Group #26042354 — subgroups

Subgroups — C₂×#19153903 #26042354

Order 11584.

266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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	#19153903	C₂	1	8	yes	maximal, direct product factor
2	C₂×#15668459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15668458	C₂	1	2	yes	maximal, complemented
4	C₂×D₁₈₁⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13089685	C₂	1	2	yes	maximal, complemented
6	C₂×#15668448	C₂	1	1	yes	maximal, characteristic
7	#15668459	C₂²	1	4	yes	complemented
8	#15668458	C₂²	1	8	yes	complemented
9	D₁₈₁⋊C₈	C₂²	1	4	yes	complemented
10	C₂×#13089685	C₂²	1	1	yes	characteristic
11	C₂×#13089685	C₂²	1	2	yes	—
12	C₂×#13089685	C₂²	1	1	yes	characteristic
13	C₂×#13089685	C₂²	1	8	yes	complemented
14	#15668448	C₄	1	4	yes	—
15	#15668448	C₂²	1	4	yes	—
16	C₂×Dic₃₆₂	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₁₈₁	C₄	1	2	yes	—
18	C₂²×Dic₁₈₁	C₂²	1	2	yes	—
19	C₂×C₄×D₁₈₁	C₂²	1	1	yes	characteristic
20	C₂×D₄×C₁₈₁	C₄	1	1	yes	characteristic
21	#13089685	C₂³	1	2	yes	—
22	#13089685	C₂³	1	4	yes	—
23	#13089685	C₂³	1	2	yes	—
24	C₂²×D₁₈₁	C₂×C₄	1	1	yes	characteristic
25	Dic₃₆₂	C₂×C₄	1	4	yes	—
26	C₂²⋊D₁₈₁	C₂×C₄	1	8	yes	—
27	C₂×Dic₁₈₁	C₂×C₄	1	2	yes	—
28	C₂×Dic₁₈₁	C₂×C₄	1	4	yes	—
29	C₂×Dic₁₈₁	C₂³	1	1	yes	characteristic
30	C₂×Dic₁₈₁	C₂³	1	4	yes	—
31	C₄×D₁₈₁	C₂×C₄	1	2	yes	—
32	C₄×D₁₈₁	C₂³	1	2	yes	—
33	C₂³×C₁₈₁	C₂×C₄	1	2	yes	—
34	D₄×C₁₈₁	C₂×C₄	1	4	yes	—
35	C₂×C₄×C₁₈₁	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₁₈₁	—	2	4	no	—
37	C₂²×C₁₈₁	C₂²×C₄	1	4	yes	—
38	C₂²×C₁₈₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×D₁₈₁	—	2	2	no	—
40	C₂×D₁₈₁	C₂²×C₄	1	2	yes	—
41	C₄×C₁₈₁	C₂²×C₄	1	2	yes	—
42	Dic₁₈₁	C₂²×C₄	1	1	yes	characteristic
43	Dic₁₈₁	C₂²×C₄	1	4	yes	—
44	Dic₁₈₁	C₂⁴	1	1	yes	characteristic
45	C₂×C₁₈₁	—	2	4	no	—
46	C₂×C₁₈₁	#131	1	2	yes	complemented
47	C₂×C₁₈₁	C₂³×C₄	1	1	yes	characteristic
48	D₁₈₁	—	2	2	no	—
49	C₁₈₁	C₂×#131	1	1	yes	characteristic, complemented, Sylow
50	C₂×#131	—	181	1	no	maximal, Sylow
51	C₂×#41	—	181	1	no	—
52	#131	—	181	8	no	—
53	C₂×M₁₆	—	181	2	no	—
54	C₂×M₁₆	—	181	1	no	—
55	C₂²×C₈	—	181	2	no	—
56	C₂²×C₈	—	181	1	no	—
57	#41	—	181	4	no	—
58	#41	—	181	4	no	—
59	C₂×Q₈	—	181	1	no	—
60	C₂×D₄	—	181	2	no	—
61	C₂×D₄	#10624382	1	1	yes	characteristic
62	C₂²×C₄	—	181	2	no	—
63	C₂²×C₄	—	181	1	no	—
64	M₁₆	—	181	8	no	—
65	M₁₆	—	181	4	no	—
66	C₂×C₈	—	181	1	no	—
67	C₂×C₈	—	181	2	no	—
68	C₂×C₈	—	181	1	no	—
69	C₂×C₈	—	181	8	no	—
70	C₂×C₈	—	181	4	no	—
71	C₂³	—	181	1	no	—
72	C₂³	C₂×#10624382	1	2	yes	—
73	Q₈	—	181	4	no	—
74	D₄	—	181	8	no	—
75	D₄	C₂×#10624382	1	4	yes	—
76	C₂×C₄	—	181	4	no	—
77	C₂×C₄	—	181	4	no	—
78	C₂×C₄	—	181	1	no	—
79	C₂×C₄	—	181	2	no	—
80	C₂×C₄	—	181	2	no	—
81	C₂×C₄	—	181	2	no	—
82	C₂×C₄	C₂×#10624382	1	1	yes	characteristic
83	C₈	—	181	2	no	—
84	C₈	—	181	4	no	—
85	C₈	—	181	2	no	—
86	C₂²	—	2	4	no	—
87	C₂²	—	362	2	no	—
88	C₂²	—	181	2	no	—
89	C₂²	C₂²×#10624382	1	4	yes	—
90	C₂²	C₂²×#10624382	1	1	yes	characteristic
91	C₄	—	181	1	no	—
92	C₄	—	181	1	no	—
93	C₄	—	181	4	no	—
94	C₄	C₂²×#10624382	1	2	yes	—
95	C₂	—	2	4	no	—
96	C₂	—	362	2	no	—
97	C₂	#19153903	1	2	yes	direct product factor
98	C₂	C₂³×#10624382	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#19153903

