Finite Group Databasebeta

← #11872727

Subgroups — #11872727

Order 1152.

889 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594985C211yesmaximal, characteristic, complemented
2#10594982C211yesmaximal, characteristic, complemented
3#10592436C211yesmaximal, characteristic, complemented
4C3×#4732C211yesmaximal, characteristic, complemented
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591162C211yesmaximal, characteristic, complemented
7#10591093C211yesmaximal, characteristic, complemented
8#10590772C211yesmaximal, characteristic, complemented
9#10590771C211yesmaximal, characteristic, complemented
10#10590767C211yesmaximal, characteristic, complemented
11Dic3×D24C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590753C211yesmaximal, characteristic, complemented
14#10590746C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#79993—31nomaximal
17#79386—31nomaximal
18C22×C3×D12C2211yescharacteristic
19#64139C2211yescharacteristic
20#64135C2211yescharacteristic
21C3×#930C2211yescharacteristic
22C3×#926C2211yescharacteristic
23C2×C3×D24C2211yescharacteristic
24C2×C3×D24C2211yescharacteristic
25#63971—21no—
26D3×#217—21no—
27D3×#217—21no—
28#63958—21no—
29#63911C2211yescharacteristic, complemented
30#63898—21no—
31#63898—21no—
32#63894C2211yescharacteristic, complemented
33Dic3×D12C2211yescharacteristic
34Dic3×D12C2211yescharacteristic
35Dic3×D12C2211yescharacteristic
36Dic3×D12C2211yescharacteristic
37Dic3×D12C2211yescharacteristic, complemented
38#63890—21no—
39#63869C2211yescharacteristic, complemented
40#63854—21no—
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic, complemented
45#63648C2211yescharacteristic, complemented
46#63645C2211yescharacteristic, complemented
47#63644C2211yescharacteristic, complemented
48C3×#830C2211yescharacteristic
49C3×#821C2211yescharacteristic
50C3×#821C2211yescharacteristic
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63563C2211yescharacteristic
58#63563C2211yescharacteristic
59#63563C2211yescharacteristic, complemented
60#63563C2211yescharacteristic, complemented
61#5798—31no—
62#5619—31no—
63#5535—31no—
64#5521—31no—
65C3×#447—31no—
66C3×#433—31no—
67#5217—31no—
68#5152—31no—
69#5150—31no—
70#5150—31no—
71Dic3×D8—31no—
72#5035—31no—
73#4847—31no—
74#4847—31no—
75#4843—31no—
76#4843—31no—
77#4785—31no—
78#4766—31no—
79#4763—31no—
80#4756—31no—
81#4737—31no—
82#4737—31no—
83#4737—31no—
84#4737—61no—
85#4732—31no—
86#4732D311yescharacteristic, complemented
87#4720D311yescharacteristic, complemented
88#4711—31no—
89#4711—31no—
90C4×D24—31no—
91C4×D24—31no—
92C23×C3×D3—21no—
93C22×C32×C4C2311yescharacteristic
94C2×#638—21no—
95C2×C4⋊(C3⋊D3)C2311yescharacteristic
96C2×C3×#67—21no—
97C2×C3×D12—21no—
98C2×C3×D12—22no—
99C2×C3×D12—22no—
100C2×C3×D12C2311yescharacteristic
101C2×C3×D12C2311yescharacteristic
102C2×C3×D12C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—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#3757—21no—
114#3752—21no—
115C4⋊(C3⋊Dic3)C2311yescharacteristic
116C4⋊(C3⋊Dic3)C2311yescharacteristic
117C4⋊(C3⋊Dic3)C2311yescharacteristic
118C4×C3⋊Dic3—21no—
119C3×#217D411yescharacteristic
120C3×#217D411yescharacteristic
121C3×(C2×D3)⋊C4—21no—
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3D411yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4×Dic3C2311yescharacteristic
126C3×C4×Dic3C2311yescharacteristic
127C2×C3×C3⋊C8C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C3×D24—22no—
130C3×D24—22no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—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#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C22×C3×D4—31no—
143C22×D12C2×D311yescharacteristic
144C2×C3×D8—31no—
145C2×C3×D8—31no—
146C3×#121—31no—
147C3×#117—31no—
148C2×#217—61no—
149C2×#217—61no—
150#940—31no—
151#939—61no—
