Subgroups — #14673129

Order 2816.

462 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	C₂×#10622312	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622130	C₂	1	2	yes	maximal
3	C₂×#10622130	C₂	1	2	yes	maximal
4	#13066694	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1942	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₄₄	—	2	1	no	—
7	C₂²×Dic₄₄	C₂²	1	2	yes	—
8	C₂×#66922	—	2	1	no	—
9	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
10	C₂×C₁₁×#107	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#389	—	2	1	no	—
13	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
14	#10622312	—	2	4	no	—
15	C₁₁×#340	—	2	1	no	—
16	#10622130	—	2	4	no	—
17	#10622130	—	2	4	no	—
18	C₂²×Dic₂₂	—	2	2	no	—
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
22	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
23	C₂×C₁₁×C₄⋊C₄	—	4	1	no	—
24	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
25	C₂×C₄⋊Dic₁₁	—	4	1	no	—
26	C₂×C₄⋊Dic₁₁	—	4	1	no	—
27	C₂×Dic₄₄	—	2	2	no	—
28	C₂×Dic₄₄	—	2	2	no	—
29	C₂×Dic₄₄	—	2	2	no	—
30	C₂×Dic₄₄	—	2	2	no	—
31	C₂×Dic₄₄	—	2	4	no	—
32	C₂×Dic₄₄	—	2	2	no	—
33	C₂×Dic₄₄	—	4	2	no	—
34	C₂×Dic₄₄	—	4	2	no	—
35	C₂×Dic₄₄	D₄	1	4	yes	—
36	#66922	—	2	4	no	—
37	#66922	—	4	2	no	—
38	C₁₁×#107	—	2	1	no	—
39	C₁₁×#107	—	2	2	no	—
40	C₁₁×#107	D₄	1	2	yes	—
41	C₄×C₈×C₁₁	—	2	2	no	—
42	C₁₁×#95	—	4	1	no	—
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	—	2	2	no	—
45	C₂×C₁₁⋊C₁₆	—	2	2	no	—
46	#13409	—	11	1	no	maximal, Sylow
47	C₂²×C₄×C₁₁	—	4	1	no	—
48	C₂²×C₄×C₁₁	—	4	1	no	—
49	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
52	C₂²×Dic₁₁	—	4	2	no	—
53	C₂×Dic₂₂	—	2	4	no	—
54	C₂×Dic₂₂	—	4	2	no	—
55	C₂×Dic₂₂	—	4	2	no	—
56	C₂×Dic₂₂	—	4	2	no	—
57	C₂×Dic₂₂	—	4	2	no	—
58	C₂×Dic₂₂	—	4	2	no	—
59	C₂×C₈×C₁₁	—	2	1	no	—
60	C₂×C₈×C₁₁	—	2	1	no	—
61	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
62	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
65	C₂×C₈×C₁₁	#41	1	2	yes	—
66	C₁₁×C₄⋊C₄	—	2	2	no	—
67	C₁₁×C₄⋊C₄	—	4	1	no	—
68	C₁₁×C₄⋊C₄	—	4	1	no	—
69	C₁₁×C₄⋊C₄	—	4	1	no	—
70	C₁₁×C₄⋊C₄	—	8	2	no	—
71	C₄²×C₁₁	—	2	1	no	—
72	C₄²×C₁₁	—	2	1	no	—
73	C₄⋊Dic₁₁	—	4	4	no	—
74	C₄⋊Dic₁₁	—	4	4	no	—
75	Dic₄₄	—	2	4	no	—
76	Dic₄₄	—	2	4	no	—
77	Dic₄₄	—	4	8	no	—
78	Dic₄₄	—	4	2	no	—
79	Dic₄₄	—	4	2	no	—
80	C₁₁⋊C₁₆	—	4	2	no	—
81	C₂×#494	—	11	1	no	—
82	C₂×#358	—	11	2	no	—
83	C₂×#358	—	11	2	no	—
84	#1942	D₁₁	1	1	yes	characteristic
85	#1374	—	11	1	no	—
86	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	4	2	no	—
92	C₂×C₄×C₁₁	—	8	1	no	—
93	C₂×C₄×C₁₁	—	8	1	no	—
94	C₂×C₄×C₁₁	—	8	1	no	—
95	C₂×C₄×C₁₁	—	8	1	no	—
96	C₂×C₄×C₁₁	—	8	1	no	—
97	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
98	C₂×C₄×C₁₁	Q₃₂	1	2	yes	—
99	C₂×C₄×C₁₁	#120	1	1	yes	characteristic
