Subgroups — #14724521

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	#13079202	C₂	1	1	yes	maximal, characteristic
2	#13077550	C₂	1	2	yes	maximal
3	#13067489	C₂	1	8	yes	maximal, complemented
4	#13067372	C₂	1	1	yes	maximal, characteristic
5	#13067072	C₂	1	2	yes	maximal
6	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
7	#10623001	C₂²	1	2	yes	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	#10622729	C₄	1	4	yes	—
12	#10622715	—	2	2	no	—
13	#10622714	—	2	2	no	—
14	#10622537	C₂²	1	2	yes	—
15	#10622312	C₄	1	1	yes	characteristic
16	C₄×Dic₄₄	C₂²	1	4	yes	—
17	#10622295	C₄	1	1	yes	characteristic
18	#10622294	C₄	1	2	yes	—
19	#10622292	—	2	2	no	—
20	#10622292	C₂²	1	4	yes	—
21	C₈×Dic₂₂	—	2	2	no	—
22	C₈×Dic₂₂	C₂²	1	4	yes	—
23	C₁₁×#322	C₂²	1	4	yes	—
24	#10622095	C₂²	1	4	yes	—
25	#10622094	C₂²	1	8	yes	—
26	C₂²×C₈×C₁₁	—	2	1	no	—
27	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
28	C₂²×C₈×C₁₁	D₄	1	2	yes	—
29	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
30	#66979	—	2	2	no	—
31	#66977	—	2	2	no	—
32	#66977	C₂×C₄	1	4	yes	—
33	C₂×#4318	—	2	2	no	—
34	C₂×Dic₄₄	C₂×C₄	1	4	yes	—
35	#66923	—	2	2	no	—
36	#66922	C₂×C₄	1	2	yes	—
37	#66922	C₂×C₄	1	2	yes	—
38	C₄×Dic₂₂	—	2	2	no	—
39	C₄×Dic₂₂	C₂³	1	4	yes	—
40	C₄×C₈×C₁₁	—	2	1	no	—
41	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
44	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
45	C₄×C₈×C₁₁	C₂³	1	2	yes	—
46	C₄×C₈×C₁₁	C₂³	1	2	yes	—
47	C₄×C₈×C₁₁	C₂³	1	2	yes	—
48	#66882	C₂×C₄	1	4	yes	—
49	#66880	C₂×C₄	1	8	yes	—
50	#66879	—	2	4	no	—
51	Dic₁₁⋊C₈	—	2	4	no	—
52	Dic₁₁⋊C₈	—	2	4	no	—
53	C₈×Dic₁₁	—	2	4	no	—
54	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
55	C₄⋊(C₁₁⋊C₈)	C₂³	1	4	yes	—
56	#17980	—	11	1	no	maximal, Sylow
57	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
60	C₂×Dic₂₂	—	2	2	no	—
61	C₂×Dic₂₂	C₂²×C₄	1	4	yes	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₂×C₈×C₁₁	—	2	4	no	—
64	C₂×C₈×C₁₁	—	2	2	no	—
65	C₂×C₈×C₁₁	—	4	2	no	—
66	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
68	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
69	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
70	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
71	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₄²×C₁₁	#41	1	1	yes	characteristic
73	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
74	C₂²⋊Dic₁₁	—	2	4	no	—
75	C₄⋊Dic₁₁	—	2	2	no	—
76	C₄⋊Dic₁₁	—	2	2	no	—
77	C₄⋊Dic₁₁	—	2	2	no	—
78	C₄⋊Dic₁₁	C₂²×C₄	1	4	yes	—
79	Dic₁₁⋊C₄	—	2	4	no	—
80	Dic₁₁⋊C₄	—	2	4	no	—
81	C₄×Dic₁₁	—	2	4	no	—
82	#4318	—	4	4	no	—
83	C₂×C₁₁⋊C₈	—	2	4	no	—
84	Dic₄₄	—	4	4	no	—
85	#3170	—	11	1	no	—
86	#2960	—	11	2	no	—
87	#1587	—	11	8	no	—
88	#1566	—	11	1	no	—
89	#1493	—	11	2	no	—
90	C₂×#322	D₁₁	1	1	yes	characteristic
91	C₂³×C₁₁	C₄×D₄	1	1	yes	characteristic
92	C₂×C₄×C₁₁	—	2	2	no	—
93	C₂×C₄×C₁₁	—	2	2	no	—
94	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
95	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
97	C₂×C₄×C₁₁	#137	1	4	yes	—
98	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
101	C₂×Dic₁₁	—	2	4	no	—
102	C₂×Dic₁₁	—	2	4	no	—
103	Dic₂₂	—	2	8	no	—
104	Dic₂₂	—	4	4	no	—
105	C₈×C₁₁	—	2	4	no	—
106	C₈×C₁₁	—	2	2	no	—
107	C₈×C₁₁	—	2	2	no	—
108	C₈×C₁₁	—	2	2	no	—
109	C₈×C₁₁	—	2	2	no	—
110	C₁₁⋊C₈	—	4	4	no	—
111	#533	—	11	2	no	—
112	#500	—	11	1	no	—
113	#494	—	11	1	no	—
114	#487	—	11	2	no	—
115	#467	—	11	4	no	—
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	—	11	4	no	—
121	#424	—	22	2	no	—
122	#423	—	11	2	no	—
123	#405	—	22	2	no	—
124	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
126	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