152#938—61no—
153D4×Dic3—31no—
154D4×Dic3—31no—
155D4×Dic3—31no—
156D4×Dic3—31no—
157D4×Dic3—31no—
158D4×Dic3—61no—
159D4×Dic3—61no—
160C2×#213—31no—
161C2×#213—31no—
162#930—31no—
163#930—31no—
164#930—61no—
165#930C2×D311yescharacteristic
166#926—31no—
167#926—31no—
168#926—61no—
169#926C2×D311yescharacteristic
170C2×D24—31no—
171C2×D24—31no—
172C2×D24C2×D311yescharacteristic
173C2×D24C2×D311yescharacteristic
174#894—61no—
175#894—61no—
176#893—31no—
177#893—61no—
178#893—61no—
179#890—31no—
180#886—61no—
181#884—61no—
182#884—61no—
183#883—61no—
184D3×C22⋊C4—61no—
185D3×C22⋊C4—61no—
186#874—31no—
187C4×D12—31no—
188C4×D12—31no—
189C4×D12—31no—
190C4×D12—31no—
191C4×D12—31no—
192C4×D12—31no—
193#870—31no—
194C3×C4⋊C8—31no—
195C3×C4⋊C8—31no—
196C3×#102—31no—
197C3×#102—31no—
198C3×C22⋊C8—21no—
199C3×C22⋊C8—31no—
200C3×C22⋊C8C2×D311yescharacteristic
201C3×C22⋊C8C2×D311yescharacteristic
202C3×#97—31no—
203C3×C4×C8—31no—
204#832—31no—
205#832—31no—
206#832—31no—
207#832—31no—
208#830C2×D311yescharacteristic
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—31no—
214#821—31no—
215#821—31no—
216#821—31no—
217#821—61no—
218#821—61no—
219#821C2×D311yescharacteristic
220#821C2×D311yescharacteristic
221#818—31no—
222#818—31no—
223#818—31no—
224#818—61no—
225#817—31no—
226#817—31no—
227#817—31no—
228#817—61no—
229#815C2×D311yescharacteristic, complemented
230Dic3⋊C8C2×D311yescharacteristic, complemented
231Dic3⋊C8C2×D311yescharacteristic, complemented
232C8×Dic3C2×D311yescharacteristic, complemented
233#808—31no—
234#807—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C22×C3×D3—21no—
239C22×C3×D3—24no—
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
247#638—81no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3C2×D411yescharacteristic
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C3×D12—24no—
260C3×D12—21no—
261C3×D12—21no—
262C3×D12—21no—
263C3×D12—21no—
264C3×D12#4112yes—
265C3×D12#4112yes—
266#626—81no—
267#626—81no—
268#624—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—91no—
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—31no—
293C24×C3—61no—
294C23×D3—21no—
295C2×C3×D4—31no—
296C2×C3×D4—31no—
297C2×C3×D4—31no—
298C2×C3×D4—62no—
299C2×C3×D4—62no—
300C2×C3×D4—61no—
301C2×C3×D4—61no—
302C22×C3×C4—21no—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C2×#67—21no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—61no—
309C2×#67—61no—
310C2×#67—121no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C2×D12—21no—
317C2×D12—22no—
318C2×D12—22no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12C22×D311yescharacteristic
325C2×D12C22×D311yescharacteristic
326C2×D12C22×D311yescharacteristic
327C2×C4×D3—61no—
328C2×C4×D3—61no—
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C3×D8—62no—
335C3×D8—62no—
336C2×C3×C8—21no—
337C2×C3×C8—21no—
338C2×C3×C8—31no—
339C2×C3×C8—31no—
340C2×C3×C8C22×D311yescharacteristic
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C2×C3×C8C22×D311yescharacteristic
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C22⋊C4—31no—
348C3×C22⋊C4—31no—
349C3×C22⋊C4—61no—
350C3×C42—31no—
351C3×C42—31no—
352#217—61no—
353#217—61no—
354#217—61no—
355#217—61no—
356#217—61no—
357#217—61no—
358#217—61no—
359#217—121no—
360#217D1211yescharacteristic
361#217D1211yescharacteristic
362#213—62no—
363#213—62no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—61no—
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—121no—
375C4⋊Dic3—31no—
376C4⋊Dic3—31no—
377C4⋊Dic3—31no—
378C4⋊Dic3—31no—
379C4⋊Dic3—31no—
380C4⋊Dic3—31no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3D1211yescharacteristic
386C4⋊Dic3D1211yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—61no—
389Dic3⋊C4—61no—
390Dic3⋊C4—61no—
391C4×Dic3—61no—
392C4×Dic3—61no—
393C4×Dic3—121no—
394C4×Dic3C22×D311yescharacteristic
