Group #34208748 — subgroups

Subgroups — C₂×Dic₇₉⋊C₃₂ #34208748

Order 20224.

230 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 147 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	C₂²×C₇₉⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₆×Dic₇₉	C₂	1	1	yes	maximal, characteristic
3	Dic₇₉⋊C₃₂	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₃₂×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₇₉⋊C₁₆	C₄	1	1	yes	characteristic
6	C₂×C₈×Dic₇₉	C₄	1	1	yes	characteristic
7	C₂×C₇₉⋊C₃₂	—	2	2	no	—
8	C₂×C₇₉⋊C₃₂	C₂²	1	2	yes	—
9	C₁₆×Dic₇₉	C₄	1	2	yes	—
10	C₁₆×Dic₇₉	C₂²	1	2	yes	—
11	C₂²×C₁₆×C₇₉	C₂²	1	1	yes	characteristic
12	C₂×C₃₂×C₇₉	—	2	2	no	—
13	C₂×C₃₂×C₇₉	C₂²	1	2	yes	—
14	C₂²×C₇₉⋊C₈	C₈	1	1	yes	characteristic
15	C₂×C₄×Dic₇₉	C₈	1	1	yes	characteristic
16	C₂×C₇₉⋊C₁₆	—	2	2	no	—
17	C₂×C₇₉⋊C₁₆	C₂×C₄	1	2	yes	—
18	C₈×Dic₇₉	C₈	1	2	yes	—
19	C₈×Dic₇₉	C₂×C₄	1	2	yes	—
20	C₇₉⋊C₃₂	—	2	2	no	—
21	C₂²×C₈×C₇₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₁₆×C₇₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₁₆×C₇₉	D₄	1	2	yes	—
24	C₂×C₁₆×C₇₉	Q₈	1	2	yes	—
25	C₂×C₁₆×C₇₉	C₂³	1	1	yes	characteristic
26	C₃₂×C₇₉	—	2	2	no	—
27	C₂²×Dic₇₉	C₁₆	1	1	yes	characteristic
28	C₂²×Dic₇₉	C₁₆	1	1	yes	characteristic
29	C₂×C₇₉⋊C₈	—	2	2	no	—
30	C₂×C₇₉⋊C₈	C₂×C₈	1	2	yes	—
31	C₄×Dic₇₉	C₁₆	1	2	yes	—
32	C₄×Dic₇₉	C₂×C₈	1	2	yes	—
33	C₇₉⋊C₁₆	—	2	2	no	—
34	C₂²×C₄×C₇₉	C₂×C₈	1	1	yes	characteristic
35	C₂×C₈×C₇₉	C₄⋊C₄	1	2	yes	—
36	C₂×C₈×C₇₉	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₇₉	M₁₆	1	2	yes	—
38	C₂×C₈×C₇₉	C₂²×C₄	1	1	yes	characteristic
39	C₁₆×C₇₉	C₄⋊C₄	1	2	yes	—
40	C₁₆×C₇₉	C₂×D₄	1	1	yes	characteristic
41	C₁₆×C₇₉	C₂×Q₈	1	1	yes	characteristic
42	C₂³×C₇₉	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₇₉	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₇₉	C₂×C₁₆	1	1	yes	characteristic
45	C₂×C₄×C₇₉	M₃₂	1	2	yes	—
46	C₂×C₄×C₇₉	C₂²×C₈	1	1	yes	characteristic
47	C₂×Dic₇₉	—	2	2	no	—
48	C₂×Dic₇₉	C₃₂	1	4	yes	complemented
49	C₂×Dic₇₉	C₂×C₁₆	1	2	yes	—
50	C₂×Dic₇₉	C₂×C₁₆	1	2	yes	—
51	C₈×C₇₉	C₄⋊C₈	1	2	yes	—
52	C₈×C₇₉	C₂×C₄⋊C₄	1	1	yes	characteristic
53	C₈×C₇₉	C₂×M₁₆	1	1	yes	characteristic
54	C₇₉⋊C₈	—	2	2	no	—
55	C₂²×C₇₉	C₄⋊C₁₆	1	2	yes	—
56	C₂²×C₇₉	C₂×C₃₂	1	2	yes	—
57	C₂²×C₇₉	M₆₄	1	2	yes	—
58	C₂²×C₇₉	C₂²×C₁₆	1	1	yes	characteristic
59	C₄×C₇₉	C₄⋊C₁₆	1	2	yes	—
60	C₄×C₇₉	C₂×C₄⋊C₈	1	1	yes	characteristic
61	C₄×C₇₉	C₂×M₃₂	1	1	yes	characteristic
