Group #16923638 — subgroups

Subgroups — #16923638

Order 4352.

322 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14530347	C₂	1	3	yes	maximal
2	#14526607	C₂	1	3	yes	maximal
3	C₁₇×#2810	C₂	1	1	yes	maximal, characteristic
4	#11762679	C₂²	1	1	yes	characteristic
5	#11762571	—	2	3	no	—
6	#11762571	—	2	3	no	—
7	#11762564	C₂²	1	3	yes	—
8	C₁₇×#400	—	2	3	no	—
9	C₁₇×#389	C₂²	1	3	yes	—
10	C₁₇×#387	—	2	3	no	—
11	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
12	C₂×C₄⋊C₄×C₁₇	D₄	1	3	yes	—
13	C₂×C₄⋊C₄×C₁₇	D₄	1	3	yes	—
14	C₂×C₄²×C₁₇	—	2	1	no	—
15	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₇	—	2	3	no	—
17	C₂²×#3622	—	2	3	no	—
18	C₁₇×#95	—	2	3	no	—
19	C₁₇×#95	—	2	3	no	—
20	C₁₇×#95	—	2	1	no	—
21	C₁₇×#95	—	2	3	no	—
22	C₂²×C₄×C₁₇	—	2	3	no	—
23	C₂²×C₄×C₁₇	—	2	3	no	—
24	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
25	C₂²×Dic₁₇	—	4	1	no	—
26	C₄⋊C₄×C₁₇	—	2	3	no	—
27	C₄⋊C₄×C₁₇	—	2	3	no	—
28	C₄⋊C₄×C₁₇	—	4	3	no	—
29	C₄⋊C₄×C₁₇	—	4	3	no	—
30	C₄⋊C₄×C₁₇	—	4	3	no	—
31	C₄²×C₁₇	—	4	1	no	—
32	C₄²×C₁₇	—	8	1	no	—
33	C₄⋊Dic₁₇	—	4	6	no	—
34	C₂×#3622	—	4	3	no	—
35	C₂×#3622	—	4	3	no	—
36	C₂×#3622	—	4	3	no	—
37	#7832	—	17	1	no	maximal, Sylow
38	C₂³×C₁₇	#120	1	1	yes	characteristic
39	C₂×C₄×C₁₇	—	2	3	no	—
40	C₂×C₄×C₁₇	—	2	3	no	—
41	C₂×C₄×C₁₇	—	4	3	no	—
42	C₂×C₄×C₁₇	—	4	3	no	—
43	C₂×C₄×C₁₇	—	4	3	no	—
44	C₂×C₄×C₁₇	—	4	3	no	—
45	C₂×C₄×C₁₇	—	4	3	no	—
46	C₂×C₄×C₁₇	—	4	3	no	—
47	C₂×C₄×C₁₇	#135	1	3	yes	—
48	C₂×C₄×C₁₇	#137	1	3	yes	—
49	C₂×Dic₁₇	—	8	3	no	—
50	#3622	—	8	3	no	—
51	#2810	D₁₇	1	1	yes	characteristic
52	#2100	—	17	3	no	—
53	#1271	—	17	3	no	—
54	C₂²×C₁₇	#452	1	3	yes	—
55	C₂²×C₁₇	#454	1	3	yes	—
56	C₂²×C₁₇	#458	1	1	yes	characteristic
57	C₄×C₁₇	—	2	3	no	—
58	C₄×C₁₇	—	2	3	no	—
59	C₄×C₁₇	—	8	3	no	—
60	C₄×C₁₇	—	8	3	no	—
61	Dic₁₇	—	16	1	no	—
62	#400	—	2	3	no	—
63	#389	C₂×D₁₇	1	3	yes	—
64	#387	—	2	3	no	—
65	#384	—	17	1	no	—
66	#340	—	34	3	no	—
67	#340	—	34	3	no	—
68	#336	—	17	3	no	—
69	C₂×C₁₇	#1615	1	3	yes	—
70	C₂×C₁₇	#1638	1	3	yes	—
71	C₂×C₁₇	#1658	1	1	yes	characteristic
72	C₂²×C₈	—	34	3	no	—
73	C₂×C₄⋊C₄	—	2	3	no	—
74	C₂×C₄⋊C₄	—	34	3	no	—
75	C₂×C₄⋊C₄	C₂²⋊D₁₇	1	3	yes	—
76	C₂×C₄⋊C₄	C₂²⋊D₁₇	1	3	yes	—
77	C₂×C₄²	—	2	1	no	—
78	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
79	#95	—	2	3	no	—
80	#95	—	2	3	no	—
81	#95	—	2	1	no	—
82	#95	—	2	3	no	—
83	C₁₇	#7832	1	1	yes	characteristic, complemented, Sylow
84	C₂²×C₄	—	2	3	no	—
85	C₂²×C₄	—	2	3	no	—
86	C₂²×C₄	—	68	1	no	—
87	C₂²×C₄	C₂×C₂²⋊D₁₇	1	3	yes	—
88	C₂×C₈	—	68	3	no	—
89	C₂×C₈	—	68	3	no	—
90	C₂×C₈	—	68	3	no	—
91	C₄⋊C₄	—	2	3	no	—
92	C₄⋊C₄	—	2	3	no	—
93	C₄⋊C₄	—	4	3	no	—
94	C₄⋊C₄	—	4	3	no	—
95	C₄⋊C₄	—	4	3	no	—
96	C₄⋊C₄	—	68	6	no	—
97	C₄²	—	4	1	no	—
98	C₄²	—	8	1	no	—
99	C₂³	#10587639	1	1	yes	characteristic
100	C₂×C₄	—	2	3	no	—
101	C₂×C₄	—	2	3	no	—
102	C₂×C₄	—	4	3	no	—
103	C₂×C₄	—	4	3	no	—
104	C₂×C₄	—	4	3	no	—
105	C₂×C₄	—	4	3	no	—
106	C₂×C₄	—	4	3	no	—
107	C₂×C₄	—	4	3	no	—
108	C₂×C₄	—	136	3	no	—
109	C₂×C₄	#10587636	1	3	yes	—
110	C₂×C₄	#10587637	1	3	yes	—
111	C₈	—	136	3	no	—
112	C₂²	#11762971	1	3	yes	—
113	C₂²	#11762982	1	3	yes	—
114	C₂²	#11762999	1	1	yes	characteristic
115	C₄	—	2	3	no	—
116	C₄	—	2	3	no	—
117	C₄	—	8	3	no	—
118	C₄	—	8	3	no	—
119	C₄	—	272	1	no	—
120	C₂	#14527815	1	3	yes	—
121	C₂	#14527956	1	3	yes	—
122	C₂	#14528086	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14530347

