Group #16950744 — subgroups

Subgroups — #16950744

Order 4352.

342 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 203 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×#11762630	C₂	1	4	yes	maximal
2	#14530540	C₂	1	2	yes	maximal
3	C₁₇×#1726	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587483	C₂²	1	4	yes	—
5	#11762630	—	2	8	no	—
6	C₄⋊#63214	—	2	4	no	—
7	C₂×C₁₇×#97	C₄	1	2	yes	—
8	C₂×C₁₇×#97	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
11	C₁₇×#376	C₄	1	1	yes	characteristic
12	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
14	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₇	C₂×C₄	1	2	yes	—
16	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₁₇×#97	—	2	4	no	—
18	C₁₇×#97	C₈	1	4	yes	—
19	C₄×C₈×C₁₇	D₄	1	2	yes	—
20	C₄×C₈×C₁₇	D₄	1	4	yes	—
21	C₄×C₈×C₁₇	Q₈	1	4	yes	—
22	C₄×C₈×C₁₇	Q₈	1	2	yes	—
23	C₁₇×#95	—	2	2	no	—
24	#10587483	—	2	8	no	—
25	C₂×#63214	—	2	4	no	—
26	C₂²×C₄×C₁₇	—	2	2	no	—
27	C₂²×C₄×C₁₇	M₁₆	1	2	yes	—
28	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₂×C₈×C₁₇	—	2	2	no	—
30	C₂×C₈×C₁₇	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₇	C₄⋊C₄	1	4	yes	—
32	C₂×C₈×C₁₇	C₂×C₈	1	4	yes	—
33	C₂×C₈×C₁₇	M₁₆	1	4	yes	—
34	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
35	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
36	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
37	C₂×C₈×C₁₇	C₂×Q₈	1	1	yes	characteristic
38	C₄²×C₁₇	—	2	2	no	—
39	C₄²×C₁₇	C₄⋊C₄	1	4	yes	—
40	C₄²×C₁₇	C₄⋊C₄	1	2	yes	—
41	C₄²×C₁₇	C₂×C₈	1	2	yes	—
42	#63214	—	4	4	no	—
43	#12901	—	17	1	no	maximal, Sylow
44	C₂³×C₁₇	C₂×M₁₆	1	1	yes	characteristic
45	C₂×C₄×C₁₇	—	2	4	no	—
46	C₂×C₄×C₁₇	—	4	2	no	—
47	C₂×C₄×C₁₇	—	4	4	no	—
48	C₂×C₄×C₁₇	C₄⋊C₈	1	4	yes	—
49	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
50	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
53	C₈×C₁₇	—	2	2	no	—
54	C₈×C₁₇	C₄⋊C₈	1	8	yes	—
55	C₈×C₁₇	#127	1	1	yes	characteristic
56	C₈×C₁₇	C₄⋊Q₈	1	2	yes	—
57	C₈×C₁₇	C₄⋊Q₈	1	1	yes	characteristic
58	C₂×#364	—	17	4	no	—
59	#2150	—	17	2	no	—
60	#1726	D₁₇	1	1	yes	characteristic
61	C₂²×C₁₇	—	2	2	no	—
62	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
63	C₂²×C₁₇	#423	1	2	yes	—
64	C₄×C₁₇	—	2	4	no	—
65	C₄×C₁₇	—	4	4	no	—
66	C₄×C₁₇	#384	1	1	yes	characteristic
