Group #19134452 — subgroups

Subgroups — #19134452

Order 5504.

260 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 141 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×C₄⋊(C₄₃⋊C₈)	C₂	1	2	yes	maximal
2	C₂×#13063236	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#14582654	C₂	1	2	yes	maximal
5	C₄₃×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄₃⋊C₈	C₂²	1	2	yes	—
8	C₄⋊(C₄₃⋊C₈)	C₄	1	8	yes	complemented
9	#13063236	—	2	2	no	—
10	C₄×C₄₃⋊C₈	—	2	2	no	—
11	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	#95×C₄₃	C₄	1	4	yes	—
15	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
17	C₂²×C₄×C₄₃	C₂×C₄	1	2	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	C₄²×C₄₃	—	2	2	no	—
20	C₄²×C₄₃	C₂×C₄	1	4	yes	—
21	C₄²×C₄₃	D₄	1	2	yes	—
22	C₄²×C₄₃	Q₈	1	2	yes	—
23	C₂×C₄₃⋊C₈	—	2	2	no	—
24	C₂×C₄₃⋊C₈	—	2	2	no	—
25	C₂×C₄₃⋊C₈	—	2	2	no	—
26	C₂×C₄₃⋊C₈	—	2	2	no	—
27	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
29	C₂³×C₄₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₄₃	—	2	4	no	—
31	C₂×C₄×C₄₃	—	2	4	no	—
32	C₂×C₄×C₄₃	—	2	2	no	—
33	C₂×C₄×C₄₃	—	2	4	no	—
34	C₂×C₄×C₄₃	C₄²	1	4	yes	—
35	C₂×C₄×C₄₃	C₄⋊C₄	1	4	yes	—
36	C₂×C₄×C₄₃	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₄₃	#41	1	2	yes	—
40	C₄₃⋊C₈	—	2	4	no	—
41	C₄₃⋊C₈	—	2	4	no	—
42	C₂²×C₄₃	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₄₃	#117	1	1	yes	characteristic
45	C₂²×C₄₃	#131	1	4	yes	—
46	C₄×C₄₃	—	2	4	no	—
47	C₄×C₄₃	—	2	4	no	—
48	C₄×C₄₃	—	4	2	no	—
49	C₄×C₄₃	C₄×D₄	1	2	yes	—
50	C₄×C₄₃	C₄×Q₈	1	2	yes	—
51	#1768	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	C₄×C₄⋊C₄	1	1	yes	characteristic
53	C₂×C₄₃	#405	1	2	yes	—
54	C₂×C₄₃	#424	1	2	yes	—
55	C₂×C₄₃	#433	1	2	yes	—
56	C₂×C₄⋊C₈	—	43	2	no	—
57	C₂×#97	—	43	1	no	—
58	C₂×C₄×C₈	—	43	1	no	—
59	#376	D₄₃	1	1	yes	characteristic
60	#336	—	43	2	no	—
61	C₄₃	#1768	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₈	—	43	2	no	—
63	C₂²×C₈	—	43	2	no	—
64	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
67	C₄⋊C₈	—	43	8	no	—
68	#97	—	86	2	no	—
69	C₄×C₈	—	86	2	no	—
70	#95	Dic₄₃	1	4	yes	—
71	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
72	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
73	C₂²×C₄	C₂×Dic₄₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
75	C₂×C₈	—	43	4	no	—
76	C₂×C₈	—	43	4	no	—
77	C₂×C₈	—	86	2	no	—
78	C₂×C₈	—	86	2	no	—
79	C₂×C₈	—	86	2	no	—
80	C₂×C₈	—	86	2	no	—
81	C₄²	—	2	2	no	—
82	C₄²	Dic₈₆	1	2	yes	—
83	C₄²	C₄×D₄₃	1	4	yes	—
84	C₄²	D₁₇₂	1	2	yes	—
85	C₂³	C₂²×Dic₄₃	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	C₄×Dic₄₃	1	4	yes	—
91	C₂×C₄	C₄⋊Dic₄₃	1	4	yes	—
92	C₂×C₄	C₂×Dic₈₆	1	1	yes	characteristic
93	C₂×C₄	C₂×C₄×D₄₃	1	2	yes	—
94	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
95	C₂×C₄	#10621898	1	2	yes	—
96	C₈	—	86	4	no	—
97	C₈	—	86	4	no	—
98	C₂²	C₂×C₄×Dic₄₃	1	1	yes	characteristic
99	C₂²	C₂×C₄⋊Dic₄₃	1	1	yes	characteristic
100	C₂²	#13063284	1	1	yes	characteristic
101	C₂²	#13063332	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	2	4	no	—
104	C₄	—	4	2	no	—
105	C₄	C₄×D₁₇₂	1	2	yes	—
106	C₄	C₄×Dic₈₆	1	2	yes	—
107	C₂	C₄×C₄⋊Dic₄₃	1	1	yes	characteristic
108	C₂	#14582855	1	2	yes	—
109	C₂	#14582926	1	2	yes	—
110	C₂	#14582960	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊(C₄₃⋊C₈)

