Subgroups — #21447579

Order 7808.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#11758185	C₂	1	1	yes	maximal, characteristic
2	#16839717	C₂	1	1	yes	maximal, characteristic
3	#16839580	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	C₄	1	1	yes	characteristic
6	#14519736	C₄	1	1	yes	characteristic
7	C₂×#11758185	—	2	2	no	—
8	C₂×#11758185	C₂²	1	2	yes	—
9	#14519687	C₄	1	2	yes	—
10	C₈×Dic₆₁	C₂²	1	2	yes	—
11	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
12	M₃₂×C₆₁	—	2	2	no	—
13	C₂×C₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	D₄	1	2	yes	—
17	C₂×C₈×C₆₁	Q₈	1	2	yes	—
18	C₂×C₈×C₆₁	C₂³	1	1	yes	characteristic
19	C₂²⋊Dic₆₁	C₈	1	2	yes	—
20	C₄⋊Dic₆₁	C₈	1	2	yes	—
21	C₄×Dic₆₁	C₂×C₄	1	2	yes	—
22	#11758194	—	2	2	no	—
23	C₂×#92418	C₂×C₄	1	2	yes	—
24	C₁₆×C₆₁	—	2	2	no	—
25	#11758185	—	2	2	no	—
26	C₂³×C₆₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
32	C₈×C₆₁	C₄⋊C₄	1	2	yes	—
33	C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
34	C₈×C₆₁	C₂×Q₈	1	1	yes	characteristic
35	#92418	—	2	2	no	—
36	C₂²×C₆₁	—	2	2	no	—
37	C₂²×C₆₁	C₄⋊C₈	1	2	yes	—
38	C₂²×C₆₁	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₆₁	C₄⋊C₈	1	2	yes	—
40	C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
42	Dic₆₁	—	2	4	no	—
43	#2151	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	—	2	2	no	—
45	C₂×C₆₁	C₂×C₄⋊C₈	1	1	yes	characteristic
46	C₂×C₆₁	#504	1	2	yes	—
47	C₂×M₃₂	D₆₁	1	1	yes	characteristic
48	C₂²×C₁₆	—	61	1	no	—
49	#405	—	61	1	no	—
50	C₄⋊C₁₆	—	61	4	no	—
51	C₆₁	#2151	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₁₆	—	61	1	no	—
53	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
54	#117	—	61	1	no	—
55	M₃₂	—	2	2	no	—
56	C₂×C₁₆	—	61	2	no	—
57	C₂×C₁₆	—	122	2	no	—
58	C₂×C₁₆	C₂×D₆₁	1	2	yes	—
59	#97	—	61	2	no	—
60	C₄×C₈	—	61	2	no	—
61	C₂²×C₄	C₄×D₆₁	1	1	yes	characteristic
62	M₁₆	—	122	2	no	—
63	C₂×C₈	—	61	2	no	—
64	C₂×C₈	Dic₁₂₂	1	2	yes	—
65	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₆₁	1	2	yes	—
67	C₂×C₈	C₂²×D₆₁	1	1	yes	characteristic
68	C₄⋊C₄	—	61	2	no	—
69	C₂²⋊C₄	—	61	2	no	—
70	C₄²	—	61	2	no	—
71	C₁₆	—	2	2	no	—
72	C₁₆	—	122	2	no	—
73	C₂³	C₈×D₆₁	1	1	yes	characteristic
74	C₂×C₄	—	61	4	no	—
75	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
76	C₂×C₄	#11758189	1	2	yes	—
77	C₂×C₄	#11758196	1	2	yes	—
78	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
79	C₈	—	122	2	no	—
80	C₈	#11758196	1	2	yes	—
81	C₈	C₂×Dic₁₂₂	1	1	yes	characteristic
82	C₈	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
83	C₂²	—	2	2	no	—
84	C₂²	#14519706	1	2	yes	—
85	C₂²	C₂×C₈×D₆₁	1	1	yes	characteristic
86	C₄	—	122	4	no	—
87	C₄	#14519706	1	2	yes	—
88	C₄	C₂×#11758196	1	1	yes	characteristic
89	C₄	C₂×#11758189	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×#14519706	1	1	yes	characteristic
92	C₂	#16840180	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂²×C₈
Fitting	C₂×M₃₂×C₆₁	C₂
hypercenter	C₂×M₃₂	D₆₁
hypocenter	C₆₁	#2151
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #16839580	C₂	semidirect
51. C₆₁	#2151	semidirect