Subgroups — #14652831

Order 2816.

498 conjugacy classes of subgroups.

The subgroup lattice has 250 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068768	C₂	1	1	yes	maximal, characteristic
2	C₄×C₄⋊(C₁₁⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622184	C₂	1	2	yes	maximal
4	C₂×#10622185	C₂	1	2	yes	maximal
5	C₁₁×#2862	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
8	C₁₁×#391	—	2	1	no	—
9	C₁₁×#391	—	2	1	no	—
10	C₁₁×#391	C₄	1	4	yes	—
11	C₁₁×#382	—	2	2	no	—
12	C₄³×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄×C₁₁⋊C₈	—	2	1	no	—
17	#10622185	—	2	4	no	—
18	#10622184	—	2	4	no	—
19	#10622162	—	2	1	no	—
20	C₂²×Q₈×C₁₁	—	2	1	no	—
21	C₂²×Q₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₁₁×C₄⋊Q₈	—	2	2	no	—
23	C₁₁×C₄⋊Q₈	—	2	2	no	—
24	C₁₁×C₄⋊Q₈	—	2	2	no	—
25	C₁₁×C₄⋊Q₈	—	2	2	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
29	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
31	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	D₄	1	2	yes	—
34	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
35	C₂²×C₁₁⋊C₈	—	2	2	no	—
36	C₂²×C₁₁⋊C₈	—	2	2	no	—
37	C₁₁×#95	—	2	4	no	—
38	C₁₁×#95	—	2	4	no	—
39	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
42	C₄⋊(C₁₁⋊C₈)	—	4	4	no	—
43	C₄⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
44	C₄×C₁₁⋊C₈	—	4	2	no	—
45	#9697	—	11	1	no	maximal, Sylow
46	C₂×Q₈×C₁₁	—	2	4	no	—
47	C₂×Q₈×C₁₁	—	4	4	no	—
48	C₂×Q₈×C₁₁	—	4	2	no	—
49	C₂×Q₈×C₁₁	—	4	2	no	—
50	C₂×Q₈×C₁₁	—	4	1	no	—
51	C₂×Q₈×C₁₁	—	4	1	no	—
52	C₂²×C₄×C₁₁	—	2	2	no	—
53	C₂²×C₄×C₁₁	—	2	2	no	—
54	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
56	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
57	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₁₁×C₄⋊C₄	—	2	4	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₁₁×C₄⋊C₄	—	4	1	no	—
62	C₁₁×C₄⋊C₄	—	4	1	no	—
63	C₁₁×C₄⋊C₄	—	4	1	no	—
64	C₁₁×C₄⋊C₄	—	4	1	no	—
65	C₄²×C₁₁	—	2	2	no	—
66	C₄²×C₁₁	—	2	1	no	—
67	C₄²×C₁₁	—	2	1	no	—
68	C₄²×C₁₁	—	4	2	no	—
69	C₄²×C₁₁	SD₁₆	1	4	yes	—
70	C₄²×C₁₁	Q₁₆	1	4	yes	—
71	C₄²×C₁₁	C₂×D₄	1	2	yes	—
72	C₄²×C₁₁	#41	1	2	yes	—
73	C₂×C₁₁⋊C₈	—	2	4	no	—
74	C₂×C₁₁⋊C₈	—	4	2	no	—
75	C₂×C₁₁⋊C₈	—	4	4	no	—
76	C₂×C₁₁⋊C₈	—	4	2	no	—
77	C₂×C₁₁⋊C₈	—	4	2	no	—
78	#2862	D₁₁	1	1	yes	characteristic
79	#1842	—	11	1	no	—
80	C₄×C₄⋊C₈	—	11	1	no	—
81	C₂×#333	—	11	2	no	—
82	C₂×#332	—	11	2	no	—
83	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
84	Q₈×C₁₁	—	8	4	no	—
85	Q₈×C₁₁	—	8	2	no	—
86	Q₈×C₁₁	—	8	2	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	2	2	no	—
89	C₂×C₄×C₁₁	—	2	2	no	—
