Subgroups — #14724692

Order 2816.

670 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13078647	C₂	1	1	yes	maximal, characteristic
2	Q₈×#4318	C₂	1	1	yes	maximal, characteristic, complemented
3	#13077359	C₂	1	1	yes	maximal, characteristic
4	#13067503	C₂	1	2	yes	maximal, complemented
5	#13067456	C₂	1	2	yes	maximal, complemented
6	#13067455	C₂	1	2	yes	maximal, complemented
7	#13067413	C₂	1	2	yes	maximal, complemented
8	#13067386	C₂	1	1	yes	maximal, characteristic, complemented
9	#13067068	C₂	1	1	yes	maximal, characteristic
10	C₈×#4318	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×#66954	—	2	1	no	—
14	#10623008	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	#10622840	C₄	1	2	yes	—
18	#10622723	—	2	1	no	—
19	#10622640	C₄	1	1	yes	characteristic
20	#10622640	C₄	1	1	yes	characteristic
21	C₄×#4325	C₂²	1	2	yes	—
22	C₄×#4325	C₂²	1	2	yes	—
23	#10622637	—	2	2	no	—
24	#10622637	C₂²	1	2	yes	—
25	Q₈×C₁₁⋊C₈	C₂²	1	2	yes	—
26	#10622633	C₄	1	1	yes	characteristic
27	#10622633	C₄	1	1	yes	characteristic
28	#10622581	C₄	1	2	yes	—
29	#10622538	C₂²	1	1	yes	characteristic
30	#10622537	—	2	1	no	—
31	#10622537	C₂²	1	1	yes	characteristic
32	C₄×#4318	—	2	1	no	—
33	C₄×#4318	C₂²	1	1	yes	characteristic
34	#10622451	C₂²	1	2	yes	—
35	#10622449	—	2	2	no	—
36	#10622447	C₂²	1	2	yes	—
37	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
39	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₁₁×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	#10622118	C₂²	1	2	yes	—
42	#10622118	C₂²	1	2	yes	—
43	#10622097	C₂²	1	2	yes	—
44	#10622097	C₂²	1	2	yes	—
45	#10622092	C₂²	1	2	yes	—
46	C₈×C₁₁⋊C₈	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂×#4339	—	2	1	no	—
49	C₂²×C₈×C₁₁	—	2	1	no	—
50	C₂²×C₈×C₁₁	—	2	1	no	—
51	C₄×Q₈×C₁₁	—	2	1	no	—
52	C₄×Q₈×C₁₁	—	2	1	no	—
53	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
54	C₄×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
55	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₄×Q₈×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₁₁	—	2	1	no	—
60	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
61	C₂×#4325	C₂×C₄	1	2	yes	—
62	C₂×#4325	C₂×C₄	1	2	yes	—
63	#66983	—	2	1	no	—
64	#66983	C₂×C₄	1	2	yes	—
65	C₂×#4318	—	2	1	no	—
66	C₂×#4318	D₄	1	1	yes	characteristic
67	C₂×#4318	D₄	1	1	yes	characteristic
68	#66954	—	4	4	no	—
69	C₂×#4313	—	2	2	no	—
70	C₂×C₈×D₁₁	—	2	2	no	—
71	#66928	—	2	1	no	—
72	#66927	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄₄	—	2	1	no	—
74	C₄×D₄₄	C₂³	1	2	yes	—
75	#66922	C₂×C₄	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	—	2	1	no	—
77	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
78	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₁	—	2	1	no	—
80	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
82	#66899	C₂×C₄	1	2	yes	—
83	#66899	C₂×C₄	1	2	yes	—
84	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
85	(C₂×D₁₁)⋊C₈	—	2	2	no	—
86	(C₂×D₁₁)⋊C₈	—	2	2	no	—
87	#66873	C₂×C₄	1	2	yes	—
88	#66873	C₂×C₄	1	2	yes	—
89	#66872	C₂×C₄	1	2	yes	—
90	#66872	C₂×C₄	1	2	yes	—
91	C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
92	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
93	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
94	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
