Group #23764888 — subgroups

Subgroups — #23764888

Order 10112.

224 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14579095	C₂	1	1	yes	maximal, characteristic
2	#19098461	C₂	1	2	yes	maximal
3	#19098326	C₂	1	2	yes	maximal
4	#19098326	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊C₈×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	C₂×Dic₇₉⋊C₄	—	2	2	no	—
9	#14579095	—	2	2	no	—
10	C₇₉⋊#95	—	2	2	no	—
11	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₇₉	—	2	2	no	—
15	C₂²×Dic₇₉	—	2	2	no	—
16	C₂²×Dic₇₉	—	2	2	no	—
17	C₄⋊Dic₇₉	—	2	2	no	—
18	C₄⋊Dic₇₉	—	2	2	no	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	Q₈	1	4	yes	—
21	Dic₇₉⋊C₄	—	4	4	no	—
22	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
23	C₂²×C₄×C₇₉	D₄	1	1	yes	characteristic
24	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₇₉	—	2	1	no	—
26	C₂×C₈×C₇₉	—	2	2	no	—
27	C₂×C₈×C₇₉	—	2	2	no	—
28	C₂×C₈×C₇₉	D₄	1	2	yes	—
29	C₄²×C₇₉	—	2	1	no	—
30	C₄²×C₇₉	—	2	1	no	—
31	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
32	C₂×C₄×C₇₉	—	2	1	no	—
33	C₂×C₄×C₇₉	—	2	1	no	—
34	C₂×C₄×C₇₉	—	2	1	no	—
35	C₂×C₄×C₇₉	—	2	2	no	—
36	C₂×C₄×C₇₉	D₈	1	2	yes	—
37	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂×Q₈	1	2	yes	—
39	C₂×C₄×C₇₉	#41	1	2	yes	—
40	C₂×C₄×C₇₉	#41	1	1	yes	characteristic
41	C₂×Dic₇₉	—	2	4	no	—
42	C₂×Dic₇₉	—	4	2	no	—
43	C₂×Dic₇₉	—	4	2	no	—
44	C₂×Dic₇₉	—	4	2	no	—
45	C₂×Dic₇₉	—	4	2	no	—
46	C₂×Dic₇₉	—	4	2	no	—
47	C₈×C₇₉	—	2	2	no	—
48	C₈×C₇₉	—	4	1	no	—
49	C₂²×C₇₉	#121	1	1	yes	characteristic
50	C₂²×C₇₉	C₂²⋊Q₈	1	2	yes	—
51	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
52	C₂²×C₇₉	#135	1	1	yes	characteristic
53	C₂²×C₇₉	#137	1	2	yes	—
54	C₄×C₇₉	—	2	2	no	—
55	C₄×C₇₉	—	4	1	no	—
56	C₄×C₇₉	#123	1	1	yes	characteristic
57	C₄×C₇₉	#125	1	2	yes	—
58	C₄×C₇₉	C₄⋊Q₈	1	1	yes	characteristic
59	Dic₇₉	—	4	4	no	—
60	Dic₇₉	—	8	2	no	—
61	C₂×C₇₉	#398	1	1	yes	characteristic
62	C₂×C₇₉	#466	1	1	yes	characteristic
63	C₂×C₇₉	#470	1	1	yes	characteristic
64	C₂×C₇₉	#474	1	2	yes	—
65	C₂×C₇₉	#479	1	2	yes	—
66	#2086	—	79	1	no	maximal, Sylow
67	C₇₉	#2086	1	1	yes	characteristic, complemented, Sylow
68	C₂×#107	—	79	1	no	—
69	C₂×C₄⋊C₈	D₇₉	1	1	yes	characteristic
70	#389	—	79	2	no	—
71	#340	—	79	1	no	—
72	#340	—	79	2	no	—
73	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
74	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
75	C₂×C₄⋊C₄	—	79	2	no	—
76	C₂×C₄⋊C₄	—	79	2	no	—
77	C₂×C₄⋊C₄	—	158	2	no	—
78	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
79	#107	—	158	2	no	—
80	C₄⋊C₈	—	2	2	no	—
81	#95	—	158	2	no	—
82	C₂²×C₄	—	158	2	no	—
83	C₂²×C₄	—	158	2	no	—
84	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
85	C₂²×C₄	D₃₁₆	1	1	yes	characteristic
86	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
87	C₂×C₈	—	2	2	no	—
88	C₂×C₈	—	2	1	no	—
89	C₂×C₈	—	2	2	no	—
90	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
91	C₄⋊C₄	—	316	4	no	—
92	C₄⋊C₄	—	79	4	no	—
93	C₄⋊C₄	—	158	2	no	—
94	C₄⋊C₄	—	158	2	no	—
95	C₄⋊C₄	—	158	2	no	—
96	C₄²	—	2	1	no	—
97	C₄²	—	2	1	no	—
98	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
99	C₂×C₄	—	2	1	no	—
100	C₂×C₄	—	2	1	no	—
101	C₂×C₄	—	2	1	no	—
102	C₂×C₄	—	2	2	no	—
103	C₂×C₄	—	316	2	no	—
104	C₂×C₄	—	316	2	no	—
105	C₂×C₄	—	316	2	no	—
106	C₂×C₄	—	316	2	no	—
107	C₂×C₄	—	316	2	no	—
108	C₂×C₄	—	158	4	no	—
109	C₂×C₄	D₆₃₂	1	2	yes	—
110	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
111	C₂×C₄	Q₈×D₇₉	1	2	yes	—
112	C₂×C₄	#11929623	1	2	yes	—
113	C₂×C₄	#11929624	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	4	1	no	—
116	C₂²	#14579135	1	1	yes	characteristic
117	C₂²	#14579141	1	2	yes	—
118	C₂²	C₂×D₆₃₂	1	1	yes	characteristic
119	C₂²	#14579183	1	1	yes	characteristic
120	C₂²	#14579194	1	2	yes	—
121	C₄	—	2	2	no	—
122	C₄	—	4	1	no	—
123	C₄	—	316	4	no	—
124	C₄	—	632	2	no	—
125	C₄	#14579142	1	1	yes	characteristic
126	C₄	#14579151	1	2	yes	—
127	C₄	#14579159	1	1	yes	characteristic
128	C₂	#19098493	1	1	yes	characteristic
129	C₂	#19098799	1	1	yes	characteristic
130	C₂	#19098821	1	1	yes	characteristic
131	C₂	#19098844	1	2	yes	—
132	C₂	#19098871	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579095

