Group #41037380 — subgroups

Subgroups — C₁₀₇×#11416 #41037380

Order 27392.

228 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 150 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	C₁₀₇×#2163	C₂	1	2	yes	maximal
2	C₁₀₇×#1450	C₂	1	1	yes	maximal, characteristic
3	C₁₀₇×#1313	C₂	1	4	yes	maximal, complemented
4	#431×C₁₀₇	C₄	1	2	yes	—
5	C₂×C₄×C₈×C₁₀₇	C₂²	1	1	yes	characteristic
6	C₄⋊C₁₆×C₁₀₇	C₄	1	4	yes	—
7	C₂²⋊C₁₆×C₁₀₇	C₄	1	4	yes	—
8	#346×C₁₀₇	C₂²	1	4	yes	—
9	#322×C₁₀₇	C₂²	1	2	yes	—
10	C₈²×C₁₀₇	C₄	1	2	yes	—
11	C₂²×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
12	C₂×C₄²×C₁₀₇	C₂×C₄	1	1	yes	characteristic
13	C₂×C₁₆×C₁₀₇	C₂×C₄	1	8	yes	—
14	C₄⋊C₈×C₁₀₇	—	2	2	no	—
15	C₂²⋊C₈×C₁₀₇	—	2	2	no	—
16	C₄×C₈×C₁₀₇	C₂×C₄	1	2	yes	—
17	C₄×C₈×C₁₀₇	C₂×C₄	1	4	yes	—
18	C₄×C₈×C₁₀₇	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₀₇	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₀₇	C₄²	1	1	yes	characteristic
21	C₂²×C₄×C₁₀₇	M₁₆	1	2	yes	—
22	C₂×C₈×C₁₀₇	—	2	4	no	—
23	C₂×C₈×C₁₀₇	—	2	4	no	—
24	C₂×C₈×C₁₀₇	C₄²	1	2	yes	—
25	C₂×C₈×C₁₀₇	C₂²×C₄	1	2	yes	—
26	C₄²×C₁₀₇	C₄²	1	1	yes	characteristic
27	C₄²×C₁₀₇	M₁₆	1	2	yes	—
28	C₄²×C₁₀₇	C₂²×C₄	1	1	yes	characteristic
29	C₁₆×C₁₀₇	—	2	8	no	—
30	C₂³×C₁₀₇	#97	1	1	yes	characteristic
31	C₂×C₄×C₁₀₇	—	2	2	no	—
32	C₂×C₄×C₁₀₇	—	4	2	no	—
33	C₂×C₄×C₁₀₇	#97	1	2	yes	—
34	C₂×C₄×C₁₀₇	#97	1	1	yes	characteristic
35	C₂×C₄×C₁₀₇	C₂×C₄²	1	1	yes	characteristic
36	C₂×C₄×C₁₀₇	C₂×M₁₆	1	2	yes	—
37	C₈×C₁₀₇	—	2	2	no	—
38	C₈×C₁₀₇	—	4	4	no	—
39	C₈×C₁₀₇	#131	1	4	yes	—
40	C₂²×C₁₀₇	—	2	2	no	—
41	C₂²×C₁₀₇	—	2	1	no	—
42	C₂²×C₁₀₇	C₂×#97	1	1	yes	characteristic
43	C₄×C₁₀₇	—	2	2	no	—
44	C₄×C₁₀₇	—	2	2	no	—
45	C₄×C₁₀₇	—	2	1	no	—
46	C₄×C₁₀₇	#405	1	2	yes	—
