Subgroups — C₁₃×#944 #11928917

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×C₁₃×Dic₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×Dic₃⋊C₄	C₂	1	4	yes	maximal
4	C₄×Dic₃×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₁₃×C₄⋊Q₈	—	3	1	no	maximal, 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×Dic₃×C₁₃	C₂²	1	2	yes	—
10	C₂×Dic₃×C₁₃	C₂²	1	2	yes	—
11	C₁₃×Dic₆	—	2	2	no	—
12	C₂×Q₈×C₁₃	—	3	1	no	—
13	C₂×Q₈×C₁₃	D₃	1	1	yes	characteristic
14	C₁₃×C₄⋊C₄	—	3	4	no	—
15	C₄²×C₁₃	—	3	1	no	—
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	Dic₃×C₁₃	—	2	2	no	—
20	Dic₃×C₁₃	Q₈	1	4	yes	complemented
21	Q₈×C₁₃	—	2	2	no	—
22	Q₈×C₁₃	—	6	2	no	—
23	C₂×C₄×C₁₃	—	3	2	no	—
24	C₂×C₄×C₁₃	—	3	2	no	—
25	C₂×C₄×C₁₃	C₂×D₃	1	2	yes	—
26	C₂×C₄×C₁₃	C₂×D₃	1	1	yes	characteristic
27	#944	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₃×C₁₃	C₂×D₄	1	1	yes	characteristic
29	C₂×C₃×C₁₃	C₂×Q₈	1	2	yes	—
30	C₂²×C₁₃	C₂²×D₃	1	1	yes	characteristic
31	C₄×C₁₃	—	2	2	no	—
32	C₄×C₁₃	—	3	4	no	—
33	C₄×C₁₃	—	6	2	no	—
34	C₄×C₁₃	#67	1	2	yes	—
35	C₂×C₃×Q₈	C₂×C₁₃	1	1	yes	characteristic
36	C₂×Dic₆	C₂×C₁₃	1	1	yes	characteristic
37	Dic₃⋊C₄	C₂×C₁₃	1	4	yes	—
38	C₄×Dic₃	C₂×C₁₃	1	1	yes	characteristic
39	C₃×C₁₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Hall
40	C₄⋊Q₈	—	3	1	no	Sylow
41	C₂×C₁₃	D₃×Q₈	1	2	yes	—
42	C₂×C₁₃	C₂×#67	1	1	yes	characteristic
43	C₃×Q₈	—	2	2	no	—
44	C₂×C₃×C₄	C₂²×C₁₃	1	2	yes	—
45	C₂×C₃×C₄	C₂²×C₁₃	1	1	yes	characteristic
46	C₂×Dic₃	C₂²×C₁₃	1	2	yes	—
47	C₂×Dic₃	C₂²×C₁₃	1	2	yes	—
48	Dic₆	—	2	2	no	—
49	C₂×Q₈	—	3	1	no	—
50	C₂×Q₈	D₃×C₁₃	1	1	yes	characteristic
51	C₄⋊C₄	—	3	4	no	—
52	C₄²	—	3	1	no	—
53	C₁₃	#944	1	1	yes	characteristic, direct product factor, Sylow
54	C₂²×C₃	C₂³×C₁₃	1	1	yes	characteristic
55	C₃×C₄	—	2	2	no	—
56	C₃×C₄	D₄×C₁₃	1	2	yes	—
57	Dic₃	—	2	2	no	—
58	Dic₃	Q₈×C₁₃	1	4	yes	complemented
59	Q₈	—	2	2	no	—
60	Q₈	—	6	2	no	—
61	C₂×C₄	—	3	2	no	—
62	C₂×C₄	—	3	2	no	—
63	C₂×C₄	C₂×D₃×C₁₃	1	2	yes	—
64	C₂×C₄	C₂×D₃×C₁₃	1	1	yes	characteristic
65	C₂×C₃	C₂×D₄×C₁₃	1	1	yes	characteristic
66	C₂×C₃	C₂×Q₈×C₁₃	1	2	yes	—
67	C₂²	C₂²×D₃×C₁₃	1	1	yes	characteristic
68	C₄	—	2	2	no	—
69	C₄	—	3	4	no	—
70	C₄	—	6	2	no	—
71	C₄	C₁₃×#67	1	2	yes	—
72	C₃	C₁₃×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
73	C₂	D₃×Q₈×C₁₃	1	2	yes	—
74	C₂	C₂×C₁₃×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₃	C₂²×D₃
commutator, cosocle	C₂²×C₃	C₂³×C₁₃
Frattini	C₂²	C₂²×D₃×C₁₃
Fitting	C₂×C₃×Q₈×C₁₃	C₂
socle, prime radical	C₂²×C₃×C₁₃	C₂³
hypercenter	C₂×Q₈×C₁₃	D₃
hypocenter	C₃	C₁₃×C₄⋊Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×Q₈×C₁₃

Complements

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

N	H ≅ G/N	type
20. Dic₃×C₁₃	Q₈	semidirect
27. #944	C₁₃	direct (N × H)
39. C₃×C₁₃	C₄⋊Q₈	semidirect
53. C₁₃	#944	direct (N × H)
58. Dic₃	Q₈×C₁₃	semidirect
72. C₃	C₁₃×C₄⋊Q₈	semidirect

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×C₁₃×Dic₆	2
C₁₃×Dic₃⋊C₄	2
C₄×Dic₃×C₁₃	2
C₁₃×C₄⋊Q₈	3
#944	13

Subgroups — C13×#944 #11928917

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#944 #11928917