Subgroups — #401×Dic₈₉ #36476292

Order 22784.

1222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26018514	C₂	1	7	yes	maximal
2	#95×Dic₈₉	C₂	1	7	yes	maximal
3	C₂×#401×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×Dic₈₉	C₂²	1	7	yes	—
5	C₂×#15667919	C₂²	1	21	yes	—
6	#401×C₈₉	C₄	1	8	yes	complemented
7	C₂×#95×C₈₉	C₂²	1	7	yes	—
8	C₂³×Dic₈₉	C₂³	1	7	yes	—
9	C₂³×Dic₈₉	C₂³	1	1	yes	characteristic
10	C₂×C₄×Dic₈₉	—	2	42	no	—
11	#15667919	—	2	42	no	—
12	C₂³×C₄×C₈₉	C₂³	1	7	yes	—
13	#95×C₈₉	C₂×C₄	1	28	yes	—
14	C₂²×Dic₈₉	—	2	21	no	—
15	C₂²×Dic₈₉	—	2	21	no	—
16	C₂²×Dic₈₉	#41	1	14	yes	—
17	C₂²×Dic₈₉	#41	1	14	yes	—
18	C₄×Dic₈₉	—	4	28	no	—
19	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
20	C₂²×C₄×C₈₉	—	2	21	no	—
21	C₂²×C₄×C₈₉	—	2	21	no	—
22	C₂²×C₄×C₈₉	C₂²×C₄	1	14	yes	—
23	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
24	C₂³×C₈₉	C₂×#41	1	7	yes	—
25	C₂³×C₈₉	C₂×#41	1	7	yes	—
26	C₂×C₄×C₈₉	—	2	42	no	—
27	C₂×C₄×C₈₉	—	4	7	no	—
28	C₂×C₄×C₈₉	—	4	21	no	—
29	C₂×Dic₈₉	—	2	42	no	—
30	C₂×Dic₈₉	—	4	7	no	—
31	C₂×Dic₈₉	—	4	21	no	—
32	C₂×Dic₈₉	#126	1	28	yes	—
33	C₂²×C₈₉	C₄×#41	1	7	yes	—
34	C₂²×C₈₉	C₂×#126	1	7	yes	—
35	C₂²×C₈₉	#529	1	21	yes	—
36	C₄×C₈₉	—	4	14	no	—
37	Dic₈₉	—	4	14	no	—
38	Dic₈₉	#401	1	8	yes	direct product factor
39	C₄×#401	—	89	1	no	maximal, Sylow
40	C₂×C₈₉	C₄×#126	1	7	yes	—
41	C₂×C₈₉	C₂×#401	1	1	yes	characteristic
42	C₂×C₈₉	#2401	1	7	yes	—
43	C₂×#401	D₈₉	1	1	yes	characteristic
44	#1443	—	89	7	no	—
45	C₄×#95	—	89	7	no	—
46	C₈₉	C₄×#401	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₄²	—	89	7	no	—
48	#401	Dic₈₉	1	8	yes	direct product factor
49	C₂×#95	—	89	21	no	—
50	C₂×#95	C₂×D₈₉	1	7	yes	—
51	C₂³×C₄	—	89	1	no	—
52	C₂³×C₄	—	89	7	no	—
53	C₂³×C₄	C₂²×D₈₉	1	7	yes	—
54	C₂×C₄²	—	178	42	no	—
55	#95	—	178	42	no	—
56	#95	C₂×Dic₈₉	1	28	yes	—
57	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
58	C₂²×C₄	—	2	21	no	—
59	C₂²×C₄	—	2	21	no	—
60	C₂²×C₄	—	89	14	no	—
61	C₂²×C₄	—	89	14	no	—
62	C₂²×C₄	—	178	21	no	—
63	C₂²×C₄	—	178	21	no	—
64	C₂²×C₄	C₂²×Dic₈₉	1	14	yes	—
65	C₄²	—	356	28	no	—
66	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
67	C₂³	#41×D₈₉	1	7	yes	—
68	C₂³	#41×D₈₉	1	7	yes	—
69	C₂×C₄	—	2	42	no	—
70	C₂×C₄	—	4	21	no	—
71	C₂×C₄	—	4	7	no	—
72	C₂×C₄	—	89	28	no	—
73	C₂×C₄	—	356	21	no	—
74	C₂×C₄	—	356	7	no	—
75	C₂×C₄	—	178	42	no	—
76	C₂²	#41×Dic₈₉	1	7	yes	—
77	C₂²	#126×D₈₉	1	7	yes	—
78	C₂²	#19152131	1	21	yes	—
79	C₄	—	4	14	no	—
80	C₄	—	89	8	no	—
81	C₄	—	356	14	no	—
82	C₂	#126×Dic₈₉	1	7	yes	—
83	C₂	#401×D₈₉	1	1	yes	characteristic
84	C₂	#26023555	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₈₉
commutator	C₂³×C₈₉	C₂³×C₄
Fitting	C₂×#401×C₈₉	C₂
socle, prime radical, cosocle	C₂⁴×C₈₉	C₂⁴
hypercenter	C₂×#401	D₈₉
hypocenter	C₈₉	C₄×#401
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×#401

Complements

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

N	H ≅ G/N	type
6. #401×C₈₉	C₄	semidirect
38. Dic₈₉	#401	direct (N × H)
46. C₈₉	C₄×#401	semidirect
48. #401	Dic₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
#26018514	2
#95×Dic₈₉	2
C₂×#401×C₈₉	2
C₄×#401	89

Subgroups — #401×Dic89 #36476292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #401×Dic₈₉ #36476292