Subgroups — #14907022

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	#13081718	C₂	1	2	yes	maximal, complemented
2	#13077520	C₂	1	1	yes	maximal, characteristic
3	#13070459	C₂	1	4	yes	maximal, complemented
4	#13070454	C₂	1	4	yes	maximal, complemented
5	#13070382	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10622146	C₂	1	2	yes	maximal, complemented
7	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic, complemented
8	#10623279	C₄	1	1	yes	characteristic
9	C₂×#66954	C₂²	1	2	yes	—
10	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	C₁₁×#405	C₂²	1	1	yes	characteristic
13	#10622738	C₄	1	1	yes	characteristic
14	C₂×#66876	C₂²	1	2	yes	—
15	#10622618	C₄	1	2	yes	—
16	#10622520	—	2	4	no	—
17	D₁₁×M₃₂	—	2	4	no	—
18	#10622514	C₂²	1	8	yes	complemented
19	#10622330	C₄	1	4	yes	—
20	#10622313	C₂²	1	4	yes	—
21	C₁₁×#346	C₂²	1	2	yes	complemented
22	C₄×C₁₁×C₁₆	C₂²	1	2	yes	complemented
23	#10622146	C₂²	1	4	yes	complemented
24	#10622146	C₂²	1	4	yes	complemented
25	#10622101	C₂²	1	4	yes	complemented
26	C₂×#4339	C₂×C₄	1	2	yes	—
27	C₂×C₁₁×M₁₆	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₁₁×#117	C₂×C₄	1	1	yes	characteristic
30	C₂×#4318	C₂×C₄	1	2	yes	—
31	#66962	C₈	1	4	yes	—
32	#66961	C₈	1	4	yes	—
33	#66957	C₂×C₄	1	4	yes	—
34	#66954	—	2	2	no	—
35	#66954	—	2	2	no	—
36	#66954	C₂×C₄	1	4	yes	—
37	#66954	C₂³	1	4	yes	—
38	C₂×#4313	—	2	2	no	—
39	C₂×C₈×D₁₁	—	2	2	no	—
40	C₁₁×M₃₂	D₄	1	4	yes	—
41	C₂×C₁₁×C₁₆	—	2	2	no	—
42	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
43	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
44	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
45	C₁₁×#97	C₂×C₄	1	2	yes	—
46	C₄×C₈×C₁₁	C₂³	1	2	yes	—
47	#66883	C₂×C₄	1	4	yes	—
48	#66876	—	2	2	no	—
49	#66876	C₂³	1	4	yes	—
50	C₂×C₁₁⋊C₁₆	—	2	2	no	—
51	#66869	C₂×C₄	1	8	yes	—
52	#66862	—	2	8	no	—
53	C₁₆×D₁₁	—	2	8	no	—
54	#33442	—	11	1	no	maximal, Sylow
55	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
56	C₂×C₂²⋊D₁₁	—	2	2	no	—
57	#4339	—	2	2	no	—
58	#4339	—	2	2	no	—
59	#4339	C₂×C₈	1	4	yes	—
60	#4339	C₂²×C₄	1	4	yes	—
61	C₂×D₄₄	C₂×C₈	1	2	yes	—
62	C₂×C₄×D₁₁	—	2	2	no	—
63	C₂×Dic₂₂	C₂×C₈	1	2	yes	—
64	C₁₁×M₁₆	C₂×C₈	1	4	yes	—
65	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
67	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₁₁	#41	1	2	yes	—
69	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
70	C₁₁×C₄⋊C₄	—	2	1	no	—
71	C₁₁×C₂²⋊C₄	—	2	1	no	—
72	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
73	#4318	—	2	2	no	—
74	#4318	C₂²×C₄	1	4	yes	—
75	C₂×C₁₁⋊C₈	—	2	2	no	—
76	Dic₄₄	C₂×C₈	1	4	yes	—
77	D₈₈	C₂×C₈	1	4	yes	—
78	#4314	C₂×C₈	1	8	yes	—
79	#4313	—	2	4	no	—
80	#4313	—	2	4	no	—