C₂

yes

maximal, direct product factor

C₂×#15668459

C₂

yes

maximal, characteristic, complemented

C₂×#15668458

C₂

yes

maximal, complemented

C₂×D₁₈₁⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂²×#13089685

C₂

yes

maximal, complemented

C₂×#15668448

C₂

yes

maximal, characteristic

#15668459

C₂²

yes

complemented

#15668458

C₂²

yes

complemented

D₁₈₁⋊C₈

C₂²

yes

complemented

C₂×#13089685

C₂²

yes

characteristic

C₂×#13089685

C₂²

yes

—

C₂×#13089685

C₂²

yes

characteristic

C₂×#13089685

C₂²

yes

complemented

#15668448

C₄

yes

—

#15668448

C₂²

yes

—

C₂×Dic₃₆₂

C₄

yes

characteristic

C₂×C₂²⋊D₁₈₁

C₄

yes

—

C₂²×Dic₁₈₁

C₂²

yes

—

C₂×C₄×D₁₈₁

C₂²

yes

characteristic

C₂×D₄×C₁₈₁

C₄

yes

characteristic

#13089685

C₂³

yes

—

#13089685

C₂³

yes

—

#13089685

C₂³

yes

—

C₂²×D₁₈₁

C₂×C₄

yes

characteristic

Dic₃₆₂

C₂×C₄

yes

—

C₂²⋊D₁₈₁

C₂×C₄

yes

—

C₂×Dic₁₈₁

C₂×C₄

yes

—

C₂×Dic₁₈₁

C₂×C₄

yes

—

C₂×Dic₁₈₁

C₂³

yes

characteristic

C₂×Dic₁₈₁

C₂³

yes

—

C₄×D₁₈₁

C₂×C₄

yes

—

C₄×D₁₈₁

C₂³

yes

—

C₂³×C₁₈₁

C₂×C₄

yes

—

D₄×C₁₈₁

C₂×C₄

yes

—

C₂×C₄×C₁₈₁

C₂×C₄

yes

characteristic

C₂²×C₁₈₁

—

C₂²×C₁₈₁

C₂²×C₄

yes

—

C₂²×C₁₈₁

C₂²×C₄

yes

characteristic

C₂×D₁₈₁

—

C₂×D₁₈₁

C₂²×C₄

yes

—

C₄×C₁₈₁

C₂²×C₄

yes

—

Dic₁₈₁

C₂²×C₄

yes

characteristic

Dic₁₈₁

C₂²×C₄

yes

—

Dic₁₈₁

C₂⁴

yes

characteristic

C₂×C₁₈₁

—

C₂×C₁₈₁

#131

yes

complemented

C₂×C₁₈₁

C₂³×C₄

yes

characteristic

D₁₈₁

—

C₁₈₁

C₂×#131

yes

characteristic, complemented, Sylow

C₂×#131

—

181

maximal, Sylow

C₂×#41

—

181

—

#131

—

181

—

C₂×M₁₆

—

181

—

C₂×M₁₆

—

181

—

C₂²×C₈

—

181

—

C₂²×C₈

—

181

—

#41

—

181

—

#41

—

181

—

C₂×Q₈

—

181

—

C₂×D₄

—

181

—

C₂×D₄

#10624382

yes

characteristic

C₂²×C₄

—

181

—

C₂²×C₄

—

181

—

M₁₆

—

181

—

M₁₆

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂×C₈

—

181

—

C₂³

—

181

—

C₂³

C₂×#10624382

yes

—

Q₈

—

181

—

D₄

—

181

—

D₄

C₂×#10624382

yes

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

—

181

—

