Subgroups — #14659721

Order 2816.

714 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66883	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622714	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622194	C₂	1	2	yes	maximal
4	#13068342	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×#4318	C₂²	1	2	yes	—
10	C₂²×#4318	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×#108	—	2	2	no	—
12	C₂×C₁₁×#108	—	2	1	no	—
13	C₂×C₁₁×#108	—	2	1	no	—
14	C₂×C₁₁×#108	C₄	1	4	yes	complemented
15	C₂×#66883	—	2	2	no	—
16	C₂×#66883	—	2	2	no	—
17	C₂×#66883	C₄	1	4	yes	complemented
18	#10622714	—	2	2	no	—
19	#10622714	C₄	1	4	yes	—
20	C₂×#66879	—	2	1	no	—
21	C₂×C₈×Dic₁₁	—	2	1	no	—
22	#10622196	—	2	4	no	—
23	#10622194	—	2	4	no	—
24	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
25	C₂×C₁₁×M₁₆	—	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	C₂×C₄	1	4	yes	—
31	C₂²×C₈×C₁₁	—	2	2	no	—
32	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₂²×C₈×C₁₁	D₄	1	2	yes	—
36	C₂²×C₈×C₁₁	D₄	1	2	yes	—
37	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
40	C₂×C₂²⋊Dic₁₁	Q₈	1	2	yes	—
41	#66979	—	2	1	no	—
42	#66979	—	2	1	no	—
43	#66979	C₂×C₄	1	2	yes	—
44	#66979	D₄	1	2	yes	—
45	C₂×C₄⋊Dic₁₁	—	2	1	no	—
46	C₂×C₄×Dic₁₁	—	2	1	no	—
47	C₂×#4318	—	2	1	no	—
48	C₂×#4318	—	2	1	no	—
49	C₂×#4318	—	2	1	no	—
50	C₂×#4318	—	2	2	no	—
51	C₂×#4318	—	2	2	no	—
52	C₂×#4318	—	2	2	no	—
53	C₂×#4318	—	2	2	no	—
54	C₂×#4318	—	2	2	no	—
55	C₂×#4318	C₂×C₄	1	4	yes	—
56	C₂×#4318	C₂×C₄	1	2	yes	—
57	C₂×#4318	D₄	1	2	yes	—
58	C₂×#4318	Q₈	1	2	yes	—
59	C₂²×C₁₁⋊C₈	—	2	1	no	—
60	C₂²×C₁₁⋊C₈	—	2	2	no	—
61	C₁₁×#108	—	2	4	no	—
62	C₁₁×#108	—	2	4	no	—
63	#66883	—	2	8	no	—
64	#66879	—	2	4	no	—
65	C₈×Dic₁₁	—	2	4	no	—
66	#10873	—	11	1	no	maximal, Sylow
67	C₂⁴×C₁₁	C₂×Q₈	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	#41	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	2	no	—
83	C₁₁×M₁₆	—	2	4	no	—
84	C₁₁×M₁₆	—	2	4	no	—
85	C₁₁×M₁₆	—	4	2	no	—
86	C₁₁×M₁₆	—	4	2	no	—
87	C₂×C₈×C₁₁	—	2	4	no	—
88	C₂×C₈×C₁₁	—	4	2	no	—
89	C₂×C₈×C₁₁	—	4	2	no	—
90	C₂×C₈×C₁₁	C₄²	1	4	yes	—
91	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
92	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
93	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
94	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
97	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
99	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
100	C₂²⋊Dic₁₁	—	2	2	no	—
101	C₂²⋊Dic₁₁	C₄⋊C₄	1	4	yes	—
102	C₄⋊Dic₁₁	—	2	2	no	—
103	C₄⋊Dic₁₁	—	2	2	no	—
104	C₄×Dic₁₁	—	2	2	no	—
105	C₄×Dic₁₁	—	2	2	no	—
106	#4318	—	2	4	no	—
107	#4318	—	2	2	no	—
108	#4318	—	2	4	no	—
109	#4318	—	2	2	no	—
110	#4318	—	2	2	no	—
111	#4318	—	4	2	no	—
112	#4318	—	4	2	no	—
113	#4318	C₄⋊C₄	1	4	yes	—
114	C₂×C₁₁⋊C₈	—	2	2	no	—
115	C₂×C₁₁⋊C₈	—	2	4	no	—
116	C₂×C₁₁⋊C₈	—	2	2	no	—
117	C₂×C₁₁⋊C₈	—	2	2	no	—
118	C₂×C₁₁⋊C₈	—	4	2	no	—
119	C₂×C₁₁⋊C₈	—	4	2	no	—