C₂

yes

maximal

#14526607

C₂

yes

maximal

C₁₇×#2810

C₂

yes

maximal, characteristic

#11762679

C₂²

yes

—

—

C₂²

yes

—

C₁₇×#400

—

C₁₇×#389

C₂²

yes

—

C₁₇×#387

—

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄⋊C₄×C₁₇

D₄

yes

—

C₂×C₄⋊C₄×C₁₇

D₄

yes

—

C₂×C₄²×C₁₇

—

C₂×C₄²×C₁₇

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₇

—

C₂²×#3622

—

C₁₇×#95

—

C₁₇×#95

—

C₁₇×#95

—

C₁₇×#95

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

—

C₂²×Dic₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

—

C₄²×C₁₇

—

C₄⋊Dic₁₇

—

—

—

—

—

C₂³×C₁₇

yes

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#135

yes

—

C₂×C₄×C₁₇

#137

yes

—

C₂×Dic₁₇

—

#3622

—

#2810

D₁₇

yes

characteristic

#2100

—

#1271

—

C₂²×C₁₇

#452

yes

—

C₂²×C₁₇

#454

yes

—

C₂²×C₁₇

#458

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

#400

—

#389

C₂×D₁₇

yes

—

—

—

—

—

—

C₂×C₁₇

#1615

yes

—

C₂×C₁₇

#1638

yes

—

C₂×C₁₇

#1658

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₇

yes

—

C₂×C₄⋊C₄

C₂²⋊D₁₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₁₇

yes

—

—

—

—

C₁₇

#7832

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₂³

#10587639

yes

characteristic

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

136

—

109

C₂×C₄

#10587636

yes

—

110

C₂×C₄

#10587637

yes

—

111

C₈

—

136

—

112

C₂²

#11762971

yes

—

113

C₂²

#11762982

yes

—

114

C₂²

#11762999

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

272

—

120

C₂

#14527815

yes

—

121

C₂

#14527956

yes

—

122

C₂

#14528086

yes

characteristic

	subgroup	G/H
center	C₂³	#10587639
commutator, cosocle	C₂×C₄²×C₁₇	C₂³
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₁₇×#2810	C₂
socle, prime radical	C₂³×C₁₇	#120
hypercenter	#2810	D₁₇
hypocenter	C₁₇	#7832
LCS	G ▷ C₂×C₄²×C₁₇ ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

subgroup

G/H

center

C₂³

#10587639

commutator, cosocle

C₂×C₄²×C₁₇

C₂³

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₁₇×#2810

C₂

C₂³×C₁₇

D₁₇

C₁₇

G ▷ C₂×C₄²×C₁₇ ▷ C₂³×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2810

N	H ≅ G/N	type
83. C₁₇	#7832	semidirect

H ≅ G/N

type

83. C₁₇

#7832

semidirect

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

subgroup	index
#14530347	2
#14526607	2
C₁₇×#2810	2
#7832	17

subgroup

index

#14530347

#14526607

C₁₇×#2810

#7832

Subgroups — #16923638

Conjugacy classes of subgroups

Complements

Maximal subgroups