Subgroups — C₁₁×#22457 #14599650

Order 2816.

1294 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#578	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2950	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2884	C₂	1	2	yes	maximal, complemented
4	C₁₁×#1976	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1905	C₂	1	4	yes	maximal, complemented
6	C₁₁×#1812	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#1796	C₂	1	2	yes	maximal, complemented
8	C₁₁×#1757	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×2₋¹⁺⁴	C₂²	1	2	yes	—
10	C₁₁×#578	—	2	4	no	—
11	C₁₁×#578	—	2	4	no	—
12	C₂×C₁₁×#137	C₄	1	4	yes	complemented
13	C₂×C₁₁×#137	C₂²	1	2	yes	—
14	C₂×C₁₁×#135	C₄	1	2	yes	complemented
15	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×Q₁₆	C₄	1	2	yes	complemented
17	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
19	C₁₁×#519	C₂²	1	4	yes	—
20	C₁₁×#441	—	2	4	no	—
21	C₄×C₁₁×Q₁₆	—	2	4	no	—
22	C₁₁×#427	C₂²	1	2	yes	—
23	C₁₁×#421	C₂²	1	4	yes	—
24	C₁₁×#419	C₂²	1	4	yes	—
25	C₁₁×#413	C₂²	1	1	yes	characteristic
26	C₁₁×#410	—	2	8	no	—
27	C₁₁×#410	C₂²	1	4	yes	—
28	C₁₁×#410	C₂²	1	2	yes	—
29	C₁₁×#410	C₂²	1	1	yes	characteristic
30	C₁₁×#405	C₂²	1	2	yes	—
31	C₁₁×#344	C₂²	1	2	yes	—
32	C₁₁×H(3,ℤ/4)	C₂²	1	2	yes	—
33	C₁₁×2₋¹⁺⁴	—	2	8	no	—
34	C₁₁×2₋¹⁺⁴	—	4	4	no	—
35	C₂×C₁₁×#41	—	2	4	no	—
36	C₂×C₁₁×#41	—	2	2	no	—
37	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
38	C₂×C₁₁×#41	C₂³	1	2	yes	—
39	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₁	—	2	2	no	—
41	C₂²×Q₈×C₁₁	C₂×C₄	1	4	yes	—
42	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
43	C₁₁×#137	—	2	8	no	—
44	C₁₁×#137	—	2	16	no	—
45	C₁₁×#135	—	2	4	no	—
46	C₁₁×#135	—	2	4	no	—
47	C₁₁×#135	—	2	2	no	—
48	C₁₁×#135	—	2	2	no	—
49	C₂×C₁₁×Q₁₆	—	2	4	no	—
50	C₂×C₁₁×Q₁₆	—	2	4	no	—
51	C₂×C₁₁×Q₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
53	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
54	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
55	C₂×C₁₁×Q₁₆	D₄	1	4	yes	—
56	C₂×C₁₁×Q₁₆	D₄	1	4	yes	—
57	C₂×C₁₁×SD₁₆	C₂×C₄	1	4	yes	—
58	C₂×C₁₁×SD₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₁₁×D₈	C₂×C₄	1	1	yes	characteristic
60	C₁₁×#131	—	2	2	no	—
61	C₁₁×#131	—	2	2	no	—
62	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₁₁×M₁₆	C₂³	1	2	yes	—
64	C₂×C₁₁×M₁₆	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
67	C₄×Q₈×C₁₁	—	2	8	no	—
68	C₄×Q₈×C₁₁	—	4	4	no	—
69	C₁₁×#117	—	2	8	no	—
70	C₁₁×#117	C₂³	1	4	yes	—
71	C₁₁×#117	C₂³	1	2	yes	—
72	C₁₁×#107	—	2	2	no	—
73	C₁₁×#106	—	2	2	no	—
74	C₁₁×#104	—	4	4	no	—
75	C₁₁×#103	—	2	8	no	—
76	C₁₁×#101	—	2	1	no	—
77	C₁₁×#100	—	2	1	no	—
78	C₁₁×#99	—	2	4	no	—
79	C₁₁×#99	—	2	8	no	—
80	C₁₁×#99	D₄	1	4	yes	—
81	C₁₁×#97	—	2	2	no	—
82	C₄×C₈×C₁₁	—	2	2	no	—
83	#22457	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₁₁×#41	—	2	2	no	—
85	C₁₁×#41	—	2	2	no	—
86	C₁₁×#41	—	2	8	no	—
87	C₁₁×#41	—	2	4	no	—
88	C₁₁×#41	—	2	4	no	—
89	C₁₁×#41	—	4	4	no	—
90	C₁₁×#41	—	4	16	no	—
91	C₁₁×#41	—	4	8	no	—
92	C₂×Q₈×C₁₁	—	2	4	no	—