120	C₂²×#108	—	11	1	no	—
121	C₂²×#108	D₁₁	1	1	yes	characteristic
122	C₂×#405	—	11	1	no	—
123	C₂×#344	—	11	2	no	—
124	#1738	—	11	2	no	—
125	C₂³×C₁₁	—	4	2	no	—
126	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
128	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
129	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
130	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
131	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
132	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
133	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
134	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₁₁	C₂×C₄⋊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	#117	1	1	yes	characteristic
142	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₄×D₄	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×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₁	#121	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	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
156	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
157	C₂×C₄×C₁₁	#125	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×Dic₁₁	—	2	4	no	—
162	C₂×Dic₁₁	—	4	4	no	—
163	C₈×C₁₁	—	4	4	no	—
164	C₈×C₁₁	#95	1	4	yes	—
165	C₈×C₁₁	#95	1	4	yes	—
166	C₁₁⋊C₈	—	2	4	no	—
167	C₁₁⋊C₈	—	4	4	no	—
168	C₂²×M₁₆	—	11	1	no	—
169	C₂²×M₁₆	—	11	2	no	—
170	C₂²×M₁₆	C₂×D₁₁	1	2	yes	—
171	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
172	C₂×#117	—	11	1	no	—
173	C₂×#108	—	2	1	no	—
174	C₂×#108	—	2	1	no	—
175	C₂×#108	—	2	2	no	—
176	C₂×#108	—	11	4	no	—
177	C₂×#108	—	22	2	no	—
178	C₂×#108	—	22	2	no	—
179	C₂×#108	Dic₁₁	1	4	yes	complemented
180	#405	—	11	4	no	—
181	#405	—	22	2	no	—
182	C₂×#97	—	22	1	no	—
183	C₂×C₄×C₈	—	22	1	no	—
184	#344	—	22	4	no	—
185	#341	—	22	4	no	—
186	C₂²×C₁₁	—	2	2	no	—
187	C₂²×C₁₁	—	2	2	no	—
188	C₂²×C₁₁	—	2	2	no	—
189	C₂²×C₁₁	—	4	1	no	—
190	C₂²×C₁₁	—	4	1	no	—
191	C₂²×C₁₁	—	4	1	no	—
192	C₂²×C₁₁	—	4	1	no	—
193	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
194	C₂²×C₁₁	#380	1	1	yes	characteristic
195	C₂²×C₁₁	#384	1	1	yes	characteristic
196	C₂²×C₁₁	#389	1	1	yes	characteristic
197	C₂²×C₁₁	#389	1	1	yes	characteristic
198	C₂²×C₁₁	#391	1	1	yes	characteristic
199	C₂²×C₁₁	#391	1	1	yes	characteristic
200	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
201	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
202	C₄×C₁₁	#380	1	1	yes	characteristic
203	C₄×C₁₁	#382	1	1	yes	characteristic
204	C₄×C₁₁	#389	1	1	yes	characteristic
205	C₄×C₁₁	#389	1	1	yes	characteristic
206	C₄×C₁₁	#390	1	1	yes	characteristic
207	C₄×C₁₁	#390	1	1	yes	characteristic
208	Dic₁₁	—	4	4	no	—
209	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	—	2	2	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	—	2	2	no	—
215	C₂×M₁₆	—	11	2	no	—
216	C₂×M₁₆	—	11	2	no	—
217	C₂×M₁₆	—	11	2	no	—
218	C₂×M₁₆	—	11	4	no	—
219	C₂×M₁₆	—	22	1	no	—
220	C₂×M₁₆	—	22	1	no	—
