Finite Group Databasebeta

← #11872725

Subgroups — #11872725

Order 1152.

935 conjugacy classes of subgroups.

The subgroup lattice has 823 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594996C211yesmaximal, characteristic, complemented
2#10594985C211yesmaximal, characteristic, complemented
3#10592431C211yesmaximal, characteristic, complemented
4C3×#4737C211yesmaximal, characteristic, complemented
5C3×#4720C211yesmaximal, characteristic, complemented
6#10591168C211yesmaximal, characteristic, complemented
7#10591136C211yesmaximal, characteristic, complemented
8#10590774C211yesmaximal, characteristic, complemented
9#10590769C211yesmaximal, characteristic, complemented
10#10590768C211yesmaximal, characteristic, complemented
11#10590765C211yesmaximal, characteristic, complemented
12#10590765C211yesmaximal, characteristic, complemented
13#10590763C211yesmaximal, characteristic, complemented
14#10590746C211yesmaximal, characteristic, complemented
15#10590745C211yesmaximal, characteristic, complemented
16#81354—31nomaximal
17#79386—31nomaximal
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19#64139C2211yescharacteristic
20C2×#3745C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#926C2211yescharacteristic
24C3×#926C2211yescharacteristic
25#63974—21no—
26#63974—21no—
27#63971—21no—
28#63958—21no—
29#63911C2211yescharacteristic, complemented
30#63894—21no—
31#63894—21no—
32#63894C2211yescharacteristic
33#63894C2211yescharacteristic
34#63894C2211yescharacteristic
35#63894C2211yescharacteristic
36#63894C2211yescharacteristic, complemented
37Dic3×D12C2211yescharacteristic, complemented
38#63890—21no—
39#63869C2211yescharacteristic, complemented
40#63854—21no—
41C2×#3714C2211yescharacteristic
42C2×#3714C2211yescharacteristic
43C32×C22⋊C8C2211yescharacteristic
44#63648C2211yescharacteristic
45#63648C2211yescharacteristic
46C3×#830C2211yescharacteristic
47C3×#821C2211yescharacteristic, complemented
48C3×#821C2211yescharacteristic, complemented
49C3×#818C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#815C2211yescharacteristic, complemented
52C3×Dic3⋊C8C2211yescharacteristic, complemented
53C3×Dic3⋊C8C2211yescharacteristic, complemented
54C3×C8×Dic3C2211yescharacteristic, complemented
55#63575C2211yescharacteristic, complemented
56#63573C2211yescharacteristic, complemented
57#63564C2211yescharacteristic
58#63564C2211yescharacteristic
59#63564C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#5619—31no—
62#5535—31no—
63#5521—31no—
64#5521—31no—
65C3×#482—31no—
66C3×#433—31no—
67#5036—31no—
68#5003—31no—
69#4891—31no—
70#4872—31no—
71#4871—31no—
72#4869—31no—
73#4847—31no—
74#4847—31no—
75#4843—31no—
76#4843—31no—
77#4786—31no—
78#4786—31no—
79#4785—31no—
80#4756—31no—
81#4737—31no—
82#4737D311yescharacteristic, complemented
83#4732—31no—
84#4732—31no—
85#4732—31no—
86#4732—61no—
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)—21no—
96C2×C4⋊(C3⋊D3)—22no—
97C2×C4⋊(C3⋊D3)—22no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C3×#67—21no—
102C2×C3×D12C2311yescharacteristic
103C2×#626—21no—
104C2×#626—21no—
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108C2×#624—21no—
109C2×#624—21no—
110C2×D3×Dic3—21no—
111C2×C32×C8C2311yescharacteristic
112C2×C32×C8C2311yescharacteristic
113#3752—21no—
114C4⋊(C3⋊Dic3)C2311yescharacteristic
115#3745—22no—
