Group #17981200 — subgroups

Subgroups — #17981200

Order 4352.

278 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 97 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	C₄×#10587666	C₂	1	2	yes	maximal
2	C₈×#63242	C₂	1	1	yes	maximal, characteristic
3	C₂×#10587666	C₄	1	4	yes	—
4	#11763903	—	2	2	no	—
5	C₄×#63241	—	2	2	no	—
6	C₄×#63242	C₄	1	1	yes	characteristic
7	C₄×#63242	C₂²	1	1	yes	characteristic
8	C₈×#3624	—	2	2	no	—
9	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
10	C₂×#63242	—	2	1	no	—
11	C₂×#63242	C₂×C₄	1	2	yes	—
12	C₂×#63241	—	2	4	no	—
13	#10587666	—	2	4	no	—
14	#10587666	C₈	1	8	yes	complemented
15	C₂×C₈×D₁₇	—	2	1	no	—
16	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₄×#3624	—	2	1	no	—
18	C₄×#3624	C₈	1	2	yes	—
19	C₄×#3624	D₄	1	1	yes	characteristic
20	C₄×#3624	D₄	1	2	yes	—
21	C₄×#3624	Q₈	1	1	yes	characteristic
22	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
23	C₈×Dic₁₇	—	2	1	no	—
24	C₄×#3622	C₈	1	1	yes	characteristic
25	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
26	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
27	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
28	C₂×#3624	—	2	2	no	—
29	C₂×#3624	C₂²⋊C₄	1	2	yes	—
30	C₂×#3624	C₄⋊C₄	1	2	yes	—
31	#63242	—	2	2	no	—
32	#63242	—	2	2	no	—
33	#63242	C₂×C₈	1	4	yes	—
34	#63242	M₁₆	1	4	yes	—
35	#63241	—	2	8	no	—
36	C₂×C₈×C₁₇	—	2	1	no	—
37	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
38	C₄×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
40	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
41	C₂×#3622	—	2	1	no	—
42	C₈×D₁₇	—	2	4	no	—
43	#7138	—	17	1	no	maximal, Sylow
44	C₂²×D₁₇	#97	1	1	yes	characteristic
45	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
48	C₂×Dic₁₇	#95	1	1	yes	characteristic
49	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
50	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
51	C₄×D₁₇	—	2	1	no	—
52	C₄×D₁₇	—	2	1	no	—
53	C₄×D₁₇	—	2	2	no	—
54	C₄×D₁₇	C₄×C₈	1	2	yes	—
55	C₄×D₁₇	#97	1	2	yes	—
56	#3624	—	2	4	no	—
57	#3624	C₂²⋊C₈	1	4	yes	—
58	#3624	C₄⋊C₈	1	4	yes	—
59	C₈×C₁₇	—	2	2	no	—
60	#3622	—	2	2	no	—
61	C₄×M₃₂	—	17	2	no	—
62	C₂×C₈²	—	17	1	no	—
63	C₂²×C₁₇	#336	1	1	yes	characteristic
64	C₂×D₁₇	—	2	1	no	—
65	C₂×D₁₇	—	2	1	no	—
66	C₂×D₁₇	#322	1	2	yes	—
67	C₄×C₁₇	—	2	1	no	—
