Subgroups — #14908438

Order 2816.

534 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13079130	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₄₄	C₂	1	1	yes	maximal, characteristic
3	#13070781	C₂	1	4	yes	maximal, complemented
4	#13070769	C₂	1	2	yes	maximal, complemented
5	#13070759	C₂	1	2	yes	maximal, complemented
6	#13070404	C₂	1	2	yes	maximal
7	#13070337	C₂	1	2	yes	maximal
8	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic
9	C₂²×Dic₄₄	C₂²	1	1	yes	characteristic
10	#10623001	—	2	1	no	—
11	C₂×C₄×Dic₂₂	—	2	1	no	—
12	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	#10622719	—	2	1	no	—
15	#10622719	C₂²	1	2	yes	—
16	C₂×#66882	C₂²	1	1	yes	characteristic
17	C₂×#66880	—	2	1	no	—
18	C₄×Dic₄₄	—	2	1	no	—
19	C₄×Dic₄₄	—	2	1	no	—
20	C₄×Dic₄₄	C₂²	1	2	yes	—
21	C₄×Dic₄₄	C₂²	1	2	yes	—
22	#10622296	—	2	1	no	—
23	#10622296	C₂²	1	2	yes	—
24	#10622295	C₂²	1	1	yes	characteristic
25	#10622295	C₂²	1	1	yes	characteristic
26	#10622293	—	2	1	no	—
27	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
28	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
29	#10622143	C₂²	1	4	yes	—
30	#10622142	C₂²	1	4	yes	—
31	#10622141	C₂²	1	4	yes	—
32	#10622141	C₂²	1	4	yes	—
33	C₂²×Dic₂₂	—	2	1	no	—
34	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	#66979	—	2	2	no	—
38	C₂×C₄⋊Dic₁₁	—	2	1	no	—
39	#66977	—	4	1	no	—
40	#66977	—	4	1	no	—
41	C₂×Dic₁₁⋊C₄	—	4	1	no	—
42	C₂×C₄×Dic₁₁	—	4	1	no	—
43	C₂×Dic₄₄	—	2	1	no	—
44	C₂×Dic₄₄	—	2	2	no	—
45	C₂×Dic₄₄	Q₈	1	4	yes	complemented
46	C₂×Dic₄₄	C₂³	1	2	yes	—
47	#66923	—	2	2	no	—
48	#66922	—	2	1	no	—
49	#66922	—	2	1	no	—
50	C₄×Dic₂₂	—	2	2	no	—
51	C₄×Dic₂₂	—	2	2	no	—
52	C₄×Dic₂₂	—	4	1	no	—
53	C₄×Dic₂₂	—	4	1	no	—
54	C₄×Dic₂₂	—	4	1	no	—
55	C₄×Dic₂₂	—	4	1	no	—
56	C₁₁×M₃₂	—	2	4	no	—
57	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
58	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
59	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
60	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
61	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
62	#66882	—	2	1	no	—
63	#66882	—	2	1	no	—
64	#66882	—	2	1	no	—
65	#66882	C₂³	1	2	yes	—
66	#66882	C₂³	1	2	yes	—
67	#66882	C₂³	1	2	yes	—
68	#66881	—	2	2	no	—
69	#66881	—	2	2	no	—
70	#66880	—	2	2	no	—
71	#66880	—	2	2	no	—
72	#33628	—	11	1	no	maximal, Sylow
73	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₁₁	—	4	1	no	—
77	C₂²×Dic₁₁	—	4	1	no	—
78	C₂×Dic₂₂	—	2	4	no	—
79	C₂×Dic₂₂	—	2	2	no	—
80	C₂×Dic₂₂	—	4	1	no	—
81	C₂×Dic₂₂	—	4	1	no	—
82	C₂×Dic₂₂	—	4	1	no	—
83	C₂×Dic₂₂	—	4	2	no	—
84	C₂×C₈×C₁₁	—	2	2	no	—
85	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
89	C₂×C₈×C₁₁	#41	1	2	yes	—
90	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
91	C₄²×C₁₁	D₈	1	1	yes	characteristic
92	C₄²×C₁₁	D₈	1	1	yes	characteristic
93	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
95	C₂²⋊Dic₁₁	—	4	2	no	—
96	C₄⋊Dic₁₁	—	2	2	no	—
97	C₄⋊Dic₁₁	—	2	2	no	—
98	C₄⋊Dic₁₁	—	2	2	no	—
99	C₄⋊Dic₁₁	—	4	1	no	—
100	C₄⋊Dic₁₁	—	4	1	no	—
101	C₄⋊Dic₁₁	—	4	1	no	—
102	Dic₁₁⋊C₄	—	4	2	no	—
103	Dic₁₁⋊C₄	—	4	2	no	—
104	Dic₁₁⋊C₄	—	4	2	no	—
105	Dic₁₁⋊C₄	—	4	2	no	—
106	C₄×Dic₁₁	—	4	2	no	—
107	C₄×Dic₁₁	—	4	2	no	—
108	C₄×Dic₁₁	—	4	2	no	—
109	Dic₄₄	—	2	4	no	—
110	Dic₄₄	—	2	2	no	—
111	Dic₄₄	C₂×Q₈	1	4	yes	—
112	C₁₁×C₁₆	—	2	4	no	—
