Subgroups — #14724332

Order 2816.

598 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	#13077551	C₂	1	2	yes	maximal
2	#13067525	C₂	1	4	yes	maximal, complemented
3	#13067435	C₂	1	4	yes	maximal, complemented
4	#13067372	C₂	1	1	yes	maximal, characteristic
5	#13067071	C₂	1	2	yes	maximal
6	C₂×#10622093	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#3170	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#533	C₂²	1	2	yes	—
9	C₁₁×#500	C₄	1	1	yes	characteristic
10	C₁₁×#494	C₄	1	1	yes	characteristic
11	C₁₁×#487	C₄	1	2	yes	—
12	C₁₁×#467	C₄	1	4	yes	—
13	C₄×C₁₁×Q₁₆	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	#10622637	—	2	2	no	—
16	#10622637	C₂²	1	4	yes	—
17	Q₈×C₁₁⋊C₈	—	2	2	no	—
18	Q₈×C₁₁⋊C₈	C₂²	1	4	yes	—
19	#10622612	—	2	2	no	—
20	#10622610	—	2	2	no	—
21	#10622537	C₂²	1	2	yes	—
22	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₁₁⋊C₈	C₂²	1	1	yes	characteristic
24	Q₈⋊(C₁₁⋊C₈)	C₂²	1	8	yes	—
25	#10622095	C₂²	1	4	yes	—
26	#10622093	C₂²	1	2	yes	—
27	#10622093	C₂²	1	2	yes	—
28	C₂×C₁₁×Q₁₆	C₂×C₄	1	4	yes	—
29	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
31	C₁₁×C₄⋊Q₈	C₂×C₄	1	2	yes	—
32	C₁₁×#125	—	2	2	no	—
33	C₁₁×C₂²⋊Q₈	—	2	2	no	—
34	C₁₁×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
35	C₄×Q₈×C₁₁	—	2	2	no	—
36	C₄×Q₈×C₁₁	C₂³	1	4	yes	—
37	C₁₁×#117	—	2	2	no	—
38	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
39	C₂×#4318	—	2	2	no	—
40	C₂²×C₁₁⋊C₈	—	2	1	no	—
41	C₂²×C₁₁⋊C₈	D₄	1	2	yes	—
42	C₁₁×#107	C₂×C₄	1	4	yes	—
43	C₁₁×#103	C₂×C₄	1	8	yes	—
44	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₁₁	C₂³	1	2	yes	—
47	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
48	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
50	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
51	#66867	—	2	4	no	—
52	C₄×C₁₁⋊C₈	—	2	1	no	—
53	C₄×C₁₁⋊C₈	—	2	4	no	—
54	C₄×C₁₁⋊C₈	D₄	1	2	yes	—
55	C₄×C₁₁⋊C₈	C₂³	1	2	yes	—
56	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
57	C₄×C₁₁⋊C₈	C₂³	1	1	yes	characteristic
58	#17961	—	11	1	no	maximal, Sylow
59	C₂×Q₈×C₁₁	—	2	2	no	—
60	C₂×Q₈×C₁₁	C₂²×C₄	1	4	yes	—
61	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
62	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
64	C₁₁×Q₁₆	—	2	8	no	—
65	C₂×C₈×C₁₁	—	2	4	no	—
66	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
68	C₁₁×C₄⋊C₄	—	2	2	no	—
69	C₁₁×C₄⋊C₄	—	2	2	no	—
70	C₁₁×C₄⋊C₄	—	2	2	no	—
71	C₁₁×C₄⋊C₄	—	2	4	no	—
72	C₁₁×C₄⋊C₄	—	2	4	no	—
73	C₁₁×C₄⋊C₄	C₂²×C₄	1	4	yes	—
74	C₁₁×C₂²⋊C₄	—	2	4	no	—
75	C₄²×C₁₁	—	2	4	no	—
76	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
