Subgroups — C₁₁₃×#7545 #43275565

Order 28928.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₁₁₃×#1423	C₂	1	2	yes	maximal
3	C₂×C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
4	#366×C₁₁₃	—	2	2	no	—
5	C₆₄×C₁₁₃	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₁₃	D₄	1	1	yes	characteristic
7	#107×C₁₁₃	—	4	2	no	—
8	C₃₂×C₁₁₃	C₂×C₄	1	1	yes	characteristic
9	C₃₂×C₁₁₃	Q₈	1	1	yes	characteristic
10	C₂×C₈×C₁₁₃	D₈	1	1	yes	characteristic
11	C₄⋊C₄×C₁₁₃	—	8	2	no	—
12	C₁₆×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
13	C₁₆×C₁₁₃	Q₁₆	1	1	yes	characteristic
14	C₂×C₄×C₁₁₃	—	16	2	no	—
15	C₂×C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
16	C₈×C₁₁₃	#107	1	1	yes	characteristic
17	C₈×C₁₁₃	Q₃₂	1	1	yes	characteristic
18	C₂²×C₁₁₃	D₃₂	1	1	yes	characteristic
19	C₄×C₁₁₃	—	32	2	no	—
20	C₄×C₁₁₃	#366	1	1	yes	characteristic
21	C₄×C₁₁₃	Q₆₄	1	1	yes	characteristic
22	#7545	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₁₁₃	#1423	1	1	yes	characteristic
24	C₂×C₁₁₃	D₆₄	1	1	yes	characteristic
25	C₂×C₁₁₃	Q₁₂₈	1	1	yes	characteristic
26	C₂×C₆₄	C₂×C₁₁₃	1	1	yes	characteristic
27	#1423	C₂×C₁₁₃	1	2	yes	—
28	C₁₁₃	#7545	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₃₂	C₂²×C₁₁₃	1	1	yes	characteristic
30	#366	—	2	2	no	—
31	C₆₄	C₄×C₁₁₃	1	2	yes	complemented
32	C₂×C₁₆	D₄×C₁₁₃	1	1	yes	characteristic
33	#107	—	4	2	no	—
34	C₃₂	C₂×C₄×C₁₁₃	1	1	yes	characteristic
35	C₃₂	Q₈×C₁₁₃	1	1	yes	characteristic
36	C₂×C₈	D₈×C₁₁₃	1	1	yes	characteristic
37	C₄⋊C₄	—	8	2	no	—
38	C₁₆	C₄⋊C₄×C₁₁₃	1	1	yes	characteristic
39	C₁₆	Q₁₆×C₁₁₃	1	1	yes	characteristic
40	C₂×C₄	—	16	2	no	—
41	C₂×C₄	D₁₆×C₁₁₃	1	1	yes	characteristic
42	C₈	#107×C₁₁₃	1	1	yes	characteristic
43	C₈	Q₃₂×C₁₁₃	1	1	yes	characteristic
44	C₂²	D₃₂×C₁₁₃	1	1	yes	characteristic
45	C₄	—	32	2	no	—
46	C₄	#366×C₁₁₃	1	1	yes	characteristic
47	C₄	Q₆₄×C₁₁₃	1	1	yes	characteristic
48	C₂	C₁₁₃×#1423	1	1	yes	characteristic
49	C₂	C₁₁₃×D₆₄	1	1	yes	characteristic
50	C₂	C₁₁₃×Q₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₁₃	D₃₂
commutator	C₃₂	C₂×C₄×C₁₁₃
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₁₃
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₂×C₄×C₁₁₃ ◁ C₂×C₈×C₁₁₃ ◁ C₂×C₁₆×C₁₁₃ ◁ C₂×C₃₂×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₄×C₁₁₃	C₄	semidirect
22. #7545	C₁₁₃	direct (N × H)
28. C₁₁₃	#7545	direct (N × H)
31. C₆₄	C₄×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₄×C₁₁₃	2
C₁₁₃×#1423	2
#7545	113

Subgroups — C113×#7545 #43275565

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#7545 #43275565