Group #16949063 — subgroups

Subgroups — #16949063

Order 4352.

238 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 87 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	#14531064	C₂	1	2	yes	maximal
2	#14531059	C₂	1	1	yes	maximal, characteristic
3	#14528393	C₂	1	2	yes	maximal
4	C₁₆×#3622	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#2252	C₂	1	1	yes	maximal, characteristic
6	#11763214	C₂²	1	2	yes	—
7	#11763161	—	2	2	no	—
8	#11763159	—	2	2	no	—
9	#11762636	—	2	4	no	—
10	#11762635	—	2	2	no	—
11	C₄×#63214	C₂²	1	1	yes	characteristic
12	C₈×#3622	C₂²	1	1	yes	characteristic
13	C₁₇×#500	C₂²	1	2	yes	—
14	C₁₇×#366	—	2	2	no	—
15	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×C₄⋊Q₈	—	2	2	no	—
17	#10587555	—	2	2	no	—
18	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
19	C₁₇×#107	—	2	2	no	—
20	C₁₇×#107	—	2	2	no	—
21	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
22	#10587506	—	4	4	no	—
23	#10587489	—	2	2	no	—
24	#10587489	—	2	2	no	—
25	C₂×#63214	D₄	1	2	yes	—
26	#10587481	—	4	4	no	—
27	C₄×#3622	D₄	1	1	yes	characteristic
28	C₄×#3622	D₄	1	1	yes	characteristic
29	C₂×Q₈×C₁₇	—	4	2	no	—
30	C₂×Dic₃₄	—	4	2	no	—
31	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
32	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
33	C₄⋊C₄×C₁₇	—	4	2	no	—
34	C₄⋊C₄×C₁₇	—	4	2	no	—
35	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
36	C₄⋊Dic₁₇	—	4	2	no	—
37	C₄⋊Dic₁₇	—	4	2	no	—
38	C₂×#3622	D₈	1	2	yes	—
39	C₂×#3622	D₈	1	2	yes	—
40	C₁₆×C₁₇	Q₁₆	1	4	yes	—
41	#63214	Q₁₆	1	4	yes	—
42	#12522	—	17	1	no	maximal, Sylow
43	Q₈×C₁₇	—	8	4	no	—
44	C₂×C₄×C₁₇	—	8	2	no	—
45	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
46	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
47	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
48	C₂×Dic₁₇	—	8	2	no	—
49	Dic₃₄	—	8	4	no	—
50	C₈×C₁₇	C₂×Q₁₆	1	2	yes	—
51	C₈×C₁₇	C₂×Q₁₆	1	2	yes	—
52	#3622	—	2	2	no	—
53	#3622	—	2	2	no	—
54	#2254	—	17	2	no	—
55	#2252	—	17	1	no	—
56	#2252	D₁₇	1	1	yes	characteristic
57	#1710	—	17	2	no	—
58	C₈×C₁₆	—	17	1	no	—
59	C₂²×C₁₇	#493	1	1	yes	characteristic
60	C₄×C₁₇	—	16	2	no	—
61	C₄×C₁₇	#494	1	1	yes	characteristic
62	C₄×C₁₇	#494	1	1	yes	characteristic
63	C₄×C₁₇	#508	1	2	yes	—
64	C₄×C₁₇	#508	1	2	yes	—
65	Dic₁₇	—	16	2	no	—
66	#500	—	17	2	no	—
67	#500	C₂×D₁₇	1	2	yes	—
68	#487	—	34	2	no	—
69	#487	—	34	2	no	—
70	#367	—	34	4	no	—
71	#366	—	2	2	no	—
72	#366	—	34	2	no	—
73	C₄×C₁₆	—	17	1	no	—
74	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
75	C₈²	—	17	1	no	—
76	C₂×C₁₇	#1713	1	1	yes	characteristic
77	C₂×C₁₇	#2249	1	1	yes	characteristic
78	C₂×C₁₇	#2249	1	1	yes	characteristic
79	C₄⋊Q₈	—	2	2	no	—
80	C₄⋊Q₈	—	34	2	no	—
81	C₂×C₁₆	—	17	2	no	—
82	C₂×C₁₆	C₂²⋊D₁₇	1	2	yes	—
83	#107	—	2	2	no	—
84	#107	—	2	2	no	—
85	#107	—	34	2	no	—
86	#107	—	34	2	no	—
87	#103	—	68	4	no	—
88	#103	—	68	4	no	—
89	C₄×C₈	—	17	1	no	—
90	C₄×C₈	—	17	1	no	—
91	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
92	C₁₇	#12522	1	1	yes	characteristic, complemented, Sylow
93	C₂×Q₈	—	4	2	no	—
94	C₂×Q₈	—	68	2	no	—
95	C₂×C₈	—	17	2	no	—
96	C₂×C₈	—	17	2	no	—
97	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
98	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
99	C₄⋊C₄	—	4	2	no	—
100	C₄⋊C₄	—	4	2	no	—
101	C₄⋊C₄	—	68	2	no	—
102	C₄⋊C₄	—	68	2	no	—
103	C₄²	D₄×D₁₇	1	1	yes	characteristic
104	C₁₆	—	17	4	no	—
105	C₁₆	#63231	1	4	yes	—
106	Q₈	—	8	4	no	—
107	Q₈	—	136	4	no	—
108	C₂×C₄	—	8	2	no	—
109	C₂×C₄	—	136	2	no	—
110	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
111	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
112	C₂×C₄	#10587626	1	1	yes	characteristic
113	C₈	—	34	2	no	—
114	C₈	—	34	2	no	—
115	C₈	Q₁₆×D₁₇	1	2	yes	—
116	C₈	C₂×#63231	1	2	yes	—
117	C₂²	#11763184	1	1	yes	characteristic
118	C₄	—	16	2	no	—
119	C₄	—	272	2	no	—
120	C₄	#11763187	1	1	yes	characteristic
121	C₄	#11763188	1	1	yes	characteristic
122	C₄	#11763238	1	2	yes	—
123	C₄	#11763242	1	2	yes	—
124	C₂	#14528401	1	1	yes	characteristic
125	C₂	#14531042	1	1	yes	characteristic
126	C₂	#14531046	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14531064