C₂

yes

maximal, characteristic

#19098461

C₂

yes

maximal

#19098326

C₂

yes

maximal

#19098326

C₂

yes

maximal, characteristic

C₂×C₄⋊C₈×C₇₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×Dic₇₉⋊C₄

—

#14579095

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄²×C₇₉

C₂²

yes

characteristic

C₄⋊C₈×C₇₉

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

Q₈

yes

—

Dic₇₉⋊C₄

—

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

D₄

yes

characteristic

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₈×C₇₉

—

C₈×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₂²×C₇₉

C₂²⋊Q₈

yes

—

C₂²×C₇₉

C₂×D₈

yes

C₂²×C₇₉

yes

C₂²×C₇₉

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#123

yes

characteristic

C₄×C₇₉

#125

yes

—

C₄×C₇₉

C₄⋊Q₈

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#479

yes

—

#2086

—

maximal, Sylow

C₇₉

#2086

yes

characteristic, complemented, Sylow

C₂×#107

—

C₂×C₄⋊C₈

D₇₉

yes

—

—

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

C₂×D₇₉

yes

characteristic

#107

—

158

—

C₄⋊C₈

—

#95

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

—

158

—

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

D₃₁₆

yes

characteristic

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₄²

—

C₂³

C₂×D₃₁₆

yes

characteristic

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

316

—

104

C₂×C₄

—

316

—

105

C₂×C₄

—

316

—

106

C₂×C₄

—

316

—

107

C₂×C₄

—

316

—

108

C₂×C₄

—

158

—

109

C₂×C₄

D₆₃₂

yes

—

110

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

111

C₂×C₄

Q₈×D₇₉

yes

—

112

C₂×C₄

#11929623

yes

—

113

C₂×C₄

#11929624

yes

characteristic

114

C₈

—

115

C₈

—

116

C₂²

#14579135

yes

characteristic

117

C₂²

#14579141

yes

—

118

C₂²

C₂×D₆₃₂

yes

characteristic

119

C₂²

#14579183

yes

characteristic

120

C₂²

#14579194

yes

—

121

C₄

—

122

C₄

—

123

C₄

—

316

—

124

C₄

—

632

—

125

C₄

#14579142

yes

characteristic

126

C₄

#14579151

yes

—

127

C₄

#14579159

yes

characteristic

128

C₂

#19098493

yes

characteristic

129

C₂

#19098799

yes

characteristic

130

C₂

#19098821

yes

characteristic

131

C₂

#19098844

yes

—

132

C₂

#19098871

yes

—

	subgroup	G/H
center	C₂³	C₂×D₃₁₆
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×C₄⋊C₈×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	C₂×C₄⋊C₈	D₇₉
hypocenter	C₇₉	#2086
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

subgroup

G/H

center

C₂³

C₂×D₃₁₆

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×C₄⋊C₈×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

hypercenter

C₂×C₄⋊C₈

D₇₉

hypocenter

C₇₉

#2086

LCS

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
67. C₇₉	#2086	semidirect

H ≅ G/N

type

67. C₇₉

#2086

semidirect

Subgroups — #23764888

Conjugacy classes of subgroups

Complements