Subgroups — C₂×Q₈⋊(C₁₁⋊C₁₆) #14663572

Order 2816.

382 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	Q₈⋊(C₁₁⋊C₁₆)	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
6	C₈×Q₈×C₁₁	—	2	1	no	—
7	C₈×Q₈×C₁₁	—	2	1	no	—
8	C₈×Q₈×C₁₁	C₄	1	2	yes	—
9	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
10	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
11	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
15	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
16	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
17	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
18	C₄×C₁₁⋊C₁₆	—	2	1	no	—
19	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	—
20	C₂²×Q₈×C₁₁	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	—	2	1	no	—
22	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₄×Q₈×C₁₁	—	2	1	no	—
25	C₄×Q₈×C₁₁	—	2	1	no	—
26	C₄×Q₈×C₁₁	C₈	1	2	yes	—
27	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
28	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	—	2	1	no	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₁₁×C₄⋊C₈	—	2	2	no	—
33	C₁₁×C₄⋊C₈	—	2	2	no	—
34	C₁₁×C₄⋊C₈	—	2	1	no	—
35	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₁	—	2	2	no	—
37	C₄×C₈×C₁₁	—	2	2	no	—
38	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₂×C₁₁⋊C₁₆	—	2	4	no	—
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	—	2	2	no	—
45	C₂×C₁₁⋊C₁₆	—	4	2	no	—
46	C₂×Q₈⋊C₁₆	—	11	1	no	maximal, Sylow
47	C₂×Q₈×C₁₁	—	2	1	no	—
48	C₂×Q₈×C₁₁	—	2	2	no	—
49	C₂×Q₈×C₁₁	C₁₆	1	4	yes	complemented
50	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
51	C₂²×C₄×C₁₁	—	2	1	no	—
52	C₂²×C₄×C₁₁	—	2	1	no	—
53	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
56	C₂×C₈×C₁₁	—	2	2	no	—
57	C₂×C₈×C₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	—	4	2	no	—
59	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
62	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
63	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₁₁×C₄⋊C₄	—	2	2	no	—
66	C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₁₁×C₄⋊C₄	—	2	2	no	—
68	C₁₁×C₄⋊C₄	C₂×C₈	1	2	yes	—
69	C₄²×C₁₁	—	2	2	no	—
70	C₄²×C₁₁	—	2	2	no	—
71	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
73	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
74	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₁₁⋊C₁₆	—	2	4	no	—
76	C₁₁⋊C₁₆	—	4	2	no	—
77	C₂×C₈×Q₈	D₁₁	1	1	yes	characteristic
78	C₂×C₄⋊C₁₆	—	11	1	no	—
79	C₂×C₄×C₁₆	—	11	1	no	—
80	Q₈⋊C₁₆	—	11	4	no	—
81	C₂³×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
82	Q₈×C₁₁	—	2	4	no	—
83	Q₈×C₁₁	—	2	2	no	—
84	Q₈×C₁₁	C₂×C₁₆	1	4	yes	complemented
85	C₂×C₄×C₁₁	—	2	4	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	4	2	no	—
90	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂²⋊C₈	1	1	yes	characteristic
93	C₂×C₄×C₁₁	#103	1	2	yes	—
94	C₂×C₄×C₁₁	#104	1	2	yes	—
95	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
96	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
100	C₈×C₁₁	—	2	1	no	—
101	C₈×C₁₁	—	2	1	no	—
102	C₈×C₁₁	—	4	2	no	—
103	C₈×C₁₁	#103	1	2	yes	—
104	C₈×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
105	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
106	C₂×C₄×Q₈	Dic₁₁	1	1	yes	characteristic
107	C₂²×C₁₆	—	22	1	no	—
108	C₂²×C₁₆	—	22	1	no	—
109	C₈×Q₈	—	2	1	no	—
110	C₈×Q₈	—	2	1	no	—
111	C₈×Q₈	Dic₁₁	1	2	yes	—
112	C₈×Q₈	C₂×D₁₁	1	2	yes	—
113	C₂×C₄⋊C₈	—	2	1	no	—
114	C₂×C₄⋊C₈	Dic₁₁	1	1	yes	characteristic
115	C₂×C₄×C₈	—	2	1	no	—
116	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
117	C₄⋊C₁₆	—	11	2	no	—
118	C₄⋊C₁₆	—	22	1	no	—
119	C₄×C₁₆	—	11	2	no	—
120	C₄×C₁₆	—	22	1	no	—
121	C₂²×C₁₁	Q₈⋊C₈	1	2	yes	—
122	C₂²×C₁₁	C₂²⋊C₁₆	1	2	yes	—
123	C₂²×C₁₁	#350	1	2	yes	—
124	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
125	C₄×C₁₁	—	2	4	no	—
126	C₄×C₁₁	—	2	1	no	—
127	C₄×C₁₁	—	2	1	no	—
128	C₄×C₁₁	—	4	2	no	—
129	C₄×C₁₁	Q₈⋊C₈	1	2	yes	—
130	C₄×C₁₁	C₂²⋊C₁₆	1	2	yes	—
131	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
132	C₄×C₁₁	C₂×#104	1	1	yes	characteristic
133	C₄×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
134	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
135	C₂²×Q₈	C₁₁⋊C₈	1	1	yes	characteristic
136	C₂²×C₈	—	2	1	no	—
137	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
138	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
139	C₄×Q₈	—	2	1	no	—
