Group #19137817 — subgroups

Subgroups — C₂×#14582823 #19137817

Order 5504.

908 conjugacy classes of subgroups; only the 245 normal subgroups are shown.

normal subgroups only

This group has 908 conjugacy classes of subgroups — too many to draw. Only its 245 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×Dic₄₃⋊C₄	C₂	1	3	yes	maximal, complemented
2	C₂²×(C₂×D₄₃)⋊C₄	C₂	1	3	yes	maximal
3	#14582823	C₂	1	8	yes	maximal, direct product factor
4	C₂×#95×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×D₄₃	C₂²	1	1	yes	characteristic
6	C₂³×Dic₄₃	C₂²	1	3	yes	—
7	C₂×Dic₄₃⋊C₄	—	2	12	no	—
8	C₂×Dic₄₃⋊C₄	C₂²	1	12	yes	complemented
9	C₂×(C₂×D₄₃)⋊C₄	—	2	12	no	—
10	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	12	yes	—
11	C₂³×C₄×C₄₃	C₂²	1	3	yes	—
12	#95×C₄₃	C₂²	1	4	yes	complemented
13	C₂⁴×C₄₃	C₂³	1	1	yes	characteristic
14	C₂³×D₄₃	—	2	6	no	—
15	C₂³×D₄₃	—	2	6	no	—
16	C₂³×D₄₃	Q₈	1	4	yes	—
17	C₂³×D₄₃	C₂³	1	2	yes	—
18	C₂²×C₄×C₄₃	—	2	6	no	—
19	C₂²×C₄×C₄₃	—	2	6	no	—
20	C₂²×C₄×C₄₃	—	2	6	no	—
21	C₂²×C₄×C₄₃	C₂³	1	6	yes	—
22	C₂²×Dic₄₃	—	2	6	no	—
23	C₂²×Dic₄₃	—	2	6	no	—
24	C₂²×Dic₄₃	D₄	1	12	yes	—
25	C₂²×Dic₄₃	C₂³	1	6	yes	—
26	(C₂×D₄₃)⋊C₄	—	2	24	no	—
27	Dic₄₃⋊C₄	—	2	24	no	—
28	C₂³×C₄₃	C₂×D₄	1	6	yes	—
29	C₂³×C₄₃	C₂×Q₈	1	2	yes	—
30	C₂³×C₄₃	#41	1	6	yes	—
31	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
32	C₂²×D₄₃	—	2	24	no	—
33	C₂²×D₄₃	—	2	6	no	—
34	C₂²×D₄₃	—	2	6	no	—
35	C₂²×D₄₃	—	4	12	no	—
36	C₂²×D₄₃	—	4	4	no	—
37	C₂²×D₄₃	C₂×Q₈	1	4	yes	—
38	C₂×C₄×C₄₃	—	2	6	no	—
39	C₂×C₄×C₄₃	—	2	6	no	—
40	C₂×C₄×C₄₃	—	2	6	no	—
41	C₂×C₄×C₄₃	—	4	12	no	—
42	C₂×Dic₄₃	—	2	24	no	—
43	C₂×Dic₄₃	—	2	6	no	—
44	C₂×Dic₄₃	—	2	6	no	—
45	C₂×Dic₄₃	C₂×D₄	1	12	yes	—
46	C₂²×C₄₃	#121	1	12	yes	—
47	C₂²×C₄₃	C₂²⋊Q₈	1	12	yes	—
48	C₂²×C₄₃	#126	1	4	yes	—
49	C₂²×C₄₃	C₂²×D₄	1	3	yes	—
50	C₂²×C₄₃	C₂²×Q₈	1	1	yes	characteristic
51	C₂²×C₄₃	C₂×#41	1	3	yes	—
52	C₂×D₄₃	—	2	12	no	—
53	C₂×D₄₃	—	4	6	no	—
54	C₂×D₄₃	—	4	2	no	—
