Subgroups — C₂×#13066731 #14668708

Order 2816.

570 conjugacy classes of subgroups.

The subgroup lattice has 416 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×#10622719	C₂	1	1	yes	maximal, characteristic
3	#13066731	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66979	—	2	1	no	—
7	C₂²×#4318	—	2	1	no	—
8	C₂×C₁₁×M₃₂	—	2	1	no	—
9	C₂×C₁₁×M₃₂	—	2	1	no	—
10	C₂×C₁₁×M₃₂	—	2	1	no	—
11	C₂×C₁₁×M₃₂	C₄	1	2	yes	complemented
12	C₂×C₁₁×M₃₂	C₄	1	2	yes	complemented
13	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
14	C₂²×C₁₁×C₁₆	—	2	1	no	—
15	C₂×#66883	—	2	1	no	—
16	C₂×#66883	—	2	1	no	—
17	C₂×#66883	—	2	1	no	—
18	C₂×#66883	C₄	1	2	yes	complemented
19	C₂×#66883	C₄	1	2	yes	complemented
20	C₂×#66883	C₂²	1	2	yes	—
21	#10622719	—	2	1	no	—
22	#10622719	—	2	1	no	—
23	#10622719	C₄	1	2	yes	—
24	#10622719	C₂²	1	2	yes	—
25	C₂×#66882	—	2	1	no	—
26	C₂×#66881	C₄	1	2	yes	—
27	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
38	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
39	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
40	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
41	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₂×C₂²⋊Dic₁₁	—	4	1	no	—
43	#66979	—	2	2	no	—
44	#66979	—	2	2	no	—
45	#66979	—	4	1	no	—
46	#66979	—	4	1	no	—
47	C₂×C₄⋊Dic₁₁	—	2	2	no	—
48	C₂×C₄×Dic₁₁	—	4	1	no	—
49	C₂×#4318	—	2	2	no	—
50	C₂×#4318	—	2	2	no	—
51	C₂×#4318	—	2	2	no	—
52	C₂×#4318	—	4	1	no	—
53	C₂×#4318	—	4	1	no	—
54	C₂×#4318	—	4	1	no	—
55	C₂²×C₁₁⋊C₈	—	4	1	no	—
56	C₁₁×M₃₂	—	2	2	no	—
57	C₁₁×M₃₂	—	2	2	no	—
58	C₁₁×M₃₂	—	2	2	no	—
59	C₁₁×M₃₂	C₂×C₄	1	4	yes	complemented
60	C₂×C₁₁×C₁₆	—	2	2	no	—
61	C₂×C₁₁×C₁₆	—	2	2	no	—
62	C₂×C₁₁×C₁₆	—	2	2	no	—
63	#66883	—	2	2	no	—
64	#66883	—	2	2	no	—
65	#66883	—	2	2	no	—
66	#66883	C₂×C₄	1	4	yes	complemented
67	#66882	—	2	2	no	—
68	#66882	—	2	2	no	—
69	#66881	—	2	2	no	—
70	#66881	C₂×C₄	1	4	yes	—
71	C₂×#1389	—	11	1	no	maximal, Sylow
72	C₂⁴×C₁₁	SD₁₆	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	D₈	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×Dic₁₁	—	4	2	no	—
88	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
89	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
90	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
91	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
92	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
116	C₂²⋊Dic₁₁	—	4	2	no	—
117	C₂²⋊Dic₁₁	—	4	2	no	—
118	C₄⋊Dic₁₁	—	2	4	no	—
119	C₄⋊Dic₁₁	—	4	2	no	—
120	C₄×Dic₁₁	—	4	2	no	—
121	C₄×Dic₁₁	—	4	2	no	—
122	#4318	—	2	4	no	—
123	#4318	—	4	2	no	—
124	#4318	—	4	2	no	—
125	#4318	—	4	2	no	—
126	C₂×C₁₁⋊C₈	—	4	2	no	—
127	C₂×C₁₁⋊C₈	—	4	2	no	—
128	C₂×C₁₁⋊C₈	—	4	2	no	—
129	C₁₁×C₁₆	—	2	4	no	—
130	C₂²×M₃₂	D₁₁	1	1	yes	characteristic
131	C₂²×#108	—	11	1	no	—
132	C₂×#427	—	11	1	no	—
133	#1389	—	11	4	no	—
134	C₂³×C₁₁	—	4	2	no	—
135	C₂³×C₁₁	#102	1	1	yes	characteristic
136	C₂³×C₁₁	#102	1	1	yes	characteristic
137	C₂³×C₁₁	#103	1	1	yes	characteristic
138	C₂³×C₁₁	#103	1	1	yes	characteristic
139	C₂³×C₁₁	#106	1	1	yes	characteristic
140	C₂³×C₁₁	#106	1	1	yes	characteristic
141	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
142	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
147	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
148	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
149	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
150	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
151	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
