Subgroups — C₁₁×#3231 #13066069

Order 1408.

326 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#533	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#533	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#500	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#485	C₂	1	4	yes	maximal
8	C₁₁×#479	C₂	1	4	yes	maximal, complemented
9	C₁₁×#431	C₂	1	1	yes	maximal, characteristic
10	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₁₁×#125	—	2	1	no	—
15	C₁₁×#125	C₂²	1	2	yes	—
16	C₁₁×C₂²⋊Q₈	—	2	1	no	—
17	C₁₁×C₂²⋊Q₈	—	2	1	no	—
18	C₁₁×C₂²⋊Q₈	—	2	1	no	—
19	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₄×Q₈×C₁₁	—	2	1	no	—
21	C₄×Q₈×C₁₁	—	2	1	no	—
22	C₄×Q₈×C₁₁	—	2	1	no	—
23	C₄×Q₈×C₁₁	C₂²	1	2	yes	—
24	C₁₁×#117	—	2	1	no	—
25	C₁₁×#117	C₂²	1	2	yes	—
26	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
27	C₁₁×#107	C₂²	1	4	yes	—
28	C₁₁×#106	C₂²	1	4	yes	—
29	C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
30	C₁₁×#103	C₂²	1	4	yes	—
31	C₁₁×#103	C₂²	1	4	yes	—
32	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
33	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
34	C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
35	C₂×Q₈×C₁₁	—	2	1	no	—
36	C₂×Q₈×C₁₁	—	2	1	no	—
37	C₂×Q₈×C₁₁	—	2	1	no	—
38	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂³	1	2	yes	—
43	C₂×C₈×C₁₁	C₂³	1	2	yes	—
44	C₁₁×C₄⋊C₄	—	2	1	no	—
45	C₁₁×C₄⋊C₄	—	2	1	no	—
46	C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₁₁×C₄⋊C₄	—	2	2	no	—
48	C₁₁×C₄⋊C₄	—	2	1	no	—
49	C₁₁×C₄⋊C₄	—	2	1	no	—
50	C₁₁×C₄⋊C₄	—	2	1	no	—
51	C₁₁×C₄⋊C₄	—	2	2	no	—
52	C₁₁×C₄⋊C₄	—	2	2	no	—
53	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
54	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
55	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
56	C₁₁×C₂²⋊C₄	—	2	2	no	—
57	C₁₁×C₂²⋊C₄	—	2	2	no	—
58	C₄²×C₁₁	—	2	2	no	—
59	C₄²×C₁₁	—	2	2	no	—
60	C₄²×C₁₁	D₄	1	1	yes	characteristic
61	C₄²×C₁₁	D₄	1	1	yes	characteristic
62	C₄²×C₁₁	C₂³	1	1	yes	characteristic
63	C₄²×C₁₁	C₂³	1	1	yes	characteristic
64	#3231	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
66	Q₈×C₁₁	—	2	4	no	—
67	Q₈×C₁₁	—	4	2	no	—
68	Q₈×C₁₁	—	4	2	no	—
69	Q₈×C₁₁	—	4	2	no	—
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
83	C₈×C₁₁	—	2	2	no	—
84	C₈×C₁₁	—	2	2	no	—
85	#533	C₂×C₁₁	1	1	yes	characteristic
86	#533	C₂×C₁₁	1	1	yes	characteristic
87	#500	C₂×C₁₁	1	1	yes	characteristic, complemented
88	#498	C₂×C₁₁	1	1	yes	characteristic, complemented
89	#487	C₂×C₁₁	1	1	yes	characteristic, complemented
90	#487	C₂×C₁₁	1	1	yes	characteristic, complemented
91	#485	C₂×C₁₁	1	4	yes	—
92	#479	C₂×C₁₁	1	4	yes	complemented
93	#431	C₂×C₁₁	1	1	yes	characteristic
94	C₂²×C₁₁	—	2	1	no	—
95	C₂²×C₁₁	—	2	1	no	—
96	C₂²×C₁₁	—	2	1	no	—
97	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
98	C₄×C₁₁	—	2	1	no	—
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	—	4	2	no	—
102	C₄×C₁₁	—	4	2	no	—
103	C₄×C₁₁	—	4	2	no	—
104	C₄×C₁₁	—	4	2	no	—
105	C₄×C₁₁	#135	1	2	yes	—
106	C₄×C₁₁	#137	1	2	yes	—
107	C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
108	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
109	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
110	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
111	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
112	#125	—	2	1	no	—
113	#125	C₂²×C₁₁	1	2	yes	—
114	C₂²⋊Q₈	—	2	1	no	—
