Group #21461394 — subgroups

Subgroups — #21461394

Order 7808.

160 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 64 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	#16840783	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#92420	C₂	1	1	yes	maximal, characteristic
3	#16840625	C₂	1	2	yes	maximal, complemented
4	#16840624	C₂	1	2	yes	maximal, complemented
5	#16839812	C₂	1	1	yes	maximal, characteristic
6	C₂²×#92420	—	2	1	no	—
7	C₄⋊#92420	—	2	1	no	—
8	C₄⋊#92420	C₂²	1	2	yes	—
9	C₄⋊#92420	C₂²	1	1	yes	characteristic
10	C₄⋊#92420	C₂²	1	1	yes	characteristic
11	C₂²⋊#92420	—	2	1	no	—
12	#14519832	—	2	1	no	—
13	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
14	#14519706	C₄	1	2	yes	—
15	C₂²⋊#92418	C₄	1	1	yes	characteristic
16	C₈×Dic₆₁	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₆₁	C₄	1	1	yes	characteristic
18	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×Dic₆₁	D₄	1	1	yes	characteristic
20	C₂²×Dic₆₁	Q₈	1	1	yes	characteristic
21	C₂×#92420	—	2	1	no	—
22	C₂×#92420	—	2	1	no	—
23	C₂×#92420	—	2	2	no	—
24	C₂×#92420	—	4	2	no	—
25	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
26	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	D₄	1	1	yes	characteristic
28	C₄×Dic₆₁	Q₈	1	1	yes	characteristic
29	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
30	C₂×#92418	C₂×C₄	1	2	yes	—
31	C₂³×C₆₁	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₆₁	—	2	2	no	—
33	C₂×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₆₁	—	2	2	no	—
36	C₂×Dic₆₁	—	2	1	no	—
37	C₂×Dic₆₁	—	2	1	no	—
38	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₆₁	C₄⋊C₄	1	1	yes	characteristic
40	C₂×Dic₆₁	C₂×D₄	1	1	yes	characteristic
41	C₂×Dic₆₁	C₂×Q₈	1	1	yes	characteristic
42	#92420	—	4	1	no	—
43	#92420	—	4	2	no	—
44	#92420	—	4	1	no	—
45	C₈×C₆₁	—	2	2	no	—
46	#92418	—	2	2	no	—
47	C₂²×C₆₁	—	2	1	no	—
48	C₂²×C₆₁	—	2	1	no	—
49	C₂²×C₆₁	#108	1	2	yes	—
50	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₄×C₆₁	—	2	1	no	—
52	C₄×C₆₁	#131	1	2	yes	—
53	Dic₆₁	—	2	1	no	—
54	Dic₆₁	—	2	1	no	—
55	Dic₆₁	—	2	1	no	—
56	Dic₆₁	AGL(1,ℤ/8)	1	1	yes	characteristic
57	Dic₆₁	#137	1	1	yes	characteristic
58	#1573	—	61	1	no	maximal, Sylow
59	C₂×C₆₁	—	2	2	no	—
60	C₂×C₆₁	#424	1	1	yes	characteristic
61	C₂×C₆₁	#428	1	1	yes	characteristic
62	C₂×C₆₁	C₂×#108	1	1	yes	characteristic
63	#432	—	61	1	no	—
64	#431	—	61	1	no	—
65	C₂×C₄⋊C₈	—	61	1	no	—
66	#335	—	61	2	no	—
67	#334	—	61	2	no	—
68	C₆₁	#1573	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₈	—	122	1	no	—
70	C₂×C₄²	—	61	1	no	—
71	C₄⋊C₈	—	61	2	no	—
72	C₄⋊C₈	—	61	1	no	—
73	C₄⋊C₈	—	61	2	no	—
74	C₄⋊C₈	—	61	1	no	—
75	C₄⋊C₈	—	122	1	no	—
76	C₂²⋊C₈	—	61	1	no	—
77	C₂²⋊C₈	—	122	1	no	—
78	C₂²⋊C₈	#6923	1	1	yes	characteristic
79	#97	—	122	1	no	—
80	C₄×C₈	—	61	2	no	—
81	C₂²×C₄	—	61	1	no	—
82	C₂²×C₄	—	61	1	no	—
83	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
84	C₂×C₈	—	61	2	no	—
85	C₂×C₈	—	122	1	no	—
86	C₂×C₈	—	122	1	no	—
87	C₂×C₈	—	122	2	no	—
88	C₂×C₈	—	244	2	no	—
89	C₂×C₈	C₂×#6923	1	2	yes	—
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₄²	—	61	1	no	—
93	C₄²	—	61	1	no	—
94	C₂³	C₄⋊#6923	1	1	yes	characteristic
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	61	1	no	—
97	C₂×C₄	—	61	1	no	—
98	C₂×C₄	—	61	1	no	—
99	C₂×C₄	—	61	1	no	—
100	C₂×C₄	—	122	1	no	—
101	C₂×C₄	—	122	1	no	—
102	C₂×C₄	—	122	2	no	—
103	C₂×C₄	C₄⋊#6923	1	1	yes	characteristic
104	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	122	2	no	—
107	C₈	—	244	1	no	—
108	C₈	—	244	1	no	—
109	C₈	—	244	2	no	—
110	C₂²	—	2	1	no	—
111	C₂²	—	2	1	no	—
112	C₂²	#14519848	1	2	yes	—
113	C₂²	C₂×C₄⋊#6923	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	61	1	no	—
116	C₄	—	61	1	no	—
117	C₄	—	122	1	no	—
118	C₄	—	122	1	no	—
119	C₄	—	122	1	no	—
120	C₄	#14519864	1	2	yes	—
121	C₂	—	2	2	no	—
122	C₂	#16840768	1	1	yes	characteristic
123	C₂	#16840773	1	1	yes	characteristic
124	C₂	C₂×#14519848	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16840783

