Subgroups — #14646899

Order 2816.

394 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₂₂	C₂	1	1	yes	maximal, characteristic
2	#13067364	C₂	1	1	yes	maximal, characteristic
3	#13067044	C₂	1	2	yes	maximal
4	#13066511	C₂	1	2	yes	maximal
5	C₁₁×#1848	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Dic₂₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#108	—	2	1	no	—
8	C₂×C₁₁×#108	—	2	1	no	—
9	C₁₁×#423	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₁⋊C₈	—	2	1	no	—
12	C₂×C₈×Dic₁₁	—	2	1	no	—
13	#10622538	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
15	C₈×Dic₂₂	—	2	1	no	—
16	C₈×Dic₂₂	—	2	1	no	—
17	C₈×Dic₂₂	C₄	1	2	yes	—
18	C₈×Dic₂₂	C₄	1	2	yes	—
19	#10622122	—	2	4	no	—
20	#10622096	—	2	1	no	—
21	#10622095	—	2	1	no	—
22	C₂²×Dic₂₂	Q₈	1	1	yes	characteristic
23	C₂×C₁₁×M₁₆	—	2	2	no	—
24	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊Dic₁₁	Q₈	1	1	yes	characteristic
28	C₂×Dic₁₁⋊C₄	—	2	1	no	—
29	C₂×C₄×Dic₁₁	—	2	1	no	—
30	C₂²×C₁₁⋊C₈	—	2	1	no	—
31	C₄×Dic₂₂	—	2	1	no	—
32	C₄×Dic₂₂	—	2	1	no	—
33	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
34	C₄×Dic₂₂	D₄	1	2	yes	—
35	C₁₁×#108	—	4	2	no	—
36	C₁₁×#108	—	4	2	no	—
37	C₁₁×C₄⋊C₈	—	2	2	no	—
38	C₁₁×C₄⋊C₈	—	2	2	no	—
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
41	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
43	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
44	Dic₁₁⋊C₈	—	2	2	no	—
45	Dic₁₁⋊C₈	—	2	2	no	—
46	C₈×Dic₁₁	—	2	2	no	—
47	C₈×Dic₁₁	—	2	2	no	—
48	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
51	C₄×C₁₁⋊C₈	—	2	2	no	—
52	#8659	—	11	1	no	maximal, Sylow
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
56	C₂²×Dic₁₁	—	2	1	no	—
57	C₂²×Dic₁₁	—	2	1	no	—
58	C₂×Dic₂₂	—	2	4	no	—
59	C₂×Dic₂₂	—	2	1	no	—
60	C₂×Dic₂₂	C₄⋊C₄	1	2	yes	—
61	C₁₁×M₁₆	—	4	2	no	—
62	C₁₁×M₁₆	—	4	2	no	—
63	C₂×C₈×C₁₁	—	2	1	no	—
64	C₂×C₈×C₁₁	—	2	1	no	—
65	C₂×C₈×C₁₁	—	4	2	no	—
66	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
71	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
72	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₁	#41	1	1	yes	characteristic
76	C₄⋊Dic₁₁	—	2	1	no	—
77	C₄⋊Dic₁₁	C₄⋊C₄	1	2	yes	—
78	Dic₁₁⋊C₄	—	2	2	no	—
79	Dic₁₁⋊C₄	—	2	2	no	—
80	C₄×Dic₁₁	—	2	2	no	—
81	C₄×Dic₁₁	—	2	2	no	—
82	C₂×C₁₁⋊C₈	—	2	2	no	—
83	C₂×C₁₁⋊C₈	—	4	2	no	—
84	C₂×C₁₁⋊C₈	—	4	1	no	—
85	C₂×C₁₁⋊C₈	—	4	1	no	—
86	C₂×C₈×Q₈	—	11	1	no	—
87	#1848	D₁₁	1	1	yes	characteristic
88	#1564	—	11	1	no	—
89	#1487	—	11	2	no	—
90	#1301	—	11	2	no	—
91	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	—	2	2	no	—
93	C₂×C₄×C₁₁	—	4	1	no	—
94	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
97	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
