Subgroups — #14658686

Order 2816.

350 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13069375	C₂	1	2	yes	maximal
2	#13069334	C₂	1	1	yes	maximal, characteristic
3	#13068776	C₂	1	1	yes	maximal, characteristic
4	#13066500	C₂	1	2	yes	maximal
5	C₁₁×#1277	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66882	—	2	1	no	—
9	C₂×#66882	—	2	1	no	—
10	C₂×#66882	—	2	2	no	—
11	C₂×Dic₁₁⋊C₈	—	2	1	no	—
12	#10622548	C₂²	1	2	yes	—
13	C₄×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	1	yes	characteristic
15	#10622189	—	2	2	no	—
16	#10622188	—	2	1	no	—
17	C₂²×C₈×C₁₁	—	2	2	no	—
18	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₁	—	2	2	no	—
22	C₂×C₄⋊Dic₁₁	—	2	2	no	—
23	C₂×C₄⋊Dic₁₁	—	2	2	no	—
24	C₂×C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₁	D₄	1	1	yes	characteristic
26	C₂×C₄×Dic₁₁	—	2	1	no	—
27	C₂²×C₁₁⋊C₈	—	2	1	no	—
28	C₁₁×C₄⋊C₈	—	2	2	no	—
29	C₁₁×C₄⋊C₈	Q₈	1	4	yes	—
30	C₄×C₈×C₁₁	—	2	2	no	—
31	C₁₁⋊#95	—	2	1	no	—
32	#66882	—	4	4	no	—
33	#66882	—	4	2	no	—
34	#66882	—	4	2	no	—
35	Dic₁₁⋊C₈	—	4	2	no	—
36	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
37	#10650	—	11	1	no	maximal, Sylow
38	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
41	C₂²×Dic₁₁	—	2	1	no	—
42	C₂²×Dic₁₁	—	2	1	no	—
43	C₂²×Dic₁₁	—	4	2	no	—
44	C₂×C₈×C₁₁	—	2	4	no	—
45	C₂×C₈×C₁₁	—	2	1	no	—
46	C₂×C₈×C₁₁	—	2	1	no	—
47	C₂×C₈×C₁₁	—	2	1	no	—
48	C₂×C₈×C₁₁	—	2	1	no	—
49	C₂×C₈×C₁₁	—	4	2	no	—
50	C₂×C₈×C₁₁	—	4	2	no	—
51	C₂×C₈×C₁₁	D₈	1	2	yes	—
52	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
53	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
54	C₄²×C₁₁	#41	1	2	yes	—
55	C₄⋊Dic₁₁	—	2	1	no	—
56	C₄⋊Dic₁₁	—	2	2	no	—
57	C₄⋊Dic₁₁	—	4	2	no	—
58	C₄⋊Dic₁₁	—	4	2	no	—
59	C₄⋊Dic₁₁	—	4	2	no	—
60	C₄⋊Dic₁₁	—	4	2	no	—
61	C₄⋊Dic₁₁	—	8	2	no	—
62	C₄⋊Dic₁₁	Q₁₆	1	2	yes	—
63	C₄×Dic₁₁	—	4	1	no	—
64	C₄×Dic₁₁	—	4	1	no	—
65	C₂×C₁₁⋊C₈	—	4	1	no	—
66	C₂×C₁₁⋊C₈	—	4	1	no	—
67	C₂×C₁₁⋊C₈	—	4	1	no	—
68	#1947	—	11	2	no	—
69	#1939	—	11	1	no	—
70	#1845	—	11	1	no	—
71	#1296	—	11	2	no	—
72	#1277	D₁₁	1	1	yes	characteristic
73	C₂³×C₁₁	#121	1	1	yes	characteristic
74	C₂×C₄×C₁₁	—	2	1	no	—
75	C₂×C₄×C₁₁	—	2	1	no	—
76	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
77	C₂×C₄×C₁₁	#123	1	1	yes	characteristic
78	C₂×C₄×C₁₁	#125	1	2	yes	—
79	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
83	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
84	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
85	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
