Subgroups — #14723741

Order 2816.

720 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13078659	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	#13067478	C₂	1	2	yes	maximal, complemented
4	#13067471	C₂	1	2	yes	maximal, complemented
5	C₈×#4325	C₂	1	2	yes	maximal, complemented
6	C₈×#4323	C₂	1	2	yes	maximal, complemented
7	#13067402	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067058	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067029	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#4318	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#529	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₁₁	—	2	1	no	—
14	C₂×C₄×D₄₄	C₂²	1	1	yes	characteristic
15	C₁₁×#446	C₂²	1	1	yes	characteristic, complemented
16	C₈×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
17	C₁₁×#436	C₂²	1	1	yes	characteristic, complemented
18	C₁₁×#435	—	2	1	no	—
19	C₈×D₄×C₁₁	—	2	1	no	—
20	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
21	C₁₁×#433	—	2	1	no	—
22	C₁₁×#432	C₂²	1	1	yes	characteristic
23	C₁₁×#405	—	2	1	no	—
24	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₁₁)⋊C₈	—	2	1	no	—
26	#10622679	C₄	1	2	yes	—
27	#10622670	C₄	1	2	yes	—
28	#10622659	C₄	1	1	yes	characteristic
29	#10622657	C₄	1	1	yes	characteristic
30	#10622649	C₄	1	1	yes	characteristic
31	#10622647	C₄	1	1	yes	characteristic
32	C₄×#4325	C₂²	1	2	yes	—
33	C₄×#4323	C₂²	1	2	yes	—
34	#10622538	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
36	C₄×#4318	C₂²	1	1	yes	characteristic
37	C₈×D₄₄	—	2	1	no	—
38	C₈×D₄₄	—	2	1	no	—
39	C₈×D₄₄	C₂²	1	2	yes	—
40	C₈×D₄₄	C₂²	1	2	yes	—
41	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
42	D₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	complemented
43	#10622121	C₂²	1	2	yes	—
44	#10622121	C₂²	1	2	yes	—
45	#10622118	C₂²	1	2	yes	complemented
46	#10622117	C₂²	1	2	yes	complemented
47	#10622092	C₂²	1	2	yes	complemented
48	C₈×C₁₁⋊C₈	C₂²	1	2	yes	complemented
49	C₂²×D₄₄	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₁₁	—	2	1	no	—
51	C₂×C₁₁×M₁₆	—	2	1	no	—
52	C₂²×C₈×C₁₁	—	2	1	no	—
53	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
55	C₁₁×#126	—	2	1	no	—
56	C₁₁×#125	C₂×C₄	1	1	yes	characteristic
57	C₁₁×#124	C₂×C₄	1	1	yes	characteristic
58	C₁₁×#123	—	2	1	no	—
59	C₁₁×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
60	C₁₁×#121	C₂×C₄	1	1	yes	characteristic
61	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₁₁	—	2	1	no	—
63	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₁₁×#117	—	2	1	no	—
65	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
66	C₂×#4325	C₂×C₄	1	2	yes	—
67	C₂×#4323	C₂×C₄	1	2	yes	—
68	C₂×(C₂×D₁₁)⋊C₄	—	2	1	no	—
69	C₂×C₄⋊Dic₁₁	C₂×C₄	1	1	yes	characteristic
70	C₂×#4318	—	2	1	no	—
71	C₂²×C₁₁⋊C₈	—	2	1	no	—
72	C₂×C₈×D₁₁	—	2	2	no	—
73	C₂×C₈×D₁₁	—	2	2	no	—
74	C₂×C₈×D₁₁	—	4	4	no	—
75	C₄×D₄₄	—	2	1	no	—
76	C₄×D₄₄	—	2	1	no	—
77	C₄×D₄₄	C₂×C₄	1	2	yes	—
78	C₄×D₄₄	C₂³	1	2	yes	—
