Group #16938833 — subgroups

Subgroups — #16938833

Order 4352.

350 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 97 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	#14528917	C₂	1	3	yes	maximal
2	#14526665	C₂	1	3	yes	maximal
3	C₁₇×#2845	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587474	C₂²	1	3	yes	—
5	#11762679	C₂²	1	1	yes	characteristic
6	#11762571	—	2	6	no	—
7	C₁₇×#398	—	2	6	no	—
8	C₁₇×#382	C₂²	1	3	yes	—
9	C₂×C₄⋊C₄×C₁₇	—	2	6	no	—
10	C₂×C₄⋊C₄×C₁₇	D₄	1	6	yes	—
11	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
12	C₂×C₄⋊Dic₁₇	—	2	3	no	—
13	C₂²×#3622	—	2	3	no	—
14	C₁₇×#95	—	2	2	no	—
15	C₁₇×#95	—	2	6	no	—
16	#10587474	—	2	3	no	—
17	#10587474	Q₈	1	6	yes	—
18	C₂²×C₄×C₁₇	—	2	6	no	—
19	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
20	C₂²×Dic₁₇	—	4	1	no	—
21	C₄⋊C₄×C₁₇	—	4	6	no	—
22	C₄⋊C₄×C₁₇	—	8	6	no	—
23	C₄²×C₁₇	C₂×Q₈	1	3	yes	—
24	C₄²×C₁₇	#41	1	1	yes	characteristic
25	C₄⋊Dic₁₇	—	4	6	no	—
26	C₂×#3622	—	2	6	no	—
27	C₂×#3622	—	4	3	no	—
28	C₂×#3622	—	4	3	no	—
29	#10586	—	17	1	no	maximal, Sylow
30	C₂³×C₁₇	#120	1	1	yes	characteristic
31	C₂×C₄×C₁₇	—	2	3	no	—
32	C₂×C₄×C₁₇	—	2	3	no	—
33	C₂×C₄×C₁₇	—	4	6	no	—
34	C₂×C₄×C₁₇	—	4	6	no	—
35	C₂×C₄×C₁₇	—	4	6	no	—
36	C₂×C₄×C₁₇	C₂²⋊Q₈	1	3	yes	—
37	C₂×C₄×C₁₇	C₄⋊Q₈	1	3	yes	—
38	C₂×Dic₁₇	—	8	3	no	—
39	#3622	—	4	6	no	—
40	#2845	D₁₇	1	1	yes	characteristic
41	#1836	—	17	3	no	—
42	#1295	—	17	3	no	—
43	C₂²×C₁₇	#395	1	1	yes	characteristic
44	C₂²×C₁₇	#454	1	3	yes	—
45	C₂²×C₁₇	#455	1	3	yes	—
46	C₄×C₁₇	—	2	3	no	—
47	C₄×C₁₇	—	2	3	no	—
48	C₄×C₁₇	—	8	6	no	—
49	Dic₁₇	—	16	1	no	—
50	C₂×#97	—	17	3	no	—
51	#398	—	2	6	no	—
52	#384	—	17	1	no	—
53	#382	C₂×D₁₇	1	3	yes	—
54	#340	—	34	6	no	—
55	C₂×C₁₇	#1658	1	1	yes	characteristic
56	C₂×C₁₇	#1662	1	3	yes	—
57	C₂×C₁₇	#2061	1	3	yes	—
58	C₂²×C₈	—	34	3	no	—
59	C₂×C₄⋊C₄	—	2	6	no	—
60	C₂×C₄⋊C₄	—	34	3	no	—
61	C₂×C₄⋊C₄	C₂²⋊D₁₇	1	6	yes	—
62	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
63	#97	—	17	6	no	—
64	#97	—	34	3	no	—
65	#95	—	2	2	no	—
66	#95	—	2	6	no	—
67	C₁₇	#10586	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	—	2	6	no	—
69	C₂²×C₄	—	68	1	no	—
70	C₂²×C₄	C₂×C₂²⋊D₁₇	1	3	yes	—
71	C₂×C₈	—	34	6	no	—
72	C₂×C₈	—	68	3	no	—
73	C₂×C₈	—	68	3	no	—
74	C₄⋊C₄	—	4	6	no	—
75	C₄⋊C₄	—	8	6	no	—
76	C₄⋊C₄	—	68	6	no	—
77	C₄²	Q₈×D₁₇	1	3	yes	—
78	C₄²	#63256	1	1	yes	characteristic
79	C₂³	#10587639	1	1	yes	characteristic
80	C₂×C₄	—	2	3	no	—
81	C₂×C₄	—	2	3	no	—
82	C₂×C₄	—	4	6	no	—
83	C₂×C₄	—	4	6	no	—
84	C₂×C₄	—	4	6	no	—
85	C₂×C₄	—	136	3	no	—
86	C₂×C₄	#10587630	1	3	yes	—
87	C₂×C₄	#10587632	1	3	yes	—
88	C₈	—	68	6	no	—
89	C₂²	#11762728	1	1	yes	characteristic
90	C₂²	#11762982	1	3	yes	—
91	C₂²	#11762987	1	3	yes	—
92	C₄	—	2	3	no	—
93	C₄	—	2	3	no	—
94	C₄	—	8	6	no	—
95	C₄	—	272	1	no	—
96	C₂	#14528086	1	1	yes	characteristic
97	C₂	#14528107	1	3	yes	—
98	C₂	#14530131	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14528917

