Group #19099117 — subgroups

Subgroups — #19099117

Order 5056.

222 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 109 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	#14579160	C₂	1	1	yes	maximal, characteristic, complemented
2	#14579159	C₂	1	1	yes	maximal, characteristic, complemented
3	#14579151	C₂	1	2	yes	maximal, complemented
4	#14579141	C₂	1	1	yes	maximal, characteristic
5	#14579139	C₂	1	2	yes	maximal
6	#14579137	C₂	1	1	yes	maximal, characteristic
7	C₄×Dic₁₅₈	C₂	1	2	yes	maximal, complemented
8	C₄×Dic₁₅₈	C₂	1	1	yes	maximal, characteristic, complemented
9	#14579118	C₂	1	2	yes	maximal
10	C₄²×D₇₉	C₂	1	1	yes	maximal, characteristic
11	C₄×Q₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Dic₁₅₈	C₂²	1	2	yes	—
13	C₂×Dic₁₅₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₇₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₇₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₇₉	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₇₉	C₂²	1	1	yes	characteristic
18	C₄⋊Dic₇₉	C₂²	1	2	yes	—
19	Dic₇₉⋊C₄	C₂²	1	2	yes	—
20	Dic₇₉⋊C₄	C₂²	1	2	yes	—
21	Dic₇₉⋊C₄	C₂²	1	2	yes	—
22	Dic₇₉⋊C₄	C₂²	1	2	yes	—
23	Dic₇₉⋊C₄	C₂²	1	2	yes	—
24	(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
25	(C₂×D₇₉)⋊C₄	C₂²	1	2	yes	—
26	C₄×Dic₇₉	C₂²	1	1	yes	characteristic
27	C₄×Dic₇₉	C₂²	1	1	yes	characteristic
28	C₄×Dic₇₉	C₂²	1	1	yes	characteristic
29	C₄×Dic₇₉	C₂²	1	2	yes	—
30	C₂×Q₈×C₇₉	C₂²	1	1	yes	characteristic
31	C₄⋊C₄×C₇₉	C₂²	1	2	yes	—
32	C₄⋊C₄×C₇₉	C₂²	1	1	yes	characteristic
33	C₄²×C₇₉	C₂²	1	1	yes	characteristic
34	C₄²×C₇₉	C₂²	1	2	yes	—
35	C₂²×D₇₉	C₂³	1	1	yes	characteristic
36	Q₈×C₇₉	—	2	2	no	—
37	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
38	C₂×C₄×C₇₉	C₂³	1	2	yes	—
39	C₂×C₄×C₇₉	C₂³	1	2	yes	—
40	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
41	C₂×C₄×C₇₉	C₂³	1	1	yes	characteristic
42	C₂×Dic₇₉	C₂³	1	1	yes	characteristic
43	C₂×Dic₇₉	C₂³	1	2	yes	—
44	C₂×Dic₇₉	C₂³	1	2	yes	—
45	C₂×Dic₇₉	C₂³	1	1	yes	characteristic
46	C₂×Dic₇₉	C₂³	1	1	yes	characteristic
47	C₄×D₇₉	—	2	2	no	—
48	C₄×D₇₉	—	2	2	no	—
49	C₄×D₇₉	Q₈	1	4	yes	complemented
50	Dic₁₅₈	—	2	2	no	—
51	Dic₁₅₈	—	2	4	no	—
52	C₂²×C₇₉	C₂⁴	1	1	yes	characteristic
53	C₂×D₇₉	—	2	1	no	—
54	C₂×D₇₉	—	2	1	no	—
55	C₂×D₇₉	C₂×Q₈	1	2	yes	—