47	#11416	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₁₀₇	—	4	1	no	—
49	C₂×C₁₀₇	#1452	1	1	yes	characteristic
50	C₂×C₁₀₇	#2110	1	2	yes	—
51	#2163	C₂×C₁₀₇	1	2	yes	—
52	#1450	C₂×C₁₀₇	1	1	yes	characteristic
53	#1313	C₂×C₁₀₇	1	4	yes	complemented
54	C₁₀₇	#11416	1	1	yes	characteristic, direct product factor, Sylow
55	#431	C₄×C₁₀₇	1	2	yes	—
56	C₂×C₄×C₈	C₂²×C₁₀₇	1	1	yes	characteristic
57	C₄⋊C₁₆	C₄×C₁₀₇	1	4	yes	—
58	C₂²⋊C₁₆	C₄×C₁₀₇	1	4	yes	—
59	#346	C₂²×C₁₀₇	1	4	yes	—
60	#322	C₂²×C₁₀₇	1	2	yes	—
61	C₈²	C₄×C₁₀₇	1	2	yes	—
62	C₂²×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
63	C₂×C₄²	C₂×C₄×C₁₀₇	1	1	yes	characteristic
64	C₂×C₁₆	C₂×C₄×C₁₀₇	1	8	yes	—
65	C₄⋊C₈	—	2	2	no	—
66	C₂²⋊C₈	—	2	2	no	—
67	C₄×C₈	C₂×C₄×C₁₀₇	1	2	yes	—
68	C₄×C₈	C₂×C₄×C₁₀₇	1	4	yes	—
69	C₄×C₈	C₂×C₄×C₁₀₇	1	1	yes	characteristic
70	C₄×C₈	C₂³×C₁₀₇	1	1	yes	characteristic
71	C₂²×C₄	C₄²×C₁₀₇	1	1	yes	characteristic
72	C₂²×C₄	M₁₆×C₁₀₇	1	2	yes	—
73	C₂×C₈	—	2	4	no	—
74	C₂×C₈	—	2	4	no	—
75	C₂×C₈	C₄²×C₁₀₇	1	2	yes	—
76	C₂×C₈	C₂²×C₄×C₁₀₇	1	2	yes	—
77	C₄²	C₄²×C₁₀₇	1	1	yes	characteristic
78	C₄²	M₁₆×C₁₀₇	1	2	yes	—
79	C₄²	C₂²×C₄×C₁₀₇	1	1	yes	characteristic
80	C₁₆	—	2	8	no	—
81	C₂³	#97×C₁₀₇	1	1	yes	characteristic
82	C₂×C₄	—	2	2	no	—
83	C₂×C₄	—	4	2	no	—
84	C₂×C₄	#97×C₁₀₇	1	2	yes	—
85	C₂×C₄	#97×C₁₀₇	1	1	yes	characteristic
86	C₂×C₄	C₂×C₄²×C₁₀₇	1	1	yes	characteristic
87	C₂×C₄	C₂×M₁₆×C₁₀₇	1	2	yes	—
88	C₈	—	2	2	no	—
89	C₈	—	4	4	no	—
90	C₈	#131×C₁₀₇	1	4	yes	—
91	C₂²	—	2	1	no	—
92	C₂²	—	2	2	no	—
93	C₂²	C₂×#97×C₁₀₇	1	1	yes	characteristic
94	C₄	—	2	1	no	—
95	C₄	—	2	2	no	—
96	C₄	—	2	2	no	—
97	C₄	#405×C₁₀₇	1	2	yes	—
98	C₂	—	4	1	no	—
99	C₂	C₁₀₇×#1452	1	1	yes	characteristic
100	C₂	C₁₀₇×#2110	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₇×#2163

