Group #24905739 — subgroups

Subgroups — C₂×#19127423 #24905739

Order 10624.

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

normal subgroups only

This group has 248 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	C₂×C₄×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#19127423	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₈×C₈₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₈₃⋊C₈	C₄	1	2	yes	—
6	C₂²×C₈₃⋊C₈	C₄	1	2	yes	—
7	C₄×C₈₃⋊C₈	C₄	1	2	yes	—
8	C₄×C₈₃⋊C₈	C₄	1	2	yes	—
9	C₄×C₈₃⋊C₈	C₂²	1	2	yes	—
10	C₄×C₈₃⋊C₈	C₂²	1	2	yes	—
11	C₂²×C₈×C₈₃	C₄	1	2	yes	—
12	C₂×C₄²×C₈₃	C₂²	1	1	yes	characteristic
13	C₄×C₈×C₈₃	C₄	1	2	yes	—
14	C₄×C₈×C₈₃	C₂²	1	2	yes	—
15	C₂×C₈₃⋊C₈	—	2	4	no	—
16	C₂×C₈₃⋊C₈	C₈	1	8	yes	complemented
17	C₂×C₈₃⋊C₈	C₂×C₄	1	4	yes	—
18	C₂×C₈₃⋊C₈	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄×C₈₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₈₃	—	2	4	no	—
23	C₂×C₈×C₈₃	C₂×C₄	1	4	yes	—
24	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
25	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
26	C₄²×C₈₃	C₂×C₄	1	1	yes	characteristic
27	C₄²×C₈₃	C₂³	1	1	yes	characteristic
28	C₂³×C₈₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
31	C₂×C₄×C₈₃	C₄²	1	1	yes	characteristic
32	C₂×C₄×C₈₃	C₂×C₈	1	4	yes	—
33	C₂×C₄×C₈₃	M₁₆	1	4	yes	—
34	C₂×C₄×C₈₃	M₁₆	1	4	yes	—
35	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄×C₈₃	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₈₃	—	2	4	no	—
39	C₈₃⋊C₈	—	2	4	no	—
40	C₈₃⋊C₈	C₂×C₈	1	8	yes	complemented
41	C₂²×C₈₃	C₄×C₈	1	2	yes	—
42	C₂²×C₈₃	#97	1	2	yes	—
43	C₂²×C₈₃	#97	1	2	yes	—
44	C₂²×C₈₃	C₂×C₄²	1	1	yes	characteristic
45	C₄×C₈₃	C₄×C₈	1	2	yes	—
46	C₄×C₈₃	#97	1	2	yes	—
47	C₄×C₈₃	#97	1	2	yes	—
48	C₄×C₈₃	C₂²×C₈	1	2	yes	—
49	C₄×C₈₃	C₂×M₁₆	1	2	yes	—
50	C₄×C₈₃	C₂×M₁₆	1	2	yes	—
51	C₂×C₈₃	#322	1	4	yes	complemented
52	C₂×C₈₃	C₂×C₄×C₈	1	1	yes	characteristic
53	C₂×C₈₃	C₂×#97	1	1	yes	characteristic
54	C₂×C₈₃	C₂×#97	1	1	yes	characteristic
55	C₂×#322	—	83	1	no	maximal, Sylow
56	C₈₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄×C₈	—	83	1	no	—
58	C₂×C₄×C₈	—	83	1	no	—
59	C₂×C₄×C₈	D₈₃	1	1	yes	characteristic
60	#322	—	83	4	no	—
61	C₂²×C₈	—	83	2	no	—
62	C₂²×C₈	—	83	2	no	—
63	C₂²×C₈	Dic₈₃	1	2	yes	—
64	C₂×C₄²	C₂×D₈₃	1	1	yes	characteristic
65	C₄×C₈	—	83	2	no	—
66	C₄×C₈	—	83	2	no	—
67	C₄×C₈	—	83	2	no	—
68	C₄×C₈	—	83	2	no	—
69	C₄×C₈	Dic₈₃	1	2	yes	—
70	C₄×C₈	C₂×D₈₃	1	2	yes	—
71	C₂²×C₄	C₄×D₈₃	1	1	yes	characteristic
72	C₂²×C₄	C₄×D₈₃	1	1	yes	characteristic
73	C₂²×C₄	C₂×Dic₈₃	1	1	yes	characteristic
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	—	83	8	no	—
76	C₂×C₈	—	83	4	no	—
77	C₂×C₈	—	83	4	no	—
78	C₂×C₈	—	166	4	no	—
79	C₂×C₈	C₂×Dic₈₃	1	4	yes	—
80	C₄²	C₄×D₈₃	1	1	yes	characteristic
81	C₄²	C₄×D₈₃	1	1	yes	characteristic
82	C₄²	C₂×Dic₈₃	1	1	yes	characteristic
83	C₄²	C₂²×D₈₃	1	1	yes	characteristic
84	C₂³	C₄×Dic₈₃	1	1	yes	characteristic
85	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
86	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
87	C₂×C₄	C₄×Dic₈₃	1	1	yes	characteristic
88	C₂×C₄	C₈×D₈₃	1	4	yes	—
89	C₂×C₄	#13050573	1	4	yes	—
90	C₂×C₄	#13050574	1	4	yes	—
91	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
92	C₂×C₄	C₂×C₄×D₈₃	1	1	yes	characteristic
93	C₂×C₄	C₂²×Dic₈₃	1	1	yes	characteristic
94	C₈	—	2	4	no	—
95	C₈	—	83	8	no	—
96	C₈	—	166	4	no	—
97	C₂²	C₈×Dic₈₃	1	2	yes	—
98	C₂²	#14581702	1	2	yes	—
99	C₂²	#14581703	1	2	yes	—
100	C₂²	C₂×C₄×Dic₈₃	1	1	yes	characteristic
101	C₄	C₈×Dic₈₃	1	2	yes	—
102	C₄	#14581702	1	2	yes	—
103	C₄	#14581703	1	2	yes	—
104	C₄	C₂×C₈×D₈₃	1	2	yes	—
105	C₄	C₂×#13050573	1	2	yes	—
106	C₄	C₂×#13050574	1	2	yes	—
107	C₂	#19127423	1	4	yes	direct product factor
108	C₂	C₂×C₈×Dic₈₃	1	1	yes	characteristic
109	C₂	C₂×#14581702	1	1	yes	characteristic
110	C₂	C₂×#14581703	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄×C₈₃⋊C₈

