Group #14546005 — subgroups

Subgroups — #14546005

Order 2176.

144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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	#11763931	C₂	1	2	yes	maximal, complemented
2	#11763913	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763910	C₂	1	2	yes	maximal, complemented
4	#11763904	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763853	C₂	1	1	yes	maximal, characteristic
6	#10587680	C₂²	1	2	yes	—
7	#10587666	—	2	2	no	—
8	#10587666	C₂²	1	2	yes	—
9	#10587665	—	2	2	no	—
10	#10587665	C₂²	1	1	yes	characteristic
11	#10587665	C₂²	1	1	yes	characteristic
12	#10587605	C₄	1	1	yes	characteristic
13	#10587550	C₄	1	2	yes	—
14	#10587536	C₄	1	1	yes	characteristic
15	C₈×#595	C₂²	1	1	yes	characteristic
16	#63256	C₂×C₄	1	2	yes	—
17	C₄×#595	C₂×C₄	1	1	yes	characteristic
18	#63243	—	2	2	no	—
19	#63243	C₂×C₄	1	2	yes	—
20	#63242	—	2	2	no	—
21	#63242	C₂³	1	1	yes	characteristic
22	#63241	—	2	2	no	—
23	#63241	—	2	1	no	—
24	#63241	D₄	1	2	yes	—
25	Q₁₆×C₁₇	C₈	1	1	yes	characteristic
26	#63230	C₈	1	2	yes	—
27	D₁₃₆	C₈	1	1	yes	characteristic
28	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
29	C₂×#595	—	2	1	no	—
30	Q₈×C₁₇	C₂×C₈	1	2	yes	—
31	D₆₈	—	2	2	no	—
32	D₆₈	C₂×C₈	1	2	yes	—
33	C₄×D₁₇	—	2	2	no	—
34	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
35	#3624	—	2	2	no	—
36	#3624	C₂×D₄	1	1	yes	characteristic
37	#3624	#41	1	1	yes	characteristic
38	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
39	#3622	C₂×C₈	1	1	yes	characteristic
40	#2171	—	17	1	no	maximal, Sylow
41	C₂×D₁₇	—	2	2	no	—
42	C₂×D₁₇	#131	1	1	yes	characteristic
43	#595	—	4	1	no	—
44	C₄×C₁₇	—	2	2	no	—
45	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
46	Dic₁₇	C₄×D₄	1	1	yes	characteristic
47	#504	—	17	2	no	—
48	#443	—	17	1	no	—
49	#364	—	17	1	no	—
50	#350	—	17	2	no	—
51	#346	—	17	1	no	—
52	C₂×C₁₇	C₈×D₄	1	1	yes	characteristic
53	D₁₇	—	2	1	no	—
54	D₁₇	—	4	2	no	—
55	#135	—	17	1	no	—
56	#131	—	17	2	no	—
57	M₃₂	—	17	2	no	—
58	M₃₂	—	34	2	no	—
59	C₂×C₁₆	—	17	1	no	—
60	C₂×C₁₆	—	17	1	no	—
61	C₂×C₁₆	—	34	2	no	—
62	#108	—	17	1	no	—
63	#104	—	17	2	no	—
64	C₄×C₈	—	17	1	no	—
65	C₁₇	#2171	1	1	yes	characteristic, complemented, Sylow
66	#41	—	17	2	no	—
67	Q₁₆	#3633	1	1	yes	characteristic
68	SD₁₆	—	17	2	no	—
69	D₈	—	17	1	no	—
70	M₁₆	—	17	2	no	—
71	M₁₆	—	34	2	no	—
72	C₂×C₈	—	17	1	no	—
73	C₂×C₈	—	17	1	no	—
74	C₂×C₈	—	34	2	no	—
75	C₄²	—	17	1	no	—
76	C₁₆	—	17	2	no	—
77	C₁₆	—	34	1	no	—
78	C₁₆	—	34	2	no	—
79	Q₈	C₂×#3633	1	2	yes	—
80	D₄	—	17	2	no	—
81	D₄	—	34	2	no	—
82	C₂×C₄	—	17	1	no	—
83	C₂×C₄	—	34	2	no	—
84	C₂×C₄	—	34	1	no	—
85	C₈	—	17	1	no	—
86	C₈	—	17	1	no	—
87	C₈	—	17	1	no	—
88	C₈	—	34	2	no	—
89	C₈	C₂×#3633	1	1	yes	characteristic
90	C₂²	—	17	1	no	—
91	C₂²	—	34	2	no	—
92	C₄	—	2	2	no	—
93	C₄	—	17	1	no	—
94	C₄	—	68	1	no	—
95	C₄	C₂²×#3633	1	1	yes	characteristic
96	C₂	—	34	1	no	—
97	C₂	—	68	2	no	—
98	C₂	D₄×#3633	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763931

