Group #19145010 — subgroups

Subgroups — C₂×#14583278 #19145010

Order 5504.

552 conjugacy classes of subgroups; only the 197 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 197 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×#10621885	C₂	1	4	yes	maximal
2	C₂×#13063325	C₂	1	1	yes	maximal, characteristic
3	#14583278	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	2	yes	—
7	C₂×#10621885	—	2	16	no	—
8	C₂×#10621885	C₂²	1	16	yes	—
9	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
10	#13063325	—	2	2	no	—
11	#13063325	C₂²	1	4	yes	—
12	C₂×C₄⋊Dic₄₃	—	2	2	no	—
13	C₄×C₄₃⋊C₈	C₂²	1	4	yes	—
14	C₂²×Q₈×C₄₃	C₂²	1	2	yes	—
15	C₄⋊Q₈×C₄₃	—	2	2	no	—
16	C₄⋊Q₈×C₄₃	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
18	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×Q₈×C₄₃	—	2	2	no	—
20	C₂×Q₈×C₄₃	—	2	8	no	—
21	C₂×Q₈×C₄₃	C₂³	1	4	yes	—
22	C₂²×C₄×C₄₃	—	2	2	no	—
23	C₂²×C₄×C₄₃	D₄	1	2	yes	—
24	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₄₃	—	2	2	no	—
26	C₂×Dic₈₆	—	2	8	no	—
27	C₂×Dic₈₆	—	2	2	no	—
28	C₂×Dic₈₆	C₂³	1	4	yes	—
29	C₄⋊C₄×C₄₃	—	2	8	no	—
30	C₄²×C₄₃	D₄	1	2	yes	—
31	C₄²×C₄₃	C₂³	1	2	yes	—
32	#10621885	—	2	32	no	—
33	C₄⋊Dic₄₃	—	2	8	no	—
34	C₂×C₄₃⋊C₈	D₄	1	8	yes	—
35	C₂×C₄₃⋊C₈	C₂³	1	4	yes	—
36	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
37	Q₈×C₄₃	—	2	8	no	—
38	Q₈×C₄₃	—	4	4	no	—
39	C₂×C₄×C₄₃	—	2	4	no	—
40	C₂×C₄×C₄₃	—	4	4	no	—
41	C₂×C₄×C₄₃	Q₁₆	1	8	yes	complemented
42	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
43	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
45	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
46	C₂×Dic₄₃	—	2	4	no	—
47	C₂×Dic₄₃	—	4	4	no	—
48	Dic₈₆	—	2	8	no	—
49	Dic₈₆	—	4	4	no	—
50	C₄₃⋊C₈	C₂×D₄	1	8	yes	—
51	C₂²×C₄₃	#127	1	2	yes	—
52	C₂²×C₄₃	C₂×Q₁₆	1	4	yes	—
53	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
54	C₄×C₄₃	—	4	4	no	—
55	C₄×C₄₃	#127	1	2	yes	—
56	C₄×C₄₃	C₂×Q₁₆	1	8	yes	complemented
57	C₄×C₄₃	C₂²×D₄	1	2	yes	—
58	Dic₄₃	—	4	4	no	—
59	C₂×#494	—	43	1	no	maximal, Sylow
60	C₂×C₄₃	#494	1	4	yes	complemented
61	C₂×C₄₃	C₂×#127	1	1	yes	characteristic
62	C₂×C₄₃	C₂²×Q₁₆	1	2	yes	—
63	C₂²×Q₁₆	—	43	4	no	—
64	C₂×C₄⋊Q₈	—	43	1	no	—
65	C₂×C₄⋊Q₈	D₄₃	1	1	yes	characteristic
66	#494	—	43	8	no	—
67	C₂×C₄×C₈	—	43	1	no	—
68	C₄₃	C₂×#494	1	1	yes	characteristic, complemented, Sylow
69	C₂²×Q₈	—	43	2	no	—
70	C₂²×Q₈	C₂×D₄₃	1	2	yes	—
71	C₂×Q₁₆	—	43	16	no	—
72	C₂×Q₁₆	—	86	16	no	—
73	C₂²×C₈	—	43	2	no	—
74	C₄⋊Q₈	—	2	2	no	—
75	C₄⋊Q₈	—	43	4	no	—
76	C₄⋊Q₈	—	86	2	no	—
77	C₄⋊Q₈	C₂×D₄₃	1	4	yes	—
78	C₂×C₄⋊C₄	—	2	2	no	—
79	C₂×C₄⋊C₄	—	86	2	no	—
80	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
81	C₄×C₈	—	43	4	no	—
82	C₂×Q₈	—	2	2	no	—
83	C₂×Q₈	—	2	8	no	—
84	C₂×Q₈	—	43	4	no	—
85	C₂×Q₈	—	86	2	no	—
86	C₂×Q₈	—	86	8	no	—
87	C₂×Q₈	C₂²×D₄₃	1	4	yes	—
88	C₂²×C₄	—	2	2	no	—
89	C₂²×C₄	—	86	2	no	—
90	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
91	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
92	Q₁₆	—	86	32	no	—
93	C₂×C₈	—	43	8	no	—
94	C₂×C₈	—	43	4	no	—
95	C₄⋊C₄	—	2	8	no	—
96	C₄⋊C₄	—	86	8	no	—
97	C₄²	C₂²⋊D₄₃	1	2	yes	—
98	C₄²	C₂²×D₄₃	1	2	yes	—
99	C₂³	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
100	Q₈	—	2	8	no	—
101	Q₈	—	4	4	no	—
102	Q₈	—	86	8	no	—
103	Q₈	—	172	4	no	—
104	C₂×C₄	—	2	4	no	—
105	C₂×C₄	—	4	4	no	—
106	C₂×C₄	—	86	4	no	—
107	C₂×C₄	—	172	4	no	—
108	C₂×C₄	#10621885	1	8	yes	complemented
109	C₂×C₄	D₄×D₄₃	1	4	yes	—
110	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
111	C₂×C₄	C₂×C₂²⋊D₄₃	1	4	yes	—
112	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
113	C₈	—	43	8	no	—
114	C₂²	#13063321	1	2	yes	—
115	C₂²	C₂×#10621885	1	4	yes	—
116	C₂²	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
117	C₄	—	4	4	no	—
118	C₄	—	172	4	no	—
119	C₄	#13063321	1	2	yes	—
120	C₄	C₂×#10621885	1	8	yes	complemented
121	C₄	C₂×D₄×D₄₃	1	2	yes	—
122	C₂	#14583278	1	4	yes	direct product factor
123	C₂	C₂×#13063321	1	1	yes	characteristic
124	C₂	C₂²×#10621885	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#10621885

