Subgroups — C₁₁×#2742 #13065580

Order 1408.

416 conjugacy classes of subgroups.

The subgroup lattice has 220 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, complemented
2	C₁₁×#399	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#395	C₂	1	2	yes	maximal, complemented
4	C₁₁×#393	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#389	C₂	1	2	yes	maximal, complemented
6	C₁₁×#388	C₂	1	2	yes	maximal
7	C₁₁×#387	C₂	1	2	yes	maximal, complemented
8	C₁₁×#385	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#380	C₂	1	2	yes	maximal
10	C₂²×Q₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₁₁×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×C₂²⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₄²×C₁₁	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	1	yes	characteristic
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	1	yes	characteristic
31	C₂⁴×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×Q₈×C₁₁	—	4	2	no	—
33	C₂×Q₈×C₁₁	—	4	1	no	—
34	C₂²×C₄×C₁₁	—	2	4	no	—
35	C₂²×C₄×C₁₁	—	4	1	no	—
36	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
42	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
44	C₁₁×C₄⋊C₄	—	2	4	no	—
45	C₁₁×C₄⋊C₄	—	2	4	no	—
46	C₁₁×C₄⋊C₄	—	4	2	no	—
47	C₁₁×C₄⋊C₄	—	4	2	no	—
48	C₁₁×C₄⋊C₄	—	4	2	no	—
49	C₁₁×C₄⋊C₄	—	4	1	no	—
50	C₁₁×C₂²⋊C₄	—	4	2	no	—
51	C₁₁×C₂²⋊C₄	—	4	2	no	—
52	C₁₁×C₂²⋊C₄	—	4	1	no	—
53	C₁₁×C₂²⋊C₄	Q₈	1	4	yes	complemented
54	C₄²×C₁₁	—	4	2	no	—
55	#2742	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂³×C₁₁	—	2	2	no	—
57	C₂³×C₁₁	—	2	2	no	—
58	C₂³×C₁₁	—	2	1	no	—
59	C₂³×C₁₁	—	2	1	no	—
60	C₂³×C₁₁	C₂×Q₈	1	2	yes	—
61	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
62	Q₈×C₁₁	—	4	4	no	—
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	—	2	2	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	1	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	1	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	—	2	2	no	—
81	C₂×C₄×C₁₁	—	2	2	no	—
82	C₂×C₄×C₁₁	—	2	2	no	—
83	C₂×C₄×C₁₁	—	4	4	no	—
84	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
85	C₂×C₄×C₁₁	#41	1	4	yes	—
86	#400	C₂×C₁₁	1	2	yes	complemented
87	#399	C₂×C₁₁	1	1	yes	characteristic
88	#395	C₂×C₁₁	1	2	yes	complemented
89	#393	C₂×C₁₁	1	1	yes	characteristic
90	#389	C₂×C₁₁	1	2	yes	complemented
91	#388	C₂×C₁₁	1	2	yes	—
92	#387	C₂×C₁₁	1	2	yes	complemented
93	#385	C₂×C₁₁	1	1	yes	characteristic
94	#380	C₂×C₁₁	1	2	yes	—
95	C₂²×C₁₁	—	2	2	no	—
96	C₂²×C₁₁	—	2	4	no	—
97	C₂²×C₁₁	—	4	2	no	—
98	C₂²×C₁₁	—	4	1	no	—
99	C₂²×C₁₁	—	4	1	no	—
100	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
101	C₂²×C₁₁	C₂×#41	1	2	yes	—
102	C₂²×C₁₁	H(5,𝔽₂)	1	2	yes	—
103	C₂²×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
104	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
105	C₄×C₁₁	—	2	4	no	—
106	C₄×C₁₁	—	2	4	no	—
107	C₄×C₁₁	—	4	2	no	—
108	C₄×C₁₁	—	4	2	no	—
109	C₄×C₁₁	—	4	1	no	—
110	C₄×C₁₁	—	4	2	no	—
111	C₄×C₁₁	—	4	2	no	—
112	C₄×C₁₁	—	4	1	no	—
113	C₂²×Q₈	C₂²×C₁₁	1	1	yes	characteristic
114	C₂³×C₄	C₂²×C₁₁	1	1	yes	characteristic
115	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
116	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
117	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
118	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
119	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
