Subgroups — #14723405

Order 2816.

700 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077733	C₂	1	1	yes	maximal, characteristic, complemented
2	#13077639	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#67002	C₂	1	1	yes	maximal, characteristic
4	#13067483	C₂	1	2	yes	maximal, complemented
5	#13067476	C₂	1	2	yes	maximal, complemented
6	#13067455	C₂	1	2	yes	maximal, complemented
7	#13067448	C₂	1	2	yes	maximal, complemented
8	#13067369	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#10622097	C₂	1	1	yes	maximal, characteristic, complemented
10	#13066905	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
13	C₂×#67002	C₄	1	1	yes	characteristic
14	C₂×C₄×D₄₄	C₂²	1	1	yes	characteristic
15	C₁₁×#431	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	#10622845	C₄	1	1	yes	characteristic
18	#10622639	C₄	1	2	yes	—
19	C₄×#4325	C₂²	1	2	yes	—
20	#10622637	C₂²	1	2	yes	complemented
21	#10622627	C₄	1	2	yes	—
22	C₄×#4323	C₂²	1	2	yes	—
23	#10622625	C₂²	1	2	yes	complemented
24	#10622624	—	2	2	no	—
25	#10622614	C₄	1	1	yes	characteristic
26	#10622608	C₄	1	1	yes	characteristic
27	#10622539	—	2	1	no	—
28	#10622538	C₂²	1	1	yes	characteristic
29	#10622537	—	2	1	no	—
30	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
31	C₄×#4318	C₂²	1	1	yes	characteristic
32	#10622447	C₂²	1	2	yes	—
33	#10622447	C₂²	1	2	yes	—
34	D₁₁×C₂²⋊C₈	—	2	2	no	—
35	C₈×D₄₄	—	2	1	no	—
36	C₈×D₄₄	—	2	1	no	—
37	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
38	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₁₁×D₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	#10622118	C₂²	1	2	yes	complemented
42	#10622117	C₂²	1	2	yes	complemented
43	#10622097	C₂²	1	2	yes	—
44	#10622097	C₂²	1	2	yes	—
45	#10622093	C₂²	1	2	yes	complemented
46	#10622092	C₂²	1	2	yes	complemented
47	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₄₄	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₁₁	—	2	1	no	—
50	C₂²×C₈×C₁₁	—	2	1	no	—
51	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₄×D₄×C₁₁	—	2	1	no	—
54	C₄×D₄×C₁₁	—	2	1	no	—
55	C₄×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
56	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
57	C₁₁×#117	—	2	1	no	—
58	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	—	2	1	no	—
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	#67002	—	2	4	no	—
62	C₂×#4325	C₂×C₄	1	2	yes	—
63	C₂×#4323	C₂×C₄	1	2	yes	—
64	C₂×(C₂×D₁₁)⋊C₄	—	2	1	no	—
65	C₂×C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
66	C₂×#4318	—	2	2	no	—
67	C₂×#4318	C₂×C₄	1	1	yes	characteristic
68	C₂×#4318	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₁₁⋊C₈	—	2	1	no	—
70	C₂×C₈×D₁₁	—	2	2	no	—
71	C₂×C₈×D₁₁	—	2	2	no	—
72	C₄×D₄₄	—	2	1	no	—
73	C₄×D₄₄	—	2	1	no	—
74	C₄×D₄₄	C₂×C₄	1	2	yes	—
75	C₄×D₄₄	C₂³	1	2	yes	—
