Group #23771777 — subgroups

Subgroups — #23771777

Order 10112.

504 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14579161	C₂	1	1	yes	maximal, characteristic
2	#19098470	C₂	1	4	yes	maximal
3	#19098468	C₂	1	4	yes	maximal
4	#19098428	C₂	1	4	yes	maximal
5	C₄²×Dic₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₁₅₈	C₂²	1	2	yes	—
8	#14579161	—	2	4	no	—
9	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
11	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
12	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
13	C₂×C₄×Dic₇₉	C₂²	1	2	yes	—
14	C₇₉⋊#95	C₂²	1	16	yes	—
15	C₂²×Q₈×C₇₉	C₂²	1	2	yes	—
16	C₄⋊Q₈×C₇₉	—	2	4	no	—
17	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
18	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
19	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₅₈	—	2	4	no	—
21	C₂×Dic₁₅₈	—	2	8	no	—
22	C₂²×Dic₇₉	C₂³	1	4	yes	—
23	C₂²×Dic₇₉	C₂³	1	4	yes	—
24	C₄⋊Dic₇₉	—	2	4	no	—
25	C₄⋊Dic₇₉	—	2	4	no	—
26	C₄×Dic₇₉	—	2	4	no	—
27	C₄×Dic₇₉	—	2	4	no	—
28	C₄×Dic₇₉	Q₈	1	8	yes	complemented
29	C₂×Q₈×C₇₉	—	2	4	no	—
30	C₂×Q₈×C₇₉	—	2	8	no	—
31	C₂²×C₄×C₇₉	C₂³	1	4	yes	—
32	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
33	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₇₉	—	2	4	no	—
36	C₄⋊C₄×C₇₉	—	2	4	no	—
37	C₄²×C₇₉	D₄	1	4	yes	—
38	C₂³×C₇₉	C₂⁴	1	1	yes	characteristic
39	Q₈×C₇₉	—	4	8	no	—
40	C₂×C₄×C₇₉	—	2	4	no	—
41	C₂×C₄×C₇₉	—	2	8	no	—
42	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
43	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
44	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₇₉	C₂×Q₈	1	4	yes	—
46	C₂×C₄×C₇₉	#41	1	4	yes	—
47	C₂×C₄×C₇₉	#41	1	4	yes	—
48	C₂×Dic₇₉	—	2	4	no	—
49	C₂×Dic₇₉	—	2	4	no	—
50	C₂×Dic₇₉	—	2	4	no	—
51	C₂×Dic₇₉	—	2	8	no	—
52	C₂×Dic₇₉	C₂×Q₈	1	8	yes	—
53	Dic₁₅₈	—	4	8	no	—
54	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
55	C₂²×C₇₉	C₂²×Q₈	1	2	yes	—
56	C₂²×C₇₉	C₂×#41	1	2	yes	—
57	C₂²×C₇₉	C₂×#41	1	2	yes	—
58	C₄×C₇₉	—	4	4	no	—
59	C₄×C₇₉	#124	1	4	yes	—
60	C₄×C₇₉	#124	1	4	yes	—
61	C₄×C₇₉	C₄⋊Q₈	1	4	yes	—
62	Dic₇₉	—	2	8	no	—
63	Dic₇₉	—	4	4	no	—
64	C₂×C₇₉	C₂×#124	1	1	yes	characteristic
65	C₂×C₇₉	C₂×#124	1	1	yes	characteristic
66	C₂×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₇₉	#533	1	4	yes	—
68	#2862	—	79	1	no	maximal, Sylow
69	C₇₉	#2862	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₄⋊Q₈	—	79	1	no	—
71	C₂×C₄⋊Q₈	D₇₉	1	1	yes	characteristic
72	#391	—	79	4	no	—
73	#391	—	79	4	no	—
74	#382	—	79	4	no	—
75	C₄³	—	79	1	no	—
76	C₂²×Q₈	—	79	2	no	—
77	C₂²×Q₈	C₂×D₇₉	1	2	yes	—
78	C₄⋊Q₈	—	2	4	no	—
79	C₄⋊Q₈	—	158	4	no	—
80	C₂×C₄⋊C₄	—	79	2	no	—
81	C₂×C₄⋊C₄	—	79	2	no	—
82	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
83	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
84	C₂×C₄²	—	79	2	no	—
85	C₂×C₄²	—	79	2	no	—
86	C₂×C₄²	—	79	2	no	—
87	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
88	#95	—	79	16	no	—
89	C₂×Q₈	—	2	4	no	—
90	C₂×Q₈	—	2	8	no	—
91	C₂×Q₈	—	158	4	no	—
92	C₂×Q₈	—	158	8	no	—
93	C₂²×C₄	—	79	4	no	—
94	C₂²×C₄	—	79	4	no	—
95	C₂²×C₄	C₂²×D₇₉	1	4	yes	—
96	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
97	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
98	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
99	C₄⋊C₄	—	2	4	no	—
100	C₄⋊C₄	—	2	4	no	—
101	C₄⋊C₄	—	158	4	no	—
102	C₄⋊C₄	—	158	4	no	—
103	C₄²	—	79	8	no	—
104	C₄²	—	158	4	no	—
105	C₄²	—	158	4	no	—
106	C₄²	C₂²⋊D₇₉	1	4	yes	—
107	C₂³	C₂³×D₇₉	1	1	yes	characteristic
108	Q₈	—	4	8	no	—
109	Q₈	—	316	8	no	—
110	C₂×C₄	—	2	8	no	—
111	C₂×C₄	—	2	4	no	—
112	C₂×C₄	—	79	8	no	—
113	C₂×C₄	—	158	8	no	—
114	C₂×C₄	—	158	4	no	—
115	C₂×C₄	—	158	4	no	—
116	C₂×C₄	—	158	4	no	—
117	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
118	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
119	C₂×C₄	C₂×C₂²⋊D₇₉	1	2	yes	—
120	C₂×C₄	Q₈×D₇₉	1	4	yes	—
121	C₂×C₄	#11929623	1	4	yes	—
122	C₂×C₄	#11929625	1	4	yes	—
123	C₂²	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
124	C₂²	C₂×Q₈×D₇₉	1	2	yes	—
125	C₂²	C₂×#11929623	1	2	yes	—
126	C₂²	C₂×#11929625	1	2	yes	—
127	C₄	—	4	4	no	—
128	C₄	—	316	4	no	—
129	C₄	—	158	8	no	—
130	C₄	#14579148	1	4	yes	—
131	C₄	#14579150	1	4	yes	—
132	C₄	#14579159	1	4	yes	—
133	C₂	C₂×#14579148	1	1	yes	characteristic
134	C₂	C₂×#14579150	1	1	yes	characteristic
135	C₂	C₂×#14579159	1	1	yes	characteristic
136	C₂	#19099118	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579161

