Subgroups — #44442192

Order 29504.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28414140	C₂	1	1	yes	maximal, characteristic
2	#28414126	C₂	1	2	yes	maximal, complemented
3	#28414044	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#108×C₄₆₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#20301501	C₂²	1	2	yes	—
7	Dic₁₈₄₄	C₄	1	1	yes	characteristic, complemented
8	#20301490	C₄	1	2	yes	complemented
9	D₃₆₈₈	C₄	1	1	yes	characteristic, complemented
10	#20301484	—	2	2	no	—
11	C₂×#16814779	C₂²	1	1	yes	characteristic
12	C₈×D₄₆₁	—	2	2	no	—
13	C₄×Dic₄₆₁	C₂²	1	1	yes	characteristic
14	M₁₆×C₄₆₁	C₂²	1	2	yes	—
15	C₂×C₈×C₄₆₁	C₂²	1	1	yes	characteristic
16	Dic₉₂₂	C₂×C₄	1	2	yes	—
17	D₁₈₄₄	C₂×C₄	1	2	yes	—
18	C₂²⋊D₄₆₁	—	2	2	no	—
19	C₂×Dic₄₆₁	—	2	1	no	—
20	C₄×D₄₆₁	—	2	2	no	—
21	#16814779	D₄	1	1	yes	characteristic
22	#16814779	D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₆₁	C₂³	1	1	yes	characteristic
24	C₈×C₄₆₁	—	2	2	no	—
25	C₈×C₄₆₁	C₂×C₄	1	1	yes	characteristic
26	C₈×C₄₆₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄₆₁	#41	1	1	yes	characteristic
28	C₂×D₄₆₁	—	2	2	no	—
29	C₄×C₄₆₁	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₄₆₁	C₂×D₄	1	1	yes	characteristic
31	Dic₄₆₁	—	2	2	no	—
32	Dic₄₆₁	—	2	2	no	—
33	C₂×C₄₆₁	—	2	1	no	—
34	C₂×C₄₆₁	C₄×D₄	1	1	yes	characteristic
35	D₄₆₁	—	4	2	no	—
36	C₄₆₁	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	461	1	no	maximal, Sylow
38	#135	—	461	1	no	—
39	#131	—	461	2	no	—
40	#108	D₄₆₁	1	1	yes	characteristic, complemented
41	#104	—	461	2	no	—
42	C₄×C₈	—	461	1	no	—
43	#41	—	461	2	no	—
44	Q₁₆	—	461	1	no	—
45	SD₁₆	—	461	2	no	—
46	D₈	—	461	1	no	—
47	M₁₆	—	922	2	no	—
48	M₁₆	C₂×D₄₆₁	1	2	yes	—
49	C₂×C₈	—	922	2	no	—
50	C₂×C₈	—	461	1	no	—
51	C₂×C₈	C₂×D₄₆₁	1	1	yes	characteristic
52	C₄²	—	461	1	no	—
53	Q₈	—	461	2	no	—
54	D₄	—	922	2	no	—
55	D₄	—	461	2	no	—
56	C₂×C₄	—	922	1	no	—
57	C₂×C₄	—	922	2	no	—
58	C₂×C₄	C₂²×D₄₆₁	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	—	461	1	no	—
61	C₈	—	461	1	no	—
62	C₈	C₄×D₄₆₁	1	1	yes	characteristic
63	C₈	C₄×D₄₆₁	1	1	yes	characteristic
64	C₂²	—	922	2	no	—
65	C₂²	#20301502	1	1	yes	characteristic
66	C₄	—	922	2	no	—
67	C₄	—	922	2	no	—
68	C₄	C₂×C₄×D₄₆₁	1	1	yes	characteristic
69	C₄	D₄×D₄₆₁	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	1844	2	no	—
72	C₂	#28414080	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₄₆₁
commutator	C₄×C₄₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₆₁
Fitting	#108×C₄₆₁	C₂
socle	C₂×C₄₆₁	C₄×D₄
prime radical	#28414140	C₂
cosocle	C₂×C₄×C₄₆₁	C₂³
hypercenter	#108	D₄₆₁
hypocenter	C₄₆₁	#443
LCS	G ▷ C₄×C₄₆₁ ▷ C₂×C₄₆₁ ▷ C₄₆₁
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #108

Complements

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

N	H ≅ G/N	type
2. #28414126	C₂	semidirect
3. #28414044	C₂	semidirect
4. C₈×Dic₄₆₁	C₂	semidirect
5. #108×C₄₆₁	C₂	semidirect
7. Dic₁₈₄₄	C₄	semidirect
8. #20301490	C₄	semidirect
9. D₃₆₈₈	C₄	semidirect
36. C₄₆₁	#443	semidirect
40. #108	D₄₆₁	semidirect

Maximal subgroups

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

subgroup	index
#28414140	2
#28414126	2
#28414044	2
C₈×Dic₄₆₁	2
#108×C₄₆₁	2
#443	461