Subgroups — C₂²×C₈²×C₁₀₇ #41043274

Order 27392.

1342 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈×C₁₀₇	C₂	1	3	yes	maximal
2	C₂×C₈²×C₁₀₇	C₂	1	12	yes	maximal, direct product factor
3	C₂³×C₈×C₁₀₇	C₄	1	6	yes	—
4	C₂²×C₄²×C₁₀₇	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₀₇	C₄	1	18	yes	—
6	C₂×C₄×C₈×C₁₀₇	C₂²	1	18	yes	—
7	C₈²×C₁₀₇	C₂²	1	16	yes	direct product factor
8	C₂³×C₄×C₁₀₇	C₂×C₄	1	3	yes	—
9	C₂²×C₈×C₁₀₇	C₈	1	48	yes	direct product factor
10	C₂²×C₈×C₁₀₇	C₂×C₄	1	36	yes	—
11	C₂×C₄²×C₁₀₇	C₂×C₄	1	9	yes	—
12	C₂×C₄²×C₁₀₇	C₂³	1	3	yes	—
13	C₄×C₈×C₁₀₇	C₂×C₄	1	36	yes	—
14	C₄×C₈×C₁₀₇	C₂³	1	12	yes	—
15	C₂⁴×C₁₀₇	C₄²	1	1	yes	characteristic
16	C₂²×C₄×C₁₀₇	C₄²	1	9	yes	—
17	C₂²×C₄×C₁₀₇	C₂×C₈	1	24	yes	—
18	C₂²×C₄×C₁₀₇	C₂²×C₄	1	9	yes	—
19	C₂×C₈×C₁₀₇	C₂×C₈	1	144	yes	direct product factor
20	C₂×C₈×C₁₀₇	C₂²×C₄	1	24	yes	—
21	C₄²×C₁₀₇	C₄²	1	6	yes	—
22	C₄²×C₁₀₇	C₂²×C₄	1	9	yes	—
23	C₄²×C₁₀₇	C₂⁴	1	1	yes	characteristic
24	C₂³×C₁₀₇	C₄×C₈	1	12	yes	—
25	C₂³×C₁₀₇	C₂×C₄²	1	3	yes	—
26	C₂×C₄×C₁₀₇	C₄×C₈	1	36	yes	—
27	C₂×C₄×C₁₀₇	C₂×C₄²	1	9	yes	—
28	C₂×C₄×C₁₀₇	C₂²×C₈	1	36	yes	—
29	C₂×C₄×C₁₀₇	C₂³×C₄	1	3	yes	—
30	C₈×C₁₀₇	C₂²×C₈	1	48	yes	direct product factor
31	C₂²×C₁₀₇	C₈²	1	16	yes	direct product factor
32	C₂²×C₁₀₇	C₂×C₄×C₈	1	18	yes	—
33	C₂²×C₁₀₇	C₂²×C₄²	1	1	yes	characteristic
34	C₄×C₁₀₇	C₂×C₄×C₈	1	18	yes	—
35	C₄×C₁₀₇	C₂³×C₈	1	6	yes	—
36	C₂²×C₈²	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×C₁₀₇	C₂×C₈²	1	12	yes	direct product factor
38	C₂×C₁₀₇	C₂²×C₄×C₈	1	3	yes	—
39	C₂²×C₄×C₈	C₂×C₁₀₇	1	3	yes	—
40	C₂×C₈²	C₂×C₁₀₇	1	12	yes	direct product factor
41	C₁₀₇	C₂²×C₈²	1	1	yes	characteristic, direct product factor, Sylow
42	C₂³×C₈	C₄×C₁₀₇	1	6	yes	—
43	C₂²×C₄²	C₂²×C₁₀₇	1	1	yes	characteristic
44	C₂×C₄×C₈	C₄×C₁₀₇	1	18	yes	—
45	C₂×C₄×C₈	C₂²×C₁₀₇	1	18	yes	—
46	C₈²	C₂²×C₁₀₇	1	16	yes	direct product factor
47	C₂³×C₄	C₂×C₄×C₁₀₇	1	3	yes	—
