Subgroups — C₂×#13067387 #14722829

Order 2816.

770 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622537	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	#13067387	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622095	C₂	1	4	yes	maximal, complemented
5	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
7	C₂²×#4318	—	2	1	no	—
8	C₂³×C₁₁⋊C₈	—	2	1	no	—
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	#10622537	—	2	2	no	—
15	#10622537	C₂²	1	4	yes	—
16	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
17	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
18	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
19	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
22	#10622095	C₂²	1	16	yes	complemented
23	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	D₄	1	2	yes	—
31	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	Q₈	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
35	C₂×#4318	—	2	4	no	—
36	C₂×#4318	—	4	4	no	—
37	C₂²×C₁₁⋊C₈	—	2	4	no	—
38	C₂²×C₁₁⋊C₈	—	2	2	no	—
39	C₂²×C₁₁⋊C₈	—	2	2	no	—
40	C₂²×C₁₁⋊C₈	—	4	4	no	—
41	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
42	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
43	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
44	C₄×C₈×C₁₁	C₂³	1	4	yes	—
45	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
47	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
48	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
50	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
51	C₂×#1570	—	11	1	no	maximal, Sylow
52	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	—	2	4	no	—
54	C₂²×C₄×C₁₁	—	4	2	no	—
55	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	SD₁₆	1	4	yes	—
62	C₂²×C₄×C₁₁	SD₁₆	1	4	yes	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
64	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
69	C₂×C₈×C₁₁	—	2	8	no	—
70	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
71	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
72	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
73	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
74	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
76	C₄²×C₁₁	C₂×D₄	1	2	yes	—
77	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
79	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
80	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
81	#4318	—	4	8	no	—
82	C₂×C₁₁⋊C₈	—	2	4	no	—
83	C₂×C₁₁⋊C₈	—	2	4	no	—
84	C₂×C₁₁⋊C₈	—	4	8	no	—
85	C₂×C₁₁⋊C₈	—	4	4	no	—
86	C₂×C₁₁⋊C₈	—	4	4	no	—
87	C₂×#431	D₁₁	1	1	yes	characteristic
88	C₂×#423	—	11	1	no	—
89	C₂²×C₄⋊C₈	—	11	1	no	—
90	#1570	—	11	8	no	—
91	C₂×#334	—	11	4	no	—
92	C₂³×C₁₁	—	2	2	no	—
93	C₂³×C₁₁	—	2	2	no	—
94	C₂³×C₁₁	#106	1	4	yes	—
95	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
96	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	2	no	—
100	C₂×C₄×C₁₁	—	2	4	no	—
101	C₂×C₄×C₁₁	—	2	4	no	—
102	C₂×C₄×C₁₁	—	4	2	no	—
103	C₂×C₄×C₁₁	—	4	2	no	—
104	C₂×C₄×C₁₁	#106	1	8	yes	—
105	C₂×C₄×C₁₁	#106	1	4	yes	—
106	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
108	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
109	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
111	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×C₁₁	#131	1	4	yes	—
113	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
114	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
115	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
116	C₂×C₄×C₁₁	C₂×SD₁₆	1	4	yes	—
117	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
118	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
119	C₂×C₄×C₁₁	C₂²×Q₈	1	1	yes	characteristic
120	C₈×C₁₁	—	2	8	no	—
121	C₁₁⋊C₈	—	4	4	no	—
122	C₁₁⋊C₈	—	4	4	no	—
123	C₂²×M₁₆	—	22	1	no	—
124	C₂³×C₈	—	22	1	no	—
125	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
126	#431	Dic₁₁	1	4	yes	—
127	#431	C₂×D₁₁	1	4	yes	—
128	#423	—	11	4	no	—
129	#423	—	22	2	no	—
130	C₂×C₄⋊C₈	—	11	2	no	—
131	C₂×C₄⋊C₈	—	11	2	no	—
132	C₂×C₄⋊C₈	—	11	4	no	—
133	C₂×C₄⋊C₈	—	22	2	no	—
134	C₂×C₄⋊C₈	—	22	1	no	—
135	C₂×C₄⋊C₈	—	22	1	no	—
136	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
137	C₂×C₂²⋊C₈	Dic₁₁	1	2	yes	—
138	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
139	#334	—	11	16	no	—
140	C₂²×C₁₁	—	2	8	no	—
141	C₂²×C₁₁	—	2	2	no	—
142	C₂²×C₁₁	—	2	2	no	—
143	C₂²×C₁₁	#424	1	2	yes	—
144	C₂²×C₁₁	C₂×#106	1	4	yes	—
145	C₂²×C₁₁	C₂×#106	1	2	yes	—
146	C₂²×C₁₁	#430	1	2	yes	—
147	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
148	C₄×C₁₁	—	2	2	no	—
149	C₄×C₁₁	—	2	2	no	—
150	C₄×C₁₁	—	2	1	no	—
151	C₄×C₁₁	—	2	1	no	—
152	C₄×C₁₁	#424	1	2	yes	—
153	C₄×C₁₁	C₂×#106	1	2	yes	—
154	C₄×C₁₁	C₂×#106	1	4	yes	—
155	C₄×C₁₁	C₂×#131	1	2	yes	—
156	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
157	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
158	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
