Subgroups — #25080115

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145912	C₂	1	1	yes	maximal, characteristic
2	#19145725	C₂	1	1	yes	maximal, characteristic
3	#19145141	C₂	1	1	yes	maximal, characteristic, complemented
4	#19143341	C₂	1	1	yes	maximal, characteristic
5	#19134119	C₂	1	2	yes	maximal, complemented
6	#19134095	C₂	1	2	yes	maximal, complemented
7	#19133995	C₂	1	2	yes	maximal, complemented
8	#19133971	C₂	1	2	yes	maximal, complemented
9	#19133250	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582647	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	#14583449	C₂²	1	1	yes	characteristic
15	C₂×#13063325	C₂²	1	1	yes	characteristic
16	#14583308	—	2	2	no	—
17	#14583304	C₂²	1	2	yes	—
18	#14583297	—	2	1	no	—
19	#14583297	C₂²	1	2	yes	—
20	#14583246	—	2	1	no	—
21	#14583218	—	2	2	no	—
22	#14583190	C₂²	1	2	yes	—
23	#14583190	C₂²	1	2	yes	—
24	#14583190	C₂²	1	2	yes	—
25	#14583185	—	2	1	no	—
26	#14583128	—	2	2	no	—
27	#14583105	C₂²	1	2	yes	—
28	#14583100	—	2	1	no	—
29	#14582978	C₂²	1	2	yes	—
30	#14582972	—	2	2	no	—
31	C₈×D₁₇₂	C₂²	1	2	yes	—
32	#14582941	—	2	1	no	—
33	#14582941	—	2	1	no	—
34	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
35	#14582867	—	2	1	no	—
36	#14582647	C₂²	1	2	yes	—
37	#14582647	C₂²	1	1	yes	characteristic
38	#14582647	C₂²	1	2	yes	—
39	#14582647	C₂²	1	1	yes	characteristic
40	#14582646	C₂²	1	1	yes	characteristic
41	#14582646	C₂²	1	1	yes	characteristic
42	C₄₃×#431	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	2	yes	—
46	C₄₃×#334	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	1	no	—
48	C₂²×Dic₈₆	—	2	1	no	—
49	C₂×#10621873	—	2	2	no	—
50	#13063333	—	4	4	no	—
51	C₂×#10621872	—	2	2	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂×C₈×D₄₃	—	2	2	no	—
54	#13063325	—	2	1	no	—
55	#13063325	—	2	1	no	—
56	#13063325	—	2	1	no	—
57	#13063325	D₄	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063325	C₂³	1	2	yes	—
60	#13063325	C₂³	1	1	yes	characteristic
61	#13063322	D₄	1	1	yes	characteristic
62	#13063317	—	2	1	no	—
63	#13063313	—	2	1	no	—
64	#13063304	—	2	1	no	—
65	#13063304	—	2	1	no	—
66	#13063299	—	2	1	no	—
67	#13063299	D₄	1	2	yes	—
68	C₄×Dic₈₆	—	2	1	no	—
69	C₄×Dic₈₆	—	2	1	no	—
70	C₄×D₁₇₂	—	2	1	no	—
71	C₄×D₁₇₂	C₂³	1	2	yes	—
72	#13063284	—	2	1	no	—
73	C₂×C₄⋊Dic₄₃	—	2	1	no	—
74	C₂×C₄⋊Dic₄₃	—	2	1	no	—
75	#13063259	—	2	2	no	—
76	#13063259	—	2	2	no	—
77	#13063257	—	2	2	no	—
78	#13063257	—	2	2	no	—
79	#13063257	—	2	2	no	—
80	#13063257	—	2	2	no	—
81	#13063257	—	2	2	no	—
82	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
83	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
84	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
85	#13063250	—	2	2	no	—
86	#13063247	—	2	2	no	—
87	#13063247	—	2	2	no	—
