Subgroups — C₂×C₁₁×#3324 #14638337

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 596 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	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₁	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#3324	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#486	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#482	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#468	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#460	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#450	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₁₁×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×#418	C₂	1	2	yes	maximal, complemented
13	C₂³×D₄×C₁₁	—	2	1	no	—
14	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
15	C₂²×C₁₁×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
17	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	complemented
18	C₁₁×#556	—	2	4	no	—
19	C₁₁×#556	C₂²	1	8	yes	complemented
20	D₄²×C₁₁	—	2	4	no	—
21	D₄²×C₁₁	C₂²	1	8	yes	—
22	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₁₁×#127	C₂²	1	1	yes	characteristic
24	C₂×C₁₁×#126	—	2	2	no	—
25	C₂×C₁₁×#124	—	2	1	no	—
26	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₂×C₁₁×#121	—	2	1	no	—
28	C₂×C₁₁×#121	C₂²	1	2	yes	—
29	C₂×C₁₁×#120	—	2	2	no	—
30	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
31	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
32	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×#117	C₂²	1	2	yes	complemented
35	C₁₁×#486	C₂²	1	8	yes	complemented
36	C₁₁×#482	C₂²	1	16	yes	complemented
37	C₁₁×#474	C₂²	1	8	yes	complemented
38	C₁₁×#468	C₂²	1	16	yes	complemented
39	C₁₁×#460	C₂²	1	8	yes	complemented
40	C₁₁×#450	C₂²	1	16	yes	complemented
41	C₄×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
42	C₁₁×#436	C₂²	1	8	yes	complemented
43	C₂×C₁₁×#107	C₂²	1	2	yes	complemented
44	C₂×C₁₁×#106	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₁×#418	C₂²	1	16	yes	complemented
47	C₂×C₁₁×#103	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₁₁×#102	C₂²	1	1	yes	characteristic
49	C₂×C₁₁×#102	C₂²	1	2	yes	—
50	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
51	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
52	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
53	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
54	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
55	C₂⁵×C₁₁	—	2	2	no	—
56	C₂²×Q₈×C₁₁	—	2	1	no	—
57	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₁	—	2	8	no	—
59	C₂²×D₄×C₁₁	—	2	2	no	—
60	C₂²×D₄×C₁₁	—	2	8	no	—
61	C₂²×D₄×C₁₁	—	2	2	no	—
62	C₂²×D₄×C₁₁	—	2	1	no	—
63	C₂²×D₄×C₁₁	—	2	4	no	—
64	C₂²×D₄×C₁₁	—	2	1	no	—
65	C₂²×D₄×C₁₁	—	4	4	no	—
66	C₂²×D₄×C₁₁	—	4	8	no	—
67	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
68	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
69	C₂²×D₄×C₁₁	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₁	—	2	1	no	—
72	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
73	C₂×C₁₁×SD₁₆	—	2	4	no	—
74	C₂×C₁₁×SD₁₆	—	4	4	no	—
75	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
76	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	complemented
77	C₂×C₁₁×M₁₆	—	4	4	no	—
