Subgroups — #14907403

Order 2816.

556 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	#13077329	C₂	1	1	yes	maximal, characteristic
2	#13070443	C₂	1	4	yes	maximal, complemented
3	#13070440	C₂	1	4	yes	maximal, complemented
4	#13070419	C₂	1	1	yes	maximal, characteristic, complemented
5	#13070228	C₂	1	4	yes	maximal, complemented
6	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66954	C₂²	1	2	yes	—
8	#10623008	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#10622723	C₄	1	2	yes	—
11	#10622537	C₄	1	1	yes	characteristic
12	C₂×#66862	C₂²	1	4	yes	—
13	C₂×C₁₆×D₁₁	C₂²	1	4	yes	—
14	#10622301	C₄	1	2	yes	—
15	#10622301	C₄	1	2	yes	—
16	C₈×D₄₄	C₂²	1	2	yes	—
17	C₈×D₄₄	C₂²	1	2	yes	—
18	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
19	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
20	C₁₁×#346	C₂²	1	2	yes	—
21	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
22	(C₂×D₁₁)⋊C₁₆	C₂²	1	8	yes	—
23	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
24	#10622099	C₂²	1	2	yes	—
25	C₂×#4339	C₂×C₄	1	2	yes	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
29	#66983	C₈	1	2	yes	—
30	#66983	C₈	1	2	yes	—
31	C₂×#4318	C₂×C₄	1	2	yes	—
32	#66954	—	4	2	no	—
33	#66954	—	4	2	no	—
34	C₂×#4313	C₂×C₄	1	4	yes	—
35	C₂×C₈×D₁₁	C₂³	1	4	yes	—
36	#66928	C₈	1	2	yes	—
37	#66927	C₈	1	1	yes	characteristic
38	C₄×D₄₄	C₂×C₄	1	2	yes	—
39	C₄×D₄₄	C₂×C₄	1	2	yes	—
40	#66922	C₈	1	1	yes	characteristic
41	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
47	(C₂×D₁₁)⋊C₈	C₂×C₄	1	4	yes	—
48	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
49	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
50	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
51	#66862	—	4	4	no	—
52	C₁₆×D₁₁	—	4	4	no	—
53	#33494	—	11	1	no	maximal, Sylow
54	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×C₂²⋊D₁₁	C₂×C₈	1	4	yes	—
58	#4339	—	4	2	no	—
59	#4339	—	4	2	no	—
60	C₂×D₄₄	C₂×C₈	1	2	yes	—
61	C₂×D₄₄	C₂×C₈	1	2	yes	—
62	C₂×D₄₄	C₂×C₈	1	2	yes	—
63	C₂×C₄×D₁₁	C₂²×C₄	1	4	yes	—
64	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
65	C₂×C₈×C₁₁	—	2	2	no	—
66	C₂×C₈×C₁₁	—	4	1	no	—
67	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
71	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
72	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
73	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
74	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	(C₂×D₁₁)⋊C₄	C₂×C₈	1	4	yes	—
76	(C₂×D₁₁)⋊C₄	C₂×C₈	1	4	yes	—
77	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
78	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
79	#4318	—	4	2	no	—
80	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
81	#4313	—	4	4	no	—
82	C₈×D₁₁	—	2	4	no	—
83	C₈×D₁₁	—	2	4	no	—
84	C₁₁×C₁₆	—	2	4	no	—
85	C₁₁⋊C₁₆	—	2	4	no	—
86	#2931	—	11	1	no	—
87	#2168	—	11	4	no	—
88	#2168	—	11	4	no	—
89	#2163	—	11	1	no	—
90	#2163	D₁₁	1	1	yes	characteristic, complemented
91	#2113	—	11	4	no	—
92	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
93	C₂²×D₁₁	C₂²×C₈	1	4	yes	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	—	4	1	no	—
97	C₂×C₄×C₁₁	—	4	1	no	—
98	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
104	C₂²⋊D₁₁	—	4	4	no	—
105	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
106	D₄₄	—	4	2	no	—
107	D₄₄	—	4	2	no	—
108	D₄₄	—	4	2	no	—
109	C₄×D₁₁	—	2	4	no	—
110	C₄×D₁₁	—	2	4	no	—
111	Dic₂₂	—	4	2	no	—
112	C₈×C₁₁	—	2	1	no	—
113	C₈×C₁₁	—	2	1	no	—
114	C₈×C₁₁	—	2	1	no	—
115	C₈×C₁₁	H(5,𝔽₂)	1	2	yes	—
116	C₁₁⋊C₈	—	2	4	no	—
117	C₂×#131	—	11	2	no	—
118	#532	—	11	1	no	—
119	C₂×M₃₂	—	11	4	no	—
120	C₂²×C₁₆	—	11	4	no	—
121	#436	—	11	2	no	—
122	#436	—	11	2	no	—
123	C₈×D₄	—	11	2	no	—
124	C₈×D₄	—	11	2	no	—
125	#423	—	11	1	no	—
126	#408	—	11	2	no	—
127	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
128	C₄⋊C₁₆	—	11	2	no	—
129	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
130	C₂²⋊C₁₆	—	11	2	no	—
131	C₂²⋊C₁₆	—	11	8	no	—
132	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
133	#346	—	11	2	no	—
134	#346	C₂×D₁₁	1	2	yes	—
135	C₂²×C₁₁	—	2	1	no	—
136	C₂²×C₁₁	—	2	1	no	—
137	C₂²×C₁₁	—	2	1	no	—
138	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
139	C₂×D₁₁	—	2	4	no	—
140	C₂×D₁₁	—	2	4	no	—
141	C₂×D₁₁	—	2	4	no	—
142	C₄×C₁₁	—	2	1	no	—
