Subgroups — C₂²×C₄×C₁₁×Q₁₆ #14637343

Order 2816.

2830 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	C₂³×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Q₈×C₁₁	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₁×Q₁₆	C₂	1	24	yes	maximal, direct product factor
4	C₂²×C₁₁×#107	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₁×#103	C₂	1	2	yes	maximal
6	C₂²×C₄×C₈×C₁₁	C₂	1	1	yes	maximal, characteristic
7	C₂³×Q₈×C₁₁	C₂²	1	2	yes	—
8	C₂²×C₁₁×Q₁₆	C₄	1	16	yes	direct product factor
9	C₂²×C₁₁×Q₁₆	C₂²	1	12	yes	—
10	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₁₁	—	2	12	no	—
13	C₂×C₄×Q₈×C₁₁	C₂²	1	24	yes	—
14	C₂²×C₁₁×C₄⋊C₄	—	2	2	no	—
15	C₂²×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₄²×C₁₁	—	2	2	no	—
17	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
18	C₄×C₁₁×Q₁₆	C₂²	1	64	yes	direct product factor
19	C₂×C₁₁×#107	C₂²	1	12	yes	—
20	C₂×C₁₁×#103	C₂²	1	24	yes	—
21	C₂×C₄×C₈×C₁₁	C₂²	1	12	yes	—
22	C₂²×Q₈×C₁₁	—	2	6	no	—
23	C₂²×Q₈×C₁₁	—	2	8	no	—
24	C₂²×Q₈×C₁₁	C₂×C₄	1	16	yes	—
25	C₂²×Q₈×C₁₁	C₂³	1	12	yes	—
26	C₂³×C₄×C₁₁	—	2	2	no	—
27	C₂³×C₄×C₁₁	—	2	2	no	—
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
31	C₂×C₁₁×Q₁₆	C₂×C₄	1	96	yes	direct product factor
32	C₂×C₁₁×Q₁₆	C₂³	1	16	yes	—
33	C₂²×C₈×C₁₁	—	2	4	no	—
34	C₂²×C₈×C₁₁	C₂×C₄	1	8	yes	—
35	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
36	C₂²×C₈×C₁₁	C₂³	1	6	yes	—
37	C₄×Q₈×C₁₁	—	2	48	no	—
38	C₄×Q₈×C₁₁	C₂³	1	32	yes	—
39	C₂×C₁₁×C₄⋊C₄	—	2	24	no	—
40	C₂×C₁₁×C₄⋊C₄	—	2	6	no	—
41	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
42	C₂×C₄²×C₁₁	—	2	24	no	—
43	C₂×C₄²×C₁₁	D₄	1	6	yes	—
44	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
45	C₁₁×#107	C₂³	1	16	yes	—
46	C₁₁×#103	C₂³	1	32	yes	—
47	C₄×C₈×C₁₁	C₂³	1	16	yes	—
48	C₂²×C₄×Q₁₆	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂⁴×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₂×Q₈×C₁₁	—	2	48	no	—
51	C₂×Q₈×C₁₁	—	2	12	no	—
52	C₂×Q₈×C₁₁	—	2	24	no	—
53	C₂×Q₈×C₁₁	C₂²×C₄	1	48	yes	—
54	C₂×Q₈×C₁₁	C₂⁴	1	8	yes	—
55	C₂²×C₄×C₁₁	—	2	16	no	—
56	C₂²×C₄×C₁₁	—	2	4	no	—
57	C₂²×C₄×C₁₁	—	2	12	no	—
58	C₂²×C₄×C₁₁	—	2	12	no	—
59	C₂²×C₄×C₁₁	—	4	8	no	—
60	C₂²×C₄×C₁₁	Q₁₆	1	8	yes	direct product factor
61	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
62	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
63	C₂²×C₄×C₁₁	C₂×D₄	1	3	yes	—
64	C₂²×C₄×C₁₁	C₂×D₄	1	6	yes	—
