Group #17962897 — subgroups

Subgroups — #17962897

Order 4352.

158 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 100 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	C₄⋊#10587467	C₂	1	2	yes	maximal
2	C₄⋊#10587467	C₂	1	1	yes	maximal, characteristic
3	#14543891	C₂	1	2	yes	maximal
4	C₄×#10587467	C₂	1	1	yes	maximal, characteristic
5	Q₈×#63214	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	C₄⋊#63214	C₄	1	2	yes	—
10	C₄⋊#63214	C₄	1	1	yes	characteristic
11	C₄×#63214	C₂²	1	1	yes	characteristic
12	C₄×#63214	C₂²	1	2	yes	—
13	C₈×Q₈×C₁₇	C₄	1	1	yes	characteristic
14	C₄×Q₈×C₁₇	C₈	1	1	yes	characteristic
15	C₁₇×C₄⋊C₈	C₈	1	2	yes	—
16	C₁₇×C₄⋊C₈	C₈	1	1	yes	characteristic
17	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₄×C₈×C₁₇	C₂×C₄	1	2	yes	—
19	C₂×#63214	C₂×C₄	1	1	yes	characteristic
20	C₂×#63214	C₂×C₄	1	2	yes	—
21	C₂×#63214	C₂³	1	1	yes	characteristic
22	#10587467	—	2	1	no	—
23	#10587467	—	2	2	no	—
24	#10587467	Q₈	1	2	yes	complemented
25	C₂×Q₈×C₁₇	C₁₆	1	1	yes	characteristic
26	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
28	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₄⋊C₄×C₁₇	C₁₆	1	2	yes	—
30	C₄⋊C₄×C₁₇	C₁₆	1	1	yes	characteristic
31	C₄²×C₁₇	C₂×C₈	1	2	yes	—
32	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
33	#63214	—	2	1	no	—
34	#63214	—	2	2	no	—
35	#63214	C₂×Q₈	1	1	yes	characteristic
36	#63214	#41	1	1	yes	characteristic
37	#13660	—	17	1	no	maximal, Sylow
38	Q₈×C₁₇	—	2	2	no	—
39	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
40	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
41	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
42	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
44	C₈×C₁₇	—	2	1	no	—
45	C₈×C₁₇	—	2	2	no	—
46	C₈×C₁₇	C₄×Q₈	1	1	yes	characteristic
47	C₈×C₁₇	#131	1	1	yes	characteristic
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	2	no	—
55	C₄×C₁₇	—	2	2	no	—
56	C₄×C₁₇	—	2	1	no	—
57	C₄×C₁₇	M₆₄	1	2	yes	—
58	C₄×C₁₇	C₈×Q₈	1	1	yes	characteristic
59	C₄×C₁₇	#504	1	1	yes	characteristic
60	C₈×Q₈	#595	1	1	yes	characteristic
61	C₂×C₃₂	—	17	1	no	—
62	C₂×C₃₂	—	17	1	no	—
63	C₂×C₃₂	—	17	2	no	—
64	C₄⋊C₁₆	—	17	1	no	—
65	C₄⋊C₁₆	—	17	2	no	—
66	C₄×C₁₆	—	17	1	no	—
67	C₄×C₁₆	—	17	2	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	#3624	1	1	yes	characteristic
72	C₂×C₁₆	—	17	1	no	—
73	C₂×C₁₆	—	17	1	no	—
74	C₂×C₁₆	—	17	2	no	—
75	C₄⋊C₈	#3624	1	2	yes	—
76	C₄⋊C₈	#3624	1	1	yes	characteristic
77	C₄×C₈	C₂×#595	1	1	yes	characteristic
78	C₄×C₈	C₂×#595	1	2	yes	—
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	#63216	1	1	yes	characteristic
84	C₂×C₈	C₂×#3624	1	1	yes	characteristic
85	C₂×C₈	C₂×#3624	1	2	yes	—
86	C₂×C₈	C₂²×#595	1	1	yes	characteristic
87	C₄⋊C₄	#63216	1	2	yes	—
88	C₄⋊C₄	#63216	1	1	yes	characteristic
89	C₄²	C₂×#3624	1	2	yes	—
90	C₄²	C₂×#3624	1	1	yes	characteristic
91	C₁₆	—	17	1	no	—
92	C₁₆	—	17	1	no	—
93	C₁₆	—	34	1	no	—
94	C₁₆	—	34	2	no	—
95	Q₈	—	2	2	no	—
96	C₂×C₄	C₂×#63216	1	2	yes	—
97	C₂×C₄	C₂×#63216	1	1	yes	characteristic
98	C₂×C₄	C₂×#63216	1	2	yes	—
99	C₂×C₄	C₂×#63216	1	1	yes	characteristic
100	C₂×C₄	C₂²×#3624	1	1	yes	characteristic
101	C₈	—	2	1	no	—
102	C₈	—	2	2	no	—
103	C₈	#10587680	1	1	yes	characteristic
104	C₈	Q₈×#595	1	1	yes	characteristic
105	C₂²	C₂²×#63216	1	1	yes	characteristic
106	C₄	—	2	2	no	—
107	C₄	—	2	2	no	—
108	C₄	—	2	1	no	—
109	C₄	#11763741	1	2	yes	—
110	C₄	Q₈×#3624	1	1	yes	characteristic
111	C₄	#11763867	1	1	yes	characteristic
112	C₂	Q₈×#63216	1	1	yes	characteristic
113	C₂	C₂×#11763741	1	1	yes	characteristic
114	C₂	#14545207	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄⋊#10587467

