Subgroups — C₂×#13066454 #14643266

Order 2816.

782 conjugacy classes of subgroups.

The subgroup lattice has 378 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×C₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13066454	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×M₁₆	C₄	1	2	yes	—
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₁₁⋊C₈	—	2	1	no	—
8	C₄×C₁₁×M₁₆	—	2	1	no	—
9	C₄×C₁₁×M₁₆	—	2	1	no	—
10	C₄×C₁₁×M₁₆	C₄	1	2	yes	—
11	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
12	C₂×C₁₁×#97	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	—	2	1	no	—
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)	C₄	1	2	yes	—
20	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
21	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
22	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
23	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
24	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
25	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
26	C₂×C₄×C₁₁⋊C₈	C₂²	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	C₂×C₁₁×M₁₆	—	2	2	no	—
31	C₂×C₁₁×M₁₆	—	2	4	no	—
32	C₂×C₁₁×M₁₆	C₈	1	8	yes	complemented
33	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
34	C₂²×C₈×C₁₁	—	2	2	no	—
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₂²×C₁₁⋊C₈	—	2	8	no	—
48	C₂²×C₁₁⋊C₈	—	2	2	no	—
49	C₂²×C₁₁⋊C₈	—	2	2	no	—
50	C₂²×C₁₁⋊C₈	—	2	2	no	—
51	C₂²×C₁₁⋊C₈	—	2	2	no	—
52	C₁₁×#97	—	2	2	no	—
53	C₁₁×#97	—	2	2	no	—
54	C₄×C₈×C₁₁	—	2	2	no	—
55	C₄×C₈×C₁₁	—	2	2	no	—
56	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
60	C₄×C₁₁⋊C₈	—	2	2	no	—
61	C₄×C₁₁⋊C₈	—	2	2	no	—
62	C₄×C₁₁⋊C₈	—	2	2	no	—
63	C₄×C₁₁⋊C₈	—	2	2	no	—
64	C₄×C₁₁⋊C₈	—	2	2	no	—
65	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
66	C₂×#1278	—	11	1	no	maximal, Sylow
67	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	—	2	4	no	—
69	C₂²×C₄×C₁₁	—	2	4	no	—
70	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₄²	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	C₂²⋊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	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
86	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
87	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
90	C₁₁×M₁₆	—	2	8	no	—
91	C₁₁×M₁₆	—	2	4	no	—
92	C₁₁×M₁₆	C₂×C₈	1	8	yes	complemented
93	C₂×C₈×C₁₁	—	2	8	no	—
94	C₂×C₈×C₁₁	—	2	4	no	—
95	C₄²×C₁₁	C₄²	1	1	yes	characteristic
96	C₄²×C₁₁	C₄²	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	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
111	C₂×C₁₁⋊C₈	—	2	8	no	—
112	C₂×C₁₁⋊C₈	—	2	8	no	—
113	C₂×C₁₁⋊C₈	—	2	8	no	—
114	C₂×C₁₁⋊C₈	—	2	4	no	—
115	C₂×C₁₁⋊C₈	—	2	4	no	—
116	C₂×C₁₁⋊C₈	—	4	4	no	—
117	C₂×#431	—	11	1	no	—
118	C₂×C₄×M₁₆	D₁₁	1	1	yes	characteristic
119	C₂²×C₄×C₈	—	11	1	no	—
120	#1278	—	11	4	no	—
121	C₂³×C₁₁	—	2	2	no	—
122	C₂³×C₁₁	—	2	2	no	—
123	C₂³×C₁₁	#95	1	1	yes	characteristic
124	C₂³×C₁₁	#95	1	1	yes	characteristic
125	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
126	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	2	2	no	—
135	C₂×C₄×C₁₁	—	2	2	no	—
136	C₂×C₄×C₁₁	—	2	2	no	—
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	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
144	C₂×C₄×C₁₁	C₄×C₈	1	2	yes	—
145	C₂×C₄×C₁₁	#97	1	2	yes	—
146	C₂×C₄×C₁₁	#97	1	2	yes	—
147	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
148	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
149	C₂×C₄×C₁₁	#104	1	4	yes	—
150	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
151	C₂×C₄×C₁₁	#108	1	4	yes	—
152	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
159	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
160	C₈×C₁₁	—	2	8	no	—
161	C₁₁⋊C₈	—	2	8	no	—
162	C₁₁⋊C₈	—	4	4	no	—
