Group #20240795 — subgroups

Subgroups — C₄₇×#3185 #20240795

Order 6016.

358 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 184 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	C₄₇×#533	C₂	1	2	yes	maximal
2	C₄₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#494	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#487	C₂	1	2	yes	maximal, complemented
5	C₄₇×#470	C₂	1	4	yes	maximal
6	C₄₇×#441	C₂	1	4	yes	maximal, complemented
7	C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂×Q₁₆×C₄₇	C₂²	1	4	yes	—
9	C₂×M₁₆×C₄₇	C₂²	1	2	yes	—
10	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
11	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
12	#125×C₄₇	—	2	2	no	—
13	C₂²⋊Q₈×C₄₇	—	2	2	no	—
14	C₂²⋊Q₈×C₄₇	C₂²	1	4	yes	—
15	C₄×Q₈×C₄₇	—	2	2	no	—
16	C₄×Q₈×C₄₇	C₂²	1	4	yes	—
17	#117×C₄₇	—	2	2	no	—
18	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	#106×C₄₇	C₂²	1	4	yes	—
20	#103×C₄₇	C₂²	1	8	yes	—
21	#97×C₄₇	C₂²	1	2	yes	—
22	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×Q₈×C₄₇	—	2	2	no	—
25	C₂×Q₈×C₄₇	C₂³	1	4	yes	—
26	C₂²×C₄×C₄₇	D₄	1	2	yes	—
27	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
28	Q₁₆×C₄₇	—	2	8	no	—
29	M₁₆×C₄₇	—	2	4	no	—
30	C₂×C₈×C₄₇	C₂³	1	2	yes	—
31	C₂×C₈×C₄₇	C₂³	1	2	yes	—
32	C₄⋊C₄×C₄₇	—	2	2	no	—
33	C₄⋊C₄×C₄₇	—	2	2	no	—
34	C₄⋊C₄×C₄₇	—	2	2	no	—
35	C₄⋊C₄×C₄₇	—	2	4	no	—
36	C₄⋊C₄×C₄₇	—	2	4	no	—
37	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
38	C₂²⋊C₄×C₄₇	—	2	4	no	—
39	C₄²×C₄₇	—	2	4	no	—
40	C₄²×C₄₇	D₄	1	2	yes	—
41	C₄²×C₄₇	C₂³	1	1	yes	characteristic
42	C₄²×C₄₇	C₂³	1	1	yes	characteristic
43	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
44	Q₈×C₄₇	—	2	8	no	—
45	Q₈×C₄₇	—	4	4	no	—
46	C₂×C₄×C₄₇	—	2	4	no	—
47	C₂×C₄×C₄₇	—	2	2	no	—
48	C₂×C₄×C₄₇	—	2	4	no	—
49	C₂×C₄×C₄₇	—	2	4	no	—
50	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
51	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
52	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
53	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
54	C₈×C₄₇	—	2	2	no	—
55	C₈×C₄₇	#41	1	4	yes	—
56	C₂²×C₄₇	—	2	1	no	—
57	C₂²×C₄₇	—	2	2	no	—
58	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
59	C₄×C₄₇	—	2	1	no	—
60	C₄×C₄₇	—	2	2	no	—
61	C₄×C₄₇	—	4	4	no	—
62	C₄×C₄₇	—	4	4	no	—
63	C₄×C₄₇	#137	1	4	yes	—
64	C₄×C₄₇	C₂×#41	1	2	yes	—