67	C₄×C₁₇	C₂×C₄⋊C₈	1	2	yes	—
68	C₄×C₁₇	#423	1	1	yes	characteristic
69	C₂×M₃₂	—	17	4	no	—
70	C₂×#97	Dic₁₇	1	2	yes	—
71	C₂×#97	Dic₁₇	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂×D₁₇	1	2	yes	—
73	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
74	#376	Dic₁₇	1	1	yes	characteristic
75	#364	—	34	8	no	—
76	C₄⋊C₁₆	—	34	4	no	—
77	C₂×C₁₇	—	2	2	no	—
78	C₂×C₁₇	#1842	1	1	yes	characteristic
79	C₂×C₁₇	#2153	1	2	yes	—
80	C₂²×C₈	C₂×Dic₁₇	1	1	yes	characteristic
81	C₂²×C₈	C₂×Dic₁₇	1	2	yes	—
82	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
83	C₂×C₄²	C₂×Dic₁₇	1	2	yes	—
84	C₂×C₄²	C₂×Dic₁₇	1	1	yes	characteristic
85	M₃₂	—	34	8	no	—
86	C₂×C₁₆	—	34	4	no	—
87	#97	—	2	4	no	—
88	#97	#3622	1	4	yes	—
89	C₄×C₈	Dic₃₄	1	4	yes	—
90	C₄×C₈	Dic₃₄	1	2	yes	—
91	C₄×C₈	D₆₈	1	4	yes	—
92	C₄×C₈	D₆₈	1	2	yes	—
93	#95	—	2	2	no	—
94	C₁₇	#12901	1	1	yes	characteristic, complemented, Sylow
95	C₂²×C₄	—	2	2	no	—
96	C₂²×C₄	#63223	1	2	yes	—
97	C₂²×C₄	C₂²×Dic₁₇	1	1	yes	characteristic
98	C₂×C₈	—	2	2	no	—
99	C₂×C₈	C₂×#3622	1	4	yes	—
100	C₂×C₈	#63223	1	4	yes	—
101	C₂×C₈	C₄⋊Dic₁₇	1	2	yes	—
102	C₂×C₈	C₄⋊Dic₁₇	1	4	yes	—
103	C₂×C₈	C₂×Dic₃₄	1	1	yes	characteristic
104	C₂×C₈	C₂×Dic₃₄	1	2	yes	—
105	C₂×C₈	C₂×D₆₈	1	2	yes	—
106	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
107	C₄²	—	2	2	no	—
108	C₄²	C₂×#3622	1	2	yes	—
109	C₄²	C₄⋊Dic₁₇	1	4	yes	—
110	C₄²	C₄⋊Dic₁₇	1	2	yes	—
111	C₁₆	—	68	4	no	—
112	C₂³	C₂×#63223	1	1	yes	characteristic
113	C₂×C₄	—	2	4	no	—
114	C₂×C₄	—	4	2	no	—
115	C₂×C₄	—	4	4	no	—
116	C₂×C₄	C₄⋊#3622	1	4	yes	—
117	C₂×C₄	C₂²×#3622	1	1	yes	characteristic
118	C₂×C₄	C₂×#63223	1	2	yes	—
119	C₂×C₄	C₂×C₄⋊Dic₁₇	1	2	yes	—
120	C₂×C₄	C₂×C₄⋊Dic₁₇	1	1	yes	characteristic
121	C₈	—	2	2	no	—
122	C₈	C₄⋊#3622	1	8	yes	—
123	C₈	#10587555	1	2	yes	—
124	C₈	#10587555	1	1	yes	characteristic
125	C₈	#10587560	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	C₂×C₄⋊#3622	1	1	yes	characteristic
128	C₂²	#11762833	1	2	yes	—
129	C₄	—	2	4	no	—
130	C₄	—	4	4	no	—
131	C₄	#11762679	1	1	yes	characteristic
132	C₄	C₂×C₄⋊#3622	1	2	yes	—
133	C₄	#11762833	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	#14528936	1	1	yes	characteristic
136	C₂	#14530550	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#11762630

