Subgroups — C₂×C₁₁×#3342 #14638426

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#556	C₂	1	2	yes	maximal
2	C₁₁×#3342	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₁×#485	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#475	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#467	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic
9	C₂×C₁₁×#427	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
12	C₁₁×#556	—	2	8	no	—
13	C₁₁×#556	C₂²	1	16	yes	—
14	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₁₁×#126	—	2	4	no	—
16	C₂×C₁₁×#124	—	2	2	no	—
17	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	4	yes	—
18	C₂×C₄×Q₈×C₁₁	—	2	2	no	—
19	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#117	C₂²	1	4	yes	—
22	C₁₁×#500	C₂²	1	8	yes	complemented
23	C₁₁×#485	C₂²	1	32	yes	complemented
24	C₁₁×#475	C₂²	1	16	yes	complemented
25	C₁₁×#467	C₂²	1	16	yes	complemented
26	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
27	C₈×D₄×C₁₁	C₂²	1	8	yes	—
28	C₁₁×#427	C₂²	1	16	yes	complemented
29	C₂×C₁₁×#107	C₂²	1	2	yes	—
30	C₂×C₁₁×#107	C₂²	1	2	yes	—
31	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
32	C₂×C₁₁×#106	C₂²	1	4	yes	—
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#103	C₂²	1	2	yes	—
35	C₂×C₁₁×#103	C₂²	1	4	yes	—
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
38	C₂²×Q₈×C₁₁	—	2	2	no	—
39	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
42	C₂×C₁₁×Q₁₆	—	2	4	no	—
43	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
44	C₂²×C₈×C₁₁	—	2	8	no	—
45	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
48	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
49	C₁₁×C₄⋊Q₈	—	2	4	no	—
50	C₁₁×C₄⋊Q₈	C₂³	1	8	yes	—
51	C₁₁×#126	—	2	32	no	—
52	C₁₁×#124	—	2	16	no	—
53	C₁₁×C₂²⋊Q₈	—	2	8	no	—
54	C₁₁×C₂²⋊Q₈	C₂³	1	16	yes	—
55	C₄×Q₈×C₁₁	—	2	16	no	—
56	C₄×Q₈×C₁₁	—	2	4	no	—
57	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
58	C₄×D₄×C₁₁	D₄	1	4	yes	—
59	C₄×D₄×C₁₁	C₂³	1	4	yes	—
60	C₁₁×#117	—	2	8	no	—
61	C₁₁×#117	C₂³	1	16	yes	—
62	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
68	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
69	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
70	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
71	C₂×C₄²×C₁₁	—	2	4	no	—
72	C₂×C₄²×C₁₁	—	2	2	no	—
73	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
74	C₁₁×#107	C₂³	1	8	yes	—
75	C₁₁×#107	C₂³	1	8	yes	—
76	C₁₁×#107	C₂³	1	4	yes	—
77	C₁₁×#106	C₂³	1	16	yes	—
78	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
79	C₁₁×#103	C₂³	1	8	yes	—
80	C₁₁×#103	C₂³	1	16	yes	—
81	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
82	C₄×C₈×C₁₁	C₂³	1	4	yes	—
83	C₂×#3342	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
85	C₂×Q₈×C₁₁	—	2	2	no	—
86	C₂×Q₈×C₁₁	—	2	8	no	—
87	C₂×Q₈×C₁₁	—	2	4	no	—
88	C₂×Q₈×C₁₁	—	2	4	no	—
89	C₂×Q₈×C₁₁	—	4	8	no	—
90	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
91	C₂×D₄×C₁₁	—	2	4	no	—
92	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₁₁	—	2	4	no	—
94	C₂²×C₄×C₁₁	—	2	4	no	—
95	C₂²×C₄×C₁₁	—	2	2	no	—
96	C₂²×C₄×C₁₁	—	2	2	no	—
97	C₂²×C₄×C₁₁	—	2	4	no	—
98	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
99	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
103	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
104	C₁₁×Q₁₆	—	2	8	no	—