113	#3160	—	11	1	no	—
114	C₂×C₄×Q₁₆	—	11	1	no	—
115	#2229	—	11	4	no	—
116	#2227	—	11	2	no	—
117	#2225	—	11	2	no	—
118	#2159	—	11	2	no	—
119	#2150	D₁₁	1	1	yes	characteristic
120	#2141	—	11	2	no	—
121	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	4	1	no	—
124	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
125	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
130	C₂×C₄×C₁₁	#137	1	2	yes	—
131	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
132	C₂×Dic₁₁	—	4	2	no	—
133	C₂×Dic₁₁	—	4	4	no	—
134	C₂×Dic₁₁	—	4	2	no	—
135	C₂×Dic₁₁	—	4	2	no	—
136	C₂×Dic₁₁	—	4	2	no	—
137	C₂×Dic₁₁	—	8	2	no	—
138	Dic₂₂	—	2	4	no	—
139	Dic₂₂	—	4	2	no	—
140	Dic₂₂	—	4	4	no	—
141	Dic₂₂	—	8	2	no	—
142	Dic₂₂	—	8	2	no	—
143	C₈×C₁₁	—	2	1	no	—
144	C₈×C₁₁	—	2	1	no	—
145	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
146	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
147	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
148	C₂²×Q₁₆	—	11	1	no	—
149	#533	—	22	1	no	—
150	C₂×C₄×Q₈	—	22	1	no	—
151	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
152	#500	—	11	1	no	—
153	#500	—	11	1	no	—
154	#499	—	11	2	no	—
155	#499	—	22	1	no	—
156	#498	—	22	1	no	—
157	C₄×Q₁₆	—	11	2	no	—
158	C₄×Q₁₆	—	11	2	no	—
159	C₄×Q₁₆	—	22	1	no	—
160	C₄×Q₁₆	—	22	1	no	—
161	#427	—	11	2	no	—
162	#427	—	22	1	no	—
163	C₂×#107	—	11	1	no	—
164	C₂×#103	—	22	1	no	—
165	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
166	#367	—	11	4	no	—
167	#366	—	11	4	no	—
168	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
169	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
170	#358	—	11	4	no	—
171	#358	—	11	4	no	—
172	C₂²×C₁₁	—	2	1	no	—
173	C₂²×C₁₁	—	2	1	no	—
174	C₂²×C₁₁	#474	1	2	yes	—
175	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
176	C₄×C₁₁	—	2	1	no	—
177	C₄×C₁₁	—	2	1	no	—
178	C₄×C₁₁	—	2	1	no	—
179	C₄×C₁₁	#474	1	2	yes	—
180	C₄×C₁₁	#510	1	2	yes	—
181	C₄×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
182	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
183	Dic₁₁	—	4	4	no	—
184	Dic₁₁	—	8	2	no	—
185	Dic₁₁	—	8	2	no	—
186	Dic₁₁	—	8	2	no	—
187	C₂²×Q₈	—	22	1	no	—
188	C₂×Q₁₆	—	11	4	no	—
189	C₂×Q₁₆	—	11	2	no	—
190	C₂×Q₁₆	—	22	1	no	—
191	C₂×Q₁₆	—	22	2	no	—
192	C₂²×C₈	D₄₄	1	1	yes	characteristic
193	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
194	C₄⋊Q₈	—	22	1	no	—
195	C₄⋊Q₈	—	22	1	no	—
196	#125	—	22	2	no	—
197	C₂²⋊Q₈	—	44	1	no	—
198	C₂²⋊Q₈	—	44	1	no	—
199	C₄×Q₈	—	22	2	no	—
200	C₄×Q₈	—	22	2	no	—
201	C₄×Q₈	—	44	1	no	—
202	C₄×Q₈	—	44	1	no	—
203	C₄×Q₈	—	44	1	no	—
204	C₄×Q₈	—	44	1	no	—
205	#117	—	22	2	no	—
206	C₂×C₄⋊C₄	—	22	1	no	—
207	C₂×C₄⋊C₄	—	44	1	no	—
208	C₂×C₄²	—	44	1	no	—
209	C₂×C₄²	D₄₄	1	1	yes	characteristic
210	M₃₂	—	2	4	no	—
211	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
212	#107	—	11	2	no	—
213	#107	—	11	2	no	—
214	#107	—	11	2	no	—
215	#107	—	22	1	no	—
216	#107	—	22	1	no	—
217	#107	—	22	1	no	—
218	#106	—	22	2	no	—
219	#106	—	22	2	no	—
220	#103	—	22	2	no	—
221	#103	—	22	2	no	—
222	C₄×C₈	D₄₄	1	1	yes	characteristic
223	C₄×C₈	D₄₄	1	1	yes	characteristic
224	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
225	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
226	C₂×C₁₁	—	2	2	no	—
227	C₂×C₁₁	C₂×#474	1	1	yes	characteristic
228	C₂×C₁₁	C₂×#510	1	1	yes	characteristic
