Subgroups — #14669703

Order 2816.

454 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622302	C₂	1	1	yes	maximal, characteristic
2	#13070372	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10622152	C₂	1	2	yes	maximal
4	#13066699	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#4313	C₂²	1	1	yes	characteristic
7	C₂²×C₈×D₁₁	C₄	1	1	yes	characteristic
8	C₂×#66925	C₄	1	1	yes	characteristic
9	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×#66879	C₂²	1	1	yes	characteristic
12	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
13	C₂×#66876	C₂²	1	2	yes	—
14	C₂×#66867	C₄	1	1	yes	characteristic
15	#10622302	—	2	2	no	—
16	#10622302	—	2	2	no	—
17	C₁₁×C₄⋊C₁₆	—	2	2	no	—
18	#10622152	—	2	4	no	—
19	C₄⋊(C₁₁⋊C₁₆)	—	2	2	no	—
20	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
23	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂×(C₂×D₁₁)⋊C₄	C₈	1	2	yes	—
25	C₂×Dic₁₁⋊C₄	C₈	1	2	yes	—
26	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
29	C₂×#4313	—	2	1	no	—
30	C₂×#4313	—	2	1	no	—
31	C₂×#4313	—	2	1	no	—
32	C₂×#4313	—	2	1	no	—
33	C₂×#4313	D₄	1	2	yes	—
34	C₂×#4313	Q₈	1	2	yes	—
35	C₂×C₈×D₁₁	—	2	2	no	—
36	C₂×C₈×D₁₁	—	2	2	no	—
37	C₂×C₈×D₁₁	—	2	2	no	—
38	#66925	—	2	2	no	—
39	#66925	—	2	2	no	—
40	C₁₁×M₃₂	—	2	2	no	—
41	C₁₁×M₃₂	—	2	2	no	—
42	C₂×C₁₁×C₁₆	—	2	2	no	—
43	C₄×C₈×C₁₁	D₄	1	2	yes	—
44	C₄×C₈×C₁₁	D₄	1	2	yes	—
45	#66879	—	2	1	no	—
46	#66879	—	2	1	no	—
47	C₈×Dic₁₁	—	2	2	no	—
48	#66876	—	2	2	no	—
49	#66876	—	2	2	no	—
50	C₂×C₁₁⋊C₁₆	—	2	2	no	—
51	#66867	—	2	2	no	—
52	#12786	—	11	1	no	maximal, Sylow
53	C₂³×D₁₁	C₂×C₈	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
56	C₂²×Dic₁₁	C₂×C₈	1	1	yes	characteristic
57	C₂²×Dic₁₁	C₂×C₈	1	2	yes	—
58	C₂×C₄×D₁₁	—	2	1	no	—
59	C₂×C₄×D₁₁	—	2	1	no	—
60	C₂×C₄×D₁₁	—	2	1	no	—
61	C₂×C₄×D₁₁	—	2	1	no	—
62	C₂×C₄×D₁₁	C₄⋊C₄	1	2	yes	—
63	C₂×C₄×D₁₁	M₁₆	1	2	yes	—
64	C₂×C₈×C₁₁	—	2	1	no	—
65	C₂×C₈×C₁₁	—	2	1	no	—
66	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
67	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
71	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
72	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
73	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
74	C₄²×C₁₁	M₁₆	1	2	yes	—
75	(C₂×D₁₁)⋊C₄	—	2	4	no	—
76	Dic₁₁⋊C₄	—	2	4	no	—
77	C₄×Dic₁₁	—	2	1	no	—
78	C₄×Dic₁₁	—	2	1	no	—
79	C₂×C₁₁⋊C₈	—	2	1	no	—
80	C₂×C₁₁⋊C₈	—	2	1	no	—
81	C₂×C₁₁⋊C₈	—	2	1	no	—
82	C₂×C₁₁⋊C₈	—	2	1	no	—
83	C₂×C₁₁⋊C₈	C₄⋊C₄	1	2	yes	—
84	C₂×C₁₁⋊C₈	M₁₆	1	2	yes	—
85	#4313	—	2	2	no	—
86	#4313	—	2	2	no	—
87	#4313	—	2	2	no	—
88	#4313	—	2	2	no	—
89	C₈×D₁₁	—	2	8	no	—
90	C₁₁×C₁₆	—	4	2	no	—
91	C₁₁⋊C₁₆	—	4	2	no	—
92	C₂×#405	—	11	1	no	—
93	#2150	—	11	1	no	—
94	#2150	D₁₁	1	1	yes	characteristic, complemented
95	C₂×#349	—	11	2	no	—
96	#1377	—	11	2	no	—
97	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
98	C₂²×D₁₁	—	2	1	no	—
99	C₂²×D₁₁	—	2	1	no	—
100	C₂²×D₁₁	—	4	2	no	—
