Subgroups — #16777686

Order 3328.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129944	C₂	1	1	yes	maximal, characteristic
2	#13129747	C₂	1	1	yes	maximal, characteristic
3	#13112969	C₂	1	1	yes	maximal, characteristic
4	#11718257	C₄	1	1	yes	characteristic
5	C₈×#1057	C₄	1	1	yes	characteristic
6	C₂×#88036	C₄	1	2	yes	—
7	C₂×C₁₃×C₃₂	C₄	1	1	yes	characteristic
8	C₁₆×Dic₁₃	C₂²	1	1	yes	characteristic
9	C₂×#88034	C₄	1	1	yes	characteristic
10	C₄×#1057	C₈	1	2	yes	—
11	C₂×#6092	C₈	1	2	yes	—
12	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
13	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂×#6090	C₂×C₄	1	1	yes	characteristic
15	#88036	C₈	1	4	yes	complemented
16	C₁₃×C₃₂	C₈	1	2	yes	complemented
17	#88034	C₈	1	2	yes	complemented
18	#7330	—	13	1	no	maximal, Sylow
19	C₂×#1057	—	2	2	no	—
20	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
21	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
22	C₂×#1055	C₂×C₈	1	1	yes	characteristic
23	#6092	—	2	2	no	—
24	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
25	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
26	#6090	C₂×C₈	1	2	yes	—
27	#1397	—	13	1	no	—
28	#1397	—	13	1	no	—
29	#1311	—	13	1	no	—
30	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
31	C₂×Dic₁₃	M₃₂	1	2	yes	—
32	#1057	—	4	2	no	—
33	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
34	C₈×C₁₃	C₄×C₈	1	1	yes	characteristic
35	#1055	M₃₂	1	2	yes	—
36	C₂×C₃₂	—	13	2	no	—
37	C₂×C₃₂	—	13	1	no	—
38	C₂×C₃₂	#261	1	1	yes	characteristic
39	C₄×C₁₆	—	13	1	no	—
40	C₄×C₁₆	—	13	1	no	—
41	C₈²	—	13	1	no	—
42	C₂²×C₁₃	#346	1	1	yes	characteristic
43	C₄×C₁₃	C₈²	1	1	yes	characteristic
44	C₄×C₁₃	#346	1	1	yes	characteristic
45	Dic₁₃	—	2	2	no	—
46	C₂×C₁₆	—	13	1	no	—
47	C₂×C₁₆	—	13	2	no	—
48	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
49	C₄×C₈	—	13	1	no	—
50	C₄×C₈	—	13	2	no	—
51	C₃₂	—	13	4	no	—
52	C₃₂	—	13	2	no	—
53	C₃₂	#1057	1	2	yes	complemented
54	C₂×C₁₃	#1311	1	1	yes	characteristic
55	C₂×C₁₃	#1398	1	2	yes	—
56	C₂×C₈	—	13	1	no	—
57	C₂×C₈	—	26	2	no	—
58	C₂×C₈	C₄×#261	1	1	yes	characteristic
59	C₄²	—	13	1	no	—
60	C₁₆	—	13	2	no	—
61	C₁₆	—	26	2	no	—
62	C₁₆	D₁₃⋊C₈	1	1	yes	characteristic
63	C₁₆	C₂×#1057	1	1	yes	characteristic
64	C₁₃	#7330	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₄	—	13	2	no	—
66	C₂×C₄	C₈×#261	1	1	yes	characteristic
67	C₈	—	13	2	no	—
68	C₈	—	52	2	no	—
69	C₈	C₈×#261	1	1	yes	characteristic
70	C₈	C₄×#1057	1	1	yes	characteristic
71	C₂²	#11718216	1	1	yes	characteristic
72	C₄	—	26	2	no	—
73	C₄	#11718216	1	1	yes	characteristic
74	C₄	C₈×#1057	1	1	yes	characteristic
75	C₂	#13129747	1	1	yes	characteristic
76	C₂	#13129945	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	C₄×#261
commutator	C₄×C₁₃	C₈²
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₂×C₁₃×C₃₂	C₄
socle, prime radical	C₂²×C₁₃	#346
cosocle	C₁₆×Dic₁₃	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7330
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
15. #88036	C₈	semidirect
16. C₁₃×C₃₂	C₈	semidirect
17. #88034	C₈	semidirect
53. C₃₂	#1057	semidirect
64. C₁₃	#7330	semidirect

Maximal subgroups

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

subgroup	index
#13129944	2
#13129747	2
#13112969	2
#7330	13