Subgroups — C₂×D₁₁×#322 #14719340

Order 2816.

1182 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×D₁₁	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×D₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622092	C₂	1	2	yes	maximal, complemented
4	C₂×#10622093	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₁×#322	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₁₁	C₄	1	4	yes	—
8	C₂²×C₈×D₁₁	C₄	1	2	yes	—
9	C₂×C₄²×D₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
12	C₂×C₈×Dic₁₁	C₄	1	4	yes	—
13	C₂×C₈×Dic₁₁	C₄	1	2	yes	—
14	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
15	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
16	C₄×C₈×D₁₁	C₄	1	8	yes	—
17	C₄×C₈×D₁₁	C₄	1	4	yes	—
18	C₄×C₈×D₁₁	C₂²	1	4	yes	—
19	C₄×C₈×D₁₁	C₂²	1	8	yes	—
20	C₁₁×#322	C₂²	1	4	yes	complemented
21	#10622093	C₂²	1	4	yes	complemented
22	#10622092	C₂²	1	8	yes	complemented
23	C₂²×C₄×D₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×D₁₁	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
29	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
31	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
32	C₂×C₈×D₁₁	—	2	16	no	—
33	C₂×C₈×D₁₁	C₈	1	16	yes	complemented
34	C₂×C₈×D₁₁	C₂×C₄	1	16	yes	—
35	C₂×C₈×D₁₁	C₂×C₄	1	8	yes	—
36	C₄²×D₁₁	C₂×C₄	1	4	yes	—
37	C₄²×D₁₁	C₂×C₄	1	2	yes	—
38	C₄²×D₁₁	C₂³	1	2	yes	—
39	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
40	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
41	C₄×C₈×C₁₁	C₂³	1	4	yes	—
42	C₄×C₈×C₁₁	C₂³	1	2	yes	—
43	C₈×Dic₁₁	C₂×C₄	1	16	yes	—
44	C₈×Dic₁₁	C₂×C₄	1	8	yes	—
45	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
46	C₄×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
47	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
48	C₄×C₁₁⋊C₈	C₂³	1	4	yes	—
49	C₂²×#322	—	11	1	no	maximal, Sylow
50	C₂³×D₁₁	C₄²	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
53	C₂²×Dic₁₁	C₄²	1	1	yes	characteristic
54	C₂²×Dic₁₁	C₄²	1	2	yes	—
55	C₂×C₄×D₁₁	C₄²	1	2	yes	—
56	C₂×C₄×D₁₁	C₄²	1	4	yes	—
57	C₂×C₄×D₁₁	C₂×C₈	1	8	yes	—
58	C₂×C₄×D₁₁	M₁₆	1	16	yes	—
59	C₂×C₄×D₁₁	C₂²×C₄	1	2	yes	—
60	C₂×C₄×D₁₁	C₂²×C₄	1	4	yes	—
61	C₂×C₈×C₁₁	—	2	8	no	—
62	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	complemented
63	C₂×C₈×C₁₁	C₂²×C₄	1	8	yes	—
64	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
65	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
66	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
68	C₄×Dic₁₁	C₄²	1	2	yes	—
69	C₄×Dic₁₁	C₄²	1	4	yes	—
70	C₄×Dic₁₁	C₂²×C₄	1	2	yes	—
71	C₄×Dic₁₁	C₂²×C₄	1	4	yes	—
72	C₂×C₁₁⋊C₈	—	2	8	no	—
73	C₂×C₁₁⋊C₈	C₂×C₈	1	8	yes	complemented
74	C₂×C₁₁⋊C₈	C₂²×C₄	1	8	yes	—
75	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
76	C₈×D₁₁	—	2	32	no	—
77	C₈×D₁₁	C₂×C₈	1	32	yes	complemented
78	C₂²×C₄×C₈	—	11	1	no	—
79	C₂²×C₄×C₈	—	11	2	no	—
80	C₂×#322	—	11	1	no	—
