Group #36442063 — subgroups

Subgroups — #36442063

Order 22784.

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

normal subgroups only

This group has 132 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	#26022505	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#15667918	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#1371	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₁₂	—	2	1	no	—
5	C₂×Dic₇₁₂	C₄	1	2	yes	—
6	#19151978	—	2	1	no	—
7	C₂×#15667918	—	2	1	no	—
8	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
9	#335×C₈₉	—	2	1	no	—
10	C₂×Dic₃₅₆	—	2	2	no	—
11	C₂×Dic₃₅₆	—	4	1	no	—
12	#15668012	—	4	1	no	—
13	Dic₇₁₂	—	4	2	no	—
14	Dic₇₁₂	—	4	1	no	—
15	Dic₇₁₂	—	4	1	no	—
16	#15667918	—	4	1	no	—
17	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
19	C₄⋊C₈×C₈₉	—	4	1	no	—
20	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
21	C₂×Dic₁₇₈	—	4	2	no	—
22	Dic₃₅₆	—	4	2	no	—
23	Dic₃₅₆	—	4	2	no	—
24	Dic₃₅₆	—	8	2	no	—
25	C₄⋊Dic₈₉	—	8	1	no	—
26	C₄⋊Dic₈₉	—	8	1	no	—
27	C₂×C₈×C₈₉	—	8	1	no	—
28	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₈₉	SD₁₆	1	1	yes	characteristic
30	C₄²×C₈₉	D₈	1	1	yes	characteristic
31	C₁₆×C₈₉	—	2	1	no	—
32	C₁₆×C₈₉	D₈	1	1	yes	characteristic
33	C₁₆×C₈₉	SD₁₆	1	1	yes	characteristic
34	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
35	C₂×C₄×C₈₉	D₁₆	1	1	yes	characteristic
36	C₂×C₄×C₈₉	SD₃₂	1	1	yes	characteristic
37	C₂×Dic₈₉	—	8	2	no	—
38	Dic₁₇₈	—	8	2	no	—
39	Dic₁₇₈	—	8	2	no	—
40	C₈×C₈₉	—	2	1	no	—
41	C₈×C₈₉	—	16	1	no	—
42	C₈×C₈₉	#100	1	1	yes	characteristic
43	C₈×C₈₉	#102	1	1	yes	characteristic
44	C₂²×C₈₉	#357	1	1	yes	characteristic
45	C₄×C₈₉	—	2	1	no	—
46	C₄×C₈₉	#331	1	1	yes	characteristic
47	C₄×C₈₉	#361	1	1	yes	characteristic
48	C₄×C₈₉	SD₆₄	1	1	yes	characteristic
49	C₄×C₈₉	Q₆₄	1	1	yes	characteristic
50	Dic₈₉	—	16	2	no	—
51	#7445	—	89	1	no	maximal, Sylow
52	C₂×C₈₉	#1361	1	1	yes	characteristic
53	C₂×C₈₉	#1416	1	1	yes	characteristic
54	C₂×C₈₉	#1420	1	1	yes	characteristic
55	#2247	—	89	1	no	—
56	C₄⋊C₃₂	—	89	1	no	—
57	#1371	D₈₉	1	1	yes	characteristic
58	C₈₉	#7445	1	1	yes	characteristic, complemented, Sylow
59	C₂×Q₃₂	—	89	2	no	—
60	C₂×Q₃₂	—	178	1	no	—
61	#494	—	178	1	no	—
62	C₂×C₃₂	—	178	1	no	—
63	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
64	#335	—	2	1	no	—
65	C₂×Q₁₆	—	356	1	no	—
66	C₂×Q₁₆	—	178	2	no	—
67	C₄⋊Q₈	—	356	1	no	—
68	Q₃₂	—	356	2	no	—
69	Q₃₂	—	356	1	no	—
70	Q₃₂	—	356	1	no	—
71	C₂×C₁₆	C₄×D₈₉	1	1	yes	characteristic
72	C₂×C₁₆	D₃₅₆	1	1	yes	characteristic
73	C₄⋊C₈	—	4	1	no	—
74	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
75	C₃₂	—	356	1	no	—
76	C₂×Q₈	—	356	2	no	—
77	Q₁₆	—	356	2	no	—
78	Q₁₆	—	356	2	no	—
79	Q₁₆	—	712	2	no	—
80	C₂×C₈	—	8	1	no	—
81	C₂×C₈	#13083551	1	1	yes	characteristic
82	C₂×C₈	#13083561	1	1	yes	characteristic
83	C₄⋊C₄	—	712	1	no	—
84	C₄⋊C₄	—	712	1	no	—
85	C₄²	#13083559	1	1	yes	characteristic
86	C₁₆	—	2	1	no	—
87	C₁₆	D₇₁₂	1	1	yes	characteristic
88	C₁₆	#13083563	1	1	yes	characteristic
89	Q₈	—	712	2	no	—
90	Q₈	—	712	2	no	—
91	C₂×C₄	—	712	2	no	—
92	C₂×C₄	#15667932	1	1	yes	characteristic
93	C₂×C₄	#15667953	1	1	yes	characteristic
94	C₂×C₄	#15667955	1	1	yes	characteristic
95	C₈	—	2	1	no	—
96	C₈	—	16	1	no	—
97	C₈	#15667928	1	1	yes	characteristic
98	C₈	#15667934	1	1	yes	characteristic
99	C₂²	#19151398	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	1424	2	no	—
102	C₄	#19151341	1	1	yes	characteristic
103	C₄	#19151410	1	1	yes	characteristic
104	C₄	#19151436	1	1	yes	characteristic
105	C₄	#19151438	1	1	yes	characteristic
106	C₂	#26018297	1	1	yes	characteristic
107	C₂	#26018432	1	1	yes	characteristic
108	C₂	#26018444	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26022505