127	#334	—	11	4	no	—
128	Q₈⋊C₈	—	11	8	no	—
129	#322	C₂×D₁₁	1	4	yes	—
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	#441	1	2	yes	—
137	C₄×C₁₁	#443	1	2	yes	—
138	C₄×C₁₁	#568	1	2	yes	—
139	C₄×C₁₁	C₂×#137	1	2	yes	—
140	Dic₁₁	—	4	4	no	—
141	Dic₁₁	—	4	4	no	—
142	C₂×Q₁₆	—	11	4	no	—
143	C₂×M₁₆	—	22	2	no	—
144	C₂²×C₈	—	2	1	no	—
145	C₂²×C₈	C₄×D₁₁	1	2	yes	—
146	C₂²×C₈	D₄₄	1	2	yes	—
147	C₄⋊Q₈	—	11	2	no	—
148	C₄⋊Q₈	—	11	2	no	—
149	#125	—	22	2	no	—
150	C₂²⋊Q₈	—	11	4	no	—
151	C₂²⋊Q₈	—	22	2	no	—
152	C₄×Q₈	—	11	4	no	—
153	C₄×Q₈	—	22	2	no	—
154	#117	—	22	2	no	—
155	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
156	#107	—	11	4	no	—
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	—	11	8	no	—
162	#97	—	22	4	no	—
163	C₄×C₈	—	2	1	no	—
164	C₄×C₈	—	22	4	no	—
165	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
166	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
167	C₄×C₈	D₄₄	1	1	yes	characteristic
168	C₄×C₈	D₄₄	1	1	yes	characteristic
169	C₄×C₈	C₂²×D₁₁	1	2	yes	—
170	C₄×C₈	C₂²×D₁₁	1	2	yes	—
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	—	11	4	no	—
177	C₂×Q₈	—	22	2	no	—
178	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
179	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
180	C₂²×C₄	#4339	1	1	yes	characteristic
181	Q₁₆	—	44	4	no	—
182	M₁₆	—	44	4	no	—
183	C₂×C₈	—	2	4	no	—
184	C₂×C₈	—	2	4	no	—
185	C₂×C₈	—	2	2	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	22	4	no	—
188	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
189	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
190	C₂×C₈	C₂×D₄₄	1	2	yes	—
191	C₂×C₈	C₂×D₄₄	1	2	yes	—
192	C₄⋊C₄	—	11	4	no	—
193	C₄⋊C₄	—	22	2	no	—
194	C₄⋊C₄	—	22	2	no	—
195	C₄⋊C₄	—	22	4	no	—
196	C₄⋊C₄	—	22	2	no	—
197	C₄⋊C₄	—	22	4	no	—
198	C₂²⋊C₄	—	22	4	no	—
199	C₄²	—	22	4	no	—
200	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
201	C₄²	C₂×D₄₄	1	1	yes	characteristic
202	C₄²	#4339	1	1	yes	characteristic
203	C₄²	C₂³×D₁₁	1	1	yes	characteristic
204	C₁₁	#17980	1	1	yes	characteristic, complemented, Sylow
205	C₂³	C₄×D₄₄	1	1	yes	characteristic
206	Q₈	—	22	8	no	—
207	Q₈	—	44	4	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	22	4	no	—
211	C₂×C₄	—	22	4	no	—
212	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
213	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
214	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
215	C₂×C₄	#66962	1	4	yes	—
216	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
217	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
218	C₂×C₄	C₂×#4339	1	1	yes	characteristic
219	C₈	—	2	4	no	—
220	C₈	—	2	2	no	—
221	C₈	—	2	2	no	—
222	C₈	—	2	2	no	—
223	C₈	—	2	2	no	—
224	C₈	—	44	4	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	#10622329	1	2	yes	—
228	C₂²	C₂×C₄×D₄₄	1	1	yes	characteristic
229	C₄	—	2	1	no	—
230	C₄	—	2	1	no	—
231	C₄	—	44	4	no	—
232	C₄	—	44	4	no	—
233	C₄	#10622313	1	2	yes	—
234	C₄	#10622329	1	2	yes	—
235	C₄	#10623276	1	2	yes	—
236	C₄	C₂×#66962	1	2	yes	—
237	C₂	—	2	2	no	—
238	C₂	#13077335	1	1	yes	characteristic
239	C₂	C₂×#10622329	1	1	yes	characteristic
240	C₂	C₂×#10622313	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₄₄
commutator	C₂×C₄×C₁₁	C₂³×C₄
Frattini	C₄²	C₂³×D₁₁
Fitting	C₂×C₁₁×#322	C₂
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂³×C₁₁	C₄×D₄
cosocle	C₄²×C₁₁	C₂⁴
hypercenter	C₂×#322	D₁₁
hypocenter	C₁₁	#17980
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#322

Complements

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

N	H ≅ G/N	type
3. #13067489	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
#13079202	2
#13077550	2
#13067489	2
#13067372	2
#13067072	2
C₂×C₁₁×#322	2
#17980	11