93	C₂×Q₈×C₁₁	—	2	2	no	—
94	C₂×Q₈×C₁₁	—	2	4	no	—
95	C₂×Q₈×C₁₁	—	2	8	no	—
96	C₂×Q₈×C₁₁	—	4	4	no	—
97	C₂×Q₈×C₁₁	—	4	8	no	—
98	C₂×Q₈×C₁₁	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₁₁	C₂×D₄	1	8	yes	—
101	C₂×Q₈×C₁₁	#41	1	1	yes	characteristic
102	C₂×D₄×C₁₁	—	2	4	no	—
103	C₂×D₄×C₁₁	—	2	2	no	—
104	C₂×D₄×C₁₁	C₂²×C₄	1	2	yes	—
105	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
106	C₂×D₄×C₁₁	#41	1	1	yes	characteristic
107	C₂²×C₄×C₁₁	—	2	2	no	—
108	C₂²×C₄×C₁₁	—	2	4	no	—
109	C₂²×C₄×C₁₁	—	2	4	no	—
110	C₂²×C₄×C₁₁	—	2	2	no	—
111	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
113	C₁₁×Q₁₆	—	2	1	no	—
114	C₁₁×Q₁₆	—	2	1	no	—
115	C₁₁×Q₁₆	—	2	8	no	—
116	C₁₁×Q₁₆	C₂²⋊C₄	1	4	yes	—
117	C₁₁×Q₁₆	C₂²⋊C₄	1	4	yes	—
118	C₁₁×Q₁₆	C₂²⋊C₄	1	8	yes	—
119	C₁₁×SD₁₆	—	2	4	no	—
120	C₁₁×SD₁₆	—	2	8	no	—
121	C₁₁×D₈	—	2	1	no	—
122	C₁₁×D₈	—	2	1	no	—
123	C₁₁×M₁₆	—	2	4	no	—
124	C₁₁×M₁₆	—	2	2	no	—
125	C₁₁×M₁₆	—	2	2	no	—
126	C₁₁×M₁₆	—	2	2	no	—
127	C₂×C₈×C₁₁	—	2	2	no	—
128	C₂×C₈×C₁₁	—	2	2	no	—
129	C₂×C₈×C₁₁	—	2	2	no	—
130	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
131	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
135	C₁₁×C₄⋊C₄	—	2	2	no	—
136	C₁₁×C₄⋊C₄	—	2	4	no	—
137	C₁₁×C₄⋊C₄	—	4	8	no	—
138	C₁₁×C₂²⋊C₄	—	2	4	no	—
139	C₁₁×C₂²⋊C₄	C₂×D₄	1	4	yes	—
140	C₄²×C₁₁	—	2	2	no	—
141	C₄²×C₁₁	—	2	4	no	—
142	C₄²×C₁₁	—	4	8	no	—
143	C₂×#578	C₂×C₁₁	1	1	yes	characteristic
144	#2950	C₂×C₁₁	1	2	yes	complemented
145	#2884	C₂×C₁₁	1	2	yes	complemented
146	#1976	C₂×C₁₁	1	2	yes	complemented
147	#1905	C₂×C₁₁	1	4	yes	complemented
148	#1812	C₂×C₁₁	1	1	yes	characteristic, complemented
149	#1796	C₂×C₁₁	1	2	yes	complemented
150	#1757	C₂×C₁₁	1	1	yes	characteristic, complemented
151	C₂³×C₁₁	—	2	2	no	—
152	C₂³×C₁₁	C₄×D₄	1	2	yes	—
153	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
154	Q₈×C₁₁	—	2	4	no	—
155	Q₈×C₁₁	—	2	8	no	—
156	Q₈×C₁₁	—	2	2	no	—
157	Q₈×C₁₁	—	2	2	no	—
158	Q₈×C₁₁	—	2	2	no	—
159	Q₈×C₁₁	—	4	8	no	—
160	Q₈×C₁₁	C₂×C₂²⋊C₄	1	8	yes	—
161	D₄×C₁₁	—	2	4	no	—
162	D₄×C₁₁	—	2	2	no	—
163	D₄×C₁₁	—	2	2	no	—
164	D₄×C₁₁	—	2	2	no	—
165	D₄×C₁₁	—	4	8	no	—
166	D₄×C₁₁	—	4	4	no	—
167	C₂×C₄×C₁₁	—	2	4	no	—
168	C₂×C₄×C₁₁	—	2	8	no	—
169	C₂×C₄×C₁₁	—	2	2	no	—
170	C₂×C₄×C₁₁	—	2	2	no	—
171	C₂×C₄×C₁₁	—	2	2	no	—
172	C₂×C₄×C₁₁	—	2	4	no	—
173	C₂×C₄×C₁₁	—	4	8	no	—
174	C₂×C₄×C₁₁	—	4	8	no	—
175	C₂×C₄×C₁₁	—	4	4	no	—
176	C₂×C₄×C₁₁	—	4	4	no	—
177	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
180	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
182	C₈×C₁₁	—	2	2	no	—
183	C₈×C₁₁	—	4	2	no	—
184	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂×2₋¹⁺⁴	C₂²×C₁₁	1	2	yes	—
188	#578	—	2	4	no	—
189	#578	—	2	4	no	—
190	C₂×#137	C₄×C₁₁	1	4	yes	complemented
191	C₂×#137	C₂²×C₁₁	1	2	yes	—
192	C₂×#135	C₄×C₁₁	1	2	yes	complemented
193	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
194	C₂²×Q₁₆	C₄×C₁₁	1	2	yes	complemented
195	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
196	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
197	#519	C₂²×C₁₁	1	4	yes	—
