Finite Group Databasebeta

← #11887426

Subgroups — #11887426

Order 1152.

921 conjugacy classes of subgroups.

The subgroup lattice has 833 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595431C211yesmaximal, characteristic, complemented
2#10594562C211yesmaximal, characteristic, complemented
3#10592509C211yesmaximal, characteristic, complemented
4C3×#4811C211yesmaximal, characteristic, complemented
5C3×#4800C211yesmaximal, characteristic, complemented
6#10591585C211yesmaximal, characteristic, complemented
7#10591568C211yesmaximal, characteristic, complemented
8#10591560C211yesmaximal, characteristic, complemented
9#10590947C211yesmaximal, characteristic, complemented
10#10590763C211yesmaximal, characteristic, complemented
11#10590721C211yesmaximal, characteristic, complemented
12#10590651C211yesmaximal, characteristic, complemented
13D3×#809C211yesmaximal, characteristic, complemented
14#10590509C211yesmaximal, characteristic, complemented
15#10590468C211yesmaximal, characteristic, complemented
16#81653—31nomaximal
17#81485—31nomaximal
18C2×#3832C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3755C2211yescharacteristic, complemented
21C2×#3745C2211yescharacteristic
22#64104C2211yescharacteristic, complemented
23C3×#947C2211yescharacteristic
24C3×#946C2211yescharacteristic
25C3×D3×C4⋊C4C2211yescharacteristic
26C3×#890C2211yescharacteristic, complemented
27#63923—21no—
28#63921—21no—
29#63916C2211yescharacteristic
30#63910—21no—
31#63909—21no—
32#63909C2211yescharacteristic
33#63904—21no—
34C4×#626C2211yescharacteristic
35#63897—21no—
36#63894C2211yescharacteristic
37#63894C2211yescharacteristic, complemented
38#63853—21no—
39#63849C2211yescharacteristic, complemented
40#63848—21no—
41C2×#3714C2211yescharacteristic
42C2×#3710C2211yescharacteristic, complemented
43C2×D3×C3⋊C8C2211yescharacteristic
44C32×#103C2211yescharacteristic, complemented
45#63647C2211yescharacteristic, complemented
46#63636C2211yescharacteristic
47C3×#835C2211yescharacteristic, complemented
48C3×#835C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×(C2×D3)⋊C8C2211yescharacteristic
51C3×#818C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×#809C2211yescharacteristic
54C3×#807C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63562C2211yescharacteristic
61#5695—31no—
62#5676—31no—
63#5630—31no—
64#5514—31no—
65C3×#488—31no—
66C3×#484—31no—
67#5066—31no—
68#5057—31no—
69#5048—31no—
70C2×#809—31no—
71#4891—31no—
72#4885—31no—
73#4883—31no—
74#4872—31no—
75#4819—31no—
76#4811D311yescharacteristic, complemented
77#4810—31no—
78#4810—31no—
79#4810—61no—
80#4807—31no—
81#4804—31no—
82#4804—31no—
83#4800D311yescharacteristic, complemented
84#4784—31no—
85#4775—31no—
86#4773—31no—
87D3×#102—31no—
88#4732—31no—
89#67⋊C8—31no—
90C4×D24—31no—
91C8×D12—31no—
92C22×D32—21no—
93C2×C32×Q8C2311yescharacteristic
94#3832—22no—
95#3832—41no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×C4×C3⋊D3C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×C3×C4×D3—21no—
104C2×C3×C4×D3C2311yescharacteristic
105C2×#626—21no—
106C2×#626—21no—
107C2×#626—21no—
108C2×#626D411yescharacteristic
109C2×#624—21no—
110C2×#624—21no—
111D3×D12—22no—
112D3×D12—41no—
113C2×C32×C8C2311yescharacteristic
114C32×C4⋊C4C2311yescharacteristic
115#3755—41no—
116#3752—21no—
