Group #38787189 — subgroups

Subgroups — C₂×#27165824 #38787189

Order 25664.

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	#27165824	C₂	1	8	yes	maximal, direct product factor
2	C₂×#20264376	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#20264375	C₂	1	2	yes	maximal, complemented
4	C₂×#20264374	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#15692006	C₂	1	2	yes	maximal, complemented
6	C₂×#20264365	C₂	1	1	yes	maximal, characteristic
7	#20264376	C₂²	1	4	yes	complemented
8	#20264375	C₂²	1	8	yes	complemented
9	#20264374	C₂²	1	4	yes	complemented
10	C₂×#15692006	C₂²	1	1	yes	characteristic
11	C₂×#15692006	C₂²	1	2	yes	—
12	C₂×#15692006	C₂²	1	1	yes	characteristic
13	C₂×#15692006	C₂²	1	8	yes	complemented
14	#20264365	C₄	1	4	yes	—
15	#20264365	C₂²	1	4	yes	—
16	C₂×Dic₈₀₂	C₄	1	1	yes	characteristic
17	C₂×C₂²⋊D₄₀₁	C₄	1	2	yes	—
18	C₂²×Dic₄₀₁	C₂²	1	2	yes	—
19	C₂×C₄×D₄₀₁	C₂²	1	1	yes	characteristic
20	C₂×D₄×C₄₀₁	C₄	1	1	yes	characteristic
21	#15692006	C₂³	1	2	yes	—
22	#15692006	C₂³	1	4	yes	—
23	#15692006	C₂³	1	2	yes	—
24	C₂²×D₄₀₁	C₂×C₄	1	1	yes	characteristic
25	Dic₈₀₂	C₂×C₄	1	4	yes	—
26	C₂²⋊D₄₀₁	C₂×C₄	1	8	yes	—
27	C₂×Dic₄₀₁	C₂×C₄	1	2	yes	—
28	C₂×Dic₄₀₁	C₂×C₄	1	4	yes	—
29	C₂×Dic₄₀₁	C₂³	1	1	yes	characteristic
30	C₂×Dic₄₀₁	C₂³	1	4	yes	—
31	C₄×D₄₀₁	C₂×C₄	1	2	yes	—
32	C₄×D₄₀₁	C₂³	1	2	yes	—
33	C₂³×C₄₀₁	C₂×C₄	1	2	yes	—
34	D₄×C₄₀₁	C₂×C₄	1	4	yes	—
35	C₂×C₄×C₄₀₁	C₂×C₄	1	1	yes	characteristic
36	C₂²×C₄₀₁	—	2	4	no	—
37	C₂²×C₄₀₁	C₂²×C₄	1	4	yes	—
38	C₂²×C₄₀₁	C₂²×C₄	1	1	yes	characteristic
39	C₂×D₄₀₁	—	2	2	no	—
40	C₂×D₄₀₁	C₂²×C₄	1	2	yes	—
41	C₄×C₄₀₁	C₂²×C₄	1	2	yes	—
42	Dic₄₀₁	C₂²×C₄	1	1	yes	characteristic
43	Dic₄₀₁	C₂²×C₄	1	4	yes	—
44	Dic₄₀₁	C₂⁴	1	1	yes	characteristic
45	C₂×C₄₀₁	—	2	4	no	—
46	C₂×C₄₀₁	#131	1	2	yes	complemented
47	C₂×C₄₀₁	C₂³×C₄	1	1	yes	characteristic
48	D₄₀₁	—	2	2	no	—
49	C₄₀₁	C₂×#131	1	1	yes	characteristic, complemented, Sylow
50	C₂×#131	—	401	1	no	maximal, Sylow
51	C₂×#41	—	401	1	no	—
52	#131	—	401	8	no	—
53	C₂×M₁₆	—	401	2	no	—
54	C₂×M₁₆	—	401	1	no	—
55	C₂²×C₈	—	401	2	no	—
56	C₂²×C₈	—	401	1	no	—
57	#41	—	401	4	no	—
58	#41	—	401	4	no	—
59	C₂×Q₈	—	401	1	no	—
60	C₂×D₄	—	401	2	no	—
61	C₂×D₄	#13107944	1	1	yes	characteristic
62	C₂²×C₄	—	401	2	no	—
63	C₂²×C₄	—	401	1	no	—
64	M₁₆	—	401	8	no	—
65	M₁₆	—	401	4	no	—
66	C₂×C₈	—	401	1	no	—
67	C₂×C₈	—	401	2	no	—
68	C₂×C₈	—	401	1	no	—
69	C₂×C₈	—	401	8	no	—
70	C₂×C₈	—	401	4	no	—
71	C₂³	—	401	1	no	—
72	C₂³	C₂×#13107944	1	2	yes	—
73	Q₈	—	401	4	no	—
74	D₄	—	401	8	no	—
75	D₄	C₂×#13107944	1	4	yes	—
76	C₂×C₄	—	401	4	no	—
77	C₂×C₄	—	401	4	no	—
78	C₂×C₄	—	401	1	no	—
79	C₂×C₄	—	401	2	no	—
80	C₂×C₄	—	401	2	no	—
81	C₂×C₄	—	401	2	no	—
82	C₂×C₄	C₂×#13107944	1	1	yes	characteristic
83	C₈	—	401	2	no	—
84	C₈	—	401	4	no	—
85	C₈	—	401	2	no	—
86	C₂²	—	2	4	no	—
87	C₂²	—	802	2	no	—
88	C₂²	—	401	2	no	—
89	C₂²	C₂²×#13107944	1	4	yes	—
90	C₂²	C₂²×#13107944	1	1	yes	characteristic
91	C₄	—	401	1	no	—
92	C₄	—	401	1	no	—
93	C₄	—	401	4	no	—
94	C₄	C₂²×#13107944	1	2	yes	—
95	C₂	—	2	4	no	—
96	C₂	—	802	2	no	—
97	C₂	#27165824	1	2	yes	direct product factor
98	C₂	C₂³×#13107944	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#27165824