221	C₂×M₁₆	—	22	1	no	—
222	C₂×M₁₆	—	22	2	no	—
223	C₂×M₁₆	—	22	2	no	—
224	C₂×M₁₆	—	22	2	no	—
225	C₂×M₁₆	—	22	2	no	—
226	C₂×M₁₆	—	22	2	no	—
227	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	—	22	1	no	—
230	C₂²×C₈	—	22	2	no	—
231	C₂²×C₈	Dic₂₂	1	2	yes	—
232	C₂²×C₈	C₄×D₁₁	1	2	yes	—
233	C₂²×C₈	C₄×D₁₁	1	2	yes	—
234	C₂²×C₈	D₄₄	1	2	yes	—
235	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
236	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
237	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
238	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
239	#117	—	11	2	no	—
240	#117	—	11	2	no	—
241	#117	—	22	1	no	—
242	#117	—	22	1	no	—
243	C₂×C₄⋊C₄	—	22	1	no	—
244	C₂×C₂²⋊C₄	—	11	2	no	—
245	C₂×C₄²	—	22	1	no	—
246	#108	—	2	4	no	—
247	#108	—	2	4	no	—
248	#108	—	22	8	no	—
249	#97	—	22	4	no	—
250	C₄×C₈	—	22	4	no	—
251	C₂×C₁₁	—	2	1	no	—
252	C₂×C₁₁	—	2	1	no	—
253	C₂×C₁₁	—	2	1	no	—
254	C₂×C₁₁	—	2	1	no	—
255	C₂×C₁₁	—	2	1	no	—
256	C₂×C₁₁	—	2	1	no	—
257	C₂×C₁₁	C₄⋊#95	1	1	yes	characteristic
258	C₂×C₁₁	#1953	1	2	yes	—
259	C₂⁴	Q₈×D₁₁	1	1	yes	characteristic
260	C₂²×C₄	—	22	2	no	—
261	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
265	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
266	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
267	C₂²×C₄	#4341	1	1	yes	characteristic
268	C₂²×C₄	#4341	1	1	yes	characteristic
269	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
270	C₂²×C₄	#4343	1	1	yes	characteristic
271	C₂²×C₄	#4343	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
275	M₁₆	—	2	4	no	—
276	M₁₆	—	2	4	no	—
277	M₁₆	—	4	2	no	—
278	M₁₆	—	4	2	no	—
279	M₁₆	—	11	4	no	—
280	M₁₆	—	22	2	no	—
281	M₁₆	—	22	2	no	—
282	M₁₆	—	22	2	no	—
283	M₁₆	—	22	4	no	—
284	M₁₆	—	22	4	no	—
285	M₁₆	—	44	2	no	—
286	M₁₆	—	44	2	no	—
287	C₂×C₈	—	2	4	no	—
288	C₂×C₈	—	4	2	no	—
289	C₂×C₈	—	4	2	no	—
290	C₂×C₈	—	22	2	no	—
291	C₂×C₈	—	22	2	no	—
292	C₂×C₈	—	22	2	no	—
293	C₂×C₈	—	22	4	no	—
294	C₂×C₈	—	44	2	no	—
295	C₂×C₈	—	44	2	no	—
296	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
297	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
298	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
299	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
300	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
301	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
302	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
303	C₂×C₈	(C₂×D₁₁)⋊C₄	1	4	yes	—
304	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
305	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
306	C₄⋊C₄	—	22	2	no	—
307	C₄⋊C₄	—	22	2	no	—
308	C₂²⋊C₄	—	11	4	no	—
309	C₂²⋊C₄	—	22	2	no	—
310	C₄²	—	22	2	no	—
311	C₄²	—	22	2	no	—
312	C₁₁	#10873	1	1	yes	characteristic, complemented, Sylow
313	C₂³	—	4	2	no	—
314	C₂³	#66940	1	1	yes	characteristic
315	C₂³	#66941	1	1	yes	characteristic
316	C₂³	C₄⋊C₄×D₁₁	1	1	yes	characteristic
317	C₂³	#66950	1	1	yes	characteristic
