Subgroups — C₂×#13070498 #14907174

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622517	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622313	C₂	1	2	yes	maximal, complemented
3	#13070498	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622144	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10622148	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66957	C₂²	1	2	yes	—
8	C₂×#66954	—	2	2	no	—
9	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×#66883	C₂²	1	2	yes	—
13	C₂×#66869	—	2	2	no	—
14	C₂×Dic₈₈	C₄	1	1	yes	characteristic, complemented
15	#10622517	C₄	1	4	yes	complemented
16	#10622517	C₂²	1	4	yes	—
17	C₂×#66864	C₄	1	2	yes	complemented
18	C₂×D₁₇₆	C₄	1	1	yes	characteristic, complemented
19	#10622313	—	2	4	no	—
20	#10622313	C₂²	1	8	yes	complemented
21	C₄×C₁₁×C₁₆	C₂²	1	4	yes	complemented
22	#10622148	C₂²	1	8	yes	complemented
23	#10622144	C₂²	1	4	yes	complemented
24	C₂×#4339	—	2	2	no	—
25	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
28	C₂×#4318	—	2	2	no	—
29	C₂×Dic₄₄	C₂×C₄	1	2	yes	—
30	#66957	—	2	2	no	—
31	#66957	—	2	2	no	—
32	#66957	C₂×C₄	1	4	yes	—
33	#66957	C₂³	1	4	yes	—
34	C₂×D₈₈	C₂×C₄	1	2	yes	—
35	C₂×#4314	—	2	2	no	—
36	#66954	—	2	8	no	—
37	#66954	—	4	4	no	—
38	C₂×#4313	—	4	2	no	—
39	C₂×C₈×D₁₁	—	4	2	no	—
40	C₂×C₁₁×C₁₆	—	2	1	no	—
41	C₂×C₁₁×C₁₆	—	2	1	no	—
42	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
43	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
44	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
45	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
46	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
47	C₄×C₈×C₁₁	D₄	1	2	yes	—
48	C₄×C₈×C₁₁	C₂³	1	2	yes	—
49	#66883	—	2	2	no	—
50	#66883	C₂³	1	4	yes	—
51	#66869	—	2	8	no	—
52	Dic₈₈	C₂×C₄	1	4	yes	complemented
53	#66864	C₂×C₄	1	8	yes	complemented
54	D₁₇₆	C₂×C₄	1	4	yes	complemented
55	C₂×#2178	—	11	1	no	maximal, Sylow
56	C₂²×C₄×C₁₁	—	2	1	no	—
57	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₂×C₂²⋊D₁₁	—	4	2	no	—
59	#4339	—	2	4	no	—
60	#4339	—	2	4	no	—
61	#4339	—	4	2	no	—
62	#4339	—	4	2	no	—
63	C₂×D₄₄	—	2	2	no	—
64	C₂×C₄×D₁₁	—	4	2	no	—
65	C₂×Dic₂₂	—	2	2	no	—
66	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
67	C₂×C₈×C₁₁	D₈	1	2	yes	—
68	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
73	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
74	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
76	C₄²×C₁₁	—	2	1	no	—
77	C₄²×C₁₁	C₂×D₄	1	2	yes	—
78	#4318	—	2	4	no	—
79	#4318	—	4	2	no	—
80	C₂×C₁₁⋊C₈	—	4	2	no	—
81	Dic₄₄	—	2	2	no	—
82	Dic₄₄	C₂²×C₄	1	4	yes	—
83	D₈₈	—	2	2	no	—
84	D₈₈	C₂²×C₄	1	4	yes	—
85	#4314	—	2	4	no	—
86	#4314	—	2	4	no	—
87	#4313	—	4	8	no	—
88	C₈×D₁₁	—	4	8	no	—
89	C₁₁×C₁₆	—	2	2	no	—
90	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
91	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
92	C₂×#508	—	11	1	no	—
93	C₂×#443	—	11	2	no	—
94	#2178	—	11	8	no	—
95	C₂×#368	—	11	1	no	—
96	C₂×#359	—	11	2	no	—
97	C₂×C₄×C₁₆	D₁₁	1	1	yes	characteristic, complemented
98	C₂³×C₁₁	#135	1	1	yes	characteristic
99	C₂²×D₁₁	—	4	2	no	—
100	C₂×C₄×C₁₁	—	2	4	no	—
101	C₂×C₄×C₁₁	—	2	2	no	—
