Subgroups — C₂×C₁₁×#2148 #14610584

Order 2816.

1154 conjugacy classes of subgroups.

The subgroup lattice has 492 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	1	yes	maximal, characteristic
2	C₂²×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#2148	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₁₁×#362	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#361	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₁×#41	—	2	1	no	—
8	C₂×C₁₁×#135	—	2	2	no	—
9	C₂×C₁₁×#135	—	2	1	no	—
10	C₂×C₁₁×#135	—	2	1	no	—
11	C₂×C₁₁×#135	—	2	2	no	—
12	C₂×C₁₁×#135	C₄	1	2	yes	—
13	C₂×C₁₁×#135	C₄	1	4	yes	—
14	C₂×C₁₁×#135	C₄	1	2	yes	—
15	C₂×C₁₁×#135	C₂²	1	4	yes	—
16	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₁×SD₁₆	—	2	1	no	—
18	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₁×M₁₆	—	2	1	no	—
20	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×M₃₂	—	2	1	no	—
22	C₂×C₁₁×M₃₂	—	2	2	no	—
23	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
24	C₂×C₁₁×M₃₂	C₂²	1	4	yes	complemented
25	C₂²×C₁₁×C₁₆	—	2	1	no	—
26	C₂×C₁₁×#108	—	2	2	no	—
27	C₂×C₁₁×#108	—	2	1	no	—
28	C₂×C₁₁×#108	C₂²	1	2	yes	—
29	C₂×C₁₁×#108	C₂²	1	4	yes	complemented
30	C₁₁×#362	C₂²	1	8	yes	complemented
31	C₁₁×#361	C₂²	1	8	yes	complemented
32	C₂×C₁₁×#41	—	2	2	no	—
33	C₂×C₁₁×#41	—	2	4	no	—
34	C₂×C₁₁×#41	—	2	2	no	—
35	C₂×C₁₁×#41	—	2	4	no	—
36	C₂×C₁₁×#41	—	4	1	no	—
37	C₂×C₁₁×#41	—	4	2	no	—
38	C₂×C₁₁×#41	—	4	1	no	—
39	C₂×C₁₁×#41	—	4	2	no	—
40	C₂²×Q₈×C₁₁	—	2	1	no	—
41	C₂²×D₄×C₁₁	—	2	1	no	—
42	C₂²×D₄×C₁₁	—	4	1	no	—
43	C₂³×C₄×C₁₁	—	4	1	no	—
44	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
45	C₁₁×#135	—	2	4	no	—
46	C₁₁×#135	—	2	4	no	—
47	C₁₁×#135	—	2	4	no	—
48	C₁₁×#135	—	2	4	no	—
49	C₁₁×#135	—	2	4	no	—
50	C₁₁×#135	—	2	4	no	—
51	C₁₁×#135	C₂×C₄	1	8	yes	—
52	C₁₁×#135	C₂×C₄	1	8	yes	—
53	C₂×C₁₁×Q₁₆	—	2	1	no	—
54	C₂×C₁₁×Q₁₆	—	2	1	no	—
55	C₂×C₁₁×Q₁₆	—	2	1	no	—
56	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
57	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
58	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
59	C₂×C₁₁×SD₁₆	—	2	2	no	—
60	C₂×C₁₁×SD₁₆	—	2	4	no	—
61	C₂×C₁₁×SD₁₆	—	2	2	no	—
62	C₂×C₁₁×SD₁₆	—	2	4	no	—
63	C₂×C₁₁×D₈	—	2	1	no	—
64	C₂×C₁₁×D₈	—	2	1	no	—
65	C₂×C₁₁×D₈	—	2	1	no	—
66	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
67	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
68	C₂×C₁₁×D₈	C₂³	1	2	yes	—
69	C₂×C₁₁×M₁₆	—	2	2	no	—
70	C₂×C₁₁×M₁₆	—	2	4	no	—
71	C₂×C₁₁×M₁₆	—	4	1	no	—
72	C₂×C₁₁×M₁₆	—	4	2	no	—
73	C₂²×C₈×C₁₁	—	4	1	no	—
74	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
75	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
76	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₁	D₄	1	2	yes	—
79	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₁₁	D₄	1	2	yes	—
82	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
84	C₁₁×M₃₂	—	2	2	no	—
85	C₁₁×M₃₂	—	2	4	no	—
86	C₁₁×M₃₂	C₂³	1	4	yes	—
87	C₂×C₁₁×C₁₆	—	2	2	no	—
88	C₂×C₁₁×C₁₆	—	2	4	no	—
89	C₁₁×#108	—	2	2	no	—
90	C₁₁×#108	—	2	4	no	—
91	C₁₁×#108	C₂³	1	4	yes	—
92	C₂×#2148	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₁	—	4	1	no	—
94	C₂⁴×C₁₁	SD₁₆	1	1	yes	characteristic
95	C₁₁×#41	—	2	8	no	—
96	C₁₁×#41	—	2	8	no	—
97	C₁₁×#41	—	4	4	no	—
98	C₁₁×#41	—	4	4	no	—
99	C₁₁×#41	—	4	4	no	—
100	C₁₁×#41	—	4	4	no	—
101	C₁₁×#41	—	4	4	no	—
102	C₁₁×#41	—	4	4	no	—
