Group #14545014 — subgroups

Subgroups — #14545014

Order 2176.

228 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 90 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	C₂×#10587538	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#63216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊#63216	C₂	1	4	yes	maximal, complemented
4	C₂×#10587634	C₂	1	1	yes	maximal, characteristic
5	C₂×#41×C₁₇	C₄	1	1	yes	characteristic
6	#10587634	—	2	2	no	—
7	#10587634	—	2	2	no	—
8	C₂×#63223	C₄	1	2	yes	—
9	C₂×#63223	C₄	1	1	yes	characteristic
10	C₂²×#3622	C₂²	1	2	yes	—
11	C₂²×#3622	C₂²	1	1	yes	characteristic
12	#10587538	—	2	2	no	—
13	C₂×#63216	—	2	2	no	—
14	C₂×#63216	C₂²	1	2	yes	—
15	C₂×#63216	C₂²	1	2	yes	—
16	#41×C₁₇	—	2	2	no	—
17	#41×C₁₇	—	2	2	no	—
18	C₂×Q₈×C₁₇	C₈	1	1	yes	characteristic
19	C₂×D₄×C₁₇	C₈	1	2	yes	—
20	C₂×D₄×C₁₇	C₈	1	1	yes	characteristic
21	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
23	#63223	—	2	2	no	—
24	#63223	—	2	4	no	—
25	C₂×#3622	—	2	2	no	—
26	C₂×#3622	—	2	2	no	—
27	C₂×#3622	C₂×C₄	1	2	yes	—
28	C₂×#3622	C₂×C₄	1	1	yes	characteristic
29	C₂×#3622	D₄	1	2	yes	—
30	C₂×#3622	D₄	1	2	yes	—
31	C₂×#3622	C₂³	1	1	yes	characteristic
32	#63216	—	2	2	no	—
33	#63216	—	2	2	no	—
34	C₂³×C₁₇	C₂×C₈	1	2	yes	—
35	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
36	Q₈×C₁₇	—	2	2	no	—
37	D₄×C₁₇	—	2	4	no	—
38	D₄×C₁₇	—	2	2	no	—
39	C₂×C₄×C₁₇	—	2	2	no	—
40	C₂×C₄×C₁₇	—	2	2	no	—
41	C₂×C₄×C₁₇	C₂²⋊C₄	1	2	yes	—
42	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
43	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
44	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
45	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
46	#3622	—	2	2	no	—
47	#3622	C₂²⋊C₄	1	2	yes	—
48	#3622	C₂×D₄	1	1	yes	characteristic
49	#3622	C₂×D₄	1	1	yes	characteristic
50	#2113	—	17	1	no	maximal, Sylow
51	C₂²×C₁₇	—	2	2	no	—
52	C₂²×C₁₇	—	2	2	no	—
53	C₂²×C₁₇	—	2	4	no	—
54	C₂²×C₁₇	C₂²⋊C₈	1	2	yes	—
55	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
56	C₄×C₁₇	—	2	2	no	—
57	C₄×C₁₇	C₂²⋊C₈	1	2	yes	—
58	C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
60	C₂×#131	—	17	1	no	—
61	C₂×M₃₂	—	17	1	no	—
62	C₂²×C₁₆	—	17	1	no	—
63	C₂²⋊C₁₆	—	17	4	no	—
64	C₂×C₁₇	—	2	2	no	—
65	C₂×C₁₇	—	4	2	no	—
66	C₂×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
67	C₂×C₁₇	#504	1	2	yes	—
68	C₂×#41	#595	1	1	yes	characteristic
69	#131	—	34	2	no	—
70	#131	—	34	2	no	—
71	C₂×M₁₆	—	17	2	no	—
72	C₂×M₁₆	—	17	1	no	—
73	C₂²×C₈	—	17	1	no	—
74	C₂²×C₈	—	17	2	no	—
75	M₃₂	—	34	2	no	—
76	C₂×C₁₆	—	17	2	no	—
77	C₂×C₁₆	—	17	2	no	—
78	C₂×C₁₆	—	34	2	no	—
79	C₁₇	#2113	1	1	yes	characteristic, complemented, Sylow
80	#41	—	2	2	no	—
81	#41	—	2	2	no	—
82	C₂×Q₈	#3624	1	1	yes	characteristic
83	C₂×D₄	#3624	1	2	yes	—
84	C₂×D₄	#3624	1	1	yes	characteristic
85	C₂²×C₄	C₂×#595	1	2	yes	—
86	C₂²×C₄	C₂×#595	1	1	yes	characteristic
87	M₁₆	—	34	4	no	—
88	M₁₆	—	34	2	no	—
89	C₂×C₈	—	17	2	no	—
90	C₂×C₈	—	17	2	no	—
91	C₂×C₈	—	17	1	no	—
92	C₂×C₈	—	17	1	no	—
93	C₂×C₈	—	17	2	no	—
94	C₂×C₈	—	34	2	no	—
95	C₂×C₈	—	34	2	no	—
96	C₁₆	—	34	2	no	—
97	C₁₆	—	34	2	no	—
98	C₂³	C₂×#3624	1	2	yes	—
99	C₂³	C₂×#3624	1	1	yes	characteristic
100	Q₈	—	2	2	no	—
101	D₄	—	2	4	no	—
102	D₄	—	2	2	no	—
103	C₂×C₄	—	2	2	no	—
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₂×#3624	1	2	yes	—
106	C₂×C₄	C₂×#3624	1	1	yes	characteristic
107	C₂×C₄	#63247	1	2	yes	—
108	C₂×C₄	C₂²⋊#595	1	2	yes	—
109	C₂×C₄	C₂²×#595	1	1	yes	characteristic
110	C₈	—	17	1	no	—
111	C₈	—	17	1	no	—
112	C₈	—	17	2	no	—
113	C₈	—	34	2	no	—
114	C₂²	—	2	2	no	—
115	C₂²	—	2	2	no	—
116	C₂²	—	2	4	no	—
117	C₂²	C₂²⋊#3624	1	2	yes	—
118	C₂²	C₂²×#3624	1	1	yes	characteristic
119	C₄	—	2	2	no	—
120	C₄	C₂²⋊#3624	1	2	yes	—
121	C₄	C₂×#63247	1	1	yes	characteristic
122	C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
123	C₂	—	2	2	no	—
124	C₂	—	4	2	no	—
125	C₂	C₂×C₂²⋊#3624	1	1	yes	characteristic
126	C₂	#11763867	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587538

