Group #14544994 — subgroups

Subgroups — #14544994

Order 2176.

184 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 102 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×#10587530	C₂	1	1	yes	maximal, characteristic
2	C₂×#10587529	C₂	1	1	yes	maximal, characteristic
3	#11763698	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763697	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#63216	C₂	1	1	yes	maximal, characteristic, complemented
7	#11762766	C₂	1	1	yes	maximal, characteristic
8	C₂×#63218	C₄	1	1	yes	characteristic
9	C₂×C₈×D₁₇	C₂²	1	1	yes	characteristic
10	#10587558	C₄	1	1	yes	characteristic
11	C₂×#63216	C₂²	1	1	yes	characteristic
12	C₂×#63216	C₂²	1	1	yes	characteristic
13	C₂×#63216	C₂²	1	1	yes	characteristic
14	C₂×#63216	C₂²	1	1	yes	characteristic
15	#10587530	C₄	1	4	yes	complemented
16	#10587529	C₄	1	4	yes	complemented
17	C₁₇×#97	C₄	1	1	yes	characteristic
18	#10587486	C₄	1	1	yes	characteristic
19	C₈×Dic₁₇	C₂²	1	1	yes	characteristic
20	C₄×#3622	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
25	#63227	C₈	1	2	yes	—
26	#63225	C₈	1	2	yes	—
27	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₂×#3622	C₂×C₄	1	1	yes	characteristic
29	C₂×#3622	C₂³	1	1	yes	characteristic
30	#63218	C₈	1	4	yes	—
31	C₈×D₁₇	C₂×C₄	1	2	yes	—
32	C₈×D₁₇	C₂×C₄	1	2	yes	—
33	#63216	C₂×C₄	1	2	yes	—
34	#63216	C₂×C₄	1	2	yes	—
35	#63216	C₂×C₄	1	2	yes	—
36	#63216	C₂×C₄	1	2	yes	—
37	C₂²×D₁₇	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₁₇	C₂×C₈	1	2	yes	—
39	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
41	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
42	C₄×D₁₇	C₄²	1	2	yes	—
43	C₄×D₁₇	C₂×C₈	1	2	yes	—
44	C₈×C₁₇	C₄²	1	2	yes	—
45	C₈×C₁₇	C₂×C₈	1	2	yes	—
46	#3622	C₂×C₈	1	2	yes	—
47	#3622	C₂²×C₄	1	1	yes	characteristic
48	#3622	C₂²×C₄	1	1	yes	characteristic
49	#2108	—	17	1	no	maximal, Sylow
50	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
51	C₂×D₁₇	—	2	2	no	—
52	C₂×D₁₇	C₄×C₈	1	2	yes	—
53	C₄×C₁₇	—	2	2	no	—
54	C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
55	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
56	Dic₁₇	—	2	2	no	—
57	Dic₁₇	C₄×C₈	1	2	yes	—
58	C₂×M₃₂	—	17	1	no	—
59	C₂²×C₁₆	—	17	1	no	—
60	#405	—	17	1	no	—
61	#346	—	17	1	no	—
62	#346	—	17	1	no	—
63	C₄×C₁₆	—	17	1	no	—
64	C₄×C₁₆	—	17	1	no	—
65	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
66	C₂×C₁₇	#504	1	2	yes	—
67	D₁₇	—	2	2	no	—
68	C₂×M₁₆	—	17	1	no	—
69	C₂²×C₈	—	17	1	no	—
70	#117	—	17	1	no	—
71	M₃₂	—	17	4	no	—
72	C₂×C₁₆	—	17	1	no	—
73	C₂×C₁₆	—	17	1	no	—
74	C₂×C₁₆	—	17	1	no	—
75	C₂×C₁₆	—	17	1	no	—
76	C₂×C₁₆	—	17	4	no	—
77	#97	—	17	1	no	—
78	#97	#595	1	1	yes	characteristic
79	C₄×C₈	—	17	1	no	—
80	C₄×C₈	—	17	1	no	—
81	C₁₇	#2108	1	1	yes	characteristic, complemented, Sylow
82	C₂²×C₄	—	17	1	no	—
83	M₁₆	—	17	4	no	—
84	C₂×C₈	—	17	1	no	—
85	C₂×C₈	—	17	1	no	—
86	C₂×C₈	—	17	2	no	—
87	C₂×C₈	—	17	2	no	—
88	C₂×C₈	C₂×#595	1	1	yes	characteristic
89	C₂×C₈	C₂×#595	1	1	yes	characteristic
90	C₄⋊C₄	—	17	2	no	—
91	C₂²⋊C₄	—	17	2	no	—
92	C₄²	—	17	1	no	—
93	C₄²	C₂×#595	1	1	yes	characteristic
94	C₁₆	—	17	2	no	—
95	C₁₆	—	17	2	no	—
96	C₁₆	—	17	2	no	—
97	C₁₆	—	17	2	no	—
98	C₂³	—	17	1	no	—
99	C₂×C₄	—	17	1	no	—
100	C₂×C₄	—	17	2	no	—
101	C₂×C₄	—	17	2	no	—
102	C₂×C₄	—	17	2	no	—
103	C₂×C₄	#63242	1	2	yes	—
104	C₂×C₄	C₂²×#595	1	1	yes	characteristic
105	C₈	—	17	2	no	—
106	C₈	—	17	1	no	—
107	C₈	—	17	1	no	—
108	C₈	#63242	1	2	yes	—
109	C₈	C₄×#595	1	2	yes	—
110	C₂²	—	17	2	no	—
111	C₂²	—	34	2	no	—
112	C₂²	C₂×#63242	1	1	yes	characteristic
113	C₄	—	2	2	no	—
114	C₄	—	17	2	no	—
115	C₄	—	34	2	no	—
116	C₄	C₂×#63242	1	1	yes	characteristic
117	C₄	C₂×C₄×#595	1	1	yes	characteristic
118	C₂	—	34	2	no	—
119	C₂	C₄×#63242	1	1	yes	characteristic
120	C₂	#11763868	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#10587530

