Subgroups — C₂×C₁₁×#3191 #14637926

Order 2816.

2394 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#525	C₂	1	2	yes	maximal, complemented
2	C₁₁×#3191	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#485	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₁×#482	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₁×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₁×#452	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₁×#449	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₁×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₁×#41	C₂²	1	2	yes	—
12	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
13	C₂²×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂²×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
15	C₂²×C₁₁×D₈	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#525	—	2	8	no	—
19	C₁₁×#525	C₂²	1	16	yes	complemented
20	C₂×C₁₁×#123	—	2	2	no	—
21	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₁₁×#121	C₂²	1	2	yes	—
24	C₂×C₁₁×#121	C₂²	1	2	yes	—
25	C₂×C₁₁×#120	—	2	2	no	—
26	C₂×C₄×D₄×C₁₁	—	2	2	no	—
27	C₂×C₄×D₄×C₁₁	—	2	2	no	—
28	C₂×C₁₁×#117	C₂²	1	2	yes	—
29	C₁₁×#485	C₂²	1	16	yes	complemented
30	C₁₁×#482	C₂²	1	16	yes	complemented
31	C₁₁×#467	C₂²	1	8	yes	complemented
32	C₁₁×#466	C₂²	1	8	yes	complemented
33	C₁₁×#465	C₂²	1	16	yes	complemented
34	C₁₁×#452	C₂²	1	16	yes	complemented
35	C₁₁×#449	C₂²	1	16	yes	complemented
36	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₁₁×#106	C₂²	1	2	yes	complemented
39	C₂×C₁₁×#103	C₂²	1	2	yes	complemented
40	C₂×C₁₁×#103	C₂²	1	2	yes	complemented
41	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
42	C₂×C₁₁×#102	C₂²	1	2	yes	complemented
43	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
44	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₂×C₁₁×C₂²⋊C₈	C₂²	1	8	yes	complemented
46	C₂⁵×C₁₁	D₄	1	1	yes	characteristic
47	C₂×C₁₁×#41	—	2	4	no	—
48	C₂×C₁₁×#41	—	4	4	no	—
49	C₂×C₁₁×#41	—	4	4	no	—
50	C₂×C₁₁×#41	C₂³	1	8	yes	—
51	C₂²×Q₈×C₁₁	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₁	—	2	2	no	—
53	C₂²×D₄×C₁₁	—	2	2	no	—
54	C₂²×D₄×C₁₁	—	2	2	no	—
55	C₂²×D₄×C₁₁	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₁	—	2	2	no	—
57	C₂³×C₄×C₁₁	—	4	2	no	—
58	C₂³×C₄×C₁₁	—	4	2	no	—
59	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₁	D₄	1	2	yes	—
61	C₂³×C₄×C₁₁	D₄	1	4	yes	—
62	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
65	C₂×C₁₁×Q₁₆	—	4	2	no	—
66	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	complemented
67	C₂×C₁₁×SD₁₆	—	4	4	no	—
68	C₂×C₁₁×SD₁₆	C₂³	1	8	yes	complemented
69	C₂×C₁₁×D₈	—	4	2	no	—
70	C₂×C₁₁×D₈	C₂³	1	4	yes	complemented
71	C₂²×C₈×C₁₁	—	4	2	no	—
72	C₂²×C₈×C₁₁	—	4	2	no	—
73	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
77	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
78	C₁₁×#123	—	2	16	no	—
79	C₁₁×C₂²⋊Q₈	—	2	4	no	—
80	C₁₁×C₂²⋊Q₈	—	2	4	no	—
81	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
82	C₁₁×C₂²⋊Q₈	C₂³	1	8	yes	—
83	C₁₁×#121	—	2	4	no	—
84	C₁₁×#121	—	2	4	no	—
85	C₁₁×#121	C₂³	1	8	yes	—
86	C₁₁×#121	C₂³	1	8	yes	—
87	C₁₁×#120	—	2	16	no	—
88	C₄×D₄×C₁₁	—	2	16	no	—
