Subgroups — C₄×C₄⋊C₄×D₁₁ #13070949

Order 1408.

928 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₄×D₁₁	C₂	1	2	yes	maximal
2	C₂×C₄²×D₁₁	C₂	1	2	yes	maximal
3	C₂×C₄²×D₁₁	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₁×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₄×Dic₁₁	C₂	1	2	yes	maximal, complemented
6	C₄×C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×Dic₁₁⋊C₄	C₂	1	2	yes	maximal, complemented
8	D₁₁×#95	C₂	1	2	yes	maximal
9	#10622262	C₂	1	2	yes	maximal, complemented
10	C₂²×C₄×D₁₁	C₂²	1	4	yes	—
11	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
12	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
13	C₂²×C₄×D₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
16	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
18	C₂×Dic₁₁⋊C₄	C₂²	1	4	yes	—
19	C₂×C₄×Dic₁₁	C₂²	1	4	yes	—
20	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
21	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
24	C₄⋊C₄×D₁₁	C₄	1	16	yes	direct product factor
25	C₄²×D₁₁	—	2	8	no	—
26	C₄²×D₁₁	C₄	1	8	yes	complemented
27	C₁₁×#95	C₂²	1	2	yes	—
28	C₁₁⋊#95	C₂²	1	2	yes	—
29	C₁₁⋊#95	C₂²	1	4	yes	—
30	C₂³×D₁₁	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₁₁	C₂³	1	4	yes	—
33	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
35	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
36	C₂²×Dic₁₁	C₂³	1	4	yes	—
37	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
38	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
39	C₂×C₄×D₁₁	—	2	8	no	—
40	C₂×C₄×D₁₁	—	2	4	no	—
41	C₂×C₄×D₁₁	—	2	8	no	—
42	C₂×C₄×D₁₁	C₂×C₄	1	4	yes	—
43	C₂×C₄×D₁₁	C₂×C₄	1	16	yes	—
44	C₂×C₄×D₁₁	C₂×C₄	1	4	yes	—
45	C₂×C₄×D₁₁	C₂×C₄	1	8	yes	—
46	C₂×C₄×D₁₁	C₂×C₄	1	4	yes	—
47	C₂×C₄×D₁₁	D₄	1	4	yes	—
48	C₂×C₄×D₁₁	Q₈	1	4	yes	—
49	C₁₁×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
50	C₄²×C₁₁	—	2	4	no	—
51	C₄²×C₁₁	C₂×C₄	1	4	yes	complemented
52	C₄⋊Dic₁₁	C₂×C₄	1	8	yes	complemented
53	Dic₁₁⋊C₄	C₂×C₄	1	16	yes	complemented
54	C₄×Dic₁₁	—	2	8	no	—
55	C₄×Dic₁₁	—	2	4	no	—
56	C₄×Dic₁₁	C₂×C₄	1	4	yes	complemented
57	C₄×Dic₁₁	C₂×C₄	1	4	yes	complemented
58	C₄×Dic₁₁	C₂×C₄	1	4	yes	complemented
59	C₂×C₄×C₄⋊C₄	—	11	1	no	maximal, Sylow
60	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
61	C₂²×D₁₁	C₂²×C₄	1	2	yes	—
62	C₂²×D₁₁	C₂²×C₄	1	4	yes	—
63	C₂²×D₁₁	C₂×D₄	1	2	yes	—
64	C₂²×D₁₁	C₂×Q₈	1	2	yes	—
65	C₂²×D₁₁	#41	1	4	yes	—
66	C₂×C₄×C₁₁	—	2	4	no	—
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	—	2	4	no	—
69	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
70	C₂×C₄×C₁₁	C₂²×C₄	1	8	yes	—
71	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
72	C₂×C₄×C₁₁	C₂²×C₄	1	4	yes	—
73	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
74	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
75	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
76	C₂×Dic₁₁	—	2	4	no	—
