Group #14544715 — subgroups

Subgroups — #14544715

Order 2176.

162 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 52 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	#11763691	C₂	1	2	yes	maximal
2	#11763680	C₂	1	2	yes	maximal
3	#11763678	C₂	1	1	yes	maximal, characteristic
4	#11763677	C₂	1	1	yes	maximal, characteristic
5	#11762761	C₂	1	1	yes	maximal, characteristic
6	#10587677	C₂²	1	2	yes	—
7	D₁₇⋊M₁₆	C₂²	1	2	yes	—
8	C₂×#63218	C₂²	1	1	yes	characteristic
9	C₂×#63218	C₂²	1	1	yes	characteristic
10	C₄²×D₁₇	C₂²	1	1	yes	characteristic
11	C₁₇×#97	C₄	1	1	yes	characteristic, complemented
12	C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
13	C₈×Dic₁₇	C₄	1	1	yes	characteristic, complemented
14	#10587474	C₄	1	1	yes	characteristic, complemented
15	C₂×C₄×D₁₇	—	2	1	no	—
16	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
17	C₂²⋊#595	—	2	2	no	—
18	#63247	—	2	2	no	—
19	C₄⋊#595	—	2	2	no	—
20	C₄×#595	—	2	2	no	—
21	#63243	—	2	2	no	—
22	#63242	—	2	2	no	—
23	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
26	C₄×Dic₁₇	—	2	1	no	—
27	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×#3622	C₂×C₄	1	1	yes	characteristic
29	C₂×#3622	C₂×C₄	1	1	yes	characteristic
30	#63218	—	2	2	no	—
31	#63218	—	2	2	no	—
32	C₂²×D₁₇	#41	1	1	yes	characteristic
33	C₂×#595	—	4	2	no	—
34	C₂×C₄×C₁₇	—	2	1	no	—
35	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₁₇	—	2	1	no	—
37	C₂×Dic₁₇	#41	1	1	yes	characteristic
38	C₄×D₁₇	—	4	2	no	—
39	C₄×D₁₇	#41	1	2	yes	—
40	C₄×D₁₇	#41	1	2	yes	—
41	#3624	—	4	2	no	—
42	C₈×C₁₇	—	2	1	no	—
43	C₈×C₁₇	—	2	1	no	—
44	#3622	—	2	1	no	—
45	#3622	—	2	1	no	—
46	#1841	—	17	1	no	maximal, Sylow
47	C₂²×C₁₇	#117	1	1	yes	characteristic
48	C₂×D₁₇	—	4	1	no	—
49	C₂×D₁₇	#126	1	2	yes	—
50	#595	—	8	2	no	—
51	C₄×C₁₇	—	4	1	no	—
52	C₄×C₁₇	#117	1	1	yes	characteristic
53	C₄×C₁₇	#117	1	1	yes	characteristic
54	Dic₁₇	—	2	2	no	—
55	Dic₁₇	#126	1	2	yes	—
56	C₄×M₁₆	—	17	1	no	—
57	#344	—	17	2	no	—
58	#339	—	17	2	no	—
59	#338	—	17	1	no	—
60	H(3,ℤ/4)	—	17	1	no	—
61	C₂×C₁₇	—	2	1	no	—
62	C₂×C₁₇	#383	1	1	yes	characteristic
63	D₁₇	—	2	2	no	—
64	C₂×M₁₆	—	17	1	no	—
65	C₂×M₁₆	—	17	1	no	—
66	C₂×M₁₆	—	17	2	no	—
67	#117	—	17	2	no	—
68	C₂×C₄²	—	17	1	no	—
69	#97	—	17	1	no	—
70	#97	#595	1	1	yes	characteristic, complemented
71	C₄×C₈	—	17	1	no	—
72	C₄×C₈	—	17	1	no	—
73	C₁₇	#1841	1	1	yes	characteristic, complemented, Sylow
74	C₂²×C₄	—	17	1	no	—
75	C₂²×C₄	—	34	1	no	—
76	M₁₆	—	34	2	no	—
77	M₁₆	—	34	2	no	—
78	M₁₆	—	34	2	no	—
79	M₁₆	—	34	2	no	—
80	C₂×C₈	—	17	1	no	—
81	C₂×C₈	—	17	1	no	—
82	C₂×C₈	—	34	2	no	—
83	C₂×C₈	C₂×#595	1	1	yes	characteristic
84	C₂×C₈	C₂×#595	1	1	yes	characteristic
85	C₄⋊C₄	—	34	2	no	—
86	C₂²⋊C₄	—	34	2	no	—
87	C₄²	—	17	1	no	—
88	C₄²	—	34	1	no	—
89	C₄²	—	34	2	no	—
90	C₄²	C₂×#595	1	1	yes	characteristic
91	C₂³	—	17	1	no	—
92	C₂×C₄	—	2	1	no	—
93	C₂×C₄	—	17	1	no	—
94	C₂×C₄	—	17	2	no	—
95	C₂×C₄	—	17	2	no	—
96	C₂×C₄	—	34	1	no	—
97	C₂×C₄	—	68	2	no	—
98	C₂×C₄	—	68	2	no	—
99	C₂×C₄	C₂²×#595	1	1	yes	characteristic
100	C₈	—	2	1	no	—
101	C₈	—	2	1	no	—
102	C₈	—	34	1	no	—
103	C₈	—	34	1	no	—
104	C₈	—	68	2	no	—
105	C₂²	—	17	2	no	—
106	C₂²	—	68	1	no	—
107	C₂²	#10587677	1	1	yes	characteristic
108	C₄	—	4	1	no	—
109	C₄	—	17	2	no	—
110	C₄	—	34	2	no	—
111	C₄	—	136	2	no	—
112	C₄	#10587677	1	1	yes	characteristic
113	C₄	#10587677	1	1	yes	characteristic
114	C₂	—	2	1	no	—
115	C₂	—	34	2	no	—
116	C₂	#11763754	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763691