86	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
87	C₂×Dic₁₁	—	2	2	no	—
88	C₂×Dic₁₁	—	4	1	no	—
89	C₂×Dic₁₁	—	4	1	no	—
90	C₂×Dic₁₁	—	4	1	no	—
91	C₂×Dic₁₁	—	4	1	no	—
92	C₂×Dic₁₁	—	4	1	no	—
93	C₂×Dic₁₁	—	8	2	no	—
94	C₂×Dic₁₁	—	8	2	no	—
95	C₂×Dic₁₁	—	8	2	no	—
96	C₈×C₁₁	—	2	2	no	—
97	C₈×C₁₁	—	2	2	no	—
98	C₈×C₁₁	—	4	4	no	—
99	C₁₁⋊C₈	—	8	1	no	—
100	C₂×#107	—	22	2	no	—
101	C₂×#107	—	22	1	no	—
102	C₂×#107	—	22	1	no	—
103	C₂×C₄⋊C₈	—	11	1	no	—
104	C₂×C₄⋊C₈	—	22	1	no	—
105	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
106	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
107	#384	—	11	2	no	—
108	C₄×C₄⋊C₄	—	11	1	no	—
109	#340	—	22	2	no	—
110	#336	—	22	1	no	—
111	C₂²×C₁₁	#398	1	1	yes	characteristic
112	C₂²×C₁₁	#459	1	1	yes	characteristic
113	C₂²×C₁₁	#462	1	1	yes	characteristic
114	C₂²×C₁₁	#467	1	1	yes	characteristic
115	C₂²×C₁₁	#469	1	1	yes	characteristic
116	C₂²×C₁₁	#472	1	1	yes	characteristic
117	C₂²×C₁₁	#473	1	1	yes	characteristic
118	C₄×C₁₁	—	2	2	no	—
119	C₄×C₁₁	#477	1	2	yes	—
120	C₄×C₁₁	#478	1	2	yes	—
121	C₄×C₁₁	#480	1	1	yes	characteristic
122	C₄×C₁₁	#484	1	1	yes	characteristic
123	C₄×C₁₁	#500	1	1	yes	characteristic
124	C₄×C₁₁	#501	1	1	yes	characteristic
125	Dic₁₁	—	4	2	no	—
126	Dic₁₁	—	8	1	no	—
127	Dic₁₁	—	16	2	no	—
128	C₂²×C₈	—	2	2	no	—
129	C₂²×C₈	—	22	1	no	—
130	C₂²×C₈	D₄₄	1	1	yes	characteristic
131	C₂²×C₈	D₄₄	1	1	yes	characteristic
132	C₂×C₄⋊C₄	—	11	1	no	—
133	C₂×C₄⋊C₄	—	11	1	no	—
134	C₂×C₄⋊C₄	—	22	2	no	—
135	C₂×C₄⋊C₄	—	22	2	no	—
136	C₂×C₄⋊C₄	—	22	2	no	—
137	C₂×C₄²	—	22	1	no	—
138	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
139	#107	—	44	4	no	—
140	#107	—	44	2	no	—
141	#107	—	44	2	no	—
142	C₄⋊C₈	—	2	2	no	—
143	C₄⋊C₈	—	22	2	no	—
144	C₄⋊C₈	—	44	2	no	—
145	C₄⋊C₈	Dic₂₂	1	4	yes	—
146	C₄×C₈	—	2	2	no	—
147	#95	—	22	1	no	—
148	C₂×C₁₁	#1669	1	1	yes	characteristic
149	C₂×C₁₁	#1676	1	1	yes	characteristic
150	C₂×C₁₁	#1687	1	1	yes	characteristic
151	C₂×C₁₁	#1694	1	1	yes	characteristic
152	C₂×C₁₁	#2083	1	1	yes	characteristic
153	C₂×C₁₁	#2087	1	1	yes	characteristic
154	C₂×C₁₁	#2089	1	1	yes	characteristic
155	C₂²×C₄	—	22	1	no	—
156	C₂²×C₄	—	22	1	no	—
157	C₂²×C₄	—	44	2	no	—
158	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
159	C₂²×C₄	D₄×D₁₁	1	1	yes	characteristic
160	C₂²×C₄	#4343	1	1	yes	characteristic
161	C₂×C₈	—	2	1	no	—
162	C₂×C₈	—	2	1	no	—
163	C₂×C₈	—	2	1	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	4	no	—
166	C₂×C₈	—	4	2	no	—
167	C₂×C₈	—	4	2	no	—
168	C₂×C₈	—	44	1	no	—
169	C₂×C₈	—	44	1	no	—
170	C₂×C₈	—	44	1	no	—
171	C₂×C₈	D₈₈	1	2	yes	—
