Subgroups — #14659677

Order 2816.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66882	C₂	1	1	yes	maximal, characteristic
2	C₂²×#66881	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622189	C₂	1	2	yes	maximal
4	#13066846	C₂	1	2	yes	maximal
5	C₂²×C₁₁×#97	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊Dic₁₁	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×#97	—	2	2	no	—
12	C₂×C₁₁×#97	—	2	2	no	—
13	C₂×C₁₁×#97	C₄	1	4	yes	complemented
14	C₂×C₁₁⋊#95	—	2	4	no	—
15	C₂×#66882	—	2	2	no	—
16	C₂×#66882	—	2	2	no	—
17	C₂×#66882	C₄	1	4	yes	complemented
18	C₂×#66881	—	2	2	no	—
19	C₂×#66881	—	2	2	no	—
20	C₂×#66881	C₄	1	4	yes	complemented
21	#10622189	—	2	4	no	—
22	C₂³×C₄×C₁₁	D₄	1	2	yes	—
23	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
24	C₂³×Dic₁₁	—	2	2	no	—
25	C₂³×Dic₁₁	—	2	2	no	—
26	C₂²×C₈×C₁₁	—	2	1	no	—
27	C₂²×C₈×C₁₁	—	2	1	no	—
28	C₂²×C₈×C₁₁	—	2	1	no	—
29	C₂²×C₈×C₁₁	—	2	1	no	—
30	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	D₄	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	2	yes	—
38	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
39	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
40	C₂×C₄²×C₁₁	—	2	1	no	—
41	C₂×C₄²×C₁₁	—	2	1	no	—
42	C₂×C₄²×C₁₁	—	2	1	no	—
43	C₂×C₄²×C₁₁	—	2	1	no	—
44	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
45	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
46	C₂×C₄⋊Dic₁₁	—	2	2	no	—
47	C₂×C₄⋊Dic₁₁	—	2	2	no	—
48	C₂×C₄⋊Dic₁₁	—	2	2	no	—
49	C₂×C₄⋊Dic₁₁	—	2	2	no	—
50	C₂×C₄⋊Dic₁₁	—	2	2	no	—
51	C₂×C₄⋊Dic₁₁	—	2	2	no	—
52	C₂×C₄⋊Dic₁₁	—	2	2	no	—
53	C₂×C₄⋊Dic₁₁	—	2	2	no	—
54	C₂×C₄⋊Dic₁₁	—	2	2	no	—
55	C₂×C₄⋊Dic₁₁	—	2	2	no	—
56	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
58	C₁₁×#97	—	2	8	no	—
59	C₁₁⋊#95	—	4	8	no	—
60	#66882	—	2	8	no	—
61	#66881	—	2	8	no	—
62	#10863	—	11	1	no	maximal, Sylow
63	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₁	—	2	2	no	—
65	C₂²×C₄×C₁₁	—	2	2	no	—
66	C₂²×C₄×C₁₁	—	2	4	no	—
67	C₂²×C₄×C₁₁	—	2	4	no	—
68	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
69	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂²×C₄	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	C₂×Q₈	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×C₄×C₁₁	#41	1	1	yes	characteristic
83	C₂²×Dic₁₁	—	2	4	no	—
84	C₂²×Dic₁₁	—	2	4	no	—
85	C₂²×Dic₁₁	—	4	2	no	—
86	C₂²×Dic₁₁	—	4	2	no	—
87	C₂²×Dic₁₁	—	4	2	no	—
88	C₂²×Dic₁₁	—	4	2	no	—
89	C₂²×Dic₁₁	—	4	4	no	—
90	C₂²×Dic₁₁	—	4	4	no	—
91	C₂²×Dic₁₁	—	4	4	no	—
92	C₂²×Dic₁₁	—	4	4	no	—
93	C₂×C₈×C₁₁	—	2	2	no	—
94	C₂×C₈×C₁₁	—	2	2	no	—
95	C₂×C₈×C₁₁	—	2	2	no	—
96	C₂×C₈×C₁₁	—	2	2	no	—
97	C₂×C₈×C₁₁	—	2	2	no	—
98	C₂×C₈×C₁₁	—	2	2	no	—
99	C₂×C₈×C₁₁	C₄²	1	4	yes	—
100	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
101	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
102	C₂×C₈×C₁₁	C₂²⋊C₄	1	4	yes	—
103	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
104	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
105	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
106	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
107	C₄²×C₁₁	—	2	2	no	—
108	C₄²×C₁₁	—	2	2	no	—
109	C₄²×C₁₁	—	2	2	no	—
110	C₄²×C₁₁	—	2	2	no	—
111	C₄⋊Dic₁₁	—	2	4	no	—
112	C₄⋊Dic₁₁	—	2	4	no	—
113	C₄⋊Dic₁₁	—	2	4	no	—
114	C₄⋊Dic₁₁	—	2	4	no	—
