Group #41046735 — subgroups

Subgroups — C₂×C₁₀₇×#1840 #41046735

Order 27392.

894 conjugacy classes of subgroups; only the 462 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 462 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×#376×C₁₀₇	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×#1840	C₂	1	8	yes	maximal, direct product factor
3	C₂×#336×C₁₀₇	C₂	1	6	yes	maximal
4	C₂³×C₈×C₁₀₇	C₂²	1	4	yes	—
5	C₂²×C₄²×C₁₀₇	C₂²	1	3	yes	—
6	#376×C₁₀₇	C₄	1	4	yes	—
7	#376×C₁₀₇	C₂²	1	4	yes	—
8	C₂×#95×C₁₀₇	C₄	1	4	yes	—
9	#336×C₁₀₇	C₂²	1	24	yes	—
10	C₂³×C₄×C₁₀₇	C₂×C₄	1	6	yes	—
11	C₂³×C₄×C₁₀₇	C₂³	1	1	yes	characteristic
12	C₂²×C₈×C₁₀₇	—	2	24	no	—
13	C₂²×C₈×C₁₀₇	C₂³	1	8	yes	—
14	C₂×C₄²×C₁₀₇	—	2	12	no	—
15	C₂×C₄²×C₁₀₇	C₂×C₄	1	6	yes	—
16	C₂×C₄²×C₁₀₇	C₂³	1	6	yes	—
17	#95×C₁₀₇	C₂×C₄	1	16	yes	—
18	C₂⁴×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
19	C₂²×C₄×C₁₀₇	—	2	12	no	—
20	C₂²×C₄×C₁₀₇	—	2	24	no	—
21	C₂²×C₄×C₁₀₇	C₂²×C₄	1	12	yes	—
22	C₂²×C₄×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
23	C₂²×C₄×C₁₀₇	#41	1	12	yes	—
24	C₂²×C₄×C₁₀₇	C₂⁴	1	1	yes	characteristic
25	C₂×C₈×C₁₀₇	—	2	24	no	—
26	C₂×C₈×C₁₀₇	—	4	16	no	—
27	C₄²×C₁₀₇	—	2	12	no	—
28	C₄²×C₁₀₇	—	2	12	no	—
29	C₂³×C₁₀₇	#117	1	6	yes	—
30	C₂³×C₁₀₇	#131	1	8	yes	—
31	C₂³×C₁₀₇	C₂³×C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₀₇	—	2	12	no	—
33	C₂×C₄×C₁₀₇	—	2	24	no	—
34	C₂×C₄×C₁₀₇	—	4	24	no	—
35	C₂×C₄×C₁₀₇	#117	1	6	yes	—
36	C₂×C₄×C₁₀₇	#126	1	16	yes	—
37	C₂×C₄×C₁₀₇	C₂×#41	1	6	yes	—
38	C₈×C₁₀₇	—	4	8	no	—
39	C₂²×C₁₀₇	#383	1	4	yes	—
40	C₂²×C₁₀₇	#433	1	24	yes	—
41	C₂²×C₁₀₇	C₂×#117	1	3	yes	—
42	C₂²×C₁₀₇	C₂×#131	1	4	yes	—
43	C₄×C₁₀₇	—	4	12	no	—
44	C₄×C₁₀₇	#383	1	4	yes	—
45	C₄×C₁₀₇	C₂×#126	1	4	yes	—
