Subgroups — #24987130

Order 11008.

482 conjugacy classes of subgroups.

The subgroup lattice has 276 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582853	C₂	1	1	yes	maximal, characteristic
2	#19132907	C₂	1	2	yes	maximal
3	#19132887	C₂	1	1	yes	maximal, characteristic, complemented
4	#19132439	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1452	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#10621872	C₄	1	1	yes	characteristic
7	C₂²×C₈×D₄₃	C₄	1	1	yes	characteristic
8	C₂×#13063282	C₂²	1	1	yes	characteristic
9	#14582952	C₂²	1	2	yes	—
10	#14582853	—	2	2	no	—
11	#14582853	—	2	2	no	—
12	C₂×#13063236	C₂²	1	1	yes	characteristic
13	C₂×#13063235	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₄₃	C₄	1	1	yes	characteristic
15	#14582624	C₄	1	4	yes	—
16	#14582622	C₄	1	4	yes	—
17	#14582621	—	2	2	no	—
18	C₄₃×#431	C₂²	1	2	yes	—
19	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
20	C₄₃×#322	—	2	2	no	—
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	—	2	2	no	—
25	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₈×D₄₃	—	2	2	no	—
28	C₂×C₈×D₄₃	—	2	2	no	—
29	C₂×C₈×D₄₃	—	2	2	no	—
30	#13063282	—	2	1	no	—
31	#13063282	—	2	1	no	—
32	#13063282	—	2	2	no	—
33	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
34	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
35	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
36	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
37	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
38	#13063236	—	2	1	no	—
39	#13063236	—	2	1	no	—
40	#13063235	—	2	2	no	—
41	C₄×C₄₃⋊C₈	—	2	2	no	—
42	C₈×Dic₄₃	—	2	2	no	—
43	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
46	C₄⋊C₈×C₄₃	—	2	2	no	—
47	C₂²⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
48	C₄×C₈×C₄₃	—	2	2	no	—
49	C₄×C₈×C₄₃	D₄	1	2	yes	—
50	C₄×C₈×C₄₃	D₄	1	2	yes	—
51	C₂³×D₄₃	C₄²	1	1	yes	characteristic
52	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
53	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₄₃	C₄²	1	1	yes	characteristic
55	C₂²×Dic₄₃	C₄²	1	2	yes	—
56	C₂×C₄×D₄₃	—	2	1	no	—
57	C₂×C₄×D₄₃	—	2	1	no	—
58	C₂×C₄×D₄₃	—	2	1	no	—
59	C₂×C₄×D₄₃	—	2	1	no	—
60	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
61	C₂×C₄×D₄₃	M₁₆	1	2	yes	—
62	C₂×C₈×C₄₃	—	2	1	no	—
63	C₂×C₈×C₄₃	—	2	1	no	—
64	C₂×C₈×C₄₃	—	2	1	no	—
65	C₂×C₈×C₄₃	—	2	1	no	—
66	C₂×C₈×C₄₃	—	2	4	no	—
67	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
68	C₂×C₈×C₄₃	C₂²⋊C₄	1	2	yes	—
69	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
71	C₄²×C₄₃	#41	1	2	yes	—
72	(C₂×D₄₃)⋊C₄	—	2	2	no	—
73	(C₂×D₄₃)⋊C₄	—	2	2	no	—
74	Dic₄₃⋊C₄	—	2	2	no	—
75	Dic₄₃⋊C₄	—	2	2	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	—	2	1	no	—
81	C₂×C₄₃⋊C₈	—	2	1	no	—
82	C₂×C₄₃⋊C₈	—	2	4	no	—
83	C₂×C₄₃⋊C₈	M₁₆	1	2	yes	—
84	C₂×C₄₃⋊C₈	M₁₆	1	2	yes	—
85	#10621872	—	2	8	no	—
86	C₈×D₄₃	—	2	8	no	—
87	C₂³×C₄₃	C₂×C₄²	1	1	yes	characteristic
88	C₂²×D₄₃	—	2	1	no	—
89	C₂²×D₄₃	—	2	1	no	—
