Group #16949035 — subgroups

Subgroups — #16949035

Order 4352.

398 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 103 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	#14531033	C₂	1	4	yes	maximal, complemented
2	#14528399	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#63214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1712	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10587497	—	2	8	no	—
6	#11763186	—	2	2	no	—
7	#11763186	C₂²	1	2	yes	—
8	C₄×#63214	C₂²	1	2	yes	—
9	C₁₇×#493	—	2	2	no	—
10	C₁₇×#493	C₂²	1	2	yes	—
11	C₈²×C₁₇	C₂²	1	1	yes	characteristic
12	C₂×D₈×C₁₇	—	2	4	no	—
13	C₂×D₈×C₁₇	—	4	4	no	—
14	C₁₇×#127	—	2	2	no	—
15	C₂×D₁₃₆	—	2	4	no	—
16	C₂×D₁₃₆	—	4	4	no	—
17	#10587560	—	2	2	no	—
18	C₄×C₈×C₁₇	D₄	1	2	yes	—
19	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
20	#10587497	—	4	16	no	—
21	C₂×#63214	D₄	1	4	yes	—
22	C₂×D₄×C₁₇	—	4	2	no	—
23	C₂×D₄×C₁₇	—	4	4	no	—
24	C₂×D₆₈	—	4	2	no	—
25	C₂×D₆₈	—	4	4	no	—
26	D₈×C₁₇	—	4	8	no	—
27	D₈×C₁₇	—	8	8	no	—
28	C₂×C₈×C₁₇	D₈	1	4	yes	—
29	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
30	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
31	D₁₃₆	—	4	8	no	—
32	D₁₃₆	—	8	8	no	—
33	#63214	D₈	1	8	yes	complemented
34	#12515	—	17	1	no	maximal, Sylow
35	C₂³×C₁₇	—	8	2	no	—
36	C₂²×D₁₇	—	8	2	no	—
37	D₄×C₁₇	—	8	4	no	—
38	D₄×C₁₇	—	8	8	no	—
39	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
40	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
41	D₆₈	—	8	4	no	—
42	D₆₈	—	8	8	no	—
43	C₈×C₁₇	D₁₆	1	8	yes	complemented
44	C₈×C₁₇	C₂×D₈	1	4	yes	—
45	#2246	—	17	4	no	—
46	#1712	—	17	1	no	—
47	#1712	D₁₇	1	1	yes	characteristic, complemented
48	C₈×C₁₆	—	17	1	no	—
49	C₂²×C₁₇	—	16	2	no	—
50	C₂²×C₁₇	—	16	4	no	—
51	C₂²×C₁₇	#493	1	1	yes	characteristic
52	C₂×D₁₇	—	16	2	no	—
53	C₂×D₁₇	—	16	4	no	—
54	C₄×C₁₇	#493	1	2	yes	—
55	C₄×C₁₇	C₂×D₁₆	1	4	yes	—
56	C₂×D₁₆	—	34	8	no	—
57	#493	—	2	2	no	—
58	#493	—	17	2	no	—
59	#493	—	34	2	no	—
60	#493	C₂×D₁₇	1	2	yes	—
61	C₄×C₁₆	—	17	2	no	—
62	C₈²	C₂×D₁₇	1	1	yes	characteristic
63	C₂×C₁₇	—	32	2	no	—
64	C₂×C₁₇	#1712	1	1	yes	characteristic
65	C₂×C₁₇	#2246	1	2	yes	—
66	D₁₇	—	32	2	no	—
67	C₂×D₈	—	2	4	no	—
68	C₂×D₈	—	4	4	no	—
69	C₂×D₈	—	34	4	no	—
70	C₂×D₈	—	68	4	no	—
71	#127	—	2	2	no	—
72	#127	—	34	2	no	—
73	D₁₆	—	68	16	no	—
74	C₂×C₁₆	—	17	4	no	—
75	C₄×C₈	C₂²⋊D₁₇	1	2	yes	—
76	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
77	C₁₇	#12515	1	1	yes	characteristic, complemented, Sylow
78	C₂×D₄	—	4	4	no	—
79	C₂×D₄	—	4	2	no	—
80	C₂×D₄	—	68	4	no	—
81	C₂×D₄	—	68	2	no	—
82	D₈	—	4	8	no	—
83	D₈	—	8	8	no	—
84	D₈	—	68	8	no	—
85	D₈	—	136	8	no	—
86	C₂×C₈	#63228	1	4	yes	—
87	C₂×C₈	D₄×D₁₇	1	2	yes	—
88	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
89	C₁₆	—	17	8	no	—
90	C₂³	—	8	2	no	—
91	C₂³	—	136	2	no	—
92	D₄	—	8	8	no	—
93	D₄	—	8	4	no	—
94	D₄	—	136	8	no	—
95	D₄	—	136	4	no	—
96	C₂×C₄	C₂×#63228	1	2	yes	—
97	C₂×C₄	#10587626	1	1	yes	characteristic
98	C₈	#10587497	1	8	yes	complemented
99	C₈	D₈×D₁₇	1	4	yes	—
100	C₂²	—	16	2	no	—
101	C₂²	—	16	4	no	—
102	C₂²	—	272	2	no	—
103	C₂²	—	272	4	no	—
104	C₂²	#11763185	1	1	yes	characteristic
105	C₄	#11763184	1	2	yes	—
106	C₄	C₂×#10587497	1	4	yes	—
107	C₂	—	32	2	no	—
108	C₂	—	544	2	no	—
109	C₂	#14528398	1	1	yes	characteristic
110	C₂	#14531033	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14531033

