Subgroups — C₂×#13069404 #14757339

Order 2816.

858 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622737	C₂	1	2	yes	maximal
2	C₂²×#66883	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622714	C₂	1	1	yes	maximal, characteristic
4	#13069404	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10622194	C₂	1	2	yes	maximal
6	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
8	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×#66979	C₂²	1	1	yes	characteristic
10	C₂²×#4318	C₂²	1	2	yes	—
11	C₂²×#4318	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×#108	—	2	1	no	—
13	C₂×C₁₁×#108	—	2	1	no	—
14	C₂×C₁₁×#108	—	2	2	no	—
15	C₂×C₁₁×#108	C₂²	1	4	yes	—
16	#10622737	—	2	4	no	—
17	#10622737	C₂²	1	8	yes	—
18	C₂×#66886	—	2	4	no	—
19	C₂×#66883	C₄	1	4	yes	complemented
20	C₂×#66883	C₄	1	4	yes	complemented
21	C₂×#66883	C₂²	1	4	yes	—
22	#10622714	—	2	2	no	—
23	#10622714	C₂²	1	4	yes	—
24	C₂×#66879	—	2	1	no	—
25	C₂×C₈×Dic₁₁	—	2	1	no	—
26	#10622194	C₂²	1	8	yes	—
27	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
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	—	2	2	no	—
32	C₂×C₁₁×M₁₆	—	2	2	no	—
33	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
34	C₂²×C₈×C₁₁	—	2	2	no	—
35	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₁	C₂×C₄	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	D₄	1	2	yes	—
40	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
41	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
42	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂×C₂²⋊Dic₁₁	Q₈	1	2	yes	—
44	#66979	—	2	1	no	—
45	#66979	—	2	1	no	—
46	#66979	Q₈	1	2	yes	—
47	#66979	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₁₁	—	2	1	no	—
49	C₂×C₄×Dic₁₁	—	2	1	no	—
50	C₂×#4318	—	2	2	no	—
51	C₂×#4318	—	2	1	no	—
52	C₂×#4318	—	2	1	no	—
53	C₂×#4318	—	2	1	no	—
54	C₂×#4318	—	2	2	no	—
55	C₂×#4318	—	2	2	no	—
56	C₂×#4318	C₂×C₄	1	4	yes	—
57	C₂×#4318	C₂×C₄	1	4	yes	—
58	C₂×#4318	D₄	1	2	yes	—
59	C₂×#4318	D₄	1	2	yes	—
60	C₂×#4318	C₂³	1	4	yes	—
61	C₂×#4318	C₂³	1	2	yes	—
62	C₂²×C₁₁⋊C₈	—	2	2	no	—
63	C₂²×C₁₁⋊C₈	—	2	1	no	—
64	C₁₁×#108	—	2	4	no	—
65	C₁₁×#108	—	2	4	no	—
66	#66886	—	2	16	no	—
67	#66883	C₂×C₄	1	16	yes	complemented
68	#66879	—	2	4	no	—
69	C₈×Dic₁₁	—	2	4	no	—
70	C₂×#1953	—	11	1	no	maximal, Sylow
71	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂²×C₄	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×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
86	C₂²×Dic₁₁	—	2	2	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	C₄⋊C₄	1	2	yes	—
95	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
96	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
97	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
98	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
99	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
102	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
104	C₂²⋊Dic₁₁	—	2	2	no	—
105	C₂²⋊Dic₁₁	C₂×Q₈	1	4	yes	—
106	C₄⋊Dic₁₁	—	2	2	no	—
107	C₄⋊Dic₁₁	—	2	2	no	—
108	C₄×Dic₁₁	—	2	2	no	—
109	C₄×Dic₁₁	—	2	2	no	—
110	#4318	—	2	4	no	—
111	#4318	—	2	4	no	—
112	#4318	—	2	2	no	—
113	#4318	—	2	2	no	—
114	#4318	—	2	2	no	—
115	#4318	—	2	4	no	—
116	#4318	C₂²×C₄	1	8	yes	—
117	#4318	C₂×D₄	1	4	yes	—
118	C₂×C₁₁⋊C₈	—	2	4	no	—
119	C₂×C₁₁⋊C₈	—	2	4	no	—
120	C₂×C₁₁⋊C₈	—	2	2	no	—
121	C₂×C₁₁⋊C₈	—	2	2	no	—
122	C₂×C₁₁⋊C₈	—	2	2	no	—
123	C₂×C₁₁⋊C₈	—	2	4	no	—
124	C₂×#430	—	11	2	no	—
125	C₂²×#108	—	11	1	no	—
126	C₂²×#108	D₁₁	1	1	yes	characteristic
127	C₂×#405	—	11	1	no	—
128	#1953	—	11	8	no	—
129	C₂×#344	—	11	2	no	—
130	C₂³×C₁₁	—	4	2	no	—
131	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
132	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
133	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
136	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
137	C₂³×C₁₁	C₂²×Q₈	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	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₄×D₄	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×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₁₁	#121	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	C₂²⋊Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
