Group #14543673 — subgroups

Subgroups — #14543673

Order 2176.

172 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 44 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	#11763831	C₂	1	1	yes	maximal, characteristic
2	#11763745	C₂	1	1	yes	maximal, characteristic
3	#11762761	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×#595	—	2	1	no	—
5	C₂×#63218	—	2	1	no	—
6	C₄²×D₁₇	C₂²	1	1	yes	characteristic
7	(C₂×#595)⋊C₄	—	2	1	no	—
8	(C₂×#595)⋊C₄	C₄	1	2	yes	—
9	#10587543	—	2	1	no	—
10	#10587542	—	2	1	no	—
11	C₄⋊#3624	C₄	1	2	yes	complemented
12	C₁₇×#97	C₄	1	1	yes	characteristic, complemented
13	C₈×Dic₁₇	—	2	1	no	—
14	#10587474	C₄	1	1	yes	characteristic, complemented
15	C₂²×#595	—	2	2	no	—
16	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
18	C₂×C₄×D₁₇	D₄	1	1	yes	characteristic
19	C₂×#3624	—	2	2	no	—
20	C₄×#595	—	2	4	no	—
21	C₂×C₈×C₁₇	—	2	1	no	—
22	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×Dic₁₇	D₄	1	1	yes	characteristic
25	C₄×Dic₁₇	Q₈	1	1	yes	characteristic
26	C₂×#3622	—	2	1	no	—
27	#63218	—	2	4	no	—
28	C₂²×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×#595	—	2	4	no	—
30	C₂×#595	—	4	2	no	—
31	C₂×#595	—	4	2	no	—
32	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₄⋊C₄	1	1	yes	characteristic
35	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
36	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
37	C₂×Dic₁₇	C₄⋊C₄	1	1	yes	characteristic
38	C₄×D₁₇	—	2	2	no	—
39	C₄×D₁₇	—	2	2	no	—
40	C₄×D₁₇	—	4	1	no	—
41	#3624	—	4	2	no	—
42	C₈×C₁₇	—	2	2	no	—
43	#3622	—	2	2	no	—
44	#1300	—	17	1	no	maximal, Sylow
45	C₂²×C₁₇	#95	1	1	yes	characteristic
46	C₂×D₁₇	—	2	1	no	—
47	C₂×D₁₇	—	2	1	no	—
48	C₂×D₁₇	#104	1	2	yes	—
49	#595	—	4	4	no	—
50	C₄×C₁₇	—	2	1	no	—
51	C₄×C₁₇	—	2	1	no	—
52	C₄×C₁₇	—	2	1	no	—
53	Dic₁₇	—	2	1	no	—
54	Dic₁₇	—	2	1	no	—
55	Dic₁₇	#104	1	2	yes	—
56	#432	—	17	1	no	—
57	C₄×M₁₆	—	17	1	no	—
58	#376	—	17	1	no	—
59	C₂×C₁₇	#339	1	1	yes	characteristic
60	C₂×C₁₇	#339	1	1	yes	characteristic
61	C₂×C₁₇	#344	1	1	yes	characteristic
62	D₁₇	—	2	2	no	—
63	C₂×M₁₆	—	34	1	no	—
64	C₂×C₄²	—	17	1	no	—
65	C₂×C₄²	—	34	1	no	—
66	C₄⋊C₈	—	17	2	no	—
67	C₂²⋊C₈	—	34	1	no	—
68	#97	—	17	1	no	—
69	#97	—	34	1	no	—
70	#97	#595	1	1	yes	characteristic, complemented
71	C₄×C₈	—	34	1	no	—
72	#95	—	17	2	no	—
73	#95	—	34	1	no	—
74	C₁₇	#1300	1	1	yes	characteristic, complemented, Sylow
75	C₂²×C₄	—	17	1	no	—
76	C₂²×C₄	—	17	1	no	—
77	C₂²×C₄	—	17	1	no	—
78	C₂²×C₄	—	34	2	no	—
79	M₁₆	—	34	4	no	—
80	C₂×C₈	—	2	1	no	—
81	C₂×C₈	—	34	1	no	—
82	C₂×C₈	—	34	2	no	—
83	C₄²	—	17	1	no	—
84	C₄²	—	17	1	no	—
85	C₄²	—	17	1	no	—
86	C₄²	—	34	4	no	—
87	C₄²	C₂×#595	1	1	yes	characteristic
88	C₂³	—	17	1	no	—
89	C₂×C₄	—	17	1	no	—
90	C₂×C₄	—	17	1	no	—
91	C₂×C₄	—	17	1	no	—
92	C₂×C₄	—	34	2	no	—
93	C₂×C₄	—	34	2	no	—
94	C₂×C₄	—	34	4	no	—
95	C₂×C₄	—	68	1	no	—
96	C₂×C₄	—	68	2	no	—
97	C₂×C₄	—	68	2	no	—
98	C₂×C₄	C₄×#595	1	1	yes	characteristic
99	C₂×C₄	C₄⋊#595	1	1	yes	characteristic
100	C₂×C₄	C₂²⋊#595	1	1	yes	characteristic
101	C₈	—	2	2	no	—
102	C₈	—	34	2	no	—
103	C₈	—	68	2	no	—
104	C₂²	—	17	2	no	—
105	C₂²	—	34	1	no	—
106	C₂²	—	34	1	no	—
107	C₂²	(C₂×#595)⋊C₄	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	2	1	no	—
110	C₄	—	2	1	no	—
111	C₄	—	17	2	no	—
112	C₄	—	34	1	no	—
113	C₄	—	34	1	no	—
114	C₄	—	68	4	no	—
115	C₂	—	34	2	no	—
116	C₂	#11763680	1	1	yes	characteristic
117	C₂	#11763681	1	1	yes	characteristic
118	C₂	#11763692	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763831

