Group #23763529 — subgroups

Subgroups — #23763529

Order 10112.

216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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×C₈×Dic₇₉	C₂	1	1	yes	maximal, characteristic
2	#19098428	C₂	1	2	yes	maximal
3	#19098326	C₂	1	1	yes	maximal, characteristic
4	#19098325	C₂	1	2	yes	maximal
5	#340×C₇₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊Dic₇₉	C₂²	1	2	yes	—
8	C₂×C₄×Dic₇₉	C₂²	1	1	yes	characteristic
9	C₈×Dic₇₉	C₄	1	4	yes	complemented
10	C₇₉⋊#95	—	2	2	no	—
11	C₇₉⋊#95	—	2	2	no	—
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
14	C₂²×Dic₇₉	—	2	2	no	—
15	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
16	C₂²×Dic₇₉	D₄	1	1	yes	characteristic
17	C₂×C₇₉⋊C₈	—	2	2	no	—
18	C₂×C₇₉⋊C₈	C₂×C₄	1	2	yes	—
19	C₄⋊Dic₇₉	—	2	2	no	—
20	C₄⋊Dic₇₉	—	2	2	no	—
21	C₄×Dic₇₉	C₂×C₄	1	2	yes	—
22	C₄×Dic₇₉	Q₈	1	2	yes	—
23	C₂²×C₄×C₇₉	—	2	2	no	—
24	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
25	C₂×C₈×C₇₉	—	2	2	no	—
26	C₂×C₈×C₇₉	C₂×C₄	1	2	yes	—
27	C₄⋊C₄×C₇₉	—	2	2	no	—
28	C₄⋊C₄×C₇₉	—	2	2	no	—
29	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₇₉	—	4	2	no	—
31	C₂×C₄×C₇₉	—	4	2	no	—
32	C₂×C₄×C₇₉	—	4	2	no	—
33	C₂×C₄×C₇₉	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₇₉	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₇₉	#41	1	2	yes	—
36	C₂×C₄×C₇₉	#41	1	2	yes	—
37	C₂×Dic₇₉	—	2	1	no	—
38	C₂×Dic₇₉	—	2	2	no	—
39	C₂×Dic₇₉	—	2	1	no	—
40	C₂×Dic₇₉	—	4	2	no	—
41	C₂×Dic₇₉	—	4	2	no	—
42	C₂×Dic₇₉	—	4	2	no	—
43	C₂×Dic₇₉	C₄⋊C₄	1	2	yes	—
44	C₂×Dic₇₉	C₄⋊C₄	1	2	yes	—
45	C₈×C₇₉	—	2	2	no	—
46	C₇₉⋊C₈	—	2	2	no	—
47	C₂²×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂²×C₇₉	#124	1	2	yes	—
49	C₂²×C₇₉	#135	1	1	yes	characteristic
50	C₂²×C₇₉	#135	1	2	yes	—
51	C₂²×C₇₉	#135	1	1	yes	characteristic
52	C₄×C₇₉	—	8	2	no	—
53	C₄×C₇₉	#117	1	1	yes	characteristic
54	C₄×C₇₉	#117	1	1	yes	characteristic
55	C₄×C₇₉	#125	1	2	yes	—
56	Dic₇₉	—	2	2	no	—
57	Dic₇₉	—	2	2	no	—
58	Dic₇₉	—	8	2	no	—
59	C₂×C₇₉	#382	1	1	yes	characteristic
60	C₂×C₇₉	#427	1	1	yes	characteristic
61	C₂×C₇₉	#427	1	1	yes	characteristic
62	C₂×C₇₉	#488	1	2	yes	—
63	C₂×C₇₉	#488	1	2	yes	—
64	#1835	—	79	1	no	maximal, Sylow
65	C₇₉	#1835	1	1	yes	characteristic, complemented, Sylow
66	C₂×C₄×C₈	—	79	1	no	—
67	#382	—	79	2	no	—
68	#340	—	79	1	no	—
69	#340	—	79	2	no	—
70	#340	D₇₉	1	1	yes	characteristic
71	C₂²×C₈	—	79	1	no	—
72	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
73	C₂×C₄⋊C₄	—	79	2	no	—
74	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
75	C₂×C₄²	—	79	1	no	—
76	C₄×C₈	—	79	4	no	—
77	#95	—	158	2	no	—
78	#95	—	158	2	no	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	—	79	1	no	—
81	C₂²×C₄	—	79	1	no	—
82	C₂²×C₄	—	158	2	no	—
83	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
84	C₂×C₈	—	2	2	no	—
85	C₂×C₈	—	79	2	no	—
86	C₂×C₈	—	158	2	no	—
87	C₂×C₈	C₄×D₇₉	1	2	yes	—
88	C₄⋊C₄	—	2	2	no	—
89	C₄⋊C₄	—	2	2	no	—
90	C₄⋊C₄	—	158	2	no	—
91	C₄⋊C₄	—	158	2	no	—
92	C₄²	—	79	2	no	—
93	C₄²	—	79	2	no	—
94	C₂³	D₄×D₇₉	1	1	yes	characteristic
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	4	2	no	—
98	C₂×C₄	—	316	2	no	—
99	C₂×C₄	—	316	2	no	—
100	C₂×C₄	—	316	2	no	—
101	C₂×C₄	—	79	2	no	—
102	C₂×C₄	—	79	2	no	—
103	C₂×C₄	—	158	1	no	—
104	C₂×C₄	—	158	2	no	—
105	C₂×C₄	—	158	1	no	—
106	C₂×C₄	C₂×C₄×D₇₉	1	1	yes	characteristic
107	C₂×C₄	Q₈×D₇₉	1	1	yes	characteristic
108	C₂×C₄	#11929623	1	2	yes	—
109	C₂×C₄	#11929624	1	2	yes	—
110	C₈	—	2	2	no	—
111	C₈	—	158	2	no	—
112	C₂²	C₄⋊C₄×D₇₉	1	1	yes	characteristic
113	C₂²	#14579147	1	2	yes	—
114	C₂²	#14579180	1	1	yes	characteristic
115	C₂²	#14579182	1	2	yes	—
116	C₂²	#14579184	1	1	yes	characteristic
117	C₄	—	8	2	no	—
118	C₄	—	632	2	no	—
119	C₄	—	158	2	no	—
120	C₄	—	158	2	no	—
121	C₄	#14579117	1	1	yes	characteristic
122	C₄	#14579118	1	1	yes	characteristic
123	C₄	#14579151	1	2	yes	—
124	C₂	#19098427	1	1	yes	characteristic
125	C₂	#19098598	1	1	yes	characteristic
126	C₂	#19098600	1	1	yes	characteristic
127	C₂	#19098916	1	2	yes	—
128	C₂	#19098919	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₈×Dic₇₉

