Finite Group Databasebeta

← #11887424

Subgroups — #11887424

Order 1152.

939 conjugacy classes of subgroups.

The subgroup lattice has 839 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595018C211yesmaximal, characteristic, complemented
2#10594843C211yesmaximal, characteristic, complemented
3#10592431C211yesmaximal, characteristic, complemented
4C3×#67⋊C8C211yesmaximal, characteristic, complemented
5C3×#4722C211yesmaximal, characteristic, complemented
6#10591177C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590967C211yesmaximal, characteristic, complemented
9#10590872C211yesmaximal, characteristic, complemented
10#10590832C211yesmaximal, characteristic, complemented
11#10590774C211yesmaximal, characteristic, complemented
12#10590770C211yesmaximal, characteristic, complemented
13#10590763C211yesmaximal, characteristic, complemented
14#10590705C211yesmaximal, characteristic, complemented
15#10590690C211yesmaximal, characteristic, complemented
16#81485—31nomaximal
17#79441—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20#64139C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22C2×#3745C2211yescharacteristic
23C3×C4×#67C2211yescharacteristic
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C3×#924C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic, complemented
28#63981—21no—
29#63978—21no—
30#63974—21no—
31#63952—21no—
32#63910—21no—
33#63909C2211yescharacteristic
34#63909C2211yescharacteristic, complemented
35#63897—21no—
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic, complemented
38#63869C2211yescharacteristic, complemented
39#63864C2211yescharacteristic
40#63854—21no—
41#63848—21no—
42#63841C2211yescharacteristic, complemented
43C2×#3717C2211yescharacteristic, complemented
44C32×C22⋊C8C2211yescharacteristic
45#63648C2211yescharacteristic
46#63648C2211yescharacteristic
47C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
48C3×#818C2211yescharacteristic, complemented
49C3×#818C2211yescharacteristic, complemented
50C3×#816C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63573C2211yescharacteristic, complemented
55#63566C2211yescharacteristic, complemented
56#63564C2211yescharacteristic
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic, complemented
61#5630—31no—
62#5565—31no—
63#5550—31no—
64#5514—31no—
65C3×#484—31no—
66C3×C8×D4—31no—
67#5115—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5048—31no—
72C2×#809—31no—
73#4891—31no—
74#4885—31no—
75#4883—31no—
76#4872—31no—
77#4847—31no—
78#4844—31no—
79#4819—31no—
80#4810—31no—
81#4804—31no—
82#4800—31no—
83#4737—31no—
84#4734—31no—
85#4732—31no—
86#4732—31no—
87#4732—61no—
88#67⋊C8D311yescharacteristic, complemented
89#4722D311yescharacteristic, complemented
90#4697—31no—
91C4×D24—31no—
92C23×C3⋊D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)—22no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67D411yescharacteristic
102C22×C3×Dic3—21no—
103C2×C3×C4×D3C2311yescharacteristic
104C2×C3×Dic6C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×#624—21no—
111#3799—22no—
112#3799—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3745—22no—
118#3745—41no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4D411yescharacteristic
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4D411yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8—41no—
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132C3×D3×C8—41no—
133#3724—21no—
134Dic3⋊Dic3—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140#3722—21no—
141(C2×D3)⋊Dic3—21no—
142Dic32—21no—
143#3717—41no—
144#3297—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×#215—31no—
157#939—61no—
158#937—61no—
159#930—31no—
160#930—31no—
161#930—31no—
162#930—31no—
163#930—61no—
164#930—61no—
165C4×#67—61no—
166C4×#67C2×D311yescharacteristic
167#926—31no—
168C2×C4⋊Dic3C2×D311yescharacteristic
169#924C2×D311yescharacteristic
170C22×C3⋊C8C2×D311yescharacteristic
171C2×D24—31no—
172C2×D24—31no—
173C2×D24—31no—
174C2×D24—31no—
175C2×D24—61no—
176C2×D24—61no—
