Group #38802941 — subgroups

Subgroups — C₂×C₁₀₁×#1843 #38802941

Order 25856.

1230 conjugacy classes of subgroups; only the 702 normal subgroups are shown.

normal subgroups only

This group has 1230 conjugacy classes of subgroups — too many to draw. Only its 702 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	C₂²×C₄⋊C₈×C₁₀₁	C₂	1	6	yes	maximal
2	C₂×#376×C₁₀₁	C₂	1	1	yes	maximal, characteristic
3	C₁₀₁×#1843	C₂	1	8	yes	maximal, direct product factor
4	C₂³×C₈×C₁₀₁	C₂²	1	4	yes	—
5	C₂²×C₄²×C₁₀₁	C₂²	1	3	yes	—
6	C₂×C₄⋊C₈×C₁₀₁	—	2	24	no	—
7	C₂×C₄⋊C₈×C₁₀₁	C₂²	1	24	yes	—
8	#376×C₁₀₁	C₄	1	4	yes	—
9	#376×C₁₀₁	C₂²	1	4	yes	—
10	C₂×#95×C₁₀₁	C₄	1	4	yes	—
11	C₂³×C₄×C₁₀₁	C₂×C₄	1	6	yes	—
12	C₂³×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
13	C₂²×C₈×C₁₀₁	—	2	24	no	—
14	C₂²×C₈×C₁₀₁	C₂³	1	8	yes	—
15	C₂×C₄²×C₁₀₁	C₂×C₄	1	6	yes	—
16	C₂×C₄²×C₁₀₁	D₄	1	12	yes	—
17	C₂×C₄²×C₁₀₁	Q₈	1	12	yes	—
18	C₂×C₄²×C₁₀₁	C₂³	1	6	yes	—
19	C₄⋊C₈×C₁₀₁	—	2	48	no	—
20	#95×C₁₀₁	C₂×C₄	1	16	yes	—
21	C₂⁴×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₀₁	—	2	24	no	—
23	C₂²×C₄×C₁₀₁	C₄⋊C₄	1	24	yes	—
24	C₂²×C₄×C₁₀₁	C₂²×C₄	1	12	yes	—
25	C₂²×C₄×C₁₀₁	C₂²×C₄	1	1	yes	characteristic
26	C₂²×C₄×C₁₀₁	C₂×D₄	1	6	yes	—
27	C₂²×C₄×C₁₀₁	C₂×Q₈	1	6	yes	—
28	C₂²×C₄×C₁₀₁	C₂⁴	1	1	yes	characteristic
29	C₂×C₈×C₁₀₁	—	2	24	no	—
30	C₂×C₈×C₁₀₁	—	4	16	no	—
31	C₄²×C₁₀₁	C₄⋊C₄	1	24	yes	—
32	C₄²×C₁₀₁	C₂×D₄	1	12	yes	—
33	C₄²×C₁₀₁	C₂×Q₈	1	12	yes	—
34	C₂³×C₁₀₁	C₂×C₄⋊C₄	1	6	yes	—
35	C₂³×C₁₀₁	#131	1	8	yes	—
36	C₂³×C₁₀₁	C₂³×C₄	1	1	yes	characteristic
37	C₂×C₄×C₁₀₁	—	2	24	no	—
38	C₂×C₄×C₁₀₁	—	2	48	no	—
39	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	24	yes	—
40	C₂×C₄×C₁₀₁	C₂×C₄⋊C₄	1	6	yes	—
41	C₂×C₄×C₁₀₁	#127	1	4	yes	—
42	C₂×C₄×C₁₀₁	C₄⋊Q₈	1	12	yes	—
43	C₂×C₄×C₁₀₁	C₂²×D₄	1	3	yes	—
44	C₂×C₄×C₁₀₁	C₂²×Q₈	1	3	yes	—
45	C₈×C₁₀₁	—	4	8	no	—
46	C₂²×C₁₀₁	#384	1	4	yes	—
47	C₂²×C₁₀₁	#424	1	24	yes	—
48	C₂²×C₁₀₁	C₂²×C₄⋊C₄	1	3	yes	—
49	C₂²×C₁₀₁	C₂×#131	1	4	yes	—
50	C₄×C₁₀₁	—	2	24	no	—
51	C₄×C₁₀₁	#384	1	4	yes	—
52	C₄×C₁₀₁	C₂×#127	1	1	yes	characteristic
53	C₄×C₁₀₁	C₂×C₄⋊Q₈	1	3	yes	—