68	C₄×C₁₇	C₈²	1	1	yes	characteristic
69	C₄×C₁₇	#322	1	1	yes	characteristic
70	C₄×C₁₇	#364	1	1	yes	characteristic
71	C₄×C₁₇	#364	1	1	yes	characteristic
72	Dic₁₇	—	2	1	no	—
73	Dic₁₇	#336	1	2	yes	—
74	Dic₁₇	#364	1	2	yes	—
75	C₂×M₃₂	—	17	4	no	—
76	C₂×C₄×C₈	—	17	1	no	—
77	C₂×C₄×C₈	—	17	1	no	—
78	C₂×C₄×C₈	—	17	1	no	—
79	#346	—	34	2	no	—
80	C₄×C₁₆	—	34	2	no	—
81	C₈²	—	34	2	no	—
82	C₂×C₁₇	#1273	1	1	yes	characteristic
83	C₂×C₁₇	#1376	1	1	yes	characteristic
84	C₂×C₁₇	#1376	1	1	yes	characteristic
85	D₁₇	—	2	2	no	—
86	C₂²×C₈	—	17	2	no	—
87	C₂²×C₈	—	34	1	no	—
88	C₂²×C₈	—	34	1	no	—
89	C₂×C₄²	—	17	1	no	—
90	M₃₂	—	17	8	no	—
91	M₃₂	—	34	4	no	—
92	C₂×C₁₆	—	34	4	no	—
93	C₄×C₈	—	17	2	no	—
94	C₄×C₈	—	17	1	no	—
95	C₄×C₈	—	17	1	no	—
96	C₄×C₈	—	17	2	no	—
97	C₄×C₈	—	17	1	no	—
98	C₄×C₈	—	34	1	no	—
99	C₄×C₈	—	34	1	no	—
100	C₄×C₈	#3633	1	1	yes	characteristic
101	C₁₇	#7138	1	1	yes	characteristic, complemented, Sylow
102	C₂²×C₄	—	17	1	no	—
103	C₂²×C₄	—	17	1	no	—
104	C₂²×C₄	—	17	1	no	—
105	C₂×C₈	—	2	1	no	—
106	C₂×C₈	—	17	4	no	—
107	C₂×C₈	—	17	4	no	—
108	C₂×C₈	—	17	2	no	—
109	C₂×C₈	—	17	2	no	—
110	C₂×C₈	—	34	4	no	—
111	C₂×C₈	—	34	2	no	—
112	C₂×C₈	—	34	2	no	—
113	C₂×C₈	—	34	2	no	—
114	C₂×C₈	—	34	1	no	—
115	C₄²	—	17	1	no	—
116	C₄²	—	17	1	no	—
117	C₄²	—	17	1	no	—
118	C₄²	C₂×#3633	1	1	yes	characteristic
119	C₁₆	—	34	8	no	—
120	C₂³	—	17	1	no	—
121	C₂×C₄	—	17	1	no	—
122	C₂×C₄	—	17	1	no	—
123	C₂×C₄	—	17	2	no	—
124	C₂×C₄	—	17	2	no	—
125	C₂×C₄	—	17	1	no	—
126	C₂×C₄	—	34	2	no	—
127	C₂×C₄	—	34	1	no	—
128	C₂×C₄	—	34	1	no	—
129	C₂×C₄	C₄×#3633	1	1	yes	characteristic
130	C₂×C₄	C₄⋊#3633	1	1	yes	characteristic
131	C₂×C₄	C₂²⋊#3633	1	1	yes	characteristic
132	C₈	—	2	2	no	—
133	C₈	—	17	4	no	—
134	C₈	—	17	4	no	—
135	C₈	—	34	2	no	—
136	C₈	—	34	4	no	—
137	C₂²	—	17	2	no	—
138	C₂²	—	34	1	no	—
139	C₂²	—	34	1	no	—
140	C₂²	(C₂×#3633)⋊C₄	1	1	yes	characteristic
141	C₄	—	2	1	no	—
142	C₄	—	17	2	no	—
143	C₄	—	17	2	no	—
144	C₄	—	34	1	no	—
145	C₄	C₈×#3633	1	1	yes	characteristic
146	C₄	#11763893	1	1	yes	characteristic
147	C₄	#11763913	1	1	yes	characteristic
148	C₄	#11763914	1	1	yes	characteristic
149	C₂	—	34	2	no	—
150	C₂	(C₂×#3633)⋊C₈	1	1	yes	characteristic
151	C₂	#14545858	1	1	yes	characteristic
152	C₂	#14545859	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#10587666

