Subgroups — #25011457

Order 11008.

586 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₃	C₂	1	2	yes	maximal
2	C₂×#14582856	C₂	1	1	yes	maximal, characteristic
3	#19132679	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132678	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1377	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10621872	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
8	C₂×#13063282	C₄	1	1	yes	characteristic
9	C₂×#13063265	C₂²	1	2	yes	—
10	C₂×#13063264	—	2	2	no	—
11	M₃₂×D₄₃	—	2	4	no	—
12	M₃₂×D₄₃	C₄	1	8	yes	complemented
13	C₂×C₁₆×D₄₃	—	2	2	no	—
14	#14582856	—	2	2	no	—
15	#14582856	—	2	2	no	—
16	C₂×#13063235	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₄₃⋊C₈	C₄	1	1	yes	characteristic
18	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
19	C₂×M₃₂×C₄₃	C₂²	1	2	yes	—
20	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#10621872	—	2	2	no	—
23	C₂×#10621872	—	2	2	no	—
24	C₂×#10621872	C₈	1	4	yes	—
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₄₃	C₂×C₄	1	4	yes	—
28	C₂×C₈×D₄₃	D₄	1	2	yes	—
29	C₂×C₈×D₄₃	D₄	1	2	yes	—
30	C₂×C₈×D₄₃	D₄	1	2	yes	—
31	C₂×C₈×D₄₃	Q₈	1	2	yes	—
32	#13063282	—	2	2	no	—
33	#13063282	—	2	2	no	—
34	C₂×Dic₄₃⋊C₄	C₈	1	2	yes	—
35	C₂×(C₂×D₄₃)⋊C₄	C₈	1	2	yes	—
36	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
37	#13063265	—	2	2	no	—
38	#13063265	C₂×C₄	1	4	yes	—
39	#13063264	—	2	8	no	—
40	C₂×C₄₃⋊C₁₆	—	2	2	no	—
41	C₁₆×D₄₃	—	2	8	no	—
42	#13063235	—	2	2	no	—
43	C₄×C₄₃⋊C₈	—	2	1	no	—
44	C₄×C₄₃⋊C₈	—	2	1	no	—
45	C₈×Dic₄₃	—	2	1	no	—
46	C₈×Dic₄₃	—	2	1	no	—
47	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
49	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
50	M₃₂×C₄₃	—	2	2	no	—
51	M₃₂×C₄₃	C₂×C₄	1	4	yes	—
52	C₂×C₁₆×C₄₃	—	2	2	no	—
53	#97×C₄₃	—	2	2	no	—
54	C₂³×D₄₃	C₂×C₈	1	1	yes	characteristic
55	C₂²×C₄×C₄₃	C₂×C₈	1	2	yes	—
56	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
57	C₂²×Dic₄₃	C₂×C₈	1	2	yes	—
58	C₂²×Dic₄₃	C₂×C₈	1	1	yes	characteristic
59	C₂×C₄×D₄₃	C₄²	1	2	yes	—
60	C₂×C₄×D₄₃	C₂²⋊C₄	1	2	yes	—
61	C₂×C₄×D₄₃	C₄⋊C₄	1	2	yes	—
62	C₂×C₄×D₄₃	C₂×C₈	1	2	yes	—
63	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
64	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
65	C₂×C₈×C₄₃	—	2	1	no	—
66	C₂×C₈×C₄₃	—	2	1	no	—
67	C₂×C₈×C₄₃	C₂×C₈	1	2	yes	—
68	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
69	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₄₃	C₂×Q₈	1	1	yes	characteristic
72	C₄²×C₄₃	—	2	1	no	—
73	C₄²×C₄₃	—	2	1	no	—
74	(C₂×D₄₃)⋊C₄	—	2	4	no	—
75	Dic₄₃⋊C₄	—	2	4	no	—
76	C₄×Dic₄₃	—	2	1	no	—
77	C₄×Dic₄₃	—	2	1	no	—
78	C₂×C₄₃⋊C₈	—	2	1	no	—
79	C₂×C₄₃⋊C₈	—	2	1	no	—
80	C₂×C₄₃⋊C₈	C₄²	1	2	yes	—
81	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄₃⋊C₈	C₄⋊C₄	1	2	yes	—
84	C₂×C₄₃⋊C₈	C₂×C₈	1	2	yes	—
85	#10621872	—	2	8	no	—
86	C₈×D₄₃	C₂²⋊C₄	1	4	yes	—
87	C₈×D₄₃	C₂²⋊C₄	1	4	yes	—
88	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
89	C₈×D₄₃	C₄⋊C₄	1	4	yes	—
90	C₁₆×C₄₃	—	2	4	no	—
91	C₄₃⋊C₁₆	—	2	4	no	—
92	C₂³×C₄₃	C₂²×C₈	1	1	yes	characteristic
93	C₂²×D₄₃	—	4	2	no	—
