Group #14537147 — subgroups

Subgroups — #14537147

Order 2176.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#10587556	C₂	1	2	yes	maximal
2	#11762707	C₂	1	8	yes	maximal
3	#11762679	C₂	1	2	yes	maximal
4	#11762675	C₂	1	2	yes	maximal
5	C₄³×C₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄²×C₁₇	C₂²	1	4	yes	—
7	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₇	C₂²	1	8	yes	—
11	C₂×C₄⋊Dic₁₇	C₂²	1	4	yes	—
12	C₂×#63225	C₂²	1	8	yes	—
13	#10587556	—	2	8	no	—
14	#10587502	C₂²	1	8	yes	—
15	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
16	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
17	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
19	C₂²×Dic₁₇	C₂³	1	8	yes	—
20	C₄²×C₁₇	—	2	8	no	—
21	C₄²×C₁₇	D₄	1	4	yes	—
22	C₄²×C₁₇	Q₈	1	4	yes	—
23	C₄²×C₁₇	Q₈	1	4	yes	—
24	C₄⋊Dic₁₇	—	2	8	no	—
25	C₄⋊Dic₁₇	—	2	16	no	—
26	#63225	—	2	16	no	—
27	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₁₇	—	2	4	no	—
29	C₂×C₄×C₁₇	—	2	4	no	—
30	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₁₇	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₁₇	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₁₇	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₁₇	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₁₇	#41	1	8	yes	—
37	C₂×Dic₁₇	—	2	8	no	—
38	C₂×Dic₁₇	—	2	16	no	—
39	#2859	—	17	1	no	maximal, Sylow
40	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₁₇	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₁₇	C₂²×Q₈	1	1	yes	characteristic
43	C₂²×C₁₇	C₂×#41	1	4	yes	—
44	C₄×C₁₇	—	2	4	no	—
45	C₄×C₁₇	—	2	4	no	—
46	C₄×C₁₇	#125	1	8	yes	complemented
47	C₄×C₁₇	C₄⋊Q₈	1	4	yes	—
48	Dic₁₇	—	4	8	no	—
49	C₂×#125	—	17	2	no	—
50	#389	—	17	8	no	—
51	#384	—	17	2	no	—
52	#382	—	17	2	no	—
53	C₄³	D₁₇	1	1	yes	characteristic
54	C₂×C₁₇	C₂×#125	1	2	yes	—
55	C₂×C₁₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
56	C₂×C₁₇	#532	1	2	yes	—
57	C₂×C₁₇	#533	1	2	yes	—
58	#125	—	34	8	no	—
59	C₂×C₄⋊C₄	—	17	4	no	—
60	C₂×C₄⋊C₄	—	17	8	no	—
61	C₂×C₄⋊C₄	—	17	8	no	—
62	C₂×C₄²	C₂×D₁₇	1	4	yes	—
63	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
64	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
66	#95	—	17	8	no	—
67	C₁₇	#2859	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	17	8	no	—
69	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
70	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
71	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
73	C₄⋊C₄	—	34	16	no	—
74	C₄⋊C₄	—	34	8	no	—
75	C₄⋊C₄	—	34	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₃₄	1	4	yes	—
78	C₄²	Dic₃₄	1	4	yes	—
79	C₄²	D₆₈	1	4	yes	—
80	C₂³	C₂³×D₁₇	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	34	8	no	—
84	C₂×C₄	—	34	16	no	—
85	C₂×C₄	C₂×Dic₃₄	1	4	yes	—
86	C₂×C₄	C₂×Dic₃₄	1	2	yes	—
87	C₂×C₄	C₂×Dic₃₄	1	2	yes	—
88	C₂×C₄	C₂×Dic₃₄	1	4	yes	—
89	C₂×C₄	C₂×D₆₈	1	4	yes	—
90	C₂×C₄	C₂×D₆₈	1	2	yes	—
91	C₂×C₄	#63252	1	8	yes	—
92	C₂²	C₂²×Dic₃₄	1	1	yes	characteristic
93	C₂²	C₂²×Dic₃₄	1	1	yes	characteristic
94	C₂²	C₂²×D₆₈	1	1	yes	characteristic
95	C₂²	C₂×#63252	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	68	8	no	—
99	C₄	#10587555	1	4	yes	—
100	C₄	#10587556	1	8	yes	complemented
101	C₂	C₂×#10587556	1	2	yes	—
102	C₂	C₂×#10587555	1	1	yes	characteristic
103	C₂	#11763359	1	2	yes	—
104	C₂	#11763366	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587556

