Group #23764841 — subgroups

Subgroups — #23764841

Order 10112.

198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19098562	C₂	1	2	yes	maximal
2	#19098529	C₂	1	1	yes	maximal, characteristic
3	#19098332	C₂	1	2	yes	maximal, complemented
4	#19098328	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#107×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11929624	C₂²	1	1	yes	characteristic
7	C₂×#11929608	C₂²	1	1	yes	characteristic
8	C₂×#11929608	C₂²	1	2	yes	—
9	#14579084	—	2	2	no	—
10	#14579081	—	2	2	no	—
11	(C₂×D₇₉)⋊C₈	—	2	2	no	—
12	C₂²×C₈×C₇₉	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
14	#107×C₇₉	—	2	2	no	—
15	#11929624	—	2	2	no	—
16	#11929624	—	2	2	no	—
17	C₂×Dic₁₅₈	D₄	1	1	yes	characteristic
18	C₂×D₃₁₆	D₄	1	1	yes	characteristic
19	C₂×C₂²⋊D₇₉	—	2	1	no	—
20	C₂×C₄×D₇₉	—	2	1	no	—
21	#11929608	—	2	2	no	—
22	#11929608	—	2	2	no	—
23	#11929608	—	2	2	no	—
24	C₂×C₇₉⋊C₈	—	2	1	no	—
25	C₂×C₇₉⋊C₈	—	2	2	no	—
26	C₂²×C₄×C₇₉	—	2	2	no	—
27	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
28	C₂×C₈×C₇₉	—	2	2	no	—
29	C₂×C₈×C₇₉	D₄	1	2	yes	—
30	C₄⋊C₄×C₇₉	—	2	2	no	—
31	C₄⋊C₄×C₇₉	—	2	2	no	—
32	C₂³×C₇₉	#41	1	1	yes	characteristic
33	C₂²×D₇₉	—	2	1	no	—
34	C₂×C₄×C₇₉	—	4	2	no	—
35	C₂×C₄×C₇₉	—	8	2	no	—
36	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₉	#41	1	2	yes	—
39	C₂×C₄×C₇₉	#41	1	2	yes	—
40	C₂²⋊D₇₉	—	4	2	no	—
41	C₂×Dic₇₉	—	2	1	no	—
42	D₃₁₆	—	2	2	no	—
43	C₄×D₇₉	—	4	1	no	—
44	C₄×D₇₉	—	4	1	no	—
45	Dic₁₅₈	—	2	2	no	—
46	C₈×C₇₉	—	2	2	no	—
47	C₇₉⋊C₈	—	4	2	no	—
48	C₇₉⋊C₈	—	4	1	no	—
49	C₂²×C₇₉	—	2	1	no	—
50	C₂²×C₇₉	—	2	1	no	—
51	C₂²×C₇₉	#121	1	1	yes	characteristic
52	C₂²×C₇₉	#126	1	2	yes	—
53	C₂×D₇₉	—	4	1	no	—
54	C₂×D₇₉	—	4	1	no	—
55	C₂×D₇₉	—	4	1	no	—
56	C₄×C₇₉	—	8	2	no	—
57	C₄×C₇₉	#123	1	1	yes	characteristic
58	C₄×C₇₉	#123	1	2	yes	—
59	C₄×C₇₉	#124	1	1	yes	characteristic
60	Dic₇₉	—	4	1	no	—
61	C₂×C₇₉	—	2	2	no	—
62	C₂×C₇₉	#397	1	1	yes	characteristic
63	C₂×C₇₉	#472	1	1	yes	characteristic
64	C₂×C₇₉	#473	1	1	yes	characteristic
65	D₇₉	—	8	1	no	—
66	#2078	—	79	1	no	maximal, Sylow
67	C₇₉	#2078	1	1	yes	characteristic, complemented, Sylow
68	C₂×#107	D₇₉	1	1	yes	characteristic, complemented
69	#417	—	79	2	no	—
70	#408	—	79	1	no	—
71	#343	—	79	2	no	—
72	#341	—	79	1	no	—
73	C₂×#41	—	79	1	no	—
74	C₂×M₁₆	—	79	2	no	—
75	C₂×M₁₆	—	79	1	no	—
76	C₂²×C₈	C₂×D₇₉	1	1	yes	characteristic
77	C₂×C₄⋊C₄	C₂×D₇₉	1	2	yes	—
78	#107	—	2	2	no	—
79	#103	—	158	2	no	—
80	#102	—	158	2	no	—
81	C₂²⋊C₈	—	158	2	no	—
82	#41	—	158	2	no	—
83	#41	—	158	2	no	—
84	C₂×Q₈	—	79	1	no	—
85	C₂×D₄	—	79	1	no	—
86	C₂×D₄	—	158	1	no	—
87	C₂²×C₄	—	2	2	no	—
88	C₂²×C₄	—	158	1	no	—
89	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
90	M₁₆	—	158	2	no	—
91	M₁₆	—	158	2	no	—
92	M₁₆	—	158	2	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	158	2	no	—
95	C₂×C₈	—	158	1	no	—
96	C₂×C₈	C₂²⋊D₇₉	1	2	yes	—
97	C₄⋊C₄	—	2	2	no	—
98	C₄⋊C₄	—	2	2	no	—
99	C₂³	—	158	1	no	—
100	C₂³	#11929623	1	1	yes	characteristic
101	Q₈	—	158	2	no	—
102	D₄	—	316	2	no	—
103	D₄	—	158	2	no	—
104	C₂×C₄	—	4	2	no	—
105	C₂×C₄	—	8	2	no	—
106	C₂×C₄	—	316	1	no	—
107	C₂×C₄	—	316	1	no	—
108	C₂×C₄	—	158	1	no	—
109	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
110	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
111	C₂×C₄	#11929624	1	2	yes	—
112	C₂×C₄	#11929625	1	2	yes	—
113	C₈	—	2	2	no	—
114	C₈	—	316	2	no	—
115	C₈	—	316	1	no	—
116	C₂²	—	2	1	no	—
117	C₂²	—	2	1	no	—
118	C₂²	—	316	1	no	—
119	C₂²	—	316	1	no	—
120	C₂²	—	316	1	no	—
121	C₂²	#14579132	1	1	yes	characteristic
122	C₂²	#14579156	1	2	yes	—
123	C₄	—	8	2	no	—
124	C₄	—	316	1	no	—
125	C₄	#14579144	1	1	yes	characteristic
126	C₄	#14579146	1	2	yes	—
127	C₄	#14579150	1	1	yes	characteristic
128	C₂	—	2	2	no	—
129	C₂	—	632	1	no	—
130	C₂	#19098489	1	1	yes	characteristic
131	C₂	#19098830	1	1	yes	characteristic
132	C₂	#19098835	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098562

