Subgroups — D₈×#6923 #16840798

Order 3904.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×#6923	C₂	1	2	yes	maximal, complemented
2	#14519846	C₂	1	1	yes	maximal, characteristic, complemented
3	#14519839	C₂	1	2	yes	maximal, complemented
4	C₈×#6923	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×#6923	—	2	2	no	—
7	D₄×D₆₁	C₂²	1	2	yes	—
8	C₂²⋊#6923	—	2	2	no	—
9	C₄⋊#6923	C₂²	1	2	yes	—
10	C₄×#6923	C₂²	1	1	yes	characteristic
11	D₆₁⋊C₈	C₂²	1	1	yes	characteristic
12	D₈×C₆₁	C₄	1	1	yes	characteristic, complemented
13	#11758199	C₄	1	2	yes	complemented
14	D₄₈₈	C₄	1	1	yes	characteristic, complemented
15	C₈×D₆₁	C₂²	1	1	yes	characteristic
16	C₂²×D₆₁	—	2	2	no	—
17	C₂×#6923	—	2	2	no	—
18	C₂×#6923	—	4	4	no	—
19	C₂×#6923	D₄	1	1	yes	characteristic
20	C₂×#6923	D₄	1	1	yes	characteristic
21	D₄×C₆₁	C₂×C₄	1	2	yes	complemented
22	C₂²⋊D₆₁	—	2	2	no	—
23	D₂₄₄	C₂×C₄	1	2	yes	complemented
24	C₄×D₆₁	C₂³	1	1	yes	characteristic
25	#92420	—	2	1	no	—
26	C₈×C₆₁	C₂×C₄	1	1	yes	characteristic, complemented
27	#92418	C₂×C₄	1	1	yes	characteristic, complemented
28	C₂²×C₆₁	—	2	2	no	—
29	C₂×D₆₁	—	2	2	no	—
30	C₂×D₆₁	—	4	2	no	—
31	C₂×D₆₁	—	4	2	no	—
32	C₂×D₆₁	C₂×D₄	1	1	yes	characteristic
33	#6923	—	2	1	no	—
34	#6923	—	4	2	no	—
35	#6923	D₈	1	2	yes	direct product factor
36	C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
37	Dic₆₁	#41	1	1	yes	characteristic
38	C₂×C₆₁	—	4	2	no	—
39	C₂×C₆₁	C₄×D₄	1	1	yes	characteristic
40	D₆₁	—	4	2	no	—
41	D₆₁	C₂×D₈	1	1	yes	characteristic
42	D₆₁	#135	1	1	yes	characteristic
43	C₄×D₈	—	61	1	no	maximal, Sylow
44	C₆₁	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
45	C₂×D₈	—	61	1	no	—
46	C₄×D₄	—	61	2	no	—
47	#107	—	61	1	no	—
48	#102	—	61	2	no	—
49	C₄×C₈	—	61	1	no	—
50	C₂×D₄	—	61	2	no	—
51	C₂²×C₄	—	122	2	no	—
52	D₈	—	61	2	no	—
53	D₈	—	61	1	no	—
54	D₈	#6923	1	1	yes	characteristic, direct product factor
55	C₂×C₈	—	61	1	no	—
56	C₂×C₈	—	61	1	no	—
57	C₄⋊C₄	—	61	2	no	—
58	C₂²⋊C₄	—	122	2	no	—
59	C₄²	—	61	1	no	—
60	C₂³	—	122	2	no	—
61	D₄	—	61	2	no	—
62	D₄	—	122	2	no	—
63	D₄	C₂×#6923	1	2	yes	complemented
64	C₂×C₄	—	61	1	no	—
65	C₂×C₄	—	61	1	no	—
66	C₂×C₄	—	61	1	no	—
67	C₂×C₄	—	122	2	no	—
68	C₂×C₄	—	244	4	no	—
69	C₈	—	61	1	no	—
70	C₈	—	122	1	no	—
71	C₈	C₂×#6923	1	1	yes	characteristic, complemented
72	C₂²	—	2	2	no	—
73	C₂²	—	61	1	no	—
74	C₂²	—	122	2	no	—
75	C₂²	—	244	2	no	—
76	C₂²	—	244	2	no	—
77	C₄	—	61	2	no	—
78	C₄	—	61	1	no	—
79	C₄	—	122	1	no	—
80	C₄	—	244	2	no	—
81	C₄	C₂²×#6923	1	1	yes	characteristic
82	C₂	—	4	2	no	—
83	C₂	—	61	1	no	—
84	C₂	—	61	1	no	—
85	C₂	—	244	2	no	—
86	C₂	D₄×#6923	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#6923
commutator	C₄×C₆₁	C₂²×C₄
Frattini	C₄	C₂²×#6923
Fitting	D₈×C₆₁	C₄
socle	C₂×C₆₁	C₄×D₄
prime radical	D₈×D₆₁	C₂
cosocle	C₄×D₆₁	C₂³
hypercenter	D₈	#6923
hypocenter	C₆₁	C₄×D₈
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. D₄×#6923	C₂	semidirect
2. #14519846	C₂	semidirect
3. #14519839	C₂	semidirect
4. C₈×#6923	C₂	semidirect
12. D₈×C₆₁	C₄	semidirect
13. #11758199	C₄	semidirect
14. D₄₈₈	C₄	semidirect
21. D₄×C₆₁	C₂×C₄	semidirect
23. D₂₄₄	C₂×C₄	semidirect
26. C₈×C₆₁	C₂×C₄	semidirect
27. #92418	C₂×C₄	semidirect
35. #6923	D₈	direct (N × H)
44. C₆₁	C₄×D₈	semidirect
54. D₈	#6923	direct (N × H)
63. D₄	C₂×#6923	semidirect
71. C₈	C₂×#6923	semidirect

Maximal subgroups

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

subgroup	index
D₄×#6923	2
#14519846	2
#14519839	2
C₈×#6923	2
D₈×D₆₁	2
C₄×D₈	61

Subgroups — D8×#6923 #16840798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×#6923 #16840798