318	C₂³	#66997	1	1	yes	characteristic
319	C₂³	Q₈×Dic₁₁	1	1	yes	characteristic
320	C₂³	#66999	1	1	yes	characteristic
321	C₂×C₄	—	22	4	no	—
322	C₂×C₄	—	44	4	no	—
323	C₂×C₄	#66940	1	1	yes	characteristic
324	C₂×C₄	#66941	1	1	yes	characteristic
325	C₂×C₄	#66943	1	1	yes	characteristic
326	C₂×C₄	#66943	1	1	yes	characteristic
327	C₂×C₄	C₄⋊C₄×D₁₁	1	1	yes	characteristic
328	C₂×C₄	#66945	1	1	yes	characteristic
329	C₂×C₄	#66945	1	1	yes	characteristic
330	C₂×C₄	#66946	1	1	yes	characteristic
331	C₂×C₄	#66946	1	1	yes	characteristic
332	C₂×C₄	#66948	1	1	yes	characteristic
333	C₂×C₄	#66948	1	1	yes	characteristic
334	C₂×C₄	#66950	1	1	yes	characteristic
335	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
339	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
341	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
342	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
343	C₂×C₄	#66989	1	1	yes	characteristic
344	C₂×C₄	#66991	1	1	yes	characteristic
345	C₂×C₄	#66991	1	1	yes	characteristic
346	C₂×C₄	#66993	1	1	yes	characteristic
347	C₂×C₄	Q₈×Dic₁₁	1	1	yes	characteristic
348	C₂×C₄	#66999	1	1	yes	characteristic
349	C₂×C₄	#67000	1	1	yes	characteristic
350	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
351	C₈	—	4	4	no	—
352	C₈	—	22	4	no	—
353	C₈	—	44	4	no	—
354	C₈	C₁₁⋊#95	1	4	yes	—
355	C₈	C₁₁⋊#95	1	4	yes	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	4	1	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	4	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	#10622586	1	1	yes	characteristic
364	C₂²	#10622587	1	1	yes	characteristic
365	C₂²	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
366	C₂²	#10622589	1	1	yes	characteristic
367	C₂²	#10622598	1	1	yes	characteristic
368	C₂²	#10622600	1	1	yes	characteristic
369	C₂²	#10622843	1	1	yes	characteristic
370	C₄	—	44	4	no	—
371	C₄	#10622586	1	1	yes	characteristic
372	C₄	C₄⋊C₄×Dic₁₁	1	1	yes	characteristic
373	C₄	#10622590	1	1	yes	characteristic
374	C₄	#10622598	1	1	yes	characteristic
375	C₄	#10622600	1	1	yes	characteristic
376	C₄	#10622601	1	1	yes	characteristic
377	C₄	C₂×C₁₁⋊#95	1	1	yes	characteristic
378	C₄	#10622834	1	1	yes	characteristic
379	C₂	—	2	1	no	—
380	C₂	—	2	1	no	—
381	C₂	—	2	1	no	—
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	2	1	no	—
385	C₂	#13066845	1	1	yes	characteristic
386	C₂	#13069404	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#66991
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₁
Fitting	C₂²×C₁₁×#108	C₂
socle	C₂²×C₁₁	#389
prime radical	C₂⁴×C₁₁	C₂×Q₈
cosocle	C₂³×C₄×C₁₁	C₂³
hypercenter	C₂²×#108	D₁₁
hypocenter	C₁₁	#10873
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
14. C₂×C₁₁×#108	C₄	semidirect
17. C₂×#66883	C₄	semidirect
179. C₂×#108	Dic₁₁	semidirect
312. C₁₁	#10873	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66883	2
C₂×#10622714	2
C₂×#10622194	2
#13068342	2
C₂²×C₁₁×#108	2
#10873	11