Group #19137888 — subgroups

Subgroups — #19137888

Order 5504.

504 conjugacy classes of subgroups; only the 189 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 189 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×C₄×Dic₈₆	C₂	1	2	yes	maximal
2	#14582831	C₂	1	4	yes	maximal
3	#14582820	C₂	1	4	yes	maximal
4	C₄×C₄⋊Dic₄₃	C₂	1	4	yes	maximal
5	C₄₃×#376	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₈₆	C₂²	1	2	yes	—
7	C₄×Dic₈₆	—	2	8	no	—
8	C₂×C₄⋊Dic₄₃	C₂²	1	8	yes	—
9	C₂×C₄⋊Dic₄₃	C₂²	1	2	yes	—
10	C₂×Dic₄₃⋊C₄	C₂²	1	4	yes	—
11	C₂×C₄×Dic₄₃	C₂²	1	4	yes	—
12	C₄₃⋊#95	C₂²	1	4	yes	—
13	C₄₃⋊#95	C₂²	1	4	yes	—
14	C₂×C₄²×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₄₃	C₂²	1	2	yes	—
16	#95×C₄₃	C₂²	1	4	yes	—
17	C₂²×C₄×C₄₃	C₂³	1	2	yes	—
18	C₂²×C₄×C₄₃	C₂³	1	4	yes	—
19	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
20	C₂²×Dic₄₃	C₂³	1	4	yes	—
21	C₂²×Dic₄₃	C₂³	1	4	yes	—
22	C₂×Dic₈₆	—	2	4	no	—
23	C₂×Dic₈₆	—	2	8	no	—
24	C₄²×C₄₃	D₄	1	4	yes	—
25	C₄²×C₄₃	Q₈	1	8	yes	complemented
26	C₄⋊Dic₄₃	—	2	4	no	—
27	C₄⋊Dic₄₃	—	2	16	no	—
28	Dic₄₃⋊C₄	—	2	8	no	—
29	C₄×Dic₄₃	—	2	8	no	—
30	C₂³×C₄₃	C₂⁴	1	1	yes	characteristic
31	C₂×C₄×C₄₃	—	2	8	no	—
32	C₂×C₄×C₄₃	—	2	4	no	—
33	C₂×C₄×C₄₃	C₂×D₄	1	4	yes	—
34	C₂×C₄×C₄₃	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₄₃	C₂×Q₈	1	8	yes	—
36	C₂×C₄×C₄₃	C₂×Q₈	1	4	yes	—
37	C₂×Dic₄₃	—	2	4	no	—
38	C₂×Dic₄₃	—	2	4	no	—
39	C₂×Dic₄₃	—	2	4	no	—
40	C₂×Dic₄₃	—	2	8	no	—
41	C₂×Dic₄₃	#41	1	8	yes	—
42	Dic₈₆	—	2	16	no	—
43	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
44	C₂²×C₄₃	C₂²×Q₈	1	2	yes	—
45	C₂²×C₄₃	C₂×#41	1	4	yes	—
46	C₄×C₄₃	—	2	4	no	—
47	C₄×C₄₃	—	2	8	no	—
48	C₄×C₄₃	C₄⋊Q₈	1	4	yes	—
49	Dic₄₃	—	2	8	no	—
50	Dic₄₃	—	4	4	no	—
51	#2399	—	43	1	no	maximal, Sylow
52	C₂×C₄₃	#525	1	2	yes	—
53	C₂×C₄₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
54	C₂×C₄₃	#533	1	4	yes	—
55	C₂×C₄×Q₈	—	43	2	no	—
56	#398	—	43	4	no	—
57	#395	—	43	4	no	—
58	C₄×C₄⋊C₄	—	43	4	no	—
59	#376	D₄₃	1	1	yes	characteristic
60	C₄₃	#2399	1	1	yes	characteristic, complemented, Sylow
61	C₂²×Q₈	—	43	2	no	—
62	C₄×Q₈	—	86	8	no	—
63	C₂×C₄⋊C₄	—	43	4	no	—
64	C₂×C₄⋊C₄	—	43	2	no	—
65	C₂×C₄⋊C₄	—	43	8	no	—
66	C₂×C₄²	—	43	4	no	—
67	C₂×C₄²	C₂×D₄₃	1	2	yes	—
68	C₂×C₄²	C₂×D₄₃	1	1	yes	characteristic
69	#95	—	43	4	no	—
70	#95	—	43	4	no	—
71	#95	C₂×D₄₃	1	4	yes	—
72	C₂×Q₈	—	86	8	no	—
73	C₂×Q₈	—	86	4	no	—
74	C₂²×C₄	—	43	4	no	—
75	C₂²×C₄	—	43	4	no	—
76	C₂²×C₄	C₂²×D₄₃	1	4	yes	—
77	C₂²×C₄	C₂²×D₄₃	1	2	yes	—
78	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
79	C₄⋊C₄	—	86	16	no	—
80	C₄⋊C₄	—	86	8	no	—
81	C₄⋊C₄	—	86	4	no	—
82	C₄²	—	86	8	no	—
83	C₄²	Dic₈₆	1	8	yes	complemented
84	C₄²	D₁₇₂	1	4	yes	—
85	C₂³	C₂³×D₄₃	1	1	yes	characteristic
86	Q₈	—	86	16	no	—
87	C₂×C₄	—	2	8	no	—
88	C₂×C₄	—	2	4	no	—
89	C₂×C₄	—	43	8	no	—
90	C₂×C₄	—	86	4	no	—
91	C₂×C₄	—	86	4	no	—
92	C₂×C₄	—	86	4	no	—
93	C₂×C₄	—	86	8	no	—
94	C₂×C₄	C₂×Dic₈₆	1	8	yes	—
95	C₂×C₄	C₂×Dic₈₆	1	4	yes	—
96	C₂×C₄	C₂×D₁₇₂	1	4	yes	—
97	C₂×C₄	C₂×D₁₇₂	1	2	yes	—
98	C₂²	C₂²×D₁₇₂	1	1	yes	characteristic
99	C₂²	C₂²×Dic₈₆	1	2	yes	—
100	C₂²	#41×D₄₃	1	4	yes	—
101	C₄	—	2	4	no	—
102	C₄	—	2	8	no	—
103	C₄	—	86	8	no	—
104	C₄	—	172	4	no	—
105	C₄	#13063325	1	4	yes	—
106	C₂	#14583411	1	2	yes	—
107	C₂	C₂×#13063325	1	1	yes	characteristic
108	C₂	#14583452	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×Dic₈₆

