Group #46812390 — subgroups

Subgroups — #46812390

Order 34432.

176 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 69 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	#31770648	C₂	1	2	yes	maximal
2	C₂×#22575387	C₂	1	1	yes	maximal, characteristic
3	#31770373	C₂	1	2	yes	maximal
4	#31770370	C₂	1	1	yes	maximal, characteristic
5	#424×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#16864386	C₂²	1	2	yes	—
7	C₂×C₄⋊Dic₂₆₉	C₂²	1	2	yes	—
8	#22575387	—	2	2	no	—
9	#22575386	—	2	2	no	—
10	#22575384	—	2	2	no	—
11	C₂×M₁₆×C₂₆₉	C₂²	1	1	yes	characteristic
12	C₂²×C₈×C₂₆₉	C₂²	1	1	yes	characteristic
13	#117×C₂₆₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₂₆₉	—	2	2	no	—
15	C₂²×Dic₂₆₉	—	2	2	no	—
16	#16864386	—	2	2	no	—
17	#16864386	Q₈	1	4	yes	—
18	C₂×#14524130	—	2	2	no	—
19	C₄⋊Dic₂₆₉	—	2	2	no	—
20	C₄⋊Dic₂₆₉	—	2	2	no	—
21	C₂²×C₄×C₂₆₉	C₂³	1	1	yes	characteristic
22	M₁₆×C₂₆₉	—	2	2	no	—
23	C₂×C₈×C₂₆₉	—	2	2	no	—
24	C₂×C₈×C₂₆₉	—	2	1	no	—
25	C₂×C₈×C₂₆₉	D₄	1	2	yes	—
26	C₄⋊C₄×C₂₆₉	D₄	1	1	yes	characteristic
27	C₄⋊C₄×C₂₆₉	D₄	1	1	yes	characteristic
28	C₂²⋊C₄×C₂₆₉	—	2	1	no	—
29	C₄²×C₂₆₉	—	2	1	no	—
30	C₂×Dic₂₆₉	—	4	2	no	—
31	C₂×Dic₂₆₉	—	8	2	no	—
32	#14524130	—	2	4	no	—
33	C₂³×C₂₆₉	#41	1	1	yes	characteristic
34	C₂×C₄×C₂₆₉	—	2	1	no	—
35	C₂×C₄×C₂₆₉	—	2	1	no	—
36	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
37	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₂₆₉	C₂×Q₈	1	2	yes	—
39	C₂×C₄×C₂₆₉	#41	1	2	yes	—
40	C₈×C₂₆₉	—	2	2	no	—
41	C₈×C₂₆₉	—	4	1	no	—
42	C₂²×C₂₆₉	—	2	1	no	—
43	C₂²×C₂₆₉	—	2	1	no	—
44	C₂²×C₂₆₉	#121	1	1	yes	characteristic
45	C₂²×C₂₆₉	#125	1	2	yes	—
46	C₄×C₂₆₉	—	4	1	no	—
47	C₄×C₂₆₉	—	4	1	no	—
48	C₄×C₂₆₉	C₂²⋊Q₈	1	2	yes	—
49	C₄×C₂₆₉	#123	1	1	yes	characteristic
50	C₄×C₂₆₉	C₄⋊Q₈	1	1	yes	characteristic
51	Dic₂₆₉	—	8	2	no	—
