Finite Group Databasebeta

← #11887253

Subgroups — #11887253

Order 1152.

868 conjugacy classes of subgroups.

The subgroup lattice has 793 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5513C211yesmaximal, characteristic, complemented
2#10594886C211yesmaximal, characteristic
3#10592670C211yesmaximal, characteristic, complemented
4C2×C3×#809C211yesmaximal, characteristic, complemented
5#10591187C211yesmaximal, characteristic, complemented
6#10591169C211yesmaximal, characteristic, complemented
7C3⋊C8×#67C211yesmaximal, characteristic, complemented
8#10590614C211yesmaximal, characteristic, complemented
9#10590608C211yesmaximal, characteristic, complemented
10#10590533C211yesmaximal, characteristic, complemented
11#10590532C211yesmaximal, characteristic, complemented
12#10590505C211yesmaximal, characteristic, complemented
13#10590501C211yesmaximal, characteristic, complemented
14#10590469C211yesmaximal, characteristic, complemented
15#10590453C211yesmaximal, characteristic, complemented
16#83598—31nomaximal
17#78759—31nomaximal
18C22×C3×D12C2211yescharacteristic
19C2×#3795C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21#64133C2211yescharacteristic
22C3×#929—21no—
23C3×C4×#67C2211yescharacteristic
24C3×#926—21no—
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C3×#898—21no—
28C3×#897C2211yescharacteristic, complemented
29C3×#892C2211yescharacteristic, complemented
30C3×#890C2211yescharacteristic, complemented
31C3×#889—21no—
32C3×#887C2211yescharacteristic, complemented
33#63976—21no—
34D3×#217—21no—
35#63908C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37#63885—21no—
38#63884—21no—
39#63860C2211yescharacteristic
40C2×#3719C2211yescharacteristic, complemented
41C2×#3715C2211yescharacteristic
42C2×#3715C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44#63657C2211yescharacteristic
45#63637C2211yescharacteristic, complemented
46#63637C2211yescharacteristic, complemented
47#63635C2211yescharacteristic, complemented
48#63635C2211yescharacteristic, complemented
49C3×#809C2211yescharacteristic
50C3×#809C2211yescharacteristic
51C3×#809C2211yescharacteristic
52C3×#809C2211yescharacteristic
53#63575C2211yescharacteristic, complemented
54Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
60Dic3×C3⋊C8C2211yescharacteristic, complemented
61C3×#552—31no—
62#5806—31no—
63#5550—31no—
64#5513D311yescharacteristic, complemented
65C2×C3×#102—31no—
66#5218—31no—
67#5116—31no—
68C8×#67—31no—
69#5068—31no—
70#5066—31no—
71#5051—31no—
72#5048—31no—
73#5047—31no—
74#5046—31no—
75#5028—31no—
76C4×#215—31no—
77D4×C3⋊C8—31no—
78#5003—31no—
79#5002—31no—
80#4971—31no—
81#4971—31no—
82#4971—61no—
83C2×#809D311yescharacteristic, complemented
84#4784—31no—
85#4783—31no—
86#4778—31no—
87#4772—31no—
88#4768—31no—
89#4767—31no—
90#4766—31no—
91#4758—31no—
92C23×C3×D3—21no—
93C22×C32×C4—21no—
94C22×C32×C4C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67D411yescharacteristic
97C2×C3×D12—22no—
98C2×C3×D12—21no—
99C2×C3×D12—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#625—21no—
105C2×#625—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108#3795—22no—
109#3795—41no—
110C32×C4⋊C4—21no—
111C32×C4⋊C4C2311yescharacteristic
112C32×C4⋊C4C2311yescharacteristic
113#3757—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3750—21no—
116C2×C3⋊(C3⋊C8)C2311yescharacteristic
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3—21no—
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×Dic3⋊C4D411yescharacteristic
130C3×C4×Dic3—21no—
131C3×C4×Dic3—21no—
132C3×C4×Dic3C2311yescharacteristic
133C2×C3×C3⋊C8—41no—
134C2×C3×C3⋊C8C2311yescharacteristic
135C2×C3×C3⋊C8C2311yescharacteristic
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3—21no—
140#3719—41no—
141#3715—22no—
142#3715—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C22×C3×D4—31no—
146C2×#237—31no—
147C2×#235—31no—
148C22×D12C2×D311yescharacteristic
149C22×C3×C8—31no—
150C3×#126—61no—
151C3×#125—31no—
152C3×#125—61no—
153C3×#123—61no—
154C3×C22⋊Q8—31no—
