Subgroups — #1057⋊C₃₂ #16777691

Order 3328.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129941	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#1057	C₂	1	1	yes	maximal, characteristic
3	C₃₂×Dic₁₃	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	1	yes	characteristic
11	C₄×#1057	C₈	1	1	yes	characteristic
12	C₂×#6092	C₈	1	2	yes	—
13	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
14	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂×#6090	C₂×C₄	1	1	yes	characteristic
16	#88036	—	2	2	no	—
17	C₁₃×C₃₂	—	2	1	no	—
18	#88034	—	2	1	no	—
19	#7331	—	13	1	no	maximal, Sylow
20	C₂×#1057	C₁₆	1	2	yes	—
21	C₂×#1057	C₁₆	1	2	yes	—
22	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
23	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
24	C₂×#1055	C₂×C₈	1	1	yes	characteristic
25	#6092	—	2	2	no	—
26	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
27	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
28	#6090	M₁₆	1	2	yes	—
29	C₄×C₃₂	—	13	1	no	—
30	C₄×C₃₂	—	13	1	no	—
31	C₈×C₁₆	—	13	1	no	—
32	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
33	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
34	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
35	#1057	—	2	2	no	—
36	#1057	C₃₂	1	4	yes	complemented
37	C₈×C₁₃	#97	1	1	yes	characteristic
38	C₈×C₁₃	#97	1	1	yes	characteristic
39	#1055	M₃₂	1	2	yes	—
40	C₂×C₃₂	—	13	2	no	—
41	C₂×C₃₂	—	13	1	no	—
42	C₂×C₃₂	#261	1	1	yes	characteristic
43	C₄×C₁₆	—	13	1	no	—
44	C₄×C₁₆	—	13	1	no	—
45	C₈²	—	13	1	no	—
46	C₂²×C₁₃	C₄×C₁₆	1	1	yes	characteristic
47	C₄×C₁₃	#322	1	1	yes	characteristic
48	C₄×C₁₃	#346	1	1	yes	characteristic
49	Dic₁₃	C₂×C₃₂	1	2	yes	—
50	Dic₁₃	M₆₄	1	2	yes	—
51	C₂×C₁₆	—	13	1	no	—
52	C₂×C₁₆	—	13	2	no	—
53	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
54	C₄×C₈	—	13	1	no	—
55	C₄×C₈	—	13	1	no	—
56	C₄×C₈	—	13	1	no	—
57	C₃₂	—	2	1	no	—
58	C₃₂	—	26	2	no	—
59	C₃₂	—	26	1	no	—
60	C₂×C₁₃	#1312	1	1	yes	characteristic
61	C₂×C₁₃	C₄×C₃₂	1	1	yes	characteristic
62	C₂×C₁₃	#1397	1	1	yes	characteristic
63	C₂×C₈	—	13	2	no	—
64	C₂×C₈	—	13	1	no	—
65	C₂×C₈	—	13	2	no	—
66	C₂×C₈	C₄×#261	1	1	yes	characteristic
67	C₄²	—	13	1	no	—
68	C₁₆	—	13	2	no	—
69	C₁₆	—	26	2	no	—
70	C₁₆	#6118	1	1	yes	characteristic
71	C₁₆	#6122	1	1	yes	characteristic
72	C₁₃	#7331	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₄	—	13	1	no	—
74	C₂×C₄	—	13	1	no	—
75	C₂×C₄	C₈×#261	1	1	yes	characteristic
76	C₈	—	13	4	no	—
77	C₈	—	13	2	no	—
78	C₈	—	26	2	no	—
79	C₈	#88100	1	1	yes	characteristic
80	C₈	#88110	1	1	yes	characteristic
81	C₂²	C₁₆×#261	1	1	yes	characteristic
82	C₄	—	13	2	no	—
83	C₄	—	13	2	no	—
84	C₄	#11718216	1	1	yes	characteristic
85	C₄	#1057⋊C₈	1	1	yes	characteristic
86	C₂	#1057⋊C₁₆	1	1	yes	characteristic
87	C₂	C₃₂×#261	1	1	yes	characteristic
88	C₂	#13129942	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₁₆	C₂×#261
commutator	C₂×C₁₃	C₄×C₃₂
Fitting	C₂×C₁₃×C₃₂	C₄
socle, prime radical	C₂²×C₁₃	C₄×C₁₆
cosocle	C₁₆×Dic₁₃	C₂²
hypercenter	C₂×C₃₂	#261
hypocenter	C₁₃	#7331
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
36. #1057	C₃₂	semidirect
72. C₁₃	#7331	semidirect

Maximal subgroups

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

subgroup	index
#13129941	2
C₁₆×#1057	2
C₃₂×Dic₁₃	2
#7331	13

Subgroups — #1057⋊C32 #16777691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1057⋊C₃₂ #16777691