Group #36444864 — subgroups

Subgroups — #36444864

Order 22784.

478 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 203 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	C₄×#15667922	C₂	1	3	yes	maximal
2	#26018079	C₂	1	3	yes	maximal
3	C₈₉×#1273	C₂	1	1	yes	maximal, characteristic
4	C₂×#15667922	C₄	1	6	yes	—
5	C₂×#15667922	C₄	1	6	yes	—
6	C₂×C₄×#10623494	C₂²	1	3	yes	—
7	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₈₉	C₂²	1	3	yes	—
9	C₂²×#10623494	C₂×C₄	1	6	yes	—
10	C₂×C₄×Dic₈₉	C₂×C₄	1	3	yes	—
11	C₂×C₄×Dic₈₉	C₂×C₄	1	3	yes	—
12	#15667922	—	2	12	no	—
13	#15667922	—	2	12	no	—
14	C₄×#10623494	—	2	3	no	—
15	C₄×#10623494	—	2	3	no	—
16	C₂²×C₈×C₈₉	C₂×C₄	1	6	yes	—
17	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
18	C₄×C₈×C₈₉	—	2	6	no	—
19	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
20	C₂²×Dic₈₉	C₄²	1	3	yes	—
21	C₂×#10623494	—	2	6	no	—
22	C₂×#10623494	—	2	6	no	—
23	C₂×#10623494	M₁₆	1	12	yes	—
24	C₄×Dic₈₉	—	2	6	no	—
25	C₄×Dic₈₉	—	2	6	no	—
26	C₂²×C₄×C₈₉	C₂²×C₄	1	3	yes	—
27	C₂×C₈×C₈₉	—	2	6	no	—
28	C₂×C₈×C₈₉	—	2	6	no	—
29	C₂×C₈×C₈₉	M₁₆	1	12	yes	—
30	C₄²×C₈₉	#41	1	3	yes	—
31	C₄²×C₈₉	#41	1	1	yes	characteristic
32	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
33	C₂×C₄×C₈₉	#117	1	3	yes	—
34	C₂×C₄×C₈₉	#117	1	3	yes	—
35	C₂×C₄×C₈₉	C₂×M₁₆	1	6	yes	—
36	C₂×C₄×C₈₉	C₂×M₁₆	1	6	yes	—
37	C₂×Dic₈₉	—	2	3	no	—
38	C₂×Dic₈₉	—	2	3	no	—
39	C₂×Dic₈₉	—	2	6	no	—
40	C₈×C₈₉	—	2	12	no	—
41	#10623494	—	2	12	no	—
42	C₂²×C₈₉	#376	1	1	yes	characteristic
43	C₂²×C₈₉	C₄×M₁₆	1	3	yes	—
44	C₂²×C₈₉	C₄×M₁₆	1	3	yes	—
45	C₄×C₈₉	#432	1	6	yes	—
46	C₄×C₈₉	#432	1	6	yes	—
47	Dic₈₉	—	4	1	no	—
48	Dic₈₉	—	4	3	no	—
49	#8136	—	89	1	no	maximal, Sylow
50	C₂×C₈₉	#1455	1	1	yes	characteristic
51	C₂×C₈₉	#1455	1	3	yes	—
52	C₂×C₈₉	#1745	1	3	yes	—
53	C₄×#97	—	89	3	no	—
54	#1273	—	89	3	no	—
55	#1273	D₈₉	1	1	yes	characteristic
56	C₈₉	#8136	1	1	yes	characteristic, complemented, Sylow
57	C₂×#97	—	89	6	no	—
58	C₂×#97	—	89	6	no	—
59	C₂×C₄×C₈	—	89	3	no	—
60	C₂×C₄×C₈	C₂×D₈₉	1	3	yes	—
61	C₄³	—	89	1	no	—
62	C₂²×C₈	—	89	6	no	—
63	C₂²×C₈	C₄×D₈₉	1	6	yes	—
64	C₂×C₄²	—	89	3	no	—
65	C₂×C₄²	—	89	3	no	—
66	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
67	#97	—	178	12	no	—
68	#97	—	178	12	no	—
69	C₄×C₈	—	2	6	no	—
70	C₄×C₈	—	178	3	no	—
71	C₄×C₈	—	178	3	no	—
72	C₂²×C₄	—	89	1	no	—
73	C₂²×C₄	—	89	3	no	—
74	C₂²×C₄	C₂×C₄×D₈₉	1	3	yes	—
75	C₂×C₈	—	2	6	no	—
76	C₂×C₈	—	2	6	no	—
77	C₂×C₈	—	89	12	no	—
78	C₂×C₈	—	178	6	no	—
79	C₂×C₈	—	178	6	no	—
80	C₂×C₈	#13083557	1	12	yes	—
81	C₄²	—	178	6	no	—
82	C₄²	—	178	6	no	—
83	C₄²	#13083573	1	3	yes	—
84	C₄²	#13083575	1	1	yes	characteristic
85	C₂³	C₄²×D₈₉	1	1	yes	characteristic
86	C₂×C₄	—	178	3	no	—
87	C₂×C₄	—	178	3	no	—
88	C₂×C₄	—	178	6	no	—
89	C₂×C₄	#15667968	1	3	yes	—
90	C₂×C₄	#15667970	1	3	yes	—
91	C₂×C₄	M₁₆×D₈₉	1	6	yes	—
92	C₂×C₄	C₂×#13083557	1	6	yes	—
93	C₈	—	2	12	no	—
94	C₈	—	178	12	no	—
95	C₂²	#19151443	1	1	yes	characteristic
96	C₂²	C₄×#13083557	1	3	yes	—
97	C₂²	#19151550	1	3	yes	—
98	C₄	—	356	1	no	—
99	C₄	—	356	3	no	—
100	C₄	#19151652	1	6	yes	—
101	C₄	#19151654	1	6	yes	—
102	C₂	#26018554	1	1	yes	characteristic
103	C₂	#26018556	1	3	yes	—
104	C₂	#26019999	1	3	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×#15667922

