Finite Group Databasebeta

← #11887270

Subgroups — #11887270

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic
2#10594849C211yesmaximal, characteristic, complemented
3#10592430C211yesmaximal, characteristic, complemented
4C3×#67⋊C8C211yesmaximal, characteristic, complemented
5C3×#4721C211yesmaximal, characteristic, complemented
6#10591187C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590970C211yesmaximal, characteristic, complemented
9#10590872C211yesmaximal, characteristic, complemented
10#10590830C211yesmaximal, characteristic, complemented
11#10590813C211yesmaximal, characteristic, complemented
12#10590769C211yesmaximal, characteristic, complemented
13#10590758C211yesmaximal, characteristic, complemented
14#10590704C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#81445—31nomaximal
17#79440—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64133C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C2×#3744C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63981—21no—
29#63974—21no—
30#63961—21no—
31#63955—21no—
32#63910—21no—
33#63909C2211yescharacteristic
34#63897—21no—
35#63894C2211yescharacteristic
36#63869C2211yescharacteristic, complemented
37#63864C2211yescharacteristic
38#63858—21no—
39#63857C2211yescharacteristic, complemented
40#63847—21no—
41#63844C2211yescharacteristic, complemented
42#63841C2211yescharacteristic, complemented
43C2×#3719C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C3×#817C2211yescharacteristic, complemented
49C3×#817C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63566C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5630—31no—
62#5550—31no—
63#5541—31no—
64#5513—31no—
65C3×#483—31no—
66C3×C8×D4—31no—
67#5116—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5051—31no—
72C2×#809—31no—
73#4871—31no—
74#4866—31no—
75#4864—31no—
76#4852—31no—
77#4847—31no—
78#4845—31no—
79#4808—31no—
80#4804—31no—
81#4800—31no—
82#4798—31no—
83#4737—31no—
84#4733—31no—
85#4731—31no—
86#4731—31no—
87#4731—61no—
88#67⋊C8D311yescharacteristic, complemented
89#4721D311yescharacteristic, complemented
90#4697—31no—
91C4×#204—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C4⋊(C3⋊D3)—22no—
95C2×C4⋊(C3⋊D3)—21no—
96C2×C4⋊(C3⋊D3)—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67D411yescharacteristic
101C22×C3×Dic3—21no—
102C2×C3×C4×D3C2311yescharacteristic
103C2×C3×Dic6C2311yescharacteristic
104C2×#626—21no—
105C2×#626—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C2×C32×C8C2311yescharacteristic
112#3757—21no—
113C4⋊(C3⋊Dic3)C2311yescharacteristic
114#3750—21no—
115#3744—22no—
116#3744—41no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×(C2×D3)⋊C4D411yescharacteristic
120C3×C4⋊Dic3—21no—
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×Dic3⋊C4D411yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8—41no—
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C3×D3×C8—41no—
131#3724—21no—
132#3724—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139(C2×D3)⋊Dic3—21no—
140(C2×D3)⋊Dic3—21no—
141Dic32—21no—
142Dic32—21no—
143#3719—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×#235—31no—
147C22×D12—31no—
148C22×D12—31no—
149C22×D12—61no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×C22⋊Q8—31no—
153C3×C4×D4—31no—
154C2×C3×C4⋊C4—31no—
155#947—31no—
156C2×#216—31no—
157#937—61no—
158#935—61no—
159#930—31no—
160#929—61no—
161C4×#67C2×D311yescharacteristic
162#926—31no—
163#926—61no—
164C2×C4⋊Dic3C2×D311yescharacteristic
165#924—31no—
166#924—31no—
167#924—31no—
168#924—61no—
169#924C2×D311yescharacteristic
170C22×C3⋊C8C2×D311yescharacteristic
171C2×Dic12—31no—
172C2×#204—31no—
173C2×#204—31no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—61no—
177C2×#204—61no—
178C2×D3×C8C2×D311yescharacteristic, complemented
179#898—61no—
180#897—31no—
181#895—31no—
182#895—61no—
183#894—61no—
184#894—61no—
185#893—31no—
186#892—31no—
187#890—31no—
188#889—61no—
189#889—61no—
190#887—31no—
191#884—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196#877—61no—
197#875—31no—
198C4×D12—31no—
199#870—31no—
200C4×Dic6—31no—
201C3×#106—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#103—31no—
205C3×#103—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8C2×D311yescharacteristic
209C3×C22⋊C8C2×D311yescharacteristic
210C3×C4×C8—31no—
211#835—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—31no—
219#821—31no—
220#821—61no—
221#821—61no—
222(C2×D3)⋊C8C2×D311yescharacteristic, complemented
223#818—31no—
224#817C2×D311yescharacteristic, complemented
225#817C2×D311yescharacteristic, complemented
226#816—31no—
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229#816C2×D311yescharacteristic, complemented
230Dic3⋊C8C2×D311yescharacteristic, complemented
