Group #36441886 — subgroups

Subgroups — #36441886

Order 22784.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic₇₁₂	C₂	1	1	yes	maximal, characteristic
2	#26018386	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1372	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₁₂	C₄	1	1	yes	characteristic
5	C₄×Dic₃₅₆	—	2	1	no	—
6	C₂×#15667918	—	2	1	no	—
7	#19151424	C₄	1	1	yes	characteristic
8	#19151403	—	2	1	no	—
9	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	#335×C₈₉	—	2	1	no	—
11	C₂×Dic₃₅₆	—	2	1	no	—
12	C₄×Dic₁₇₈	—	4	1	no	—
13	Dic₇₁₂	—	2	1	no	—
14	Dic₇₁₂	C₈	1	2	yes	complemented
15	#15667946	—	2	1	no	—
16	#15667937	—	4	1	no	—
17	#15667918	—	2	2	no	—
18	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
20	C₄⋊C₈×C₈₉	—	4	1	no	—
21	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
22	C₂×Dic₁₇₈	—	4	1	no	—
23	Dic₃₅₆	—	2	2	no	—
24	Dic₃₅₆	—	4	1	no	—
25	C₄⋊Dic₈₉	—	4	1	no	—
26	#13083553	—	8	1	no	—
27	C₄×Dic₈₉	—	8	1	no	—
28	C₂×C₈×C₈₉	—	8	1	no	—
29	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
31	C₄²×C₈₉	D₈	1	1	yes	characteristic
32	C₁₆×C₈₉	—	2	1	no	—
33	C₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
34	C₁₆×C₈₉	M₁₆	1	1	yes	characteristic
35	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
36	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
37	C₂×C₄×C₈₉	SD₃₂	1	1	yes	characteristic
38	C₂×Dic₈₉	—	8	1	no	—
39	C₂×Dic₈₉	—	8	1	no	—
40	Dic₁₇₈	—	4	2	no	—
41	Dic₁₇₈	—	8	1	no	—
42	C₈×C₈₉	—	2	1	no	—
43	C₈×C₈₉	—	16	1	no	—
44	C₈×C₈₉	C₂²⋊C₈	1	1	yes	characteristic
45	C₈×C₈₉	#104	1	1	yes	characteristic
46	C₂²×C₈₉	#357	1	1	yes	characteristic
47	C₄×C₈₉	—	2	1	no	—
48	C₄×C₈₉	—	2	1	no	—
49	C₄×C₈₉	D₄⋊C₈	1	1	yes	characteristic
50	C₄×C₈₉	#359	1	1	yes	characteristic
51	Dic₈₉	—	8	2	no	—
52	Dic₈₉	—	16	1	no	—
53	#7386	—	89	1	no	maximal, Sylow
54	C₂×C₈₉	#1331	1	1	yes	characteristic
55	C₂×C₈₉	#1418	1	1	yes	characteristic
56	C₂×C₈₉	#1420	1	1	yes	characteristic
57	C₄×Q₃₂	—	89	1	no	—
58	#1397	—	89	1	no	—
59	#1372	D₈₉	1	1	yes	characteristic
60	C₈₉	#7386	1	1	yes	characteristic, complemented, Sylow
61	C₂×Q₃₂	—	89	1	no	—
62	C₄×Q₁₆	—	178	1	no	—
63	C₂×C₃₂	—	178	1	no	—
64	#366	—	89	1	no	—
65	#358	—	178	1	no	—
66	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
67	#335	—	2	1	no	—
68	C₂×Q₁₆	—	178	1	no	—
69	C₄×Q₈	—	356	1	no	—
70	Q₃₂	—	89	2	no	—
71	Q₃₂	—	178	1	no	—
72	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
73	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
74	#107	—	178	1	no	—
75	C₄⋊C₈	—	4	1	no	—
76	#103	—	356	1	no	—
77	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
78	C₃₂	—	178	2	no	—
79	C₂×Q₈	—	356	1	no	—
80	Q₁₆	—	356	1	no	—
81	Q₁₆	—	178	2	no	—
82	C₂×C₈	—	8	1	no	—
83	C₂×C₈	#13083551	1	1	yes	characteristic
84	C₂×C₈	#13083561	1	1	yes	characteristic
85	C₄⋊C₄	—	356	1	no	—
86	C₄⋊C₄	—	712	1	no	—
87	C₄²	—	712	1	no	—
88	C₄²	#13083559	1	1	yes	characteristic
89	C₁₆	—	2	1	no	—
90	C₁₆	C₈×D₈₉	1	1	yes	characteristic
91	C₁₆	#13083557	1	1	yes	characteristic
92	Q₈	—	356	2	no	—
93	Q₈	—	712	1	no	—
94	C₂×C₄	—	712	1	no	—
95	C₂×C₄	—	712	1	no	—
96	C₂×C₄	#15667932	1	1	yes	characteristic
97	C₂×C₄	#15667953	1	1	yes	characteristic
98	C₂×C₄	#15667955	1	1	yes	characteristic
99	C₈	—	2	1	no	—
100	C₈	—	16	1	no	—
101	C₈	#15667924	1	1	yes	characteristic
102	C₈	#15667938	1	1	yes	characteristic
103	C₂²	#19151398	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	1	no	—
106	C₄	—	1424	1	no	—
107	C₄	—	712	2	no	—
108	C₄	#19151325	1	1	yes	characteristic
109	C₄	#19151404	1	1	yes	characteristic
110	C₂	#26018212	1	1	yes	characteristic
111	C₂	#26018438	1	1	yes	characteristic
112	C₂	#26018444	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×Dic₇₁₂

