Group #19145109 — subgroups

Subgroups — #19145109

Order 5504.

356 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 173 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	#14583456	C₂	1	2	yes	maximal
2	#14583304	C₂	1	2	yes	maximal, complemented
3	#14583301	C₂	1	4	yes	maximal, complemented
4	#14583297	C₂	1	2	yes	maximal, complemented
5	#14582937	C₂	1	4	yes	maximal
6	C₂×C₄×C₈×C₄₃	C₂	1	1	yes	maximal, characteristic
7	#13063325	C₂²	1	4	yes	—
8	#13063317	C₂²	1	4	yes	—
9	#13063304	—	2	4	no	—
10	C₄×Dic₈₆	—	2	4	no	—
11	#13063284	C₂²	1	4	yes	—
12	#13063259	C₂²	1	8	yes	—
13	#13063257	C₂²	1	8	yes	—
14	C₂²×C₈×C₄₃	C₂²	1	2	yes	—
15	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
16	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₄×C₈×C₄₃	C₂²	1	2	yes	—
18	C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₄₃	D₄	1	2	yes	—
20	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
21	C₂×Dic₈₆	—	2	4	no	—
22	C₂×C₈×C₄₃	Q₈	1	8	yes	complemented
23	C₂×C₈×C₄₃	C₂³	1	2	yes	—
24	C₂×C₈×C₄₃	C₂³	1	2	yes	—
25	C₄²×C₄₃	D₄	1	2	yes	—
26	C₄²×C₄₃	C₂³	1	1	yes	characteristic
27	C₄²×C₄₃	C₂³	1	1	yes	characteristic
28	C₂²⋊Dic₄₃	—	2	4	no	—
29	C₄⋊Dic₄₃	—	2	4	no	—
30	C₄⋊Dic₄₃	C₂³	1	8	yes	—
31	Dic₄₃⋊C₄	—	2	8	no	—
32	C₄×Dic₄₃	—	2	4	no	—
33	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
34	C₂×C₄×C₄₃	—	2	4	no	—
35	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
36	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
37	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
39	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
40	C₂×Dic₄₃	—	2	8	no	—
41	Dic₈₆	—	4	8	no	—
42	C₈×C₄₃	C₂×Q₈	1	4	yes	—
43	C₈×C₄₃	C₂×Q₈	1	4	yes	—
44	C₂²×C₄₃	—	2	2	no	—
45	C₂²×C₄₃	C₄⋊Q₈	1	2	yes	—
46	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
47	C₄×C₄₃	—	2	2	no	—
48	C₄×C₄₃	C₄⋊Q₈	1	2	yes	—
49	C₄×C₄₃	#135	1	4	yes	—
50	C₄×C₄₃	C₂²×Q₈	1	2	yes	—
51	Dic₄₃	—	4	8	no	—
52	#3160	—	43	1	no	maximal, Sylow
53	C₂×C₄₃	—	2	2	no	—
54	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
55	C₂×C₄₃	C₂×#135	1	2	yes	—
56	#533	—	43	2	no	—
57	#500	—	43	2	no	—
58	#499	—	43	4	no	—
59	#498	—	43	2	no	—
60	#427	—	43	4	no	—
61	C₂×C₄×C₈	D₄₃	1	1	yes	characteristic
62	C₄₃	#3160	1	1	yes	characteristic, complemented, Sylow
63	C₂²×C₈	C₂×D₄₃	1	2	yes	—
64	C₄⋊Q₈	—	43	4	no	—
65	#125	—	43	4	no	—
66	C₂²⋊Q₈	—	86	4	no	—
67	C₄×Q₈	—	86	4	no	—
68	#117	—	43	4	no	—
69	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
70	#107	—	43	8	no	—
71	#106	—	43	8	no	—
72	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
73	C₄×C₈	C₂×D₄₃	1	2	yes	—
74	C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
75	C₂×Q₈	—	86	4	no	—
76	C₂²×C₄	D₁₇₂	1	2	yes	—
77	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
78	C₂×C₈	Dic₈₆	1	8	yes	complemented
79	C₂×C₈	C₂²×D₄₃	1	2	yes	—
80	C₂×C₈	C₂²×D₄₃	1	2	yes	—
81	C₄⋊C₄	—	43	8	no	—
82	C₄⋊C₄	—	86	8	no	—
83	C₄⋊C₄	—	86	4	no	—
84	C₂²⋊C₄	—	86	4	no	—
85	C₄²	—	86	4	no	—
86	C₄²	D₁₇₂	1	2	yes	—
87	C₄²	C₂²×D₄₃	1	1	yes	characteristic
88	C₄²	C₂²×D₄₃	1	1	yes	characteristic
89	C₂³	C₂×D₁₇₂	1	1	yes	characteristic
90	Q₈	—	172	8	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	86	8	no	—
93	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
94	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
95	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
96	C₂×C₄	C₂×D₁₇₂	1	1	yes	characteristic
97	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
98	C₈	C₂×Dic₈₆	1	4	yes	—
99	C₈	C₂×Dic₈₆	1	4	yes	—
100	C₂²	—	2	2	no	—
101	C₂²	#13063325	1	2	yes	—
102	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
103	C₄	—	2	2	no	—
104	C₄	—	172	8	no	—
105	C₄	#13063325	1	2	yes	—
106	C₄	#13063347	1	4	yes	—
107	C₄	C₂²×Dic₈₆	1	2	yes	—
108	C₂	—	2	2	no	—
109	C₂	C₂×#13063325	1	1	yes	characteristic
110	C₂	C₂×#13063347	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14583456