C₂

yes

maximal

#14582831

C₂

yes

maximal

#14582820

C₂

yes

maximal

C₄×C₄⋊Dic₄₃

C₂

yes

maximal

C₄₃×#376

C₂

yes

maximal, characteristic

C₂²×Dic₈₆

C₂²

yes

—

C₄×Dic₈₆

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×C₄⋊Dic₄₃

C₂²

yes

—

C₂×Dic₄₃⋊C₄

C₂²

yes

—

C₂×C₄×Dic₄₃

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₄₃⋊#95

C₂²

yes

—

C₂×C₄²×C₄₃

C₂²

yes

characteristic

C₂×C₄²×C₄₃

C₂²

yes

—

#95×C₄₃

C₂²

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

—

C₂²×C₄×C₄₃

C₂³

yes

characteristic

C₂²×Dic₄₃

C₂³

yes

—

C₂²×Dic₄₃

C₂³

yes

—

C₂×Dic₈₆

—

C₂×Dic₈₆

—

C₄²×C₄₃

D₄

yes

—

C₄²×C₄₃

Q₈

yes

complemented

C₄⋊Dic₄₃

—

C₄⋊Dic₄₃

—

Dic₄₃⋊C₄

—

C₄×Dic₄₃

—

C₂³×C₄₃

C₂⁴

yes

characteristic

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×D₄

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×C₄×C₄₃

C₂×Q₈

yes

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

—

C₂×Dic₄₃

#41

yes

—

Dic₈₆

—

C₂²×C₄₃

C₂²×D₄

yes

characteristic

C₂²×C₄₃

C₂²×Q₈

yes

—

C₂²×C₄₃

C₂×#41

yes

—

C₄×C₄₃

—

C₄×C₄₃

—

C₄×C₄₃

C₄⋊Q₈

yes

—

Dic₄₃

—

Dic₄₃

—

#2399

—

maximal, Sylow

C₂×C₄₃

#525

yes

—

C₂×C₄₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₄₃

#533

yes

—

C₂×C₄×Q₈

—

#398

—

#395

—

C₄×C₄⋊C₄

—

#376

D₄₃

yes

characteristic

C₄₃

#2399

yes

characteristic, complemented, Sylow

C₂²×Q₈

—

C₄×Q₈

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄²

—

C₂×C₄²

C₂×D₄₃

yes

—

C₂×C₄²

C₂×D₄₃

yes

—

—

C₂×D₄₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

—

C₂²×C₄

C₂²×D₄₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

Dic₈₆

yes

complemented

C₄²

D₁₇₂

yes

—

C₂³

C₂³×D₄₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×Dic₈₆

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂×C₄

C₂×D₁₇₂

yes

—

C₂²

C₂²×D₁₇₂

yes

characteristic

C₂²

C₂²×Dic₈₆

yes

—

100

C₂²

#41×D₄₃

yes

—

101

C₄

—

102

C₄

—

103

C₄

—

104

C₄

—

172

—

105

C₄

#13063325

yes

—

106

C₂

#14583411

yes

—

107

C₂

C₂×#13063325

yes

characteristic

108

C₂

#14583452

yes

—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₃
commutator, socle	C₂³×C₄₃	C₂⁴
Frattini	C₂³	C₂³×D₄₃
Fitting	C₄₃×#376	C₂
hypercenter	#376	D₄₃
hypocenter	C₄₃	#2399
LCS	G ▷ C₂³×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center

C₂²×C₄

C₂²×D₄₃

commutator, socle

C₂³×C₄₃

C₂⁴

Frattini

C₂³

C₂³×D₄₃

Fitting

C₄₃×#376

C₂

D₄₃

C₄₃

G ▷ C₂³×C₄₃ ▷ C₄₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
25. C₄²×C₄₃	Q₈	semidirect
60. C₄₃	#2399	semidirect
83. C₄²	Dic₈₆	semidirect

H ≅ G/N

type

25. C₄²×C₄₃

Q₈

semidirect

60. C₄₃

#2399

semidirect

83. C₄²

Dic₈₆

semidirect

Subgroups — #19137888

Conjugacy classes of subgroups

Complements