Finite Group Databasebeta

← #11872726

Subgroups — #11872726

Order 1152.

884 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595041C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3#10592419C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#4732C211yesmaximal, characteristic, complemented
6#10591160C211yesmaximal, characteristic, complemented
7#10591090C211yesmaximal, characteristic, complemented
8#10590782C211yesmaximal, characteristic, complemented
9#10590781C211yesmaximal, characteristic, complemented
10#10590780C211yesmaximal, characteristic, complemented
11#10590777C211yesmaximal, characteristic, complemented
12#10590749C211yesmaximal, characteristic, complemented
13#10590749C211yesmaximal, characteristic, complemented
14#10590741C211yesmaximal, characteristic, complemented
15#10590740C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#79993—31nomaximal
18C22×C3×D12C2211yescharacteristic
19#64135C2211yescharacteristic
20C3×#930C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25#63970—21no—
26#63970—21no—
27D3×#217—21no—
28D3×#217—21no—
29#63914C2211yescharacteristic, complemented
30#63898C2211yescharacteristic
31#63898C2211yescharacteristic
32#63898C2211yescharacteristic
33#63898C2211yescharacteristic
34#63898C2211yescharacteristic, complemented
35#63898C2211yescharacteristic, complemented
36Dic3×D12—21no—
37Dic3×D12—21no—
38#63891—21no—
39#63891—21no—
40#63872C2211yescharacteristic, complemented
41C2×#3713C2211yescharacteristic
42C2×#3713C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63657C2211yescharacteristic
45#63642C2211yescharacteristic, complemented
46#63641C2211yescharacteristic, complemented
47#63641C2211yescharacteristic, complemented
48C8×C3⋊Dic3C2211yescharacteristic, complemented
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#821C2211yescharacteristic, complemented
52C3×#821C2211yescharacteristic, complemented
53C3×#818C2211yescharacteristic, complemented
54C3×#817C2211yescharacteristic, complemented
55#63576C2211yescharacteristic, complemented
56#63574C2211yescharacteristic, complemented
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63562C2211yescharacteristic, complemented
60#63562C2211yescharacteristic, complemented
61#5798—31no—
62#5619—31no—
63#5619—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#447—31no—
67#5217—31no—
68#5152—31no—
69#5150—31no—
70#5150—31no—
71Dic3×D8—31no—
72#5036—31no—
73#5035—31no—
74#5003—31no—
75#4891—31no—
76#4872—31no—
77#4871—31no—
78#4869—31no—
79#4786—31no—
80#4786—31no—
81#4785—31no—
82#4785—31no—
83#4766—31no—
84#4763—31no—
85#4756—31no—
86#4756—31no—
87#4737D311yescharacteristic, complemented
88#4732D311yescharacteristic, complemented
89#4720—31no—
90#4720—31no—
91#4720—61no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×C3×#67—21no—
95C2×C3×#67—21no—
96C2×C3×D12—21no—
97C2×C3×D12—22no—
98C2×C3×D12—22no—
99C2×C3×D12C2311yescharacteristic
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×#625—21no—
104C2×#625—21no—
105C2×D3×Dic3—21no—
106C2×D3×Dic3—21no—
107C2×D3×Dic3—21no—
108C2×D3×Dic3—21no—
109C2×D3×Dic3—21no—
110C2×D3×Dic3—21no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3757D411yescharacteristic