231C8×Dic3C2×D311yescharacteristic, complemented
232#810—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#807—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×C4C2×D411yescharacteristic
248C2×C32×C4C2411yescharacteristic
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—42no—
255C4⋊(C3⋊D3)#4112yes—
256#634—21no—
257#634—21no—
258C3×#67—22no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—42no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×C4×D3—21no—
268C3×C4×D3—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271#626—42no—
272#626—81no—
273#624—42no—
274#624—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—31no—
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—31no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—31no—
298C2×C3×D4—31no—
299C22×C3×C4—21no—
300C22×C3×C4—31no—
301C22×C3×C4—61no—
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C2×#67—61no—
305C2×#67—61no—
306C2×#67D1211yescharacteristic
307C22×Dic3—21no—
308#239—62no—
309#239—121no—
310#235—62no—
311#235—121no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—31no—
315C2×D12—31no—
316C2×D12—61no—
317C2×D12—61no—
318C2×D12—62no—
319C2×D12—62no—
320C2×D12—61no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—122no—
325C2×D12—121no—
326C2×D12—121no—
327C2×D12—121no—
328C2×D12—122no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—21no—
339C2×C3×C8—21no—
340C2×C3×C8—31no—
341C2×C3×C8—31no—
342C2×C3×C8—121no—
343C2×C3×C8—121no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—61no—
353C3×C4⋊C4—61no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—31no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358#217—21no—
359#217—61no—
360#217—61no—
361#217—61no—
362#217—61no—
363#217—121no—
364#217D1211yescharacteristic
365#216—121no—
366(C2×D3)⋊C4—61no—
367(C2×D3)⋊C4—61no—
368(C2×D3)⋊C4—61no—
369(C2×D3)⋊C4—61no—
370(C2×D3)⋊C4—61no—
371(C2×D3)⋊C4—61no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
375(C2×D3)⋊C4—61no—
376(C2×D3)⋊C4D1211yescharacteristic
377C4⋊Dic3—21no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385C4⋊Dic3C22×D311yescharacteristic
386Dic3⋊C4—21no—
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⋊C4—121no—
396Dic3⋊C4D1211yescharacteristic
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3—61no—
400C4×Dic3—61no—
401C4×Dic3C22×D311yescharacteristic
402C2×C3⋊C8—41no—
403C2×C3⋊C8C22×D311yescharacteristic
404C2×C3⋊C8C22×D311yescharacteristic
405Dic12—121no—
406#204—62no—
407#204—62no—
408#204—122no—
409#204—121no—
410#204—121no—
411#204—122no—
412D3×C8—41no—
413C22×C32—21no—
414C22×C32—21no—
415C22×C32#13512yes—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—41no—
419C2×C3⋊D3—41no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—84no—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C32×C4—21no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—41no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—31no—
445C22×C8—31no—
446#126—181no—
447#125—91no—
448#125—181no—
449#124—91no—
450#123—181no—
451#123—181no—
452C22⋊Q8—31no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—91no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—31no—
460C4×D4—91no—
461#117—91no—
462#117—181no—
463C2×C4⋊C4—31no—
464C2×C22⋊C4—181no—
465#107—91no—
466#106—31no—
467#106—31no—
468C4⋊C8—31no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—91no—
474#102—91no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102—91no—
479C22⋊C8—31no—
480C22⋊C8D3211yescharacteristic
481C4×C8—31no—
482C23×C3—21no—
483C23×C3—31no—
484C23×C3C2×D1211yescharacteristic
485C23×C3D3×D411yescharacteristic
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—124no—
495C22×D3—122no—
496C22×D3—122no—
497C22×D3—242no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—242no—
501C22×D3C2×D1211yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—62no—
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—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—122no—
523C2×C3×C4C2×D1211yescharacteristic
524C2×C3×C4D3×D411yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526C2×C3×C4C23×D311yescharacteristic
527#67—22no—
528#67—122no—
529#67—241no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—42no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3C2×D1211yescharacteristic
542C2×Dic3C2×D1211yescharacteristic
543C2×Dic3C2×D1211yescharacteristic
544D12—32no—
545D12—32no—
546D12—62no—
547D12—62no—
548D12—61no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—121no—
555D12—121no—
556D12—122no—
557D12—122no—
558D12—124no—
559D12—122no—
560D12—241no—
561C4×D3—21no—
562C4×D3—21no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—21no—
568Dic6—21no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—121no—
