Subgroups — #16777690

Order 3328.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88036	C₂	1	2	yes	maximal
2	C₈×#6090	C₂	1	1	yes	maximal, characteristic
3	C₂×#88036	C₄	1	4	yes	—
4	C₈²×C₁₃	C₄	1	1	yes	characteristic
5	C₄×#6090	C₄	1	1	yes	characteristic
6	C₄×#6090	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
8	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
9	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₂×#6090	C₈	1	2	yes	—
11	C₂×#6090	C₂×C₄	1	2	yes	—
12	#88036	—	2	4	no	—
13	#7331	—	13	1	no	maximal, Sylow
14	C₂×C₈×C₁₃	C₁₆	1	2	yes	—
15	C₂×C₈×C₁₃	C₁₆	1	2	yes	—
16	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
17	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
18	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
19	#6090	—	2	2	no	—
20	#6090	M₁₆	1	4	yes	—
21	C₄×C₃₂	—	13	2	no	—
22	C₈×C₁₆	—	13	1	no	—
23	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
24	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
26	C₈×C₁₃	—	2	2	no	—
27	C₈×C₁₃	C₃₂	1	4	yes	complemented
28	C₈×C₁₃	#97	1	2	yes	—
29	C₈×C₁₃	M₃₂	1	2	yes	—
30	C₂×C₃₂	—	13	4	no	—
31	C₄×C₁₆	—	13	1	no	—
32	C₄×C₁₆	—	13	1	no	—
33	C₈²	#261	1	1	yes	characteristic
34	C₂²×C₁₃	C₄×C₁₆	1	1	yes	characteristic
35	C₄×C₁₃	#322	1	1	yes	characteristic
36	C₄×C₁₃	#346	1	1	yes	characteristic
37	C₄×C₁₃	C₂×C₃₂	1	2	yes	—
38	C₄×C₁₃	M₆₄	1	2	yes	—
39	C₂×C₁₆	—	13	2	no	—
40	C₂×C₁₆	—	13	2	no	—
41	C₄×C₈	#1057	1	1	yes	characteristic
42	C₄×C₈	#1057	1	1	yes	characteristic
43	C₄×C₈	C₂×#261	1	1	yes	characteristic
44	C₃₂	—	26	4	no	—
45	C₂×C₁₃	#1312	1	1	yes	characteristic
46	C₂×C₁₃	C₄×C₃₂	1	1	yes	characteristic
47	C₂×C₁₃	#1397	1	1	yes	characteristic
48	C₂×C₈	#6092	1	2	yes	—
49	C₂×C₈	#6092	1	2	yes	—
50	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
51	C₂×C₈	C₄×#261	1	1	yes	characteristic
52	C₄²	C₂×#1057	1	1	yes	characteristic
53	C₁₆	—	13	4	no	—
54	C₁₆	—	26	2	no	—
55	C₁₃	#7331	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₄	C₂×#6092	1	1	yes	characteristic
57	C₂×C₄	C₂×#6092	1	1	yes	characteristic
58	C₂×C₄	C₄×#1057	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	#88036	1	4	yes	complemented
61	C₈	#88098	1	2	yes	—
62	C₈	#88100	1	2	yes	—
63	C₂²	C₄×#6092	1	1	yes	characteristic
64	C₄	C₂×#88036	1	2	yes	—
65	C₄	#11718249	1	2	yes	—
66	C₄	#11718251	1	1	yes	characteristic
67	C₄	#11718258	1	1	yes	characteristic
68	C₂	#13129749	1	1	yes	characteristic
69	C₂	C₄×#88036	1	1	yes	characteristic
70	C₂	#13129943	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₄×C₃₂
Fitting	C₈²×C₁₃	C₄
socle, prime radical	C₂²×C₁₃	C₄×C₁₆
cosocle	C₄×#6090	C₂²
hypercenter	C₈²	#261
hypocenter	C₁₃	#7331
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
27. C₈×C₁₃	C₃₂	semidirect
55. C₁₃	#7331	semidirect
60. C₈	#88036	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88036	2
C₈×#6090	2
#7331	13