177C2×#204—31no—
178C2×D3×C8C2×D311yescharacteristic, complemented
179#898—61no—
180#898—61no—
181#895—31no—
182#895—31no—
183#895—61no—
184#894—61no—
185#894—61no—
186#894—61no—
187#893—31no—
188#893—31no—
189#892—31no—
190#890—31no—
191#884—61no—
192#883—61no—
193#882—61no—
194#67⋊C4—61no—
195D3×C22⋊C4—61no—
196D3×C22⋊C4—61no—
197#875—31no—
198C4×D12—31no—
199C4×D12—31no—
200#870—31no—
201C3×#107—31no—
202C3×#107—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—31no—
221#821—61no—
222#821—61no—
223(C2×D3)⋊C8C2×D311yescharacteristic, complemented
224#818C2×D311yescharacteristic, complemented
225#818C2×D311yescharacteristic, complemented
226#817—31no—
227#816—31no—
228#816C2×D311yescharacteristic, complemented
229#816C2×D311yescharacteristic, complemented
230Dic3⋊C8C2×D311yescharacteristic, complemented
231C8×Dic3C2×D311yescharacteristic, complemented
232#809—31no—
233#809—31no—
234#809—31no—
235#809—31no—
236#809—31no—
237#808—31no—
238C23×C32C2×D411yescharacteristic
239C22×C3⋊D3—21no—
240C22×C3⋊D3—21no—
241C22×C3⋊D3—21no—
242C22×C3⋊D3—42no—
243C22×C3⋊D3—42no—
244C22×C3⋊D3—81no—
245C22×C3×D3C2×D411yescharacteristic
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—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)—42no—
258C4⋊(C3⋊D3)#4112yes—
259C3×#67—22no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—81no—
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C3×C4×D3—21no—
269C3×C4×D3—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272#626—42no—
273#626—81no—
274#626—81no—
275#624—42no—
276#624—81no—
277#624—81no—
278C32×C8—21no—
279C32×C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—91no—
285#484—31no—
286#482—91no—
287#478—91no—
288#466—91no—
289#465—91no—
290#463—91no—
291#449—91no—
292#447—91no—
293C4×D8—91no—
294C8×D4—31no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C23×D3—121no—
300C2×C3×Q8—31no—
301C2×C3×D4—31no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—121no—
313C2×#67D1211yescharacteristic
314C22×Dic3—21no—
315#239—62no—
316#239—121no—
317#235—62no—
318#235—121no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—31no—
323C2×D12—31no—
324C2×D12—31no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—62no—
329C2×D12—62no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—61no—
335C2×D12—122no—
336C2×D12—121no—
337C2×D12—121no—
338C2×D12—121no—
339C2×D12—122no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—61no—
344C2×C4×D3—61no—
345C2×C4×D3—61no—
346C2×C4×D3C22×D311yescharacteristic
347C2×Dic6C22×D311yescharacteristic
348C2×C3×C8—21no—
349C2×C3×C8—21no—
350C2×C3×C8—31no—
351C2×C3×C8—31no—
352C2×C3×C8—121no—
353C2×C3×C8—121no—
354C2×C3×C8C22×D311yescharacteristic
355C2×C3×C8C22×D311yescharacteristic
356C2×C3×C8C22×D311yescharacteristic
357C2×C3×C8C22×D311yescharacteristic
358C3×C4⋊C4—31no—
359C3×C4⋊C4—31no—
360C3×C4⋊C4—31no—
361C3×C4⋊C4—31no—
362C3×C4⋊C4—61no—
363C3×C4⋊C4—61no—
364C3×C22⋊C4—31no—
365C3×C22⋊C4—31no—
366C3×C22⋊C4—61no—
367C3×C42—31no—
368#217—21no—
369#217—61no—
370#217D1211yescharacteristic
371#215—121no—
372(C2×D3)⋊C4—61no—
373(C2×D3)⋊C4—61no—
374(C2×D3)⋊C4—61no—
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—61no—
382(C2×D3)⋊C4—61no—
383(C2×D3)⋊C4—61no—
384(C2×D3)⋊C4—61no—
385(C2×D3)⋊C4—61no—
386(C2×D3)⋊C4—61no—
387(C2×D3)⋊C4—121no—
388(C2×D3)⋊C4D1211yescharacteristic
389C4⋊Dic3—21no—
390C4⋊Dic3—31no—
391C4⋊Dic3—31no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4D1211yescharacteristic
402C4×Dic3—61no—
403C4×Dic3—61no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—41no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409D24—62no—
410D24—122no—
411D24—121no—
412D24—121no—
413D24—122no—
414#204—121no—
415D3×C8—41no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32#13512yes—
419C22×C32C22×D411yescharacteristic
420C2×C3⋊D3—22no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3⋊D3—41no—
427C2×C3⋊D3—41no—
428C2×C3⋊D3—41no—
429C2×C3⋊D3—84no—
430C2×C3×D3—21no—
431C2×C3×D3—21no—
432C2×C3×D3—21no—