54	C₂×#1843	C₁₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂×C₁₀₁	#1843	1	8	yes	direct product factor
56	C₂×C₁₀₁	C₂×#384	1	1	yes	characteristic
57	C₂×C₁₀₁	C₂×#424	1	6	yes	—
58	C₂²×C₄⋊C₈	C₂×C₁₀₁	1	6	yes	—
59	C₂×#376	C₂×C₁₀₁	1	1	yes	characteristic
60	#1843	C₂×C₁₀₁	1	8	yes	direct product factor
61	C₁₀₁	C₂×#1843	1	1	yes	characteristic, direct product factor, Sylow
62	C₂³×C₈	C₂²×C₁₀₁	1	4	yes	—
63	C₂²×C₄²	C₂²×C₁₀₁	1	3	yes	—
64	C₂×C₄⋊C₈	—	2	24	no	—
65	C₂×C₄⋊C₈	C₂²×C₁₀₁	1	24	yes	—
66	#376	C₄×C₁₀₁	1	4	yes	—
67	#376	C₂²×C₁₀₁	1	4	yes	—
68	C₂×#95	C₄×C₁₀₁	1	4	yes	—
69	C₂³×C₄	C₂×C₄×C₁₀₁	1	6	yes	—
70	C₂³×C₄	C₂³×C₁₀₁	1	1	yes	characteristic
71	C₂²×C₈	—	2	24	no	—
72	C₂²×C₈	C₂³×C₁₀₁	1	8	yes	—
73	C₂×C₄²	C₂×C₄×C₁₀₁	1	6	yes	—
74	C₂×C₄²	D₄×C₁₀₁	1	12	yes	—
75	C₂×C₄²	Q₈×C₁₀₁	1	12	yes	—
76	C₂×C₄²	C₂³×C₁₀₁	1	6	yes	—
77	C₄⋊C₈	—	2	48	no	—
78	#95	C₂×C₄×C₁₀₁	1	16	yes	—
79	C₂⁴	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
80	C₂²×C₄	—	2	24	no	—
81	C₂²×C₄	C₄⋊C₄×C₁₀₁	1	24	yes	—
82	C₂²×C₄	C₂²×C₄×C₁₀₁	1	12	yes	—
83	C₂²×C₄	C₂²×C₄×C₁₀₁	1	1	yes	characteristic
84	C₂²×C₄	C₂×D₄×C₁₀₁	1	6	yes	—
85	C₂²×C₄	C₂×Q₈×C₁₀₁	1	6	yes	—
86	C₂²×C₄	C₂⁴×C₁₀₁	1	1	yes	characteristic
87	C₂×C₈	—	2	24	no	—
88	C₂×C₈	—	4	16	no	—
89	C₄²	C₄⋊C₄×C₁₀₁	1	24	yes	—
90	C₄²	C₂×D₄×C₁₀₁	1	12	yes	—
91	C₄²	C₂×Q₈×C₁₀₁	1	12	yes	—
92	C₂³	C₂×C₄⋊C₄×C₁₀₁	1	6	yes	—
93	C₂³	#131×C₁₀₁	1	8	yes	—
94	C₂³	C₂³×C₄×C₁₀₁	1	1	yes	characteristic
95	C₂×C₄	—	2	48	no	—
96	C₂×C₄	—	2	24	no	—
97	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	24	yes	—
98	C₂×C₄	C₂×C₄⋊C₄×C₁₀₁	1	6	yes	—
99	C₂×C₄	#127×C₁₀₁	1	4	yes	—
100	C₂×C₄	C₄⋊Q₈×C₁₀₁	1	12	yes	—
101	C₂×C₄	C₂²×D₄×C₁₀₁	1	3	yes	—
102	C₂×C₄	C₂²×Q₈×C₁₀₁	1	3	yes	—
103	C₈	—	4	8	no	—
104	C₂²	#384×C₁₀₁	1	4	yes	—
105	C₂²	#424×C₁₀₁	1	24	yes	—
106	C₂²	C₂²×C₄⋊C₄×C₁₀₁	1	3	yes	—
107	C₂²	C₂×#131×C₁₀₁	1	4	yes	—
108	C₄	—	2	24	no	—
109	C₄	#384×C₁₀₁	1	4	yes	—
110	C₄	C₂×#127×C₁₀₁	1	1	yes	characteristic
111	C₄	C₂×C₄⋊Q₈×C₁₀₁	1	3	yes	—
112	C₂	C₁₀₁×#1843	1	8	yes	direct product factor
113	C₂	C₂×#384×C₁₀₁	1	1	yes	characteristic
114	C₂	C₂×#424×C₁₀₁	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₄⋊C₈×C₁₀₁

