Subgroups — C₂×C₁₁×#2925 #14637315

Order 2816.

2178 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2925	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₁×#433	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#432	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₁×#431	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#423	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₁₁×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₁×#408	C₂	1	2	yes	maximal
9	C₂×C₁₁×#405	C₂	1	2	yes	maximal, complemented
10	C₂²×C₁₁×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×M₁₆	C₂²	1	2	yes	—
12	C₂³×C₈×C₁₁	C₂²	1	2	yes	—
13	C₄×C₁₁×#41	C₄	1	8	yes	—
14	C₄×C₁₁×#41	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₁	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₁	C₄	1	2	yes	—
20	C₂×C₄×D₄×C₁₁	C₄	1	1	yes	characteristic
21	C₂×C₁₁×#117	C₂²	1	2	yes	—
22	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
25	C₁₁×#433	C₂²	1	32	yes	complemented
26	C₁₁×#432	C₂²	1	16	yes	complemented
27	C₁₁×#431	C₂²	1	16	yes	complemented
28	C₁₁×#423	C₂²	1	8	yes	complemented
29	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
32	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
33	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
34	C₂×C₁₁×C₄⋊C₈	C₂²	1	8	yes	complemented
35	C₁₁×#408	C₂²	1	16	yes	—
36	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
37	C₂×C₁₁×C₂²⋊C₈	C₂²	1	4	yes	—
38	C₁₁×#405	C₂²	1	16	yes	complemented
39	C₂×C₁₁×#97	C₂²	1	4	yes	—
40	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
41	C₂×C₁₁×#41	—	2	4	no	—
42	C₂×C₁₁×#41	—	2	4	no	—
43	C₂×C₁₁×#41	C₂×C₄	1	4	yes	—
44	C₂×C₁₁×#41	C₂³	1	4	yes	—
45	C₂²×Q₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₁	C₂×C₄	1	2	yes	—
47	C₂²×D₄×C₁₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₁	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
54	C₂×C₁₁×M₁₆	—	2	8	no	—
55	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
56	C₂²×C₈×C₁₁	—	2	8	no	—
57	C₂²×C₈×C₁₁	C₂³	1	8	yes	—
58	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
60	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
61	C₄×Q₈×C₁₁	C₂×C₄	1	8	yes	—
62	C₄×Q₈×C₁₁	C₂×C₄	1	8	yes	—
63	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	—
64	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
65	C₄×D₄×C₁₁	C₂×C₄	1	16	yes	—
66	C₄×D₄×C₁₁	C₂×C₄	1	8	yes	—
67	C₁₁×#117	C₂×C₄	1	8	yes	—
68	C₁₁×#117	C₂×C₄	1	4	yes	—
69	C₁₁×#117	C₂³	1	4	yes	—
70	C₁₁×#117	C₂³	1	8	yes	—
71	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
74	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
76	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
77	C₂×C₁₁×C₂²⋊C₄	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
81	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₁	C₂×C₄	1	8	yes	—
83	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
84	C₂×C₄²×C₁₁	C₂³	1	4	yes	—
85	C₂×C₄²×C₁₁	C₂³	1	8	yes	—
86	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
88	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
89	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
90	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
91	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
92	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
93	C₁₁×C₄⋊C₈	C₂³	1	8	yes	—
94	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
95	C₁₁×C₂²⋊C₈	C₂³	1	16	yes	—
96	C₁₁×#97	C₂³	1	16	yes	—
