Group #19105740 — subgroups

Subgroups — C₄₁×#1960 #19105740

Order 5248.

308 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 128 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⋊Q₈×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#103×C₄₁	C₂	1	4	yes	maximal
3	C₂×#97×C₄₁	C₂	1	1	yes	maximal, characteristic
4	C₄₁×#382	C₂	1	1	yes	maximal, characteristic
5	C₂²×Q₈×C₄₁	C₂²	1	2	yes	—
6	C₂²×C₈×C₄₁	C₂²	1	2	yes	—
7	C₄⋊Q₈×C₄₁	—	2	2	no	—
8	C₄⋊Q₈×C₄₁	C₄	1	4	yes	complemented
9	C₂×C₄⋊C₄×C₄₁	—	2	2	no	—
10	C₂×C₄⋊C₄×C₄₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₄₁	C₂²	1	1	yes	characteristic
12	#103×C₄₁	—	2	8	no	—
13	#97×C₄₁	—	2	2	no	—
14	#95×C₄₁	—	2	2	no	—
15	C₂×Q₈×C₄₁	—	2	2	no	—
16	C₂×Q₈×C₄₁	—	2	4	no	—
17	C₂×Q₈×C₄₁	—	2	4	no	—
18	C₂×Q₈×C₄₁	C₂×C₄	1	4	yes	—
19	C₂²×C₄×C₄₁	—	2	2	no	—
20	C₂²×C₄×C₄₁	—	2	2	no	—
21	C₂²×C₄×C₄₁	D₄	1	2	yes	—
22	C₂²×C₄×C₄₁	C₂³	1	1	yes	characteristic
23	C₂×C₈×C₄₁	—	2	2	no	—
24	C₂×C₈×C₄₁	—	2	2	no	—
25	C₂×C₈×C₄₁	D₄	1	4	yes	—
26	C₄⋊C₄×C₄₁	—	2	8	no	—
27	C₄⋊C₄×C₄₁	—	2	4	no	—
28	C₄²×C₄₁	C₂×C₄	1	2	yes	—
29	C₄²×C₄₁	D₄	1	2	yes	—
30	C₂³×C₄₁	C₂×D₄	1	1	yes	characteristic
31	Q₈×C₄₁	—	2	8	no	—
32	Q₈×C₄₁	—	4	4	no	—
33	C₂×C₄×C₄₁	—	2	4	no	—
34	C₂×C₄×C₄₁	—	2	4	no	—
35	C₂×C₄×C₄₁	—	4	2	no	—
36	C₂×C₄×C₄₁	—	4	2	no	—
37	C₂×C₄×C₄₁	—	4	2	no	—
38	C₂×C₄×C₄₁	—	4	4	no	—
39	C₂×C₄×C₄₁	C₂²⋊C₄	1	4	yes	—
40	C₂×C₄×C₄₁	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₄×C₄₁	C₂×D₄	1	2	yes	—
42	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
43	C₂×C₄×C₄₁	#41	1	2	yes	—
44	C₈×C₄₁	—	2	4	no	—
45	C₂²×C₄₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄₁	#124	1	1	yes	characteristic
47	C₂²×C₄₁	#127	1	1	yes	characteristic
48	C₂²×C₄₁	#137	1	4	yes	—
49	C₄×C₄₁	—	2	4	no	—
50	C₄×C₄₁	—	4	4	no	—
51	C₄×C₄₁	—	8	2	no	—
52	C₄×C₄₁	C₄×D₄	1	2	yes	—
53	C₄×C₄₁	#121	1	2	yes	—
