Group #17960103 — subgroups

Subgroups — #17960103

Order 4352.

220 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 116 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×#11763731	C₂	1	2	yes	maximal
2	#14543819	C₂	1	4	yes	maximal, complemented
3	M₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587538	—	2	2	no	—
5	#11763731	—	2	2	no	—
6	#11763731	C₂²	1	4	yes	—
7	C₂×#10587483	C₄	1	1	yes	characteristic
8	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
9	#11762584	C₄	1	2	yes	—
10	C₁₆×Dic₁₇	C₂²	1	2	yes	—
11	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₁₇	Q₈	1	1	yes	characteristic
14	C₂²×#3622	D₄	1	1	yes	characteristic
15	#10587538	—	2	4	no	—
16	#10587538	—	4	2	no	—
17	C₂×#63216	—	4	2	no	—
18	C₁₇×M₃₂	C₈	1	4	yes	—
19	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
20	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₈×Dic₁₇	D₄	1	1	yes	characteristic
22	C₈×Dic₁₇	Q₈	1	1	yes	characteristic
23	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
24	#10587483	—	2	2	no	—
25	C₂×#63214	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
27	C₂²×Dic₁₇	—	2	1	no	—
28	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₁₇	M₁₆	1	2	yes	—
31	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	C₄×Dic₁₇	—	2	1	no	—
33	C₄×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
34	C₄×Dic₁₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×#3622	C₄⋊C₄	1	1	yes	characteristic
36	C₂×#3622	D₈	1	2	yes	—
37	C₂×#3622	Q₁₆	1	2	yes	—
38	C₂×#3622	C₂×D₄	1	1	yes	characteristic
39	#63216	—	4	4	no	—
40	C₁₆×C₁₇	C₂×C₈	1	4	yes	—
41	#63214	—	2	2	no	—
42	#12011	—	17	1	no	maximal, Sylow
43	C₂³×C₁₇	#108	1	1	yes	characteristic
44	C₂×C₄×C₁₇	C₄⋊C₈	1	2	yes	—
45	C₂×C₄×C₁₇	#107	1	2	yes	—
46	C₂×C₄×C₁₇	#108	1	1	yes	characteristic
47	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×Dic₁₇	—	2	1	no	—
49	C₂×Dic₁₇	—	2	1	no	—
50	C₂×Dic₁₇	—	4	2	no	—
51	C₈×C₁₇	C₄⋊C₈	1	2	yes	—
52	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
53	C₈×C₁₇	C₂×M₁₆	1	1	yes	characteristic
54	#3622	#107	1	2	yes	—
55	#3622	C₂×D₈	1	1	yes	characteristic
56	#3622	C₂×Q₁₆	1	1	yes	characteristic
57	C₂×#364	—	17	2	no	—
58	C₄×M₃₂	—	17	1	no	—
