Group #17962898 — subgroups

Subgroups — #17962898

Order 4352.

158 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 84 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	#14543942	C₂	1	2	yes	maximal
2	C₄⋊#10587467	C₂	1	1	yes	maximal, characteristic
3	#14543892	C₂	1	2	yes	maximal
4	C₄×#10587467	C₂	1	1	yes	maximal, characteristic
5	#14530686	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587467	C₂²	1	1	yes	characteristic
7	C₂×#10587467	C₂²	1	2	yes	—
8	C₂×#10587467	C₂²	1	1	yes	characteristic
9	C₈×Dic₃₄	C₄	1	1	yes	characteristic
10	#11762627	C₄	1	2	yes	—
11	C₄×#63214	C₂²	1	1	yes	characteristic
12	C₁₆×Dic₁₇	C₂²	1	2	yes	—
13	C₁₇×C₄⋊C₁₆	C₄	1	1	yes	characteristic
14	C₄×Dic₃₄	C₈	1	1	yes	characteristic
15	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
16	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
17	#10587485	C₈	1	2	yes	—
18	C₈×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂×#63214	C₂×C₄	1	1	yes	characteristic
20	C₂×#63214	C₂³	1	1	yes	characteristic
21	C₄⋊#3622	C₈	1	1	yes	characteristic
22	#10587467	—	2	1	no	—
23	#10587467	—	2	2	no	—
24	#10587467	Q₈	1	2	yes	complemented
25	C₂×Dic₃₄	C₁₆	1	1	yes	characteristic
26	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
29	C₄⋊Dic₁₇	C₁₆	1	1	yes	characteristic
30	#63225	C₁₆	1	2	yes	—
31	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
32	C₂×#3622	C₂×C₈	1	2	yes	—
33	C₁₆×C₁₇	—	2	2	no	—
34	#63214	—	2	1	no	—
35	#63214	C₂×Q₈	1	1	yes	characteristic
36	#63214	#41	1	1	yes	characteristic
37	#13660	—	17	1	no	maximal, Sylow
38	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
39	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
40	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
41	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
42	C₂×Dic₁₇	C₂×C₁₆	1	2	yes	—
43	Dic₃₄	—	2	2	no	—
44	C₈×C₁₇	—	2	1	no	—
45	C₈×C₁₇	C₄×Q₈	1	1	yes	characteristic
46	C₈×C₁₇	#131	1	1	yes	characteristic
47	#3622	—	2	2	no	—
48	Q₈×C₁₆	—	17	1	no	—
49	C₄⋊C₃₂	—	17	1	no	—
50	C₄⋊C₃₂	—	17	2	no	—
51	#1397	—	17	2	no	—
52	C₄×C₃₂	—	17	1	no	—
53	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
54	C₄×C₁₇	—	2	1	no	—
55	C₄×C₁₇	M₆₄	1	2	yes	—
56	C₄×C₁₇	C₈×Q₈	1	1	yes	characteristic
57	C₄×C₁₇	#504	1	1	yes	characteristic
58	Dic₁₇	—	2	2	no	—
59	Dic₁₇	—	2	2	no	—
60	C₈×Q₈	—	17	1	no	—
61	C₂×C₃₂	—	17	1	no	—
62	C₂×C₃₂	—	17	1	no	—
63	C₂×C₃₂	—	17	2	no	—
64	C₄⋊C₁₆	—	17	2	no	—
65	C₄⋊C₁₆	#595	1	1	yes	characteristic
66	C₄×C₁₆	—	17	2	no	—
67	C₄×C₁₆	—	17	1	no	—
68	C₂×C₁₇	Q₈×C₁₆	1	1	yes	characteristic
69	C₂×C₁₇	C₂×M₆₄	1	1	yes	characteristic
70	C₂×C₁₇	#2258	1	1	yes	characteristic
71	C₄×Q₈	—	17	1	no	—
72	C₂×C₁₆	—	17	1	no	—
73	C₂×C₁₆	—	17	1	no	—
74	C₂×C₁₆	C₂×#595	1	2	yes	—
75	C₄⋊C₈	—	17	2	no	—
76	C₄⋊C₈	—	17	1	no	—
77	C₄×C₈	—	17	2	no	—
78	C₄×C₈	C₂×#595	1	1	yes	characteristic
79	C₃₂	—	17	2	no	—
80	C₃₂	—	34	1	no	—
81	C₃₂	—	34	2	no	—
82	C₁₇	#13660	1	1	yes	characteristic, complemented, Sylow
83	C₂×Q₈	—	17	1	no	—
84	C₂×C₈	—	17	2	no	—
85	C₂×C₈	#63242	1	1	yes	characteristic
86	C₂×C₈	C₂²×#595	1	1	yes	characteristic
87	C₄⋊C₄	—	17	2	no	—
88	C₄⋊C₄	—	17	1	no	—
89	C₄²	—	17	2	no	—
90	C₄²	#63242	1	1	yes	characteristic
91	C₁₆	—	2	2	no	—
92	C₁₆	—	17	1	no	—
93	C₁₆	—	17	1	no	—
94	C₁₆	—	34	1	no	—
95	Q₈	—	34	2	no	—
96	C₂×C₄	—	17	2	no	—
97	C₂×C₄	—	17	2	no	—
98	C₂×C₄	#10587529	1	1	yes	characteristic
99	C₂×C₄	#10587529	1	1	yes	characteristic
100	C₂×C₄	C₂×#63242	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	34	2	no	—
103	C₈	#10587678	1	1	yes	characteristic
104	C₈	Q₈×#595	1	1	yes	characteristic
105	C₂²	C₂×#10587529	1	1	yes	characteristic
106	C₄	—	2	1	no	—
107	C₄	—	34	2	no	—
108	C₄	—	34	2	no	—
109	C₄	#11763742	1	2	yes	—
110	C₄	#11763858	1	1	yes	characteristic
111	C₄	#11763868	1	1	yes	characteristic
112	C₂	#14545198	1	1	yes	characteristic
113	C₂	C₂×#11763742	1	1	yes	characteristic
114	C₂	#14545208	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14543942

