Subgroups — #14669018

Order 2816.

430 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622313	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622135	C₂	1	1	yes	maximal, characteristic
3	#13070321	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622099	C₂	1	1	yes	maximal, characteristic, complemented
5	#13066711	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066709	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1772	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#66957	C₂²	1	1	yes	characteristic
9	C₂×#66954	—	2	1	no	—
10	C₂×C₁₁×#108	C₂²	1	1	yes	characteristic
11	C₁₁×#427	C₂²	1	1	yes	characteristic
12	C₁₁×#405	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×#66883	C₂²	1	1	yes	characteristic
15	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₂×#66869	—	2	1	no	—
18	#10622313	—	2	2	no	—
19	#10622313	C₄	1	4	yes	complemented
20	C₁₁×#339	—	2	1	no	—
21	#10622135	C₄	1	4	yes	complemented
22	#10622130	C₄	1	2	yes	complemented
23	#10622129	C₄	1	2	yes	complemented
24	#10622099	—	2	2	no	—
25	C₂×#4339	—	2	1	no	—
26	C₂×C₁₁×M₁₆	—	2	1	no	—
27	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₁₁×#117	—	2	1	no	—
30	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
31	C₂×#4318	—	2	1	no	—
32	C₂×Dic₄₄	C₂×C₄	1	1	yes	characteristic
33	#66957	—	2	1	no	—
34	#66957	—	2	1	no	—
35	#66957	C₂×C₄	1	2	yes	—
36	#66957	C₂×C₄	1	2	yes	—
37	C₂×D₈₈	C₂×C₄	1	1	yes	characteristic
38	C₂×#4314	—	2	1	no	—
39	#66954	—	2	4	no	—
40	#66954	—	4	2	no	—
41	C₂×#4313	—	4	1	no	—
42	C₂×C₈×D₁₁	—	4	1	no	—
43	C₁₁×#108	—	2	1	no	—
44	C₁₁×#108	C₂×C₄	1	2	yes	—
45	C₁₁×#107	C₂×C₄	1	2	yes	—
46	C₁₁×#106	—	2	1	no	—
47	C₁₁×#97	—	4	1	no	—
48	C₄×C₈×C₁₁	—	4	1	no	—
49	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
50	C₄×C₈×C₁₁	D₄	1	2	yes	—
51	#66883	—	2	1	no	—
52	#66883	C₂×C₄	1	2	yes	—
53	C₂×C₁₁⋊C₁₆	—	2	1	no	—
54	C₂×C₁₁⋊C₁₆	—	2	1	no	—
55	C₂×C₁₁⋊C₁₆	—	2	1	no	—
56	C₂×C₁₁⋊C₁₆	—	2	1	no	—
57	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₁₁⋊C₁₆	C₂×C₄	1	2	yes	—
59	#66869	—	2	4	no	—
60	#12642	—	11	1	no	maximal, Sylow
61	C₂²×C₄×C₁₁	—	2	1	no	—
62	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₂×C₂²⋊D₁₁	—	4	1	no	—
64	#4339	—	2	2	no	—
65	#4339	—	2	2	no	—
66	#4339	—	4	1	no	—
67	#4339	—	4	1	no	—
68	C₂×D₄₄	—	2	1	no	—
69	C₂×C₄×D₁₁	—	4	1	no	—
70	C₂×Dic₂₂	—	2	1	no	—
71	C₁₁×M₁₆	—	2	2	no	—
72	C₁₁×M₁₆	—	4	1	no	—
73	C₂×C₈×C₁₁	—	4	1	no	—
74	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
75	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
76	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
77	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
78	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
80	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
83	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
84	C₁₁×C₄⋊C₄	—	2	2	no	—
85	C₁₁×C₂²⋊C₄	—	4	1	no	—
86	C₄²×C₁₁	—	2	1	no	—
87	C₄²×C₁₁	—	4	1	no	—
88	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
89	#4318	—	2	2	no	—
90	#4318	—	4	1	no	—
91	C₂×C₁₁⋊C₈	—	4	1	no	—
92	Dic₄₄	—	2	1	no	—
93	Dic₄₄	C₄²	1	2	yes	—
94	D₈₈	—	2	1	no	—
95	D₈₈	C₄²	1	2	yes	—
96	#4314	—	2	2	no	—
97	#4314	—	2	2	no	—
98	#4313	—	4	4	no	—
99	C₈×D₁₁	—	4	4	no	—
