Subgroups — #11928136

Order 1248.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₈	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#10597662	C₂	1	1	yes	maximal, characteristic
4	#88064	—	3	1	no	maximal, Hall
5	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	C₂×Dic₃₉	C₄	1	2	yes	—
7	Dic₇₈	—	2	1	no	—
8	Dic₇₈	—	2	1	no	—
9	C₃×C₈×C₁₃	—	2	1	no	—
10	C₃⋊#1055	—	2	1	no	—
11	C₂×Dic₂₆	—	3	1	no	—
12	C₁₃×M₁₆	D₃	1	1	yes	characteristic
13	#6099	—	3	1	no	—
14	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
16	C₃×C₄×C₁₃	D₄	1	1	yes	characteristic
17	Dic₃₉	—	2	2	no	—
18	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
19	C₂×Dic₁₃	—	3	2	no	—
20	Dic₂₆	—	6	1	no	—
21	Dic₂₆	—	6	1	no	—
22	C₈×C₁₃	—	2	1	no	—
23	#1055	—	6	1	no	—
24	#824	—	13	1	no	maximal, Hall
25	C₂×C₃×C₁₃	—	2	1	no	—
26	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
28	C₄×C₁₃	D₁₂	1	1	yes	characteristic
29	C₄×C₁₃	#67	1	1	yes	characteristic
30	Dic₁₃	—	6	2	no	—
31	C₂×Dic₆	—	13	1	no	—
32	C₃×M₁₆	D₁₃	1	1	yes	characteristic
33	#208	—	13	1	no	—
34	C₃×C₁₃	#101	1	1	yes	characteristic, complemented, Hall
35	#101	—	39	1	no	Sylow
36	C₂×C₁₃	—	2	1	no	—
37	C₂×C₁₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
38	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
39	C₂×Dic₃	—	13	2	no	—
40	Dic₆	—	26	1	no	—
41	Dic₆	—	26	1	no	—
42	C₃×C₈	—	2	1	no	—
43	C₃⋊C₈	—	26	1	no	—
44	C₂×Q₈	—	39	1	no	—
45	M₁₆	—	39	1	no	—
46	M₁₆	D₃₉	1	1	yes	characteristic
47	C₁₃	#824	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₃	C₄×D₁₃	1	1	yes	characteristic
49	C₃×C₄	D₅₂	1	1	yes	characteristic
50	C₃×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
51	Dic₃	—	26	2	no	—
52	Q₈	—	78	1	no	—
53	Q₈	—	78	1	no	—
54	C₂×C₄	—	39	2	no	—
55	C₂×C₄	C₂×D₃₉	1	1	yes	characteristic
56	C₈	—	2	1	no	—
57	C₈	—	78	1	no	—
58	C₂×C₃	—	2	1	no	—
59	C₂×C₃	#6103	1	1	yes	characteristic
60	C₂²	C₄×D₃₉	1	1	yes	characteristic
61	C₄	—	78	2	no	—
62	C₄	D₁₅₆	1	1	yes	characteristic
63	C₄	#64625	1	1	yes	characteristic
64	C₃	#88064	1	1	yes	characteristic, complemented, Sylow
65	C₂	—	2	1	no	—
66	C₂	#10597666	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597666
commutator, prime radical	C₂²×C₃×C₁₃	C₂×C₄
Frattini	C₂×C₄	C₂×D₃₉
Fitting	C₃×C₁₃×M₁₆	C₂
socle	C₂×C₃×C₁₃	C₂²⋊C₄
cosocle	C₂×C₃×C₄×C₁₃	C₂²
hypercenter	M₁₆	D₃₉
hypocenter	C₃×C₁₃	#101
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
34. C₃×C₁₃	#101	semidirect
47. C₁₃	#824	semidirect
64. C₃	#88064	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₇₈	2
C₃×C₁₃×M₁₆	2
#10597662	2
#88064	3
#824	13