Group #36760472 — subgroups

Subgroups — C₂×#26028644 #36760472

Order 22784.

2186 conjugacy classes of subgroups; only the 683 normal subgroups are shown.

normal subgroups only

This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 683 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	#26028644	C₂	1	16	yes	maximal, direct product factor
2	C₂×#19151489	C₂	1	7	yes	maximal
3	C₂×#19151482	C₂	1	7	yes	maximal, complemented
4	C₂×C₄³×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13083553	C₂²	1	7	yes	—
6	C₂²×#13083551	C₂²	1	7	yes	—
7	#19151489	C₂²	1	56	yes	—
8	#19151482	C₂²	1	56	yes	complemented
9	C₂×#15667919	C₂²	1	14	yes	—
10	C₂²×C₄²×C₈₉	C₂²	1	7	yes	—
11	C₄³×C₈₉	C₂²	1	8	yes	complemented
12	C₂⁴×D₈₉	C₂³	1	1	yes	characteristic
13	C₂³×Dic₈₉	C₂³	1	7	yes	—
14	C₂×#13083553	—	2	28	no	—
15	C₂×#13083553	C₂³	1	28	yes	—
16	C₂×#13083551	—	2	28	no	—
17	C₂×#13083551	C₂³	1	28	yes	—
18	#15667919	C₂³	1	56	yes	—
19	C₂³×C₄×C₈₉	C₂³	1	7	yes	—
20	C₂×C₄²×C₈₉	—	2	28	no	—
21	C₂×C₄²×C₈₉	C₂³	1	28	yes	—
22	C₂³×D₈₉	—	2	14	no	—
23	C₂³×D₈₉	C₂⁴	1	2	yes	—
24	C₂²×Dic₈₉	—	2	14	no	—
25	C₂²×Dic₈₉	—	2	28	no	—
26	C₂²×Dic₈₉	C₂⁴	1	14	yes	—
27	#13083553	—	2	56	no	—
28	#13083551	—	2	56	no	—
29	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
30	C₂²×C₄×C₈₉	—	2	28	no	—
31	C₂²×C₄×C₈₉	#41	1	28	yes	—
32	C₂²×C₄×C₈₉	C₂⁴	1	14	yes	—
33	C₄²×C₈₉	—	2	56	no	—
34	C₂³×C₈₉	C₂×#41	1	14	yes	—
35	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
36	C₂²×D₈₉	—	2	14	no	—
37	C₂²×D₈₉	—	4	28	no	—
38	C₂×C₄×C₈₉	—	2	56	no	—
39	C₂×C₄×C₈₉	—	2	28	no	—
40	C₂×C₄×C₈₉	C₂×#41	1	28	yes	—
41	C₂×Dic₈₉	—	2	14	no	—
42	C₂×Dic₈₉	—	2	28	no	—
43	C₂×Dic₈₉	—	4	28	no	—
44	C₂²×C₈₉	#529	1	28	yes	—
45	C₂²×C₈₉	C₂²×#41	1	7	yes	—
