Subgroups — #21418597

Order 7456.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16836602	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄⋊#11745400	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×D₂₃₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#11745400	—	2	1	no	—
5	#14272345	—	2	1	no	—
6	C₂²×D₂₃₃	—	2	1	no	—
7	D₉₃₂	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊D₂₃₃	—	2	1	no	—
9	C₄×D₂₃₃	C₂²	1	1	yes	characteristic
10	D₄×C₂₃₃	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₂₃₃	—	2	1	no	—
12	C₂×D₂₃₃	—	2	1	no	—
13	C₂×D₂₃₃	—	4	1	no	—
14	C₂×D₂₃₃	—	4	1	no	—
15	C₂×D₂₃₃	D₄	1	1	yes	characteristic
16	#11745400	—	4	1	no	—
17	C₄×C₂₃₃	C₂×C₄	1	1	yes	characteristic
18	Dic₂₃₃	D₄	1	1	yes	characteristic
19	C₂×C₂₃₃	—	4	1	no	—
20	C₂×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
21	D₂₃₃	—	4	1	no	—
22	D₂₃₃	D₈	1	1	yes	characteristic
23	D₂₃₃	SD₁₆	1	1	yes	characteristic
24	C₂₃₃	#102	1	1	yes	characteristic, complemented, Sylow
25	#102	—	233	1	no	maximal, Sylow
26	C₂×D₄	—	233	1	no	—
27	C₂×C₈	—	233	1	no	—
28	C₄⋊C₄	—	233	1	no	—
29	C₂³	—	466	1	no	—
30	D₄	—	466	1	no	—
31	D₄	—	233	1	no	—
32	D₄	#11745400	1	1	yes	characteristic, complemented
33	C₂×C₄	—	466	1	no	—
34	C₂×C₄	—	233	1	no	—
35	C₈	—	466	1	no	—
36	C₂²	—	2	1	no	—
37	C₂²	—	932	1	no	—
38	C₂²	—	932	1	no	—
39	C₂²	—	466	1	no	—
40	C₂²	—	233	1	no	—
41	C₄	—	932	1	no	—
42	C₄	—	233	1	no	—
43	C₄	C₂×#11745400	1	1	yes	characteristic
44	C₂	—	4	1	no	—
45	C₂	—	932	1	no	—
46	C₂	—	233	1	no	—
47	C₂	—	233	1	no	—
48	C₂	C₂²⋊#11745400	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂²⋊#11745400
commutator	C₄×C₂₃₃	C₂×C₄
Frattini	C₄	C₂×#11745400
Fitting	D₄×C₂₃₃	C₄
socle	C₂×C₂₃₃	C₂²⋊C₄
hypercenter	D₄	#11745400
hypocenter	C₂₃₃	#102
LCS	G ▷ C₄×C₂₃₃ ▷ C₂×C₂₃₃ ▷ C₂₃₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₄

Complements

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

N	H ≅ G/N	type
1. #16836602	C₂	semidirect
2. C₄⋊#11745400	C₂	semidirect
7. D₉₃₂	C₄	semidirect
10. D₄×C₂₃₃	C₄	semidirect
24. C₂₃₃	#102	semidirect
32. D₄	#11745400	semidirect