Group #19140538 — subgroups

Subgroups — #19140538

Order 5504.

584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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
2	C₂×#13063317	C₂	1	1	yes	maximal, characteristic, complemented
3	#14582817	C₂	1	8	yes	maximal, complemented
4	#14582801	C₂	1	4	yes	maximal, complemented
5	C₄₃×#376	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₁₇₂	C₂²	1	2	yes	—
7	C₂²×D₁₇₂	C₂²	1	4	yes	—
8	#13063322	—	2	4	no	—
9	#13063317	—	2	4	no	—
10	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
11	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
12	C₂×(C₂×D₄₃)⋊C₄	C₂²	1	16	yes	—
13	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	#95×C₄₃	C₂²	1	4	yes	—
16	C₂³×D₄₃	C₂³	1	4	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₃	C₂³	1	4	yes	—
21	C₂×D₁₇₂	—	2	8	no	—
22	C₂×D₁₇₂	—	2	4	no	—
23	C₂×D₁₇₂	—	2	8	no	—
24	C₂×D₁₇₂	—	4	8	no	—
25	C₄²×C₄₃	—	2	4	no	—
26	C₄²×C₄₃	D₄	1	4	yes	—
27	(C₂×D₄₃)⋊C₄	—	4	16	no	—
28	C₄⋊Dic₄₃	—	2	4	no	—
29	Dic₄₃⋊C₄	—	2	8	no	—
30	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂²×D₄₃	—	2	4	no	—
32	C₂²×D₄₃	—	2	8	no	—
33	C₂²×D₄₃	—	2	16	no	—
34	C₂×C₄×C₄₃	—	2	4	no	—
35	C₂×C₄×C₄₃	—	2	4	no	—
36	C₂×C₄×C₄₃	—	2	8	no	—
37	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
38	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
39	C₂×C₄×C₄₃	#41	1	4	yes	—
40	C₂×Dic₄₃	—	2	4	no	—
41	C₂×Dic₄₃	—	2	8	no	—
42	D₁₇₂	—	4	16	no	—
43	D₁₇₂	—	4	8	no	—
44	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
45	C₂²×C₄₃	C₂×#41	1	2	yes	—
46	C₂²×C₄₃	H(5,𝔽₂)	1	4	yes	—
47	C₂×D₄₃	—	4	4	no	—
48	C₂×D₄₃	—	4	8	no	—
49	C₂×D₄₃	—	4	16	no	—
50	C₄×C₄₃	—	2	4	no	—
51	C₄×C₄₃	—	4	4	no	—
52	C₄×C₄₃	#124	1	4	yes	—
53	Dic₄₃	—	4	4	no	—
54	#2641	—	43	1	no	maximal, Sylow
55	C₂×C₄₃	C₂×#124	1	1	yes	characteristic
56	C₂×C₄₃	#535	1	2	yes	—
57	C₂×C₄₃	#540	1	4	yes	—
58	D₄₃	—	8	4	no	—
59	C₂×#127	—	43	1	no	—
60	C₂×#125	—	43	1	no	—
61	#394	—	43	8	no	—
62	#390	—	43	4	no	—
63	#376	D₄₃	1	1	yes	characteristic, complemented
64	C₄₃	#2641	1	1	yes	characteristic, complemented, Sylow
65	C₂²×D₄	—	43	2	no	—
66	C₂²×D₄	—	43	4	no	—
67	#127	—	86	4	no	—
68	#125	—	86	4	no	—
69	C₂×C₄⋊C₄	—	43	4	no	—
70	C₂×C₄⋊C₄	—	43	2	no	—
71	C₂×C₂²⋊C₄	—	43	16	no	—
72	C₂×C₄²	C₂×D₄₃	1	2	yes	—
73	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
74	#95	C₂×D₄₃	1	4	yes	—
75	C₂⁴	—	43	4	no	—
76	C₂×D₄	—	86	8	no	—
77	C₂×D₄	—	86	4	no	—
78	C₂×D₄	—	86	8	no	—
79	C₂×D₄	—	172	8	no	—
80	C₂²×C₄	—	43	4	no	—
81	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
82	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
83	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
84	C₄⋊C₄	—	86	8	no	—
85	C₄⋊C₄	—	86	4	no	—
86	C₂²⋊C₄	—	172	16	no	—
87	C₄²	—	2	4	no	—
88	C₄²	D₁₇₂	1	4	yes	—
89	C₂³	—	86	4	no	—
90	C₂³	—	86	8	no	—
91	C₂³	—	86	16	no	—
92	C₂³	C₂³×D₄₃	1	1	yes	characteristic
93	D₄	—	172	16	no	—
94	D₄	—	172	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	2	4	no	—
97	C₂×C₄	—	2	8	no	—
98	C₂×C₄	—	86	4	no	—
99	C₂×C₄	—	86	8	no	—
100	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
101	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
102	C₂×C₄	#10621898	1	4	yes	—
103	C₂²	—	172	4	no	—
104	C₂²	—	172	8	no	—
105	C₂²	—	172	16	no	—
106	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
107	C₂²	C₂×#10621898	1	2	yes	—
108	C₂²	#13063371	1	4	yes	—
109	C₄	—	2	4	no	—
110	C₄	—	4	4	no	—
111	C₄	—	172	4	no	—
112	C₄	#13063313	1	4	yes	—
113	C₂	—	344	4	no	—
114	C₂	C₂×#13063313	1	1	yes	characteristic
115	C₂	#14583468	1	2	yes	—
116	C₂	#14583504	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13063322

