Group #14545115 — subgroups

Subgroups — C₂×#11763730 #14545115

Order 2176.

184 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 106 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	C₂²×#63216	C₂	1	2	yes	maximal
2	#11763730	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₁₇	C₄	1	1	yes	characteristic
5	C₂×C₄×Dic₁₇	C₄	1	1	yes	characteristic
6	C₂²×#3622	C₂²	1	1	yes	characteristic
7	C₂×#63216	—	2	4	no	—
8	C₂×#63216	C₂²	1	4	yes	—
9	C₈×Dic₁₇	C₄	1	2	yes	—
10	C₈×Dic₁₇	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
12	C₂²×Dic₁₇	C₈	1	1	yes	characteristic
13	C₂²×Dic₁₇	C₈	1	1	yes	characteristic
14	C₂×C₈×C₁₇	—	2	2	no	—
15	C₂×C₈×C₁₇	C₂×C₄	1	2	yes	—
16	C₄×Dic₁₇	C₈	1	2	yes	—
17	C₄×Dic₁₇	C₂×C₄	1	2	yes	—
18	C₂×#3622	C₂×C₄	1	1	yes	characteristic
19	C₂×#3622	D₄	1	2	yes	—
20	C₂×#3622	Q₈	1	2	yes	—
21	C₂×#3622	C₂³	1	1	yes	characteristic
22	#63216	—	2	4	no	—
23	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
25	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
27	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₁₇	—	2	2	no	—
29	C₂×Dic₁₇	C₁₆	1	4	yes	complemented
30	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
31	C₂×Dic₁₇	C₂×C₈	1	2	yes	—
32	C₈×C₁₇	—	2	2	no	—
33	#3622	C₄⋊C₄	1	2	yes	—
34	#3622	C₂×D₄	1	1	yes	characteristic
35	#3622	C₂×Q₈	1	1	yes	characteristic
36	C₂×C₄⋊C₁₆	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	C₄⋊C₈	1	2	yes	—
38	C₂²×C₁₇	C₂×C₁₆	1	2	yes	—
39	C₂²×C₁₇	M₃₂	1	2	yes	—
40	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
41	C₄×C₁₇	C₄⋊C₈	1	2	yes	—
42	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
44	Dic₁₇	—	2	2	no	—
45	Dic₁₇	C₂×C₁₆	1	4	yes	complemented
46	C₂²×C₁₆	—	17	2	no	—
47	C₂×C₄×C₈	—	17	1	no	—
48	C₄⋊C₁₆	—	17	4	no	—
49	C₂×C₁₇	C₄⋊C₁₆	1	4	yes	complemented
50	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
51	C₂×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
52	C₂×C₁₇	C₂×M₃₂	1	1	yes	characteristic
53	C₂²×C₈	—	17	1	no	—
54	C₂²×C₈	#595	1	1	yes	characteristic
55	C₂×C₄²	—	17	1	no	—
56	C₂×C₁₆	—	17	4	no	—
57	C₂×C₁₆	—	34	4	no	—
58	C₄×C₈	—	17	2	no	—
59	C₄×C₈	—	17	2	no	—
60	C₁₇	C₂×C₄⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	—	17	1	no	—
62	C₂²×C₄	—	17	1	no	—
63	C₂²×C₄	C₂×#595	1	1	yes	characteristic
64	C₂×C₈	—	2	2	no	—
65	C₂×C₈	—	17	2	no	—
66	C₂×C₈	—	17	2	no	—
67	C₂×C₈	—	17	1	no	—
68	C₂×C₈	—	17	1	no	—
69	C₂×C₈	C₂×#595	1	2	yes	—
70	C₄²	—	17	2	no	—
71	C₄²	—	17	2	no	—
72	C₁₆	—	34	4	no	—
73	C₂³	#63242	1	1	yes	characteristic
74	C₂×C₄	—	17	2	no	—
75	C₂×C₄	—	17	4	no	—
76	C₂×C₄	—	17	2	no	—
77	C₂×C₄	—	34	2	no	—
78	C₂×C₄	#63242	1	1	yes	characteristic
79	C₂×C₄	C₄⋊#595	1	2	yes	—
80	C₂×C₄	#63247	1	2	yes	—
81	C₂×C₄	C₂²×#595	1	1	yes	characteristic
82	C₈	—	2	2	no	—
83	C₈	—	17	1	no	—
84	C₈	—	17	2	no	—
85	C₈	—	17	1	no	—
86	C₂²	#10587529	1	2	yes	—
87	C₂²	#10587530	1	2	yes	—
88	C₂²	#10587544	1	2	yes	—
89	C₂²	C₂×#63242	1	1	yes	characteristic
90	C₄	—	17	4	no	—
91	C₄	—	34	2	no	—
92	C₄	#10587544	1	2	yes	—
93	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
94	C₄	C₂×#63247	1	1	yes	characteristic
95	C₂	#11763730	1	4	yes	direct product factor
96	C₂	C₂×#10587544	1	1	yes	characteristic
97	C₂	C₂×#10587529	1	1	yes	characteristic
98	C₂	C₂×#10587530	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#63216

