Group #26019160 — subgroups

Subgroups — #26019160

Order 11392.

148 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 63 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	#19151725	C₂	1	2	yes	maximal
2	C₄×Dic₃₅₆	C₂	1	1	yes	maximal, characteristic
3	#19151328	C₂	1	2	yes	maximal
4	#19151319	C₂	1	1	yes	maximal, characteristic
5	#334×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₅₆	C₄	1	1	yes	characteristic
7	C₄×Dic₁₇₈	C₂²	1	2	yes	—
8	#15667946	C₄	1	1	yes	characteristic
9	#15667941	—	2	2	no	—
10	#15667937	C₄	1	2	yes	—
11	#15667922	—	2	2	no	—
12	C₄×#10623494	C₂²	1	1	yes	characteristic
13	C₄×#10623494	C₂²	1	1	yes	characteristic
14	C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
15	C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×Dic₁₇₈	C₂×C₄	1	2	yes	—
17	Dic₃₅₆	—	2	2	no	—
18	C₂×#10623494	—	2	1	no	—
19	C₂×#10623494	D₄	1	2	yes	—
20	C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
21	#13083553	—	2	2	no	—
22	C₄×Dic₈₉	—	2	2	no	—
23	C₂×C₈×C₈₉	—	2	2	no	—
24	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₈₉	C₂³	1	1	yes	characteristic
27	C₂×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
29	C₂×C₄×C₈₉	#41	1	1	yes	characteristic
30	C₂×Dic₈₉	—	2	2	no	—
31	C₂×Dic₈₉	—	2	2	no	—
32	Dic₁₇₈	—	2	2	no	—
33	Dic₁₇₈	—	2	2	no	—
34	C₈×C₈₉	—	2	1	no	—
35	C₈×C₈₉	—	4	2	no	—
36	C₈×C₈₉	M₁₆	1	2	yes	—
37	#10623494	—	2	2	no	—
38	#10623494	—	4	1	no	—
39	C₂²×C₈₉	C₄×D₄	1	1	yes	characteristic
40	C₄×C₈₉	—	2	1	no	—
41	C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
42	C₄×C₈₉	#131	1	1	yes	characteristic
43	C₄×C₈₉	#137	1	2	yes	—
44	Dic₈₉	—	4	2	no	—
45	Dic₈₉	—	4	2	no	—
46	C₂×C₈₉	#436	1	1	yes	characteristic
47	C₂×C₈₉	#441	1	1	yes	characteristic
48	C₂×C₈₉	#444	1	1	yes	characteristic
49	#1593	—	89	1	no	maximal, Sylow
50	C₈₉	#1593	1	1	yes	characteristic, complemented, Sylow
51	#446	—	89	2	no	—
52	C₄×Q₁₆	—	89	1	no	—
53	#334	D₈₉	1	1	yes	characteristic
54	Q₈⋊C₈	—	89	2	no	—
55	#322	—	89	1	no	—
56	C₂×Q₁₆	—	89	1	no	—
57	C₄×Q₈	—	89	2	no	—
58	#107	—	89	1	no	—
59	C₄⋊C₈	—	178	2	no	—
60	C₄⋊C₈	C₂×D₈₉	1	2	yes	—
61	#103	—	89	2	no	—
62	#97	—	178	2	no	—
63	C₄×C₈	—	89	1	no	—
64	C₄×C₈	—	89	1	no	—
65	C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
66	C₂×Q₈	—	89	2	no	—
67	Q₁₆	—	178	2	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	89	2	no	—
70	C₂×C₈	—	178	1	no	—
71	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
72	C₂×C₈	C₄×D₈₉	1	1	yes	characteristic
73	C₄⋊C₄	—	89	2	no	—
74	C₄⋊C₄	—	178	2	no	—
75	C₄²	—	178	2	no	—
76	C₄²	C₂²×D₈₉	1	1	yes	characteristic
77	Q₈	—	178	2	no	—
78	Q₈	—	178	2	no	—
79	C₂×C₄	—	178	2	no	—
80	C₂×C₄	—	178	2	no	—
81	C₂×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
82	C₂×C₄	D₄×D₈₉	1	1	yes	characteristic
83	C₂×C₄	#13083575	1	1	yes	characteristic
84	C₈	—	2	1	no	—
85	C₈	—	4	2	no	—
86	C₈	—	356	1	no	—
87	C₈	—	178	2	no	—
88	C₈	#13083557	1	2	yes	—
89	C₂²	#15667974	1	1	yes	characteristic
90	C₄	—	2	1	no	—
91	C₄	—	356	2	no	—
92	C₄	—	356	2	no	—
93	C₄	C₂×#13083557	1	1	yes	characteristic
94	C₄	#15668020	1	1	yes	characteristic
95	C₄	#15668041	1	2	yes	—
96	C₂	#19151675	1	1	yes	characteristic
97	C₂	#19151704	1	1	yes	characteristic
98	C₂	#19151719	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19151725

