Group #19136703 — subgroups

Subgroups — #19136703

Order 5504.

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic₃₄₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#14583140	C₂	1	2	yes	maximal
3	#14582727	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582704	C₂	1	2	yes	maximal, complemented
5	C₂×M₃₂×C₄₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₁₇₂	C₂²	1	2	yes	—
7	#13063304	—	2	2	no	—
8	Dic₃₄₄	—	2	2	no	—
9	#13063259	C₂²	1	2	yes	—
10	#13063250	—	2	2	no	—
11	C₂²×C₈×C₄₃	C₂²	1	1	yes	characteristic
12	M₃₂×C₄₃	—	2	2	no	—
13	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₄₃	D₄	1	1	yes	characteristic
16	C₂×Dic₈₆	—	2	2	no	—
17	C₂×C₈×C₄₃	—	2	1	no	—
18	C₂×C₈×C₄₃	—	2	1	no	—
19	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
21	C₂²⋊Dic₄₃	—	4	2	no	—
22	C₄⋊Dic₄₃	—	2	2	no	—
23	Dic₄₃⋊C₄	—	4	2	no	—
24	Dic₁₇₂	—	2	2	no	—
25	Dic₁₇₂	—	2	2	no	—
26	C₁₆×C₄₃	—	2	1	no	—
27	C₁₆×C₄₃	D₄	1	2	yes	—
28	C₂³×C₄₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₄₃	—	2	1	no	—
30	C₂×C₄×C₄₃	—	2	1	no	—
31	C₂×C₄×C₄₃	D₈	1	1	yes	characteristic
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×Dic₄₃	—	4	2	no	—
34	C₂×Dic₄₃	—	4	2	no	—
35	Dic₈₆	—	4	2	no	—
36	Dic₈₆	—	4	2	no	—
37	C₈×C₄₃	—	2	1	no	—
38	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₄₃	#41	1	1	yes	characteristic
40	C₂²×C₄₃	—	2	1	no	—
41	C₂²×C₄₃	—	2	2	no	—
42	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
43	C₄×C₄₃	—	2	1	no	—
44	C₄×C₄₃	#121	1	1	yes	characteristic
45	C₄×C₄₃	#135	1	1	yes	characteristic
46	Dic₄₃	—	8	2	no	—
47	Dic₄₃	—	8	2	no	—
48	#2219	—	43	1	no	maximal, Sylow
49	C₂×C₄₃	—	4	1	no	—
50	C₂×C₄₃	#466	1	1	yes	characteristic
51	C₂×C₄₃	#510	1	2	yes	—
52	C₂×Q₃₂	—	43	1	no	—
53	C₂×M₃₂	D₄₃	1	1	yes	characteristic
54	#467	—	43	2	no	—
55	#367	—	43	1	no	—
56	#358	—	43	2	no	—
57	C₄₃	#2219	1	1	yes	characteristic, complemented, Sylow
58	C₂×Q₁₆	—	43	2	no	—
59	C₂²×C₈	C₂×D₄₃	1	1	yes	characteristic
60	C₂²⋊Q₈	—	86	2	no	—
61	Q₃₂	—	86	2	no	—
62	M₃₂	—	2	2	no	—
63	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
64	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
65	#107	—	43	2	no	—
66	#103	—	86	2	no	—
67	C₂×Q₈	—	86	2	no	—
68	C₂²×C₄	D₁₇₂	1	1	yes	characteristic
69	Q₁₆	—	86	2	no	—
70	Q₁₆	—	86	2	no	—
71	C₂×C₈	—	2	1	no	—
72	C₂×C₈	—	2	1	no	—
73	C₂×C₈	D₁₇₂	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
75	C₄⋊C₄	—	86	2	no	—
76	C₄⋊C₄	—	172	2	no	—
77	C₂²⋊C₄	—	172	2	no	—
78	C₁₆	—	2	1	no	—
79	C₁₆	C₂²⋊D₄₃	1	2	yes	—
80	C₂³	D₃₄₄	1	1	yes	characteristic
81	Q₈	—	172	2	no	—
82	Q₈	—	172	2	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	172	2	no	—
86	C₂×C₄	—	172	2	no	—
87	C₂×C₄	D₃₄₄	1	1	yes	characteristic
88	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	#10621898	1	1	yes	characteristic
91	C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
92	C₂²	—	2	2	no	—
93	C₂²	—	2	1	no	—
94	C₂²	C₂×D₃₄₄	1	1	yes	characteristic
95	C₄	—	2	1	no	—
96	C₄	—	344	2	no	—
97	C₄	—	344	2	no	—
98	C₄	#13063299	1	1	yes	characteristic
99	C₄	#13063347	1	1	yes	characteristic
100	C₂	—	4	1	no	—
101	C₂	#14583135	1	1	yes	characteristic
102	C₂	#14583342	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×Dic₃₄₄

