Finite Group Databasebeta

← #11887312

Subgroups — #11887312

Order 1152.

910 conjugacy classes of subgroups.

The subgroup lattice has 811 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595243C211yesmaximal, characteristic
2#10594584C211yesmaximal, characteristic, complemented
3#10592475C211yesmaximal, characteristic, complemented
4C3×#4779C211yesmaximal, characteristic, complemented
5C3×#4768C211yesmaximal, characteristic, complemented
6#10591460C211yesmaximal, characteristic, complemented
7#10591441C211yesmaximal, characteristic, complemented
8#10591416C211yesmaximal, characteristic, complemented
9#10590970C211yesmaximal, characteristic, complemented
10#10590758C211yesmaximal, characteristic, complemented
11#10590721C211yesmaximal, characteristic, complemented
12#10590686C211yesmaximal, characteristic, complemented
13#10590610C211yesmaximal, characteristic, complemented
14#10590525C211yesmaximal, characteristic, complemented
15#10590468C211yesmaximal, characteristic, complemented
16#81652—31nomaximal
17#81381—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic
19C2×#3799C2211yescharacteristic
20C2×#3754C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22#64106C2211yescharacteristic
23C3×#938C2211yescharacteristic
24C3×#936C2211yescharacteristic
25C3×#892C2211yescharacteristic, complemented
26C3×#890C2211yescharacteristic, complemented
27#63981—21no—
28#63975—21no—
29#63974—21no—
30#63958—21no—
31C4×#626C2211yescharacteristic
32#63900C2211yescharacteristic
33#63894C2211yescharacteristic
34#63871C2211yescharacteristic
35#63869—21no—
36#63861—21no—
37#63857C2211yescharacteristic, complemented
38#63854—21no—
39#63844C2211yescharacteristic, complemented
40#63836—21no—
41C2×#3719C2211yescharacteristic, complemented
42C2×#3710C2211yescharacteristic
43C2×D3×C3⋊C8C2211yescharacteristic, complemented
44C32×#102C2211yescharacteristic
45#63647C2211yescharacteristic
46#63636C2211yescharacteristic
47C3×#832C2211yescharacteristic
48C3×#832C2211yescharacteristic
49C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
50C3×#817C2211yescharacteristic, complemented
51C3×#816C2211yescharacteristic, complemented
52C3×C8×Dic3C2211yescharacteristic, complemented
53C3×#810C2211yescharacteristic, complemented
54C3×#807C2211yescharacteristic, complemented
55#63574C2211yescharacteristic, complemented
56Dic3⋊(C3⋊C8)C2211yescharacteristic, complemented
57#63567C2211yescharacteristic, complemented
58#63565C2211yescharacteristic, complemented
59#63564C2211yescharacteristic
60#63564C2211yescharacteristic
61#5694—31no—
62#5676—31no—
63#5612—31no—
64#5529—31no—
65C3×#488—31no—
66C3×#482—31no—
67#5066—31no—
68#5054—31no—
69#5041—31no—
70#5002—31no—
71#4891—31no—
72#4887—31no—
73#4862—31no—
74#4852—31no—
75#4813—31no—
76#4808—31no—
77#4805—31no—
78#4804—31no—
79#4779D311yescharacteristic, complemented
80#4778—31no—
81#4776—31no—
82#4776—31no—
83#4776—61no—
84D3×#102—31no—
