Group #14545176 — subgroups

Subgroups — #14545176

Order 2176.

144 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 58 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	#11763868	C₂	1	2	yes	maximal, complemented
2	#11763731	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763708	C₂	1	2	yes	maximal, complemented
4	#11763698	C₂	1	1	yes	maximal, characteristic, complemented
5	#11762925	C₂	1	1	yes	maximal, characteristic
6	#10587593	C₂²	1	2	yes	—
7	#10587590	C₄	1	1	yes	characteristic
8	#10587538	C₂²	1	2	yes	—
9	C₂×#63216	C₂²	1	1	yes	characteristic
10	C₂×#63216	C₂²	1	1	yes	characteristic
11	#10587530	—	2	2	no	—
12	#10587529	—	2	2	no	—
13	C₁₇×#108	C₄	1	1	yes	characteristic
14	#10587496	C₄	1	2	yes	—
15	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
16	#63252	C₂×C₄	1	2	yes	—
17	M₁₆×C₁₇	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×#3622	C₂³	1	1	yes	characteristic
21	Dic₆₈	C₈	1	1	yes	characteristic
22	D₁₃₆	C₈	1	1	yes	characteristic
23	#63219	C₈	1	2	yes	—
24	#63218	—	2	2	no	—
25	C₈×D₁₇	—	2	2	no	—
26	#63216	—	2	2	no	—
27	#63216	—	2	1	no	—
28	#63216	D₄	1	2	yes	—
29	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₂²⋊D₁₇	—	2	2	no	—
31	C₂×Dic₁₇	—	2	1	no	—
32	D₆₈	C₂×C₈	1	2	yes	—
33	C₄×D₁₇	—	2	2	no	—
34	Dic₃₄	C₂×C₈	1	2	yes	—
35	C₈×C₁₇	—	2	2	no	—
36	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
37	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
38	#3622	C₂×D₄	1	1	yes	characteristic
39	#3622	#41	1	1	yes	characteristic
40	#2171	—	17	1	no	maximal, Sylow
41	C₂²×C₁₇	#131	1	1	yes	characteristic
42	C₂×D₁₇	—	2	2	no	—
43	C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
44	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
45	Dic₁₇	—	2	2	no	—
46	Dic₁₇	—	4	1	no	—
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	—	2	1	no	—
53	C₂×C₁₇	C₈×D₄	1	1	yes	characteristic
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	#595	1	1	yes	characteristic
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	—	17	1	no	—
68	SD₁₆	—	17	2	no	—
69	D₈	—	17	1	no	—
70	M₁₆	—	34	2	no	—
71	M₁₆	C₂×#595	1	2	yes	—
72	C₂×C₈	—	17	1	no	—
73	C₂×C₈	—	34	2	no	—
74	C₂×C₈	C₂×#595	1	1	yes	characteristic
75	C₄²	—	17	1	no	—
76	C₁₆	—	17	2	no	—
77	C₁₆	—	34	1	no	—
78	C₁₆	—	34	2	no	—
79	Q₈	—	17	2	no	—
80	D₄	—	17	2	no	—
81	D₄	—	34	2	no	—
82	C₂×C₄	—	34	2	no	—
83	C₂×C₄	—	34	1	no	—
84	C₂×C₄	C₂²×#595	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	17	1	no	—
87	C₈	—	17	1	no	—
88	C₈	#63242	1	1	yes	characteristic
89	C₈	#63242	1	1	yes	characteristic
90	C₂²	—	34	2	no	—
91	C₂²	#10587680	1	1	yes	characteristic
92	C₄	—	34	2	no	—
93	C₄	—	68	1	no	—
94	C₄	C₂×#63242	1	1	yes	characteristic
95	C₄	D₄×#595	1	1	yes	characteristic
96	C₂	—	2	1	no	—
97	C₂	—	68	2	no	—
98	C₂	#11763837	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763868

C₂

yes

maximal, complemented

#11763731

C₂

yes

maximal, characteristic, complemented

#11763708

C₂

yes

maximal, complemented

#11763698

C₂

yes

maximal, characteristic, complemented

#11762925

C₂

yes

maximal, characteristic

#10587593

C₂²

yes

—

#10587590

C₄

yes

characteristic

#10587538

C₂²

yes

—

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

#10587530

—

#10587529

—

C₁₇×#108

C₄

yes

characteristic

#10587496

C₄

yes

—

C₈×Dic₁₇

C₂²

yes

characteristic

#63252

C₂×C₄

yes

—

M₁₆×C₁₇

C₂×C₄

yes

—

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂³

yes

characteristic

Dic₆₈

C₈

yes

characteristic

D₁₃₆

C₈

yes

characteristic

#63219

C₈

yes

—

#63218

—

C₈×D₁₇

—

#63216

—

#63216

—

#63216

D₄

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂²⋊D₁₇

—

C₂×Dic₁₇

—

D₆₈

C₂×C₈

yes

—

C₄×D₁₇

—

Dic₃₄

C₂×C₈

yes

—

C₈×C₁₇

—

C₈×C₁₇

C₂×C₈

yes

characteristic

C₈×C₁₇

C₂×C₈

yes

characteristic

#3622

C₂×D₄

yes

yes

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₄×C₁₇

C₄×D₄

yes

characteristic

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

—

Dic₁₇

—

—

—

—

—

—

C₂×C₁₇

—

C₂×C₁₇

C₈×D₄

yes

characteristic

D₁₇

—

#135

—

#131

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

yes

—

C₄×C₈

—

C₁₇

#2171

yes

characteristic, complemented, Sylow

#41

—

Q₁₆

—

SD₁₆

—

D₈

—

M₁₆

—

M₁₆

C₂×#595

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

characteristic

C₄²

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

D₄

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²×#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

#10587680

yes

characteristic

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

—

C₂

#11763837

yes

characteristic

	subgroup	G/H
center	C₄	D₄×#595
commutator	C₄×C₁₇	C₂²×C₈
Frattini	C₂×C₄	C₂²×#595
Fitting	C₁₇×#108	C₄
socle	C₂×C₁₇	C₈×D₄
prime radical	#10587590	C₄
cosocle	C₂×#3622	C₂³
hypercenter	#108	#595
hypocenter	C₁₇	#2171
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

subgroup

G/H

center

C₄

D₄×#595

commutator

C₄×C₁₇

C₂²×C₈

Frattini

C₂×C₄

C₂²×#595

Fitting

C₁₇×#108

C₄

socle

C₂×C₁₇

C₈×D₄

C₄

C₂³

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

N	H ≅ G/N	type
1. #11763868	C₂	semidirect
2. #11763731	C₂	semidirect
3. #11763708	C₂	semidirect
4. #11763698	C₂	semidirect
65. C₁₇	#2171	semidirect

H ≅ G/N

type

1. #11763868

C₂

semidirect

2. #11763731

C₂

semidirect

3. #11763708

C₂

semidirect

4. #11763698

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
#11763868	2
#11763731	2
#11763708	2
#11763698	2
#11762925	2
#2171	17

subgroup

index

Subgroups — #14545176

Conjugacy classes of subgroups

Complements

Maximal subgroups