Group #14545915 — subgroups

Subgroups — #14545915

Order 2176.

192 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 57 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	D₄×#3633	C₂	1	2	yes	maximal, complemented
2	#11763898	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄⋊#3633	C₂	1	2	yes	maximal, complemented
4	#11763893	C₂	1	1	yes	maximal, characteristic, complemented
5	D₈×#595	C₂	1	1	yes	maximal, characteristic
6	C₂²×#3633	—	2	2	no	—
7	D₄×#595	C₂²	1	2	yes	—
8	C₂²⋊#3633	—	2	2	no	—
9	C₄⋊#3633	C₂²	1	2	yes	—
10	C₄×#3633	C₂²	1	1	yes	characteristic
11	C₄×#3633	C₂²	1	1	yes	characteristic
12	D₈×D₁₇	C₄	1	1	yes	characteristic
13	#10587547	C₄	1	2	yes	—
14	#10587534	C₄	1	1	yes	characteristic
15	C₈×#595	C₂²	1	1	yes	characteristic
16	C₂²×#595	—	2	2	no	—
17	C₂×#3633	—	2	2	no	—
18	C₂×#3633	—	2	1	no	—
19	C₂×#3633	—	4	4	no	—
20	C₂×#3633	D₄	1	2	yes	—
21	D₄×D₁₇	C₂×C₄	1	2	yes	—
22	C₂²⋊#595	—	2	2	no	—
23	C₄⋊#595	C₂×C₄	1	2	yes	—
24	C₄×#595	C₂³	1	1	yes	characteristic
25	#63242	C₂×C₄	1	1	yes	characteristic
26	D₈×C₁₇	C₈	1	1	yes	characteristic, complemented
27	#63228	C₈	1	2	yes	complemented
28	D₁₃₆	C₈	1	1	yes	characteristic, complemented
29	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×D₁₇	—	2	2	no	—
31	C₂×#595	—	2	2	no	—
32	C₂×#595	—	4	2	no	—
33	C₂×#595	—	4	2	no	—
34	C₂×#595	C₂×D₄	1	1	yes	characteristic
35	C₂×#595	#41	1	1	yes	characteristic
36	#3633	—	2	2	no	—
37	#3633	—	4	1	no	—
38	#3633	—	4	2	no	—
39	D₄×C₁₇	C₂×C₈	1	2	yes	complemented
40	C₂²⋊D₁₇	—	2	2	no	—
41	D₆₈	C₂×C₈	1	2	yes	complemented
42	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
43	#3624	—	2	1	no	—
44	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic, complemented
45	#3622	C₂×C₈	1	1	yes	characteristic, complemented
46	#1580	—	17	1	no	maximal, Sylow
47	C₂²×C₁₇	—	2	2	no	—
48	C₂×D₁₇	—	2	2	no	—
