Subgroups — C₂×#13066900 #14719352

Order 2816.

982 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622538	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₁₁⋊C₈	C₂	1	1	yes	maximal, characteristic
3	#13066900	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622092	C₂	1	2	yes	maximal, complemented
5	C₂×C₈×C₁₁⋊C₈	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂³×C₁₁⋊C₈	C₄	1	2	yes	—
9	C₁₁×#431	C₄	1	4	yes	—
10	C₁₁×#431	C₂²	1	4	yes	—
11	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
12	C₂×C₁₁×C₂²⋊C₈	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
14	C₂×C₂²⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
15	#10622538	C₄	1	4	yes	—
16	#10622538	C₂²	1	4	yes	—
17	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
18	C₂×C₄×C₁₁⋊C₈	C₄	1	2	yes	—
19	C₂×C₄×C₁₁⋊C₈	C₄	1	4	yes	—
20	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	4	yes	—
23	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
24	#10622092	C₂²	1	8	yes	complemented
25	C₈×C₁₁⋊C₈	C₂²	1	8	yes	complemented
26	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
36	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
37	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
38	C₂²×C₁₁⋊C₈	C₈	1	16	yes	complemented
39	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
40	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
42	C₂²×C₁₁⋊C₈	C₂×C₄	1	8	yes	—
43	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
44	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
45	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
46	C₄×C₈×C₁₁	C₂³	1	4	yes	—
47	C₂²⋊(C₁₁⋊C₈)	C₂×C₄	1	8	yes	—
48	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	8	yes	—
49	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
50	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
51	C₄×C₁₁⋊C₈	C₂×C₄	1	8	yes	—
52	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
53	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
54	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
55	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
56	C₂×#1450	—	11	1	no	maximal, Sylow
57	C₂⁴×C₁₁	C₄²	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	—	2	4	no	—
59	C₂²×C₄×C₁₁	—	2	4	no	—
60	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
63	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
64	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
65	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×C₈	1	8	yes	—
67	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
68	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
69	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
71	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	—	2	8	no	—
74	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
75	C₄²×C₁₁	C₄²	1	2	yes	—
76	C₄²×C₁₁	C₄²	1	2	yes	—
77	C₄²×C₁₁	C₄²	1	2	yes	—
78	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
79	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
82	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
83	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
84	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
85	C₂×C₁₁⋊C₈	—	2	8	no	—
86	C₂×C₁₁⋊C₈	C₂×C₈	1	8	yes	—
87	C₂×C₁₁⋊C₈	C₂×C₈	1	8	yes	—
88	C₂×C₁₁⋊C₈	C₂×C₈	1	32	yes	complemented
89	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
90	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
91	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
92	C₂×#431	—	11	1	no	—
93	C₂×#431	D₁₁	1	1	yes	characteristic
94	C₂²×C₄×C₈	—	11	1	no	—
95	#1450	—	11	8	no	—
96	C₂×#322	—	11	2	no	—
97	C₂×C₈²	—	11	2	no	—
98	C₂³×C₁₁	—	2	2	no	—
99	C₂³×C₁₁	—	2	2	no	—
100	C₂³×C₁₁	C₄×C₈	1	4	yes	—