85D3×#102—31no—
86#4768D311yescharacteristic, complemented
87#4767—31no—
88#4733—31no—
89#67⋊C8—31no—
90C4×#204—31no—
91C8×D12—31no—
92C23×C3⋊D3—21no—
93C2×C32×D4C2311yescharacteristic
94C2×#638—21no—
95D4×C3⋊D3—22no—
96D4×C3⋊D3—41no—
97C2×C4⋊(C3⋊D3)C2311yescharacteristic
98C2×C4×C3⋊D3C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×C4×D3C2311yescharacteristic
102C2×C3×Dic6C2311yescharacteristic
103C2×#626—21no—
104C2×#626D411yescharacteristic
105C2×#624—21no—
106C2×#624—21no—
107C2×#624—21no—
108#3799—22no—
109#3799—41no—
110C2×C32×C8C2311yescharacteristic
111C32×C4⋊C4C2311yescharacteristic
112#3754—41no—
113#3752—21no—
114C4⋊(C3⋊Dic3)—21no—
115C2×C3⋊(C3⋊C8)C2311yescharacteristic
116#3744—22no—
117C3×#217—21no—
118C3×#217—21no—
119C3×#217—21no—
120C3×(C2×D3)⋊C4—21no—
121C3×C4⋊Dic3—21no—
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×C4⋊Dic3C2311yescharacteristic
125C3×Dic3⋊C4—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C2×C3×C3⋊C8C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130#3724—21no—
131#3724—21no—
132Dic3⋊Dic3—21no—
133Dic3⋊Dic3—21no—
134Dic3⋊Dic3D411yescharacteristic
135#3722—21no—
136#3722—21no—
137#3722D411yescharacteristic
138(C2×D3)⋊Dic3—21no—
139(C2×D3)⋊Dic3D411yescharacteristic
140Dic32—21no—
141#3719—41no—
142#3710—41no—
143D3×C3⋊C8—41no—
144#3296—91noSylow
145C2×#239—31no—
146C2×D3×D4—31no—
147C2×D3×D4—31no—
148C2×D3×D4—61no—
149C2×#235—31no—
150C3×#125—31no—
151C3×#124—31no—
152C3×#121—31no—
153C3×#117—31no—
154#946—31no—
155C2×#216—31no—
156#938—61no—
157#938C2×D311yescharacteristic
158#937—61no—
159#936C2×D311yescharacteristic
160C2×#214—31no—
161C2×#214—31no—
162C2×#214—61no—
163C4×#67—31no—
164#924—31no—
165C22×C3⋊C8—31no—
166C2×Dic12—31no—
167C2×#204—31no—
168C2×#204—31no—
169C2×#204—61no—
170C2×D3×C8—31no—
171C2×D3×C8—31no—
172C2×D3×C8—31no—
173#898—61no—
174#897—31no—
175#897—31no—
176#897—31no—
177#897—31no—
178#897—61no—
179#894—61no—
180#893—31no—
181#892—61no—
182#892C2×D311yescharacteristic, complemented
183D3×C4⋊C4—31no—
184D3×C4⋊C4—31no—
185#890—61no—
186#890C2×D311yescharacteristic, complemented
187#887—31no—
188#884—61no—
189#883—61no—
190#883—61no—
191#883—61no—
192#882—61no—
193D3×C22⋊C4—61no—
194D3×C22⋊C4—61no—
195#879—61no—
196C4×D12—31no—
197C4×D12—31no—
198#872—61no—
199#870—61no—
200C4×Dic6—31no—
201C3×#107—31no—
202C3×#106—31no—
203C3×#103—31no—
204C3×#103—31no—
205C3×#102—21no—
206C3×#102—31no—
207C3×#102—31no—
208C3×#102C2×D311yescharacteristic
209C3×#102C2×D311yescharacteristic
210C3×C22⋊C8—31no—
211C3×C4×C8—31no—
212#835—31no—
213#832C2×D311yescharacteristic
214#832C2×D311yescharacteristic
215#821—31no—
216#821—31no—
217(C2×D3)⋊C8—31no—
218(C2×D3)⋊C8—31no—
219(C2×D3)⋊C8—61no—
220(C2×D3)⋊C8C2×D311yescharacteristic, complemented
221#817C2×D311yescharacteristic, complemented
222#816—31no—
223#816C2×D311yescharacteristic, complemented
224Dic3⋊C8—31no—
225C8×Dic3C2×D311yescharacteristic, complemented