78	C₂×C₁₁×M₁₆	C₂³	1	8	yes	complemented
79	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
82	C₁₁×C₄⋊Q₈	—	2	2	no	—
83	C₁₁×C₄⋊Q₈	C₂³	1	4	yes	complemented
84	C₁₁×#127	—	2	2	no	—
85	C₁₁×#127	C₂³	1	4	yes	—
86	C₁₁×#126	—	2	16	no	—
87	C₁₁×#124	—	2	8	no	—
88	C₁₁×C₂²⋊Q₈	—	2	4	no	—
89	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	complemented
90	C₁₁×#121	—	2	4	no	—
91	C₁₁×#121	—	2	8	no	—
92	C₁₁×#121	C₂³	1	8	yes	—
93	C₁₁×#120	—	2	16	no	—
94	C₄×Q₈×C₁₁	—	2	8	no	—
95	C₄×Q₈×C₁₁	—	2	2	no	—
96	C₄×Q₈×C₁₁	C₂³	1	4	yes	complemented
97	C₄×D₄×C₁₁	—	2	2	no	—
98	C₄×D₄×C₁₁	D₄	1	4	yes	—
99	C₄×D₄×C₁₁	C₂³	1	4	yes	—
100	C₄×D₄×C₁₁	C₂³	1	4	yes	—
101	C₁₁×#117	—	2	4	no	—
102	C₁₁×#117	C₂³	1	8	yes	complemented
103	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
104	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
115	C₂×C₄²×C₁₁	—	2	2	no	—
116	C₂×C₄²×C₁₁	—	2	1	no	—
117	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
118	C₁₁×#107	C₂³	1	8	yes	complemented
119	C₁₁×#106	C₂³	1	4	yes	complemented
120	C₁₁×C₄⋊C₈	C₂³	1	4	yes	complemented
121	C₁₁×#103	C₂³	1	4	yes	complemented
122	C₁₁×#102	C₂³	1	4	yes	—
123	C₁₁×#102	C₂³	1	8	yes	—
124	C₁₁×#102	C₂³	1	8	yes	complemented
125	C₁₁×#102	C₂³	1	8	yes	complemented
126	C₁₁×#102	C₂³	1	8	yes	complemented
127	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	complemented
128	C₄×C₈×C₁₁	C₂³	1	4	yes	complemented
129	C₂×#3324	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₁	—	2	1	no	—
131	C₂⁴×C₁₁	—	2	2	no	—
132	C₂⁴×C₁₁	—	2	8	no	—
133	C₂⁴×C₁₁	—	4	8	no	—
134	C₂⁴×C₁₁	—	4	8	no	—
135	C₂⁴×C₁₁	—	8	4	no	—
136	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
137	C₂×Q₈×C₁₁	—	2	1	no	—
138	C₂×Q₈×C₁₁	—	2	4	no	—
139	C₂×Q₈×C₁₁	—	2	2	no	—
140	C₂×Q₈×C₁₁	—	2	2	no	—
141	C₂×Q₈×C₁₁	—	4	4	no	—
142	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
143	C₂×D₄×C₁₁	—	2	16	no	—
144	C₂×D₄×C₁₁	—	2	8	no	—
145	C₂×D₄×C₁₁	—	2	4	no	—
146	C₂×D₄×C₁₁	—	2	1	no	—
147	C₂×D₄×C₁₁	—	2	8	no	—
148	C₂×D₄×C₁₁	—	2	2	no	—
149	C₂×D₄×C₁₁	—	2	4	no	—
150	C₂×D₄×C₁₁	—	2	4	no	—
151	C₂×D₄×C₁₁	—	2	4	no	—
152	C₂×D₄×C₁₁	—	2	2	no	—
153	C₂×D₄×C₁₁	—	2	4	no	—
154	C₂×D₄×C₁₁	—	4	8	no	—
155	C₂×D₄×C₁₁	—	4	16	no	—
156	C₂×D₄×C₁₁	—	4	8	no	—
157	C₂×D₄×C₁₁	—	4	32	no	—
158	C₂×D₄×C₁₁	—	4	8	no	—
159	C₂×D₄×C₁₁	—	4	4	no	—
160	C₂×D₄×C₁₁	—	8	2	no	—
161	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
162	C₂×D₄×C₁₁	#41	1	4	yes	—
163	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
164	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₁₁	—	2	4	no	—
166	C₂²×C₄×C₁₁	—	2	4	no	—
167	C₂²×C₄×C₁₁	—	2	1	no	—
168	C₂²×C₄×C₁₁	—	2	1	no	—
169	C₂²×C₄×C₁₁	—	2	2	no	—
170	C₂²×C₄×C₁₁	—	2	1	no	—
171	C₂²×C₄×C₁₁	—	2	4	no	—
172	C₂²×C₄×C₁₁	—	4	4	no	—
173	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
179	C₁₁×SD₁₆	—	2	8	no	—
180	C₁₁×SD₁₆	—	4	8	no	—
181	C₁₁×M₁₆	—	4	8	no	—
182	C₂×C₈×C₁₁	—	2	2	no	—
183	C₂×C₈×C₁₁	—	2	2	no	—
184	C₂×C₈×C₁₁	—	2	4	no	—
185	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
186	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
187	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
188	C₁₁×C₄⋊C₄	—	2	8	no	—
189	C₁₁×C₄⋊C₄	—	2	4	no	—
190	C₁₁×C₄⋊C₄	—	2	4	no	—
191	C₁₁×C₄⋊C₄	—	2	1	no	—
192	C₁₁×C₄⋊C₄	—	2	2	no	—
193	C₁₁×C₄⋊C₄	—	2	1	no	—