79	C₁₁×C₄⋊C₈	—	2	1	no	—
80	C₁₁×C₄⋊C₈	—	2	1	no	—
81	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₁₁×C₂²⋊C₈	—	2	1	no	—
84	C₁₁×C₂²⋊C₈	—	2	1	no	—
85	C₁₁×C₂²⋊C₈	—	2	1	no	—
86	C₁₁×#97	—	2	1	no	—
87	C₁₁×#97	—	2	1	no	—
88	C₄×C₈×C₁₁	—	2	1	no	—
89	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
90	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
91	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
93	#66899	C₂×C₄	1	2	yes	—
94	#66896	C₂×C₄	1	2	yes	—
95	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₁₁)⋊C₈	—	2	2	no	—
98	(C₂×D₁₁)⋊C₈	—	2	2	no	—
99	#66873	C₂×C₄	1	2	yes	—
100	#66873	C₂×C₄	1	2	yes	—
101	#66872	C₂×C₄	1	2	yes	—
102	#66871	C₂×C₄	1	2	yes	—
103	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
104	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
105	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
106	#66867	—	2	1	no	—
107	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
108	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
109	#17910	—	11	1	no	maximal, Sylow
110	C₂³×D₁₁	—	2	1	no	—
111	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₁₁	—	2	1	no	—
113	C₂×D₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₁	—	2	1	no	—
115	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
118	C₂²×Dic₁₁	—	2	1	no	—
119	C₂×D₄₄	—	2	4	no	—
120	C₂×D₄₄	—	2	1	no	—
121	C₂×D₄₄	C₂²×C₄	1	2	yes	—
122	C₂×C₄×D₁₁	—	2	2	no	—
123	C₂×C₄×D₁₁	—	2	2	no	—
124	C₂×C₄×D₁₁	—	4	2	no	—
125	C₂×C₄×D₁₁	—	4	2	no	—
126	C₁₁×M₁₆	—	4	2	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	1	no	—
129	C₂×C₈×C₁₁	—	2	1	no	—
130	C₂×C₈×C₁₁	—	4	1	no	—
131	C₂×C₈×C₁₁	—	4	2	no	—
132	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
134	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
135	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
136	C₁₁×C₄⋊C₄	—	2	1	no	—
137	C₁₁×C₄⋊C₄	—	2	1	no	—
138	C₁₁×C₄⋊C₄	—	2	1	no	—
139	C₁₁×C₄⋊C₄	—	2	1	no	—
140	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
141	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
142	C₁₁×C₂²⋊C₄	—	2	1	no	—
143	C₁₁×C₂²⋊C₄	—	2	1	no	—
144	C₁₁×C₂²⋊C₄	—	2	1	no	—
145	C₁₁×C₂²⋊C₄	—	2	1	no	—
146	C₁₁×C₂²⋊C₄	—	2	1	no	—
147	C₄²×C₁₁	—	2	1	no	—
148	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₁₁	#41	1	1	yes	characteristic
151	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
152	#4325	—	2	4	no	—
153	#4323	—	2	4	no	—
154	(C₂×D₁₁)⋊C₄	—	2	2	no	—
155	(C₂×D₁₁)⋊C₄	—	2	2	no	—
156	C₄⋊Dic₁₁	—	2	1	no	—
157	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
158	#4318	—	2	4	no	—
159	C₂×C₁₁⋊C₈	—	2	2	no	—
160	C₂×C₁₁⋊C₈	—	2	2	no	—
161	C₂×C₁₁⋊C₈	—	4	2	no	—
162	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
163	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
164	C₈×D₁₁	—	4	4	no	—
165	C₈×D₁₁	—	4	4	no	—
166	#3105	—	11	1	no	—
167	#2966	D₁₁	1	1	yes	characteristic, complemented
168	C₂×C₈×D₄	—	11	1	no	—
169	#1586	—	11	2	no	—
170	#1585	—	11	2	no	—
