Subgroups — #16777975

Order 3328.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129867	C₂	1	2	yes	maximal
2	C₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#11718254	—	2	2	no	—
4	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
6	C₂×#88034	C₄	1	1	yes	characteristic
7	C₄⋊#1057	—	4	2	no	—
8	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
9	C₈×Dic₁₃	D₄	1	1	yes	characteristic
10	C₂×#6090	Q₈	1	1	yes	characteristic
11	C₁₃×C₃₂	—	2	1	no	—
12	#88034	C₈	1	2	yes	complemented
13	#7460	—	13	1	no	maximal, Sylow
14	C₂×#1057	—	8	2	no	—
15	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×Dic₁₃	D₈	1	1	yes	characteristic
17	C₂×#1055	Q₁₆	1	1	yes	characteristic
18	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
19	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
20	#6090	—	2	1	no	—
21	C₄×C₃₂	—	13	1	no	—
22	#1371	—	13	2	no	—
23	C₂×C₄×C₁₃	#107	1	1	yes	characteristic
24	C₂×Dic₁₃	D₁₆	1	1	yes	characteristic
25	C₂×Dic₁₃	Q₃₂	1	1	yes	characteristic
26	#1057	—	16	2	no	—
27	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
28	C₈×C₁₃	#108	1	1	yes	characteristic
29	#1055	—	2	1	no	—
30	C₂×C₃₂	—	13	1	no	—
31	C₂×C₃₂	#261	1	1	yes	characteristic
32	C₄×C₁₆	—	13	1	no	—
33	#335	—	26	2	no	—
34	C₂²×C₁₃	#366	1	1	yes	characteristic
35	C₄×C₁₃	#335	1	1	yes	characteristic
36	C₄×C₁₃	#368	1	1	yes	characteristic
37	Dic₁₃	—	2	1	no	—
38	Dic₁₃	D₃₂	1	1	yes	characteristic
39	Dic₁₃	Q₆₄	1	1	yes	characteristic
40	C₂×C₁₆	—	13	1	no	—
41	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
42	C₄⋊C₈	—	52	2	no	—
43	C₄×C₈	—	13	1	no	—
44	C₃₂	—	2	1	no	—
45	C₃₂	—	13	2	no	—
46	C₂×C₁₃	#1371	1	1	yes	characteristic
47	C₂×C₁₃	#1423	1	1	yes	characteristic
48	C₂×C₁₃	#1425	1	1	yes	characteristic
49	C₂×C₈	—	13	1	no	—
50	C₂×C₈	—	104	2	no	—
51	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
52	C₄²	—	13	1	no	—
53	C₁₆	—	26	1	no	—
54	C₁₆	D₁₃⋊C₈	1	1	yes	characteristic
55	C₁₆	#6122	1	1	yes	characteristic
56	C₁₃	#7460	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄	—	13	1	no	—
58	C₂×C₄	—	13	1	no	—
59	C₂×C₄	#88102	1	1	yes	characteristic
60	C₈	—	26	1	no	—
61	C₈	—	208	2	no	—
62	C₈	#88103	1	1	yes	characteristic
63	C₈	#88112	1	1	yes	characteristic
64	C₂²	#11718221	1	1	yes	characteristic
65	C₄	—	13	1	no	—
66	C₄	—	13	1	no	—
67	C₄	—	26	1	no	—
68	C₄	#11718224	1	1	yes	characteristic
69	C₄	#11718256	1	1	yes	characteristic
70	C₂	#13129868	1	1	yes	characteristic
71	C₂	#13129997	1	1	yes	characteristic
72	C₂	#13130000	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11718221
commutator	C₁₃×C₁₆	C₂×C₈
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₂×C₁₃×C₃₂	C₄
socle, prime radical	C₂²×C₁₃	#366
cosocle	C₁₆×Dic₁₃	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7460
LCS	G ▷ C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
12. #88034	C₈	semidirect
56. C₁₃	#7460	semidirect

Maximal subgroups

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

subgroup	index
#13129867	2
C₃₂×Dic₁₃	2
#7460	13