C₂

yes

maximal, characteristic

#11763745

C₂

yes

maximal, characteristic

#11762761

C₂

yes

maximal, characteristic

C₂×C₄×#595

—

C₂×#63218

—

C₄²×D₁₇

C₂²

yes

characteristic

(C₂×#595)⋊C₄

—

(C₂×#595)⋊C₄

C₄

yes

—

#10587543

—

#10587542

—

C₄⋊#3624

C₄

yes

complemented

C₁₇×#97

C₄

yes

characteristic, complemented

C₈×Dic₁₇

—

#10587474

C₄

yes

characteristic, complemented

C₂²×#595

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

characteristic

C₂×C₄×D₁₇

D₄

yes

characteristic

C₂×#3624

—

C₄×#595

—

C₂×C₈×C₁₇

—

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

D₄

yes

characteristic

C₄×Dic₁₇

Q₈

yes

characteristic

C₂×#3622

—

#63218

—

C₂²×D₁₇

C₂²⋊C₄

yes

—

—

—

C₂×C₄×C₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

characteristic

C₂×Dic₁₇

C₄⋊C₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

#3624

—

C₈×C₁₇

—

—

—

C₂²×C₁₇

yes

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

#104

yes

—

#595

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

—

Dic₁₇

#104

yes

—

#432

—

C₄×M₁₆

—

#376

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

C₂×M₁₆

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

—

—

yes

characteristic, complemented

C₄×C₈

—

#95

—

#95

—

C₁₇

#1300

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

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

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

100

C₂×C₄

C₂²⋊#595

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

—

104

C₂²

—

105

C₂²

—

106

C₂²

—

107

C₂²

(C₂×#595)⋊C₄

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

113

C₄

—

114

C₄

—

115

C₂

—

116

C₂

#11763680

yes

characteristic

117

C₂

#11763681

yes

characteristic

118

C₂

#11763692

yes

characteristic

	subgroup	G/H
center	C₂²	(C₂×#595)⋊C₄
commutator	C₂×C₄×C₁₇	C₄²
Frattini	C₄²	C₂×#595
Fitting	C₁₇×#97	C₄
socle	C₂²×C₁₇	#95
prime radical	C₂²×D₁₇	C₂²⋊C₄
cosocle	C₄²×D₁₇	C₂²
hypercenter	#97	#595
hypocenter	C₁₇	#1300
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

(C₂×#595)⋊C₄

commutator

C₂×C₄×C₁₇

C₄²

Frattini

C₄²

C₂×#595

Fitting

C₁₇×#97

C₄

socle

C₂²×C₁₇

#95

prime radical

C₂²×D₁₇

C₂²⋊C₄

cosocle

C₄²×D₁₇

C₂²

C₁₇

G ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
11. C₄⋊#3624	C₄	semidirect
12. C₁₇×#97	C₄	semidirect
14. #10587474	C₄	semidirect
70. #97	#595	semidirect
74. C₁₇	#1300	semidirect

H ≅ G/N

type

11. C₄⋊#3624

C₄

semidirect

12. C₁₇×#97

C₄

semidirect

14. #10587474

C₄

semidirect

70. #97

#595

semidirect

74. C₁₇

#1300

semidirect

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

subgroup	index
#11763831	2
#11763745	2
#11762761	2
#1300	17

subgroup

index

Subgroups — #14543673

Conjugacy classes of subgroups

Complements

Maximal subgroups