76	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₁×C₂²⋊C₈	—	2	1	no	—
79	C₄×C₈×C₁₁	—	2	1	no	—
80	C₄×C₈×C₁₁	—	2	1	no	—
81	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
82	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
83	#66899	C₂×C₄	1	2	yes	—
84	#66896	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₁₁⋊C₈)	D₄	1	2	yes	—
87	(C₂×D₁₁)⋊C₈	—	2	2	no	—
88	(C₂×D₁₁)⋊C₈	—	2	2	no	—
89	#66873	C₂×C₄	1	2	yes	—
90	#66873	C₂×C₄	1	2	yes	—
91	#66872	C₂×C₄	1	2	yes	—
92	#66871	C₂×C₄	1	2	yes	—
93	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
94	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
95	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
96	C₄⋊(C₁₁⋊C₈)	D₄	1	1	yes	characteristic
97	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
98	#66867	—	2	2	no	—
99	#66867	C₂×C₄	1	2	yes	—
100	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
101	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
102	#17873	—	11	1	no	maximal, Sylow
103	C₂³×D₁₁	—	2	1	no	—
104	C₁₁×#41	—	2	2	no	—
105	C₁₁×#41	—	2	2	no	—
106	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₁₁	—	2	1	no	—
108	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	—	2	1	no	—
111	C₂²×C₄×C₁₁	—	2	1	no	—
112	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
115	C₂²×Dic₁₁	—	2	1	no	—
116	C₂×D₄₄	—	2	1	no	—
117	C₂×D₄₄	—	2	2	no	—
118	C₂×D₄₄	M₁₆	1	4	yes	complemented
119	C₂×D₄₄	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₁₁	—	2	2	no	—
121	C₂×C₄×D₁₁	—	2	2	no	—
122	C₂×C₄×D₁₁	—	8	1	no	—
123	C₂×C₄×D₁₁	—	8	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	2	1	no	—
126	C₂×C₈×C₁₁	—	2	1	no	—
127	C₂×C₈×C₁₁	—	2	1	no	—
128	C₂×C₈×C₁₁	—	4	2	no	—
129	C₁₁×C₄⋊C₄	—	2	1	no	—
130	C₁₁×C₄⋊C₄	—	2	1	no	—
131	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
132	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
133	C₁₁×C₂²⋊C₄	—	2	1	no	—
134	C₁₁×C₂²⋊C₄	—	2	1	no	—
135	C₁₁×C₂²⋊C₄	—	2	1	no	—
136	C₄²×C₁₁	—	2	1	no	—
137	C₄²×C₁₁	—	2	1	no	—
138	C₄²×C₁₁	—	2	1	no	—
139	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₁₁	#41	1	1	yes	characteristic
142	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
143	#4325	—	2	4	no	—
144	#4323	—	2	4	no	—
145	(C₂×D₁₁)⋊C₄	—	2	2	no	—
146	(C₂×D₁₁)⋊C₄	—	2	2	no	—
147	C₄⋊Dic₁₁	—	2	1	no	—
148	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
149	#4318	—	2	2	no	—
150	#4318	—	2	2	no	—
151	#4318	—	8	2	no	—
152	C₂×C₁₁⋊C₈	—	2	2	no	—
153	C₂×C₁₁⋊C₈	—	8	1	no	—
154	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
157	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
158	C₈×D₁₁	—	8	2	no	—
159	C₈×D₁₁	—	8	2	no	—
160	#2989	—	11	1	no	—
161	#2972	—	11	1	no	—
162	C₄×AGL(1,ℤ/8)	—	11	1	no	—
163	#1586	—	11	2	no	—
164	#1585	—	11	2	no	—
165	#1582	—	11	2	no	—
166	#1581	—	11	2	no	—
167	#1565	—	11	1	no	—
168	#1476	D₁₁	1	1	yes	characteristic, complemented
