Group #14545858 — subgroups

Subgroups — #14545858

Order 2176.

148 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 51 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	#11763928	C₂	1	2	yes	maximal
2	C₄×#63242	C₂	1	1	yes	maximal, characteristic
3	C₂×#63242	C₄	1	1	yes	characteristic
4	C₂×#63242	C₂²	1	1	yes	characteristic
5	#10587670	—	2	2	no	—
6	#10587666	C₄	1	4	yes	complemented
7	#10587665	—	2	2	no	—
8	C₄²×D₁₇	C₄	1	1	yes	characteristic
9	C₄×#3624	—	2	2	no	—
10	C₂×C₄×D₁₇	—	2	1	no	—
11	C₂×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂×#3624	—	2	1	no	—
13	C₂×#3624	D₄	1	2	yes	—
14	#63242	—	2	1	no	—
15	#63242	C₈	1	2	yes	—
16	#63242	C₂×C₄	1	2	yes	—
17	#63242	D₄	1	1	yes	characteristic
18	#63242	Q₈	1	1	yes	characteristic
19	#63241	—	2	4	no	—
20	C₄²×C₁₇	C₈	1	1	yes	characteristic
21	C₄×Dic₁₇	—	2	1	no	—
22	C₄×Dic₁₇	C₈	1	1	yes	characteristic
23	C₂²×D₁₇	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₁₇	—	2	1	no	—
25	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₁₇	—	2	1	no	—
27	C₂×Dic₁₇	C₂²⋊C₄	1	1	yes	characteristic
28	C₄×D₁₇	—	2	4	no	—
29	C₄×D₁₇	C₄²	1	1	yes	characteristic
30	C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
31	C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
32	C₄×D₁₇	M₁₆	1	1	yes	characteristic
33	#3624	—	2	2	no	—
34	#3624	C₂²⋊C₄	1	2	yes	—
35	#3624	C₄⋊C₄	1	2	yes	—
36	#1376	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
38	C₂×D₁₇	—	2	2	no	—
39	C₂×D₁₇	#97	1	1	yes	characteristic
40	C₂×D₁₇	C₄⋊C₈	1	1	yes	characteristic
41	C₄×C₁₇	—	2	2	no	—
42	C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
43	C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
44	Dic₁₇	—	2	2	no	—
45	Dic₁₇	#95	1	1	yes	characteristic
46	Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
47	C₂×M₃₂	—	17	2	no	—
48	C₂×C₄×C₈	—	17	1	no	—
49	C₂×C₁₇	—	2	1	no	—
50	C₂×C₁₇	#336	1	1	yes	characteristic
51	D₁₇	—	2	1	no	—
52	D₁₇	#364	1	2	yes	—
53	C₂²×C₈	—	17	1	no	—
54	C₂²×C₈	—	17	1	no	—
55	C₂×C₄²	—	17	1	no	—
56	M₃₂	—	17	4	no	—
57	M₃₂	—	34	2	no	—
58	C₂×C₁₆	—	34	2	no	—
59	C₄×C₈	—	34	2	no	—
60	C₁₇	#1376	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	17	1	no	—
62	C₂²×C₄	—	34	1	no	—
63	C₂×C₈	—	17	2	no	—
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	17	2	no	—
67	C₂×C₈	—	17	2	no	—
68	C₂×C₈	—	34	1	no	—
69	C₂×C₈	—	34	1	no	—
70	C₄²	—	17	1	no	—
71	C₄²	—	34	1	no	—
72	C₄²	#3633	1	1	yes	characteristic
73	C₁₆	—	34	4	no	—
74	C₂³	—	17	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	17	1	no	—
77	C₂×C₄	—	17	1	no	—
78	C₂×C₄	—	17	1	no	—
79	C₂×C₄	—	17	1	no	—
80	C₂×C₄	—	17	1	no	—
81	C₂×C₄	—	34	4	no	—
82	C₂×C₄	—	34	1	no	—
83	C₂×C₄	C₂×#3633	1	1	yes	characteristic
84	C₈	—	17	2	no	—
85	C₈	—	17	2	no	—
86	C₈	—	34	2	no	—
87	C₂²	—	17	1	no	—
88	C₂²	—	17	1	no	—
89	C₂²	—	34	2	no	—
90	C₂²	C₂²⋊#3633	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	17	1	no	—
93	C₄	—	17	1	no	—
94	C₄	—	34	2	no	—
95	C₄	C₄×#3633	1	1	yes	characteristic
96	C₄	C₄⋊#3633	1	1	yes	characteristic
97	C₂	—	2	1	no	—
98	C₂	—	17	2	no	—
99	C₂	—	34	1	no	—
100	C₂	(C₂×#3633)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#11763928