C₂

yes

maximal, complemented

#11763913

C₂

yes

maximal, characteristic, complemented

#11763910

C₂

yes

maximal, complemented

#11763904

C₂

yes

maximal, characteristic, complemented

#11763853

C₂

yes

maximal, characteristic

#10587680

C₂²

yes

—

#10587666

—

#10587666

C₂²

yes

—

#10587665

—

#10587665

C₂²

yes

characteristic

#10587665

C₂²

yes

characteristic

#10587605

C₄

yes

characteristic

#10587550

C₄

yes

—

#10587536

C₄

yes

characteristic

C₈×#595

C₂²

yes

characteristic

#63256

C₂×C₄

yes

—

C₄×#595

C₂×C₄

yes

characteristic

#63243

—

#63243

C₂×C₄

yes

—

#63242

—

#63242

C₂³

yes

—

—

D₄

yes

—

Q₁₆×C₁₇

C₈

yes

characteristic

#63230

C₈

yes

—

D₁₃₆

C₈

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₂×#595

—

Q₈×C₁₇

C₂×C₈

yes

—

D₆₈

—

D₆₈

C₂×C₈

yes

—

C₄×D₁₇

—

C₄×D₁₇

C₂²×C₄

yes

characteristic

#3624

—

#3624

C₂×D₄

yes

yes

C₈×C₁₇

C₂×C₈

yes

characteristic

#3622

C₂×C₈

yes

characteristic

#2171

—

maximal, Sylow

C₂×D₁₇

—

C₂×D₁₇

#131

yes

characteristic

#595

—

C₄×C₁₇

—

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

C₄×D₄

yes

—

—

—

—

—

C₂×C₁₇

C₈×D₄

yes

characteristic

D₁₇

—

D₁₇

—

#135

—

#131

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#108

—

#104

—

C₄×C₈

—

C₁₇

#2171

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

#3633

yes

characteristic

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

C₂×#3633

yes

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₈

—

C₈

—

C₈

—

C₈

—

C₈

C₂×#3633

yes

characteristic

C₂²

—

C₂²

—

C₄

—

C₄

—

C₄

—

C₄

C₂²×#3633

yes

characteristic

C₂

—

C₂

—

C₂

D₄×#3633

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#3633
commutator	C₄×C₁₇	C₂²×C₈
Frattini	C₄	C₂²×#3633
Fitting	Q₁₆×C₁₇	C₈
socle	C₂×C₁₇	C₈×D₄
prime radical	#10587605	C₄
cosocle	#63242	C₂³
hypercenter	Q₁₆	#3633
hypocenter	C₁₇	#2171
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

subgroup

G/H

center

C₂

D₄×#3633

commutator

C₄×C₁₇

C₂²×C₈

Frattini

C₄

C₂²×#3633

Fitting

Q₁₆×C₁₇

C₈

socle

C₂×C₁₇

C₈×D₄

C₄

C₂³

Q₁₆

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

N	H ≅ G/N	type
1. #11763931	C₂	semidirect
2. #11763913	C₂	semidirect
3. #11763910	C₂	semidirect
4. #11763904	C₂	semidirect
65. C₁₇	#2171	semidirect

H ≅ G/N

type

1. #11763931

C₂

semidirect

2. #11763913

C₂

semidirect

3. #11763910

C₂

semidirect

4. #11763904

C₂

semidirect

65. C₁₇

#2171

semidirect

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

subgroup	index
#11763931	2
#11763913	2
#11763910	2
#11763904	2
#11763853	2
#2171	17

subgroup

index

Subgroups — #14546005

Conjugacy classes of subgroups

Complements

Maximal subgroups