Subgroups — C₂²×C₁₁×#525 #14639852

Order 2816.

14334 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₁×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁵×C₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₁×#525	C₂	1	48	yes	maximal, direct product factor
4	C₂²×C₁₁×#123	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₁×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
6	C₂²×C₁₁×#121	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₁×#120	C₂	1	2	yes	maximal, complemented
8	C₂²×C₄×D₄×C₁₁	C₂	1	4	yes	maximal, complemented
9	C₂²×C₁₁×#117	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂⁶×C₁₁	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×#41	—	2	16	no	—
12	C₂²×C₁₁×#41	C₂²	1	24	yes	complemented
13	C₂³×Q₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
14	C₂³×D₄×C₁₁	C₂²	1	4	yes	—
15	C₂³×D₄×C₁₁	C₂²	1	2	yes	—
16	C₂³×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
17	C₂⁴×C₄×C₁₁	—	2	16	no	—
18	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
19	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	—
21	C₂⁴×C₄×C₁₁	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₁₁	C₂²	1	24	yes	complemented
23	C₂⁴×C₄×C₁₁	C₂²	1	2	yes	complemented
24	C₁₁×#525	C₂²	1	256	yes	direct product factor
25	C₂×C₁₁×#123	C₂²	1	48	yes	complemented
26	C₂×C₁₁×C₂²⋊Q₈	C₂²	1	48	yes	complemented
27	C₂×C₁₁×#121	C₂²	1	48	yes	complemented
28	C₂×C₁₁×#120	C₂²	1	48	yes	complemented
29	C₂×C₄×D₄×C₁₁	C₂²	1	96	yes	complemented
30	C₂×C₁₁×#117	C₂²	1	24	yes	complemented
31	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	complemented
32	C₂²×C₁₁×C₄⋊C₄	C₂²	1	4	yes	complemented
33	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	—
35	C₂²×C₁₁×C₂²⋊C₄	C₂²	1	4	yes	complemented
36	C₂²×C₄²×C₁₁	C₂²	1	2	yes	complemented
37	C₂⁵×C₁₁	—	2	8	no	—
38	C₂⁵×C₁₁	—	2	16	no	—
39	C₂⁵×C₁₁	C₂³	1	2	yes	—
40	C₂⁵×C₁₁	C₂³	1	12	yes	—
41	C₂⁵×C₁₁	C₂³	1	1	yes	characteristic
42	C₂⁵×C₁₁	C₂³	1	2	yes	—
43	C₂×C₁₁×#41	—	2	192	no	—
44	C₂×C₁₁×#41	C₂³	1	64	yes	complemented
45	C₂²×Q₈×C₁₁	—	2	8	no	—
46	C₂²×Q₈×C₁₁	C₂³	1	12	yes	complemented
47	C₂²×D₄×C₁₁	—	2	16	no	—
48	C₂²×D₄×C₁₁	—	2	32	no	—
49	C₂²×D₄×C₁₁	—	2	8	no	—
50	C₂²×D₄×C₁₁	C₂³	1	48	yes	—
51	C₂²×D₄×C₁₁	C₂³	1	24	yes	—
