Group #14534734 — subgroups

Subgroups — #14534734

Order 2176.

416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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	1	yes	maximal, characteristic
2	#11762747	C₂	1	8	yes	maximal
3	#11762716	C₂	1	4	yes	maximal
4	#11762655	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₈×C₁₇	C₂²	1	2	yes	—
7	C₁₇×C₄⋊Q₈	—	2	4	no	—
8	C₂×C₄⋊C₄×C₁₇	C₂²	1	4	yes	—
9	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Dic₁₇	C₂²	1	2	yes	—
11	C₂×#63225	C₂²	1	4	yes	—
12	C₂×C₄×Dic₁₇	C₂²	1	2	yes	—
13	#10587556	—	2	4	no	—
14	#10587502	C₂²	1	16	yes	—
15	#10587502	C₂²	1	4	yes	—
16	C₂×Q₈×C₁₇	—	2	4	no	—
17	C₂×Q₈×C₁₇	—	2	8	no	—
18	C₂²×C₄×C₁₇	C₂³	1	4	yes	—
19	C₂²×C₄×C₁₇	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
21	C₂²×Dic₁₇	C₂³	1	4	yes	—
22	C₂²×Dic₁₇	C₂³	1	4	yes	—
23	C₄⋊C₄×C₁₇	—	2	8	no	—
24	C₄²×C₁₇	D₄	1	4	yes	—
25	C₄⋊Dic₁₇	—	2	4	no	—
26	#63225	—	2	8	no	—
27	C₄×Dic₁₇	—	2	4	no	—
28	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
29	Q₈×C₁₇	—	4	8	no	—
30	C₂×C₄×C₁₇	—	2	4	no	—
31	C₂×C₄×C₁₇	—	2	4	no	—
32	C₂×C₄×C₁₇	—	2	8	no	—
33	C₂×C₄×C₁₇	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₁₇	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₁₇	#41	1	4	yes	—
36	C₂×Dic₁₇	—	2	4	no	—
37	C₂×Dic₁₇	—	2	4	no	—
38	C₂×Dic₁₇	—	2	8	no	—
39	C₂×Dic₁₇	—	2	8	no	—
40	#2642	—	17	1	no	maximal, Sylow
41	C₂²×C₁₇	C₂²×D₄	1	1	yes	characteristic
42	C₂²×C₁₇	C₂×#41	1	2	yes	—
43	C₂²×C₁₇	2₋¹⁺⁴	1	4	yes	—
44	C₄×C₁₇	—	2	4	no	—
45	C₄×C₁₇	—	4	4	no	—
46	C₄×C₁₇	#124	1	4	yes	—
47	Dic₁₇	—	4	4	no	—
48	Dic₁₇	—	4	4	no	—
49	C₂×C₄⋊Q₈	D₁₇	1	1	yes	characteristic
50	C₂×#125	—	17	1	no	—
51	#400	—	17	8	no	—
52	#391	—	17	4	no	—
53	#376	—	17	1	no	—
54	C₂×C₁₇	C₂×#124	1	1	yes	characteristic
55	C₂×C₁₇	#536	1	2	yes	—
56	C₂×C₁₇	#541	1	4	yes	—
57	C₂²×Q₈	C₂×D₁₇	1	2	yes	—
58	C₄⋊Q₈	—	2	4	no	—
59	#125	—	34	4	no	—
60	C₂×C₄⋊C₄	—	17	2	no	—
61	C₂×C₄⋊C₄	—	17	4	no	—
62	C₂×C₄⋊C₄	C₂×D₁₇	1	4	yes	—
63	C₂×C₄²	—	17	2	no	—
64	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
65	#95	—	17	4	no	—
66	#95	—	17	16	no	—
67	C₁₇	#2642	1	1	yes	characteristic, complemented, Sylow
68	C₂×Q₈	—	2	8	no	—
69	C₂×Q₈	—	2	4	no	—
70	C₂²×C₄	—	17	4	no	—
71	C₂²×C₄	—	17	4	no	—
72	C₂²×C₄	C₂²×D₁₇	1	4	yes	—
73	C₂²×C₄	C₂²×D₁₇	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
75	C₄⋊C₄	—	2	8	no	—
76	C₄⋊C₄	—	34	8	no	—
77	C₄⋊C₄	—	34	4	no	—
78	C₄²	—	34	4	no	—
79	C₄²	C₂²⋊D₁₇	1	4	yes	—
80	C₂³	C₂³×D₁₇	1	1	yes	characteristic
81	Q₈	—	4	8	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	2	8	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	34	4	no	—
86	C₂×C₄	—	34	8	no	—
87	C₂×C₄	—	34	8	no	—
88	C₂×C₄	—	34	4	no	—
89	C₂×C₄	#63254	1	4	yes	—
90	C₂×C₄	C₂×C₂²⋊D₁₇	1	4	yes	—
91	C₂×C₄	C₂×C₂²⋊D₁₇	1	2	yes	—
92	C₂²	C₂×#63254	1	2	yes	—
93	C₂²	#10587694	1	4	yes	—
94	C₂²	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
95	C₄	—	2	4	no	—
96	C₄	—	4	4	no	—
97	C₄	—	68	4	no	—
98	C₄	—	68	4	no	—
99	C₄	#10587622	1	4	yes	—
100	C₂	C₂×#10587622	1	1	yes	characteristic
101	C₂	#11763383	1	2	yes	—
102	C₂	#11763420	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587556

