Group #16949042 — subgroups

Subgroups — #16949042

Order 4352.

354 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 115 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	#14531040	C₂	1	4	yes	maximal, complemented
2	#14528402	C₂	1	1	yes	maximal, characteristic, complemented
3	#14528399	C₂	1	1	yes	maximal, characteristic
4	C₈×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10587471	—	2	8	no	—
6	#11763214	—	2	2	no	—
7	#11763189	C₂²	1	2	yes	—
8	#11763186	—	2	2	no	—
9	#11763186	C₂²	1	2	yes	—
10	C₄×C₁₆×C₁₇	C₂²	1	2	yes	—
11	C₈²×C₁₇	C₂²	1	1	yes	characteristic
12	C₂×Dic₆₈	—	2	4	no	—
13	C₂×D₁₃₆	—	2	4	no	—
14	C₂×D₁₃₆	—	4	4	no	—
15	#10587560	—	2	2	no	—
16	#10587555	—	2	2	no	—
17	C₂×C₁₆×C₁₇	D₄	1	4	yes	—
18	C₄×C₈×C₁₇	D₄	1	2	yes	—
19	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
20	#10587489	—	4	4	no	—
21	#10587471	—	4	16	no	—
22	C₂×D₆₈	—	4	2	no	—
23	C₂×D₆₈	—	4	4	no	—
24	C₂×Dic₃₄	—	4	2	no	—
25	C₂×C₈×C₁₇	D₈	1	4	yes	—
26	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
27	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
28	C₄⋊Dic₁₇	—	4	4	no	—
29	Dic₆₈	—	4	8	no	—
30	D₁₃₆	—	4	8	no	—
31	D₁₃₆	—	8	8	no	—
32	C₁₆×C₁₇	D₈	1	8	yes	complemented
33	#12517	—	17	1	no	maximal, Sylow
34	C₂²×D₁₇	—	8	2	no	—
35	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
36	C₂×C₄×C₁₇	C₂×D₈	1	2	yes	—
37	C₂×Dic₁₇	—	8	2	no	—
38	D₆₈	—	8	4	no	—
39	D₆₈	—	8	8	no	—
40	Dic₃₄	—	8	4	no	—
41	C₈×C₁₇	SD₃₂	1	8	yes	complemented
42	C₈×C₁₇	C₂×D₈	1	4	yes	—
43	#2248	—	17	4	no	—
44	#1713	—	17	1	no	—
45	#1712	—	17	1	no	—
46	C₈×C₁₆	D₁₇	1	1	yes	characteristic, complemented
47	C₂²×C₁₇	#493	1	1	yes	characteristic
48	C₂×D₁₇	—	16	2	no	—
49	C₂×D₁₇	—	16	4	no	—
50	C₄×C₁₇	#493	1	2	yes	—
51	C₄×C₁₇	C₂×SD₃₂	1	4	yes	—
52	Dic₁₇	—	16	2	no	—
53	C₂×SD₃₂	—	34	8	no	—
54	#500	—	34	2	no	—
55	#494	—	17	2	no	—
56	#493	—	17	2	no	—
57	#493	—	34	2	no	—
58	C₄×C₁₆	C₂×D₁₇	1	2	yes	—
59	C₈²	C₂×D₁₇	1	1	yes	characteristic
60	C₂×C₁₇	#1712	1	1	yes	characteristic
61	C₂×C₁₇	#2248	1	2	yes	—
62	D₁₇	—	32	2	no	—
63	C₂×Q₁₆	—	34	4	no	—
64	C₂×D₈	—	34	4	no	—
65	C₂×D₈	—	68	4	no	—
66	C₄⋊Q₈	—	34	2	no	—
67	#127	—	34	2	no	—
68	SD₃₂	—	68	16	no	—
69	C₂×C₁₆	D₆₈	1	4	yes	—
70	#107	—	68	4	no	—
71	C₄×C₈	D₆₈	1	2	yes	—
72	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
73	C₁₇	#12517	1	1	yes	characteristic, complemented, Sylow
74	C₂×Q₈	—	68	2	no	—
75	C₂×D₄	—	68	2	no	—
76	C₂×D₄	—	68	4	no	—
77	Q₁₆	—	68	8	no	—
78	D₈	—	68	8	no	—
79	D₈	—	136	8	no	—
80	C₂×C₈	D₁₃₆	1	4	yes	—
81	C₂×C₈	C₂×D₆₈	1	2	yes	—
82	C₄⋊C₄	—	68	4	no	—
83	C₄²	C₂×D₆₈	1	1	yes	characteristic
84	C₁₆	D₁₃₆	1	8	yes	complemented
85	C₂³	—	136	2	no	—
86	Q₈	—	136	4	no	—
87	D₄	—	136	8	no	—
88	D₄	—	136	4	no	—
89	C₂×C₄	—	136	2	no	—
90	C₂×C₄	#10587560	1	1	yes	characteristic
91	C₂×C₄	C₂×D₁₃₆	1	2	yes	—
92	C₈	#10587471	1	8	yes	complemented
93	C₈	C₂×D₁₃₆	1	4	yes	—
94	C₂²	—	272	2	no	—
95	C₂²	—	272	4	no	—
96	C₂²	#11763186	1	1	yes	characteristic
97	C₄	—	272	2	no	—
98	C₄	#11763186	1	2	yes	—
99	C₄	C₂×#10587471	1	4	yes	—
100	C₂	—	544	2	no	—
101	C₂	#14528399	1	1	yes	characteristic
102	C₂	#14531040	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14531040