104	C₂×Dic₁₁	—	2	4	no	—
105	C₂×Dic₁₁	—	2	2	no	—
106	C₂×Dic₁₁	—	2	2	no	—
107	C₂×Dic₁₁	—	4	2	no	—
108	Dic₂₂	—	2	4	no	—
109	Dic₂₂	—	2	2	no	—
110	Dic₂₂	#108	1	4	yes	complemented
111	C₈×C₁₁	—	2	1	no	—
112	C₈×C₁₁	—	2	1	no	—
113	C₈×C₁₁	—	8	2	no	—
114	C₈×C₁₁	#103	1	2	yes	—
115	C₈×C₁₁	#103	1	2	yes	—
116	C₁₁⋊C₈	—	4	2	no	—
117	C₁₁⋊C₈	—	8	2	no	—
118	C₂×C₄×Q₈	—	11	1	no	—
119	C₈×Q₈	—	11	2	no	—
120	C₈×Q₈	—	11	2	no	—
121	C₈×Q₈	—	22	1	no	—
122	C₈×Q₈	—	22	1	no	—
123	#431	—	11	2	no	—
124	C₂×#108	—	2	1	no	—
125	C₂×#108	—	2	1	no	—
126	#423	C₂×D₁₁	1	2	yes	—
127	C₂×C₄⋊C₈	—	11	1	no	—
128	C₂×C₄⋊C₈	—	22	1	no	—
129	C₂×C₄×C₈	—	22	1	no	—
130	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
131	#335	—	22	1	no	—
132	#334	—	22	1	no	—
133	Q₈⋊C₈	—	22	4	no	—
134	C₂²×C₁₁	—	2	1	no	—
135	C₂²×C₁₁	—	2	1	no	—
136	C₂²×C₁₁	#380	1	1	yes	characteristic
137	C₂²×C₁₁	#475	1	1	yes	characteristic
138	C₂²×C₁₁	#477	1	1	yes	characteristic
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	—	2	1	no	—
141	C₄×C₁₁	—	2	1	no	—
142	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
143	C₄×C₁₁	#417	1	1	yes	characteristic
144	C₄×C₁₁	C₂×#108	1	2	yes	—
145	C₄×C₁₁	#460	1	1	yes	characteristic
146	C₄×C₁₁	#462	1	1	yes	characteristic
147	Dic₁₁	—	2	4	no	—
148	Dic₁₁	—	4	2	no	—
149	C₂²×Q₈	—	11	1	no	—
150	C₂×M₁₆	—	2	2	no	—
151	C₂²×C₈	—	22	1	no	—
152	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
153	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
154	C₄×Q₈	—	11	2	no	—
155	C₄×Q₈	—	11	2	no	—
156	C₄×Q₈	—	22	1	no	—
157	C₄×Q₈	—	22	1	no	—
158	C₂×C₄⋊C₄	—	11	1	no	—
159	C₂×C₄⋊C₄	—	22	1	no	—
160	C₂×C₄²	—	22	1	no	—
161	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
162	#108	—	4	2	no	—
163	#108	—	4	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	11	2	no	—
167	C₄⋊C₈	—	22	2	no	—
168	C₄⋊C₈	—	22	2	no	—
169	C₄⋊C₈	—	22	1	no	—
170	C₄⋊C₈	—	22	2	no	—
171	C₂²⋊C₈	—	22	2	no	—
172	C₄×C₈	—	22	2	no	—
173	C₄×C₈	—	22	2	no	—
174	C₄×C₈	—	22	2	no	—
175	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
176	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
177	C₄×C₈	D₄₄	1	1	yes	characteristic
178	C₄×C₈	D₄₄	1	1	yes	characteristic
179	C₂×C₁₁	—	2	1	no	—
180	C₂×C₁₁	—	2	1	no	—
181	C₂×C₁₁	#1803	1	1	yes	characteristic
182	C₂×C₁₁	#1810	1	1	yes	characteristic
183	C₂×C₁₁	#1814	1	1	yes	characteristic
184	C₂×Q₈	—	11	2	no	—
185	C₂×Q₈	—	22	4	no	—
186	C₂×Q₈	—	22	1	no	—
187	C₂²×C₄	—	22	1	no	—
188	C₂²×C₄	—	22	1	no	—
189	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
190	C₂²×C₄	#4343	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
192	M₁₆	—	4	2	no	—
193	M₁₆	—	4	2	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	4	2	no	—
197	C₂×C₈	—	22	2	no	—