89	C₄×D₄×C₁₁	—	2	16	no	—
90	C₁₁×#117	—	2	4	no	—
91	C₁₁×#117	C₂³	1	8	yes	—
92	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
93	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
94	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
96	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
97	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
99	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
100	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
101	C₂×C₄²×C₁₁	—	2	2	no	—
102	C₁₁×#107	C₂³	1	4	yes	complemented
103	C₁₁×#107	C₂³	1	4	yes	complemented
104	C₁₁×#106	C₂³	1	8	yes	complemented
105	C₁₁×#103	C₂³	1	8	yes	complemented
106	C₁₁×#103	C₂³	1	8	yes	complemented
107	C₁₁×#102	C₂³	1	8	yes	complemented
108	C₁₁×#102	C₂³	1	8	yes	complemented
109	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
110	C₁₁×C₂²⋊C₈	C₂³	1	8	yes	—
111	C₂×#3191	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₁	—	2	4	no	—
113	C₂⁴×C₁₁	—	2	2	no	—
114	C₂⁴×C₁₁	—	4	2	no	—
115	C₂⁴×C₁₁	—	4	2	no	—
116	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
117	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
118	C₂⁴×C₁₁	C₂×D₄	1	4	yes	—
119	C₁₁×#41	—	4	8	no	—
120	C₁₁×#41	—	4	8	no	—
121	C₁₁×#41	—	4	16	no	—
122	C₂×Q₈×C₁₁	—	2	2	no	—
123	C₂×Q₈×C₁₁	—	2	4	no	—
124	C₂×Q₈×C₁₁	—	2	4	no	—
125	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
126	C₂×D₄×C₁₁	—	2	8	no	—
127	C₂×D₄×C₁₁	—	2	8	no	—
128	C₂×D₄×C₁₁	—	2	8	no	—
129	C₂×D₄×C₁₁	—	2	2	no	—
130	C₂×D₄×C₁₁	—	2	4	no	—
131	C₂×D₄×C₁₁	—	2	4	no	—
132	C₂×D₄×C₁₁	—	4	8	no	—
133	C₂×D₄×C₁₁	—	4	8	no	—
134	C₂×D₄×C₁₁	—	4	8	no	—
135	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₁₁	—	2	2	no	—
137	C₂²×C₄×C₁₁	—	2	2	no	—
138	C₂²×C₄×C₁₁	—	2	4	no	—
139	C₂²×C₄×C₁₁	—	2	4	no	—
140	C₂²×C₄×C₁₁	—	2	2	no	—
141	C₂²×C₄×C₁₁	—	2	2	no	—
142	C₂²×C₄×C₁₁	—	2	2	no	—
143	C₂²×C₄×C₁₁	—	2	8	no	—
144	C₂²×C₄×C₁₁	—	4	8	no	—
145	C₂²×C₄×C₁₁	—	4	4	no	—
146	C₂²×C₄×C₁₁	—	4	4	no	—
147	C₂²×C₄×C₁₁	—	4	2	no	—
148	C₂²×C₄×C₁₁	—	4	4	no	—
149	C₂²×C₄×C₁₁	—	4	8	no	—
150	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
155	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
156	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
159	C₁₁×Q₁₆	—	4	4	no	—
160	C₁₁×SD₁₆	—	4	8	no	—
161	C₁₁×D₈	—	4	4	no	—
162	C₂×C₈×C₁₁	—	2	2	no	—
163	C₂×C₈×C₁₁	—	2	4	no	—
164	C₂×C₈×C₁₁	—	2	2	no	—
165	C₂×C₈×C₁₁	—	4	4	no	—
166	C₂×C₈×C₁₁	—	4	4	no	—
167	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
168	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
169	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
170	C₁₁×C₄⋊C₄	—	2	8	no	—
171	C₁₁×C₄⋊C₄	—	2	8	no	—
172	C₁₁×C₄⋊C₄	—	2	2	no	—
173	C₁₁×C₄⋊C₄	—	2	2	no	—
174	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
175	C₁₁×C₄⋊C₄	C₂⁴	1	4	yes	—
176	C₁₁×C₂²⋊C₄	—	2	8	no	—
177	C₁₁×C₂²⋊C₄	—	2	8	no	—
178	C₁₁×C₂²⋊C₄	—	2	8	no	—
179	C₁₁×C₂²⋊C₄	—	2	8	no	—
180	C₁₁×C₂²⋊C₄	—	2	8	no	—
181	C₄²×C₁₁	—	2	8	no	—
182	C₂×#525	C₂×C₁₁	1	2	yes	complemented
183	#3191	C₂×C₁₁	1	16	yes	direct product factor
184	C₂×#485	C₂×C₁₁	1	2	yes	complemented
185	C₂×#482	C₂×C₁₁	1	2	yes	complemented
