Group #20267726 — subgroups

Subgroups — #20267726

Order 6592.

186 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 61 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×Dic₁₀₃⋊C₄	C₂	1	2	yes	maximal, complemented
2	C₂×(C₂×D₁₀₃)⋊C₄	C₂	1	2	yes	maximal
3	C₂×(C₂×D₁₀₃)⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₀₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₄⋊C₄×C₁₀₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₁₀₃	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₀₃	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₀₃	C₂²	1	2	yes	—
9	Dic₁₀₃⋊C₄	—	2	4	no	—
10	(C₂×D₁₀₃)⋊C₄	—	2	2	no	—
11	(C₂×D₁₀₃)⋊C₄	—	2	4	no	—
12	C₂²×C₄×C₁₀₃	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₀₃	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₀₃	—	2	2	no	—
15	C₂³×C₁₀₃	C₂³	1	1	yes	characteristic
16	C₂²×D₁₀₃	—	2	2	no	—
17	C₂²×D₁₀₃	—	2	1	no	—
18	C₂²×D₁₀₃	—	2	2	no	—
19	C₂²×D₁₀₃	—	2	1	no	—
20	C₂²×D₁₀₃	Q₈	1	2	yes	—
21	C₂×C₄×C₁₀₃	—	2	2	no	—
22	C₂×C₄×C₁₀₃	—	2	2	no	—
23	C₂×C₄×C₁₀₃	—	2	2	no	—
24	C₂×C₄×C₁₀₃	—	2	2	no	—
25	C₂×C₄×C₁₀₃	D₄	1	2	yes	—
26	C₂×Dic₁₀₃	—	2	2	no	—
27	C₂×Dic₁₀₃	—	2	2	no	—
28	C₂×Dic₁₀₃	—	2	1	no	—
29	C₂×Dic₁₀₃	—	2	2	no	—
30	C₂×Dic₁₀₃	D₄	1	4	yes	—
31	C₂²×C₁₀₃	C₂×D₄	1	2	yes	—
32	C₂²×C₁₀₃	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₁₀₃	C₂×Q₈	1	1	yes	characteristic
34	C₂²×C₁₀₃	#41	1	2	yes	—
35	C₂²×C₁₀₃	#41	1	1	yes	characteristic
36	C₂×D₁₀₃	—	2	2	no	—
37	C₂×D₁₀₃	—	2	4	no	—
38	C₂×D₁₀₃	—	4	1	no	—
39	C₂×D₁₀₃	—	4	2	no	—
40	C₂×D₁₀₃	—	4	1	no	—
41	C₄×C₁₀₃	—	2	2	no	—
42	C₄×C₁₀₃	—	4	2	no	—
43	Dic₁₀₃	—	2	4	no	—
44	Dic₁₀₃	—	4	1	no	—
45	C₂×C₁₀₃	C₂²⋊Q₈	1	1	yes	characteristic
46	C₂×C₁₀₃	C₂²⋊Q₈	1	2	yes	—
47	C₂×C₁₀₃	#123	1	1	yes	characteristic
48	C₂×C₁₀₃	#123	1	2	yes	—
49	C₂×C₁₀₃	#127	1	1	yes	characteristic
50	D₁₀₃	—	4	2	no	—
51	C₁₀₃	#399	1	1	yes	characteristic, complemented, Sylow
52	#399	—	103	1	no	maximal, Sylow
53	C₂×C₄⋊C₄	—	103	2	no	—
54	C₂×C₄⋊C₄	D₁₀₃	1	1	yes	characteristic, complemented
55	C₂×C₂²⋊C₄	—	103	2	no	—
56	C₂×C₂²⋊C₄	—	103	1	no	—
57	#95	—	103	1	no	—
58	C₂⁴	—	103	1	no	—
59	C₂²×C₄	—	103	2	no	—
60	C₂²×C₄	—	103	1	no	—
61	C₂²×C₄	C₂×D₁₀₃	1	2	yes	—
62	C₂²×C₄	C₂×D₁₀₃	1	1	yes	characteristic
63	C₄⋊C₄	—	2	2	no	—
64	C₄⋊C₄	—	206	4	no	—
65	C₂²⋊C₄	—	206	4	no	—
66	C₂²⋊C₄	—	206	2	no	—
67	C₂³	—	103	2	no	—
68	C₂³	—	206	2	no	—
69	C₂³	—	206	1	no	—
70	C₂³	—	206	2	no	—
71	C₂³	—	206	1	no	—
72	C₂³	C₂²×D₁₀₃	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	2	2	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	103	4	no	—
78	C₂×C₄	—	206	2	no	—
79	C₂×C₄	—	206	1	no	—
80	C₂×C₄	—	206	2	no	—
81	C₂×C₄	—	206	2	no	—
82	C₂×C₄	C₂²⋊D₁₀₃	1	2	yes	—
83	C₂²	—	412	1	no	—
84	C₂²	—	412	2	no	—
85	C₂²	—	412	1	no	—
86	C₂²	—	206	2	no	—
87	C₂²	—	206	4	no	—
88	C₂²	D₄×D₁₀₃	1	2	yes	—
89	C₂²	C₂×C₂²⋊D₁₀₃	1	1	yes	characteristic
90	C₂²	Q₈×D₁₀₃	1	1	yes	characteristic
91	C₂²	#13110105	1	2	yes	—
92	C₂²	#13110106	1	1	yes	characteristic
93	C₄	—	2	2	no	—
94	C₄	—	4	2	no	—
95	C₄	—	412	1	no	—
96	C₄	—	206	4	no	—
97	C₂	—	412	2	no	—
98	C₂	#15692997	1	1	yes	characteristic
99	C₂	#15692999	1	2	yes	—
100	C₂	#15693004	1	1	yes	characteristic
101	C₂	#15693006	1	2	yes	—
102	C₂	#15693017	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₁₀₃⋊C₄

