Group #23765528 — subgroups

Subgroups — #23765528

Order 10112.

144 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 47 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×#14579105	C₂	1	1	yes	maximal, characteristic, complemented
2	#19098980	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098838	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098392	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098378	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098376	C₂	1	1	yes	maximal, characteristic, complemented
7	#472×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#14579191	—	2	1	no	—
9	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
10	#14579105	—	2	1	no	—
11	#14579105	—	2	1	no	—
12	#14579101	—	2	1	no	—
13	#14579101	C₂²	1	1	yes	characteristic
14	C₂×C₇₉⋊C₁₆	—	2	1	no	—
15	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
16	#14579097	C₂²	1	1	yes	characteristic
17	#14579079	—	2	1	no	—
18	AGL(1,ℤ/8)×C₇₉	—	2	1	no	—
19	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
20	#131×C₇₉	C₂²	1	1	yes	characteristic
21	#108×C₇₉	C₂²	1	1	yes	characteristic
22	#100×C₇₉	—	2	1	no	—
23	C₂×Dic₁₅₈	—	2	1	no	—
24	Dic₃₁₆	—	2	1	no	—
25	Dic₃₁₆	—	2	1	no	—
26	#11929614	—	4	1	no	—
27	#11929612	—	4	1	no	—
28	#11929608	—	2	1	no	—
29	C₇₉⋊C₁₆	—	2	1	no	—
30	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
31	C₇₉⋊C₁₆	D₄	1	1	yes	characteristic
32	#41×C₇₉	D₄	1	1	yes	characteristic
33	C₂×D₄×C₇₉	—	2	1	no	—
34	SD₁₆×C₇₉	—	4	1	no	—
35	D₈×C₇₉	—	2	1	no	—
36	D₈×C₇₉	—	2	1	no	—
37	D₈×C₇₉	—	4	1	no	—
38	M₁₆×C₇₉	—	2	1	no	—
39	M₁₆×C₇₉	—	2	1	no	—
40	M₁₆×C₇₉	D₄	1	1	yes	characteristic
41	C₂×C₈×C₇₉	—	2	1	no	—
42	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
43	C₂³×C₇₉	—	4	1	no	—
44	Q₈×C₇₉	D₈	1	1	yes	characteristic
45	D₄×C₇₉	—	2	1	no	—
46	D₄×C₇₉	—	4	1	no	—
47	D₄×C₇₉	—	4	1	no	—
48	D₄×C₇₉	D₈	1	1	yes	characteristic
49	C₂×C₄×C₇₉	—	2	1	no	—
50	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
51	C₂×Dic₇₉	—	4	1	no	—
52	Dic₁₅₈	—	4	1	no	—
53	Dic₁₅₈	—	4	1	no	—
54	C₈×C₇₉	—	2	1	no	—
55	C₈×C₇₉	—	4	1	no	—
56	C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
57	C₈×C₇₉	#41	1	1	yes	characteristic
58	C₇₉⋊C₈	—	4	1	no	—
59	C₂²×C₇₉	—	2	1	no	—
60	C₂²×C₇₉	—	8	1	no	—
