Group #14543662 — subgroups

Subgroups — #14543662

Order 2176.

188 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 76 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	C₂×#10587544	C₂	1	2	yes	maximal
2	#11762678	C₂	1	1	yes	maximal, characteristic
3	C₂²×#3624	—	2	2	no	—
4	C₂×C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
5	C₂×C₄⋊Dic₁₇	C₄	1	1	yes	characteristic
6	C₂×#63225	—	2	2	no	—
7	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
8	#10587544	—	2	2	no	—
9	#10587544	C₄	1	4	yes	complemented
10	C₂²×C₄×C₁₇	—	2	1	no	—
11	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₁₇	—	2	1	no	—
13	C₂²×Dic₁₇	D₄	1	2	yes	—
14	C₂×#3624	—	2	4	no	—
15	C₂×#3624	—	4	2	no	—
16	C₂×#3624	—	4	2	no	—
17	C₄⋊C₄×C₁₇	—	4	1	no	—
18	C₄⋊Dic₁₇	—	4	1	no	—
19	#63225	—	4	2	no	—
20	#63225	—	4	2	no	—
21	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
22	C₄×Dic₁₇	D₄	1	1	yes	characteristic
23	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
24	C₂³×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₁₇	—	2	1	no	—
26	C₂×C₄×C₁₇	—	2	1	no	—
27	C₂×C₄×C₁₇	—	4	1	no	—
28	C₂×C₄×C₁₇	—	4	2	no	—
29	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
31	C₂×Dic₁₇	—	4	1	no	—
32	C₂×Dic₁₇	—	4	2	no	—
33	C₂×Dic₁₇	C₂²⋊C₄	1	2	yes	—
34	C₂×Dic₁₇	C₄⋊C₄	1	2	yes	—
35	C₂×Dic₁₇	D₈	1	2	yes	—
36	C₂×Dic₁₇	SD₁₆	1	2	yes	—
37	C₂×Dic₁₇	SD₁₆	1	2	yes	—
38	C₂×Dic₁₇	Q₁₆	1	2	yes	—
39	#3624	—	4	4	no	—
40	#1296	—	17	1	no	maximal, Sylow
41	C₂²×C₁₇	#95	1	1	yes	characteristic
42	C₂²×C₁₇	#100	1	1	yes	characteristic
43	C₂²×C₁₇	#101	1	1	yes	characteristic
44	C₂²×C₁₇	#102	1	2	yes	—
45	C₂²×C₁₇	#103	1	2	yes	—
46	C₄×C₁₇	—	2	1	no	—
47	C₄×C₁₇	—	2	1	no	—
48	C₄×C₁₇	—	8	1	no	—
49	Dic₁₇	—	8	1	no	—
50	Dic₁₇	#102	1	2	yes	—
51	Dic₁₇	#103	1	2	yes	—
52	Dic₁₇	#106	1	2	yes	—
53	Dic₁₇	#107	1	2	yes	—
54	C₂×C₄⋊C₈	—	17	2	no	—
55	#384	—	17	1	no	—
56	C₂×C₁₇	#331	1	1	yes	characteristic
57	C₂×C₁₇	#332	1	2	yes	—
58	C₂×C₁₇	#333	1	1	yes	characteristic
59	C₂×C₁₇	#340	1	2	yes	—
60	C₂×C₁₇	#343	1	1	yes	characteristic
61	C₂²×C₈	—	34	2	no	—
62	C₂×C₄⋊C₄	—	17	1	no	—
63	C₂×C₄⋊C₄	—	34	2	no	—
64	C₂×C₄⋊C₄	#595	1	1	yes	characteristic
65	C₂×C₄²	—	17	1	no	—
66	C₄⋊C₈	—	17	4	no	—
67	C₄⋊C₈	—	34	2	no	—
68	C₁₇	#1296	1	1	yes	characteristic, complemented, Sylow
69	C₂²×C₄	—	2	1	no	—
70	C₂²×C₄	—	17	2	no	—
71	C₂²×C₄	—	34	1	no	—
72	C₂²×C₄	C₂×#595	1	1	yes	characteristic
73	C₂×C₈	—	34	4	no	—
74	C₂×C₈	—	68	2	no	—
75	C₂×C₈	—	68	2	no	—
76	C₄⋊C₄	—	4	1	no	—
77	C₄⋊C₄	—	68	1	no	—
78	C₄⋊C₄	—	68	2	no	—
79	C₄⋊C₄	—	68	2	no	—
80	C₄²	—	17	2	no	—
81	C₄²	—	17	1	no	—
82	C₄²	—	17	1	no	—
83	C₂³	C₂²⋊#595	1	1	yes	characteristic
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	4	2	no	—
87	C₂×C₄	—	4	1	no	—
88	C₂×C₄	—	17	2	no	—
89	C₂×C₄	—	17	2	no	—
90	C₂×C₄	—	17	2	no	—
91	C₂×C₄	—	17	2	no	—
92	C₂×C₄	—	17	2	no	—
93	C₂×C₄	—	17	2	no	—
94	C₂×C₄	—	68	2	no	—
95	C₂×C₄	—	68	1	no	—
96	C₂×C₄	C₄×#595	1	1	yes	characteristic
97	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
98	C₈	—	68	4	no	—
99	C₂²	#10587545	1	1	yes	characteristic
100	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
101	C₂²	#10587547	1	2	yes	—
102	C₂²	#10587549	1	2	yes	—
103	C₂²	#10587553	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	8	1	no	—
107	C₄	—	17	2	no	—
108	C₄	—	17	2	no	—
109	C₄	—	17	2	no	—
110	C₄	—	17	2	no	—
111	C₄	—	136	1	no	—
112	C₂	#11763667	1	1	yes	characteristic
113	C₂	#11763668	1	2	yes	—
114	C₂	#11763669	1	1	yes	characteristic
115	C₂	#11763682	1	2	yes	—
116	C₂	#11763689	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587544