186	C₂×#467	C₂×C₁₁	1	1	yes	characteristic, complemented
187	C₂×#466	C₂×C₁₁	1	1	yes	characteristic, complemented
188	C₂×#465	C₂×C₁₁	1	2	yes	complemented
189	C₂×#452	C₂×C₁₁	1	2	yes	complemented
190	C₂×#449	C₂×C₁₁	1	2	yes	complemented
191	C₂²×C₂²⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
192	C₂³×C₁₁	—	2	2	no	—
193	C₂³×C₁₁	—	2	2	no	—
194	C₂³×C₁₁	—	2	4	no	—
195	C₂³×C₁₁	—	2	8	no	—
196	C₂³×C₁₁	—	2	4	no	—
197	C₂³×C₁₁	—	2	4	no	—
198	C₂³×C₁₁	—	2	4	no	—
199	C₂³×C₁₁	—	4	4	no	—
200	C₂³×C₁₁	—	4	4	no	—
201	C₂³×C₁₁	—	4	16	no	—
202	C₂³×C₁₁	—	4	4	no	—
203	C₂³×C₁₁	—	4	4	no	—
204	C₂³×C₁₁	—	4	4	no	—
205	C₂³×C₁₁	#135	1	4	yes	—
206	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
207	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
208	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₁₁	—	2	4	no	—
210	Q₈×C₁₁	—	2	4	no	—
211	Q₈×C₁₁	—	4	4	no	—
212	D₄×C₁₁	—	2	4	no	—
213	D₄×C₁₁	—	2	4	no	—
214	D₄×C₁₁	—	4	16	no	—
215	D₄×C₁₁	—	4	16	no	—
216	D₄×C₁₁	—	4	16	no	—
217	D₄×C₁₁	—	4	4	no	—
218	C₂×C₄×C₁₁	—	2	4	no	—
219	C₂×C₄×C₁₁	—	2	2	no	—
220	C₂×C₄×C₁₁	—	2	4	no	—
221	C₂×C₄×C₁₁	—	2	8	no	—
222	C₂×C₄×C₁₁	—	2	2	no	—
223	C₂×C₄×C₁₁	—	2	2	no	—
224	C₂×C₄×C₁₁	—	2	4	no	—
225	C₂×C₄×C₁₁	—	2	4	no	—
226	C₂×C₄×C₁₁	—	2	4	no	—
227	C₂×C₄×C₁₁	—	2	4	no	—
228	C₂×C₄×C₁₁	—	2	4	no	—
229	C₂×C₄×C₁₁	—	4	4	no	—
230	C₂×C₄×C₁₁	—	4	8	no	—
231	C₂×C₄×C₁₁	—	4	16	no	—
232	C₂×C₄×C₁₁	—	4	4	no	—
233	C₂×C₄×C₁₁	—	4	4	no	—
234	C₂×C₄×C₁₁	—	4	4	no	—
235	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
236	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
239	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
240	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
241	C₈×C₁₁	—	2	2	no	—
242	C₈×C₁₁	—	2	4	no	—
243	C₈×C₁₁	—	2	2	no	—
244	C₂²×#41	C₂²×C₁₁	1	2	yes	—
245	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
246	C₂²×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
247	C₂²×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
248	C₂²×D₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
249	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
250	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
251	#525	—	2	8	no	—
252	#525	C₂²×C₁₁	1	16	yes	complemented
253	C₂×#123	—	2	2	no	—
254	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
255	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
256	C₂×#121	C₂²×C₁₁	1	2	yes	—
257	C₂×#121	C₂²×C₁₁	1	2	yes	—
258	C₂×#120	—	2	2	no	—
259	C₂×C₄×D₄	—	2	2	no	—
260	C₂×C₄×D₄	—	2	2	no	—
261	C₂×#117	C₂²×C₁₁	1	2	yes	—
262	#485	C₂²×C₁₁	1	16	yes	complemented
263	#482	C₂²×C₁₁	1	16	yes	complemented
264	#467	C₂²×C₁₁	1	8	yes	complemented
265	#466	C₂²×C₁₁	1	8	yes	complemented
266	#465	C₂²×C₁₁	1	16	yes	complemented
267	#452	C₂²×C₁₁	1	16	yes	complemented
268	#449	C₂²×C₁₁	1	16	yes	complemented
269	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic, complemented
270	C₂×#107	C₂²×C₁₁	1	1	yes	characteristic, complemented
271	C₂×#106	C₂²×C₁₁	1	2	yes	complemented
272	C₂×#103	C₂²×C₁₁	1	2	yes	complemented
273	C₂×#103	C₂²×C₁₁	1	2	yes	complemented
274	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
