Subgroups — #28417536

Order 14912.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418632	C₂	1	1	yes	maximal, characteristic, complemented
2	#21418630	C₂	1	1	yes	maximal, characteristic, complemented
3	#21418623	C₂	1	1	yes	maximal, characteristic
4	#16836606	—	2	1	no	—
5	#16836606	—	2	1	no	—
6	#16836604	—	2	1	no	—
7	#16836604	C₄	1	1	yes	characteristic
8	#16836602	—	2	1	no	—
9	#16836602	C₂²	1	1	yes	characteristic
10	#16836595	C₄	1	1	yes	characteristic
11	#14272345	—	2	1	no	—
12	#14272345	D₄	1	1	yes	characteristic
13	#14272345	D₄	1	1	yes	characteristic
14	D₉₃₂	—	2	1	no	—
15	D₉₃₂	C₈	1	1	yes	characteristic
16	C₄×D₂₃₃	—	2	1	no	—
17	C₄×D₂₃₃	C₂×C₄	1	1	yes	characteristic
18	Q₈×C₂₃₃	C₈	1	1	yes	characteristic
19	C₂×D₂₃₃	—	2	1	no	—
20	C₂×D₂₃₃	M₁₆	1	1	yes	characteristic
21	C₄×C₂₃₃	—	2	1	no	—
22	C₄×C₂₃₃	C₂×C₈	1	1	yes	characteristic
23	Dic₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
24	C₂×C₂₃₃	C₂²⋊C₈	1	1	yes	characteristic
25	D₂₃₃	—	2	1	no	—
26	D₂₃₃	—	4	1	no	—
27	C₂₃₃	#350	1	1	yes	characteristic, complemented, Sylow
28	#350	—	233	1	no	maximal, Sylow
29	#131	—	233	1	no	—
30	M₃₂	—	233	1	no	—
31	C₂×C₁₆	—	233	1	no	—
32	#41	—	233	1	no	—
33	M₁₆	—	466	1	no	—
34	M₁₆	—	233	1	no	—
35	C₂×C₈	—	466	1	no	—
36	C₂×C₈	—	233	1	no	—
37	C₁₆	—	466	1	no	—
38	C₁₆	—	466	1	no	—
39	Q₈	#14272347	1	1	yes	characteristic
40	D₄	—	466	1	no	—
41	D₄	—	233	1	no	—
42	C₂×C₄	—	466	1	no	—
43	C₂×C₄	—	233	1	no	—
44	C₈	—	466	1	no	—
45	C₈	—	233	1	no	—
46	C₈	—	233	1	no	—
47	C₂²	—	466	1	no	—
48	C₂²	—	233	1	no	—
49	C₄	—	2	1	no	—
50	C₄	—	233	1	no	—
51	C₄	C₂×#14272347	1	1	yes	characteristic
52	C₂	—	932	1	no	—
53	C₂	—	466	1	no	—
54	C₂	C₂²⋊#14272347	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#14272347
commutator	C₄×C₂₃₃	C₂×C₈
Frattini	C₄	C₂×#14272347
Fitting	Q₈×C₂₃₃	C₈
socle	C₂×C₂₃₃	C₂²⋊C₈
prime radical	#16836595	C₄
cosocle	#16836602	C₂²
hypercenter	Q₈	#14272347
hypocenter	C₂₃₃	#350
LCS	G ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₈

Complements

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

N	H ≅ G/N	type
1. #21418632	C₂	semidirect
2. #21418630	C₂	semidirect
27. C₂₃₃	#350	semidirect

Maximal subgroups

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

subgroup	index
#21418632	2
#21418630	2
#21418623	2
#350	233