Group #16955300 — subgroups

Subgroups — #16955300

Order 4352.

180 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 180 conjugacy classes of subgroups — too many to draw. Only its 67 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	#14531063	C₂	1	1	yes	maximal, characteristic, complemented
2	#14526965	C₂	1	2	yes	maximal, complemented
3	#14526962	C₂	1	2	yes	maximal
4	C₄×#10587465	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2249	C₂	1	1	yes	maximal, characteristic
6	#11763211	—	2	1	no	—
7	C₂×#10587465	C₂²	1	2	yes	—
8	#11762637	—	2	1	no	—
9	#11762635	C₂²	1	2	yes	—
10	C₂×C₁₇×Q₃₂	C₂²	1	1	yes	characteristic
11	C₂×C₁₇×SD₃₂	—	2	1	no	—
12	C₂×C₁₇×D₁₆	C₂²	1	1	yes	characteristic
13	C₁₇×#495	—	2	1	no	—
14	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₁₇	—	2	1	no	—
16	C₂×SD₁₆×C₁₇	—	4	1	no	—
17	C₂×D₈×C₁₇	—	2	1	no	—
18	C₁₇×#124	—	4	1	no	—
19	#10587556	—	4	1	no	—
20	C₁₇×Q₃₂	—	2	2	no	—
21	C₁₇×SD₃₂	—	4	2	no	—
22	C₁₇×D₁₆	—	2	2	no	—
23	C₂×C₁₆×C₁₇	D₄	1	1	yes	characteristic
24	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
25	C₄×C₈×C₁₇	D₄	1	1	yes	characteristic
26	#10587489	—	2	2	no	—
27	#10587488	—	4	1	no	—
28	#10587465	—	2	2	no	—
29	C₂×Q₈×C₁₇	—	4	1	no	—
30	C₂×D₄×C₁₇	—	4	1	no	—
31	Q₁₆×C₁₇	—	4	1	no	—
32	Q₁₆×C₁₇	—	4	1	no	—
33	SD₁₆×C₁₇	—	8	2	no	—
34	D₈×C₁₇	—	4	1	no	—
35	D₈×C₁₇	—	4	1	no	—
36	C₂×C₈×C₁₇	D₈	1	1	yes	characteristic
37	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
38	C₂²⋊C₄×C₁₇	—	8	2	no	—
39	C₄²×C₁₇	D₈	1	1	yes	characteristic
40	C₄⋊Dic₁₇	—	4	2	no	—
41	#63225	—	8	2	no	—
42	C₁₆×C₁₇	SD₁₆	1	2	yes	—
43	C₁₆×C₁₇	#41	1	2	yes	—
44	#13721	—	17	1	no	maximal, Sylow
45	C₂³×C₁₇	—	8	1	no	—
46	Q₈×C₁₇	—	8	1	no	—
47	Q₈×C₁₇	—	8	1	no	—
48	D₄×C₁₇	—	8	1	no	—
49	D₄×C₁₇	—	8	1	no	—
50	C₂×C₄×C₁₇	—	8	1	no	—
51	C₂×C₄×C₁₇	D₁₆	1	2	yes	—
52	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
53	C₂×Dic₁₇	—	8	2	no	—
54	C₈×C₁₇	SD₃₂	1	2	yes	—
55	C₈×C₁₇	#124	1	1	yes	characteristic
56	C₈×C₁₇	C₂×SD₁₆	1	1	yes	characteristic
57	#2253	—	17	1	no	—
58	#2249	D₁₇	1	1	yes	characteristic
59	#1416	—	17	2	no	—
60	#1415	—	17	2	no	—
61	C₄×C₃₂	—	17	1	no	—
