Subgroups — #14643261

Order 2816.

618 conjugacy classes of subgroups.

The subgroup lattice has 276 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	C₂×#10622537	C₂	1	1	yes	maximal, characteristic
3	#13066451	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	C₂²×#4318	—	2	1	no	—
7	C₁₁×#431	—	2	2	no	—
8	C₁₁×#431	—	2	2	no	—
9	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
10	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
12	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
13	#10622538	—	2	2	no	—
14	#10622538	C₄	1	4	yes	—
15	#10622537	—	2	2	no	—
16	#10622537	C₄	1	4	yes	—
17	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
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	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₁	D₄	1	2	yes	—
30	C₂×C₄²×C₁₁	D₄	1	2	yes	—
31	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₂×#4318	—	2	4	no	—
34	C₂×#4318	—	4	4	no	—
35	C₂²×C₁₁⋊C₈	—	2	2	no	—
36	C₂²×C₁₁⋊C₈	—	2	2	no	—
37	C₁₁×C₄⋊C₈	—	2	4	no	—
38	C₁₁×C₂²⋊C₈	—	2	4	no	—
39	C₄×C₈×C₁₁	—	2	2	no	—
40	C₄×C₈×C₁₁	—	2	2	no	—
41	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
42	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
44	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
45	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
46	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
47	C₄×C₁₁⋊C₈	—	2	4	no	—
48	#7880	—	11	1	no	maximal, Sylow
49	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	—	2	4	no	—
51	C₂²×C₄×C₁₁	—	2	4	no	—
52	C₂²×C₄×C₁₁	—	2	2	no	—
53	C₂²×C₄×C₁₁	—	2	2	no	—
54	C₂²×C₄×C₁₁	C₄²	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	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
66	C₂×C₈×C₁₁	—	2	4	no	—
67	C₂×C₈×C₁₁	—	2	8	no	—
68	C₄²×C₁₁	C₄²	1	2	yes	—
69	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
70	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
71	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
72	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
73	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
74	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
77	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
78	#4318	—	4	8	no	—
79	C₂×C₁₁⋊C₈	—	2	4	no	—
80	C₂×C₁₁⋊C₈	—	2	4	no	—
81	C₂×C₁₁⋊C₈	—	4	2	no	—
82	C₂×C₁₁⋊C₈	—	4	4	no	—
83	C₂×C₁₁⋊C₈	—	4	2	no	—
84	C₂×#431	—	11	1	no	—
85	C₂×#431	D₁₁	1	1	yes	characteristic
86	C₂×#423	—	11	1	no	—
87	#1277	—	11	4	no	—
88	C₂³×C₁₁	—	2	2	no	—
89	C₂³×C₁₁	—	2	2	no	—
90	C₂³×C₁₁	—	2	2	no	—
91	C₂³×C₁₁	#95	1	2	yes	—
92	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	—	2	2	no	—
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	—	2	4	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	#95	1	2	yes	—
104	C₂×C₄×C₁₁	#95	1	2	yes	—
105	C₂×C₄×C₁₁	#95	1	2	yes	—
106	C₂×C₄×C₁₁	#108	1	4	yes	—
107	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	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×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#131	1	4	yes	—
114	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
115	C₂×C₄×C₁₁	#137	1	2	yes	—
116	C₈×C₁₁	—	4	4	no	—
117	C₁₁⋊C₈	—	4	4	no	—
118	C₁₁⋊C₈	—	4	4	no	—
119	C₂²×M₁₆	—	22	1	no	—
120	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
121	#431	—	2	2	no	—
122	#431	—	2	2	no	—
123	#431	—	11	4	no	—
124	#431	—	22	2	no	—
125	#423	—	11	4	no	—
126	#423	—	22	2	no	—
127	C₂×C₄⋊C₈	—	11	2	no	—
128	C₂×C₄⋊C₈	—	11	2	no	—
129	C₂×C₄⋊C₈	—	22	1	no	—
130	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
131	C₂×C₂²⋊C₈	—	22	1	no	—
132	C₂×C₂²⋊C₈	Dic₁₁	1	2	yes	—
133	C₂×C₄×C₈	—	22	1	no	—
134	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
135	C₂²×C₁₁	—	2	2	no	—
136	C₂²×C₁₁	—	2	2	no	—
137	C₂²×C₁₁	—	2	2	no	—
138	C₂²×C₁₁	—	4	4	no	—
139	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
140	C₂²×C₁₁	#424	1	2	yes	—
141	C₂²×C₁₁	#428	1	2	yes	—
142	C₂²×C₁₁	C₂×#108	1	2	yes	—
143	C₄×C₁₁	—	2	2	no	—
144	C₄×C₁₁	—	2	2	no	—
145	C₄×C₁₁	—	2	1	no	—
146	C₄×C₁₁	—	2	1	no	—
147	C₄×C₁₁	#341	1	4	yes	—
148	C₄×C₁₁	#405	1	2	yes	—
149	C₄×C₁₁	#408	1	2	yes	—
150	C₄×C₁₁	#417	1	2	yes	—
151	C₄×C₁₁	#418	1	1	yes	characteristic
152	C₄×C₁₁	#419	1	1	yes	characteristic
153	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
154	C₂³×C₄	D₄₄	1	1	yes	characteristic
155	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
156	C₂×M₁₆	—	22	4	no	—
