Group #23772188 — subgroups

Subgroups — C₂×#19098671 #23772188

Order 10112.

480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 205 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	C₂²×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₁₅₈	C₂	1	2	yes	maximal
3	#19098671	C₂	1	8	yes	maximal, direct product factor
4	C₂×#14579093	C₂	1	1	yes	maximal, characteristic
5	C₂×#14579086	C₂	1	2	yes	maximal
6	C₂×#97×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₅₈	C₂²	1	2	yes	—
8	C₂×Dic₃₁₆	C₄	1	8	yes	complemented
9	C₂×Dic₃₁₆	C₂²	1	4	yes	—
10	C₄×Dic₁₅₈	—	2	4	no	—
11	C₄×Dic₁₅₈	C₂²	1	8	yes	—
12	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
13	C₂×Dic₇₉⋊C₄	—	2	2	no	—
14	C₂×C₄×Dic₇₉	—	2	2	no	—
15	#14579093	C₂²	1	4	yes	—
16	#14579086	C₂²	1	8	yes	—
17	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	#97×C₇₉	C₂²	1	4	yes	—
21	C₂×Dic₁₅₈	—	2	2	no	—
22	C₂×Dic₁₅₈	—	2	4	no	—
23	C₂×Dic₁₅₈	C₂×C₄	1	8	yes	—
24	C₂×Dic₁₅₈	C₂³	1	4	yes	—
25	C₂²×Dic₇₉	—	2	2	no	—
26	C₂²×Dic₇₉	—	2	2	no	—
27	Dic₃₁₆	C₂×C₄	1	16	yes	complemented
28	C₄⋊Dic₇₉	—	2	2	no	—
29	C₄⋊Dic₇₉	C₂³	1	4	yes	—
30	Dic₇₉⋊C₄	—	2	8	no	—
31	C₄×Dic₇₉	—	2	8	no	—
32	C₂²×C₄×C₇₉	D₄	1	2	yes	—
33	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
34	C₂×C₈×C₇₉	—	2	2	no	—
35	C₂×C₈×C₇₉	C₂×C₄	1	4	yes	—
36	C₂×C₈×C₇₉	C₂³	1	2	yes	—
37	C₂×C₈×C₇₉	C₂³	1	2	yes	—
38	C₄²×C₇₉	D₄	1	2	yes	—
39	C₄²×C₇₉	C₂³	1	2	yes	—
40	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₂×C₄×C₇₉	—	2	4	no	—
42	C₂×C₄×C₇₉	C₂²×C₄	1	2	yes	—
43	C₂×C₄×C₇₉	C₂×D₄	1	4	yes	—
44	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
45	C₂×C₄×C₇₉	#41	1	2	yes	—
46	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
47	C₂×Dic₇₉	—	2	8	no	—
48	C₂×Dic₇₉	—	2	4	no	—
49	C₂×Dic₇₉	—	2	4	no	—
50	C₂×Dic₇₉	—	4	4	no	—
51	Dic₁₅₈	—	2	8	no	—
52	Dic₁₅₈	—	2	4	no	—
53	Dic₁₅₈	C₂²×C₄	1	8	yes	—
54	C₈×C₇₉	—	2	2	no	—
55	C₈×C₇₉	C₂²×C₄	1	4	yes	—
56	C₂²×C₇₉	C₄×D₄	1	2	yes	—
57	C₂²×C₇₉	#137	1	4	yes	—
58	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₇₉	—	2	4	no	—
60	C₄×C₇₉	C₄×D₄	1	2	yes	—
61	C₄×C₇₉	C₂³×C₄	1	1	yes	characteristic
62	C₄×C₇₉	C₂×#41	1	1	yes	characteristic
63	Dic₇₉	—	2	8	no	—
64	Dic₇₉	—	4	4	no	—
