Subgroups — C₁₁×#2949 #13065787

Order 1408.

492 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁×#518	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#440	C₂	1	4	yes	maximal, complemented
5	C₄×C₁₁×SD₁₆	C₂	1	4	yes	maximal, complemented
6	C₁₁×#427	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#418	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂²×D₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×SD₁₆	C₄	1	8	yes	complemented
13	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	—
15	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
17	C₄×Q₈×C₁₁	—	2	2	no	—
18	C₄×Q₈×C₁₁	C₂²	1	4	yes	complemented
19	C₄×D₄×C₁₁	—	2	2	no	—
20	C₄×D₄×C₁₁	C₂²	1	4	yes	—
21	C₁₁×#117	—	2	2	no	—
22	C₁₁×#117	C₂²	1	1	yes	characteristic
23	C₁₁×#117	C₂²	1	1	yes	characteristic
24	C₁₁×#117	C₂²	1	1	yes	characteristic
25	C₂×C₁₁×C₂²⋊C₄	—	2	2	no	—
26	C₁₁×#107	C₂²	1	2	yes	complemented
27	C₁₁×#106	C₂²	1	2	yes	complemented
28	C₁₁×#103	C₂²	1	4	yes	complemented
29	C₁₁×#102	C₂²	1	4	yes	—
30	C₁₁×#97	C₂²	1	2	yes	complemented
31	C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
32	C₂⁴×C₁₁	—	2	1	no	—
33	C₂×Q₈×C₁₁	—	2	1	no	—
34	C₂×Q₈×C₁₁	—	2	2	no	—
35	C₂×Q₈×C₁₁	C₂×C₄	1	4	yes	complemented
36	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
37	C₂×D₄×C₁₁	—	2	1	no	—
38	C₂×D₄×C₁₁	—	2	2	no	—
39	C₂×D₄×C₁₁	C₂×C₄	1	4	yes	—
40	C₂×D₄×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₄×C₁₁	—	2	1	no	—
42	C₂²×C₄×C₁₁	—	2	4	no	—
43	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
45	C₁₁×SD₁₆	C₂×C₄	1	8	yes	complemented
46	C₁₁×M₁₆	—	2	2	no	—
47	C₂×C₈×C₁₁	C₂×C₄	1	4	yes	complemented
48	C₂×C₈×C₁₁	C₂³	1	2	yes	—
49	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
51	C₁₁×C₄⋊C₄	—	2	4	no	—
52	C₁₁×C₄⋊C₄	D₄	1	2	yes	—
53	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
54	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
55	C₁₁×C₂²⋊C₄	—	2	1	no	—
56	C₁₁×C₂²⋊C₄	—	2	1	no	—
57	C₁₁×C₂²⋊C₄	—	2	4	no	—
58	C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
59	C₄²×C₁₁	—	2	4	no	—
60	C₄²×C₁₁	—	2	1	no	—
61	C₄²×C₁₁	—	2	1	no	—
62	C₄²×C₁₁	C₂³	1	2	yes	—
63	#2949	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
64	C₂³×C₁₁	—	2	2	no	—
65	C₂³×C₁₁	—	2	4	no	—
66	C₂³×C₁₁	—	8	2	no	—
67	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
68	Q₈×C₁₁	—	2	4	no	—
69	Q₈×C₁₁	—	2	2	no	—
70	Q₈×C₁₁	C₂²×C₄	1	4	yes	—
71	D₄×C₁₁	—	2	4	no	—
72	D₄×C₁₁	—	2	2	no	—
73	D₄×C₁₁	C₂²×C₄	1	4	yes	—
74	C₂×C₄×C₁₁	—	2	4	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	8	4	no	—
79	C₂×C₄×C₁₁	C₂²×C₄	1	2	yes	—
80	C₂×C₄×C₁₁	C₂×D₄	1	4	yes	—
81	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	#41	1	2	yes	—
83	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
84	C₈×C₁₁	—	2	2	no	—
85	C₈×C₁₁	C₂²×C₄	1	2	yes	—
86	C₈×C₁₁	C₂²×C₄	1	2	yes	—
