Subgroups — C₂×C₁₁×#3287 #14638240

Order 2816.

2910 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#135	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×#550	C₂	1	2	yes	maximal, complemented
3	C₁₁×#3287	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₁×#493	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₁×#466	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#460	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₁×#449	C₂	1	4	yes	maximal, complemented
8	C₂×C₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₁×#41	C₂²	1	4	yes	—
11	C₂×C₁₁×#135	—	2	16	no	—
12	C₂×C₁₁×#135	C₂²	1	16	yes	complemented
13	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×SD₁₆	C₂²	1	4	yes	—
15	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
16	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
17	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
18	C₁₁×#550	—	2	8	no	—
19	C₁₁×#550	C₂²	1	16	yes	complemented
20	C₂×C₁₁×#127	—	2	2	no	—
21	C₂×C₁₁×#127	C₂²	1	2	yes	—
22	C₂×C₁₁×#121	—	2	4	no	—
23	C₂×C₁₁×#121	C₂²	1	4	yes	—
24	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₁	—	2	2	no	—
26	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×#493	C₂²	1	8	yes	complemented
28	C₁₁×#466	C₂²	1	16	yes	complemented
29	C₁₁×#460	C₂²	1	16	yes	complemented
30	C₁₁×#449	C₂²	1	32	yes	complemented
31	C₄×C₁₁×Q₁₆	C₂²	1	8	yes	complemented
32	C₈×D₄×C₁₁	C₂²	1	8	yes	complemented
33	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₁×#103	C₂²	1	2	yes	—
36	C₂×C₁₁×#102	C₂²	1	4	yes	—
37	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
39	C₂×C₁₁×#41	—	2	8	no	—
40	C₂×C₁₁×#41	—	2	16	no	—
41	C₂×C₁₁×#41	—	4	8	no	—
42	C₂×C₁₁×#41	C₂³	1	16	yes	—
43	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₁	—	2	4	no	—
45	C₂²×D₄×C₁₁	—	2	4	no	—
46	C₂²×D₄×C₁₁	—	2	2	no	—
47	C₂²×D₄×C₁₁	—	2	2	no	—
48	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
49	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
50	C₂³×C₄×C₁₁	—	2	4	no	—
51	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
52	C₁₁×#135	—	2	64	no	—
53	C₂×C₁₁×Q₁₆	D₄	1	8	yes	complemented
54	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
55	C₂×C₁₁×SD₁₆	—	2	16	no	—
56	C₂×C₁₁×SD₁₆	C₂³	1	16	yes	—
57	C₂×C₁₁×D₈	—	2	8	no	—
58	C₂×C₁₁×D₈	—	4	4	no	—
59	C₂×C₁₁×D₈	C₂³	1	8	yes	—
60	C₂×C₁₁×D₈	C₂³	1	8	yes	—
61	C₂²×C₈×C₁₁	—	2	8	no	—
62	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
65	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
66	C₁₁×#127	—	2	16	no	—
67	C₁₁×#127	—	2	4	no	—
68	C₁₁×#127	C₂³	1	8	yes	—
69	C₁₁×#121	—	2	8	no	—
70	C₁₁×#121	—	2	32	no	—
71	C₁₁×#121	C₂³	1	16	yes	—
72	C₄×Q₈×C₁₁	—	2	4	no	—
73	C₄×Q₈×C₁₁	C₂³	1	8	yes	—
74	C₄×D₄×C₁₁	—	2	16	no	—
75	C₄×D₄×C₁₁	D₄	1	4	yes	—
76	C₄×D₄×C₁₁	C₂³	1	4	yes	—
77	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
78	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
80	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
81	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
82	C₂×C₄²×C₁₁	—	2	2	no	—
83	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