101	C₂²×D₁₁	C₄⋊C₈	1	2	yes	—
102	C₂×C₄×C₁₁	—	4	2	no	—
103	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
104	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
110	C₂×Dic₁₁	—	2	1	no	—
111	C₂×Dic₁₁	—	2	1	no	—
112	C₂×Dic₁₁	—	2	2	no	—
113	C₂×Dic₁₁	—	4	2	no	—
114	C₂×Dic₁₁	C₄⋊C₈	1	2	yes	—
115	C₄×D₁₁	—	2	2	no	—
116	C₄×D₁₁	—	2	2	no	—
117	C₄×D₁₁	—	2	2	no	—
118	C₄×D₁₁	—	2	2	no	—
119	C₈×C₁₁	—	2	2	no	—
120	C₈×C₁₁	#121	1	1	yes	characteristic
121	C₈×C₁₁	#121	1	1	yes	characteristic
122	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
123	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
124	C₁₁⋊C₈	—	2	2	no	—
125	C₁₁⋊C₈	—	2	2	no	—
126	C₂²×M₁₆	—	11	1	no	—
127	C₂³×C₈	—	11	1	no	—
128	C₂×#117	—	11	1	no	—
129	C₂×M₃₂	—	11	2	no	—
130	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
131	#405	—	22	2	no	—
132	#405	—	22	2	no	—
133	C₂×#97	—	11	1	no	—
134	C₂×#97	—	11	1	no	—
135	C₂×C₄×C₈	—	11	1	no	—
136	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
137	C₄⋊C₁₆	—	2	2	no	—
138	C₄⋊C₁₆	—	22	2	no	—
139	#349	—	22	4	no	—
140	C₂²×C₁₁	—	2	2	no	—
141	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
142	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
143	C₂²×C₁₁	#431	1	1	yes	characteristic
144	C₂×D₁₁	—	2	2	no	—
145	C₂×D₁₁	—	4	2	no	—
146	C₂×D₁₁	—	4	2	no	—
147	C₂×D₁₁	—	4	2	no	—
148	C₄×C₁₁	—	2	4	no	—
149	C₄×C₁₁	#380	1	1	yes	characteristic
150	C₄×C₁₁	#407	1	1	yes	characteristic
151	C₄×C₁₁	#423	1	1	yes	characteristic
152	C₄×C₁₁	#432	1	1	yes	characteristic
153	Dic₁₁	—	2	2	no	—
154	Dic₁₁	—	4	2	no	—
155	C₂³×C₄	—	11	1	no	—
156	C₂×M₁₆	—	11	2	no	—
157	C₂×M₁₆	—	11	2	no	—
158	C₂×M₁₆	—	22	1	no	—
159	C₂×M₁₆	—	22	1	no	—
160	C₂×M₁₆	—	22	1	no	—
161	C₂×M₁₆	—	22	1	no	—
162	C₂²×C₈	—	11	1	no	—
163	C₂²×C₈	—	11	1	no	—
164	C₂²×C₈	—	22	2	no	—
165	C₂²×C₈	—	22	2	no	—
166	C₂²×C₈	—	22	2	no	—
167	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
168	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
169	#117	—	22	2	no	—
170	#117	—	22	2	no	—
171	C₂×C₄⋊C₄	—	11	2	no	—
172	C₂×C₂²⋊C₄	—	11	2	no	—
173	C₂×C₄²	—	11	1	no	—
174	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
175	M₃₂	—	2	2	no	—
176	M₃₂	—	2	2	no	—
177	M₃₂	—	22	2	no	—
178	M₃₂	—	22	2	no	—
179	C₂×C₁₆	—	2	2	no	—
180	C₂×C₁₆	—	22	2	no	—
181	#97	—	22	1	no	—
182	#97	—	22	1	no	—
183	#97	—	22	2	no	—
184	C₄×C₈	—	22	2	no	—
185	C₄×C₈	D₄₄	1	2	yes	—
186	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
187	C₂×C₁₁	—	2	1	no	—
188	C₂×C₁₁	—	2	1	no	—
189	C₂×C₁₁	#1797	1	1	yes	characteristic
190	C₂×C₁₁	#2115	1	2	yes	—
191	D₁₁	—	4	2	no	—
192	C₂⁴	—	11	1	no	—
193	C₂²×C₄	—	11	1	no	—
194	C₂²×C₄	—	11	2	no	—
195	C₂²×C₄	—	11	2	no	—
196	C₂²×C₄	—	11	2	no	—
197	C₂²×C₄	—	22	1	no	—
198	C₂²×C₄	—	22	1	no	—
199	C₂²×C₄	—	22	1	no	—
200	C₂²×C₄	—	22	1	no	—
201	C₂²×C₄	C₈×D₁₁	1	2	yes	—
202	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
203	M₁₆	—	22	2	no	—
204	M₁₆	—	22	2	no	—
205	M₁₆	—	22	2	no	—
206	M₁₆	—	22	2	no	—