77	C₂×Dic₁₁	—	2	2	no	—
78	C₂×Dic₁₁	—	2	4	no	—
79	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
80	C₂×Dic₁₁	C₂²×C₄	1	8	yes	—
81	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
82	C₂×Dic₁₁	C₂²×C₄	1	4	yes	—
83	C₂×Dic₁₁	C₂²×C₄	1	2	yes	—
84	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
85	C₂×Dic₁₁	C₂×Q₈	1	2	yes	—
86	C₄×D₁₁	—	2	8	no	—
87	C₄×D₁₁	—	2	32	no	—
88	C₄×D₁₁	C₄²	1	16	yes	complemented
89	C₄×D₁₁	C₄⋊C₄	1	16	yes	direct product factor
90	C₂²×C₄⋊C₄	—	11	2	no	—
91	C₂²×C₄²	—	11	1	no	—
92	C₂²×C₄²	—	11	2	no	—
93	C₄×C₄⋊C₄	—	11	2	no	—
94	C₄×C₄⋊C₄	—	11	2	no	—
95	C₄×C₄⋊C₄	—	11	1	no	—
96	C₄×C₄⋊C₄	—	11	2	no	—
97	C₄×C₄⋊C₄	D₁₁	1	1	yes	characteristic, direct product factor
98	C₂×#95	—	11	2	no	—
99	C₂²×C₁₁	C₂³×C₄	1	1	yes	characteristic
100	C₂²×C₁₁	C₂³×C₄	1	2	yes	—
101	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
102	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
103	C₂²×C₁₁	C₂×#41	1	2	yes	—
104	C₂×D₁₁	C₂×C₄²	1	4	yes	—
105	C₂×D₁₁	C₂×C₄⋊C₄	1	4	yes	—
106	C₂×D₁₁	#117	1	4	yes	—
107	C₂×D₁₁	C₄×D₄	1	8	yes	—
108	C₂×D₁₁	C₄×Q₈	1	8	yes	—
109	C₄×C₁₁	—	2	2	no	—
110	C₄×C₁₁	—	2	8	no	—
111	C₄×C₁₁	C₂×C₄²	1	4	yes	complemented
112	C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	complemented
113	Dic₁₁	—	2	2	no	—
114	Dic₁₁	—	2	8	no	—
115	Dic₁₁	C₂×C₄²	1	4	yes	complemented
116	Dic₁₁	C₂×C₄⋊C₄	1	4	yes	complemented
117	C₂³×C₄	—	11	1	no	—
118	C₂³×C₄	—	11	1	no	—
119	C₂³×C₄	—	11	4	no	—
120	C₂³×C₄	—	11	1	no	—
121	C₂×C₄⋊C₄	—	11	4	no	—
122	C₂×C₄⋊C₄	—	11	2	no	—
123	C₂×C₄⋊C₄	—	11	16	no	—
124	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	—
125	C₂×C₄²	—	11	1	no	—
126	C₂×C₄²	—	11	1	no	—
127	C₂×C₄²	—	11	1	no	—
128	C₂×C₄²	—	11	8	no	—
129	C₂×C₄²	—	11	4	no	—
130	C₂×C₄²	—	11	2	no	—
131	C₂×C₄²	—	22	8	no	—
132	C₂×C₄²	C₂×D₁₁	1	2	yes	—
133	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
134	#95	—	11	4	no	—
135	#95	—	11	2	no	—
136	#95	C₂×D₁₁	1	2	yes	—
137	C₂×C₁₁	C₂²×C₄²	1	1	yes	characteristic
138	C₂×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
139	C₂×C₁₁	C₂×#117	1	1	yes	characteristic
140	C₂×C₁₁	C₂×C₄×D₄	1	2	yes	—
141	C₂×C₁₁	C₂×C₄×Q₈	1	2	yes	—
142	D₁₁	C₄×C₄⋊C₄	1	8	yes	direct product factor
143	C₂⁴	—	11	1	no	—
144	C₂²×C₄	—	11	1	no	—
145	C₂²×C₄	—	11	1	no	—
146	C₂²×C₄	—	11	4	no	—
147	C₂²×C₄	—	11	4	no	—
148	C₂²×C₄	—	11	8	no	—
149	C₂²×C₄	—	11	4	no	—
150	C₂²×C₄	—	11	4	no	—
151	C₂²×C₄	—	11	1	no	—
152	C₂²×C₄	—	11	4	no	—
153	C₂²×C₄	—	11	4	no	—
154	C₂²×C₄	—	11	16	no	—
155	C₂²×C₄	—	22	8	no	—
156	C₂²×C₄	—	22	8	no	—
157	C₂²×C₄	—	22	4	no	—
158	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
159	C₂²×C₄	C₂²×D₁₁	1	4	yes	—
160	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
161	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
162	C₄⋊C₄	—	11	16	no	—
163	C₄⋊C₄	—	11	8	no	—
164	C₄⋊C₄	C₄×D₁₁	1	8	yes	direct product factor