114#3757D411yescharacteristic
115C4⋊(C3⋊Dic3)D411yescharacteristic
116C4⋊(C3⋊Dic3)D411yescharacteristic
117C4×C3⋊Dic3C2311yescharacteristic
118C4×C3⋊Dic3C2311yescharacteristic
119C2×C3⋊(C3⋊C8)C2311yescharacteristic
120C2×C3⋊(C3⋊C8)C2311yescharacteristic
121C3×#217—21no—
122C3×(C2×D3)⋊C4—21no—
123C3×(C2×D3)⋊C4—21no—
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4⋊Dic3C2311yescharacteristic
127C3×C4⋊Dic3C2311yescharacteristic
128C3×C4×Dic3—21no—
129C3×D24—22no—
130C3×D24—22no—
131Dic3⋊Dic3—21no—
132Dic3⋊Dic3—21no—
133(C2×D3)⋊Dic3—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137(C2×D3)⋊Dic3—21no—
138(C2×D3)⋊Dic3—21no—
139#3713—22no—
140#3713—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#121—31no—
147C3×#121—31no—
148C3×#117—31no—
149C2×#217—61no—
150C2×#217—61no—
151#940—31no—
152#940—31no—
153#939—61no—
154#939—61no—
155#938—61no—
156#938—61no—
157D4×Dic3—31no—
158D4×Dic3—31no—
159D4×Dic3—31no—
160D4×Dic3—31no—
161D4×Dic3—31no—
162D4×Dic3—31no—
163D4×Dic3—61no—
164D4×Dic3—61no—
165C2×#213—31no—
166C2×#213—31no—
167C2×#213—31no—
168C2×#213—31no—
169#930C2×D311yescharacteristic
170#930C2×D311yescharacteristic
171#926—31no—
172#926—31no—
173#926—61no—
174#926C2×D311yescharacteristic
175C2×D24C2×D311yescharacteristic
176C2×D24C2×D311yescharacteristic
177#893—31no—
178#893—31no—
179#893—31no—
180#893—31no—
181#893—31no—
182#893—31no—
183#890—31no—
184#890—31no—
185#886—61no—
186#886—61no—
187#883—61no—
188#883—61no—
189D3×C22⋊C4—61no—
190D3×C22⋊C4—61no—
191C4×D12—61no—
192C4×D12—61no—
193C3×#107—31no—
194C3×#106—31no—
195C3×#102—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×#102—31no—
199C3×C22⋊C8—21no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202#832—31no—
203#832—31no—
204#832—31no—
205#832—31no—
206#830—31no—
207#830—31no—
208#830—61no—
209#821C2×D311yescharacteristic
210#821C2×D311yescharacteristic
211#821C2×D311yescharacteristic, complemented
212#821C2×D311yescharacteristic, complemented
213#818C2×D311yescharacteristic, complemented
214#817C2×D311yescharacteristic, complemented
215#815—31no—
216#815—31no—
217#815—61no—
218Dic3⋊C8—31no—
219Dic3⋊C8—31no—
220Dic3⋊C8—31no—
221Dic3⋊C8—31no—
222Dic3⋊C8—61no—
223Dic3⋊C8—61no—
224C8×Dic3—31no—
225C8×Dic3—31no—
226C8×Dic3—61no—
227#809—31no—
228#809—31no—
229#809—31no—
230#809—31no—
231#808—31no—
232#808—31no—
233#807—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—24no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—81no—
242C22×C3×D3—81no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247C2×C3⋊Dic3C2×D411yescharacteristic
248C2×C3⋊Dic3C2×D411yescharacteristic
249C2×C3⋊Dic3C2×D411yescharacteristic
250C2×C3⋊Dic3C2×D411yescharacteristic
251C3×#67—81no—
252C3×#67—81no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C3×D12—24no—
258C3×D12—21no—
259C3×D12—21no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×D12#4112yes—
266#625—81no—
267#625—81no—
268D3×Dic3—81no—
269D3×Dic3—81no—
270D3×Dic3—81no—
271D3×Dic3—81no—
272D3×Dic3—81no—
273D3×Dic3—81no—
274C32×C8—21no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3⋊(C3⋊C8)—21no—
278#540—91no—
279#518—91no—
280#482—31no—
281#482—91no—
