Subgroups — #16840069

Order 3904.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14519769	C₂	1	1	yes	maximal, characteristic
2	#14519710	C₂	1	1	yes	maximal, characteristic
3	#14519708	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#92418	C₂	1	1	yes	maximal, characteristic
5	#14519701	C₂	1	1	yes	maximal, characteristic
6	#14519701	C₂	1	1	yes	maximal, characteristic
7	C₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₈×C₆₁	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₆₁	—	2	1	no	—
10	C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
11	C₄²×C₆₁	—	2	1	no	—
12	C₄²×C₆₁	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
14	C₄⋊Dic₆₁	C₂²	1	1	yes	characteristic
15	#11758196	—	2	1	no	—
16	#11758196	—	2	1	no	—
17	C₂×#92418	C₂²	1	1	yes	characteristic
18	C₂×#92418	C₂²	1	1	yes	characteristic
19	Q₈×C₆₁	—	2	1	no	—
20	Q₈×C₆₁	Q₈	1	2	yes	—
21	C₂×C₄×C₆₁	—	2	1	no	—
22	C₂×C₄×C₆₁	—	2	1	no	—
23	C₂×C₄×C₆₁	D₄	1	1	yes	characteristic
24	C₂×C₄×C₆₁	D₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂³	1	1	yes	characteristic
26	C₂×Dic₆₁	—	2	1	no	—
27	C₂×Dic₆₁	—	2	1	no	—
28	#92418	—	2	1	no	—
29	#92418	—	2	1	no	—
30	C₂²×C₆₁	C₂×D₄	1	1	yes	characteristic
31	C₄×C₆₁	—	2	2	no	—
32	C₄×C₆₁	—	2	1	no	—
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	—	4	1	no	—
35	C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
36	C₄×C₆₁	#41	1	1	yes	characteristic
37	Dic₆₁	—	4	1	no	—
38	Dic₆₁	—	4	1	no	—
39	C₂×C₆₁	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₆₁	#135	1	1	yes	characteristic
41	C₂×C₆₁	#137	1	1	yes	characteristic
42	#479	—	61	1	no	maximal, Sylow
43	C₆₁	#479	1	1	yes	characteristic, complemented, Sylow
44	#125	—	61	1	no	—
45	C₄×Q₈	D₆₁	1	1	yes	characteristic
46	#107	—	61	1	no	—
47	#106	—	61	1	no	—
48	C₄⋊C₈	—	61	1	no	—
49	#103	—	61	1	no	—
50	#103	—	61	1	no	—
51	C₂×Q₈	C₂×D₆₁	1	1	yes	characteristic
52	C₂×C₈	—	61	1	no	—
53	C₂×C₈	—	61	1	no	—
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	61	1	no	—
56	C₄⋊C₄	—	61	1	no	—
57	C₄⋊C₄	—	122	1	no	—
58	C₄⋊C₄	—	122	1	no	—
59	C₄⋊C₄	C₂×D₆₁	1	1	yes	characteristic
60	C₄²	—	2	1	no	—
61	C₄²	C₂×D₆₁	1	1	yes	characteristic
62	Q₈	—	2	1	no	—
63	Q₈	Dic₁₂₂	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	122	1	no	—
67	C₂×C₄	—	122	1	no	—
68	C₂×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
69	C₂×C₄	C₂²⋊D₆₁	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₆₁	1	1	yes	characteristic
71	C₈	—	122	1	no	—
72	C₈	—	122	1	no	—
73	C₂²	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
74	C₄	—	2	1	no	—
75	C₄	—	2	2	no	—
76	C₄	—	2	1	no	—
77	C₄	—	4	1	no	—
78	C₄	—	244	1	no	—
79	C₄	—	244	1	no	—
80	C₄	C₂×Dic₁₂₂	1	1	yes	characteristic
81	C₄	#11758222	1	1	yes	characteristic
82	C₂	#14519756	1	1	yes	characteristic
83	C₂	#14519797	1	1	yes	characteristic
84	C₂	#14519808	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₆₁
commutator, cosocle	C₂×C₄×C₆₁	C₂³
Frattini	C₂×C₄	C₂²×D₆₁
Fitting	C₄×Q₈×C₆₁	C₂
socle, prime radical	C₂²×C₆₁	C₂×D₄
hypercenter	C₄×Q₈	D₆₁
hypocenter	C₆₁	#479
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
43. C₆₁	#479	semidirect

Maximal subgroups

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

subgroup	index
#14519769	2
#14519710	2
#14519708	2
C₄⋊#92418	2
#14519701	2
C₄×Q₈×C₆₁	2
#479	61