433C32×C4—21no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—41no—
437C3×Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—41no—
441C3×Dic3—41no—
442C3×Dic3—41no—
443C3×Dic3—41no—
444C2×#41—91no—
445C22×D4—91no—
446C2×SD16—91no—
447C2×D8—91no—
448C2×D8—91no—
449C22×C8—31no—
450C22×C8—31no—
451#126—181no—
452#125—91no—
453#124—91no—
454#123—181no—
455#123—181no—
456C22⋊Q8—31no—
457#121—91no—
458#121—91no—
459#121—91no—
460#121—181no—
461#121—181no—
462#120—181no—
463C4×D4—31no—
464C4×D4—91no—
465C4×D4—91no—
466C4×D4—181no—
467#117—91no—
468C2×C4⋊C4—31no—
469C2×C22⋊C4—181no—
470#107—31no—
471#107—31no—
472#106—91no—
473C4⋊C8—31no—
474#103—31no—
475#103—31no—
476#103—91no—
477#102—91no—
478#102—91no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484C22⋊C8—31no—
485C22⋊C8D3211yescharacteristic
486C4×C8—31no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3C2×D1211yescharacteristic
490C23×C3D3×D411yescharacteristic
491C22×D3—61no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—121no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—124no—
503C22×D3—122no—
504C22×D3—122no—
505C22×D3—242no—
506C22×D3—241no—
507C22×D3—241no—
508C22×D3—242no—
509C22×D3C2×D1211yescharacteristic
510C3×Q8—61no—
511C3×Q8—61no—
512C3×D4—62no—
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—31no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—241no—
531C2×C3×C4C2×D1211yescharacteristic
532C2×C3×C4D3×D411yescharacteristic
533C2×C3×C4C23×D311yescharacteristic
534C2×C3×C4C23×D311yescharacteristic
535#67—22no—
536#67—122no—
537#67—122no—
538#67—122no—
539#67—242no—
540#67—241no—
541#67—241no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—81no—
549C2×Dic3—121no—
550C2×Dic3C2×D1211yescharacteristic
551C2×Dic3C2×D1211yescharacteristic
552C2×Dic3C2×D1211yescharacteristic
553D12—32no—
554D12—32no—
555D12—62no—
556D12—62no—
557D12—61no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—61no—
565D12—61no—
566D12—61no—
567D12—121no—
568D12—121no—
569D12—121no—
570D12—121no—
571D12—122no—
572D12—122no—
573D12—124no—
574D12—122no—
575D12—241no—
576D12—241no—
577C4×D3—21no—
578C4×D3—21no—
579C4×D3—122no—
580C4×D3—122no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585Dic6—21no—
586Dic6—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—21no—
590C3×C8—21no—
591C3×C8—41no—
592C3×C8—41no—
593C3×C8—61no—
594C3×C8—61no—
595C3⋊C8—21no—
596C3⋊C8—21no—
597C2×C32—22no—
598C2×C32#54611yescharacteristic
599C2×C32C2×#13511yescharacteristic
600C2×C32#57611yescharacteristic
601C3⋊D3—42no—
602C3⋊D3—81no—
603C3⋊D3—81no—
604C3×D3—41no—
605C24—181no—
606#41—182no—
607#41—361no—
608C2×Q8—31no—
609C2×D4—31no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—91no—
613C2×D4—182no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—181no—
618C2×D4—181no—
619C2×D4—361no—
620C22×C4—31no—
621C22×C4—61no—
622C22×C4—181no—
623C22×C4—181no—
624C22×C4—181no—
625C22×C4C2×D3211yescharacteristic
626SD16—361no—
627D8—182no—
628D8—361no—
629C2×C8—31no—
630C2×C8—31no—
631C2×C8—121no—
632C2×C8—121no—
633C2×C8C2×D3211yescharacteristic
634C2×C8C2×D3211yescharacteristic
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—31no—
638C4⋊C4—31no—
639C4⋊C4—61no—
640C4⋊C4—61no—
641C4⋊C4—91no—
642C4⋊C4—181no—
643C4⋊C4—181no—
644C22⋊C4—31no—
645C22⋊C4—31no—
646C22⋊C4—61no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C22⋊C4—181no—
654C22⋊C4—181no—
655C42—31no—
656C42—181no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—22no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—61no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3#90412yes—
669C22×C3#91912yes—
670C22×C3C22×D1211yescharacteristic
671C22×C3C2×D3×D411yescharacteristic
672C2×D3—21no—
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—62no—
676C2×D3—62no—
677C2×D3—122no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—122no—
683C2×D3—121no—
684C2×D3—121no—
685C2×D3—121no—
686C2×D3—121no—
687C2×D3—121no—
688C2×D3—121no—
689C2×D3—121no—
690C2×D3—121no—
691C2×D3—121no—
692C2×D3—121no—
