Subgroups — C₂×#13068010 #14736129

Order 2816.

702 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×#10622295	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622644	C₂	1	2	yes	maximal
3	#13068010	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622096	C₂	1	1	yes	maximal, characteristic
5	C₂×#10622124	C₂	1	2	yes	maximal
6	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×#4326	—	2	2	no	—
9	C₂×#66922	C₂²	1	2	yes	—
10	C₈×Q₈×C₁₁	—	2	2	no	—
11	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
12	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
13	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₁	—	2	1	no	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×#66882	—	2	1	no	—
17	C₂×#66882	—	2	1	no	—
18	#10622644	—	2	4	no	—
19	#10622644	C₂²	1	8	yes	—
20	C₂×#66874	—	2	2	no	—
21	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
22	#10622295	—	2	2	no	—
23	#10622295	C₂²	1	4	yes	—
24	#10622124	C₂²	1	8	yes	—
25	#10622096	C₂²	1	4	yes	—
26	C₂²×Q₈×C₁₁	D₄	1	1	yes	characteristic
27	C₂²×Dic₂₂	—	2	2	no	—
28	C₂²×C₈×C₁₁	—	2	1	no	—
29	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₄×Q₈×C₁₁	—	2	1	no	—
32	C₄×Q₈×C₁₁	—	2	1	no	—
33	C₄×Q₈×C₁₁	D₄	1	2	yes	—
34	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
35	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
36	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	—	2	1	no	—
38	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
39	C₂×#4326	—	2	8	no	—
40	C₂×#4326	—	4	8	no	—
41	C₂×C₄⋊Dic₁₁	—	2	2	no	—
42	C₂×C₄⋊Dic₁₁	—	2	2	no	—
43	C₂²×C₁₁⋊C₈	—	2	2	no	—
44	#66922	—	2	2	no	—
45	#66922	—	2	2	no	—
46	#66922	—	2	2	no	—
47	#66922	C₂³	1	4	yes	—
48	C₁₁×C₄⋊C₈	—	2	4	no	—
49	C₁₁×C₄⋊C₈	—	2	1	no	—
50	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
51	C₄×C₈×C₁₁	—	2	4	no	—
52	C₄×C₈×C₁₁	D₄	1	2	yes	—
53	C₄×C₈×C₁₁	C₂³	1	2	yes	—
54	#66882	—	2	4	no	—
55	#66882	—	2	4	no	—
56	#66874	—	2	8	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
59	C₂×#1674	—	11	1	no	maximal, Sylow
60	C₂×Q₈×C₁₁	—	2	1	no	—
61	C₂×Q₈×C₁₁	—	2	2	no	—
62	C₂×Q₈×C₁₁	D₈	1	4	yes	—
63	C₂×Q₈×C₁₁	C₂×D₄	1	2	yes	—
64	C₂²×C₄×C₁₁	—	2	1	no	—
65	C₂²×C₄×C₁₁	—	2	1	no	—
66	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
67	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
69	C₂²×Dic₁₁	—	4	2	no	—
70	C₂×Dic₂₂	—	2	4	no	—
71	C₂×Dic₂₂	—	4	2	no	—
72	C₂×Dic₂₂	—	4	4	no	—
73	C₂×Dic₂₂	—	4	4	no	—
74	C₂×C₈×C₁₁	—	2	2	no	—
75	C₂×C₈×C₁₁	—	2	2	no	—
76	C₂×C₈×C₁₁	—	4	2	no	—
77	C₂×C₈×C₁₁	Q₁₆	1	4	yes	complemented
78	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
79	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
80	C₁₁×C₄⋊C₄	—	2	2	no	—
81	C₁₁×C₄⋊C₄	—	2	1	no	—
82	C₁₁×C₄⋊C₄	—	2	2	no	—
83	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
84	C₄²×C₁₁	—	2	2	no	—
85	C₄²×C₁₁	—	2	2	no	—
86	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
87	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
88	C₄²×C₁₁	#41	1	1	yes	characteristic
89	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
90	#4326	—	4	16	no	—
91	C₄⋊Dic₁₁	—	2	4	no	—
92	C₄⋊Dic₁₁	—	2	4	no	—
93	C₄⋊Dic₁₁	—	4	2	no	—
94	C₄⋊Dic₁₁	—	4	2	no	—
95	C₂×C₁₁⋊C₈	—	2	4	no	—
96	C₂×C₁₁⋊C₈	—	4	4	no	—
97	C₂×#500	—	11	1	no	—
98	C₂×#462	—	11	2	no	—
99	C₂×C₈×Q₈	D₁₁	1	1	yes	characteristic