226#810—31no—
227#810—31no—
228#810C2×D311yescharacteristic, complemented
229#809—31no—
230#809—31no—
231#809—31no—
232#809—31no—
233#809—61no—
234#808—31no—
235#808—31no—
236#807C2×D311yescharacteristic, complemented
237C4⋊(C3⋊C8)—31no—
238C23×C32—21no—
239C22×C3⋊D3—21no—
240C22×C3⋊D3—42no—
241C22×C3⋊D3—42no—
242C22×C3⋊D3—81no—
243C22×C3⋊D3C2×D411yescharacteristic
244C22×C3×D3C2×D411yescharacteristic
245C32×D4—21no—
246C32×D4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C2411yescharacteristic
249#638—42no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3C2×D411yescharacteristic
252C4⋊(C3⋊D3)—21no—
253C4⋊(C3⋊D3)#4112yes—
254C4×C3⋊D3—21no—
255C4×C3⋊D3—21no—
256#634—21no—
257#634—21no—
258C3×#67—81no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3—21no—
263C2×C3×Dic3C2×D411yescharacteristic
264C2×C3×Dic3C2×D411yescharacteristic
265C2×C3×Dic3C2×D411yescharacteristic
266C3×C4×D3—21no—
267C3×C4×D3—21no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270#626—22no—
271#626—42no—
272#624—42no—
273#624—42no—
274#624—81no—
275C32×C8—21no—
276C3⋊(C3⋊C8)—21no—
277C3×C3⋊C8—21no—
278C3×C3⋊C8—21no—
279#552—91no—
280#546—91no—
281#488—31no—
282#483—91no—
283#482—31no—
284#478—91no—
285#467—91no—
286#465—91no—
287#464—91no—
288#452—91no—
289#450—91no—
290C4×SD16—91no—
291C8×D4—91no—
292#416—91no—
293C2×#102—91no—
294C23×D3—61no—
295C23×D3—61no—
296C23×D3—121no—
297C2×C3×Q8—31no—
298C2×C3×D4—21no—
299C2×C3×D4—61no—
300C2×C3×D4C22×D311yescharacteristic
301C2×C3×D4C22×D311yescharacteristic
302C22×C3×C4—31no—
303C2×#67—21no—
304C2×#67—31no—
305C2×#67—61no—
306C2×#67—61no—
307C2×#67—61no—
308C2×#67—121no—
309#239—62no—
310#239—121no—
311D3×D4—62no—
312D3×D4—62no—
313D3×D4—122no—
314D3×D4—121no—
315D3×D4—121no—
316D3×D4—122no—
317#235—62no—
318#235—121no—
319C2×D12—31no—
320C2×D12—31no—
321C2×D12—31no—
322C2×D12—61no—
323C2×D12—61no—
324C2×C4×D3—31no—
325C2×C4×D3—31no—
326C2×C4×D3—61no—
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×D3C22×D311yescharacteristic
334C2×Dic6—31no—
335C2×Dic6—31no—
336C2×Dic6—61no—
337C2×Dic6C22×D311yescharacteristic
338C2×C3×C8—21no—
339C2×C3×C8—31no—
340C2×C3×C8—31no—
341C2×C3×C8C22×D311yescharacteristic
342C2×C3×C8C22×D311yescharacteristic
343C3×C4⋊C4—21no—
344C3×C4⋊C4—31no—
345C3×C4⋊C4—31no—
346C3×C4⋊C4—31no—
347C3×C4⋊C4—61no—
348C3×C4⋊C4—61no—
349C3×C4⋊C4C22×D311yescharacteristic
350C3×C4⋊C4C22×D311yescharacteristic
351C3×C22⋊C4—61no—
352C3×C22⋊C4—61no—
353C3×C22⋊C4—61no—
354C3×C22⋊C4—61no—
355C3×C42—31no—
356C3×C42—61no—
357#217—21no—
358#217—21no—
359#217—21no—
360#217—31no—
361#217—61no—
362#216—121no—
363#214—121no—
364#214—121no—
365#214—122no—
366(C2×D3)⋊C4—21no—
367(C2×D3)⋊C4—31no—
368(C2×D3)⋊C4—31no—
369(C2×D3)⋊C4—31no—
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—121no—
378C4⋊Dic3—21no—
379C4⋊Dic3—31no—
380C4⋊Dic3—61no—
381C4⋊Dic3—61no—
382C4⋊Dic3—61no—
383C4⋊Dic3—61no—
384C4⋊Dic3—121no—
