Group #36441525 — subgroups

Subgroups — #36441525

Order 22784.

148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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	#26022068	C₂	1	2	yes	maximal
2	C₈₉×#2151	C₂	1	1	yes	maximal, characteristic
3	#19151419	—	2	2	no	—
4	#19151380	—	2	2	no	—
5	#19151376	C₄	1	4	yes	—
6	C₂×M₃₂×C₈₉	C₄	1	1	yes	characteristic
7	C₂²×C₁₆×C₈₉	C₄	1	1	yes	characteristic
8	#405×C₈₉	C₂²	1	1	yes	characteristic
9	C₄⋊C₁₆×C₈₉	—	2	2	no	—
10	#15667952	—	2	4	no	—
11	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
12	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
13	#117×C₈₉	Q₈	1	1	yes	characteristic
14	M₃₂×C₈₉	—	4	1	no	—
15	C₂×C₁₆×C₈₉	—	2	1	no	—
16	C₂×C₁₆×C₈₉	—	2	1	no	—
17	C₂×C₁₆×C₈₉	—	4	1	no	—
18	#97×C₈₉	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₈₉	D₄	1	2	yes	—
20	#13083549	—	4	4	no	—
21	C₂²×C₄×C₈₉	C₄⋊C₄	1	1	yes	characteristic
22	M₁₆×C₈₉	—	4	1	no	—
23	C₂×C₈×C₈₉	—	2	1	no	—
24	C₂×C₈×C₈₉	—	2	1	no	—
25	C₂×C₈×C₈₉	C₄²	1	1	yes	characteristic
26	C₂×C₈×C₈₉	C₂²⋊C₄	1	2	yes	—
27	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₄⋊C₄×C₈₉	—	2	1	no	—
29	C₂²⋊C₄×C₈₉	—	2	1	no	—
30	C₄²×C₈₉	C₄⋊C₄	1	2	yes	—
31	C₁₆×C₈₉	—	4	1	no	—
32	C₁₆×C₈₉	—	4	1	no	—
33	C₂³×C₈₉	#108	1	1	yes	characteristic
34	C₂×C₄×C₈₉	—	2	1	no	—
35	C₂×C₄×C₈₉	—	2	1	no	—
36	C₂×C₄×C₈₉	—	2	2	no	—
37	C₂×C₄×C₈₉	#95	1	1	yes	characteristic
38	C₂×C₄×C₈₉	#108	1	1	yes	characteristic
39	C₈×C₈₉	—	2	2	no	—
40	C₈×C₈₉	—	2	1	no	—
41	C₈×C₈₉	#100	1	1	yes	characteristic
42	C₈×C₈₉	#101	1	1	yes	characteristic
43	C₂²×C₈₉	—	2	1	no	—
44	C₂²×C₈₉	—	4	1	no	—
45	C₂²×C₈₉	#341	1	1	yes	characteristic
46	C₄×C₈₉	—	2	1	no	—
47	C₄×C₈₉	—	4	2	no	—
48	C₄×C₈₉	H(3,ℤ/4)	1	1	yes	characteristic
49	C₄×C₈₉	#343	1	1	yes	characteristic
50	#7240	—	89	1	no	maximal, Sylow
51	C₂×C₈₉	—	2	1	no	—
52	C₂×C₈₉	—	4	1	no	—
53	C₂×C₈₉	#1290	1	1	yes	characteristic
54	#2166	—	89	2	no	—
55	#2151	D₈₉	1	1	yes	characteristic
56	C₈₉	#7240	1	1	yes	characteristic, complemented, Sylow
57	C₂×M₃₂	Dic₈₉	1	1	yes	characteristic
58	C₂²×C₁₆	Dic₈₉	1	1	yes	characteristic
59	#405	C₂×D₈₉	1	1	yes	characteristic
60	#364	—	178	2	no	—
61	C₄⋊C₁₆	—	2	2	no	—
62	#349	—	178	2	no	—
63	#347	—	89	4	no	—
64	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
65	C₂²×C₈	C₂×Dic₈₉	1	1	yes	characteristic
66	#117	Dic₁₇₈	1	1	yes	characteristic
67	M₃₂	—	4	1	no	—
68	M₃₂	—	178	4	no	—
69	C₂×C₁₆	—	2	1	no	—
70	C₂×C₁₆	—	2	1	no	—
71	C₂×C₁₆	—	4	1	no	—
72	#97	C₄×D₈₉	1	2	yes	—
73	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
74	C₂²×C₄	C₄⋊Dic₈₉	1	1	yes	characteristic
75	M₁₆	—	4	1	no	—
76	C₂×C₈	—	2	1	no	—
77	C₂×C₈	—	2	1	no	—
78	C₂×C₈	C₄×Dic₈₉	1	1	yes	characteristic
79	C₂×C₈	#13083551	1	2	yes	—
80	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
81	C₄⋊C₄	—	2	1	no	—
82	C₂²⋊C₄	—	2	1	no	—
83	C₄²	#13083553	1	2	yes	—
84	C₁₆	—	4	1	no	—
85	C₁₆	—	4	1	no	—
86	C₁₆	—	356	4	no	—
87	C₂³	#15667948	1	1	yes	characteristic
88	C₂×C₄	—	2	1	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	#15667919	1	1	yes	characteristic
92	C₂×C₄	#15667948	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	2	2	no	—
95	C₈	#15667929	1	1	yes	characteristic
96	C₈	#15667931	1	1	yes	characteristic
97	C₂²	—	2	1	no	—
98	C₂²	—	4	1	no	—
99	C₂²	#19151363	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	4	2	no	—
102	C₄	#19151355	1	1	yes	characteristic
103	C₄	#19151367	1	1	yes	characteristic
104	C₂	—	2	1	no	—
105	C₂	—	4	1	no	—
106	C₂	#26018122	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26022068

