Subgroups — C₄×C₁₁×#576 #14637364

Order 2816.

2826 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#576	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₁×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2951	C₂	1	3	yes	maximal, complemented
4	C₁₁×#2948	C₂	1	3	yes	maximal, complemented
5	C₁₁×#2946	C₂	1	6	yes	maximal, complemented
6	C₄×C₁₁×AGL(1,ℤ/8)	C₂	1	6	yes	maximal, complemented
7	C₄×C₁₁×#135	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₁₁×D₈	C₂	1	3	yes	maximal, complemented
9	C₁₁×#2913	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₁×#2897	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₁×H(5,𝔽₂)	C₂²	1	2	yes	—
13	C₁₁×#576	C₄	1	16	yes	direct product factor
14	C₂×C₁₁×AGL(1,ℤ/8)	C₂²	1	6	yes	—
15	C₂×C₁₁×#135	C₂²	1	3	yes	—
16	C₂²×C₁₁×D₈	C₂²	1	3	yes	—
17	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
19	C₁₁×#520	—	2	2	no	—
20	C₁₁×#520	C₂²	1	2	yes	—
21	C₁₁×#520	C₂²	1	6	yes	complemented
22	C₁₁×#518	—	2	6	no	—
23	C₁₁×#518	C₂²	1	6	yes	complemented
24	C₄×C₁₁×#41	—	2	2	no	—
25	C₄×C₁₁×#41	C₂²	1	1	yes	characteristic
26	C₄×C₁₁×#41	C₂²	1	6	yes	complemented
27	C₂×C₄×D₄×C₁₁	—	2	6	no	—
28	C₂×C₄×D₄×C₁₁	C₂²	1	6	yes	complemented
29	C₁₁×#442	C₂²	1	12	yes	complemented
30	C₁₁×#440	C₂²	1	12	yes	complemented
31	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₁₁×Q₁₆	C₂²	1	3	yes	complemented
33	C₄×C₁₁×SD₁₆	C₂²	1	6	yes	complemented
34	C₄×C₁₁×SD₁₆	C₂²	1	6	yes	complemented
35	C₄×C₁₁×D₈	C₂²	1	3	yes	complemented
36	C₄×C₁₁×D₈	C₂²	1	6	yes	complemented
37	C₄×C₁₁×D₈	C₂²	1	6	yes	complemented
38	C₄×C₁₁×D₈	C₂²	1	6	yes	complemented
39	C₄×C₁₁×D₈	C₂²	1	3	yes	complemented
40	C₁₁×#428	C₂²	1	6	yes	complemented
41	C₁₁×#427	C₂²	1	3	yes	complemented
42	C₂×C₁₁×#107	C₂²	1	3	yes	complemented
43	C₁₁×#418	C₂²	1	6	yes	complemented
44	C₁₁×#417	C₂²	1	6	yes	complemented
45	C₁₁×#416	C₂²	1	6	yes	complemented
46	C₂×C₁₁×#102	C₂²	1	6	yes	complemented
47	C₁₁×#405	C₂²	1	3	yes	complemented
48	C₁₁×#405	C₂²	1	3	yes	complemented
49	C₄×C₁₁×M₁₆	C₂²	1	3	yes	complemented
50	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	complemented
51	C₁₁×H(5,𝔽₂)	—	2	8	no	—
52	C₁₁×H(5,𝔽₂)	C₂×C₄	1	16	yes	complemented
53	C₂×C₁₁×#41	—	2	2	no	—
54	C₂×C₁₁×#41	C₂³	1	6	yes	—
55	C₂×C₁₁×#41	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₁	—	2	6	no	—
57	C₂²×D₄×C₁₁	C₂³	1	6	yes	—
58	C₂³×C₄×C₁₁	—	2	6	no	—
59	C₁₁×AGL(1,ℤ/8)	C₂×C₄	1	48	yes	complemented