693C2×D3—121no—
694C2×D3—121no—
695C2×D3—241no—
696C2×D3—241no—
697C2×D3—241no—
698C2×D3—241no—
699C2×D3—241no—
700C2×D3—241no—
701C2×D3—241no—
702C2×D3—244no—
703C2×D3—244no—
704C2×D3—248no—
705C3×C4—21no—
706C3×C4—21no—
707C3×C4—21no—
708C3×C4—21no—
709C3×C4—41no—
710C3×C4—61no—
711C3×C4—61no—
712C3×C4—61no—
713C3×C4—121no—
714C3×C4—121no—
715C3×C4—121no—
716C3×C4—121no—
717C3×C4#100411yescharacteristic
718C3×C4D3×#4111yescharacteristic
719C3×C4D3×#4111yescharacteristic
720C3×C4#100911yescharacteristic
721Dic3—21no—
722Dic3—21no—
723Dic3—21no—
724Dic3—41no—
725Dic3—41no—
726Dic3—41no—
727Dic3—41no—
728Dic3—121no—
729Dic3—121no—
730Dic3—241no—
731C32#329711yescharacteristic, complemented, Sylow
732C23—31no—
733C23—181no—
734C23—181no—
735C23—181no—
736C23—362no—
737C23—362no—
738C23—721no—
739C23D3×D1211yescharacteristic
740Q8—61no—
741Q8—61no—
742D4—62no—
743D4—92no—
744D4—181no—
745D4—181no—
746D4—181no—
747D4—181no—
748D4—181no—
749D4—362no—
750D4—362no—
751D4—362no—
752D4—721no—
753D4—721no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—31no—
757C2×C4—31no—
758C2×C4—31no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—61no—
762C2×C4—61no—
763C2×C4—61no—
764C2×C4—61no—
765C2×C4—181no—
766C2×C4—241no—
767C2×C4—362no—
768C2×C4—721no—
769C2×C4—721no—
770C2×C4D3×D1211yescharacteristic
771C2×C4C22×D3211yescharacteristic
772C8—21no—
773C8—21no—
774C8—61no—
775C8—61no—
776C2×C3—22no—
777C2×C3—22no—
778C2×C3—21no—
779C2×C3—21no—
780C2×C3—21no—
781C2×C3—42no—
782C2×C3—121no—
783C2×C3#555411yescharacteristic
784C2×C3#565411yescharacteristic
785C2×C3C2×#90411yescharacteristic
786C2×C3#575211yescharacteristic
787C2×C3C2×#91911yescharacteristic
788C2×C3#577411yescharacteristic
789D3—41no—
790D3—122no—
791D3—122no—
792D3—242no—
793D3—242no—
794D3—241no—
795D3—241no—
796D3—241no—
797D3—241no—
798D3—481no—
799C22—21no—
800C22—21no—
801C22—61no—
802C22—61no—
803C22—61no—
804C22—182no—
805C22—361no—
806C22—361no—
807C22—361no—
808C22—361no—
809C22—361no—
810C22—361no—
811C22—361no—
812C22—361no—
813C22—724no—
814C22#6380812yes—
815C22C2×D3×D1211yescharacteristic
816C4—21no—
817C4—61no—
818C4—61no—
819C4—61no—
820C4—121no—
821C4—121no—
822C4—121no—
823C4—121no—
824C4—361no—
825C4#6431211yescharacteristic
826C4#6431411yescharacteristic
827C3—21no—
828C3#7944111yescharacteristic, complemented
829C3#8148511yescharacteristic, complemented
830C2—22no—
831C2—121no—
832C2—362no—
833C2—721no—
834C2—721no—
835C2#1059429311yescharacteristic
836C2C2×#6380811yescharacteristic
837C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3297
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
1. #10595018C2semidirect
2. #10594843C2semidirect
3. #10592431C2semidirect
4. C3×#67⋊C8C2semidirect
5. C3×#4722C2semidirect
6. #10591177C2semidirect
7. C2×#63564C2semidirect
8. #10590967C2semidirect
9. #10590872C2semidirect
10. #10590832C2semidirect
11. #10590774C2semidirect
12. #10590770C2semidirect
13. #10590763C2semidirect
14. #10590705C2semidirect
15. #10590690C2semidirect
27. C2×C3×D3×C8C22semidirect
34. #63909C22semidirect
37. #63894C22semidirect
38. #63869C22semidirect
42. #63841C22semidirect
43. C2×#3717C22semidirect
47. C3×(C2×D3)⋊C8C22semidirect
48. C3×#818C22semidirect
49. C3×#818C22semidirect
50. C3×#816C22semidirect
51. C3×#816C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63573C22semidirect
55. #63566C22semidirect
60. #63564C22semidirect
88. #67⋊C8D3semidirect
89. #4722D3semidirect
178. C2×D3×C8C2×D3semidirect
223. (C2×D3)⋊C8C2×D3semidirect
224. #818C2×D3semidirect
225. #818C2×D3semidirect
228. #816C2×D3semidirect
229. #816C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. C8×Dic3C2×D3semidirect
731. C32#3297semidirect
828. C3#79441semidirect
829. C3#81485semidirect

Maximal subgroups

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

subgroupindex
#105950182
#105948432
#105924312
C3×#67⋊C82
C3×#47222
#105911772
C2×#635642
#105909672
#105908722
#105908322
#105907742
#105907702
#105907632
#105907052
#105906902
#814853
#794413