Group #49154875 — subgroups

Subgroups — #1868×C₂₉₃ #49154875

Order 37504.

260 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 108 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	#568×C₂₉₃	C₂	1	1	yes	maximal, characteristic
2	#424×C₂₉₃	C₂	1	2	yes	maximal, complemented
3	#410×C₂₉₃	C₂	1	1	yes	maximal, characteristic
4	#408×C₂₉₃	C₂	1	1	yes	maximal, characteristic
5	#344×C₂₉₃	C₂	1	2	yes	maximal, complemented
6	C₂×#41×C₂₉₃	C₂²	1	1	yes	characteristic
7	#131×C₂₉₃	—	2	4	no	—
8	C₂×M₁₆×C₂₉₃	—	2	2	no	—
9	C₂×M₁₆×C₂₉₃	C₂²	1	1	yes	characteristic
10	C₂×M₁₆×C₂₉₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₂₉₃	C₂²	1	1	yes	characteristic
12	#117×C₂₉₃	C₂²	1	2	yes	—
13	C₄⋊C₈×C₂₉₃	—	2	4	no	—
14	#99×C₂₉₃	C₄	1	4	yes	—
15	C₂²⋊C₈×C₂₉₃	—	2	2	no	—
16	#41×C₂₉₃	—	2	2	no	—
17	#41×C₂₉₃	—	2	2	no	—
18	C₂×Q₈×C₂₉₃	Q₈	1	1	yes	characteristic
19	C₂×D₄×C₂₉₃	C₂×C₄	1	2	yes	—
20	C₂×D₄×C₂₉₃	Q₈	1	1	yes	characteristic
21	C₂²×C₄×C₂₉₃	D₄	1	2	yes	—
22	C₂²×C₄×C₂₉₃	C₂³	1	1	yes	characteristic
23	M₁₆×C₂₉₃	—	2	4	no	—
24	M₁₆×C₂₉₃	—	2	2	no	—
25	M₁₆×C₂₉₃	—	2	2	no	—
26	M₁₆×C₂₉₃	—	2	2	no	—
27	C₂×C₈×C₂₉₃	—	2	4	no	—
28	C₂×C₈×C₂₉₃	—	2	1	no	—
29	C₂×C₈×C₂₉₃	—	2	1	no	—
30	C₂×C₈×C₂₉₃	—	2	2	no	—
31	C₂×C₈×C₂₉₃	D₄	1	4	yes	—
32	C₄⋊C₄×C₂₉₃	—	2	2	no	—
33	C₂²⋊C₄×C₂₉₃	C₂×C₄	1	4	yes	—
34	C₄²×C₂₉₃	—	2	2	no	—
35	C₂³×C₂₉₃	C₄⋊C₄	1	2	yes	—
36	C₂³×C₂₉₃	C₂²×C₄	1	1	yes	characteristic
37	Q₈×C₂₉₃	—	2	2	no	—
38	D₄×C₂₉₃	—	2	4	no	—
39	D₄×C₂₉₃	—	2	2	no	—
40	C₂×C₄×C₂₉₃	—	2	2	no	—
41	C₂×C₄×C₂₉₃	—	2	2	no	—
42	C₂×C₄×C₂₉₃	—	2	4	no	—
43	C₂×C₄×C₂₉₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₄×C₂₉₃	C₂×D₄	1	2	yes	—
45	C₂×C₄×C₂₉₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₄×C₂₉₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₄×C₂₉₃	#41	1	2	yes	—
48	C₈×C₂₉₃	—	2	4	no	—
49	C₈×C₂₉₃	—	4	1	no	—
50	C₈×C₂₉₃	—	4	1	no	—
51	C₂²×C₂₉₃	—	2	2	no	—
52	C₂²×C₂₉₃	—	4	1	no	—
53	C₂²×C₂₉₃	—	4	2	no	—
54	C₂²×C₂₉₃	C₂×C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₂₉₃	C₄×D₄	1	2	yes	—
56	C₄×C₂₉₃	—	2	2	no	—
57	C₄×C₂₉₃	—	4	4	no	—
58	C₄×C₂₉₃	#120	1	1	yes	characteristic
59	C₄×C₂₉₃	C₂²⋊Q₈	1	2	yes	—
