Subgroups — #14907430

Order 2816.

452 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077550	C₂	1	1	yes	maximal, characteristic
2	#13070522	C₂	1	4	yes	maximal, complemented
3	#13070521	C₂	1	2	yes	maximal, complemented
4	#13070518	C₂	1	2	yes	maximal, complemented
5	#13070420	C₂	1	4	yes	maximal
6	#13070415	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic
8	#10623001	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	#10622715	C₄	1	2	yes	—
11	#10622714	C₂²	1	2	yes	—
12	#10622537	C₄	1	1	yes	characteristic
13	#10622292	C₄	1	2	yes	—
14	#10622292	C₄	1	2	yes	—
15	C₈×Dic₂₂	C₂²	1	2	yes	—
16	C₈×Dic₂₂	C₂²	1	2	yes	—
17	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
18	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
19	C₁₁×#346	C₂²	1	2	yes	—
20	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
21	#10622140	C₂²	1	4	yes	—
22	Dic₁₁⋊C₁₆	C₂²	1	4	yes	—
23	Dic₁₁⋊C₁₆	C₂²	1	4	yes	—
24	C₁₆×Dic₁₁	C₂²	1	4	yes	—
25	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
26	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
27	C₄×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	#66979	C₂×C₄	1	2	yes	—
32	#66977	C₈	1	2	yes	—
33	#66977	C₈	1	2	yes	—
34	C₂×#4318	C₂×C₄	1	2	yes	—
35	#66923	C₈	1	2	yes	—
36	#66922	C₈	1	1	yes	characteristic
37	#66922	C₈	1	1	yes	characteristic
38	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
39	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
40	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
41	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
43	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
44	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
45	#66879	C₂×C₄	1	4	yes	—
46	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
47	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
48	C₈×Dic₁₁	C₂³	1	4	yes	—
49	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
50	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
51	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
52	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
53	#33499	—	11	1	no	maximal, Sylow
54	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
58	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
65	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
66	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
67	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
68	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
69	C₂²⋊Dic₁₁	C₂×C₈	1	4	yes	—
70	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
71	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
72	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
73	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
74	Dic₁₁⋊C₄	C₂×C₈	1	4	yes	—
75	Dic₁₁⋊C₄	C₂×C₈	1	4	yes	—
76	C₄×Dic₁₁	C₂²×C₄	1	4	yes	—
77	#4318	—	4	2	no	—
78	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
79	C₁₁×C₁₆	—	2	4	no	—
80	C₁₁⋊C₁₆	—	2	2	no	—
81	C₁₁⋊C₁₆	—	2	2	no	—
82	#2960	—	11	1	no	—
83	#2183	—	11	2	no	—
84	#2183	—	11	4	no	—
85	Q₈×C₁₆	—	11	2	no	—
86	#2164	—	11	4	no	—
87	#2163	D₁₁	1	1	yes	characteristic
88	#2162	—	11	1	no	—
89	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
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	—	4	1	no	—
94	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
95	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
97	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
98	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
100	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
101	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
102	Dic₂₂	—	2	4	no	—
103	Dic₂₂	—	4	2	no	—
104	C₈×C₁₁	—	2	1	no	—
105	C₈×C₁₁	—	2	1	no	—
106	C₈×C₁₁	—	2	1	no	—
107	C₈×C₁₁	2₋¹⁺⁴	1	2	yes	—
108	C₁₁⋊C₈	—	2	4	no	—
109	#533	—	11	1	no	—
110	#446	—	11	2	no	—
111	#446	—	11	2	no	—
112	C₈×Q₈	—	11	2	no	—
113	C₈×Q₈	—	11	2	no	—
114	#424	—	11	2	no	—
115	#423	—	11	1	no	—
116	#405	—	11	2	no	—
117	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
118	C₄⋊C₁₆	—	11	4	no	—
119	C₄⋊C₁₆	—	11	4	no	—
120	C₄⋊C₁₆	—	11	2	no	—
121	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
122	C₂²⋊C₁₆	—	11	2	no	—
123	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
