Subgroups — C₂×C₄×C₁₁×#137 #14637350

Order 2816.

2810 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#137	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×C₁₁×#137	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₁×#441	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#440	C₂	1	2	yes	maximal, complemented
7	C₂×C₄×C₁₁×Q₁₆	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#417	C₂	1	1	yes	maximal, characteristic
11	C₂×C₁₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
14	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#137	C₄	1	16	yes	direct product factor
16	C₂×C₁₁×#137	C₂²	1	8	yes	—
17	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
18	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	—
19	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
21	C₄×C₁₁×#41	—	2	4	no	—
22	C₄×C₁₁×#41	C₂²	1	8	yes	—
23	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₁	—	2	4	no	—
25	C₂×C₄×Q₈×C₁₁	—	2	1	no	—
26	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₁	C₂²	1	8	yes	complemented
31	C₂×C₄×D₄×C₁₁	—	2	1	no	—
32	C₂×C₄×D₄×C₁₁	—	2	1	no	—
33	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#117	—	2	1	no	—
36	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
37	C₂²×C₁₁×C₄⋊C₄	—	2	1	no	—
38	C₂²×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₁₁	—	2	1	no	—
40	C₂²×C₄²×C₁₁	—	2	1	no	—
41	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
42	C₁₁×#441	C₂²	1	16	yes	complemented
43	C₁₁×#440	C₂²	1	16	yes	complemented
44	C₄×C₁₁×Q₁₆	C₂²	1	16	yes	complemented
45	C₄×C₁₁×SD₁₆	C₂²	1	16	yes	complemented
46	C₁₁×#428	C₂²	1	8	yes	complemented
47	C₂×C₁₁×#107	C₂²	1	2	yes	—
48	C₂×C₁₁×#106	C₂²	1	2	yes	—
49	C₁₁×#419	C₂²	1	8	yes	complemented
50	C₁₁×#417	C₂²	1	8	yes	—
51	C₂×C₁₁×#103	C₂²	1	2	yes	—
52	C₂×C₁₁×#103	C₂²	1	2	yes	—
53	C₂×C₁₁×#103	C₂²	1	2	yes	—
54	C₂×C₁₁×#102	C₂²	1	2	yes	—
55	C₄×C₁₁×M₁₆	C₂²	1	8	yes	complemented
56	C₂×C₁₁×#97	C₂²	1	2	yes	—
57	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
58	C₂×C₁₁×#41	—	2	2	no	—
59	C₂×C₁₁×#41	—	2	4	no	—
60	C₂×C₁₁×#41	C₂×C₄	1	8	yes	—
61	C₂×C₁₁×#41	C₂³	1	4	yes	—
62	C₂²×Q₈×C₁₁	—	2	1	no	—
63	C₂²×Q₈×C₁₁	—	2	2	no	—
64	C₂²×Q₈×C₁₁	—	2	4	no	—
65	C₂²×Q₈×C₁₁	C₂×C₄	1	8	yes	complemented
66	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
67	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
69	C₂²×D₄×C₁₁	—	2	1	no	—
70	C₂²×D₄×C₁₁	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₁	—	2	1	no	—
72	C₂³×C₄×C₁₁	—	2	1	no	—
73	C₂³×C₄×C₁₁	—	2	1	no	—
74	C₂³×C₄×C₁₁	—	2	1	no	—
75	C₂³×C₄×C₁₁	—	2	1	no	—
76	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
77	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
78	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
79	C₁₁×#137	C₂×C₄	1	64	yes	direct product factor
80	C₂×C₁₁×Q₁₆	C₂×C₄	1	16	yes	complemented
81	C₂×C₁₁×Q₁₆	C₂³	1	8	yes	—
82	C₂×C₁₁×SD₁₆	C₂×C₄	1	16	yes	complemented
83	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	—
