Group #20268342 — subgroups

Subgroups — #20268342

Order 6592.

310 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 111 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	C₂×#13110106	C₂	1	2	yes	maximal, complemented
2	#15693018	C₂	1	1	yes	maximal, characteristic, complemented
3	#15693010	C₂	1	2	yes	maximal, complemented
4	#15692996	C₂	1	4	yes	maximal, complemented
5	#15692983	C₂	1	4	yes	maximal, complemented
6	C₄²×D₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄⋊Q₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#13110106	—	2	8	no	—
9	C₂×D₄₁₂	C₂²	1	4	yes	—
10	C₂×D₄₁₂	C₂²	1	2	yes	—
11	C₂×D₄₁₂	C₂²	1	4	yes	—
12	C₂×C₄×D₁₀₃	C₂²	1	4	yes	—
13	C₂×C₄×D₁₀₃	C₂²	1	2	yes	—
14	C₂×C₄×D₁₀₃	C₂²	1	1	yes	characteristic
15	(C₂×D₁₀₃)⋊C₄	C₂²	1	8	yes	—
16	C₄×Dic₁₀₃	C₂²	1	2	yes	—
17	C₄×Dic₁₀₃	C₂²	1	1	yes	characteristic
18	C₂×Q₈×C₁₀₃	C₂²	1	2	yes	—
19	C₄⋊C₄×C₁₀₃	C₂²	1	4	yes	—
20	C₄²×C₁₀₃	C₂²	1	1	yes	characteristic
21	C₂²×D₁₀₃	C₂³	1	4	yes	—
22	C₂²×D₁₀₃	C₂³	1	1	yes	characteristic
23	Q₈×C₁₀₃	—	2	4	no	—
24	C₂×C₄×C₁₀₃	C₂³	1	4	yes	—
25	C₂×C₄×C₁₀₃	C₂³	1	1	yes	characteristic
26	C₂×C₄×C₁₀₃	C₂³	1	2	yes	—
27	C₂×Dic₁₀₃	C₂³	1	2	yes	—
28	C₂×Dic₁₀₃	C₂³	1	1	yes	characteristic
29	D₄₁₂	—	2	8	no	—
30	D₄₁₂	—	2	4	no	—
31	D₄₁₂	—	2	8	no	—
32	C₄×D₁₀₃	—	2	4	no	—
33	C₄×D₁₀₃	—	2	8	no	—
34	C₄×D₁₀₃	D₄	1	4	yes	complemented
35	C₂²×C₁₀₃	C₂⁴	1	1	yes	characteristic
36	C₂×D₁₀₃	—	2	2	no	—
37	C₂×D₁₀₃	—	2	4	no	—
38	C₂×D₁₀₃	—	2	8	no	—
39	C₂×D₁₀₃	C₂×D₄	1	2	yes	—
40	C₄×C₁₀₃	—	2	4	no	—
41	C₄×C₁₀₃	C₂×D₄	1	2	yes	—