157	C₂×M₁₆	—	44	4	no	—
158	C₂²×C₈	—	22	2	no	—
159	C₂²×C₈	—	22	2	no	—
160	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
161	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
162	C₂×C₄²	C₄×D₁₁	1	2	yes	—
163	C₂×C₄²	C₄×D₁₁	1	2	yes	—
164	C₂×C₄²	D₄₄	1	1	yes	characteristic
165	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
166	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
167	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
168	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
169	C₄⋊C₈	—	2	4	no	—
170	C₄⋊C₈	—	11	4	no	—
171	C₄⋊C₈	—	11	4	no	—
172	C₄⋊C₈	—	22	4	no	—
173	C₄⋊C₈	—	22	2	no	—
174	C₄⋊C₈	—	22	2	no	—
175	C₂²⋊C₈	—	2	4	no	—
176	C₂²⋊C₈	—	22	4	no	—
177	C₄×C₈	—	2	2	no	—
178	C₄×C₈	—	2	2	no	—
179	C₄×C₈	—	22	4	no	—
180	C₂×C₁₁	—	4	2	no	—
181	C₂×C₁₁	#1574	1	4	yes	—
182	C₂×C₁₁	#1729	1	1	yes	characteristic
183	C₂×C₁₁	#1736	1	1	yes	characteristic
184	C₂×C₁₁	C₂×#341	1	1	yes	characteristic
185	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
186	C₂²×C₄	—	2	4	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	2	4	no	—
190	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
191	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
192	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
193	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
194	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
195	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
196	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
197	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
198	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
199	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
200	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
201	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
202	M₁₆	—	44	8	no	—
203	C₂×C₈	—	2	8	no	—
204	C₂×C₈	—	2	4	no	—
205	C₂×C₈	—	22	4	no	—
206	C₂×C₈	—	22	4	no	—
207	C₂×C₈	—	44	4	no	—
208	C₂×C₈	—	44	2	no	—
209	C₂×C₈	—	44	2	no	—
210	C₄²	C₄×Dic₁₁	1	2	yes	—
211	C₄²	Dic₁₁⋊C₄	1	2	yes	—
212	C₄²	Dic₁₁⋊C₄	1	2	yes	—
213	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
214	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
215	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
216	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
217	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
218	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
219	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
220	C₁₁	#7880	1	1	yes	characteristic, complemented, Sylow
221	C₂³	—	2	2	no	—
222	C₂³	—	2	2	no	—
223	C₂³	—	2	2	no	—
224	C₂³	C₁₁⋊#95	1	2	yes	—
225	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	2	2	no	—
228	C₂×C₄	—	2	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	4	no	—
233	C₂×C₄	—	2	4	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	#66883	1	4	yes	—
237	C₂×C₄	C₁₁⋊#95	1	2	yes	—
238	C₂×C₄	C₁₁⋊#95	1	2	yes	—
239	C₂×C₄	C₁₁⋊#95	1	2	yes	—
240	C₂×C₄	#66961	1	2	yes	—
241	C₂×C₄	#66962	1	2	yes	—
242	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
243	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
244	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
245	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
246	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
247	C₂×C₄	#67001	1	4	yes	—
248	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
249	C₈	—	4	4	no	—
250	C₈	—	44	4	no	—
251	C₈	—	44	4	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	4	4	no	—
256	C₂²	#10622612	1	2	yes	—
257	C₂²	C₂×#66883	1	2	yes	—
258	C₂²	#10622734	1	2	yes	—
259	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
260	C₄	—	2	2	no	—
261	C₄	—	2	2	no	—
262	C₄	—	2	1	no	—
263	C₄	—	2	1	no	—
264	C₄	#10622190	1	4	yes	—
265	C₄	#10622610	1	2	yes	—
266	C₄	#10622733	1	1	yes	characteristic
267	C₄	#10622744	1	1	yes	characteristic
268	C₄	#10622746	1	2	yes	—
269	C₄	#10622847	1	2	yes	—
270	C₂	—	4	2	no	—
271	C₂	#13067405	1	4	yes	—
272	C₂	#13068313	1	1	yes	characteristic
273	C₂	#13068336	1	1	yes	characteristic
274	C₂	C₂×#10622190	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂×C₄²
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	#7880
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13066451	C₂	semidirect
220. C₁₁	#7880	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
C₂×#10622537	2
#13066451	2
C₂×C₁₁×#431	2
#7880	11