Subgroups — Q₈×C₁₆×D₁₁ #14907252

Order 2816.

582 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×D₁₁	C₂	1	1	yes	maximal, characteristic
2	Q₈×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×Dic₂₂	C₂	1	3	yes	maximal, complemented
4	#13070518	C₂	1	3	yes	maximal, complemented
5	D₁₁×C₄⋊C₁₆	C₂	1	3	yes	maximal
6	C₄×C₁₆×D₁₁	C₂	1	3	yes	maximal
7	Q₈×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×Q₈×D₁₁	C₄	1	1	yes	characteristic
9	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic
10	Q₈×C₁₁⋊C₈	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₁₁	C₂²	1	3	yes	—
12	C₂×C₁₆×D₁₁	C₂²	1	1	yes	characteristic
13	D₁₁×C₄⋊C₈	C₄	1	3	yes	—
14	#10622443	C₄	1	3	yes	—
15	C₄×C₈×D₁₁	C₂²	1	3	yes	—
16	C₈×Dic₂₂	C₂²	1	3	yes	—
17	C₁₁×C₄⋊C₁₆	C₂²	1	3	yes	—
18	C₄×C₁₁×C₁₆	C₂²	1	3	yes	—
19	Dic₁₁⋊C₁₆	C₂²	1	6	yes	—
20	C₁₆×Dic₁₁	C₂²	1	3	yes	—
21	C₁₆×Dic₁₁	C₂²	1	3	yes	—
22	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	3	yes	—
23	C₄×C₁₁⋊C₁₆	C₂²	1	3	yes	—
24	C₂×Q₈×D₁₁	C₈	1	1	yes	characteristic
25	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	Q₈×Dic₁₁	C₈	1	1	yes	characteristic
27	C₂×C₈×D₁₁	C₂×C₄	1	3	yes	—
28	C₂×C₈×D₁₁	C₂³	1	1	yes	characteristic
29	C₄⋊C₄×D₁₁	C₈	1	3	yes	—
30	#66940	C₈	1	3	yes	—
31	C₄²×D₁₁	C₂×C₄	1	3	yes	—
32	C₄×Dic₂₂	C₂×C₄	1	3	yes	—
33	C₂×C₁₁×C₁₆	C₂³	1	3	yes	—
34	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
35	C₁₁×C₄⋊C₈	C₂×C₄	1	3	yes	—
36	C₄×C₈×C₁₁	C₂³	1	3	yes	—
37	Dic₁₁⋊C₈	C₂×C₄	1	6	yes	—
38	C₈×Dic₁₁	C₂×C₄	1	3	yes	—
39	C₈×Dic₁₁	C₂³	1	3	yes	—
40	C₂×C₁₁⋊C₁₆	C₂³	1	3	yes	—
41	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
42	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	3	yes	—
43	C₄×C₁₁⋊C₈	C₂×C₄	1	3	yes	—
44	C₁₆×D₁₁	—	2	6	no	—
45	C₁₆×D₁₁	Q₈	1	4	yes	direct product factor
46	C₂×Q₈×C₁₆	—	11	1	no	maximal, Sylow
47	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
48	Q₈×D₁₁	C₁₆	1	8	yes	direct product factor
49	C₂×C₄×D₁₁	C₂×C₈	1	3	yes	—
50	C₂×C₄×D₁₁	C₂×C₈	1	3	yes	—
51	C₂×C₄×D₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂×Dic₂₂	C₂×C₈	1	3	yes	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
54	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
55	C₁₁×C₄⋊C₄	C₂×C₈	1	3	yes	—
56	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
57	C₄⋊Dic₁₁	C₂×C₈	1	3	yes	—
58	Dic₁₁⋊C₄	C₂×C₈	1	6	yes	—
59	C₄×Dic₁₁	C₂×C₈	1	3	yes	—
60	C₄×Dic₁₁	C₂×C₈	1	3	yes	—
61	C₄×Dic₁₁	C₂²×C₄	1	3	yes	—
62	C₂×C₁₁⋊C₈	C₂²×C₄	1	3	yes	—
63	C₂×C₁₁⋊C₈	C₂²×C₄	1	1	yes	characteristic
64	C₈×D₁₁	—	2	6	no	—
65	C₈×D₁₁	C₂×Q₈	1	2	yes	—
66	C₈×D₁₁	#41	1	2	yes	—
67	C₁₁×C₁₆	—	2	3	no	—
68	C₁₁×C₁₆	C₂×Q₈	1	2	yes	complemented
69	C₁₁⋊C₁₆	—	2	3	no	—