84	C₁₁×#107	C₂³	1	4	yes	—
85	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
86	C₁₁×#103	C₂³	1	8	yes	—
87	C₁₁×#102	C₂³	1	16	yes	—
88	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
89	C₄×C₈×C₁₁	C₂³	1	4	yes	—
90	C₂×#3287	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
91	C₂⁴×C₁₁	—	2	4	no	—
92	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
93	C₁₁×#41	—	2	32	no	—
94	C₁₁×#41	—	4	16	no	—
95	C₁₁×#41	—	4	32	no	—
96	C₂×Q₈×C₁₁	—	2	2	no	—
97	C₂×Q₈×C₁₁	—	2	4	no	—
98	C₂×Q₈×C₁₁	C₂×D₄	1	8	yes	—
99	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
100	C₂×D₄×C₁₁	—	2	16	no	—
101	C₂×D₄×C₁₁	—	2	16	no	—
102	C₂×D₄×C₁₁	—	2	4	no	—
103	C₂×D₄×C₁₁	—	2	8	no	—
104	C₂×D₄×C₁₁	—	2	8	no	—
105	C₂×D₄×C₁₁	—	2	4	no	—
106	C₂×D₄×C₁₁	—	2	8	no	—
107	C₂×D₄×C₁₁	—	2	8	no	—
108	C₂×D₄×C₁₁	—	4	16	no	—
109	C₂×D₄×C₁₁	—	4	8	no	—
110	C₂×D₄×C₁₁	—	8	4	no	—
111	C₂×D₄×C₁₁	—	8	8	no	—
112	C₂×D₄×C₁₁	C₂×D₄	1	4	yes	—
113	C₂×D₄×C₁₁	C₂⁴	1	8	yes	—
114	C₂²×C₄×C₁₁	—	2	2	no	—
115	C₂²×C₄×C₁₁	—	2	4	no	—
116	C₂²×C₄×C₁₁	—	2	4	no	—
117	C₂²×C₄×C₁₁	—	2	2	no	—
118	C₂²×C₄×C₁₁	—	2	16	no	—
119	C₂²×C₄×C₁₁	—	4	16	no	—
120	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
126	C₁₁×Q₁₆	C₂×D₄	1	16	yes	complemented
127	C₁₁×SD₁₆	—	2	32	no	—
128	C₁₁×D₈	—	2	16	no	—
129	C₁₁×D₈	—	4	8	no	—
130	C₂×C₈×C₁₁	—	2	16	no	—
131	C₂×C₈×C₁₁	—	2	4	no	—
132	C₂×C₈×C₁₁	—	2	2	no	—
133	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
134	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
135	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
136	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
137	C₁₁×C₄⋊C₄	—	2	8	no	—
138	C₁₁×C₄⋊C₄	—	2	2	no	—
139	C₁₁×C₄⋊C₄	C₂×D₄	1	4	yes	—
140	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
141	C₁₁×C₂²⋊C₄	—	2	16	no	—
142	C₁₁×C₂²⋊C₄	C₂×D₄	1	8	yes	—
143	C₄²×C₁₁	—	2	8	no	—
144	C₄²×C₁₁	C₂×D₄	1	2	yes	—
145	C₄²×C₁₁	C₂⁴	1	2	yes	—
146	C₂²×#135	C₂×C₁₁	1	2	yes	complemented
147	C₂×#550	C₂×C₁₁	1	2	yes	complemented
148	#3287	C₂×C₁₁	1	16	yes	direct product factor
149	C₂×#493	C₂×C₁₁	1	1	yes	characteristic, complemented
150	C₂×#466	C₂×C₁₁	1	2	yes	complemented
151	C₂×#460	C₂×C₁₁	1	2	yes	complemented
152	C₂×#449	C₂×C₁₁	1	4	yes	complemented
153	C₂×C₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
154	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
155	C₂³×C₁₁	—	2	4	no	—
156	C₂³×C₁₁	—	2	4	no	—
157	C₂³×C₁₁	—	2	4	no	—
158	C₂³×C₁₁	—	2	8	no	—
159	C₂³×C₁₁	—	4	8	no	—
160	C₂³×C₁₁	—	4	8	no	—
161	C₂³×C₁₁	—	4	8	no	—
162	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
163	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₁₁	—	2	8	no	—
165	Q₈×C₁₁	—	2	4	no	—
166	Q₈×C₁₁	C₂²×D₄	1	8	yes	—
167	D₄×C₁₁	—	2	8	no	—
168	D₄×C₁₁	—	2	8	no	—
169	D₄×C₁₁	—	2	8	no	—
170	D₄×C₁₁	—	4	32	no	—
171	D₄×C₁₁	—	4	8	no	—
172	D₄×C₁₁	—	4	16	no	—
173	D₄×C₁₁	—	8	8	no	—
174	D₄×C₁₁	—	8	16	no	—
175	C₂×C₄×C₁₁	—	2	4	no	—
176	C₂×C₄×C₁₁	—	2	8	no	—
177	C₂×C₄×C₁₁	—	2	2	no	—
178	C₂×C₄×C₁₁	—	2	4	no	—
179	C₂×C₄×C₁₁	—	2	8	no	—
180	C₂×C₄×C₁₁	—	2	4	no	—
181	C₂×C₄×C₁₁	—	2	4	no	—
