Subgroups — C₄×#97×C₂₂₃ #43250740

Order 28544.

360 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#97×C₂₂₃	C₂	1	4	yes	maximal
2	C₂×C₄×C₈×C₂₂₃	C₂	1	2	yes	maximal
3	C₄³×C₂₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×C₂₂₃	C₂²	1	4	yes	—
5	C₂×C₄²×C₂₂₃	C₄	1	4	yes	—
6	C₂×C₄²×C₂₂₃	C₂²	1	2	yes	—
7	C₂×C₄²×C₂₂₃	C₂²	1	1	yes	characteristic
8	#97×C₂₂₃	C₄	1	16	yes	direct product factor
9	C₄×C₈×C₂₂₃	C₄	1	8	yes	complemented
10	C₂²×C₄×C₂₂₃	C₂×C₄	1	4	yes	—
11	C₂²×C₄×C₂₂₃	C₂×C₄	1	2	yes	—
12	C₂²×C₄×C₂₂₃	C₂³	1	1	yes	characteristic
13	C₂×C₈×C₂₂₃	C₂×C₄	1	8	yes	—
14	C₂×C₈×C₂₂₃	C₂×C₄	1	16	yes	—
15	C₄²×C₂₂₃	—	2	8	no	—
16	C₄²×C₂₂₃	C₂×C₄	1	4	yes	—
17	C₄²×C₂₂₃	C₂×C₄	1	8	yes	—
18	C₂³×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₂₃	—	2	8	no	—
20	C₂×C₄×C₂₂₃	C₄²	1	8	yes	—
21	C₂×C₄×C₂₂₃	C₄²	1	4	yes	—
22	C₂×C₄×C₂₂₃	M₁₆	1	8	yes	—
23	C₂×C₄×C₂₂₃	C₂²×C₄	1	2	yes	—
24	C₂×C₄×C₂₂₃	C₂²×C₄	1	4	yes	—
25	C₈×C₂₂₃	C₄²	1	16	yes	complemented
26	C₂²×C₂₂₃	C₂×C₄²	1	1	yes	characteristic
27	C₂²×C₂₂₃	C₂×C₄²	1	2	yes	—
28	C₂²×C₂₂₃	C₂×M₁₆	1	4	yes	—
29	C₄×C₂₂₃	—	2	8	no	—
30	C₄×C₂₂₃	#97	1	8	yes	direct product factor
31	C₄×C₂₂₃	C₂×C₄²	1	4	yes	—
32	C₂×C₂₂₃	C₄³	1	1	yes	characteristic
33	C₂×C₂₂₃	C₂×#97	1	2	yes	—
34	C₂×C₂₂₃	C₄×M₁₆	1	4	yes	—
35	C₂₂₃	C₄×#97	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×#97	C₂₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×#97	C₂×C₂₂₃	1	4	yes	—
38	C₂×C₄×C₈	C₂×C₂₂₃	1	2	yes	—
39	C₄³	C₂×C₂₂₃	1	1	yes	characteristic
40	C₂²×C₈	C₂²×C₂₂₃	1	4	yes	—
41	C₂×C₄²	C₄×C₂₂₃	1	4	yes	—
42	C₂×C₄²	C₂²×C₂₂₃	1	1	yes	characteristic
43	C₂×C₄²	C₂²×C₂₂₃	1	2	yes	—
44	#97	C₄×C₂₂₃	1	16	yes	direct product factor
45	C₄×C₈	C₄×C₂₂₃	1	8	yes	complemented
46	C₂²×C₄	C₂×C₄×C₂₂₃	1	4	yes	—
47	C₂²×C₄	C₂×C₄×C₂₂₃	1	2	yes	—
48	C₂²×C₄	C₂³×C₂₂₃	1	1	yes	characteristic
49	C₂×C₈	C₂×C₄×C₂₂₃	1	8	yes	—
50	C₂×C₈	C₂×C₄×C₂₂₃	1	16	yes	—
51	C₄²	—	2	8	no	—
52	C₄²	C₂×C₄×C₂₂₃	1	4	yes	—
53	C₄²	C₂×C₄×C₂₂₃	1	8	yes	—
54	C₂³	C₂²×C₄×C₂₂₃	1	1	yes	characteristic
55	C₂×C₄	—	2	8	no	—
56	C₂×C₄	C₄²×C₂₂₃	1	8	yes	—
57	C₂×C₄	C₄²×C₂₂₃	1	4	yes	—
58	C₂×C₄	M₁₆×C₂₂₃	1	8	yes	—
59	C₂×C₄	C₂²×C₄×C₂₂₃	1	2	yes	—
60	C₂×C₄	C₂²×C₄×C₂₂₃	1	4	yes	—
61	C₈	C₄²×C₂₂₃	1	16	yes	complemented
62	C₂²	C₂×C₄²×C₂₂₃	1	1	yes	characteristic
63	C₂²	C₂×C₄²×C₂₂₃	1	2	yes	—
64	C₂²	C₂×M₁₆×C₂₂₃	1	4	yes	—
65	C₄	—	2	8	no	—
66	C₄	#97×C₂₂₃	1	8	yes	direct product factor
67	C₄	C₂×C₄²×C₂₂₃	1	4	yes	—
68	C₂	C₄³×C₂₂₃	1	1	yes	characteristic
69	C₂	C₂×#97×C₂₂₃	1	2	yes	—
70	C₂	C₄×M₁₆×C₂₂₃	1	4	yes	—

	subgroup	G/H
center	C₂×C₄²×C₂₂₃	C₂²
commutator	C₂	C₄³×C₂₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₂₃
socle, prime radical	C₂³×C₂₂₃	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₂₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. #97×C₂₂₃	C₄	direct (N × H)
9. C₄×C₈×C₂₂₃	C₄	semidirect
25. C₈×C₂₂₃	C₄²	semidirect
30. C₄×C₂₂₃	#97	direct (N × H)
35. C₂₂₃	C₄×#97	direct (N × H)
36. C₄×#97	C₂₂₃	direct (N × H)
44. #97	C₄×C₂₂₃	direct (N × H)
45. C₄×C₈	C₄×C₂₂₃	semidirect
61. C₈	C₄²×C₂₂₃	semidirect
66. C₄	#97×C₂₂₃	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×#97×C₂₂₃	2
C₂×C₄×C₈×C₂₂₃	2
C₄³×C₂₂₃	2
C₄×#97	223

Subgroups — C4×#97×C223 #43250740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#97×C₂₂₃ #43250740