Subgroups — D₄×#66491 #14580402

Order 2624.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66491	C₂	1	2	yes	maximal, complemented
2	C₄⋊#66491	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#66491	C₂	1	2	yes	maximal, complemented
4	C₄×#66491	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×D₄×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₁	C₄	1	1	yes	characteristic
7	C₂²×C₄×C₄₁	C₂²	1	2	yes	—
8	C₄⋊C₄×C₄₁	C₄	1	1	yes	characteristic
9	C₂²⋊C₄×C₄₁	C₄	1	2	yes	—
10	C₄²×C₄₁	C₂²	1	1	yes	characteristic
11	C₂×#66491	—	2	4	no	—
12	C₂×#66491	C₂²	1	2	yes	—
13	C₂×#66491	C₂²	1	1	yes	characteristic
14	C₂×#66491	C₂²	1	1	yes	characteristic
15	C₂³×C₄₁	C₂×C₄	1	2	yes	—
16	D₄×C₄₁	C₈	1	4	yes	complemented
17	C₂×C₄×C₄₁	—	2	2	no	—
18	C₂×C₄×C₄₁	—	2	2	no	—
19	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
23	#66491	—	2	2	no	—
24	#66491	—	2	1	no	—
25	#66491	D₄	1	2	yes	direct product factor
26	C₂²×C₄₁	—	2	2	no	—
27	C₂²×C₄₁	—	2	2	no	—
28	C₂²×C₄₁	C₂×C₈	1	4	yes	complemented
29	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₄₁	—	2	2	no	—
31	C₄×C₄₁	—	2	1	no	—
32	C₄×C₄₁	C₂×C₈	1	2	yes	complemented
33	C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
34	C₄×C₄₁	#41	1	1	yes	characteristic
35	C₂×C₄₁	—	2	4	no	—
36	C₂×C₄₁	C₄×D₄	1	1	yes	characteristic
37	C₂×C₄₁	C₂²×C₈	1	1	yes	characteristic
38	C₂×C₄₁	#131	1	1	yes	characteristic
39	C₈×D₄	—	41	1	no	maximal, Sylow
40	C₄₁	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₈	—	41	2	no	—
42	C₄×D₄	D₄₁	1	1	yes	characteristic
43	C₄⋊C₈	—	41	1	no	—
44	C₂²⋊C₈	—	41	2	no	—
45	C₄×C₈	—	41	1	no	—
46	C₂×D₄	Dic₄₁	1	1	yes	characteristic
47	C₂²×C₄	C₂×D₄₁	1	2	yes	—
48	C₂×C₈	—	41	1	no	—
49	C₂×C₈	—	41	1	no	—
50	C₂×C₈	—	41	2	no	—
51	C₂×C₈	—	82	4	no	—
52	C₄⋊C₄	Dic₄₁	1	1	yes	characteristic
53	C₂²⋊C₄	Dic₄₁	1	2	yes	—
54	C₄²	C₂×D₄₁	1	1	yes	characteristic
55	C₂³	C₂×Dic₄₁	1	2	yes	—
56	D₄	#66491	1	4	yes	direct product factor
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	C₂×Dic₄₁	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₄₁	1	2	yes	—
61	C₂×C₄	C₂×Dic₄₁	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
63	C₈	—	41	2	no	—
64	C₈	—	82	2	no	—
65	C₈	—	82	1	no	—
66	C₂²	—	2	2	no	—
67	C₂²	—	2	2	no	—
68	C₂²	C₂×#66491	1	4	yes	complemented
69	C₂²	C₂²×Dic₄₁	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	C₂×#66491	1	2	yes	complemented
73	C₄	D₄×D₄₁	1	1	yes	characteristic
74	C₄	#10620308	1	1	yes	characteristic
75	C₂	—	2	4	no	—
76	C₂	D₄×Dic₄₁	1	1	yes	characteristic
77	C₂	C₂²×#66491	1	1	yes	characteristic
78	C₂	#13050171	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator	C₂×C₄₁	C₂²×C₈
Fitting	C₄×D₄×C₄₁	C₂
socle	C₂²×C₄₁	C₂²×C₄
prime radical	C₂×D₄×C₄₁	C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄×D₄	D₄₁
hypocenter	C₄₁	C₈×D₄
LCS	G ▷ C₂×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#66491	C₂	semidirect
2. C₄⋊#66491	C₂	semidirect
3. C₂²⋊#66491	C₂	semidirect
4. C₄×#66491	C₂	semidirect
16. D₄×C₄₁	C₈	semidirect
25. #66491	D₄	direct (N × H)
28. C₂²×C₄₁	C₂×C₈	semidirect
32. C₄×C₄₁	C₂×C₈	semidirect
40. C₄₁	C₈×D₄	semidirect
56. D₄	#66491	direct (N × H)
68. C₂²	C₂×#66491	semidirect
72. C₄	C₂×#66491	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66491	2
C₄⋊#66491	2
C₂²⋊#66491	2
C₄×#66491	2
C₄×D₄×C₄₁	2
C₈×D₄	41

Subgroups — D4×#66491 #14580402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×#66491 #14580402