Subgroups — #14647607

Order 2816.

556 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#13068593	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₁₁)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#10622095	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10622118	C₂	1	1	yes	maximal, characteristic, complemented
6	#13066450	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₁₁	—	2	1	no	—
9	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₁₁)⋊C₈	—	2	1	no	—
14	C₂×(C₂×D₁₁)⋊C₈	C₄	1	1	yes	characteristic
15	C₂×(C₂×D₁₁)⋊C₈	C₄	1	1	yes	characteristic
16	C₂×Dic₁₁⋊C₈	—	2	1	no	—
17	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
20	D₁₁×C₄⋊C₈	—	2	2	no	—
21	D₁₁×C₄⋊C₈	—	2	2	no	—
22	#10622188	—	2	1	no	—
23	#10622188	C₄	1	1	yes	characteristic
24	#10622188	C₄	1	1	yes	characteristic
25	#10622118	—	2	2	no	—
26	#10622095	—	2	2	no	—
27	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₁	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₁	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	1	no	—
31	C₂²×C₈×C₁₁	—	2	1	no	—
32	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
35	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₁	Q₈	1	1	yes	characteristic
38	C₂²×C₁₁⋊C₈	—	2	1	no	—
39	C₂²×C₁₁⋊C₈	—	2	1	no	—
40	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₁₁	—	2	4	no	—
43	C₂×C₈×D₁₁	—	4	2	no	—
44	C₂×C₈×D₁₁	—	4	2	no	—
45	C₄²×D₁₁	—	2	1	no	—
46	C₄²×D₁₁	—	2	1	no	—
47	C₄²×D₁₁	—	2	1	no	—
48	C₄²×D₁₁	—	2	1	no	—
49	C₁₁×C₄⋊C₈	—	2	1	no	—
50	C₁₁×C₄⋊C₈	—	2	1	no	—
51	C₁₁×C₄⋊C₈	—	2	1	no	—
52	C₁₁×C₄⋊C₈	D₄	1	2	yes	—
53	C₄×C₈×C₁₁	—	2	1	no	—
54	C₄×C₈×C₁₁	—	2	1	no	—
55	(C₂×D₁₁)⋊C₈	—	2	2	no	—
56	(C₂×D₁₁)⋊C₈	—	4	2	no	—
57	(C₂×D₁₁)⋊C₈	C₈	1	4	yes	complemented
58	Dic₁₁⋊C₈	—	2	4	no	—
59	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
63	C₄×C₁₁⋊C₈	—	2	1	no	—
64	C₄×C₁₁⋊C₈	—	2	1	no	—
65	#8830	—	11	1	no	maximal, Sylow
66	C₂³×D₁₁	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
70	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×Dic₁₁	C₄⋊C₄	1	1	yes	characteristic
73	C₂×C₄×D₁₁	—	2	2	no	—
74	C₂×C₄×D₁₁	—	2	1	no	—
75	C₂×C₄×D₁₁	—	2	1	no	—
76	C₂×C₄×D₁₁	—	2	1	no	—
77	C₂×C₄×D₁₁	—	2	1	no	—
78	C₂×C₄×D₁₁	—	2	1	no	—
79	C₂×C₄×D₁₁	—	2	1	no	—
80	C₂×C₄×D₁₁	—	2	1	no	—
81	C₂×C₄×D₁₁	—	2	1	no	—
82	C₂×C₄×D₁₁	—	2	1	no	—
83	C₂×C₄×D₁₁	—	2	1	no	—
84	C₂×C₄×D₁₁	—	4	1	no	—
85	C₂×C₄×D₁₁	C₂×C₈	1	2	yes	—
86	C₂×C₄×D₁₁	M₁₆	1	2	yes	—
87	C₂×C₄×D₁₁	SD₁₆	1	2	yes	—