59	#1373	—	17	4	no	—
60	C₂²×C₁₇	—	4	1	no	—
61	C₂²×C₁₇	#335	1	2	yes	—
62	C₂²×C₁₇	C₂×#108	1	1	yes	characteristic
63	C₄×C₁₇	#335	1	2	yes	—
64	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
65	C₄×C₁₇	C₂×#107	1	1	yes	characteristic
66	Dic₁₇	—	2	2	no	—
67	Dic₁₇	—	4	1	no	—
68	C₂×M₃₂	—	17	1	no	—
69	C₂×M₃₂	—	34	2	no	—
70	C₂×M₃₂	#595	1	1	yes	characteristic
71	C₂×C₄×C₈	—	17	1	no	—
72	#364	—	17	4	no	—
73	#364	—	34	2	no	—
74	#346	—	17	2	no	—
75	C₄×C₁₆	—	17	2	no	—
76	C₂×C₁₇	—	2	1	no	—
77	C₂×C₁₇	—	2	2	no	—
78	C₂×C₁₇	C₂×#335	1	1	yes	characteristic
79	C₂²×C₈	—	17	1	no	—
80	C₂²×C₈	C₂×#595	1	1	yes	characteristic
81	C₂×C₄²	—	17	1	no	—
82	M₃₂	—	34	2	no	—
83	M₃₂	—	34	4	no	—
84	M₃₂	—	68	2	no	—
85	M₃₂	#3624	1	4	yes	—
86	C₂×C₁₆	—	17	2	no	—
87	C₂×C₁₆	—	68	2	no	—
88	C₂×C₁₆	C₂×#595	1	2	yes	—
89	C₄×C₈	—	17	1	no	—
90	C₄×C₈	—	17	1	no	—
91	C₄×C₈	—	17	1	no	—
92	C₄×C₈	—	17	1	no	—
93	C₁₇	#12011	1	1	yes	characteristic, complemented, Sylow
94	C₂²×C₄	—	34	1	no	—
95	C₂²×C₄	C₄⋊#595	1	1	yes	characteristic
96	C₂×C₈	—	17	1	no	—
97	C₂×C₈	—	17	1	no	—
98	C₂×C₈	—	17	2	no	—
99	C₂×C₈	—	17	2	no	—
100	C₂×C₈	#63243	1	2	yes	—
101	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
102	C₂×C₈	C₂×#3624	1	2	yes	—
103	C₂×C₈	C₂²×#595	1	1	yes	characteristic
104	C₄²	—	17	1	no	—
105	C₄²	—	17	1	no	—
106	C₄²	—	34	1	no	—
107	C₁₆	—	34	2	no	—
108	C₁₆	—	68	4	no	—
109	C₁₆	C₂×#3624	1	4	yes	—
110	C₂³	#10587536	1	1	yes	characteristic
111	C₂×C₄	—	34	1	no	—
112	C₂×C₄	—	34	1	no	—
113	C₂×C₄	—	68	2	no	—
114	C₂×C₄	#10587534	1	2	yes	—
115	C₂×C₄	#10587536	1	1	yes	characteristic
116	C₂×C₄	C₄⋊#3624	1	2	yes	—
117	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
118	C₈	—	17	1	no	—
119	C₈	—	17	2	no	—
120	C₈	—	17	1	no	—
121	C₈	C₄⋊#3624	1	2	yes	—
122	C₈	C₂×#63243	1	1	yes	characteristic
123	C₈	C₂²×#3624	1	1	yes	characteristic
124	C₂²	—	4	1	no	—
125	C₂²	#11763672	1	2	yes	—
126	C₂²	C₂×#10587536	1	1	yes	characteristic
127	C₄	—	34	2	no	—
128	C₄	—	68	1	no	—
129	C₄	#11763672	1	2	yes	—
130	C₄	C₂×C₄⋊#3624	1	1	yes	characteristic
131	C₄	C₂×#10587534	1	1	yes	characteristic
132	C₂	—	2	1	no	—
133	C₂	—	2	2	no	—
134	C₂	C₂×#11763672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11763731

