Group #14528644 — subgroups

Subgroups — #14528644

Order 2176.

260 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 129 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×#10587485	C₂	1	2	yes	maximal
2	C₂×C₄×#3622	C₂	1	1	yes	maximal, characteristic
3	#11762655	C₂	1	1	yes	maximal, characteristic
4	#11762563	C₂	1	2	yes	maximal
5	C₂×C₁₇×#97	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×C₁₇	C₂²	1	2	yes	—
7	C₂×C₄²×C₁₇	C₂²	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic
10	C₂²×#3622	C₂²	1	2	yes	—
11	C₁₇×#97	—	2	2	no	—
12	#10587502	C₄	1	4	yes	—
13	#10587485	C₄	1	8	yes	complemented
14	C₄×#3622	—	2	2	no	—
15	C₂²×C₄×C₁₇	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
17	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
18	C₂²×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₁₇	—	2	2	no	—
20	C₂×C₈×C₁₇	—	2	2	no	—
21	C₂×C₈×C₁₇	C₂×C₄	1	4	yes	—
22	C₄²×C₁₇	D₄	1	2	yes	—
23	C₄²×C₁₇	Q₈	1	2	yes	—
24	C₄×Dic₁₇	—	2	2	no	—
25	C₄×Dic₁₇	C₂×C₄	1	4	yes	—
26	C₂×#3622	—	2	2	no	—
27	C₂×#3622	—	2	2	no	—
28	C₂×#3622	C₂×C₄	1	4	yes	—
29	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₁₇	—	2	4	no	—
31	C₂×C₄×C₁₇	C₄⋊C₄	1	4	yes	—
32	C₂×C₄×C₁₇	C₂²×C₄	1	2	yes	—
33	C₂×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₂×Q₈	1	1	yes	characteristic
35	C₂×C₄×C₁₇	#41	1	2	yes	—
36	C₂×Dic₁₇	—	2	4	no	—
37	C₂×Dic₁₇	—	2	2	no	—
38	C₂×Dic₁₇	—	2	4	no	—
39	C₂×Dic₁₇	C₄²	1	4	yes	—
40	C₈×C₁₇	—	2	4	no	—
41	#3622	—	2	4	no	—
42	#1768	—	17	1	no	maximal, Sylow
43	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
44	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₁₇	#117	1	1	yes	characteristic
46	C₂²×C₁₇	#131	1	4	yes	—
47	C₄×C₁₇	—	2	4	no	—
48	C₄×C₁₇	C₄×D₄	1	2	yes	—
49	C₄×C₁₇	C₄×Q₈	1	2	yes	—
50	Dic₁₇	—	2	4	no	—
51	Dic₁₇	—	4	2	no	—
52	C₂×C₄⋊C₈	—	17	2	no	—
53	C₂×#97	D₁₇	1	1	yes	characteristic
54	C₂×C₄×C₈	—	17	1	no	—
55	#376	—	17	1	no	—
56	#336	—	17	2	no	—
57	C₂×C₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
58	C₂×C₁₇	#405	1	2	yes	—
59	C₂×C₁₇	#424	1	2	yes	—
60	C₂×C₁₇	#433	1	2	yes	—
61	C₂²×C₈	—	17	2	no	—
62	C₂²×C₈	C₂×D₁₇	1	2	yes	—
63	C₂×C₄²	—	17	1	no	—
64	C₂×C₄²	—	17	1	no	—
65	C₂×C₄²	C₂×D₁₇	1	1	yes	characteristic
66	C₄⋊C₈	—	17	8	no	—
67	#97	—	2	2	no	—
68	C₄×C₈	—	34	2	no	—
69	#95	—	17	4	no	—
70	C₁₇	#1768	1	1	yes	characteristic, complemented, Sylow
71	C₂²×C₄	—	17	2	no	—
72	C₂²×C₄	—	17	2	no	—
73	C₂²×C₄	C₄×D₁₇	1	2	yes	—
74	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
75	C₂×C₈	—	2	2	no	—
76	C₂×C₈	—	2	2	no	—
77	C₂×C₈	—	17	4	no	—
78	C₂×C₈	—	34	2	no	—
79	C₂×C₈	—	34	2	no	—
80	C₂×C₈	C₄×D₁₇	1	4	yes	—
81	C₄²	—	17	4	no	—
82	C₄²	—	34	2	no	—
83	C₄²	Dic₃₄	1	2	yes	—
84	C₄²	C₂²⋊D₁₇	1	2	yes	—
85	C₂³	C₂×C₄×D₁₇	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	17	4	no	—
88	C₂×C₄	—	34	4	no	—
89	C₂×C₄	—	34	2	no	—
90	C₂×C₄	—	34	4	no	—
91	C₂×C₄	#63225	1	4	yes	—
92	C₂×C₄	C₂×Dic₃₄	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₁₇	1	2	yes	—
94	C₂×C₄	#63252	1	2	yes	—
95	C₂×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
96	C₈	—	2	4	no	—
97	C₈	—	34	4	no	—
98	C₂²	C₄²×D₁₇	1	1	yes	characteristic
99	C₂²	#10587558	1	1	yes	characteristic
100	C₂²	#10587593	1	4	yes	—
101	C₂²	C₂×#63225	1	1	yes	characteristic
102	C₄	—	2	4	no	—
103	C₄	—	34	4	no	—
104	C₄	—	68	2	no	—
105	C₄	C₄×Dic₃₄	1	2	yes	—
106	C₄	C₄×C₂²⋊D₁₇	1	2	yes	—
107	C₂	C₄×#63225	1	1	yes	characteristic
108	C₂	#11762766	1	2	yes	—
109	C₂	#11762837	1	2	yes	—
110	C₂	#11762871	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587485

