Group #19132722 — subgroups

Subgroups — #19132722

Order 5504.

172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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×#13063244	C₂	1	2	yes	maximal
2	C₄₃×#391	C₂	1	1	yes	maximal, characteristic
3	C₂×#10621877	—	2	2	no	—
4	#13063244	—	2	2	no	—
5	#13063244	C₄	1	4	yes	complemented
6	C₂²×Q₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
8	C₂×C₄²×C₄₃	C₄	1	1	yes	characteristic
9	#95×C₄₃	—	2	2	no	—
10	C₂×Q₈×C₄₃	—	4	1	no	—
11	C₂×Q₈×C₄₃	—	4	1	no	—
12	C₂×Q₈×C₄₃	C₂×C₄	1	2	yes	—
13	C₂×Q₈×C₄₃	D₄	1	1	yes	characteristic
14	C₂×Q₈×C₄₃	Q₈	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	—	2	1	no	—
16	C₂²×C₄×C₄₃	—	2	1	no	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄×C₄₃	D₄	1	2	yes	—
19	C₄⋊C₄×C₄₃	—	4	1	no	—
20	C₄²×C₄₃	—	4	1	no	—
21	#10621877	—	2	4	no	—
22	#10621877	—	4	2	no	—
23	C₂×C₄₃⋊C₈	—	4	2	no	—
24	C₂³×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
25	Q₈×C₄₃	—	4	2	no	—
26	Q₈×C₄₃	—	4	1	no	—
27	Q₈×C₄₃	—	4	1	no	—
28	C₂×C₄×C₄₃	—	2	2	no	—
29	C₂×C₄×C₄₃	—	2	2	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	—	2	1	no	—
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	4	1	no	—
34	C₂×C₄×C₄₃	—	4	1	no	—
35	C₂×C₄×C₄₃	—	4	2	no	—
36	C₂×C₄×C₄₃	—	4	1	no	—
37	C₂×C₄×C₄₃	C₄²	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₄₃	C₄⋊C₄	1	2	yes	—
40	C₂×C₄×C₄₃	C₄⋊C₄	1	1	yes	characteristic
41	C₄₃⋊C₈	—	4	4	no	—
42	C₂²×C₄₃	—	2	1	no	—
43	C₂²×C₄₃	—	2	1	no	—
44	C₂²×C₄₃	#95	1	1	yes	characteristic
45	C₂²×C₄₃	#99	1	1	yes	characteristic
46	C₂²×C₄₃	#99	1	1	yes	characteristic
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	—	2	1	no	—
49	C₄×C₄₃	—	2	2	no	—
50	C₄×C₄₃	—	2	1	no	—
51	C₄×C₄₃	—	4	2	no	—
52	C₄×C₄₃	—	8	1	no	—
53	#1394	—	43	1	no	maximal, Sylow
54	C₂×C₄₃	—	2	1	no	—
55	C₂×C₄₃	—	2	1	no	—
56	C₂×C₄₃	#342	1	1	yes	characteristic
57	C₂×C₄₃	#355	1	1	yes	characteristic
58	C₂×C₄₃	#356	1	1	yes	characteristic
59	C₂×#101	—	43	2	no	—
60	#391	D₄₃	1	1	yes	characteristic
61	C₄₃	#1394	1	1	yes	characteristic, complemented, Sylow
62	C₂²×Q₈	C₂×D₄₃	1	1	yes	characteristic
63	C₂×M₁₆	—	86	2	no	—
64	C₂×C₄⋊C₄	Dic₄₃	1	1	yes	characteristic
65	C₂×C₄²	Dic₄₃	1	1	yes	characteristic
66	#101	—	43	4	no	—
67	#101	—	86	2	no	—
68	#95	—	2	2	no	—
69	C₂×Q₈	—	4	1	no	—
70	C₂×Q₈	—	4	1	no	—
71	C₂×Q₈	Dic₈₆	1	1	yes	characteristic
72	C₂×Q₈	C₄×D₄₃	1	2	yes	—
73	C₂×Q₈	D₁₇₂	1	1	yes	characteristic
74	C₂²×C₄	—	2	1	no	—
75	C₂²×C₄	—	2	1	no	—
76	C₂²×C₄	C₂×Dic₄₃	1	1	yes	characteristic
77	C₂²×C₄	C₂²⋊D₄₃	1	2	yes	—
78	M₁₆	—	86	4	no	—
79	M₁₆	—	172	2	no	—
80	C₂×C₈	—	172	2	no	—
81	C₄⋊C₄	—	4	1	no	—
82	C₄²	—	4	1	no	—
83	C₂³	C₂²⋊Dic₄₃	1	1	yes	characteristic
84	Q₈	—	4	1	no	—
85	Q₈	—	4	2	no	—
86	Q₈	—	4	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	4	1	no	—
93	C₂×C₄	—	4	1	no	—
94	C₂×C₄	—	4	2	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	C₄×Dic₄₃	1	1	yes	characteristic
97	C₂×C₄	Dic₄₃⋊C₄	1	2	yes	—
98	C₂×C₄	C₄⋊Dic₄₃	1	1	yes	characteristic
99	C₂×C₄	(C₂×D₄₃)⋊C₄	1	2	yes	—
100	C₈	—	172	4	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	2	1	no	—
103	C₂²	C₄₃⋊#95	1	1	yes	characteristic
104	C₂²	#13063240	1	1	yes	characteristic
105	C₂²	#13063240	1	1	yes	characteristic
106	C₄	—	2	2	no	—
107	C₄	—	2	1	no	—
108	C₄	—	2	2	no	—
109	C₄	—	2	1	no	—
110	C₄	—	4	2	no	—
111	C₄	—	8	1	no	—
112	C₂	—	2	1	no	—
113	C₂	—	2	1	no	—
114	C₂	#14582666	1	1	yes	characteristic
115	C₂	#14582696	1	1	yes	characteristic
116	C₂	#14582698	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063244

