Subgroups — C₂×#13070788 #14908504

Order 2816.

558 conjugacy classes of subgroups.

The subgroup lattice has 286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622293	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10622313	C₂	1	1	yes	maximal, characteristic
3	#13070788	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622151	C₂	1	2	yes	maximal, complemented
5	C₂×#10622156	C₂	1	2	yes	maximal
6	C₂×C₁₁×#364	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#66957	C₂²	1	1	yes	characteristic
8	C₂×#66954	—	2	1	no	—
9	C₂×#66922	—	2	1	no	—
10	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×#66883	C₂²	1	1	yes	characteristic
13	C₂×#66881	—	2	1	no	—
14	C₂×#66881	C₂²	1	2	yes	—
15	C₂×#66869	—	2	1	no	—
16	#10622313	—	2	2	no	—
17	#10622313	C₂²	1	4	yes	—
18	#10622293	—	2	2	no	—
19	#10622293	C₂²	1	4	yes	complemented
20	C₁₁×#364	C₂²	1	4	yes	complemented
21	#10622156	C₂²	1	8	yes	—
22	#10622151	C₂²	1	8	yes	complemented
23	C₂×#4339	—	2	1	no	—
24	C₂²×Dic₂₂	—	4	1	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×C₄⋊Dic₁₁	—	2	2	no	—
29	C₂×C₄⋊Dic₁₁	—	4	1	no	—
30	C₂×#4318	—	2	1	no	—
31	C₂×Dic₄₄	Q₈	1	1	yes	characteristic, complemented
32	#66957	—	2	1	no	—
33	#66957	—	2	1	no	—
34	#66957	Q₈	1	2	yes	complemented
35	#66957	C₂³	1	2	yes	—
36	C₂×D₈₈	Q₈	1	1	yes	characteristic, complemented
37	C₂×#4314	—	2	1	no	—
38	#66954	—	2	4	no	—
39	#66954	—	4	2	no	—
40	C₂×#4313	—	4	1	no	—
41	C₂×C₈×D₁₁	—	4	1	no	—
42	#66922	—	2	4	no	—
43	#66922	—	4	2	no	—
44	C₁₁×M₃₂	—	2	2	no	—
45	C₁₁×M₃₂	C₂³	1	4	yes	—
46	C₂×C₁₁×C₁₆	—	2	2	no	—
47	C₄×C₈×C₁₁	D₄	1	2	yes	—
48	C₄×C₈×C₁₁	C₂³	1	2	yes	—
49	#66883	—	2	1	no	—
50	#66883	C₂³	1	2	yes	—
51	#66881	—	2	2	no	—
52	#66881	—	2	4	no	—
53	#66881	C₂³	1	4	yes	—
54	#66869	—	2	4	no	—
55	C₂×#2230	—	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	1	no	—
59	C₂²×Dic₁₁	—	4	2	no	—
60	#4339	—	2	2	no	—
61	#4339	—	2	2	no	—
62	#4339	—	4	1	no	—
63	#4339	—	4	1	no	—
64	C₂×D₄₄	—	2	1	no	—
65	C₂×C₄×D₁₁	—	4	1	no	—
66	C₂×Dic₂₂	—	2	1	no	—
67	C₂×Dic₂₂	—	4	4	no	—
68	C₂×Dic₂₂	—	8	4	no	—
69	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
70	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
71	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
72	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
74	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
76	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
77	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
78	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
79	C₄²×C₁₁	—	2	1	no	—
80	C₄²×C₁₁	C₂×D₄	1	2	yes	—
81	C₄⋊Dic₁₁	—	2	4	no	—
82	C₄⋊Dic₁₁	—	4	4	no	—
83	C₄⋊Dic₁₁	—	4	2	no	—
84	#4318	—	2	2	no	—
85	#4318	—	4	1	no	—
86	C₂×C₁₁⋊C₈	—	4	1	no	—
87	Dic₄₄	—	2	1	no	—
88	Dic₄₄	C₂×Q₈	1	2	yes	complemented
89	D₈₈	—	2	1	no	—
90	D₈₈	C₂×Q₈	1	2	yes	complemented
91	#4314	—	2	2	no	—
92	#4314	—	2	2	no	—
93	#4313	—	4	4	no	—
94	C₈×D₁₁	—	4	4	no	—
95	C₁₁×C₁₆	—	2	4	no	—
96	C₂×#498	—	11	1	no	—
97	C₂×#443	—	11	1	no	—
98	#2230	—	11	8	no	—
99	C₂×#365	—	11	2	no	—
100	C₂×#364	D₁₁	1	1	yes	characteristic, complemented
101	C₂×#360	—	11	2	no	—
102	C₂³×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
103	C₂²×D₁₁	—	4	1	no	—
104	C₂×C₄×C₁₁	—	2	4	no	—
