Group #14544442 — subgroups

Subgroups — #14544442

Order 2176.

328 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 158 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×#10587532	C₂	1	2	yes	maximal
2	C₄×#63242	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×#595	C₂	1	2	yes	maximal
4	#11763745	C₂	1	1	yes	maximal, characteristic
5	#97×D₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#595	C₂²	1	2	yes	—
7	C₂×#63242	C₂²	1	1	yes	characteristic
8	C₂×#63242	C₂²	1	1	yes	characteristic
9	C₂×C₈×D₁₇	C₂²	1	2	yes	—
10	C₄²×D₁₇	C₂²	1	1	yes	characteristic
11	(C₂×#595)⋊C₄	C₄	1	4	yes	—
12	C₄×#3624	C₄	1	4	yes	complemented
13	#10587532	C₄	1	8	yes	complemented
14	C₈×#595	C₄	1	8	yes	complemented
15	C₁₇×#97	C₄	1	1	yes	characteristic, complemented
16	#10587486	C₄	1	2	yes	complemented
17	#10587474	C₄	1	1	yes	characteristic, complemented
18	C₂²×#595	C₂×C₄	1	4	yes	—
19	C₂×C₄×D₁₇	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
21	C₂×#3624	C₂×C₄	1	2	yes	—
22	C₂×#3624	C₂×C₄	1	2	yes	—
23	C₄×#595	C₂×C₄	1	4	yes	—
24	C₄×#595	C₂×C₄	1	4	yes	—
25	#63242	C₂×C₄	1	4	yes	—
26	#63242	C₂×C₄	1	4	yes	—
27	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
28	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
31	C₂×#3622	C₂×C₄	1	2	yes	—
32	C₈×D₁₇	C₂×C₄	1	4	yes	—
33	C₈×D₁₇	C₂×C₄	1	4	yes	—
34	C₂²×D₁₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×#595	—	2	8	no	—
36	C₂×#595	C₄²	1	8	yes	—
37	C₂×C₄×C₁₇	C₄²	1	2	yes	—
38	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×Dic₁₇	C₄²	1	2	yes	—
40	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
41	C₄×D₁₇	—	2	4	no	—
42	C₄×D₁₇	C₂²×C₄	1	2	yes	—
43	C₄×D₁₇	C₂²×C₄	1	2	yes	—
44	#3624	C₄²	1	4	yes	—
45	#3624	C₄²	1	4	yes	—
46	C₈×C₁₇	C₄²	1	4	yes	—
47	#3622	C₄²	1	4	yes	—
48	#1726	—	17	1	no	maximal, Sylow
49	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
50	C₂×D₁₇	C₂×C₄²	1	2	yes	—
51	C₂×D₁₇	#131	1	4	yes	—
52	#595	—	2	8	no	—
53	C₄×C₁₇	—	2	2	no	—
54	C₄×C₁₇	C₂×C₄²	1	2	yes	—
55	Dic₁₇	—	2	2	no	—
56	Dic₁₇	C₂×C₄²	1	1	yes	characteristic
57	Dic₁₇	C₂×C₄²	1	1	yes	characteristic
58	C₂×#97	—	17	2	no	—
59	C₂×#97	—	17	1	no	—
60	C₂×C₄×C₈	—	17	2	no	—
61	C₂×C₄×C₈	—	17	1	no	—
62	#376	—	17	1	no	—
63	C₂×C₁₇	C₄³	1	1	yes	characteristic
64	C₂×C₁₇	#405	1	2	yes	—
65	D₁₇	#405	1	4	yes	—
66	C₂²×C₈	—	17	1	no	—
67	C₂²×C₈	—	17	1	no	—
68	C₂²×C₈	—	17	2	no	—
69	C₂×C₄²	—	17	2	no	—
70	C₂×C₄²	—	17	1	no	—
71	#97	—	17	8	no	—
72	#97	—	17	2	no	—
73	#97	—	17	1	no	—
74	#97	#595	1	1	yes	characteristic, complemented
75	C₄×C₈	—	17	8	no	—
76	C₄×C₈	—	17	4	no	—
77	#95	—	17	4	no	—
78	C₁₇	#1726	1	1	yes	characteristic, complemented, Sylow
79	C₂²×C₄	—	17	1	no	—
80	C₂²×C₄	—	17	4	no	—
81	C₂²×C₄	—	17	2	no	—
82	C₂×C₈	—	17	4	no	—
83	C₂×C₈	—	17	4	no	—
84	C₂×C₈	—	17	2	no	—
85	C₂×C₈	—	17	2	no	—
86	C₂×C₈	—	17	2	no	—
87	C₂×C₈	—	17	4	no	—
88	C₂×C₈	—	17	4	no	—
89	C₂×C₈	C₂×#595	1	2	yes	—
90	C₄²	—	17	4	no	—
91	C₄²	—	17	4	no	—
92	C₄²	—	17	2	no	—
93	C₄²	—	17	1	no	—
94	C₄²	C₂×#595	1	1	yes	characteristic
95	C₂³	—	17	1	no	—
96	C₂×C₄	—	17	1	no	—
97	C₂×C₄	—	17	2	no	—
98	C₂×C₄	—	17	2	no	—
99	C₂×C₄	—	17	8	no	—
100	C₂×C₄	—	17	2	no	—
101	C₂×C₄	—	34	4	no	—
102	C₂×C₄	—	34	8	no	—
103	C₂×C₄	C₄×#595	1	2	yes	—
104	C₂×C₄	C₂²×#595	1	1	yes	characteristic
105	C₈	—	17	4	no	—
106	C₈	—	17	4	no	—
107	C₈	—	17	4	no	—
108	C₈	C₄×#595	1	4	yes	—
109	C₂²	—	17	2	no	—
110	C₂²	—	17	4	no	—
111	C₂²	C₂×C₄×#595	1	1	yes	characteristic
112	C₄	—	2	2	no	—
113	C₄	—	17	1	no	—
114	C₄	—	17	1	no	—
115	C₄	—	34	8	no	—
116	C₄	—	34	2	no	—
117	C₄	C₂×C₄×#595	1	2	yes	—
118	C₂	—	17	4	no	—
119	C₂	C₄²×#595	1	1	yes	characteristic
120	C₂	#11763775	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587532

