Subgroups — #14646807

Order 2816.

404 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13067375	C₂	1	1	yes	maximal, characteristic, complemented
2	#13067372	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067351	C₂	1	2	yes	maximal
4	C₁₁⋊#1309	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#131	C₄	1	2	yes	—
7	C₁₁×#532	C₂²	1	1	yes	characteristic
8	C₁₁×#436	—	2	1	no	—
9	C₁₁×#436	—	2	1	no	—
10	C₈×D₄×C₁₁	—	2	1	no	—
11	C₈×D₄×C₁₁	—	2	1	no	—
12	C₁₁×#423	C₂²	1	1	yes	characteristic
13	C₁₁×#408	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	#10622537	C₂²	1	2	yes	—
16	#10622537	C₂²	1	2	yes	—
17	#10622184	—	2	2	no	—
18	#10622182	—	2	2	no	—
19	#10622096	—	2	1	no	—
20	#10622096	—	2	1	no	—
21	#10622095	—	2	1	no	—
22	#10622095	—	2	1	no	—
23	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
24	C₁₁×#131	—	4	4	no	—
25	C₂×C₁₁×M₁₆	—	2	2	no	—
26	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
27	C₂²×C₈×C₁₁	—	2	2	no	—
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
31	C₁₁×#127	D₄	1	1	yes	characteristic
32	C₁₁×#124	Q₈	1	2	yes	—
33	C₁₁×#121	—	2	1	no	—
34	C₁₁×#121	—	2	1	no	—
35	C₄×D₄×C₁₁	—	2	1	no	—
36	C₄×D₄×C₁₁	—	2	1	no	—
37	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
38	C₂×#4318	—	2	2	no	—
39	C₂×#4318	—	2	2	no	—
40	C₁₁×C₄⋊C₈	—	2	1	no	—
41	C₁₁×C₄⋊C₈	—	2	1	no	—
42	C₁₁×C₂²⋊C₈	—	2	2	no	—
43	C₁₁×C₂²⋊C₈	—	2	2	no	—
44	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
48	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
51	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
52	#8640	—	11	1	no	maximal, Sylow
53	C₁₁×#41	—	4	2	no	—
54	C₁₁×#41	—	4	2	no	—
55	C₂×Q₈×C₁₁	C₄⋊C₄	1	2	yes	—
56	C₂×D₄×C₁₁	—	2	2	no	—
57	C₂×D₄×C₁₁	—	2	1	no	—
58	C₂×D₄×C₁₁	—	2	1	no	—
59	C₂×D₄×C₁₁	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	—	2	2	no	—
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
64	C₁₁×M₁₆	—	4	2	no	—
65	C₁₁×M₁₆	—	4	4	no	—
66	C₂×C₈×C₁₁	—	2	2	no	—
67	C₂×C₈×C₁₁	—	2	2	no	—
68	C₂×C₈×C₁₁	—	4	1	no	—
69	C₂×C₈×C₁₁	—	4	4	no	—
70	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₁₁×C₄⋊C₄	—	2	1	no	—
75	C₁₁×C₄⋊C₄	—	2	1	no	—
76	C₁₁×C₂²⋊C₄	—	2	2	no	—
77	C₁₁×C₂²⋊C₄	—	2	2	no	—
78	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
82	#4318	—	8	2	no	—
83	#4318	—	8	2	no	—
84	C₂×C₁₁⋊C₈	—	4	2	no	—
85	C₂×C₁₁⋊C₈	—	4	2	no	—
86	#2931	D₁₁	1	1	yes	characteristic
87	#1567	—	11	1	no	—
88	#1566	—	11	1	no	—
89	#1560	—	11	2	no	—
90	#1309	—	11	2	no	—
91	C₂³×C₁₁	—	2	2	no	—
92	C₂³×C₁₁	#117	1	1	yes	characteristic
93	Q₈×C₁₁	—	4	2	no	—
94	D₄×C₁₁	—	4	2	no	—
95	D₄×C₁₁	—	4	4	no	—
96	D₄×C₁₁	—	4	2	no	—
97	D₄×C₁₁	—	4	1	no	—
98	D₄×C₁₁	—	4	1	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	2	1	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	2	1	no	—
