Subgroups — D₄⋊#11764049 #22578490

Order 8768.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11764049	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#11764049	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×#10587739	C₂	1	1	yes	maximal, characteristic
4	C₂×#11764049	—	2	1	no	—
5	C₂×#11764049	—	2	1	no	—
6	C₂²×#10587739	—	2	1	no	—
7	C₄⋊#10587739	C₄	1	1	yes	characteristic
8	C₂²⋊#10587739	—	2	1	no	—
9	C₄×#10587739	C₂²	1	1	yes	characteristic
10	D₄×D₁₃₇	C₄	1	1	yes	characteristic
11	#11764049	—	2	2	no	—
12	#11764049	—	4	1	no	—
13	C₂×#10587739	—	2	1	no	—
14	C₂×#10587739	—	4	1	no	—
15	C₂×#10587739	—	4	1	no	—
16	C₂×#10587739	D₄	1	1	yes	characteristic
17	C₂×#10587739	D₄	1	1	yes	characteristic
18	C₂²×D₁₃₇	—	2	1	no	—
19	D₅₄₈	C₈	1	1	yes	characteristic, complemented
20	C₂²⋊D₁₃₇	—	2	1	no	—
21	C₄×D₁₃₇	C₂×C₄	1	1	yes	characteristic
22	D₄×C₁₃₇	C₈	1	1	yes	characteristic, complemented
23	C₂²×C₁₃₇	—	2	1	no	—
24	C₂×D₁₃₇	—	2	1	no	—
25	C₂×D₁₃₇	—	4	1	no	—
26	C₂×D₁₃₇	—	4	1	no	—
27	C₂×D₁₃₇	C₂²⋊C₄	1	1	yes	characteristic
28	#10587739	—	2	1	no	—
29	#10587739	—	4	1	no	—
30	#10587739	D₈	1	1	yes	characteristic
31	#10587739	SD₁₆	1	1	yes	characteristic
32	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
33	Dic₁₃₇	M₁₆	1	1	yes	characteristic
34	C₂×C₁₃₇	—	4	1	no	—
35	C₂×C₁₃₇	C₂²⋊C₈	1	1	yes	characteristic
36	D₁₃₇	—	4	1	no	—
37	D₁₃₇	#102	1	1	yes	characteristic
38	D₁₃₇	#104	1	1	yes	characteristic
39	C₁₃₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
40	D₄⋊C₈	—	137	1	no	maximal, Sylow
41	C₄×D₄	—	137	1	no	—
42	C₄⋊C₈	—	137	1	no	—
43	C₄×C₈	—	137	1	no	—
44	C₂×D₄	—	137	1	no	—
45	C₂²×C₄	—	274	1	no	—
46	C₂×C₈	—	274	1	no	—
47	C₂×C₈	—	274	1	no	—
48	C₄⋊C₄	—	137	1	no	—
49	C₂²⋊C₄	—	274	1	no	—
50	C₄²	—	137	1	no	—
51	C₂³	—	274	1	no	—
52	D₄	—	274	1	no	—
53	D₄	—	137	1	no	—
54	D₄	#11764049	1	1	yes	characteristic, complemented
55	C₂×C₄	—	274	1	no	—
56	C₂×C₄	—	548	1	no	—
57	C₂×C₄	—	548	1	no	—
58	C₂×C₄	—	137	1	no	—
59	C₂×C₄	—	137	1	no	—
60	C₂×C₄	—	137	1	no	—
61	C₈	—	274	2	no	—
62	C₈	—	548	1	no	—
63	C₂²	—	2	1	no	—
64	C₂²	—	274	1	no	—
65	C₂²	—	548	1	no	—
66	C₂²	—	548	1	no	—
67	C₂²	—	137	1	no	—
68	C₄	—	274	1	no	—
69	C₄	—	548	1	no	—
70	C₄	—	137	1	no	—
71	C₄	—	137	1	no	—
72	C₄	—	137	1	no	—
73	C₄	C₂×#11764049	1	1	yes	characteristic
74	C₂	—	4	1	no	—
75	C₂	—	548	1	no	—
76	C₂	—	137	1	no	—
77	C₂	—	137	1	no	—
78	C₂	C₂²⋊#11764049	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11764049
commutator	C₄×C₁₃₇	C₂×C₈
Frattini	C₄	C₂×#11764049
Fitting	D₄×C₁₃₇	C₈
socle	C₂×C₁₃₇	C₂²⋊C₈
hypercenter	D₄	#11764049
hypocenter	C₁₃₇	D₄⋊C₈
LCS	G ▷ C₄×C₁₃₇ ▷ C₂×C₁₃₇ ▷ C₁₃₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11764049	C₂	semidirect
2. C₄×#11764049	C₂	semidirect
19. D₅₄₈	C₈	semidirect
22. D₄×C₁₃₇	C₈	semidirect
39. C₁₃₇	D₄⋊C₈	semidirect
54. D₄	#11764049	semidirect

Subgroups — D4⋊#11764049 #22578490

Conjugacy classes of subgroups

Complements

Subgroups — D₄⋊#11764049 #22578490