Group #19142638 — subgroups

Subgroups — #19142638

Order 5504.

630 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 630 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063322	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063319	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582817	C₂	1	6	yes	maximal, complemented
4	#14582809	C₂	1	6	yes	maximal, complemented
5	C₄₃×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	C₂²	1	6	yes	—
7	C₂²×D₁₇₂	C₂²	1	4	yes	—
8	#13063322	—	2	4	no	—
9	#13063319	—	2	4	no	—
10	C₂×Dic₄₃⋊C₄	C₂²	1	3	yes	—
11	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	3	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	12	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	#95×C₄₃	C₂²	1	6	yes	—
15	C₂³×D₄₃	C₂³	1	1	yes	characteristic
16	C₂³×D₄₃	C₂³	1	4	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	3	yes	—
19	C₂²×Dic₄₃	C₂³	1	3	yes	—
20	C₂×D₁₇₂	—	2	12	no	—
21	C₂×D₁₇₂	—	4	12	no	—
22	C₂×D₁₇₂	—	4	12	no	—
23	C₄²×C₄₃	D₄	1	4	yes	complemented
24	(C₂×D₄₃)⋊C₄	—	2	6	no	—
25	(C₂×D₄₃)⋊C₄	—	4	12	no	—
26	Dic₄₃⋊C₄	—	2	6	no	—
27	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
28	C₂²×D₄₃	—	2	1	no	—
29	C₂²×D₄₃	—	2	4	no	—
30	C₂²×D₄₃	—	2	12	no	—
31	C₂²×D₄₃	—	2	6	no	—
32	C₂²×D₄₃	—	2	12	no	—
33	C₂×C₄×C₄₃	—	2	6	no	—
34	C₂×C₄×C₄₃	—	2	12	no	—
35	C₂×C₄×C₄₃	C₂×D₄	1	6	yes	—
36	C₂×Dic₄₃	—	2	3	no	—
37	C₂×Dic₄₃	—	2	6	no	—
38	D₁₇₂	—	4	24	no	—
39	D₁₇₂	—	4	16	no	—
40	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
41	C₂²×C₄₃	H(5,𝔽₂)	1	6	yes	—
42	C₂×D₄₃	—	4	3	no	—
43	C₂×D₄₃	—	4	12	no	—
44	C₂×D₄₃	—	4	12	no	—
45	C₂×D₄₃	—	4	4	no	—
46	C₂×D₄₃	—	4	4	no	—
47	C₄×C₄₃	—	2	6	no	—
48	C₄×C₄₃	—	4	4	no	—
49	Dic₄₃	—	4	3	no	—
50	#2818	—	43	1	no	maximal, Sylow
51	C₂×C₄₃	#535	1	3	yes	—
52	C₂×C₄₃	#560	1	4	yes	—
53	D₄₃	—	8	1	no	—
54	D₄₃	—	8	4	no	—
55	C₂×#127	—	43	1	no	—
56	C₂×#126	—	43	1	no	—
57	#394	—	43	6	no	—
58	#392	—	43	6	no	—
59	#383	D₄₃	1	1	yes	characteristic, complemented
60	C₄₃	#2818	1	1	yes	characteristic, complemented, Sylow
61	C₂²×D₄	—	43	6	no	—
62	C₂²×D₄	—	43	4	no	—
63	#127	—	86	4	no	—
64	#126	—	86	4	no	—
65	C₂×C₄⋊C₄	—	43	3	no	—
66	C₂×C₂²⋊C₄	—	43	3	no	—
67	C₂×C₂²⋊C₄	—	43	12	no	—
68	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
69	#95	C₂×D₄₃	1	6	yes	—
70	C₂⁴	—	43	1	no	—
71	C₂⁴	—	43	4	no	—
72	C₂×D₄	—	86	12	no	—
73	C₂×D₄	—	172	12	no	—
74	C₂×D₄	—	172	12	no	—
75	C₂²×C₄	—	43	3	no	—
76	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
77	C₂²×C₄	C₂²×D₄₃	1	3	yes	—
78	C₄⋊C₄	—	86	6	no	—
79	C₂²⋊C₄	—	86	6	no	—
80	C₂²⋊C₄	—	172	12	no	—
81	C₄²	D₁₇₂	1	4	yes	complemented
82	C₂³	—	86	1	no	—
83	C₂³	—	86	4	no	—
84	C₂³	—	86	12	no	—
85	C₂³	—	86	6	no	—
86	C₂³	—	86	12	no	—
87	C₂³	C₂³×D₄₃	1	1	yes	characteristic
88	D₄	—	172	24	no	—
89	D₄	—	172	16	no	—
90	C₂×C₄	—	2	6	no	—
91	C₂×C₄	—	2	12	no	—
92	C₂×C₄	—	86	3	no	—
93	C₂×C₄	—	86	6	no	—
94	C₂×C₄	C₂×D₁₇₂	1	6	yes	—
95	C₂²	—	172	4	no	—
96	C₂²	—	172	4	no	—
97	C₂²	—	172	12	no	—
98	C₂²	—	172	12	no	—
99	C₂²	—	172	3	no	—
100	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
101	C₂²	#13063371	1	6	yes	—
102	C₄	—	2	6	no	—
103	C₄	—	4	4	no	—
104	C₄	—	172	3	no	—
105	C₂	—	344	1	no	—
106	C₂	—	344	4	no	—
107	C₂	#14583468	1	3	yes	—
108	C₂	#14583640	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063322

