Group #14543645 — subgroups

Subgroups — #14543645

Order 2176.

152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 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	C₄×#63243	C₂	1	1	yes	maximal, characteristic
2	#11763754	C₂	1	1	yes	maximal, characteristic
3	#11762864	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	—	2	1	no	—
5	C₄²×D₁₇	C₂²	1	1	yes	characteristic
6	(C₂×#595)⋊C₄	—	2	1	no	—
7	(C₂×#595)⋊C₄	—	2	1	no	—
8	(C₂×#595)⋊C₄	C₄	1	2	yes	—
9	#10587542	—	2	1	no	—
10	C₄×#3624	C₄	1	2	yes	complemented
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	#63243	—	2	4	no	—
21	C₂×C₈×C₁₇	—	2	1	no	—
22	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₇	D₄	1	1	yes	characteristic
25	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
26	C₂×#3622	—	2	1	no	—
27	C₂²×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×#595	—	4	2	no	—
29	C₂×#595	—	4	2	no	—
30	C₂×#595	—	4	2	no	—
31	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
34	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
35	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
36	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
37	C₄×D₁₇	—	2	2	no	—
38	C₄×D₁₇	—	4	1	no	—
39	C₄×D₁₇	—	4	1	no	—
40	#3624	—	2	4	no	—
41	C₈×C₁₇	—	4	1	no	—
42	#3622	—	4	1	no	—
43	#1288	—	17	1	no	maximal, Sylow
44	C₂²×C₁₇	#95	1	1	yes	characteristic
45	C₂×D₁₇	—	2	1	no	—
46	C₂×D₁₇	—	2	1	no	—
47	C₂×D₁₇	#104	1	2	yes	—
48	#595	—	8	2	no	—
49	C₄×C₁₇	—	2	1	no	—
50	C₄×C₁₇	—	2	1	no	—
51	C₄×C₁₇	—	2	1	no	—
52	Dic₁₇	—	2	1	no	—
53	Dic₁₇	—	2	1	no	—
54	Dic₁₇	—	2	1	no	—
55	#432	—	17	1	no	—
56	C₄×M₁₆	—	17	1	no	—
57	#383	—	17	1	no	—
58	C₂×C₁₇	H(3,ℤ/4)	1	1	yes	characteristic
59	C₂×C₁₇	#339	1	1	yes	characteristic
60	C₂×C₁₇	#344	1	1	yes	characteristic
61	D₁₇	—	2	2	no	—
62	C₂×M₁₆	—	34	1	no	—
63	C₂×C₄²	—	17	1	no	—
64	C₄⋊C₈	—	34	1	no	—
65	C₂²⋊C₈	—	34	1	no	—
66	#97	—	17	1	no	—
67	#97	—	34	1	no	—
68	#97	#595	1	1	yes	characteristic, complemented
69	C₄×C₈	—	17	2	no	—
70	#95	—	17	2	no	—
71	#95	—	34	1	no	—
72	#95	—	34	1	no	—
73	C₁₇	#1288	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	—	17	1	no	—
75	C₂²×C₄	—	17	1	no	—
76	C₂²×C₄	—	17	1	no	—
77	C₂²×C₄	—	34	2	no	—
78	M₁₆	—	34	4	no	—
79	C₂×C₈	—	2	1	no	—
80	C₂×C₈	—	34	2	no	—
81	C₂×C₈	—	34	1	no	—
82	C₄²	—	17	1	no	—
83	C₄²	—	17	1	no	—
84	C₄²	—	17	1	no	—
85	C₄²	C₂×#595	1	1	yes	characteristic
86	C₂³	—	17	1	no	—
87	C₂×C₄	—	17	1	no	—
88	C₂×C₄	—	17	1	no	—
89	C₂×C₄	—	17	1	no	—
90	C₂×C₄	—	34	2	no	—
91	C₂×C₄	—	68	1	no	—
92	C₂×C₄	—	68	1	no	—
93	C₂×C₄	—	68	2	no	—
94	C₂×C₄	—	68	2	no	—
95	C₂×C₄	—	68	2	no	—
96	C₂×C₄	C₄×#595	1	1	yes	characteristic
97	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
98	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
99	C₈	—	4	1	no	—
100	C₈	—	34	4	no	—
101	C₈	—	68	1	no	—
102	C₂²	—	17	2	no	—
103	C₂²	—	34	1	no	—
104	C₂²	—	34	1	no	—
105	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	2	1	no	—
108	C₄	—	2	1	no	—
109	C₄	—	34	1	no	—
110	C₄	—	34	1	no	—
111	C₄	—	34	1	no	—
112	C₄	—	136	2	no	—
113	C₂	—	34	2	no	—
114	C₂	#11763676	1	1	yes	characteristic
115	C₂	#11763681	1	1	yes	characteristic
116	C₂	#11763692	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#63243

C₂

yes

maximal, characteristic

#11763754

C₂

yes

maximal, characteristic

#11762864

C₂

yes

maximal, characteristic

C₂×#63243

—

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

—

(C₂×#595)⋊C₄

—

(C₂×#595)⋊C₄

C₄

yes

—

#10587542

—

C₄×#3624

C₄

yes

complemented

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

characteristic

C₂×#3624

—

#63243

—

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

—

#3624

—

C₈×C₁₇

—

—

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

#104

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

—

#432

—

C₄×M₁₆

—

#383

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

C₂×M₁₆

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

—

—

yes

characteristic, complemented

C₄×C₈

—

#95

—

#95

—

#95

—

C₁₇

#1288

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

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

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

C₂²⋊#595

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

(C₂×#595)⋊C₄

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

136

—

113

C₂

—

114

C₂

#11763676

yes

characteristic

115

C₂

#11763681

yes

characteristic

116

C₂

#11763692

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	#1288
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
10. C₄×#3624	C₄	semidirect
11. C₁₇×#97	C₄	semidirect
14. #10587474	C₄	semidirect
68. #97	#595	semidirect
73. C₁₇	#1288	semidirect

H ≅ G/N

type

10. C₄×#3624

C₄

semidirect

11. C₁₇×#97

C₄

semidirect

14. #10587474

C₄

semidirect

68. #97

#595

semidirect

73. C₁₇

#1288

semidirect

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

subgroup	index
C₄×#63243	2
#11763754	2
#11762864	2
#1288	17

subgroup

index

Subgroups — #14543645

Conjugacy classes of subgroups

Complements

Maximal subgroups