C₂

yes

maximal

C₄×#63242

C₂

yes

maximal, characteristic

C₂×C₈×#595

C₂

yes

maximal

#11763745

C₂

yes

maximal, characteristic

#97×D₁₇

C₂

yes

maximal, characteristic

C₂×C₄×#595

C₂²

yes

—

C₂×#63242

C₂²

yes

characteristic

C₂×#63242

C₂²

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

C₄

yes

—

C₄×#3624

C₄

yes

complemented

#10587532

C₄

yes

complemented

C₈×#595

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

—

C₂×#3624

C₂×C₄

yes

—

C₄×#595

C₂×C₄

yes

—

C₄×#595

C₂×C₄

yes

—

#63242

C₂×C₄

yes

—

#63242

C₂×C₄

yes

—

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

C₂×C₄

yes

—

C₈×D₁₇

C₂×C₄

yes

—

C₂²×D₁₇

C₂²×C₄

yes

characteristic

C₂×#595

—

C₂×#595

C₄²

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

C₂²×C₄

yes

—

C₄×D₁₇

C₂²×C₄

yes

—

#3624

C₄²

yes

—

#3624

C₄²

yes

—

C₈×C₁₇

C₄²

yes

—

#3622

C₄²

yes

—

#1726

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂×D₁₇

C₂×C₄²

yes

—

C₂×D₁₇

#131

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄²

yes

—

Dic₁₇

—

Dic₁₇

C₂×C₄²

yes

characteristic

Dic₁₇

C₂×C₄²

yes

characteristic

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

—

#376

—

C₂×C₁₇

C₄³

yes

characteristic

C₂×C₁₇

#405

yes

—

D₁₇

#405

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₂×C₄²

—

—

—

—

yes

characteristic, complemented

C₄×C₈

—

C₄×C₈

—

#95

—

C₁₇

#1726

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

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

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₄×#595

yes

—

104

C₂×C₄

C₂²×#595

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

C₄×#595

yes

—

109

C₂²

—

110

C₂²

—

111

C₂²

C₂×C₄×#595

yes

characteristic

112

C₄

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×C₄×#595

yes

—

118

C₂

—

119

C₂

C₄²×#595

yes

characteristic

120

C₂

#11763775

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator	C₂×C₁₇	C₄³
Fitting	C₁₇×#97	C₄
socle	C₂²×C₁₇	C₂×C₄²
prime radical	C₂²×D₁₇	C₂²×C₄
cosocle	C₂×C₄×D₁₇	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#1726
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator

C₂×C₁₇

C₄³

Fitting

C₁₇×#97

C₄

socle

C₂²×C₁₇

C₂×C₄²

prime radical

C₂²×D₁₇

C₂²×C₄

cosocle

C₂×C₄×D₁₇

C₂³

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
12. C₄×#3624	C₄	semidirect
13. #10587532	C₄	semidirect
14. C₈×#595	C₄	semidirect
15. C₁₇×#97	C₄	semidirect
16. #10587486	C₄	semidirect
17. #10587474	C₄	semidirect
74. #97	#595	semidirect
78. C₁₇	#1726	semidirect

H ≅ G/N

type

12. C₄×#3624

C₄

semidirect

13. #10587532

C₄

semidirect

14. C₈×#595

C₄

semidirect

15. C₁₇×#97

C₄

semidirect

16. #10587486

C₄

semidirect

17. #10587474

C₄

semidirect

74. #97

#595

semidirect

78. C₁₇

#1726

semidirect

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

subgroup	index
C₂×#10587532	2
C₄×#63242	2
C₂×C₈×#595	2
#11763745	2
#97×D₁₇	2
#1726	17

subgroup

index

C₂×C₈×#595

#97×D₁₇

Subgroups — #14544442

Conjugacy classes of subgroups

Complements

Maximal subgroups