165	C₄²	—	2	4	no	—
166	C₄²	—	11	4	no	—
167	C₄²	—	11	4	no	—
168	C₄²	—	11	4	no	—
169	C₄²	—	22	8	no	—
170	C₄²	—	22	4	no	—
171	C₄²	C₄×D₁₁	1	4	yes	complemented
172	C₁₁	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
173	C₂³	—	11	2	no	—
174	C₂³	—	11	4	no	—
175	C₂³	—	11	2	no	—
176	C₂³	—	11	2	no	—
177	C₂³	—	11	4	no	—
178	C₂³	C₂³×D₁₁	1	1	yes	characteristic
179	C₂×C₄	—	2	4	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	11	2	no	—
183	C₂×C₄	—	11	2	no	—
184	C₂×C₄	—	11	4	no	—
185	C₂×C₄	—	11	2	no	—
186	C₂×C₄	—	11	2	no	—
187	C₂×C₄	—	11	16	no	—
188	C₂×C₄	—	11	16	no	—
189	C₂×C₄	—	11	2	no	—
190	C₂×C₄	—	11	8	no	—
191	C₂×C₄	—	22	8	no	—
192	C₂×C₄	—	22	32	no	—
193	C₂×C₄	—	22	4	no	—
194	C₂×C₄	—	22	2	no	—
195	C₂×C₄	—	22	4	no	—
196	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
197	C₂×C₄	C₂×C₄×D₁₁	1	8	yes	—
198	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
199	C₂×C₄	C₂×C₄×D₁₁	1	4	yes	—
200	C₂×C₄	C₂×C₄×D₁₁	1	2	yes	—
201	C₂×C₄	D₄×D₁₁	1	2	yes	—
202	C₂×C₄	Q₈×D₁₁	1	2	yes	—
203	C₂²	—	11	4	no	—
204	C₂²	—	11	4	no	—
205	C₂²	—	11	4	no	—
206	C₂²	—	11	8	no	—
207	C₂²	—	11	8	no	—
208	C₂²	C₂²×C₄×D₁₁	1	1	yes	characteristic
209	C₂²	C₂²×C₄×D₁₁	1	2	yes	—
210	C₂²	C₂×D₄×D₁₁	1	1	yes	characteristic
211	C₂²	C₂×Q₈×D₁₁	1	1	yes	characteristic
212	C₂²	#41×D₁₁	1	2	yes	—
213	C₄	—	2	2	no	—
214	C₄	—	2	8	no	—
215	C₄	—	11	4	no	—
216	C₄	—	11	4	no	—
217	C₄	—	22	2	no	—
218	C₄	—	22	8	no	—
219	C₄	C₄²×D₁₁	1	4	yes	complemented
220	C₄	C₄⋊C₄×D₁₁	1	4	yes	direct product factor
221	C₂	—	11	8	no	—
222	C₂	C₂×C₄²×D₁₁	1	1	yes	characteristic
223	C₂	C₂×C₄⋊C₄×D₁₁	1	1	yes	characteristic
224	C₂	D₁₁×#117	1	1	yes	characteristic
225	C₂	C₄×D₄×D₁₁	1	2	yes	—
226	C₂	C₄×Q₈×D₁₁	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₄×C₁₁×C₄⋊C₄	C₂	semidirect
5. C₄⋊C₄×Dic₁₁	C₂	semidirect
6. C₄×C₄⋊Dic₁₁	C₂	semidirect
7. C₄×Dic₁₁⋊C₄	C₂	semidirect
9. #10622262	C₂	semidirect
24. C₄⋊C₄×D₁₁	C₄	direct (N × H)
26. C₄²×D₁₁	C₄	semidirect
49. C₁₁×C₄⋊C₄	C₂×C₄	semidirect
51. C₄²×C₁₁	C₂×C₄	semidirect
52. C₄⋊Dic₁₁	C₂×C₄	semidirect
53. Dic₁₁⋊C₄	C₂×C₄	semidirect
56. C₄×Dic₁₁	C₂×C₄	semidirect
57. C₄×Dic₁₁	C₂×C₄	semidirect
58. C₄×Dic₁₁	C₂×C₄	semidirect
88. C₄×D₁₁	C₄²	semidirect
89. C₄×D₁₁	C₄⋊C₄	direct (N × H)
97. C₄×C₄⋊C₄	D₁₁	direct (N × H)
111. C₄×C₁₁	C₂×C₄²	semidirect
112. C₄×C₁₁	C₂×C₄⋊C₄	semidirect
115. Dic₁₁	C₂×C₄²	semidirect
116. Dic₁₁	C₂×C₄⋊C₄	semidirect
142. D₁₁	C₄×C₄⋊C₄	direct (N × H)
164. C₄⋊C₄	C₄×D₁₁	direct (N × H)
171. C₄²	C₄×D₁₁	semidirect
172. C₁₁	C₂×C₄×C₄⋊C₄	semidirect
219. C₄	C₄²×D₁₁	semidirect
220. C₄	C₄⋊C₄×D₁₁	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⋊C₄×D₁₁	2
C₂×C₄²×D₁₁	2
C₄×C₁₁×C₄⋊C₄	2
C₄⋊C₄×Dic₁₁	2
C₄×C₄⋊Dic₁₁	2
C₄×Dic₁₁⋊C₄	2
D₁₁×#95	2
#10622262	2
C₂×C₄×C₄⋊C₄	11

Subgroups — C4×C4⋊C4×D11 #13070949

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₄⋊C₄×D₁₁ #13070949