152	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
153	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
154	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
156	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
157	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
158	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
159	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
160	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
161	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
162	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
163	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
170	C₂×Dic₁₁	—	4	4	no	—
171	C₂×Dic₁₁	—	8	4	no	—
172	C₈×C₁₁	#95	1	1	yes	characteristic
173	C₈×C₁₁	#95	1	1	yes	characteristic
174	C₈×C₁₁	#95	1	1	yes	characteristic
175	C₈×C₁₁	#95	1	1	yes	characteristic
176	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
177	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₁₁⋊C₈	—	4	4	no	—
181	C₂²×M₁₆	—	22	1	no	—
182	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
183	C₂×#117	—	22	1	no	—
184	C₂×M₃₂	—	2	1	no	—
185	C₂×M₃₂	—	2	1	no	—
186	C₂×M₃₂	—	2	1	no	—
187	C₂×M₃₂	Dic₁₁	1	2	yes	complemented
188	C₂×M₃₂	Dic₁₁	1	2	yes	complemented
189	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
190	C₂²×C₁₆	—	2	1	no	—
191	C₂×#108	—	11	2	no	—
192	C₂×#108	—	11	2	no	—
193	C₂×#108	—	11	2	no	—
194	C₂×#108	—	22	1	no	—
195	C₂×#108	—	22	1	no	—
196	C₂×#108	—	22	1	no	—
197	#427	—	11	2	no	—
198	#427	—	11	2	no	—
199	#427	—	22	1	no	—
200	#427	—	22	1	no	—
201	C₂×#107	—	22	1	no	—
202	C₂×#106	—	11	2	no	—
203	C₂²×C₁₁	—	2	2	no	—
204	C₂²×C₁₁	—	2	2	no	—
205	C₂²×C₁₁	—	2	2	no	—
206	C₂²×C₁₁	—	4	1	no	—
207	C₂²×C₁₁	—	4	1	no	—
208	C₂²×C₁₁	—	4	1	no	—
209	C₂²×C₁₁	—	4	1	no	—
210	C₂²×C₁₁	#340	1	1	yes	characteristic
211	C₂²×C₁₁	#340	1	1	yes	characteristic
212	C₂²×C₁₁	#340	1	1	yes	characteristic
213	C₂²×C₁₁	#340	1	1	yes	characteristic
214	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
215	C₂²×C₁₁	C₂×#103	1	1	yes	characteristic
216	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
217	C₄×C₁₁	#340	1	1	yes	characteristic
218	C₄×C₁₁	#340	1	1	yes	characteristic
219	C₄×C₁₁	#340	1	1	yes	characteristic
220	C₄×C₁₁	#340	1	1	yes	characteristic
221	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
222	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
223	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
224	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
225	Dic₁₁	—	8	4	no	—
226	C₂³×C₄	D₄₄	1	1	yes	characteristic
227	C₂×M₁₆	—	22	2	no	—
228	C₂×M₁₆	—	22	2	no	—
229	C₂×M₁₆	—	22	2	no	—
230	C₂×M₁₆	—	44	1	no	—
231	C₂×M₁₆	—	44	1	no	—
232	C₂×M₁₆	—	44	1	no	—
233	C₂²×C₈	—	44	1	no	—
234	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
235	C₂²×C₈	Dic₂₂	1	1	yes	characteristic
236	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
237	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
238	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
239	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
240	C₂²×C₈	D₄₄	1	1	yes	characteristic
241	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
242	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
243	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
244	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
245	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
246	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
247	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
248	#117	—	22	2	no	—