65	C₂×C₇₉	#441	1	4	yes	complemented
66	C₂×C₇₉	C₂×C₄×D₄	1	1	yes	characteristic
67	C₂×C₇₉	C₂×#137	1	2	yes	—
68	C₂×#441	—	79	1	no	maximal, Sylow
69	C₇₉	C₂×#441	1	1	yes	characteristic, complemented, Sylow
70	C₂²×Q₁₆	—	79	1	no	—
71	C₂×C₄×Q₈	—	79	2	no	—
72	#441	—	79	8	no	—
73	C₂×#106	—	79	1	no	—
74	C₂×#103	—	79	2	no	—
75	C₂×#97	D₇₉	1	1	yes	characteristic
76	C₂²×Q₈	—	79	2	no	—
77	C₂×Q₁₆	—	79	4	no	—
78	C₂×Q₁₆	—	79	8	no	—
79	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
80	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
81	C₄×Q₈	—	79	8	no	—
82	C₄×Q₈	—	158	4	no	—
83	C₂×C₄⋊C₄	—	79	2	no	—
84	C₂×C₄⋊C₄	—	158	2	no	—
85	C₂×C₄²	—	158	2	no	—
86	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
87	#106	—	79	4	no	—
88	#103	—	79	8	no	—
89	#97	C₂×D₇₉	1	4	yes	—
90	C₂×Q₈	—	79	8	no	—
91	C₂×Q₈	—	79	4	no	—
92	C₂×Q₈	—	158	2	no	—
93	C₂×Q₈	—	158	4	no	—
94	C₂²×C₄	—	158	2	no	—
95	C₂²×C₄	—	158	2	no	—
96	C₂²×C₄	D₃₁₆	1	2	yes	—
97	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
98	Q₁₆	—	79	16	no	—
99	C₂×C₈	—	2	2	no	—
100	C₂×C₈	C₄×D₇₉	1	4	yes	—
101	C₂×C₈	C₂²×D₇₉	1	2	yes	—
102	C₂×C₈	C₂²×D₇₉	1	2	yes	—
103	C₄⋊C₄	—	79	4	no	—
104	C₄⋊C₄	—	158	8	no	—
105	C₄⋊C₄	—	158	2	no	—
106	C₄²	—	158	8	no	—
107	C₄²	D₃₁₆	1	2	yes	—
108	C₄²	C₂²×D₇₉	1	2	yes	—
109	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
110	Q₈	—	79	8	no	—
111	Q₈	—	158	4	no	—
112	Q₈	—	158	8	no	—
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	316	4	no	—
115	C₂×C₄	—	158	4	no	—
116	C₂×C₄	—	158	8	no	—
117	C₂×C₄	—	158	4	no	—
118	C₂×C₄	C₂×C₄×D₇₉	1	2	yes	—
119	C₂×C₄	C₂×D₃₁₆	1	4	yes	—
120	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
121	C₂×C₄	#11929624	1	2	yes	—
122	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	C₂×C₄×D₇₉	1	4	yes	—
125	C₂²	C₄×D₃₁₆	1	2	yes	—
126	C₂²	#14579194	1	4	yes	—
127	C₂²	C₂²×D₃₁₆	1	1	yes	characteristic
128	C₄	—	2	4	no	—
129	C₄	—	316	4	no	—
130	C₄	—	158	8	no	—
131	C₄	C₄×D₃₁₆	1	2	yes	—
132	C₄	C₂²×C₄×D₇₉	1	1	yes	characteristic
133	C₄	C₂×#11929624	1	1	yes	characteristic
134	C₂	#19098671	1	4	yes	direct product factor
135	C₂	C₂×C₄×D₃₁₆	1	1	yes	characteristic
136	C₂	C₂×#14579194	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₃₁₆