61	C₂²×C₇₉	—	16	1	no	—
62	C₂²×C₇₉	#135	1	1	yes	characteristic
63	C₄×C₇₉	—	2	1	no	—
64	C₄×C₇₉	#121	1	1	yes	characteristic
65	C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
66	Dic₇₉	—	8	1	no	—
67	C₂×C₇₉	—	2	1	no	—
68	C₂×C₇₉	—	4	1	no	—
69	C₂×C₇₉	—	16	1	no	—
70	C₂×C₇₉	#466	1	1	yes	characteristic
71	#2223	—	79	1	no	maximal, Sylow
72	C₇₉	#2223	1	1	yes	characteristic, complemented, Sylow
73	C₂×SD₃₂	—	79	1	no	—
74	#504	—	79	1	no	—
75	#473	—	79	1	no	—
76	#472	D₇₉	1	1	yes	characteristic
77	#368	—	79	1	no	—
78	#362	—	79	1	no	—
79	#361	—	79	1	no	—
80	#137	—	158	1	no	—
81	AGL(1,ℤ/8)	—	2	1	no	—
82	C₂×Q₁₆	—	79	1	no	—
83	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
84	#131	C₂×D₇₉	1	1	yes	characteristic
85	SD₃₂	—	158	1	no	—
86	SD₃₂	—	158	1	no	—
87	M₃₂	—	79	1	no	—
88	M₃₂	—	158	1	no	—
89	C₂×C₁₆	—	79	1	no	—
90	C₂×C₁₆	—	158	1	no	—
91	#108	—	79	1	no	—
92	#108	C₂×D₇₉	1	1	yes	characteristic
93	#101	—	158	1	no	—
94	#100	—	2	1	no	—
95	#41	C₂²⋊D₇₉	1	1	yes	characteristic
96	C₂×Q₈	—	158	1	no	—
97	C₂×D₄	—	2	1	no	—
98	Q₁₆	—	316	1	no	—
99	Q₁₆	—	158	1	no	—
100	Q₁₆	—	158	1	no	—
101	SD₁₆	—	4	1	no	—
102	SD₁₆	—	316	1	no	—
103	D₈	—	2	1	no	—
104	D₈	—	2	1	no	—
105	D₈	—	4	1	no	—
106	M₁₆	—	2	1	no	—
107	M₁₆	—	2	1	no	—
108	M₁₆	—	158	1	no	—
109	M₁₆	C₂²⋊D₇₉	1	1	yes	characteristic
110	C₂×C₈	—	2	1	no	—
111	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
112	C₁₆	—	79	1	no	—
113	C₁₆	—	79	1	no	—
114	C₁₆	—	158	1	no	—
115	C₂³	—	4	1	no	—
116	Q₈	—	316	1	no	—
117	Q₈	—	316	1	no	—
118	Q₈	#11929609	1	1	yes	characteristic
119	D₄	—	2	1	no	—
120	D₄	—	4	1	no	—
121	D₄	—	4	1	no	—
122	D₄	#11929609	1	1	yes	characteristic
123	C₂×C₄	—	2	1	no	—
124	C₂×C₄	—	316	1	no	—
125	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
126	C₈	—	2	1	no	—
127	C₈	—	4	1	no	—
128	C₈	—	316	1	no	—
129	C₈	D₄×D₇₉	1	1	yes	characteristic
130	C₈	#11929623	1	1	yes	characteristic
131	C₂²	—	2	1	no	—
132	C₂²	—	8	1	no	—
133	C₂²	—	16	1	no	—
134	C₂²	#14579181	1	1	yes	characteristic
135	C₄	—	2	1	no	—
136	C₄	—	632	1	no	—
137	C₄	#14579133	1	1	yes	characteristic
138	C₄	C₂×#11929609	1	1	yes	characteristic
139	C₂	—	2	1	no	—
140	C₂	—	4	1	no	—
141	C₂	—	16	1	no	—
142	C₂	#19098797	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579105