77	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₄²×C₁₁	#41	1	1	yes	characteristic
79	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
80	#4318	—	4	4	no	—
81	C₂×C₁₁⋊C₈	—	2	4	no	—
82	C₂×C₁₁⋊C₈	—	2	4	no	—
83	C₂×C₁₁⋊C₈	—	2	2	no	—
84	C₂×C₁₁⋊C₈	—	4	2	no	—
85	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
86	C₂×C₁₁⋊C₈	C₂×D₄	1	2	yes	—
87	#3170	D₁₁	1	1	yes	characteristic
88	#2960	—	11	2	no	—
89	#1593	—	11	4	no	—
90	#1579	—	11	4	no	—
91	#1566	—	11	1	no	—
92	#1493	—	11	2	no	—
93	C₂×#322	—	11	1	no	—
94	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
95	Q₈×C₁₁	—	2	8	no	—
96	Q₈×C₁₁	—	4	4	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	2	4	no	—
100	C₂×C₄×C₁₁	—	2	4	no	—
101	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	#137	1	4	yes	—
105	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
108	C₈×C₁₁	—	2	2	no	—
109	C₈×C₁₁	#131	1	4	yes	—
110	C₁₁⋊C₈	—	2	2	no	—
111	C₁₁⋊C₈	—	2	2	no	—
112	C₁₁⋊C₈	—	4	2	no	—
113	C₁₁⋊C₈	—	4	4	no	—
114	#533	C₂×D₁₁	1	2	yes	—
115	#500	Dic₁₁	1	1	yes	characteristic
116	#494	Dic₁₁	1	1	yes	characteristic
117	#487	Dic₁₁	1	2	yes	—
118	#467	Dic₁₁	1	4	yes	—
119	#446	—	11	4	no	—
120	#446	—	22	2	no	—
121	C₈×Q₈	—	11	4	no	—
122	C₈×Q₈	—	22	2	no	—
123	C₄×Q₁₆	C₂×D₁₁	1	4	yes	—
124	#424	—	22	2	no	—
125	#423	—	11	2	no	—
126	#405	—	22	2	no	—
127	C₂×C₄×C₈	—	11	1	no	—
128	C₂×C₄×C₈	—	11	1	no	—
129	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
130	#334	—	11	4	no	—
131	Q₈⋊C₈	—	11	8	no	—
132	#322	—	11	2	no	—
133	#322	—	11	2	no	—
134	C₂²×C₁₁	—	2	1	no	—
135	C₂²×C₁₁	—	2	1	no	—
136	C₂²×C₁₁	#441	1	2	yes	—
137	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
138	C₄×C₁₁	—	2	1	no	—
139	C₄×C₁₁	—	2	1	no	—
140	C₄×C₁₁	—	4	4	no	—
141	C₄×C₁₁	—	4	4	no	—
142	C₄×C₁₁	#441	1	2	yes	—
143	C₄×C₁₁	#444	1	2	yes	—
144	C₄×C₁₁	C₂×#131	1	2	yes	—
145	C₄×C₁₁	C₂×#137	1	2	yes	—
146	C₂×Q₁₆	C₂×Dic₁₁	1	4	yes	—
147	C₂×M₁₆	—	22	2	no	—
148	C₂²×C₈	—	11	2	no	—
149	C₂²×C₈	—	22	1	no	—
150	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
151	C₄⋊Q₈	C₂×Dic₁₁	1	2	yes	—
152	C₄⋊Q₈	C₂×Dic₁₁	1	2	yes	—
153	#125	—	2	2	no	—
154	C₂²⋊Q₈	—	2	2	no	—
155	C₂²⋊Q₈	C₂×Dic₁₁	1	4	yes	—
156	C₄×Q₈	—	2	2	no	—
157	C₄×Q₈	C₂²×D₁₁	1	4	yes	—
158	#117	—	2	2	no	—
159	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
160	#107	C₂×Dic₁₁	1	4	yes	—
161	C₄⋊C₈	—	11	4	no	—
162	C₄⋊C₈	—	22	4	no	—
163	C₄⋊C₈	—	22	4	no	—
164	C₄⋊C₈	—	22	2	no	—
165	#103	C₂×Dic₁₁	1	8	yes	—
166	#97	—	22	4	no	—
167	C₄×C₈	—	11	2	no	—
168	C₄×C₈	—	11	1	no	—
169	C₄×C₈	—	11	1	no	—
170	C₄×C₈	—	11	2	no	—
171	C₄×C₈	—	22	4	no	—
172	C₄×C₈	—	22	1	no	—
173	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