163	C₂²×M₁₆	Dic₁₁	1	2	yes	—
164	C₂³×C₈	—	22	1	no	—
165	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
166	#431	—	11	2	no	—
167	#431	—	11	2	no	—
168	#431	—	22	1	no	—
169	#431	—	22	1	no	—
170	C₂×C₄⋊C₈	—	11	2	no	—
171	C₂×C₂²⋊C₈	—	22	1	no	—
172	C₄×M₁₆	—	2	1	no	—
173	C₄×M₁₆	—	2	1	no	—
174	C₄×M₁₆	Dic₁₁	1	2	yes	—
175	C₄×M₁₆	C₂×D₁₁	1	2	yes	—
176	C₂×#97	—	2	1	no	—
177	C₂×C₄×C₈	—	2	1	no	—
178	C₂×C₄×C₈	—	11	2	no	—
179	C₂×C₄×C₈	—	11	2	no	—
180	C₂×C₄×C₈	—	11	2	no	—
181	C₂×C₄×C₈	—	22	1	no	—
182	C₂×C₄×C₈	—	22	1	no	—
183	C₂×C₄×C₈	—	22	1	no	—
184	C₂×C₄×C₈	—	22	1	no	—
185	C₂²×C₁₁	—	2	1	no	—
186	C₂²×C₁₁	—	2	1	no	—
187	C₂²×C₁₁	—	2	1	no	—
188	C₂²×C₁₁	—	2	1	no	—
189	C₂²×C₁₁	—	2	8	no	—
190	C₂²×C₁₁	#336	1	2	yes	—
191	C₂²×C₁₁	#336	1	2	yes	—
192	C₂²×C₁₁	#339	1	2	yes	—
193	C₂²×C₁₁	#341	1	2	yes	—
194	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
195	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
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	#336	1	2	yes	—
201	C₄×C₁₁	#336	1	2	yes	—
202	C₄×C₁₁	#339	1	2	yes	—
203	C₄×C₁₁	#341	1	2	yes	—
204	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
205	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
206	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
207	C₄×C₁₁	C₂×#104	1	2	yes	—
208	C₄×C₁₁	C₂×#108	1	2	yes	—
209	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
210	C₂³×C₄	D₄₄	1	1	yes	characteristic
211	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
212	C₂×M₁₆	—	2	4	no	—
213	C₂×M₁₆	—	2	2	no	—
214	C₂×M₁₆	C₁₁⋊C₈	1	8	yes	complemented
215	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
216	C₂²×C₈	—	2	2	no	—
217	C₂²×C₈	—	22	8	no	—
218	C₂²×C₈	—	22	2	no	—
219	C₂²×C₈	—	22	2	no	—
220	C₂²×C₈	—	22	2	no	—
221	C₂²×C₈	—	22	2	no	—
222	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
223	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
224	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
227	C₂×C₄²	D₄₄	1	1	yes	characteristic
228	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
229	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
230	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
233	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
234	C₄⋊C₈	—	11	4	no	—
235	C₄⋊C₈	—	22	2	no	—
236	C₂²⋊C₈	—	22	2	no	—
237	C₂²⋊C₈	—	22	2	no	—
238	#97	—	2	2	no	—
239	#97	—	2	2	no	—
240	C₄×C₈	—	2	2	no	—
241	C₄×C₈	—	2	2	no	—
242	C₄×C₈	—	11	4	no	—
243	C₄×C₈	—	22	2	no	—
244	C₄×C₈	—	22	2	no	—
245	C₄×C₈	—	22	2	no	—
246	C₄×C₈	—	22	2	no	—
247	C₄×C₈	—	22	2	no	—
248	C₂×C₁₁	—	2	2	no	—
249	C₂×C₁₁	—	2	2	no	—
250	C₂×C₁₁	#1278	1	4	yes	complemented
251	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
252	C₂×C₁₁	C₂×#339	1	1	yes	characteristic
253	C₂×C₁₁	C₂×#341	1	1	yes	characteristic
254	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	C₂×C₁₁⋊C₈	1	4	yes	—
258	C₂²×C₄	#4318	1	4	yes	—
259	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
260	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
261	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
263	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
264	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
266	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
267	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
268	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
269	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
270	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
271	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
274	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
277	M₁₆	—	2	8	no	—
278	M₁₆	—	2	4	no	—
279	M₁₆	C₂×C₁₁⋊C₈	1	8	yes	complemented
280	C₂×C₈	—	2	8	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	22	8	no	—
283	C₂×C₈	—	22	8	no	—
284	C₂×C₈	—	22	8	no	—
