Group #20267751 — subgroups

Subgroups — C₂×(C₂×D₁₀₃)⋊C₈ #20267751

Order 6592.

202 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 87 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	C₂²×C₄×D₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₀₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	(C₂×D₁₀₃)⋊C₈	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₀₃	C₄	1	1	yes	characteristic
6	C₂²×Dic₁₀₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₁₀₃	—	2	2	no	—
8	C₂×C₄×D₁₀₃	—	2	2	no	—
9	C₂×C₄×D₁₀₃	C₄	1	2	yes	—
10	C₂×C₄×D₁₀₃	C₂²	1	2	yes	—
11	C₂×C₁₀₃⋊C₈	—	2	2	no	—
12	C₂×C₁₀₃⋊C₈	C₂²	1	2	yes	complemented
13	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₁₀₃	—	2	2	no	—
15	C₂×C₈×C₁₀₃	C₂²	1	2	yes	complemented
16	C₂³×C₁₀₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×D₁₀₃	—	2	2	no	—
18	C₂²×D₁₀₃	—	2	2	no	—
19	C₂²×D₁₀₃	C₈	1	4	yes	complemented
20	C₂²×D₁₀₃	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₁₀₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
23	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
24	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
25	C₂×Dic₁₀₃	—	2	2	no	—
26	C₂×Dic₁₀₃	C₂×C₄	1	2	yes	—
27	C₄×D₁₀₃	—	2	4	no	—
28	C₄×D₁₀₃	—	2	2	no	—
29	C₄×D₁₀₃	—	2	2	no	—
30	C₈×C₁₀₃	—	2	2	no	—
31	C₁₀₃⋊C₈	—	2	2	no	—
32	C₂²×C₁₀₃	C₂²⋊C₄	1	2	yes	—
33	C₂²×C₁₀₃	C₂×C₈	1	2	yes	—
34	C₂²×C₁₀₃	M₁₆	1	2	yes	—
35	C₂²×C₁₀₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×D₁₀₃	—	2	8	no	—
37	C₂×D₁₀₃	—	2	2	no	—
38	C₂×D₁₀₃	—	2	2	no	—
39	C₂×D₁₀₃	C₂×C₈	1	4	yes	complemented
40	C₄×C₁₀₃	C₂²⋊C₄	1	2	yes	—
41	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
42	C₄×C₁₀₃	C₂×D₄	1	1	yes	characteristic
43	Dic₁₀₃	—	2	2	no	—
44	C₂×C₁₀₃	C₂²⋊C₈	1	4	yes	complemented
45	C₂×C₁₀₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂×C₁₀₃	C₂²×C₈	1	1	yes	characteristic
47	C₂×C₁₀₃	C₂×M₁₆	1	1	yes	characteristic
48	D₁₀₃	—	2	4	no	—
49	C₁₀₃	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₂²⋊C₈	—	103	1	no	maximal, Sylow
51	C₂³×C₄	—	103	1	no	—
52	C₂²×C₈	—	103	1	no	—
53	C₂²×C₈	D₁₀₃	1	1	yes	characteristic, complemented
54	C₂²⋊C₈	—	103	4	no	—
55	C₂⁴	—	103	1	no	—
56	C₂²×C₄	—	103	1	no	—
57	C₂²×C₄	—	103	2	no	—
58	C₂²×C₄	—	103	2	no	—
59	C₂²×C₄	—	206	2	no	—
60	C₂²×C₄	—	206	2	no	—
61	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	103	2	no	—
64	C₂×C₈	—	206	2	no	—
65	C₂×C₈	C₂×D₁₀₃	1	2	yes	complemented
66	C₂³	—	103	4	no	—
67	C₂³	—	103	2	no	—
68	C₂³	—	206	2	no	—
69	C₂³	—	206	2	no	—
70	C₂³	C₄×D₁₀₃	1	1	yes	characteristic
71	C₂×C₄	—	103	2	no	—
72	C₂×C₄	—	206	2	no	—
73	C₂×C₄	—	206	4	no	—
74	C₂×C₄	—	206	2	no	—
75	C₂×C₄	—	206	2	no	—
76	C₂×C₄	C₄×D₁₀₃	1	1	yes	characteristic
77	C₂×C₄	D₄₁₂	1	2	yes	—
78	C₂×C₄	C₂²⋊D₁₀₃	1	2	yes	—
79	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
80	C₈	—	2	2	no	—
81	C₈	—	206	2	no	—
82	C₂²	—	103	4	no	—
83	C₂²	—	206	8	no	—
84	C₂²	—	206	2	no	—
85	C₂²	—	206	2	no	—
86	C₂²	(C₂×D₁₀₃)⋊C₄	1	2	yes	—
87	C₂²	C₈×D₁₀₃	1	2	yes	—
88	C₂²	#13110088	1	2	yes	—
89	C₂²	C₂×C₄×D₁₀₃	1	1	yes	characteristic
90	C₄	—	206	2	no	—
91	C₄	(C₂×D₁₀₃)⋊C₄	1	2	yes	—
92	C₄	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
93	C₄	C₂×D₄₁₂	1	1	yes	characteristic
94	C₂	—	206	4	no	—
95	C₂	(C₂×D₁₀₃)⋊C₈	1	4	yes	direct product factor
96	C₂	C₂×(C₂×D₁₀₃)⋊C₄	1	1	yes	characteristic
97	C₂	C₂×C₈×D₁₀₃	1	1	yes	characteristic
98	C₂	C₂×#13110088	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄×D₁₀₃