C₂

yes

maximal, complemented

#14528402

C₂

yes

maximal, characteristic, complemented

#14528399

C₂

yes

maximal, characteristic

C₈×C₁₆×C₁₇

C₂

yes

maximal, characteristic, complemented

C₂×#10587471

—

#11763214

—

#11763189

C₂²

yes

—

#11763186

—

#11763186

C₂²

yes

—

C₄×C₁₆×C₁₇

C₂²

yes

—

C₈²×C₁₇

C₂²

yes

characteristic

C₂×Dic₆₈

—

C₂×D₁₃₆

—

C₂×D₁₃₆

—

#10587560

—

#10587555

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

D₄

yes

—

C₄×C₈×C₁₇

C₂³

yes

characteristic

#10587489

—

#10587471

—

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

—

Dic₆₈

—

D₁₃₆

—

D₁₃₆

—

C₁₆×C₁₇

D₈

yes

complemented

#12517

—

maximal, Sylow

C₂²×D₁₇

—

C₂×C₄×C₁₇

#127

yes

characteristic

C₂×C₄×C₁₇

C₂×D₈

yes

—

C₂×Dic₁₇

—

D₆₈

—

D₆₈

—

Dic₃₄

—

C₈×C₁₇

SD₃₂

yes

complemented

C₈×C₁₇

C₂×D₈

yes

—

#2248

—

#1713

—

#1712

—

C₈×C₁₆

D₁₇

yes

characteristic, complemented

C₂²×C₁₇

#493

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

#493

yes

—

C₄×C₁₇

C₂×SD₃₂

yes

—

Dic₁₇

—

C₂×SD₃₂

—

—

—

—

—

C₄×C₁₆

C₂×D₁₇

yes

—

C₈²

C₂×D₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

D₁₇

—

C₂×Q₁₆

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

SD₃₂

—

C₂×C₁₆

D₆₈

yes

—

#107

—

C₄×C₈

D₆₈

yes

—

C₄×C₈

C₂²×D₁₇

yes

characteristic

C₁₇

#12517

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

D₈

—

D₈

—

136

—

C₂×C₈

D₁₃₆

yes

—

C₂×C₈

C₂×D₆₈

yes

—

C₄⋊C₄

—

C₄²

C₂×D₆₈

yes

characteristic

C₁₆

D₁₃₆

yes

complemented

C₂³

—

136

—

Q₈

—

136

—

D₄

—

136

—

D₄

—

136

—

C₂×C₄

—

136

—

C₂×C₄

#10587560

yes

characteristic

C₂×C₄

C₂×D₁₃₆

yes

—

C₈

#10587471

yes

complemented

C₈

C₂×D₁₃₆

yes

—

C₂²

—

272

—

C₂²

—

272

—

C₂²

#11763186

yes

characteristic

C₄

—

272

—

C₄

#11763186

yes

—

C₄

C₂×#10587471

yes

—

100

C₂

—

544

—

101

C₂

#14528399

yes

characteristic

102

C₂

#14531040

yes

—

	subgroup	G/H
center	C₂²	#11763186
commutator, cosocle	C₄×C₈×C₁₇	C₂³
Frattini	C₄×C₈	C₂²×D₁₇
Fitting	C₈×C₁₆×C₁₇	C₂
socle	C₂²×C₁₇	#493
prime radical	#14528399	C₂
hypercenter	C₈×C₁₆	D₁₇
hypocenter	C₁₇	#12517
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

subgroup

G/H

center

C₂²

#11763186

commutator, cosocle

C₄×C₈×C₁₇

C₂³

Frattini

C₄×C₈

C₂²×D₁₇

Fitting

C₈×C₁₆×C₁₇

C₂

C₂²×C₁₇

C₂

C₈×C₁₆

D₁₇

hypocenter

C₁₇

#12517

LCS

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

N	H ≅ G/N	type
1. #14531040	C₂	semidirect
2. #14528402	C₂	semidirect
4. C₈×C₁₆×C₁₇	C₂	semidirect
32. C₁₆×C₁₇	D₈	semidirect
41. C₈×C₁₇	SD₃₂	semidirect
46. C₈×C₁₆	D₁₇	semidirect
73. C₁₇	#12517	semidirect
84. C₁₆	D₁₃₆	semidirect
92. C₈	#10587471	semidirect

H ≅ G/N

type

1. #14531040

C₂

semidirect

2. #14528402

C₂

semidirect

4. C₈×C₁₆×C₁₇

C₂

semidirect

32. C₁₆×C₁₇

D₈

semidirect

41. C₈×C₁₇

SD₃₂

semidirect

46. C₈×C₁₆

D₁₇

semidirect

73. C₁₇

#12517

semidirect

84. C₁₆

D₁₃₆

semidirect

92. C₈

#10587471

semidirect

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

subgroup	index
#14531040	2
#14528402	2
#14528399	2
C₈×C₁₆×C₁₇	2
#12517	17

subgroup

index

C₈×C₁₆×C₁₇

Subgroups — #16949042

Conjugacy classes of subgroups

Complements

Maximal subgroups