Group #23765264 — subgroups

Subgroups — #23765264

Order 10112.

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

normal subgroups only

This group has 160 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	C₂×#14579105	C₂	1	1	yes	maximal, characteristic
2	C₄×Dic₃₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098388	C₂	1	1	yes	maximal, characteristic, complemented
4	#19098366	C₂	1	1	yes	maximal, characteristic, complemented
5	#19098364	C₂	1	1	yes	maximal, characteristic
6	#19098339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₃₁₆	C₂²	1	1	yes	characteristic
9	C₄×Dic₁₅₈	—	2	1	no	—
10	#14579105	C₄	1	4	yes	complemented
11	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₇₉⋊C₁₆	C₂²	1	1	yes	characteristic
13	#14579095	C₂²	1	1	yes	characteristic
14	#14579086	—	2	1	no	—
15	C₂×D₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₄×D₄×C₇₉	—	2	1	no	—
17	#107×C₇₉	C₂²	1	1	yes	characteristic
18	#102×C₇₉	—	2	1	no	—
19	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
20	C₂×Dic₁₅₈	—	2	1	no	—
21	Dic₃₁₆	—	2	1	no	—
22	Dic₃₁₆	C₂×C₄	1	2	yes	complemented
23	C₄⋊Dic₇₉	—	2	1	no	—
24	Dic₇₉⋊C₄	—	4	1	no	—
25	C₄×Dic₇₉	—	4	1	no	—
26	C₇₉⋊C₁₆	—	2	1	no	—
27	C₇₉⋊C₁₆	C₂×C₄	1	2	yes	complemented
28	C₂×D₄×C₇₉	—	2	1	no	—
29	C₂²×C₄×C₇₉	—	4	1	no	—
30	D₈×C₇₉	—	2	1	no	—
31	D₈×C₇₉	C₂×C₄	1	2	yes	—
32	C₂×C₈×C₇₉	D₄	1	1	yes	characteristic
33	C₂×C₈×C₇₉	C₂³	1	1	yes	characteristic
34	C₄⋊C₄×C₇₉	—	2	1	no	—
35	C₂²⋊C₄×C₇₉	—	4	1	no	—
36	C₄²×C₇₉	D₄	1	1	yes	characteristic
37	C₂³×C₇₉	—	4	1	no	—
38	D₄×C₇₉	—	2	2	no	—
39	D₄×C₇₉	—	4	1	no	—
40	C₂×C₄×C₇₉	—	4	1	no	—
41	C₂×C₄×C₇₉	—	8	2	no	—
42	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
43	C₂×C₄×C₇₉	D₈	1	1	yes	characteristic
44	C₂×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
45	C₂×Dic₇₉	—	4	1	no	—
46	C₂×Dic₇₉	—	4	1	no	—
47	Dic₁₅₈	—	2	2	no	—
48	Dic₁₅₈	—	4	1	no	—
49	C₈×C₇₉	—	2	1	no	—
50	C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
51	C₈×C₇₉	#41	1	1	yes	characteristic
52	C₂²×C₇₉	—	4	2	no	—
53	C₂²×C₇₉	—	8	1	no	—
54	C₂²×C₇₉	—	8	1	no	—
55	C₂²×C₇₉	C₂×D₈	1	1	yes	characteristic
56	C₄×C₇₉	—	2	1	no	—
57	C₄×C₇₉	—	2	1	no	—
58	C₄×C₇₉	—	8	1	no	—
59	C₄×C₇₉	C₄×D₄	1	1	yes	characteristic