102	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
106	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
108	C₂²⋊D₁₁	—	4	4	no	—
109	C₂²⋊D₁₁	—	4	4	no	—
110	C₂×Dic₁₁	—	4	2	no	—
111	D₄₄	—	2	4	no	—
112	D₄₄	—	4	2	no	—
113	C₄×D₁₁	—	4	4	no	—
114	C₄×D₁₁	—	4	4	no	—
115	Dic₂₂	—	2	4	no	—
116	Dic₂₂	—	4	2	no	—
117	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
118	C₈×C₁₁	C₄×D₄	1	1	yes	characteristic
119	C₈×C₁₁	C₂×D₈	1	2	yes	—
120	C₈×C₁₁	C₂×D₈	1	2	yes	—
121	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
122	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
123	C₁₁⋊C₈	—	4	4	no	—
124	C₂×#135	—	11	2	no	—
125	C₂×#131	—	22	2	no	—
126	#508	—	11	4	no	—
127	#508	—	11	4	no	—
128	C₂×Q₃₂	—	11	1	no	—
129	C₂×SD₃₂	—	11	2	no	—
130	C₂×D₁₆	—	11	1	no	—
131	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
132	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
133	#443	—	11	8	no	—
134	#443	—	22	4	no	—
135	C₂×#108	—	11	2	no	—
136	C₂×#104	—	22	2	no	—
137	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
138	#368	—	11	4	no	—
139	#359	—	11	8	no	—
140	C₄×C₁₆	C₂×D₁₁	1	4	yes	complemented
141	C₂²×C₁₁	—	2	2	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	C₂×D₁₁	—	4	4	no	—
146	C₂×D₁₁	—	8	4	no	—
147	C₄×C₁₁	—	2	4	no	—
148	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
149	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
150	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
151	C₄×C₁₁	C₂²×D₈	1	1	yes	characteristic
152	Dic₁₁	—	4	4	no	—
153	C₂×#41	—	22	2	no	—
154	#135	—	11	4	no	—
155	#135	—	11	4	no	—
156	#135	—	22	2	no	—
157	#135	—	22	2	no	—
158	C₂×Q₁₆	—	11	2	no	—
159	C₂×SD₁₆	—	22	2	no	—
160	C₂×D₈	—	11	2	no	—
161	#131	—	22	8	no	—
162	#131	—	44	4	no	—
163	C₂×M₁₆	—	22	2	no	—
164	C₂×M₁₆	—	44	2	no	—
165	C₂²×C₈	—	44	2	no	—
166	C₂²×C₈	D₄₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
168	C₂×C₄²	D₄₄	1	1	yes	characteristic
169	Q₃₂	—	11	4	no	—
170	SD₃₂	—	11	8	no	—
171	D₁₆	—	11	4	no	—
172	C₂×C₁₆	—	2	1	no	—
173	C₂×C₁₆	—	2	1	no	—
174	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
175	C₂×C₁₆	C₄×D₁₁	1	1	yes	characteristic
176	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
177	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
178	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
179	#108	—	11	4	no	—
180	#108	—	22	2	no	—
181	#104	—	22	8	no	—
182	C₄×C₈	D₄₄	1	2	yes	—
183	C₄×C₈	C₂²×D₁₁	1	2	yes	—
184	C₂×C₁₁	—	2	1	no	—
185	C₂×C₁₁	—	2	1	no	—
186	C₂×C₁₁	#2178	1	2	yes	complemented
187	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
188	D₁₁	—	8	4	no	—
189	#41	—	22	4	no	—
190	#41	—	22	4	no	—
191	#41	—	44	2	no	—
192	#41	—	44	2	no	—
193	C₂×Q₈	—	22	2	no	—
194	C₂×D₄	—	22	2	no	—
195	C₂×D₄	—	44	2	no	—
196	C₂²×C₄	—	2	1	no	—
197	C₂²×C₄	—	44	2	no	—
198	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
199	Q₁₆	—	11	4	no	—
200	Q₁₆	—	22	2	no	—
201	SD₁₆	—	22	4	no	—
202	SD₁₆	—	22	4	no	—
203	D₈	—	11	4	no	—
204	D₈	—	22	2	no	—
205	M₁₆	—	22	4	no	—
206	M₁₆	—	44	2	no	—
207	M₁₆	—	44	8	no	—
208	C₂×C₈	—	44	2	no	—
209	C₂×C₈	—	44	8	no	—
210	C₂×C₈	D₈₈	1	1	yes	characteristic
211	C₂×C₈	D₈₈	1	2	yes	—
