Group #23765295 — subgroups

Subgroups — #23765295

Order 10112.

154 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 51 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	#19098998	C₂	1	1	yes	maximal, characteristic
2	#19098685	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098674	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098385	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098377	C₂	1	1	yes	maximal, characteristic, complemented
6	#19098340	C₂	1	1	yes	maximal, characteristic, complemented
7	#360×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₆₃₂	C₂²	1	1	yes	characteristic
9	#14579168	—	2	1	no	—
10	#14579123	—	2	1	no	—
11	#14579104	C₄	1	2	yes	complemented
12	#14579102	C₄	1	2	yes	complemented
13	#14579101	C₂²	1	1	yes	characteristic
14	#14579097	C₂²	1	1	yes	characteristic
15	#14579088	—	2	1	no	—
16	#14579081	—	2	1	no	—
17	#14579071	C₂²	1	1	yes	characteristic
18	#135×C₇₉	C₂²	1	1	yes	characteristic
19	M₃₂×C₇₉	C₂²	1	1	yes	characteristic
20	#106×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×D₃₁₆	—	2	1	no	—
22	C₂×C₄×D₇₉	—	4	1	no	—
23	D₆₃₂	—	2	1	no	—
24	D₆₃₂	C₂×C₄	1	2	yes	—
25	#11929608	—	2	1	no	—
26	#11929608	—	4	1	no	—
27	C₂×C₇₉⋊C₈	—	4	1	no	—
28	C₂×C₇₉⋊C₈	D₄	1	1	yes	characteristic
29	(C₂×D₇₉)⋊C₄	—	4	1	no	—
30	C₄×Dic₇₉	D₄	1	1	yes	characteristic
31	C₇₉⋊C₁₆	C₂×C₄	1	2	yes	complemented
32	#41×C₇₉	—	2	1	no	—
33	Q₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
34	SD₁₆×C₇₉	—	2	1	no	—
35	D₈×C₇₉	C₂×C₄	1	1	yes	characteristic, complemented
36	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₄×C₇₉	—	2	1	no	—
38	C₁₆×C₇₉	—	2	1	no	—
39	C₂²×D₇₉	—	4	1	no	—
40	Q₈×C₇₉	—	2	1	no	—
41	D₄×C₇₉	—	2	1	no	—
42	D₄×C₇₉	—	4	1	no	—
43	C₂×C₄×C₇₉	—	4	1	no	—
44	C₂×C₄×C₇₉	—	4	1	no	—
45	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
46	C₂×Dic₇₉	—	2	1	no	—
47	D₃₁₆	—	2	2	no	—
48	D₃₁₆	—	4	1	no	—
49	C₄×D₇₉	—	8	2	no	—
50	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
51	C₈×C₇₉	#41	1	1	yes	characteristic
52	C₇₉⋊C₈	—	2	1	no	—
53	C₇₉⋊C₈	—	4	1	no	—
54	C₂²×C₇₉	—	4	1	no	—
55	C₂²×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
56	C₂×D₇₉	—	4	2	no	—
57	C₂×D₇₉	—	8	1	no	—
58	C₂×D₇₉	—	8	1	no	—
59	C₄×C₇₉	—	4	1	no	—
60	C₄×C₇₉	—	8	1	no	—
61	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
62	C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
63	Dic₇₉	—	4	1	no	—
64	C₂×C₇₉	—	2	1	no	—
65	C₂×C₇₉	—	8	1	no	—
66	C₂×C₇₉	#442	1	1	yes	characteristic
67	D₇₉	—	8	2	no	—
68	AGL(1,ℤ/16)	—	79	1	no	maximal, Sylow
69	C₇₉	AGL(1,ℤ/16)	1	1	yes	characteristic, complemented, Sylow
70	#509	—	79	1	no	—
71	#444	—	79	1	no	—
72	#442	—	79	1	no	—
73	#365	—	79	1	no	—
74	#361	—	79	1	no	—
75	#360	D₇₉	1	1	yes	characteristic, complemented
76	#347	—	79	1	no	—
77	#135	C₂×D₇₉	1	1	yes	characteristic
78	C₂×D₈	—	79	1	no	—
79	#131	—	158	1	no	—
80	C₄×D₄	—	158	1	no	—
81	SD₃₂	—	79	2	no	—
82	D₁₆	—	79	2	no	—
83	M₃₂	—	79	1	no	—
84	M₃₂	C₂×D₇₉	1	1	yes	characteristic
85	#108	—	79	1	no	—
86	#106	C₂×D₇₉	1	1	yes	characteristic
87	#104	—	158	1	no	—
88	#102	—	158	1	no	—
89	#97	—	79	1	no	—
90	#41	—	2	1	no	—
91	C₂×D₄	—	158	1	no	—
92	C₂²×C₄	—	316	1	no	—
93	Q₁₆	C₄×D₇₉	1	1	yes	characteristic, complemented
94	SD₁₆	—	2	1	no	—
95	D₈	—	79	2	no	—
96	D₈	—	158	1	no	—
97	D₈	C₄×D₇₉	1	1	yes	characteristic, complemented
98	M₁₆	—	316	1	no	—
99	M₁₆	—	158	1	no	—
100	C₂×C₈	—	316	1	no	—
101	C₂×C₈	—	79	1	no	—
102	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
103	C₄⋊C₄	—	2	1	no	—
104	C₂²⋊C₄	—	316	1	no	—
105	C₄²	—	79	1	no	—
106	C₁₆	—	2	1	no	—
107	C₁₆	—	79	2	no	—
108	C₂³	—	316	1	no	—
109	Q₈	—	2	1	no	—
110	D₄	—	2	1	no	—
111	D₄	—	4	1	no	—
112	D₄	—	316	1	no	—
113	D₄	—	158	2	no	—
114	C₂×C₄	—	4	1	no	—
115	C₂×C₄	—	4	1	no	—
116	C₂×C₄	—	632	2	no	—
117	C₂×C₄	—	158	1	no	—
118	C₂×C₄	D₄×D₇₉	1	1	yes	characteristic
119	C₈	—	316	1	no	—
120	C₈	—	158	1	no	—
121	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
122	C₈	#11929623	1	1	yes	characteristic
123	C₂²	—	4	1	no	—
124	C₂²	—	316	2	no	—
125	C₂²	—	632	1	no	—
126	C₂²	—	632	1	no	—
127	C₂²	#14579185	1	1	yes	characteristic
128	C₄	—	4	1	no	—
129	C₄	—	8	1	no	—
130	C₄	—	316	1	no	—
131	C₄	(C₂²⋊D₇₉)⋊C₄	1	1	yes	characteristic
132	C₄	#14579188	1	1	yes	characteristic
133	C₂	—	2	1	no	—
134	C₂	—	8	1	no	—
135	C₂	—	632	2	no	—
136	C₂	#19098672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19098998

