Finite Group Databasebeta

← #11887378

Subgroups — #11887378

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#10595078C211yesmaximal, characteristic, complemented
2#10594946C211yesmaximal, characteristic, complemented
3#10592433C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#67⋊C8C211yesmaximal, characteristic, complemented
6#10591164C211yesmaximal, characteristic, complemented
7#10591105C211yesmaximal, characteristic, complemented
8#10590947C211yesmaximal, characteristic, complemented
9D3×#821C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590860C211yesmaximal, characteristic, complemented
12#10590830C211yesmaximal, characteristic, complemented
13#10590769C211yesmaximal, characteristic, complemented
14#10590763C211yesmaximal, characteristic, complemented
15#10590684C211yesmaximal, characteristic, complemented
16#81382—31nomaximal
17#79441—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20#64139C2211yescharacteristic, complemented
21C2×#3745C2211yescharacteristic
22C2×#3744C2211yescharacteristic, complemented
23C3×#930C2211yescharacteristic
24C3×C4×#67C2211yescharacteristic
25C3×#926C2211yescharacteristic, complemented
26C22×C3×C3⋊C8C2211yescharacteristic, complemented
27C2×C3×D3×C8C2211yescharacteristic
28#63983—21no—
29#63975—21no—
30#63971—21no—
31#63958—21no—
32#63921—21no—
33#63909C2211yescharacteristic
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic, complemented
36D3×C4⋊Dic3C2211yescharacteristic
37#63880—21no—
38#63869C2211yescharacteristic, complemented
39#63868—21no—
40#63860C2211yescharacteristic
41#63857C2211yescharacteristic
42#63853—21no—
43C2×#3714C2211yescharacteristic
44C32×C22⋊C8C2211yescharacteristic, complemented
45#63648C2211yescharacteristic
46#63643C2211yescharacteristic, complemented
47C3×#821C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic
50C3×#818C2211yescharacteristic, complemented
51C3×#817C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×C8×Dic3C2211yescharacteristic, complemented
54#63575C2211yescharacteristic, complemented
55#63567C2211yescharacteristic, complemented
56#63567C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63563C2211yescharacteristic
61#5612—31no—
62#5565—31no—
63#5550—31no—
64#5530—31no—
65C3×#482—31no—
66C3×C8×D4—31no—
67#5115—31no—
68#5114—31no—
69#5113—31no—
70C2×#821—31no—
71#5038—31no—
72#5002—31no—
73#4884—31no—
74#4872—31no—
75#4871—31no—
76#4864—31no—
77#4847—31no—
78#4844—31no—
79#4787—31no—
80#4773—31no—
81D3×#102—31no—
82#4768—31no—
83#4737D311yescharacteristic, complemented
84#4734—31no—
85#4734—31no—
86#4734—61no—
87#4732—31no—
88#67⋊C8D311yescharacteristic, complemented
89#4722—31no—
90#4697—31no—
91C4×D24—31no—
92C22×D32—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×#638—21no—
96#3828—22no—
97#3828—41no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4×C3⋊D3—21no—
101C2×#634C2311yescharacteristic
102C2×C3×#67—21no—
103C2×C3×#67D411yescharacteristic
104C2×C3×D12C2311yescharacteristic
105C2×C3×C4×D3C2311yescharacteristic
106C2×#626—21no—
107C2×#626—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111D3×D12—22no—
112D3×D12—41no—
113C2×C32×C8C2311yescharacteristic