194	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
195	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
196	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
197	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
198	C₁₁×C₂²⋊C₄	—	2	8	no	—
199	C₁₁×C₂²⋊C₄	—	2	8	no	—
200	C₁₁×C₂²⋊C₄	—	2	4	no	—
201	C₁₁×C₂²⋊C₄	—	2	8	no	—
202	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
203	C₄²×C₁₁	—	2	8	no	—
204	C₄²×C₁₁	—	2	4	no	—
205	C₄²×C₁₁	C₂×D₄	1	2	yes	—
206	C₄²×C₁₁	C₂⁴	1	2	yes	—
207	C₂×#556	C₂×C₁₁	1	1	yes	characteristic, complemented
208	C₂×D₄²	C₂×C₁₁	1	1	yes	characteristic
209	#3324	C₂×C₁₁	1	16	yes	direct product factor
210	C₂×#486	C₂×C₁₁	1	1	yes	characteristic, complemented
211	C₂×#482	C₂×C₁₁	1	2	yes	complemented
212	C₂×#474	C₂×C₁₁	1	1	yes	characteristic, complemented
213	C₂×#468	C₂×C₁₁	1	2	yes	complemented
214	C₂×#460	C₂×C₁₁	1	1	yes	characteristic, complemented
215	C₂×#450	C₂×C₁₁	1	2	yes	complemented
216	C₂×C₄×SD₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
217	C₂×#436	C₂×C₁₁	1	1	yes	characteristic, complemented
218	C₂×#418	C₂×C₁₁	1	2	yes	complemented
219	C₂³×C₁₁	—	2	4	no	—
220	C₂³×C₁₁	—	2	4	no	—
221	C₂³×C₁₁	—	2	4	no	—
222	C₂³×C₁₁	—	2	4	no	—
223	C₂³×C₁₁	—	2	2	no	—
224	C₂³×C₁₁	—	2	4	no	—
225	C₂³×C₁₁	—	4	16	no	—
226	C₂³×C₁₁	—	4	16	no	—
227	C₂³×C₁₁	—	4	2	no	—
228	C₂³×C₁₁	—	4	2	no	—
229	C₂³×C₁₁	—	4	4	no	—
230	C₂³×C₁₁	—	4	4	no	—
231	C₂³×C₁₁	—	4	4	no	—
232	C₂³×C₁₁	—	8	8	no	—
233	C₂³×C₁₁	—	8	32	no	—
234	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
235	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₁	—	2	2	no	—
237	Q₈×C₁₁	—	2	2	no	—
238	Q₈×C₁₁	—	4	2	no	—
239	Q₈×C₁₁	—	4	8	no	—
240	D₄×C₁₁	—	2	4	no	—
241	D₄×C₁₁	—	2	8	no	—
242	D₄×C₁₁	—	2	4	no	—
243	D₄×C₁₁	—	2	2	no	—
244	D₄×C₁₁	—	2	4	no	—
245	D₄×C₁₁	—	4	16	no	—
246	D₄×C₁₁	—	4	16	no	—
247	D₄×C₁₁	—	4	4	no	—
248	D₄×C₁₁	—	4	8	no	—
249	D₄×C₁₁	—	8	4	no	—
250	D₄×C₁₁	C₂×#41	1	4	yes	—
251	C₂×C₄×C₁₁	—	2	4	no	—
252	C₂×C₄×C₁₁	—	2	2	no	—
253	C₂×C₄×C₁₁	—	2	8	no	—
254	C₂×C₄×C₁₁	—	2	4	no	—
255	C₂×C₄×C₁₁	—	2	4	no	—
256	C₂×C₄×C₁₁	—	2	2	no	—
257	C₂×C₄×C₁₁	—	2	2	no	—
258	C₂×C₄×C₁₁	—	2	4	no	—
259	C₂×C₄×C₁₁	—	2	2	no	—
260	C₂×C₄×C₁₁	—	4	2	no	—
261	C₂×C₄×C₁₁	—	4	2	no	—
262	C₂×C₄×C₁₁	—	4	4	no	—
263	C₂×C₄×C₁₁	—	4	2	no	—
264	C₂×C₄×C₁₁	—	4	8	no	—
265	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	4	yes	—
266	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
267	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
270	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
271	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
272	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
273	C₈×C₁₁	—	2	2	no	—
274	C₈×C₁₁	—	2	2	no	—
275	C₈×C₁₁	—	2	4	no	—
276	C₂³×D₄	—	2	1	no	—
277	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
278	C₂²×SD₁₆	C₂²×C₁₁	1	1	yes	characteristic
279	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
280	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	complemented
281	#556	—	2	4	no	—
282	#556	C₂²×C₁₁	1	8	yes	complemented
283	D₄²	—	2	4	no	—
284	D₄²	C₂²×C₁₁	1	8	yes	—
285	C₂×C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
286	C₂×#127	C₂²×C₁₁	1	1	yes	characteristic
287	C₂×#126	—	2	2	no	—
