Group #23774145 — subgroups

Subgroups — #23774145

Order 10112.

358 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 133 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	#19099120	C₂	1	2	yes	maximal
2	#19098961	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098943	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098914	C₂	1	2	yes	maximal, complemented
5	#19098821	C₂	1	4	yes	maximal
6	#19098671	C₂	1	4	yes	maximal, complemented
7	C₄×M₁₆×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₂²	1	4	yes	—
9	#14579161	C₂²	1	2	yes	—
10	#14579161	C₂²	1	2	yes	—
11	#14579153	—	2	2	no	—
12	#14579140	—	2	2	no	—
13	#14579140	C₂²	1	4	yes	—
14	C₄×Dic₁₅₈	—	2	2	no	—
15	C₄×Dic₁₅₈	C₂²	1	4	yes	—
16	#14579120	—	2	2	no	—
17	#14579093	C₂²	1	4	yes	—
18	#14579086	C₂²	1	8	yes	—
19	C₂×M₁₆×C₇₉	C₂²	1	2	yes	—
20	C₂×C₄²×C₇₉	C₂²	1	1	yes	characteristic
21	#97×C₇₉	C₂²	1	2	yes	—
22	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₅₈	—	2	2	no	—
25	C₂×Dic₁₅₈	C₂³	1	4	yes	—
26	Dic₃₁₆	—	2	8	no	—
27	C₄⋊Dic₇₉	—	2	2	no	—
28	C₄⋊Dic₇₉	—	2	2	no	—
29	C₄⋊Dic₇₉	—	2	2	no	—
30	C₄⋊Dic₇₉	C₂³	1	4	yes	—
31	Dic₇₉⋊C₄	—	2	4	no	—
32	Dic₇₉⋊C₄	—	2	4	no	—
33	C₂²⋊Dic₇₉	—	2	4	no	—
34	C₄×Dic₇₉	—	2	4	no	—
35	C₂²×C₄×C₇₉	D₄	1	2	yes	—
36	C₂²×C₄×C₇₉	C₂³	1	1	yes	characteristic
37	M₁₆×C₇₉	—	2	4	no	—
38	C₂×C₈×C₇₉	C₂³	1	2	yes	—
39	C₂×C₈×C₇₉	C₂³	1	2	yes	—
40	C₄²×C₇₉	D₄	1	2	yes	—
41	C₄²×C₇₉	C₂³	1	1	yes	characteristic
42	C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₂³×C₇₉	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₇₉	—	2	4	no	—
45	C₂×C₄×C₇₉	—	2	2	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
48	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
49	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
50	C₂×Dic₇₉	—	2	4	no	—
51	C₂×Dic₇₉	—	2	4	no	—
52	Dic₁₅₈	—	2	8	no	—
53	Dic₁₅₈	—	4	4	no	—
54	C₈×C₇₉	—	2	2	no	—
55	C₈×C₇₉	#41	1	4	yes	—
56	C₂²×C₇₉	—	2	1	no	—
57	C₂²×C₇₉	—	2	2	no	—
58	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₇₉	—	2	1	no	—
60	C₄×C₇₉	—	2	2	no	—
61	C₄×C₇₉	#137	1	4	yes	—
