Subgroups — #14580465

Order 2624.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₈₂	C₂	1	1	yes	maximal, characteristic
2	#13050093	C₂	1	1	yes	maximal, characteristic
3	#13050093	C₂	1	1	yes	maximal, characteristic
4	#13050075	C₂	1	1	yes	maximal, characteristic
5	#13050074	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₄₁	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₈₂	C₄	1	1	yes	characteristic
9	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₄₁	C₂²	1	1	yes	characteristic
11	C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₁	C₄	1	1	yes	characteristic
13	#10620279	C₄	1	1	yes	characteristic
14	#10620279	C₄	1	1	yes	characteristic
15	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
16	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
17	C₂×#66491	C₂²	1	1	yes	characteristic
18	C₂×#66491	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₄₁	C₂×C₄	1	1	yes	characteristic
26	Dic₈₂	—	2	2	no	—
27	C₈×C₄₁	—	2	1	no	—
28	C₈×C₄₁	—	2	1	no	—
29	#66491	—	2	1	no	—
30	#66491	Q₈	1	2	yes	complemented
31	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₄₁	—	2	1	no	—
33	C₄×C₄₁	—	2	1	no	—
34	C₄×C₄₁	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₄₁	#41	1	1	yes	characteristic
36	Dic₄₁	—	2	1	no	—
37	Dic₄₁	—	2	1	no	—
38	Dic₄₁	—	2	1	no	—
39	Dic₄₁	M₁₆	1	2	yes	—
40	C₂×C₄₁	C₄×Q₈	1	1	yes	characteristic
41	C₂×C₄₁	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₄₁	#131	1	1	yes	characteristic
43	#446	—	41	1	no	maximal, Sylow
44	C₄₁	#446	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₈	—	41	1	no	—
46	C₄⋊C₈	—	41	1	no	—
47	C₄⋊C₈	—	41	1	no	—
48	C₄⋊C₈	D₄₁	1	1	yes	characteristic
49	#97	—	41	1	no	—
50	#97	—	41	1	no	—
51	C₄×C₈	—	41	1	no	—
52	C₂×Q₈	—	41	1	no	—
53	C₂×C₈	—	41	1	no	—
54	C₂×C₈	—	41	1	no	—
55	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
56	C₂×C₈	C₂×D₄₁	1	1	yes	characteristic
57	C₄⋊C₄	—	41	1	no	—
58	C₄⋊C₄	—	41	1	no	—
59	C₄⋊C₄	—	41	1	no	—
60	C₄²	—	41	1	no	—
61	C₄²	—	41	1	no	—
62	C₄²	C₂×D₄₁	1	1	yes	characteristic
63	Q₈	—	82	2	no	—
64	C₂×C₄	—	41	1	no	—
65	C₂×C₄	—	41	1	no	—
66	C₂×C₄	—	41	1	no	—
67	C₂×C₄	—	41	1	no	—
68	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
69	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	2	1	no	—
73	C₈	—	41	2	no	—
74	C₈	—	82	1	no	—
75	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	41	2	no	—
79	C₄	—	82	1	no	—
80	C₄	—	82	1	no	—
81	C₄	—	82	1	no	—
82	C₄	#10620308	1	1	yes	characteristic
83	C₄	Q₈×D₄₁	1	1	yes	characteristic
84	C₂	#13050129	1	1	yes	characteristic
85	C₂	M₁₆×D₄₁	1	1	yes	characteristic
86	C₂	#13050170	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator, socle, prime radical	C₂²×C₄₁	C₂²×C₄
Fitting	C₄⋊C₈×C₄₁	C₂
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₄⋊C₈	D₄₁
hypocenter	C₄₁	#446
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
30. #66491	Q₈	semidirect
44. C₄₁	#446	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₈₂	2
#13050093	2
#13050075	2
#13050074	2
C₈×Dic₄₁	2
C₄⋊C₈×C₄₁	2
#446	41