Group #46810213 — subgroups

Subgroups — #46810213

Order 34432.

172 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 49 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	#31771015	C₂	1	2	yes	maximal
2	#31770975	C₂	1	1	yes	maximal, characteristic
3	#31770347	C₂	1	2	yes	maximal
4	#31770347	C₂	1	1	yes	maximal, characteristic
5	#564×C₂₆₉	C₂	1	1	yes	maximal, characteristic
6	#22575453	C₂²	1	1	yes	characteristic
7	#22575386	—	2	2	no	—
8	#22575384	—	2	2	no	—
9	#22575376	—	2	2	no	—
10	#22575364	C₂²	1	1	yes	characteristic
11	#22575364	C₂²	1	2	yes	—
12	#125×C₂₆₉	—	2	2	no	—
13	#125×C₂₆₉	—	2	2	no	—
14	#125×C₂₆₉	—	2	2	no	—
15	#125×C₂₆₉	C₂²	1	1	yes	characteristic
16	#125×C₂₆₉	C₂²	1	2	yes	—
17	C₂×Dic₅₃₈	—	2	1	no	—
18	C₂×#14524130	—	2	2	no	—
19	C₂×#14524130	—	2	1	no	—
20	C₄⋊Dic₂₆₉	—	2	2	no	—
21	C₄⋊C₄×C₂₆₉	—	2	2	no	—
22	C₄⋊C₄×C₂₆₉	—	2	2	no	—
23	C₄⋊C₄×C₂₆₉	—	2	2	no	—
24	C₄⋊C₄×C₂₆₉	—	2	2	no	—
25	C₄⋊C₄×C₂₆₉	—	2	2	no	—
26	C₄⋊C₄×C₂₆₉	—	2	2	no	—
27	C₄⋊C₄×C₂₆₉	D₄	1	2	yes	—
28	C₄⋊C₄×C₂₆₉	D₄	1	2	yes	—
29	C₄⋊C₄×C₂₆₉	D₄	1	2	yes	—
30	C₄²×C₂₆₉	—	2	2	no	—
31	C₄²×C₂₆₉	C₂³	1	1	yes	characteristic
32	Dic₅₃₈	—	4	2	no	—
33	C₂×Dic₂₆₉	—	4	1	no	—
34	#14524130	—	2	4	no	—
35	#14524130	—	4	1	no	—
36	C₂×C₄×C₂₆₉	—	2	2	no	—
37	C₂×C₄×C₂₆₉	—	2	2	no	—
38	C₂×C₄×C₂₆₉	—	2	2	no	—
39	C₂×C₄×C₂₆₉	C₂×D₄	1	2	yes	—
40	C₂×C₄×C₂₆₉	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₂₆₉	#120	1	1	yes	characteristic
42	C₄×C₂₆₉	—	2	1	no	—
43	C₄×C₂₆₉	—	2	2	no	—
44	C₄×C₂₆₉	—	4	2	no	—
45	C₄×C₂₆₉	—	4	2	no	—
46	C₄×C₂₆₉	—	4	2	no	—
47	Dic₂₆₉	—	8	1	no	—
48	C₂×C₂₆₉	#454	1	1	yes	characteristic
49	C₂×C₂₆₉	#456	1	2	yes	—
50	C₂₆₉	#1663	1	1	yes	characteristic, complemented, Sylow
51	#1663	—	269	1	no	maximal, Sylow
52	#564	D₂₆₉	1	1	yes	characteristic
53	#501	—	269	2	no	—
54	#491	—	269	1	no	—
55	#330	—	269	2	no	—
56	#330	—	269	1	no	—
57	C₄⋊Q₈	—	269	1	no	—
58	#125	—	2	2	no	—
59	#125	—	2	2	no	—
60	#125	—	2	2	no	—
61	#125	C₂×D₂₆₉	1	1	yes	characteristic
62	#125	C₂×D₂₆₉	1	2	yes	—
63	#107	—	538	2	no	—
64	#106	—	538	2	no	—
65	#103	—	538	2	no	—
66	#97	—	269	1	no	—
67	#97	—	269	2	no	—
68	C₂×Q₈	—	538	1	no	—
69	C₂×C₈	—	538	2	no	—
70	C₂×C₈	—	538	1	no	—
71	C₄⋊C₄	—	2	2	no	—
72	C₄⋊C₄	—	2	2	no	—
73	C₄⋊C₄	—	2	2	no	—
74	C₄⋊C₄	—	2	2	no	—
75	C₄⋊C₄	—	2	2	no	—
76	C₄⋊C₄	—	2	2	no	—
77	C₄⋊C₄	—	538	2	no	—
78	C₄⋊C₄	C₂²⋊D₂₆₉	1	2	yes	—
79	C₄⋊C₄	C₂²⋊D₂₆₉	1	2	yes	—
80	C₄⋊C₄	C₂²⋊D₂₆₉	1	2	yes	—
81	C₄²	—	2	2	no	—
82	C₄²	C₂²×D₂₆₉	1	1	yes	characteristic
83	Q₈	—	1076	2	no	—
84	C₂×C₄	—	2	2	no	—
85	C₂×C₄	—	2	2	no	—
86	C₂×C₄	—	2	2	no	—
87	C₂×C₄	—	1076	1	no	—
88	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	2	yes	—
89	C₂×C₄	C₂×C₂²⋊D₂₆₉	1	1	yes	characteristic
90	C₈	—	538	4	no	—
91	C₈	—	1076	1	no	—
92	C₂²	#22575422	1	1	yes	characteristic
93	C₄	—	2	1	no	—
94	C₄	—	2	2	no	—
95	C₄	—	4	2	no	—
96	C₄	—	4	2	no	—
97	C₄	—	4	2	no	—
98	C₄	—	2152	1	no	—
99	C₂	#31770778	1	1	yes	characteristic
100	C₂	#31770788	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#31771015