117C2×C3⋊(C3⋊C8)C2311yescharacteristic
118#3745—22no—
119C3×(C2×D3)⋊C4—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3—21no—
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4—21no—
127C3×Dic3⋊C4—21no—
128C3×Dic3⋊C4—21no—
129C3×C4×Dic3C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131C2×C3×C3⋊C8C2311yescharacteristic
132Dic3⋊Dic3D411yescharacteristic
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3714—41no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3297—91noSylow
145C2×#239—31no—
146C2×#239—31no—
147C2×#239—61no—
148C2×D3×D4—31no—
149C22×D12—31no—
150C3×#125—31no—
151C3×#124—31no—
152C3×C22⋊Q8—31no—
153C2×C3×C4⋊C4—31no—
154#947C2×D311yescharacteristic
155#946C2×D311yescharacteristic
156C2×#215—31no—
157C2×#215—31no—
158C2×#215—61no—
159#938—31no—
160C2×#213—31no—
161#930—31no—
162#930—61no—
163C4×#67—31no—
164C4×#67—61no—
165C22×C3⋊C8—31no—
166C2×D24—31no—
167C2×D24—31no—
168C2×D24—31no—
169C2×D24—61no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173#898—61no—
174#898—61no—
175#895—31no—
176#895—31no—
177#895—31no—
178#895—31no—
179#895—61no—
180#895—61no—
181#895—61no—
182#894—61no—
183#894—61no—
184#894—61no—
185#893—31no—
186#893—31no—
187#893—61no—
188#892—31no—
189#892—31no—
190D3×C4⋊C4C2×D311yescharacteristic
191#890C2×D311yescharacteristic, complemented
192#884—61no—
193#883—61no—
194#882—61no—
195#882—61no—
196D3×C22⋊C4—61no—
197D3×C22⋊C4—61no—
198C4×D12—31no—
199C4×D12—31no—
200C4×D12—31no—
201C3×#107—31no—
202C3×#107—31no—
203C3×#103—21no—
204C3×#103—31no—
205C3×#103—31no—
206C3×#103C2×D311yescharacteristic, complemented
207C3×#103C2×D311yescharacteristic, complemented
208C3×#102—31no—
209C3×#102—31no—
210C3×C22⋊C8—31no—
211C3×C4×C8—31no—
212#835C2×D311yescharacteristic, complemented
213#835C2×D311yescharacteristic, complemented
214#832—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821C2×D311yescharacteristic
219(C2×D3)⋊C8—31no—
220(C2×D3)⋊C8—31no—
221(C2×D3)⋊C8—61no—
222(C2×D3)⋊C8C2×D311yescharacteristic
223#818C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225C8×Dic3C2×D311yescharacteristic, complemented
226#809—31no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#809—31no—
232#809—61no—
233#809C2×D311yescharacteristic
234#808—31no—
235#808—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C22×C3⋊D3—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3C2×D411yescharacteristic
241C22×C3×D3—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C32×Q8—21no—
247C32×Q8—21no—
248C2×C32×C4—21no—
249C2×C32×C4—21no—
250C2×C32×C4C2411yescharacteristic
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—42no—
256C4⋊(C3⋊D3)—81no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—21no—
259C4×C3⋊D3—21no—
260C4×C3⋊D3—42no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C2×C3×Dic3C2×D411yescharacteristic
267C3×D12—21no—
268C3×D12—21no—
269C3×C4×D3—21no—
270C3×C4×D3—21no—
271C3×C4×D3—81no—
272#626—22no—
273#626—42no—
274#626—42no—
275#626—81no—
276#624—81no—
277#624—81no—
278C32×C8—21no—
279C3⋊(C3⋊C8)—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—21no—
282#553—91no—
283#546—91no—
284#488—31no—
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—91no—
295#416—91no—
296C2×#102—91no—
297C23×D3—61no—
298C23×D3—61no—
299C2×C3×Q8—21no—
300C2×C3×Q8C22×D311yescharacteristic
