Group #19147847 — subgroups

Subgroups — C₂²×#13063316 #19147847

Order 5504.

1192 conjugacy classes of subgroups; only the 645 normal subgroups are shown.

normal subgroups only

This group has 1192 conjugacy classes of subgroups — too many to draw. Only its 645 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×#13063316	C₂	1	24	yes	maximal, direct product factor
2	C₂²×C₄⋊Dic₄₃	C₂	1	2	yes	maximal
3	C₂²×C₄⋊Dic₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₄₃⋊C₄	C₂	1	2	yes	maximal
5	C₂²×C₄×Dic₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊C₄×C₄₃	C₂	1	1	yes	maximal, characteristic
7	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic
8	C₂³×Dic₄₃	C₂²	1	1	yes	characteristic
9	C₂³×Dic₄₃	C₂²	1	2	yes	—
10	#13063316	C₂²	1	64	yes	direct product factor
11	C₂×C₄⋊Dic₄₃	C₂²	1	24	yes	—
12	C₂×C₄⋊Dic₄₃	C₂²	1	12	yes	—
13	C₂×Dic₄₃⋊C₄	C₂²	1	24	yes	—
14	C₂×C₄×Dic₄₃	C₂²	1	12	yes	—
15	C₂³×C₄×C₄₃	C₂²	1	2	yes	—
16	C₂³×C₄×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄×C₄₃	C₂²	1	12	yes	—
18	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	—	2	8	no	—
20	C₂²×C₄×C₄₃	Q₈	1	8	yes	—
21	C₂²×C₄×C₄₃	C₂³	1	12	yes	—
22	C₂²×C₄×C₄₃	C₂³	1	6	yes	—
23	C₂²×Dic₄₃	—	2	4	no	—
24	C₂²×Dic₄₃	—	2	4	no	—
25	C₂²×Dic₄₃	—	2	8	no	—
26	C₂²×Dic₄₃	C₂³	1	6	yes	—
27	C₂²×Dic₄₃	C₂³	1	6	yes	—
28	C₂²×Dic₄₃	C₂³	1	12	yes	—
29	C₄⋊C₄×C₄₃	C₂³	1	16	yes	—
30	C₄⋊Dic₄₃	C₂³	1	32	yes	—
31	C₄⋊Dic₄₃	C₂³	1	16	yes	—
32	Dic₄₃⋊C₄	C₂³	1	32	yes	—
33	C₄×Dic₄₃	C₂³	1	16	yes	—
34	C₂³×C₄₃	C₂×Q₈	1	4	yes	—
35	C₂³×C₄₃	#41	1	4	yes	—
36	C₂³×C₄₃	#41	1	4	yes	—
37	C₂³×C₄₃	C₂⁴	1	3	yes	—
38	C₂×C₄×C₄₃	—	2	24	no	—
39	C₂×C₄×C₄₃	C₂×Q₈	1	24	yes	—
40	C₂×C₄×C₄₃	C₂⁴	1	8	yes	—
41	C₂×C₄×C₄₃	C₂⁴	1	4	yes	—
42	C₂×Dic₄₃	—	2	12	no	—
43	C₂×Dic₄₃	—	2	12	no	—
44	C₂×Dic₄₃	—	2	24	no	—
45	C₂×Dic₄₃	C₂⁴	1	4	yes	—
46	C₂×Dic₄₃	C₂⁴	1	4	yes	—
47	C₂×Dic₄₃	C₂⁴	1	8	yes	—
48	C₂²×C₄₃	#125	1	16	yes	complemented
49	C₂²×C₄₃	C₂²×Q₈	1	6	yes	—
50	C₂²×C₄₃	C₂×#41	1	6	yes	—
51	C₂²×C₄₃	C₂×#41	1	6	yes	—
52	C₂²×C₄₃	C₂⁵	1	1	yes	characteristic
53	C₄×C₄₃	—	2	8	no	—
54	C₄×C₄₃	C₂²×Q₈	1	8	yes	—
55	Dic₄₃	—	2	4	no	—