84	C₂×C₁₁×M₁₆	—	2	4	no	—
85	C₂×C₁₁×M₁₆	C₂×C₄	1	8	yes	complemented
86	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
87	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
88	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
89	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
90	C₄×Q₈×C₁₁	—	2	4	no	—
91	C₄×Q₈×C₁₁	—	2	4	no	—
92	C₄×Q₈×C₁₁	—	2	8	no	—
93	C₄×Q₈×C₁₁	—	2	8	no	—
94	C₄×Q₈×C₁₁	—	2	2	no	—
95	C₄×Q₈×C₁₁	—	2	2	no	—
96	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
97	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
98	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
99	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
100	C₄×D₄×C₁₁	—	2	8	no	—
101	C₄×D₄×C₁₁	—	2	8	no	—
102	C₄×D₄×C₁₁	—	2	2	no	—
103	C₄×D₄×C₁₁	—	2	2	no	—
104	C₄×D₄×C₁₁	C₂³	1	4	yes	—
105	C₄×D₄×C₁₁	C₂³	1	4	yes	—
106	C₁₁×#117	—	2	2	no	—
107	C₁₁×#117	—	2	8	no	—
108	C₁₁×#117	C₂³	1	4	yes	—
109	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
110	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
111	C₂×C₁₁×C₄⋊C₄	—	2	8	no	—
112	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
113	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
114	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
115	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
116	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
117	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
118	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₂×C₁₁×C₄⋊C₄	C₂³	1	1	yes	characteristic
120	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₁₁×C₂²⋊C₄	—	2	1	no	—
123	C₂×C₄²×C₁₁	—	2	1	no	—
124	C₂×C₄²×C₁₁	—	2	1	no	—
125	C₂×C₄²×C₁₁	—	2	2	no	—
126	C₂×C₄²×C₁₁	—	2	8	no	—
127	C₂×C₄²×C₁₁	—	2	1	no	—
128	C₂×C₄²×C₁₁	—	2	2	no	—
129	C₂×C₄²×C₁₁	—	2	8	no	—
130	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
131	C₂×C₄²×C₁₁	D₄	1	4	yes	—
132	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
133	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
135	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
136	C₁₁×#107	C₂³	1	8	yes	—
137	C₁₁×#106	C₂³	1	8	yes	—
138	C₁₁×#103	C₂³	1	8	yes	—
139	C₁₁×#103	C₂³	1	8	yes	—
140	C₁₁×#103	C₂³	1	8	yes	—
141	C₁₁×#102	C₂³	1	8	yes	—
142	C₁₁×#97	C₂³	1	8	yes	—
143	C₄×C₈×C₁₁	C₂³	1	8	yes	—
144	C₂×C₄×#137	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
145	C₂⁴×C₁₁	—	2	1	no	—
146	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
147	C₁₁×#41	—	2	16	no	—
148	C₁₁×#41	—	2	8	no	—
149	C₁₁×#41	C₂²×C₄	1	16	yes	—
150	C₂×Q₈×C₁₁	—	2	8	no	—
151	C₂×Q₈×C₁₁	—	2	16	no	—
152	C₂×Q₈×C₁₁	—	2	4	no	—
153	C₂×Q₈×C₁₁	—	2	2	no	—
154	C₂×Q₈×C₁₁	—	2	1	no	—
155	C₂×Q₈×C₁₁	—	2	4	no	—
156	C₂×Q₈×C₁₁	—	2	8	no	—
157	C₂×Q₈×C₁₁	—	2	2	no	—
158	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
159	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
160	C₂×Q₈×C₁₁	C₂²×C₄	1	16	yes	complemented