62	Dic₇₉	—	2	2	no	—
63	Dic₇₉	C₂×C₃₂	1	4	yes	complemented
64	C₂×C₄⋊C₃₂	—	79	1	no	maximal, Sylow
65	C₂×C₇₉	C₄⋊C₃₂	1	4	yes	complemented
66	C₂×C₇₉	C₂×C₄⋊C₁₆	1	1	yes	characteristic
67	C₂×C₇₉	C₂²×C₃₂	1	1	yes	characteristic
68	C₂×C₇₉	C₂×M₆₄	1	1	yes	characteristic
69	C₂²×C₃₂	—	79	1	no	—
70	C₂²×C₃₂	D₇₉	1	1	yes	characteristic
71	C₂×C₄×C₁₆	—	79	1	no	—
72	C₄⋊C₃₂	—	79	4	no	—
73	C₇₉	C₂×C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₁₆	—	79	1	no	—
75	C₂²×C₁₆	C₂×D₇₉	1	1	yes	characteristic
76	C₂×C₄×C₈	—	79	1	no	—
77	C₂×C₃₂	—	2	2	no	—
78	C₂×C₃₂	—	79	2	no	—
79	C₂×C₃₂	—	158	2	no	—
80	C₂×C₃₂	C₂×D₇₉	1	2	yes	—
81	C₄×C₁₆	—	79	2	no	—
82	C₄×C₁₆	—	79	2	no	—
83	C₂²×C₈	—	79	1	no	—
84	C₂²×C₈	C₄×D₇₉	1	1	yes	characteristic
85	C₂×C₄²	—	79	1	no	—
86	C₂×C₁₆	—	79	2	no	—
87	C₂×C₁₆	—	158	2	no	—
88	C₂×C₁₆	Dic₁₅₈	1	2	yes	—
89	C₂×C₁₆	C₄×D₇₉	1	1	yes	characteristic
90	C₂×C₁₆	C₂²⋊D₇₉	1	2	yes	—
91	C₂×C₁₆	C₂²×D₇₉	1	1	yes	characteristic
92	C₄×C₈	—	79	2	no	—
93	C₄×C₈	—	79	2	no	—
94	C₃₂	—	2	2	no	—
95	C₃₂	—	158	2	no	—
96	C₂²×C₄	—	79	1	no	—
97	C₂²×C₄	—	79	1	no	—
98	C₂²×C₄	C₈×D₇₉	1	1	yes	characteristic
99	C₂×C₈	—	79	2	no	—
100	C₂×C₈	—	158	2	no	—
101	C₂×C₈	Dic₇₉⋊C₄	1	2	yes	—
102	C₂×C₈	C₈×D₇₉	1	1	yes	characteristic
103	C₂×C₈	#11929607	1	2	yes	—
104	C₂×C₈	C₂×C₄×D₇₉	1	1	yes	characteristic
105	C₄²	—	79	2	no	—
106	C₄²	—	79	2	no	—
107	C₁₆	—	158	2	no	—
108	C₁₆	Dic₇₉⋊C₄	1	2	yes	—
109	C₁₆	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
110	C₁₆	C₂×Dic₁₅₈	1	1	yes	characteristic
111	C₂³	C₁₆×D₇₉	1	1	yes	characteristic
112	C₂×C₄	—	79	4	no	—
113	C₂×C₄	—	79	2	no	—
114	C₂×C₄	—	79	2	no	—
115	C₂×C₄	—	158	2	no	—
116	C₂×C₄	Dic₇₉⋊C₈	1	2	yes	—
117	C₂×C₄	C₁₆×D₇₉	1	1	yes	characteristic
118	C₂×C₄	#14579100	1	2	yes	—
119	C₂×C₄	C₂×C₈×D₇₉	1	1	yes	characteristic
120	C₈	—	158	2	no	—
121	C₈	Dic₇₉⋊C₈	1	2	yes	—
122	C₈	C₂×Dic₇₉⋊C₄	1	1	yes	characteristic
123	C₈	C₂×#11929607	1	1	yes	characteristic
124	C₂²	Dic₇₉⋊C₁₆	1	2	yes	—
125	C₂²	C₃₂×D₇₉	1	2	yes	—
126	C₂²	#19098396	1	2	yes	—
127	C₂²	C₂×C₁₆×D₇₉	1	1	yes	characteristic
128	C₄	—	79	4	no	—
129	C₄	—	158	2	no	—
130	C₄	Dic₇₉⋊C₁₆	1	2	yes	—
131	C₄	C₂×Dic₇₉⋊C₈	1	1	yes	characteristic
132	C₄	C₂×#14579100	1	1	yes	characteristic
133	C₂	Dic₇₉⋊C₃₂	1	4	yes	direct product factor
134	C₂	C₂×Dic₇₉⋊C₁₆	1	1	yes	characteristic
135	C₂	C₂×C₃₂×D₇₉	1	1	yes	characteristic
136	C₂	C₂×#19098396	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₇₉⋊C₃₂

