×D3)⋊(C3⋊C8)C2211yescharacteristic
61C3×#536—31no—
62#5825—31no—
63#5816—31no—
64#5628D311yescharacteristic
65C3×#451—31no—
66#5234—31no—
67#5228—31no—
68#5228—31no—
69#5228—31no—
70#5189—31no—
71#5188—31no—
72#5186—31no—
73#5186—31no—
74#5052—31no—
75#5052—31no—
76#5051—31no—
77#5051—31no—
78#5050—31no—
79#5050D311yescharacteristic, complemented
80#5045—31no—
81#5045—31no—
82#5045—31no—
83#5045—61no—
84#4996—31no—
85#4996—31no—
86#4816—31no—
87#4815—31no—
88#4814—31no—
89#4813—31no—
90#4727—31no—
91#4723—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67D411yescharacteristic
95C2×C3×#67D411yescharacteristic
96C22×C3×Dic3—21no—
97C3×D3×Q8—41no—
98C3×D3×Q8—41no—
99C3×#235—41no—
100C3×#235—41no—
101C2×C3×D12D411yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×C4×D3C2311yescharacteristic
105C2×C3×Dic6—21no—
106C2×C3×Dic6—21no—
107C2×C3×Dic6—41no—
108C2×C3×Dic6—41no—
109C2×C3×Dic6D411yescharacteristic
110C2×C3×Dic6C2311yescharacteristic
111C2×C3×Dic6C2311yescharacteristic
112C2×C3×Dic6C2311yescharacteristic
113C32×C4⋊C4—21no—
114C32×C4⋊C4C2311yescharacteristic
115C32×C22⋊C4—21no—
116#3757—21no—
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4⋊(C3⋊Dic3)C2311yescharacteristic
119C4×C3⋊Dic3—21no—
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C2×C3⋊(C3⋊C8)C2311yescharacteristic
122C3×#217—21no—
123C3×#216—41no—
124C3×#216—41no—
125C3×(C2×D3)⋊C4—21no—
126C3×(C2×D3)⋊C4—21no—
127C3×(C2×D3)⋊C4—21no—
128C3×C4⋊Dic3—21no—
129C3×C4⋊Dic3C2311yescharacteristic
130C3×Dic3⋊C4—21no—
131C3×Dic3⋊C4—21no—
132C3×C4×Dic3—21no—
133C2×C3×C3⋊C8C2311yescharacteristic
134C2×C3×C3⋊C8C2311yescharacteristic
135#3724—21no—
136#3724—21no—
137#3724—21no—
138#3724—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3718—41no—
144#3718—41no—
145#3711—41no—
146D3×C3⋊C8—41no—
147#3202—91noSylow
148C2×C3×#41—31no—
149C22×C3×Q8—31no—
150C22×C3×Q8—31no—
151C2×D3×Q8C2×D311yescharacteristic
152C2×#235C2×D311yescharacteristic
153C22×Dic6C2×D311yescharacteristic
154C2×C3×Q16—31no—
155C2×C3×Q16—31no—
156C3×C4⋊Q8—61no—
157C3×#124—61no—
158C3×#123—61no—
159C3×#123—61no—
160C3×C22⋊Q8—21no—
161C3×C22⋊Q8—31no—
162C3×C22⋊Q8—31no—
163C3×C22⋊Q8—31no—
164C3×C22⋊Q8C2×D311yescharacteristic
165C3×C22⋊Q8C2×D311yescharacteristic
166C3×#117—31no—
167#947—61no—
168#946—31no—
169#946—31no—
170#946—31no—
171#946—31no—
172#946C2×D311yescharacteristic
173#944—61no—
174#944—61no—
175C2×#216—31no—
176C2×#216—31no—
177C2×#216—31no—
178C2×#216—31no—
179C2×#216C2×D311yescharacteristic
180C2×#216C2×D311yescharacteristic
181#936—61no—
182#935—61no—
183#935—61no—
184#929—61no—
185#929—61no—
186#926—31no—
187#926—31no—
188#926—61no—
189#924—31no—
190#924—31no—
191#924—31no—
192#924—31no—
193#924C2×D311yescharacteristic
194C2×#208—31no—
195C22×C3⋊C8—31no—
196C2×ΓL(1,𝔽25)—31no—
197C2×D3×C8—31no—
198#897C2×D311yescharacteristic
199#894—21no—
200#892C2×D311yescharacteristic
201#888—21no—
202#885—21no—
203#883—21no—
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#835—61no—
217#830—31no—
218#830—31no—
219#830—31no—
220#830—31no—
221#830—61no—
222#830C2×D311yescharacteristic
223(C2×D3)⋊C8—31no—
224(C2×D3)⋊C8—31no—
225#818—31no—
226#817—31no—
227#816—31no—
228#816—31no—
229#810—31no—
230#810—31no—
231#810C2×D311yescharacteristic