385C4⋊Dic3C22×D311yescharacteristic
386C4⋊Dic3C22×D311yescharacteristic
387C4⋊Dic3C22×D311yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—31no—
390Dic3⋊C4—61no—
391Dic3⋊C4—61no—
392Dic3⋊C4—61no—
393Dic3⋊C4—61no—
394Dic3⋊C4—61no—
395Dic3⋊C4—61no—
396C4×Dic3—21no—
397C4×Dic3—61no—
398C4×Dic3—61no—
399C4×Dic3C22×D311yescharacteristic
400C2×C3⋊C8—31no—
401C2×C3⋊C8—31no—
402C2×C3⋊C8—61no—
403C2×C3⋊C8—121no—
404C2×C3⋊C8C22×D311yescharacteristic
405C2×C3⋊C8C22×D311yescharacteristic
406Dic12—121no—
407#204—62no—
408#204—62no—
409#204—122no—
410D3×C8—121no—
411D3×C8—121no—
412D3×C8—121no—
413C22×C32—41no—
414C22×C32—41no—
415C22×C32—41no—
416C22×C32C22×D411yescharacteristic
417C2×C3⋊D3—21no—
418C2×C3⋊D3—21no—
419C2×C3⋊D3—22no—
420C2×C3⋊D3—41no—
421C2×C3⋊D3—41no—
422C2×C3⋊D3—84no—
423C2×C3⋊D3#13512yes—
424C2×C3×D3—21no—
425C2×C3×D3—21no—
426C2×C3×D3—21no—
427C32×C4—41no—
428C32×C4C2×#4111yescharacteristic
429C32×C4H(5,𝔽2)11yescharacteristic
430C3⋊Dic3—21no—
431C3⋊Dic3—41no—
432C3×Dic3—21no—
433C3×Dic3—21no—
434C3×Dic3—21no—
435C3×Dic3—41no—
436C3×Dic3—41no—
437C3×Dic3—41no—
438C3×Dic3—41no—
439C2×#41—91no—
440C22×D4—91no—
441C2×Q16—91no—
442C2×SD16—91no—
443C2×SD16—91no—
444C22×C8—91no—
445C22×C8—91no—
446#126—181no—
447#125—31no—
448#125—181no—
449#124—31no—
450#123—181no—
451#123—181no—
452C22⋊Q8—91no—
453C22⋊Q8—91no—
454C22⋊Q8—91no—
455#121—31no—
456#121—181no—
457#120—181no—
458C4×Q8—91no—
459C4×D4—91no—
460C4×D4—91no—
461#117—31no—
462#117—181no—
463C2×C4⋊C4—91no—
464C2×C22⋊C4—181no—
465#107—31no—
466#106—31no—
467#106—91no—
468C4⋊C8—91no—
469#103—31no—
470#103—31no—
471#103—91no—
472#103—91no—
473#102—31no—
474#102—31no—
475#102—91no—
476#102—91no—
477#102—91no—
478#102D3211yescharacteristic
479C22⋊C8—31no—
480C22⋊C8—91no—
481C4×C8—31no—
482C23×C3—21no—
483C23×C3—21no—
484C23×C3—31no—
485C23×C3—41no—
486C22×D3—31no—
487C22×D3—31no—
488C22×D3—61no—
489C22×D3—61no—
490C22×D3—61no—
491C22×D3—121no—
492C22×D3—122no—
493C22×D3—122no—
494C22×D3—122no—
495C22×D3—122no—
496C22×D3—124no—
497C22×D3—242no—
498C22×D3—241no—
499C22×D3—241no—
500C22×D3—242no—
501C22×D3D3×D411yescharacteristic
502C3×Q8—61no—
503C3×Q8—61no—
504C3×D4—22no—
505C3×D4—21no—
506C3×D4—21no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—41no—
510C3×D4—241no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
514C2×C3×C4—31no—
515C2×C3×C4—31no—
516C2×C3×C4—31no—
517C2×C3×C4—41no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4C23×D311yescharacteristic
525C2×C3×C4C23×D311yescharacteristic
526#67—62no—
527#67—81no—
528#67—122no—
529#67—122no—
530#67—122no—
531#67—124no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—31no—
537C2×Dic3—31no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—121no—
542C2×Dic3D3×D411yescharacteristic
543C2×Dic3D3×D411yescharacteristic
544C2×Dic3D3×D411yescharacteristic
545D12—32no—
546D12—32no—
547D12—62no—
548D12—62no—
549D12—61no—
550D12—61no—