105	C₂×C₈×C₁₁	—	2	16	no	—
106	C₂×C₈×C₁₁	—	2	4	no	—
107	C₂×C₈×C₁₁	—	2	2	no	—
108	C₂×C₈×C₁₁	#41	1	4	yes	—
109	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
110	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
111	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
112	C₁₁×C₄⋊C₄	—	2	16	no	—
113	C₁₁×C₄⋊C₄	—	2	8	no	—
114	C₁₁×C₄⋊C₄	—	2	8	no	—
115	C₁₁×C₄⋊C₄	—	2	2	no	—
116	C₁₁×C₄⋊C₄	—	2	4	no	—
117	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
118	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
119	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
120	C₁₁×C₂²⋊C₄	—	2	16	no	—
121	C₁₁×C₂²⋊C₄	—	2	16	no	—
122	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
123	C₄²×C₁₁	—	2	16	no	—
124	C₄²×C₁₁	—	2	8	no	—
125	C₄²×C₁₁	C₂×D₄	1	2	yes	—
126	C₄²×C₁₁	C₂⁴	1	2	yes	—
127	C₂×#556	C₂×C₁₁	1	2	yes	—
128	#3342	C₂×C₁₁	1	16	yes	direct product factor
129	C₂×#500	C₂×C₁₁	1	1	yes	characteristic, complemented
130	C₂×#485	C₂×C₁₁	1	4	yes	complemented
131	C₂×#475	C₂×C₁₁	1	2	yes	complemented
132	C₂×#467	C₂×C₁₁	1	2	yes	complemented
133	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
134	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic
135	C₂×#427	C₂×C₁₁	1	2	yes	complemented
136	C₂³×C₁₁	—	2	4	no	—
137	C₂³×C₁₁	—	2	4	no	—
138	C₂³×C₁₁	—	2	4	no	—
139	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
140	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₁₁	—	2	4	no	—
142	Q₈×C₁₁	—	2	4	no	—
143	Q₈×C₁₁	—	4	4	no	—
144	Q₈×C₁₁	—	4	16	no	—
145	D₄×C₁₁	—	2	8	no	—
146	C₂×C₄×C₁₁	—	2	4	no	—
147	C₂×C₄×C₁₁	—	2	2	no	—
148	C₂×C₄×C₁₁	—	2	8	no	—
149	C₂×C₄×C₁₁	—	2	4	no	—
150	C₂×C₄×C₁₁	—	2	4	no	—
151	C₂×C₄×C₁₁	—	2	4	no	—
152	C₂×C₄×C₁₁	—	2	4	no	—
153	C₂×C₄×C₁₁	—	2	8	no	—
154	C₂×C₄×C₁₁	—	4	4	no	—
155	C₂×C₄×C₁₁	—	4	8	no	—
156	C₂×C₄×C₁₁	—	4	4	no	—
157	C₂×C₄×C₁₁	#135	1	4	yes	—
158	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
159	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
160	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
162	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
163	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
164	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
165	C₈×C₁₁	—	2	4	no	—
166	C₈×C₁₁	—	2	2	no	—
167	C₈×C₁₁	C₂×#41	1	4	yes	—
168	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
169	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
170	#556	—	2	8	no	—
171	#556	C₂²×C₁₁	1	16	yes	—
172	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
173	C₂×#126	—	2	4	no	—
174	C₂×#124	—	2	2	no	—
175	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	4	yes	—
176	C₂×C₄×Q₈	—	2	2	no	—
177	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
178	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
179	C₂×#117	C₂²×C₁₁	1	4	yes	—
180	#500	C₂²×C₁₁	1	8	yes	complemented
181	#485	C₂²×C₁₁	1	32	yes	complemented
182	#475	C₂²×C₁₁	1	16	yes	complemented
183	#467	C₂²×C₁₁	1	16	yes	complemented
184	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
185	C₈×D₄	C₂²×C₁₁	1	8	yes	—
186	#427	C₂²×C₁₁	1	16	yes	complemented
187	C₂×#107	C₂²×C₁₁	1	2	yes	—
188	C₂×#107	C₂²×C₁₁	1	2	yes	—
189	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
190	C₂×#106	C₂²×C₁₁	1	4	yes	—
191	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
192	C₂×#103	C₂²×C₁₁	1	4	yes	—
