Subgroups — C₁₁₃×#1361 #28386157

Order 14464.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#493×C₁₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#335×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×C₁₁₃	—	2	1	no	—
5	C₂×D₈×C₁₁₃	C₄	1	2	yes	—
6	#127×C₁₁₃	—	2	1	no	—
7	C₂×C₁₆×C₁₁₃	—	2	1	no	—
8	C₄⋊C₈×C₁₁₃	—	2	1	no	—
9	C₄×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
10	C₂×D₄×C₁₁₃	—	2	2	no	—
11	C₂×D₄×C₁₁₃	—	4	1	no	—
12	C₂×D₄×C₁₁₃	—	4	1	no	—
13	D₈×C₁₁₃	—	4	2	no	—
14	D₈×C₁₁₃	—	4	1	no	—
15	D₈×C₁₁₃	—	4	1	no	—
16	C₂×C₈×C₁₁₃	—	4	1	no	—
17	C₂×C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂×C₈×C₁₁₃	D₄	1	1	yes	characteristic
19	C₄²×C₁₁₃	D₄	1	1	yes	characteristic
20	C₁₆×C₁₁₃	—	4	1	no	—
21	C₂³×C₁₁₃	—	4	2	no	—
22	D₄×C₁₁₃	—	4	2	no	—
23	D₄×C₁₁₃	—	4	2	no	—
24	D₄×C₁₁₃	—	8	2	no	—
25	D₄×C₁₁₃	—	8	1	no	—
26	D₄×C₁₁₃	—	8	1	no	—
27	C₂×C₄×C₁₁₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₁₃	D₈	1	1	yes	characteristic
29	C₂×C₄×C₁₁₃	SD₁₆	1	1	yes	characteristic
30	C₈×C₁₁₃	—	2	1	no	—
31	C₈×C₁₁₃	—	8	1	no	—
32	C₈×C₁₁₃	D₈	1	1	yes	characteristic
33	C₈×C₁₁₃	SD₁₆	1	1	yes	characteristic
34	C₂²×C₁₁₃	—	8	2	no	—
35	C₂²×C₁₁₃	—	8	2	no	—
36	C₂²×C₁₁₃	—	8	2	no	—
37	C₂²×C₁₁₃	#102	1	1	yes	characteristic
38	C₄×C₁₁₃	—	2	1	no	—
39	C₄×C₁₁₃	#100	1	1	yes	characteristic
40	C₄×C₁₁₃	#102	1	1	yes	characteristic
41	C₄×C₁₁₃	D₁₆	1	1	yes	characteristic
42	C₄×C₁₁₃	SD₃₂	1	1	yes	characteristic
43	C₂×C₁₁₃	—	16	2	no	—
44	C₂×C₁₁₃	#331	1	1	yes	characteristic
45	C₂×C₁₁₃	#357	1	1	yes	characteristic
46	C₂×C₁₁₃	#361	1	1	yes	characteristic
47	#1361	C₁₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₁₁₃	#1361	1	1	yes	characteristic, direct product factor, Sylow
49	#493	C₂×C₁₁₃	1	1	yes	characteristic
50	C₄⋊C₁₆	C₂×C₁₁₃	1	1	yes	characteristic, complemented
51	#335	C₂×C₁₁₃	1	1	yes	characteristic, complemented
52	C₂×D₈	—	2	1	no	—
53	C₂×D₈	C₄×C₁₁₃	1	2	yes	—
54	#127	—	2	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₄⋊C₈	—	2	1	no	—
57	C₄×C₈	C₂²×C₁₁₃	1	1	yes	characteristic
58	C₂×D₄	—	2	2	no	—
59	C₂×D₄	—	4	1	no	—
60	C₂×D₄	—	4	1	no	—
61	D₈	—	4	2	no	—
62	D₈	—	4	1	no	—
63	D₈	—	4	1	no	—
64	C₂×C₈	—	4	1	no	—
65	C₂×C₈	C₂×C₄×C₁₁₃	1	1	yes	characteristic
66	C₂×C₈	D₄×C₁₁₃	1	1	yes	characteristic
67	C₄²	D₄×C₁₁₃	1	1	yes	characteristic
68	C₁₆	—	4	1	no	—
69	C₂³	—	4	2	no	—
70	D₄	—	4	2	no	—
71	D₄	—	4	2	no	—
72	D₄	—	8	2	no	—
73	D₄	—	8	1	no	—
74	D₄	—	8	1	no	—
75	C₂×C₄	C₂²⋊C₄×C₁₁₃	1	1	yes	characteristic
76	C₂×C₄	D₈×C₁₁₃	1	1	yes	characteristic
77	C₂×C₄	SD₁₆×C₁₁₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	8	1	no	—
80	C₈	D₈×C₁₁₃	1	1	yes	characteristic
81	C₈	SD₁₆×C₁₁₃	1	1	yes	characteristic
82	C₂²	—	8	2	no	—
83	C₂²	—	8	2	no	—
84	C₂²	—	8	2	no	—
85	C₂²	#102×C₁₁₃	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	#100×C₁₁₃	1	1	yes	characteristic
88	C₄	#102×C₁₁₃	1	1	yes	characteristic
89	C₄	D₁₆×C₁₁₃	1	1	yes	characteristic
90	C₄	SD₃₂×C₁₁₃	1	1	yes	characteristic
91	C₂	—	16	2	no	—
92	C₂	#331×C₁₁₃	1	1	yes	characteristic
93	C₂	#357×C₁₁₃	1	1	yes	characteristic
94	C₂	#361×C₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁₃	#102
commutator	C₂×C₈	C₂×C₄×C₁₁₃
Frattini, cosocle	C₄×C₈	C₂²×C₁₁₃
prime radical	#493×C₁₁₃	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁₃ ◁ C₄²×C₁₁₃ ◁ C₄×C₈×C₁₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄⋊C₁₆×C₁₁₃	C₂	semidirect
3. #335×C₁₁₃	C₂	semidirect
47. #1361	C₁₁₃	direct (N × H)
48. C₁₁₃	#1361	direct (N × H)
50. C₄⋊C₁₆	C₂×C₁₁₃	semidirect
51. #335	C₂×C₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
#493×C₁₁₃	2
C₄⋊C₁₆×C₁₁₃	2
#335×C₁₁₃	2
#1361	113

Subgroups — C113×#1361 #28386157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁₃×#1361 #28386157