95	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₁₁⋊C₈)	C₂³	1	2	yes	—
97	#66867	—	2	2	no	—
98	#66867	D₄	1	2	yes	—
99	C₄×C₁₁⋊C₈	—	2	2	no	—
100	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
101	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
102	#17997	—	11	1	no	maximal, Sylow
103	C₂×Q₈×C₁₁	—	2	1	no	—
104	C₂×Q₈×C₁₁	—	2	2	no	—
105	C₂×Q₈×C₁₁	—	4	1	no	—
106	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
107	C₂×Q₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₁	—	2	1	no	—
109	C₂²×C₄×C₁₁	—	2	1	no	—
110	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
113	C₂×C₂²⋊D₁₁	—	2	2	no	—
114	#4339	—	4	2	no	—
115	#4339	—	4	2	no	—
116	C₂×D₄₄	—	2	1	no	—
117	C₂×D₄₄	—	2	1	no	—
118	C₂×D₄₄	C₂²×C₄	1	2	yes	—
119	C₂×C₄×D₁₁	—	2	2	no	—
120	C₂×Dic₂₂	—	2	1	no	—
121	C₂×C₈×C₁₁	—	2	1	no	—
122	C₂×C₈×C₁₁	—	2	1	no	—
123	C₂×C₈×C₁₁	—	2	1	no	—
124	C₂×C₈×C₁₁	—	2	1	no	—
125	C₂×C₈×C₁₁	—	4	2	no	—
126	C₂×C₈×C₁₁	—	4	2	no	—
127	C₁₁×C₄⋊C₄	—	2	1	no	—
128	C₁₁×C₄⋊C₄	—	2	1	no	—
129	C₁₁×C₄⋊C₄	—	2	1	no	—
130	C₁₁×C₄⋊C₄	—	2	1	no	—
131	C₁₁×C₄⋊C₄	—	2	1	no	—
132	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
133	C₁₁×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₁₁	—	2	1	no	—
135	C₄²×C₁₁	—	2	1	no	—
136	C₄²×C₁₁	—	2	1	no	—
137	C₄²×C₁₁	—	2	1	no	—
138	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₁₁	#41	1	1	yes	characteristic
141	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
142	#4325	—	2	4	no	—
143	#4325	—	4	2	no	—
144	(C₂×D₁₁)⋊C₄	—	2	2	no	—
145	(C₂×D₁₁)⋊C₄	—	2	2	no	—
146	C₄⋊Dic₁₁	—	2	1	no	—
147	C₄⋊Dic₁₁	C₂²×C₄	1	2	yes	—
148	#4318	—	2	2	no	—
149	#4318	—	4	2	no	—
150	#4318	SD₁₆	1	4	yes	complemented
151	C₂×C₁₁⋊C₈	—	2	2	no	—
152	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
153	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
155	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
156	#4313	—	4	4	no	—
157	C₈×D₁₁	—	4	4	no	—
158	#3103	—	11	1	no	—
159	Q₈×M₁₆	—	11	1	no	—
160	#2935	—	11	1	no	—
161	#1590	—	11	2	no	—
162	#1583	—	11	2	no	—
163	#1582	—	11	2	no	—
164	C₈×SD₁₆	—	11	2	no	—
165	#1570	—	11	1	no	—
166	#1492	—	11	1	no	—
167	C₂×Q₈⋊C₈	D₁₁	1	1	yes	characteristic, complemented
168	C₈×M₁₆	—	11	1	no	—
169	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
170	C₂²×D₁₁	—	2	2	no	—
171	Q₈×C₁₁	—	2	1	no	—
172	Q₈×C₁₁	—	2	1	no	—
173	Q₈×C₁₁	—	2	1	no	—
174	Q₈×C₁₁	—	4	2	no	—
175	Q₈×C₁₁	#131	1	2	yes	complemented
176	C₂×C₄×C₁₁	—	2	1	no	—
177	C₂×C₄×C₁₁	—	2	1	no	—
178	C₂×C₄×C₁₁	—	2	1	no	—
179	C₂×C₄×C₁₁	—	2	1	no	—
180	C₂×C₄×C₁₁	—	2	1	no	—
181	C₂×C₄×C₁₁	—	2	1	no	—
182	C₂×C₄×C₁₁	—	4	1	no	—
183	C₂×C₄×C₁₁	—	4	2	no	—
184	C₂×C₄×C₁₁	—	8	1	no	—
185	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
189	C₂×C₄×C₁₁	#135	1	2	yes	—
190	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
193	C₂²⋊D₁₁	—	4	4	no	—
194	C₂×Dic₁₁	—	2	2	no	—
195	D₄₄	—	2	2	no	—
196	D₄₄	—	2	2	no	—
197	D₄₄	—	4	2	no	—
198	D₄₄	—	8	1	no	—
199	C₄×D₁₁	—	4	2	no	—
200	C₄×D₁₁	—	4	2	no	—
201	Dic₂₂	—	4	2	no	—
202	C₈×C₁₁	—	2	2	no	—
203	C₈×C₁₁	—	4	1	no	—
204	C₈×C₁₁	—	4	1	no	—
205	C₈×C₁₁	—	4	1	no	—
206	C₁₁⋊C₈	—	2	2	no	—
207	C₁₁⋊C₈	—	2	2	no	—
208	C₁₁⋊C₈	—	2	2	no	—
209	C₁₁⋊C₈	—	4	2	no	—
210	C₁₁⋊C₈	C₂×SD₁₆	1	4	yes	—
211	C₂×#131	—	22	1	no	—
212	#532	—	11	1	no	—
213	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
214	#481	—	11	2	no	—
215	#475	—	11	1	no	—
216	#475	—	11	1	no	—