174	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
175	C₄×C₈	C₂²×D₁₁	1	2	yes	—
176	C₂×C₁₁	—	2	2	no	—
177	C₂×C₁₁	#2931	1	1	yes	characteristic
178	C₂×C₁₁	C₂×#441	1	1	yes	characteristic
179	C₂×C₁₁	C₂×#444	1	1	yes	characteristic
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	C₂²×Dic₁₁	1	4	yes	—
182	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
183	C₂²×C₄	#4341	1	1	yes	characteristic
184	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
185	Q₁₆	—	2	8	no	—
186	M₁₆	—	44	4	no	—
187	C₂×C₈	—	2	4	no	—
188	C₂×C₈	—	11	2	no	—
189	C₂×C₈	—	11	2	no	—
190	C₂×C₈	—	22	4	no	—
191	C₂×C₈	—	22	4	no	—
192	C₂×C₈	—	22	2	no	—
193	C₂×C₈	—	44	2	no	—
194	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
195	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
196	C₄⋊C₄	—	2	2	no	—
197	C₄⋊C₄	—	2	2	no	—
198	C₄⋊C₄	—	2	2	no	—
199	C₄⋊C₄	—	2	4	no	—
200	C₄⋊C₄	—	2	4	no	—
201	C₄⋊C₄	C₂²×Dic₁₁	1	4	yes	—
202	C₂²⋊C₄	—	2	4	no	—
203	C₄²	—	2	4	no	—
204	C₄²	D₄×D₁₁	1	1	yes	characteristic
205	C₄²	#4341	1	1	yes	characteristic
206	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
207	C₄²	C₂³×D₁₁	1	1	yes	characteristic
208	C₁₁	#17961	1	1	yes	characteristic, complemented, Sylow
209	C₂³	D₄×Dic₁₁	1	1	yes	characteristic
210	Q₈	—	2	8	no	—
211	Q₈	—	4	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	2	4	no	—
215	C₂×C₄	—	2	4	no	—
216	C₂×C₄	#66971	1	4	yes	—
217	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
218	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
219	C₂×C₄	D₄×Dic₁₁	1	1	yes	characteristic
220	C₂×C₄	C₂×D₄×D₁₁	1	1	yes	characteristic
221	C₂×C₄	C₂×#4341	1	1	yes	characteristic
222	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
223	C₈	—	2	2	no	—
224	C₈	—	22	2	no	—
225	C₈	—	22	2	no	—
226	C₈	—	44	2	no	—
227	C₈	—	44	4	no	—
228	C₈	#67001	1	4	yes	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	#10622797	1	2	yes	—
232	C₂²	C₂×D₄×Dic₁₁	1	1	yes	characteristic
233	C₄	—	2	1	no	—
234	C₄	—	2	1	no	—
235	C₄	—	4	4	no	—
236	C₄	—	4	4	no	—
237	C₄	#10622797	1	2	yes	—
238	C₄	#10622810	1	2	yes	—
239	C₄	C₂×#66971	1	2	yes	—
240	C₄	C₂×#67001	1	2	yes	—
241	C₂	—	2	2	no	—
242	C₂	#13077328	1	1	yes	characteristic
243	C₂	C₂×#10622797	1	1	yes	characteristic
244	C₂	C₂×#10622810	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	#17961
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. #13067525	C₂	semidirect
3. #13067435	C₂	semidirect
208. C₁₁	#17961	semidirect

Maximal subgroups

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

subgroup	index
#13077551	2
#13067525	2
#13067435	2
#13067372	2
#13067071	2
C₂×#10622093	2
C₁₁×#3170	2
#17961	11