282#478—91no—
283#478—91no—
284#459—91no—
285#459—91no—
286#447—31no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—91no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—31no—
299C2×C3×D4—62no—
300C2×C3×D4—62no—
301C2×C3×D4—61no—
302C2×C3×D4—61no—
303C2×C3×D4—61no—
304C22×C3×C4—21no—
305C22×C3×C4C22×D311yescharacteristic
306C22×C3×C4C22×D311yescharacteristic
307C2×#67—21no—
308C2×#67—21no—
309C2×#67—61no—
310C2×#67—61no—
311C2×#67—61no—
312C2×#67—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3—61no—
318C22×Dic3—61no—
319C2×D12—21no—
320C2×D12—22no—
321C2×D12—22no—
322C2×D12C22×D311yescharacteristic
323C2×D12C22×D311yescharacteristic
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×C4×D3—61no—
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C3×D8—62no—
333C3×D8—62no—
334C2×C3×C8—21no—
335C2×C3×C8—21no—
336C2×C3×C8C22×D311yescharacteristic
337C2×C3×C8C22×D311yescharacteristic
338C2×C3×C8C22×D311yescharacteristic
339C2×C3×C8C22×D311yescharacteristic
340C3×C4⋊C4—31no—
341C3×C4⋊C4—31no—
342C3×C4⋊C4—31no—
343C3×C4⋊C4—31no—
344C3×C22⋊C4—61no—
345C3×C22⋊C4—61no—
346C3×C22⋊C4—61no—
347C3×C42—61no—
348#217—21no—
349#217—31no—
350#217—31no—
351#217—31no—
352#217—31no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—61no—
360#217—61no—
361#213—62no—
362#213—62no—
363#213—62no—
364#213—62no—
365(C2×D3)⋊C4—21no—
366(C2×D3)⋊C4—21no—
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—
373C4⋊Dic3—31no—
374C4⋊Dic3—31no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—61no—
378C4⋊Dic3—61no—
379C4⋊Dic3—61no—
380C4⋊Dic3—61no—
381C4⋊Dic3C22×D311yescharacteristic
382C4⋊Dic3C22×D311yescharacteristic
383C4⋊Dic3C22×D311yescharacteristic
384C4⋊Dic3C22×D311yescharacteristic
385Dic3⋊C4—61no—
386Dic3⋊C4—61no—
387C4×Dic3—21no—
388C4×Dic3—31no—
389C4×Dic3—31no—
390C4×Dic3—31no—
391C4×Dic3—31no—
392C4×Dic3—61no—
393C4×Dic3—61no—
394C2×C3⋊C8—31no—
395C2×C3⋊C8—31no—
396C2×C3⋊C8—31no—
397C2×C3⋊C8—31no—
398C2×C3⋊C8—61no—
399C2×C3⋊C8—61no—
400D24—22no—
401D24—22no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32C22×D411yescharacteristic
406C2×C3×D3—22no—
407C2×C3×D3—22no—
408C2×C3×D3—41no—
409C2×C3×D3—41no—
410C2×C3×D3—41no—
411C2×C3×D3—41no—
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—41no—
415C2×C3×D3—41no—
416C2×C3×D3—41no—
417C2×C3×D3—41no—
418C2×C3×D3—84no—
419C32×C4—21no—
420C32×C4C2×#4111yescharacteristic
421C32×C4C2×#4111yescharacteristic
422C3⋊Dic3—21no—
423C3⋊Dic3—21no—
424C3⋊Dic3—21no—
425C3⋊Dic3—21no—
426C3×Dic3—41no—
427C3×Dic3—41no—
428C3×Dic3—41no—
429C3×Dic3—41no—
430C22×D4—31no—
431C2×D8—31no—
432C2×D8—31no—
433C2×D8—91no—
434C2×D8—91no—
435#127—91no—
436#125—91no—
437#123—181no—
438#123—181no—
439#121—31no—
440#121—31no—
441#121—181no—
442#121—181no—
443C4×D4—91no—
444C4×D4—91no—
445C4×D4—91no—
446C4×D4—91no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—181no—
450C4×D4—181no—
451#117—31no—
452#117—91no—
453C2×C22⋊C4—181no—
454C2×C22⋊C4—181no—
455#107—31no—
456#107—91no—
457#106—31no—
458#106—91no—
459C4⋊C8—91no—
460C4⋊C8—91no—
461#102—31no—
462#102—31no—
463#102—31no—
464#102—31no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—91no—
470C22⋊C8D3211yescharacteristic
