Subgroups — C₂×#13067524 #14723536

Order 2816.

654 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622444	C₂	1	2	yes	maximal
2	C₂×C₄×Dic₄₄	C₂	1	1	yes	maximal, characteristic
3	#13067524	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10622122	C₂	1	2	yes	maximal
5	C₂×#10622093	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×#334	C₂	1	1	yes	maximal, characteristic
7	C₂²×Dic₄₄	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₂₂	C₂²	1	2	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×#66882	C₄	1	1	yes	characteristic
12	C₂×#66880	C₄	1	2	yes	—
13	C₂×#66879	—	2	2	no	—
14	C₂×Dic₁₁⋊C₈	—	2	2	no	—
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
17	#10622444	—	2	4	no	—
18	#10622444	C₂²	1	8	yes	—
19	C₄×Dic₄₄	C₄	1	4	yes	—
20	C₄×Dic₄₄	C₂²	1	4	yes	—
21	C₁₁×#334	C₂²	1	4	yes	—
22	#10622122	C₂²	1	8	yes	—
23	#10622093	C₂²	1	4	yes	—
24	C₂²×Dic₂₂	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₁	—	2	2	no	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
29	C₂×C₄⋊Dic₁₁	C₂×C₄	1	2	yes	—
30	C₂×Dic₁₁⋊C₄	—	2	2	no	—
31	C₂×C₄×Dic₁₁	—	2	2	no	—
32	C₂²×C₁₁⋊C₈	—	2	1	no	—
33	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
34	C₂×Dic₄₄	—	2	4	no	—
35	C₂×Dic₄₄	C₂×C₄	1	4	yes	—
36	C₄×Dic₂₂	—	2	2	no	—
37	C₄×Dic₂₂	—	2	2	no	—
38	C₄×Dic₂₂	C₂×C₄	1	4	yes	—
39	C₄×Dic₂₂	C₂³	1	4	yes	—
40	C₁₁×C₄⋊C₈	—	2	2	no	—
41	C₁₁×C₄⋊C₈	C₂³	1	4	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₁	C₂³	1	2	yes	—
44	#66882	C₂×C₄	1	4	yes	—
45	#66880	C₂×C₄	1	8	yes	—
46	#66879	—	2	8	no	—
47	Dic₁₁⋊C₈	—	2	8	no	—
48	C₄×C₁₁⋊C₈	—	2	1	no	—
49	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
50	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
51	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
52	C₂×#1593	—	11	1	no	maximal, Sylow
53	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
56	C₂²×Dic₁₁	—	2	2	no	—
57	C₂²×Dic₁₁	—	2	2	no	—
58	C₂×Dic₂₂	—	2	2	no	—
59	C₂×Dic₂₂	—	2	4	no	—
60	C₂×Dic₂₂	—	2	4	no	—
61	C₂×Dic₂₂	C₂²×C₄	1	4	yes	—
62	C₂×C₈×C₁₁	—	2	2	no	—
63	C₂×C₈×C₁₁	—	2	4	no	—
64	C₂×C₈×C₁₁	—	4	4	no	—
65	C₂×C₈×C₁₁	M₁₆	1	4	yes	—
66	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
68	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₁₁	#41	1	1	yes	characteristic
71	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
72	C₄⋊Dic₁₁	—	2	2	no	—
73	C₄⋊Dic₁₁	C₂²×C₄	1	4	yes	—
74	Dic₁₁⋊C₄	—	2	4	no	—
75	Dic₁₁⋊C₄	—	2	4	no	—
76	C₄×Dic₁₁	—	2	4	no	—
77	C₄×Dic₁₁	—	2	4	no	—
78	C₂×C₁₁⋊C₈	—	2	4	no	—
79	C₂×C₁₁⋊C₈	—	2	2	no	—
80	C₂×C₁₁⋊C₈	—	4	2	no	—
81	C₂×C₁₁⋊C₈	C₂×D₄	1	4	yes	—
82	Dic₄₄	—	2	8	no	—
83	C₂×#446	—	11	2	no	—
84	C₂×C₄×Q₁₆	—	11	1	no	—
85	#1593	—	11	8	no	—