C₂

yes

maximal, characteristic, complemented

#14583140

C₂

yes

maximal

#14582727

C₂

yes

maximal, characteristic, complemented

#14582704

C₂

yes

maximal, complemented

C₂×M₃₂×C₄₃

C₂

yes

maximal, characteristic

C₂×Dic₁₇₂

C₂²

yes

—

#13063304

—

Dic₃₄₄

—

#13063259

C₂²

yes

—

#13063250

—

C₂²×C₈×C₄₃

C₂²

yes

characteristic

M₃₂×C₄₃

—

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

Dic₁₇₂

—

Dic₁₇₂

—

C₁₆×C₄₃

—

C₁₆×C₄₃

D₄

yes

—

C₂³×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

characteristic

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×Dic₄₃

—

C₂×Dic₄₃

—

Dic₈₆

—

Dic₈₆

—

C₈×C₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

—

#2219

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#466

yes

characteristic

C₂×C₄₃

#510

yes

—

C₂×Q₃₂

—

C₂×M₃₂

D₄₃

yes

—

—

—

C₄₃

#2219

yes

characteristic, complemented, Sylow

C₂×Q₁₆

—

C₂²×C₈

C₂×D₄₃

yes

characteristic

C₂²⋊Q₈

—

Q₃₂

—

M₃₂

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

C₂×C₁₆

C₂×D₄₃

yes

characteristic

#107

—

#103

—

C₂×Q₈

—

C₂²×C₄

D₁₇₂

yes

characteristic

Q₁₆

—

Q₁₆

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₁₇₂

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

172

—

C₂²⋊C₄

—

172

—

C₁₆

—

C₁₆

C₂²⋊D₄₃

yes

—

C₂³

D₃₄₄

yes

characteristic

Q₈

—

172

—

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

172

—

C₂×C₄

—

172

—

C₂×C₄

D₃₄₄

yes

characteristic

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₈

—

C₈

#10621898

yes

characteristic

C₈

C₂×C₂²⋊D₄₃

yes

characteristic

C₂²

—

C₂²

—

C₂²

C₂×D₃₄₄

yes

characteristic

C₄

—

C₄

—

344

—

C₄

—

344

—

C₄

yes

C₄

yes

100

C₂

—

101

C₂

#14583135

yes

characteristic

102

C₂

#14583342

yes

—

	subgroup	G/H
center	C₂²	C₂×D₃₄₄
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₂×M₃₂×C₄₃	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	C₂×M₃₂	D₄₃
hypocenter	C₄₃	#2219
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

subgroup

G/H

center

C₂²

C₂×D₃₄₄

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₂×M₃₂×C₄₃

C₂

socle

C₂²×C₄₃

C₂×D₈

hypercenter

C₂×M₃₂

D₄₃

hypocenter

C₄₃

#2219

LCS

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×M₃₂

N	H ≅ G/N	type
1. C₂×Dic₃₄₄	C₂	semidirect
3. #14582727	C₂	semidirect
4. #14582704	C₂	semidirect
57. C₄₃	#2219	semidirect

H ≅ G/N

type

1. C₂×Dic₃₄₄

C₂

semidirect

3. #14582727

C₂

semidirect

4. #14582704

C₂

semidirect

57. C₄₃

#2219

semidirect

Subgroups — #19136703

Conjugacy classes of subgroups

Complements