Group #17982371 — subgroups

Subgroups — C₄×#11763902 #17982371

Order 4352.

558 conjugacy classes of subgroups; only the 301 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 301 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×#11763902	C₂	1	4	yes	maximal
2	C₄×#10587665	C₂	1	2	yes	maximal
3	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587665	C₂²	1	4	yes	—
5	#11763902	C₄	1	16	yes	direct product factor
6	C₄×#63241	C₄	1	8	yes	complemented
7	C₄×#63242	C₂²	1	1	yes	characteristic
8	C₂×C₈×#595	C₄	1	2	yes	—
9	C₂×C₈×#595	C₂²	1	2	yes	—
10	C₄²×#595	C₄	1	1	yes	characteristic
11	C₄×C₈×D₁₇	C₄	1	1	yes	characteristic
12	C₂×C₄×#595	C₈	1	4	yes	—
13	C₂×C₄×#595	C₂×C₄	1	2	yes	—
14	C₂×#63242	C₂×C₄	1	1	yes	characteristic
15	C₂×#63242	C₂³	1	1	yes	characteristic
16	C₂×#63241	C₂×C₄	1	8	yes	—
17	#10587665	C₂×C₄	1	16	yes	—
18	C₂×C₈×D₁₇	C₂×C₄	1	2	yes	—
19	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄×#3624	C₂×C₄	1	4	yes	—
21	C₈×#595	C₈	1	8	yes	—
22	C₈×#595	C₂×C₄	1	8	yes	—
23	C₄×C₈×C₁₇	C₈	1	1	yes	characteristic
24	C₈×Dic₁₇	C₈	1	2	yes	—
25	C₄×#3622	C₈	1	1	yes	characteristic
26	C₂²×#595	C₂×C₈	1	4	yes	—
27	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
28	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×#3624	C₄²	1	2	yes	—
30	C₂×#3624	C₂²×C₄	1	2	yes	—
31	C₄×#595	C₁₆	1	16	yes	complemented
32	C₄×#595	C₄²	1	4	yes	—
33	C₄×#595	C₂×C₈	1	4	yes	—
34	#63242	C₂×C₈	1	4	yes	—
35	#63242	C₂²×C₄	1	4	yes	—
36	#63241	C₄²	1	16	yes	complemented
37	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
38	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
39	C₄×Dic₁₇	C₄²	1	2	yes	—
40	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
41	C₂×#3622	C₂×C₈	1	2	yes	—
42	C₈×D₁₇	C₄²	1	4	yes	—
43	C₈×D₁₇	C₂×C₈	1	4	yes	—
44	C₄²×C₁₆	—	17	1	no	maximal, Sylow
45	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
46	C₂×#595	C₄×C₈	1	8	yes	—
47	C₂×#595	C₂×C₁₆	1	16	yes	—
48	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
49	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
50	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
51	C₂×Dic₁₇	C₂×C₄²	1	1	yes	characteristic
52	C₄×D₁₇	C₂×C₁₆	1	8	yes	—
53	C₄×D₁₇	C₂×C₄²	1	2	yes	—
54	C₄×D₁₇	C₂²×C₈	1	2	yes	—
55	#3624	C₄×C₈	1	4	yes	—
56	#3624	C₂×C₄²	1	4	yes	—
57	C₈×C₁₇	C₄×C₈	1	4	yes	—