90	C₂²×D₄₃	—	4	2	no	—
91	C₂²×D₄₃	#97	1	2	yes	—
92	C₂×C₄×C₄₃	—	4	2	no	—
93	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₄₃	#117	1	1	yes	characteristic
95	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
96	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
98	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
99	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
100	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
101	C₂×Dic₄₃	—	2	1	no	—
102	C₂×Dic₄₃	—	2	1	no	—
103	C₂×Dic₄₃	—	2	2	no	—
104	C₂×Dic₄₃	—	4	2	no	—
105	C₂×Dic₄₃	#97	1	2	yes	—
106	C₄×D₄₃	—	2	2	no	—
107	C₄×D₄₃	—	2	2	no	—
108	C₄×D₄₃	—	2	2	no	—
109	C₄×D₄₃	—	2	2	no	—
110	C₈×C₄₃	—	2	2	no	—
111	C₈×C₄₃	—	2	2	no	—
112	C₈×C₄₃	—	4	4	no	—
113	C₄₃⋊C₈	—	2	2	no	—
114	C₄₃⋊C₈	—	2	2	no	—
115	C₄₃⋊C₈	—	4	4	no	—
116	#8157	—	43	1	no	maximal, Sylow
117	C₂²×C₄₃	—	2	2	no	—
118	C₂²×C₄₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
119	C₂²×C₄₃	C₂×#97	1	1	yes	characteristic
120	C₂²×C₄₃	C₄×M₁₆	1	1	yes	characteristic
121	C₂×D₄₃	—	2	2	no	—
122	C₂×D₄₃	—	4	2	no	—
123	C₂×D₄₃	—	4	2	no	—
124	C₂×D₄₃	—	4	2	no	—
125	C₄×C₄₃	—	2	2	no	—
126	C₄×C₄₃	—	2	2	no	—
127	C₄×C₄₃	#407	1	1	yes	characteristic
128	C₄×C₄₃	#407	1	1	yes	characteristic
129	C₄×C₄₃	#432	1	1	yes	characteristic
130	C₄×C₄₃	#432	1	1	yes	characteristic
131	Dic₄₃	—	2	2	no	—
132	Dic₄₃	—	4	2	no	—
133	C₂×#405	—	43	1	no	—
134	#1458	—	43	2	no	—
135	#1452	—	43	1	no	—
136	#1452	D₄₃	1	1	yes	characteristic, complemented
137	#1281	—	43	2	no	—
138	C₂×C₄₃	—	2	1	no	—
139	C₂×C₄₃	—	2	1	no	—
140	C₂×C₄₃	#1749	1	1	yes	characteristic
141	C₂×C₄₃	#1757	1	2	yes	—
142	D₄₃	—	4	2	no	—
143	C₂²×M₁₆	—	43	1	no	—
144	C₂³×C₈	—	43	1	no	—
145	C₂×#117	—	43	1	no	—
146	#431	—	43	2	no	—
147	#431	C₂×D₄₃	1	2	yes	—
148	#405	—	86	2	no	—
149	#405	—	86	2	no	—
150	C₂×#97	—	43	1	no	—
151	C₂×#97	—	43	1	no	—
152	C₂×C₄×C₈	—	43	1	no	—
153	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
154	#324	—	43	4	no	—
155	#323	—	43	4	no	—
156	#322	—	2	2	no	—
157	#322	—	86	2	no	—
158	C₄₃	#8157	1	1	yes	characteristic, complemented, Sylow
159	C₂³×C₄	—	43	1	no	—
160	C₂×M₁₆	—	86	2	no	—
161	C₂×M₁₆	—	86	2	no	—
162	C₂×M₁₆	—	86	2	no	—
163	C₂²×C₈	—	43	1	no	—
164	C₂²×C₈	—	43	1	no	—
165	C₂²×C₈	—	86	2	no	—
166	C₂²×C₈	—	86	2	no	—
167	C₂²×C₈	—	86	2	no	—
168	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
169	C₂²×C₈	C₄×D₄₃	1	1	yes	characteristic
170	#117	—	86	1	no	—
171	#117	—	86	2	no	—
172	#117	—	86	1	no	—
173	C₂×C₄⋊C₄	—	43	2	no	—
174	C₂×C₂²⋊C₄	—	43	2	no	—
175	C₂×C₄²	—	43	1	no	—
176	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
177	C₄⋊C₈	—	2	2	no	—
178	C₄⋊C₈	—	86	2	no	—
179	C₂²⋊C₈	—	43	4	no	—
180	C₂²⋊C₈	C₄×D₄₃	1	4	yes	—
181	#97	—	86	2	no	—
182	#97	—	86	1	no	—
183	#97	—	86	1	no	—
184	C₄×C₈	—	2	2	no	—
185	C₄×C₈	—	86	2	no	—
186	C₄×C₈	—	86	2	no	—
187	C₄×C₈	D₁₇₂	1	2	yes	—
188	C₄×C₈	C₂²⋊D₄₃	1	2	yes	—
189	C₂⁴	—	43	1	no	—
190	C₂²×C₄	—	43	1	no	—
191	C₂²×C₄	—	43	2	no	—
192	C₂²×C₄	—	43	2	no	—