60	C₁₁×#135	C₂×C₄	1	24	yes	complemented
61	C₂×C₁₁×Q₁₆	C₂³	1	1	yes	characteristic
62	C₂×C₁₁×SD₁₆	C₂³	1	6	yes	—
63	C₂×C₁₁×D₈	C₂×C₄	1	24	yes	complemented
64	C₂×C₁₁×D₈	C₂³	1	3	yes	—
65	C₂×C₁₁×D₈	C₂³	1	6	yes	—
66	C₁₁×#131	—	2	4	no	—
67	C₁₁×#131	C₂×C₄	1	8	yes	complemented
68	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
69	C₂×C₁₁×M₁₆	C₂³	1	3	yes	—
70	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
71	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
72	C₄×Q₈×C₁₁	—	2	2	no	—
73	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₁	D₄	1	1	yes	characteristic
75	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
76	C₄×Q₈×C₁₁	C₂³	1	6	yes	—
77	C₄×D₄×C₁₁	—	2	6	no	—
78	C₄×D₄×C₁₁	—	2	6	no	—
79	C₄×D₄×C₁₁	—	2	6	no	—
80	C₄×D₄×C₁₁	—	2	6	no	—
81	C₄×D₄×C₁₁	—	2	6	no	—
82	C₄×D₄×C₁₁	—	2	12	no	—
83	C₄×D₄×C₁₁	—	2	6	no	—
84	C₄×D₄×C₁₁	—	2	6	no	—
85	C₄×D₄×C₁₁	D₄	1	3	yes	—
86	C₄×D₄×C₁₁	D₄	1	3	yes	—
87	C₄×D₄×C₁₁	C₂³	1	6	yes	—
88	C₄×D₄×C₁₁	C₂³	1	12	yes	—
89	C₄×D₄×C₁₁	C₂³	1	6	yes	—
90	C₁₁×#117	—	2	6	no	—
91	C₁₁×#117	—	2	6	no	—
92	C₁₁×#117	C₂³	1	6	yes	—
93	C₁₁×#117	C₂³	1	3	yes	—
94	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
95	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
96	C₂×C₁₁×C₂²⋊C₄	—	2	6	no	—
97	C₂×C₁₁×C₂²⋊C₄	—	2	12	no	—
98	C₂×C₄²×C₁₁	—	2	6	no	—
99	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
100	C₁₁×#107	C₂³	1	3	yes	—
101	C₁₁×#107	C₂³	1	6	yes	—
102	C₁₁×#107	C₂³	1	1	yes	characteristic
103	C₁₁×#106	C₂³	1	6	yes	—
104	C₁₁×#103	C₂³	1	2	yes	—
105	C₁₁×#103	C₂³	1	6	yes	—
106	C₁₁×#102	C₂³	1	6	yes	—
107	C₁₁×#102	C₂³	1	12	yes	—
108	C₁₁×#102	C₂³	1	6	yes	—
109	C₁₁×#97	C₂³	1	6	yes	—
110	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₁	C₂³	1	3	yes	—
112	C₄×C₈×C₁₁	C₂³	1	3	yes	—
113	C₄×C₈×C₁₁	C₂³	1	3	yes	—
114	C₄×#576	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
115	C₂⁴×C₁₁	—	2	6	no	—
116	C₁₁×#41	—	2	16	no	—
117	C₁₁×#41	—	2	12	no	—
118	C₁₁×#41	C₂²×C₄	1	4	yes	—
119	C₁₁×#41	C₂²×C₄	1	24	yes	complemented
120	C₁₁×#41	#41	1	4	yes	—
121	C₂×Q₈×C₁₁	C₂×D₄	1	1	yes	characteristic
122	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
123	C₂×D₄×C₁₁	—	2	6	no	—
124	C₂×D₄×C₁₁	—	2	48	no	—
125	C₂×D₄×C₁₁	—	2	6	no	—
126	C₂×D₄×C₁₁	—	2	12	no	—
127	C₂×D₄×C₁₁	C₂²×C₄	1	24	yes	complemented
128	C₂×D₄×C₁₁	C₂×D₄	1	3	yes	—
129	C₂×D₄×C₁₁	C₂⁴	1	6	yes	—
130	C₂²×C₄×C₁₁	—	2	6	no	—
131	C₂²×C₄×C₁₁	—	2	6	no	—
132	C₂²×C₄×C₁₁	—	2	6	no	—
133	C₂²×C₄×C₁₁	—	2	6	no	—