C₂

yes

maximal, characteristic

C₂×#13063317

C₂

yes

maximal, characteristic, complemented

#14582817

C₂

yes

maximal, complemented

#14582801

C₂

yes

maximal, complemented

C₄₃×#376

C₂

yes

maximal, characteristic, complemented

C₂²×D₁₇₂

C₂²

yes

—

C₂²×D₁₇₂

C₂²

yes

—

#13063322

—

#13063317

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×(C₂×D₄₃)⋊C₄

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

#95×C₄₃

C₂²

yes

—

C₂³×D₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₄²×C₄₃

—

C₄²×C₄₃

D₄

yes

—

(C₂×D₄₃)⋊C₄

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

#41

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

D₁₇₂

—

D₁₇₂

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂×#41

yes

—

C₂²×C₄₃

H(5,𝔽₂)

yes

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

#124

yes

—

Dic₄₃

—

—

C₂×C₄₃

yes

C₂×C₄₃

yes

—

C₂×C₄₃

#540

yes

—

D₄₃

—

—

—

—

—

D₄₃

yes

characteristic, complemented

C₄₃

#2641

yes

characteristic, complemented, Sylow

C₂²×D₄

—

C₂²×D₄

—

#127

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#95

C₂×D₄₃

yes

—

C₂⁴

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

C₂×D₄

—

172

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

172

—

C₄²

—

C₄²

D₁₇₂

yes

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂³×D₄₃

yes

characteristic

D₄

—

172

—

D₄

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

100

C₂×C₄

C₂×D₁₇₂

yes

—

101

C₂×C₄

C₂×D₁₇₂

yes

—

102

C₂×C₄

#10621898

yes

—

103

C₂²

—

172

—

104

C₂²

—

172

—

105

C₂²

—

172

—

106

C₂²

C₂²×D₁₇₂

yes

characteristic

107

C₂²

C₂×#10621898

yes

—

108

C₂²

#13063371

yes

—

109

C₄

—

110

C₄

—

111

C₄

—

172

—

112

C₄

#13063313

yes

—

113

C₂

—

344

—

114

C₂

C₂×#13063313

yes

characteristic

115

C₂

#14583468

yes

—

116

C₂

#14583504

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Fitting	C₄₃×#376	C₂
hypercenter	#376	D₄₃
hypocenter	C₄₃	#2641
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ #376

subgroup

G/H

center, Frattini

C₂³

C₂³×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Fitting

C₄₃×#376

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂³ ◁ #376

N	H ≅ G/N	type
2. C₂×#13063317	C₂	semidirect
3. #14582817	C₂	semidirect
4. #14582801	C₂	semidirect
5. C₄₃×#376	C₂	semidirect
63. #376	D₄₃	semidirect
64. C₄₃	#2641	semidirect

H ≅ G/N

type

2. C₂×#13063317

C₂

semidirect

3. #14582817

C₂

semidirect

4. #14582801

C₂

semidirect

5. C₄₃×#376

C₂

semidirect

63. #376

D₄₃

semidirect

64. C₄₃

#2641

semidirect

Subgroups — #19140538

Conjugacy classes of subgroups

Complements