C₂

yes

maximal, characteristic

#19098685

C₂

yes

maximal, characteristic, complemented

#19098674

C₂

yes

maximal, characteristic, complemented

#19098385

C₂

yes

maximal, characteristic, complemented

#19098377

C₂

yes

maximal, characteristic, complemented

#19098340

C₂

yes

maximal, characteristic, complemented

#360×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×D₆₃₂

C₂²

yes

—

—

C₄

yes

complemented

#14579102

C₄

yes

complemented

#14579101

C₂²

yes

characteristic

#14579097

C₂²

yes

—

—

C₂²

yes

characteristic

#135×C₇₉

C₂²

yes

characteristic

M₃₂×C₇₉

C₂²

yes

characteristic

#106×C₇₉

C₂²

yes

characteristic

C₂×D₃₁₆

—

C₂×C₄×D₇₉

—

D₆₃₂

—

D₆₃₂

C₂×C₄

yes

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

D₄

yes

characteristic

(C₂×D₇₉)⋊C₄

—

C₄×Dic₇₉

D₄

yes

characteristic

C₇₉⋊C₁₆

C₂×C₄

yes

complemented

#41×C₇₉

—

Q₁₆×C₇₉

C₂×C₄

yes

characteristic, complemented

SD₁₆×C₇₉

—

D₈×C₇₉

C₂×C₄

yes

characteristic, complemented

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₁₆×C₇₉

—

C₂²×D₇₉

—

Q₈×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

D₃₁₆

—

D₃₁₆

—

C₄×D₇₉

—

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₇₉⋊C₈

—

C₇₉⋊C₈

—

C₂²×C₇₉

—

C₂²×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

—

C₂×C₇₉

#442

yes

characteristic

D₇₉

—

AGL(1,ℤ/16)

