Group #36441909 — subgroups

Subgroups — #36441909

Order 22784.

110 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 53 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	#26022160	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#15667918	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1397	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₁₇₈	C₄	1	1	yes	characteristic
5	C₂×#15667918	—	2	1	no	—
6	C₄⋊#13083549	C₄	1	1	yes	characteristic
7	#19151416	—	2	1	no	—
8	#19151373	—	2	1	no	—
9	C₂×C₃₂×C₈₉	—	2	1	no	—
10	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
11	C₄×Dic₁₇₈	C₈	1	1	yes	characteristic
12	C₂×#13083549	—	2	1	no	—
13	C₄⋊#10623494	C₈	1	1	yes	characteristic
14	#15667941	—	2	1	no	—
15	C₈×Dic₈₉	—	2	1	no	—
16	#15667918	—	4	1	no	—
17	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
18	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
19	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
20	C₃₂×C₈₉	—	2	2	no	—
21	C₂×Dic₁₇₈	C₁₆	1	1	yes	characteristic
22	C₂×#10623494	—	2	1	no	—
23	C₄⋊Dic₈₉	C₁₆	1	1	yes	characteristic
24	#13083553	—	2	1	no	—
25	C₄×Dic₈₉	—	2	1	no	—
26	#13083549	—	4	1	no	—
27	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₈₉	M₁₆	1	1	yes	characteristic
29	C₄²×C₈₉	C₂×C₈	1	1	yes	characteristic
30	C₁₆×C₈₉	—	2	1	no	—
31	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
32	C₁₆×C₈₉	Q₁₆	1	1	yes	characteristic
33	C₂×C₄×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
35	C₂×C₄×C₈₉	M₃₂	1	1	yes	characteristic
36	C₂×Dic₈₉	—	2	1	no	—
37	C₂×Dic₈₉	—	2	1	no	—
38	Dic₁₇₈	—	4	1	no	—
39	C₈×C₈₉	—	2	1	no	—
40	C₈×C₈₉	#103	1	1	yes	characteristic
41	C₈×C₈₉	#104	1	1	yes	characteristic
42	#10623494	—	4	1	no	—
43	C₂²×C₈₉	C₂²⋊C₁₆	1	1	yes	characteristic
44	C₄×C₈₉	—	2	1	no	—
45	C₄×C₈₉	—	2	1	no	—
46	C₄×C₈₉	Q₈⋊C₈	1	1	yes	characteristic
47	C₄×C₈₉	#350	1	1	yes	characteristic
48	Dic₈₉	—	4	1	no	—
49	Dic₈₉	—	4	1	no	—
50	#7393	—	89	1	no	maximal, Sylow
51	C₂×C₈₉	Q₈⋊C₁₆	1	1	yes	characteristic
52	C₂×C₈₉	#1400	1	1	yes	characteristic
53	C₂×C₈₉	#1401	1	1	yes	characteristic
54	#2183	—	89	1	no	—
55	C₄⋊C₃₂	—	89	1	no	—
56	#1397	D₈₉	1	1	yes	characteristic
57	C₈₉	#7393	1	1	yes	characteristic, complemented, Sylow
58	C₈×Q₈	—	89	1	no	—
59	C₂×C₃₂	—	2	1	no	—
60	C₂×C₃₂	—	178	1	no	—
61	C₄⋊C₁₆	—	89	1	no	—
62	C₄⋊C₁₆	—	178	1	no	—
63	#346	—	178	1	no	—
64	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
65	C₄×Q₈	—	89	1	no	—
66	C₂×C₁₆	—	178	1	no	—
67	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
68	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
69	C₄⋊C₈	—	89	1	no	—
70	C₄⋊C₈	—	178	1	no	—
71	C₄×C₈	—	178	1	no	—
72	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
73	C₃₂	—	2	2	no	—
74	C₃₂	—	356	1	no	—
75	C₂×Q₈	—	89	1	no	—
76	C₂×C₈	—	178	1	no	—
77	C₂×C₈	#13083551	1	1	yes	characteristic
78	C₂×C₈	#13083557	1	1	yes	characteristic
79	C₄⋊C₄	—	89	1	no	—
80	C₄⋊C₄	—	178	1	no	—
81	C₄²	—	178	1	no	—
82	C₄²	C₈×D₈₉	1	1	yes	characteristic
83	C₁₆	—	2	1	no	—
84	C₁₆	—	356	1	no	—
85	C₁₆	#13083563	1	1	yes	characteristic
86	C₁₆	Dic₃₅₆	1	1	yes	characteristic
87	Q₈	—	356	1	no	—
88	C₂×C₄	—	178	1	no	—
89	C₂×C₄	—	178	1	no	—
90	C₂×C₄	#15667924	1	1	yes	characteristic
91	C₂×C₄	C₁₆×D₈₉	1	1	yes	characteristic
92	C₂×C₄	#15667951	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	356	1	no	—
95	C₈	#15667937	1	1	yes	characteristic
96	C₈	#15667940	1	1	yes	characteristic
97	C₂²	#19151377	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	2	1	no	—
100	C₄	—	356	1	no	—
101	C₄	—	356	1	no	—
102	C₄	#19151330	1	1	yes	characteristic
103	C₄	#19151381	1	1	yes	characteristic
104	C₂	#26018232	1	1	yes	characteristic
105	C₂	#26018391	1	1	yes	characteristic
106	C₂	#26018395	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26022160

