Group #19136982 — subgroups

Subgroups — C₂×#14582765 #19136982

Order 5504.

712 conjugacy classes of subgroups; only the 389 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 389 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⋊Dic₄₃	C₂	1	2	yes	maximal
2	#14582765	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄₃⋊#95	C₂	1	4	yes	maximal
4	C₂²×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
5	C₂³×Dic₄₃	C₂²	1	4	yes	—
6	C₂×C₄⋊Dic₄₃	—	2	8	no	—
7	C₂×C₄⋊Dic₄₃	C₂²	1	8	yes	—
8	C₄₃⋊#95	C₂²	1	16	yes	—
9	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
10	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×C₄²×C₄₃	C₄	1	8	yes	complemented
12	C₂×C₄²×C₄₃	C₂²	1	4	yes	—
13	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
14	C₂²×C₄×C₄₃	—	2	8	no	—
15	C₂²×C₄×C₄₃	C₂×C₄	1	8	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	4	yes	—
17	C₂²×C₄×C₄₃	D₄	1	4	yes	—
18	C₂²×C₄×C₄₃	Q₈	1	4	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
21	C₂²×Dic₄₃	—	2	8	no	—
22	C₂²×Dic₄₃	—	2	16	no	—
23	C₂²×Dic₄₃	C₂³	1	8	yes	—
24	C₄²×C₄₃	C₂×C₄	1	16	yes	complemented
25	C₄⋊Dic₄₃	—	2	16	no	—
26	C₂³×C₄₃	C₂²×C₄	1	2	yes	—
27	C₂³×C₄₃	C₂×D₄	1	2	yes	—
28	C₂³×C₄₃	C₂×Q₈	1	2	yes	—
29	C₂³×C₄₃	#41	1	8	yes	—
30	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₄₃	—	2	16	no	—
32	C₂×C₄×C₄₃	—	2	8	no	—
33	C₂×C₄×C₄₃	C₄⋊C₄	1	16	yes	—
34	C₂×C₄×C₄₃	C₂²×C₄	1	8	yes	—
35	C₂×C₄×C₄₃	C₂²×C₄	1	4	yes	—
36	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
37	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
38	C₂×Dic₄₃	—	2	8	no	—
39	C₂×Dic₄₃	—	2	16	no	—
40	C₂×Dic₄₃	—	4	16	no	—
41	C₂²×C₄₃	C₂×C₄⋊C₄	1	4	yes	—
42	C₂²×C₄₃	#117	1	8	yes	—
43	C₂²×C₄₃	#124	1	8	yes	—
44	C₂²×C₄₃	#125	1	8	yes	—
45	C₂²×C₄₃	C₂³×C₄	1	1	yes	characteristic
46	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
47	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
48	C₂²×C₄₃	C₂×#41	1	4	yes	—
49	C₄×C₄₃	—	2	8	no	—
50	C₄×C₄₃	C₂×C₄⋊C₄	1	8	yes	—
51	Dic₄₃	—	4	8	no	—
52	C₂×#382	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	#382	1	8	yes	complemented
54	C₂×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄₃	C₂×#117	1	2	yes	—
56	C₂×C₄₃	C₂×#124	1	2	yes	—
57	C₂×C₄₃	C₂×#125	1	2	yes	—
58	C₂²×C₄⋊C₄	—	43	2	no	—
59	C₂²×C₄²	D₄₃	1	1	yes	characteristic
60	#382	—	43	8	no	—
61	C₂×#95	—	43	4	no	—
62	C₄₃	C₂×#382	1	1	yes	characteristic, complemented, Sylow
63	C₂³×C₄	—	43	4	no	—
64	C₂³×C₄	C₂×D₄₃	1	2	yes	—
65	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
66	C₂×C₄⋊C₄	—	43	8	no	—
67	C₂×C₄⋊C₄	—	86	8	no	—
68	C₂×C₄²	Dic₄₃	1	8	yes	complemented
69	C₂×C₄²	C₂×D₄₃	1	4	yes	—
70	#95	—	43	16	no	—
71	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
72	C₂²×C₄	—	2	8	no	—
73	C₂²×C₄	—	43	8	no	—
74	C₂²×C₄	—	86	8	no	—
75	C₂²×C₄	—	86	16	no	—
76	C₂²×C₄	Dic₈₆	1	4	yes	—
77	C₂²×C₄	D₁₇₂	1	4	yes	—
78	C₂²×C₄	C₂×Dic₄₃	1	8	yes	—
79	C₂²×C₄	C₂×Dic₄₃	1	4	yes	—
80	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
81	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
82	C₄⋊C₄	—	86	16	no	—
83	C₄²	C₂×Dic₄₃	1	16	yes	complemented
84	C₂³	C₂×Dic₈₆	1	2	yes	—
85	C₂³	C₂×D₁₇₂	1	2	yes	—
86	C₂³	#10621898	1	8	yes	—
87	C₂³	C₂²×Dic₄₃	1	2	yes	—
88	C₂³	C₂³×D₄₃	1	1	yes	characteristic
89	C₂×C₄	—	2	16	no	—
90	C₂×C₄	—	2	8	no	—
91	C₂×C₄	—	86	8	no	—
92	C₂×C₄	—	86	16	no	—
93	C₂×C₄	—	172	16	no	—
94	C₂×C₄	C₄⋊Dic₄₃	1	16	yes	—
95	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
96	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
97	C₂×C₄	C₂²×Dic₄₃	1	8	yes	—
98	C₂×C₄	C₂²×Dic₄₃	1	4	yes	—
99	C₂²	C₂×C₄⋊Dic₄₃	1	4	yes	—
100	C₂²	#13063284	1	8	yes	—
101	C₂²	#13063313	1	8	yes	—
102	C₂²	#13063317	1	8	yes	—
103	C₂²	C₂³×Dic₄₃	1	1	yes	characteristic
104	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
105	C₂²	C₂²×Dic₈₆	1	1	yes	characteristic
106	C₂²	C₂×#10621898	1	4	yes	—
107	C₄	—	2	8	no	—
108	C₄	—	172	8	no	—
109	C₄	C₂×C₄⋊Dic₄₃	1	8	yes	—
110	C₂	#14582765	1	8	yes	direct product factor
111	C₂	C₂²×C₄⋊Dic₄₃	1	1	yes	characteristic
112	C₂	C₂×#13063284	1	2	yes	—
113	C₂	C₂×#13063313	1	2	yes	—
114	C₂	C₂×#13063317	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal

