Subgroups — #14907021

Order 2816.

642 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13081719	C₂	1	2	yes	maximal, complemented
2	#13070458	C₂	1	4	yes	maximal, complemented
3	#13070453	C₂	1	4	yes	maximal, complemented
4	#13070382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10622199	C₂	1	2	yes	maximal, complemented
6	#13070213	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₁×#2955	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#575	C₄	1	1	yes	characteristic
9	C₂×C₁₁×#131	C₂²	1	2	yes	—
10	C₁₁×#444	C₄	1	4	yes	—
11	C₁₁×#443	C₂²	1	4	yes	—
12	C₁₁×#430	C₄	1	1	yes	characteristic
13	C₁₁×#421	C₄	1	2	yes	—
14	C₁₁×#405	C₂²	1	1	yes	characteristic
15	#10622753	—	2	4	no	—
16	#10622753	C₂²	1	8	yes	complemented
17	C₂×#66876	—	2	4	no	—
18	C₂×#66876	C₂²	1	2	yes	—
19	C₂×#66876	C₂²	1	1	yes	characteristic
20	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
21	#10622199	C₂²	1	4	yes	complemented
22	#10622199	C₂²	1	4	yes	complemented
23	#10622101	C₂²	1	4	yes	complemented
24	#10622099	C₂²	1	2	yes	complemented
25	C₄×C₁₁⋊C₁₆	C₂²	1	2	yes	complemented
26	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
27	C₁₁×#137	C₈	1	4	yes	—
28	C₁₁×AGL(1,ℤ/8)	C₈	1	4	yes	—
29	C₁₁×#135	C₂×C₄	1	4	yes	—
30	C₁₁×#131	—	2	2	no	—
31	C₁₁×#131	—	2	2	no	—
32	C₁₁×#131	C₂×C₄	1	4	yes	—
33	C₁₁×#131	C₂³	1	4	yes	—
34	C₂×C₁₁×M₁₆	—	2	2	no	—
35	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
36	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₈×C₁₁	—	2	2	no	—
38	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
39	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
40	C₁₁×#108	C₂×C₄	1	4	yes	—
41	C₁₁×#104	C₂×C₄	1	8	yes	—
42	C₁₁×#97	C₂×C₄	1	2	yes	—
43	C₄×C₈×C₁₁	C₂³	1	2	yes	—
44	#66876	—	2	2	no	—
45	#66876	—	2	8	no	—
46	#66876	D₄	1	4	yes	—
47	#66876	C₂³	1	4	yes	—
48	C₂×C₁₁⋊C₁₆	—	2	2	no	—
49	C₂×C₁₁⋊C₁₆	—	2	2	no	—
50	C₂×C₁₁⋊C₁₆	—	2	8	no	—
51	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
52	C₂×C₁₁⋊C₁₆	C₂³	1	1	yes	characteristic
53	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
54	#33442	—	11	1	no	maximal, Sylow
55	C₁₁×#41	—	2	2	no	—
56	C₁₁×#41	—	2	2	no	—
57	C₁₁×#41	C₂×C₈	1	4	yes	—
58	C₁₁×#41	C₂²×C₄	1	4	yes	—
59	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
60	C₂×D₄×C₁₁	—	2	2	no	—
61	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
62	C₂²×C₄×C₁₁	—	2	2	no	—
63	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
64	C₁₁×Q₁₆	C₂×C₈	1	4	yes	—
65	C₁₁×SD₁₆	C₂×C₈	1	8	yes	—
66	C₁₁×D₈	C₂×C₈	1	4	yes	—
67	C₁₁×M₁₆	—	2	4	no	—
68	C₁₁×M₁₆	—	2	4	no	—
69	C₁₁×M₁₆	—	2	2	no	—
70	C₁₁×M₁₆	C₂×C₈	1	4	yes	—
71	C₁₁×M₁₆	C₂²×C₄	1	4	yes	—
72	C₂×C₈×C₁₁	—	2	4	no	—
73	C₂×C₈×C₁₁	—	2	4	no	—
74	C₂×C₈×C₁₁	—	2	2	no	—
75	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
76	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
77	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
78	C₂×C₈×C₁₁	#41	1	2	yes	—
79	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
80	C₁₁×C₄⋊C₄	—	2	1	no	—