275	C₂×#102	C₂²×C₁₁	1	2	yes	complemented
276	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₁₁	1	8	yes	complemented
279	C₂²×C₁₁	—	2	2	no	—
280	C₂²×C₁₁	—	2	8	no	—
281	C₂²×C₁₁	—	2	2	no	—
282	C₂²×C₁₁	—	2	4	no	—
283	C₂²×C₁₁	—	2	4	no	—
284	C₂²×C₁₁	—	2	4	no	—
285	C₂²×C₁₁	—	4	16	no	—
286	C₂²×C₁₁	—	4	8	no	—
287	C₂²×C₁₁	—	4	4	no	—
288	C₂²×C₁₁	—	4	4	no	—
289	C₂²×C₁₁	—	4	4	no	—
290	C₂²×C₁₁	—	8	8	no	—
291	C₂²×C₁₁	#534	1	2	yes	—
292	C₂²×C₁₁	C₂×#135	1	4	yes	—
293	C₂²×C₁₁	C₂×#135	1	2	yes	—
294	C₂²×C₁₁	#575	1	2	yes	—
295	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
296	C₄×C₁₁	—	2	4	no	—
297	C₄×C₁₁	—	2	2	no	—
298	C₄×C₁₁	—	4	4	no	—
299	C₄×C₁₁	—	4	4	no	—
300	C₄×C₁₁	—	4	4	no	—
301	C₄×C₁₁	#534	1	2	yes	—
302	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
303	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
304	C₂⁵	D₄×C₁₁	1	1	yes	characteristic
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	4	4	no	—
307	C₂×#41	—	4	4	no	—
308	C₂×#41	C₂³×C₁₁	1	8	yes	—
309	C₂²×Q₈	C₂³×C₁₁	1	2	yes	—
310	C₂²×D₄	—	2	2	no	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	C₂³×C₁₁	1	2	yes	—
314	C₂³×C₄	—	2	2	no	—
315	C₂³×C₄	—	4	2	no	—
316	C₂³×C₄	—	4	2	no	—
317	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
318	C₂³×C₄	D₄×C₁₁	1	2	yes	—
319	C₂³×C₄	D₄×C₁₁	1	4	yes	—
320	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
323	C₂×Q₁₆	—	4	2	no	—
324	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	complemented
325	C₂×SD₁₆	—	4	4	no	—
326	C₂×SD₁₆	C₂³×C₁₁	1	8	yes	complemented
327	C₂×D₈	—	4	2	no	—
328	C₂×D₈	C₂³×C₁₁	1	4	yes	complemented
329	C₂²×C₈	—	4	2	no	—
330	C₂²×C₈	—	4	2	no	—
331	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
333	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
335	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
336	#123	—	2	16	no	—
337	C₂²⋊Q₈	—	2	4	no	—
338	C₂²⋊Q₈	—	2	4	no	—
339	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
340	C₂²⋊Q₈	C₂³×C₁₁	1	8	yes	—
341	#121	—	2	4	no	—
342	#121	—	2	4	no	—
343	#121	C₂³×C₁₁	1	8	yes	—
344	#121	C₂³×C₁₁	1	8	yes	—
345	#120	—	2	16	no	—
346	C₄×D₄	—	2	16	no	—
347	C₄×D₄	—	2	16	no	—
348	#117	—	2	4	no	—
349	#117	C₂³×C₁₁	1	8	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₄²	—	2	2	no	—
360	#107	C₂³×C₁₁	1	4	yes	complemented
361	#107	C₂³×C₁₁	1	4	yes	complemented
362	#106	C₂³×C₁₁	1	8	yes	complemented
363	#103	C₂³×C₁₁	1	8	yes	complemented
364	#103	C₂³×C₁₁	1	8	yes	complemented
365	#102	C₂³×C₁₁	1	8	yes	complemented
366	#102	C₂³×C₁₁	1	8	yes	complemented
367	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
368	C₂²⋊C₈	C₂³×C₁₁	1	8	yes	—
369	C₂×C₁₁	—	2	4	no	—
370	C₂×C₁₁	—	4	4	no	—
371	C₂×C₁₁	—	8	4	no	—
372	C₂×C₁₁	#3191	1	4	yes	direct product factor
373	C₂×C₁₁	C₂×#534	1	1	yes	characteristic
374	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
375	C₂×C₁₁	C₂×#575	1	1	yes	characteristic
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
381	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
382	C₂⁴	C₂×D₄×C₁₁	1	4	yes	—
383	#41	—	4	8	no	—
384	#41	—	4	8	no	—
