Subgroups — #14659709

Order 2816.

774 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66882	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622714	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622192	C₂	1	2	yes	maximal
4	#13068336	C₂	1	2	yes	maximal
5	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66979	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₁	C₂²	1	2	yes	—
10	C₂²×#4318	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#108	—	2	2	no	—
12	C₂×C₁₁×#108	—	2	2	no	—
13	C₂×C₁₁×#108	C₄	1	4	yes	complemented
14	C₂×#66882	—	2	1	no	—
15	C₂×#66882	—	2	1	no	—
16	C₂×#66882	—	2	2	no	—
17	C₂×#66882	C₄	1	4	yes	complemented
18	#10622714	—	2	2	no	—
19	#10622714	C₄	1	4	yes	complemented
20	C₂×#66879	—	2	1	no	—
21	C₂×C₈×Dic₁₁	—	2	1	no	—
22	#10622192	—	2	4	no	—
23	#10622189	—	2	4	no	—
24	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₁	—	2	2	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	—	2	2	no	—
28	C₂×C₁₁×M₁₆	—	2	2	no	—
29	C₂×C₁₁×M₁₆	—	2	2	no	—
30	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
32	C₂²×C₈×C₁₁	—	2	2	no	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	D₄	1	2	yes	—
39	C₂²×C₈×C₁₁	D₄	1	2	yes	—
40	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
41	C₂×C₂²⋊Dic₁₁	—	2	1	no	—
42	#66979	—	2	1	no	—
43	#66979	—	2	1	no	—
44	#66979	C₂×C₄	1	2	yes	—
45	#66979	Q₈	1	2	yes	—
46	C₂×C₄⋊Dic₁₁	—	2	2	no	—
47	C₂×C₄⋊Dic₁₁	—	2	2	no	—
48	C₂×C₄⋊Dic₁₁	—	2	2	no	—
49	C₂×C₄⋊Dic₁₁	—	2	2	no	—
50	C₂×C₄⋊Dic₁₁	—	2	2	no	—
51	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊Dic₁₁	D₄	1	2	yes	—
53	C₂×C₄×Dic₁₁	—	2	1	no	—
54	C₂×#4318	—	2	1	no	—
55	C₂×#4318	—	2	1	no	—
56	C₂×#4318	—	2	1	no	—
57	C₂×#4318	C₂×C₄	1	2	yes	—
58	C₂×#4318	D₄	1	2	yes	—
59	C₂×#4318	Q₈	1	2	yes	—
60	C₂²×C₁₁⋊C₈	—	2	1	no	—
61	C₁₁×#108	—	2	8	no	—
62	#66882	—	2	4	no	—
63	#66882	—	2	4	no	—
64	#66879	—	2	4	no	—
65	C₈×Dic₁₁	—	2	4	no	—
66	#10870	—	11	1	no	maximal, Sylow
67	C₂⁴×C₁₁	#41	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
82	C₂²×Dic₁₁	—	2	4	no	—
83	C₂²×Dic₁₁	—	2	2	no	—
84	C₂²×Dic₁₁	—	4	2	no	—
85	C₂²×Dic₁₁	—	4	2	no	—
86	C₂²×Dic₁₁	—	8	4	no	—
87	C₁₁×M₁₆	—	2	4	no	—
88	C₁₁×M₁₆	—	2	4	no	—
89	C₁₁×M₁₆	—	4	2	no	—
90	C₁₁×M₁₆	—	4	2	no	—
91	C₂×C₈×C₁₁	—	2	4	no	—
92	C₂×C₈×C₁₁	—	4	2	no	—
93	C₂×C₈×C₁₁	—	4	2	no	—
94	C₂×C₈×C₁₁	C₄²	1	4	yes	—
95	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
99	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
102	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
103	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
104	C₂²⋊Dic₁₁	—	2	2	no	—
105	C₂²⋊Dic₁₁	—	2	2	no	—
106	C₄⋊Dic₁₁	—	2	4	no	—
107	C₄⋊Dic₁₁	—	2	4	no	—
108	C₄⋊Dic₁₁	—	2	2	no	—
109	C₄⋊Dic₁₁	—	4	2	no	—
110	C₄⋊Dic₁₁	—	4	2	no	—
111	C₄⋊Dic₁₁	C₄⋊C₄	1	4	yes	—
112	C₄×Dic₁₁	—	2	2	no	—
113	C₄×Dic₁₁	—	2	2	no	—
114	#4318	—	2	2	no	—
115	#4318	—	2	2	no	—
116	#4318	—	2	2	no	—
117	#4318	C₄⋊C₄	1	4	yes	—
118	C₂×C₁₁⋊C₈	—	2	2	no	—
119	C₂×C₁₁⋊C₈	—	2	2	no	—
120	C₂×C₁₁⋊C₈	—	2	2	no	—
121	C₂²×#108	D₁₁	1	1	yes	characteristic
