Subgroups — C₂×#13069365 #14757183

Order 2816.

974 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66883	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622612	C₂	1	2	yes	maximal
3	C₂²×C₈×Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	#13069365	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10622170	C₂	1	2	yes	maximal
6	C₂×C₁₁×#427	C₂	1	1	yes	maximal, characteristic
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×#117	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
10	C₂²×#4318	C₂²	1	2	yes	—
11	C₂³×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
12	C₁₁×#427	C₄	1	4	yes	complemented
13	C₁₁×#427	C₂²	1	4	yes	—
14	C₂×C₁₁×#107	C₄	1	2	yes	complemented
15	C₂×C₁₁×#106	C₄	1	2	yes	complemented
16	C₂×#66883	—	2	4	no	—
17	C₂×#66883	C₂²	1	4	yes	—
18	C₂×C₈×Dic₁₁	—	2	4	no	—
19	C₂×C₈×Dic₁₁	C₂²	1	4	yes	—
20	#10622612	—	2	4	no	—
21	#10622612	C₂²	1	8	yes	—
22	C₂×C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
23	#10622170	C₂²	1	8	yes	—
24	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
25	C₂³×Dic₁₁	—	2	1	no	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
29	C₂²×C₈×C₁₁	D₄	1	4	yes	—
30	C₂²×C₈×C₁₁	Q₈	1	4	yes	—
31	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
32	C₁₁×#117	—	2	2	no	—
33	C₁₁×#117	—	2	2	no	—
34	C₁₁×#117	C₂×C₄	1	4	yes	—
35	C₁₁×#117	C₂³	1	4	yes	—
36	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
37	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
38	C₂×C₄²×C₁₁	—	2	2	no	—
39	C₂×C₄×Dic₁₁	—	2	2	no	—
40	C₂×C₄×Dic₁₁	—	2	1	no	—
41	C₂×C₄×Dic₁₁	Q₈	1	4	yes	—
42	C₂×C₄×Dic₁₁	C₂³	1	2	yes	—
43	C₂×#4318	—	2	2	no	—
44	C₂×#4318	—	2	4	no	—
45	C₂×#4318	—	2	4	no	—
46	C₂×#4318	C₂³	1	4	yes	—
47	C₂²×C₁₁⋊C₈	—	2	2	no	—
48	C₂²×C₁₁⋊C₈	—	2	2	no	—
49	C₂²×C₁₁⋊C₈	—	2	2	no	—
50	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
51	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
52	C₂²×C₁₁⋊C₈	C₂³	1	2	yes	—
53	C₁₁×#107	C₂×C₄	1	8	yes	complemented
54	C₁₁×#106	C₂×C₄	1	8	yes	complemented
55	#66883	—	2	8	no	—
56	C₈×Dic₁₁	—	2	8	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	16	no	—
58	C₂×#1945	—	11	1	no	maximal, Sylow
59	C₂⁴×C₁₁	#41	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	—	2	4	no	—
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
68	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
69	C₂²×C₄×C₁₁	#41	1	2	yes	—
70	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
71	C₂²×Dic₁₁	—	2	8	no	—
72	C₂²×Dic₁₁	—	2	4	no	—
73	C₂²×Dic₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
75	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
76	C₂×C₈×C₁₁	C₄⋊C₄	1	8	yes	—
77	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
78	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
80	C₂×C₈×C₁₁	C₂×Q₈	1	4	yes	—
81	C₁₁×C₄⋊C₄	—	2	4	no	—
