Subgroups — #15777634

Order 3328.

310 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13117089	C₂	1	4	yes	maximal
2	#13114454	C₂	1	2	yes	maximal
3	C₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₁₀₄	—	2	8	no	—
5	#11718360	C₂²	1	4	yes	—
6	#11718343	—	2	4	no	—
7	C₄×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₈²×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₂	—	2	8	no	—
10	#88123	—	2	4	no	—
11	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
12	C₄×C₈×C₁₃	D₄	1	2	yes	—
13	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
14	#88058	—	4	8	no	—
15	Dic₁₀₄	—	4	16	no	—
16	#12516	—	13	1	no	maximal, Sylow
17	C₂×Dic₂₆	—	4	4	no	—
18	C₂×C₈×C₁₃	D₈	1	4	yes	—
19	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
20	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
21	C₄⋊Dic₁₃	—	4	8	no	—
22	Dic₅₂	—	4	16	no	—
23	C₁₃×C₁₆	D₈	1	8	yes	—
24	#2247	—	13	4	no	—
25	#1713	—	13	2	no	—
26	C₈×C₁₆	D₁₃	1	1	yes	characteristic
27	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
28	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
29	C₂×Dic₁₃	—	8	4	no	—
30	Dic₂₆	—	8	8	no	—
31	C₈×C₁₃	Q₃₂	1	8	yes	complemented
32	C₈×C₁₃	C₂×D₈	1	4	yes	—
33	C₂×Q₃₂	—	26	8	no	—
34	#500	—	26	4	no	—
35	#494	—	13	4	no	—
36	C₄×C₁₆	C₂×D₁₃	1	2	yes	—
37	C₈²	C₂×D₁₃	1	1	yes	characteristic
38	C₂²×C₁₃	#493	1	1	yes	characteristic
39	C₄×C₁₃	#493	1	2	yes	—
40	C₄×C₁₃	C₂×Q₃₂	1	4	yes	—
41	Dic₁₃	—	16	4	no	—
42	C₂×Q₁₆	—	26	8	no	—
43	C₄⋊Q₈	—	26	4	no	—
44	Q₃₂	—	52	16	no	—
45	C₂×C₁₆	D₅₂	1	4	yes	—
46	#107	—	52	8	no	—
47	C₄×C₈	D₅₂	1	2	yes	—
48	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
49	C₂×C₁₃	#1712	1	1	yes	characteristic
50	C₂×C₁₃	#2247	1	2	yes	—
51	C₂×Q₈	—	52	4	no	—
52	Q₁₆	—	52	16	no	—
53	C₂×C₈	D₁₀₄	1	4	yes	—
54	C₂×C₈	C₂×D₅₂	1	2	yes	—
55	C₄⋊C₄	—	52	8	no	—
56	C₄²	C₂×D₅₂	1	1	yes	characteristic
57	C₁₆	D₁₀₄	1	8	yes	—
58	C₁₃	#12516	1	1	yes	characteristic, complemented, Sylow
59	Q₈	—	104	8	no	—
60	C₂×C₄	—	104	4	no	—
61	C₂×C₄	#88128	1	1	yes	characteristic
62	C₂×C₄	C₂×D₁₀₄	1	2	yes	—
63	C₈	Dic₁₀₄	1	8	yes	complemented
64	C₈	C₂×D₁₀₄	1	4	yes	—
65	C₂²	#11718356	1	1	yes	characteristic
66	C₄	—	208	4	no	—
67	C₄	#11718356	1	2	yes	—
68	C₄	C₂×Dic₁₀₄	1	4	yes	—
69	C₂	#13114451	1	1	yes	characteristic
70	C₂	#13117089	1	2	yes	—

	subgroup	G/H
center	C₂²	#11718356
commutator, cosocle	C₄×C₈×C₁₃	C₂³
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₈×C₁₃×C₁₆	C₂
socle, prime radical	C₂²×C₁₃	#493
hypercenter	C₈×C₁₆	D₁₃
hypocenter	C₁₃	#12516
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈² ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
31. C₈×C₁₃	Q₃₂	semidirect
58. C₁₃	#12516	semidirect
63. C₈	Dic₁₀₄	semidirect

Maximal subgroups

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

subgroup	index
#13117089	2
#13114454	2
C₈×C₁₃×C₁₆	2
#12516	13