97	C₄×C₈×C₁₁	C₂³	1	16	yes	—
98	C₂×#2925	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₁	C₂²×C₄	1	2	yes	—
100	C₂⁴×C₁₁	C₂²×C₄	1	1	yes	characteristic
101	C₁₁×#41	—	2	16	no	—
102	C₁₁×#41	—	2	8	no	—
103	C₁₁×#41	—	2	8	no	—
104	C₂×Q₈×C₁₁	—	2	4	no	—
105	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
106	C₂×D₄×C₁₁	—	2	8	no	—
107	C₂×D₄×C₁₁	—	2	4	no	—
108	C₂×D₄×C₁₁	C₂²×C₄	1	8	yes	—
109	C₂×D₄×C₁₁	C₂²×C₄	1	4	yes	—
110	C₂²×C₄×C₁₁	—	2	4	no	—
111	C₂²×C₄×C₁₁	—	2	8	no	—
112	C₂²×C₄×C₁₁	—	2	4	no	—
113	C₂²×C₄×C₁₁	—	2	4	no	—
114	C₂²×C₄×C₁₁	—	4	2	no	—
115	C₂²×C₄×C₁₁	—	4	4	no	—
116	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
124	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
126	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
127	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₁	#41	1	4	yes	—
131	C₂²×C₄×C₁₁	#41	1	4	yes	—
132	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
135	C₁₁×M₁₆	—	2	16	no	—
136	C₂×C₈×C₁₁	—	2	4	no	—
137	C₂×C₈×C₁₁	—	2	4	no	—
138	C₂×C₈×C₁₁	—	2	16	no	—
139	C₂×C₈×C₁₁	—	2	8	no	—
140	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
141	C₂×C₈×C₁₁	C₂⁴	1	8	yes	—
142	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
143	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
144	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
145	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
146	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
147	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
148	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
149	C₁₁×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
150	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
151	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
152	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
153	C₄²×C₁₁	C₂²×C₄	1	8	yes	—
154	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
155	C₄²×C₁₁	C₂²×C₄	1	8	yes	—
156	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
157	C₄²×C₁₁	C₂⁴	1	4	yes	—
158	C₄²×C₁₁	C₂⁴	1	2	yes	—
159	C₄²×C₁₁	C₂⁴	1	2	yes	—
160	C₂×C₄×#41	C₂×C₁₁	1	1	yes	characteristic
161	#2925	C₂×C₁₁	1	16	yes	direct product factor
162	C₂×#433	C₂×C₁₁	1	4	yes	complemented
163	C₂×#432	C₂×C₁₁	1	2	yes	complemented
164	C₂×#431	C₂×C₁₁	1	2	yes	complemented
165	C₂×#423	C₂×C₁₁	1	1	yes	characteristic, complemented
166	C₂²×C₄⋊C₈	C₂×C₁₁	1	1	yes	characteristic, complemented
167	C₂×#408	C₂×C₁₁	1	2	yes	—
168	C₂×#405	C₂×C₁₁	1	2	yes	complemented
169	C₂³×C₁₁	—	2	2	no	—
170	C₂³×C₁₁	—	2	2	no	—
171	C₂³×C₁₁	—	2	4	no	—
172	C₂³×C₁₁	—	2	4	no	—
173	C₂³×C₁₁	—	2	4	no	—
174	C₂³×C₁₁	#117	1	4	yes	—
175	C₂³×C₁₁	C₂³×C₄	1	4	yes	—
176	C₂³×C₁₁	C₂³×C₄	1	2	yes	—
177	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
178	Q₈×C₁₁	—	2	8	no	—
179	D₄×C₁₁	—	2	16	no	—
180	D₄×C₁₁	—	2	8	no	—
181	C₂×C₄×C₁₁	—	2	4	no	—
182	C₂×C₄×C₁₁	—	2	2	no	—
183	C₂×C₄×C₁₁	—	2	4	no	—
184	C₂×C₄×C₁₁	—	2	2	no	—
185	C₂×C₄×C₁₁	—	2	2	no	—
186	C₂×C₄×C₁₁	—	2	4	no	—
187	C₂×C₄×C₁₁	—	2	8	no	—
188	C₂×C₄×C₁₁	—	2	8	no	—
189	C₂×C₄×C₁₁	—	2	16	no	—
190	C₂×C₄×C₁₁	—	2	4	no	—
191	C₂×C₄×C₁₁	—	2	4	no	—
192	C₂×C₄×C₁₁	—	4	4	no	—
193	C₂×C₄×C₁₁	—	4	8	no	—
194	C₂×C₄×C₁₁	#117	1	4	yes	—
195	C₂×C₄×C₁₁	#117	1	8	yes	—
196	C₂×C₄×C₁₁	#131	1	4	yes	—
197	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
198	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
199	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