C₂

yes

maximal

#14526665

C₂

yes

maximal

C₁₇×#2845

C₂

yes

maximal, characteristic

C₂×#10587474

C₂²

yes

—

#11762679

C₂²

yes

characteristic

#11762571

—

C₁₇×#398

—

C₁₇×#382

C₂²

yes

—

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄⋊C₄×C₁₇

D₄

yes

—

C₂×C₄²×C₁₇

C₂³

yes

characteristic

C₂×C₄⋊Dic₁₇

—

C₂²×#3622

—

C₁₇×#95

—

C₁₇×#95

—

#10587474

—

#10587474

Q₈

yes

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

—

C₂²×Dic₁₇

—

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂×Q₈

yes

—

C₄²×C₁₇

#41

yes

characteristic

C₄⋊Dic₁₇

—

—

—

—

—

C₂³×C₁₇

yes

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₁₇

C₄⋊Q₈

yes

—

C₂×Dic₁₇

—

#3622

—

#2845

D₁₇

yes

characteristic

#1836

—

#1295

—

C₂²×C₁₇

#395

yes

characteristic

C₂²×C₁₇

#454

yes

—

C₂²×C₁₇

#455

yes

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

C₂×#97

—

#398

—

#384

—

#382

C₂×D₁₇

yes

—

#340

—

C₂×C₁₇

#1658

yes

characteristic

C₂×C₁₇

#1662

yes

—

C₂×C₁₇

#2061

yes

—

C₂²×C₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²⋊D₁₇

yes

—

C₂×C₄²

C₂²×D₁₇

yes

—

—

—

—

C₁₇

#10586

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₂²⋊D₁₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

Q₈×D₁₇

yes

—

C₄²

yes

C₂³

yes

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

136

—

C₂×C₄

#10587630

yes

—

C₂×C₄

#10587632

yes

—

C₈

—

C₂²

#11762728

yes

characteristic

C₂²

#11762982

yes

—

C₂²

#11762987

yes

—

C₄

—

C₄

—

C₄

—

C₄

—

272

—

C₂

#14528086

yes

characteristic

C₂

#14528107

yes

—

C₂

#14530131

yes

—

	subgroup	G/H
center	C₂³	#10587639
commutator, cosocle	C₂×C₄²×C₁₇	C₂³
Frattini	C₂×C₄²	C₂²×D₁₇
Fitting	C₁₇×#2845	C₂
socle, prime radical	C₂³×C₁₇	#120
hypercenter	#2845	D₁₇
hypocenter	C₁₇	#10586
LCS	G ▷ C₂×C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

subgroup

G/H

center

C₂³

#10587639

commutator, cosocle

C₂×C₄²×C₁₇

C₂³

Frattini

C₂×C₄²

C₂²×D₁₇

Fitting

C₁₇×#2845

C₂

C₂³×C₁₇

D₁₇

C₁₇

G ▷ C₂×C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2845

N	H ≅ G/N	type
67. C₁₇	#10586	semidirect

H ≅ G/N

type

67. C₁₇

#10586

semidirect

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

subgroup	index
#14528917	2
#14526665	2
C₁₇×#2845	2
#10586	17

subgroup

index

#14528917

#14526665

C₁₇×#2845

#10586

Subgroups — #16938833

Conjugacy classes of subgroups

Complements

Maximal subgroups