385	#41	—	4	16	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	4	no	—
388	C₂×Q₈	—	2	4	no	—
389	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	4	no	—
396	C₂×D₄	—	4	8	no	—
397	C₂×D₄	—	4	8	no	—
398	C₂×D₄	—	4	8	no	—
399	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	4	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	8	no	—
414	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
415	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
417	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
419	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
420	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
423	Q₁₆	—	4	4	no	—
424	SD₁₆	—	4	8	no	—
425	D₈	—	4	4	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	4	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	4	4	no	—
430	C₂×C₈	—	4	4	no	—
431	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
432	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
433	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
439	C₄⋊C₄	C₂⁴×C₁₁	1	4	yes	—
440	C₂²⋊C₄	—	2	8	no	—
441	C₂²⋊C₄	—	2	8	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	—	2	8	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₄²	—	2	8	no	—
446	C₁₁	C₂×#3191	1	1	yes	characteristic, direct product factor, Sylow
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	8	no	—
451	C₂³	—	2	4	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	2	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	—	4	16	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	4	no	—
460	C₂³	C₁₁×#135	1	4	yes	—
461	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
462	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
463	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	2	4	no	—
466	Q₈	—	4	4	no	—
467	D₄	—	2	4	no	—
468	D₄	—	2	4	no	—
469	D₄	—	4	16	no	—
470	D₄	—	4	16	no	—
471	D₄	—	4	16	no	—
472	D₄	—	4	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	8	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	8	no	—
486	C₂×C₄	—	4	16	no	—
487	C₂×C₄	—	4	4	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
491	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
493	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
494	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	4	no	—
498	C₈	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	8	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	2	4	no	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	4	no	—
505	C₂²	—	4	16	no	—
506	C₂²	—	4	8	no	—
507	C₂²	—	4	4	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	8	8	no	—
511	C₂²	C₁₁×#534	1	2	yes	—
512	C₂²	C₂×C₁₁×#135	1	4	yes	—
513	C₂²	C₂×C₁₁×#135	1	2	yes	—
514	C₂²	C₁₁×#575	1	2	yes	—
515	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
516	C₄	—	2	4	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	4	no	—
520	C₄	—	4	4	no	—
521	C₄	C₁₁×#534	1	2	yes	—
522	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
523	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
524	C₂	—	2	4	no	—
525	C₂	—	4	4	no	—
526	C₂	—	8	4	no	—
527	C₂	C₁₁×#3191	1	4	yes	direct product factor
