Subgroups — #19149711

Order 5536.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583827	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583816	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583815	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583813	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583809	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₁₆×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₃₄₆	—	2	1	no	—
9	Dic₃₄₆	C₂²	1	1	yes	characteristic
10	D₆₉₂	—	2	1	no	—
11	D₆₉₂	C₂²	1	1	yes	characteristic
12	C₄×D₁₇₃	—	2	1	no	—
13	C₄×D₁₇₃	—	2	1	no	—
14	C₄×D₁₇₃	C₂²	1	1	yes	characteristic
15	#13063436	C₂²	1	1	yes	characteristic
16	Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
17	Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
18	C₈×C₁₇₃	C₂²	1	1	yes	characteristic
19	C₂×D₁₇₃	—	2	1	no	—
20	C₂×D₁₇₃	D₄	1	1	yes	characteristic
21	C₄×C₁₇₃	—	2	1	no	—
22	C₄×C₁₇₃	—	2	1	no	—
23	C₄×C₁₇₃	C₂³	1	1	yes	characteristic
24	Dic₁₇₃	—	2	1	no	—
25	Dic₁₇₃	D₄	1	1	yes	characteristic
26	C₂×C₁₇₃	C₂×D₄	1	1	yes	characteristic
27	D₁₇₃	—	2	1	no	—
28	D₁₇₃	—	4	1	no	—
29	C₁₇₃	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	173	1	no	maximal, Sylow
31	#41	—	173	1	no	—
32	C₂×Q₈	—	173	1	no	—
33	Q₁₆	—	173	1	no	—
34	Q₁₆	D₁₇₃	1	1	yes	characteristic, complemented
35	SD₁₆	—	173	1	no	—
36	SD₁₆	—	173	1	no	—
37	M₁₆	—	173	1	no	—
38	Q₈	—	346	1	no	—
39	Q₈	—	173	1	no	—
40	Q₈	C₂×D₁₇₃	1	1	yes	characteristic
41	Q₈	C₂×D₁₇₃	1	1	yes	characteristic
42	D₄	—	346	1	no	—
43	D₄	—	173	1	no	—
44	C₂×C₄	—	346	1	no	—
45	C₂×C₄	—	346	1	no	—
46	C₂×C₄	—	173	1	no	—
47	C₈	—	173	1	no	—
48	C₈	C₂×D₁₇₃	1	1	yes	characteristic
49	C₂²	—	346	1	no	—
50	C₂²	—	173	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	2	1	no	—
53	C₄	—	346	1	no	—
54	C₄	—	173	1	no	—
55	C₄	C₂²×D₁₇₃	1	1	yes	characteristic
56	C₂	—	346	1	no	—
57	C₂	—	692	1	no	—
58	C₂	D₄×D₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₁₇₃
commutator	C₄×C₁₇₃	C₂³
Frattini	C₄	C₂²×D₁₇₃
Fitting	Q₁₆×C₁₇₃	C₂
socle	C₂×C₁₇₃	C₂×D₄
hypercenter	Q₁₆	D₁₇₃
hypocenter	C₁₇₃	#137
LCS	G ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ Q₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₁₇₃	C₂	semidirect
3. #14583816	C₂	semidirect
4. #14583815	C₂	semidirect
5. #14583813	C₂	semidirect
6. #14583809	C₂	semidirect
7. Q₁₆×C₁₇₃	C₂	semidirect
29. C₁₇₃	#137	semidirect
34. Q₁₆	D₁₇₃	semidirect