171	C₈×SD₁₆	—	11	2	no	—
172	C₈×D₈	—	11	2	no	—
173	#1573	—	11	1	no	—
174	#1490	—	11	1	no	—
175	#1483	—	11	1	no	—
176	C₈×M₁₆	—	11	1	no	—
177	C₂³×C₁₁	—	2	1	no	—
178	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
179	C₂²×D₁₁	—	2	4	no	—
180	C₂²×D₁₁	—	2	2	no	—
181	C₂²×D₁₁	—	4	2	no	—
182	C₂²×D₁₁	—	4	2	no	—
183	Q₈×C₁₁	—	2	2	no	—
184	D₄×C₁₁	—	2	2	no	—
185	D₄×C₁₁	—	4	2	no	—
186	C₂×C₄×C₁₁	—	2	2	no	—
187	C₂×C₄×C₁₁	—	2	2	no	—
188	C₂×C₄×C₁₁	—	2	1	no	—
189	C₂×C₄×C₁₁	—	2	1	no	—
190	C₂×C₄×C₁₁	—	2	1	no	—
191	C₂×C₄×C₁₁	—	2	1	no	—
192	C₂×C₄×C₁₁	—	2	1	no	—
193	C₂×C₄×C₁₁	—	4	1	no	—
194	C₂×C₄×C₁₁	—	4	1	no	—
195	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
201	C₂×Dic₁₁	—	2	2	no	—
202	C₂×Dic₁₁	—	4	2	no	—
203	D₄₄	—	2	4	no	—
204	D₄₄	—	2	2	no	—
205	D₄₄	#131	1	4	yes	—
206	C₄×D₁₁	—	4	4	no	—
207	C₄×D₁₁	—	4	2	no	—
208	C₄×D₁₁	—	4	2	no	—
209	C₈×C₁₁	—	2	1	no	—
210	C₈×C₁₁	—	2	1	no	—
211	C₈×C₁₁	—	2	1	no	—
212	C₈×C₁₁	—	4	1	no	—
213	C₈×C₁₁	—	4	1	no	—
214	C₈×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
215	C₁₁⋊C₈	—	2	4	no	—
216	C₁₁⋊C₈	—	2	2	no	—
217	C₁₁⋊C₈	—	2	2	no	—
218	C₁₁⋊C₈	—	4	2	no	—
219	C₂³×C₈	—	22	1	no	—
220	#529	C₂×D₁₁	1	1	yes	characteristic
221	C₂×C₄×D₄	—	11	1	no	—
222	#484	—	11	1	no	—
223	#481	—	11	1	no	—
224	#478	—	11	2	no	—
225	#463	—	11	2	no	—
226	#450	—	11	1	no	—
227	#447	—	11	1	no	—
228	#446	C₂×D₁₁	1	1	yes	characteristic, complemented
229	C₈×Q₈	C₂×D₁₁	1	1	yes	characteristic, complemented
230	C₄×SD₁₆	—	11	2	no	—
231	C₄×D₈	—	11	2	no	—
232	#436	C₂×D₁₁	1	1	yes	characteristic, complemented
233	#435	—	2	1	no	—
234	C₈×D₄	—	2	1	no	—
235	C₈×D₄	—	11	2	no	—
236	C₈×D₄	—	11	2	no	—
237	C₈×D₄	—	22	1	no	—
238	C₈×D₄	—	22	1	no	—
239	C₈×D₄	C₂×D₁₁	1	1	yes	characteristic, complemented
240	#433	—	2	1	no	—
241	#432	C₂×D₁₁	1	1	yes	characteristic
242	#431	—	11	1	no	—
243	C₂×C₄⋊C₈	—	11	1	no	—
244	C₂×C₂²⋊C₈	—	22	1	no	—
245	#405	—	2	1	no	—
246	C₄×M₁₆	—	11	1	no	—
247	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
248	#335	—	11	2	no	—
249	#334	—	11	2	no	—
250	Q₈⋊C₈	—	11	2	no	—
251	D₄⋊C₈	—	11	2	no	—
252	D₄⋊C₈	—	11	2	no	—
253	D₄⋊C₈	—	11	2	no	—
254	#322	—	11	2	no	—
255	C₈²	—	11	2	no	—
256	C₂²×C₁₁	—	2	1	no	—
257	C₂²×C₁₁	—	2	1	no	—
258	C₂²×C₁₁	—	4	1	no	—
259	C₂²×C₁₁	—	4	1	no	—
260	C₂²×C₁₁	—	4	1	no	—
261	C₂²×C₁₁	#443	1	2	yes	—
262	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂×D₁₁	—	2	4	no	—
264	C₂×D₁₁	—	4	8	no	—
265	C₂×D₁₁	—	4	2	no	—
266	C₂×D₁₁	—	4	2	no	—
267	C₄×C₁₁	—	2	1	no	—
268	C₄×C₁₁	—	2	1	no	—
269	C₄×C₁₁	—	2	1	no	—
270	C₄×C₁₁	—	2	1	no	—
271	C₄×C₁₁	—	4	1	no	—
272	C₄×C₁₁	—	4	1	no	—
273	C₄×C₁₁	—	4	1	no	—
274	C₄×C₁₁	C₂×#131	1	2	yes	—
275	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
276	C₄×C₁₁	#575	1	1	yes	characteristic
277	Dic₁₁	—	4	2	no	—
278	C₂²×D₄	—	11	1	no	—
279	C₂³×C₄	—	22	1	no	—
280	C₂×SD₁₆	—	11	2	no	—
281	C₂×D₈	—	11	2	no	—
282	C₂×M₁₆	—	2	1	no	—
283	C₂×M₁₆	—	22	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	22	1	no	—
