Subgroups — C₂×#13066446 #14643188

Order 2816.

678 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622538	C₂	1	1	yes	maximal, characteristic
2	C₂²×#66867	C₂	1	1	yes	maximal, characteristic
3	#13066446	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂³×C₁₁⋊C₈	C₄	1	2	yes	—
7	C₁₁×#431	—	2	1	no	—
8	C₁₁×#431	—	2	1	no	—
9	C₁₁×#431	C₄	1	2	yes	—
10	C₁₁×#431	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
14	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	1	no	—
15	#10622538	—	2	1	no	—
16	#10622538	—	2	1	no	—
17	#10622538	C₄	1	2	yes	—
18	#10622538	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
20	C₂×#66867	—	2	1	no	—
21	C₂×#66867	—	2	1	no	—
22	C₂×#66867	—	2	1	no	—
23	C₂×#66867	—	2	1	no	—
24	C₂×#66867	C₄	1	2	yes	—
25	C₂×#66867	C₂²	1	2	yes	—
26	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	2	no	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
43	C₂²×C₁₁⋊C₈	—	2	2	no	—
44	C₂²×C₁₁⋊C₈	—	2	2	no	—
45	C₂²×C₁₁⋊C₈	—	2	4	no	—
46	C₂²×C₁₁⋊C₈	—	2	2	no	—
47	C₂²×C₁₁⋊C₈	C₈	1	8	yes	complemented
48	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
49	C₁₁×C₄⋊C₈	—	2	2	no	—
50	C₁₁×C₄⋊C₈	—	2	2	no	—
51	C₁₁×C₂²⋊C₈	—	2	2	no	—
52	C₁₁×C₂²⋊C₈	—	2	2	no	—
53	C₄×C₈×C₁₁	—	2	2	no	—
54	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
55	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
56	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
59	#66867	—	2	2	no	—
60	#66867	—	2	2	no	—
61	#66867	—	2	2	no	—
62	#66867	—	2	2	no	—
63	C₄×C₁₁⋊C₈	—	2	2	no	—
64	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
65	C₂×#1275	—	11	1	no	maximal, Sylow
66	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	—	4	2	no	—
68	C₂²×C₄×C₁₁	—	4	2	no	—
69	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂²⋊C₄	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	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
85	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
86	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
89	C₂×C₈×C₁₁	—	2	4	no	—
90	C₂×C₈×C₁₁	—	4	4	no	—
91	C₄²×C₁₁	C₄²	1	1	yes	characteristic
92	C₄²×C₁₁	C₄²	1	1	yes	characteristic
93	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
107	C₂×C₁₁⋊C₈	—	2	8	no	—
108	C₂×C₁₁⋊C₈	—	2	8	no	—
109	C₂×C₁₁⋊C₈	—	2	4	no	—
110	C₂×C₁₁⋊C₈	—	2	4	no	—
111	C₂×C₁₁⋊C₈	—	2	4	no	—
112	C₂×C₁₁⋊C₈	—	4	4	no	—
113	C₂×C₁₁⋊C₈	C₂×C₈	1	8	yes	complemented
114	C₂×#431	—	11	1	no	—
115	C₂×#431	D₁₁	1	1	yes	characteristic
116	C₂²×#97	—	11	1	no	—
117	#1275	—	11	4	no	—
118	C₂³×C₁₁	—	2	2	no	—
119	C₂³×C₁₁	—	2	2	no	—
120	C₂³×C₁₁	#95	1	1	yes	characteristic
121	C₂³×C₁₁	#95	1	1	yes	characteristic
122	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
123	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	4	1	no	—
129	C₂×C₄×C₁₁	—	4	1	no	—
130	C₂×C₄×C₁₁	—	4	1	no	—
131	C₂×C₄×C₁₁	—	4	1	no	—
132	C₂×C₄×C₁₁	—	4	1	no	—
133	C₂×C₄×C₁₁	—	4	1	no	—
134	C₂×C₄×C₁₁	—	4	1	no	—
135	C₂×C₄×C₁₁	—	4	1	no	—
136	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
137	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
143	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
144	C₂×C₄×C₁₁	#97	1	2	yes	—
145	C₂×C₄×C₁₁	#97	1	2	yes	—
146	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
147	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
148	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
149	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
157	C₈×C₁₁	—	4	4	no	—
158	C₁₁⋊C₈	—	2	8	no	—
159	C₁₁⋊C₈	—	4	4	no	—
160	C₂³×C₈	—	11	2	no	—
161	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
162	#431	—	2	1	no	—
163	#431	—	2	1	no	—
164	#431	—	11	2	no	—
165	#431	—	11	2	no	—
