Group #21461015 — subgroups

Subgroups — #21461015

Order 7808.

248 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#92420⋊C₈	C₂	1	4	yes	maximal, complemented
4	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂×D₆₁⋊C₈	C₄	1	2	yes	—
6	C₂×D₆₁⋊C₈	C₄	1	2	yes	—
7	C₄×#92420	C₄	1	2	yes	—
8	C₄×#92420	C₄	1	2	yes	—
9	C₄×#92420	C₂²	1	2	yes	—
10	C₄×#92420	C₂²	1	2	yes	—
11	C₂×C₈×D₆₁	C₄	1	2	yes	—
12	C₄²×D₆₁	C₂²	1	1	yes	characteristic
13	C₄×#92418	C₄	1	1	yes	characteristic
14	C₈×Dic₆₁	C₂²	1	2	yes	—
15	C₄×C₈×C₆₁	C₄	1	1	yes	characteristic
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×#92420	C₂×C₄	1	4	yes	—
20	C₂×#92420	C₂×C₄	1	4	yes	—
21	D₆₁⋊C₈	—	2	4	no	—
22	D₆₁⋊C₈	C₈	1	8	yes	complemented
23	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
24	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
28	C₂×#92418	C₂×C₄	1	2	yes	—
29	C₈×D₆₁	—	2	4	no	—
30	C₂²×D₆₁	C₄²	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
35	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
37	C₄×D₆₁	C₂×C₈	1	4	yes	—
38	C₄×D₆₁	M₁₆	1	4	yes	—
39	C₄×D₆₁	M₁₆	1	4	yes	—
40	#92420	—	2	4	no	—
41	#92420	C₂×C₈	1	8	yes	complemented
42	C₈×C₆₁	—	2	2	no	—
43	#92418	—	2	2	no	—
44	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
45	C₂×D₆₁	C₄×C₈	1	2	yes	—
46	C₂×D₆₁	#97	1	2	yes	—
47	C₂×D₆₁	#97	1	2	yes	—
48	C₄×C₆₁	C₄×C₈	1	2	yes	—
49	C₄×C₆₁	#97	1	2	yes	—
50	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
51	Dic₆₁	#97	1	2	yes	—
52	Dic₆₁	C₂²×C₈	1	2	yes	—
53	Dic₆₁	C₂×M₁₆	1	2	yes	—
54	C₂×#322	—	61	1	no	maximal, Sylow
55	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
56	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
57	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
58	D₆₁	#322	1	4	yes	complemented
59	C₂×C₄×C₈	—	61	1	no	—
60	C₂×C₄×C₈	—	61	1	no	—
61	C₂×C₄×C₈	—	61	1	no	—
62	#322	—	61	4	no	—
63	C₆₁	C₂×#322	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₈	—	61	2	no	—
65	C₂²×C₈	—	61	2	no	—
66	C₂²×C₈	—	61	2	no	—
67	C₂×C₄²	—	61	1	no	—
68	C₄×C₈	—	61	2	no	—
69	C₄×C₈	—	61	2	no	—
70	C₄×C₈	—	61	2	no	—
71	C₄×C₈	—	61	2	no	—
72	C₄×C₈	—	61	2	no	—
73	C₄×C₈	—	61	1	no	—
74	C₄×C₈	#6923	1	1	yes	characteristic
75	C₂²×C₄	—	61	1	no	—
76	C₂²×C₄	—	61	1	no	—
77	C₂²×C₄	—	61	1	no	—
78	C₂×C₈	—	61	4	no	—
79	C₂×C₈	—	61	8	no	—
80	C₂×C₈	—	61	4	no	—
81	C₂×C₈	—	61	2	no	—
82	C₂×C₈	—	122	4	no	—
83	C₂×C₈	—	122	4	no	—
84	C₂×C₈	C₂×#6923	1	2	yes	—
85	C₄²	—	61	1	no	—
86	C₄²	—	61	1	no	—
87	C₄²	—	61	1	no	—
88	C₄²	C₂×#6923	1	1	yes	characteristic
89	C₂³	—	61	1	no	—
90	C₂×C₄	—	61	1	no	—
91	C₂×C₄	—	61	1	no	—
92	C₂×C₄	—	61	1	no	—
93	C₂×C₄	—	61	4	no	—
94	C₂×C₄	—	61	4	no	—
95	C₂×C₄	—	61	4	no	—
96	C₂×C₄	C₄×#6923	1	1	yes	characteristic
97	C₂×C₄	C₄×#6923	1	1	yes	characteristic
98	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
99	C₈	—	2	2	no	—
100	C₈	—	61	8	no	—
101	C₈	—	122	4	no	—
102	C₈	—	122	2	no	—
103	C₂²	—	61	2	no	—
104	C₂²	—	61	2	no	—
105	C₂²	—	61	2	no	—
106	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
107	C₄	—	61	2	no	—
108	C₄	—	61	2	no	—
109	C₄	—	61	2	no	—
110	C₄	C₈×#6923	1	2	yes	—
111	C₄	#14519831	1	2	yes	—
112	C₄	D₆₁⋊M₁₆	1	2	yes	—
113	C₂	—	61	4	no	—
114	C₂	C₂×C₈×#6923	1	1	yes	characteristic
115	C₂	C₂×#14519831	1	1	yes	characteristic
116	C₂	#16840721	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, complemented

