Group #26018271 — subgroups

Subgroups — #26018271

Order 11392.

104 conjugacy classes of subgroups; only the 35 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 35 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	#19151839	C₂	1	1	yes	maximal, characteristic
2	#19151363	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₅₆	C₄	1	1	yes	characteristic
5	C₂×#13083558	—	2	1	no	—
6	#15667991	—	2	1	no	—
7	#15667946	C₄	1	1	yes	characteristic
8	#15667937	—	2	1	no	—
9	C₂²×C₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₈₉	—	2	1	no	—
11	C₂×Dic₁₇₈	—	2	1	no	—
12	Dic₃₅₆	—	4	1	no	—
13	#13083558	—	2	2	no	—
14	#13083558	—	4	1	no	—
15	C₂×#10623494	—	4	1	no	—
16	C₄⋊Dic₈₉	—	2	1	no	—
17	#13083553	—	4	1	no	—
18	C₂²⋊Dic₈₉	—	4	1	no	—
19	C₂²×C₄×C₈₉	D₄	1	1	yes	characteristic
20	C₂×C₈×C₈₉	—	4	1	no	—
21	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₉	D₄	1	1	yes	characteristic
23	C₁₆×C₈₉	—	4	1	no	—
24	C₂³×C₈₉	SD₁₆	1	1	yes	characteristic
25	C₂×C₄×C₈₉	—	2	1	no	—
26	C₂×C₄×C₈₉	—	2	1	no	—
27	C₂×C₄×C₈₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₉	D₈	1	1	yes	characteristic
29	C₂×Dic₈₉	—	4	1	no	—
30	C₂×Dic₈₉	—	4	1	no	—
31	Dic₁₇₈	—	4	1	no	—
32	Dic₁₇₈	—	4	1	no	—
33	C₈×C₈₉	—	2	1	no	—
34	C₈×C₈₉	—	2	1	no	—
35	#10623494	—	4	2	no	—
36	C₂²×C₈₉	—	2	1	no	—
37	C₂²×C₈₉	—	2	1	no	—
38	C₂²×C₈₉	—	2	1	no	—
39	C₂²×C₈₉	#102	1	1	yes	characteristic
40	C₄×C₈₉	—	2	1	no	—
41	C₄×C₈₉	#99	1	1	yes	characteristic
42	C₄×C₈₉	#104	1	1	yes	characteristic
43	Dic₈₉	—	8	1	no	—
44	Dic₈₉	—	8	1	no	—
45	C₂×C₈₉	—	4	1	no	—
46	C₂×C₈₉	#327	1	1	yes	characteristic
47	C₂×C₈₉	#359	1	1	yes	characteristic
48	C₂×C₈₉	#362	1	1	yes	characteristic
49	#1350	—	89	1	no	maximal, Sylow
50	C₈₉	#1350	1	1	yes	characteristic, complemented, Sylow
51	#467	—	89	1	no	—
52	C₂²⋊C₁₆	D₈₉	1	1	yes	characteristic
53	#341	—	89	1	no	—
54	C₂×Q₁₆	—	89	1	no	—
55	C₂×M₁₆	—	178	1	no	—
56	C₂²×C₈	C₂×D₈₉	1	1	yes	characteristic
57	C₂²⋊Q₈	—	178	1	no	—
58	C₂×C₁₆	—	2	1	no	—
59	#107	—	89	1	no	—
60	#103	—	178	1	no	—
61	C₂×Q₈	—	178	1	no	—
62	C₂²×C₄	D₃₅₆	1	1	yes	characteristic
63	Q₁₆	—	356	1	no	—
64	M₁₆	—	356	1	no	—
65	M₁₆	—	178	2	no	—
66	C₂×C₈	—	4	1	no	—
67	C₂×C₈	—	356	1	no	—
68	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
69	C₂×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
70	C₄⋊C₄	—	356	1	no	—
71	C₄⋊C₄	—	178	1	no	—
72	C₂²⋊C₄	—	356	1	no	—
73	C₁₆	—	4	1	no	—
74	C₂³	#13083563	1	1	yes	characteristic
75	Q₈	—	356	1	no	—
76	Q₈	—	356	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	356	1	no	—
80	C₂×C₄	—	356	1	no	—
81	C₂×C₄	#13083551	1	1	yes	characteristic
82	C₂×C₄	D₇₁₂	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₈	—	356	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	—	2	1	no	—
88	C₂²	—	2	1	no	—
89	C₂²	#15667934	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	712	1	no	—
92	C₄	—	712	1	no	—
93	C₄	#15667926	1	1	yes	characteristic
94	C₄	#15667938	1	1	yes	characteristic
95	C₂	—	4	1	no	—
96	C₂	#19151333	1	1	yes	characteristic
97	C₂	#19151406	1	1	yes	characteristic
98	C₂	#19151415	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19151839