124	#346	—	11	4	no	—
125	#346	C₂×D₁₁	1	2	yes	—
126	C₄×C₁₆	—	11	4	no	—
127	C₄×C₁₆	—	11	1	no	—
128	C₄×C₁₆	—	11	1	no	—
129	C₂²×C₁₁	—	2	1	no	—
130	C₂²×C₁₁	—	2	1	no	—
131	C₂²×C₁₁	—	2	1	no	—
132	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
133	C₄×C₁₁	—	2	1	no	—
134	C₄×C₁₁	—	2	1	no	—
135	C₄×C₁₁	—	2	1	no	—
136	C₄×C₁₁	—	2	1	no	—
137	C₄×C₁₁	#504	1	2	yes	—
138	C₄×C₁₁	#519	1	1	yes	characteristic
139	C₄×C₁₁	#568	1	1	yes	characteristic
140	Dic₁₁	—	2	4	no	—
141	Dic₁₁	—	2	4	no	—
142	C₂×M₁₆	—	11	2	no	—
143	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
144	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
145	C₄⋊Q₈	—	11	1	no	—
146	C₄⋊Q₈	—	11	1	no	—
147	#125	—	11	2	no	—
148	C₂²⋊Q₈	—	11	2	no	—
149	C₂²⋊Q₈	—	11	2	no	—
150	C₄×Q₈	—	11	2	no	—
151	C₄×Q₈	—	11	2	no	—
152	#117	—	11	2	no	—
153	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
154	C₂×C₁₆	—	11	2	no	—
155	C₂×C₁₆	—	11	2	no	—
156	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
157	C₄⋊C₈	—	11	4	no	—
158	C₄⋊C₈	—	11	4	no	—
159	C₄⋊C₈	—	11	2	no	—
160	C₄⋊C₈	—	11	2	no	—
161	#97	—	11	4	no	—
162	C₄×C₈	—	11	4	no	—
163	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
164	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
165	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
166	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
167	C₂×C₁₁	—	4	1	no	—
168	C₂×C₁₁	#2982	1	1	yes	characteristic
169	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
170	C₂×C₁₁	#3407	1	1	yes	characteristic
171	C₂×Q₈	—	11	2	no	—
172	C₂×Q₈	—	11	2	no	—
173	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
174	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
175	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
176	M₁₆	—	44	2	no	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	4	1	no	—
179	C₂×C₈	—	11	4	no	—
180	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
182	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
183	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
184	C₄⋊C₄	—	11	2	no	—
185	C₄⋊C₄	—	11	2	no	—
186	C₄⋊C₄	—	11	4	no	—
187	C₄⋊C₄	—	11	4	no	—
188	C₄⋊C₄	—	11	2	no	—
189	C₄⋊C₄	—	11	2	no	—
190	C₂²⋊C₄	—	11	4	no	—
191	C₄²	—	11	4	no	—
192	C₄²	C₈×D₁₁	1	1	yes	characteristic
193	C₄²	C₈×D₁₁	1	1	yes	characteristic
194	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
195	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
196	C₁₆	—	2	4	no	—
197	C₁₆	—	22	2	no	—
198	C₁₆	—	22	2	no	—
199	C₁₁	#33499	1	1	yes	characteristic, complemented, Sylow
200	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
201	Q₈	—	22	4	no	—
202	Q₈	—	44	2	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	11	4	no	—
208	C₂×C₄	—	11	4	no	—
209	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
210	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
211	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
212	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
213	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
214	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
215	C₈	—	2	1	no	—
216	C₈	—	2	1	no	—
217	C₈	—	2	1	no	—
218	C₈	—	22	4	no	—
219	C₈	#67043	1	2	yes	—
220	C₂²	—	2	1	no	—
221	C₂²	—	2	1	no	—
222	C₂²	—	2	1	no	—
223	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
224	C₄	—	2	1	no	—
225	C₄	—	2	1	no	—
226	C₄	—	2	1	no	—
227	C₄	—	2	1	no	—
228	C₄	—	22	4	no	—
229	C₄	—	22	4	no	—
230	C₄	#10622520	1	2	yes	—
231	C₄	#10623047	1	1	yes	characteristic
232	C₄	#10623276	1	1	yes	characteristic
233	C₂	—	4	1	no	—
234	C₂	#13077696	1	1	yes	characteristic
235	C₂	C₂×#10622520	1	1	yes	characteristic
236	C₂	#13081718	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2163	C₂
prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2163	D₁₁
hypocenter	C₁₁	#33499
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2163

Complements

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

N	H ≅ G/N	type
2. #13070522	C₂	semidirect
3. #13070521	C₂	semidirect
4. #13070518	C₂	semidirect
199. C₁₁	#33499	semidirect

Maximal subgroups

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

subgroup	index
#13077550	2
#13070522	2
#13070521	2
#13070518	2
#13070420	2
#13070415	2
C₁₁×#2163	2
#33499	11