C₂

yes

maximal

C₄⋊#10587467

C₂

yes

maximal, characteristic

#14543892

C₂

yes

maximal

C₄×#10587467

C₂

yes

maximal, characteristic

#14530686

C₂

yes

maximal, characteristic

C₂×#10587467

C₂²

yes

characteristic

C₂×#10587467

C₂²

yes

—

C₂×#10587467

C₂²

yes

characteristic

C₈×Dic₃₄

C₄

yes

characteristic

#11762627

C₄

yes

—

C₄×#63214

C₂²

yes

characteristic

C₁₆×Dic₁₇

C₂²

yes

—

C₁₇×C₄⋊C₁₆

C₄

yes

characteristic

C₄×Dic₃₄

C₈

yes

characteristic

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

#10587485

C₈

yes

—

C₈×Dic₁₇

C₂×C₄

yes

—

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂³

yes

characteristic

C₄⋊#3622

C₈

yes

—

—

Q₈

yes

complemented

C₂×Dic₃₄

C₁₆

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

characteristic

C₄⋊Dic₁₇

C₁₆

yes

characteristic

#63225

C₁₆

yes

—

C₄×Dic₁₇

C₂×C₈

yes

—

C₂×#3622

C₂×C₈

yes

—

C₁₆×C₁₇

—

#63214

—

#63214

C₂×Q₈

yes

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₂×Dic₁₇

C₂×C₁₆

yes

—

C₂×Dic₁₇

C₂×C₁₆

yes

—

Dic₃₄

—

C₈×C₁₇

—

C₈×C₁₇

C₄×Q₈

yes

C₈×C₁₇

yes

—

Q₈×C₁₆

—

C₄⋊C₃₂

—

C₄⋊C₃₂

—

#1397

—

C₄×C₃₂

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

M₆₄

yes

—

C₄×C₁₇

C₈×Q₈

yes

characteristic

C₄×C₁₇

#504

yes

characteristic

Dic₁₇

—

Dic₁₇

—

C₈×Q₈

—

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₄⋊C₁₆

#595

yes

characteristic

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

Q₈×C₁₆

yes

characteristic

C₂×C₁₇

C₂×M₆₄

yes

characteristic

C₂×C₁₇

#2258

yes

characteristic

C₄×Q₈

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×#595

yes

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄×C₈

—

C₄×C₈

C₂×#595

yes

characteristic

C₃₂

—

C₃₂

—

C₃₂

—

C₁₇

#13660

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×C₈

—

C₂×C₈

#63242

yes

characteristic

C₂×C₈

C₂²×#595

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

#63242

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

100

C₂×C₄

C₂×#63242

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

#10587678

yes

characteristic

104

C₈

Q₈×#595

yes

characteristic

105

C₂²

C₂×#10587529

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

#11763742

yes

—

110

C₄

#11763858

yes

characteristic

111

C₄

#11763868

yes

characteristic

112

C₂

#14545198

yes

characteristic

113

C₂

C₂×#11763742

yes

characteristic

114

C₂

#14545208

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle, prime radical	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₁₇×C₄⋊C₁₆	C₄
cosocle	C₂×#63214	C₂³
hypercenter	C₄⋊C₁₆	#595
hypocenter	C₁₇	#13660
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator, socle, prime radical

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₁₇×C₄⋊C₁₆

C₄

C₂³

C₄⋊C₁₆

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
24. #10587467	Q₈	semidirect
82. C₁₇	#13660	semidirect

H ≅ G/N

type

24. #10587467

Q₈

semidirect

82. C₁₇

#13660

semidirect

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

subgroup	index
#14543942	2
C₄⋊#10587467	2
#14543892	2
C₄×#10587467	2
#14530686	2
#13660	17

subgroup

index

Subgroups — #17962898

Conjugacy classes of subgroups

Complements

Maximal subgroups