Group #17948401 — subgroups

Subgroups — #17948401

Order 4352.

152 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 152 conjugacy classes of subgroups — too many to draw. Only its 42 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	#14543807	C₂	1	2	yes	maximal, complemented
2	#14528391	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#63216	—	2	2	no	—
4	#11763186	C₄	1	1	yes	characteristic
5	#11763157	—	2	2	no	—
6	C₈×#3622	C₂²	1	1	yes	characteristic
7	C₁₇×#494	C₄	1	1	yes	characteristic
8	C₂×Q₁₆×C₁₇	—	4	1	no	—
9	C₁₇×C₄⋊Q₈	—	2	1	no	—
10	C₂×D₁₃₆	—	4	1	no	—
11	#10587560	—	2	1	no	—
12	C₂×#63216	—	4	2	no	—
13	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
14	#10587480	—	4	2	no	—
15	#10587480	—	4	2	no	—
16	C₄×#3622	D₄	1	2	yes	—
17	C₂×Q₈×C₁₇	—	4	1	no	—
18	C₂×D₆₈	—	4	1	no	—
19	C₂×D₆₈	—	4	2	no	—
20	Q₁₆×C₁₇	—	8	2	no	—
21	C₂×C₈×C₁₇	—	2	1	no	—
22	C₄⋊C₄×C₁₇	—	4	2	no	—
23	C₄²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×#3622	D₈	1	2	yes	—
25	C₂×#3622	SD₁₆	1	2	yes	—
26	D₁₃₆	—	8	2	no	—
27	#63216	—	8	2	no	—
28	#7092	—	17	1	no	maximal, Sylow
29	C₂²×D₁₇	—	8	1	no	—
30	Q₈×C₁₇	—	8	2	no	—
31	C₂×C₄×C₁₇	—	8	1	no	—
32	C₂×C₄×C₁₇	#100	1	1	yes	characteristic
33	C₂×C₄×C₁₇	#102	1	2	yes	—
34	D₆₈	—	8	2	no	—
35	D₆₈	—	8	2	no	—
36	D₆₈	—	8	2	no	—
37	C₈×C₁₇	—	2	2	no	—
38	#3622	—	2	2	no	—
39	#3622	—	2	2	no	—
40	#1709	—	17	1	no	—
41	#1367	—	17	2	no	—
42	C₂²×C₁₇	#331	1	1	yes	characteristic
43	C₂×D₁₇	—	16	1	no	—
44	C₂×D₁₇	—	16	2	no	—
45	C₄×C₁₇	—	2	1	no	—
46	C₄×C₁₇	—	16	1	no	—
47	C₄×C₁₇	#359	1	2	yes	—
48	C₄×C₁₇	#360	1	2	yes	—
49	#494	#595	1	1	yes	characteristic
50	#493	—	17	1	no	—
51	#486	—	34	2	no	—
52	C₄⋊C₁₆	—	34	2	no	—
53	C₈²	—	17	1	no	—
54	C₂×C₁₇	#1357	1	1	yes	characteristic
55	C₂×C₁₇	#1360	1	2	yes	—
56	D₁₇	—	32	1	no	—
57	C₂×Q₁₆	—	4	1	no	—
58	C₂×D₈	—	68	1	no	—
59	C₄⋊Q₈	—	2	1	no	—
60	#127	—	34	1	no	—
61	C₂×C₁₆	—	68	2	no	—
62	#102	—	68	2	no	—
63	#102	—	68	2	no	—
64	C₄×C₈	—	17	2	no	—
65	C₄×C₈	C₂×#595	1	1	yes	characteristic
66	C₁₇	#7092	1	1	yes	characteristic, complemented, Sylow
67	C₂×Q₈	—	4	1	no	—
68	C₂×D₄	—	68	2	no	—
69	C₂×D₄	—	68	1	no	—
70	Q₁₆	—	8	2	no	—
71	D₈	—	136	2	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	—	17	2	no	—
74	C₂×C₈	—	17	2	no	—
75	C₄⋊C₄	—	4	2	no	—
76	C₄²	C₂²⋊#595	1	1	yes	characteristic
77	C₁₆	—	136	2	no	—
78	C₂³	—	136	1	no	—
79	Q₈	—	8	2	no	—
80	D₄	—	136	2	no	—
81	D₄	—	136	2	no	—
82	D₄	—	136	2	no	—
83	C₂×C₄	—	8	1	no	—
84	C₂×C₄	#10587547	1	2	yes	—
85	C₂×C₄	#10587553	1	1	yes	characteristic
86	C₈	—	2	2	no	—
87	C₈	—	34	2	no	—
88	C₈	—	34	2	no	—
89	C₂²	—	272	1	no	—
90	C₂²	—	272	2	no	—
91	C₂²	#11763667	1	1	yes	characteristic
92	C₄	—	2	1	no	—
93	C₄	—	16	1	no	—
94	C₄	#11763724	1	2	yes	—
95	C₄	#11763726	1	2	yes	—
96	C₂	—	544	1	no	—
97	C₂	#14543792	1	1	yes	characteristic
98	C₂	#14543797	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14543807