C₂

yes

maximal, characteristic

C₄⋊#15667918

C₂

yes

maximal, characteristic

C₈₉×#1371

C₂

yes

maximal, characteristic

C₂×Dic₇₁₂

—

C₂×Dic₇₁₂

C₄

yes

—

#19151978

—

C₂×#15667918

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

#335×C₈₉

—

C₂×Dic₃₅₆

—

C₂×Dic₃₅₆

—

#15668012

—

Dic₇₁₂

—

Dic₇₁₂

—

Dic₇₁₂

—

#15667918

—

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

—

Dic₃₅₆

—

C₄⋊Dic₈₉

—

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

D₈

yes

characteristic

C₁₆×C₈₉

SD₁₆

yes

characteristic

C₂×C₄×C₈₉

#102

yes

characteristic

C₂×C₄×C₈₉

D₁₆

yes

characteristic

C₂×C₄×C₈₉

SD₃₂

yes

characteristic

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

yes

C₈×C₈₉

yes

C₂²×C₈₉

yes

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

C₄×C₈₉

SD₆₄

yes

characteristic

C₄×C₈₉

Q₆₄

yes

characteristic

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₄⋊C₃₂

—

#1371

D₈₉

yes

characteristic

C₈₉

#7445

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

—

178

—

#494

—

178

—

C₂×C₃₂

—

178

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

#335

—

C₂×Q₁₆

—

356

—

C₂×Q₁₆

—

178

—

C₄⋊Q₈

—

356

—

Q₃₂

—

356

—

Q₃₂

—

356

—

Q₃₂

—

356

—

C₂×C₁₆

C₄×D₈₉

yes

characteristic

C₂×C₁₆

D₃₅₆

yes

characteristic

C₄⋊C₈

—

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

C₃₂

—

356

—

C₂×Q₈

—

356

—

Q₁₆

—

356

—

Q₁₆

—

356

—

Q₁₆

—

712

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

712

—

C₄⋊C₄

—

712

—

C₄²

#13083559

yes

characteristic

C₁₆

—

C₁₆

D₇₁₂

yes

characteristic

C₁₆

#13083563

yes

characteristic

Q₈

—

712

—

Q₈

—

712

—

C₂×C₄

—

712

—

C₂×C₄

yes

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

C₈

yes

C₈

yes

C₂²

yes

100

C₄

—

101

C₄

—

1424

—

102

C₄

#19151341

yes

characteristic

103

C₄

#19151410

yes

characteristic

104

C₄

#19151436

yes

characteristic

105

C₄

#19151438

yes

characteristic

106

C₂

#26018297

yes

characteristic

107

C₂

#26018432

yes

characteristic

108

C₂

#26018444

yes

characteristic

	subgroup	G/H
center	C₂²	#19151398
commutator	C₂×C₁₆×C₈₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#1371	C₂
socle, prime radical	C₂²×C₈₉	#357
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#1371	D₈₉
hypocenter	C₈₉	#7445
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

subgroup

G/H

center

C₂²

#19151398

commutator

C₂×C₁₆×C₈₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₈₉

Fitting

C₈₉×#1371

C₂

socle, prime radical

C₂²×C₈₉

#357

cosocle

C₄×C₁₆×C₈₉

C₂²

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

N	H ≅ G/N	type
58. C₈₉	#7445	semidirect

H ≅ G/N

type

58. C₈₉

#7445

semidirect

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

subgroup	index
#26022505	2
C₄⋊#15667918	2
C₈₉×#1371	2
#7445	89

subgroup

index

#26022505

C₄⋊#15667918

C₈₉×#1371

#7445

Subgroups — #36442063

Conjugacy classes of subgroups

Complements

Maximal subgroups