Group #23766608 — subgroups

Subgroups — #395×D₇₉ #23766608

Order 10112.

908 conjugacy classes of subgroups; only the 223 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 223 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×Q₈×D₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₄×D₇₉	C₂	1	3	yes	maximal
3	#19098484	C₂	1	3	yes	maximal, complemented
4	#19098483	C₂	1	3	yes	maximal, complemented
5	#19098482	C₂	1	1	yes	maximal, characteristic, complemented
6	#95×D₇₉	C₂	1	3	yes	maximal
7	#395×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Dic₁₅₈	C₂²	1	3	yes	—
9	C₂×Q₈×D₇₉	—	2	12	no	—
10	C₂²×C₄×D₇₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×D₇₉	C₂²	1	3	yes	—
12	C₂²×C₄×D₇₉	C₂²	1	3	yes	—
13	C₂×C₄⋊Dic₇₉	C₂²	1	3	yes	—
14	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
15	C₂×Dic₇₉⋊C₄	C₂²	1	3	yes	—
16	C₄⋊C₄×D₇₉	—	2	12	no	—
17	C₇₉⋊#95	C₂²	1	3	yes	—
18	C₇₉⋊#95	C₂²	1	6	yes	—
19	C₂²×Q₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×C₇₉	C₂²	1	3	yes	—
21	#95×C₇₉	C₂²	1	3	yes	—
22	C₂³×D₇₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₁₅₈	—	2	12	no	—
24	C₂×Dic₁₅₈	—	2	6	no	—
25	Q₈×D₇₉	—	2	32	no	—
26	C₂²×Dic₇₉	C₂³	1	1	yes	characteristic
27	C₂²×Dic₇₉	C₂³	1	3	yes	—
28	C₂²×Dic₇₉	C₂³	1	3	yes	—
29	C₂×C₄×D₇₉	—	2	12	no	—
30	C₂×C₄×D₇₉	—	2	6	no	—
31	C₂×C₄×D₇₉	—	2	6	no	—
32	C₂×C₄×D₇₉	—	2	6	no	—
33	C₂×C₄×D₇₉	D₄	1	12	yes	—
34	C₂×C₄×D₇₉	Q₈	1	12	yes	complemented
35	C₄⋊Dic₇₉	—	2	6	no	—
36	Dic₇₉⋊C₄	—	2	6	no	—
37	Dic₇₉⋊C₄	—	2	6	no	—
38	C₂×Q₈×C₇₉	—	2	6	no	—
39	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
41	C₂²×C₄×C₇₉	C₂³	1	3	yes	—
42	C₄⋊C₄×C₇₉	—	2	6	no	—
43	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
44	C₂²×D₇₉	C₂×D₄	1	6	yes	—
45	C₂²×D₇₉	C₂×Q₈	1	6	yes	—
46	C₂²×D₇₉	#41	1	2	yes	—
47	Q₈×C₇₉	—	2	8	no	—
48	C₂×C₄×C₇₉	—	2	3	no	—
49	C₂×C₄×C₇₉	—	2	6	no	—
50	C₂×C₄×C₇₉	—	2	3	no	—
51	C₂×C₄×C₇₉	—	2	3	no	—
52	C₂×C₄×C₇₉	C₂×D₄	1	6	yes	—
53	C₂×C₄×C₇₉	C₂×Q₈	1	6	yes	complemented
54	C₂×Dic₇₉	—	2	3	no	—
55	C₂×Dic₇₉	—	2	6	no	—
56	C₂×Dic₇₉	—	2	3	no	—
57	C₂×Dic₇₉	—	2	3	no	—
58	C₂×Dic₇₉	C₂×D₄	1	6	yes	—
59	C₂×Dic₇₉	C₂×Q₈	1	6	yes	complemented
60	C₄×D₇₉	—	2	24	no	—
61	C₄×D₇₉	—	2	24	no	—
62	C₄×D₇₉	—	4	4	no	—
63	Dic₁₅₈	—	2	24	no	—
64	C₂²×C₇₉	C₂²×D₄	1	3	yes	—
65	C₂²×C₇₉	C₂²×Q₈	1	3	yes	—
66	C₂²×C₇₉	C₂×#41	1	1	yes	characteristic
67	C₂×D₇₉	#120	1	4	yes	—
68	C₂×D₇₉	C₂²⋊Q₈	1	12	yes	—
69	C₂×D₇₉	C₄⋊Q₈	1	12	yes	—
70	C₄×C₇₉	—	2	6	no	—
71	C₄×C₇₉	—	2	6	no	—