88	#13063247	—	2	2	no	—
89	(C₂×D₄₃)⋊C₈	—	2	2	no	—
90	(C₂×D₄₃)⋊C₈	—	2	2	no	—
91	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₄₃	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	—	2	1	no	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	—	2	1	no	—
96	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₄₃	—	2	1	no	—
100	#97×C₄₃	D₄	1	2	yes	—
101	C₄×C₈×C₄₃	—	2	1	no	—
102	C₄×C₈×C₄₃	C₂³	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₃	—	2	2	no	—
107	C₂²×Dic₄₃	—	4	1	no	—
108	#10621898	—	4	2	no	—
109	#10621898	—	4	2	no	—
110	C₂×D₁₇₂	—	2	1	no	—
111	C₂×D₁₇₂	—	2	1	no	—
112	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
113	C₂×C₄×D₄₃	—	2	2	no	—
114	C₂×Dic₈₆	—	2	1	no	—
115	C₂×Dic₈₆	—	2	1	no	—
116	C₂×Dic₈₆	—	2	1	no	—
117	C₂×Dic₈₆	—	2	2	no	—
118	C₂×Dic₈₆	—	4	1	no	—
119	C₂×Dic₈₆	—	8	2	no	—
120	M₁₆×C₄₃	—	2	2	no	—
121	M₁₆×C₄₃	SD₁₆	1	4	yes	complemented
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	1	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	8	1	no	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
128	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₃	#41	1	1	yes	characteristic
131	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
132	C₂²⋊Dic₄₃	—	4	1	no	—
133	(C₂×D₄₃)⋊C₄	—	2	2	no	—
134	(C₂×D₄₃)⋊C₄	—	2	2	no	—
135	C₄⋊Dic₄₃	—	2	1	no	—
136	C₄⋊Dic₄₃	—	2	2	no	—
137	C₄⋊Dic₄₃	—	2	1	no	—
138	C₄⋊Dic₄₃	—	2	1	no	—
139	C₄⋊Dic₄₃	—	2	2	no	—
140	C₄⋊Dic₄₃	—	2	1	no	—
141	C₄⋊Dic₄₃	—	2	1	no	—
142	C₄⋊Dic₄₃	—	4	1	no	—
143	C₄⋊Dic₄₃	—	4	1	no	—
144	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
145	Dic₄₃⋊C₄	—	4	1	no	—
146	Dic₄₃⋊C₄	—	4	1	no	—
147	C₄×Dic₄₃	—	4	1	no	—
148	C₂×C₄₃⋊C₈	—	2	1	no	—
149	C₂×C₄₃⋊C₈	—	2	1	no	—
150	C₂×C₄₃⋊C₈	—	4	2	no	—
151	#10621873	—	8	2	no	—
152	#10621872	—	4	4	no	—
153	C₈×D₄₃	—	4	4	no	—
154	C₂³×C₄₃	#121	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	2	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₄₃	#137	1	2	yes	—
164	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
167	C₂²⋊D₄₃	—	4	4	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	4	1	no	—
170	C₂×Dic₄₃	—	4	1	no	—
171	C₂×Dic₄₃	—	4	2	no	—
172	C₂×Dic₄₃	—	8	2	no	—
173	D₁₇₂	—	2	2	no	—
174	D₁₇₂	—	2	2	no	—
175	D₁₇₂	—	4	2	no	—
176	D₁₇₂	—	8	1	no	—
177	C₄×D₄₃	—	4	2	no	—
178	C₄×D₄₃	—	4	2	no	—
179	Dic₈₆	—	4	2	no	—
180	Dic₈₆	—	4	1	no	—
181	Dic₈₆	—	4	1	no	—
182	Dic₈₆	—	8	2	no	—
183	Dic₈₆	—	8	1	no	—
184	Dic₈₆	—	8	2	no	—
185	C₈×C₄₃	—	2	2	no	—
186	C₈×C₄₃	—	4	2	no	—
187	C₈×C₄₃	—	4	1	no	—
188	C₈×C₄₃	—	4	1	no	—
189	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
190	C₄₃⋊C₈	—	4	1	no	—
191	C₄₃⋊C₈	—	4	1	no	—
192	#19233	—	43	1	no	maximal, Sylow
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	#461	1	2	yes	—
