Group #46812640 — subgroups

Subgroups — #46812640

Order 34432.

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

normal subgroups only

This group has 172 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	C₂×#22575393	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#31770423	C₂	1	4	yes	maximal, complemented
4	C₂×M₃₂×C₂₆₉	C₂	1	1	yes	maximal, characteristic
5	C₂²×#14524130	C₄	1	1	yes	characteristic
6	C₂×C₄×Dic₂₆₉	C₄	1	1	yes	characteristic
7	#22575393	—	2	2	no	—
8	C₂×#16864377	C₂²	1	2	yes	—
9	C₈×Dic₂₆₉	C₄	1	2	yes	—
10	C₈×Dic₂₆₉	C₂²	1	2	yes	—
11	C₂²×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
12	M₃₂×C₂₆₉	—	2	2	no	—
13	C₂×C₁₆×C₂₆₉	C₂²	1	2	yes	—
14	C₂²×Dic₂₆₉	C₈	1	2	yes	—
15	C₂×#14524130	—	2	2	no	—
16	C₂×#14524130	C₂×C₄	1	2	yes	—
17	C₄×Dic₂₆₉	C₈	1	1	yes	characteristic
18	C₄×Dic₂₆₉	C₈	1	1	yes	characteristic
19	C₄×Dic₂₆₉	C₂×C₄	1	2	yes	—
20	#16864377	—	2	2	no	—
21	C₂²×C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₂₆₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
24	C₂×C₈×C₂₆₉	Q₈	1	2	yes	—
25	C₂×C₈×C₂₆₉	C₂³	1	1	yes	characteristic
26	C₁₆×C₂₆₉	—	2	2	no	—
27	C₂×Dic₂₆₉	—	2	4	no	—
28	C₂×Dic₂₆₉	C₂×C₈	1	2	yes	—
29	C₂×Dic₂₆₉	C₂×C₈	1	2	yes	—
30	#14524130	—	2	2	no	—
31	C₂³×C₂₆₉	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₂₆₉	C₄⋊C₄	1	2	yes	—
33	C₂×C₄×C₂₆₉	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₂₆₉	M₁₆	1	2	yes	—
35	C₂×C₄×C₂₆₉	C₂²×C₄	1	1	yes	characteristic
36	C₈×C₂₆₉	C₄⋊C₄	1	2	yes	—
37	C₈×C₂₆₉	C₂×D₄	1	1	yes	characteristic
38	C₈×C₂₆₉	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₂₆₉	—	2	2	no	—
40	C₂²×C₂₆₉	C₄⋊C₈	1	2	yes	—
41	C₂²×C₂₆₉	C₂²×C₈	1	1	yes	characteristic
42	C₄×C₂₆₉	C₄⋊C₈	1	2	yes	—
43	C₄×C₂₆₉	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₄×C₂₆₉	C₂×M₁₆	1	1	yes	characteristic
45	Dic₂₆₉	—	2	2	no	—
46	Dic₂₆₉	M₃₂	1	4	yes	complemented
47	C₂×C₂₆₉	—	2	2	no	—
48	C₂×C₂₆₉	C₂×C₄⋊C₈	1	1	yes	characteristic
49	C₂×C₂₆₉	C₂×M₃₂	1	2	yes	—
50	C₂₆₉	#2150	1	1	yes	characteristic, complemented, Sylow
51	#2150	—	269	1	no	maximal, Sylow
52	C₂×M₃₂	—	269	1	no	—
53	C₂×M₃₂	D₂₆₉	1	1	yes	characteristic
54	C₂×C₄×C₈	—	269	1	no	—
55	C₄⋊C₁₆	—	269	4	no	—
56	C₂²×C₈	—	269	1	no	—
57	C₂²×C₈	C₂×D₂₆₉	1	1	yes	characteristic
58	C₂×C₄²	—	269	1	no	—
59	M₃₂	—	2	2	no	—
60	M₃₂	—	538	2	no	—
61	C₂×C₁₆	—	269	2	no	—
62	C₂×C₁₆	C₂×D₂₆₉	1	2	yes	—
63	C₄×C₈	—	269	2	no	—
64	C₄×C₈	—	269	2	no	—
65	C₂²×C₄	—	269	2	no	—
66	C₂²×C₄	C₄×D₂₆₉	1	1	yes	characteristic
67	C₂×C₈	—	269	2	no	—
68	C₂×C₈	—	538	2	no	—
69	C₂×C₈	C₄×D₂₆₉	1	1	yes	characteristic
70	C₂×C₈	C₂²⋊D₂₆₉	1	2	yes	—
71	C₂×C₈	Dic₅₃₈	1	2	yes	—
72	C₂×C₈	C₂²×D₂₆₉	1	1	yes	characteristic
73	C₄²	—	269	1	no	—
74	C₄²	—	269	1	no	—
75	C₄²	—	269	2	no	—
76	C₁₆	—	2	2	no	—
77	C₁₆	—	538	2	no	—
78	C₂³	C₈×D₂₆₉	1	1	yes	characteristic
79	C₂×C₄	—	269	2	no	—
80	C₂×C₄	—	269	2	no	—
81	C₂×C₄	—	538	4	no	—
82	C₂×C₄	#16864381	1	2	yes	—
83	C₂×C₄	C₈×D₂₆₉	1	1	yes	characteristic
84	C₂×C₄	#16864385	1	2	yes	—
85	C₂×C₄	C₂×C₄×D₂₆₉	1	1	yes	characteristic
86	C₈	—	538	2	no	—
87	C₈	#16864381	1	2	yes	—
88	C₈	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
89	C₈	C₂×Dic₅₃₈	1	1	yes	characteristic
90	C₂²	—	2	2	no	—
91	C₂²	#22575382	1	2	yes	—
92	C₂²	C₂×C₈×D₂₆₉	1	1	yes	characteristic
93	C₄	—	269	4	no	—
94	C₄	—	538	2	no	—
95	C₄	#22575382	1	2	yes	—
96	C₄	C₂×#16864381	1	1	yes	characteristic
97	C₄	C₂×#16864385	1	1	yes	characteristic
98	C₂	—	2	2	no	—
99	C₂	C₂×#22575382	1	1	yes	characteristic
100	C₂	M₃₂×D₂₆₉	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#22575393

