Finite Group Databasebeta

← #11887226

Subgroups — #11887226

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595067C211yesmaximal, characteristic
2#10594942C211yesmaximal, characteristic, complemented
3#10592436C211yesmaximal, characteristic, complemented
4C3×#4733C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591177C211yesmaximal, characteristic, complemented
7#10591084C211yesmaximal, characteristic, complemented
8#10590942C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590872C211yesmaximal, characteristic, complemented
11#10590851C211yesmaximal, characteristic, complemented
12#10590801C211yesmaximal, characteristic, complemented
13#10590767C211yesmaximal, characteristic, complemented
14Dic3×#204C211yesmaximal, characteristic, complemented
15#10590675C211yesmaximal, characteristic, complemented
16#80246—31nomaximal
17#79440—31nomaximal
18C2×C3×#235C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64139C2211yescharacteristic
21#64135C2211yescharacteristic, complemented
22C3×C4×#67C2211yescharacteristic
23C3×#924C2211yescharacteristic, complemented
24C22×C3×C3⋊C8C2211yescharacteristic, complemented
25C2×C3×Dic12C2211yescharacteristic, complemented
26C2×C3×#204C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63983—21no—
29#63971—21no—
30#63969—21no—
31#63956—21no—
32D3×(C2×D3)⋊C4—21no—
33Dic3×D12C2211yescharacteristic
34D3×C4⋊Dic3C2211yescharacteristic
35#63878—21no—
36#63870—21no—
37#63869C2211yescharacteristic, complemented
38#63864C2211yescharacteristic
39#63856C2211yescharacteristic
40#63856C2211yescharacteristic
41#63850—21no—
42Dic3×Dic6C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47#63645C2211yescharacteristic, complemented
48#63644C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63566C2211yescharacteristic, complemented
58#63564C2211yescharacteristic
59#63563C2211yescharacteristic
60#63563C2211yescharacteristic
61#5829—31no—
62#5639—31no—
63#5550—31no—
64#5541—31no—
65C3×#452—31no—
66C3×C8×D4—31no—
67#5233—31no—
68#5188—31no—
69#5185—31no—
70#5169—31no—
71Dic3×SD16—31no—
72#5116—31no—
73#5114—31no—
74#5113—31no—
75C2×#821—31no—
76#5048—31no—
77#4847—31no—
78#4845—31no—
79#4805—31no—
80#4800—31no—
81D3×#102—31no—
82#4766—31no—
83#4737—31no—
84#4737—31no—
85#4737—61no—
86#4733D311yescharacteristic, complemented
87#4731—31no—
88#67⋊C8D311yescharacteristic, complemented
89#4721—31no—
90#4697—31no—
91C4×#204—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×#67D411yescharacteristic
98C3×#235—22no—
99C3×#235—41no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×C4×D3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108D3×D12—22no—
109D3×D12—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4×C3⋊Dic3—21no—
118C3×#217—21no—
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×Dic3⋊C4—21no—
123C3×Dic3⋊C4D411yescharacteristic
124C3×C4×Dic3C2311yescharacteristic
125C2×C3×C3⋊C8—41no—
126C2×C3×C3⋊C8C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C3×Dic12—41no—
129C3×#204—22no—
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3717—41no—
144#3296—91noSylow
145C2×C3×#41—31no—
146C2×D3×D4—31no—
147C2×#235C2×D311yescharacteristic
148C22×D12—31no—
149C2×C3×Q16—31no—
150C2×C3×SD16—31no—
151C22×C3×C8—31no—
152C22×C3×C8—31no—
153C3×C22⋊Q8—31no—
154C3×C4×D4—31no—
155#947—31no—
156#946—31no—
157#946—31no—
158Q8×Dic3—31no—
159C2×#215—31no—
160#939—61no—
161#937—61no—
162#937—61no—
163#935—61no—
164D4×Dic3—31no—
165#930—31no—
166#930—31no—
167#930—61no—
168#929—61no—
169C4×#67C2×D311yescharacteristic
170C2×(C2×D3)⋊C4—61no—
171#926—31no—
172#926—31no—
173#926—61no—
174C2×C4⋊Dic3—31no—
175#924—31no—
176#924—31no—
177#924C2×D311yescharacteristic, complemented
178C22×C3⋊C8C2×D311yescharacteristic, complemented
179C2×Dic12C2×D311yescharacteristic, complemented