86	C₂×#334	D₁₁	1	1	yes	characteristic
87	C₂×Q₈⋊C₈	—	11	2	no	—
88	C₂×#322	—	11	1	no	—
89	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
94	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
95	C₂×C₄×C₁₁	#131	1	2	yes	—
96	C₂×C₄×C₁₁	#137	1	4	yes	—
97	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
100	C₂×Dic₁₁	—	2	4	no	—
101	C₂×Dic₁₁	—	2	4	no	—
102	C₂×Dic₁₁	—	4	4	no	—
103	C₂×Dic₁₁	—	4	4	no	—
104	Dic₂₂	—	2	4	no	—
105	Dic₂₂	—	2	4	no	—
106	Dic₂₂	—	4	4	no	—
107	C₈×C₁₁	—	2	2	no	—
108	C₈×C₁₁	—	4	4	no	—
109	C₈×C₁₁	C₂×M₁₆	1	4	yes	—
110	C₁₁⋊C₈	—	2	4	no	—
111	C₁₁⋊C₈	—	4	2	no	—
112	C₂²×Q₁₆	—	11	1	no	—
113	C₂×C₄×Q₈	—	11	2	no	—
114	#446	—	11	8	no	—
115	#446	—	22	4	no	—
116	C₄×Q₁₆	—	11	4	no	—
117	C₄×Q₁₆	—	11	4	no	—
118	C₂×#107	—	11	1	no	—
119	C₂×C₄⋊C₈	—	22	2	no	—
120	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
121	C₂×#103	—	11	2	no	—
122	C₂×#97	—	22	2	no	—
123	C₂×C₄×C₈	—	11	1	no	—
124	C₂×C₄×C₈	—	11	1	no	—
125	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
126	#334	C₂×D₁₁	1	4	yes	—
127	Q₈⋊C₈	—	11	8	no	—
128	#322	—	11	4	no	—
129	C₂²×C₁₁	#436	1	2	yes	—
130	C₂²×C₁₁	#441	1	2	yes	—
131	C₂²×C₁₁	#444	1	2	yes	—
132	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
133	C₄×C₁₁	—	2	1	no	—
134	C₄×C₁₁	—	2	1	no	—
135	C₄×C₁₁	#436	1	2	yes	—
136	C₄×C₁₁	#441	1	2	yes	—
137	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
138	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
139	C₄×C₁₁	C₂×#137	1	2	yes	—
140	Dic₁₁	—	4	4	no	—
141	Dic₁₁	—	4	4	no	—
142	C₂²×Q₈	—	11	2	no	—
143	C₂×Q₁₆	—	11	4	no	—
144	C₂×Q₁₆	—	22	4	no	—
145	C₂²×C₈	—	2	2	no	—
146	C₂²×C₈	—	11	2	no	—
147	C₂²×C₈	—	22	1	no	—
148	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
149	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
150	C₄×Q₈	—	11	4	no	—
151	C₄×Q₈	—	11	4	no	—
152	C₄×Q₈	—	22	2	no	—
153	C₄×Q₈	—	22	2	no	—
154	C₂×C₄⋊C₄	—	11	2	no	—
155	C₂×C₄⋊C₄	—	22	2	no	—
156	C₂×C₄²	—	22	2	no	—
157	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
158	#107	—	11	4	no	—
159	C₄⋊C₈	—	2	2	no	—
160	C₄⋊C₈	—	22	8	no	—
161	C₄⋊C₈	C₂²×D₁₁	1	4	yes	—
162	#103	—	11	8	no	—
163	#97	—	22	8	no	—
164	C₄×C₈	—	11	2	no	—
165	C₄×C₈	—	11	2	no	—
166	C₄×C₈	—	11	2	no	—
167	C₄×C₈	—	22	1	no	—
168	C₄×C₈	C₄×D₁₁	1	2	yes	—
169	C₄×C₈	C₂²×D₁₁	1	2	yes	—
170	C₂×C₁₁	#1593	1	4	yes	complemented
171	C₂×C₁₁	C₂×#436	1	1	yes	characteristic
172	C₂×C₁₁	C₂×#441	1	1	yes	characteristic
173	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
174	C₂×Q₈	—	11	4	no	—
175	C₂×Q₈	—	22	2	no	—
176	C₂×Q₈	—	22	4	no	—
177	C₂×Q₈	—	22	4	no	—
178	C₂²×C₄	—	22	2	no	—
179	C₂²×C₄	—	22	2	no	—
180	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