115	C₄⋊Dic₁₁	—	4	2	no	—
116	C₄⋊Dic₁₁	—	4	2	no	—
117	C₄⋊Dic₁₁	—	4	2	no	—
118	C₄⋊Dic₁₁	—	4	2	no	—
119	C₂²×#107	—	11	1	no	—
120	C₂²×#106	—	11	1	no	—
121	C₂²×#97	D₁₁	1	1	yes	characteristic
122	C₂×#340	—	11	2	no	—
123	C₄⋊#95	—	11	2	no	—
124	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
125	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
126	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
127	C₂³×C₁₁	#121	1	1	yes	characteristic
128	C₂³×C₁₁	#121	1	1	yes	characteristic
129	C₂³×C₁₁	#127	1	1	yes	characteristic
130	C₂³×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
131	C₂³×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
132	C₂³×C₁₁	#137	1	4	yes	—
133	C₂×C₄×C₁₁	—	2	4	no	—
134	C₂×C₄×C₁₁	—	2	8	no	—
135	C₂×C₄×C₁₁	—	4	4	no	—
136	C₂×C₄×C₁₁	—	4	2	no	—
137	C₂×C₄×C₁₁	—	4	2	no	—
138	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
139	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
147	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
152	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
155	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
156	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
159	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
161	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
162	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
163	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
164	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
166	C₂×Dic₁₁	—	4	4	no	—
167	C₂×Dic₁₁	—	4	4	no	—
168	C₂×Dic₁₁	—	4	8	no	—
169	C₂×Dic₁₁	—	4	8	no	—
170	C₂×Dic₁₁	—	8	4	no	—
171	C₂×Dic₁₁	—	8	4	no	—
172	C₂×Dic₁₁	—	8	2	no	—
173	C₂×Dic₁₁	—	8	2	no	—
174	C₂×Dic₁₁	—	8	2	no	—
175	C₂×Dic₁₁	—	8	2	no	—
176	C₈×C₁₁	—	2	4	no	—
177	C₈×C₁₁	#95	1	8	yes	complemented
178	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
179	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
180	C₂²×C₄⋊C₄	—	11	2	no	—
181	C₂²×C₄⋊C₄	—	11	2	no	—
182	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
183	C₂×#107	—	11	4	no	—
184	C₂×#107	—	22	2	no	—
185	C₂×#107	—	22	2	no	—
186	C₂×#106	—	11	4	no	—
187	C₂×#106	—	22	2	no	—
188	C₂×#106	—	22	2	no	—
189	C₂×#97	—	2	2	no	—
190	C₂×#97	—	2	2	no	—
191	C₂×#97	Dic₁₁	1	4	yes	complemented
192	C₂×#95	—	22	4	no	—
193	#340	—	22	4	no	—
194	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
195	C₂²×C₁₁	#380	1	1	yes	characteristic
196	C₂²×C₁₁	#384	1	1	yes	characteristic
197	C₂²×C₁₁	#389	1	1	yes	characteristic
198	C₂²×C₁₁	#389	1	1	yes	characteristic
199	C₂²×C₁₁	#390	1	1	yes	characteristic
200	C₂²×C₁₁	#390	1	1	yes	characteristic
201	C₂²×C₁₁	#428	1	4	yes	—
202	C₂²×C₁₁	#440	1	4	yes	—
203	C₂²×C₁₁	#441	1	2	yes	—
204	C₂²×C₁₁	#442	1	2	yes	—
205	C₂²×C₁₁	#468	1	4	yes	—
206	C₂²×C₁₁	#469	1	2	yes	—
207	C₂²×C₁₁	#470	1	2	yes	—
208	C₂²×C₁₁	#496	1	2	yes	—
209	C₂²×C₁₁	#497	1	2	yes	—
210	C₂²×C₁₁	#501	1	4	yes	—
211	C₄×C₁₁	—	4	4	no	—
212	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
213	C₄×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₄×C₁₁	#380	1	1	yes	characteristic
215	C₄×C₁₁	#382	1	1	yes	characteristic
216	C₄×C₁₁	#389	1	1	yes	characteristic
217	C₄×C₁₁	#389	1	1	yes	characteristic
218	C₄×C₁₁	#391	1	1	yes	characteristic
219	C₄×C₁₁	#391	1	1	yes	characteristic
220	Dic₁₁	—	8	4	no	—