122	C₂²×#107	—	11	1	no	—
123	C₂×#405	—	11	1	no	—
124	C₂×#343	—	11	2	no	—
125	#1736	—	11	2	no	—
126	C₂³×C₁₁	—	2	2	no	—
127	C₂³×C₁₁	—	2	2	no	—
128	C₂³×C₁₁	#117	1	1	yes	characteristic
129	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
130	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
131	C₂³×C₁₁	#121	1	1	yes	characteristic
132	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
133	C₂³×C₁₁	#124	1	1	yes	characteristic
134	C₂³×C₁₁	#125	1	1	yes	characteristic
135	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
136	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
158	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
159	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
163	C₂×Dic₁₁	—	2	4	no	—
164	C₂×Dic₁₁	—	4	2	no	—
165	C₂×Dic₁₁	—	4	2	no	—
166	C₂×Dic₁₁	—	4	4	no	—
167	C₂×Dic₁₁	—	8	4	no	—
168	C₂×Dic₁₁	—	8	4	no	—
169	C₂×Dic₁₁	—	8	4	no	—
170	C₈×C₁₁	—	4	4	no	—
171	C₈×C₁₁	#95	1	4	yes	—
172	C₈×C₁₁	#95	1	4	yes	—
173	C₁₁⋊C₈	—	2	4	no	—
174	C₂²×M₁₆	—	11	1	no	—
175	C₂²×M₁₆	C₂×D₁₁	1	2	yes	—
176	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
177	C₂×#117	—	11	1	no	—
178	C₂²×C₄⋊C₄	—	11	2	no	—
179	C₂×#108	—	2	2	no	—
180	C₂×#108	—	2	2	no	—
181	C₂×#108	Dic₁₁	1	4	yes	complemented
182	C₂×#107	—	11	4	no	—
183	C₂×#107	—	22	1	no	—
184	C₂×#107	—	22	1	no	—
185	C₂×#107	—	22	2	no	—
186	#405	—	11	4	no	—
187	#405	—	22	2	no	—
188	C₂×#97	—	22	1	no	—
189	C₂×C₄×C₈	—	22	1	no	—
190	#343	—	22	4	no	—
191	#340	—	22	4	no	—
192	C₂²×C₁₁	—	2	2	no	—
193	C₂²×C₁₁	—	2	2	no	—
194	C₂²×C₁₁	—	2	2	no	—
195	C₂²×C₁₁	—	2	2	no	—
196	C₂²×C₁₁	—	2	1	no	—
197	C₂²×C₁₁	—	2	1	no	—
198	C₂²×C₁₁	—	2	1	no	—
199	C₂²×C₁₁	—	2	1	no	—
200	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
201	C₂²×C₁₁	#380	1	1	yes	characteristic
202	C₂²×C₁₁	#382	1	1	yes	characteristic
203	C₂²×C₁₁	#389	1	1	yes	characteristic
204	C₂²×C₁₁	#389	1	1	yes	characteristic
205	C₂²×C₁₁	#390	1	1	yes	characteristic
206	C₂²×C₁₁	#391	1	1	yes	characteristic
207	C₂²×C₁₁	#472	1	2	yes	—
208	C₂²×C₁₁	#473	1	2	yes	—
209	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
210	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
211	C₄×C₁₁	#380	1	1	yes	characteristic
212	C₄×C₁₁	#384	1	1	yes	characteristic
213	C₄×C₁₁	#389	1	1	yes	characteristic
214	C₄×C₁₁	#389	1	1	yes	characteristic
215	C₄×C₁₁	#390	1	1	yes	characteristic
216	C₄×C₁₁	#391	1	1	yes	characteristic
217	Dic₁₁	—	4	4	no	—
218	Dic₁₁	—	8	4	no	—
219	C₂³×C₄	—	22	2	no	—
220	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	2	2	no	—
223	C₂×M₁₆	—	2	2	no	—
224	C₂×M₁₆	—	2	2	no	—
225	C₂×M₁₆	—	2	2	no	—
226	C₂×M₁₆	—	11	2	no	—
227	C₂×M₁₆	—	11	2	no	—
228	C₂×M₁₆	—	11	2	no	—
229	C₂×M₁₆	—	22	1	no	—
230	C₂×M₁₆	—	22	1	no	—
231	C₂×M₁₆	—	22	1	no	—
232	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	22	1	no	—
235	C₂²×C₈	Dic₂₂	1	2	yes	—
236	C₂²×C₈	C₄×D₁₁	1	2	yes	—
237	C₂²×C₈	C₄×D₁₁	1	2	yes	—
238	C₂²×C₈	D₄₄	1	1	yes	characteristic
239	C₂²×C₈	D₄₄	1	1	yes	characteristic
240	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