87	C₂²×SD₁₆	C₂×C₁₁	1	1	yes	characteristic
88	#519	C₂×C₁₁	1	1	yes	characteristic, complemented
89	#518	C₂×C₁₁	1	1	yes	characteristic
90	#440	C₂×C₁₁	1	4	yes	complemented
91	C₄×SD₁₆	C₂×C₁₁	1	4	yes	complemented
92	#427	C₂×C₁₁	1	1	yes	characteristic, complemented
93	#419	C₂×C₁₁	1	1	yes	characteristic, complemented
94	#418	C₂×C₁₁	1	1	yes	characteristic
95	#405	C₂×C₁₁	1	1	yes	characteristic, complemented
96	C₂²×C₁₁	—	2	2	no	—
97	C₂²×C₁₁	—	2	4	no	—
98	C₂²×C₁₁	—	4	4	no	—
99	C₂²×C₁₁	—	8	4	no	—
100	C₂²×C₁₁	C₄×D₄	1	2	yes	—
101	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
102	C₄×C₁₁	—	2	4	no	—
103	C₄×C₁₁	—	2	4	no	—
104	C₄×C₁₁	—	4	2	no	—
105	C₄×C₁₁	—	4	2	no	—
106	C₄×C₁₁	C₄×D₄	1	2	yes	—
107	C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
108	C₄×C₁₁	C₂×#41	1	1	yes	characteristic
109	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic
110	C₂²×D₄	C₂²×C₁₁	1	1	yes	characteristic
111	C₂×SD₁₆	C₄×C₁₁	1	8	yes	complemented
112	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
113	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	—
114	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
115	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
116	C₄×Q₈	—	2	2	no	—
117	C₄×Q₈	C₂²×C₁₁	1	4	yes	complemented
118	C₄×D₄	—	2	2	no	—
119	C₄×D₄	C₂²×C₁₁	1	4	yes	—
120	#117	—	2	2	no	—
121	#117	C₂²×C₁₁	1	1	yes	characteristic
122	#117	C₂²×C₁₁	1	1	yes	characteristic
123	#117	C₂²×C₁₁	1	1	yes	characteristic
124	C₂×C₂²⋊C₄	—	2	2	no	—
125	#107	C₂²×C₁₁	1	2	yes	complemented
126	#106	C₂²×C₁₁	1	2	yes	complemented
127	#103	C₂²×C₁₁	1	4	yes	complemented
128	#102	C₂²×C₁₁	1	4	yes	—
129	#97	C₂²×C₁₁	1	2	yes	complemented
130	C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
131	C₂×C₁₁	—	2	2	no	—
132	C₂×C₁₁	—	4	4	no	—
133	C₂×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
134	C₂×C₁₁	#577	1	2	yes	—
135	C₂⁴	—	2	1	no	—
136	C₂×Q₈	—	2	1	no	—
137	C₂×Q₈	—	2	2	no	—
138	C₂×Q₈	C₂×C₄×C₁₁	1	4	yes	complemented
139	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
140	C₂×D₄	—	2	1	no	—
141	C₂×D₄	—	2	2	no	—
142	C₂×D₄	C₂×C₄×C₁₁	1	4	yes	—
143	C₂×D₄	C₂³×C₁₁	1	2	yes	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	2	4	no	—
146	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
147	SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
148	SD₁₆	C₂×C₄×C₁₁	1	8	yes	complemented
149	M₁₆	—	2	2	no	—
150	C₂×C₈	C₂×C₄×C₁₁	1	4	yes	complemented
151	C₂×C₈	C₂³×C₁₁	1	2	yes	—
152	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
153	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	D₄×C₁₁	1	2	yes	—
156	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
157	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
158	C₂²⋊C₄	—	2	1	no	—
159	C₂²⋊C₄	—	2	1	no	—
160	C₂²⋊C₄	—	2	4	no	—