103	C₂×C₄×C₁₁	—	2	1	no	—
104	C₂×C₄×C₁₁	—	2	2	no	—
105	C₂×C₄×C₁₁	—	4	2	no	—
106	C₂×C₄×C₁₁	—	4	2	no	—
107	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
110	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
113	C₈×C₁₁	—	2	1	no	—
114	C₈×C₁₁	—	2	1	no	—
115	C₈×C₁₁	—	2	1	no	—
116	C₈×C₁₁	—	4	2	no	—
117	C₈×C₁₁	#100	1	2	yes	—
118	C₁₁⋊C₈	—	8	2	no	—
119	C₁₁⋊C₈	—	8	2	no	—
120	C₂×#131	Dic₁₁	1	2	yes	—
121	#532	C₂×D₁₁	1	1	yes	characteristic
122	#436	—	2	1	no	—
123	#436	—	2	1	no	—
124	C₈×D₄	—	2	1	no	—
125	C₈×D₄	—	2	1	no	—
126	#423	—	11	2	no	—
127	#423	—	11	2	no	—
128	#423	C₂×D₁₁	1	1	yes	characteristic
129	#408	Dic₁₁	1	2	yes	—
130	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
131	#335	—	22	1	no	—
132	#335	—	22	1	no	—
133	#334	—	22	1	no	—
134	#334	—	22	1	no	—
135	#333	—	22	2	no	—
136	#331	—	22	2	no	—
137	C₂²×C₁₁	—	2	1	no	—
138	C₂²×C₁₁	—	2	1	no	—
139	C₂²×C₁₁	—	2	1	no	—
140	C₂²×C₁₁	—	4	2	no	—
141	C₂²×C₁₁	—	4	2	no	—
142	C₂²×C₁₁	—	4	2	no	—
143	C₂²×C₁₁	#380	1	1	yes	characteristic
144	C₄×C₁₁	—	2	1	no	—
145	C₄×C₁₁	—	2	1	no	—
146	C₄×C₁₁	—	2	1	no	—
147	C₄×C₁₁	—	4	2	no	—
148	C₄×C₁₁	C₂×#100	1	1	yes	characteristic
149	C₄×C₁₁	#413	1	1	yes	characteristic
150	C₄×C₁₁	#471	1	2	yes	—
151	C₄×C₁₁	#472	1	1	yes	characteristic
152	C₄×C₁₁	#473	1	1	yes	characteristic
153	C₂×#41	C₂×Dic₁₁	1	2	yes	—
154	#131	—	4	4	no	—
155	C₂×M₁₆	—	2	2	no	—
156	C₂×M₁₆	—	22	2	no	—
157	C₂×M₁₆	—	22	2	no	—
158	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
159	C₂²×C₈	—	2	2	no	—
160	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
161	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
162	C₄⋊Q₈	D₄₄	1	1	yes	characteristic
163	#127	D₄₄	1	1	yes	characteristic
164	#124	Dic₂₂	1	2	yes	—
165	#121	—	2	1	no	—
166	#121	—	2	1	no	—
167	C₄×D₄	—	2	1	no	—
168	C₄×D₄	—	2	1	no	—
169	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
170	C₄⋊C₈	—	2	1	no	—
171	C₄⋊C₈	—	2	1	no	—
172	C₄⋊C₈	—	22	2	no	—
173	C₄⋊C₈	—	22	2	no	—
174	C₄⋊C₈	—	22	2	no	—
175	C₄⋊C₈	—	22	2	no	—
176	C₂²⋊C₈	—	2	2	no	—
177	C₂²⋊C₈	—	2	2	no	—
178	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
179	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
180	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
181	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
182	C₂×C₁₁	—	4	1	no	—
183	C₂×C₁₁	—	8	2	no	—
184	C₂×C₁₁	#1800	1	1	yes	characteristic
185	C₂×C₁₁	#1815	1	1	yes	characteristic
186	C₂×C₁₁	#1816	1	1	yes	characteristic
187	#41	—	4	2	no	—
188	#41	—	4	2	no	—
189	C₂×Q₈	C₄⋊Dic₁₁	1	2	yes	—
190	C₂×D₄	—	2	2	no	—
191	C₂×D₄	—	2	1	no	—
192	C₂×D₄	—	2	1	no	—
193	C₂×D₄	C₄⋊Dic₁₁	1	2	yes	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	#4339	1	1	yes	characteristic
196	C₂²×C₄	#4339	1	1	yes	characteristic
197	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
