Subgroups — C₂×#13066451 #14643229

Order 2816.

830 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₁₁⋊C₈)	C₂	1	2	yes	maximal
2	#13066451	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈×C₁₁	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂³×C₁₁⋊C₈	—	2	2	no	—
7	C₂×C₄×C₈×C₁₁	—	2	4	no	—
8	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
11	C₂×C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
12	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	8	yes	—
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	4	yes	—
14	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	—	2	4	no	—
18	C₂²×C₈×C₁₁	—	2	4	no	—
19	C₂²×C₈×C₁₁	C₈	1	8	yes	complemented
20	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
22	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₁	D₄	1	4	yes	—
25	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
27	C₂²×C₁₁⋊C₈	—	2	8	no	—
28	C₂²×C₁₁⋊C₈	—	2	4	no	—
29	C₂²×C₁₁⋊C₈	—	4	4	no	—
30	C₂²×C₁₁⋊C₈	—	4	4	no	—
31	C₄×C₈×C₁₁	—	2	4	no	—
32	C₄×C₈×C₁₁	—	2	4	no	—
33	C₄⋊(C₁₁⋊C₈)	—	2	8	no	—
34	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
35	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	8	yes	—
36	C₂×#1277	—	11	1	no	maximal, Sylow
37	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	—	2	4	no	—
39	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
40	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
41	C₂²×C₄×C₁₁	C₂²⋊C₄	1	4	yes	—
42	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	C₄⋊C₄	1	4	yes	—
44	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
47	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
48	C₂²×C₄×C₁₁	D₈	1	2	yes	—
49	C₂²×C₄×C₁₁	SD₁₆	1	4	yes	—
50	C₂²×C₄×C₁₁	Q₁₆	1	2	yes	—
51	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₈×C₁₁	—	2	16	no	—
55	C₂×C₈×C₁₁	—	2	4	no	—
56	C₂×C₈×C₁₁	—	2	4	no	—
57	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	complemented
58	C₄²×C₁₁	C₄²	1	2	yes	—
59	C₄²×C₁₁	C₂²⋊C₄	1	4	yes	—
60	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
61	C₄²×C₁₁	C₄⋊C₄	1	4	yes	—
62	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
63	C₄²×C₁₁	C₂×D₄	1	2	yes	—
64	C₂×C₁₁⋊C₈	—	2	8	no	—
65	C₂×C₁₁⋊C₈	—	4	16	no	—
66	C₂×C₁₁⋊C₈	—	4	4	no	—
67	C₂×C₁₁⋊C₈	—	4	4	no	—
68	C₂²×C₄⋊C₈	—	11	2	no	—
69	C₂²×C₄×C₈	D₁₁	1	1	yes	characteristic
70	#1277	—	11	4	no	—
71	C₂³×C₁₁	#95	1	2	yes	—
72	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
73	C₂³×C₁₁	#106	1	2	yes	—
74	C₂³×C₁₁	#107	1	2	yes	—
75	C₂³×C₁₁	#108	1	4	yes	—
76	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₁	—	2	8	no	—
78	C₂×C₄×C₁₁	—	2	2	no	—
79	C₂×C₄×C₁₁	—	2	2	no	—
80	C₂×C₄×C₁₁	#95	1	2	yes	—
81	C₂×C₄×C₁₁	#95	1	2	yes	—
82	C₂×C₄×C₁₁	#95	1	2	yes	—
83	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
84	C₂×C₄×C₁₁	#97	1	4	yes	—
85	C₂×C₄×C₁₁	C₂²⋊C₈	1	8	yes	—
86	C₂×C₄×C₁₁	#102	1	8	yes	—
87	C₂×C₄×C₁₁	#103	1	8	yes	—
88	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
89	C₂×C₄×C₁₁	#106	1	2	yes	—
90	C₂×C₄×C₁₁	#107	1	2	yes	—
91	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
93	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
95	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
96	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
