Subgroups — C₁₁×#33705 #14610898

Order 2816.

578 conjugacy classes of subgroups.

The subgroup lattice has 234 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2245	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2241	C₂	1	4	yes	maximal, complemented
5	C₁₁×#2141	C₂	1	4	yes	maximal
6	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×Q₁₆	—	2	1	no	—
8	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	—
9	C₁₁×#533	—	2	1	no	—
10	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
12	C₁₁×#500	C₂²	1	2	yes	—
13	C₁₁×#499	—	2	1	no	—
14	C₁₁×#499	C₂²	1	2	yes	—
15	C₁₁×#498	—	2	1	no	—
16	C₁₁×#494	—	2	1	no	—
17	C₁₁×#494	—	2	1	no	—
18	C₁₁×#494	C₂²	1	2	yes	—
19	C₁₁×#494	C₂²	1	2	yes	—
20	C₁₁×#427	—	2	1	no	—
21	C₁₁×#427	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#358	C₂²	1	16	yes	—
24	C₁₁×#346	C₂²	1	2	yes	—
25	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
26	C₂²×Q₈×C₁₁	—	2	2	no	—
27	C₂×C₁₁×Q₁₆	—	2	2	no	—
28	C₂×C₁₁×Q₁₆	—	2	2	no	—
29	C₂×C₁₁×Q₁₆	—	2	2	no	—
30	C₂×C₁₁×Q₁₆	—	2	8	no	—
31	C₂×C₁₁×Q₁₆	—	4	4	no	—
32	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
33	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
35	C₁₁×C₄⋊Q₈	—	2	2	no	—
36	C₁₁×C₄⋊Q₈	—	2	2	no	—
37	C₁₁×C₄⋊Q₈	—	2	2	no	—
38	C₁₁×C₄⋊Q₈	—	4	2	no	—
39	C₁₁×#125	—	2	2	no	—
40	C₁₁×C₂²⋊Q₈	—	4	2	no	—
41	C₄×Q₈×C₁₁	—	4	2	no	—
42	C₁₁×#117	—	2	2	no	—
43	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
44	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
45	C₁₁×M₃₂	—	2	4	no	—
46	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
47	C₁₁×#107	—	2	2	no	—
48	C₁₁×#107	C₂³	1	4	yes	—
49	C₁₁×#106	—	2	2	no	—
50	C₁₁×#106	—	2	2	no	—
51	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
52	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
53	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
54	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	#33705	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂×Q₈×C₁₁	—	2	4	no	—
57	C₂×Q₈×C₁₁	—	4	2	no	—
58	C₂×Q₈×C₁₁	—	4	2	no	—
59	C₂×Q₈×C₁₁	—	4	4	no	—
60	C₂×Q₈×C₁₁	—	4	4	no	—
61	C₂²×C₄×C₁₁	—	4	2	no	—
62	C₂²×C₄×C₁₁	D₈	1	2	yes	—
63	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₁₁×Q₁₆	—	2	8	no	—
65	C₁₁×Q₁₆	—	4	4	no	—
66	C₁₁×Q₁₆	—	4	4	no	—
67	C₁₁×Q₁₆	—	4	4	no	—
68	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
69	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₁	#41	1	4	yes	—
73	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
74	C₁₁×C₄⋊C₄	—	2	4	no	—
75	C₁₁×C₄⋊C₄	—	4	4	no	—
76	C₁₁×C₄⋊C₄	—	4	4	no	—
77	C₁₁×C₄⋊C₄	—	4	4	no	—
78	C₁₁×C₄⋊C₄	—	4	2	no	—
79	C₁₁×C₂²⋊C₄	—	4	2	no	—
80	C₄²×C₁₁	—	4	2	no	—
81	C₄²×C₁₁	D₈	1	2	yes	—
82	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
83	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
84	C₁₁×C₁₆	—	2	4	no	—
85	#3160	C₂×C₁₁	1	1	yes	characteristic
86	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
87	#2245	C₂×C₁₁	1	4	yes	complemented
88	#2241	C₂×C₁₁	1	4	yes	complemented
89	#2141	C₂×C₁₁	1	4	yes	—
90	C₄×M₃₂	C₂×C₁₁	1	1	yes	characteristic
91	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
92	Q₈×C₁₁	—	4	4	no	—
93	Q₈×C₁₁	—	4	4	no	—
94	Q₈×C₁₁	—	8	4	no	—
95	Q₈×C₁₁	—	8	4	no	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	—	4	4	no	—
98	C₂×C₄×C₁₁	—	4	4	no	—
99	C₂×C₄×C₁₁	—	8	4	no	—
100	C₂×C₄×C₁₁	#124	1	2	yes	—
101	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
102	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
105	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
106	C₈×C₁₁	#124	1	2	yes	—
107	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
108	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
109	C₈×C₁₁	C₂×#41	1	2	yes	—
110	C₂²×Q₁₆	—	2	1	no	—
111	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	—
112	#533	—	2	1	no	—
113	C₂×C₄⋊Q₈	—	2	1	no	—
114	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
115	#500	C₂²×C₁₁	1	2	yes	—
116	#499	—	2	1	no	—
117	#499	C₂²×C₁₁	1	2	yes	—
118	#498	—	2	1	no	—
119	#494	—	2	1	no	—
120	#494	—	2	1	no	—
121	#494	C₂²×C₁₁	1	2	yes	—