134	C₂²×C₄×C₁₁	—	2	12	no	—
135	C₂²×C₄×C₁₁	—	8	12	no	—
136	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
137	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
138	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
139	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	complemented
140	C₁₁×SD₁₆	C₂²×C₄	1	24	yes	complemented
141	C₁₁×D₈	C₂²×C₄	1	12	yes	complemented
142	C₁₁×D₈	C₂²×C₄	1	24	yes	complemented
143	C₁₁×M₁₆	—	2	6	no	—
144	C₁₁×M₁₆	C₂²×C₄	1	12	yes	complemented
145	C₂×C₈×C₁₁	—	2	6	no	—
146	C₂×C₈×C₁₁	C₂²×C₄	1	12	yes	complemented
147	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₁	C₂⁴	1	3	yes	—
149	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
150	C₂×C₈×C₁₁	C₂⁴	1	3	yes	—
151	C₁₁×C₄⋊C₄	—	2	6	no	—
152	C₁₁×C₄⋊C₄	—	2	6	no	—
153	C₁₁×C₄⋊C₄	—	2	2	no	—
154	C₁₁×C₄⋊C₄	C₂×D₄	1	3	yes	—
155	C₁₁×C₄⋊C₄	C₂×D₄	1	3	yes	—
156	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
157	C₁₁×C₄⋊C₄	C₂⁴	1	6	yes	—
158	C₁₁×C₂²⋊C₄	—	2	6	no	—
159	C₁₁×C₂²⋊C₄	—	2	6	no	—
160	C₁₁×C₂²⋊C₄	—	2	12	no	—
161	C₁₁×C₂²⋊C₄	—	2	6	no	—
162	C₁₁×C₂²⋊C₄	C₂×D₄	1	6	yes	—
163	C₄²×C₁₁	—	2	6	no	—
164	C₄²×C₁₁	—	2	6	no	—
165	C₄²×C₁₁	—	2	2	no	—
166	C₄²×C₁₁	C₂×D₄	1	3	yes	—
167	C₄²×C₁₁	C₂×D₄	1	3	yes	—
168	C₄²×C₁₁	C₂⁴	1	3	yes	—
169	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
170	C₂×#576	C₂×C₁₁	1	1	yes	characteristic
171	C₄×H(5,𝔽₂)	C₂×C₁₁	1	2	yes	complemented
172	#2951	C₂×C₁₁	1	3	yes	complemented
173	#2948	C₂×C₁₁	1	3	yes	complemented
174	#2946	C₂×C₁₁	1	6	yes	complemented
175	C₄×AGL(1,ℤ/8)	C₂×C₁₁	1	6	yes	complemented
176	C₄×#135	C₂×C₁₁	1	3	yes	complemented
177	C₂×C₄×D₈	C₂×C₁₁	1	3	yes	complemented
178	#2913	C₂×C₁₁	1	1	yes	characteristic, complemented
179	#2897	C₂×C₁₁	1	2	yes	complemented
180	C₄×#131	C₂×C₁₁	1	1	yes	characteristic, complemented
181	C₂³×C₁₁	—	2	6	no	—
182	C₂³×C₁₁	—	2	24	no	—
183	C₂³×C₁₁	—	8	6	no	—
184	C₂³×C₁₁	—	8	6	no	—
185	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
186	Q₈×C₁₁	—	2	2	no	—
187	Q₈×C₁₁	C₄×D₄	1	4	yes	—
188	Q₈×C₁₁	C₂³×C₄	1	4	yes	—
189	D₄×C₁₁	—	2	24	no	—
190	D₄×C₁₁	—	2	24	no	—
191	D₄×C₁₁	—	2	6	no	—
192	D₄×C₁₁	C₄×D₄	1	12	yes	—
193	D₄×C₁₁	C₂³×C₄	1	12	yes	—
194	C₂×C₄×C₁₁	—	2	2	no	—
195	C₂×C₄×C₁₁	—	2	24	no	—
196	C₂×C₄×C₁₁	—	2	6	no	—
197	C₂×C₄×C₁₁	—	2	2	no	—
198	C₂×C₄×C₁₁	—	2	6	no	—
199	C₂×C₄×C₁₁	—	4	3	no	—
200	C₂×C₄×C₁₁	—	4	12	no	—
201	C₂×C₄×C₁₁	—	8	6	no	—
202	C₂×C₄×C₁₁	—	8	12	no	—
203	C₂×C₄×C₁₁	—	8	6	no	—