46	C₂×#1840	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×C₁₀₇	#1840	1	8	yes	direct product factor
48	C₂×C₁₀₇	C₂×#383	1	1	yes	characteristic
49	C₂×C₁₀₇	C₂×#433	1	6	yes	—
50	C₂×#376	C₂×C₁₀₇	1	1	yes	characteristic
51	#1840	C₂×C₁₀₇	1	8	yes	direct product factor
52	C₂×#336	C₂×C₁₀₇	1	6	yes	—
53	C₁₀₇	C₂×#1840	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³×C₈	C₂²×C₁₀₇	1	4	yes	—
55	C₂²×C₄²	C₂²×C₁₀₇	1	3	yes	—
56	#376	C₄×C₁₀₇	1	4	yes	—
57	#376	C₂²×C₁₀₇	1	4	yes	—
58	C₂×#95	C₄×C₁₀₇	1	4	yes	—
59	#336	C₂²×C₁₀₇	1	24	yes	—
60	C₂³×C₄	C₂×C₄×C₁₀₇	1	6	yes	—
61	C₂³×C₄	C₂³×C₁₀₇	1	1	yes	characteristic
62	C₂²×C₈	—	2	24	no	—
63	C₂²×C₈	C₂³×C₁₀₇	1	8	yes	—
64	C₂×C₄²	—	2	12	no	—
65	C₂×C₄²	C₂×C₄×C₁₀₇	1	6	yes	—
66	C₂×C₄²	C₂³×C₁₀₇	1	6	yes	—
67	#95	C₂×C₄×C₁₀₇	1	16	yes	—
68	C₂⁴	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
69	C₂²×C₄	—	2	12	no	—
70	C₂²×C₄	—	2	24	no	—
71	C₂²×C₄	C₂²×C₄×C₁₀₇	1	12	yes	—
72	C₂²×C₄	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
73	C₂²×C₄	#41×C₁₀₇	1	12	yes	—
74	C₂²×C₄	C₂⁴×C₁₀₇	1	1	yes	characteristic
75	C₂×C₈	—	2	24	no	—
76	C₂×C₈	—	4	16	no	—
77	C₄²	—	2	12	no	—
78	C₄²	—	2	12	no	—
79	C₂³	#117×C₁₀₇	1	6	yes	—
80	C₂³	#131×C₁₀₇	1	8	yes	—
81	C₂³	C₂³×C₄×C₁₀₇	1	1	yes	characteristic
82	C₂×C₄	—	2	12	no	—
83	C₂×C₄	—	2	24	no	—
84	C₂×C₄	—	4	24	no	—
85	C₂×C₄	#117×C₁₀₇	1	6	yes	—
86	C₂×C₄	#126×C₁₀₇	1	16	yes	—
87	C₂×C₄	C₂×#41×C₁₀₇	1	6	yes	—
88	C₈	—	4	8	no	—
89	C₂²	#383×C₁₀₇	1	4	yes	—
90	C₂²	#433×C₁₀₇	1	24	yes	—
91	C₂²	C₂×#117×C₁₀₇	1	3	yes	—
92	C₂²	C₂×#131×C₁₀₇	1	4	yes	—
93	C₄	—	4	12	no	—
94	C₄	#383×C₁₀₇	1	4	yes	—
95	C₄	C₂×#126×C₁₀₇	1	4	yes	—
96	C₂	C₁₀₇×#1840	1	8	yes	direct product factor
97	C₂	C₂×#383×C₁₀₇	1	1	yes	characteristic
98	C₂	C₂×#433×C₁₀₇	1	6	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#376×C₁₀₇