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
110	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
111	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
112	C₂²⋊D₁₁	—	4	2	no	—
113	C₂²⋊D₁₁	—	4	2	no	—
114	C₂×Dic₁₁	—	4	1	no	—
115	C₂×Dic₁₁	—	4	4	no	—
116	C₂×Dic₁₁	—	8	4	no	—
117	D₄₄	—	2	2	no	—
118	D₄₄	—	4	1	no	—
119	C₄×D₁₁	—	4	2	no	—
120	C₄×D₁₁	—	4	2	no	—
121	Dic₂₂	—	2	2	no	—
122	Dic₂₂	—	4	1	no	—
123	Dic₂₂	—	8	8	no	—
124	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
125	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
126	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
127	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
128	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
129	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
130	C₁₁⋊C₈	—	4	2	no	—
131	C₂×#135	—	11	1	no	—
132	C₂×#131	—	22	1	no	—
133	C₂×C₄⋊Q₈	—	22	1	no	—
134	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
135	#498	—	11	4	no	—
136	#498	—	22	2	no	—
137	#443	—	11	4	no	—
138	#443	—	22	2	no	—
139	C₂×#108	—	11	1	no	—
140	C₂×#106	—	11	2	no	—
141	C₂×#106	—	22	1	no	—
142	C₂×#104	—	22	1	no	—
143	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
144	#365	—	11	8	no	—
145	#364	C₂×D₁₁	1	4	yes	complemented
146	#360	—	11	8	no	—
147	C₂²×C₁₁	—	2	2	no	—
148	C₂²×C₁₁	#476	1	1	yes	characteristic
149	C₂²×C₁₁	#476	1	1	yes	characteristic
150	C₂²×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×D₁₁	—	4	2	no	—
152	C₂×D₁₁	—	8	2	no	—
153	C₄×C₁₁	—	2	4	no	—
154	C₄×C₁₁	#476	1	1	yes	characteristic
155	C₄×C₁₁	#476	1	1	yes	characteristic
156	C₄×C₁₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
157	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
158	Dic₁₁	—	4	2	no	—
159	Dic₁₁	—	8	4	no	—
160	C₂×#41	—	22	1	no	—
161	C₂²×Q₈	—	44	1	no	—
162	#135	—	11	2	no	—
163	#135	—	11	2	no	—
164	#135	—	22	1	no	—
165	#135	—	22	1	no	—
166	C₂×Q₁₆	—	11	1	no	—
167	C₂×SD₁₆	—	22	1	no	—
168	C₂×D₈	—	11	1	no	—
169	#131	—	22	4	no	—
170	#131	—	44	2	no	—
171	C₂×M₁₆	—	22	1	no	—
172	C₂×M₁₆	—	44	1	no	—
173	C₂²×C₈	—	44	1	no	—
174	C₂²×C₈	D₄₄	1	1	yes	characteristic
175	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
176	C₄⋊Q₈	—	22	4	no	—
177	C₄⋊Q₈	—	44	2	no	—
178	C₂×C₄⋊C₄	—	22	2	no	—
179	C₂×C₄⋊C₄	—	44	1	no	—
180	C₂×C₄²	D₄₄	1	1	yes	characteristic
181	M₃₂	—	2	2	no	—
182	M₃₂	C₂²×D₁₁	1	4	yes	—
183	C₂×C₁₆	—	2	2	no	—
184	#108	—	11	2	no	—
185	#108	—	22	1	no	—
186	#106	—	11	4	no	—
187	#106	—	22	2	no	—
188	#106	—	22	4	no	—
189	#104	—	22	4	no	—
190	C₄×C₈	D₄₄	1	2	yes	—
191	C₄×C₈	C₂²×D₁₁	1	2	yes	—
192	C₂×C₁₁	—	2	1	no	—
193	C₂×C₁₁	—	2	1	no	—
194	C₂×C₁₁	#2230	1	2	yes	complemented
195	C₂×C₁₁	C₂×#476	1	1	yes	characteristic
196	D₁₁	—	8	2	no	—
197	#41	—	22	2	no	—
198	#41	—	22	2	no	—
199	#41	—	44	1	no	—
200	#41	—	44	1	no	—
201	C₂×Q₈	—	22	1	no	—
202	C₂×Q₈	—	44	4	no	—
203	C₂×Q₈	—	88	4	no	—
204	C₂×D₄	—	22	1	no	—
205	C₂×D₄	—	44	1	no	—
206	C₂²×C₄	—	2	1	no	—
207	C₂²×C₄	—	44	1	no	—
208	C₂²×C₄	—	44	2	no	—
209	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
210	Q₁₆	—	11	2	no	—
211	Q₁₆	—	22	1	no	—
212	SD₁₆	—	22	2	no	—
213	SD₁₆	—	22	2	no	—
214	D₈	—	11	2	no	—
215	D₈	—	22	1	no	—
216	M₁₆	—	22	2	no	—
217	M₁₆	—	44	1	no	—
