Group #21461031 — subgroups

Subgroups — #21461031

Order 7808.

208 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 92 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×#11758213	C₂	1	1	yes	maximal, characteristic
2	C₄×D₆₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#92420⋊C₈	C₂	1	2	yes	maximal, complemented
4	#16840603	C₂	1	2	yes	maximal, complemented
5	#16839814	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₄	1	2	yes	—
7	C₂×D₆₁⋊C₈	C₄	1	2	yes	—
8	#14519832	C₄	1	2	yes	—
9	C₄×#92420	C₄	1	2	yes	—
10	C₄×#92420	C₂²	1	1	yes	characteristic
11	C₄×#92420	C₂²	1	1	yes	characteristic
12	C₄×#92420	C₂²	1	2	yes	—
13	C₄²×D₆₁	C₂²	1	1	yes	characteristic
14	C₄⋊#92418	C₄	1	1	yes	characteristic
15	#14519689	C₄	1	2	yes	—
16	C₈×Dic₆₁	C₂²	1	2	yes	—
17	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
21	C₂×#92420	C₂×C₄	1	2	yes	—
22	C₂×#92420	C₂×C₄	1	4	yes	—
23	C₂×#92420	C₂×C₄	1	2	yes	—
24	#11758213	—	2	4	no	—
25	D₆₁⋊C₈	—	2	4	no	—
26	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
27	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
31	C₂×#92418	C₂×C₄	1	2	yes	—
32	C₂²×D₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
37	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₄×D₆₁	—	2	1	no	—
40	C₄×D₆₁	—	2	1	no	—
41	C₄×D₆₁	—	2	2	no	—
42	C₄×D₆₁	M₁₆	1	4	yes	—
43	#92420	—	2	2	no	—
44	#92420	—	2	4	no	—
45	#92420	M₁₆	1	4	yes	complemented
46	C₈×C₆₁	—	2	2	no	—
47	#92418	—	2	2	no	—
48	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
49	C₂×D₆₁	—	2	1	no	—
50	C₂×D₆₁	—	2	1	no	—
51	C₂×D₆₁	#97	1	2	yes	—
52	C₄×C₆₁	—	2	1	no	—
53	C₄×C₆₁	#97	1	2	yes	—
54	C₄×C₆₁	#131	1	1	yes	characteristic
55	C₄×C₆₁	#131	1	1	yes	characteristic
56	Dic₆₁	—	2	1	no	—
57	Dic₆₁	C₂×M₁₆	1	2	yes	—
58	Dic₆₁	C₂×M₁₆	1	2	yes	—
59	#1451	—	61	1	no	maximal, Sylow
60	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
61	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
62	C₂×C₆₁	#405	1	1	yes	characteristic
63	D₆₁	—	2	2	no	—
64	#431	—	61	1	no	—
65	C₄×M₁₆	—	61	1	no	—
66	C₂×C₄×C₈	—	61	1	no	—
67	#322	—	61	2	no	—
68	#322	—	61	2	no	—
69	C₆₁	#1451	1	1	yes	characteristic, complemented, Sylow
70	C₂×M₁₆	—	61	2	no	—
71	C₂²×C₈	—	61	2	no	—
72	C₂×C₄²	—	61	1	no	—
73	C₄⋊C₈	—	61	1	no	—
74	C₄⋊C₈	#6923	1	1	yes	characteristic
75	C₂²⋊C₈	—	61	2	no	—
76	#97	—	61	2	no	—
77	C₄×C₈	—	61	2	no	—
78	C₄×C₈	—	61	1	no	—
79	C₄×C₈	—	61	1	no	—
80	C₄×C₈	—	61	2	no	—
81	C₄×C₈	—	61	2	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	M₁₆	—	122	4	no	—
86	C₂×C₈	—	61	2	no	—
87	C₂×C₈	—	61	2	no	—
88	C₂×C₈	—	61	4	no	—
89	C₂×C₈	—	61	2	no	—
90	C₂×C₈	—	122	4	no	—
91	C₂×C₈	C₂×#6923	1	2	yes	—
92	C₄²	—	61	1	no	—
93	C₄²	—	61	1	no	—
94	C₄²	—	61	1	no	—
95	C₄²	C₂×#6923	1	1	yes	characteristic
96	C₂³	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	4	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	122	2	no	—
102	C₂×C₄	—	122	1	no	—
103	C₂×C₄	—	122	1	no	—
104	C₂×C₄	C₄×#6923	1	1	yes	characteristic
105	C₂×C₄	C₄×#6923	1	1	yes	characteristic
106	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	61	4	no	—
109	C₈	—	122	2	no	—
110	C₈	—	122	4	no	—
111	C₈	—	122	2	no	—
112	C₂²	—	61	2	no	—
113	C₂²	—	122	1	no	—
114	C₂²	—	122	1	no	—
115	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	61	2	no	—
118	C₄	—	61	2	no	—
119	C₄	—	122	1	no	—
120	C₄	#14519831	1	2	yes	—
121	C₄	#14519864	1	1	yes	characteristic
122	C₄	#14519865	1	1	yes	characteristic
123	C₂	—	122	2	no	—
124	C₂	C₂×#14519831	1	1	yes	characteristic
125	C₂	M₁₆×#6923	1	1	yes	characteristic
126	C₂	#16840727	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#11758213

