Subgroups — #14646902

Order 2816.

394 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068788	C₂	1	1	yes	maximal, characteristic
2	#13067364	C₂	1	1	yes	maximal, characteristic
3	#13067045	C₂	1	2	yes	maximal
4	#13066513	C₂	1	2	yes	maximal
5	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
7	C₈×Q₈×C₁₁	—	2	1	no	—
8	C₈×Q₈×C₁₁	—	2	1	no	—
9	C₈×Q₈×C₁₁	C₄	1	2	yes	—
10	C₈×Q₈×C₁₁	C₄	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
12	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	—	2	1	no	—
14	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
15	C₂×#66883	—	2	1	no	—
16	C₂×#66883	—	2	1	no	—
17	#10622538	C₂²	1	2	yes	—
18	#10622537	C₂²	1	2	yes	—
19	Q₈⋊(C₁₁⋊C₈)	—	2	4	no	—
20	#10622096	—	2	1	no	—
21	#10622095	—	2	1	no	—
22	C₂²×Q₈×C₁₁	Q₈	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	—	2	1	no	—
24	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
26	C₄×Q₈×C₁₁	—	2	1	no	—
27	C₄×Q₈×C₁₁	—	2	1	no	—
28	C₄×Q₈×C₁₁	C₂×C₄	1	2	yes	—
29	C₄×Q₈×C₁₁	D₄	1	2	yes	—
30	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
31	C₂×C₁₁×C₄⋊C₄	Q₈	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	—	2	1	no	—
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₂×#4318	—	2	2	no	—
35	C₁₁×C₄⋊C₈	—	2	2	no	—
36	C₁₁×C₄⋊C₈	—	2	2	no	—
37	C₁₁×C₄⋊C₈	—	2	1	no	—
38	C₁₁×C₄⋊C₈	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₁	—	2	2	no	—
40	C₄×C₈×C₁₁	—	2	2	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	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
46	#66883	—	4	2	no	—
47	#66883	—	4	2	no	—
48	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
49	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
50	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
51	C₄×C₁₁⋊C₈	—	2	2	no	—
52	#8659	—	11	1	no	maximal, Sylow
53	C₂×Q₈×C₁₁	—	2	4	no	—
54	C₂×Q₈×C₁₁	—	2	1	no	—
55	C₂×Q₈×C₁₁	C₄⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	—	2	1	no	—
57	C₂²×C₄×C₁₁	—	2	1	no	—
58	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
60	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
61	C₂×C₈×C₁₁	—	2	2	no	—
62	C₂×C₈×C₁₁	—	2	1	no	—
63	C₂×C₈×C₁₁	—	2	1	no	—
64	C₂×C₈×C₁₁	—	4	1	no	—
65	C₂×C₈×C₁₁	—	4	1	no	—
66	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
71	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
72	C₁₁×C₄⋊C₄	—	2	2	no	—
73	C₁₁×C₄⋊C₄	—	2	2	no	—
74	C₁₁×C₄⋊C₄	—	2	1	no	—
75	C₁₁×C₄⋊C₄	C₄⋊C₄	1	2	yes	—
76	C₄²×C₁₁	—	2	2	no	—
77	C₄²×C₁₁	—	2	2	no	—
78	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
79	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₄²×C₁₁	#41	1	1	yes	characteristic
82	#4318	—	4	2	no	—
83	#4318	—	4	2	no	—
84	C₂×C₁₁⋊C₈	—	4	2	no	—
85	C₂×C₁₁⋊C₈	—	4	2	no	—
86	C₂×C₈×Q₈	D₁₁	1	1	yes	characteristic
87	#1848	—	11	1	no	—
88	#1564	—	11	1	no	—
89	#1487	—	11	2	no	—
90	#1301	—	11	2	no	—
91	C₂³×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
92	Q₈×C₁₁	—	2	4	no	—
93	Q₈×C₁₁	—	2	2	no	—
94	Q₈×C₁₁	#108	1	4	yes	complemented
95	C₂×C₄×C₁₁	—	2	4	no	—
