Subgroups — C₂×#379×D₄₃ #25254850

Order 11008.

33214 conjugacy classes of subgroups.

The subgroup lattice has 308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₄×D₄₃	C₂	1	6	yes	maximal, complemented
3	C₂×#14582755	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#14582754	C₂	1	6	yes	maximal, complemented
5	#379×D₄₃	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₄₃×#379	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂⁵×D₄₃	—	2	48	no	—
8	C₂⁵×D₄₃	C₄	1	16	yes	complemented
9	C₂⁵×D₄₃	C₂²	1	8	yes	—
10	C₂⁵×D₄₃	C₂²	1	3	yes	—
11	C₂⁵×D₄₃	C₂²	1	3	yes	—
12	C₂³×C₄×D₄₃	C₂²	1	4	yes	complemented
13	C₂²×C₂²⋊Dic₄₃	C₂²	1	6	yes	complemented
14	C₂²×(C₂×D₄₃)⋊C₄	C₂²	1	12	yes	complemented
15	C₂×C₂²⋊C₄×D₄₃	—	2	48	no	—
16	C₂×C₂²⋊C₄×D₄₃	C₂²	1	48	yes	complemented
17	#14582755	C₂²	1	8	yes	complemented
18	#14582754	C₂²	1	48	yes	complemented
19	C₂⁶×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	6	yes	complemented
21	C₄₃×#379	C₂²	1	8	yes	complemented
22	C₂⁴×D₄₃	—	2	512	no	—
23	C₂⁴×D₄₃	—	2	24	no	—
24	C₂⁴×D₄₃	—	2	384	no	—
25	C₂⁴×D₄₃	—	2	192	no	—
26	C₂⁴×D₄₃	—	2	48	no	—
27	C₂⁴×D₄₃	—	2	48	no	—
28	C₂⁴×D₄₃	C₂×C₄	1	24	yes	—
29	C₂⁴×D₄₃	C₂×C₄	1	64	yes	complemented
30	C₂⁴×D₄₃	C₂×C₄	1	24	yes	complemented
31	C₂⁴×D₄₃	D₄	1	48	yes	—
32	C₂⁴×D₄₃	C₂³	1	12	yes	—
33	C₂⁴×D₄₃	C₂³	1	12	yes	—
34	C₂⁴×D₄₃	C₂³	1	3	yes	—
35	C₂⁴×D₄₃	C₂³	1	1	yes	characteristic
36	C₂³×Dic₄₃	C₂³	1	4	yes	complemented
37	C₂²×C₄×D₄₃	—	2	48	no	—
38	C₂²×C₄×D₄₃	C₂³	1	16	yes	complemented
39	C₂×C₂²⋊Dic₄₃	—	2	24	no	—
40	C₂×C₂²⋊Dic₄₃	C₂³	1	24	yes	complemented
41	C₂×(C₂×D₄₃)⋊C₄	—	2	48	no	—
42	C₂×(C₂×D₄₃)⋊C₄	C₂³	1	48	yes	complemented
43	C₂²⋊C₄×D₄₃	—	2	192	no	—
44	C₂⁵×C₄₃	—	2	24	no	—
45	C₂⁵×C₄₃	C₂×C₄	1	8	yes	complemented
46	C₂⁵×C₄₃	C₂³	1	4	yes	—
47	C₂⁵×C₄₃	C₂³	1	3	yes	—
48	C₂³×C₄×C₄₃	C₂³	1	4	yes	complemented
49	C₂×C₂²⋊C₄×C₄₃	—	2	24	no	—
50	C₂×C₂²⋊C₄×C₄₃	C₂³	1	24	yes	complemented
51	C₂⁴×C₄₃	—	2	128	no	—
52	C₂⁴×C₄₃	—	2	96	no	—
53	C₂⁴×C₄₃	—	2	48	no	—
54	C₂⁴×C₄₃	—	2	24	no	—
55	C₂⁴×C₄₃	C₂²×C₄	1	12	yes	—
56	C₂⁴×C₄₃	C₂²×C₄	1	16	yes	complemented
57	C₂⁴×C₄₃	C₂×D₄	1	24	yes	—
58	C₂⁴×C₄₃	C₂⁴	1	6	yes	—
59	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
60	C₂³×D₄₃	—	2	384	no	—
61	C₂³×D₄₃	—	2	1024	no	—