88	C₂×C₄×D₁₁	SD₁₆	1	2	yes	—
89	C₂×C₈×C₁₁	—	2	1	no	—
90	C₂×C₈×C₁₁	—	2	1	no	—
91	C₂×C₈×C₁₁	—	2	2	no	—
92	C₂×C₈×C₁₁	—	2	1	no	—
93	C₂×C₈×C₁₁	—	2	1	no	—
94	C₂×C₈×C₁₁	—	2	1	no	—
95	C₂×C₈×C₁₁	—	4	1	no	—
96	C₂×C₈×C₁₁	—	4	1	no	—
97	C₂×C₈×C₁₁	—	4	1	no	—
98	C₂×C₈×C₁₁	—	4	1	no	—
99	C₂×C₈×C₁₁	—	4	1	no	—
100	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	complemented
101	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₁₁	#41	1	1	yes	characteristic
104	C₄²×C₁₁	#41	1	1	yes	characteristic
105	C₄×Dic₁₁	—	2	1	no	—
106	C₄×Dic₁₁	—	2	1	no	—
107	C₄×Dic₁₁	—	2	1	no	—
108	C₄×Dic₁₁	—	2	1	no	—
109	C₄×Dic₁₁	—	2	1	no	—
110	C₄×Dic₁₁	—	2	1	no	—
111	C₂×C₁₁⋊C₈	—	2	1	no	—
112	C₂×C₁₁⋊C₈	—	2	1	no	—
113	C₂×C₁₁⋊C₈	—	2	2	no	—
114	C₂×C₁₁⋊C₈	—	2	1	no	—
115	C₂×C₁₁⋊C₈	—	2	1	no	—
116	C₂×C₁₁⋊C₈	—	2	1	no	—
117	C₂×C₁₁⋊C₈	—	4	1	no	—
118	C₂×C₁₁⋊C₈	—	4	1	no	—
119	C₂×C₁₁⋊C₈	—	4	1	no	—
120	C₂×C₁₁⋊C₈	—	4	1	no	—
121	C₂×C₁₁⋊C₈	—	4	1	no	—
122	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	complemented
123	C₈×D₁₁	—	4	8	no	—
124	C₂²×C₄⋊C₈	—	11	1	no	—
125	#1797	—	11	1	no	—
126	C₄×C₂²⋊C₈	—	11	1	no	—
127	C₂×#334	—	11	1	no	—
128	C₂×#334	—	11	1	no	—
129	#1277	—	11	1	no	—
130	#1277	D₁₁	1	1	yes	characteristic, complemented
131	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂²×D₁₁	—	2	1	no	—
133	C₂²×D₁₁	—	2	1	no	—
134	C₂²×D₁₁	—	2	1	no	—
135	C₂²×D₁₁	—	2	1	no	—
136	C₂²×D₁₁	C₄⋊C₈	1	2	yes	—
137	C₂²×D₁₁	#106	1	2	yes	—
138	C₂²×D₁₁	#108	1	2	yes	—
139	C₂×C₄×C₁₁	—	2	1	no	—
140	C₂×C₄×C₁₁	—	2	1	no	—
141	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
146	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
150	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
154	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
155	C₂×Dic₁₁	—	2	1	no	—
156	C₂×Dic₁₁	—	2	1	no	—
157	C₂×Dic₁₁	—	2	1	no	—
158	C₂×Dic₁₁	—	2	1	no	—
159	C₂×Dic₁₁	—	2	1	no	—
160	C₂×Dic₁₁	—	2	1	no	—
161	C₂×Dic₁₁	—	2	1	no	—
162	C₂×Dic₁₁	C₄⋊C₈	1	2	yes	—
163	C₂×Dic₁₁	#106	1	2	yes	—
164	C₄×D₁₁	—	2	2	no	—
165	C₄×D₁₁	—	2	2	no	—
166	C₄×D₁₁	—	2	2	no	—
167	C₄×D₁₁	—	2	2	no	—
168	C₄×D₁₁	—	2	2	no	—
169	C₄×D₁₁	—	2	2	no	—
170	C₄×D₁₁	—	2	2	no	—
171	C₄×D₁₁	—	2	2	no	—
172	C₄×D₁₁	—	4	2	no	—
173	C₄×D₁₁	—	4	2	no	—
174	C₈×C₁₁	—	2	2	no	—
175	C₈×C₁₁	—	4	1	no	—
176	C₈×C₁₁	—	4	2	no	—
177	C₈×C₁₁	—	8	1	no	—
178	C₁₁⋊C₈	—	2	2	no	—
179	C₁₁⋊C₈	—	4	1	no	—
180	C₁₁⋊C₈	—	4	2	no	—
181	C₁₁⋊C₈	—	8	1	no	—
182	C₂³×C₈	—	22	1	no	—