241	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
242	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
243	#117	—	11	2	no	—
244	#117	—	11	2	no	—
245	#117	—	22	1	no	—
246	#117	—	22	1	no	—
247	C₂×C₄⋊C₄	—	11	2	no	—
248	C₂×C₄⋊C₄	—	11	4	no	—
249	C₂×C₄⋊C₄	—	22	2	no	—
250	C₂×C₄⋊C₄	—	22	2	no	—
251	C₂×C₄⋊C₄	—	22	2	no	—
252	C₂×C₄⋊C₄	—	22	2	no	—
253	C₂×C₄⋊C₄	—	22	2	no	—
254	C₂×C₂²⋊C₄	—	22	1	no	—
255	C₂×C₄²	—	22	1	no	—
256	#108	—	2	8	no	—
257	#107	—	22	4	no	—
258	#107	—	22	4	no	—
259	#97	—	22	4	no	—
260	C₄×C₈	—	22	4	no	—
261	C₂×C₁₁	—	2	1	no	—
262	C₂×C₁₁	—	2	1	no	—
263	C₂×C₁₁	—	2	1	no	—
264	C₂×C₁₁	—	2	1	no	—
265	C₂×C₁₁	C₄⋊#95	1	1	yes	characteristic
266	C₂×C₁₁	#1816	1	2	yes	—
267	C₂×C₁₁	#1952	1	2	yes	—
268	C₂×C₁₁	#1978	1	1	yes	characteristic
269	C₂×C₁₁	#1979	1	1	yes	characteristic
270	C₂⁴	#4343	1	1	yes	characteristic
271	C₂²×C₄	—	22	2	no	—
272	C₂²×C₄	—	22	4	no	—
273	C₂²×C₄	—	44	2	no	—
274	C₂²×C₄	—	44	2	no	—
275	C₂²×C₄	—	88	4	no	—
276	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
280	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
281	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
282	C₂²×C₄	#4341	1	1	yes	characteristic
283	C₂²×C₄	#4341	1	1	yes	characteristic
284	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
285	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
286	C₂²×C₄	#4343	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
290	M₁₆	—	2	4	no	—
291	M₁₆	—	2	4	no	—
292	M₁₆	—	4	2	no	—
293	M₁₆	—	4	2	no	—
294	M₁₆	—	11	4	no	—
295	M₁₆	—	22	2	no	—
296	M₁₆	—	22	2	no	—
297	M₁₆	—	22	2	no	—
298	C₂×C₈	—	2	4	no	—
299	C₂×C₈	—	4	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	22	2	no	—
302	C₂×C₈	—	22	2	no	—
303	C₂×C₈	—	22	2	no	—
304	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
305	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
306	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
307	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
308	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
309	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
310	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
311	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
312	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
313	C₂×C₈	C₂²⋊Dic₁₁	1	4	yes	—
314	C₄⋊C₄	—	11	4	no	—
315	C₄⋊C₄	—	22	2	no	—
316	C₄⋊C₄	—	22	4	no	—
317	C₄⋊C₄	—	22	4	no	—
318	C₄⋊C₄	—	44	2	no	—
319	C₄⋊C₄	—	44	2	no	—
320	C₂²⋊C₄	—	22	2	no	—
321	C₂²⋊C₄	—	22	2	no	—
322	C₄²	—	22	2	no	—
323	C₄²	—	22	2	no	—
324	C₁₁	#10870	1	1	yes	characteristic, complemented, Sylow
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	#66943	1	1	yes	characteristic
328	C₂³	#66945	1	1	yes	characteristic
329	C₂³	#66946	1	1	yes	characteristic
330	C₂³	#66948	1	1	yes	characteristic
331	C₂³	Q₈×Dic₁₁	1	1	yes	characteristic
332	C₂³	#66999	1	1	yes	characteristic
333	C₂³	#67000	1	1	yes	characteristic
334	C₂×C₄	—	22	4	no	—
335	C₂×C₄	—	44	2	no	—
336	C₂×C₄	—	44	2	no	—
337	C₂×C₄	—	44	4	no	—
338	C₂×C₄	—	88	4	no	—