122	#494	C₂²×C₁₁	1	2	yes	—
123	#427	—	2	1	no	—
124	#427	C₂²×C₁₁	1	2	yes	—
125	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
126	#358	C₂²×C₁₁	1	16	yes	—
127	#346	C₂²×C₁₁	1	2	yes	—
128	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
129	C₂²×C₁₁	—	2	2	no	—
130	C₂²×C₁₁	#486	1	2	yes	—
131	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	8	4	no	—
134	C₄×C₁₁	—	8	4	no	—
135	C₄×C₁₁	#486	1	2	yes	—
136	C₄×C₁₁	#510	1	4	yes	—
137	C₄×C₁₁	C₂×#124	1	1	yes	characteristic
138	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
139	C₂²×Q₈	—	2	2	no	—
140	C₂×Q₁₆	—	2	2	no	—
141	C₂×Q₁₆	—	2	2	no	—
142	C₂×Q₁₆	—	2	2	no	—
143	C₂×Q₁₆	—	2	8	no	—
144	C₂×Q₁₆	—	4	4	no	—
145	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
146	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
147	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	2	2	no	—
151	C₄⋊Q₈	—	4	2	no	—
152	#125	—	2	2	no	—
153	C₂²⋊Q₈	—	4	2	no	—
154	C₄×Q₈	—	4	2	no	—
155	#117	—	2	2	no	—
156	C₂×C₄⋊C₄	—	4	2	no	—
157	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
158	M₃₂	—	2	4	no	—
159	C₂×C₁₆	C₂³×C₁₁	1	4	yes	—
160	#107	—	2	2	no	—
161	#107	C₂³×C₁₁	1	4	yes	—
162	#106	—	2	2	no	—
163	#106	—	2	2	no	—
164	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
165	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
166	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
167	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
168	C₂×C₁₁	—	2	2	no	—
169	C₂×C₁₁	C₂×#486	1	1	yes	characteristic
170	C₂×C₁₁	C₂×#510	1	2	yes	—
171	C₂×Q₈	—	2	4	no	—
172	C₂×Q₈	—	4	2	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂×Q₈	—	4	4	no	—
175	C₂×Q₈	—	4	4	no	—
176	C₂²×C₄	—	4	2	no	—
177	C₂²×C₄	C₁₁×D₈	1	2	yes	—
178	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
179	Q₁₆	—	2	8	no	—
180	Q₁₆	—	4	4	no	—
181	Q₁₆	—	4	4	no	—
182	Q₁₆	—	4	4	no	—
183	C₂×C₈	C₁₁×SD₁₆	1	4	yes	—
184	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
185	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
186	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
187	C₂×C₈	C₁₁×#41	1	4	yes	—
188	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
189	C₄⋊C₄	—	2	4	no	—
190	C₄⋊C₄	—	4	4	no	—
191	C₄⋊C₄	—	4	4	no	—
192	C₄⋊C₄	—	4	4	no	—
193	C₄⋊C₄	—	4	2	no	—
194	C₂²⋊C₄	—	4	2	no	—
195	C₄²	—	4	2	no	—
196	C₄²	C₁₁×D₈	1	2	yes	—
197	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
198	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
199	C₁₆	—	2	4	no	—
200	C₁₁	#33705	1	1	yes	characteristic, direct product factor, Sylow
201	C₂³	C₂×C₁₁×D₈	1	1	yes	characteristic
202	Q₈	—	4	4	no	—
203	Q₈	—	4	4	no	—
204	Q₈	—	8	4	no	—
205	Q₈	—	8	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	—	8	4	no	—
210	C₂×C₄	C₁₁×#124	1	2	yes	—
211	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
212	C₂×C₄	C₂×C₁₁×D₈	1	2	yes	—
213	C₂×C₄	C₂×C₁₁×D₈	1	1	yes	characteristic
214	C₂×C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
215	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
216	C₈	C₁₁×#124	1	2	yes	—
217	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
218	C₈	C₂×C₁₁×SD₁₆	1	2	yes	—
219	C₈	C₂×C₁₁×#41	1	2	yes	—
220	C₂²	—	2	2	no	—
221	C₂²	C₁₁×#486	1	2	yes	—
222	C₂²	C₂²×C₁₁×D₈	1	1	yes	characteristic
223	C₄	—	2	2	no	—
224	C₄	—	8	4	no	—
225	C₄	—	8	4	no	—
226	C₄	C₁₁×#486	1	2	yes	—
227	C₄	C₁₁×#510	1	4	yes	—
228	C₄	C₂×C₁₁×#124	1	1	yes	characteristic
229	C₄	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
230	C₂	—	2	2	no	—
231	C₂	C₂×C₁₁×#486	1	1	yes	characteristic
232	C₂	C₂×C₁₁×#510	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 ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2245	C₂	semidirect
4. C₁₁×#2241	C₂	semidirect
55. #33705	C₁₁	direct (N × H)
87. #2245	C₂×C₁₁	semidirect
88. #2241	C₂×C₁₁	semidirect
200. C₁₁	#33705	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×#3160	2
C₂×C₁₁×#494	2
C₁₁×#2245	2
C₁₁×#2241	2
C₁₁×#2141	2
C₄×C₁₁×M₃₂	2
#33705	11

Subgroups — C11×#33705 #14610898

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33705 #14610898