Group #36442076 — subgroups

Subgroups — #36442076

Order 22784.

126 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 47 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	#26018450	C₂	1	1	yes	maximal, characteristic
2	#26018328	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2247	C₂	1	1	yes	maximal, characteristic
4	#19151432	—	2	1	no	—
5	#19151419	—	2	1	no	—
6	C₂×Q₃₂×C₈₉	—	2	1	no	—
7	C₂×Q₃₂×C₈₉	C₄	1	2	yes	—
8	#494×C₈₉	—	2	1	no	—
9	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
10	#15667952	—	4	1	no	—
11	#15667918	—	4	1	no	—
12	C₂×Q₁₆×C₈₉	—	2	2	no	—
13	C₂×Q₁₆×C₈₉	—	4	1	no	—
14	C₄⋊Q₈×C₈₉	—	4	1	no	—
15	Q₃₂×C₈₉	—	4	2	no	—
16	Q₃₂×C₈₉	—	4	1	no	—
17	Q₃₂×C₈₉	—	4	1	no	—
18	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₁₆×C₈₉	D₄	1	1	yes	characteristic
20	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
21	#13083549	—	8	1	no	—
22	C₂×Q₈×C₈₉	—	4	2	no	—
23	Q₁₆×C₈₉	—	4	2	no	—
24	Q₁₆×C₈₉	—	4	2	no	—
25	Q₁₆×C₈₉	—	8	1	no	—
26	Q₁₆×C₈₉	—	8	1	no	—
27	C₂×C₈×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₈×C₈₉	D₈	1	1	yes	characteristic
29	C₄⋊C₄×C₈₉	—	8	2	no	—
30	C₄²×C₈₉	SD₁₆	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	Q₈×C₈₉	—	8	2	no	—
35	Q₈×C₈₉	—	8	2	no	—
36	C₂×C₄×C₈₉	—	2	1	no	—
37	C₂×C₄×C₈₉	—	8	2	no	—
38	C₂×C₄×C₈₉	#102	1	1	yes	characteristic
39	C₈×C₈₉	#100	1	1	yes	characteristic
40	C₈×C₈₉	#102	1	1	yes	characteristic
41	C₈×C₈₉	D₁₆	1	1	yes	characteristic
42	C₈×C₈₉	SD₃₂	1	1	yes	characteristic
43	C₂²×C₈₉	#361	1	1	yes	characteristic
44	C₄×C₈₉	—	2	2	no	—
45	C₄×C₈₉	—	16	2	no	—
46	C₄×C₈₉	#331	1	1	yes	characteristic
47	C₄×C₈₉	#357	1	1	yes	characteristic
48	#7449	—	89	1	no	maximal, Sylow
49	C₂×C₈₉	—	2	1	no	—
50	C₂×C₈₉	#1361	1	1	yes	characteristic
51	#2247	D₈₉	1	1	yes	characteristic
52	#1422	—	89	1	no	—
53	#1373	—	89	1	no	—
54	C₈₉	#7449	1	1	yes	characteristic, complemented, Sylow
55	C₂×Q₃₂	—	2	1	no	—
56	C₂×Q₃₂	Dic₈₉	1	2	yes	—
57	#494	—	2	1	no	—
58	M₆₄	—	178	1	no	—
59	#364	—	178	1	no	—
60	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic
61	C₂×Q₁₆	—	2	2	no	—
62	C₂×Q₁₆	—	4	1	no	—
63	C₄⋊Q₈	—	4	1	no	—
64	Q₃₂	—	4	2	no	—
65	Q₃₂	—	4	1	no	—
66	Q₃₂	—	4	1	no	—
67	M₃₂	—	356	1	no	—
68	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
69	C₂×C₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
70	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
71	C₃₂	—	356	1	no	—
72	C₂×Q₈	—	4	2	no	—
73	Q₁₆	—	4	2	no	—
74	Q₁₆	—	4	2	no	—
75	Q₁₆	—	8	1	no	—
76	Q₁₆	—	8	1	no	—
77	C₂×C₈	C₂²⋊Dic₈₉	1	1	yes	characteristic
78	C₂×C₈	#13083559	1	1	yes	characteristic
79	C₄⋊C₄	—	8	2	no	—
80	C₄²	#13083562	1	1	yes	characteristic
81	C₁₆	—	2	1	no	—
82	C₁₆	—	712	1	no	—
83	C₁₆	#13083559	1	1	yes	characteristic
84	C₁₆	#13083562	1	1	yes	characteristic
85	Q₈	—	8	2	no	—
86	Q₈	—	8	2	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	8	2	no	—
89	C₂×C₄	#15667933	1	1	yes	characteristic
90	C₈	#15667929	1	1	yes	characteristic
91	C₈	#15667933	1	1	yes	characteristic
92	C₈	#15667953	1	1	yes	characteristic
93	C₈	#15667956	1	1	yes	characteristic
94	C₂²	#19151411	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	16	2	no	—
97	C₄	#19151342	1	1	yes	characteristic
98	C₄	#19151399	1	1	yes	characteristic
99	C₂	—	2	1	no	—
100	C₂	#26018298	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26018450