198	#441	—	2	4	no	—
199	C₄×Q₁₆	—	2	4	no	—
200	#427	C₂²×C₁₁	1	2	yes	—
201	#421	C₂²×C₁₁	1	4	yes	—
202	#419	C₂²×C₁₁	1	4	yes	—
203	#413	C₂²×C₁₁	1	1	yes	characteristic
204	#410	—	2	8	no	—
205	#410	C₂²×C₁₁	1	2	yes	—
206	#410	C₂²×C₁₁	1	4	yes	—
207	#410	C₂²×C₁₁	1	1	yes	characteristic
208	#405	C₂²×C₁₁	1	2	yes	—
209	#344	C₂²×C₁₁	1	2	yes	—
210	H(3,ℤ/4)	C₂²×C₁₁	1	2	yes	—
211	C₂²×C₁₁	—	2	2	no	—
212	C₂²×C₁₁	—	4	1	no	—
213	C₂²×C₁₁	—	4	2	no	—
214	C₂²×C₁₁	—	4	2	no	—
215	C₂²×C₁₁	—	8	2	no	—
216	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₁₁	D₄²	1	2	yes	—
218	C₄×C₁₁	—	2	8	no	—
219	C₄×C₁₁	—	2	2	no	—
220	C₄×C₁₁	—	4	4	no	—
221	C₄×C₁₁	—	4	2	no	—
222	C₄×C₁₁	—	8	4	no	—
223	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
224	C₄×C₁₁	#518	1	1	yes	characteristic
225	C₄×C₁₁	#546	1	2	yes	—
226	2₋¹⁺⁴	—	2	8	no	—
227	2₋¹⁺⁴	—	4	4	no	—
228	C₂×#41	—	2	4	no	—
229	C₂×#41	—	2	2	no	—
230	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
231	C₂×#41	C₂³×C₁₁	1	2	yes	—
232	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	C₂×C₄×C₁₁	1	4	yes	—
235	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
236	#137	—	2	8	no	—
237	#137	—	2	16	no	—
238	#135	—	2	4	no	—
239	#135	—	2	4	no	—
240	#135	—	2	2	no	—
241	#135	—	2	2	no	—
242	C₂×Q₁₆	—	2	4	no	—
243	C₂×Q₁₆	—	2	4	no	—
244	C₂×Q₁₆	C₂×C₄×C₁₁	1	1	yes	characteristic
245	C₂×Q₁₆	C₂×C₄×C₁₁	1	4	yes	—
246	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
247	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
248	C₂×Q₁₆	D₄×C₁₁	1	4	yes	—
249	C₂×Q₁₆	D₄×C₁₁	1	4	yes	—
250	C₂×SD₁₆	C₂×C₄×C₁₁	1	4	yes	—
251	C₂×SD₁₆	C₂×C₄×C₁₁	1	2	yes	—
252	C₂×D₈	C₂×C₄×C₁₁	1	1	yes	characteristic
253	#131	—	2	2	no	—
254	#131	—	2	2	no	—
255	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
256	C₂×M₁₆	C₂³×C₁₁	1	2	yes	—
257	C₂×M₁₆	C₂³×C₁₁	1	1	yes	characteristic
258	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
259	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
260	C₄×Q₈	—	2	8	no	—
261	C₄×Q₈	—	4	4	no	—
262	#117	—	2	8	no	—
263	#117	C₂³×C₁₁	1	4	yes	—
264	#117	C₂³×C₁₁	1	2	yes	—
265	#107	—	2	2	no	—
266	#106	—	2	2	no	—
267	#104	—	4	4	no	—
268	#103	—	2	8	no	—
269	#101	—	2	1	no	—
270	#100	—	2	1	no	—
271	#99	—	2	4	no	—
272	#99	—	2	8	no	—
273	#99	D₄×C₁₁	1	4	yes	—
274	#97	—	2	2	no	—
275	C₄×C₈	—	2	2	no	—
276	C₂×C₁₁	—	2	2	no	—
277	C₂×C₁₁	—	2	1	no	—
278	C₂×C₁₁	—	4	2	no	—
279	C₂×C₁₁	—	8	2	no	—
280	C₂×C₁₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	#41	—	2	8	no	—
284	#41	—	2	4	no	—
285	#41	—	2	4	no	—
286	#41	—	4	4	no	—
287	#41	—	4	16	no	—
288	#41	—	4	8	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	8	no	—
293	C₂×Q₈	—	4	4	no	—
294	C₂×Q₈	—	4	8	no	—
295	C₂×Q₈	C₂²×C₄×C₁₁	1	2	yes	—
296	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
297	C₂×Q₈	C₂×D₄×C₁₁	1	8	yes	—
298	C₂×Q₈	C₁₁×#41	1	1	yes	characteristic
299	C₂×D₄	—	2	4	no	—
300	C₂×D₄	—	2	2	no	—
301	C₂×D₄	C₂²×C₄×C₁₁	1	2	yes	—
302	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
303	C₂×D₄	C₁₁×#41	1	1	yes	characteristic
