Subgroups — #13077451

Order 1408.

506 conjugacy classes of subgroups.

The subgroup lattice has 278 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10623358	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#67002	C₂	1	1	yes	maximal, characteristic
3	#10623052	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#416	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#66885	C₂	1	1	yes	maximal, characteristic, complemented
6	#10622714	C₂	1	1	yes	maximal, characteristic, complemented
7	#10622608	C₂	1	1	yes	maximal, characteristic, complemented
8	#10622430	C₂	1	2	yes	maximal, complemented
9	#10622401	C₂	1	2	yes	maximal, complemented
10	#10622398	C₂	1	2	yes	maximal, complemented
11	#10622369	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂²×D₄₄	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₁₁×#117	C₂²	1	1	yes	characteristic
16	#67002	C₄	1	8	yes	complemented
17	Q₈×Dic₁₁	C₂²	1	2	yes	complemented
18	C₂×#4325	C₂²	1	2	yes	—
19	D₄×Dic₁₁	—	2	2	no	—
20	D₄×Dic₁₁	C₂²	1	2	yes	complemented
21	C₂×#4323	C₂²	1	2	yes	—
22	#66979	—	2	1	no	—
23	#66979	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	—	2	1	no	—
25	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
26	C₂×#4318	C₂²	1	1	yes	characteristic
27	#66946	C₂²	1	2	yes	—
28	#66946	C₂²	1	2	yes	—
29	C₂²⋊C₄×D₁₁	—	2	2	no	—
30	C₄×D₄₄	—	2	1	no	—
31	C₄×D₄₄	—	2	1	no	—
32	C₁₁×#103	C₂²	1	1	yes	characteristic, complemented
33	C₁₁×#103	C₂²	1	1	yes	characteristic, complemented
34	C₁₁×#102	C₂²	1	1	yes	characteristic, complemented
35	C₁₁×#102	C₂²	1	1	yes	characteristic, complemented
36	#66885	C₂²	1	2	yes	—
37	#66885	C₂²	1	2	yes	—
38	#66879	C₂²	1	2	yes	complemented
39	C₈×Dic₁₁	C₂²	1	2	yes	complemented
40	#66872	C₂²	1	2	yes	complemented
41	#66871	C₂²	1	2	yes	complemented
42	C₂³×D₁₁	—	2	1	no	—
43	C₁₁×#41	—	2	2	no	—
44	C₁₁×#41	C₂×C₄	1	4	yes	complemented
45	C₂×Q₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂×D₄×C₁₁	—	2	1	no	—
47	C₂×D₄×C₁₁	C₂³	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	—	2	1	no	—
49	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₂²×Dic₁₁	—	2	2	no	—
51	C₂²×Dic₁₁	—	2	1	no	—
52	C₂×D₄₄	—	2	1	no	—
53	C₂×D₄₄	—	2	2	no	—
54	C₂×D₄₄	C₂×C₄	1	4	yes	complemented
55	C₂×D₄₄	C₂³	1	2	yes	—
56	C₂×C₄×D₁₁	—	2	2	no	—
57	C₂×C₄×D₁₁	—	2	2	no	—
58	C₂×C₈×C₁₁	—	2	2	no	—
59	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₁₁×C₂²⋊C₄	—	2	1	no	—
64	C₄²×C₁₁	—	2	1	no	—
65	C₂²⋊Dic₁₁	—	2	2	no	—
66	C₂²⋊Dic₁₁	D₄	1	2	yes	—
67	#4325	C₂×C₄	1	8	yes	complemented
68	#4323	C₂×C₄	1	8	yes	complemented
69	(C₂×D₁₁)⋊C₄	—	2	2	no	—
70	(C₂×D₁₁)⋊C₄	—	2	2	no	—
71	C₄⋊Dic₁₁	—	2	2	no	—
72	C₄⋊Dic₁₁	—	2	1	no	—
73	C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
74	C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
75	C₄⋊Dic₁₁	C₂³	1	2	yes	—
76	C₄×Dic₁₁	—	2	2	no	—
77	C₄×Dic₁₁	C₂³	1	2	yes	—
78	#4318	C₂×C₄	1	4	yes	complemented
