Group #23763040 — subgroups

Subgroups — #23763040

Order 10112.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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	#19098939	C₂	1	1	yes	maximal, characteristic
2	#19098937	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098915	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098910	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098909	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098284	C₂	1	1	yes	maximal, characteristic, complemented
7	#486×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#11929611	—	2	2	no	—
9	C₂×#11929609	—	2	2	no	—
10	#14579161	C₂²	1	1	yes	characteristic
11	#14579158	C₂²	1	1	yes	characteristic
12	#14579084	—	2	2	no	—
13	#14579083	—	2	2	no	—
14	#14579082	—	2	2	no	—
15	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	#127×C₇₉	C₂²	1	1	yes	characteristic
19	#102×C₇₉	—	2	2	no	—
20	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	2	1	no	—
22	C₂×D₃₁₆	—	2	1	no	—
23	C₂×D₃₁₆	—	2	1	no	—
24	C₂×D₃₁₆	—	2	1	no	—
25	#11929611	—	4	4	no	—
26	#11929609	—	4	4	no	—
27	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
28	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
29	C₄⋊Dic₇₉	—	2	1	no	—
30	C₄⋊Dic₇₉	—	2	1	no	—
31	C₂×Q₈×C₇₉	—	2	1	no	—
32	C₂×D₄×C₇₉	—	2	1	no	—
33	C₂×D₄×C₇₉	—	2	1	no	—
34	C₂×D₄×C₇₉	—	2	1	no	—
35	C₂×C₈×C₇₉	D₄	1	2	yes	—
36	C₄⋊C₄×C₇₉	—	2	1	no	—
37	C₄⋊C₄×C₇₉	—	2	1	no	—
38	C₄²×C₇₉	C₂³	1	1	yes	characteristic
39	C₂³×C₇₉	—	4	1	no	—
40	C₂²×D₇₉	—	4	1	no	—
41	Q₈×C₇₉	—	4	2	no	—
42	D₄×C₇₉	—	4	2	no	—
43	D₄×C₇₉	—	4	2	no	—
44	D₄×C₇₉	—	4	2	no	—
45	C₂×C₄×C₇₉	—	4	1	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
49	C₂×Dic₇₉	—	4	1	no	—
50	D₃₁₆	—	4	2	no	—
51	D₃₁₆	—	4	2	no	—
52	D₃₁₆	—	4	2	no	—
53	Dic₁₅₈	—	4	2	no	—
54	C₈×C₇₉	—	2	2	no	—
55	C₇₉⋊C₈	—	2	2	no	—
56	C₇₉⋊C₈	—	2	2	no	—
57	C₂²×C₇₉	—	8	1	no	—
58	C₂²×C₇₉	—	8	1	no	—
59	C₂²×C₇₉	—	8	1	no	—
60	C₂²×C₇₉	#127	1	1	yes	characteristic
61	C₂×D₇₉	—	8	1	no	—
62	C₂×D₇₉	—	8	1	no	—
63	C₂×D₇₉	—	8	1	no	—
64	C₄×C₇₉	—	8	1	no	—
65	C₄×C₇₉	#135	1	2	yes	—
66	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
67	C₄×C₇₉	AGL(1,ℤ/8)	1	2	yes	—
68	Dic₇₉	—	8	1	no	—
69	C₂×C₇₉	—	16	1	no	—
70	C₂×C₇₉	#495	1	1	yes	characteristic
71	C₂×C₇₉	#496	1	1	yes	characteristic
72	C₂×C₇₉	#496	1	1	yes	characteristic
73	D₇₉	—	16	1	no	—
74	#1717	—	79	1	no	maximal, Sylow
75	C₇₉	#1717	1	1	yes	characteristic, complemented, Sylow
76	#493	—	79	1	no	—
77	#492	—	79	1	no	—
78	#487	—	79	1	no	—
79	#486	—	79	1	no	—
80	#486	—	79	1	no	—
81	#486	D₇₉	1	1	yes	characteristic, complemented
82	#322	—	79	1	no	—
83	C₂×SD₁₆	—	158	2	no	—
84	C₂×D₈	—	158	2	no	—
85	C₄⋊Q₈	—	79	1	no	—
86	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
87	#127	—	79	1	no	—
88	#127	C₂×D₇₉	1	1	yes	characteristic
89	#103	—	158	2	no	—
90	#102	—	2	2	no	—
91	#102	—	158	2	no	—
92	#102	—	158	2	no	—
93	C₄×C₈	—	79	1	no	—
94	C₄×C₈	—	79	1	no	—
95	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
96	C₂×Q₈	—	2	1	no	—
97	C₂×Q₈	—	158	1	no	—
98	C₂×D₄	—	2	1	no	—
99	C₂×D₄	—	2	1	no	—
100	C₂×D₄	—	2	1	no	—
101	C₂×D₄	—	158	1	no	—
102	C₂×D₄	—	158	1	no	—
103	C₂×D₄	—	158	1	no	—
104	SD₁₆	—	316	4	no	—
105	D₈	—	316	4	no	—
106	C₂×C₈	—	79	2	no	—
107	C₂×C₈	—	79	2	no	—
108	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
109	C₄⋊C₄	—	2	1	no	—
110	C₄⋊C₄	—	2	1	no	—
111	C₄⋊C₄	—	158	1	no	—
112	C₄⋊C₄	—	158	1	no	—
113	C₄²	C₂²×D₇₉	1	1	yes	characteristic
114	C₂³	—	4	1	no	—
115	C₂³	—	316	1	no	—
116	Q₈	—	4	2	no	—
117	Q₈	—	316	2	no	—
118	D₄	—	4	2	no	—
119	D₄	—	4	2	no	—
120	D₄	—	4	2	no	—
121	D₄	—	316	2	no	—
122	D₄	—	316	2	no	—
123	D₄	—	316	2	no	—
124	C₂×C₄	—	4	1	no	—
125	C₂×C₄	—	316	1	no	—
126	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
127	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
128	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
129	C₈	—	2	2	no	—
130	C₈	—	158	2	no	—
131	C₈	—	158	2	no	—
132	C₂²	—	8	1	no	—
133	C₂²	—	8	1	no	—
134	C₂²	—	8	1	no	—
135	C₂²	—	632	1	no	—
136	C₂²	—	632	1	no	—
137	C₂²	—	632	1	no	—
138	C₂²	#14579157	1	1	yes	characteristic
139	C₄	—	8	1	no	—
140	C₄	—	632	1	no	—
141	C₄	#14579181	1	2	yes	—
142	C₄	#14579185	1	2	yes	—
143	C₄	#14579188	1	2	yes	—
144	C₂	—	16	1	no	—
145	C₂	—	1264	1	no	—
146	C₂	#19098945	1	1	yes	characteristic
147	C₂	#19098949	1	1	yes	characteristic
148	C₂	#19098951	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098939