161	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
162	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
163	C₂×D₄×C₁₁	—	2	8	no	—
164	C₂×D₄×C₁₁	—	2	4	no	—
165	C₂×D₄×C₁₁	—	2	1	no	—
166	C₂×D₄×C₁₁	—	2	2	no	—
167	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
168	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₁	—	2	8	no	—
170	C₂²×C₄×C₁₁	—	2	1	no	—
171	C₂²×C₄×C₁₁	—	2	2	no	—
172	C₂²×C₄×C₁₁	—	2	4	no	—
173	C₂²×C₄×C₁₁	—	2	8	no	—
174	C₂²×C₄×C₁₁	—	2	4	no	—
175	C₂²×C₄×C₁₁	—	2	4	no	—
176	C₂²×C₄×C₁₁	—	2	1	no	—
177	C₂²×C₄×C₁₁	—	2	1	no	—
178	C₂²×C₄×C₁₁	—	2	4	no	—
179	C₂²×C₄×C₁₁	—	2	2	no	—
180	C₂²×C₄×C₁₁	—	2	4	no	—
181	C₂²×C₄×C₁₁	—	2	4	no	—
182	C₂²×C₄×C₁₁	—	4	2	no	—
183	C₂²×C₄×C₁₁	—	4	4	no	—
184	C₂²×C₄×C₁₁	—	4	4	no	—
185	C₂²×C₄×C₁₁	—	4	4	no	—
186	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
187	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
189	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
190	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
193	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
194	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₁₁	#41	1	4	yes	—
196	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
198	C₁₁×Q₁₆	C₂²×C₄	1	32	yes	complemented
199	C₁₁×SD₁₆	C₂²×C₄	1	32	yes	complemented
200	C₁₁×M₁₆	—	2	8	no	—
201	C₁₁×M₁₆	C₂²×C₄	1	16	yes	complemented
202	C₂×C₈×C₁₁	—	2	4	no	—
203	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
204	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
205	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
206	C₁₁×C₄⋊C₄	—	2	8	no	—
207	C₁₁×C₄⋊C₄	—	2	8	no	—
208	C₁₁×C₄⋊C₄	—	2	4	no	—
209	C₁₁×C₄⋊C₄	—	2	2	no	—
210	C₁₁×C₄⋊C₄	—	2	4	no	—
211	C₁₁×C₄⋊C₄	—	2	4	no	—
212	C₁₁×C₄⋊C₄	—	2	1	no	—
213	C₁₁×C₄⋊C₄	—	2	1	no	—
214	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
215	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
216	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
217	C₁₁×C₂²⋊C₄	—	2	4	no	—
218	C₁₁×C₂²⋊C₄	—	2	4	no	—
219	C₁₁×C₂²⋊C₄	—	2	4	no	—
220	C₄²×C₁₁	—	2	4	no	—
221	C₄²×C₁₁	—	2	4	no	—
222	C₄²×C₁₁	—	2	4	no	—
223	C₄²×C₁₁	—	2	8	no	—
224	C₄²×C₁₁	—	2	8	no	—
225	C₄²×C₁₁	C₂×D₄	1	4	yes	—
226	C₄²×C₁₁	C₂×D₄	1	4	yes	—
227	C₄²×C₁₁	C₂×D₄	1	2	yes	—
228	C₄²×C₁₁	C₂×D₄	1	2	yes	—
229	C₄²×C₁₁	C₂⁴	1	2	yes	—
230	C₄²×C₁₁	C₂⁴	1	2	yes	—
231	C₂²×#137	C₂×C₁₁	1	1	yes	characteristic
232	C₂×C₄×#41	C₂×C₁₁	1	1	yes	characteristic
233	C₂²×C₄×Q₈	C₂×C₁₁	1	1	yes	characteristic, complemented
234	C₄×#137	C₂×C₁₁	1	16	yes	direct product factor
235	C₂×#441	C₂×C₁₁	1	2	yes	complemented
236	C₂×#440	C₂×C₁₁	1	2	yes	complemented
237	C₂×C₄×Q₁₆	C₂×C₁₁	1	2	yes	complemented
238	C₂×C₄×SD₁₆	C₂×C₁₁	1	2	yes	complemented
239	C₂×#428	C₂×C₁₁	1	1	yes	characteristic, complemented
240	C₂×#417	C₂×C₁₁	1	1	yes	characteristic
241	C₂×#419	C₂×C₁₁	1	1	yes	characteristic, complemented
242	C₂×C₄×M₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
243	C₂³×C₁₁	—	2	2	no	—
244	C₂³×C₁₁	—	2	2	no	—
