Subgroups — C₁₁×#33730 #14610923

Order 2816.

474 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3164	C₂	1	2	yes	maximal
2	C₁₁×#2255	C₂	1	4	yes	maximal, complemented
3	C₁₁×#2254	C₂	1	2	yes	maximal, complemented
4	C₁₁×#2253	C₂	1	2	yes	maximal, complemented
5	C₁₁×#2159	C₂	1	2	yes	maximal
6	C₁₁×#2158	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×#367	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic
9	C₁₁×#544	—	2	2	no	—
10	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	C₁₁×#501	—	2	4	no	—
13	C₁₁×#500	C₂²	1	4	yes	—
14	C₁₁×#499	C₂²	1	4	yes	—
15	C₁₁×#428	—	2	2	no	—
16	C₁₁×#427	C₂²	1	2	yes	—
17	C₂×C₁₁×#107	C₂²	1	2	yes	—
18	C₁₁×#405	C₂²	1	1	yes	characteristic
19	C₁₁×#367	C₂²	1	2	yes	—
20	C₁₁×#367	C₂²	1	2	yes	—
21	C₁₁×#367	C₂²	1	1	yes	characteristic
22	C₁₁×#367	C₂²	1	1	yes	characteristic
23	C₁₁×#367	C₂²	1	4	yes	—
24	C₁₁×#366	C₂²	1	2	yes	—
25	C₁₁×#366	C₂²	1	4	yes	—
26	C₁₁×#346	C₂²	1	2	yes	—
27	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
28	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
30	C₁₁×C₄⋊Q₈	—	2	4	no	—
31	C₁₁×C₄⋊Q₈	—	4	2	no	—
32	C₁₁×#125	—	2	4	no	—
33	C₁₁×#125	—	4	2	no	—
34	C₁₁×C₂²⋊Q₈	—	4	4	no	—
35	C₁₁×#117	—	2	2	no	—
36	C₁₁×#117	D₄	1	1	yes	characteristic
37	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
38	C₁₁×M₃₂	Q₈	1	4	yes	complemented
39	C₂×C₁₁×C₁₆	Q₈	1	4	yes	complemented
40	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
41	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
42	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
43	C₁₁×#107	—	2	4	no	—
44	C₁₁×#107	—	2	2	no	—
45	C₁₁×#107	C₂³	1	2	yes	—
46	C₁₁×#107	C₂³	1	4	yes	—
47	C₁₁×#107	C₂³	1	2	yes	—
48	C₁₁×#106	—	2	4	no	—
49	C₁₁×#106	—	2	2	no	—
50	C₁₁×#97	D₄	1	2	yes	—
51	C₄×C₈×C₁₁	C₂³	1	2	yes	—
52	#33730	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×Q₈×C₁₁	—	4	4	no	—
54	C₂²×C₄×C₁₁	—	4	2	no	—
55	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₁₁×M₁₆	Q₁₆	1	4	yes	—
57	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
59	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
60	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
61	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	—	2	2	no	—
63	C₁₁×C₄⋊C₄	—	2	4	no	—
64	C₁₁×C₄⋊C₄	—	2	2	no	—
65	C₁₁×C₄⋊C₄	—	4	2	no	—
66	C₁₁×C₄⋊C₄	—	4	4	no	—
67	C₁₁×C₄⋊C₄	—	4	4	no	—
68	C₁₁×C₄⋊C₄	—	4	4	no	—
69	C₁₁×C₄⋊C₄	D₈	1	2	yes	—
70	C₁₁×C₂²⋊C₄	—	4	2	no	—
71	C₁₁×C₂²⋊C₄	D₈	1	2	yes	—
72	C₄²×C₁₁	—	4	2	no	—
73	C₄²×C₁₁	C₂×D₄	1	2	yes	—
74	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
75	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
76	C₁₁×C₁₆	C₂×Q₈	1	4	yes	—
77	#3164	C₂×C₁₁	1	2	yes	—
78	#2255	C₂×C₁₁	1	4	yes	complemented
79	#2254	C₂×C₁₁	1	2	yes	complemented
80	#2253	C₂×C₁₁	1	2	yes	complemented
81	#2159	C₂×C₁₁	1	2	yes	—
82	#2158	C₂×C₁₁	1	1	yes	characteristic
83	C₂×#367	C₂×C₁₁	1	1	yes	characteristic
84	#2108	C₂×C₁₁	1	1	yes	characteristic
85	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
86	Q₈×C₁₁	—	16	4	no	—
87	C₂×C₄×C₁₁	—	4	2	no	—
88	C₂×C₄×C₁₁	—	4	2	no	—
89	C₂×C₄×C₁₁	—	4	4	no	—
90	C₂×C₄×C₁₁	—	16	2	no	—
91	C₂×C₄×C₁₁	C₄⋊Q₈	1	2	yes	—
92	C₂×C₄×C₁₁	C₂×D₈	1	4	yes	—
93	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
94	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
95	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
96	C₈×C₁₁	C₄⋊Q₈	1	2	yes	—
97	C₈×C₁₁	C₂×Q₁₆	1	4	yes	—
98	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
99	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
100	#544	—	2	2	no	—
101	C₂×M₃₂	C₂²×C₁₁	1	1	yes	characteristic
102	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
103	#501	—	2	4	no	—
104	#500	C₂²×C₁₁	1	4	yes	—
105	#499	C₂²×C₁₁	1	4	yes	—
106	#428	—	2	2	no	—
107	#427	C₂²×C₁₁	1	2	yes	—
108	C₂×#107	C₂²×C₁₁	1	2	yes	—
109	#405	C₂²×C₁₁	1	1	yes	characteristic
110	#367	C₂²×C₁₁	1	2	yes	—
111	#367	C₂²×C₁₁	1	2	yes	—