42	C₄×C₁₀₃	#41	1	4	yes	complemented
43	Dic₁₀₃	—	2	2	no	—
44	Dic₁₀₃	C₂×D₄	1	2	yes	—
45	C₂×C₁₀₃	C₂²×D₄	1	1	yes	characteristic
46	C₂×C₁₀₃	C₂×#41	1	2	yes	—
47	D₁₀₃	—	2	2	no	—
48	D₁₀₃	—	4	4	no	—
49	C₁₀₃	#532	1	1	yes	characteristic, complemented, Sylow
50	#532	—	103	1	no	maximal, Sylow
51	C₂×#41	—	103	2	no	—
52	C₄⋊Q₈	D₁₀₃	1	1	yes	characteristic, complemented
53	#127	—	103	1	no	—
54	#124	—	103	2	no	—
55	#121	—	103	4	no	—
56	C₄×D₄	—	103	4	no	—
57	C₂×C₄²	—	103	1	no	—
58	#41	—	206	8	no	—
59	C₂×Q₈	C₂×D₁₀₃	1	2	yes	—
60	C₂×D₄	—	103	4	no	—
61	C₂×D₄	—	103	4	no	—
62	C₂×D₄	—	103	2	no	—
63	C₂²×C₄	—	103	1	no	—
64	C₂²×C₄	—	103	2	no	—
65	C₂²×C₄	—	103	4	no	—
66	C₄⋊C₄	C₂×D₁₀₃	1	4	yes	—
67	C₂²⋊C₄	—	103	8	no	—
68	C₄²	—	103	2	no	—
69	C₄²	—	103	1	no	—
70	C₄²	C₂×D₁₀₃	1	1	yes	characteristic
71	C₂³	—	103	1	no	—
72	C₂³	—	103	4	no	—
73	Q₈	—	2	4	no	—
74	D₄	—	206	8	no	—
75	D₄	—	206	4	no	—
76	D₄	—	206	8	no	—
77	C₂×C₄	—	103	1	no	—
78	C₂×C₄	—	103	4	no	—
79	C₂×C₄	—	103	2	no	—
80	C₂×C₄	—	206	8	no	—
81	C₂×C₄	—	206	4	no	—
82	C₂×C₄	C₂²×D₁₀₃	1	4	yes	—
83	C₂×C₄	C₂²×D₁₀₃	1	1	yes	characteristic
84	C₂×C₄	C₂²×D₁₀₃	1	2	yes	—
85	C₂²	—	103	2	no	—
86	C₂²	—	206	4	no	—
87	C₂²	—	206	8	no	—
88	C₂²	—	206	2	no	—
89	C₂²	C₂³×D₁₀₃	1	1	yes	characteristic
90	C₄	—	2	4	no	—
91	C₄	—	103	2	no	—
92	C₄	—	206	2	no	—
93	C₄	D₄×D₁₀₃	1	2	yes	—
94	C₄	#13110106	1	4	yes	complemented
95	C₂	—	412	4	no	—
96	C₂	—	206	2	no	—
97	C₂	C₂×D₄×D₁₀₃	1	1	yes	characteristic
98	C₂	C₂×#13110106	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13110106