C₂

yes

maximal

#14543819

C₂

yes

maximal, complemented

M₃₂×Dic₁₇

C₂

yes

maximal, characteristic

C₂×#10587538

—

#11763731

—

#11763731

C₂²

yes

—

C₂×#10587483

C₄

yes

characteristic

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

#11762584

C₄

yes

—

C₁₆×Dic₁₇

C₂²

yes

—

C₂×C₁₇×M₃₂

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₄×Dic₁₇

Q₈

yes

characteristic

C₂²×#3622

D₄

yes

—

—

—

C₁₇×M₃₂

C₈

yes

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₈×Dic₁₇

C₂×C₄

yes

characteristic

C₈×Dic₁₇

D₄

yes

characteristic

C₈×Dic₁₇

Q₈

yes

characteristic

C₈×Dic₁₇

C₂³

yes

characteristic

#10587483

—

C₂×#63214

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂²×Dic₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×Dic₁₇

C₂×Q₈

yes

characteristic

C₂×#3622

C₄⋊C₄

yes

characteristic

C₂×#3622

D₈

yes

—

C₂×#3622

Q₁₆

yes

—

C₂×#3622

C₂×D₄

yes

characteristic

#63216

—

C₁₆×C₁₇

C₂×C₈

yes

—

—

—

C₂³×C₁₇

yes

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

#107

yes

—

C₂×C₄×C₁₇

#108

yes

characteristic

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

C₄⋊C₈

yes

—

C₈×C₁₇

C₂²×C₈

yes

characteristic

C₈×C₁₇

C₂×M₁₆

yes

characteristic

#3622

#107

yes

—

#3622

C₂×D₈

yes

characteristic

#3622

C₂×Q₁₆

yes

characteristic

C₂×#364

—

C₄×M₃₂

—

#1373

—

C₂²×C₁₇

—

C₂²×C₁₇

#335

yes

—

C₂²×C₁₇

C₂×#108

yes

characteristic

C₄×C₁₇

#335

yes

—

C₄×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₄×C₁₇

C₂×#107

yes

characteristic

Dic₁₇

—

Dic₁₇

—

C₂×M₃₂

—

C₂×M₃₂

—

C₂×M₃₂

#595

yes

characteristic

C₂×C₄×C₈

—

#364

—

#364

—

#346

—

C₄×C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

—

C₂×C₁₇

C₂×#335

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂×#595

yes

characteristic

C₂×C₄²

—

M₃₂

—

M₃₂

—

M₃₂

—

M₃₂

#3624

yes

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#595

yes

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#12011

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄⋊#595

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

100

C₂×C₈

#63243

yes

—

101

C₂×C₈

C₄⋊#595

yes

characteristic

102

C₂×C₈

C₂×#3624

yes

—

103

C₂×C₈

C₂²×#595

yes

characteristic

104

C₄²

—

105

C₄²

—

106

C₄²

—

107

C₁₆

—

108

C₁₆

—

109

C₁₆

C₂×#3624

yes

—

110

C₂³

#10587536

yes

characteristic

111

C₂×C₄

—

112

C₂×C₄

—

113

C₂×C₄

—

114

C₂×C₄

#10587534

yes

—

115

C₂×C₄

#10587536

yes

characteristic

116

C₂×C₄

C₄⋊#3624

yes

—

117

C₂×C₄

C₂×C₄⋊#595

yes

characteristic

118

C₈

—

119

C₈

—

120

C₈

—

121

C₈

C₄⋊#3624

yes

—

122

C₈

C₂×#63243

yes

characteristic

123

C₈

C₂²×#3624

yes

characteristic

124

C₂²

—

125

C₂²

#11763672

yes

—

126

C₂²

C₂×#10587536

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

#11763672

yes

—

130

C₄

C₂×C₄⋊#3624

yes

characteristic

131

C₄

C₂×#10587534

yes

characteristic

132

C₂

—

133

C₂

—

134

C₂

C₂×#11763672

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#10587534
commutator	C₈×C₁₇	C₂²×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂×C₁₇	C₂×#335
prime radical	C₂³×C₁₇	#108
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	#12011
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₄

C₂×#10587534

commutator

C₈×C₁₇

C₂²×C₈

Frattini

C₂×C₈

C₂²×#595

Fitting

C₂×C₁₇×M₃₂

C₄

C₂×C₁₇

C₂³×C₁₇

C₈×Dic₁₇

C₂³

C₂×M₃₂

C₁₇

G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
2. #14543819	C₂	semidirect
93. C₁₇	#12011	semidirect

H ≅ G/N

type

2. #14543819

C₂

semidirect

93. C₁₇

#12011

semidirect

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

subgroup	index
C₂×#11763731	2
#14543819	2
M₃₂×Dic₁₇	2
#12011	17

subgroup

index

C₂×#11763731

#14543819

M₃₂×Dic₁₇

#12011

Subgroups — #17960103

Conjugacy classes of subgroups

Complements

Maximal subgroups