551D12—121no—
552D12—122no—
553C4×D3—21no—
554C4×D3—21no—
555C4×D3—61no—
556C4×D3—61no—
557C4×D3—61no—
558C4×D3—61no—
559C4×D3—121no—
560C4×D3—121no—
561C4×D3—122no—
562C4×D3—122no—
563C4×D3—122no—
564C4×D3—122no—
565C4×D3—241no—
566C4×D3—241no—
567Dic6—21no—
568Dic6—21no—
569Dic6—61no—
570Dic6—61no—
571Dic6—61no—
572Dic6—61no—
573Dic6—121no—
574Dic6—121no—
575C3×C8—21no—
576C3×C8—21no—
577C3×C8—41no—
578C3×C8—61no—
579C3×C8—61no—
580C3⋊C8—21no—
581C3⋊C8—21no—
582C3⋊C8—61no—
583C3⋊C8—61no—
584C3⋊C8—121no—
585C2×C32—81no—
586C2×C32#54611yescharacteristic
587C2×C32C2×#13511yescharacteristic
588C2×C32#57711yescharacteristic
589C3⋊D3—22no—
590C3⋊D3—42no—
591C3×D3—41no—
592C24—181no—
593#41—182no—
594#41—361no—
595C2×Q8—31no—
596C2×Q8—91no—
597C2×D4—61no—
598C2×D4—91no—
599C2×D4—91no—
600C2×D4—181no—
601C2×D4—181no—
602C2×D4—182no—
603C2×D4—361no—
604C2×D4C2×D3211yescharacteristic
605C22×C4—31no—
606C22×C4—91no—
607C22×C4—181no—
608C22×C4—181no—
609C22×C4—181no—
610Q16—361no—
611SD16—182no—
612SD16—361no—
613C2×C8—31no—
614C2×C8—31no—
615C2×C8—91no—
616C2×C8—361no—
617C2×C8—361no—
618C2×C8C2×D3211yescharacteristic
619C4⋊C4—31no—
620C4⋊C4—31no—
621C4⋊C4—31no—
622C4⋊C4—61no—
623C4⋊C4—61no—
624C4⋊C4—91no—
625C4⋊C4—181no—
626C4⋊C4—181no—
627C4⋊C4—181no—
628C4⋊C4—181no—
629C4⋊C4—181no—
630C4⋊C4C2×D3211yescharacteristic
631C22⋊C4—61no—
632C22⋊C4—61no—
633C22⋊C4—61no—
634C22⋊C4—61no—
635C22⋊C4—91no—
636C22⋊C4—91no—
637C22⋊C4—181no—
638C22⋊C4—181no—
639C22⋊C4—181no—
640C22⋊C4—181no—
641C42—31no—
642C42—61no—
643C42—181no—
644C22×C3—21no—
645C22×C3—42no—
646C22×C3—41no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—61no—
653C22×C3—61no—
654C22×C3—61no—
655C22×C3—81no—
656C22×C3—81no—
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C2×D3×D411yescharacteristic
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—32no—
663C2×D3—32no—
664C2×D3—62no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—61no—
669C2×D3—62no—
670C2×D3—62no—
671C2×D3—121no—
672C2×D3—121no—
673C2×D3—122no—
674C2×D3—121no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—241no—
679C2×D3—241no—
680C2×D3—244no—
681C2×D3—244no—
682C2×D3—248no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—41no—
686C3×C4—41no—
687C3×C4—61no—
688C3×C4—61no—
689C3×C4—61no—
690C3×C4—81no—
691C3×C4—121no—
692C3×C4—121no—
693C3×C4—121no—
694C3×C4—121no—
695C3×C4D3×#4111yescharacteristic
696C3×C4D3×#4111yescharacteristic
697C3×C4#100911yescharacteristic
698C3×C4#100911yescharacteristic
699Dic3—21no—
700Dic3—21no—
701Dic3—21no—
702Dic3—41no—
703Dic3—41no—
704Dic3—41no—
705Dic3—41no—
706Dic3—61no—
707Dic3—61no—
708Dic3—121no—
709Dic3—121no—
710Dic3—121no—
711Dic3—241no—
712C32#329611yescharacteristic, complemented, Sylow
713C23—21no—
714C23—31no—
715C23—91no—
716C23—181no—
717C23—362no—
718C23—362no—
719C23—721no—
720Q8—61no—
721Q8—61no—
722Q8—181no—
723Q8—181no—
724D4—21no—
725D4—21no—
726D4—92no—