116#3745—22no—
117C3×#217—21no—
118C3×#217D411yescharacteristic
119C3×#217D411yescharacteristic
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3D411yescharacteristic
122C3×C4⋊Dic3D411yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×C4⋊Dic3C2311yescharacteristic
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132Dic3⋊Dic3—21no—
133#3722—21no—
134#3722—21no—
135#3722—21no—
136#3722—21no—
137#3722—21no—
138(C2×D3)⋊Dic3—21no—
139#3714—22no—
140#3714—22no—
141#3122—91noSylow
142C22×D12—31no—
143C22×D12—31no—
144C22×D12—61no—
145C3×#121—31no—
146C3×#117—31no—
147C3×#117—31no—
148#940—31no—
149#939—61no—
150#938—61no—
151D4×Dic3—31no—
152C2×#213—31no—
153C2×#213—31no—
154#930—31no—
155#930—31no—
156#930—61no—
157#930C2×D311yescharacteristic
158#926C2×D311yescharacteristic
159#926C2×D311yescharacteristic
160C2×D24—31no—
161C2×D24—31no—
162C2×D24—31no—
163C2×D24—31no—
164C2×D24—31no—
165C2×D24—31no—
166C2×D24—61no—
167C2×D24—61no—
168#894—61no—
169#894—61no—
170#893—31no—
171#893—31no—
172#893—31no—
173#893—31no—
174#893—31no—
175#893—61no—
176#893—61no—
177#890—31no—
178#886—61no—
179#884—61no—
180#884—61no—
181#883—61no—
182D3×C22⋊C4—61no—
183D3×C22⋊C4—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—
193C4×D12—61no—
194C4×D12—61no—
195#870—31no—
196C3×#107—31no—
197C3×#106—31no—
198C3×C4⋊C8—31no—
199C3×C4⋊C8—31no—
200C3×#102—31no—
201C3×#102—31no—
202C3×C22⋊C8—21no—
203C3×C22⋊C8—31no—
204C3×C22⋊C8C2×D311yescharacteristic
205C3×C22⋊C8C2×D311yescharacteristic
206C3×#97—31no—
207C3×C4×C8—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, complemented
220#821C2×D311yescharacteristic, complemented
221#818—31no—
222#818C2×D311yescharacteristic, complemented
223#817—31no—
224#817C2×D311yescharacteristic, complemented
225#815C2×D311yescharacteristic, complemented
226Dic3⋊C8C2×D311yescharacteristic, complemented
227Dic3⋊C8C2×D311yescharacteristic, complemented
228C8×Dic3C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#808—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—81no—
241C22×C3⋊D3—81no—
242C22×C3×D3—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4C2×D411yescharacteristic
246C2×C32×C4C2411yescharacteristic
247#638—81no—
248C2×C3⋊Dic3—21no—
249C4⋊(C3⋊D3)—24no—
250C4⋊(C3⋊D3)—21no—
251C4⋊(C3⋊D3)—21no—
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)—21no—
254C4⋊(C3⋊D3)#4112yes—
255C4⋊(C3⋊D3)#4112yes—
256C3×#67—81no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3C2×D411yescharacteristic
261C2×C3×Dic3C2×D411yescharacteristic
262C2×C3×Dic3C2×D411yescharacteristic
263C2×C3×Dic3C2×D411yescharacteristic
264C3×D12—21no—
265C3×D12—21no—
266#626—81no—
267#626—81no—
268#624—81no—
269#624—81no—
270#624—81no—
271#624—81no—
272#624—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—91no—
287#447—91no—
288#442—91no—
289#442—91no—
290C4×D8—91no—
291C4×D8—91no—
292#433—31no—
293C23×D3—61no—
294C23×D3—61no—
295C23×D3—121no—
296C2×C3×D4—31no—
297C2×C3×D4—61no—
298C22×C3×C4—21no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C2×#67—21no—
302C2×#67—61no—
303C2×#67—61no—
304C2×#67—61no—
305C2×#67—61no—
306C2×#67—121no—
307C22×Dic3—61no—
308C2×D12—31no—
309C2×D12—31no—
310C2×D12—31no—
311C2×D12—31no—
312C2×D12—31no—
313C2×D12—31no—
314C2×D12—61no—
315C2×D12—61no—
316C2×D12—61no—
317C2×D12—62no—
318C2×D12—62no—
319C2×D12—62no—
