Subgroups — #14653887

Order 2816.

440 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	#13068469	C₂	1	1	yes	maximal, characteristic
2	#13068365	C₂	1	1	yes	maximal, characteristic
3	#13066497	C₂	1	4	yes	maximal
4	C₁₁×#2862	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
6	C₂×C₁₁×C₄⋊Q₈	C₄	1	1	yes	characteristic
7	C₁₁×#391	—	2	1	no	—
8	C₁₁×#391	—	2	1	no	—
9	C₁₁×#391	—	2	1	no	—
10	C₁₁×#391	—	2	1	no	—
11	C₁₁×#382	C₄	1	2	yes	—
12	C₁₁×#382	C₂²	1	2	yes	—
13	C₄³×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
15	C₂×#66867	C₂²	1	2	yes	—
16	C₂×#66867	C₂²	1	2	yes	—
17	#10622162	—	2	1	no	—
18	#10622162	—	2	1	no	—
19	#10622162	—	2	1	no	—
20	C₂²×Q₈×C₁₁	—	2	1	no	—
21	C₂²×Q₈×C₁₁	—	2	1	no	—
22	C₁₁×C₄⋊Q₈	—	4	2	no	—
23	C₁₁×C₄⋊Q₈	—	4	2	no	—
24	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
25	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
26	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
27	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	D₄	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	C₂³	1	1	yes	characteristic
35	C₂²×C₁₁⋊C₈	—	2	2	no	—
36	C₂²×C₁₁⋊C₈	—	2	2	no	—
37	C₁₁×#95	—	2	2	no	—
38	C₁₁×#95	—	2	2	no	—
39	C₁₁×#95	—	2	2	no	—
40	C₁₁×#95	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
42	#66867	—	2	2	no	—
43	#66867	—	2	4	no	—
44	#66867	Q₈	1	4	yes	complemented
45	#9895	—	11	1	no	maximal, Sylow
46	C₂×Q₈×C₁₁	—	4	2	no	—
47	C₂×Q₈×C₁₁	—	4	2	no	—
48	C₂×Q₈×C₁₁	—	4	2	no	—
49	C₂×Q₈×C₁₁	—	4	2	no	—
50	C₂×Q₈×C₁₁	—	4	2	no	—
51	C₂×Q₈×C₁₁	—	4	2	no	—
52	C₂²×C₄×C₁₁	—	2	2	no	—
53	C₂²×C₄×C₁₁	—	2	2	no	—
54	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₁₁×C₄⋊C₄	—	4	2	no	—
62	C₁₁×C₄⋊C₄	—	4	2	no	—
63	C₁₁×C₄⋊C₄	—	4	2	no	—
64	C₁₁×C₄⋊C₄	—	4	2	no	—
65	C₄²×C₁₁	—	2	2	no	—
66	C₄²×C₁₁	—	2	2	no	—
67	C₄²×C₁₁	—	2	2	no	—
68	C₄²×C₁₁	—	4	1	no	—
69	C₄²×C₁₁	—	4	1	no	—
70	C₄²×C₁₁	—	4	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	—	2	4	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	#2862	D₁₁	1	1	yes	characteristic
80	#1767	—	11	1	no	—
81	#1745	—	11	1	no	—
82	#1295	—	11	4	no	—
83	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₁₁	—	8	4	no	—
85	Q₈×C₁₁	—	8	4	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	—	2	1	no	—
98	C₂×C₄×C₁₁	—	2	1	no	—
99	C₂×C₄×C₁₁	—	2	1	no	—
100	C₂×C₄×C₁₁	—	2	1	no	—
101	C₂×C₄×C₁₁	—	4	2	no	—
102	C₂×C₄×C₁₁	—	4	2	no	—
103	C₂×C₄×C₁₁	—	4	2	no	—
104	C₂×C₄×C₁₁	—	4	2	no	—
105	C₂×C₄×C₁₁	—	4	2	no	—
106	C₂×C₄×C₁₁	—	4	2	no	—
107	C₂×C₄×C₁₁	#100	1	2	yes	—
108	C₂×C₄×C₁₁	#101	1	2	yes	—
109	C₂×C₄×C₁₁	#104	1	2	yes	—
110	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
111	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
112	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
114	C₁₁⋊C₈	—	4	4	no	—
115	C₁₁⋊C₈	—	4	4	no	—
116	C₂×C₄⋊Q₈	Dic₁₁	1	1	yes	characteristic
117	C₂×C₄⋊Q₈	Dic₁₁	1	1	yes	characteristic
118	C₂×C₄⋊C₈	—	22	1	no	—
119	C₂×#97	—	11	2	no	—
120	C₂×#97	—	11	2	no	—
121	#391	—	2	1	no	—
122	#391	—	2	1	no	—
123	#391	—	2	1	no	—
124	#391	—	2	1	no	—
125	#382	Dic₁₁	1	2	yes	—
126	#382	C₂×D₁₁	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	C₂×#104	1	1	yes	characteristic
135	C₂²×C₁₁	#421	1	1	yes	characteristic
136	C₂²×C₁₁	#421	1	1	yes	characteristic
137	C₂²×C₁₁	#421	1	1	yes	characteristic
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	—	2	2	no	—
141	C₄×C₁₁	—	2	2	no	—
142	C₄×C₁₁	—	2	2	no	—
143	C₄×C₁₁	—	2	2	no	—
144	C₄×C₁₁	—	2	2	no	—
145	C₄×C₁₁	—	4	1	no	—
146	C₄×C₁₁	—	8	2	no	—
147	C₄×C₁₁	—	8	2	no	—
148	C₂²×Q₈	—	2	1	no	—
149	C₂²×Q₈	—	2	1	no	—
150	C₂²×C₈	—	22	2	no	—
151	C₂²×C₈	—	22	2	no	—
152	C₄⋊Q₈	—	4	2	no	—
153	C₄⋊Q₈	—	4	2	no	—
154	C₂×C₄⋊C₄	—	2	1	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