C₂

yes

maximal

C₄⋊#10587467

C₂

yes

maximal, characteristic

#14543891

C₂

yes

maximal

C₄×#10587467

C₂

yes

maximal, characteristic

Q₈×#63214

C₂

yes

maximal, characteristic

C₂×#10587467

C₂²

yes

characteristic

C₂×#10587467

C₂²

yes

—

C₂×#10587467

C₂²

yes

characteristic

C₄⋊#63214

C₄

yes

—

C₄⋊#63214

C₄

yes

characteristic

C₄×#63214

C₂²

yes

characteristic

C₄×#63214

C₂²

yes

—

C₈×Q₈×C₁₇

C₄

yes

characteristic

C₄×Q₈×C₁₇

C₈

yes

characteristic

C₁₇×C₄⋊C₈

C₈

yes

—

C₁₇×C₄⋊C₈

C₈

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₇

C₂×C₄

yes

—

C₂×#63214

C₂×C₄

yes

characteristic

C₂×#63214

C₂×C₄

yes

—

C₂×#63214

C₂³

yes

—

—

Q₈

yes

complemented

C₂×Q₈×C₁₇

C₁₆

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

characteristic

C₂×C₈×C₁₇

C₂×C₈

yes

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₄⋊C₄×C₁₇

C₁₆

yes

—

C₄⋊C₄×C₁₇

C₁₆

yes

characteristic

C₄²×C₁₇

C₂×C₈

yes

—

C₄²×C₁₇

C₂×C₈

yes

—

—

C₂×Q₈

yes

yes

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂×C₁₆

yes

—

C₂×C₄×C₁₇

C₂×C₁₆

yes

characteristic

C₂×C₄×C₁₇

C₂²×C₈

yes

characteristic

C₈×C₁₇

—

C₈×C₁₇

—

C₈×C₁₇

C₄×Q₈

yes

characteristic

C₈×C₁₇

#131

yes

characteristic

Q₈×C₁₆

—

C₄⋊C₃₂

—

C₄⋊C₃₂

—

#1397

—

C₄×C₃₂

—

C₂²×C₁₇

C₂²×C₁₆

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

M₆₄

yes

—

C₄×C₁₇

C₈×Q₈

yes

C₄×C₁₇

yes

C₈×Q₈

yes

C₂×C₃₂

—

C₂×C₃₂

—

C₂×C₃₂

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₄×C₁₆

—

C₄×C₁₆

—

C₂×C₁₇

Q₈×C₁₆

yes

characteristic

C₂×C₁₇

C₂×M₆₄

yes

C₂×C₁₇

yes

C₄×Q₈

yes

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄⋊C₈

#3624

yes

—

C₄⋊C₈

yes

C₄×C₈

yes

C₄×C₈

yes

—

C₃₂

—

C₃₂

—

C₃₂

—

C₁₇

#13660

yes

characteristic, complemented, Sylow

C₂×Q₈

yes

C₂×C₈

yes

C₂×C₈

yes

—

C₂×C₈

C₂²×#595

yes

characteristic

C₄⋊C₄

#63216

yes

—

C₄⋊C₄

#63216

yes

characteristic

C₄²

C₂×#3624

yes

—

C₄²

C₂×#3624

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₁₆

—

Q₈

—

C₂×C₄

C₂×#63216

yes

—

C₂×C₄

C₂×#63216

yes

characteristic

C₂×C₄

C₂×#63216

yes

—

C₂×C₄

C₂×#63216

yes

characteristic

100

C₂×C₄

C₂²×#3624

yes

characteristic

101

C₈

—

102

C₈

—

103

C₈

#10587680

yes

characteristic

104

C₈

Q₈×#595

yes

characteristic

105

C₂²

C₂²×#63216

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

#11763741

yes

—

110

C₄

Q₈×#3624

yes

characteristic

111

C₄

#11763867

yes

characteristic

112

C₂

Q₈×#63216

yes

characteristic

113

C₂

C₂×#11763741

yes

characteristic

114

C₂

#14545207

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator, socle, prime radical	C₂²×C₁₇	C₂²×C₁₆
Fitting	C₈×Q₈×C₁₇	C₄
cosocle	C₂×#63214	C₂³
hypercenter	C₈×Q₈	#595
hypocenter	C₁₇	#13660
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₈×Q₈

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×#595

commutator, socle, prime radical

C₂²×C₁₇

C₂²×C₁₆

Fitting

C₈×Q₈×C₁₇

C₄

C₂³

C₈×Q₈

C₁₇

G ▷ C₂²×C₁₇ ▷ C₁₇

C₁ ◁ C₂×C₈ ◁ C₈×Q₈

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
C₄⋊#10587467	2
#14543891	2
C₄×#10587467	2
Q₈×#63214	2
#13660	17

subgroup

index

Subgroups — #17962897

Conjugacy classes of subgroups

Complements

Maximal subgroups