Subgroups — #19149712

Order 5536.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14583826	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₃₄₆	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₆₉₂	C₂	1	2	yes	maximal, complemented
4	#14583815	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Dic₃₄₆	—	2	1	no	—
7	Dic₃₄₆	C₂²	1	2	yes	—
8	Dic₃₄₆	C₂²	1	1	yes	characteristic
9	D₆₉₂	C₂²	1	1	yes	characteristic
10	C₂²⋊D₁₇₃	—	2	1	no	—
11	C₂×Dic₁₇₃	—	2	1	no	—
12	C₄×D₁₇₃	—	2	1	no	—
13	C₂×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
14	C₈×C₁₇₃	C₂²	1	2	yes	—
15	C₂²×C₁₇₃	D₄	1	1	yes	characteristic
16	C₂×D₁₇₃	—	2	1	no	—
17	C₄×C₁₇₃	D₄	1	1	yes	characteristic
18	C₄×C₁₇₃	C₂³	1	1	yes	characteristic
19	Dic₁₇₃	—	2	1	no	—
20	Dic₁₇₃	—	2	2	no	—
21	C₂×C₁₇₃	—	2	1	no	—
22	C₂×C₁₇₃	C₂×D₄	1	1	yes	characteristic
23	D₁₇₃	—	4	1	no	—
24	C₁₇₃	#137	1	1	yes	characteristic, complemented, Sylow
25	#137	—	173	1	no	maximal, Sylow
26	#41	—	173	1	no	—
27	C₂×Q₈	—	173	1	no	—
28	Q₁₆	—	173	2	no	—
29	SD₁₆	—	173	2	no	—
30	M₁₆	D₁₇₃	1	1	yes	characteristic, complemented
31	Q₈	—	346	1	no	—
32	Q₈	—	173	2	no	—
33	Q₈	—	173	1	no	—
34	D₄	—	346	1	no	—
35	D₄	—	173	1	no	—
36	C₂×C₄	—	346	1	no	—
37	C₂×C₄	—	346	1	no	—
38	C₂×C₄	C₂×D₁₇₃	1	1	yes	characteristic
39	C₈	C₂×D₁₇₃	1	2	yes	—
40	C₂²	—	346	1	no	—
41	C₂²	D₆₉₂	1	1	yes	characteristic
42	C₄	—	346	1	no	—
43	C₄	—	346	2	no	—
44	C₄	D₆₉₂	1	1	yes	characteristic
45	C₄	C₂²×D₁₇₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	692	1	no	—
48	C₂	C₂×D₆₉₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₆₉₂
commutator	C₄×C₁₇₃	C₂³
Frattini	C₄	C₂²×D₁₇₃
Fitting	M₁₆×C₁₇₃	C₂
socle	C₂×C₁₇₃	C₂×D₄
hypercenter	M₁₆	D₁₇₃
hypocenter	C₁₇₃	#137
LCS	G ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₃₄₆	C₂	semidirect
3. Dic₆₉₂	C₂	semidirect
4. #14583815	C₂	semidirect
5. M₁₆×C₁₇₃	C₂	semidirect
24. C₁₇₃	#137	semidirect
30. M₁₆	D₁₇₃	semidirect