Subgroups — #28417354

Order 14912.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21418610	C₂	1	1	yes	maximal, characteristic
2	#21418605	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×D₂₃₃	C₂	1	1	yes	maximal, characteristic
4	#16836604	—	2	1	no	—
5	#16836597	—	2	1	no	—
6	Q₈×D₂₃₃	—	2	1	no	—
7	Dic₉₃₂	C₄	1	1	yes	characteristic
8	#16836584	—	2	1	no	—
9	C₈×D₂₃₃	C₂²	1	1	yes	characteristic
10	Q₁₆×C₂₃₃	C₄	1	1	yes	characteristic
11	#14272345	—	4	1	no	—
12	Dic₄₆₆	—	2	1	no	—
13	Dic₄₆₆	—	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	SD₁₆	1	1	yes	characteristic
20	C₄×C₂₃₃	—	4	1	no	—
21	C₄×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
22	Dic₂₃₃	—	4	1	no	—
23	Dic₂₃₃	D₈	1	1	yes	characteristic
24	C₂×C₂₃₃	#102	1	1	yes	characteristic
25	D₂₃₃	—	2	1	no	—
26	C₂₃₃	#362	1	1	yes	characteristic, complemented, Sylow
27	#362	—	233	1	no	maximal, Sylow
28	C₂×Q₁₆	—	233	1	no	—
29	M₃₂	—	233	1	no	—
30	#108	—	233	1	no	—
31	C₂×Q₈	—	466	1	no	—
32	Q₁₆	—	466	1	no	—
33	Q₁₆	—	233	1	no	—
34	Q₁₆	#11745400	1	1	yes	characteristic
35	M₁₆	—	466	1	no	—
36	C₂×C₈	—	233	1	no	—
37	C₁₆	—	466	1	no	—
38	Q₈	—	2	1	no	—
39	Q₈	—	932	1	no	—
40	Q₈	—	466	1	no	—
41	C₂×C₄	—	932	1	no	—
42	C₂×C₄	—	233	1	no	—
43	C₈	—	932	1	no	—
44	C₈	—	233	1	no	—
45	C₈	C₂×#11745400	1	1	yes	characteristic
46	C₂²	—	233	1	no	—
47	C₄	—	4	1	no	—
48	C₄	—	932	1	no	—
49	C₄	—	233	1	no	—
50	C₄	C₂²⋊#11745400	1	1	yes	characteristic
51	C₂	—	466	1	no	—
52	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	C₂×D₂₃₃	SD₁₆
cosocle	C₈×D₂₃₃	C₂²
hypercenter	Q₁₆	#11745400
hypocenter	C₂₃₃	#362
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
26. C₂₃₃	#362	semidirect

Maximal subgroups

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

subgroup	index
#21418610	2
#21418605	2
Q₁₆×D₂₃₃	2
#362	233