—

maximal, Sylow

C₇₉

AGL(1,ℤ/16)

yes

characteristic, complemented, Sylow

—

—

—

—

—

D₇₉

yes

characteristic, complemented

#347

—

#135

C₂×D₇₉

yes

characteristic

C₂×D₈

—

#131

—

158

—

C₄×D₄

—

158

—

SD₃₂

—

D₁₆

—

M₃₂

—

M₃₂

C₂×D₇₉

yes

characteristic

#108

—

#106

C₂×D₇₉

yes

characteristic

#104

—

158

—

#102

—

158

—

#97

—

#41

—

C₂×D₄

—

158

—

C₂²×C₄

—

316

—

Q₁₆

C₄×D₇₉

yes

characteristic, complemented

SD₁₆

—

D₈

—

D₈

—

158

—

D₈

C₄×D₇₉

yes

characteristic, complemented

M₁₆

—

316

—

M₁₆

—

158

—

100

C₂×C₈

—

316

—

101

C₂×C₈

—

102

C₂×C₈

C₂²×D₇₉

yes

characteristic

103

C₄⋊C₄

—

104

C₂²⋊C₄

—

316

—

105

C₄²

—

106

C₁₆

—

107

C₁₆

—

108

C₂³

—

316

—

109

Q₈

—

110

D₄

—

111

D₄

—

112

D₄

—

316

—

113

D₄

—

158

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

632

—

117

C₂×C₄

—

158

—

118

C₂×C₄

D₄×D₇₉

yes

characteristic

119

C₈

—

316

—

120

C₈

—

158

—

121

C₈

C₂×C₄×D₇₉

yes

characteristic

122

C₈

#11929623

yes

characteristic

123

C₂²

—

124

C₂²

—

316

—

125

C₂²

—

632

—

126

C₂²

—

632

—

127

C₂²

#14579185

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

316

—

131

C₄

(C₂²⋊D₇₉)⋊C₄

yes

characteristic

132

C₄

#14579188

yes

characteristic

133

C₂

—

134

C₂

—

135

C₂

—

632

—

136

C₂

#19098672

yes

characteristic

	subgroup	G/H
center	C₂	#19098672
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	#360×C₇₉	C₂
socle	C₂×C₇₉	#442
prime radical	#19098998	C₂
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	#360	D₇₉
hypocenter	C₇₉	AGL(1,ℤ/16)
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

subgroup

G/H

center

C₂

#19098672

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

#360×C₇₉

C₂

C₂×C₇₉

C₂

C₂×C₈×C₇₉

C₂³

D₇₉

C₇₉

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #360

N	H ≅ G/N	type
2. #19098685	C₂	semidirect
3. #19098674	C₂	semidirect
4. #19098385	C₂	semidirect
5. #19098377	C₂	semidirect
6. #19098340	C₂	semidirect
7. #360×C₇₉	C₂	semidirect
11. #14579104	C₄	semidirect
12. #14579102	C₄	semidirect
31. C₇₉⋊C₁₆	C₂×C₄	semidirect
33. Q₁₆×C₇₉	C₂×C₄	semidirect
35. D₈×C₇₉	C₂×C₄	semidirect
69. C₇₉	AGL(1,ℤ/16)	semidirect
75. #360	D₇₉	semidirect
93. Q₁₆	C₄×D₇₉	semidirect
97. D₈	C₄×D₇₉	semidirect

H ≅ G/N

type

2. #19098685

C₂

semidirect

3. #19098674

C₂

semidirect

4. #19098385

C₂

semidirect

5. #19098377

C₂

semidirect

6. #19098340

C₂

semidirect

7. #360×C₇₉

C₂

semidirect

11. #14579104

C₄

semidirect

12. #14579102

C₄

semidirect

31. C₇₉⋊C₁₆

C₂×C₄

semidirect

33. Q₁₆×C₇₉

C₂×C₄

semidirect

35. D₈×C₇₉

C₂×C₄

semidirect

69. C₇₉

AGL(1,ℤ/16)

semidirect

75. #360

D₇₉

semidirect

93. Q₁₆

C₄×D₇₉

semidirect

97. D₈

C₄×D₇₉

semidirect

Subgroups — #23765295

Conjugacy classes of subgroups

Complements