245	C₂³×C₁₁	—	2	4	no	—
246	C₂³×C₁₁	—	2	2	no	—
247	C₂³×C₁₁	—	4	2	no	—
248	C₂³×C₁₁	—	4	2	no	—
249	C₂³×C₁₁	C₄×D₄	1	4	yes	—
250	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
251	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
252	Q₈×C₁₁	—	2	8	no	—
253	Q₈×C₁₁	—	2	16	no	—
254	Q₈×C₁₁	—	2	4	no	—
255	Q₈×C₁₁	—	2	4	no	—
256	Q₈×C₁₁	—	2	2	no	—
257	Q₈×C₁₁	C₂³×C₄	1	8	yes	—
258	Q₈×C₁₁	C₂³×C₄	1	4	yes	—
259	D₄×C₁₁	—	2	16	no	—
260	D₄×C₁₁	—	2	4	no	—
261	D₄×C₁₁	—	2	2	no	—
262	D₄×C₁₁	C₂³×C₄	1	4	yes	—
263	C₂×C₄×C₁₁	—	2	4	no	—
264	C₂×C₄×C₁₁	—	2	8	no	—
265	C₂×C₄×C₁₁	—	2	16	no	—
266	C₂×C₄×C₁₁	—	2	2	no	—
267	C₂×C₄×C₁₁	—	2	2	no	—
268	C₂×C₄×C₁₁	—	2	2	no	—
269	C₂×C₄×C₁₁	—	2	2	no	—
270	C₂×C₄×C₁₁	—	2	4	no	—
271	C₂×C₄×C₁₁	—	2	16	no	—
272	C₂×C₄×C₁₁	—	2	8	no	—
273	C₂×C₄×C₁₁	—	2	2	no	—
274	C₂×C₄×C₁₁	—	2	2	no	—
275	C₂×C₄×C₁₁	—	2	4	no	—
276	C₂×C₄×C₁₁	—	4	4	no	—
277	C₂×C₄×C₁₁	—	4	8	no	—
278	C₂×C₄×C₁₁	—	4	8	no	—
279	C₂×C₄×C₁₁	—	4	2	no	—
280	C₂×C₄×C₁₁	—	4	2	no	—
281	C₂×C₄×C₁₁	—	4	4	no	—
282	C₂×C₄×C₁₁	—	4	8	no	—
283	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
284	C₂×C₄×C₁₁	C₄×D₄	1	8	yes	—
285	C₂×C₄×C₁₁	#137	1	4	yes	direct product factor
286	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
287	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
288	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
289	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
290	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
291	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
292	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
294	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
295	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
296	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
297	C₈×C₁₁	—	2	4	no	—
298	C₈×C₁₁	C₂³×C₄	1	8	yes	—
299	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
300	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic
301	C₂×#137	C₄×C₁₁	1	16	yes	direct product factor
302	C₂×#137	C₂²×C₁₁	1	8	yes	—
303	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
304	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	—
305	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
306	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
307	C₄×#41	—	2	4	no	—
308	C₄×#41	C₂²×C₁₁	1	8	yes	—
309	C₂×C₄×Q₈	—	2	1	no	—
310	C₂×C₄×Q₈	—	2	1	no	—
311	C₂×C₄×Q₈	—	2	4	no	—
312	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
313	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
314	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
316	C₂×C₄×Q₈	C₂²×C₁₁	1	8	yes	complemented
317	C₂×C₄×D₄	—	2	1	no	—
318	C₂×C₄×D₄	—	2	1	no	—
319	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
320	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
321	C₂×#117	—	2	1	no	—
322	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	—	2	1	no	—
324	C₂²×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