60	C₄×C₇₉	#135	1	1	yes	characteristic
61	Dic₇₉	—	4	2	no	—
62	Dic₇₉	—	8	1	no	—
63	C₂×C₇₉	—	8	2	no	—
64	C₂×C₇₉	C₄×D₈	1	1	yes	characteristic
65	C₂×C₇₉	#509	1	1	yes	characteristic
66	C₂×C₇₉	#510	1	1	yes	characteristic
67	#2175	—	79	1	no	maximal, Sylow
68	C₇₉	#2175	1	1	yes	characteristic, complemented, Sylow
69	C₂×SD₃₂	—	79	1	no	—
70	C₄×Q₁₆	—	79	1	no	—
71	C₄×D₈	D₇₉	1	1	yes	characteristic
72	#366	—	79	1	no	—
73	#358	—	79	1	no	—
74	#357	—	79	1	no	—
75	#346	—	79	1	no	—
76	C₂×Q₁₆	—	79	1	no	—
77	C₂×D₈	C₂×D₇₉	1	1	yes	characteristic
78	C₄×Q₈	—	158	1	no	—
79	C₄×D₄	—	2	1	no	—
80	SD₃₂	—	79	4	no	—
81	C₂×C₁₆	—	79	1	no	—
82	C₂×C₁₆	—	79	1	no	—
83	#107	—	79	1	no	—
84	#107	C₂×D₇₉	1	1	yes	characteristic
85	#103	—	158	1	no	—
86	#102	—	2	1	no	—
87	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
88	C₂×Q₈	—	158	1	no	—
89	C₂×D₄	—	2	1	no	—
90	C₂²×C₄	—	4	1	no	—
91	Q₁₆	—	79	2	no	—
92	Q₁₆	—	158	1	no	—
93	D₈	—	2	1	no	—
94	D₈	C₄×D₇₉	1	2	yes	—
95	C₂×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
96	C₂×C₈	C₂²×D₇₉	1	1	yes	characteristic
97	C₄⋊C₄	—	2	1	no	—
98	C₄⋊C₄	—	316	1	no	—
99	C₄⋊C₄	—	158	1	no	—
100	C₂²⋊C₄	—	4	1	no	—
101	C₄²	—	316	1	no	—
102	C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
103	C₁₆	—	79	2	no	—
104	C₁₆	—	158	1	no	—
105	C₂³	—	4	1	no	—
106	Q₈	—	316	1	no	—
107	Q₈	—	158	2	no	—
108	D₄	—	2	2	no	—
109	D₄	—	4	1	no	—
110	C₂×C₄	—	4	1	no	—
111	C₂×C₄	—	8	2	no	—
112	C₂×C₄	—	316	1	no	—
113	C₂×C₄	—	316	1	no	—
114	C₂×C₄	#11929609	1	1	yes	characteristic
115	C₂×C₄	#11929609	1	1	yes	characteristic
116	C₂×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
117	C₈	—	2	1	no	—
118	C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
119	C₈	#11929624	1	1	yes	characteristic
120	C₂²	—	4	2	no	—
121	C₂²	—	8	1	no	—
122	C₂²	—	8	1	no	—
123	C₂²	C₂×#11929609	1	1	yes	characteristic
124	C₄	—	2	1	no	—
125	C₄	—	2	1	no	—
126	C₄	—	8	1	no	—
127	C₄	—	316	2	no	—
128	C₄	—	632	1	no	—
129	C₄	C₄×C₂²⋊D₇₉	1	1	yes	characteristic
130	C₄	#14579181	1	1	yes	characteristic
131	C₂	—	8	2	no	—
132	C₂	C₄×#11929609	1	1	yes	characteristic
133	C₂	#19098999	1	1	yes	characteristic
134	C₂	#19099003	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14579105