C₂

yes

maximal, characteristic

C₂×C₈×Dic₂₆₉

C₂

yes

maximal, characteristic

#31770423

C₂

yes

maximal, complemented

C₂×M₃₂×C₂₆₉

C₂

yes

maximal, characteristic

C₂²×#14524130

C₄

yes

characteristic

C₂×C₄×Dic₂₆₉

C₄

yes

characteristic

#22575393

—

C₂×#16864377

C₂²

yes

—

C₈×Dic₂₆₉

C₄

yes

—

C₈×Dic₂₆₉

C₂²

yes

—

C₂²×C₈×C₂₆₉

C₂²

yes

characteristic

M₃₂×C₂₆₉

—

C₂×C₁₆×C₂₆₉

C₂²

yes

—

C₂²×Dic₂₆₉

C₈

yes

—

C₂×#14524130

—

C₂×#14524130

C₂×C₄

yes

—

C₄×Dic₂₆₉

C₈

yes

characteristic

C₄×Dic₂₆₉

C₈

yes

characteristic

C₄×Dic₂₆₉

C₂×C₄

yes

—

#16864377

—

C₂²×C₄×C₂₆₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₆₉

C₂×C₄

yes

characteristic

C₂×C₈×C₂₆₉

D₄

yes

—

C₂×C₈×C₂₆₉

Q₈

yes

—

C₂×C₈×C₂₆₉

C₂³

yes

characteristic

C₁₆×C₂₆₉

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

C₂×C₈

yes

—

C₂×Dic₂₆₉

C₂×C₈

yes

—

#14524130

—

C₂³×C₂₆₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₆₉

C₄⋊C₄

yes

—

C₂×C₄×C₂₆₉

C₂×C₈

yes

characteristic

C₂×C₄×C₂₆₉

M₁₆

yes

—

C₂×C₄×C₂₆₉

C₂²×C₄

yes

characteristic

C₈×C₂₆₉

C₄⋊C₄

yes

—

C₈×C₂₆₉

C₂×D₄

yes

characteristic

C₈×C₂₆₉

C₂×Q₈

yes

characteristic

C₂²×C₂₆₉

—

C₂²×C₂₆₉

C₄⋊C₈

yes

—

C₂²×C₂₆₉

C₂²×C₈

yes

characteristic

C₄×C₂₆₉

C₄⋊C₈

yes

—

C₄×C₂₆₉

C₂×C₄⋊C₄

yes

characteristic

C₄×C₂₆₉

C₂×M₁₆

yes

characteristic

Dic₂₆₉

—

Dic₂₆₉

M₃₂

yes

complemented

C₂×C₂₆₉

—

C₂×C₂₆₉

C₂×C₄⋊C₈

yes

characteristic

C₂×C₂₆₉

C₂×M₃₂

yes

—

C₂₆₉

#2150

yes

characteristic, complemented, Sylow

#2150

—

269

maximal, Sylow

C₂×M₃₂

—

269

—

C₂×M₃₂

D₂₆₉

yes

characteristic

C₂×C₄×C₈

—

269

—

C₄⋊C₁₆

—

269

—

C₂²×C₈

—

269

—

C₂²×C₈

C₂×D₂₆₉

yes

characteristic

C₂×C₄²

—

269

—

M₃₂

—

M₃₂

—

538

—

C₂×C₁₆

—

269

—

C₂×C₁₆

C₂×D₂₆₉

yes

—

C₄×C₈

—

269

—

C₄×C₈