94	C₂²×D₄₃	C₄×C₈	1	2	yes	—
95	C₂²×D₄₃	C₂²⋊C₈	1	2	yes	—
96	C₂²×D₄₃	C₄⋊C₈	1	2	yes	—
97	C₂×C₄×C₄₃	—	2	2	no	—
98	C₂×C₄×C₄₃	—	4	2	no	—
99	C₂×C₄×C₄₃	C₂×C₄²	1	1	yes	characteristic
100	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
103	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
104	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
105	C₂×Dic₄₃	—	2	2	no	—
106	C₂×Dic₄₃	—	4	2	no	—
107	C₂×Dic₄₃	C₄×C₈	1	2	yes	—
108	C₂×Dic₄₃	C₂²⋊C₈	1	2	yes	—
109	C₂×Dic₄₃	C₄⋊C₈	1	2	yes	—
110	C₄×D₄₃	#95	1	4	yes	—
111	C₄×D₄₃	#97	1	4	yes	—
112	C₄×D₄₃	C₂²⋊C₈	1	4	yes	—
113	C₄×D₄₃	C₄⋊C₈	1	4	yes	—
114	C₈×C₄₃	—	2	2	no	—
115	C₈×C₄₃	C₂×C₂²⋊C₄	1	2	yes	—
116	C₈×C₄₃	C₂×C₄⋊C₄	1	2	yes	—
117	C₄₃⋊C₈	—	2	2	no	—
118	C₄₃⋊C₈	#95	1	2	yes	—
119	C₄₃⋊C₈	#95	1	2	yes	—
120	#12551	—	43	1	no	maximal, Sylow
121	C₂²×C₄₃	—	2	2	no	—
122	C₂²×C₄₃	C₂×C₄×C₈	1	1	yes	characteristic
123	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
124	C₂²×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
125	C₂×D₄₃	—	2	4	no	—
126	C₂×D₄₃	—	4	2	no	—
127	C₂×D₄₃	—	4	2	no	—
128	C₂×D₄₃	#336	1	4	yes	—
129	C₄×C₄₃	—	4	2	no	—
130	C₄×C₄₃	C₂×#95	1	1	yes	characteristic
131	C₄×C₄₃	C₂×#97	1	1	yes	characteristic
132	C₄×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
133	C₄×C₄₃	C₂×C₄⋊C₈	1	1	yes	characteristic
134	Dic₄₃	—	4	2	no	—
135	Dic₄₃	#336	1	4	yes	—
136	C₂²×M₃₂	—	43	2	no	—
137	C₂×#405	—	43	1	no	—
138	#1377	—	43	2	no	—
139	#1377	—	43	1	no	—
140	#1377	D₄₃	1	1	yes	characteristic, complemented
141	C₂×C₄₃	—	2	1	no	—
142	C₂×C₄₃	—	2	1	no	—
143	C₂×C₄₃	C₂×#336	1	1	yes	characteristic
144	C₂×C₄₃	#2115	1	2	yes	—
145	D₄₃	—	2	4	no	—
146	C₂²×M₁₆	—	43	1	no	—
147	C₂³×C₈	—	43	1	no	—
148	C₂×#117	—	43	1	no	—
149	C₂×M₃₂	—	43	2	no	—
150	C₂×M₃₂	—	43	8	no	—
151	C₂×M₃₂	—	86	2	no	—
152	C₂×M₃₂	—	86	4	no	—
153	C₂×M₃₂	C₂×D₄₃	1	2	yes	—
154	C₂²×C₁₆	—	86	2	no	—
155	#405	—	86	2	no	—
156	#405	—	86	2	no	—
157	C₂×#97	—	43	1	no	—
158	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
159	C₂×C₄×C₈	—	43	1	no	—
160	C₂×C₄×C₈	—	43	1	no	—
161	C₄₃	#12551	1	1	yes	characteristic, complemented, Sylow
162	C₂³×C₄	—	43	1	no	—
163	C₂×M₁₆	—	43	4	no	—
164	C₂×M₁₆	—	86	2	no	—
165	C₂×M₁₆	—	86	2	no	—
166	C₂²×C₈	—	43	1	no	—
167	C₂²×C₈	—	43	4	no	—
168	C₂²×C₈	—	43	2	no	—
169	C₂²×C₈	—	43	2	no	—
170	C₂²×C₈	—	43	2	no	—
171	C₂²×C₈	—	43	2	no	—
172	C₂²×C₈	—	43	1	no	—
173	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
174	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
175	#117	—	86	2	no	—
176	#117	—	86	2	no	—
177	C₂×C₄⋊C₄	—	43	2	no	—
178	C₂×C₂²⋊C₄	—	43	2	no	—
179	C₂×C₄²	—	43	1	no	—
180	C₂×C₄²	C₄×D₄₃	1	1	yes	characteristic
181	M₃₂	—	2	2	no	—
182	M₃₂	—	43	4	no	—
183	M₃₂	—	86	8	no	—
184	M₃₂	—	86	2	no	—
185	M₃₂	C₄×D₄₃	1	4	yes	—
186	C₂×C₁₆	—	2	2	no	—
187	C₂×C₁₆	—	86	8	no	—
188	C₂×C₁₆	—	86	2	no	—
189	#97	—	2	2	no	—
190	#97	—	86	2	no	—
191	C₄×C₈	—	86	1	no	—
192	C₄×C₈	—	86	1	no	—
193	C₄×C₈	—	86	1	no	—
194	C₄×C₈	—	86	1	no	—
195	C₂⁴	—	43	1	no	—
196	C₂²×C₄	—	43	1	no	—
197	C₂²×C₄	—	43	2	no	—
198	C₂²×C₄	—	43	2	no	—
199	C₂²×C₄	—	43	2	no	—
200	C₂²×C₄	—	43	2	no	—
