Subgroups — C₄×C₁₁×C₁₇×C₃₂ #72201210

Order 23936.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×C₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×C₁₇×C₃₂	C₂	1	2	yes	maximal
3	C₄×C₈×C₁₁×C₁₇	C₄	1	1	yes	characteristic
4	C₂×C₁₁×C₁₆×C₁₇	C₄	1	1	yes	characteristic
5	C₂×C₁₁×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
6	C₁₁×C₁₇×C₃₂	C₄	1	4	yes	direct product factor
7	C₄²×C₁₁×C₁₇	C₈	1	1	yes	characteristic
8	C₂×C₈×C₁₁×C₁₇	C₈	1	1	yes	characteristic
9	C₂×C₈×C₁₁×C₁₇	C₂×C₄	1	1	yes	characteristic
10	C₁₁×C₁₆×C₁₇	C₈	1	2	yes	—
11	C₁₁×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
12	C₄×C₁₇×C₃₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₄×C₁₁×C₁₇	C₁₆	1	2	yes	—
14	C₂×C₄×C₁₁×C₁₇	C₂×C₈	1	1	yes	characteristic
15	C₈×C₁₁×C₁₇	C₁₆	1	2	yes	—
16	C₈×C₁₁×C₁₇	C₄²	1	1	yes	characteristic
17	C₈×C₁₁×C₁₇	C₂×C₈	1	1	yes	characteristic
18	C₄×C₁₁×C₃₂	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₇×C₃₂	C₂×C₁₁	1	2	yes	—
20	C₄×C₁₆×C₁₇	C₂×C₁₁	1	1	yes	characteristic
21	C₂²×C₁₁×C₁₇	C₂×C₁₆	1	1	yes	characteristic
22	C₄×C₁₁×C₁₇	C₃₂	1	4	yes	direct product factor
23	C₄×C₁₁×C₁₇	C₄×C₈	1	1	yes	characteristic
24	C₄×C₁₁×C₁₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₁₁×C₃₂	C₂×C₁₇	1	2	yes	—
26	C₄×C₁₁×C₁₆	C₂×C₁₇	1	1	yes	characteristic
27	C₂×C₁₆×C₁₇	C₄×C₁₁	1	1	yes	characteristic
28	C₂×C₁₆×C₁₇	C₂²×C₁₁	1	1	yes	characteristic
29	C₄×C₈×C₁₇	C₄×C₁₁	1	1	yes	characteristic
30	C₁₇×C₃₂	C₄×C₁₁	1	4	yes	direct product factor
31	C₂×C₁₁×C₁₇	C₄×C₁₆	1	1	yes	characteristic
32	C₂×C₁₁×C₁₇	C₂×C₃₂	1	2	yes	—
33	C₂×C₁₁×C₁₆	C₄×C₁₇	1	1	yes	characteristic
34	C₂×C₁₁×C₁₆	C₂²×C₁₇	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₄×C₁₇	1	1	yes	characteristic
36	C₁₁×C₃₂	C₄×C₁₇	1	4	yes	direct product factor
37	C₂×C₈×C₁₇	C₈×C₁₁	1	1	yes	characteristic
38	C₂×C₈×C₁₇	C₂×C₄×C₁₁	1	1	yes	characteristic
39	C₄²×C₁₇	C₈×C₁₁	1	1	yes	characteristic
40	C₁₆×C₁₇	C₈×C₁₁	1	2	yes	—
41	C₁₆×C₁₇	C₂×C₄×C₁₁	1	2	yes	—
42	C₁₁×C₁₇	C₄×C₃₂	1	1	yes	characteristic, direct product factor, Hall
43	C₂×C₈×C₁₁	C₈×C₁₇	1	1	yes	characteristic
44	C₂×C₈×C₁₁	C₂×C₄×C₁₇	1	1	yes	characteristic
45	C₄²×C₁₁	C₈×C₁₇	1	1	yes	characteristic
46	C₁₁×C₁₆	C₈×C₁₇	1	2	yes	—
47	C₁₁×C₁₆	C₂×C₄×C₁₇	1	2	yes	—
48	C₂×C₄×C₁₇	C₁₁×C₁₆	1	2	yes	—
49	C₂×C₄×C₁₇	C₂×C₈×C₁₁	1	1	yes	characteristic
50	C₈×C₁₇	C₁₁×C₁₆	1	2	yes	—
51	C₈×C₁₇	C₄²×C₁₁	1	1	yes	characteristic
52	C₈×C₁₇	C₂×C₈×C₁₁	1	1	yes	characteristic
53	C₄×C₃₂	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂×C₄×C₁₁	C₁₆×C₁₇	1	2	yes	—
55	C₂×C₄×C₁₁	C₂×C₈×C₁₇	1	1	yes	characteristic
