Group #16949037 — subgroups

Subgroups — #16949037

Order 4352.

310 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 95 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	#14531037	C₂	1	1	yes	maximal, characteristic
2	#14531036	C₂	1	2	yes	maximal
3	#14528400	C₂	1	2	yes	maximal
4	C₁₆×#3622	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#2247	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₃₆	—	2	2	no	—
7	C₂×#10587500	—	2	4	no	—
8	#11763212	—	2	4	no	—
9	#11763189	C₂²	1	2	yes	—
10	C₄×#63214	C₂²	1	1	yes	characteristic
11	C₈×#3622	C₂²	1	1	yes	characteristic
12	C₂×C₁₇×Q₃₂	—	2	2	no	—
13	C₁₇×#494	C₂²	1	2	yes	—
14	C₄×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
15	C₂×Q₁₆×C₁₇	—	2	2	no	—
16	C₂×Q₁₆×C₁₇	—	2	2	no	—
17	C₁₇×C₄⋊Q₈	—	2	2	no	—
18	C₂×Dic₆₈	—	2	2	no	—
19	C₂×Dic₆₈	—	2	2	no	—
20	#10587555	—	2	2	no	—
21	C₁₇×Q₃₂	—	4	4	no	—
22	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
23	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
24	#10587500	—	4	8	no	—
25	C₂×#63214	D₄	1	2	yes	—
26	#10587478	—	4	8	no	—
27	C₄×#3622	D₄	1	2	yes	—
28	Dic₁₃₆	—	4	4	no	—
29	C₂×Q₈×C₁₇	—	4	2	no	—
30	C₂×Dic₃₄	—	4	2	no	—
31	Q₁₆×C₁₇	—	4	4	no	—
32	Q₁₆×C₁₇	—	4	4	no	—
33	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
35	C₄⋊C₄×C₁₇	—	4	4	no	—
36	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
37	C₄⋊Dic₁₇	—	4	4	no	—
38	C₂×#3622	D₈	1	4	yes	—
39	Dic₆₈	—	4	4	no	—
40	Dic₆₈	—	4	4	no	—
41	C₁₆×C₁₇	D₈	1	4	yes	—
42	#63214	D₈	1	4	yes	—
43	#12516	—	17	1	no	maximal, Sylow
44	Q₈×C₁₇	—	8	2	no	—
45	Q₈×C₁₇	—	8	2	no	—
46	C₂×C₄×C₁₇	—	8	2	no	—
47	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
48	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
49	C₂×Dic₁₇	—	8	2	no	—
50	Dic₃₄	—	8	2	no	—
51	Dic₃₄	—	8	2	no	—
52	C₈×C₁₇	C₂×D₈	1	2	yes	—
53	C₈×C₁₇	C₂×D₈	1	2	yes	—
54	#3622	Q₃₂	1	8	yes	complemented
55	#2247	—	17	2	no	—
56	#2247	—	17	1	no	—
57	#2247	D₁₇	1	1	yes	characteristic
58	#1713	—	17	2	no	—
59	C₈×C₁₆	—	17	1	no	—
60	C₂²×C₁₇	#493	1	1	yes	characteristic
61	C₄×C₁₇	—	16	2	no	—
62	C₄×C₁₇	#493	1	1	yes	characteristic
63	C₄×C₁₇	#493	1	1	yes	characteristic
64	C₄×C₁₇	C₂×Q₃₂	1	4	yes	—
65	Dic₁₇	—	16	2	no	—
66	C₂×Q₃₂	—	2	2	no	—
67	C₂×Q₃₂	—	34	4	no	—
68	C₂×Q₃₂	—	34	2	no	—
69	#500	—	34	4	no	—
70	#494	—	17	2	no	—
71	#494	C₂×D₁₇	1	2	yes	—
72	C₄×C₁₆	—	17	1	no	—
73	C₄×C₁₆	C₂×D₁₇	1	1	yes	characteristic
74	C₈²	—	17	1	no	—
75	C₂×C₁₇	#1712	1	1	yes	characteristic
76	C₂×C₁₇	#2247	1	2	yes	—
77	C₂×Q₁₆	—	2	2	no	—
78	C₂×Q₁₆	—	2	2	no	—
79	C₂×Q₁₆	—	34	2	no	—
80	C₂×Q₁₆	—	34	2	no	—
81	C₄⋊Q₈	—	2	2	no	—
82	C₄⋊Q₈	—	34	2	no	—
83	Q₃₂	—	4	4	no	—
84	Q₃₂	—	68	8	no	—
85	Q₃₂	—	68	4	no	—
86	C₂×C₁₆	—	17	2	no	—
87	C₂×C₁₆	C₂²⋊D₁₇	1	2	yes	—
88	#107	—	68	8	no	—
89	C₄×C₈	—	17	2	no	—
90	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
91	C₁₇	#12516	1	1	yes	characteristic, complemented, Sylow
92	C₂×Q₈	—	4	2	no	—
93	C₂×Q₈	—	68	2	no	—
94	Q₁₆	—	4	4	no	—
95	Q₁₆	—	4	4	no	—
96	Q₁₆	—	68	4	no	—
97	Q₁₆	—	68	4	no	—
98	C₂×C₈	—	17	4	no	—
99	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
100	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
101	C₄⋊C₄	—	4	4	no	—
102	C₄⋊C₄	—	68	4	no	—
103	C₄²	D₄×D₁₇	1	1	yes	characteristic
104	C₁₆	—	17	4	no	—
105	C₁₆	#63228	1	4	yes	—
106	Q₈	—	8	2	no	—
107	Q₈	—	8	2	no	—
108	Q₈	—	136	2	no	—
109	Q₈	—	136	2	no	—
110	C₂×C₄	—	8	2	no	—
111	C₂×C₄	—	136	2	no	—
112	C₂×C₄	D₈×D₁₇	1	2	yes	—
113	C₂×C₄	#10587626	1	1	yes	characteristic
114	C₈	—	17	8	no	—
115	C₈	D₈×D₁₇	1	2	yes	—
116	C₈	C₂×#63228	1	2	yes	—
117	C₂²	#11763184	1	1	yes	characteristic
118	C₄	—	16	2	no	—
119	C₄	—	272	2	no	—
120	C₄	#11763184	1	1	yes	characteristic
121	C₄	#11763185	1	1	yes	characteristic
122	C₄	Q₃₂×D₁₇	1	4	yes	—
123	C₂	#14528398	1	1	yes	characteristic
124	C₂	#14531035	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14531037