C₂

yes

maximal, characteristic

#19098937

C₂

yes

maximal, characteristic, complemented

#19098915

C₂

yes

maximal, characteristic, complemented

#19098910

C₂

yes

maximal, characteristic, complemented

#19098909

C₂

yes

maximal, characteristic, complemented

#19098284

C₂

yes

maximal, characteristic, complemented

#486×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929611

—

C₂×#11929609

—

#14579161

C₂²

yes

characteristic

#14579158

C₂²

yes

—

—

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#127×C₇₉

C₂²

yes

characteristic

#102×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

C₂×D₃₁₆

—

#11929611

—

#11929609

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

D₃₁₆

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#127

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#135

yes

—

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

C₄×C₇₉

AGL(1,ℤ/8)

yes

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#1717

—

maximal, Sylow

C₇₉

#1717

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic, complemented

#322

—

C₂×SD₁₆

—

158

—

C₂×D₈

—

158

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

#127

—

#127

C₂×D₇₉

yes

characteristic

#103

—

158

—

#102

—

#102

—

158

—

#102

—

158

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×D₄

—

C₂×D₄

—

100

C₂×D₄

—

101

C₂×D₄

—

158

—

102

C₂×D₄

—

158

—

103

C₂×D₄

—

158

—

104

SD₁₆

—

316

—

105

D₈

—

316

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

C₂²⋊D₇₉

yes

—

109

C₄⋊C₄

—

110

C₄⋊C₄

—

111

C₄⋊C₄

—

158

—

112

C₄⋊C₄

—

158

—

113

C₄²

C₂²×D₇₉

yes

characteristic

114

C₂³

—

115

C₂³

—

316

—

116

Q₈

—

117

Q₈

—

316

—

118

D₄

—

119

D₄

—

120

D₄

—

121

D₄

—

316

—

122

D₄

—

316

—

123

D₄

—

316

—

124

C₂×C₄

—

125

C₂×C₄

—

316

—

126

C₂×C₄

D₄×D₇₉

yes

characteristic

127

C₂×C₄

D₄×D₇₉

yes

characteristic

128

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

129

C₈

—

130

C₈

—

158

—

131

C₈

—

158

—

132

C₂²

—

133

C₂²

—

134

C₂²

—

135

C₂²

—

632

—

136

C₂²

—

632

—

137

C₂²

—

632

—

138

C₂²

#14579157

yes

characteristic

139

C₄

—

140

C₄

—

632

—

141

C₄

#14579181

yes

—

142

C₄

#14579185

yes

—

143

C₄

#14579188

yes

—

144

C₂

—

145

C₂

—

1264

—

146

C₂

#19098945

yes

characteristic

147

C₂

#19098949

yes

characteristic

148

C₂

#19098951

yes

characteristic

	subgroup	G/H
center	C₂²	#14579157
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#486×C₇₉	C₂
socle	C₂²×C₇₉	#127
prime radical	#19098939	C₂
hypercenter	#486	D₇₉
hypocenter	C₇₉	#1717
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #486

subgroup

G/H

center

C₂²

#14579157

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#486×C₇₉

C₂

C₂²×C₇₉

C₂

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #486

N	H ≅ G/N	type
2. #19098937	C₂	semidirect
3. #19098915	C₂	semidirect
4. #19098910	C₂	semidirect
5. #19098909	C₂	semidirect
6. #19098284	C₂	semidirect
7. #486×C₇₉	C₂	semidirect
75. C₇₉	#1717	semidirect
81. #486	D₇₉	semidirect

H ≅ G/N

type

2. #19098937

C₂

semidirect

3. #19098915

C₂

semidirect

4. #19098910

C₂

semidirect

5. #19098909

C₂

semidirect

6. #19098284

C₂

semidirect

7. #486×C₇₉

C₂

semidirect

75. C₇₉

#1717

semidirect

81. #486

D₇₉

semidirect

Subgroups — #23763040

Conjugacy classes of subgroups

Complements