Subgroups — #11928382

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Dic₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1057	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#1057	—	3	1	no	maximal, Hall
4	C₂³×C₃×C₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×Dic₁₃	—	2	2	no	—
6	C₂×C₃×Dic₁₃	C₄	1	1	yes	characteristic
7	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
8	C₃⋊#1057	—	2	2	no	—
9	C₂²×Dic₁₃	D₃	1	1	yes	characteristic
10	C₂×#1057	—	3	2	no	—
11	C₂²×C₃×C₁₃	—	2	1	no	—
12	C₂²×C₃×C₁₃	—	2	1	no	—
13	C₂²×C₃×C₁₃	C₈	1	2	yes	complemented
14	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
15	C₃×Dic₁₃	—	2	1	no	—
16	C₃×Dic₁₃	D₄	1	2	yes	—
17	C₂³×C₁₃	Dic₃	1	1	yes	characteristic
18	C₂×Dic₁₃	—	2	2	no	—
19	C₂×Dic₁₃	Dic₃	1	1	yes	characteristic
20	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
21	#1057	—	6	2	no	—
22	#830	—	13	1	no	maximal, Hall
23	C₂×C₃×C₁₃	—	2	2	no	—
24	C₂×C₃×C₁₃	C₂²⋊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	—	2	1	no	—
28	C₂²×C₁₃	—	2	1	no	—
29	C₂²×C₁₃	C₃⋊C₈	1	2	yes	complemented
30	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
31	Dic₁₃	—	2	1	no	—
32	Dic₁₃	#67	1	2	yes	—
33	C₂²×C₃×C₄	—	13	1	no	—
34	C₂×C₃⋊C₈	—	13	2	no	—
35	C₃×C₁₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Hall
36	C₂²⋊C₈	—	39	1	no	Sylow
37	C₂×C₁₃	—	2	2	no	—
38	C₂×C₁₃	C₂×C₃⋊C₈	1	1	yes	characteristic
39	C₂×C₁₃	#208	1	1	yes	characteristic
40	C₂×C₁₃	#217	1	1	yes	characteristic
41	C₂³×C₃	#261	1	1	yes	characteristic
42	C₂×C₃×C₄	—	13	1	no	—
43	C₂×C₃×C₄	—	13	1	no	—
44	C₂×C₃×C₄	—	26	2	no	—
45	C₃⋊C₈	—	26	2	no	—
46	C₂²×C₄	—	13	1	no	—
47	C₂×C₈	—	39	2	no	—
48	C₁₃	#830	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	2	1	no	—
51	C₂²×C₃	#1057	1	2	yes	complemented
52	C₂²×C₃	C₂×#261	1	1	yes	characteristic
53	C₃×C₄	—	13	2	no	—
54	C₃×C₄	—	26	1	no	—
55	C₂³	C₃⋊#261	1	1	yes	characteristic
56	C₂×C₄	—	13	1	no	—
57	C₂×C₄	—	13	1	no	—
58	C₂×C₄	—	26	2	no	—
59	C₈	—	78	2	no	—
60	C₂×C₃	—	2	2	no	—
61	C₂×C₃	C₂×#1057	1	1	yes	characteristic
62	C₂×C₃	#6122	1	1	yes	characteristic
63	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
64	C₂²	—	2	1	no	—
65	C₂²	—	2	1	no	—
66	C₂²	C₃⋊#1057	1	2	yes	complemented
67	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
68	C₄	—	13	2	no	—
69	C₄	—	26	1	no	—
70	C₃	C₂²⋊#1057	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	2	2	no	—
72	C₂	C₂×C₃⋊#1057	1	1	yes	characteristic
73	C₂	#10597728	1	1	yes	characteristic
74	C₂	#10597729	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×C₃⋊#261
commutator	C₂×C₃×C₁₃	C₂×C₈
Fitting, prime radical	C₂³×C₃×C₁₃	C₄
socle	C₂²×C₃×C₁₃	C₂×C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypercenter	C₂³	C₃⋊#261
hypocenter	C₃×C₁₃	C₂²⋊C₈
LCS	G ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂² ◁ C₂³

Complements

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

N	H ≅ G/N	type
2. C₂×C₃⋊#1057	C₂	semidirect
13. C₂²×C₃×C₁₃	C₈	semidirect
29. C₂²×C₁₃	C₃⋊C₈	semidirect
35. C₃×C₁₃	C₂²⋊C₈	semidirect
48. C₁₃	#830	semidirect
51. C₂²×C₃	#1057	semidirect
66. C₂²	C₃⋊#1057	semidirect
70. C₃	C₂²⋊#1057	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×Dic₁₃	2
C₂×C₃⋊#1057	2
C₂²⋊#1057	3
#830	13