Subgroups — #14724520

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077551	C₂	1	2	yes	maximal
2	#13067488	C₂	1	8	yes	maximal, complemented
3	#13067372	C₂	1	1	yes	maximal, characteristic
4	#13067071	C₂	1	2	yes	maximal
5	C₂×#10622092	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#533	C₂²	1	2	yes	—
8	C₁₁×#500	C₄	1	1	yes	characteristic
9	C₁₁×#494	C₄	1	1	yes	characteristic
10	C₁₁×#487	C₄	1	2	yes	—
11	C₁₁×#467	C₄	1	4	yes	—
12	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	#10622637	—	2	2	no	—
15	#10622637	C₂²	1	4	yes	—
16	Q₈×C₁₁⋊C₈	—	2	2	no	—
17	Q₈×C₁₁⋊C₈	C₂²	1	4	yes	—
18	#10622612	—	2	2	no	—
19	#10622610	—	2	2	no	—
20	#10622537	C₂²	1	2	yes	—
21	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	Q₈⋊(C₁₁⋊C₈)	C₂²	1	8	yes	—
24	#10622095	C₂²	1	4	yes	—
25	#10622092	C₂²	1	4	yes	—
26	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
28	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
29	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
30	C₁₁×#125	—	2	2	no	—
31	C₁₁×C₂²⋊Q₈	—	2	2	no	—
32	C₁₁×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
33	C₄×Q₈×C₁₁	—	2	2	no	—
34	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
35	C₁₁×#117	—	2	2	no	—
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₂×#4318	—	2	2	no	—
38	C₂²×C₁₁⋊C₈	—	2	1	no	—
39	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
40	C₁₁×#107	C₂×C₄	1	4	yes	—
41	C₁₁×#103	C₂×C₄	1	8	yes	—
42	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	C₂³	1	2	yes	—
45	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
46	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
47	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
48	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
49	#66867	—	2	4	no	—
50	C₄×C₁₁⋊C₈	—	2	1	no	—
51	C₄×C₁₁⋊C₈	—	2	4	no	—
52	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
53	C₄×C₁₁⋊C₈	D₄	1	1	yes	characteristic
54	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
55	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
56	#17980	—	11	1	no	maximal, Sylow
57	C₂×Q₈×C₁₁	—	2	2	no	—
58	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
62	C₁₁×Q₁₆	—	4	4	no	—
63	C₂×C₈×C₁₁	—	4	2	no	—
64	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
66	C₁₁×C₄⋊C₄	—	2	2	no	—
67	C₁₁×C₄⋊C₄	—	2	2	no	—
68	C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₁₁×C₄⋊C₄	—	2	4	no	—
70	C₁₁×C₄⋊C₄	—	2	4	no	—
71	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
72	C₁₁×C₂²⋊C₄	—	2	4	no	—
73	C₄²×C₁₁	—	2	4	no	—
74	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₄²×C₁₁	#41	1	1	yes	characteristic
77	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
78	#4318	—	4	4	no	—
79	C₂×C₁₁⋊C₈	—	2	4	no	—
80	C₂×C₁₁⋊C₈	—	2	4	no	—
81	C₂×C₁₁⋊C₈	—	2	4	no	—
82	C₂×C₁₁⋊C₈	—	2	2	no	—
83	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
84	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
85	#3170	D₁₁	1	1	yes	characteristic
86	#2960	—	11	2	no	—
87	#1587	—	11	8	no	—
88	#1566	—	11	1	no	—
89	#1493	—	11	2	no	—
90	C₂×#322	—	11	1	no	—
91	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
92	Q₈×C₁₁	—	2	8	no	—
93	Q₈×C₁₁	—	4	4	no	—
94	C₂×C₄×C₁₁	—	2	2	no	—
95	C₂×C₄×C₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	—	2	4	no	—
98	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
101	C₂×C₄×C₁₁	#137	1	4	yes	—
102	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
105	C₈×C₁₁	—	2	2	no	—
106	C₈×C₁₁	—	2	2	no	—
107	C₁₁⋊C₈	—	2	4	no	—
108	C₁₁⋊C₈	—	2	2	no	—
109	C₁₁⋊C₈	—	2	2	no	—
110	C₁₁⋊C₈	—	4	4	no	—
111	#533	C₂×D₁₁	1	2	yes	—
112	#500	Dic₁₁	1	1	yes	characteristic
113	#494	Dic₁₁	1	1	yes	characteristic
114	#487	Dic₁₁	1	2	yes	—
115	#467	Dic₁₁	1	4	yes	—
116	#446	—	11	4	no	—
117	#446	—	22	2	no	—
118	C₈×Q₈	—	11	4	no	—
119	C₈×Q₈	—	22	2	no	—
120	C₄×Q₁₆	C₂×D₁₁	1	4	yes	—
121	#424	—	22	2	no	—
122	#423	—	11	2	no	—
123	#405	—	22	2	no	—
124	C₂×C₄×C₈	—	11	1	no	—
125	C₂×C₄×C₈	—	11	1	no	—
126	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
127	#334	—	11	4	no	—
