Subgroups — C₁₀₇×#7540 #41033504

Order 27392.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×#2262	C₂	1	1	yes	maximal, characteristic
2	C₁₀₇×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₇×#1424	C₂	1	1	yes	maximal, characteristic, complemented
4	#508×C₁₀₇	—	2	1	no	—
5	Q₆₄×C₁₀₇	C₄	1	1	yes	characteristic, complemented
6	SD₆₄×C₁₀₇	—	2	1	no	—
7	D₃₂×C₁₀₇	C₄	1	1	yes	characteristic, complemented
8	C₂×C₃₂×C₁₀₇	C₂²	1	1	yes	characteristic
9	#366×C₁₀₇	—	2	1	no	—
10	C₆₄×C₁₀₇	—	2	1	no	—
11	#135×C₁₀₇	—	4	1	no	—
12	Q₃₂×C₁₀₇	—	2	1	no	—
13	SD₃₂×C₁₀₇	—	4	1	no	—
14	D₁₆×C₁₀₇	—	2	1	no	—
15	C₂×C₁₆×C₁₀₇	D₄	1	1	yes	characteristic
16	#107×C₁₀₇	—	4	1	no	—
17	C₃₂×C₁₀₇	C₂×C₄	1	1	yes	characteristic
18	C₃₂×C₁₀₇	D₄	1	1	yes	characteristic
19	#41×C₁₀₇	—	8	1	no	—
20	Q₁₆×C₁₀₇	—	4	1	no	—
21	SD₁₆×C₁₀₇	—	8	1	no	—
22	D₈×C₁₀₇	—	4	1	no	—
23	C₂×C₈×C₁₀₇	D₈	1	1	yes	characteristic
24	C₄⋊C₄×C₁₀₇	—	8	1	no	—
25	C₁₆×C₁₀₇	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₁₀₇	SD₁₆	1	1	yes	characteristic
27	Q₈×C₁₀₇	—	8	1	no	—
28	D₄×C₁₀₇	—	8	1	no	—
29	D₄×C₁₀₇	—	16	1	no	—
30	C₂×C₄×C₁₀₇	—	16	1	no	—
31	C₂×C₄×C₁₀₇	—	16	1	no	—
32	C₂×C₄×C₁₀₇	D₁₆	1	1	yes	characteristic
33	C₈×C₁₀₇	#102	1	1	yes	characteristic
34	C₈×C₁₀₇	SD₃₂	1	1	yes	characteristic
35	C₂²×C₁₀₇	—	16	1	no	—
36	C₂²×C₁₀₇	D₃₂	1	1	yes	characteristic
37	C₄×C₁₀₇	—	16	1	no	—
38	C₄×C₁₀₇	—	32	1	no	—
39	C₄×C₁₀₇	#357	1	1	yes	characteristic
40	C₄×C₁₀₇	SD₆₄	1	1	yes	characteristic
41	#7540	C₁₀₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₁₀₇	—	2	1	no	—
43	C₂×C₁₀₇	—	32	1	no	—
44	C₂×C₁₀₇	#1415	1	1	yes	characteristic
45	#2262	C₂×C₁₀₇	1	1	yes	characteristic
46	M₁₂₈	C₂×C₁₀₇	1	1	yes	characteristic, complemented
47	#1424	C₂×C₁₀₇	1	1	yes	characteristic, complemented
48	C₁₀₇	#7540	1	1	yes	characteristic, direct product factor, Sylow
49	#508	—	2	1	no	—
50	Q₆₄	C₄×C₁₀₇	1	1	yes	characteristic, complemented
51	SD₆₄	—	2	1	no	—
52	D₃₂	C₄×C₁₀₇	1	1	yes	characteristic, complemented
53	C₂×C₃₂	C₂²×C₁₀₇	1	1	yes	characteristic
54	#366	—	2	1	no	—
55	C₆₄	—	2	1	no	—
56	#135	—	4	1	no	—
57	Q₃₂	—	2	1	no	—
58	SD₃₂	—	4	1	no	—
59	D₁₆	—	2	1	no	—
60	C₂×C₁₆	D₄×C₁₀₇	1	1	yes	characteristic
61	#107	—	4	1	no	—
62	C₃₂	C₂×C₄×C₁₀₇	1	1	yes	characteristic
63	C₃₂	D₄×C₁₀₇	1	1	yes	characteristic
64	#41	—	8	1	no	—
65	Q₁₆	—	4	1	no	—
66	SD₁₆	—	8	1	no	—
67	D₈	—	4	1	no	—
68	C₂×C₈	D₈×C₁₀₇	1	1	yes	characteristic
69	C₄⋊C₄	—	8	1	no	—
70	C₁₆	C₂²⋊C₄×C₁₀₇	1	1	yes	characteristic
71	C₁₆	SD₁₆×C₁₀₇	1	1	yes	characteristic
72	Q₈	—	8	1	no	—
73	D₄	—	8	1	no	—
74	D₄	—	16	1	no	—
75	C₂×C₄	—	16	1	no	—
76	C₂×C₄	—	16	1	no	—
77	C₂×C₄	D₁₆×C₁₀₇	1	1	yes	characteristic
78	C₈	#102×C₁₀₇	1	1	yes	characteristic
79	C₈	SD₃₂×C₁₀₇	1	1	yes	characteristic
80	C₂²	—	16	1	no	—
81	C₂²	D₃₂×C₁₀₇	1	1	yes	characteristic
82	C₄	—	16	1	no	—
83	C₄	—	32	1	no	—
84	C₄	#357×C₁₀₇	1	1	yes	characteristic
85	C₄	SD₆₄×C₁₀₇	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	32	1	no	—
88	C₂	C₁₀₇×#1415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₀₇	#1415
commutator	C₃₂	C₂×C₄×C₁₀₇
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₀₇
prime radical	C₁₀₇×#2262	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₇ ◁ C₂×C₄×C₁₀₇ ◁ C₂×C₈×C₁₀₇ ◁ C₂×C₁₆×C₁₀₇ ◁ C₂×C₃₂×C₁₀₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₇×M₁₂₈	C₂	semidirect
3. C₁₀₇×#1424	C₂	semidirect
5. Q₆₄×C₁₀₇	C₄	semidirect
7. D₃₂×C₁₀₇	C₄	semidirect
41. #7540	C₁₀₇	direct (N × H)
46. M₁₂₈	C₂×C₁₀₇	semidirect
47. #1424	C₂×C₁₀₇	semidirect
48. C₁₀₇	#7540	direct (N × H)
50. Q₆₄	C₄×C₁₀₇	semidirect
52. D₃₂	C₄×C₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×#2262	2
C₁₀₇×M₁₂₈	2
C₁₀₇×#1424	2
#7540	107

Subgroups — C107×#7540 #41033504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₇×#7540 #41033504