C₂

yes

maximal

C₄×#63242

C₂

yes

maximal, characteristic

C₂×#63242

C₄

yes

characteristic

C₂×#63242

C₂²

yes

characteristic

#10587670

—

#10587666

C₄

yes

complemented

#10587665

—

C₄²×D₁₇

C₄

yes

characteristic

C₄×#3624

—

C₂×C₄×D₁₇

—

C₂×C₄×D₁₇

C₂×C₄

yes

characteristic

C₂×#3624

—

C₂×#3624

D₄

yes

—

#63242

—

#63242

C₈

yes

—

#63242

C₂×C₄

yes

—

#63242

D₄

yes

characteristic

#63242

Q₈

yes

characteristic

#63241

—

C₄²×C₁₇

C₈

yes

characteristic

C₄×Dic₁₇

—

C₄×Dic₁₇

C₈

yes

characteristic

C₂²×D₁₇

M₁₆

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₂²⋊C₄

yes

characteristic

C₄×D₁₇

—

C₄×D₁₇

C₄²

yes

characteristic

C₄×D₁₇

C₄⋊C₄

yes

characteristic

C₄×D₁₇

C₂×C₈

yes

characteristic

C₄×D₁₇

M₁₆

yes

characteristic

#3624

—

#3624

C₂²⋊C₄

yes

—

#3624

C₄⋊C₄

yes

—

#1376

—

maximal, Sylow

C₂²×C₁₇

C₂²⋊C₈

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

#97

yes

characteristic

C₂×D₁₇

C₄⋊C₈

yes

characteristic

C₄×C₁₇

—

C₄×C₁₇

C₄×C₈

yes

characteristic

C₄×C₁₇

C₄⋊C₈

yes

characteristic

Dic₁₇

—

Dic₁₇

#95

yes

characteristic

Dic₁₇

C₂²⋊C₈

yes

characteristic

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂×C₁₇

—

C₂×C₁₇

#336

yes

characteristic

D₁₇

—

D₁₇

#364

yes

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

C₂×C₁₆

—

C₄×C₈

—

C₁₇

#1376

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₄²

#3633

yes

characteristic

C₁₆

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×#3633

yes

characteristic

C₈

—

C₈

—

C₈

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂²⋊#3633

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

C₂

—

C₂

—

100

C₂

(C₂×#3633)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₄⋊#3633
commutator	C₄×C₁₇	C₄×C₈
Frattini	C₂×C₄	C₂×#3633
Fitting	C₄²×C₁₇	C₈
socle	C₂×C₁₇	#336
prime radical	C₂²×D₁₇	M₁₆
cosocle	C₂×#63242	C₂²
hypercenter	C₄²	#3633
hypocenter	C₁₇	#1376
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

subgroup

G/H

center

C₄

C₄⋊#3633

commutator

C₄×C₁₇

C₄×C₈

Frattini

C₂×C₄

C₂×#3633

Fitting

C₄²×C₁₇

C₈

socle

C₂×C₁₇

#336

prime radical

C₂²×D₁₇

M₁₆

C₂²

C₄²

C₁₇

G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

N	H ≅ G/N	type
6. #10587666	C₄	semidirect
60. C₁₇	#1376	semidirect

H ≅ G/N

type

6. #10587666

C₄

semidirect

60. C₁₇

#1376

semidirect

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

subgroup	index
#11763928	2
C₄×#63242	2
#1376	17

subgroup

index

#11763928

C₄×#63242

#1376

Subgroups — #14545858

Conjugacy classes of subgroups

Complements

Maximal subgroups