52	C₂²×D₄×C₁₁	C₂³	1	12	yes	complemented
53	C₂³×C₄×C₁₁	—	2	8	no	—
54	C₂³×C₄×C₁₁	—	2	16	no	—
55	C₂³×C₄×C₁₁	—	2	16	no	—
56	C₂³×C₄×C₁₁	—	2	16	no	—
57	C₂³×C₄×C₁₁	—	2	192	no	—
58	C₂³×C₄×C₁₁	D₄	1	16	yes	complemented
59	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
61	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
62	C₂³×C₄×C₁₁	C₂³	1	24	yes	—
63	C₂³×C₄×C₁₁	C₂³	1	24	yes	—
64	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
65	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₁	C₂³	1	12	yes	—
67	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₁	C₂³	1	64	yes	complemented
69	C₂³×C₄×C₁₁	C₂³	1	24	yes	complemented
70	C₁₁×#123	C₂³	1	128	yes	complemented
71	C₁₁×C₂²⋊Q₈	C₂³	1	128	yes	complemented
72	C₁₁×#121	C₂³	1	128	yes	complemented
73	C₁₁×#120	C₂³	1	128	yes	complemented
74	C₄×D₄×C₁₁	C₂³	1	256	yes	complemented
75	C₁₁×#117	C₂³	1	64	yes	complemented
76	C₂×C₁₁×C₄⋊C₄	C₂³	1	24	yes	complemented
77	C₂×C₁₁×C₄⋊C₄	C₂³	1	48	yes	complemented
78	C₂×C₁₁×C₂²⋊C₄	C₂³	1	24	yes	—
79	C₂×C₁₁×C₂²⋊C₄	C₂³	1	48	yes	—
80	C₂×C₁₁×C₂²⋊C₄	C₂³	1	48	yes	complemented
81	C₂×C₄²×C₁₁	C₂³	1	24	yes	complemented
82	C₂²×#525	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
83	C₂⁴×C₁₁	—	2	128	no	—
84	C₂⁴×C₁₁	—	2	48	no	—
85	C₂⁴×C₁₁	—	2	8	no	—
86	C₂⁴×C₁₁	—	2	8	no	—
87	C₂⁴×C₁₁	—	2	8	no	—
88	C₂⁴×C₁₁	—	2	96	no	—
89	C₂⁴×C₁₁	—	2	8	no	—
90	C₂⁴×C₁₁	—	2	16	no	—
91	C₂⁴×C₁₁	C₂×D₄	1	8	yes	—
92	C₂⁴×C₁₁	#41	1	16	yes	complemented
93	C₂⁴×C₁₁	C₂⁴	1	12	yes	—
94	C₂⁴×C₁₁	C₂⁴	1	16	yes	—
95	C₂⁴×C₁₁	C₂⁴	1	6	yes	—
96	C₂⁴×C₁₁	C₂⁴	1	12	yes	—
97	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
98	C₁₁×#41	—	2	256	no	—
99	C₂×Q₈×C₁₁	—	2	48	no	—
100	C₂×Q₈×C₁₁	C₂⁴	1	16	yes	complemented
101	C₂×D₄×C₁₁	—	2	96	no	—
102	C₂×D₄×C₁₁	—	2	192	no	—
103	C₂×D₄×C₁₁	—	2	48	no	—
104	C₂×D₄×C₁₁	C₂⁴	1	64	yes	—
105	C₂×D₄×C₁₁	C₂⁴	1	32	yes	—
106	C₂×D₄×C₁₁	C₂⁴	1	16	yes	complemented
107	C₂²×C₄×C₁₁	—	2	48	no	—
108	C₂²×C₄×C₁₁	—	2	8	no	—
109	C₂²×C₄×C₁₁	—	2	8	no	—
110	C₂²×C₄×C₁₁	—	2	16	no	—
111	C₂²×C₄×C₁₁	—	2	96	no	—
112	C₂²×C₄×C₁₁	—	2	96	no	—
113	C₂²×C₄×C₁₁	—	2	96	no	—
114	C₂²×C₄×C₁₁	—	2	256	no	—
115	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
116	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₁₁	C₂×D₄	1	96	yes	complemented
