Subgroups — C₂×#13067379 #14722780

Order 2816.

766 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622539	C₂	1	2	yes	maximal
2	#13067379	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10622096	C₂	1	2	yes	maximal, complemented
4	C₂×#10622095	C₂	1	2	yes	maximal, complemented
5	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₁	C₄	1	1	yes	characteristic
7	C₂³×C₈×C₁₁	C₄	1	1	yes	characteristic
8	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₄	1	4	yes	—
11	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₁	C₂²	1	4	yes	—
15	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
16	#10622539	—	2	4	no	—
17	#10622539	C₂²	1	8	yes	—
18	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
19	C₂×#66867	—	2	2	no	—
20	#10622096	C₂²	1	8	yes	complemented
21	#10622095	C₂²	1	8	yes	complemented
22	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
25	C₂²×C₈×C₁₁	—	2	4	no	—
26	C₂²×C₈×C₁₁	—	2	4	no	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
28	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₈×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	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	2	yes	—
37	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
39	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₁₁⋊C₈	—	2	4	no	—
42	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
43	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
44	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
45	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
46	C₄×C₈×C₁₁	C₂³	1	2	yes	—
47	C₄×C₈×C₁₁	C₂³	1	2	yes	—
48	C₂²⋊(C₁₁⋊C₈)	—	2	8	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
50	C₄⋊(C₁₁⋊C₈)	C₂³	1	8	yes	—
51	#66867	—	2	8	no	—
52	C₂×#1568	—	11	1	no	maximal, Sylow
53	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	—	2	4	no	—
55	C₂²×C₄×C₁₁	—	2	2	no	—
56	C₂²×C₄×C₁₁	—	2	2	no	—
57	C₂²×C₄×C₁₁	—	2	4	no	—
58	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
64	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
65	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
69	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
70	C₂×C₈×C₁₁	—	2	8	no	—
71	C₂×C₈×C₁₁	—	2	8	no	—
72	C₂×C₈×C₁₁	—	2	2	no	—
73	C₂×C₈×C₁₁	—	2	2	no	—
74	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
75	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
76	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
78	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
79	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
80	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
81	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
82	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
83	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
84	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₄²×C₁₁	C₂×D₄	1	2	yes	—
86	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
88	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
89	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
90	C₂×C₁₁⋊C₈	—	2	8	no	—
91	C₂×C₁₁⋊C₈	—	4	8	no	—
92	C₂×#432	—	11	2	no	—
93	C₂²×C₄×C₈	D₁₁	1	1	yes	characteristic
94	#1568	—	11	8	no	—
95	C₂×#335	—	11	2	no	—
96	C₂×#334	—	11	2	no	—
97	C₂³×C₁₁	—	2	2	no	—
98	C₂³×C₁₁	—	2	2	no	—
99	C₂³×C₁₁	#108	1	4	yes	—
100	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
101	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	2	2	no	—
104	C₂×C₄×C₁₁	—	2	4	no	—
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	—	2	4	no	—
107	C₂×C₄×C₁₁	—	2	2	no	—
108	C₂×C₄×C₁₁	—	2	2	no	—
109	C₂×C₄×C₁₁	—	2	2	no	—
110	C₂×C₄×C₁₁	—	2	4	no	—
111	C₂×C₄×C₁₁	—	2	4	no	—
112	C₂×C₄×C₁₁	—	2	4	no	—
113	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
114	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
116	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
117	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
120	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
121	C₂×C₄×C₁₁	#135	1	4	yes	—
122	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
123	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
124	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
125	C₈×C₁₁	—	2	2	no	—
126	C₈×C₁₁	—	2	2	no	—
127	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
128	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
129	C₁₁⋊C₈	—	4	8	no	—
130	C₂³×C₈	Dic₁₁	1	1	yes	characteristic
131	C₂³×C₈	Dic₁₁	1	1	yes	characteristic
132	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
133	#432	—	11	8	no	—
134	#432	—	22	4	no	—
135	C₂×C₄⋊C₈	—	11	4	no	—
136	C₂×C₂²⋊C₈	—	22	2	no	—
137	C₂×#97	—	22	2	no	—
138	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
139	C₂×C₄×C₈	Dic₁₁	1	4	yes	—
140	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
141	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
142	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
143	C₂×C₄×C₈	C₂×D₁₁	1	4	yes	—
144	#335	—	11	8	no	—
145	#334	—	11	8	no	—
146	C₂²×C₁₁	—	2	8	no	—
147	C₂²×C₁₁	—	2	2	no	—
148	C₂²×C₁₁	—	2	2	no	—
149	C₂²×C₁₁	#423	1	2	yes	—
150	C₂²×C₁₁	#427	1	2	yes	—
151	C₂²×C₁₁	C₂×#108	1	4	yes	—
152	C₂²×C₁₁	C₂×#108	1	2	yes	—
153	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
154	C₄×C₁₁	—	2	2	no	—
155	C₄×C₁₁	—	2	2	no	—
156	C₄×C₁₁	—	2	1	no	—
157	C₄×C₁₁	—	2	2	no	—
158	C₄×C₁₁	—	2	1	no	—
159	C₄×C₁₁	#423	1	2	yes	—
160	C₄×C₁₁	#427	1	2	yes	—
161	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
162	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
163	C₄×C₁₁	C₂×#135	1	2	yes	—
164	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
