Group #19136426 — subgroups

Subgroups — #19136426

Order 5504.

162 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 71 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×#13063264	C₂	1	2	yes	maximal, complemented
2	C₈×D₁₇₂	C₂	1	1	yes	maximal, characteristic
3	(C₂×D₄₃)⋊C₁₆	C₂	1	2	yes	maximal, complemented
4	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈×D₄₃	C₂²	1	2	yes	—
7	C₄×D₁₇₂	C₄	1	1	yes	characteristic
8	#13063264	—	2	4	no	—
9	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
11	C₄⋊(C₄₃⋊C₈)	C₄	1	1	yes	characteristic
12	(C₂×D₄₃)⋊C₈	C₄	1	2	yes	—
13	C₂×C₁₆×C₄₃	C₂²	1	2	yes	—
14	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×D₁₇₂	C₈	1	1	yes	characteristic
16	C₂×C₄×D₄₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
20	(C₂×D₄₃)⋊C₄	C₈	1	2	yes	—
21	C₄⋊Dic₄₃	C₈	1	1	yes	characteristic
22	C₂×C₄₃⋊C₈	C₂×C₄	1	2	yes	—
23	C₈×D₄₃	—	2	2	no	—
24	C₈×D₄₃	—	2	2	no	—
25	C₁₆×C₄₃	—	2	2	no	—
26	C₄₃⋊C₁₆	—	2	1	no	—
27	C₄₃⋊C₁₆	D₄	1	2	yes	complemented
28	C₂²×D₄₃	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₄₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₄₃	C₂×C₈	1	2	yes	—
33	D₁₇₂	—	2	2	no	—
34	C₄×D₄₃	—	2	2	no	—
35	C₄×D₄₃	—	2	2	no	—
36	C₈×C₄₃	—	2	1	no	—
37	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₈×C₄₃	#41	1	1	yes	characteristic
39	C₄₃⋊C₈	—	2	2	no	—
40	C₂²×C₄₃	C₂²×C₈	1	1	yes	characteristic
41	C₂×D₄₃	—	2	2	no	—
42	C₂×D₄₃	—	2	2	no	—
43	C₂×D₄₃	—	2	2	no	—
44	C₄×C₄₃	—	2	1	no	—
45	C₄×C₄₃	M₃₂	1	2	yes	complemented
46	C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
47	C₄×C₄₃	#131	1	1	yes	characteristic
48	Dic₄₃	—	2	2	no	—
49	#2169	—	43	1	no	maximal, Sylow
50	C₂×C₄₃	C₈×D₄	1	1	yes	characteristic
51	C₂×C₄₃	C₂×M₃₂	1	1	yes	characteristic
52	C₂×C₄₃	#504	1	1	yes	characteristic
53	D₄₃	—	4	2	no	—
54	C₂×M₃₂	—	43	2	no	—
55	C₈×D₄	—	43	1	no	—
56	C₄⋊C₁₆	D₄₃	1	1	yes	characteristic, complemented
57	C₂²⋊C₁₆	—	43	2	no	—
58	C₄×C₁₆	—	43	1	no	—
59	C₄₃	#2169	1	1	yes	characteristic, complemented, Sylow
60	C₂²×C₈	—	43	2	no	—
61	C₄×D₄	—	43	1	no	—
62	M₃₂	—	86	4	no	—
63	C₂×C₁₆	—	43	1	no	—
64	C₂×C₁₆	—	43	1	no	—
65	C₂×C₁₆	C₂×D₄₃	1	2	yes	—
66	C₄⋊C₈	—	43	1	no	—
67	C₂²⋊C₈	—	43	2	no	—
68	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
69	C₂×D₄	—	43	1	no	—
70	C₂²×C₄	—	43	2	no	—
71	C₂×C₈	—	43	2	no	—
72	C₂×C₈	—	86	2	no	—
73	C₂×C₈	—	86	2	no	—
74	C₂×C₈	C₄×D₄₃	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
76	C₄⋊C₄	—	43	1	no	—
77	C₂²⋊C₄	—	43	2	no	—
78	C₄²	C₄×D₄₃	1	1	yes	characteristic
79	C₁₆	—	2	2	no	—
80	C₁₆	—	43	2	no	—
81	C₁₆	—	86	1	no	—
82	C₂³	—	43	2	no	—
83	D₄	—	86	2	no	—
84	C₂×C₄	—	43	2	no	—
85	C₂×C₄	—	86	2	no	—
86	C₂×C₄	—	86	2	no	—
87	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
88	C₂×C₄	C₈×D₄₃	1	1	yes	characteristic
89	C₂×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
90	C₈	—	2	1	no	—
91	C₈	—	86	2	no	—
92	C₈	D₄×D₄₃	1	1	yes	characteristic
93	C₈	#10621902	1	1	yes	characteristic
94	C₂²	—	86	2	no	—
95	C₂²	—	86	2	no	—
96	C₂²	—	86	2	no	—
97	C₂²	C₂×C₈×D₄₃	1	1	yes	characteristic
98	C₄	—	2	1	no	—
99	C₄	—	86	2	no	—
100	C₄	#13063264	1	2	yes	complemented
101	C₄	#13063287	1	1	yes	characteristic
102	C₄	#13063333	1	1	yes	characteristic
103	C₂	—	172	2	no	—
104	C₂	#14582964	1	1	yes	characteristic
105	C₂	C₂×#13063264	1	1	yes	characteristic
106	C₂	#14583317	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063264