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₅₈

C₂

yes

maximal

#19098671

C₂

yes

maximal, direct product factor

C₂×#14579093

C₂

yes

maximal, characteristic

C₂×#14579086

C₂

yes

maximal

C₂×#97×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

—

C₂×Dic₃₁₆

C₄

yes

complemented

C₂×Dic₃₁₆

C₂²

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

—

C₂×C₄×Dic₇₉

—

#14579093

C₂²

yes

—

#14579086

C₂²

yes

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#97×C₇₉

C₂²

yes

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂×C₄

yes

—

C₂×Dic₁₅₈

C₂³

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

Dic₃₁₆

C₂×C₄

yes

complemented

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

C₂³

yes

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄²×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

Dic₁₅₈

C₂²×C₄

yes

—

C₈×C₇₉

—

C₈×C₇₉

C₂²×C₄

yes

—

C₂²×C₇₉

C₄×D₄

yes

—

C₂²×C₇₉

#137

yes

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

—

C₄×C₇₉

C₂³×C₄

yes

characteristic

C₄×C₇₉

C₂×#41

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#441

yes

complemented

C₂×C₇₉

C₂×C₄×D₄

yes

characteristic

C₂×C₇₉

C₂×#137

yes

—

C₂×#441

—

maximal, Sylow

C₇₉

C₂×#441

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂×C₄×Q₈

—

#441

—

C₂×#106

—

C₂×#103

—

C₂×#97

D₇₉

yes

characteristic

C₂²×Q₈

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

—

158

—

C₂×C₄²

C₂×D₇₉

yes

—

—

C₂×D₇₉

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

D₃₁₆

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

Q₁₆

—

C₂×C₈

—

100

C₂×C₈

C₄×D₇₉

yes

—

101

C₂×C₈

C₂²×D₇₉

yes

—

102

C₂×C₈

C₂²×D₇₉

yes

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

158

—

105

C₄⋊C₄

—

158

—

106

C₄²

—

158

—

107

C₄²

D₃₁₆

yes

—

108

C₄²

C₂²×D₇₉

yes

—

109

C₂³

C₂×D₃₁₆

yes

characteristic

110

Q₈

—

111

Q₈

—

158

—

112

Q₈

—

158

—

113

C₂×C₄

—

114

C₂×C₄

—

316

—

115

C₂×C₄

—

158

—

116

C₂×C₄

—

158

—

117

C₂×C₄

—

158

—

118

C₂×C₄

C₂×C₄×D₇₉

yes

—

119

C₂×C₄

C₂×D₃₁₆

yes

—

120

C₂×C₄

C₂×D₃₁₆

yes

characteristic

121

C₂×C₄

#11929624

yes

—

122

C₂×C₄

C₂³×D₇₉

yes

characteristic

123

C₈

—

124

C₈

C₂×C₄×D₇₉

yes

—

125

C₂²

C₄×D₃₁₆

yes

—

126

C₂²

#14579194

yes

—

127

C₂²

C₂²×D₃₁₆

yes

characteristic

128

C₄

—

129

C₄

—

316

—

130

C₄

—

158

—

131

C₄

C₄×D₃₁₆

yes

—

132

C₄

C₂²×C₄×D₇₉

yes

characteristic

133

C₄

C₂×#11929624

yes

characteristic

134

C₂

#19098671

yes

direct product factor

135

C₂

C₂×C₄×D₃₁₆

yes

characteristic

136

C₂

C₂×#14579194

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₁₆
commutator	C₄×C₇₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	C₂×#97×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂×C₄×C₇₉	C₂⁴
hypercenter	C₂×#97	D₇₉
hypocenter	C₇₉	C₂×#441
LCS	G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

subgroup

G/H

center

C₂³

C₂×D₃₁₆

commutator

C₄×C₇₉

C₂³×C₄

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

C₂×#97×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂×C₄×C₇₉

C₂⁴

hypercenter

C₂×#97

D₇₉

hypocenter

C₇₉

C₂×#441

LCS

G ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#97

N	H ≅ G/N	type
3. #19098671	C₂	direct (N × H)
8. C₂×Dic₃₁₆	C₄	semidirect
27. Dic₃₁₆	C₂×C₄	semidirect
65. C₂×C₇₉	#441	semidirect
69. C₇₉	C₂×#441	semidirect
134. C₂	#19098671	direct (N × H)

H ≅ G/N

type

3. #19098671

C₂

direct (N × H)

8. C₂×Dic₃₁₆

C₄

semidirect

27. Dic₃₁₆

C₂×C₄

semidirect

65. C₂×C₇₉

#441

semidirect

69. C₇₉

C₂×#441

semidirect

134. C₂

#19098671

direct (N × H)

Subgroups — C₂×#19098671 #23772188

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19098671 #23772188

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19098671 #23772188