Subgroups — C₂²×C₃₂×C₁₇₉ #37505478

Order 22912.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×C₁₇₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃₂×C₁₇₉	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₈×C₁₇₉	C₄	1	1	yes	characteristic
4	C₂×C₁₆×C₁₇₉	C₄	1	3	yes	—
5	C₂×C₁₆×C₁₇₉	C₂²	1	3	yes	—
6	C₃₂×C₁₇₉	C₂²	1	4	yes	direct product factor
7	C₂²×C₄×C₁₇₉	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₇₉	C₈	1	3	yes	—
9	C₂×C₈×C₁₇₉	C₂×C₄	1	3	yes	—
10	C₁₆×C₁₇₉	C₂×C₄	1	3	yes	—
11	C₁₆×C₁₇₉	C₂³	1	1	yes	characteristic
12	C₂³×C₁₇₉	C₁₆	1	1	yes	characteristic
13	C₂×C₄×C₁₇₉	C₁₆	1	3	yes	—
14	C₂×C₄×C₁₇₉	C₂×C₈	1	3	yes	—
15	C₈×C₁₇₉	C₂×C₈	1	3	yes	—
16	C₈×C₁₇₉	C₂²×C₄	1	1	yes	characteristic
17	C₂²×C₁₇₉	C₃₂	1	4	yes	direct product factor
18	C₂²×C₁₇₉	C₂×C₁₆	1	3	yes	—
19	C₄×C₁₇₉	C₂×C₁₆	1	3	yes	—
20	C₄×C₁₇₉	C₂²×C₈	1	1	yes	characteristic
21	C₂×C₁₇₉	C₂×C₃₂	1	6	yes	direct product factor
22	C₂×C₁₇₉	C₂²×C₁₆	1	1	yes	characteristic
23	C₁₇₉	C₂²×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
24	C₂²×C₃₂	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
25	C₂²×C₁₆	C₂×C₁₇₉	1	1	yes	characteristic
26	C₂×C₃₂	C₂×C₁₇₉	1	6	yes	direct product factor
27	C₂²×C₈	C₄×C₁₇₉	1	1	yes	characteristic
28	C₂×C₁₆	C₄×C₁₇₉	1	3	yes	—
29	C₂×C₁₆	C₂²×C₁₇₉	1	3	yes	—
30	C₃₂	C₂²×C₁₇₉	1	4	yes	direct product factor
31	C₂²×C₄	C₈×C₁₇₉	1	1	yes	characteristic
32	C₂×C₈	C₈×C₁₇₉	1	3	yes	—
33	C₂×C₈	C₂×C₄×C₁₇₉	1	3	yes	—
34	C₁₆	C₂×C₄×C₁₇₉	1	3	yes	—
35	C₁₆	C₂³×C₁₇₉	1	1	yes	characteristic
36	C₂³	C₁₆×C₁₇₉	1	1	yes	characteristic
37	C₂×C₄	C₁₆×C₁₇₉	1	3	yes	—
38	C₂×C₄	C₂×C₈×C₁₇₉	1	3	yes	—
39	C₈	C₂×C₈×C₁₇₉	1	3	yes	—
40	C₈	C₂²×C₄×C₁₇₉	1	1	yes	characteristic
41	C₂²	C₃₂×C₁₇₉	1	4	yes	direct product factor
42	C₂²	C₂×C₁₆×C₁₇₉	1	3	yes	—
43	C₄	C₂×C₁₆×C₁₇₉	1	3	yes	—
44	C₄	C₂²×C₈×C₁₇₉	1	1	yes	characteristic
45	C₂	C₂×C₃₂×C₁₇₉	1	6	yes	direct product factor
46	C₂	C₂²×C₁₆×C₁₇₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂³×C₁₇₉
socle, prime radical	C₂³×C₁₇₉	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃₂×C₁₇₉	C₂	direct (N × H)
6. C₃₂×C₁₇₉	C₂²	direct (N × H)
17. C₂²×C₁₇₉	C₃₂	direct (N × H)
21. C₂×C₁₇₉	C₂×C₃₂	direct (N × H)
23. C₁₇₉	C₂²×C₃₂	direct (N × H)
24. C₂²×C₃₂	C₁₇₉	direct (N × H)
26. C₂×C₃₂	C₂×C₁₇₉	direct (N × H)
30. C₃₂	C₂²×C₁₇₉	direct (N × H)
41. C₂²	C₃₂×C₁₇₉	direct (N × H)
45. C₂	C₂×C₃₂×C₁₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×C₁₇₉	2
C₂×C₃₂×C₁₇₉	2
C₂²×C₃₂	179

Subgroups — C22×C32×C179 #37505478

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃₂×C₁₇₉ #37505478