C₂

yes

maximal

C₂×#376×C₁₀₁

C₂

yes

maximal, characteristic

C₁₀₁×#1843

C₂

yes

maximal, direct product factor

C₂³×C₈×C₁₀₁

C₂²

yes

—

C₂²×C₄²×C₁₀₁

C₂²

yes

—

C₂×C₄⋊C₈×C₁₀₁

—

C₂×C₄⋊C₈×C₁₀₁

C₂²

yes

—

#376×C₁₀₁

C₄

yes

—

#376×C₁₀₁

C₂²

yes

—

C₂×#95×C₁₀₁

C₄

yes

—

C₂³×C₄×C₁₀₁

C₂×C₄

yes

—

C₂³×C₄×C₁₀₁

C₂³

yes

characteristic

C₂²×C₈×C₁₀₁

—

C₂²×C₈×C₁₀₁

C₂³

yes

—

C₂×C₄²×C₁₀₁

C₂×C₄

yes

—

C₂×C₄²×C₁₀₁

D₄

yes

—

C₂×C₄²×C₁₀₁

Q₈

yes

—

C₂×C₄²×C₁₀₁

C₂³

yes

—

C₄⋊C₈×C₁₀₁

—

#95×C₁₀₁

C₂×C₄

yes

—

C₂⁴×C₁₀₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₀₁

—

C₂²×C₄×C₁₀₁

C₄⋊C₄

yes

—

C₂²×C₄×C₁₀₁

C₂²×C₄

yes

—

C₂²×C₄×C₁₀₁

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₀₁

C₂×D₄

yes

—

C₂²×C₄×C₁₀₁

C₂×Q₈

yes

—

C₂²×C₄×C₁₀₁

C₂⁴

yes

characteristic

C₂×C₈×C₁₀₁

—

C₂×C₈×C₁₀₁

—

C₄²×C₁₀₁

C₄⋊C₄

yes

—

C₄²×C₁₀₁

C₂×D₄

yes

—

C₄²×C₁₀₁

C₂×Q₈

yes

—

C₂³×C₁₀₁

C₂×C₄⋊C₄

yes

—

C₂³×C₁₀₁

#131

yes

—

C₂³×C₁₀₁

C₂³×C₄

yes

characteristic

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₀₁

C₂×C₄⋊C₄

yes

—

C₂×C₄×C₁₀₁

#127

yes

—

C₂×C₄×C₁₀₁

C₄⋊Q₈

yes

—

C₂×C₄×C₁₀₁

C₂²×D₄

yes

—

C₂×C₄×C₁₀₁

C₂²×Q₈

yes

—

C₈×C₁₀₁

—

C₂²×C₁₀₁

#384

yes

—

C₂²×C₁₀₁

#424

yes

—

C₂²×C₁₀₁

C₂²×C₄⋊C₄

yes

—

C₂²×C₁₀₁

C₂×#131

yes

—

C₄×C₁₀₁

—

C₄×C₁₀₁

#384

yes

—

C₄×C₁₀₁

C₂×#127

yes

characteristic

C₄×C₁₀₁

C₂×C₄⋊Q₈

yes

—

C₂×#1843

C₁₀₁

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₀₁

#1843

yes

direct product factor

C₂×C₁₀₁

C₂×#384

yes

characteristic

C₂×C₁₀₁

C₂×#424

yes

—

C₂²×C₄⋊C₈

C₂×C₁₀₁

yes

—

C₂×#376

C₂×C₁₀₁

yes

characteristic

#1843

C₂×C₁₀₁

yes

direct product factor

C₁₀₁

C₂×#1843

yes

characteristic, direct product factor, Sylow

C₂³×C₈

C₂²×C₁₀₁

yes

—

C₂²×C₄²

C₂²×C₁₀₁

yes

—

C₂×C₄⋊C₈

—

C₂×C₄⋊C₈

C₂²×C₁₀₁

yes

—

#376

C₄×C₁₀₁

yes

—

#376

C₂²×C₁₀₁

yes

—

C₂×#95

C₄×C₁₀₁

yes

—

C₂³×C₄

C₂×C₄×C₁₀₁

yes

—

C₂³×C₄

C₂³×C₁₀₁

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂³×C₁₀₁

yes

—

C₂×C₄²

C₂×C₄×C₁₀₁

yes

—

C₂×C₄²

D₄×C₁₀₁

yes

—

C₂×C₄²

Q₈×C₁₀₁

yes

—

C₂×C₄²

C₂³×C₁₀₁

yes

—

C₄⋊C₈

—

#95

C₂×C₄×C₁₀₁

yes

—

C₂⁴

C₂²×C₄×C₁₀₁

yes