325	C₂²×C₄²	—	2	1	no	—
326	C₂²×C₄²	—	2	1	no	—
327	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
328	#441	C₂²×C₁₁	1	16	yes	complemented
329	#440	C₂²×C₁₁	1	16	yes	complemented
330	C₄×Q₁₆	C₂²×C₁₁	1	16	yes	complemented
331	C₄×SD₁₆	C₂²×C₁₁	1	16	yes	complemented
332	#428	C₂²×C₁₁	1	8	yes	complemented
333	C₂×#107	C₂²×C₁₁	1	2	yes	—
334	C₂×#106	C₂²×C₁₁	1	2	yes	—
335	#419	C₂²×C₁₁	1	8	yes	complemented
336	#417	C₂²×C₁₁	1	8	yes	—
337	C₂×#103	C₂²×C₁₁	1	2	yes	—
338	C₂×#103	C₂²×C₁₁	1	2	yes	—
339	C₂×#103	C₂²×C₁₁	1	2	yes	—
340	C₂×#102	C₂²×C₁₁	1	2	yes	—
341	C₄×M₁₆	C₂²×C₁₁	1	8	yes	complemented
342	C₂×#97	C₂²×C₁₁	1	2	yes	—
343	C₂×C₄×C₈	C₂²×C₁₁	1	2	yes	—
344	C₂²×C₁₁	—	2	8	no	—
345	C₂²×C₁₁	—	2	2	no	—
346	C₂²×C₁₁	—	2	2	no	—
347	C₂²×C₁₁	—	2	4	no	—
348	C₂²×C₁₁	—	4	8	no	—
349	C₂²×C₁₁	—	4	2	no	—
350	C₂²×C₁₁	—	4	2	no	—
351	C₂²×C₁₁	C₂×C₄×D₄	1	4	yes	—
352	C₂²×C₁₁	C₂×C₄×D₄	1	2	yes	—
353	C₂²×C₁₁	C₂×#137	1	2	yes	—
354	C₂²×C₁₁	#575	1	2	yes	—
355	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₁	—	2	4	no	—
357	C₄×C₁₁	—	2	8	no	—
358	C₄×C₁₁	—	2	2	no	—
359	C₄×C₁₁	—	2	2	no	—
360	C₄×C₁₁	—	2	2	no	—
361	C₄×C₁₁	—	4	2	no	—
362	C₄×C₁₁	—	4	2	no	—
363	C₄×C₁₁	—	4	4	no	—
364	C₄×C₁₁	C₂×C₄×D₄	1	4	yes	—
365	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
366	C₄×C₁₁	C₂×#137	1	4	yes	direct product factor
367	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
368	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
369	C₂×#41	—	2	2	no	—
370	C₂×#41	—	2	4	no	—
371	C₂×#41	C₂×C₄×C₁₁	1	8	yes	—
372	C₂×#41	C₂³×C₁₁	1	4	yes	—
373	C₂²×Q₈	—	2	1	no	—
374	C₂²×Q₈	—	2	2	no	—
375	C₂²×Q₈	—	2	4	no	—
376	C₂²×Q₈	C₂×C₄×C₁₁	1	8	yes	complemented
377	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
378	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	C₂³×C₁₁	1	1	yes	characteristic
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	—	2	1	no	—
385	C₂³×C₄	—	2	1	no	—
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
388	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
389	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
390	#137	C₂×C₄×C₁₁	1	64	yes	direct product factor
391	C₂×Q₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
392	C₂×Q₁₆	C₂³×C₁₁	1	8	yes	—
393	C₂×SD₁₆	C₂×C₄×C₁₁	1	16	yes	complemented
394	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	—
395	C₂×M₁₆	—	2	4	no	—
396	C₂×M₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
397	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
398	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
399	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
400	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
401	C₄×Q₈	—	2	4	no	—
402	C₄×Q₈	—	2	4	no	—
403	C₄×Q₈	—	2	8	no	—
404	C₄×Q₈	—	2	8	no	—
405	C₄×Q₈	—	2	2	no	—
406	C₄×Q₈	—	2	2	no	—
407	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
408	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
409	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