C₂

yes

maximal, characteristic

C₂²×C₁₀₃⋊C₈

C₂

yes

maximal, characteristic, complemented

(C₂×D₁₀₃)⋊C₈

C₂

yes

maximal, direct product factor

C₂²×C₈×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₃

C₄

yes

characteristic

C₂²×Dic₁₀₃

C₄

yes

characteristic

C₂×C₄×D₁₀₃

—

C₂×C₄×D₁₀₃

—

C₂×C₄×D₁₀₃

C₄

yes

—

C₂×C₄×D₁₀₃

C₂²

yes

—

C₂×C₁₀₃⋊C₈

—

C₂×C₁₀₃⋊C₈

C₂²

yes

complemented

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₂×C₈×C₁₀₃

—

C₂×C₈×C₁₀₃

C₂²

yes

complemented

C₂³×C₁₀₃

C₂×C₄

yes

characteristic

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

C₈

yes

complemented

C₂²×D₁₀₃

C₂×C₄

yes

—

C₂×C₄×C₁₀₃

C₂×C₄

yes

characteristic

C₂×C₄×C₁₀₃

D₄

yes

—

C₂×C₄×C₁₀₃

D₄

yes

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

C₂×C₄

yes

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

C₈×C₁₀₃

—

C₁₀₃⋊C₈

—

C₂²×C₁₀₃

C₂²⋊C₄

yes

—

C₂²×C₁₀₃

C₂×C₈

yes

—

C₂²×C₁₀₃

M₁₆

yes

—

C₂²×C₁₀₃

C₂²×C₄

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

C₂×C₈

yes

complemented

C₄×C₁₀₃

C₂²⋊C₄

yes

—

C₄×C₁₀₃

C₂×D₄

yes

characteristic

C₄×C₁₀₃

C₂×D₄

yes

characteristic

Dic₁₀₃

—

C₂×C₁₀₃

C₂²⋊C₈

yes

complemented

C₂×C₁₀₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₀₃

C₂²×C₈

yes

characteristic

C₂×C₁₀₃

C₂×M₁₆

yes

characteristic

D₁₀₃

—

C₁₀₃

C₂×C₂²⋊C₈

yes

characteristic, complemented, Sylow

C₂×C₂²⋊C₈

—

103

maximal, Sylow

C₂³×C₄

—

103

—

C₂²×C₈

—

103

—

C₂²×C₈

D₁₀₃

yes

characteristic, complemented

C₂²⋊C₈

—

103

—

C₂⁴

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

206

—

C₂²×C₄

—

206

—

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

103

—

C₂×C₈

—

206

—

C₂×C₈

C₂×D₁₀₃

yes

complemented

C₂³

—

103

—

C₂³

—

103

—

C₂³

—

206

—

C₂³

—

206

—

C₂³

C₄×D₁₀₃

yes

characteristic

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

C₄×D₁₀₃

yes

characteristic

C₂×C₄

D₄₁₂

yes

—

C₂×C₄

C₂²⋊D₁₀₃

yes

—

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₈

