Subgroups — #14670271

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66882	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622127	C₂	1	2	yes	maximal, complemented
3	C₂×C₂²⋊(C₁₁⋊C₁₆)	C₂	1	1	yes	maximal, characteristic
4	#13066707	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1808	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₁	—	2	1	no	—
8	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
9	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
10	C₁₁×#380	—	2	1	no	—
11	C₂×#66882	—	2	1	no	—
12	C₂×#66882	—	2	4	no	—
13	C₂×#66882	C₂²	1	2	yes	—
14	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
15	C₁₁×#340	—	2	1	no	—
16	C₂²⋊(C₁₁⋊C₁₆)	C₄	1	4	yes	complemented
17	#10622127	—	2	4	no	—
18	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
19	C₂³×Dic₁₁	—	4	1	no	—
20	C₂²×C₈×C₁₁	—	2	2	no	—
21	C₂²×C₈×C₁₁	—	2	2	no	—
22	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
26	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₁×C₂²⋊C₄	—	4	1	no	—
29	C₂×C₄⋊Dic₁₁	—	2	4	no	—
30	C₂×C₄⋊Dic₁₁	—	2	2	no	—
31	C₂×C₄⋊Dic₁₁	—	4	2	no	—
32	C₂×C₄⋊Dic₁₁	—	4	1	no	—
33	C₁₁×#107	—	2	2	no	—
34	C₁₁×#107	—	2	2	no	—
35	C₁₁×#95	—	4	1	no	—
36	#66882	—	2	4	no	—
37	#66882	—	2	2	no	—
38	#66882	D₄	1	4	yes	—
39	C₂×C₁₁⋊C₁₆	—	2	2	no	—
40	C₂×C₁₁⋊C₁₆	—	2	2	no	—
41	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	complemented
42	#12919	—	11	1	no	maximal, Sylow
43	C₂⁴×C₁₁	D₈	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	—	2	1	no	—
45	C₂²×C₄×C₁₁	—	2	1	no	—
46	C₂²×C₄×C₁₁	—	2	1	no	—
47	C₂²×C₄×C₁₁	—	2	1	no	—
48	C₂²×C₄×C₁₁	—	4	1	no	—
49	C₂²×C₄×C₁₁	—	4	1	no	—
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
51	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×Dic₁₁	—	4	4	no	—
55	C₂²×Dic₁₁	—	4	2	no	—
56	C₂²×Dic₁₁	—	8	2	no	—
57	C₂²×Dic₁₁	—	8	2	no	—
58	C₂×C₈×C₁₁	—	2	4	no	—
59	C₂×C₈×C₁₁	—	2	4	no	—
60	C₂×C₈×C₁₁	—	2	1	no	—
61	C₂×C₈×C₁₁	—	2	1	no	—
62	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
63	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
65	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₈×C₁₁	#41	1	2	yes	—
67	C₁₁×C₄⋊C₄	—	4	1	no	—
68	C₁₁×C₄⋊C₄	—	4	1	no	—
69	C₁₁×C₄⋊C₄	—	4	1	no	—
70	C₁₁×C₄⋊C₄	—	4	1	no	—
71	C₁₁×C₂²⋊C₄	—	8	2	no	—
72	C₄⋊Dic₁₁	—	2	4	no	—
73	C₄⋊Dic₁₁	—	4	4	no	—
74	C₄⋊Dic₁₁	—	4	2	no	—
75	C₁₁⋊C₁₆	—	2	4	no	—
76	C₂²×#107	—	11	1	no	—
77	C₂×#366	—	11	2	no	—
78	C₂×C₂²⋊C₁₆	—	11	1	no	—
79	#1808	D₁₁	1	1	yes	characteristic
80	#1380	—	11	2	no	—
81	C₂³×C₁₁	—	2	1	no	—
82	C₂³×C₁₁	—	2	1	no	—
83	C₂³×C₁₁	—	2	1	no	—
84	C₂³×C₁₁	—	2	1	no	—
85	C₂³×C₁₁	#107	1	2	yes	—
86	C₂³×C₁₁	D₁₆	1	2	yes	—
87	C₂³×C₁₁	Q₃₂	1	2	yes	—
88	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	2	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	—	8	1	no	—
96	C₂×C₄×C₁₁	—	8	1	no	—
97	C₂×C₄×C₁₁	—	8	1	no	—
98	C₂×C₄×C₁₁	—	8	1	no	—
99	C₂×C₄×C₁₁	—	8	1	no	—
100	C₂×C₄×C₁₁	—	8	1	no	—
101	C₂×C₄×C₁₁	#107	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