56	Dic₄₃	—	2	4	no	—
57	Dic₄₃	—	2	8	no	—
58	C₂²×#125	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	C₂×#125	1	12	yes	complemented
60	C₂×C₄₃	C₂³×Q₈	1	1	yes	characteristic
61	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
62	C₂×C₄₃	C₂²×#41	1	1	yes	characteristic
63	C₂×#125	—	43	24	no	—
64	C₂²×C₄⋊C₄	—	43	2	no	—
65	C₂²×C₄⋊C₄	—	43	1	no	—
66	C₂²×C₄⋊C₄	—	43	2	no	—
67	C₂²×C₄⋊C₄	D₄₃	1	1	yes	characteristic
68	C₂²×C₄²	—	43	1	no	—
69	C₄₃	C₂²×#125	1	1	yes	characteristic, complemented, Sylow
70	C₂³×C₄	—	43	2	no	—
71	C₂³×C₄	—	43	1	no	—
72	C₂³×C₄	—	43	1	no	—
73	C₂³×C₄	C₂×D₄₃	1	2	yes	—
74	C₂³×C₄	C₂×D₄₃	1	1	yes	characteristic
75	#125	—	43	64	no	—
76	C₂×C₄⋊C₄	—	43	24	no	—
77	C₂×C₄⋊C₄	—	43	24	no	—
78	C₂×C₄⋊C₄	—	43	12	no	—
79	C₂×C₄⋊C₄	C₂×D₄₃	1	12	yes	—
80	C₂×C₄²	—	43	12	no	—
81	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²×C₄	—	2	8	no	—
83	C₂²×C₄	—	43	6	no	—
84	C₂²×C₄	—	43	6	no	—
85	C₂²×C₄	—	43	12	no	—
86	C₂²×C₄	—	86	4	no	—
87	C₂²×C₄	—	86	8	no	—
88	C₂²×C₄	—	86	4	no	—
89	C₂²×C₄	Dic₈₆	1	8	yes	—
90	C₂²×C₄	C₂²×D₄₃	1	12	yes	—
91	C₂²×C₄	C₂²×D₄₃	1	6	yes	—
92	C₄⋊C₄	—	43	32	no	—
93	C₄⋊C₄	—	43	32	no	—
94	C₄⋊C₄	—	43	16	no	—
95	C₄⋊C₄	C₂²×D₄₃	1	16	yes	—
96	C₄²	—	43	16	no	—
97	C₂³	C₂×Dic₈₆	1	4	yes	—
98	C₂³	#10621900	1	4	yes	—
99	C₂³	#10621902	1	4	yes	—
100	C₂³	C₂³×D₄₃	1	3	yes	—
101	C₂×C₄	—	2	24	no	—
102	C₂×C₄	—	43	4	no	—
103	C₂×C₄	—	43	4	no	—
104	C₂×C₄	—	43	8	no	—
105	C₂×C₄	—	86	12	no	—
106	C₂×C₄	—	86	12	no	—
107	C₂×C₄	—	86	24	no	—
108	C₂×C₄	C₂×Dic₈₆	1	24	yes	—
109	C₂×C₄	C₂³×D₄₃	1	8	yes	—
110	C₂×C₄	C₂³×D₄₃	1	4	yes	—
111	C₂²	#13063316	1	16	yes	direct product factor
112	C₂²	C₂²×Dic₈₆	1	6	yes	—
113	C₂²	C₂×#10621900	1	6	yes	—
114	C₂²	C₂×#10621902	1	6	yes	—
115	C₂²	C₂⁴×D₄₃	1	1	yes	characteristic
116	C₄	—	2	8	no	—
117	C₄	—	86	4	no	—
118	C₄	—	86	4	no	—
119	C₄	—	86	8	no	—
120	C₄	C₂²×Dic₈₆	1	8	yes	—
121	C₂	C₂×#13063316	1	12	yes	direct product factor
122	C₂	C₂³×Dic₈₆	1	1	yes	characteristic
123	C₂	C₂²×#10621900	1	1	yes	characteristic
124	C₂	C₂²×#10621902	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063316