81	C₂×#322	—	11	2	no	—
82	C₂×#322	—	11	8	no	—
83	C₂×#322	D₁₁	1	1	yes	characteristic, direct product factor
84	C₂³×C₁₁	C₂×C₄²	1	1	yes	characteristic
85	C₂²×D₁₁	C₄×C₈	1	4	yes	—
86	C₂²×D₁₁	#97	1	8	yes	—
87	C₂²×D₁₁	C₂×C₄²	1	2	yes	—
88	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂×C₄²	1	2	yes	—
90	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
91	C₂×C₄×C₁₁	C₂×M₁₆	1	8	yes	—
92	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂³×C₄	1	2	yes	—
94	C₂×Dic₁₁	C₄×C₈	1	4	yes	—
95	C₂×Dic₁₁	#97	1	8	yes	—
96	C₂×Dic₁₁	C₂×C₄²	1	2	yes	—
97	C₂×Dic₁₁	C₂×C₄²	1	4	yes	—
98	C₄×D₁₁	C₄×C₈	1	8	yes	—
99	C₄×D₁₁	#97	1	16	yes	—
100	C₄×D₁₁	C₂²×C₈	1	8	yes	—
101	C₄×D₁₁	C₂×M₁₆	1	16	yes	—
102	C₈×C₁₁	—	2	8	no	—
103	C₈×C₁₁	C₂²×C₈	1	8	yes	complemented
104	C₁₁⋊C₈	—	2	8	no	—
105	C₁₁⋊C₈	C₂²×C₈	1	8	yes	complemented
106	C₂³×C₈	—	11	2	no	—
107	C₂³×C₈	—	11	4	no	—
108	C₂²×C₄²	—	11	1	no	—
109	C₂×C₄×C₈	—	11	2	no	—
110	C₂×C₄×C₈	—	11	4	no	—
111	C₂×C₄×C₈	—	11	1	no	—
112	C₂×C₄×C₈	—	11	2	no	—
113	C₂×C₄×C₈	—	11	4	no	—
114	C₂×C₄×C₈	—	11	8	no	—
115	C₂×C₄×C₈	—	11	4	no	—
116	C₂×C₄×C₈	—	11	8	no	—
117	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
118	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
119	#322	—	11	8	no	—
120	#322	—	11	4	no	—
121	#322	C₂×D₁₁	1	4	yes	direct product factor
122	C₂²×C₁₁	C₂×C₄×C₈	1	2	yes	—
123	C₂²×C₁₁	C₂×#97	1	4	yes	—
124	C₂²×C₁₁	C₂²×C₄²	1	1	yes	characteristic
125	C₂×D₁₁	#322	1	16	yes	direct product factor
126	C₂×D₁₁	C₂×C₄×C₈	1	4	yes	—
127	C₂×D₁₁	C₂×#97	1	8	yes	—
128	C₄×C₁₁	C₂×C₄×C₈	1	2	yes	—
129	C₄×C₁₁	C₂×#97	1	4	yes	—
130	C₄×C₁₁	C₂³×C₈	1	2	yes	—
131	C₄×C₁₁	C₂²×M₁₆	1	4	yes	—
132	Dic₁₁	C₂×C₄×C₈	1	4	yes	—
133	Dic₁₁	C₂×#97	1	8	yes	—
134	C₂³×C₄	—	11	1	no	—
135	C₂³×C₄	—	11	2	no	—
136	C₂²×C₈	—	11	2	no	—
137	C₂²×C₈	—	11	16	no	—
138	C₂²×C₈	—	11	8	no	—
139	C₂²×C₈	—	11	4	no	—
140	C₂²×C₈	—	11	16	no	—
141	C₂²×C₈	—	22	16	no	—
142	C₂²×C₈	C₄×D₁₁	1	4	yes	—
143	C₂²×C₈	C₄×D₁₁	1	2	yes	—
144	C₂×C₄²	—	11	1	no	—
145	C₂×C₄²	—	11	2	no	—
146	C₂×C₄²	—	11	4	no	—
147	C₂×C₄²	—	11	2	no	—
148	C₂×C₄²	—	11	2	no	—
149	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
150	C₄×C₈	—	11	8	no	—
151	C₄×C₈	—	11	16	no	—
152	C₄×C₈	—	11	2	no	—
153	C₄×C₈	—	11	4	no	—
154	C₄×C₈	—	11	2	no	—
155	C₄×C₈	—	11	4	no	—
156	C₄×C₈	C₄×D₁₁	1	4	yes	—
157	C₄×C₈	C₄×D₁₁	1	2	yes	—
158	C₄×C₈	C₂²×D₁₁	1	4	yes	—
159	C₄×C₈	C₂²×D₁₁	1	2	yes	—
160	C₂×C₁₁	C₂×#322	1	4	yes	complemented
161	C₂×C₁₁	C₂²×C₄×C₈	1	1	yes	characteristic
162	C₂×C₁₁	C₂²×#97	1	2	yes	—
163	D₁₁	C₂×#322	1	8	yes	direct product factor
164	C₂⁴	—	11	1	no	—
165	C₂²×C₄	—	11	1	no	—
166	C₂²×C₄	—	11	2	no	—
167	C₂²×C₄	—	11	2	no	—
168	C₂²×C₄	—	11	4	no	—
169	C₂²×C₄	—	11	8	no	—
170	C₂²×C₄	—	11	16	no	—
171	C₂²×C₄	—	11	2	no	—
172	C₂²×C₄	—	11	4	no	—
173	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
174	C₂²×C₄	C₂×C₄×D₁₁	1	2	yes	—
175	C₂×C₈	—	2	8	no	—