112	#367	C₂²×C₁₁	1	1	yes	characteristic
113	#367	C₂²×C₁₁	1	1	yes	characteristic
114	#367	C₂²×C₁₁	1	4	yes	—
115	#366	C₂²×C₁₁	1	2	yes	—
116	#366	C₂²×C₁₁	1	4	yes	—
117	#346	C₂²×C₁₁	1	2	yes	—
118	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
119	C₂²×C₁₁	—	2	2	no	—
120	C₂²×C₁₁	#500	1	2	yes	—
121	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
122	C₄×C₁₁	—	2	4	no	—
123	C₄×C₁₁	—	8	2	no	—
124	C₄×C₁₁	—	8	4	no	—
125	C₄×C₁₁	—	8	2	no	—
126	C₄×C₁₁	#500	1	2	yes	—
127	C₄×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
128	C₄×C₁₁	C₂²×Q₁₆	1	1	yes	characteristic
129	C₂×M₁₆	D₄×C₁₁	1	1	yes	characteristic
130	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
131	C₄⋊Q₈	—	2	4	no	—
132	C₄⋊Q₈	—	4	2	no	—
133	#125	—	2	4	no	—
134	#125	—	4	2	no	—
135	C₂²⋊Q₈	—	4	4	no	—
136	#117	—	2	2	no	—
137	#117	D₄×C₁₁	1	1	yes	characteristic
138	C₂×C₄⋊C₄	—	2	2	no	—
139	M₃₂	Q₈×C₁₁	1	4	yes	complemented
140	C₂×C₁₆	Q₈×C₁₁	1	4	yes	complemented
141	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
142	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
143	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
144	#107	—	2	2	no	—
145	#107	—	2	4	no	—
146	#107	C₂³×C₁₁	1	2	yes	—
147	#107	C₂³×C₁₁	1	4	yes	—
148	#107	C₂³×C₁₁	1	2	yes	—
149	#106	—	2	2	no	—
150	#106	—	2	4	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	C₂×#500	1	1	yes	characteristic
155	C₂×C₁₁	#3416	1	2	yes	—
156	C₂×Q₈	—	4	4	no	—
157	C₂²×C₄	—	4	2	no	—
158	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
159	M₁₆	C₁₁×Q₁₆	1	4	yes	—
160	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
161	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
162	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
163	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
164	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
165	C₄⋊C₄	—	2	2	no	—
166	C₄⋊C₄	—	2	4	no	—
167	C₄⋊C₄	—	2	2	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	4	4	no	—
170	C₄⋊C₄	—	4	4	no	—
171	C₄⋊C₄	—	4	4	no	—
172	C₄⋊C₄	C₁₁×D₈	1	2	yes	—
173	C₂²⋊C₄	—	4	2	no	—
174	C₂²⋊C₄	C₁₁×D₈	1	2	yes	—
175	C₄²	—	4	2	no	—
176	C₄²	C₂×D₄×C₁₁	1	2	yes	—
177	C₁₆	C₂×Q₈×C₁₁	1	2	yes	—
178	C₁₆	C₂×Q₈×C₁₁	1	2	yes	—
179	C₁₆	C₂×Q₈×C₁₁	1	4	yes	—
180	C₁₁	#33730	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
182	Q₈	—	16	4	no	—
183	C₂×C₄	—	4	2	no	—
184	C₂×C₄	—	4	2	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	16	2	no	—
187	C₂×C₄	C₁₁×C₄⋊Q₈	1	2	yes	—
188	C₂×C₄	C₂×C₁₁×D₈	1	4	yes	—
189	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
190	C₂×C₄	C₂×C₁₁×Q₁₆	1	2	yes	—
191	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
192	C₈	C₁₁×C₄⋊Q₈	1	2	yes	—
193	C₈	C₂×C₁₁×Q₁₆	1	4	yes	—
194	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
195	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
196	C₂²	—	2	2	no	—
197	C₂²	C₁₁×#500	1	2	yes	—
198	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
199	C₄	—	2	4	no	—
200	C₄	—	8	4	no	—
201	C₄	—	8	2	no	—
202	C₄	—	8	2	no	—
203	C₄	C₁₁×#500	1	2	yes	—
204	C₄	C₂×C₁₁×C₄⋊Q₈	1	1	yes	characteristic
205	C₄	C₂²×C₁₁×Q₁₆	1	1	yes	characteristic
206	C₂	—	2	2	no	—
207	C₂	C₂×C₁₁×#500	1	1	yes	characteristic
208	C₂	C₁₁×#3416	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	C₂×D₈
LCS	G ▷ C₂×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×#2255	C₂	semidirect
3. C₁₁×#2254	C₂	semidirect
4. C₁₁×#2253	C₂	semidirect
38. C₁₁×M₃₂	Q₈	semidirect
39. C₂×C₁₁×C₁₆	Q₈	semidirect
52. #33730	C₁₁	direct (N × H)
78. #2255	C₂×C₁₁	semidirect
79. #2254	C₂×C₁₁	semidirect
80. #2253	C₂×C₁₁	semidirect
139. M₃₂	Q₈×C₁₁	semidirect
140. C₂×C₁₆	Q₈×C₁₁	semidirect
180. C₁₁	#33730	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×#3164	2
C₁₁×#2255	2
C₁₁×#2254	2
C₁₁×#2253	2
C₁₁×#2159	2
C₁₁×#2158	2
C₂×C₁₁×#367	2
C₁₁×#2108	2
#33730	11

Subgroups — C11×#33730 #14610923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33730 #14610923