Group #14544504 — subgroups

Subgroups — #14544504

Order 2176.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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	C₄×#63242	C₂	1	1	yes	maximal, characteristic
2	#11763745	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	C₂²	1	2	yes	—
6	C₂×#63242	C₂²	1	2	yes	—
7	C₂×C₈×D₁₇	C₂²	1	2	yes	—
8	C₄²×D₁₇	C₂²	1	1	yes	characteristic
9	(C₂×#595)⋊C₄	C₄	1	4	yes	—
10	C₄×#3624	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	4	no	—
19	#63242	—	2	4	no	—
20	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
21	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
22	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
24	C₂×#3622	C₂×C₄	1	2	yes	—
25	C₈×D₁₇	—	2	4	no	—
26	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
27	C₂×#595	—	2	4	no	—
28	C₂×#595	—	2	8	no	—
29	C₂×C₄×C₁₇	C₄²	1	2	yes	—
30	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
31	C₂×Dic₁₇	C₄²	1	2	yes	—
32	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
33	C₄×D₁₇	—	2	4	no	—
34	C₄×D₁₇	#41	1	4	yes	—
35	#3624	—	2	4	no	—
36	C₈×C₁₇	—	2	2	no	—
37	#3622	—	2	2	no	—
38	#1746	—	17	1	no	maximal, Sylow
39	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
40	C₂×D₁₇	#117	1	2	yes	—
41	C₂×D₁₇	#131	1	4	yes	—
42	#595	—	4	4	no	—
43	C₄×C₁₇	—	2	2	no	—
44	C₄×C₁₇	#117	1	2	yes	—
45	Dic₁₇	—	2	2	no	—
46	Dic₁₇	#117	1	2	yes	—
47	C₂×#97	—	17	1	no	—
48	C₂×C₄×C₈	—	17	1	no	—
49	#376	—	17	1	no	—
50	#336	—	17	4	no	—
51	C₂×C₁₇	#376	1	1	yes	characteristic
52	C₂×C₁₇	#405	1	2	yes	—
53	D₁₇	#433	1	4	yes	—
54	C₂²×C₈	—	17	2	no	—
55	C₂²×C₈	—	17	2	no	—
56	C₂×C₄²	—	17	1	no	—
57	C₂×C₄²	—	17	2	no	—
58	#97	—	17	2	no	—
59	#97	—	17	1	no	—
60	#97	#595	1	1	yes	characteristic, complemented
61	C₄×C₈	—	17	4	no	—
62	#95	—	17	4	no	—
63	C₁₇	#1746	1	1	yes	characteristic, complemented, Sylow
64	C₂²×C₄	—	17	1	no	—
65	C₂²×C₄	—	17	2	no	—
66	C₂²×C₄	—	17	4	no	—
67	C₂×C₈	—	17	4	no	—
68	C₂×C₈	—	17	2	no	—
69	C₂×C₈	—	34	4	no	—
70	C₂×C₈	—	34	4	no	—
71	C₂×C₈	C₂×#595	1	2	yes	—
72	C₄²	—	17	2	no	—
73	C₄²	—	17	1	no	—
74	C₄²	—	34	4	no	—
75	C₄²	C₂×#595	1	1	yes	characteristic
76	C₂³	—	17	1	no	—
77	C₂×C₄	—	17	1	no	—
78	C₂×C₄	—	17	4	no	—
79	C₂×C₄	—	17	2	no	—
80	C₂×C₄	—	34	4	no	—
81	C₂×C₄	—	34	4	no	—
82	C₂×C₄	—	34	8	no	—
83	C₂×C₄	C₄×#595	1	2	yes	—
84	C₂×C₄	C₂²×#595	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	34	4	no	—
87	C₈	—	34	2	no	—
88	C₂²	—	17	2	no	—
89	C₂²	—	17	4	no	—
90	C₂²	C₂×C₄×#595	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	17	2	no	—
93	C₄	—	34	2	no	—
94	C₄	—	68	4	no	—
95	C₄	#10587677	1	2	yes	—
96	C₂	—	17	4	no	—
97	C₂	#11763745	1	1	yes	characteristic
98	C₂	#11763775	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#63242

C₂

yes

maximal, characteristic

#11763745

C₂

yes

maximal, characteristic

#11763674

C₂

yes

maximal

#97×D₁₇

C₂

yes

maximal, characteristic

C₂×C₄×#595

C₂²

yes

—

C₂×#63242

C₂²

yes

—

C₂×C₈×D₁₇

C₂²

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

C₄

yes

—

C₄×#3624

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

—

#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

characteristic

C₂×#595

—

C₂×#595

—

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

—

#1746

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂×D₁₇

#117

yes

—

C₂×D₁₇

#131

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

#117

yes

—

Dic₁₇

—

Dic₁₇

#117

yes

—

C₂×#97

—

C₂×C₄×C₈

—

#376

—

#336

—

C₂×C₁₇

#376

yes

characteristic

C₂×C₁₇

#405

yes

—

D₁₇

#433

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

—

—

yes

characteristic, complemented

C₄×C₈

—

#95

—

C₁₇

#1746

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

C₂×#595

yes

characteristic

C₂³

—

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

—

C₂

—

C₂

#11763745

yes

characteristic

C₂

#11763775

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	#1746
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. C₄×#3624	C₄	semidirect
11. C₁₇×#97	C₄	semidirect
12. #10587486	C₄	semidirect
13. #10587474	C₄	semidirect
60. #97	#595	semidirect
63. C₁₇	#1746	semidirect

H ≅ G/N

type

10. C₄×#3624

C₄

semidirect

11. C₁₇×#97

C₄

semidirect

12. #10587486

C₄

semidirect

13. #10587474

C₄

semidirect

60. #97

#595

semidirect

63. C₁₇

#1746

semidirect

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

subgroup	index
C₄×#63242	2
#11763745	2
#11763674	2
#97×D₁₇	2
#1746	17

subgroup

index

#97×D₁₇

Subgroups — #14544504

Conjugacy classes of subgroups

Complements

Maximal subgroups