—

C₈

—

206

—

C₂²

—

103

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

(C₂×D₁₀₃)⋊C₄

yes

—

C₂²

C₈×D₁₀₃

yes

—

C₂²

#13110088

yes

—

C₂²

C₂×C₄×D₁₀₃

yes

characteristic

C₄

—

206

—

C₄

(C₂×D₁₀₃)⋊C₄

yes

—

C₄

C₂×C₂²⋊D₁₀₃

yes

characteristic

C₄

C₂×D₄₁₂

yes

characteristic

C₂

—

206

—

C₂

(C₂×D₁₀₃)⋊C₈

yes

direct product factor

C₂

C₂×(C₂×D₁₀₃)⋊C₄

yes

characteristic

C₂

C₂×C₈×D₁₀₃

yes

characteristic

C₂

C₂×#13110088

yes

characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₀₃
commutator	C₂×C₁₀₃	C₂²×C₈
Frattini	C₂×C₄	C₂²×D₁₀₃
Fitting	C₂²×C₈×C₁₀₃	C₂
socle	C₂³×C₁₀₃	C₂×C₄
hypercenter	C₂²×C₈	D₁₀₃
hypocenter	C₁₀₃	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

subgroup

G/H

center

C₂²×C₄

C₂×D₁₀₃

commutator

C₂×C₁₀₃

C₂²×C₈

Frattini

C₂×C₄

C₂²×D₁₀₃

Fitting

C₂²×C₈×C₁₀₃

C₂

socle

C₂³×C₁₀₃

C₂×C₄

hypercenter

C₂²×C₈

D₁₀₃

hypocenter

C₁₀₃

C₂×C₂²⋊C₈

LCS

G ▷ C₂×C₁₀₃ ▷ C₁₀₃

UCS

C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

N	H ≅ G/N	type
2. C₂²×C₁₀₃⋊C₈	C₂	semidirect
3. (C₂×D₁₀₃)⋊C₈	C₂	direct (N × H)
4. C₂²×C₈×C₁₀₃	C₂	semidirect
12. C₂×C₁₀₃⋊C₈	C₂²	semidirect
15. C₂×C₈×C₁₀₃	C₂²	semidirect
19. C₂²×D₁₀₃	C₈	semidirect
39. C₂×D₁₀₃	C₂×C₈	semidirect
44. C₂×C₁₀₃	C₂²⋊C₈	semidirect
49. C₁₀₃	C₂×C₂²⋊C₈	semidirect
53. C₂²×C₈	D₁₀₃	semidirect
65. C₂×C₈	C₂×D₁₀₃	semidirect
95. C₂	(C₂×D₁₀₃)⋊C₈	direct (N × H)

H ≅ G/N

type

2. C₂²×C₁₀₃⋊C₈

C₂

semidirect

3. (C₂×D₁₀₃)⋊C₈

C₂

direct (N × H)

4. C₂²×C₈×C₁₀₃

C₂

semidirect

12. C₂×C₁₀₃⋊C₈

C₂²

semidirect

15. C₂×C₈×C₁₀₃

C₂²

semidirect

19. C₂²×D₁₀₃

C₈

semidirect

39. C₂×D₁₀₃

C₂×C₈

semidirect

44. C₂×C₁₀₃

C₂²⋊C₈

semidirect

49. C₁₀₃

C₂×C₂²⋊C₈

semidirect

53. C₂²×C₈

D₁₀₃

semidirect

65. C₂×C₈

C₂×D₁₀₃

semidirect

95. C₂

(C₂×D₁₀₃)⋊C₈

direct (N × H)

Subgroups — C₂×(C₂×D₁₀₃)⋊C₈ #20267751

Conjugacy classes of subgroups

Complements

Subgroups — C2×(C2×D103)⋊C8 #20267751

Conjugacy classes of subgroups

Complements

Subgroups — C₂×(C₂×D₁₀₃)⋊C₈ #20267751