C₂

yes

maximal, characteristic

#19098428

C₂

yes

maximal

#19098326

C₂

yes

maximal, characteristic

#19098325

C₂

yes

maximal

#340×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₈

C₂²

yes

characteristic

C₂×C₄⋊Dic₇₉

C₂²

yes

—

C₂×C₄×Dic₇₉

C₂²

yes

characteristic

C₈×Dic₇₉

C₄

yes

complemented

C₇₉⋊#95

—

C₇₉⋊#95

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

C₂²×Dic₇₉

—

C₂²×Dic₇₉

D₄

yes

characteristic

C₂²×Dic₇₉

D₄

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄×Dic₇₉

C₂×C₄

yes

—

C₄×Dic₇₉

Q₈

yes

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

C₂×C₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₂×Dic₇₉

C₄⋊C₄

yes

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₂²×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₇₉

#124

yes

—

C₂²×C₇₉

#135

yes

characteristic

C₂²×C₇₉

#135

yes

—

C₂²×C₇₉

#135

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

yes

C₄×C₇₉

yes

C₄×C₇₉

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₂×C₇₉

#488

yes

—

#1835

—

maximal, Sylow

C₇₉

#1835

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

—

—

—

D₇₉

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

C₂×C₄²

—

C₄×C₈

—

#95

—

158

—

#95

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

C₄×D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

—

C₄²

—

C₂³

D₄×D₇₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

316

—

C₂×C₄

—

316

—

100

C₂×C₄

—

316

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

158

—

104

C₂×C₄

—

158

—

105

C₂×C₄

—

158

—

106

C₂×C₄

C₂×C₄×D₇₉

yes

characteristic

107

C₂×C₄

Q₈×D₇₉

yes

characteristic

108

C₂×C₄

#11929623

yes

—

109

C₂×C₄

#11929624

yes

—

110

C₈

—

111

C₈

—

158

—

112

C₂²

C₄⋊C₄×D₇₉

yes

characteristic

113

C₂²

#14579147

yes

—

114

C₂²

#14579180

yes

characteristic

115

C₂²

#14579182

yes

—

116

C₂²

#14579184

yes

characteristic

117

C₄

—

118

C₄

—

632

—

119

C₄

—

158

—

120

C₄

—

158

—

121

C₄

#14579117

yes

characteristic

122

C₄

#14579118

yes

characteristic

123

C₄

#14579151

yes

—

124

C₂

#19098427

yes

characteristic

125

C₂

#19098598

yes

characteristic

126

C₂

#19098600

yes

characteristic

127

C₂

#19098916

yes

—

128

C₂

#19098919

yes

—

	subgroup	G/H
center	C₂³	D₄×D₇₉
commutator	C₂×C₄×C₇₉	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	#340×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×D₄
cosocle	C₂²×C₄×C₇₉	C₂³
hypercenter	#340	D₇₉
hypocenter	C₇₉	#1835
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

subgroup

G/H

center

C₂³

D₄×D₇₉

commutator

C₂×C₄×C₇₉

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

#340×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×D₄

cosocle

C₂²×C₄×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ #340

N	H ≅ G/N	type
9. C₈×Dic₇₉	C₄	semidirect
65. C₇₉	#1835	semidirect

H ≅ G/N

type

9. C₈×Dic₇₉

C₄

semidirect

65. C₇₉

#1835

semidirect

Subgroups — #23763529

Conjugacy classes of subgroups

Complements