Subgroups — C₁₁×#33456 #14610649

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×D₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2948	C₂	1	2	yes	maximal, complemented
3	C₁₁×#2177	C₂	1	4	yes	maximal, complemented
4	C₄×C₁₁×D₁₆	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2158	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2140	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₁₁×D₈	C₂²	1	2	yes	—
9	C₁₁×#518	—	2	2	no	—
10	C₂×C₁₁×D₁₆	C₄	1	8	yes	complemented
11	C₂×C₁₁×D₁₆	C₂²	1	2	yes	—
12	C₂×C₁₁×D₁₆	C₂²	1	2	yes	—
13	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
14	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
15	C₁₁×#442	—	2	4	no	—
16	C₄×C₁₁×D₈	C₂²	1	8	yes	complemented
17	C₁₁×#427	C₂²	1	2	yes	—
18	C₁₁×#418	—	2	2	no	—
19	C₁₁×#405	C₂²	1	1	yes	characteristic
20	C₁₁×#367	C₂²	1	2	yes	complemented
21	C₁₁×#366	C₂²	1	2	yes	complemented
22	C₁₁×#357	C₂²	1	8	yes	complemented
23	C₁₁×#346	C₂²	1	2	yes	complemented
24	C₄×C₁₁×C₁₆	C₂²	1	2	yes	complemented
25	C₂²×D₄×C₁₁	—	2	2	no	—
26	C₂×C₁₁×D₈	—	2	2	no	—
27	C₂×C₁₁×D₈	—	2	4	no	—
28	C₂×C₁₁×D₈	C₂×C₄	1	8	yes	complemented
29	C₂×C₁₁×D₈	C₂³	1	4	yes	—
30	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
32	C₄×D₄×C₁₁	—	2	8	no	—
33	C₄×D₄×C₁₁	—	4	4	no	—
34	C₁₁×#117	—	2	2	no	—
35	C₁₁×#117	D₄	1	1	yes	characteristic
36	C₂×C₁₁×C₂²⋊C₄	—	4	4	no	—
37	C₁₁×D₁₆	C₂×C₄	1	8	yes	complemented
38	C₁₁×D₁₆	C₂×C₄	1	8	yes	complemented
39	C₁₁×M₃₂	—	2	2	no	—
40	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	complemented
41	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
42	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
44	C₁₁×#107	C₂³	1	4	yes	—
45	C₁₁×#106	—	2	2	no	—
46	C₁₁×#102	—	2	8	no	—
47	C₁₁×#97	D₄	1	2	yes	—
48	C₄×C₈×C₁₁	C₂³	1	2	yes	—
49	#33456	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂⁴×C₁₁	—	4	2	no	—
51	C₂×D₄×C₁₁	—	2	8	no	—
52	C₂×D₄×C₁₁	—	2	4	no	—
53	C₂×D₄×C₁₁	—	4	2	no	—
54	C₂×D₄×C₁₁	—	4	4	no	—
55	C₂²×C₄×C₁₁	—	4	8	no	—
56	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
57	C₁₁×D₈	—	2	8	no	—
58	C₁₁×D₈	—	2	4	no	—
59	C₁₁×D₈	C₂²×C₄	1	8	yes	—
60	C₁₁×M₁₆	—	2	2	no	—
61	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
62	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	#41	1	2	yes	—
65	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
66	C₁₁×C₄⋊C₄	—	2	4	no	—
67	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
68	C₁₁×C₂²⋊C₄	—	4	2	no	—
69	C₁₁×C₂²⋊C₄	—	4	8	no	—
70	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
71	C₄²×C₁₁	—	4	2	no	—
72	C₄²×C₁₁	C₂×D₄	1	2	yes	—
73	C₁₁×C₁₆	—	2	2	no	—
74	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
75	C₁₁×C₁₆	C₂²×C₄	1	2	yes	—
76	C₂²×D₁₆	C₂×C₁₁	1	1	yes	characteristic
77	#2948	C₂×C₁₁	1	2	yes	complemented
78	#2177	C₂×C₁₁	1	4	yes	complemented
79	C₄×D₁₆	C₂×C₁₁	1	4	yes	complemented
80	#2158	C₂×C₁₁	1	1	yes	characteristic, complemented
81	#2140	C₂×C₁₁	1	2	yes	complemented
82	#2108	C₂×C₁₁	1	1	yes	characteristic, complemented
83	C₂³×C₁₁	—	4	4	no	—
84	C₂³×C₁₁	—	4	8	no	—