C₂

yes

maximal, complemented

#14528391

C₂

yes

maximal, characteristic

C₄⋊#63216

—

#11763186

C₄

yes

characteristic

#11763157

—

C₈×#3622

C₂²

yes

characteristic

C₁₇×#494

C₄

yes

characteristic

C₂×Q₁₆×C₁₇

—

C₁₇×C₄⋊Q₈

—

C₂×D₁₃₆

—

#10587560

—

C₂×#63216

—

C₄×C₈×C₁₇

C₂×C₄

yes

—

—

D₄

yes

—

C₂×Q₈×C₁₇

—

C₂×D₆₈

—

C₂×D₆₈

—

Q₁₆×C₁₇

—

C₂×C₈×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄²×C₁₇

C₂²⋊C₄

yes

characteristic

C₂×#3622

D₈

yes

—

C₂×#3622

SD₁₆

yes

—

D₁₃₆

—

#63216

—

#7092

—

maximal, Sylow

C₂²×D₁₇

—

Q₈×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

#100

yes

characteristic

C₂×C₄×C₁₇

#102

yes

—

D₆₈

—

D₆₈

—

D₆₈

—

C₈×C₁₇

—

—

—

—

—

C₂²×C₁₇

#331

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

C₄×C₁₇

#359

yes

—

C₄×C₁₇

#360

yes

—

yes

—

—

C₄⋊C₁₆

—

C₈²

—

C₂×C₁₇

#1357

yes

characteristic

C₂×C₁₇

#1360

yes

—

D₁₇

—

C₂×Q₁₆

—

C₂×D₈

—

C₄⋊Q₈

—

#127

—

C₂×C₁₆

—

#102

—

#102

—

C₄×C₈

—

C₄×C₈

C₂×#595

yes

characteristic

C₁₇

#7092

yes

characteristic, complemented, Sylow

C₂×Q₈

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

D₈

—

136

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄²

C₂²⋊#595

yes

characteristic

C₁₆

—

136

—

C₂³

—

136

—

Q₈

—

D₄

—

136

—

D₄

—

136

—

D₄

—

136

—

C₂×C₄

—

C₂×C₄

#10587547

yes

—

C₂×C₄

#10587553

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

272

—

C₂²

—

272

—

C₂²

#11763667

yes

characteristic

C₄

—

C₄

—

C₄

#11763724

yes

—

C₄

#11763726

yes

—

C₂

—

544

—

C₂

#14543792

yes

characteristic

C₂

#14543797

yes

—

	subgroup	G/H
center	C₂²	#11763667
commutator	C₄×C₈×C₁₇	C₂×C₄
Frattini	C₄×C₈	C₂×#595
Fitting	C₁₇×#494	C₄
socle	C₂²×C₁₇	#331
prime radical	#11763186	C₄
cosocle	C₈×#3622	C₂²
hypercenter	#494	#595
hypocenter	C₁₇	#7092
LCS	G ▷ C₄×C₈×C₁₇ ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

subgroup

G/H

center

C₂²

#11763667

commutator

C₄×C₈×C₁₇

C₂×C₄

Frattini

C₄×C₈

C₂×#595

Fitting

C₁₇×#494

C₄

C₂²×C₁₇

C₄

C₂²

C₁₇

G ▷ C₄×C₈×C₁₇ ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #494

N	H ≅ G/N	type
1. #14543807	C₂	semidirect
66. C₁₇	#7092	semidirect

H ≅ G/N

type

1. #14543807

C₂

semidirect

66. C₁₇

#7092

semidirect

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

subgroup	index
#14543807	2
#14528391	2
#7092	17

subgroup

index

#14543807

#14528391

#7092

Subgroups — #17948401

Conjugacy classes of subgroups

Complements

Maximal subgroups