70	C₁₁⋊C₁₆	C₂×Q₈	1	2	yes	complemented
71	C₂×C₈×Q₈	—	11	1	no	—
72	Q₈×C₁₆	—	11	1	no	—
73	Q₈×C₁₆	—	11	3	no	—
74	Q₈×C₁₆	—	11	3	no	—
75	Q₈×C₁₆	D₁₁	1	1	yes	characteristic, direct product factor
76	C₂×C₄⋊C₁₆	—	11	3	no	—
77	C₂×C₄×C₁₆	—	11	3	no	—
78	C₂²×D₁₁	C₂²×C₈	1	1	yes	characteristic
79	Q₈×C₁₁	C₂×C₁₆	1	4	yes	complemented
80	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
81	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
82	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
83	C₂×Dic₁₁	C₂²×C₈	1	3	yes	—
84	C₂×Dic₁₁	C₂²×C₈	1	1	yes	characteristic
85	C₂×Dic₁₁	C₂²×C₈	1	3	yes	—
86	C₄×D₁₁	—	2	6	no	—
87	C₄×D₁₁	C₂×C₁₆	1	12	yes	—
88	C₄×D₁₁	C₄×Q₈	1	2	yes	—
89	C₄×D₁₁	#131	1	2	yes	—
90	Dic₂₂	C₂×C₁₆	1	12	yes	complemented
91	C₈×C₁₁	—	2	3	no	—
92	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
93	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
94	C₁₁⋊C₈	—	2	3	no	—
95	C₁₁⋊C₈	C₄×Q₈	1	2	yes	—
96	C₂×C₄×Q₈	—	11	1	no	—
97	C₂²×C₁₆	—	11	1	no	—
98	C₂²×C₁₆	—	11	3	no	—
99	C₈×Q₈	—	11	1	no	—
100	C₈×Q₈	—	11	3	no	—
101	C₈×Q₈	—	11	3	no	—
102	C₈×Q₈	C₂×D₁₁	1	1	yes	characteristic
103	C₂×C₄⋊C₈	—	11	3	no	—
104	C₂×C₄×C₈	—	11	3	no	—
105	C₄⋊C₁₆	—	11	6	no	—
106	C₄⋊C₁₆	—	11	3	no	—
107	C₄⋊C₁₆	C₂×D₁₁	1	3	yes	—
108	C₄×C₁₆	—	11	3	no	—
109	C₄×C₁₆	—	11	3	no	—
110	C₄×C₁₆	—	11	3	no	—
111	C₄×C₁₆	C₂×D₁₁	1	3	yes	—
112	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
113	C₂×D₁₁	C₈×Q₈	1	2	yes	—
114	C₂×D₁₁	C₂²×C₁₆	1	2	yes	—
115	C₂×D₁₁	#504	1	2	yes	—
116	C₄×C₁₁	—	2	3	no	—
117	C₄×C₁₁	C₂²×C₁₆	1	6	yes	—
118	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
119	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
120	Dic₁₁	—	2	3	no	—
121	Dic₁₁	C₈×Q₈	1	2	yes	—
122	Dic₁₁	C₂²×C₁₆	1	6	yes	—
123	C₂²×Q₈	—	11	1	no	—
124	C₂²×C₈	—	11	1	no	—
125	C₂²×C₈	—	11	3	no	—
126	C₄×Q₈	—	11	1	no	—
127	C₄×Q₈	—	11	3	no	—
128	C₄×Q₈	—	11	3	no	—
129	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
130	C₂×C₄⋊C₄	—	11	3	no	—
131	C₂×C₄²	—	11	3	no	—
132	C₂×C₁₆	—	11	1	no	—
133	C₂×C₁₆	—	11	4	no	—
134	C₂×C₁₆	—	11	3	no	—
135	C₂×C₁₆	—	22	6	no	—
136	C₂×C₁₆	C₂²×D₁₁	1	3	yes	—
137	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
138	C₄⋊C₈	—	11	6	no	—
139	C₄⋊C₈	—	11	3	no	—
140	C₄⋊C₈	C₄×D₁₁	1	3	yes	—
141	C₄×C₈	—	11	3	no	—
142	C₄×C₈	—	11	3	no	—
143	C₄×C₈	—	11	3	no	—
144	C₄×C₈	C₂²×D₁₁	1	3	yes	—
145	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
146	C₂×C₁₁	C₂³×C₁₆	1	1	yes	characteristic
147	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
148	D₁₁	Q₈×C₁₆	1	4	yes	direct product factor
149	C₂×Q₈	—	11	8	no	—
150	C₂×Q₈	—	11	3	no	—
151	C₂×Q₈	C₈×D₁₁	1	1	yes	characteristic
152	C₂²×C₄	—	11	3	no	—