C₂

yes

maximal, characteristic

C₄×D₆₁⋊C₈

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, complemented

#16840603

C₂

yes

maximal, complemented

#16839814

C₂

yes

maximal, characteristic

C₂×#11758213

C₄

yes

—

C₂×D₆₁⋊C₈

C₄

yes

—

#14519832

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

characteristic

C₄×#92420

C₂²

yes

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic

#14519689

C₄

yes

—

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

—

C₂×#92420

C₂×C₄

yes

—

#11758213

—

D₆₁⋊C₈

—

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

—

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

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

M₁₆

yes

—

#92420

—

#92420

—

#92420

M₁₆

yes

complemented

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#97

yes

—

C₄×C₆₁

—

C₄×C₆₁

#97

yes

—

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

C₂×M₁₆

yes

—

Dic₆₁

C₂×M₁₆

yes

—

#1451

—

maximal, Sylow

C₂×C₆₁

C₂×#97

yes

characteristic

C₂×C₆₁

C₄×M₁₆

yes

characteristic

C₂×C₆₁

#405

yes

characteristic

D₆₁

—

#431

—

C₄×M₁₆

—

C₂×C₄×C₈

—

#322

—

#322

—

C₆₁

#1451

yes

characteristic, complemented, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

#6923

yes

characteristic

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

122

—

102

C₂×C₄

—

122

—

103

C₂×C₄

—

122

—

104

C₂×C₄

C₄×#6923

yes

characteristic

105

C₂×C₄

C₄×#6923

yes

characteristic

106

C₂×C₄

C₂²×#6923

yes

characteristic

107

C₈

—

108

C₈

—

109

C₈

—

122

—

110

C₈

—

122

—

111

C₈

—

122

—

112

C₂²

—

113

C₂²

—

122

—

114

C₂²

—

122

—

115

C₂²

C₂×C₄×#6923

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

122

—

120

C₄

#14519831

yes

—

121

C₄

#14519864

yes

characteristic

122

C₄

#14519865

yes

characteristic

123

C₂

—

122

—

124

C₂

C₂×#14519831

yes

characteristic

125

C₂

M₁₆×#6923

yes

characteristic

126

C₂

#16840727

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	C₄⋊C₈×C₆₁	C₄
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1451
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#6923

commutator, socle

C₂²×C₆₁

C₂×C₄²

Fitting

C₄⋊C₈×C₆₁

C₄

C₄⋊C₈

C₆₁

G ▷ C₂²×C₆₁ ▷ C₆₁

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
3. #92420⋊C₈	C₂	semidirect
4. #16840603	C₂	semidirect
45. #92420	M₁₆	semidirect
69. C₆₁	#1451	semidirect

H ≅ G/N

type

3. #92420⋊C₈

C₂

semidirect

4. #16840603

C₂

semidirect

45. #92420

M₁₆

semidirect

69. C₆₁

#1451

semidirect

Subgroups — #21461031

Conjugacy classes of subgroups

Complements