Subgroups — C₂×C₈²×C₁₁×C₁₇ #72201215

Order 23936.

560 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₁×C₁₇	C₂	1	3	yes	maximal
2	C₈²×C₁₁×C₁₇	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₁₁×C₁₇	C₄	1	6	yes	—
4	C₂×C₄²×C₁₁×C₁₇	C₂²	1	1	yes	characteristic
5	C₄×C₈×C₁₁×C₁₇	C₄	1	6	yes	—
6	C₄×C₈×C₁₁×C₁₇	C₂²	1	6	yes	—
7	C₂²×C₄×C₁₁×C₁₇	C₂×C₄	1	3	yes	—
8	C₄²×C₁₁×C₁₇	C₂×C₄	1	3	yes	—
9	C₄²×C₁₁×C₁₇	C₂³	1	1	yes	characteristic
10	C₂×C₈×C₁₁×C₁₇	C₈	1	24	yes	direct product factor
11	C₂×C₈×C₁₁×C₁₇	C₂×C₄	1	12	yes	—
12	C₂×C₈²×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂³×C₁₁×C₁₇	C₄²	1	1	yes	characteristic
14	C₂×C₄×C₁₁×C₁₇	C₄²	1	3	yes	—
15	C₂×C₄×C₁₁×C₁₇	C₂×C₈	1	12	yes	—
16	C₂×C₄×C₁₁×C₁₇	C₂²×C₄	1	3	yes	—
17	C₈×C₁₁×C₁₇	C₂×C₈	1	24	yes	direct product factor
18	C₂×C₈²×C₁₁	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₄×C₈×C₁₇	C₂×C₁₁	1	3	yes	—
20	C₈²×C₁₇	C₂×C₁₁	1	4	yes	direct product factor
21	C₂²×C₁₁×C₁₇	C₄×C₈	1	6	yes	—
22	C₂²×C₁₁×C₁₇	C₂×C₄²	1	1	yes	characteristic
23	C₄×C₁₁×C₁₇	C₄×C₈	1	6	yes	—
24	C₄×C₁₁×C₁₇	C₂²×C₈	1	6	yes	—
25	C₂×C₄×C₈×C₁₁	C₂×C₁₇	1	3	yes	—
26	C₈²×C₁₁	C₂×C₁₇	1	4	yes	direct product factor
27	C₂²×C₈×C₁₇	C₄×C₁₁	1	6	yes	—
28	C₂×C₄²×C₁₇	C₂²×C₁₁	1	1	yes	characteristic
29	C₄×C₈×C₁₇	C₄×C₁₁	1	6	yes	—
30	C₄×C₈×C₁₇	C₂²×C₁₁	1	6	yes	—
31	C₂×C₁₁×C₁₇	C₈²	1	4	yes	direct product factor
32	C₂×C₁₁×C₁₇	C₂×C₄×C₈	1	3	yes	—
33	C₂²×C₈×C₁₁	C₄×C₁₇	1	6	yes	—
34	C₂×C₄²×C₁₁	C₂²×C₁₇	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₄×C₁₇	1	6	yes	—
36	C₄×C₈×C₁₁	C₂²×C₁₇	1	6	yes	—
37	C₂²×C₄×C₁₇	C₂×C₄×C₁₁	1	3	yes	—
38	C₂×C₈×C₁₇	C₈×C₁₁	1	24	yes	direct product factor
39	C₂×C₈×C₁₇	C₂×C₄×C₁₁	1	12	yes	—
40	C₄²×C₁₇	C₂×C₄×C₁₁	1	3	yes	—
41	C₄²×C₁₇	C₂³×C₁₁	1	1	yes	characteristic
42	C₁₁×C₁₇	C₂×C₈²	1	1	yes	characteristic, direct product factor, Hall
43	C₂²×C₄×C₁₁	C₂×C₄×C₁₇	1	3	yes	—
44	C₂×C₈×C₁₁	C₈×C₁₇	1	24	yes	direct product factor
45	C₂×C₈×C₁₁	C₂×C₄×C₁₇	1	12	yes	—
46	C₄²×C₁₁	C₂×C₄×C₁₇	1	3	yes	—
47	C₄²×C₁₁	C₂³×C₁₇	1	1	yes	characteristic
48	C₂³×C₁₇	C₄²×C₁₁	1	1	yes	characteristic
49	C₂×C₄×C₁₇	C₄²×C₁₁	1	3	yes	—
50	C₂×C₄×C₁₇	C₂×C₈×C₁₁	1	12	yes	—
51	C₂×C₄×C₁₇	C₂²×C₄×C₁₁	1	3	yes	—
52	C₈×C₁₇	C₂×C₈×C₁₁	1	24	yes	direct product factor
53	C₂×C₈²	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
54	C₂³×C₁₁	C₄²×C₁₇	1	1	yes	characteristic
55	C₂×C₄×C₁₁	C₄²×C₁₇	1	3	yes	—
56	C₂×C₄×C₁₁	C₂×C₈×C₁₇	1	12	yes	—
57	C₂×C₄×C₁₁	C₂²×C₄×C₁₇	1	3	yes	—
58	C₈×C₁₁	C₂×C₈×C₁₇	1	24	yes	direct product factor
59	C₂²×C₁₇	C₄×C₈×C₁₁	1	6	yes	—