C₂

yes

maximal

#11763730

C₂

yes

maximal, direct product factor

C₂×C₈×Dic₁₇

C₂

yes

maximal, characteristic

C₂²×C₈×C₁₇

C₄

yes

characteristic

C₂×C₄×Dic₁₇

C₄

yes

characteristic

C₂²×#3622

C₂²

yes

characteristic

C₂×#63216

—

C₂×#63216

C₂²

yes

—

C₈×Dic₁₇

C₄

yes

—

C₈×Dic₁₇

C₂²

yes

—

C₂²×C₄×C₁₇

C₂×C₄

yes

characteristic

C₂²×Dic₁₇

C₈

yes

characteristic

C₂²×Dic₁₇

C₈

yes

characteristic

C₂×C₈×C₁₇

—

C₂×C₈×C₁₇

C₂×C₄

yes

—

C₄×Dic₁₇

C₈

yes

—

C₄×Dic₁₇

C₂×C₄

yes

—

C₂×#3622

C₂×C₄

yes

characteristic

C₂×#3622

D₄

yes

—

C₂×#3622

Q₈

yes

—

C₂×#3622

C₂³

yes

characteristic

#63216

—

C₂³×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

C₄⋊C₄

yes

—

C₂×C₄×C₁₇

C₂×C₈

yes

characteristic

C₂×C₄×C₁₇

M₁₆

yes

—

C₂×C₄×C₁₇

C₂²×C₄

yes

characteristic

C₂×Dic₁₇

—

C₂×Dic₁₇

C₁₆

yes

complemented

C₂×Dic₁₇

C₂×C₈

yes

—

C₂×Dic₁₇

C₂×C₈

yes

—

C₈×C₁₇

—

#3622

C₄⋊C₄

yes

—

#3622

C₂×D₄

yes

characteristic

#3622

C₂×Q₈

yes

characteristic

C₂×C₄⋊C₁₆

—

maximal, Sylow

C₂²×C₁₇

C₄⋊C₈

yes

—

C₂²×C₁₇

C₂×C₁₆

yes

—

C₂²×C₁₇

M₃₂

yes

—

C₂²×C₁₇

C₂²×C₈

yes

characteristic

C₄×C₁₇

C₄⋊C₈

yes

—

C₄×C₁₇

C₂×C₄⋊C₄

yes

characteristic

C₄×C₁₇

C₂×M₁₆

yes

characteristic

Dic₁₇

—

Dic₁₇

C₂×C₁₆

yes

complemented

C₂²×C₁₆

—

C₂×C₄×C₈

—

C₄⋊C₁₆

—

C₂×C₁₇

C₄⋊C₁₆

yes

complemented

C₂×C₁₇

C₂×C₄⋊C₈

yes

characteristic

C₂×C₁₇

C₂²×C₁₆

yes

characteristic

C₂×C₁₇

C₂×M₃₂

yes

characteristic

C₂²×C₈

—

C₂²×C₈

#595

yes

characteristic

C₂×C₄²

—

C₂×C₁₆

—

C₂×C₁₆

—

C₄×C₈

—

C₄×C₈

—

C₁₇

C₂×C₄⋊C₁₆

yes

characteristic, complemented, Sylow

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#595

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₂×#595

yes

—

C₄²

—

C₄²

—

C₁₆

—

C₂³

#63242

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#63242

yes

characteristic

C₂×C₄

C₄⋊#595

yes

—

C₂×C₄

#63247

yes

—

C₂×C₄

C₂²×#595

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

C₂²

#10587529

yes

—

C₂²

#10587530

yes

—

C₂²

#10587544

yes

—

C₂²

C₂×#63242

yes

characteristic

C₄

—

C₄

—

C₄

#10587544

yes

—

C₄

C₂×C₄⋊#595

yes

C₄

yes

C₂

yes

direct product factor

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²×C₄	C₂×#595
commutator	C₂×C₁₇	C₂²×C₁₆
Frattini	C₂×C₄	C₂²×#595
Fitting	C₂²×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂×C₈
cosocle	C₂×#3622	C₂³
hypercenter	C₂²×C₈	#595
hypocenter	C₁₇	C₂×C₄⋊C₁₆
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²×C₄

C₂×#595

commutator

C₂×C₁₇

C₂²×C₁₆

Frattini

C₂×C₄

C₂²×#595

Fitting

C₂²×C₈×C₁₇

C₄

socle, prime radical

C₂³×C₁₇

C₂×C₈

C₂³

C₂²×C₈

C₁₇

C₂×C₄⋊C₁₆

LCS

G ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. #11763730	C₂	direct (N × H)
29. C₂×Dic₁₇	C₁₆	semidirect
45. Dic₁₇	C₂×C₁₆	semidirect
49. C₂×C₁₇	C₄⋊C₁₆	semidirect
60. C₁₇	C₂×C₄⋊C₁₆	semidirect
95. C₂	#11763730	direct (N × H)

H ≅ G/N

type

2. #11763730

C₂

direct (N × H)

29. C₂×Dic₁₇

C₁₆

semidirect

45. Dic₁₇

C₂×C₁₆

semidirect

49. C₂×C₁₇

C₄⋊C₁₆

semidirect

60. C₁₇

C₂×C₄⋊C₁₆

semidirect

95. C₂

#11763730

direct (N × H)

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

subgroup	index
C₂²×#63216	2
#11763730	2
C₂×C₈×Dic₁₇	2
C₂×C₄⋊C₁₆	17

subgroup

index

C₂²×#63216

#11763730

C₂×C₈×Dic₁₇

C₂×C₄⋊C₁₆

Subgroups — C₂×#11763730 #14545115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#11763730 #14545115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11763730 #14545115