Subgroups — C₄₁×#2244 #19106024

Order 5248.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₁×#493	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#357	C₂	1	4	yes	maximal, complemented
4	C₄₁×#346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₁	—	2	1	no	—
6	C₂×D₈×C₄₁	C₂²	1	2	yes	—
7	#127×C₄₁	—	2	1	no	—
8	#125×C₄₁	—	2	1	no	—
9	C₂×C₁₆×C₄₁	C₂²	1	2	yes	—
10	#107×C₄₁	C₂²	1	2	yes	—
11	#106×C₄₁	—	2	1	no	—
12	C₄×C₈×C₄₁	C₂²	1	1	yes	characteristic
13	C₂×D₄×C₄₁	—	2	2	no	—
14	C₂×D₄×C₄₁	—	4	2	no	—
15	D₈×C₄₁	—	2	4	no	—
16	D₈×C₄₁	—	4	2	no	—
17	C₂×C₈×C₄₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₄₁	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₄₁	—	2	2	no	—
20	C₄⋊C₄×C₄₁	—	4	2	no	—
21	C₄²×C₄₁	D₄	1	1	yes	characteristic
22	C₁₆×C₄₁	—	2	2	no	—
23	C₂³×C₄₁	—	4	2	no	—
24	D₄×C₄₁	—	4	2	no	—
25	D₄×C₄₁	—	4	2	no	—
26	D₄×C₄₁	—	8	4	no	—
27	C₂×C₄×C₄₁	—	4	2	no	—
28	C₂×C₄×C₄₁	D₈	1	2	yes	—
29	C₂×C₄×C₄₁	C₂×D₄	1	1	yes	characteristic
30	C₈×C₄₁	SD₁₆	1	2	yes	—
31	C₈×C₄₁	#41	1	2	yes	—
32	C₂²×C₄₁	—	8	2	no	—
33	C₂²×C₄₁	—	8	4	no	—
34	C₂²×C₄₁	C₂×D₈	1	1	yes	characteristic
35	C₄×C₄₁	—	2	2	no	—
36	C₄×C₄₁	—	8	2	no	—
37	C₄×C₄₁	#124	1	1	yes	characteristic
38	C₄×C₄₁	C₂×SD₁₆	1	1	yes	characteristic
39	#2244	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₄₁	—	16	2	no	—
41	C₂×C₄₁	#486	1	1	yes	characteristic
42	C₂×C₄₁	#509	1	2	yes	—
43	#499	C₂×C₄₁	1	1	yes	characteristic, complemented
44	#493	C₂×C₄₁	1	1	yes	characteristic
45	#357	C₂×C₄₁	1	4	yes	complemented
46	#346	C₂×C₄₁	1	1	yes	characteristic, complemented
47	C₄₁	#2244	1	1	yes	characteristic, direct product factor, Sylow
48	C₂×D₈	—	2	1	no	—
49	C₂×D₈	C₂²×C₄₁	1	2	yes	—
50	#127	—	2	1	no	—
51	#125	—	2	1	no	—
52	C₂×C₁₆	C₂²×C₄₁	1	2	yes	—
53	#107	C₂²×C₄₁	1	2	yes	—
54	#106	—	2	1	no	—
55	C₄×C₈	C₂²×C₄₁	1	1	yes	characteristic
56	C₂×D₄	—	2	2	no	—
57	C₂×D₄	—	4	2	no	—
58	D₈	—	2	4	no	—
59	D₈	—	4	2	no	—
60	C₂×C₈	D₄×C₄₁	1	1	yes	characteristic
61	C₂×C₈	C₂³×C₄₁	1	1	yes	characteristic
62	C₄⋊C₄	—	2	2	no	—
63	C₄⋊C₄	—	4	2	no	—
64	C₄²	D₄×C₄₁	1	1	yes	characteristic
65	C₁₆	—	2	2	no	—
66	C₂³	—	4	2	no	—
67	D₄	—	4	2	no	—
68	D₄	—	4	2	no	—
69	D₄	—	8	4	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	D₈×C₄₁	1	2	yes	—
72	C₂×C₄	C₂×D₄×C₄₁	1	1	yes	characteristic
73	C₈	SD₁₆×C₄₁	1	2	yes	—
74	C₈	#41×C₄₁	1	2	yes	—
75	C₂²	—	8	4	no	—
76	C₂²	—	8	2	no	—
77	C₂²	C₂×D₈×C₄₁	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	8	2	no	—
80	C₄	#124×C₄₁	1	1	yes	characteristic
81	C₄	C₂×SD₁₆×C₄₁	1	1	yes	characteristic
82	C₂	—	16	2	no	—
83	C₂	C₄₁×#486	1	1	yes	characteristic
84	C₂	C₄₁×#509	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₁	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₄₁
prime radical	C₄₁×#493	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₄²×C₄₁ ◁ C₄×C₈×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₁×#499	C₂	semidirect
3. C₄₁×#357	C₂	semidirect
4. C₄₁×#346	C₂	semidirect
39. #2244	C₄₁	direct (N × H)
43. #499	C₂×C₄₁	semidirect
45. #357	C₂×C₄₁	semidirect
46. #346	C₂×C₄₁	semidirect
47. C₄₁	#2244	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₁×#499	2
C₄₁×#493	2
C₄₁×#357	2
C₄₁×#346	2
#2244	41

Subgroups — C41×#2244 #19106024

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#2244 #19106024