180C2×#204—31no—
181C2×#204C2×D311yescharacteristic
182C2×D3×C8C2×D311yescharacteristic
183#894—61no—
184#892—61no—
185D3×C4⋊C4—31no—
186#890—31no—
187#889—61no—
188#889—61no—
189#884—61no—
190#883—61no—
191D3×C22⋊C4—61no—
192#879—61no—
193#879—61no—
194#877—61no—
195#875—31no—
196C4×D12—31no—
197#870—31no—
198C4×Dic6—31no—
199C3×C4⋊C8—31no—
200C3×#103—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic, complemented
205C3×C22⋊C8C2×D311yescharacteristic, complemented
206C3×C4×C8—31no—
207#835—31no—
208#835—31no—
209#835—31no—
210#832—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—61no—
220#821—61no—
221#821C2×D311yescharacteristic
222(C2×D3)⋊C8C2×D311yescharacteristic
223#818—31no—
224#818—31no—
225#818—61no—
226#817—31no—
227#817—31no—
228#817—31no—
229#817—61no—
230#816—31no—
231#816—31no—
232#816—31no—
233#816C2×D311yescharacteristic, complemented
234Dic3⋊C8C2×D311yescharacteristic, complemented
235C8×Dic3C2×D311yescharacteristic, complemented
236#809—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3C2×D411yescharacteristic
242C2×D32—42no—
243C2×D32—42no—
244C2×D32—81no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249#638—81no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C3×#67—22no—
256C3×#67—42no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C3×D12—21no—
264C3×D12#4112yes—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×C4×D3—42no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273D3×Dic3—42no—
274D3×Dic3—81no—
275C32×C8—21no—
276C32×C8—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
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—31no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—31no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C3×#41—62no—
297C3×#41—121no—
298C2×C3×Q8—31no—
299C2×C3×Q8—31no—
300C2×C3×D4—31no—
301C2×C3×D4—31no—
302C2×C3×D4—61no—
303C22×C3×C4—21no—
304C22×C3×C4—31no—
305C22×C3×C4—61no—
306C22×C3×C4C22×D311yescharacteristic
307C22×C3×C4C22×D311yescharacteristic
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C2×#67D1211yescharacteristic
314C22×Dic3—61no—
315C22×Dic3—61no—
316D3×D4—62no—
317D3×D4—121no—
318#235—22no—
319#235—41no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—62no—
324C2×D12—61no—
325C2×D12—121no—
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—21no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3C22×D311yescharacteristic
331C2×Dic6C22×D311yescharacteristic
332C2×Dic6C22×D311yescharacteristic
333C3×Q16—121no—
334C3×SD16—62no—
335C2×C3×C8—21no—
336C2×C3×C8—21no—
337C2×C3×C8—31no—
338C2×C3×C8—31no—
339C2×C3×C8—121no—
340C2×C3×C8—121no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C2×C3×C8C22×D311yescharacteristic
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—31no—
350C3×C22⋊C4—61no—
351C3×C42—31no—
352#217—21no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—121no—
359#217D1211yescharacteristic
360#215—121no—
361(C2×D3)⋊C4—61no—
362(C2×D3)⋊C4—61no—
363(C2×D3)⋊C4—61no—
364(C2×D3)⋊C4—61no—
365(C2×D3)⋊C4—61no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—121no—
371(C2×D3)⋊C4D1211yescharacteristic
372C4⋊Dic3—31no—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—21no—
386Dic3⋊C4—61no—
387Dic3⋊C4—61no—
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4D1211yescharacteristic
396C4×Dic3—61no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—121no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—41no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—41no—
406#204—22no—
407#204—121no—
408D3×C8—41no—
409C22×C32—21no—
410C22×C32—21no—
411C22×C32—21no—
412C22×C32C22×D411yescharacteristic
413C2×C3⋊D3—41no—
414C2×C3⋊D3—41no—
415C2×C3⋊D3—41no—
416C2×C3×D3—21no—
417C2×C3×D3—21no—
418C2×C3×D3—22no—
419C2×C3×D3—41no—
420C2×C3×D3—41no—
421C2×C3×D3#13512yes—