166	#431	—	22	1	no	—
167	#431	—	22	1	no	—
168	#431	Dic₁₁	1	2	yes	—
169	#431	C₂×D₁₁	1	2	yes	—
170	C₂×C₄⋊C₈	—	2	1	no	—
171	C₂×C₄⋊C₈	—	22	1	no	—
172	C₂×C₂²⋊C₈	—	2	1	no	—
173	C₂×C₂²⋊C₈	—	22	1	no	—
174	C₂×#97	—	11	2	no	—
175	C₂×#97	—	11	2	no	—
176	C₂×#97	—	22	1	no	—
177	C₂×#97	—	22	1	no	—
178	C₂×#97	—	22	1	no	—
179	C₂×#97	—	22	1	no	—
180	C₂×C₄×C₈	—	11	2	no	—
181	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
182	C₂²×C₁₁	—	2	1	no	—
183	C₂²×C₁₁	—	2	1	no	—
184	C₂²×C₁₁	—	2	1	no	—
185	C₂²×C₁₁	—	2	1	no	—
186	C₂²×C₁₁	—	2	8	no	—
187	C₂²×C₁₁	#336	1	2	yes	—
188	C₂²×C₁₁	#336	1	2	yes	—
189	C₂²×C₁₁	H(3,ℤ/4)	1	2	yes	—
190	C₂²×C₁₁	#338	1	2	yes	—
191	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
192	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
193	C₄×C₁₁	—	2	1	no	—
194	C₄×C₁₁	—	2	1	no	—
195	C₄×C₁₁	—	2	1	no	—
196	C₄×C₁₁	—	2	1	no	—
197	C₄×C₁₁	—	2	1	no	—
198	C₄×C₁₁	—	2	1	no	—
199	C₄×C₁₁	—	2	1	no	—
200	C₄×C₁₁	—	2	1	no	—
201	C₄×C₁₁	#336	1	2	yes	—
202	C₄×C₁₁	#336	1	2	yes	—
203	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
204	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
205	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
206	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
207	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
208	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
209	C₂²×C₈	—	2	2	no	—
210	C₂²×C₈	—	11	8	no	—
211	C₂²×C₈	—	11	4	no	—
212	C₂²×C₈	—	22	4	no	—
213	C₂²×C₈	—	22	2	no	—
214	C₂²×C₈	—	22	2	no	—
215	C₂²×C₈	—	22	2	no	—
216	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
217	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
218	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
219	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
220	C₂×C₄²	D₄₄	1	1	yes	characteristic
221	C₂×C₄²	D₄₄	1	1	yes	characteristic
222	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
223	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
224	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
225	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
226	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
227	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
228	C₄⋊C₈	—	2	2	no	—
229	C₄⋊C₈	—	2	2	no	—
230	C₄⋊C₈	—	22	2	no	—
231	C₄⋊C₈	—	22	2	no	—
232	C₂²⋊C₈	—	2	2	no	—
233	C₂²⋊C₈	—	2	2	no	—
234	C₂²⋊C₈	—	22	2	no	—
235	C₂²⋊C₈	—	22	2	no	—
236	#97	—	22	2	no	—
237	#97	—	22	2	no	—
238	#97	—	22	2	no	—
239	#97	—	22	2	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	—	11	4	no	—
242	C₄×C₈	—	22	2	no	—
243	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
244	C₂×C₁₁	—	2	2	no	—
245	C₂×C₁₁	—	2	2	no	—
246	C₂×C₁₁	#1275	1	4	yes	complemented
247	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
248	C₂×C₁₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
249	C₂×C₁₁	C₂×#338	1	1	yes	characteristic
250	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
251	C₂²×C₄	—	4	2	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	C₈×D₁₁	1	4	yes	—
254	C₂²×C₄	#4313	1	4	yes	—
255	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
256	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
257	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
260	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
264	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
266	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
267	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
269	C₂²×C₄	C₂²⋊Dic₁₁	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×C₂²⋊D₁₁	1	1	yes	characteristic
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	4	4	no	—
275	C₂×C₈	—	11	8	no	—