114C2×C32×C8C2311yescharacteristic
115#3752—21no—
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117#3745—22no—
118#3744—41no—
119C3×#217—21no—
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×(C2×D3)⋊C4D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×Dic3⋊C4D411yescharacteristic
127C3×C4×Dic3—21no—
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—
135Dic3⋊Dic3—21no—
136Dic3⋊Dic3—21no—
137#3722—21no—
138#3722—21no—
139#3722—21no—
140(C2×D3)⋊Dic3—21no—
141(C2×D3)⋊Dic3—21no—
142(C2×D3)⋊Dic3—21no—
143#3714—41no—
144#3297—91noSylow
145C2×D3×D4—31no—
146C2×#235—31no—
147C2×#235—31no—
148C2×#235—61no—
149C22×D12—31no—
150C22×C3×C8—31no—
151C22×C3×C8—31no—
152C3×#121—31no—
153C3×C4×D4—31no—
154C3×#117—31no—
155#939—61no—
156#938—61no—
157#937—61no—
158#937—61no—
159#936—31no—
160C2×#213—31no—
161#930—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#930C2×D311yescharacteristic
166C4×#67C2×D311yescharacteristic
167#926C2×D311yescharacteristic, complemented
168C2×C4⋊Dic3—31no—
169#924—31no—
170C22×C3⋊C8C2×D311yescharacteristic, complemented
171C2×D24—31no—
172C2×D24—31no—
173C2×D24—31no—
174C2×D24—61no—
175C2×#204—31no—
176C2×#204—31no—
177C2×#204—61no—
178C2×D3×C8C2×D311yescharacteristic
179#898—61no—
180#897—31no—
181#895—31no—
182#894—61no—
183#893—31no—
184#893—31no—
185D3×C4⋊C4—31no—
186#890—31no—
187#884—61no—
188#884—61no—
189#883—61no—
190#883—61no—
191#883—61no—
192#67⋊C4—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#876—61no—
196#875—31no—
197C4×D12—31no—
198C4×D12—31no—
199C4×D12—61no—
200#870—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×C4⋊C8—31no—
204C3×#102—31no—
205C3×#102—31no—
206C3×C22⋊C8—21no—
207C3×C22⋊C8—31no—
208C3×C22⋊C8C2×D311yescharacteristic, complemented
209C3×C22⋊C8C2×D311yescharacteristic, complemented
210C3×C4×C8—31no—
211#832—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—31no—
218#821—61no—
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic
221(C2×D3)⋊C8C2×D311yescharacteristic
222#818—31no—
223#818C2×D311yescharacteristic, complemented
224#817C2×D311yescharacteristic, complemented
225#816—31no—
226#816—31no—
227#816—31no—
228#816—31no—
229#816—61no—
230Dic3⋊C8C2×D311yescharacteristic, complemented
231C8×Dic3C2×D311yescharacteristic, complemented
232#810—31no—
233#810—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—21no—
242C22×C3×D3C2×D411yescharacteristic
243C2×D32—42no—
244C2×D32—42no—
245C2×D32—81no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2×D411yescharacteristic
249C2×C32×C4C2411yescharacteristic
250#638—42no—
251#638—81no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C4⋊(C3⋊D3)—21no—
255C4⋊(C3⋊D3)—21no—
256C4⋊(C3⋊D3)—21no—
257C4⋊(C3⋊D3)#4112yes—
258C4×C3⋊D3—42no—
259#634—21no—
260#634—21no—
261C3×#67—22no—
262C3×#67—81no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3C2×D411yescharacteristic
267C2×C3×Dic3C2×D411yescharacteristic
268C2×C3×Dic3C2×D411yescharacteristic
269C3×D12—21no—
270C3×D12—21no—
271C3×C4×D3—21no—
272C3×C4×D3—21no—
273#626—42no—
274#626—42no—
275#624—81no—
276#624—81no—
277D3×Dic3—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—91no—