320C2×D12—62no—
321C2×D12—61no—
322C2×D12—61no—
323C2×D12—61no—
324C2×D12—61no—
325C2×D12—122no—
326C2×D12—122no—
327C2×D12—121no—
328C2×D12C22×D311yescharacteristic
329C2×C4×D3—61no—
330C2×C4×D3—61no—
331C2×C4×D3—61no—
332C2×C4×D3—61no—
333C2×C4×D3—61no—
334C2×C4×D3—61no—
335C2×C4×D3—61no—
336C2×C4×D3—61no—
337C2×C4×D3—61no—
338C2×C4×D3—61no—
339C2×C4×D3—61no—
340C2×C3×C8—21no—
341C2×C3×C8—21no—
342C2×C3×C8—31no—
343C2×C3×C8—31no—
344C2×C3×C8C22×D311yescharacteristic
345C2×C3×C8C22×D311yescharacteristic
346C2×C3×C8C22×D311yescharacteristic
347C2×C3×C8C22×D311yescharacteristic
348C3×C4⋊C4—31no—
349C3×C4⋊C4—31no—
350C3×C4⋊C4—31no—
351C3×C4⋊C4—31no—
352C3×C4⋊C4—31no—
353C3×C22⋊C4—31no—
354C3×C22⋊C4—31no—
355C3×C22⋊C4—61no—
356C3×C22⋊C4—61no—
357C3×C42—31no—
358C3×C42—31no—
359C3×C42—61no—
360#217—21no—
361#217—61no—
362#217D1211yescharacteristic
363#217D1211yescharacteristic
364#213—62no—
365#213—62no—
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—
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—121no—
381C4⋊Dic3—31no—
382C4⋊Dic3—31no—
383C4⋊Dic3—61no—
384C4⋊Dic3—61no—
385C4⋊Dic3D1211yescharacteristic
386C4⋊Dic3D1211yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388C4⋊Dic3C22×D311yescharacteristic
389C4⋊Dic3C22×D311yescharacteristic
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393C4×Dic3—21no—
394C4×Dic3C22×D311yescharacteristic
395C4×Dic3C22×D311yescharacteristic
396C2×C3⋊C8C22×D311yescharacteristic
397C2×C3⋊C8C22×D311yescharacteristic
398D24—62no—
399D24—62no—
400D24—62no—
401D24—62no—
402D24—62no—
403D24—62no—
404D24—122no—
405D24—122no—
406C22×C32—21no—
407C22×C32—21no—
408C22×C32—21no—
409C22×C32C22×D411yescharacteristic
410C2×C3⋊D3—22no—
411C2×C3⋊D3—22no—
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—41no—
419C2×C3⋊D3—84no—
420C2×C3×D3—41no—
421C2×C3×D3—41no—
422C2×C3×D3—41no—
423C32×C4—21no—
424C32×C4C2×#4111yescharacteristic
425C32×C4C2×#4111yescharacteristic
426C3⋊Dic3—41no—
427C3×Dic3—21no—
428C3×Dic3—21no—
429C3×Dic3—21no—
430C3×Dic3—21no—
431C3×Dic3—41no—
432C3×Dic3—41no—
433C3×Dic3—41no—
434C22×D4—91no—
435C2×D8—91no—
436C2×D8—91no—
437C2×D8—91no—
438C2×D8—91no—
439#127—91no—
440#125—91no—
441#123—181no—
442#123—181no—
443#121—31no—
444#121—91no—
445#121—181no—
446#121—181no—
447C4×D4—91no—
448C4×D4—91no—
449C4×D4—91no—
450C4×D4—91no—
451C4×D4—91no—
452C4×D4—91no—
453C4×D4—181no—
454C4×D4—181no—
455#117—31no—
456#117—31no—
457C2×C22⋊C4—181no—
458C2×C22⋊C4—181no—
459#107—31no—
460#107—91no—
461#106—31no—
462#106—91no—
463C4⋊C8—31no—
464C4⋊C8—31no—
465#102—31no—
466#102—31no—
467#102—91no—
468#102—91no—
469#102—91no—
470#102—91no—
471#102—91no—
472#102—91no—
473C22⋊C8—31no—
474C22⋊C8D3211yescharacteristic
475#97—31no—
476C4×C8—31no—
477C23×C3—21no—
478C23×C3—61no—
479C23×C3C2×D1211yescharacteristic
480C23×C3D3×D411yescharacteristic
481C22×D3—21no—
482C22×D3—61no—
483C22×D3—61no—
484C22×D3—61no—
485C22×D3—61no—
486C22×D3—64no—
487C22×D3—64no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—121no—
491C22×D3—121no—
492C22×D3—124no—
493C22×D3—121no—
494C22×D3—241no—
495C22×D3—241no—
496C22×D3—241no—
497C22×D3—241no—
498C22×D3—242no—
499C22×D3—242no—
500C3×D4—61no—
501C3×D4—61no—
502C3×D4—241no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—31no—
510C2×C3×C4—31no—
511C2×C3×C4—31no—
512C2×C3×C4—31no—
513C2×C3×C4—41no—
