Subgroups — #443×C₂₂₉ #28411056

Order 14656.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#135×C₂₂₉	C₂	1	1	yes	maximal, characteristic
2	#131×C₂₂₉	C₂	1	2	yes	maximal, complemented
3	#108×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#104×C₂₂₉	C₂	1	2	yes	maximal, complemented
5	C₄×C₈×C₂₂₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#41×C₂₂₉	C₂²	1	2	yes	—
7	Q₁₆×C₂₂₉	C₄	1	1	yes	characteristic, complemented
8	SD₁₆×C₂₂₉	C₄	1	2	yes	complemented
9	D₈×C₂₂₉	C₄	1	1	yes	characteristic, complemented
10	M₁₆×C₂₂₉	—	2	2	no	—
11	M₁₆×C₂₂₉	C₂²	1	2	yes	—
12	C₂×C₈×C₂₂₉	—	2	2	no	—
13	C₂×C₈×C₂₂₉	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₂₂₉	C₂²	1	1	yes	characteristic
15	C₄²×C₂₂₉	C₂²	1	1	yes	characteristic
16	Q₈×C₂₂₉	C₂×C₄	1	2	yes	—
17	D₄×C₂₂₉	—	2	2	no	—
18	D₄×C₂₂₉	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₂₂₉	—	2	1	no	—
20	C₂×C₄×C₂₂₉	—	2	2	no	—
21	C₂×C₄×C₂₂₉	C₂³	1	1	yes	characteristic
22	C₈×C₂₂₉	—	2	2	no	—
23	C₈×C₂₂₉	C₂×C₄	1	1	yes	characteristic
24	C₈×C₂₂₉	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₂₉	D₄	1	1	yes	characteristic
26	C₈×C₂₂₉	D₄	1	1	yes	characteristic
27	C₂²×C₂₂₉	—	2	2	no	—
28	C₂²×C₂₂₉	#41	1	1	yes	characteristic
29	C₄×C₂₂₉	—	2	2	no	—
30	C₄×C₂₂₉	—	2	2	no	—
31	C₄×C₂₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₂₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂×C₂₂₉	—	2	1	no	—
34	C₂×C₂₂₉	—	4	2	no	—
35	C₂×C₂₂₉	C₄×D₄	1	1	yes	characteristic
36	C₂₂₉	#443	1	1	yes	characteristic, direct product factor, Sylow
37	#443	C₂₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	#135	C₂×C₂₂₉	1	1	yes	characteristic
39	#131	C₂×C₂₂₉	1	2	yes	complemented
40	#108	C₂×C₂₂₉	1	1	yes	characteristic, complemented
41	#104	C₂×C₂₂₉	1	2	yes	complemented
42	C₄×C₈	C₂×C₂₂₉	1	1	yes	characteristic, complemented
43	#41	C₂²×C₂₂₉	1	2	yes	—
44	Q₁₆	C₄×C₂₂₉	1	1	yes	characteristic, complemented
45	SD₁₆	C₄×C₂₂₉	1	2	yes	complemented
46	D₈	C₄×C₂₂₉	1	1	yes	characteristic, complemented
47	M₁₆	—	2	2	no	—
48	M₁₆	C₂²×C₂₂₉	1	2	yes	—
49	C₂×C₈	—	2	2	no	—
50	C₂×C₈	C₂²×C₂₂₉	1	1	yes	characteristic
51	C₂×C₈	C₂²×C₂₂₉	1	1	yes	characteristic
52	C₄²	C₂²×C₂₂₉	1	1	yes	characteristic
53	Q₈	C₂×C₄×C₂₂₉	1	2	yes	—
54	D₄	—	2	2	no	—
55	D₄	C₂×C₄×C₂₂₉	1	2	yes	—
56	C₂×C₄	—	2	1	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	C₂³×C₂₂₉	1	1	yes	characteristic
59	C₈	—	2	2	no	—
60	C₈	C₂×C₄×C₂₂₉	1	1	yes	characteristic
61	C₈	C₂×C₄×C₂₂₉	1	1	yes	characteristic
62	C₈	D₄×C₂₂₉	1	1	yes	characteristic
63	C₈	D₄×C₂₂₉	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	#41×C₂₂₉	1	1	yes	characteristic
66	C₄	—	2	2	no	—
67	C₄	—	2	2	no	—
68	C₄	C₂²×C₄×C₂₂₉	1	1	yes	characteristic
69	C₄	C₂×D₄×C₂₂₉	1	1	yes	characteristic
70	C₂	—	2	1	no	—
71	C₂	—	4	2	no	—
72	C₂	C₄×D₄×C₂₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈×C₂₂₉	D₄
commutator	C₄	C₂²×C₄×C₂₂₉
Frattini, cosocle	C₂×C₄	C₂³×C₂₂₉
socle	C₂×C₂₂₉	C₄×D₄
prime radical	#135×C₂₂₉	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₂₉ ◁ C₂×C₈×C₂₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. #131×C₂₂₉	C₂	semidirect
3. #108×C₂₂₉	C₂	semidirect
4. #104×C₂₂₉	C₂	semidirect
5. C₄×C₈×C₂₂₉	C₂	semidirect
7. Q₁₆×C₂₂₉	C₄	semidirect
8. SD₁₆×C₂₂₉	C₄	semidirect
9. D₈×C₂₂₉	C₄	semidirect
36. C₂₂₉	#443	direct (N × H)
37. #443	C₂₂₉	direct (N × H)
39. #131	C₂×C₂₂₉	semidirect
40. #108	C₂×C₂₂₉	semidirect
41. #104	C₂×C₂₂₉	semidirect
42. C₄×C₈	C₂×C₂₂₉	semidirect
44. Q₁₆	C₄×C₂₂₉	semidirect
45. SD₁₆	C₄×C₂₂₉	semidirect
46. D₈	C₄×C₂₂₉	semidirect

Maximal subgroups

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

subgroup	index
#135×C₂₂₉	2
#131×C₂₂₉	2
#108×C₂₂₉	2
#104×C₂₂₉	2
C₄×C₈×C₂₂₉	2
#443	229

Subgroups — #443×C229 #28411056

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #443×C₂₂₉ #28411056