200	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
201	C₂×C₄×C₁₁	C₂³×C₄	1	4	yes	—
202	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
203	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
205	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
206	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
207	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
208	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
209	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
210	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
211	C₈×C₁₁	—	2	4	no	—
212	C₈×C₁₁	—	2	4	no	—
213	C₈×C₁₁	—	2	8	no	—
214	C₂²×#41	C₂²×C₁₁	1	1	yes	characteristic
215	C₂²×M₁₆	C₂²×C₁₁	1	2	yes	—
216	C₂³×C₈	C₂²×C₁₁	1	2	yes	—
217	C₄×#41	C₄×C₁₁	1	8	yes	—
218	C₄×#41	C₂²×C₁₁	1	8	yes	—
219	C₂×C₄×Q₈	C₄×C₁₁	1	1	yes	characteristic
220	C₂×C₄×Q₈	C₄×C₁₁	1	1	yes	characteristic
221	C₂×C₄×D₄	C₄×C₁₁	1	2	yes	—
222	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
223	C₂×C₄×D₄	C₄×C₁₁	1	2	yes	—
224	C₂×C₄×D₄	C₄×C₁₁	1	1	yes	characteristic
225	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
226	C₂×#117	C₂²×C₁₁	1	2	yes	—
227	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₁₁	1	2	yes	—
229	#433	C₂²×C₁₁	1	32	yes	complemented
230	#432	C₂²×C₁₁	1	16	yes	complemented
231	#431	C₂²×C₁₁	1	16	yes	complemented
232	#423	C₂²×C₁₁	1	8	yes	complemented
233	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic
235	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
236	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
237	C₂×C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₁₁	1	8	yes	complemented
239	#408	C₂²×C₁₁	1	16	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
241	C₂×C₂²⋊C₈	C₂²×C₁₁	1	4	yes	—
242	#405	C₂²×C₁₁	1	16	yes	complemented
243	C₂×#97	C₂²×C₁₁	1	4	yes	—
244	C₂×C₄×C₈	C₂²×C₁₁	1	4	yes	—
245	C₂²×C₁₁	—	2	8	no	—
246	C₂²×C₁₁	—	2	2	no	—
247	C₂²×C₁₁	—	2	2	no	—
248	C₂²×C₁₁	—	2	4	no	—
249	C₂²×C₁₁	—	2	4	no	—
250	C₂²×C₁₁	—	2	4	no	—
251	C₂²×C₁₁	—	4	8	no	—
252	C₂²×C₁₁	C₂×#117	1	4	yes	—
253	C₂²×C₁₁	C₂×#117	1	2	yes	—
254	C₂²×C₁₁	C₂×#131	1	2	yes	—
255	C₂²×C₁₁	#568	1	2	yes	—
256	C₂²×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
257	C₄×C₁₁	—	2	4	no	—
258	C₄×C₁₁	—	2	2	no	—
259	C₄×C₁₁	—	2	4	no	—
260	C₄×C₁₁	—	2	2	no	—
261	C₄×C₁₁	—	2	2	no	—
262	C₄×C₁₁	—	2	4	no	—
263	C₄×C₁₁	C₂×#117	1	2	yes	—
264	C₄×C₁₁	C₂×#117	1	4	yes	—
265	C₄×C₁₁	C₂×#131	1	4	yes	—
266	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
267	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
268	C₂×#41	—	2	4	no	—
269	C₂×#41	—	2	4	no	—
270	C₂×#41	C₂×C₄×C₁₁	1	4	yes	—
271	C₂×#41	C₂³×C₁₁	1	4	yes	—
272	C₂²×Q₈	C₂×C₄×C₁₁	1	1	yes	characteristic
273	C₂²×D₄	C₂×C₄×C₁₁	1	2	yes	—
274	C₂²×D₄	C₂×C₄×C₁₁	1	1	yes	characteristic
275	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
276	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
277	C₂³×C₄	C₂×C₄×C₁₁	1	2	yes	—
278	C₂³×C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
280	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
281	C₂×M₁₆	—	2	8	no	—
282	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
283	C₂²×C₈	—	2	8	no	—
284	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
286	C₂²×C₈	C₂³×C₁₁	1	8	yes	—
287	C₂²×C₈	C₂³×C₁₁	1	4	yes	—
288	C₄×Q₈	C₂×C₄×C₁₁	1	8	yes	—
289	C₄×Q₈	C₂×C₄×C₁₁	1	8	yes	—
290	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	—