46	C₂×D₈₉	—	4	14	no	—
47	C₂×D₈₉	—	8	8	no	—
48	C₄×C₈₉	—	2	28	no	—
49	Dic₈₉	—	4	14	no	—
50	C₂×#2866	—	89	1	no	maximal, Sylow
51	C₂×C₈₉	#2866	1	8	yes	complemented
52	C₂×C₈₉	C₂×#529	1	7	yes	—
53	D₈₉	—	8	2	no	—
54	#2866	—	89	16	no	—
55	C₂×#388	—	89	7	no	—
56	C₂×#387	—	89	7	no	—
57	C₂×C₄³	D₈₉	1	1	yes	characteristic, complemented
58	C₈₉	C₂×#2866	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₄⋊C₄	—	89	7	no	—
60	C₂²×C₂²⋊C₄	—	89	7	no	—
61	C₂²×C₄²	C₂×D₈₉	1	7	yes	—
62	#388	—	89	56	no	—
63	#387	—	89	56	no	—
64	C₂×#95	—	89	14	no	—
65	C₄³	C₂×D₈₉	1	8	yes	complemented
66	C₂⁵	—	89	1	no	—
67	C₂³×C₄	—	89	7	no	—
68	C₂³×C₄	C₂²×D₈₉	1	7	yes	—
69	C₂×C₄⋊C₄	—	89	28	no	—
70	C₂×C₄⋊C₄	—	178	28	no	—
71	C₂×C₂²⋊C₄	—	89	28	no	—
72	C₂×C₂²⋊C₄	—	178	28	no	—
73	C₂×C₄²	—	2	28	no	—
74	C₂×C₄²	C₂²×D₈₉	1	28	yes	—
75	#95	—	89	56	no	—
76	C₂⁴	—	89	2	no	—
77	C₂⁴	—	178	14	no	—
78	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
79	C₂²×C₄	—	2	28	no	—
80	C₂²×C₄	—	89	14	no	—
81	C₂²×C₄	—	178	14	no	—
82	C₂²×C₄	—	178	28	no	—
83	C₂²×C₄	#13083574	1	28	yes	—
84	C₂²×C₄	C₂³×D₈₉	1	14	yes	—
85	C₄⋊C₄	—	178	56	no	—
86	C₂²⋊C₄	—	178	56	no	—
87	C₄²	—	2	56	no	—
88	C₂³	—	356	28	no	—
89	C₂³	—	178	14	no	—
90	C₂³	C₂×#13083574	1	14	yes	—
91	C₂³	C₂⁴×D₈₉	1	1	yes	characteristic
92	C₂×C₄	—	2	56	no	—
93	C₂×C₄	—	2	28	no	—
94	C₂×C₄	—	356	28	no	—
95	C₂×C₄	—	178	14	no	—
96	C₂×C₄	—	178	28	no	—
97	C₂×C₄	C₂×#13083574	1	28	yes	—
98	C₂²	—	356	14	no	—
99	C₂²	—	712	8	no	—
100	C₂²	#19152132	1	28	yes	—
101	C₂²	C₂²×#13083574	1	7	yes	—
102	C₄	—	2	28	no	—
103	C₄	—	356	14	no	—
104	C₂	—	712	2	no	—
105	C₂	#26028644	1	8	yes	direct product factor
106	C₂	C₂×#19152132	1	7	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26028644

