Group #21461029 — subgroups

Subgroups — #21461029

Order 7808.

208 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 94 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	#16840781	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758213	C₂	1	1	yes	maximal, characteristic
3	#92420⋊C₈	C₂	1	2	yes	maximal, complemented
4	#16840603	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×D₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758213	C₄	1	2	yes	—
7	C₄⋊#92420	C₄	1	2	yes	—
8	#14519834	C₄	1	2	yes	—
9	#14519832	C₄	1	2	yes	—
10	C₄×#92420	C₂²	1	2	yes	—
11	C₄×#92420	C₂²	1	2	yes	—
12	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
13	C₂×C₈×D₆₁	C₄	1	1	yes	characteristic
14	C₄²×D₆₁	C₂²	1	1	yes	characteristic
15	C₄×#92418	C₄	1	1	yes	characteristic
16	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
17	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
18	C₄×C₈×C₆₁	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×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
22	C₂×#92420	C₂×C₄	1	4	yes	—
23	C₂×#92420	C₂×C₄	1	4	yes	—
24	#11758213	—	2	4	no	—
25	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
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	1	yes	characteristic
32	C₂×#92418	C₂×C₄	1	1	yes	characteristic
33	C₈×D₆₁	—	2	2	no	—
34	C₈×D₆₁	—	2	2	no	—
35	C₂²×D₆₁	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
38	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
42	C₄×D₆₁	—	2	1	no	—
43	C₄×D₆₁	—	2	1	no	—
44	C₄×D₆₁	—	2	2	no	—
45	C₄×D₆₁	M₁₆	1	4	yes	—
46	#92420	—	2	4	no	—
47	#92420	—	2	4	no	—
48	C₈×C₆₁	—	2	1	no	—
49	C₈×C₆₁	M₁₆	1	2	yes	complemented
50	#92418	—	2	1	no	—
51	#92418	M₁₆	1	2	yes	complemented
52	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
53	C₂×D₆₁	—	2	1	no	—
54	C₂×D₆₁	—	2	1	no	—
55	C₂×D₆₁	#97	1	2	yes	—
56	C₄×C₆₁	—	2	1	no	—
57	C₄×C₆₁	#97	1	2	yes	—
58	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
59	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
60	Dic₆₁	—	2	1	no	—
61	Dic₆₁	C₂×M₁₆	1	2	yes	—
62	Dic₆₁	#131	1	2	yes	—
63	#1451	—	61	1	no	maximal, Sylow
64	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
65	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
66	C₂×C₆₁	#405	1	1	yes	characteristic
67	D₆₁	—	2	2	no	—
68	#431	—	61	1	no	—
69	C₄×M₁₆	—	61	1	no	—
70	C₂×C₄×C₈	—	61	1	no	—
71	#322	—	61	2	no	—
72	#322	—	61	2	no	—
73	C₆₁	#1451	1	1	yes	characteristic, complemented, Sylow
74	C₂×M₁₆	—	61	2	no	—
75	C₂²×C₈	—	61	1	no	—
76	C₂²×C₈	—	61	1	no	—
77	C₂×C₄²	—	61	1	no	—
78	C₄⋊C₈	—	61	2	no	—
79	C₂²⋊C₈	—	61	2	no	—
80	#97	—	61	2	no	—
81	C₄×C₈	—	61	2	no	—
82	C₄×C₈	—	61	2	no	—
83	C₄×C₈	—	61	1	no	—
84	C₄×C₈	—	61	1	no	—
85	C₄×C₈	—	61	1	no	—
86	C₄×C₈	#6923	1	1	yes	characteristic
87	C₂²×C₄	—	61	1	no	—
88	C₂²×C₄	—	61	1	no	—
89	C₂²×C₄	—	61	1	no	—
90	M₁₆	—	122	4	no	—
91	C₂×C₈	—	61	1	no	—
92	C₂×C₈	—	61	4	no	—
93	C₂×C₈	—	61	4	no	—
94	C₂×C₈	—	61	1	no	—
95	C₂×C₈	—	122	2	no	—
96	C₂×C₈	—	122	2	no	—
97	C₂×C₈	C₂×#6923	1	1	yes	characteristic
98	C₂×C₈	C₂×#6923	1	1	yes	characteristic
99	C₄²	—	61	1	no	—
100	C₄²	—	61	1	no	—
101	C₄²	—	61	1	no	—
102	C₄²	C₂×#6923	1	1	yes	characteristic
103	C₂³	—	61	1	no	—
104	C₂×C₄	—	61	1	no	—
105	C₂×C₄	—	61	1	no	—
106	C₂×C₄	—	61	4	no	—
107	C₂×C₄	—	61	1	no	—
108	C₂×C₄	—	122	2	no	—
109	C₂×C₄	—	122	1	no	—
110	C₂×C₄	—	122	1	no	—
111	C₂×C₄	C₄×#6923	1	1	yes	characteristic
112	C₂×C₄	C₄×#6923	1	1	yes	characteristic
113	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
114	C₈	—	2	1	no	—
115	C₈	—	61	2	no	—
116	C₈	—	122	4	no	—
117	C₈	—	122	4	no	—
118	C₈	—	122	1	no	—
119	C₈	#11758213	1	2	yes	complemented
120	C₂²	—	61	2	no	—
121	C₂²	—	122	1	no	—
122	C₂²	—	122	1	no	—
123	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	61	2	no	—
126	C₄	—	61	2	no	—
127	C₄	—	122	1	no	—
128	C₄	#14519831	1	2	yes	—
129	C₄	D₆₁⋊M₁₆	1	1	yes	characteristic
130	C₄	C₂×#11758213	1	1	yes	characteristic
131	C₂	—	122	2	no	—
132	C₂	C₂×#14519831	1	1	yes	characteristic
133	C₂	C₄×#11758213	1	1	yes	characteristic
134	C₂	#16840725	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840781

