Group #17960659 — subgroups

Subgroups — #17960659

Order 4352.

358 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 168 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×#11763697	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#63216	C₂	1	1	yes	maximal, characteristic
3	#14543822	C₂	1	4	yes	maximal
4	#14528471	C₂	1	1	yes	maximal, characteristic
5	C₂²×#63216	C₂²	1	2	yes	—
6	C₂²×#63216	C₂²	1	2	yes	—
7	#11763697	C₄	1	4	yes	complemented
8	C₄×#63216	C₄	1	4	yes	complemented
9	C₂×#10587474	C₄	1	2	yes	—
10	C₂×#10587474	C₄	1	1	yes	characteristic
11	C₂×C₄×#3622	C₂²	1	2	yes	—
12	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
13	C₁₇×#376	C₄	1	1	yes	characteristic
14	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
15	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂²×#3622	C₂×C₄	1	2	yes	—
17	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
18	C₂²×#3622	C₂³	1	1	yes	characteristic
19	C₂×#63216	—	2	4	no	—
20	C₂×#63216	—	2	4	no	—
21	C₂×#63216	C₂×C₄	1	4	yes	—
22	C₂×#63216	C₂×C₄	1	4	yes	—
23	C₁₇×#95	C₈	1	4	yes	—
24	#10587474	—	2	4	no	—
25	#10587474	C₈	1	4	yes	—
26	C₄×#3622	—	2	4	no	—
27	C₄×#3622	C₂×C₄	1	2	yes	—
28	C₄×#3622	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₁₇	C₂×C₈	1	4	yes	—
30	C₂²×C₄×C₁₇	C₂×C₈	1	2	yes	—
31	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₄²×C₁₇	—	2	2	no	—
33	C₄²×C₁₇	—	2	2	no	—
34	C₄²×C₁₇	C₄²	1	2	yes	—
35	C₄²×C₁₇	C₂×C₈	1	2	yes	—
36	C₂×#3622	—	2	2	no	—
37	C₂×#3622	—	2	2	no	—
38	C₂×#3622	C₄²	1	2	yes	—
39	C₂×#3622	C₂×C₈	1	4	yes	—
40	C₂×#3622	M₁₆	1	4	yes	—
41	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
42	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
43	C₂×#3622	#41	1	4	yes	—
44	#63216	—	2	4	no	—
45	#63216	—	2	4	no	—
46	#12592	—	17	1	no	maximal, Sylow
47	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₇	—	2	4	no	—
49	C₂×C₄×C₁₇	—	2	4	no	—
50	C₂×C₄×C₁₇	—	2	8	no	—
51	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
52	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
53	C₂×C₄×C₁₇	#117	1	2	yes	—
54	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
56	#3622	—	2	4	no	—
57	#3622	#97	1	4	yes	—
58	#3622	#117	1	2	yes	—
59	#3622	#117	1	2	yes	—
60	C₂×#346	—	17	1	no	—
61	C₂×C₄×C₁₆	—	17	1	no	—