286#482—31no—
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—
299C2×C3×D4—31no—
300C2×C3×D4—31no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4C22×D311yescharacteristic
305C22×C3×C4C22×D311yescharacteristic
306C2×#67—21no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C2×#67—121no—
314C2×#67—121no—
315C2×#67D1211yescharacteristic
316C22×Dic3—61no—
317D3×D4—62no—
318D3×D4—121no—
319#235—62no—
320#235—62no—
321#235—122no—
322#235—121no—
323#235—121no—
324#235—122no—
325C2×D12—31no—
326C2×D12—31no—
327C2×D12—31no—
328C2×D12—31no—
329C2×D12—61no—
330C2×D12—61no—
331C2×D12—62no—
332C2×D12—61no—
333C2×D12—61no—
334C2×D12—121no—
335C2×D12C22×D311yescharacteristic
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C4×D3—61no—
341C2×C4×D3—61no—
342C2×C4×D3—61no—
343C2×C4×D3—121no—
344C2×C4×D3C22×D311yescharacteristic
345C2×Dic6—31no—
346C2×Dic6—31no—
347C2×Dic6—61no—
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×C22⋊C4—31no—
363C3×C22⋊C4—31no—
364C3×C22⋊C4—61no—
365C3×C22⋊C4—61no—
366C3×C42—31no—
367C3×C42—61no—
368#217—21no—
369#217—61no—
370#217—61no—
371#217—61no—
372#217D1211yescharacteristic
373#213—121no—
374(C2×D3)⋊C4—21no—
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—121no—
387(C2×D3)⋊C4D1211yescharacteristic
388C4⋊Dic3—31no—
389C4⋊Dic3—31no—
390C4⋊Dic3—61no—
391C4⋊Dic3—61no—
392C4⋊Dic3—61no—
393C4⋊Dic3—61no—
394C4⋊Dic3C22×D311yescharacteristic
395C4⋊Dic3C22×D311yescharacteristic
396C4⋊Dic3C22×D311yescharacteristic
397Dic3⋊C4—61no—
398Dic3⋊C4—61no—
399Dic3⋊C4—61no—
400Dic3⋊C4—61no—
401Dic3⋊C4—61no—
402Dic3⋊C4D1211yescharacteristic
403C4×Dic3—21no—
404C4×Dic3C22×D311yescharacteristic
405C2×C3⋊C8—41no—
406C2×C3⋊C8C22×D311yescharacteristic
407C2×C3⋊C8C22×D311yescharacteristic
408D24—62no—
409D24—62no—
410D24—122no—
411D24—121no—
412#204—121no—
413#204—121no—
414#204—122no—
415D3×C8—41no—
416C22×C32—21no—
417C22×C32—21no—
418C22×C32—21no—
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—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—21no—
434C32×C4C2×#4111yescharacteristic
435C32×C4H(5,𝔽2)11yescharacteristic
436C3⋊Dic3—41no—
437C3⋊Dic3—41no—
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—31no—
450C22×C8—31no—
451#126—181no—
452#125—91no—
453#124—91no—
454#123—181no—
455#123—181no—
456C22⋊Q8—91no—
457#121—31no—
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—31no—
468C2×C4⋊C4—91no—
469C2×C22⋊C4—181no—
470#107—31no—
471#107—91no—
472#106—31no—
473C4⋊C8—31no—
474#103—91no—
475#103—91no—
476#103—91no—
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⋊C8D3211yescharacteristic, complemented
486C4×C8—31no—
487C23×C3—21no—
488C23×C3—31no—
489C23×C3—61no—
490C23×C3C2×D1211yescharacteristic
491C23×C3D3×D411yescharacteristic
492C22×D3—21no—
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×D3C2×D1211yescharacteristic
506C3×D4—62no—
507C3×D4—61no—
508C3×D4—61no—
509C3×D4—241no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—31no—
517C2×C3×C4—31no—
518C2×C3×C4—31no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4C2×D1211yescharacteristic
527C2×C3×C4D3×D411yescharacteristic
528C2×C3×C4C23×D311yescharacteristic