C₂

yes

maximal, characteristic

#26018386

C₂

yes

maximal, characteristic

C₈₉×#1372

C₂

yes

maximal, characteristic

C₂×Dic₇₁₂

C₄

yes

characteristic

C₄×Dic₃₅₆

—

C₂×#15667918

—

#19151424

C₄

yes

characteristic

#19151403

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

C₂×Dic₃₅₆

—

C₄×Dic₁₇₈

—

Dic₇₁₂

—

Dic₇₁₂

C₈

yes

—

—

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₄⋊C₈×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

characteristic

C₂×Dic₁₇₈

—

Dic₃₅₆

—

Dic₃₅₆

—

C₄⋊Dic₈₉

—

#13083553

—

C₄×Dic₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

SD₁₆

yes

characteristic

C₄²×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

C₂×C₈

yes

characteristic

C₁₆×C₈₉

M₁₆

yes

characteristic

C₂×C₄×C₈₉

#102

yes

characteristic

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

SD₃₂

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

C₂²⋊C₈

yes

C₈×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

D₄⋊C₈

yes

characteristic

C₄×C₈₉

#359

yes

characteristic

Dic₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

C₄×Q₃₂

—

#1397

—

#1372

D₈₉

yes

characteristic

C₈₉

#7386

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₄×Q₁₆

—

178

—

C₂×C₃₂

—

178

—

#366

—

#358

—

178

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

#335

—

C₂×Q₁₆

—

178

—

C₄×Q₈

—

356

—

Q₃₂

—

Q₃₂

—

178

—

C₂×C₁₆

C₄×D₈₉

yes

characteristic

C₂×C₁₆

D₃₅₆

yes

characteristic

#107

—

178

—

C₄⋊C₈

—

#103

—

356

—

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

C₃₂

—

178

—

C₂×Q₈

—

356

—

Q₁₆

—

356

—

Q₁₆

—

178

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

356

—

C₄⋊C₄

—

712

—

C₄²

—

712

—

C₄²

#13083559

yes

characteristic

C₁₆

—

C₁₆

C₈×D₈₉

yes

characteristic

C₁₆

#13083557

yes

characteristic

Q₈

—

356

—

Q₈

—

712

—

C₂×C₄

—

712

—

C₂×C₄

—

712

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

100

C₈

—

101

C₈

#15667924

yes

characteristic

102

C₈

#15667938

yes

characteristic

103

C₂²

#19151398

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

1424

—

107

C₄

—

712

—

108

C₄

#19151325

yes

characteristic

109

C₄

#19151404

yes

characteristic

110

C₂

#26018212

yes

characteristic

111

C₂

#26018438

yes

characteristic

112

C₂

#26018444

yes

characteristic

	subgroup	G/H
center	C₂²	#19151398
commutator	C₁₆×C₈₉	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#1372	C₂
socle, prime radical	C₂²×C₈₉	#357
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#1372	D₈₉
hypocenter	C₈₉	#7386
LCS	G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

subgroup

G/H

center

C₂²

#19151398

commutator

C₁₆×C₈₉

C₂×C₈

Frattini

C₄×C₁₆

C₂×D₈₉

Fitting

C₈₉×#1372

C₂

socle, prime radical

C₂²×C₈₉

#357

cosocle

C₄×C₁₆×C₈₉

C₂²

D₈₉

C₈₉

G ▷ C₁₆×C₈₉ ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1372

N	H ≅ G/N	type
14. Dic₇₁₂	C₈	semidirect
60. C₈₉	#7386	semidirect

H ≅ G/N

type

14. Dic₇₁₂

C₈

semidirect

60. C₈₉

#7386

semidirect

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

subgroup	index
C₄×Dic₇₁₂	2
#26018386	2
C₈₉×#1372	2
#7386	89

subgroup

index

C₄×Dic₇₁₂

#26018386

C₈₉×#1372

#7386

Subgroups — #36441886

Conjugacy classes of subgroups

Complements

Maximal subgroups