Subgroups — C₂×#13070502 #14907179

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622809	C₂	1	2	yes	maximal, complemented
2	#13070502	C₂	1	8	yes	maximal, direct product factor
3	C₂×#10622144	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10622205	C₂	1	2	yes	maximal, complemented
5	C₂×#10622140	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₁×#508	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×#135	C₂²	1	2	yes	—
8	C₂×#67001	—	2	2	no	—
9	C₁₁×#508	C₄	1	4	yes	complemented
10	C₁₁×#508	C₂²	1	4	yes	—
11	C₂×C₁₁×Q₃₂	C₄	1	1	yes	characteristic, complemented
12	C₂×C₁₁×SD₃₂	C₄	1	2	yes	complemented
13	C₂×C₁₁×D₁₆	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	C₂×#66901	—	2	2	no	—
16	#10622809	—	2	4	no	—
17	#10622809	C₂²	1	8	yes	complemented
18	C₂×#66883	C₂²	1	2	yes	—
19	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
21	#10622205	C₂²	1	8	yes	complemented
22	#10622144	C₂²	1	4	yes	complemented
23	#10622140	C₂²	1	4	yes	complemented
24	C₂×C₁₁×#41	—	2	2	no	—
25	C₁₁×#135	—	2	2	no	—
26	C₁₁×#135	—	2	2	no	—
27	C₁₁×#135	C₂×C₄	1	4	yes	—
28	C₁₁×#135	C₂³	1	4	yes	—
29	C₂×C₁₁×Q₁₆	C₂×C₄	1	2	yes	—
30	C₂×C₁₁×SD₁₆	—	2	2	no	—
31	C₂×C₁₁×D₈	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
33	#67001	—	2	8	no	—
34	#67001	—	4	4	no	—
35	C₂×C₄×Dic₁₁	D₄	1	1	yes	characteristic
36	C₂×#4318	—	2	2	no	—
37	C₂×#4318	—	4	2	no	—
38	C₂²×C₁₁⋊C₈	—	4	2	no	—
39	C₂²×C₁₁⋊C₈	D₄	1	1	yes	characteristic
40	C₁₁×Q₃₂	C₂×C₄	1	4	yes	complemented
41	C₁₁×SD₃₂	C₂×C₄	1	8	yes	complemented
42	C₁₁×D₁₆	C₂×C₄	1	4	yes	complemented
43	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
45	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
46	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
47	#66901	—	2	8	no	—
48	#66883	—	2	2	no	—
49	#66883	C₂³	1	4	yes	—
50	C₈×Dic₁₁	D₄	1	2	yes	—
51	C₈×Dic₁₁	C₂³	1	2	yes	—
52	C₂×C₁₁⋊C₁₆	—	2	1	no	—
53	C₂×C₁₁⋊C₁₆	—	2	1	no	—
54	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
55	C₂×#2179	—	11	1	no	maximal, Sylow
56	C₁₁×#41	—	2	4	no	—
57	C₁₁×#41	—	2	4	no	—
58	C₁₁×#41	—	4	2	no	—
59	C₁₁×#41	—	4	2	no	—
60	C₂×Q₈×C₁₁	—	2	2	no	—
61	C₂×D₄×C₁₁	—	2	2	no	—
62	C₂×D₄×C₁₁	—	4	2	no	—
63	C₂²×C₄×C₁₁	—	4	2	no	—
64	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
65	C₂²×Dic₁₁	—	2	1	no	—
66	C₁₁×Q₁₆	—	2	2	no	—
67	C₁₁×Q₁₆	C₂²×C₄	1	4	yes	—
68	C₁₁×SD₁₆	—	2	4	no	—
69	C₁₁×SD₁₆	—	2	4	no	—
70	C₁₁×D₈	—	2	2	no	—
71	C₁₁×D₈	C₂²×C₄	1	4	yes	—
72	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
74	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
76	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
77	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
78	C₄×Dic₁₁	—	2	1	no	—
79	C₄×Dic₁₁	C₂×D₄	1	2	yes	—
80	#4318	—	2	4	no	—
81	#4318	—	4	8	no	—
82	#4318	—	4	2	no	—
83	C₂×C₁₁⋊C₈	—	4	8	no	—
84	C₂×C₁₁⋊C₈	—	4	2	no	—
85	C₂×C₁₁⋊C₈	D₈	1	2	yes	—
86	C₂×C₁₁⋊C₈	D₈	1	2	yes	—
87	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
88	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
89	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
90	C₁₁⋊C₁₆	—	2	2	no	—
91	C₂×#508	D₁₁	1	1	yes	characteristic
92	C₂×#443	—	11	2	no	—
93	#2179	—	11	8	no	—
94	C₂×#368	—	11	1	no	—
95	C₂×#359	—	11	2	no	—
96	C₂×#346	—	11	1	no	—
97	C₂³×C₁₁	—	4	2	no	—
98	C₂³×C₁₁	#135	1	1	yes	characteristic
99	Q₈×C₁₁	—	2	4	no	—
100	Q₈×C₁₁	—	4	2	no	—
101	D₄×C₁₁	—	2	4	no	—
102	D₄×C₁₁	—	4	4	no	—
103	D₄×C₁₁	—	4	4	no	—
104	D₄×C₁₁	—	4	2	no	—
105	C₂×C₄×C₁₁	—	4	2	no	—
106	C₂×C₄×C₁₁	—	4	4	no	—
107	C₂×C₄×C₁₁	—	4	4	no	—
108	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
110	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
112	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
113	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
114	C₂×Dic₁₁	—	2	2	no	—
115	C₂×Dic₁₁	—	4	2	no	—
116	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
117	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
118	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
119	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
120	C₁₁⋊C₈	—	4	4	no	—
121	C₁₁⋊C₈	C₂×D₈	1	4	yes	—
122	C₂×#135	C₂×D₁₁	1	2	yes	—
123	C₂×#131	—	22	2	no	—
124	#508	Dic₁₁	1	4	yes	complemented
125	#508	C₂×D₁₁	1	4	yes	—
126	C₂×Q₃₂	Dic₁₁	1	1	yes	characteristic, complemented
127	C₂×SD₃₂	Dic₁₁	1	2	yes	complemented
128	C₂×D₁₆	Dic₁₁	1	1	yes	characteristic, complemented
129	C₂²×C₁₆	—	11	1	no	—
130	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
