Subgroups — #14643231

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622538	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13066450	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂³×C₁₁⋊C₈	C₄	1	2	yes	—
7	C₁₁×#431	—	2	2	no	—
8	C₁₁×#431	C₄	1	4	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
11	C₂×C₄×C₈×C₁₁	—	2	1	no	—
12	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
13	#10622538	—	2	2	no	—
14	#10622538	C₄	1	4	yes	—
15	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄×C₁₁⋊C₈	—	2	2	no	—
17	C₂×C₄×C₁₁⋊C₈	—	2	2	no	—
18	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
19	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
20	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
21	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	—	2	2	no	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₁	D₄	1	2	yes	—
29	C₂×C₄²×C₁₁	D₄	1	2	yes	—
30	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₂²×C₁₁⋊C₈	—	2	4	no	—
34	C₂²×C₁₁⋊C₈	—	2	4	no	—
35	C₂²×C₁₁⋊C₈	—	2	2	no	—
36	C₂²×C₁₁⋊C₈	C₈	1	8	yes	complemented
37	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
38	C₁₁×C₄⋊C₈	—	2	2	no	—
39	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
40	C₁₁×C₂²⋊C₈	—	2	4	no	—
41	C₄×C₈×C₁₁	—	2	4	no	—
42	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
45	C₄×C₁₁⋊C₈	—	2	4	no	—
46	C₄×C₁₁⋊C₈	—	2	4	no	—
47	C₄×C₁₁⋊C₈	—	2	2	no	—
48	C₄×C₁₁⋊C₈	—	2	2	no	—
49	#7872	—	11	1	no	maximal, Sylow
50	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	—	2	4	no	—
52	C₂²×C₄×C₁₁	—	2	4	no	—
53	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
54	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
57	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
63	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
64	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
67	C₂×C₈×C₁₁	—	2	4	no	—
68	C₂×C₈×C₁₁	—	4	4	no	—
69	C₄²×C₁₁	C₄²	1	2	yes	—
70	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
73	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
74	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
75	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×C₁₁⋊C₈	—	2	16	no	—
80	C₂×C₁₁⋊C₈	—	2	4	no	—
81	C₂×C₁₁⋊C₈	—	2	4	no	—
82	C₂×C₁₁⋊C₈	—	2	4	no	—
83	C₂×C₁₁⋊C₈	—	4	4	no	—
84	C₂×C₁₁⋊C₈	C₂×C₈	1	8	yes	—
85	C₂×#431	—	11	1	no	—
86	C₂×#431	D₁₁	1	1	yes	characteristic
87	C₂²×C₄×C₈	—	11	1	no	—
88	#1277	—	11	4	no	—
89	C₂³×C₁₁	—	2	2	no	—
90	C₂³×C₁₁	—	2	2	no	—
91	C₂³×C₁₁	#95	1	2	yes	—
92	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
93	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	—	2	4	no	—
98	C₂×C₄×C₁₁	—	2	4	no	—
99	C₂×C₄×C₁₁	—	2	4	no	—
100	C₂×C₄×C₁₁	#95	1	2	yes	—
101	C₂×C₄×C₁₁	#95	1	2	yes	—
102	C₂×C₄×C₁₁	#95	1	2	yes	—
103	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
104	C₂×C₄×C₁₁	#97	1	4	yes	—
105	C₂×C₄×C₁₁	C₂²⋊C₈	1	8	yes	—
106	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
107	C₂×C₄×C₁₁	#108	1	4	yes	—
108	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
115	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
116	C₂×C₄×C₁₁	#135	1	4	yes	—
117	C₈×C₁₁	—	4	4	no	—
118	C₁₁⋊C₈	—	2	8	no	—
119	C₁₁⋊C₈	—	4	4	no	—
120	C₂³×C₈	—	11	2	no	—
121	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
122	#431	—	2	2	no	—
123	#431	—	11	4	no	—
124	#431	—	22	2	no	—
125	#431	Dic₁₁	1	4	yes	—
126	C₂×C₄⋊C₈	—	11	2	no	—
127	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
128	C₂×C₂²⋊C₈	—	2	1	no	—
129	C₂×C₂²⋊C₈	—	22	1	no	—
130	C₂×C₄×C₈	—	2	1	no	—
131	C₂×C₄×C₈	—	11	2	no	—
132	C₂×C₄×C₈	—	11	2	no	—
133	C₂×C₄×C₈	—	22	2	no	—
134	C₂×C₄×C₈	—	22	2	no	—
135	C₂×C₄×C₈	—	22	1	no	—
136	C₂²×C₁₁	—	2	8	no	—
137	C₂²×C₁₁	—	2	2	no	—
138	C₂²×C₁₁	—	2	2	no	—
139	C₂²×C₁₁	#336	1	4	yes	—
140	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
141	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
142	C₂²×C₁₁	#427	1	2	yes	—
143	C₂²×C₁₁	C₂×#108	1	2	yes	—
144	C₄×C₁₁	—	2	2	no	—
145	C₄×C₁₁	—	2	1	no	—
146	C₄×C₁₁	—	2	1	no	—
147	C₄×C₁₁	#336	1	4	yes	—
148	C₄×C₁₁	#341	1	4	yes	—
149	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
150	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
151	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
152	C₄×C₁₁	#416	1	2	yes	—
153	C₄×C₁₁	#416	1	2	yes	—
154	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
155	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
156	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	—	11	8	no	—