207	C₂×C₈	—	2	1	no	—
208	C₂×C₈	—	2	1	no	—
209	C₂×C₈	—	11	2	no	—
210	C₂×C₈	—	11	2	no	—
211	C₂×C₈	—	22	8	no	—
212	C₂×C₈	—	22	1	no	—
213	C₂×C₈	—	22	1	no	—
214	C₂×C₈	—	22	1	no	—
215	C₂×C₈	—	22	1	no	—
216	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
217	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
218	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
219	C₂×C₈	#4341	1	1	yes	characteristic
220	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
221	C₂×C₈	#4343	1	1	yes	characteristic
222	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
223	C₄⋊C₄	—	22	4	no	—
224	C₂²⋊C₄	—	22	4	no	—
225	C₄²	—	22	1	no	—
226	C₄²	—	22	1	no	—
227	C₄²	#4313	1	2	yes	—
228	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
229	C₁₆	—	4	2	no	—
230	C₁₆	—	44	2	no	—
231	C₁₁	#12786	1	1	yes	characteristic, complemented, Sylow
232	C₂³	—	11	2	no	—
233	C₂³	—	22	1	no	—
234	C₂³	—	22	1	no	—
235	C₂³	—	44	2	no	—
236	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	11	2	no	—
239	C₂×C₄	—	22	1	no	—
240	C₂×C₄	—	22	1	no	—
241	C₂×C₄	—	22	2	no	—
242	C₂×C₄	—	22	2	no	—
243	C₂×C₄	—	22	2	no	—
244	C₂×C₄	—	22	2	no	—
245	C₂×C₄	—	22	2	no	—
246	C₂×C₄	—	44	2	no	—
247	C₂×C₄	(C₂×D₁₁)⋊C₈	1	4	yes	—
248	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
249	C₂×C₄	#66945	1	1	yes	characteristic
250	C₂×C₄	C₂×#4313	1	1	yes	characteristic
251	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
252	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
253	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
254	C₈	—	2	2	no	—
255	C₈	—	22	2	no	—
256	C₈	—	22	2	no	—
257	C₈	#66948	1	1	yes	characteristic
258	C₈	#66950	1	1	yes	characteristic
259	C₈	#66991	1	1	yes	characteristic
260	C₈	#66999	1	1	yes	characteristic
261	C₂²	—	2	2	no	—
262	C₂²	—	22	2	no	—
263	C₂²	—	44	2	no	—
264	C₂²	—	44	2	no	—
265	C₂²	—	44	2	no	—
266	C₂²	D₁₁×C₄⋊C₈	1	1	yes	characteristic
267	C₂²	#10622446	1	1	yes	characteristic
268	C₂²	C₂×(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
269	C₄	—	2	4	no	—
270	C₄	—	22	2	no	—
271	C₄	—	44	2	no	—
272	C₄	#10622448	1	1	yes	characteristic
273	C₄	#10622450	1	1	yes	characteristic
274	C₄	#10622600	1	1	yes	characteristic
275	C₄	#10622739	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	44	2	no	—
279	C₂	#13068593	1	1	yes	characteristic
280	C₂	#13070236	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄
commutator	C₂³×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#2150	C₂
socle	C₂²×C₁₁	C₂×C₂²⋊C₈
prime radical	C₂³×D₁₁	C₂×C₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#2150	D₁₁
hypocenter	C₁₁	#12786
LCS	G ▷ C₂³×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
2. #13070372	C₂	semidirect
4. #13066699	C₂	semidirect
5. C₁₁×#2150	C₂	semidirect
94. #2150	D₁₁	semidirect
231. C₁₁	#12786	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622302	2
#13070372	2
C₂×#10622152	2
#13066699	2
C₁₁×#2150	2
#12786	11