204	C₂×C₄×C₁₁	C₂³×C₄	1	6	yes	—
205	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
206	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
208	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
209	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
211	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
212	C₈×C₁₁	—	2	1	no	—
213	C₈×C₁₁	—	2	3	no	—
214	C₈×C₁₁	C₂³×C₄	1	2	yes	—
215	C₈×C₁₁	C₂³×C₄	1	6	yes	—
216	C₂×H(5,𝔽₂)	C₂²×C₁₁	1	2	yes	—
217	#576	C₄×C₁₁	1	16	yes	direct product factor
218	C₂×AGL(1,ℤ/8)	C₂²×C₁₁	1	6	yes	—
219	C₂×#135	C₂²×C₁₁	1	3	yes	—
220	C₂²×D₈	C₂²×C₁₁	1	3	yes	—
221	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
222	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
223	#520	—	2	2	no	—
224	#520	C₂²×C₁₁	1	2	yes	—
225	#520	C₂²×C₁₁	1	6	yes	complemented
226	#518	—	2	6	no	—
227	#518	C₂²×C₁₁	1	6	yes	complemented
228	C₄×#41	—	2	2	no	—
229	C₄×#41	C₂²×C₁₁	1	1	yes	characteristic
230	C₄×#41	C₂²×C₁₁	1	6	yes	complemented
231	C₂×C₄×D₄	—	2	6	no	—
232	C₂×C₄×D₄	C₂²×C₁₁	1	6	yes	complemented
233	#442	C₂²×C₁₁	1	12	yes	complemented
234	#440	C₂²×C₁₁	1	12	yes	complemented
235	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
236	C₄×Q₁₆	C₂²×C₁₁	1	3	yes	complemented
237	C₄×SD₁₆	C₂²×C₁₁	1	6	yes	complemented
238	C₄×SD₁₆	C₂²×C₁₁	1	6	yes	complemented
239	C₄×D₈	C₂²×C₁₁	1	3	yes	complemented
240	C₄×D₈	C₂²×C₁₁	1	6	yes	complemented
241	C₄×D₈	C₂²×C₁₁	1	6	yes	complemented
242	C₄×D₈	C₂²×C₁₁	1	6	yes	complemented
243	C₄×D₈	C₂²×C₁₁	1	3	yes	complemented
244	#428	C₂²×C₁₁	1	6	yes	complemented
245	#427	C₂²×C₁₁	1	3	yes	complemented
246	C₂×#107	C₂²×C₁₁	1	3	yes	complemented
247	#418	C₂²×C₁₁	1	6	yes	complemented
248	#417	C₂²×C₁₁	1	6	yes	complemented
249	#416	C₂²×C₁₁	1	6	yes	complemented
250	C₂×#102	C₂²×C₁₁	1	6	yes	complemented
251	#405	C₂²×C₁₁	1	3	yes	complemented
252	#405	C₂²×C₁₁	1	3	yes	complemented
253	C₄×M₁₆	C₂²×C₁₁	1	3	yes	complemented
254	C₂×C₄×C₈	C₂²×C₁₁	1	3	yes	complemented
255	C₂²×C₁₁	—	2	3	no	—
256	C₂²×C₁₁	—	2	3	no	—
257	C₂²×C₁₁	—	2	12	no	—
258	C₂²×C₁₁	—	4	6	no	—
259	C₂²×C₁₁	—	4	6	no	—
260	C₂²×C₁₁	—	8	24	no	—
261	C₂²×C₁₁	C₂×C₄×D₄	1	6	yes	—
262	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
263	C₄×C₁₁	—	2	1	no	—
264	C₄×C₁₁	—	2	3	no	—
265	C₄×C₁₁	—	2	4	no	—
266	C₄×C₁₁	—	2	3	no	—
267	C₄×C₁₁	—	4	2	no	—
268	C₄×C₁₁	—	4	6	no	—
269	C₄×C₁₁	C₂×C₄×D₄	1	6	yes	—
270	C₄×C₁₁	#576	1	2	yes	direct product factor
271	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