159	C₂²×C₈	—	11	4	no	—
160	C₂²×C₈	—	22	4	no	—
161	C₂²×C₈	—	22	4	no	—
162	C₂²×C₈	—	22	2	no	—
163	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
164	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
165	C₂×C₄²	C₄×D₁₁	1	2	yes	—
166	C₂×C₄²	D₄₄	1	2	yes	—
167	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
168	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
169	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
170	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
171	C₄⋊C₈	—	2	2	no	—
172	C₄⋊C₈	—	11	4	no	—
173	C₄⋊C₈	—	22	2	no	—
174	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
175	C₂²⋊C₈	—	2	4	no	—
176	C₂²⋊C₈	—	22	4	no	—
177	C₄×C₈	—	2	4	no	—
178	C₄×C₈	—	22	4	no	—
179	C₄×C₈	—	22	4	no	—
180	C₄×C₈	—	22	2	no	—
181	C₄×C₈	—	22	2	no	—
182	C₂×C₁₁	—	2	4	no	—
183	C₂×C₁₁	#1564	1	4	yes	—
184	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
185	C₂×C₁₁	#1735	1	1	yes	characteristic
186	C₂×C₁₁	C₂×#341	1	1	yes	characteristic
187	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	2	4	no	—
190	C₂²×C₄	C₈×D₁₁	1	4	yes	—
191	C₂²×C₄	#4313	1	4	yes	—
192	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
193	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
194	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
195	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
196	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
197	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
198	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
199	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
200	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
201	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
202	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
203	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	4	4	no	—
206	C₂×C₈	—	11	8	no	—
207	C₂×C₈	—	22	16	no	—
208	C₂×C₈	—	22	4	no	—
209	C₂×C₈	—	22	4	no	—
210	C₂×C₈	—	22	4	no	—
211	C₂×C₈	—	44	4	no	—
212	C₄²	C₄×Dic₁₁	1	2	yes	—
213	C₄²	Dic₁₁⋊C₄	1	2	yes	—
214	C₄²	C₄⋊Dic₁₁	1	2	yes	—
215	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
216	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
217	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
218	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
219	C₄²	C₂×D₄₄	1	1	yes	characteristic
220	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
221	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
222	C₁₁	#7872	1	1	yes	characteristic, complemented, Sylow
223	C₂³	—	2	2	no	—
224	C₂³	—	2	2	no	—
225	C₂³	Dic₁₁⋊C₈	1	4	yes	—
226	C₂³	C₁₁⋊#95	1	2	yes	—
227	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	C₈×Dic₁₁	1	4	yes	—
235	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
236	C₂×C₄	#66879	1	4	yes	—
237	C₂×C₄	(C₂×D₁₁)⋊C₈	1	8	yes	—
238	C₂×C₄	#66886	1	4	yes	—
239	C₂×C₄	C₁₁⋊#95	1	2	yes	—
240	C₂×C₄	C₁₁⋊#95	1	2	yes	—
241	C₂×C₄	C₁₁⋊#95	1	2	yes	—
242	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
243	C₂×C₄	C₂×#4313	1	2	yes	—
244	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
245	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
246	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
247	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
248	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
249	C₂×C₄	#67003	1	4	yes	—
250	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
251	C₈	—	4	4	no	—
252	C₈	—	22	8	no	—
253	C₈	—	44	4	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	2	2	no	—
256	C₂²	—	2	8	no	—
257	C₂²	#10622188	1	4	yes	—
258	C₂²	#10622611	1	2	yes	—
259	C₂²	C₂×Dic₁₁⋊C₈	1	2	yes	—
260	C₂²	C₂×#66886	1	2	yes	—
261	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
262	C₄	—	2	2	no	—
263	C₄	—	2	1	no	—
264	C₄	—	2	1	no	—
265	C₄	#10622188	1	4	yes	—
266	C₄	#10622196	1	4	yes	—
267	C₄	#10622615	1	2	yes	—
268	C₄	C₂×C₈×Dic₁₁	1	1	yes	characteristic
269	C₄	C₂×#66879	1	1	yes	characteristic
270	C₄	C₂×(C₂×D₁₁)⋊C₈	1	2	yes	—
271	C₄	#10622846	1	2	yes	—
272	C₂	—	2	4	no	—
273	C₂	#13067362	1	4	yes	—
274	C₂	C₂×#10622188	1	1	yes	characteristic
275	C₂	#13068332	1	1	yes	characteristic
276	C₂	C₂×#10622196	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	#7872
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13066450	C₂	semidirect
36. C₂²×C₁₁⋊C₈	C₈	semidirect
222. C₁₁	#7872	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622538	2
C₂²×C₄×C₁₁⋊C₈	2
#13066450	2
C₂×C₁₁×#431	2
#7872	11