C₂

yes

maximal, direct product factor

C₂×#20264376

C₂

yes

maximal, characteristic, complemented

C₂×#20264375

C₂

yes

maximal, complemented

C₂×#20264374

C₂

yes

maximal, characteristic, complemented

C₂²×#15692006

C₂

yes

maximal, complemented

C₂×#20264365

C₂

yes

maximal, characteristic

#20264376

C₂²

yes

complemented

#20264375

C₂²

yes

complemented

#20264374

C₂²

yes

complemented

C₂×#15692006

C₂²

yes

characteristic

C₂×#15692006

C₂²

yes

—

C₂×#15692006

C₂²

yes

characteristic

C₂×#15692006

C₂²

yes

complemented

#20264365

C₄

yes

—

#20264365

C₂²

yes

—

C₂×Dic₈₀₂

C₄

yes

characteristic

C₂×C₂²⋊D₄₀₁

C₄

yes

—

C₂²×Dic₄₀₁

C₂²

yes

—

C₂×C₄×D₄₀₁

C₂²

yes

characteristic

C₂×D₄×C₄₀₁

C₄

yes

characteristic

#15692006

C₂³

yes

—

#15692006

C₂³

yes

—

#15692006

C₂³

yes

—

C₂²×D₄₀₁

C₂×C₄

yes

characteristic

Dic₈₀₂

C₂×C₄

yes

—

C₂²⋊D₄₀₁

C₂×C₄

yes

—

C₂×Dic₄₀₁

C₂×C₄

yes

—

C₂×Dic₄₀₁

C₂×C₄

yes

—

C₂×Dic₄₀₁

C₂³

yes

characteristic

C₂×Dic₄₀₁

C₂³

yes

—

C₄×D₄₀₁

C₂×C₄

yes

—

C₄×D₄₀₁

C₂³

yes

—

C₂³×C₄₀₁

C₂×C₄

yes

—

D₄×C₄₀₁

C₂×C₄

yes

—

C₂×C₄×C₄₀₁

C₂×C₄

yes

characteristic

C₂²×C₄₀₁

—

C₂²×C₄₀₁

C₂²×C₄

yes

—

C₂²×C₄₀₁

C₂²×C₄

yes

characteristic

C₂×D₄₀₁

—

C₂×D₄₀₁

C₂²×C₄

yes

—

C₄×C₄₀₁

C₂²×C₄

yes

—

Dic₄₀₁

C₂²×C₄

yes

characteristic

Dic₄₀₁

C₂²×C₄

yes

—

Dic₄₀₁

C₂⁴

yes

characteristic

C₂×C₄₀₁

—

C₂×C₄₀₁

#131

yes

complemented

C₂×C₄₀₁

C₂³×C₄

yes

characteristic

D₄₀₁

—

C₄₀₁

C₂×#131

yes

characteristic, complemented, Sylow

C₂×#131

—

401

maximal, Sylow

C₂×#41

—

401

—

#131

—

401

—

C₂×M₁₆

—

401

—

C₂×M₁₆

—

401

—

C₂²×C₈

—

401

—

C₂²×C₈

—

401

—

#41

—

401

—

#41

—

401

—

C₂×Q₈

—

401

—

C₂×D₄

—

401

—

C₂×D₄

#13107944

yes

characteristic

C₂²×C₄

—

401

—

C₂²×C₄

—

401

—

M₁₆

—

401

—

M₁₆

—

401

—

C₂×C₈

—

401

—

C₂×C₈

—

401

—

C₂×C₈

—

401

—

C₂×C₈

—

401

—

C₂×C₈

—

401

—

C₂³

—

401

—

C₂³

C₂×#13107944

yes

—

Q₈

—

401

—

D₄

—

401

—

D₄

C₂×#13107944

yes

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

