Subgroups — #15750591

Order 3328.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#88034	C₂	1	1	yes	maximal, characteristic
2	C₁₆×#1055	C₂	1	1	yes	maximal, characteristic
3	C₁₃×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₃₂	—	2	1	no	—
5	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×#88034	—	2	1	no	—
7	C₄×#6090	C₄	1	1	yes	characteristic
8	C₈×#1055	C₄	1	1	yes	characteristic
9	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
10	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
11	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×#6090	—	2	1	no	—
13	C₄×#1055	C₈	1	1	yes	characteristic
14	C₄×#1055	C₈	1	1	yes	characteristic
15	C₁₃×C₃₂	—	4	1	no	—
16	#88034	—	4	1	no	—
17	#7458	—	13	1	no	maximal, Sylow
18	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
20	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
21	C₂×#1055	—	2	1	no	—
22	C₂×#1055	C₁₆	1	1	yes	characteristic
23	C₂×#1055	C₁₆	1	1	yes	characteristic
24	C₁₃×C₁₆	—	2	1	no	—
25	C₁₃×C₁₆	D₈	1	1	yes	characteristic
26	C₁₃×C₁₆	Q₁₆	1	1	yes	characteristic
27	#6090	—	2	2	no	—
28	C₄⋊C₃₂	—	13	1	no	—
29	C₄⋊C₃₂	D₁₃	1	1	yes	characteristic
30	C₈×C₁₆	—	13	1	no	—
31	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
32	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
33	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
34	C₈×C₁₃	—	2	1	no	—
35	C₈×C₁₃	#107	1	1	yes	characteristic
36	C₈×C₁₃	#108	1	1	yes	characteristic
37	#1055	—	2	2	no	—
38	#1055	—	2	1	no	—
39	#1055	C₃₂	1	2	yes	complemented
40	C₂×C₃₂	—	2	1	no	—
41	C₂×C₃₂	—	26	1	no	—
42	C₄×C₁₆	—	13	1	no	—
43	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
44	C₈²	—	13	1	no	—
45	C₂²×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
46	C₄×C₁₃	—	2	1	no	—
47	C₄×C₁₃	#335	1	1	yes	characteristic
48	C₄×C₁₃	#364	1	1	yes	characteristic
49	C₄×C₁₃	C₂×C₃₂	1	1	yes	characteristic
50	C₄×C₁₃	M₆₄	1	1	yes	characteristic
51	C₂×C₁₆	—	26	1	no	—
52	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
53	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
54	C₄×C₈	—	13	1	no	—
55	C₄×C₈	—	13	1	no	—
56	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
57	C₃₂	—	4	1	no	—
58	C₃₂	—	52	1	no	—
59	C₂×C₁₃	#1370	1	1	yes	characteristic
60	C₂×C₁₃	C₄⋊C₃₂	1	1	yes	characteristic
61	C₂×C₁₃	#1422	1	1	yes	characteristic
62	C₂×C₈	—	13	1	no	—
63	C₂×C₈	—	13	1	no	—
64	C₂×C₈	—	26	1	no	—
65	C₂×C₈	#6094	1	1	yes	characteristic
66	C₂×C₈	#6101	1	1	yes	characteristic
67	C₄²	C₈×D₁₃	1	1	yes	characteristic
68	C₁₆	—	2	1	no	—
69	C₁₆	—	26	2	no	—
70	C₁₆	#6104	1	1	yes	characteristic
71	C₁₆	#6107	1	1	yes	characteristic
72	C₁₃	#7458	1	1	yes	characteristic, complemented, Sylow
73	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
74	C₂×C₄	#88038	1	1	yes	characteristic
75	C₂×C₄	#88054	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	13	2	no	—
78	C₈	—	26	2	no	—
79	C₈	—	26	1	no	—
80	C₈	#88047	1	1	yes	characteristic
81	C₈	#88062	1	1	yes	characteristic
82	C₂²	#11718093	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	D₁₃×C₃₂	1	1	yes	characteristic
85	C₄	#11718039	1	1	yes	characteristic
86	C₄	#11718071	1	1	yes	characteristic
87	C₄	#11718103	1	1	yes	characteristic
88	C₂	#13112905	1	1	yes	characteristic
89	C₂	#13113031	1	1	yes	characteristic
90	C₂	#13113033	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂×C₃₂
Frattini	C₄×C₁₆	C₂×D₁₃
Fitting	C₁₃×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₁₃	C₄⋊C₁₆
cosocle	C₄×C₁₃×C₁₆	C₂²
hypercenter	C₄⋊C₃₂	D₁₃
hypocenter	C₁₃	#7458
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
39. #1055	C₃₂	semidirect
72. C₁₃	#7458	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#88034	2
C₁₆×#1055	2
C₁₃×C₄⋊C₃₂	2
#7458	13