286	C₂²×C₈	—	22	2	no	—
287	C₂²×C₈	—	22	2	no	—
288	C₂²×C₈	—	44	4	no	—
289	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
290	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
291	#126	—	2	1	no	—
292	#125	C₄×D₁₁	1	1	yes	characteristic
293	#124	C₄×D₁₁	1	1	yes	characteristic
294	#123	—	2	1	no	—
295	C₂²⋊Q₈	C₄×D₁₁	1	1	yes	characteristic
296	#121	C₄×D₁₁	1	1	yes	characteristic
297	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	11	2	no	—
300	C₄×D₄	—	11	2	no	—
301	C₄×D₄	—	22	1	no	—
302	C₄×D₄	—	22	1	no	—
303	C₄×D₄	C₂²×D₁₁	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	C₂×C₄⋊C₄	—	11	1	no	—
306	C₂×C₂²⋊C₄	—	22	1	no	—
307	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
308	#107	—	11	2	no	—
309	#106	—	11	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	11	2	no	—
313	C₄⋊C₈	—	11	2	no	—
314	C₄⋊C₈	—	22	1	no	—
315	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
317	#103	—	11	2	no	—
318	#102	—	11	2	no	—
319	#102	—	11	2	no	—
320	#102	—	11	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	11	1	no	—
325	C₂²⋊C₈	—	11	1	no	—
326	C₂²⋊C₈	—	22	2	no	—
327	C₂²⋊C₈	—	22	2	no	—
328	#97	—	2	1	no	—
329	#97	—	2	1	no	—
330	#97	—	22	1	no	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	11	2	no	—
333	C₄×C₈	—	11	2	no	—
334	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
335	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
338	C₂×C₁₁	—	2	2	no	—
339	C₂×C₁₁	—	8	1	no	—
340	C₂×C₁₁	#2929	1	1	yes	characteristic
341	C₂×C₁₁	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
343	D₁₁	—	4	4	no	—
344	C₂⁴	—	22	1	no	—
345	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	11	2	no	—
348	C₂×D₄	—	22	4	no	—
349	C₂×D₄	—	22	1	no	—
350	C₂×D₄	C₂×C₄×D₁₁	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	22	1	no	—
353	C₂²×C₄	—	22	2	no	—
354	C₂²×C₄	—	22	2	no	—
355	C₂²×C₄	—	44	2	no	—
356	C₂²×C₄	—	44	2	no	—
357	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
358	C₂²×C₄	#4339	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
360	SD₁₆	—	22	4	no	—
361	D₈	—	22	4	no	—
362	M₁₆	—	4	2	no	—
363	M₁₆	—	22	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	2	no	—
369	C₂×C₈	—	11	2	no	—
370	C₂×C₈	—	11	2	no	—
371	C₂×C₈	—	22	2	no	—
372	C₂×C₈	—	22	2	no	—
373	C₂×C₈	—	44	4	no	—
374	C₂×C₈	—	44	2	no	—
375	C₂×C₈	—	44	4	no	—
376	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
377	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
378	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
379	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	11	2	no	—
385	C₄⋊C₄	—	22	1	no	—
386	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
387	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
388	C₂²⋊C₄	—	2	1	no	—
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	22	2	no	—
394	C₂²⋊C₄	—	22	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
397	C₄²	#4339	1	1	yes	characteristic
398	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