422D32—84no—
423C32×C4—21no—
424C32×C4C2×#4111yescharacteristic
425C32×C4H(5,𝔽2)11yescharacteristic
426C3⋊Dic3—41no—
427C3⋊Dic3—41no—
428C3⋊Dic3—41no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—21no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C3×Dic3—41no—
435C2×#41—31no—
436C22×D4—91no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—91no—
440C22×C8—31no—
441C22×C8—31no—
442#126—181no—
443#125—91no—
444#125—181no—
445#124—91no—
446#123—181no—
447#123—181no—
448C22⋊Q8—31no—
449C22⋊Q8—91no—
450C22⋊Q8—91no—
451#121—91no—
452#121—181no—
453#120—181no—
454C4×Q8—91no—
455C4×D4—31no—
456C4×D4—91no—
457#117—91no—
458#117—181no—
459C2×C4⋊C4—91no—
460C2×C22⋊C4—181no—
461#107—91no—
462#106—91no—
463#106—91no—
464C4⋊C8—31no—
465#103—31no—
466#103—91no—
467#103—91no—
468#103—91no—
469#102—31no—
470#102—91no—
471#102—91no—
472#102—91no—
473#102—91no—
474#102—91no—
475C22⋊C8—31no—
476C22⋊C8D3211yescharacteristic, complemented
477C4×C8—31no—
478C23×C3—21no—
479C23×C3—31no—
480C23×C3—61no—
481C23×C3C2×D1211yescharacteristic
482C23×C3D3×D411yescharacteristic
483C22×D3—21no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—121no—
487C22×D3—122no—
488C22×D3—122no—
489C22×D3—122no—
490C22×D3—122no—
491C22×D3—241no—
492C22×D3—241no—
493C22×D3C2×D1211yescharacteristic
494C3×Q8—61no—
495C3×Q8—61no—
496C3×Q8—61no—
497C3×Q8—61no—
498C3×D4—32no—
499C3×D4—62no—
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—31no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—41no—
512C2×C3×C4—41no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—122no—
519C2×C3×C4C2×D1211yescharacteristic
520C2×C3×C4D3×D411yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522C2×C3×C4C23×D311yescharacteristic
523#67—22no—
524#67—42no—
525#67—122no—
526#67—241no—
527#67—241no—
528#67—242no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—61no—
533C2×Dic3—61no—
534C2×Dic3—61no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—122no—
542C2×Dic3—241no—
543C2×Dic3C2×D1211yescharacteristic
544C2×Dic3C2×D1211yescharacteristic
545C2×Dic3C2×D1211yescharacteristic
546D12—21no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—121no—
553D12—122no—
554D12#23712yes—
555C4×D3—21no—
556C4×D3—21no—
557C4×D3—42no—
558C4×D3—122no—
559C4×D3—241no—
560Dic6—21no—
561Dic6—21no—
562Dic6—21no—
563Dic6—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—21no—
568C3×C8—41no—
569C3×C8—41no—
570C3×C8—61no—
571C3×C8—61no—
572C3⋊C8—21no—
573C3⋊C8—21no—
574C2×C32—41no—
575C2×C32#54611yescharacteristic
576C2×C32C2×#13511yescharacteristic
577C2×C32#57711yescharacteristic
578C3⋊D3—81no—
579C3×D3—22no—
580C3×D3—42no—
581C24—181no—
582#41—62no—
583#41—121no—
584C2×Q8—31no—
585C2×Q8—31no—
586C2×D4—31no—
587C2×D4—31no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—182no—
592C2×D4—181no—
593C2×D4—361no—
594C22×C4—31no—
595C22×C4—61no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4C2×D3211yescharacteristic
599Q16—121no—
600SD16—62no—
601SD16—361no—
602C2×C8—31no—
603C2×C8—31no—
604C2×C8—121no—
605C2×C8—121no—
606C2×C8C2×D3211yescharacteristic
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—61no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C4⋊C4—181no—
617C4⋊C4—181no—
618C4⋊C4—181no—
619C4⋊C4—181no—
620C22⋊C4—31no—
621C22⋊C4—31no—
622C22⋊C4—61no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C22⋊C4—181no—
628C22⋊C4—181no—
629C22⋊C4—181no—
630C42—31no—
631C42—181no—
632C42—181no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—32no—
641C22×C3—41no—
642C22×C3—41no—
643C22×C3—41no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—62no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3C22×D1211yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C2×D3—21no—
652C2×D3—21no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—121no—