272	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
273	H(5,𝔽₂)	—	2	8	no	—
274	H(5,𝔽₂)	C₂×C₄×C₁₁	1	16	yes	complemented
275	C₂×#41	—	2	2	no	—
276	C₂×#41	C₂³×C₁₁	1	6	yes	—
277	C₂×#41	C₂³×C₁₁	1	1	yes	characteristic
278	C₂²×D₄	—	2	6	no	—
279	C₂²×D₄	C₂³×C₁₁	1	6	yes	—
280	C₂³×C₄	—	2	6	no	—
281	AGL(1,ℤ/8)	C₂×C₄×C₁₁	1	48	yes	complemented
282	#135	C₂×C₄×C₁₁	1	24	yes	complemented
283	C₂×Q₁₆	C₂³×C₁₁	1	1	yes	characteristic
284	C₂×SD₁₆	C₂³×C₁₁	1	6	yes	—
285	C₂×D₈	C₂×C₄×C₁₁	1	24	yes	complemented
286	C₂×D₈	C₂³×C₁₁	1	3	yes	—
287	C₂×D₈	C₂³×C₁₁	1	6	yes	—
288	#131	—	2	4	no	—
289	#131	C₂×C₄×C₁₁	1	8	yes	complemented
290	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
291	C₂×M₁₆	C₂³×C₁₁	1	3	yes	—
292	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
293	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
294	C₄×Q₈	—	2	2	no	—
295	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
296	C₄×Q₈	D₄×C₁₁	1	1	yes	characteristic
297	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
298	C₄×Q₈	C₂³×C₁₁	1	6	yes	—
299	C₄×D₄	—	2	6	no	—
300	C₄×D₄	—	2	6	no	—
301	C₄×D₄	—	2	6	no	—
302	C₄×D₄	—	2	6	no	—
303	C₄×D₄	—	2	6	no	—
304	C₄×D₄	—	2	12	no	—
305	C₄×D₄	—	2	6	no	—
306	C₄×D₄	—	2	6	no	—
307	C₄×D₄	D₄×C₁₁	1	3	yes	—
308	C₄×D₄	D₄×C₁₁	1	3	yes	—
309	C₄×D₄	C₂³×C₁₁	1	6	yes	—
310	C₄×D₄	C₂³×C₁₁	1	12	yes	—
311	C₄×D₄	C₂³×C₁₁	1	6	yes	—
312	#117	—	2	6	no	—
313	#117	—	2	6	no	—
314	#117	C₂³×C₁₁	1	6	yes	—
315	#117	C₂³×C₁₁	1	3	yes	—
316	C₂×C₄⋊C₄	—	2	6	no	—
317	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
318	C₂×C₂²⋊C₄	—	2	6	no	—
319	C₂×C₂²⋊C₄	—	2	12	no	—
320	C₂×C₄²	—	2	6	no	—
321	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
322	#107	C₂³×C₁₁	1	3	yes	—
323	#107	C₂³×C₁₁	1	6	yes	—
324	#107	C₂³×C₁₁	1	1	yes	characteristic
325	#106	C₂³×C₁₁	1	6	yes	—
326	#103	C₂³×C₁₁	1	2	yes	—
327	#103	C₂³×C₁₁	1	6	yes	—
328	#102	C₂³×C₁₁	1	6	yes	—
329	#102	C₂³×C₁₁	1	12	yes	—
330	#102	C₂³×C₁₁	1	6	yes	—
331	#97	C₂³×C₁₁	1	6	yes	—
332	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
333	C₄×C₈	C₂³×C₁₁	1	3	yes	—
334	C₄×C₈	C₂³×C₁₁	1	3	yes	—
335	C₄×C₈	C₂³×C₁₁	1	3	yes	—
336	C₂×C₁₁	—	2	6	no	—
337	C₂×C₁₁	—	4	12	no	—
338	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
339	C₂×C₁₁	C₂×#576	1	1	yes	characteristic
340	C₂×C₁₁	#3584	1	1	yes	characteristic
341	C₂⁴	—	2	6	no	—
342	#41	—	2	16	no	—
343	#41	—	2	12	no	—
344	#41	C₂²×C₄×C₁₁	1	4	yes	—
