Group #19136844 — subgroups

Subgroups — #19136844

Order 5504.

216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 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×#13063266	C₂	1	4	yes	maximal, complemented
2	#14583276	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₃₄₄	—	2	1	no	—
6	C₂×D₃₄₄	C₂²	1	2	yes	—
7	#13063322	—	2	1	no	—
8	#13063266	—	2	8	no	—
9	C₂×C₄₃⋊C₁₆	C₂²	1	2	yes	—
10	C₂×D₈×C₄₃	—	2	1	no	—
11	C₂×D₈×C₄₃	C₂²	1	2	yes	—
12	#127×C₄₃	—	2	1	no	—
13	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×D₄×C₄₃	—	2	2	no	—
15	C₂×D₄×C₄₃	—	4	2	no	—
16	C₂×D₁₇₂	—	2	2	no	—
17	C₂×D₁₇₂	—	4	2	no	—
18	D₈×C₄₃	—	2	4	no	—
19	D₈×C₄₃	—	4	2	no	—
20	C₂×C₈×C₄₃	D₄	1	1	yes	characteristic
21	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
22	C₄²×C₄₃	D₄	1	1	yes	characteristic
23	D₃₄₄	—	2	4	no	—
24	D₃₄₄	—	4	2	no	—
25	C₄₃⋊C₁₆	D₄	1	4	yes	complemented
26	C₂³×C₄₃	—	4	2	no	—
27	C₂²×D₄₃	—	4	2	no	—
28	D₄×C₄₃	—	4	2	no	—
29	D₄×C₄₃	—	4	2	no	—
30	D₄×C₄₃	—	8	4	no	—
31	C₂×C₄×C₄₃	D₈	1	2	yes	—
32	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
33	D₁₇₂	—	4	2	no	—
34	D₁₇₂	—	4	2	no	—
35	D₁₇₂	—	8	4	no	—
36	C₈×C₄₃	D₈	1	2	yes	—
37	C₈×C₄₃	C₂×D₄	1	2	yes	—
38	C₂²×C₄₃	—	8	2	no	—
39	C₂²×C₄₃	—	8	4	no	—
40	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
41	C₂×D₄₃	—	8	2	no	—
42	C₂×D₄₃	—	8	4	no	—
43	C₄×C₄₃	D₁₆	1	4	yes	complemented
44	C₄×C₄₃	#127	1	1	yes	characteristic
45	C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
46	#2246	—	43	1	no	maximal, Sylow
47	C₂×C₄₃	—	16	2	no	—
48	C₂×C₄₃	#493	1	1	yes	characteristic
49	C₂×C₄₃	C₂×D₁₆	1	2	yes	—
50	D₄₃	—	16	2	no	—
51	C₂×D₁₆	—	43	4	no	—
52	#493	—	43	1	no	—
53	#493	D₄₃	1	1	yes	characteristic, complemented
54	C₄×C₁₆	—	43	1	no	—
55	C₄₃	#2246	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₈	—	2	1	no	—
57	C₂×D₈	—	43	2	no	—
58	C₂×D₈	—	86	1	no	—
59	C₂×D₈	C₂×D₄₃	1	2	yes	—
60	#127	—	2	1	no	—
61	#127	—	86	1	no	—
62	D₁₆	—	86	8	no	—
63	C₂×C₁₆	—	43	2	no	—
64	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
65	C₂×D₄	—	2	2	no	—
66	C₂×D₄	—	4	2	no	—
67	C₂×D₄	—	86	2	no	—
68	C₂×D₄	—	172	2	no	—
69	D₈	—	2	4	no	—
70	D₈	—	4	2	no	—
71	D₈	—	86	4	no	—
72	D₈	—	172	2	no	—
73	C₂×C₈	C₂²⋊D₄₃	1	1	yes	characteristic
74	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
75	C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
76	C₁₆	—	43	4	no	—
77	C₂³	—	4	2	no	—
78	C₂³	—	172	2	no	—
79	D₄	—	4	2	no	—
80	D₄	—	4	2	no	—
81	D₄	—	8	4	no	—
82	D₄	—	344	4	no	—
83	D₄	—	172	2	no	—
84	D₄	—	172	2	no	—
85	C₂×C₄	#10621882	1	2	yes	—
86	C₂×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
87	C₈	#10621882	1	2	yes	—
88	C₈	D₄×D₄₃	1	2	yes	—
89	C₂²	—	8	4	no	—
90	C₂²	—	8	2	no	—
91	C₂²	—	344	4	no	—
92	C₂²	—	344	2	no	—
93	C₂²	C₂×#10621882	1	1	yes	characteristic
94	C₄	#13063266	1	4	yes	complemented
95	C₄	#13063321	1	1	yes	characteristic
96	C₄	C₂×#10621882	1	1	yes	characteristic
97	C₂	—	16	2	no	—
98	C₂	—	688	2	no	—
99	C₂	#14583275	1	1	yes	characteristic
100	C₂	C₂×#13063266	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063266

