Group #21461014 — subgroups

Subgroups — C₂×#92420⋊C₈ #21461014

Order 7808.

248 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₂×C₄×#92420	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#92420	C₂	1	1	yes	maximal, characteristic
3	#92420⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×Dic₆₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×#92420	C₄	1	2	yes	—
6	C₂²×#92420	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	C₂²×#92418	C₄	1	1	yes	characteristic
12	C₂×C₄×Dic₆₁	C₂²	1	1	yes	characteristic
13	C₈×Dic₆₁	C₄	1	2	yes	—
14	C₈×Dic₆₁	C₂²	1	2	yes	—
15	C₂²×C₈×C₆₁	C₄	1	1	yes	characteristic
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×Dic₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×#92420	—	2	4	no	—
20	C₂×#92420	C₈	1	8	yes	complemented
21	C₂×#92420	C₂×C₄	1	4	yes	—
22	C₂×#92420	C₂×C₄	1	4	yes	—
23	C₂×C₈×C₆₁	—	2	2	no	—
24	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
25	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₆₁	C₂³	1	1	yes	characteristic
29	C₂×#92418	—	2	2	no	—
30	C₂×#92418	C₂×C₄	1	2	yes	—
31	C₂³×C₆₁	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
34	C₂×C₄×C₆₁	M₁₆	1	2	yes	—
35	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
37	C₂×Dic₆₁	C₄²	1	1	yes	characteristic
38	C₂×Dic₆₁	C₂×C₈	1	4	yes	—
39	C₂×Dic₆₁	M₁₆	1	4	yes	—
40	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×Dic₆₁	C₂²×C₄	1	1	yes	characteristic
42	#92420	—	2	4	no	—
43	#92420	C₂×C₈	1	8	yes	complemented
44	C₈×C₆₁	—	2	2	no	—
45	#92418	—	2	2	no	—
46	C₂²×C₆₁	C₄×C₈	1	2	yes	—
47	C₂²×C₆₁	#97	1	2	yes	—
48	C₂²×C₆₁	#97	1	2	yes	—
49	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
50	C₄×C₆₁	#97	1	2	yes	—
51	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
52	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
53	Dic₆₁	C₄×C₈	1	2	yes	—
54	Dic₆₁	#97	1	2	yes	—
55	Dic₆₁	C₂²×C₈	1	2	yes	—
56	Dic₆₁	C₂×M₁₆	1	2	yes	—
57	C₂×#322	—	61	1	no	maximal, Sylow
58	C₂×C₆₁	#322	1	4	yes	complemented
59	C₂×C₆₁	C₂×C₄×C₈	1	1	yes	characteristic
60	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
61	C₂×C₆₁	C₂×#97	1	1	yes	characteristic
62	C₂×C₄×C₈	—	61	1	no	—
63	C₂×C₄×C₈	—	61	1	no	—
64	C₂×C₄×C₈	—	61	1	no	—
65	#322	—	61	4	no	—
66	C₆₁	C₂×#322	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₈	—	61	2	no	—
68	C₂²×C₈	—	61	2	no	—
69	C₂²×C₈	—	61	1	no	—
70	C₂²×C₈	#6923	1	1	yes	characteristic
71	C₂×C₄²	—	61	1	no	—
72	C₄×C₈	—	61	2	no	—
73	C₄×C₈	—	61	2	no	—
74	C₄×C₈	—	61	2	no	—
75	C₄×C₈	—	61	2	no	—
76	C₄×C₈	—	61	2	no	—
77	C₄×C₈	—	61	2	no	—
78	C₂²×C₄	—	61	1	no	—
79	C₂²×C₄	—	61	1	no	—
80	C₂²×C₄	C₂×#6923	1	1	yes	characteristic
81	C₂×C₈	—	2	2	no	—
82	C₂×C₈	—	61	4	no	—
83	C₂×C₈	—	61	8	no	—
84	C₂×C₈	—	61	4	no	—
85	C₂×C₈	—	61	2	no	—
86	C₂×C₈	—	122	4	no	—
87	C₂×C₈	—	122	2	no	—
88	C₂×C₈	C₂×#6923	1	2	yes	—
89	C₄²	—	61	1	no	—
90	C₄²	—	61	1	no	—
91	C₄²	—	61	1	no	—
92	C₄²	—	61	1	no	—
93	C₂³	C₄×#6923	1	1	yes	characteristic
94	C₂×C₄	—	61	4	no	—
95	C₂×C₄	—	61	4	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	#11758213	1	2	yes	—
101	C₂×C₄	C₄×#6923	1	1	yes	characteristic
102	C₂×C₄	#11758217	1	2	yes	—
103	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
104	C₈	—	2	2	no	—
105	C₈	—	61	8	no	—
106	C₈	—	122	4	no	—
107	C₈	—	122	2	no	—
108	C₂²	C₈×#6923	1	2	yes	—
109	C₂²	#14519831	1	2	yes	—
110	C₂²	#14519832	1	2	yes	—
111	C₂²	C₂×C₄×#6923	1	1	yes	characteristic
112	C₄	—	61	2	no	—
113	C₄	—	61	2	no	—
114	C₄	—	61	2	no	—
115	C₄	—	61	2	no	—
116	C₄	#14519832	1	2	yes	—
117	C₄	C₂×#11758217	1	1	yes	characteristic
118	C₄	C₂×#11758213	1	1	yes	characteristic
119	C₂	#92420⋊C₈	1	4	yes	direct product factor
120	C₂	C₂×C₈×#6923	1	1	yes	characteristic
121	C₂	C₂×#14519831	1	1	yes	characteristic
122	C₂	C₂×#14519832	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×#92420