118	C₂²×C₄×C₁₁	C₂⁴	1	24	yes	—
119	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
120	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
121	C₂²×C₄×C₁₁	C₂⁴	1	32	yes	—
122	C₂²×C₄×C₁₁	C₂⁴	1	32	yes	—
123	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
124	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
125	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
126	C₂²×C₄×C₁₁	C₂⁴	1	16	yes	—
127	C₂²×C₄×C₁₁	C₂⁴	1	32	yes	complemented
128	C₁₁×C₄⋊C₄	C₂⁴	1	32	yes	complemented
129	C₁₁×C₄⋊C₄	C₂⁴	1	64	yes	complemented
130	C₁₁×C₂²⋊C₄	C₂⁴	1	32	yes	—
131	C₁₁×C₂²⋊C₄	C₂⁴	1	64	yes	—
132	C₁₁×C₂²⋊C₄	C₂⁴	1	64	yes	complemented
133	C₄²×C₁₁	C₂⁴	1	32	yes	complemented
134	C₂³×#41	C₂×C₁₁	1	1	yes	characteristic, complemented
135	C₂⁵×C₄	C₂×C₁₁	1	1	yes	characteristic, complemented
136	C₂×#525	C₂×C₁₁	1	48	yes	direct product factor
137	C₂²×#123	C₂×C₁₁	1	2	yes	complemented
138	C₂²×C₂²⋊Q₈	C₂×C₁₁	1	2	yes	complemented
139	C₂²×#121	C₂×C₁₁	1	2	yes	complemented
140	C₂²×#120	C₂×C₁₁	1	2	yes	complemented
141	C₂²×C₄×D₄	C₂×C₁₁	1	4	yes	complemented
142	C₂²×#117	C₂×C₁₁	1	1	yes	characteristic, complemented
143	C₂³×C₁₁	—	2	384	no	—
144	C₂³×C₁₁	—	2	32	no	—
145	C₂³×C₁₁	—	2	64	no	—
146	C₂³×C₁₁	—	2	32	no	—
147	C₂³×C₁₁	—	2	24	no	—
148	C₂³×C₁₁	—	2	24	no	—
149	C₂³×C₁₁	—	2	24	no	—
150	C₂³×C₁₁	—	2	64	no	—
151	C₂³×C₁₁	—	2	24	no	—
152	C₂³×C₁₁	—	2	48	no	—
153	C₂³×C₁₁	—	4	32	no	—
154	C₂³×C₁₁	C₂²×D₄	1	24	yes	—
155	C₂³×C₁₁	C₂²×D₄	1	4	yes	—
156	C₂³×C₁₁	C₂×#41	1	8	yes	—
157	C₂³×C₁₁	C₂×#41	1	48	yes	complemented
158	C₂³×C₁₁	C₂⁵	1	8	yes	—
159	C₂³×C₁₁	C₂⁵	1	4	yes	—
160	C₂³×C₁₁	C₂⁵	1	8	yes	—
161	C₂³×C₁₁	C₂⁵	1	3	yes	—
162	Q₈×C₁₁	—	2	32	no	—
163	D₄×C₁₁	—	2	64	no	—
164	D₄×C₁₁	—	2	128	no	—
165	D₄×C₁₁	—	2	32	no	—
166	C₂×C₄×C₁₁	—	2	32	no	—
167	C₂×C₄×C₁₁	—	2	24	no	—
168	C₂×C₄×C₁₁	—	2	24	no	—
169	C₂×C₄×C₁₁	—	2	48	no	—
170	C₂×C₄×C₁₁	—	2	64	no	—
171	C₂×C₄×C₁₁	—	2	64	no	—
172	C₂×C₄×C₁₁	—	2	64	no	—
173	C₂×C₄×C₁₁	C₂²×D₄	1	24	yes	—
174	C₂×C₄×C₁₁	C₂²×D₄	1	24	yes	—
175	C₂×C₄×C₁₁	C₂²×D₄	1	64	yes	complemented
176	C₂×C₄×C₁₁	C₂⁵	1	16	yes	—
177	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
178	C₂×C₄×C₁₁	C₂⁵	1	8	yes	—
179	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
180	C₂×C₄×C₁₁	C₂⁵	1	4	yes	—