60	C₄×C₂₉₃	#123	1	1	yes	characteristic
61	C₂×C₂₉₃	—	2	2	no	—
62	C₂×C₂₉₃	—	2	1	no	—
63	C₂×C₂₉₃	—	4	2	no	—
64	C₂×C₂₉₃	#385	1	1	yes	characteristic
65	C₂₉₃	#1868	1	1	yes	characteristic, direct product factor, Sylow
66	#1868	C₂₉₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
67	#568	C₂×C₂₉₃	1	1	yes	characteristic
68	#424	C₂×C₂₉₃	1	2	yes	complemented
69	#410	C₂×C₂₉₃	1	1	yes	characteristic
70	#408	C₂×C₂₉₃	1	1	yes	characteristic
71	#344	C₂×C₂₉₃	1	2	yes	complemented
72	C₂×#41	C₂²×C₂₉₃	1	1	yes	characteristic
73	#131	—	2	4	no	—
74	C₂×M₁₆	—	2	2	no	—
75	C₂×M₁₆	C₂²×C₂₉₃	1	1	yes	characteristic
76	C₂×M₁₆	C₂²×C₂₉₃	1	2	yes	—
77	C₂²×C₈	C₂²×C₂₉₃	1	1	yes	characteristic
78	#117	C₂²×C₂₉₃	1	2	yes	—
79	C₄⋊C₈	—	2	4	no	—
80	#99	C₄×C₂₉₃	1	4	yes	—
81	C₂²⋊C₈	—	2	2	no	—
82	#41	—	2	2	no	—
83	#41	—	2	2	no	—
84	C₂×Q₈	Q₈×C₂₉₃	1	1	yes	characteristic
85	C₂×D₄	C₂×C₄×C₂₉₃	1	2	yes	—
86	C₂×D₄	Q₈×C₂₉₃	1	1	yes	characteristic
87	C₂²×C₄	D₄×C₂₉₃	1	2	yes	—
88	C₂²×C₄	C₂³×C₂₉₃	1	1	yes	characteristic
89	M₁₆	—	2	4	no	—
90	M₁₆	—	2	2	no	—
91	M₁₆	—	2	2	no	—
92	M₁₆	—	2	2	no	—
93	C₂×C₈	—	2	4	no	—
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	—	2	2	no	—
97	C₂×C₈	D₄×C₂₉₃	1	4	yes	—
98	C₄⋊C₄	—	2	2	no	—
99	C₂²⋊C₄	C₂×C₄×C₂₉₃	1	4	yes	—
100	C₄²	—	2	2	no	—
101	C₂³	C₄⋊C₄×C₂₉₃	1	2	yes	—
102	C₂³	C₂²×C₄×C₂₉₃	1	1	yes	characteristic
103	Q₈	—	2	2	no	—
104	D₄	—	2	4	no	—
105	D₄	—	2	2	no	—
106	C₂×C₄	—	2	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	2	4	no	—
109	C₂×C₄	C₄⋊C₄×C₂₉₃	1	2	yes	—
110	C₂×C₄	C₂×D₄×C₂₉₃	1	2	yes	—
111	C₂×C₄	C₂×D₄×C₂₉₃	1	1	yes	characteristic
112	C₂×C₄	C₂×Q₈×C₂₉₃	1	1	yes	characteristic
113	C₂×C₄	#41×C₂₉₃	1	2	yes	—
114	C₈	—	2	4	no	—
115	C₈	—	4	1	no	—
116	C₈	—	4	1	no	—
117	C₂²	—	2	2	no	—
118	C₂²	—	4	1	no	—
119	C₂²	—	4	2	no	—
120	C₂²	C₂×C₄⋊C₄×C₂₉₃	1	1	yes	characteristic
121	C₂²	C₄×D₄×C₂₉₃	1	2	yes	—
122	C₄	—	2	2	no	—
123	C₄	—	4	4	no	—
124	C₄	#120×C₂₉₃	1	1	yes	characteristic
125	C₄	C₂²⋊Q₈×C₂₉₃	1	2	yes	—
126	C₄	#123×C₂₉₃	1	1	yes	characteristic
127	C₂	—	2	2	no	—
128	C₂	—	2	1	no	—
129	C₂	—	4	2	no	—
130	C₂	#385×C₂₉₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#568×C₂₉₃