471#97—91no—
472C4×C8—91no—
473C23×C3—21no—
474C23×C3—64no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—61no—
479C23×C3—241no—
480C23×C3—241no—
481C23×C3D3×D411yescharacteristic
482C23×C3D3×D411yescharacteristic
483C22×D3—21no—
484C22×D3—21no—
485C22×D3—24no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—81no—
489C22×D3—81no—
490C3×D4—32no—
491C3×D4—32no—
492C3×D4—64no—
493C3×D4—61no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—61no—
499C3×D4—241no—
500C3×D4—241no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—41no—
508C2×C3×C4—41no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4D3×D411yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516C2×C3×C4C23×D311yescharacteristic
517#67—81no—
518#67—81no—
519#67—241no—
520#67—241no—
521#67—241no—
522#67—241no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—31no—
528C2×Dic3—31no—
529C2×Dic3—31no—
530C2×Dic3—31no—
531C2×Dic3—31no—
532C2×Dic3—31no—
533C2×Dic3—31no—
534C2×Dic3—31no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—241no—
540C2×Dic3—241no—
541C2×Dic3—241no—
542C2×Dic3—241no—
543C2×Dic3—241no—
544C2×Dic3—241no—
545D12—24no—
546D12—21no—
547D12—21no—
548D12—21no—
549D12—21no—
550D12—21no—
551D12—21no—
552D12#23712yes—
553D12#23712yes—
554C4×D3—241no—
555C4×D3—241no—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C3×C8—21no—
561C3×C8—21no—
562C3×C8—21no—
563C3×C8—21no—
564C3×C8—41no—
565C3×C8—41no—
566C3⋊C8—61no—
567C3⋊C8—61no—
568C3⋊C8—61no—
569C3⋊C8—61no—
570C3⋊C8—121no—
571C3⋊C8—121no—
572C2×C32—41no—
573C2×C32#52511yescharacteristic
574C2×C32#57611yescharacteristic
575C2×C32#57611yescharacteristic
576C3×D3—42no—
577C3×D3—42no—
578C3×D3—81no—
579C3×D3—81no—
580C24—61no—
581C2×D4—31no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—62no—
586C2×D4—62no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—61no—
590C2×D4—181no—
591C2×D4—181no—
592C22×C4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4C2×D3211yescharacteristic
599D8—62no—
600D8—62no—
601D8—182no—
602D8—182no—
603C2×C8—91no—
604C2×C8—91no—
605C2×C8C2×D3211yescharacteristic
606C2×C8C2×D3211yescharacteristic
607C4⋊C4—31no—
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—181no—
614C4⋊C4—181no—
615C22⋊C4—61no—
616C22⋊C4—61no—
617C22⋊C4—61no—
618C22⋊C4—91no—
619C22⋊C4—91no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C42—61no—
627C42—91no—
628C42—91no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—41no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—62no—
640C22×C3—62no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3—244no—
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C2×D3—22no—
655C2×D3—22no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C2×D3—41no—
665C2×D3—41no—
666C2×D3—84no—
667C3×C4—21no—
668C3×C4—21no—
669C3×C4—21no—
670C3×C4—21no—
671C3×C4—41no—
672C3×C4—121no—
673C3×C4—121no—
674C3×C4—121no—
675C3×C4—121no—
676C3×C4C2×#23711yescharacteristic
677C3×C4C2×#23711yescharacteristic
678C3×C4D3×#4111yescharacteristic
679C3×C4D3×#4111yescharacteristic
680Dic3—41no—
681Dic3—41no—
682Dic3—41no—
683Dic3—41no—
684Dic3—61no—
685Dic3—61no—
686Dic3—61no—
687Dic3—61no—
688Dic3—61no—