C₂

yes

maximal

C₂×#13063236

C₂

yes

maximal, characteristic

C₂×C₄×C₄₃⋊C₈

C₂

yes

maximal, characteristic

#14582654

C₂

yes

maximal

C₄₃×#376

C₂

yes

maximal, characteristic

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₂²×C₄₃⋊C₈

C₂²

yes

—

C₄⋊(C₄₃⋊C₈)

C₄

yes

complemented

#13063236

—

C₄×C₄₃⋊C₈

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂×C₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

—

C₄²×C₄₃

C₂×C₄

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

Q₈

yes

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂×C₄₃⋊C₈

C₂×C₄

yes

—

C₂³×C₄₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₄²

yes

—

C₂×C₄×C₄₃

C₄⋊C₄

yes

—

C₂×C₄×C₄₃

C₂²×C₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₄₃⋊C₈

—

C₂²×C₄₃

C₂×C₄²

yes

characteristic

C₂²×C₄₃

C₂×C₄⋊C₄

yes

C₂²×C₄₃

yes

C₂²×C₄₃

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄×D₄

yes

—

C₄×C₄₃

C₄×Q₈

yes

—

#1768

—

maximal, Sylow

C₂×C₄₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₄₃

#405

yes

—

C₂×C₄₃

#424

yes

—

C₂×C₄₃

#433

yes

—

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

—

#376

D₄₃

yes

characteristic

#336

—

C₄₃

#1768

yes

characteristic, complemented, Sylow

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₂×C₄²

C₂×D₄₃

yes

characteristic

C₄⋊C₈

—

#97

—

C₄×C₈

—

#95

Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂×Dic₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

Dic₈₆

yes

—

C₄²

C₄×D₄₃

yes

—

C₄²

D₁₇₂

yes

—

C₂³

C₂²×Dic₄₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₄₃

yes

—

C₂×C₄

C₄⋊Dic₄₃

yes

—

C₂×C₄

C₂×Dic₈₆

yes

characteristic

C₂×C₄

C₂×C₄×D₄₃

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

#10621898

yes

—

C₈

—

C₈

—

C₂²

C₂×C₄×Dic₄₃

yes

characteristic

C₂²

C₂×C₄⋊Dic₄₃

yes

characteristic

100

C₂²

#13063284

yes

characteristic

101

C₂²

#13063332

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄×D₁₇₂

yes

—

106

C₄

C₄×Dic₈₆

yes

—

107

C₂

C₄×C₄⋊Dic₄₃

yes

characteristic

108

C₂

#14582855

yes

—

109

C₂

#14582926

yes

—

110

C₂

#14582960

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₄₃
commutator	C₂²×C₄₃	C₂×C₄²
Fitting	C₄₃×#376	C₂
socle	C₂³×C₄₃	C₂²×C₄
hypercenter	#376	D₄₃
hypocenter	C₄₃	#1768
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₄₃

commutator

C₂²×C₄₃

C₂×C₄²

Fitting

C₄₃×#376

C₂

socle

C₂³×C₄₃

C₂²×C₄

D₄₃

C₄₃

G ▷ C₂²×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
8. C₄⋊(C₄₃⋊C₈)	C₄	semidirect
61. C₄₃	#1768	semidirect

H ≅ G/N

type

8. C₄⋊(C₄₃⋊C₈)

C₄

semidirect

61. C₄₃

#1768

semidirect

Subgroups — #19134452

Conjugacy classes of subgroups

Complements