65	C₂²×C₄×C₁₁	#41	1	4	yes	—
66	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
67	C₁₁×Q₁₆	C₂²×C₄	1	64	yes	direct product factor
68	C₂×C₈×C₁₁	—	2	12	no	—
69	C₂×C₈×C₁₁	C₂²×C₄	1	24	yes	—
70	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
71	C₂×C₈×C₁₁	C₂⁴	1	4	yes	—
72	C₁₁×C₄⋊C₄	—	2	32	no	—
73	C₁₁×C₄⋊C₄	—	2	12	no	—
74	C₁₁×C₄⋊C₄	C₂⁴	1	8	yes	—
75	C₄²×C₁₁	—	2	32	no	—
76	C₄²×C₁₁	C₂×D₄	1	12	yes	—
77	C₄²×C₁₁	C₂⁴	1	4	yes	—
78	C₂³×Q₁₆	C₂×C₁₁	1	1	yes	characteristic
79	C₂²×C₄×Q₈	C₂×C₁₁	1	2	yes	—
80	C₂×C₄×Q₁₆	C₂×C₁₁	1	24	yes	direct product factor
81	C₂²×#107	C₂×C₁₁	1	1	yes	characteristic
82	C₂²×#103	C₂×C₁₁	1	2	yes	—
83	C₂²×C₄×C₈	C₂×C₁₁	1	1	yes	characteristic
84	C₂³×C₁₁	C₄×D₄	1	4	yes	—
85	C₂³×C₁₁	C₂×Q₁₆	1	4	yes	—
86	C₂³×C₁₁	#135	1	4	yes	—
87	C₂³×C₁₁	C₂²×D₄	1	3	yes	—
88	Q₈×C₁₁	—	2	48	no	—
89	Q₈×C₁₁	—	2	8	no	—
90	Q₈×C₁₁	C₂³×C₄	1	16	yes	—
91	C₂×C₄×C₁₁	—	2	48	no	—
92	C₂×C₄×C₁₁	—	2	12	no	—
93	C₂×C₄×C₁₁	—	2	8	no	—
94	C₂×C₄×C₁₁	—	2	8	no	—
95	C₂×C₄×C₁₁	—	4	24	no	—
96	C₂×C₄×C₁₁	C₄×D₄	1	12	yes	—
97	C₂×C₄×C₁₁	C₂×Q₁₆	1	24	yes	direct product factor
98	C₂×C₄×C₁₁	C₂³×C₄	1	6	yes	—
99	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
100	C₂×C₄×C₁₁	C₂²×D₄	1	3	yes	—
101	C₂×C₄×C₁₁	C₂²×D₄	1	4	yes	—
102	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
103	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
104	C₈×C₁₁	—	2	4	no	—
105	C₈×C₁₁	C₂³×C₄	1	8	yes	—
106	C₂³×Q₈	C₂²×C₁₁	1	2	yes	—
107	C₂²×Q₁₆	C₄×C₁₁	1	16	yes	direct product factor
108	C₂²×Q₁₆	C₂²×C₁₁	1	12	yes	—
109	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
110	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
111	C₂×C₄×Q₈	—	2	12	no	—
112	C₂×C₄×Q₈	C₂²×C₁₁	1	24	yes	—
113	C₂²×C₄⋊C₄	—	2	2	no	—
114	C₂²×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
115	C₂²×C₄²	—	2	2	no	—
116	C₂²×C₄²	C₂²×C₁₁	1	1	yes	characteristic
117	C₄×Q₁₆	C₂²×C₁₁	1	64	yes	direct product factor
118	C₂×#107	C₂²×C₁₁	1	12	yes	—
119	C₂×#103	C₂²×C₁₁	1	24	yes	—
120	C₂×C₄×C₈	C₂²×C₁₁	1	12	yes	—
121	C₂²×C₁₁	C₄×Q₁₆	1	16	yes	direct product factor
122	C₂²×C₁₁	C₂×C₄×D₄	1	6	yes	—
123	C₂²×C₁₁	C₂²×Q₁₆	1	6	yes	—
124	C₂²×C₁₁	C₂×#135	1	6	yes	—
125	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
126	C₄×C₁₁	—	2	16	no	—
127	C₄×C₁₁	—	2	4	no	—
128	C₄×C₁₁	—	4	8	no	—
129	C₄×C₁₁	C₂×C₄×D₄	1	6	yes	—
130	C₄×C₁₁	C₂²×Q₁₆	1	8	yes	direct product factor
131	C₄×C₁₁	C₂⁴×C₄	1	1	yes	characteristic
