Finite Group Databasebeta

← #14910233

Subgroups — #14910233

Order 2816.

760 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622524C211yesmaximal, characteristic, complemented
2C2×D11×D16C211yesmaximal, characteristic, complemented
3#13080302C211yesmaximal, characteristic, complemented
4D8×D44C211yesmaximal, characteristic, complemented
5#13070882C211yesmaximal, characteristic, complemented
6#13070720C211yesmaximal, characteristic, complemented
7#13070713C211yesmaximal, characteristic, complemented
8#13070671C211yesmaximal, characteristic, complemented
9#13070651C211yesmaximal, characteristic, complemented
10#13070546C211yesmaximal, characteristic, complemented
11#13070540C211yesmaximal, characteristic, complemented
12#13070529C211yesmaximal, characteristic, complemented
13#13070529C211yesmaximal, characteristic, complemented
14#13070443C211yesmaximal, characteristic, complemented
15C11×#2177C211yesmaximal, characteristic, complemented
16C2×#66965C2211yescharacteristic, complemented
17C2×D8×D11C2211yescharacteristic
18C2×D8×D11C2211yescharacteristic, complemented
19C2×D8×D11C2211yescharacteristic, complemented
20#10623085—21no—
21D4×D44—21no—
22C2×C11×D16C2211yescharacteristic
23C4×C11×D8C2211yescharacteristic, complemented
24C4×C11×D8C2211yescharacteristic, complemented
25C2×#66891C2211yescharacteristic, complemented
26C2×#66890C2211yescharacteristic
27C2×#66890C2211yescharacteristic, complemented
28C2×#66890C2211yescharacteristic, complemented
29#10622629—21no—
30#10622628—21no—
31#10622524—24no—
32D11×D16—24no—
33C2×#66864C2211yescharacteristic, complemented
34C2×#66864C2211yescharacteristic, complemented
35C2×D176C2211yescharacteristic, complemented
36C2×D176C2211yescharacteristic, complemented
37C2×#66862C2211yescharacteristic, complemented
38C2×C16×D11C2211yescharacteristic, complemented
39#10622500C2211yescharacteristic, complemented
40#10622496C2211yescharacteristic
41#10622496C2211yescharacteristic, complemented
42#10622496C2211yescharacteristic, complemented
43#10622394—21no—
44#10622389—21no—
45#10622386—21no—
46#10622386—21no—
47#10622309C2211yescharacteristic, complemented
48#10622308C2211yescharacteristic, complemented
49C8×D44C2211yescharacteristic
50C11×#367C2211yescharacteristic, complemented
51C11×#357C2211yescharacteristic, complemented
52C11×#357C2211yescharacteristic, complemented
53C11×#346C2211yescharacteristic, complemented
54(C2×D11)⋊C16C2211yescharacteristic, complemented
55(C2×D11)⋊C16C2211yescharacteristic, complemented
56#10622130C2211yescharacteristic, complemented
57#10622129C2211yescharacteristic, complemented
58#10622129C2211yescharacteristic, complemented
59#10622129C2211yescharacteristic, complemented
60C4⋊(C11⋊C16)C2211yescharacteristic, complemented
61C2×#4341—21no—
62C2×D4×D11—21no—
63C2×D4×D11—21no—
64C2×D4×D11—21no—
65C22×D44—41no—
66C2×C11×D8C2311yescharacteristic
67C2×C11×D8C2311yescharacteristic
68C4×D4×C11—21no—
69C4×D4×C11—21no—
70C2×#4324—21no—
71C2×#4323—21no—
72C2×#4323—21no—
73C2×#4323—21no—
74#66983—41no—
75#66983—41no—
76C2×(C2×D11)⋊C4—41no—
77#66965—22no—
78#66965—41no—
79D8×D11—22no—
80D8×D11—22no—
81D8×D11—22no—
82D8×D11—41no—
83D8×D11—41no—
84D8×D11—41no—
85C2×Dic44C2311yescharacteristic
86C2×D88—21no—
87C2×D88C2311yescharacteristic
88C2×D88C2311yescharacteristic
89C2×D88C2311yescharacteristic
90C2×#4314—21no—
91C2×C8×D11C2311yescharacteristic
