Subgroups — #25084474

Order 11008.

772 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145736	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145723	C₂	1	1	yes	maximal, characteristic
3	#19145155	C₂	1	1	yes	maximal, characteristic
4	#19145054	C₂	1	1	yes	maximal, characteristic
5	C₂×#14583249	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134229	C₂	1	2	yes	maximal, complemented
7	#19134218	C₂	1	2	yes	maximal, complemented
8	#19134197	C₂	1	2	yes	maximal, complemented
9	#19134193	C₂	1	2	yes	maximal, complemented
10	M₁₆×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063358	—	2	2	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	C₂×#13063325	C₂²	1	1	yes	characteristic
15	#14583295	C₂²	1	2	yes	—
16	#14583295	C₂²	1	1	yes	characteristic
17	#14583295	C₂²	1	2	yes	—
18	#14583293	—	2	2	no	—
19	#14583279	C₂²	1	2	yes	—
20	#14583273	C₂²	1	1	yes	characteristic
21	#14583272	C₂²	1	2	yes	—
22	#14583249	—	2	2	no	—
23	#14583249	C₂²	1	2	yes	—
24	#14583249	C₂²	1	2	yes	—
25	#14583249	C₂²	1	1	yes	characteristic
26	#14583249	C₂²	1	2	yes	—
27	#14583247	C₂²	1	2	yes	—
28	#14583247	C₂²	1	1	yes	characteristic
29	#14583227	—	2	2	no	—
30	#14583217	—	2	2	no	—
31	#14583186	—	2	2	no	—
32	#14583184	—	2	2	no	—
33	#14583130	—	2	2	no	—
34	C₄×#10621884	—	2	2	no	—
35	#14582952	C₂²	1	1	yes	characteristic
36	C₂×#13063249	—	2	2	no	—
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	#14582620	C₂²	1	2	yes	—
39	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
40	C₄₃×#533	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
42	C₄₃×#501	—	2	2	no	—
43	C₄₃×#500	C₂²	1	2	yes	—
44	C₄₃×#498	C₂²	1	2	yes	—
45	C₄₃×#428	—	2	2	no	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	#13063358	—	4	8	no	—
50	C₂×Dic₁₇₂	—	2	4	no	—
51	C₂×#10621873	—	2	4	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂²×C₄₃⋊C₈	D₄	1	2	yes	—
54	#13063325	—	2	1	no	—
55	#13063325	—	2	1	no	—
56	#13063325	—	2	1	no	—
57	#13063325	C₂³	1	2	yes	—
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063322	C₂³	1	1	yes	characteristic
60	#13063313	—	2	1	no	—
61	#13063299	—	2	1	no	—
62	#13063299	—	2	1	no	—
63	C₄×D₁₇₂	—	2	1	no	—
64	C₄×D₁₇₂	—	2	1	no	—
65	C₂×C₄⋊Dic₄₃	—	2	1	no	—
66	C₂×C₄⋊Dic₄₃	—	2	1	no	—
67	#13063256	—	2	2	no	—
68	#13063256	—	2	4	no	—
69	#13063256	—	2	4	no	—
70	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
71	#13063249	—	2	2	no	—
72	#13063249	—	2	4	no	—
73	#13063249	—	2	4	no	—
74	#13063249	—	2	4	no	—
75	#13063245	—	2	2	no	—
76	#13063245	—	2	4	no	—
77	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
78	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
79	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
82	C₂²×Q₈×C₄₃	—	2	1	no	—
83	C₂×M₁₆×C₄₃	D₄	1	2	yes	—
84	C₄⋊Q₈×C₄₃	—	2	1	no	—
85	C₄⋊Q₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	—	2	1	no	—
87	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
90	#125×C₄₃	—	2	1	no	—