276	C₂×C₈	—	22	8	no	—
277	C₂×C₈	—	22	8	no	—
278	C₂×C₈	—	22	4	no	—
279	C₂×C₈	—	22	4	no	—
280	C₂×C₈	—	22	4	no	—
281	C₂×C₈	—	44	4	no	—
282	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
283	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
284	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
285	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
286	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
287	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
288	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
289	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
290	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
291	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
292	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
293	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
294	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
295	C₄²	C₂×D₄₄	1	1	yes	characteristic
296	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
297	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
298	C₁₁	C₂×#1275	1	1	yes	characteristic, complemented, Sylow
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	Dic₁₁⋊C₈	1	4	yes	—
302	C₂³	C₁₁⋊#95	1	1	yes	characteristic
303	C₂³	C₁₁⋊#95	1	1	yes	characteristic
304	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	1	no	—
312	C₂×C₄	—	4	1	no	—
313	C₂×C₄	—	4	1	no	—
314	C₂×C₄	—	4	1	no	—
315	C₂×C₄	—	4	1	no	—
316	C₂×C₄	—	4	1	no	—
317	C₂×C₄	C₈×Dic₁₁	1	2	yes	—
318	C₂×C₄	C₈×Dic₁₁	1	2	yes	—
319	C₂×C₄	Dic₁₁⋊C₈	1	4	yes	—
320	C₂×C₄	#66879	1	2	yes	—
321	C₂×C₄	#66879	1	2	yes	—
322	C₂×C₄	(C₂×D₁₁)⋊C₈	1	4	yes	—
323	C₂×C₄	(C₂×D₁₁)⋊C₈	1	4	yes	—
324	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
325	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
327	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
328	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
329	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
330	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
331	C₂×C₄	C₂×#4313	1	2	yes	—
332	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
333	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
335	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
337	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
338	C₈	—	4	4	no	—
339	C₈	—	22	8	no	—
340	C₈	—	44	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	8	no	—
346	C₂²	#10622169	1	2	yes	—
347	C₂²	#10622188	1	2	yes	—
348	C₂²	#10622188	1	2	yes	—
349	C₂²	C₁₁⋊#338	1	2	yes	—
350	C₂²	C₂×Dic₁₁⋊C₈	1	2	yes	—
351	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	#10622188	1	2	yes	—
361	C₄	#10622188	1	2	yes	—
362	C₄	C₂×C₈×Dic₁₁	1	1	yes	characteristic
363	C₄	C₂×#66879	1	1	yes	characteristic
364	C₄	C₂×(C₂×D₁₁)⋊C₈	1	2	yes	—
365	C₂	—	2	2	no	—
366	C₂	—	2	2	no	—
367	C₂	#13066446	1	4	yes	direct product factor
368	C₂	C₂×#10622188	1	1	yes	characteristic
369	C₂	C₂×#10622169	1	1	yes	characteristic
370	C₂	C₂×C₁₁⋊#338	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄×Dic₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂³×C₁₁	#95
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	C₂×#1275
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13066446	C₂	direct (N × H)
47. C₂²×C₁₁⋊C₈	C₈	semidirect
113. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
246. C₂×C₁₁	#1275	semidirect
298. C₁₁	C₂×#1275	semidirect
367. C₂	#13066446	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×#10622538	2
C₂²×#66867	2
#13066446	2
C₂×C₁₁×#431	2
C₂×#1275	11

Subgroups — C2×#13066446 #14643188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066446 #14643188