291	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
292	C₄×D₄	C₂×C₄×C₁₁	1	16	yes	—
293	C₄×D₄	C₂×C₄×C₁₁	1	8	yes	—
294	#117	C₂×C₄×C₁₁	1	8	yes	—
295	#117	C₂×C₄×C₁₁	1	4	yes	—
296	#117	C₂³×C₁₁	1	4	yes	—
297	#117	C₂³×C₁₁	1	8	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₁	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
303	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×C₄×C₁₁	1	2	yes	—
305	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
306	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
307	C₂×C₄²	C₂×C₄×C₁₁	1	2	yes	—
308	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₁₁	1	8	yes	—
310	C₂×C₄²	C₂×C₄×C₁₁	1	4	yes	—
311	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
312	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₁₁	1	4	yes	—
314	C₂×C₄²	C₂³×C₁₁	1	8	yes	—
315	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
317	C₄⋊C₈	C₂³×C₁₁	1	4	yes	—
318	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
319	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
320	C₄⋊C₈	C₂³×C₁₁	1	8	yes	—
321	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
322	C₂²⋊C₈	C₂³×C₁₁	1	16	yes	—
323	#97	C₂³×C₁₁	1	16	yes	—
324	C₄×C₈	C₂³×C₁₁	1	16	yes	—
325	C₂×C₁₁	—	2	4	no	—
326	C₂×C₁₁	—	4	4	no	—
327	C₂×C₁₁	#2925	1	4	yes	direct product factor
328	C₂×C₁₁	C₂²×#117	1	1	yes	characteristic
329	C₂×C₁₁	C₂²×#131	1	1	yes	characteristic
330	C₂×C₁₁	C₂×#568	1	1	yes	characteristic
331	C₂⁴	C₂²×C₄×C₁₁	1	2	yes	—
332	C₂⁴	C₂²×C₄×C₁₁	1	1	yes	characteristic
333	#41	—	2	16	no	—
334	#41	—	2	8	no	—
335	#41	—	2	8	no	—
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	C₂²×C₄×C₁₁	1	4	yes	—
338	C₂×D₄	—	2	8	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	C₂²×C₄×C₁₁	1	8	yes	—
341	C₂×D₄	C₂²×C₄×C₁₁	1	4	yes	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
350	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
351	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
354	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
356	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
357	C₂²×C₄	C₂²×C₄×C₁₁	1	8	yes	—
358	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
360	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
362	C₂²×C₄	C₁₁×#41	1	4	yes	—
363	C₂²×C₄	C₁₁×#41	1	4	yes	—
364	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
365	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
367	M₁₆	—	2	16	no	—
368	C₂×C₈	—	2	4	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	16	no	—
371	C₂×C₈	—	2	8	no	—
372	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
373	C₂×C₈	C₂⁴×C₁₁	1	8	yes	—
374	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
375	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
376	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
377	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
378	C₄⋊C₄	C₂²×C₄×C₁₁	1	4	yes	—
379	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
380	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
381	C₂²⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
382	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
383	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
384	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
385	C₄²	C₂²×C₄×C₁₁	1	8	yes	—
386	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
387	C₄²	C₂²×C₄×C₁₁	1	8	yes	—
388	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
389	C₄²	C₂⁴×C₁₁	1	4	yes	—