62	C₄×C₇₉	C₂×#41	1	2	yes	—
63	Dic₇₉	—	4	4	no	—
64	Dic₇₉	—	4	4	no	—
65	C₂×C₇₉	—	4	1	no	—
66	C₂×C₇₉	#532	1	1	yes	characteristic
67	C₂×C₇₉	C₂×#137	1	2	yes	—
68	#3185	—	79	1	no	maximal, Sylow
69	C₇₉	#3185	1	1	yes	characteristic, complemented, Sylow
70	#533	—	79	2	no	—
71	#498	—	79	1	no	—
72	#494	—	79	1	no	—
73	#487	—	79	2	no	—
74	#470	—	79	4	no	—
75	#441	—	79	4	no	—
76	C₄×M₁₆	D₇₉	1	1	yes	characteristic
77	C₂×Q₁₆	—	79	4	no	—
78	C₂×M₁₆	C₂×D₇₉	1	2	yes	—
79	C₄⋊Q₈	—	79	2	no	—
80	C₄⋊Q₈	—	79	2	no	—
81	#125	—	158	2	no	—
82	C₂²⋊Q₈	—	79	4	no	—
83	C₂²⋊Q₈	—	158	2	no	—
84	C₄×Q₈	—	79	4	no	—
85	C₄×Q₈	—	158	2	no	—
86	#117	—	158	2	no	—
87	C₂×C₄²	C₂×D₇₉	1	1	yes	characteristic
88	#106	—	79	4	no	—
89	#103	—	79	8	no	—
90	#97	C₂×D₇₉	1	2	yes	—
91	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
92	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
93	C₂×Q₈	—	79	4	no	—
94	C₂×Q₈	—	158	2	no	—
95	C₂²×C₄	D₃₁₆	1	2	yes	—
96	C₂²×C₄	C₂²×D₇₉	1	1	yes	characteristic
97	Q₁₆	—	158	8	no	—
98	M₁₆	—	2	4	no	—
99	C₂×C₈	C₂²×D₇₉	1	2	yes	—
100	C₂×C₈	C₂²×D₇₉	1	2	yes	—
101	C₄⋊C₄	—	79	4	no	—
102	C₄⋊C₄	—	158	4	no	—
103	C₄⋊C₄	—	158	4	no	—
104	C₄⋊C₄	—	158	2	no	—
105	C₄⋊C₄	—	158	2	no	—
106	C₄⋊C₄	—	158	2	no	—
107	C₂²⋊C₄	—	158	4	no	—
108	C₄²	—	158	4	no	—
109	C₄²	D₃₁₆	1	2	yes	—
110	C₄²	C₂²×D₇₉	1	1	yes	characteristic
111	C₄²	C₂²×D₇₉	1	1	yes	characteristic
112	C₂³	C₂×D₃₁₆	1	1	yes	characteristic
113	Q₈	—	316	4	no	—
114	Q₈	—	158	8	no	—
115	C₂×C₄	—	2	2	no	—
116	C₂×C₄	—	2	4	no	—
117	C₂×C₄	—	158	4	no	—
118	C₂×C₄	—	158	4	no	—
119	C₂×C₄	C₂×D₃₁₆	1	2	yes	—
120	C₂×C₄	C₂×D₃₁₆	1	1	yes	characteristic
121	C₂×C₄	C₂×D₃₁₆	1	2	yes	—
122	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	#11929624	1	4	yes	—
125	C₂²	—	2	2	no	—
126	C₂²	—	2	1	no	—
127	C₂²	C₂²×D₃₁₆	1	1	yes	characteristic
128	C₄	—	2	2	no	—
129	C₄	—	2	1	no	—
130	C₄	—	316	4	no	—
131	C₄	—	316	4	no	—
132	C₄	#14579194	1	4	yes	—
133	C₄	C₂×#11929624	1	2	yes	—
134	C₂	—	4	1	no	—
135	C₂	#19099113	1	1	yes	characteristic
136	C₂	C₂×#14579194	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19099120