120	C₂×C₄⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
121	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
122	C₂×C₂²⋊C₄	C₂²×C₁₁	1	2	yes	—
123	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
124	C₂×C₂²⋊C₄	C₂²×C₁₁	1	1	yes	characteristic
125	C₂×C₄²	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	1	yes	characteristic
130	#95	C₂²×C₁₁	1	2	yes	—
131	#95	C₂²×C₁₁	1	2	yes	—
132	#95	C₂²×C₁₁	1	2	yes	—
133	#95	C₂²×C₁₁	1	1	yes	characteristic
134	C₂×C₁₁	—	4	2	no	—
135	C₂×C₁₁	#542	1	2	yes	—
136	C₂×C₁₁	#544	1	1	yes	characteristic
137	C₂×C₁₁	#551	1	1	yes	characteristic
138	C₂×C₁₁	#554	1	2	yes	—
139	C₂×C₁₁	#560	1	1	yes	characteristic
140	C₂⁴	C₂³×C₁₁	1	1	yes	characteristic
141	C₂×Q₈	—	4	2	no	—
142	C₂×Q₈	—	4	1	no	—
143	C₂²×C₄	—	2	4	no	—
144	C₂²×C₄	—	4	1	no	—
145	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
146	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
147	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
148	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
149	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
150	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
151	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
152	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	2	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	1	no	—
159	C₂²⋊C₄	—	4	2	no	—
160	C₂²⋊C₄	—	4	2	no	—
161	C₂²⋊C₄	—	4	1	no	—
162	C₂²⋊C₄	Q₈×C₁₁	1	4	yes	complemented
163	C₄²	—	4	2	no	—
164	C₁₁	#2742	1	1	yes	characteristic, direct product factor, Sylow
165	C₂³	—	2	2	no	—
166	C₂³	—	2	2	no	—
167	C₂³	—	2	1	no	—
168	C₂³	—	2	1	no	—
169	C₂³	C₂×Q₈×C₁₁	1	2	yes	—
170	C₂³	C₂⁴×C₁₁	1	1	yes	characteristic
171	Q₈	—	4	4	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	1	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	2	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	2	no	—
189	C₂×C₄	—	2	2	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	4	4	no	—
193	C₂×C₄	C₂×Q₈×C₁₁	1	4	yes	—
194	C₂×C₄	C₁₁×#41	1	4	yes	—
195	C₂²	—	2	2	no	—
196	C₂²	—	2	4	no	—
197	C₂²	—	4	2	no	—
198	C₂²	—	4	1	no	—
199	C₂²	—	4	1	no	—
200	C₂²	C₂²×Q₈×C₁₁	1	1	yes	characteristic
201	C₂²	C₂×C₁₁×#41	1	2	yes	—
202	C₂²	C₁₁×H(5,𝔽₂)	1	2	yes	—
203	C₂²	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂²	C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
205	C₄	—	2	4	no	—
206	C₄	—	2	4	no	—
207	C₄	—	4	2	no	—
208	C₄	—	4	2	no	—
209	C₄	—	4	1	no	—
210	C₄	—	4	2	no	—
211	C₄	—	4	1	no	—
212	C₄	—	4	2	no	—
213	C₂	—	4	2	no	—
214	C₂	C₁₁×#542	1	2	yes	—
215	C₂	C₁₁×#544	1	1	yes	characteristic
216	C₂	C₁₁×#551	1	1	yes	characteristic
217	C₂	C₁₁×#554	1	2	yes	—
218	C₂	C₁₁×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂⁴×C₁₁	C₂³
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
1. C₁₁×#400	C₂	semidirect
3. C₁₁×#395	C₂	semidirect
5. C₁₁×#389	C₂	semidirect
7. C₁₁×#387	C₂	semidirect
53. C₁₁×C₂²⋊C₄	Q₈	semidirect
55. #2742	C₁₁	direct (N × H)
86. #400	C₂×C₁₁	semidirect
88. #395	C₂×C₁₁	semidirect
90. #389	C₂×C₁₁	semidirect
92. #387	C₂×C₁₁	semidirect
162. C₂²⋊C₄	Q₈×C₁₁	semidirect
164. C₁₁	#2742	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×#399	2
C₁₁×#395	2
C₁₁×#393	2
C₁₁×#389	2
C₁₁×#388	2
C₁₁×#387	2
C₁₁×#385	2
C₁₁×#380	2
#2742	11

Subgroups — C11×#2742 #13065580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#2742 #13065580