176	C₂×C₈	—	11	8	no	—
177	C₂×C₈	—	11	4	no	—
178	C₂×C₈	—	11	32	no	—
179	C₂×C₈	—	11	8	no	—
180	C₂×C₈	—	22	32	no	—
181	C₂×C₈	—	22	8	no	—
182	C₂×C₈	C₈×D₁₁	1	8	yes	complemented
183	C₂×C₈	C₂×C₄×D₁₁	1	8	yes	—
184	C₂×C₈	C₂×C₄×D₁₁	1	4	yes	—
185	C₄²	—	11	2	no	—
186	C₄²	—	11	4	no	—
187	C₄²	—	11	2	no	—
188	C₄²	—	11	4	no	—
189	C₄²	C₂×C₄×D₁₁	1	2	yes	—
190	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
191	C₄²	C₂³×D₁₁	1	1	yes	characteristic
192	C₁₁	C₂²×#322	1	1	yes	characteristic, complemented, Sylow
193	C₂³	—	11	2	no	—
194	C₂³	—	11	4	no	—
195	C₂³	—	11	8	no	—
196	C₂³	C₄²×D₁₁	1	1	yes	characteristic
197	C₂×C₄	—	11	2	no	—
198	C₂×C₄	—	11	4	no	—
199	C₂×C₄	—	11	4	no	—
200	C₂×C₄	—	11	8	no	—
201	C₂×C₄	—	11	8	no	—
202	C₂×C₄	—	11	16	no	—
203	C₂×C₄	—	11	8	no	—
204	C₂×C₄	—	11	16	no	—
205	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
206	C₂×C₄	C₄²×D₁₁	1	2	yes	—
207	C₂×C₄	C₂×C₈×D₁₁	1	4	yes	—
208	C₂×C₄	M₁₆×D₁₁	1	8	yes	—
209	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
210	C₂×C₄	C₂²×C₄×D₁₁	1	2	yes	—
211	C₈	—	2	8	no	—
212	C₈	—	11	8	no	—
213	C₈	—	22	8	no	—
214	C₈	C₂×C₈×D₁₁	1	8	yes	complemented
215	C₂²	—	11	4	no	—
216	C₂²	—	11	8	no	—
217	C₂²	—	11	16	no	—
218	C₂²	C₄×C₈×D₁₁	1	2	yes	—
219	C₂²	D₁₁×#97	1	4	yes	—
220	C₂²	C₂×C₄²×D₁₁	1	1	yes	characteristic
221	C₄	—	11	4	no	—
222	C₄	—	11	8	no	—
223	C₄	C₄×C₈×D₁₁	1	2	yes	—
224	C₄	D₁₁×#97	1	4	yes	—
225	C₄	C₂²×C₈×D₁₁	1	2	yes	—
226	C₄	C₂×M₁₆×D₁₁	1	4	yes	—
227	C₂	—	11	8	no	—
228	C₂	D₁₁×#322	1	4	yes	direct product factor
229	C₂	C₂×C₄×C₈×D₁₁	1	1	yes	characteristic
230	C₂	C₂×D₁₁×#97	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₁
commutator	C₂×C₁₁	C₂²×C₄×C₈
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#322	C₂
socle	C₂³×C₁₁	C₂×C₄²
prime radical	C₂³×D₁₁	C₄²
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#322	D₁₁
hypocenter	C₁₁	C₂²×#322
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄² ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
3. C₂×#10622092	C₂	semidirect
4. C₂×#10622093	C₂	semidirect
5. D₁₁×#322	C₂	direct (N × H)
6. C₂×C₁₁×#322	C₂	semidirect
20. C₁₁×#322	C₂²	semidirect
21. #10622093	C₂²	semidirect
22. #10622092	C₂²	semidirect
33. C₂×C₈×D₁₁	C₈	semidirect
62. C₂×C₈×C₁₁	C₂×C₈	semidirect
73. C₂×C₁₁⋊C₈	C₂×C₈	semidirect
77. C₈×D₁₁	C₂×C₈	semidirect
83. C₂×#322	D₁₁	direct (N × H)
103. C₈×C₁₁	C₂²×C₈	semidirect
105. C₁₁⋊C₈	C₂²×C₈	semidirect
121. #322	C₂×D₁₁	direct (N × H)
125. C₂×D₁₁	#322	direct (N × H)
160. C₂×C₁₁	C₂×#322	semidirect
163. D₁₁	C₂×#322	direct (N × H)
182. C₂×C₈	C₈×D₁₁	semidirect
192. C₁₁	C₂²×#322	semidirect
214. C₈	C₂×C₈×D₁₁	semidirect
228. C₂	D₁₁×#322	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×C₄×C₈×D₁₁	2
C₂×#10622092	2
C₂×#10622093	2
D₁₁×#322	2
C₂×C₁₁×#322	2
C₂²×#322	11

Subgroups — C2×D11×#322 #14719340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₁×#322 #14719340