79	C₂×C₁₁⋊C₈	C₂³	1	2	yes	—
80	#2946	—	11	1	no	maximal, Sylow
81	C₂³×C₁₁	—	2	1	no	—
82	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₂²×D₁₁	—	2	2	no	—
84	C₂²×D₁₁	—	2	4	no	—
85	C₂²×D₁₁	—	8	1	no	—
86	C₂²×D₁₁	—	8	1	no	—
87	Q₈×C₁₁	—	2	1	no	—
88	Q₈×C₁₁	C₂²×C₄	1	2	yes	—
89	D₄×C₁₁	—	2	4	no	—
90	D₄×C₁₁	—	2	1	no	—
91	D₄×C₁₁	C₂²×C₄	1	2	yes	—
92	C₂×C₄×C₁₁	—	2	1	no	—
93	C₂×C₄×C₁₁	—	2	4	no	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	1	no	—
96	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#41	1	2	yes	—
99	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
100	C₂×Dic₁₁	—	2	2	no	—
101	C₂×Dic₁₁	—	8	2	no	—
102	C₂×Dic₁₁	—	8	1	no	—
103	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
104	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
105	D₄₄	—	2	4	no	—
106	D₄₄	—	2	2	no	—
107	D₄₄	C₂²×C₄	1	4	yes	—
108	C₄×D₁₁	—	8	2	no	—
109	C₄×D₁₁	—	8	2	no	—
110	C₈×C₁₁	—	2	1	no	—
111	C₈×C₁₁	—	2	1	no	—
112	C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
113	C₂×AGL(1,ℤ/8)	—	11	1	no	—
114	#520	—	11	1	no	—
115	#518	—	11	1	no	—
116	#442	—	11	2	no	—
117	#440	—	11	2	no	—
118	C₄×SD₁₆	—	11	2	no	—
119	C₄×D₈	—	11	2	no	—
120	#428	—	11	1	no	—
121	#416	D₁₁	1	1	yes	characteristic, complemented
122	C₂×#102	—	11	1	no	—
123	#405	—	11	1	no	—
124	C₂²×C₁₁	—	2	1	no	—
125	C₂²×C₁₁	—	2	1	no	—
126	C₂²×C₁₁	—	2	2	no	—
127	C₂²×C₁₁	—	4	1	no	—
128	C₂²×C₁₁	—	4	1	no	—
129	C₂²×C₁₁	C₄×D₄	1	2	yes	—
130	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
131	C₂×D₁₁	—	2	4	no	—
132	C₂×D₁₁	—	4	2	no	—
133	C₂×D₁₁	—	4	2	no	—
134	C₂×D₁₁	—	8	4	no	—
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	—	4	1	no	—
137	C₄×C₁₁	—	4	1	no	—
138	C₄×C₁₁	C₄×D₄	1	2	yes	—
139	C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
140	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
141	Dic₁₁	—	2	2	no	—
142	Dic₁₁	—	2	2	no	—
143	Dic₁₁	—	4	2	no	—
144	C₂×#41	C₂×D₁₁	1	1	yes	characteristic
145	C₂²×D₄	—	11	1	no	—
146	AGL(1,ℤ/8)	—	11	8	no	—
147	C₂×SD₁₆	—	11	2	no	—
148	C₂×D₈	—	11	2	no	—
149	C₂×M₁₆	—	11	1	no	—
150	C₂²×C₈	C₂×D₁₁	1	1	yes	characteristic
151	C₄×Q₈	—	11	2	no	—
152	C₄×D₄	—	11	2	no	—
153	C₄×D₄	—	11	2	no	—
154	C₄×D₄	—	11	2	no	—
155	C₄×D₄	—	22	1	no	—
156	C₄×D₄	—	22	1	no	—
157	C₄×D₄	—	22	2	no	—
158	#117	—	11	1	no	—
159	#117	—	22	1	no	—
160	#117	C₂×D₁₁	1	1	yes	characteristic
161	C₂×C₄⋊C₄	—	11	1	no	—
162	C₂×C₄⋊C₄	—	22	1	no	—
163	C₂×C₂²⋊C₄	—	22	2	no	—
164	#107	—	11	2	no	—
165	#106	—	11	2	no	—
166	#103	C₂×D₁₁	1	1	yes	characteristic, complemented
167	#103	C₂×D₁₁	1	1	yes	characteristic, complemented
168	#102	—	11	2	no	—
169	#102	—	11	2	no	—
170	#102	C₂×D₁₁	1	1	yes	characteristic, complemented
171	#102	C₂×D₁₁	1	1	yes	characteristic, complemented
172	#97	—	11	2	no	—
173	C₄×C₈	—	11	2	no	—
174	C₂×C₁₁	—	2	2	no	—
175	C₂×C₁₁	—	4	2	no	—
176	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂×C₁₁	#576	1	1	yes	characteristic