657C2×D3—121no—
658C2×D3—121no—
659C2×D3—121no—
660C2×D3—121no—
661C2×D3—121no—
662C2×D3—241no—
663C2×D3—241no—
664C2×D3—241no—
665C2×D3—244no—
666C2×D3—244no—
667C2×D3#90412yes—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—21no—
672C3×C4—41no—
673C3×C4—61no—
674C3×C4—61no—
675C3×C4—61no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4C2×#23711yescharacteristic
680C3×C4#100411yescharacteristic
681C3×C4#100411yescharacteristic
682C3×C4D3×#4111yescharacteristic
683Dic3—21no—
684Dic3—21no—
685Dic3—21no—
686Dic3—41no—
687Dic3—41no—
688Dic3—41no—
689Dic3—121no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—241no—
696Dic3—241no—
697Dic3—241no—
698C32#329611yescharacteristic, complemented, Sylow
699C23—31no—
700C23—61no—
701C23—181no—
702C23—362no—
703C23—362no—
704C23—721no—
705C23D3×D1211yescharacteristic
706Q8—61no—
707Q8—61no—
708Q8—61no—
709Q8—61no—
710D4—32no—
711D4—62no—
712D4—61no—
713D4—122no—
714D4—181no—
715D4—181no—
716D4—362no—
717D4—721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—31no—
721C2×C4—31no—
722C2×C4—31no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—122no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—181no—
732C2×C4—362no—
733C2×C4—721no—
734C2×C4D3×D1211yescharacteristic
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—21no—
738C8—61no—
739C8—61no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—62no—
746C2×C3—81no—
747C2×C3—122no—
748C2×C3#555411yescharacteristic
749C2×C3#559111yescharacteristic
750C2×C3C2×#90411yescharacteristic
751C2×C3#575111yescharacteristic
752C2×C3D3×#13511yescharacteristic
753C2×C3#577811yescharacteristic
754D3—22no—
755D3—42no—
756D3—241no—
757D3—241no—
758D3—481no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—32no—
763C22—61no—
764C22—61no—
765C22—62no—
766C22—121no—
767C22—121no—
768C22—361no—
769C22—361no—
770C22—361no—
771C22—724no—
772C22C2×D3×D1211yescharacteristic
773C4—21no—
774C4—61no—
775C4—61no—
776C4—61no—
777C4—121no—
778C4—121no—
779C4—121no—
780C4—361no—
781C4—361no—
782C4—361no—
783C4D3×#23711yescharacteristic
784C4#6431311yescharacteristic
785C3—21no—
786C3#7944011yescharacteristic, complemented
787C3#8024611yescharacteristic, complemented
788C2—41no—
789C2—62no—
790C2—122no—
791C2—721no—
792C2#1059429211yescharacteristic
793C2D3×#90411yescharacteristic
794C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595067C2
hypercenterC22⋊C8D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #10594942C2semidirect
3. #10592436C2semidirect
4. C3×#4733C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591177C2semidirect
7. #10591084C2semidirect
8. #10590942C2semidirect
9. D3×#821C2semidirect
10. #10590872C2semidirect
11. #10590851C2semidirect
12. #10590801C2semidirect
13. #10590767C2semidirect
14. Dic3×#204C2semidirect
15. #10590675C2semidirect
21. #64135C22semidirect
23. C3×#924C22semidirect
24. C22×C3×C3⋊C8C22semidirect
25. C2×C3×Dic12C22semidirect
37. #63869C22semidirect
42. Dic3×Dic6C22semidirect
44. C32×C22⋊C8C22semidirect
47. #63645C22semidirect
48. #63644C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
56. #63566C22semidirect
57. #63566C22semidirect
86. #4733D3semidirect
88. #67⋊C8D3semidirect
177. #924C2×D3semidirect
178. C22×C3⋊C8C2×D3semidirect
179. C2×Dic12C2×D3semidirect
204. C3×C22⋊C8C2×D3semidirect
205. C3×C22⋊C8C2×D3semidirect
233. #816C2×D3semidirect
234. Dic3⋊C8C2×D3semidirect
235. C8×Dic3C2×D3semidirect
476. C22⋊C8D32semidirect
698. C32#3296semidirect
786. C3#79440semidirect
787. C3#80246semidirect

Maximal subgroups

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

subgroupindex
#105950672
#105949422
#105924362
C3×#47332
C3×#67⋊C82
#105911772
#105910842
#105909422
D3×#8212
#105908722
#105908512
#105908012
#105907672
Dic3×#2042
#105906752
#802463
#794403