Subgroups — #43247478

Order 28352.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28381845	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂×M₁₆×C₄₄₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×Dic₄₄₃	—	2	1	no	—
5	C₄⋊Dic₄₄₃	C₄	1	2	yes	complemented
6	C₂²⋊Dic₄₄₃	—	2	1	no	—
7	C₄×Dic₄₄₃	—	2	1	no	—
8	C₄×Dic₄₄₃	—	2	1	no	—
9	C₄×Dic₄₄₃	C₄	1	2	yes	complemented
10	C₂²×C₄×C₄₄₃	C₂²	1	1	yes	characteristic
11	M₁₆×C₄₄₃	—	2	1	no	—
12	M₁₆×C₄₄₃	C₄	1	2	yes	complemented
13	C₂×C₈×C₄₄₃	—	2	1	no	—
14	C₂×Dic₄₄₃	—	2	4	no	—
15	C₂×Dic₄₄₃	—	2	2	no	—
16	C₂×Dic₄₄₃	—	2	2	no	—
17	C₂³×C₄₄₃	D₄	1	1	yes	characteristic
18	C₂×C₄×C₄₄₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₄₄₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₄₄₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
22	C₂×C₄×C₄₄₃	D₄	1	1	yes	characteristic
23	C₂×C₄×C₄₄₃	Q₈	1	1	yes	characteristic
24	C₈×C₄₄₃	—	2	2	no	—
25	C₂²×C₄₄₃	—	2	2	no	—
26	C₂²×C₄₄₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄₄₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₄₄₃	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₄₄₃	C₄²	1	1	yes	characteristic
30	C₄×C₄₄₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₄₄₃	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₄₄₃	C₄⋊C₄	1	1	yes	characteristic
33	Dic₄₄₃	—	2	4	no	—
34	Dic₄₄₃	—	4	2	no	—
35	C₂×C₄₄₃	—	2	1	no	—
36	C₂×C₄₄₃	—	2	1	no	—
37	C₂×C₄₄₃	#95	1	1	yes	characteristic
38	C₂×C₄₄₃	#104	1	2	yes	—
39	C₄₄₃	#339	1	1	yes	characteristic, complemented, Sylow
40	#339	—	443	1	no	maximal, Sylow
41	C₂×M₁₆	D₄₄₃	1	1	yes	characteristic
42	#117	—	443	1	no	—
43	C₂×C₄²	—	443	1	no	—
44	C₂²×C₄	—	886	1	no	—
45	C₂²×C₄	C₂×D₄₄₃	1	1	yes	characteristic
46	M₁₆	—	2	1	no	—
47	M₁₆	Dic₄₄₃	1	2	yes	complemented
48	C₂×C₈	—	2	1	no	—
49	C₄⋊C₄	—	443	2	no	—
50	C₂²⋊C₄	—	886	1	no	—
51	C₄²	—	886	1	no	—
52	C₄²	—	886	1	no	—
53	C₄²	—	443	2	no	—
54	C₂³	D₁₇₇₂	1	1	yes	characteristic
55	C₂×C₄	—	886	4	no	—
56	C₂×C₄	—	886	2	no	—
57	C₂×C₄	—	886	2	no	—
58	C₂×C₄	C₄×D₄₄₃	1	1	yes	characteristic
59	C₂×C₄	C₄×D₄₄₃	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₄₄₃	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₄₄₃	1	1	yes	characteristic
62	C₂×C₄	C₂²⋊D₄₄₃	1	1	yes	characteristic
63	C₂×C₄	Dic₈₈₆	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	(C₂×D₄₄₃)⋊C₄	1	1	yes	characteristic
67	C₂²	(C₂×D₄₄₃)⋊C₄	1	1	yes	characteristic
68	C₂²	C₄⋊Dic₄₄₃	1	1	yes	characteristic
69	C₄	—	886	4	no	—
70	C₄	—	1772	2	no	—
71	C₄	C₄×Dic₄₄₃	1	1	yes	characteristic
72	C₄	C₂²⋊Dic₄₄₃	1	1	yes	characteristic
73	C₄	Dic₄₄₃⋊C₄	1	1	yes	characteristic
74	C₄	Dic₄₄₃⋊C₄	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	2	1	no	—
77	C₂	C₄₄₃⋊#95	1	1	yes	characteristic
78	C₂	#28381812	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₄₄₃
commutator	C₄×C₄₄₃	C₄²
Frattini	C₂²×C₄	C₂×D₄₄₃
Fitting	C₂×M₁₆×C₄₄₃	C₂
socle	C₂²×C₄₄₃	C₂²⋊C₄
prime radical	C₂³×C₄₄₃	D₄
cosocle	C₂²×C₄×C₄₄₃	C₂²
hypercenter	C₂×M₁₆	D₄₄₃
hypocenter	C₄₄₃	#339
LCS	G ▷ C₄×C₄₄₃ ▷ C₂×C₄₄₃ ▷ C₄₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
5. C₄⋊Dic₄₄₃	C₄	semidirect
9. C₄×Dic₄₄₃	C₄	semidirect
12. M₁₆×C₄₄₃	C₄	semidirect
39. C₄₄₃	#339	semidirect
47. M₁₆	Dic₄₄₃	semidirect

Maximal subgroups

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

subgroup	index
#28381845	2
C₂×C₄×Dic₄₄₃	2
C₂×M₁₆×C₄₄₃	2
#339	443