345	#41	C₂²×C₄×C₁₁	1	24	yes	complemented
346	#41	C₁₁×#41	1	4	yes	—
347	C₂×Q₈	C₂×D₄×C₁₁	1	1	yes	characteristic
348	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
349	C₂×D₄	—	2	6	no	—
350	C₂×D₄	—	2	48	no	—
351	C₂×D₄	—	2	6	no	—
352	C₂×D₄	—	2	12	no	—
353	C₂×D₄	C₂²×C₄×C₁₁	1	24	yes	complemented
354	C₂×D₄	C₂×D₄×C₁₁	1	3	yes	—
355	C₂×D₄	C₂⁴×C₁₁	1	6	yes	—
356	C₂²×C₄	—	2	6	no	—
357	C₂²×C₄	—	2	6	no	—
358	C₂²×C₄	—	2	6	no	—
359	C₂²×C₄	—	2	6	no	—
360	C₂²×C₄	—	2	12	no	—
361	C₂²×C₄	—	8	12	no	—
362	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
363	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
364	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
365	Q₁₆	C₂²×C₄×C₁₁	1	4	yes	complemented
366	SD₁₆	C₂²×C₄×C₁₁	1	24	yes	complemented
367	D₈	C₂²×C₄×C₁₁	1	12	yes	complemented
368	D₈	C₂²×C₄×C₁₁	1	24	yes	complemented
369	M₁₆	—	2	6	no	—
370	M₁₆	C₂²×C₄×C₁₁	1	12	yes	complemented
371	C₂×C₈	—	2	6	no	—
372	C₂×C₈	C₂²×C₄×C₁₁	1	12	yes	complemented
373	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
374	C₂×C₈	C₂⁴×C₁₁	1	3	yes	—
375	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
376	C₂×C₈	C₂⁴×C₁₁	1	3	yes	—
377	C₄⋊C₄	—	2	6	no	—
378	C₄⋊C₄	—	2	6	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	C₂×D₄×C₁₁	1	3	yes	—
381	C₄⋊C₄	C₂×D₄×C₁₁	1	3	yes	—
382	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
383	C₄⋊C₄	C₂⁴×C₁₁	1	6	yes	—
384	C₂²⋊C₄	—	2	6	no	—
385	C₂²⋊C₄	—	2	6	no	—
386	C₂²⋊C₄	—	2	12	no	—
387	C₂²⋊C₄	—	2	6	no	—
388	C₂²⋊C₄	C₂×D₄×C₁₁	1	6	yes	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	6	no	—
391	C₄²	—	2	6	no	—
392	C₄²	C₂×D₄×C₁₁	1	3	yes	—
393	C₄²	C₂×D₄×C₁₁	1	3	yes	—
394	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
395	C₄²	C₂⁴×C₁₁	1	3	yes	—
396	C₁₁	C₄×#576	1	1	yes	characteristic, direct product factor, Sylow
397	C₂³	—	2	6	no	—
398	C₂³	—	2	24	no	—
399	C₂³	—	8	6	no	—
400	C₂³	—	8	6	no	—
401	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
402	Q₈	—	2	2	no	—
403	Q₈	C₄×D₄×C₁₁	1	4	yes	—
404	Q₈	C₂³×C₄×C₁₁	1	4	yes	—
405	D₄	—	2	24	no	—
406	D₄	—	2	24	no	—
407	D₄	—	2	6	no	—
408	D₄	C₄×D₄×C₁₁	1	12	yes	—
409	D₄	C₂³×C₄×C₁₁	1	12	yes	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	24	no	—
412	C₂×C₄	—	2	6	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	6	no	—
415	C₂×C₄	—	4	3	no	—
416	C₂×C₄	—	4	12	no	—
417	C₂×C₄	—	8	6	no	—
418	C₂×C₄	—	8	12	no	—
419	C₂×C₄	—	8	6	no	—
420	C₂×C₄	C₂³×C₄×C₁₁	1	6	yes	—
421	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