181	C₂⁶	C₂²×C₁₁	1	1	yes	characteristic
182	C₂²×#41	—	2	16	no	—
183	C₂²×#41	C₂²×C₁₁	1	24	yes	complemented
184	C₂³×Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
185	C₂³×D₄	C₂²×C₁₁	1	2	yes	—
186	C₂³×D₄	C₂²×C₁₁	1	4	yes	—
187	C₂³×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
188	C₂⁴×C₄	—	2	16	no	—
189	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
190	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	—
191	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
192	C₂⁴×C₄	C₂²×C₁₁	1	1	yes	characteristic
193	C₂⁴×C₄	C₂²×C₁₁	1	24	yes	complemented
194	C₂⁴×C₄	C₂²×C₁₁	1	2	yes	complemented
195	#525	C₂²×C₁₁	1	256	yes	direct product factor
196	C₂×#123	C₂²×C₁₁	1	48	yes	complemented
197	C₂×C₂²⋊Q₈	C₂²×C₁₁	1	48	yes	complemented
198	C₂×#121	C₂²×C₁₁	1	48	yes	complemented
199	C₂×#120	C₂²×C₁₁	1	48	yes	complemented
200	C₂×C₄×D₄	C₂²×C₁₁	1	96	yes	complemented
201	C₂×#117	C₂²×C₁₁	1	24	yes	complemented
202	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	complemented
203	C₂²×C₄⋊C₄	C₂²×C₁₁	1	4	yes	complemented
204	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
205	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	—
206	C₂²×C₂²⋊C₄	C₂²×C₁₁	1	4	yes	complemented
207	C₂²×C₄²	C₂²×C₁₁	1	2	yes	complemented
208	C₂²×C₁₁	—	2	128	no	—
209	C₂²×C₁₁	—	2	8	no	—
210	C₂²×C₁₁	—	2	8	no	—
211	C₂²×C₁₁	—	2	8	no	—
212	C₂²×C₁₁	—	2	48	no	—
213	C₂²×C₁₁	—	2	96	no	—
214	C₂²×C₁₁	—	2	8	no	—
215	C₂²×C₁₁	—	2	16	no	—
216	C₂²×C₁₁	—	4	48	no	—
217	C₂²×C₁₁	#525	1	16	yes	direct product factor
218	C₂²×C₁₁	C₂³×D₄	1	8	yes	—
219	C₂²×C₁₁	C₂³×D₄	1	6	yes	—
220	C₂²×C₁₁	C₂²×#41	1	12	yes	—
221	C₂²×C₁₁	C₂²×#41	1	16	yes	complemented
222	C₂²×C₁₁	C₂⁶	1	1	yes	characteristic
223	C₄×C₁₁	—	2	8	no	—
224	C₄×C₁₁	—	2	8	no	—
225	C₄×C₁₁	—	2	16	no	—
226	C₄×C₁₁	C₂³×D₄	1	8	yes	—
227	C₄×C₁₁	C₂³×D₄	1	8	yes	—
228	C₂⁵	—	2	8	no	—
229	C₂⁵	—	2	16	no	—
230	C₂⁵	C₂³×C₁₁	1	2	yes	—
231	C₂⁵	C₂³×C₁₁	1	12	yes	—
232	C₂⁵	C₂³×C₁₁	1	1	yes	characteristic
233	C₂⁵	C₂³×C₁₁	1	2	yes	—
234	C₂×#41	—	2	192	no	—
235	C₂×#41	C₂³×C₁₁	1	64	yes	complemented
236	C₂²×Q₈	—	2	8	no	—
237	C₂²×Q₈	C₂³×C₁₁	1	12	yes	complemented
238	C₂²×D₄	—	2	16	no	—
239	C₂²×D₄	—	2	32	no	—
240	C₂²×D₄	—	2	8	no	—
241	C₂²×D₄	C₂³×C₁₁	1	48	yes	—
242	C₂²×D₄	C₂³×C₁₁	1	24	yes	—