165	C₂³×C₄	D₄₄	1	1	yes	characteristic
166	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
167	C₂²×C₈	—	2	4	no	—
168	C₂²×C₈	—	2	4	no	—
169	C₂²×C₈	—	22	4	no	—
170	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
171	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
172	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
173	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
174	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
175	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
176	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
177	C₂×C₄²	Dic₂₂	1	2	yes	—
178	C₂×C₄²	D₄₄	1	2	yes	—
179	C₂×C₄²	D₄₄	1	1	yes	characteristic
180	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
181	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
182	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
183	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
184	C₄⋊C₈	—	11	8	no	—
185	C₄⋊C₈	—	22	4	no	—
186	C₂²⋊C₈	—	22	8	no	—
187	#97	—	22	8	no	—
188	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
189	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
190	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
191	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
192	C₄×C₈	C₂²×D₁₁	1	2	yes	—
193	C₄×C₈	C₂²×D₁₁	1	2	yes	—
194	C₂×C₁₁	—	2	4	no	—
195	C₂×C₁₁	#1568	1	4	yes	complemented
196	C₂×C₁₁	C₂×#423	1	1	yes	characteristic
197	C₂×C₁₁	C₂×#427	1	1	yes	characteristic
198	C₂×C₁₁	C₂²×#108	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	—	2	2	no	—
203	C₂²×C₄	—	2	2	no	—
204	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
205	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
206	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
207	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
208	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
209	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
210	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
211	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
212	C₂²×C₄	C₂×D₄₄	1	2	yes	—
213	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
214	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
215	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
216	C₂×C₈	—	2	2	no	—
217	C₂×C₈	—	2	2	no	—
218	C₂×C₈	—	2	8	no	—
219	C₂×C₈	—	2	8	no	—
220	C₂×C₈	—	22	8	no	—
221	C₂×C₈	—	44	8	no	—
222	C₂×C₈	#4318	1	4	yes	—
223	C₂×C₈	#4318	1	4	yes	—
224	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
225	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
226	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
227	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
228	C₄²	C₄⋊Dic₁₁	1	2	yes	—
229	C₄²	C₄⋊Dic₁₁	1	2	yes	—
230	C₄²	C₄⋊Dic₁₁	1	2	yes	—
231	C₄²	C₂×Dic₂₂	1	2	yes	—
232	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
233	C₄²	C₂×D₄₄	1	2	yes	—
234	C₄²	C₂×D₄₄	1	1	yes	characteristic
235	C₄²	C₂²×Dic₁₁	1	2	yes	—
236	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
237	C₄²	C₂³×D₁₁	1	1	yes	characteristic
238	C₁₁	C₂×#1568	1	1	yes	characteristic, complemented, Sylow
239	C₂³	—	2	2	no	—
240	C₂³	—	2	2	no	—
241	C₂³	#66883	1	4	yes	—
242	C₂³	C₂×C₄⋊Dic₁₁	1	2	yes	—
243	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
244	C₂×C₄	—	2	4	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	2	4	no	—
247	C₂×C₄	—	2	2	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	4	no	—
251	C₂×C₄	—	2	4	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	2	4	no	—
255	C₂×C₄	#66957	1	4	yes	—
256	C₂×C₄	C₂×#4318	1	2	yes	—
257	C₂×C₄	C₂×#4318	1	2	yes	—
258	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
259	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
260	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
261	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
262	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
263	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
264	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
265	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
266	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
267	C₈	—	2	2	no	—
268	C₈	—	2	2	no	—
269	C₈	—	44	8	no	—
270	C₈	C₂×#4318	1	4	yes	—
271	C₈	C₂×#4318	1	4	yes	—
272	C₂²	—	2	8	no	—
273	C₂²	—	2	2	no	—
274	C₂²	—	2	2	no	—
275	C₂²	#10622537	1	2	yes	—
276	C₂²	#10622719	1	2	yes	—
277	C₂²	C₂×#66883	1	4	yes	—
278	C₂²	C₂×#66883	1	2	yes	—
279	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
280	C₄	—	2	2	no	—
281	C₄	—	2	2	no	—
282	C₄	—	2	1	no	—
283	C₄	—	2	2	no	—
284	C₄	—	2	1	no	—
285	C₄	#10622537	1	2	yes	—
286	C₄	#10622719	1	2	yes	—
287	C₄	C₂×#66957	1	2	yes	—
288	C₄	C₂²×#4318	1	1	yes	characteristic
289	C₄	C₂²×#4318	1	1	yes	characteristic
290	C₂	—	2	4	no	—
291	C₂	#13067379	1	4	yes	direct product factor
292	C₂	C₂×#10622537	1	1	yes	characteristic
293	C₂	C₂×#10622719	1	1	yes	characteristic
294	C₂	C₂²×#66883	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂²×C₄×C₈×C₁₁	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂²×C₄×C₈	D₁₁
hypocenter	C₁₁	C₂×#1568
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13067379	C₂	direct (N × H)
3. C₂×#10622096	C₂	semidirect
4. C₂×#10622095	C₂	semidirect
20. #10622096	C₂²	semidirect
21. #10622095	C₂²	semidirect
195. C₂×C₁₁	#1568	semidirect
238. C₁₁	C₂×#1568	semidirect
291. C₂	#13067379	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×#10622539	2
#13067379	2
C₂×#10622096	2
C₂×#10622095	2
C₂²×C₄×C₈×C₁₁	2
C₂×#1568	11

Subgroups — C2×#13067379 #14722780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13067379 #14722780