Group #19136815 — subgroups

Subgroups — #19136815

Order 5504.

124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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	#14583157	C₂	1	1	yes	maximal, characteristic
2	#14582948	C₂	1	1	yes	maximal, characteristic
3	#14582722	C₂	1	2	yes	maximal, complemented
4	#14582716	C₂	1	2	yes	maximal, complemented
5	C₄₃×#349	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic
7	C₂×#10621877	—	2	1	no	—
8	#13063304	—	2	1	no	—
9	#13063261	—	2	1	no	—
10	#13063261	C₂²	1	2	yes	—
11	#13063257	C₂²	1	1	yes	characteristic
12	#13063250	—	2	1	no	—
13	C₂×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	M₃₂×C₄₃	C₂²	1	2	yes	—
15	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂×Dic₈₆	—	2	1	no	—
17	M₁₆×C₄₃	—	2	2	no	—
18	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²⋊Dic₄₃	—	4	1	no	—
21	C₄⋊Dic₄₃	—	2	1	no	—
22	Dic₄₃⋊C₄	—	4	1	no	—
23	#10621877	—	2	2	no	—
24	#10621877	—	4	1	no	—
25	C₂×C₄₃⋊C₈	—	4	1	no	—
26	Dic₁₇₂	—	2	2	no	—
27	C₁₆×C₄₃	—	2	2	no	—
28	C₂³×C₄₃	SD₁₆	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	SD₁₆	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₃	—	4	1	no	—
34	C₂×Dic₄₃	—	4	1	no	—
35	Dic₈₆	—	4	1	no	—
36	Dic₈₆	—	4	1	no	—
37	C₈×C₄₃	—	2	1	no	—
38	C₈×C₄₃	#41	1	2	yes	—
39	C₄₃⋊C₈	—	4	2	no	—
40	C₂²×C₄₃	—	2	1	no	—
41	C₂²×C₄₃	—	4	1	no	—
42	C₂²×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	#123	1	1	yes	characteristic
45	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
46	Dic₄₃	—	8	1	no	—
47	Dic₄₃	—	8	1	no	—
48	#2239	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	2	1	no	—
50	C₂×C₄₃	—	4	1	no	—
51	C₂×C₄₃	#481	1	1	yes	characteristic
52	#470	—	43	1	no	—
53	#430	—	43	1	no	—
54	#365	—	43	2	no	—
55	#362	—	43	2	no	—
56	#349	D₄₃	1	1	yes	characteristic
57	C₄₃	#2239	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	43	1	no	—
59	C₂×M₁₆	—	86	1	no	—
60	C₂×M₁₆	C₂×D₄₃	1	1	yes	characteristic
61	C₂²⋊Q₈	—	86	1	no	—
62	M₃₂	C₂×D₄₃	1	2	yes	—
63	#108	—	43	2	no	—
64	#108	—	86	1	no	—
65	#106	—	43	1	no	—
66	#103	—	86	1	no	—
67	C₂×Q₈	—	86	1	no	—
68	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
69	Q₁₆	—	86	2	no	—
70	M₁₆	—	2	2	no	—
71	M₁₆	—	86	2	no	—
72	M₁₆	—	172	1	no	—
73	C₂×C₈	—	172	1	no	—
74	C₂×C₈	D₁₇₂	1	1	yes	characteristic
75	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
76	C₄⋊C₄	—	86	1	no	—
77	C₄⋊C₄	—	172	1	no	—
78	C₂²⋊C₄	—	172	1	no	—
79	C₁₆	—	2	2	no	—
80	C₂³	#10621873	1	1	yes	characteristic
81	Q₈	—	172	1	no	—
82	Q₈	—	172	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	172	1	no	—
86	C₂×C₄	—	172	1	no	—
87	C₂×C₄	#10621873	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	172	2	no	—
91	C₈	#10621900	1	2	yes	—
92	C₂²	—	2	1	no	—
93	C₂²	—	4	1	no	—
94	C₂²	C₂×#10621873	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	344	1	no	—
97	C₄	—	344	1	no	—
98	C₄	#13063309	1	1	yes	characteristic
99	C₄	#13063353	1	1	yes	characteristic
100	C₂	—	2	1	no	—
101	C₂	—	4	1	no	—
102	C₂	#14583218	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14583157

C₂

yes

maximal, characteristic

#14582948

C₂

yes

maximal, characteristic

#14582722

C₂

yes

maximal, complemented

#14582716

C₂

yes

maximal, complemented

C₄₃×#349

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

—

—

C₂²

yes

—

#13063257

C₂²

yes

characteristic

#13063250

—

C₂×M₁₆×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

M₁₆×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

#10621877

—

#10621877

—

C₂×C₄₃⋊C₈

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₂³×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

SD₁₆

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

#41

yes

—

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×SD₁₆

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2239

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

—

C₂×C₄₃

yes

—

—

—

—

D₄₃

yes

characteristic

C₄₃

#2239

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂×M₁₆

—

C₂×M₁₆

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

M₃₂

C₂×D₄₃

yes

—

—

—

—

—

C₂×Q₈

—

C₂²×C₄

D₁₇₂

yes

characteristic

Q₁₆

—

M₁₆

—

M₁₆

—

M₁₆

—

172

—

C₂×C₈

—

172

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₂³

#10621873

yes

characteristic

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

#10621873

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₈

—

C₈

—

172

—

C₈

#10621900

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#10621873

yes

characteristic

C₄

—

C₄

—

344

—

C₄

—

344

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

—

102

C₂

#14583218

yes

characteristic

	subgroup	G/H
center	C₂	#14583218
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#349	C₂
socle	C₂×C₄₃	#481
hypercenter	#349	D₄₃
hypocenter	C₄₃	#2239
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

subgroup

G/H

center

C₂

#14583218

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#349

C₂

C₂×C₄₃

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

N	H ≅ G/N	type
3. #14582722	C₂	semidirect
4. #14582716	C₂	semidirect
57. C₄₃	#2239	semidirect

H ≅ G/N

type

3. #14582722

C₂

semidirect

4. #14582716

C₂

semidirect

57. C₄₃

#2239

semidirect

Subgroups — #19136815

Conjugacy classes of subgroups

Complements