55	C₂×D₄₃	—	4	16	no	—
56	C₄×C₄₃	—	4	6	no	—
57	Dic₄₃	—	2	12	no	—
58	C₂×#396	—	43	1	no	maximal, Sylow
59	C₂×C₄₃	#396	1	8	yes	complemented
60	C₂×C₄₃	C₂×#121	1	3	yes	—
61	C₂×C₄₃	C₂×C₂²⋊Q₈	1	3	yes	—
62	C₂×C₄₃	C₂×#126	1	1	yes	characteristic
63	D₄₃	—	4	4	no	—
64	C₂²×C₄⋊C₄	—	43	3	no	—
65	C₂²×C₂²⋊C₄	—	43	3	no	—
66	#396	—	43	8	no	—
67	C₂×#95	D₄₃	1	1	yes	characteristic, complemented
68	C₄₃	C₂×#396	1	1	yes	characteristic, complemented, Sylow
69	C₂⁵	—	43	1	no	—
70	C₂³×C₄	—	43	3	no	—
71	C₂³×C₄	C₂×D₄₃	1	3	yes	—
72	C₂×C₄⋊C₄	—	43	12	no	—
73	C₂×C₄⋊C₄	—	86	12	no	—
74	C₂×C₂²⋊C₄	—	43	12	no	—
75	C₂×C₂²⋊C₄	—	86	12	no	—
76	#95	C₂×D₄₃	1	4	yes	complemented
77	C₂⁴	—	43	4	no	—
78	C₂⁴	—	43	2	no	—
79	C₂⁴	—	86	6	no	—
80	C₂⁴	—	86	6	no	—
81	C₂⁴	C₂²×D₄₃	1	1	yes	characteristic
82	C₂²×C₄	—	2	6	no	—
83	C₂²×C₄	—	2	6	no	—
84	C₂²×C₄	—	2	6	no	—
85	C₂²×C₄	—	43	12	no	—
86	C₂²×C₄	—	43	6	no	—
87	C₂²×C₄	—	86	6	no	—
88	C₂²×C₄	—	86	6	no	—
89	C₂²×C₄	C₂²×D₄₃	1	6	yes	—
90	C₄⋊C₄	—	86	24	no	—
91	C₂²⋊C₄	—	86	24	no	—
92	C₂³	—	43	4	no	—
93	C₂³	—	86	24	no	—
94	C₂³	—	86	6	no	—
95	C₂³	—	86	6	no	—
96	C₂³	—	172	12	no	—
97	C₂³	—	172	4	no	—
98	C₂³	#10621898	1	6	yes	—
99	C₂³	D₄×D₄₃	1	6	yes	—
100	C₂³	Q₈×D₄₃	1	2	yes	—
101	C₂³	C₂³×D₄₃	1	1	yes	characteristic
102	C₂×C₄	—	2	6	no	—
103	C₂×C₄	—	2	6	no	—
104	C₂×C₄	—	2	6	no	—
105	C₂×C₄	—	4	12	no	—
106	C₂×C₄	—	43	12	no	—
107	C₂×C₄	—	86	24	no	—
108	C₂×C₄	—	86	6	no	—
109	C₂×C₄	—	86	6	no	—
110	C₂²	—	86	12	no	—
111	C₂²	—	172	16	no	—
112	C₂²	—	172	6	no	—
113	C₂²	—	172	2	no	—
114	C₂²	#13063298	1	12	yes	—
115	C₂²	#13063303	1	12	yes	—
116	C₂²	#13063319	1	4	yes	—
117	C₂²	C₂×D₄×D₄₃	1	3	yes	—
118	C₂²	C₂×Q₈×D₄₃	1	1	yes	characteristic
119	C₂²	C₂×#10621898	1	3	yes	—
120	C₄	—	4	6	no	—
121	C₄	—	86	12	no	—
122	C₂	—	172	4	no	—
123	C₂	#14582823	1	8	yes	direct product factor
124	C₂	C₂×#13063298	1	3	yes	—
125	C₂	C₂×#13063303	1	3	yes	—
126	C₂	C₂×#13063319	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₄₃⋊C₄

