Group #14545780 — subgroups

Subgroups — #14545780

Order 2176.

1424 conjugacy classes of subgroups; only the 750 normal subgroups are shown.

normal subgroups only

This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 750 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	#11763889	C₂	1	5	yes	maximal, complemented
2	#11763888	C₂	1	10	yes	maximal, complemented
3	C₂×#10587680	C₂	1	5	yes	maximal, complemented
4	D₁₇⋊#131	C₂	1	10	yes	maximal, complemented
5	#11763646	C₂	1	1	yes	maximal, characteristic
6	C₁₇×2₋¹⁺⁴	C₄	1	1	yes	characteristic
7	#10587696	C₄	1	10	yes	—
8	#41×D₁₇	C₂²	1	10	yes	—
9	#10587694	C₄	1	5	yes	—
10	C₂×#63256	C₂²	1	5	yes	—
11	#10587680	C₂²	1	10	yes	complemented
12	#10587680	C₂²	1	10	yes	complemented
13	#10587680	C₂²	1	20	yes	complemented
14	#10587678	C₂²	1	10	yes	complemented
15	#10587678	C₂²	1	30	yes	complemented
16	D₁₇⋊M₁₆	C₂²	1	30	yes	complemented
17	C₂×#63243	C₂²	1	15	yes	complemented
18	C₂×#63242	C₂²	1	15	yes	complemented
19	#41×C₁₇	C₂×C₄	1	10	yes	—
20	C₂×Q₈×C₁₇	C₂×C₄	1	5	yes	—
21	#63256	C₂×C₄	1	20	yes	—
22	#63256	C₂³	1	10	yes	—
23	Q₈×D₁₇	C₂×C₄	1	10	yes	—
24	#63254	C₂³	1	10	yes	—
25	D₄×D₁₇	C₂×C₄	1	30	yes	—
26	#63252	C₂×C₄	1	30	yes	—
27	C₂×D₆₈	C₂×C₄	1	15	yes	—
28	C₂×C₄×D₁₇	C₂³	1	15	yes	—
29	#63247	C₂³	1	20	yes	—
30	C₂×#3624	C₂³	1	5	yes	—
31	C₂×#3624	C₂³	1	15	yes	—
32	#63243	C₂³	1	30	yes	—
33	#63243	C₂³	1	10	yes	—
34	#63242	C₂³	1	10	yes	—
35	#63242	C₂³	1	30	yes	—
36	C₂²×D₁₇	C₂²×C₄	1	15	yes	—
37	Q₈×C₁₇	C₂²×C₄	1	10	yes	—
38	D₄×C₁₇	C₂²×C₄	1	10	yes	—
39	C₂×C₄×C₁₇	C₂²×C₄	1	15	yes	—
40	C₂²⋊D₁₇	C₂²×C₄	1	20	yes	—
41	C₂×Dic₁₇	C₂⁴	1	5	yes	—
42	D₆₈	C₂²×C₄	1	30	yes	—
43	C₄×D₁₇	C₂²×C₄	1	30	yes	—
44	C₄×D₁₇	C₂⁴	1	10	yes	—
45	Dic₃₄	C₂²×C₄	1	10	yes	—
46	#3624	C₂⁴	1	1	yes	characteristic
