Subgroups — C₂×#26011210 #36351772

Order 22144.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26011210	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃₂×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₆×C₁₇₃	C₄	1	1	yes	characteristic
4	C₃₂×C₁₇₃	C₄	1	1	yes	characteristic
5	C₃₂×C₁₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₇₃	C₈	1	1	yes	characteristic
7	C₁₆×C₁₇₃	C₈	1	1	yes	characteristic
8	C₁₆×C₁₇₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₇₃	C₁₆	1	1	yes	characteristic
10	C₈×C₁₇₃	C₁₆	1	1	yes	characteristic
11	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₇₃	C₃₂	1	1	yes	characteristic
13	C₄×C₁₇₃	C₃₂	1	1	yes	characteristic
14	C₄×C₁₇₃	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₇₃	C₆₄	1	2	yes	complemented
16	C₂×C₁₇₃	C₂×C₃₂	1	1	yes	characteristic
17	C₁₇₃	C₂×C₆₄	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₆₄	—	173	1	no	maximal, Sylow
19	C₂×C₃₂	D₁₇₃	1	1	yes	characteristic
20	C₆₄	—	173	2	no	—
21	C₂×C₁₆	Dic₁₇₃	1	1	yes	characteristic
22	C₃₂	Dic₁₇₃	1	1	yes	characteristic
23	C₃₂	C₂×D₁₇₃	1	1	yes	characteristic
24	C₂×C₈	#13063436	1	1	yes	characteristic
25	C₁₆	#13063436	1	1	yes	characteristic
26	C₁₆	C₂×Dic₁₇₃	1	1	yes	characteristic
27	C₂×C₄	#14583801	1	1	yes	characteristic
28	C₈	#14583801	1	1	yes	characteristic
29	C₈	C₂×#13063436	1	1	yes	characteristic
30	C₂²	#19149585	1	1	yes	characteristic
31	C₄	#19149585	1	1	yes	characteristic
32	C₄	C₂×#14583801	1	1	yes	characteristic
33	C₂	#26011210	1	2	yes	direct product factor
34	C₂	C₂×#19149585	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃₂	D₁₇₃
commutator, hypocenter	C₁₇₃	C₂×C₆₄
Frattini	C₃₂	C₂×D₁₇₃
Fitting	C₂×C₃₂×C₁₇₃	C₂
socle, prime radical	C₂²×C₁₇₃	C₃₂
cosocle	C₃₂×C₁₇₃	C₂²
LCS	G ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
1. #26011210	C₂	direct (N × H)
15. C₂×C₁₇₃	C₆₄	semidirect
17. C₁₇₃	C₂×C₆₄	semidirect
33. C₂	#26011210	direct (N × H)

Maximal subgroups

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

subgroup	index
#26011210	2
C₂×C₃₂×C₁₇₃	2
C₂×C₆₄	173

Subgroups — C2×#26011210 #36351772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26011210 #36351772