128	Q₈⋊C₈	—	11	8	no	—
129	#322	—	11	4	no	—
130	C₂²×C₁₁	—	2	1	no	—
131	C₂²×C₁₁	—	2	1	no	—
132	C₂²×C₁₁	#441	1	2	yes	—
133	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
134	C₄×C₁₁	—	2	1	no	—
135	C₄×C₁₁	—	2	1	no	—
136	C₄×C₁₁	—	4	4	no	—
137	C₄×C₁₁	—	4	4	no	—
138	C₄×C₁₁	#441	1	2	yes	—
139	C₄×C₁₁	#443	1	2	yes	—
140	C₄×C₁₁	#568	1	2	yes	—
141	C₄×C₁₁	C₂×#137	1	2	yes	—
142	C₂×Q₁₆	C₂×Dic₁₁	1	4	yes	—
143	C₂×M₁₆	—	22	2	no	—
144	C₂²×C₈	—	11	2	no	—
145	C₂²×C₈	—	22	1	no	—
146	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
147	C₄⋊Q₈	C₂×Dic₁₁	1	2	yes	—
148	C₄⋊Q₈	C₂×Dic₁₁	1	2	yes	—
149	#125	—	2	2	no	—
150	C₂²⋊Q₈	—	2	2	no	—
151	C₂²⋊Q₈	C₂×Dic₁₁	1	4	yes	—
152	C₄×Q₈	—	2	2	no	—
153	C₄×Q₈	C₂²×D₁₁	1	4	yes	—
154	#117	—	2	2	no	—
155	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
156	#107	C₂×Dic₁₁	1	4	yes	—
157	C₄⋊C₈	—	11	4	no	—
158	C₄⋊C₈	—	22	4	no	—
159	C₄⋊C₈	—	22	4	no	—
160	C₄⋊C₈	—	22	2	no	—
161	#103	C₂×Dic₁₁	1	8	yes	—
162	#97	—	22	4	no	—
163	C₄×C₈	—	11	1	no	—
164	C₄×C₈	—	11	1	no	—
165	C₄×C₈	—	11	2	no	—
166	C₄×C₈	—	11	2	no	—
167	C₄×C₈	—	22	4	no	—
168	C₄×C₈	—	22	1	no	—
169	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
170	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
171	C₄×C₈	C₂²×D₁₁	1	2	yes	—
172	C₂×C₁₁	—	2	2	no	—
173	C₂×C₁₁	#2932	1	1	yes	characteristic
174	C₂×C₁₁	C₂×#441	1	1	yes	characteristic
175	C₂×C₁₁	C₂×#443	1	1	yes	characteristic
176	C₂×Q₈	—	2	2	no	—
177	C₂×Q₈	C₂²×Dic₁₁	1	4	yes	—
178	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
179	C₂²×C₄	#4341	1	1	yes	characteristic
180	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
181	Q₁₆	—	4	4	no	—
182	M₁₆	—	44	4	no	—
183	C₂×C₈	—	4	2	no	—
184	C₂×C₈	—	11	2	no	—
185	C₂×C₈	—	11	2	no	—
186	C₂×C₈	—	22	4	no	—
187	C₂×C₈	—	22	4	no	—
188	C₂×C₈	—	22	2	no	—
189	C₂×C₈	—	22	4	no	—
190	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
191	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
192	C₄⋊C₄	—	2	2	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	2	no	—
195	C₄⋊C₄	—	2	4	no	—
196	C₄⋊C₄	—	2	4	no	—
197	C₄⋊C₄	C₂²×Dic₁₁	1	4	yes	—
198	C₂²⋊C₄	—	2	4	no	—
199	C₄²	—	2	4	no	—
200	C₄²	D₄×D₁₁	1	1	yes	characteristic
201	C₄²	#4341	1	1	yes	characteristic
202	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
203	C₄²	C₂³×D₁₁	1	1	yes	characteristic
204	C₁₁	#17980	1	1	yes	characteristic, complemented, Sylow
205	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
206	Q₈	—	2	8	no	—
207	Q₈	—	4	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	4	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	#66971	1	4	yes	—
213	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
214	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
215	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
216	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
217	C₂×C₄	C₂×#4341	1	1	yes	characteristic
218	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
219	C₈	—	2	2	no	—
220	C₈	—	2	2	no	—
221	C₈	—	22	4	no	—
222	C₈	—	22	2	no	—
223	C₈	—	22	2	no	—
224	C₈	—	44	4	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#10622797	1	2	yes	—
228	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	4	4	no	—
232	C₄	—	4	4	no	—
233	C₄	#10622797	1	2	yes	—
234	C₄	#10622809	1	2	yes	—
235	C₄	C₂×#66971	1	2	yes	—
236	C₄	#10623350	1	2	yes	—
237	C₂	—	2	2	no	—
238	C₂	#13077334	1	1	yes	characteristic
239	C₂	C₂×#10622797	1	1	yes	characteristic
240	C₂	C₂×#10622809	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₁
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₁₁×#3170	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂³×C₁₁	C₄×D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	#3170	D₁₁
hypocenter	C₁₁	#17980
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
2. #13067488	C₂	semidirect
204. C₁₁	#17980	semidirect

Maximal subgroups

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

subgroup	index
#13077551	2
#13067488	2
#13067372	2
#13067071	2
C₂×#10622092	2
C₁₁×#3170	2
#17980	11