47	#3624	C₂⁴	1	5	yes	—
48	#3624	C₂⁴	1	10	yes	—
49	#3573	—	17	1	no	maximal, Sylow
50	C₂²×C₁₇	C₂³×C₄	1	5	yes	—
51	C₂×D₁₇	—	4	15	no	—
52	C₂×D₁₇	C₂³×C₄	1	10	yes	—
53	C₄×C₁₇	C₂³×C₄	1	10	yes	—
54	Dic₁₇	C₂³×C₄	1	5	yes	—
55	Dic₁₇	C₂⁵	1	1	yes	characteristic
56	#585	—	17	1	no	—
57	#568	—	17	10	no	—
58	#568	—	17	5	no	—
59	C₂×#131	—	17	10	no	—
60	C₂×#131	—	17	5	no	—
61	C₂×C₁₇	—	2	5	no	—
62	C₂×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
63	D₁₇	—	2	10	no	—
64	2₋¹⁺⁴	—	17	5	no	—
65	2₋¹⁺⁴	#595	1	1	yes	characteristic
66	H(5,𝔽₂)	—	17	10	no	—
67	C₂×#41	—	17	10	no	—
68	C₂×#41	—	17	5	no	—
69	#131	—	17	10	no	—
70	#131	—	17	30	no	—
71	#131	—	17	10	no	—
72	#131	—	17	10	no	—
73	#131	—	17	20	no	—
74	C₂×M₁₆	—	17	15	no	—
75	C₂×M₁₆	—	17	30	no	—
76	C₂²×C₈	—	17	15	no	—
77	C₁₇	#3573	1	1	yes	characteristic, complemented, Sylow
78	#41	—	17	20	no	—
79	#41	—	17	10	no	—
80	#41	—	17	10	no	—
81	#41	—	17	30	no	—
82	#41	C₂×#595	1	10	yes	—
83	C₂×Q₈	—	17	10	no	—
84	C₂×Q₈	C₂×#595	1	5	yes	—
85	C₂×D₄	—	17	30	no	—
86	C₂×D₄	—	17	15	no	—
87	C₂²×C₄	—	17	15	no	—
88	M₁₆	—	17	30	no	—
89	M₁₆	—	17	10	no	—
90	M₁₆	—	17	20	no	—
91	C₂×C₈	—	17	10	no	—
92	C₂×C₈	—	17	30	no	—
93	C₂×C₈	—	17	5	no	—
94	C₂×C₈	—	17	15	no	—
95	C₂³	—	17	15	no	—
96	Q₈	—	17	10	no	—
97	Q₈	C₂²×#595	1	10	yes	—
98	D₄	—	17	20	no	—
99	D₄	—	17	30	no	—
100	D₄	C₂²×#595	1	10	yes	—
101	C₂×C₄	—	17	5	no	—
102	C₂×C₄	—	17	10	no	—
103	C₂×C₄	—	17	30	no	—
104	C₂×C₄	C₂²×#595	1	15	yes	—
105	C₈	—	17	1	no	—
106	C₈	—	17	10	no	—
107	C₈	—	17	5	no	—
108	C₂²	—	17	10	no	—
109	C₂²	—	68	15	no	—
110	C₂²	C₂³×#595	1	5	yes	—
111	C₄	—	17	1	no	—
112	C₄	—	17	5	no	—
113	C₄	C₂³×#595	1	10	yes	—
114	C₂	—	2	5	no	—
115	C₂	—	34	10	no	—
116	C₂	C₂⁴×#595	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763889

