Subgroups — C₃×#88198 #11928832

Order 1248.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×Dic₂₆	C₂	1	1	yes	maximal, characteristic
3	C₃×#6101	C₂	1	4	yes	maximal
4	C₃×C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
5	#88198	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×Q₈×C₁₃	—	2	2	no	—
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	2	yes	—
10	C₂×C₃×Dic₁₃	C₂²	1	2	yes	—
11	C₃×Dic₂₆	—	2	2	no	—
12	C₂×Q₈×C₁₃	C₂×C₃	1	1	yes	characteristic
13	C₂×Dic₂₆	C₂×C₃	1	1	yes	characteristic
14	#6101	C₂×C₃	1	4	yes	—
15	C₄×Dic₁₃	C₂×C₃	1	1	yes	characteristic
16	C₂²×C₃×C₁₃	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₁₃	—	2	2	no	—
18	C₃×C₄×C₁₃	D₄	1	2	yes	—
19	C₃×Dic₁₃	—	2	2	no	—
20	C₃×Dic₁₃	Q₈	1	4	yes	complemented
21	Q₈×C₁₃	—	2	2	no	—
22	C₂×C₄×C₁₃	C₂²×C₃	1	2	yes	—
23	C₂×C₄×C₁₃	C₂²×C₃	1	1	yes	characteristic
24	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
25	C₂×Dic₁₃	C₂²×C₃	1	2	yes	—
26	Dic₂₆	—	2	2	no	—
27	C₃×C₄⋊Q₈	—	13	1	no	maximal, Hall
28	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	—
30	C₂²×C₁₃	C₂³×C₃	1	1	yes	characteristic
31	C₄×C₁₃	—	2	2	no	—
32	C₄×C₁₃	C₃×D₄	1	2	yes	—
33	Dic₁₃	—	2	2	no	—
34	Dic₁₃	C₃×Q₈	1	4	yes	complemented
35	C₂×C₃×Q₈	—	13	1	no	—
36	C₂×C₃×Q₈	D₁₃	1	1	yes	characteristic
37	C₃×C₄⋊C₄	—	13	4	no	—
38	C₃×C₄²	—	13	1	no	—
39	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
40	C₄⋊Q₈	—	13	1	no	Sylow
41	C₂×C₁₃	C₂×C₃×D₄	1	1	yes	characteristic
42	C₂×C₁₃	C₂×C₃×Q₈	1	2	yes	—
43	C₃×Q₈	—	2	2	no	—
44	C₃×Q₈	—	26	2	no	—
45	C₂×C₃×C₄	—	13	2	no	—
46	C₂×C₃×C₄	—	13	2	no	—
47	C₂×C₃×C₄	C₂×D₁₃	1	2	yes	—
48	C₂×C₃×C₄	C₂×D₁₃	1	1	yes	characteristic
49	C₂×Q₈	—	13	1	no	—
50	C₂×Q₈	C₃×D₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	13	4	no	—
52	C₄²	—	13	1	no	—
53	C₁₃	C₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
54	C₂²×C₃	C₂²×D₁₃	1	1	yes	characteristic
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	—	13	4	no	—
57	C₃×C₄	—	26	2	no	—
58	C₃×C₄	C₂²⋊D₁₃	1	2	yes	—
59	Q₈	—	2	2	no	—
60	Q₈	—	26	2	no	—
61	C₂×C₄	—	13	2	no	—
62	C₂×C₄	—	13	2	no	—
63	C₂×C₄	C₂×C₃×D₁₃	1	2	yes	—
64	C₂×C₄	C₂×C₃×D₁₃	1	1	yes	characteristic
65	C₂×C₃	Q₈×D₁₃	1	2	yes	—
66	C₂×C₃	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
67	C₂²	C₂²×C₃×D₁₃	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	—	13	4	no	—
70	C₄	—	26	2	no	—
71	C₄	C₃×C₂²⋊D₁₃	1	2	yes	—
72	C₃	#88198	1	1	yes	characteristic, direct product factor, Sylow
73	C₂	C₃×Q₈×D₁₃	1	2	yes	—
74	C₂	C₂×C₃×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂³×C₃
Frattini	C₂²	C₂²×C₃×D₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×C₃×Q₈	D₁₃
hypocenter	C₁₃	C₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×Q₈

Complements

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

N	H ≅ G/N	type
5. #88198	C₃	direct (N × H)
20. C₃×Dic₁₃	Q₈	semidirect
34. Dic₁₃	C₃×Q₈	semidirect
39. C₃×C₁₃	C₄⋊Q₈	semidirect
53. C₁₃	C₃×C₄⋊Q₈	semidirect
72. C₃	#88198	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₁₃	2
C₂×C₃×Dic₂₆	2
C₃×#6101	2
C₃×C₄×Dic₁₃	2
#88198	3
C₃×C₄⋊Q₈	13

Subgroups — C3×#88198 #11928832

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#88198 #11928832