193	C₂²×C₄	—	43	2	no	—
194	C₂²×C₄	—	86	1	no	—
195	C₂²×C₄	—	86	1	no	—
196	C₂²×C₄	—	86	1	no	—
197	C₂²×C₄	—	86	1	no	—
198	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
199	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
200	M₁₆	—	86	8	no	—
201	C₂×C₈	—	2	1	no	—
202	C₂×C₈	—	2	1	no	—
203	C₂×C₈	—	2	1	no	—
204	C₂×C₈	—	2	1	no	—
205	C₂×C₈	—	2	4	no	—
206	C₂×C₈	—	43	2	no	—
207	C₂×C₈	—	43	2	no	—
208	C₂×C₈	—	86	8	no	—
209	C₂×C₈	—	86	1	no	—
210	C₂×C₈	—	86	1	no	—
211	C₂×C₈	—	86	1	no	—
212	C₂×C₈	—	86	1	no	—
213	C₂×C₈	—	86	4	no	—
214	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
215	C₂×C₈	(C₂×D₄₃)⋊C₄	1	2	yes	—
216	C₄⋊C₄	—	86	2	no	—
217	C₄⋊C₄	—	86	2	no	—
218	C₂²⋊C₄	—	86	2	no	—
219	C₂²⋊C₄	—	86	2	no	—
220	C₄²	—	86	1	no	—
221	C₄²	—	86	1	no	—
222	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
223	C₄²	#10621898	1	2	yes	—
224	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
225	C₂³	—	43	2	no	—
226	C₂³	—	86	1	no	—
227	C₂³	—	86	1	no	—
228	C₂³	—	172	2	no	—
229	C₂³	C₄²×D₄₃	1	1	yes	characteristic
230	C₂×C₄	—	4	2	no	—
231	C₂×C₄	—	43	2	no	—
232	C₂×C₄	—	86	1	no	—
233	C₂×C₄	—	86	1	no	—
234	C₂×C₄	—	86	2	no	—
235	C₂×C₄	—	86	2	no	—
236	C₂×C₄	—	86	2	no	—
237	C₂×C₄	—	86	2	no	—
238	C₂×C₄	—	86	2	no	—
239	C₂×C₄	—	172	2	no	—
240	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
241	C₂×C₄	#13063282	1	1	yes	characteristic
242	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
243	C₂×C₄	C₄×D₁₇₂	1	2	yes	—
244	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
245	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
246	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
247	C₂×C₄	M₁₆×D₄₃	1	1	yes	characteristic
248	C₈	—	2	2	no	—
249	C₈	—	2	2	no	—
250	C₈	—	4	4	no	—
251	C₈	—	86	2	no	—
252	C₈	—	86	2	no	—
253	C₈	—	172	4	no	—
254	C₂²	—	2	2	no	—
255	C₂²	—	86	2	no	—
256	C₂²	—	172	2	no	—
257	C₂²	—	172	2	no	—
258	C₂²	—	172	2	no	—
259	C₂²	C₄×(C₂×D₄₃)⋊C₄	1	1	yes	characteristic
260	C₂²	#97×D₄₃	1	1	yes	characteristic
261	C₂²	#14582851	1	1	yes	characteristic
262	C₄	—	2	2	no	—
263	C₄	—	2	2	no	—
264	C₄	—	86	2	no	—
265	C₄	—	172	2	no	—
266	C₄	#14582862	1	1	yes	characteristic
267	C₄	#14582862	1	1	yes	characteristic
268	C₄	#14582954	1	1	yes	characteristic
269	C₄	#14582954	1	1	yes	characteristic
270	C₂	—	2	1	no	—
271	C₂	—	2	1	no	—
272	C₂	—	172	2	no	—
273	C₂	#19134358	1	1	yes	characteristic
274	C₂	#19134396	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₄₃)⋊C₄
commutator	C₂³×C₄₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1452	C₂
socle	C₂²×C₄₃	C₄×C₂²⋊C₄
prime radical	C₂³×D₄₃	C₄²
cosocle	C₂×C₄²×C₄₃	C₂³
hypercenter	#1452	D₄₃
hypocenter	C₄₃	#8157
LCS	G ▷ C₂³×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
3. #19132887	C₂	semidirect
4. #19132439	C₂	semidirect
5. C₄₃×#1452	C₂	semidirect
136. #1452	D₄₃	semidirect
158. C₄₃	#8157	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582853	2
#19132907	2
#19132887	2
#19132439	2
C₄₃×#1452	2
#8157	43