96	C₂×C₄×C₁₁	—	2	2	no	—
97	C₂×C₄×C₁₁	—	2	2	no	—
98	C₂×C₄×C₁₁	—	2	2	no	—
99	C₂×C₄×C₁₁	—	4	1	no	—
100	C₂×C₄×C₁₁	—	4	2	no	—
101	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
104	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
105	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
106	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
107	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
109	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
110	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
111	C₈×C₁₁	—	2	1	no	—
112	C₈×C₁₁	—	2	1	no	—
113	C₈×C₁₁	—	4	2	no	—
114	C₈×C₁₁	#103	1	2	yes	—
115	C₈×C₁₁	#103	1	2	yes	—
116	C₁₁⋊C₈	—	8	2	no	—
117	C₁₁⋊C₈	—	8	2	no	—
118	C₂×C₄×Q₈	C₂×D₁₁	1	1	yes	characteristic
119	C₈×Q₈	—	2	1	no	—
120	C₈×Q₈	—	2	1	no	—
121	C₈×Q₈	Dic₁₁	1	2	yes	—
122	C₈×Q₈	Dic₁₁	1	2	yes	—
123	#431	—	11	2	no	—
124	C₂×#108	—	22	1	no	—
125	C₂×#108	—	22	1	no	—
126	#423	—	11	2	no	—
127	C₂×C₄⋊C₈	—	2	1	no	—
128	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
129	C₂×C₄×C₈	—	2	1	no	—
130	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
131	#335	—	22	1	no	—
132	#334	—	22	1	no	—
133	Q₈⋊C₈	—	22	4	no	—
134	C₂²×C₁₁	—	2	1	no	—
135	C₂²×C₁₁	—	2	1	no	—
136	C₂²×C₁₁	#380	1	1	yes	characteristic
137	C₂²×C₁₁	#475	1	1	yes	characteristic
138	C₂²×C₁₁	#477	1	1	yes	characteristic
139	C₄×C₁₁	—	2	4	no	—
140	C₄×C₁₁	—	2	1	no	—
141	C₄×C₁₁	—	2	1	no	—
142	C₄×C₁₁	—	2	1	no	—
143	C₄×C₁₁	—	4	2	no	—
144	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
145	C₄×C₁₁	#417	1	1	yes	characteristic
146	C₄×C₁₁	C₂×#108	1	2	yes	—
147	C₄×C₁₁	#460	1	1	yes	characteristic
148	C₄×C₁₁	#462	1	1	yes	characteristic
149	C₂²×Q₈	Dic₂₂	1	1	yes	characteristic
150	C₂×M₁₆	—	22	2	no	—
151	C₂²×C₈	—	2	1	no	—
152	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
153	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
154	C₄×Q₈	—	2	1	no	—
155	C₄×Q₈	—	2	1	no	—
156	C₄×Q₈	D₄₄	1	2	yes	—
157	C₄×Q₈	C₂×Dic₁₁	1	2	yes	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	Dic₂₂	1	1	yes	characteristic
160	C₂×C₄²	—	2	1	no	—
161	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
162	#108	—	44	2	no	—
163	#108	—	44	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	—	2	2	no	—
166	C₄⋊C₈	—	2	1	no	—
167	C₄⋊C₈	—	22	2	no	—
168	C₄⋊C₈	—	22	2	no	—
169	C₄⋊C₈	—	22	2	no	—
170	C₄⋊C₈	C₂×Dic₁₁	1	2	yes	—
171	C₂²⋊C₈	—	22	2	no	—
172	C₄×C₈	—	2	2	no	—
173	C₄×C₈	—	2	2	no	—
174	C₄×C₈	—	22	2	no	—
175	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
176	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
177	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
178	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
179	C₂×C₁₁	—	2	1	no	—
180	C₂×C₁₁	—	2	1	no	—
181	C₂×C₁₁	#1803	1	1	yes	characteristic
182	C₂×C₁₁	#1810	1	1	yes	characteristic
183	C₂×C₁₁	#1814	1	1	yes	characteristic
184	C₂×Q₈	—	2	4	no	—
185	C₂×Q₈	—	2	1	no	—
186	C₂×Q₈	C₄⋊Dic₁₁	1	2	yes	—
187	C₂²×C₄	—	2	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