81	C₈×D₁₁	—	2	4	no	—
82	C₈×D₁₁	—	2	4	no	—
83	C₁₁×C₁₆	—	2	1	no	—
84	C₁₁×C₁₆	—	2	1	no	—
85	C₁₁×C₁₆	C₂×D₄	1	4	yes	—
86	C₁₁⋊C₁₆	—	2	4	no	—
87	#3407	—	11	2	no	—
88	#2955	—	11	1	no	—
89	#2171	—	11	4	no	—
90	#2170	—	11	4	no	—
91	#2153	—	11	1	no	—
92	C₂×#350	—	11	2	no	—
93	#2108	D₁₁	1	1	yes	characteristic, complemented
94	C₂³×C₁₁	#131	1	1	yes	characteristic
95	C₂²×D₁₁	—	2	2	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
99	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
101	C₂²⋊D₁₁	—	2	4	no	—
102	C₂²⋊D₁₁	—	2	4	no	—
103	C₂×Dic₁₁	—	2	2	no	—
104	D₄₄	—	2	2	no	—
105	D₄₄	C₂²×C₈	1	4	yes	—
106	C₄×D₁₁	—	2	4	no	—
107	C₄×D₁₁	—	2	4	no	—
108	Dic₂₂	—	2	2	no	—
109	Dic₂₂	C₂²×C₈	1	4	yes	—
110	C₈×C₁₁	C₄×D₄	1	2	yes	—
111	C₈×C₁₁	C₂²×C₈	1	4	yes	—
112	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
113	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
114	C₁₁⋊C₈	—	2	4	no	—
115	#575	—	11	1	no	—
116	C₂×#131	—	11	2	no	—
117	#504	—	11	8	no	—
118	#504	—	22	4	no	—
119	C₂×M₃₂	—	11	2	no	—
120	C₂×M₃₂	—	22	4	no	—
121	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
122	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
123	#444	—	11	4	no	—
124	#443	—	11	4	no	—
125	#430	—	11	1	no	—
126	#421	—	11	2	no	—
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	C₂×D₁₁	1	2	yes	complemented
132	C₄×C₁₆	C₂×D₁₁	1	2	yes	complemented
133	C₂²×C₁₁	—	4	1	no	—
134	C₂²×C₁₁	C₈×D₄	1	2	yes	—
135	C₂²×C₁₁	C₂×#131	1	1	yes	characteristic
136	C₂×D₁₁	—	2	4	no	—
137	C₂×D₁₁	—	8	2	no	—
138	C₄×C₁₁	—	4	2	no	—
139	C₄×C₁₁	C₈×D₄	1	2	yes	—
140	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
141	C₄×C₁₁	C₂³×C₈	1	1	yes	characteristic
142	Dic₁₁	—	2	4	no	—
143	C₂×#41	—	11	2	no	—
144	#137	—	11	4	no	—
145	AGL(1,ℤ/8)	—	11	4	no	—
146	#135	—	11	4	no	—
147	#131	—	11	4	no	—
148	#131	—	11	4	no	—
149	#131	—	22	2	no	—
150	#131	—	22	2	no	—
151	C₂×M₁₆	—	11	2	no	—
152	C₂×M₁₆	—	22	2	no	—
153	C₂×M₁₆	C₄×D₁₁	1	1	yes	characteristic
154	C₂²×C₈	—	22	2	no	—
155	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
156	#117	C₄×D₁₁	1	1	yes	characteristic
157	M₃₂	—	11	4	no	—
158	M₃₂	—	22	2	no	—
159	M₃₂	—	22	8	no	—
160	M₃₂	D₄₄	1	4	yes	—
161	C₂×C₁₆	—	2	2	no	—
162	C₂×C₁₆	—	22	2	no	—
163	C₂×C₁₆	—	22	8	no	—
164	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
165	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
166	C₂×C₁₆	C₂²×D₁₁	1	2	yes	—
167	#108	—	11	4	no	—
168	#104	—	11	8	no	—
169	#97	C₄×D₁₁	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	C₂×C₈×D₄	1	1	yes	characteristic
174	D₁₁	—	4	4	no	—
175	#41	—	11	4	no	—
176	#41	—	11	4	no	—
177	#41	—	22	2	no	—
178	#41	—	22	2	no	—
179	C₂×Q₈	—	11	2	no	—
180	C₂×D₄	—	11	2	no	—
181	C₂×D₄	—	22	2	no	—