97	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
99	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
100	C₈×C₁₁	—	2	8	no	—
101	C₁₁⋊C₈	—	4	8	no	—
102	C₂³×C₈	—	22	2	no	—
103	C₂³×C₈	Dic₁₁	1	2	yes	—
104	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
105	C₂×C₄⋊C₈	—	11	4	no	—
106	C₂×C₄⋊C₈	—	11	8	no	—
107	C₂×C₄⋊C₈	—	22	2	no	—
108	C₂×C₄⋊C₈	—	22	4	no	—
109	C₂×C₄×C₈	—	2	4	no	—
110	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
111	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
112	C₂²×C₁₁	#334	1	8	yes	—
113	C₂²×C₁₁	#335	1	8	yes	—
114	C₂²×C₁₁	#336	1	4	yes	—
115	C₂²×C₁₁	#340	1	4	yes	—
116	C₂²×C₁₁	#341	1	4	yes	—
117	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
118	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
119	C₂²×C₁₁	C₂×#106	1	1	yes	characteristic
120	C₂²×C₁₁	C₂×#107	1	1	yes	characteristic
121	C₂²×C₁₁	C₂×#108	1	2	yes	—
122	C₄×C₁₁	—	2	2	no	—
123	C₄×C₁₁	—	2	2	no	—
124	C₄×C₁₁	#336	1	4	yes	—
125	C₄×C₁₁	#340	1	4	yes	—
126	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
127	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
128	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
129	C₄×C₁₁	C₂×#102	1	2	yes	—
130	C₄×C₁₁	C₂×#103	1	2	yes	—
131	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
132	C₂³×C₄	D₄₄	1	1	yes	characteristic
133	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
134	C₂²×C₈	—	2	4	no	—
135	C₂²×C₈	—	2	4	no	—
136	C₂²×C₈	—	22	8	no	—
137	C₂²×C₈	—	22	4	no	—
138	C₂²×C₈	—	44	4	no	—
139	C₂²×C₈	—	44	4	no	—
140	C₂²×C₈	C₁₁⋊C₈	1	8	yes	complemented
141	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
142	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
143	C₂×C₄²	C₄×D₁₁	1	4	yes	—
144	C₂×C₄²	D₄₄	1	1	yes	characteristic
145	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
146	C₂×C₄²	C₂²⋊D₁₁	1	4	yes	—
147	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
148	C₄⋊C₈	—	11	8	no	—
149	C₄⋊C₈	—	22	8	no	—
150	C₄⋊C₈	—	22	4	no	—
151	C₄×C₈	—	2	4	no	—
152	C₄×C₈	—	2	4	no	—
153	C₂×C₁₁	#1277	1	8	yes	complemented
154	C₂×C₁₁	C₂×#334	1	2	yes	—
155	C₂×C₁₁	C₂×#335	1	2	yes	—
156	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
157	C₂×C₁₁	C₂×#340	1	1	yes	characteristic
158	C₂×C₁₁	C₂×#341	1	1	yes	characteristic
159	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
160	C₂²×C₄	—	2	4	no	—
161	C₂²×C₄	#4314	1	4	yes	—
162	C₂²×C₄	D₈₈	1	2	yes	—
163	C₂²×C₄	Dic₄₄	1	2	yes	—
164	C₂²×C₄	C₂×C₁₁⋊C₈	1	4	yes	—
165	C₂²×C₄	#4318	1	4	yes	—
166	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
167	C₂²×C₄	Dic₁₁⋊C₄	1	4	yes	—
168	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
169	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
170	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
171	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	4	yes	—
172	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
173	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
174	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
175	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
176	C₂×C₈	—	2	16	no	—
177	C₂×C₈	—	2	4	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	22	8	no	—
180	C₂×C₈	—	44	16	no	—