C₂

yes

maximal

#11762678

C₂

yes

maximal, characteristic

C₂²×#3624

—

C₂×C₄⋊C₄×C₁₇

C₄

yes

characteristic

C₂×C₄⋊Dic₁₇

C₄

yes

characteristic

C₂×#63225

—

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

#10587544

—

#10587544

C₄

yes

complemented

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

—

C₂²×Dic₁₇

D₄

yes

—

C₂×#3624

—

C₂×#3624

—

C₂×#3624

—

C₄⋊C₄×C₁₇

—

C₄⋊Dic₁₇

—

#63225

—

#63225

—

C₄×Dic₁₇

C₂×C₄

yes

—

C₄×Dic₁₇

D₄

yes

characteristic

C₄×Dic₁₇

Q₈

yes

characteristic

C₂³×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂²⋊C₄

yes

—

C₂×Dic₁₇

C₄⋊C₄

yes

—

C₂×Dic₁₇

D₈

yes

—

C₂×Dic₁₇

SD₁₆

yes

—

C₂×Dic₁₇

SD₁₆

yes

—

C₂×Dic₁₇

Q₁₆

yes

—

—

—

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

—

C₂²×C₁₇

#103

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

#102

yes

—

Dic₁₇

#103

yes

—

Dic₁₇

#106

yes

—

Dic₁₇

#107

yes

—

C₂×C₄⋊C₈

—

#384

—

C₂×C₁₇

#331

yes

characteristic

C₂×C₁₇

#332

yes

—

C₂×C₁₇

#333

yes

characteristic

C₂×C₁₇

#340

yes

—

C₂×C₁₇

#343

yes

characteristic

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

#595

yes

characteristic

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₁₇

#1296

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#595

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₂²⋊#595

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₂²

#10587545

yes

characteristic

100

C₂²

(C₂×#595)⋊C₄

yes

characteristic

101

C₂²

#10587547

yes

—

102

C₂²

#10587549

yes

—

103

C₂²

#10587553

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

136

—

112

C₂

#11763667

yes

characteristic

113

C₂

#11763668

yes

—

114

C₂

#11763669

yes

characteristic

115

C₂

#11763682

yes

—

116

C₂

#11763689

yes

characteristic

	subgroup	G/H
center	C₂³	C₂²⋊#595
commutator	C₂×C₄×C₁₇	C₄²
Frattini	C₂²×C₄	C₂×#595
Fitting	C₂×C₄⋊C₄×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂²⋊C₄
cosocle	C₂×C₄×Dic₁₇	C₂²
hypercenter	C₂×C₄⋊C₄	#595
hypocenter	C₁₇	#1296
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

subgroup

G/H

center

C₂³

C₂²⋊#595

commutator

C₂×C₄×C₁₇

C₄²

Frattini

C₂²×C₄

C₂×#595

Fitting

C₂×C₄⋊C₄×C₁₇

C₄

socle, prime radical

C₂³×C₁₇

C₂²⋊C₄

cosocle

C₂×C₄×Dic₁₇

C₂²

C₂×C₄⋊C₄

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
9. #10587544	C₄	semidirect
68. C₁₇	#1296	semidirect

H ≅ G/N

type

9. #10587544

C₄

semidirect

68. C₁₇

#1296

semidirect

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

subgroup	index
C₂×#10587544	2
#11762678	2
#1296	17

subgroup

index

C₂×#10587544

#11762678

#1296

Subgroups — #14543662

Conjugacy classes of subgroups

Complements

Maximal subgroups