Group #23765644 — subgroups

Subgroups — #23765644

Order 10112.

132 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 132 conjugacy classes of subgroups — too many to draw. Only its 47 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	#19098964	C₂	1	1	yes	maximal, characteristic
2	#19098941	C₂	1	1	yes	maximal, characteristic
3	#19098368	C₂	1	1	yes	maximal, characteristic
4	#19098367	C₂	1	1	yes	maximal, characteristic
5	#19098366	C₂	1	1	yes	maximal, characteristic
6	#19098338	C₂	1	1	yes	maximal, characteristic
7	#358×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₂×#11929614	—	2	1	no	—
10	#14579159	—	2	1	no	—
11	#14579152	—	2	1	no	—
12	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	#14579095	C₂²	1	1	yes	characteristic
14	#14579092	—	2	1	no	—
15	C₈×Dic₇₉	C₂²	1	1	yes	characteristic
16	C₂×Q₁₆×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
18	#107×C₇₉	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₅₈	—	2	1	no	—
20	Dic₃₁₆	—	2	1	no	—
21	Dic₃₁₆	—	2	1	no	—
22	#11929614	—	4	2	no	—
23	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
24	C₄⋊Dic₇₉	—	2	1	no	—
25	C₄⋊Dic₇₉	—	4	1	no	—
26	Dic₇₉⋊C₄	—	4	1	no	—
27	Dic₇₉⋊C₄	—	4	1	no	—
28	Dic₇₉⋊C₄	—	4	1	no	—
29	C₄×Dic₇₉	D₄	1	1	yes	characteristic
30	C₇₉⋊C₁₆	—	2	1	no	—
31	C₂×Q₈×C₇₉	—	2	1	no	—
32	Q₁₆×C₇₉	—	2	1	no	—
33	Q₁₆×C₇₉	—	2	1	no	—
34	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
35	C₄⋊C₄×C₇₉	—	2	1	no	—
36	C₁₆×C₇₉	—	2	1	no	—
37	Q₈×C₇₉	—	4	1	no	—
38	Q₈×C₇₉	—	4	1	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×Dic₇₉	—	4	1	no	—
43	C₂×Dic₇₉	—	4	1	no	—
44	C₂×Dic₇₉	D₈	1	1	yes	characteristic
45	C₂×Dic₇₉	D₈	1	1	yes	characteristic
46	Dic₁₅₈	—	4	1	no	—
47	Dic₁₅₈	—	4	1	no	—
48	C₈×C₇₉	#41	1	1	yes	characteristic
49	C₈×C₇₉	#41	1	1	yes	characteristic
50	C₇₉⋊C₈	SD₁₆	1	2	yes	—
51	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
52	C₄×C₇₉	—	8	1	no	—
53	C₄×C₇₉	—	8	1	no	—
54	C₄×C₇₉	#124	1	1	yes	characteristic
55	C₄×C₇₉	C₂×SD₁₆	1	1	yes	characteristic
56	Dic₇₉	—	2	1	no	—
57	Dic₇₉	—	2	1	no	—
58	Dic₇₉	—	8	1	no	—
59	Dic₇₉	—	8	1	no	—
60	C₂×C₇₉	#486	1	1	yes	characteristic
61	C₂×C₇₉	#510	1	1	yes	characteristic
62	C₂×C₇₉	#510	1	1	yes	characteristic
63	#2245	—	79	1	no	maximal, Sylow
64	C₇₉	#2245	1	1	yes	characteristic, complemented, Sylow
65	#499	—	79	1	no	—
66	#494	—	79	1	no	—
67	#358	—	79	1	no	—
68	#358	—	79	1	no	—
69	#358	—	79	1	no	—
70	#358	D₇₉	1	1	yes	characteristic
71	#346	—	79	1	no	—
72	C₂×Q₁₆	—	79	1	no	—
73	C₂×Q₁₆	—	158	1	no	—
74	C₂×Q₁₆	C₂×D₇₉	1	1	yes	characteristic
75	C₄⋊Q₈	—	158	1	no	—
76	#125	—	158	1	no	—
77	C₂×C₁₆	—	79	1	no	—
78	C₂×C₁₆	C₂×D₇₉	1	1	yes	characteristic
79	#107	—	79	1	no	—
80	#107	C₂×D₇₉	1	1	yes	characteristic
81	#106	—	158	1	no	—
82	C₄×C₈	—	79	1	no	—
83	C₂×Q₈	—	2	1	no	—
84	C₂×Q₈	—	158	1	no	—
85	Q₁₆	—	2	1	no	—
86	Q₁₆	—	2	1	no	—
87	Q₁₆	—	316	2	no	—
88	Q₁₆	—	158	1	no	—
89	Q₁₆	—	158	1	no	—
90	C₂×C₈	—	79	1	no	—
91	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
92	C₄⋊C₄	—	2	1	no	—
93	C₄⋊C₄	—	316	1	no	—
94	C₄⋊C₄	—	316	1	no	—
95	C₄⋊C₄	—	316	1	no	—
96	C₄⋊C₄	—	316	1	no	—
97	C₄⋊C₄	—	158	1	no	—
98	C₄²	—	79	1	no	—
99	C₁₆	—	2	1	no	—
100	C₁₆	—	158	1	no	—
101	Q₈	—	4	1	no	—
102	Q₈	—	4	1	no	—
103	Q₈	—	316	1	no	—
104	Q₈	—	316	1	no	—
105	C₂×C₄	—	4	1	no	—
106	C₂×C₄	—	4	1	no	—
107	C₂×C₄	—	316	1	no	—
108	C₂×C₄	—	316	1	no	—
109	C₂×C₄	—	79	1	no	—
110	C₂×C₄	—	79	1	no	—
111	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
112	C₈	—	79	2	no	—
113	C₈	#11929623	1	1	yes	characteristic
114	C₈	#11929624	1	1	yes	characteristic
115	C₂²	D₈×D₇₉	1	1	yes	characteristic
116	C₄	—	8	1	no	—
117	C₄	—	8	1	no	—
118	C₄	—	632	1	no	—
119	C₄	—	632	1	no	—
120	C₄	—	158	1	no	—
121	C₄	—	158	1	no	—
122	C₄	#14579147	1	1	yes	characteristic
123	C₄	SD₁₆×D₇₉	1	1	yes	characteristic
124	C₂	#19098908	1	1	yes	characteristic
125	C₂	#19099002	1	1	yes	characteristic
126	C₂	#19099005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098964

