Group #16949028 — subgroups

Subgroups — #16949028

Order 4352.

290 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 83 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	#14531008	C₂	1	4	yes	maximal, complemented
2	#14528399	C₂	1	1	yes	maximal, characteristic
3	#14528394	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1311	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763214	C₂²	1	2	yes	—
6	#11763186	—	2	2	no	—
7	#11763186	C₂²	1	2	yes	—
8	#11763160	—	2	2	no	—
9	#11762611	—	2	8	no	—
10	C₄×C₁₆×C₁₇	C₂²	1	2	yes	—
11	C₈²×C₁₇	C₂²	1	1	yes	characteristic
12	C₂×D₁₃₆	—	2	4	no	—
13	C₂×D₁₃₆	—	4	4	no	—
14	#10587560	—	2	2	no	—
15	#10587555	—	2	2	no	—
16	C₂×C₁₆×C₁₇	D₄	1	4	yes	—
17	C₄×C₈×C₁₇	D₄	1	2	yes	—
18	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
19	#10587489	—	2	4	no	—
20	#10587487	—	4	4	no	—
21	C₂×D₆₈	—	4	2	no	—
22	C₂×D₆₈	—	4	4	no	—
23	C₂×Dic₃₄	—	4	2	no	—
24	C₂×C₈×C₁₇	D₈	1	4	yes	—
25	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
26	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
27	C₄⋊Dic₁₇	—	4	2	no	—
28	C₄⋊Dic₁₇	—	4	2	no	—
29	D₁₃₆	—	4	8	no	—
30	D₁₃₆	—	8	8	no	—
31	C₁₆×C₁₇	—	2	4	no	—
32	#12513	—	17	1	no	maximal, Sylow
33	C₂²×D₁₇	—	8	2	no	—
34	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
35	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
36	C₂×Dic₁₇	—	8	2	no	—
37	D₆₈	—	8	4	no	—
38	D₆₈	—	8	8	no	—
39	Dic₃₄	—	8	4	no	—
40	C₈×C₁₇	—	2	4	no	—
41	C₈×C₁₇	#135	1	4	yes	—
42	#2240	—	17	4	no	—
43	#1712	—	17	1	no	—
44	#1710	—	17	1	no	—
45	#1311	D₁₇	1	1	yes	characteristic, complemented
46	C₂²×C₁₇	#493	1	1	yes	characteristic
47	C₂×D₁₇	—	16	2	no	—
48	C₂×D₁₇	—	16	4	no	—
49	C₄×C₁₇	#495	1	2	yes	—
50	C₄×C₁₇	#509	1	4	yes	—
51	Dic₁₇	—	16	2	no	—
52	#500	—	17	2	no	—
53	#493	—	17	2	no	—
54	#493	—	34	2	no	—
55	#487	—	34	2	no	—
56	#357	—	34	8	no	—
57	C₄×C₁₆	C₂×D₁₇	1	2	yes	—
58	C₈²	C₂×D₁₇	1	1	yes	characteristic
59	C₂×C₁₇	#1709	1	1	yes	characteristic
60	C₂×C₁₇	#2250	1	2	yes	—
61	D₁₇	—	32	2	no	—
62	C₂×D₈	—	34	4	no	—
63	C₂×D₈	—	68	4	no	—
64	C₄⋊Q₈	—	34	2	no	—
65	#127	—	34	2	no	—
66	C₂×C₁₆	D₆₈	1	4	yes	—
67	#107	—	34	4	no	—
68	#103	—	68	4	no	—
69	C₄×C₈	D₆₈	1	2	yes	—
70	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
71	C₁₇	#12513	1	1	yes	characteristic, complemented, Sylow
72	C₂×Q₈	—	68	2	no	—
73	C₂×D₄	—	68	2	no	—
74	C₂×D₄	—	68	4	no	—
75	D₈	—	68	8	no	—
76	D₈	—	136	8	no	—
77	C₂×C₈	D₁₃₆	1	4	yes	—
78	C₂×C₈	C₂×D₆₈	1	2	yes	—
79	C₄⋊C₄	—	68	2	no	—
80	C₄⋊C₄	—	68	2	no	—
81	C₄²	C₂×D₆₈	1	1	yes	characteristic
82	C₁₆	—	2	4	no	—
83	C₂³	—	136	2	no	—
84	Q₈	—	136	4	no	—
85	D₄	—	136	8	no	—
86	D₄	—	136	4	no	—
87	C₂×C₄	—	136	2	no	—
88	C₂×C₄	#10587560	1	1	yes	characteristic
89	C₂×C₄	C₂×D₁₃₆	1	2	yes	—
90	C₈	—	2	4	no	—
91	C₈	#10587590	1	4	yes	—
92	C₂²	—	272	2	no	—
93	C₂²	—	272	4	no	—
94	C₂²	#11763186	1	1	yes	characteristic
95	C₄	—	272	2	no	—
96	C₄	#11763193	1	2	yes	—
97	C₄	#11763247	1	4	yes	—
98	C₂	—	544	2	no	—
99	C₂	#14528390	1	1	yes	characteristic
100	C₂	#14531050	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14531008