81	C₁₁×C₂²⋊C₄	—	2	1	no	—
82	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
83	C₁₁⋊C₁₆	—	2	4	no	—
84	C₁₁⋊C₁₆	—	2	1	no	—
85	C₁₁⋊C₁₆	—	2	1	no	—
86	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	—
87	#3407	—	11	2	no	—
88	#2955	D₁₁	1	1	yes	characteristic
89	#2171	—	11	4	no	—
90	#2170	—	11	4	no	—
91	#2153	—	11	1	no	—
92	C₂×#350	—	11	2	no	—
93	#2108	—	11	1	no	—
94	C₂³×C₁₁	—	2	2	no	—
95	C₂³×C₁₁	#131	1	1	yes	characteristic
96	Q₈×C₁₁	—	2	2	no	—
97	Q₈×C₁₁	C₂²×C₈	1	4	yes	—
98	D₄×C₁₁	—	2	4	no	—
99	D₄×C₁₁	—	2	4	no	—
100	D₄×C₁₁	—	2	2	no	—
101	D₄×C₁₁	C₂²×C₈	1	4	yes	—
102	C₂×C₄×C₁₁	—	2	2	no	—
103	C₂×C₄×C₁₁	—	2	4	no	—
104	C₂×C₄×C₁₁	—	2	4	no	—
105	C₂×C₄×C₁₁	—	2	2	no	—
106	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
107	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
108	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
109	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
110	C₈×C₁₁	—	2	4	no	—
111	C₈×C₁₁	C₄×D₄	1	2	yes	—
112	C₈×C₁₁	C₂²×C₈	1	4	yes	—
113	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
114	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
115	#575	Dic₁₁	1	1	yes	characteristic
116	C₂×#131	C₂×D₁₁	1	2	yes	—
117	#504	—	11	8	no	—
118	#504	—	22	4	no	—
119	C₂×M₃₂	—	11	1	no	—
120	C₂×M₃₂	—	11	2	no	—
121	C₂×M₃₂	—	22	4	no	—
122	C₂²×C₁₆	—	11	1	no	—
123	#444	Dic₁₁	1	4	yes	—
124	#443	C₂×D₁₁	1	4	yes	—
125	#430	Dic₁₁	1	1	yes	characteristic
126	#421	Dic₁₁	1	2	yes	—
127	#405	C₂×D₁₁	1	1	yes	characteristic
128	#364	—	11	4	no	—
129	#350	—	11	4	no	—
130	#350	—	11	4	no	—
131	#346	—	11	2	no	—
132	C₄×C₁₆	—	11	2	no	—
133	C₂²×C₁₁	—	2	4	no	—
134	C₂²×C₁₁	—	4	1	no	—
135	C₂²×C₁₁	—	8	2	no	—
136	C₂²×C₁₁	C₈×D₄	1	2	yes	—
137	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
138	C₄×C₁₁	—	2	4	no	—
139	C₄×C₁₁	—	4	2	no	—
140	C₄×C₁₁	C₈×D₄	1	2	yes	—
141	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
142	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
143	C₂×#41	C₂×Dic₁₁	1	2	yes	—
144	#137	C₁₁⋊C₈	1	4	yes	—
145	AGL(1,ℤ/8)	C₁₁⋊C₈	1	4	yes	—
146	#135	C₂×Dic₁₁	1	4	yes	—
147	#131	—	2	2	no	—
148	#131	—	2	2	no	—
149	#131	C₂×Dic₁₁	1	4	yes	—
150	#131	C₂²×D₁₁	1	4	yes	—
151	C₂×M₁₆	—	2	2	no	—
152	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
153	C₂×M₁₆	C₂×Dic₁₁	1	1	yes	characteristic
154	C₂²×C₈	—	2	2	no	—
155	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
156	#117	C₂×Dic₁₁	1	1	yes	characteristic
157	M₃₂	—	11	4	no	—
158	M₃₂	—	11	4	no	—
159	M₃₂	—	22	8	no	—
160	M₃₂	—	22	2	no	—
161	C₂×C₁₆	—	11	2	no	—
162	C₂×C₁₆	—	11	1	no	—
163	C₂×C₁₆	—	11	1	no	—
164	C₂×C₁₆	—	22	8	no	—
165	C₂×C₁₆	—	22	2	no	—
166	C₂×C₁₆	—	22	2	no	—
167	#108	C₂×Dic₁₁	1	4	yes	—
168	#104	C₂×Dic₁₁	1	8	yes	—
169	#97	C₂×Dic₁₁	1	2	yes	—
170	C₄×C₈	C₂²×D₁₁	1	2	yes	—
171	C₂×C₁₁	—	2	1	no	—
172	C₂×C₁₁	—	2	2	no	—
173	C₂×C₁₁	—	4	4	no	—
174	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
175	#41	—	2	2	no	—
176	#41	—	2	2	no	—
177	#41	C₂×C₁₁⋊C₈	1	4	yes	—
178	#41	C₂²×Dic₁₁	1	4	yes	—