C₂

yes

maximal

#19098961

C₂

yes

maximal, characteristic, complemented

#19098943

C₂

yes

maximal, characteristic, complemented

#19098914

C₂

yes

maximal, complemented

#19098821

C₂

yes

maximal

#19098671

C₂

yes

maximal, complemented

C₄×M₁₆×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

—

#14579161

C₂²

yes

—

#14579161

C₂²

yes

—

#14579153

—

#14579140

—

#14579140

C₂²

yes

—

C₄×Dic₁₅₈

—

C₄×Dic₁₅₈

C₂²

yes

—

#14579120

—

#14579093

C₂²

yes

—

#14579086

C₂²

yes

—

C₂×M₁₆×C₇₉

C₂²

yes

—

C₂×C₄²×C₇₉

C₂²

yes

characteristic

#97×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

C₂³

yes

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₂²⋊Dic₇₉

—

C₄×Dic₇₉

—

C₂²×C₄×C₇₉

D₄

yes

—

C₂²×C₄×C₇₉

C₂³

yes

characteristic

M₁₆×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄²×C₇₉

D₄

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₄²×C₇₉

C₂³

yes

characteristic

C₂³×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

#41

yes

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

#137

yes

—

C₄×C₇₉

C₂×#41

yes

—

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#532

yes

characteristic

C₂×C₇₉

C₂×#137

yes

—

#3185

—

maximal, Sylow

C₇₉

#3185

yes

characteristic, complemented, Sylow

—

—

—

—

—

—

C₄×M₁₆

D₇₉

yes

characteristic

C₂×Q₁₆

—

C₂×M₁₆

C₂×D₇₉

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

158

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

158

—

C₄×Q₈

—

C₄×Q₈

—

158

—

#117

—

158

—

C₂×C₄²

C₂×D₇₉

yes

—

—

C₂×D₇₉

yes

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

158

—

C₂²×C₄

D₃₁₆

yes

—

C₂²×C₄

C₂²×D₇₉

yes

characteristic

Q₁₆

—

158

—

M₁₆

—

C₂×C₈

C₂²×D₇₉

yes

—

100

C₂×C₈

C₂²×D₇₉

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

158

—

103

C₄⋊C₄

—

158

—

104

C₄⋊C₄

—

158

—

105

C₄⋊C₄

—

158

—

106

C₄⋊C₄

—

158

—

107

C₂²⋊C₄

—

158

—

108

C₄²

—

158

—

109

C₄²

D₃₁₆

yes

—

110

C₄²

C₂²×D₇₉

yes

characteristic

111

C₄²

C₂²×D₇₉

yes

characteristic

112

C₂³

C₂×D₃₁₆

yes

characteristic

113

Q₈

—

316

—

114

Q₈

—

158

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

158

—

118

C₂×C₄

—

158

—

119

C₂×C₄

C₂×D₃₁₆

yes

—

120

C₂×C₄

C₂×D₃₁₆

yes

characteristic

121

C₂×C₄

C₂×D₃₁₆

yes

—

122

C₂×C₄

C₂³×D₇₉

yes

characteristic

123

C₈

—

124

C₈

#11929624

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂²×D₃₁₆

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

316

—

131

C₄

—

316

—

132

C₄

#14579194

yes

—

133

C₄

C₂×#11929624

yes

—

134

C₂

—

135

C₂

#19099113

yes

characteristic

136

C₂

C₂×#14579194

yes

—

	subgroup	G/H
center	C₂²	C₂²×D₃₁₆
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	C₄×M₁₆×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂³×C₇₉	C₂×D₄
hypercenter	C₄×M₁₆	D₇₉
hypocenter	C₇₉	#3185
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

subgroup

G/H

center

C₂²

C₂²×D₃₁₆

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

C₄×M₁₆×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂³×C₇₉

C₂×D₄

hypercenter

C₄×M₁₆

D₇₉

hypocenter

C₇₉

#3185

LCS

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×M₁₆

N	H ≅ G/N	type
2. #19098961	C₂	semidirect
3. #19098943	C₂	semidirect
4. #19098914	C₂	semidirect
6. #19098671	C₂	semidirect
69. C₇₉	#3185	semidirect

H ≅ G/N

type

2. #19098961

C₂

semidirect

3. #19098943

C₂

semidirect

4. #19098914

C₂

semidirect

6. #19098671

C₂

semidirect

69. C₇₉

#3185

semidirect

Subgroups — #23774145

Conjugacy classes of subgroups

Complements