Group #23763008 — subgroups

Subgroups — #23763008

Order 10112.

168 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 61 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	#19098966	C₂	1	1	yes	maximal, characteristic
2	#19098966	C₂	1	1	yes	maximal, characteristic
3	#19098915	C₂	1	1	yes	maximal, characteristic
4	#19098914	C₂	1	1	yes	maximal, characteristic
5	#19098913	C₂	1	1	yes	maximal, characteristic
6	C₈×C₇₉⋊C₈	C₂	1	1	yes	maximal, characteristic
7	#487×C₇₉	C₂	1	1	yes	maximal, characteristic
8	#14579161	C₂²	1	1	yes	characteristic
9	#14579161	C₂²	1	1	yes	characteristic
10	#14579094	—	2	2	no	—
11	#14579094	—	2	2	no	—
12	#14579086	—	2	2	no	—
13	#14579085	—	2	2	no	—
14	#14579084	—	2	2	no	—
15	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×C₇₉	C₂²	1	1	yes	characteristic
19	#103×C₇₉	—	2	2	no	—
20	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×Dic₁₅₈	—	2	1	no	—
22	C₂×Dic₁₅₈	—	2	1	no	—
23	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
24	C₂×C₇₉⋊C₈	D₄	1	2	yes	—
25	C₄⋊Dic₇₉	—	2	1	no	—
26	C₄⋊Dic₇₉	—	2	1	no	—
27	C₄⋊Dic₇₉	—	2	1	no	—
28	C₄⋊Dic₇₉	—	2	1	no	—
29	C₂×Q₈×C₇₉	—	2	1	no	—
30	C₂×Q₈×C₇₉	—	2	1	no	—
31	C₂×C₈×C₇₉	D₄	1	2	yes	—
32	C₄⋊C₄×C₇₉	—	2	1	no	—
33	C₄⋊C₄×C₇₉	—	2	1	no	—
34	C₄⋊C₄×C₇₉	—	2	1	no	—
35	C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₄²×C₇₉	C₂³	1	1	yes	characteristic
37	Q₈×C₇₉	—	4	2	no	—
38	Q₈×C₇₉	—	4	2	no	—
39	C₂×C₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	—	4	1	no	—
41	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
42	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
44	C₂×Dic₇₉	—	4	1	no	—
45	C₂×Dic₇₉	—	4	1	no	—
46	Dic₁₅₈	—	4	2	no	—
47	Dic₁₅₈	—	4	2	no	—
48	C₈×C₇₉	—	2	2	no	—
49	C₇₉⋊C₈	—	2	2	no	—
50	C₇₉⋊C₈	Q₁₆	1	4	yes	—
51	C₂²×C₇₉	#127	1	1	yes	characteristic
52	C₄×C₇₉	—	8	1	no	—
53	C₄×C₇₉	—	8	1	no	—
54	C₄×C₇₉	C₂×Q₁₆	1	2	yes	—
55	C₄×C₇₉	#135	1	2	yes	—
56	C₄×C₇₉	#135	1	2	yes	—
57	Dic₇₉	—	8	1	no	—
58	Dic₇₉	—	8	1	no	—
59	C₂×C₇₉	#494	1	1	yes	characteristic
60	C₂×C₇₉	#495	1	1	yes	characteristic
61	C₂×C₇₉	#495	1	1	yes	characteristic
62	#1710	—	79	1	no	maximal, Sylow
63	C₇₉	#1710	1	1	yes	characteristic, complemented, Sylow
64	#500	—	79	1	no	—
65	#500	—	79	1	no	—
66	#487	—	79	1	no	—
67	#487	—	79	1	no	—
68	#487	—	79	1	no	—
69	#487	D₇₉	1	1	yes	characteristic
70	C₈²	—	79	1	no	—
71	C₄⋊Q₈	—	79	1	no	—
72	C₄⋊Q₈	—	79	1	no	—
73	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
74	C₄⋊Q₈	C₂×D₇₉	1	1	yes	characteristic
75	#107	—	158	2	no	—
76	#107	—	158	2	no	—
77	#103	—	2	2	no	—
78	#103	—	158	2	no	—
79	#103	—	158	2	no	—
80	#103	—	158	2	no	—
81	C₄×C₈	—	79	1	no	—
82	C₄×C₈	—	79	1	no	—
83	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
84	C₂×Q₈	—	2	1	no	—
85	C₂×Q₈	—	2	1	no	—
86	C₂×Q₈	—	158	1	no	—
87	C₂×Q₈	—	158	1	no	—
88	C₂×C₈	—	79	2	no	—
89	C₂×C₈	—	79	2	no	—
90	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
91	C₄⋊C₄	—	2	1	no	—
92	C₄⋊C₄	—	2	1	no	—
93	C₄⋊C₄	—	2	1	no	—
94	C₄⋊C₄	—	2	1	no	—
95	C₄⋊C₄	—	158	1	no	—
96	C₄⋊C₄	—	158	1	no	—
97	C₄⋊C₄	—	158	1	no	—
98	C₄⋊C₄	—	158	1	no	—
99	C₄²	C₂²×D₇₉	1	1	yes	characteristic
100	Q₈	—	4	2	no	—
101	Q₈	—	4	2	no	—
102	Q₈	—	316	2	no	—
103	Q₈	—	316	2	no	—
104	C₂×C₄	—	4	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	316	1	no	—
107	C₂×C₄	—	316	1	no	—
108	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
109	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
111	C₈	—	2	2	no	—
112	C₈	—	79	4	no	—
113	C₈	—	158	2	no	—
114	C₂²	#14579157	1	1	yes	characteristic
115	C₄	—	8	1	no	—
116	C₄	—	8	1	no	—
117	C₄	—	632	1	no	—
118	C₄	—	632	1	no	—
119	C₄	Q₁₆×D₇₉	1	2	yes	—
120	C₄	#14579181	1	2	yes	—
121	C₄	#14579182	1	2	yes	—
122	C₂	#19098941	1	1	yes	characteristic
123	C₂	#19098944	1	1	yes	characteristic
124	C₂	#19098945	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098966