140	C₄×Q₈	—	2	1	no	—
141	C₄×Q₈	C₁₁⋊C₈	1	2	yes	—
142	C₄×Q₈	C₂×Dic₁₁	1	2	yes	—
143	C₂×C₄⋊C₄	—	2	1	no	—
144	C₂×C₄⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
145	C₂×C₄²	—	2	1	no	—
146	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
147	C₂×C₁₆	—	22	4	no	—
148	C₂×C₁₆	—	22	2	no	—
149	C₂×C₁₆	—	22	2	no	—
150	C₂×C₁₆	—	44	2	no	—
151	C₄⋊C₈	—	2	2	no	—
152	C₄⋊C₈	—	2	2	no	—
153	C₄⋊C₈	—	2	1	no	—
154	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
155	C₄×C₈	—	2	2	no	—
156	C₄×C₈	—	2	2	no	—
157	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
158	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
159	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
160	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
161	C₂×C₁₁	Q₈⋊C₁₆	1	4	yes	complemented
162	C₂×C₁₁	C₂×Q₈⋊C₈	1	1	yes	characteristic
163	C₂×C₁₁	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
164	C₂×C₁₁	C₂×#350	1	1	yes	characteristic
165	C₂×Q₈	—	2	2	no	—
166	C₂×Q₈	—	2	1	no	—
167	C₂×Q₈	C₁₁⋊C₁₆	1	4	yes	complemented
168	C₂×Q₈	C₂×C₁₁⋊C₈	1	2	yes	—
169	C₂²×C₄	—	2	1	no	—
170	C₂²×C₄	—	2	1	no	—
171	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
172	C₂²×C₄	#4318	1	1	yes	characteristic
173	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
174	C₂×C₈	—	2	2	no	—
175	C₂×C₈	—	2	2	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	#4325	1	2	yes	—
178	C₂×C₈	#4326	1	2	yes	—
179	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
180	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
182	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
183	C₄⋊C₄	—	2	2	no	—
184	C₄⋊C₄	—	2	1	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	C₂×C₁₁⋊C₈	1	2	yes	—
187	C₄²	—	2	2	no	—
188	C₄²	—	2	2	no	—
189	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
190	C₄²	#4318	1	1	yes	characteristic
191	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
192	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
193	C₁₆	—	22	4	no	—
194	C₁₆	—	44	2	no	—
195	C₁₁	C₂×Q₈⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
196	C₂³	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
197	Q₈	—	2	4	no	—
198	Q₈	—	2	2	no	—
199	Q₈	C₂×C₁₁⋊C₁₆	1	4	yes	complemented
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	4	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	C₂×C₁₁⋊C₁₆	1	2	yes	—
206	C₂×C₄	#66876	1	2	yes	—
207	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
208	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
209	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
210	C₂×C₄	#66899	1	2	yes	—
211	C₂×C₄	#66901	1	2	yes	—
212	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
213	C₂×C₄	C₂×#4318	1	1	yes	characteristic
214	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
215	C₈	—	2	1	no	—
216	C₈	—	2	1	no	—
217	C₈	—	4	2	no	—
218	C₈	#66899	1	2	yes	—
219	C₈	C₂×#4325	1	1	yes	characteristic
220	C₈	C₂×#4326	1	1	yes	characteristic
221	C₂²	Q₈⋊(C₁₁⋊C₈)	1	2	yes	—
222	C₂²	C₂²⋊(C₁₁⋊C₁₆)	1	2	yes	—
223	C₂²	#10622199	1	2	yes	—
224	C₂²	C₂×C₂²⋊(C₁₁⋊C₈)	1	1	yes	characteristic
225	C₄	—	2	4	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	4	2	no	—
229	C₄	Q₈⋊(C₁₁⋊C₈)	1	2	yes	—
230	C₄	C₂²⋊(C₁₁⋊C₁₆)	1	2	yes	—
231	C₄	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
232	C₄	C₂×#66876	1	1	yes	characteristic
233	C₄	C₂×#66899	1	1	yes	characteristic
234	C₄	C₂×#66901	1	1	yes	characteristic
235	C₂	Q₈⋊(C₁₁⋊C₁₆)	1	4	yes	direct product factor
236	C₂	C₂×Q₈⋊(C₁₁⋊C₈)	1	1	yes	characteristic
237	C₂	C₂×C₂²⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
238	C₂	C₂×#10622199	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂²×C₁₆
Frattini	C₄×C₈	C₂²×D₁₁
Fitting	C₂×C₈×Q₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	C₂²⋊C₈
cosocle	C₄×C₈×C₁₁	C₂³
hypercenter	C₂×C₈×Q₈	D₁₁
hypocenter	C₁₁	C₂×Q₈⋊C₁₆
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
3. Q₈⋊(C₁₁⋊C₁₆)	C₂	direct (N × H)
49. C₂×Q₈×C₁₁	C₁₆	semidirect
84. Q₈×C₁₁	C₂×C₁₆	semidirect
161. C₂×C₁₁	Q₈⋊C₁₆	semidirect
167. C₂×Q₈	C₁₁⋊C₁₆	semidirect
195. C₁₁	C₂×Q₈⋊C₁₆	semidirect
199. Q₈	C₂×C₁₁⋊C₁₆	semidirect
235. C₂	Q₈⋊(C₁₁⋊C₁₆)	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⋊(C₁₁⋊C₁₆)	2
C₂×C₄×C₁₁⋊C₁₆	2
Q₈⋊(C₁₁⋊C₁₆)	2
C₂×C₈×Q₈×C₁₁	2
C₂×Q₈⋊C₁₆	11

Subgroups — C2×Q8⋊(C11⋊C16) #14663572

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈⋊(C₁₁⋊C₁₆) #14663572