C₂

yes

maximal

C₂×C₄×#3622

C₂

yes

maximal, characteristic

#11762655

C₂

yes

maximal, characteristic

#11762563

C₂

yes

maximal

C₂×C₁₇×#97

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₇

C₂²

yes

—

C₂×C₄²×C₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂×C₄×Dic₁₇

C₂²

yes

characteristic

C₂²×#3622

C₂²

yes

—

C₁₇×#97

—

#10587502

C₄

yes

—

#10587485

C₄

yes

complemented

C₄×#3622

—

C₂²×C₄×C₁₇

C₂×C₄

yes

—

C₂²×C₄×C₁₇

C₂³

yes

characteristic

C₂²×Dic₁₇

C₂×C₄

yes

—

C₂²×Dic₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

D₄

yes

—

C₄²×C₁₇

Q₈

yes

—

C₄×Dic₁₇

—

C₄×Dic₁₇

C₂×C₄

yes

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

C₂×C₄

yes

—

C₂³×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

—

C₂×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂×C₄×C₁₇

C₂×Q₈

yes

characteristic

C₂×C₄×C₁₇

#41

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

C₄²

yes

—

C₈×C₁₇

—

#3622

—

#1768

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂²×C₁₇

C₂×C₄⋊C₄

yes

C₂²×C₁₇

yes

C₂²×C₁₇

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₄×D₄

yes

—

C₄×C₁₇

C₄×Q₈

yes

—

Dic₁₇

—

Dic₁₇

—

C₂×C₄⋊C₈

—

C₂×#97

D₁₇

yes

characteristic

C₂×C₄×C₈

—

#376

—

#336

—

C₂×C₁₇

C₄×C₄⋊C₄

yes

characteristic

C₂×C₁₇

#405

yes

—

C₂×C₁₇

#424

yes

—

C₂×C₁₇

#433

yes

—

C₂²×C₈

—

C₂²×C₈

C₂×D₁₇

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂×D₁₇

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

#95

—

C₁₇

#1768

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₄×D₁₇

yes

—

C₂²×C₄

C₂²×D₁₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₁₇

yes

—

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

C₂×Dic₃₄

yes

characteristic

C₂×C₄

C₂×C₄×D₁₇

yes

—

C₂×C₄

#63252

yes

—

C₂×C₄

C₂×C₂²⋊D₁₇

yes

characteristic

C₈

—

C₈

—

C₂²

C₄²×D₁₇

yes

characteristic

C₂²

#10587558

yes

characteristic

100

C₂²

#10587593

yes

—

101

C₂²

C₂×#63225

yes

characteristic

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄×Dic₃₄

yes

—

106

C₄

C₄×C₂²⋊D₁₇

yes

—

107

C₂

C₄×#63225

yes

characteristic

108

C₂

#11762766

yes

—

109

C₂

#11762837

yes

—

110

C₂

#11762871

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₁₇
commutator	C₂²×C₁₇	C₂×C₄²
Fitting	C₂×C₁₇×#97	C₂
socle, prime radical	C₂³×C₁₇	C₂²×C₄
cosocle	C₂²×C₄×C₁₇	C₂³
hypercenter	C₂×#97	D₁₇
hypocenter	C₁₇	#1768
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₁₇

commutator

C₂²×C₁₇

C₂×C₄²

Fitting

C₂×C₁₇×#97

C₂

socle, prime radical

C₂³×C₁₇

C₂²×C₄

cosocle

C₂²×C₄×C₁₇

C₂³

hypercenter

C₂×#97

D₁₇

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂²×C₄ ◁ C₂×#97

N	H ≅ G/N	type
13. #10587485	C₄	semidirect
70. C₁₇	#1768	semidirect

H ≅ G/N

type

13. #10587485

C₄

semidirect

70. C₁₇

#1768

semidirect

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

subgroup	index
C₂×#10587485	2
C₂×C₄×#3622	2
#11762655	2
#11762563	2
C₂×C₁₇×#97	2
#1768	17

subgroup

index

C₂×C₄×#3622

C₂×C₁₇×#97

Subgroups — #14528644

Conjugacy classes of subgroups

Complements

Maximal subgroups