Subgroups — #14653913

Order 2816.

430 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068733	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#13066499	C₂	1	2	yes	maximal
4	#13066499	C₂	1	2	yes	maximal
5	C₁₁×#2859	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#125	C₄	1	2	yes	—
7	C₁₁×#389	—	2	1	no	—
8	C₁₁×#389	—	2	1	no	—
9	C₁₁×#389	—	2	1	no	—
10	C₁₁×#389	—	2	1	no	—
11	C₁₁×#384	C₂²	1	1	yes	characteristic
12	C₁₁×#384	C₂²	1	1	yes	characteristic
13	C₁₁×#382	C₄	1	2	yes	—
14	C₄³×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
18	#10622162	—	2	1	no	—
19	#10622162	—	2	1	no	—
20	#10622162	—	2	1	no	—
21	C₁₁×#125	—	4	4	no	—
22	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
24	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
25	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
29	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₂²×C₁₁⋊C₈	—	2	2	no	—
38	C₂²×C₁₁⋊C₈	—	2	2	no	—
39	C₁₁×#95	—	2	2	no	—
40	C₁₁×#95	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
43	C₄⋊(C₁₁⋊C₈)	Q₈	1	4	yes	—
44	C₄×C₁₁⋊C₈	—	4	2	no	—
45	#9901	—	11	1	no	maximal, Sylow
46	C₂²×C₄×C₁₁	—	2	2	no	—
47	C₂²×C₄×C₁₁	—	2	2	no	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₁₁×C₄⋊C₄	—	4	4	no	—
56	C₁₁×C₄⋊C₄	—	4	2	no	—
57	C₁₁×C₄⋊C₄	—	4	2	no	—
58	C₁₁×C₄⋊C₄	—	4	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₁₁×C₄⋊C₄	—	4	2	no	—
62	C₁₁×C₄⋊C₄	—	4	1	no	—
63	C₁₁×C₄⋊C₄	—	4	1	no	—
64	C₄²×C₁₁	—	2	2	no	—
65	C₄²×C₁₁	—	2	2	no	—
66	C₄²×C₁₁	—	2	2	no	—
67	C₄²×C₁₁	—	2	2	no	—
68	C₄²×C₁₁	—	2	2	no	—
69	C₄²×C₁₁	—	2	1	no	—
70	C₄²×C₁₁	—	2	1	no	—
71	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
72	C₄²×C₁₁	#41	1	2	yes	—
73	C₂×C₁₁⋊C₈	—	2	4	no	—
74	C₂×C₁₁⋊C₈	—	4	2	no	—
75	C₂×C₁₁⋊C₈	—	4	2	no	—
76	C₂×C₁₁⋊C₈	—	4	2	no	—
77	C₂×C₁₁⋊C₈	—	4	2	no	—
78	C₂×C₁₁⋊C₈	—	4	2	no	—
79	#2859	D₁₁	1	1	yes	characteristic
80	#1831	—	11	1	no	—
81	C₄×C₄⋊C₈	—	11	1	no	—
82	#1296	—	11	2	no	—
83	#1296	—	11	2	no	—
84	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	—	2	1	no	—
86	C₂×C₄×C₁₁	—	2	1	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	2	1	no	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	—	2	1	no	—
97	C₂×C₄×C₁₁	—	4	2	no	—
98	C₂×C₄×C₁₁	—	4	2	no	—
99	C₂×C₄×C₁₁	—	4	2	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	—	4	2	no	—
102	C₂×C₄×C₁₁	—	4	2	no	—
103	C₂×C₄×C₁₁	#100	1	2	yes	—
104	C₂×C₄×C₁₁	#101	1	2	yes	—
105	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
106	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
107	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
109	C₂×C₄×C₁₁	#135	1	2	yes	—
110	C₂×C₄×C₁₁	#135	1	2	yes	—
111	C₂×C₄×C₁₁	#135	1	2	yes	—
112	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
114	C₁₁⋊C₈	—	4	4	no	—
115	C₁₁⋊C₈	—	8	2	no	—
116	C₂×#125	Dic₁₁	1	2	yes	—
117	C₂×C₄⋊C₈	—	11	2	no	—
118	C₂×C₄⋊C₈	—	11	2	no	—
119	C₂×C₄×C₈	—	22	1	no	—
120	#389	—	2	1	no	—
121	#389	—	2	1	no	—
122	#389	—	2	1	no	—
123	#389	—	2	1	no	—
124	#384	C₂×D₁₁	1	1	yes	characteristic
125	#384	C₂×D₁₁	1	1	yes	characteristic
126	#382	Dic₁₁	1	2	yes	—
127	C₄³	C₂×D₁₁	1	1	yes	characteristic
128	#336	—	22	1	no	—
129	#336	—	22	1	no	—
130	#336	—	22	1	no	—
131	C₂²×C₁₁	#391	1	1	yes	characteristic
132	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
133	C₂²×C₁₁	C₂×#101	1	1	yes	characteristic
134	C₂²×C₁₁	#416	1	1	yes	characteristic
135	C₂²×C₁₁	#416	1	1	yes	characteristic
136	C₂²×C₁₁	#416	1	1	yes	characteristic
137	C₂²×C₁₁	#417	1	1	yes	characteristic
138	C₄×C₁₁	—	2	2	no	—
139	C₄×C₁₁	—	2	2	no	—
140	C₄×C₁₁	—	2	2	no	—
141	C₄×C₁₁	—	4	1	no	—
142	C₄×C₁₁	—	4	1	no	—
143	C₄×C₁₁	—	8	2	no	—
144	C₄×C₁₁	—	8	2	no	—
145	C₄×C₁₁	#478	1	2	yes	—
146	C₄×C₁₁	#479	1	2	yes	—
147	C₄×C₁₁	#488	1	2	yes	—
148	C₄×C₁₁	#499	1	2	yes	—
149	C₂²×C₈	—	22	2	no	—
150	C₂²×C₈	—	22	2	no	—
151	#125	—	4	4	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	—	2	1	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