56	C₄×C₇₉	—	2	2	no	—
57	C₄×C₇₉	—	2	2	no	—
58	C₄×C₇₉	—	2	1	no	—
59	C₄×C₇₉	C₂×Q₈	1	2	yes	—
60	C₄×C₇₉	#41	1	2	yes	—
61	Dic₇₉	—	2	2	no	—
62	Dic₇₉	—	2	2	no	—
63	Dic₇₉	—	2	1	no	—
64	Dic₇₉	C₂×Q₈	1	2	yes	—
65	Dic₇₉	#41	1	2	yes	—
66	C₂×C₇₉	C₂²×Q₈	1	1	yes	characteristic
67	C₂×C₇₉	C₂×#41	1	1	yes	characteristic
68	C₂×C₇₉	C₂×#41	1	1	yes	characteristic
69	D₇₉	—	2	2	no	—
70	C₇₉	#533	1	1	yes	characteristic, complemented, Sylow
71	#533	—	79	1	no	maximal, Sylow
72	C₄⋊Q₈	—	79	1	no	—
73	C₄⋊Q₈	—	79	1	no	—
74	#125	—	79	2	no	—
75	C₂²⋊Q₈	—	79	1	no	—
76	C₂²⋊Q₈	—	79	2	no	—
77	C₂²⋊Q₈	—	79	1	no	—
78	C₄×Q₈	—	79	2	no	—
79	C₄×Q₈	—	79	1	no	—
80	C₄×Q₈	D₇₉	1	1	yes	characteristic, complemented
81	#117	—	79	2	no	—
82	C₂×C₄²	—	79	1	no	—
83	C₂×Q₈	—	79	2	no	—
84	C₂×Q₈	—	79	1	no	—
85	C₂×Q₈	C₂×D₇₉	1	1	yes	characteristic
86	C₂²×C₄	—	79	1	no	—
87	C₂²×C₄	—	79	1	no	—
88	C₂²×C₄	—	79	1	no	—
89	C₄⋊C₄	—	79	2	no	—
90	C₄⋊C₄	—	79	2	no	—
91	C₄⋊C₄	—	79	2	no	—
92	C₄⋊C₄	—	79	2	no	—
93	C₄⋊C₄	—	79	2	no	—
94	C₄⋊C₄	—	79	2	no	—
95	C₄⋊C₄	—	79	1	no	—
96	C₄⋊C₄	C₂×D₇₉	1	2	yes	—
97	C₄⋊C₄	C₂×D₇₉	1	1	yes	characteristic
98	C₂²⋊C₄	—	79	2	no	—
99	C₂²⋊C₄	—	79	2	no	—
100	C₄²	—	79	1	no	—
101	C₄²	—	79	1	no	—
102	C₄²	—	79	1	no	—
103	C₄²	—	79	2	no	—
104	C₄²	C₂×D₇₉	1	1	yes	characteristic
105	C₄²	C₂×D₇₉	1	2	yes	—
106	C₂³	—	79	1	no	—
107	Q₈	—	2	2	no	—
108	Q₈	—	158	4	no	—
109	Q₈	—	158	2	no	—
110	C₂×C₄	—	79	1	no	—
111	C₂×C₄	—	79	1	no	—
112	C₂×C₄	—	79	4	no	—
113	C₂×C₄	—	79	1	no	—
114	C₂×C₄	—	79	2	no	—
115	C₂×C₄	—	79	2	no	—
116	C₂×C₄	—	158	2	no	—
117	C₂×C₄	—	158	2	no	—
118	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
119	C₂×C₄	C₂²×D₇₉	1	2	yes	—
120	C₂×C₄	C₂²×D₇₉	1	2	yes	—
121	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
122	C₂×C₄	C₂²×D₇₉	1	1	yes	characteristic
123	C₂²	—	79	2	no	—
124	C₂²	—	158	1	no	—
125	C₂²	—	158	1	no	—
126	C₂²	C₂³×D₇₉	1	1	yes	characteristic
127	C₄	—	2	1	no	—
128	C₄	—	2	2	no	—
129	C₄	—	2	2	no	—
130	C₄	—	79	2	no	—
131	C₄	—	79	2	no	—
132	C₄	—	158	2	no	—
133	C₄	—	158	1	no	—
134	C₄	—	158	2	no	—
135	C₄	Q₈×D₇₉	1	2	yes	—
136	C₄	#11929624	1	2	yes	—
137	C₂	—	158	2	no	—
138	C₂	C₂×Q₈×D₇₉	1	1	yes	characteristic
139	C₂	#41×D₇₉	1	1	yes	characteristic
140	C₂	C₂×#11929624	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14579160