58	#3622	C₄×C₈	1	4	yes	—
59	C₂×C₄×C₁₆	—	17	2	no	—
60	C₂×C₄×C₁₆	—	17	4	no	—
61	C₄²×C₈	—	17	1	no	—
62	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
63	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
64	C₂×D₁₇	C₂²×C₁₆	1	4	yes	—
65	#595	C₄×C₁₆	1	16	yes	complemented
66	C₄×C₁₇	C₄×C₁₆	1	4	yes	complemented
67	C₄×C₁₇	C₂×C₄×C₈	1	2	yes	—
68	Dic₁₇	C₄×C₁₆	1	4	yes	complemented
69	Dic₁₇	C₄³	1	1	yes	characteristic
70	Dic₁₇	C₂×C₄×C₈	1	1	yes	characteristic
71	C₂²×C₁₆	—	17	4	no	—
72	C₂×C₄×C₈	—	17	2	no	—
73	C₂×C₄×C₈	—	17	2	no	—
74	C₂×C₄×C₈	—	17	1	no	—
75	C₂×C₄×C₈	—	17	1	no	—
76	C₄³	—	17	1	no	—
77	C₄×C₁₆	—	17	8	no	—
78	C₄×C₁₆	—	17	16	no	—
79	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
80	C₂×C₁₇	C₂×C₄×C₁₆	1	2	yes	—
81	D₁₇	C₂×C₄×C₁₆	1	4	yes	—
82	C₂²×C₈	—	17	1	no	—
83	C₂²×C₈	—	17	1	no	—
84	C₂²×C₈	—	17	2	no	—
85	C₂×C₄²	—	17	4	no	—
86	C₂×C₄²	—	17	2	no	—
87	C₂×C₄²	—	17	1	no	—
88	C₂×C₁₆	—	17	16	no	—
89	C₂×C₁₆	—	17	8	no	—
90	C₄×C₈	—	17	8	no	—
91	C₄×C₈	—	17	4	no	—
92	C₄×C₈	—	17	8	no	—
93	C₄×C₈	—	17	2	no	—
94	C₄×C₈	—	17	1	no	—
95	C₄×C₈	#3633	1	1	yes	characteristic
96	C₁₇	C₄²×C₁₆	1	1	yes	characteristic, complemented, Sylow
97	C₂²×C₄	—	17	4	no	—
98	C₂²×C₄	—	17	2	no	—
99	C₂²×C₄	—	17	1	no	—
100	C₂×C₈	—	17	4	no	—
101	C₂×C₈	—	17	4	no	—
102	C₂×C₈	—	17	2	no	—
103	C₂×C₈	—	17	2	no	—
104	C₂×C₈	—	17	2	no	—
105	C₂×C₈	—	17	4	no	—
106	C₂×C₈	—	17	4	no	—
107	C₂×C₈	C₂×#3633	1	2	yes	—
108	C₄²	—	17	16	no	—
109	C₄²	—	17	4	no	—
110	C₄²	—	17	4	no	—
111	C₄²	—	17	2	no	—
112	C₄²	—	17	1	no	—
113	C₄²	C₂×#3633	1	1	yes	characteristic
114	C₁₆	—	17	16	no	—
115	C₂³	—	17	1	no	—
116	C₂×C₄	—	17	8	no	—
117	C₂×C₄	—	17	16	no	—
118	C₂×C₄	—	17	1	no	—
119	C₂×C₄	—	17	2	no	—
120	C₂×C₄	—	17	8	no	—
121	C₂×C₄	—	17	2	no	—
122	C₂×C₄	—	17	2	no	—
123	C₂×C₄	C₄×#3633	1	2	yes	—
124	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
125	C₈	—	17	4	no	—
126	C₈	—	17	4	no	—
127	C₈	—	17	4	no	—
128	C₈	C₄×#3633	1	4	yes	—
129	C₂²	—	17	4	no	—
130	C₂²	—	17	2	no	—
131	C₂²	C₂×C₄×#3633	1	1	yes	characteristic
132	C₄	—	17	16	no	—
133	C₄	—	17	4	no	—
134	C₄	—	17	1	no	—
135	C₄	—	17	1	no	—
136	C₄	#11763902	1	4	yes	direct product factor
137	C₄	C₂×C₄×#3633	1	2	yes	—
138	C₂	—	17	4	no	—
139	C₂	C₄²×#3633	1	1	yes	characteristic
140	C₂	C₂×#11763902	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763902