C₂

yes

maximal, direct product factor

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal

C₂²×C₄⋊Dic₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₄₃⋊C₄

C₂

yes

maximal

C₂²×C₄×Dic₄₃

C₂

yes

maximal, characteristic

C₂²×C₄⋊C₄×C₄₃

C₂

yes

maximal, characteristic

C₂³×Dic₄₃

C₂²

yes

characteristic

C₂³×Dic₄₃

C₂²

yes

characteristic

C₂³×Dic₄₃

C₂²

yes

—

#13063316

C₂²

yes

direct product factor

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₂²

yes

—

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

Q₈

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₄⋊C₄×C₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

C₂³

yes

—

C₄×Dic₄₃

C₂³

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₂×Dic₄₃

C₂⁴

yes

—

C₂²×C₄₃

#125

yes

complemented

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

C₂⁵

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₂²×Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

Dic₄₃

—

C₂²×#125

—

maximal, Sylow

C₂×C₄₃

C₂×#125

yes

complemented

C₂×C₄₃

C₂³×Q₈

yes

characteristic

C₂×C₄₃

C₂²×#41

yes

characteristic

C₂×C₄₃

C₂²×#41

yes

characteristic

C₂×#125

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

—

C₂²×C₄⋊C₄

D₄₃

yes

characteristic

C₂²×C₄²

—

C₄₃

C₂²×#125

yes

characteristic, complemented, Sylow

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂³×C₄

C₂×D₄₃

yes

characteristic

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂×D₄₃

yes

—

C₂×C₄²

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

Dic₈₆

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂²×D₄₃

yes

—

C₄²

—

C₂³

C₂×Dic₈₆

yes

—

C₂³

#10621900

yes

—

C₂³

#10621902

yes

—

100

C₂³

C₂³×D₄₃

yes

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

C₂×Dic₈₆

yes

—

109

C₂×C₄

C₂³×D₄₃

yes

—

110

C₂×C₄

C₂³×D₄₃

yes

—

111

C₂²

#13063316

yes

direct product factor

112

C₂²

C₂²×Dic₈₆

yes

—

113

C₂²

C₂×#10621900

yes

—

114

C₂²

C₂×#10621902

yes

—

115

C₂²

C₂⁴×D₄₃

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

C₂²×Dic₈₆

yes

—

121

C₂

C₂×#13063316

yes

direct product factor

122

C₂

C₂³×Dic₈₆

yes

characteristic

123

C₂

C₂²×#10621900

yes

characteristic

124

C₂

C₂²×#10621902

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂⁵
Frattini	C₂²	C₂⁴×D₄₃
Fitting	C₂²×C₄⋊C₄×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂³
hypercenter	C₂²×C₄⋊C₄	D₄₃
hypocenter	C₄₃	C₂²×#125
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

subgroup

G/H

center

C₂⁴

C₂²×D₄₃

commutator

C₂²×C₄₃

C₂⁵

Frattini

C₂²

C₂⁴×D₄₃

Fitting

C₂²×C₄⋊C₄×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂³

hypercenter

C₂²×C₄⋊C₄

D₄₃

hypocenter

C₄₃

C₂²×#125

LCS

G ▷ C₂²×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂⁴ ◁ C₂²×C₄⋊C₄

N	H ≅ G/N	type
1. C₂×#13063316	C₂	direct (N × H)
10. #13063316	C₂²	direct (N × H)
48. C₂²×C₄₃	#125	semidirect
59. C₂×C₄₃	C₂×#125	semidirect
69. C₄₃	C₂²×#125	semidirect
111. C₂²	#13063316	direct (N × H)
121. C₂	C₂×#13063316	direct (N × H)

H ≅ G/N

type

1. C₂×#13063316

C₂

direct (N × H)

10. #13063316

C₂²

direct (N × H)

48. C₂²×C₄₃

#125

semidirect

59. C₂×C₄₃

C₂×#125

semidirect

69. C₄₃

C₂²×#125

semidirect

111. C₂²

#13063316

direct (N × H)

121. C₂

C₂×#13063316

direct (N × H)

Subgroups — C₂²×#13063316 #19147847

Conjugacy classes of subgroups

Complements

Subgroups — C22×#13063316 #19147847

Conjugacy classes of subgroups

Complements

Subgroups — C₂²×#13063316 #19147847