232#810C2×D311yescharacteristic
233#808—31no—
234#808—31no—
235#808—31no—
236#808—61no—
237#807—31no—
238#807—31no—
239#807—31no—
240#807—61no—
241C23×C32C2×D411yescharacteristic
242C22×C3×D3C2×D411yescharacteristic
243C22×C3×D3C2×D411yescharacteristic
244C32×Q8—21no—
245C32×Q8—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C3×#67—41no—
255C3×#67—41no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—42no—
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—41no—
264C3×C4×D3—21no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×C4×D3—42no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—21no—
274C3×Dic6—21no—
275C3×Dic6—41no—
276C3×Dic6—42no—
277C3×Dic6—42no—
278C3⋊(C3⋊C8)—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#536—31no—
283#536—91no—
284#485—91no—
285#485—91no—
286#485—91no—
287#485—91no—
288#470—91no—
289#470—91no—
290#467—91no—
291#467—91no—
292#451—31no—
293#451—91no—
294#451—91no—
295#451—91no—
296#408—91no—
297C3×#41—121no—
298C3×#41—121no—
299C2×C3×Q8—21no—
300C2×C3×Q8—31no—
301C2×C3×Q8—31no—
302C2×C3×Q8—31no—
303C2×C3×Q8—31no—
304C2×C3×Q8—61no—
305C2×C3×Q8—61no—
306C2×C3×Q8—121no—
307C2×C3×Q8—121no—
308C2×C3×Q8—121no—
309C2×C3×Q8—121no—
310C2×C3×Q8C22×D311yescharacteristic
311C2×C3×Q8C22×D311yescharacteristic
312C2×C3×D4—31no—
313C2×C3×D4—31no—
314C2×C3×D4—31no—
315C22×C3×C4—21no—
316C22×C3×C4—31no—
317C22×C3×C4—31no—
318C22×C3×C4—61no—
319C22×C3×C4—61no—
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C2×#67#6711yescharacteristic
323C2×#67#6711yescharacteristic
324C22×Dic3—21no—
325D3×Q8—41no—
326D3×Q8—41no—
327#235—41no—
328#235—41no—
329C2×D12#6711yescharacteristic
330C2×C4×D3—21no—
331C2×C4×D3C22×D311yescharacteristic
332C2×C4×D3C22×D311yescharacteristic
333C2×Dic6—21no—
334C2×Dic6—21no—
335C2×Dic6—41no—
336C2×Dic6—41no—
337C2×Dic6#6711yescharacteristic
338C2×Dic6C22×D311yescharacteristic
339C2×Dic6C22×D311yescharacteristic
340C2×Dic6C22×D311yescharacteristic
341C3×Q16—121no—
342C3×Q16—121no—
343C2×C3×C8—31no—
344C2×C3×C8—31no—
345C3×C4⋊C4—21no—
346C3×C4⋊C4—21no—
347C3×C4⋊C4—21no—
348C3×C4⋊C4—31no—
349C3×C4⋊C4—41no—
350C3×C4⋊C4—61no—
351C3×C4⋊C4—61no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4C22×D311yescharacteristic
354C3×C4⋊C4C22×D311yescharacteristic
355C3×C22⋊C4—21no—
356C3×C22⋊C4—21no—
357C3×C22⋊C4—41no—
358C3×C22⋊C4—61no—
359C3×C22⋊C4—61no—
360C3×C22⋊C4—61no—
361C3×C22⋊C4—61no—
362C3×C42—61no—
363#217—21no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—61no—
368#217—61no—
369#217—61no—
370#217—121no—
371#216—41no—
372#216—41no—
373#216—121no—
374#216—121no—
375#216—121no—
376#216—121no—
377(C2×D3)⋊C4—21no—
378(C2×D3)⋊C4—21no—
379(C2×D3)⋊C4—21no—
380(C2×D3)⋊C4—61no—
381(C2×D3)⋊C4—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384C4⋊Dic3—21no—
385C4⋊Dic3—31no—
386C4⋊Dic3—31no—
387C4⋊Dic3—31no—
388C4⋊Dic3—31no—
389C4⋊Dic3—61no—
390C4⋊Dic3—61no—
391C4⋊Dic3C22×D311yescharacteristic
392Dic3⋊C4—21no—
393Dic3⋊C4—21no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396Dic3⋊C4—61no—
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402C4×Dic3—21no—
403C4×Dic3—61no—
404C4×Dic3—61no—
405C4×Dic3—121no—
406#208—121no—
407C2×C3⋊C8—31no—
408C2×C3⋊C8—31no—
409C2×C3⋊C8—31no—
410C2×C3⋊C8—31no—
411C2×C3⋊C8—61no—