410	C₄×Q₈	C₂³×C₁₁	1	4	yes	—
411	C₄×D₄	—	2	8	no	—
412	C₄×D₄	—	2	8	no	—
413	C₄×D₄	—	2	2	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	C₂³×C₁₁	1	4	yes	—
416	C₄×D₄	C₂³×C₁₁	1	4	yes	—
417	#117	—	2	2	no	—
418	#117	—	2	8	no	—
419	#117	C₂³×C₁₁	1	4	yes	—
420	C₂×C₄⋊C₄	—	2	2	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	8	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	2	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
428	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
429	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
430	C₂×C₄⋊C₄	C₂³×C₁₁	1	1	yes	characteristic
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₄²	—	2	1	no	—
435	C₂×C₄²	—	2	1	no	—
436	C₂×C₄²	—	2	1	no	—
437	C₂×C₄²	—	2	2	no	—
438	C₂×C₄²	—	2	2	no	—
439	C₂×C₄²	—	2	8	no	—
440	C₂×C₄²	—	2	8	no	—
441	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
442	C₂×C₄²	D₄×C₁₁	1	4	yes	—
443	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
447	#107	C₂³×C₁₁	1	8	yes	—
448	#106	C₂³×C₁₁	1	8	yes	—
449	#103	C₂³×C₁₁	1	8	yes	—
450	#103	C₂³×C₁₁	1	8	yes	—
451	#103	C₂³×C₁₁	1	8	yes	—
452	#102	C₂³×C₁₁	1	8	yes	—
453	#97	C₂³×C₁₁	1	8	yes	—
454	C₄×C₈	C₂³×C₁₁	1	8	yes	—
455	C₂×C₁₁	—	2	4	no	—
456	C₂×C₁₁	—	4	4	no	—
457	C₂×C₁₁	C₄×#137	1	4	yes	direct product factor
458	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
459	C₂×C₁₁	C₂²×#137	1	1	yes	characteristic
460	C₂×C₁₁	C₂×#575	1	1	yes	characteristic
461	C₂⁴	—	2	1	no	—
462	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
463	#41	—	2	16	no	—
464	#41	—	2	8	no	—
465	#41	C₂²×C₄×C₁₁	1	16	yes	—
466	C₂×Q₈	—	2	8	no	—
467	C₂×Q₈	—	2	16	no	—
468	C₂×Q₈	—	2	4	no	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	4	no	—
472	C₂×Q₈	—	2	8	no	—
473	C₂×Q₈	—	2	2	no	—
474	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
475	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
476	C₂×Q₈	C₂²×C₄×C₁₁	1	16	yes	complemented
477	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
478	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
479	C₂×D₄	—	2	8	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
484	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
485	C₂²×C₄	—	2	8	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	8	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	4	2	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
505	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
508	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
511	C₂²×C₄	C₁₁×#41	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
513	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
514	Q₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
515	SD₁₆	C₂²×C₄×C₁₁	1	32	yes	complemented
516	M₁₆	—	2	8	no	—
517	M₁₆	C₂²×C₄×C₁₁	1	16	yes	complemented
518	C₂×C₈	—	2	4	no	—
519	C₂×C₈	C₂²×C₄×C₁₁	1	8	yes	—
520	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
521	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
