Subgroups — C₁₁₃×#7537 #43275557

Order 28928.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₄×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×#1423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₁₆×C₁₁₃	—	2	1	no	—
5	D₃₂×C₁₁₃	—	2	1	no	—
6	D₃₂×C₁₁₃	C₄	1	2	yes	complemented
7	C₂×C₃₂×C₁₁₃	C₂²	1	1	yes	characteristic
8	#366×C₁₁₃	—	2	1	no	—
9	C₆₄×C₁₁₃	—	2	1	no	—
10	C₂×D₈×C₁₁₃	—	4	1	no	—
11	D₁₆×C₁₁₃	—	2	2	no	—
12	D₁₆×C₁₁₃	—	4	1	no	—
13	C₂×C₁₆×C₁₁₃	D₄	1	1	yes	characteristic
14	#107×C₁₁₃	—	4	1	no	—
15	C₃₂×C₁₁₃	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₁₁₃	D₄	1	1	yes	characteristic
17	C₂×D₄×C₁₁₃	—	8	1	no	—
18	D₈×C₁₁₃	—	4	2	no	—
19	D₈×C₁₁₃	—	8	1	no	—
20	C₂×C₈×C₁₁₃	D₈	1	1	yes	characteristic
21	C₄⋊C₄×C₁₁₃	—	8	1	no	—
22	C₁₆×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₁₁₃	SD₁₆	1	1	yes	characteristic
24	C₂³×C₁₁₃	—	16	1	no	—
25	D₄×C₁₁₃	—	8	2	no	—
26	D₄×C₁₁₃	—	16	1	no	—
27	C₂×C₄×C₁₁₃	—	16	1	no	—
28	C₂×C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
29	C₈×C₁₁₃	#102	1	1	yes	characteristic
30	C₈×C₁₁₃	SD₃₂	1	1	yes	characteristic
31	C₂²×C₁₁₃	—	16	2	no	—
32	C₂²×C₁₁₃	—	32	1	no	—
33	C₂²×C₁₁₃	—	32	1	no	—
34	C₂²×C₁₁₃	D₃₂	1	1	yes	characteristic
35	C₄×C₁₁₃	—	32	1	no	—
36	C₄×C₁₁₃	#357	1	1	yes	characteristic
37	C₄×C₁₁₃	SD₆₄	1	1	yes	characteristic
38	#7537	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₁₁₃	—	32	2	no	—
40	C₂×C₁₁₃	#1415	1	1	yes	characteristic
41	C₂×C₁₁₃	D₆₄	1	1	yes	characteristic
42	C₂×C₁₁₃	SD₁₂₈	1	1	yes	characteristic
43	C₂×D₃₂	C₂×C₁₁₃	1	1	yes	characteristic
44	C₂×C₆₄	C₂×C₁₁₃	1	1	yes	characteristic, complemented
45	#1423	C₂×C₁₁₃	1	1	yes	characteristic, complemented
46	C₁₁₃	#7537	1	1	yes	characteristic, direct product factor, Sylow
47	C₂×D₁₆	—	2	1	no	—
48	D₃₂	—	2	1	no	—
49	D₃₂	C₄×C₁₁₃	1	2	yes	complemented
50	C₂×C₃₂	C₂²×C₁₁₃	1	1	yes	characteristic
51	#366	—	2	1	no	—
52	C₆₄	—	2	1	no	—
53	C₂×D₈	—	4	1	no	—
54	D₁₆	—	2	2	no	—
55	D₁₆	—	4	1	no	—
56	C₂×C₁₆	D₄×C₁₁₃	1	1	yes	characteristic
57	#107	—	4	1	no	—
58	C₃₂	C₂×C₄×C₁₁₃	1	1	yes	characteristic
59	C₃₂	D₄×C₁₁₃	1	1	yes	characteristic
60	C₂×D₄	—	8	1	no	—
61	D₈	—	4	2	no	—
62	D₈	—	8	1	no	—
63	C₂×C₈	D₈×C₁₁₃	1	1	yes	characteristic
64	C₄⋊C₄	—	8	1	no	—
65	C₁₆	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
66	C₁₆	SD₁₆×C₁₁₃	1	1	yes	characteristic
67	C₂³	—	16	1	no	—
68	D₄	—	8	2	no	—
69	D₄	—	16	1	no	—
70	C₂×C₄	—	16	1	no	—
71	C₂×C₄	D₁₆×C₁₁₃	1	1	yes	characteristic
72	C₈	#102×C₁₁₃	1	1	yes	characteristic
73	C₈	SD₃₂×C₁₁₃	1	1	yes	characteristic
74	C₂²	—	16	2	no	—
75	C₂²	—	32	1	no	—
76	C₂²	—	32	1	no	—
77	C₂²	D₃₂×C₁₁₃	1	1	yes	characteristic
78	C₄	—	32	1	no	—
79	C₄	#357×C₁₁₃	1	1	yes	characteristic
80	C₄	SD₆₄×C₁₁₃	1	1	yes	characteristic
81	C₂	—	32	2	no	—
82	C₂	C₁₁₃×#1415	1	1	yes	characteristic
83	C₂	C₁₁₃×D₆₄	1	1	yes	characteristic
84	C₂	C₁₁₃×SD₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	D₃₂
commutator	C₃₂	C₂×C₄×C₁₁₃
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₁₃
prime radical	C₂×D₃₂×C₁₁₃	C₂
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
2. C₂×C₆₄×C₁₁₃	C₂	semidirect
3. C₁₁₃×#1423	C₂	semidirect
6. D₃₂×C₁₁₃	C₄	semidirect
38. #7537	C₁₁₃	direct (N × H)
44. C₂×C₆₄	C₂×C₁₁₃	semidirect
45. #1423	C₂×C₁₁₃	semidirect
46. C₁₁₃	#7537	direct (N × H)
49. D₃₂	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×D₃₂×C₁₁₃	2
C₂×C₆₄×C₁₁₃	2
C₁₁₃×#1423	2
#7537	113

Subgroups — C113×#7537 #43275557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#7537 #43275557