91	C₂²⋊Q₈×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	#117×C₄₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
98	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
99	#107×C₄₃	—	2	4	no	—
100	#106×C₄₃	—	2	4	no	—
101	#97×C₄₃	D₄	1	2	yes	—
102	C₄×C₈×C₄₃	C₂³	1	2	yes	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×Q₈×C₄₃	—	2	1	no	—
105	C₂×Q₈×C₄₃	—	2	2	no	—
106	C₂×Q₈×C₄₃	—	4	4	no	—
107	C₂×Q₈×C₄₃	—	4	1	no	—
108	C₂²×C₄×C₄₃	—	4	1	no	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	—	4	1	no	—
113	C₂²×Dic₄₃	—	4	1	no	—
114	#10621898	—	4	4	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	—	2	1	no	—
118	C₂×C₄×D₄₃	—	4	1	no	—
119	C₂×Dic₈₆	—	2	1	no	—
120	C₂×Dic₈₆	—	2	2	no	—
121	C₂×Dic₈₆	—	4	4	no	—
122	C₂×Dic₈₆	—	4	1	no	—
123	M₁₆×C₄₃	SD₁₆	1	8	yes	complemented
124	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	4	1	no	—
132	C₄⋊C₄×C₄₃	—	4	1	no	—
133	C₄⋊C₄×C₄₃	—	4	1	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₂²⋊C₄×C₄₃	—	4	1	no	—
136	C₄²×C₄₃	—	4	1	no	—
137	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
141	#10621884	—	4	4	no	—
142	(C₂×D₄₃)⋊C₄	—	4	1	no	—
143	(C₂×D₄₃)⋊C₄	—	4	1	no	—
144	C₄⋊Dic₄₃	—	2	2	no	—
145	C₄⋊Dic₄₃	—	2	2	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	—	4	1	no	—
149	C₄⋊Dic₄₃	—	4	1	no	—
150	C₂×C₄₃⋊C₈	—	4	2	no	—
151	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₃⋊C₈	C₂×D₄	1	4	yes	—
154	Dic₁₇₂	—	4	8	no	—
155	#10621873	—	4	8	no	—
156	C₂³×C₄₃	#127	1	1	yes	characteristic
157	C₂²×D₄₃	—	4	1	no	—
158	Q₈×C₄₃	—	4	2	no	—
159	Q₈×C₄₃	—	4	4	no	—
160	Q₈×C₄₃	—	4	2	no	—
161	Q₈×C₄₃	—	8	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	4	1	no	—
165	C₂×C₄×C₄₃	—	4	1	no	—
166	C₂×C₄×C₄₃	—	4	2	no	—
167	C₂×C₄×C₄₃	—	8	2	no	—
168	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
169	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
170	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×SD₁₆	1	4	yes	—
172	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂²⋊D₄₃	—	8	2	no	—
176	C₂×Dic₄₃	—	4	2	no	—
177	C₂×Dic₄₃	—	4	1	no	—
178	C₂×Dic₄₃	—	8	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	4	2	no	—
182	C₄×D₄₃	—	8	2	no	—
183	Dic₈₆	—	4	4	no	—
184	Dic₈₆	—	4	2	no	—
185	Dic₈₆	—	8	2	no	—
186	C₈×C₄₃	C₂×SD₁₆	1	8	yes	—
187	C₄₃⋊C₈	—	2	2	no	—
188	C₄₃⋊C₈	—	2	2	no	—
189	C₄₃⋊C₈	—	2	4	no	—
190	#19624	—	43	1	no	maximal, Sylow
191	C₂²×C₄₃	—	2	1	no	—
192	C₂²×C₄₃	—	2	1	no	—
193	C₂²×C₄₃	#492	1	2	yes	—
194	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
195	C₂×D₄₃	—	8	1	no	—
196	C₂×D₄₃	—	8	1	no	—
197	C₂×D₄₃	—	8	1	no	—
198	C₄×C₄₃	—	2	1	no	—
199	C₄×C₄₃	—	2	1	no	—
200	C₄×C₄₃	—	8	2	no	—
201	C₄×C₄₃	—	8	1	no	—
202	C₄×C₄₃	—	8	1	no	—
203	C₄×C₄₃	#492	1	2	yes	—
204	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
205	C₄×C₄₃	#575	1	2	yes	—
206	C₄×C₄₃	#578	1	2	yes	—
207	Dic₄₃	—	8	2	no	—
208	Dic₄₃	—	8	1	no	—
209	#3229	—	43	1	no	—
210	#3227	—	43	1	no	—
211	#3167	—	43	1	no	—
212	#3165	D₄₃	1	1	yes	characteristic, complemented
213	#3152	—	43	1	no	—