115	C₂²⋊Q₈	—	2	1	no	—
116	C₂²⋊Q₈	—	2	1	no	—
117	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
118	C₄×Q₈	—	2	1	no	—
119	C₄×Q₈	—	2	1	no	—
120	C₄×Q₈	—	2	1	no	—
121	C₄×Q₈	C₂²×C₁₁	1	2	yes	—
122	#117	—	2	1	no	—
123	#117	C₂²×C₁₁	1	2	yes	—
124	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
125	#107	C₂²×C₁₁	1	4	yes	—
126	#106	C₂²×C₁₁	1	4	yes	—
127	C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
128	#103	C₂²×C₁₁	1	4	yes	—
129	#103	C₂²×C₁₁	1	4	yes	—
130	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
131	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
132	C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
133	C₂×C₁₁	—	4	1	no	—
134	C₂×C₁₁	#536	1	1	yes	characteristic
135	C₂×C₁₁	C₂×#135	1	1	yes	characteristic
136	C₂×C₁₁	C₂×#137	1	1	yes	characteristic
137	C₂×Q₈	—	2	1	no	—
138	C₂×Q₈	—	2	1	no	—
139	C₂×Q₈	—	2	1	no	—
140	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
141	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
142	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
143	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
144	C₂×C₈	C₂³×C₁₁	1	2	yes	—
145	C₂×C₈	C₂³×C₁₁	1	2	yes	—
146	C₄⋊C₄	—	2	1	no	—
147	C₄⋊C₄	—	2	1	no	—
148	C₄⋊C₄	—	2	2	no	—
149	C₄⋊C₄	—	2	2	no	—
150	C₄⋊C₄	—	2	1	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	—	2	1	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
156	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
157	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
158	C₂²⋊C₄	—	2	2	no	—
159	C₂²⋊C₄	—	2	2	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	2	no	—
162	C₄²	D₄×C₁₁	1	1	yes	characteristic
163	C₄²	D₄×C₁₁	1	1	yes	characteristic
164	C₄²	C₂³×C₁₁	1	1	yes	characteristic
165	C₄²	C₂³×C₁₁	1	1	yes	characteristic
166	C₁₁	#3231	1	1	yes	characteristic, direct product factor, Sylow
167	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
168	Q₈	—	2	4	no	—
169	Q₈	—	4	2	no	—
170	Q₈	—	4	2	no	—
171	Q₈	—	4	2	no	—
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
180	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
181	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
182	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
183	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
184	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
185	C₈	—	2	2	no	—
186	C₈	—	2	2	no	—
187	C₂²	—	2	1	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
191	C₄	—	2	1	no	—
192	C₄	—	2	1	no	—
193	C₄	—	2	1	no	—
194	C₄	—	4	2	no	—
195	C₄	—	4	2	no	—
196	C₄	—	4	2	no	—
197	C₄	—	4	2	no	—
198	C₄	C₁₁×#135	1	2	yes	—
199	C₄	C₁₁×#137	1	2	yes	—
200	C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
201	C₂	—	4	1	no	—
202	C₂	C₁₁×#536	1	1	yes	characteristic
203	C₂	C₂×C₁₁×#135	1	1	yes	characteristic
204	C₂	C₂×C₁₁×#137	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₁₁×#500	C₂	semidirect
4. C₁₁×#498	C₂	semidirect
5. C₁₁×#487	C₂	semidirect
6. C₁₁×#487	C₂	semidirect
8. C₁₁×#479	C₂	semidirect
64. #3231	C₁₁	direct (N × H)
87. #500	C₂×C₁₁	semidirect
88. #498	C₂×C₁₁	semidirect
89. #487	C₂×C₁₁	semidirect
90. #487	C₂×C₁₁	semidirect
92. #479	C₂×C₁₁	semidirect
166. C₁₁	#3231	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#533	2
C₁₁×#500	2
C₁₁×#498	2
C₁₁×#487	2
C₁₁×#485	2
C₁₁×#479	2
C₁₁×#431	2
#3231	11

Subgroups — C11×#3231 #13066069

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3231 #13066069