Group #23773896 — subgroups

Subgroups — #498×D₇₉ #23773896

Order 10112.

424 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 165 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	C₄⋊Q₈×D₇₉	C₂	1	2	yes	maximal
2	#19098961	C₂	1	1	yes	maximal, characteristic, complemented
3	#19098960	C₂	1	4	yes	maximal, complemented
4	#19098959	C₂	1	2	yes	maximal, complemented
5	#106×D₇₉	C₂	1	4	yes	maximal
6	C₄×C₈×D₇₉	C₂	1	1	yes	maximal, characteristic
7	#498×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×D₇₉	—	2	2	no	—
9	C₂×C₈×D₇₉	C₂²	1	2	yes	—
10	#14579161	C₂²	1	2	yes	—
11	#14579160	—	2	2	no	—
12	#14579160	C₂²	1	4	yes	—
13	#14579159	—	2	2	no	—
14	C₄⋊C₄×D₇₉	—	2	2	no	—
15	C₄⋊C₄×D₇₉	C₂²	1	4	yes	—
16	C₄²×D₇₉	C₂²	1	1	yes	characteristic
17	#14579093	C₂²	1	4	yes	—
18	#14579092	C₂²	1	8	yes	—
19	C₄×C₇₉⋊C₈	C₂²	1	1	yes	characteristic
20	C₈×Dic₇₉	C₂²	1	2	yes	—
21	C₄⋊Q₈×C₇₉	C₂²	1	2	yes	—
22	#106×C₇₉	C₂²	1	4	yes	—
23	C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
24	C₂×Dic₁₅₈	—	2	4	no	—
25	C₂×Dic₁₅₈	—	2	2	no	—
26	Q₈×D₇₉	—	4	8	no	—
27	C₂×C₄×D₇₉	—	2	4	no	—
28	C₂×C₄×D₇₉	D₄	1	2	yes	—
29	C₂×C₄×D₇₉	C₂³	1	1	yes	characteristic
30	C₂×C₇₉⋊C₈	C₂³	1	2	yes	—
31	C₈×D₇₉	Q₈	1	8	yes	complemented
32	C₄⋊Dic₇₉	—	2	2	no	—
33	C₄⋊Dic₇₉	C₂³	1	4	yes	—
34	Dic₇₉⋊C₄	—	2	4	no	—
35	Dic₇₉⋊C₄	—	2	4	no	—
36	C₄×Dic₇₉	D₄	1	2	yes	—
37	C₄×Dic₇₉	C₂³	1	1	yes	characteristic
38	C₂×Q₈×C₇₉	—	2	2	no	—
39	C₂×C₈×C₇₉	C₂³	1	2	yes	—
40	C₄⋊C₄×C₇₉	—	2	2	no	—
41	C₄⋊C₄×C₇₉	C₂³	1	4	yes	—
42	C₄²×C₇₉	C₂³	1	1	yes	characteristic
43	C₂²×D₇₉	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₇₉	—	4	4	no	—
45	C₂×C₄×C₇₉	—	2	4	no	—
46	C₂×C₄×C₇₉	C₂×D₄	1	2	yes	—
47	C₂×C₄×C₇₉	C₂⁴	1	1	yes	characteristic
48	C₂×Dic₇₉	—	2	4	no	—
49	C₂×Dic₇₉	C₂×D₄	1	1	yes	characteristic
50	C₂×Dic₇₉	C₂×D₄	1	2	yes	—
51	C₄×D₇₉	—	4	8	no	—
52	C₄×D₇₉	SD₁₆	1	8	yes	—
53	C₄×D₇₉	C₂×Q₈	1	4	yes	—
54	Dic₁₅₈	—	4	4	no	—
55	Dic₁₅₈	—	4	8	no	—
56	C₈×C₇₉	C₂×Q₈	1	4	yes	complemented
57	C₇₉⋊C₈	C₂×Q₈	1	4	yes	complemented
58	C₂²×C₇₉	C₂²×D₄	1	1	yes	characteristic
59	C₂×D₇₉	C₄⋊Q₈	1	2	yes	—
60	C₂×D₇₉	C₂×SD₁₆	1	4	yes	—
61	C₄×C₇₉	—	4	4	no	—
62	C₄×C₇₉	C₂×SD₁₆	1	4	yes	—