54	#1960	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₄₁	#390	1	1	yes	characteristic
56	C₂×C₄₁	#419	1	2	yes	—
57	C₂×C₄₁	#491	1	2	yes	—
58	C₂×C₄₁	#497	1	2	yes	—
59	C₂×C₄⋊Q₈	C₂×C₄₁	1	1	yes	characteristic
60	C₂×#103	C₂×C₄₁	1	4	yes	—
61	C₂×#97	C₂×C₄₁	1	1	yes	characteristic
62	#382	C₂×C₄₁	1	1	yes	characteristic
63	C₄₁	#1960	1	1	yes	characteristic, direct product factor, Sylow
64	C₂²×Q₈	C₂²×C₄₁	1	2	yes	—
65	C₂²×C₈	C₂²×C₄₁	1	2	yes	—
66	C₄⋊Q₈	—	2	2	no	—
67	C₄⋊Q₈	C₄×C₄₁	1	4	yes	complemented
68	C₂×C₄⋊C₄	—	2	2	no	—
69	C₂×C₄⋊C₄	C₂²×C₄₁	1	2	yes	—
70	C₂×C₄²	C₂²×C₄₁	1	1	yes	characteristic
71	#103	—	2	8	no	—
72	#97	—	2	2	no	—
73	#95	—	2	2	no	—
74	C₂×Q₈	—	2	2	no	—
75	C₂×Q₈	—	2	4	no	—
76	C₂×Q₈	—	2	4	no	—
77	C₂×Q₈	C₂×C₄×C₄₁	1	4	yes	—
78	C₂²×C₄	—	2	2	no	—
79	C₂²×C₄	—	2	2	no	—
80	C₂²×C₄	D₄×C₄₁	1	2	yes	—
81	C₂²×C₄	C₂³×C₄₁	1	1	yes	characteristic
82	C₂×C₈	—	2	2	no	—
83	C₂×C₈	—	2	2	no	—
84	C₂×C₈	D₄×C₄₁	1	4	yes	—
85	C₄⋊C₄	—	2	8	no	—
86	C₄⋊C₄	—	2	4	no	—
87	C₄²	C₂×C₄×C₄₁	1	2	yes	—
88	C₄²	D₄×C₄₁	1	2	yes	—
89	C₂³	C₂×D₄×C₄₁	1	1	yes	characteristic
90	Q₈	—	2	8	no	—
91	Q₈	—	4	4	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	2	4	no	—
94	C₂×C₄	—	4	2	no	—
95	C₂×C₄	—	4	2	no	—
96	C₂×C₄	—	4	2	no	—
97	C₂×C₄	—	4	4	no	—
98	C₂×C₄	C₂²⋊C₄×C₄₁	1	4	yes	—
99	C₂×C₄	C₂²×C₄×C₄₁	1	1	yes	characteristic
100	C₂×C₄	C₂×D₄×C₄₁	1	2	yes	—
101	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
102	C₂×C₄	#41×C₄₁	1	2	yes	—
103	C₈	—	2	4	no	—
104	C₂²	C₂×C₂²⋊C₄×C₄₁	1	1	yes	characteristic
105	C₂²	#124×C₄₁	1	1	yes	characteristic
106	C₂²	#127×C₄₁	1	1	yes	characteristic
107	C₂²	#137×C₄₁	1	4	yes	—
108	C₄	—	2	4	no	—
109	C₄	—	4	4	no	—
110	C₄	—	8	2	no	—
111	C₄	C₄×D₄×C₄₁	1	2	yes	—
112	C₄	#121×C₄₁	1	2	yes	—
113	C₂	C₄₁×#390	1	1	yes	characteristic
114	C₂	C₄₁×#419	1	2	yes	—
115	C₂	C₄₁×#491	1	2	yes	—
116	C₂	C₄₁×#497	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Q₈×C₄₁