49	C₂×D₁₇	—	4	2	no	—
50	C₂×D₁₇	—	4	2	no	—
51	C₂×D₁₇	C₄×D₄	1	1	yes	characteristic
52	#595	—	2	1	no	—
53	#595	—	4	2	no	—
54	#595	AGL(1,ℤ/8)	1	2	yes	—
55	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
56	Dic₁₇	#131	1	1	yes	characteristic
57	C₄×D₈	—	17	1	no	—
58	C₈×D₄	—	17	2	no	—
59	#334	—	17	1	no	—
60	D₄⋊C₈	—	17	2	no	—
61	#322	—	17	1	no	—
62	C₂×C₁₇	—	4	2	no	—
63	C₂×C₁₇	C₈×D₄	1	1	yes	characteristic
64	D₁₇	—	4	2	no	—
65	D₁₇	#442	1	1	yes	characteristic
66	D₁₇	#444	1	1	yes	characteristic
67	C₂×D₈	—	17	1	no	—
68	C₂²×C₈	—	34	2	no	—
69	C₄×D₄	—	17	2	no	—
70	#107	—	17	1	no	—
71	C₄⋊C₈	—	17	2	no	—
72	#102	—	17	2	no	—
73	C₂²⋊C₈	—	34	2	no	—
74	C₄×C₈	—	17	1	no	—
75	C₄×C₈	—	17	1	no	—
76	C₄×C₈	—	17	1	no	—
77	C₁₇	#1580	1	1	yes	characteristic, complemented, Sylow
78	C₂×D₄	—	17	2	no	—
79	C₂²×C₄	—	34	2	no	—
80	D₈	—	17	2	no	—
81	D₈	—	17	1	no	—
82	D₈	#3633	1	1	yes	characteristic, complemented
83	C₂×C₈	—	17	1	no	—
84	C₂×C₈	—	17	1	no	—
85	C₂×C₈	—	17	2	no	—
86	C₂×C₈	—	34	1	no	—
87	C₂×C₈	—	34	2	no	—
88	C₂×C₈	—	68	4	no	—
89	C₄⋊C₄	—	17	2	no	—
90	C₂²⋊C₄	—	34	2	no	—
91	C₄²	—	17	1	no	—
92	C₂³	—	34	2	no	—
93	D₄	—	17	2	no	—
94	D₄	—	34	2	no	—
95	D₄	C₂×#3633	1	2	yes	complemented
96	C₂×C₄	—	17	1	no	—
97	C₂×C₄	—	17	1	no	—
98	C₂×C₄	—	17	1	no	—
99	C₂×C₄	—	34	2	no	—
100	C₂×C₄	—	68	2	no	—
101	C₂×C₄	—	68	2	no	—
102	C₈	—	17	1	no	—
103	C₈	—	34	2	no	—
104	C₈	—	34	1	no	—
105	C₈	—	68	2	no	—
106	C₈	—	68	1	no	—
107	C₈	C₂×#3633	1	1	yes	characteristic, complemented
108	C₂²	—	2	2	no	—
109	C₂²	—	17	1	no	—
110	C₂²	—	34	2	no	—
111	C₂²	—	68	2	no	—
112	C₂²	—	68	2	no	—
113	C₄	—	17	2	no	—
114	C₄	—	17	1	no	—
115	C₄	—	34	1	no	—
116	C₄	—	68	2	no	—
117	C₄	C₂²×#3633	1	1	yes	characteristic
118	C₂	—	4	2	no	—
119	C₂	—	17	1	no	—
120	C₂	—	17	1	no	—
121	C₂	—	68	2	no	—
122	C₂	D₄×#3633	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