156	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
157	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₁₁	—	2	4	no	—
167	C₂×Dic₁₁	—	4	4	no	—
168	C₈×C₁₁	—	4	4	no	—
169	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
170	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
171	C₁₁⋊C₈	—	2	8	no	—
172	C₁₁⋊C₈	—	2	4	no	—
173	C₂²×M₁₆	—	11	1	no	—
174	C₂²×M₁₆	—	11	2	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	#430	—	11	8	no	—
179	#430	—	22	4	no	—
180	C₂×#108	—	2	1	no	—
181	C₂×#108	—	2	1	no	—
182	C₂×#108	—	2	2	no	—
183	C₂×#108	—	11	4	no	—
184	C₂×#108	—	11	4	no	—
185	C₂×#108	—	11	4	no	—
186	C₂×#108	—	22	4	no	—
187	C₂×#108	C₂×D₁₁	1	4	yes	—
188	#405	—	11	4	no	—
189	#405	—	22	2	no	—
190	C₂×#97	—	22	1	no	—
191	C₂×C₄×C₈	—	22	1	no	—
192	#344	—	11	8	no	—
193	C₂²×C₁₁	—	2	2	no	—
194	C₂²×C₁₁	—	2	2	no	—
195	C₂²×C₁₁	—	2	2	no	—
196	C₂²×C₁₁	—	4	1	no	—
197	C₂²×C₁₁	—	4	1	no	—
198	C₂²×C₁₁	—	4	1	no	—
199	C₂²×C₁₁	—	4	1	no	—
200	C₂²×C₁₁	#389	1	1	yes	characteristic
201	C₂²×C₁₁	#389	1	1	yes	characteristic
202	C₂²×C₁₁	#389	1	1	yes	characteristic
203	C₂²×C₁₁	#389	1	1	yes	characteristic
204	C₂²×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
205	C₂²×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
206	C₂²×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
207	C₄×C₁₁	#389	1	1	yes	characteristic
208	C₄×C₁₁	#389	1	1	yes	characteristic
209	C₄×C₁₁	#389	1	1	yes	characteristic
210	C₄×C₁₁	#389	1	1	yes	characteristic
211	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
212	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
213	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
214	C₄×C₁₁	C₂×#125	1	1	yes	characteristic
215	Dic₁₁	—	4	4	no	—
216	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	2	2	no	—
220	C₂×M₁₆	—	2	2	no	—
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	—	11	4	no	—
223	C₂×M₁₆	—	11	4	no	—
224	C₂×M₁₆	—	11	2	no	—
225	C₂×M₁₆	—	11	2	no	—
226	C₂×M₁₆	—	11	4	no	—
227	C₂×M₁₆	—	11	2	no	—
228	C₂×M₁₆	—	22	2	no	—
229	C₂×M₁₆	—	22	1	no	—
230	C₂×M₁₆	—	22	1	no	—
231	C₂×M₁₆	—	22	2	no	—
232	C₂×M₁₆	—	22	2	no	—
233	C₂×M₁₆	—	22	1	no	—
234	C₂×M₁₆	C₂²×D₁₁	1	4	yes	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	22	2	no	—
237	C₂²×C₈	—	22	1	no	—
238	C₂²×C₈	Dic₂₂	1	2	yes	—
239	C₂²×C₈	Dic₂₂	1	2	yes	—
240	C₂²×C₈	C₄×D₁₁	1	2	yes	—
241	C₂²×C₈	C₄×D₁₁	1	2	yes	—
242	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
243	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
244	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
245	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
246	#117	—	11	2	no	—
247	#117	—	11	2	no	—
248	#117	—	22	1	no	—
249	#117	—	22	1	no	—
250	C₂×C₄⋊C₄	—	22	1	no	—
251	C₂×C₂²⋊C₄	—	11	2	no	—
252	C₂×C₄²	—	22	1	no	—
253	#108	—	2	4	no	—
254	#108	—	2	4	no	—
255	#108	—	11	16	no	—
256	#108	—	22	16	no	—
257	#97	—	22	4	no	—
258	C₄×C₈	—	22	4	no	—
259	C₂×C₁₁	—	2	1	no	—
260	C₂×C₁₁	—	2	1	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	#1953	1	2	yes	complemented
266	C₂×C₁₁	C₂×#389	1	1	yes	characteristic
267	C₂⁴	Q₈×D₁₁	1	1	yes	characteristic
268	C₂²×C₄	—	22	2	no	—
269	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
270	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
271	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
272	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
273	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
274	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
275	C₂²×C₄	#4341	1	1	yes	characteristic
276	C₂²×C₄	#4341	1	1	yes	characteristic
277	C₂²×C₄	Q₈×D₁₁	1	1	yes	characteristic
278	C₂²×C₄	#4343	1	1	yes	characteristic
279	C₂²×C₄	#4343	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
282	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
283	M₁₆	—	2	4	no	—
284	M₁₆	—	2	4	no	—
285	M₁₆	—	4	2	no	—
286	M₁₆	—	4	2	no	—
287	M₁₆	—	11	8	no	—
288	M₁₆	—	11	4	no	—
289	M₁₆	—	22	4	no	—
290	M₁₆	—	22	4	no	—