C₂

yes

maximal

C₁₀₇×#1450

C₂

yes

maximal, characteristic

C₁₀₇×#1313

C₂

yes

maximal, complemented

#431×C₁₀₇

C₄

yes

—

C₂×C₄×C₈×C₁₀₇

C₂²

yes

characteristic

C₄⋊C₁₆×C₁₀₇

C₄

yes

—

C₂²⋊C₁₆×C₁₀₇

C₄

yes

—

#346×C₁₀₇

C₂²

yes

—

#322×C₁₀₇

C₂²

yes

—

C₈²×C₁₀₇

C₄

yes

—

C₂²×C₈×C₁₀₇

C₂×C₄

yes

—

C₂×C₄²×C₁₀₇

C₂×C₄

yes

characteristic

C₂×C₁₆×C₁₀₇

C₂×C₄

yes

—

C₄⋊C₈×C₁₀₇

—

C₂²⋊C₈×C₁₀₇

—

C₄×C₈×C₁₀₇

C₂×C₄

yes

—

C₄×C₈×C₁₀₇

C₂×C₄

yes

—

C₄×C₈×C₁₀₇

C₂×C₄

yes

characteristic

C₄×C₈×C₁₀₇

C₂³

yes

characteristic

C₂²×C₄×C₁₀₇

C₄²

yes

characteristic

C₂²×C₄×C₁₀₇

M₁₆

yes

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

—

C₂×C₈×C₁₀₇

C₄²

yes

—

C₂×C₈×C₁₀₇

C₂²×C₄

yes

—

C₄²×C₁₀₇

C₄²

yes

characteristic

C₄²×C₁₀₇

M₁₆

yes

—

C₄²×C₁₀₇

C₂²×C₄

yes

characteristic

C₁₆×C₁₀₇

—

C₂³×C₁₀₇

#97

yes

characteristic

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

—

C₂×C₄×C₁₀₇

#97

yes

—

C₂×C₄×C₁₀₇

#97

yes

characteristic

C₂×C₄×C₁₀₇

C₂×C₄²

yes

characteristic

C₂×C₄×C₁₀₇

C₂×M₁₆

yes

—

C₈×C₁₀₇

—

C₈×C₁₀₇

—

C₈×C₁₀₇

#131

yes

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

—

C₂²×C₁₀₇

C₂×#97

yes

characteristic

C₄×C₁₀₇

—

C₄×C₁₀₇

—

C₄×C₁₀₇

—

C₄×C₁₀₇

#405

yes

—

#11416

C₁₀₇

yes

maximal, characteristic, direct product factor, Sylow

C₂×C₁₀₇

—

C₂×C₁₀₇

#1452

yes

characteristic

C₂×C₁₀₇

#2110

yes

—

#2163

C₂×C₁₀₇

yes

—

#1450

C₂×C₁₀₇

yes

characteristic

#1313

C₂×C₁₀₇

yes

complemented

C₁₀₇

#11416

yes

characteristic, direct product factor, Sylow

#431

C₄×C₁₀₇

yes

—

C₂×C₄×C₈

C₂²×C₁₀₇

yes

characteristic

C₄⋊C₁₆

C₄×C₁₀₇

yes

—

C₂²⋊C₁₆

C₄×C₁₀₇

yes

—

#346

C₂²×C₁₀₇

yes

—

#322

C₂²×C₁₀₇

yes

—

C₈²

C₄×C₁₀₇

yes

—

C₂²×C₈

C₂×C₄×C₁₀₇

yes

—

C₂×C₄²

C₂×C₄×C₁₀₇

yes

characteristic

C₂×C₁₆

C₂×C₄×C₁₀₇

yes

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₄×C₈

C₂×C₄×C₁₀₇

yes

—

C₄×C₈

C₂×C₄×C₁₀₇

yes

—

C₄×C₈

C₂×C₄×C₁₀₇

yes

characteristic

C₄×C₈

C₂³×C₁₀₇

yes

characteristic

C₂²×C₄

C₄²×C₁₀₇

yes

characteristic

C₂²×C₄

M₁₆×C₁₀₇

yes

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

C₄²×C₁₀₇

yes

—

C₂×C₈

C₂²×C₄×C₁₀₇

yes

—

C₄²

C₄²×C₁₀₇

yes

characteristic

C₄²

M₁₆×C₁₀₇

yes

—

C₄²

C₂²×C₄×C₁₀₇

yes

characteristic

C₁₆

—

C₂³

#97×C₁₀₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#97×C₁₀₇

yes

—

C₂×C₄

#97×C₁₀₇

yes

characteristic

C₂×C₄

C₂×C₄²×C₁₀₇

yes

characteristic

C₂×C₄

C₂×M₁₆×C₁₀₇

yes

—

C₈

—

C₈

—

C₈

#131×C₁₀₇

yes

—

C₂²

—

C₂²

—

C₂²

C₂×#97×C₁₀₇

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

#405×C₁₀₇

yes

—

C₂

—

C₂

C₁₀₇×#1452

yes

characteristic

100

C₂

C₁₀₇×#2110

yes

—

	subgroup	G/H
center	C₂×C₄×C₁₀₇	C₂×C₄²
commutator	C₂×C₄	C₂×C₄²×C₁₀₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₀₇
socle	C₂²×C₁₀₇	C₂×#97
prime radical	C₂³×C₁₀₇	#97
LCS	G ▷ C₂×C₄ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₀₇ ◁ G

subgroup

G/H

center

C₂×C₄×C₁₀₇

C₂×C₄²

commutator

C₂×C₄

C₂×C₄²×C₁₀₇

Frattini, cosocle

C₄×C₈

C₂³×C₁₀₇

socle

C₂²×C₁₀₇

C₂×#97

C₂³×C₁₀₇

G ▷ C₂×C₄ ▷ C₁

C₁ ◁ C₂×C₄×C₁₀₇ ◁ G

N	H ≅ G/N	type
3. C₁₀₇×#1313	C₂	semidirect
47. #11416	C₁₀₇	direct (N × H)
53. #1313	C₂×C₁₀₇	semidirect
54. C₁₀₇	#11416	direct (N × H)

H ≅ G/N

type

3. C₁₀₇×#1313

C₂

semidirect

47. #11416

C₁₀₇

direct (N × H)

53. #1313

C₂×C₁₀₇

semidirect

54. C₁₀₇

#11416

direct (N × H)

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

subgroup	index
C₁₀₇×#2163	2
C₁₀₇×#1450	2
C₁₀₇×#1313	2
#11416	107

subgroup

index

C₁₀₇×#2163

C₁₀₇×#1450

C₁₀₇×#1313

#11416

107

Subgroups — C₁₀₇×#11416 #41037380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C107×#11416 #41037380

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#11416 #41037380