182	C₂×C₄×C₁₁	—	2	4	no	—
183	C₂×C₄×C₁₁	—	4	32	no	—
184	C₂×C₄×C₁₁	—	4	4	no	—
185	C₂×C₄×C₁₁	#135	1	4	yes	complemented
186	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
187	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
188	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
192	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
193	C₈×C₁₁	—	2	4	no	—
194	C₈×C₁₁	—	2	2	no	—
195	C₈×C₁₁	C₂²×D₄	1	4	yes	—
196	C₂²×#41	C₂²×C₁₁	1	4	yes	—
197	C₂×#135	—	2	16	no	—
198	C₂×#135	C₂²×C₁₁	1	16	yes	complemented
199	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
200	C₂²×SD₁₆	C₂²×C₁₁	1	4	yes	—
201	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
202	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
203	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
204	#550	—	2	8	no	—
205	#550	C₂²×C₁₁	1	16	yes	complemented
206	C₂×#127	—	2	2	no	—
207	C₂×#127	C₂²×C₁₁	1	2	yes	—
208	C₂×#121	—	2	4	no	—
209	C₂×#121	C₂²×C₁₁	1	4	yes	—
210	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
211	C₂×C₄×D₄	—	2	2	no	—
212	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
213	#493	C₂²×C₁₁	1	8	yes	complemented
214	#466	C₂²×C₁₁	1	16	yes	complemented
215	#460	C₂²×C₁₁	1	16	yes	complemented
216	#449	C₂²×C₁₁	1	32	yes	complemented
217	C₄×Q₁₆	C₂²×C₁₁	1	8	yes	complemented
218	C₈×D₄	C₂²×C₁₁	1	8	yes	complemented
219	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
221	C₂×#103	C₂²×C₁₁	1	2	yes	—
222	C₂×#102	C₂²×C₁₁	1	4	yes	—
223	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
224	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
225	C₂²×C₁₁	—	2	4	no	—
226	C₂²×C₁₁	—	2	4	no	—
227	C₂²×C₁₁	—	2	4	no	—
228	C₂²×C₁₁	—	4	8	no	—
229	C₂²×C₁₁	—	4	8	no	—
230	C₂²×C₁₁	—	4	8	no	—
231	C₂²×C₁₁	—	4	8	no	—
232	C₂²×C₁₁	—	8	16	no	—
233	C₂²×C₁₁	D₄²	1	2	yes	—
234	C₂²×C₁₁	C₂×#135	1	2	yes	—
235	C₂²×C₁₁	#576	1	2	yes	—
236	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
237	C₄×C₁₁	—	2	4	no	—
238	C₄×C₁₁	—	2	8	no	—
239	C₄×C₁₁	—	2	2	no	—
240	C₄×C₁₁	—	4	4	no	—
241	C₄×C₁₁	D₄²	1	2	yes	—
242	C₄×C₁₁	C₂×#135	1	4	yes	complemented
243	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
244	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×#41	—	2	8	no	—
246	C₂×#41	—	2	16	no	—
247	C₂×#41	—	4	8	no	—
248	C₂×#41	C₂³×C₁₁	1	16	yes	—
249	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
250	C₂²×D₄	—	2	4	no	—
251	C₂²×D₄	—	2	4	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
255	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
256	C₂³×C₄	—	2	4	no	—
257	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
258	#135	—	2	64	no	—
259	C₂×Q₁₆	D₄×C₁₁	1	8	yes	complemented
260	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
261	C₂×SD₁₆	—	2	16	no	—
262	C₂×SD₁₆	C₂³×C₁₁	1	16	yes	—
263	C₂×D₈	—	2	8	no	—
264	C₂×D₈	—	4	4	no	—
265	C₂×D₈	C₂³×C₁₁	1	8	yes	—
266	C₂×D₈	C₂³×C₁₁	1	8	yes	—
267	C₂²×C₈	—	2	8	no	—
268	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
269	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
270	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