C₂×C₄

C₂×#10624382

yes

characteristic

C₈

—

181

—

C₈

—

181

—

C₈

—

181

—

C₂²

—

C₂²

—

362

—

C₂²

—

181

—

C₂²

C₂²×#10624382

yes

—

C₂²

C₂²×#10624382

yes

characteristic

C₄

—

181

—

C₄

—

181

—

C₄

—

181

—

C₄

C₂²×#10624382

yes

—

C₂

—

C₂

—

362

—

C₂

#19153903

yes

direct product factor

C₂

C₂³×#10624382

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×#10624382
commutator	C₂×C₁₈₁	C₂³×C₄
Frattini	C₂	C₂³×#10624382
Fitting	C₂×D₄×C₁₈₁	C₄
socle	C₂²×C₁₈₁	C₂²×C₄
prime radical	C₂×#15668448	C₂
cosocle	Dic₁₈₁	C₂⁴
hypercenter	C₂×D₄	#10624382
hypocenter	C₁₈₁	C₂×#131
LCS	G ▷ C₂×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ C₂×D₄

subgroup

G/H

center

C₂²

C₂²×#10624382

commutator

C₂×C₁₈₁

C₂³×C₄

Frattini

C₂

C₂³×#10624382

Fitting

C₂×D₄×C₁₈₁

C₄

socle

C₂²×C₁₈₁

C₂²×C₄

prime radical

C₂×#15668448

C₂

cosocle

Dic₁₈₁

C₂⁴

C₂×D₄

C₁₈₁

G ▷ C₂×C₁₈₁ ▷ C₁₈₁

C₁ ◁ C₂² ◁ C₂×D₄

N	H ≅ G/N	type
1. #19153903	C₂	direct (N × H)
2. C₂×#15668459	C₂	semidirect
3. C₂×#15668458	C₂	semidirect
4. C₂×D₁₈₁⋊C₈	C₂	semidirect
5. C₂²×#13089685	C₂	semidirect
7. #15668459	C₂²	semidirect
8. #15668458	C₂²	semidirect
9. D₁₈₁⋊C₈	C₂²	semidirect
13. C₂×#13089685	C₂²	semidirect
46. C₂×C₁₈₁	#131	semidirect
49. C₁₈₁	C₂×#131	semidirect
97. C₂	#19153903	direct (N × H)

H ≅ G/N

type

1. #19153903

C₂

direct (N × H)

2. C₂×#15668459

C₂

semidirect

3. C₂×#15668458

C₂

semidirect

4. C₂×D₁₈₁⋊C₈

C₂

semidirect

5. C₂²×#13089685

C₂

semidirect

7. #15668459

C₂²

semidirect

8. #15668458

C₂²

semidirect

9. D₁₈₁⋊C₈

C₂²

semidirect

13. C₂×#13089685

C₂²

semidirect

46. C₂×C₁₈₁

#131

semidirect

49. C₁₈₁

C₂×#131

semidirect

97. C₂

#19153903

direct (N × H)

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

subgroup	index
#19153903	2
C₂×#15668459	2
C₂×#15668458	2
C₂×D₁₈₁⋊C₈	2
C₂²×#13089685	2
C₂×#15668448	2
C₂×#131	181

subgroup

index

C₂×D₁₈₁⋊C₈

181

Subgroups — C₂×#19153903 #26042354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#19153903 #26042354

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19153903 #26042354