C₂

yes

maximal, complemented

#15693018

C₂

yes

maximal, characteristic, complemented

#15693010

C₂

yes

maximal, complemented

#15692996

C₂

yes

maximal, complemented

#15692983

C₂

yes

maximal, complemented

C₄²×D₁₀₃

C₂

yes

maximal, characteristic, complemented

C₄⋊Q₈×C₁₀₃

C₂

yes

maximal, characteristic, complemented

#13110106

—

C₂×D₄₁₂

C₂²

yes

—

C₂×D₄₁₂

C₂²

yes

—

C₂×D₄₁₂

C₂²

yes

—

C₂×C₄×D₁₀₃

C₂²

yes

—

C₂×C₄×D₁₀₃

C₂²

yes

—

C₂×C₄×D₁₀₃

C₂²

yes

characteristic

(C₂×D₁₀₃)⋊C₄

C₂²

yes

—

C₄×Dic₁₀₃

C₂²

yes

—

C₄×Dic₁₀₃

C₂²

yes

characteristic

C₂×Q₈×C₁₀₃

C₂²

yes

—

C₄⋊C₄×C₁₀₃

C₂²

yes

—

C₄²×C₁₀₃

C₂²

yes

characteristic

C₂²×D₁₀₃

C₂³

yes

—

C₂²×D₁₀₃

C₂³

yes

characteristic

Q₈×C₁₀₃

—

C₂×C₄×C₁₀₃

C₂³

yes

—

C₂×C₄×C₁₀₃

C₂³

yes

characteristic

C₂×C₄×C₁₀₃

C₂³

yes

—

C₂×Dic₁₀₃

C₂³

yes

—

C₂×Dic₁₀₃

C₂³

yes

characteristic

D₄₁₂

—

D₄₁₂

—

D₄₁₂

—

C₄×D₁₀₃

—

C₄×D₁₀₃

—

C₄×D₁₀₃

D₄

yes

complemented

C₂²×C₁₀₃

C₂⁴

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

C₂×D₄

yes

—

C₄×C₁₀₃

—

C₄×C₁₀₃

C₂×D₄

yes

—

C₄×C₁₀₃

#41

yes

complemented

Dic₁₀₃

—

Dic₁₀₃

C₂×D₄

yes

—

C₂×C₁₀₃

C₂²×D₄

yes

characteristic

C₂×C₁₀₃

C₂×#41

yes

—

D₁₀₃

—

D₁₀₃

—

C₁₀₃

#532

yes

characteristic, complemented, Sylow

#532

—

103

maximal, Sylow

C₂×#41

—

103

—

C₄⋊Q₈

D₁₀₃

yes

characteristic, complemented

#127

—

103

—

#124

—

103

—

#121

—

103

—

C₄×D₄

—

103

—

C₂×C₄²

—

103

—

#41

—

206

—

C₂×Q₈

C₂×D₁₀₃

yes

—

C₂×D₄

—

103

—

C₂×D₄

—

103

—

C₂×D₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₄⋊C₄

C₂×D₁₀₃

yes

—

C₂²⋊C₄

—

103

—

C₄²

—

103

—

C₄²

—

103

—

C₄²

C₂×D₁₀₃

yes

characteristic

C₂³

—

103

—

C₂³

—

103

—

Q₈

—

D₄

—

206

—

D₄

—

206

—

D₄

—

206

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

C₂²×D₁₀₃

yes

—

C₂×C₄

C₂²×D₁₀₃

yes

characteristic

C₂×C₄

C₂²×D₁₀₃

yes

—

C₂²

—

103

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

C₂³×D₁₀₃

yes

characteristic

C₄

—

C₄

—

103

—

C₄

—

206

—

C₄

D₄×D₁₀₃

yes

—

C₄

#13110106

yes

complemented

C₂

—

412

—

C₂

—

206

—

C₂

C₂×D₄×D₁₀₃

yes

characteristic

C₂

C₂×#13110106

yes

—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₁₀₃
commutator, socle	C₂²×C₁₀₃	C₂⁴
Fitting	C₄⋊Q₈×C₁₀₃	C₂
hypercenter	C₄⋊Q₈	D₁₀₃
hypocenter	C₁₀₃	#532
LCS	G ▷ C₂²×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

subgroup

G/H

center, Frattini

C₂²

C₂³×D₁₀₃

commutator, socle

C₂²×C₁₀₃

C₂⁴

Fitting

C₄⋊Q₈×C₁₀₃

C₂

hypercenter

C₄⋊Q₈

D₁₀₃

C₁₀₃

G ▷ C₂²×C₁₀₃ ▷ C₁₀₃

C₁ ◁ C₂² ◁ C₄⋊Q₈

N	H ≅ G/N	type
1. C₂×#13110106	C₂	semidirect
2. #15693018	C₂	semidirect
3. #15693010	C₂	semidirect
4. #15692996	C₂	semidirect
5. #15692983	C₂	semidirect
6. C₄²×D₁₀₃	C₂	semidirect
7. C₄⋊Q₈×C₁₀₃	C₂	semidirect
34. C₄×D₁₀₃	D₄	semidirect
42. C₄×C₁₀₃	#41	semidirect
49. C₁₀₃	#532	semidirect
52. C₄⋊Q₈	D₁₀₃	semidirect
94. C₄	#13110106	semidirect

H ≅ G/N

type

1. C₂×#13110106

C₂

semidirect

2. #15693018

C₂

semidirect

3. #15693010

C₂

semidirect

4. #15692996

C₂

semidirect

5. #15692983

C₂

semidirect

6. C₄²×D₁₀₃

C₂

semidirect

7. C₄⋊Q₈×C₁₀₃

C₂

semidirect

34. C₄×D₁₀₃

D₄

semidirect

42. C₄×C₁₀₃

#41

semidirect

49. C₁₀₃

#532

semidirect

52. C₄⋊Q₈

D₁₀₃

semidirect

94. C₄

#13110106

semidirect

Subgroups — #20268342

Conjugacy classes of subgroups

Complements