193	C₂×#103	C₂²×C₁₁	1	2	yes	—
194	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
195	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
196	C₂²×C₁₁	—	2	4	no	—
197	C₂²×C₁₁	—	2	4	no	—
198	C₂²×C₁₁	—	2	4	no	—
199	C₂²×C₁₁	—	4	8	no	—
200	C₂²×C₁₁	#547	1	2	yes	—
201	C₂²×C₁₁	C₂×#135	1	2	yes	—
202	C₂²×C₁₁	#578	1	2	yes	—
203	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
204	C₄×C₁₁	—	2	4	no	—
205	C₄×C₁₁	—	2	2	no	—
206	C₄×C₁₁	—	4	4	no	—
207	C₄×C₁₁	—	4	8	no	—
208	C₄×C₁₁	—	4	4	no	—
209	C₄×C₁₁	#547	1	2	yes	—
210	C₄×C₁₁	C₂×#135	1	4	yes	—
211	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
212	C₄×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
213	C₂²×Q₈	—	2	2	no	—
214	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
215	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
216	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
217	C₂×Q₁₆	—	2	4	no	—
218	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
219	C₂²×C₈	—	2	8	no	—
220	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
221	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
222	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
223	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
224	C₄⋊Q₈	—	2	4	no	—
225	C₄⋊Q₈	C₂³×C₁₁	1	8	yes	—
226	#126	—	2	32	no	—
227	#124	—	2	16	no	—
228	C₂²⋊Q₈	—	2	8	no	—
229	C₂²⋊Q₈	C₂³×C₁₁	1	16	yes	—
230	C₄×Q₈	—	2	16	no	—
231	C₄×Q₈	—	2	4	no	—
232	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
233	C₄×D₄	D₄×C₁₁	1	4	yes	—
234	C₄×D₄	C₂³×C₁₁	1	4	yes	—
235	#117	—	2	8	no	—
236	#117	C₂³×C₁₁	1	16	yes	—
237	C₂×C₄⋊C₄	—	2	4	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
241	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
242	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
243	C₂×C₂²⋊C₄	—	2	4	no	—
244	C₂×C₂²⋊C₄	—	2	4	no	—
245	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
246	C₂×C₄²	—	2	4	no	—
247	C₂×C₄²	—	2	2	no	—
248	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
249	#107	C₂³×C₁₁	1	4	yes	—
250	#107	C₂³×C₁₁	1	8	yes	—
251	#107	C₂³×C₁₁	1	8	yes	—
252	#106	C₂³×C₁₁	1	16	yes	—
253	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
254	#103	C₂³×C₁₁	1	8	yes	—
255	#103	C₂³×C₁₁	1	16	yes	—
256	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
257	C₄×C₈	C₂³×C₁₁	1	4	yes	—
258	C₂×C₁₁	—	4	4	no	—
259	C₂×C₁₁	#3342	1	4	yes	direct product factor
260	C₂×C₁₁	C₂×#547	1	1	yes	characteristic
261	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
262	C₂×C₁₁	C₂×#578	1	1	yes	characteristic
263	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	2	4	no	—
267	C₂×Q₈	—	2	4	no	—
268	C₂×Q₈	—	4	8	no	—
269	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
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	—	2	4	no	—
277	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
278	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
281	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
282	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
283	Q₁₆	—	2	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	16	no	—
287	C₂×C₈	C₁₁×#41	1	4	yes	—
288	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
289	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
290	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
291	C₄⋊C₄	—	2	16	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
