Subgroups — #44443046

Order 29504.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20301510	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#16814786	C₂	1	4	yes	maximal, complemented
3	C₂³×Dic₄₆₁	C₂	1	1	yes	maximal, characteristic
4	#20301510	—	2	4	no	—
5	C₂×#16814786	C₂²	1	4	yes	complemented
6	C₂²×Dic₄₆₁	—	2	4	no	—
7	C₂²×Dic₄₆₁	C₄	1	1	yes	characteristic
8	C₂²×Dic₄₆₁	C₄	1	2	yes	—
9	C₂²×Dic₄₆₁	C₂²	1	2	yes	—
10	C₂²×Dic₄₆₁	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄₆₁	C₄	1	1	yes	characteristic
12	#16814786	—	2	4	no	—
13	C₂×Dic₄₆₁	—	2	2	no	—
14	C₂×Dic₄₆₁	—	2	4	no	—
15	C₂×Dic₄₆₁	—	2	4	no	—
16	C₂×Dic₄₆₁	C₂×C₄	1	2	yes	—
17	C₂×Dic₄₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₄₆₁	D₄	1	4	yes	—
19	C₂×Dic₄₆₁	C₂³	1	1	yes	characteristic
20	C₂³×C₄₆₁	—	2	2	no	—
21	C₂³×C₄₆₁	—	2	4	no	—
22	C₂³×C₄₆₁	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄₆₁	C₂×C₄	1	2	yes	—
24	C₂²×C₄₆₁	—	2	8	no	—
25	C₂²×C₄₆₁	—	2	2	no	—
26	C₂²×C₄₆₁	—	2	2	no	—
27	C₂²×C₄₆₁	—	2	2	no	—
28	C₂²×C₄₆₁	C₂²⋊C₄	1	2	yes	—
29	C₂²×C₄₆₁	M₁₆	1	4	yes	complemented
30	C₂²×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
31	Dic₄₆₁	—	2	2	no	—
32	Dic₄₆₁	C₂²⋊C₄	1	2	yes	—
33	Dic₄₆₁	C₂×D₄	1	2	yes	—
34	C₂×C₄₆₁	—	2	2	no	—
35	C₂×C₄₆₁	—	2	4	no	—
36	C₂×C₄₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
37	C₂×C₄₆₁	C₂×M₁₆	1	2	yes	—
38	C₄₆₁	#407	1	1	yes	characteristic, complemented, Sylow
39	#407	—	461	1	no	maximal, Sylow
40	C₂³×C₄	—	461	1	no	—
41	C₂×M₁₆	—	461	2	no	—
42	C₂²⋊C₈	—	461	4	no	—
43	C₂⁴	#14270406	1	1	yes	characteristic
44	C₂²×C₄	—	922	4	no	—
45	C₂²×C₄	—	461	2	no	—
46	C₂²×C₄	—	461	1	no	—
47	C₂²×C₄	—	461	2	no	—
48	C₂²×C₄	—	461	1	no	—
49	M₁₆	—	922	4	no	—
50	C₂×C₈	—	461	4	no	—
51	C₂³	—	2	2	no	—
52	C₂³	—	2	4	no	—
53	C₂³	C₂×#14270406	1	1	yes	characteristic
54	C₂³	C₂×#14270406	1	2	yes	—
55	C₂×C₄	—	922	2	no	—
56	C₂×C₄	—	922	4	no	—
57	C₂×C₄	—	922	4	no	—
58	C₂×C₄	—	461	2	no	—
59	C₂×C₄	—	461	4	no	—
60	C₂×C₄	—	461	1	no	—
61	C₂×C₄	—	461	1	no	—
62	C₈	—	922	4	no	—
63	C₂²	—	2	8	no	—
64	C₂²	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	—	2	2	no	—
67	C₂²	C₂²⋊#14270406	1	2	yes	—
68	C₂²	#20301510	1	4	yes	complemented
69	C₂²	C₂²×#14270406	1	1	yes	characteristic
70	C₄	—	922	2	no	—
71	C₄	—	461	2	no	—
72	C₄	—	461	2	no	—
73	C₂	—	2	2	no	—
74	C₂	—	2	4	no	—
75	C₂	C₂×C₂²⋊#14270406	1	1	yes	characteristic
76	C₂	C₂×#20301510	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#14270406
commutator, socle	C₂²×C₄₆₁	C₂²×C₄
Fitting, prime radical	C₂⁴×C₄₆₁	C₄
cosocle	C₂×Dic₄₆₁	C₂³
hypercenter	C₂⁴	#14270406
hypocenter	C₄₆₁	#407
LCS	G ▷ C₂²×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₂² ◁ C₂⁴

Complements

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

N	H ≅ G/N	type
1. C₂×#20301510	C₂	semidirect
2. C₂²⋊#16814786	C₂	semidirect
5. C₂×#16814786	C₂²	semidirect
29. C₂²×C₄₆₁	M₁₆	semidirect
38. C₄₆₁	#407	semidirect
68. C₂²	#20301510	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20301510	2
C₂²⋊#16814786	2
C₂³×Dic₄₆₁	2
#407	461