Subgroups — C₁₁₃×#7331 #43275351

Order 28928.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃₂×C₁₁₃	C₂	1	2	yes	maximal
2	C₈×C₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₁₁₃	C₄	1	4	yes	—
4	C₄×C₁₆×C₁₁₃	C₄	1	1	yes	characteristic
5	C₄×C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
6	C₈²×C₁₁₃	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₁₁₃	C₈	1	2	yes	—
8	C₂×C₁₆×C₁₁₃	C₂×C₄	1	2	yes	—
9	C₄×C₈×C₁₁₃	C₈	1	1	yes	characteristic
10	C₄×C₈×C₁₁₃	C₈	1	1	yes	characteristic
11	C₄×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
12	C₃₂×C₁₁₃	—	2	4	no	—
13	C₂×C₈×C₁₁₃	C₁₆	1	2	yes	—
14	C₂×C₈×C₁₁₃	C₁₆	1	2	yes	—
15	C₂×C₈×C₁₁₃	C₄²	1	1	yes	characteristic
16	C₂×C₈×C₁₁₃	C₂×C₈	1	1	yes	characteristic
17	C₄²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
18	C₁₆×C₁₁₃	—	2	2	no	—
19	C₁₆×C₁₁₃	M₁₆	1	4	yes	—
20	C₂×C₄×C₁₁₃	C₄×C₈	1	1	yes	characteristic
21	C₂×C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
22	C₂×C₄×C₁₁₃	C₂×C₁₆	1	1	yes	characteristic
23	C₈×C₁₁₃	—	2	2	no	—
24	C₈×C₁₁₃	C₃₂	1	4	yes	complemented
25	C₈×C₁₁₃	#97	1	2	yes	—
26	C₈×C₁₁₃	M₃₂	1	2	yes	—
27	C₂²×C₁₁₃	C₄×C₁₆	1	1	yes	characteristic
28	C₄×C₁₁₃	#322	1	1	yes	characteristic
29	C₄×C₁₁₃	#346	1	1	yes	characteristic
30	C₄×C₁₁₃	C₂×C₃₂	1	2	yes	—
31	C₄×C₁₁₃	M₆₄	1	2	yes	—
32	#7331	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₁₁₃	#1312	1	1	yes	characteristic
34	C₂×C₁₁₃	C₄×C₃₂	1	1	yes	characteristic
35	C₂×C₁₁₃	#1397	1	1	yes	characteristic
36	C₄×C₃₂	C₂×C₁₁₃	1	2	yes	—
37	C₈×C₁₆	C₂×C₁₁₃	1	1	yes	characteristic
38	C₁₁₃	#7331	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₃₂	C₄×C₁₁₃	1	4	yes	—
40	C₄×C₁₆	C₄×C₁₁₃	1	1	yes	characteristic
41	C₄×C₁₆	C₂²×C₁₁₃	1	1	yes	characteristic
42	C₈²	C₄×C₁₁₃	1	1	yes	characteristic
43	C₂×C₁₆	C₈×C₁₁₃	1	2	yes	—
44	C₂×C₁₆	C₂×C₄×C₁₁₃	1	2	yes	—
45	C₄×C₈	C₈×C₁₁₃	1	1	yes	characteristic
46	C₄×C₈	C₈×C₁₁₃	1	1	yes	characteristic
47	C₄×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
48	C₃₂	—	2	4	no	—
49	C₂×C₈	C₁₆×C₁₁₃	1	2	yes	—
50	C₂×C₈	C₁₆×C₁₁₃	1	2	yes	—
51	C₂×C₈	C₄²×C₁₁₃	1	1	yes	characteristic
52	C₂×C₈	C₂×C₈×C₁₁₃	1	1	yes	characteristic
53	C₄²	C₂×C₈×C₁₁₃	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₁₆	M₁₆×C₁₁₃	1	4	yes	—
56	C₂×C₄	C₄×C₈×C₁₁₃	1	1	yes	characteristic
57	C₂×C₄	C₂×C₁₆×C₁₁₃	1	1	yes	characteristic
58	C₂×C₄	C₂×C₁₆×C₁₁₃	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	C₃₂×C₁₁₃	1	4	yes	complemented
61	C₈	#97×C₁₁₃	1	2	yes	—
62	C₈	M₃₂×C₁₁₃	1	2	yes	—
63	C₂²	C₄×C₁₆×C₁₁₃	1	1	yes	characteristic
64	C₄	#322×C₁₁₃	1	1	yes	characteristic
65	C₄	#346×C₁₁₃	1	1	yes	characteristic
66	C₄	C₂×C₃₂×C₁₁₃	1	2	yes	—
67	C₄	M₆₄×C₁₁₃	1	2	yes	—
68	C₂	C₁₁₃×#1312	1	1	yes	characteristic
69	C₂	C₄×C₃₂×C₁₁₃	1	1	yes	characteristic
70	C₂	C₁₁₃×#1397	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
24. C₈×C₁₁₃	C₃₂	semidirect
32. #7331	C₁₁₃	direct (N × H)
38. C₁₁₃	#7331	direct (N × H)
60. C₈	C₃₂×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
C₈×C₁₆×C₁₁₃	2
#7331	113

Subgroups — C113×#7331 #43275351

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#7331 #43275351