390	C₄²	C₂⁴×C₁₁	1	2	yes	—
391	C₄²	C₂⁴×C₁₁	1	2	yes	—
392	C₁₁	C₂×#2925	1	1	yes	characteristic, direct product factor, Sylow
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	C₁₁×#117	1	4	yes	—
399	C₂³	C₂³×C₄×C₁₁	1	4	yes	—
400	C₂³	C₂³×C₄×C₁₁	1	2	yes	—
401	C₂³	C₂³×C₄×C₁₁	1	1	yes	characteristic
402	Q₈	—	2	8	no	—
403	D₄	—	2	16	no	—
404	D₄	—	2	8	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	8	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	16	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	C₁₁×#117	1	4	yes	—
419	C₂×C₄	C₁₁×#117	1	8	yes	—
420	C₂×C₄	C₁₁×#131	1	4	yes	—
421	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
422	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
423	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
424	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
425	C₂×C₄	C₂³×C₄×C₁₁	1	4	yes	—
426	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
428	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
429	C₂×C₄	C₂³×C₄×C₁₁	1	2	yes	—
430	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
431	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
432	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
433	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
434	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	2	4	no	—
437	C₈	—	2	8	no	—
438	C₂²	—	2	8	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	4	8	no	—
445	C₂²	C₂×C₁₁×#117	1	4	yes	—
446	C₂²	C₂×C₁₁×#117	1	2	yes	—
447	C₂²	C₂×C₁₁×#131	1	2	yes	—
448	C₂²	C₁₁×#568	1	2	yes	—
449	C₂²	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
450	C₄	—	2	4	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	2	4	no	—
456	C₄	C₂×C₁₁×#117	1	2	yes	—
457	C₄	C₂×C₁₁×#117	1	4	yes	—
458	C₄	C₂×C₁₁×#131	1	4	yes	—
459	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
460	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
461	C₂	—	2	4	no	—
462	C₂	—	4	4	no	—
463	C₂	C₁₁×#2925	1	4	yes	direct product factor
464	C₂	C₂²×C₁₁×#117	1	1	yes	characteristic
465	C₂	C₂²×C₁₁×#131	1	1	yes	characteristic
466	C₂	C₂×C₁₁×#568	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2925	C₂	direct (N × H)
3. C₂×C₁₁×#433	C₂	semidirect
4. C₂×C₁₁×#432	C₂	semidirect
5. C₂×C₁₁×#431	C₂	semidirect
6. C₂×C₁₁×#423	C₂	semidirect
7. C₂²×C₁₁×C₄⋊C₈	C₂	semidirect
9. C₂×C₁₁×#405	C₂	semidirect
25. C₁₁×#433	C₂²	semidirect
26. C₁₁×#432	C₂²	semidirect
27. C₁₁×#431	C₂²	semidirect
28. C₁₁×#423	C₂²	semidirect
34. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
38. C₁₁×#405	C₂²	semidirect
98. C₂×#2925	C₁₁	direct (N × H)
161. #2925	C₂×C₁₁	direct (N × H)
162. C₂×#433	C₂×C₁₁	semidirect
163. C₂×#432	C₂×C₁₁	semidirect
164. C₂×#431	C₂×C₁₁	semidirect
165. C₂×#423	C₂×C₁₁	semidirect
166. C₂²×C₄⋊C₈	C₂×C₁₁	semidirect
168. C₂×#405	C₂×C₁₁	semidirect
229. #433	C₂²×C₁₁	semidirect
230. #432	C₂²×C₁₁	semidirect
231. #431	C₂²×C₁₁	semidirect
232. #423	C₂²×C₁₁	semidirect
238. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
242. #405	C₂²×C₁₁	semidirect
327. C₂×C₁₁	#2925	direct (N × H)
392. C₁₁	C₂×#2925	direct (N × H)
463. C₂	C₁₁×#2925	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×C₄×C₁₁×#41	2
C₁₁×#2925	2
C₂×C₁₁×#433	2
C₂×C₁₁×#432	2
C₂×C₁₁×#431	2
C₂×C₁₁×#423	2
C₂²×C₁₁×C₄⋊C₈	2
C₂×C₁₁×#408	2
C₂×C₁₁×#405	2
C₂×#2925	11

Subgroups — C2×C11×#2925 #14637315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₁×#2925 #14637315