155C3×C22⋊Q8—31no—
156C3×C4×Q8—31no—
157C3×C4×D4—31no—
158C3×#117—31no—
159C3×#117—61no—
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4C2×D311yescharacteristic
162C2×C3×C4⋊C4C2×D311yescharacteristic
163#953—61no—
164C2×#217—61no—
165C2×#216—31no—
166C2×#215—31no—
167C2×#215—31no—
168#939—61no—
169#938—31no—
170#937—61no—
171#936—31no—
172#935—61no—
173D4×Dic3—31no—
174C2×#214—31no—
175C2×#214—31no—
176#930—31no—
177#929—21no—
178C4×#67C2×D311yescharacteristic
179#926—21no—
180#924—31no—
181#924—31no—
182#924—61no—
183#924C2×D311yescharacteristic
184C22×C3⋊C8—31no—
185C22×C3⋊C8C2×D311yescharacteristic
186C2×Dic12—31no—
187C2×D3×C8—31no—
188#898—21no—
189#897C2×D311yescharacteristic, complemented
190#894—61no—
191#892C2×D311yescharacteristic, complemented
192#890C2×D311yescharacteristic, complemented
193#889—21no—
194#887C2×D311yescharacteristic, complemented
195#884—61no—
196D3×C22⋊C4—61no—
197#875—31no—
198C4×D12—31no—
199C3×#102—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×#102—31no—
203#835—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—31no—
209#830—61no—
210(C2×D3)⋊C8—31no—
211#818—31no—
212#816—31no—
213#816—31no—
214Dic3⋊C8—31no—
215C8×Dic3—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810—61no—
223#809—31no—
224#809—31no—
225#809C2×D311yescharacteristic
226#809C2×D311yescharacteristic
227#809C2×D311yescharacteristic
228#809C2×D311yescharacteristic
229#808—31no—
230#808—31no—
231#808—31no—
232#808—31no—
233#808—61no—
234#808—61no—
235#807—31no—
236C4⋊(C3⋊C8)—31no—
237C4×C3⋊C8—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—42no—
242C22×C3×D3—42no—
243C22×C3×D3—81no—
244C22×C3×D3C2×D411yescharacteristic
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4—21no—
249C2×C32×C4—42no—
250C2×C32×C4C2×D411yescharacteristic
251C2×C32×C4C2411yescharacteristic
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254#634—21no—
255#634—21no—
256C3×#67—22no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C3×D12—21no—
263C3×D12—21no—
264C3×D12—21no—
265C3×D12—42no—
266C3×D12#4112yes—
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#625—42no—
272#625—81no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C3⋊(C3⋊C8)—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—31no—
280#546—91no—
281#488—91no—
282#483—91no—
283#482—91no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—31no—
294C24×C3—61no—
295C23×D3—21no—
296C2×C3×Q8—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—31no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4—121no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—31no—
307C22×C3×C4—41no—
308C22×C3×C4C22×D311yescharacteristic
309C22×C3×C4C22×D311yescharacteristic
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—61no—
314C2×#67#6711yescharacteristic
315C22×Dic3—61no—
316C22×Dic3—61no—
317#237—62no—
318#237—121no—
319#235—62no—
320#235—121no—
321C2×D12—22no—
322C2×D12—21no—
323C2×D12—41no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3C22×D311yescharacteristic
329C2×Dic6—31no—
330C2×Dic6—31no—
331C2×Dic6—61no—
332C2×Dic6C22×D311yescharacteristic
333C2×C3×C8—31no—
334C2×C3×C8—31no—
335C2×C3×C8—121no—
336C3×C4⋊C4—21no—
337C3×C4⋊C4—21no—
338C3×C4⋊C4—21no—
339C3×C4⋊C4—21no—
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—41no—
343C3×C4⋊C4—61no—
344C3×C4⋊C4—61no—
345C3×C4⋊C4—61no—
346C3×C4⋊C4—61no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4C22×D311yescharacteristic
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C4⋊C4C22×D311yescharacteristic
352C3×C22⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—61no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—61no—
359C3×C42—61no—
360#217—21no—
361#217—61no—
362#217—61no—
363#217—61no—
364#217—61no—
365#217—61no—
366#217—61no—
367#217—121no—
368#217#6711yescharacteristic
369#216—121no—
370#215—62no—
371#215—121no—
372#214—62no—
373#214—121no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—61no—
377(C2×D3)⋊C4—61no—
378(C2×D3)⋊C4—61no—
379(C2×D3)⋊C4—61no—
380(C2×D3)⋊C4#6711yescharacteristic