422	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
424	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
425	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
426	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
427	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
428	C₈	—	2	1	no	—
429	C₈	—	2	3	no	—
430	C₈	C₂³×C₄×C₁₁	1	2	yes	—
431	C₈	C₂³×C₄×C₁₁	1	6	yes	—
432	C₂²	—	2	3	no	—
433	C₂²	—	2	3	no	—
434	C₂²	—	2	12	no	—
435	C₂²	—	4	6	no	—
436	C₂²	—	4	6	no	—
437	C₂²	—	8	24	no	—
438	C₂²	C₂×C₄×D₄×C₁₁	1	6	yes	—
439	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
440	C₄	—	2	4	no	—
441	C₄	—	2	3	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	3	no	—
444	C₄	—	4	6	no	—
445	C₄	—	4	2	no	—
446	C₄	C₂×C₄×D₄×C₁₁	1	6	yes	—
447	C₄	C₁₁×#576	1	2	yes	direct product factor
448	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
449	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
450	C₂	—	2	6	no	—
451	C₂	—	4	12	no	—
452	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
453	C₂	C₂×C₁₁×#576	1	1	yes	characteristic
454	C₂	C₁₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂³×D₄
prime radical	C₂×C₁₁×#576	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₄×C₁₁×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₁×H(5,𝔽₂)	C₂	semidirect
3. C₁₁×#2951	C₂	semidirect
4. C₁₁×#2948	C₂	semidirect
5. C₁₁×#2946	C₂	semidirect
6. C₄×C₁₁×AGL(1,ℤ/8)	C₂	semidirect
7. C₄×C₁₁×#135	C₂	semidirect
8. C₂×C₄×C₁₁×D₈	C₂	semidirect
9. C₁₁×#2913	C₂	semidirect
10. C₁₁×#2897	C₂	semidirect
11. C₄×C₁₁×#131	C₂	semidirect
13. C₁₁×#576	C₄	direct (N × H)
21. C₁₁×#520	C₂²	semidirect
23. C₁₁×#518	C₂²	semidirect
26. C₄×C₁₁×#41	C₂²	semidirect
28. C₂×C₄×D₄×C₁₁	C₂²	semidirect
29. C₁₁×#442	C₂²	semidirect
30. C₁₁×#440	C₂²	semidirect
31. C₄×C₁₁×Q₁₆	C₂²	semidirect
32. C₄×C₁₁×Q₁₆	C₂²	semidirect
33. C₄×C₁₁×SD₁₆	C₂²	semidirect
34. C₄×C₁₁×SD₁₆	C₂²	semidirect
35. C₄×C₁₁×D₈	C₂²	semidirect
36. C₄×C₁₁×D₈	C₂²	semidirect
37. C₄×C₁₁×D₈	C₂²	semidirect
38. C₄×C₁₁×D₈	C₂²	semidirect
39. C₄×C₁₁×D₈	C₂²	semidirect
40. C₁₁×#428	C₂²	semidirect
41. C₁₁×#427	C₂²	semidirect
42. C₂×C₁₁×#107	C₂²	semidirect
43. C₁₁×#418	C₂²	semidirect
44. C₁₁×#417	C₂²	semidirect
45. C₁₁×#416	C₂²	semidirect
46. C₂×C₁₁×#102	C₂²	semidirect
47. C₁₁×#405	C₂²	semidirect
48. C₁₁×#405	C₂²	semidirect
49. C₄×C₁₁×M₁₆	C₂²	semidirect
50. C₂×C₄×C₈×C₁₁	C₂²	semidirect
