Group #23764552 — subgroups

Subgroups — #23764552

Order 10112.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14579153	C₂	1	1	yes	maximal, characteristic
2	C₂×#14579086	C₂	1	2	yes	maximal
3	#19098469	C₂	1	1	yes	maximal, characteristic
4	#19098326	C₂	1	2	yes	maximal
5	#336×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₁₅₈	C₂²	1	1	yes	characteristic
7	#14579153	—	2	4	no	—
8	C₂×C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
10	C₂×Dic₇₉⋊C₄	—	2	2	no	—
11	#14579086	—	2	4	no	—
12	C₇₉⋊#95	—	2	2	no	—
13	C₂²×C₈×C₇₉	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₅₈	—	2	2	no	—
16	C₂×Dic₁₅₈	—	2	2	no	—
17	C₂×Dic₁₅₈	—	2	1	no	—
18	C₂×Dic₁₅₈	Q₈	1	2	yes	—
19	C₂²×Dic₇₉	—	2	1	no	—
20	C₂²×Dic₇₉	—	2	2	no	—
21	C₂²×Dic₇₉	—	2	1	no	—
22	C₄⋊Dic₇₉	—	2	2	no	—
23	C₄⋊Dic₇₉	—	2	2	no	—
24	C₄⋊Dic₇₉	D₄	1	4	yes	—
25	Dic₇₉⋊C₄	—	2	8	no	—
26	C₂²×C₄×C₇₉	D₄	1	2	yes	—
27	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₂×C₈×C₇₉	—	2	2	no	—
30	C₂×C₈×C₇₉	—	2	2	no	—
31	C₄²×C₇₉	—	2	2	no	—
32	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₉	—	2	2	no	—
34	C₂×C₄×C₇₉	—	2	2	no	—
35	C₂×C₄×C₇₉	—	2	2	no	—
36	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
38	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
39	C₂×C₄×C₇₉	#41	1	2	yes	—
40	C₂×Dic₇₉	—	2	4	no	—
41	C₂×Dic₇₉	—	2	2	no	—
42	C₂×Dic₇₉	—	4	1	no	—
43	C₂×Dic₇₉	—	4	1	no	—
44	C₂×Dic₇₉	—	4	2	no	—
45	C₂×Dic₇₉	—	4	2	no	—
46	C₂×Dic₇₉	—	4	1	no	—
47	C₂×Dic₇₉	—	4	2	no	—
48	Dic₁₅₈	—	2	4	no	—
49	Dic₁₅₈	—	4	2	no	—
50	C₈×C₇₉	—	4	2	no	—
51	C₂²×C₇₉	#120	1	1	yes	characteristic
52	C₂²×C₇₉	C₂²⋊Q₈	1	1	yes	characteristic
53	C₂²×C₇₉	#124	1	1	yes	characteristic
54	C₂²×C₇₉	#135	1	2	yes	—
55	C₂²×C₇₉	#137	1	2	yes	—
56	C₄×C₇₉	—	4	2	no	—
57	C₄×C₇₉	C₂²⋊Q₈	1	2	yes	—
58	C₄×C₇₉	#124	1	2	yes	—
59	Dic₇₉	—	4	2	no	—
60	Dic₇₉	—	4	4	no	—
61	Dic₇₉	—	8	1	no	—
62	C₂×C₇₉	#393	1	1	yes	characteristic
63	C₂×C₇₉	#452	1	2	yes	—
64	C₂×C₇₉	#479	1	2	yes	—
65	C₂×C₇₉	#488	1	1	yes	characteristic
66	C₂×C₇₉	#491	1	1	yes	characteristic
67	#2026	—	79	1	no	maximal, Sylow
68	C₇₉	#2026	1	1	yes	characteristic, complemented, Sylow
69	C₂×#125	—	79	1	no	—
70	C₂×#103	—	79	2	no	—
71	#391	—	79	1	no	—
72	#340	—	79	2	no	—
73	#336	D₇₉	1	1	yes	characteristic
74	C₂²×Q₈	—	79	1	no	—
75	C₂²×C₈	C₂×D₇₉	1	2	yes	—
76	#125	—	158	4	no	—
77	C₂×C₄⋊C₄	—	79	2	no	—
78	C₂×C₄⋊C₄	—	79	1	no	—
79	C₂×C₄⋊C₄	—	158	2	no	—
80	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
81	#103	—	158	4	no	—
82	#95	—	158	2	no	—
83	C₂×Q₈	—	79	2	no	—
84	C₂×Q₈	—	158	2	no	—
85	C₂×Q₈	—	158	2	no	—
86	C₂×Q₈	—	158	1	no	—
87	C₂²×C₄	—	158	1	no	—
88	C₂²×C₄	—	158	1	no	—
89	C₂²×C₄	—	158	2	no	—
90	C₂²×C₄	D₃₁₆	1	2	yes	—
91	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
92	C₂×C₈	—	2	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	2	2	no	—
95	C₄⋊C₄	—	79	4	no	—
96	C₄⋊C₄	—	158	8	no	—
97	C₄⋊C₄	—	158	2	no	—
98	C₄⋊C₄	—	158	2	no	—
99	C₄²	—	2	2	no	—
100	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
101	Q₈	—	316	2	no	—
102	Q₈	—	158	4	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	—	2	2	no	—
106	C₂×C₄	—	316	1	no	—
107	C₂×C₄	—	316	1	no	—
108	C₂×C₄	—	316	2	no	—
109	C₂×C₄	—	316	2	no	—
110	C₂×C₄	—	316	1	no	—
111	C₂×C₄	—	316	2	no	—
112	C₂×C₄	—	158	4	no	—
113	C₂×C₄	—	158	2	no	—
114	C₂×C₄	D₄×D₇₉	1	2	yes	—
115	C₂×C₄	Q₈×D₇₉	1	1	yes	characteristic
116	C₂×C₄	#11929623	1	1	yes	characteristic
117	C₂×C₄	#11929624	1	2	yes	—
118	C₈	—	4	2	no	—
119	C₂²	#14579131	1	1	yes	characteristic
120	C₂²	#14579141	1	1	yes	characteristic
121	C₂²	#14579149	1	1	yes	characteristic
122	C₂²	#14579183	1	2	yes	—
123	C₂²	#14579194	1	2	yes	—
124	C₄	—	4	2	no	—
125	C₄	—	316	4	no	—
126	C₄	—	316	2	no	—
127	C₄	—	632	1	no	—
128	C₄	#14579139	1	2	yes	—
129	C₄	#14579147	1	2	yes	—
130	C₂	#19098476	1	1	yes	characteristic
131	C₂	#19098727	1	2	yes	—
132	C₂	#19098871	1	2	yes	—
133	C₂	#19098918	1	1	yes	characteristic
134	C₂	#19098932	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579153

