Subgroups — C₁₁₃×#8136 #43276156

Order 28928.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#97×C₁₁₃	C₂	1	3	yes	maximal
2	C₁₁₃×#1273	C₂	1	4	yes	maximal
3	C₂×#97×C₁₁₃	C₄	1	12	yes	—
4	C₂×C₄×C₈×C₁₁₃	C₂²	1	6	yes	—
5	C₄³×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₁₁₃	C₂×C₄	1	12	yes	—
7	C₂×C₄²×C₁₁₃	C₂×C₄	1	6	yes	—
8	C₂×C₄²×C₁₁₃	C₂³	1	1	yes	characteristic
9	#97×C₁₁₃	—	2	24	no	—
10	C₄×C₈×C₁₁₃	—	2	12	no	—
11	C₂²×C₄×C₁₁₃	C₄²	1	4	yes	—
12	C₂²×C₄×C₁₁₃	C₂²×C₄	1	3	yes	—
13	C₂×C₈×C₁₁₃	—	2	12	no	—
14	C₂×C₈×C₁₁₃	—	2	12	no	—
15	C₂×C₈×C₁₁₃	M₁₆	1	24	yes	—
16	C₄²×C₁₁₃	—	2	12	no	—
17	C₄²×C₁₁₃	#41	1	4	yes	—
18	C₂³×C₁₁₃	C₂×C₄²	1	1	yes	characteristic
19	C₂×C₄×C₁₁₃	—	2	12	no	—
20	C₂×C₄×C₁₁₃	#117	1	6	yes	—
21	C₂×C₄×C₁₁₃	C₂×M₁₆	1	12	yes	—
22	C₈×C₁₁₃	—	2	24	no	—
23	C₂²×C₁₁₃	#376	1	1	yes	characteristic
24	C₂²×C₁₁₃	C₄×M₁₆	1	6	yes	—
25	C₄×C₁₁₃	—	4	4	no	—
26	C₄×C₁₁₃	#432	1	12	yes	—
27	#8136	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂×C₁₁₃	#1455	1	4	yes	—
29	C₂×C₁₁₃	#1745	1	3	yes	—
30	C₄×#97	C₂×C₁₁₃	1	3	yes	—
31	#1273	C₂×C₁₁₃	1	4	yes	—
32	C₁₁₃	#8136	1	1	yes	characteristic, direct product factor, Sylow
33	C₂×#97	C₄×C₁₁₃	1	12	yes	—
34	C₂×C₄×C₈	C₂²×C₁₁₃	1	6	yes	—
35	C₄³	C₂²×C₁₁₃	1	1	yes	characteristic
36	C₂²×C₈	C₂×C₄×C₁₁₃	1	12	yes	—
37	C₂×C₄²	C₂×C₄×C₁₁₃	1	6	yes	—
38	C₂×C₄²	C₂³×C₁₁₃	1	1	yes	characteristic
39	#97	—	2	24	no	—
40	C₄×C₈	—	2	12	no	—
41	C₂²×C₄	C₄²×C₁₁₃	1	4	yes	—
42	C₂²×C₄	C₂²×C₄×C₁₁₃	1	3	yes	—
43	C₂×C₈	—	2	12	no	—
44	C₂×C₈	—	2	12	no	—
45	C₂×C₈	M₁₆×C₁₁₃	1	24	yes	—
46	C₄²	—	2	12	no	—
47	C₄²	#41×C₁₁₃	1	4	yes	—
48	C₂³	C₂×C₄²×C₁₁₃	1	1	yes	characteristic
49	C₂×C₄	—	2	12	no	—
50	C₂×C₄	#117×C₁₁₃	1	6	yes	—
51	C₂×C₄	C₂×M₁₆×C₁₁₃	1	12	yes	—
52	C₈	—	2	24	no	—
53	C₂²	#376×C₁₁₃	1	1	yes	characteristic
54	C₂²	C₄×M₁₆×C₁₁₃	1	6	yes	—
55	C₄	—	4	4	no	—
56	C₄	#432×C₁₁₃	1	12	yes	—
57	C₂	C₁₁₃×#1455	1	4	yes	—
58	C₂	C₁₁₃×#1745	1	3	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₁₃	C₂³
commutator	C₂³	C₂×C₄²×C₁₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁₃
socle, prime radical	C₂³×C₁₁₃	C₂×C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
27. #8136	C₁₁₃	direct (N × H)
32. C₁₁₃	#8136	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#97×C₁₁₃	2
C₁₁₃×#1273	2
#8136	113

Subgroups — C113×#8136 #43276156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#8136 #43276156