131	#443	—	11	8	no	—
132	#443	—	22	4	no	—
133	C₂×#108	—	11	2	no	—
134	C₂×#104	—	22	2	no	—
135	C₂×C₄×C₈	—	11	1	no	—
136	#368	—	11	4	no	—
137	#359	—	11	8	no	—
138	#346	—	11	4	no	—
139	C₂²×C₁₁	—	2	2	no	—
140	C₂²×C₁₁	—	4	4	no	—
141	C₂²×C₁₁	—	8	4	no	—
142	C₂²×C₁₁	C₄×D₈	1	1	yes	characteristic
143	C₂²×C₁₁	C₄×D₈	1	1	yes	characteristic
144	C₂²×C₁₁	C₂×#135	1	1	yes	characteristic
145	C₄×C₁₁	—	4	4	no	—
146	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
147	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
148	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
149	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
150	Dic₁₁	—	4	2	no	—
151	C₂×#41	—	2	2	no	—
152	#135	—	2	2	no	—
153	#135	—	2	2	no	—
154	#135	C₂×Dic₁₁	1	4	yes	—
155	#135	C₂²×D₁₁	1	4	yes	—
156	C₂×Q₁₆	C₂×Dic₁₁	1	2	yes	—
157	C₂×SD₁₆	—	2	2	no	—
158	C₂×D₈	C₂×Dic₁₁	1	2	yes	—
159	#131	—	22	8	no	—
160	#131	—	44	4	no	—
161	C₂×M₁₆	—	22	2	no	—
162	C₂×M₁₆	—	44	2	no	—
163	C₂²×C₈	—	11	1	no	—
164	C₂²×C₈	—	44	2	no	—
165	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
166	C₂×C₄²	—	11	1	no	—
167	Q₃₂	C₂×Dic₁₁	1	4	yes	complemented
168	SD₃₂	C₂×Dic₁₁	1	8	yes	complemented
169	D₁₆	C₂×Dic₁₁	1	4	yes	complemented
170	C₂×C₁₆	—	11	2	no	—
171	C₂×C₁₆	—	22	1	no	—
172	C₂×C₁₆	—	22	1	no	—
173	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
174	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
175	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
176	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
177	#108	—	11	4	no	—
178	#108	—	22	2	no	—
179	#104	—	22	8	no	—
180	C₄×C₈	—	11	2	no	—
181	C₄×C₈	—	11	2	no	—
182	C₂×C₁₁	—	2	1	no	—
183	C₂×C₁₁	—	2	1	no	—
184	C₂×C₁₁	—	8	4	no	—
185	C₂×C₁₁	#2179	1	2	yes	complemented
186	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
187	#41	—	2	4	no	—
188	#41	—	2	4	no	—
189	#41	—	4	2	no	—
190	#41	—	4	2	no	—
191	C₂×Q₈	—	2	2	no	—
192	C₂×D₄	—	2	2	no	—
193	C₂×D₄	—	4	2	no	—
194	C₂²×C₄	—	4	2	no	—
195	C₂²×C₄	—	22	1	no	—
196	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
197	Q₁₆	—	2	2	no	—
198	Q₁₆	C₂²×Dic₁₁	1	4	yes	—
199	SD₁₆	—	2	4	no	—
200	SD₁₆	—	2	4	no	—
201	D₈	—	2	2	no	—
202	D₈	C₂²×Dic₁₁	1	4	yes	—
203	M₁₆	—	22	4	no	—
204	M₁₆	—	44	8	no	—
205	M₁₆	—	44	2	no	—
206	C₂×C₈	—	11	2	no	—
207	C₂×C₈	—	11	2	no	—
208	C₂×C₈	—	11	2	no	—
209	C₂×C₈	—	44	8	no	—
210	C₂×C₈	—	44	2	no	—
211	C₂×C₈	D₄×D₁₁	1	1	yes	characteristic
212	C₂×C₈	#4341	1	1	yes	characteristic
213	C₂×C₈	#4341	1	1	yes	characteristic
214	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
215	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
216	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
217	C₄²	—	11	2	no	—
218	C₄²	—	22	1	no	—
219	C₁₆	—	22	2	no	—
220	C₁₆	C₂²×Dic₁₁	1	2	yes	—
221	C₁₆	C₂²×Dic₁₁	1	2	yes	—
222	C₁₁	C₂×#2179	1	1	yes	characteristic, complemented, Sylow
223	C₂³	—	4	2	no	—
224	C₂³	#66965	1	1	yes	characteristic
225	Q₈	—	2	4	no	—
226	Q₈	—	4	2	no	—
227	D₄	—	2	4	no	—
228	D₄	—	4	4	no	—
229	D₄	—	4	4	no	—
230	D₄	—	4	2	no	—
231	C₂×C₄	—	4	2	no	—
232	C₂×C₄	—	4	4	no	—
233	C₂×C₄	—	4	4	no	—
234	C₂×C₄	—	22	2	no	—
235	C₂×C₄	—	44	2	no	—
236	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
237	C₂×C₄	D₈×D₁₁	1	1	yes	characteristic
238	C₂×C₄	#66965	1	1	yes	characteristic
239	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
240	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
241	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
242	C₈	—	11	4	no	—
243	C₈	—	44	4	no	—
244	C₈	D₄×Dic₁₁	1	1	yes	characteristic
245	C₈	D₄×Dic₁₁	1	1	yes	characteristic
246	C₈	C₂×#4341	1	1	yes	characteristic
247	C₈	C₂³×Dic₁₁	1	1	yes	characteristic
248	C₂²	—	2	2	no	—
249	C₂²	—	4	4	no	—
250	C₂²	—	8	4	no	—
251	C₂²	D₈×Dic₁₁	1	1	yes	characteristic
252	C₂²	D₈×Dic₁₁	1	1	yes	characteristic
253	C₂²	C₂×#66965	1	1	yes	characteristic
254	C₄	—	4	4	no	—
255	C₄	—	44	2	no	—
256	C₄	D₈×Dic₁₁	1	1	yes	characteristic
257	C₄	D₈×Dic₁₁	1	1	yes	characteristic
258	C₄	C₂×D₈×D₁₁	1	1	yes	characteristic
259	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	2	1	no	—
262	C₂	—	8	4	no	—
263	C₂	#13070502	1	2	yes	direct product factor
264	C₂	C₂×D₈×Dic₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₁₁
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting, prime radical	C₂×C₁₁×#508	C₂
socle	C₂²×C₁₁	C₄×D₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×#508	D₁₁
hypocenter	C₁₁	C₂×#2179
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#508

