Subgroups — #28417352

Order 14912.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418610	C₂	1	1	yes	maximal, characteristic, complemented
2	#21418603	C₂	1	1	yes	maximal, characteristic, complemented
3	#21418558	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11745400	—	2	1	no	—
5	#16836597	—	2	1	no	—
6	#16836595	—	2	1	no	—
7	#16836581	—	2	1	no	—
8	D₁₈₆₄	C₄	1	1	yes	characteristic, complemented
9	C₈×D₂₃₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₂₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂×#11745400	—	4	1	no	—
12	D₉₃₂	—	2	1	no	—
13	D₉₃₂	—	4	1	no	—
14	C₄×D₂₃₃	—	4	1	no	—
15	C₄×D₂₃₃	D₄	1	1	yes	characteristic
16	#14272338	D₄	1	1	yes	characteristic
17	Q₈×C₂₃₃	—	2	1	no	—
18	C₈×C₂₃₃	C₂×C₄	1	1	yes	characteristic
19	C₂×D₂₃₃	—	4	1	no	—
20	C₂×D₂₃₃	D₈	1	1	yes	characteristic
21	#11745400	—	8	1	no	—
22	C₄×C₂₃₃	—	4	1	no	—
23	C₄×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
24	Dic₂₃₃	SD₁₆	1	1	yes	characteristic
25	C₂×C₂₃₃	#102	1	1	yes	characteristic
26	D₂₃₃	—	2	1	no	—
27	D₂₃₃	—	8	1	no	—
28	C₂₃₃	#360	1	1	yes	characteristic, complemented, Sylow
29	#360	—	233	1	no	maximal, Sylow
30	#135	—	233	1	no	—
31	M₃₂	—	233	1	no	—
32	#106	—	233	1	no	—
33	#41	—	466	1	no	—
34	Q₁₆	#11745400	1	1	yes	characteristic, complemented
35	SD₁₆	—	466	1	no	—
36	D₈	—	233	1	no	—
37	C₂×C₈	—	233	1	no	—
38	C₄⋊C₄	—	466	1	no	—
39	C₁₆	—	466	1	no	—
40	Q₈	—	2	1	no	—
41	D₄	—	932	1	no	—
42	D₄	—	466	1	no	—
43	C₂×C₄	—	932	1	no	—
44	C₂×C₄	—	932	1	no	—
45	C₂×C₄	—	233	1	no	—
46	C₈	—	233	1	no	—
47	C₈	C₂×#11745400	1	1	yes	characteristic
48	C₂²	—	932	1	no	—
49	C₂²	—	233	1	no	—
50	C₄	—	4	1	no	—
51	C₄	—	1864	1	no	—
52	C₄	—	233	1	no	—
53	C₄	C₂²⋊#11745400	1	1	yes	characteristic
54	C₂	—	1864	1	no	—
55	C₂	—	466	1	no	—
56	C₂	#21418597	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21418597
commutator	C₈×C₂₃₃	C₂×C₄
Frattini	C₈	C₂×#11745400
Fitting	Q₁₆×C₂₃₃	C₄
socle	C₂×C₂₃₃	#102
prime radical	#21418558	C₂
cosocle	C₈×D₂₃₃	C₂²
hypercenter	Q₁₆	#11745400
hypocenter	C₂₃₃	#360
LCS	G ▷ C₈×C₂₃₃ ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
1. #21418610	C₂	semidirect
2. #21418603	C₂	semidirect
8. D₁₈₆₄	C₄	semidirect
10. Q₁₆×C₂₃₃	C₄	semidirect
28. C₂₃₃	#360	semidirect
34. Q₁₆	#11745400	semidirect

Maximal subgroups

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

subgroup	index
#21418610	2
#21418603	2
#21418558	2
#360	233