272	#127	—	2	16	no	—
273	#127	—	2	4	no	—
274	#127	C₂³×C₁₁	1	8	yes	—
275	#121	—	2	8	no	—
276	#121	—	2	32	no	—
277	#121	C₂³×C₁₁	1	16	yes	—
278	C₄×Q₈	—	2	4	no	—
279	C₄×Q₈	C₂³×C₁₁	1	8	yes	—
280	C₄×D₄	—	2	16	no	—
281	C₄×D₄	D₄×C₁₁	1	4	yes	—
282	C₄×D₄	C₂³×C₁₁	1	4	yes	—
283	C₂×C₄⋊C₄	—	2	2	no	—
284	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
290	#107	C₂³×C₁₁	1	4	yes	—
291	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
292	#103	C₂³×C₁₁	1	8	yes	—
293	#102	C₂³×C₁₁	1	16	yes	—
294	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
295	C₄×C₈	C₂³×C₁₁	1	4	yes	—
296	C₂×C₁₁	—	4	4	no	—
297	C₂×C₁₁	—	8	8	no	—
298	C₂×C₁₁	#3287	1	4	yes	direct product factor
299	C₂×C₁₁	C₂×D₄²	1	1	yes	characteristic
300	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
301	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
302	C₂⁴	—	2	4	no	—
303	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
304	#41	—	2	32	no	—
305	#41	—	4	16	no	—
306	#41	—	4	32	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	C₂×D₄×C₁₁	1	8	yes	—
310	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
311	C₂×D₄	—	2	16	no	—
312	C₂×D₄	—	2	16	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	8	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	2	8	no	—
318	C₂×D₄	—	2	8	no	—
319	C₂×D₄	—	4	16	no	—
320	C₂×D₄	—	4	8	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂×D₄	—	8	8	no	—
323	C₂×D₄	C₂×D₄×C₁₁	1	4	yes	—
324	C₂×D₄	C₂⁴×C₁₁	1	8	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	16	no	—
330	C₂²×C₄	—	4	16	no	—
331	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
334	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
335	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
336	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
337	Q₁₆	C₂×D₄×C₁₁	1	16	yes	complemented
338	SD₁₆	—	2	32	no	—
339	D₈	—	2	16	no	—
340	D₈	—	4	8	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	16	no	—
344	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
345	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
346	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
347	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	C₂×D₄×C₁₁	1	4	yes	—
351	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
352	C₂²⋊C₄	—	2	16	no	—
353	C₂²⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
354	C₄²	—	2	8	no	—
355	C₄²	C₂×D₄×C₁₁	1	2	yes	—
356	C₄²	C₂⁴×C₁₁	1	2	yes	—
357	C₁₁	C₂×#3287	1	1	yes	characteristic, direct product factor, Sylow
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	—	4	8	no	—
364	C₂³	—	4	8	no	—
365	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
366	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
367	Q₈	—	2	8	no	—
368	Q₈	—	2	4	no	—
369	Q₈	C₂²×D₄×C₁₁	1	8	yes	—
370	D₄	—	2	8	no	—
371	D₄	—	2	8	no	—
372	D₄	—	2	8	no	—
373	D₄	—	4	32	no	—
374	D₄	—	4	8	no	—
375	D₄	—	4	16	no	—
376	D₄	—	8	8	no	—
377	D₄	—	8	16	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	32	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	C₁₁×#135	1	4	yes	complemented
