Subgroups — C₄₁×#7538 #23783739

Order 10496.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₁×Q₆₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₁×C₆₄	C₂	1	1	yes	maximal, characteristic
3	C₄₁×#1423	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₃₂×C₄₁	—	2	1	no	—
5	C₄₁×Q₆₄	—	2	1	no	—
6	C₄₁×Q₆₄	C₄	1	2	yes	complemented
7	C₂×C₃₂×C₄₁	C₂²	1	1	yes	characteristic
8	C₄₁×#366	—	2	1	no	—
9	C₄₁×C₆₄	—	2	1	no	—
10	C₂×Q₁₆×C₄₁	—	4	1	no	—
11	Q₃₂×C₄₁	—	2	2	no	—
12	Q₃₂×C₄₁	—	4	1	no	—
13	C₂×C₁₆×C₄₁	D₄	1	1	yes	characteristic
14	#107×C₄₁	—	4	1	no	—
15	C₃₂×C₄₁	C₂×C₄	1	1	yes	characteristic
16	C₃₂×C₄₁	D₄	1	1	yes	characteristic
17	C₂×Q₈×C₄₁	—	8	1	no	—
18	Q₁₆×C₄₁	—	4	2	no	—
19	Q₁₆×C₄₁	—	8	1	no	—
20	C₂×C₈×C₄₁	D₈	1	1	yes	characteristic
21	C₄⋊C₄×C₄₁	—	8	1	no	—
22	C₁₆×C₄₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₁₆×C₄₁	SD₁₆	1	1	yes	characteristic
24	Q₈×C₄₁	—	8	2	no	—
25	Q₈×C₄₁	—	16	1	no	—
26	C₂×C₄×C₄₁	—	16	1	no	—
27	C₂×C₄×C₄₁	—	16	1	no	—
28	C₂×C₄×C₄₁	D₁₆	1	1	yes	characteristic
29	C₈×C₄₁	#102	1	1	yes	characteristic
30	C₈×C₄₁	SD₃₂	1	1	yes	characteristic
31	#7538	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₄₁	D₃₂	1	1	yes	characteristic
33	C₄×C₄₁	—	16	2	no	—
34	C₄×C₄₁	—	32	1	no	—
35	C₄×C₄₁	#357	1	1	yes	characteristic
36	C₄×C₄₁	SD₆₄	1	1	yes	characteristic
37	C₂×Q₆₄	C₂×C₄₁	1	1	yes	characteristic
38	C₂×C₆₄	C₂×C₄₁	1	1	yes	characteristic
39	#1423	C₂×C₄₁	1	1	yes	characteristic
40	C₂×C₄₁	#1415	1	1	yes	characteristic
41	C₂×C₄₁	SD₁₂₈	1	1	yes	characteristic
42	C₂×C₄₁	Q₁₂₈	1	1	yes	characteristic
43	C₂×Q₃₂	—	2	1	no	—
44	Q₆₄	—	2	1	no	—
45	Q₆₄	C₄×C₄₁	1	2	yes	complemented
46	C₂×C₃₂	C₂²×C₄₁	1	1	yes	characteristic
47	#366	—	2	1	no	—
48	C₆₄	—	2	1	no	—
49	C₄₁	#7538	1	1	yes	characteristic, direct product factor, Sylow
50	C₂×Q₁₆	—	4	1	no	—
51	Q₃₂	—	2	2	no	—
52	Q₃₂	—	4	1	no	—
53	C₂×C₁₆	D₄×C₄₁	1	1	yes	characteristic
54	#107	—	4	1	no	—
55	C₃₂	C₂×C₄×C₄₁	1	1	yes	characteristic
56	C₃₂	D₄×C₄₁	1	1	yes	characteristic
57	C₂×Q₈	—	8	1	no	—
58	Q₁₆	—	4	2	no	—
59	Q₁₆	—	8	1	no	—
60	C₂×C₈	D₈×C₄₁	1	1	yes	characteristic
61	C₄⋊C₄	—	8	1	no	—
62	C₁₆	C₂²⋊C₄×C₄₁	1	1	yes	characteristic
63	C₁₆	SD₁₆×C₄₁	1	1	yes	characteristic
64	Q₈	—	8	2	no	—
65	Q₈	—	16	1	no	—
66	C₂×C₄	—	16	1	no	—
67	C₂×C₄	—	16	1	no	—
68	C₂×C₄	D₁₆×C₄₁	1	1	yes	characteristic
69	C₈	#102×C₄₁	1	1	yes	characteristic
70	C₈	SD₃₂×C₄₁	1	1	yes	characteristic
71	C₂²	C₄₁×D₃₂	1	1	yes	characteristic
72	C₄	—	16	2	no	—
73	C₄	—	32	1	no	—
74	C₄	C₄₁×#357	1	1	yes	characteristic
75	C₄	C₄₁×SD₆₄	1	1	yes	characteristic
76	C₂	C₄₁×#1415	1	1	yes	characteristic
77	C₂	C₄₁×SD₁₂₈	1	1	yes	characteristic
78	C₂	C₄₁×Q₁₂₈	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₄₁	D₃₂
commutator	C₃₂	C₂×C₄×C₄₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₄₁
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₁ ◁ C₂×C₄×C₄₁ ◁ C₂×C₈×C₄₁ ◁ C₂×C₁₆×C₄₁ ◁ C₂×C₃₂×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₄₁×Q₆₄	C₄	semidirect
31. #7538	C₄₁	direct (N × H)
45. Q₆₄	C₄×C₄₁	semidirect
49. C₄₁	#7538	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₁×Q₆₄	2
C₂×C₄₁×C₆₄	2
C₄₁×#1423	2
#7538	41

Subgroups — C41×#7538 #23783739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₁×#7538 #23783739