Group #14528903 — subgroups

Subgroups — #14528903

Order 2176.

216 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 101 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×C₄⋊#3622	C₂	1	1	yes	maximal, characteristic
2	#11762655	C₂	1	1	yes	maximal, characteristic
3	#11762563	C₂	1	4	yes	maximal
4	C₂×C₁₇×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
6	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
7	C₂×C₄×Dic₁₇	C₂²	1	2	yes	—
8	C₂²×#3622	C₂²	1	2	yes	—
9	C₁₇×C₄⋊C₈	—	2	2	no	—
10	#10587502	C₄	1	2	yes	—
11	#10587502	C₄	1	2	yes	—
12	C₄⋊#3622	—	2	2	no	—
13	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
16	C₂²×Dic₁₇	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₁₇	—	2	2	no	—
18	C₂×C₈×C₁₇	—	2	4	no	—
19	C₄²×C₁₇	D₄	1	2	yes	—
20	C₄²×C₁₇	Q₈	1	2	yes	—
21	C₄×Dic₁₇	—	2	2	no	—
22	C₄×Dic₁₇	—	2	2	no	—
23	C₂×#3622	—	2	2	no	—
24	C₂×#3622	—	2	4	no	—
25	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
26	C₂×C₄×C₁₇	—	2	2	no	—
27	C₂×C₄×C₁₇	—	2	2	no	—
28	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
29	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
30	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
31	C₂×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₄×C₁₇	#41	1	2	yes	—
33	C₂×C₄×C₁₇	#41	1	2	yes	—
34	C₂×Dic₁₇	—	2	4	no	—
35	C₂×Dic₁₇	—	2	4	no	—
36	C₂×Dic₁₇	—	2	4	no	—
37	C₈×C₁₇	—	4	2	no	—
38	#3622	—	4	2	no	—
39	#1832	—	17	1	no	maximal, Sylow
40	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₂²×C₁₇	#117	1	2	yes	—
42	C₂²×C₁₇	#131	1	2	yes	—
43	C₂²×C₁₇	#131	1	2	yes	—
44	C₄×C₁₇	—	2	2	no	—
45	C₄×C₁₇	—	2	2	no	—
46	C₄×C₁₇	#124	1	1	yes	characteristic
47	C₄×C₁₇	#124	1	1	yes	characteristic
48	C₄×C₁₇	#125	1	2	yes	—
49	Dic₁₇	—	4	4	no	—
50	C₂×C₄⋊C₈	—	17	1	no	—
51	C₂×C₄⋊C₈	D₁₇	1	1	yes	characteristic
52	#376	—	17	1	no	—
53	#336	—	17	4	no	—
54	C₂×C₁₇	#382	1	1	yes	characteristic
55	C₂×C₁₇	#424	1	1	yes	characteristic
56	C₂×C₁₇	#424	1	1	yes	characteristic
57	C₂×C₁₇	#433	1	4	yes	—
58	C₂²×C₈	—	17	2	no	—
59	C₂²×C₈	C₂×D₁₇	1	2	yes	—
60	C₂×C₄²	—	17	2	no	—
61	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
62	C₄⋊C₈	—	2	2	no	—
63	C₄⋊C₈	—	34	2	no	—
64	#95	—	17	2	no	—
65	#95	—	17	2	no	—
66	C₁₇	#1832	1	1	yes	characteristic, complemented, Sylow
67	C₂²×C₄	—	17	4	no	—
68	C₂²×C₄	C₄×D₁₇	1	1	yes	characteristic
69	C₂²×C₄	C₄×D₁₇	1	1	yes	characteristic
70	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
71	C₂×C₈	—	2	4	no	—
72	C₂×C₈	—	2	2	no	—
73	C₂×C₈	—	34	4	no	—
74	C₂×C₈	—	34	2	no	—
75	C₄²	—	34	2	no	—
76	C₄²	—	34	2	no	—
77	C₄²	Dic₃₄	1	2	yes	—
78	C₄²	C₂²⋊D₁₇	1	2	yes	—
79	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
80	C₂×C₄	—	2	2	no	—
81	C₂×C₄	—	2	2	no	—
82	C₂×C₄	—	34	4	no	—
83	C₂×C₄	—	34	4	no	—
84	C₂×C₄	—	34	4	no	—
85	C₂×C₄	#63225	1	2	yes	—
86	C₂×C₄	#63225	1	2	yes	—
87	C₂×C₄	C₂×Dic₃₄	1	1	yes	characteristic
88	C₂×C₄	#63254	1	2	yes	—
89	C₂×C₄	#63256	1	2	yes	—
90	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
91	C₈	—	4	2	no	—
92	C₈	—	68	2	no	—
93	C₂²	#10587578	1	2	yes	—
94	C₂²	#10587587	1	2	yes	—
95	C₂²	#10587593	1	2	yes	—
96	C₂²	C₂×#63225	1	1	yes	characteristic
97	C₄	—	2	2	no	—
98	C₄	—	2	2	no	—
99	C₄	—	68	4	no	—
100	C₄	#10587576	1	2	yes	—
101	C₄	#10587622	1	1	yes	characteristic
102	C₄	#10587633	1	1	yes	characteristic
103	C₂	#11762674	1	1	yes	characteristic
104	C₂	#11762835	1	1	yes	characteristic
105	C₂	#11762837	1	1	yes	characteristic
106	C₂	#11762869	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#3622