198	C₂×C₈	—	44	1	no	—
199	C₂×C₈	—	44	1	no	—
200	C₂×C₈	—	44	2	no	—
201	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
202	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
203	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
204	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
205	C₂×C₈	#4324	1	2	yes	—
206	C₂×C₈	#4326	1	2	yes	—
207	C₄⋊C₄	—	11	2	no	—
208	C₄⋊C₄	—	22	2	no	—
209	C₄⋊C₄	—	22	2	no	—
210	C₄⋊C₄	—	22	1	no	—
211	C₄²	—	22	2	no	—
212	C₄²	—	22	2	no	—
213	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
214	C₄²	C₂×D₄₄	1	1	yes	characteristic
215	C₄²	D₄×D₁₁	1	1	yes	characteristic
216	C₄²	#4341	1	1	yes	characteristic
217	C₁₁	#8659	1	1	yes	characteristic, complemented, Sylow
218	C₂³	#66999	1	1	yes	characteristic
219	Q₈	—	11	4	no	—
220	Q₈	—	22	4	no	—
221	Q₈	—	22	2	no	—
222	C₂×C₄	—	2	2	no	—
223	C₂×C₄	—	4	1	no	—
224	C₂×C₄	—	22	4	no	—
225	C₂×C₄	—	22	2	no	—
226	C₂×C₄	—	22	2	no	—
227	C₂×C₄	—	44	2	no	—
228	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
229	C₂×C₄	#66945	1	1	yes	characteristic
230	C₂×C₄	#66948	1	1	yes	characteristic
231	C₂×C₄	#66950	1	1	yes	characteristic
232	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
233	C₂×C₄	#66985	1	1	yes	characteristic
234	C₂×C₄	C₂×#4324	1	1	yes	characteristic
235	C₂×C₄	#66991	1	1	yes	characteristic
236	C₂×C₄	#66995	1	1	yes	characteristic
237	C₂×C₄	C₂×#4326	1	1	yes	characteristic
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	8	2	no	—
241	C₈	—	44	2	no	—
242	C₈	—	88	2	no	—
243	C₈	#66874	1	2	yes	—
244	C₈	#66874	1	2	yes	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	#10622600	1	1	yes	characteristic
248	C₂²	#10622704	1	1	yes	characteristic
249	C₂²	#10622707	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	22	4	no	—
254	C₄	—	44	2	no	—
255	C₄	D₁₁×#108	1	2	yes	—
256	C₄	#10622579	1	1	yes	characteristic
257	C₄	C₂×#66874	1	1	yes	characteristic
258	C₄	#10622688	1	1	yes	characteristic
259	C₄	#10622703	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	2	1	no	—
262	C₂	#13068618	1	1	yes	characteristic
263	C₂	#13068651	1	1	yes	characteristic
264	C₂	#13068671	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#66991
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1848	C₂
socle	C₂²×C₁₁	#380
prime radical	C₂³×C₁₁	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1848	D₁₁
hypocenter	C₁₁	#8659
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1848

Complements

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

N	H ≅ G/N	type
110. Dic₂₂	#108	semidirect
217. C₁₁	#8659	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₂₂	2
#13067364	2
#13067044	2
#13066511	2
C₁₁×#1848	2
#8659	11