#14582765

C₂

yes

maximal, direct product factor

C₂×C₄₃⋊#95

C₂

yes

maximal

C₂²×C₄²×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₄

yes

complemented

C₂×C₄²×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₄²×C₄₃

C₂×C₄

yes

complemented

C₄⋊Dic₄₃

—

C₂³×C₄₃

C₂²×C₄

yes

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂²×C₄₃

C₂×C₄⋊C₄

yes

—

C₂²×C₄₃

#117

yes

—

C₂²×C₄₃

#124

yes

—

C₂²×C₄₃

#125

yes

—

C₂²×C₄₃

C₂³×C₄

yes

characteristic

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

C₂×C₄⋊C₄

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

C₂²×C₄⋊C₄

yes

characteristic

C₂×C₄₃

C₂×#117

yes

—

C₂×C₄₃

C₂×#124

yes

—

C₂×C₄₃

C₂×#125

yes

—

C₂²×C₄⋊C₄

—

C₂²×C₄²

D₄₃

yes

characteristic

#382

—

C₂×#95

—

C₄₃

C₂×#382

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

Dic₄₃

yes

complemented

C₂×C₄²

C₂×D₄₃

yes

—

#95

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄²

C₂×Dic₄₃

yes

complemented

C₂³

C₂×Dic₈₆

yes

—

C₂³

C₂×D₁₇₂

yes

—

C₂³

#10621898

yes

—

C₂³

C₂²×Dic₄₃

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

C₄⋊Dic₄₃

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂×C₄

C₂²×Dic₄₃

yes

—

C₂²

C₂×C₄⋊Dic₄₃

yes

—

100

C₂²

#13063284

yes

—

101

C₂²

#13063313

yes

—

102

C₂²

#13063317

yes

—

103

C₂²

C₂³×Dic₄₃

yes

characteristic

104

C₂²

C₂²×D₁₇₂

yes

characteristic

105

C₂²

C₂²×Dic₈₆

yes

characteristic

106

C₂²

C₂×#10621898

yes

—

107

C₄

—

108

C₄

—

172

—

109

C₄

C₂×C₄⋊Dic₄₃

yes

—

110

C₂

#14582765

yes

direct product factor

111

C₂

C₂²×C₄⋊Dic₄₃

yes

characteristic

112

C₂

C₂×#13063284

yes

—

113

C₂

C₂×#13063313

yes

—

114

C₂

C₂×#13063317

yes

—

	subgroup	G/H
center	C₂⁴	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂³×C₄
Frattini	C₂³	C₂³×D₄₃
Fitting	C₂²×C₄²×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂³
hypercenter	C₂²×C₄²	D₄₃
hypocenter	C₄₃	C₂×#382
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄²

subgroup

G/H

center

C₂⁴

C₂²×D₄₃

commutator

C₂²×C₄₃

C₂³×C₄

Frattini

C₂³

C₂³×D₄₃

Fitting

C₂²×C₄²×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂³

hypercenter

C₂²×C₄²

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂⁴ ◁ C₂²×C₄²

N	H ≅ G/N	type
2. #14582765	C₂	direct (N × H)
11. C₂×C₄²×C₄₃	C₄	semidirect
24. C₄²×C₄₃	C₂×C₄	semidirect
53. C₂×C₄₃	#382	semidirect
62. C₄₃	C₂×#382	semidirect
68. C₂×C₄²	Dic₄₃	semidirect
83. C₄²	C₂×Dic₄₃	semidirect
110. C₂	#14582765	direct (N × H)

H ≅ G/N

type

2. #14582765

C₂

direct (N × H)

11. C₂×C₄²×C₄₃

C₄

semidirect

24. C₄²×C₄₃

C₂×C₄

semidirect

53. C₂×C₄₃

#382

semidirect

62. C₄₃

C₂×#382

semidirect

68. C₂×C₄²

Dic₄₃

semidirect

83. C₄²

C₂×Dic₄₃

semidirect

110. C₂

#14582765

direct (N × H)

Subgroups — C₂×#14582765 #19136982

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582765 #19136982

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582765 #19136982