Subgroups — #360×C₂₄₁ #29507209

Order 15424.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×C₂₄₁	C₂	1	1	yes	maximal, characteristic
2	M₃₂×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#106×C₂₄₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#41×C₂₄₁	—	2	1	no	—
5	Q₁₆×C₂₄₁	C₄	1	1	yes	characteristic, complemented
6	SD₁₆×C₂₄₁	—	2	1	no	—
7	D₈×C₂₄₁	C₄	1	1	yes	characteristic, complemented
8	C₂×C₈×C₂₄₁	C₂²	1	1	yes	characteristic
9	C₄⋊C₄×C₂₄₁	—	2	1	no	—
10	C₁₆×C₂₄₁	—	2	1	no	—
11	Q₈×C₂₄₁	—	2	1	no	—
12	D₄×C₂₄₁	—	2	1	no	—
13	D₄×C₂₄₁	—	4	1	no	—
14	C₂×C₄×C₂₄₁	—	4	1	no	—
15	C₂×C₄×C₂₄₁	—	4	1	no	—
16	C₂×C₄×C₂₄₁	D₄	1	1	yes	characteristic
17	C₈×C₂₄₁	C₂×C₄	1	1	yes	characteristic
18	C₈×C₂₄₁	D₄	1	1	yes	characteristic
19	C₂²×C₂₄₁	—	4	1	no	—
20	C₂²×C₂₄₁	D₈	1	1	yes	characteristic
21	C₄×C₂₄₁	—	4	1	no	—
22	C₄×C₂₄₁	—	8	1	no	—
23	C₄×C₂₄₁	C₂²⋊C₄	1	1	yes	characteristic
24	C₄×C₂₄₁	SD₁₆	1	1	yes	characteristic
25	C₂×C₂₄₁	—	2	1	no	—
26	C₂×C₂₄₁	—	8	1	no	—
27	C₂×C₂₄₁	#102	1	1	yes	characteristic
28	C₂₄₁	#360	1	1	yes	characteristic, direct product factor, Sylow
29	#360	C₂₄₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	#135	C₂×C₂₄₁	1	1	yes	characteristic
31	M₃₂	C₂×C₂₄₁	1	1	yes	characteristic, complemented
32	#106	C₂×C₂₄₁	1	1	yes	characteristic, complemented
33	#41	—	2	1	no	—
34	Q₁₆	C₄×C₂₄₁	1	1	yes	characteristic, complemented
35	SD₁₆	—	2	1	no	—
36	D₈	C₄×C₂₄₁	1	1	yes	characteristic, complemented
37	C₂×C₈	C₂²×C₂₄₁	1	1	yes	characteristic
38	C₄⋊C₄	—	2	1	no	—
39	C₁₆	—	2	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	2	1	no	—
42	D₄	—	4	1	no	—
43	C₂×C₄	—	4	1	no	—
44	C₂×C₄	—	4	1	no	—
45	C₂×C₄	D₄×C₂₄₁	1	1	yes	characteristic
46	C₈	C₂×C₄×C₂₄₁	1	1	yes	characteristic
47	C₈	D₄×C₂₄₁	1	1	yes	characteristic
48	C₂²	—	4	1	no	—
49	C₂²	D₈×C₂₄₁	1	1	yes	characteristic
50	C₄	—	4	1	no	—
51	C₄	—	8	1	no	—
52	C₄	C₂²⋊C₄×C₂₄₁	1	1	yes	characteristic
53	C₄	SD₁₆×C₂₄₁	1	1	yes	characteristic
54	C₂	—	2	1	no	—
55	C₂	—	8	1	no	—
56	C₂	#102×C₂₄₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₄₁	#102
commutator	C₈	C₂×C₄×C₂₄₁
Frattini, cosocle	C₂×C₈	C₂²×C₂₄₁
prime radical	#135×C₂₄₁	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₄₁ ◁ C₂×C₄×C₂₄₁ ◁ C₂×C₈×C₂₄₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. M₃₂×C₂₄₁	C₂	semidirect
3. #106×C₂₄₁	C₂	semidirect
5. Q₁₆×C₂₄₁	C₄	semidirect
7. D₈×C₂₄₁	C₄	semidirect
28. C₂₄₁	#360	direct (N × H)
29. #360	C₂₄₁	direct (N × H)
31. M₃₂	C₂×C₂₄₁	semidirect
32. #106	C₂×C₂₄₁	semidirect
34. Q₁₆	C₄×C₂₄₁	semidirect
36. D₈	C₄×C₂₄₁	semidirect

Maximal subgroups

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

subgroup	index
#135×C₂₄₁	2
M₃₂×C₂₄₁	2
#106×C₂₄₁	2
#360	241

Subgroups — #360×C241 #29507209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #360×C₂₄₁ #29507209