Group #14543774 — subgroups

Subgroups — #14543774

Order 2176.

114 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 114 conjugacy classes of subgroups — too many to draw. Only its 30 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	#11763704	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763685	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763042	C₂	1	1	yes	maximal, characteristic
4	C₂×#63243	—	2	1	no	—
5	C₂×D₈×C₁₇	C₄	1	1	yes	characteristic
6	#10587624	—	2	1	no	—
7	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
8	C₂×#63216	—	2	1	no	—
9	#10587503	—	2	1	no	—
10	#10587489	C₄	1	1	yes	characteristic
11	C₂×D₄×C₁₇	—	2	1	no	—
12	C₂×C₂²⋊D₁₇	—	4	1	no	—
13	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
14	C₂×#3624	—	4	1	no	—
15	#63243	—	2	2	no	—
16	#63243	—	4	1	no	—
17	D₈×C₁₇	—	4	1	no	—
18	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂²⋊Dic₁₇	—	4	1	no	—
20	C₄⋊Dic₁₇	—	2	1	no	—
21	C₂×#3622	D₄	1	1	yes	characteristic
22	C₈×D₁₇	—	4	1	no	—
23	#63216	—	4	1	no	—
24	C₂³×C₁₇	—	4	1	no	—
25	C₂²×D₁₇	SD₁₆	1	1	yes	characteristic
26	D₄×C₁₇	—	4	1	no	—
27	D₄×C₁₇	—	4	1	no	—
28	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂²⋊D₁₇	—	8	2	no	—
30	C₂×Dic₁₇	—	4	1	no	—
31	C₂×Dic₁₇	D₈	1	1	yes	characteristic
32	C₄×D₁₇	—	2	1	no	—
33	C₄×D₁₇	—	2	1	no	—
34	#3624	—	4	2	no	—
35	C₈×C₁₇	—	2	1	no	—
36	#3622	—	2	1	no	—
37	#1349	—	17	1	no	maximal, Sylow
38	C₂²×C₁₇	—	8	1	no	—
39	C₂²×C₁₇	—	8	1	no	—
40	C₂²×C₁₇	—	8	1	no	—
41	C₂²×C₁₇	#102	1	1	yes	characteristic
42	C₂×D₁₇	—	2	1	no	—
43	C₂×D₁₇	—	2	1	no	—
44	C₂×D₁₇	—	2	1	no	—
45	C₄×C₁₇	#99	1	1	yes	characteristic
46	C₄×C₁₇	#104	1	1	yes	characteristic
47	Dic₁₇	—	2	1	no	—
48	Dic₁₇	—	8	1	no	—
49	#466	—	17	1	no	—
50	C₂²⋊C₁₆	—	17	1	no	—
51	#341	—	17	1	no	—
52	C₂×C₁₇	—	16	1	no	—
53	C₂×C₁₇	#327	1	1	yes	characteristic
54	C₂×C₁₇	#359	1	1	yes	characteristic
55	C₂×C₁₇	#361	1	1	yes	characteristic
56	D₁₇	—	4	1	no	—
57	C₂×D₈	#595	1	1	yes	characteristic
58	C₂×M₁₆	—	34	1	no	—
59	C₂²×C₈	—	17	1	no	—
60	#121	—	34	1	no	—
61	C₂×C₁₆	—	34	1	no	—
62	#107	—	17	1	no	—
63	#102	—	34	1	no	—
64	C₁₇	#1349	1	1	yes	characteristic, complemented, Sylow
65	C₂×D₄	—	2	1	no	—
66	C₂×D₄	—	68	1	no	—
67	C₂²×C₄	—	17	1	no	—
68	D₈	—	4	1	no	—
69	M₁₆	—	34	2	no	—
70	M₁₆	—	68	1	no	—
71	C₂×C₈	—	17	1	no	—
72	C₂×C₈	—	68	1	no	—
73	C₂×C₈	—	68	1	no	—
74	C₂×C₈	C₂×#595	1	1	yes	characteristic
75	C₄⋊C₄	—	34	1	no	—
76	C₂²⋊C₄	—	68	1	no	—
77	C₁₆	—	68	1	no	—
78	C₂³	—	4	1	no	—
79	C₂³	—	17	1	no	—
80	D₄	—	4	1	no	—
81	D₄	—	4	1	no	—
82	D₄	—	136	2	no	—
83	C₂×C₄	—	17	1	no	—
84	C₂×C₄	—	34	1	no	—
85	C₂×C₄	—	34	1	no	—
86	C₂×C₄	—	68	1	no	—
87	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
88	C₈	—	2	1	no	—
89	C₈	—	34	1	no	—
90	C₈	—	68	2	no	—
91	C₂²	—	8	1	no	—
92	C₂²	—	8	1	no	—
93	C₂²	—	8	1	no	—
94	C₂²	—	34	1	no	—
95	C₂²	—	34	1	no	—
96	C₂²	—	34	1	no	—
97	C₂²	#10587547	1	1	yes	characteristic
98	C₄	—	34	1	no	—
99	C₄	—	136	1	no	—
100	C₄	#10587548	1	1	yes	characteristic
101	C₄	#10587551	1	1	yes	characteristic
102	C₂	—	16	1	no	—
103	C₂	—	68	1	no	—
104	C₂	#11763660	1	1	yes	characteristic
105	C₂	#11763723	1	1	yes	characteristic
106	C₂	#11763727	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763704