C₂

yes

maximal, complemented

#14583276

C₂

yes

maximal, characteristic, complemented

C₄×C₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

C₄₃×#493

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

—

C₂×D₃₄₄

C₂²

yes

—

#13063322

—

#13063266

—

C₂×C₄₃⋊C₁₆

C₂²

yes

—

C₂×D₈×C₄₃

—

C₂×D₈×C₄₃

C₂²

yes

—

#127×C₄₃

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×D₄×C₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

D₄

yes

characteristic

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

C₄₃⋊C₁₆

D₄

yes

complemented

C₂³×C₄₃

—

C₂²×D₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

D₈

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₈×C₄₃

D₈

yes

—

C₈×C₄₃

C₂×D₄

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

D₁₆

yes

complemented

C₄×C₄₃

#127

yes

characteristic

C₄×C₄₃

C₂×D₈

yes

characteristic

#2246

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#493

yes

characteristic

C₂×C₄₃

C₂×D₁₆

yes

—

D₄₃

—

C₂×D₁₆

—

#493

—

#493

D₄₃

yes

characteristic, complemented

C₄×C₁₆

—

C₄₃

#2246

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

—

#127

—

#127

—

D₁₆

—

C₂×C₁₆

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

D₈

—

D₈

—

D₈

—

D₈

—

172

—

C₂×C₈

C₂²⋊D₄₃

yes

characteristic

C₂×C₈

C₂²×D₄₃

yes

characteristic

C₄²

C₂²⋊D₄₃

yes

characteristic

C₁₆

—

C₂³

—

C₂³

—

172

—

D₄

—

D₄

—

D₄

—

D₄

—

344

—

D₄

—

172

—

D₄

—

172

—

C₂×C₄

#10621882

yes

—

C₂×C₄

C₂×C₂²⋊D₄₃

yes

characteristic

C₈

#10621882

yes

—

C₈

D₄×D₄₃

yes

—

C₂²

—

C₂²

—

C₂²

—

344

—

C₂²

—

344

—

C₂²

yes

C₄

yes

C₄

yes

C₄

yes

C₂

—

C₂

—

688

—

C₂

#14583275

yes

characteristic

100

C₂

C₂×#13063266

yes

—

	subgroup	G/H
center	C₂²	C₂×#10621882
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#493	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#493	D₄₃
hypocenter	C₄₃	#2246
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

subgroup

G/H

center

C₂²

C₂×#10621882

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#493

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #493

N	H ≅ G/N	type
1. C₂×#13063266	C₂	semidirect
2. #14583276	C₂	semidirect
3. C₄×C₄₃⋊C₁₆	C₂	semidirect
4. C₄₃×#493	C₂	semidirect
25. C₄₃⋊C₁₆	D₄	semidirect
43. C₄×C₄₃	D₁₆	semidirect
53. #493	D₄₃	semidirect
55. C₄₃	#2246	semidirect
94. C₄	#13063266	semidirect

H ≅ G/N

type

1. C₂×#13063266

C₂

semidirect

2. #14583276

C₂

semidirect

3. C₄×C₄₃⋊C₁₆

C₂

semidirect

4. C₄₃×#493

C₂

semidirect

25. C₄₃⋊C₁₆

D₄

semidirect

43. C₄×C₄₃

D₁₆

semidirect

53. #493

D₄₃

semidirect

55. C₄₃

#2246

semidirect

94. C₄

#13063266

semidirect

Subgroups — #19136844

Conjugacy classes of subgroups

Complements