103	C₂×Q₈×C₁₁	—	2	2	no	—
104	C₂×Q₈×C₁₁	—	2	2	no	—
105	C₂×Q₈×C₁₁	—	2	2	no	—
106	C₂×Q₈×C₁₁	—	4	1	no	—
107	C₂×Q₈×C₁₁	—	4	1	no	—
108	C₂×Q₈×C₁₁	—	4	1	no	—
109	C₂×D₄×C₁₁	—	2	2	no	—
110	C₂×D₄×C₁₁	—	2	2	no	—
111	C₂×D₄×C₁₁	—	2	2	no	—
112	C₂×D₄×C₁₁	—	4	2	no	—
113	C₂×D₄×C₁₁	—	4	2	no	—
114	C₂×D₄×C₁₁	—	4	4	no	—
115	C₂×D₄×C₁₁	—	4	4	no	—
116	C₂×D₄×C₁₁	—	4	1	no	—
117	C₂×D₄×C₁₁	—	4	1	no	—
118	C₂×D₄×C₁₁	—	4	1	no	—
119	C₂²×C₄×C₁₁	—	4	1	no	—
120	C₂²×C₄×C₁₁	—	4	4	no	—
121	C₂²×C₄×C₁₁	—	4	2	no	—
122	C₂²×C₄×C₁₁	—	4	2	no	—
123	C₂²×C₄×C₁₁	—	4	4	no	—
124	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
126	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	D₈	1	2	yes	—
129	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
131	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
132	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
134	C₁₁×Q₁₆	—	2	2	no	—
135	C₁₁×Q₁₆	—	2	2	no	—
136	C₁₁×Q₁₆	—	2	2	no	—
137	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	—
138	C₁₁×SD₁₆	—	2	8	no	—
139	C₁₁×SD₁₆	—	2	8	no	—
140	C₁₁×D₈	—	2	2	no	—
141	C₁₁×D₈	—	2	2	no	—
142	C₁₁×D₈	—	2	2	no	—
143	C₁₁×D₈	C₂²×C₄	1	4	yes	—
144	C₁₁×M₁₆	—	2	4	no	—
145	C₁₁×M₁₆	—	4	2	no	—
146	C₁₁×M₁₆	—	4	4	no	—
147	C₂×C₈×C₁₁	—	4	2	no	—
148	C₂×C₈×C₁₁	—	4	4	no	—
149	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
151	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
153	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
154	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
155	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
156	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
160	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
162	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
164	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
167	C₁₁×C₁₆	—	2	4	no	—
168	C₂²×#135	C₂×C₁₁	1	1	yes	characteristic
169	C₂²×M₃₂	C₂×C₁₁	1	1	yes	characteristic, complemented
170	C₂²×#108	C₂×C₁₁	1	1	yes	characteristic, complemented
171	#2148	C₂×C₁₁	1	8	yes	direct product factor
172	C₂×#362	C₂×C₁₁	1	2	yes	complemented
173	C₂×#361	C₂×C₁₁	1	2	yes	complemented
174	C₂³×C₁₁	—	4	2	no	—
175	C₂³×C₁₁	—	4	2	no	—
176	C₂³×C₁₁	—	4	2	no	—
177	C₂³×C₁₁	—	4	2	no	—
178	C₂³×C₁₁	—	8	4	no	—
179	C₂³×C₁₁	#102	1	1	yes	characteristic
180	C₂³×C₁₁	#102	1	1	yes	characteristic
181	C₂³×C₁₁	#102	1	2	yes	—
182	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
183	C₂³×C₁₁	C₂×SD₁₆	1	2	yes	—
184	Q₈×C₁₁	—	2	4	no	—
185	Q₈×C₁₁	—	4	2	no	—
186	Q₈×C₁₁	—	4	2	no	—
187	Q₈×C₁₁	—	4	2	no	—
188	D₄×C₁₁	—	2	4	no	—
189	D₄×C₁₁	—	4	8	no	—
190	D₄×C₁₁	—	4	8	no	—
191	D₄×C₁₁	—	4	2	no	—
192	D₄×C₁₁	—	4	2	no	—
193	D₄×C₁₁	—	4	2	no	—
194	C₂×C₄×C₁₁	—	4	2	no	—
195	C₂×C₄×C₁₁	—	4	2	no	—
196	C₂×C₄×C₁₁	—	4	2	no	—
197	C₂×C₄×C₁₁	—	4	8	no	—
198	C₂×C₄×C₁₁	—	4	8	no	—
199	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
200	C₂×C₄×C₁₁	#102	1	2	yes	—
201	C₂×C₄×C₁₁	#102	1	2	yes	—
202	C₂×C₄×C₁₁	#102	1	2	yes	—
203	C₂×C₄×C₁₁	#102	1	2	yes	—
204	C₂×C₄×C₁₁	#102	1	2	yes	—
205	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
206	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
208	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
209	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
210	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
211	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