100	C₁₁⋊C₁₆	—	2	2	no	—
101	C₁₁⋊C₁₆	—	2	2	no	—
102	C₂×#443	—	11	1	no	—
103	C₂×#359	—	11	1	no	—
104	#2138	—	11	1	no	—
105	C₂×#346	—	11	1	no	—
106	#1772	D₁₁	1	1	yes	characteristic, complemented
107	#1382	—	11	1	no	—
108	#1381	—	11	1	no	—
109	C₂³×C₁₁	#135	1	1	yes	characteristic
110	C₂²×D₁₁	—	4	1	no	—
111	C₂×C₄×C₁₁	—	2	2	no	—
112	C₂×C₄×C₁₁	—	4	2	no	—
113	C₂×C₄×C₁₁	—	4	2	no	—
114	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
119	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
120	C₂²⋊D₁₁	—	4	2	no	—
121	C₂²⋊D₁₁	—	4	2	no	—
122	C₂×Dic₁₁	—	4	1	no	—
123	D₄₄	—	2	2	no	—
124	D₄₄	—	4	1	no	—
125	C₄×D₁₁	—	4	2	no	—
126	C₄×D₁₁	—	4	2	no	—
127	Dic₂₂	—	2	2	no	—
128	Dic₂₂	—	4	1	no	—
129	C₈×C₁₁	—	4	2	no	—
130	C₈×C₁₁	#102	1	2	yes	—
131	C₈×C₁₁	#102	1	2	yes	—
132	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
133	C₈×C₁₁	#117	1	1	yes	characteristic
134	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
135	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
136	C₁₁⋊C₈	—	4	2	no	—
137	C₂×#135	—	11	1	no	—
138	C₂×#131	—	22	1	no	—
139	C₂²×C₁₆	—	11	1	no	—
140	C₂²×C₁₆	—	11	1	no	—
141	#443	—	11	4	no	—
142	#443	—	22	2	no	—
143	C₂×#108	—	11	1	no	—
144	C₂×#108	C₂×D₁₁	1	1	yes	characteristic
145	#427	C₂×D₁₁	1	1	yes	characteristic
146	C₂×#104	—	22	1	no	—
147	#405	—	2	1	no	—
148	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
149	#359	—	11	4	no	—
150	#358	—	11	2	no	—
151	#357	—	11	2	no	—
152	#346	—	22	2	no	—
153	#339	—	2	1	no	—
154	C₂²×C₁₁	—	2	2	no	—
155	C₂²×C₁₁	#416	1	1	yes	characteristic
156	C₂²×C₁₁	C₄×D₈	1	1	yes	characteristic
157	C₂²×C₁₁	C₄×SD₁₆	1	1	yes	characteristic
158	C₂×D₁₁	—	4	2	no	—
159	C₂×D₁₁	—	8	2	no	—
160	C₄×C₁₁	—	4	2	no	—
161	C₄×C₁₁	—	8	2	no	—
162	C₄×C₁₁	C₄×C₂²⋊C₄	1	1	yes	characteristic
163	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
164	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
165	C₄×C₁₁	C₄×SD₁₆	1	1	yes	characteristic
166	Dic₁₁	—	4	2	no	—
167	C₂×#41	—	22	1	no	—
168	#135	—	11	2	no	—
169	#135	—	11	2	no	—
170	#135	—	22	1	no	—
171	#135	—	22	1	no	—
172	C₂×Q₁₆	—	11	1	no	—
173	C₂×SD₁₆	—	22	1	no	—
174	C₂×D₈	—	11	1	no	—
175	#131	—	22	4	no	—
176	#131	—	44	2	no	—
177	C₂×M₁₆	—	2	1	no	—
178	C₂×M₁₆	—	22	1	no	—
179	C₂×M₁₆	—	44	1	no	—
180	C₂²×C₈	—	44	1	no	—
181	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
182	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
183	#117	—	2	1	no	—
184	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
185	C₂×C₁₆	—	11	2	no	—
186	C₂×C₁₆	—	11	2	no	—
187	C₂×C₁₆	—	22	1	no	—
188	C₂×C₁₆	—	22	1	no	—
189	C₂×C₁₆	—	22	1	no	—
190	C₂×C₁₆	—	22	1	no	—
191	#108	—	2	1	no	—
192	#108	—	11	2	no	—
193	#108	—	22	1	no	—
194	#108	C₄×D₁₁	1	2	yes	—
195	#107	C₄×D₁₁	1	2	yes	—
196	#106	—	2	1	no	—
197	#104	—	22	4	no	—
198	#97	—	4	1	no	—
199	C₄×C₈	—	4	1	no	—
200	C₄×C₈	C₄×D₁₁	1	2	yes	—
201	C₄×C₈	D₄₄	1	2	yes	—
202	C₂×C₁₁	—	2	1	no	—
203	C₂×C₁₁	—	2	1	no	—
204	C₂×C₁₁	C₄×#102	1	1	yes	characteristic
205	C₂×C₁₁	#2179	1	2	yes	—
206	D₁₁	—	8	2	no	—
207	#41	—	22	2	no	—
208	#41	—	22	2	no	—
209	#41	—	44	1	no	—
210	#41	—	44	1	no	—
211	C₂×Q₈	—	22	1	no	—
212	C₂×D₄	—	22	1	no	—
213	C₂×D₄	—	44	1	no	—
214	C₂²×C₄	—	2	1	no	—
215	C₂²×C₄	—	44	1	no	—