297	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
298	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
299	C₂²⋊C₄	—	2	16	no	—
300	C₂²⋊C₄	—	2	16	no	—
301	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
302	C₄²	—	2	16	no	—
303	C₄²	—	2	8	no	—
304	C₄²	C₂×D₄×C₁₁	1	2	yes	—
305	C₄²	C₂⁴×C₁₁	1	2	yes	—
306	C₁₁	C₂×#3342	1	1	yes	characteristic, direct product factor, Sylow
307	C₂³	—	2	4	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	4	no	—
310	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
311	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
312	Q₈	—	2	4	no	—
313	Q₈	—	2	4	no	—
314	Q₈	—	4	4	no	—
315	Q₈	—	4	16	no	—
316	D₄	—	2	8	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	C₁₁×#135	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
331	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
332	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
333	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
334	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
335	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
336	C₈	—	2	4	no	—
337	C₈	—	2	2	no	—
338	C₈	C₂×C₁₁×#41	1	4	yes	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	4	no	—
341	C₂²	—	2	4	no	—
342	C₂²	—	4	8	no	—
343	C₂²	C₁₁×#547	1	2	yes	—
344	C₂²	C₂×C₁₁×#135	1	2	yes	—
345	C₂²	C₁₁×#578	1	2	yes	—
346	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	2	2	no	—
349	C₄	—	4	4	no	—
350	C₄	—	4	8	no	—
351	C₄	—	4	4	no	—
352	C₄	C₁₁×#547	1	2	yes	—
353	C₄	C₂×C₁₁×#135	1	4	yes	—
354	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
355	C₄	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
356	C₂	—	4	4	no	—
357	C₂	C₁₁×#3342	1	4	yes	direct product factor
358	C₂	C₂×C₁₁×#547	1	1	yes	characteristic
359	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic
360	C₂	C₂×C₁₁×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂²×D₄×C₁₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₂×C₄×D₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#3342	C₂	direct (N × H)
3. C₂×C₁₁×#500	C₂	semidirect
4. C₂×C₁₁×#485	C₂	semidirect
5. C₂×C₁₁×#475	C₂	semidirect
6. C₂×C₁₁×#467	C₂	semidirect
7. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
9. C₂×C₁₁×#427	C₂	semidirect
22. C₁₁×#500	C₂²	semidirect
23. C₁₁×#485	C₂²	semidirect
24. C₁₁×#475	C₂²	semidirect
25. C₁₁×#467	C₂²	semidirect
26. C₄×C₁₁×Q₁₆	C₂²	semidirect
28. C₁₁×#427	C₂²	semidirect
83. C₂×#3342	C₁₁	direct (N × H)
128. #3342	C₂×C₁₁	direct (N × H)
129. C₂×#500	C₂×C₁₁	semidirect
130. C₂×#485	C₂×C₁₁	semidirect
131. C₂×#475	C₂×C₁₁	semidirect
132. C₂×#467	C₂×C₁₁	semidirect
133. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
135. C₂×#427	C₂×C₁₁	semidirect
180. #500	C₂²×C₁₁	semidirect
181. #485	C₂²×C₁₁	semidirect
182. #475	C₂²×C₁₁	semidirect
183. #467	C₂²×C₁₁	semidirect
184. C₄×Q₁₆	C₂²×C₁₁	semidirect
186. #427	C₂²×C₁₁	semidirect
259. C₂×C₁₁	#3342	direct (N × H)
306. C₁₁	C₂×#3342	direct (N × H)
357. C₂	C₁₁×#3342	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×#556	2
C₁₁×#3342	2
C₂×C₁₁×#500	2
C₂×C₁₁×#485	2
C₂×C₁₁×#475	2
C₂×C₁₁×#467	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×C₈×D₄×C₁₁	2
C₂×C₁₁×#427	2
C₂×#3342	11

Subgroups — C2×C11×#3342 #14638426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3342 #14638426