C₂

yes

maximal

#31770975

C₂

yes

maximal, characteristic

#31770347

C₂

yes

maximal

#31770347

C₂

yes

maximal, characteristic

#564×C₂₆₉

C₂

yes

maximal, characteristic

#22575453

C₂²

yes

—

—

—

C₂²

yes

characteristic

#22575364

C₂²

yes

—

#125×C₂₆₉

—

#125×C₂₆₉

—

#125×C₂₆₉

—

#125×C₂₆₉

C₂²

yes

characteristic

#125×C₂₆₉

C₂²

yes

—

C₂×Dic₅₃₈

—

C₂×#14524130

—

C₂×#14524130

—

C₄⋊Dic₂₆₉

—

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

—

C₄⋊C₄×C₂₆₉

D₄

yes

—

C₄⋊C₄×C₂₆₉

D₄

yes

—

C₄⋊C₄×C₂₆₉

D₄

yes

—

C₄²×C₂₆₉

—

C₄²×C₂₆₉

C₂³

yes

characteristic

Dic₅₃₈

—

C₂×Dic₂₆₉

—

#14524130

—

#14524130

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

—

C₂×C₄×C₂₆₉

C₂×D₄

yes

characteristic

C₂²×C₂₆₉

#120

yes

characteristic

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

C₄×C₂₆₉

—

Dic₂₆₉

—

C₂×C₂₆₉

#454

yes

characteristic

C₂×C₂₆₉

#456

yes

—

C₂₆₉

#1663

yes

characteristic, complemented, Sylow

#1663

—

269

maximal, Sylow

#564

D₂₆₉

yes

characteristic

#501

—

269

—

#491

—

269

—

#330

—

269

—

#330

—

269

—

C₄⋊Q₈

—

269

—

—

—

—

C₂×D₂₆₉

yes

characteristic

#125

C₂×D₂₆₉

yes

—

#107

—

538

—

#106

—

538

—

#103

—

538

—

#97

—

269

—

#97

—

269

—

C₂×Q₈

—

538

—

C₂×C₈

—

538

—

C₂×C₈

—

538

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

538

—

C₄⋊C₄

C₂²⋊D₂₆₉

yes

—

C₄⋊C₄

C₂²⋊D₂₆₉

yes

—

C₄⋊C₄

C₂²⋊D₂₆₉

yes

—

C₄²

—

C₄²

C₂²×D₂₆₉

yes

characteristic

Q₈

—

1076

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

1076

—

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

—

C₂×C₄

C₂×C₂²⋊D₂₆₉

yes

characteristic

C₈

—

538

—

C₈

—

1076

—

C₂²

#22575422

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

C₄

—

2152

—

C₂

#31770778

yes

characteristic

100

C₂

#31770788

yes

—

	subgroup	G/H
center	C₂²	#22575422
commutator, cosocle	C₄²×C₂₆₉	C₂³
Frattini	C₄²	C₂²×D₂₆₉
Fitting	#564×C₂₆₉	C₂
socle, prime radical	C₂²×C₂₆₉	#120
hypercenter	#564	D₂₆₉
hypocenter	C₂₆₉	#1663
LCS	G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #564

subgroup

G/H

center

C₂²

#22575422

commutator, cosocle

C₄²×C₂₆₉

C₂³

Frattini

C₄²

C₂²×D₂₆₉

Fitting

#564×C₂₆₉

C₂

C₂²×C₂₆₉

D₂₆₉

C₂₆₉

G ▷ C₄²×C₂₆₉ ▷ C₂²×C₂₆₉ ▷ C₂₆₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #564

N	H ≅ G/N	type
50. C₂₆₉	#1663	semidirect

H ≅ G/N

type

50. C₂₆₉

#1663

semidirect

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

subgroup	index
#31771015	2
#31770975	2
#31770347	2
#564×C₂₆₉	2
#1663	269

subgroup

index

#564×C₂₆₉

269

Subgroups — #46810213

Conjugacy classes of subgroups

Complements

Maximal subgroups