514C2×C3×C4—41no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4C2×D1211yescharacteristic
519C2×C3×C4D3×D411yescharacteristic
520C2×C3×C4C23×D311yescharacteristic
521C2×C3×C4C23×D311yescharacteristic
522#67—81no—
523#67—241no—
524#67—241no—
525#67—241no—
526#67—241no—
527#67—242no—
528C2×Dic3—21no—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—61no—
532C2×Dic3—61no—
533C2×Dic3—121no—
534C2×Dic3—241no—
535C2×Dic3C2×D1211yescharacteristic
536C2×Dic3C2×D1211yescharacteristic
537C2×Dic3C2×D1211yescharacteristic
538C2×Dic3C2×D1211yescharacteristic
539D12—21no—
540D12—21no—
541D12—32no—
542D12—32no—
543D12—32no—
544D12—32no—
545D12—62no—
546D12—62no—
547D12—64no—
548D12—64no—
549D12—61no—
550D12—61no—
551D12—61no—
552D12—61no—
553D12—61no—
554D12—61no—
555D12—61no—
556D12—61no—
557D12—121no—
558D12—121no—
559D12—121no—
560D12—121no—
561D12—124no—
562D12—241no—
563D12—241no—
564C4×D3—241no—
565C4×D3—241no—
566C4×D3—241no—
567C4×D3—241no—
568C4×D3—241no—
569C4×D3—241no—
570C4×D3—241no—
571C4×D3—241no—
572C4×D3—241no—
573C4×D3—241no—
574C4×D3—241no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—21no—
578C3×C8—21no—
579C3×C8—41no—
580C3×C8—41no—
581C3×C8—61no—
582C3×C8—61no—
583C3⋊C8—21no—
584C3⋊C8—21no—
585C2×C32—41no—
586C2×C32#52511yescharacteristic
587C2×C32#57611yescharacteristic
588C2×C32#57611yescharacteristic
589C3⋊D3—42no—
590C3⋊D3—42no—
591C3⋊D3—81no—
592C3×D3—81no—
593C24—181no—
594C2×D4—31no—
595C2×D4—61no—
596C2×D4—91no—
597C2×D4—91no—
598C2×D4—91no—
599C2×D4—182no—
600C2×D4—182no—
601C2×D4—181no—
602C2×D4—181no—
603C2×D4—181no—
604C2×D4—181no—
605C22×C4—181no—
606C22×C4—181no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610C22×C4—181no—
611C22×C4C2×D3211yescharacteristic
612D8—182no—
613D8—182no—
614D8—182no—
615D8—182no—
616C2×C8—31no—
617C2×C8—31no—
618C2×C8C2×D3211yescharacteristic
619C2×C8C2×D3211yescharacteristic
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—31no—
623C4⋊C4—31no—
624C4⋊C4—31no—
625C4⋊C4—91no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C22⋊C4—31no—
629C22⋊C4—31no—
630C22⋊C4—61no—
631C22⋊C4—61no—
632C22⋊C4—181no—
633C22⋊C4—181no—
634C22⋊C4—181no—
635C22⋊C4—181no—
636C22⋊C4—181no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C42—31no—
640C42—31no—
641C42—61no—
642C22×C3—22no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—121no—
653C22×C3—121no—
654C22×C3—121no—
655C22×C3C22×D1211yescharacteristic
656C22×C3C2×D3×D411yescharacteristic
657C2×D3—41no—
658C2×D3—41no—
659C2×D3—41no—
660C2×D3—62no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—62no—
664C2×D3—122no—
665C2×D3—122no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—121no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—121no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—241no—
681C2×D3—241no—
682C2×D3—241no—
683C2×D3—241no—
684C2×D3—241no—
685C2×D3—241no—
686C2×D3—241no—
687C2×D3—244no—
688C2×D3—244no—
689C2×D3—248no—
690C3×C4—21no—
691C3×C4—21no—
692C3×C4—21no—
693C3×C4—21no—
694C3×C4—41no—
695C3×C4—61no—
696C3×C4—61no—
697C3×C4—61no—
698C3×C4—61no—
699C3×C4—121no—
700C3×C4—121no—
701C3×C4—121no—
702C3×C4D3×#4111yescharacteristic
703C3×C4D3×#4111yescharacteristic
704C3×C4D3×#4111yescharacteristic
705C3×C4D3×#4111yescharacteristic
706Dic3—21no—
707Dic3—21no—
708Dic3—21no—
709Dic3—21no—
710Dic3—41no—
