Subgroups — #44416593

Order 29248.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28410492	C₂	1	1	yes	maximal, characteristic
2	#28410488	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₁₆×C₄₅₇	C₂	1	1	yes	maximal, characteristic
4	#20300725	—	2	1	no	—
5	#20300716	—	2	1	no	—
6	C₂×Q₈×C₄₅₇	—	2	1	no	—
7	Q₁₆×C₄₅₇	—	2	1	no	—
8	Q₁₆×C₄₅₇	C₄	1	2	yes	—
9	C₂×C₈×C₄₅₇	C₂²	1	1	yes	characteristic
10	#16814532	—	4	1	no	—
11	Q₈×C₄₅₇	—	2	2	no	—
12	Q₈×C₄₅₇	—	4	1	no	—
13	C₂×C₄×C₄₅₇	—	4	1	no	—
14	C₂×C₄×C₄₅₇	D₄	1	1	yes	characteristic
15	C₈×C₄₅₇	C₂×C₄	1	1	yes	characteristic
16	C₈×C₄₅₇	D₄	1	1	yes	characteristic
17	C₂²×C₄₅₇	SD₁₆	1	1	yes	characteristic
18	C₄×C₄₅₇	—	4	2	no	—
19	C₄×C₄₅₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₄×C₄₅₇	D₈	1	1	yes	characteristic
21	C₂×C₄₅₇	—	2	1	no	—
22	C₂×C₄₅₇	#102	1	1	yes	characteristic
23	C₄₅₇	#362	1	1	yes	characteristic, complemented, Sylow
24	#362	—	457	1	no	maximal, Sylow
25	C₂×Q₁₆	D₄₅₇	1	1	yes	characteristic
26	M₃₂	—	457	1	no	—
27	#108	—	457	1	no	—
28	C₂×Q₈	—	2	1	no	—
29	Q₁₆	—	2	1	no	—
30	Q₁₆	Dic₄₅₇	1	2	yes	—
31	M₁₆	—	914	1	no	—
32	C₂×C₈	C₂×D₄₅₇	1	1	yes	characteristic
33	C₁₆	—	914	1	no	—
34	Q₈	—	2	2	no	—
35	Q₈	—	4	1	no	—
36	C₂×C₄	—	4	1	no	—
37	C₂×C₄	C₂²⋊D₄₅₇	1	1	yes	characteristic
38	C₈	—	1828	1	no	—
39	C₈	C₂×Dic₄₅₇	1	1	yes	characteristic
40	C₈	C₂²⋊D₄₅₇	1	1	yes	characteristic
41	C₂²	#20300729	1	1	yes	characteristic
42	C₄	—	4	2	no	—
43	C₄	C₂²⋊Dic₄₅₇	1	1	yes	characteristic
44	C₄	#20300726	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#28410473	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#28410473
commutator	C₈×C₄₅₇	C₂×C₄
Frattini	C₂×C₈	C₂×D₄₅₇
Fitting	C₂×Q₁₆×C₄₅₇	C₂
socle	C₂×C₄₅₇	#102
prime radical	C₂²×C₄₅₇	SD₁₆
cosocle	C₂×C₈×C₄₅₇	C₂²
hypercenter	C₂×Q₁₆	D₄₅₇
hypocenter	C₄₅₇	#362
LCS	G ▷ C₈×C₄₅₇ ▷ C₄×C₄₅₇ ▷ C₂×C₄₅₇ ▷ C₄₅₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×Q₁₆

Complements

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

N	H ≅ G/N	type
23. C₄₅₇	#362	semidirect

Maximal subgroups

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

subgroup	index
#28410492	2
#28410488	2
C₂×Q₁₆×C₄₅₇	2
#362	457