Subgroups — #11928222

Order 1248.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64605	C₂	1	1	yes	maximal, characteristic
2	#10597728	C₂	1	1	yes	maximal, characteristic
3	C₃×#6122	C₂	1	1	yes	maximal, characteristic
4	#88113	—	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	#64605	—	2	1	no	—
9	#64605	—	2	1	no	—
10	C₃⋊#1057	—	2	1	no	—
11	C₃×#1057	—	2	1	no	—
12	C₂×Dic₂₆	—	3	1	no	—
13	#6122	—	3	1	no	—
14	#6122	D₃	1	1	yes	characteristic
15	C₂²×C₃×C₁₃	C₂×C₄	1	1	yes	characteristic
16	Dic₃₉	—	2	1	no	—
17	C₃×Dic₁₃	D₄	1	1	yes	characteristic
18	C₃×Dic₁₃	D₄	1	1	yes	characteristic
19	Dic₃×C₁₃	—	2	1	no	—
20	C₂×C₄×C₁₃	—	3	1	no	—
21	C₂×Dic₁₃	—	3	1	no	—
22	C₂×Dic₁₃	C₂×D₃	1	1	yes	characteristic
23	Dic₂₆	—	6	1	no	—
24	Dic₂₆	—	6	1	no	—
25	#1057	—	2	1	no	—
26	#1057	—	6	1	no	—
27	#824	—	13	1	no	maximal, Hall
28	C₂×C₃×C₁₃	—	2	1	no	—
29	C₂×C₃×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂²×C₁₃	C₄×D₃	1	1	yes	characteristic
31	C₄×C₁₃	—	6	1	no	—
32	Dic₁₃	—	6	1	no	—
33	Dic₁₃	D₁₂	1	1	yes	characteristic
34	Dic₁₃	#67	1	1	yes	characteristic
35	C₂×Dic₆	—	13	1	no	—
36	C₃×M₁₆	—	13	1	no	—
37	#208	—	13	1	no	—
38	C₃×C₁₃	#101	1	1	yes	characteristic, complemented, Hall
39	#101	—	39	1	no	Sylow
40	C₂×C₁₃	—	2	1	no	—
41	C₂×C₁₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
42	C₂×C₃×C₄	—	13	1	no	—
43	C₂×Dic₃	—	13	1	no	—
44	C₂×Dic₃	#261	1	1	yes	characteristic
45	Dic₆	—	26	1	no	—
46	Dic₆	—	26	1	no	—
47	C₃×C₈	—	26	1	no	—
48	C₃⋊C₈	—	26	1	no	—
49	C₂×Q₈	—	39	1	no	—
50	M₁₆	—	13	1	no	—
51	M₁₆	—	39	1	no	—
52	C₁₃	#824	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	C₂×#261	1	1	yes	characteristic
54	C₃×C₄	—	13	1	no	—
55	C₃×C₄	—	13	1	no	—
56	Dic₃	—	2	1	no	—
57	Dic₃	—	26	1	no	—
58	Q₈	—	78	1	no	—
59	Q₈	—	78	1	no	—
60	C₂×C₄	—	3	1	no	—
61	C₂×C₄	—	13	1	no	—
62	C₂×C₄	—	39	1	no	—
63	C₈	—	26	1	no	—
64	C₈	—	78	1	no	—
65	C₂×C₃	—	2	1	no	—
66	C₂×C₃	C₂²⋊#261	1	1	yes	characteristic
67	C₂²	D₃×#261	1	1	yes	characteristic
68	C₄	—	6	1	no	—
69	C₄	—	13	1	no	—
70	C₄	—	13	1	no	—
71	C₄	—	78	1	no	—
72	C₃	#88113	1	1	yes	characteristic, complemented, Sylow
73	C₂	—	2	1	no	—
74	C₂	(C₂×D₃)⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂	(C₂×D₃)⋊#261
commutator, Fitting, prime radical	C₂²×C₃×C₁₃	C₂×C₄
Frattini, hypercenter	C₂²	D₃×#261
socle	C₂×C₃×C₁₃	C₂²⋊C₄
cosocle	C₂×C₃×Dic₁₃	C₂²
hypocenter	C₃×C₁₃	#101
LCS	G ▷ C₂²×C₃×C₁₃ ▷ C₂×C₃×C₁₃ ▷ C₃×C₁₃
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
38. C₃×C₁₃	#101	semidirect
52. C₁₃	#824	semidirect
72. C₃	#88113	semidirect

Maximal subgroups

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

subgroup	index
C₂×#64605	2
#10597728	2
C₃×#6122	2
#88113	3
#824	13