Group #14543636 — subgroups

Subgroups — #14543636

Order 2176.

164 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 46 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	#11763831	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#595	C₂	1	1	yes	maximal, characteristic
3	#11762865	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊#595	—	2	1	no	—
5	C₂×C₄×#595	C₄	1	2	yes	—
6	C₄²×D₁₇	C₂²	1	1	yes	characteristic
7	(C₂×#595)⋊C₄	—	2	1	no	—
8	#10587543	—	2	1	no	—
9	#10587542	C₄	1	2	yes	complemented
10	C₄⋊#3624	—	2	1	no	—
11	C₁₇×C₄⋊C₈	C₄	1	1	yes	characteristic, complemented
12	#10587491	—	2	1	no	—
13	#10587486	—	2	1	no	—
14	C₄⋊#3622	C₄	1	1	yes	characteristic, complemented
15	C₂²×#595	—	2	2	no	—
16	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
18	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
19	C₂×#3624	—	2	2	no	—
20	C₄⋊#595	—	2	2	no	—
21	C₄⋊#595	—	2	2	no	—
22	C₄×#595	—	4	2	no	—
23	C₂×C₈×C₁₇	—	2	1	no	—
24	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₁₇	D₄	1	1	yes	characteristic
27	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
28	C₂×#3622	—	2	1	no	—
29	C₂²×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×#595	—	2	4	no	—
31	C₂×#595	—	4	2	no	—
32	C₂×#595	—	4	2	no	—
33	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
36	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
37	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
39	C₄×D₁₇	—	2	1	no	—
40	C₄×D₁₇	—	2	1	no	—
41	C₄×D₁₇	—	2	1	no	—
42	C₄×D₁₇	—	2	1	no	—
43	C₄×D₁₇	—	4	1	no	—
44	#3624	—	4	2	no	—
45	C₈×C₁₇	—	4	1	no	—
46	#3622	—	4	1	no	—
47	#1285	—	17	1	no	maximal, Sylow
48	C₂²×C₁₇	#95	1	1	yes	characteristic
49	C₂×D₁₇	—	2	1	no	—
50	C₂×D₁₇	—	2	1	no	—
51	C₂×D₁₇	#100	1	1	yes	characteristic
52	C₂×D₁₇	#101	1	1	yes	characteristic
53	#595	—	4	4	no	—
54	C₄×C₁₇	—	2	1	no	—
55	C₄×C₁₇	—	2	1	no	—
56	C₄×C₁₇	#104	1	1	yes	characteristic
57	C₄×C₁₇	#104	1	1	yes	characteristic
58	Dic₁₇	—	2	1	no	—
59	Dic₁₇	—	2	1	no	—
60	Dic₁₇	—	2	1	no	—
61	#432	—	17	1	no	—
62	#432	—	17	1	no	—
63	C₄×C₄⋊C₄	—	17	1	no	—
64	C₂×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
65	C₂×C₁₇	#339	1	1	yes	characteristic
66	C₂×C₁₇	#343	1	1	yes	characteristic
67	D₁₇	—	2	1	no	—
68	D₁₇	—	2	1	no	—
69	C₂×C₄⋊C₄	—	34	1	no	—
70	C₂×C₄²	—	17	1	no	—
71	C₂×C₄²	—	17	2	no	—
72	C₄⋊C₈	—	17	1	no	—
73	C₄⋊C₈	—	34	1	no	—
74	C₄⋊C₈	#595	1	1	yes	characteristic, complemented
75	C₂²⋊C₈	—	34	1	no	—
76	C₂²⋊C₈	—	34	1	no	—
77	#97	—	17	2	no	—
78	#97	—	34	1	no	—
79	#95	—	34	1	no	—
80	C₁₇	#1285	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	17	1	no	—
82	C₂²×C₄	—	17	1	no	—
83	C₂²×C₄	—	17	1	no	—
84	C₂²×C₄	—	34	2	no	—
85	C₂×C₈	—	2	1	no	—
86	C₂×C₈	—	34	2	no	—
87	C₂×C₈	—	34	1	no	—
88	C₄⋊C₄	—	34	2	no	—
89	C₄⋊C₄	—	34	2	no	—
90	C₄²	—	17	1	no	—
91	C₄²	—	17	1	no	—
92	C₄²	—	17	1	no	—
93	C₄²	—	68	2	no	—
94	C₄²	C₂×#595	1	1	yes	characteristic
95	C₂³	—	17	1	no	—
96	C₂×C₄	—	17	1	no	—
97	C₂×C₄	—	17	1	no	—
98	C₂×C₄	—	17	1	no	—
99	C₂×C₄	—	34	1	no	—
100	C₂×C₄	—	34	1	no	—
101	C₂×C₄	—	34	1	no	—
102	C₂×C₄	—	34	1	no	—
103	C₂×C₄	—	34	4	no	—
104	C₂×C₄	—	68	1	no	—
105	C₂×C₄	—	68	2	no	—
106	C₂×C₄	—	68	2	no	—
107	C₂×C₄	C₄×#595	1	1	yes	characteristic
108	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
109	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
110	C₈	—	4	1	no	—
111	C₈	—	68	2	no	—
112	C₈	—	68	1	no	—
113	C₂²	—	17	1	no	—
114	C₂²	—	17	1	no	—
115	C₂²	—	34	1	no	—
116	C₂²	—	34	1	no	—
117	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
118	C₄	—	2	1	no	—
119	C₄	—	2	1	no	—
120	C₄	—	34	1	no	—
121	C₄	—	34	1	no	—
122	C₄	—	34	1	no	—
123	C₄	—	68	4	no	—
124	C₄	#10587548	1	1	yes	characteristic
125	C₄	#10587550	1	1	yes	characteristic
126	C₂	—	34	1	no	—
127	C₂	—	34	1	no	—
128	C₂	#11763677	1	1	yes	characteristic
129	C₂	#11763679	1	1	yes	characteristic
130	C₂	#11763688	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763831

