Subgroups — #44450013

Order 29824.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#21418441	C₂	1	1	yes	maximal, characteristic
2	#28416265	C₂	1	1	yes	maximal, characteristic
3	#368×C₂₃₃	C₂	1	1	yes	maximal, characteristic
4	#21418471	—	2	1	no	—
5	#21418441	C₄	1	2	yes	—
6	C₂×C₁₆×C₂₃₃	C₂²	1	1	yes	characteristic
7	#108×C₂₃₃	—	2	1	no	—
8	#16836578	—	4	1	no	—
9	M₁₆×C₂₃₃	—	4	1	no	—
10	C₂×C₈×C₂₃₃	D₄	1	1	yes	characteristic
11	C₁₆×C₂₃₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₂₃₃	Q₈	1	1	yes	characteristic
13	#14272338	—	8	1	no	—
14	C₂×C₄×C₂₃₃	D₈	1	1	yes	characteristic
15	C₈×C₂₃₃	—	8	1	no	—
16	C₈×C₂₃₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₂₃₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₂₃₃	Q₃₂	1	1	yes	characteristic
19	C₄×C₂₃₃	#107	1	1	yes	characteristic
20	C₄×C₂₃₃	D₁₆	1	1	yes	characteristic
21	C₂×C₂₃₃	—	2	1	no	—
22	C₂×C₂₃₃	#366	1	1	yes	characteristic
23	C₂₃₃	#1425	1	1	yes	characteristic, complemented, Sylow
24	#1425	—	233	1	no	maximal, Sylow
25	C₂×C₃₂	—	233	1	no	—
26	#368	—	233	1	no	—
27	#368	D₂₃₃	1	1	yes	characteristic
28	C₂×C₁₆	C₂×D₂₃₃	1	1	yes	characteristic
29	#108	—	2	1	no	—
30	#108	—	466	1	no	—
31	C₃₂	—	233	2	no	—
32	M₁₆	—	4	1	no	—
33	M₁₆	—	932	1	no	—
34	C₂×C₈	C₂²⋊D₂₃₃	1	1	yes	characteristic
35	C₁₆	C₄×D₂₃₃	1	1	yes	characteristic
36	C₁₆	Dic₄₆₆	1	1	yes	characteristic
37	C₂×C₄	#16836579	1	1	yes	characteristic
38	C₈	—	8	1	no	—
39	C₈	—	1864	1	no	—
40	C₈	#16836573	1	1	yes	characteristic
41	C₈	#16836584	1	1	yes	characteristic
42	C₂²	#21418481	1	1	yes	characteristic
43	C₄	#21418468	1	1	yes	characteristic
44	C₄	#21418476	1	1	yes	characteristic
45	C₂	—	2	1	no	—
46	C₂	#28416260	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#21418476
commutator	C₁₆×C₂₃₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₂₃₃
Fitting	#368×C₂₃₃	C₂
socle	C₂×C₂₃₃	#366
prime radical	C₂²×C₂₃₃	Q₃₂
cosocle	C₂×C₁₆×C₂₃₃	C₂²
hypercenter	#368	D₂₃₃
hypocenter	C₂₃₃	#1425
LCS	G ▷ C₁₆×C₂₃₃ ▷ C₈×C₂₃₃ ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #368

Complements

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

N	H ≅ G/N	type
23. C₂₃₃	#1425	semidirect

Maximal subgroups

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

subgroup	index
C₂×#21418441	2
#28416265	2
#368×C₂₃₃	2
#1425	233