C₂

yes

maximal, complemented

#11763888

C₂

yes

maximal, complemented

C₂×#10587680

C₂

yes

maximal, complemented

D₁₇⋊#131

C₂

yes

maximal, complemented

#11763646

C₂

yes

maximal, characteristic

C₁₇×2₋¹⁺⁴

C₄

yes

characteristic

#10587696

C₄

yes

—

#41×D₁₇

C₂²

yes

—

#10587694

C₄

yes

—

C₂×#63256

C₂²

yes

—

#10587680

C₂²

yes

complemented

#10587680

C₂²

yes

complemented

#10587680

C₂²

yes

complemented

#10587678

C₂²

yes

complemented

#10587678

C₂²

yes

complemented

D₁₇⋊M₁₆

C₂²

yes

complemented

C₂×#63243

C₂²

yes

complemented

C₂×#63242

C₂²

yes

complemented

#41×C₁₇

C₂×C₄

yes

—

C₂×Q₈×C₁₇

C₂×C₄

yes

—

#63256

C₂×C₄

yes

—

#63256

C₂³

yes

—

Q₈×D₁₇

C₂×C₄

yes

—

#63254

C₂³

yes

—

D₄×D₁₇

C₂×C₄

yes

—

#63252

C₂×C₄

yes

—

C₂×D₆₈

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂³

yes

—

#63247

C₂³

yes

—

C₂×#3624

C₂³

yes

—

C₂×#3624

C₂³

yes

—

#63243

C₂³

yes

—

#63243

C₂³

yes

—

#63242

C₂³

yes

—

#63242

C₂³

yes

—

C₂²×D₁₇

C₂²×C₄

yes

—

Q₈×C₁₇

C₂²×C₄

yes

—

D₄×C₁₇

C₂²×C₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

—

C₂²⋊D₁₇

C₂²×C₄

yes

—

C₂×Dic₁₇

C₂⁴

yes

—

D₆₈

C₂²×C₄

yes

—

C₄×D₁₇

C₂²×C₄

yes

—

C₄×D₁₇

C₂⁴

yes

—

Dic₃₄

C₂²×C₄

yes

—

#3624

C₂⁴

yes

characteristic

#3624

C₂⁴

yes

—

#3624

C₂⁴

yes

—

#3573

—

maximal, Sylow

C₂²×C₁₇

C₂³×C₄

yes

—

C₂×D₁₇

—

C₂×D₁₇

C₂³×C₄

yes

—

C₄×C₁₇

C₂³×C₄

yes

—

Dic₁₇

C₂³×C₄

yes

—

Dic₁₇

C₂⁵

yes

—

—

—

—

—

C₂×C₁₇

—

C₂×C₁₇

C₂⁴×C₄

yes

characteristic

D₁₇

—

2₋¹⁺⁴

—

2₋¹⁺⁴

#595

yes

characteristic

H(5,𝔽₂)

—

C₂×#41

—

C₂×#41

—

—

—

—

—

—

C₂×M₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

C₁₇

#3573

yes

characteristic, complemented, Sylow

—

—

—

—

yes

—

C₂×Q₈

—

C₂×Q₈

C₂×#595

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

M₁₆

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂³

—

Q₈

—

Q₈

C₂²×#595

yes

—

D₄

—

D₄

—

100

D₄

C₂²×#595

yes

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

C₂²×#595

yes

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₂²

—

109

C₂²

—

110

C₂²

C₂³×#595

yes

—

111

C₄

—

112

C₄

—

113

C₄

C₂³×#595

yes

—

114

C₂

—

115

C₂

—

116

C₂

C₂⁴×#595

yes

characteristic

	subgroup	G/H
center, Frattini	C₂	C₂⁴×#595
commutator, socle	C₂×C₁₇	C₂⁴×C₄
Fitting	C₁₇×2₋¹⁺⁴	C₄
prime radical	#11763646	C₂
cosocle	Dic₁₇	C₂⁵
hypercenter	2₋¹⁺⁴	#595
hypocenter	C₁₇	#3573
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ 2₋¹⁺⁴

subgroup

G/H

center, Frattini

C₂

C₂⁴×#595

commutator, socle

C₂×C₁₇

C₂⁴×C₄

Fitting

C₁₇×2₋¹⁺⁴

C₄

prime radical

#11763646

C₂

cosocle

Dic₁₇

C₂⁵

2₋¹⁺⁴

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₂ ◁ 2₋¹⁺⁴

N	H ≅ G/N	type
1. #11763889	C₂	semidirect
2. #11763888	C₂	semidirect
3. C₂×#10587680	C₂	semidirect
4. D₁₇⋊#131	C₂	semidirect
11. #10587680	C₂²	semidirect
12. #10587680	C₂²	semidirect
13. #10587680	C₂²	semidirect
14. #10587678	C₂²	semidirect
15. #10587678	C₂²	semidirect
16. D₁₇⋊M₁₆	C₂²	semidirect
17. C₂×#63243	C₂²	semidirect
18. C₂×#63242	C₂²	semidirect
77. C₁₇	#3573	semidirect

H ≅ G/N

type

1. #11763889

C₂

semidirect

2. #11763888

C₂

semidirect

3. C₂×#10587680

C₂

semidirect

4. D₁₇⋊#131

C₂

semidirect

11. #10587680

C₂²

semidirect

12. #10587680

C₂²

semidirect

13. #10587680

C₂²

semidirect

14. #10587678

C₂²

semidirect

15. #10587678

C₂²

semidirect

16. D₁₇⋊M₁₆

C₂²

semidirect

17. C₂×#63243

C₂²

semidirect

18. C₂×#63242

C₂²

semidirect

77. C₁₇

#3573

semidirect

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

subgroup	index
#11763889	2
#11763888	2
C₂×#10587680	2
D₁₇⋊#131	2
#11763646	2
#3573	17

subgroup

index

D₁₇⋊#131

Subgroups — #14545780

Conjugacy classes of subgroups

Complements

Maximal subgroups