C₂

yes

maximal

#14530540

C₂

yes

maximal

C₁₇×#1726

C₂

yes

maximal, characteristic

C₂×#10587483

C₂²

yes

—

#11762630

—

C₄⋊#63214

—

C₂×C₁₇×#97

C₄

yes

—

C₂×C₁₇×#97

C₄

yes

characteristic

C₂×C₄×C₈×C₁₇

C₂²

yes

—

C₂×C₄×C₈×C₁₇

C₂²

yes

characteristic

C₁₇×#376

C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₈×C₁₇

C₂×C₄

yes

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄²×C₁₇

C₂×C₄

yes

—

C₂×C₄²×C₁₇

C₂×C₄

yes

characteristic

C₁₇×#97

—

C₁₇×#97

C₈

yes

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

C₄×C₈×C₁₇

Q₈

yes

—

C₁₇×#95

—

#10587483

—

C₂×#63214

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

M₁₆

yes

—

C₂²×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₄⋊C₄

yes

—

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

M₁₆

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×Q₈

yes

—

C₂×C₈×C₁₇

C₂×Q₈

yes

characteristic

C₄²×C₁₇

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

C₄⋊C₄

yes

—

C₄²×C₁₇

C₂×C₈

yes

—

#63214

—

#12901

—

maximal, Sylow

C₂³×C₁₇

C₂×M₁₆

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₈

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×M₁₆

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₈

yes

—

C₈×C₁₇

#127

yes

characteristic

C₈×C₁₇

C₄⋊Q₈

yes

—

C₈×C₁₇

C₄⋊Q₈

yes

—

—

D₁₇

yes

characteristic

C₂²×C₁₇

—

C₂²×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂²×C₁₇

#423

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#384

yes

characteristic

C₄×C₁₇

C₂×C₄⋊C₈

yes

—

C₄×C₁₇

#423

yes

characteristic

C₂×M₃₂

—

C₂×#97

Dic₁₇

yes

—

C₂×#97

Dic₁₇

yes

characteristic

C₂×C₄×C₈

C₂×D₁₇

yes

—

C₂×C₄×C₈

C₂×D₁₇

yes

characteristic

#376

Dic₁₇

yes

characteristic

#364

—

C₄⋊C₁₆

—

C₂×C₁₇

—

C₂×C₁₇

#1842

yes

characteristic

C₂×C₁₇

#2153

yes

—

C₂²×C₈

C₂×Dic₁₇

yes

characteristic

C₂²×C₈

C₂×Dic₁₇

yes

—

C₂²×C₈

C₂²×D₁₇

yes

characteristic

C₂×C₄²

C₂×Dic₁₇

yes

—

C₂×C₄²

C₂×Dic₁₇

yes

characteristic

M₃₂

—

C₂×C₁₆

—

#97

—

#97

#3622

yes

—

C₄×C₈

Dic₃₄

yes

—

C₄×C₈

Dic₃₄

yes

—

C₄×C₈

D₆₈

yes

—

C₄×C₈

D₆₈

yes

—

#95

—

C₁₇

#12901

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

#63223

yes

—

C₂²×C₄

C₂²×Dic₁₇

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×#3622

yes

—

100

C₂×C₈

#63223

yes

—

101

C₂×C₈

C₄⋊Dic₁₇

yes

—

102

C₂×C₈

C₄⋊Dic₁₇

yes

—

103

C₂×C₈

C₂×Dic₃₄

yes

characteristic

104

C₂×C₈

C₂×Dic₃₄

yes

—

105

C₂×C₈

C₂×D₆₈

yes

—

106

C₂×C₈

C₂×D₆₈

yes

characteristic

107

C₄²

—

108

C₄²

C₂×#3622

yes

—

109

C₄²

C₄⋊Dic₁₇

yes

—

110

C₄²

C₄⋊Dic₁₇

yes

—

111

C₁₆

—

112

C₂³

C₂×#63223

yes

characteristic

113

C₂×C₄

—

114

C₂×C₄

—

115

C₂×C₄

—

116

C₂×C₄

C₄⋊#3622

yes

—

117

C₂×C₄

C₂²×#3622

yes

characteristic

118

C₂×C₄

C₂×#63223

yes

—

119

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

—

120

C₂×C₄

C₂×C₄⋊Dic₁₇

yes

characteristic

121

C₈

—

122

C₈

C₄⋊#3622

yes

—

123

C₈

#10587555

yes

—

124

C₈

#10587555

yes

characteristic

125

C₈

#10587560

yes

characteristic

126

C₂²

—

127

C₂²

C₂×C₄⋊#3622

yes

characteristic

128

C₂²

#11762833

yes

—

129

C₄

—

130

C₄

—

131

C₄

#11762679

yes

characteristic

132

C₄

C₂×C₄⋊#3622

yes

—

133

C₄

#11762833

yes

characteristic

134

C₂

—

135

C₂

#14528936

yes

characteristic

136

C₂

#14530550

yes

—

	subgroup	G/H
center	C₂×C₈	C₂×D₆₈
commutator	C₂×C₄×C₁₇	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₁₇×#1726	C₂
socle	C₂²×C₁₇	C₂×C₄⋊C₈
prime radical	C₂³×C₁₇	C₂×M₁₆
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	#1726	D₁₇
hypocenter	C₁₇	#12901
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

subgroup

G/H

center

C₂×C₈

C₂×D₆₈

commutator

C₂×C₄×C₁₇

C₂²×C₈

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₁₇×#1726

C₂

socle

C₂²×C₁₇

C₂×C₄⋊C₈

prime radical

C₂³×C₁₇

C₂×M₁₆

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #1726

N	H ≅ G/N	type
94. C₁₇	#12901	semidirect

H ≅ G/N

type

94. C₁₇

#12901

semidirect

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

subgroup	index
C₂×#11762630	2
#14530540	2
C₁₇×#1726	2
#12901	17

subgroup

index

C₂×#11762630

#14530540

C₁₇×#1726

#12901

Subgroups — #16950744

Conjugacy classes of subgroups

Complements

Maximal subgroups