Subgroups — #29567675

Order 15616.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21448098	C₂	1	1	yes	maximal, characteristic
2	#21443895	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#1422	C₂	1	1	yes	maximal, characteristic
4	#16840164	—	2	1	no	—
5	#16839590	C₄	1	2	yes	—
6	#16839588	—	2	1	no	—
7	#16839583	—	2	1	no	—
8	C₆₁×M₆₄	—	2	1	no	—
9	C₄×C₁₆×C₆₁	C₂²	1	1	yes	characteristic
10	#14519769	—	4	1	no	—
11	#14519717	—	4	1	no	—
12	#14519711	—	2	2	no	—
13	#14519709	—	4	1	no	—
14	C₂×C₁₆×C₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₁₆×C₆₁	D₄	1	1	yes	characteristic
16	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
17	C₃₂×C₆₁	—	4	1	no	—
18	C₂×C₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
19	C₂×C₈×C₆₁	D₈	1	1	yes	characteristic
20	C₄²×C₆₁	SD₁₆	1	1	yes	characteristic
21	C₄⋊Dic₆₁	—	4	2	no	—
22	#11758196	—	8	2	no	—
23	C₁₆×C₆₁	—	2	1	no	—
24	C₁₆×C₆₁	SD₁₆	1	1	yes	characteristic
25	C₁₆×C₆₁	Q₁₆	1	1	yes	characteristic
26	#11758185	—	8	1	no	—
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	#102	1	1	yes	characteristic
29	C₂×Dic₆₁	—	8	2	no	—
30	C₈×C₆₁	#101	1	1	yes	characteristic
31	C₈×C₆₁	#103	1	1	yes	characteristic
32	C₈×C₆₁	SD₃₂	1	1	yes	characteristic
33	C₈×C₆₁	Q₃₂	1	1	yes	characteristic
34	#7454	—	61	1	no	maximal, Sylow
35	C₂²×C₆₁	#361	1	1	yes	characteristic
36	C₄×C₆₁	—	4	1	no	—
37	C₄×C₆₁	#332	1	1	yes	characteristic
38	C₄×C₆₁	#358	1	1	yes	characteristic
39	Dic₆₁	—	16	2	no	—
40	#2253	—	61	1	no	—
41	#1422	D₆₁	1	1	yes	characteristic
42	#1373	—	61	1	no	—
43	C₂×C₆₁	—	2	1	no	—
44	C₂×C₆₁	#1365	1	1	yes	characteristic
45	#499	—	122	1	no	—
46	M₆₄	—	2	1	no	—
47	#367	—	61	2	no	—
48	#366	—	122	1	no	—
49	#364	—	122	1	no	—
50	C₄×C₁₆	C₂×D₆₁	1	1	yes	characteristic
51	C₆₁	#7454	1	1	yes	characteristic, complemented, Sylow
52	#125	—	244	1	no	—
53	M₃₂	—	244	1	no	—
54	C₂×C₁₆	C₄×D₆₁	1	1	yes	characteristic
55	C₂×C₁₆	C₂²⋊D₆₁	1	1	yes	characteristic
56	#107	—	122	2	no	—
57	#106	—	244	1	no	—
58	C₄×C₈	D₂₄₄	1	1	yes	characteristic
59	C₃₂	—	4	1	no	—
60	C₂×C₈	D₄₈₈	1	1	yes	characteristic
61	C₂×C₈	#11758198	1	1	yes	characteristic
62	C₄⋊C₄	—	488	2	no	—
63	C₄⋊C₄	—	244	2	no	—
64	C₄²	#11758190	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	488	1	no	—
67	C₁₆	#11758200	1	1	yes	characteristic
68	C₁₆	#11758202	1	1	yes	characteristic
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	488	2	no	—
71	C₂×C₄	#14519699	1	1	yes	characteristic
72	C₈	#14519695	1	1	yes	characteristic
73	C₈	#14519700	1	1	yes	characteristic
74	C₈	#14519722	1	1	yes	characteristic
75	C₈	Dic₄₈₈	1	1	yes	characteristic
76	C₂²	#16839576	1	1	yes	characteristic
77	C₄	—	4	1	no	—
78	C₄	—	976	2	no	—
79	C₄	#16839507	1	1	yes	characteristic
80	C₄	#16839567	1	1	yes	characteristic
81	C₂	—	2	1	no	—
82	C₂	#21443876	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21443876
commutator	C₂×C₁₆×C₆₁	C₂×C₄
Frattini	C₄×C₁₆	C₂×D₆₁
Fitting	C₆₁×#1422	C₂
socle	C₂×C₆₁	#1365
prime radical	C₂²×C₆₁	#361
cosocle	C₄×C₁₆×C₆₁	C₂²
hypercenter	#1422	D₆₁
hypocenter	C₆₁	#7454
LCS	G ▷ C₂×C₁₆×C₆₁ ▷ C₂×C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1422

Complements

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

N	H ≅ G/N	type
51. C₆₁	#7454	semidirect

Maximal subgroups

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

subgroup	index
#21448098	2
#21443895	2
C₆₁×#1422	2
#7454	61