285	C₂×C₈	—	22	4	no	—
286	C₂×C₈	—	22	4	no	—
287	C₂×C₈	—	44	4	no	—
288	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
289	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
290	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
294	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
295	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
296	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
297	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
298	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
299	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
300	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
301	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
302	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
303	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
304	C₁₁	C₂×#1278	1	1	yes	characteristic, complemented, Sylow
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
308	C₂³	C₁₁⋊#95	1	1	yes	characteristic
309	C₂³	C₁₁⋊#95	1	1	yes	characteristic
310	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	C₄×C₁₁⋊C₈	1	2	yes	—
322	C₂×C₄	C₄×C₁₁⋊C₈	1	2	yes	—
323	C₂×C₄	#66867	1	2	yes	—
324	C₂×C₄	#66867	1	2	yes	—
325	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
326	C₂×C₄	#66886	1	4	yes	—
327	C₂×C₄	#66889	1	4	yes	—
328	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	4	yes	—
329	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	4	yes	—
330	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
331	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
332	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
333	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
334	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
335	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
336	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
337	C₂×C₄	C₂×#4318	1	2	yes	—
338	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
339	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
340	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
342	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
344	C₈	—	2	8	no	—
345	C₈	—	22	8	no	—
346	C₈	—	44	4	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	8	no	—
352	C₂²	#10622162	1	2	yes	—
353	C₂²	#10622162	1	2	yes	—
354	C₂²	#10622193	1	2	yes	—
355	C₂²	#10622196	1	2	yes	—
356	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	2	yes	—
357	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	2	1	no	—
361	C₄	—	2	1	no	—
362	C₄	#10622162	1	2	yes	—
363	C₄	#10622162	1	2	yes	—
364	C₄	#10622193	1	2	yes	—
365	C₄	#10622196	1	2	yes	—
366	C₄	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
367	C₄	C₂×#66867	1	1	yes	characteristic
368	C₄	C₂×#66886	1	2	yes	—
369	C₄	C₂×#66889	1	2	yes	—
370	C₄	C₂×C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
371	C₂	—	2	2	no	—
372	C₂	—	2	2	no	—
373	C₂	#13066454	1	4	yes	direct product factor
374	C₂	C₂×#10622162	1	1	yes	characteristic
375	C₂	C₂×#10622193	1	1	yes	characteristic
376	C₂	C₂×#10622196	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²⋊D₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₄×C₁₁×M₁₆	C₂
socle	C₂³×C₁₁	#95
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₁
hypocenter	C₁₁	C₂×#1278
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
3. #13066454	C₂	direct (N × H)
32. C₂×C₁₁×M₁₆	C₈	semidirect
92. C₁₁×M₁₆	C₂×C₈	semidirect
214. C₂×M₁₆	C₁₁⋊C₈	semidirect
250. C₂×C₁₁	#1278	semidirect
279. M₁₆	C₂×C₁₁⋊C₈	semidirect
304. C₁₁	C₂×#1278	semidirect
373. C₂	#13066454	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×C₄×C₁₁⋊C₈	2
#13066454	2
C₂×C₄×C₁₁×M₁₆	2
C₂×#1278	11

Subgroups — C2×#13066454 #14643266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066454 #14643266