132	C₄×C₁₁	C₂²×#41	1	1	yes	characteristic
133	C₂²×Q₈	—	2	6	no	—
134	C₂²×Q₈	—	2	8	no	—
135	C₂²×Q₈	C₂×C₄×C₁₁	1	16	yes	—
136	C₂²×Q₈	C₂³×C₁₁	1	12	yes	—
137	C₂³×C₄	—	2	2	no	—
138	C₂³×C₄	—	2	2	no	—
139	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
140	C₂³×C₄	D₄×C₁₁	1	1	yes	characteristic
141	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
142	C₂×Q₁₆	C₂×C₄×C₁₁	1	96	yes	direct product factor
143	C₂×Q₁₆	C₂³×C₁₁	1	16	yes	—
144	C₂²×C₈	—	2	4	no	—
145	C₂²×C₈	C₂×C₄×C₁₁	1	8	yes	—
146	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
147	C₂²×C₈	C₂³×C₁₁	1	6	yes	—
148	C₄×Q₈	—	2	48	no	—
149	C₄×Q₈	C₂³×C₁₁	1	32	yes	—
150	C₂×C₄⋊C₄	—	2	24	no	—
151	C₂×C₄⋊C₄	—	2	6	no	—
152	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
153	C₂×C₄²	—	2	24	no	—
154	C₂×C₄²	D₄×C₁₁	1	6	yes	—
155	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
156	#107	C₂³×C₁₁	1	16	yes	—
157	#103	C₂³×C₁₁	1	32	yes	—
158	C₄×C₈	C₂³×C₁₁	1	16	yes	—
159	C₂×C₁₁	C₂×C₄×Q₁₆	1	12	yes	direct product factor
160	C₂×C₁₁	C₂²×C₄×D₄	1	1	yes	characteristic
161	C₂×C₁₁	C₂³×Q₁₆	1	1	yes	characteristic
162	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
163	C₂⁴	C₂×D₄×C₁₁	1	1	yes	characteristic
164	C₂×Q₈	—	2	48	no	—
165	C₂×Q₈	—	2	12	no	—
166	C₂×Q₈	—	2	24	no	—
167	C₂×Q₈	C₂²×C₄×C₁₁	1	48	yes	—
168	C₂×Q₈	C₂⁴×C₁₁	1	8	yes	—
169	C₂²×C₄	—	2	16	no	—
170	C₂²×C₄	—	2	4	no	—
171	C₂²×C₄	—	2	12	no	—
172	C₂²×C₄	—	2	12	no	—
173	C₂²×C₄	—	4	8	no	—
174	C₂²×C₄	C₁₁×Q₁₆	1	8	yes	direct product factor
175	C₂²×C₄	C₂²×C₄×C₁₁	1	4	yes	—
176	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
177	C₂²×C₄	C₂×D₄×C₁₁	1	3	yes	—
178	C₂²×C₄	C₂×D₄×C₁₁	1	6	yes	—
179	C₂²×C₄	C₁₁×#41	1	4	yes	—
180	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
181	Q₁₆	C₂²×C₄×C₁₁	1	64	yes	direct product factor
182	C₂×C₈	—	2	12	no	—
183	C₂×C₈	C₂²×C₄×C₁₁	1	24	yes	—
184	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
185	C₂×C₈	C₂⁴×C₁₁	1	4	yes	—
186	C₄⋊C₄	—	2	32	no	—
187	C₄⋊C₄	—	2	12	no	—
188	C₄⋊C₄	C₂⁴×C₁₁	1	8	yes	—
189	C₄²	—	2	32	no	—
190	C₄²	C₂×D₄×C₁₁	1	12	yes	—
191	C₄²	C₂⁴×C₁₁	1	4	yes	—
192	C₁₁	C₂²×C₄×Q₁₆	1	1	yes	characteristic, direct product factor, Sylow
193	C₂³	C₄×D₄×C₁₁	1	4	yes	—
194	C₂³	C₂×C₁₁×Q₁₆	1	4	yes	—
195	C₂³	C₁₁×#135	1	4	yes	—
196	C₂³	C₂²×D₄×C₁₁	1	3	yes	—
197	Q₈	—	2	48	no	—
198	Q₈	—	2	8	no	—
199	Q₈	C₂³×C₄×C₁₁	1	16	yes	—
200	C₂×C₄	—	2	48	no	—
201	C₂×C₄	—	2	12	no	—
