Group #14544000 — subgroups

Subgroups — #14544000

Order 2176.

196 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 88 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	#11763828	C₂	1	1	yes	maximal, characteristic
2	C₄×#63242	C₂	1	1	yes	maximal, characteristic
3	#11763651	C₂	1	2	yes	maximal, complemented
4	#11763650	C₂	1	2	yes	maximal, complemented
5	#11762861	C₂	1	1	yes	maximal, characteristic
6	C₂×#63242	C₄	1	2	yes	—
7	C₄²×D₁₇	C₂²	1	1	yes	characteristic
8	#10587543	C₄	1	2	yes	—
9	C₄⋊#3624	C₄	1	2	yes	—
10	C₄×#3624	C₄	1	2	yes	—
11	C₄×#3624	C₂²	1	1	yes	characteristic
12	C₄×#3624	C₂²	1	1	yes	characteristic
13	C₄×#3624	C₂²	1	2	yes	—
14	C₁₇×C₄⋊C₈	C₄	1	1	yes	characteristic
15	#10587491	C₄	1	2	yes	—
16	C₈×Dic₁₇	C₂²	1	2	yes	—
17	C₄⋊#3622	C₄	1	1	yes	characteristic
18	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×#3624	C₂×C₄	1	2	yes	—
22	C₂×#3624	C₂×C₄	1	2	yes	—
23	C₂×#3624	C₂×C₄	1	4	yes	—
24	#63242	—	2	4	no	—
25	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
26	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
29	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
30	C₂×#3622	C₂×C₄	1	2	yes	—
31	C₂²×D₁₇	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
33	C₂×C₄×C₁₇	C₄²	1	1	yes	characteristic
34	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×Dic₁₇	C₄²	1	1	yes	characteristic
36	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
38	C₄×D₁₇	—	2	1	no	—
39	C₄×D₁₇	—	2	1	no	—
40	C₄×D₁₇	—	2	2	no	—
41	C₄×D₁₇	M₁₆	1	4	yes	—
42	#3624	—	2	2	no	—
43	#3624	—	2	2	no	—
44	#3624	—	2	4	no	—
45	C₈×C₁₇	—	2	2	no	—
46	#3622	—	2	2	no	—
47	#1452	—	17	1	no	maximal, Sylow
48	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
49	C₂×D₁₇	—	2	1	no	—
50	C₂×D₁₇	—	2	1	no	—
51	C₂×D₁₇	#97	1	2	yes	—
52	C₄×C₁₇	—	2	1	no	—
53	C₄×C₁₇	#97	1	2	yes	—
54	C₄×C₁₇	#131	1	1	yes	characteristic
55	C₄×C₁₇	#131	1	1	yes	characteristic
56	Dic₁₇	—	2	1	no	—
57	Dic₁₇	C₂×M₁₆	1	2	yes	—
58	Dic₁₇	#131	1	2	yes	—
59	#431	—	17	1	no	—
60	#431	—	17	1	no	—
61	C₂×C₄×C₈	—	17	1	no	—
62	#322	—	17	2	no	—
63	#322	—	17	2	no	—
64	C₂×C₁₇	C₂×#97	1	1	yes	characteristic
65	C₂×C₁₇	#405	1	1	yes	characteristic
66	C₂×C₁₇	#405	1	1	yes	characteristic
67	D₁₇	—	2	2	no	—
68	C₂²×C₈	—	17	2	no	—
69	C₂×C₄²	—	17	1	no	—
70	C₄⋊C₈	—	17	2	no	—
71	C₄⋊C₈	—	17	1	no	—
72	C₄⋊C₈	#595	1	1	yes	characteristic
73	C₂²⋊C₈	—	17	2	no	—
74	C₂²⋊C₈	—	17	2	no	—
75	C₄×C₈	—	17	1	no	—
76	C₄×C₈	—	17	1	no	—
77	C₄×C₈	—	17	2	no	—
78	C₄×C₈	—	17	2	no	—
79	C₄×C₈	—	17	2	no	—
80	C₁₇	#1452	1	1	yes	characteristic, complemented, Sylow
81	C₂²×C₄	—	17	1	no	—
82	C₂²×C₄	—	17	1	no	—
83	C₂²×C₄	—	17	1	no	—
84	C₂×C₈	—	17	2	no	—
85	C₂×C₈	—	17	2	no	—
86	C₂×C₈	—	17	4	no	—
87	C₂×C₈	—	17	2	no	—
88	C₂×C₈	—	34	4	no	—
89	C₂×C₈	C₂×#595	1	2	yes	—
90	C₄²	—	17	1	no	—
91	C₄²	—	17	1	no	—
92	C₄²	—	17	1	no	—
93	C₄²	C₂×#595	1	1	yes	characteristic
94	C₂³	—	17	1	no	—
95	C₂×C₄	—	17	1	no	—
96	C₂×C₄	—	17	1	no	—
97	C₂×C₄	—	17	4	no	—
98	C₂×C₄	—	17	1	no	—
99	C₂×C₄	—	34	2	no	—
100	C₂×C₄	—	34	1	no	—
101	C₂×C₄	—	34	1	no	—
102	C₂×C₄	C₄×#595	1	1	yes	characteristic
103	C₂×C₄	C₄×#595	1	1	yes	characteristic
104	C₂×C₄	C₂²×#595	1	1	yes	characteristic
105	C₈	—	2	2	no	—
106	C₈	—	34	2	no	—
107	C₈	—	34	2	no	—
108	C₈	—	34	4	no	—
109	C₈	—	34	2	no	—
110	C₂²	—	17	2	no	—
111	C₂²	—	34	1	no	—
112	C₂²	—	34	1	no	—
113	C₂²	C₂×C₄×#595	1	1	yes	characteristic
114	C₄	—	2	1	no	—
115	C₄	—	17	2	no	—
116	C₄	—	17	2	no	—
117	C₄	—	34	1	no	—
118	C₄	#10587532	1	2	yes	—
119	C₄	#10587678	1	1	yes	characteristic
120	C₄	#10587680	1	1	yes	characteristic
121	C₂	—	34	2	no	—
122	C₂	C₂×#10587532	1	1	yes	characteristic
123	C₂	#11763774	1	1	yes	characteristic
124	C₂	#11763775	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763828

