Subgroups — #25084300

Order 11008.

706 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145182	C₂	1	1	yes	maximal, characteristic
2	#19145180	C₂	1	2	yes	maximal
3	#19145179	C₂	1	1	yes	maximal, characteristic
4	#19145104	C₂	1	2	yes	maximal
5	#19134212	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134211	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134203	C₂	1	2	yes	maximal, complemented
8	#19134192	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134190	C₂	1	2	yes	maximal, complemented
10	C₈²×D₄₃	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1707	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583454	C₂²	1	2	yes	—
13	#14583454	C₂²	1	2	yes	—
14	#14583304	C₂²	1	1	yes	characteristic
15	#14583302	C₂²	1	2	yes	—
16	#14583302	C₂²	1	2	yes	—
17	#14583302	C₂²	1	2	yes	—
18	#14583299	—	2	4	no	—
19	#14583297	C₂²	1	2	yes	—
20	#14583279	C₂²	1	1	yes	characteristic
21	#14583278	C₂²	1	2	yes	—
22	#14583251	C₂²	1	2	yes	—
23	#14583250	C₂²	1	2	yes	—
24	#14583249	C₂²	1	2	yes	—
25	#14583141	—	2	2	no	—
26	#14583139	—	2	4	no	—
27	#14583137	—	2	2	no	—
28	Q₁₆×Dic₄₃	—	2	2	no	—
29	#14582993	—	2	2	no	—
30	#14582991	—	2	4	no	—
31	#14582934	—	2	4	no	—
32	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
35	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₄₃×#500	C₂²	1	1	yes	characteristic
39	C₄₃×#498	C₂²	1	2	yes	—
40	C₄₃×#494	C₂²	1	1	yes	characteristic
41	C₄₃×#487	C₂²	1	2	yes	—
42	C₈²×C₄₃	C₂²	1	1	yes	characteristic
43	C₂×Dic₁₇₂	—	2	2	no	—
44	C₂×#10621885	—	2	4	no	—
45	C₂×C₈×D₄₃	D₄	1	2	yes	—
46	C₂×C₈×D₄₃	D₄	1	2	yes	—
47	C₂×C₈×D₄₃	D₄	1	2	yes	—
48	#13063325	C₂³	1	2	yes	—
49	#13063325	C₂³	1	2	yes	—
50	#13063316	—	2	2	no	—
51	#13063316	—	2	2	no	—
52	#13063305	—	2	2	no	—
53	#13063305	—	2	2	no	—
54	#13063301	—	2	2	no	—
55	#13063301	—	2	2	no	—
56	Q₈×Dic₄₃	—	2	2	no	—
57	Q₈×Dic₄₃	—	2	2	no	—
58	#13063290	—	2	2	no	—
59	#13063290	—	2	2	no	—
60	#13063283	—	2	2	no	—
61	#13063283	—	2	2	no	—
62	C₄²×D₄₃	C₂³	1	1	yes	characteristic
63	#13063259	—	2	2	no	—
64	#13063258	—	2	4	no	—
65	#13063258	—	2	4	no	—
66	#13063258	—	2	4	no	—
67	#13063257	—	2	4	no	—
68	#13063250	—	2	4	no	—
69	#13063249	—	2	4	no	—
70	#13063248	—	2	4	no	—
71	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
72	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
73	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
74	C₈×Dic₄₃	D₄	1	2	yes	—
75	C₈×Dic₄₃	D₄	1	2	yes	—
76	C₈×Dic₄₃	D₄	1	2	yes	—
77	C₂×Q₁₆×C₄₃	—	2	2	no	—
78	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
