Subgroups — C₁₁₃×#7461 #43275481

Order 28928.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#1371	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₁₁₃	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₁₁₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
6	#335×C₁₁₃	—	2	2	no	—
7	C₂×C₁₆×C₁₁₃	C₂×C₄	1	1	yes	characteristic
8	C₂×C₁₆×C₁₁₃	Q₈	1	1	yes	characteristic
9	C₄⋊C₈×C₁₁₃	—	4	2	no	—
10	C₄×C₈×C₁₁₃	D₄	1	1	yes	characteristic
11	C₃₂×C₁₁₃	—	2	1	no	—
12	C₃₂×C₁₁₃	C₈	1	2	yes	complemented
13	C₂×C₈×C₁₁₃	—	8	2	no	—
14	C₂×C₈×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₂×C₈×C₁₁₃	Q₁₆	1	1	yes	characteristic
16	C₄²×C₁₁₃	D₈	1	1	yes	characteristic
17	C₁₆×C₁₁₃	—	2	1	no	—
18	C₁₆×C₁₁₃	C₂×C₈	1	1	yes	characteristic
19	C₁₆×C₁₁₃	M₁₆	1	1	yes	characteristic
20	C₂×C₄×C₁₁₃	#107	1	1	yes	characteristic
21	C₂×C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	Q₃₂	1	1	yes	characteristic
23	C₈×C₁₁₃	—	2	1	no	—
24	C₈×C₁₁₃	—	16	2	no	—
25	C₈×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
26	C₈×C₁₁₃	#108	1	1	yes	characteristic
27	C₂²×C₁₁₃	#366	1	1	yes	characteristic
28	C₄×C₁₁₃	—	2	1	no	—
29	C₄×C₁₁₃	#335	1	1	yes	characteristic
30	C₄×C₁₁₃	#368	1	1	yes	characteristic
31	C₄×C₁₁₃	SD₆₄	1	2	yes	—
32	#7461	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₁₁₃	#1371	1	1	yes	characteristic
34	C₂×C₁₁₃	#1424	1	1	yes	characteristic
35	C₂×C₁₁₃	#1425	1	1	yes	characteristic
36	C₄×C₃₂	C₂×C₁₁₃	1	1	yes	characteristic
37	#1371	C₂×C₁₁₃	1	2	yes	—
38	C₁₁₃	#7461	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₃₂	C₄×C₁₁₃	1	1	yes	characteristic
40	C₂×C₃₂	C₄×C₁₁₃	1	1	yes	characteristic
41	C₄×C₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
42	#335	—	2	2	no	—
43	C₂×C₁₆	C₂×C₄×C₁₁₃	1	1	yes	characteristic
44	C₂×C₁₆	Q₈×C₁₁₃	1	1	yes	characteristic
45	C₄⋊C₈	—	4	2	no	—
46	C₄×C₈	D₄×C₁₁₃	1	1	yes	characteristic
47	C₃₂	—	2	1	no	—
48	C₃₂	C₈×C₁₁₃	1	2	yes	complemented
49	C₂×C₈	—	8	2	no	—
50	C₂×C₈	C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
51	C₂×C₈	Q₁₆×C₁₁₃	1	1	yes	characteristic
52	C₄²	D₈×C₁₁₃	1	1	yes	characteristic
53	C₁₆	—	2	1	no	—
54	C₁₆	C₂×C₈×C₁₁₃	1	1	yes	characteristic
55	C₁₆	M₁₆×C₁₁₃	1	1	yes	characteristic
56	C₂×C₄	#107×C₁₁₃	1	1	yes	characteristic
57	C₂×C₄	D₁₆×C₁₁₃	1	1	yes	characteristic
58	C₂×C₄	Q₃₂×C₁₁₃	1	1	yes	characteristic
59	C₈	—	2	1	no	—
60	C₈	—	16	2	no	—
61	C₈	C₄⋊C₈×C₁₁₃	1	1	yes	characteristic
62	C₈	#108×C₁₁₃	1	1	yes	characteristic
63	C₂²	#366×C₁₁₃	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	#335×C₁₁₃	1	1	yes	characteristic
66	C₄	#368×C₁₁₃	1	1	yes	characteristic
67	C₄	SD₆₄×C₁₁₃	1	2	yes	—
68	C₂	C₁₁₃×#1371	1	1	yes	characteristic
69	C₂	C₁₁₃×#1424	1	1	yes	characteristic
70	C₂	C₁₁₃×#1425	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁₃	D₁₆
commutator	C₁₆	C₂×C₈×C₁₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₁₃
socle, prime radical	C₂²×C₁₁₃	#366
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁₃ ◁ C₄²×C₁₁₃ ◁ C₄×C₈×C₁₁₃ ◁ C₄×C₁₆×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₃₂×C₁₁₃	C₈	semidirect
32. #7461	C₁₁₃	direct (N × H)
38. C₁₁₃	#7461	direct (N × H)
48. C₃₂	C₈×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃₂×C₁₁₃	2
C₁₁₃×#1371	2
#7461	113

Subgroups — C113×#7461 #43275481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#7461 #43275481