Subgroups — C₂×#13066726 #14668697

Order 2816.

614 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#66876	C₂	1	1	yes	maximal, characteristic
2	C₂²×#66882	C₂	1	1	yes	maximal, characteristic
3	#13066726	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×M₁₆	—	2	1	no	—
6	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₁₁	—	2	1	no	—
8	C₂×C₁₁×#108	—	2	1	no	—
9	C₂×C₁₁×#108	—	2	2	no	—
10	C₂×C₁₁×#108	C₄	1	4	yes	complemented
11	C₂×C₁₁×#108	C₂²	1	2	yes	—
12	C₂×#66882	—	2	1	no	—
13	C₂×#66882	—	2	1	no	—
14	C₂×#66882	—	2	1	no	—
15	C₂×#66882	C₄	1	2	yes	—
16	C₂×#66882	C₄	1	2	yes	—
17	C₂×#66882	C₂²	1	2	yes	—
18	C₂×#66876	—	2	2	no	—
19	C₂×#66876	—	2	1	no	—
20	C₂×#66876	C₄	1	4	yes	complemented
21	C₂×#66876	C₂²	1	2	yes	—
22	C₂²×C₁₁⋊C₁₆	—	2	1	no	—
23	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
24	C₂³×Dic₁₁	—	4	1	no	—
25	C₂×C₁₁×M₁₆	—	2	4	no	—
26	C₂×C₁₁×M₁₆	—	2	2	no	—
27	C₂×C₁₁×M₁₆	—	4	1	no	—
28	C₂×C₁₁×M₁₆	—	4	2	no	—
29	C₂²×C₈×C₁₁	—	4	1	no	—
30	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
31	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
34	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
35	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	D₄	1	2	yes	—
38	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
39	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
40	C₂×C₄⋊Dic₁₁	—	2	2	no	—
41	C₂×C₄⋊Dic₁₁	—	2	2	no	—
42	C₂×C₄⋊Dic₁₁	—	2	2	no	—
43	C₂×C₄⋊Dic₁₁	—	4	1	no	—
44	C₂×C₄⋊Dic₁₁	—	4	1	no	—
45	C₂×C₄⋊Dic₁₁	—	4	1	no	—
46	C₁₁×#108	—	2	4	no	—
47	C₁₁×#108	—	2	2	no	—
48	C₁₁×#108	C₂×C₄	1	4	yes	complemented
49	#66882	—	2	2	no	—
50	#66882	—	2	2	no	—
51	#66882	—	2	2	no	—
52	#66882	C₂×C₄	1	4	yes	—
53	#66876	—	2	4	no	—
54	#66876	—	2	2	no	—
55	#66876	C₂×C₄	1	4	yes	complemented
56	C₂×C₁₁⋊C₁₆	—	2	4	no	—
57	C₂×C₁₁⋊C₁₆	—	2	2	no	—
58	C₂×#1387	—	11	1	no	maximal, Sylow
59	C₂⁴×C₁₁	SD₁₆	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	SD₁₆	1	2	yes	—
68	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
69	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂²×Dic₁₁	—	4	2	no	—
71	C₂²×Dic₁₁	—	4	2	no	—
72	C₂²×Dic₁₁	—	4	2	no	—
73	C₂²×Dic₁₁	—	8	4	no	—
74	C₁₁×M₁₆	—	2	4	no	—
75	C₁₁×M₁₆	—	4	4	no	—
76	C₁₁×M₁₆	—	4	2	no	—
77	C₂×C₈×C₁₁	—	4	4	no	—
78	C₂×C₈×C₁₁	—	4	2	no	—
79	C₂×C₈×C₁₁	C₄²	1	2	yes	—
80	C₂×C₈×C₁₁	C₄²	1	2	yes	—
81	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
82	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
83	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
86	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
87	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
88	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
89	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
90	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
91	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
95	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
96	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