249	#117	—	22	2	no	—
250	#117	—	44	1	no	—
251	#117	—	44	1	no	—
252	C₂×C₄⋊C₄	—	22	2	no	—
253	C₂×C₂²⋊C₄	—	44	1	no	—
254	C₂×C₄²	—	44	1	no	—
255	M₃₂	—	2	2	no	—
256	M₃₂	—	2	2	no	—
257	M₃₂	—	2	2	no	—
258	M₃₂	C₂×Dic₁₁	1	4	yes	complemented
259	C₂×C₁₆	—	2	2	no	—
260	C₂×C₁₆	—	2	2	no	—
261	C₂×C₁₆	—	2	2	no	—
262	#108	—	11	4	no	—
263	#108	—	22	2	no	—
264	#108	—	22	2	no	—
265	#108	—	22	2	no	—
266	#107	—	22	2	no	—
267	#107	—	22	2	no	—
268	#106	—	11	4	no	—
269	#106	—	22	2	no	—
270	C₂×C₁₁	—	2	1	no	—
271	C₂×C₁₁	—	2	1	no	—
272	C₂×C₁₁	—	2	1	no	—
273	C₂×C₁₁	—	2	1	no	—
274	C₂×C₁₁	—	2	1	no	—
275	C₂×C₁₁	—	2	1	no	—
276	C₂×C₁₁	#1389	1	2	yes	complemented
277	C₂×C₁₁	C₂×#340	1	1	yes	characteristic
278	C₂⁴	#4314	1	1	yes	characteristic
279	C₂²×C₄	—	44	2	no	—
280	C₂²×C₄	#4314	1	1	yes	characteristic
281	C₂²×C₄	#4314	1	1	yes	characteristic
282	C₂²×C₄	#4314	1	1	yes	characteristic
283	C₂²×C₄	D₈₈	1	1	yes	characteristic
284	C₂²×C₄	D₈₈	1	1	yes	characteristic
285	C₂²×C₄	Dic₄₄	1	1	yes	characteristic
286	C₂²×C₄	Dic₄₄	1	1	yes	characteristic
287	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
288	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
289	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
290	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
291	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
292	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
294	M₁₆	—	22	4	no	—
295	M₁₆	—	44	2	no	—
296	M₁₆	—	44	2	no	—
297	M₁₆	—	44	2	no	—
298	C₂×C₈	—	44	2	no	—
299	C₂×C₈	—	44	2	no	—
300	C₂×C₈	—	44	2	no	—
301	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
302	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
303	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
304	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
305	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
306	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
307	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
308	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
309	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
310	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
311	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
312	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
313	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
314	C₂×C₈	C₄⋊Dic₁₁	1	1	yes	characteristic
315	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
316	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
317	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
318	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
319	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
320	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
321	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
322	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
323	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
324	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
325	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
326	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
327	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
329	C₄⋊C₄	—	22	4	no	—
330	C₄⋊C₄	—	44	2	no	—
331	C₂²⋊C₄	—	44	2	no	—
332	C₂²⋊C₄	—	44	2	no	—
333	C₄²	—	44	2	no	—
334	C₄²	—	44	2	no	—
335	C₁₆	—	2	4	no	—
336	C₁₁	C₂×#1389	1	1	yes	characteristic, complemented, Sylow
337	C₂³	—	4	2	no	—
338	C₂³	#66880	1	1	yes	characteristic
339	C₂³	#66880	1	1	yes	characteristic
340	C₂³	#66881	1	1	yes	characteristic
341	C₂³	#66881	1	1	yes	characteristic