243	C₂²×D₄	C₂³×C₁₁	1	12	yes	complemented
244	C₂³×C₄	—	2	8	no	—
245	C₂³×C₄	—	2	16	no	—
246	C₂³×C₄	—	2	16	no	—
247	C₂³×C₄	—	2	16	no	—
248	C₂³×C₄	—	2	192	no	—
249	C₂³×C₄	D₄×C₁₁	1	16	yes	complemented
250	C₂³×C₄	C₂³×C₁₁	1	4	yes	—
251	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
252	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
253	C₂³×C₄	C₂³×C₁₁	1	24	yes	—
254	C₂³×C₄	C₂³×C₁₁	1	24	yes	—
255	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
256	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
257	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₁₁	1	12	yes	—
259	C₂³×C₄	C₂³×C₁₁	1	64	yes	complemented
260	C₂³×C₄	C₂³×C₁₁	1	24	yes	complemented
261	#123	C₂³×C₁₁	1	128	yes	complemented
262	C₂²⋊Q₈	C₂³×C₁₁	1	128	yes	complemented
263	#121	C₂³×C₁₁	1	128	yes	complemented
264	#120	C₂³×C₁₁	1	128	yes	complemented
265	C₄×D₄	C₂³×C₁₁	1	256	yes	complemented
266	#117	C₂³×C₁₁	1	64	yes	complemented
267	C₂×C₄⋊C₄	C₂³×C₁₁	1	24	yes	complemented
268	C₂×C₄⋊C₄	C₂³×C₁₁	1	48	yes	complemented
269	C₂×C₂²⋊C₄	C₂³×C₁₁	1	24	yes	—
270	C₂×C₂²⋊C₄	C₂³×C₁₁	1	48	yes	—
271	C₂×C₂²⋊C₄	C₂³×C₁₁	1	48	yes	complemented
272	C₂×C₄²	C₂³×C₁₁	1	24	yes	complemented
273	C₂×C₁₁	—	2	8	no	—
274	C₂×C₁₁	—	2	16	no	—
275	C₂×C₁₁	—	4	8	no	—
276	C₂×C₁₁	C₂×#525	1	12	yes	direct product factor
277	C₂×C₁₁	C₂⁴×D₄	1	1	yes	characteristic
278	C₂×C₁₁	C₂³×#41	1	2	yes	—
279	C₂⁴	—	2	128	no	—
280	C₂⁴	—	2	48	no	—
281	C₂⁴	—	2	8	no	—
282	C₂⁴	—	2	8	no	—
283	C₂⁴	—	2	8	no	—
284	C₂⁴	—	2	96	no	—
285	C₂⁴	—	2	8	no	—
286	C₂⁴	—	2	16	no	—
287	C₂⁴	C₂×D₄×C₁₁	1	8	yes	—
288	C₂⁴	C₁₁×#41	1	16	yes	complemented
289	C₂⁴	C₂⁴×C₁₁	1	12	yes	—
290	C₂⁴	C₂⁴×C₁₁	1	16	yes	—
291	C₂⁴	C₂⁴×C₁₁	1	6	yes	—
292	C₂⁴	C₂⁴×C₁₁	1	12	yes	—
293	C₂⁴	C₂⁴×C₁₁	1	1	yes	characteristic
294	#41	—	2	256	no	—
295	C₂×Q₈	—	2	48	no	—
296	C₂×Q₈	C₂⁴×C₁₁	1	16	yes	complemented
297	C₂×D₄	—	2	96	no	—
298	C₂×D₄	—	2	192	no	—
299	C₂×D₄	—	2	48	no	—
300	C₂×D₄	C₂⁴×C₁₁	1	64	yes	—
301	C₂×D₄	C₂⁴×C₁₁	1	32	yes	—
302	C₂×D₄	C₂⁴×C₁₁	1	16	yes	complemented
303	C₂²×C₄	—	2	48	no	—
304	C₂²×C₄	—	2	8	no	—
305	C₂²×C₄	—	2	8	no	—
306	C₂²×C₄	—	2	16	no	—
307	C₂²×C₄	—	2	96	no	—
308	C₂²×C₄	—	2	96	no	—
309	C₂²×C₄	—	2	96	no	—
310	C₂²×C₄	—	2	256	no	—
311	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
