Subgroups — #14907438

Order 2816.

444 conjugacy classes of subgroups.

The subgroup lattice has 228 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	#13070523	C₂	1	4	yes	maximal, complemented
3	#13070522	C₂	1	4	yes	maximal, complemented
4	#13070420	C₂	1	4	yes	maximal
5	#13070419	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic
7	#10623001	C₄	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	#10622715	C₄	1	2	yes	—
10	#10622714	C₂²	1	2	yes	—
11	#10622537	C₄	1	1	yes	characteristic
12	#10622292	C₄	1	2	yes	—
13	#10622292	C₄	1	2	yes	—
14	C₈×Dic₂₂	C₂²	1	2	yes	—
15	C₈×Dic₂₂	C₂²	1	2	yes	—
16	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₁₁×C₂²⋊C₁₆	C₂²	1	2	yes	—
18	C₁₁×#346	C₂²	1	2	yes	—
19	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
20	#10622140	C₂²	1	4	yes	—
21	Dic₁₁⋊C₁₆	C₂²	1	8	yes	—
22	C₁₆×Dic₁₁	C₂²	1	4	yes	—
23	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	2	yes	—
24	#10622099	C₂²	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
28	#66979	C₂×C₄	1	2	yes	—
29	#66977	C₈	1	2	yes	—
30	#66977	C₈	1	2	yes	—
31	C₂×#4318	C₂×C₄	1	2	yes	—
32	#66923	C₈	1	2	yes	—
33	#66922	C₈	1	1	yes	characteristic
34	#66922	C₈	1	1	yes	characteristic
35	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
36	C₄×Dic₂₂	C₂×C₄	1	2	yes	—
37	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
38	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
41	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	#66879	C₂×C₄	1	4	yes	—
43	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
44	Dic₁₁⋊C₈	C₂×C₄	1	4	yes	—
45	C₈×Dic₁₁	C₂³	1	4	yes	—
46	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
47	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
48	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	2	yes	—
49	#33501	—	11	1	no	maximal, Sylow
50	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
54	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
55	C₂×C₈×C₁₁	—	2	2	no	—
56	C₂×C₈×C₁₁	—	4	1	no	—
57	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
61	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
62	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
63	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²⋊Dic₁₁	C₂×C₈	1	4	yes	—
66	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
67	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
68	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
69	C₄⋊Dic₁₁	C₂×C₈	1	2	yes	—
70	Dic₁₁⋊C₄	C₂×C₈	1	4	yes	—
71	Dic₁₁⋊C₄	C₂×C₈	1	4	yes	—
72	C₄×Dic₁₁	C₂²×C₄	1	4	yes	—
73	#4318	—	4	2	no	—
74	C₂×C₁₁⋊C₈	C₂²×C₄	1	4	yes	—
75	C₁₁×C₁₆	—	2	4	no	—
76	C₁₁⋊C₁₆	—	2	4	no	—
77	#2960	—	11	1	no	—
78	#2183	—	11	4	no	—
79	#2183	—	11	4	no	—
80	#2164	—	11	4	no	—
81	#2163	—	11	1	no	—
82	#2163	D₁₁	1	1	yes	characteristic
83	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₁	—	2	1	no	—
85	C₂×C₄×C₁₁	—	2	1	no	—
86	C₂×C₄×C₁₁	—	4	1	no	—
87	C₂×C₄×C₁₁	—	4	1	no	—
88	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
89	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
91	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
92	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
94	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
95	C₂×Dic₁₁	C₂²×C₈	1	4	yes	—
96	Dic₂₂	—	4	2	no	—
97	Dic₂₂	—	4	2	no	—
98	C₈×C₁₁	—	2	1	no	—
99	C₈×C₁₁	—	2	1	no	—
100	C₈×C₁₁	—	2	1	no	—
101	C₈×C₁₁	2₋¹⁺⁴	1	2	yes	—
102	C₁₁⋊C₈	—	2	4	no	—
103	#533	—	11	1	no	—
104	#446	—	11	2	no	—
105	#446	—	11	2	no	—
106	C₈×Q₈	—	11	2	no	—
107	C₈×Q₈	—	11	2	no	—
108	#424	—	11	2	no	—
109	#423	—	11	1	no	—
110	#405	—	11	2	no	—
111	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
112	C₄⋊C₁₆	—	11	8	no	—
113	C₄⋊C₁₆	—	11	2	no	—
114	C₄⋊C₁₆	C₂×D₁₁	1	2	yes	—
115	C₂²⋊C₁₆	—	11	2	no	—
116	C₂²⋊C₁₆	C₂×D₁₁	1	2	yes	—
117	#346	—	11	4	no	—
118	#346	—	11	2	no	—
119	#346	C₂×D₁₁	1	2	yes	—
