Group #36469145 — subgroups

Subgroups — #36469145

Order 22784.

354 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 103 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	#26022507	C₂	1	4	yes	maximal, complemented
2	#26019870	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#13083549	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#1712	C₂	1	1	yes	maximal, characteristic
5	C₂×#15667956	—	2	8	no	—
6	#19152003	—	2	2	no	—
7	#19151978	C₂²	1	2	yes	—
8	C₄×#13083549	C₂²	1	2	yes	—
9	#493×C₈₉	—	2	2	no	—
10	#493×C₈₉	C₂²	1	2	yes	—
11	C₈²×C₈₉	C₂²	1	1	yes	characteristic
12	C₂×Dic₃₅₆	—	2	4	no	—
13	#15668012	—	2	2	no	—
14	#15667956	—	4	16	no	—
15	C₂×#13083549	D₄	1	4	yes	—
16	#15667946	—	4	4	no	—
17	C₂×D₈×C₈₉	—	2	4	no	—
18	C₂×D₈×C₈₉	—	4	4	no	—
19	#127×C₈₉	—	2	2	no	—
20	C₄×C₈×C₈₉	D₄	1	2	yes	—
21	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
22	C₂×Dic₁₇₈	—	4	2	no	—
23	Dic₃₅₆	—	4	8	no	—
24	C₄⋊Dic₈₉	—	4	4	no	—
25	#13083549	D₈	1	8	yes	complemented
26	C₂×D₄×C₈₉	—	4	2	no	—
27	C₂×D₄×C₈₉	—	4	4	no	—
28	D₈×C₈₉	—	4	8	no	—
29	D₈×C₈₉	—	8	8	no	—
30	C₂×C₈×C₈₉	D₈	1	4	yes	—
31	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
32	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
33	C₂³×C₈₉	—	8	2	no	—
34	D₄×C₈₉	—	8	4	no	—
35	D₄×C₈₉	—	8	8	no	—
36	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
37	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
38	C₂×Dic₈₉	—	8	2	no	—
39	Dic₁₇₈	—	8	4	no	—
40	C₈×C₈₉	SD₃₂	1	8	yes	complemented
41	C₈×C₈₉	C₂×D₈	1	4	yes	—
42	C₂²×C₈₉	—	16	2	no	—
43	C₂²×C₈₉	—	16	4	no	—
44	C₂²×C₈₉	#493	1	1	yes	characteristic
45	C₄×C₈₉	#493	1	2	yes	—
46	C₄×C₈₉	C₂×SD₃₂	1	4	yes	—
47	Dic₈₉	—	16	2	no	—
48	#12517	—	89	1	no	maximal, Sylow
49	C₂×C₈₉	—	32	2	no	—
50	C₂×C₈₉	#1712	1	1	yes	characteristic
51	C₂×C₈₉	#2248	1	2	yes	—
52	#2248	—	89	4	no	—
53	#1713	—	89	1	no	—
54	#1712	D₈₉	1	1	yes	characteristic
55	C₈×C₁₆	—	89	1	no	—
56	C₈₉	#12517	1	1	yes	characteristic, complemented, Sylow
57	C₂×SD₃₂	—	178	8	no	—
58	#500	—	178	2	no	—
59	#494	—	89	2	no	—
60	#493	—	2	2	no	—
61	#493	C₂×D₈₉	1	2	yes	—
62	C₄×C₁₆	—	89	2	no	—
63	C₈²	C₂×D₈₉	1	1	yes	characteristic
64	C₂×Q₁₆	—	178	4	no	—
65	C₂×D₈	—	2	4	no	—
66	C₂×D₈	—	4	4	no	—
67	C₄⋊Q₈	—	178	2	no	—
68	#127	—	2	2	no	—
69	SD₃₂	—	356	16	no	—
70	C₂×C₁₆	—	89	4	no	—
71	#107	—	356	4	no	—
72	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
73	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
74	C₂×Q₈	—	356	2	no	—
75	C₂×D₄	—	4	2	no	—
76	C₂×D₄	—	4	4	no	—
77	Q₁₆	—	356	8	no	—
78	D₈	—	4	8	no	—
79	D₈	—	8	8	no	—
80	C₂×C₈	#13083559	1	4	yes	—
81	C₂×C₈	D₄×D₈₉	1	2	yes	—
82	C₄⋊C₄	—	356	4	no	—
83	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
84	C₁₆	—	89	8	no	—
85	C₂³	—	8	2	no	—
86	Q₈	—	712	4	no	—
87	D₄	—	8	4	no	—
88	D₄	—	8	8	no	—
89	C₂×C₄	—	712	2	no	—
90	C₂×C₄	#15668008	1	1	yes	characteristic
91	C₂×C₄	C₂×#13083559	1	2	yes	—
92	C₈	#15667956	1	8	yes	complemented
93	C₈	D₈×D₈₉	1	4	yes	—
94	C₂²	—	16	2	no	—
95	C₂²	—	16	4	no	—
96	C₂²	#19151974	1	1	yes	characteristic
97	C₄	—	1424	2	no	—
98	C₄	#19151973	1	2	yes	—
99	C₄	C₂×#15667956	1	4	yes	—
100	C₂	—	32	2	no	—
101	C₂	#26019866	1	1	yes	characteristic
102	C₂	#26022507	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26022507