381C4⋊Dic3—21no—
382C4⋊Dic3—21no—
383C4⋊Dic3—31no—
384C4⋊Dic3—31no—
385C4⋊Dic3—61no—
386C4⋊Dic3C22×D311yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—121no—
393Dic3⋊C4#6711yescharacteristic
394C4×Dic3—21no—
395C4×Dic3—21no—
396C4×Dic3C22×D311yescharacteristic
397C2×C3⋊C8—31no—
398C2×C3⋊C8—31no—
399C2×C3⋊C8—31no—
400C2×C3⋊C8—31no—
401C2×C3⋊C8—41no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—61no—
404C2×C3⋊C8—121no—
405C2×C3⋊C8C22×D311yescharacteristic
406C2×C3⋊C8C22×D311yescharacteristic
407Dic12—121no—
408D3×C8—121no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32#13512yes—
412C22×C32C22×D411yescharacteristic
413C2×C3×D3—22no—
414C2×C3×D3—21no—
415C2×C3×D3—21no—
416C2×C3×D3—21no—
417C2×C3×D3—41no—
418C2×C3×D3—41no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—84no—
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—21no—
431C3×Dic3—21no—
432C3×Dic3—21no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—91no—
436C22×D4—31no—
437C2×Q16—91no—
438C2×SD16—91no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—91no—
442#126—61no—
443#125—31no—
444#125—61no—
445#124—91no—
446#123—61no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—31no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—31no—
455C4×D4—31no—
456C4×D4—91no—
457#117—31no—
458#117—61no—
459C2×C4⋊C4D3211yescharacteristic
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—91no—
465#103—91no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—31no—
471#102—31no—
472#102—31no—
473#102—91no—
474#102—91no—
475C22⋊C8—91no—
476C22⋊C8—91no—
477C4×C8—91no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—61no—
481C23×C3—61no—
482C23×C3—122no—
483C23×C3—122no—
484C23×C3—241no—
485C23×C3D3×D411yescharacteristic
486C23×C3C2×#6711yescharacteristic
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—42no—
490C22×D3—42no—
491C22×D3—81no—
492C22×D3C2×#6711yescharacteristic
493C3×Q8—61no—
494C3×Q8—61no—
495C3×D4—32no—
496C3×D4—62no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—61no—
500C3×D4—122no—
501C2×C3×C4—21no—
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—31no—
512C2×C3×C4—31no—
513C2×C3×C4—31no—
514C2×C3×C4—41no—
515C2×C3×C4—41no—
516C2×C3×C4—41no—
517C2×C3×C4—41no—
518C2×C3×C4—42no—
519C2×C3×C4—42no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—82no—
525C2×C3×C4D3×D411yescharacteristic
526C2×C3×C4C2×#6711yescharacteristic
527C2×C3×C4C23×D311yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529#67—22no—
530#67—122no—
531#67—122no—
532#67—241no—
533#67—241no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—121no—
541C2×Dic3—121no—
542C2×Dic3—122no—
543C2×Dic3—241no—
544C2×Dic3C2×#6711yescharacteristic
545C2×Dic3C2×#6711yescharacteristic
546C2×Dic3C2×#6711yescharacteristic
547D12—21no—
548D12—21no—
549D12—21no—
550D12—42no—
551D12#23512yes—
552C4×D3—21no—
553C4×D3—21no—
554C4×D3—122no—
555C4×D3—241no—
556Dic6—21no—
557Dic6—21no—
558Dic6—61no—
559Dic6—61no—
560Dic6—61no—
561Dic6—61no—
562Dic6—121no—
563Dic6—121no—
564C3×C8—61no—
565C3×C8—61no—
566C3⋊C8—21no—
567C3⋊C8—21no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—61no—
571C3⋊C8—61no—
572C3⋊C8—121no—
573C3⋊C8—121no—
574C2×C32—22no—
575C2×C32#54611yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57711yescharacteristic
578C3×D3—41no—
579C3×D3—42no—
580C3×D3—81no—
581C24—61no—
582#41—182no—
583#41—361no—
584C2×Q8—31no—
585C2×Q8—91no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—31no—
589C2×D4—62no—
590C2×D4—61no—
591C2×D4—121no—
592C2×D4—181no—
593C2×D4—181no—
594C22×C4—21no—
595C22×C4—31no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4C2×D3211yescharacteristic
599Q16—361no—
600SD16—182no—
601SD16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—91no—
605C2×C8—91no—
606C2×C8—121no—
607C2×C8—361no—
608C4⋊C4—21no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—61no—
612C4⋊C4—61no—
613C4⋊C4—61no—
614C4⋊C4—61no—
615C4⋊C4—61no—
616C4⋊C4—91no—
617C4⋊C4—181no—
618C4⋊C4C2×D3211yescharacteristic
619C4⋊C4C2×D3211yescharacteristic
