Subgroups — #16791501

Order 3328.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13130006	C₂	1	2	yes	maximal, complemented
2	#13130005	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃⋊C₆₄	C₂	1	2	yes	maximal, complemented
4	C₂×#11718037	C₂	1	1	yes	maximal, characteristic, complemented
5	#13117131	C₂	1	1	yes	maximal, characteristic
6	#11718562	C₄	1	1	yes	characteristic
7	C₁₃×M₆₄	C₄	1	1	yes	characteristic
8	C₂×#88034	C₂²	1	1	yes	characteristic
9	#11718039	C₄	1	2	yes	—
10	D₁₃×C₃₂	C₂²	1	2	yes	—
11	#11718037	C₂²	1	1	yes	characteristic
12	#11718037	C₂²	1	1	yes	characteristic
13	#11718037	C₂²	1	2	yes	—
14	#88155	C₈	1	1	yes	characteristic
15	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
16	#88052	C₈	1	1	yes	characteristic
17	#88038	C₈	1	2	yes	—
18	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
19	C₁₃×C₃₂	C₂×C₄	1	2	yes	—
20	#88034	C₂×C₄	1	1	yes	characteristic
21	#88034	C₂³	1	1	yes	characteristic
22	#13737	—	13	1	no	maximal, Sylow
23	#6127	C₁₆	1	1	yes	characteristic
24	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
25	#6099	C₁₆	1	1	yes	characteristic
26	#6094	C₁₆	1	2	yes	—
27	C₈×D₁₃	C₂×C₈	1	2	yes	—
28	C₁₃×C₁₆	C₂×C₈	1	1	yes	characteristic
29	C₁₃×C₁₆	C₂²×C₄	1	1	yes	characteristic
30	#6090	C₂×C₈	1	2	yes	—
31	#2258	—	13	1	no	—
32	M₁₂₈	—	13	1	no	—
33	M₁₂₈	—	13	2	no	—
34	C₂×C₆₄	—	13	1	no	—
35	C₂×C₆₄	—	13	2	no	—
36	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
37	C₂²⋊D₁₃	C₃₂	1	2	yes	—
38	D₅₂	C₃₂	1	1	yes	characteristic
39	C₄×D₁₃	C₂×C₁₆	1	2	yes	—
40	Dic₂₆	C₃₂	1	1	yes	characteristic
41	C₈×C₁₃	C₂×C₁₆	1	1	yes	characteristic
42	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
43	#1055	C₂×C₁₆	1	2	yes	—
44	#504	—	13	1	no	—
45	M₆₄	—	13	2	no	—
46	M₆₄	#261	1	1	yes	characteristic
47	C₂×C₃₂	—	13	1	no	—
48	C₂×C₃₂	—	13	2	no	—
49	C₆₄	—	13	1	no	—
50	C₆₄	—	13	1	no	—
51	C₆₄	—	13	2	no	—
52	C₂²×C₁₃	C₂×C₃₂	1	1	yes	characteristic
53	C₂×D₁₃	C₂×C₃₂	1	2	yes	—
54	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
55	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
56	Dic₁₃	C₂×C₃₂	1	2	yes	—
57	#131	—	13	1	no	—
58	M₃₂	—	13	1	no	—
59	M₃₂	—	13	2	no	—
60	C₂×C₁₆	—	13	2	no	—
61	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
62	C₃₂	—	13	1	no	—
63	C₃₂	—	13	1	no	—
64	C₃₂	C₂×#261	1	2	yes	—
65	C₂×C₁₃	—	2	1	no	—
66	C₂×C₁₃	C₂²×C₃₂	1	1	yes	characteristic
67	D₁₃	—	2	2	no	—
68	#41	—	13	1	no	—
69	M₁₆	—	13	1	no	—
70	M₁₆	—	13	2	no	—
71	C₂×C₈	—	13	2	no	—
72	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
73	C₁₆	—	13	2	no	—
74	C₁₆	D₁₃⋊C₈	1	1	yes	characteristic
75	C₁₆	C₂²×#261	1	1	yes	characteristic
76	C₁₃	#13737	1	1	yes	characteristic, complemented, Sylow
77	Q₈	—	13	1	no	—
78	D₄	—	13	2	no	—
79	D₄	—	13	1	no	—
80	C₂×C₄	—	13	2	no	—
81	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
82	C₈	—	13	2	no	—
83	C₈	D₁₃⋊C₁₆	1	1	yes	characteristic
84	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
85	C₂²	—	13	2	no	—
86	C₂²	D₁₃⋊C₃₂	1	1	yes	characteristic
87	C₄	—	13	2	no	—
88	C₄	D₁₃⋊C₃₂	1	1	yes	characteristic
89	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
90	C₂	—	2	1	no	—
91	C₂	—	26	2	no	—
92	C₂	C₂×D₁₃⋊C₃₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₁₆	C₂²×#261
commutator, socle	C₂×C₁₃	C₂²×C₃₂
Fitting	C₁₃×M₆₄	C₄
prime radical	#6127	C₁₆
cosocle	#88034	C₂³
hypercenter	M₆₄	#261
hypocenter	C₁₃	#13737
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₁₆ ◁ M₆₄

Complements

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

N	H ≅ G/N	type
1. #13130006	C₂	semidirect
2. #13130005	C₂	semidirect
3. D₁₃⋊C₆₄	C₂	semidirect
4. C₂×#11718037	C₂	semidirect
76. C₁₃	#13737	semidirect

Maximal subgroups

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

subgroup	index
#13130006	2
#13130005	2
D₁₃⋊C₆₄	2
C₂×#11718037	2
#13117131	2
#13737	13