528	C₂	C₂×C₁₁×#534	1	1	yes	characteristic
529	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic
530	C₂	C₂×C₁₁×#575	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 ◁ C₂⁴×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×#525	C₂	semidirect
2. C₁₁×#3191	C₂	direct (N × H)
3. C₂×C₁₁×#485	C₂	semidirect
4. C₂×C₁₁×#482	C₂	semidirect
5. C₂×C₁₁×#467	C₂	semidirect
6. C₂×C₁₁×#466	C₂	semidirect
7. C₂×C₁₁×#465	C₂	semidirect
8. C₂×C₁₁×#452	C₂	semidirect
9. C₂×C₁₁×#449	C₂	semidirect
10. C₂²×C₁₁×C₂²⋊C₈	C₂	semidirect
13. C₂²×C₁₁×Q₁₆	C₂²	semidirect
14. C₂²×C₁₁×SD₁₆	C₂²	semidirect
15. C₂²×C₁₁×D₈	C₂²	semidirect
19. C₁₁×#525	C₂²	semidirect
29. C₁₁×#485	C₂²	semidirect
30. C₁₁×#482	C₂²	semidirect
31. C₁₁×#467	C₂²	semidirect
32. C₁₁×#466	C₂²	semidirect
33. C₁₁×#465	C₂²	semidirect
34. C₁₁×#452	C₂²	semidirect
35. C₁₁×#449	C₂²	semidirect
36. C₂×C₁₁×#107	C₂²	semidirect
37. C₂×C₁₁×#107	C₂²	semidirect
38. C₂×C₁₁×#106	C₂²	semidirect
39. C₂×C₁₁×#103	C₂²	semidirect
40. C₂×C₁₁×#103	C₂²	semidirect
41. C₂×C₁₁×#102	C₂²	semidirect
42. C₂×C₁₁×#102	C₂²	semidirect
45. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
66. C₂×C₁₁×Q₁₆	C₂³	semidirect
68. C₂×C₁₁×SD₁₆	C₂³	semidirect
70. C₂×C₁₁×D₈	C₂³	semidirect
102. C₁₁×#107	C₂³	semidirect
103. C₁₁×#107	C₂³	semidirect
104. C₁₁×#106	C₂³	semidirect
105. C₁₁×#103	C₂³	semidirect
106. C₁₁×#103	C₂³	semidirect
107. C₁₁×#102	C₂³	semidirect
108. C₁₁×#102	C₂³	semidirect
111. C₂×#3191	C₁₁	direct (N × H)
182. C₂×#525	C₂×C₁₁	semidirect
183. #3191	C₂×C₁₁	direct (N × H)
184. C₂×#485	C₂×C₁₁	semidirect
185. C₂×#482	C₂×C₁₁	semidirect
186. C₂×#467	C₂×C₁₁	semidirect
187. C₂×#466	C₂×C₁₁	semidirect
188. C₂×#465	C₂×C₁₁	semidirect
189. C₂×#452	C₂×C₁₁	semidirect
190. C₂×#449	C₂×C₁₁	semidirect
191. C₂²×C₂²⋊C₈	C₂×C₁₁	semidirect
246. C₂²×Q₁₆	C₂²×C₁₁	semidirect
247. C₂²×SD₁₆	C₂²×C₁₁	semidirect
248. C₂²×D₈	C₂²×C₁₁	semidirect
252. #525	C₂²×C₁₁	semidirect
262. #485	C₂²×C₁₁	semidirect
263. #482	C₂²×C₁₁	semidirect
264. #467	C₂²×C₁₁	semidirect
265. #466	C₂²×C₁₁	semidirect
266. #465	C₂²×C₁₁	semidirect
267. #452	C₂²×C₁₁	semidirect
268. #449	C₂²×C₁₁	semidirect
269. C₂×#107	C₂²×C₁₁	semidirect
270. C₂×#107	C₂²×C₁₁	semidirect
271. C₂×#106	C₂²×C₁₁	semidirect
272. C₂×#103	C₂²×C₁₁	semidirect
273. C₂×#103	C₂²×C₁₁	semidirect
274. C₂×#102	C₂²×C₁₁	semidirect
275. C₂×#102	C₂²×C₁₁	semidirect
278. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
324. C₂×Q₁₆	C₂³×C₁₁	semidirect
326. C₂×SD₁₆	C₂³×C₁₁	semidirect
328. C₂×D₈	C₂³×C₁₁	semidirect
360. #107	C₂³×C₁₁	semidirect
361. #107	C₂³×C₁₁	semidirect
362. #106	C₂³×C₁₁	semidirect
363. #103	C₂³×C₁₁	semidirect
364. #103	C₂³×C₁₁	semidirect
365. #102	C₂³×C₁₁	semidirect
366. #102	C₂³×C₁₁	semidirect
372. C₂×C₁₁	#3191	direct (N × H)
446. C₁₁	C₂×#3191	direct (N × H)
527. C₂	C₁₁×#3191	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×#525	2
C₁₁×#3191	2
C₂×C₁₁×#485	2
C₂×C₁₁×#482	2
C₂×C₁₁×#467	2
C₂×C₁₁×#466	2
C₂×C₁₁×#465	2
C₂×C₁₁×#452	2
C₂×C₁₁×#449	2
C₂²×C₁₁×C₂²⋊C₈	2
C₂×#3191	11

Subgroups — C2×C11×#3191 #14637926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#3191 #14637926