Subgroups — #14646812

Order 2816.

336 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13067375	C₂	1	1	yes	maximal, characteristic
2	#13067372	C₂	1	1	yes	maximal, characteristic
3	#13067354	C₂	1	2	yes	maximal
4	C₁₁⋊#1309	C₂	1	2	yes	maximal
5	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#533	C₂²	1	1	yes	characteristic
7	C₁₁×#446	—	2	1	no	—
8	C₁₁×#446	—	2	1	no	—
9	C₈×Q₈×C₁₁	—	2	1	no	—
10	C₈×Q₈×C₁₁	—	2	1	no	—
11	C₁₁×#424	C₄	1	2	yes	—
12	C₁₁×#423	C₂²	1	1	yes	characteristic
13	C₁₁×#405	C₄	1	2	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	#10622537	C₂²	1	2	yes	—
16	#10622537	C₂²	1	2	yes	—
17	#10622185	—	2	2	no	—
18	#10622185	—	2	2	no	—
19	#10622096	—	2	1	no	—
20	#10622096	—	2	1	no	—
21	#10622095	—	2	1	no	—
22	#10622095	—	2	1	no	—
23	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	D₄	1	1	yes	characteristic
28	C₁₁×#125	Q₈	1	2	yes	—
29	C₁₁×C₂²⋊Q₈	—	2	1	no	—
30	C₁₁×C₂²⋊Q₈	—	2	1	no	—
31	C₄×Q₈×C₁₁	—	2	1	no	—
32	C₄×Q₈×C₁₁	—	2	1	no	—
33	C₁₁×#117	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
35	C₂×#4318	—	2	2	no	—
36	C₂×#4318	—	2	2	no	—
37	C₁₁×C₄⋊C₈	—	2	2	no	—
38	C₁₁×C₄⋊C₈	—	2	2	no	—
39	C₁₁×C₄⋊C₈	—	2	1	no	—
40	C₁₁×C₄⋊C₈	—	2	1	no	—
41	C₁₁×#97	—	2	2	no	—
42	C₄×C₈×C₁₁	—	2	2	no	—
43	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
47	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
51	#8641	—	11	1	no	maximal, Sylow
52	C₂×Q₈×C₁₁	—	2	1	no	—
53	C₂×Q₈×C₁₁	—	2	1	no	—
54	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
57	C₁₁×M₁₆	—	4	2	no	—
58	C₂×C₈×C₁₁	—	2	2	no	—
59	C₂×C₈×C₁₁	—	2	2	no	—
60	C₂×C₈×C₁₁	—	4	1	no	—
61	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
62	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
63	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
65	C₁₁×C₄⋊C₄	—	2	1	no	—
66	C₁₁×C₄⋊C₄	—	2	1	no	—
67	C₁₁×C₄⋊C₄	—	2	2	no	—
68	C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
70	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
71	C₁₁×C₂²⋊C₄	—	2	2	no	—
72	C₄²×C₁₁	—	2	2	no	—
73	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
77	#4318	—	8	2	no	—
78	#4318	—	8	2	no	—
79	C₂×C₁₁⋊C₈	—	4	2	no	—
80	C₂×C₁₁⋊C₈	—	4	2	no	—
81	#2960	D₁₁	1	1	yes	characteristic
82	#1567	—	11	1	no	—
83	#1566	—	11	1	no	—
84	#1561	—	11	2	no	—
85	#1309	—	11	2	no	—
86	C₂³×C₁₁	#117	1	1	yes	characteristic
87	Q₈×C₁₁	—	4	2	no	—
88	Q₈×C₁₁	—	4	1	no	—
89	Q₈×C₁₁	—	4	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	—	2	2	no	—
93	C₂×C₄×C₁₁	—	2	1	no	—
94	C₂×C₄×C₁₁	—	2	1	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
100	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
103	C₈×C₁₁	—	2	1	no	—
104	C₈×C₁₁	—	2	1	no	—
105	C₈×C₁₁	—	2	1	no	—
106	C₈×C₁₁	—	4	2	no	—
107	C₈×C₁₁	#101	1	2	yes	—
108	C₁₁⋊C₈	—	8	2	no	—
109	C₁₁⋊C₈	—	8	2	no	—
110	#533	C₂×D₁₁	1	1	yes	characteristic
111	#446	—	2	1	no	—
112	#446	—	2	1	no	—
113	C₈×Q₈	—	2	1	no	—
114	C₈×Q₈	—	2	1	no	—
115	#424	Dic₁₁	1	2	yes	—
116	#423	—	11	2	no	—
117	#423	—	11	2	no	—
118	#423	C₂×D₁₁	1	1	yes	characteristic
119	#405	Dic₁₁	1	2	yes	—
120	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
121	#335	—	22	1	no	—
122	#335	—	22	1	no	—
123	#334	—	22	1	no	—
124	#334	—	22	1	no	—
125	#332	—	22	2	no	—
126	#332	—	22	2	no	—
127	C₂²×C₁₁	—	2	1	no	—
128	C₂²×C₁₁	—	2	1	no	—
129	C₂²×C₁₁	—	2	1	no	—
130	C₂²×C₁₁	#380	1	1	yes	characteristic
131	C₄×C₁₁	—	2	1	no	—
132	C₄×C₁₁	—	2	1	no	—
133	C₄×C₁₁	—	2	1	no	—
134	C₄×C₁₁	—	4	2	no	—
135	C₄×C₁₁	—	4	2	no	—
136	C₄×C₁₁	C₂×#101	1	1	yes	characteristic
137	C₄×C₁₁	#413	1	1	yes	characteristic
138	C₄×C₁₁	#471	1	2	yes	—
139	C₄×C₁₁	#472	1	1	yes	characteristic
140	C₄×C₁₁	#473	1	1	yes	characteristic
141	C₂×M₁₆	—	22	2	no	—
142	C₂×M₁₆	—	22	2	no	—
143	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