C₂

yes

maximal, characteristic

C₂×C₄⋊#92420

C₂

yes

maximal, characteristic

#16840625

C₂

yes

maximal, complemented

#16840624

C₂

yes

maximal, complemented

#16839812

C₂

yes

maximal, characteristic

C₂²×#92420

—

C₄⋊#92420

—

C₄⋊#92420

C₂²

yes

—

C₄⋊#92420

C₂²

yes

characteristic

C₄⋊#92420

C₂²

yes

characteristic

C₂²⋊#92420

—

#14519832

—

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

#14519706

C₄

yes

—

C₂²⋊#92418

C₄

yes

characteristic

C₈×Dic₆₁

C₂²

yes

—

C₂²⋊C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

D₄

yes

characteristic

C₂²×Dic₆₁

Q₈

yes

—

—

—

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

D₄

yes

characteristic

C₄×Dic₆₁

Q₈

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

—

C₂×C₄×C₆₁

C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

—

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₄⋊C₄

yes

characteristic

C₂×Dic₆₁

C₂×D₄

yes

characteristic

C₂×Dic₆₁

C₂×Q₈

yes

—

—

—

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

—

C₂²×C₆₁

—

C₂²×C₆₁

#108

yes

—

C₂²×C₆₁

C₂×C₄⋊C₄

yes

characteristic

C₄×C₆₁

—

C₄×C₆₁

#131

yes

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

—

Dic₆₁

yes

Dic₆₁

yes

—

C₂×C₆₁

—

C₂×C₆₁

yes

C₂×C₆₁

yes

C₂×C₆₁

yes

—

—

C₂×C₄⋊C₈

—

#335

—

#334

—

C₆₁

#1573

yes

characteristic, complemented, Sylow

C₂²×C₈

—

122

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

122

—

C₂²⋊C₈

—

C₂²⋊C₈

—

122

—

C₂²⋊C₈

#6923

yes

characteristic

#97

—

122

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

—

244

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

122

—

101

C₂×C₄

—

122

—

102

C₂×C₄

—

122

—

103

C₂×C₄

C₄⋊#6923

yes

characteristic

104

C₂×C₄

C₂²×#6923

yes

characteristic

105

C₈

—

106

C₈

—

122

—

107

C₈

—

244

—

108

C₈

—

244

—

109

C₈

—

244

—

110

C₂²

—

111

C₂²

—

112

C₂²

#14519848

yes

—

113

C₂²

C₂×C₄⋊#6923

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

122

—

118

C₄

—

122

—

119

C₄

—

122

—

120

C₄

#14519864

yes

—

121

C₂

—

122

C₂

#16840768

yes

characteristic

123

C₂

#16840773

yes

characteristic

124

C₂

C₂×#14519848

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#6923
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂²⋊C₈×C₆₁	C₄
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	C₂²⋊C₈	#6923
hypocenter	C₆₁	#1573
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#6923

commutator

C₂×C₄×C₆₁

C₂²×C₄

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂²⋊C₈×C₆₁

C₄

socle

C₂²×C₆₁

C₂×C₄⋊C₄

C₂²⋊C₈

C₆₁

G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
3. #16840625	C₂	semidirect
4. #16840624	C₂	semidirect
68. C₆₁	#1573	semidirect

H ≅ G/N

type

3. #16840625

C₂

semidirect

4. #16840624

C₂

semidirect

68. C₆₁

#1573

semidirect

Subgroups — #21461394

Conjugacy classes of subgroups

Complements