100	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
101	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
103	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
104	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
105	C₂×Dic₁₁	—	4	4	no	—
106	C₂×Dic₁₁	—	8	2	no	—
107	C₂×Dic₁₁	—	8	2	no	—
108	Dic₂₂	—	4	4	no	—
109	Dic₂₂	—	4	4	no	—
110	Dic₂₂	—	8	2	no	—
111	Dic₂₂	—	8	2	no	—
112	C₈×C₁₁	—	2	2	no	—
113	C₈×C₁₁	#121	1	2	yes	—
114	C₈×C₁₁	#123	1	2	yes	—
115	C₂²×Q₁₆	—	11	2	no	—
116	C₂²×Q₁₆	—	22	1	no	—
117	C₂×C₄⋊Q₈	—	22	1	no	—
118	C₂²×C₁₆	—	11	2	no	—
119	#494	—	22	4	no	—
120	C₂×#107	C₂×D₁₁	1	1	yes	characteristic
121	C₂×#107	C₂×D₁₁	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
123	#389	—	2	1	no	—
124	#358	—	22	4	no	—
125	#358	—	22	4	no	—
126	#340	—	2	1	no	—
127	C₂²×C₁₁	#447	1	1	yes	characteristic
128	C₂²×C₁₁	#459	1	1	yes	characteristic
129	C₂²×C₁₁	#486	1	1	yes	characteristic
130	C₂²×C₁₁	C₂×SD₃₂	1	1	yes	characteristic
131	C₂²×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
132	C₂²×C₁₁	#510	1	1	yes	characteristic
133	C₂²×C₁₁	#510	1	1	yes	characteristic
134	C₄×C₁₁	—	2	2	no	—
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	—	8	2	no	—
137	C₄×C₁₁	—	16	1	no	—
138	C₄×C₁₁	#394	1	1	yes	characteristic
139	C₄×C₁₁	#450	1	1	yes	characteristic
140	C₄×C₁₁	#460	1	1	yes	characteristic
141	C₄×C₁₁	#490	1	1	yes	characteristic
142	Dic₁₁	—	8	4	no	—
143	C₂²×Q₈	—	22	2	no	—
144	C₂×Q₁₆	—	11	4	no	—
145	C₂×Q₁₆	—	22	4	no	—
146	C₂×Q₁₆	—	22	2	no	—
147	C₂×Q₁₆	—	22	2	no	—
148	C₂×Q₁₆	—	22	2	no	—
149	C₂×Q₁₆	—	22	2	no	—
150	C₂×Q₁₆	—	22	2	no	—
151	C₂×Q₁₆	—	44	2	no	—
152	C₂×Q₁₆	—	44	2	no	—
153	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
154	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
155	C₄⋊Q₈	—	22	4	no	—
156	C₄⋊Q₈	—	44	2	no	—
157	C₂×C₄⋊C₄	—	2	1	no	—
158	C₂×C₄⋊C₄	—	2	1	no	—
159	C₂×C₄⋊C₄	—	4	1	no	—
160	C₂×C₄⋊C₄	—	44	1	no	—
161	C₂×C₄⋊C₄	—	44	1	no	—
162	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
163	C₂×C₁₆	—	22	2	no	—
164	C₂×C₁₆	—	22	2	no	—
165	C₂×C₁₆	—	22	2	no	—
166	#107	—	2	1	no	—
167	#107	—	2	2	no	—
168	#107	D₄₄	1	2	yes	—
169	C₄×C₈	—	2	2	no	—
170	#95	—	4	1	no	—
171	C₂×C₁₁	#2041	1	1	yes	characteristic
172	C₂×C₁₁	#2185	1	1	yes	characteristic
173	C₂×C₁₁	#2188	1	1	yes	characteristic
174	C₂×C₁₁	#2208	1	1	yes	characteristic
175	C₂×C₁₁	#2209	1	1	yes	characteristic
176	C₂×C₁₁	#2241	1	1	yes	characteristic
177	C₂×C₁₁	#2245	1	1	yes	characteristic
178	C₂×Q₈	—	22	4	no	—
179	C₂×Q₈	—	44	2	no	—
180	C₂×Q₈	—	44	2	no	—
181	C₂×Q₈	—	44	2	no	—
182	C₂×Q₈	—	44	2	no	—
183	C₂×Q₈	—	44	2	no	—
184	C₂²×C₄	—	4	1	no	—
185	C₂²×C₄	—	4	1	no	—
186	C₂²×C₄	—	44	2	no	—
187	C₂²×C₄	#4323	1	1	yes	characteristic
188	C₂²×C₄	#4323	1	1	yes	characteristic
189	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
