Subgroups — C₄×#564×C₈₉ #36412203

Order 22784.

1800 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#564×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2382	C₂	1	15	yes	maximal
3	C₄×#125×C₈₉	C₂	1	15	yes	maximal
4	#564×C₈₉	C₄	1	16	yes	direct product factor
5	C₂×#125×C₈₉	C₂²	1	15	yes	—
6	#389×C₈₉	C₂²	1	30	yes	—
7	#387×C₈₉	C₂²	1	60	yes	—
8	#382×C₈₉	C₂²	1	15	yes	—
9	C₄×C₄⋊C₄×C₈₉	C₂²	1	30	yes	—
10	C₄³×C₈₉	C₂²	1	5	yes	—
11	#125×C₈₉	C₂×C₄	1	120	yes	—
12	C₂×C₄⋊C₄×C₈₉	C₂³	1	30	yes	—
13	C₂×C₄⋊C₄×C₈₉	C₂³	1	30	yes	—
14	C₂×C₄²×C₈₉	C₂³	1	15	yes	—
15	C₂×C₄²×C₈₉	C₂³	1	15	yes	—
16	C₂×C₄²×C₈₉	C₂³	1	5	yes	—
17	#95×C₈₉	C₂³	1	60	yes	—
18	C₂²×C₄×C₈₉	C₂⁴	1	15	yes	—
19	C₂²×C₄×C₈₉	C₂⁴	1	15	yes	—
20	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
21	C₄⋊C₄×C₈₉	—	4	30	no	—
22	C₄⋊C₄×C₈₉	C₂²×C₄	1	120	yes	—
23	C₄²×C₈₉	—	2	30	no	—
24	C₄²×C₈₉	—	4	15	no	—
25	C₄²×C₈₉	C₂²×C₄	1	20	yes	—
26	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
27	C₂×C₄×C₈₉	—	2	15	no	—
28	C₂×C₄×C₈₉	—	2	15	no	—
29	C₂×C₄×C₈₉	—	2	15	no	—
30	C₂×C₄×C₈₉	—	2	30	no	—
31	C₂×C₄×C₈₉	C₂³×C₄	1	30	yes	—
32	C₂×C₄×C₈₉	2₋¹⁺⁴	1	6	yes	—
33	C₂²×C₈₉	C₂⁴×C₄	1	1	yes	characteristic
34	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	3	yes	—
35	C₂²×C₈₉	#585	1	3	yes	—
36	C₄×C₈₉	—	2	30	no	—
37	C₄×C₈₉	—	4	15	no	—
38	C₄×C₈₉	#564	1	4	yes	direct product factor
39	C₄×#564	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×C₈₉	C₄×2₋¹⁺⁴	1	3	yes	—
41	C₂×C₈₉	C₂×#564	1	1	yes	characteristic
42	C₂×C₈₉	#3531	1	3	yes	—
43	C₂×#564	C₂×C₈₉	1	1	yes	characteristic
44	#2382	C₂×C₈₉	1	15	yes	—
45	C₄×#125	C₂×C₈₉	1	15	yes	—
46	C₈₉	C₄×#564	1	1	yes	characteristic, direct product factor, Sylow
47	#564	C₄×C₈₉	1	16	yes	direct product factor
48	C₂×#125	C₂²×C₈₉	1	15	yes	—
49	#389	C₂²×C₈₉	1	30	yes	—
50	#387	C₂²×C₈₉	1	60	yes	—
51	#382	C₂²×C₈₉	1	15	yes	—
52	C₄×C₄⋊C₄	C₂²×C₈₉	1	30	yes	—
53	C₄³	C₂²×C₈₉	1	5	yes	—
54	#125	C₂×C₄×C₈₉	1	120	yes	—
55	C₂×C₄⋊C₄	C₂³×C₈₉	1	30	yes	—
56	C₂×C₄⋊C₄	C₂³×C₈₉	1	30	yes	—
57	C₂×C₄²	C₂³×C₈₉	1	15	yes	—
58	C₂×C₄²	C₂³×C₈₉	1	15	yes	—
59	C₂×C₄²	C₂³×C₈₉	1	5	yes	—
60	#95	C₂³×C₈₉	1	60	yes	—
61	C₂²×C₄	C₂⁴×C₈₉	1	15	yes	—
62	C₂²×C₄	C₂⁴×C₈₉	1	15	yes	—
63	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
64	C₄⋊C₄	—	4	30	no	—
65	C₄⋊C₄	C₂²×C₄×C₈₉	1	120	yes	—
66	C₄²	—	2	30	no	—
67	C₄²	—	4	15	no	—
68	C₄²	C₂²×C₄×C₈₉	1	20	yes	—
69	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
70	C₂×C₄	—	2	15	no	—
71	C₂×C₄	—	2	15	no	—
72	C₂×C₄	—	2	15	no	—
73	C₂×C₄	—	2	30	no	—
74	C₂×C₄	C₂³×C₄×C₈₉	1	30	yes	—
75	C₂×C₄	2₋¹⁺⁴×C₈₉	1	6	yes	—
76	C₂²	C₂⁴×C₄×C₈₉	1	1	yes	characteristic
77	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	3	yes	—
78	C₂²	#585×C₈₉	1	3	yes	—
79	C₄	—	2	30	no	—
80	C₄	—	4	15	no	—
81	C₄	#564×C₈₉	1	4	yes	direct product factor
82	C₂	C₄×2₋¹⁺⁴×C₈₉	1	3	yes	—
83	C₂	C₂×#564×C₈₉	1	1	yes	characteristic
84	C₂	C₈₉×#3531	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₈₉	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₈₉
Frattini, cosocle	C₂³	C₂⁵×C₈₉
socle, prime radical	C₂³×C₈₉	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
4. #564×C₈₉	C₄	direct (N × H)
38. C₄×C₈₉	#564	direct (N × H)
39. C₄×#564	C₈₉	direct (N × H)
46. C₈₉	C₄×#564	direct (N × H)
47. #564	C₄×C₈₉	direct (N × H)
81. C₄	#564×C₈₉	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×#564×C₈₉	2
C₈₉×#2382	2
C₄×#125×C₈₉	2
C₄×#564	89

Subgroups — C4×#564×C89 #36412203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#564×C₈₉ #36412203