Subgroups — #36368716

Order 22144.

74 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012424	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012418	C₂	1	1	yes	maximal, characteristic, complemented
3	#26011920	C₂	1	1	yes	maximal, characteristic
4	#19149748	—	2	1	no	—
5	#19149729	—	2	1	no	—
6	#19149698	—	2	1	no	—
7	Dic₁₃₈₄	C₄	1	1	yes	characteristic, complemented
8	#19149623	—	2	1	no	—
9	C₁₆×D₁₇₃	C₂²	1	1	yes	characteristic
10	D₁₆×C₁₇₃	C₄	1	1	yes	characteristic, complemented
11	C₄⋊#10621924	—	4	1	no	—
12	#14583825	—	4	1	no	—
13	Dic₆₉₂	—	2	1	no	—
14	#14583814	—	4	1	no	—
15	C₈×D₁₇₃	D₄	1	1	yes	characteristic
16	#14583801	D₄	1	1	yes	characteristic
17	D₈×C₁₇₃	—	2	1	no	—
18	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#10621924	—	8	1	no	—
20	Dic₃₄₆	—	4	1	no	—
21	C₂²⋊D₁₇₃	—	8	1	no	—
22	C₂×Dic₁₇₃	—	8	1	no	—
23	C₄×D₁₇₃	D₈	1	1	yes	characteristic
24	#13063436	SD₁₆	1	1	yes	characteristic
25	D₄×C₁₇₃	—	4	1	no	—
26	C₈×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₁₇₃	—	8	1	no	—
28	C₂×D₁₇₃	D₁₆	1	1	yes	characteristic
29	#10621924	—	16	1	no	—
30	C₄×C₁₇₃	#102	1	1	yes	characteristic
31	Dic₁₇₃	—	8	1	no	—
32	Dic₁₇₃	SD₃₂	1	1	yes	characteristic
33	C₂×C₁₇₃	—	16	1	no	—
34	C₂×C₁₇₃	#357	1	1	yes	characteristic
35	D₁₇₃	—	2	1	no	—
36	C₁₇₃	#1418	1	1	yes	characteristic, complemented, Sylow
37	#1418	—	173	1	no	maximal, Sylow
38	#508	—	173	1	no	—
39	M₆₄	—	173	1	no	—
40	#367	—	173	1	no	—
41	#135	—	346	1	no	—
42	Q₃₂	—	173	1	no	—
43	SD₃₂	—	346	1	no	—
44	D₁₆	#10621924	1	1	yes	characteristic, complemented
45	C₂×C₁₆	—	173	1	no	—
46	#107	—	346	1	no	—
47	C₃₂	—	346	1	no	—
48	#41	—	692	1	no	—
49	Q₁₆	—	346	1	no	—
50	SD₁₆	—	692	1	no	—
51	D₈	—	2	1	no	—
52	C₂×C₈	—	173	1	no	—
53	C₄⋊C₄	—	692	1	no	—
54	C₁₆	—	173	1	no	—
55	C₁₆	C₂×#10621924	1	1	yes	characteristic
56	Q₈	—	692	1	no	—
57	D₄	—	4	1	no	—
58	D₄	—	1384	1	no	—
59	C₂×C₄	—	1384	1	no	—
60	C₂×C₄	—	1384	1	no	—
61	C₂×C₄	—	173	1	no	—
62	C₈	—	173	1	no	—
63	C₈	C₂²⋊#10621924	1	1	yes	characteristic
64	C₂²	—	8	1	no	—
65	C₂²	—	173	1	no	—
66	C₄	—	1384	1	no	—
67	C₄	—	173	1	no	—
68	C₄	—	2768	1	no	—
69	C₄	#19149741	1	1	yes	characteristic
70	C₂	—	16	1	no	—
71	C₂	—	346	1	no	—
72	C₂	#26012403	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26012403
commutator	C₁₆×C₁₇₃	C₂×C₄
Frattini	C₁₆	C₂×#10621924
Fitting	D₁₆×C₁₇₃	C₄
socle	C₂×C₁₇₃	#357
prime radical	#26011920	C₂
cosocle	C₁₆×D₁₇₃	C₂²
hypercenter	D₁₆	#10621924
hypocenter	C₁₇₃	#1418
LCS	G ▷ C₁₆×C₁₇₃ ▷ C₈×C₁₇₃ ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ C₁₆ ◁ D₁₆

Complements

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

N	H ≅ G/N	type
1. #26012424	C₂	semidirect
2. #26012418	C₂	semidirect
7. Dic₁₃₈₄	C₄	semidirect
10. D₁₆×C₁₇₃	C₄	semidirect
36. C₁₇₃	#1418	semidirect
44. D₁₆	#10621924	semidirect

Maximal subgroups

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

subgroup	index
#26012424	2
#26012418	2
#26011920	2
#1418	173