C₂

yes

maximal, characteristic

C₄×#63242

C₂

yes

maximal, characteristic

#11763651

C₂

yes

maximal, complemented

#11763650

C₂

yes

maximal, complemented

#11762861

C₂

yes

maximal, characteristic

C₂×#63242

C₄

yes

—

C₄²×D₁₇

C₂²

yes

characteristic

#10587543

C₄

yes

—

C₄⋊#3624

C₄

yes

—

C₄×#3624

C₄

yes

—

C₄×#3624

C₂²

yes

characteristic

C₄×#3624

C₂²

yes

characteristic

C₄×#3624

C₂²

yes

—

C₁₇×C₄⋊C₈

C₄

yes

characteristic

#10587491

C₄

yes

—

C₈×Dic₁₇

C₂²

yes

—

C₄⋊#3622

C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×#3624

C₂×C₄

yes

—

C₂×#3624

C₂×C₄

yes

—

C₂×#3624

C₂×C₄

yes

—

#63242

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₄²×C₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂×C₄

yes

characteristic

C₄×Dic₁₇

C₂³

yes

characteristic

C₂×#3622

C₂×C₄

yes

—

C₂²×D₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₄²

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₄²

yes

characteristic

C₂×Dic₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

C₂²×C₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

—

C₄×D₁₇

M₁₆

yes

—

#3624

—

#3624

—

#3624

—

C₈×C₁₇

—

#3622

—

#1452

—

maximal, Sylow

C₂²×C₁₇

C₂×C₄²

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

#97

yes

—

C₄×C₁₇

—

C₄×C₁₇

#97

yes

—

C₄×C₁₇

yes

C₄×C₁₇

yes

Dic₁₇

—

Dic₁₇

C₂×M₁₆

yes

—

Dic₁₇

#131

yes

—

#431

—

#431

—

C₂×C₄×C₈

—

#322

—

#322

—

C₂×C₁₇

C₂×#97

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

D₁₇

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

#595

yes

characteristic

C₂²⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#1452

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

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

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

C₄×#595

yes

characteristic

103

C₂×C₄

C₄×#595

yes

characteristic

104

C₂×C₄

C₂²×#595

yes

characteristic

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

—

109

C₈

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₂²

C₂×C₄×#595

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

#10587532

yes

—

119

C₄

#10587678

yes

characteristic

120

C₄

#10587680

yes

characteristic

121

C₂

—

122

C₂

C₂×#10587532

yes

characteristic

123

C₂

#11763774

yes

characteristic

124

C₂

#11763775

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂×C₄²
Fitting	C₁₇×C₄⋊C₈	C₄
prime radical	C₂²×D₁₇	C₄²
cosocle	C₄×Dic₁₇	C₂³
hypercenter	C₄⋊C₈	#595
hypocenter	C₁₇	#1452
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#595

commutator, socle

C₂²×C₁₇

C₂×C₄²

Fitting

C₁₇×C₄⋊C₈

C₄

prime radical

C₂²×D₁₇

C₄²

cosocle

C₄×Dic₁₇

C₂³

C₄⋊C₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

N	H ≅ G/N	type
3. #11763651	C₂	semidirect
4. #11763650	C₂	semidirect
80. C₁₇	#1452	semidirect

H ≅ G/N

type

3. #11763651

C₂

semidirect

4. #11763650

C₂

semidirect

80. C₁₇

#1452

semidirect

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

subgroup	index
#11763828	2
C₄×#63242	2
#11763651	2
#11763650	2
#11762861	2
#1452	17

subgroup

index

Subgroups — #14544000

Conjugacy classes of subgroups

Complements

Maximal subgroups