181	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
182	C₂²×C₄	#4343	1	1	yes	characteristic
183	Q₁₆	—	22	8	no	—
184	C₂×C₈	—	2	2	no	—
185	C₂×C₈	—	2	4	no	—
186	C₂×C₈	—	4	4	no	—
187	C₂×C₈	—	11	4	no	—
188	C₂×C₈	—	22	4	no	—
189	C₂×C₈	—	22	2	no	—
190	C₂×C₈	—	44	2	no	—
191	C₂×C₈	#4313	1	4	yes	—
192	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
193	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
194	C₄⋊C₄	—	11	4	no	—
195	C₄⋊C₄	—	22	2	no	—
196	C₄⋊C₄	—	22	4	no	—
197	C₄⋊C₄	—	22	4	no	—
198	C₄²	—	22	4	no	—
199	C₄²	—	22	4	no	—
200	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
201	C₄²	D₄×D₁₁	1	1	yes	characteristic
202	C₄²	#4343	1	1	yes	characteristic
203	C₄²	C₂³×D₁₁	1	1	yes	characteristic
204	C₁₁	C₂×#1593	1	1	yes	characteristic, complemented, Sylow
205	C₂³	#66946	1	1	yes	characteristic
206	Q₈	—	22	4	no	—
207	Q₈	—	22	4	no	—
208	Q₈	—	44	4	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	22	4	no	—
211	C₂×C₄	—	22	4	no	—
212	C₂×C₄	—	44	4	no	—
213	C₂×C₄	—	44	4	no	—
214	C₂×C₄	#66946	1	1	yes	characteristic
215	C₂×C₄	#66946	1	1	yes	characteristic
216	C₂×C₄	#66946	1	1	yes	characteristic
217	C₂×C₄	C₂×#4313	1	2	yes	—
218	C₂×C₄	#66960	1	2	yes	—
219	C₂×C₄	#66968	1	4	yes	—
220	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
221	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
222	C₂×C₄	C₂×#4343	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	4	4	no	—
225	C₈	—	22	4	no	—
226	C₈	—	44	2	no	—
227	C₈	C₂×#4313	1	4	yes	—
228	C₂²	#10622451	1	2	yes	—
229	C₂²	#10622466	1	2	yes	—
230	C₂²	#10622507	1	2	yes	—
231	C₂²	C₂×#66946	1	1	yes	characteristic
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	44	4	no	—
235	C₄	—	44	4	no	—
236	C₄	#10622451	1	2	yes	—
237	C₄	#10622466	1	2	yes	—
238	C₄	C₂²×#4313	1	1	yes	characteristic
239	C₄	C₂×#66960	1	1	yes	characteristic
240	C₄	C₂×#66968	1	2	yes	—
241	C₂	#13067524	1	4	yes	direct product factor
242	C₂	C₂×#10622451	1	1	yes	characteristic
243	C₂	C₂×#10622466	1	1	yes	characteristic
244	C₂	C₂×#10622507	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#334	C₂
socle, prime radical	C₂³×C₁₁	C₄×D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#334	D₁₁
hypocenter	C₁₁	C₂×#1593
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
3. #13067524	C₂	direct (N × H)
170. C₂×C₁₁	#1593	semidirect
204. C₁₁	C₂×#1593	semidirect
241. C₂	#13067524	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×#10622444	2
C₂×C₄×Dic₄₄	2
#13067524	2
C₂×#10622122	2
C₂×#10622093	2
C₂×C₁₁×#334	2
C₂×#1593	11

Subgroups — C2×#13067524 #14723536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13067524 #14723536