Subgroups — #43248147

Order 28352.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381908	C₂	1	1	yes	maximal, characteristic, complemented
2	#28381832	C₂	1	1	yes	maximal, characteristic, complemented
3	#28381830	C₂	1	1	yes	maximal, characteristic, complemented
4	#28381829	C₂	1	1	yes	maximal, characteristic, complemented
5	#28381827	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#135×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	#20296787	—	2	1	no	—
9	Dic₁₇₇₂	C₂²	1	1	yes	characteristic
10	#20296776	—	2	1	no	—
11	D₃₅₄₄	C₂²	1	1	yes	characteristic
12	C₄₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
13	C₄₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
14	#41×C₄₄₃	—	2	1	no	—
15	Q₁₆×C₄₄₃	C₂²	1	1	yes	characteristic
16	SD₁₆×C₄₄₃	—	2	1	no	—
17	D₈×C₄₄₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×C₄₄₃	C₂²	1	1	yes	characteristic
19	Dic₈₈₆	—	2	1	no	—
20	D₁₇₇₂	—	2	1	no	—
21	C₂²⋊D₄₄₃	—	4	1	no	—
22	C₄×D₄₄₃	—	4	1	no	—
23	Q₈×C₄₄₃	—	2	1	no	—
24	D₄×C₄₄₃	—	2	1	no	—
25	D₄×C₄₄₃	—	4	1	no	—
26	C₂×C₄×C₄₄₃	—	4	1	no	—
27	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
28	C₈×C₄₄₃	D₄	1	1	yes	characteristic
29	C₈×C₄₄₃	C₂³	1	1	yes	characteristic
30	C₂²×C₄₄₃	—	4	1	no	—
31	C₂²×C₄₄₃	D₈	1	1	yes	characteristic
32	C₂×D₄₄₃	—	4	1	no	—
33	C₄×C₄₄₃	—	4	1	no	—
34	C₄×C₄₄₃	D₈	1	1	yes	characteristic
35	C₄×C₄₄₃	C₂×D₄	1	1	yes	characteristic
36	Dic₄₄₃	—	4	1	no	—
37	C₂×C₄₄₃	—	2	1	no	—
38	C₂×C₄₄₃	—	8	1	no	—
39	C₂×C₄₄₃	C₂×D₈	1	1	yes	characteristic
40	D₄₄₃	—	8	1	no	—
41	C₄₄₃	#508	1	1	yes	characteristic, complemented, Sylow
42	#508	—	443	1	no	maximal, Sylow
43	#135	—	443	1	no	—
44	#135	D₄₄₃	1	1	yes	characteristic, complemented
45	Q₃₂	—	443	1	no	—
46	SD₃₂	—	443	1	no	—
47	SD₃₂	—	443	1	no	—
48	D₁₆	—	443	1	no	—
49	C₂×C₁₆	—	443	1	no	—
50	#41	—	2	1	no	—
51	#41	—	886	1	no	—
52	Q₁₆	—	443	1	no	—
53	Q₁₆	C₂×D₄₄₃	1	1	yes	characteristic
54	SD₁₆	—	2	1	no	—
55	SD₁₆	—	886	1	no	—
56	D₈	—	443	1	no	—
57	D₈	C₂×D₄₄₃	1	1	yes	characteristic
58	C₂×C₈	C₂×D₄₄₃	1	1	yes	characteristic
59	C₁₆	—	443	1	no	—
60	C₁₆	—	443	1	no	—
61	Q₈	—	2	1	no	—
62	Q₈	—	886	1	no	—
63	D₄	—	2	1	no	—
64	D₄	—	4	1	no	—
65	D₄	—	886	1	no	—
66	D₄	—	1772	1	no	—
67	C₂×C₄	—	4	1	no	—
68	C₂×C₄	—	1772	1	no	—
69	C₂×C₄	C₂²⋊D₄₄₃	1	1	yes	characteristic
70	C₈	C₂²⋊D₄₄₃	1	1	yes	characteristic
71	C₈	C₂²×D₄₄₃	1	1	yes	characteristic
72	C₂²	—	4	1	no	—
73	C₂²	—	1772	1	no	—
74	C₂²	#20296772	1	1	yes	characteristic
75	C₄	—	4	1	no	—
76	C₄	—	1772	1	no	—
77	C₄	#20296772	1	1	yes	characteristic
78	C₄	C₂×C₂²⋊D₄₄₃	1	1	yes	characteristic
79	C₂	—	2	1	no	—
80	C₂	—	8	1	no	—
81	C₂	—	3544	1	no	—
82	C₂	C₂×#20296772	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#20296772
commutator, cosocle	C₈×C₄₄₃	C₂³
Frattini	C₈	C₂²×D₄₄₃
Fitting	#135×C₄₄₃	C₂
socle	C₂×C₄₄₃	C₂×D₈
hypercenter	#135	D₄₄₃
hypocenter	C₄₄₃	#508
LCS	G ▷ C₈×C₄₄₃ ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #28381908	C₂	semidirect
2. #28381832	C₂	semidirect
3. #28381830	C₂	semidirect
4. #28381829	C₂	semidirect
5. #28381827	C₂	semidirect
6. C₂×C₄₄₃⋊C₁₆	C₂	semidirect
7. #135×C₄₄₃	C₂	semidirect
41. C₄₄₃	#508	semidirect
44. #135	D₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
#28381908	2
#28381832	2
#28381830	2
#28381829	2
#28381827	2
C₂×C₄₄₃⋊C₁₆	2
#135×C₄₄₃	2
#508	443