C₂

yes

maximal, complemented

C₂²×(C₂×D₄₃)⋊C₄

C₂

yes

maximal

#14582823

C₂

yes

maximal, direct product factor

C₂×#95×C₄₃

C₂

yes

maximal, characteristic, complemented

C₂⁴×D₄₃

C₂²

yes

characteristic

C₂³×Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

—

C₂×Dic₄₃⋊C₄

C₂²

yes

complemented

C₂×(C₂×D₄₃)⋊C₄

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂³×C₄×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

complemented

C₂⁴×C₄₃

C₂³

yes

characteristic

C₂³×D₄₃

—

C₂³×D₄₃

—

C₂³×D₄₃

Q₈

yes

—

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

—

C₂²×Dic₄₃

D₄

yes

—

C₂²×Dic₄₃

C₂³

yes

—

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂×D₄

yes

—

C₂³×C₄₃

C₂×Q₈

yes

—

C₂³×C₄₃

#41

yes

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

C₂×D₄

yes

—

C₂²×C₄₃

#121

yes

—

C₂²×C₄₃

C₂²⋊Q₈

yes

—

C₂²×C₄₃

#126

yes

—

C₂²×C₄₃

C₂²×D₄

yes

—

C₂²×C₄₃

C₂²×Q₈

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

C₂×C₂²⋊Q₈

yes

—

C₂×C₄₃

C₂×#126

yes

characteristic

D₄₃

—

C₂²×C₄⋊C₄

—

C₂²×C₂²⋊C₄

—

#396

—

C₂×#95

D₄₃

yes

characteristic, complemented

C₄₃

C₂×#396

yes

characteristic, complemented, Sylow

C₂⁵

—

C₂³×C₄

—

C₂³×C₄

C₂×D₄₃

yes

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

C₂×D₄₃

yes

complemented

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

—

C₂⁴

C₂²×D₄₃

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

172

—

C₂³

—

172

—

C₂³

#10621898

yes

—

C₂³

D₄×D₄₃

yes

—

100

C₂³

Q₈×D₄₃

yes

—

101

C₂³

C₂³×D₄₃

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

108

C₂×C₄

—

109

C₂×C₄

—

110

C₂²

—

111

C₂²

—

172

—

112

C₂²

—

172

—

113

C₂²

—

172

—

114

C₂²

#13063298

yes

—

115

C₂²

#13063303

yes

—

116

C₂²

#13063319

yes

—

117

C₂²

C₂×D₄×D₄₃

yes

—

118

C₂²

C₂×Q₈×D₄₃

yes

characteristic

119

C₂²

C₂×#10621898

yes

—

120

C₄

—

121

C₄

—

122

C₂

—

172

—

123

C₂

#14582823

yes

direct product factor

124

C₂

C₂×#13063298

yes

—

125

C₂

C₂×#13063303

yes

—

126

C₂

C₂×#13063319

yes

characteristic

	subgroup	G/H
center	C₂⁴	C₂²×D₄₃
commutator	C₂³×C₄₃	C₂⁴
Frattini	C₂³	C₂³×D₄₃
Fitting	C₂×#95×C₄₃	C₂
socle	C₂⁴×C₄₃	C₂³
hypercenter	C₂×#95	D₄₃
hypocenter	C₄₃	C₂×#396
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

subgroup

G/H

center

C₂⁴

C₂²×D₄₃

commutator

C₂³×C₄₃

C₂⁴

Frattini

C₂³

C₂³×D₄₃

Fitting

C₂×#95×C₄₃

C₂

socle

C₂⁴×C₄₃

C₂³

hypercenter

C₂×#95

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂⁴ ◁ C₂×#95

N	H ≅ G/N	type
1. C₂²×Dic₄₃⋊C₄	C₂	semidirect
3. #14582823	C₂	direct (N × H)
4. C₂×#95×C₄₃	C₂	semidirect
8. C₂×Dic₄₃⋊C₄	C₂²	semidirect
12. #95×C₄₃	C₂²	semidirect
59. C₂×C₄₃	#396	semidirect
67. C₂×#95	D₄₃	semidirect
68. C₄₃	C₂×#396	semidirect
76. #95	C₂×D₄₃	semidirect
123. C₂	#14582823	direct (N × H)

H ≅ G/N

type

1. C₂²×Dic₄₃⋊C₄

C₂

semidirect

3. #14582823

C₂

direct (N × H)

4. C₂×#95×C₄₃

C₂

semidirect

8. C₂×Dic₄₃⋊C₄

C₂²

semidirect

12. #95×C₄₃

C₂²

semidirect

59. C₂×C₄₃

#396

semidirect

67. C₂×#95

D₄₃

semidirect

68. C₄₃

C₂×#396

semidirect

76. #95

C₂×D₄₃

semidirect

123. C₂

#14582823

direct (N × H)

Subgroups — C₂×#14582823 #19137817

Conjugacy classes of subgroups

Complements

Subgroups — C2×#14582823 #19137817

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#14582823 #19137817