144	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
145	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
146	C₄⋊Q₈	D₄₄	1	1	yes	characteristic
147	C₄⋊Q₈	D₄₄	1	1	yes	characteristic
148	#125	Dic₂₂	1	2	yes	—
149	C₂²⋊Q₈	—	2	1	no	—
150	C₂²⋊Q₈	—	2	1	no	—
151	C₄×Q₈	—	2	1	no	—
152	C₄×Q₈	—	2	1	no	—
153	#117	C₂×Dic₁₁	1	2	yes	—
154	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
155	C₄⋊C₈	—	2	2	no	—
156	C₄⋊C₈	—	2	2	no	—
157	C₄⋊C₈	—	2	1	no	—
158	C₄⋊C₈	—	2	1	no	—
159	C₄⋊C₈	—	22	2	no	—
160	C₄⋊C₈	—	22	2	no	—
161	C₄⋊C₈	—	22	2	no	—
162	C₄⋊C₈	—	22	2	no	—
163	#97	—	2	2	no	—
164	C₄×C₈	—	2	2	no	—
165	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
166	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
167	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
168	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
169	C₂×C₁₁	—	4	1	no	—
170	C₂×C₁₁	#1801	1	1	yes	characteristic
171	C₂×C₁₁	#1815	1	1	yes	characteristic
172	C₂×C₁₁	#1816	1	1	yes	characteristic
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	2	1	no	—
175	C₂²×C₄	#4339	1	1	yes	characteristic
176	C₂²×C₄	#4339	1	1	yes	characteristic
177	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
178	M₁₆	—	4	2	no	—
179	M₁₆	—	88	2	no	—
180	M₁₆	—	88	2	no	—
181	C₂×C₈	—	2	2	no	—
182	C₂×C₈	—	2	2	no	—
183	C₂×C₈	—	4	1	no	—
184	C₂×C₈	—	44	2	no	—
185	C₂×C₈	—	44	2	no	—
186	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
187	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
188	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
189	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
190	C₄⋊C₄	—	2	2	no	—
191	C₄⋊C₄	—	2	2	no	—
192	C₄⋊C₄	—	2	1	no	—
193	C₄⋊C₄	—	2	1	no	—
194	C₄⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
195	C₄⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
196	C₂²⋊C₄	—	2	2	no	—
197	C₄²	—	2	2	no	—
198	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
199	C₄²	C₂×D₄₄	1	1	yes	characteristic
200	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
201	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
202	C₁₁	#8641	1	1	yes	characteristic, complemented, Sylow
203	C₂³	#66979	1	1	yes	characteristic
204	Q₈	—	4	2	no	—
205	Q₈	—	4	1	no	—
206	Q₈	—	4	1	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	#66977	1	1	yes	characteristic
215	C₂×C₄	#66977	1	1	yes	characteristic
216	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
217	C₂×C₄	#66983	1	1	yes	characteristic
218	C₂×C₄	#66983	1	1	yes	characteristic
219	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
220	C₈	—	2	1	no	—
221	C₈	—	2	1	no	—
222	C₈	—	2	1	no	—
223	C₈	—	4	2	no	—
224	C₈	—	88	2	no	—
225	C₈	—	88	2	no	—
226	C₈	#66900	1	2	yes	—
227	C₂²	—	2	1	no	—
228	C₂²	—	2	1	no	—
229	C₂²	—	2	1	no	—
230	C₂²	#10622825	1	1	yes	characteristic
231	C₄	—	2	1	no	—
232	C₄	—	2	1	no	—
233	C₄	—	2	1	no	—
234	C₄	—	4	2	no	—
235	C₄	—	4	2	no	—
236	C₄	#10622754	1	2	yes	—
237	C₄	#10622755	1	1	yes	characteristic
238	C₄	#10622756	1	1	yes	characteristic
239	C₄	C₂×#66900	1	1	yes	characteristic
240	C₄	#10622850	1	1	yes	characteristic
241	C₂	—	4	1	no	—
242	C₂	#13068612	1	1	yes	characteristic
243	C₂	#13068675	1	1	yes	characteristic
244	C₂	#13068680	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622825
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2960	C₂
socle	C₂²×C₁₁	#380
prime radical	C₂³×C₁₁	#117
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2960	D₁₁
hypocenter	C₁₁	#8641
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2960

Complements

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

N	H ≅ G/N	type
202. C₁₁	#8641	semidirect

Maximal subgroups

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

subgroup	index
#13067375	2
#13067372	2
#13067354	2
C₁₁⋊#1309	2
C₁₁×#2960	2
#8641	11