92C2×C8×D11C2311yescharacteristic
93#66950—21no—
94#66948—21no—
95#66948—21no—
96#66948—21no—
97#66939—41no—
98#66935—41no—
99#66935—41no—
100#66935—41no—
101#66928—21no—
102#66927—21no—
103C4×D44D411yescharacteristic
104C11×D16D414yescomplemented
105C2×C11×C16C2311yescharacteristic
106C2×C11×C16C2311yescharacteristic
107C11×#107C2311yescharacteristic
108C11×#107C2311yescharacteristic
109C11×#102—21no—
110C11×#102—21no—
111C4×C8×C11C2311yescharacteristic
112#66891—22no—
113#66890—22no—
114#66890—22no—
115#66890—22no—
116(C2×D11)⋊C8D411yescharacteristic
117(C2×D11)⋊C8D411yescharacteristic
118C2×C11⋊C16C2311yescharacteristic
119C2×C11⋊C16C2311yescharacteristic
120#66874—21no—
121#66873—21no—
122#66873—21no—
123#66873—21no—
124C4⋊(C11⋊C8)D411yescharacteristic
125#66864—22no—
126#66864—41no—
127D176—22no—
128D176—41no—
129#66862—22no—
130C16×D11—22no—
131#33830—111nomaximal, Sylow
132C23×D11—41no—
133C23×D11—41no—
134C23×D11—41no—
135C2×D4×C11—21no—
136C2×D4×C11—21no—
137C22×C4×C11—41no—
138C22×C4×C11—41no—
139C2×C22⋊D11—41no—
140C2×C22⋊D11—41no—
141C2×C22⋊D11—41no—
142C2×C22⋊D11—41no—
143C22×Dic11—41no—
144#4341—42no—
145#4341—81no—
146D4×D11—42no—
147D4×D11—42no—
148D4×D11—42no—
149D4×D11—81no—
150D4×D11—81no—
151D4×D11—81no—
152C2×D44—21no—
153C2×D44—21no—
154C2×D44—21no—
155C2×D44—41no—
156C2×D44—41no—
157C2×D44—41no—
158C2×D44—41no—
159C2×D44—41no—
160C2×D44—84no—
161C2×D44D811yescharacteristic
162C2×C4×D11C2×D411yescharacteristic
163C2×C4×D11C2×D411yescharacteristic
164C2×Dic22—21no—
165C11×D8—21no—
166C11×D8—21no—
167C11×D8C2×D412yes—
168C11×D8C2×D412yescomplemented
169C2×C8×C11C2×D411yescharacteristic
170C2×C8×C11C2411yescharacteristic
171C11×C4⋊C4—21no—
172C11×C4⋊C4—21no—
173C11×C22⋊C4—41no—
174C11×C22⋊C4—41no—
175C42×C11C2×D411yescharacteristic
176#4324—42no—
177#4323—42no—
178#4323—42no—
179#4323—42no—
180(C2×D11)⋊C4—41no—
181(C2×D11)⋊C4—41no—
182(C2×D11)⋊C4—41no—
183(C2×D11)⋊C4—41no—
184(C2×D11)⋊C4—41no—
185(C2×D11)⋊C4—41no—
186(C2×D11)⋊C4D811yescharacteristic
187(C2×D11)⋊C4D811yescharacteristic
188C4⋊Dic11—41no—
189C4⋊Dic11D811yescharacteristic
190C2×C11⋊C8C2×D411yescharacteristic
191C2×C11⋊C8C2×D411yescharacteristic
192Dic44—21no—
193Dic44—21no—
194D88—21no—
195D88—21no—
196D88—21no—
197D88—21no—
198D88—21no—
199D88—21no—
200D88—81no—
201#4314—81no—
202C8×D11—21no—
203C8×D11—21no—
204C8×D11—21no—
205C8×D11—21no—
206C11×C16—21no—
207C11×C16C2×D412yescomplemented
208C11⋊C16—21no—
209C11⋊C16—21no—
210C2×#509—111no—
211C22×D16—111no—
212#3280—111no—
213D4×D8—111no—
214#2250—111no—
215#2218—111no—
216#2217—111no—
217#2210—111no—
218#2206—111no—
219#2187—111no—
220#2186—111no—
221#2184—111no—
222#2184—111no—
223#2177D1111yescharacteristic, complemented
224#2168—111no—
225C23×C11—41no—
226C23×C11—41no—
227C22×D11—41no—
228C22×D11—41no—
229C22×D11—41no—
230C22×D11—82no—
231C22×D11—82no—
232C22×D11—82no—
233C22×D11—82no—
234C22×D11—82no—
235C22×D11—82no—
236C22×D11—161no—
237C22×D11—161no—
238C22×D11—161no—
239C22×D11C2×D811yescharacteristic
240C22×D11C2×D811yescharacteristic
241D4×C11—22no—
242D4×C11—22no—
243D4×C11—41no—
244D4×C11—41no—
245C2×C4×C11—41no—
246C2×C4×C11—41no—
247C2×C4×C11—82no—
248C2×C4×C11—161no—
249C2×C4×C11C2×D811yescharacteristic
250C2×C4×C11C2×D811yescharacteristic
251C2×C4×C11C22×D411yescharacteristic
252C22⋊D11—82no—
253C22⋊D11—82no—
254C22⋊D11—82no—
255C22⋊D11—82no—
