Group #14544500 — subgroups

Subgroups — #14544500

Order 2176.

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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	#11763768	C₂	1	1	yes	maximal, characteristic
2	C₄²×#595	C₂	1	1	yes	maximal, characteristic
3	#11763674	C₂	1	4	yes	maximal
4	#97×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#595	C₄	1	4	yes	—
6	C₂×C₄×#595	C₂²	1	2	yes	—
7	C₂×#63242	C₂²	1	2	yes	—
8	C₂×C₈×D₁₇	C₂²	1	2	yes	—
9	C₄²×D₁₇	C₂²	1	1	yes	characteristic
10	#10587542	C₄	1	4	yes	complemented
11	C₁₇×#97	C₄	1	1	yes	characteristic, complemented
12	#10587486	C₄	1	2	yes	complemented
13	#10587474	C₄	1	1	yes	characteristic, complemented
14	C₂²×#595	C₂×C₄	1	4	yes	—
15	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
17	C₂×#3624	C₂×C₄	1	4	yes	—
18	C₄×#595	—	2	8	no	—
19	C₄×#595	—	2	4	no	—
20	#63242	—	2	4	no	—
21	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
22	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
25	C₂×#3622	C₂×C₄	1	2	yes	—
26	C₈×D₁₇	—	2	4	no	—
27	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×#595	—	2	4	no	—
29	C₂×#595	—	2	4	no	—
30	C₂×#595	M₁₆	1	8	yes	—
31	C₂×C₄×C₁₇	C₄²	1	2	yes	—
32	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₂×Dic₁₇	C₄²	1	2	yes	—
34	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
35	C₄×D₁₇	—	2	4	no	—
36	C₄×D₁₇	#41	1	4	yes	—
37	#3624	—	2	4	no	—
38	C₈×C₁₇	—	2	2	no	—
39	#3622	—	2	2	no	—
40	#1745	—	17	1	no	maximal, Sylow
41	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
42	C₂×D₁₇	#117	1	2	yes	—
43	C₂×D₁₇	C₂×M₁₆	1	4	yes	—
44	#595	—	2	8	no	—
45	C₄×C₁₇	—	2	2	no	—
46	C₄×C₁₇	#117	1	2	yes	—
47	Dic₁₇	—	2	2	no	—
48	Dic₁₇	#117	1	2	yes	—
49	C₂×#97	—	17	1	no	—
50	C₂×#97	—	17	1	no	—
51	C₄³	—	17	1	no	—
52	#336	—	17	4	no	—
53	C₂×C₁₇	#376	1	1	yes	characteristic
54	C₂×C₁₇	C₄×M₁₆	1	2	yes	—
55	D₁₇	#432	1	4	yes	—
56	C₂²×C₈	—	17	2	no	—
57	C₂²×C₈	—	17	2	no	—
58	C₂×C₄²	—	17	1	no	—
59	C₂×C₄²	—	17	4	no	—
60	C₂×C₄²	—	17	2	no	—
61	#97	—	17	4	no	—
62	#97	—	17	2	no	—
63	#97	—	17	1	no	—
64	#97	#595	1	1	yes	characteristic, complemented
65	C₁₇	#1745	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₄	—	17	1	no	—
67	C₂²×C₄	—	17	4	no	—
68	C₂²×C₄	—	17	2	no	—
69	C₂×C₈	—	17	4	no	—
70	C₂×C₈	—	17	2	no	—
71	C₂×C₈	—	34	4	no	—
72	C₂×C₈	—	34	4	no	—
73	C₂×C₈	C₂×#595	1	2	yes	—
74	C₄²	—	17	2	no	—
75	C₄²	—	17	1	no	—
76	C₄²	—	34	4	no	—
77	C₄²	—	34	8	no	—
78	C₄²	C₂×#595	1	1	yes	characteristic
79	C₂³	—	17	1	no	—
80	C₂×C₄	—	17	1	no	—
81	C₂×C₄	—	17	4	no	—
82	C₂×C₄	—	17	8	no	—
83	C₂×C₄	—	17	2	no	—
84	C₂×C₄	—	34	4	no	—
85	C₂×C₄	—	34	4	no	—
86	C₂×C₄	—	34	4	no	—
87	C₂×C₄	C₄×#595	1	2	yes	—
88	C₂×C₄	C₂²×#595	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	34	4	no	—
91	C₈	—	34	2	no	—
92	C₂²	—	17	2	no	—
93	C₂²	—	17	4	no	—
94	C₂²	C₂×C₄×#595	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	17	2	no	—
97	C₄	—	34	8	no	—
98	C₄	—	34	2	no	—
99	C₄	#10587677	1	2	yes	—
100	C₂	—	17	4	no	—
101	C₂	#11763745	1	1	yes	characteristic
102	C₂	M₁₆×#595	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#11763768

C₂

yes

maximal, characteristic

C₄²×#595

C₂

yes

maximal, characteristic

#11763674

C₂

yes

maximal

#97×D₁₇

C₂

yes

maximal, characteristic

C₂×C₄×#595

C₄

yes

—

C₂×C₄×#595

C₂²

yes

—

C₂×#63242

C₂²

yes

—

C₂×C₈×D₁₇

C₂²

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

#10587542

C₄

yes

complemented

C₁₇×#97

C₄

yes

characteristic, complemented

#10587486

C₄

yes

complemented

#10587474

C₄

yes

characteristic, complemented

C₂²×#595

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂³

yes

characteristic

C₂×#3624

C₂×C₄

yes

—

C₄×#595

—

C₄×#595

—

#63242

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

—

C₈×D₁₇

—

C₂²×D₁₇

C₂²×C₄

yes

—

—

M₁₆

yes

—

C₂×C₄×C₁₇

C₄²

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄²

yes

—

C₂×Dic₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

#41

yes

—

#3624

—

C₈×C₁₇

—

#3622

—

#1745

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂×D₁₇

#117

yes

—

C₂×D₁₇

C₂×M₁₆

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

#117

yes

—

Dic₁₇

—

Dic₁₇

#117

yes

—

C₂×#97

—

C₂×#97

—

C₄³

—

#336

—

C₂×C₁₇

#376

yes

characteristic

C₂×C₁₇

C₄×M₁₆

yes

—

D₁₇

#432

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₁₇

#1745

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×#595

yes

—

C₂×C₄

C₂²×#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

C₂×C₄×#595

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

#10587677

yes

—

100

C₂

—

101

C₂

#11763745

yes

characteristic

102

C₂

M₁₆×#595

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂×C₄²
Fitting	C₁₇×#97	C₄
prime radical	C₂²×D₁₇	C₂²×C₄
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#1745
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂×C₄²

Fitting

C₁₇×#97

C₄

prime radical

C₂²×D₁₇

C₂²×C₄

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
10. #10587542	C₄	semidirect
11. C₁₇×#97	C₄	semidirect
12. #10587486	C₄	semidirect
13. #10587474	C₄	semidirect
64. #97	#595	semidirect
65. C₁₇	#1745	semidirect

H ≅ G/N

type

10. #10587542

C₄

semidirect

11. C₁₇×#97

C₄

semidirect

12. #10587486

C₄

semidirect

13. #10587474

C₄

semidirect

64. #97

#595

semidirect

65. C₁₇

#1745

semidirect

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

subgroup	index
#11763768	2
C₄²×#595	2
#11763674	2
#97×D₁₇	2
#1745	17

subgroup

index

#11763768

C₄²×#595

#11763674

#97×D₁₇

#1745

Subgroups — #14544500

Conjugacy classes of subgroups

Complements

Maximal subgroups