169	C₂×D₄⋊C₈	—	11	1	no	—
170	#1451	—	11	1	no	—
171	C₂³×C₁₁	—	2	1	no	—
172	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
173	C₂²×D₁₁	—	2	2	no	—
174	C₂²×D₁₁	—	2	4	no	—
175	C₂²×D₁₁	—	8	1	no	—
176	C₂²×D₁₁	—	8	1	no	—
177	Q₈×C₁₁	—	2	1	no	—
178	Q₈×C₁₁	—	2	1	no	—
179	D₄×C₁₁	—	2	1	no	—
180	D₄×C₁₁	—	2	1	no	—
181	D₄×C₁₁	—	4	2	no	—
182	C₂×C₄×C₁₁	—	2	1	no	—
183	C₂×C₄×C₁₁	—	2	1	no	—
184	C₂×C₄×C₁₁	—	2	1	no	—
185	C₂×C₄×C₁₁	—	2	1	no	—
186	C₂×C₄×C₁₁	—	2	1	no	—
187	C₂×C₄×C₁₁	—	4	1	no	—
188	C₂×C₄×C₁₁	—	4	1	no	—
189	C₂×C₄×C₁₁	—	4	1	no	—
190	C₂×C₄×C₁₁	—	4	2	no	—
191	C₂×C₄×C₁₁	—	8	1	no	—
192	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
196	C₂×C₄×C₁₁	#131	1	2	yes	—
197	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
200	C₂×Dic₁₁	—	2	2	no	—
201	C₂×Dic₁₁	—	8	1	no	—
202	D₄₄	—	2	2	no	—
203	D₄₄	—	2	4	no	—
204	D₄₄	C₂×M₁₆	1	4	yes	—
205	C₄×D₁₁	—	4	2	no	—
206	C₄×D₁₁	—	4	2	no	—
207	C₄×D₁₁	—	8	2	no	—
208	C₈×C₁₁	—	2	2	no	—
209	C₈×C₁₁	—	4	1	no	—
210	C₈×C₁₁	—	4	1	no	—
211	C₈×C₁₁	—	4	1	no	—
212	C₁₁⋊C₈	—	2	2	no	—
213	C₁₁⋊C₈	—	2	2	no	—
214	C₁₁⋊C₈	—	2	2	no	—
215	C₁₁⋊C₈	—	2	2	no	—
216	C₁₁⋊C₈	—	4	2	no	—
217	C₂×AGL(1,ℤ/8)	—	11	1	no	—
218	C₄×#41	C₂×D₁₁	1	1	yes	characteristic
219	C₂×C₄×D₄	—	11	1	no	—
220	#446	—	11	2	no	—
221	#442	—	11	2	no	—
222	#440	—	11	2	no	—
223	C₄×SD₁₆	—	11	2	no	—
224	C₄×D₈	—	11	2	no	—
225	#436	—	11	2	no	—
226	#435	—	22	2	no	—
227	C₈×D₄	—	11	2	no	—
228	C₈×D₄	—	11	2	no	—
229	C₈×D₄	—	22	1	no	—
230	C₈×D₄	—	22	1	no	—
231	#432	—	22	1	no	—
232	#431	—	11	1	no	—
233	#431	C₂×D₁₁	1	1	yes	characteristic
234	#428	—	11	1	no	—
235	#423	—	22	1	no	—
236	C₂×C₄⋊C₈	—	11	1	no	—
237	#418	—	11	1	no	—
238	#417	—	11	1	no	—
239	C₂×C₂²⋊C₈	—	22	2	no	—
240	C₄×M₁₆	—	11	1	no	—
241	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
242	#335	—	11	2	no	—
243	#334	—	11	2	no	—
244	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
245	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
246	D₄⋊C₈	—	11	2	no	—
247	D₄⋊C₈	—	11	2	no	—
248	D₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
249	D₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic, complemented
250	#322	—	11	2	no	—
251	#322	—	11	2	no	—
252	C₂²×C₁₁	—	2	1	no	—
253	C₂²×C₁₁	—	2	1	no	—
254	C₂²×C₁₁	—	4	1	no	—
255	C₂²×C₁₁	—	4	1	no	—
256	C₂²×C₁₁	—	4	1	no	—
257	C₂²×C₁₁	#435	1	2	yes	—
258	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₁₁	—	2	4	no	—
260	C₂×D₁₁	—	4	2	no	—
261	C₂×D₁₁	—	4	2	no	—
262	C₂×D₁₁	—	8	4	no	—
263	C₄×C₁₁	—	2	1	no	—
264	C₄×C₁₁	—	2	1	no	—
265	C₄×C₁₁	—	2	1	no	—
266	C₄×C₁₁	—	4	1	no	—
267	C₄×C₁₁	—	4	1	no	—
268	C₄×C₁₁	—	4	1	no	—
269	C₄×C₁₁	#435	1	2	yes	—
270	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
271	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
272	C₄×C₁₁	#576	1	1	yes	characteristic
273	C₄×C₁₁	#577	1	1	yes	characteristic