143	C₄×C₁₁	—	2	1	no	—
144	C₄×C₁₁	—	2	1	no	—
145	C₄×C₁₁	—	2	1	no	—
146	C₄×C₁₁	—	2	1	no	—
147	C₄×C₁₁	#518	1	1	yes	characteristic
148	C₄×C₁₁	#568	1	1	yes	characteristic
149	Dic₁₁	—	2	4	no	—
150	C₂×#41	—	11	2	no	—
151	#131	—	44	2	no	—
152	#131	—	44	2	no	—
153	C₂×M₁₆	—	11	2	no	—
154	C₂×M₁₆	—	11	4	no	—
155	C₂²×C₈	—	11	4	no	—
156	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
157	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
158	C₄⋊Q₈	—	11	1	no	—
159	#127	—	11	1	no	—
160	#124	—	11	2	no	—
161	#121	—	11	2	no	—
162	#121	—	11	2	no	—
163	C₄×D₄	—	11	2	no	—
164	C₄×D₄	—	11	2	no	—
165	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
166	M₃₂	—	44	4	no	—
167	C₂×C₁₆	—	11	4	no	—
168	C₂×C₁₆	—	44	4	no	—
169	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
170	C₄⋊C₈	—	11	2	no	—
171	C₄⋊C₈	—	11	2	no	—
172	C₂²⋊C₈	—	11	4	no	—
173	C₂²⋊C₈	—	11	4	no	—
174	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
175	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
176	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
177	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
178	C₂×C₁₁	—	4	1	no	—
179	C₂×C₁₁	#2972	1	1	yes	characteristic
180	C₂×C₁₁	#3407	1	1	yes	characteristic
181	C₂×C₁₁	#3407	1	1	yes	characteristic
182	D₁₁	—	4	4	no	—
183	#41	—	44	2	no	—
184	#41	—	44	2	no	—
185	C₂×Q₈	—	11	2	no	—
186	C₂×D₄	—	11	4	no	—
187	C₂×D₄	—	11	2	no	—
188	C₂×D₄	—	11	2	no	—
189	C₂×D₄	—	11	2	no	—
190	C₂²×C₄	—	11	4	no	—
191	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
192	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
194	M₁₆	—	44	4	no	—
195	M₁₆	—	44	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	11	4	no	—
199	C₂×C₈	—	22	4	no	—
200	C₂×C₈	—	22	4	no	—
201	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
202	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
203	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
204	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
205	C₄⋊C₄	—	11	2	no	—
206	C₄⋊C₄	—	11	2	no	—
207	C₂²⋊C₄	—	11	4	no	—
208	C₂²⋊C₄	—	11	4	no	—
209	C₄²	C₈×D₁₁	1	1	yes	characteristic
210	C₄²	C₈×D₁₁	1	1	yes	characteristic
211	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
212	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
213	C₁₆	—	2	4	no	—
214	C₁₆	—	22	4	no	—
215	C₁₁	#33494	1	1	yes	characteristic, complemented, Sylow
216	C₂³	—	11	4	no	—
217	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
218	Q₈	—	44	2	no	—
219	D₄	—	44	2	no	—
220	D₄	—	44	2	no	—
221	D₄	—	44	2	no	—
222	D₄	—	44	4	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	4	1	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	11	4	no	—
228	C₂×C₄	—	22	4	no	—
229	C₂×C₄	—	22	4	no	—
230	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
231	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
232	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
233	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
234	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
235	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
236	C₈	—	2	1	no	—
237	C₈	—	2	1	no	—
238	C₈	—	2	1	no	—
239	C₈	—	22	4	no	—
240	C₈	#67042	1	2	yes	—
241	C₂²	—	2	1	no	—
242	C₂²	—	2	1	no	—
243	C₂²	—	2	1	no	—
244	C₂²	—	22	4	no	—
245	C₂²	—	22	4	no	—
246	C₂²	—	22	4	no	—
247	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
248	C₄	—	2	1	no	—
249	C₄	—	2	1	no	—
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	22	4	no	—
254	C₄	#10623052	1	1	yes	characteristic
255	C₄	#10623276	1	1	yes	characteristic
256	C₂	—	4	1	no	—
257	C₂	—	44	4	no	—
258	C₂	#13077639	1	1	yes	characteristic
259	C₂	#13081718	1	1	yes	characteristic
260	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2163	C₂
prime radical	#10623008	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2163	D₁₁
hypocenter	C₁₁	#33494
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #13070443	C₂	semidirect
3. #13070440	C₂	semidirect
4. #13070419	C₂	semidirect
5. #13070228	C₂	semidirect
6. C₁₁×#2163	C₂	semidirect
90. #2163	D₁₁	semidirect
215. C₁₁	#33494	semidirect

Maximal subgroups

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

subgroup	index
#13077329	2
#13070443	2
#13070440	2
#13070419	2
#13070228	2
C₁₁×#2163	2
#33494	11