C₂

yes

maximal, characteristic

#19098470

C₂

yes

maximal

#19098468

C₂

yes

maximal

#19098428

C₂

yes

maximal

C₄²×Dic₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₇₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₅₈

C₂²

yes

—

#14579161

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

—

C₇₉⋊#95

C₂²

yes

—

C₂²×Q₈×C₇₉

C₂²

yes

—

C₄⋊Q₈×C₇₉

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

C₂³

yes

—

C₂²×Dic₇₉

C₂³

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

—

C₄×Dic₇₉

Q₈

yes

complemented

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

—

C₂³×C₇₉

C₂⁴

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×Q₈

yes

—

Dic₁₅₈

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂²×C₇₉

C₂²×Q₈

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₂²×C₇₉

C₂×#41

yes

—

C₄×C₇₉

—

C₄×C₇₉

#124

yes

—

C₄×C₇₉

#124

yes

—

C₄×C₇₉

C₄⋊Q₈

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₉

#533

yes

—

#2862

—

maximal, Sylow

C₇₉

#2862

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₇₉

yes

—

—

—

C₄³

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₇₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

158

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#95

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₉

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

158

—

102

C₄⋊C₄

—

158

—

103

C₄²

—

104

C₄²

—

158

—

105

C₄²

—

158

—

106

C₄²

C₂²⋊D₇₉

yes

—

107

C₂³

C₂³×D₇₉

yes

characteristic

108

Q₈

—

109

Q₈

—

316

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

158

—

114

C₂×C₄

—

158

—

115

C₂×C₄

—

158

—

116

C₂×C₄

—

158

—

117

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

118

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

119

C₂×C₄

C₂×C₂²⋊D₇₉

yes

—

120

C₂×C₄

Q₈×D₇₉

yes

—

121

C₂×C₄

#11929623

yes

—

122

C₂×C₄

#11929625

yes

—

123

C₂²

C₂²×C₂²⋊D₇₉

yes

characteristic

124

C₂²

C₂×Q₈×D₇₉

yes

—

125

C₂²

C₂×#11929623

yes

—

126

C₂²

C₂×#11929625

yes

—

127

C₄

—

128

C₄

—

316

—

129

C₄

—

158

—

130

C₄

#14579148

yes

—

131

C₄

#14579150

yes

—

132

C₄

#14579159

yes

—

133

C₂

C₂×#14579148

yes

characteristic

134

C₂

C₂×#14579150

yes

characteristic

135

C₂

C₂×#14579159

yes

characteristic

136

C₂

#19099118

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₇₉
commutator, socle, prime radical, cosocle	C₂³×C₇₉	C₂⁴
Fitting	C₂×C₄⋊Q₈×C₇₉	C₂
hypercenter	C₂×C₄⋊Q₈	D₇₉
hypocenter	C₇₉	#2862
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₇₉

commutator, socle, prime radical, cosocle

C₂³×C₇₉

C₂⁴

Fitting

C₂×C₄⋊Q₈×C₇₉

C₂

hypercenter

C₂×C₄⋊Q₈

D₇₉

C₇₉

G ▷ C₂³×C₇₉ ▷ C₇₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
28. C₄×Dic₇₉	Q₈	semidirect
69. C₇₉	#2862	semidirect

H ≅ G/N

type

28. C₄×Dic₇₉

Q₈

semidirect

69. C₇₉

#2862

semidirect

Subgroups — #23771777

Conjugacy classes of subgroups

Complements