C₂

yes

maximal, characteristic

#19098941

C₂

yes

maximal, characteristic

#19098368

C₂

yes

maximal, characteristic

#19098367

C₂

yes

maximal, characteristic

#19098366

C₂

yes

maximal, characteristic

#19098338

C₂

yes

maximal, characteristic

#358×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

—

—

—

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579092

—

C₈×Dic₇₉

C₂²

yes

characteristic

C₂×Q₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₁₆×C₇₉

C₂²

yes

characteristic

#107×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

—

#11929614

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

—

C₂×Q₈×C₇₉

—

Q₁₆×C₇₉

—

Q₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

Q₈×C₇₉

—

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

C₂×Dic₇₉

D₈

yes

characteristic

C₂×Dic₇₉

D₈

yes

characteristic

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

yes

C₈×C₇₉

yes

C₇₉⋊C₈

SD₁₆

yes

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#124

yes

characteristic

C₄×C₇₉

C₂×SD₁₆

yes

characteristic

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic

#346

—

C₂×Q₁₆

—

C₂×Q₁₆

—

158

—

C₂×Q₁₆

C₂×D₇₉

yes

characteristic

C₄⋊Q₈

—

158

—

#125

—

158

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₉

yes

characteristic

#107

—

#107

C₂×D₇₉

yes

characteristic

#106

—

158

—

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

158

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

316

—

Q₁₆

—

158

—

Q₁₆

—

158

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

C₄²

—

C₁₆

—

100

C₁₆

—

158

—

101

Q₈

—

102

Q₈

—

103

Q₈

—

316

—

104

Q₈

—

316

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

316

—

108

C₂×C₄

—

316

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

D₄×D₇₉

yes

characteristic

112

C₈

—

113

C₈

#11929623

yes

characteristic

114

C₈

#11929624

yes

characteristic

115

C₂²

D₈×D₇₉

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

632

—

119

C₄

—

632

—

120

C₄

—

158

—

121

C₄

—

158

—

122

C₄

#14579147

yes

characteristic

123

C₄

SD₁₆×D₇₉

yes

characteristic

124

C₂

#19098908

yes

characteristic

125

C₂

#19099002

yes

characteristic

126

C₂

#19099005

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₉
commutator, cosocle	C₂×C₈×C₇₉	C₂³
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#358×C₇₉	C₂
socle, prime radical	C₂²×C₇₉	C₂×D₈
hypercenter	#358	D₇₉
hypocenter	C₇₉	#2245
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

subgroup

G/H

center

C₂²

D₈×D₇₉

commutator, cosocle

C₂×C₈×C₇₉

C₂³

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#358×C₇₉

C₂

socle, prime radical

C₂²×C₇₉

C₂×D₈

D₇₉

C₇₉

G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #358

N	H ≅ G/N	type
64. C₇₉	#2245	semidirect

H ≅ G/N

type

64. C₇₉

#2245

semidirect

Subgroups — #23765644

Conjugacy classes of subgroups

Complements