183	C₂²×C₄²	—	11	1	no	—
184	C₂×C₄⋊C₈	—	11	1	no	—
185	C₂×C₄⋊C₈	—	11	1	no	—
186	C₂×C₄⋊C₈	—	22	2	no	—
187	C₂×C₄⋊C₈	—	22	1	no	—
188	C₂×C₄⋊C₈	—	22	2	no	—
189	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
190	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
191	C₂×C₂²⋊C₈	—	11	1	no	—
192	C₂×C₂²⋊C₈	—	11	1	no	—
193	C₂×C₂²⋊C₈	—	22	1	no	—
194	C₂×C₄×C₈	—	11	1	no	—
195	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
196	#336	—	11	1	no	—
197	#336	—	11	1	no	—
198	#336	—	22	1	no	—
199	#334	—	22	2	no	—
200	#334	—	22	2	no	—
201	C₂²×C₁₁	#385	1	1	yes	characteristic
202	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
203	C₂²×C₁₁	#424	1	1	yes	characteristic
204	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
205	C₂²×C₁₁	#428	1	1	yes	characteristic
206	C₂²×C₁₁	C₂×#108	1	1	yes	characteristic
207	C₂²×C₁₁	#430	1	1	yes	characteristic
208	C₂×D₁₁	—	2	2	no	—
209	C₂×D₁₁	—	2	2	no	—
210	C₂×D₁₁	—	2	2	no	—
211	C₂×D₁₁	—	2	2	no	—
212	C₂×D₁₁	—	2	2	no	—
213	C₂×D₁₁	—	2	2	no	—
214	C₂×D₁₁	#334	1	4	yes	complemented
215	C₄×C₁₁	—	2	1	no	—
216	C₄×C₁₁	—	2	1	no	—
217	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
218	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
219	C₄×C₁₁	#435	1	1	yes	characteristic
220	C₄×C₁₁	#435	1	1	yes	characteristic
221	C₄×C₁₁	#448	1	1	yes	characteristic
222	C₄×C₁₁	#450	1	1	yes	characteristic
223	C₄×C₁₁	#481	1	1	yes	characteristic
224	C₄×C₁₁	#483	1	1	yes	characteristic
225	Dic₁₁	—	2	2	no	—
226	Dic₁₁	—	2	2	no	—
227	Dic₁₁	—	4	1	no	—
228	C₂³×C₄	—	11	1	no	—
229	C₂³×C₄	—	11	1	no	—
230	C₂³×C₄	—	11	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	11	1	no	—
234	C₂²×C₈	—	11	1	no	—
235	C₂²×C₈	—	22	4	no	—
236	C₂²×C₈	—	22	1	no	—
237	C₂²×C₈	—	22	1	no	—
238	C₂²×C₈	—	44	2	no	—
239	C₂²×C₈	—	44	2	no	—
240	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
241	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
242	C₂×C₄²	—	11	1	no	—
243	C₂×C₄²	—	11	1	no	—
244	C₂×C₄²	—	11	1	no	—
245	C₂×C₄²	—	22	1	no	—
246	C₂×C₄²	—	22	1	no	—
247	C₂×C₄²	—	22	1	no	—
248	C₂×C₄²	—	22	1	no	—
249	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	1	no	—
253	C₄⋊C₈	—	11	2	no	—
254	C₄⋊C₈	—	22	4	no	—
255	C₄⋊C₈	—	22	1	no	—
256	C₄⋊C₈	—	22	1	no	—
257	C₄⋊C₈	—	22	1	no	—
258	C₄⋊C₈	D₄₄	1	2	yes	—
259	C₂²⋊C₈	—	11	4	no	—
260	C₂²⋊C₈	—	22	2	no	—
261	C₂²⋊C₈	—	44	2	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	2	1	no	—
264	C₄×C₈	—	22	1	no	—
265	C₄×C₈	—	22	1	no	—
