Group #14545893 — subgroups

Subgroups — #14545893

Order 2176.

212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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	#11763922	C₂	1	2	yes	maximal
2	#11763893	C₂	1	2	yes	maximal, complemented
3	C₈×#3633	C₂	1	2	yes	maximal, complemented
4	C₂×C₈×#595	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#595	C₂²	1	1	yes	characteristic
6	C₂×#63242	C₄	1	1	yes	characteristic
7	C₂²⋊#3633	C₄	1	4	yes	—
8	C₄⋊#3633	C₄	1	4	yes	—
9	C₄×#3633	C₂²	1	4	yes	—
10	C₂×C₈×D₁₇	C₄	1	1	yes	characteristic
11	C₈×#595	C₄	1	1	yes	characteristic
12	C₈×#595	C₄	1	1	yes	characteristic
13	C₈×#595	C₂²	1	1	yes	characteristic
14	C₈×#595	C₂²	1	1	yes	characteristic
15	C₂²×#595	C₂×C₄	1	2	yes	—
16	C₂×#3633	C₂×C₄	1	8	yes	—
17	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×#3624	C₈	1	2	yes	complemented
19	C₄×#595	C₂×C₄	1	2	yes	—
20	C₄×#595	C₂×C₄	1	1	yes	characteristic
21	C₄×#595	C₂³	1	1	yes	characteristic
22	#63242	C₈	1	2	yes	complemented
23	#63242	C₂×C₄	1	1	yes	characteristic
24	#63242	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₇	C₈	1	1	yes	characteristic, complemented
26	C₂×#3622	C₈	1	1	yes	characteristic, complemented
27	C₈×D₁₇	C₈	1	1	yes	characteristic, complemented
28	C₈×D₁₇	C₈	1	1	yes	characteristic, complemented
29	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₁₇	C₄²	1	1	yes	characteristic
32	C₂×#595	—	2	4	no	—
33	C₂×#595	C₄²	1	2	yes	—
34	C₂×#595	C₂²×C₄	1	2	yes	—
35	#3633	—	2	8	no	—
36	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
37	C₂×Dic₁₇	C₂×C₈	1	1	yes	characteristic
38	C₄×D₁₇	C₄²	1	1	yes	characteristic
39	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
40	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
41	C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
42	#3624	C₂×C₈	1	2	yes	—
43	#3624	C₂×C₈	1	2	yes	—
44	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
45	C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
46	#3622	C₂×C₈	1	1	yes	characteristic
47	#3622	C₂×C₈	1	1	yes	characteristic
48	#1450	—	17	1	no	maximal, Sylow
