Subgroups — #16778149

Order 3328.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130005	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11718037	C₂	1	1	yes	maximal, characteristic, complemented
3	#13117130	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#504	C₄	1	1	yes	characteristic
5	#11718091	—	2	1	no	—
6	#11718091	C₄	1	1	yes	characteristic
7	C₂×#88034	—	2	1	no	—
8	C₂×#88034	C₂²	1	1	yes	characteristic
9	#11718037	—	2	1	no	—
10	#11718037	—	2	1	no	—
11	C₁₃×#131	C₈	1	1	yes	characteristic
12	C₁₃×M₃₂	—	2	1	no	—
13	C₁₃×M₃₂	C₈	1	1	yes	characteristic
14	C₂×C₁₃×C₁₆	—	2	1	no	—
15	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	#88034	—	2	1	no	—
17	#88034	D₄	1	1	yes	characteristic
18	#88034	D₄	1	1	yes	characteristic
19	#7514	—	13	1	no	maximal, Sylow
20	C₁₃×#41	C₁₆	1	1	yes	characteristic
21	C₁₃×M₁₆	—	2	1	no	—
22	C₁₃×M₁₆	C₁₆	1	1	yes	characteristic
23	C₂×C₈×C₁₃	—	2	1	no	—
24	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
25	C₁₃×C₁₆	—	2	1	no	—
26	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₁₃×C₁₆	M₁₆	1	1	yes	characteristic
28	#2258	—	13	1	no	—
29	M₁₂₈	—	13	1	no	—
30	C₂×C₆₄	—	13	1	no	—
31	Q₈×C₁₃	C₃₂	1	1	yes	characteristic
32	D₄×C₁₃	—	2	1	no	—
33	D₄×C₁₃	C₃₂	1	1	yes	characteristic
34	C₂×C₄×C₁₃	—	2	1	no	—
35	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
36	C₈×C₁₃	—	2	1	no	—
37	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
38	C₈×C₁₃	M₃₂	1	1	yes	characteristic
39	#504	#261	1	1	yes	characteristic
40	M₆₄	—	13	1	no	—
41	M₆₄	—	26	1	no	—
42	C₂×C₃₂	—	13	1	no	—
43	C₂×C₃₂	—	26	1	no	—
44	C₆₄	—	26	1	no	—
45	C₆₄	—	26	1	no	—
46	C₂²×C₁₃	—	2	1	no	—
47	C₂²×C₁₃	M₆₄	1	1	yes	characteristic
48	C₄×C₁₃	—	2	1	no	—
49	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
50	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
51	#131	#1057	1	1	yes	characteristic
52	M₃₂	—	2	1	no	—
53	M₃₂	#1057	1	1	yes	characteristic
54	C₂×C₁₆	—	2	1	no	—
55	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
56	C₃₂	—	13	1	no	—
57	C₃₂	—	13	1	no	—
58	C₃₂	—	26	1	no	—
59	C₂×C₁₃	—	2	1	no	—
60	C₂×C₁₃	—	4	1	no	—
61	C₂×C₁₃	C₂²⋊C₃₂	1	1	yes	characteristic
62	#41	#6092	1	1	yes	characteristic
63	M₁₆	—	2	1	no	—
64	M₁₆	#6092	1	1	yes	characteristic
65	C₂×C₈	—	2	1	no	—
66	C₂×C₈	C₂×#1057	1	1	yes	characteristic
67	C₁₆	—	2	1	no	—
68	C₁₆	#6122	1	1	yes	characteristic
69	C₁₆	C₂²⋊#261	1	1	yes	characteristic
70	C₁₃	#7514	1	1	yes	characteristic, complemented, Sylow
71	Q₈	#88036	1	1	yes	characteristic
72	D₄	—	2	1	no	—
73	D₄	#88036	1	1	yes	characteristic
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	C₂×#6092	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	#88106	1	1	yes	characteristic
78	C₈	C₂²⋊#1057	1	1	yes	characteristic
79	C₂²	—	2	1	no	—
80	C₂²	#11718249	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	C₂×#88036	1	1	yes	characteristic
83	C₄	C₂²⋊#6092	1	1	yes	characteristic
84	C₂	—	2	1	no	—
85	C₂	—	4	1	no	—
86	C₂	C₂²⋊#88036	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	C₂²⋊#261
commutator	C₄×C₁₃	C₂×C₃₂
Frattini	C₂×C₁₆	C₂×#261
Fitting	C₁₃×#504	C₄
socle	C₂×C₁₃	C₂²⋊C₃₂
prime radical	C₁₃×#41	C₁₆
cosocle	C₂×#88034	C₂²
hypercenter	#504	#261
hypocenter	C₁₃	#7514
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #504

Complements

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

N	H ≅ G/N	type
1. #13130005	C₂	semidirect
2. C₂×#11718037	C₂	semidirect
70. C₁₃	#7514	semidirect

Maximal subgroups

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

subgroup	index
#13130005	2
C₂×#11718037	2
#13117130	2
#7514	13