256C2×Dic11—41no—
257C2×Dic11—82no—
258C2×Dic11C2×D811yescharacteristic
259C2×Dic11C2×D811yescharacteristic
260D44—22no—
261D44—41no—
262D44—41no—
263D44—41no—
264D44—41no—
265D44—41no—
266D44—41no—
267D44—82no—
268D44—82no—
269D44—82no—
270D44—161no—
271D44—161no—
272C4×D11—21no—
273C4×D11—21no—
274C4×D11—21no—
275C4×D11—21no—
276Dic22—41no—
277Dic22—41no—
278C8×C11—21no—
279C8×C11C22×D411yescharacteristic
280C8×C11H(5,𝔽2)11yescharacteristic
281C11⋊C8—21no—
282C11⋊C8—21no—
283C2×#135—111no—
284C22×D8—111no—
285C22×D8—111no—
286C22×D8—111no—
287#546—221no—
288D42—221no—
289#509—224no—
290C2×SD32—111no—
291C2×SD32—111no—
292C2×SD32—111no—
293C2×D16—111no—
294C2×D16—111no—
295C2×D16—111no—
296C2×D16—111no—
297C2×D16—111no—
298C2×D16—224no—
299C2×D16C2×D1111yescharacteristic
300C2×M32—111no—
301C22×C16—111no—
302#495—111no—
303#493—111no—
304#467—111no—
305#466—111no—
306#466—111no—
307#466—111no—
308#463—221no—
309#459—221no—
310#450—221no—
311#449—221no—
312#447—221no—
313#447—221no—
314C4×D8C2×D1111yescharacteristic, complemented
315C4×D8C2×D1111yescharacteristic, complemented
316C8×D4—111no—
317#367C2×D1111yescharacteristic, complemented
318C4⋊C16—111no—
319#358—111no—
320#357—111no—
321#357—111no—
322#357—111no—
323#357C2×D1111yescharacteristic, complemented
324#357C2×D1111yescharacteristic, complemented
325C22⋊C16—111no—
326C22⋊C16—111no—
327#346C2×D1111yescharacteristic, complemented
328C22×C11—42no—
329C22×C11—42no—
330C22×C11—81no—
331C22×C11—81no—
332C22×C11—81no—
333C22×C11—81no—
334C22×C11C22×D811yescharacteristic
335C2×D11—21no—
336C2×D11—21no—
337C2×D11—21no—
338C2×D11—21no—
339C2×D11—21no—
340C2×D11—81no—
341C2×D11—81no—
342C2×D11—81no—
343C2×D11—81no—
344C2×D11—81no—
345C2×D11—81no—
346C2×D11—81no—
347C2×D11—81no—
348C2×D11—81no—
349C2×D11—164no—
350C2×D11—164no—
351C2×D11—164no—
352C2×D11#50912yescomplemented
353C4×C11—21no—
354C4×C11—21no—
355C4×C11—81no—
356C4×C11—81no—
357C4×C11D4211yescharacteristic
358C4×C11#57611yescharacteristic
359Dic11—21no—
360Dic11—21no—
361Dic11—81no—
362C2×#41—221no—
363C22×D4—221no—
364C22×D4—221no—
365C22×D4—221no—
366C22×D4—441no—
367#135—222no—
368#135—441no—
369C2×Q16—111no—
370C2×SD16—221no—
371C2×SD16—221no—
372C2×D8—111no—
373C2×D8—111no—
374C2×D8—111no—
375C2×D8—221no—
376C2×D8—221no—
377C2×D8—221no—
378C2×D8—222no—
379C2×D8—222no—
380C2×D8—222no—
381C2×D8—221no—
382C2×D8—441no—
383C2×D8—441no—
384C2×D8—441no—
385C2×D8C22×D1111yescharacteristic
386C2×D8C22×D1111yescharacteristic
387C22×C8—111no—
388C22×C8—111no—
389#127—221no—
390#124—221no—
391#123—441no—
392C22⋊Q8—221no—
393#121—221no—
394#121—221no—
395#121—221no—
396#121—441no—
397#121—441no—
398#120—441no—
399#120—441no—
400#120—441no—
401C4×D4—21no—
402C4×D4—21no—
403C4×D4—111no—
404C2×C22⋊C4—441no—
405SD32—222no—
406SD32—222no—
407SD32—441no—
408D16—222no—
409D16—222no—
410D16—222no—
411D16—222no—
412D16—441no—
413D16D4414yescomplemented
414M32—222no—
415C2×C16—111no—
416C2×C16—111no—
417C2×C16—222no—
418C2×C16C22×D1111yescharacteristic
419C2×C16C22×D1111yescharacteristic
420#107C22×D1111yescharacteristic
421#107C22×D1111yescharacteristic
422C4⋊C8—111no—
423#103—221no—
424#102—21no—
425#102—21no—
426#102—221no—
427#102—221no—
428#102—221no—
429C22⋊C8—111no—
430C22⋊C8—111no—
431C4×C8C22×D1111yescharacteristic
432C2×C11—82no—
433C2×C11—82no—
434C2×C11D4×D811yescharacteristic