62	C₂³×D₄₃	—	2	2048	no	—
63	C₂³×D₄₃	—	2	96	no	—
64	C₂³×D₄₃	—	2	48	no	—
65	C₂³×D₄₃	—	2	24	no	—
66	C₂³×D₄₃	—	2	192	no	—
67	C₂³×D₄₃	—	2	192	no	—
68	C₂³×D₄₃	—	2	768	no	—
69	C₂³×D₄₃	—	2	384	no	—
70	C₂³×D₄₃	—	2	96	no	—
71	C₂³×D₄₃	—	2	96	no	—
72	C₂³×D₄₃	C₂²⋊C₄	1	192	yes	complemented
73	C₂³×D₄₃	C₂²×C₄	1	12	yes	—
74	C₂³×D₄₃	C₂²×C₄	1	48	yes	—
75	C₂³×D₄₃	C₂²×C₄	1	4	yes	—
76	C₂³×D₄₃	C₂²×C₄	1	48	yes	complemented
77	C₂³×D₄₃	C₂×D₄	1	96	yes	—
78	C₂³×D₄₃	C₂×D₄	1	24	yes	—
79	C₂³×D₄₃	C₂×D₄	1	24	yes	—
80	C₂³×D₄₃	C₂⁴	1	6	yes	—
81	C₂³×D₄₃	C₂⁴	1	2	yes	—
82	C₂²×C₄×C₄₃	—	2	24	no	—
83	C₂²×C₄×C₄₃	C₂⁴	1	8	yes	complemented
84	C₂²×Dic₄₃	—	2	24	no	—
85	C₂²×Dic₄₃	C₂⁴	1	8	yes	complemented
86	C₂×C₄×D₄₃	—	2	96	no	—
87	C₂×C₄×D₄₃	—	4	64	no	—
88	C₂²⋊C₄×C₄₃	—	2	48	no	—
89	C₂²⋊Dic₄₃	—	2	48	no	—
90	(C₂×D₄₃)⋊C₄	—	2	96	no	—
91	C₂³×C₄₃	—	2	128	no	—
92	C₂³×C₄₃	—	2	256	no	—
93	C₂³×C₄₃	—	2	48	no	—
94	C₂³×C₄₃	—	2	96	no	—
95	C₂³×C₄₃	—	2	96	no	—
96	C₂³×C₄₃	—	2	24	no	—
97	C₂³×C₄₃	C₂×C₂²⋊C₄	1	48	yes	complemented
98	C₂³×C₄₃	C₂³×C₄	1	12	yes	—
99	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
100	C₂³×C₄₃	C₂²×D₄	1	24	yes	—
101	C₂³×C₄₃	C₂²×D₄	1	12	yes	—
102	C₂³×C₄₃	C₂⁵	1	1	yes	characteristic
103	C₂²×D₄₃	—	2	384	no	—
104	C₂²×D₄₃	—	2	768	no	—
105	C₂²×D₄₃	—	2	2048	no	—
106	C₂²×D₄₃	—	2	48	no	—
107	C₂²×D₄₃	—	2	96	no	—
108	C₂²×D₄₃	—	2	96	no	—
109	C₂²×D₄₃	—	2	24	no	—
110	C₂²×D₄₃	—	2	192	no	—
111	C₂²×D₄₃	—	2	192	no	—
112	C₂²×D₄₃	—	2	384	no	—
113	C₂²×D₄₃	—	2	768	no	—
114	C₂²×D₄₃	C₂×C₂²⋊C₄	1	48	yes	—
115	C₂²×D₄₃	C₂×C₂²⋊C₄	1	192	yes	complemented
116	C₂²×D₄₃	C₂×C₂²⋊C₄	1	48	yes	complemented
117	C₂²×D₄₃	#120	1	64	yes	—
118	C₂²×D₄₃	C₂³×C₄	1	12	yes	—
119	C₂²×D₄₃	C₂³×C₄	1	4	yes	—
120	C₂²×D₄₃	C₂²×D₄	1	24	yes	—
121	C₂²×D₄₃	C₂²×D₄	1	24	yes	—
122	C₂×C₄×C₄₃	—	2	24	no	—
123	C₂×C₄×C₄₃	—	4	16	no	—
124	C₂×Dic₄₃	—	2	24	no	—
125	C₂×Dic₄₃	—	4	16	no	—
126	C₄×D₄₃	—	4	64	no	—
127	C₂²×#379	—	43	1	no	maximal, Sylow
128	C₂²×C₄₃	—	2	128	no	—
129	C₂²×C₄₃	—	2	24	no	—
130	C₂²×C₄₃	—	2	48	no	—
131	C₂²×C₄₃	—	2	96	no	—
132	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	12	yes	—
133	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	24	yes	complemented
134	C₂²×C₄₃	C₂×#120	1	16	yes	—