288	C₂×#124	—	2	1	no	—
289	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	complemented
290	C₂×#121	—	2	1	no	—
291	C₂×#121	C₂²×C₁₁	1	2	yes	—
292	C₂×#120	—	2	2	no	—
293	C₂×C₄×Q₈	—	2	1	no	—
294	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
295	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
296	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
297	C₂×#117	C₂²×C₁₁	1	2	yes	complemented
298	#486	C₂²×C₁₁	1	8	yes	complemented
299	#482	C₂²×C₁₁	1	16	yes	complemented
300	#474	C₂²×C₁₁	1	8	yes	complemented
301	#468	C₂²×C₁₁	1	16	yes	complemented
302	#460	C₂²×C₁₁	1	8	yes	complemented
303	#450	C₂²×C₁₁	1	16	yes	complemented
304	C₄×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
305	#436	C₂²×C₁₁	1	8	yes	complemented
306	C₂×#107	C₂²×C₁₁	1	2	yes	complemented
307	C₂×#106	C₂²×C₁₁	1	1	yes	characteristic, complemented
308	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
309	#418	C₂²×C₁₁	1	16	yes	complemented
310	C₂×#103	C₂²×C₁₁	1	1	yes	characteristic, complemented
311	C₂×#102	C₂²×C₁₁	1	1	yes	characteristic
312	C₂×#102	C₂²×C₁₁	1	2	yes	—
313	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
314	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
315	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
316	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	complemented
317	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
318	C₂²×C₁₁	—	2	4	no	—
319	C₂²×C₁₁	—	2	4	no	—
320	C₂²×C₁₁	—	2	4	no	—
321	C₂²×C₁₁	—	2	4	no	—
322	C₂²×C₁₁	—	4	2	no	—
323	C₂²×C₁₁	—	4	8	no	—
324	C₂²×C₁₁	—	4	8	no	—
325	C₂²×C₁₁	—	4	2	no	—
326	C₂²×C₁₁	—	4	4	no	—
327	C₂²×C₁₁	—	4	4	no	—
328	C₂²×C₁₁	—	4	4	no	—
329	C₂²×C₁₁	—	8	32	no	—
330	C₂²×C₁₁	—	8	8	no	—
331	C₂²×C₁₁	#546	1	2	yes	—
332	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
333	C₂²×C₁₁	#577	1	2	yes	—
334	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
335	C₄×C₁₁	—	2	4	no	—
336	C₄×C₁₁	—	2	2	no	—
337	C₄×C₁₁	—	4	2	no	—
338	C₄×C₁₁	—	4	2	no	—
339	C₄×C₁₁	—	4	4	no	—
340	C₄×C₁₁	—	4	2	no	—
341	C₄×C₁₁	#546	1	2	yes	—
342	C₄×C₁₁	C₂×AGL(1,ℤ/8)	1	4	yes	—
343	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
344	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂⁵	—	2	2	no	—
346	C₂²×Q₈	—	2	1	no	—
347	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
348	C₂²×D₄	—	2	8	no	—
349	C₂²×D₄	—	2	2	no	—
350	C₂²×D₄	—	2	8	no	—
351	C₂²×D₄	—	2	2	no	—
352	C₂²×D₄	—	2	1	no	—
353	C₂²×D₄	—	2	4	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	4	4	no	—
356	C₂²×D₄	—	4	8	no	—
357	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
358	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
359	C₂²×D₄	C₂³×C₁₁	1	8	yes	—
360	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
361	C₂³×C₄	—	2	1	no	—
362	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
363	C₂×SD₁₆	—	2	4	no	—
364	C₂×SD₁₆	—	4	4	no	—
365	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
366	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	complemented
367	C₂×M₁₆	—	4	4	no	—
368	C₂×M₁₆	C₂³×C₁₁	1	8	yes	complemented
369	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
371	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	C₂³×C₁₁	1	4	yes	complemented
374	#127	—	2	2	no	—
375	#127	C₂³×C₁₁	1	4	yes	—