159	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
160	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
161	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
162	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
163	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
164	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
165	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
166	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
167	C₄⋊C₈	—	11	4	no	—
168	C₄⋊C₈	—	22	2	no	—
169	C₄⋊C₈	—	22	4	no	—
170	C₄×C₈	—	44	2	no	—
171	#95	—	2	2	no	—
172	#95	—	2	2	no	—
173	C₂×C₁₁	#1543	1	1	yes	characteristic
174	C₂×C₁₁	#1544	1	1	yes	characteristic
175	C₂×C₁₁	#1551	1	1	yes	characteristic
176	C₂×C₁₁	#1552	1	1	yes	characteristic
177	C₂×C₁₁	#1989	1	1	yes	characteristic
178	C₂×C₁₁	#1991	1	1	yes	characteristic
179	C₂×C₁₁	#1997	1	1	yes	characteristic
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
183	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
184	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
185	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
186	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
187	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
188	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
189	C₂×C₈	—	22	4	no	—
190	C₂×C₈	—	44	2	no	—
191	C₂×C₈	—	44	2	no	—
192	C₂×C₈	—	44	2	no	—
193	C₂×C₈	—	44	2	no	—
194	C₂×C₈	—	44	2	no	—
195	C₄⋊C₄	—	4	2	no	—
196	C₄⋊C₄	—	4	2	no	—
197	C₄⋊C₄	—	4	4	no	—
198	C₄⋊C₄	—	4	4	no	—
199	C₄⋊C₄	—	4	1	no	—
200	C₄⋊C₄	—	4	2	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄²	—	2	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	1	no	—
207	C₄²	—	2	2	no	—
208	C₄²	—	2	2	no	—
209	C₄²	—	2	2	no	—
210	C₄²	—	2	1	no	—
211	C₄²	Q₈×D₁₁	1	2	yes	—
212	C₄²	#4343	1	2	yes	—
213	C₁₁	#9901	1	1	yes	characteristic, complemented, Sylow
214	C₂³	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	1	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	4	2	no	—
229	C₂×C₄	—	4	2	no	—
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	#66897	1	2	yes	—
234	C₂×C₄	#66900	1	2	yes	—
235	C₂×C₄	#66997	1	1	yes	characteristic
236	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
237	C₂×C₄	#66999	1	2	yes	—
238	C₂×C₄	#67000	1	1	yes	characteristic
239	C₂×C₄	#67002	1	1	yes	characteristic
240	C₂×C₄	#67003	1	2	yes	—
241	C₂×C₄	#67003	1	2	yes	—
242	C₂×C₄	#67003	1	2	yes	—
243	C₂×C₄	#67004	1	1	yes	characteristic
244	C₈	—	44	4	no	—
245	C₈	—	88	2	no	—
246	C₂²	C₂×#66897	1	1	yes	characteristic
247	C₂²	C₂×#66900	1	1	yes	characteristic
248	C₂²	#10622843	1	1	yes	characteristic
249	C₂²	#10622845	1	1	yes	characteristic
250	C₂²	#10622846	1	1	yes	characteristic
251	C₂²	#10622846	1	1	yes	characteristic
252	C₂²	#10622846	1	1	yes	characteristic
253	C₄	—	2	2	no	—
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	4	1	no	—
257	C₄	—	4	1	no	—
258	C₄	—	8	2	no	—
259	C₄	—	8	2	no	—
260	C₄	#10622676	1	2	yes	—
261	C₄	#10622677	1	2	yes	—
262	C₄	#10622679	1	2	yes	—
263	C₄	#10622681	1	2	yes	—
264	C₂	#13067278	1	1	yes	characteristic
265	C₂	#13067281	1	1	yes	characteristic
266	C₂	#13067311	1	1	yes	characteristic
267	C₂	#13067316	1	1	yes	characteristic
268	C₂	#13069574	1	1	yes	characteristic
269	C₂	#13069582	1	1	yes	characteristic
270	C₂	#13069606	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2859	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2859	D₁₁
hypocenter	C₁₁	#9901
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2859

Complements

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

N	H ≅ G/N	type
213. C₁₁	#9901	semidirect

Maximal subgroups

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

subgroup	index
#13068733	2
C₄×C₄⋊(C₁₁⋊C₈)	2
#13066499	2
C₁₁×#2859	2
#9901	11