62	C₂²×C₁₇	—	16	1	no	—
63	C₂²×C₁₇	—	16	2	no	—
64	C₂²×C₁₇	C₂×D₁₆	1	1	yes	characteristic
65	C₄×C₁₇	—	2	2	no	—
66	C₄×C₁₇	—	16	1	no	—
67	C₄×C₁₇	#486	1	1	yes	characteristic
68	C₄×C₁₇	C₂×SD₃₂	1	1	yes	characteristic
69	Dic₁₇	—	16	2	no	—
70	C₂×Q₃₂	C₂×D₁₇	1	1	yes	characteristic
71	C₂×SD₃₂	—	2	1	no	—
72	C₂×D₁₆	C₂×D₁₇	1	1	yes	characteristic
73	#499	—	34	1	no	—
74	#495	—	2	1	no	—
75	C₂×C₃₂	—	17	2	no	—
76	#367	—	34	1	no	—
77	#366	—	17	2	no	—
78	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
79	C₂×C₁₇	—	32	1	no	—
80	C₂×C₁₇	#2240	1	1	yes	characteristic
81	C₂×C₁₇	#2262	1	2	yes	—
82	C₂×Q₁₆	—	2	1	no	—
83	C₂×SD₁₆	—	4	1	no	—
84	C₂×D₈	—	2	1	no	—
85	#125	—	68	1	no	—
86	#124	—	4	1	no	—
87	Q₃₂	—	2	2	no	—
88	SD₃₂	—	4	2	no	—
89	D₁₆	—	2	2	no	—
90	C₂×C₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
91	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
92	#107	—	34	2	no	—
93	#106	—	68	1	no	—
94	C₄×C₈	C₂²⋊D₁₇	1	1	yes	characteristic
95	C₃₂	—	34	2	no	—
96	C₁₇	#13721	1	1	yes	characteristic, complemented, Sylow
97	C₂×Q₈	—	4	1	no	—
98	C₂×D₄	—	4	1	no	—
99	Q₁₆	—	4	1	no	—
100	Q₁₆	—	4	1	no	—
101	SD₁₆	—	8	2	no	—
102	D₈	—	4	1	no	—
103	D₈	—	4	1	no	—
104	C₂×C₈	#63228	1	1	yes	characteristic
105	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
106	C₄⋊C₄	—	68	2	no	—
107	C₄⋊C₄	—	136	2	no	—
108	C₂²⋊C₄	—	8	2	no	—
109	C₄²	#63228	1	1	yes	characteristic
110	C₁₆	#63229	1	2	yes	—
111	C₁₆	#63254	1	2	yes	—
112	C₂³	—	8	1	no	—
113	Q₈	—	8	1	no	—
114	Q₈	—	8	1	no	—
115	D₄	—	8	1	no	—
116	D₄	—	8	1	no	—
117	C₂×C₄	—	8	1	no	—
118	C₂×C₄	—	136	2	no	—
119	C₂×C₄	#10587497	1	2	yes	—
120	C₂×C₄	C₂×#63228	1	1	yes	characteristic
121	C₈	#10587498	1	2	yes	—
122	C₈	C₂×#63229	1	1	yes	characteristic
123	C₈	#10587622	1	1	yes	characteristic
124	C₂²	—	16	2	no	—
125	C₂²	—	16	1	no	—
126	C₂²	C₂×#10587497	1	1	yes	characteristic
127	C₄	—	2	2	no	—
128	C₄	—	16	1	no	—
129	C₄	—	272	2	no	—
130	C₄	#11763155	1	1	yes	characteristic
131	C₄	C₂×#10587498	1	1	yes	characteristic
132	C₂	—	32	1	no	—
133	C₂	#14531007	1	1	yes	characteristic
134	C₂	#14531091	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14531063

