Group #14530592 — subgroups

Subgroups — #14530592

Order 2176.

138 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 69 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	#11762763	C₂	1	1	yes	maximal, characteristic
2	#11762627	C₂	1	2	yes	maximal, complemented
3	#11762588	C₂	1	2	yes	maximal
4	C₄×#63214	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#346	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#63218	C₄	1	1	yes	characteristic
7	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
8	#10587558	C₄	1	1	yes	characteristic
9	C₂×C₁₆×C₁₇	C₂²	1	2	yes	—
10	C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
11	#10587486	C₄	1	1	yes	characteristic
12	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₂×#63214	C₂²	1	2	yes	—
14	#10587474	C₄	1	1	yes	characteristic
15	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₇	C₂³	1	1	yes	characteristic
18	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
19	#63227	C₈	1	2	yes	—
20	#63225	C₈	1	2	yes	—
21	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×#3622	C₂×C₄	1	1	yes	characteristic
23	C₂×#3622	C₂×C₄	1	1	yes	characteristic
24	#63218	—	2	2	no	—
25	C₈×D₁₇	—	2	2	no	—
26	C₁₆×C₁₇	—	2	2	no	—
27	#63214	—	2	2	no	—
28	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
30	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
33	C₄×D₁₇	—	2	1	no	—
34	C₄×D₁₇	—	2	1	no	—
35	C₈×C₁₇	M₁₆	1	2	yes	—
36	C₈×C₁₇	#41	1	2	yes	—
37	#3622	—	2	1	no	—
38	#3622	—	2	1	no	—
39	#2164	—	17	1	no	maximal, Sylow
40	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₁₇	—	2	1	no	—
42	C₂×D₁₇	—	2	2	no	—
43	C₄×C₁₇	—	2	2	no	—
44	C₄×C₁₇	#117	1	1	yes	characteristic
45	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
46	Dic₁₇	—	2	1	no	—
47	Dic₁₇	—	2	2	no	—
48	#405	—	17	1	no	—
49	C₄⋊C₁₆	—	17	2	no	—
50	C₂²⋊C₁₆	—	17	2	no	—
51	#346	D₁₇	1	1	yes	characteristic, complemented
52	C₄×C₁₆	—	17	1	no	—
53	C₂×C₁₇	#431	1	1	yes	characteristic
54	C₂×C₁₇	#504	1	2	yes	—
55	D₁₇	—	4	1	no	—
56	C₂×M₁₆	—	17	1	no	—
57	C₂²×C₈	—	17	1	no	—
58	#117	—	17	1	no	—
59	C₂×C₁₆	—	17	2	no	—
60	C₂×C₁₆	C₂×D₁₇	1	2	yes	—
61	#97	—	17	1	no	—
62	#97	—	17	1	no	—
63	C₄×C₈	—	17	1	no	—
64	C₄×C₈	C₂×D₁₇	1	1	yes	characteristic
65	C₁₇	#2164	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	17	1	no	—
67	M₁₆	—	34	2	no	—
68	C₂×C₈	—	17	1	no	—
69	C₂×C₈	—	17	1	no	—
70	C₂×C₈	—	34	2	no	—
71	C₂×C₈	C₄×D₁₇	1	1	yes	characteristic
72	C₂×C₈	C₂²×D₁₇	1	1	yes	characteristic
73	C₄⋊C₄	—	17	2	no	—
74	C₂²⋊C₄	—	17	2	no	—
75	C₄²	—	17	1	no	—
76	C₄²	C₄×D₁₇	1	1	yes	characteristic
77	C₁₆	—	2	2	no	—
78	C₁₆	—	34	2	no	—
79	C₂³	—	17	1	no	—
80	C₂×C₄	—	17	2	no	—
81	C₂×C₄	—	17	1	no	—
82	C₂×C₄	—	34	1	no	—
83	C₂×C₄	—	34	1	no	—
84	C₂×C₄	C₈×D₁₇	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
86	C₈	—	34	1	no	—
87	C₈	—	34	1	no	—
88	C₈	#63218	1	2	yes	—
89	C₈	#63252	1	2	yes	—
90	C₂²	—	34	2	no	—
91	C₂²	—	34	1	no	—
92	C₂²	C₂×C₈×D₁₇	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	34	2	no	—
95	C₄	—	34	1	no	—
96	C₄	#10587558	1	1	yes	characteristic
97	C₄	C₂×#63218	1	1	yes	characteristic
98	C₂	—	68	1	no	—
99	C₂	#11762860	1	1	yes	characteristic
100	C₂	#11763227	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11762763

C₂

yes

maximal, characteristic

#11762627

C₂

yes

maximal, complemented

#11762588

C₂

yes

maximal

C₄×#63214

C₂

yes

maximal, characteristic, complemented

C₁₇×#346

C₂

yes

maximal, characteristic, complemented

C₂×#63218

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587558

C₄

yes

characteristic

C₂×C₁₆×C₁₇

C₂²

yes

—

C₄×C₈×C₁₇

C₂²

yes

characteristic

#10587486

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₂×#63214

C₂²

yes

—

#10587474

C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂³

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

#63227

C₈

yes

—

#63225

C₈

yes

—

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

#63218

—

C₈×D₁₇

—

C₁₆×C₁₇

—

#63214

—

C₂²×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

—

C₄×D₁₇

—

C₄×D₁₇

—

C₈×C₁₇

M₁₆

yes

—

C₈×C₁₇

#41

yes

—

—

—

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#117

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

—

#405

—

C₄⋊C₁₆

—

C₂²⋊C₁₆

—

#346

D₁₇

yes

characteristic, complemented

C₄×C₁₆

—

C₂×C₁₇

#431

yes

characteristic

C₂×C₁₇

#504

yes

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₁₇

yes

—

#97

—

#97

—

C₄×C₈

—

C₄×C₈

C₂×D₁₇

yes

characteristic

C₁₇

#2164

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₇

yes

characteristic

C₂×C₈

C₂²×D₁₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₄×D₁₇

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₁₇

yes

—

C₂×C₄

C₂×C₄×D₁₇

yes

characteristic

C₈

—

C₈

—

C₈

#63218

yes

—

C₈

#63252

yes

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₁₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

#11762860

yes

characteristic

100

C₂

#11763227

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₁₇
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₁₇×#346	C₂
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	C₂×C₈×C₁₇	C₂³
hypercenter	#346	D₁₇
hypocenter	C₁₇	#2164
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ #346

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₁₇

commutator, socle

C₂²×C₁₇

C₂²×C₈

Fitting

C₁₇×#346

C₂

prime radical

C₂²×D₁₇

C₂×C₈

cosocle

C₂×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ #346

N	H ≅ G/N	type
2. #11762627	C₂	semidirect
4. C₄×#63214	C₂	semidirect
5. C₁₇×#346	C₂	semidirect
51. #346	D₁₇	semidirect
65. C₁₇	#2164	semidirect

H ≅ G/N

type

2. #11762627

C₂

semidirect

4. C₄×#63214

C₂

semidirect

5. C₁₇×#346

C₂

semidirect

51. #346

D₁₇

semidirect

65. C₁₇

#2164

semidirect

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

subgroup	index
#11762763	2
#11762627	2
#11762588	2
C₄×#63214	2
C₁₇×#346	2
#2164	17

subgroup

index

C₁₇×#346

Subgroups — #14530592

Conjugacy classes of subgroups

Complements

Maximal subgroups