63	C₄×C₇₉	C₂²×Q₈	1	2	yes	—
64	Dic₇₉	—	4	4	no	—
65	Dic₇₉	C₄⋊Q₈	1	2	yes	—
66	Dic₇₉	C₂×SD₁₆	1	4	yes	—
67	C₂×C₇₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
68	C₂×C₇₉	C₂²×SD₁₆	1	2	yes	—
69	D₇₉	#498	1	4	yes	direct product factor
70	C₂×#498	—	79	1	no	maximal, Sylow
71	C₇₉	C₂×#498	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₄⋊Q₈	—	79	2	no	—
73	#498	—	79	2	no	—
74	#498	—	79	4	no	—
75	#498	—	79	1	no	—
76	#498	D₇₉	1	1	yes	characteristic, direct product factor
77	C₂×#106	—	79	4	no	—
78	C₂×C₄×C₈	—	79	1	no	—
79	C₂²×Q₈	—	158	2	no	—
80	C₂²×C₈	—	79	2	no	—
81	C₄⋊Q₈	—	79	4	no	—
82	C₄⋊Q₈	—	79	2	no	—
83	C₄⋊Q₈	—	158	2	no	—
84	C₄⋊Q₈	—	158	2	no	—
85	C₄⋊Q₈	C₂×D₇₉	1	2	yes	—
86	C₂×C₄⋊C₄	—	79	4	no	—
87	C₂×C₄⋊C₄	—	158	2	no	—
88	C₂×C₄²	—	79	1	no	—
89	#106	—	79	4	no	—
90	#106	—	79	8	no	—
91	#106	C₂×D₇₉	1	4	yes	—
92	C₄×C₈	—	79	2	no	—
93	C₄×C₈	—	79	1	no	—
94	C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
95	C₂×Q₈	—	2	2	no	—
96	C₂×Q₈	—	316	8	no	—
97	C₂×Q₈	—	158	4	no	—
98	C₂×Q₈	—	158	2	no	—
99	C₂²×C₄	—	79	2	no	—
100	C₂²×C₄	—	79	1	no	—
101	C₂²×C₄	—	158	4	no	—
102	C₂×C₈	—	79	2	no	—
103	C₂×C₈	—	79	8	no	—
104	C₂×C₈	C₂²×D₇₉	1	2	yes	—
105	C₄⋊C₄	—	2	2	no	—
106	C₄⋊C₄	—	79	4	no	—
107	C₄⋊C₄	—	158	4	no	—
108	C₄⋊C₄	—	158	4	no	—
109	C₄⋊C₄	—	158	2	no	—
110	C₄⋊C₄	C₂²×D₇₉	1	4	yes	—
111	C₄²	—	79	2	no	—
112	C₄²	—	79	1	no	—
113	C₄²	C₂²×D₇₉	1	1	yes	characteristic
114	C₂³	—	79	1	no	—
115	Q₈	—	4	4	no	—
116	Q₈	—	316	8	no	—
117	Q₈	—	316	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	316	8	no	—
120	C₂×C₄	—	79	1	no	—
121	C₂×C₄	—	79	2	no	—
122	C₂×C₄	—	79	4	no	—
123	C₂×C₄	—	79	8	no	—
124	C₂×C₄	—	158	4	no	—
125	C₂×C₄	D₄×D₇₉	1	2	yes	—
126	C₂×C₄	C₂³×D₇₉	1	1	yes	characteristic
127	C₈	—	79	4	no	—
128	C₈	Q₈×D₇₉	1	4	yes	complemented
129	C₂²	—	79	4	no	—
130	C₂²	—	79	2	no	—
131	C₂²	C₂×D₄×D₇₉	1	1	yes	characteristic
132	C₄	—	4	4	no	—
133	C₄	—	316	4	no	—
134	C₄	—	79	4	no	—
135	C₄	—	79	2	no	—
136	C₄	SD₁₆×D₇₉	1	4	yes	—
137	C₄	C₂×Q₈×D₇₉	1	2	yes	—
138	C₂	—	79	4	no	—
139	C₂	C₄⋊Q₈×D₇₉	1	1	yes	characteristic
140	C₂	C₂×SD₁₆×D₇₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊Q₈×D₇₉

