Subgroups — #14580390

Order 2624.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₄₁	C₂	1	1	yes	maximal, characteristic
2	#13050093	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#66491	C₂	1	1	yes	maximal, characteristic
4	#13050074	C₂	1	2	yes	maximal, complemented
5	C₂²⋊C₈×C₄₁	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄×C₄₁	C₂²	1	1	yes	characteristic
7	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
8	C₂²×Dic₄₁	C₄	1	1	yes	characteristic
9	C₂×C₈×C₄₁	C₂²	1	2	yes	—
10	C₄×Dic₄₁	C₄	1	1	yes	characteristic
11	C₄×Dic₄₁	C₄	1	1	yes	characteristic
12	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
13	C₄×Dic₄₁	C₂²	1	1	yes	characteristic
14	C₂×#66491	C₂²	1	2	yes	—
15	C₂³×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₄₁	—	2	2	no	—
17	C₂×C₄×C₄₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₄₁	C₂³	1	1	yes	characteristic
19	C₂×Dic₄₁	—	2	2	no	—
20	C₂×Dic₄₁	—	2	2	no	—
21	C₂×Dic₄₁	C₂×C₄	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	C₈×C₄₁	—	2	2	no	—
26	#66491	—	2	2	no	—
27	C₂²×C₄₁	—	2	1	no	—
28	C₂²×C₄₁	—	2	1	no	—
29	C₂²×C₄₁	M₁₆	1	2	yes	—
30	C₂²×C₄₁	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₄₁	—	2	1	no	—
32	C₄×C₄₁	#41	1	2	yes	—
33	Dic₄₁	—	2	1	no	—
34	Dic₄₁	—	2	1	no	—
35	Dic₄₁	—	2	1	no	—
36	Dic₄₁	M₁₆	1	2	yes	—
37	C₂×C₄₁	—	2	2	no	—
38	C₂×C₄₁	#117	1	1	yes	characteristic
39	C₂×C₄₁	C₂×M₁₆	1	1	yes	characteristic
40	C₂×C₄₁	C₂×M₁₆	1	1	yes	characteristic
41	#432	—	41	1	no	maximal, Sylow
42	C₄₁	#432	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₄²	—	41	1	no	—
44	C₄⋊C₈	—	41	2	no	—
45	C₂²⋊C₈	—	41	1	no	—
46	C₂²⋊C₈	D₄₁	1	1	yes	characteristic
47	#97	—	41	2	no	—
48	C₂²×C₄	—	41	1	no	—
49	C₂²×C₄	—	41	1	no	—
50	C₂²×C₄	C₂×D₄₁	1	1	yes	characteristic
51	C₂×C₈	—	41	2	no	—
52	C₂×C₈	C₂×D₄₁	1	2	yes	—
53	C₄²	—	41	1	no	—
54	C₄²	—	41	1	no	—
55	C₄²	—	41	1	no	—
56	C₄²	—	41	1	no	—
57	C₂³	C₄×D₄₁	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	41	1	no	—
60	C₂×C₄	—	41	1	no	—
61	C₂×C₄	—	41	1	no	—
62	C₂×C₄	—	41	1	no	—
63	C₂×C₄	—	82	2	no	—
64	C₂×C₄	—	82	2	no	—
65	C₂×C₄	C₄×D₄₁	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₄₁	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	82	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	#10620272	1	2	yes	—
72	C₂²	C₂×C₄×D₄₁	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	41	2	no	—
75	C₄	—	82	1	no	—
76	C₄	—	82	1	no	—
77	C₄	—	82	1	no	—
78	C₄	#10620308	1	2	yes	—
79	C₂	—	2	2	no	—
80	C₂	#13050120	1	1	yes	characteristic
81	C₂	M₁₆×D₄₁	1	1	yes	characteristic
82	C₂	C₂×#10620272	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₄₁
commutator, socle	C₂²×C₄₁	C₂²×C₄
Fitting	C₂²⋊C₈×C₄₁	C₂
prime radical	C₂³×C₄₁	C₂×C₄
cosocle	C₂×C₄×C₄₁	C₂³
hypercenter	C₂²⋊C₈	D₄₁
hypocenter	C₄₁	#432
LCS	G ▷ C₂²×C₄₁ ▷ C₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
2. #13050093	C₂	semidirect
4. #13050074	C₂	semidirect
42. C₄₁	#432	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₄₁	2
#13050093	2
C₂²⋊#66491	2
#13050074	2
C₂²⋊C₈×C₄₁	2
#432	41