Subgroups — #14725013

Order 2816.

592 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13078681	C₂	1	1	yes	maximal, characteristic
2	#13077737	C₂	1	1	yes	maximal, characteristic
3	#13067523	C₂	1	2	yes	maximal, complemented
4	#13067466	C₂	1	2	yes	maximal, complemented
5	#13067450	C₂	1	2	yes	maximal, complemented
6	#13067426	C₂	1	2	yes	maximal, complemented
7	#13067404	C₂	1	1	yes	maximal, characteristic, complemented
8	#13067071	C₂	1	1	yes	maximal, characteristic, complemented
9	#13066996	C₂	1	1	yes	maximal, characteristic
10	#13066909	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₁×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#533	C₂²	1	1	yes	characteristic
13	C₄×#4339	C₂²	1	1	yes	characteristic
14	C₁₁×#446	—	2	1	no	—
15	C₁₁×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₁	—	2	1	no	—
17	C₈×Q₈×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#433	—	2	2	no	—
19	C₁₁×#431	C₂²	1	1	yes	characteristic
20	C₁₁×#431	C₂²	1	1	yes	characteristic
21	#10622707	C₄	1	1	yes	characteristic
22	#10622703	C₄	1	1	yes	characteristic
23	#10622700	C₄	1	1	yes	characteristic
24	#10622696	C₄	1	1	yes	characteristic
25	#10622660	C₄	1	2	yes	—
26	#10622658	C₄	1	2	yes	—
27	C₄×#4326	C₂²	1	2	yes	—
28	C₄×#4325	C₂²	1	2	yes	—
29	#10622538	C₂²	1	1	yes	characteristic
30	#10622537	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
32	#10622448	—	2	1	no	—
33	D₁₁×C₄⋊C₈	—	2	1	no	—
34	#10622341	—	2	2	no	—
35	C₈×D₄₄	C₂²	1	2	yes	—
36	#10622292	C₂²	1	2	yes	—
37	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
38	Q₈⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
39	#10622122	C₂²	1	1	yes	characteristic
40	#10622122	C₂²	1	1	yes	characteristic
41	#10622121	C₂²	1	1	yes	characteristic
42	#10622121	C₂²	1	1	yes	characteristic
43	#10622118	C₂²	1	2	yes	—
44	#10622117	C₂²	1	2	yes	—
45	#10622093	C₂²	1	2	yes	—
46	#10622092	C₂²	1	2	yes	—
47	C₂×#4339	C₂×C₄	1	1	yes	characteristic
48	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
50	C₁₁×#125	—	2	1	no	—
51	C₁₁×C₂²⋊Q₈	—	2	1	no	—
52	C₁₁×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
53	C₄×Q₈×C₁₁	—	2	1	no	—
54	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
55	C₁₁×#117	—	2	1	no	—
56	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₂×#4326	C₂×C₄	1	2	yes	—
58	C₂×#4325	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₁₁	—	2	1	no	—
60	C₄×C₂²⋊D₁₁	—	2	1	no	—
61	#66979	C₂×C₄	1	1	yes	characteristic
62	C₂×#4318	—	2	1	no	—
63	C₂²×C₁₁⋊C₈	—	2	1	no	—
64	C₂×C₈×D₁₁	—	2	2	no	—
65	C₄×D₄₄	C₂×C₄	1	1	yes	characteristic
66	C₄×D₄₄	C₂³	1	1	yes	characteristic
67	#66925	—	2	1	no	—
68	C₄²×D₁₁	—	2	1	no	—
69	C₄×Dic₂₂	C₂×C₄	1	1	yes	characteristic
70	C₄×Dic₂₂	C₂³	1	1	yes	characteristic
71	C₁₁×C₄⋊C₈	—	2	2	no	—
72	C₁₁×C₄⋊C₈	—	2	2	no	—
73	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
74	C₁₁×C₄⋊C₈	D₄	1	1	yes	characteristic
75	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
76	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
77	C₁₁×C₂²⋊C₈	—	2	1	no	—
78	C₁₁×C₂²⋊C₈	D₄	1	2	yes	—
79	C₁₁×#97	—	2	2	no	—
80	C₄×C₈×C₁₁	—	2	2	no	—
81	C₄×C₈×C₁₁	—	2	1	no	—
82	C₄×C₈×C₁₁	C₂³	1	2	yes	—
83	#66899	C₂×C₄	1	2	yes	—
