Group #26023557 — subgroups

Subgroups — #26023557

Order 11392.

400 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 157 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	#19151540	C₂	1	4	yes	maximal
2	#19151532	C₂	1	4	yes	maximal
3	C₄×#13083553	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₈₉	C₂	1	2	yes	maximal
5	#376×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊Dic₈₉	C₂²	1	4	yes	—
7	C₂×#13083553	C₂²	1	4	yes	—
8	C₂×#13083553	C₂²	1	4	yes	—
9	C₂×C₄×Dic₈₉	C₂²	1	4	yes	—
10	#15667919	C₂²	1	2	yes	—
11	#15667919	C₂²	1	2	yes	—
12	#15667919	C₂²	1	4	yes	—
13	#15667919	C₂²	1	4	yes	—
14	C₂×C₄²×C₈₉	C₂²	1	2	yes	—
15	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
16	#95×C₈₉	C₂²	1	4	yes	—
17	C₂²×Dic₈₉	C₂³	1	4	yes	—
18	C₂²×Dic₈₉	C₂³	1	4	yes	—
19	C₄⋊Dic₈₉	—	2	8	no	—
20	#13083553	—	2	8	no	—
21	#13083553	—	2	8	no	—
22	C₄×Dic₈₉	—	2	8	no	—
23	C₂²×C₄×C₈₉	C₂³	1	4	yes	—
24	C₂²×C₄×C₈₉	C₂³	1	2	yes	—
25	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
26	C₄²×C₈₉	—	2	4	no	—
27	C₄²×C₈₉	Q₈	1	4	yes	—
28	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
29	C₂×C₄×C₈₉	—	2	4	no	—
30	C₂×C₄×C₈₉	—	2	4	no	—
31	C₂×C₄×C₈₉	—	2	4	no	—
32	C₂×C₄×C₈₉	—	2	4	no	—
33	C₂×C₄×C₈₉	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₈₉	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₈₉	#41	1	4	yes	—
36	C₂×Dic₈₉	—	2	4	no	—
37	C₂×Dic₈₉	—	2	4	no	—
38	C₂×Dic₈₉	—	2	4	no	—
39	C₂×Dic₈₉	—	2	4	no	—
40	C₂×Dic₈₉	—	2	4	no	—
41	C₂×Dic₈₉	#41	1	8	yes	—
42	C₂²×C₈₉	C₂²×Q₈	1	1	yes	characteristic
43	C₂²×C₈₉	C₂×#41	1	2	yes	—
44	C₂²×C₈₉	C₂×#41	1	4	yes	—
45	C₄×C₈₉	—	2	4	no	—
46	C₄×C₈₉	—	4	4	no	—
47	C₄×C₈₉	#125	1	4	yes	—
48	Dic₈₉	—	2	8	no	—
49	Dic₈₉	—	4	4	no	—
50	C₂×C₈₉	C₂×#125	1	1	yes	characteristic
51	C₂×C₈₉	#529	1	4	yes	—
52	C₂×C₈₉	#533	1	2	yes	—
53	#2402	—	89	1	no	maximal, Sylow
54	C₈₉	#2402	1	1	yes	characteristic, complemented, Sylow
55	#400	—	89	4	no	—
56	#398	—	89	4	no	—
57	C₄×C₄⋊C₄	—	89	2	no	—
58	C₄×C₄⋊C₄	—	89	4	no	—
59	#376	D₈₉	1	1	yes	characteristic
60	C₂×C₄⋊C₄	—	89	4	no	—
61	C₂×C₄⋊C₄	—	89	4	no	—
62	C₂×C₄⋊C₄	—	89	4	no	—
63	C₂×C₄²	—	89	4	no	—
64	C₂×C₄²	C₂×D₈₉	1	2	yes	—
65	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
66	#95	—	89	2	no	—
67	#95	—	89	4	no	—
68	#95	—	89	4	no	—
69	#95	—	89	2	no	—
70	#95	C₂×D₈₉	1	4	yes	—
71	C₂²×C₄	—	89	4	no	—
72	C₂²×C₄	—	89	4	no	—
73	C₂²×C₄	C₂²×D₈₉	1	4	yes	—
74	C₂²×C₄	C₂²×D₈₉	1	2	yes	—
75	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
76	C₄⋊C₄	—	178	8	no	—
77	C₄⋊C₄	—	178	8	no	—
78	C₄⋊C₄	—	178	8	no	—
79	C₄²	—	2	4	no	—
80	C₄²	—	178	8	no	—
81	C₄²	Dic₁₇₈	1	4	yes	—
82	C₂³	C₂³×D₈₉	1	1	yes	characteristic
83	C₂×C₄	—	2	4	no	—
84	C₂×C₄	—	2	4	no	—
85	C₂×C₄	—	2	4	no	—
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	89	8	no	—
88	C₂×C₄	—	178	4	no	—
89	C₂×C₄	—	178	4	no	—
90	C₂×C₄	—	178	4	no	—
91	C₂×C₄	—	178	4	no	—
92	C₂×C₄	—	178	4	no	—
93	C₂×C₄	C₂×Dic₁₇₈	1	4	yes	—
94	C₂×C₄	C₂×Dic₁₇₈	1	2	yes	—
95	C₂×C₄	#13083574	1	4	yes	—
96	C₂²	C₂²×Dic₁₇₈	1	1	yes	characteristic
97	C₂²	#41×D₈₉	1	4	yes	—
98	C₂²	C₂×#13083574	1	2	yes	—
99	C₄	—	2	4	no	—
100	C₄	—	4	4	no	—
101	C₄	—	356	4	no	—
102	C₄	—	178	8	no	—
103	C₄	#15668004	1	4	yes	—
104	C₂	C₂×#15668004	1	1	yes	characteristic
105	C₂	#19152126	1	4	yes	—
106	C₂	#19152151	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#19151540