179	C₂×Q₈	C₂×C₁₁⋊C₈	1	2	yes	—
180	C₂×D₄	—	2	2	no	—
181	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
182	C₂²×C₄	—	2	2	no	—
183	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
184	Q₁₆	C₂×C₁₁⋊C₈	1	4	yes	—
185	SD₁₆	C₂×C₁₁⋊C₈	1	8	yes	—
186	D₈	C₂×C₁₁⋊C₈	1	4	yes	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	2	4	no	—
189	M₁₆	—	2	4	no	—
190	M₁₆	C₂×C₁₁⋊C₈	1	4	yes	—
191	M₁₆	C₂²×Dic₁₁	1	4	yes	—
192	C₂×C₈	—	2	2	no	—
193	C₂×C₈	—	2	4	no	—
194	C₂×C₈	—	2	4	no	—
195	C₂×C₈	D₄×D₁₁	1	2	yes	—
196	C₂×C₈	#4341	1	2	yes	—
197	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
198	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
199	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
200	C₄⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	2	1	no	—
202	C₄²	C₂²×Dic₁₁	1	2	yes	—
203	C₁₆	—	11	4	no	—
204	C₁₆	—	22	4	no	—
205	C₁₆	—	22	1	no	—
206	C₁₆	—	22	1	no	—
207	C₁₁	#33442	1	1	yes	characteristic, complemented, Sylow
208	C₂³	—	2	2	no	—
209	C₂³	#67001	1	1	yes	characteristic
210	Q₈	—	2	2	no	—
211	Q₈	C₂²×C₁₁⋊C₈	1	4	yes	—
212	D₄	—	2	4	no	—
213	D₄	—	2	4	no	—
214	D₄	—	2	2	no	—
215	D₄	C₂²×C₁₁⋊C₈	1	4	yes	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	2	4	no	—
218	C₂×C₄	—	2	4	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
221	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
222	C₂×C₄	#67001	1	1	yes	characteristic
223	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
224	C₈	—	2	4	no	—
225	C₈	C₂²×C₁₁⋊C₈	1	4	yes	—
226	C₈	D₄×Dic₁₁	1	2	yes	—
227	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
228	C₈	C₂×#4341	1	1	yes	characteristic
229	C₂²	—	2	4	no	—
230	C₂²	—	4	1	no	—
231	C₂²	—	8	2	no	—
232	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
233	C₂²	C₂×#67001	1	1	yes	characteristic
234	C₄	—	2	4	no	—
235	C₄	—	4	2	no	—
236	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
237	C₄	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
238	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	4	4	no	—
242	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₁₁
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2955	C₂
socle	C₂×C₁₁	C₂×C₈×D₄
prime radical	C₁₁×#575	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2955	D₁₁
hypocenter	C₁₁	#33442
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #2955

Complements

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

N	H ≅ G/N	type
1. #13081719	C₂	semidirect
2. #13070458	C₂	semidirect
3. #13070453	C₂	semidirect
4. #13070382	C₂	semidirect
5. C₂×#10622199	C₂	semidirect
6. #13070213	C₂	semidirect
16. #10622753	C₂²	semidirect
21. #10622199	C₂²	semidirect
22. #10622199	C₂²	semidirect
23. #10622101	C₂²	semidirect
24. #10622099	C₂²	semidirect
25. C₄×C₁₁⋊C₁₆	C₂²	semidirect
207. C₁₁	#33442	semidirect

Maximal subgroups

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

subgroup	index
#13081719	2
#13070458	2
#13070453	2
#13070382	2
C₂×#10622199	2
#13070213	2
C₁₁×#2955	2
#33442	11