101	C₂³×C₁₁	C₂×C₄²	1	2	yes	—
102	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
103	C₂×C₄×C₁₁	—	2	2	no	—
104	C₂×C₄×C₁₁	—	2	2	no	—
105	C₂×C₄×C₁₁	—	2	4	no	—
106	C₂×C₄×C₁₁	—	2	4	no	—
107	C₂×C₄×C₁₁	—	2	4	no	—
108	C₂×C₄×C₁₁	—	2	4	no	—
109	C₂×C₄×C₁₁	C₄×C₈	1	8	yes	—
110	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
111	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
112	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
113	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
114	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
115	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
116	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
118	C₂×C₄×C₁₁	C₂²×C₈	1	8	yes	—
119	C₂×C₄×C₁₁	#131	1	4	yes	—
120	C₂×C₄×C₁₁	#131	1	4	yes	—
121	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
122	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
124	C₈×C₁₁	—	2	8	no	—
125	C₁₁⋊C₈	—	2	8	no	—
126	C₁₁⋊C₈	C₂²×C₈	1	8	yes	—
127	C₁₁⋊C₈	C₂²×C₈	1	8	yes	—
128	C₂³×C₈	—	11	2	no	—
129	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
130	#431	—	11	4	no	—
131	#431	—	11	4	no	—
132	#431	Dic₁₁	1	4	yes	—
133	#431	C₂×D₁₁	1	4	yes	—
134	C₂×C₄⋊C₈	—	11	2	no	—
135	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
136	C₂×C₂²⋊C₈	—	11	2	no	—
137	C₂×C₂²⋊C₈	Dic₁₁	1	2	yes	—
138	C₂×C₄×C₈	—	11	4	no	—
139	C₂×C₄×C₈	—	11	1	no	—
140	C₂×C₄×C₈	—	11	1	no	—
141	C₂×C₄×C₈	—	11	2	no	—
142	C₂×C₄×C₈	—	11	2	no	—
143	C₂×C₄×C₈	—	11	4	no	—
144	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
145	#322	—	11	8	no	—
146	C₈²	—	11	8	no	—
147	C₂²×C₁₁	—	2	2	no	—
148	C₂²×C₁₁	—	2	2	no	—
149	C₂²×C₁₁	—	2	8	no	—
150	C₂²×C₁₁	C₂×C₄×C₈	1	4	yes	—
151	C₂²×C₁₁	C₂×C₄×C₈	1	2	yes	—
152	C₂²×C₁₁	#405	1	2	yes	—
153	C₂²×C₁₁	#405	1	2	yes	—
154	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
155	C₄×C₁₁	—	2	2	no	—
156	C₄×C₁₁	—	2	2	no	—
157	C₄×C₁₁	C₂×C₄×C₈	1	2	yes	—
158	C₄×C₁₁	C₂×C₄×C₈	1	4	yes	—
159	C₄×C₁₁	#405	1	2	yes	—
160	C₄×C₁₁	#405	1	2	yes	—
161	C₄×C₁₁	C₂³×C₈	1	2	yes	—
162	C₄×C₁₁	C₂×#131	1	2	yes	—
163	C₄×C₁₁	C₂×#131	1	2	yes	—
164	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
165	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
166	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
167	C₂²×C₈	—	11	16	no	—
168	C₂²×C₈	—	11	2	no	—
169	C₂²×C₈	—	11	2	no	—
170	C₂²×C₈	—	11	8	no	—
171	C₂²×C₈	—	11	4	no	—
172	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
173	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
174	C₂×C₄²	C₄×D₁₁	1	2	yes	—
175	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
176	C₂×C₄²	C₄×D₁₁	1	2	yes	—
177	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
178	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
179	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
180	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
181	C₄⋊C₈	—	11	8	no	—
182	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
183	C₂²⋊C₈	—	11	8	no	—
184	C₂²⋊C₈	C₂×Dic₁₁	1	8	yes	—
185	C₄×C₈	—	11	8	no	—
186	C₄×C₈	—	11	2	no	—
187	C₄×C₈	—	11	2	no	—
188	C₄×C₈	—	11	4	no	—
189	C₄×C₈	—	11	2	no	—
190	C₄×C₈	—	11	4	no	—
191	C₄×C₈	—	11	2	no	—
192	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
193	C₄×C₈	C₂²×D₁₁	1	4	yes	—
194	C₂×C₁₁	—	2	4	no	—
195	C₂×C₁₁	#1450	1	4	yes	complemented
196	C₂×C₁₁	C₂²×C₄×C₈	1	1	yes	characteristic
197	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
198	C₂×C₁₁	C₂×#405	1	1	yes	characteristic
199	C₂⁴	C₄×Dic₁₁	1	1	yes	characteristic
200	C₂²×C₄	—	2	4	no	—
201	C₂²×C₄	—	2	4	no	—
202	C₂²×C₄	C₈×D₁₁	1	8	yes	—
203	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
204	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