135	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
136	C₂²×C₄₃	C₂³×D₄	1	6	yes	—
137	C₂×D₄₃	—	2	384	no	—
138	C₂×D₄₃	—	2	24	no	—
139	C₂×D₄₃	—	2	48	no	—
140	C₂×D₄₃	—	2	96	no	—
141	C₂×D₄₃	—	2	384	no	—
142	C₂×D₄₃	#379	1	64	yes	direct product factor
143	C₂×D₄₃	C₂²×C₂²⋊C₄	1	24	yes	—
144	C₂×D₄₃	C₂²×C₂²⋊C₄	1	24	yes	complemented
145	C₂×D₄₃	C₂×#120	1	32	yes	—
146	C₄×C₄₃	—	4	8	no	—
147	Dic₄₃	—	4	8	no	—
148	C₂⁷	—	43	1	no	—
149	C₂³×C₂²⋊C₄	—	43	6	no	—
150	C₂×#379	—	43	16	no	—
151	C₂×#379	—	43	1	no	—
152	C₂×#379	—	43	6	no	—
153	C₂×#379	D₄₃	1	1	yes	characteristic, direct product factor
154	C₂×C₄₃	—	2	24	no	—
155	C₂×C₄₃	C₂×#379	1	8	yes	complemented
156	C₂×C₄₃	C₂³×C₂²⋊C₄	1	3	yes	—
157	C₂×C₄₃	C₂²×#120	1	4	yes	—
158	D₄₃	—	2	24	no	—
159	D₄₃	C₂×#379	1	16	yes	direct product factor
160	C₂⁶	—	43	3	no	—
161	C₂⁶	—	43	8	no	—
162	C₂⁶	—	43	3	no	—
163	C₂⁶	—	43	16	no	—
164	C₂⁶	—	86	48	no	—
165	C₂⁶	C₂×D₄₃	1	1	yes	characteristic
166	C₂⁴×C₄	—	43	4	no	—
167	C₂²×C₂²⋊C₄	—	43	6	no	—
168	C₂²×C₂²⋊C₄	—	43	12	no	—
169	C₂²×C₂²⋊C₄	—	43	48	no	—
170	C₂²×C₂²⋊C₄	—	86	48	no	—
171	C₂²×C₂²⋊C₄	C₂×D₄₃	1	6	yes	complemented
172	#379	—	43	8	no	—
173	#379	—	43	48	no	—
174	#379	C₂×D₄₃	1	8	yes	direct product factor
175	C₄₃	C₂²×#379	1	1	yes	characteristic, complemented, Sylow
176	C₂⁵	—	2	24	no	—
177	C₂⁵	—	43	1	no	—
178	C₂⁵	—	43	24	no	—
179	C₂⁵	—	43	48	no	—
180	C₂⁵	—	43	12	no	—
181	C₂⁵	—	43	3	no	—
182	C₂⁵	—	43	24	no	—
183	C₂⁵	—	43	64	no	—
184	C₂⁵	—	43	12	no	—
185	C₂⁵	—	86	384	no	—
186	C₂⁵	—	86	48	no	—
187	C₂⁵	—	86	192	no	—
188	C₂⁵	—	86	48	no	—
189	C₂⁵	—	86	512	no	—
190	C₂⁵	—	86	24	no	—
191	C₂⁵	C₄×D₄₃	1	8	yes	complemented
192	C₂⁵	C₂²×D₄₃	1	4	yes	—
193	C₂⁵	C₂²×D₄₃	1	3	yes	—
194	C₂³×C₄	—	43	4	no	—
195	C₂³×C₄	—	43	16	no	—
196	C₂³×C₄	—	86	48	no	—
197	C₂³×C₄	C₂²×D₄₃	1	4	yes	complemented
198	C₂×C₂²⋊C₄	—	2	24	no	—
199	C₂×C₂²⋊C₄	—	43	24	no	—
200	C₂×C₂²⋊C₄	—	43	48	no	—
201	C₂×C₂²⋊C₄	—	86	192	no	—
202	C₂×C₂²⋊C₄	—	86	48	no	—
203	C₂×C₂²⋊C₄	—	86	24	no	—
204	C₂×C₂²⋊C₄	C₂²×D₄₃	1	24	yes	complemented
205	C₂⁴	—	2	128	no	—
206	C₂⁴	—	2	96	no	—
207	C₂⁴	—	2	48	no	—
208	C₂⁴	—	2	24	no	—
209	C₂⁴	—	43	4	no	—
210	C₂⁴	—	43	24	no	—
211	C₂⁴	—	43	2	no	—
212	C₂⁴	—	43	192	no	—
213	C₂⁴	—	43	48	no	—
214	C₂⁴	—	43	12	no	—
215	C₂⁴	—	43	96	no	—
