Subgroups — #21461032

Order 7808.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840778	C₂	1	2	yes	maximal
2	#92420⋊C₈	C₂	1	4	yes	maximal, complemented
3	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#92420	C₄	1	4	yes	—
5	C₂²⋊#92420	C₄	1	4	yes	—
6	C₄×#92420	C₂²	1	4	yes	—
7	C₂²×#92418	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
9	C₈×Dic₆₁	C₄	1	2	yes	—
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
12	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
13	C₂²×Dic₆₁	C₂×C₄	1	2	yes	—
14	C₂×#92420	C₂×C₄	1	8	yes	—
15	C₂×C₈×C₆₁	—	2	2	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
19	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
20	C₂×#92418	—	2	2	no	—
21	C₂×#92418	C₂×C₄	1	2	yes	—
22	C₂³×C₆₁	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
24	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
25	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
26	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×Dic₆₁	—	2	4	no	—
28	C₂×Dic₆₁	C₄²	1	2	yes	—
29	C₂×Dic₆₁	C₂²×C₄	1	2	yes	—
30	#92420	—	2	8	no	—
31	C₈×C₆₁	—	2	2	no	—
32	#92418	—	2	2	no	—
33	C₂²×C₆₁	—	2	2	no	—
34	C₂²×C₆₁	#97	1	2	yes	—
35	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
36	C₄×C₆₁	#97	1	2	yes	—
37	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
38	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
39	Dic₆₁	—	2	2	no	—
40	Dic₆₁	#131	1	4	yes	—
41	#1452	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	—	2	2	no	—
43	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
44	C₂×C₆₁	#405	1	2	yes	—
45	#431	—	61	2	no	—
46	C₂×C₄×C₈	—	61	1	no	—
47	#322	—	61	4	no	—
48	C₆₁	#1452	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₈	—	61	1	no	—
50	C₂²×C₈	#6923	1	1	yes	characteristic
51	C₂×C₄²	—	61	1	no	—
52	C₄⋊C₈	—	61	4	no	—
53	C₂²⋊C₈	—	61	4	no	—
54	C₄×C₈	—	61	4	no	—
55	C₄×C₈	—	61	2	no	—
56	C₄×C₈	—	61	2	no	—
57	C₂²×C₄	—	61	2	no	—
58	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
59	C₂×C₈	—	2	2	no	—
60	C₂×C₈	—	61	8	no	—
61	C₂×C₈	—	61	2	no	—
62	C₂×C₈	—	122	2	no	—
63	C₂×C₈	C₂×#6923	1	2	yes	—
64	C₄²	—	61	2	no	—
65	C₄²	—	61	1	no	—
66	C₄²	—	61	1	no	—
67	C₂³	C₄×#6923	1	1	yes	characteristic
68	C₂×C₄	—	61	2	no	—
69	C₂×C₄	—	61	2	no	—
70	C₂×C₄	—	122	4	no	—
71	C₂×C₄	#11758213	1	2	yes	—
72	C₂×C₄	C₄×#6923	1	1	yes	characteristic
73	C₂×C₄	#11758217	1	2	yes	—
74	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	122	8	no	—
77	C₈	—	122	2	no	—
78	C₂²	—	2	2	no	—
79	C₂²	#14519832	1	2	yes	—
80	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
81	C₄	—	61	4	no	—
82	C₄	—	122	2	no	—
83	C₄	#14519832	1	2	yes	—
84	C₄	C₂×#11758217	1	1	yes	characteristic
85	C₄	C₂×#11758213	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	C₂×#14519832	1	1	yes	characteristic
88	C₂	#16840725	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	C₂²×C₈×C₆₁	C₄
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	#1452
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #92420⋊C₈	C₂	semidirect
48. C₆₁	#1452	semidirect