205	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
206	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
207	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
208	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
209	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
210	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
211	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
212	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
213	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
214	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
215	C₂×C₈	—	2	8	no	—
216	C₂×C₈	—	11	8	no	—
217	C₂×C₈	—	11	8	no	—
218	C₂×C₈	—	11	32	no	—
219	C₂×C₈	—	11	4	no	—
220	C₂×C₈	—	11	4	no	—
221	C₂×C₈	—	11	8	no	—
222	C₂×C₈	—	22	8	no	—
223	C₂×C₈	C₂²×Dic₁₁	1	8	yes	—
224	C₄²	C₄×Dic₁₁	1	2	yes	—
225	C₄²	C₄×Dic₁₁	1	2	yes	—
226	C₄²	C₄×Dic₁₁	1	2	yes	—
227	C₄²	C₂×C₄×D₁₁	1	2	yes	—
228	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
229	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
230	C₄²	C₂×C₄×D₁₁	1	2	yes	—
231	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
232	C₄²	C₂²×Dic₁₁	1	2	yes	—
233	C₄²	C₂³×D₁₁	1	1	yes	characteristic
234	C₁₁	C₂×#1450	1	1	yes	characteristic, complemented, Sylow
235	C₂³	—	2	2	no	—
236	C₂³	—	2	2	no	—
237	C₂³	C₈×Dic₁₁	1	4	yes	—
238	C₂³	C₂×C₄×Dic₁₁	1	2	yes	—
239	C₂³	C₂×C₄×Dic₁₁	1	1	yes	characteristic
240	C₂×C₄	—	2	2	no	—
241	C₂×C₄	—	2	2	no	—
242	C₂×C₄	—	2	4	no	—
243	C₂×C₄	—	2	4	no	—
244	C₂×C₄	—	2	4	no	—
245	C₂×C₄	—	2	4	no	—
246	C₂×C₄	C₈×Dic₁₁	1	8	yes	—
247	C₂×C₄	C₈×Dic₁₁	1	4	yes	—
248	C₂×C₄	C₂×C₈×D₁₁	1	8	yes	—
249	C₂×C₄	C₂×C₈×D₁₁	1	4	yes	—
250	C₂×C₄	#66960	1	4	yes	—
251	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
252	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
253	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
254	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
255	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
256	C₂×C₄	C₂×C₄×Dic₁₁	1	2	yes	—
257	C₂×C₄	#67001	1	4	yes	—
258	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
259	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
260	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
261	C₈	—	2	8	no	—
262	C₈	—	11	8	no	—
263	C₈	—	11	8	no	—
264	C₈	—	22	8	no	—
265	C₂²	—	2	2	no	—
266	C₂²	—	2	2	no	—
267	C₂²	—	2	8	no	—
268	C₂²	#10622610	1	2	yes	—
269	C₂²	C₂×C₈×Dic₁₁	1	4	yes	—
270	C₂²	C₂×C₈×Dic₁₁	1	2	yes	—
271	C₂²	#10622735	1	2	yes	—
272	C₂²	C₂²×C₄×Dic₁₁	1	1	yes	characteristic
273	C₄	—	2	2	no	—
274	C₄	—	2	2	no	—
275	C₄	#10622610	1	2	yes	—
276	C₄	C₂×C₈×Dic₁₁	1	2	yes	—
277	C₄	C₂×C₈×Dic₁₁	1	4	yes	—
278	C₄	#10622735	1	2	yes	—
279	C₄	C₂²×C₈×D₁₁	1	2	yes	—
280	C₄	C₂×#66960	1	2	yes	—
281	C₄	C₂×#67001	1	2	yes	—
282	C₂	—	2	4	no	—
283	C₂	#13066900	1	4	yes	direct product factor
284	C₂	C₂²×C₈×Dic₁₁	1	1	yes	characteristic
285	C₂	C₂×#10622610	1	1	yes	characteristic
286	C₂	C₂×#10622735	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂³×C₁₁	C₂×C₄²
prime radical	C₂⁴×C₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	C₂×#1450
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13066900	C₂	direct (N × H)
4. C₂×#10622092	C₂	semidirect
5. C₂×C₈×C₁₁⋊C₈	C₂	semidirect
24. #10622092	C₂²	semidirect
25. C₈×C₁₁⋊C₈	C₂²	semidirect
38. C₂²×C₁₁⋊C₈	C₈	semidirect
88. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
195. C₂×C₁₁	#1450	semidirect
234. C₁₁	C₂×#1450	semidirect
283. C₂	#13066900	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×#10622538	2
C₂²×C₄×C₁₁⋊C₈	2
#13066900	2
C₂×#10622092	2
C₂×C₈×C₁₁⋊C₈	2
C₂×C₁₁×#431	2
C₂×#1450	11

Subgroups — C2×#13066900 #14719352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066900 #14719352