C₂

yes

maximal, characteristic

#14531036

C₂

yes

maximal

#14528400

C₂

yes

maximal

C₁₆×#3622

C₂

yes

maximal, characteristic

C₁₇×#2247

C₂

yes

maximal, characteristic

C₂×Dic₁₃₆

—

C₂×#10587500

—

#11763212

—

#11763189

C₂²

yes

—

C₄×#63214

C₂²

yes

characteristic

C₈×#3622

C₂²

yes

characteristic

C₂×C₁₇×Q₃₂

—

C₁₇×#494

C₂²

yes

—

C₄×C₁₆×C₁₇

C₂²

yes

characteristic

C₂×Q₁₆×C₁₇

—

C₂×Q₁₆×C₁₇

—

C₁₇×C₄⋊Q₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

#10587555

—

C₁₇×Q₃₂

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

C₂³

yes

characteristic

#10587500

—

C₂×#63214

D₄

yes

—

#10587478

—

C₄×#3622

D₄

yes

—

Dic₁₃₆

—

C₂×Q₈×C₁₇

—

C₂×Dic₃₄

—

Q₁₆×C₁₇

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄⋊Dic₁₇

—

C₂×#3622

D₈

yes

—

Dic₆₈

—

Dic₆₈

—

C₁₆×C₁₇

D₈

yes

—

#63214

D₈

yes

—

#12516

—

maximal, Sylow

Q₈×C₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×Dic₁₇

—

Dic₃₄

—

Dic₃₄

—

C₈×C₁₇

C₂×D₈

yes

—

C₈×C₁₇

C₂×D₈

yes

—

#3622

Q₃₂

yes

—

—

D₁₇

yes

characteristic

#1713

—

C₈×C₁₆

—

C₂²×C₁₇

#493

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

C₂×Q₃₂

yes

—

Dic₁₇

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×Q₃₂

—

#500

—

#494

—

#494

C₂×D₁₇

yes

—

C₄×C₁₆

—

C₄×C₁₆

C₂×D₁₇

yes

characteristic

C₈²

—

C₂×C₁₇

#1712

yes

characteristic

C₂×C₁₇

#2247

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

C₂×C₁₆

—

C₂×C₁₆

C₂²⋊D₁₇

yes

—

#107

—

C₄×C₈

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12516

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

D₄×D₁₇

yes

characteristic

100

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

101

C₄⋊C₄

—

102

C₄⋊C₄

—

103

C₄²

D₄×D₁₇

yes

characteristic

104

C₁₆

—

105

C₁₆

#63228

yes

—

106

Q₈

—

107

Q₈

—

108

Q₈

—

136

—

109

Q₈

—

136

—

110

C₂×C₄

—

111

C₂×C₄

—

136

—

112

C₂×C₄

D₈×D₁₇

yes

—

113

C₂×C₄

#10587626

yes

characteristic

114

C₈

—

115

C₈

D₈×D₁₇

yes

—

116

C₈

C₂×#63228

yes

—

117

C₂²

#11763184

yes

characteristic

118

C₄

—

119

C₄

—

272

—

120

C₄

#11763184

yes

characteristic

121

C₄

#11763185

yes

characteristic

122

C₄

Q₃₂×D₁₇

yes

—

123

C₂

#14528398

yes

characteristic

124

C₂

#14531035

yes

—

	subgroup	G/H
center	C₂²	#11763184
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#2247	C₂
socle, prime radical	C₂²×C₁₇	#493
hypercenter	#2247	D₁₇
hypocenter	C₁₇	#12516
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

subgroup

G/H

center

C₂²

#11763184

commutator, cosocle

C₄×C₈×C₁₇

C₂³

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#2247

C₂

C₂²×C₁₇

D₁₇

C₁₇

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

N	H ≅ G/N	type
54. #3622	Q₃₂	semidirect
91. C₁₇	#12516	semidirect

H ≅ G/N

type

54. #3622

Q₃₂

semidirect

91. C₁₇

#12516

semidirect

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

subgroup	index
#14531037	2
#14531036	2
#14528400	2
C₁₆×#3622	2
C₁₇×#2247	2
#12516	17

subgroup

index

#14531037

#14531036

#14528400

C₁₆×#3622

C₁₇×#2247

#12516

Subgroups — #16949037

Conjugacy classes of subgroups

Complements

Maximal subgroups