Subgroups — #21445725

Order 7808.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519713	C₂	1	2	yes	maximal
2	C₄×#11758194	C₂	1	2	yes	maximal
3	#16839527	C₂	1	2	yes	maximal
4	C₂×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	C₂²	1	4	yes	—
6	#14519713	C₄	1	8	yes	complemented
7	#14519688	—	2	2	no	—
8	C₄×#92418	—	2	2	no	—
9	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	#97×C₆₁	C₄	1	4	yes	—
13	C₂²×C₄×C₆₁	Q₈	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	C₂×C₈×C₆₁	—	2	2	no	—
16	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₆₁	C₂×C₄	1	4	yes	—
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₄²×C₆₁	C₂×C₄	1	2	yes	—
20	C₄²×C₆₁	D₄	1	2	yes	—
21	#11758194	—	2	4	no	—
22	#11758194	C₂×C₄	1	8	yes	—
23	C₂×#92418	—	2	4	no	—
24	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	4	2	no	—
26	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	#41	1	2	yes	—
31	C₈×C₆₁	—	2	2	no	—
32	C₈×C₆₁	C₄²	1	4	yes	—
33	#92418	—	2	8	no	—
34	C₂²×C₆₁	—	2	2	no	—
35	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₆₁	C₄×Q₈	1	2	yes	—
37	C₄×C₆₁	—	2	4	no	—
38	C₄×C₆₁	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₆₁	#117	1	1	yes	characteristic
40	C₄×C₆₁	C₄×D₄	1	2	yes	—
41	#1778	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	—	2	2	no	—
43	C₂×C₆₁	C₄×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₆₁	#430	1	2	yes	—
45	C₂×#108	—	61	2	no	—
46	C₄×M₁₆	—	61	2	no	—
47	C₂×#97	D₆₁	1	1	yes	characteristic
48	#341	—	61	2	no	—
49	C₆₁	#1778	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	61	4	no	—
51	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₆₁	1	1	yes	characteristic
53	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
54	#108	—	61	8	no	—
55	#97	—	122	2	no	—
56	#97	Dic₆₁	1	4	yes	—
57	C₄×C₈	—	122	2	no	—
58	C₂²×C₄	Dic₁₂₂	1	2	yes	—
59	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
60	M₁₆	—	61	8	no	—
61	M₁₆	—	122	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	122	4	no	—
64	C₂×C₈	C₄×D₆₁	1	4	yes	—
65	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
66	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
67	C₄²	D₂₄₄	1	2	yes	—
68	C₄²	C₂×Dic₆₁	1	2	yes	—
69	C₂³	C₂×Dic₁₂₂	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	C₄⋊Dic₆₁	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
73	C₂×C₄	C₂×D₂₄₄	1	1	yes	characteristic
74	C₂×C₄	#11758222	1	2	yes	—
75	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
76	C₈	—	2	2	no	—
77	C₈	—	122	8	no	—
78	C₈	C₄×Dic₆₁	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	C₂×C₄⋊Dic₆₁	1	1	yes	characteristic
81	C₂²	C₄×Dic₁₂₂	1	2	yes	—
82	C₄	—	2	4	no	—
83	C₄	C₂×C₄×Dic₆₁	1	1	yes	characteristic
84	C₄	#14519736	1	1	yes	characteristic
85	C₄	C₄×D₂₄₄	1	2	yes	—
86	C₂	—	2	2	no	—
87	C₂	C₄×C₄⋊Dic₆₁	1	1	yes	characteristic
88	C₂	#16839811	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₄₄
commutator	C₄×C₆₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₂×#97×C₆₁	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₂×#97	D₆₁
hypocenter	C₆₁	#1778
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
6. #14519713	C₄	semidirect
49. C₆₁	#1778	semidirect