Subgroups — #1450×C₂₂₃ #43250465

Order 28544.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×C₂₂₃	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	#322×C₂₂₃	C₂	1	2	yes	maximal, complemented
4	C₈²×C₂₂₃	C₂	1	2	yes	maximal, complemented
5	C₂²×C₈×C₂₂₃	C₄	1	2	yes	—
6	C₂×C₄²×C₂₂₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₈×C₂₂₃	C₄	1	4	yes	—
8	C₂²⋊C₈×C₂₂₃	C₄	1	4	yes	—
9	C₄×C₈×C₂₂₃	C₄	1	2	yes	—
10	C₄×C₈×C₂₂₃	C₂²	1	4	yes	—
11	C₄×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₂₂₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄×C₂₂₃	C₂×C₄	1	2	yes	—
14	C₂²×C₄×C₂₂₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₂₂₃	C₈	1	8	yes	complemented
16	C₂×C₈×C₂₂₃	C₂×C₄	1	8	yes	—
17	C₂×C₈×C₂₂₃	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₂₂₃	C₂×C₄	1	2	yes	—
19	C₄²×C₂₂₃	C₂×C₄	1	1	yes	characteristic
20	C₄²×C₂₂₃	C₂×C₄	1	2	yes	—
21	C₄²×C₂₂₃	C₂³	1	1	yes	characteristic
22	C₂³×C₂₂₃	C₄²	1	1	yes	characteristic
23	C₂×C₄×C₂₂₃	—	2	4	no	—
24	C₂×C₄×C₂₂₃	C₄²	1	2	yes	—
25	C₂×C₄×C₂₂₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₂₃	C₂×C₈	1	4	yes	—
27	C₂×C₄×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₂₃	C₂²×C₄	1	2	yes	—
29	C₈×C₂₂₃	—	2	8	no	—
30	C₈×C₂₂₃	C₂×C₈	1	4	yes	—
31	C₈×C₂₂₃	C₂×C₈	1	4	yes	—
32	C₂²×C₂₂₃	—	2	2	no	—
33	C₂²×C₂₂₃	C₄×C₈	1	2	yes	—
34	C₂²×C₂₂₃	C₂×C₄²	1	1	yes	characteristic
35	C₄×C₂₂₃	—	2	2	no	—
36	C₄×C₂₂₃	C₄×C₈	1	2	yes	—
37	C₄×C₂₂₃	C₂²×C₈	1	2	yes	—
38	C₄×C₂₂₃	#131	1	4	yes	—
39	C₂×C₂₂₃	—	2	2	no	—
40	C₂×C₂₂₃	C₂×C₄×C₈	1	1	yes	characteristic
41	C₂×C₂₂₃	#405	1	2	yes	—
42	C₂₂₃	#1450	1	1	yes	characteristic, direct product factor, Sylow
43	#1450	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	#431	C₂×C₂₂₃	1	2	yes	—
45	C₂×C₄×C₈	C₂×C₂₂₃	1	1	yes	characteristic
46	#322	C₂×C₂₂₃	1	2	yes	complemented
47	C₈²	C₂×C₂₂₃	1	2	yes	complemented
48	C₂²×C₈	C₄×C₂₂₃	1	2	yes	—
49	C₂×C₄²	C₂²×C₂₂₃	1	1	yes	characteristic
50	C₄⋊C₈	C₄×C₂₂₃	1	4	yes	—
51	C₂²⋊C₈	C₄×C₂₂₃	1	4	yes	—
52	C₄×C₈	C₄×C₂₂₃	1	2	yes	—
53	C₄×C₈	C₂²×C₂₂₃	1	1	yes	characteristic
54	C₄×C₈	C₂²×C₂₂₃	1	4	yes	—
55	C₄×C₈	C₂²×C₂₂₃	1	1	yes	characteristic
56	C₂²×C₄	C₂×C₄×C₂₂₃	1	2	yes	—
57	C₂²×C₄	C₂×C₄×C₂₂₃	1	1	yes	characteristic
58	C₂×C₈	C₈×C₂₂₃	1	8	yes	complemented
59	C₂×C₈	C₂×C₄×C₂₂₃	1	8	yes	—
60	C₂×C₈	C₂×C₄×C₂₂₃	1	2	yes	—
61	C₂×C₈	C₂×C₄×C₂₂₃	1	2	yes	—
62	C₄²	C₂×C₄×C₂₂₃	1	1	yes	characteristic
63	C₄²	C₂×C₄×C₂₂₃	1	2	yes	—
64	C₄²	C₂³×C₂₂₃	1	1	yes	characteristic
65	C₂³	C₄²×C₂₂₃	1	1	yes	characteristic
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	C₄²×C₂₂₃	1	2	yes	—
68	C₂×C₄	C₄²×C₂₂₃	1	1	yes	characteristic
69	C₂×C₄	C₂×C₈×C₂₂₃	1	4	yes	—
70	C₂×C₄	C₂²×C₄×C₂₂₃	1	1	yes	characteristic
71	C₂×C₄	C₂²×C₄×C₂₂₃	1	2	yes	—
72	C₈	—	2	8	no	—
73	C₈	C₂×C₈×C₂₂₃	1	4	yes	—
74	C₈	C₂×C₈×C₂₂₃	1	4	yes	—
75	C₂²	—	2	2	no	—
76	C₂²	C₄×C₈×C₂₂₃	1	2	yes	—
77	C₂²	C₂×C₄²×C₂₂₃	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	C₄×C₈×C₂₂₃	1	2	yes	—
80	C₄	C₂²×C₈×C₂₂₃	1	2	yes	—
81	C₄	#131×C₂₂₃	1	4	yes	—
82	C₂	—	2	2	no	—
83	C₂	C₂×C₄×C₈×C₂₂₃	1	1	yes	characteristic
84	C₂	#405×C₂₂₃	1	2	yes	—

	subgroup	G/H
center	C₄×C₈×C₂₂₃	C₂²
commutator	C₂	C₂×C₄×C₈×C₂₂₃
Frattini, cosocle	C₄²	C₂³×C₂₂₃
socle	C₂²×C₂₂₃	C₂×C₄²
prime radical	C₂³×C₂₂₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. #322×C₂₂₃	C₂	semidirect
4. C₈²×C₂₂₃	C₂	semidirect
15. C₂×C₈×C₂₂₃	C₈	semidirect
42. C₂₂₃	#1450	direct (N × H)
43. #1450	C₂₂₃	direct (N × H)
46. #322	C₂×C₂₂₃	semidirect
47. C₈²	C₂×C₂₂₃	semidirect
58. C₂×C₈	C₈×C₂₂₃	semidirect

Maximal subgroups

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

subgroup	index
#431×C₂₂₃	2
C₂×C₄×C₈×C₂₂₃	2
#322×C₂₂₃	2
C₈²×C₂₂₃	2
#1450	223

Subgroups — #1450×C223 #43250465

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1450×C₂₂₃ #43250465