C₂

yes

maximal, complemented

#26019870

C₂

yes

maximal, characteristic, complemented

C₈×#13083549

C₂

yes

maximal, characteristic, complemented

C₈₉×#1712

C₂

yes

maximal, characteristic

C₂×#15667956

—

#19152003

—

#19151978

C₂²

yes

—

C₄×#13083549

C₂²

yes

—

#493×C₈₉

—

#493×C₈₉

C₂²

yes

—

C₈²×C₈₉

C₂²

yes

characteristic

C₂×Dic₃₅₆

—

#15668012

—

#15667956

—

C₂×#13083549

D₄

yes

—

#15667946

—

C₂×D₈×C₈₉

—

C₂×D₈×C₈₉

—

#127×C₈₉

—

C₄×C₈×C₈₉

D₄

yes

—

C₄×C₈×C₈₉

C₂³

yes

characteristic

C₂×Dic₁₇₈

—

Dic₃₅₆

—

C₄⋊Dic₈₉

—

#13083549

D₈

yes

complemented

C₂×D₄×C₈₉

—

C₂×D₄×C₈₉

—

D₈×C₈₉

—

D₈×C₈₉

—

C₂×C₈×C₈₉

D₈

yes

—

C₂×C₈×C₈₉

C₂×D₄

yes

—

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₂³×C₈₉

—

D₄×C₈₉

—

D₄×C₈₉

—

C₂×C₄×C₈₉

#127

yes

characteristic

C₂×C₄×C₈₉

C₂×D₈

yes

—

C₂×Dic₈₉

—

Dic₁₇₈

—

C₈×C₈₉

SD₃₂

yes

complemented

C₈×C₈₉

C₂×D₈

yes

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#493

yes

characteristic

C₄×C₈₉

#493

yes

—

C₄×C₈₉

C₂×SD₃₂

yes

—

Dic₈₉

—

#12517

—

maximal, Sylow

C₂×C₈₉

—

C₂×C₈₉

#1712

yes

characteristic

C₂×C₈₉

#2248

yes

—

#2248

—

#1713

—

#1712

D₈₉

yes

characteristic

C₈×C₁₆

—

C₈₉

#12517

yes

characteristic, complemented, Sylow

C₂×SD₃₂

—

178

—

#500

—

178

—

#494

—

#493

—

#493

C₂×D₈₉

yes

—

C₄×C₁₆

—

C₈²

C₂×D₈₉

yes

characteristic

C₂×Q₁₆

—

178

—

C₂×D₈

—

C₂×D₈

—

C₄⋊Q₈

—

178

—

#127

—

SD₃₂

—

356

—

C₂×C₁₆

—

#107

—

356

—

C₄×C₈

C₂²⋊D₈₉

yes

—

C₄×C₈

C₂²×D₈₉

yes

characteristic

C₂×Q₈

—

356

—

C₂×D₄

—

C₂×D₄

—

Q₁₆

—

356

—

D₈

—

D₈

—

C₂×C₈

#13083559

yes

—

C₂×C₈

D₄×D₈₉

yes

—

C₄⋊C₄

—

356

—

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

C₁₆

—

C₂³

—

Q₈

—

712

—

D₄

—

D₄

—

C₂×C₄

—

712

—

C₂×C₄

#15668008

yes

characteristic

C₂×C₄

C₂×#13083559

yes

—

C₈

#15667956

yes

complemented

C₈

D₈×D₈₉

yes

—

C₂²

—

C₂²

—

C₂²

#19151974

yes

characteristic

C₄

—

1424

—

C₄

#19151973

yes

—

C₄

C₂×#15667956

yes

—

100

C₂

—

101

C₂

#26019866

yes

characteristic

102

C₂

#26022507

yes

—

	subgroup	G/H
center	C₂²	#19151974
commutator, cosocle	C₄×C₈×C₈₉	C₂³
Frattini	C₄×C₈	C₂²×D₈₉
Fitting, prime radical	C₈₉×#1712	C₂
socle	C₂²×C₈₉	#493
hypercenter	#1712	D₈₉
hypocenter	C₈₉	#12517
LCS	G ▷ C₄×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

subgroup

G/H

center

C₂²

#19151974

commutator, cosocle

C₄×C₈×C₈₉

C₂³

Frattini

C₄×C₈

C₂²×D₈₉

Fitting, prime radical

C₈₉×#1712

C₂

C₂²×C₈₉

D₈₉

C₈₉

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

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ #1712

N	H ≅ G/N	type
1. #26022507	C₂	semidirect
2. #26019870	C₂	semidirect
3. C₈×#13083549	C₂	semidirect
25. #13083549	D₈	semidirect
40. C₈×C₈₉	SD₃₂	semidirect
56. C₈₉	#12517	semidirect
92. C₈	#15667956	semidirect

H ≅ G/N

type

1. #26022507

C₂

semidirect

2. #26019870

C₂

semidirect

3. C₈×#13083549

C₂

semidirect

25. #13083549

D₈

semidirect

40. C₈×C₈₉

SD₃₂

semidirect

56. C₈₉

#12517

semidirect

92. C₈

#15667956

semidirect

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

subgroup	index
#26022507	2
#26019870	2
C₈×#13083549	2
C₈₉×#1712	2
#12517	89

subgroup

index

C₈₉×#1712

Subgroups — #36469145

Conjugacy classes of subgroups

Complements

Maximal subgroups