80	#107×C₄₃	—	2	2	no	—
81	#106×C₄₃	—	2	4	no	—
82	#103×C₄₃	—	2	4	no	—
83	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
86	C₂×Q₈×C₄₃	—	2	2	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
91	C₂×Dic₈₆	—	2	2	no	—
92	C₂×Dic₈₆	—	2	2	no	—
93	Q₁₆×C₄₃	—	4	4	no	—
94	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
95	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
96	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
97	C₄⋊C₄×C₄₃	—	2	2	no	—
98	C₄⋊C₄×C₄₃	—	2	2	no	—
99	C₄⋊C₄×C₄₃	—	2	2	no	—
100	C₄⋊C₄×C₄₃	—	2	2	no	—
101	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
102	#10621885	—	4	8	no	—
103	(C₂×D₄₃)⋊C₄	—	4	2	no	—
104	(C₂×D₄₃)⋊C₄	—	4	2	no	—
105	C₄⋊Dic₄₃	—	2	2	no	—
106	C₄⋊Dic₄₃	—	2	2	no	—
107	C₄⋊Dic₄₃	—	2	2	no	—
108	C₄⋊Dic₄₃	—	2	2	no	—
109	C₄⋊Dic₄₃	—	4	2	no	—
110	C₄⋊Dic₄₃	—	4	2	no	—
111	Dic₄₃⋊C₄	—	4	2	no	—
112	Dic₄₃⋊C₄	—	4	2	no	—
113	C₄×Dic₄₃	—	4	2	no	—
114	C₄×Dic₄₃	—	4	2	no	—
115	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
116	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
117	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
119	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
120	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
121	Dic₁₇₂	—	4	4	no	—
122	C₈×D₄₃	—	2	4	no	—
123	C₈×D₄₃	—	2	4	no	—
124	C₈×D₄₃	Q₁₆	1	8	yes	complemented
125	C₂²×D₄₃	#127	1	1	yes	characteristic
126	Q₈×C₄₃	—	4	4	no	—
127	Q₈×C₄₃	—	4	4	no	—
128	C₂×C₄×C₄₃	—	4	2	no	—
129	C₂×C₄×C₄₃	—	4	2	no	—
130	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
133	C₂×Dic₄₃	—	4	2	no	—
134	C₂×Dic₄₃	—	4	2	no	—
135	C₂×Dic₄₃	#127	1	1	yes	characteristic
136	C₂×Dic₄₃	#127	1	1	yes	characteristic
137	C₂×Dic₄₃	#127	1	1	yes	characteristic
138	C₄×D₄₃	—	2	2	no	—
139	C₄×D₄₃	—	2	2	no	—
140	C₄×D₄₃	C₂×Q₁₆	1	4	yes	—
141	Dic₈₆	—	4	4	no	—
142	Dic₈₆	—	4	4	no	—
143	C₈×C₄₃	—	2	2	no	—
144	C₈×C₄₃	C₂×Q₁₆	1	4	yes	—
145	C₈×C₄₃	#135	1	4	yes	—
146	C₄₃⋊C₈	—	2	2	no	—
147	C₄₃⋊C₈	C₂×Q₁₆	1	4	yes	—
148	C₄₃⋊C₈	#135	1	4	yes	—
149	#19604	—	43	1	no	maximal, Sylow
150	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
151	C₂×D₄₃	—	2	1	no	—
152	C₂×D₄₃	—	2	1	no	—
153	C₂×D₄₃	#494	1	2	yes	—
154	C₄×C₄₃	—	8	2	no	—
155	C₄×C₄₃	—	8	2	no	—
156	C₄×C₄₃	C₂²×Q₁₆	1	2	yes	—
157	C₄×C₄₃	C₂×#135	1	2	yes	—
158	C₄×C₄₃	C₂×#135	1	2	yes	—
159	Dic₄₃	—	2	1	no	—
160	Dic₄₃	—	2	1	no	—
161	Dic₄₃	—	8	2	no	—
162	Dic₄₃	—	8	2	no	—
163	Dic₄₃	#494	1	2	yes	—
164	#3170	—	43	1	no	—
165	#3170	—	43	1	no	—
166	#3170	—	43	2	no	—
167	#3160	—	43	2	no	—
168	#1713	—	43	1	no	—