C₂

yes

maximal, characteristic

C₄×Dic₃₁₆

C₂

yes

maximal, characteristic, complemented

#19098388

C₂

yes

maximal, characteristic, complemented

#19098366

C₂

yes

maximal, characteristic, complemented

#19098364

C₂

yes

maximal, characteristic

#19098339

C₂

yes

maximal, characteristic, complemented

C₄×D₈×C₇₉

C₂

yes

maximal, characteristic

C₂×Dic₃₁₆

C₂²

yes

characteristic

C₄×Dic₁₅₈

—

#14579105

C₄

yes

complemented

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

C₂×C₇₉⋊C₁₆

C₂²

yes

characteristic

#14579095

C₂²

yes

characteristic

#14579086

—

C₂×D₈×C₇₉

C₂²

yes

characteristic

C₄×D₄×C₇₉

—

#107×C₇₉

C₂²

yes

characteristic

#102×C₇₉

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

Dic₃₁₆

—

Dic₃₁₆

C₂×C₄

yes

complemented

C₄⋊Dic₇₉

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

—

C₇₉⋊C₁₆

—

C₇₉⋊C₁₆

C₂×C₄

yes

complemented

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

C₂×C₄

yes

—

C₂×C₈×C₇₉

D₄

yes

characteristic

C₂×C₈×C₇₉

C₂³

yes

characteristic

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

D₄

yes

characteristic

C₂³×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

D₈

yes

characteristic

C₂×C₄×C₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

—

C₈×C₇₉

C₂²×C₄

yes

characteristic

C₈×C₇₉

#41

yes

characteristic

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

—

C₂²×C₇₉

C₂×D₈

yes

characteristic

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₄×D₄

yes

characteristic

C₄×C₇₉

#135

yes

characteristic

Dic₇₉

—

Dic₇₉

—

C₂×C₇₉

—

C₂×C₇₉

C₄×D₈

yes

C₂×C₇₉

yes

C₂×C₇₉

yes

—

C₇₉

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

C₄×Q₁₆

—

C₄×D₈

D₇₉

yes

—

—

—

—

C₂×Q₁₆

—

C₂×D₈

C₂×D₇₉

yes

characteristic

C₄×Q₈

—

158

—

C₄×D₄

—

SD₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

#107

—

#107

C₂×D₇₉

yes

characteristic

#103

—

158

—

#102

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

158

—

C₂×D₄

—

C₂²×C₄

—

Q₁₆

—

Q₁₆

—

158

—

D₈

—

D₈

C₄×D₇₉

yes

—

C₂×C₈

C₂²⋊D₇₉

yes

characteristic

C₂×C₈

C₂²×D₇₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

316

—

C₄⋊C₄

—

158

—

100

C₂²⋊C₄

—

101

C₄²

—

316

—

102

C₄²

C₂²⋊D₇₉

yes

characteristic

103

C₁₆

—

104

C₁₆

—

158

—

105

C₂³

—

106

Q₈

—

316

—

107

Q₈

—

158

—

108

D₄

—

109

D₄

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

316

—

113

C₂×C₄

—

316

—

114

C₂×C₄

#11929609

yes

characteristic

115

C₂×C₄

#11929609

yes

characteristic

116

C₂×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

117

C₈

—

118

C₈

C₂×C₄×D₇₉

yes

characteristic

119

C₈

#11929624

yes

characteristic

120

C₂²

—

121

C₂²

—

122

C₂²

—

123

C₂²

C₂×#11929609

yes

characteristic

124

C₄

—

125

C₄

—

126

C₄

—

127

C₄

—

316

—

128

C₄

—

632

—

129

C₄

C₄×C₂²⋊D₇₉

yes

characteristic

130

C₄

#14579181

yes

characteristic

131

C₂

—

132

C₂

C₄×#11929609

yes

characteristic

133

C₂

#19098999

yes

characteristic

134

C₂

#19099003

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×#11929609
commutator	C₈×C₇₉	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₉
Fitting	C₄×D₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂×D₈
prime radical	C₂×D₈×C₇₉	C₂²
cosocle	C₂×C₈×C₇₉	C₂³
hypercenter	C₄×D₈	D₇₉
hypocenter	C₇₉	#2175
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

subgroup

G/H

center

C₂²

C₂×#11929609

commutator

C₈×C₇₉

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₉

Fitting

C₄×D₈×C₇₉

C₂

socle

C₂²×C₇₉

C₂×D₈

prime radical

C₂×D₈×C₇₉

C₂²

cosocle

C₂×C₈×C₇₉

C₂³

hypercenter

C₄×D₈

D₇₉

hypocenter

C₇₉

#2175

LCS

G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₈

N	H ≅ G/N	type
2. C₄×Dic₃₁₆	C₂	semidirect
3. #19098388	C₂	semidirect
4. #19098366	C₂	semidirect
6. #19098339	C₂	semidirect
10. #14579105	C₄	semidirect
22. Dic₃₁₆	C₂×C₄	semidirect
27. C₇₉⋊C₁₆	C₂×C₄	semidirect
68. C₇₉	#2175	semidirect

H ≅ G/N

type

2. C₄×Dic₃₁₆

C₂

semidirect

3. #19098388

C₂

semidirect

4. #19098366

C₂

semidirect

6. #19098339

C₂

semidirect

10. #14579105

C₄

semidirect

22. Dic₃₁₆

C₂×C₄

semidirect

27. C₇₉⋊C₁₆

C₂×C₄

semidirect

68. C₇₉

#2175

semidirect

Subgroups — #23765264

Conjugacy classes of subgroups

Complements