C₂

yes

maximal, characteristic

C₄×C₄⋊#595

C₂

yes

maximal, characteristic

#11762865

C₂

yes

maximal, characteristic

C₂×C₄⋊#595

—

C₂×C₄×#595

C₄

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

—

#10587543

—

#10587542

C₄

yes

complemented

C₄⋊#3624

—

C₁₇×C₄⋊C₈

C₄

yes

characteristic, complemented

#10587491

—

#10587486

—

C₄⋊#3622

C₄

yes

characteristic, complemented

C₂²×#595

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

—

—

—

—

C₂×C₈×C₁₇

—

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

D₄

yes

characteristic

C₄×Dic₁₇

Q₈

yes

characteristic

C₂×#3622

—

C₂²×D₁₇

C₂²⋊C₄

yes

—

—

—

C₂×C₄×C₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

C₈×C₁₇

—

—

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

yes

C₂×D₁₇

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

—

Dic₁₇

—

#432

—

#432

—

C₄×C₄⋊C₄

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

D₁₇

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#595

yes

characteristic, complemented

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

—

#97

—

#95

—

C₁₇

#1285

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

C₄×#595

yes

characteristic

108

C₂×C₄

C₄⋊#595

yes

characteristic

109

C₂×C₄

C₂²⋊#595

yes

characteristic

110

C₈

—

111

C₈

—

112

C₈

—

113

C₂²

—

114

C₂²

—

115

C₂²

—

116

C₂²

—

117

C₂²

(C₂×#595)⋊C₄

yes

characteristic

118

C₄

—

119

C₄

—

120

C₄

—

121

C₄

—

122

C₄

—

123

C₄

—

124

C₄

#10587548

yes

characteristic

125

C₄

#10587550

yes

characteristic

126

C₂

—

127

C₂

—

128

C₂

#11763677

yes

characteristic

129

C₂

#11763679

yes

characteristic

130

C₂

#11763688

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#595)⋊C₄
commutator	C₂×C₄×C₁₇	C₄²
Frattini	C₄²	C₂×#595
Fitting	C₁₇×C₄⋊C₈	C₄
socle	C₂²×C₁₇	#95
prime radical	C₂²×D₁₇	C₂²⋊C₄
cosocle	C₄²×D₁₇	C₂²
hypercenter	C₄⋊C₈	#595
hypocenter	C₁₇	#1285
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

subgroup

G/H

center

C₂²

(C₂×#595)⋊C₄

commutator

C₂×C₄×C₁₇

C₄²

Frattini

C₄²

C₂×#595

Fitting

C₁₇×C₄⋊C₈

C₄

socle

C₂²×C₁₇

#95

prime radical

C₂²×D₁₇

C₂²⋊C₄

cosocle

C₄²×D₁₇

C₂²

C₄⋊C₈

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

N	H ≅ G/N	type
9. #10587542	C₄	semidirect
11. C₁₇×C₄⋊C₈	C₄	semidirect
14. C₄⋊#3622	C₄	semidirect
74. C₄⋊C₈	#595	semidirect
80. C₁₇	#1285	semidirect

H ≅ G/N

type

9. #10587542

C₄

semidirect

11. C₁₇×C₄⋊C₈

C₄

semidirect

14. C₄⋊#3622

C₄

semidirect

74. C₄⋊C₈

#595

semidirect

80. C₁₇

#1285

semidirect

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

subgroup	index
#11763831	2
C₄×C₄⋊#595	2
#11762865	2
#1285	17

subgroup

index

#11763831

C₄×C₄⋊#595

#11762865

#1285

Subgroups — #14543636

Conjugacy classes of subgroups

Complements

Maximal subgroups