389	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
390	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
391	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
392	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
393	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
394	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
395	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
396	C₈	—	2	4	no	—
397	C₈	—	2	2	no	—
398	C₈	C₂²×D₄×C₁₁	1	4	yes	—
399	C₂²	—	2	4	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	4	8	no	—
403	C₂²	—	4	8	no	—
404	C₂²	—	4	8	no	—
405	C₂²	—	4	8	no	—
406	C₂²	—	8	16	no	—
407	C₂²	D₄²×C₁₁	1	2	yes	—
408	C₂²	C₂×C₁₁×#135	1	2	yes	—
409	C₂²	C₁₁×#576	1	2	yes	—
410	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
411	C₄	—	2	4	no	—
412	C₄	—	2	8	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	4	no	—
415	C₄	D₄²×C₁₁	1	2	yes	—
416	C₄	C₂×C₁₁×#135	1	4	yes	complemented
417	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
418	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂	—	4	4	no	—
420	C₂	—	8	8	no	—
421	C₂	C₁₁×#3287	1	4	yes	direct product factor
422	C₂	C₂×D₄²×C₁₁	1	1	yes	characteristic
423	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic
424	C₂	C₂×C₁₁×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
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. C₂²×C₁₁×#135	C₂	semidirect
2. C₂×C₁₁×#550	C₂	semidirect
3. C₁₁×#3287	C₂	direct (N × H)
4. C₂×C₁₁×#493	C₂	semidirect
5. C₂×C₁₁×#466	C₂	semidirect
6. C₂×C₁₁×#460	C₂	semidirect
7. C₂×C₁₁×#449	C₂	semidirect
8. C₂×C₄×C₁₁×Q₁₆	C₂	semidirect
9. C₂×C₈×D₄×C₁₁	C₂	semidirect
12. C₂×C₁₁×#135	C₂²	semidirect
19. C₁₁×#550	C₂²	semidirect
27. C₁₁×#493	C₂²	semidirect
28. C₁₁×#466	C₂²	semidirect
29. C₁₁×#460	C₂²	semidirect
30. C₁₁×#449	C₂²	semidirect
31. C₄×C₁₁×Q₁₆	C₂²	semidirect
32. C₈×D₄×C₁₁	C₂²	semidirect
53. C₂×C₁₁×Q₁₆	D₄	semidirect
90. C₂×#3287	C₁₁	direct (N × H)
126. C₁₁×Q₁₆	C₂×D₄	semidirect
146. C₂²×#135	C₂×C₁₁	semidirect
147. C₂×#550	C₂×C₁₁	semidirect
148. #3287	C₂×C₁₁	direct (N × H)
149. C₂×#493	C₂×C₁₁	semidirect
150. C₂×#466	C₂×C₁₁	semidirect
151. C₂×#460	C₂×C₁₁	semidirect
152. C₂×#449	C₂×C₁₁	semidirect
153. C₂×C₄×Q₁₆	C₂×C₁₁	semidirect
154. C₂×C₈×D₄	C₂×C₁₁	semidirect
185. C₂×C₄×C₁₁	#135	semidirect
198. C₂×#135	C₂²×C₁₁	semidirect
205. #550	C₂²×C₁₁	semidirect
213. #493	C₂²×C₁₁	semidirect
214. #466	C₂²×C₁₁	semidirect
215. #460	C₂²×C₁₁	semidirect
216. #449	C₂²×C₁₁	semidirect
217. C₄×Q₁₆	C₂²×C₁₁	semidirect
218. C₈×D₄	C₂²×C₁₁	semidirect
242. C₄×C₁₁	C₂×#135	semidirect
259. C₂×Q₁₆	D₄×C₁₁	semidirect
298. C₂×C₁₁	#3287	direct (N × H)
337. Q₁₆	C₂×D₄×C₁₁	semidirect
357. C₁₁	C₂×#3287	direct (N × H)
388. C₂×C₄	C₁₁×#135	semidirect
416. C₄	C₂×C₁₁×#135	semidirect
421. C₂	C₁₁×#3287	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×#135	2
C₂×C₁₁×#550	2
C₁₁×#3287	2
C₂×C₁₁×#493	2
C₂×C₁₁×#466	2
C₂×C₁₁×#460	2
C₂×C₁₁×#449	2
C₂×C₄×C₁₁×Q₁₆	2
C₂×C₈×D₄×C₁₁	2
C₂×#3287	11

Subgroups — C2×C11×#3287 #14638240

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3287 #14638240