Subgroups — C₂²×C₇×C₁₁×C₃₂ #72188558

Order 9856.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₇×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×C₁₁×C₃₂	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₇×C₈×C₁₁	C₄	1	1	yes	characteristic
4	C₂×C₇×C₁₁×C₁₆	C₄	1	3	yes	—
5	C₂×C₇×C₁₁×C₁₆	C₂²	1	3	yes	—
6	C₇×C₁₁×C₃₂	C₂²	1	4	yes	direct product factor
7	C₂²×C₁₁×C₃₂	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₄×C₇×C₁₁	C₈	1	1	yes	characteristic
9	C₂×C₇×C₈×C₁₁	C₈	1	3	yes	—
10	C₂×C₇×C₈×C₁₁	C₂×C₄	1	3	yes	—
11	C₇×C₁₁×C₁₆	C₂×C₄	1	3	yes	—
12	C₇×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
13	C₂²×C₇×C₃₂	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₁₁×C₁₆	C₂×C₇	1	1	yes	characteristic
15	C₂×C₁₁×C₃₂	C₂×C₇	1	6	yes	direct product factor
16	C₂³×C₇×C₁₁	C₁₆	1	1	yes	characteristic
17	C₂×C₄×C₇×C₁₁	C₁₆	1	3	yes	—
18	C₂×C₄×C₇×C₁₁	C₂×C₈	1	3	yes	—
19	C₇×C₈×C₁₁	C₂×C₈	1	3	yes	—
20	C₇×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
21	C₂²×C₇×C₁₆	C₂×C₁₁	1	1	yes	characteristic
22	C₂×C₇×C₃₂	C₂×C₁₁	1	6	yes	direct product factor
23	C₂²×C₈×C₁₁	C₄×C₇	1	1	yes	characteristic
24	C₂×C₁₁×C₁₆	C₄×C₇	1	3	yes	—
25	C₂×C₁₁×C₁₆	C₂²×C₇	1	3	yes	—
26	C₁₁×C₃₂	C₂²×C₇	1	4	yes	direct product factor
27	C₂²×C₇×C₁₁	C₃₂	1	4	yes	direct product factor
28	C₂²×C₇×C₁₁	C₂×C₁₆	1	3	yes	—
29	C₄×C₇×C₁₁	C₂×C₁₆	1	3	yes	—
30	C₄×C₇×C₁₁	C₂²×C₈	1	1	yes	characteristic
31	C₂²×C₇×C₈	C₄×C₁₁	1	1	yes	characteristic
32	C₂×C₇×C₁₆	C₄×C₁₁	1	3	yes	—
33	C₂×C₇×C₁₆	C₂²×C₁₁	1	3	yes	—
34	C₇×C₃₂	C₂²×C₁₁	1	4	yes	direct product factor
35	C₂²×C₄×C₁₁	C₇×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₇×C₈	1	3	yes	—
37	C₂×C₈×C₁₁	C₂×C₄×C₇	1	3	yes	—
38	C₁₁×C₁₆	C₂×C₄×C₇	1	3	yes	—
39	C₁₁×C₁₆	C₂³×C₇	1	1	yes	characteristic
40	C₂×C₇×C₁₁	C₂×C₃₂	1	6	yes	direct product factor
41	C₂×C₇×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
42	C₂²×C₃₂	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₄×C₇	C₈×C₁₁	1	1	yes	characteristic
44	C₂×C₇×C₈	C₈×C₁₁	1	3	yes	—
45	C₂×C₇×C₈	C₂×C₄×C₁₁	1	3	yes	—
46	C₇×C₁₆	C₂×C₄×C₁₁	1	3	yes	—
47	C₇×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
48	C₂³×C₁₁	C₇×C₁₆	1	1	yes	characteristic
49	C₂×C₄×C₁₁	C₇×C₁₆	1	3	yes	—
50	C₂×C₄×C₁₁	C₂×C₇×C₈	1	3	yes	—
51	C₈×C₁₁	C₂×C₇×C₈	1	3	yes	—
52	C₈×C₁₁	C₂²×C₄×C₇	1	1	yes	characteristic
53	C₇×C₁₁	C₂²×C₃₂	1	1	yes	characteristic, direct product factor, Hall
54	C₂²×C₁₆	C₂×C₇×C₁₁	1	1	yes	characteristic
55	C₂×C₃₂	C₂×C₇×C₁₁	1	6	yes	direct product factor
56	C₂³×C₇	C₁₁×C₁₆	1	1	yes	characteristic
57	C₂×C₄×C₇	C₁₁×C₁₆	1	3	yes	—
58	C₂×C₄×C₇	C₂×C₈×C₁₁	1	3	yes	—
59	C₇×C₈	C₂×C₈×C₁₁	1	3	yes	—