C₂

yes

maximal

C₄×Dic₃₅₆

C₂

yes

maximal, characteristic

#19151328

C₂

yes

maximal

#19151319

C₂

yes

maximal, characteristic

#334×C₈₉

C₂

yes

maximal, characteristic

C₂×Dic₃₅₆

C₄

yes

characteristic

C₄×Dic₁₇₈

C₂²

yes

—

#15667946

C₄

yes

characteristic

#15667941

—

#15667937

C₄

yes

—

#15667922

—

C₄×#10623494

C₂²

yes

characteristic

C₄×#10623494

C₂²

yes

characteristic

C₄⋊C₈×C₈₉

C₂²

yes

—

C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂×Dic₁₇₈

C₂×C₄

yes

—

Dic₃₅₆

—

C₂×#10623494

—

C₂×#10623494

D₄

yes

—

C₄⋊Dic₈₉

C₂×C₄

yes

—

#13083553

—

C₄×Dic₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×C₄

yes

characteristic

C₄²×C₈₉

C₂³

yes

characteristic

C₂×C₄×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂×C₄×C₈₉

#41

yes

characteristic

C₂×Dic₈₉

—

C₂×Dic₈₉

—

Dic₁₇₈

—

Dic₁₇₈

—

C₈×C₈₉

—

C₈×C₈₉

—

C₈×C₈₉

M₁₆

yes

—

#10623494

—

#10623494

—

C₂²×C₈₉

C₄×D₄

yes

characteristic

C₄×C₈₉

—

C₄×C₈₉

C₂×M₁₆

yes

C₄×C₈₉

yes

C₄×C₈₉

yes

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

yes

C₂×C₈₉

yes

C₂×C₈₉

yes

—

C₈₉

yes

characteristic, complemented, Sylow

#446

—

C₄×Q₁₆

—

#334

D₈₉

yes

characteristic

Q₈⋊C₈

—

#322

—

C₂×Q₁₆

—

C₄×Q₈

—

#107

—

C₄⋊C₈

—

178

—

C₄⋊C₈

C₂×D₈₉

yes

—

#103

—

#97

—

178

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

C₂×D₈₉

yes

characteristic

C₂×Q₈

—

Q₁₆

—

178

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

178

—

C₂×C₈

C₄×D₈₉

yes

characteristic

C₂×C₈

C₄×D₈₉

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

178

—

C₄²

—

178

—

C₄²

C₂²×D₈₉

yes

characteristic

Q₈

—

178

—

Q₈

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂×C₄×D₈₉

yes

characteristic

C₂×C₄

D₄×D₈₉

yes

characteristic

C₂×C₄

#13083575

yes

characteristic

C₈

—

C₈

—

C₈

—

356

—

C₈

—

178

—

C₈

#13083557

yes

—

C₂²

#15667974

yes

characteristic

C₄

—

C₄

—

356

—

C₄

—

356

—

C₄

yes

C₄

yes

C₄

yes

—

C₂

yes

C₂

yes

C₂

yes

	subgroup	G/H
center	C₂×C₄	D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂²×C₄
Frattini	C₄²	C₂²×D₈₉
Fitting	#334×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂³
hypercenter	#334	D₈₉
hypocenter	C₈₉	#1593
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

subgroup

G/H

center

C₂×C₄

D₄×D₈₉

commutator

C₂×C₄×C₈₉

C₂²×C₄

Frattini

C₄²

C₂²×D₈₉

Fitting

#334×C₈₉

C₂

socle, prime radical

C₂²×C₈₉

C₄×D₄

cosocle

C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₄² ◁ #334

N	H ≅ G/N	type
50. C₈₉	#1593	semidirect

H ≅ G/N

type

50. C₈₉

#1593

semidirect

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

subgroup	index
#19151725	2
C₄×Dic₃₅₆	2
#19151328	2
#19151319	2
#334×C₈₉	2
#1593	89

subgroup

index

C₄×Dic₃₅₆

#334×C₈₉

Subgroups — #26019160

Conjugacy classes of subgroups

Complements

Maximal subgroups