Subgroups — #14643164

Order 2816.

610 conjugacy classes of subgroups.

The subgroup lattice has 262 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×#10622538	C₂	1	1	yes	maximal, characteristic
3	C₁₁⋊#1273	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	C₁₁×#431	—	2	2	no	—
7	C₁₁×#431	—	2	2	no	—
8	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
9	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
12	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
13	#10622538	—	2	2	no	—
14	#10622538	—	2	2	no	—
15	#10622538	—	2	2	no	—
16	#10622538	—	2	2	no	—
17	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
19	C₂×C₄×C₁₁⋊C₈	C₂²	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	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	D₄	1	2	yes	—
29	C₂×C₄²×C₁₁	D₄	1	2	yes	—
30	C₂×C₄²×C₁₁	D₄	1	2	yes	—
31	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
34	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
35	C₁₁×C₄⋊C₈	—	2	4	no	—
36	C₁₁×C₂²⋊C₈	—	2	4	no	—
37	C₄×C₈×C₁₁	—	2	2	no	—
38	C₄×C₈×C₁₁	—	2	2	no	—
39	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
40	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
41	C₄⋊(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	—	2	2	no	—
46	C₄×C₁₁⋊C₈	—	2	2	no	—
47	#7851	—	11	1	no	maximal, Sylow
48	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	—	2	4	no	—
50	C₂²×C₄×C₁₁	—	2	4	no	—
51	C₂²×C₄×C₁₁	—	2	4	no	—
52	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
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	2	yes	—
59	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	—	2	4	no	—
65	C₂×C₈×C₁₁	—	2	8	no	—
66	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
70	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
71	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
72	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₁₁⋊C₈	—	2	4	no	—
77	C₂×C₁₁⋊C₈	—	2	4	no	—
78	C₂×C₁₁⋊C₈	—	2	8	no	—
79	C₂×C₁₁⋊C₈	—	2	8	no	—
80	C₂×#431	—	11	1	no	—
81	C₂×#431	—	11	1	no	—
82	C₂×#431	D₁₁	1	1	yes	characteristic
83	#1273	—	11	4	no	—
84	C₂³×C₁₁	—	2	2	no	—
85	C₂³×C₁₁	—	2	2	no	—
86	C₂³×C₁₁	—	2	2	no	—
87	C₂³×C₁₁	#95	1	2	yes	—
88	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	2	4	no	—
93	C₂×C₄×C₁₁	—	2	4	no	—
94	C₂×C₄×C₁₁	—	2	4	no	—
95	C₂×C₄×C₁₁	—	2	4	no	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	—	2	4	no	—
98	C₂×C₄×C₁₁	#95	1	2	yes	—
99	C₂×C₄×C₁₁	#95	1	2	yes	—
100	C₂×C₄×C₁₁	#95	1	2	yes	—
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₁	#131	1	4	yes	—
108	C₂×C₄×C₁₁	#131	1	4	yes	—
109	C₂×C₄×C₁₁	#131	1	4	yes	—
110	C₈×C₁₁	—	4	4	no	—
111	C₁₁⋊C₈	—	4	4	no	—
112	C₁₁⋊C₈	—	4	4	no	—
113	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
114	#431	—	2	2	no	—
115	#431	—	2	2	no	—
116	#431	—	22	2	no	—
117	#431	—	22	2	no	—
118	#431	—	22	2	no	—
119	#431	—	22	2	no	—
120	C₂×C₄⋊C₈	—	11	2	no	—
121	C₂×C₄⋊C₈	—	11	2	no	—
122	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
123	C₂×C₂²⋊C₈	—	11	2	no	—
124	C₂×C₂²⋊C₈	—	11	2	no	—
125	C₂×C₂²⋊C₈	Dic₁₁	1	2	yes	—
126	C₂×C₄×C₈	—	11	2	no	—
127	C₂×C₄×C₈	—	11	2	no	—
128	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
129	C₂²×C₁₁	—	2	2	no	—
130	C₂²×C₁₁	—	2	2	no	—
131	C₂²×C₁₁	—	2	2	no	—
132	C₂²×C₁₁	—	4	4	no	—
133	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
134	C₂²×C₁₁	#405	1	2	yes	—
135	C₂²×C₁₁	#405	1	2	yes	—
136	C₂²×C₁₁	#405	1	2	yes	—
137	C₄×C₁₁	—	2	2	no	—
138	C₄×C₁₁	—	2	2	no	—
139	C₄×C₁₁	—	2	2	no	—
140	C₄×C₁₁	#408	1	2	yes	—
141	C₄×C₁₁	#408	1	2	yes	—
142	C₄×C₁₁	#408	1	2	yes	—
143	C₄×C₁₁	#424	1	2	yes	—
144	C₄×C₁₁	#424	1	2	yes	—
145	C₄×C₁₁	#424	1	2	yes	—
146	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
147	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
148	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
149	C₂²×C₈	—	11	4	no	—
150	C₂²×C₈	—	11	4	no	—
151	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
152	C₂×C₄²	Dic₂₂	1	2	yes	—
153	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