72	C₄×C₇₉	—	4	1	no	—
73	Dic₇₉	—	2	6	no	—
74	Dic₇₉	—	2	6	no	—
75	Dic₇₉	—	4	1	no	—
76	C₂×C₇₉	C₂×#120	1	1	yes	characteristic
77	C₂×C₇₉	C₂×C₂²⋊Q₈	1	3	yes	—
78	C₂×C₇₉	C₂×C₄⋊Q₈	1	3	yes	—
79	D₇₉	#395	1	8	yes	direct product factor
80	C₂×#395	—	79	1	no	maximal, Sylow
81	C₇₉	C₂×#395	1	1	yes	characteristic, complemented, Sylow
82	C₂³×Q₈	—	79	1	no	—
83	C₂²×C₄⋊C₄	—	79	3	no	—
84	#395	—	79	1	no	—
85	#395	—	79	3	no	—
86	#395	—	79	3	no	—
87	#395	D₇₉	1	1	yes	characteristic, direct product factor
88	C₂×#95	—	79	3	no	—
89	C₂²×Q₈	—	79	3	no	—
90	C₂²×Q₈	—	158	12	no	—
91	C₂²×Q₈	C₂×D₇₉	1	1	yes	characteristic
92	C₂³×C₄	—	79	3	no	—
93	C₂³×C₄	—	79	3	no	—
94	C₂³×C₄	—	79	1	no	—
95	C₂×C₄⋊C₄	—	79	3	no	—
96	C₂×C₄⋊C₄	—	79	3	no	—
97	C₂×C₄⋊C₄	—	79	3	no	—
98	C₂×C₄⋊C₄	—	158	12	no	—
99	C₂×C₄⋊C₄	C₂×D₇₉	1	3	yes	—
100	#95	—	79	3	no	—
101	#95	—	79	6	no	—
102	#95	C₂×D₇₉	1	3	yes	—
103	C₂⁴	—	79	1	no	—
104	C₂×Q₈	—	2	6	no	—
105	C₂×Q₈	—	158	12	no	—
106	C₂×Q₈	—	158	32	no	—
107	C₂×Q₈	—	158	6	no	—
108	C₂²×C₄	—	79	3	no	—
109	C₂²×C₄	—	79	3	no	—
110	C₂²×C₄	—	79	12	no	—
111	C₂²×C₄	—	79	12	no	—
112	C₂²×C₄	—	79	1	no	—
113	C₂²×C₄	—	158	6	no	—
114	C₂²×C₄	—	158	6	no	—
115	C₂²×C₄	—	158	6	no	—
116	C₂²×C₄	—	158	12	no	—
117	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
118	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
119	C₂²×C₄	C₂²×D₇₉	1	3	yes	—
120	C₄⋊C₄	—	2	6	no	—
121	C₄⋊C₄	—	158	6	no	—
122	C₄⋊C₄	—	158	6	no	—
123	C₄⋊C₄	—	158	6	no	—
124	C₂³	—	79	6	no	—
125	C₂³	—	79	2	no	—
126	C₂³	—	79	6	no	—
127	C₂³	C₂³×D₇₉	1	1	yes	characteristic
128	Q₈	—	2	8	no	—
129	Q₈	—	158	24	no	—
130	C₂×C₄	—	2	3	no	—
131	C₂×C₄	—	2	3	no	—
132	C₂×C₄	—	2	6	no	—
133	C₂×C₄	—	2	3	no	—
134	C₂×C₄	—	316	4	no	—
135	C₂×C₄	—	79	6	no	—
136	C₂×C₄	—	79	6	no	—
137	C₂×C₄	—	158	24	no	—
138	C₂×C₄	—	158	24	no	—
139	C₂×C₄	—	158	3	no	—
140	C₂×C₄	—	158	3	no	—
141	C₂×C₄	—	158	3	no	—
142	C₂×C₄	—	158	6	no	—
143	C₂×C₄	D₄×D₇₉	1	6	yes	—
144	C₂×C₄	Q₈×D₇₉	1	6	yes	complemented
145	C₂²	—	79	4	no	—
146	C₂²	—	79	12	no	—
147	C₂²	—	79	12	no	—
148	C₂²	C₂×D₄×D₇₉	1	3	yes	—
149	C₂²	C₂×Q₈×D₇₉	1	3	yes	—
150	C₂²	#41×D₇₉	1	1	yes	characteristic
151	C₄	—	2	6	no	—
152	C₄	—	2	6	no	—
153	C₄	—	4	1	no	—
154	C₄	—	316	1	no	—
155	C₄	—	158	6	no	—
156	C₄	—	158	6	no	—
157	C₂	—	79	8	no	—
158	C₂	#120×D₇₉	1	1	yes	characteristic
159	C₂	C₂²⋊Q₈×D₇₉	1	3	yes	—
160	C₂	C₄⋊Q₈×D₇₉	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₈×D₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊C₄×D₇₉