D₄×#3633

C₂

yes

maximal, complemented

#11763898

C₂

yes

maximal, characteristic, complemented

D₄⋊#3633

C₂

yes

maximal, complemented

#11763893

C₂

yes

maximal, characteristic, complemented

D₈×#595

C₂

yes

maximal, characteristic

C₂²×#3633

—

D₄×#595

C₂²

yes

—

C₂²⋊#3633

—

C₄⋊#3633

C₂²

yes

—

C₄×#3633

C₂²

yes

characteristic

C₄×#3633

C₂²

yes

characteristic

D₈×D₁₇

C₄

yes

characteristic

#10587547

C₄

yes

—

#10587534

C₄

yes

characteristic

C₈×#595

C₂²

yes

characteristic

C₂²×#595

—

—

—

—

D₄

yes

—

D₄×D₁₇

C₂×C₄

yes

—

C₂²⋊#595

—

C₄⋊#595

C₂×C₄

yes

—

C₄×#595

C₂³

yes

characteristic

#63242

C₂×C₄

yes

characteristic

D₈×C₁₇

C₈

yes

characteristic, complemented

#63228

C₈

yes

complemented

D₁₃₆

C₈

yes

characteristic, complemented

C₈×D₁₇

C₂×C₄

yes

characteristic

C₂²×D₁₇

—

—

—

—

C₂×D₄

yes

yes

—

—

—

D₄×C₁₇

C₂×C₈

yes

complemented

C₂²⋊D₁₇

—

D₆₈

C₂×C₈

yes

complemented

C₄×D₁₇

C₂²×C₄

yes

characteristic

#3624

—

C₈×C₁₇

C₂×C₈

yes

characteristic, complemented

#3622

C₂×C₈

yes

characteristic, complemented

#1580

—

maximal, Sylow

C₂²×C₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

C₄×D₄

yes

—

—

yes

—

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

#131

yes

characteristic

C₄×D₈

—

C₈×D₄

—

#334

—

D₄⋊C₈

—

#322

—

C₂×C₁₇

—

C₂×C₁₇

C₈×D₄

yes

characteristic

D₁₇

—

D₁₇

yes

D₁₇

yes

C₂×D₈

—

C₂²×C₈

—

C₄×D₄

—

#107

—

C₄⋊C₈

—

#102

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#1580

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂²×C₄

—

D₈

—

D₈

—

D₈

#3633

yes

characteristic, complemented

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₂³

—

D₄

—

D₄

—

D₄

C₂×#3633

yes

complemented

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₈

—

103

C₈

—

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

C₂×#3633

yes

characteristic, complemented

108

C₂²

—

109

C₂²

—

110

C₂²

—

111

C₂²

—

112

C₂²

—

113

C₄

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂²×#3633

yes

characteristic

118

C₂

—

119

C₂

—

120

C₂

—

121

C₂

—

122

C₂

D₄×#3633

yes

characteristic

	subgroup	G/H
center	C₂	D₄×#3633
commutator	C₄×C₁₇	C₂²×C₈
Frattini	C₄	C₂²×#3633
Fitting	D₈×C₁₇	C₈
socle	C₂×C₁₇	C₈×D₄
prime radical	D₈×D₁₇	C₄
cosocle	C₄×#595	C₂³
hypercenter	D₈	#3633
hypocenter	C₁₇	#1580
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

subgroup

G/H

center

C₂

D₄×#3633

commutator

C₄×C₁₇

C₂²×C₈

Frattini

C₄

C₂²×#3633

Fitting

D₈×C₁₇

C₈

socle

C₂×C₁₇

C₈×D₄

prime radical

D₈×D₁₇

C₄

C₂³

D₈

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂ ◁ C₄ ◁ D₈

N	H ≅ G/N	type
1. D₄×#3633	C₂	semidirect
2. #11763898	C₂	semidirect
3. D₄⋊#3633	C₂	semidirect
4. #11763893	C₂	semidirect
26. D₈×C₁₇	C₈	semidirect
27. #63228	C₈	semidirect
28. D₁₃₆	C₈	semidirect
39. D₄×C₁₇	C₂×C₈	semidirect
41. D₆₈	C₂×C₈	semidirect
44. C₈×C₁₇	C₂×C₈	semidirect
45. #3622	C₂×C₈	semidirect
77. C₁₇	#1580	semidirect
82. D₈	#3633	semidirect
95. D₄	C₂×#3633	semidirect
107. C₈	C₂×#3633	semidirect

H ≅ G/N

type

1. D₄×#3633

C₂

semidirect

2. #11763898

C₂

semidirect

3. D₄⋊#3633

C₂

semidirect

4. #11763893

C₂

semidirect

26. D₈×C₁₇

C₈

semidirect

27. #63228

C₈

semidirect

28. D₁₃₆

C₈

semidirect

39. D₄×C₁₇

C₂×C₈

semidirect

41. D₆₈

C₂×C₈

semidirect

44. C₈×C₁₇

C₂×C₈

semidirect

45. #3622

C₂×C₈

semidirect

77. C₁₇

#1580

semidirect

82. D₈

#3633

semidirect

95. D₄

C₂×#3633

semidirect

107. C₈

C₂×#3633

semidirect

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

subgroup	index
D₄×#3633	2
#11763898	2
D₄⋊#3633	2
#11763893	2
D₈×#595	2
#1580	17

subgroup

index

Subgroups — #14545915

Conjugacy classes of subgroups

Complements

Maximal subgroups