154	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
155	C₂×C₄²	D₄₄	1	2	yes	—
156	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
157	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
158	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
159	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
160	C₄⋊C₈	—	2	4	no	—
161	C₄⋊C₈	—	22	4	no	—
162	C₄⋊C₈	—	22	4	no	—
163	C₂²⋊C₈	—	2	4	no	—
164	C₂²⋊C₈	—	22	4	no	—
165	C₂²⋊C₈	—	22	4	no	—
166	C₄×C₈	—	2	2	no	—
167	C₄×C₈	—	2	2	no	—
168	C₄×C₈	—	22	2	no	—
169	C₄×C₈	—	22	2	no	—
170	C₄×C₈	—	22	2	no	—
171	C₄×C₈	—	22	2	no	—
172	C₂×C₁₁	—	4	2	no	—
173	C₂×C₁₁	#1454	1	4	yes	—
174	C₂×C₁₁	#1729	1	1	yes	characteristic
175	C₂×C₁₁	#1729	1	1	yes	characteristic
176	C₂×C₁₁	#1729	1	1	yes	characteristic
177	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
178	C₂²×C₄	—	2	4	no	—
179	C₂²×C₄	—	2	4	no	—
180	C₂²×C₄	—	2	4	no	—
181	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
182	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
183	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
184	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
185	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
186	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
187	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
188	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
189	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
190	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
192	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
193	C₂×C₈	—	2	8	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	—	22	8	no	—
196	C₂×C₈	—	22	8	no	—
197	C₂×C₈	—	22	4	no	—
198	C₂×C₈	—	22	4	no	—
199	C₄²	Dic₁₁⋊C₄	1	2	yes	—
200	C₄²	Dic₁₁⋊C₄	1	2	yes	—
201	C₄²	C₄⋊Dic₁₁	1	2	yes	—
202	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
203	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
204	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
205	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
206	C₄²	C₂×D₄₄	1	1	yes	characteristic
207	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
208	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
209	C₁₁	#7851	1	1	yes	characteristic, complemented, Sylow
210	C₂³	—	2	2	no	—
211	C₂³	—	2	2	no	—
212	C₂³	—	2	2	no	—
213	C₂³	C₁₁⋊#95	1	2	yes	—
214	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
215	C₂×C₄	—	2	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	4	no	—
220	C₂×C₄	—	2	4	no	—
221	C₂×C₄	—	2	4	no	—
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	C₁₁⋊#95	1	2	yes	—
225	C₂×C₄	C₁₁⋊#95	1	2	yes	—
226	C₂×C₄	C₁₁⋊#95	1	2	yes	—
227	C₂×C₄	#66954	1	4	yes	—
228	C₂×C₄	#66960	1	4	yes	—
229	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
230	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
231	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
232	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
233	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
234	C₂×C₄	#67001	1	4	yes	—
235	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
236	C₈	—	4	4	no	—
237	C₈	—	44	4	no	—
238	C₈	—	44	4	no	—
239	C₂²	—	2	2	no	—
240	C₂²	—	2	2	no	—
241	C₂²	—	2	2	no	—
242	C₂²	—	4	4	no	—
243	C₂²	#10622610	1	2	yes	—
244	C₂²	#10622714	1	2	yes	—
245	C₂²	#10622735	1	2	yes	—
246	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	2	2	no	—
250	C₄	#10622612	1	2	yes	—
251	C₄	#10622715	1	2	yes	—
252	C₄	#10622723	1	2	yes	—
253	C₄	#10622732	1	2	yes	—
254	C₄	#10622742	1	2	yes	—
255	C₄	#10622847	1	2	yes	—
256	C₂	—	4	2	no	—
257	C₂	#13066916	1	4	yes	—
258	C₂	#13068312	1	1	yes	characteristic
259	C₂	#13068313	1	1	yes	characteristic
260	C₂	#13068314	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₁
commutator, socle	C₂³×C₁₁	C₂×C₄²
Fitting	C₂×C₁₁×#431	C₂
prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	#7851
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. C₁₁⋊#1273	C₂	semidirect
209. C₁₁	#7851	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
C₁₁⋊#1273	2
C₂×C₁₁×#431	2
#7851	11