301C2×C3×Q8C22×D311yescharacteristic
302C2×C3×D4—31no—
303C22×C3×C4—31no—
304C22×C3×C4—61no—
305C2×#67—31no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309#239—62no—
310#239—62no—
311#239—122no—
312#239—121no—
313#239—121no—
314#239—122no—
315D3×D4—62no—
316D3×D4—121no—
317C2×D12—31no—
318C2×D12—31no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—62no—
325C2×D12—61no—
326C2×D12—61no—
327C2×D12—61no—
328C2×D12—61no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—61no—
332C2×D12—121no—
333C2×D12—121no—
334C2×D12—121no—
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—21no—
337C2×C4×D3—31no—
338C2×C4×D3—31no—
339C2×C4×D3—61no—
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×D3—121no—
347C2×C4×D3C22×D311yescharacteristic
348C2×C3×C8—21no—
349C2×C3×C8—31no—
350C2×C3×C8—31no—
351C2×C3×C8C22×D311yescharacteristic
352C2×C3×C8C22×D311yescharacteristic
353C3×C4⋊C4—21no—
354C3×C4⋊C4—31no—
355C3×C4⋊C4—31no—
356C3×C4⋊C4—31no—
357C3×C4⋊C4—61no—
358C3×C4⋊C4—61no—
359C3×C4⋊C4—61no—
360C3×C4⋊C4—61no—
361C3×C4⋊C4C22×D311yescharacteristic
362C3×C4⋊C4C22×D311yescharacteristic
363C3×C22⋊C4—61no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367#217—31no—
368#217—61no—
369#215—121no—
370#215—121no—
371#215—122no—
372#213—121no—
373(C2×D3)⋊C4—21no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—31no—
377(C2×D3)⋊C4—31no—
378(C2×D3)⋊C4—31no—
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—61no—
388(C2×D3)⋊C4—61no—
389(C2×D3)⋊C4—61no—
390(C2×D3)⋊C4—121no—
391C4⋊Dic3—21no—
392C4⋊Dic3—31no—
393C4⋊Dic3C22×D311yescharacteristic
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396Dic3⋊C4—21no—
397Dic3⋊C4—21no—
398Dic3⋊C4—21no—
399Dic3⋊C4—31no—
400C4×Dic3—61no—
401C4×Dic3—61no—
402C4×Dic3C22×D311yescharacteristic
403C2×C3⋊C8—31no—
404C2×C3⋊C8—31no—
405C2×C3⋊C8—61no—
406C2×C3⋊C8—121no—
407C2×C3⋊C8C22×D311yescharacteristic
408C2×C3⋊C8C22×D311yescharacteristic
409D24—62no—
410D24—62no—
411D24—122no—
412D24—121no—
413D3×C8—121no—
414D3×C8—121no—
415D3×C8—121no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—22no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—21no—
420C2×C3⋊D3—21no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—41no—
423C2×C3⋊D3—41no—
424C2×C3⋊D3—41no—
425C2×C3⋊D3—41no—
426C2×C3×D3—21no—
427C2×C3×D3—21no—
428C2×C3×D3—41no—
429C2×C3×D3—41no—
430C2×C3×D3—41no—
431C2×C3×D3#13512yes—
432D32—84no—
433C32×C4—41no—
434C32×C4—41no—
435C32×C4C2×#4111yescharacteristic
436C32×C4H(5,𝔽2)11yescharacteristic
437C3⋊Dic3—21no—
438C3×Dic3—21no—
439C3×Dic3—21no—
440C3×Dic3—21no—
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—91no—
450C22×C8—91no—
451#126—181no—
452#125—31no—
453#124—31no—
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—91no—
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—91no—
474#103—31no—
475#103—31no—
476#103D3211yescharacteristic, complemented
477#102—31no—
478#102—31no—
479#102—91no—
480#102—91no—
481#102—91no—
482#102—91no—
483#102—91no—
484C22⋊C8—31no—
485C22⋊C8—91no—
486C4×C8—31no—
487C23×C3—31no—
488C23×C3—61no—
489C22×D3—21no—
490C22×D3—31no—
491C22×D3—31no—
492C22×D3—61no—
493C22×D3—61no—
494C22×D3—61no—
495C22×D3—61no—
496C22×D3—61no—
497C22×D3—121no—
498C22×D3—121no—
499C22×D3—122no—
500C22×D3—122no—
501C22×D3—122no—
502C22×D3—122no—
503C22×D3—241no—
504C22×D3—241no—