—

269

—

C₂²×C₄

—

269

—

C₂²×C₄

C₄×D₂₆₉

yes

characteristic

C₂×C₈

—

269

—

C₂×C₈

—

538

—

C₂×C₈

C₄×D₂₆₉

yes

characteristic

C₂×C₈

C₂²⋊D₂₆₉

yes

—

C₂×C₈

Dic₅₃₈

yes

—

C₂×C₈

C₂²×D₂₆₉

yes

characteristic

C₄²

—

269

—

C₄²

—

269

—

C₄²

—

269

—

C₁₆

—

C₁₆

—

538

—

C₂³

C₈×D₂₆₉

yes

characteristic

C₂×C₄

—

269

—

C₂×C₄

—

269

—

C₂×C₄

—

538

—

C₂×C₄

#16864381

yes

—

C₂×C₄

C₈×D₂₆₉

yes

characteristic

C₂×C₄

#16864385

yes

—

C₂×C₄

C₂×C₄×D₂₆₉

yes

characteristic

C₈

—

538

—

C₈

#16864381

yes

—

C₈

C₂×C₂²⋊D₂₆₉

yes

characteristic

C₈

C₂×Dic₅₃₈

yes

characteristic

C₂²

—

C₂²

#22575382

yes

—

C₂²

C₂×C₈×D₂₆₉

yes

characteristic

C₄

—

269

—

C₄

—

538

—

C₄

#22575382

yes

—

C₄

yes

C₄

yes

C₂

—

C₂

C₂×#22575382

yes

characteristic

100

C₂

M₃₂×D₂₆₉

yes

—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₂₆₉
commutator, socle	C₂²×C₂₆₉	C₂²×C₈
Fitting	C₂×M₃₂×C₂₆₉	C₂
prime radical	C₂³×C₂₆₉	C₂×C₈
cosocle	C₂×C₈×C₂₆₉	C₂³
hypercenter	C₂×M₃₂	D₂₆₉
hypocenter	C₂₆₉	#2150
LCS	G ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₂₆₉

commutator, socle

C₂²×C₂₆₉

C₂²×C₈

Fitting

C₂×M₃₂×C₂₆₉

C₂

prime radical

C₂³×C₂₆₉

C₂×C₈

cosocle

C₂×C₈×C₂₆₉

C₂³

hypercenter

C₂×M₃₂

D₂₆₉

C₂₆₉

G ▷ C₂²×C₂₆₉ ▷ C₂₆₉

C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
3. #31770423	C₂	semidirect
46. Dic₂₆₉	M₃₂	semidirect
50. C₂₆₉	#2150	semidirect

H ≅ G/N

type

3. #31770423

C₂

semidirect

46. Dic₂₆₉

M₃₂

semidirect

50. C₂₆₉

#2150

semidirect

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

subgroup	index
C₂×#22575393	2
C₂×C₈×Dic₂₆₉	2
#31770423	2
C₂×M₃₂×C₂₆₉	2
#2150	269

subgroup

index

C₂×#22575393

C₂×C₈×Dic₂₆₉

#31770423

C₂×M₃₂×C₂₆₉

#2150

269

Subgroups — #46812640

Conjugacy classes of subgroups

Complements

Maximal subgroups