85	C₂³×C₁₁	—	16	4	no	—
86	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
87	D₄×C₁₁	—	2	8	no	—
88	D₄×C₁₁	—	4	4	no	—
89	D₄×C₁₁	—	4	8	no	—
90	C₂×C₄×C₁₁	—	4	4	no	—
91	C₂×C₄×C₁₁	—	16	8	no	—
92	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
93	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
94	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
95	C₂×C₄×C₁₁	#135	1	2	yes	—
96	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
97	C₈×C₁₁	—	2	2	no	—
98	C₈×C₁₁	C₄×D₄	1	2	yes	—
99	C₈×C₁₁	C₂³×C₄	1	1	yes	characteristic
100	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
101	C₂²×D₈	C₂²×C₁₁	1	2	yes	—
102	#518	—	2	2	no	—
103	C₂×D₁₆	C₄×C₁₁	1	8	yes	complemented
104	C₂×D₁₆	C₂²×C₁₁	1	2	yes	—
105	C₂×D₁₆	C₂²×C₁₁	1	2	yes	—
106	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
107	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
108	#442	—	2	4	no	—
109	C₄×D₈	C₂²×C₁₁	1	8	yes	complemented
110	#427	C₂²×C₁₁	1	2	yes	—
111	#418	—	2	2	no	—
112	#405	C₂²×C₁₁	1	1	yes	characteristic
113	#367	C₂²×C₁₁	1	2	yes	complemented
114	#366	C₂²×C₁₁	1	2	yes	complemented
115	#357	C₂²×C₁₁	1	8	yes	complemented
116	#346	C₂²×C₁₁	1	2	yes	complemented
117	C₄×C₁₆	C₂²×C₁₁	1	2	yes	complemented
118	C₂²×C₁₁	—	2	2	no	—
119	C₂²×C₁₁	—	4	8	no	—
120	C₂²×C₁₁	—	8	8	no	—
121	C₂²×C₁₁	—	16	8	no	—
122	C₂²×C₁₁	C₄×D₈	1	2	yes	—
123	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
124	C₄×C₁₁	—	2	4	no	—
125	C₄×C₁₁	—	8	4	no	—
126	C₄×C₁₁	C₄×D₈	1	2	yes	—
127	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
128	C₄×C₁₁	C₂×#135	1	1	yes	characteristic
129	C₂²×D₄	—	2	2	no	—
130	C₂×D₈	—	2	2	no	—
131	C₂×D₈	—	2	4	no	—
132	C₂×D₈	C₂×C₄×C₁₁	1	8	yes	complemented
133	C₂×D₈	C₂³×C₁₁	1	4	yes	—
134	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
135	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
136	C₄×D₄	—	2	8	no	—
137	C₄×D₄	—	4	4	no	—
138	#117	—	2	2	no	—
139	#117	D₄×C₁₁	1	1	yes	characteristic
140	C₂×C₂²⋊C₄	—	4	4	no	—
141	D₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
142	D₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
143	M₃₂	—	2	2	no	—
144	C₂×C₁₆	C₂×C₄×C₁₁	1	4	yes	complemented
145	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
146	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
147	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
148	#107	C₂³×C₁₁	1	4	yes	—
149	#106	—	2	2	no	—
150	#102	—	2	8	no	—
151	#97	D₄×C₁₁	1	2	yes	—
152	C₄×C₈	C₂³×C₁₁	1	2	yes	—
153	C₂×C₁₁	—	2	2	no	—
154	C₂×C₁₁	—	8	8	no	—
155	C₂×C₁₁	C₂×C₄×D₈	1	1	yes	characteristic
156	C₂×C₁₁	#3415	1	2	yes	—
157	C₂⁴	—	4	2	no	—
158	C₂×D₄	—	2	8	no	—
159	C₂×D₄	—	2	4	no	—
160	C₂×D₄	—	4	2	no	—
161	C₂×D₄	—	4	4	no	—
162	C₂²×C₄	—	4	8	no	—
163	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
164	D₈	—	2	8	no	—
165	D₈	—	2	4	no	—
166	D₈	C₂²×C₄×C₁₁	1	8	yes	—
167	M₁₆	—	2	2	no	—
168	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
169	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
170	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