52	C₂×C₂₆₉	—	2	2	no	—
53	C₂×C₂₆₉	#398	1	1	yes	characteristic
54	C₂×C₂₆₉	#472	1	1	yes	characteristic
55	C₂×C₂₆₉	#473	1	1	yes	characteristic
56	C₂₆₉	#2089	1	1	yes	characteristic, complemented, Sylow
57	#2089	—	269	1	no	maximal, Sylow
58	#428	—	269	2	no	—
59	C₂×#107	—	269	1	no	—
60	#424	D₂₆₉	1	1	yes	characteristic
61	#343	—	269	2	no	—
62	#341	—	269	1	no	—
63	C₂×M₁₆	—	269	2	no	—
64	C₂×M₁₆	C₂×D₂₆₉	1	1	yes	characteristic
65	C₂²×C₈	C₂×D₂₆₉	1	1	yes	characteristic
66	#117	C₂×D₂₆₉	1	1	yes	characteristic
67	C₂×C₄⋊C₄	—	269	2	no	—
68	#107	—	538	2	no	—
69	#107	—	538	2	no	—
70	#106	—	538	2	no	—
71	C₄⋊C₈	—	2	2	no	—
72	C₂²×C₄	—	538	2	no	—
73	C₂²×C₄	C₂²×D₂₆₉	1	1	yes	characteristic
74	M₁₆	—	2	2	no	—
75	M₁₆	—	269	4	no	—
76	M₁₆	—	538	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	2	1	no	—
79	C₂×C₈	—	538	2	no	—
80	C₂×C₈	C₂²⋊D₂₆₉	1	2	yes	—
81	C₄⋊C₄	—	538	2	no	—
82	C₄⋊C₄	—	538	2	no	—
83	C₄⋊C₄	D₁₀₇₆	1	1	yes	characteristic
84	C₄⋊C₄	D₁₀₇₆	1	1	yes	characteristic
85	C₂²⋊C₄	—	2	1	no	—
86	C₄²	—	2	1	no	—
87	C₂³	#16864402	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	1076	2	no	—
91	C₂×C₄	—	2152	2	no	—
92	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
93	C₂×C₄	C₂×D₁₀₇₆	1	1	yes	characteristic
94	C₂×C₄	Q₈×D₂₆₉	1	2	yes	—
95	C₂×C₄	#16864401	1	2	yes	—
96	C₈	—	2	2	no	—
97	C₈	—	4	1	no	—
98	C₈	—	538	4	no	—
99	C₂²	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	#22575427	1	1	yes	characteristic
102	C₂²	#22575443	1	2	yes	—
103	C₄	—	4	1	no	—
104	C₄	—	4	1	no	—
105	C₄	—	2152	2	no	—
106	C₄	#22575433	1	2	yes	—
107	C₄	#22575434	1	1	yes	characteristic
108	C₄	#22575451	1	1	yes	characteristic
109	C₂	—	2	2	no	—
110	C₂	#31770535	1	1	yes	characteristic
111	C₂	#31770875	1	1	yes	characteristic
112	C₂	#31770880	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#31770648