90	C₂×C₄×C₁₁	—	2	2	no	—
91	C₂×C₄×C₁₁	—	2	2	no	—
92	C₂×C₄×C₁₁	—	4	2	no	—
93	C₂×C₄×C₁₁	—	4	2	no	—
94	C₂×C₄×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	4	2	no	—
96	C₂×C₄×C₁₁	—	4	2	no	—
97	C₂×C₄×C₁₁	#103	1	4	yes	—
98	C₂×C₄×C₁₁	#103	1	4	yes	—
99	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
100	C₂×C₄×C₁₁	#121	1	2	yes	—
101	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
102	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
104	C₂×C₄×C₁₁	C₂×Q₁₆	1	2	yes	—
105	C₂×C₄×C₁₁	#135	1	2	yes	—
106	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
107	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
108	C₁₁⋊C₈	—	4	4	no	—
109	C₁₁⋊C₈	—	8	2	no	—
110	C₂×C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
111	C₂×C₄⋊Q₈	C₂×D₁₁	1	1	yes	characteristic
112	C₂×C₄⋊C₈	—	11	2	no	—
113	C₂×C₄⋊C₈	—	11	2	no	—
114	C₂×C₄⋊C₈	—	22	2	no	—
115	C₂×C₄×C₈	—	22	1	no	—
116	#391	—	2	1	no	—
117	#391	—	2	1	no	—
118	#391	Dic₁₁	1	4	yes	—
119	#382	—	2	2	no	—
120	C₄³	C₂×D₁₁	1	1	yes	characteristic
121	#336	—	22	1	no	—
122	#333	—	22	4	no	—
123	#332	—	22	4	no	—
124	C₂²×C₁₁	#390	1	1	yes	characteristic
125	C₂²×C₁₁	#413	1	2	yes	—
126	C₂²×C₁₁	C₂×#103	1	2	yes	—
127	C₂²×C₁₁	#416	1	1	yes	characteristic
128	C₂²×C₁₁	#417	1	1	yes	characteristic
129	C₄×C₁₁	—	2	4	no	—
130	C₄×C₁₁	—	2	4	no	—
131	C₄×C₁₁	—	2	2	no	—
132	C₄×C₁₁	—	8	2	no	—
133	C₄×C₁₁	—	8	2	no	—
134	C₄×C₁₁	#463	1	2	yes	—
135	C₄×C₁₁	#464	1	2	yes	—
136	C₄×C₁₁	#487	1	2	yes	—
137	C₄×C₁₁	#492	1	1	yes	characteristic
138	C₄×C₁₁	#494	1	1	yes	characteristic
139	C₂²×Q₈	—	2	1	no	—
140	C₂²×Q₈	C₂×Dic₁₁	1	2	yes	—
141	C₂²×C₈	—	22	2	no	—
142	C₂²×C₈	—	22	2	no	—
143	C₄⋊Q₈	—	2	2	no	—
144	C₄⋊Q₈	—	2	2	no	—
145	C₄⋊Q₈	—	2	2	no	—
146	C₄⋊Q₈	—	2	2	no	—
147	C₂×C₄⋊C₄	—	2	1	no	—
148	C₂×C₄⋊C₄	—	2	1	no	—
149	C₂×C₄⋊C₄	—	2	1	no	—
150	C₂×C₄⋊C₄	C₂×Dic₁₁	1	2	yes	—
151	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
152	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
153	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
154	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
155	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
156	C₄⋊C₈	—	11	4	no	—
157	C₄⋊C₈	—	22	2	no	—
158	C₄⋊C₈	—	22	2	no	—
159	C₄⋊C₈	—	22	2	no	—
160	C₄⋊C₈	—	44	4	no	—
161	C₄×C₈	—	44	2	no	—
162	#95	—	2	4	no	—
163	#95	—	2	4	no	—
164	C₂×C₁₁	#1542	1	2	yes	—
165	C₂×C₁₁	#1550	1	2	yes	—
166	C₂×C₁₁	#1956	1	1	yes	characteristic
167	C₂×C₁₁	#1967	1	1	yes	characteristic
168	C₂×C₁₁	#1983	1	1	yes	characteristic
169	C₂×Q₈	—	2	4	no	—
170	C₂×Q₈	—	4	4	no	—
171	C₂×Q₈	—	4	2	no	—