C₂

yes

maximal

C₈×#63242

C₂

yes

maximal, characteristic

C₂×#10587666

C₄

yes

—

#11763903

—

C₄×#63241

—

C₄×#63242

C₄

yes

characteristic

C₄×#63242

C₂²

yes

characteristic

C₈×#3624

—

C₄×C₈×D₁₇

C₄

yes

characteristic

C₂×#63242

—

C₂×#63242

C₂×C₄

yes

—

C₂×#63241

—

#10587666

—

#10587666

C₈

yes

complemented

C₂×C₈×D₁₇

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₄×#3624

—

C₄×#3624

C₈

yes

—

C₄×#3624

D₄

yes

characteristic

C₄×#3624

D₄

yes

—

C₄×#3624

Q₈

yes

characteristic

C₄×C₈×C₁₇

C₈

yes

characteristic

C₈×Dic₁₇

—

C₄×#3622

C₈

yes

characteristic

C₂×C₄×D₁₇

C₄²

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

characteristic

C₂×C₄×D₁₇

M₁₆

yes

characteristic

C₂×#3624

—

C₂×#3624

C₂²⋊C₄

yes

—

C₂×#3624

C₄⋊C₄

yes

—

#63242

—

#63242

—

#63242

C₂×C₈

yes

—

#63242

M₁₆

yes

—

#63241

—

C₂×C₈×C₁₇

—

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

—

C₈×D₁₇

—

—

C₂²×D₁₇

yes

C₂×C₄×C₁₇

C₄×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₈

yes

characteristic

C₂×Dic₁₇

#95

yes

characteristic

C₂×Dic₁₇

C₂²⋊C₈

yes

characteristic

C₂×Dic₁₇

C₄⋊C₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

C₄×C₈

yes

—

C₄×D₁₇

#97

yes

—

#3624

—

#3624

C₂²⋊C₈

yes

—

#3624

C₄⋊C₈

yes

—

C₈×C₁₇

—

#3622

—

C₄×M₃₂

—

C₂×C₈²

—

C₂²×C₁₇

#336

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

#322

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₈²

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

#336

yes

—

Dic₁₇

#364

yes

—

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#346

—

C₄×C₁₆

—

C₈²

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

100

C₄×C₈

#3633

yes

characteristic

101

C₁₇

#7138

yes

characteristic, complemented, Sylow

102

C₂²×C₄

—

103

C₂²×C₄

—

104

C₂²×C₄

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

—

108

C₂×C₈

—

109

C₂×C₈

—

110

C₂×C₈

—

111

C₂×C₈

—

112

C₂×C₈

—

113

C₂×C₈

—

114

C₂×C₈

—

115

C₄²

—

116

C₄²

—

117

C₄²

—

118

C₄²

C₂×#3633

yes

characteristic

119

C₁₆

—

120

C₂³

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

—

124

C₂×C₄

—

125

C₂×C₄

—

126

C₂×C₄

—

127

C₂×C₄

—

128

C₂×C₄

—

129

C₂×C₄

C₄×#3633

yes

characteristic

130

C₂×C₄

C₄⋊#3633

yes

characteristic

131

C₂×C₄

C₂²⋊#3633

yes

characteristic

132

C₈

—

133

C₈

—

134

C₈

—

135

C₈

—

136

C₈

—

137

C₂²

—

138

C₂²

—

139

C₂²

—

140

C₂²

(C₂×#3633)⋊C₄

yes

characteristic

141

C₄

—

142

C₄

—

143

C₄

—

144

C₄

—

145

C₄

C₈×#3633

yes

characteristic

146

C₄

#11763893

yes

characteristic

147

C₄

#11763913

yes

characteristic

148

C₄

#11763914

yes

characteristic

149

C₂

—

150

C₂

(C₂×#3633)⋊C₈

yes

characteristic

151

C₂

#14545858

yes

characteristic

152

C₂

#14545859

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#3633
commutator	C₄×C₁₇	C₈²
Frattini	C₄²	C₂×#3633
Fitting	C₄×C₈×C₁₇	C₈
socle	C₂²×C₁₇	#336
prime radical	C₂²×D₁₇	#97
cosocle	C₄×#63242	C₂²
hypercenter	C₄×C₈	#3633
hypocenter	C₁₇	#7138
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂×C₄

C₄⋊#3633

commutator

C₄×C₁₇

C₈²

Frattini

C₄²

C₂×#3633

Fitting

C₄×C₈×C₁₇

C₈

C₂²×C₁₇

C₂²×D₁₇

C₂²

C₄×C₈

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
14. #10587666	C₈	semidirect
101. C₁₇	#7138	semidirect

H ≅ G/N

type

14. #10587666

C₈

semidirect

101. C₁₇

#7138

semidirect

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

subgroup	index
C₄×#10587666	2
C₈×#63242	2
#7138	17

subgroup

index

C₄×#10587666

C₈×#63242

#7138

Subgroups — #17981200

Conjugacy classes of subgroups

Complements

Maximal subgroups