65	#3185	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂×C₄₇	—	4	1	no	—
67	C₂×C₄₇	#532	1	1	yes	characteristic
68	C₂×C₄₇	C₂×#137	1	2	yes	—
69	#533	C₂×C₄₇	1	2	yes	—
70	#498	C₂×C₄₇	1	1	yes	characteristic, complemented
71	#494	C₂×C₄₇	1	1	yes	characteristic, complemented
72	#487	C₂×C₄₇	1	2	yes	complemented
73	#470	C₂×C₄₇	1	4	yes	—
74	#441	C₂×C₄₇	1	4	yes	complemented
75	C₄×M₁₆	C₂×C₄₇	1	1	yes	characteristic
76	C₄₇	#3185	1	1	yes	characteristic, direct product factor, Sylow
77	C₂×Q₁₆	C₂²×C₄₇	1	4	yes	—
78	C₂×M₁₆	C₂²×C₄₇	1	2	yes	—
79	C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
80	C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
81	#125	—	2	2	no	—
82	C₂²⋊Q₈	—	2	2	no	—
83	C₂²⋊Q₈	C₂²×C₄₇	1	4	yes	—
84	C₄×Q₈	—	2	2	no	—
85	C₄×Q₈	C₂²×C₄₇	1	4	yes	—
86	#117	—	2	2	no	—
87	C₂×C₄²	C₂²×C₄₇	1	1	yes	characteristic
88	#106	C₂²×C₄₇	1	4	yes	—
89	#103	C₂²×C₄₇	1	8	yes	—
90	#97	C₂²×C₄₇	1	2	yes	—
91	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
92	C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
93	C₂×Q₈	—	2	2	no	—
94	C₂×Q₈	C₂³×C₄₇	1	4	yes	—
95	C₂²×C₄	D₄×C₄₇	1	2	yes	—
96	C₂²×C₄	C₂³×C₄₇	1	1	yes	characteristic
97	Q₁₆	—	2	8	no	—
98	M₁₆	—	2	4	no	—
99	C₂×C₈	C₂³×C₄₇	1	2	yes	—
100	C₂×C₈	C₂³×C₄₇	1	2	yes	—
101	C₄⋊C₄	—	2	2	no	—
102	C₄⋊C₄	—	2	2	no	—
103	C₄⋊C₄	—	2	2	no	—
104	C₄⋊C₄	—	2	4	no	—
105	C₄⋊C₄	—	2	4	no	—
106	C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
107	C₂²⋊C₄	—	2	4	no	—
108	C₄²	—	2	4	no	—
109	C₄²	D₄×C₄₇	1	2	yes	—
110	C₄²	C₂³×C₄₇	1	1	yes	characteristic
111	C₄²	C₂³×C₄₇	1	1	yes	characteristic
112	C₂³	C₂×D₄×C₄₇	1	1	yes	characteristic
113	Q₈	—	2	8	no	—
114	Q₈	—	4	4	no	—
115	C₂×C₄	—	2	4	no	—
116	C₂×C₄	—	2	2	no	—
117	C₂×C₄	—	2	4	no	—
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	C₂×D₄×C₄₇	1	2	yes	—
120	C₂×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
121	C₂×C₄	C₂×D₄×C₄₇	1	2	yes	—
122	C₂×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
123	C₈	—	2	2	no	—
124	C₈	#41×C₄₇	1	4	yes	—
125	C₂²	—	2	1	no	—
126	C₂²	—	2	2	no	—
127	C₂²	C₂²×D₄×C₄₇	1	1	yes	characteristic
128	C₄	—	2	1	no	—
129	C₄	—	2	2	no	—
130	C₄	—	4	4	no	—
131	C₄	—	4	4	no	—
132	C₄	#137×C₄₇	1	4	yes	—
133	C₄	C₂×#41×C₄₇	1	2	yes	—
134	C₂	—	4	1	no	—
135	C₂	C₄₇×#532	1	1	yes	characteristic
136	C₂	C₂×#137×C₄₇	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄₇×#533

