Subgroups — #11928224

Order 1248.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊#1057	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#1057	C₂	1	1	yes	maximal, characteristic
3	Dic₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
4	#88112	—	3	1	no	maximal, Hall
5	C₂×Dic₃₉	C₄	1	1	yes	characteristic
6	C₂×Dic₃×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
8	C₃⋊#1057	—	2	1	no	—
9	C₃×#1057	—	2	1	no	—
10	C₂×#1057	—	3	1	no	—
11	C₂×#1057	D₃	1	1	yes	characteristic
12	C₄×Dic₁₃	—	3	1	no	—
13	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
14	Dic₃₉	C₈	1	2	yes	complemented
15	C₃×Dic₁₃	D₄	1	1	yes	characteristic
16	C₃×Dic₁₃	Q₈	1	1	yes	characteristic
17	Dic₃×C₁₃	—	2	1	no	—
18	C₂×C₄×C₁₃	—	3	1	no	—
19	C₂×Dic₁₃	—	3	1	no	—
20	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
21	#1057	—	2	1	no	—
22	#1057	—	6	1	no	—
23	Dic₃⋊C₈	—	13	1	no	maximal, Hall
24	C₂×C₃×C₁₃	C₄⋊C₄	1	1	yes	characteristic
25	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₃×C₁₃	M₁₆	1	1	yes	characteristic
27	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
28	C₄×C₁₃	—	6	1	no	—
29	Dic₁₃	—	3	2	no	—
30	Dic₁₃	Dic₆	1	1	yes	characteristic
31	Dic₁₃	#67	1	1	yes	characteristic
32	C₂×C₃×C₈	—	13	1	no	—
33	C₄×Dic₃	—	13	1	no	—
34	C₂×C₃⋊C₈	—	13	1	no	—
35	C₃×C₁₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Hall
36	C₄⋊C₈	—	39	1	no	Sylow
37	C₂×C₁₃	D₃×C₈	1	1	yes	characteristic
38	C₂×C₁₃	ΓL(1,𝔽₂₅)	1	1	yes	characteristic
39	C₂×C₁₃	Dic₃⋊C₄	1	1	yes	characteristic
40	C₂×C₃×C₄	—	13	1	no	—
41	C₂×Dic₃	—	13	1	no	—
42	C₂×Dic₃	#261	1	1	yes	characteristic
43	C₃×C₈	—	26	1	no	—
44	C₃⋊C₈	—	26	1	no	—
45	C₂×C₈	—	13	1	no	—
46	C₂×C₈	—	39	1	no	—
47	C₄²	—	39	1	no	—
48	C₁₃	Dic₃⋊C₈	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	C₂×#261	1	1	yes	characteristic
50	C₃×C₄	—	13	1	no	—
51	C₃×C₄	—	13	1	no	—
52	Dic₃	—	2	1	no	—
53	Dic₃	—	13	2	no	—
54	C₂×C₄	—	3	1	no	—
55	C₂×C₄	—	13	1	no	—
56	C₂×C₄	—	39	1	no	—
57	C₈	—	26	1	no	—
58	C₈	—	78	1	no	—
59	C₂×C₃	D₁₃⋊C₈	1	1	yes	characteristic
60	C₂×C₃	C₄⋊#261	1	1	yes	characteristic
61	C₂×C₃	#6122	1	1	yes	characteristic
62	C₂²	D₃×#261	1	1	yes	characteristic
63	C₄	—	6	1	no	—
64	C₄	—	13	1	no	—
65	C₄	—	13	1	no	—
66	C₄	—	39	2	no	—
67	C₃	#88112	1	1	yes	characteristic, complemented, Sylow
68	C₂	Dic₃⋊#261	1	1	yes	characteristic
69	C₂	#10597691	1	1	yes	characteristic
70	C₂	#10597692	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂²	D₃×#261
commutator	C₂×C₃×C₁₃	C₂×C₈
Fitting, socle, prime radical	C₂²×C₃×C₁₃	C₂×C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypocenter	C₃×C₁₃	C₄⋊C₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
14. Dic₃₉	C₈	semidirect
35. C₃×C₁₃	C₄⋊C₈	semidirect
48. C₁₃	Dic₃⋊C₈	semidirect
67. C₃	#88112	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
C₂×C₃×#1057	2
Dic₃×Dic₁₃	2
#88112	3
Dic₃⋊C₈	13