56	C₈×C₁₁	C₁₆×C₁₇	1	2	yes	—
57	C₈×C₁₁	C₄²×C₁₇	1	1	yes	characteristic
58	C₈×C₁₁	C₂×C₈×C₁₇	1	1	yes	characteristic
59	C₂²×C₁₇	C₂×C₁₁×C₁₆	1	1	yes	characteristic
60	C₄×C₁₇	C₁₁×C₃₂	1	4	yes	direct product factor
61	C₄×C₁₇	C₄×C₈×C₁₁	1	1	yes	characteristic
62	C₄×C₁₇	C₂×C₁₁×C₁₆	1	1	yes	characteristic
63	C₂×C₃₂	C₂×C₁₁×C₁₇	1	2	yes	—
64	C₄×C₁₆	C₂×C₁₁×C₁₇	1	1	yes	characteristic
65	C₂²×C₁₁	C₂×C₁₆×C₁₇	1	1	yes	characteristic
66	C₄×C₁₁	C₁₇×C₃₂	1	4	yes	direct product factor
67	C₄×C₁₁	C₄×C₈×C₁₇	1	1	yes	characteristic
68	C₄×C₁₁	C₂×C₁₆×C₁₇	1	1	yes	characteristic
69	C₂×C₁₇	C₄×C₁₁×C₁₆	1	1	yes	characteristic
70	C₂×C₁₇	C₂×C₁₁×C₃₂	1	2	yes	—
71	C₂×C₁₆	C₄×C₁₁×C₁₇	1	1	yes	characteristic
72	C₂×C₁₆	C₂²×C₁₁×C₁₇	1	1	yes	characteristic
73	C₄×C₈	C₄×C₁₁×C₁₇	1	1	yes	characteristic
74	C₃₂	C₄×C₁₁×C₁₇	1	4	yes	direct product factor
75	C₂×C₁₁	C₄×C₁₆×C₁₇	1	1	yes	characteristic
76	C₂×C₁₁	C₂×C₁₇×C₃₂	1	2	yes	—
77	C₁₇	C₄×C₁₁×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
78	C₂×C₈	C₈×C₁₁×C₁₇	1	1	yes	characteristic
79	C₂×C₈	C₂×C₄×C₁₁×C₁₇	1	1	yes	characteristic
80	C₄²	C₈×C₁₁×C₁₇	1	1	yes	characteristic
81	C₁₆	C₈×C₁₁×C₁₇	1	2	yes	—
82	C₁₆	C₂×C₄×C₁₁×C₁₇	1	2	yes	—
83	C₁₁	C₄×C₁₇×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
84	C₂×C₄	C₁₁×C₁₆×C₁₇	1	2	yes	—
85	C₂×C₄	C₂×C₈×C₁₁×C₁₇	1	1	yes	characteristic
86	C₈	C₁₁×C₁₆×C₁₇	1	2	yes	—
87	C₈	C₂×C₈×C₁₁×C₁₇	1	1	yes	characteristic
88	C₈	C₄²×C₁₁×C₁₇	1	1	yes	characteristic
89	C₂²	C₂×C₁₁×C₁₆×C₁₇	1	1	yes	characteristic
90	C₄	C₁₁×C₁₇×C₃₂	1	4	yes	direct product factor
91	C₄	C₂×C₁₁×C₁₆×C₁₇	1	1	yes	characteristic
92	C₄	C₄×C₈×C₁₁×C₁₇	1	1	yes	characteristic
93	C₂	C₂×C₁₁×C₁₇×C₃₂	1	2	yes	—
94	C₂	C₄×C₁₁×C₁₆×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₁₆	C₂²×C₁₁×C₁₇
socle, prime radical	C₂²×C₁₁×C₁₇	C₂×C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₁₁×C₁₇×C₃₂	C₄	direct (N × H)
12. C₄×C₁₇×C₃₂	C₁₁	direct (N × H)
18. C₄×C₁₁×C₃₂	C₁₇	direct (N × H)
22. C₄×C₁₁×C₁₇	C₃₂	direct (N × H)
30. C₁₇×C₃₂	C₄×C₁₁	direct (N × H)
36. C₁₁×C₃₂	C₄×C₁₇	direct (N × H)
42. C₁₁×C₁₇	C₄×C₃₂	direct (N × H)
53. C₄×C₃₂	C₁₁×C₁₇	direct (N × H)
60. C₄×C₁₇	C₁₁×C₃₂	direct (N × H)
66. C₄×C₁₁	C₁₇×C₃₂	direct (N × H)
74. C₃₂	C₄×C₁₁×C₁₇	direct (N × H)
77. C₁₇	C₄×C₁₁×C₃₂	direct (N × H)
83. C₁₁	C₄×C₁₇×C₃₂	direct (N × H)
90. C₄	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
C₄×C₁₁×C₁₆×C₁₇	2
C₂×C₁₁×C₁₇×C₃₂	2
C₄×C₁₇×C₃₂	11
C₄×C₁₁×C₃₂	17

Subgroups — C4×C11×C17×C32 #72201210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×C₁₇×C₃₂ #72201210