Subgroups — #1839×C₁₇₃ #36349624

Order 22144.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄³×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	#336×C₁₇₃	C₂	1	6	yes	maximal
3	C₂²×C₈×C₁₇₃	C₂²	1	4	yes	—
4	C₂×C₄²×C₁₇₃	C₄	1	3	yes	—
5	C₂×C₄²×C₁₇₃	C₄	1	1	yes	characteristic
6	C₂×C₄²×C₁₇₃	C₂²	1	3	yes	—
7	C₂²×C₄×C₁₇₃	C₂×C₄	1	3	yes	—
8	C₂²×C₄×C₁₇₃	C₂×C₄	1	3	yes	—
9	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
10	C₂×C₈×C₁₇₃	—	2	12	no	—
11	C₄²×C₁₇₃	—	2	6	no	—
12	C₄²×C₁₇₃	—	2	6	no	—
13	C₄²×C₁₇₃	C₈	1	4	yes	complemented
14	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
15	C₂×C₄×C₁₇₃	—	2	3	no	—
16	C₂×C₄×C₁₇₃	—	2	3	no	—
17	C₂×C₄×C₁₇₃	—	2	3	no	—
18	C₂×C₄×C₁₇₃	—	2	3	no	—
19	C₂×C₄×C₁₇₃	C₂×C₈	1	6	yes	—
20	C₂×C₄×C₁₇₃	M₁₆	1	6	yes	—
21	C₂×C₄×C₁₇₃	#41	1	6	yes	—
22	C₈×C₁₇₃	—	4	4	no	—
23	C₂²×C₁₇₃	#117	1	3	yes	—
24	C₂²×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₁₇₃	C₂×M₁₆	1	3	yes	—
26	C₄×C₁₇₃	—	2	6	no	—
27	C₄×C₁₇₃	—	2	6	no	—
28	C₄×C₁₇₃	#126	1	4	yes	—
29	C₂×C₁₇₃	#383	1	1	yes	characteristic
30	C₂×C₁₇₃	#431	1	3	yes	—
31	C₂×C₁₇₃	#432	1	3	yes	—
32	C₁₇₃	#1839	1	1	yes	characteristic, direct product factor, Sylow
33	#1839	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
34	C₄³	C₂×C₁₇₃	1	1	yes	characteristic
35	#336	C₂×C₁₇₃	1	6	yes	—
36	C₂²×C₈	C₂²×C₁₇₃	1	4	yes	—
37	C₂×C₄²	C₄×C₁₇₃	1	3	yes	—
38	C₂×C₄²	C₄×C₁₇₃	1	1	yes	characteristic
39	C₂×C₄²	C₂²×C₁₇₃	1	3	yes	—
40	C₂²×C₄	C₂×C₄×C₁₇₃	1	3	yes	—
41	C₂²×C₄	C₂×C₄×C₁₇₃	1	3	yes	—
42	C₂²×C₄	C₂³×C₁₇₃	1	1	yes	characteristic
43	C₂×C₈	—	2	12	no	—
44	C₄²	—	2	6	no	—
45	C₄²	—	2	6	no	—
46	C₄²	C₈×C₁₇₃	1	4	yes	complemented
47	C₂³	C₂²×C₄×C₁₇₃	1	1	yes	characteristic
48	C₂×C₄	—	2	3	no	—
49	C₂×C₄	—	2	3	no	—
50	C₂×C₄	—	2	3	no	—
51	C₂×C₄	—	2	3	no	—
52	C₂×C₄	C₂×C₈×C₁₇₃	1	6	yes	—
53	C₂×C₄	M₁₆×C₁₇₃	1	6	yes	—
54	C₂×C₄	#41×C₁₇₃	1	6	yes	—
55	C₈	—	4	4	no	—
56	C₂²	#117×C₁₇₃	1	3	yes	—
57	C₂²	C₂²×C₈×C₁₇₃	1	1	yes	characteristic
58	C₂²	C₂×M₁₆×C₁₇₃	1	3	yes	—
59	C₄	—	2	6	no	—
60	C₄	—	2	6	no	—
61	C₄	#126×C₁₇₃	1	4	yes	—
62	C₂	#383×C₁₇₃	1	1	yes	characteristic
63	C₂	#431×C₁₇₃	1	3	yes	—
64	C₂	#432×C₁₇₃	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₇₃	C₂³
commutator	C₂²	C₂²×C₈×C₁₇₃
Frattini, cosocle	C₂²×C₄	C₂³×C₁₇₃
socle, prime radical	C₂³×C₁₇₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₄²×C₁₇₃	C₈	semidirect
32. C₁₇₃	#1839	direct (N × H)
33. #1839	C₁₇₃	direct (N × H)
46. C₄²	C₈×C₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₄³×C₁₇₃	2
#336×C₁₇₃	2
#1839	173

Subgroups — #1839×C173 #36349624

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1839×C₁₇₃ #36349624