C₂

yes

maximal, characteristic

C₂×C₁₆×Dic₇₉

C₂

yes

maximal, characteristic

Dic₇₉⋊C₃₂

C₂

yes

maximal, direct product factor

C₂²×C₃₂×C₇₉

C₂

yes

maximal, characteristic

C₂²×C₇₉⋊C₁₆

C₄

yes

characteristic

C₂×C₈×Dic₇₉

C₄

yes

characteristic

C₂×C₇₉⋊C₃₂

—

C₂×C₇₉⋊C₃₂

C₂²

yes

—

C₁₆×Dic₇₉

C₄

yes

—

C₁₆×Dic₇₉

C₂²

yes

—

C₂²×C₁₆×C₇₉

C₂²

yes

characteristic

C₂×C₃₂×C₇₉

—

C₂×C₃₂×C₇₉

C₂²

yes

—

C₂²×C₇₉⋊C₈

C₈

yes

characteristic

C₂×C₄×Dic₇₉

C₈

yes

characteristic

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

C₂×C₄

yes

—

C₈×Dic₇₉

C₈

yes

—

C₈×Dic₇₉

C₂×C₄

yes

—

C₇₉⋊C₃₂

—

C₂²×C₈×C₇₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₇₉

D₄

yes

—

C₂×C₁₆×C₇₉

Q₈

yes

—

C₂×C₁₆×C₇₉

C₂³

yes

characteristic

C₃₂×C₇₉

—

C₂²×Dic₇₉

C₁₆

yes

characteristic

C₂²×Dic₇₉

C₁₆

yes

characteristic

C₂×C₇₉⋊C₈

—

C₂×C₇₉⋊C₈

C₂×C₈

yes

—

C₄×Dic₇₉

C₁₆

yes

—

C₄×Dic₇₉

C₂×C₈

yes

—

C₇₉⋊C₁₆

—

C₂²×C₄×C₇₉

C₂×C₈

yes

characteristic

C₂×C₈×C₇₉

C₄⋊C₄

yes

—

C₂×C₈×C₇₉

C₂×C₈

yes

characteristic

C₂×C₈×C₇₉

M₁₆

yes

—

C₂×C₈×C₇₉

C₂²×C₄

yes

characteristic

C₁₆×C₇₉

C₄⋊C₄

yes

—

C₁₆×C₇₉

C₂×D₄

yes

characteristic

C₁₆×C₇₉

C₂×Q₈

yes

characteristic

C₂³×C₇₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₉

C₄⋊C₈

yes

—

C₂×C₄×C₇₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₇₉

M₃₂

yes

—

C₂×C₄×C₇₉

C₂²×C₈

yes

characteristic

C₂×Dic₇₉

—

C₂×Dic₇₉

C₃₂

yes

complemented

C₂×Dic₇₉

C₂×C₁₆

yes

—

C₂×Dic₇₉

C₂×C₁₆

yes

—

C₈×C₇₉

C₄⋊C₈

yes

—

C₈×C₇₉

C₂×C₄⋊C₄

yes

characteristic

C₈×C₇₉

C₂×M₁₆

yes

characteristic

C₇₉⋊C₈

—

C₂²×C₇₉

C₄⋊C₁₆

yes

—

C₂²×C₇₉

C₂×C₃₂

yes

—

C₂²×C₇₉

M₆₄

yes

—

C₂²×C₇₉

C₂²×C₁₆

yes

characteristic

C₄×C₇₉

C₄⋊C₁₆

yes

—

C₄×C₇₉

C₂×C₄⋊C₈

yes

characteristic

C₄×C₇₉

C₂×M₃₂

yes

characteristic

Dic₇₉

—

Dic₇₉

C₂×C₃₂

yes

complemented

C₂×C₄⋊C₃₂

—

maximal, Sylow

C₂×C₇₉

C₄⋊C₃₂

yes

complemented

C₂×C₇₉

C₂×C₄⋊C₁₆

yes

characteristic

C₂×C₇₉

C₂²×C₃₂

yes

characteristic

C₂×C₇₉

C₂×M₆₄

yes

characteristic

C₂²×C₃₂

—

C₂²×C₃₂

D₇₉

yes

characteristic

C₂×C₄×C₁₆

—

C₄⋊C₃₂

—

C₇₉

C₂×C₄⋊C₃₂

yes

characteristic, complemented, Sylow

C₂²×C₁₆

—

C₂²×C₁₆

C₂×D₇₉

yes

characteristic

C₂×C₄×C₈

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

158

—

C₂×C₃₂

C₂×D₇₉

yes

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂²×C₈

—

C₂²×C₈

C₄×D₇₉

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

158

—

C₂×C₁₆

Dic₁₅₈

yes

—

C₂×C₁₆

C₄×D₇₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₇₉

yes

—

C₂×C₁₆

C₂²×D₇₉

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₃₂

—