505C22×D3D3×D411yescharacteristic
506C3×Q8—22no—
507C3×Q8—21no—
508C3×Q8—21no—
509C3×Q8—21no—
510C3×Q8—21no—
511C3×Q8—41no—
512C3×D4—61no—
513C3×D4—61no—
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—241no—
530C2×C3×C4C23×D311yescharacteristic
531C2×C3×C4C23×D311yescharacteristic
532#67—62no—
533#67—122no—
534#67—122no—
535#67—241no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—31no—
540C2×Dic3—31no—
541C2×Dic3—61no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—21no—
546D12—21no—
547D12—32no—
548D12—32no—
549D12—62no—
550D12—62no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—121no—
558D12—121no—
559D12—121no—
560D12—122no—
561D12—122no—
562D12—124no—
563D12—122no—
564D12—122no—
565D12—241no—
566D12—241no—
567D12—242no—
568D12—241no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—61no—
572C4×D3—61no—
573C4×D3—61no—
574C4×D3—61no—
575C4×D3—81no—
576C4×D3—121no—
577C4×D3—121no—
578C4×D3—122no—
579C4×D3—122no—
580C4×D3—124no—
581C4×D3—241no—
582C4×D3—241no—
583C4×D3—241no—
584C4×D3—241no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—41no—
588C3×C8—61no—
589C3×C8—61no—
590C3⋊C8—21no—
591C3⋊C8—21no—
592C3⋊C8—61no—
593C3⋊C8—61no—
594C3⋊C8—121no—
595C2×C32#54611yescharacteristic
596C2×C32C2×#13511yescharacteristic
597C2×C32#57611yescharacteristic
598C3⋊D3—42no—
599C3⋊D3—41no—
600C3⋊D3—81no—
601C3×D3—22no—
602C3×D3—81no—
603C24—181no—
604#41—182no—
605#41—361no—
606C2×Q8C2×D3211yescharacteristic
607C2×D4—31no—
608C2×D4—91no—
609C2×D4—91no—
610C2×D4—91no—
611C2×D4—181no—
612C2×D4—181no—
613C2×D4—181no—
614C2×D4—182no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—361no—
618C22×C4—31no—
619C22×C4—61no—
620C22×C4—91no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4—181no—
624SD16—361no—
625D8—182no—
626D8—361no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—91no—
630C2×C8—361no—
631C2×C8—361no—
632C2×C8C2×D3211yescharacteristic
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—61no—
637C4⋊C4—61no—
638C4⋊C4—61no—
639C4⋊C4—61no—
640C4⋊C4—91no—
641C4⋊C4C2×D3211yescharacteristic
642C22⋊C4—61no—
643C22⋊C4—61no—
644C22⋊C4—61no—
645C22⋊C4—91no—
646C22⋊C4—91no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—181no—
655C22×C3—21no—
656C22×C3—32no—
657C22×C3—61no—
658C22×C3—61no—
659C22×C3—121no—
660C22×C3—121no—
661C22×C3—121no—
662C22×C3C2×D3×D411yescharacteristic
663C22×C3C2×D3×D411yescharacteristic
664C2×D3—21no—
665C2×D3—21no—
666C2×D3—41no—
667C2×D3—41no—
668C2×D3—41no—
669C2×D3—61no—
670C2×D3—62no—
671C2×D3—61no—
672C2×D3—62no—
673C2×D3—61no—
674C2×D3—61no—
675C2×D3—61no—
676C2×D3—61no—
677C2×D3—122no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
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—241no—
692C2×D3—241no—
693C2×D3—241no—
694C2×D3—241no—
695C2×D3—241no—
696C2×D3—244no—
697C2×D3—244no—
698C2×D3#91912yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—42no—
702C3×C4—41no—
703C3×C4—41no—
704C3×C4—41no—
705C3×C4—41no—
706C3×C4—61no—
707C3×C4—61no—
708C3×C4—61no—
709C3×C4—81no—
710C3×C4—121no—
711C3×C4—121no—
712C3×C4—121no—
713C3×C4D3×#4111yescharacteristic
714C3×C4D3×#4111yescharacteristic
715C3×C4#100911yescharacteristic
716C3×C4#100911yescharacteristic
717Dic3—21no—
718Dic3—21no—
719Dic3—21no—
720Dic3—41no—
721Dic3—41no—
722Dic3—41no—
723Dic3—61no—
724Dic3—61no—