218	M₁₆	—	44	4	no	—
219	C₂×C₈	—	44	1	no	—
220	C₂×C₈	—	44	4	no	—
221	C₂×C₈	#4314	1	1	yes	characteristic
222	C₂×C₈	#4314	1	1	yes	characteristic
223	C₂×C₈	#4314	1	2	yes	—
224	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
225	C₂×C₈	C₂×D₄₄	1	2	yes	—
226	C₂×C₈	#4341	1	1	yes	characteristic
227	C₂×C₈	#4341	1	1	yes	characteristic
228	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
229	C₂×C₈	Q₈×D₁₁	1	1	yes	characteristic
230	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
231	C₄⋊C₄	—	22	4	no	—
232	C₄⋊C₄	—	44	4	no	—
233	C₄⋊C₄	—	44	2	no	—
234	C₄²	—	2	1	no	—
235	C₄²	C₂×D₄₄	1	2	yes	—
236	C₁₆	—	2	4	no	—
237	C₁₁	C₂×#2230	1	1	yes	characteristic, complemented, Sylow
238	C₂³	—	44	1	no	—
239	C₂³	#66961	1	1	yes	characteristic
240	Q₈	—	22	2	no	—
241	Q₈	—	44	1	no	—
242	Q₈	—	88	8	no	—
243	D₄	—	22	2	no	—
244	D₄	—	44	2	no	—
245	D₄	—	44	2	no	—
246	D₄	—	44	1	no	—
247	C₂×C₄	—	2	4	no	—
248	C₂×C₄	—	2	2	no	—
249	C₂×C₄	—	44	1	no	—
250	C₂×C₄	—	44	2	no	—
251	C₂×C₄	—	44	2	no	—
252	C₂×C₄	—	44	4	no	—
253	C₂×C₄	—	88	4	no	—
254	C₂×C₄	#66950	1	1	yes	characteristic
255	C₂×C₄	#66950	1	1	yes	characteristic
256	C₂×C₄	C₂×#4314	1	1	yes	characteristic
257	C₂×C₄	C₂×#4314	1	1	yes	characteristic
258	C₂×C₄	#66961	1	1	yes	characteristic
259	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
260	C₈	—	44	2	no	—
261	C₈	#66950	1	1	yes	characteristic
262	C₈	#66950	1	1	yes	characteristic
263	C₈	C₂×#4314	1	2	yes	—
264	C₈	C₂×#4314	1	2	yes	—
265	C₈	C₂×#4341	1	1	yes	characteristic
266	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
267	C₂²	—	2	2	no	—
268	C₂²	—	44	2	no	—
269	C₂²	—	88	2	no	—
270	C₂²	#10622455	1	1	yes	characteristic
271	C₂²	#10622455	1	1	yes	characteristic
272	C₂²	C₂×#66961	1	1	yes	characteristic
273	C₄	—	2	4	no	—
274	C₄	—	44	2	no	—
275	C₄	—	88	4	no	—
276	C₄	#10622455	1	1	yes	characteristic
277	C₄	#10622455	1	1	yes	characteristic
278	C₄	C₂×#66950	1	1	yes	characteristic
279	C₄	C₂²×#4314	1	1	yes	characteristic
280	C₂	—	2	1	no	—
281	C₂	—	2	1	no	—
282	C₂	—	88	2	no	—
283	C₂	#13070788	1	2	yes	direct product factor
284	C₂	C₂×#10622455	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622455
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₂×C₁₁×#364	C₂
socle	C₂²×C₁₁	#476
prime radical	C₂×#66957	C₂²
hypercenter	C₂×#364	D₁₁
hypocenter	C₁₁	C₂×#2230
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#364

Complements

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

N	H ≅ G/N	type
1. C₂×#10622293	C₂	semidirect
3. #13070788	C₂	direct (N × H)
4. C₂×#10622151	C₂	semidirect
6. C₂×C₁₁×#364	C₂	semidirect
19. #10622293	C₂²	semidirect
20. C₁₁×#364	C₂²	semidirect
22. #10622151	C₂²	semidirect
31. C₂×Dic₄₄	Q₈	semidirect
34. #66957	Q₈	semidirect
36. C₂×D₈₈	Q₈	semidirect
88. Dic₄₄	C₂×Q₈	semidirect
90. D₈₈	C₂×Q₈	semidirect
100. C₂×#364	D₁₁	semidirect
145. #364	C₂×D₁₁	semidirect
194. C₂×C₁₁	#2230	semidirect
237. C₁₁	C₂×#2230	semidirect
283. C₂	#13070788	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×#10622293	2
C₂×#10622313	2
#13070788	2
C₂×#10622151	2
C₂×#10622156	2
C₂×C₁₁×#364	2
C₂×#2230	11

Subgroups — C2×#13070788 #14908504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13070788 #14908504