104	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
108	C₂×Dic₁₁	—	4	4	no	—
109	C₂×Dic₁₁	—	8	8	no	—
110	C₂×Dic₁₁	—	8	2	no	—
111	C₂×Dic₁₁	—	8	2	no	—
112	C₈×C₁₁	—	2	2	no	—
113	C₈×C₁₁	C₄×D₄	1	2	yes	—
114	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
115	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
116	C₂²×C₄⋊C₄	—	22	1	no	—
117	C₂²×C₁₆	—	11	2	no	—
118	C₂×#107	—	11	2	no	—
119	C₂×#107	—	22	4	no	—
120	C₂×#107	—	22	1	no	—
121	C₂×#107	C₂×D₁₁	1	1	yes	characteristic
122	C₂×#107	C₂×D₁₁	1	1	yes	characteristic
123	#380	—	2	1	no	—
124	#366	—	22	4	no	—
125	C₂²⋊C₁₆	—	11	4	no	—
126	#340	—	2	1	no	—
127	C₂²×C₁₁	—	2	2	no	—
128	C₂²×C₁₁	—	2	2	no	—
129	C₂²×C₁₁	—	2	2	no	—
130	C₂²×C₁₁	—	2	2	no	—
131	C₂²×C₁₁	—	2	2	no	—
132	C₂²×C₁₁	—	2	2	no	—
133	C₂²×C₁₁	#366	1	4	yes	complemented
134	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
135	C₂²×C₁₁	#447	1	1	yes	characteristic
136	C₂²×C₁₁	#480	1	1	yes	characteristic
137	C₂²×C₁₁	C₂×D₁₆	1	1	yes	characteristic
138	C₂²×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
139	C₂²×C₁₁	#509	1	1	yes	characteristic
140	C₂²×C₁₁	#510	1	1	yes	characteristic
141	C₄×C₁₁	—	2	2	no	—
142	C₄×C₁₁	—	16	1	no	—
143	C₄×C₁₁	—	16	1	no	—
144	C₄×C₁₁	#385	1	1	yes	characteristic
145	C₄×C₁₁	#428	1	1	yes	characteristic
146	C₄×C₁₁	#451	1	1	yes	characteristic
147	C₄×C₁₁	#484	1	1	yes	characteristic
148	Dic₁₁	—	8	4	no	—
149	C₂³×C₄	—	44	1	no	—
150	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
151	C₂²×C₈	—	2	2	no	—
152	C₂²×C₈	—	2	2	no	—
153	C₂²×C₈	Dic₂₂	1	2	yes	—
154	C₂²×C₈	C₄×D₁₁	1	2	yes	—
155	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
156	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	—	22	4	no	—
160	C₂×C₄⋊C₄	—	22	2	no	—
161	C₂×C₄⋊C₄	—	44	2	no	—
162	C₂×C₄⋊C₄	—	44	1	no	—
163	C₂×C₂²⋊C₄	—	4	1	no	—
164	C₂×C₁₆	—	11	4	no	—
165	C₂×C₁₆	—	22	2	no	—
166	C₂×C₁₆	—	22	2	no	—
167	#107	—	2	2	no	—
168	#107	—	2	2	no	—
169	#107	—	11	4	no	—
170	#107	—	22	4	no	—
171	#107	—	22	2	no	—
172	#95	—	4	1	no	—
173	C₂×C₁₁	—	2	4	no	—
174	C₂×C₁₁	#1852	1	1	yes	characteristic
175	C₂×C₁₁	C₂×#366	1	1	yes	characteristic
176	C₂×C₁₁	#2159	1	1	yes	characteristic
177	C₂×C₁₁	#2184	1	1	yes	characteristic
178	C₂×C₁₁	#2188	1	1	yes	characteristic
179	C₂×C₁₁	#2232	1	1	yes	characteristic
180	C₂×C₁₁	#2236	1	1	yes	characteristic
181	C₂⁴	#4323	1	1	yes	characteristic
182	C₂²×C₄	—	2	1	no	—
183	C₂²×C₄	—	2	1	no	—
184	C₂²×C₄	—	2	1	no	—
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	4	1	no	—
187	C₂²×C₄	—	4	1	no	—
188	C₂²×C₄	—	44	4	no	—
189	C₂²×C₄	—	44	2	no	—
190	C₂²×C₄	—	88	2	no	—
191	C₂²×C₄	—	88	2	no	—
192	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
193	C₂²×C₄	#4323	1	1	yes	characteristic
194	C₂²×C₄	#4326	1	2	yes	—
195	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	—	2	1	no	—
198	C₂×C₈	—	2	4	no	—
199	C₂×C₈	—	2	4	no	—
200	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
201	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