212	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
213	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
214	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
215	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
216	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
217	C₈×C₁₁	—	4	4	no	—
218	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
219	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
221	C₈×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
222	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
223	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
224	C₂²×#41	—	2	1	no	—
225	C₂×#135	—	2	2	no	—
226	C₂×#135	—	2	1	no	—
227	C₂×#135	—	2	1	no	—
228	C₂×#135	—	2	2	no	—
229	C₂×#135	C₄×C₁₁	1	2	yes	—
230	C₂×#135	C₄×C₁₁	1	4	yes	—
231	C₂×#135	C₄×C₁₁	1	2	yes	—
232	C₂×#135	C₂²×C₁₁	1	4	yes	—
233	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic
234	C₂²×SD₁₆	—	2	1	no	—
235	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic
236	C₂²×M₁₆	—	2	1	no	—
237	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
238	C₂×M₃₂	—	2	1	no	—
239	C₂×M₃₂	—	2	2	no	—
240	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
241	C₂×M₃₂	C₂²×C₁₁	1	4	yes	complemented
242	C₂²×C₁₆	—	2	1	no	—
243	C₂×#108	—	2	2	no	—
244	C₂×#108	—	2	1	no	—
245	C₂×#108	C₂²×C₁₁	1	2	yes	—
246	C₂×#108	C₂²×C₁₁	1	4	yes	complemented
247	#362	C₂²×C₁₁	1	8	yes	complemented
248	#361	C₂²×C₁₁	1	8	yes	complemented
249	C₂²×C₁₁	—	2	2	no	—
250	C₂²×C₁₁	—	2	2	no	—
251	C₂²×C₁₁	—	2	2	no	—
252	C₂²×C₁₁	—	4	2	no	—
253	C₂²×C₁₁	—	4	2	no	—
254	C₂²×C₁₁	—	4	4	no	—
255	C₂²×C₁₁	—	8	4	no	—
256	C₂²×C₁₁	—	8	4	no	—
257	C₂²×C₁₁	—	8	4	no	—
258	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
259	C₂²×C₁₁	C₂×#102	1	2	yes	—
260	C₂²×C₁₁	C₂×#102	1	2	yes	—
261	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
262	C₂²×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
263	C₄×C₁₁	—	4	4	no	—
264	C₄×C₁₁	C₂×#102	1	2	yes	—
265	C₄×C₁₁	C₂×#102	1	2	yes	—
266	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
267	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
268	C₄×C₁₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
269	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
270	C₂×#41	—	2	2	no	—
271	C₂×#41	—	2	4	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	—	4	1	no	—
275	C₂×#41	—	4	1	no	—
276	C₂×#41	—	4	2	no	—
277	C₂×#41	—	4	2	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	4	1	no	—
281	C₂³×C₄	—	4	1	no	—
282	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
283	#135	—	2	4	no	—
284	#135	—	2	4	no	—
285	#135	—	2	4	no	—
286	#135	—	2	4	no	—
287	#135	—	2	4	no	—
288	#135	—	2	4	no	—
289	#135	C₂×C₄×C₁₁	1	8	yes	—
290	#135	C₂×C₄×C₁₁	1	8	yes	—
291	C₂×Q₁₆	—	2	1	no	—
292	C₂×Q₁₆	—	2	1	no	—
293	C₂×Q₁₆	—	2	1	no	—
294	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
295	C₂×Q₁₆	C₂×C₄×C₁₁	1	2	yes	—
296	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
297	C₂×SD₁₆	—	2	2	no	—
298	C₂×SD₁₆	—	2	4	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×SD₁₆	—	2	4	no	—
301	C₂×D₈	—	2	1	no	—
302	C₂×D₈	—	2	1	no	—
303	C₂×D₈	—	2	1	no	—
304	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
305	C₂×D₈	C₂×C₄×C₁₁	1	2	yes	—
306	C₂×D₈	C₂³×C₁₁	1	2	yes	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	4	no	—
309	C₂×M₁₆	—	4	1	no	—
310	C₂×M₁₆	—	4	2	no	—