82	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
83	C₁₁×C₂²⋊C₄	—	2	4	no	—
84	C₁₁×C₂²⋊C₄	—	2	4	no	—
85	C₄²×C₁₁	—	2	4	no	—
86	C₄²×C₁₁	—	2	4	no	—
87	C₄×Dic₁₁	—	2	4	no	—
88	C₄×Dic₁₁	—	2	2	no	—
89	C₄×Dic₁₁	C₂×Q₈	1	4	yes	—
90	#4318	—	2	4	no	—
91	#4318	—	2	4	no	—
92	#4318	—	4	4	no	—
93	C₂×C₁₁⋊C₈	—	2	4	no	—
94	C₂×C₁₁⋊C₈	—	2	4	no	—
95	C₂×C₁₁⋊C₈	—	2	2	no	—
96	C₂×C₁₁⋊C₈	—	2	4	no	—
97	C₂×C₁₁⋊C₈	—	2	2	no	—
98	C₂×C₁₁⋊C₈	—	4	4	no	—
99	C₂×C₁₁⋊C₈	C₂×D₄	1	4	yes	—
100	C₂²×#108	—	11	1	no	—
101	C₂×#427	D₁₁	1	1	yes	characteristic
102	C₂×#424	—	11	2	no	—
103	C₂²×C₄×C₈	—	11	1	no	—
104	#1945	—	11	8	no	—
105	C₂×#339	—	11	2	no	—
106	C₂³×C₁₁	—	2	4	no	—
107	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
108	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
109	C₂³×C₁₁	C₂²⋊Q₈	1	2	yes	—
110	C₂³×C₁₁	#125	1	2	yes	—
111	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
112	C₂×C₄×C₁₁	—	2	8	no	—
113	C₂×C₄×C₁₁	—	4	8	no	—
114	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
115	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
116	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
117	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
119	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
120	C₂×C₄×C₁₁	#121	1	2	yes	—
121	C₂×C₄×C₁₁	#121	1	2	yes	—
122	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
123	C₂×C₄×C₁₁	#125	1	2	yes	—
124	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
125	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
126	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
131	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
132	C₂×Dic₁₁	—	2	8	no	—
133	C₂×Dic₁₁	—	2	16	no	—
134	C₂×Dic₁₁	—	2	4	no	—
135	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
136	C₈×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
137	C₁₁⋊C₈	—	2	4	no	—
138	C₁₁⋊C₈	—	4	4	no	—
139	C₂²×M₁₆	—	11	2	no	—
140	C₂³×C₈	—	11	1	no	—
141	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
142	C₂×#117	C₂×D₁₁	1	2	yes	—
143	C₂²×C₄²	—	11	1	no	—
144	C₂×#108	—	11	4	no	—
145	C₂×#108	—	22	4	no	—
146	#427	Dic₁₁	1	4	yes	complemented
147	#427	C₂×D₁₁	1	4	yes	—
148	C₂×#107	Dic₁₁	1	2	yes	complemented
149	C₂×#106	Dic₁₁	1	2	yes	complemented
150	#424	—	11	8	no	—
151	#424	—	22	4	no	—
152	C₂×C₄⋊C₈	—	22	4	no	—
153	C₂×C₄×C₈	—	11	4	no	—
154	C₂×C₄×C₈	—	22	4	no	—
155	#339	—	11	8	no	—
156	C₂²×C₁₁	—	2	2	no	—
157	C₂²×C₁₁	—	2	2	no	—
158	C₂²×C₁₁	—	2	4	no	—
159	C₂²×C₁₁	—	2	4	no	—
160	C₂²×C₁₁	#389	1	2	yes	—
161	C₂²×C₁₁	#389	1	2	yes	—
162	C₂²×C₁₁	#443	1	4	yes	—
163	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
164	C₂²×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
165	C₂²×C₁₁	C₂×#125	1	1	yes	characteristic
166	C₄×C₁₁	—	4	8	no	—
167	C₄×C₁₁	#389	1	2	yes	—
168	C₄×C₁₁	#389	1	2	yes	—
169	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