84	#66899	C₂×C₄	1	2	yes	—
85	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
86	(C₂×D₁₁)⋊C₈	—	2	2	no	—
87	#66879	—	2	2	no	—
88	Dic₁₁⋊C₈	—	2	2	no	—
89	#66874	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)	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	C₄×C₁₁⋊C₈	—	2	1	no	—
98	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
99	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
100	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
101	#18021	—	11	1	no	maximal, Sylow
102	C₂×Q₈×C₁₁	—	2	1	no	—
103	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₁₁	—	2	1	no	—
108	#4339	—	2	2	no	—
109	#4339	—	4	1	no	—
110	C₂×D₄₄	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₁	—	2	1	no	—
112	C₂×C₄×D₁₁	—	2	1	no	—
113	C₂×C₄×D₁₁	—	2	1	no	—
114	C₂×Dic₂₂	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₁₁	—	2	1	no	—
116	C₂×C₈×C₁₁	—	2	1	no	—
117	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
119	C₁₁×C₄⋊C₄	—	2	1	no	—
120	C₁₁×C₄⋊C₄	—	2	1	no	—
121	C₁₁×C₄⋊C₄	—	2	1	no	—
122	C₁₁×C₄⋊C₄	—	2	2	no	—
123	C₁₁×C₄⋊C₄	—	2	2	no	—
124	C₁₁×C₄⋊C₄	C₂²×C₄	1	2	yes	—
125	C₁₁×C₂²⋊C₄	—	2	2	no	—
126	C₄²×C₁₁	—	2	2	no	—
127	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₁₁	#41	1	1	yes	characteristic
130	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₁₁	—	2	1	no	—
132	#4326	—	4	2	no	—
133	#4325	—	2	4	no	—
134	(C₂×D₁₁)⋊C₄	—	2	1	no	—
135	(C₂×D₁₁)⋊C₄	—	2	1	no	—
136	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊Dic₁₁	C₂²×C₄	1	1	yes	characteristic
138	Dic₁₁⋊C₄	—	2	1	no	—
139	Dic₁₁⋊C₄	—	2	1	no	—
140	C₄×Dic₁₁	—	2	1	no	—
141	C₄×Dic₁₁	—	2	1	no	—
142	C₄×Dic₁₁	—	2	1	no	—
143	#4318	—	8	1	no	—
144	C₂×C₁₁⋊C₈	—	2	2	no	—
145	C₂×C₁₁⋊C₈	—	2	1	no	—
146	C₂×C₁₁⋊C₈	—	2	1	no	—
147	C₂×C₁₁⋊C₈	—	4	2	no	—
148	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
149	C₂×C₁₁⋊C₈	C₂²×C₄	1	2	yes	—
150	C₈×D₁₁	—	8	2	no	—
151	#3107	—	11	1	no	—
152	#2990	—	11	1	no	—
153	#2986	D₁₁	1	1	yes	characteristic, complemented
154	#1593	—	11	2	no	—
155	#1584	—	11	2	no	—
156	#1582	—	11	2	no	—
157	SD₁₆⋊C₈	—	11	2	no	—
158	#1574	—	11	1	no	—
159	#1493	—	11	1	no	—
160	#1476	—	11	1	no	—
161	#1452	—	11	1	no	—
162	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
163	C₂²×D₁₁	—	2	1	no	—
164	Q₈×C₁₁	—	2	2	no	—
165	Q₈×C₁₁	—	2	2	no	—
166	Q₈×C₁₁	—	4	2	no	—
167	C₂×C₄×C₁₁	—	2	1	no	—
168	C₂×C₄×C₁₁	—	2	1	no	—
169	C₂×C₄×C₁₁	—	2	1	no	—
170	C₂×C₄×C₁₁	—	2	1	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	2	no	—
173	C₂×C₄×C₁₁	—	2	2	no	—
174	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₁₁	—	4	2	no	—
181	C₂×Dic₁₁	—	2	1	no	—
182	C₂×Dic₁₁	—	2	1	no	—
183	C₂×Dic₁₁	—	2	1	no	—
184	D₄₄	—	2	1	no	—
185	D₄₄	#131	1	2	yes	—
186	C₄×D₁₁	—	4	2	no	—
187	C₄×D₁₁	—	4	1	no	—
188	C₄×D₁₁	—	4	1	no	—
189	C₄×D₁₁	—	4	2	no	—
190	Dic₂₂	—	2	1	no	—
191	Dic₂₂	—	2	1	no	—
192	C₈×C₁₁	—	2	2	no	—
193	C₈×C₁₁	—	2	2	no	—
194	C₈×C₁₁	—	4	1	no	—
195	C₈×C₁₁	—	4	1	no	—
196	C₁₁⋊C₈	—	2	2	no	—
197	C₁₁⋊C₈	—	2	2	no	—
198	C₁₁⋊C₈	—	4	1	no	—
199	C₁₁⋊C₈	—	4	1	no	—
200	C₁₁⋊C₈	—	4	2	no	—
201	#533	C₂×D₁₁	1	1	yes	characteristic
202	C₄×#41	—	11	1	no	—
203	#485	—	11	2	no	—
204	#475	—	11	1	no	—
205	#474	—	11	1	no	—