178	C₂×C₁₁	#577	1	1	yes	characteristic
179	D₁₁	—	4	4	no	—
180	C₂⁴	—	22	1	no	—
181	#41	—	2	2	no	—
182	#41	C₄×D₁₁	1	4	yes	complemented
183	C₂×Q₈	C₂²×D₁₁	1	1	yes	characteristic
184	C₂×D₄	—	2	1	no	—
185	C₂×D₄	—	11	4	no	—
186	C₂×D₄	—	11	2	no	—
187	C₂×D₄	—	22	1	no	—
188	C₂×D₄	—	22	2	no	—
189	C₂×D₄	C₂²×D₁₁	1	1	yes	characteristic
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	22	2	no	—
192	C₂²×C₄	—	22	2	no	—
193	C₂²×C₄	—	22	2	no	—
194	C₂²×C₄	—	22	1	no	—
195	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
196	SD₁₆	—	11	8	no	—
197	D₈	—	11	8	no	—
198	M₁₆	—	11	4	no	—
199	C₂×C₈	—	2	2	no	—
200	C₂×C₈	—	11	2	no	—
201	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
202	C₂×C₈	C₂²×D₁₁	1	1	yes	characteristic
203	C₄⋊C₄	—	11	1	no	—
204	C₄⋊C₄	—	11	1	no	—
205	C₄⋊C₄	—	11	2	no	—
206	C₄⋊C₄	—	22	2	no	—
207	C₄⋊C₄	—	22	1	no	—
208	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
209	C₄⋊C₄	C₂²×D₁₁	1	1	yes	characteristic
210	C₂²⋊C₄	—	2	1	no	—
211	C₂²⋊C₄	—	11	2	no	—
212	C₂²⋊C₄	—	22	2	no	—
213	C₂²⋊C₄	—	22	2	no	—
214	C₂²⋊C₄	—	22	2	no	—
215	C₄²	—	2	1	no	—
216	C₄²	—	11	2	no	—
217	C₄²	—	22	2	no	—
218	C₁₁	#2946	1	1	yes	characteristic, complemented, Sylow
219	C₂³	—	2	1	no	—
220	C₂³	—	22	2	no	—
221	C₂³	—	22	4	no	—
222	C₂³	—	88	1	no	—
223	C₂³	—	88	1	no	—
224	C₂³	D₄×D₁₁	1	1	yes	characteristic
225	Q₈	—	2	1	no	—
226	Q₈	C₂×C₄×D₁₁	1	2	yes	—
227	D₄	—	2	4	no	—
228	D₄	—	2	1	no	—
229	D₄	—	11	4	no	—
230	D₄	—	22	4	no	—
231	D₄	—	22	2	no	—
232	D₄	C₂×C₄×D₁₁	1	2	yes	—
233	C₂×C₄	—	2	1	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	11	2	no	—
238	C₂×C₄	—	11	2	no	—
239	C₂×C₄	—	22	2	no	—
240	C₂×C₄	—	88	2	no	—
241	C₂×C₄	—	88	2	no	—
242	C₂×C₄	—	88	2	no	—
243	C₂×C₄	—	88	1	no	—
244	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
245	C₂×C₄	D₄×D₁₁	1	1	yes	characteristic
246	C₂×C₄	#4341	1	2	yes	—
247	C₂×C₄	C₂³×D₁₁	1	1	yes	characteristic
248	C₈	—	2	1	no	—
249	C₈	—	2	1	no	—
250	C₈	—	11	4	no	—
251	C₂²	—	2	1	no	—
252	C₂²	—	2	1	no	—
253	C₂²	—	2	2	no	—
254	C₂²	—	4	1	no	—
255	C₂²	—	4	1	no	—
256	C₂²	—	22	4	no	—
257	C₂²	—	44	2	no	—
258	C₂²	—	44	2	no	—
259	C₂²	—	88	4	no	—
260	C₂²	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
261	C₂²	C₂×D₄×D₁₁	1	1	yes	characteristic
262	C₄	—	2	2	no	—
263	C₄	—	4	1	no	—
264	C₄	—	4	1	no	—
265	C₄	—	22	2	no	—
266	C₄	—	22	2	no	—
267	C₄	—	44	2	no	—
268	C₄	(C₂²⋊D₁₁)⋊C₄	1	2	yes	—
269	C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
270	C₄	C₂×#4341	1	1	yes	characteristic
271	C₂	—	2	2	no	—
272	C₂	—	4	2	no	—
273	C₂	—	44	4	no	—
274	C₂	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
275	C₂	#10623300	1	1	yes	characteristic
276	C₂	#10623301	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₁
Fitting	C₁₁×#416	C₂
socle	C₂²×C₁₁	C₂²×D₄
prime radical	C₂×#67002	C₂
cosocle	C₂×C₄×C₁₁	C₂⁴
hypercenter	#416	D₁₁
hypocenter	C₁₁	#2946
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #416

