Subgroups — #21461744

Order 7808.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840767	C₂	1	2	yes	maximal
2	#16840638	C₂	1	4	yes	maximal
3	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×#11758213	C₂²	1	4	yes	—
5	#14519844	—	2	4	no	—
6	C₂×C₈×D₆₁	C₂²	1	2	yes	—
7	C₄²×D₆₁	C₂²	1	1	yes	characteristic
8	C₄×#92418	C₄	1	1	yes	characteristic
9	C₈×Dic₆₁	C₄	1	2	yes	—
10	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
11	C₂×C₄×D₆₁	Q₈	1	2	yes	—
12	C₂×C₄×D₆₁	C₂³	1	1	yes	characteristic
13	C₂×#92420	—	2	4	no	—
14	#11758213	—	2	8	no	—
15	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
16	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₆₁	D₄	1	2	yes	—
19	C₂×#92418	C₂×C₄	1	2	yes	—
20	C₈×D₆₁	—	2	4	no	—
21	C₂²×D₆₁	C₂×Q₈	1	1	yes	characteristic
22	C₂×C₄×C₆₁	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
24	C₂×Dic₆₁	C₄⋊C₄	1	2	yes	—
25	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
26	C₄×D₆₁	—	2	4	no	—
27	C₄×D₆₁	#41	1	4	yes	—
28	#92420	—	4	4	no	—
29	C₈×C₆₁	—	2	2	no	—
30	#92418	—	2	2	no	—
31	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₂×D₆₁	—	2	2	no	—
33	C₂×D₆₁	#125	1	2	yes	—
34	C₄×C₆₁	—	2	2	no	—
35	C₄×C₆₁	#117	1	2	yes	—
36	Dic₆₁	#108	1	4	yes	—
37	Dic₆₁	#124	1	2	yes	—
38	#1837	—	61	1	no	maximal, Sylow
39	C₂×C₆₁	#382	1	1	yes	characteristic
40	C₂×C₆₁	C₂×#108	1	2	yes	—
41	D₆₁	—	2	2	no	—
42	#423	—	61	2	no	—
43	C₂×C₄×C₈	—	61	1	no	—
44	#341	—	61	4	no	—
45	C₆₁	#1837	1	1	yes	characteristic, complemented, Sylow
46	C₂×M₁₆	—	61	4	no	—
47	C₂²×C₈	—	61	2	no	—
48	C₂×C₄²	—	61	1	no	—
49	C₄⋊C₈	—	122	4	no	—
50	C₄×C₈	—	61	2	no	—
51	C₄×C₈	—	61	1	no	—
52	C₄×C₈	#6923	1	1	yes	characteristic
53	C₂²×C₄	—	61	1	no	—
54	C₂²×C₄	—	61	2	no	—
55	M₁₆	—	122	8	no	—
56	C₂×C₈	—	61	2	no	—
57	C₂×C₈	—	122	4	no	—
58	C₂×C₈	—	122	4	no	—
59	C₂×C₈	C₂×#6923	1	2	yes	—
60	C₄²	—	61	2	no	—
61	C₄²	—	61	1	no	—
62	C₄²	C₂×#6923	1	1	yes	characteristic
63	C₂³	—	61	1	no	—
64	C₂×C₄	—	61	2	no	—
65	C₂×C₄	—	61	1	no	—
66	C₂×C₄	—	61	4	no	—
67	C₂×C₄	—	122	4	no	—
68	C₂×C₄	C₄⋊#6923	1	2	yes	—
69	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	122	2	no	—
72	C₈	—	244	4	no	—
73	C₂²	—	61	2	no	—
74	C₂²	—	122	2	no	—
75	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
76	C₄	—	2	2	no	—
77	C₄	—	61	2	no	—
78	C₄	—	61	4	no	—
79	C₄	#14519856	1	2	yes	—
80	C₂	—	122	2	no	—
81	C₂	#16840706	1	1	yes	characteristic
82	C₂	D₆₁⋊#108	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	#1837
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
45. C₆₁	#1837	semidirect