Subgroups — #26012355

Order 11072.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13063443	C₂	1	2	yes	maximal
2	C₈×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#13063443	—	2	2	no	—
4	C₂×#13063436	C₄	1	1	yes	characteristic
5	C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₁₇₃	C₄	1	1	yes	characteristic
7	#13063443	—	4	2	no	—
8	C₂×Dic₁₇₃	D₄	1	1	yes	characteristic
9	C₂×Dic₁₇₃	Q₈	1	1	yes	characteristic
10	#13063436	C₈	1	2	yes	complemented
11	C₂×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₁₇₃	—	2	1	no	—
13	C₂²×C₁₇₃	C₄⋊C₄	1	1	yes	characteristic
14	C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
15	C₄×C₁₇₃	M₁₆	1	1	yes	characteristic
16	Dic₁₇₃	—	2	1	no	—
17	Dic₁₇₃	D₈	1	1	yes	characteristic
18	Dic₁₇₃	Q₁₆	1	1	yes	characteristic
19	C₂×C₁₇₃	C₄⋊C₈	1	1	yes	characteristic
20	C₂×C₁₇₃	#107	1	1	yes	characteristic
21	C₂×C₁₇₃	#108	1	1	yes	characteristic
22	C₁₇₃	#335	1	1	yes	characteristic, complemented, Sylow
23	#335	—	173	1	no	maximal, Sylow
24	C₄⋊C₈	—	173	2	no	—
25	C₄×C₈	—	173	1	no	—
26	C₂×C₈	—	346	2	no	—
27	C₂×C₈	—	173	1	no	—
28	C₂×C₈	#10621924	1	1	yes	characteristic
29	C₄²	—	173	1	no	—
30	C₂×C₄	—	173	1	no	—
31	C₂×C₄	—	173	1	no	—
32	C₂×C₄	C₂×#10621924	1	1	yes	characteristic
33	C₈	—	2	1	no	—
34	C₈	—	173	2	no	—
35	C₈	—	692	2	no	—
36	C₂²	C₄⋊#10621924	1	1	yes	characteristic
37	C₄	—	346	1	no	—
38	C₄	—	173	1	no	—
39	C₄	—	173	1	no	—
40	C₄	D₁₇₃⋊C₈	1	1	yes	characteristic
41	C₄	#14583835	1	1	yes	characteristic
42	C₂	#19149746	1	1	yes	characteristic
43	C₂	#19149748	1	1	yes	characteristic
44	C₂	#19149749	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#10621924
commutator	C₄×C₁₇₃	C₂×C₈
Frattini	C₂×C₄	C₂×#10621924
Fitting	C₂×C₈×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	C₄⋊C₄
cosocle	C₄×Dic₁₇₃	C₂²
hypercenter	C₂×C₈	#10621924
hypocenter	C₁₇₃	#335
LCS	G ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
10. #13063436	C₈	semidirect
22. C₁₇₃	#335	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#13063443	2
C₈×Dic₁₇₃	2
#335	173