C₂

yes

maximal, characteristic

#11762655

C₂

yes

maximal, characteristic

#11762563

C₂

yes

maximal

C₂×C₁₇×C₄⋊C₈

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₇

C₂²

yes

—

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

—

C₂²×#3622

C₂²

yes

—

C₁₇×C₄⋊C₈

—

#10587502

C₄

yes

—

#10587502

C₄

yes

—

C₄⋊#3622

—

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₄²×C₁₇

D₄

yes

—

C₄²×C₁₇

Q₈

yes

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₂×#3622

—

C₂×#3622

—

C₂³×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

#41

yes

—

C₂×C₄×C₁₇

#41

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₈×C₁₇

—

#3622

—

#1832

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₂²×C₁₇

#117

yes

—

C₂²×C₁₇

#131

yes

—

C₂²×C₁₇

#131

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

yes

C₄×C₁₇

yes

C₄×C₁₇

yes

—

Dic₁₇

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

D₁₇

yes

characteristic

#376

—

#336

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₇

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

#95

—

#95

—

C₁₇

#1832

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

C₄×D₁₇

yes

characteristic

C₂²×C₄

C₄×D₁₇

yes

characteristic

C₂²×C₄

C₂²×D₁₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

Dic₃₄

yes

—

C₄²

C₂²⋊D₁₇

yes

—

C₂³

C₂×C₄×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#63225

yes

—

C₂×C₄

#63225

yes

—

C₂×C₄

C₂×Dic₃₄

yes

characteristic

C₂×C₄

#63254

yes

—

C₂×C₄

#63256

yes

—

C₂×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

C₈

—

C₈

—

C₂²

#10587578

yes

—

C₂²

#10587587

yes

—

C₂²

#10587593

yes

—

C₂²

C₂×#63225

yes

characteristic

C₄

—

C₄

—

C₄

—

100

C₄

#10587576

yes

—

101

C₄

#10587622

yes

characteristic

102

C₄

#10587633

yes

characteristic

103

C₂

#11762674

yes

characteristic

104

C₂

#11762835

yes

characteristic

105

C₂

#11762837

yes

characteristic

106

C₂

#11762869

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇
commutator, socle, prime radical	C₂³×C₁₇	C₂²×C₄
Fitting	C₂×C₁₇×C₄⋊C₈	C₂
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×C₄⋊C₈	D₁₇
hypocenter	C₁₇	#1832
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₇

commutator, socle, prime radical

C₂³×C₁₇

C₂²×C₄

Fitting

C₂×C₁₇×C₄⋊C₈

C₂

cosocle

C₂²×C₄×C₁₇

C₂³

hypercenter

C₂×C₄⋊C₈

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₈

N	H ≅ G/N	type
66. C₁₇	#1832	semidirect

H ≅ G/N

type

66. C₁₇

#1832

semidirect

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

subgroup	index
C₂×C₄⋊#3622	2
#11762655	2
#11762563	2
C₂×C₁₇×C₄⋊C₈	2
#1832	17

subgroup

index

C₂×C₄⋊#3622

#11762655

#11762563

C₂×C₁₇×C₄⋊C₈

#1832

Subgroups — #14528903

Conjugacy classes of subgroups

Complements

Maximal subgroups