C₂

yes

maximal

#19151532

C₂

yes

maximal

C₄×#13083553

C₂

yes

maximal

C₄×C₄⋊Dic₈₉

C₂

yes

maximal

#376×C₈₉

C₂

yes

maximal, characteristic

C₂×C₄⋊Dic₈₉

C₂²

yes

—

C₂×#13083553

C₂²

yes

—

C₂×#13083553

C₂²

yes

—

C₂×C₄×Dic₈₉

C₂²

yes

—

#15667919

C₂²

yes

—

#15667919

C₂²

yes

—

#15667919

C₂²

yes

—

#15667919

C₂²

yes

—

C₂×C₄²×C₈₉

C₂²

yes

—

C₂×C₄²×C₈₉

C₂²

yes

characteristic

#95×C₈₉

C₂²

yes

—

C₂²×Dic₈₉

C₂³

yes

—

C₂²×Dic₈₉

C₂³

yes

—

C₄⋊Dic₈₉

—

#13083553

—

#13083553

—

C₄×Dic₈₉

—

C₂²×C₄×C₈₉

C₂³

yes

—

C₂²×C₄×C₈₉

C₂³

yes

—

C₂²×C₄×C₈₉

C₂³

yes

characteristic

C₄²×C₈₉

—

C₄²×C₈₉

Q₈

yes

—

C₂³×C₈₉

C₂⁴

yes

characteristic

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×Q₈

yes

—

C₂×C₄×C₈₉

C₂×Q₈

yes

—

C₂×C₄×C₈₉

#41

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#41

yes

—

C₂²×C₈₉

C₂²×Q₈

yes

characteristic

C₂²×C₈₉

C₂×#41

yes

—

C₂²×C₈₉

C₂×#41

yes

—

C₄×C₈₉

—

C₄×C₈₉

—

C₄×C₈₉

#125

yes

—

Dic₈₉

—

Dic₈₉

—

C₂×C₈₉

C₂×#125

yes

characteristic

C₂×C₈₉

#529

yes

—

C₂×C₈₉

#533

yes

—

#2402

—

maximal, Sylow

C₈₉

#2402

yes

characteristic, complemented, Sylow

#400

—

#398

—

C₄×C₄⋊C₄

—

C₄×C₄⋊C₄

—

#376

D₈₉

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₈₉

yes

—

C₂×C₄²

C₂×D₈₉

yes

—

—

—

—

C₂×D₈₉

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₈₉

yes

—

C₂²×C₄

C₂²×D₈₉

yes

—

C₂²×C₄

C₂²×D₈₉

yes

characteristic

C₄⋊C₄

—

178

—

C₄⋊C₄

—

178

—

C₄⋊C₄

—

178

—

C₄²

—

C₄²

—

178

—

C₄²

Dic₁₇₈

yes

—

C₂³

C₂³×D₈₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂×Dic₁₇₈

yes

—

C₂×C₄

C₂×Dic₁₇₈

yes

—

C₂×C₄

#13083574

yes

—

C₂²

C₂²×Dic₁₇₈

yes

characteristic

C₂²

#41×D₈₉

yes

—

C₂²

C₂×#13083574

yes

—

C₄

—

100

C₄

—

101

C₄

—

356

—

102

C₄

—

178

—

103

C₄

#15668004

yes

—

104

C₂

C₂×#15668004

yes

characteristic

105

C₂

#19152126

yes

—

106

C₂

#19152151

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₈₉
commutator, socle, prime radical, cosocle	C₂³×C₈₉	C₂⁴
Frattini	C₂³	C₂³×D₈₉
Fitting	#376×C₈₉	C₂
hypercenter	#376	D₈₉
hypocenter	C₈₉	#2402
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₈₉

commutator, socle, prime radical, cosocle

C₂³×C₈₉

C₂⁴

Frattini

C₂³

C₂³×D₈₉

Fitting

#376×C₈₉

C₂

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
54. C₈₉	#2402	semidirect

H ≅ G/N

type

54. C₈₉

#2402

semidirect

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

subgroup	index
#19151540	2
#19151532	2
C₄×#13083553	2
C₄×C₄⋊Dic₈₉	2
#376×C₈₉	2
#2402	89

subgroup

index

#19151540

#19151532

C₄×#13083553

C₄×C₄⋊Dic₈₉

#376×C₈₉

#2402

Subgroups — #26023557

Conjugacy classes of subgroups

Complements

Maximal subgroups