C₂

yes

maximal, characteristic

C₂×#14579086

C₂

yes

maximal

#19098469

C₂

yes

maximal, characteristic

#19098326

C₂

yes

maximal

#336×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

characteristic

#14579153

—

C₂×C₄⋊Dic₇₉

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

—

#14579086

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

Q₈

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

D₄

yes

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

C₂×C₄×C₇₉

yes

C₂×C₄×C₇₉

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₂²×C₇₉

#120

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₂²×C₇₉

#137

yes

—

C₄×C₇₉

—

C₄×C₇₉

C₂²⋊Q₈

yes

—

C₄×C₇₉

#124

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

#393

yes

characteristic

C₂×C₇₉

#452

yes

—

C₂×C₇₉

#479

yes

—

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₉

yes

characteristic

C₂²×Q₈

—

C₂²×C₈

C₂×D₇₉

yes

—

#125

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#103

—

158

—

#95

—

158

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

D₃₁₆

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

100

C₂³

C₂×D₃₁₆

yes

characteristic

101

Q₈

—

316

—

102

Q₈

—

158

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

316

—

107

C₂×C₄

—

316

—

108

C₂×C₄

—

316

—

109

C₂×C₄

—

316

—

110

C₂×C₄

—

316

—

111

C₂×C₄

—

316

—

112

C₂×C₄

—

158

—

113

C₂×C₄

—

158

—

114

C₂×C₄

D₄×D₇₉

yes

—

115

C₂×C₄

Q₈×D₇₉

yes

characteristic

116

C₂×C₄

#11929623

yes

characteristic

117

C₂×C₄

#11929624

yes

—

118

C₈

—

119

C₂²

#14579131

yes

characteristic

120

C₂²

#14579141

yes

characteristic

121

C₂²

#14579149

yes

characteristic

122

C₂²

#14579183

yes

—

123

C₂²

#14579194

yes

—

124

C₄

—

125

C₄

—

316

—

126

C₄

—

316

—

127

C₄

—

632

—

128

C₄

#14579139

yes

—

129

C₄

#14579147

yes

—

130

C₂

#19098476

yes

characteristic

131

C₂

#19098727

yes

—

132

C₂

#19098871

yes

—

133

C₂

#19098918

yes

characteristic

134

C₂

#19098932

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₁₆
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#336×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	#336	D₇₉
hypocenter	C₇₉	#2026
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

subgroup

G/H

center

C₂³

C₂×D₃₁₆

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#336×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

N	H ≅ G/N	type
68. C₇₉	#2026	semidirect

H ≅ G/N

type

68. C₇₉

#2026

semidirect

Subgroups — #23764552

Conjugacy classes of subgroups

Complements