181	C₂×C₈	—	44	4	no	—
182	C₂×C₈	—	44	4	no	—
183	C₂×C₈	C₂×C₁₁⋊C₈	1	8	yes	complemented
184	C₄²	C₄×Dic₁₁	1	2	yes	—
185	C₄²	Dic₁₁⋊C₄	1	4	yes	—
186	C₄²	(C₂×D₁₁)⋊C₄	1	4	yes	—
187	C₄²	C₂²⋊Dic₁₁	1	2	yes	—
188	C₄²	C₂×C₄×D₁₁	1	2	yes	—
189	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
190	C₁₁	C₂×#1277	1	1	yes	characteristic, complemented, Sylow
191	C₂³	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
192	C₂³	#66881	1	2	yes	—
193	C₂³	#66882	1	2	yes	—
194	C₂³	#66883	1	4	yes	—
195	C₂³	C₁₁⋊#95	1	2	yes	—
196	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
197	C₂×C₄	—	2	2	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	8	no	—
200	C₂×C₄	C₄×C₁₁⋊C₈	1	4	yes	—
201	C₂×C₄	#66867	1	4	yes	—
202	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
203	C₂×C₄	#66880	1	8	yes	—
204	C₂×C₄	#66881	1	2	yes	—
205	C₂×C₄	#66882	1	2	yes	—
206	C₂×C₄	#66885	1	8	yes	—
207	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	8	yes	—
208	C₂×C₄	C₁₁⋊#95	1	2	yes	—
209	C₂×C₄	C₁₁⋊#95	1	2	yes	—
210	C₂×C₄	C₁₁⋊#95	1	2	yes	—
211	C₂×C₄	C₂×#4314	1	2	yes	—
212	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
213	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
214	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
215	C₂×C₄	C₂×#4318	1	2	yes	—
216	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
217	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
218	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	2	yes	—
219	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
220	C₈	—	2	8	no	—
221	C₈	—	44	8	no	—
222	C₂²	#10622095	1	8	yes	—
223	C₂²	#10622096	1	8	yes	—
224	C₂²	#10622162	1	4	yes	—
225	C₂²	#10622189	1	4	yes	—
226	C₂²	#10622190	1	4	yes	—
227	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	2	yes	—
228	C₂²	C₂×#66881	1	1	yes	characteristic
229	C₂²	C₂×#66882	1	1	yes	characteristic
230	C₂²	C₂×#66883	1	2	yes	—
231	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	2	2	no	—
234	C₄	#10622162	1	4	yes	—
235	C₄	#10622189	1	4	yes	—
236	C₄	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
237	C₄	C₂×#66867	1	1	yes	characteristic
238	C₄	C₂×#66880	1	2	yes	—
239	C₄	C₂×#66885	1	2	yes	—
240	C₄	C₂×C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
241	C₂	#13066451	1	8	yes	direct product factor
242	C₂	C₂×#10622095	1	2	yes	—
243	C₂	C₂×#10622096	1	2	yes	—
244	C₂	C₂×#10622162	1	1	yes	characteristic
245	C₂	C₂×#10622189	1	1	yes	characteristic
246	C₂	C₂×#10622190	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	D₄₄
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂²×C₄×C₈×C₁₁	C₂
socle, prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂²×C₄×C₈	D₁₁
hypocenter	C₁₁	C₂×#1277
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13066451	C₂	direct (N × H)
19. C₂²×C₈×C₁₁	C₈	semidirect
57. C₂×C₈×C₁₁	C₂×C₈	semidirect
140. C₂²×C₈	C₁₁⋊C₈	semidirect
153. C₂×C₁₁	#1277	semidirect
183. C₂×C₈	C₂×C₁₁⋊C₈	semidirect
190. C₁₁	C₂×#1277	semidirect
241. C₂	#13066451	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₄⋊(C₁₁⋊C₈)	2
#13066451	2
C₂²×C₄×C₈×C₁₁	2
C₂×#1277	11

Subgroups — C2×#13066451 #14643229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13066451 #14643229