435C2×C11C2×#50911yescharacteristic
436C2×C11#341511yescharacteristic
437D11—22no—
438D11—41no—
439D11—161no—
440D11—161no—
441D11—161no—
442C24—441no—
443C24—441no—
444C24—441no—
445#41—442no—
446#41—881no—
447C2×Q8—221no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—111no—
451C2×D4—221no—
452C2×D4—221no—
453C2×D4—221no—
454C2×D4—441no—
455C2×D4—441no—
456C2×D4—441no—
457C2×D4—441no—
458C2×D4—441no—
459C2×D4—441no—
460C2×D4—442no—
461C2×D4—442no—
462C2×D4—442no—
463C2×D4—441no—
464C2×D4—441no—
465C2×D4—441no—
466C2×D4—884no—
467C2×D4—881no—
468C2×D4—881no—
469C2×D4—881no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—111no—
473C22×C4—111no—
474C22×C4—441no—
475Q16—221no—
476Q16—221no—
477SD16—442no—
478SD16—881no—
479D8—21no—
480D8—21no—
481D8—221no—
482D8—221no—
483D8—221no—
484D8—221no—
485D8—221no—
486D8—221no—
487D8—442no—
488D8—442no—
489D8—442no—
490D8—881no—
491D8C2×D4412yes—
492D8C2×D4412yescomplemented
493C2×C8—111no—
494C2×C8—111no—
495C2×C8—221no—
496C2×C8—221no—
497C2×C8—221no—
498C2×C8—221no—
499C2×C8D4×D1111yescharacteristic
500C2×C8C23×D1111yescharacteristic
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—111no—
504C4⋊C4—441no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—111no—
508C22⋊C4—111no—
509C22⋊C4—441no—
510C22⋊C4—441no—
511C22⋊C4—441no—
512C22⋊C4—441no—
513C22⋊C4—441no—
514C22⋊C4—441no—
515C42D4×D1111yescharacteristic
516C16—21no—
517C16—221no—
518C16—221no—
519C16C2×D4412yescomplemented
520C11#3383011yescharacteristic, complemented, Sylow
521C23—41no—
522C23—41no—
523C23—111no—
524C23—111no—
525C23—441no—
526C23—441no—
527C23—441no—
528C23—882no—
529C23—882no—
530C23—882no—
531C23—882no—
532C23—882no—
533C23—882no—
534C23—1761no—
535C23—1761no—
536C23—1761no—
537Q8—441no—
538Q8—441no—
539D4—22no—
540D4—22no—
541D4—41no—
542D4—41no—
543D4—222no—
544D4—441no—
545D4—441no—
546D4—441no—
547D4—441no—
548D4—441no—
549D4—441no—
550D4—882no—
551D4—882no—
552D4—882no—
553D4—882no—
554D4—882no—
555D4—882no—
556D4—882no—
557D4—1761no—
558D4—1761no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—82no—
562C2×C4—111no—
563C2×C4—111no—
564C2×C4—161no—
565C2×C4—221no—
566C2×C4—221no—
567C2×C4—221no—
568C2×C4—221no—
569C2×C4—441no—
570C2×C4—882no—
571C2×C4D8×D1111yescharacteristic
572C2×C4D8×D1111yescharacteristic
573C2×C4C2×D4×D1111yescharacteristic
574C8—21no—
575C8—221no—
576C8—221no—
577C8C22×D4411yescharacteristic
578C8#6704211yescharacteristic
579C22—42no—
580C22—42no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—112no—
586C22—221no—
587C22—221no—
588C22—221no—
589C22—221no—
590C22—221no—
591C22—881no—
592C22—881no—
593C22—881no—
594C22—881no—
595C22—881no—
596C22—881no—
597C22—881no—
598C22—881no—
599C22—881no—
600C22—1764no—
601C22—1764no—
602C22—1764no—
603C22C2×D8×D1111yescharacteristic
604C4—21no—
605C4—21no—
606C4—81no—
607C4—81no—
608C4—221no—
609C4—221no—
610C4—881no—
611C4D4×D4411yescharacteristic
612C4#1062330011yescharacteristic
613C2—82no—
614C2—82no—
615C2—222no—
616C2—441no—
617C2—1761no—
618C2—1761no—
619C2—1761no—
620C2D8×D4411yescharacteristic
621C2D11×#50911yescharacteristic
622C2#1308175611yescharacteristic
subgroupG/H
centerC22C2×D8×D11
commutator, cosocleC2×C8×C11C24
FrattiniC2×C8C23×D11
FittingC11×#2177C2
socleC22×C11C22×D8
hypercenter#2177D11
hypocenterC11#33830
LCSG ▷ C2×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2177