214	C₂×#487	—	43	1	no	—
215	#1716	—	43	2	no	—
216	#1714	—	43	2	no	—
217	#1708	—	43	2	no	—
218	#1707	—	43	2	no	—
219	C₈×M₁₆	—	43	1	no	—
220	C₂×C₄₃	—	2	2	no	—
221	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
222	C₂×C₄₃	#3153	1	1	yes	characteristic
223	C₂×C₄₃	#3156	1	1	yes	characteristic
224	D₄₃	—	16	1	no	—
225	C₂×#137	—	86	2	no	—
226	#533	C₂×D₄₃	1	1	yes	characteristic
227	#532	—	43	1	no	—
228	C₂×C₄⋊Q₈	—	43	1	no	—
229	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
230	#501	—	2	2	no	—
231	#500	C₂×D₄₃	1	2	yes	—
232	#498	—	43	1	no	—
233	#498	—	43	2	no	—
234	#498	—	43	2	no	—
235	#498	C₂×D₄₃	1	2	yes	—
236	#497	—	86	2	no	—
237	#494	—	43	2	no	—
238	#492	—	43	1	no	—
239	#492	—	43	2	no	—
240	#487	—	43	2	no	—
241	#487	—	43	2	no	—
242	#487	—	43	1	no	—
243	#487	—	43	2	no	—
244	#487	—	86	2	no	—
245	#486	—	43	1	no	—
246	#486	—	43	2	no	—
247	#483	—	86	2	no	—
248	#481	—	86	2	no	—
249	#476	—	86	2	no	—
250	#475	—	86	2	no	—
251	#465	—	86	2	no	—
252	C₄×SD₁₆	—	86	2	no	—
253	#431	—	43	1	no	—
254	#428	—	2	2	no	—
255	C₂×#103	—	86	2	no	—
256	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
257	C₂×C₄×C₈	—	43	1	no	—
258	#322	—	43	2	no	—
259	C₈²	—	43	2	no	—
260	C₄₃	#19624	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	86	1	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂²×Q₈	—	86	1	no	—
264	#137	—	172	8	no	—
265	C₂×Q₁₆	—	86	4	no	—
266	C₂×SD₁₆	—	86	2	no	—
267	C₂×SD₁₆	—	86	4	no	—
268	C₂×M₁₆	C₂²⋊D₄₃	1	2	yes	—
269	C₂²×C₈	—	43	2	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	—	2	1	no	—
273	C₄⋊Q₈	—	43	2	no	—
274	C₄⋊Q₈	—	43	1	no	—
275	C₄⋊Q₈	—	86	1	no	—
276	C₄⋊Q₈	—	86	1	no	—
277	C₄⋊Q₈	—	86	1	no	—
278	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
279	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
280	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
281	#127	—	43	1	no	—
282	#125	—	2	1	no	—
283	#124	—	86	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	#121	—	86	1	no	—
287	#121	—	86	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×D₄	—	86	1	no	—
291	C₄×D₄	—	86	1	no	—
292	#117	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	86	1	no	—
296	C₂×C₄⋊C₄	—	86	1	no	—
297	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
298	#107	—	2	4	no	—
299	#106	—	2	4	no	—
300	#106	—	86	2	no	—
301	#106	—	86	4	no	—
302	#106	—	86	4	no	—
303	C₄⋊C₈	—	43	2	no	—
304	#103	—	86	4	no	—
305	#103	—	86	4	no	—
306	#103	—	86	2	no	—
307	#103	—	86	4	no	—
308	#102	—	86	2	no	—
309	#102	—	86	4	no	—
310	C₂²⋊C₈	—	43	2	no	—
311	#97	C₂²⋊D₄₃	1	2	yes	—
312	C₄×C₈	—	43	2	no	—
313	C₄×C₈	—	43	1	no	—
314	C₄×C₈	—	43	2	no	—
315	C₄×C₈	—	43	1	no	—
316	C₄×C₈	C₂²×D₄₃	1	2	yes	—
317	#41	—	172	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×Q₈	—	4	4	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	86	1	no	—
324	C₂×Q₈	—	86	2	no	—
325	C₂×Q₈	—	172	4	no	—
326	C₂×Q₈	—	172	1	no	—
327	C₂×D₄	—	86	1	no	—
328	C₂×D₄	—	86	1	no	—
329	C₂×D₄	—	86	1	no	—