60	C₂²×C₁₇	C₂×C₄²×C₁₁	1	1	yes	characteristic
61	C₄×C₁₇	C₄×C₈×C₁₁	1	6	yes	—
62	C₄×C₁₇	C₂²×C₈×C₁₁	1	6	yes	—
63	C₂×C₄×C₈	C₂×C₁₁×C₁₇	1	3	yes	—
64	C₈²	C₂×C₁₁×C₁₇	1	4	yes	direct product factor
65	C₂²×C₁₁	C₄×C₈×C₁₇	1	6	yes	—
66	C₂²×C₁₁	C₂×C₄²×C₁₇	1	1	yes	characteristic
67	C₄×C₁₁	C₄×C₈×C₁₇	1	6	yes	—
68	C₄×C₁₁	C₂²×C₈×C₁₇	1	6	yes	—
69	C₂×C₁₇	C₈²×C₁₁	1	4	yes	direct product factor
70	C₂×C₁₇	C₂×C₄×C₈×C₁₁	1	3	yes	—
71	C₂²×C₈	C₄×C₁₁×C₁₇	1	6	yes	—
72	C₂×C₄²	C₂²×C₁₁×C₁₇	1	1	yes	characteristic
73	C₄×C₈	C₄×C₁₁×C₁₇	1	6	yes	—
74	C₄×C₈	C₂²×C₁₁×C₁₇	1	6	yes	—
75	C₂×C₁₁	C₈²×C₁₇	1	4	yes	direct product factor
76	C₂×C₁₁	C₂×C₄×C₈×C₁₇	1	3	yes	—
77	C₁₇	C₂×C₈²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
78	C₂²×C₄	C₂×C₄×C₁₁×C₁₇	1	3	yes	—
79	C₂×C₈	C₈×C₁₁×C₁₇	1	24	yes	direct product factor
80	C₂×C₈	C₂×C₄×C₁₁×C₁₇	1	12	yes	—
81	C₄²	C₂×C₄×C₁₁×C₁₇	1	3	yes	—
82	C₄²	C₂³×C₁₁×C₁₇	1	1	yes	characteristic
83	C₁₁	C₂×C₈²×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
84	C₂³	C₄²×C₁₁×C₁₇	1	1	yes	characteristic
85	C₂×C₄	C₂×C₈×C₁₁×C₁₇	1	12	yes	—
86	C₂×C₄	C₄²×C₁₁×C₁₇	1	3	yes	—
87	C₂×C₄	C₂²×C₄×C₁₁×C₁₇	1	3	yes	—
88	C₈	C₂×C₈×C₁₁×C₁₇	1	24	yes	direct product factor
89	C₂²	C₄×C₈×C₁₁×C₁₇	1	6	yes	—
90	C₂²	C₂×C₄²×C₁₁×C₁₇	1	1	yes	characteristic
91	C₄	C₄×C₈×C₁₁×C₁₇	1	6	yes	—
92	C₄	C₂²×C₈×C₁₁×C₁₇	1	6	yes	—
93	C₂	C₈²×C₁₁×C₁₇	1	4	yes	direct product factor
94	C₂	C₂×C₄×C₈×C₁₁×C₁₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²	C₂³×C₁₁×C₁₇
socle, prime radical	C₂³×C₁₁×C₁₇	C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈²×C₁₁×C₁₇	C₂	direct (N × H)
10. C₂×C₈×C₁₁×C₁₇	C₈	direct (N × H)
12. C₂×C₈²×C₁₇	C₁₁	direct (N × H)
17. C₈×C₁₁×C₁₇	C₂×C₈	direct (N × H)
18. C₂×C₈²×C₁₁	C₁₇	direct (N × H)
20. C₈²×C₁₇	C₂×C₁₁	direct (N × H)
26. C₈²×C₁₁	C₂×C₁₇	direct (N × H)
31. C₂×C₁₁×C₁₇	C₈²	direct (N × H)
38. C₂×C₈×C₁₇	C₈×C₁₁	direct (N × H)
42. C₁₁×C₁₇	C₂×C₈²	direct (N × H)
44. C₂×C₈×C₁₁	C₈×C₁₇	direct (N × H)
52. C₈×C₁₇	C₂×C₈×C₁₁	direct (N × H)
53. C₂×C₈²	C₁₁×C₁₇	direct (N × H)
58. C₈×C₁₁	C₂×C₈×C₁₇	direct (N × H)
64. C₈²	C₂×C₁₁×C₁₇	direct (N × H)
69. C₂×C₁₇	C₈²×C₁₁	direct (N × H)
75. C₂×C₁₁	C₈²×C₁₇	direct (N × H)
77. C₁₇	C₂×C₈²×C₁₁	direct (N × H)
79. C₂×C₈	C₈×C₁₁×C₁₇	direct (N × H)
83. C₁₁	C₂×C₈²×C₁₇	direct (N × H)
88. C₈	C₂×C₈×C₁₁×C₁₇	direct (N × H)
93. C₂	C₈²×C₁₁×C₁₇	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×C₄×C₈×C₁₁×C₁₇	2
C₈²×C₁₁×C₁₇	2
C₂×C₈²×C₁₇	11
C₂×C₈²×C₁₁	17

Subgroups — C2×C82×C11×C17 #72201215

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈²×C₁₁×C₁₇ #72201215