C₂

yes

maximal

C₂×#13063325

C₂

yes

maximal, characteristic

#14583278

C₂

yes

maximal, direct product factor

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

C₂×C₄⋊Q₈×C₄₃

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₂×#10621885

—

C₂×#10621885

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

#13063325

—

#13063325

C₂²

yes

—

C₂×C₄⋊Dic₄₃

—

C₄×C₄₃⋊C₈

C₂²

yes

—

C₂²×Q₈×C₄₃

C₂²

yes

—

C₄⋊Q₈×C₄₃

—

C₄⋊Q₈×C₄₃

C₂²

yes

—

C₂×C₄⋊C₄×C₄₃

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₂×Dic₈₆

C₂³

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

—

#10621885

—

C₄⋊Dic₄₃

—

C₂×C₄₃⋊C₈

D₄

yes

—

C₂×C₄₃⋊C₈

C₂³

yes

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

Q₁₆

yes

complemented

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₄₃⋊C₈

C₂×D₄

yes

—

C₂²×C₄₃

#127

yes

—

C₂²×C₄₃

C₂×Q₁₆

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

#127

yes

—

C₄×C₄₃

C₂×Q₁₆

yes

complemented

C₄×C₄₃

C₂²×D₄

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

C₂²×Q₁₆

yes

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

C₂×C₄⋊Q₈

D₄₃

yes

characteristic

#494

—

C₂×C₄×C₈

—

C₄₃

C₂×#494

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₂²×Q₈

C₂×D₄₃

yes

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂²×C₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

—

C₄⋊Q₈

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄×C₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂²×D₄₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂²⋊D₄₃

yes

—

C₄²

C₂²×D₄₃

yes

—

C₂³

C₂×C₂²⋊D₄₃

yes

characteristic

100

Q₈

—

101

Q₈

—

102

Q₈

—

103

Q₈

—

172

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

172

—

108

C₂×C₄

#10621885

yes

complemented

109

C₂×C₄

D₄×D₄₃

yes

—

110

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

111

C₂×C₄

C₂×C₂²⋊D₄₃

yes

—

112

C₂×C₄

C₂³×D₄₃

yes

characteristic

113

C₈

—

114

C₂²

#13063321

yes

—

115

C₂²

C₂×#10621885

yes

—

116

C₂²

C₂²×C₂²⋊D₄₃

yes

characteristic

117

C₄

—

118

C₄

—

172

—

119

C₄

#13063321

yes

—

120

C₄

C₂×#10621885

yes

complemented

121

C₄

C₂×D₄×D₄₃

yes

—

122

C₂

#14583278

yes

direct product factor

123

C₂

C₂×#13063321

yes

characteristic

124

C₂

C₂²×#10621885

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄⋊Q₈×C₄₃	C₂
socle	C₂³×C₄₃	C₂×D₄
hypercenter	C₂×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	C₂×#494
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊D₄₃

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄⋊Q₈×C₄₃

C₂

socle

C₂³×C₄₃

C₂×D₄

hypercenter

C₂×C₄⋊Q₈

D₄₃

hypocenter

C₄₃

C₂×#494

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊Q₈

N	H ≅ G/N	type
3. #14583278	C₂	direct (N × H)
41. C₂×C₄×C₄₃	Q₁₆	semidirect
56. C₄×C₄₃	C₂×Q₁₆	semidirect
60. C₂×C₄₃	#494	semidirect
68. C₄₃	C₂×#494	semidirect
108. C₂×C₄	#10621885	semidirect
120. C₄	C₂×#10621885	semidirect
122. C₂	#14583278	direct (N × H)

H ≅ G/N

type

3. #14583278

C₂

direct (N × H)

41. C₂×C₄×C₄₃

Q₁₆

semidirect

56. C₄×C₄₃

C₂×Q₁₆

semidirect

60. C₂×C₄₃

#494

semidirect

68. C₄₃

C₂×#494

semidirect

108. C₂×C₄

#10621885

semidirect

120. C₄

C₂×#10621885

semidirect

122. C₂

#14583278

direct (N × H)

Subgroups — C₂×#14583278 #19145010

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14583278 #19145010

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14583278 #19145010