217	#460	—	11	1	no	—
218	#460	—	11	1	no	—
219	#448	—	11	2	no	—
220	#446	—	11	2	no	—
221	#446	—	22	2	no	—
222	C₈×Q₈	—	11	2	no	—
223	C₄×SD₁₆	—	11	2	no	—
224	C₄×SD₁₆	—	11	2	no	—
225	#436	—	11	2	no	—
226	#435	—	22	2	no	—
227	C₈×D₄	—	11	2	no	—
228	#431	—	11	1	no	—
229	#423	—	11	1	no	—
230	#423	—	22	1	no	—
231	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
232	#408	—	22	1	no	—
233	C₄×M₁₆	—	11	1	no	—
234	C₄×M₁₆	—	22	1	no	—
235	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
236	#334	—	11	2	no	—
237	#334	—	11	2	no	—
238	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic
239	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic
240	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic
241	Q₈⋊C₈	C₂×D₁₁	1	1	yes	characteristic
242	D₄⋊C₈	—	11	2	no	—
243	D₄⋊C₈	—	11	2	no	—
244	#322	—	11	2	no	—
245	C₈²	—	11	2	no	—
246	C₂²×C₁₁	—	2	1	no	—
247	C₂²×C₁₁	—	2	1	no	—
248	C₂²×C₁₁	C₄×SD₁₆	1	2	yes	—
249	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×D₁₁	—	4	2	no	—
251	C₂×D₁₁	—	4	2	no	—
252	C₂×D₁₁	—	4	2	no	—
253	C₄×C₁₁	—	2	1	no	—
254	C₄×C₁₁	—	2	2	no	—
255	C₄×C₁₁	—	2	1	no	—
256	C₄×C₁₁	—	2	1	no	—
257	C₄×C₁₁	—	4	1	no	—
258	C₄×C₁₁	—	4	1	no	—
259	C₄×C₁₁	—	4	1	no	—
260	C₄×C₁₁	C₄×SD₁₆	1	2	yes	—
261	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
262	C₄×C₁₁	#568	1	1	yes	characteristic
263	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
264	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
265	Dic₁₁	—	4	2	no	—
266	C₂×#41	—	22	1	no	—
267	C₂²×Q₈	C₄×D₁₁	1	1	yes	characteristic
268	C₂×SD₁₆	—	11	2	no	—
269	C₂×SD₁₆	—	11	2	no	—
270	#131	—	44	4	no	—
271	C₂×M₁₆	—	11	1	no	—
272	C₂×M₁₆	—	11	1	no	—
273	C₂×M₁₆	—	22	2	no	—
274	C₂×M₁₆	—	22	1	no	—
275	C₂²×C₈	—	2	1	no	—
276	C₂²×C₈	—	2	1	no	—
277	C₂²×C₈	—	22	2	no	—
278	C₄⋊Q₈	—	11	1	no	—
279	#127	—	11	1	no	—
280	#124	—	22	1	no	—
281	#121	—	11	2	no	—
282	#121	—	22	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
286	C₄×Q₈	C₄×D₁₁	1	1	yes	characteristic
287	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
288	C₄×Q₈	C₂²×D₁₁	1	1	yes	characteristic
289	C₄×D₄	—	11	2	no	—
290	C₄×D₄	—	22	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	C₄×D₁₁	1	1	yes	characteristic
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
295	#106	—	11	2	no	—
296	#106	—	11	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	11	1	no	—
299	C₄⋊C₈	—	11	1	no	—
300	C₄⋊C₈	—	11	2	no	—
301	C₄⋊C₈	—	22	2	no	—
302	C₄⋊C₈	—	22	2	no	—
303	C₄⋊C₈	—	22	1	no	—
304	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
306	#103	—	11	2	no	—
307	#103	—	11	2	no	—
308	#102	—	11	2	no	—
309	#102	—	11	2	no	—
310	C₂²⋊C₈	—	11	2	no	—
311	C₂²⋊C₈	—	22	2	no	—
312	C₂²⋊C₈	—	22	2	no	—
313	#97	—	11	2	no	—
314	#97	—	22	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	11	2	no	—
317	C₄×C₈	—	11	2	no	—
318	C₄×C₈	—	22	2	no	—
319	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
321	C₂×C₁₁	—	2	2	no	—
322	C₂×C₁₁	#2933	1	1	yes	characteristic
323	C₂×C₁₁	C₂×C₄×SD₁₆	1	1	yes	characteristic
324	C₂×C₁₁	#2956	1	1	yes	characteristic
325	D₁₁	—	8	2	no	—
326	#41	—	44	2	no	—
327	#41	—	44	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	22	1	no	—
332	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
333	C₂×Q₈	C₂×C₄×D₁₁	1	1	yes	characteristic
334	C₂×D₄	—	11	2	no	—
335	C₂×D₄	—	22	2	no	—
336	C₂×D₄	—	22	1	no	—