C₂

yes

maximal, characteristic

C₂×#10587529

C₂

yes

maximal, characteristic

#11763698

C₂

yes

maximal, characteristic, complemented

#11763697

C₂

yes

maximal, characteristic, complemented

#11763695

C₂

yes

maximal, characteristic, complemented

C₄×#63216

C₂

yes

maximal, characteristic, complemented

#11762766

C₂

yes

maximal, characteristic

C₂×#63218

C₄

yes

characteristic

C₂×C₈×D₁₇

C₂²

yes

characteristic

#10587558

C₄

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

C₂×#63216

C₂²

yes

characteristic

#10587530

C₄

yes

complemented

#10587529

C₄

yes

complemented

C₁₇×#97

C₄

yes

characteristic

#10587486

C₄

yes

characteristic

C₈×Dic₁₇

C₂²

yes

characteristic

C₄×#3622

C₂²

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₄

yes

characteristic

#63227

C₈

yes

—

#63225

C₈

yes

—

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

C₂³

yes

characteristic

#63218

C₈

yes

—

C₈×D₁₇

C₂×C₄

yes

—

C₈×D₁₇

C₂×C₄

yes

—

#63216

C₂×C₄

yes

—

#63216

C₂×C₄

yes

—

#63216

C₂×C₄

yes

—

#63216

C₂×C₄

yes

—

C₂²×D₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₂×C₈

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₄²

yes

—

C₄×D₁₇

C₂×C₈

yes

—

C₈×C₁₇

C₄²

yes

—

C₈×C₁₇

C₂×C₈

yes

—

#3622

C₂×C₈

yes

—

#3622

C₂²×C₄

yes

characteristic

#3622

C₂²×C₄

yes

characteristic

#2108

—

maximal, Sylow

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄×C₈

yes

—

C₄×C₁₇

—

C₄×C₁₇

C₂×C₄²

yes

characteristic

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

—

Dic₁₇

C₄×C₈

yes

—

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

#346

—

#346

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

C₂×C₄×C₈

yes

characteristic

C₂×C₁₇

#504

yes

—

D₁₇

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₁₇

#2108

yes

characteristic, complemented, Sylow

C₂²×C₄

—

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#595

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

#63242

yes

—

104

C₂×C₄

C₂²×#595

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

#63242

yes

—

109

C₈

C₄×#595

yes

—

110

C₂²

—

111

C₂²

—

112

C₂²

C₂×#63242

yes

characteristic

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

C₂×#63242

yes

characteristic

117

C₄

C₂×C₄×#595

yes

characteristic

118

C₂

—

119

C₂

C₄×#63242

yes

characteristic

120

C₂

#11763868

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator	C₂×C₁₇	C₂×C₄×C₈
Fitting	C₁₇×#97	C₄
socle	C₂²×C₁₇	C₂²×C₈
prime radical	C₂²×D₁₇	C₂×C₈
cosocle	C₂×#3622	C₂³
hypercenter	#97	#595
hypocenter	C₁₇	#2108
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator

C₂×C₁₇

C₂×C₄×C₈

Fitting

C₁₇×#97

C₄

socle

C₂²×C₁₇

C₂²×C₈

prime radical

C₂²×D₁₇

C₂×C₈

C₂³

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #11763698	C₂	semidirect
4. #11763697	C₂	semidirect
5. #11763695	C₂	semidirect
6. C₄×#63216	C₂	semidirect
15. #10587530	C₄	semidirect
16. #10587529	C₄	semidirect
81. C₁₇	#2108	semidirect

H ≅ G/N

type

3. #11763698

C₂

semidirect

4. #11763697

C₂

semidirect

5. #11763695

C₂

semidirect

6. C₄×#63216

C₂

semidirect

15. #10587530

C₄

semidirect

16. #10587529

C₄

semidirect

81. C₁₇

#2108

semidirect

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

subgroup	index
C₂×#10587530	2
C₂×#10587529	2
#11763698	2
#11763697	2
#11763695	2
C₄×#63216	2
#11762766	2
#2108	17

subgroup

index

Subgroups — #14544994

Conjugacy classes of subgroups

Complements

Maximal subgroups