C₂

yes

maximal, complemented

#14528399

C₂

yes

maximal, characteristic, complemented

C₈×#63214

C₂

yes

maximal, characteristic, complemented

C₁₇×#1712

C₂

yes

maximal, characteristic, complemented

C₂×#10587497

—

#11763186

—

#11763186

C₂²

yes

—

C₄×#63214

C₂²

yes

—

C₁₇×#493

—

C₁₇×#493

C₂²

yes

—

C₈²×C₁₇

C₂²

yes

characteristic

C₂×D₈×C₁₇

—

C₂×D₈×C₁₇

—

C₁₇×#127

—

C₂×D₁₃₆

—

C₂×D₁₃₆

—

#10587560

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

C₂³

yes

characteristic

#10587497

—

C₂×#63214

D₄

yes

—

C₂×D₄×C₁₇

—

C₂×D₄×C₁₇

—

C₂×D₆₈

—

C₂×D₆₈

—

D₈×C₁₇

—

D₈×C₁₇

—

C₂×C₈×C₁₇

D₈

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

D₁₃₆

—

D₁₃₆

—

#63214

D₈

yes

complemented

#12515

—

maximal, Sylow

C₂³×C₁₇

—

C₂²×D₁₇

—

D₄×C₁₇

—

D₄×C₁₇

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

—

D₆₈

—

D₆₈

—

C₈×C₁₇

D₁₆

yes

complemented

C₈×C₁₇

C₂×D₈

yes

—

#2246

—

#1712

—

#1712

D₁₇

yes

characteristic, complemented

C₈×C₁₆

—

C₂²×C₁₇

—

C₂²×C₁₇

—

C₂²×C₁₇

#493

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

#493

yes

—

C₄×C₁₇

C₂×D₁₆

yes

—

C₂×D₁₆

—

—

—

—

C₂×D₁₇

yes

—

C₄×C₁₆

—

C₈²

C₂×D₁₇

yes

characteristic

C₂×C₁₇

—

C₂×C₁₇

#1712

yes

characteristic

C₂×C₁₇

#2246

yes

—

D₁₇

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

#127

—

#127

—

D₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂²⋊D₁₇

yes

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12515

yes

characteristic, complemented, Sylow

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

D₈

—

D₈

—

136

—

C₂×C₈

#63228

yes

—

C₂×C₈

D₄×D₁₇

yes

—

C₄²

C₂×C₂²⋊D₁₇

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

136

—

D₄

—

D₄

—

D₄

—

136

—

D₄

—

136

—

C₂×C₄

C₂×#63228

yes

—

C₂×C₄

yes

C₈

yes

C₈

D₈×D₁₇

yes

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

272

—

103

C₂²

—

272

—

104

C₂²

#11763185

yes

characteristic

105

C₄

#11763184

yes

—

106

C₄

C₂×#10587497

yes

—

107

C₂

—

108

C₂

—

544

—

109

C₂

#14528398

yes

characteristic

110

C₂

#14531033

yes

—

	subgroup	G/H
center	C₂²	#11763185
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#1712	C₂
socle	C₂²×C₁₇	#493
hypercenter	#1712	D₁₇
hypocenter	C₁₇	#12515
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

subgroup

G/H

center

C₂²

#11763185

commutator, cosocle

C₄×C₈×C₁₇

C₂³

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#1712

C₂

C₂²×C₁₇

D₁₇

C₁₇

G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

N	H ≅ G/N	type
1. #14531033	C₂	semidirect
2. #14528399	C₂	semidirect
3. C₈×#63214	C₂	semidirect
4. C₁₇×#1712	C₂	semidirect
33. #63214	D₈	semidirect
43. C₈×C₁₇	D₁₆	semidirect
47. #1712	D₁₇	semidirect
77. C₁₇	#12515	semidirect
98. C₈	#10587497	semidirect

H ≅ G/N

type

1. #14531033

C₂

semidirect

2. #14528399

C₂

semidirect

3. C₈×#63214

C₂

semidirect

4. C₁₇×#1712

C₂

semidirect

33. #63214

D₈

semidirect

43. C₈×C₁₇

D₁₆

semidirect

47. #1712

D₁₇

semidirect

77. C₁₇

#12515

semidirect

98. C₈

#10587497

semidirect

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

subgroup	index
#14531033	2
#14528399	2
C₈×#63214	2
C₁₇×#1712	2
#12515	17

subgroup

index

C₁₇×#1712

Subgroups — #16949035

Conjugacy classes of subgroups

Complements

Maximal subgroups