Group #21460646 — subgroups

Subgroups — #21460646

Order 7808.

208 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 62 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	C₄²×#6923	C₂	1	1	yes	maximal, characteristic
3	#16839814	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#6923	—	2	1	no	—
5	C₂×C₄×#6923	—	2	1	no	—
6	C₂×C₄×#6923	C₄	1	2	yes	—
7	C₄⋊#92420	C₄	1	2	yes	complemented
8	#14519834	—	2	1	no	—
9	C₄×#92420	—	2	1	no	—
10	C₄²×D₆₁	C₂²	1	1	yes	characteristic
11	C₄⋊#92418	C₄	1	1	yes	characteristic, complemented
12	#14519689	—	2	1	no	—
13	C₈×Dic₆₁	—	2	1	no	—
14	C₄⋊C₈×C₆₁	C₄	1	1	yes	characteristic, complemented
15	C₂²×#6923	—	2	2	no	—
16	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
18	C₂×C₄×D₆₁	D₄	1	1	yes	characteristic
19	C₂×#92420	—	2	2	no	—
20	C₄×#6923	—	2	2	no	—
21	C₄×#6923	—	2	2	no	—
22	C₄×#6923	—	2	4	no	—
23	C₄×#6923	—	2	2	no	—
24	C₄×#6923	C₈	1	4	yes	complemented
25	C₂×C₈×C₆₁	—	2	1	no	—
26	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₆₁	D₄	1	1	yes	characteristic
29	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
30	C₂×#92418	—	2	1	no	—
31	C₂²×D₆₁	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×#6923	—	2	4	no	—
33	C₂×#6923	—	2	4	no	—
34	C₂×#6923	—	2	4	no	—
35	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
36	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂²⋊C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
41	C₄×D₆₁	—	2	1	no	—
42	C₄×D₆₁	—	2	1	no	—
43	C₄×D₆₁	—	2	2	no	—
44	C₄×D₆₁	C₂×C₈	1	2	yes	—
45	C₄×D₆₁	M₁₆	1	2	yes	—
46	#92420	—	4	2	no	—
47	C₈×C₆₁	—	4	1	no	—
48	#92418	—	4	1	no	—
49	C₂²×C₆₁	#95	1	1	yes	characteristic
50	C₂×D₆₁	—	2	1	no	—
51	C₂×D₆₁	—	2	1	no	—
52	C₂×D₆₁	C₂²⋊C₈	1	2	yes	—
53	#6923	—	2	8	no	—
54	C₄×C₆₁	—	2	1	no	—
55	C₄×C₆₁	C₄×C₈	1	1	yes	characteristic
56	C₄×C₆₁	#97	1	1	yes	characteristic
57	C₄×C₆₁	#104	1	1	yes	characteristic
58	C₄×C₆₁	#104	1	1	yes	characteristic
59	Dic₆₁	—	2	1	no	—
60	Dic₆₁	#104	1	2	yes	—
61	Dic₆₁	C₄⋊C₈	1	2	yes	—
62	#1276	—	61	1	no	maximal, Sylow
63	C₂×C₆₁	#336	1	1	yes	characteristic
64	C₂×C₆₁	#339	1	1	yes	characteristic
65	C₂×C₆₁	#339	1	1	yes	characteristic
66	D₆₁	—	2	2	no	—
67	#431	—	61	1	no	—
68	#431	—	61	1	no	—
69	C₄³	—	61	1	no	—
70	C₆₁	#1276	1	1	yes	characteristic, complemented, Sylow
71	C₂×C₄²	—	61	1	no	—
72	C₂×C₄²	—	61	2	no	—
73	C₂×C₄²	—	122	1	no	—
74	C₂×C₄²	—	122	1	no	—
75	C₄⋊C₈	—	61	2	no	—
76	C₄⋊C₈	—	61	1	no	—
77	C₄⋊C₈	#6923	1	1	yes	characteristic, complemented
78	C₂²⋊C₈	—	122	1	no	—
79	C₂²⋊C₈	—	122	1	no	—
80	C₄×C₈	—	122	1	no	—
81	C₄×C₈	—	122	1	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	—	61	1	no	—
84	C₂²×C₄	—	61	1	no	—
85	C₂²×C₄	—	122	2	no	—
86	C₂×C₈	—	2	1	no	—
87	C₂×C₈	—	122	2	no	—
88	C₂×C₈	—	122	1	no	—
89	C₄²	—	61	1	no	—
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₄²	—	61	4	no	—
93	C₄²	—	122	2	no	—
94	C₄²	—	122	4	no	—
95	C₄²	—	122	2	no	—
96	C₄²	—	122	2	no	—
97	C₄²	C₂×#6923	1	1	yes	characteristic
98	C₂³	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	61	1	no	—
101	C₂×C₄	—	61	2	no	—
102	C₂×C₄	—	61	2	no	—
103	C₂×C₄	—	61	1	no	—
104	C₂×C₄	—	122	2	no	—
105	C₂×C₄	—	122	4	no	—
106	C₂×C₄	—	122	4	no	—
107	C₂×C₄	—	122	4	no	—
108	C₂×C₄	—	122	1	no	—
109	C₂×C₄	—	122	1	no	—
110	C₂×C₄	C₄×#6923	1	1	yes	characteristic
111	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
112	C₂×C₄	C₂²⋊#6923	1	1	yes	characteristic
113	C₈	—	4	1	no	—
114	C₈	—	244	2	no	—
115	C₈	—	244	1	no	—
116	C₂²	—	61	2	no	—
117	C₂²	—	122	1	no	—
118	C₂²	—	122	1	no	—
119	C₂²	(C₂×#6923)⋊C₄	1	1	yes	characteristic
120	C₄	—	2	1	no	—
121	C₄	—	61	2	no	—
122	C₄	—	61	2	no	—
123	C₄	—	122	8	no	—
124	C₄	—	122	1	no	—
125	C₄	C₈×#6923	1	1	yes	characteristic
126	C₄	#14519831	1	1	yes	characteristic
127	C₄	#14519841	1	1	yes	characteristic
128	C₄	#14519842	1	1	yes	characteristic
129	C₂	—	122	2	no	—
130	C₂	(C₂×#6923)⋊C₈	1	1	yes	characteristic
131	C₂	#16840632	1	1	yes	characteristic
132	C₂	#16840634	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840781