216	C₂⁴	—	43	24	no	—
217	C₂⁴	—	43	6	no	—
218	C₂⁴	—	43	48	no	—
219	C₂⁴	—	86	192	no	—
220	C₂⁴	—	86	192	no	—
221	C₂⁴	—	86	768	no	—
222	C₂⁴	—	86	384	no	—
223	C₂⁴	—	86	96	no	—
224	C₂⁴	—	86	96	no	—
225	C₂⁴	—	86	1024	no	—
226	C₂⁴	—	86	2048	no	—
227	C₂⁴	—	86	384	no	—
228	C₂⁴	—	86	96	no	—
229	C₂⁴	—	86	48	no	—
230	C₂⁴	—	86	24	no	—
231	C₂⁴	C₂×C₄×D₄₃	1	12	yes	—
232	C₂⁴	C₂×C₄×D₄₃	1	16	yes	complemented
233	C₂⁴	D₄×D₄₃	1	24	yes	—
234	C₂⁴	C₂³×D₄₃	1	6	yes	—
235	C₂⁴	C₂³×D₄₃	1	1	yes	characteristic
236	C₂²×C₄	—	2	24	no	—
237	C₂²×C₄	—	43	8	no	—
238	C₂²×C₄	—	86	96	no	—
239	C₂²×C₄	—	86	24	no	—
240	C₂²×C₄	—	172	64	no	—
241	C₂²×C₄	C₂³×D₄₃	1	8	yes	complemented
242	C₂²⋊C₄	—	2	48	no	—
243	C₂²⋊C₄	—	86	96	no	—
244	C₂²⋊C₄	—	86	48	no	—
245	C₂³	—	2	128	no	—
246	C₂³	—	2	256	no	—
247	C₂³	—	2	48	no	—
248	C₂³	—	2	96	no	—
249	C₂³	—	2	96	no	—
250	C₂³	—	2	24	no	—
251	C₂³	—	43	48	no	—
252	C₂³	—	43	64	no	—
253	C₂³	—	43	4	no	—
254	C₂³	—	43	24	no	—
255	C₂³	—	43	48	no	—
256	C₂³	—	43	192	no	—
257	C₂³	—	43	12	no	—
258	C₂³	—	43	24	no	—
259	C₂³	—	86	384	no	—
260	C₂³	—	86	768	no	—
261	C₂³	—	86	192	no	—
262	C₂³	—	86	192	no	—
263	C₂³	—	86	2048	no	—
264	C₂³	—	86	384	no	—
265	C₂³	—	86	768	no	—
266	C₂³	—	86	48	no	—
267	C₂³	—	86	96	no	—
268	C₂³	—	86	96	no	—
269	C₂³	—	86	24	no	—
270	C₂³	C₂²⋊C₄×D₄₃	1	48	yes	complemented
271	C₂³	C₂²×C₄×D₄₃	1	12	yes	—
272	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
273	C₂³	C₂×D₄×D₄₃	1	24	yes	—
274	C₂³	C₂×D₄×D₄₃	1	12	yes	—
275	C₂³	C₂⁴×D₄₃	1	1	yes	characteristic
276	C₂×C₄	—	2	24	no	—
277	C₂×C₄	—	4	16	no	—
278	C₂×C₄	—	86	24	no	—
279	C₂×C₄	—	172	64	no	—
280	C₂×C₄	—	172	16	no	—
281	C₂²	—	2	128	no	—
282	C₂²	—	2	48	no	—
283	C₂²	—	2	96	no	—
284	C₂²	—	2	24	no	—
285	C₂²	—	43	32	no	—
286	C₂²	—	43	64	no	—
287	C₂²	—	43	24	no	—
288	C₂²	—	43	24	no	—
289	C₂²	—	86	384	no	—
290	C₂²	—	86	384	no	—
291	C₂²	—	86	48	no	—
292	C₂²	—	86	96	no	—
293	C₂²	—	86	24	no	—
294	C₂²	C₂×C₂²⋊C₄×D₄₃	1	12	yes	—
295	C₂²	C₂×C₂²⋊C₄×D₄₃	1	24	yes	complemented
296	C₂²	#120×D₄₃	1	16	yes	—
297	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
298	C₂²	C₂²×D₄×D₄₃	1	6	yes	—
299	C₄	—	4	8	no	—
300	C₄	—	172	8	no	—
301	C₂	—	2	24	no	—
302	C₂	—	43	16	no	—
303	C₂	—	86	24	no	—