C₂

yes

maximal

C₂×#22575387

C₂

yes

maximal, characteristic

#31770373

C₂

yes

maximal

#31770370

C₂

yes

maximal, characteristic

#424×C₂₆₉

C₂

yes

maximal, characteristic

C₂×#16864386

C₂²

yes

—

C₂×C₄⋊Dic₂₆₉

C₂²

yes

—

#22575387

—

#22575386

—

#22575384

—

C₂×M₁₆×C₂₆₉

C₂²

yes

characteristic

C₂²×C₈×C₂₆₉

C₂²

yes

characteristic

#117×C₂₆₉

C₂²

yes

characteristic

C₄⋊C₈×C₂₆₉

—

C₂²×Dic₂₆₉

—

#16864386

—

#16864386

Q₈

yes

—

C₂×#14524130

—

C₄⋊Dic₂₆₉

—

C₄⋊Dic₂₆₉

—

C₂²×C₄×C₂₆₉

C₂³

yes

characteristic

M₁₆×C₂₆₉

—

C₂×C₈×C₂₆₉

—

C₂×C₈×C₂₆₉

—

C₂×C₈×C₂₆₉

D₄

yes

—

C₄⋊C₄×C₂₆₉

D₄

yes

characteristic

C₄⋊C₄×C₂₆₉

D₄

yes

characteristic

C₂²⋊C₄×C₂₆₉

—

C₄²×C₂₆₉

—

C₂×Dic₂₆₉

—

C₂×Dic₂₆₉

—

#14524130

—

C₂³×C₂₆₉

#41

yes

characteristic

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂×C₄×C₂₆₉

C₂×Q₈

yes

—

C₂×C₄×C₂₆₉

#41

yes

—

C₈×C₂₆₉

—

C₈×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

—

C₂²×C₂₆₉

#121

yes

characteristic

C₂²×C₂₆₉

#125

yes

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

C₂²⋊Q₈

yes

—

C₄×C₂₆₉

#123

yes

characteristic

C₄×C₂₆₉

C₄⋊Q₈

yes

characteristic

Dic₂₆₉

—

C₂×C₂₆₉

—

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

C₂×C₂₆₉

yes

C₂₆₉

yes

characteristic, complemented, Sylow

#2089

—

269

maximal, Sylow

#428

—

269

—

C₂×#107

—

269

—

#424

D₂₆₉

yes

characteristic

#343

—

269

—

#341

—

269

—

C₂×M₁₆

—

269

—

C₂×M₁₆

C₂×D₂₆₉

yes

characteristic

C₂²×C₈

C₂×D₂₆₉

yes

characteristic

#117

C₂×D₂₆₉

yes

characteristic

C₂×C₄⋊C₄

—

269

—

#107

—

538

—

#107

—

538

—

#106

—

538

—

C₄⋊C₈

—

C₂²×C₄

—

538

—

C₂²×C₄

C₂²×D₂₆₉

yes

characteristic

M₁₆

—

M₁₆

—

269

—

M₁₆

—

538

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

538

—

C₂×C₈

C₂²⋊D₂₆₉

yes

—

C₄⋊C₄

—

538

—

C₄⋊C₄

—

538

—

C₄⋊C₄

D₁₀₇₆

yes

characteristic

C₄⋊C₄

D₁₀₇₆

yes

characteristic

C₂²⋊C₄

—

C₄²

—

C₂³

#16864402

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

1076

—

C₂×C₄

—

2152

—

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

characteristic

C₂×C₄

C₂×D₁₀₇₆

yes

characteristic

C₂×C₄

Q₈×D₂₆₉

yes

—

C₂×C₄

#16864401

yes

—

C₈

—

C₈

—

C₈

—

538

—

C₂²

—

100

C₂²

—

101

C₂²

#22575427

yes

characteristic

102

C₂²

#22575443

yes

—

103

C₄

—

104

C₄

—

105

C₄

—

2152

—

106

C₄

#22575433

yes

—

107

C₄

#22575434

yes

characteristic

108

C₄

#22575451

yes

characteristic

109

C₂

—

110

C₂

#31770535

yes

characteristic

111

C₂

#31770875

yes

characteristic

112

C₂

#31770880

yes

characteristic

	subgroup	G/H
center	C₂²	#22575427
commutator, cosocle	C₂²×C₄×C₂₆₉	C₂³
Frattini	C₂²×C₄	C₂²×D₂₆₉
Fitting	#424×C₂₆₉	C₂
socle	C₂²×C₂₆₉	#121
prime radical	C₂³×C₂₆₉	#41
hypercenter	#424	D₂₆₉
hypocenter	C₂₆₉	#2089
LCS	G ▷ C₂²×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

subgroup

G/H

center

C₂²

#22575427

commutator, cosocle

C₂²×C₄×C₂₆₉

C₂³

Frattini

C₂²×C₄

C₂²×D₂₆₉

Fitting

#424×C₂₆₉

C₂

C₂²×C₂₆₉

C₂³×C₂₆₉

D₂₆₉

C₂₆₉

G ▷ C₂²×C₄×C₂₆₉ ▷ C₂×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #424

N	H ≅ G/N	type
56. C₂₆₉	#2089	semidirect

H ≅ G/N

type

56. C₂₆₉

#2089

semidirect

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

subgroup	index
#31770648	2
C₂×#22575387	2
#31770373	2
#31770370	2
#424×C₂₆₉	2
#2089	269

subgroup

index

#424×C₂₆₉

269

Subgroups — #46812390

Conjugacy classes of subgroups

Complements

Maximal subgroups