Subgroups — D₄⋊#13089678 #26041007

Order 11584.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13089678	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13089678	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×C₁₈₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#13089678	—	2	1	no	—
5	C₂×#13089678	—	2	1	no	—
6	C₂×D₄×C₁₈₁	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₁₈₁	—	2	1	no	—
8	C₄⋊C₄×C₁₈₁	C₄	1	1	yes	characteristic
9	C₂²⋊C₄×C₁₈₁	—	2	1	no	—
10	C₄²×C₁₈₁	C₂²	1	1	yes	characteristic
11	#13089678	—	2	2	no	—
12	#13089678	—	4	1	no	—
13	C₂³×C₁₈₁	—	2	1	no	—
14	D₄×C₁₈₁	—	2	1	no	—
15	D₄×C₁₈₁	C₈	1	2	yes	complemented
16	C₂×C₄×C₁₈₁	—	2	1	no	—
17	C₂×C₄×C₁₈₁	—	4	1	no	—
18	C₂×C₄×C₁₈₁	—	4	1	no	—
19	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₁₈₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₁₈₁	D₄	1	1	yes	characteristic
22	C₂²×C₁₈₁	—	2	2	no	—
23	C₂²×C₁₈₁	—	4	1	no	—
24	C₂²×C₁₈₁	—	4	1	no	—
25	C₂²×C₁₈₁	C₂²⋊C₄	1	1	yes	characteristic
26	C₄×C₁₈₁	—	2	1	no	—
27	C₄×C₁₈₁	—	4	1	no	—
28	C₄×C₁₈₁	C₂×C₈	1	1	yes	characteristic
29	C₄×C₁₈₁	M₁₆	1	1	yes	characteristic
30	C₄×C₁₈₁	D₈	1	1	yes	characteristic
31	C₄×C₁₈₁	SD₁₆	1	1	yes	characteristic
32	C₂×C₁₈₁	—	4	2	no	—
33	C₂×C₁₈₁	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₁₈₁	#102	1	1	yes	characteristic
35	C₂×C₁₈₁	#104	1	1	yes	characteristic
36	C₁₈₁	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
37	D₄⋊C₈	—	181	1	no	maximal, Sylow
38	C₄×D₄	D₁₈₁	1	1	yes	characteristic
39	C₄⋊C₈	—	181	1	no	—
40	C₄×C₈	—	181	1	no	—
41	C₂×D₄	Dic₁₈₁	1	1	yes	characteristic
42	C₂²×C₄	—	2	1	no	—
43	C₂×C₈	—	362	1	no	—
44	C₂×C₈	—	362	1	no	—
45	C₄⋊C₄	Dic₁₈₁	1	1	yes	characteristic
46	C₂²⋊C₄	—	2	1	no	—
47	C₄²	C₂×D₁₈₁	1	1	yes	characteristic
48	C₂³	—	2	1	no	—
49	D₄	—	2	1	no	—
50	D₄	#13089678	1	2	yes	complemented
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	4	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	C₂×Dic₁₈₁	1	1	yes	characteristic
55	C₂×C₄	C₂²⋊D₁₈₁	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊D₁₈₁	1	1	yes	characteristic
57	C₈	—	362	2	no	—
58	C₈	—	724	1	no	—
59	C₂²	—	2	2	no	—
60	C₂²	—	4	1	no	—
61	C₂²	—	4	1	no	—
62	C₂²	C₂²⋊Dic₁₈₁	1	1	yes	characteristic
63	C₄	—	2	1	no	—
64	C₄	—	4	1	no	—
65	C₄	C₂×#13089678	1	1	yes	characteristic
66	C₄	#15668433	1	1	yes	characteristic
67	C₄	#15668434	1	1	yes	characteristic
68	C₄	#15668437	1	1	yes	characteristic
69	C₂	—	4	2	no	—
70	C₂	C₂²⋊#13089678	1	1	yes	characteristic
71	C₂	#19153737	1	1	yes	characteristic
72	C₂	#19153743	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₁₈₁
commutator	C₄×C₁₈₁	C₂×C₈
Frattini	C₄²	C₂×D₁₈₁
Fitting	C₄×D₄×C₁₈₁	C₂
socle	C₂²×C₁₈₁	C₂²⋊C₄
prime radical	C₂×D₄×C₁₈₁	C₄
cosocle	C₄²×C₁₈₁	C₂²
hypercenter	C₄×D₄	D₁₈₁
hypocenter	C₁₈₁	D₄⋊C₈
LCS	G ▷ C₄×C₁₈₁ ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₄⋊#13089678	C₂	semidirect
2. C₄×#13089678	C₂	semidirect
15. D₄×C₁₈₁	C₈	semidirect
36. C₁₈₁	D₄⋊C₈	semidirect
50. D₄	#13089678	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#13089678	2
C₄×#13089678	2
C₄×D₄×C₁₈₁	2
D₄⋊C₈	181

Subgroups — D4⋊#13089678 #26041007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄⋊#13089678 #26041007