C₂

yes

maximal, characteristic

C₄×#11758213

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, complemented

#16840603

C₂

yes

maximal, complemented

C₄×C₈×D₆₁

C₂

yes

maximal, characteristic

C₂×#11758213

C₄

yes

—

C₄⋊#92420

C₄

yes

—

#14519834

C₄

yes

—

#14519832

C₄

yes

—

C₄×#92420

C₂²

yes

—

C₄×#92420

C₂²

yes

—

C₂×C₈×D₆₁

C₄

yes

characteristic

C₂×C₈×D₆₁

C₄

yes

characteristic

C₄²×D₆₁

C₂²

yes

characteristic

C₄×#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₂²

yes

characteristic

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

—

#11758213

—

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

C₂×C₈×C₆₁

C₂×C₄

yes

characteristic

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

characteristic

C₂×#92418

C₂×C₄

yes

characteristic

C₈×D₆₁

—

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

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

M₁₆

yes

—

#92420

—

#92420

—

C₈×C₆₁

—

C₈×C₆₁

M₁₆

yes

complemented

#92418

—

#92418

M₁₆

yes

complemented

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

#97

yes

—

C₄×C₆₁

—

C₄×C₆₁

#97

yes

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

—

Dic₆₁

C₂×M₁₆

yes

—

Dic₆₁

#131

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

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#6923

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

122

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

yes

C₂×C₈

yes

C₄²

—

100

C₄²

—

101

C₄²

—

102

C₄²

C₂×#6923

yes

characteristic

103

C₂³

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

122

—

109

C₂×C₄

—

122

—

110

C₂×C₄

—

122

—

111

C₂×C₄

C₄×#6923

yes

characteristic

112

C₂×C₄

C₄×#6923

yes

characteristic

113

C₂×C₄

C₂²×#6923

yes

characteristic

114

C₈

—

115

C₈

—

116

C₈

—

122

—

117

C₈

—

122

—

118

C₈

—

122

—

119

C₈

#11758213

yes

complemented

120

C₂²

—

121

C₂²

—

122

—

122

C₂²

—

122

—

123

C₂²

C₂×C₄×#6923

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

122

—

128

C₄

#14519831

yes

—

129

C₄

D₆₁⋊M₁₆

yes

characteristic

130

C₄

C₂×#11758213

yes

characteristic

131

C₂

—

122

—

132

C₂

C₂×#14519831

yes

characteristic

133

C₂

C₄×#11758213

yes

characteristic

134

C₂

#16840725

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
49. C₈×C₆₁	M₁₆	semidirect
51. #92418	M₁₆	semidirect
73. C₆₁	#1451	semidirect
119. C₈	#11758213	semidirect

H ≅ G/N

type

3. #92420⋊C₈

C₂

semidirect

4. #16840603

C₂

semidirect

49. C₈×C₆₁

M₁₆

semidirect

51. #92418

M₁₆

semidirect

73. C₆₁

#1451

semidirect

119. C₈

#11758213

semidirect

Subgroups — #21461029

Conjugacy classes of subgroups

Complements