C₂

yes

maximal

C₄×#10587665

C₂

yes

maximal

C₄×C₈×#595

C₂

yes

maximal, characteristic

C₂×#10587665

C₂²

yes

—

#11763902

C₄

yes

direct product factor

C₄×#63241

C₄

yes

complemented

C₄×#63242

C₂²

yes

characteristic

C₂×C₈×#595

C₄

yes

—

C₂×C₈×#595

C₂²

yes

—

C₄²×#595

C₄

yes

characteristic

C₄×C₈×D₁₇

C₄

yes

characteristic

C₂×C₄×#595

C₈

yes

—

C₂×C₄×#595

C₂×C₄

yes

—

C₂×#63242

C₂×C₄

yes

characteristic

C₂×#63242

C₂³

yes

characteristic

C₂×#63241

C₂×C₄

yes

—

#10587665

C₂×C₄

yes

—

C₂×C₈×D₁₇

C₂×C₄

yes

—

C₄²×D₁₇

C₂×C₄

yes

characteristic

C₄×#3624

C₂×C₄

yes

—

C₈×#595

C₈

yes

—

C₈×#595

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₈

yes

characteristic

C₈×Dic₁₇

C₈

yes

—

C₄×#3622

C₈

yes

characteristic

C₂²×#595

C₂×C₈

yes

—

C₂×C₄×D₁₇

C₂×C₈

yes

—

C₂×C₄×D₁₇

C₂²×C₄

yes

characteristic

C₂×#3624

C₄²

yes

—

C₂×#3624

C₂²×C₄

yes

—

C₄×#595

C₁₆

yes

complemented

C₄×#595

C₄²

yes

—

C₄×#595

C₂×C₈

yes

—

#63242

C₂×C₈

yes

—

#63242

C₂²×C₄

yes

—

#63241

C₄²

yes

complemented

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄×Dic₁₇

C₄²

yes

—

C₄×Dic₁₇

C₂×C₈

yes

characteristic

C₂×#3622

C₂×C₈

yes

—

C₈×D₁₇

C₄²

yes

—

C₈×D₁₇

C₂×C₈

yes

—

C₄²×C₁₆

—

maximal, Sylow

C₂²×D₁₇

C₂²×C₈

yes

characteristic

C₂×#595

C₄×C₈

yes

—

C₂×#595

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₄×C₈

yes

—

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

C₄×C₈

yes

—

C₂×Dic₁₇

C₂×C₄²

yes

characteristic

C₄×D₁₇

C₂×C₁₆

yes

—

C₄×D₁₇

C₂×C₄²

yes

—

C₄×D₁₇

C₂²×C₈

yes

—

#3624

C₄×C₈

yes

—

#3624

C₂×C₄²

yes

—

C₈×C₁₇

C₄×C₈

yes

—

#3622

C₄×C₈

yes

—

C₂×C₄×C₁₆

—

C₂×C₄×C₁₆

—

C₄²×C₈

—

C₂²×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×D₁₇

C₂×C₄×C₈

yes

—

C₂×D₁₇

C₂²×C₁₆

yes

—

#595

C₄×C₁₆

yes

complemented

C₄×C₁₇

C₄×C₁₆

yes

complemented

C₄×C₁₇

C₂×C₄×C₈

yes

—

Dic₁₇

C₄×C₁₆

yes

complemented

Dic₁₇

C₄³

yes

characteristic

Dic₁₇

C₂×C₄×C₈

yes

characteristic

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₄³

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

C₄²×C₈

yes

characteristic

C₂×C₁₇

C₂×C₄×C₁₆

yes

—

D₁₇

C₂×C₄×C₁₆

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

#3633

yes

characteristic

C₁₇

C₄²×C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

100

C₂×C₈

—

101

C₂×C₈

—

102

C₂×C₈

—

103

C₂×C₈

—

104

C₂×C₈

—

105

C₂×C₈

—

106

C₂×C₈

—

107

C₂×C₈

C₂×#3633

yes

—

108

C₄²

—

109

C₄²

—

110

C₄²

—

111

C₄²

—

112

C₄²

—

113

C₄²

C₂×#3633

yes

characteristic

114

C₁₆

—

115

C₂³

—

116

C₂×C₄

—

117

C₂×C₄

—

118

C₂×C₄

—

119

C₂×C₄

—

120

C₂×C₄

—

121

C₂×C₄

—

122

C₂×C₄

—

123

C₂×C₄

C₄×#3633

yes

—

124

C₂×C₄

C₂²×#3633

yes

characteristic

125

C₈

—

126

C₈

—

127

C₈

—

128

C₈

C₄×#3633

yes

—

129

C₂²

—

130

C₂²

—

131

C₂²

C₂×C₄×#3633

yes

characteristic

132

C₄

—

133

C₄

—

134

C₄

—

135

C₄

—

136

C₄

#11763902

yes

direct product factor

137

C₄

C₂×C₄×#3633

yes

—

138

C₂

—

139

C₂

C₄²×#3633

yes

characteristic

140

C₂

C₂×#11763902

yes

—

	subgroup	G/H
center, hypercenter	C₄×C₈	#3633
commutator, hypocenter	C₁₇	C₄²×C₁₆
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₄×C₈×C₁₇	C₈
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×#63242	C₂³
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₄×C₈

subgroup

G/H

center, hypercenter

C₄×C₈

#3633

commutator, hypocenter

C₁₇

C₄²×C₁₆

Frattini

C₂×C₄

C₂²×#3633

Fitting

C₄×C₈×C₁₇

C₈

socle

C₂²×C₁₇

C₂×C₄×C₈

prime radical

C₂²×D₁₇

C₂²×C₈

C₂³

G ▷ C₁₇

C₁ ◁ C₄×C₈

N	H ≅ G/N	type
5. #11763902	C₄	direct (N × H)
6. C₄×#63241	C₄	semidirect
31. C₄×#595	C₁₆	semidirect
36. #63241	C₄²	semidirect
65. #595	C₄×C₁₆	semidirect
66. C₄×C₁₇	C₄×C₁₆	semidirect
68. Dic₁₇	C₄×C₁₆	semidirect
96. C₁₇	C₄²×C₁₆	semidirect
136. C₄	#11763902	direct (N × H)

H ≅ G/N

type

5. #11763902

C₄

direct (N × H)

6. C₄×#63241

C₄

semidirect

31. C₄×#595

C₁₆

semidirect

36. #63241

C₄²

semidirect

65. #595

C₄×C₁₆

semidirect

66. C₄×C₁₇

C₄×C₁₆

semidirect

68. Dic₁₇

C₄×C₁₆

semidirect

96. C₁₇

C₄²×C₁₆

semidirect

136. C₄

#11763902

direct (N × H)

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

subgroup	index
C₂×#11763902	2
C₄×#10587665	2
C₄×C₈×#595	2
C₄²×C₁₆	17

subgroup

index

C₂×#11763902

C₄×#10587665

C₄×C₈×#595

C₄²×C₁₆

Subgroups — C₄×#11763902 #17982371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C4×#11763902 #17982371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763902 #17982371