Subgroups — D₁₃⋊(#41⋊C₃) #11929163

Order 1248.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃⋊SL(2,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	#10597713	C₂	1	1	yes	maximal, characteristic, complemented
4	#41×D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	Q₈⋊(C₁₃⋊C₃)	C₂²	1	1	yes	characteristic, complemented
6	C₄×D₁₃⋊C₃	—	4	1	no	maximal
7	C₁₃×#41	C₂×C₃	1	1	yes	characteristic, complemented
8	#6131	C₂×C₃	1	1	yes	characteristic, complemented
9	Q₈×D₁₃	C₂×C₃	1	1	yes	characteristic
10	#6129	—	3	1	no	—
11	D₄×D₁₃	—	3	1	no	—
12	#6127	—	3	1	no	—
13	C₂×C₄×D₁₃	—	3	1	no	—
14	C₂×D₁₃⋊C₃	—	4	1	no	—
15	C₄×C₁₃⋊C₃	—	4	1	no	—
16	Dic₁₃⋊C₃	—	4	1	no	—
17	C₂²×D₁₃	—	3	1	no	—
18	Q₈×C₁₃	C₂²×C₃	1	1	yes	characteristic
19	D₄×C₁₃	—	3	1	no	—
20	C₂×C₄×C₁₃	—	3	1	no	—
21	C₂²⋊D₁₃	—	3	2	no	—
22	C₂×Dic₁₃	—	3	1	no	—
23	D₅₂	—	3	1	no	—
24	C₄×D₁₃	—	3	1	no	—
25	C₄×D₁₃	—	3	1	no	—
26	C₄×D₁₃	—	3	1	no	—
27	C₄×D₁₃	A₄	1	1	yes	characteristic
28	Dic₂₆	—	3	1	no	—
29	C₂×#41⋊C₃	—	13	1	no	maximal, Hall
30	C₂×C₁₃⋊C₃	—	4	1	no	—
31	D₁₃⋊C₃	—	4	2	no	—
32	C₂²×C₁₃	—	3	1	no	—
33	C₂×D₁₃	—	3	1	no	—
34	C₂×D₁₃	—	6	2	no	—
35	C₂×D₁₃	C₂×A₄	1	1	yes	characteristic
36	C₄×C₁₃	—	3	1	no	—
37	C₄×C₁₃	C₂×A₄	1	1	yes	characteristic
38	Dic₁₃	—	3	1	no	—
39	Dic₁₃	C₂×A₄	1	1	yes	characteristic
40	#41⋊C₃	—	13	1	no	—
41	#41⋊C₃	—	13	1	no	—
42	C₂×SL(2,𝔽₃)	—	13	1	no	—
43	C₁₃⋊C₃	—	4	1	no	Hall
44	C₂×#41	—	13	1	no	Sylow
45	C₂×C₁₃	—	6	1	no	—
46	C₂×C₁₃	C₂²×A₄	1	1	yes	characteristic
47	D₁₃	—	6	1	no	—
48	D₁₃	#41⋊C₃	1	2	yes	complemented
49	C₂×C₃×C₄	—	52	1	no	—
50	SL(2,𝔽₃)	—	13	1	no	—
51	#41	—	13	1	no	—
52	#41	—	39	1	no	—
53	#41	—	39	1	no	—
54	#41	D₁₃⋊C₃	1	1	yes	characteristic, complemented
55	C₂×Q₈	—	13	1	no	—
56	C₂×D₄	—	39	1	no	—
57	C₂²×C₄	—	39	1	no	—
58	C₁₃	C₂×#41⋊C₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₃	—	52	1	no	—
60	C₃×C₄	—	52	1	no	—
61	C₃×C₄	—	52	1	no	—
62	C₂³	—	39	1	no	—
63	Q₈	—	39	1	no	—
64	Q₈	C₂×D₁₃⋊C₃	1	1	yes	characteristic
65	D₄	—	3	1	no	—
66	D₄	—	39	1	no	—
67	D₄	—	39	2	no	—
68	C₂×C₄	—	3	1	no	—
69	C₂×C₄	—	13	1	no	—
70	C₂×C₄	—	39	1	no	—
71	C₂×C₄	—	39	1	no	—
72	C₂×C₄	—	39	1	no	—
73	C₂×C₄	—	39	1	no	—
74	C₂×C₃	—	52	2	no	—
75	C₂×C₃	—	52	1	no	—
76	C₂²	—	3	1	no	—
77	C₂²	—	13	1	no	—
78	C₂²	—	39	1	no	—
79	C₂²	—	78	2	no	—
80	C₄	—	3	1	no	—
81	C₄	—	13	1	no	—
82	C₄	—	39	1	no	—
83	C₄	D₁₃⋊A₄	1	1	yes	characteristic
84	C₃	—	52	1	no	Sylow
85	C₂	—	6	1	no	—
86	C₂	—	13	2	no	—
87	C₂	—	78	1	no	—
88	C₂	C₂×D₁₃⋊A₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₁₃⋊A₄
commutator, cosocle, hypocenter	Q₈×C₁₃	C₂²×C₃
Frattini	C₂	C₂×D₁₃⋊A₄
Fitting	C₁₃×#41	C₂×C₃
socle	C₂×C₁₃	C₂²×A₄
LCS	G ▷ Q₈×C₁₃
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
1. #41⋊(C₁₃⋊C₃)	C₂	semidirect
2. D₁₃⋊SL(2,𝔽₃)	C₂	semidirect
3. #10597713	C₂	semidirect
4. #41×D₁₃	C₃	semidirect
5. Q₈⋊(C₁₃⋊C₃)	C₂²	semidirect
7. C₁₃×#41	C₂×C₃	semidirect
8. #6131	C₂×C₃	semidirect
48. D₁₃	#41⋊C₃	semidirect
54. #41	D₁₃⋊C₃	semidirect
58. C₁₃	C₂×#41⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
#41⋊(C₁₃⋊C₃)	2
D₁₃⋊SL(2,𝔽₃)	2
#10597713	2
#41×D₁₃	3
C₄×D₁₃⋊C₃	4
C₂×#41⋊C₃	13

Subgroups — D13⋊(#41⋊C3) #11929163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃⋊(#41⋊C₃) #11929163