311	C₂²×C₈	—	4	1	no	—
312	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
313	C₂²×C₈	C₂×C₄×C₁₁	1	2	yes	—
314	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
315	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
316	C₂²×C₈	D₄×C₁₁	1	2	yes	—
317	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
318	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
319	C₂²×C₈	D₄×C₁₁	1	2	yes	—
320	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
322	M₃₂	—	2	2	no	—
323	M₃₂	—	2	4	no	—
324	M₃₂	C₂³×C₁₁	1	4	yes	—
325	C₂×C₁₆	—	2	2	no	—
326	C₂×C₁₆	—	2	4	no	—
327	#108	—	2	2	no	—
328	#108	—	2	4	no	—
329	#108	C₂³×C₁₁	1	4	yes	—
330	C₂×C₁₁	—	2	1	no	—
331	C₂×C₁₁	—	2	1	no	—
332	C₂×C₁₁	—	2	2	no	—
333	C₂×C₁₁	—	2	2	no	—
334	C₂×C₁₁	—	8	4	no	—
335	C₂×C₁₁	#2148	1	2	yes	direct product factor
336	C₂×C₁₁	C₂²×#102	1	1	yes	characteristic
337	C₂⁴	—	4	1	no	—
338	C₂⁴	C₁₁×SD₁₆	1	1	yes	characteristic
339	#41	—	2	8	no	—
340	#41	—	2	8	no	—
341	#41	—	4	4	no	—
342	#41	—	4	4	no	—
343	#41	—	4	4	no	—
344	#41	—	4	4	no	—
345	#41	—	4	4	no	—
346	#41	—	4	4	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	4	1	no	—
351	C₂×Q₈	—	4	1	no	—
352	C₂×Q₈	—	4	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	—	4	1	no	—
362	C₂×D₄	—	4	1	no	—
363	C₂²×C₄	—	4	1	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
369	C₂²×C₄	C₁₁×C₂²⋊C₄	1	2	yes	—
370	C₂²×C₄	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
371	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
372	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
373	C₂²×C₄	C₁₁×D₈	1	2	yes	—
374	C₂²×C₄	C₁₁×SD₁₆	1	1	yes	characteristic
375	C₂²×C₄	C₁₁×SD₁₆	1	2	yes	—
376	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
378	Q₁₆	—	2	2	no	—
379	Q₁₆	—	2	2	no	—
380	Q₁₆	—	2	2	no	—
381	Q₁₆	C₂²×C₄×C₁₁	1	4	yes	—
382	SD₁₆	—	2	8	no	—
383	SD₁₆	—	2	8	no	—
384	D₈	—	2	2	no	—
385	D₈	—	2	2	no	—
386	D₈	—	2	2	no	—
387	D₈	C₂²×C₄×C₁₁	1	4	yes	—
388	M₁₆	—	2	4	no	—
389	M₁₆	—	4	2	no	—
390	M₁₆	—	4	4	no	—
391	C₂×C₈	—	4	2	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
394	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
395	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
396	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
397	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
398	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
399	C₂×C₈	C₁₁×C₂²⋊C₄	1	2	yes	—
400	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
401	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
402	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
403	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
404	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
405	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
406	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
407	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
408	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
409	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
410	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
411	C₁₆	—	2	4	no	—
412	C₁₁	C₂×#2148	1	1	yes	characteristic, direct product factor, Sylow
413	C₂³	—	4	2	no	—
414	C₂³	—	4	2	no	—
415	C₂³	—	4	2	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	8	4	no	—
418	C₂³	C₁₁×#102	1	1	yes	characteristic
419	C₂³	C₁₁×#102	1	1	yes	characteristic
420	C₂³	C₁₁×#102	1	2	yes	—