C₂

yes

maximal, characteristic

C₂×C₄×C₈₃⋊C₈

C₂

yes

maximal, characteristic

#19127423

C₂

yes

maximal, direct product factor

C₂×C₄×C₈×C₈₃

C₂

yes

maximal, characteristic

C₂²×C₈₃⋊C₈

C₄

yes

—

C₂²×C₈₃⋊C₈

C₄

yes

—

C₄×C₈₃⋊C₈

C₄

yes

—

C₄×C₈₃⋊C₈

C₄

yes

—

C₄×C₈₃⋊C₈

C₂²

yes

—

C₄×C₈₃⋊C₈

C₂²

yes

—

C₂²×C₈×C₈₃

C₄

yes

—

C₂×C₄²×C₈₃

C₂²

yes

characteristic

C₄×C₈×C₈₃

C₄

yes

—

C₄×C₈×C₈₃

C₂²

yes

—

C₂×C₈₃⋊C₈

—

C₂×C₈₃⋊C₈

C₈

yes

complemented

C₂×C₈₃⋊C₈

C₂×C₄

yes

—

C₂×C₈₃⋊C₈

C₂×C₄

yes

—

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂²×C₄×C₈₃

C₂×C₄

yes

characteristic

C₂×C₈×C₈₃

—

C₂×C₈×C₈₃

C₂×C₄

yes

—

C₄²×C₈₃

C₂×C₄

yes

characteristic

C₄²×C₈₃

C₂×C₄

yes

characteristic

C₄²×C₈₃

C₂×C₄

yes

characteristic

C₄²×C₈₃

C₂³

yes

characteristic

C₂³×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₄²

yes

characteristic

C₂×C₄×C₈₃

C₂×C₈

yes

—

C₂×C₄×C₈₃

M₁₆

yes

—

C₂×C₄×C₈₃

M₁₆

yes

—

C₂×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₈₃

C₂²×C₄

yes

characteristic

C₈×C₈₃

—

C₈₃⋊C₈

—

C₈₃⋊C₈

C₂×C₈

yes

complemented

C₂²×C₈₃

C₄×C₈

yes

—

C₂²×C₈₃

#97

yes

—

C₂²×C₈₃

#97

yes

—

C₂²×C₈₃

C₂×C₄²

yes

characteristic

C₄×C₈₃

C₄×C₈

yes

—

C₄×C₈₃

#97

yes

—

C₄×C₈₃

#97

yes

—

C₄×C₈₃

C₂²×C₈

yes

—

C₄×C₈₃

C₂×M₁₆

yes

—

C₄×C₈₃

C₂×M₁₆

yes

—

C₂×C₈₃

#322

yes

complemented

C₂×C₈₃

C₂×C₄×C₈

yes

characteristic

C₂×C₈₃

C₂×#97

yes

characteristic

C₂×C₈₃

C₂×#97

yes

—

C₈₃

yes

characteristic, complemented, Sylow

C₂×C₄×C₈

—

C₂×C₄×C₈

—

C₂×C₄×C₈

D₈₃

yes

characteristic

#322

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

Dic₈₃

yes

—

C₂×C₄²

C₂×D₈₃

yes

characteristic

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

—

C₄×C₈

Dic₈₃

yes

—

C₄×C₈

C₂×D₈₃

yes

—

C₂²×C₄

C₄×D₈₃

yes

characteristic

C₂²×C₄

C₄×D₈₃

yes

characteristic

C₂²×C₄

C₂×Dic₈₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

166

—

C₂×C₈

C₂×Dic₈₃

yes

—

C₄²

C₄×D₈₃

yes

characteristic

C₄²

C₄×D₈₃

yes

characteristic