C₂

yes

maximal, characteristic, complemented

C₂²×#63216

C₂

yes

maximal, characteristic, complemented

C₂²⋊#63216

C₂

yes

maximal, complemented

C₂×#10587634

C₂

yes

maximal, characteristic

C₂×#41×C₁₇

C₄

yes

—

—

C₄

yes

—

C₂×#63223

C₄

yes

characteristic

C₂²×#3622

C₂²

yes

—

C₂²×#3622

C₂²

yes

—

—

C₂²

yes

—

C₂×#63216

C₂²

yes

—

#41×C₁₇

—

#41×C₁₇

—

C₂×Q₈×C₁₇

C₈

yes

characteristic

C₂×D₄×C₁₇

C₈

yes

—

C₂×D₄×C₁₇

C₈

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

D₄

yes

—

C₂×#3622

D₄

yes

—

C₂×#3622

C₂³

yes

characteristic

#63216

—

#63216

—

C₂³×C₁₇

C₂×C₈

yes

—

C₂³×C₁₇

C₂×C₈

yes

characteristic

Q₈×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

#3622

—

#3622

C₂²⋊C₄

yes

—

#3622

C₂×D₄

yes

characteristic

#3622

C₂×D₄

yes

characteristic

#2113

—

maximal, Sylow

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂²⋊C₈

yes

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

C₂²⋊C₈

yes

—

C₄×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

C₂×#131

—

C₂×M₃₂

—

C₂²×C₁₆

—

C₂²⋊C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₁₇

#504

yes

—

C₂×#41

yes

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₂²×C₈

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₁₇

#2113

yes

characteristic, complemented, Sylow

#41

—

#41

—

C₂×Q₈

#3624

yes

characteristic

C₂×D₄

#3624

yes

—

C₂×D₄

#3624

yes

characteristic

C₂²×C₄

C₂×#595

yes

—

C₂²×C₄

C₂×#595

yes

characteristic

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₁₆

—

C₁₆

—

C₂³

C₂×#3624

yes

—

C₂³

C₂×#3624

yes

characteristic

100

Q₈

—

101

D₄

—

102

D₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₂×#3624

yes

—

106

C₂×C₄

C₂×#3624

yes

characteristic

107

C₂×C₄

#63247

yes

—

108

C₂×C₄

C₂²⋊#595

yes

—

109

C₂×C₄

C₂²×#595

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₈

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

C₂²⋊#3624

yes

—

118

C₂²

C₂²×#3624

yes

characteristic

119

C₄

—

120

C₄

C₂²⋊#3624

yes

—

121

C₄

C₂×#63247

yes

characteristic

122

C₄

C₂×C₂²⋊#595

yes

characteristic

123

C₂

—

124

C₂

—

125

C₂

C₂×C₂²⋊#3624

yes

characteristic

126

C₂

#11763867

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting, prime radical	C₂×#41×C₁₇	C₄
cosocle	C₂×#3622	C₂³
hypercenter	C₂×#41	#595
hypocenter	C₁₇	#2113
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂²×C₈

Fitting, prime radical

C₂×#41×C₁₇

C₄

C₂³

C₂×#41

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₂×#41

N	H ≅ G/N	type
1. C₂×#10587538	C₂	semidirect
2. C₂²×#63216	C₂	semidirect
3. C₂²⋊#63216	C₂	semidirect
79. C₁₇	#2113	semidirect

H ≅ G/N

type

1. C₂×#10587538

C₂

semidirect

2. C₂²×#63216

C₂

semidirect

3. C₂²⋊#63216

C₂

semidirect

79. C₁₇

#2113

semidirect

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

subgroup	index
C₂×#10587538	2
C₂²×#63216	2
C₂²⋊#63216	2
C₂×#10587634	2
#2113	17

subgroup

index

C₂²×#63216

Subgroups — #14545014

Conjugacy classes of subgroups

Complements

Maximal subgroups