52. C₁₁×H(5,𝔽₂)	C₂×C₄	semidirect
59. C₁₁×AGL(1,ℤ/8)	C₂×C₄	semidirect
60. C₁₁×#135	C₂×C₄	semidirect
63. C₂×C₁₁×D₈	C₂×C₄	semidirect
67. C₁₁×#131	C₂×C₄	semidirect
114. C₄×#576	C₁₁	direct (N × H)
119. C₁₁×#41	C₂²×C₄	semidirect
127. C₂×D₄×C₁₁	C₂²×C₄	semidirect
139. C₁₁×Q₁₆	C₂²×C₄	semidirect
140. C₁₁×SD₁₆	C₂²×C₄	semidirect
141. C₁₁×D₈	C₂²×C₄	semidirect
142. C₁₁×D₈	C₂²×C₄	semidirect
144. C₁₁×M₁₆	C₂²×C₄	semidirect
146. C₂×C₈×C₁₁	C₂²×C₄	semidirect
171. C₄×H(5,𝔽₂)	C₂×C₁₁	semidirect
172. #2951	C₂×C₁₁	semidirect
173. #2948	C₂×C₁₁	semidirect
174. #2946	C₂×C₁₁	semidirect
175. C₄×AGL(1,ℤ/8)	C₂×C₁₁	semidirect
176. C₄×#135	C₂×C₁₁	semidirect
177. C₂×C₄×D₈	C₂×C₁₁	semidirect
178. #2913	C₂×C₁₁	semidirect
179. #2897	C₂×C₁₁	semidirect
180. C₄×#131	C₂×C₁₁	semidirect
217. #576	C₄×C₁₁	direct (N × H)
225. #520	C₂²×C₁₁	semidirect
227. #518	C₂²×C₁₁	semidirect
230. C₄×#41	C₂²×C₁₁	semidirect
232. C₂×C₄×D₄	C₂²×C₁₁	semidirect
233. #442	C₂²×C₁₁	semidirect
234. #440	C₂²×C₁₁	semidirect
235. C₄×Q₁₆	C₂²×C₁₁	semidirect
236. C₄×Q₁₆	C₂²×C₁₁	semidirect
237. C₄×SD₁₆	C₂²×C₁₁	semidirect
238. C₄×SD₁₆	C₂²×C₁₁	semidirect
239. C₄×D₈	C₂²×C₁₁	semidirect
240. C₄×D₈	C₂²×C₁₁	semidirect
241. C₄×D₈	C₂²×C₁₁	semidirect
242. C₄×D₈	C₂²×C₁₁	semidirect
243. C₄×D₈	C₂²×C₁₁	semidirect
244. #428	C₂²×C₁₁	semidirect
245. #427	C₂²×C₁₁	semidirect
246. C₂×#107	C₂²×C₁₁	semidirect
247. #418	C₂²×C₁₁	semidirect
248. #417	C₂²×C₁₁	semidirect
249. #416	C₂²×C₁₁	semidirect
250. C₂×#102	C₂²×C₁₁	semidirect
251. #405	C₂²×C₁₁	semidirect
252. #405	C₂²×C₁₁	semidirect
253. C₄×M₁₆	C₂²×C₁₁	semidirect
254. C₂×C₄×C₈	C₂²×C₁₁	semidirect
270. C₄×C₁₁	#576	direct (N × H)
274. H(5,𝔽₂)	C₂×C₄×C₁₁	semidirect
281. AGL(1,ℤ/8)	C₂×C₄×C₁₁	semidirect
282. #135	C₂×C₄×C₁₁	semidirect
285. C₂×D₈	C₂×C₄×C₁₁	semidirect
289. #131	C₂×C₄×C₁₁	semidirect
345. #41	C₂²×C₄×C₁₁	semidirect
353. C₂×D₄	C₂²×C₄×C₁₁	semidirect
365. Q₁₆	C₂²×C₄×C₁₁	semidirect
366. SD₁₆	C₂²×C₄×C₁₁	semidirect
367. D₈	C₂²×C₄×C₁₁	semidirect
368. D₈	C₂²×C₄×C₁₁	semidirect
370. M₁₆	C₂²×C₄×C₁₁	semidirect
372. C₂×C₈	C₂²×C₄×C₁₁	semidirect
396. C₁₁	C₄×#576	direct (N × H)
447. C₄	C₁₁×#576	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×#576	2
C₄×C₁₁×H(5,𝔽₂)	2
C₁₁×#2951	2
C₁₁×#2948	2
C₁₁×#2946	2
C₄×C₁₁×AGL(1,ℤ/8)	2
C₄×C₁₁×#135	2
C₂×C₄×C₁₁×D₈	2
C₁₁×#2913	2
C₁₁×#2897	2
C₄×C₁₁×#131	2
C₄×#576	11

Subgroups — C4×C11×#576 #14637364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₁₁×#576 #14637364