C₂

yes

maximal, characteristic, complemented

#14579159

C₂

yes

maximal, characteristic, complemented

#14579151

C₂

yes

maximal, complemented

#14579141

C₂

yes

maximal, characteristic

#14579139

C₂

yes

maximal

#14579137

C₂

yes

maximal, characteristic

C₄×Dic₁₅₈

C₂

yes

maximal, complemented

C₄×Dic₁₅₈

C₂

yes

maximal, characteristic, complemented

#14579118

C₂

yes

maximal

C₄²×D₇₉

C₂

yes

maximal, characteristic

C₄×Q₈×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Dic₁₅₈

C₂²

yes

—

C₂×Dic₁₅₈

C₂²

yes

characteristic

C₂×C₄×D₇₉

C₂²

yes

characteristic

C₂×C₄×D₇₉

C₂²

yes

characteristic

C₂×C₄×D₇₉

C₂²

yes

characteristic

C₄⋊Dic₇₉

C₂²

yes

characteristic

C₄⋊Dic₇₉

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

—

Dic₇₉⋊C₄

C₂²

yes

—

(C₂×D₇₉)⋊C₄

C₂²

yes

—

(C₂×D₇₉)⋊C₄

C₂²

yes

—

C₄×Dic₇₉

C₂²

yes

characteristic

C₄×Dic₇₉

C₂²

yes

characteristic

C₄×Dic₇₉

C₂²

yes

characteristic

C₄×Dic₇₉

C₂²

yes

—

C₂×Q₈×C₇₉

C₂²

yes

characteristic

C₄⋊C₄×C₇₉

C₂²

yes

—

C₄⋊C₄×C₇₉

C₂²

yes

characteristic

C₄²×C₇₉

C₂²

yes

characteristic

C₄²×C₇₉

C₂²

yes

—

C₂²×D₇₉

C₂³

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂³

yes

—

C₂×C₄×C₇₉

C₂³

yes

—

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×C₄×C₇₉

C₂³

yes

characteristic

C₂×Dic₇₉

C₂³

yes

characteristic

C₂×Dic₇₉

C₂³

yes

—

C₂×Dic₇₉

C₂³

yes

—

C₂×Dic₇₉

C₂³

yes

characteristic

C₂×Dic₇₉

C₂³

yes

characteristic

C₄×D₇₉

—

C₄×D₇₉

—

C₄×D₇₉

Q₈

yes

complemented

Dic₁₅₈

—

Dic₁₅₈

—

C₂²×C₇₉

C₂⁴

yes

characteristic

C₂×D₇₉

—

C₂×D₇₉

—

C₂×D₇₉

C₂×Q₈

yes

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

—

C₄×C₇₉

C₂×Q₈

yes

—

C₄×C₇₉

#41

yes

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

—

Dic₇₉

C₂×Q₈

yes

—

Dic₇₉

#41

yes

—

C₂×C₇₉

C₂²×Q₈

yes

characteristic

C₂×C₇₉

C₂×#41

yes

characteristic

C₂×C₇₉

C₂×#41

yes

characteristic

D₇₉

—

C₇₉

#533

yes

characteristic, complemented, Sylow

#533

—

maximal, Sylow

C₄⋊Q₈

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₂²⋊Q₈

—

C₄×Q₈

—

C₄×Q₈

—

C₄×Q₈

D₇₉

yes

characteristic, complemented

#117

—

C₂×C₄²

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×D₇₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×D₇₉

yes

—

C₄⋊C₄

C₂×D₇₉

yes

characteristic

C₂²⋊C₄

—

C₂²⋊C₄

—

100

C₄²

—

101

C₄²

—

102

C₄²

—

103

C₄²

—

104

C₄²

C₂×D₇₉

yes

characteristic

105

C₄²

C₂×D₇₉

yes

—

106

C₂³

—

107

Q₈

—

108

Q₈

—

158

—

109

Q₈

—

158

—

110

C₂×C₄

—

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

—

158

—

117

C₂×C₄

—

158

—

118

C₂×C₄

C₂²×D₇₉

yes

characteristic

119

C₂×C₄

C₂²×D₇₉

yes

—

120

C₂×C₄

C₂²×D₇₉

yes

—

121

C₂×C₄

C₂²×D₇₉

yes

characteristic

122

C₂×C₄

C₂²×D₇₉

yes

characteristic

123

C₂²

—

124

C₂²

—

158

—

125

C₂²

—

158

—

126

C₂²

C₂³×D₇₉

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

—

158

—

133

C₄

—

158

—

134

C₄

—

158

—

135

C₄

Q₈×D₇₉

yes

—

136

C₄

#11929624

yes

—

137

C₂

—

158

—

138

C₂

C₂×Q₈×D₇₉

yes

characteristic

139

C₂

#41×D₇₉

yes

characteristic

140

C₂

C₂×#11929624

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₇₉
commutator, socle	C₂²×C₇₉	C₂⁴
Frattini	C₂²	C₂³×D₇₉
Fitting	C₄×Q₈×C₇₉	C₂
hypercenter	C₄×Q₈	D₇₉
hypocenter	C₇₉	#533
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

subgroup

G/H

center

C₂×C₄

C₂²×D₇₉

commutator, socle

C₂²×C₇₉

C₂⁴

Frattini

C₂²

C₂³×D₇₉

Fitting

C₄×Q₈×C₇₉

C₂

hypercenter

C₄×Q₈

D₇₉

C₇₉

G ▷ C₂²×C₇₉ ▷ C₇₉

C₁ ◁ C₂×C₄ ◁ C₄×Q₈

N	H ≅ G/N	type
1. #14579160	C₂	semidirect
2. #14579159	C₂	semidirect
3. #14579151	C₂	semidirect
7. C₄×Dic₁₅₈	C₂	semidirect
8. C₄×Dic₁₅₈	C₂	semidirect
11. C₄×Q₈×C₇₉	C₂	semidirect
49. C₄×D₇₉	Q₈	semidirect
70. C₇₉	#533	semidirect
80. C₄×Q₈	D₇₉	semidirect

H ≅ G/N

type

1. #14579160

C₂

semidirect

2. #14579159

C₂

semidirect

3. #14579151

C₂

semidirect

7. C₄×Dic₁₅₈

C₂

semidirect

8. C₄×Dic₁₅₈

C₂

semidirect

11. C₄×Q₈×C₇₉

C₂

semidirect

49. C₄×D₇₉

Q₈

semidirect

70. C₇₉

#533

semidirect

80. C₄×Q₈

D₇₉

semidirect

Subgroups — #19099117

Conjugacy classes of subgroups

Complements