Subgroups — #26011909

Order 11072.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149685	C₂	1	1	yes	maximal, characteristic
2	#19149618	C₂	1	2	yes	maximal, complemented
3	C₂×#14583801	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₆×D₁₇₃	C₂	1	2	yes	maximal, complemented
5	M₃₂×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583826	C₄	1	1	yes	characteristic
7	#14583810	C₄	1	1	yes	characteristic
8	#14583809	C₄	1	2	yes	—
9	C₈×D₁₇₃	C₂²	1	2	yes	—
10	#14583801	C₂²	1	1	yes	characteristic
11	#14583801	C₂²	1	1	yes	characteristic
12	C₂×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
13	C₁₆×C₁₇₃	C₂²	1	2	yes	—
14	Dic₃₄₆	C₈	1	1	yes	characteristic
15	D₆₉₂	C₈	1	1	yes	characteristic
16	C₂²⋊D₁₇₃	C₈	1	2	yes	—
17	C₄×D₁₇₃	C₂×C₄	1	2	yes	—
18	#13063436	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
20	C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
21	C₈×C₁₇₃	C₂³	1	1	yes	characteristic
22	C₂²×C₁₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×D₁₇₃	C₂×C₈	1	2	yes	—
24	C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
25	C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
26	Dic₁₇₃	C₂×C₈	1	2	yes	—
27	C₂×C₁₇₃	—	2	1	no	—
28	C₂×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
29	D₁₇₃	—	2	2	no	—
30	C₁₇₃	#504	1	1	yes	characteristic, complemented, Sylow
31	#504	—	173	1	no	maximal, Sylow
32	#131	—	173	1	no	—
33	M₃₂	—	173	2	no	—
34	M₃₂	D₁₇₃	1	1	yes	characteristic, complemented
35	C₂×C₁₆	—	173	1	no	—
36	C₂×C₁₆	—	173	2	no	—
37	#41	—	173	1	no	—
38	M₁₆	—	173	1	no	—
39	M₁₆	—	173	2	no	—
40	C₂×C₈	—	173	2	no	—
41	C₂×C₈	C₂×D₁₇₃	1	1	yes	characteristic
42	C₁₆	—	173	1	no	—
43	C₁₆	—	173	1	no	—
44	C₁₆	C₂×D₁₇₃	1	2	yes	—
45	Q₈	—	173	1	no	—
46	D₄	—	173	2	no	—
47	D₄	—	173	1	no	—
48	C₂×C₄	—	173	2	no	—
49	C₂×C₄	C₄×D₁₇₃	1	1	yes	characteristic
50	C₈	—	173	2	no	—
51	C₈	C₄×D₁₇₃	1	1	yes	characteristic
52	C₈	C₂²×D₁₇₃	1	1	yes	characteristic
53	C₂²	—	173	2	no	—
54	C₂²	C₈×D₁₇₃	1	1	yes	characteristic
55	C₄	—	173	2	no	—
56	C₄	C₈×D₁₇₃	1	1	yes	characteristic
57	C₄	C₂×C₄×D₁₇₃	1	1	yes	characteristic
58	C₂	—	2	1	no	—
59	C₂	—	346	2	no	—
60	C₂	C₂×C₈×D₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×D₁₇₃
commutator, socle	C₂×C₁₇₃	C₂²×C₈
Fitting	M₃₂×C₁₇₃	C₂
prime radical	#14583826	C₄
cosocle	C₈×C₁₇₃	C₂³
hypercenter	M₃₂	D₁₇₃
hypocenter	C₁₇₃	#504
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
2. #19149618	C₂	semidirect
3. C₂×#14583801	C₂	semidirect
4. C₁₆×D₁₇₃	C₂	semidirect
5. M₃₂×C₁₇₃	C₂	semidirect
30. C₁₇₃	#504	semidirect
34. M₃₂	D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
#19149685	2
#19149618	2
C₂×#14583801	2
C₁₆×D₁₇₃	2
M₃₂×C₁₇₃	2
#504	173