212	C₂×C₈	D₈₈	1	1	yes	characteristic
213	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
214	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
215	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
216	C₂×C₈	C₂×D₄₄	1	2	yes	—
217	C₂×C₈	#4339	1	1	yes	characteristic
218	C₂×C₈	#4339	1	1	yes	characteristic
219	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
220	C₄²	—	2	1	no	—
221	C₄²	C₂×D₄₄	1	2	yes	—
222	C₁₆	—	2	2	no	—
223	C₁₆	C₂×C₄×D₁₁	1	2	yes	—
224	C₁₆	C₂×C₄×D₁₁	1	2	yes	—
225	C₁₁	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
226	C₂³	—	44	2	no	—
227	C₂³	#66957	1	1	yes	characteristic
228	Q₈	—	22	4	no	—
229	Q₈	—	44	2	no	—
230	D₄	—	22	4	no	—
231	D₄	—	44	4	no	—
232	D₄	—	44	4	no	—
233	D₄	—	44	2	no	—
234	C₂×C₄	—	2	4	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	44	2	no	—
237	C₂×C₄	—	44	4	no	—
238	C₂×C₄	—	44	4	no	—
239	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
240	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
241	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
242	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
243	C₂×C₄	#66957	1	1	yes	characteristic
244	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
245	C₈	—	44	4	no	—
246	C₈	C₄×D₄₄	1	1	yes	characteristic
247	C₈	C₄×D₄₄	1	1	yes	characteristic
248	C₈	C₂×D₈₈	1	2	yes	—
249	C₈	C₂×D₈₈	1	2	yes	—
250	C₈	C₂²×C₄×D₁₁	1	1	yes	characteristic
251	C₈	C₂×#4339	1	1	yes	characteristic
252	C₂²	—	2	2	no	—
253	C₂²	—	44	4	no	—
254	C₂²	—	88	4	no	—
255	C₂²	C₄×D₈₈	1	1	yes	characteristic
256	C₂²	C₄×D₈₈	1	1	yes	characteristic
257	C₂²	C₂×#66957	1	1	yes	characteristic
258	C₄	—	2	4	no	—
259	C₄	—	44	4	no	—
260	C₄	C₄×D₈₈	1	1	yes	characteristic
261	C₄	C₄×D₈₈	1	1	yes	characteristic
262	C₄	C₂×C₄×D₄₄	1	1	yes	characteristic
263	C₄	C₂²×D₈₈	1	1	yes	characteristic
264	C₂	—	2	1	no	—
265	C₂	—	2	1	no	—
266	C₂	—	88	4	no	—
267	C₂	#13070498	1	2	yes	direct product factor
268	C₂	C₂×C₄×D₈₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₈₈
commutator	C₈×C₁₁	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₄×C₁₁×C₁₆	C₂
socle	C₂²×C₁₁	C₄×D₈
prime radical	C₂×#10622517	C₂
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₄×C₁₆	D₁₁
hypocenter	C₁₁	C₂×#2178
LCS	G ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×#10622313	C₂	semidirect
3. #13070498	C₂	direct (N × H)
4. C₂×#10622144	C₂	semidirect
5. C₂×#10622148	C₂	semidirect
6. C₂×C₄×C₁₁×C₁₆	C₂	semidirect
14. C₂×Dic₈₈	C₄	semidirect
15. #10622517	C₄	semidirect
17. C₂×#66864	C₄	semidirect
18. C₂×D₁₇₆	C₄	semidirect
20. #10622313	C₂²	semidirect
21. C₄×C₁₁×C₁₆	C₂²	semidirect
22. #10622148	C₂²	semidirect
23. #10622144	C₂²	semidirect
52. Dic₈₈	C₂×C₄	semidirect
53. #66864	C₂×C₄	semidirect
54. D₁₇₆	C₂×C₄	semidirect
97. C₂×C₄×C₁₆	D₁₁	semidirect
140. C₄×C₁₆	C₂×D₁₁	semidirect
186. C₂×C₁₁	#2178	semidirect
225. C₁₁	C₂×#2178	semidirect
267. C₂	#13070498	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×#10622517	2
C₂×#10622313	2
#13070498	2
C₂×#10622144	2
C₂×#10622148	2
C₂×C₄×C₁₁×C₁₆	2
C₂×#2178	11

Subgroups — C2×#13070498 #14907174

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070498 #14907174