229	C₂×C₁₁	#3414	1	1	yes	characteristic
230	C₂×Q₈	—	22	4	no	—
231	C₂×Q₈	—	22	2	no	—
232	C₂×Q₈	—	44	1	no	—
233	C₂×Q₈	—	44	1	no	—
234	C₂×Q₈	—	44	1	no	—
235	C₂×Q₈	—	44	2	no	—
236	C₂²×C₄	—	44	1	no	—
237	C₂²×C₄	—	44	1	no	—
238	C₂²×C₄	D₈₈	1	1	yes	characteristic
239	C₂²×C₄	D₈₈	1	1	yes	characteristic
240	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
241	Q₁₆	—	11	4	no	—
242	Q₁₆	—	22	4	no	—
243	Q₁₆	—	22	2	no	—
244	C₂×C₈	—	2	2	no	—
245	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
246	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
247	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
248	C₂×C₈	#4341	1	2	yes	—
249	C₂×C₈	Q₈×D₁₁	1	2	yes	—
250	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
251	C₄⋊C₄	—	22	2	no	—
252	C₄⋊C₄	—	22	2	no	—
253	C₄⋊C₄	—	22	2	no	—
254	C₄⋊C₄	—	44	1	no	—
255	C₄⋊C₄	—	44	2	no	—
256	C₄⋊C₄	—	44	2	no	—
257	C₄⋊C₄	—	44	2	no	—
258	C₄⋊C₄	—	44	2	no	—
259	C₄⋊C₄	—	44	1	no	—
260	C₄⋊C₄	—	44	1	no	—
261	C₂²⋊C₄	—	44	2	no	—
262	C₄²	—	44	2	no	—
263	C₄²	—	44	2	no	—
264	C₄²	—	44	2	no	—
265	C₄²	D₈₈	1	1	yes	characteristic
266	C₄²	D₈₈	1	1	yes	characteristic
267	C₄²	C₂×D₄₄	1	1	yes	characteristic
268	C₄²	C₂×D₄₄	1	1	yes	characteristic
269	C₁₆	—	2	4	no	—
270	C₁₁	#33628	1	1	yes	characteristic, complemented, Sylow
271	C₂³	C₂×D₈₈	1	1	yes	characteristic
272	Q₈	—	22	4	no	—
273	Q₈	—	44	2	no	—
274	Q₈	—	44	4	no	—
275	Q₈	—	88	2	no	—
276	Q₈	—	88	2	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	4	1	no	—
279	C₂×C₄	—	44	2	no	—
280	C₂×C₄	—	44	4	no	—
281	C₂×C₄	—	44	2	no	—
282	C₂×C₄	—	44	2	no	—
283	C₂×C₄	—	44	2	no	—
284	C₂×C₄	—	88	2	no	—
285	C₂×C₄	#66950	1	2	yes	—
286	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
287	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
288	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
289	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
290	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
291	C₂×C₄	#66962	1	2	yes	—
292	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
293	C₈	—	2	1	no	—
294	C₈	—	2	1	no	—
295	C₈	#66950	1	2	yes	—
296	C₈	C₂×#4341	1	1	yes	characteristic
297	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
298	C₂²	—	2	1	no	—
299	C₂²	—	2	1	no	—
300	C₂²	#10622459	1	2	yes	—
301	C₂²	C₂²×D₈₈	1	1	yes	characteristic
302	C₄	—	2	1	no	—
303	C₄	—	2	1	no	—
304	C₄	—	2	1	no	—
305	C₄	—	44	4	no	—
306	C₄	—	88	2	no	—
307	C₄	—	88	2	no	—
308	C₄	—	88	2	no	—
309	C₄	#10622459	1	2	yes	—
310	C₄	#10622522	1	2	yes	—
311	C₄	C₂×#66950	1	1	yes	characteristic
312	C₄	C₂×#66962	1	1	yes	characteristic
313	C₂	—	2	2	no	—
314	C₂	C₂×#10622459	1	1	yes	characteristic
315	C₂	C₂×#10622522	1	1	yes	characteristic
316	C₂	#13081752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2150	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	#2150	D₁₁
hypocenter	C₁₁	#33628
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #2150

Complements

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

N	H ≅ G/N	type
3. #13070781	C₂	semidirect
4. #13070769	C₂	semidirect
5. #13070759	C₂	semidirect
45. C₂×Dic₄₄	Q₈	semidirect
270. C₁₁	#33628	semidirect

Maximal subgroups

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

subgroup	index
#13079130	2
C₂×C₄×Dic₄₄	2
#13070781	2
#13070769	2
#13070759	2
#13070404	2
#13070337	2
C₁₁×#2150	2
#33628	11