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—22no—
399D24—22no—
400D24—62no—
401D24—62no—
402C22×C32—21no—
403C22×C32—21no—
404C22×C32—21no—
405C22×C32C22×D411yescharacteristic
406C2×C3⋊D3—41no—
407C2×C3⋊D3—41no—
408C2×C3⋊D3—41no—
409C2×C3×D3—22no—
410C2×C3×D3—22no—
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—41no—
423C3⋊Dic3—41no—
424C3⋊Dic3—41no—
425C3×Dic3—21no—
426C3×Dic3—21no—
427C3×Dic3—21no—
428C3×Dic3—21no—
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—91no—
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—91no—
456#107—91no—
457#106—91no—
458#106—91no—
459C4⋊C8—31no—
460C4⋊C8—31no—
461#102—31no—
462#102—31no—
463#102—91no—
464#102—91no—
465#102—91no—
466#102—91no—
467#102—91no—
468#102—91no—
469C22⋊C8—31no—
470C22⋊C8D3211yescharacteristic
471#97—31no—
472C4×C8—31no—
473C23×C3—21no—
474C23×C3—64no—
475C23×C3—61no—
476C23×C3—61no—
477C23×C3—61no—
478C23×C3—241no—
479C23×C3—241no—
480C23×C3C2×D1211yescharacteristic
481C23×C3D3×D411yescharacteristic
482C22×D3—21no—
483C22×D3—21no—
484C22×D3—24no—
485C22×D3—21no—
486C22×D3—61no—
487C22×D3—61no—
488C22×D3—81no—
489C22×D3—81no—
490C22×D3—121no—
491C3×D4—32no—
492C3×D4—32no—
493C3×D4—64no—
494C3×D4—61no—
495C3×D4—61no—
496C3×D4—61no—
497C3×D4—61no—
498C3×D4—241no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—31no—
506C2×C3×C4—31no—
507C2×C3×C4—31no—
508C2×C3×C4—31no—
509C2×C3×C4—41no—
510C2×C3×C4—41no—
511C2×C3×C4—61no—
512C2×C3×C4C2×D1211yescharacteristic
513C2×C3×C4D3×D411yescharacteristic
514C2×C3×C4C23×D311yescharacteristic
515C2×C3×C4C23×D311yescharacteristic
516#67—81no—
517#67—241no—
518#67—241no—
519#67—241no—
520#67—241no—
521#67—242no—
522C2×Dic3—21no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—121no—
530C2×Dic3—121no—
531C2×Dic3—121no—
532C2×Dic3—241no—
533C2×Dic3—241no—
534C2×Dic3—241no—
535C2×Dic3—241no—
536C2×Dic3—241no—
537C2×Dic3C2×D1211yescharacteristic
538C2×Dic3C2×D1211yescharacteristic
539C2×Dic3C2×D1211yescharacteristic
540C2×Dic3C2×D1211yescharacteristic
541D12—24no—
542D12—21no—
543D12—21no—
544D12—21no—
545D12—21no—
546D12—61no—
547D12—61no—
548D12—61no—
549D12—61no—
550D12—121no—
551D12—121no—
552D12—241no—
553D12—241no—
554D12#23712yes—
555D12#23712yes—
556C4×D3—241no—
557C4×D3—241no—
558C4×D3—241no—
559C4×D3—241no—
560C4×D3—241no—
561C4×D3—241no—
562C4×D3—241no—
563C3×C8—21no—
564C3×C8—21no—
565C3×C8—21no—
566C3×C8—21no—
567C3×C8—41no—
568C3×C8—41no—
569C3×C8—61no—
570C3×C8—61no—
571C3⋊C8—21no—
572C3⋊C8—21no—
573C2×C32—41no—
574C2×C32#52511yescharacteristic
575C2×C32#57611yescharacteristic
576C2×C32#57611yescharacteristic
577C3⋊D3—81no—
578C3×D3—42no—
579C3×D3—42no—
580C3×D3—81no—
581C24—61no—
582C2×D4—31no—
583C2×D4—31no—
584C2×D4—31no—
585C2×D4—62no—
586C2×D4—62no—
587C2×D4—61no—
588C2×D4—61no—
589C2×D4—91no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—181no—
593C22×C4—181no—
594C22×C4—181no—
595C22×C4—181no—
596C22×C4—181no—
597C22×C4—181no—
598C22×C4—181no—
599C22×C4C2×D3211yescharacteristic
600D8—62no—
601D8—62no—
602D8—182no—
603D8—182no—
604C2×C8—31no—
605C2×C8—31no—
606C2×C8C2×D3211yescharacteristic
607C2×C8C2×D3211yescharacteristic
608C4⋊C4—31no—
609C4⋊C4—31no—
610C4⋊C4—31no—
611C4⋊C4—91no—
612C4⋊C4—91no—
613C4⋊C4—91no—
614C4⋊C4—181no—
615C4⋊C4—181no—
616C22⋊C4—31no—
617C22⋊C4—31no—
618C22⋊C4—61no—
619C22⋊C4—181no—
620C22⋊C4—181no—
621C22⋊C4—181no—
622C22⋊C4—181no—
623C22⋊C4—181no—
624C22⋊C4—181no—
625C22⋊C4—181no—
626C22⋊C4—181no—
627C42—31no—
628C42—31no—
629C42—181no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—41no—
638C22×C3—41no—
639C22×C3—41no—
640C22×C3—62no—
641C22×C3—62no—
642C22×C3—121no—
643C22×C3—121no—
644C22×C3—121no—
645C22×C3—121no—
646C22×C3—121no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—244no—
650C22×C3C22×D1211yescharacteristic