C₂

yes

maximal, characteristic

#19098966

C₂

yes

maximal, characteristic

#19098915

C₂

yes

maximal, characteristic

#19098914

C₂

yes

maximal, characteristic

#19098913

C₂

yes

maximal, characteristic

C₈×C₇₉⋊C₈

C₂

yes

maximal, characteristic

#487×C₇₉

C₂

yes

maximal, characteristic

#14579161

C₂²

yes

characteristic

#14579161

C₂²

yes

—

—

—

—

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊Q₈×C₇₉

C₂²

yes

characteristic

#103×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₂×C₇₉⋊C₈

D₄

yes

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₂×Q₈×C₇₉

—

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₄²×C₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

Q₁₆

yes

—

C₂²×C₇₉

#127

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×Q₁₆

yes

—

C₄×C₇₉

#135

yes

—

C₄×C₇₉

#135

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic

C₈²

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

C₄⋊Q₈

C₂×D₇₉

yes

characteristic

#107

—

158

—

#107

—

158

—

#103

—

#103

—

158

—

#103

—

158

—

#103

—

158

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄⋊C₄

—

158

—

C₄²

C₂²×D₇₉

yes

characteristic

100

Q₈

—

101

Q₈

—

102

Q₈

—

316

—

103

Q₈

—

316

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

316

—

107

C₂×C₄

—

316

—

108

C₂×C₄

D₄×D₇₉

yes

characteristic

109

C₂×C₄

D₄×D₇₉

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

111

C₈

—

112

C₈

—

113

C₈

—

158

—

114

C₂²

#14579157

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

632

—

118

C₄

—

632

—

119

C₄

Q₁₆×D₇₉

yes

—

120

C₄

#14579181

yes

—

121

C₄

#14579182

yes

—

122

C₂

#19098941

yes

characteristic

123

C₂

#19098944

yes

characteristic

124

C₂

#19098945

yes

characteristic

	subgroup	G/H
center	C₂²	#14579157
commutator, cosocle	C₄²×C₇₉	C₂³
Frattini	C₄²	C₂²×D₇₉
Fitting	#487×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	#127
hypercenter	#487	D₇₉
hypocenter	C₇₉	#1710
LCS	G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #487

subgroup

G/H

center

C₂²

#14579157

commutator, cosocle

C₄²×C₇₉

C₂³

Frattini

C₄²

C₂²×D₇₉

Fitting

#487×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₄²×C₇₉ ▷ C₂²×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #487

N	H ≅ G/N	type
63. C₇₉	#1710	semidirect

H ≅ G/N

type

63. C₇₉

#1710

semidirect

Subgroups — #23763008

Conjugacy classes of subgroups

Complements