Subgroups — #11928932

Order 1248.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₉	C₂	1	2	yes	maximal
3	#10597664	C₂	1	4	yes	maximal
4	#88124	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
6	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×Dic₃₉	C₂²	1	4	yes	—
8	C₄²×C₁₃	D₃	1	1	yes	characteristic
9	C₄⋊Dic₁₃	—	3	2	no	—
10	#6101	—	3	4	no	—
11	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
12	C₃×C₄×C₁₃	—	2	2	no	—
13	C₃×C₄×C₁₃	Q₈	1	2	yes	—
14	Dic₃₉	—	2	4	no	—
15	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
16	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
17	C₂×Dic₁₃	—	3	4	no	—
18	#870	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
20	C₂×C₃×C₁₃	#41	1	2	yes	—
21	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
22	C₄×C₁₃	—	2	2	no	—
23	C₄×C₁₃	Dic₆	1	2	yes	—
24	Dic₁₃	—	6	4	no	—
25	C₃×C₄²	D₁₃	1	1	yes	characteristic
26	C₄⋊Dic₃	—	13	2	no	—
27	Dic₃⋊C₄	—	13	4	no	—
28	C₃×C₁₃	#125	1	1	yes	characteristic, complemented, Hall
29	#125	—	39	1	no	Sylow
30	C₂×C₁₃	C₂×Dic₆	1	1	yes	characteristic
31	C₂×C₁₃	#235	1	2	yes	—
32	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
33	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
34	C₂×Dic₃	—	13	4	no	—
35	C₄⋊C₄	—	39	4	no	—
36	C₄⋊C₄	—	39	2	no	—
37	C₄²	D₃₉	1	1	yes	characteristic
38	C₁₃	#870	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
40	C₃×C₄	—	2	2	no	—
41	C₃×C₄	Dic₂₆	1	2	yes	—
42	Dic₃	—	26	4	no	—
43	C₂×C₄	—	39	4	no	—
44	C₂×C₄	C₂×D₃₉	1	2	yes	—
45	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
46	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
47	C₂×C₃	#6127	1	2	yes	—
48	C₂²	C₂²×D₃₉	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	78	4	no	—
51	C₄	Dic₇₈	1	2	yes	—
52	C₃	#88124	1	1	yes	characteristic, complemented, Sylow
53	C₂	C₂×Dic₇₈	1	1	yes	characteristic
54	C₂	#10597790	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃₉
commutator, socle, prime radical, cosocle	C₂²×C₃×C₁₃	C₂³
Fitting	C₃×C₄²×C₁₃	C₂
hypercenter	C₄²	D₃₉
hypocenter	C₃×C₁₃	#125
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₄²

Complements

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

N	H ≅ G/N	type
28. C₃×C₁₃	#125	semidirect
38. C₁₃	#870	semidirect
52. C₃	#88124	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₁₃	2
C₄⋊Dic₃₉	2
#10597664	2
#88124	3
#870	13