157	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
158	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
159	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
160	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
161	C₂×C₄²	C₂²⋊D₁₁	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	C₄⋊C₈	—	22	4	no	—
166	#97	—	11	4	no	—
167	#97	—	22	2	no	—
168	#97	—	22	4	no	—
169	#95	—	2	2	no	—
170	#95	—	2	2	no	—
171	#95	—	2	2	no	—
172	#95	—	2	2	no	—
173	C₂×C₁₁	#1527	1	1	yes	characteristic
174	C₂×C₁₁	#1531	1	1	yes	characteristic
175	C₂×C₁₁	#1533	1	1	yes	characteristic
176	C₂×C₁₁	#1537	1	1	yes	characteristic
177	C₂×C₁₁	#1986	1	1	yes	characteristic
178	C₂×C₁₁	#1995	1	1	yes	characteristic
179	C₂×C₁₁	#1997	1	1	yes	characteristic
180	C₂×Q₈	—	4	2	no	—
181	C₂×Q₈	—	4	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂×Q₈	—	4	2	no	—
186	C₂²×C₄	—	2	2	no	—
187	C₂²×C₄	—	2	2	no	—
188	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
189	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
190	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
191	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
192	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
193	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
194	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
195	C₂×C₈	—	22	4	no	—
196	C₂×C₈	—	22	4	no	—
197	C₂×C₈	—	44	2	no	—
198	C₂×C₈	—	44	2	no	—
199	C₂×C₈	—	44	2	no	—
200	C₂×C₈	—	44	2	no	—
201	C₄⋊C₄	—	4	2	no	—
202	C₄⋊C₄	—	4	2	no	—
203	C₄⋊C₄	—	4	2	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄²	—	2	2	no	—
206	C₄²	—	2	2	no	—
207	C₄²	—	2	2	no	—
208	C₄²	—	4	1	no	—
209	C₄²	—	4	1	no	—
210	C₄²	—	4	1	no	—
211	C₄²	Q₈×D₁₁	1	2	yes	—
212	C₄²	#4343	1	2	yes	—
213	C₁₁	#9895	1	1	yes	characteristic, complemented, Sylow
214	C₂³	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
215	Q₈	—	8	4	no	—
216	Q₈	—	8	4	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	—	2	1	no	—
228	C₂×C₄	—	2	1	no	—
229	C₂×C₄	—	2	1	no	—
230	C₂×C₄	—	2	1	no	—
231	C₂×C₄	—	2	1	no	—
232	C₂×C₄	—	4	2	no	—
233	C₂×C₄	—	4	2	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	4	2	no	—
236	C₂×C₄	—	4	2	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	#66897	1	2	yes	—
239	C₂×C₄	#66900	1	2	yes	—
240	C₂×C₄	#66901	1	2	yes	—
241	C₂×C₄	#66997	1	1	yes	characteristic
242	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
243	C₂×C₄	#66999	1	2	yes	—
244	C₂×C₄	#67000	1	1	yes	characteristic
245	C₈	—	44	4	no	—
246	C₈	—	44	4	no	—
247	C₂²	C₂×#66897	1	1	yes	characteristic
248	C₂²	C₂×#66900	1	1	yes	characteristic
249	C₂²	#10622843	1	1	yes	characteristic
250	C₂²	C₂×#66901	1	1	yes	characteristic
251	C₂²	#10622849	1	1	yes	characteristic
252	C₂²	#10622849	1	1	yes	characteristic
253	C₂²	#10622849	1	1	yes	characteristic
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	2	2	no	—
257	C₄	—	2	2	no	—
258	C₄	—	2	2	no	—
259	C₄	—	2	1	no	—
260	C₄	—	2	1	no	—
261	C₄	—	4	1	no	—
262	C₄	—	8	2	no	—
263	C₄	—	8	2	no	—
264	C₂	#13067214	1	1	yes	characteristic
265	C₂	#13067231	1	1	yes	characteristic
266	C₂	#13067240	1	1	yes	characteristic
267	C₂	#13067254	1	1	yes	characteristic
268	C₂	#13069561	1	1	yes	characteristic
269	C₂	#13069598	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×#2862	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2862	D₁₁
hypocenter	C₁₁	#9895
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

Complements

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

N	H ≅ G/N	type
44. #66867	Q₈	semidirect
213. C₁₁	#9895	semidirect

Maximal subgroups

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

subgroup	index
#13068469	2
#13068365	2
#13066497	2
C₁₁×#2862	2
#9895	11