Subgroups — #11928372

Order 1248.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊#1057	C₂	1	2	yes	maximal, complemented
3	#88111	—	3	1	no	maximal, Hall
4	C₂²×C₃×D₁₃	C₄	1	1	yes	characteristic
5	C₂×C₃×C₄×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
7	C₃×C₄×D₁₃	—	2	2	no	—
8	C₃⋊#1057	—	2	2	no	—
9	C₂×C₄×D₁₃	D₃	1	1	yes	characteristic
10	C₂×#1057	—	3	2	no	—
11	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₃×D₁₃	—	2	1	no	—
13	C₂×C₃×D₁₃	—	2	1	no	—
14	C₂×C₃×D₁₃	C₈	1	2	yes	complemented
15	C₃×C₄×C₁₃	—	2	1	no	—
16	C₃×Dic₁₃	D₄	1	2	yes	—
17	C₂²×D₁₃	Dic₃	1	1	yes	characteristic
18	C₂×C₄×C₁₃	Dic₃	1	1	yes	characteristic
19	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
20	C₄×D₁₃	—	2	2	no	—
21	#1057	—	6	2	no	—
22	#830	—	13	1	no	maximal, Hall
23	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₃×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₂×C₃×C₁₃	M₁₆	1	1	yes	characteristic
26	C₃×D₁₃	—	2	2	no	—
27	C₂²×C₁₃	C₂×Dic₃	1	1	yes	characteristic
28	C₂×D₁₃	—	2	1	no	—
29	C₂×D₁₃	—	2	1	no	—
30	C₂×D₁₃	C₃⋊C₈	1	2	yes	complemented
31	C₄×C₁₃	—	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	C₂×C₃⋊C₈	1	1	yes	characteristic
38	C₂×C₁₃	#208	1	1	yes	characteristic
39	C₂×C₁₃	#217	1	1	yes	characteristic
40	D₁₃	—	2	2	no	—
41	C₂³×C₃	—	13	1	no	—
42	C₂×C₃×C₄	—	13	1	no	—
43	C₂×C₃×C₄	—	26	2	no	—
44	C₂×C₃×C₄	#261	1	1	yes	characteristic
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	—	13	2	no	—
50	C₂²×C₃	—	26	1	no	—
51	C₂²×C₃	—	26	1	no	—
52	C₂²×C₃	C₂×#261	1	1	yes	characteristic
53	C₃×C₄	—	2	1	no	—
54	C₃×C₄	—	13	2	no	—
55	C₂³	—	13	1	no	—
56	C₂×C₄	—	13	1	no	—
57	C₂×C₄	—	26	2	no	—
58	C₂×C₄	C₃⋊#261	1	1	yes	characteristic
59	C₈	—	78	2	no	—
60	C₂×C₃	—	26	2	no	—
61	C₂×C₃	D₁₃⋊C₈	1	1	yes	characteristic
62	C₂×C₃	#6118	1	1	yes	characteristic
63	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
64	C₂²	—	13	2	no	—
65	C₂²	—	26	1	no	—
66	C₂²	—	26	1	no	—
67	C₂²	C₂×C₃⋊#261	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	13	2	no	—
70	C₃	#88111	1	1	yes	characteristic, complemented, Sylow
71	C₂	—	26	2	no	—
72	C₂	D₁₃⋊(C₃⋊C₈)	1	1	yes	characteristic
73	C₂	#10597724	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	C₂×C₃×C₄×C₁₃	C₄
socle	C₂²×C₃×C₁₃	C₂×C₄
prime radical	C₂²×C₃×D₁₃	C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypercenter	C₂×C₄	C₃⋊#261
hypocenter	C₃×C₁₃	C₂²⋊C₈
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
2. C₂×C₃⋊#1057	C₂	semidirect
14. C₂×C₃×D₁₃	C₈	semidirect
30. C₂×D₁₃	C₃⋊C₈	semidirect
35. C₃×C₁₃	C₂²⋊C₈	semidirect
48. C₁₃	#830	semidirect
70. C₃	#88111	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×D₁₃	2
C₂×C₃⋊#1057	2
#88111	3
#830	13