727D4—182no—
728D4—181no—
729D4—241no—
730D4—362no—
731D4—362no—
732C2×C4—21no—
733C2×C4—31no—
734C2×C4—31no—
735C2×C4—31no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—91no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—362no—
747C2×C4—362no—
748C2×C4—721no—
749C2×C4C22×D3211yescharacteristic
750C8—21no—
751C8—61no—
752C8—61no—
753C8—181no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—82no—
758C2×C3—81no—
759C2×C3—81no—
760C2×C3—121no—
761C2×C3#565411yescharacteristic
762C2×C3#567611yescharacteristic
763C2×C3D3×#13511yescharacteristic
764C2×C3D3×#13511yescharacteristic
765C2×C3#577011yescharacteristic
766C2×C3#577511yescharacteristic
767D3—41no—
768D3—62no—
769D3—62no—
770D3—122no—
771D3—122no—
772D3—122no—
773D3—242no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—61no—
778C22—61no—
779C22—61no—
780C22—92no—
781C22—181no—
782C22—181no—
783C22—182no—
784C22—361no—
785C22—361no—
786C22—724no—
787C22D32×D411yescharacteristic
788C4—41no—
789C4—61no—
790C4—61no—
791C4—61no—
792C4—121no—
793C4—121no—
794C4—121no—
795C4—121no—
796C4—181no—
797C4—361no—
798C4#6430811yescharacteristic
799C4#6431211yescharacteristic
800C3—21no—
801C3#8138111yescharacteristic, complemented
802C3#8165211yescharacteristic, complemented
803C2—81no—
804C2—121no—
805C2—182no—
806C2—362no—
807C2#1059428211yescharacteristic
808C2#1059473611yescharacteristic
809C2#1059474711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radical#10595243C2
hypercenter#102D32
hypocenterC32#3296
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10594584C2semidirect
3. #10592475C2semidirect
4. C3×#4779C2semidirect
5. C3×#4768C2semidirect
6. #10591460C2semidirect
7. #10591441C2semidirect
8. #10591416C2semidirect
9. #10590970C2semidirect
10. #10590758C2semidirect
11. #10590721C2semidirect
12. #10590686C2semidirect
13. #10590610C2semidirect
14. #10590525C2semidirect
15. #10590468C2semidirect
25. C3×#892C22semidirect
26. C3×#890C22semidirect
37. #63857C22semidirect
39. #63844C22semidirect
41. C2×#3719C22semidirect
43. C2×D3×C3⋊C8C22semidirect
49. C3×(C2×D3)⋊C8C22semidirect
50. C3×#817C22semidirect
51. C3×#816C22semidirect
52. C3×C8×Dic3C22semidirect
53. C3×#810C22semidirect
54. C3×#807C22semidirect
55. #63574C22semidirect
56. Dic3⋊(C3⋊C8)C22semidirect
57. #63567C22semidirect
58. #63565C22semidirect
79. #4779D3semidirect
86. #4768D3semidirect
182. #892C2×D3semidirect
186. #890C2×D3semidirect
220. (C2×D3)⋊C8C2×D3semidirect
221. #817C2×D3semidirect
223. #816C2×D3semidirect
225. C8×Dic3C2×D3semidirect
228. #810C2×D3semidirect
236. #807C2×D3semidirect
712. C32#3296semidirect
801. C3#81381semidirect
802. C3#81652semidirect

Maximal subgroups

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

subgroupindex
#105952432
#105945842
#105924752
C3×#47792
C3×#47682
#105914602
#105914412
#105914162
#105909702
#105907582
#105907212
#105906862
#105906102
#105905252
#105904682
#816523
#813813