Complements

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

NH ≅ G/Ntype
1. C2×#10622524C2semidirect
2. C2×D11×D16C2semidirect
3. #13080302C2semidirect
4. D8×D44C2semidirect
5. #13070882C2semidirect
6. #13070720C2semidirect
7. #13070713C2semidirect
8. #13070671C2semidirect
9. #13070651C2semidirect
10. #13070546C2semidirect
11. #13070540C2semidirect
12. #13070529C2semidirect
13. #13070529C2semidirect
14. #13070443C2semidirect
15. C11×#2177C2semidirect
16. C2×#66965C22semidirect
18. C2×D8×D11C22semidirect
19. C2×D8×D11C22semidirect
23. C4×C11×D8C22semidirect
24. C4×C11×D8C22semidirect
25. C2×#66891C22semidirect
27. C2×#66890C22semidirect
28. C2×#66890C22semidirect
33. C2×#66864C22semidirect
34. C2×#66864C22semidirect
35. C2×D176C22semidirect
36. C2×D176C22semidirect
37. C2×#66862C22semidirect
38. C2×C16×D11C22semidirect
39. #10622500C22semidirect
41. #10622496C22semidirect
42. #10622496C22semidirect
47. #10622309C22semidirect
48. #10622308C22semidirect
50. C11×#367C22semidirect
51. C11×#357C22semidirect
52. C11×#357C22semidirect
53. C11×#346C22semidirect
54. (C2×D11)⋊C16C22semidirect
55. (C2×D11)⋊C16C22semidirect
56. #10622130C22semidirect
57. #10622129C22semidirect
58. #10622129C22semidirect
59. #10622129C22semidirect
60. C4⋊(C11⋊C16)C22semidirect
104. C11×D16D4semidirect
168. C11×D8C2×D4semidirect
207. C11×C16C2×D4semidirect
223. #2177D11semidirect
314. C4×D8C2×D11semidirect
315. C4×D8C2×D11semidirect
317. #367C2×D11semidirect
323. #357C2×D11semidirect
324. #357C2×D11semidirect
327. #346C2×D11semidirect
352. C2×D11#509semidirect
413. D16D44semidirect
492. D8C2×D44semidirect
519. C16C2×D44semidirect
520. C11#33830semidirect

Maximal subgroups

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

subgroupindex
C2×#106225242
C2×D11×D162
#130803022
D8×D442
#130708822
#130707202
#130707132
#130706712
#130706512
#130705462
#130705402
#130705292
#130704432
C11×#21772
#3383011