C₂

yes

maximal, characteristic, complemented

#19098980

C₂

yes

maximal, characteristic, complemented

#19098838

C₂

yes

maximal, characteristic, complemented

#19098392

C₂

yes

maximal, characteristic, complemented

#19098378

C₂

yes

maximal, characteristic, complemented

#19098376

C₂

yes

maximal, characteristic, complemented

#472×C₇₉

C₂

yes

maximal, characteristic

#14579191

—

C₂×Dic₃₁₆

C₂²

yes

—

—

—

C₂²

yes

characteristic

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579097

C₂²

yes

characteristic

#14579079

—

AGL(1,ℤ/8)×C₇₉

—

C₂×D₈×C₇₉

C₂²

yes

characteristic

#131×C₇₉

C₂²

yes

characteristic

#108×C₇₉

C₂²

yes

characteristic

#100×C₇₉

—

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929614

—

#11929612

—

#11929608

—

C₇₉⋊C₁₆

—

C₇₉⋊C₁₆

D₄

yes

characteristic

C₇₉⋊C₁₆

D₄

yes

characteristic

#41×C₇₉

D₄

yes

characteristic

C₂×D₄×C₇₉

—

SD₁₆×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

—

M₁₆×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

—

Q₈×C₇₉

D₈

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

—

C₈×C₇₉

C₂×D₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#135

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

#121

yes

characteristic

C₄×C₇₉

C₂×D₈

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

#504

—

#473

—

#472

D₇₉

yes

—

—

—

—

158

—

AGL(1,ℤ/8)

—

C₂×Q₁₆

—

C₂×D₈

C₂×D₇₉

yes

characteristic

#131

C₂×D₇₉

yes

characteristic

SD₃₂

—

158

—

SD₃₂

—

158

—

M₃₂

—

M₃₂

—

158

—

C₂×C₁₆

—

C₂×C₁₆

—

158

—

#108

—

#108

C₂×D₇₉

yes

characteristic

#101

—

158

—

#100

—

#41

C₂²⋊D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

Q₁₆

—

316

—

Q₁₆

—

158

—

100

Q₁₆

—

158

—

101

SD₁₆

—

102

SD₁₆

—

316

—

103

D₈

—

104

D₈

—

105

D₈

—

106

M₁₆

—

107

M₁₆

—

108

M₁₆

—

158

—

109

M₁₆

C₂²⋊D₇₉

yes

characteristic

110

C₂×C₈

—

111

C₂×C₈

C₂²×D₇₉

yes

characteristic

112

C₁₆

—

113

C₁₆

—

114

C₁₆

—

158

—

115

C₂³

—

116

Q₈

—

316

—

117

Q₈

—

316

—

118

Q₈

#11929609

yes

characteristic

119

D₄

—

120

D₄

—

121

D₄

—

122

D₄

#11929609

yes

characteristic

123

C₂×C₄

—

124

C₂×C₄

—

316

—

125

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

126

C₈

—

127

C₈

—

128

C₈

—

316

—

129

C₈

D₄×D₇₉

yes

characteristic

130

C₈

#11929623

yes

characteristic

131

C₂²

—

132

C₂²

—

133

C₂²

—

134

C₂²

#14579181

yes

characteristic

135

C₄

—

136

C₄

—

632

—

137

C₄

#14579133

yes

characteristic

138

C₄

C₂×#11929609

yes

characteristic

139

C₂

—

140

C₂

—

141

C₂

—

142

C₂

#19098797

yes

characteristic

	subgroup	G/H
center	C₂	#19098797
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting, prime radical	#472×C₇₉	C₂
socle	C₂×C₇₉	#466
hypercenter	#472	D₇₉
hypocenter	C₇₉	#2223
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

subgroup

G/H

center

C₂

#19098797

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting, prime radical

#472×C₇₉

C₂

C₂×C₇₉

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131 ◁ #472

N	H ≅ G/N	type
1. C₂×#14579105	C₂	semidirect
2. #19098980	C₂	semidirect
3. #19098838	C₂	semidirect
4. #19098392	C₂	semidirect
5. #19098378	C₂	semidirect
6. #19098376	C₂	semidirect
72. C₇₉	#2223	semidirect

H ≅ G/N

type

1. C₂×#14579105

C₂

semidirect

2. #19098980

C₂

semidirect

3. #19098838

C₂

semidirect

4. #19098392

C₂

semidirect

5. #19098378

C₂

semidirect

6. #19098376

C₂

semidirect

72. C₇₉

#2223

semidirect

Subgroups — #23765528

Conjugacy classes of subgroups

Complements