C₂

yes

maximal, complemented

#14528399

C₂

yes

maximal, characteristic

#14528394

C₂

yes

maximal, characteristic, complemented

C₁₇×#1311

C₂

yes

maximal, characteristic, complemented

#11763214

C₂²

yes

—

#11763186

—

#11763186

C₂²

yes

—

#11763160

—

#11762611

—

C₄×C₁₆×C₁₇

C₂²

yes

—

C₈²×C₁₇

C₂²

yes

characteristic

C₂×D₁₃₆

—

C₂×D₁₃₆

—

#10587560

—

#10587555

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

C₂³

yes

characteristic

#10587489

—

#10587487

—

C₂×D₆₈

—

C₂×D₆₈

—

C₂×Dic₃₄

—

C₂×C₈×C₁₇

D₈

yes

—

C₂×C₈×C₁₇

C₂×D₄

yes

—

C₄²×C₁₇

C₂×D₄

yes

characteristic

C₄⋊Dic₁₇

—

C₄⋊Dic₁₇

—

D₁₃₆

—

D₁₃₆

—

C₁₆×C₁₇

—

#12513

—

maximal, Sylow

C₂²×D₁₇

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×Dic₁₇

—

D₆₈

—

D₆₈

—

Dic₃₄

—

C₈×C₁₇

—

C₈×C₁₇

#135

yes

—

—

—

—

D₁₇

yes

characteristic, complemented

C₂²×C₁₇

#493

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

#495

yes

—

C₄×C₁₇

#509

yes

—

Dic₁₇

—

—

—

—

—

—

C₄×C₁₆

C₂×D₁₇

yes

—

C₈²

C₂×D₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

D₁₇

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

D₆₈

yes

—

#107

—

#103

—

C₄×C₈

D₆₈

yes

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12513

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

D₈

—

D₈

—

136

—

C₂×C₈

D₁₃₆

yes

—

C₂×C₈

C₂×D₆₈

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×D₆₈

yes

characteristic

C₁₆

—

C₂³

—

136

—

Q₈

—

136

—

D₄

—

136

—

D₄

—

136

—

C₂×C₄

—

136

—

C₂×C₄

#10587560

yes

characteristic

C₂×C₄

C₂×D₁₃₆

yes

—

C₈

—

C₈

#10587590

yes

—

C₂²

—

272

—

C₂²

—

272

—

C₂²

#11763186

yes

characteristic

C₄

—

272

—

C₄

#11763193

yes

—

C₄

#11763247

yes

—

C₂

—

544

—

C₂

#14528390

yes

characteristic

100

C₂

#14531050

yes

—

	subgroup	G/H
center	C₂²	#11763186
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₁₇×#1311	C₂
socle	C₂²×C₁₇	#493
prime radical	#14528399	C₂
hypercenter	#1311	D₁₇
hypocenter	C₁₇	#12513
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

subgroup

G/H

center

C₂²

#11763186

commutator, cosocle

C₄×C₈×C₁₇

C₂³

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₁₇×#1311

C₂

C₂²×C₁₇

C₂

D₁₇

C₁₇

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1311

N	H ≅ G/N	type
1. #14531008	C₂	semidirect
3. #14528394	C₂	semidirect
4. C₁₇×#1311	C₂	semidirect
45. #1311	D₁₇	semidirect
71. C₁₇	#12513	semidirect

H ≅ G/N

type

1. #14531008

C₂

semidirect

3. #14528394

C₂

semidirect

4. C₁₇×#1311

C₂

semidirect

45. #1311

D₁₇

semidirect

71. C₁₇

#12513

semidirect

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

subgroup	index
#14531008	2
#14528399	2
#14528394	2
C₁₇×#1311	2
#12513	17

subgroup

index

C₁₇×#1311

Subgroups — #16949028

Conjugacy classes of subgroups

Complements

Maximal subgroups