Subgroups — #14640383

Order 2816.

304 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068733	C₂	1	1	yes	maximal, characteristic
2	#13068469	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1767	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₁×C₄⋊C₈	—	2	1	no	—
5	C₂×C₁₁×#97	—	2	1	no	—
6	C₄³×C₁₁	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
8	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	2	yes	—
9	C₂×#66867	—	2	1	no	—
10	C₁₁×#336	C₄	1	2	yes	—
11	#10622162	—	2	1	no	—
12	#10622162	—	2	1	no	—
13	#10622162	C₄	1	2	yes	—
14	C₂²×C₈×C₁₁	—	2	2	no	—
15	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
20	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
22	C₂²×C₁₁⋊C₈	—	2	2	no	—
23	C₂²×C₁₁⋊C₈	—	2	2	no	—
24	C₁₁×C₄⋊C₈	—	2	4	no	—
25	C₁₁×#97	—	4	1	no	—
26	C₁₁×#97	—	4	1	no	—
27	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
28	C₄⋊(C₁₁⋊C₈)	—	4	2	no	—
29	#66867	—	4	1	no	—
30	#66867	—	4	1	no	—
31	#7049	—	11	1	no	maximal, Sylow
32	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₁	—	2	4	no	—
40	C₂×C₈×C₁₁	—	4	2	no	—
41	C₂×C₈×C₁₁	—	4	2	no	—
42	C₄²×C₁₁	—	2	1	no	—
43	C₄²×C₁₁	—	2	1	no	—
44	C₄²×C₁₁	—	2	2	no	—
45	C₄²×C₁₁	—	2	2	no	—
46	C₄²×C₁₁	—	4	1	no	—
47	C₄²×C₁₁	—	4	1	no	—
48	C₄²×C₁₁	—	4	1	no	—
49	C₄²×C₁₁	D₈	1	1	yes	characteristic
50	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
51	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
52	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
53	C₂×C₁₁⋊C₈	—	2	4	no	—
54	C₂×C₁₁⋊C₈	—	4	2	no	—
55	C₂×C₁₁⋊C₈	—	4	2	no	—
56	C₂×C₁₁⋊C₈	—	4	2	no	—
57	C₂×C₁₁⋊C₈	—	4	2	no	—
58	C₂×C₁₁⋊C₈	—	4	2	no	—
59	#1831	—	11	1	no	—
60	#1767	—	11	1	no	—
61	#1767	D₁₁	1	1	yes	characteristic
62	C₂³×C₁₁	#95	1	1	yes	characteristic
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	2	1	no	—
65	C₂×C₄×C₁₁	—	2	1	no	—
66	C₂×C₄×C₁₁	—	2	1	no	—
67	C₂×C₄×C₁₁	—	2	1	no	—
68	C₂×C₄×C₁₁	—	2	1	no	—
69	C₂×C₄×C₁₁	—	2	1	no	—
70	C₂×C₄×C₁₁	—	2	1	no	—
71	C₂×C₄×C₁₁	—	2	1	no	—
72	C₂×C₄×C₁₁	—	2	1	no	—
73	C₂×C₄×C₁₁	—	2	1	no	—
74	C₂×C₄×C₁₁	—	2	1	no	—
75	C₂×C₄×C₁₁	—	2	1	no	—
76	C₂×C₄×C₁₁	—	2	1	no	—
77	C₂×C₄×C₁₁	—	2	1	no	—
78	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
80	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
81	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
82	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
83	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
84	C₂×C₄×C₁₁	#104	1	2	yes	—
85	C₂×C₄×C₁₁	#104	1	2	yes	—
86	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
88	C₈×C₁₁	—	4	4	no	—
89	C₁₁⋊C₈	—	4	4	no	—
90	C₁₁⋊C₈	—	8	2	no	—
91	C₂×C₄⋊C₈	—	2	1	no	—
92	C₂×C₄⋊C₈	—	11	2	no	—
93	C₂×C₄⋊C₈	—	22	1	no	—
94	C₂×#97	—	2	1	no	—
95	C₂×#97	—	22	1	no	—
96	C₄³	C₂×D₁₁	1	1	yes	characteristic
97	#336	—	11	2	no	—
98	#336	—	22	1	no	—
99	#336	—	22	1	no	—
100	#336	Dic₁₁	1	2	yes	—
101	C₂²×C₁₁	#338	1	1	yes	characteristic
102	C₂²×C₁₁	#339	1	1	yes	characteristic
103	C₂²×C₁₁	#339	1	1	yes	characteristic
104	C₂²×C₁₁	#340	1	1	yes	characteristic
105	C₂²×C₁₁	#343	1	1	yes	characteristic
106	C₂²×C₁₁	#344	1	1	yes	characteristic
107	C₂²×C₁₁	#344	1	1	yes	characteristic
108	C₄×C₁₁	—	2	1	no	—
109	C₄×C₁₁	—	2	1	no	—
110	C₄×C₁₁	—	2	1	no	—
111	C₄×C₁₁	—	2	1	no	—
112	C₄×C₁₁	—	2	1	no	—
113	C₄×C₁₁	—	2	1	no	—
114	C₄×C₁₁	—	4	1	no	—
115	C₄×C₁₁	—	4	1	no	—
116	C₄×C₁₁	—	4	1	no	—
117	C₄×C₁₁	#329	1	2	yes	—
118	C₄×C₁₁	#330	1	2	yes	—
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	22	2	no	—
121	C₂²×C₈	—	22	2	no	—
122	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
123	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
