Subgroups — Q₈×D₁₁₆ #14271830

Order 1856.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₂₉	C₂	1	2	yes	maximal, complemented
2	C₄×Q₈×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745259	C₂	1	6	yes	maximal, complemented
4	C₄×D₁₁₆	C₂	1	3	yes	maximal
5	#11745231	C₂	1	3	yes	maximal, complemented
6	C₂×Q₈×C₂₉	C₂²	1	1	yes	characteristic
7	Q₈×D₂₉	—	2	8	no	—
8	C₂×D₁₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₂₉	C₂²	1	6	yes	—
10	C₂×Dic₅₈	C₂²	1	6	yes	—
11	C₄⋊C₄×C₂₉	C₂²	1	3	yes	—
12	C₄²×C₂₉	C₂²	1	3	yes	—
13	#90781	C₂²	1	6	yes	—
14	C₄⋊Dic₂₉	C₂²	1	3	yes	—
15	C₄⋊Dic₂₉	C₂²	1	6	yes	—
16	C₂²×D₂₉	C₂³	1	2	yes	—
17	Q₈×C₂₉	D₄	1	4	yes	complemented
18	C₂×C₄×C₂₉	C₂³	1	3	yes	—
19	C₂×C₄×C₂₉	C₂³	1	3	yes	—
20	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
21	C₂×Dic₂₉	C₂³	1	6	yes	—
22	D₁₁₆	Q₈	1	4	yes	direct product factor
23	C₄×D₂₉	—	2	12	no	—
24	Dic₅₈	—	2	12	no	—
25	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
26	C₂×D₂₉	—	2	2	no	—
27	C₂×D₂₉	—	2	2	no	—
28	C₂×D₂₉	C₂×Q₈	1	4	yes	complemented
29	C₄×C₂₉	—	2	3	no	—
30	C₄×C₂₉	C₂×D₄	1	6	yes	—
31	C₄×C₂₉	C₂×Q₈	1	2	yes	complemented
32	Dic₂₉	—	2	6	no	—
33	D₄×Q₈	—	29	1	no	maximal, Sylow
34	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
35	C₂×C₂₉	C₂²×Q₈	1	1	yes	characteristic
36	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
37	D₂₉	—	2	4	no	—
38	C₂²×Q₈	—	29	2	no	—
39	C₄⋊Q₈	—	29	3	no	—
40	C₂²⋊Q₈	—	29	6	no	—
41	C₄×Q₈	D₂₉	1	1	yes	characteristic, complemented
42	C₄×D₄	—	29	3	no	—
43	C₂₉	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	29	6	no	—
45	C₂×Q₈	—	58	8	no	—
46	C₂×Q₈	C₂×D₂₉	1	1	yes	characteristic
47	C₂×D₄	—	29	1	no	—
48	C₂²×C₄	—	29	6	no	—
49	C₄⋊C₄	—	29	3	no	—
50	C₄⋊C₄	—	29	6	no	—
51	C₄⋊C₄	C₂×D₂₉	1	3	yes	—
52	C₂²⋊C₄	—	29	6	no	—
53	C₄²	C₂×D₂₉	1	3	yes	—
54	C₂³	—	29	2	no	—
55	Q₈	—	58	12	no	—
56	Q₈	D₁₁₆	1	4	yes	direct product factor
57	D₄	—	29	4	no	—
58	C₂×C₄	—	29	6	no	—
59	C₂×C₄	—	58	12	no	—
60	C₂×C₄	C₂²×D₂₉	1	3	yes	—
61	C₂×C₄	C₂²×D₂₉	1	3	yes	—
62	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
63	C₂²	—	29	4	no	—
64	C₂²	—	58	2	no	—
65	C₂²	—	58	2	no	—
66	C₂²	C₂³×D₂₉	1	1	yes	characteristic
67	C₄	—	2	3	no	—
68	C₄	—	58	6	no	—
69	C₄	C₂×D₁₁₆	1	6	yes	—
70	C₄	Q₈×D₂₉	1	2	yes	complemented
71	C₂	—	58	4	no	—
72	C₂	C₂²×D₁₁₆	1	1	yes	characteristic
73	C₂	C₂×Q₈×D₂₉	1	1	yes	characteristic
74	C₂	#11745365	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₄×Q₈×C₂₉	C₂
prime radical	C₂×D₁₁₆	C₂²
hypercenter	C₄×Q₈	D₂₉
hypocenter	C₂₉	D₄×Q₈
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×D₂₉	C₂	semidirect
2. C₄×Q₈×C₂₉	C₂	semidirect
3. #11745259	C₂	semidirect
5. #11745231	C₂	semidirect
17. Q₈×C₂₉	D₄	semidirect
22. D₁₁₆	Q₈	direct (N × H)
28. C₂×D₂₉	C₂×Q₈	semidirect
31. C₄×C₂₉	C₂×Q₈	semidirect
41. C₄×Q₈	D₂₉	semidirect
43. C₂₉	D₄×Q₈	semidirect
56. Q₈	D₁₁₆	direct (N × H)
70. C₄	Q₈×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₂₉	2
C₄×Q₈×C₂₉	2
#11745259	2
C₄×D₁₁₆	2
#11745231	2
D₄×Q₈	29

Subgroups — Q8×D116 #14271830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×D₁₁₆ #14271830