C₂

yes

maximal, direct product factor

C₂×#19151489

C₂

yes

maximal

C₂×#19151482

C₂

yes

maximal, complemented

C₂×C₄³×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂²×#13083553

C₂²

yes

—

C₂²×#13083551

C₂²

yes

—

#19151489

C₂²

yes

—

#19151482

C₂²

yes

complemented

C₂×#15667919

C₂²

yes

—

C₂²×C₄²×C₈₉

C₂²

yes

—

C₄³×C₈₉

C₂²

yes

complemented

C₂⁴×D₈₉

C₂³

yes

characteristic

C₂³×Dic₈₉

C₂³

yes

—

C₂×#13083553

—

C₂×#13083553

C₂³

yes

—

C₂×#13083551

—

C₂×#13083551

C₂³

yes

—

#15667919

C₂³

yes

—

C₂³×C₄×C₈₉

C₂³

yes

—

C₂×C₄²×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

—

C₂³×D₈₉

—

C₂³×D₈₉

C₂⁴

yes

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

C₂⁴

yes

—

#13083553

—

#13083551

—

C₂⁴×C₈₉

C₂⁴

yes

characteristic

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

#41

yes

—

C₂²×C₄×C₈₉

C₂⁴

yes

—

C₄²×C₈₉

—

C₂³×C₈₉

C₂×#41

yes

—

C₂³×C₈₉

C₂⁵

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×#41

yes

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂²×C₈₉

#529

yes

—

C₂²×C₈₉

C₂²×#41

yes

—

C₂×D₈₉

—

C₂×D₈₉

—

C₄×C₈₉

—

Dic₈₉

—

—

C₂×C₈₉

yes

C₂×C₈₉

yes

—

D₈₉

—

#2866

—

C₂×#388

—

C₂×#387

—

C₂×C₄³

D₈₉

yes

characteristic, complemented

C₈₉

C₂×#2866

yes

characteristic, complemented, Sylow

C₂²×C₄⋊C₄

—

C₂²×C₂²⋊C₄

—

C₂²×C₄²

C₂×D₈₉

yes

—

#388

—

#387

—

C₂×#95

—

C₄³

C₂×D₈₉

yes

complemented

C₂⁵

—

C₂³×C₄

—

C₂³×C₄

C₂²×D₈₉

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

178

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

178

—

C₂×C₄²

—

C₂×C₄²

C₂²×D₈₉

yes

—

#95

—

C₂⁴

—

C₂⁴

—

178

—

C₂⁴

C₂³×D₈₉

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

178

—

C₂²×C₄

—

178

—

C₂²×C₄

#13083574

yes

—

C₂²×C₄

C₂³×D₈₉

yes

—

C₄⋊C₄

—

178

—

C₂²⋊C₄

—

178

—

C₄²

—

C₂³

—

356

—

C₂³

—

178

—

C₂³

C₂×#13083574

yes

—

C₂³

C₂⁴×D₈₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

356

—

C₂×C₄

—

178

—

C₂×C₄

—

178

—

C₂×C₄

C₂×#13083574

yes

—

C₂²

—

356

—

C₂²

—

712

—

100

C₂²

#19152132

yes

—

101

C₂²

C₂²×#13083574

yes

—

102

C₄

—

103

C₄

—

356

—

104

C₂

—

712

—

105

C₂

#26028644

yes

direct product factor

106

C₂

C₂×#19152132

yes

—

	subgroup	G/H
center	C₂⁴	C₂³×D₈₉
commutator, cosocle	C₂³×C₈₉	C₂⁵
Frattini	C₂³	C₂⁴×D₈₉
Fitting	C₂×C₄³×C₈₉	C₂
socle	C₂⁴×C₈₉	C₂⁴
prime radical	C₂⁴×D₈₉	C₂³
hypercenter	C₂×C₄³	D₈₉
hypocenter	C₈₉	C₂×#2866
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

subgroup

G/H

center

C₂⁴

C₂³×D₈₉

commutator, cosocle

C₂³×C₈₉

C₂⁵

Frattini

C₂³

C₂⁴×D₈₉

Fitting

C₂×C₄³×C₈₉

C₂

socle

C₂⁴×C₈₉

C₂⁴

prime radical

C₂⁴×D₈₉

C₂³

hypercenter

C₂×C₄³

D₈₉

C₈₉

G ▷ C₂³×C₈₉ ▷ C₈₉

C₁ ◁ C₂⁴ ◁ C₂×C₄³

N	H ≅ G/N	type
1. #26028644	C₂	direct (N × H)
3. C₂×#19151482	C₂	semidirect
4. C₂×C₄³×C₈₉	C₂	semidirect
8. #19151482	C₂²	semidirect
11. C₄³×C₈₉	C₂²	semidirect
51. C₂×C₈₉	#2866	semidirect
57. C₂×C₄³	D₈₉	semidirect
58. C₈₉	C₂×#2866	semidirect
65. C₄³	C₂×D₈₉	semidirect
105. C₂	#26028644	direct (N × H)

H ≅ G/N

type

1. #26028644

C₂

direct (N × H)

3. C₂×#19151482

C₂

semidirect

4. C₂×C₄³×C₈₉

C₂

semidirect

8. #19151482

C₂²

semidirect

11. C₄³×C₈₉

C₂²

semidirect

51. C₂×C₈₉

#2866

semidirect

57. C₂×C₄³

D₈₉

semidirect

58. C₈₉

C₂×#2866

semidirect

65. C₄³

C₂×D₈₉

semidirect

105. C₂

#26028644

direct (N × H)

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

subgroup	index
#26028644	2
C₂×#19151489	2
C₂×#19151482	2
C₂×C₄³×C₈₉	2
C₂×#2866	89

subgroup

index

C₂×C₄³×C₈₉

Subgroups — C₂×#26028644 #36760472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#26028644 #36760472

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26028644 #36760472