206	#462	—	11	1	no	—
207	#461	—	11	1	no	—
208	#452	—	11	2	no	—
209	#446	—	2	1	no	—
210	#446	—	11	2	no	—
211	#446	C₂×D₁₁	1	2	yes	—
212	C₈×Q₈	—	2	1	no	—
213	C₈×Q₈	C₂×D₁₁	1	2	yes	—
214	C₄×Q₁₆	—	11	2	no	—
215	C₄×SD₁₆	—	11	2	no	—
216	#435	—	22	2	no	—
217	C₈×D₄	—	11	2	no	—
218	#433	—	2	2	no	—
219	#432	—	22	1	no	—
220	#431	—	11	1	no	—
221	#431	C₂×D₁₁	1	1	yes	characteristic
222	#431	C₂×D₁₁	1	1	yes	characteristic
223	#423	—	11	1	no	—
224	C₂×C₄⋊C₈	—	22	1	no	—
225	C₂×C₄×C₈	—	11	1	no	—
226	#335	—	11	2	no	—
227	#334	—	11	2	no	—
228	Q₈⋊C₈	—	11	2	no	—
229	Q₈⋊C₈	—	11	2	no	—
230	Q₈⋊C₈	—	11	1	no	—
231	Q₈⋊C₈	—	11	1	no	—
232	D₄⋊C₈	—	11	1	no	—
233	D₄⋊C₈	—	11	1	no	—
234	#322	—	11	2	no	—
235	#322	—	11	2	no	—
236	C₂²×C₁₁	—	2	1	no	—
237	C₂²×C₁₁	—	2	1	no	—
238	C₂²×C₁₁	—	2	1	no	—
239	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
240	C₂×D₁₁	—	2	2	no	—
241	C₂×D₁₁	—	4	1	no	—
242	C₂×D₁₁	—	4	1	no	—
243	C₄×C₁₁	—	2	1	no	—
244	C₄×C₁₁	—	2	1	no	—
245	C₄×C₁₁	—	2	1	no	—
246	C₄×C₁₁	—	4	2	no	—
247	C₄×C₁₁	—	4	2	no	—
248	C₄×C₁₁	#444	1	2	yes	—
249	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
250	C₄×C₁₁	#568	1	1	yes	characteristic
251	C₄×C₁₁	#577	1	1	yes	characteristic
252	C₄×C₁₁	#578	1	1	yes	characteristic
253	Dic₁₁	—	4	1	no	—
254	Dic₁₁	—	4	1	no	—
255	Dic₁₁	—	4	1	no	—
256	C₂×#41	—	11	1	no	—
257	C₂×Q₁₆	—	11	2	no	—
258	C₂×SD₁₆	—	11	2	no	—
259	C₂×M₁₆	—	22	1	no	—
260	C₂²×C₈	—	22	1	no	—
261	C₂²×C₈	—	22	2	no	—
262	C₄⋊Q₈	C₄×D₁₁	1	1	yes	characteristic
263	C₄⋊Q₈	C₄×D₁₁	1	1	yes	characteristic
264	#125	—	2	1	no	—
265	C₂²⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	C₄×D₁₁	1	2	yes	—
267	C₄×Q₈	—	2	1	no	—
268	C₄×Q₈	—	11	1	no	—
269	C₄×Q₈	—	11	1	no	—
270	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
271	C₄×D₄	—	11	1	no	—
272	C₄×D₄	—	11	1	no	—
273	C₄×D₄	—	22	1	no	—
274	C₄×D₄	—	22	1	no	—
275	#117	—	2	1	no	—
276	#117	—	11	1	no	—
277	#117	—	22	1	no	—
278	C₂×C₄²	—	22	1	no	—
279	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
280	#107	—	11	2	no	—
281	#106	—	11	2	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	11	1	no	—
285	C₄⋊C₈	—	11	1	no	—
286	C₄⋊C₈	—	11	2	no	—
287	C₄⋊C₈	—	22	2	no	—
288	C₄⋊C₈	—	22	1	no	—
289	C₄⋊C₈	C₂²⋊D₁₁	1	1	yes	characteristic
290	C₄⋊C₈	C₂²⋊D₁₁	1	1	yes	characteristic
291	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
292	C₄⋊C₈	C₂²×D₁₁	1	1	yes	characteristic
293	#103	—	11	2	no	—
294	#103	—	11	2	no	—
295	#103	—	11	2	no	—
296	#102	—	11	2	no	—
297	C₂²⋊C₈	—	2	1	no	—
298	C₂²⋊C₈	—	11	2	no	—
299	C₂²⋊C₈	—	22	2	no	—
300	C₂²⋊C₈	C₂²⋊D₁₁	1	2	yes	—
301	#97	—	2	2	no	—
302	#97	—	22	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	—	11	2	no	—
306	C₄×C₈	—	11	1	no	—
307	C₄×C₈	—	11	1	no	—
308	C₄×C₈	—	22	1	no	—
309	C₄×C₈	C₂²×D₁₁	1	2	yes	—
310	C₂×C₁₁	—	4	1	no	—
311	C₂×C₁₁	#2933	1	1	yes	characteristic
312	C₂×C₁₁	#2947	1	1	yes	characteristic
313	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
314	D₁₁	—	4	2	no	—
315	#41	—	22	2	no	—
316	#41	—	44	1	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	11	1	no	—
319	C₂×Q₈	C₂×C₄×D₁₁	1	2	yes	—
320	C₂×D₄	—	11	1	no	—
321	C₂×D₄	—	22	1	no	—
322	C₂²×C₄	—	22	1	no	—
323	C₂²×C₄	—	22	1	no	—
