Subgroups — #11928371

Order 1248.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#1057	C₂	1	2	yes	maximal
2	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#88110	—	3	1	no	maximal, Hall
4	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₁₃	C₄	1	1	yes	characteristic
6	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₃⋊#1057	C₄	1	4	yes	complemented
8	C₂×#1057	—	3	2	no	—
9	C₄×Dic₁₃	D₃	1	1	yes	characteristic
10	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₃×C₄×C₁₃	—	2	1	no	—
12	C₃×Dic₁₃	—	2	1	no	—
13	C₃×Dic₁₃	C₂×C₄	1	2	yes	—
14	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
15	C₂×Dic₁₃	Dic₃	1	1	yes	characteristic
16	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
17	#1057	—	3	4	no	—
18	#803	—	13	1	no	maximal, Hall
19	C₂×C₃×C₁₃	C₄²	1	1	yes	characteristic
20	C₂×C₃×C₁₃	M₁₆	1	1	yes	characteristic
21	C₂×C₃×C₁₃	M₁₆	1	1	yes	characteristic
22	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
23	C₄×C₁₃	—	2	1	no	—
24	Dic₁₃	—	2	1	no	—
25	Dic₁₃	C₄×D₃	1	2	yes	—
26	C₃×C₄²	—	13	1	no	—
27	C₂×C₃⋊C₈	—	13	2	no	—
28	C₃×C₁₃	#97	1	1	yes	characteristic, complemented, Hall
29	#97	—	39	1	no	Sylow
30	C₂×C₁₃	#208	1	1	yes	characteristic
31	C₂×C₁₃	#208	1	1	yes	characteristic
32	C₂×C₁₃	C₄×Dic₃	1	1	yes	characteristic
33	C₂×C₃×C₄	—	13	1	no	—
34	C₂×C₃×C₄	—	13	1	no	—
35	C₂×C₃×C₄	#261	1	1	yes	characteristic
36	C₃⋊C₈	—	13	4	no	—
37	C₂×C₈	—	39	2	no	—
38	C₄²	—	13	1	no	—
39	C₁₃	#803	1	1	yes	characteristic, complemented, Sylow
40	C₂²×C₃	C₂×#261	1	1	yes	characteristic
41	C₃×C₄	—	2	1	no	—
42	C₃×C₄	—	13	2	no	—
43	C₃×C₄	—	26	1	no	—
44	C₂×C₄	—	13	1	no	—
45	C₂×C₄	—	13	1	no	—
46	C₂×C₄	C₃⋊#261	1	1	yes	characteristic
47	C₈	—	39	4	no	—
48	C₂×C₃	#6118	1	1	yes	characteristic
49	C₂×C₃	C₄×#261	1	1	yes	characteristic
50	C₂×C₃	#6122	1	1	yes	characteristic
51	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
52	C₄	—	2	1	no	—
53	C₄	—	13	2	no	—
54	C₄	—	26	1	no	—
55	C₃	#88110	1	1	yes	characteristic, complemented, Sylow
56	C₂	#10597724	1	1	yes	characteristic
57	C₂	C₄×C₃⋊#261	1	1	yes	characteristic
58	C₂	#10597728	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×C₃⋊#261
commutator	C₂×C₃×C₁₃	C₄²
Fitting	C₂×C₃×C₄×C₁₃	C₄
socle, prime radical	C₂²×C₃×C₁₃	C₂×C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypercenter	C₂×C₄	C₃⋊#261
hypocenter	C₃×C₁₃	#97
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
7. C₃⋊#1057	C₄	semidirect
28. C₃×C₁₃	#97	semidirect
39. C₁₃	#803	semidirect
55. C₃	#88110	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃⋊#1057	2
C₃×C₄×Dic₁₃	2
#88110	3
#803	13