689Dic3—61no—
690Dic3—61no—
691Dic3—61no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696C32#312211yescharacteristic, complemented, Sylow
697C23—64no—
698C23—61no—
699C23—61no—
700C23—61no—
701C23—61no—
702C23—241no—
703C23—241no—
704C23#380211yescharacteristic
705D4—32no—
706D4—32no—
707D4—64no—
708D4—61no—
709D4—61no—
710D4—61no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—241no—
715D4—241no—
716D4—721no—
717D4—721no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—91no—
725C2×C4—91no—
726C2×C4—91no—
727C2×C4—91no—
728C2×C4—721no—
729C2×C4—721no—
730C2×C4—721no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4#380211yescharacteristic
735C2×C4C22×D3211yescharacteristic
736C8—21no—
737C8—21no—
738C8—181no—
739C8—181no—
740C2×C3—21no—
741C2×C3—21no—
742C2×C3—21no—
743C2×C3—41no—
744C2×C3—41no—
745C2×C3—81no—
746C2×C3—122no—
747C2×C3—122no—
748C2×C3—241no—
749C2×C3—241no—
750C2×C3#558611yescharacteristic
751C2×C3#565611yescharacteristic
752C2×C3#575711yescharacteristic
753C2×C3#576911yescharacteristic
754C2×C3#577411yescharacteristic
755C2×C3#577411yescharacteristic
756D3—42no—
757D3—42no—
758D3—81no—
759D3—81no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—62no—
764C22—62no—
765C22—121no—
766C22—121no—
767C22—121no—
768C22—121no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—244no—
776C22C2×#380211yescharacteristic
777C4—21no—
778C4—121no—
779C4—121no—
780C4—121no—
781C4—121no—
782C4—181no—
783C4—181no—
784C4—181no—
785C4—181no—
786C4D3×#23711yescharacteristic
787C4D3×#23711yescharacteristic
788C3—21no—
789C3#7999311yescharacteristic, complemented
790C3#8135411yescharacteristic, complemented
791C2—41no—
792C2—122no—
793C2—122no—
794C2—241no—
795C2—241no—
796C2#1059408211yescharacteristic
797C2#1059468711yescharacteristic
798C2#1059472011yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊C8C22
socleC22×C32C22×D4
hypercenterC22⋊C8D32
hypocenterC32#3122
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. #10595041C2semidirect
2. #10594982C2semidirect
3. #10592419C2semidirect
4. C3×#4737C2semidirect
5. C3×#4732C2semidirect
6. #10591160C2semidirect
7. #10591090C2semidirect
8. #10590782C2semidirect
9. #10590781C2semidirect
10. #10590780C2semidirect
11. #10590777C2semidirect
12. #10590749C2semidirect
13. #10590749C2semidirect
14. #10590741C2semidirect
15. #10590740C2semidirect
29. #63914C22semidirect
34. #63898C22semidirect
35. #63898C22semidirect
40. #63872C22semidirect
45. #63642C22semidirect
46. #63641C22semidirect
47. #63641C22semidirect
48. C8×C3⋊Dic3C22semidirect
51. C3×#821C22semidirect
52. C3×#821C22semidirect
53. C3×#818C22semidirect
54. C3×#817C22semidirect
55. #63576C22semidirect
56. #63574C22semidirect
59. #63562C22semidirect
60. #63562C22semidirect
87. #4737D3semidirect
88. #4732D3semidirect
211. #821C2×D3semidirect
212. #821C2×D3semidirect
213. #818C2×D3semidirect
214. #817C2×D3semidirect
696. C32#3122semidirect
789. C3#79993semidirect
790. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105950412
#105949822
#105924192
C3×#47372
C3×#47322
#105911602
#105910902
#105907822
#105907812
#105907802
#105907772
#105907492
#105907412
#105907402
#813543
#799933