C₂

yes

maximal, characteristic

#424×C₂₉₃

C₂

yes

maximal, complemented

#410×C₂₉₃

C₂

yes

maximal, characteristic

#408×C₂₉₃

C₂

yes

maximal, characteristic

#344×C₂₉₃

C₂

yes

maximal, complemented

C₂×#41×C₂₉₃

C₂²

yes

characteristic

#131×C₂₉₃

—

C₂×M₁₆×C₂₉₃

—

C₂×M₁₆×C₂₉₃

C₂²

yes

characteristic

C₂×M₁₆×C₂₉₃

C₂²

yes

—

C₂²×C₈×C₂₉₃

C₂²

yes

characteristic

#117×C₂₉₃

C₂²

yes

—

C₄⋊C₈×C₂₉₃

—

#99×C₂₉₃

C₄

yes

—

C₂²⋊C₈×C₂₉₃

—

#41×C₂₉₃

—

#41×C₂₉₃

—

C₂×Q₈×C₂₉₃

Q₈

yes

characteristic

C₂×D₄×C₂₉₃

C₂×C₄

yes

—

C₂×D₄×C₂₉₃

Q₈

yes

characteristic

C₂²×C₄×C₂₉₃

D₄

yes

—

C₂²×C₄×C₂₉₃

C₂³

yes

characteristic

M₁₆×C₂₉₃

—

M₁₆×C₂₉₃

—

M₁₆×C₂₉₃

—

M₁₆×C₂₉₃

—

C₂×C₈×C₂₉₃

—

C₂×C₈×C₂₉₃

—

C₂×C₈×C₂₉₃

—

C₂×C₈×C₂₉₃

—

C₂×C₈×C₂₉₃

D₄

yes

—

C₄⋊C₄×C₂₉₃

—

C₂²⋊C₄×C₂₉₃

C₂×C₄

yes

—

C₄²×C₂₉₃

—

C₂³×C₂₉₃

C₄⋊C₄

yes

—

C₂³×C₂₉₃

C₂²×C₄

yes

characteristic

Q₈×C₂₉₃

—

D₄×C₂₉₃

—

D₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

—

C₂×C₄×C₂₉₃

C₄⋊C₄

yes

—

C₂×C₄×C₂₉₃

C₂×D₄

yes

—

C₂×C₄×C₂₉₃

C₂×D₄

yes

characteristic

C₂×C₄×C₂₉₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₉₃

#41

yes

—

C₈×C₂₉₃

—

C₈×C₂₉₃

—

C₈×C₂₉₃

—

C₂²×C₂₉₃

—

C₂²×C₂₉₃

—

C₂²×C₂₉₃

—

C₂²×C₂₉₃

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₂₉₃

C₄×D₄

yes

—

C₄×C₂₉₃

—

C₄×C₂₉₃

—

C₄×C₂₉₃

#120

yes

characteristic

C₄×C₂₉₃

C₂²⋊Q₈

yes

—

C₄×C₂₉₃

#123

yes

characteristic

C₂×C₂₉₃

—

C₂×C₂₉₃

—

C₂×C₂₉₃

—

C₂×C₂₉₃

#385

yes

characteristic

C₂₉₃

#1868

yes

characteristic, direct product factor, Sylow

#1868

C₂₉₃

yes

maximal, characteristic, direct product factor, Sylow

#568

C₂×C₂₉₃

yes

characteristic

#424

C₂×C₂₉₃

yes

complemented

#410

C₂×C₂₉₃

yes

characteristic

#408

C₂×C₂₉₃

yes

characteristic

#344

C₂×C₂₉₃

yes

complemented

C₂×#41

C₂²×C₂₉₃

yes

characteristic

#131

—

C₂×M₁₆

—

C₂×M₁₆

C₂²×C₂₉₃

yes

characteristic

C₂×M₁₆

C₂²×C₂₉₃

yes

—

C₂²×C₈

C₂²×C₂₉₃

yes

characteristic

#117

C₂²×C₂₉₃

yes

—

C₄⋊C₈

—

#99

C₄×C₂₉₃

yes

—

C₂²⋊C₈

—

#41

—

#41

—

C₂×Q₈

Q₈×C₂₉₃

yes

characteristic

C₂×D₄

C₂×C₄×C₂₉₃

yes

—

C₂×D₄

Q₈×C₂₉₃

yes

characteristic