342	C₂³	#66885	1	1	yes	characteristic
343	C₂³	#66885	1	1	yes	characteristic
344	C₂³	C₂×#4314	1	1	yes	characteristic
345	C₂×C₄	—	44	4	no	—
346	C₂×C₄	—	88	4	no	—
347	C₂×C₄	#66880	1	1	yes	characteristic
348	C₂×C₄	#66880	1	1	yes	characteristic
349	C₂×C₄	#66880	1	1	yes	characteristic
350	C₂×C₄	#66880	1	1	yes	characteristic
351	C₂×C₄	#66880	1	1	yes	characteristic
352	C₂×C₄	#66880	1	1	yes	characteristic
353	C₂×C₄	#66881	1	1	yes	characteristic
354	C₂×C₄	#66881	1	1	yes	characteristic
355	C₂×C₄	#66882	1	1	yes	characteristic
356	C₂×C₄	#66882	1	1	yes	characteristic
357	C₂×C₄	#66882	1	1	yes	characteristic
358	C₂×C₄	#66882	1	1	yes	characteristic
359	C₂×C₄	#66885	1	1	yes	characteristic
360	C₂×C₄	#66885	1	1	yes	characteristic
361	C₂×C₄	#66885	1	1	yes	characteristic
362	C₂×C₄	#66885	1	1	yes	characteristic
363	C₂×C₄	#66885	1	1	yes	characteristic
364	C₂×C₄	#66885	1	1	yes	characteristic
365	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
366	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
367	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
368	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
369	C₂×C₄	C₂×#4314	1	1	yes	characteristic
370	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
371	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
373	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
374	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
375	C₈	—	44	4	no	—
376	C₈	C₁₁⋊#95	1	1	yes	characteristic
377	C₈	C₁₁⋊#95	1	1	yes	characteristic
378	C₈	C₁₁⋊#95	1	1	yes	characteristic
379	C₈	C₁₁⋊#95	1	1	yes	characteristic
380	C₈	C₂×C₄×Dic₁₁	1	1	yes	characteristic
381	C₈	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
382	C₈	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
383	C₈	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	#10622189	1	1	yes	characteristic
392	C₂²	#10622189	1	1	yes	characteristic
393	C₂²	#10622189	1	1	yes	characteristic
394	C₂²	#10622189	1	1	yes	characteristic
395	C₂²	C₂×#66880	1	1	yes	characteristic
396	C₂²	C₂×#66881	1	1	yes	characteristic
397	C₂²	C₂×#66885	1	1	yes	characteristic
398	C₄	—	88	4	no	—
399	C₄	#10622189	1	1	yes	characteristic
400	C₄	#10622189	1	1	yes	characteristic
401	C₄	#10622189	1	1	yes	characteristic
402	C₄	#10622189	1	1	yes	characteristic
403	C₄	C₂×#66880	1	1	yes	characteristic
404	C₄	C₂×#66882	1	1	yes	characteristic
405	C₄	C₂×#66885	1	1	yes	characteristic
406	C₄	C₂×C₁₁⋊#95	1	1	yes	characteristic
407	C₂	—	2	1	no	—
408	C₂	—	2	1	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	#13066731	1	2	yes	direct product factor
414	C₂	C₂×#10622189	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#66885
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂²×C₁₁×M₃₂	C₂
socle	C₂²×C₁₁	#340
prime radical	C₂⁴×C₁₁	SD₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂²×M₃₂	D₁₁
hypocenter	C₁₁	C₂×#1389
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13066731	C₂	direct (N × H)
11. C₂×C₁₁×M₃₂	C₄	semidirect
12. C₂×C₁₁×M₃₂	C₄	semidirect
18. C₂×#66883	C₄	semidirect
19. C₂×#66883	C₄	semidirect
59. C₁₁×M₃₂	C₂×C₄	semidirect
66. #66883	C₂×C₄	semidirect
187. C₂×M₃₂	Dic₁₁	semidirect
188. C₂×M₃₂	Dic₁₁	semidirect
258. M₃₂	C₂×Dic₁₁	semidirect
276. C₂×C₁₁	#1389	semidirect
336. C₁₁	C₂×#1389	semidirect
413. C₂	#13066731	direct (N × H)

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×#10622719	2
#13066731	2
C₂²×C₁₁×M₃₂	2
C₂×#1389	11

Subgroups — C2×#13066731 #14668708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066731 #14668708