324	C₂²×C₄	—	22	1	no	—
325	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
326	C₂²×C₄	#4339	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
328	Q₁₆	—	44	2	no	—
329	SD₁₆	—	22	4	no	—
330	M₁₆	—	88	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	11	2	no	—
334	C₂×C₈	—	11	2	no	—
335	C₂×C₈	—	22	1	no	—
336	C₂×C₈	—	22	1	no	—
337	C₂×C₈	—	22	2	no	—
338	C₂×C₈	—	44	2	no	—
339	C₂×C₈	—	88	2	no	—
340	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	11	1	no	—
348	C₄⋊C₄	—	11	1	no	—
349	C₄⋊C₄	—	22	1	no	—
350	C₄⋊C₄	—	22	1	no	—
351	C₄⋊C₄	C₂×C₄×D₁₁	1	2	yes	—
352	C₂²⋊C₄	—	2	2	no	—
353	C₂²⋊C₄	—	22	1	no	—
354	C₂²⋊C₄	—	22	1	no	—
355	C₂²⋊C₄	—	22	1	no	—
356	C₄²	—	2	2	no	—
357	C₄²	—	22	1	no	—
358	C₄²	—	22	1	no	—
359	C₄²	—	22	1	no	—
360	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
361	C₄²	#4339	1	1	yes	characteristic
362	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
363	C₄²	C₂³×D₁₁	1	1	yes	characteristic
364	C₁₁	#18021	1	1	yes	characteristic, complemented, Sylow
365	C₂³	—	22	1	no	—
366	C₂³	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	22	1	no	—
371	Q₈	—	22	1	no	—
372	D₄	—	11	2	no	—
373	D₄	—	22	1	no	—
374	D₄	—	44	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	22	1	no	—
383	C₂×C₄	—	22	1	no	—
384	C₂×C₄	—	22	1	no	—
385	C₂×C₄	—	44	2	no	—
386	C₂×C₄	—	44	2	no	—
387	C₂×C₄	—	44	1	no	—
388	C₂×C₄	—	44	1	no	—
389	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
390	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
391	C₂×C₄	C₄×C₂²⋊D₁₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
393	C₂×C₄	C₂×#4339	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	22	2	no	—
400	C₈	—	22	2	no	—
401	C₈	—	44	1	no	—
402	C₈	—	44	1	no	—
403	C₈	—	44	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	22	2	no	—
408	C₂²	—	44	1	no	—
409	C₂²	—	44	1	no	—
410	C₂²	C₂×C₄×C₂²⋊D₁₁	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	44	1	no	—
417	C₄	—	44	1	no	—
418	C₄	—	44	1	no	—
419	C₄	#10622758	1	2	yes	—
420	C₄	D₁₁×#131	1	1	yes	characteristic
421	C₄	#10623281	1	1	yes	characteristic
422	C₄	#10623368	1	1	yes	characteristic
423	C₄	#10623369	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	44	2	no	—
426	C₂	#13077338	1	1	yes	characteristic
427	C₂	#13077459	1	1	yes	characteristic
428	C₂	C₂×#10622758	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#2986	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂×#4339	C₂×C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#2986	D₁₁
hypocenter	C₁₁	#18021
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2986

Complements

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

N	H ≅ G/N	type
3. #13067523	C₂	semidirect
4. #13067466	C₂	semidirect
5. #13067450	C₂	semidirect
6. #13067426	C₂	semidirect
7. #13067404	C₂	semidirect
8. #13067071	C₂	semidirect
10. #13066909	C₂	semidirect
11. C₁₁×#2986	C₂	semidirect
153. #2986	D₁₁	semidirect
364. C₁₁	#18021	semidirect

Maximal subgroups

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

subgroup	index
#13078681	2
#13077737	2
#13067523	2
#13067466	2
#13067450	2
#13067426	2
#13067404	2
#13067071	2
#13066996	2
#13066909	2
C₁₁×#2986	2
#18021	11