Subgroups — #43247758

Order 28352.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20296770	C₂	1	1	yes	maximal, characteristic
2	#28381844	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×D₄₄₃	C₂	1	1	yes	maximal, characteristic
4	#28381819	C₂	1	1	yes	maximal, characteristic, complemented
5	#28381818	C₂	1	1	yes	maximal, characteristic, complemented
6	#28381817	C₂	1	1	yes	maximal, characteristic, complemented
7	#107×C₄₄₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄₄₃	—	2	1	no	—
9	C₂×C₄×D₄₄₃	C₂²	1	1	yes	characteristic
10	#20296770	C₄	1	4	yes	complemented
11	C₂×C₄₄₃⋊C₈	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₄₄₃	C₂²	1	1	yes	characteristic
13	C₄⋊Dic₄₄₃	C₂²	1	1	yes	characteristic
14	Dic₄₄₃⋊C₄	—	2	1	no	—
15	(C₂×D₄₄₃)⋊C₄	—	2	1	no	—
16	C₄×Dic₄₄₃	—	2	1	no	—
17	C₂×C₈×C₄₄₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₄₄₃	C₂²	1	1	yes	characteristic
19	C₄⋊C₄×C₄₄₃	C₂²	1	1	yes	characteristic
20	C₂²×D₄₄₃	D₄	1	1	yes	characteristic
21	C₂×Dic₄₄₃	—	2	1	no	—
22	C₂×Dic₄₄₃	—	2	1	no	—
23	C₂×Dic₄₄₃	D₄	1	1	yes	characteristic
24	C₄×D₄₄₃	—	4	2	no	—
25	C₄×D₄₄₃	C₂×C₄	1	2	yes	—
26	C₄×D₄₄₃	Q₈	1	2	yes	—
27	C₄₄₃⋊C₈	C₂×C₄	1	2	yes	complemented
28	C₂×C₄×C₄₄₃	—	2	1	no	—
29	C₂×C₄×C₄₄₃	—	2	1	no	—
30	C₂×C₄×C₄₄₃	C₂³	1	1	yes	characteristic
31	C₈×C₄₄₃	C₂×C₄	1	2	yes	complemented
32	C₂²×C₄₄₃	C₂×D₄	1	1	yes	characteristic
33	C₂×D₄₄₃	—	2	1	no	—
34	C₂×D₄₄₃	—	2	1	no	—
35	C₂×D₄₄₃	C₄⋊C₄	1	2	yes	—
36	C₄×C₄₄₃	—	4	1	no	—
37	C₄×C₄₄₃	—	4	1	no	—
38	C₄×C₄₄₃	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₄₄₃	C₂×Q₈	1	1	yes	characteristic
40	Dic₄₄₃	—	4	1	no	—
41	Dic₄₄₃	—	4	1	no	—
42	Dic₄₄₃	C₄⋊C₄	1	2	yes	—
43	C₂×C₄₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₄₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
45	C₂×C₄₄₃	#137	1	1	yes	characteristic
46	D₄₄₃	—	2	2	no	—
47	C₄₄₃	#428	1	1	yes	characteristic, complemented, Sylow
48	#428	—	443	1	no	maximal, Sylow
49	C₂×M₁₆	—	443	1	no	—
50	#117	—	443	1	no	—
51	C₂×C₄⋊C₄	—	443	1	no	—
52	#107	—	443	1	no	—
53	#107	D₄₄₃	1	1	yes	characteristic, complemented
54	#106	—	443	1	no	—
55	#106	—	443	1	no	—
56	C₂²×C₄	—	886	1	no	—
57	C₂²×C₄	—	443	1	no	—
58	M₁₆	—	443	4	no	—
59	C₂×C₈	—	443	1	no	—
60	C₂×C₈	C₂×D₄₄₃	1	1	yes	characteristic
61	C₄⋊C₄	—	886	1	no	—
62	C₄⋊C₄	—	443	1	no	—
63	C₄⋊C₄	—	443	1	no	—
64	C₄⋊C₄	C₂×D₄₄₃	1	1	yes	characteristic
65	C₄⋊C₄	C₂×D₄₄₃	1	1	yes	characteristic
66	C₂²⋊C₄	—	886	1	no	—
67	C₄²	—	886	1	no	—
68	C₂³	—	443	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	886	1	no	—
72	C₂×C₄	—	886	1	no	—
73	C₂×C₄	—	443	1	no	—
74	C₂×C₄	—	443	2	no	—
75	C₂×C₄	—	443	2	no	—
76	C₂×C₄	—	1772	2	no	—
77	C₂×C₄	C₂²×D₄₄₃	1	1	yes	characteristic
78	C₈	—	443	2	no	—
79	C₈	C₄×D₄₄₃	1	2	yes	complemented
80	C₂²	—	886	1	no	—
81	C₂²	—	886	1	no	—
82	C₂²	—	443	2	no	—
83	C₂²	D₄×D₄₄₃	1	1	yes	characteristic
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	443	2	no	—
87	C₄	—	1772	1	no	—
88	C₄	—	1772	1	no	—
89	C₄	C₂×C₄×D₄₄₃	1	1	yes	characteristic
90	C₄	Q₈×D₄₄₃	1	1	yes	characteristic
91	C₂	—	886	2	no	—
92	C₂	C₄⋊C₄×D₄₄₃	1	1	yes	characteristic
93	C₂	#28381910	1	1	yes	characteristic
94	C₂	#28381918	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₄₃
commutator	C₄×C₄₄₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₄₃
Fitting	#107×C₄₄₃	C₂
socle	C₂²×C₄₄₃	C₂×D₄
prime radical	C₂²×D₄₄₃	D₄
cosocle	C₂×C₄×C₄₄₃	C₂³
hypercenter	#107	D₄₄₃
hypocenter	C₄₄₃	#428
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
4. #28381819	C₂	semidirect
5. #28381818	C₂	semidirect
6. #28381817	C₂	semidirect
7. #107×C₄₄₃	C₂	semidirect
10. #20296770	C₄	semidirect
27. C₄₄₃⋊C₈	C₂×C₄	semidirect
31. C₈×C₄₄₃	C₂×C₄	semidirect
47. C₄₄₃	#428	semidirect
53. #107	D₄₄₃	semidirect
79. C₈	C₄×D₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#20296770	2
#28381844	2
C₄⋊C₄×D₄₄₃	2
#28381819	2
#28381818	2
#28381817	2
#107×C₄₄₃	2
#428	443