339	C₂×C₄	—	88	4	no	—
340	C₂×C₄	—	88	4	no	—
341	C₂×C₄	#66940	1	1	yes	characteristic
342	C₂×C₄	#66940	1	1	yes	characteristic
343	C₂×C₄	#66941	1	1	yes	characteristic
344	C₂×C₄	#66941	1	1	yes	characteristic
345	C₂×C₄	#66943	1	1	yes	characteristic
346	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
347	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
348	C₂×C₄	#66945	1	1	yes	characteristic
349	C₂×C₄	#66946	1	1	yes	characteristic
350	C₂×C₄	#66948	1	1	yes	characteristic
351	C₂×C₄	#66950	1	1	yes	characteristic
352	C₂×C₄	#66950	1	1	yes	characteristic
353	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
354	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
355	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
357	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
358	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
359	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
360	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
361	C₂×C₄	#66989	1	1	yes	characteristic
362	C₂×C₄	#66991	1	1	yes	characteristic
363	C₂×C₄	#66991	1	1	yes	characteristic
364	C₂×C₄	#66993	1	1	yes	characteristic
365	C₂×C₄	#66997	1	1	yes	characteristic
366	C₂×C₄	Q₈×Dic₁₁	1	1	yes	characteristic
367	C₂×C₄	#66999	1	1	yes	characteristic
368	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
369	C₈	—	4	4	no	—
370	C₈	—	22	4	no	—
371	C₈	C₁₁⋊#95	1	4	yes	—
372	C₈	C₁₁⋊#95	1	4	yes	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	#10622509	1	2	yes	—
382	C₂²	#10622510	1	2	yes	—
383	C₂²	#10622586	1	1	yes	characteristic
384	C₂²	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
385	C₂²	#10622590	1	1	yes	characteristic
386	C₂²	#10622598	1	1	yes	characteristic
387	C₂²	#10622600	1	1	yes	characteristic
388	C₂²	#10622601	1	1	yes	characteristic
389	C₂²	#10622843	1	1	yes	characteristic
390	C₄	—	44	4	no	—
391	C₄	—	88	4	no	—
392	C₄	#10622586	1	1	yes	characteristic
393	C₄	#10622587	1	1	yes	characteristic
394	C₄	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
395	C₄	#10622589	1	1	yes	characteristic
396	C₄	#10622598	1	1	yes	characteristic
397	C₄	#10622600	1	1	yes	characteristic
398	C₄	C₂×C₁₁⋊#95	1	1	yes	characteristic
399	C₄	#10622834	1	1	yes	characteristic
400	C₂	—	2	1	no	—
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	#13066845	1	1	yes	characteristic
405	C₂	#13068677	1	2	yes	—
406	C₂	#13069402	1	2	yes	—
407	C₂	#13069524	1	1	yes	characteristic
408	C₂	#13069529	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66948
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₁
Fitting	C₂²×C₁₁×#108	C₂
socle	C₂³×C₁₁	#121
prime radical	C₂⁴×C₁₁	#41
cosocle	C₂³×C₄×C₁₁	C₂³
hypercenter	C₂²×#108	D₁₁
hypocenter	C₁₁	#10870
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₁×#108	C₄	semidirect
17. C₂×#66882	C₄	semidirect
19. #10622714	C₄	semidirect
181. C₂×#108	Dic₁₁	semidirect
324. C₁₁	#10870	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66882	2
C₂×#10622714	2
C₂×#10622192	2
#13068336	2
C₂²×C₁₁×#108	2
#10870	11