C₂

yes

maximal

#14531059

C₂

yes

maximal, characteristic

#14528393

C₂

yes

maximal

C₁₆×#3622

C₂

yes

maximal, characteristic

C₁₇×#2252

C₂

yes

maximal, characteristic

#11763214

C₂²

yes

—

—

—

—

—

C₂²

yes

characteristic

C₈×#3622

C₂²

yes

characteristic

C₁₇×#500

C₂²

yes

—

C₁₇×#366

—

C₄×C₁₆×C₁₇

C₂²

yes

characteristic

C₁₇×C₄⋊Q₈

—

#10587555

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₁₇×#107

—

C₁₇×#107

—

C₄×C₈×C₁₇

C₂³

yes

—

—

—

D₄

yes

—

#10587481

—

C₄×#3622

D₄

yes

characteristic

C₄×#3622

D₄

yes

characteristic

C₂×Q₈×C₁₇

—

C₂×Dic₃₄

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₂×#3622

D₈

yes

—

C₂×#3622

D₈

yes

—

C₁₆×C₁₇

Q₁₆

yes

—

#63214

Q₁₆

yes

—

#12522

—

maximal, Sylow

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

characteristic

C₂×Dic₁₇

—

Dic₃₄

—

C₈×C₁₇

C₂×Q₁₆

yes

—

C₈×C₁₇

C₂×Q₁₆

yes

—

—

—

—

—

D₁₇

yes

characteristic

#1710

—

C₈×C₁₆

—

C₂²×C₁₇

#493

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

C₄×C₁₇

#508

yes

—

Dic₁₇

—

#500

—

#500

C₂×D₁₇

yes

—

—

—

—

—

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₇

yes

characteristic

C₈²

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₄⋊Q₈

—

C₄⋊Q₈

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₇

yes

—

—

—

—

—

—

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12522

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×D₁₇

yes

characteristic

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

C₄⋊C₄

—

100

C₄⋊C₄

—

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

D₄×D₁₇

yes

characteristic

104

C₁₆

—

105

C₁₆

#63231

yes

—

106

Q₈

—

107

Q₈

—

136

—

108

C₂×C₄

—

109

C₂×C₄

—

136

—

110

C₂×C₄

D₈×D₁₇

yes

characteristic

111

C₂×C₄

D₈×D₁₇

yes

characteristic

112

C₂×C₄

#10587626

yes

characteristic

113

C₈

—

114

C₈

—

115

C₈

Q₁₆×D₁₇

yes

—

116

C₈

C₂×#63231

yes

—

117

C₂²

#11763184

yes

characteristic

118

C₄

—

119

C₄

—

272

—

120

C₄

#11763187

yes

characteristic

121

C₄

#11763188

yes

characteristic

122

C₄

#11763238

yes

—

123

C₄

#11763242

yes

—

124

C₂

#14528401

yes

characteristic

125

C₂

#14531042

yes

characteristic

126

C₂

#14531046

yes

characteristic

	subgroup	G/H
center	C₂²	#11763184
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#2252	C₂
socle, prime radical	C₂²×C₁₇	#493
hypercenter	#2252	D₁₇
hypocenter	C₁₇	#12522
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2252

subgroup

G/H

center

C₂²

#11763184

commutator, cosocle

C₄×C₈×C₁₇

C₂³

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#2252

C₂

C₂²×C₁₇

D₁₇

C₁₇

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2252

N	H ≅ G/N	type
92. C₁₇	#12522	semidirect

H ≅ G/N

type

92. C₁₇

#12522

semidirect

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

subgroup	index
#14531064	2
#14531059	2
#14528393	2
C₁₆×#3622	2
C₁₇×#2252	2
#12522	17

subgroup

index

#14531064

#14531059

#14528393

C₁₆×#3622

C₁₇×#2252

#12522

Subgroups — #16949063

Conjugacy classes of subgroups

Complements

Maximal subgroups