Group #14545120 — subgroups

Subgroups — #14545120

Order 2176.

160 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 76 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×#10587530	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587529	C₂	1	1	yes	maximal, characteristic
3	#11763730	C₂	1	2	yes	maximal, complemented
4	C₄⋊#63216	C₂	1	2	yes	maximal, complemented
5	#11762766	C₂	1	1	yes	maximal, characteristic
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×#63216	C₂²	1	2	yes	—
10	C₂×#63216	C₂²	1	2	yes	—
11	#10587530	—	2	2	no	—
12	#10587529	—	2	2	no	—
13	C₁₇×#97	C₄	1	1	yes	characteristic
14	#10587486	C₄	1	1	yes	characteristic
15	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
16	C₄×#3622	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
21	#63227	C₈	1	2	yes	—
22	#63225	C₈	1	2	yes	—
23	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₂×#3622	C₂×C₄	1	1	yes	characteristic
25	C₂×#3622	C₂³	1	1	yes	characteristic
26	#63218	—	2	2	no	—
27	C₈×D₁₇	D₄	1	2	yes	—
28	C₈×D₁₇	Q₈	1	2	yes	—
29	#63216	—	2	2	no	—
30	#63216	—	2	2	no	—
31	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
35	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
36	C₄×D₁₇	C₄⋊C₄	1	2	yes	—
37	C₄×D₁₇	M₁₆	1	2	yes	—
38	C₈×C₁₇	—	2	1	no	—
39	C₈×C₁₇	C₄⋊C₄	1	2	yes	—
40	#3622	—	2	1	no	—
41	#3622	C₂×D₄	1	1	yes	characteristic
42	#3622	C₂×Q₈	1	1	yes	characteristic
43	#2151	—	17	1	no	maximal, Sylow
44	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
45	C₂×D₁₇	—	2	2	no	—
46	C₂×D₁₇	C₄⋊C₈	1	2	yes	—
47	C₄×C₁₇	—	2	2	no	—
48	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
50	Dic₁₇	—	2	2	no	—
51	Dic₁₇	C₄⋊C₈	1	2	yes	—
52	C₂×M₃₂	—	17	1	no	—
53	C₂²×C₁₆	—	17	1	no	—
54	#405	—	17	1	no	—
55	C₄⋊C₁₆	—	17	2	no	—
56	C₄⋊C₁₆	—	17	2	no	—
57	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
58	C₂×C₁₇	#504	1	2	yes	—
59	D₁₇	—	2	2	no	—
60	C₂×M₁₆	—	17	1	no	—
61	C₂²×C₈	—	17	1	no	—
62	#117	—	17	1	no	—
63	M₃₂	—	34	2	no	—
64	C₂×C₁₆	—	17	2	no	—
65	C₂×C₁₆	—	17	2	no	—
66	C₂×C₁₆	—	34	2	no	—
67	#97	—	17	1	no	—
68	#97	#595	1	1	yes	characteristic
69	C₄×C₈	—	17	1	no	—
70	C₄×C₈	—	17	1	no	—
71	C₁₇	#2151	1	1	yes	characteristic, complemented, Sylow
72	C₂²×C₄	—	17	1	no	—
73	M₁₆	—	34	2	no	—
74	C₂×C₈	—	17	1	no	—
75	C₂×C₈	—	17	2	no	—
76	C₂×C₈	—	17	2	no	—
77	C₂×C₈	—	17	1	no	—
78	C₂×C₈	C₂×#595	1	1	yes	characteristic
79	C₂×C₈	C₂×#595	1	1	yes	characteristic
80	C₄⋊C₄	—	17	2	no	—
81	C₂²⋊C₄	—	17	2	no	—
82	C₄²	—	17	1	no	—
83	C₄²	C₂×#595	1	1	yes	characteristic
84	C₁₆	—	34	2	no	—
85	C₁₆	—	34	2	no	—
86	C₂³	—	17	1	no	—
87	C₂×C₄	—	17	1	no	—
88	C₂×C₄	—	17	2	no	—
89	C₂×C₄	—	17	2	no	—
90	C₂×C₄	—	17	2	no	—
91	C₂×C₄	#63242	1	2	yes	—
92	C₂×C₄	C₂²×#595	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	17	1	no	—
95	C₈	—	17	1	no	—
96	C₈	—	34	1	no	—
97	C₈	C₄⋊#595	1	2	yes	—
98	C₂²	—	17	2	no	—
99	C₂²	—	34	2	no	—
100	C₂²	C₂×#63242	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	17	2	no	—
103	C₄	—	34	2	no	—
104	C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
105	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
106	C₂	—	34	2	no	—
107	C₂	#11763810	1	1	yes	characteristic
108	C₂	#11763868	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587530

C₂

yes

maximal, characteristic

C₂×#10587529

C₂

yes

maximal, characteristic

#11763730

C₂

yes

maximal, complemented

C₄⋊#63216

C₂

yes

maximal, complemented

#11762766

C₂

yes

maximal, characteristic

C₂×#63218

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587558

C₄

yes

characteristic

C₂×#63216

C₂²

yes

—

C₂×#63216

C₂²

yes

—

#10587530

—

#10587529

—

C₁₇×#97

C₄

yes

characteristic

#10587486

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₄×#3622

C₂²

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

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

C₂³

yes

characteristic

#63218

—

C₈×D₁₇

D₄

yes

—

C₈×D₁₇

Q₈

yes

—

#63216

—

#63216

—

C₂²×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₄⋊C₄

yes

—

C₄×D₁₇

M₁₆

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₄⋊C₄

yes

—

#3622

—

#3622

C₂×D₄

yes

characteristic

#3622

C₂×Q₈

yes

characteristic

#2151

—

maximal, Sylow

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄⋊C₈

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

C₄⋊C₈

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₇

#504

yes

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₁₇

#2151

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#63242

yes

—

C₂×C₄

C₂²×#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₄⋊#595

yes

—

C₂²

—

C₂²

—

100

C₂²

C₂×#63242

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

D₁₇⋊M₁₆

yes

characteristic

105

C₄

C₂×C₄⋊#595

yes

characteristic

106

C₂

—

107

C₂

#11763810

yes

characteristic

108

C₂

#11763868

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₁₇×#97	C₄
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	C₂×#3622	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#2151
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂²×C₈

Fitting

C₁₇×#97

C₄

prime radical

C₂²×D₁₇

C₂×C₈

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #11763730	C₂	semidirect
4. C₄⋊#63216	C₂	semidirect
71. C₁₇	#2151	semidirect

H ≅ G/N

type

3. #11763730

C₂

semidirect

4. C₄⋊#63216

C₂

semidirect

71. C₁₇

#2151

semidirect

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

subgroup	index
C₂×#10587530	2
C₂×#10587529	2
#11763730	2
C₄⋊#63216	2
#11762766	2
#2151	17

subgroup

index

Subgroups — #14545120

Conjugacy classes of subgroups

Complements

Maximal subgroups