529C2×C3×C4C23×D311yescharacteristic
530#67—22no—
531#67—81no—
532#67—122no—
533#67—122no—
534#67—122no—
535#67—122no—
536#67—124no—
537#67—241no—
538#67—241no—
539#67—242no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—61no—
544C2×Dic3—61no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—121no—
548C2×Dic3—121no—
549C2×Dic3—241no—
550C2×Dic3C2×D1211yescharacteristic
551C2×Dic3C2×D1211yescharacteristic
552C2×Dic3C2×D1211yescharacteristic
553D12—21no—
554D12—21no—
555D12—32no—
556D12—32no—
557D12—62no—
558D12—61no—
559D12—61no—
560D12—61no—
561D12—61no—
562D12—61no—
563D12—61no—
564D12—121no—
565D12—121no—
566D12—121no—
567D12—122no—
568D12—122no—
569C4×D3—21no—
570C4×D3—21no—
571C4×D3—122no—
572C4×D3—122no—
573C4×D3—124no—
574C4×D3—241no—
575C4×D3—241no—
576C4×D3—241no—
577C4×D3—241no—
578C4×D3—241no—
579Dic6—62no—
580Dic6—61no—
581Dic6—61no—
582Dic6—61no—
583Dic6—61no—
584Dic6—121no—
585C3×C8—21no—
586C3×C8—21no—
587C3×C8—21no—
588C3×C8—21no—
589C3×C8—41no—
590C3×C8—41no—
591C3×C8—61no—
592C3×C8—61no—
593C3⋊C8—21no—
594C3⋊C8—21no—
595C2×C32—41no—
596C2×C32#54611yescharacteristic
597C2×C32C2×#13511yescharacteristic
598C2×C32#57611yescharacteristic
599C3⋊D3—42no—
600C3⋊D3—81no—
601C3×D3—22no—
602C3×D3—81no—
603C24—181no—
604#41—182no—
605#41—361no—
606C2×Q8—91no—
607C2×D4—31no—
608C2×D4—31no—
609C2×D4—61no—
610C2×D4—91no—
611C2×D4—91no—
612C2×D4—181no—
613C2×D4—182no—
614C2×D4—181no—
615C2×D4—181no—
616C2×D4—181no—
617C2×D4—361no—
618C22×C4—31no—
619C22×C4—181no—
620C22×C4—181no—
621C22×C4—181no—
622C22×C4—181no—
623C22×C4C2×D3211yescharacteristic
624SD16—361no—
625D8—182no—
626D8—361no—
627C2×C8—31no—
628C2×C8—31no—
629C2×C8—121no—
630C2×C8—121no—
631C2×C8C2×D3211yescharacteristic
632C2×C8C2×D3211yescharacteristic
633C4⋊C4—31no—
634C4⋊C4—31no—
635C4⋊C4—31no—
636C4⋊C4—31no—
637C4⋊C4—91no—
638C4⋊C4—181no—
639C4⋊C4—181no—
640C4⋊C4—181no—
641C4⋊C4—181no—
642C22⋊C4—31no—
643C22⋊C4—31no—
644C22⋊C4—61no—
645C22⋊C4—61no—
646C22⋊C4—181no—
647C22⋊C4—181no—
648C22⋊C4—181no—
649C22⋊C4—181no—
650C22⋊C4—181no—
651C22⋊C4—181no—
652C22⋊C4—181no—
653C42—31no—
654C42—61no—
655C22×C3—21no—
656C22×C3—21no—
657C22×C3—21no—
658C22×C3—21no—
659C22×C3—21no—
660C22×C3—21no—
661C22×C3—21no—
662C22×C3—32no—
663C22×C3—41no—
664C22×C3—41no—
665C22×C3—41no—
666C22×C3—61no—
667C22×C3—61no—
668C22×C3—121no—
669C22×C3—121no—
670C22×C3—121no—
671C22×C3C22×D1211yescharacteristic
672C22×C3C2×D3×D411yescharacteristic
673C2×D3—21no—
674C2×D3—21no—
675C2×D3—41no—
676C2×D3—41no—
677C2×D3—41no—
678C2×D3—62no—
679C2×D3—62no—
680C2×D3—122no—
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#90412yes—
699C3×C4—21no—
700C3×C4—21no—
701C3×C4—21no—
702C3×C4—21no—
703C3×C4—41no—
704C3×C4—61no—
705C3×C4—61no—
706C3×C4—61no—
707C3×C4—121no—
708C3×C4—121no—
709C3×C4—121no—
710C3×C4#100411yescharacteristic
711C3×C4D3×#4111yescharacteristic
712C3×C4D3×#4111yescharacteristic
713C3×C4#100911yescharacteristic
714Dic3—21no—
715Dic3—21no—
716Dic3—21no—
717Dic3—41no—
718Dic3—41no—
719Dic3—41no—
720Dic3—122no—
721Dic3—121no—
722Dic3—121no—
723Dic3—121no—
724Dic3—121no—
725Dic3—241no—
726C32#329711yescharacteristic, complemented, Sylow