312	C₂²×C₄	C₂×D₄×C₁₁	1	8	yes	—
313	C₂²×C₄	C₂×D₄×C₁₁	1	96	yes	complemented
314	C₂²×C₄	C₂⁴×C₁₁	1	24	yes	—
315	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
316	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
317	C₂²×C₄	C₂⁴×C₁₁	1	32	yes	—
318	C₂²×C₄	C₂⁴×C₁₁	1	32	yes	—
319	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
320	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
321	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
322	C₂²×C₄	C₂⁴×C₁₁	1	16	yes	—
323	C₂²×C₄	C₂⁴×C₁₁	1	32	yes	complemented
324	C₄⋊C₄	C₂⁴×C₁₁	1	32	yes	complemented
325	C₄⋊C₄	C₂⁴×C₁₁	1	64	yes	complemented
326	C₂²⋊C₄	C₂⁴×C₁₁	1	32	yes	—
327	C₂²⋊C₄	C₂⁴×C₁₁	1	64	yes	—
328	C₂²⋊C₄	C₂⁴×C₁₁	1	64	yes	complemented
329	C₄²	C₂⁴×C₁₁	1	32	yes	complemented
330	C₁₁	C₂²×#525	1	1	yes	characteristic, direct product factor, Sylow
331	C₂³	—	2	384	no	—
332	C₂³	—	2	32	no	—
333	C₂³	—	2	64	no	—
334	C₂³	—	2	32	no	—
335	C₂³	—	2	24	no	—
336	C₂³	—	2	24	no	—
337	C₂³	—	2	24	no	—
338	C₂³	—	2	64	no	—
339	C₂³	—	2	24	no	—
340	C₂³	—	2	48	no	—
341	C₂³	—	4	32	no	—
342	C₂³	C₂²×D₄×C₁₁	1	24	yes	—
343	C₂³	C₂²×D₄×C₁₁	1	4	yes	—
344	C₂³	C₂×C₁₁×#41	1	8	yes	—
345	C₂³	C₂×C₁₁×#41	1	48	yes	complemented
346	C₂³	C₂⁵×C₁₁	1	8	yes	—
347	C₂³	C₂⁵×C₁₁	1	4	yes	—
348	C₂³	C₂⁵×C₁₁	1	8	yes	—
349	C₂³	C₂⁵×C₁₁	1	3	yes	—
350	Q₈	—	2	32	no	—
351	D₄	—	2	64	no	—
352	D₄	—	2	128	no	—
353	D₄	—	2	32	no	—
354	C₂×C₄	—	2	32	no	—
355	C₂×C₄	—	2	24	no	—
356	C₂×C₄	—	2	24	no	—
357	C₂×C₄	—	2	48	no	—
358	C₂×C₄	—	2	64	no	—
359	C₂×C₄	—	2	64	no	—
360	C₂×C₄	—	2	64	no	—
361	C₂×C₄	C₂²×D₄×C₁₁	1	24	yes	—
362	C₂×C₄	C₂²×D₄×C₁₁	1	24	yes	—
363	C₂×C₄	C₂²×D₄×C₁₁	1	64	yes	complemented
364	C₂×C₄	C₂⁵×C₁₁	1	16	yes	—
365	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
366	C₂×C₄	C₂⁵×C₁₁	1	8	yes	—
367	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
368	C₂×C₄	C₂⁵×C₁₁	1	4	yes	—
369	C₂²	—	2	128	no	—
370	C₂²	—	2	48	no	—
371	C₂²	—	2	96	no	—
372	C₂²	—	2	8	no	—
373	C₂²	—	2	8	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	8	no	—
376	C₂²	—	2	16	no	—
377	C₂²	—	4	48	no	—
378	C₂²	C₁₁×#525	1	16	yes	direct product factor
379	C₂²	C₂³×D₄×C₁₁	1	8	yes	—
380	C₂²	C₂³×D₄×C₁₁	1	6	yes	—
381	C₂²	C₂²×C₁₁×#41	1	12	yes	—