C₂

yes

maximal, characteristic

C₄²×#6923

C₂

yes

maximal, characteristic

#16839814

C₂

yes

maximal, characteristic

C₂×C₄×#6923

—

C₂×C₄×#6923

—

C₂×C₄×#6923

C₄

yes

—

C₄⋊#92420

C₄

yes

complemented

#14519834

—

C₄×#92420

—

C₄²×D₆₁

C₂²

yes

characteristic

C₄⋊#92418

C₄

yes

characteristic, complemented

#14519689

—

C₈×Dic₆₁

—

C₄⋊C₈×C₆₁

C₄

yes

characteristic, complemented

C₂²×#6923

—

C₂×C₄×D₆₁

C₂×C₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

characteristic

C₂×C₄×D₆₁

D₄

yes

—

—

—

—

—

C₈

yes

complemented

C₂×C₈×C₆₁

—

C₄²×C₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₂×#92418

—

C₂²×D₆₁

C₂²⋊C₄

yes

—

—

—

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂²⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

—

C₄×D₆₁

C₂×C₈

yes

—

C₄×D₆₁

M₁₆

yes

—

#92420

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

#95

yes

characteristic

C₂×D₆₁

—

C₂×D₆₁

—

C₂×D₆₁

C₂²⋊C₈

yes

—

#6923

—

C₄×C₆₁

—

C₄×C₆₁

C₄×C₈

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

C₄×C₆₁

yes

Dic₆₁

—

Dic₆₁

#104

yes

—

Dic₆₁

C₄⋊C₈

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

D₆₁

—

#431

—

#431

—

C₄³

—

C₆₁

#1276

yes

characteristic, complemented, Sylow

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

122

—

C₂×C₄²

—

122

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#6923

yes

characteristic, complemented

C₂²⋊C₈

—

122

—

C₂²⋊C₈

—

122

—

C₄×C₈

—

122

—

C₄×C₈

—

122

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

122

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

—

122

—

C₄²

C₂×#6923

yes

characteristic

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

122

—

105

C₂×C₄

—

122

—

106

C₂×C₄

—

122

—

107

C₂×C₄

—

122

—

108

C₂×C₄

—

122

—

109

C₂×C₄

—

122

—

110

C₂×C₄

C₄×#6923

yes

characteristic

111

C₂×C₄

C₄⋊#6923

yes

characteristic

112

C₂×C₄

C₂²⋊#6923

yes

characteristic

113

C₈

—

114

C₈

—

244

—

115

C₈

—

244

—

116

C₂²

—

117

C₂²

—

122

—

118

C₂²

—

122

—

119

C₂²

(C₂×#6923)⋊C₄

yes

characteristic

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

122

—

124

C₄

—

122

—

125

C₄

C₈×#6923

yes

characteristic

126

C₄

#14519831

yes

characteristic

127

C₄

#14519841

yes

characteristic

128

C₄

#14519842

yes

characteristic

129

C₂

—

122

—

130

C₂

(C₂×#6923)⋊C₈

yes

characteristic

131

C₂

#16840632

yes

characteristic

132

C₂

#16840634

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#6923
commutator	C₄×C₆₁	C₄×C₈
Frattini	C₄²	C₂×#6923
Fitting	C₄⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	#95
hypercenter	C₄⋊C₈	#6923
hypocenter	C₆₁	#1276
LCS	G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂×C₄

C₂²⋊#6923

commutator

C₄×C₆₁

C₄×C₈

Frattini

C₄²

C₂×#6923

Fitting

C₄⋊C₈×C₆₁

C₄

C₂²×C₆₁

C₄⋊C₈

C₆₁

G ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
7. C₄⋊#92420	C₄	semidirect
11. C₄⋊#92418	C₄	semidirect
14. C₄⋊C₈×C₆₁	C₄	semidirect
24. C₄×#6923	C₈	semidirect
70. C₆₁	#1276	semidirect
77. C₄⋊C₈	#6923	semidirect

H ≅ G/N

type

7. C₄⋊#92420

C₄

semidirect

11. C₄⋊#92418

C₄

semidirect

14. C₄⋊C₈×C₆₁

C₄

semidirect

24. C₄×#6923

C₈

semidirect

70. C₆₁

#1276

semidirect

77. C₄⋊C₈

#6923

semidirect

Subgroups — #21460646

Conjugacy classes of subgroups

Complements