376	#126	—	2	16	no	—
377	#124	—	2	8	no	—
378	C₂²⋊Q₈	—	2	4	no	—
379	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	complemented
380	#121	—	2	4	no	—
381	#121	—	2	8	no	—
382	#121	C₂³×C₁₁	1	8	yes	—
383	#120	—	2	16	no	—
384	C₄×Q₈	—	2	8	no	—
385	C₄×Q₈	—	2	2	no	—
386	C₄×Q₈	C₂³×C₁₁	1	4	yes	complemented
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	D₄×C₁₁	1	4	yes	—
389	C₄×D₄	C₂³×C₁₁	1	4	yes	—
390	C₄×D₄	C₂³×C₁₁	1	4	yes	—
391	#117	—	2	4	no	—
392	#117	C₂³×C₁₁	1	8	yes	complemented
393	C₂×C₄⋊C₄	—	2	2	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	2	no	—
401	C₂×C₂²⋊C₄	—	2	2	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	2	no	—
404	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
405	C₂×C₄²	—	2	2	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
408	#107	C₂³×C₁₁	1	8	yes	complemented
409	#106	C₂³×C₁₁	1	4	yes	complemented
410	C₄⋊C₈	C₂³×C₁₁	1	4	yes	complemented
411	#103	C₂³×C₁₁	1	4	yes	complemented
412	#102	C₂³×C₁₁	1	4	yes	—
413	#102	C₂³×C₁₁	1	8	yes	—
414	#102	C₂³×C₁₁	1	8	yes	complemented
415	#102	C₂³×C₁₁	1	8	yes	complemented
416	#102	C₂³×C₁₁	1	8	yes	complemented
417	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	complemented
418	C₄×C₈	C₂³×C₁₁	1	4	yes	complemented
419	C₂×C₁₁	—	4	4	no	—
420	C₂×C₁₁	—	4	4	no	—
421	C₂×C₁₁	—	8	4	no	—
422	C₂×C₁₁	#3324	1	4	yes	direct product factor
423	C₂×C₁₁	C₂×#546	1	1	yes	characteristic
424	C₂×C₁₁	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂×C₁₁	C₂×#577	1	1	yes	characteristic
426	C₂⁴	—	2	1	no	—
427	C₂⁴	—	2	2	no	—
428	C₂⁴	—	2	8	no	—
429	C₂⁴	—	4	8	no	—
430	C₂⁴	—	4	8	no	—
431	C₂⁴	—	8	4	no	—
432	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	4	4	no	—
438	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
439	C₂×D₄	—	2	16	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	8	no	—
444	C₂×D₄	—	2	2	no	—
445	C₂×D₄	—	2	4	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	4	16	no	—
452	C₂×D₄	—	4	8	no	—
453	C₂×D₄	—	4	32	no	—
454	C₂×D₄	—	4	8	no	—
455	C₂×D₄	—	4	4	no	—
456	C₂×D₄	—	8	2	no	—
457	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
458	C₂×D₄	C₁₁×#41	1	4	yes	—
459	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
460	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	2	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	4	4	no	—
469	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
470	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
472	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
473	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
474	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
475	SD₁₆	—	2	8	no	—
476	SD₁₆	—	4	8	no	—
477	M₁₆	—	4	8	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	2	4	no	—
481	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
482	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
483	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
484	C₄⋊C₄	—	2	8	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	2	4	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
491	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
492	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
493	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
494	C₂²⋊C₄	—	2	8	no	—