C₃₂

—

158

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₈×D₇₉

yes

characteristic

C₂×C₈

—

100

C₂×C₈

—

158

—

101

C₂×C₈

Dic₇₉⋊C₄

yes

—

102

C₂×C₈

C₈×D₇₉

yes

characteristic

103

C₂×C₈

#11929607

yes

—

104

C₂×C₈

C₂×C₄×D₇₉

yes

characteristic

105

C₄²

—

106

C₄²

—

107

C₁₆

—

158

—

108

C₁₆

Dic₇₉⋊C₄

yes

—

109

C₁₆

C₂×C₂²⋊D₇₉

yes

characteristic

110

C₁₆

C₂×Dic₁₅₈

yes

characteristic

111

C₂³

C₁₆×D₇₉

yes

characteristic

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

158

—

116

C₂×C₄

Dic₇₉⋊C₈

yes

—

117

C₂×C₄

C₁₆×D₇₉

yes

characteristic

118

C₂×C₄

#14579100

yes

—

119

C₂×C₄

C₂×C₈×D₇₉

yes

characteristic

120

C₈

—

158

—

121

C₈

Dic₇₉⋊C₈

yes

—

122

C₈

C₂×Dic₇₉⋊C₄

yes

characteristic

123

C₈

C₂×#11929607

yes

characteristic

124

C₂²

Dic₇₉⋊C₁₆

yes

—

125

C₂²

C₃₂×D₇₉

yes

—

126

C₂²

#19098396

yes

—

127

C₂²

C₂×C₁₆×D₇₉

yes

characteristic

128

C₄

—

129

C₄

—

158

—

130

C₄

Dic₇₉⋊C₁₆

yes

—

131

C₄

C₂×Dic₇₉⋊C₈

yes

characteristic

132

C₄

C₂×#14579100

yes

characteristic

133

C₂

Dic₇₉⋊C₃₂

yes

direct product factor

134

C₂

C₂×Dic₇₉⋊C₁₆

yes

characteristic

135

C₂

C₂×C₃₂×D₇₉

yes

characteristic

136

C₂

C₂×#19098396

yes

characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂×D₇₉
commutator	C₂×C₇₉	C₂²×C₃₂
Frattini	C₂×C₁₆	C₂²×D₇₉
Fitting	C₂²×C₃₂×C₇₉	C₂
socle, prime radical	C₂³×C₇₉	C₂×C₁₆
cosocle	C₂×C₁₆×C₇₉	C₂³
hypercenter	C₂²×C₃₂	D₇₉
hypocenter	C₇₉	C₂×C₄⋊C₃₂
LCS	G ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

subgroup

G/H

center

C₂²×C₁₆

C₂×D₇₉

commutator

C₂×C₇₉

C₂²×C₃₂

Frattini

C₂×C₁₆

C₂²×D₇₉

Fitting

C₂²×C₃₂×C₇₉

C₂

socle, prime radical

C₂³×C₇₉

C₂×C₁₆

cosocle

C₂×C₁₆×C₇₉

C₂³

hypercenter

C₂²×C₃₂

D₇₉

hypocenter

C₇₉

C₂×C₄⋊C₃₂

LCS

G ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂²×C₁₆ ◁ C₂²×C₃₂

N	H ≅ G/N	type
3. Dic₇₉⋊C₃₂	C₂	direct (N × H)
48. C₂×Dic₇₉	C₃₂	semidirect
63. Dic₇₉	C₂×C₃₂	semidirect
65. C₂×C₇₉	C₄⋊C₃₂	semidirect
73. C₇₉	C₂×C₄⋊C₃₂	semidirect
133. C₂	Dic₇₉⋊C₃₂	direct (N × H)

H ≅ G/N

type

3. Dic₇₉⋊C₃₂

C₂

direct (N × H)

48. C₂×Dic₇₉

C₃₂

semidirect

63. Dic₇₉

C₂×C₃₂

semidirect

65. C₂×C₇₉

C₄⋊C₃₂

semidirect

73. C₇₉

C₂×C₄⋊C₃₂

semidirect

133. C₂

Dic₇₉⋊C₃₂

direct (N × H)

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₇₉⋊C₃₂	2
C₂×C₁₆×Dic₇₉	2
Dic₇₉⋊C₃₂	2
C₂²×C₃₂×C₇₉	2
C₂×C₄⋊C₃₂	79

subgroup

index

C₂²×C₇₉⋊C₃₂

C₂×C₁₆×Dic₇₉

Dic₇₉⋊C₃₂

C₂²×C₃₂×C₇₉

C₂×C₄⋊C₃₂

Subgroups — C₂×Dic₇₉⋊C₃₂ #34208748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×Dic79⋊C32 #34208748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₇₉⋊C₃₂ #34208748