304	C₂	#379×D₄₃	1	8	yes	direct product factor
305	C₂	C₂²×C₂²⋊C₄×D₄₃	1	3	yes	—
306	C₂	C₂×#120×D₄₃	1	4	yes	—

	subgroup	G/H
center	C₂⁴	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#379	C₂
socle	C₂⁴×C₄₃	C₂⁴
prime radical	C₂⁶×D₄₃	C₂
cosocle	C₂³×C₄₃	C₂⁵
hypercenter	C₂×#379	D₄₃
hypocenter	C₄₃	C₂²×#379
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂⁴ ◁ C₂×#379

Complements

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

N	H ≅ G/N	type
2. C₂²×C₂²⋊C₄×D₄₃	C₂	semidirect
3. C₂×#14582755	C₂	semidirect
4. C₂×#14582754	C₂	semidirect
5. #379×D₄₃	C₂	direct (N × H)
6. C₂×C₄₃×#379	C₂	semidirect
8. C₂⁵×D₄₃	C₄	semidirect
12. C₂³×C₄×D₄₃	C₂²	semidirect
13. C₂²×C₂²⋊Dic₄₃	C₂²	semidirect
14. C₂²×(C₂×D₄₃)⋊C₄	C₂²	semidirect
16. C₂×C₂²⋊C₄×D₄₃	C₂²	semidirect
17. #14582755	C₂²	semidirect
18. #14582754	C₂²	semidirect
20. C₂²×C₂²⋊C₄×C₄₃	C₂²	semidirect
21. C₄₃×#379	C₂²	semidirect
29. C₂⁴×D₄₃	C₂×C₄	semidirect
30. C₂⁴×D₄₃	C₂×C₄	semidirect
36. C₂³×Dic₄₃	C₂³	semidirect
38. C₂²×C₄×D₄₃	C₂³	semidirect
40. C₂×C₂²⋊Dic₄₃	C₂³	semidirect
42. C₂×(C₂×D₄₃)⋊C₄	C₂³	semidirect
45. C₂⁵×C₄₃	C₂×C₄	semidirect
48. C₂³×C₄×C₄₃	C₂³	semidirect
50. C₂×C₂²⋊C₄×C₄₃	C₂³	semidirect
56. C₂⁴×C₄₃	C₂²×C₄	semidirect
72. C₂³×D₄₃	C₂²⋊C₄	semidirect
76. C₂³×D₄₃	C₂²×C₄	semidirect
83. C₂²×C₄×C₄₃	C₂⁴	semidirect
85. C₂²×Dic₄₃	C₂⁴	semidirect
97. C₂³×C₄₃	C₂×C₂²⋊C₄	semidirect
115. C₂²×D₄₃	C₂×C₂²⋊C₄	semidirect
116. C₂²×D₄₃	C₂×C₂²⋊C₄	semidirect
133. C₂²×C₄₃	C₂²×C₂²⋊C₄	semidirect
142. C₂×D₄₃	#379	direct (N × H)
144. C₂×D₄₃	C₂²×C₂²⋊C₄	semidirect
153. C₂×#379	D₄₃	direct (N × H)
155. C₂×C₄₃	C₂×#379	semidirect
159. D₄₃	C₂×#379	direct (N × H)
171. C₂²×C₂²⋊C₄	C₂×D₄₃	semidirect
174. #379	C₂×D₄₃	direct (N × H)
175. C₄₃	C₂²×#379	semidirect
191. C₂⁵	C₄×D₄₃	semidirect
197. C₂³×C₄	C₂²×D₄₃	semidirect
204. C₂×C₂²⋊C₄	C₂²×D₄₃	semidirect
232. C₂⁴	C₂×C₄×D₄₃	semidirect
241. C₂²×C₄	C₂³×D₄₃	semidirect
270. C₂³	C₂²⋊C₄×D₄₃	semidirect
295. C₂²	C₂×C₂²⋊C₄×D₄₃	semidirect
304. C₂	#379×D₄₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁶×D₄₃	2
C₂²×C₂²⋊C₄×D₄₃	2
C₂×#14582755	2
C₂×#14582754	2
#379×D₄₃	2
C₂×C₄₃×#379	2
C₂²×#379	43

Subgroups — C2×#379×D43 #25254850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#379×D₄₃ #25254850