Subgroups — #36485632

Order 22784.

1278 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26018479	C₂	1	14	yes	maximal
2	C₂×C₄³×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#15667919	C₂²	1	28	yes	—
4	C₂²×C₄²×C₈₉	C₂²	1	7	yes	—
5	C₄³×C₈₉	C₄	1	8	yes	complemented
6	C₂³×Dic₈₉	C₂³	1	8	yes	—
7	#15667919	—	2	56	no	—
8	C₂³×C₄×C₈₉	C₂³	1	7	yes	—
9	C₂×C₄²×C₈₉	—	2	28	no	—
10	C₂×C₄²×C₈₉	C₂×C₄	1	28	yes	—
11	C₂²×Dic₈₉	—	2	56	no	—
12	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
13	C₂²×C₄×C₈₉	—	2	28	no	—
14	C₂²×C₄×C₈₉	C₂²×C₄	1	14	yes	—
15	C₂²×C₄×C₈₉	#41	1	28	yes	—
16	C₄²×C₈₉	—	2	56	no	—
17	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
18	C₂³×C₈₉	C₂×#41	1	14	yes	—
19	C₂×C₄×C₈₉	—	2	28	no	—
20	C₂×C₄×C₈₉	—	2	56	no	—
21	C₂×C₄×C₈₉	#117	1	28	yes	—
22	C₂×Dic₈₉	—	4	56	no	—
23	C₂²×C₈₉	C₂×#117	1	7	yes	—
24	C₂²×C₈₉	#529	1	28	yes	—
25	C₄×C₈₉	—	2	28	no	—
26	Dic₈₉	—	8	8	no	—
27	#14691	—	89	1	no	maximal, Sylow
28	C₂×C₈₉	#2283	1	7	yes	—
29	C₂×C₈₉	#2866	1	8	yes	—
30	C₂×C₄³	D₈₉	1	1	yes	characteristic
31	#1434	—	89	14	no	—
32	C₈₉	#14691	1	1	yes	characteristic, complemented, Sylow
33	C₂²×C₄²	C₂×D₈₉	1	7	yes	—
34	C₂×#95	—	89	28	no	—
35	C₄³	Dic₈₉	1	8	yes	complemented
36	C₂³×C₄	—	89	8	no	—
37	C₂³×C₄	C₂²×D₈₉	1	7	yes	—
38	C₂×C₄²	—	2	28	no	—
39	C₂×C₄²	C₂×Dic₈₉	1	28	yes	—
40	#95	—	178	56	no	—
41	C₂⁴	C₂³×D₈₉	1	1	yes	characteristic
42	C₂²×C₄	—	2	28	no	—
43	C₂²×C₄	—	178	56	no	—
44	C₂²×C₄	C₂²×Dic₈₉	1	14	yes	—
45	C₂²×C₄	#13083574	1	28	yes	—
46	C₄²	—	2	56	no	—
47	C₂³	C₂³×Dic₈₉	1	1	yes	characteristic
48	C₂³	C₂×#13083574	1	14	yes	—
49	C₂×C₄	—	2	56	no	—
50	C₂×C₄	—	2	28	no	—
51	C₂×C₄	—	356	56	no	—
52	C₂×C₄	#15667971	1	28	yes	—
53	C₂²	C₂×#15667971	1	7	yes	—
54	C₂²	#19152132	1	28	yes	—
55	C₄	—	2	28	no	—
56	C₄	—	712	8	no	—
57	C₂	#26022650	1	7	yes	—
58	C₂	#26028644	1	8	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₈₉
commutator	C₂³×C₈₉	C₂³×C₄
Fitting	C₂×C₄³×C₈₉	C₂
socle, prime radical, cosocle	C₂⁴×C₈₉	C₂⁴
hypercenter	C₂×C₄³	D₈₉
hypocenter	C₈₉	#14691
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
5. C₄³×C₈₉	C₄	semidirect
32. C₈₉	#14691	semidirect
35. C₄³	Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26018479	2
C₂×C₄³×C₈₉	2
#14691	89