522	C₄⋊C₄	—	2	8	no	—
523	C₄⋊C₄	—	2	8	no	—
524	C₄⋊C₄	—	2	4	no	—
525	C₄⋊C₄	—	2	2	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
531	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
532	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₄²	—	2	4	no	—
537	C₄²	—	2	4	no	—
538	C₄²	—	2	4	no	—
539	C₄²	—	2	8	no	—
540	C₄²	—	2	8	no	—
541	C₄²	C₂×D₄×C₁₁	1	4	yes	—
542	C₄²	C₂×D₄×C₁₁	1	4	yes	—
543	C₄²	C₂×D₄×C₁₁	1	2	yes	—
544	C₄²	C₂×D₄×C₁₁	1	2	yes	—
545	C₄²	C₂⁴×C₁₁	1	2	yes	—
546	C₄²	C₂⁴×C₁₁	1	2	yes	—
547	C₁₁	C₂×C₄×#137	1	1	yes	characteristic, direct product factor, Sylow
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	4	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	2	no	—
554	C₂³	C₄×D₄×C₁₁	1	4	yes	—
555	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
556	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
557	Q₈	—	2	8	no	—
558	Q₈	—	2	16	no	—
559	Q₈	—	2	4	no	—
560	Q₈	—	2	4	no	—
561	Q₈	—	2	2	no	—
562	Q₈	C₂³×C₄×C₁₁	1	8	yes	—
563	Q₈	C₂³×C₄×C₁₁	1	4	yes	—
564	D₄	—	2	16	no	—
565	D₄	—	2	4	no	—
566	D₄	—	2	2	no	—
567	D₄	C₂³×C₄×C₁₁	1	4	yes	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	—	2	16	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	4	no	—
576	C₂×C₄	—	2	16	no	—
577	C₂×C₄	—	2	8	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	8	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	4	2	no	—
586	C₂×C₄	—	4	4	no	—
587	C₂×C₄	—	4	8	no	—
588	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
589	C₂×C₄	C₄×D₄×C₁₁	1	8	yes	—
590	C₂×C₄	C₁₁×#137	1	4	yes	direct product factor
591	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
592	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
593	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
594	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
595	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
596	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
597	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
598	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
599	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
600	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
601	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
602	C₈	—	2	4	no	—
603	C₈	C₂³×C₄×C₁₁	1	8	yes	—
604	C₂²	—	2	8	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	4	no	—
608	C₂²	—	4	8	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	C₂×C₄×D₄×C₁₁	1	4	yes	—
612	C₂²	C₂×C₄×D₄×C₁₁	1	2	yes	—
613	C₂²	C₂×C₁₁×#137	1	2	yes	—
614	C₂²	C₁₁×#575	1	2	yes	—
615	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
616	C₄	—	2	4	no	—
617	C₄	—	2	8	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	4	2	no	—
622	C₄	—	4	2	no	—
623	C₄	—	4	4	no	—
624	C₄	C₂×C₄×D₄×C₁₁	1	4	yes	—
625	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
626	C₄	C₂×C₁₁×#137	1	4	yes	direct product factor
627	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