198	M₁₆	—	4	4	no	—
199	M₁₆	—	4	2	no	—
200	M₁₆	—	88	2	no	—
201	M₁₆	—	88	2	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	2	no	—
204	C₂×C₈	—	4	1	no	—
205	C₂×C₈	—	4	4	no	—
206	C₂×C₈	—	44	2	no	—
207	C₂×C₈	—	44	2	no	—
208	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
209	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
210	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
211	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
212	C₄⋊C₄	—	2	1	no	—
213	C₄⋊C₄	—	2	1	no	—
214	C₂²⋊C₄	—	2	2	no	—
215	C₂²⋊C₄	—	2	2	no	—
216	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
217	C₄²	C₂×D₄₄	1	1	yes	characteristic
218	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
219	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
220	C₁₁	#8640	1	1	yes	characteristic, complemented, Sylow
221	C₂³	—	2	2	no	—
222	C₂³	#66979	1	1	yes	characteristic
223	Q₈	—	4	2	no	—
224	D₄	—	4	2	no	—
225	D₄	—	4	4	no	—
226	D₄	—	4	2	no	—
227	D₄	—	4	1	no	—
228	D₄	—	4	1	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	2	1	no	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	#66977	1	1	yes	characteristic
238	C₂×C₄	#66977	1	1	yes	characteristic
239	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
240	C₂×C₄	#66983	1	1	yes	characteristic
241	C₂×C₄	#66983	1	1	yes	characteristic
242	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
243	C₈	—	2	1	no	—
244	C₈	—	2	1	no	—
245	C₈	—	2	1	no	—
246	C₈	—	4	2	no	—
247	C₈	—	88	2	no	—
248	C₈	—	88	2	no	—
249	C₈	#66897	1	2	yes	—
250	C₂²	—	2	1	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	4	2	no	—
254	C₂²	—	4	2	no	—
255	C₂²	—	4	2	no	—
256	C₂²	#10622825	1	1	yes	characteristic
257	C₄	—	2	1	no	—
258	C₄	—	2	1	no	—
259	C₄	—	2	1	no	—
260	C₄	—	4	2	no	—
261	C₄	#10622754	1	2	yes	—
262	C₄	#10622755	1	1	yes	characteristic
263	C₄	#10622756	1	1	yes	characteristic
264	C₄	C₂×#66897	1	1	yes	characteristic
265	C₄	#10622850	1	1	yes	characteristic
266	C₂	—	4	1	no	—
267	C₂	—	8	2	no	—
268	C₂	#13068608	1	1	yes	characteristic
269	C₂	#13068675	1	1	yes	characteristic
270	C₂	#13068680	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622825
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2931	C₂
socle	C₂²×C₁₁	#380
prime radical	C₁₁×#532	C₂²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2931	D₁₁
hypocenter	C₁₁	#8640
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2931

Complements

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

N	H ≅ G/N	type
1. #13067375	C₂	semidirect
2. #13067372	C₂	semidirect
4. C₁₁⋊#1309	C₂	semidirect
220. C₁₁	#8640	semidirect

Maximal subgroups

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

subgroup	index
#13067375	2
#13067372	2
#13067351	2
C₁₁⋊#1309	2
C₁₁×#2931	2
#8640	11