216	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
217	Q₁₆	—	11	2	no	—
218	Q₁₆	—	22	1	no	—
219	SD₁₆	—	22	2	no	—
220	SD₁₆	—	22	2	no	—
221	D₈	—	11	2	no	—
222	D₈	—	22	1	no	—
223	M₁₆	—	2	2	no	—
224	M₁₆	—	4	1	no	—
225	M₁₆	—	22	2	no	—
226	M₁₆	—	44	1	no	—
227	M₁₆	—	44	4	no	—
228	C₂×C₈	—	4	1	no	—
229	C₂×C₈	—	44	1	no	—
230	C₂×C₈	—	44	4	no	—
231	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
232	C₂×C₈	#4323	1	1	yes	characteristic
233	C₂×C₈	#4323	1	1	yes	characteristic
234	C₂×C₈	#4325	1	2	yes	—
235	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
236	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
237	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
238	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
239	C₂×C₈	#4339	1	1	yes	characteristic
240	C₂×C₈	#4339	1	1	yes	characteristic
241	C₄⋊C₄	—	2	2	no	—
242	C₂²⋊C₄	—	4	1	no	—
243	C₄²	—	2	1	no	—
244	C₄²	—	4	1	no	—
245	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
246	C₁₆	—	22	2	no	—
247	C₁₆	—	22	2	no	—
248	C₁₁	#12642	1	1	yes	characteristic, complemented, Sylow
249	C₂³	—	44	1	no	—
250	C₂³	#67003	1	1	yes	characteristic
251	Q₈	—	22	2	no	—
252	Q₈	—	44	1	no	—
253	D₄	—	22	2	no	—
254	D₄	—	44	2	no	—
255	D₄	—	44	2	no	—
256	D₄	—	44	1	no	—
257	C₂×C₄	—	2	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	—	4	2	no	—
260	C₂×C₄	—	44	1	no	—
261	C₂×C₄	—	44	2	no	—
262	C₂×C₄	—	44	2	no	—
263	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
264	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
265	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
266	C₂×C₄	C₂×#4323	1	1	yes	characteristic
267	C₂×C₄	C₂×#4325	1	1	yes	characteristic
268	C₂×C₄	#67003	1	1	yes	characteristic
269	C₈	—	4	2	no	—
270	C₈	—	44	2	no	—
271	C₈	#66873	1	2	yes	—
272	C₈	#66873	1	2	yes	—
273	C₈	C₄²×D₁₁	1	1	yes	characteristic
274	C₈	#66925	1	1	yes	characteristic
275	C₈	C₄×D₄₄	1	1	yes	characteristic
276	C₈	C₄×D₄₄	1	1	yes	characteristic
277	C₂²	—	2	2	no	—
278	C₂²	—	44	2	no	—
279	C₂²	—	88	2	no	—
280	C₂²	#10622615	1	1	yes	characteristic
281	C₂²	C₄×#4323	1	1	yes	characteristic
282	C₂²	C₄×#4325	1	1	yes	characteristic
283	C₄	—	4	2	no	—
284	C₄	—	8	2	no	—
285	C₄	—	44	2	no	—
286	C₄	C₄×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
287	C₄	C₂×#66873	1	1	yes	characteristic
288	C₄	C₄×#4323	1	1	yes	characteristic
289	C₄	C₄×#4325	1	1	yes	characteristic
290	C₂	—	2	1	no	—
291	C₂	—	2	1	no	—
292	C₂	—	88	2	no	—
293	C₂	C₄×#66873	1	1	yes	characteristic
294	C₂	#13070500	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#4323
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1772	C₂
socle	C₂²×C₁₁	C₄×D₈
prime radical	C₂×#66957	C₂²
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1772	D₁₁
hypocenter	C₁₁	#12642
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
4. C₂×#10622099	C₂	semidirect
5. #13066711	C₂	semidirect
6. #13066709	C₂	semidirect
7. C₁₁×#1772	C₂	semidirect
19. #10622313	C₄	semidirect
21. #10622135	C₄	semidirect
22. #10622130	C₄	semidirect
23. #10622129	C₄	semidirect
106. #1772	D₁₁	semidirect
248. C₁₁	#12642	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622313	2
C₂×#10622135	2
#13070321	2
C₂×#10622099	2
#13066711	2
#13066709	2
C₁₁×#1772	2
#12642	11