161	C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
162	C₄²	—	2	4	no	—
163	C₄²	—	2	1	no	—
164	C₄²	—	2	1	no	—
165	C₄²	C₂³×C₁₁	1	2	yes	—
166	C₁₁	#2949	1	1	yes	characteristic, direct product factor, Sylow
167	C₂³	—	2	2	no	—
168	C₂³	—	2	4	no	—
169	C₂³	—	8	2	no	—
170	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
171	Q₈	—	2	4	no	—
172	Q₈	—	2	2	no	—
173	Q₈	C₂²×C₄×C₁₁	1	4	yes	—
174	D₄	—	2	4	no	—
175	D₄	—	2	2	no	—
176	D₄	C₂²×C₄×C₁₁	1	4	yes	—
177	C₂×C₄	—	2	4	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	8	4	no	—
182	C₂×C₄	C₂²×C₄×C₁₁	1	2	yes	—
183	C₂×C₄	C₂×D₄×C₁₁	1	4	yes	—
184	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
185	C₂×C₄	C₁₁×#41	1	2	yes	—
186	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
187	C₈	—	2	2	no	—
188	C₈	C₂²×C₄×C₁₁	1	2	yes	—
189	C₈	C₂²×C₄×C₁₁	1	2	yes	—
190	C₂²	—	2	2	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	4	4	no	—
193	C₂²	—	8	4	no	—
194	C₂²	C₄×D₄×C₁₁	1	2	yes	—
195	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
196	C₄	—	2	4	no	—
197	C₄	—	2	4	no	—
198	C₄	—	4	2	no	—
199	C₄	—	4	2	no	—
200	C₄	C₄×D₄×C₁₁	1	2	yes	—
201	C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
202	C₄	C₂×C₁₁×#41	1	1	yes	characteristic
203	C₂	—	2	2	no	—
204	C₂	—	4	4	no	—
205	C₂	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
206	C₂	C₁₁×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator	C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₂²×D₄×C₁₁	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#519	C₂	semidirect
4. C₁₁×#440	C₂	semidirect
5. C₄×C₁₁×SD₁₆	C₂	semidirect
6. C₁₁×#427	C₂	semidirect
7. C₁₁×#419	C₂	semidirect
9. C₁₁×#405	C₂	semidirect
12. C₂×C₁₁×SD₁₆	C₄	semidirect
18. C₄×Q₈×C₁₁	C₂²	semidirect
26. C₁₁×#107	C₂²	semidirect
27. C₁₁×#106	C₂²	semidirect
28. C₁₁×#103	C₂²	semidirect
30. C₁₁×#97	C₂²	semidirect
31. C₄×C₈×C₁₁	C₂²	semidirect
35. C₂×Q₈×C₁₁	C₂×C₄	semidirect
44. C₁₁×SD₁₆	C₂×C₄	semidirect
45. C₁₁×SD₁₆	C₂×C₄	semidirect
47. C₂×C₈×C₁₁	C₂×C₄	semidirect
63. #2949	C₁₁	direct (N × H)
88. #519	C₂×C₁₁	semidirect
90. #440	C₂×C₁₁	semidirect
91. C₄×SD₁₆	C₂×C₁₁	semidirect
92. #427	C₂×C₁₁	semidirect
93. #419	C₂×C₁₁	semidirect
95. #405	C₂×C₁₁	semidirect
111. C₂×SD₁₆	C₄×C₁₁	semidirect
117. C₄×Q₈	C₂²×C₁₁	semidirect
125. #107	C₂²×C₁₁	semidirect
126. #106	C₂²×C₁₁	semidirect
127. #103	C₂²×C₁₁	semidirect
129. #97	C₂²×C₁₁	semidirect
130. C₄×C₈	C₂²×C₁₁	semidirect
138. C₂×Q₈	C₂×C₄×C₁₁	semidirect
147. SD₁₆	C₂×C₄×C₁₁	semidirect
148. SD₁₆	C₂×C₄×C₁₁	semidirect
150. C₂×C₈	C₂×C₄×C₁₁	semidirect
166. C₁₁	#2949	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×SD₁₆	2
C₁₁×#519	2
C₁₁×#518	2
C₁₁×#440	2
C₄×C₁₁×SD₁₆	2
C₁₁×#427	2
C₁₁×#419	2
C₁₁×#418	2
C₁₁×#405	2
#2949	11

Subgroups — C11×#2949 #13065787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2949 #13065787