Subgroups — #34039313

Order 18976.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23748733	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₂₃₇₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#23748722	C₂	1	2	yes	maximal, complemented
4	D₄₇₄₄	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₅₉₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₅₉₃	—	2	1	no	—
7	Dic₁₁₈₆	C₂²	1	1	yes	characteristic, complemented
8	D₂₃₇₂	—	2	1	no	—
9	D₂₃₇₂	C₂²	1	2	yes	—
10	D₂₃₇₂	C₂²	1	1	yes	characteristic, complemented
11	C₂²⋊D₅₉₃	—	2	1	no	—
12	C₄×D₅₉₃	—	2	1	no	—
13	C₂×C₄×C₅₉₃	C₂²	1	1	yes	characteristic
14	C₈×C₅₉₃	C₂²	1	2	yes	complemented
15	C₂²×C₅₉₃	D₄	1	1	yes	characteristic
16	C₂×D₅₉₃	—	2	1	no	—
17	C₂×D₅₉₃	—	2	2	no	—
18	C₂×D₅₉₃	—	4	2	no	—
19	C₄×C₅₉₃	D₄	1	1	yes	characteristic
20	C₄×C₅₉₃	C₂³	1	1	yes	characteristic
21	Dic₅₉₃	—	2	1	no	—
22	C₂×C₅₉₃	—	2	1	no	—
23	C₂×C₅₉₃	C₂×D₄	1	1	yes	characteristic
24	D₅₉₃	—	4	1	no	—
25	D₅₉₃	—	4	2	no	—
26	C₅₉₃	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
27	AGL(1,ℤ/8)	—	593	1	no	maximal, Sylow
28	#41	—	593	1	no	—
29	C₂×D₄	—	593	1	no	—
30	SD₁₆	—	593	2	no	—
31	D₈	—	593	2	no	—
32	M₁₆	D₅₉₃	1	1	yes	characteristic, complemented
33	C₂³	—	1186	1	no	—
34	Q₈	—	593	1	no	—
35	D₄	—	593	2	no	—
36	D₄	—	593	1	no	—
37	D₄	—	1186	1	no	—
38	D₄	—	1186	1	no	—
39	C₂×C₄	—	1186	1	no	—
40	C₂×C₄	C₂×D₅₉₃	1	1	yes	characteristic
41	C₈	C₂×D₅₉₃	1	2	yes	complemented
42	C₂²	—	2372	2	no	—
43	C₂²	—	1186	1	no	—
44	C₂²	—	1186	2	no	—
45	C₂²	D₂₃₇₂	1	1	yes	characteristic
46	C₄	—	1186	1	no	—
47	C₄	D₂₃₇₂	1	1	yes	characteristic
48	C₄	C₂²×D₅₉₃	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	—	2372	2	no	—
51	C₂	—	2372	1	no	—
52	C₂	C₂×D₂₃₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₂₃₇₂
commutator, cosocle	C₄×C₅₉₃	C₂³
Frattini	C₄	C₂²×D₅₉₃
Fitting	M₁₆×C₅₉₃	C₂
socle	C₂×C₅₉₃	C₂×D₄
hypercenter	M₁₆	D₅₉₃
hypocenter	C₅₉₃	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₅₉₃ ▷ C₂×C₅₉₃ ▷ C₅₉₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
1. #23748733	C₂	semidirect
2. C₂×D₂₃₇₂	C₂	semidirect
3. #23748722	C₂	semidirect
4. D₄₇₄₄	C₂	semidirect
5. M₁₆×C₅₉₃	C₂	semidirect
7. Dic₁₁₈₆	C₂²	semidirect
10. D₂₃₇₂	C₂²	semidirect
14. C₈×C₅₉₃	C₂²	semidirect
26. C₅₉₃	AGL(1,ℤ/8)	semidirect
32. M₁₆	D₅₉₃	semidirect
41. C₈	C₂×D₅₉₃	semidirect

Maximal subgroups

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

subgroup	index
#23748733	2
C₂×D₂₃₇₂	2
#23748722	2
D₄₇₄₄	2
M₁₆×C₅₉₃	2
AGL(1,ℤ/8)	593