169	#1713	—	43	1	no	—
170	#1710	—	43	2	no	—
171	#1707	—	43	2	no	—
172	#1707	—	43	1	no	—
173	#1707	D₄₃	1	1	yes	characteristic, complemented
174	C₂×C₈²	—	43	1	no	—
175	C₂×C₄₃	C₂×#494	1	1	yes	characteristic
176	C₂×C₄₃	#3147	1	1	yes	characteristic
177	C₂×C₄₃	#3147	1	1	yes	characteristic
178	D₄₃	—	2	2	no	—
179	#533	—	43	2	no	—
180	#533	—	43	2	no	—
181	#500	—	43	2	no	—
182	#500	—	43	2	no	—
183	#500	—	43	2	no	—
184	#500	—	43	1	no	—
185	#500	C₂×D₄₃	1	1	yes	characteristic
186	#499	—	86	4	no	—
187	#498	—	43	2	no	—
188	#498	C₂×D₄₃	1	2	yes	—
189	#494	—	43	2	no	—
190	#494	—	43	1	no	—
191	#494	C₂×D₄₃	1	1	yes	characteristic
192	#487	—	43	2	no	—
193	#487	—	43	2	no	—
194	#487	—	43	2	no	—
195	#487	C₂×D₄₃	1	2	yes	—
196	#467	—	86	4	no	—
197	#467	—	86	2	no	—
198	#467	—	86	2	no	—
199	C₄×Q₁₆	—	86	4	no	—
200	C₄×Q₁₆	—	86	2	no	—
201	C₄×Q₁₆	—	86	2	no	—
202	#427	—	86	4	no	—
203	C₂×C₄×C₈	—	43	1	no	—
204	C₂×C₄×C₈	—	43	1	no	—
205	C₂×C₄×C₈	—	43	1	no	—
206	C₈²	—	43	1	no	—
207	C₈²	—	43	1	no	—
208	C₈²	—	43	1	no	—
209	C₈²	C₂×D₄₃	1	1	yes	characteristic
210	C₄₃	#19604	1	1	yes	characteristic, complemented, Sylow
211	C₂×Q₁₆	—	2	2	no	—
212	C₂×Q₁₆	—	86	4	no	—
213	C₂×Q₁₆	—	86	2	no	—
214	C₂²×C₈	—	43	2	no	—
215	C₂²×C₈	—	43	2	no	—
216	C₂²×C₈	—	43	2	no	—
217	C₄⋊Q₈	—	43	2	no	—
218	C₄⋊Q₈	—	43	2	no	—
219	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
220	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
221	#125	—	86	2	no	—
222	#125	—	86	2	no	—
223	C₂²⋊Q₈	—	86	2	no	—
224	C₂²⋊Q₈	—	86	2	no	—
225	C₂²⋊Q₈	—	86	2	no	—
226	C₂²⋊Q₈	—	86	2	no	—
227	C₄×Q₈	—	86	2	no	—
228	C₄×Q₈	—	86	2	no	—
229	C₄×Q₈	—	86	2	no	—
230	C₄×Q₈	—	86	2	no	—
231	#117	—	86	2	no	—
232	#117	—	86	2	no	—
233	C₂×C₄²	—	43	1	no	—
234	#107	—	2	2	no	—
235	#107	—	86	4	no	—
236	#107	—	86	4	no	—
237	#107	—	86	4	no	—
238	#107	—	86	2	no	—
239	#106	—	2	4	no	—
240	#106	—	86	4	no	—
241	#103	—	2	4	no	—
242	#103	—	86	4	no	—
243	#103	—	86	4	no	—
244	#103	—	86	4	no	—
245	C₄×C₈	—	43	2	no	—
246	C₄×C₈	—	43	2	no	—
247	C₄×C₈	—	43	2	no	—
248	C₄×C₈	—	43	1	no	—
249	C₄×C₈	—	43	1	no	—
250	C₄×C₈	—	43	1	no	—
251	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
252	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
253	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
254	C₂×Q₈	—	2	2	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	86	2	no	—
257	C₂×Q₈	—	86	2	no	—
258	C₂²×C₄	—	43	1	no	—
259	C₂²×C₄	—	43	1	no	—
260	C₂²×C₄	—	43	1	no	—
261	Q₁₆	—	4	4	no	—
262	Q₁₆	—	172	8	no	—
263	Q₁₆	—	172	4	no	—
264	C₂×C₈	—	43	2	no	—
