Subgroups — M₃₂×C₁₁⋊C₈ #14662750

Order 2816.

354 conjugacy classes of subgroups.

The subgroup lattice has 148 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#66876	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13066532	C₂	1	2	yes	maximal, complemented
4	C₁₆×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₄	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66876	C₄	1	2	yes	—
9	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
10	C₁₁×#346	C₄	1	2	yes	—
11	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
12	#10622099	C₄	1	2	yes	—
13	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
14	C₈×C₁₁⋊C₈	C₄	1	2	yes	—
15	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₈×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₁₁⋊C₈	C₈	1	4	yes	—
21	C₁₁×M₃₂	C₈	1	8	yes	complemented
22	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
23	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	#66876	C₈	1	8	yes	complemented
28	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
29	C₄×C₁₁⋊C₈	C₈	1	4	yes	—
30	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
31	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
32	C₈×M₃₂	—	11	1	no	maximal, Sylow
33	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
35	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
36	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
37	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
38	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
39	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
41	C₄²×C₁₁	C₄²	1	1	yes	characteristic
42	C₄²×C₁₁	C₂×C₈	1	2	yes	—
43	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₁₁⋊C₈	—	2	8	no	—
45	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
46	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
47	C₁₁×C₁₆	C₂×C₈	1	8	yes	complemented
48	C₁₁⋊C₁₆	C₂×C₈	1	8	yes	complemented
49	C₄×M₃₂	—	11	1	no	—
50	C₄×M₃₂	D₁₁	1	1	yes	characteristic
51	C₂×C₈²	—	11	1	no	—
52	#1311	—	11	2	no	—
53	C₈×C₁₆	—	11	2	no	—
54	C₂³×C₁₁	C₄×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₁	—	2	4	no	—
56	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
57	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
58	C₂×C₄×C₁₁	C₄×C₈	1	1	yes	characteristic
59	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
60	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
62	C₈×C₁₁	C₄×C₈	1	2	yes	—
63	C₈×C₁₁	C₄×C₈	1	2	yes	—
64	C₈×C₁₁	C₂²×C₈	1	2	yes	—
65	C₈×C₁₁	C₂²×C₈	1	2	yes	—
66	C₁₁⋊C₈	—	2	4	no	—
67	C₁₁⋊C₈	M₃₂	1	8	yes	direct product factor
68	C₂×M₃₂	—	11	2	no	—
69	C₂×M₃₂	Dic₁₁	1	2	yes	—
70	C₂×C₄×C₈	—	11	2	no	—
71	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
72	#346	—	11	2	no	—
73	#346	Dic₁₁	1	2	yes	—
74	C₄×C₁₆	—	11	2	no	—
75	C₄×C₁₆	C₂×D₁₁	1	2	yes	—
76	C₈²	—	11	1	no	—
77	C₈²	—	11	1	no	—
78	C₈²	—	11	2	no	—
79	C₂²×C₁₁	—	2	2	no	—
80	C₂²×C₁₁	C₈²	1	2	yes	—
81	C₂²×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
82	C₄×C₁₁	—	2	2	no	—
83	C₄×C₁₁	C₈²	1	2	yes	—
84	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
85	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
86	C₄×C₁₁	C₂×M₃₂	1	4	yes	—
87	C₂²×C₈	—	11	4	no	—
88	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
89	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
90	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
91	M₃₂	—	11	8	no	—
92	M₃₂	C₁₁⋊C₈	1	8	yes	direct product factor
93	C₂×C₁₆	—	11	4	no	—
94	C₂×C₁₆	C₂×Dic₁₁	1	4	yes	—
95	C₄×C₈	—	11	4	no	—
96	C₄×C₈	—	11	2	no	—
97	C₄×C₈	—	11	2	no	—
98	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
99	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
100	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
101	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
102	C₂×C₁₁	—	2	2	no	—
103	C₂×C₁₁	C₂×C₈²	1	1	yes	characteristic
104	C₂×C₁₁	C₄×M₃₂	1	2	yes	—
105	C₂²×C₄	C₈×D₁₁	1	2	yes	—
106	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
107	C₂×C₈	—	11	4	no	—
108	C₂×C₈	—	11	4	no	—
109	C₂×C₈	—	22	8	no	—
110	C₂×C₈	C₈×D₁₁	1	4	yes	—
111	C₂×C₈	C₂×C₁₁⋊C₈	1	4	yes	—
112	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
113	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
114	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
115	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
116	C₄²	C₈×D₁₁	1	2	yes	—
117	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
118	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
119	C₁₆	—	11	8	no	—
120	C₁₆	C₂×C₁₁⋊C₈	1	8	yes	complemented
121	C₁₁	C₈×M₃₂	1	1	yes	characteristic, complemented, Sylow
122	C₂³	C₈×Dic₁₁	1	1	yes	characteristic
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	C₄×C₁₁⋊C₈	1	2	yes	—
125	C₂×C₄	C₈×Dic₁₁	1	2	yes	—
126	C₂×C₄	C₈×Dic₁₁	1	1	yes	characteristic
127	C₂×C₄	C₈×Dic₁₁	1	2	yes	—
128	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
129	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
130	C₈	—	11	8	no	—
131	C₈	—	22	4	no	—
132	C₈	C₄×C₁₁⋊C₈	1	2	yes	—
133	C₈	C₈×Dic₁₁	1	2	yes	—
134	C₈	C₂×C₈×D₁₁	1	2	yes	—
135	C₈	C₂²×C₁₁⋊C₈	1	2	yes	—
136	C₂²	—	2	2	no	—
137	C₂²	C₈×C₁₁⋊C₈	1	2	yes	—
138	C₂²	C₂×C₈×Dic₁₁	1	1	yes	characteristic
139	C₄	—	2	2	no	—
140	C₄	C₈×C₁₁⋊C₈	1	2	yes	—
141	C₄	D₁₁×M₃₂	1	4	yes	—
142	C₄	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
143	C₄	C₂×C₈×Dic₁₁	1	1	yes	characteristic
144	C₂	—	2	2	no	—
145	C₂	C₂×C₈×C₁₁⋊C₈	1	1	yes	characteristic
146	C₂	M₃₂×Dic₁₁	1	2	yes	—

	subgroup	G/H
center, Frattini	C₄×C₈	C₂²×D₁₁
commutator	C₂×C₁₁	C₂×C₈²
Fitting	C₄×C₁₁×M₃₂	C₂
socle	C₂²×C₁₁	C₂×C₄×C₈
prime radical	C₂³×C₁₁	C₄×C₈
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	C₈×M₃₂
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13066532	C₂	semidirect
4. C₁₆×C₁₁⋊C₈	C₂	semidirect
21. C₁₁×M₃₂	C₈	semidirect
27. #66876	C₈	semidirect
47. C₁₁×C₁₆	C₂×C₈	semidirect
48. C₁₁⋊C₁₆	C₂×C₈	semidirect
67. C₁₁⋊C₈	M₃₂	direct (N × H)
92. M₃₂	C₁₁⋊C₈	direct (N × H)
120. C₁₆	C₂×C₁₁⋊C₈	semidirect
121. C₁₁	C₈×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66876	2
C₂×C₈×C₁₁⋊C₈	2
#13066532	2
C₁₆×C₁₁⋊C₈	2
C₄×C₁₁×M₃₂	2
C₈×M₃₂	11

Subgroups — M32×C11⋊C8 #14662750

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×C₁₁⋊C₈ #14662750