Group #19142958 — subgroups

Subgroups — #19142958

Order 5504.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#13063317	C₂	1	2	yes	maximal
2	#14582797	C₂	1	8	yes	maximal
3	#14582769	C₂	1	2	yes	maximal
4	#14582765	C₂	1	2	yes	maximal
5	C₄³×C₄₃	C₂	1	1	yes	maximal, characteristic
6	#13063317	—	2	8	no	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	8	yes	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	4	yes	—
9	C₂×Dic₄₃⋊C₄	C₂²	1	8	yes	—
10	C₄₃⋊#95	C₂²	1	8	yes	—
11	C₂×C₄²×C₄₃	C₂²	1	4	yes	—
12	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
16	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
19	C₂²×Dic₄₃	C₂³	1	8	yes	—
20	C₄²×C₄₃	—	2	8	no	—
21	C₄²×C₄₃	D₄	1	4	yes	—
22	C₄²×C₄₃	Q₈	1	4	yes	—
23	C₄²×C₄₃	Q₈	1	4	yes	—
24	C₄⋊Dic₄₃	—	2	8	no	—
25	C₄⋊Dic₄₃	—	2	16	no	—
26	Dic₄₃⋊C₄	—	2	16	no	—
27	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
28	C₂×C₄×C₄₃	—	2	4	no	—
29	C₂×C₄×C₄₃	—	2	4	no	—
30	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
31	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
32	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
33	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
34	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
35	C₂×C₄×C₄₃	C₂×Q₈	1	2	yes	—
36	C₂×C₄×C₄₃	#41	1	8	yes	—
37	C₂×Dic₄₃	—	2	8	no	—
38	C₂×Dic₄₃	—	2	16	no	—
39	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
41	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₄₃	C₂×#41	1	4	yes	—
43	C₄×C₄₃	—	2	4	no	—
44	C₄×C₄₃	—	2	4	no	—
45	C₄×C₄₃	#125	1	8	yes	complemented
46	C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
47	Dic₄₃	—	4	8	no	—
48	#2859	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	C₂×#125	1	2	yes	—
50	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
51	C₂×C₄₃	#532	1	2	yes	—
52	C₂×C₄₃	#533	1	2	yes	—
53	C₂×#125	—	43	2	no	—
54	#389	—	43	8	no	—
55	#384	—	43	2	no	—
56	#382	—	43	2	no	—
57	C₄³	D₄₃	1	1	yes	characteristic
58	C₄₃	#2859	1	1	yes	characteristic, complemented, Sylow
59	#125	—	86	8	no	—
60	C₂×C₄⋊C₄	—	43	8	no	—
61	C₂×C₄⋊C₄	—	43	4	no	—
62	C₂×C₄⋊C₄	—	43	8	no	—
63	C₂×C₄²	C₂×D₄₃	1	4	yes	—
64	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
67	#95	—	43	8	no	—
68	C₂²×C₄	—	43	8	no	—
69	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
70	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
71	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
73	C₄⋊C₄	—	86	16	no	—
74	C₄⋊C₄	—	86	8	no	—
75	C₄⋊C₄	—	86	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	Dic₈₆	1	4	yes	—
78	C₄²	Dic₈₆	1	4	yes	—
79	C₄²	D₁₇₂	1	4	yes	—
80	C₂³	C₂³×D₄₃	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	86	8	no	—
84	C₂×C₄	—	86	16	no	—
85	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
86	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
87	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
88	C₂×C₄	C₂×Dic₈₆	1	2	yes	—
89	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
90	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
91	C₂×C₄	#10621898	1	8	yes	—
92	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
93	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
94	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
95	C₂²	C₂×#10621898	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	172	8	no	—
99	C₄	#13063317	1	8	yes	complemented
100	C₄	#13063325	1	4	yes	—
101	C₂	C₂×#13063317	1	2	yes	—
102	C₂	C₂×#13063325	1	1	yes	characteristic
103	C₂	#14583449	1	2	yes	—
104	C₂	#14583456	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063317

C₂

yes

maximal

#14582797

C₂

yes

maximal

#14582769

C₂

yes

maximal

#14582765

C₂

yes

maximal

C₄³×C₄₃

C₂

yes

maximal, characteristic

#13063317

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄²×C₄₃

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

Q₈

yes

—

C₄²×C₄₃

Q₈

yes

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#125

yes

complemented

C₄×C₄₃

C₄⋊Q₈

yes

—

Dic₄₃

—

#2859

—

maximal, Sylow

C₂×C₄₃

C₂×#125

yes

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

#532

yes

—

C₂×C₄₃

#533

yes

—

—

—

—

—

C₄³

D₄₃

yes

characteristic

C₄₃

#2859

yes

characteristic, complemented, Sylow

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₈₆

yes

—

C₄²

Dic₈₆

yes

—

C₄²

D₁₇₂

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

#10621898

yes

—

C₂²

C₂²×D₁₇₂

yes

characteristic

C₂²

C₂²×Dic₈₆

yes

characteristic

C₂²

C₂²×Dic₈₆

yes

characteristic

C₂²

C₂×#10621898

yes

—

C₄

—

C₄

—

C₄

—

172

—

C₄

#13063317

yes

complemented

100

C₄

#13063325

yes

—

101

C₂

C₂×#13063317

yes

—

102

C₂

C₂×#13063325

yes

characteristic

103

C₂

#14583449

yes

—

104

C₂

#14583456

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄³×C₄₃	C₂
hypercenter	C₄³	D₄₃
hypocenter	C₄₃	#2859
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄³×C₄₃

C₂

hypercenter

C₄³

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
45. C₄×C₄₃	#125	semidirect
58. C₄₃	#2859	semidirect
99. C₄	#13063317	semidirect

H ≅ G/N

type

45. C₄×C₄₃

#125

semidirect

58. C₄₃

#2859

semidirect

99. C₄

#13063317

semidirect

Subgroups — #19142958

Conjugacy classes of subgroups

Complements