330	C₂×D₄	—	172	1	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	—	172	1	no	—
333	C₂²×C₄	—	172	1	no	—
334	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
337	Q₁₆	—	172	8	no	—
338	SD₁₆	—	172	4	no	—
339	SD₁₆	—	172	8	no	—
340	M₁₆	#10621884	1	8	yes	complemented
341	C₂×C₈	—	43	2	no	—
342	C₂×C₈	—	43	2	no	—
343	C₂×C₈	—	43	4	no	—
344	C₂×C₈	—	172	2	no	—
345	C₂×C₈	C₂×C₂²⋊D₄₃	1	4	yes	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	86	2	no	—
357	C₄⋊C₄	—	86	2	no	—
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	172	1	no	—
361	C₄⋊C₄	—	172	1	no	—
362	C₂²⋊C₄	—	4	1	no	—
363	C₂²⋊C₄	—	172	1	no	—
364	C₂²⋊C₄	—	172	1	no	—
365	C₄²	—	4	1	no	—
366	C₄²	D₄×D₄₃	1	1	yes	characteristic
367	C₄²	D₄×D₄₃	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
369	C₄²	C₂³×D₄₃	1	1	yes	characteristic
370	C₂³	—	172	1	no	—
371	C₂³	#13063321	1	1	yes	characteristic
372	Q₈	—	4	2	no	—
373	Q₈	—	4	4	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	8	2	no	—
376	Q₈	—	344	2	no	—
377	Q₈	—	172	4	no	—
378	Q₈	—	172	2	no	—
379	D₄	—	344	2	no	—
380	D₄	—	172	2	no	—
381	D₄	—	172	2	no	—
382	D₄	—	172	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	344	2	no	—
390	C₂×C₄	—	344	2	no	—
391	C₂×C₄	—	172	1	no	—
392	C₂×C₄	—	172	2	no	—
393	C₂×C₄	#13063321	1	1	yes	characteristic
394	C₂×C₄	#13063321	1	1	yes	characteristic
395	C₂×C₄	#13063321	1	1	yes	characteristic
396	C₂×C₄	C₂×#10621884	1	4	yes	—
397	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
400	C₈	—	86	2	no	—
401	C₈	—	86	2	no	—
402	C₈	—	86	4	no	—
403	C₈	C₂×#10621884	1	8	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	344	1	no	—
407	C₂²	—	344	1	no	—
408	C₂²	—	344	1	no	—
409	C₂²	#14583273	1	2	yes	—
410	C₂²	C₂×#13063321	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	344	1	no	—
417	C₄	—	344	2	no	—
418	C₄	#14583273	1	2	yes	—
419	C₄	C₂²×#10621884	1	2	yes	—
420	C₄	#14583695	1	2	yes	—
421	C₄	#14583715	1	2	yes	—
422	C₂	—	2	2	no	—
423	C₂	—	688	1	no	—
424	C₂	C₂×#14583273	1	1	yes	characteristic
425	C₂	#19145057	1	1	yes	characteristic
426	C₂	#19145088	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063321
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3165	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	#14583449	C₂²
hypercenter	#3165	D₄₃
hypocenter	C₄₃	#19624
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3165

Complements

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

N	H ≅ G/N	type
1. #19145736	C₂	semidirect
5. C₂×#14583249	C₂	semidirect
6. #19134229	C₂	semidirect
7. #19134218	C₂	semidirect
8. #19134197	C₂	semidirect
9. #19134193	C₂	semidirect
10. M₁₆×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#3165	C₂	semidirect
123. M₁₆×C₄₃	SD₁₆	semidirect
212. #3165	D₄₃	semidirect
260. C₄₃	#19624	semidirect
340. M₁₆	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145736	2
#19145723	2
#19145155	2
#19145054	2
C₂×#14583249	2
#19134229	2
#19134218	2
#19134197	2
#19134193	2
M₁₆×C₄₃⋊C₈	2
C₄₃×#3165	2
#19624	43