725Dic3—121no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—31no—
728C23—61no—
729C23—91no—
730C23—181no—
731C23—181no—
732C23—362no—
733C23—362no—
734C23—721no—
735Q8—21no—
736Q8—21no—
737D4—61no—
738D4—61no—
739D4—92no—
740D4—182no—
741D4—181no—
742D4—181no—
743D4—181no—
744D4—362no—
745D4—362no—
746D4—362no—
747D4—721no—
748D4—721no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—31no—
752C2×C4—31no—
753C2×C4—31no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—91no—
760C2×C4—181no—
761C2×C4—181no—
762C2×C4—241no—
763C2×C4—362no—
764C2×C4—721no—
765C2×C4—721no—
766C2×C4C22×D3211yescharacteristic
767C8—21no—
768C8—61no—
769C8—61no—
770C8—181no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—62no—
775C2×C3—241no—
776C2×C3#565411yescharacteristic
777C2×C3#567611yescharacteristic
778C2×C3C2×#91911yescharacteristic
779C2×C3D3×#13511yescharacteristic
780C2×C3#576911yescharacteristic
781C2×C3#577411yescharacteristic
782D3—22no—
783D3—81no—
784D3—121no—
785D3—122no—
786D3—121no—
787D3—122no—
788D3—241no—
789D3—242no—
790D3—241no—
791D3—241no—
792D3—481no—
793C22—32no—
794C22—61no—
795C22—61no—
796C22—121no—
797C22—121no—
798C22—121no—
799C22—181no—
800C22—181no—
801C22—181no—
802C22—182no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—361no—
808C22—724no—
809C22D32×D411yescharacteristic
810C4—41no—
811C4—41no—
812C4—61no—
813C4—61no—
814C4—61no—
815C4—121no—
816C4—121no—
817C4—121no—
818C4—181no—
819C4#6430811yescharacteristic
820C4#6431211yescharacteristic
821C3—21no—
822C3#8148511yescharacteristic, complemented
823C3#8165311yescharacteristic, complemented
824C2—62no—
825C2—241no—
826C2—361no—
827C2—362no—
828C2—721no—
829C2#1059428211yescharacteristic
830C2#1059475511yescharacteristic
831C2D3×#91911yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#103C22
socleC22×C32C22×D4
hypercenter#103D32
hypocenterC32#3297
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
1. #10595431C2semidirect
2. #10594562C2semidirect
3. #10592509C2semidirect
4. C3×#4811C2semidirect
5. C3×#4800C2semidirect
6. #10591585C2semidirect
7. #10591568C2semidirect
8. #10591560C2semidirect
9. #10590947C2semidirect
10. #10590763C2semidirect
11. #10590721C2semidirect
12. #10590651C2semidirect
13. D3×#809C2semidirect
14. #10590509C2semidirect
15. #10590468C2semidirect
20. C2×#3755C22semidirect
22. #64104C22semidirect
26. C3×#890C22semidirect
37. #63894C22semidirect
39. #63849C22semidirect
42. C2×#3710C22semidirect
44. C32×#103C22semidirect
45. #63647C22semidirect
47. C3×#835C22semidirect
48. C3×#835C22semidirect
51. C3×#818C22semidirect
52. C3×C8×Dic3C22semidirect
54. C3×#807C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
59. #63564C22semidirect
76. #4811D3semidirect
83. #4800D3semidirect
191. #890C2×D3semidirect
206. C3×#103C2×D3semidirect
207. C3×#103C2×D3semidirect
212. #835C2×D3semidirect
213. #835C2×D3semidirect
223. #818C2×D3semidirect
225. C8×Dic3C2×D3semidirect
236. #807C2×D3semidirect
476. #103D32semidirect
726. C32#3297semidirect
822. C3#81485semidirect
823. C3#81653semidirect

Maximal subgroups

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

subgroupindex
#105954312
#105945622
#105925092
C3×#48112
C3×#48002
#105915852
#105915682
#105915602
#105909472
#105907632
#105907212
#105906512
D3×#8092
#105905092
#105904682
#816533
#814853