Group #46812461 — subgroups

Subgroups — #46812461

Order 34432.

158 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 59 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	#31770654	C₂	1	1	yes	maximal, characteristic
2	#31770628	C₂	1	1	yes	maximal, characteristic
3	#31770375	C₂	1	2	yes	maximal
4	#31770364	C₂	1	2	yes	maximal
5	H(3,ℤ/4)×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#16864386	C₂²	1	1	yes	characteristic
7	C₂×#16864386	C₂²	1	2	yes	—
8	C₂×C₄×Dic₂₆₉	C₂²	1	1	yes	characteristic
9	#22575389	—	2	2	no	—
10	#22575382	—	2	2	no	—
11	C₂×M₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
12	#117×C₂₆₉	C₂²	1	2	yes	—
13	C₂²×Dic₂₆₉	—	2	1	no	—
14	#16864386	—	2	2	no	—
15	#16864386	—	2	2	no	—
16	#16864386	—	2	2	no	—
17	C₂×#14524130	—	2	1	no	—
18	C₂×#14524130	—	2	2	no	—
19	C₄×Dic₂₆₉	—	2	1	no	—
20	C₄×Dic₂₆₉	Q₈	1	1	yes	characteristic
21	C₄×Dic₂₆₉	Q₈	1	1	yes	characteristic
22	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
23	M₁₆×C₂₆₉	—	2	2	no	—
24	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
25	C₄⋊C₄×C₂₆₉	—	2	2	no	—
26	C₂²⋊C₄×C₂₆₉	—	2	2	no	—
27	C₄²×C₂₆₉	—	2	2	no	—
28	C₂×Dic₂₆₉	—	2	1	no	—
29	C₂×Dic₂₆₉	—	2	1	no	—
30	C₂×Dic₂₆₉	—	4	2	no	—
31	#14524130	—	4	1	no	—
32	#14524130	—	4	2	no	—
33	C₂³×C₂₆₉	#41	1	1	yes	characteristic
34	C₂×C₄×C₂₆₉	—	4	2	no	—
35	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
36	C₂×C₄×C₂₆₉	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₄×C₂₆₉	#41	1	2	yes	—
38	C₂×C₄×C₂₆₉	#41	1	2	yes	—
39	C₈×C₂₆₉	—	2	2	no	—
40	C₂²×C₂₆₉	—	4	1	no	—
41	C₂²×C₂₆₉	C₂²⋊Q₈	1	1	yes	characteristic
42	C₂²×C₂₆₉	#126	1	2	yes	—
43	C₄×C₂₆₉	—	8	2	no	—
44	C₄×C₂₆₉	#123	1	1	yes	characteristic
45	C₄×C₂₆₉	#124	1	1	yes	characteristic
46	C₄×C₂₆₉	#125	1	2	yes	—
47	Dic₂₆₉	—	2	2	no	—
48	Dic₂₆₉	—	4	1	no	—
49	C₂×C₂₆₉	—	2	1	no	—
50	C₂×C₂₆₉	—	2	2	no	—
51	C₂×C₂₆₉	#400	1	1	yes	characteristic
52	C₂₆₉	#2102	1	1	yes	characteristic, complemented, Sylow
53	#2102	—	269	1	no	maximal, Sylow
54	#430	—	269	1	no	—
55	#423	—	269	1	no	—
56	#344	—	269	2	no	—
57	#339	—	269	2	no	—
58	H(3,ℤ/4)	D₂₆₉	1	1	yes	characteristic
59	C₂×M₁₆	—	269	2	no	—
60	C₂×M₁₆	—	269	1	no	—
61	C₂×M₁₆	C₂×D₂₆₉	1	1	yes	characteristic
62	#117	C₂×D₂₆₉	1	2	yes	—
63	C₂×C₄²	—	269	1	no	—
64	#108	—	538	2	no	—
65	C₄⋊C₈	—	538	2	no	—
66	C₂²×C₄	—	538	1	no	—
67	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
68	M₁₆	—	2	2	no	—
69	M₁₆	—	538	2	no	—
70	M₁₆	—	538	2	no	—
71	M₁₆	—	538	2	no	—
72	C₂×C₈	—	538	1	no	—
73	C₂×C₈	—	538	2	no	—
74	C₂×C₈	D₁₀₇₆	1	2	yes	—
75	C₄⋊C₄	—	2	2	no	—
76	C₂²⋊C₄	—	2	2	no	—
77	C₄²	—	2	2	no	—
78	C₄²	—	269	1	no	—
79	C₄²	—	269	1	no	—
80	C₄²	—	538	1	no	—
81	C₂³	#16864401	1	1	yes	characteristic
82	C₂×C₄	—	4	2	no	—
83	C₂×C₄	—	538	1	no	—
84	C₂×C₄	—	538	1	no	—
85	C₂×C₄	—	1076	2	no	—
86	C₂×C₄	C₂×D₁₀₇₆	1	1	yes	characteristic
87	C₂×C₄	Q₈×D₂₆₉	1	1	yes	characteristic
88	C₂×C₄	#16864401	1	2	yes	—
89	C₂×C₄	#16864402	1	2	yes	—
90	C₈	—	2	2	no	—
91	C₈	—	1076	1	no	—
92	C₈	—	1076	2	no	—
93	C₂²	—	4	1	no	—
94	C₂²	#22575433	1	1	yes	characteristic
95	C₂²	#22575446	1	2	yes	—
96	C₄	—	8	2	no	—
97	C₄	—	538	2	no	—
98	C₄	—	1076	1	no	—
99	C₄	#22575437	1	1	yes	characteristic
100	C₄	#22575441	1	1	yes	characteristic
101	C₄	#22575443	1	2	yes	—
102	C₂	—	2	2	no	—
103	C₂	—	2	1	no	—
104	C₂	#31770545	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31770654

