Subgroups — C₄×Q₃₂×C₁₇₃ #36349959

Order 22144.

150 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₃₂×C₁₇₃	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆×C₁₇₃	C₂	1	2	yes	maximal
3	#366×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	#358×C₁₇₃	C₂	1	2	yes	maximal
5	C₄×C₁₆×C₁₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₁₆×C₁₇₃	C₂²	1	2	yes	—
7	C₄×Q₈×C₁₇₃	—	2	2	no	—
8	Q₃₂×C₁₇₃	C₄	1	4	yes	direct product factor
9	C₂×C₁₆×C₁₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₁₆×C₁₇₃	C₂²	1	1	yes	characteristic
11	#107×C₁₇₃	C₂²	1	2	yes	—
12	#103×C₁₇₃	—	2	2	no	—
13	C₄×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
14	C₂×Q₈×C₁₇₃	—	2	2	no	—
15	Q₁₆×C₁₇₃	—	2	2	no	—
16	Q₁₆×C₁₇₃	C₂×C₄	1	4	yes	—
17	C₂×C₈×C₁₇₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₇₃	C₂³	1	1	yes	characteristic
19	C₄⋊C₄×C₁₇₃	—	2	2	no	—
20	C₄⋊C₄×C₁₇₃	—	4	2	no	—
21	C₄²×C₁₇₃	—	4	2	no	—
22	C₄²×C₁₇₃	D₄	1	1	yes	characteristic
23	C₁₆×C₁₇₃	—	2	1	no	—
24	C₁₆×C₁₇₃	C₂×C₄	1	2	yes	—
25	Q₈×C₁₇₃	—	2	4	no	—
26	Q₈×C₁₇₃	—	4	2	no	—
27	C₂×C₄×C₁₇₃	—	4	2	no	—
28	C₂×C₄×C₁₇₃	—	4	2	no	—
29	C₂×C₄×C₁₇₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇₃	D₈	1	1	yes	characteristic
31	C₂×C₄×C₁₇₃	C₂×D₄	1	1	yes	characteristic
32	C₈×C₁₇₃	—	2	1	no	—
33	C₈×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₇₃	#41	1	1	yes	characteristic
35	C₂²×C₁₇₃	C₂×D₈	1	1	yes	characteristic
36	C₄×C₁₇₃	—	2	1	no	—
37	C₄×C₁₇₃	—	4	4	no	—
38	C₄×C₁₇₃	—	8	2	no	—
39	C₄×C₁₇₃	Q₃₂	1	2	yes	direct product factor
40	C₄×C₁₇₃	C₄×D₄	1	1	yes	characteristic
41	C₄×C₁₇₃	#135	1	1	yes	characteristic
42	C₂×C₁₇₃	C₄×D₈	1	1	yes	characteristic
43	C₂×C₁₇₃	C₂×Q₃₂	1	1	yes	characteristic
44	C₂×C₁₇₃	#508	1	1	yes	characteristic
45	C₁₇₃	C₄×Q₃₂	1	1	yes	characteristic, direct product factor, Sylow
46	C₄×Q₃₂	C₁₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₃₂	C₂×C₁₇₃	1	1	yes	characteristic
48	C₄×Q₁₆	C₂×C₁₇₃	1	2	yes	—
49	#366	C₂×C₁₇₃	1	1	yes	characteristic
50	#358	C₂×C₁₇₃	1	2	yes	—
51	C₄×C₁₆	C₂×C₁₇₃	1	1	yes	characteristic
52	C₂×Q₁₆	C₂²×C₁₇₃	1	2	yes	—
53	C₄×Q₈	—	2	2	no	—
54	Q₃₂	C₄×C₁₇₃	1	4	yes	direct product factor
55	C₂×C₁₆	C₂²×C₁₇₃	1	1	yes	characteristic
56	C₂×C₁₆	C₂²×C₁₇₃	1	1	yes	characteristic
57	#107	C₂²×C₁₇₃	1	2	yes	—
58	#103	—	2	2	no	—
59	C₄×C₈	C₂²×C₁₇₃	1	1	yes	characteristic
60	C₂×Q₈	—	2	2	no	—
61	Q₁₆	—	2	2	no	—
62	Q₁₆	C₂×C₄×C₁₇₃	1	4	yes	—
63	C₂×C₈	D₄×C₁₇₃	1	1	yes	characteristic
64	C₂×C₈	C₂³×C₁₇₃	1	1	yes	characteristic
65	C₄⋊C₄	—	2	2	no	—
66	C₄⋊C₄	—	4	2	no	—
67	C₄²	—	4	2	no	—
68	C₄²	D₄×C₁₇₃	1	1	yes	characteristic
69	C₁₆	—	2	1	no	—
70	C₁₆	C₂×C₄×C₁₇₃	1	2	yes	—
71	Q₈	—	2	4	no	—
72	Q₈	—	4	2	no	—
73	C₂×C₄	—	4	2	no	—
74	C₂×C₄	—	4	2	no	—
75	C₂×C₄	D₈×C₁₇₃	1	1	yes	characteristic
76	C₂×C₄	D₈×C₁₇₃	1	1	yes	characteristic
77	C₂×C₄	C₂×D₄×C₁₇₃	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	C₂²×C₄×C₁₇₃	1	1	yes	characteristic
80	C₈	#41×C₁₇₃	1	1	yes	characteristic
81	C₂²	C₂×D₈×C₁₇₃	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	4	4	no	—
84	C₄	—	8	2	no	—
85	C₄	Q₃₂×C₁₇₃	1	2	yes	direct product factor
86	C₄	C₄×D₄×C₁₇₃	1	1	yes	characteristic
87	C₄	#135×C₁₇₃	1	1	yes	characteristic
88	C₂	C₄×D₈×C₁₇₃	1	1	yes	characteristic
89	C₂	C₂×Q₃₂×C₁₇₃	1	1	yes	characteristic
90	C₂	#508×C₁₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇₃	D₈
commutator	C₈	C₂²×C₄×C₁₇₃
Frattini, cosocle	C₂×C₈	C₂³×C₁₇₃
socle, prime radical	C₂²×C₁₇₃	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇₃ ◁ C₄²×C₁₇₃ ◁ C₄×C₈×C₁₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. Q₃₂×C₁₇₃	C₄	direct (N × H)
39. C₄×C₁₇₃	Q₃₂	direct (N × H)
45. C₁₇₃	C₄×Q₃₂	direct (N × H)
46. C₄×Q₃₂	C₁₇₃	direct (N × H)
54. Q₃₂	C₄×C₁₇₃	direct (N × H)
85. C₄	Q₃₂×C₁₇₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₃₂×C₁₇₃	2
C₄×Q₁₆×C₁₇₃	2
#366×C₁₇₃	2
#358×C₁₇₃	2
C₄×C₁₆×C₁₇₃	2
C₄×Q₃₂	173

Subgroups — C4×Q32×C173 #36349959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×Q₃₂×C₁₇₃ #36349959