Group #36585415 — subgroups

Subgroups — #2104×D₈₉ #36585415

Order 22784.

822 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 822 conjugacy classes of subgroups — too many to draw. Only its 167 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	C₈₉⋊#2104	C₂	1	7	yes	maximal, complemented
2	#342×D₈₉	C₂	1	7	yes	maximal
3	C₈₉×#2104	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂²⋊C₄×D₈₉	C₂²	1	7	yes	—
5	#19151365	C₂²	1	7	yes	—
6	#19151364	C₂²	1	14	yes	—
7	#342×C₈₉	C₂²	1	7	yes	—
8	C₂⁴×D₈₉	C₂³	1	1	yes	characteristic
9	C₂²×C₄×D₈₉	—	2	7	no	—
10	C₂×C₂²⋊Dic₈₉	C₂³	1	7	yes	—
11	C₂×#13083551	—	2	7	no	—
12	C₂²⋊C₄×D₈₉	—	2	14	no	—
13	C₂²⋊C₄×D₈₉	—	2	14	no	—
14	C₂×C₂²⋊C₄×C₈₉	C₂³	1	7	yes	—
15	C₂³×D₈₉	—	8	2	no	—
16	C₂³×D₈₉	#41	1	7	yes	—
17	C₂³×D₈₉	#41	1	7	yes	—
18	C₂²×Dic₈₉	—	2	7	no	—
19	C₂×C₄×D₈₉	—	4	7	no	—
20	C₂×C₄×D₈₉	—	4	7	no	—
21	C₂×C₄×D₈₉	—	8	14	no	—
22	C₂²⋊Dic₈₉	—	2	14	no	—
23	#13083551	—	4	14	no	—
24	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
25	C₂²×C₄×C₈₉	—	2	7	no	—
26	C₂²⋊C₄×C₈₉	—	2	14	no	—
27	C₂³×C₈₉	—	8	1	no	—
28	C₂³×C₈₉	C₂×#41	1	7	yes	—
29	C₂²×D₈₉	—	4	14	no	—
30	C₂²×D₈₉	—	8	7	no	—
31	C₂²×D₈₉	#126	1	7	yes	—
32	C₂²×D₈₉	#126	1	14	yes	—
33	C₂²×D₈₉	#126	1	7	yes	—
34	C₂×C₄×C₈₉	—	4	7	no	—
35	C₂×C₄×C₈₉	—	8	7	no	—
36	C₂×Dic₈₉	—	4	7	no	—
37	C₂×Dic₈₉	—	8	7	no	—
38	C₄×D₈₉	—	8	14	no	—
39	C₄×D₈₉	—	8	14	no	—
40	C₂²×C₈₉	—	4	7	no	—
41	C₂²×C₈₉	C₂×#126	1	7	yes	—
42	C₂×D₈₉	—	2	14	no	—
43	C₂×D₈₉	—	4	7	no	—
44	C₂×D₈₉	—	4	14	no	—
45	C₂×D₈₉	#401	1	7	yes	—
46	C₂×D₈₉	#401	1	1	yes	characteristic
47	C₄×C₈₉	—	8	7	no	—
48	Dic₈₉	—	8	7	no	—
49	C₂×#2104	—	89	1	no	maximal, Sylow
50	C₂×C₈₉	—	2	7	no	—
51	C₂×C₈₉	C₂×#401	1	1	yes	characteristic
52	D₈₉	—	2	7	no	—
53	D₈₉	#2104	1	2	yes	direct product factor
54	#2104	—	89	7	no	—
55	#2104	D₈₉	1	1	yes	characteristic, direct product factor
56	C₂×#342	—	89	7	no	—
57	C₈₉	C₂×#2104	1	1	yes	characteristic, complemented, Sylow
58	C₂²×C₂²⋊C₄	—	89	7	no	—
59	#342	—	89	14	no	—
60	#342	—	89	7	no	—
61	#342	C₂×D₈₉	1	7	yes	—
62	C₂⁵	—	89	1	no	—
63	C₂³×C₄	—	178	7	no	—
64	C₂×C₂²⋊C₄	—	89	7	no	—
65	C₂×C₂²⋊C₄	—	178	14	no	—
66	C₂×C₂²⋊C₄	—	178	14	no	—
67	C₂×C₂²⋊C₄	—	178	7	no	—
68	C₂×C₂²⋊C₄	C₂²×D₈₉	1	7	yes	—
69	C₂⁴	—	89	7	no	—
70	C₂⁴	—	89	7	no	—
71	C₂⁴	—	712	2	no	—
72	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
73	C₂²×C₄	—	2	7	no	—
74	C₂²×C₄	—	356	7	no	—
75	C₂²×C₄	—	356	7	no	—
76	C₂²×C₄	—	178	7	no	—
77	C₂²×C₄	—	712	14	no	—
78	C₂²⋊C₄	—	2	14	no	—
79	C₂²⋊C₄	—	356	14	no	—
80	C₂²⋊C₄	—	178	14	no	—
81	C₂³	—	8	1	no	—
82	C₂³	—	89	14	no	—
83	C₂³	—	89	7	no	—
84	C₂³	—	89	7	no	—
85	C₂³	—	356	14	no	—
86	C₂³	—	712	7	no	—
87	C₂³	#41×D₈₉	1	7	yes	—
88	C₂×C₄	—	4	7	no	—
89	C₂×C₄	—	8	7	no	—
90	C₂×C₄	—	356	7	no	—
91	C₂×C₄	—	712	14	no	—
92	C₂×C₄	—	712	14	no	—
93	C₂×C₄	—	712	7	no	—
94	C₂²	—	4	7	no	—
95	C₂²	—	89	1	no	—
96	C₂²	—	89	7	no	—
97	C₂²	—	356	7	no	—
98	C₂²	—	356	14	no	—
99	C₂²	—	178	14	no	—
100	C₂²	#126×D₈₉	1	7	yes	—
101	C₄	—	8	7	no	—
102	C₄	—	712	7	no	—
103	C₂	—	2	7	no	—
104	C₂	—	89	2	no	—
105	C₂	—	178	7	no	—
106	C₂	#401×D₈₉	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₈₉⋊#2104