100	#1674	—	11	8	no	—
101	C₂×#335	—	11	1	no	—
102	C₂×#332	—	11	2	no	—
103	C₂³×C₁₁	#121	1	1	yes	characteristic
104	Q₈×C₁₁	—	2	2	no	—
105	Q₈×C₁₁	—	2	4	no	—
106	Q₈×C₁₁	C₂×D₈	1	4	yes	—
107	C₂×C₄×C₁₁	—	2	2	no	—
108	C₂×C₄×C₁₁	—	2	4	no	—
109	C₂×C₄×C₁₁	—	2	2	no	—
110	C₂×C₄×C₁₁	—	2	2	no	—
111	C₂×C₄×C₁₁	—	4	2	no	—
112	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
113	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
114	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
115	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
116	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
117	C₂×C₄×C₁₁	#135	1	2	yes	—
118	C₂×C₄×C₁₁	#137	1	2	yes	—
119	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
120	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
122	C₂×Dic₁₁	—	4	4	no	—
123	C₂×Dic₁₁	—	8	4	no	—
124	Dic₂₂	—	4	4	no	—
125	Dic₂₂	—	4	4	no	—
126	Dic₂₂	—	8	4	no	—
127	C₈×C₁₁	—	2	2	no	—
128	C₈×C₁₁	—	4	2	no	—
129	C₈×C₁₁	C₂×Q₁₆	1	4	yes	complemented
130	C₁₁⋊C₈	—	4	4	no	—
131	C₂²×Q₁₆	—	22	2	no	—
132	C₂×C₄⋊Q₈	—	11	2	no	—
133	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
134	#500	—	11	4	no	—
135	#500	—	22	2	no	—
136	#462	—	11	8	no	—
137	#462	—	22	4	no	—
138	C₈×Q₈	—	2	2	no	—
139	C₈×Q₈	C₂×D₁₁	1	4	yes	—
140	C₂×#107	—	22	1	no	—
141	C₂×#107	—	22	1	no	—
142	C₂×C₄⋊C₈	—	2	1	no	—
143	C₂×C₄⋊C₈	—	11	2	no	—
144	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
145	C₂×#103	—	22	2	no	—
146	C₂×C₄×C₈	—	2	1	no	—
147	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
148	#335	—	11	4	no	—
149	#332	—	11	8	no	—
150	C₂²×C₁₁	#462	1	2	yes	—
151	C₂²×C₁₁	#466	1	2	yes	—
152	C₂²×C₁₁	#473	1	2	yes	—
153	C₂²×C₁₁	C₂×#121	1	1	yes	characteristic
154	C₄×C₁₁	—	2	4	no	—
155	C₄×C₁₁	—	2	1	no	—
156	C₄×C₁₁	—	2	1	no	—
157	C₄×C₁₁	—	4	2	no	—
158	C₄×C₁₁	#462	1	2	yes	—
159	C₄×C₁₁	#466	1	2	yes	—
160	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
161	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
162	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
163	C₄×C₁₁	C₂×#137	1	1	yes	characteristic
164	Dic₁₁	—	8	4	no	—
165	C₂²×Q₈	—	22	2	no	—
166	C₂²×Q₈	D₄₄	1	1	yes	characteristic
167	C₂×Q₁₆	—	22	8	no	—
168	C₂×Q₁₆	—	44	8	no	—
169	C₂²×C₈	—	2	1	no	—
170	C₂²×C₈	—	22	2	no	—
171	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
172	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
173	C₄⋊Q₈	—	11	4	no	—
174	C₄⋊Q₈	—	22	2	no	—
175	C₄⋊Q₈	—	22	2	no	—
176	C₄⋊Q₈	—	22	2	no	—
177	C₄×Q₈	—	2	1	no	—
178	C₄×Q₈	—	2	1	no	—
179	C₄×Q₈	D₄₄	1	2	yes	—
180	C₄×Q₈	C₂²×D₁₁	1	2	yes	—
181	C₂×C₄⋊C₄	—	2	1	no	—
182	C₂×C₄⋊C₄	—	22	2	no	—
183	C₂×C₄⋊C₄	—	22	2	no	—
184	C₂×C₄⋊C₄	D₄₄	1	1	yes	characteristic
185	C₂×C₄²	—	2	1	no	—
186	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
187	#107	—	22	4	no	—
188	#107	—	22	4	no	—
189	C₄⋊C₈	—	2	4	no	—
190	C₄⋊C₈	—	2	1	no	—
191	C₄⋊C₈	—	11	4	no	—
192	C₄⋊C₈	—	22	2	no	—
193	C₄⋊C₈	C₂²×D₁₁	1	2	yes	—
194	#103	—	22	8	no	—
195	C₄×C₈	—	2	4	no	—
196	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
197	C₄×C₈	C₂²×D₁₁	1	2	yes	—
198	C₂×C₁₁	#1674	1	4	yes	complemented
199	C₂×C₁₁	C₂×#462	1	1	yes	characteristic
200	C₂×C₁₁	C₂×#466	1	1	yes	characteristic
201	C₂×C₁₁	C₂×#473	1	1	yes	characteristic
202	C₂×Q₈	—	2	2	no	—
203	C₂×Q₈	—	2	1	no	—
204	C₂×Q₈	—	22	4	no	—