C₂

yes

maximal, characteristic

#31770628

C₂

yes

maximal, characteristic

#31770375

C₂

yes

maximal

#31770364

C₂

yes

maximal

H(3,ℤ/4)×C₂₆₉

C₂

yes

maximal, characteristic

C₂×#16864386

C₂²

yes

characteristic

C₂×#16864386

C₂²

yes

—

C₂×C₄×Dic₂₆₉

C₂²

yes

characteristic

#22575389

—

#22575382

—

C₂×M₁₆×C₂₆₉

C₂²

yes

characteristic

#117×C₂₆₉

C₂²

yes

—

C₂²×Dic₂₆₉

—

—

—

—

—

—

C₄×Dic₂₆₉

—

C₄×Dic₂₆₉

Q₈

yes

characteristic

C₄×Dic₂₆₉

Q₈

yes

characteristic

C₂²×C₄×C₂₆₉

C₂³

yes

characteristic

M₁₆×C₂₆₉

—

C₂×C₈×C₂₆₉

D₄

yes

—

C₄⋊C₄×C₂₆₉

—

C₂²⋊C₄×C₂₆₉

—

C₄²×C₂₆₉

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

#14524130

—

#14524130

—

C₂³×C₂₆₉

#41

yes

characteristic

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

C₂×Q₈

yes

characteristic

C₂×C₄×C₂₆₉

#41

yes

—

C₂×C₄×C₂₆₉

#41

yes

—

C₈×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

C₂²⋊Q₈

yes

characteristic

C₂²×C₂₆₉

#126

yes

—

C₄×C₂₆₉

—

C₄×C₂₆₉

yes

C₄×C₂₆₉

yes

C₄×C₂₆₉

yes

—

Dic₂₆₉

—

Dic₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

#400

yes

characteristic

C₂₆₉

#2102

yes

characteristic, complemented, Sylow

#2102

—

269

maximal, Sylow

#430

—

269

—

#423

—

269

—

#344

—

269

—

#339

—

269

—

H(3,ℤ/4)

D₂₆₉

yes

characteristic

C₂×M₁₆

—

269

—

C₂×M₁₆

—

269

—

C₂×M₁₆

C₂×D₂₆₉

yes

characteristic

#117

C₂×D₂₆₉

yes

—

C₂×C₄²

—

269

—

#108

—

538

—

C₄⋊C₈

—

538

—

C₂²×C₄

—

538

—

C₂²×C₄

C₂²×D₂₆₉

yes

characteristic

M₁₆

—

M₁₆

—

538

—

M₁₆

—

538

—

M₁₆

—

538

—

C₂×C₈

—

538

—

C₂×C₈

—

538

—

C₂×C₈

D₁₀₇₆

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

269

—

C₄²

—

269

—

C₄²

—

538

—

C₂³

#16864401

yes

characteristic

C₂×C₄

—

C₂×C₄

—

538

—

C₂×C₄

—

538

—

C₂×C₄

—

1076

—

C₂×C₄

C₂×D₁₀₇₆

yes

characteristic

C₂×C₄

Q₈×D₂₆₉

yes

characteristic

C₂×C₄

#16864401

yes

—

C₂×C₄

#16864402

yes

—

C₈

—

C₈

—

1076

—

C₈

—

1076

—

C₂²

—

C₂²

#22575433

yes

characteristic

C₂²

#22575446

yes

—

C₄

—

C₄

—

538

—

C₄

—

1076

—

C₄

#22575437

yes

characteristic

100

C₄

#22575441

yes

characteristic

101

C₄

#22575443

yes

—

102

C₂

—

103

C₂

—

104

C₂

#31770545

yes

characteristic

	subgroup	G/H
center	C₄	#22575441
commutator, cosocle	C₂²×C₄×C₂₆₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₆₉
Fitting	H(3,ℤ/4)×C₂₆₉	C₂
socle	C₂×C₂₆₉	#400
prime radical	C₂³×C₂₆₉	#41
hypercenter	H(3,ℤ/4)	D₂₆₉
hypocenter	C₂₆₉	#2102
LCS	G ▷ C₂²×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

subgroup

G/H

center

C₄

#22575441

commutator, cosocle

C₂²×C₄×C₂₆₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₆₉

Fitting

H(3,ℤ/4)×C₂₆₉

C₂

C₂×C₂₆₉

C₂³×C₂₆₉

D₂₆₉

C₂₆₉

G ▷ C₂²×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ H(3,ℤ/4)

N	H ≅ G/N	type
52. C₂₆₉	#2102	semidirect

H ≅ G/N

type

52. C₂₆₉

#2102

semidirect

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

subgroup	index
#31770654	2
#31770628	2
#31770375	2
#31770364	2
H(3,ℤ/4)×C₂₆₉	2
#2102	269

subgroup

index

H(3,ℤ/4)×C₂₆₉

269

Subgroups — #46812461

Conjugacy classes of subgroups

Complements

Maximal subgroups