Subgroups — #103×C₁₃⋊C₃ #11928014

Order 1248.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#103	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	Q₈×C₁₃⋊C₃	—	2	1	no	—
6	Q₈×C₁₃⋊C₃	C₄	1	2	yes	complemented
7	C₂×C₄×C₁₃⋊C₃	—	2	1	no	—
8	C₂×C₄×C₁₃⋊C₃	—	2	1	no	—
9	C₂×C₄×C₁₃⋊C₃	C₂²	1	1	yes	characteristic
10	C₈×C₁₃⋊C₃	—	2	1	no	—
11	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
12	C₂×C₈×C₁₃	C₂×C₃	1	1	yes	characteristic
13	C₁₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
14	C₂²×C₁₃⋊C₃	D₄	1	1	yes	characteristic
15	C₄×C₁₃⋊C₃	—	2	2	no	—
16	C₄×C₁₃⋊C₃	—	4	1	no	—
17	C₄×C₁₃⋊C₃	C₂×C₄	1	1	yes	characteristic
18	C₄×C₁₃⋊C₃	D₄	1	1	yes	characteristic
19	Q₈×C₁₃	—	2	1	no	—
20	Q₈×C₁₃	C₃×C₄	1	2	yes	complemented
21	C₂×C₄×C₁₃	—	2	1	no	—
22	C₂×C₄×C₁₃	—	2	1	no	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
24	C₈×C₁₃	—	2	1	no	—
25	C₃×#103	—	13	1	no	maximal, Hall
26	C₂×C₁₃⋊C₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₁₃⋊C₃	SD₁₆	1	1	yes	characteristic
28	C₂×C₁₃⋊C₃	Q₁₆	1	1	yes	characteristic
29	C₂²×C₁₃	C₃×D₄	1	1	yes	characteristic
30	C₄×C₁₃	—	2	2	no	—
31	C₄×C₁₃	—	4	1	no	—
32	C₄×C₁₃	C₂×C₃×C₄	1	1	yes	characteristic
33	C₄×C₁₃	C₃×D₄	1	1	yes	characteristic
34	C₂×C₃×Q₈	—	13	1	no	—
35	C₂×C₃×C₈	—	13	1	no	—
36	C₃×C₄⋊C₄	—	13	1	no	—
37	C₁₃⋊C₃	#103	1	1	yes	characteristic, direct product factor, Hall
38	#103	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
39	C₂×C₁₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₁₃	C₃×SD₁₆	1	1	yes	characteristic
41	C₂×C₁₃	C₃×Q₁₆	1	1	yes	characteristic
42	C₃×Q₈	—	13	2	no	—
43	C₃×Q₈	—	26	1	no	—
44	C₂×C₃×C₄	—	13	1	no	—
45	C₂×C₃×C₄	—	26	1	no	—
46	C₂×C₃×C₄	—	26	1	no	—
47	C₃×C₈	—	26	1	no	—
48	C₂×Q₈	C₂×C₁₃⋊C₃	1	1	yes	characteristic
49	C₂×C₈	C₂×C₁₃⋊C₃	1	1	yes	characteristic
50	C₄⋊C₄	C₂×C₁₃⋊C₃	1	1	yes	characteristic
51	C₁₃	C₃×#103	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₃	—	13	1	no	—
53	C₃×C₄	—	13	1	no	—
54	C₃×C₄	—	13	1	no	—
55	C₃×C₄	—	26	2	no	—
56	C₃×C₄	—	52	1	no	—
57	Q₈	—	2	1	no	—
58	Q₈	C₄×C₁₃⋊C₃	1	2	yes	complemented
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	C₂²×C₁₃⋊C₃	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₂×C₃	—	13	1	no	—
64	C₂×C₃	—	13	1	no	—
65	C₂×C₃	—	13	1	no	—
66	C₂²	D₄×C₁₃⋊C₃	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	4	1	no	—
69	C₄	C₂×C₄×C₁₃⋊C₃	1	1	yes	characteristic
70	C₄	D₄×C₁₃⋊C₃	1	1	yes	characteristic
71	C₃	—	13	1	no	Sylow
72	C₂	C₂²⋊C₄×C₁₃⋊C₃	1	1	yes	characteristic
73	C₂	SD₁₆×C₁₃⋊C₃	1	1	yes	characteristic
74	C₂	Q₁₆×C₁₃⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×C₁₃⋊C₃
commutator	C₄×C₁₃	C₂×C₃×C₄
Frattini	C₂×C₄	C₂²×C₁₃⋊C₃
Fitting	C₁₃×#103	C₃
socle	C₂²×C₁₃	C₃×D₄
prime radical	C₂²×C₁₃⋊C₃	D₄
cosocle	C₂×C₄×C₁₃	C₂²×C₃
hypercenter	#103	C₁₃⋊C₃
hypocenter	C₁₃	C₃×#103
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
4. C₁₃×#103	C₃	semidirect
6. Q₈×C₁₃⋊C₃	C₄	semidirect
20. Q₈×C₁₃	C₃×C₄	semidirect
37. C₁₃⋊C₃	#103	direct (N × H)
38. #103	C₁₃⋊C₃	direct (N × H)
51. C₁₃	C₃×#103	semidirect
58. Q₈	C₄×C₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₁₃⋊C₃	2
C₂×C₈×C₁₃⋊C₃	2
C₄⋊C₄×C₁₃⋊C₃	2
C₁₃×#103	3
C₃×#103	13

Subgroups — #103×C13⋊C3 #11928014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #103×C₁₃⋊C₃ #11928014