171	C₂×C₈	C₁₁×#41	1	2	yes	—
172	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
173	C₄⋊C₄	—	2	4	no	—
174	C₄⋊C₄	C₁₁×D₈	1	2	yes	—
175	C₂²⋊C₄	—	4	2	no	—
176	C₂²⋊C₄	—	4	8	no	—
177	C₂²⋊C₄	C₁₁×D₈	1	2	yes	—
178	C₄²	—	4	2	no	—
179	C₄²	C₂×D₄×C₁₁	1	2	yes	—
180	C₁₆	—	2	2	no	—
181	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
182	C₁₆	C₂²×C₄×C₁₁	1	2	yes	—
183	C₁₁	#33456	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³	—	4	4	no	—
185	C₂³	—	4	8	no	—
186	C₂³	—	16	4	no	—
187	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
188	D₄	—	2	8	no	—
189	D₄	—	4	4	no	—
190	D₄	—	4	8	no	—
191	C₂×C₄	—	4	4	no	—
192	C₂×C₄	—	16	8	no	—
193	C₂×C₄	C₄×D₄×C₁₁	1	2	yes	—
194	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
195	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
196	C₂×C₄	C₁₁×#135	1	2	yes	—
197	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
198	C₈	—	2	2	no	—
199	C₈	C₄×D₄×C₁₁	1	2	yes	—
200	C₈	C₂³×C₄×C₁₁	1	1	yes	characteristic
201	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
202	C₂²	—	2	2	no	—
203	C₂²	—	4	8	no	—
204	C₂²	—	8	8	no	—
205	C₂²	—	16	8	no	—
206	C₂²	C₄×C₁₁×D₈	1	2	yes	—
207	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
208	C₄	—	2	4	no	—
209	C₄	—	8	4	no	—
210	C₄	C₄×C₁₁×D₈	1	2	yes	—
211	C₄	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
212	C₄	C₂×C₁₁×#135	1	1	yes	characteristic
213	C₂	—	2	2	no	—
214	C₂	—	8	8	no	—
215	C₂	C₂×C₄×C₁₁×D₈	1	1	yes	characteristic
216	C₂	C₁₁×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator	C₈	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂²×C₁₁×D₁₆	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₁₁×#117 ◁ C₁₁×#405 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2948	C₂	semidirect
3. C₁₁×#2177	C₂	semidirect
4. C₄×C₁₁×D₁₆	C₂	semidirect
5. C₁₁×#2158	C₂	semidirect
6. C₁₁×#2140	C₂	semidirect
7. C₁₁×#2108	C₂	semidirect
10. C₂×C₁₁×D₁₆	C₄	semidirect
16. C₄×C₁₁×D₈	C₂²	semidirect
20. C₁₁×#367	C₂²	semidirect
21. C₁₁×#366	C₂²	semidirect
22. C₁₁×#357	C₂²	semidirect
23. C₁₁×#346	C₂²	semidirect
24. C₄×C₁₁×C₁₆	C₂²	semidirect
28. C₂×C₁₁×D₈	C₂×C₄	semidirect
37. C₁₁×D₁₆	C₂×C₄	semidirect
38. C₁₁×D₁₆	C₂×C₄	semidirect
40. C₂×C₁₁×C₁₆	C₂×C₄	semidirect
49. #33456	C₁₁	direct (N × H)
77. #2948	C₂×C₁₁	semidirect
78. #2177	C₂×C₁₁	semidirect
79. C₄×D₁₆	C₂×C₁₁	semidirect
80. #2158	C₂×C₁₁	semidirect
81. #2140	C₂×C₁₁	semidirect
82. #2108	C₂×C₁₁	semidirect
103. C₂×D₁₆	C₄×C₁₁	semidirect
109. C₄×D₈	C₂²×C₁₁	semidirect
113. #367	C₂²×C₁₁	semidirect
114. #366	C₂²×C₁₁	semidirect
115. #357	C₂²×C₁₁	semidirect
116. #346	C₂²×C₁₁	semidirect
117. C₄×C₁₆	C₂²×C₁₁	semidirect
132. C₂×D₈	C₂×C₄×C₁₁	semidirect
141. D₁₆	C₂×C₄×C₁₁	semidirect
142. D₁₆	C₂×C₄×C₁₁	semidirect
144. C₂×C₁₆	C₂×C₄×C₁₁	semidirect
183. C₁₁	#33456	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×C₁₁×D₁₆	2
C₁₁×#2948	2
C₁₁×#2177	2
C₄×C₁₁×D₁₆	2
C₁₁×#2158	2
C₁₁×#2140	2
C₁₁×#2108	2
#33456	11

Subgroups — C11×#33456 #14610649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33456 #14610649