C₂

yes

maximal, characteristic

C₄⋊#15667918

C₂

yes

maximal, characteristic

C₈₉×#1397

C₂

yes

maximal, characteristic

C₈×Dic₁₇₈

C₄

yes

characteristic

C₂×#15667918

—

C₄⋊#13083549

C₄

yes

characteristic

#19151416

—

#19151373

—

C₂×C₃₂×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

C₄×Dic₁₇₈

C₈

yes

characteristic

C₂×#13083549

—

C₄⋊#10623494

C₈

yes

characteristic

#15667941

—

C₈×Dic₈₉

—

#15667918

—

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

C₂×C₄

yes

characteristic

C₃₂×C₈₉

—

C₂×Dic₁₇₈

C₁₆

yes

characteristic

C₂×#10623494

—

C₄⋊Dic₈₉

C₁₆

yes

characteristic

#13083553

—

C₄×Dic₈₉

—

#13083549

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

M₁₆

yes

characteristic

C₄²×C₈₉

C₂×C₈

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

SD₁₆

yes

characteristic

C₁₆×C₈₉

Q₁₆

yes

characteristic

C₂×C₄×C₈₉

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₈₉

C₂×C₁₆

yes

characteristic

C₂×C₄×C₈₉

M₃₂

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

—

C₂²×C₈₉

C₂²⋊C₁₆

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

Q₈⋊C₈

yes

characteristic

C₄×C₈₉

#350

yes

characteristic

Dic₈₉

—

Dic₈₉

—

#7393

—

maximal, Sylow

C₂×C₈₉

Q₈⋊C₁₆

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₄⋊C₃₂

—

#1397

D₈₉

yes

characteristic

C₈₉

#7393

yes

characteristic, complemented, Sylow

C₈×Q₈

—

C₂×C₃₂

—

C₂×C₃₂

—

178

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

178

—

#346

—

178

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

C₄×Q₈

—

C₂×C₁₆

—

178

—

C₂×C₁₆

D₃₅₆

yes

characteristic

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

C₄⋊C₈

—

C₄⋊C₈

—

178

—

C₄×C₈

—

178

—

C₄×C₈

C₄×D₈₉

yes

characteristic

C₃₂

—

C₃₂

—

356

—

C₂×Q₈

—

C₂×C₈

—

178

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₄⋊C₄

—

178

—

C₄²

—

178

—

C₄²

C₈×D₈₉

yes

characteristic

C₁₆

—

C₁₆

—

356

—

C₁₆

#13083563

yes

characteristic

C₁₆

Dic₃₅₆

yes

characteristic

Q₈

—

356

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

#15667924

yes

characteristic

C₂×C₄

C₁₆×D₈₉

yes

characteristic

C₂×C₄

#15667951

yes

characteristic

C₈

—

C₈

—

356

—

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

100

C₄

—

356

—

101

C₄

—

356

—

102

C₄

#19151330

yes

characteristic

103

C₄

#19151381

yes

characteristic

104

C₂

#26018232

yes

characteristic

105

C₂

#26018391

yes

characteristic

106

C₂

#26018395

yes

characteristic

	subgroup	G/H
center	C₂×C₈	#13083551
commutator	C₂×C₄×C₈₉	C₂×C₁₆
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#1397	C₂
socle, prime radical	C₂²×C₈₉	C₂²⋊C₁₆
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#1397	D₈₉
hypocenter	C₈₉	#7393
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #1397

subgroup

G/H

center

C₂×C₈

#13083551

commutator

C₂×C₄×C₈₉

C₂×C₁₆

Frattini

C₄×C₁₆

C₂×D₈₉

Fitting

C₈₉×#1397

C₂

socle, prime radical

C₂²×C₈₉

C₂²⋊C₁₆

cosocle

C₄×C₁₆×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₁₆ ◁ #1397

N	H ≅ G/N	type
57. C₈₉	#7393	semidirect

H ≅ G/N

type

57. C₈₉

#7393

semidirect

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

subgroup	index
#26022160	2
C₄⋊#15667918	2
C₈₉×#1397	2
#7393	89

subgroup

index

#26022160

C₄⋊#15667918

C₈₉×#1397

#7393

Subgroups — #36441909

Conjugacy classes of subgroups

Complements

Maximal subgroups