C₂²×C₄

D₄×C₂₉₃

yes

—

C₂²×C₄

C₂³×C₂₉₃

yes

characteristic

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₂₉₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

C₂×C₄×C₂₉₃

yes

—

100

C₄²

—

101

C₂³

C₄⋊C₄×C₂₉₃

yes

—

102

C₂³

C₂²×C₄×C₂₉₃

yes

characteristic

103

Q₈

—

104

D₄

—

105

D₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

C₄⋊C₄×C₂₉₃

yes

—

110

C₂×C₄

C₂×D₄×C₂₉₃

yes

—

111

C₂×C₄

C₂×D₄×C₂₉₃

yes

characteristic

112

C₂×C₄

C₂×Q₈×C₂₉₃

yes

characteristic

113

C₂×C₄

#41×C₂₉₃

yes

—

114

C₈

—

115

C₈

—

116

C₈

—

117

C₂²

—

118

C₂²

—

119

C₂²

—

120

C₂²

C₂×C₄⋊C₄×C₂₉₃

yes

characteristic

121

C₂²

C₄×D₄×C₂₉₃

yes

—

122

C₄

—

123

C₄

—

124

C₄

#120×C₂₉₃

yes

characteristic

125

C₄

C₂²⋊Q₈×C₂₉₃

yes

—

126

C₄

#123×C₂₉₃

yes

characteristic

127

C₂

—

128

C₂

—

129

C₂

—

130

C₂

#385×C₂₉₃

yes

characteristic

	subgroup	G/H
center	C₄×C₂₉₃	#120
commutator	C₂³	C₂²×C₄×C₂₉₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉₃
socle	C₂×C₂₉₃	#385
prime radical	C₂×#41×C₂₉₃	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉₃ ◁ C₂²×C₄×C₂₉₃ ◁ G

subgroup

G/H

center

C₄×C₂₉₃

#120

commutator

C₂³

C₂²×C₄×C₂₉₃

Frattini, cosocle

C₂²×C₄

C₂³×C₂₉₃

socle

C₂×C₂₉₃

#385

prime radical

C₂×#41×C₂₉₃

C₂²

LCS

G ▷ C₂³ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₄×C₂₉₃ ◁ C₂²×C₄×C₂₉₃ ◁ G

N	H ≅ G/N	type
2. #424×C₂₉₃	C₂	semidirect
5. #344×C₂₉₃	C₂	semidirect
65. C₂₉₃	#1868	direct (N × H)
66. #1868	C₂₉₃	direct (N × H)
68. #424	C₂×C₂₉₃	semidirect
71. #344	C₂×C₂₉₃	semidirect

H ≅ G/N

type

2. #424×C₂₉₃

C₂

semidirect

5. #344×C₂₉₃

C₂

semidirect

65. C₂₉₃

#1868

direct (N × H)

66. #1868

C₂₉₃

direct (N × H)

68. #424

C₂×C₂₉₃

semidirect

71. #344

C₂×C₂₉₃

semidirect

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

subgroup	index
#568×C₂₉₃	2
#424×C₂₉₃	2
#410×C₂₉₃	2
#408×C₂₉₃	2
#344×C₂₉₃	2
#1868	293

subgroup

index

#568×C₂₉₃

#424×C₂₉₃

#410×C₂₉₃

#408×C₂₉₃

#344×C₂₉₃

#1868

293

Subgroups — #1868×C₂₉₃ #49154875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1868×C293 #49154875

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1868×C₂₉₃ #49154875