C₂

yes

maximal, characteristic

#19151363

C₂

yes

maximal, characteristic

C₂²⋊C₁₆×C₈₉

C₂

yes

maximal, characteristic

C₂×Dic₃₅₆

C₄

yes

—

—

C₄

yes

characteristic

#15667937

—

C₂²×C₈×C₈₉

C₂²

yes

characteristic

C₂×C₁₆×C₈₉

—

C₂×Dic₁₇₈

—

Dic₃₅₆

—

#13083558

—

#13083558

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

#13083553

—

C₂²⋊Dic₈₉

—

C₂²×C₄×C₈₉

D₄

yes

characteristic

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂×C₈×C₈₉

D₄

yes

characteristic

C₁₆×C₈₉

—

C₂³×C₈₉

SD₁₆

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

D₈

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

—

C₂²×C₈₉

#102

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

yes

C₄×C₈₉

yes

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₈₉

yes

characteristic, complemented, Sylow

#467

—

C₂²⋊C₁₆

D₈₉

yes

characteristic

#341

—

C₂×Q₁₆

—

C₂×M₁₆

—

178

—

C₂²×C₈

C₂×D₈₉

yes

characteristic

C₂²⋊Q₈

—

178

—

C₂×C₁₆

—

#107

—

#103

—

178

—

C₂×Q₈

—

178

—

C₂²×C₄

D₃₅₆

yes

characteristic

Q₁₆

—

356

—

M₁₆

—

356

—

M₁₆

—

178

—

C₂×C₈

—

C₂×C₈

—

356

—

C₂×C₈

C₄×D₈₉

yes

characteristic

C₂×C₈

C₂²⋊D₈₉

yes

characteristic

C₄⋊C₄

—

356

—

C₄⋊C₄

—

178

—

C₂²⋊C₄

—

356

—

C₁₆

—

C₂³

#13083563

yes

characteristic

Q₈

—

356

—

Q₈

—

356

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

356

—

C₂×C₄

—

356

—

C₂×C₄

#13083551

yes

characteristic

C₂×C₄

D₇₁₂

yes

characteristic

C₈

—

C₈

—

C₈

—

356

—

C₂²

—

C₂²

—

C₂²

—

C₂²

#15667934

yes

characteristic

C₄

—

C₄

—

712

—

C₄

—

712

—

C₄

yes

C₄

yes

C₂

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂²	#15667934
commutator	C₂×C₈×C₈₉	C₂×C₄
Frattini	C₂²×C₈	C₂×D₈₉
Fitting	C₂²⋊C₁₆×C₈₉	C₂
socle	C₂²×C₈₉	#102
prime radical	C₂³×C₈₉	SD₁₆
cosocle	C₂²×C₈×C₈₉	C₂²
hypercenter	C₂²⋊C₁₆	D₈₉
hypocenter	C₈₉	#1350
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

subgroup

G/H

center

C₂²

#15667934

commutator

C₂×C₈×C₈₉

C₂×C₄

Frattini

C₂²×C₈

C₂×D₈₉

Fitting

C₂²⋊C₁₆×C₈₉

C₂

socle

C₂²×C₈₉

#102

prime radical

C₂³×C₈₉

SD₁₆

cosocle

C₂²×C₈×C₈₉

C₂²

hypercenter

C₂²⋊C₁₆

D₈₉

hypocenter

C₈₉

#1350

LCS

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

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²⋊C₁₆

N	H ≅ G/N	type
50. C₈₉	#1350	semidirect

H ≅ G/N

type

50. C₈₉

#1350

semidirect

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

subgroup	index
#19151839	2
#19151363	2
C₂²⋊C₁₆×C₈₉	2
#1350	89

subgroup

index

#19151839

#19151363

C₂²⋊C₁₆×C₈₉

#1350

Subgroups — #26018271

Conjugacy classes of subgroups

Complements

Maximal subgroups