190	C₂²×C₄	#4339	1	1	yes	characteristic
191	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
192	M₁₆	—	44	2	no	—
193	M₁₆	—	44	2	no	—
194	C₂×C₈	—	2	1	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	4	1	no	—
198	C₂×C₈	—	4	1	no	—
199	C₂×C₈	—	44	2	no	—
200	C₂×C₈	—	44	2	no	—
201	C₂×C₈	#4325	1	2	yes	—
202	C₂×C₈	#4326	1	2	yes	—
203	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
204	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
205	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
206	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
207	C₄⋊C₄	—	2	1	no	—
208	C₄⋊C₄	—	2	2	no	—
209	C₄⋊C₄	—	2	2	no	—
210	C₄⋊C₄	C₄⋊Dic₁₁	1	2	yes	—
211	C₄²	—	2	2	no	—
212	C₄²	—	2	2	no	—
213	C₄²	C₂×D₄₄	1	1	yes	characteristic
214	C₄²	#4339	1	1	yes	characteristic
215	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
216	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
217	C₁₁	#8659	1	1	yes	characteristic, complemented, Sylow
218	C₂³	#66977	1	1	yes	characteristic
219	Q₈	—	2	4	no	—
220	Q₈	—	2	2	no	—
221	Q₈	#66883	1	4	yes	complemented
222	C₂×C₄	—	2	4	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	—	2	2	no	—
226	C₂×C₄	—	4	1	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	#66977	1	1	yes	characteristic
229	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
230	C₂×C₄	#66979	1	1	yes	characteristic
231	C₂×C₄	#66983	1	1	yes	characteristic
232	C₂×C₄	#66983	1	1	yes	characteristic
233	C₂×C₄	C₂×#4325	1	1	yes	characteristic
234	C₂×C₄	C₂×#4326	1	1	yes	characteristic
235	C₂×C₄	#67002	1	1	yes	characteristic
236	C₂×C₄	#67004	1	1	yes	characteristic
237	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
238	C₈	—	2	1	no	—
239	C₈	—	2	1	no	—
240	C₈	—	4	2	no	—
241	C₈	—	88	2	no	—
242	C₈	—	88	2	no	—
243	C₈	#66899	1	2	yes	—
244	C₈	#66899	1	2	yes	—
245	C₂²	—	2	1	no	—
246	C₂²	—	2	1	no	—
247	C₂²	#10622633	1	1	yes	characteristic
248	C₂²	#10622634	1	1	yes	characteristic
249	C₂²	#10622825	1	1	yes	characteristic
250	C₄	—	2	4	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	—	2	1	no	—
254	C₄	—	4	2	no	—
255	C₄	#10622640	1	1	yes	characteristic
256	C₄	#10622644	1	1	yes	characteristic
257	C₄	C₂×#66883	1	2	yes	—
258	C₄	C₂×#66899	1	1	yes	characteristic
259	C₄	#10622845	1	1	yes	characteristic
260	C₂	—	2	1	no	—
261	C₂	—	2	1	no	—
262	C₂	#13068621	1	1	yes	characteristic
263	C₂	#13068654	1	1	yes	characteristic
264	C₂	#13068670	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#66983
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₈×Q₈×C₁₁	C₂
socle	C₂²×C₁₁	#380
prime radical	C₂³×C₁₁	C₂²⋊Q₈
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₈×Q₈	D₁₁
hypocenter	C₁₁	#8659
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
94. Q₈×C₁₁	#108	semidirect
217. C₁₁	#8659	semidirect
221. Q₈	#66883	semidirect

Maximal subgroups

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

subgroup	index
#13068788	2
#13067364	2
#13067045	2
#13066513	2
C₂×C₈×Q₈×C₁₁	2
#8659	11