C₂

yes

maximal, characteristic

C₁₀₇×#1840

C₂

yes

maximal, direct product factor

C₂×#336×C₁₀₇

C₂

yes

maximal

C₂³×C₈×C₁₀₇

C₂²

yes

—

C₂²×C₄²×C₁₀₇

C₂²

yes

—

#376×C₁₀₇

C₄

yes

—

#376×C₁₀₇

C₂²

yes

—

C₂×#95×C₁₀₇

C₄

yes

—

#336×C₁₀₇

C₂²

yes

—

C₂³×C₄×C₁₀₇

C₂×C₄

yes

—

C₂³×C₄×C₁₀₇

C₂³

yes

characteristic

C₂²×C₈×C₁₀₇

—

C₂²×C₈×C₁₀₇

C₂³

yes

—

C₂×C₄²×C₁₀₇

—

C₂×C₄²×C₁₀₇

C₂×C₄

yes

—

C₂×C₄²×C₁₀₇

C₂³

yes

—

#95×C₁₀₇

C₂×C₄

yes

—

C₂⁴×C₁₀₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₀₇

—

C₂²×C₄×C₁₀₇

—

C₂²×C₄×C₁₀₇

C₂²×C₄

yes

—

C₂²×C₄×C₁₀₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₀₇

#41

yes

—

C₂²×C₄×C₁₀₇

C₂⁴

yes

characteristic

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₄²×C₁₀₇

—

C₄²×C₁₀₇

—

C₂³×C₁₀₇

#117

yes

—

C₂³×C₁₀₇

#131

yes

—

C₂³×C₁₀₇

C₂³×C₄

yes

characteristic

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

#117

yes

—

C₂×C₄×C₁₀₇

#126

yes

—

C₂×C₄×C₁₀₇

C₂×#41

yes

—

C₈×C₁₀₇

—

C₂²×C₁₀₇

#383

yes

—

C₂²×C₁₀₇

#433

yes

—

C₂²×C₁₀₇

C₂×#117

yes

—

C₂²×C₁₀₇

C₂×#131

yes

—

C₄×C₁₀₇

—

C₄×C₁₀₇

#383

yes

—

C₄×C₁₀₇

C₂×#126

yes

—

C₂×#1840

C₁₀₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₀₇

#1840

yes

direct product factor

C₂×C₁₀₇

C₂×#383

yes

characteristic

C₂×C₁₀₇

C₂×#433

yes

—

C₂×#376

C₂×C₁₀₇

yes

characteristic

#1840

C₂×C₁₀₇

yes

direct product factor

C₂×#336

C₂×C₁₀₇

yes

—

C₁₀₇

C₂×#1840

yes

characteristic, direct product factor, Sylow

C₂³×C₈

C₂²×C₁₀₇

yes

—

C₂²×C₄²

C₂²×C₁₀₇

yes

—

#376

C₄×C₁₀₇

yes

—

#376

C₂²×C₁₀₇

yes

—

C₂×#95

C₄×C₁₀₇

yes

—

#336

C₂²×C₁₀₇

yes

—

C₂³×C₄

C₂×C₄×C₁₀₇

yes

—

C₂³×C₄

C₂³×C₁₀₇

yes

characteristic

C₂²×C₈

—

C₂²×C₈

C₂³×C₁₀₇

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×C₄×C₁₀₇

yes

—

C₂×C₄²

C₂³×C₁₀₇

yes

—

#95

C₂×C₄×C₁₀₇

yes

—

C₂⁴

C₂²×C₄×C₁₀₇

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×C₄×C₁₀₇

yes

—

C₂²×C₄

C₂²×C₄×C₁₀₇

yes

characteristic

C₂²×C₄

#41×C₁₀₇

yes

—

C₂²×C₄

C₂⁴×C₁₀₇

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₄²

—

C₄²

—

C₂³

#117×C₁₀₇

yes

—

C₂³

#131×C₁₀₇

yes

—

C₂³

C₂³×C₄×C₁₀₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#117×C₁₀₇

yes

—

C₂×C₄

#126×C₁₀₇

yes

—

C₂×C₄

C₂×#41×C₁₀₇

yes

—

C₈

—

C₂²

#383×C₁₀₇

yes

—

C₂²

#433×C₁₀₇

yes

—

C₂²

C₂×#117×C₁₀₇

yes

—

C₂²

C₂×#131×C₁₀₇

yes

—

C₄

—

C₄

#383×C₁₀₇

yes

—

C₄

C₂×#126×C₁₀₇

yes

—

C₂

C₁₀₇×#1840

yes

direct product factor

C₂

C₂×#383×C₁₀₇

yes

characteristic

C₂

C₂×#433×C₁₀₇

yes

—

	subgroup	G/H
center	C₂³×C₄×C₁₀₇	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₇
socle, prime radical	C₂⁴×C₁₀₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₇ ◁ G

subgroup

G/H

center

C₂³×C₄×C₁₀₇

C₂³

commutator

C₂³

C₂³×C₄×C₁₀₇

Frattini, cosocle

C₂²×C₄

C₂⁴×C₁₀₇

socle, prime radical

C₂⁴×C₁₀₇

C₂²×C₄

LCS

G ▷ C₂³ ▷ C₁

UCS

C₁ ◁ C₂³×C₄×C₁₀₇ ◁ G

N	H ≅ G/N	type
2. C₁₀₇×#1840	C₂	direct (N × H)
46. C₂×#1840	C₁₀₇	direct (N × H)
47. C₂×C₁₀₇	#1840	direct (N × H)
51. #1840	C₂×C₁₀₇	direct (N × H)
53. C₁₀₇	C₂×#1840	direct (N × H)
96. C₂	C₁₀₇×#1840	direct (N × H)

H ≅ G/N

type

2. C₁₀₇×#1840

C₂

direct (N × H)

46. C₂×#1840

C₁₀₇

direct (N × H)

47. C₂×C₁₀₇

#1840

direct (N × H)

51. #1840

C₂×C₁₀₇

direct (N × H)

53. C₁₀₇

C₂×#1840

direct (N × H)

96. C₂

C₁₀₇×#1840

direct (N × H)

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

subgroup	index
C₂×#376×C₁₀₇	2
C₁₀₇×#1840	2
C₂×#336×C₁₀₇	2
C₂×#1840	107

subgroup

index

C₂×#376×C₁₀₇

C₁₀₇×#1840

C₂×#336×C₁₀₇

C₂×#1840

107

Subgroups — C₂×C₁₀₇×#1840 #41046735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C2×C107×#1840 #41046735

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₀₇×#1840 #41046735