Subgroups — #21462192

Order 7808.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840685	C₂	1	2	yes	maximal, complemented
2	#16840658	C₂	1	2	yes	maximal
3	#16840654	C₂	1	2	yes	maximal, complemented
4	#16839718	C₂	1	1	yes	maximal, characteristic
5	#14519851	C₂²	1	4	yes	—
6	C₂×#11758194	C₂²	1	1	yes	characteristic
7	C₂²×#92418	C₄	1	1	yes	characteristic
8	#14519688	C₄	1	1	yes	characteristic
9	#14519688	C₂²	1	1	yes	characteristic
10	C₄×#92418	C₄	1	1	yes	characteristic
11	C₄×#92418	C₂²	1	1	yes	characteristic
12	#117×C₆₁	C₄	1	1	yes	characteristic
13	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₄⋊C₄×C₆₁	—	2	1	no	—
15	C₂²⋊C₄×C₆₁	—	2	1	no	—
16	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	#11758194	—	2	2	no	—
19	C₂×#92418	—	2	2	no	—
20	C₂×#92418	C₂×C₄	1	1	yes	characteristic
21	C₂×#92418	C₂×C₄	1	1	yes	characteristic
22	C₂×#92418	C₂×C₄	1	1	yes	characteristic
23	C₂×#92418	C₂³	1	1	yes	characteristic
24	#11758187	—	2	4	no	—
25	C₂³×C₆₁	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	—	2	1	no	—
29	C₂×C₄×C₆₁	—	2	1	no	—
30	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
32	#92418	—	2	1	no	—
33	#92418	—	2	1	no	—
34	#92418	M₁₆	1	2	yes	—
35	#92418	#41	1	2	yes	—
36	C₂²×C₆₁	—	2	1	no	—
37	C₂²×C₆₁	—	4	1	no	—
38	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	—	4	1	no	—
41	C₄×C₆₁	—	4	1	no	—
42	C₄×C₆₁	#117	1	1	yes	characteristic
43	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
44	#2166	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	—	4	1	no	—
47	C₂×C₆₁	#432	1	1	yes	characteristic
48	#405	—	61	1	no	—
49	#364	—	61	2	no	—
50	#349	—	61	2	no	—
51	#347	—	61	2	no	—
52	C₆₁	#2166	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	61	1	no	—
54	C₂²×C₈	—	61	1	no	—
55	#117	#6923	1	1	yes	characteristic
56	M₃₂	—	61	4	no	—
57	#97	—	61	1	no	—
58	#97	—	61	1	no	—
59	C₄×C₈	—	61	1	no	—
60	C₄×C₈	—	61	1	no	—
61	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
62	M₁₆	—	122	2	no	—
63	C₂×C₈	—	61	1	no	—
64	C₂×C₈	—	61	1	no	—
65	C₂×C₈	—	61	1	no	—
66	C₂×C₈	—	61	1	no	—
67	C₂×C₈	—	122	2	no	—
68	C₄⋊C₄	—	2	1	no	—
69	C₂²⋊C₄	—	2	1	no	—
70	C₄²	C₂×#6923	1	1	yes	characteristic
71	C₄²	C₂×#6923	1	1	yes	characteristic
72	C₁₆	—	122	4	no	—
73	C₂³	#11758217	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	#11758217	1	1	yes	characteristic
79	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
80	C₈	—	61	2	no	—
81	C₈	—	61	2	no	—
82	C₈	—	122	1	no	—
83	C₈	—	122	1	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂×#11758217	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	4	1	no	—
89	C₄	—	4	1	no	—
90	C₄	#14519856	1	1	yes	characteristic
91	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	4	1	no	—
94	C₂	#16840782	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519856
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#117×C₆₁	C₄
socle	C₂×C₆₁	#432
hypercenter	#117	#6923
hypocenter	C₆₁	#2166
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₄² ◁ #117

Complements

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

N	H ≅ G/N	type
1. #16840685	C₂	semidirect
3. #16840654	C₂	semidirect
52. C₆₁	#2166	semidirect