62	#1726	—	17	1	no	—
63	#1374	—	17	4	no	—
64	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
65	C₂²×C₁₇	#431	1	2	yes	—
66	C₂²×C₁₇	#504	1	4	yes	—
67	C₄×C₁₇	—	2	4	no	—
68	C₄×C₁₇	—	4	4	no	—
69	C₄×C₁₇	#376	1	1	yes	characteristic
70	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
71	C₄×C₁₇	#431	1	2	yes	—
72	C₂²×C₁₆	—	17	2	no	—
73	C₂²×C₁₆	—	17	2	no	—
74	C₂×#97	—	17	1	no	—
75	C₂×#97	—	17	2	no	—
76	C₂×C₄×C₈	—	17	1	no	—
77	C₂×C₄×C₈	—	17	2	no	—
78	#376	#595	1	1	yes	characteristic
79	#346	—	17	4	no	—
80	C₄×C₁₆	—	17	4	no	—
81	C₂×C₁₇	#1744	1	1	yes	characteristic
82	C₂×C₁₇	#2108	1	2	yes	—
83	C₂×C₁₇	#2164	1	4	yes	—
84	C₂²×C₈	—	17	1	no	—
85	C₂²×C₈	—	17	1	no	—
86	C₂²×C₈	—	17	2	no	—
87	C₂×C₄²	C₂×#595	1	2	yes	—
88	C₂×C₄²	C₂×#595	1	1	yes	characteristic
89	C₂×C₁₆	—	17	4	no	—
90	C₂×C₁₆	—	17	4	no	—
91	C₂×C₁₆	—	34	4	no	—
92	C₂×C₁₆	—	34	4	no	—
93	#97	—	17	4	no	—
94	#97	—	34	4	no	—
95	C₄×C₈	—	17	2	no	—
96	C₄×C₈	—	17	2	no	—
97	C₄×C₈	—	34	4	no	—
98	#95	#3624	1	4	yes	—
99	C₁₇	#12592	1	1	yes	characteristic, complemented, Sylow
100	C₂²×C₄	C₂×#3624	1	4	yes	—
101	C₂²×C₄	C₂×#3624	1	2	yes	—
102	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
103	C₂×C₈	—	17	4	no	—
104	C₂×C₈	—	17	1	no	—
105	C₂×C₈	—	17	1	no	—
106	C₂×C₈	—	17	2	no	—
107	C₂×C₈	—	17	4	no	—
108	C₂×C₈	—	17	4	no	—
109	C₂×C₈	—	34	2	no	—
110	C₂×C₈	—	34	2	no	—
111	C₄²	—	2	2	no	—
112	C₄²	—	2	2	no	—
113	C₄²	#63242	1	2	yes	—
114	C₄²	C₄×#595	1	2	yes	—
115	C₁₆	—	34	4	no	—
116	C₁₆	—	34	4	no	—
117	C₂³	C₂²×#3624	1	1	yes	characteristic
118	C₂×C₄	—	2	4	no	—
119	C₂×C₄	—	2	4	no	—
120	C₂×C₄	—	2	8	no	—
121	C₂×C₄	C₄×#3624	1	4	yes	—
122	C₂×C₄	C₂×#63242	1	1	yes	characteristic
123	C₂×C₄	D₁₇⋊M₁₆	1	2	yes	—
124	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
125	C₂×C₄	#10587677	1	2	yes	—
126	C₈	—	17	2	no	—
127	C₈	—	17	2	no	—
128	C₈	—	17	4	no	—
129	C₈	—	34	4	no	—
130	C₂²	C₂×C₄×#3624	1	1	yes	characteristic
131	C₂²	#11763825	1	2	yes	—
132	C₂²	#11763867	1	4	yes	—
133	C₄	—	2	4	no	—
134	C₄	—	4	4	no	—
135	C₄	#11763745	1	1	yes	characteristic
136	C₄	#11763768	1	1	yes	characteristic
137	C₄	#11763827	1	2	yes	—
138	C₂	#14544498	1	1	yes	characteristic
139	C₂	#14544993	1	2	yes	—
140	C₂	#14545149	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763697