97	C₄⋊Dic₁₁	—	2	4	no	—
98	C₄⋊Dic₁₁	—	4	2	no	—
99	C₄⋊Dic₁₁	—	4	2	no	—
100	C₄⋊Dic₁₁	—	4	2	no	—
101	C₁₁⋊C₁₆	—	2	4	no	—
102	C₂²×M₃₂	—	11	1	no	—
103	C₂²×#108	D₁₁	1	1	yes	characteristic
104	C₂²×#107	—	11	1	no	—
105	#1387	—	11	4	no	—
106	C₂³×C₁₁	—	2	2	no	—
107	C₂³×C₁₁	—	2	2	no	—
108	C₂³×C₁₁	#102	1	1	yes	characteristic
109	C₂³×C₁₁	#102	1	1	yes	characteristic
110	C₂³×C₁₁	#103	1	2	yes	—
111	C₂³×C₁₁	#106	1	2	yes	—
112	C₂³×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#95	1	2	yes	—
114	C₂×C₄×C₁₁	#95	1	2	yes	—
115	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
116	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
117	C₂×C₄×C₁₁	#102	1	2	yes	—
118	C₂×C₄×C₁₁	#102	1	2	yes	—
119	C₂×C₄×C₁₁	#103	1	2	yes	—
120	C₂×C₄×C₁₁	#103	1	2	yes	—
121	C₂×C₄×C₁₁	#103	1	2	yes	—
122	C₂×C₄×C₁₁	#106	1	2	yes	—
123	C₂×C₄×C₁₁	#107	1	2	yes	—
124	C₂×C₄×C₁₁	#107	1	2	yes	—
125	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
129	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
130	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
131	C₂×Dic₁₁	—	4	4	no	—
132	C₂×Dic₁₁	—	8	4	no	—
133	C₂×Dic₁₁	—	8	4	no	—
134	C₂×Dic₁₁	—	8	4	no	—
135	C₈×C₁₁	—	4	4	no	—
136	C₈×C₁₁	#95	1	2	yes	—
137	C₈×C₁₁	#95	1	2	yes	—
138	C₈×C₁₁	C₂×C₄²	1	1	yes	characteristic
139	C₈×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂²×M₁₆	—	2	1	no	—
143	C₂³×C₈	C₂×D₁₁	1	1	yes	characteristic
144	C₂²×C₄⋊C₄	—	22	1	no	—
145	C₂×M₃₂	—	11	2	no	—
146	C₂×M₃₂	—	11	4	no	—
147	C₂×M₃₂	—	22	1	no	—
148	C₂×M₃₂	—	22	2	no	—
149	C₂²×C₁₆	—	22	1	no	—
150	C₂×#108	—	2	1	no	—
151	C₂×#108	—	2	2	no	—
152	C₂×#108	Dic₁₁	1	4	yes	complemented
153	C₂×#108	C₂×D₁₁	1	2	yes	—
154	C₂×#107	—	11	2	no	—
155	C₂×#107	—	11	2	no	—
156	C₂×#107	—	11	2	no	—
157	C₂×#107	—	22	1	no	—
158	C₂×#107	—	22	1	no	—
159	C₂×#107	—	22	1	no	—
160	C₂²×C₁₁	—	2	1	no	—
161	C₂²×C₁₁	—	2	1	no	—
162	C₂²×C₁₁	—	2	1	no	—
163	C₂²×C₁₁	—	2	1	no	—
164	C₂²×C₁₁	—	2	4	no	—
165	C₂²×C₁₁	—	2	4	no	—
166	C₂²×C₁₁	#340	1	2	yes	—
167	C₂²×C₁₁	#340	1	2	yes	—
168	C₂²×C₁₁	#361	1	2	yes	—
169	C₂²×C₁₁	#362	1	2	yes	—
170	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
171	C₂²×C₁₁	C₂×#103	1	1	yes	characteristic
172	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
173	C₄×C₁₁	#340	1	2	yes	—
174	C₄×C₁₁	#340	1	2	yes	—
175	C₄×C₁₁	C₂×#95	1	1	yes	characteristic
176	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
177	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
178	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
179	Dic₁₁	—	8	4	no	—
180	C₂³×C₄	—	44	1	no	—
181	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
182	C₂×M₁₆	—	2	4	no	—
183	C₂×M₁₆	—	2	2	no	—
184	C₂×M₁₆	—	4	1	no	—
185	C₂×M₁₆	—	4	2	no	—
186	C₂²×C₈	—	4	1	no	—
187	C₂²×C₈	Dic₂₂	1	2	yes	—
188	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
189	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
190	C₂²×C₈	C₄×D₁₁	1	2	yes	—
191	C₂²×C₈	D₄₄	1	1	yes	characteristic