182	C₂²×C₄	—	22	2	no	—
183	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
184	Q₁₆	—	11	4	no	—
185	SD₁₆	—	11	8	no	—
186	D₈	—	11	4	no	—
187	M₁₆	—	11	4	no	—
188	M₁₆	—	22	2	no	—
189	M₁₆	—	22	4	no	—
190	M₁₆	—	22	4	no	—
191	M₁₆	C₈×D₁₁	1	4	yes	—
192	C₂×C₈	—	22	2	no	—
193	C₂×C₈	—	22	4	no	—
194	C₂×C₈	—	22	4	no	—
195	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
196	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
197	C₂×C₈	C₂×D₄₄	1	2	yes	—
198	C₂×C₈	#4339	1	2	yes	—
199	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
200	C₄⋊C₄	—	2	1	no	—
201	C₂²⋊C₄	—	2	1	no	—
202	C₄²	C₂×C₄×D₁₁	1	2	yes	—
203	C₁₆	—	2	1	no	—
204	C₁₆	—	2	1	no	—
205	C₁₆	—	22	4	no	—
206	C₁₆	C₂×D₄₄	1	4	yes	—
207	C₁₁	#33442	1	1	yes	characteristic, complemented, Sylow
208	C₂³	—	22	2	no	—
209	C₂³	#66954	1	1	yes	characteristic
210	Q₈	—	11	4	no	—
211	Q₈	—	22	2	no	—
212	D₄	—	11	4	no	—
213	D₄	—	22	4	no	—
214	D₄	—	22	4	no	—
215	D₄	—	22	2	no	—
216	C₂×C₄	—	2	2	no	—
217	C₂×C₄	—	22	2	no	—
218	C₂×C₄	—	22	4	no	—
219	C₂×C₄	—	22	4	no	—
220	C₂×C₄	C₄×D₄₄	1	2	yes	—
221	C₂×C₄	C₂×C₈×D₁₁	1	2	yes	—
222	C₂×C₄	#66954	1	1	yes	characteristic
223	C₂×C₄	C₂²×C₄×D₁₁	1	1	yes	characteristic
224	C₈	—	22	4	no	—
225	C₈	C₄×D₄₄	1	2	yes	—
226	C₈	C₂×C₈×D₁₁	1	4	yes	—
227	C₈	C₂²×D₄₄	1	1	yes	characteristic
228	C₈	C₂×#4339	1	1	yes	characteristic
229	C₂²	—	4	1	no	—
230	C₂²	—	22	4	no	—
231	C₂²	—	88	2	no	—
232	C₂²	C₈×D₄₄	1	2	yes	—
233	C₂²	C₂×#66954	1	1	yes	characteristic
234	C₄	—	4	2	no	—
235	C₄	—	22	4	no	—
236	C₄	C₈×D₄₄	1	2	yes	—
237	C₄	C₂×C₄×D₄₄	1	1	yes	characteristic
238	C₄	C₂²×C₈×D₁₁	1	1	yes	characteristic
239	C₂	—	2	1	no	—
240	C₂	—	2	2	no	—
241	C₂	—	44	4	no	—
242	C₂	C₂×C₈×D₄₄	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²×D₄₄
commutator	C₄×C₁₁	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₁₁×#2108	C₂
socle	C₂×C₁₁	C₂×C₈×D₄
prime radical	#10623279	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2108	D₁₁
hypocenter	C₁₁	#33442
LCS	G ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂ ◁ #2108

Complements

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

N	H ≅ G/N	type
1. #13081718	C₂	semidirect
3. #13070459	C₂	semidirect
4. #13070454	C₂	semidirect
5. #13070382	C₂	semidirect
6. C₂×#10622146	C₂	semidirect
7. C₁₁×#2108	C₂	semidirect
18. #10622514	C₂²	semidirect
21. C₁₁×#346	C₂²	semidirect
22. C₄×C₁₁×C₁₆	C₂²	semidirect
23. #10622146	C₂²	semidirect
24. #10622146	C₂²	semidirect
25. #10622101	C₂²	semidirect
93. #2108	D₁₁	semidirect
131. #346	C₂×D₁₁	semidirect
132. C₄×C₁₆	C₂×D₁₁	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
#13081718	2
#13077520	2
#13070459	2
#13070454	2
#13070382	2
C₂×#10622146	2
C₁₁×#2108	2
#33442	11