C₂

yes

maximal

#19098529

C₂

yes

maximal, characteristic

#19098332

C₂

yes

maximal, complemented

#19098328

C₂

yes

maximal, characteristic, complemented

C₂×#107×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#11929624

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

characteristic

C₂×#11929608

C₂²

yes

—

#14579084

—

#14579081

—

(C₂×D₇₉)⋊C₈

—

C₂²×C₈×C₇₉

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₉

C₂²

yes

—

#107×C₇₉

—

#11929624

—

#11929624

—

C₂×Dic₁₅₈

D₄

yes

characteristic

C₂×D₃₁₆

D₄

yes

characteristic

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

—

#11929608

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₄

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂³×C₇₉

#41

yes

characteristic

C₂²×D₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

#41

yes

—

C₂×C₄×C₇₉

#41

yes

—

C₂²⋊D₇₉

—

C₂×Dic₇₉

—

D₃₁₆

—

C₄×D₇₉

—

C₄×D₇₉

—

Dic₁₅₈

—

C₈×C₇₉

—

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

#121

yes

characteristic

C₂²×C₇₉

#126

yes

—

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#123

yes

characteristic

C₄×C₇₉

#123

yes

—

C₄×C₇₉

#124

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

D₇₉

—

#2078

—

maximal, Sylow

C₇₉

#2078

yes

characteristic, complemented, Sylow

C₂×#107

D₇₉

yes

characteristic, complemented

—

—

—

—

C₂×#41

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

C₂×D₇₉

yes

characteristic

C₂×C₄⋊C₄

C₂×D₇₉

yes

—

#107

—

#103

—

158

—

#102

—

158

—

C₂²⋊C₈

—

158

—

#41

—

158

—

#41

—

158

—

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

158

—

C₂²×C₄

—

C₂²×C₄

—

158

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

M₁₆

—

158

—

M₁₆

—

158

—

M₁₆

—

158

—

C₂×C₈

—

C₂×C₈

—

158

—

C₂×C₈

—

158

—

C₂×C₈

C₂²⋊D₇₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂³

—

158

—

100

C₂³

#11929623

yes

characteristic

101

Q₈

—

158

—

102

D₄

—

316

—

103

D₄

—

158

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

316

—

107

C₂×C₄

—

316

—

108

C₂×C₄

—

158

—

109

C₂×C₄

D₄×D₇₉

yes

characteristic

110

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

111

C₂×C₄

#11929624

yes

—

112

C₂×C₄

#11929625

yes

—

113

C₈

—

114

C₈

—

316

—

115

C₈

—

316

—

116

C₂²

—

117

C₂²

—

118

C₂²

—

316

—

119

C₂²

—

316

—

120

C₂²

—

316

—

121

C₂²

#14579132

yes

characteristic

122

C₂²

#14579156

yes

—

123

C₄

—

124

C₄

—

316

—

125

C₄

#14579144

yes

characteristic

126

C₄

#14579146

yes

—

127

C₄

#14579150

yes

characteristic

128

C₂

—

129

C₂

—

632

—

130

C₂

#19098489

yes

characteristic

131

C₂

#19098830

yes

characteristic

132

C₂

#19098835

yes

characteristic

	subgroup	G/H
center	C₂²	#14579132
commutator, cosocle	C₂²×C₄×C₇₉	C₂³
Frattini	C₂²×C₄	C₂²×D₇₉
Fitting	C₂×#107×C₇₉	C₂
socle	C₂²×C₇₉	#121
prime radical	C₂×#11929624	C₂²
hypercenter	C₂×#107	D₇₉
hypocenter	C₇₉	#2078
LCS	G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

subgroup

G/H

center

C₂²

#14579132

commutator, cosocle

C₂²×C₄×C₇₉

C₂³

Frattini

C₂²×C₄

C₂²×D₇₉

Fitting

C₂×#107×C₇₉

C₂

C₂²×C₇₉

C₂²

D₇₉

C₇₉

G ▷ C₂²×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#107

N	H ≅ G/N	type
3. #19098332	C₂	semidirect
4. #19098328	C₂	semidirect
5. C₂×#107×C₇₉	C₂	semidirect
67. C₇₉	#2078	semidirect
68. C₂×#107	D₇₉	semidirect

H ≅ G/N

type

3. #19098332

C₂

semidirect

4. #19098328

C₂

semidirect

5. C₂×#107×C₇₉

C₂

semidirect

67. C₇₉

#2078

semidirect

68. C₂×#107

D₇₉

semidirect

Subgroups — #23764841

Conjugacy classes of subgroups

Complements