C₂

yes

maximal

#19098961

C₂

yes

maximal, characteristic, complemented

#19098960

C₂

yes

maximal, complemented

#19098959

C₂

yes

maximal, complemented

#106×D₇₉

C₂

yes

maximal

C₄×C₈×D₇₉

C₂

yes

maximal, characteristic

#498×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×Q₈×D₇₉

—

C₂×C₈×D₇₉

C₂²

yes

—

#14579161

C₂²

yes

—

#14579160

—

#14579160

C₂²

yes

—

#14579159

—

C₄⋊C₄×D₇₉

—

C₄⋊C₄×D₇₉

C₂²

yes

—

C₄²×D₇₉

C₂²

yes

characteristic

#14579093

C₂²

yes

—

#14579092

C₂²

yes

—

C₄×C₇₉⋊C₈

C₂²

yes

characteristic

C₈×Dic₇₉

C₂²

yes

—

C₄⋊Q₈×C₇₉

C₂²

yes

—

#106×C₇₉

C₂²

yes

—

C₄×C₈×C₇₉

C₂²

yes

characteristic

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

Q₈×D₇₉

—

C₂×C₄×D₇₉

—

C₂×C₄×D₇₉

D₄

yes

—

C₂×C₄×D₇₉

C₂³

yes

characteristic

C₂×C₇₉⋊C₈

C₂³

yes

—

C₈×D₇₉

Q₈

yes

complemented

C₄⋊Dic₇₉

—

C₄⋊Dic₇₉

C₂³

yes

—

Dic₇₉⋊C₄

—

Dic₇₉⋊C₄

—

C₄×Dic₇₉

D₄

yes

—

C₄×Dic₇₉

C₂³

yes

characteristic

C₂×Q₈×C₇₉

—

C₂×C₈×C₇₉

C₂³

yes

—

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

C₂³

yes

—

C₄²×C₇₉

C₂³

yes

characteristic

C₂²×D₇₉

C₂×D₄

yes

characteristic

Q₈×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

C₂×D₄

yes

—

C₂×C₄×C₇₉

C₂⁴

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

C₂×D₄

yes

characteristic

C₂×Dic₇₉

C₂×D₄

yes

—

C₄×D₇₉

—

C₄×D₇₉

SD₁₆

yes

—

C₄×D₇₉

C₂×Q₈

yes

—

Dic₁₅₈

—

Dic₁₅₈

—

C₈×C₇₉

C₂×Q₈

yes

complemented

C₇₉⋊C₈

C₂×Q₈

yes

complemented

C₂²×C₇₉

C₂²×D₄

yes

characteristic

C₂×D₇₉

C₄⋊Q₈

yes

—

C₂×D₇₉

C₂×SD₁₆

yes

—

C₄×C₇₉

—

C₄×C₇₉

C₂×SD₁₆

yes

—

C₄×C₇₉

C₂²×Q₈

yes

—

Dic₇₉

—

Dic₇₉

C₄⋊Q₈

yes

—

Dic₇₉

C₂×SD₁₆

yes

—

C₂×C₇₉

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₇₉

C₂²×SD₁₆

yes

—

D₇₉

#498

yes

direct product factor

C₂×#498

—

maximal, Sylow

C₇₉

C₂×#498

yes

characteristic, complemented, Sylow

C₂×C₄⋊Q₈

—

—

—

—

D₇₉

yes

characteristic, direct product factor

C₂×#106

—

C₂×C₄×C₈

—

C₂²×Q₈

—

158

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

—

158

—

C₄⋊Q₈

C₂×D₇₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

158

—

C₂×C₄²

—

#106

—

#106

—

#106

C₂×D₇₉

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₇₉

yes

characteristic

C₂×Q₈

—

C₂×Q₈

—

316

—

C₂×Q₈

