Subgroups — #16839890

Order 3904.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₁₂₂	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#92418	C₂	1	1	yes	maximal, characteristic
3	#14519706	C₂	1	1	yes	maximal, characteristic
4	#14519706	C₂	1	1	yes	maximal, characteristic
5	#14519687	C₂	1	1	yes	maximal, characteristic
6	C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
7	#97×C₆₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₁₂₂	C₄	1	1	yes	characteristic
9	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₆₁	C₄	1	1	yes	characteristic
13	#11758196	C₄	1	1	yes	characteristic
14	#11758196	C₄	1	1	yes	characteristic
15	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
16	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
17	C₂×#92418	C₂²	1	1	yes	characteristic
18	C₂×#92418	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
22	C₂×Dic₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₆₁	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₆₁	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₆₁	C₂×C₄	1	1	yes	characteristic
26	Dic₁₂₂	—	2	2	no	—
27	C₈×C₆₁	—	2	1	no	—
28	C₈×C₆₁	Q₈	1	2	yes	complemented
29	#92418	—	2	1	no	—
30	#92418	—	2	1	no	—
31	C₂²×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₆₁	—	2	1	no	—
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₆₁	#41	1	1	yes	characteristic
36	Dic₆₁	—	2	1	no	—
37	Dic₆₁	—	2	1	no	—
38	Dic₆₁	—	2	1	no	—
39	Dic₆₁	M₁₆	1	2	yes	—
40	C₂×C₆₁	C₄×Q₈	1	1	yes	characteristic
41	C₂×C₆₁	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₆₁	#131	1	1	yes	characteristic
43	#446	—	61	1	no	maximal, Sylow
44	C₆₁	#446	1	1	yes	characteristic, complemented, Sylow
45	C₄×Q₈	—	61	1	no	—
46	C₄⋊C₈	—	61	1	no	—
47	C₄⋊C₈	—	61	1	no	—
48	C₄⋊C₈	—	61	1	no	—
49	#97	—	61	1	no	—
50	#97	D₆₁	1	1	yes	characteristic
51	C₄×C₈	—	61	1	no	—
52	C₂×Q₈	—	61	1	no	—
53	C₂×C₈	—	61	1	no	—
54	C₂×C₈	—	61	1	no	—
55	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
56	C₂×C₈	C₂×D₆₁	1	1	yes	characteristic
57	C₄⋊C₄	—	61	1	no	—
58	C₄⋊C₄	—	61	1	no	—
59	C₄⋊C₄	—	61	1	no	—
60	C₄²	—	61	1	no	—
61	C₄²	—	61	1	no	—
62	C₄²	C₂×D₆₁	1	1	yes	characteristic
63	Q₈	—	122	2	no	—
64	C₂×C₄	—	61	1	no	—
65	C₂×C₄	—	61	1	no	—
66	C₂×C₄	—	61	1	no	—
67	C₂×C₄	—	61	1	no	—
68	C₂×C₄	C₄×D₆₁	1	1	yes	characteristic
69	C₂×C₄	C₄×D₆₁	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	122	1	no	—
73	C₈	—	122	1	no	—
74	C₈	Dic₁₂₂	1	2	yes	complemented
75	C₂²	C₂×C₄×D₆₁	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	2	1	no	—
78	C₄	—	61	2	no	—
79	C₄	—	122	1	no	—
80	C₄	—	122	1	no	—
81	C₄	—	122	1	no	—
82	C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
83	C₄	#11758222	1	1	yes	characteristic
84	C₂	C₄×Dic₁₂₂	1	1	yes	characteristic
85	C₂	M₁₆×D₆₁	1	1	yes	characteristic
86	C₂	#14519785	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₆₁
commutator, socle, prime radical	C₂²×C₆₁	C₂²×C₄
Fitting	#97×C₆₁	C₂
cosocle	C₂×C₄×C₆₁	C₂³
hypercenter	#97	D₆₁
hypocenter	C₆₁	#446
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ #97

Complements

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

N	H ≅ G/N	type
28. C₈×C₆₁	Q₈	semidirect
44. C₆₁	#446	semidirect
74. C₈	Dic₁₂₂	semidirect

Maximal subgroups

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

subgroup	index
C₄×Dic₁₂₂	2
C₄⋊#92418	2
#14519706	2
#14519687	2
C₈×Dic₆₁	2
#97×C₆₁	2
#446	61