Subgroups — C₃×#88144 #11928781

Order 1248.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄⋊Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄⋊Dic₁₃	C₂	1	2	yes	maximal
4	C₃×#6101	C₂	1	2	yes	maximal
5	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	#88144	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
11	C₂×C₃×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
13	C₄⋊Dic₁₃	C₂×C₃	1	2	yes	—
14	C₄⋊Dic₁₃	C₂×C₃	1	1	yes	characteristic
15	#6101	C₂×C₃	1	2	yes	—
16	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic
17	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
18	C₃×C₄×C₁₃	—	2	2	no	—
19	C₃×C₄×C₁₃	Q₈	1	2	yes	—
20	C₃×Dic₁₃	—	2	1	no	—
21	C₃×Dic₁₃	—	2	2	no	—
22	C₃×Dic₁₃	—	2	1	no	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
24	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
25	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
26	C₂×Dic₁₃	C₂²×C₃	1	1	yes	characteristic
27	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
28	C₃×#125	—	13	1	no	maximal, Hall
29	C₂×C₃×C₁₃	C₂×Q₈	1	1	yes	characteristic
30	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
31	C₂×C₃×C₁₃	#41	1	1	yes	characteristic
32	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
33	C₄×C₁₃	—	2	2	no	—
34	C₄×C₁₃	C₃×Q₈	1	2	yes	—
35	Dic₁₃	—	2	1	no	—
36	Dic₁₃	—	2	1	no	—
37	Dic₁₃	—	2	2	no	—
38	C₃×C₄⋊C₄	—	13	2	no	—
39	C₃×C₄⋊C₄	—	13	2	no	—
40	C₃×C₄⋊C₄	—	13	1	no	—
41	C₃×C₄⋊C₄	D₁₃	1	1	yes	characteristic
42	C₃×C₄²	—	13	1	no	—
43	C₃×C₁₃	#125	1	1	yes	characteristic, complemented, Hall
44	#125	—	13	1	no	Sylow
45	C₂×C₁₃	C₂×C₃×Q₈	1	1	yes	characteristic
46	C₂×C₁₃	C₃×#41	1	1	yes	characteristic
47	C₂×C₁₃	C₃×#41	1	1	yes	characteristic
48	C₂×C₃×C₄	—	13	1	no	—
49	C₂×C₃×C₄	—	13	1	no	—
50	C₂×C₃×C₄	—	13	2	no	—
51	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
52	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
53	C₄⋊C₄	—	13	2	no	—
54	C₄⋊C₄	—	13	2	no	—
55	C₄⋊C₄	—	13	1	no	—
56	C₄⋊C₄	C₃×D₁₃	1	1	yes	characteristic
57	C₄²	—	13	1	no	—
58	C₁₃	C₃×#125	1	1	yes	characteristic, complemented, Sylow
59	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
60	C₃×C₄	—	2	2	no	—
61	C₃×C₄	—	26	1	no	—
62	C₃×C₄	—	26	1	no	—
63	C₃×C₄	—	26	2	no	—
64	C₃×C₄	Dic₂₆	1	2	yes	—
65	C₂×C₄	—	13	1	no	—
66	C₂×C₄	—	13	1	no	—
67	C₂×C₄	—	13	2	no	—
68	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
69	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
70	C₂×C₃	C₂×Dic₂₆	1	1	yes	characteristic
71	C₂×C₃	#6129	1	1	yes	characteristic
72	C₂×C₃	#6131	1	1	yes	characteristic
73	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	26	1	no	—
76	C₄	—	26	1	no	—
77	C₄	—	26	2	no	—
78	C₄	C₃×Dic₂₆	1	2	yes	—
79	C₃	#88144	1	1	yes	characteristic, direct product factor, Sylow
80	C₂	C₂×C₃×Dic₂₆	1	1	yes	characteristic
81	C₂	C₃×#6129	1	1	yes	characteristic
82	C₂	C₃×#6131	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₃×C₁₃×C₄⋊C₄	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₃×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₃×#125
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
6. #88144	C₃	direct (N × H)
43. C₃×C₁₃	#125	semidirect
58. C₁₃	C₃×#125	semidirect
79. C₃	#88144	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₁₃×C₄⋊C₄	2
C₃×C₄⋊Dic₁₃	2
C₃×#6101	2
C₃×C₄×Dic₁₃	2
#88144	3
C₃×#125	13

Subgroups — C3×#88144 #11928781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88144 #11928781