265	C₂×C₈	—	43	2	no	—
266	C₂×C₈	—	43	8	no	—
267	C₂×C₈	—	43	2	no	—
268	C₂×C₈	—	86	4	no	—
269	C₂×C₈	—	86	4	no	—
270	C₂×C₈	D₄×D₄₃	1	2	yes	—
271	C₂×C₈	D₄×D₄₃	1	2	yes	—
272	C₂×C₈	D₄×D₄₃	1	2	yes	—
273	C₄⋊C₄	—	2	2	no	—
274	C₄⋊C₄	—	2	2	no	—
275	C₄⋊C₄	—	2	2	no	—
276	C₄⋊C₄	—	2	2	no	—
277	C₄⋊C₄	—	86	2	no	—
278	C₄⋊C₄	—	86	2	no	—
279	C₄⋊C₄	—	86	2	no	—
280	C₄⋊C₄	—	86	2	no	—
281	C₄⋊C₄	—	172	2	no	—
282	C₄⋊C₄	—	172	2	no	—
283	C₄⋊C₄	—	172	2	no	—
284	C₄⋊C₄	—	172	2	no	—
285	C₂²⋊C₄	—	172	2	no	—
286	C₂²⋊C₄	—	172	2	no	—
287	C₄²	—	43	1	no	—
288	C₄²	—	43	1	no	—
289	C₄²	—	43	1	no	—
290	C₄²	—	172	2	no	—
291	C₄²	—	172	2	no	—
292	C₄²	C₂³×D₄₃	1	1	yes	characteristic
293	C₂³	—	43	1	no	—
294	Q₈	—	4	4	no	—
295	Q₈	—	4	4	no	—
296	Q₈	—	172	4	no	—
297	Q₈	—	172	4	no	—
298	C₂×C₄	—	4	2	no	—
299	C₂×C₄	—	4	2	no	—
300	C₂×C₄	—	43	1	no	—
301	C₂×C₄	—	43	4	no	—
302	C₂×C₄	—	43	1	no	—
303	C₂×C₄	—	43	1	no	—
304	C₂×C₄	—	86	2	no	—
305	C₂×C₄	—	86	2	no	—
306	C₂×C₄	—	172	2	no	—
307	C₂×C₄	—	172	2	no	—
308	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
309	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
310	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
311	C₈	—	2	2	no	—
312	C₈	—	43	4	no	—
313	C₈	—	43	4	no	—
314	C₈	—	86	2	no	—
315	C₈	Q₁₆×D₄₃	1	4	yes	—
316	C₈	#13063346	1	4	yes	—
317	C₂²	—	43	2	no	—
318	C₂²	—	86	1	no	—
319	C₂²	—	86	1	no	—
320	C₂²	#127×D₄₃	1	1	yes	characteristic
321	C₄	—	8	2	no	—
322	C₄	—	8	2	no	—
323	C₄	—	43	2	no	—
324	C₄	—	86	1	no	—
325	C₄	—	86	1	no	—
326	C₄	—	344	2	no	—
327	C₄	—	344	2	no	—
328	C₄	C₂×Q₁₆×D₄₃	1	2	yes	—
329	C₄	#135×D₄₃	1	2	yes	—
330	C₄	C₂×#13063346	1	2	yes	—
331	C₂	—	86	2	no	—
332	C₂	#494×D₄₃	1	1	yes	characteristic
333	C₂	#19145018	1	1	yes	characteristic
334	C₂	#19145020	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1707	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	C₂²×D₄₃	#127
hypercenter	#1707	D₄₃
hypocenter	C₄₃	#19604
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1707

Complements

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

N	H ≅ G/N	type
5. #19134212	C₂	semidirect
6. #19134211	C₂	semidirect
7. #19134203	C₂	semidirect
8. #19134192	C₂	semidirect
9. #19134190	C₂	semidirect
11. C₄₃×#1707	C₂	semidirect
124. C₈×D₄₃	Q₁₆	semidirect
173. #1707	D₄₃	semidirect
210. C₄₃	#19604	semidirect

Maximal subgroups

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

subgroup	index
#19145182	2
#19145180	2
#19145179	2
#19145104	2
#19134212	2
#19134211	2
#19134203	2
#19134192	2
#19134190	2
C₈²×D₄₃	2
C₄₃×#1707	2
#19604	43