651C22×C3C2×D3×D411yescharacteristic
652C2×D3—22no—
653C2×D3—22no—
654C2×D3—41no—
655C2×D3—41no—
656C2×D3—41no—
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—41no—
661C2×D3—84no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—241no—
669C2×D3—241no—
670C2×D3—241no—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—41no—
676C3×C4—61no—
677C3×C4—61no—
678C3×C4—61no—
679C3×C4—61no—
680C3×C4—121no—
681C3×C4C2×#23711yescharacteristic
682C3×C4C2×#23711yescharacteristic
683C3×C4D3×#4111yescharacteristic
684C3×C4D3×#4111yescharacteristic
685Dic3—21no—
686Dic3—21no—
687Dic3—21no—
688Dic3—21no—
689Dic3—41no—
690Dic3—121no—
691Dic3—121no—
692Dic3—121no—
693Dic3—121no—
694Dic3—121no—
695Dic3—121no—
696Dic3—241no—
697Dic3—241no—
698Dic3—241no—
699C32#312211yescharacteristic, complemented, Sylow
700C23—64no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—181no—
705C23—241no—
706C23—241no—
707C23D3×D1211yescharacteristic
708D4—32no—
709D4—32no—
710D4—64no—
711D4—61no—
712D4—61no—
713D4—61no—
714D4—61no—
715D4—181no—
716D4—181no—
717D4—241no—
718D4—721no—
719D4—721no—
720D4—721no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—31no—
724C2×C4—31no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—61no—
728C2×C4—181no—
729C2×C4—181no—
730C2×C4—181no—
731C2×C4—721no—
732C2×C4—721no—
733C2×C4—721no—
734C2×C4—721no—
735C2×C4—721no—
736C2×C4—721no—
737C2×C4D3×D1211yescharacteristic
738C2×C4C22×D3211yescharacteristic
739C8—21no—
740C8—21no—
741C8—61no—
742C8—61no—
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—41no—
747C2×C3—41no—
748C2×C3—81no—
749C2×C3—122no—
750C2×C3—122no—
751C2×C3—241no—
752C2×C3#552411yescharacteristic
753C2×C3#558611yescharacteristic
754C2×C3#575211yescharacteristic
755C2×C3#575211yescharacteristic
756C2×C3#575711yescharacteristic
757C2×C3#577411yescharacteristic
758D3—42no—
759D3—42no—
760D3—81no—
761D3—241no—
762D3—241no—
763D3—481no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—62no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22—121no—
774C22—121no—
775C22—121no—
776C22—244no—
777C22—361no—
778C22—361no—
779C22—361no—
780C22C2×D3×D1211yescharacteristic
781C4—21no—
782C4—61no—
783C4—61no—
784C4—61no—
785C4—61no—
786C4—121no—
787C4—361no—
788C4—361no—
789C4—361no—
790C4D3×#23711yescharacteristic
791C4D3×#23711yescharacteristic
792C3—21no—
793C3#7938611yescharacteristic, complemented
794C3#7999311yescharacteristic, complemented
795C2—41no—
796C2—122no—
797C2—122no—
798C2—241no—
799C2—721no—
800C2#1059407811yescharacteristic
801C2#1059467811yescharacteristic
802C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
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. #10594985C2semidirect
2. #10594982C2semidirect
3. #10592436C2semidirect
4. C3×#4732C2semidirect
5. C3×#4720C2semidirect
6. #10591162C2semidirect
7. #10591093C2semidirect
8. #10590772C2semidirect
9. #10590771C2semidirect
10. #10590767C2semidirect
11. Dic3×D24C2semidirect
12. #10590753C2semidirect
13. #10590753C2semidirect
14. #10590746C2semidirect
15. #10590745C2semidirect
29. #63911C22semidirect
32. #63894C22semidirect
37. Dic3×D12C22semidirect
39. #63869C22semidirect
44. #63648C22semidirect
45. #63648C22semidirect
46. #63645C22semidirect
47. #63644C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
59. #63563C22semidirect
60. #63563C22semidirect
86. #4732D3semidirect
87. #4720D3semidirect
229. #815C2×D3semidirect
230. Dic3⋊C8C2×D3semidirect
231. Dic3⋊C8C2×D3semidirect
232. C8×Dic3C2×D3semidirect
699. C32#3122semidirect
793. C3#79386semidirect
794. C3#79993semidirect

Maximal subgroups

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

subgroupindex
#105949852
#105949822
#105924362
C3×#47322
C3×#47202
#105911622
#105910932
#105907722
#105907712
#105907672
Dic3×D242
#105907532
#105907462
#105907452
#799933
#793863