202	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
203	C₂×C₈	D₄×D₁₁	1	2	yes	—
204	C₂×C₈	#4341	1	2	yes	—
205	C₄⋊C₄	—	4	1	no	—
206	C₄⋊C₄	—	4	1	no	—
207	C₄⋊C₄	—	4	1	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₄⋊C₄	—	22	4	no	—
210	C₄⋊C₄	—	44	4	no	—
211	C₄⋊C₄	—	44	2	no	—
212	C₂²⋊C₄	—	8	2	no	—
213	C₁₆	—	22	4	no	—
214	C₁₁	#12919	1	1	yes	characteristic, complemented, Sylow
215	C₂³	—	2	1	no	—
216	C₂³	—	2	1	no	—
217	C₂³	—	2	1	no	—
218	C₂³	—	2	1	no	—
219	C₂³	#66871	1	2	yes	—
220	C₂³	#66890	1	2	yes	—
221	C₂³	#66893	1	2	yes	—
222	C₂³	C₂×#4323	1	1	yes	characteristic
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	8	1	no	—
230	C₂×C₄	—	8	1	no	—
231	C₂×C₄	—	8	1	no	—
232	C₂×C₄	—	8	1	no	—
233	C₂×C₄	—	8	1	no	—
234	C₂×C₄	—	8	1	no	—
235	C₂×C₄	—	44	4	no	—
236	C₂×C₄	—	88	8	no	—
237	C₂×C₄	—	88	2	no	—
238	C₂×C₄	—	88	2	no	—
239	C₂×C₄	#66871	1	2	yes	—
240	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
241	C₂×C₄	#66988	1	1	yes	characteristic
242	C₂×C₄	#66990	1	1	yes	characteristic
243	C₂×C₄	C₂×#4326	1	1	yes	characteristic
244	C₂×C₄	#67002	1	1	yes	characteristic
245	C₂×C₄	#67004	1	1	yes	characteristic
246	C₈	—	2	2	no	—
247	C₈	#66931	1	2	yes	—
248	C₈	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
249	C₂²	—	2	2	no	—
250	C₂²	—	2	2	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	2	no	—
255	C₂²	#10622127	1	4	yes	complemented
256	C₂²	C₂×#66871	1	1	yes	characteristic
257	C₂²	#10622646	1	1	yes	characteristic
258	C₂²	#10622649	1	1	yes	characteristic
259	C₂²	C₂×#66890	1	1	yes	characteristic
260	C₂²	C₂×#66893	1	1	yes	characteristic
261	C₂²	#10622806	1	1	yes	characteristic
262	C₂²	#10622808	1	1	yes	characteristic
263	C₄	—	2	2	no	—
264	C₄	—	16	1	no	—
265	C₄	—	16	1	no	—
266	C₄	—	88	4	no	—
267	C₄	#10622559	1	1	yes	characteristic
268	C₄	#10622608	1	1	yes	characteristic
269	C₄	#10622657	1	1	yes	characteristic
270	C₄	#10622663	1	1	yes	characteristic
271	C₂	—	2	4	no	—
272	C₂	#13068803	1	1	yes	characteristic
273	C₂	C₂×#10622127	1	1	yes	characteristic
274	C₂	#13070405	1	1	yes	characteristic
275	C₂	#13070527	1	1	yes	characteristic
276	C₂	#13070549	1	1	yes	characteristic
277	C₂	#13070794	1	1	yes	characteristic
278	C₂	#13070816	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4323
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1808	C₂
socle	C₂³×C₁₁	C₂×D₈
prime radical	C₂⁴×C₁₁	D₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1808	D₁₁
hypocenter	C₁₁	#12919
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

Complements

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

N	H ≅ G/N	type
2. C₂×#10622127	C₂	semidirect
4. #13066707	C₂	semidirect
16. C₂²⋊(C₁₁⋊C₁₆)	C₄	semidirect
41. C₂×C₁₁⋊C₁₆	C₂×C₄	semidirect
133. C₂²×C₁₁	#366	semidirect
214. C₁₁	#12919	semidirect
255. C₂²	#10622127	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66882	2
C₂×#10622127	2
C₂×C₂²⋊(C₁₁⋊C₁₆)	2
#13066707	2
C₁₁×#1808	2
#12919	11