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—61no—
624C22⋊C4—61no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—61no—
632C42—61no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—22no—
639C22×C3—41no—
640C22×C3—41no—
641C22×C3—61no—
642C22×C3—61no—
643C22×C3—61no—
644C22×C3—62no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—244no—
651C22×C3#91212yes—
652C22×C3#95012yes—
653C22×C3C2×D3×D411yescharacteristic
654C22×C3C22×#6711yescharacteristic
655C2×D3—22no—
656C2×D3—21no—
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—84no—
665C3×C4—21no—
666C3×C4—21no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—41no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—61no—
677C3×C4—81no—
678C3×C4—81no—
679C3×C4—121no—
680C3×C4—121no—
681C3×C4C2×#23511yescharacteristic
682C3×C4#100411yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4#100911yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—41no—
689Dic3—41no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—241no—
695Dic3—241no—
696C32#329611yescharacteristic, complemented, Sylow
697C23—31no—
698C23—61no—
699C23—61no—
700C23—122no—
701C23—122no—
702C23—241no—
703C23D3×#6711yescharacteristic
704Q8—61no—
705Q8—61no—
706Q8—181no—
707Q8—181no—
708D4—32no—
709D4—62no—
710D4—61no—
711D4—61no—
712D4—61no—
713D4—122no—
714D4—362no—
715D4—721no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—42no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—362no—
731C2×C4—721no—
732C2×C4D3×#6711yescharacteristic
733C2×C4C22×D3211yescharacteristic
734C8—61no—
735C8—61no—
736C8—181no—
737C8—181no—
738C2×C3—22no—
739C2×C3—22no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—42no—
744C2×C3—122no—
745C2×C3—121no—
746C2×C3—241no—
747C2×C3#549011yescharacteristic
748C2×C3C2×#91211yescharacteristic
749C2×C3#576211yescharacteristic
750C2×C3C2×#95011yescharacteristic
751C2×C3#582911yescharacteristic
752C2×C3#583711yescharacteristic
753D3—41no—
754D3—42no—
755D3—81no—
756C22—21no—
757C22—21no—
758C22—61no—
759C22—61no—
760C22—61no—
761C22—62no—
762C22—121no—
763C22—121no—
764C22—121no—
765C22—121no—
766C22—121no—
767C22—244no—
768C22#6393312yes—
769C22C2×D3×#6711yescharacteristic
770C4—21no—
771C4—41no—
772C4—41no—
773C4—61no—
774C4—61no—
775C4—61no—
776C4—121no—
777C4—121no—
778C4—361no—
779C4—361no—
780C4D3×#23511yescharacteristic
781C4#6430711yescharacteristic
782C3—21no—
783C3#7875911yescharacteristic, complemented
784C3#8359811yescharacteristic, complemented
785C2—22no—
786C2—121no—
787C2—122no—
788C2—241no—
789C2#1059506511yescharacteristic
790C2C2×#6393311yescharacteristic
791C2#1059531811yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radical#10594886C2
hypercenterC2×C4⋊C4D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#5513C2semidirect
3. #10592670C2semidirect
4. C2×C3×#809C2semidirect
5. #10591187C2semidirect
6. #10591169C2semidirect
7. C3⋊C8×#67C2semidirect
8. #10590614C2semidirect
9. #10590608C2semidirect
10. #10590533C2semidirect
11. #10590532C2semidirect
12. #10590505C2semidirect
13. #10590501C2semidirect
14. #10590469C2semidirect
15. #10590453C2semidirect
28. C3×#897C22semidirect
29. C3×#892C22semidirect
30. C3×#890C22semidirect
32. C3×#887C22semidirect
40. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
45. #63637C22semidirect
46. #63637C22semidirect
47. #63635C22semidirect
48. #63635C22semidirect
53. #63575C22semidirect
54. Dic3⋊(C3⋊C8)C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
59. (C2×D3)⋊(C3⋊C8)C22semidirect
60. Dic3×C3⋊C8C22semidirect
64. #5513D3semidirect
83. C2×#809D3semidirect
189. #897C2×D3semidirect
191. #892C2×D3semidirect
192. #890C2×D3semidirect
194. #887C2×D3semidirect
696. C32#3296semidirect
783. C3#78759semidirect
784. C3#83598semidirect

Maximal subgroups

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

subgroupindex
C3×#55132
#105948862
#105926702
C2×C3×#8092
#105911872
#105911692
C3⋊C8×#672
#105906142
#105906082
#105905332
#105905322
#105905052
#105905012
#105904692
#105904532
#835983
#787593