574Dic6—121no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—41no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C2×C32—22no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57711yescharacteristic
589C3⋊D3—42no—
590C3⋊D3—81no—
591C3×D3—41no—
592C24—181no—
593#41—182no—
594#41—361no—
595C2×Q8—31no—
596C2×Q8—91no—
597C2×D4—31no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—361no—
605C22×C4—31no—
606C22×C4—61no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4C2×D3211yescharacteristic
610Q16—361no—
611SD16—182no—
612SD16—361no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—121no—
616C2×C8—121no—
617C2×C8C2×D3211yescharacteristic
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—61no—
624C4⋊C4—61no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4—181no—
631C22⋊C4—31no—
632C22⋊C4—31no—
633C22⋊C4—61no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—181no—
643C42—181no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—22no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3#90412yes—
656C22×C3#91612yes—
657C22×C3C22×D1211yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—122no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—122no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—241no—
677C2×D3—241no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3—244no—
681C2×D3—244no—
682C2×D3—248no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—21no—
687C3×C4—41no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—61no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4#100411yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4D3×#4111yescharacteristic
698C3×C4#100911yescharacteristic
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—121no—
707Dic3—121no—
708Dic3—121no—
709Dic3—121no—
710Dic3—241no—
711Dic3—241no—
712C32#329611yescharacteristic, complemented, Sylow
713C23—31no—
714C23—181no—
715C23—181no—
716C23—362no—
717C23—362no—
718C23—721no—
719C23D3×D1211yescharacteristic
720Q8—61no—
721Q8—61no—
722Q8—181no—
723Q8—181no—
724D4—62no—
725D4—92no—
726D4—181no—
727D4—181no—
728D4—181no—
729D4—362no—
730D4—362no—
731D4—721no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—31no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—122no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—362no—
747C2×C4—721no—
748C2×C4D3×D1211yescharacteristic
749C2×C4C22×D3211yescharacteristic
750C8—21no—
751C8—21no—
752C8—61no—
753C8—61no—
754C2×C3—22no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—42no—
760C2×C3—121no—
761C2×C3#555411yescharacteristic
762C2×C3#565411yescharacteristic
763C2×C3C2×#90411yescharacteristic
764C2×C3#575111yescharacteristic
765C2×C3C2×#91611yescharacteristic
766C2×C3#577811yescharacteristic
767D3—41no—
768D3—122no—
769D3—122no—
770D3—242no—
771D3—242no—
772D3—241no—
773D3—241no—
774C22—21no—
775C22—21no—
776C22—61no—
777C22—61no—
778C22—61no—
779C22—182no—
780C22—361no—
781C22—361no—
782C22—361no—
783C22—361no—
784C22—361no—
785C22—724no—
786C22#6380612yes—
787C22C2×D3×D1211yescharacteristic
788C4—21no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—361no—
797C4—361no—
798C4#6431211yescharacteristic
799C4#6431411yescharacteristic
800C3—21no—
801C3#7944011yescharacteristic, complemented
802C3#8144511yescharacteristic, complemented
803C2—22no—
804C2—121no—
805C2—362no—
806C2—721no—
807C2#1059429311yescharacteristic
808C2C2×#6380611yescharacteristic
809C2#1059471511yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
prime radical#10595018C2
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. #10594849C2semidirect
3. #10592430C2semidirect
4. C3×#67⋊C8C2semidirect
5. C3×#4721C2semidirect
6. #10591187C2semidirect
7. C2×#63564C2semidirect
8. #10590970C2semidirect
9. #10590872C2semidirect
10. #10590830C2semidirect
11. #10590813C2semidirect
12. #10590769C2semidirect
13. #10590758C2semidirect
14. #10590704C2semidirect
15. #10590690C2semidirect
27. C2×C3×D3×C8C22semidirect
36. #63869C22semidirect
39. #63857C22semidirect
41. #63844C22semidirect
42. #63841C22semidirect
43. C2×#3719C22semidirect
47. C3×(C2×D3)⋊C8C22semidirect
48. C3×#817C22semidirect
49. C3×#817C22semidirect
50. C3×#816C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63566C22semidirect
88. #67⋊C8D3semidirect
89. #4721D3semidirect
178. C2×D3×C8C2×D3semidirect
222. (C2×D3)⋊C8C2×D3semidirect
224. #817C2×D3semidirect
225. #817C2×D3semidirect
228. #816C2×D3semidirect
229. #816C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. C8×Dic3C2×D3semidirect
712. C32#3296semidirect
801. C3#79440semidirect
802. C3#81445semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105948492
#105924302
C3×#67⋊C82
C3×#47212
#105911872
C2×#635642
#105909702
#105908722
#105908302
#105908132
#105907692
#105907582
#105907042
#105906902
#814453
#794403