628	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
629	C₂	—	2	4	no	—
630	C₂	—	4	4	no	—
631	C₂	C₄×C₁₁×#137	1	4	yes	direct product factor
632	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
633	C₂	C₂²×C₁₁×#137	1	1	yes	characteristic
634	C₂	C₂×C₁₁×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	C₂×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂³×C₁₁	C₂²×D₄
prime radical	C₂²×C₁₁×#41	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂²×C₄×Q₈×C₁₁	C₂	semidirect
4. C₄×C₁₁×#137	C₂	direct (N × H)
5. C₂×C₁₁×#441	C₂	semidirect
6. C₂×C₁₁×#440	C₂	semidirect
7. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
8. C₂×C₄×C₁₁×SD₁₆	C₂	semidirect
9. C₂×C₁₁×#428	C₂	semidirect
11. C₂×C₁₁×#419	C₂	semidirect
12. C₂×C₄×C₁₁×M₁₆	C₂	semidirect
15. C₂×C₁₁×#137	C₄	direct (N × H)
30. C₂×C₄×Q₈×C₁₁	C₂²	semidirect
42. C₁₁×#441	C₂²	semidirect
43. C₁₁×#440	C₂²	semidirect
44. C₄×C₁₁×Q₁₆	C₂²	semidirect
45. C₄×C₁₁×SD₁₆	C₂²	semidirect
46. C₁₁×#428	C₂²	semidirect
49. C₁₁×#419	C₂²	semidirect
55. C₄×C₁₁×M₁₆	C₂²	semidirect
65. C₂²×Q₈×C₁₁	C₂×C₄	semidirect
79. C₁₁×#137	C₂×C₄	direct (N × H)
80. C₂×C₁₁×Q₁₆	C₂×C₄	semidirect
82. C₂×C₁₁×SD₁₆	C₂×C₄	semidirect
85. C₂×C₁₁×M₁₆	C₂×C₄	semidirect
144. C₂×C₄×#137	C₁₁	direct (N × H)
160. C₂×Q₈×C₁₁	C₂²×C₄	semidirect
198. C₁₁×Q₁₆	C₂²×C₄	semidirect
199. C₁₁×SD₁₆	C₂²×C₄	semidirect
201. C₁₁×M₁₆	C₂²×C₄	semidirect
233. C₂²×C₄×Q₈	C₂×C₁₁	semidirect
234. C₄×#137	C₂×C₁₁	direct (N × H)
235. C₂×#441	C₂×C₁₁	semidirect
236. C₂×#440	C₂×C₁₁	semidirect
237. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
238. C₂×C₄×SD₁₆	C₂×C₁₁	semidirect
239. C₂×#428	C₂×C₁₁	semidirect
241. C₂×#419	C₂×C₁₁	semidirect
242. C₂×C₄×M₁₆	C₂×C₁₁	semidirect
285. C₂×C₄×C₁₁	#137	direct (N × H)
301. C₂×#137	C₄×C₁₁	direct (N × H)
316. C₂×C₄×Q₈	C₂²×C₁₁	semidirect
328. #441	C₂²×C₁₁	semidirect
329. #440	C₂²×C₁₁	semidirect
330. C₄×Q₁₆	C₂²×C₁₁	semidirect
331. C₄×SD₁₆	C₂²×C₁₁	semidirect
332. #428	C₂²×C₁₁	semidirect
335. #419	C₂²×C₁₁	semidirect
341. C₄×M₁₆	C₂²×C₁₁	semidirect
366. C₄×C₁₁	C₂×#137	direct (N × H)
376. C₂²×Q₈	C₂×C₄×C₁₁	semidirect
390. #137	C₂×C₄×C₁₁	direct (N × H)
391. C₂×Q₁₆	C₂×C₄×C₁₁	semidirect
393. C₂×SD₁₆	C₂×C₄×C₁₁	semidirect
396. C₂×M₁₆	C₂×C₄×C₁₁	semidirect
457. C₂×C₁₁	C₄×#137	direct (N × H)
476. C₂×Q₈	C₂²×C₄×C₁₁	semidirect
514. Q₁₆	C₂²×C₄×C₁₁	semidirect
515. SD₁₆	C₂²×C₄×C₁₁	semidirect
517. M₁₆	C₂²×C₄×C₁₁	semidirect
547. C₁₁	C₂×C₄×#137	direct (N × H)
590. C₂×C₄	C₁₁×#137	direct (N × H)
626. C₄	C₂×C₁₁×#137	direct (N × H)
631. C₂	C₄×C₁₁×#137	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×C₁₁×#137	2
C₂×C₄×C₁₁×#41	2
C₂²×C₄×Q₈×C₁₁	2
C₄×C₁₁×#137	2
C₂×C₁₁×#441	2
C₂×C₁₁×#440	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×C₄×C₁₁×SD₁₆	2
C₂×C₁₁×#428	2
C₂×C₁₁×#417	2
C₂×C₁₁×#419	2
C₂×C₄×C₁₁×M₁₆	2
C₂×C₄×#137	11

Subgroups — C2×C4×C11×#137 #14637350

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₁×#137 #14637350