C₂

yes

maximal, characteristic

#26018328

C₂

yes

maximal, characteristic

C₈₉×#2247

C₂

yes

maximal, characteristic

#19151432

—

#19151419

—

C₂×Q₃₂×C₈₉

—

C₂×Q₃₂×C₈₉

C₄

yes

—

#494×C₈₉

—

C₄×C₁₆×C₈₉

C₂²

yes

characteristic

#15667952

—

#15667918

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₄⋊Q₈×C₈₉

—

Q₃₂×C₈₉

—

Q₃₂×C₈₉

—

Q₃₂×C₈₉

—

C₂×C₁₆×C₈₉

C₂×C₄

yes

characteristic

C₂×C₁₆×C₈₉

D₄

yes

characteristic

C₄×C₈×C₈₉

D₄

yes

characteristic

#13083549

—

C₂×Q₈×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₈₉

D₈

yes

characteristic

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

SD₁₆

yes

characteristic

C₁₆×C₈₉

—

C₁₆×C₈₉

D₈

yes

characteristic

C₁₆×C₈₉

SD₁₆

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

yes

C₈×C₈₉

yes

C₈×C₈₉

yes

C₈×C₈₉

D₁₆

yes

characteristic

C₈×C₈₉

SD₃₂

yes

characteristic

C₂²×C₈₉

#361

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

—

C₂×C₈₉

—

C₂×C₈₉

#1361

yes

characteristic

#2247

D₈₉

yes

characteristic

#1422

—

#1373

—

C₈₉

#7449

yes

characteristic, complemented, Sylow

C₂×Q₃₂

—

C₂×Q₃₂

Dic₈₉

yes

—

#494

—

M₆₄

—

178

—

#364

—

178

—

C₄×C₁₆

C₂×D₈₉

yes

characteristic

C₂×Q₁₆

—

C₂×Q₁₆

—

C₄⋊Q₈

—

Q₃₂

—

Q₃₂

—

Q₃₂

—

M₃₂

—

356

—

C₂×C₁₆

C₂×Dic₈₉

yes

characteristic

C₂×C₁₆

C₂²⋊D₈₉

yes

characteristic

C₄×C₈

C₂²⋊D₈₉

yes

characteristic

C₃₂

—

356

—

C₂×Q₈

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

Q₁₆

—

C₂×C₈

C₂²⋊Dic₈₉

yes

characteristic

C₂×C₈

#13083559

yes

characteristic

C₄⋊C₄

—

C₄²

#13083562

yes

characteristic

C₁₆

—

C₁₆

—

712

—

C₁₆

yes

C₁₆

yes

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

yes

C₈

yes

C₈

yes

C₈

yes

C₈

yes

C₂²

yes

C₄

—

C₄

—

C₄

yes

C₄

yes

C₂

—

100

C₂

#26018298

yes

characteristic

	subgroup	G/H
center	C₂	#26018298
commutator	C₂×C₁₆×C₈₉	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₈₉
Fitting	C₈₉×#2247	C₂
socle	C₂×C₈₉	#1361
prime radical	C₂²×C₈₉	#361
cosocle	C₄×C₁₆×C₈₉	C₂²
hypercenter	#2247	D₈₉
hypocenter	C₈₉	#7449
LCS	G ▷ C₂×C₁₆×C₈₉ ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

subgroup

G/H

center

C₂

#26018298

commutator

C₂×C₁₆×C₈₉

C₂×C₄

Frattini

C₄×C₁₆

C₂×D₈₉

Fitting

C₈₉×#2247

C₂

C₂×C₈₉

C₂²×C₈₉

C₄×C₁₆×C₈₉

C₂²

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #2247

N	H ≅ G/N	type
54. C₈₉	#7449	semidirect

H ≅ G/N

type

54. C₈₉

#7449

semidirect

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

subgroup	index
#26018450	2
#26018328	2
C₈₉×#2247	2
#7449	89

subgroup

index

#26018450

#26018328

C₈₉×#2247

#7449

Subgroups — #36442076

Conjugacy classes of subgroups

Complements

Maximal subgroups