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
310	Q₁₆	—	2	8	no	—
311	Q₁₆	—	2	1	no	—
312	Q₁₆	—	2	1	no	—
313	Q₁₆	C₁₁×C₂²⋊C₄	1	4	yes	—
314	Q₁₆	C₁₁×C₂²⋊C₄	1	4	yes	—
315	Q₁₆	C₁₁×C₂²⋊C₄	1	8	yes	—
316	SD₁₆	—	2	8	no	—
317	SD₁₆	—	2	4	no	—
318	D₈	—	2	1	no	—
319	D₈	—	2	1	no	—
320	M₁₆	—	2	2	no	—
321	M₁₆	—	2	4	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
328	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
329	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
330	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
331	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	4	no	—
339	C₄²	—	4	8	no	—
340	C₁₁	#22457	1	1	yes	characteristic, direct product factor, Sylow
341	C₂³	—	2	2	no	—
342	C₂³	C₄×D₄×C₁₁	1	2	yes	—
343	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	2	8	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	—	2	2	no	—
349	Q₈	—	4	8	no	—
350	Q₈	C₂×C₁₁×C₂²⋊C₄	1	8	yes	—
351	D₄	—	2	4	no	—
352	D₄	—	2	2	no	—
353	D₄	—	2	2	no	—
354	D₄	—	2	2	no	—
355	D₄	—	4	8	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	8	no	—
364	C₂×C₄	—	4	8	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
368	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
370	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
371	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
372	C₈	—	2	2	no	—
373	C₈	—	4	2	no	—
374	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
375	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
376	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
377	C₂²	—	2	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
383	C₂²	D₄²×C₁₁	1	2	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	4	no	—
387	C₄	—	4	2	no	—
388	C₄	—	8	4	no	—
389	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
390	C₄	C₁₁×#518	1	1	yes	characteristic
391	C₄	C₁₁×#546	1	2	yes	—
392	C₂	—	2	2	no	—
393	C₂	—	2	1	no	—
394	C₂	—	4	2	no	—
395	C₂	—	8	2	no	—
396	C₂	D₄×C₁₁×C₂²⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₁	D₄×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#578	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2950	C₂	semidirect
3. C₁₁×#2884	C₂	semidirect
4. C₁₁×#1976	C₂	semidirect
5. C₁₁×#1905	C₂	semidirect
6. C₁₁×#1812	C₂	semidirect
7. C₁₁×#1796	C₂	semidirect
8. C₁₁×#1757	C₂	semidirect
12. C₂×C₁₁×#137	C₄	semidirect
14. C₂×C₁₁×#135	C₄	semidirect
16. C₂²×C₁₁×Q₁₆	C₄	semidirect
83. #22457	C₁₁	direct (N × H)
144. #2950	C₂×C₁₁	semidirect
145. #2884	C₂×C₁₁	semidirect
146. #1976	C₂×C₁₁	semidirect
147. #1905	C₂×C₁₁	semidirect
148. #1812	C₂×C₁₁	semidirect
149. #1796	C₂×C₁₁	semidirect
150. #1757	C₂×C₁₁	semidirect
190. C₂×#137	C₄×C₁₁	semidirect
192. C₂×#135	C₄×C₁₁	semidirect
194. C₂²×Q₁₆	C₄×C₁₁	semidirect
340. C₁₁	#22457	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×C₁₁×#578	2
C₁₁×#2950	2
C₁₁×#2884	2
C₁₁×#1976	2
C₁₁×#1905	2
C₁₁×#1812	2
C₁₁×#1796	2
C₁₁×#1757	2
#22457	11

Subgroups — C11×#22457 #14599650

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22457 #14599650