49	C₂²×C₁₇	C₄×C₈	1	1	yes	characteristic
50	C₂×D₁₇	—	2	2	no	—
51	C₂×D₁₇	C₄×C₈	1	1	yes	characteristic
52	C₂×D₁₇	C₂×C₄²	1	1	yes	characteristic
53	#595	—	2	2	no	—
54	#595	#131	1	4	yes	—
55	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
56	C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
57	Dic₁₇	C₄×C₈	1	1	yes	characteristic
58	Dic₁₇	C₂²×C₈	1	1	yes	characteristic
59	#431	—	17	2	no	—
60	C₂×C₄×C₈	—	17	1	no	—
61	#322	—	17	2	no	—
62	C₈²	—	17	2	no	—
63	C₂×C₁₇	—	2	1	no	—
64	C₂×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
65	D₁₇	—	2	1	no	—
66	D₁₇	#405	1	2	yes	—
67	C₂²×C₈	—	17	1	no	—
68	C₂²×C₈	—	17	1	no	—
69	C₂×C₄²	—	17	1	no	—
70	C₄⋊C₈	—	17	4	no	—
71	C₂²⋊C₈	—	17	4	no	—
72	C₄×C₈	—	17	4	no	—
73	C₄×C₈	—	17	1	no	—
74	C₄×C₈	—	17	1	no	—
75	C₄×C₈	—	17	1	no	—
76	C₄×C₈	—	17	1	no	—
77	C₁₇	#1450	1	1	yes	characteristic, complemented, Sylow
78	C₂²×C₄	—	17	1	no	—
79	C₂²×C₄	—	17	2	no	—
80	C₂×C₈	—	17	2	no	—
81	C₂×C₈	—	17	1	no	—
82	C₂×C₈	—	17	1	no	—
83	C₂×C₈	—	17	2	no	—
84	C₂×C₈	—	17	1	no	—
85	C₂×C₈	—	17	1	no	—
86	C₂×C₈	—	17	1	no	—
87	C₂×C₈	—	17	1	no	—
88	C₂×C₈	—	17	1	no	—
89	C₂×C₈	—	17	8	no	—
90	C₂×C₈	#3633	1	1	yes	characteristic, complemented
91	C₄²	—	17	1	no	—
92	C₄²	—	17	2	no	—
93	C₄²	—	17	1	no	—
94	C₂³	—	17	1	no	—
95	C₂×C₄	—	17	2	no	—
96	C₂×C₄	—	17	1	no	—
97	C₂×C₄	—	17	1	no	—
98	C₂×C₄	—	17	1	no	—
99	C₂×C₄	—	17	1	no	—
100	C₂×C₄	—	17	1	no	—
101	C₂×C₄	—	17	2	no	—
102	C₂×C₄	—	34	4	no	—
103	C₂×C₄	C₂×#3633	1	1	yes	characteristic
104	C₈	—	17	2	no	—
105	C₈	—	17	2	no	—
106	C₈	—	17	1	no	—
107	C₈	—	17	1	no	—
108	C₈	—	34	8	no	—
109	C₈	C₂×#3633	1	1	yes	characteristic
110	C₈	C₂×#3633	1	1	yes	characteristic
111	C₂²	—	17	1	no	—
112	C₂²	—	17	1	no	—
113	C₂²	—	34	2	no	—
114	C₂²	C₄×#3633	1	1	yes	characteristic
115	C₄	—	17	4	no	—
116	C₄	—	17	1	no	—
117	C₄	—	17	1	no	—
118	C₄	—	34	2	no	—
119	C₄	C₄×#3633	1	1	yes	characteristic
120	C₄	C₂²×#3633	1	1	yes	characteristic
121	C₂	—	2	1	no	—
122	C₂	—	17	2	no	—
123	C₂	—	34	1	no	—
124	C₂	C₂×C₄×#3633	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763922

