Subgroups — #30594099

Order 15616.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460841	C₂	1	2	yes	maximal
2	#21443735	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11758187	—	2	2	no	—
4	C₄×#11758185	C₄	1	1	yes	characteristic
5	C₈×#92418	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₆₁	C₄	1	1	yes	characteristic
7	C₂×#11758187	—	4	2	no	—
8	C₂×#11758185	—	2	1	no	—
9	C₄×#92418	D₄	1	1	yes	characteristic
10	C₄×#92418	Q₈	1	1	yes	characteristic
11	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
12	C₂×C₁₆×C₆₁	C₈	1	1	yes	characteristic
13	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
15	C₂×C₈×C₆₁	M₁₆	1	1	yes	characteristic
16	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
17	C₂×#92418	—	2	1	no	—
18	C₂×#92418	SD₁₆	1	2	yes	—
19	#11758187	—	8	2	no	—
20	C₁₆×C₆₁	—	2	1	no	—
21	C₁₆×C₆₁	C₁₆	1	2	yes	complemented
22	#11758185	—	2	2	no	—
23	C₂×C₄×C₆₁	C₄⋊C₈	1	1	yes	characteristic
24	C₂×C₄×C₆₁	#106	1	1	yes	characteristic
25	C₂×C₄×C₆₁	#108	1	1	yes	characteristic
26	C₈×C₆₁	—	2	1	no	—
27	C₈×C₆₁	C₂×C₁₆	1	1	yes	characteristic
28	C₈×C₆₁	M₃₂	1	1	yes	characteristic
29	#92418	—	2	2	no	—
30	#92418	—	4	1	no	—
31	#7099	—	61	1	no	maximal, Sylow
32	C₂²×C₆₁	#334	1	1	yes	characteristic
33	C₄×C₆₁	—	2	1	no	—
34	C₄×C₆₁	C₄⋊C₁₆	1	1	yes	characteristic
35	C₄×C₆₁	#364	1	1	yes	characteristic
36	C₄×C₆₁	#365	1	2	yes	—
37	#1367	—	61	2	no	—
38	#1311	—	61	1	no	—
39	C₂×C₆₁	#1367	1	1	yes	characteristic
40	C₂×C₆₁	#1368	1	1	yes	characteristic
41	C₂×C₆₁	#1369	1	1	yes	characteristic
42	C₄⋊C₁₆	—	122	2	no	—
43	C₄×C₁₆	—	61	1	no	—
44	C₄×C₁₆	#6923	1	1	yes	characteristic
45	C₈²	—	61	1	no	—
46	C₆₁	#7099	1	1	yes	characteristic, complemented, Sylow
47	C₂×C₁₆	—	122	1	no	—
48	C₂×C₁₆	—	244	2	no	—
49	C₂×C₁₆	#92420	1	1	yes	characteristic
50	C₂×C₁₆	#92420	1	1	yes	characteristic
51	C₄×C₈	—	61	1	no	—
52	C₄×C₈	—	61	1	no	—
53	C₄×C₈	C₂×#6923	1	1	yes	characteristic
54	C₂×C₈	—	61	2	no	—
55	C₂×C₈	—	122	1	no	—
56	C₂×C₈	#11758213	1	1	yes	characteristic
57	C₂×C₈	C₂×#92420	1	1	yes	characteristic
58	C₄²	C₄⋊#6923	1	1	yes	characteristic
59	C₁₆	—	2	1	no	—
60	C₁₆	—	122	2	no	—
61	C₁₆	—	488	2	no	—
62	C₁₆	#11758187	1	2	yes	complemented
63	C₂×C₄	C₄⋊#92420	1	1	yes	characteristic
64	C₂×C₄	#14519845	1	1	yes	characteristic
65	C₂×C₄	#14519847	1	1	yes	characteristic
66	C₈	—	2	1	no	—
67	C₈	—	122	2	no	—
68	C₈	—	244	1	no	—
69	C₈	C₂×#11758187	1	1	yes	characteristic
70	C₈	#14519851	1	1	yes	characteristic
71	C₂²	#16840623	1	1	yes	characteristic
72	C₄	—	2	1	no	—
73	C₄	C₄⋊#11758187	1	1	yes	characteristic
74	C₄	#16840684	1	1	yes	characteristic
75	C₄	#16840686	1	2	yes	—
76	C₂	#21460841	1	1	yes	characteristic
77	C₂	#21460843	1	1	yes	characteristic
78	C₂	#21460846	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
21. C₁₆×C₆₁	C₁₆	semidirect
46. C₆₁	#7099	semidirect
62. C₁₆	#11758187	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