C₂

yes

maximal, characteristic, complemented

#14526965

C₂

yes

maximal, complemented

#14526962

C₂

yes

maximal

C₄×#10587465

C₂

yes

maximal, characteristic, complemented

C₁₇×#2249

C₂

yes

maximal, characteristic

#11763211

—

C₂×#10587465

C₂²

yes

—

#11762637

—

#11762635

C₂²

yes

—

C₂×C₁₇×Q₃₂

C₂²

yes

characteristic

C₂×C₁₇×SD₃₂

—

C₂×C₁₇×D₁₆

C₂²

yes

characteristic

C₁₇×#495

—

C₄×C₁₆×C₁₇

C₂²

yes

characteristic

C₂×Q₁₆×C₁₇

—

C₂×SD₁₆×C₁₇

—

C₂×D₈×C₁₇

—

C₁₇×#124

—

#10587556

—

C₁₇×Q₃₂

—

C₁₇×SD₃₂

—

C₁₇×D₁₆

—

C₂×C₁₆×C₁₇

D₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂³

yes

characteristic

C₄×C₈×C₁₇

D₄

yes

—

—

—

C₂×Q₈×C₁₇

—

C₂×D₄×C₁₇

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

SD₁₆×C₁₇

—

D₈×C₁₇

—

D₈×C₁₇

—

C₂×C₈×C₁₇

D₈

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂²⋊C₄×C₁₇

—

C₄²×C₁₇

D₈

yes

characteristic

C₄⋊Dic₁₇

—

#63225

—

C₁₆×C₁₇

SD₁₆

yes

—

C₁₆×C₁₇

#41

yes

—

#13721

—

maximal, Sylow

C₂³×C₁₇

—

Q₈×C₁₇

—

Q₈×C₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

D₁₆

yes

—

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×Dic₁₇

—

C₈×C₁₇

SD₃₂

yes

—

C₈×C₁₇

#124

yes

characteristic

C₈×C₁₇

C₂×SD₁₆

yes

characteristic

#2253

—

#2249

D₁₇

yes

characteristic

#1416

—

#1415

—

C₄×C₃₂

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

C₂×D₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#486

yes

characteristic

C₄×C₁₇

C₂×SD₃₂

yes

characteristic

Dic₁₇

—

C₂×Q₃₂

C₂×D₁₇

yes

characteristic

C₂×SD₃₂

—

C₂×D₁₆

C₂×D₁₇

yes

characteristic

#499

—

#495

—

C₂×C₃₂

—

#367

—

#366

—

C₄×C₁₆

C₂×D₁₇

yes

characteristic

C₂×C₁₇

—

C₂×C₁₇

#2240

yes

characteristic

C₂×C₁₇

#2262

yes

—

C₂×Q₁₆

—

C₂×SD₁₆

—

C₂×D₈

—

#125

—

#124

—

Q₃₂

—

SD₃₂

—

D₁₆

—

C₂×C₁₆

C₂²⋊D₁₇

yes

characteristic

C₂×C₁₆

C₂²×D₁₇

yes

characteristic

#107

—

#106

—

C₄×C₈

C₂²⋊D₁₇

yes

characteristic

C₃₂

—

C₁₇

#13721

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

Q₁₆

—

100

Q₁₆

—

101

SD₁₆

—

102

D₈

—

103

D₈

—

104

C₂×C₈

#63228

yes

characteristic

105

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

106

C₄⋊C₄

—

107

C₄⋊C₄

—

136

—

108

C₂²⋊C₄

—

109

C₄²

#63228

yes

characteristic

110

C₁₆

#63229

yes

—

111

C₁₆

#63254

yes

—

112

C₂³

—

113

Q₈

—

114

Q₈

—

115

D₄

—

116

D₄

—

117

C₂×C₄

—

118

C₂×C₄

—

136

—

119

C₂×C₄

#10587497

yes

—

120

C₂×C₄

C₂×#63228

yes

characteristic

121

C₈

#10587498

yes

—

122

C₈

C₂×#63229

yes

characteristic

123

C₈

#10587622

yes

characteristic

124

C₂²

—

125

C₂²

—

126

C₂²

C₂×#10587497

yes

characteristic

127

C₄

—

128

C₄

—

129

C₄

—

272

—

130

C₄

#11763155

yes

characteristic

131

C₄

C₂×#10587498

yes

characteristic

132

C₂

—

133

C₂

#14531007

yes

characteristic

134

C₂

#14531091

yes

—

	subgroup	G/H
center	C₂²	C₂×#10587497
commutator, cosocle	C₂×C₁₆×C₁₇	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₇
Fitting	C₁₇×#2249	C₂
socle	C₂²×C₁₇	C₂×D₁₆
prime radical	C₂×C₁₇×D₁₆	C₂²
hypercenter	#2249	D₁₇
hypocenter	C₁₇	#13721
LCS	G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2249

subgroup

G/H

center

C₂²

C₂×#10587497

commutator, cosocle

C₂×C₁₆×C₁₇

C₂³

Frattini

C₂×C₁₆

C₂²×D₁₇

Fitting

C₁₇×#2249

C₂

socle

C₂²×C₁₇

C₂×D₁₆

prime radical

C₂×C₁₇×D₁₆

C₂²

D₁₇

C₁₇

G ▷ C₂×C₁₆×C₁₇ ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2249

N	H ≅ G/N	type
1. #14531063	C₂	semidirect
2. #14526965	C₂	semidirect
4. C₄×#10587465	C₂	semidirect
96. C₁₇	#13721	semidirect

H ≅ G/N

type

1. #14531063

C₂

semidirect

2. #14526965

C₂

semidirect

4. C₄×#10587465

C₂

semidirect

96. C₁₇

#13721

semidirect

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

subgroup	index
#14531063	2
#14526965	2
#14526962	2
C₄×#10587465	2
C₁₇×#2249	2
#13721	17

subgroup

index

C₁₇×#2249

Subgroups — #16955300

Conjugacy classes of subgroups

Complements

Maximal subgroups