Subgroups — C₁₁×#2805 #13065643

Order 1408.

368 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#400	C₂	1	2	yes	maximal
2	C₁₁×#400	C₂	1	2	yes	maximal
3	C₁₁×#395	C₂	1	2	yes	maximal
4	C₁₁×#391	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#389	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#389	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#389	C₂	1	2	yes	maximal
8	C₁₁×#387	C₂	1	2	yes	maximal
9	C₁₁×#387	C₂	1	2	yes	maximal
10	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	C₂²	1	2	yes	—
21	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
22	C₁₁×#95	C₂²	1	2	yes	—
23	C₁₁×#95	C₂²	1	2	yes	—
24	C₁₁×#95	C₂²	1	2	yes	—
25	C₁₁×#95	C₂²	1	2	yes	—
26	C₁₁×#95	C₂²	1	2	yes	—
27	C₁₁×#95	C₂²	1	2	yes	—
28	C₁₁×#95	C₂²	1	2	yes	—
29	C₁₁×#95	C₂²	1	2	yes	—
30	C₁₁×#95	C₂²	1	2	yes	—
31	C₂×Q₈×C₁₁	—	2	2	no	—
32	C₂×Q₈×C₁₁	—	4	1	no	—
33	C₂×Q₈×C₁₁	—	4	1	no	—
34	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
39	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
43	C₁₁×C₄⋊C₄	—	2	4	no	—
44	C₁₁×C₄⋊C₄	—	2	2	no	—
45	C₁₁×C₄⋊C₄	—	2	4	no	—
46	C₁₁×C₄⋊C₄	—	4	2	no	—
47	C₁₁×C₄⋊C₄	—	4	1	no	—
48	C₁₁×C₄⋊C₄	—	4	1	no	—
49	C₁₁×C₄⋊C₄	—	4	1	no	—
50	C₁₁×C₄⋊C₄	—	4	2	no	—
51	C₁₁×C₄⋊C₄	Q₈	1	4	yes	complemented
52	C₄²×C₁₁	—	4	1	no	—
53	C₄²×C₁₁	—	4	2	no	—
54	#2805	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
55	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
56	Q₈×C₁₁	—	4	4	no	—
57	C₂×C₄×C₁₁	—	2	2	no	—
58	C₂×C₄×C₁₁	—	2	1	no	—
59	C₂×C₄×C₁₁	—	2	1	no	—
60	C₂×C₄×C₁₁	—	2	2	no	—
61	C₂×C₄×C₁₁	—	2	1	no	—
62	C₂×C₄×C₁₁	—	2	1	no	—
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	2	1	no	—
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	—	2	2	no	—
69	C₂×C₄×C₁₁	—	2	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	—	2	2	no	—
78	C₂×C₄×C₁₁	—	2	2	no	—
79	C₂×C₄×C₁₁	—	2	2	no	—
80	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
81	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
82	C₂×C₄×C₁₁	#41	1	2	yes	—
83	C₂×C₄×C₁₁	#41	1	2	yes	—
84	#400	C₂×C₁₁	1	2	yes	—
85	#400	C₂×C₁₁	1	2	yes	—
86	#395	C₂×C₁₁	1	2	yes	—
87	#391	C₂×C₁₁	1	1	yes	characteristic
88	#389	C₂×C₁₁	1	1	yes	characteristic
89	#389	C₂×C₁₁	1	1	yes	characteristic
90	#389	C₂×C₁₁	1	2	yes	—
91	#387	C₂×C₁₁	1	2	yes	—
92	#387	C₂×C₁₁	1	2	yes	—
93	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
94	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
95	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
96	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
97	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
98	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
99	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
100	C₄×C₁₁	—	2	2	no	—
101	C₄×C₁₁	—	2	2	no	—
102	C₄×C₁₁	—	2	2	no	—
103	C₄×C₁₁	—	2	4	no	—
104	C₄×C₁₁	—	4	2	no	—
105	C₄×C₁₁	—	4	2	no	—
106	C₄×C₁₁	—	4	2	no	—
107	C₄×C₁₁	—	4	2	no	—
108	C₄×C₁₁	—	4	2	no	—
109	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic
110	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
111	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
112	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
113	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
115	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
116	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
