Subgroups — #16778193

Order 3328.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129974	C₂	1	2	yes	maximal
2	#13114452	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#494	C₄	1	1	yes	characteristic
4	#11718739	—	2	2	no	—
5	#11718360	C₂²	1	1	yes	characteristic
6	#11718227	—	2	2	no	—
7	C₈×#1055	C₄	1	1	yes	characteristic
8	C₂×C₁₃×Q₁₆	—	4	1	no	—
9	C₁₃×C₄⋊Q₈	—	2	1	no	—
10	C₂×Dic₅₂	—	4	1	no	—
11	#88123	D₄	1	2	yes	—
12	#88113	—	4	2	no	—
13	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
14	#88047	—	4	4	no	—
15	C₄×#1055	—	2	1	no	—
16	#7532	—	13	1	no	maximal, Sylow
17	C₂×Q₈×C₁₃	—	4	1	no	—
18	C₂×Dic₂₆	—	2	2	no	—
19	#6122	—	8	2	no	—
20	C₁₃×Q₁₆	—	8	2	no	—
21	C₂×C₈×C₁₃	—	2	1	no	—
22	C₁₃×C₄⋊C₄	—	4	2	no	—
23	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₄⋊Dic₁₃	—	4	2	no	—
25	C₂×#1055	—	2	2	no	—
26	Dic₅₂	—	8	2	no	—
27	#1713	—	13	1	no	—
28	#1411	—	13	2	no	—
29	Q₈×C₁₃	—	8	2	no	—
30	C₂×C₄×C₁₃	—	2	1	no	—
31	C₂×C₄×C₁₃	—	8	1	no	—
32	C₂×C₄×C₁₃	#99	1	1	yes	characteristic
33	C₂×Dic₁₃	—	4	2	no	—
34	Dic₂₆	—	8	2	no	—
35	#1057	—	16	2	no	—
36	C₈×C₁₃	—	2	2	no	—
37	#1055	—	2	4	no	—
38	#500	—	26	2	no	—
39	#494	—	13	1	no	—
40	#494	#261	1	1	yes	characteristic
41	#356	—	26	2	no	—
42	C₈²	—	13	1	no	—
43	C₂²×C₁₃	#353	1	1	yes	characteristic
44	C₄×C₁₃	—	2	2	no	—
45	C₄×C₁₃	—	2	1	no	—
46	C₄×C₁₃	—	16	1	no	—
47	Dic₁₃	—	8	2	no	—
48	C₂×Q₁₆	—	4	1	no	—
49	C₂×Q₁₆	—	52	1	no	—
50	C₄⋊Q₈	—	2	1	no	—
51	C₄⋊Q₈	—	13	2	no	—
52	#107	—	52	4	no	—
53	#101	—	52	2	no	—
54	C₄×C₈	—	26	1	no	—
55	C₄×C₈	C₂×#261	1	1	yes	characteristic
56	C₂×C₁₃	—	2	1	no	—
57	C₂×C₁₃	#1408	1	1	yes	characteristic
58	C₂×Q₈	—	4	1	no	—
59	C₂×Q₈	—	26	2	no	—
60	Q₁₆	—	8	2	no	—
61	Q₁₆	—	104	2	no	—
62	M₁₆	—	104	2	no	—
63	C₂×C₈	—	2	1	no	—
64	C₂×C₈	—	26	2	no	—
65	C₄⋊C₄	—	4	2	no	—
66	C₄⋊C₄	—	52	2	no	—
67	C₄²	C₂²⋊#261	1	1	yes	characteristic
68	C₁₃	#7532	1	1	yes	characteristic, complemented, Sylow
69	Q₈	—	8	2	no	—
70	Q₈	—	104	2	no	—
71	C₂×C₄	—	2	1	no	—
72	C₂×C₄	—	8	1	no	—
73	C₂×C₄	—	52	2	no	—
74	C₂×C₄	#88119	1	1	yes	characteristic
75	C₈	—	2	2	no	—
76	C₈	—	26	4	no	—
77	C₈	—	208	2	no	—
78	C₂²	#11718294	1	1	yes	characteristic
79	C₄	—	2	2	no	—
80	C₄	—	2	1	no	—
81	C₄	—	16	1	no	—
82	C₄	—	104	2	no	—
83	C₂	—	2	1	no	—
84	C₂	#13129967	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#13129967
commutator	C₄×C₈×C₁₃	C₂×C₄
Frattini	C₄×C₈	C₂×#261
Fitting	C₁₃×#494	C₄
socle	C₂×C₁₃	#1408
prime radical	C₂²×C₁₃	#353
cosocle	#11718360	C₂²
hypercenter	#494	#261
hypocenter	C₁₃	#7532
LCS	G ▷ C₄×C₈×C₁₃ ▷ C₄²×C₁₃ ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #494

Complements

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

N	H ≅ G/N	type
68. C₁₃	#7532	semidirect

Maximal subgroups

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

subgroup	index
#13129974	2
#13114452	2
#7532	13