120	C₄×C₁₆	—	11	4	no	—
121	C₂²×C₁₁	—	2	1	no	—
122	C₂²×C₁₁	—	2	1	no	—
123	C₂²×C₁₁	—	2	1	no	—
124	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
125	C₄×C₁₁	—	2	1	no	—
126	C₄×C₁₁	—	2	1	no	—
127	C₄×C₁₁	—	2	1	no	—
128	C₄×C₁₁	—	2	1	no	—
129	C₄×C₁₁	—	2	1	no	—
130	C₄×C₁₁	#519	1	1	yes	characteristic
131	C₄×C₁₁	#568	1	1	yes	characteristic
132	Dic₁₁	—	2	4	no	—
133	Dic₁₁	—	2	4	no	—
134	C₂×M₁₆	—	11	2	no	—
135	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
136	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
137	C₄⋊Q₈	—	11	1	no	—
138	C₄⋊Q₈	—	11	1	no	—
139	#125	—	11	2	no	—
140	C₂²⋊Q₈	—	11	2	no	—
141	C₂²⋊Q₈	—	11	2	no	—
142	C₄×Q₈	—	11	2	no	—
143	C₄×Q₈	—	11	2	no	—
144	#117	—	11	2	no	—
145	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
146	C₂×C₁₆	—	11	4	no	—
147	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
148	C₄⋊C₈	—	11	4	no	—
149	C₄⋊C₈	—	11	4	no	—
150	C₄⋊C₈	—	11	2	no	—
151	C₄⋊C₈	—	11	2	no	—
152	#97	—	11	4	no	—
153	C₄×C₈	—	11	4	no	—
154	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
155	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
156	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
157	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
158	C₂×C₁₁	—	4	1	no	—
159	C₂×C₁₁	#2982	1	1	yes	characteristic
160	C₂×C₁₁	#3407	1	1	yes	characteristic
161	C₂×C₁₁	#3407	1	1	yes	characteristic
162	C₂×Q₈	—	11	2	no	—
163	C₂×Q₈	—	11	2	no	—
164	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
165	C₂²×C₄	C₈×D₁₁	1	1	yes	characteristic
166	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
167	M₁₆	—	44	2	no	—
168	C₂×C₈	—	2	2	no	—
169	C₂×C₈	—	4	1	no	—
170	C₂×C₈	—	11	4	no	—
171	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
172	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
173	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
174	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
175	C₄⋊C₄	—	11	2	no	—
176	C₄⋊C₄	—	11	2	no	—
177	C₄⋊C₄	—	11	4	no	—
178	C₄⋊C₄	—	11	4	no	—
179	C₄⋊C₄	—	11	2	no	—
180	C₄⋊C₄	—	11	2	no	—
181	C₂²⋊C₄	—	11	4	no	—
182	C₄²	—	11	4	no	—
183	C₄²	C₈×D₁₁	1	1	yes	characteristic
184	C₄²	C₈×D₁₁	1	1	yes	characteristic
185	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
186	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
187	C₁₆	—	2	4	no	—
188	C₁₆	—	22	4	no	—
189	C₁₁	#33501	1	1	yes	characteristic, complemented, Sylow
190	C₂³	C₂×C₈×D₁₁	1	1	yes	characteristic
191	Q₈	—	44	2	no	—
192	Q₈	—	44	2	no	—
193	C₂×C₄	—	2	1	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	11	4	no	—
198	C₂×C₄	—	11	4	no	—
199	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
200	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
201	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
202	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
203	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
204	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
205	C₈	—	2	1	no	—
206	C₈	—	2	1	no	—
207	C₈	—	2	1	no	—
208	C₈	—	22	4	no	—
209	C₈	#67043	1	2	yes	—
210	C₂²	—	2	1	no	—
211	C₂²	—	2	1	no	—
212	C₂²	—	2	1	no	—
213	C₂²	C₂²×C₈×D₁₁	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	1	no	—
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	1	no	—
219	C₄	—	22	4	no	—
220	C₄	—	22	4	no	—
221	C₄	#10623047	1	1	yes	characteristic
222	C₄	#10623276	1	1	yes	characteristic
223	C₂	—	4	1	no	—
224	C₂	#13077696	1	1	yes	characteristic
225	C₂	#13081718	1	1	yes	characteristic
226	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	#33501
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. #13070523	C₂	semidirect
3. #13070522	C₂	semidirect
189. C₁₁	#33501	semidirect

Maximal subgroups

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

subgroup	index
#13077550	2
#13070523	2
#13070522	2
#13070420	2
#13070419	2
C₁₁×#2163	2
#33501	11