Subgroups — C₄×#19151317 #36442231

Order 22784.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151317	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic
3	#19151317	C₄	1	4	yes	direct product factor
4	C₂×C₃₂×C₈₉	C₄	1	1	yes	characteristic
5	C₂×C₃₂×C₈₉	C₂²	1	1	yes	characteristic
6	C₄×C₁₆×C₈₉	C₄	1	1	yes	characteristic
7	C₂×C₁₆×C₈₉	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₈₉	C₈	1	1	yes	characteristic
10	C₃₂×C₈₉	C₈	1	2	yes	—
11	C₃₂×C₈₉	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₈₉	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₈₉	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₈₉	C₁₆	1	1	yes	characteristic
15	C₁₆×C₈₉	C₁₆	1	2	yes	—
16	C₁₆×C₈₉	C₄²	1	1	yes	characteristic
17	C₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₈₉	C₃₂	1	2	yes	—
19	C₂×C₄×C₈₉	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₈₉	C₃₂	1	2	yes	—
21	C₈×C₈₉	C₄×C₈	1	1	yes	characteristic
22	C₈×C₈₉	C₂×C₁₆	1	1	yes	characteristic
23	C₂²×C₈₉	C₂×C₃₂	1	1	yes	characteristic
24	C₄×C₈₉	C₆₄	1	4	yes	complemented
25	C₄×C₈₉	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₈₉	C₂×C₃₂	1	1	yes	characteristic
27	C₄×C₆₄	—	89	1	no	maximal, Sylow
28	C₂×C₈₉	C₄×C₃₂	1	1	yes	characteristic
29	C₂×C₈₉	C₂×C₆₄	1	2	yes	—
30	C₂×C₆₄	—	89	2	no	—
31	C₄×C₃₂	D₈₉	1	1	yes	characteristic
32	C₈₉	C₄×C₆₄	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃₂	Dic₈₉	1	1	yes	characteristic
34	C₂×C₃₂	C₂×D₈₉	1	1	yes	characteristic
35	C₄×C₁₆	Dic₈₉	1	1	yes	characteristic
36	C₆₄	—	89	4	no	—
37	C₂×C₁₆	#10623494	1	1	yes	characteristic
38	C₂×C₁₆	C₂×Dic₈₉	1	1	yes	characteristic
39	C₄×C₈	#10623494	1	1	yes	characteristic
40	C₃₂	#10623494	1	2	yes	—
41	C₃₂	C₄×D₈₉	1	2	yes	—
42	C₂×C₈	#13083549	1	1	yes	characteristic
43	C₂×C₈	C₂×#10623494	1	1	yes	characteristic
44	C₄²	#13083549	1	1	yes	characteristic
45	C₁₆	#13083549	1	2	yes	—
46	C₁₆	C₄×Dic₈₉	1	1	yes	characteristic
47	C₁₆	C₂×#10623494	1	1	yes	characteristic
48	C₂×C₄	#15667918	1	2	yes	—
49	C₂×C₄	C₂×#13083549	1	1	yes	characteristic
50	C₈	#15667918	1	2	yes	—
51	C₈	C₄×#10623494	1	1	yes	characteristic
52	C₈	C₂×#13083549	1	1	yes	characteristic
53	C₂²	C₂×#15667918	1	1	yes	characteristic
54	C₄	#19151317	1	4	yes	direct product factor
55	C₄	C₄×#13083549	1	1	yes	characteristic
56	C₄	C₂×#15667918	1	1	yes	characteristic
57	C₂	C₄×#15667918	1	1	yes	characteristic
58	C₂	C₂×#19151317	1	2	yes	—

	subgroup	G/H
center, hypercenter	C₄×C₃₂	D₈₉
commutator, hypocenter	C₈₉	C₄×C₆₄
Frattini	C₂×C₃₂	C₂×D₈₉
Fitting	C₄×C₃₂×C₈₉	C₂
socle, prime radical	C₂²×C₈₉	C₂×C₃₂
cosocle	C₂×C₃₂×C₈₉	C₂²
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₄×C₃₂

Complements

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

N	H ≅ G/N	type
3. #19151317	C₄	direct (N × H)
24. C₄×C₈₉	C₆₄	semidirect
32. C₈₉	C₄×C₆₄	semidirect
54. C₄	#19151317	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×#19151317	2
C₄×C₃₂×C₈₉	2
C₄×C₆₄	89

Subgroups — C4×#19151317 #36442231

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19151317 #36442231