Subgroups — C₂×C₄₁×#376 #19106047

Order 5248.

840 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₄₁	C₂	1	3	yes	maximal
2	C₄₁×#376	C₂	1	8	yes	maximal, direct product factor
3	C₂×#95×C₄₁	C₂	1	4	yes	maximal
4	C₂³×C₄×C₄₁	C₂²	1	6	yes	—
5	C₂³×C₄×C₄₁	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₄₁	C₄	1	24	yes	complemented
7	C₂×C₄²×C₄₁	C₂²	1	12	yes	—
8	#95×C₄₁	C₂²	1	16	yes	—
9	C₂⁴×C₄₁	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₄₁	—	2	24	no	—
11	C₂²×C₄×C₄₁	C₂×C₄	1	24	yes	—
12	C₂²×C₄×C₄₁	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₄₁	C₂³	1	12	yes	—
14	C₂²×C₄×C₄₁	C₂³	1	2	yes	—
15	C₄²×C₄₁	C₂×C₄	1	48	yes	complemented
16	C₂³×C₄₁	C₂²×C₄	1	6	yes	—
17	C₂³×C₄₁	#41	1	8	yes	—
18	C₂³×C₄₁	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₄₁	—	2	48	no	—
20	C₂×C₄×C₄₁	—	2	24	no	—
21	C₂×C₄×C₄₁	C₄²	1	16	yes	—
22	C₂×C₄×C₄₁	C₂²×C₄	1	24	yes	—
23	C₂×C₄×C₄₁	C₂²×C₄	1	12	yes	—
24	C₂²×C₄₁	C₂×C₄²	1	4	yes	—
25	C₂²×C₄₁	#117	1	24	yes	—
26	C₂²×C₄₁	C₂³×C₄	1	3	yes	—
27	C₂²×C₄₁	C₂×#41	1	4	yes	—
28	C₄×C₄₁	—	2	24	no	—
29	C₄×C₄₁	C₂×C₄²	1	8	yes	—
30	C₂×#376	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₄₁	#376	1	8	yes	direct product factor
32	C₂×C₄₁	C₂²×C₄²	1	1	yes	characteristic
33	C₂×C₄₁	C₂×#117	1	6	yes	—
34	C₂²×C₄²	C₂×C₄₁	1	3	yes	—
35	#376	C₂×C₄₁	1	8	yes	direct product factor
36	C₂×#95	C₂×C₄₁	1	4	yes	—
37	C₄₁	C₂×#376	1	1	yes	characteristic, direct product factor, Sylow
38	C₂³×C₄	C₂²×C₄₁	1	6	yes	—
39	C₂³×C₄	C₂²×C₄₁	1	1	yes	characteristic
40	C₂×C₄²	C₄×C₄₁	1	24	yes	complemented
41	C₂×C₄²	C₂²×C₄₁	1	12	yes	—
42	#95	C₂²×C₄₁	1	16	yes	—
43	C₂⁴	C₂³×C₄₁	1	1	yes	characteristic
44	C₂²×C₄	—	2	24	no	—
45	C₂²×C₄	C₂×C₄×C₄₁	1	24	yes	—
46	C₂²×C₄	C₂×C₄×C₄₁	1	12	yes	—
47	C₂²×C₄	C₂³×C₄₁	1	12	yes	—
48	C₂²×C₄	C₂³×C₄₁	1	2	yes	—
49	C₄²	C₂×C₄×C₄₁	1	48	yes	complemented
50	C₂³	C₂²×C₄×C₄₁	1	6	yes	—
51	C₂³	#41×C₄₁	1	8	yes	—
52	C₂³	C₂⁴×C₄₁	1	1	yes	characteristic
53	C₂×C₄	—	2	48	no	—
54	C₂×C₄	—	2	24	no	—
55	C₂×C₄	C₄²×C₄₁	1	16	yes	—
56	C₂×C₄	C₂²×C₄×C₄₁	1	24	yes	—
57	C₂×C₄	C₂²×C₄×C₄₁	1	12	yes	—
58	C₂²	C₂×C₄²×C₄₁	1	4	yes	—
59	C₂²	#117×C₄₁	1	24	yes	—
60	C₂²	C₂³×C₄×C₄₁	1	3	yes	—
61	C₂²	C₂×#41×C₄₁	1	4	yes	—
62	C₄	—	2	24	no	—
63	C₄	C₂×C₄²×C₄₁	1	8	yes	—
64	C₂	C₄₁×#376	1	8	yes	direct product factor
65	C₂	C₂²×C₄²×C₄₁	1	1	yes	characteristic
66	C₂	C₂×#117×C₄₁	1	6	yes	—

	subgroup	G/H
center	C₂³×C₄×C₄₁	C₂²
commutator	C₂	C₂²×C₄²×C₄₁
Frattini, cosocle	C₂³	C₂⁴×C₄₁
socle, prime radical	C₂⁴×C₄₁	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₁×#376	C₂	direct (N × H)
6. C₂×C₄²×C₄₁	C₄	semidirect
15. C₄²×C₄₁	C₂×C₄	semidirect
30. C₂×#376	C₄₁	direct (N × H)
31. C₂×C₄₁	#376	direct (N × H)
35. #376	C₂×C₄₁	direct (N × H)
37. C₄₁	C₂×#376	direct (N × H)
40. C₂×C₄²	C₄×C₄₁	semidirect
49. C₄²	C₂×C₄×C₄₁	semidirect
64. C₂	C₄₁×#376	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₄₁	2
C₄₁×#376	2
C₂×#95×C₄₁	2
C₂×#376	41

Subgroups — C2×C41×#376 #19106047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×#376 #19106047