201	C₂²×C₄	—	43	2	no	—
202	C₂²×C₄	—	43	2	no	—
203	C₂²×C₄	—	43	2	no	—
204	C₂²×C₄	C₈×D₄₃	1	2	yes	—
205	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
206	M₁₆	—	86	8	no	—
207	C₂×C₈	—	2	1	no	—
208	C₂×C₈	—	2	1	no	—
209	C₂×C₈	—	43	2	no	—
210	C₂×C₈	—	43	1	no	—
211	C₂×C₈	—	43	1	no	—
212	C₂×C₈	—	43	2	no	—
213	C₂×C₈	—	43	4	no	—
214	C₂×C₈	—	43	4	no	—
215	C₂×C₈	—	43	4	no	—
216	C₂×C₈	—	43	4	no	—
217	C₂×C₈	—	43	2	no	—
218	C₂×C₈	—	86	1	no	—
219	C₂×C₈	—	86	1	no	—
220	C₂×C₈	C₈×D₄₃	1	2	yes	—
221	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
222	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
223	C₂×C₈	D₄×D₄₃	1	2	yes	—
224	C₂×C₈	Q₈×D₄₃	1	1	yes	characteristic
225	C₄⋊C₄	—	86	4	no	—
226	C₂²⋊C₄	—	86	4	no	—
227	C₄²	—	2	1	no	—
228	C₄²	—	2	1	no	—
229	C₄²	—	86	1	no	—
230	C₄²	—	86	1	no	—
231	C₁₆	—	2	4	no	—
232	C₁₆	—	86	4	no	—
233	C₂³	—	43	2	no	—
234	C₂³	—	43	2	no	—
235	C₂³	—	43	2	no	—
236	C₂³	—	172	2	no	—
237	C₂³	C₂×C₈×D₄₃	1	1	yes	characteristic
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	4	2	no	—
240	C₂×C₄	—	43	2	no	—
241	C₂×C₄	—	43	2	no	—
242	C₂×C₄	—	43	2	no	—
243	C₂×C₄	—	43	4	no	—
244	C₂×C₄	—	43	4	no	—
245	C₂×C₄	—	43	4	no	—
246	C₂×C₄	—	43	4	no	—
247	C₂×C₄	—	86	2	no	—
248	C₂×C₄	—	172	2	no	—
249	C₂×C₄	C₄²×D₄₃	1	1	yes	characteristic
250	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
251	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
252	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
253	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
254	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
255	C₈	—	2	2	no	—
256	C₈	—	43	2	no	—
257	C₈	—	43	2	no	—
258	C₈	—	86	2	no	—
259	C₈	C₂²⋊C₄×D₄₃	1	2	yes	—
260	C₈	C₄⋊C₄×D₄₃	1	2	yes	—
261	C₂²	—	2	2	no	—
262	C₂²	—	43	4	no	—
263	C₂²	—	86	4	no	—
264	C₂²	—	172	2	no	—
265	C₂²	—	172	2	no	—
266	C₂²	C₄×C₈×D₄₃	1	1	yes	characteristic
267	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
268	C₂²	C₄⋊C₈×D₄₃	1	1	yes	characteristic
269	C₄	—	4	2	no	—
270	C₄	—	43	4	no	—
271	C₄	—	172	2	no	—
272	C₄	#95×D₄₃	1	1	yes	characteristic
273	C₄	#97×D₄₃	1	1	yes	characteristic
274	C₄	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
275	C₄	C₄⋊C₈×D₄₃	1	1	yes	characteristic
276	C₂	—	2	1	no	—
277	C₂	—	2	1	no	—
278	C₂	—	86	4	no	—
279	C₂	#336×D₄₃	1	1	yes	characteristic
280	C₂	#19136214	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₃
commutator	C₂²×C₄₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₄₃×#1377	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₈
prime radical	C₂³×D₄₃	C₂×C₈
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	#1377	D₄₃
hypocenter	C₄₃	#12551
LCS	G ▷ C₂²×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1377

Complements

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

N	H ≅ G/N	type
3. #19132679	C₂	semidirect
4. #19132678	C₂	semidirect
5. C₄₃×#1377	C₂	semidirect
12. M₃₂×D₄₃	C₄	semidirect
140. #1377	D₄₃	semidirect
161. C₄₃	#12551	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₃	2
C₂×#14582856	2
#19132679	2
#19132678	2
C₄₃×#1377	2
#12551	43