C₂

yes

maximal

C₄₃×#391

C₂

yes

maximal, characteristic

C₂×#10621877

—

#13063244

—

#13063244

C₄

yes

complemented

C₂²×Q₈×C₄₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₄₃

C₄

yes

characteristic

C₂×C₄²×C₄₃

C₄

yes

characteristic

#95×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

—

C₂×Q₈×C₄₃

C₂×C₄

yes

—

C₂×Q₈×C₄₃

D₄

yes

characteristic

C₂×Q₈×C₄₃

Q₈

yes

characteristic

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

—

C₂²×C₄×C₄₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₄⋊C₄×C₄₃

—

C₄²×C₄₃

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

C₂³×C₄₃

C₂²⋊C₄

yes

characteristic

Q₈×C₄₃

—

Q₈×C₄₃

—

Q₈×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

characteristic

C₂×C₄×C₄₃

C₂²⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

#1394

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

C₂×C₄₃

yes

C₂×C₄₃

yes

—

D₄₃

yes

characteristic

C₄₃

#1394

yes

characteristic, complemented, Sylow

C₂²×Q₈

C₂×D₄₃

yes

characteristic

C₂×M₁₆

—

C₂×C₄⋊C₄

Dic₄₃

yes

characteristic

C₂×C₄²

Dic₄₃

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

Dic₈₆

yes

characteristic

C₂×Q₈

C₄×D₄₃

yes

—

C₂×Q₈

D₁₇₂

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×Dic₄₃

yes

characteristic

C₂²×C₄

C₂²⋊D₄₃

yes

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₄⋊C₄

—

C₄²

—

C₂³

C₂²⋊Dic₄₃

yes

characteristic

Q₈

—

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₃

yes

characteristic

C₂×C₄

Dic₄₃⋊C₄

yes

—

C₂×C₄

C₄⋊Dic₄₃

yes

characteristic

C₂×C₄

(C₂×D₄₃)⋊C₄

yes

—

100

C₈

—

172

—

101

C₂²

—

102

C₂²

—

103

C₂²

C₄₃⋊#95

yes

characteristic

104

C₂²

#13063240

yes

characteristic

105

C₂²

#13063240

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

—

112

C₂

—

113

C₂

—

114

C₂

#14582666

yes

characteristic

115

C₂

#14582696

yes

characteristic

116

C₂

#14582698

yes

characteristic

	subgroup	G/H
center	C₂²	#13063240
commutator	C₂×C₄×C₄₃	C₄²
Frattini	C₂²×Q₈	C₂×D₄₃
Fitting	C₄₃×#391	C₂
socle	C₂²×C₄₃	#99
hypercenter	#391	D₄₃
hypocenter	C₄₃	#1394
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×Q₈ ◁ #391

subgroup

G/H

center

C₂²

#13063240

commutator

C₂×C₄×C₄₃

C₄²

Frattini

C₂²×Q₈

C₂×D₄₃

Fitting

C₄₃×#391

C₂

C₂²×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₄×C₄₃ ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×Q₈ ◁ #391

N	H ≅ G/N	type
5. #13063244	C₄	semidirect
61. C₄₃	#1394	semidirect

H ≅ G/N

type

5. #13063244

C₄

semidirect

61. C₄₃

#1394

semidirect

Subgroups — #19132722

Conjugacy classes of subgroups

Complements