C₂

yes

maximal

C₈₉×#2151

C₂

yes

maximal, characteristic

#19151419

—

#19151380

—

#19151376

C₄

yes

—

C₂×M₃₂×C₈₉

C₄

yes

characteristic

C₂²×C₁₆×C₈₉

C₄

yes

characteristic

#405×C₈₉

C₂²

yes

characteristic

C₄⋊C₁₆×C₈₉

—

#15667952

—

C₂×M₁₆×C₈₉

D₄

yes

characteristic

C₂²×C₈×C₈₉

C₂×C₄

yes

characteristic

#117×C₈₉

Q₈

yes

characteristic

M₃₂×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

—

C₂×C₁₆×C₈₉

—

#97×C₈₉

C₂×C₄

yes

—

C₄×C₈×C₈₉

D₄

yes

—

#13083549

—

C₂²×C₄×C₈₉

C₄⋊C₄

yes

characteristic

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₄²

yes

characteristic

C₂×C₈×C₈₉

C₂²⋊C₄

yes

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₈₉

—

C₂²⋊C₄×C₈₉

—

C₄²×C₈₉

C₄⋊C₄

yes

—

C₁₆×C₈₉

—

C₁₆×C₈₉

—

C₂³×C₈₉

#108

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#341

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

—

D₈₉

yes

characteristic

C₈₉

#7240

yes

characteristic, complemented, Sylow

C₂×M₃₂

Dic₈₉

yes

characteristic

C₂²×C₁₆

Dic₈₉

yes

characteristic

#405

C₂×D₈₉

yes

characteristic

#364

—

178

—

C₄⋊C₁₆

—

#349

—

178

—

#347

—

C₂×M₁₆

D₃₅₆

yes

characteristic

C₂²×C₈

C₂×Dic₈₉

yes

characteristic

#117

Dic₁₇₈

yes

characteristic

M₃₂

—

M₃₂

—

178

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

#97

C₄×D₈₉

yes

—

C₄×C₈

C₂²⋊D₈₉

yes

—

C₂²×C₄

C₄⋊Dic₈₉

yes

characteristic

M₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×Dic₈₉

yes

characteristic

C₂×C₈

#13083551

yes

—

C₂×C₈

C₂²⋊Dic₈₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

#13083553

yes

—

C₁₆

—

C₁₆

—

C₁₆

—

356

—

C₂³

#15667948

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

—

C₂²

—

C₂²

#19151363

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

#19151355

yes

characteristic

103

C₄

#19151367

yes

characteristic

104

C₂

—

105

C₂

—

106

C₂

#26018122

yes

characteristic

	subgroup	G/H
center	C₄	#19151355
commutator	C₂×C₈×C₈₉	C₄²
Frattini	#405	C₂×D₈₉
Fitting	C₈₉×#2151	C₂
socle	C₂×C₈₉	#1290
prime radical	C₂³×C₈₉	#108
cosocle	#405×C₈₉	C₂²
hypercenter	#2151	D₈₉
hypocenter	C₈₉	#7240
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2151

subgroup

G/H

center

C₄

#19151355

commutator

C₂×C₈×C₈₉

C₄²

Frattini

#405

C₂×D₈₉

Fitting

C₈₉×#2151

C₂

C₂×C₈₉

C₂³×C₈₉

#405×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₄ ◁ C₂×C₈ ◁ #2151

N	H ≅ G/N	type
56. C₈₉	#7240	semidirect

H ≅ G/N

type

56. C₈₉

#7240

semidirect

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

subgroup	index
#26022068	2
C₈₉×#2151	2
#7240	89

subgroup

index

#26022068

C₈₉×#2151

#7240

Subgroups — #36441525

Conjugacy classes of subgroups

Complements

Maximal subgroups