Subgroups — #36351762

Order 22144.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149585	C₂	1	1	yes	maximal, characteristic
2	#26011317	C₂	1	1	yes	maximal, characteristic
3	#366×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	#19149613	—	2	1	no	—
5	#19149585	C₄	1	2	yes	complemented
6	C₂×C₁₆×C₁₇₃	C₂²	1	1	yes	characteristic
7	#107×C₁₇₃	—	2	1	no	—
8	C₄⋊Dic₁₇₃	—	4	1	no	—
9	C₂×C₈×C₁₇₃	D₄	1	1	yes	characteristic
10	C₄⋊C₄×C₁₇₃	—	4	1	no	—
11	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
12	C₁₆×C₁₇₃	Q₈	1	1	yes	characteristic
13	C₂×Dic₁₇₃	—	8	1	no	—
14	C₂×C₄×C₁₇₃	—	8	1	no	—
15	C₂×C₄×C₁₇₃	D₈	1	1	yes	characteristic
16	C₈×C₁₇₃	C₄⋊C₄	1	1	yes	characteristic
17	C₈×C₁₇₃	Q₁₆	1	1	yes	characteristic
18	C₂²×C₁₇₃	D₁₆	1	1	yes	characteristic
19	C₄×C₁₇₃	—	16	1	no	—
20	C₄×C₁₇₃	#107	1	1	yes	characteristic
21	C₄×C₁₇₃	Q₃₂	1	1	yes	characteristic
22	Dic₁₇₃	—	16	1	no	—
23	C₂×C₁₇₃	#366	1	1	yes	characteristic
24	C₂×C₁₇₃	D₃₂	1	1	yes	characteristic
25	C₂×C₁₇₃	Q₆₄	1	1	yes	characteristic
26	C₁₇₃	#1423	1	1	yes	characteristic, complemented, Sylow
27	#1423	—	173	1	no	maximal, Sylow
28	C₂×C₃₂	—	173	1	no	—
29	#366	—	173	1	no	—
30	#366	D₁₇₃	1	1	yes	characteristic
31	C₂×C₁₆	C₂×D₁₇₃	1	1	yes	characteristic
32	#107	—	2	1	no	—
33	#107	—	346	1	no	—
34	C₃₂	—	173	2	no	—
35	C₂×C₈	C₂²⋊D₁₇₃	1	1	yes	characteristic
36	C₄⋊C₄	—	4	1	no	—
37	C₄⋊C₄	—	692	1	no	—
38	C₁₆	C₄×D₁₇₃	1	1	yes	characteristic
39	C₁₆	Dic₃₄₆	1	1	yes	characteristic
40	C₂×C₄	—	8	1	no	—
41	C₂×C₄	—	1384	1	no	—
42	C₂×C₄	#14583811	1	1	yes	characteristic
43	C₈	#14583805	1	1	yes	characteristic
44	C₈	#14583816	1	1	yes	characteristic
45	C₂²	#19149620	1	1	yes	characteristic
46	C₄	—	16	1	no	—
47	C₄	—	2768	1	no	—
48	C₄	#19149612	1	1	yes	characteristic
49	C₄	#19149625	1	1	yes	characteristic
50	C₂	#26011316	1	1	yes	characteristic
51	C₂	#26011326	1	1	yes	characteristic
52	C₂	#26011331	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19149620
commutator	C₁₆×C₁₇₃	C₂×C₄
Frattini	C₂×C₁₆	C₂×D₁₇₃
Fitting	#366×C₁₇₃	C₂
socle, prime radical	C₂²×C₁₇₃	D₁₆
cosocle	C₂×C₁₆×C₁₇₃	C₂²
hypercenter	#366	D₁₇₃
hypocenter	C₁₇₃	#1423
LCS	G ▷ C₁₆×C₁₇₃ ▷ C₈×C₁₇₃ ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #366

Complements

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

N	H ≅ G/N	type
5. #19149585	C₄	semidirect
26. C₁₇₃	#1423	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19149585	2
#26011317	2
#366×C₁₇₃	2
#1423	173