C₂

yes

maximal, complemented

C₈×D₁₇₂

C₂

yes

maximal, characteristic

(C₂×D₄₃)⋊C₁₆

C₂

yes

maximal, complemented

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₃×C₄⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₄₃

C₂²

yes

—

C₄×D₁₇₂

C₄

yes

characteristic

#13063264

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

C₄⋊(C₄₃⋊C₈)

C₄

yes

characteristic

(C₂×D₄₃)⋊C₈

C₄

yes

—

C₂×C₁₆×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₁₇₂

C₈

yes

characteristic

C₂×C₄×D₄₃

C₂×C₄

yes

—

C₂×C₈×C₄₃

C₂×C₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂×C₄

yes

characteristic

(C₂×D₄₃)⋊C₄

C₈

yes

—

C₄⋊Dic₄₃

C₈

yes

characteristic

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₈×D₄₃

—

C₈×D₄₃

—

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₄₃⋊C₁₆

D₄

yes

complemented

C₂²×D₄₃

C₂×C₈

yes

—

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂×C₈

yes

characteristic

C₂×C₄×C₄₃

C₂²×C₄

yes

characteristic

C₂×Dic₄₃

C₂×C₈

yes

—

D₁₇₂

—

C₄×D₄₃

—

C₄×D₄₃

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

C₂²×C₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

M₃₂

yes

complemented

C₄×C₄₃

C₄×D₄

yes

characteristic

C₄×C₄₃

#131

yes

characteristic

Dic₄₃

—

#2169

—

maximal, Sylow

C₂×C₄₃

C₈×D₄

yes

characteristic

C₂×C₄₃

C₂×M₃₂

yes

characteristic

C₂×C₄₃

#504

yes

characteristic

D₄₃

—

C₂×M₃₂

—

C₈×D₄

—

C₄⋊C₁₆

D₄₃

yes

characteristic, complemented

C₂²⋊C₁₆

—

C₄×C₁₆

—

C₄₃

#2169

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₄×D₄

—

M₃₂

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂²×C₄

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄×D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

C₄×D₄₃

yes

characteristic

C₁₆

—

C₁₆

—

C₁₆

—

C₂³

—

D₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₈×D₄₃

yes

characteristic

C₂×C₄

C₈×D₄₃

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

characteristic

C₈

—

C₈

—

C₈

D₄×D₄₃

yes

characteristic

C₈

#10621902

yes

characteristic

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×C₈×D₄₃

yes

characteristic

C₄

—

C₄

—

100

C₄

#13063264

yes

complemented

101

C₄

#13063287

yes

characteristic

102

C₄

#13063333

yes

characteristic

103

C₂

—

172

—

104

C₂

#14582964

yes

characteristic

105

C₂

C₂×#13063264

yes

characteristic

106

C₂

#14583317

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×D₄₃
commutator, socle	C₂²×C₄₃	C₂²×C₈
Fitting	C₄₃×C₄⋊C₁₆	C₂
hypercenter	C₄⋊C₁₆	D₄₃
hypocenter	C₄₃	#2169
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

subgroup

G/H

center, Frattini

C₂×C₈

C₂²×D₄₃

commutator, socle

C₂²×C₄₃

C₂²×C₈

Fitting

C₄₃×C₄⋊C₁₆

C₂

hypercenter

C₄⋊C₁₆

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂×C₈ ◁ C₄⋊C₁₆

N	H ≅ G/N	type
1. C₂×#13063264	C₂	semidirect
3. (C₂×D₄₃)⋊C₁₆	C₂	semidirect
4. C₄×C₄₃⋊C₁₆	C₂	semidirect
5. C₄₃×C₄⋊C₁₆	C₂	semidirect
27. C₄₃⋊C₁₆	D₄	semidirect
45. C₄×C₄₃	M₃₂	semidirect
56. C₄⋊C₁₆	D₄₃	semidirect
59. C₄₃	#2169	semidirect
100. C₄	#13063264	semidirect

H ≅ G/N

type

1. C₂×#13063264

C₂

semidirect

3. (C₂×D₄₃)⋊C₁₆

C₂

semidirect

4. C₄×C₄₃⋊C₁₆

C₂

semidirect

5. C₄₃×C₄⋊C₁₆

C₂

semidirect

27. C₄₃⋊C₁₆

D₄

semidirect

45. C₄×C₄₃

M₃₂

semidirect

56. C₄⋊C₁₆

D₄₃

semidirect

59. C₄₃

#2169

semidirect

100. C₄

#13063264

semidirect

Subgroups — #19136426

Conjugacy classes of subgroups

Complements