C₂

yes

maximal, complemented

C₂×(C₂×D₁₀₃)⋊C₄

C₂

yes

maximal

C₂×(C₂×D₁₀₃)⋊C₄

C₂

yes

maximal, characteristic

C₁₀₃⋊#95

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊C₄×C₁₀₃

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₀₃

C₂²

yes

characteristic

C₂²×Dic₁₀₃

C₂²

yes

characteristic

C₂²×Dic₁₀₃

C₂²

yes

—

Dic₁₀₃⋊C₄

—

(C₂×D₁₀₃)⋊C₄

—

(C₂×D₁₀₃)⋊C₄

—

C₂²×C₄×C₁₀₃

C₂²

yes

—

C₂²×C₄×C₁₀₃

C₂²

yes

characteristic

C₄⋊C₄×C₁₀₃

—

C₂³×C₁₀₃

C₂³

yes

characteristic

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

—

C₂²×D₁₀₃

Q₈

yes

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

—

C₂×C₄×C₁₀₃

D₄

yes

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

—

C₂×Dic₁₀₃

D₄

yes

—

C₂²×C₁₀₃

C₂×D₄

yes

—

C₂²×C₁₀₃

C₂×D₄

yes

characteristic

C₂²×C₁₀₃

C₂×Q₈

yes

characteristic

C₂²×C₁₀₃

#41

yes

—

C₂²×C₁₀₃

#41

yes

characteristic

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₂×D₁₀₃

—

C₄×C₁₀₃

—

C₄×C₁₀₃

—

Dic₁₀₃

—

Dic₁₀₃

—

C₂×C₁₀₃

C₂²⋊Q₈

yes

characteristic

C₂×C₁₀₃

C₂²⋊Q₈

yes

—

C₂×C₁₀₃

#123

yes

characteristic

C₂×C₁₀₃

#123

yes

—

C₂×C₁₀₃

#127

yes

characteristic

D₁₀₃

—

C₁₀₃

#399

yes

characteristic, complemented, Sylow

#399

—

103

maximal, Sylow

C₂×C₄⋊C₄

—

103

—

C₂×C₄⋊C₄

D₁₀₃

yes

characteristic, complemented

C₂×C₂²⋊C₄

—

103

—

C₂×C₂²⋊C₄

—

103

—

#95

—

103

—

C₂⁴

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

—

103

—

C₂²×C₄

C₂×D₁₀₃

yes

—

C₂²×C₄

C₂×D₁₀₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

206

—

C₂²⋊C₄

—

206

—

C₂²⋊C₄

—

206

—

C₂³

—

103

—

C₂³

—

206

—

C₂³

—

206

—

C₂³

—

206

—

C₂³

—

206

—

C₂³

C₂²×D₁₀₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

103

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

—

206

—

C₂×C₄

C₂²⋊D₁₀₃

yes

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

—

412

—

C₂²

—

206

—

C₂²

—

206

—

C₂²

D₄×D₁₀₃

yes

—

C₂²

C₂×C₂²⋊D₁₀₃

yes

characteristic

C₂²

Q₈×D₁₀₃

yes

characteristic

C₂²

#13110105

yes

—

C₂²

#13110106

yes

characteristic

C₄

—

C₄

—

C₄

—

412

—

C₄

—

206

—

C₂

—

412

—

C₂

#15692997

yes

characteristic

C₂

#15692999

yes

—

100

C₂

#15693004

yes

characteristic

101

C₂

#15693006

yes

—

102

C₂

#15693017

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₀₃
commutator, socle	C₂³×C₁₀₃	C₂³
Fitting	C₂×C₄⋊C₄×C₁₀₃	C₂
hypercenter	C₂×C₄⋊C₄	D₁₀₃
hypocenter	C₁₀₃	#399
LCS	G ▷ C₂³×C₁₀₃ ▷ C₁₀₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₀₃

commutator, socle

C₂³×C₁₀₃

C₂³

Fitting

C₂×C₄⋊C₄×C₁₀₃

C₂

hypercenter

C₂×C₄⋊C₄

D₁₀₃

C₁₀₃

G ▷ C₂³×C₁₀₃ ▷ C₁₀₃

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
1. C₂×Dic₁₀₃⋊C₄	C₂	semidirect
4. C₁₀₃⋊#95	C₂	semidirect
5. C₂×C₄⋊C₄×C₁₀₃	C₂	semidirect
51. C₁₀₃	#399	semidirect
54. C₂×C₄⋊C₄	D₁₀₃	semidirect

H ≅ G/N

type

1. C₂×Dic₁₀₃⋊C₄

C₂

semidirect

4. C₁₀₃⋊#95

C₂

semidirect

5. C₂×C₄⋊C₄×C₁₀₃

C₂

semidirect

51. C₁₀₃

#399

semidirect

54. C₂×C₄⋊C₄

D₁₀₃

semidirect

Subgroups — #20267726

Conjugacy classes of subgroups

Complements