495	C₂²⋊C₄	—	2	8	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	8	no	—
498	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
499	C₄²	—	2	8	no	—
500	C₄²	—	2	4	no	—
501	C₄²	C₂×D₄×C₁₁	1	2	yes	—
502	C₄²	C₂⁴×C₁₁	1	2	yes	—
503	C₁₁	C₂×#3324	1	1	yes	characteristic, direct product factor, Sylow
504	C₂³	—	2	4	no	—
505	C₂³	—	2	4	no	—
506	C₂³	—	2	4	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	2	4	no	—
510	C₂³	—	4	16	no	—
511	C₂³	—	4	16	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	4	4	no	—
517	C₂³	—	8	8	no	—
518	C₂³	—	8	32	no	—
519	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
520	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	8	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	8	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	4	no	—
530	D₄	—	4	16	no	—
531	D₄	—	4	16	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	8	no	—
534	D₄	—	8	4	no	—
535	D₄	C₂×C₁₁×#41	1	4	yes	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	8	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	8	no	—
550	C₂×C₄	C₁₁×AGL(1,ℤ/8)	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
552	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
553	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
555	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
556	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
557	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
558	C₈	—	2	2	no	—
559	C₈	—	2	2	no	—
560	C₈	—	2	4	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	4	no	—
563	C₂²	—	2	4	no	—
564	C₂²	—	2	4	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	4	8	no	—
567	C₂²	—	4	8	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	8	32	no	—
573	C₂²	—	8	8	no	—
574	C₂²	C₁₁×#546	1	2	yes	—
575	C₂²	C₂×C₁₁×AGL(1,ℤ/8)	1	2	yes	—
576	C₂²	C₁₁×#577	1	2	yes	—
577	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
578	C₄	—	2	4	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	2	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	4	no	—
583	C₄	—	4	2	no	—
584	C₄	C₁₁×#546	1	2	yes	—
585	C₄	C₂×C₁₁×AGL(1,ℤ/8)	1	4	yes	—
586	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
587	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
588	C₂	—	4	4	no	—
589	C₂	—	4	4	no	—
590	C₂	—	8	4	no	—
591	C₂	C₁₁×#3324	1	4	yes	direct product factor
592	C₂	C₂×C₁₁×#546	1	1	yes	characteristic
593	C₂	C₂²×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
594	C₂	C₂×C₁₁×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
prime radical	C₂×D₄²×C₁₁	C₂
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
1. C₂×C₁₁×#556	C₂	semidirect
3. C₁₁×#3324	C₂	direct (N × H)
4. C₂×C₁₁×#486	C₂	semidirect
5. C₂×C₁₁×#482	C₂	semidirect
6. C₂×C₁₁×#474	C₂	semidirect
7. C₂×C₁₁×#468	C₂	semidirect
8. C₂×C₁₁×#460	C₂	semidirect
9. C₂×C₁₁×#450	C₂	semidirect
10. C₂×C₄×C₁₁×SD₁₆	C₂	semidirect
11. C₂×C₁₁×#436	C₂	semidirect
12. C₂×C₁₁×#418	C₂	semidirect
16. C₂²×C₁₁×SD₁₆	C₂²	semidirect
17. C₂²×C₁₁×M₁₆	C₂²	semidirect
19. C₁₁×#556	C₂²	semidirect
22. C₂×C₁₁×C₄⋊Q₈	C₂²	semidirect
26. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
31. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
34. C₂×C₁₁×#117	C₂²	semidirect