C₂

yes

maximal, characteristic

C₂×C₄×#63216

C₂

yes

maximal, characteristic

#14543822

C₂

yes

maximal

#14528471

C₂

yes

maximal, characteristic

C₂²×#63216

C₂²

yes

—

C₂²×#63216

C₂²

yes

—

#11763697

C₄

yes

complemented

C₄×#63216

C₄

yes

complemented

C₂×#10587474

C₄

yes

—

C₂×#10587474

C₄

yes

characteristic

C₂×C₄×#3622

C₂²

yes

—

C₂×C₄×#3622

C₂²

yes

characteristic

C₁₇×#376

C₄

yes

characteristic

C₂×C₄²×C₁₇

C₂×C₄

yes

—

C₂×C₄²×C₁₇

C₂×C₄

yes

characteristic

C₂²×#3622

C₂×C₄

yes

—

C₂²×#3622

C₂×C₄

yes

characteristic

C₂²×#3622

C₂³

yes

—

—

C₂×C₄

yes

—

C₂×#63216

C₂×C₄

yes

—

C₁₇×#95

C₈

yes

—

#10587474

—

#10587474

C₈

yes

—

C₄×#3622

—

C₄×#3622

C₂×C₄

yes

—

C₄×#3622

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂×C₈

yes

—

C₂²×C₄×C₁₇

C₂×C₈

yes

—

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

C₄²

yes

—

C₄²×C₁₇

C₂×C₈

yes

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

C₄²

yes

—

C₂×#3622

C₂×C₈

yes

—

C₂×#3622

M₁₆

yes

—

C₂×#3622

C₂²×C₄

yes

characteristic

C₂×#3622

C₂²×C₄

yes

characteristic

C₂×#3622

#41

yes

—

—

—

—

C₂³×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄×C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₇

#117

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

#3622

—

#3622

#97

yes

—

#3622

#117

yes

—

#3622

#117

yes

—

C₂×#346

—

C₂×C₄×C₁₆

—

#1726

—

#1374

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₇

#431

yes

—

C₂²×C₁₇

#504

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#376

yes

characteristic

C₄×C₁₇

C₂×#97

yes

characteristic

C₄×C₁₇

#431

yes

—

C₂²×C₁₆

—

C₂²×C₁₆

—

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

yes

—

C₄×C₁₆

—

C₂×C₁₇

#1744

yes

characteristic

C₂×C₁₇

#2108

yes

—

C₂×C₁₇

#2164

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₂×#595

yes

—

C₂×C₄²

C₂×#595

yes

characteristic

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

#95

#3624

yes

—

C₁₇

#12592

yes

characteristic, complemented, Sylow

100

C₂²×C₄

C₂×#3624

yes

—

101

C₂²×C₄

C₂×#3624

yes

—

102

C₂²×C₄

C₂²×#595

yes

characteristic

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₄²

—

112

C₄²

—

113

C₄²

#63242

yes

—

114

C₄²

C₄×#595

yes

—

115

C₁₆

—

116

C₁₆

—

117

C₂³

C₂²×#3624

yes

characteristic

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

C₄×#3624

yes

—

122

C₂×C₄

C₂×#63242

yes

characteristic

123

C₂×C₄

D₁₇⋊M₁₆

yes

—

124

C₂×C₄

C₂×C₄×#595

yes

characteristic

125

C₂×C₄

#10587677

yes

—

126

C₈

—

127

C₈

—

128

C₈

—

129

C₈

—

130

C₂²

C₂×C₄×#3624

yes

characteristic

131

C₂²

#11763825

yes

—

132

C₂²

#11763867

yes

—

133

C₄

—

134

C₄

—

135

C₄

#11763745

yes

characteristic

136

C₄

#11763768

yes

characteristic

137

C₄

#11763827

yes

—

138

C₂

#14544498

yes

characteristic

139

C₂

#14544993

yes

—

140

C₂

#14545149

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#595
commutator	C₂²×C₁₇	C₂×C₄×C₈
Fitting	C₁₇×#376	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₈
cosocle	C₂²×#3622	C₂³
hypercenter	#376	#595
hypocenter	C₁₇	#12592
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×#595

commutator

C₂²×C₁₇

C₂×C₄×C₈

Fitting

C₁₇×#376

C₄

socle, prime radical

C₂³×C₁₇

C₂²×C₈

cosocle

C₂²×#3622

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
7. #11763697	C₄	semidirect
8. C₄×#63216	C₄	semidirect
99. C₁₇	#12592	semidirect

H ≅ G/N

type

7. #11763697

C₄

semidirect

8. C₄×#63216

C₄

semidirect

99. C₁₇

#12592

semidirect

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

subgroup	index
C₂×#11763697	2
C₂×C₄×#63216	2
#14543822	2
#14528471	2
#12592	17

subgroup

index

C₂×C₄×#63216

Subgroups — #17960659

Conjugacy classes of subgroups

Complements

Maximal subgroups