Subgroups — D₄⋊#11715906 #20261822

Order 6208.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11715906	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11715906	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#87604	C₂	1	1	yes	maximal, characteristic
4	C₂×#11715906	—	2	1	no	—
5	C₂×#11715906	—	2	1	no	—
6	C₂²×#87604	—	2	1	no	—
7	C₄⋊#87604	C₄	1	1	yes	characteristic
8	C₂²⋊#87604	—	2	1	no	—
9	C₄×#87604	C₂²	1	1	yes	characteristic
10	D₄×D₉₇	C₄	1	1	yes	characteristic
11	C₂²×D₉₇	—	2	1	no	—
12	C₂×#87604	—	2	1	no	—
13	C₂×#87604	—	4	1	no	—
14	C₂×#87604	—	4	1	no	—
15	C₂×#87604	D₄	1	1	yes	characteristic
16	C₂×#87604	D₄	1	1	yes	characteristic
17	#11715906	—	2	2	no	—
18	#11715906	—	4	1	no	—
19	D₄×C₉₇	C₈	1	1	yes	characteristic, complemented
20	C₂²⋊D₉₇	—	2	1	no	—
21	D₃₈₈	C₈	1	1	yes	characteristic, complemented
22	C₄×D₉₇	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₉₇	—	2	1	no	—
24	C₂×D₉₇	—	2	1	no	—
25	C₂×D₉₇	—	4	1	no	—
26	C₂×D₉₇	—	4	1	no	—
27	C₂×D₉₇	C₂²⋊C₄	1	1	yes	characteristic
28	#87604	—	2	1	no	—
29	#87604	—	4	1	no	—
30	#87604	D₈	1	1	yes	characteristic
31	#87604	SD₁₆	1	1	yes	characteristic
32	C₄×C₉₇	C₂×C₈	1	1	yes	characteristic
33	Dic₉₇	M₁₆	1	1	yes	characteristic
34	C₂×C₉₇	—	4	1	no	—
35	C₂×C₉₇	C₂²⋊C₈	1	1	yes	characteristic
36	D₉₇	—	4	1	no	—
37	D₉₇	#102	1	1	yes	characteristic
38	D₉₇	#104	1	1	yes	characteristic
39	C₉₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	D₄⋊C₈	—	97	1	no	maximal, Sylow
41	C₄×D₄	—	97	1	no	—
42	C₄⋊C₈	—	97	1	no	—
43	C₄×C₈	—	97	1	no	—
44	C₂×D₄	—	97	1	no	—
45	C₂²×C₄	—	194	1	no	—
46	C₂×C₈	—	194	1	no	—
47	C₂×C₈	—	194	1	no	—
48	C₄⋊C₄	—	97	1	no	—
49	C₂²⋊C₄	—	194	1	no	—
50	C₄²	—	97	1	no	—
51	C₂³	—	194	1	no	—
52	D₄	—	97	1	no	—
53	D₄	—	194	1	no	—
54	D₄	#11715906	1	1	yes	characteristic, complemented
55	C₂×C₄	—	97	1	no	—
56	C₂×C₄	—	97	1	no	—
57	C₂×C₄	—	97	1	no	—
58	C₂×C₄	—	388	1	no	—
59	C₂×C₄	—	388	1	no	—
60	C₂×C₄	—	194	1	no	—
61	C₈	—	388	1	no	—
62	C₈	—	194	2	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	97	1	no	—
65	C₂²	—	388	1	no	—
66	C₂²	—	388	1	no	—
67	C₂²	—	194	1	no	—
68	C₄	—	97	1	no	—
69	C₄	—	97	1	no	—
70	C₄	—	97	1	no	—
71	C₄	—	388	1	no	—
72	C₄	—	194	1	no	—
73	C₄	C₂×#11715906	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	—	97	1	no	—
76	C₂	—	97	1	no	—
77	C₂	—	388	1	no	—
78	C₂	C₂²⋊#11715906	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11715906
commutator	C₄×C₉₇	C₂×C₈
Frattini	C₄	C₂×#11715906
Fitting	D₄×C₉₇	C₈
socle	C₂×C₉₇	C₂²⋊C₈
hypercenter	D₄	#11715906
hypocenter	C₉₇	D₄⋊C₈
LCS	G ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11715906	C₂	semidirect
2. C₄×#11715906	C₂	semidirect
19. D₄×C₉₇	C₈	semidirect
21. D₃₈₈	C₈	semidirect
39. C₉₇	D₄⋊C₈	semidirect
54. D₄	#11715906	semidirect

Subgroups — D4⋊#11715906 #20261822

Conjugacy classes of subgroups

Complements

Subgroups — D₄⋊#11715906 #20261822