C₂

yes

maximal

#19098484

C₂

yes

maximal, complemented

#19098483

C₂

yes

maximal, complemented

#19098482

C₂

yes

maximal, characteristic, complemented

#95×D₇₉

C₂

yes

maximal

#395×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂²×Dic₁₅₈

C₂²

yes

—

C₂×Q₈×D₇₉

—

C₂²×C₄×D₇₉

C₂²

yes

characteristic

C₂²×C₄×D₇₉

C₂²

yes

—

C₂²×C₄×D₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₂×Dic₇₉⋊C₄

C₂²

yes

—

C₄⋊C₄×D₇₉

—

C₇₉⋊#95

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

#95×C₇₉

C₂²

yes

—

C₂³×D₇₉

C₂³

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Q₈×D₇₉

—

C₂²×Dic₇₉

C₂³

yes

characteristic

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

Q₈

yes

complemented

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

C₂⁴

yes

characteristic

C₂²×D₇₉

C₂×D₄

yes

—

C₂²×D₇₉

C₂×Q₈

yes

—

C₂²×D₇₉

#41

yes

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

complemented

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

—

C₂×Dic₇₉

C₂×Q₈

yes

complemented

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₂²×C₇₉

C₂²×D₄

yes

—

C₂²×C₇₉

C₂²×Q₈

yes

—

C₂²×C₇₉

C₂×#41

yes

characteristic

C₂×D₇₉

#120

yes

—

C₂×D₇₉

C₂²⋊Q₈

yes

—

C₂×D₇₉

C₄⋊Q₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

C₂×#120

yes

characteristic

C₂×C₇₉

C₂×C₂²⋊Q₈

yes

—

C₂×C₇₉

C₂×C₄⋊Q₈

yes

—

D₇₉

#395

yes

direct product factor

C₂×#395

—

maximal, Sylow

C₇₉

C₂×#395

yes

characteristic, complemented, Sylow

C₂³×Q₈

—

C₂²×C₄⋊C₄

—

—

—

—

D₇₉

yes

characteristic, direct product factor

C₂×#95

—

C₂²×Q₈

—

C₂²×Q₈

—

158

—

C₂²×Q₈

C₂×D₇₉

yes

characteristic

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

100

#95

—

101

#95

—

102

#95

C₂×D₇₉

yes

—

103

C₂⁴

—

104

C₂×Q₈

—

105

C₂×Q₈

—

158

—

106

C₂×Q₈

—

158

—

107

C₂×Q₈

—

158

—

108

C₂²×C₄

—

109

C₂²×C₄

—

110

C₂²×C₄

—

111

C₂²×C₄

—

112

C₂²×C₄

—

113

C₂²×C₄

—

158

—

114

C₂²×C₄

—

158

—

115

C₂²×C₄

—

158

—

116

C₂²×C₄

—

158

—

117

C₂²×C₄

C₂²×D₇₉

yes

characteristic

118

C₂²×C₄

C₂²×D₇₉

yes

—

119

C₂²×C₄

C₂²×D₇₉