C₂

yes

maximal, characteristic, complemented

C₂×#13063319

C₂

yes

maximal, characteristic, complemented

#14582817

C₂

yes

maximal, complemented

#14582809

C₂

yes

maximal, complemented

C₄₃×#383

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

—

C₂²×D₁₇₂

C₂²

yes

—

#13063322

—

#13063319

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂³×D₄₃

C₂³

yes

characteristic

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₄²×C₄₃

D₄

yes

complemented

(C₂×D₄₃)⋊C₄

—

(C₂×D₄₃)⋊C₄

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

Dic₄₃

—

#2818

—

maximal, Sylow

C₂×C₄₃

#535

yes

—

C₂×C₄₃

#560

yes

—

D₄₃

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2818

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

#127

—

#126

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

C₂×D₄₃

yes

—

C₂⁴

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

D₁₇₂

yes

complemented

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₃

yes

characteristic

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂²

—

172

—

C₂²

—

172

—

C₂²

—

172

—

C₂²

—

172

—

C₂²

—

172

—

100

C₂²

C₂²×D₁₇₂

yes

characteristic

101

C₂²

#13063371

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

172

—

105

C₂

—

344

—

106

C₂

—

344

—

107

C₂

#14583468

yes

—

108

C₂

#14583640

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#383	C₂
hypercenter	#383	D₄₃
hypocenter	C₄₃	#2818
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #383

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#383

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #383

N	H ≅ G/N	type
1. C₂×#13063322	C₂	semidirect
2. C₂×#13063319	C₂	semidirect
3. #14582817	C₂	semidirect
4. #14582809	C₂	semidirect
5. C₄₃×#383	C₂	semidirect
23. C₄²×C₄₃	D₄	semidirect
59. #383	D₄₃	semidirect
60. C₄₃	#2818	semidirect
81. C₄²	D₁₇₂	semidirect

H ≅ G/N

type

1. C₂×#13063322

C₂

semidirect

2. C₂×#13063319

C₂

semidirect

3. #14582817

C₂

semidirect

4. #14582809

C₂

semidirect

5. C₄₃×#383

C₂

semidirect

23. C₄²×C₄₃

D₄

semidirect

59. #383

D₄₃

semidirect

60. C₄₃

#2818

semidirect

81. C₄²

D₁₇₂

semidirect

Subgroups — #19142638

Conjugacy classes of subgroups

Complements