characteristic

C₂²×C₄

—

C₂²×C₄

C₄⋊C₄×C₁₀₁

yes

—

C₂²×C₄

C₂²×C₄×C₁₀₁

yes

—

C₂²×C₄

C₂²×C₄×C₁₀₁

yes

characteristic

C₂²×C₄

C₂×D₄×C₁₀₁

yes

—

C₂²×C₄

C₂×Q₈×C₁₀₁

yes

—

C₂²×C₄

C₂⁴×C₁₀₁

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

C₄⋊C₄×C₁₀₁

yes

—

C₄²

C₂×D₄×C₁₀₁

yes

—

C₄²

C₂×Q₈×C₁₀₁

yes

—

C₂³

C₂×C₄⋊C₄×C₁₀₁

yes

—

C₂³

#131×C₁₀₁

yes

—

C₂³

C₂³×C₄×C₁₀₁

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂×C₄⋊C₄×C₁₀₁

yes

—

C₂×C₄

C₂×C₄⋊C₄×C₁₀₁

yes

—

C₂×C₄

#127×C₁₀₁

yes

—

100

C₂×C₄

C₄⋊Q₈×C₁₀₁

yes

—

101

C₂×C₄

C₂²×D₄×C₁₀₁

yes

—

102

C₂×C₄

C₂²×Q₈×C₁₀₁

yes

—

103

C₈

—

104

C₂²

#384×C₁₀₁

yes

—

105

C₂²

#424×C₁₀₁

yes

—

106

C₂²

C₂²×C₄⋊C₄×C₁₀₁

yes

—

107

C₂²

C₂×#131×C₁₀₁

yes

—

108

C₄

—

109

C₄

#384×C₁₀₁

yes

—

110

C₄

C₂×#127×C₁₀₁

yes

characteristic

111

C₄

C₂×C₄⋊Q₈×C₁₀₁

yes

—

112

C₂

C₁₀₁×#1843

yes

direct product factor

113

C₂

C₂×#384×C₁₀₁

yes

characteristic

114

C₂

C₂×#424×C₁₀₁

yes

—

	subgroup	G/H
center	C₂³×C₄×C₁₀₁	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₁
socle, prime radical	C₂⁴×C₁₀₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

subgroup

G/H

center

C₂³×C₄×C₁₀₁

C₂³

commutator

C₂³

C₂³×C₄×C₁₀₁

Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₀₁

socle, prime radical

C₂⁴×C₁₀₁

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

N	H ≅ G/N	type
3. C₁₀₁×#1843	C₂	direct (N × H)
54. C₂×#1843	C₁₀₁	direct (N × H)
55. C₂×C₁₀₁	#1843	direct (N × H)
60. #1843	C₂×C₁₀₁	direct (N × H)
61. C₁₀₁	C₂×#1843	direct (N × H)
112. C₂	C₁₀₁×#1843	direct (N × H)

H ≅ G/N

type

3. C₁₀₁×#1843

C₂

direct (N × H)

54. C₂×#1843

C₁₀₁

direct (N × H)

55. C₂×C₁₀₁

#1843

direct (N × H)

60. #1843

C₂×C₁₀₁

direct (N × H)

61. C₁₀₁

C₂×#1843

direct (N × H)

112. C₂

C₁₀₁×#1843

direct (N × H)

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

subgroup	index
C₂²×C₄⋊C₈×C₁₀₁	2
C₂×#376×C₁₀₁	2
C₁₀₁×#1843	2
C₂×#1843	101

subgroup

index

C₂²×C₄⋊C₈×C₁₀₁

C₂×#376×C₁₀₁

C₁₀₁×#1843

C₂×#1843

101

Subgroups — C₂×C₁₀₁×#1843 #38802941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C101×#1843 #38802941

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₁×#1843 #38802941