382	C₂²	C₂²×C₁₁×#41	1	16	yes	complemented
383	C₂²	C₂⁶×C₁₁	1	1	yes	characteristic
384	C₄	—	2	8	no	—
385	C₄	—	2	8	no	—
386	C₄	—	2	16	no	—
387	C₄	C₂³×D₄×C₁₁	1	8	yes	—
388	C₄	C₂³×D₄×C₁₁	1	8	yes	—
389	C₂	—	2	8	no	—
390	C₂	—	2	16	no	—
391	C₂	—	4	8	no	—
392	C₂	C₂×C₁₁×#525	1	12	yes	direct product factor
393	C₂	C₂⁴×D₄×C₁₁	1	1	yes	characteristic
394	C₂	C₂³×C₁₁×#41	1	2	yes	—

	subgroup	G/H
center	C₂³×C₄×C₁₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₁
socle	C₂⁴×C₁₁	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×C₁₁×#41	C₂	semidirect
2. C₂⁵×C₄×C₁₁	C₂	semidirect
3. C₂×C₁₁×#525	C₂	direct (N × H)
4. C₂²×C₁₁×#123	C₂	semidirect
5. C₂²×C₁₁×C₂²⋊Q₈	C₂	semidirect
6. C₂²×C₁₁×#121	C₂	semidirect
7. C₂²×C₁₁×#120	C₂	semidirect
8. C₂²×C₄×D₄×C₁₁	C₂	semidirect
9. C₂²×C₁₁×#117	C₂	semidirect
12. C₂²×C₁₁×#41	C₂²	semidirect
13. C₂³×Q₈×C₁₁	C₂²	semidirect
16. C₂³×D₄×C₁₁	C₂²	semidirect
22. C₂⁴×C₄×C₁₁	C₂²	semidirect
23. C₂⁴×C₄×C₁₁	C₂²	semidirect
24. C₁₁×#525	C₂²	direct (N × H)
25. C₂×C₁₁×#123	C₂²	semidirect
26. C₂×C₁₁×C₂²⋊Q₈	C₂²	semidirect
27. C₂×C₁₁×#121	C₂²	semidirect
28. C₂×C₁₁×#120	C₂²	semidirect
29. C₂×C₄×D₄×C₁₁	C₂²	semidirect
30. C₂×C₁₁×#117	C₂²	semidirect
31. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
32. C₂²×C₁₁×C₄⋊C₄	C₂²	semidirect
35. C₂²×C₁₁×C₂²⋊C₄	C₂²	semidirect
36. C₂²×C₄²×C₁₁	C₂²	semidirect
44. C₂×C₁₁×#41	C₂³	semidirect
46. C₂²×Q₈×C₁₁	C₂³	semidirect
52. C₂²×D₄×C₁₁	C₂³	semidirect
58. C₂³×C₄×C₁₁	D₄	semidirect
68. C₂³×C₄×C₁₁	C₂³	semidirect
69. C₂³×C₄×C₁₁	C₂³	semidirect
70. C₁₁×#123	C₂³	semidirect
71. C₁₁×C₂²⋊Q₈	C₂³	semidirect
72. C₁₁×#121	C₂³	semidirect
73. C₁₁×#120	C₂³	semidirect
74. C₄×D₄×C₁₁	C₂³	semidirect
75. C₁₁×#117	C₂³	semidirect
76. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
77. C₂×C₁₁×C₄⋊C₄	C₂³	semidirect
80. C₂×C₁₁×C₂²⋊C₄	C₂³	semidirect
81. C₂×C₄²×C₁₁	C₂³	semidirect
82. C₂²×#525	C₁₁	direct (N × H)
92. C₂⁴×C₁₁	#41	semidirect
100. C₂×Q₈×C₁₁	C₂⁴	semidirect
106. C₂×D₄×C₁₁	C₂⁴	semidirect
117. C₂²×C₄×C₁₁	C₂×D₄	semidirect
127. C₂²×C₄×C₁₁	C₂⁴	semidirect
128. C₁₁×C₄⋊C₄	C₂⁴	semidirect
129. C₁₁×C₄⋊C₄	C₂⁴	semidirect
132. C₁₁×C₂²⋊C₄	C₂⁴	semidirect
133. C₄²×C₁₁	C₂⁴	semidirect
134. C₂³×#41	C₂×C₁₁	semidirect
135. C₂⁵×C₄	C₂×C₁₁	semidirect
136. C₂×#525	C₂×C₁₁	direct (N × H)