192	C₂²×C₈	D₄₄	1	1	yes	characteristic
193	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
194	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
195	C₂²×C₈	C₂²⋊D₁₁	1	2	yes	—
196	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
197	C₂×C₄⋊C₄	—	22	2	no	—
198	C₂×C₄⋊C₄	—	22	2	no	—
199	C₂×C₄⋊C₄	—	22	2	no	—
200	C₂×C₄⋊C₄	—	44	1	no	—
201	C₂×C₄⋊C₄	—	44	1	no	—
202	C₂×C₄⋊C₄	—	44	1	no	—
203	M₃₂	—	11	4	no	—
204	M₃₂	—	22	4	no	—
205	M₃₂	—	22	2	no	—
206	C₂×C₁₆	—	22	4	no	—
207	C₂×C₁₆	—	22	2	no	—
208	#108	—	2	4	no	—
209	#108	—	2	2	no	—
210	#108	C₂×Dic₁₁	1	4	yes	complemented
211	#107	—	11	4	no	—
212	#107	—	22	2	no	—
213	#107	—	22	2	no	—
214	#107	—	22	2	no	—
215	C₂×C₁₁	—	2	2	no	—
216	C₂×C₁₁	—	2	1	no	—
217	C₂×C₁₁	—	2	1	no	—
218	C₂×C₁₁	#1387	1	4	yes	complemented
219	C₂×C₁₁	C₂×#340	1	1	yes	characteristic
220	C₂×C₁₁	C₂×#361	1	1	yes	characteristic
221	C₂×C₁₁	C₂×#362	1	1	yes	characteristic
222	C₂⁴	#4325	1	1	yes	characteristic
223	C₂²×C₄	—	44	2	no	—
224	C₂²×C₄	—	44	2	no	—
225	C₂²×C₄	—	44	2	no	—
226	C₂²×C₄	—	88	4	no	—
227	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
228	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
229	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
230	C₂²×C₄	#4323	1	1	yes	characteristic
231	C₂²×C₄	#4323	1	1	yes	characteristic
232	C₂²×C₄	#4324	1	2	yes	—
233	C₂²×C₄	#4325	1	1	yes	characteristic
234	C₂²×C₄	#4326	1	2	yes	—
235	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
236	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
237	M₁₆	—	2	4	no	—
238	M₁₆	—	4	4	no	—
239	M₁₆	—	4	2	no	—
240	C₂×C₈	—	4	4	no	—
241	C₂×C₈	—	4	2	no	—
242	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
243	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
244	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
245	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
246	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
247	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
248	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
249	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
250	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
251	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
252	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
253	C₂×C₈	C₂²⋊Dic₁₁	1	2	yes	—
254	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
255	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
256	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
257	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
258	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
259	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
260	C₄⋊C₄	—	22	4	no	—
261	C₄⋊C₄	—	44	2	no	—
262	C₄⋊C₄	—	44	2	no	—
263	C₄⋊C₄	—	44	2	no	—
264	C₁₆	—	22	4	no	—
265	C₁₁	C₂×#1387	1	1	yes	characteristic, complemented, Sylow
266	C₂³	—	2	2	no	—
267	C₂³	—	2	2	no	—
268	C₂³	#66872	1	2	yes	—
269	C₂³	#66873	1	1	yes	characteristic