291	M₁₆	—	22	2	no	—
292	M₁₆	—	22	2	no	—
293	M₁₆	—	22	2	no	—
294	M₁₆	—	22	4	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	22	4	no	—
299	C₂×C₈	—	22	4	no	—
300	C₂×C₈	—	22	2	no	—
301	C₂×C₈	—	22	2	no	—
302	C₂×C₈	—	22	4	no	—
303	C₂×C₈	—	22	2	no	—
304	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
305	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
306	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
307	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
308	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
309	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
310	C₂×C₈	C₂×Dic₂₂	1	4	yes	—
311	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
312	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
313	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
314	C₄⋊C₄	—	22	2	no	—
315	C₄⋊C₄	—	22	2	no	—
316	C₂²⋊C₄	—	11	4	no	—
317	C₂²⋊C₄	—	22	2	no	—
318	C₄²	—	22	2	no	—
319	C₄²	—	22	2	no	—
320	C₁₁	C₂×#1953	1	1	yes	characteristic, complemented, Sylow
321	C₂³	—	4	2	no	—
322	C₂³	#66940	1	1	yes	characteristic
323	C₂³	#66940	1	1	yes	characteristic
324	C₂³	#66941	1	1	yes	characteristic
325	C₂³	#66941	1	1	yes	characteristic
326	C₂³	#66999	1	1	yes	characteristic
327	C₂³	#66999	1	1	yes	characteristic
328	C₂³	C₂×Q₈×D₁₁	1	1	yes	characteristic
329	C₂×C₄	—	22	4	no	—
330	C₂×C₄	—	44	4	no	—
331	C₂×C₄	#66940	1	1	yes	characteristic
332	C₂×C₄	#66940	1	1	yes	characteristic
333	C₂×C₄	#66941	1	1	yes	characteristic
334	C₂×C₄	#66941	1	1	yes	characteristic
335	C₂×C₄	#66943	1	1	yes	characteristic
336	C₂×C₄	#66943	1	1	yes	characteristic
337	C₂×C₄	#66943	1	1	yes	characteristic
338	C₂×C₄	#66943	1	1	yes	characteristic
339	C₂×C₄	#66946	1	1	yes	characteristic
340	C₂×C₄	#66946	1	1	yes	characteristic
341	C₂×C₄	#66946	1	1	yes	characteristic
342	C₂×C₄	#66946	1	1	yes	characteristic
343	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
347	C₂×C₄	#66991	1	1	yes	characteristic
348	C₂×C₄	#66991	1	1	yes	characteristic
349	C₂×C₄	#66991	1	1	yes	characteristic
350	C₂×C₄	#66991	1	1	yes	characteristic
351	C₂×C₄	#66999	1	1	yes	characteristic
352	C₂×C₄	#66999	1	1	yes	characteristic
353	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
355	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
356	C₂×C₄	C₂×#4341	1	1	yes	characteristic
357	C₂×C₄	C₂×#4343	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
359	C₈	—	4	4	no	—
360	C₈	—	22	8	no	—
361	C₈	—	22	4	no	—
362	C₈	C₂×Dic₁₁⋊C₄	1	4	yes	—
363	C₈	C₂×Dic₁₁⋊C₄	1	4	yes	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	#10622586	1	1	yes	characteristic
372	C₂²	#10622586	1	1	yes	characteristic
373	C₂²	#10622586	1	1	yes	characteristic
374	C₂²	#10622586	1	1	yes	characteristic
375	C₂²	C₂×#66940	1	1	yes	characteristic
376	C₂²	C₂×#66941	1	1	yes	characteristic
377	C₂²	C₂×#66999	1	1	yes	characteristic
378	C₄	—	44	4	no	—
379	C₄	#10622586	1	1	yes	characteristic
380	C₄	#10622586	1	1	yes	characteristic
381	C₄	#10622586	1	1	yes	characteristic
382	C₄	#10622586	1	1	yes	characteristic
383	C₄	C₂×#66943	1	1	yes	characteristic
384	C₄	C₂×#66946	1	1	yes	characteristic
385	C₄	C₂²×Dic₁₁⋊C₄	1	1	yes	characteristic
386	C₄	C₂×#66991	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	#13069404	1	2	yes	direct product factor
394	C₂	C₂×#10622586	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#66991
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₂²×C₁₁×#108	C₂
socle	C₂²×C₁₁	#389
prime radical	C₂⁴×C₁₁	C₂×Q₈
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₂²×#108	D₁₁
hypocenter	C₁₁	C₂×#1953
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
4. #13069404	C₂	direct (N × H)
19. C₂×#66883	C₄	semidirect
20. C₂×#66883	C₄	semidirect
67. #66883	C₂×C₄	semidirect
265. C₂×C₁₁	#1953	semidirect
320. C₁₁	C₂×#1953	semidirect
393. C₂	#13069404	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10622737	2
C₂²×#66883	2
C₂×#10622714	2
#13069404	2
C₂×#10622194	2
C₂²×C₁₁×#108	2
C₂×#1953	11

Subgroups — C2×#13069404 #14757339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13069404 #14757339