C₂

yes

maximal

#14583304

C₂

yes

maximal, complemented

#14583301

C₂

yes

maximal, complemented

#14583297

C₂

yes

maximal, complemented

#14582937

C₂

yes

maximal

C₂×C₄×C₈×C₄₃

C₂

yes

maximal, characteristic

#13063325

C₂²

yes

—

#13063317

C₂²

yes

—

#13063304

—

C₄×Dic₈₆

—

#13063284

C₂²

yes

—

#13063259

C₂²

yes

—

#13063257

C₂²

yes

—

C₂²×C₈×C₄₃

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₄×C₈×C₄₃

C₂²

yes

—

C₄×C₈×C₄₃

C₂²

yes

characteristic

C₂²×C₄×C₄₃

D₄

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂×Dic₈₆

—

C₂×C₈×C₄₃

Q₈

yes

complemented

C₂×C₈×C₄₃

C₂³

yes

—

C₂×C₈×C₄₃

C₂³

yes

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

C₂³

yes

characteristic

C₄²×C₄₃

C₂³

yes

characteristic

C₂²⋊Dic₄₃

—

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

C₂³

yes

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂⁴

yes

characteristic

C₂×Dic₄₃

—

Dic₈₆

—

C₈×C₄₃

C₂×Q₈

yes

—

C₈×C₄₃

C₂×Q₈

yes

—

C₂²×C₄₃

—

C₂²×C₄₃

C₄⋊Q₈

yes

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₄×C₄₃

—

C₄×C₄₃

C₄⋊Q₈

yes

—

C₄×C₄₃

#135

yes

—

C₄×C₄₃

C₂²×Q₈

yes

—

Dic₄₃

—

#3160

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

C₂×#135

yes

—

—

—

—

—

—

C₂×C₄×C₈

D₄₃

yes

characteristic

C₄₃

#3160

yes

characteristic, complemented, Sylow

C₂²×C₈

C₂×D₄₃

yes

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

C₄×Q₈

—

#117

—

C₂×C₄²

C₂×D₄₃

yes

characteristic

#107

—

#106

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₄×C₈

C₂×D₄₃

yes

—

C₄×C₈

C₂×D₄₃

yes

characteristic

C₂×Q₈

—

C₂²×C₄

D₁₇₂

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₂×C₈

Dic₈₆

yes

complemented

C₂×C₈

C₂²×D₄₃

yes

—

C₂×C₈

C₂²×D₄₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

D₁₇₂

yes

—

C₄²

C₂²×D₄₃

yes

characteristic

C₄²

C₂²×D₄₃

yes

characteristic

C₂³

C₂×D₁₇₂

yes

characteristic

Q₈

—

172

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂×D₁₇₂

yes

characteristic

C₂×C₄

C₂³×D₄₃

yes

characteristic

C₈

C₂×Dic₈₆

yes

—

C₈

C₂×Dic₈₆

yes

—

100

C₂²

—

101

C₂²

#13063325

yes

—

102

C₂²

C₂²×D₁₇₂

yes

characteristic

103

C₄

—

104

C₄

—

172

—

105

C₄

#13063325

yes

—

106

C₄

#13063347

yes

—

107

C₄

C₂²×Dic₈₆

yes

—

108

C₂

—

109

C₂

C₂×#13063325

yes

characteristic

110

C₂

C₂×#13063347

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₂×C₄×C₈×C₄₃	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	C₂×C₄×C₈	D₄₃
hypocenter	C₄₃	#3160
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄

C₂×D₁₇₂

commutator

C₂×C₄×C₄₃

C₂⁴

Frattini

C₂×C₄

C₂³×D₄₃

Fitting

C₂×C₄×C₈×C₄₃

C₂

socle

C₂²×C₄₃

C₂²×D₄

hypercenter

C₂×C₄×C₈

D₄₃

hypocenter

C₄₃

#3160

LCS

G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
2. #14583304	C₂	semidirect
3. #14583301	C₂	semidirect
4. #14583297	C₂	semidirect
22. C₂×C₈×C₄₃	Q₈	semidirect
62. C₄₃	#3160	semidirect
78. C₂×C₈	Dic₈₆	semidirect

H ≅ G/N

type

2. #14583304

C₂

semidirect

3. #14583301

C₂

semidirect

4. #14583297

C₂

semidirect

22. C₂×C₈×C₄₃

Q₈

semidirect

62. C₄₃

#3160

semidirect

78. C₂×C₈

Dic₈₆

semidirect

Subgroups — #19145109

Conjugacy classes of subgroups

Complements