Subgroups — #44442935

Order 29504.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414185	C₂	1	1	yes	maximal, characteristic
2	#28414185	C₂	1	1	yes	maximal, characteristic
3	#28414117	C₂	1	1	yes	maximal, characteristic
4	C₂×#16814786	—	2	1	no	—
5	C₂×#16814786	—	2	1	no	—
6	C₂×Dic₉₂₂	—	2	1	no	—
7	C₄⋊Dic₄₆₁	C₄	1	1	yes	characteristic
8	#20301480	—	2	1	no	—
9	C₄×Dic₄₆₁	C₂²	1	1	yes	characteristic
10	C₄⋊C₄×C₄₆₁	C₄	1	1	yes	characteristic
11	#16814786	—	4	1	no	—
12	#16814786	—	4	1	no	—
13	Dic₉₂₂	—	4	1	no	—
14	Dic₉₂₂	—	4	1	no	—
15	C₂×Dic₄₆₁	—	2	1	no	—
16	C₂×Dic₄₆₁	D₄	1	1	yes	characteristic
17	C₂×Dic₄₆₁	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₆₁	—	2	1	no	—
19	C₂×C₄×C₄₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₄₆₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₄₆₁	—	2	1	no	—
22	C₄×C₄₆₁	—	4	1	no	—
23	Dic₄₆₁	—	4	1	no	—
24	Dic₄₆₁	D₈	1	1	yes	characteristic
25	Dic₄₆₁	SD₁₆	1	1	yes	characteristic
26	Dic₄₆₁	SD₁₆	1	1	yes	characteristic
27	Dic₄₆₁	Q₁₆	1	1	yes	characteristic
28	C₂×C₄₆₁	#101	1	1	yes	characteristic
29	C₂×C₄₆₁	#102	1	1	yes	characteristic
30	C₂×C₄₆₁	#103	1	1	yes	characteristic
31	C₄₆₁	#332	1	1	yes	characteristic, complemented, Sylow
32	#332	—	461	1	no	maximal, Sylow
33	C₄⋊Q₈	—	461	1	no	—
34	C₄⋊C₈	—	461	1	no	—
35	C₄⋊C₈	—	461	1	no	—
36	C₂×Q₈	—	922	1	no	—
37	C₂×C₈	—	922	1	no	—
38	C₂×C₈	—	922	1	no	—
39	C₄⋊C₄	—	922	1	no	—
40	C₄⋊C₄	—	461	1	no	—
41	C₄⋊C₄	#14270406	1	1	yes	characteristic
42	C₄²	—	461	1	no	—
43	Q₈	—	1844	1	no	—
44	Q₈	—	1844	1	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	922	1	no	—
47	C₂×C₄	—	461	1	no	—
48	C₂×C₄	—	461	1	no	—
49	C₂×C₄	C₂×#14270406	1	1	yes	characteristic
50	C₈	—	1844	1	no	—
51	C₈	—	1844	1	no	—
52	C₂²	C₂²⋊#14270406	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	1844	1	no	—
56	C₄	—	461	1	no	—
57	C₄	—	461	1	no	—
58	C₄	—	461	1	no	—
59	C₄	—	461	1	no	—
60	C₂	#28414179	1	1	yes	characteristic
61	C₂	#28414180	1	1	yes	characteristic
62	C₂	#28414181	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#14270406
commutator	C₂×C₄×C₄₆₁	C₂×C₄
Frattini	C₂×C₄	C₂×#14270406
Fitting	C₄⋊C₄×C₄₆₁	C₄
socle, prime radical	C₂²×C₄₆₁	C₂²⋊C₄
cosocle	C₄×Dic₄₆₁	C₂²
hypercenter	C₄⋊C₄	#14270406
hypocenter	C₄₆₁	#332
LCS	G ▷ C₂×C₄×C₄₆₁ ▷ C₂²×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
31. C₄₆₁	#332	semidirect

Maximal subgroups

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

subgroup	index
#28414185	2
#28414117	2
#332	461