C₂

yes

maximal, characteristic, complemented

#11763685

C₂

yes

maximal, characteristic, complemented

#11763042

C₂

yes

maximal, characteristic

C₂×#63243

—

C₂×D₈×C₁₇

C₄

yes

characteristic

#10587624

—

C₂×C₈×D₁₇

C₂²

yes

—

—

C₄

yes

characteristic

C₂×D₄×C₁₇

—

C₂×C₂²⋊D₁₇

—

C₂×C₄×D₁₇

D₄

yes

—

—

—

D₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂²⋊Dic₁₇

—

C₄⋊Dic₁₇

—

C₂×#3622

D₄

yes

characteristic

C₈×D₁₇

—

#63216

—

C₂³×C₁₇

—

C₂²×D₁₇

SD₁₆

yes

characteristic

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂²⋊D₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

D₈

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

C₈×C₁₇

—

#3622

—

#1349

—

maximal, Sylow

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

#102

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

—

#466

—

C₂²⋊C₁₆

—

#341

—

C₂×C₁₇

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

C₂×D₈

#595

yes

characteristic

C₂×M₁₆

—

C₂²×C₈

—

#121

—

C₂×C₁₆

—

#107

—

#102

—

C₁₇

#1349

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₁₆

—

C₂³

—

C₂³

—

D₄

—

D₄

—

D₄

—

136

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#10587547

yes

characteristic

C₄

—

C₄

—

136

—

100

C₄

#10587548

yes

characteristic

101

C₄

#10587551

yes

characteristic

102

C₂

—

103

C₂

—

104

C₂

#11763660

yes

characteristic

105

C₂

#11763723

yes

characteristic

106

C₂

#11763727

yes

characteristic

	subgroup	G/H
center	C₂²	#10587547
commutator	C₂×C₈×C₁₇	C₂×C₄
Frattini	C₂×C₈	C₂×#595
Fitting	C₂×D₈×C₁₇	C₄
socle	C₂²×C₁₇	#102
prime radical	#11763042	C₂
cosocle	C₂×C₈×D₁₇	C₂²
hypercenter	C₂×D₈	#595
hypocenter	C₁₇	#1349
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

subgroup

G/H

center

C₂²

#10587547

commutator

C₂×C₈×C₁₇

C₂×C₄

Frattini

C₂×C₈

C₂×#595

Fitting

C₂×D₈×C₁₇

C₄

C₂²×C₁₇

C₂

C₂×C₈×D₁₇

C₂²

C₂×D₈

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×D₈

N	H ≅ G/N	type
1. #11763704	C₂	semidirect
2. #11763685	C₂	semidirect
64. C₁₇	#1349	semidirect

H ≅ G/N

type

1. #11763704

C₂

semidirect

2. #11763685

C₂

semidirect

64. C₁₇

#1349

semidirect

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

subgroup	index
#11763704	2
#11763685	2
#11763042	2
#1349	17

subgroup

index

Subgroups — #14543774

Conjugacy classes of subgroups

Complements

Maximal subgroups