Subgroups — #30594101

Order 15616.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460841	C₂	1	1	yes	maximal, characteristic
2	#21460841	C₂	1	1	yes	maximal, characteristic
3	#21443735	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11758187	—	2	1	no	—
5	C₄⋊#11758187	—	2	1	no	—
6	C₄×#11758185	C₄	1	1	yes	characteristic
7	C₈×#92418	C₂²	1	1	yes	characteristic
8	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
9	C₂×#11758187	—	4	1	no	—
10	C₂×#11758187	—	4	1	no	—
11	C₂×#11758185	C₈	1	1	yes	characteristic
12	C₂×#11758185	C₈	1	1	yes	characteristic
13	C₄×#92418	D₄	1	1	yes	characteristic
14	C₄×#92418	Q₈	1	1	yes	characteristic
15	C₂×C₁₆×C₆₁	—	2	1	no	—
16	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈×C₆₁	M₁₆	1	1	yes	characteristic
19	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
20	C₂×#92418	—	2	1	no	—
21	C₂×#92418	SD₁₆	1	1	yes	characteristic
22	C₂×#92418	SD₁₆	1	1	yes	characteristic
23	#11758187	—	8	1	no	—
24	#11758187	—	8	1	no	—
25	C₁₆×C₆₁	—	2	2	no	—
26	#11758185	—	2	1	no	—
27	#11758185	C₁₆	1	2	yes	complemented
28	C₂×C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
29	C₂×C₄×C₆₁	#106	1	1	yes	characteristic
30	C₂×C₄×C₆₁	#108	1	1	yes	characteristic
31	C₈×C₆₁	—	2	1	no	—
32	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
33	C₈×C₆₁	M₃₂	1	1	yes	characteristic
34	#92418	—	2	1	no	—
35	#92418	—	2	1	no	—
36	#92418	—	4	1	no	—
37	#7099	—	61	1	no	maximal, Sylow
38	C₂²×C₆₁	#334	1	1	yes	characteristic
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
41	C₄×C₆₁	#364	1	1	yes	characteristic
42	C₄×C₆₁	#365	1	1	yes	characteristic
43	C₄×C₆₁	#365	1	1	yes	characteristic
44	#1367	—	61	1	no	—
45	#1367	—	61	1	no	—
46	#1311	—	61	1	no	—
47	C₂×C₆₁	#1367	1	1	yes	characteristic
48	C₂×C₆₁	#1368	1	1	yes	characteristic
49	C₂×C₆₁	#1369	1	1	yes	characteristic
50	C₄⋊C₁₆	—	122	1	no	—
51	C₄⋊C₁₆	—	122	1	no	—
52	C₄×C₁₆	—	61	1	no	—
53	C₄×C₁₆	#6923	1	1	yes	characteristic
54	C₈²	—	61	1	no	—
55	C₆₁	#7099	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₁₆	—	2	1	no	—
57	C₂×C₁₆	—	61	1	no	—
58	C₂×C₁₆	—	61	1	no	—
59	C₂×C₁₆	—	244	1	no	—
60	C₂×C₁₆	—	244	1	no	—
61	C₄×C₈	—	61	1	no	—
62	C₄×C₈	—	61	1	no	—
63	C₄×C₈	C₂×#6923	1	1	yes	characteristic
64	C₂×C₈	—	61	1	no	—
65	C₂×C₈	—	61	1	no	—
66	C₂×C₈	—	122	1	no	—
67	C₂×C₈	D₆₁⋊C₈	1	1	yes	characteristic
68	C₂×C₈	#11758217	1	1	yes	characteristic
69	C₄²	C₄⋊#6923	1	1	yes	characteristic
70	C₁₆	—	2	2	no	—
71	C₁₆	—	61	2	no	—
72	C₁₆	—	122	1	no	—
73	C₁₆	—	488	1	no	—
74	C₁₆	—	488	1	no	—
75	C₂×C₄	#14519844	1	1	yes	characteristic
76	C₂×C₄	#14519845	1	1	yes	characteristic
77	C₂×C₄	#14519848	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	122	1	no	—
80	C₈	—	122	1	no	—
81	C₈	—	244	1	no	—
82	C₈	D₆₁⋊C₁₆	1	1	yes	characteristic
83	C₈	#14519852	1	1	yes	characteristic
84	C₂²	#16840624	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	#16840683	1	1	yes	characteristic
87	C₄	#16840685	1	1	yes	characteristic
88	C₄	#16840686	1	1	yes	characteristic
89	C₄	#16840687	1	1	yes	characteristic
90	C₂	#21460842	1	1	yes	characteristic
91	C₂	#21460845	1	1	yes	characteristic
92	C₂	#21460847	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14519845
commutator	C₈×C₆₁	C₂×C₁₆
Frattini	C₄×C₈	C₂×#6923
Fitting	C₄×C₁₆×C₆₁	C₄
socle, prime radical	C₂²×C₆₁	#334
cosocle	C₈×#92418	C₂²
hypercenter	C₄×C₁₆	#6923
hypocenter	C₆₁	#7099
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
27. #11758185	C₁₆	semidirect
55. C₆₁	#7099	semidirect

Maximal subgroups

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

subgroup	index
#21460841	2
#21443735	2
#7099	61