171	C₄×C₁₁	C₂×#121	1	1	yes	characteristic
172	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
173	Dic₁₁	—	2	8	no	—
174	C₂³×C₄	—	22	1	no	—
175	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
176	C₂×M₁₆	—	11	4	no	—
177	C₂×M₁₆	—	22	2	no	—
178	C₂×M₁₆	—	22	4	no	—
179	C₂×M₁₆	—	22	4	no	—
180	C₂²×C₈	—	11	2	no	—
181	C₂²×C₈	—	11	2	no	—
182	C₂²×C₈	—	11	2	no	—
183	C₂²×C₈	—	22	2	no	—
184	C₂²×C₈	—	22	2	no	—
185	C₂²×C₈	—	22	2	no	—
186	C₂²×C₈	Dic₂₂	1	4	yes	—
187	C₂²×C₈	D₄₄	1	4	yes	—
188	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
189	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
190	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
191	C₂²×C₈	C₂²×D₁₁	1	2	yes	—
192	#117	—	2	2	no	—
193	#117	—	2	2	no	—
194	#117	C₂×Dic₁₁	1	4	yes	—
195	#117	C₂²×D₁₁	1	4	yes	—
196	C₂×C₄⋊C₄	C₂×Dic₁₁	1	4	yes	—
197	C₂×C₂²⋊C₄	—	2	2	no	—
198	C₂×C₄²	—	2	2	no	—
199	C₂×C₄²	—	11	4	no	—
200	C₂×C₄²	—	11	2	no	—
201	C₂×C₄²	—	22	2	no	—
202	C₂×C₄²	—	22	1	no	—
203	#108	—	22	8	no	—
204	#107	C₂×Dic₁₁	1	8	yes	complemented
205	#106	C₂×Dic₁₁	1	8	yes	complemented
206	C₄⋊C₈	—	22	16	no	—
207	C₄×C₈	—	22	8	no	—
208	C₂×C₁₁	—	2	1	no	—
209	C₂×C₁₁	—	2	1	no	—
210	C₂×C₁₁	—	2	2	no	—
211	C₂×C₁₁	#1945	1	4	yes	complemented
212	C₂×C₁₁	C₂×#389	1	1	yes	characteristic
213	C₂×C₁₁	C₂×#443	1	2	yes	—
214	C₂⁴	#4341	1	1	yes	characteristic
215	C₂²×C₄	—	2	4	no	—
216	C₂²×C₄	—	22	8	no	—
217	C₂²×C₄	—	22	4	no	—
218	C₂²×C₄	—	22	2	no	—
219	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
220	C₂²×C₄	C₂×D₄₄	1	2	yes	—
221	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
222	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
223	C₂²×C₄	#4341	1	1	yes	characteristic
224	C₂²×C₄	Q₈×D₁₁	1	2	yes	—
225	C₂²×C₄	#4343	1	2	yes	—
226	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
227	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
228	C₂²×C₄	C₂³×D₁₁	1	1	yes	characteristic
229	M₁₆	—	22	4	no	—
230	M₁₆	—	22	4	no	—
231	M₁₆	—	44	4	no	—
232	C₂×C₈	—	11	4	no	—
233	C₂×C₈	—	22	4	no	—
234	C₂×C₈	—	22	4	no	—
235	C₂×C₈	—	22	2	no	—
236	C₂×C₈	—	22	2	no	—
237	C₂×C₈	—	22	4	no	—
238	C₂×C₈	—	44	4	no	—
239	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
240	C₂×C₈	C₄⋊Dic₁₁	1	4	yes	—
241	C₂×C₈	C₄⋊Dic₁₁	1	8	yes	—
242	C₂×C₈	C₂×Dic₂₂	1	4	yes	—
243	C₂×C₈	C₂×D₄₄	1	4	yes	—
244	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
245	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
246	C₄⋊C₄	—	2	4	no	—
247	C₄⋊C₄	C₂²×Dic₁₁	1	8	yes	—
248	C₂²⋊C₄	—	2	4	no	—
249	C₂²⋊C₄	—	2	4	no	—
250	C₄²	—	2	4	no	—
251	C₄²	—	2	4	no	—
252	C₄²	—	11	4	no	—
253	C₄²	—	22	4	no	—
254	C₄²	—	22	2	no	—
255	C₁₁	C₂×#1945	1	1	yes	characteristic, complemented, Sylow
256	C₂³	—	2	4	no	—
257	C₂³	#66943	1	2	yes	—
258	C₂³	#66950	1	2	yes	—
259	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