124	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
125	C₂×C₄²	D₄₄	1	1	yes	characteristic
126	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
127	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
128	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
129	C₄⋊C₈	—	2	4	no	—
130	C₄⋊C₈	—	22	4	no	—
131	C₄⋊C₈	—	44	2	no	—
132	#97	—	4	1	no	—
133	#97	—	4	1	no	—
134	#97	—	44	1	no	—
135	#97	—	44	1	no	—
136	C₂×C₁₁	#1291	1	1	yes	characteristic
137	C₂×C₁₁	#1291	1	1	yes	characteristic
138	C₂×C₁₁	#1292	1	1	yes	characteristic
139	C₂×C₁₁	#1295	1	1	yes	characteristic
140	C₂×C₁₁	#1303	1	1	yes	characteristic
141	C₂×C₁₁	#1303	1	1	yes	characteristic
142	C₂×C₁₁	#1307	1	1	yes	characteristic
143	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
144	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
145	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
146	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
147	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
148	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
149	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
150	C₂×C₈	—	2	4	no	—
151	C₂×C₈	—	4	2	no	—
152	C₂×C₈	—	4	2	no	—
153	C₂×C₈	—	22	4	no	—
154	C₂×C₈	—	44	2	no	—
155	C₂×C₈	—	44	2	no	—
156	C₂×C₈	—	44	2	no	—
157	C₂×C₈	—	44	2	no	—
158	C₂×C₈	—	44	2	no	—
159	C₄²	—	2	2	no	—
160	C₄²	—	2	1	no	—
161	C₄²	—	2	1	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	4	1	no	—
164	C₄²	—	4	1	no	—
165	C₄²	—	4	1	no	—
166	C₄²	#4323	1	1	yes	characteristic
167	C₄²	#4324	1	1	yes	characteristic
168	C₄²	#4325	1	1	yes	characteristic
169	C₄²	#4326	1	1	yes	characteristic
170	C₁₁	#7049	1	1	yes	characteristic, complemented, Sylow
171	C₂³	C₁₁⋊#95	1	1	yes	characteristic
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	1	no	—
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	#66869	1	2	yes	—
188	C₂×C₄	#66871	1	1	yes	characteristic
189	C₂×C₄	#66872	1	1	yes	characteristic
190	C₂×C₄	#66873	1	1	yes	characteristic
191	C₂×C₄	#66874	1	1	yes	characteristic
192	C₂×C₄	#66887	1	1	yes	characteristic
193	C₂×C₄	#66888	1	1	yes	characteristic
194	C₂×C₄	#66889	1	2	yes	—
195	C₂×C₄	#66896	1	1	yes	characteristic
196	C₂×C₄	#66899	1	1	yes	characteristic
197	C₈	—	4	4	no	—
198	C₈	—	44	4	no	—
199	C₈	—	88	2	no	—
200	C₂²	#10622161	1	1	yes	characteristic
201	C₂²	#10622167	1	1	yes	characteristic
202	C₂²	#10622171	1	1	yes	characteristic
203	C₂²	#10622192	1	1	yes	characteristic
204	C₂²	#10622193	1	1	yes	characteristic
205	C₂²	#10622194	1	1	yes	characteristic
206	C₂²	C₁₁⋊#338	1	1	yes	characteristic
207	C₄	—	2	1	no	—
208	C₄	—	2	1	no	—
209	C₄	—	2	1	no	—
210	C₄	—	2	1	no	—
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	4	1	no	—
214	C₄	—	4	1	no	—
215	C₄	—	4	1	no	—
216	C₄	#10622102	1	2	yes	—
217	C₄	#10622103	1	2	yes	—
218	C₂	#13066488	1	1	yes	characteristic
219	C₂	#13066489	1	1	yes	characteristic
220	C₂	#13066490	1	1	yes	characteristic
221	C₂	#13066498	1	1	yes	characteristic
222	C₂	#13066517	1	1	yes	characteristic
223	C₂	#13066519	1	1	yes	characteristic
224	C₂	#13066526	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₁₁⋊#95
commutator	C₂²×C₄×C₁₁	C₄²
Frattini	C₄³	C₂×D₁₁
Fitting	C₁₁×#1767	C₂
socle, prime radical	C₂³×C₁₁	#95
cosocle	C₄³×C₁₁	C₂²
hypercenter	#1767	D₁₁
hypocenter	C₁₁	#7049
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1767

Complements

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

N	H ≅ G/N	type
170. C₁₁	#7049	semidirect

Maximal subgroups

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

subgroup	index
#13068733	2
#13068469	2
C₁₁×#1767	2
#7049	11