274	Dic₁₁	—	4	2	no	—
275	C₂×#41	C₄×D₁₁	1	1	yes	characteristic
276	C₂²×D₄	—	11	1	no	—
277	C₂³×C₄	—	22	1	no	—
278	AGL(1,ℤ/8)	—	22	4	no	—
279	C₂×SD₁₆	—	11	2	no	—
280	C₂×D₈	—	11	2	no	—
281	C₂×M₁₆	—	11	1	no	—
282	C₂×M₁₆	—	11	1	no	—
283	C₂×M₁₆	—	22	2	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	22	2	no	—
286	C₂²×C₈	—	22	2	no	—
287	C₂²×C₈	—	22	1	no	—
288	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	11	2	no	—
293	C₄×D₄	—	11	2	no	—
294	C₄×D₄	—	22	1	no	—
295	C₄×D₄	—	22	1	no	—
296	C₄×D₄	C₄×D₁₁	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	C₄×D₁₁	1	1	yes	characteristic
300	C₂×C₄⋊C₄	—	11	1	no	—
301	C₂×C₂²⋊C₄	—	22	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
304	#107	—	11	2	no	—
305	#106	—	11	2	no	—
306	C₄⋊C₈	—	11	1	no	—
307	C₄⋊C₈	—	11	1	no	—
308	C₄⋊C₈	—	11	2	no	—
309	C₄⋊C₈	—	22	2	no	—
310	C₄⋊C₈	—	22	1	no	—
311	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
313	#103	—	11	2	no	—
314	#102	—	11	2	no	—
315	#102	—	11	2	no	—
316	#102	—	11	2	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	11	2	no	—
319	C₂²⋊C₈	—	22	2	no	—
320	C₂²⋊C₈	—	22	2	no	—
321	C₂²⋊C₈	—	22	2	no	—
322	#97	—	11	2	no	—
323	#97	—	22	2	no	—
324	C₄×C₈	—	2	1	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	—	11	2	no	—
327	C₄×C₈	—	11	2	no	—
328	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
330	C₂×C₁₁	—	2	2	no	—
331	C₂×C₁₁	—	8	1	no	—
332	C₂×C₁₁	C₂×#435	1	1	yes	characteristic
333	C₂×C₁₁	#2946	1	1	yes	characteristic
334	C₂×C₁₁	#2956	1	1	yes	characteristic
335	D₁₁	—	4	4	no	—
336	C₂⁴	—	22	1	no	—
337	#41	—	2	2	no	—
338	#41	—	2	2	no	—
339	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	11	4	no	—
342	C₂×D₄	—	11	2	no	—
343	C₂×D₄	—	22	1	no	—
344	C₂×D₄	—	22	2	no	—
345	C₂×D₄	C₂×C₄×D₁₁	1	1	yes	characteristic
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	22	1	no	—
350	C₂²×C₄	—	22	2	no	—
351	C₂²×C₄	—	22	2	no	—
352	C₂²×C₄	—	88	1	no	—
353	C₂²×C₄	—	88	1	no	—
354	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
356	C₂²×C₄	#4341	1	1	yes	characteristic
357	SD₁₆	—	22	4	no	—
358	D₈	—	22	4	no	—
359	M₁₆	—	22	2	no	—
360	M₁₆	—	22	2	no	—
361	M₁₆	—	88	2	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	11	2	no	—
368	C₂×C₈	—	11	2	no	—
369	C₂×C₈	—	11	2	no	—
370	C₂×C₈	—	11	2	no	—
371	C₂×C₈	—	22	2	no	—
372	C₂×C₈	—	88	2	no	—
373	C₂×C₈	—	88	2	no	—
374	C₂×C₈	—	88	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	11	2	no	—
378	C₄⋊C₄	—	22	1	no	—
379	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
380	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
381	C₂²⋊C₄	—	2	1	no	—
382	C₂²⋊C₄	—	2	1	no	—
383	C₂²⋊C₄	—	2	1	no	—
384	C₂²⋊C₄	—	22	2	no	—
385	C₂²⋊C₄	—	22	2	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
390	C₄²	D₄×D₁₁	1	1	yes	characteristic
391	C₄²	#4341	1	1	yes	characteristic
392	C₄²	C₂³×D₁₁	1	1	yes	characteristic