202	C₂×C₄	—	2	8	no	—
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	4	24	no	—
205	C₂×C₄	C₄×D₄×C₁₁	1	12	yes	—
206	C₂×C₄	C₂×C₁₁×Q₁₆	1	24	yes	direct product factor
207	C₂×C₄	C₂³×C₄×C₁₁	1	6	yes	—
208	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
209	C₂×C₄	C₂²×D₄×C₁₁	1	3	yes	—
210	C₂×C₄	C₂²×D₄×C₁₁	1	4	yes	—
211	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
212	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
213	C₈	—	2	4	no	—
214	C₈	C₂³×C₄×C₁₁	1	8	yes	—
215	C₂²	C₄×C₁₁×Q₁₆	1	16	yes	direct product factor
216	C₂²	C₂×C₄×D₄×C₁₁	1	6	yes	—
217	C₂²	C₂²×C₁₁×Q₁₆	1	6	yes	—
218	C₂²	C₂×C₁₁×#135	1	6	yes	—
219	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
220	C₄	—	2	16	no	—
221	C₄	—	2	4	no	—
222	C₄	—	4	8	no	—
223	C₄	C₂×C₄×D₄×C₁₁	1	6	yes	—
224	C₄	C₂²×C₁₁×Q₁₆	1	8	yes	direct product factor
225	C₄	C₂⁴×C₄×C₁₁	1	1	yes	characteristic
226	C₄	C₂²×C₁₁×#41	1	1	yes	characteristic
227	C₂	C₂×C₄×C₁₁×Q₁₆	1	12	yes	direct product factor
228	C₂	C₂²×C₄×D₄×C₁₁	1	1	yes	characteristic
229	C₂	C₂³×C₁₁×Q₁₆	1	1	yes	characteristic
230	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₁₁	D₄
commutator	C₄	C₂⁴×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle, prime radical	C₂⁴×C₁₁	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₁ ◁ C₂²×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₁₁×Q₁₆	C₂	direct (N × H)
8. C₂²×C₁₁×Q₁₆	C₄	direct (N × H)
18. C₄×C₁₁×Q₁₆	C₂²	direct (N × H)
31. C₂×C₁₁×Q₁₆	C₂×C₄	direct (N × H)
48. C₂²×C₄×Q₁₆	C₁₁	direct (N × H)
60. C₂²×C₄×C₁₁	Q₁₆	direct (N × H)
67. C₁₁×Q₁₆	C₂²×C₄	direct (N × H)
80. C₂×C₄×Q₁₆	C₂×C₁₁	direct (N × H)
97. C₂×C₄×C₁₁	C₂×Q₁₆	direct (N × H)
107. C₂²×Q₁₆	C₄×C₁₁	direct (N × H)
117. C₄×Q₁₆	C₂²×C₁₁	direct (N × H)
121. C₂²×C₁₁	C₄×Q₁₆	direct (N × H)
130. C₄×C₁₁	C₂²×Q₁₆	direct (N × H)
142. C₂×Q₁₆	C₂×C₄×C₁₁	direct (N × H)
159. C₂×C₁₁	C₂×C₄×Q₁₆	direct (N × H)
174. C₂²×C₄	C₁₁×Q₁₆	direct (N × H)
181. Q₁₆	C₂²×C₄×C₁₁	direct (N × H)
192. C₁₁	C₂²×C₄×Q₁₆	direct (N × H)
206. C₂×C₄	C₂×C₁₁×Q₁₆	direct (N × H)
215. C₂²	C₄×C₁₁×Q₁₆	direct (N × H)
224. C₄	C₂²×C₁₁×Q₁₆	direct (N × H)
227. C₂	C₂×C₄×C₁₁×Q₁₆	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₁×Q₁₆	2
C₂²×C₄×Q₈×C₁₁	2
C₂×C₄×C₁₁×Q₁₆	2
C₂²×C₁₁×#107	2
C₂²×C₁₁×#103	2
C₂²×C₄×C₈×C₁₁	2
C₂²×C₄×Q₁₆	11

Subgroups — C22×C4×C11×Q16 #14637343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₁₁×Q₁₆ #14637343