172	C₂×Q₈	—	4	1	no	—
173	C₂×Q₈	—	4	2	no	—
174	C₂×Q₈	—	4	1	no	—
175	C₂²×C₄	—	2	2	no	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
178	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
179	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
180	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
182	C₂×C₈	—	22	4	no	—
183	C₂×C₈	—	44	2	no	—
184	C₂×C₈	—	44	2	no	—
185	C₂×C₈	—	44	2	no	—
186	C₂×C₈	—	44	4	no	—
187	C₄⋊C₄	—	2	4	no	—
188	C₄⋊C₄	—	4	1	no	—
189	C₄⋊C₄	—	4	1	no	—
190	C₄⋊C₄	—	4	2	no	—
191	C₄⋊C₄	—	4	1	no	—
192	C₄⋊C₄	—	4	1	no	—
193	C₄²	—	2	1	no	—
194	C₄²	—	2	2	no	—
195	C₄²	—	2	1	no	—
196	C₄²	—	4	2	no	—
197	C₄²	#4325	1	4	yes	—
198	C₄²	#4326	1	4	yes	—
199	C₄²	D₄×D₁₁	1	2	yes	—
200	C₄²	#4341	1	2	yes	—
201	C₁₁	#9697	1	1	yes	characteristic, complemented, Sylow
202	C₂³	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
203	Q₈	—	8	4	no	—
204	Q₈	—	8	2	no	—
205	Q₈	—	8	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	4	2	no	—
212	C₂×C₄	—	4	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	4	no	—
216	C₂×C₄	#66899	1	4	yes	—
217	C₂×C₄	#66899	1	4	yes	—
218	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
219	C₂×C₄	#66989	1	1	yes	characteristic
220	C₂×C₄	#66991	1	2	yes	—
221	C₂×C₄	#66993	1	1	yes	characteristic
222	C₂×C₄	C₂×#4325	1	2	yes	—
223	C₂×C₄	C₂×#4326	1	2	yes	—
224	C₂×C₄	#67002	1	1	yes	characteristic
225	C₂×C₄	#67003	1	2	yes	—
226	C₂×C₄	#67004	1	1	yes	characteristic
227	C₈	—	44	4	no	—
228	C₈	—	88	2	no	—
229	C₂²	#10622834	1	1	yes	characteristic
230	C₂²	C₂×#66899	1	2	yes	—
231	C₂²	#10622845	1	1	yes	characteristic
232	C₂²	#10622846	1	1	yes	characteristic
233	C₂²	#10622850	1	2	yes	—
234	C₄	—	2	4	no	—
235	C₄	—	2	4	no	—
236	C₄	—	2	2	no	—
237	C₄	—	8	2	no	—
238	C₄	—	8	2	no	—
239	C₄	#10622667	1	2	yes	—
240	C₄	#10622670	1	2	yes	—
241	C₄	#10622694	1	2	yes	—
242	C₄	#10622698	1	1	yes	characteristic
243	C₄	#10622705	1	1	yes	characteristic
244	C₂	#13067273	1	2	yes	—
245	C₂	#13067306	1	2	yes	—
246	C₂	#13069419	1	1	yes	characteristic
247	C₂	#13069466	1	1	yes	characteristic
248	C₂	#13069549	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2862	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2862	D₁₁
hypocenter	C₁₁	#9697
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2862

Complements

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

N	H ≅ G/N	type
201. C₁₁	#9697	semidirect

Maximal subgroups

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

subgroup	index
#13068768	2
C₄×C₄⋊(C₁₁⋊C₈)	2
C₂×#10622184	2
C₂×#10622185	2
C₁₁×#2862	2
#9697	11