C₂

yes

maximal, complemented

#342×D₈₉

C₂

yes

maximal

C₈₉×#2104

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊C₄×D₈₉

C₂²

yes

—

#19151365

C₂²

yes

—

#19151364

C₂²

yes

—

#342×C₈₉

C₂²

yes

—

C₂⁴×D₈₉

C₂³

yes

characteristic

C₂²×C₄×D₈₉

—

C₂×C₂²⋊Dic₈₉

C₂³

yes

—

C₂×#13083551

—

C₂²⋊C₄×D₈₉

—

C₂²⋊C₄×D₈₉

—

C₂×C₂²⋊C₄×C₈₉

C₂³

yes

—

C₂³×D₈₉

—

C₂³×D₈₉

#41

yes

—

C₂³×D₈₉

#41

yes

—

C₂²×Dic₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂²⋊Dic₈₉

—

#13083551

—

C₂⁴×C₈₉

C₂⁴

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₂³×C₈₉

—

C₂³×C₈₉

C₂×#41

yes

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

#126

yes

—

C₂²×D₈₉

#126

yes

—

C₂²×D₈₉

#126

yes

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

C₂×#126

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

—

C₂×D₈₉

#401

yes

—

C₂×D₈₉

#401

yes

characteristic

C₄×C₈₉

—

Dic₈₉

—

C₂×#2104

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

C₂×#401

yes

characteristic

D₈₉

—

D₈₉

#2104

yes

direct product factor

#2104

—

#2104

D₈₉

yes

characteristic, direct product factor

C₂×#342

—

C₈₉

C₂×#2104

yes

characteristic, complemented, Sylow

C₂²×C₂²⋊C₄

—

#342

—

#342

—

#342

C₂×D₈₉

yes

—

C₂⁵

—

C₂³×C₄

—

178

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

178

—

C₂×C₂²⋊C₄

—

178

—

C₂×C₂²⋊C₄

—

178

—

C₂×C₂²⋊C₄

C₂²×D₈₉

yes

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

712

—

C₂⁴

C₂³×D₈₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

356

—

C₂²×C₄

—

356

—

C₂²×C₄

—

178

—

C₂²×C₄

—

712

—

C₂²⋊C₄

—

C₂²⋊C₄

—

356

—

C₂²⋊C₄

—

178

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

356

—

C₂³

—

712

—

C₂³

#41×D₈₉

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

356

—

C₂×C₄

—

712

—

C₂×C₄

—

712

—

C₂×C₄

—

712

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

356

—

C₂²

—

356

—

C₂²

—

178

—

100

C₂²

#126×D₈₉

yes

—

101

C₄

—

102

C₄

—

712

—

103

C₂

—

104

C₂

—

105

C₂

—

178

—

106

C₂

#401×D₈₉

yes

characteristic

	subgroup	G/H
center	C₂	#401×D₈₉
commutator, cosocle	C₂⁴×C₈₉	C₂⁴
Frattini	C₂⁴	C₂³×D₈₉
Fitting	C₈₉×#2104	C₂
socle	C₂×C₈₉	C₂×#401
prime radical	C₂⁴×D₈₉	C₂³
hypercenter	#2104	D₈₉
hypocenter	C₈₉	C₂×#2104
LCS	G ▷ C₂⁴×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ #2104

subgroup

G/H

center

C₂

#401×D₈₉

commutator, cosocle

C₂⁴×C₈₉

C₂⁴

Frattini

C₂⁴

C₂³×D₈₉

Fitting

C₈₉×#2104

C₂

socle

C₂×C₈₉

C₂×#401

prime radical

C₂⁴×D₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂⁴×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂ ◁ C₂⁴ ◁ #2104

N	H ≅ G/N	type
1. C₈₉⋊#2104	C₂	semidirect
3. C₈₉×#2104	C₂	semidirect
53. D₈₉	#2104	direct (N × H)
55. #2104	D₈₉	direct (N × H)
57. C₈₉	C₂×#2104	semidirect

H ≅ G/N

type

1. C₈₉⋊#2104

C₂

semidirect

3. C₈₉×#2104

C₂

semidirect

53. D₈₉

#2104

direct (N × H)

55. #2104

D₈₉

direct (N × H)

57. C₈₉

C₂×#2104

semidirect

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

subgroup	index
C₈₉⋊#2104	2
#342×D₈₉	2
C₈₉×#2104	2
C₂×#2104	89

subgroup

index

C₈₉⋊#2104

#342×D₈₉

C₈₉×#2104

C₂×#2104

Subgroups — #2104×D₈₉ #36585415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2104×D89 #36585415

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2104×D₈₉ #36585415