266	C₂×C₁₁	C₂×#334	1	1	yes	characteristic
267	C₂×C₁₁	#1565	1	1	yes	characteristic
268	C₂×C₁₁	#1570	1	1	yes	characteristic
269	C₂×C₁₁	#1573	1	1	yes	characteristic
270	C₂×C₁₁	#1850	1	1	yes	characteristic
271	C₂×C₁₁	#1853	1	1	yes	characteristic
272	C₂×C₁₁	#1855	1	1	yes	characteristic
273	D₁₁	—	2	4	no	—
274	C₂⁴	—	11	1	no	—
275	C₂²×C₄	—	11	1	no	—
276	C₂²×C₄	—	11	1	no	—
277	C₂²×C₄	—	11	2	no	—
278	C₂²×C₄	—	11	2	no	—
279	C₂²×C₄	—	11	2	no	—
280	C₂²×C₄	—	11	2	no	—
281	C₂²×C₄	—	11	1	no	—
282	C₂²×C₄	—	22	2	no	—
283	C₂²×C₄	—	22	1	no	—
284	C₂²×C₄	—	22	1	no	—
285	C₂²×C₄	—	22	1	no	—
286	C₂²×C₄	—	22	1	no	—
287	C₂²×C₄	—	22	1	no	—
288	C₂²×C₄	—	22	1	no	—
289	C₂²×C₄	—	22	1	no	—
290	C₂²×C₄	—	22	1	no	—
291	C₂²×C₄	—	22	1	no	—
292	C₂²×C₄	—	22	1	no	—
293	C₂²×C₄	—	44	1	no	—
294	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
296	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	11	2	no	—
309	C₂×C₈	—	22	1	no	—
310	C₂×C₈	—	22	1	no	—
311	C₂×C₈	—	22	1	no	—
312	C₂×C₈	—	22	2	no	—
313	C₂×C₈	—	22	1	no	—
314	C₂×C₈	—	22	1	no	—
315	C₂×C₈	—	44	8	no	—
316	C₂×C₈	—	44	1	no	—
317	C₂×C₈	—	44	1	no	—
318	C₂×C₈	—	44	1	no	—
319	C₂×C₈	—	44	1	no	—
320	C₂×C₈	—	44	1	no	—
321	C₂×C₈	C₈×D₁₁	1	2	yes	complemented
322	C₄²	—	22	1	no	—
323	C₄²	—	22	1	no	—
324	C₄²	—	22	1	no	—
325	C₄²	—	22	1	no	—
326	C₄²	—	22	1	no	—
327	C₄²	—	22	1	no	—
328	C₄²	C₂×D₄₄	1	1	yes	characteristic
329	C₄²	#4339	1	1	yes	characteristic
330	C₄²	D₄×D₁₁	1	1	yes	characteristic
331	C₄²	#4341	1	1	yes	characteristic
332	C₁₁	#8830	1	1	yes	characteristic, complemented, Sylow
333	C₂³	—	11	2	no	—
334	C₂³	—	11	2	no	—
335	C₂³	—	11	2	no	—
336	C₂³	—	22	1	no	—
337	C₂³	—	22	1	no	—
338	C₂³	—	22	1	no	—
339	C₂³	—	22	1	no	—
340	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	11	2	no	—
344	C₂×C₄	—	11	2	no	—
345	C₂×C₄	—	22	1	no	—
346	C₂×C₄	—	22	1	no	—
347	C₂×C₄	—	22	1	no	—
348	C₂×C₄	—	22	1	no	—
349	C₂×C₄	—	22	2	no	—
350	C₂×C₄	—	22	2	no	—
351	C₂×C₄	—	22	2	no	—
352	C₂×C₄	—	22	2	no	—
353	C₂×C₄	—	22	2	no	—
354	C₂×C₄	—	22	2	no	—
355	C₂×C₄	—	22	2	no	—
356	C₂×C₄	—	22	2	no	—
357	C₂×C₄	—	22	1	no	—
358	C₂×C₄	—	22	1	no	—
359	C₂×C₄	—	22	1	no	—
360	C₂×C₄	—	44	2	no	—
361	C₂×C₄	—	44	2	no	—
362	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
363	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
364	C₂×C₄	#66935	1	1	yes	characteristic
365	C₂×C₄	#66936	1	1	yes	characteristic
366	C₂×C₄	#66949	1	1	yes	characteristic