35. C₁₁×#486	C₂²	semidirect
36. C₁₁×#482	C₂²	semidirect
37. C₁₁×#474	C₂²	semidirect
38. C₁₁×#468	C₂²	semidirect
39. C₁₁×#460	C₂²	semidirect
40. C₁₁×#450	C₂²	semidirect
41. C₄×C₁₁×SD₁₆	C₂²	semidirect
42. C₁₁×#436	C₂²	semidirect
43. C₂×C₁₁×#107	C₂²	semidirect
44. C₂×C₁₁×#106	C₂²	semidirect
45. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
46. C₁₁×#418	C₂²	semidirect
47. C₂×C₁₁×#103	C₂²	semidirect
50. C₂×C₁₁×#102	C₂²	semidirect
51. C₂×C₁₁×#102	C₂²	semidirect
52. C₂×C₁₁×#102	C₂²	semidirect
53. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
54. C₂×C₄×C₈×C₁₁	C₂²	semidirect
76. C₂×C₁₁×SD₁₆	C₂³	semidirect
78. C₂×C₁₁×M₁₆	C₂³	semidirect
83. C₁₁×C₄⋊Q₈	C₂³	semidirect
89. C₁₁×C₂²⋊Q₈	C₂³	semidirect
96. C₄×Q₈×C₁₁	C₂³	semidirect
102. C₁₁×#117	C₂³	semidirect
118. C₁₁×#107	C₂³	semidirect
119. C₁₁×#106	C₂³	semidirect
120. C₁₁×C₄⋊C₈	C₂³	semidirect
121. C₁₁×#103	C₂³	semidirect
124. C₁₁×#102	C₂³	semidirect
125. C₁₁×#102	C₂³	semidirect
126. C₁₁×#102	C₂³	semidirect
127. C₁₁×C₂²⋊C₈	C₂³	semidirect
128. C₄×C₈×C₁₁	C₂³	semidirect
129. C₂×#3324	C₁₁	direct (N × H)
207. C₂×#556	C₂×C₁₁	semidirect
209. #3324	C₂×C₁₁	direct (N × H)
210. C₂×#486	C₂×C₁₁	semidirect
211. C₂×#482	C₂×C₁₁	semidirect
212. C₂×#474	C₂×C₁₁	semidirect
213. C₂×#468	C₂×C₁₁	semidirect
214. C₂×#460	C₂×C₁₁	semidirect
215. C₂×#450	C₂×C₁₁	semidirect
216. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
217. C₂×#436	C₂×C₁₁	semidirect
218. C₂×#418	C₂×C₁₁	semidirect
279. C₂²×SD₁₆	C₂²×C₁₁	semidirect
280. C₂²×M₁₆	C₂²×C₁₁	semidirect
282. #556	C₂²×C₁₁	semidirect
285. C₂×C₄⋊Q₈	C₂²×C₁₁	semidirect
289. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
294. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
297. C₂×#117	C₂²×C₁₁	semidirect
298. #486	C₂²×C₁₁	semidirect
299. #482	C₂²×C₁₁	semidirect
300. #474	C₂²×C₁₁	semidirect
301. #468	C₂²×C₁₁	semidirect
302. #460	C₂²×C₁₁	semidirect
303. #450	C₂²×C₁₁	semidirect
304. C₄×SD₁₆	C₂²×C₁₁	semidirect
305. #436	C₂²×C₁₁	semidirect
306. C₂×#107	C₂²×C₁₁	semidirect
307. C₂×#106	C₂²×C₁₁	semidirect
308. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
309. #418	C₂²×C₁₁	semidirect
310. C₂×#103	C₂²×C₁₁	semidirect
313. C₂×#102	C₂²×C₁₁	semidirect
314. C₂×#102	C₂²×C₁₁	semidirect
315. C₂×#102	C₂²×C₁₁	semidirect
316. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
317. C₂×C₄×C₈	C₂²×C₁₁	semidirect
366. C₂×SD₁₆	C₂³×C₁₁	semidirect
368. C₂×M₁₆	C₂³×C₁₁	semidirect
373. C₄⋊Q₈	C₂³×C₁₁	semidirect
379. C₂²⋊Q₈	C₂³×C₁₁	semidirect
386. C₄×Q₈	C₂³×C₁₁	semidirect
392. #117	C₂³×C₁₁	semidirect
408. #107	C₂³×C₁₁	semidirect
409. #106	C₂³×C₁₁	semidirect
410. C₄⋊C₈	C₂³×C₁₁	semidirect
411. #103	C₂³×C₁₁	semidirect
414. #102	C₂³×C₁₁	semidirect
415. #102	C₂³×C₁₁	semidirect
416. #102	C₂³×C₁₁	semidirect
417. C₂²⋊C₈	C₂³×C₁₁	semidirect
418. C₄×C₈	C₂³×C₁₁	semidirect
422. C₂×C₁₁	#3324	direct (N × H)
503. C₁₁	C₂×#3324	direct (N × H)
591. C₂	C₁₁×#3324	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
C₂×D₄²×C₁₁	2
C₁₁×#3324	2
C₂×C₁₁×#486	2
C₂×C₁₁×#482	2
C₂×C₁₁×#474	2
C₂×C₁₁×#468	2
C₂×C₁₁×#460	2
C₂×C₁₁×#450	2
C₂×C₄×C₁₁×SD₁₆	2
C₂×C₁₁×#436	2
C₂×C₁₁×#418	2
C₂×#3324	11

Subgroups — C2×C11×#3324 #14638337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3324 #14638337