221	Dic₁₁	—	8	4	no	—
222	C₂³×C₄	—	22	2	no	—
223	C₂³×C₄	—	22	2	no	—
224	C₂³×C₄	D₄₄	1	2	yes	—
225	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	2	1	no	—
228	C₂²×C₈	—	2	1	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	Dic₂₂	1	2	yes	—
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	D₄₄	1	2	yes	—
236	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
237	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
238	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
239	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
240	C₂×C₄⋊C₄	—	11	4	no	—
241	C₂×C₄⋊C₄	—	11	4	no	—
242	C₂×C₄⋊C₄	—	22	2	no	—
243	C₂×C₄⋊C₄	—	22	2	no	—
244	C₂×C₄⋊C₄	—	22	2	no	—
245	C₂×C₄⋊C₄	—	22	2	no	—
246	C₂×C₄⋊C₄	—	22	2	no	—
247	C₂×C₄⋊C₄	—	22	2	no	—
248	C₂×C₄⋊C₄	—	22	2	no	—
249	C₂×C₄⋊C₄	—	22	2	no	—
250	C₂×C₄⋊C₄	—	22	2	no	—
251	C₂×C₄⋊C₄	—	22	2	no	—
252	C₂×C₄²	—	2	1	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	Dic₂₂	1	2	yes	—
257	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
258	#107	—	22	8	no	—
259	#106	—	22	8	no	—
260	#97	—	2	8	no	—
261	#95	—	44	8	no	—
262	C₂×C₁₁	C₄⋊#95	1	1	yes	characteristic
263	C₂×C₁₁	#1776	1	2	yes	—
264	C₂×C₁₁	#1809	1	2	yes	—
265	C₂×C₁₁	#1847	1	2	yes	—
266	C₂×C₁₁	#1943	1	2	yes	—
267	C₂×C₁₁	#1944	1	2	yes	—
268	C₂×C₁₁	#1971	1	1	yes	characteristic
269	C₂×C₁₁	#1972	1	1	yes	characteristic
270	C₂×C₁₁	#1973	1	2	yes	—
271	C₂⁴	C₂×D₄₄	1	1	yes	characteristic
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	22	4	no	—
277	C₂²×C₄	—	22	4	no	—
278	C₂²×C₄	—	44	2	no	—
279	C₂²×C₄	—	44	2	no	—
280	C₂²×C₄	—	44	4	no	—
281	C₂²×C₄	—	44	4	no	—
282	C₂²×C₄	—	44	4	no	—
283	C₂²×C₄	—	44	4	no	—
284	C₂²×C₄	—	44	2	no	—
285	C₂²×C₄	—	44	2	no	—
286	C₂²×C₄	C₄⋊Dic₁₁	1	4	yes	—
287	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
288	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
289	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
294	C₂²×C₄	#4339	1	1	yes	characteristic
295	C₂²×C₄	#4339	1	1	yes	characteristic
296	C₂²×C₄	#4339	1	1	yes	characteristic
297	C₂²×C₄	#4339	1	1	yes	characteristic
298	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	C₄×Dic₁₁	1	4	yes	—
308	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
309	C₂×C₈	Dic₁₁⋊C₄	1	4	yes	—
310	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
311	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
312	C₂×C₈	(C₂×D₁₁)⋊C₄	1	4	yes	—
313	C₂×C₈	(C₂×D₁₁)⋊C₄	1	4	yes	—
314	C₂×C₈	C₂²⋊Dic₁₁	1	4	yes	—
315	C₄⋊C₄	—	22	4	no	—
316	C₄⋊C₄	—	22	4	no	—
317	C₄⋊C₄	—	22	4	no	—
318	C₄⋊C₄	—	22	4	no	—
319	C₄⋊C₄	—	44	2	no	—
320	C₄⋊C₄	—	44	2	no	—
321	C₄⋊C₄	—	44	2	no	—
322	C₄⋊C₄	—	44	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₁₁	#10863	1	1	yes	characteristic, complemented, Sylow
328	C₂³	#66922	1	1	yes	characteristic
329	C₂³	C₄×D₄₄	1	1	yes	characteristic
330	C₂³	C₄×D₄₄	1	1	yes	characteristic
331	C₂³	#66927	1	1	yes	characteristic
332	C₂³	#66961	1	4	yes	—
333	C₂³	#66962	1	4	yes	—
334	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
335	C₂³	#66983	1	1	yes	characteristic
336	C₂³	#66983	1	1	yes	characteristic
337	C₂×C₄	—	2	8	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	44	4	no	—
343	C₂×C₄	—	44	4	no	—
344	C₂×C₄	—	44	8	no	—
345	C₂×C₄	—	44	8	no	—
346	C₂×C₄	—	88	4	no	—
347	C₂×C₄	—	88	4	no	—