C₂

yes

maximal

#11763893

C₂

yes

maximal, complemented

C₈×#3633

C₂

yes

maximal, complemented

C₂×C₈×#595

C₂

yes

maximal, characteristic

C₂×C₄×#595

C₂²

yes

characteristic

C₂×#63242

C₄

yes

characteristic

C₂²⋊#3633

C₄

yes

—

C₄⋊#3633

C₄

yes

—

C₄×#3633

C₂²

yes

—

C₂×C₈×D₁₇

C₄

yes

characteristic

C₈×#595

C₄

yes

characteristic

C₈×#595

C₄

yes

characteristic

C₈×#595

C₂²

yes

characteristic

C₈×#595

C₂²

yes

characteristic

C₂²×#595

C₂×C₄

yes

—

C₂×#3633

C₂×C₄

yes

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×#3624

C₈

yes

complemented

C₄×#595

C₂×C₄

yes

—

C₄×#595

C₂×C₄

yes

characteristic

C₄×#595

C₂³

yes

characteristic

#63242

C₈

yes

complemented

#63242

C₂×C₄

yes

characteristic

#63242

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇

C₈

yes

characteristic, complemented

C₂×#3622

C₈

yes

characteristic, complemented

C₈×D₁₇

C₈

yes

characteristic, complemented

C₈×D₁₇

C₈

yes

characteristic, complemented

C₈×D₁₇

C₂×C₄

yes

characteristic

C₈×D₁₇

C₂×C₄

yes

characteristic

C₂²×D₁₇

C₄²

yes

characteristic

C₂×#595

—

C₂×#595

C₄²

yes

—

C₂×#595

C₂²×C₄

yes

—

#3633

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₄²

yes

characteristic

C₄×D₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

C₂²×C₄

yes

characteristic

#3624

C₂×C₈

yes

—

#3624

C₂×C₈

yes

—

C₈×C₁₇

C₂×C₈

yes

characteristic

C₈×C₁₇

C₂×C₈

yes

characteristic

#3622

C₂×C₈

yes

characteristic

#3622

C₂×C₈

yes

characteristic

#1450

—

maximal, Sylow

C₂²×C₁₇

C₄×C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

C₄×C₈

yes

characteristic

C₂×D₁₇

C₂×C₄²

yes

—

yes

—

C₄×C₁₇

C₄×C₈

yes

characteristic

C₄×C₁₇

C₂²×C₈

yes

characteristic

Dic₁₇

C₄×C₈

yes

characteristic

Dic₁₇

C₂²×C₈

yes

characteristic

#431

—

C₂×C₄×C₈

—

#322

—

C₈²

—

C₂×C₁₇

—

C₂×C₁₇

C₂×C₄×C₈

yes

characteristic

D₁₇

—

D₁₇

#405

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₁₇

#1450

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

#3633

yes

characteristic, complemented

C₄²

—

C₄²

—

C₄²

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

C₂×#3633

yes

characteristic

104

C₈

—

105

C₈

—

106

C₈

—

107

C₈

—

108

C₈

—

109

C₈

C₂×#3633

yes

characteristic

110

C₈

C₂×#3633

yes

characteristic

111

C₂²

—

112

C₂²

—

113

C₂²

—

114

C₂²

C₄×#3633

yes

characteristic

115

C₄

—

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

C₄×#3633

yes

characteristic

120

C₄

C₂²×#3633

yes

characteristic

121

C₂

—

122

C₂

—

123

C₂

—

124

C₂

C₂×C₄×#3633

yes

characteristic

	subgroup	G/H
center	C₈	C₂×#3633
commutator, socle	C₂×C₁₇	C₂×C₄×C₈
Frattini	C₄	C₂²×#3633
Fitting	C₂×C₈×C₁₇	C₈
prime radical	C₂²×D₁₇	C₄²
cosocle	C₄×#595	C₂³
hypercenter	C₂×C₈	#3633
hypocenter	C₁₇	#1450
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂×C₈

subgroup

G/H

center

C₈

C₂×#3633

commutator, socle

C₂×C₁₇

C₂×C₄×C₈

Frattini

C₄

C₂²×#3633

Fitting

C₂×C₈×C₁₇

C₈

prime radical

C₂²×D₁₇

C₄²

C₂³

C₂×C₈

C₁₇

G ▷ C₂×C₁₇ ▷ C₁₇

C₁ ◁ C₈ ◁ C₂×C₈

N	H ≅ G/N	type
2. #11763893	C₂	semidirect
3. C₈×#3633	C₂	semidirect
18. C₂×#3624	C₈	semidirect
22. #63242	C₈	semidirect
25. C₂×C₈×C₁₇	C₈	semidirect
26. C₂×#3622	C₈	semidirect
27. C₈×D₁₇	C₈	semidirect
28. C₈×D₁₇	C₈	semidirect
77. C₁₇	#1450	semidirect
90. C₂×C₈	#3633	semidirect

H ≅ G/N

type

2. #11763893

C₂

semidirect

3. C₈×#3633

C₂

semidirect

18. C₂×#3624

C₈

semidirect

22. #63242

C₈

semidirect

25. C₂×C₈×C₁₇

C₈

semidirect

26. C₂×#3622

C₈

semidirect

27. C₈×D₁₇

C₈

semidirect

28. C₈×D₁₇

C₈

semidirect

77. C₁₇

#1450

semidirect

90. C₂×C₈

#3633

semidirect

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

subgroup	index
#11763922	2
#11763893	2
C₈×#3633	2
C₂×C₈×#595	2
#1450	17

subgroup

index

C₂×C₈×#595

Subgroups — #14545893

Conjugacy classes of subgroups

Complements

Maximal subgroups