C₂

yes

maximal, characteristic

#11762747

C₂

yes

maximal

#11762716

C₂

yes

maximal

#11762655

C₂

yes

maximal, characteristic

C₂×C₁₇×C₄⋊Q₈

C₂

yes

maximal, characteristic

C₂²×Q₈×C₁₇

C₂²

yes

—

C₁₇×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₇

C₂²

yes

—

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₇

C₂²

yes

—

C₂×#63225

C₂²

yes

—

C₂×C₄×Dic₁₇

C₂²

yes

—

#10587556

—

#10587502

C₂²

yes

—

#10587502

C₂²

yes

—

C₂×Q₈×C₁₇

—

C₂×Q₈×C₁₇

—

C₂²×C₄×C₁₇

C₂³

yes

—

C₂²×C₄×C₁₇

C₂³

yes

—

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×Dic₁₇

C₂³

yes

—

C₂²×Dic₁₇

C₂³

yes

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

D₄

yes

—

C₄⋊Dic₁₇

—

#63225

—

C₄×Dic₁₇

—

C₂³×C₁₇

C₂⁴

yes

characteristic

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×D₄

yes

—

C₂×C₄×C₁₇

C₂×D₄

yes

—

C₂×C₄×C₁₇

#41

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

#2642

—

maximal, Sylow

C₂²×C₁₇

C₂²×D₄

yes

characteristic

C₂²×C₁₇

C₂×#41

yes

—

C₂²×C₁₇

2₋¹⁺⁴

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#124

yes

—

Dic₁₇

—

Dic₁₇

—

C₂×C₄⋊Q₈

D₁₇

yes

—

—

—

—

C₂×C₁₇

C₂×#124

yes

characteristic

C₂×C₁₇

#536

yes

—

C₂×C₁₇

#541

yes

—

C₂²×Q₈

C₂×D₁₇

yes

—

C₄⋊Q₈

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₁₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₇

yes

characteristic

#95

—

#95

—

C₁₇

#2642

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₁₇

yes

—

C₂²×C₄

C₂²×D₁₇

yes

—

C₂²×C₄

C₂²×D₁₇

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂²⋊D₁₇

yes

—

C₂³

C₂³×D₁₇

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#63254

yes

—

C₂×C₄

C₂×C₂²⋊D₁₇

yes

—

C₂×C₄

C₂×C₂²⋊D₁₇

yes

—

C₂²

C₂×#63254

yes

—

C₂²

#10587694

yes

—

C₂²

C₂²×C₂²⋊D₁₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#10587622

yes

—

100

C₂

C₂×#10587622

yes

characteristic

101

C₂

#11763383

yes

—

102

C₂

#11763420

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₇
commutator, socle, prime radical, cosocle	C₂³×C₁₇	C₂⁴
Fitting	C₂×C₁₇×C₄⋊Q₈	C₂
hypercenter	C₂×C₄⋊Q₈	D₁₇
hypocenter	C₁₇	#2642
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₇

commutator, socle, prime radical, cosocle

C₂³×C₁₇

C₂⁴

Fitting

C₂×C₁₇×C₄⋊Q₈

C₂

hypercenter

C₂×C₄⋊Q₈

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂³ ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
67. C₁₇	#2642	semidirect

H ≅ G/N

type

67. C₁₇

#2642

semidirect

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

subgroup	index
C₂×#10587556	2
#11762747	2
#11762716	2
#11762655	2
C₂×C₁₇×C₄⋊Q₈	2
#2642	17

subgroup

index

C₂×C₁₇×C₄⋊Q₈

Subgroups — #14534734

Conjugacy classes of subgroups

Complements

Maximal subgroups