399	C₄²	C₂³×D₁₁	1	1	yes	characteristic
400	C₁₁	#17910	1	1	yes	characteristic, complemented, Sylow
401	C₂³	—	2	1	no	—
402	C₂³	—	22	4	no	—
403	C₂³	—	22	2	no	—
404	C₂³	—	44	2	no	—
405	C₂³	—	44	2	no	—
406	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
407	Q₈	—	2	2	no	—
408	D₄	—	2	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	11	4	no	—
411	D₄	—	22	4	no	—
412	D₄	—	22	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	22	2	no	—
423	C₂×C₄	—	44	4	no	—
424	C₂×C₄	—	44	2	no	—
425	C₂×C₄	—	44	2	no	—
426	C₂×C₄	—	44	2	no	—
427	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
428	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
429	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
430	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
431	C₂×C₄	C₂×#4339	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
433	C₈	—	2	1	no	—
434	C₈	—	2	1	no	—
435	C₈	—	2	1	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	22	4	no	—
439	C₈	—	22	2	no	—
440	C₈	—	22	2	no	—
441	C₈	—	44	2	no	—
442	C₈	#67002	1	2	yes	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	22	4	no	—
449	C₂²	—	44	8	no	—
450	C₂²	—	44	2	no	—
451	C₂²	—	44	2	no	—
452	C₂²	#10622757	1	2	yes	—
453	C₂²	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	2	1	no	—
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	4	1	no	—
461	C₄	—	44	2	no	—
462	C₄	D₁₁×#131	1	2	yes	—
463	C₄	C₂×#67002	1	1	yes	characteristic
464	C₄	#10623353	1	1	yes	characteristic
465	C₂	—	2	2	no	—
466	C₂	—	8	1	no	—
467	C₂	—	44	4	no	—
468	C₂	#13077308	1	1	yes	characteristic
469	C₂	C₄×#67002	1	1	yes	characteristic
470	C₂	C₂×#10622757	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2966	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	#10622649	C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2966	D₁₁
hypocenter	C₁₁	#17910
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2966

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₄₄	C₂	semidirect
3. #13067478	C₂	semidirect
4. #13067471	C₂	semidirect
5. C₈×#4325	C₂	semidirect
6. C₈×#4323	C₂	semidirect
7. #13067402	C₂	semidirect
8. #13067058	C₂	semidirect
9. #13067029	C₂	semidirect
10. C₈×#4318	C₂	semidirect
11. C₁₁×#2966	C₂	semidirect
15. C₁₁×#446	C₂²	semidirect
16. C₈×Q₈×C₁₁	C₂²	semidirect
17. C₁₁×#436	C₂²	semidirect
20. C₈×D₄×C₁₁	C₂²	semidirect
41. Q₈⋊(C₁₁⋊C₈)	C₂²	semidirect
42. D₄⋊(C₁₁⋊C₈)	C₂²	semidirect
45. #10622118	C₂²	semidirect
46. #10622117	C₂²	semidirect
47. #10622092	C₂²	semidirect
48. C₈×C₁₁⋊C₈	C₂²	semidirect
167. #2966	D₁₁	semidirect
228. #446	C₂×D₁₁	semidirect
229. C₈×Q₈	C₂×D₁₁	semidirect
232. #436	C₂×D₁₁	semidirect
239. C₈×D₄	C₂×D₁₁	semidirect
400. C₁₁	#17910	semidirect

Maximal subgroups

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

subgroup	index
#13078659	2
C₂×C₈×D₄₄	2
#13067478	2
#13067471	2
C₈×#4325	2
C₈×#4323	2
#13067402	2
#13067058	2
#13067029	2
C₈×#4318	2
C₁₁×#2966	2
#17910	11