137. C₂²×#123	C₂×C₁₁	semidirect
138. C₂²×C₂²⋊Q₈	C₂×C₁₁	semidirect
139. C₂²×#121	C₂×C₁₁	semidirect
140. C₂²×#120	C₂×C₁₁	semidirect
141. C₂²×C₄×D₄	C₂×C₁₁	semidirect
142. C₂²×#117	C₂×C₁₁	semidirect
157. C₂³×C₁₁	C₂×#41	semidirect
175. C₂×C₄×C₁₁	C₂²×D₄	semidirect
183. C₂²×#41	C₂²×C₁₁	semidirect
184. C₂³×Q₈	C₂²×C₁₁	semidirect
187. C₂³×D₄	C₂²×C₁₁	semidirect
193. C₂⁴×C₄	C₂²×C₁₁	semidirect
194. C₂⁴×C₄	C₂²×C₁₁	semidirect
195. #525	C₂²×C₁₁	direct (N × H)
196. C₂×#123	C₂²×C₁₁	semidirect
197. C₂×C₂²⋊Q₈	C₂²×C₁₁	semidirect
198. C₂×#121	C₂²×C₁₁	semidirect
199. C₂×#120	C₂²×C₁₁	semidirect
200. C₂×C₄×D₄	C₂²×C₁₁	semidirect
201. C₂×#117	C₂²×C₁₁	semidirect
202. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
203. C₂²×C₄⋊C₄	C₂²×C₁₁	semidirect
206. C₂²×C₂²⋊C₄	C₂²×C₁₁	semidirect
207. C₂²×C₄²	C₂²×C₁₁	semidirect
217. C₂²×C₁₁	#525	direct (N × H)
221. C₂²×C₁₁	C₂²×#41	semidirect
235. C₂×#41	C₂³×C₁₁	semidirect
237. C₂²×Q₈	C₂³×C₁₁	semidirect
243. C₂²×D₄	C₂³×C₁₁	semidirect
249. C₂³×C₄	D₄×C₁₁	semidirect
259. C₂³×C₄	C₂³×C₁₁	semidirect
260. C₂³×C₄	C₂³×C₁₁	semidirect
261. #123	C₂³×C₁₁	semidirect
262. C₂²⋊Q₈	C₂³×C₁₁	semidirect
263. #121	C₂³×C₁₁	semidirect
264. #120	C₂³×C₁₁	semidirect
265. C₄×D₄	C₂³×C₁₁	semidirect
266. #117	C₂³×C₁₁	semidirect
267. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
268. C₂×C₄⋊C₄	C₂³×C₁₁	semidirect
271. C₂×C₂²⋊C₄	C₂³×C₁₁	semidirect
272. C₂×C₄²	C₂³×C₁₁	semidirect
276. C₂×C₁₁	C₂×#525	direct (N × H)
288. C₂⁴	C₁₁×#41	semidirect
296. C₂×Q₈	C₂⁴×C₁₁	semidirect
302. C₂×D₄	C₂⁴×C₁₁	semidirect
313. C₂²×C₄	C₂×D₄×C₁₁	semidirect
323. C₂²×C₄	C₂⁴×C₁₁	semidirect
324. C₄⋊C₄	C₂⁴×C₁₁	semidirect
325. C₄⋊C₄	C₂⁴×C₁₁	semidirect
328. C₂²⋊C₄	C₂⁴×C₁₁	semidirect
329. C₄²	C₂⁴×C₁₁	semidirect
330. C₁₁	C₂²×#525	direct (N × H)
345. C₂³	C₂×C₁₁×#41	semidirect
363. C₂×C₄	C₂²×D₄×C₁₁	semidirect
378. C₂²	C₁₁×#525	direct (N × H)
382. C₂²	C₂²×C₁₁×#41	semidirect
392. C₂	C₂×C₁₁×#525	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₁₁×#41	2
C₂⁵×C₄×C₁₁	2
C₂×C₁₁×#525	2
C₂²×C₁₁×#123	2
C₂²×C₁₁×C₂²⋊Q₈	2
C₂²×C₁₁×#121	2
C₂²×C₁₁×#120	2
C₂²×C₄×D₄×C₁₁	2
C₂²×C₁₁×#117	2
C₂²×#525	11

Subgroups — C22×C11×#525 #14639852

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×#525 #14639852