Complements

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

N	H ≅ G/N	type
1. C₂×#10622809	C₂	semidirect
2. #13070502	C₂	direct (N × H)
3. C₂×#10622144	C₂	semidirect
4. C₂×#10622205	C₂	semidirect
5. C₂×#10622140	C₂	semidirect
9. C₁₁×#508	C₄	semidirect
11. C₂×C₁₁×Q₃₂	C₄	semidirect
12. C₂×C₁₁×SD₃₂	C₄	semidirect
13. C₂×C₁₁×D₁₆	C₄	semidirect
17. #10622809	C₂²	semidirect
21. #10622205	C₂²	semidirect
22. #10622144	C₂²	semidirect
23. #10622140	C₂²	semidirect
40. C₁₁×Q₃₂	C₂×C₄	semidirect
41. C₁₁×SD₃₂	C₂×C₄	semidirect
42. C₁₁×D₁₆	C₂×C₄	semidirect
124. #508	Dic₁₁	semidirect
126. C₂×Q₃₂	Dic₁₁	semidirect
127. C₂×SD₃₂	Dic₁₁	semidirect
128. C₂×D₁₆	Dic₁₁	semidirect
167. Q₃₂	C₂×Dic₁₁	semidirect
168. SD₃₂	C₂×Dic₁₁	semidirect
169. D₁₆	C₂×Dic₁₁	semidirect
185. C₂×C₁₁	#2179	semidirect
222. C₁₁	C₂×#2179	semidirect
263. C₂	#13070502	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×#10622809	2
#13070502	2
C₂×#10622144	2
C₂×#10622205	2
C₂×#10622140	2
C₂×C₁₁×#508	2
C₂×#2179	11

Subgroups — C2×#13070502 #14907179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070502 #14907179