190	Q₁₆	—	22	4	no	—
191	Q₁₆	—	22	4	no	—
192	Q₁₆	—	44	8	no	—
193	Q₁₆	—	44	2	no	—
194	Q₁₆	—	44	2	no	—
195	C₂×C₈	—	2	1	no	—
196	C₂×C₈	—	2	1	no	—
197	C₂×C₈	#4325	1	2	yes	—
198	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
199	C₂×C₈	#4339	1	1	yes	characteristic
200	C₂×C₈	D₄×D₁₁	1	2	yes	—
201	C₂×C₈	#4343	1	2	yes	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	4	1	no	—
204	C₄⋊C₄	—	4	1	no	—
205	C₄⋊C₄	—	4	1	no	—
206	C₄⋊C₄	—	8	2	no	—
207	C₄⋊C₄	—	44	4	no	—
208	C₄⋊C₄	—	44	4	no	—
209	C₄²	—	2	1	no	—
210	C₄²	—	2	1	no	—
211	C₁₆	—	44	2	no	—
212	C₁₁	#13409	1	1	yes	characteristic, complemented, Sylow
213	C₂³	C₂×#4323	1	1	yes	characteristic
214	Q₈	—	44	4	no	—
215	Q₈	—	44	4	no	—
216	Q₈	—	88	2	no	—
217	Q₈	—	88	2	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	1	no	—
220	C₂×C₄	—	2	1	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	4	2	no	—
223	C₂×C₄	—	8	1	no	—
224	C₂×C₄	—	8	1	no	—
225	C₂×C₄	—	8	1	no	—
226	C₂×C₄	—	8	1	no	—
227	C₂×C₄	—	8	1	no	—
228	C₂×C₄	—	44	4	no	—
229	C₂×C₄	—	88	2	no	—
230	C₂×C₄	—	88	2	no	—
231	C₂×C₄	#66891	1	2	yes	—
232	C₂×C₄	#66893	1	2	yes	—
233	C₂×C₄	#66983	1	1	yes	characteristic
234	C₂×C₄	#66990	1	1	yes	characteristic
235	C₂×C₄	C₂×#4325	1	1	yes	characteristic
236	C₂×C₄	#67000	1	1	yes	characteristic
237	C₂×C₄	#67002	1	1	yes	characteristic
238	C₂×C₄	#67002	1	1	yes	characteristic
239	C₈	—	2	2	no	—
240	C₈	#66947	1	2	yes	—
241	C₈	#66948	1	2	yes	—
242	C₂²	#10622628	1	1	yes	characteristic
243	C₂²	#10622649	1	1	yes	characteristic
244	C₂²	#10622701	1	1	yes	characteristic
245	C₂²	C₂×#66891	1	1	yes	characteristic
246	C₂²	C₂×#66893	1	1	yes	characteristic
247	C₂²	#10622808	1	1	yes	characteristic
248	C₂²	#10622808	1	1	yes	characteristic
249	C₄	—	2	2	no	—
250	C₄	—	2	2	no	—
251	C₄	—	8	2	no	—
252	C₄	—	16	1	no	—
253	C₄	—	88	4	no	—
254	C₄	#10622604	1	1	yes	characteristic
255	C₄	#10622640	1	1	yes	characteristic
256	C₄	#10622659	1	1	yes	characteristic
257	C₄	#10622680	1	1	yes	characteristic
258	C₂	#13069850	1	1	yes	characteristic
259	C₂	#13070532	1	1	yes	characteristic
260	C₂	#13070549	1	1	yes	characteristic
261	C₂	#13070661	1	1	yes	characteristic
262	C₂	#13070666	1	1	yes	characteristic
263	C₂	#13070845	1	1	yes	characteristic
264	C₂	#13070863	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4323
commutator, cosocle	C₂²×C₈×C₁₁	C₂³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1942	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
hypercenter	#1942	D₁₁
hypocenter	C₁₁	#13409
LCS	G ▷ C₂²×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1942

Complements

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

N	H ≅ G/N	type
212. C₁₁	#13409	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622312	2
C₂×#10622130	2
#13066694	2
C₁₁×#1942	2
#13409	11