C₄²

C₂×Dic₈₃

yes

characteristic

C₄²

C₂²×D₈₃

yes

characteristic

C₂³

C₄×Dic₈₃

yes

characteristic

C₂×C₄

C₄×Dic₈₃

yes

characteristic

C₂×C₄

C₄×Dic₈₃

yes

characteristic

C₂×C₄

C₄×Dic₈₃

yes

characteristic

C₂×C₄

C₈×D₈₃

yes

—

C₂×C₄

#13050573

yes

—

C₂×C₄

#13050574

yes

—

C₂×C₄

C₂×C₄×D₈₃

yes

characteristic

C₂×C₄

C₂×C₄×D₈₃

yes

characteristic

C₂×C₄

C₂²×Dic₈₃

yes

characteristic

C₈

—

C₈

—

C₈

—

166

—

C₂²

C₈×Dic₈₃

yes

—

C₂²

#14581702

yes

—

C₂²

#14581703

yes

—

100

C₂²

C₂×C₄×Dic₈₃

yes

characteristic

101

C₄

C₈×Dic₈₃

yes

—

102

C₄

#14581702

yes

—

103

C₄

#14581703

yes

—

104

C₄

C₂×C₈×D₈₃

yes

—

105

C₄

C₂×#13050573

yes

—

106

C₄

C₂×#13050574

yes

—

107

C₂

#19127423

yes

direct product factor

108

C₂

C₂×C₈×Dic₈₃

yes

characteristic

109

C₂

C₂×#14581702

yes

characteristic

110

C₂

C₂×#14581703

yes

characteristic

	subgroup	G/H
center	C₂×C₄²	C₂×D₈₃
commutator	C₂×C₈₃	C₂×C₄×C₈
Frattini	C₄²	C₂²×D₈₃
Fitting	C₂×C₄×C₈×C₈₃	C₂
socle, prime radical	C₂³×C₈₃	C₄²
cosocle	C₄²×C₈₃	C₂³
hypercenter	C₂×C₄×C₈	D₈₃
hypocenter	C₈₃	C₂×#322
LCS	G ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

subgroup

G/H

center

C₂×C₄²

C₂×D₈₃

commutator

C₂×C₈₃

C₂×C₄×C₈

Frattini

C₄²

C₂²×D₈₃

Fitting

C₂×C₄×C₈×C₈₃

C₂

socle, prime radical

C₂³×C₈₃

C₄²

cosocle

C₄²×C₈₃

C₂³

hypercenter

C₂×C₄×C₈

D₈₃

C₈₃

G ▷ C₂×C₈₃ ▷ C₈₃

C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

N	H ≅ G/N	type
3. #19127423	C₂	direct (N × H)
16. C₂×C₈₃⋊C₈	C₈	semidirect
40. C₈₃⋊C₈	C₂×C₈	semidirect
51. C₂×C₈₃	#322	semidirect
56. C₈₃	C₂×#322	semidirect
107. C₂	#19127423	direct (N × H)

H ≅ G/N

type

3. #19127423

C₂

direct (N × H)

16. C₂×C₈₃⋊C₈

C₈

semidirect

40. C₈₃⋊C₈

C₂×C₈

semidirect

51. C₂×C₈₃

#322

semidirect

56. C₈₃

C₂×#322

semidirect

107. C₂

#19127423

direct (N × H)

Subgroups — C₂×#19127423 #24905739

Conjugacy classes of subgroups

Complements

Subgroups — C2×#19127423 #24905739

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#19127423 #24905739