159	C₂³×C₄	D₄₄	1	1	yes	characteristic
160	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
161	C₂×M₁₆	—	22	4	no	—
162	C₂×M₁₆	—	44	4	no	—
163	C₂²×C₈	—	22	4	no	—
164	C₂²×C₈	—	22	2	no	—
165	C₂²×C₈	—	22	2	no	—
166	C₂²×C₈	—	44	4	no	—
167	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
168	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
169	C₂×C₄²	Dic₂₂	1	2	yes	—
170	C₂×C₄²	D₄₄	1	2	yes	—
171	C₂×C₄²	D₄₄	1	1	yes	characteristic
172	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
173	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
174	C₂×C₄²	C₂²×D₁₁	1	2	yes	—
175	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
176	C₄⋊C₈	—	11	4	no	—
177	C₄⋊C₈	—	11	4	no	—
178	C₄⋊C₈	—	22	2	no	—
179	C₄⋊C₈	—	22	4	no	—
180	C₄⋊C₈	—	22	2	no	—
181	C₄⋊C₈	—	22	4	no	—
182	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
183	C₂²⋊C₈	C₂×Dic₁₁	1	8	yes	—
184	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
185	C₄×C₈	C₂²×D₁₁	1	4	yes	—
186	C₂×C₁₁	—	2	4	no	—
187	C₂×C₁₁	#1570	1	4	yes	complemented
188	C₂×C₁₁	C₂×#424	1	1	yes	characteristic
189	C₂×C₁₁	C₂²×#106	1	1	yes	characteristic
190	C₂×C₁₁	C₂×#430	1	1	yes	characteristic
191	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
192	C₂²×C₄	—	2	4	no	—
193	C₂²×C₄	—	4	2	no	—
194	C₂²×C₄	#4314	1	4	yes	—
195	C₂²×C₄	#4314	1	4	yes	—
196	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
197	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
198	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
199	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
200	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
201	C₂²×C₄	C₄⋊Dic₁₁	1	2	yes	—
202	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
203	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
204	C₂²×C₄	C₂×D₄₄	1	2	yes	—
205	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
206	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
207	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
208	M₁₆	—	44	8	no	—
209	C₂×C₈	—	2	8	no	—
210	C₂×C₈	—	22	4	no	—
211	C₂×C₈	—	22	4	no	—
212	C₂×C₈	—	44	8	no	—
213	C₂×C₈	—	44	4	no	—
214	C₂×C₈	—	44	4	no	—
215	C₂×C₈	C₂²×Dic₁₁	1	8	yes	—
216	C₄²	C₄⋊Dic₁₁	1	2	yes	—
217	C₄²	C₄⋊Dic₁₁	1	2	yes	—
218	C₄²	C₄⋊Dic₁₁	1	2	yes	—
219	C₄²	C₂×Dic₂₂	1	2	yes	—
220	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
221	C₄²	C₂×D₄₄	1	2	yes	—
222	C₄²	C₂×D₄₄	1	1	yes	characteristic
223	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
224	C₄²	C₂²×Dic₁₁	1	2	yes	—
225	C₄²	C₂³×D₁₁	1	1	yes	characteristic
226	C₁₁	C₂×#1570	1	1	yes	characteristic, complemented, Sylow
227	C₂³	—	2	2	no	—
228	C₂³	—	2	2	no	—
229	C₂³	#66881	1	4	yes	—
230	C₂³	C₂×C₄⋊Dic₁₁	1	2	yes	—
231	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	4	no	—
236	C₂×C₄	—	2	4	no	—
237	C₂×C₄	—	4	2	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	#66881	1	8	yes	—
240	C₂×C₄	#66881	1	4	yes	—
241	C₂×C₄	C₂×#4314	1	4	yes	—
242	C₂×C₄	C₂×#4314	1	2	yes	—
243	C₂×C₄	C₂×#4314	1	2	yes	—
244	C₂×C₄	C₂×#4314	1	4	yes	—
245	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
246	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
247	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
248	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
249	C₂×C₄	C₂×C₄⋊Dic₁₁	1	2	yes	—
250	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
251	C₂×C₄	#67001	1	4	yes	—
252	C₂×C₄	C₂²×Dic₂₂	1	1	yes	characteristic
253	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
254	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
255	C₈	—	2	8	no	—
256	C₈	—	44	4	no	—
257	C₈	—	44	4	no	—
258	C₂²	—	2	8	no	—
259	C₂²	—	2	2	no	—
260	C₂²	—	2	2	no	—
261	C₂²	#10622612	1	2	yes	—
262	C₂²	C₂×#66881	1	4	yes	—
263	C₂²	C₂×#66881	1	2	yes	—
264	C₂²	#10622738	1	2	yes	—
265	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
266	C₄	—	2	2	no	—
267	C₄	—	2	2	no	—
268	C₄	—	2	1	no	—
269	C₄	—	2	1	no	—
270	C₄	#10622612	1	2	yes	—
271	C₄	C₂×#66881	1	4	yes	—
272	C₄	C₂×#66881	1	2	yes	—
273	C₄	C₂²×#4314	1	1	yes	characteristic
274	C₄	C₂²×#4314	1	1	yes	characteristic
275	C₄	C₂×#67001	1	2	yes	—
276	C₂	—	2	4	no	—
277	C₂	#13067387	1	4	yes	direct product factor
278	C₂	C₂×#10622612	1	1	yes	characteristic
279	C₂	C₂²×#66881	1	1	yes	characteristic
280	C₂	C₂×#10622738	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂³×C₁₁	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	C₂×#1570
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13067387	C₂	direct (N × H)
4. C₂×#10622095	C₂	semidirect
22. #10622095	C₂²	semidirect
187. C₂×C₁₁	#1570	semidirect
226. C₁₁	C₂×#1570	semidirect
277. C₂	#13067387	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×#10622537	2
C₂²×C₄⋊(C₁₁⋊C₈)	2
#13067387	2
C₂×#10622095	2
C₂×C₁₁×#431	2
C₂×#1570	11

Subgroups — C2×#13067387 #14722829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13067387 #14722829