337	C₂×D₄	—	22	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	22	2	no	—
341	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
342	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
343	C₂²×C₄	#4341	1	1	yes	characteristic
344	SD₁₆	—	22	4	no	—
345	SD₁₆	—	44	2	no	—
346	M₁₆	—	11	4	no	—
347	M₁₆	—	22	2	no	—
348	M₁₆	—	44	4	no	—
349	M₁₆	—	44	2	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	11	2	no	—
357	C₂×C₈	—	11	2	no	—
358	C₂×C₈	—	11	2	no	—
359	C₂×C₈	—	11	2	no	—
360	C₂×C₈	—	22	2	no	—
361	C₂×C₈	—	44	4	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	11	2	no	—
368	C₄⋊C₄	—	22	1	no	—
369	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
370	C₄⋊C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
371	C₂²⋊C₄	—	22	2	no	—
372	C₂²⋊C₄	—	22	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
378	C₄²	D₄×D₁₁	1	1	yes	characteristic
379	C₄²	#4341	1	1	yes	characteristic
380	C₄²	C₂³×D₁₁	1	1	yes	characteristic
381	C₁₁	#17997	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	22	2	no	—
383	C₂³	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	2	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	44	2	no	—
389	Q₈	#66954	1	2	yes	complemented
390	D₄	—	22	2	no	—
391	D₄	—	22	2	no	—
392	D₄	—	44	4	no	—
393	D₄	—	44	2	no	—
394	D₄	—	88	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	8	1	no	—
404	C₂×C₄	—	22	2	no	—
405	C₂×C₄	—	44	2	no	—
406	C₂×C₄	—	44	2	no	—
407	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
408	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
409	C₂×C₄	(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₁₁	1	2	yes	—
411	C₂×C₄	#66972	1	2	yes	—
412	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
413	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
414	C₂×C₄	C₂×#4341	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	11	4	no	—
420	C₈	—	22	2	no	—
421	C₈	—	22	2	no	—
422	C₈	—	22	2	no	—
423	C₈	—	44	2	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	44	2	no	—
427	C₂²	—	44	2	no	—
428	C₂²	—	44	2	no	—
429	C₂²	#10622401	1	2	yes	—
430	C₂²	C₂×(C₂²⋊D₁₁)⋊C₄	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	44	2	no	—
439	C₄	#10622401	1	2	yes	—
440	C₄	C₂×#66954	1	1	yes	characteristic
441	C₄	#10623276	1	1	yes	characteristic
442	C₄	C₂×SD₁₆×D₁₁	1	1	yes	characteristic
443	C₄	C₂×#66972	1	1	yes	characteristic
444	C₂	—	2	2	no	—
445	C₂	—	88	2	no	—
446	C₂	#13077337	1	1	yes	characteristic
447	C₂	C₂×#10622401	1	1	yes	characteristic
448	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	C₂×C₁₁×Q₈⋊C₈	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	#10623008	C₂²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₁₁
hypocenter	C₁₁	#17997
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. Q₈×#4318	C₂	semidirect
4. #13067503	C₂	semidirect
5. #13067456	C₂	semidirect
6. #13067455	C₂	semidirect
7. #13067413	C₂	semidirect
8. #13067386	C₂	semidirect
10. C₈×#4318	C₂	semidirect
11. C₂×C₁₁×Q₈⋊C₈	C₂	semidirect
150. #4318	SD₁₆	semidirect
167. C₂×Q₈⋊C₈	D₁₁	semidirect
175. Q₈×C₁₁	#131	semidirect
381. C₁₁	#17997	semidirect
389. Q₈	#66954	semidirect

Maximal subgroups

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

subgroup	index
#13078647	2
Q₈×#4318	2
#13077359	2
#13067503	2
#13067456	2
#13067455	2
#13067413	2
#13067386	2
#13067068	2
C₈×#4318	2
C₂×C₁₁×Q₈⋊C₈	2
#17997	11