C₂

yes

maximal

C₄₇×#498

C₂

yes

maximal, characteristic, complemented

C₄₇×#494

C₂

yes

maximal, characteristic, complemented

C₄₇×#487

C₂

yes

maximal, complemented

C₄₇×#470

C₂

yes

maximal

C₄₇×#441

C₂

yes

maximal, complemented

C₄×M₁₆×C₄₇

C₂

yes

maximal, characteristic

C₂×Q₁₆×C₄₇

C₂²

yes

—

C₂×M₁₆×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

C₄⋊Q₈×C₄₇

C₂²

yes

—

#125×C₄₇

—

C₂²⋊Q₈×C₄₇

—

C₂²⋊Q₈×C₄₇

C₂²

yes

—

C₄×Q₈×C₄₇

—

C₄×Q₈×C₄₇

C₂²

yes

—

#117×C₄₇

—

C₂×C₄²×C₄₇

C₂²

yes

characteristic

#106×C₄₇

C₂²

yes

—

#103×C₄₇

C₂²

yes

—

#97×C₄₇

C₂²

yes

—

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₄×C₈×C₄₇

C₂²

yes

characteristic

C₂×Q₈×C₄₇

—

C₂×Q₈×C₄₇

C₂³

yes

—

C₂²×C₄×C₄₇

D₄

yes

—

C₂²×C₄×C₄₇

C₂³

yes

characteristic

Q₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

C₂³

yes

—

C₂×C₈×C₄₇

C₂³

yes

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

—

C₄⋊C₄×C₄₇

C₂³

yes

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

—

C₄²×C₄₇

D₄

yes

—

C₄²×C₄₇

C₂³

yes

characteristic

C₄²×C₄₇

C₂³

yes

characteristic

C₂³×C₄₇

C₂×D₄

yes

characteristic

Q₈×C₄₇

—

Q₈×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂×C₄×C₄₇

C₂×D₄

yes

—

C₂×C₄×C₄₇

C₂⁴

yes

characteristic

C₈×C₄₇

—

C₈×C₄₇

#41

yes

—

C₂²×C₄₇

—

C₂²×C₄₇

—

C₂²×C₄₇

C₂²×D₄

yes

characteristic

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

—

C₄×C₄₇

#137

yes

—

C₄×C₄₇

C₂×#41

yes

—

#3185

C₄₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄₇

—

C₂×C₄₇

#532

yes

characteristic

C₂×C₄₇

C₂×#137

yes

—

#533

C₂×C₄₇

yes

—

#498

C₂×C₄₇

yes

characteristic, complemented

#494

C₂×C₄₇

yes

characteristic, complemented

#487

C₂×C₄₇

yes

complemented

#470

C₂×C₄₇

yes

—

#441

C₂×C₄₇

yes

complemented

C₄×M₁₆

C₂×C₄₇

yes

characteristic

C₄₇

#3185

yes

characteristic, direct product factor, Sylow

C₂×Q₁₆

C₂²×C₄₇

yes

—

C₂×M₁₆

C₂²×C₄₇

yes

—

C₄⋊Q₈

C₂²×C₄₇

yes

—

C₄⋊Q₈

C₂²×C₄₇

yes

—

#125

—

C₂²⋊Q₈

—

C₂²⋊Q₈

C₂²×C₄₇

yes

—

C₄×Q₈

—

C₄×Q₈

C₂²×C₄₇

yes

—

#117

—

C₂×C₄²

C₂²×C₄₇

yes

characteristic

#106

C₂²×C₄₇

yes

—

#103

C₂²×C₄₇

yes

—

#97

C₂²×C₄₇

yes

—

C₄×C₈

C₂²×C₄₇

yes

characteristic

C₄×C₈

C₂²×C₄₇

yes

characteristic

C₂×Q₈

—

C₂×Q₈

C₂³×C₄₇

yes

—

C₂²×C₄

D₄×C₄₇

yes

—

C₂²×C₄

C₂³×C₄₇

yes

characteristic

Q₁₆

—

M₁₆

—

C₂×C₈

C₂³×C₄₇

yes

—

100

C₂×C₈

C₂³×C₄₇

yes

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄⋊C₄

—

104

C₄⋊C₄

—

105

C₄⋊C₄

—

106

C₄⋊C₄

C₂³×C₄₇

yes

—

107

C₂²⋊C₄

—

108

C₄²

—

109

C₄²

D₄×C₄₇

yes

—

110

C₄²

C₂³×C₄₇

yes

characteristic

111

C₄²

C₂³×C₄₇

yes

characteristic

112

C₂³

C₂×D₄×C₄₇

yes

characteristic

113

Q₈

—

114

Q₈

—

115

C₂×C₄

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

C₂×D₄×C₄₇

yes

—

120

C₂×C₄

C₂×D₄×C₄₇

yes

characteristic

121

C₂×C₄

C₂×D₄×C₄₇

yes

—

122

C₂×C₄

C₂⁴×C₄₇

yes

characteristic

123

C₈

—

124

C₈

#41×C₄₇

yes

—

125

C₂²

—

126

C₂²

—

127

C₂²

C₂²×D₄×C₄₇

yes

characteristic

128

C₄

—

129

C₄

—

130

C₄

—

131

C₄

—

132

C₄

#137×C₄₇

yes

—

133

C₄

C₂×#41×C₄₇

yes

—

134

C₂

—

135

C₂

C₄₇×#532

yes

characteristic

136

C₂

C₂×#137×C₄₇

yes

—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₄₇
prime radical	C₂³×C₄₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

subgroup

G/H

center, socle

C₂²×C₄₇

C₂²×D₄

commutator, Frattini, cosocle

C₂×C₄

C₂⁴×C₄₇

prime radical

C₂³×C₄₇

C₂×D₄

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

N	H ≅ G/N	type
2. C₄₇×#498	C₂	semidirect
3. C₄₇×#494	C₂	semidirect
4. C₄₇×#487	C₂	semidirect
6. C₄₇×#441	C₂	semidirect
65. #3185	C₄₇	direct (N × H)
70. #498	C₂×C₄₇	semidirect
71. #494	C₂×C₄₇	semidirect
72. #487	C₂×C₄₇	semidirect
74. #441	C₂×C₄₇	semidirect
76. C₄₇	#3185	direct (N × H)

H ≅ G/N

type

2. C₄₇×#498

C₂

semidirect

3. C₄₇×#494

C₂

semidirect

4. C₄₇×#487

C₂

semidirect

6. C₄₇×#441

C₂

semidirect

65. #3185

C₄₇

direct (N × H)

70. #498

C₂×C₄₇

semidirect

71. #494

C₂×C₄₇

semidirect

72. #487

C₂×C₄₇

semidirect

74. #441

C₂×C₄₇

semidirect

76. C₄₇

#3185

direct (N × H)

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

subgroup	index
C₄₇×#533	2
C₄₇×#498	2
C₄₇×#494	2
C₄₇×#487	2
C₄₇×#470	2
C₄₇×#441	2
C₄×M₁₆×C₄₇	2
#3185	47

subgroup

index

C₄₇×#533

C₄₇×#498

C₄₇×#494

C₄₇×#487

C₄₇×#470

C₄₇×#441

C₄×M₁₆×C₄₇

#3185

Subgroups — C₄₇×#3185 #20240795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C47×#3185 #20240795

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#3185 #20240795