Subgroups — C₂²×C₁₁×C₁₇×C₃₂ #72201211

Order 23936.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₁₇×C₃₂	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₈×C₁₁×C₁₇	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₁₆×C₁₇	C₄	1	3	yes	—
5	C₂×C₁₁×C₁₆×C₁₇	C₂²	1	3	yes	—
6	C₁₁×C₁₇×C₃₂	C₂²	1	4	yes	direct product factor
7	C₂²×C₄×C₁₁×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₁×C₁₇	C₈	1	3	yes	—
9	C₂×C₈×C₁₁×C₁₇	C₂×C₄	1	3	yes	—
10	C₁₁×C₁₆×C₁₇	C₂×C₄	1	3	yes	—
11	C₁₁×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
12	C₂²×C₁₇×C₃₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₁₁×C₁₇	C₁₆	1	1	yes	characteristic
14	C₂×C₄×C₁₁×C₁₇	C₁₆	1	3	yes	—
15	C₂×C₄×C₁₁×C₁₇	C₂×C₈	1	3	yes	—
16	C₈×C₁₁×C₁₇	C₂×C₈	1	3	yes	—
17	C₈×C₁₁×C₁₇	C₂²×C₄	1	1	yes	characteristic
18	C₂²×C₁₁×C₃₂	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₁₆×C₁₇	C₂×C₁₁	1	1	yes	characteristic
20	C₂×C₁₇×C₃₂	C₂×C₁₁	1	6	yes	direct product factor
21	C₂²×C₁₁×C₁₇	C₃₂	1	4	yes	direct product factor
22	C₂²×C₁₁×C₁₇	C₂×C₁₆	1	3	yes	—
23	C₄×C₁₁×C₁₇	C₂×C₁₆	1	3	yes	—
24	C₄×C₁₁×C₁₇	C₂²×C₈	1	1	yes	characteristic
25	C₂²×C₁₁×C₁₆	C₂×C₁₇	1	1	yes	characteristic
26	C₂×C₁₁×C₃₂	C₂×C₁₇	1	6	yes	direct product factor
27	C₂²×C₈×C₁₇	C₄×C₁₁	1	1	yes	characteristic
28	C₂×C₁₆×C₁₇	C₄×C₁₁	1	3	yes	—
29	C₂×C₁₆×C₁₇	C₂²×C₁₁	1	3	yes	—
30	C₁₇×C₃₂	C₂²×C₁₁	1	4	yes	direct product factor
31	C₂×C₁₁×C₁₇	C₂×C₃₂	1	6	yes	direct product factor
32	C₂×C₁₁×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	C₄×C₁₇	1	1	yes	characteristic
34	C₂×C₁₁×C₁₆	C₄×C₁₇	1	3	yes	—
35	C₂×C₁₁×C₁₆	C₂²×C₁₇	1	3	yes	—
36	C₁₁×C₃₂	C₂²×C₁₇	1	4	yes	direct product factor
37	C₂²×C₄×C₁₇	C₈×C₁₁	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₈×C₁₁	1	3	yes	—
39	C₂×C₈×C₁₇	C₂×C₄×C₁₁	1	3	yes	—
40	C₁₆×C₁₇	C₂×C₄×C₁₁	1	3	yes	—
41	C₁₆×C₁₇	C₂³×C₁₁	1	1	yes	characteristic
42	C₁₁×C₁₇	C₂²×C₃₂	1	1	yes	characteristic, direct product factor, Hall
43	C₂²×C₄×C₁₁	C₈×C₁₇	1	1	yes	characteristic
44	C₂×C₈×C₁₁	C₈×C₁₇	1	3	yes	—
45	C₂×C₈×C₁₁	C₂×C₄×C₁₇	1	3	yes	—
46	C₁₁×C₁₆	C₂×C₄×C₁₇	1	3	yes	—
47	C₁₁×C₁₆	C₂³×C₁₇	1	1	yes	characteristic
48	C₂³×C₁₇	C₁₁×C₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₇	C₁₁×C₁₆	1	3	yes	—
50	C₂×C₄×C₁₇	C₂×C₈×C₁₁	1	3	yes	—
51	C₈×C₁₇	C₂×C₈×C₁₁	1	3	yes	—
52	C₈×C₁₇	C₂²×C₄×C₁₁	1	1	yes	characteristic
53	C₂²×C₃₂	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³×C₁₁	C₁₆×C₁₇	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₁₆×C₁₇	1	3	yes	—
56	C₂×C₄×C₁₁	C₂×C₈×C₁₇	1	3	yes	—
57	C₈×C₁₁	C₂×C₈×C₁₇	1	3	yes	—
58	C₈×C₁₁	C₂²×C₄×C₁₇	1	1	yes	characteristic
59	C₂²×C₁₇	C₁₁×C₃₂	1	4	yes	direct product factor
60	C₂²×C₁₇	C₂×C₁₁×C₁₆	1	3	yes	—