48	C₂²×C₈	C₈×C₁₀₇	1	48	yes	direct product factor
49	C₂²×C₈	C₂×C₄×C₁₀₇	1	36	yes	—
50	C₂×C₄²	C₂×C₄×C₁₀₇	1	9	yes	—
51	C₂×C₄²	C₂³×C₁₀₇	1	3	yes	—
52	C₄×C₈	C₂×C₄×C₁₀₇	1	36	yes	—
53	C₄×C₈	C₂³×C₁₀₇	1	12	yes	—
54	C₂⁴	C₄²×C₁₀₇	1	1	yes	characteristic
55	C₂²×C₄	C₄²×C₁₀₇	1	9	yes	—
56	C₂²×C₄	C₂×C₈×C₁₀₇	1	24	yes	—
57	C₂²×C₄	C₂²×C₄×C₁₀₇	1	9	yes	—
58	C₂×C₈	C₂×C₈×C₁₀₇	1	144	yes	direct product factor
59	C₂×C₈	C₂²×C₄×C₁₀₇	1	24	yes	—
60	C₄²	C₄²×C₁₀₇	1	6	yes	—
61	C₄²	C₂²×C₄×C₁₀₇	1	9	yes	—
62	C₄²	C₂⁴×C₁₀₇	1	1	yes	characteristic
63	C₂³	C₄×C₈×C₁₀₇	1	12	yes	—
64	C₂³	C₂×C₄²×C₁₀₇	1	3	yes	—
65	C₂×C₄	C₄×C₈×C₁₀₇	1	36	yes	—
66	C₂×C₄	C₂×C₄²×C₁₀₇	1	9	yes	—
67	C₂×C₄	C₂²×C₈×C₁₀₇	1	36	yes	—
68	C₂×C₄	C₂³×C₄×C₁₀₇	1	3	yes	—
69	C₈	C₂²×C₈×C₁₀₇	1	48	yes	direct product factor
70	C₂²	C₈²×C₁₀₇	1	16	yes	direct product factor
71	C₂²	C₂×C₄×C₈×C₁₀₇	1	18	yes	—
72	C₂²	C₂²×C₄²×C₁₀₇	1	1	yes	characteristic
73	C₄	C₂×C₄×C₈×C₁₀₇	1	18	yes	—
74	C₄	C₂³×C₈×C₁₀₇	1	6	yes	—
75	C₂	C₂×C₈²×C₁₀₇	1	12	yes	direct product factor
76	C₂	C₂²×C₄×C₈×C₁₀₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²	C₂⁴×C₁₀₇
socle, prime radical	C₂⁴×C₁₀₇	C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₈²×C₁₀₇	C₂	direct (N × H)
7. C₈²×C₁₀₇	C₂²	direct (N × H)
9. C₂²×C₈×C₁₀₇	C₈	direct (N × H)
19. C₂×C₈×C₁₀₇	C₂×C₈	direct (N × H)
30. C₈×C₁₀₇	C₂²×C₈	direct (N × H)
31. C₂²×C₁₀₇	C₈²	direct (N × H)
36. C₂²×C₈²	C₁₀₇	direct (N × H)
37. C₂×C₁₀₇	C₂×C₈²	direct (N × H)
40. C₂×C₈²	C₂×C₁₀₇	direct (N × H)
41. C₁₀₇	C₂²×C₈²	direct (N × H)
46. C₈²	C₂²×C₁₀₇	direct (N × H)
48. C₂²×C₈	C₈×C₁₀₇	direct (N × H)
58. C₂×C₈	C₂×C₈×C₁₀₇	direct (N × H)
69. C₈	C₂²×C₈×C₁₀₇	direct (N × H)
70. C₂²	C₈²×C₁₀₇	direct (N × H)
75. C₂	C₂×C₈²×C₁₀₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈×C₁₀₇	2
C₂×C₈²×C₁₀₇	2
C₂²×C₈²	107

Subgroups — C22×C82×C107 #41043274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₈²×C₁₀₇ #41043274