C₂

yes

maximal, characteristic

C₂×#103×C₄₁

C₂

yes

maximal

C₂×#97×C₄₁

C₂

yes

maximal, characteristic

C₄₁×#382

C₂

yes

maximal, characteristic

C₂²×Q₈×C₄₁

C₂²

yes

—

C₂²×C₈×C₄₁

C₂²

yes

—

C₄⋊Q₈×C₄₁

—

C₄⋊Q₈×C₄₁

C₄

yes

complemented

C₂×C₄⋊C₄×C₄₁

—

C₂×C₄⋊C₄×C₄₁

C₂²

yes

—

C₂×C₄²×C₄₁

C₂²

yes

characteristic

#103×C₄₁

—

#97×C₄₁

—

#95×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

—

C₂×Q₈×C₄₁

C₂×C₄

yes

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

—

C₂²×C₄×C₄₁

D₄

yes

—

C₂²×C₄×C₄₁

C₂³

yes

characteristic

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

—

C₂×C₈×C₄₁

D₄

yes

—

C₄⋊C₄×C₄₁

—

C₄⋊C₄×C₄₁

—

C₄²×C₄₁

C₂×C₄

yes

—

C₄²×C₄₁

D₄

yes

—

C₂³×C₄₁

C₂×D₄

yes

characteristic

Q₈×C₄₁

—

Q₈×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

—

C₂×C₄×C₄₁

C₂²⋊C₄

yes

—

C₂×C₄×C₄₁

C₂²×C₄

yes

characteristic

C₂×C₄×C₄₁

C₂×D₄

yes

—

C₂×C₄×C₄₁

C₂×D₄

yes

characteristic

C₂×C₄×C₄₁

#41

yes

—

C₈×C₄₁

—

C₂²×C₄₁

C₂×C₂²⋊C₄

yes

C₂²×C₄₁

yes

C₂²×C₄₁

yes

C₂²×C₄₁

yes

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

—

C₄×C₄₁

C₄×D₄

yes

—

C₄×C₄₁

#121

yes

—

#1960

C₄₁

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₄₁

#390

yes

characteristic

C₂×C₄₁

#419

yes

—

C₂×C₄₁

#491

yes

—

C₂×C₄₁

#497

yes

—

C₂×C₄⋊Q₈

C₂×C₄₁

yes

characteristic

C₂×#103

C₂×C₄₁

yes

—

C₂×#97

C₂×C₄₁

yes

characteristic

#382

C₂×C₄₁

yes

characteristic

C₄₁

#1960

yes

characteristic, direct product factor, Sylow

C₂²×Q₈

C₂²×C₄₁

yes

—

C₂²×C₈

C₂²×C₄₁

yes

—

C₄⋊Q₈

—

C₄⋊Q₈

C₄×C₄₁

yes

complemented

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂²×C₄₁

yes

—

C₂×C₄²

C₂²×C₄₁

yes

—

—

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

—

C₂×Q₈

C₂×C₄×C₄₁

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

D₄×C₄₁

yes

—

C₂²×C₄

C₂³×C₄₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

D₄×C₄₁

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

C₂×C₄×C₄₁

yes

—

C₄²

D₄×C₄₁

yes

—

C₂³

C₂×D₄×C₄₁

yes

characteristic

Q₈

—

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊C₄×C₄₁

yes

—

C₂×C₄

C₂²×C₄×C₄₁

yes

characteristic

100

C₂×C₄

C₂×D₄×C₄₁

yes

—

101

C₂×C₄

C₂×D₄×C₄₁

yes

characteristic

102

C₂×C₄

#41×C₄₁

yes

—

103

C₈

—

104

C₂²

C₂×C₂²⋊C₄×C₄₁

yes

characteristic

105

C₂²

#124×C₄₁

yes

characteristic

106

C₂²

#127×C₄₁

yes

characteristic

107

C₂²

#137×C₄₁

yes

—

108

C₄

—

109

C₄

—

110

C₄

—

111

C₄

C₄×D₄×C₄₁

yes

—

112

C₄

#121×C₄₁

yes

—

113

C₂

C₄₁×#390

yes

characteristic

114

C₂

C₄₁×#419

yes

—

115

C₂

C₄₁×#491

yes

—

116

C₂

C₄₁×#497

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₄₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₄×C₄₁
Frattini, cosocle	C₂²×C₄	C₂³×C₄₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₄₁

C₂×D₄

commutator

C₂×C₄

C₂²×C₄×C₄₁

Frattini, cosocle

C₂²×C₄

C₂³×C₄₁

LCS

G ▷ C₂×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₄₁ ◁ C₂×C₄²×C₄₁ ◁ G

N	H ≅ G/N	type
8. C₄⋊Q₈×C₄₁	C₄	semidirect
54. #1960	C₄₁	direct (N × H)
63. C₄₁	#1960	direct (N × H)
67. C₄⋊Q₈	C₄×C₄₁	semidirect

H ≅ G/N

type

8. C₄⋊Q₈×C₄₁

C₄

semidirect

54. #1960

C₄₁

direct (N × H)

63. C₄₁

#1960

direct (N × H)

67. C₄⋊Q₈

C₄×C₄₁

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄⋊Q₈×C₄₁	2
C₂×#103×C₄₁	2
C₂×#97×C₄₁	2
C₄₁×#382	2
#1960	41

subgroup

index

C₂×C₄⋊Q₈×C₄₁

C₂×#103×C₄₁

C₂×#97×C₄₁

C₄₁×#382

#1960

Subgroups — C₄₁×#1960 #19105740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C41×#1960 #19105740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#1960 #19105740