367	C₂×C₄	#66950	1	1	yes	characteristic
368	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
369	C₂×C₄	#66954	1	1	yes	characteristic
370	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
371	C₂×C₄	#66960	1	1	yes	characteristic
372	C₂×C₄	#66964	1	1	yes	characteristic
373	C₂×C₄	SD₁₆×D₁₁	1	1	yes	characteristic
374	C₂×C₄	SD₁₆×D₁₁	1	1	yes	characteristic
375	C₂×C₄	#66971	1	1	yes	characteristic
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	8	1	no	—
380	C₈	—	22	2	no	—
381	C₈	—	44	1	no	—
382	C₈	—	44	2	no	—
383	C₈	—	88	1	no	—
384	C₂²	—	11	4	no	—
385	C₂²	—	22	2	no	—
386	C₂²	—	22	2	no	—
387	C₂²	—	22	2	no	—
388	C₂²	—	22	2	no	—
389	C₂²	—	22	2	no	—
390	C₂²	—	22	2	no	—
391	C₂²	#10622281	1	1	yes	characteristic
392	C₂²	D₁₁×C₄⋊C₈	1	1	yes	characteristic
393	C₂²	#10622452	1	1	yes	characteristic
394	C₂²	D₁₁×#106	1	1	yes	characteristic
395	C₂²	#10622494	1	1	yes	characteristic
396	C₂²	D₁₁×#108	1	1	yes	characteristic
397	C₂²	#10622506	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	22	2	no	—
401	C₄	—	22	2	no	—
402	C₄	—	44	1	no	—
403	C₄	C₈×D₄₄	1	1	yes	characteristic
404	C₄	#10622319	1	1	yes	characteristic
405	C₄	(C₂²⋊D₁₁)⋊C₈	1	1	yes	characteristic
406	C₄	#10622341	1	1	yes	characteristic
407	C₄	#10622389	1	1	yes	characteristic
408	C₄	#10622390	1	1	yes	characteristic
409	C₄	#10622418	1	1	yes	characteristic
410	C₄	#10622419	1	1	yes	characteristic
411	C₂	—	22	4	no	—
412	C₂	D₁₁×#334	1	1	yes	characteristic
413	C₂	#13067367	1	1	yes	characteristic
414	C₂	#13067385	1	1	yes	characteristic
415	C₂	#13067400	1	1	yes	characteristic
416	C₂	#13068795	1	1	yes	characteristic
417	C₂	#13068810	1	1	yes	characteristic
418	C₂	#13068822	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1277	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂³×D₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1277	D₁₁
hypocenter	C₁₁	#8830
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
4. C₂×#10622095	C₂	semidirect
5. C₂×#10622118	C₂	semidirect
6. #13066450	C₂	semidirect
7. C₁₁×#1277	C₂	semidirect
57. (C₂×D₁₁)⋊C₈	C₈	semidirect
100. C₂×C₈×C₁₁	C₂×C₈	semidirect
122. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
130. #1277	D₁₁	semidirect
214. C₂×D₁₁	#334	semidirect
321. C₂×C₈	C₈×D₁₁	semidirect
332. C₁₁	#8830	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₁×C₄⋊C₈	2
#13068593	2
C₄×(C₂×D₁₁)⋊C₈	2
C₂×#10622095	2
C₂×#10622118	2
#13066450	2
C₁₁×#1277	2
#8830	11