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×D₆₁⋊C₈

C₄

yes

—

C₂×D₆₁⋊C₈

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₂²

yes

—

C₄×#92420

C₂²

yes

—

C₂×C₈×D₆₁

C₄

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

—

C₄×C₈×C₆₁

C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

D₆₁⋊C₈

—

D₆₁⋊C₈

C₈

yes

complemented

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₈×D₆₁

—

C₂²×D₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₄×D₆₁

C₂×C₈

yes

—

C₄×D₆₁

M₁₆

yes

—

C₄×D₆₁

M₁₆

yes

—

#92420

—

#92420

C₂×C₈

yes

complemented

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

C₄×C₈

yes

—

C₂×D₆₁

#97

yes

—

C₂×D₆₁

#97

yes

—

C₄×C₆₁

C₄×C₈

yes

—

C₄×C₆₁

#97

yes

—

C₄×C₆₁

C₂×M₁₆

yes

—

Dic₆₁

#97

yes

—

Dic₆₁

C₂²×C₈

yes

—

Dic₆₁

C₂×M₁₆

yes

—

C₂×#322

—

maximal, Sylow

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

C₂×#97

yes

characteristic

C₂×C₆₁

C₂×#97

yes

characteristic

D₆₁

#322

yes

complemented

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#322

—

C₆₁

C₂×#322

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²×#6923

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

122

—

102

C₈

—

122

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂×C₄×#6923

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

C₈×#6923

yes

—

111

C₄

#14519831

yes

—

112

C₄

D₆₁⋊M₁₆

yes

—

113

C₂

—

114

C₂

C₂×C₈×#6923

yes

characteristic

115

C₂

C₂×#14519831

yes

characteristic

116

C₂

#16840721

yes

characteristic

	subgroup	G/H
center	C₄²	C₂×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₄×C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄²
hypercenter	C₄×C₈	#6923
hypocenter	C₆₁	C₂×#322
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₄²

C₂×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₄×C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄²

C₄×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
3. #92420⋊C₈	C₂	semidirect
22. D₆₁⋊C₈	C₈	semidirect
41. #92420	C₂×C₈	semidirect
58. D₆₁	#322	semidirect
63. C₆₁	C₂×#322	semidirect

H ≅ G/N

type

3. #92420⋊C₈

C₂

semidirect

22. D₆₁⋊C₈

C₈

semidirect

41. #92420

C₂×C₈

semidirect

58. D₆₁

#322

semidirect

63. C₆₁

C₂×#322

semidirect

Subgroups — #21461015

Conjugacy classes of subgroups

Complements