270	C₂³	#66873	1	1	yes	characteristic
271	C₂³	#66899	1	2	yes	—
272	C₂³	C₂×#4325	1	1	yes	characteristic
273	C₂×C₄	—	44	4	no	—
274	C₂×C₄	—	88	4	no	—
275	C₂×C₄	—	88	4	no	—
276	C₂×C₄	—	88	4	no	—
277	C₂×C₄	#66871	1	2	yes	—
278	C₂×C₄	#66871	1	2	yes	—
279	C₂×C₄	#66872	1	2	yes	—
280	C₂×C₄	#66873	1	1	yes	characteristic
281	C₂×C₄	#66873	1	1	yes	characteristic
282	C₂×C₄	#66874	1	2	yes	—
283	C₂×C₄	#66874	1	2	yes	—
284	C₂×C₄	C₁₁⋊#95	1	2	yes	—
285	C₂×C₄	C₁₁⋊#95	1	2	yes	—
286	C₂×C₄	#66896	1	2	yes	—
287	C₂×C₄	#66896	1	2	yes	—
288	C₂×C₄	#66899	1	2	yes	—
289	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
290	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
291	C₂×C₄	C₂×#4323	1	1	yes	characteristic
292	C₂×C₄	C₂×#4324	1	1	yes	characteristic
293	C₂×C₄	C₂×#4326	1	1	yes	characteristic
294	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
295	C₈	—	4	4	no	—
296	C₈	C₁₁⋊#95	1	2	yes	—
297	C₈	C₁₁⋊#95	1	2	yes	—
298	C₈	C₂×C₄×Dic₁₁	1	1	yes	characteristic
299	C₈	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
300	C₈	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
301	C₈	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
302	C₂²	—	2	1	no	—
303	C₂²	—	2	1	no	—
304	C₂²	—	2	1	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	4	no	—
307	C₂²	—	2	4	no	—
308	C₂²	#10622133	1	2	yes	—
309	C₂²	#10622134	1	2	yes	—
310	C₂²	#10622167	1	2	yes	—
311	C₂²	#10622167	1	2	yes	—
312	C₂²	C₂×#66872	1	1	yes	characteristic
313	C₂²	C₂×#66873	1	1	yes	characteristic
314	C₂²	C₂×#66899	1	1	yes	characteristic
315	C₄	—	88	4	no	—
316	C₄	#10622167	1	2	yes	—
317	C₄	#10622167	1	2	yes	—
318	C₄	C₂×#66871	1	1	yes	characteristic
319	C₄	C₂×#66874	1	1	yes	characteristic
320	C₄	C₂×C₁₁⋊#95	1	1	yes	characteristic
321	C₄	C₂×#66896	1	1	yes	characteristic
322	C₂	—	2	1	no	—
323	C₂	—	2	1	no	—
324	C₂	—	2	2	no	—
325	C₂	#13066726	1	4	yes	direct product factor
326	C₂	C₂×#10622167	1	1	yes	characteristic
327	C₂	C₂×#10622133	1	1	yes	characteristic
328	C₂	C₂×#10622134	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66873
commutator	C₈×C₁₁	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂²×C₁₁×#108	C₂
socle	C₂³×C₁₁	#102
prime radical	C₂⁴×C₁₁	SD₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂²×#108	D₁₁
hypocenter	C₁₁	C₂×#1387
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂²×#108

Complements

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

N	H ≅ G/N	type
3. #13066726	C₂	direct (N × H)
10. C₂×C₁₁×#108	C₄	semidirect
20. C₂×#66876	C₄	semidirect
48. C₁₁×#108	C₂×C₄	semidirect
55. #66876	C₂×C₄	semidirect
152. C₂×#108	Dic₁₁	semidirect
210. #108	C₂×Dic₁₁	semidirect
218. C₂×C₁₁	#1387	semidirect
265. C₁₁	C₂×#1387	semidirect
325. C₂	#13066726	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×#66876	2
C₂²×#66882	2
#13066726	2
C₂²×C₁₁×#108	2
C₂×#1387	11

Subgroups — C2×#13066726 #14668697

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066726 #14668697