205	C₂×Q₈	—	44	2	no	—
206	C₂×Q₈	—	44	4	no	—
207	C₂×Q₈	—	44	4	no	—
208	C₂×Q₈	D₈₈	1	4	yes	—
209	C₂×Q₈	C₂×D₄₄	1	2	yes	—
210	C₂²×C₄	—	2	1	no	—
211	C₂²×C₄	—	2	1	no	—
212	C₂²×C₄	—	44	2	no	—
213	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
214	C₂²×C₄	#4339	1	1	yes	characteristic
215	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
216	Q₁₆	—	44	16	no	—
217	C₂×C₈	—	2	2	no	—
218	C₂×C₈	—	2	2	no	—
219	C₂×C₈	—	4	2	no	—
220	C₂×C₈	—	22	4	no	—
221	C₂×C₈	—	44	4	no	—
222	C₂×C₈	#4326	1	4	yes	complemented
223	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
224	C₂×C₈	C₂×C₂²⋊D₁₁	1	2	yes	—
225	C₄⋊C₄	—	2	2	no	—
226	C₄⋊C₄	—	2	1	no	—
227	C₄⋊C₄	—	2	2	no	—
228	C₄⋊C₄	—	22	4	no	—
229	C₄⋊C₄	—	22	4	no	—
230	C₄⋊C₄	—	44	2	no	—
231	C₄⋊C₄	—	44	2	no	—
232	C₄⋊C₄	C₂×D₄₄	1	2	yes	—
233	C₄²	—	2	2	no	—
234	C₄²	—	2	2	no	—
235	C₄²	C₂×D₄₄	1	1	yes	characteristic
236	C₄²	#4339	1	1	yes	characteristic
237	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
238	C₄²	C₂³×D₁₁	1	1	yes	characteristic
239	C₁₁	C₂×#1674	1	1	yes	characteristic, complemented, Sylow
240	C₂³	#66983	1	1	yes	characteristic
241	Q₈	—	2	4	no	—
242	Q₈	—	2	2	no	—
243	Q₈	—	44	4	no	—
244	Q₈	—	44	4	no	—
245	Q₈	—	88	4	no	—
246	Q₈	C₂×D₈₈	1	4	yes	—
247	C₂×C₄	—	2	4	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	2	2	no	—
250	C₂×C₄	—	2	2	no	—
251	C₂×C₄	—	4	2	no	—
252	C₂×C₄	—	44	4	no	—
253	C₂×C₄	—	88	4	no	—
254	C₂×C₄	C₂×D₈₈	1	2	yes	—
255	C₂×C₄	#66957	1	2	yes	—
256	C₂×C₄	#66983	1	1	yes	characteristic
257	C₂×C₄	#66983	1	1	yes	characteristic
258	C₂×C₄	#66983	1	1	yes	characteristic
259	C₂×C₄	C₂×#4326	1	2	yes	—
260	C₂×C₄	#67004	1	2	yes	—
261	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
262	C₂×C₄	C₂×#4339	1	1	yes	characteristic
263	C₂×C₄	C₂²×C₂²⋊D₁₁	1	1	yes	characteristic
264	C₈	—	2	2	no	—
265	C₈	—	4	2	no	—
266	C₈	—	44	4	no	—
267	C₈	C₂×#4326	1	4	yes	complemented
268	C₂²	#10622644	1	2	yes	—
269	C₂²	#10622728	1	2	yes	—
270	C₂²	#10622756	1	2	yes	—
271	C₂²	C₂×#66983	1	1	yes	characteristic
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	2	4	no	—
275	C₄	—	4	2	no	—
276	C₄	—	88	4	no	—
277	C₄	#10622644	1	2	yes	—
278	C₄	#10622728	1	2	yes	—
279	C₄	C₂²×D₈₈	1	1	yes	characteristic
280	C₄	C₂×#66957	1	1	yes	characteristic
281	C₄	C₂²×#4326	1	1	yes	characteristic
282	C₄	C₂×#67004	1	1	yes	characteristic
283	C₂	#13068010	1	4	yes	direct product factor
284	C₂	C₂×#10622644	1	1	yes	characteristic
285	C₂	C₂×#10622728	1	1	yes	characteristic
286	C₂	C₂×#10622756	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66983
commutator, cosocle	C₄²×C₁₁	C₂⁴
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₈×Q₈×C₁₁	C₂
socle, prime radical	C₂³×C₁₁	#121
hypercenter	C₂×C₈×Q₈	D₁₁
hypocenter	C₁₁	C₂×#1674
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
3. #13068010	C₂	direct (N × H)
77. C₂×C₈×C₁₁	Q₁₆	semidirect
129. C₈×C₁₁	C₂×Q₁₆	semidirect
198. C₂×C₁₁	#1674	semidirect
222. C₂×C₈	#4326	semidirect
239. C₁₁	C₂×#1674	semidirect
267. C₈	C₂×#4326	semidirect
283. C₂	#13068010	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×#10622295	2
C₂×#10622644	2
#13068010	2
C₂×#10622096	2
C₂×#10622124	2
C₂×C₈×Q₈×C₁₁	2
C₂×#1674	11

Subgroups — C2×#13068010 #14736129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13068010 #14736129