117	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
118	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
119	C₂×C₄²	C₂²×C₁₁	1	2	yes	—
120	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
121	#95	C₂²×C₁₁	1	2	yes	—
122	#95	C₂²×C₁₁	1	2	yes	—
123	#95	C₂²×C₁₁	1	2	yes	—
124	#95	C₂²×C₁₁	1	2	yes	—
125	#95	C₂²×C₁₁	1	2	yes	—
126	#95	C₂²×C₁₁	1	2	yes	—
127	#95	C₂²×C₁₁	1	2	yes	—
128	#95	C₂²×C₁₁	1	2	yes	—
129	#95	C₂²×C₁₁	1	2	yes	—
130	C₂×C₁₁	#538	1	1	yes	characteristic
131	C₂×C₁₁	#539	1	1	yes	characteristic
132	C₂×C₁₁	#544	1	1	yes	characteristic
133	C₂×C₁₁	#554	1	1	yes	characteristic
134	C₂×C₁₁	#556	1	1	yes	characteristic
135	C₂×C₁₁	#557	1	1	yes	characteristic
136	C₂×C₁₁	#563	1	1	yes	characteristic
137	C₂×Q₈	—	2	2	no	—
138	C₂×Q₈	—	4	1	no	—
139	C₂×Q₈	—	4	1	no	—
140	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
141	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
142	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
143	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
144	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
145	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
146	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
147	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
148	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	2	2	no	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	4	2	no	—
153	C₄⋊C₄	—	4	1	no	—
154	C₄⋊C₄	—	4	1	no	—
155	C₄⋊C₄	—	4	1	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	Q₈×C₁₁	1	4	yes	complemented
158	C₄²	—	4	1	no	—
159	C₄²	—	4	2	no	—
160	C₁₁	#2805	1	1	yes	characteristic, direct product factor, Sylow
161	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
162	Q₈	—	4	4	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	1	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	2	1	no	—
169	C₂×C₄	—	2	1	no	—
170	C₂×C₄	—	2	1	no	—
171	C₂×C₄	—	2	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	—	2	2	no	—
180	C₂×C₄	—	2	2	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	C₂×Q₈×C₁₁	1	2	yes	—
187	C₂×C₄	C₂×Q₈×C₁₁	1	4	yes	—
188	C₂×C₄	C₁₁×#41	1	2	yes	—
189	C₂×C₄	C₁₁×#41	1	2	yes	—
190	C₂²	C₂²×Q₈×C₁₁	1	1	yes	characteristic
191	C₂²	C₂×C₁₁×#41	1	1	yes	characteristic
192	C₂²	C₂×C₁₁×#41	1	1	yes	characteristic
193	C₂²	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
194	C₂²	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
195	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
196	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
197	C₄	—	2	2	no	—
198	C₄	—	2	2	no	—
199	C₄	—	2	2	no	—
200	C₄	—	2	4	no	—
201	C₄	—	4	2	no	—
202	C₄	—	4	2	no	—
203	C₄	—	4	2	no	—
204	C₄	—	4	2	no	—
205	C₄	—	4	2	no	—
206	C₂	C₁₁×#538	1	1	yes	characteristic
207	C₂	C₁₁×#539	1	1	yes	characteristic
208	C₂	C₁₁×#544	1	1	yes	characteristic
209	C₂	C₁₁×#554	1	1	yes	characteristic
210	C₂	C₁₁×#556	1	1	yes	characteristic
211	C₂	C₁₁×#557	1	1	yes	characteristic
212	C₂	C₁₁×#563	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
51. C₁₁×C₄⋊C₄	Q₈	semidirect
54. #2805	C₁₁	direct (N × H)
157. C₄⋊C₄	Q₈×C₁₁	semidirect
160. C₁₁	#2805	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×#400	2
C₁₁×#395	2
C₁₁×#391	2
C₁₁×#389	2
C₁₁×#387	2
#2805	11

Subgroups — C11×#2805 #13065643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2805 #13065643