393	C₁₁	#17873	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	2	1	no	—
395	C₂³	—	22	2	no	—
396	C₂³	—	22	4	no	—
397	C₂³	—	88	1	no	—
398	C₂³	—	88	1	no	—
399	C₂³	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	2	1	no	—
402	D₄	—	2	1	no	—
403	D₄	—	2	1	no	—
404	D₄	—	4	2	no	—
405	D₄	—	11	4	no	—
406	D₄	—	22	2	no	—
407	D₄	—	22	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	8	1	no	—
418	C₂×C₄	—	22	2	no	—
419	C₂×C₄	—	44	2	no	—
420	C₂×C₄	—	44	2	no	—
421	C₂×C₄	—	88	2	no	—
422	C₂×C₄	—	88	1	no	—
423	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
424	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
426	C₂×C₄	#66954	1	2	yes	—
427	C₂×C₄	M₁₆×D₁₁	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
430	C₂×C₄	C₂×#4341	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	22	2	no	—
436	C₈	—	22	2	no	—
437	C₈	—	22	2	no	—
438	C₈	—	22	2	no	—
439	C₈	—	44	2	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	22	4	no	—
446	C₂²	—	44	2	no	—
447	C₂²	—	44	2	no	—
448	C₂²	—	88	4	no	—
449	C₂²	#10622341	1	2	yes	—
450	C₂²	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	4	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	44	2	no	—
458	C₄	#10622341	1	2	yes	—
459	C₄	C₂×#66954	1	1	yes	characteristic
460	C₄	C₂×M₁₆×D₁₁	1	1	yes	characteristic
461	C₄	#10623300	1	1	yes	characteristic
462	C₄	#10623301	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	1	no	—
465	C₂	—	44	4	no	—
466	C₂	C₂×#10622341	1	1	yes	characteristic
467	C₂	#13077451	1	1	yes	characteristic
468	C₂	#13077522	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#1476	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#67002	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#1476	D₁₁
hypocenter	C₁₁	#17873
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
1. #13077733	C₂	semidirect
2. #13077639	C₂	semidirect
4. #13067483	C₂	semidirect
5. #13067476	C₂	semidirect
6. #13067455	C₂	semidirect
7. #13067448	C₂	semidirect
8. #13067369	C₂	semidirect
9. C₂×#10622097	C₂	semidirect
10. #13066905	C₂	semidirect
11. C₁₁×#1476	C₂	semidirect
20. #10622637	C₂²	semidirect
23. #10622625	C₂²	semidirect
37. C₁₁×Q₈⋊C₈	C₂²	semidirect
38. C₁₁×Q₈⋊C₈	C₂²	semidirect
39. C₁₁×D₄⋊C₈	C₂²	semidirect
40. C₁₁×D₄⋊C₈	C₂²	semidirect
41. #10622118	C₂²	semidirect
42. #10622117	C₂²	semidirect
45. #10622093	C₂²	semidirect
46. #10622092	C₂²	semidirect
118. C₂×D₄₄	M₁₆	semidirect
168. #1476	D₁₁	semidirect
244. Q₈⋊C₈	C₂×D₁₁	semidirect
245. Q₈⋊C₈	C₂×D₁₁	semidirect
248. D₄⋊C₈	C₂×D₁₁	semidirect
249. D₄⋊C₈	C₂×D₁₁	semidirect
393. C₁₁	#17873	semidirect

Maximal subgroups

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

subgroup	index
#13077733	2
#13077639	2
C₄×#67002	2
#13067483	2
#13067476	2
#13067455	2
#13067448	2
#13067369	2
C₂×#10622097	2
#13066905	2
C₁₁×#1476	2
#17873	11