172	C₂×C₈	Dic₄₄	1	2	yes	—
173	C₄⋊C₄	—	11	2	no	—
174	C₄⋊C₄	—	22	1	no	—
175	C₄⋊C₄	—	22	2	no	—
176	C₄⋊C₄	—	44	2	no	—
177	C₄⋊C₄	—	44	2	no	—
178	C₄⋊C₄	—	44	2	no	—
179	C₄⋊C₄	—	44	2	no	—
180	C₄⋊C₄	—	88	2	no	—
181	C₄²	—	44	1	no	—
182	C₄²	—	44	1	no	—
183	C₄²	C₂×Dic₂₂	1	2	yes	—
184	C₄²	#4341	1	2	yes	—
185	C₁₁	#10650	1	1	yes	characteristic, complemented, Sylow
186	C₂³	#66948	1	1	yes	characteristic
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	22	2	no	—
190	C₂×C₄	—	44	1	no	—
191	C₂×C₄	—	44	1	no	—
192	C₂×C₄	—	44	1	no	—
193	C₂×C₄	—	44	1	no	—
194	C₂×C₄	—	44	1	no	—
195	C₂×C₄	—	88	2	no	—
196	C₂×C₄	—	88	2	no	—
197	C₂×C₄	—	88	2	no	—
198	C₂×C₄	#66922	1	1	yes	characteristic
199	C₂×C₄	#66931	1	2	yes	—
200	C₂×C₄	#66939	1	1	yes	characteristic
201	C₂×C₄	#66943	1	2	yes	—
202	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
203	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
204	C₂×C₄	#66961	1	1	yes	characteristic
205	C₂×C₄	#66962	1	1	yes	characteristic
206	C₂×C₄	#66965	1	1	yes	characteristic
207	C₂×C₄	#66967	1	2	yes	—
208	C₂×C₄	Q₁₆×D₁₁	1	1	yes	characteristic
209	C₈	—	2	2	no	—
210	C₈	—	2	2	no	—
211	C₈	—	4	4	no	—
212	C₈	—	88	1	no	—
213	C₂²	#10622274	1	1	yes	characteristic
214	C₂²	#10622456	1	1	yes	characteristic
215	C₂²	#10622462	1	1	yes	characteristic
216	C₂²	#10622478	1	1	yes	characteristic
217	C₂²	#10622500	1	1	yes	characteristic
218	C₂²	#10622509	1	1	yes	characteristic
219	C₂²	#10622510	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	44	2	no	—
222	C₄	—	88	1	no	—
223	C₄	—	176	2	no	—
224	C₄	#10622295	1	1	yes	characteristic
225	C₄	#10622315	1	1	yes	characteristic
226	C₄	#10622335	1	1	yes	characteristic
227	C₄	#10622349	1	1	yes	characteristic
228	C₄	#10622379	1	2	yes	—
229	C₄	#10622407	1	2	yes	—
230	C₂	#13067982	1	1	yes	characteristic
231	C₂	#13068021	1	1	yes	characteristic
232	C₂	#13068096	1	1	yes	characteristic
233	C₂	#13068135	1	1	yes	characteristic
234	C₂	#13070089	1	1	yes	characteristic
235	C₂	#13070111	1	1	yes	characteristic
236	C₂	#13070123	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66948
commutator, cosocle	C₂×C₄²×C₁₁	C₂³
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1277	C₂
socle, prime radical	C₂³×C₁₁	#121
hypercenter	#1277	D₁₁
hypocenter	C₁₁	#10650
LCS	G ▷ C₂×C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
185. C₁₁	#10650	semidirect

Maximal subgroups

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

subgroup	index
#13069375	2
#13069334	2
#13068776	2
#13066500	2
C₁₁×#1277	2
#10650	11