C₂

yes

maximal

#11762707

C₂

yes

maximal

#11762679

C₂

yes

maximal

#11762675

C₂

yes

maximal

C₄³×C₁₇

C₂

yes

maximal, characteristic

C₂×C₄²×C₁₇

C₂²

yes

—

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₇

C₂²

yes

—

C₂×C₄⋊Dic₁₇

C₂²

yes

—

C₂×#63225

C₂²

yes

—

#10587556

—

#10587502

C₂²

yes

—

C₂²×C₄×C₁₇

C₂³

yes

—

C₂²×C₄×C₁₇

C₂³

yes

—

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×C₄×C₁₇

C₂³

yes

—

C₂²×Dic₁₇

C₂³

yes

—

C₄²×C₁₇

—

C₄²×C₁₇

D₄

yes

—

C₄²×C₁₇

Q₈

yes

—

C₄²×C₁₇

Q₈

yes

—

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

#63225

—

C₂³×C₁₇

C₂⁴

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×D₄

yes

—

C₂×C₄×C₁₇

C₂×D₄

yes

—

C₂×C₄×C₁₇

C₂×Q₈

yes

—

C₂×C₄×C₁₇

C₂×Q₈

yes

—

C₂×C₄×C₁₇

C₂×Q₈

yes

—

C₂×C₄×C₁₇

C₂×Q₈

yes

—

C₂×C₄×C₁₇

#41

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

#2859

—

maximal, Sylow

C₂²×C₁₇

C₂²×D₄

yes

characteristic

C₂²×C₁₇

C₂²×Q₈

yes

characteristic

C₂²×C₁₇

C₂²×Q₈

yes

characteristic

C₂²×C₁₇

C₂×#41

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#125

yes

complemented

C₄×C₁₇

C₄⋊Q₈

yes

—

Dic₁₇

—

—

—

—

—

C₄³

D₁₇

yes

characteristic

C₂×C₁₇

C₂×#125

yes

—

C₂×C₁₇

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₇

#532

yes

—

C₂×C₁₇

#533

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₁₇

yes

—

C₂×C₄²

C₂×D₁₇

yes

characteristic

C₂×C₄²

C₂×D₁₇

yes

characteristic

C₂×C₄²

C₂×D₁₇

yes

characteristic

#95

—

C₁₇

#2859

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₇

yes

—

C₂²×C₄

C₂²×D₁₇

yes

—

C₂²×C₄

C₂²×D₁₇

yes

characteristic

C₂²×C₄

C₂²×D₁₇

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₃₄

yes

—

C₄²

Dic₃₄

yes

—

C₄²

D₆₈

yes

—

C₂³

C₂³×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₃₄

yes

—

C₂×C₄

C₂×Dic₃₄

yes

—

C₂×C₄

C₂×Dic₃₄

yes

—

C₂×C₄

C₂×Dic₃₄

yes

—

C₂×C₄

C₂×D₆₈

yes

—

C₂×C₄

C₂×D₆₈

yes

—

C₂×C₄

#63252

yes

—

C₂²

C₂²×Dic₃₄

yes

characteristic

C₂²

C₂²×Dic₃₄

yes

characteristic

C₂²

C₂²×D₆₈

yes

characteristic

C₂²

C₂×#63252

yes

—

C₄

—

C₄

—

C₄

—

C₄

#10587555

yes

—

100

C₄

#10587556

yes

complemented

101

C₂

C₂×#10587556

yes

—

102

C₂

C₂×#10587555

yes

characteristic

103

C₂

#11763359

yes

—

104

C₂

#11763366

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₇
commutator, socle, prime radical, cosocle	C₂³×C₁₇	C₂⁴
Fitting	C₄³×C₁₇	C₂
hypercenter	C₄³	D₁₇
hypocenter	C₁₇	#2859
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₇

commutator, socle, prime radical, cosocle

C₂³×C₁₇

C₂⁴

Fitting

C₄³×C₁₇

C₂

hypercenter

C₄³

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
46. C₄×C₁₇	#125	semidirect
67. C₁₇	#2859	semidirect
100. C₄	#10587556	semidirect

H ≅ G/N

type

46. C₄×C₁₇

#125

semidirect

67. C₁₇

#2859

semidirect

100. C₄

#10587556

semidirect

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

subgroup	index
C₂×#10587556	2
#11762707	2
#11762679	2
#11762675	2
C₄³×C₁₇	2
#2859	17

subgroup

index

C₄³×C₁₇

Subgroups — #14537147

Conjugacy classes of subgroups

Complements

Maximal subgroups