727C23—31no—
728C23—61no—
729C23—181no—
730C23—181no—
731C23—362no—
732C23—362no—
733C23—721no—
734C23D3×D1211yescharacteristic
735Q8—181no—
736Q8—181no—
737D4—62no—
738D4—61no—
739D4—61no—
740D4—92no—
741D4—181no—
742D4—181no—
743D4—181no—
744D4—241no—
745D4—362no—
746D4—362no—
747D4—362no—
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—181no—
760C2×C4—181no—
761C2×C4—362no—
762C2×C4—721no—
763C2×C4—721no—
764C2×C4—721no—
765C2×C4D3×D1211yescharacteristic
766C2×C4C22×D3211yescharacteristic
767C8—21no—
768C8—21no—
769C8—61no—
770C8—61no—
771C2×C3—21no—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—41no—
775C2×C3—41no—
776C2×C3—62no—
777C2×C3—81no—
778C2×C3—241no—
779C2×C3#555411yescharacteristic
780C2×C3#565411yescharacteristic
781C2×C3C2×#90411yescharacteristic
782C2×C3#575211yescharacteristic
783C2×C3D3×#13511yescharacteristic
784C2×C3#577411yescharacteristic
785D3—22no—
786D3—81no—
787D3—122no—
788D3—122no—
789D3—242no—
790D3—241no—
791D3—241no—
792D3—481no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—32no—
797C22—61no—
798C22—61no—
799C22—121no—
800C22—121no—
801C22—121no—
802C22—182no—
803C22—361no—
804C22—361no—
805C22—361no—
806C22—361no—
807C22—361no—
808C22—724no—
809C22C2×D3×D1211yescharacteristic
810C4—21no—
811C4—61no—
812C4—61no—
813C4—61no—
814C4—121no—
815C4—121no—
816C4—121no—
817C4—361no—
818C4—361no—
819C4#6431211yescharacteristic
820C4#6431411yescharacteristic
821C3—21no—
822C3#7944111yescharacteristic, complemented
823C3#8138211yescharacteristic, complemented
824C2—41no—
825C2—62no—
826C2—241no—
827C2—362no—
828C2—721no—
829C2#1059429311yescharacteristic
830C2D3×#90411yescharacteristic
831C2#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. #10595078C2semidirect
2. #10594946C2semidirect
3. #10592433C2semidirect
4. C3×#4737C2semidirect
5. C3×#67⋊C8C2semidirect
6. #10591164C2semidirect
7. #10591105C2semidirect
8. #10590947C2semidirect
9. D3×#821C2semidirect
10. #10590863C2semidirect
11. #10590860C2semidirect
12. #10590830C2semidirect
13. #10590769C2semidirect
14. #10590763C2semidirect
15. #10590684C2semidirect
20. #64139C22semidirect
22. C2×#3744C22semidirect
25. C3×#926C22semidirect
26. C22×C3×C3⋊C8C22semidirect
35. #63894C22semidirect
38. #63869C22semidirect
44. C32×C22⋊C8C22semidirect
46. #63643C22semidirect
50. C3×#818C22semidirect
51. C3×#817C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×C8×Dic3C22semidirect
54. #63575C22semidirect
55. #63567C22semidirect
56. #63567C22semidirect
59. #63564C22semidirect
83. #4737D3semidirect
88. #67⋊C8D3semidirect
167. #926C2×D3semidirect
170. C22×C3⋊C8C2×D3semidirect
208. C3×C22⋊C8C2×D3semidirect
209. C3×C22⋊C8C2×D3semidirect
223. #818C2×D3semidirect
224. #817C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. C8×Dic3C2×D3semidirect
485. C22⋊C8D32semidirect
726. C32#3297semidirect
822. C3#79441semidirect
823. C3#81382semidirect

Maximal subgroups

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

subgroupindex
#105950782
#105949462
#105924332
C3×#47372
C3×#67⋊C82
#105911642
#105911052
#105909472
D3×#8212
#105908632
#105908602
#105908302
#105907692
#105907632
#105906842
#813823
#794413