C₂

yes

maximal

#26018079

C₂

yes

maximal

C₈₉×#1273

C₂

yes

maximal, characteristic

C₂×#15667922

C₄

yes

—

C₂×#15667922

C₄

yes

—

C₂×C₄×#10623494

C₂²

yes

—

C₄²×Dic₈₉

C₂²

yes

characteristic

C₂×C₄×C₈×C₈₉

C₂²

yes

—

C₂²×#10623494

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

C₂×C₄×Dic₈₉

C₂×C₄

yes

—

—

—

—

—

C₂²×C₈×C₈₉

C₂×C₄

yes

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₂²×Dic₈₉

C₄²

yes

characteristic

C₂²×Dic₈₉

C₄²

yes

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

M₁₆

yes

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂²×C₄

yes

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

M₁₆

yes

—

C₄²×C₈₉

#41

yes

—

C₄²×C₈₉

#41

yes

characteristic

C₂³×C₈₉

C₂×C₄²

yes

characteristic

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

#117

yes

—

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂×C₄×C₈₉

C₂×M₁₆

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

#376

yes

characteristic

C₂²×C₈₉

C₄×M₁₆

yes

—

C₂²×C₈₉

C₄×M₁₆

yes

—

C₄×C₈₉

#432

yes

—

C₄×C₈₉

#432

yes

—

Dic₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₂×C₈₉

#1745

yes

—

C₄×#97

—

#1273

—

#1273

D₈₉

yes

characteristic

C₈₉

#8136

yes

characteristic, complemented, Sylow

C₂×#97

—

C₂×#97

—

C₂×C₄×C₈

—

C₂×C₄×C₈

C₂×D₈₉

yes

—

C₄³

—

C₂²×C₈

—

C₂²×C₈

C₄×D₈₉

yes

—

C₂×C₄²

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

characteristic

#97

—

178

—

#97

—

178

—

C₄×C₈

—

C₄×C₈

—

178

—

C₄×C₈

—

178

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×C₄×D₈₉

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

178

—

C₂×C₈

—

178

—

C₂×C₈

#13083557

yes

—

C₄²

—

178

—

C₄²

—

178

—

C₄²

#13083573

yes

—

C₄²

#13083575

yes

characteristic

C₂³

C₄²×D₈₉

yes

characteristic

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

#15667968

yes

—

C₂×C₄

#15667970

yes

—

C₂×C₄

M₁₆×D₈₉

yes

—

C₂×C₄

C₂×#13083557

yes

—

C₈

—

C₈

—

178

—

C₂²

#19151443

yes

characteristic

C₂²

C₄×#13083557

yes

—

C₂²

#19151550

yes

—

C₄

—

356

—

C₄

—

356

—

100

C₄

#19151652

yes

—

101

C₄

#19151654

yes

—

102

C₂

#26018554

yes

characteristic

103

C₂

#26018556

yes

—

104

C₂

#26019999

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂×C₄²
Fitting	C₈₉×#1273	C₂
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1273	D₈₉
hypocenter	C₈₉	#8136
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄² ◁ #1273

subgroup

G/H

center, Frattini

C₂×C₄²

C₂²×D₈₉

commutator, socle, prime radical

C₂³×C₈₉

C₂×C₄²

Fitting

C₈₉×#1273

C₂

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂×C₄² ◁ #1273

N	H ≅ G/N	type
56. C₈₉	#8136	semidirect

H ≅ G/N

type

56. C₈₉

#8136

semidirect

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

subgroup	index
C₄×#15667922	2
#26018079	2
C₈₉×#1273	2
#8136	89

subgroup

index

C₄×#15667922

#26018079

C₈₉×#1273

#8136

Subgroups — #36444864

Conjugacy classes of subgroups

Complements

Maximal subgroups