—

401

—

C₂×C₄

C₂×#13107944

yes

characteristic

C₈

—

401

—

C₈

—

401

—

C₈

—

401

—

C₂²

—

C₂²

—

802

—

C₂²

—

401

—

C₂²

C₂²×#13107944

yes

—

C₂²

C₂²×#13107944

yes

characteristic

C₄

—

401

—

C₄

—

401

—

C₄

—

401

—

C₄

C₂²×#13107944

yes

—

C₂

—

C₂

—

802

—

C₂

#27165824

yes

direct product factor

C₂

C₂³×#13107944

yes

characteristic

	subgroup	G/H
center	C₂²	C₂²×#13107944
commutator	C₂×C₄₀₁	C₂³×C₄
Frattini	C₂	C₂³×#13107944
Fitting	C₂×D₄×C₄₀₁	C₄
socle	C₂²×C₄₀₁	C₂²×C₄
prime radical	C₂×#20264365	C₂
cosocle	Dic₄₀₁	C₂⁴
hypercenter	C₂×D₄	#13107944
hypocenter	C₄₀₁	C₂×#131
LCS	G ▷ C₂×C₄₀₁ ▷ C₄₀₁
UCS	C₁ ◁ C₂² ◁ C₂×D₄

subgroup

G/H

center

C₂²

C₂²×#13107944

commutator

C₂×C₄₀₁

C₂³×C₄

Frattini

C₂

C₂³×#13107944

Fitting

C₂×D₄×C₄₀₁

C₄

socle

C₂²×C₄₀₁

C₂²×C₄

prime radical

C₂×#20264365

C₂

cosocle

Dic₄₀₁

C₂⁴

C₂×D₄

C₄₀₁

G ▷ C₂×C₄₀₁ ▷ C₄₀₁

C₁ ◁ C₂² ◁ C₂×D₄

N	H ≅ G/N	type
1. #27165824	C₂	direct (N × H)
2. C₂×#20264376	C₂	semidirect
3. C₂×#20264375	C₂	semidirect
4. C₂×#20264374	C₂	semidirect
5. C₂²×#15692006	C₂	semidirect
7. #20264376	C₂²	semidirect
8. #20264375	C₂²	semidirect
9. #20264374	C₂²	semidirect
13. C₂×#15692006	C₂²	semidirect
46. C₂×C₄₀₁	#131	semidirect
49. C₄₀₁	C₂×#131	semidirect
97. C₂	#27165824	direct (N × H)

H ≅ G/N

type

1. #27165824

C₂

direct (N × H)

2. C₂×#20264376

C₂

semidirect

3. C₂×#20264375

C₂

semidirect

4. C₂×#20264374

C₂

semidirect

5. C₂²×#15692006

C₂

semidirect

7. #20264376

C₂²

semidirect

8. #20264375

C₂²

semidirect

9. #20264374

C₂²

semidirect

13. C₂×#15692006

C₂²

semidirect

46. C₂×C₄₀₁

#131

semidirect

49. C₄₀₁

C₂×#131

semidirect

97. C₂

#27165824

direct (N × H)

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

subgroup	index
#27165824	2
C₂×#20264376	2
C₂×#20264375	2
C₂×#20264374	2
C₂²×#15692006	2
C₂×#20264365	2
C₂×#131	401

subgroup

index

401

Subgroups — C₂×#27165824 #38787189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×#27165824 #38787189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27165824 #38787189