412C2×C3⋊C8—61no—
413C2×C3⋊C8—121no—
414C2×C3⋊C8C22×D311yescharacteristic
415C2×C3⋊C8C22×D311yescharacteristic
416ΓL(1,𝔽25)—121no—
417D3×C8—121no—
418C22×C32—21no—
419C22×C32—21no—
420C22×C32—21no—
421C22×C32C22×D411yescharacteristic
422C2×C3×D3—21no—
423C2×C3×D3—21no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C32×C4—21no—
429C32×C4—41no—
430C32×C4—41no—
431C32×C4H(5,𝔽2)11yescharacteristic
432C32×C4H(5,𝔽2)11yescharacteristic
433C3⋊Dic3—41no—
434C3⋊Dic3—41no—
435C3×Dic3—21no—
436C3×Dic3—21no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C2×#41—31no—
442C22×Q8—31no—
443C22×Q8—31no—
444C2×Q16—31no—
445C2×Q16—31no—
446C2×Q16—91no—
447C2×Q16—91no—
448C2×M16—91no—
449C22×C8—91no—
450C4⋊Q8—61no—
451C4⋊Q8—181no—
452#124—61no—
453#124—181no—
454#123—61no—
455#123—61no—
456#123—181no—
457#123—181no—
458C22⋊Q8—31no—
459C22⋊Q8—31no—
460C22⋊Q8—31no—
461C22⋊Q8—91no—
462C22⋊Q8—91no—
463C22⋊Q8—91no—
464C22⋊Q8—91no—
465C22⋊Q8D3211yescharacteristic
466#117—31no—
467#117—91no—
468#107—91no—
469#107—91no—
470#106—91no—
471#106—91no—
472#103—31no—
473#103—31no—
474#103—91no—
475#103—91no—
476#103—91no—
477#103—91no—
478#103—91no—
479#103—91no—
480C22⋊C8—31no—
481C22⋊C8—91no—
482C22⋊C8—91no—
483C22⋊C8—91no—
484C23×C3—21no—
485C23×C3—31no—
486C23×C3—31no—
487C23×C3D3×D411yescharacteristic
488C23×C3C2×#6711yescharacteristic
489C22×D3C2×#6711yescharacteristic
490C22×D3C2×#6711yescharacteristic
491C3×Q8—21no—
492C3×Q8—21no—
493C3×Q8—21no—
494C3×Q8—21no—
495C3×Q8—41no—
496C3×Q8—41no—
497C3×Q8—61no—
498C3×Q8—61no—
499C3×Q8—61no—
500C3×Q8—61no—
501C3×Q8—61no—
502C3×Q8—61no—
503C3×Q8—121no—
504C3×Q8—122no—
505C3×Q8—122no—
506C3×D4—121no—
507C3×D4—121no—
508C3×D4—121no—
509C2×C3×C4—21no—
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—31no—
520C2×C3×C4—31no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—122no—
534C2×C3×C4—122no—
535C2×C3×C4D3×D411yescharacteristic
536C2×C3×C4C2×#6711yescharacteristic
537C2×C3×C4C23×D311yescharacteristic
538C2×C3×C4C23×D311yescharacteristic
539#67—41no—
540#67—41no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—42no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—121no—
551C2×Dic3—121no—
552C2×Dic3C2×#6711yescharacteristic
553C2×Dic3C2×#6711yescharacteristic
554D12—41no—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—21no—
558C4×D3—21no—
559C4×D3—42no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564Dic6—21no—
565Dic6—21no—
566Dic6—41no—
567Dic6—42no—
568Dic6—42no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C3⋊C8—61no—
574C3⋊C8—61no—
575C3⋊C8—61no—
576C3⋊C8—61no—
577C3⋊C8—121no—
578C3⋊C8—121no—
579C2×C32—41no—
580C2×C32#53411yescharacteristic
581C2×C32#57811yescharacteristic
582C2×C32#57811yescharacteristic
583C3×D3—41no—
584C3×D3—41no—
585#41—121no—
586#41—121no—
587C2×Q8—31no—
588C2×Q8—31no—
589C2×Q8—31no—
590C2×Q8—31no—
591C2×Q8—61no—
592C2×Q8—61no—
593C2×Q8—121no—
594C2×Q8—121no—
595C2×Q8—121no—
596C2×Q8—121no—
597C2×Q8C2×D3211yescharacteristic
598C2×D4—31no—
599C2×D4—31no—
600C2×D4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—61no—
604C22×C4—61no—
605C22×C4C2×D3211yescharacteristic
606Q16—121no—
607Q16—121no—
608Q16—361no—
609Q16—361no—
610M16—361no—
611C2×C8—31no—
612C2×C8—31no—
613C2×C8—91no—
614C2×C8—91no—
