Subgroups — #36368479

Order 22144.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012380	C₂	1	1	yes	maximal, characteristic
2	#26012332	C₂	1	1	yes	maximal, characteristic
3	#26011266	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583829	C₄	1	2	yes	—
5	C₄×#13063443	C₄	1	2	yes	—
6	C₂×#14583801	C₄	1	1	yes	characteristic
7	C₈×Dic₁₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₇₃	C₄	1	1	yes	characteristic
9	C₂×#13063443	—	2	2	no	—
10	#14583829	—	2	2	no	—
11	C₂×#13063436	C₂×C₄	1	1	yes	characteristic
12	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
13	#14583801	C₈	1	2	yes	complemented
14	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
15	C₁₆×C₁₇₃	C₈	1	2	yes	complemented
16	#13063443	—	4	2	no	—
17	C₂×Dic₁₇₃	M₁₆	1	2	yes	—
18	#13063436	M₁₆	1	2	yes	—
19	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
20	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
21	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
22	C₂²×C₁₇₃	#97	1	1	yes	characteristic
23	C₄×C₁₇₃	C₄×C₈	1	1	yes	characteristic
24	C₄×C₁₇₃	#97	1	1	yes	characteristic
25	Dic₁₇₃	—	2	2	no	—
26	C₂×C₁₇₃	#322	1	1	yes	characteristic
27	C₂×C₁₇₃	#347	1	2	yes	—
28	C₁₇₃	#1313	1	1	yes	characteristic, complemented, Sylow
29	#1313	—	173	1	no	maximal, Sylow
30	#346	—	173	1	no	—
31	#346	—	173	1	no	—
32	#322	—	173	1	no	—
33	C₂×C₁₆	—	173	2	no	—
34	C₂×C₁₆	—	173	1	no	—
35	C₂×C₁₆	#10621924	1	1	yes	characteristic
36	C₄×C₈	—	173	2	no	—
37	C₄×C₈	—	173	1	no	—
38	C₂×C₈	—	346	2	no	—
39	C₂×C₈	—	173	1	no	—
40	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
41	C₄²	—	173	1	no	—
42	C₁₆	—	346	2	no	—
43	C₁₆	—	173	2	no	—
44	C₁₆	#13063443	1	2	yes	complemented
45	C₂×C₄	—	173	2	no	—
46	C₂×C₄	C₄×#10621924	1	1	yes	characteristic
47	C₈	—	173	2	no	—
48	C₈	—	692	2	no	—
49	C₈	C₂×#13063443	1	1	yes	characteristic
50	C₈	D₁₇₃⋊C₈	1	1	yes	characteristic
51	C₂²	#19149733	1	1	yes	characteristic
52	C₄	—	346	2	no	—
53	C₄	C₄×#13063443	1	1	yes	characteristic
54	C₄	#19149733	1	1	yes	characteristic
55	C₂	#26012332	1	1	yes	characteristic
56	C₂	#26012381	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄×#10621924
commutator	C₄×C₁₇₃	C₄×C₈
Frattini	C₂×C₈	C₂×#10621924
Fitting	C₂×C₁₆×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	#97
cosocle	C₈×Dic₁₇₃	C₂²
hypercenter	C₂×C₁₆	#10621924
hypocenter	C₁₇₃	#1313
LCS	G ▷ C₄×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
13. #14583801	C₈	semidirect
15. C₁₆×C₁₇₃	C₈	semidirect
28. C₁₇₃	#1313	semidirect
44. C₁₆	#13063443	semidirect

Maximal subgroups

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

subgroup	index
#26012380	2
#26012332	2
#26011266	2
#1313	173