Complements

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

N	H ≅ G/N	type
1. #10623358	C₂	semidirect
3. #10623052	C₂	semidirect
4. C₁₁×#416	C₂	semidirect
5. C₂×#66885	C₂	semidirect
6. #10622714	C₂	semidirect
7. #10622608	C₂	semidirect
8. #10622430	C₂	semidirect
9. #10622401	C₂	semidirect
10. #10622398	C₂	semidirect
11. #10622369	C₂	semidirect
16. #67002	C₄	semidirect
17. Q₈×Dic₁₁	C₂²	semidirect
20. D₄×Dic₁₁	C₂²	semidirect
32. C₁₁×#103	C₂²	semidirect
33. C₁₁×#103	C₂²	semidirect
34. C₁₁×#102	C₂²	semidirect
35. C₁₁×#102	C₂²	semidirect
38. #66879	C₂²	semidirect
39. C₈×Dic₁₁	C₂²	semidirect
40. #66872	C₂²	semidirect
41. #66871	C₂²	semidirect
44. C₁₁×#41	C₂×C₄	semidirect
54. C₂×D₄₄	C₂×C₄	semidirect
67. #4325	C₂×C₄	semidirect
68. #4323	C₂×C₄	semidirect
78. #4318	C₂×C₄	semidirect
121. #416	D₁₁	semidirect
166. #103	C₂×D₁₁	semidirect
167. #103	C₂×D₁₁	semidirect
170. #102	C₂×D₁₁	semidirect
171. #102	C₂×D₁₁	semidirect
182. #41	C₄×D₁₁	semidirect
218. C₁₁	#2946	semidirect

Maximal subgroups

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

subgroup	index
#10623358	2
C₂×#67002	2
#10623052	2
C₁₁×#416	2
C₂×#66885	2
#10622714	2
#10622608	2
#10622430	2
#10622401	2
#10622398	2
#10622369	2
#2946	11