Subgroups — #16840121

Order 3904.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519777	C₂	1	1	yes	maximal, characteristic, complemented
2	#14519701	C₂	1	2	yes	maximal, complemented
3	#14519698	C₂	1	2	yes	maximal
4	#14519688	C₂	1	1	yes	maximal, characteristic, complemented
5	#124×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₆₁	C₂²	1	1	yes	characteristic
7	C₂×D₄×C₆₁	C₂²	1	1	yes	characteristic
8	C₂×Dic₁₂₂	—	2	1	no	—
9	C₂²⋊C₄×C₆₁	—	2	1	no	—
10	C₂²⋊C₄×C₆₁	—	2	1	no	—
11	C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₆₁	—	2	1	no	—
13	C₄⋊Dic₆₁	C₂²	1	2	yes	—
14	C₂×#92418	C₂²	1	2	yes	—
15	C₂³×C₆₁	—	2	1	no	—
16	Q₈×C₆₁	—	2	2	no	—
17	D₄×C₆₁	—	2	2	no	—
18	C₂×C₄×C₆₁	—	2	1	no	—
19	C₂×C₄×C₆₁	D₄	1	1	yes	characteristic
20	C₂×C₄×C₆₁	D₄	1	1	yes	characteristic
21	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₆₁	—	2	2	no	—
23	Dic₁₂₂	—	4	2	no	—
24	#92418	—	2	2	no	—
25	C₂²×C₆₁	—	4	1	no	—
26	C₂²×C₆₁	—	4	1	no	—
27	C₂²×C₆₁	—	4	1	no	—
28	C₂²×C₆₁	C₂×D₄	1	1	yes	characteristic
29	C₄×C₆₁	—	2	1	no	—
30	C₄×C₆₁	—	2	1	no	—
31	C₄×C₆₁	—	4	1	no	—
32	C₄×C₆₁	#41	1	2	yes	—
33	Dic₆₁	—	4	2	no	—
34	C₂×C₆₁	—	8	1	no	—
35	C₂×C₆₁	#124	1	1	yes	characteristic
36	C₂×C₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
37	C₂×C₆₁	#137	1	1	yes	characteristic
38	#489	—	61	1	no	maximal, Sylow
39	C₆₁	#489	1	1	yes	characteristic, complemented, Sylow
40	C₄⋊Q₈	—	61	1	no	—
41	#124	D₆₁	1	1	yes	characteristic
42	#103	—	61	2	no	—
43	#102	—	61	2	no	—
44	#97	—	61	1	no	—
45	C₂×Q₈	—	122	1	no	—
46	C₂×Q₈	C₂×D₆₁	1	1	yes	characteristic
47	C₂×D₄	C₂×D₆₁	1	1	yes	characteristic
48	C₂×C₈	—	61	2	no	—
49	C₄⋊C₄	—	61	2	no	—
50	C₄⋊C₄	—	122	1	no	—
51	C₂²⋊C₄	—	2	1	no	—
52	C₂²⋊C₄	—	2	1	no	—
53	C₄²	C₂×D₆₁	1	1	yes	characteristic
54	C₂³	—	2	1	no	—
55	Q₈	—	2	2	no	—
56	Q₈	—	244	2	no	—
57	D₄	—	2	2	no	—
58	C₂×C₄	—	2	1	no	—
59	C₂×C₄	—	122	2	no	—
60	C₂×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
63	C₈	—	122	2	no	—
64	C₂²	—	4	1	no	—
65	C₂²	—	4	1	no	—
66	C₂²	—	4	1	no	—
67	C₂²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	1	no	—
70	C₄	—	4	1	no	—
71	C₄	—	244	2	no	—
72	C₄	#11758224	1	2	yes	—
73	C₂	—	8	1	no	—
74	C₂	#14519764	1	1	yes	characteristic
75	C₂	#14519802	1	1	yes	characteristic
76	C₂	#14519807	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₆₁
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	#124×C₆₁	C₂
socle	C₂²×C₆₁	C₂×D₄
prime radical	C₂×D₄×C₆₁	C₂²
hypercenter	#124	D₆₁
hypocenter	C₆₁	#489
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #124

Complements

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

N	H ≅ G/N	type
1. #14519777	C₂	semidirect
2. #14519701	C₂	semidirect
4. #14519688	C₂	semidirect
39. C₆₁	#489	semidirect

Maximal subgroups

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

subgroup	index
#14519777	2
#14519701	2
#14519698	2
#14519688	2
#124×C₆₁	2
#489	61