Subgroups — #26028644

Order 11392.

418 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19151489	C₂	1	7	yes	maximal
2	#19151482	C₂	1	7	yes	maximal, complemented
3	C₄³×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#13083553	C₂²	1	7	yes	—
5	C₂×#13083551	C₂²	1	7	yes	—
6	#15667919	C₂²	1	14	yes	—
7	C₂×C₄²×C₈₉	C₂²	1	7	yes	—
8	C₂³×D₈₉	C₂³	1	1	yes	characteristic
9	C₂²×Dic₈₉	C₂³	1	7	yes	—
10	#13083553	—	2	14	no	—
11	#13083551	—	2	14	no	—
12	C₂²×C₄×C₈₉	C₂³	1	7	yes	—
13	C₄²×C₈₉	—	2	14	no	—
14	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
15	C₂²×D₈₉	—	2	7	no	—
16	C₂×C₄×C₈₉	—	2	14	no	—
17	C₂×C₄×C₈₉	#41	1	14	yes	—
18	C₂×Dic₈₉	—	2	7	no	—
19	C₂×Dic₈₉	—	2	14	no	—
20	C₂²×C₈₉	C₂×#41	1	7	yes	—
21	C₂×D₈₉	—	4	7	no	—
22	C₄×C₈₉	—	2	14	no	—
23	Dic₈₉	—	4	7	no	—
24	C₂×C₈₉	#529	1	7	yes	—
25	D₈₉	—	8	1	no	—
26	#2866	—	89	1	no	maximal, Sylow
27	C₈₉	#2866	1	1	yes	characteristic, complemented, Sylow
28	#388	—	89	7	no	—
29	#387	—	89	7	no	—
30	C₄³	D₈₉	1	1	yes	characteristic, complemented
31	C₂×C₄⋊C₄	—	89	7	no	—
32	C₂×C₂²⋊C₄	—	89	7	no	—
33	C₂×C₄²	C₂×D₈₉	1	7	yes	—
34	#95	—	89	14	no	—
35	C₂⁴	—	89	1	no	—
36	C₂²×C₄	—	89	7	no	—
37	C₂²×C₄	C₂²×D₈₉	1	7	yes	—
38	C₄⋊C₄	—	178	14	no	—
39	C₂²⋊C₄	—	178	14	no	—
40	C₄²	—	2	14	no	—
41	C₂³	—	178	7	no	—
42	C₂³	C₂³×D₈₉	1	1	yes	characteristic
43	C₂×C₄	—	2	14	no	—
44	C₂×C₄	—	178	7	no	—
45	C₂×C₄	—	178	14	no	—
46	C₂×C₄	#13083574	1	14	yes	—
47	C₂²	—	356	7	no	—
48	C₂²	C₂×#13083574	1	7	yes	—
49	C₄	—	2	14	no	—
50	C₄	—	356	7	no	—
51	C₂	—	712	1	no	—
52	C₂	#19152132	1	7	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₈₉
commutator, socle, cosocle	C₂³×C₈₉	C₂⁴
Fitting	C₄³×C₈₉	C₂
prime radical	C₂³×D₈₉	C₂³
hypercenter	C₄³	D₈₉
hypocenter	C₈₉	#2866
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₄³

Complements

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

N	H ≅ G/N	type
2. #19151482	C₂	semidirect
3. C₄³×C₈₉	C₂	semidirect
27. C₈₉	#2866	semidirect
30. C₄³	D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#19151489	2
#19151482	2
C₄³×C₈₉	2
#2866	89