60	C₇×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
61	C₂²×C₁₁	C₇×C₃₂	1	4	yes	direct product factor
62	C₂²×C₁₁	C₂×C₇×C₁₆	1	3	yes	—
63	C₄×C₁₁	C₂×C₇×C₁₆	1	3	yes	—
64	C₄×C₁₁	C₂²×C₇×C₈	1	1	yes	characteristic
65	C₂²×C₈	C₄×C₇×C₁₁	1	1	yes	characteristic
66	C₂×C₁₆	C₄×C₇×C₁₁	1	3	yes	—
67	C₂×C₁₆	C₂²×C₇×C₁₁	1	3	yes	—
68	C₃₂	C₂²×C₇×C₁₁	1	4	yes	direct product factor
69	C₂²×C₇	C₁₁×C₃₂	1	4	yes	direct product factor
70	C₂²×C₇	C₂×C₁₁×C₁₆	1	3	yes	—
71	C₄×C₇	C₂×C₁₁×C₁₆	1	3	yes	—
72	C₄×C₇	C₂²×C₈×C₁₁	1	1	yes	characteristic
73	C₂×C₁₁	C₂×C₇×C₃₂	1	6	yes	direct product factor
74	C₂×C₁₁	C₂²×C₇×C₁₆	1	1	yes	characteristic
75	C₂²×C₄	C₇×C₈×C₁₁	1	1	yes	characteristic
76	C₂×C₈	C₇×C₈×C₁₁	1	3	yes	—
77	C₂×C₈	C₂×C₄×C₇×C₁₁	1	3	yes	—
78	C₁₆	C₂×C₄×C₇×C₁₁	1	3	yes	—
79	C₁₆	C₂³×C₇×C₁₁	1	1	yes	characteristic
80	C₂×C₇	C₂×C₁₁×C₃₂	1	6	yes	direct product factor
81	C₂×C₇	C₂²×C₁₁×C₁₆	1	1	yes	characteristic
82	C₁₁	C₂²×C₇×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
83	C₂³	C₇×C₁₁×C₁₆	1	1	yes	characteristic
84	C₂×C₄	C₇×C₁₁×C₁₆	1	3	yes	—
85	C₂×C₄	C₂×C₇×C₈×C₁₁	1	3	yes	—
86	C₈	C₂×C₇×C₈×C₁₁	1	3	yes	—
87	C₈	C₂²×C₄×C₇×C₁₁	1	1	yes	characteristic
88	C₇	C₂²×C₁₁×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
89	C₂²	C₇×C₁₁×C₃₂	1	4	yes	direct product factor
90	C₂²	C₂×C₇×C₁₁×C₁₆	1	3	yes	—
91	C₄	C₂×C₇×C₁₁×C₁₆	1	3	yes	—
92	C₄	C₂²×C₇×C₈×C₁₁	1	1	yes	characteristic
93	C₂	C₂×C₇×C₁₁×C₃₂	1	6	yes	direct product factor
94	C₂	C₂²×C₇×C₁₁×C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂³×C₇×C₁₁
socle, prime radical	C₂³×C₇×C₁₁	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×C₇×C₁₁×C₃₂	C₂	direct (N × H)
6. C₇×C₁₁×C₃₂	C₂²	direct (N × H)
7. C₂²×C₁₁×C₃₂	C₇	direct (N × H)
13. C₂²×C₇×C₃₂	C₁₁	direct (N × H)
15. C₂×C₁₁×C₃₂	C₂×C₇	direct (N × H)
22. C₂×C₇×C₃₂	C₂×C₁₁	direct (N × H)
26. C₁₁×C₃₂	C₂²×C₇	direct (N × H)
27. C₂²×C₇×C₁₁	C₃₂	direct (N × H)
34. C₇×C₃₂	C₂²×C₁₁	direct (N × H)
40. C₂×C₇×C₁₁	C₂×C₃₂	direct (N × H)
42. C₂²×C₃₂	C₇×C₁₁	direct (N × H)
53. C₇×C₁₁	C₂²×C₃₂	direct (N × H)
55. C₂×C₃₂	C₂×C₇×C₁₁	direct (N × H)
61. C₂²×C₁₁	C₇×C₃₂	direct (N × H)
68. C₃₂	C₂²×C₇×C₁₁	direct (N × H)
69. C₂²×C₇	C₁₁×C₃₂	direct (N × H)
73. C₂×C₁₁	C₂×C₇×C₃₂	direct (N × H)
80. C₂×C₇	C₂×C₁₁×C₃₂	direct (N × H)
82. C₁₁	C₂²×C₇×C₃₂	direct (N × H)
88. C₇	C₂²×C₁₁×C₃₂	direct (N × H)
89. C₂²	C₇×C₁₁×C₃₂	direct (N × H)
93. C₂	C₂×C₇×C₁₁×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×C₇×C₁₁×C₁₆	2
C₂×C₇×C₁₁×C₃₂	2
C₂²×C₁₁×C₃₂	7
C₂²×C₇×C₃₂	11

Subgroups — C22×C7×C11×C32 #72188558

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₇×C₁₁×C₃₂ #72188558