C₂

yes

maximal

#11763680

C₂

yes

maximal

#11763678

C₂

yes

maximal, characteristic

#11763677

C₂

yes

maximal, characteristic

#11762761

C₂

yes

maximal, characteristic

#10587677

C₂²

yes

—

D₁₇⋊M₁₆

C₂²

yes

—

C₂×#63218

C₂²

yes

characteristic

C₂×#63218

C₂²

yes

characteristic

C₄²×D₁₇

C₂²

yes

characteristic

C₁₇×#97

C₄

yes

characteristic, complemented

C₈×Dic₁₇

C₄

yes

characteristic, complemented

C₈×Dic₁₇

C₄

yes

characteristic, complemented

#10587474

C₄

yes

characteristic, complemented

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂²⋊#595

—

—

—

—

—

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

#63218

—

#63218

—

C₂²×D₁₇

#41

yes

characteristic

C₂×#595

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

#41

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

#41

yes

—

C₄×D₁₇

#41

yes

—

#3624

—

C₈×C₁₇

—

C₈×C₁₇

—

—

—

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

#126

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

#126

yes

—

C₄×M₁₆

—

—

—

—

—

C₂×C₁₇

—

C₂×C₁₇

#383

yes

characteristic

D₁₇

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂×M₁₆

—

#117

—

C₂×C₄²

—

#97

—

#97

#595

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

C₁₇

#1841

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

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

C₂²×#595

yes

characteristic

100

C₈

—

101

C₈

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₂²

—

106

C₂²

—

107

C₂²

#10587677

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

136

—

112

C₄

#10587677

yes

characteristic

113

C₄

#10587677

yes

characteristic

114

C₂

—

115

C₂

—

116

C₂

#11763754

yes

characteristic

	subgroup	G/H
center	C₄	#10587677
commutator	C₂×C₄×C₁₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#97	C₄
socle	C₂×C₁₇	#383
prime radical	C₂²×D₁₇	#41
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#1841
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

subgroup

G/H

center

C₄

#10587677

commutator

C₂×C₄×C₁₇

C₂²×C₄

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#97

C₄

C₂×C₁₇

C₂²×D₁₇

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

N	H ≅ G/N	type
11. C₁₇×#97	C₄	semidirect
12. C₈×Dic₁₇	C₄	semidirect
13. C₈×Dic₁₇	C₄	semidirect
14. #10587474	C₄	semidirect
70. #97	#595	semidirect
73. C₁₇	#1841	semidirect

H ≅ G/N

type

11. C₁₇×#97

C₄

semidirect

12. C₈×Dic₁₇

C₄

semidirect

13. C₈×Dic₁₇

C₄

semidirect

14. #10587474

C₄

semidirect

70. #97

#595

semidirect

73. C₁₇

#1841

semidirect

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

subgroup	index
#11763691	2
#11763680	2
#11763678	2
#11763677	2
#11762761	2
#1841	17

subgroup

index

Subgroups — #14544715

Conjugacy classes of subgroups

Complements

Maximal subgroups