61	C₄×C₁₇	C₂×C₁₁×C₁₆	1	3	yes	—
62	C₄×C₁₇	C₂²×C₈×C₁₁	1	1	yes	characteristic
63	C₂²×C₁₆	C₂×C₁₁×C₁₇	1	1	yes	characteristic
64	C₂×C₃₂	C₂×C₁₁×C₁₇	1	6	yes	direct product factor
65	C₂²×C₁₁	C₁₇×C₃₂	1	4	yes	direct product factor
66	C₂²×C₁₁	C₂×C₁₆×C₁₇	1	3	yes	—
67	C₄×C₁₁	C₂×C₁₆×C₁₇	1	3	yes	—
68	C₄×C₁₁	C₂²×C₈×C₁₇	1	1	yes	characteristic
69	C₂×C₁₇	C₂×C₁₁×C₃₂	1	6	yes	direct product factor
70	C₂×C₁₇	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
71	C₂²×C₈	C₄×C₁₁×C₁₇	1	1	yes	characteristic
72	C₂×C₁₆	C₄×C₁₁×C₁₇	1	3	yes	—
73	C₂×C₁₆	C₂²×C₁₁×C₁₇	1	3	yes	—
74	C₃₂	C₂²×C₁₁×C₁₇	1	4	yes	direct product factor
75	C₂×C₁₁	C₂×C₁₇×C₃₂	1	6	yes	direct product factor
76	C₂×C₁₁	C₂²×C₁₆×C₁₇	1	1	yes	characteristic
77	C₁₇	C₂²×C₁₁×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
78	C₂²×C₄	C₈×C₁₁×C₁₇	1	1	yes	characteristic
79	C₂×C₈	C₈×C₁₁×C₁₇	1	3	yes	—
80	C₂×C₈	C₂×C₄×C₁₁×C₁₇	1	3	yes	—
81	C₁₆	C₂×C₄×C₁₁×C₁₇	1	3	yes	—
82	C₁₆	C₂³×C₁₁×C₁₇	1	1	yes	characteristic
83	C₁₁	C₂²×C₁₇×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³	C₁₁×C₁₆×C₁₇	1	1	yes	characteristic
85	C₂×C₄	C₁₁×C₁₆×C₁₇	1	3	yes	—
86	C₂×C₄	C₂×C₈×C₁₁×C₁₇	1	3	yes	—
87	C₈	C₂×C₈×C₁₁×C₁₇	1	3	yes	—
88	C₈	C₂²×C₄×C₁₁×C₁₇	1	1	yes	characteristic
89	C₂²	C₁₁×C₁₇×C₃₂	1	4	yes	direct product factor
90	C₂²	C₂×C₁₁×C₁₆×C₁₇	1	3	yes	—
91	C₄	C₂×C₁₁×C₁₆×C₁₇	1	3	yes	—
92	C₄	C₂²×C₈×C₁₁×C₁₇	1	1	yes	characteristic
93	C₂	C₂×C₁₁×C₁₇×C₃₂	1	6	yes	direct product factor
94	C₂	C₂²×C₁₁×C₁₆×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂³×C₁₁×C₁₇
socle, prime radical	C₂³×C₁₁×C₁₇	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×C₁₁×C₁₇×C₃₂	C₂	direct (N × H)
6. C₁₁×C₁₇×C₃₂	C₂²	direct (N × H)
12. C₂²×C₁₇×C₃₂	C₁₁	direct (N × H)
18. C₂²×C₁₁×C₃₂	C₁₇	direct (N × H)
20. C₂×C₁₇×C₃₂	C₂×C₁₁	direct (N × H)
21. C₂²×C₁₁×C₁₇	C₃₂	direct (N × H)
26. C₂×C₁₁×C₃₂	C₂×C₁₇	direct (N × H)
30. C₁₇×C₃₂	C₂²×C₁₁	direct (N × H)
31. C₂×C₁₁×C₁₇	C₂×C₃₂	direct (N × H)
36. C₁₁×C₃₂	C₂²×C₁₇	direct (N × H)
42. C₁₁×C₁₇	C₂²×C₃₂	direct (N × H)
53. C₂²×C₃₂	C₁₁×C₁₇	direct (N × H)
59. C₂²×C₁₇	C₁₁×C₃₂	direct (N × H)
64. C₂×C₃₂	C₂×C₁₁×C₁₇	direct (N × H)
65. C₂²×C₁₁	C₁₇×C₃₂	direct (N × H)
69. C₂×C₁₇	C₂×C₁₁×C₃₂	direct (N × H)
74. C₃₂	C₂²×C₁₁×C₁₇	direct (N × H)
75. C₂×C₁₁	C₂×C₁₇×C₃₂	direct (N × H)
77. C₁₇	C₂²×C₁₁×C₃₂	direct (N × H)
83. C₁₁	C₂²×C₁₇×C₃₂	direct (N × H)
89. C₂²	C₁₁×C₁₇×C₃₂	direct (N × H)
93. C₂	C₂×C₁₁×C₁₇×C₃₂	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×C₁₁×C₁₆×C₁₇	2
C₂×C₁₁×C₁₇×C₃₂	2
C₂²×C₁₇×C₃₂	11
C₂²×C₁₁×C₃₂	17

Subgroups — C22×C11×C17×C32 #72201211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₁₇×C₃₂ #72201211