421	C₂³	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
422	C₂³	C₂×C₁₁×SD₁₆	1	2	yes	—
423	Q₈	—	2	4	no	—
424	Q₈	—	4	2	no	—
425	Q₈	—	4	2	no	—
426	Q₈	—	4	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	8	no	—
429	D₄	—	4	8	no	—
430	D₄	—	4	2	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	C₁₁×#102	1	2	yes	—
439	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
440	C₂×C₄	C₁₁×#102	1	2	yes	—
441	C₂×C₄	C₁₁×#102	1	2	yes	—
442	C₂×C₄	C₁₁×#102	1	2	yes	—
443	C₂×C₄	C₁₁×#102	1	2	yes	—
444	C₂×C₄	C₁₁×#102	1	1	yes	characteristic
445	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
447	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
448	C₂×C₄	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
449	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
450	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
451	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
453	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
454	C₂×C₄	C₂×C₁₁×SD₁₆	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
456	C₈	—	4	4	no	—
457	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
458	C₈	C₂×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
459	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
460	C₈	C₂×C₁₁×C₂²⋊C₄	1	2	yes	—
461	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
462	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	2	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	8	4	no	—
470	C₂²	—	8	4	no	—
471	C₂²	—	8	4	no	—
472	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
473	C₂²	C₂×C₁₁×#102	1	2	yes	—
474	C₂²	C₂×C₁₁×#102	1	2	yes	—
475	C₂²	C₂×C₁₁×#102	1	1	yes	characteristic
476	C₂²	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
477	C₄	—	4	4	no	—
478	C₄	C₂×C₁₁×#102	1	2	yes	—
479	C₄	C₂×C₁₁×#102	1	2	yes	—
480	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
481	C₄	C₂×C₁₁×#102	1	1	yes	characteristic
482	C₄	C₂²×C₁₁×C₂²⋊C₄	1	1	yes	characteristic
483	C₄	C₂²×C₁₁×D₈	1	1	yes	characteristic
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	—	2	2	no	—
487	C₂	—	2	2	no	—
488	C₂	—	8	4	no	—
489	C₂	C₁₁×#2148	1	2	yes	direct product factor
490	C₂	C₂²×C₁₁×#102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	#102
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×#102
prime radical	C₂²×C₁₁×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂³×C₄×C₁₁ ◁ C₂³×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₁₁×M₃₂	C₂	semidirect
3. C₂²×C₁₁×#108	C₂	semidirect
4. C₁₁×#2148	C₂	direct (N × H)
5. C₂×C₁₁×#362	C₂	semidirect
6. C₂×C₁₁×#361	C₂	semidirect
24. C₂×C₁₁×M₃₂	C₂²	semidirect
29. C₂×C₁₁×#108	C₂²	semidirect
30. C₁₁×#362	C₂²	semidirect
31. C₁₁×#361	C₂²	semidirect
92. C₂×#2148	C₁₁	direct (N × H)
169. C₂²×M₃₂	C₂×C₁₁	semidirect
170. C₂²×#108	C₂×C₁₁	semidirect
171. #2148	C₂×C₁₁	direct (N × H)
172. C₂×#362	C₂×C₁₁	semidirect
173. C₂×#361	C₂×C₁₁	semidirect
241. C₂×M₃₂	C₂²×C₁₁	semidirect
246. C₂×#108	C₂²×C₁₁	semidirect
247. #362	C₂²×C₁₁	semidirect
248. #361	C₂²×C₁₁	semidirect
335. C₂×C₁₁	#2148	direct (N × H)
412. C₁₁	C₂×#2148	direct (N × H)
489. C₂	C₁₁×#2148	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
C₂²×C₁₁×M₃₂	2
C₂²×C₁₁×#108	2
C₁₁×#2148	2
C₂×C₁₁×#362	2
C₂×C₁₁×#361	2
C₂×#2148	11

Subgroups — C2×C11×#2148 #14610584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2148 #14610584