348	C₂×C₄	—	88	2	no	—
349	C₂×C₄	—	88	2	no	—
350	C₂×C₄	—	88	2	no	—
351	C₂×C₄	—	88	2	no	—
352	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
353	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
354	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
355	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
356	C₂×C₄	#66922	1	1	yes	characteristic
357	C₂×C₄	#66922	1	1	yes	characteristic
358	C₂×C₄	#66923	1	1	yes	characteristic
359	C₂×C₄	#66923	1	1	yes	characteristic
360	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
361	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
362	C₂×C₄	#66928	1	1	yes	characteristic
363	C₂×C₄	#66928	1	1	yes	characteristic
364	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
365	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
366	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
367	C₂×C₄	#66977	1	1	yes	characteristic
368	C₂×C₄	#66977	1	1	yes	characteristic
369	C₂×C₄	#66977	1	1	yes	characteristic
370	C₂×C₄	#66977	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
373	C₂×C₄	#66979	1	1	yes	characteristic
374	C₂×C₄	#66979	1	1	yes	characteristic
375	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
376	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
377	C₂×C₄	#66983	1	1	yes	characteristic
378	C₂×C₄	#66983	1	1	yes	characteristic
379	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
380	C₈	—	2	4	no	—
381	C₈	C₁₁⋊#95	1	8	yes	complemented
382	C₂²	#10622315	1	4	yes	—
383	C₂²	#10622323	1	4	yes	—
384	C₂²	#10622324	1	2	yes	—
385	C₂²	#10622325	1	2	yes	—
386	C₂²	#10622328	1	2	yes	—
387	C₂²	#10622329	1	2	yes	—
388	C₂²	#10622541	1	1	yes	characteristic
389	C₂²	#10622541	1	1	yes	characteristic
390	C₂²	C₄×C₄⋊Dic₁₁	1	1	yes	characteristic
391	C₂²	#10622548	1	1	yes	characteristic
392	C₂²	#10622552	1	1	yes	characteristic
393	C₂²	#10622552	1	1	yes	characteristic
394	C₂²	#10622734	1	4	yes	—
395	C₂²	#10622747	1	4	yes	—
396	C₂²	#10622748	1	2	yes	—
397	C₂²	#10622750	1	2	yes	—
398	C₂²	#10622825	1	1	yes	characteristic
399	C₄	—	4	4	no	—
400	C₄	—	88	4	no	—
401	C₄	—	88	4	no	—
402	C₄	#10622541	1	1	yes	characteristic
403	C₄	#10622541	1	1	yes	characteristic
404	C₄	#10622542	1	1	yes	characteristic
405	C₄	#10622542	1	1	yes	characteristic
406	C₄	C₄×C₄⋊Dic₁₁	1	1	yes	characteristic
407	C₄	#10622549	1	1	yes	characteristic
408	C₄	C₂×C₁₁⋊#95	1	1	yes	characteristic
409	C₄	#10622825	1	1	yes	characteristic
410	C₂	#13066846	1	1	yes	characteristic
411	C₂	#13068513	1	2	yes	—
412	C₂	#13068649	1	2	yes	—
413	C₂	#13068784	1	2	yes	—
414	C₂	#13069354	1	2	yes	—
415	C₂	#13069359	1	2	yes	—
416	C₂	#13069487	1	1	yes	characteristic
417	C₂	#13069492	1	1	yes	characteristic
418	C₂	#13069497	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₁
Fitting	C₂²×C₁₁×#97	C₂
socle, prime radical	C₂⁴×C₁₁	C₂×D₄
cosocle	C₂³×C₄×C₁₁	C₂³
hypercenter	C₂²×#97	D₁₁
hypocenter	C₁₁	#10863
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
13. C₂×C₁₁×#97	C₄	semidirect
17. C₂×#66882	C₄	semidirect
20. C₂×#66881	C₄	semidirect
177. C₈×C₁₁	#95	semidirect
191. C₂×#97	Dic₁₁	semidirect
327. C₁₁	#10863	semidirect
381. C₈	C₁₁⋊#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#66882	2
C₂²×#66881	2
C₂×#10622189	2
#13066846	2
C₂²×C₁₁×#97	2
#10863	11