260	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
261	C₂³	C₂×#4341	1	1	yes	characteristic
262	C₂×C₄	—	2	8	no	—
263	C₂×C₄	—	4	8	no	—
264	C₂×C₄	—	22	8	no	—
265	C₂×C₄	—	22	16	no	—
266	C₂×C₄	—	22	4	no	—
267	C₂×C₄	#66941	1	2	yes	—
268	C₂×C₄	#66941	1	2	yes	—
269	C₂×C₄	#66943	1	2	yes	—
270	C₂×C₄	#66948	1	2	yes	—
271	C₂×C₄	#66948	1	2	yes	—
272	C₂×C₄	#66950	1	2	yes	—
273	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
274	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
275	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
276	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
277	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
278	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
279	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
280	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
281	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
282	C₂×C₄	C₂×Q₈×D₁₁	1	1	yes	characteristic
283	C₂×C₄	C₂×#4343	1	1	yes	characteristic
284	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
285	C₈	—	22	4	no	—
286	C₈	—	44	4	no	—
287	C₈	C₂×C₄⋊Dic₁₁	1	4	yes	—
288	C₈	C₂×C₄⋊Dic₁₁	1	4	yes	—
289	C₂²	—	2	2	no	—
290	C₂²	—	2	2	no	—
291	C₂²	—	2	4	no	—
292	C₂²	—	2	4	no	—
293	C₂²	#10622598	1	2	yes	—
294	C₂²	#10622598	1	2	yes	—
295	C₂²	#10622809	1	4	yes	—
296	C₂²	C₂×#66943	1	1	yes	characteristic
297	C₂²	C₂×#66950	1	1	yes	characteristic
298	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
299	C₄	—	4	8	no	—
300	C₄	—	22	8	no	—
301	C₄	#10622598	1	2	yes	—
302	C₄	#10622598	1	2	yes	—
303	C₄	C₂×#66941	1	1	yes	characteristic
304	C₄	C₂×#66948	1	1	yes	characteristic
305	C₄	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
306	C₄	C₂×Q₈×Dic₁₁	1	1	yes	characteristic
307	C₂	—	2	1	no	—
308	C₂	—	2	1	no	—
309	C₂	—	2	2	no	—
310	C₂	#13069365	1	4	yes	direct product factor
311	C₂	C₂×#10622598	1	1	yes	characteristic
312	C₂	C₂×#10622809	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₁
Fitting	C₂×C₁₁×#427	C₂
socle	C₂³×C₁₁	C₄×D₄
prime radical	C₂⁴×C₁₁	#41
cosocle	C₂²×C₄×C₁₁	C₂⁴
hypercenter	C₂×#427	D₁₁
hypocenter	C₁₁	C₂×#1945
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
4. #13069365	C₂	direct (N × H)
12. C₁₁×#427	C₄	semidirect
14. C₂×C₁₁×#107	C₄	semidirect
15. C₂×C₁₁×#106	C₄	semidirect
53. C₁₁×#107	C₂×C₄	semidirect
54. C₁₁×#106	C₂×C₄	semidirect
146. #427	Dic₁₁	semidirect
148. C₂×#107	Dic₁₁	semidirect
149. C₂×#106	Dic₁₁	semidirect
204. #107	C₂×Dic₁₁	semidirect
205. #106	C₂×Dic₁₁	semidirect
211. C₂×C₁₁	#1945	semidirect
255. C₁₁	C₂×#1945	semidirect
310. C₂	#13069365	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#66883	2
C₂×#10622612	2
C₂²×C₈×Dic₁₁	2
#13069365	2
C₂×#10622170	2
C₂×C₁₁×#427	2
C₂×#1945	11

Subgroups — C2×#13069365 #14757183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13069365 #14757183