615C2×C8—361no—
616C4⋊C4—21no—
617C4⋊C4—31no—
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⋊C4—181no—
627C4⋊C4C2×D3211yescharacteristic
628C22⋊C4—21no—
629C22⋊C4—61no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C42—61no—
639C42—181no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—61no—
651C22×C3—61no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—61no—
656C22×C3C2×D3×D411yescharacteristic
657C22×C3C22×#6711yescharacteristic
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—21no—
663C2×D3—21no—
664C3×C4—21no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—81no—
676C3×C4—81no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4#100411yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4#100411yescharacteristic
684C3×C4#100411yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—41no—
688Dic3—41no—
689Dic3—41no—
690Dic3—41no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697C32#320211yescharacteristic, complemented, Sylow
698C23—31no—
699C23—31no—
700C23D3×#6711yescharacteristic
701Q8—21no—
702Q8—21no—
703Q8—61no—
704Q8—61no—
705Q8—61no—
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—121no—
710Q8—122no—
711Q8—122no—
712D4—121no—
713D4—121no—
714D4—121no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—31no—
720C2×C4—31no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—122no—
730C2×C4—122no—
731C2×C4—181no—
732C2×C4—181no—
733C2×C4D3×#6711yescharacteristic
734C2×C4C22×D3211yescharacteristic
735C8—61no—
736C8—61no—
737C8—181no—
738C8—181no—
739C2×C3—21no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—41no—
743C2×C3—41no—
744C2×C3—81no—
745C2×C3—121no—
746C2×C3—121no—
747C2×C3#558911yescharacteristic
748C2×C3#576611yescharacteristic
749C2×C3#577911yescharacteristic
750C2×C3#580411yescharacteristic
751C2×C3#583811yescharacteristic
752C2×C3#583811yescharacteristic
753D3—41no—
754D3—41no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—61no—
762C22—61no—
763C22—61no—
764C22C2×D3×#6711yescharacteristic
765C4—21no—
766C4—41no—
767C4—41no—
768C4—61no—
769C4—61no—
770C4—121no—
771C4—121no—
772C4—121no—
773C4—121no—
774C4—361no—
775C4—361no—
776C4#6431311yescharacteristic
777C4#6431311yescharacteristic
778C3—21no—
779C3#8019211yescharacteristic, complemented
780C3#8341311yescharacteristic, complemented
781C2—41no—
782C2—121no—
783C2—121no—
784C2#1059523011yescharacteristic
785C2#1059532711yescharacteristic
786C2#1059546511yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC2×C3×#235C22
hypercenterC22⋊Q8D32
hypocenterC32#3202
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
3. #10592744C2semidirect
4. C3×#5050C2semidirect
5. #10591638C2semidirect
6. #10591635C2semidirect
7. #10591594C2semidirect
8. #10591594C2semidirect
9. #10591185C2semidirect
11. #10591127C2semidirect
12. #10590521C2semidirect
13. #10590520C2semidirect
14. #10590519C2semidirect
15. #10590518C2semidirect
79. #5050D3semidirect
697. C32#3202semidirect
779. C3#80192semidirect
780. C3#83413semidirect

Maximal subgroups

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

subgroupindex
C3×#56282
#105948552
#105927442
C3×#50502
#105916382
#105916352
#105915942
#105911852
#105911452
#105911272
#105905212
#105905202
#105905192
#105905182
#834133
#801923