711Dic3—41no—
712Dic3—41no—
713Dic3—121no—
714Dic3—121no—
715Dic3—241no—
716C32#312211yescharacteristic, complemented, Sylow
717C23—61no—
718C23—184no—
719C23—181no—
720C23—181no—
721C23—181no—
722C23—721no—
723C23—721no—
724C23D3×D1211yescharacteristic
725D4—61no—
726D4—61no—
727D4—92no—
728D4—92no—
729D4—184no—
730D4—181no—
731D4—181no—
732D4—181no—
733D4—181no—
734D4—241no—
735D4—721no—
736D4—721no—
737D4—721no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—31no—
741C2×C4—31no—
742C2×C4—31no—
743C2×C4—31no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—181no—
748C2×C4—721no—
749C2×C4—721no—
750C2×C4—721no—
751C2×C4—721no—
752C2×C4—721no—
753C2×C4—721no—
754C2×C4D3×D1211yescharacteristic
755C2×C4C22×D3211yescharacteristic
756C8—21no—
757C8—21no—
758C8—61no—
759C8—61no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—42no—
764C2×C3—41no—
765C2×C3—41no—
766C2×C3—241no—
767C2×C3#552411yescharacteristic
768C2×C3#565611yescharacteristic
769C2×C3#575211yescharacteristic
770C2×C3#575211yescharacteristic
771C2×C3#576911yescharacteristic
772C2×C3#577411yescharacteristic
773D3—81no—
774D3—122no—
775D3—122no—
776D3—122no—
777D3—122no—
778D3—242no—
779D3—242no—
780D3—241no—
781D3—241no—
782D3—481no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—121no—
787C22—121no—
788C22—121no—
789C22—182no—
790C22—182no—
791C22—361no—
792C22—361no—
793C22—361no—
794C22—361no—
795C22—361no—
796C22—361no—
797C22—361no—
798C22—724no—
799C22C2×D3×D1211yescharacteristic
800C4—21no—
801C4—61no—
802C4—61no—
803C4—61no—
804C4—61no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—361no—
809C4#6431211yescharacteristic
810C4#6431211yescharacteristic
811C3—21no—
812C3#7938611yescharacteristic, complemented
813C3#8135411yescharacteristic, complemented
814C2—41no—
815C2—241no—
816C2—362no—
817C2—362no—
818C2—721no—
819C2#1059407911yescharacteristic
820C2#1059468011yescharacteristic
821C2#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. #10594996C2semidirect
2. #10594985C2semidirect
3. #10592431C2semidirect
4. C3×#4737C2semidirect
5. C3×#4720C2semidirect
6. #10591168C2semidirect
7. #10591136C2semidirect
8. #10590774C2semidirect
9. #10590769C2semidirect
10. #10590768C2semidirect
11. #10590765C2semidirect
12. #10590765C2semidirect
13. #10590763C2semidirect
14. #10590746C2semidirect
15. #10590745C2semidirect
29. #63911C22semidirect
36. #63894C22semidirect
37. Dic3×D12C22semidirect
39. #63869C22semidirect
47. C3×#821C22semidirect
48. C3×#821C22semidirect
49. C3×#818C22semidirect
50. C3×#817C22semidirect
51. C3×#815C22semidirect
52. C3×Dic3⋊C8C22semidirect
53. C3×Dic3⋊C8C22semidirect
54. C3×C8×Dic3C22semidirect
55. #63575C22semidirect
56. #63573C22semidirect
59. #63564C22semidirect
60. #63564C22semidirect
82. #4737D3semidirect
87. #4720D3semidirect
219. #821C2×D3semidirect
220. #821C2×D3semidirect
222. #818C2×D3semidirect
224. #817C2×D3semidirect
225. #815C2×D3semidirect
226. Dic3⋊C8C2×D3semidirect
227. Dic3⋊C8C2×D3semidirect
228. C8×Dic3C2×D3semidirect
716. C32#3122semidirect
812. C3#79386semidirect
813. C3#81354semidirect

Maximal subgroups

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

subgroupindex
#105949962
#105949852
#105924312
C3×#47372
C3×#47202
#105911682
#105911362
#105907742
#105907692
#105907682
#105907652
#105907632
#105907462
#105907452
#813543
#793863