153	C₂²×C₄	—	11	1	no	—
154	C₂²×C₄	—	11	3	no	—
155	C₂×C₈	—	11	1	no	—
156	C₂×C₈	—	11	2	no	—
157	C₂×C₈	—	11	2	no	—
158	C₂×C₈	—	11	3	no	—
159	C₂×C₈	—	22	6	no	—
160	C₂×C₈	C₂×C₄×D₁₁	1	3	yes	—
161	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
162	C₄⋊C₄	—	11	6	no	—
163	C₄⋊C₄	—	11	3	no	—
164	C₄⋊C₄	C₈×D₁₁	1	3	yes	—
165	C₄²	—	11	3	no	—
166	C₄²	—	11	3	no	—
167	C₄²	—	11	3	no	—
168	C₄²	C₂×C₄×D₁₁	1	3	yes	—
169	C₁₆	—	2	3	no	—
170	C₁₆	—	11	2	no	—
171	C₁₆	—	22	3	no	—
172	C₁₆	Q₈×D₁₁	1	2	yes	direct product factor
173	C₁₁	C₂×Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
174	C₂³	—	11	1	no	—
175	Q₈	—	11	12	no	—
176	Q₈	C₁₆×D₁₁	1	4	yes	direct product factor
177	C₂×C₄	—	11	1	no	—
178	C₂×C₄	—	11	3	no	—
179	C₂×C₄	—	11	12	no	—
180	C₂×C₄	—	11	2	no	—
181	C₂×C₄	—	11	2	no	—
182	C₂×C₄	—	11	3	no	—
183	C₂×C₄	—	22	6	no	—
184	C₂×C₄	C₂×C₈×D₁₁	1	3	yes	—
185	C₂×C₄	C₂×C₈×D₁₁	1	3	yes	—
186	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
187	C₈	—	2	3	no	—
188	C₈	—	11	2	no	—
189	C₈	—	22	3	no	—
190	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
191	C₈	#41×D₁₁	1	1	yes	characteristic
192	C₂²	—	11	2	no	—
193	C₂²	—	11	2	no	—
194	C₂²	—	11	2	no	—
195	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
196	C₄	—	2	3	no	—
197	C₄	—	11	2	no	—
198	C₄	—	11	6	no	—
199	C₄	—	22	3	no	—
200	C₄	C₂×C₁₆×D₁₁	1	6	yes	—
201	C₄	C₄×Q₈×D₁₁	1	1	yes	characteristic
202	C₄	D₁₁×#131	1	1	yes	characteristic
203	C₂	—	11	4	no	—
204	C₂	C₈×Q₈×D₁₁	1	1	yes	characteristic
205	C₂	C₂²×C₁₆×D₁₁	1	1	yes	characteristic
206	C₂	D₁₁×#504	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₁₁
commutator	C₂×C₁₁	C₂³×C₁₆
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	Q₈×C₁₁×C₁₆	C₂
socle	C₂²×C₁₁	C₂³×C₈
prime radical	C₂²×D₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	Q₈×C₁₆	D₁₁
hypocenter	C₁₁	C₂×Q₈×C₁₆
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₁₆ ◁ Q₈×C₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×C₁₁⋊C₁₆	C₂	semidirect
3. C₁₆×Dic₂₂	C₂	semidirect
4. #13070518	C₂	semidirect
7. Q₈×C₁₁×C₁₆	C₂	semidirect
45. C₁₆×D₁₁	Q₈	direct (N × H)
48. Q₈×D₁₁	C₁₆	direct (N × H)
68. C₁₁×C₁₆	C₂×Q₈	semidirect
70. C₁₁⋊C₁₆	C₂×Q₈	semidirect
75. Q₈×C₁₆	D₁₁	direct (N × H)
79. Q₈×C₁₁	C₂×C₁₆	semidirect
90. Dic₂₂	C₂×C₁₆	semidirect
148. D₁₁	Q₈×C₁₆	direct (N × H)
172. C₁₆	Q₈×D₁₁	direct (N × H)
173. C₁₁	C₂×Q₈×C₁₆	semidirect
176. Q₈	C₁₆×D₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×Q₈×D₁₁	2
Q₈×C₁₁⋊C₁₆	2
C₁₆×Dic₂₂	2
#13070518	2
D₁₁×C₄⋊C₁₆	2
C₄×C₁₆×D₁₁	2
Q₈×C₁₁×C₁₆	2
C₂×Q₈×C₁₆	11

Subgroups — Q8×C16×D11 #14907252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₁₆×D₁₁ #14907252