Group #14543634 — subgroups

Subgroups — #14543634

Order 2176.

164 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 44 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	#11763832	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊#595	C₂	1	1	yes	maximal, characteristic
3	#11762864	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	#10587544	C₄	1	2	yes	complemented
9	#10587543	—	2	1	no	—
10	#10587542	—	2	1	no	—
11	C₁₇×#97	C₄	1	1	yes	characteristic, complemented
12	#10587491	—	2	1	no	—
13	#10587485	—	2	1	no	—
14	#10587474	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	4	no	—
21	C₄×#595	—	4	2	no	—
22	C₂×C₈×C₁₇	—	2	1	no	—
23	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
25	C₄×Dic₁₇	D₄	1	1	yes	characteristic
26	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
27	C₂×#3622	—	2	1	no	—
28	C₂²×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×#595	—	2	4	no	—
30	C₂×#595	—	4	2	no	—
31	C₂×#595	—	4	2	no	—
32	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₁₇	—	2	1	no	—
39	C₄×D₁₇	—	2	1	no	—
40	C₄×D₁₇	—	2	2	no	—
41	C₄×D₁₇	—	4	1	no	—
42	#3624	—	4	2	no	—
43	C₈×C₁₇	—	4	1	no	—
44	#3622	—	4	1	no	—
45	#1285	—	17	1	no	maximal, Sylow
46	C₂²×C₁₇	#95	1	1	yes	characteristic
47	C₂×D₁₇	—	2	1	no	—
48	C₂×D₁₇	—	2	1	no	—
49	C₂×D₁₇	#100	1	1	yes	characteristic
50	C₂×D₁₇	#101	1	1	yes	characteristic
51	#595	—	4	4	no	—
52	C₄×C₁₇	—	2	1	no	—
53	C₄×C₁₇	—	2	1	no	—
54	C₄×C₁₇	—	2	1	no	—
55	Dic₁₇	—	2	1	no	—
56	Dic₁₇	—	2	1	no	—
57	Dic₁₇	#104	1	2	yes	—
58	#432	—	17	1	no	—
59	#432	—	17	1	no	—
60	C₄×C₄⋊C₄	—	17	1	no	—
61	C₂×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
62	C₂×C₁₇	#339	1	1	yes	characteristic
63	C₂×C₁₇	#343	1	1	yes	characteristic
64	D₁₇	—	2	1	no	—
65	D₁₇	—	2	1	no	—
66	C₂×C₄⋊C₄	—	34	1	no	—
67	C₂×C₄²	—	17	1	no	—
68	C₂×C₄²	—	17	2	no	—
69	C₄⋊C₈	—	17	2	no	—
70	C₄⋊C₈	—	34	1	no	—
71	C₂²⋊C₈	—	34	1	no	—
72	C₂²⋊C₈	—	34	1	no	—
73	#97	—	17	1	no	—
74	#97	—	34	1	no	—
75	#97	#595	1	1	yes	characteristic, complemented
76	#95	—	34	1	no	—
77	C₁₇	#1285	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	17	1	no	—
79	C₂²×C₄	—	17	1	no	—
80	C₂²×C₄	—	17	1	no	—
81	C₂²×C₄	—	34	2	no	—
82	C₂×C₈	—	2	1	no	—
83	C₂×C₈	—	34	2	no	—
84	C₂×C₈	—	34	1	no	—
85	C₄⋊C₄	—	34	4	no	—
86	C₄²	—	17	1	no	—
87	C₄²	—	17	1	no	—
88	C₄²	—	17	1	no	—
89	C₄²	—	68	2	no	—
90	C₄²	C₂×#595	1	1	yes	characteristic
91	C₂³	—	17	1	no	—
92	C₂×C₄	—	17	1	no	—
93	C₂×C₄	—	17	1	no	—
94	C₂×C₄	—	17	1	no	—
95	C₂×C₄	—	34	2	no	—
96	C₂×C₄	—	34	1	no	—
97	C₂×C₄	—	34	1	no	—
98	C₂×C₄	—	34	4	no	—
99	C₂×C₄	—	68	1	no	—
100	C₂×C₄	—	68	2	no	—
101	C₂×C₄	—	68	2	no	—
102	C₂×C₄	C₄×#595	1	1	yes	characteristic
103	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
104	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
105	C₈	—	4	1	no	—
106	C₈	—	68	1	no	—
107	C₈	—	68	2	no	—
108	C₂²	—	17	1	no	—
109	C₂²	—	17	1	no	—
110	C₂²	—	34	1	no	—
111	C₂²	—	34	1	no	—
112	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
113	C₄	—	2	1	no	—
114	C₄	—	2	1	no	—
115	C₄	—	2	1	no	—
116	C₄	—	17	2	no	—
117	C₄	—	34	1	no	—
118	C₄	—	34	1	no	—
119	C₄	—	68	4	no	—
120	C₂	—	34	1	no	—
121	C₂	—	34	1	no	—
122	C₂	#11763676	1	1	yes	characteristic
123	C₂	#11763681	1	1	yes	characteristic
124	C₂	#11763688	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763832

C₂

yes

maximal, characteristic

C₄×C₄⋊#595

C₂

yes

maximal, characteristic

#11762864

C₂

yes

maximal, characteristic

C₂×C₄⋊#595

—

C₂×C₄×#595

C₄

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

—

#10587544

C₄

yes

complemented

#10587543

—

#10587542

—

C₁₇×#97

C₄

yes

characteristic, complemented

#10587491

—

#10587485

—

#10587474

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

—

#3624

—

C₈×C₁₇

—

—

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

yes

C₂×D₁₇

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

#104

yes

—

#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

—

C₂²⋊C₈

—

C₂²⋊C₈

—

—

—

yes

characteristic, complemented

#95

—

C₁₇

#1285

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄×#595

yes

characteristic

103

C₂×C₄

C₄⋊#595

yes

characteristic

104

C₂×C₄

C₂²⋊#595

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

(C₂×#595)⋊C₄

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₂

—

121

C₂

—

122

C₂

#11763676

yes

characteristic

123

C₂

#11763681

yes

characteristic

124

C₂

#11763688

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#595)⋊C₄
commutator	C₂×C₄×C₁₇	C₄²
Frattini	C₄²	C₂×#595
Fitting	C₁₇×#97	C₄
socle	C₂²×C₁₇	#95
prime radical	C₂²×D₁₇	C₂²⋊C₄
cosocle	C₄²×D₁₇	C₂²
hypercenter	#97	#595
hypocenter	C₁₇	#1285
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#595)⋊C₄

commutator

C₂×C₄×C₁₇

C₄²

Frattini

C₄²

C₂×#595

Fitting

C₁₇×#97

C₄

socle

C₂²×C₁₇

#95

prime radical

C₂²×D₁₇

C₂²⋊C₄

cosocle

C₄²×D₁₇

C₂²

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
8. #10587544	C₄	semidirect
11. C₁₇×#97	C₄	semidirect
14. #10587474	C₄	semidirect
75. #97	#595	semidirect
77. C₁₇	#1285	semidirect

H ≅ G/N

type

8. #10587544

C₄

semidirect

11. C₁₇×#97

C₄

semidirect

14. #10587474

C₄

semidirect

75. #97

#595

semidirect

77. C₁₇

#1285

semidirect

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

subgroup	index
#11763832	2
C₄×C₄⋊#595	2
#11762864	2
#1285	17

subgroup

index

#11763832

C₄×C₄⋊#595

#11762864

#1285

Subgroups — #14543634

Conjugacy classes of subgroups

Complements

Maximal subgroups