C₂

yes

maximal, characteristic

C₂×C₄×#92420

C₂

yes

maximal, characteristic

#92420⋊C₈

C₂

yes

maximal, direct product factor

C₂×C₈×Dic₆₁

C₂

yes

maximal, characteristic

C₂²×#92420

C₄

yes

—

C₂²×#92420

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₄

yes

—

C₄×#92420

C₂²

yes

—

C₄×#92420

C₂²

yes

—

C₂²×#92418

C₄

yes

characteristic

C₂×C₄×Dic₆₁

C₂²

yes

characteristic

C₈×Dic₆₁

C₄

yes

—

C₈×Dic₆₁

C₂²

yes

—

C₂²×C₈×C₆₁

C₄

yes

characteristic

C₂²×C₄×C₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂²×Dic₆₁

C₂×C₄

yes

characteristic

C₂×#92420

—

C₂×#92420

C₈

yes

complemented

C₂×#92420

C₂×C₄

yes

—

C₂×#92420

C₂×C₄

yes

—

C₂×C₈×C₆₁

—

C₂×C₈×C₆₁

C₂×C₄

yes

—

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂×C₄

yes

characteristic

C₄×Dic₆₁

C₂³

yes

characteristic

C₂×#92418

—

C₂×#92418

C₂×C₄

yes

—

C₂³×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

C₄²

yes

characteristic

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

M₁₆

yes

—

C₂×C₄×C₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₄²

yes

characteristic

C₂×Dic₆₁

C₂×C₈

yes

—

C₂×Dic₆₁

M₁₆

yes

—

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

C₂×Dic₆₁

C₂²×C₄

yes

characteristic

#92420

—

#92420

C₂×C₈

yes

complemented

C₈×C₆₁

—

#92418

—

C₂²×C₆₁

C₄×C₈

yes

—

C₂²×C₆₁

#97

yes

—

C₂²×C₆₁

#97

yes

—

C₂²×C₆₁

C₂×C₄²

yes

characteristic

C₄×C₆₁

#97

yes

—

C₄×C₆₁

C₂×M₁₆

yes

characteristic

C₄×C₆₁

C₂×M₁₆

yes

characteristic

Dic₆₁

C₄×C₈

yes

—

Dic₆₁

#97

yes

—

Dic₆₁

C₂²×C₈

yes

—

Dic₆₁

C₂×M₁₆

yes

—

—

C₂×C₆₁

yes

C₂×C₆₁

C₂×C₄×C₈

yes

characteristic

C₂×C₆₁

C₂×#97

yes

characteristic

C₂×C₆₁

C₂×#97

yes

characteristic

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#322

—

C₆₁

C₂×#322

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

#6923

yes

characteristic

C₂×C₄²

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#6923

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

122

—

C₂×C₈

—

122

—

C₂×C₈

C₂×#6923

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄×#6923

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

#11758213

yes

—

101

C₂×C₄

C₄×#6923

yes

characteristic

102

C₂×C₄

#11758217

yes

—

103

C₂×C₄

C₂²×#6923

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

122

—

107

C₈

—

122

—

108

C₂²

C₈×#6923

yes

—

109

C₂²

#14519831

yes

—

110

C₂²

#14519832

yes

—

111

C₂²

C₂×C₄×#6923

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

#14519832

yes

—

117

C₄

C₂×#11758217

yes

characteristic

118

C₄

C₂×#11758213

yes

characteristic

119

C₂

#92420⋊C₈

yes

direct product factor

120

C₂

C₂×C₈×#6923

yes

characteristic

121

C₂

C₂×#14519831

yes

characteristic

122

C₂

C₂×#14519832

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×#6923
commutator	C₂×C₆₁	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#6923
Fitting	C₂²×C₈×C₆₁	C₄
socle	C₂³×C₆₁	C₄²
hypercenter	C₂²×C₈	#6923
hypocenter	C₆₁	C₂×#322
LCS	G ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²×C₄

C₂×#6923

commutator

C₂×C₆₁

C₂×C₄×C₈

Frattini

C₂×C₄

C₂²×#6923

Fitting

C₂²×C₈×C₆₁

C₄

socle

C₂³×C₆₁

C₄²

C₂²×C₈

C₆₁

G ▷ C₂×C₆₁ ▷ C₆₁

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
3. #92420⋊C₈	C₂	direct (N × H)
20. C₂×#92420	C₈	semidirect
43. #92420	C₂×C₈	semidirect
58. C₂×C₆₁	#322	semidirect
66. C₆₁	C₂×#322	semidirect
119. C₂	#92420⋊C₈	direct (N × H)

H ≅ G/N

type

3. #92420⋊C₈

C₂

direct (N × H)

20. C₂×#92420

C₈

semidirect

43. #92420

C₂×C₈

semidirect

58. C₂×C₆₁

#322

semidirect

66. C₆₁

C₂×#322

semidirect

119. C₂

#92420⋊C₈

direct (N × H)

Subgroups — C₂×#92420⋊C₈ #21461014

Conjugacy classes of subgroups

Complements

Subgroups — C2×#92420⋊C8 #21461014

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#92420⋊C₈ #21461014