—

158

—

C₂×Q₈

—

158

—

C₂²×C₄

—

100

C₂²×C₄

—

101

C₂²×C₄

—

158

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

C₂²×D₇₉

yes

—

105

C₄⋊C₄

—

106

C₄⋊C₄

—

107

C₄⋊C₄

—

158

—

108

C₄⋊C₄

—

158

—

109

C₄⋊C₄

—

158

—

110

C₄⋊C₄

C₂²×D₇₉

yes

—

111

C₄²

—

112

C₄²

—

113

C₄²

C₂²×D₇₉

yes

characteristic

114

C₂³

—

115

Q₈

—

116

Q₈

—

316

—

117

Q₈

—

316

—

118

C₂×C₄

—

119

C₂×C₄

—

316

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

158

—

125

C₂×C₄

D₄×D₇₉

yes

—

126

C₂×C₄

C₂³×D₇₉

yes

characteristic

127

C₈

—

128

C₈

Q₈×D₇₉

yes

complemented

129

C₂²

—

130

C₂²

—

131

C₂²

C₂×D₄×D₇₉

yes

characteristic

132

C₄

—

133

C₄

—

316

—

134

C₄

—

135

C₄

—

136

C₄

SD₁₆×D₇₉

yes

—

137

C₄

C₂×Q₈×D₇₉

yes

—

138

C₂

—

139

C₂

C₄⋊Q₈×D₇₉

yes

characteristic

140

C₂

C₂×SD₁₆×D₇₉

yes

—

	subgroup	G/H
center	C₂²	C₂×D₄×D₇₉
commutator, cosocle	C₂×C₄×C₇₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₇₉
Fitting	#498×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₄
prime radical	C₂²×D₇₉	C₂×D₄
hypercenter	#498	D₇₉
hypocenter	C₇₉	C₂×#498
LCS	G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #498

subgroup

G/H

center

C₂²

C₂×D₄×D₇₉

commutator, cosocle

C₂×C₄×C₇₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₇₉

Fitting

#498×C₇₉

C₂

socle

C₂²×C₇₉

C₂²×D₄

prime radical

C₂²×D₇₉

C₂×D₄

D₇₉

C₇₉

G ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #498

N	H ≅ G/N	type
2. #19098961	C₂	semidirect
3. #19098960	C₂	semidirect
4. #19098959	C₂	semidirect
7. #498×C₇₉	C₂	semidirect
31. C₈×D₇₉	Q₈	semidirect
56. C₈×C₇₉	C₂×Q₈	semidirect
57. C₇₉⋊C₈	C₂×Q₈	semidirect
69. D₇₉	#498	direct (N × H)
71. C₇₉	C₂×#498	semidirect
76. #498	D₇₉	direct (N × H)
128. C₈	Q₈×D₇₉	semidirect

H ≅ G/N

type

2. #19098961

C₂

semidirect

3. #19098960

C₂

semidirect

4. #19098959

C₂

semidirect

7. #498×C₇₉

C₂

semidirect

31. C₈×D₇₉

Q₈

semidirect

56. C₈×C₇₉

C₂×Q₈

semidirect

57. C₇₉⋊C₈

C₂×Q₈

semidirect

69. D₇₉

#498

direct (N × H)

71. C₇₉

C₂×#498

semidirect

76. #498

D₇₉

direct (N × H)

128. C₈

Q₈×D₇₉

semidirect

Subgroups — #498×D₇₉ #23773896

Conjugacy classes of subgroups

Complements

Subgroups — #498×D79 #23773896

Conjugacy classes of subgroups

Complements

Subgroups — #498×D₇₉ #23773896