yes

—

120

C₄⋊C₄

—

121

C₄⋊C₄

—

158

—

122

C₄⋊C₄

—

158

—

123

C₄⋊C₄

—

158

—

124

C₂³

—

125

C₂³

—

126

C₂³

—

127

C₂³

C₂³×D₇₉

yes

characteristic

128

Q₈

—

129

Q₈

—

158

—

130

C₂×C₄

—

131

C₂×C₄

—

132

C₂×C₄

—

133

C₂×C₄

—

134

C₂×C₄

—

316

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

158

—

138

C₂×C₄

—

158

—

139

C₂×C₄

—

158

—

140

C₂×C₄

—

158

—

141

C₂×C₄

—

158

—

142

C₂×C₄

—

158

—

143

C₂×C₄

D₄×D₇₉

yes

—

144

C₂×C₄

Q₈×D₇₉

yes

complemented

145

C₂²

—

146

C₂²

—

147

C₂²

—

148

C₂²

C₂×D₄×D₇₉

yes

—

149

C₂²

C₂×Q₈×D₇₉

yes

—

150

C₂²

#41×D₇₉

yes

characteristic

151

C₄

—

152

C₄

—

153

C₄

—

154

C₄

—

316

—

155

C₄

—

158

—

156

C₄

—

158

—

157

C₂

—

158

C₂

#120×D₇₉

yes

characteristic

159

C₂

C₂²⋊Q₈×D₇₉

yes

—

160

C₂

C₄⋊Q₈×D₇₉

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, cosocle	C₂³×C₇₉	C₂⁴
Fitting	#395×C₇₉	C₂
prime radical	C₂³×D₇₉	C₂³
hypercenter	#395	D₇₉
hypocenter	C₇₉	C₂×#395
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ #395

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, cosocle

C₂³×C₇₉

C₂⁴

Fitting

#395×C₇₉

C₂

prime radical

C₂³×D₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ #395

N	H ≅ G/N	type
3. #19098484	C₂	semidirect
4. #19098483	C₂	semidirect
5. #19098482	C₂	semidirect
7. #395×C₇₉	C₂	semidirect
34. C₂×C₄×D₇₉	Q₈	semidirect
53. C₂×C₄×C₇₉	C₂×Q₈	semidirect
59. C₂×Dic₇₉	C₂×Q₈	semidirect
79. D₇₉	#395	direct (N × H)
81. C₇₉	C₂×#395	semidirect
87. #395	D₇₉	direct (N × H)
144. C₂×C₄	Q₈×D₇₉	semidirect

H ≅ G/N

type

3. #19098484

C₂

semidirect

4. #19098483

C₂

semidirect

5. #19098482

C₂

semidirect

7. #395×C₇₉

C₂

semidirect

34. C₂×C₄×D₇₉

Q₈

semidirect

53. C₂×C₄×C₇₉

C₂×Q₈

semidirect

59. C₂×Dic₇₉

C₂×Q₈

semidirect

79. D₇₉

#395

direct (N × H)

81. C₇₉

C₂×#395

semidirect

87. #395

D₇₉

direct (N × H)

144. C₂×C₄

Q₈×D₇₉

semidirect

Subgroups — #395×D₇₉ #23766608

Conjugacy classes of subgroups

Complements

Subgroups — #395×D79 #23766608

Conjugacy classes of subgroups

Complements

Subgroups — #395×D₇₉ #23766608