196	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
197	C₂×D₄₃	—	4	2	no	—
198	C₂×D₄₃	—	4	2	no	—
199	C₂×D₄₃	—	4	2	no	—
200	C₄×C₄₃	—	2	1	no	—
201	C₄×C₄₃	—	2	1	no	—
202	C₄×C₄₃	—	2	1	no	—
203	C₄×C₄₃	#461	1	2	yes	—
204	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
205	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
206	C₄×C₄₃	#577	1	1	yes	characteristic
207	C₄×C₄₃	#578	1	1	yes	characteristic
208	Dic₄₃	—	4	2	no	—
209	Dic₄₃	—	8	1	no	—
210	Dic₄₃	—	8	2	no	—
211	Dic₄₃	—	8	1	no	—
212	#3246	—	43	1	no	—
213	#3227	—	43	1	no	—
214	#3165	—	43	1	no	—
215	#2935	—	43	1	no	—
216	#1695	—	43	2	no	—
217	#1691	—	43	2	no	—
218	#1675	—	43	2	no	—
219	#1671	—	43	2	no	—
220	#1565	D₄₃	1	1	yes	characteristic, complemented
221	#1542	—	43	1	no	—
222	C₂×#333	—	43	1	no	—
223	C₂×C₄₃	—	2	2	no	—
224	C₂×C₄₃	C₂×#461	1	1	yes	characteristic
225	C₂×C₄₃	#3063	1	1	yes	characteristic
226	C₂×C₄₃	#3068	1	1	yes	characteristic
227	D₄₃	—	8	2	no	—
228	C₂×#131	—	86	1	no	—
229	#533	—	43	1	no	—
230	#532	—	43	1	no	—
231	C₂×C₄⋊Q₈	—	43	1	no	—
232	#501	—	86	2	no	—
233	#500	—	43	2	no	—
234	#498	—	43	2	no	—
235	#498	—	86	1	no	—
236	#486	—	86	1	no	—
237	#481	—	86	2	no	—
238	#476	—	43	2	no	—
239	#476	—	43	2	no	—
240	#476	—	43	2	no	—
241	#475	—	86	1	no	—
242	#465	—	86	2	no	—
243	#461	—	43	2	no	—
244	#460	—	86	1	no	—
245	#436	—	43	2	no	—
246	#435	—	86	2	no	—
247	C₈×D₄	—	43	2	no	—
248	#431	C₂×D₄₃	1	1	yes	characteristic
249	#428	—	86	1	no	—
250	#428	—	86	1	no	—
251	C₂×C₄⋊C₈	—	43	1	no	—
252	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
253	#408	—	86	1	no	—
254	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
255	#335	C₂×D₄₃	1	2	yes	—
256	#334	C₂×D₄₃	1	2	yes	—
257	#333	—	43	2	no	—
258	#333	—	43	2	no	—
259	#333	—	43	1	no	—
260	#333	—	43	1	no	—
261	#332	—	43	1	no	—
262	#332	—	43	1	no	—
263	C₄₃	#19233	1	1	yes	characteristic, complemented, Sylow
264	C₂×#41	—	86	1	no	—
265	C₂²×Q₈	—	86	1	no	—
266	C₂×SD₁₆	—	86	2	no	—
267	#131	—	172	4	no	—
268	C₂×M₁₆	—	86	2	no	—
269	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
270	C₂×M₁₆	D₁₇₂	1	1	yes	characteristic
271	C₂²×C₈	—	2	1	no	—
272	C₂²×C₈	—	86	1	no	—
273	C₂²×C₈	—	86	2	no	—
274	C₄⋊Q₈	—	43	1	no	—
275	C₄⋊Q₈	—	43	2	no	—
276	C₄⋊Q₈	—	43	1	no	—
277	C₄⋊Q₈	—	43	1	no	—
278	C₄⋊Q₈	—	86	1	no	—
279	C₄⋊Q₈	—	86	1	no	—
280	C₄⋊Q₈	—	86	1	no	—
281	#127	—	43	1	no	—
282	#125	—	86	1	no	—
283	#124	—	86	1	no	—
284	C₂²⋊Q₈	—	86	1	no	—
285	C₂²⋊Q₈	—	86	1	no	—
286	#121	—	43	2	no	—
287	#121	—	86	1	no	—
288	C₄×Q₈	—	86	1	no	—
289	C₄×Q₈	—	86	1	no	—
290	C₄×D₄	—	43	2	no	—
291	C₄×D₄	—	86	1	no	—
292	#117	—	86	1	no	—
293	C₂×C₄⋊C₄	—	86	1	no	—
294	C₂×C₄⋊C₄	—	86	1	no	—
295	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
296	#107	—	86	2	no	—
297	#107	—	86	2	no	—
298	#106	—	86	2	no	—
299	#106	—	86	2	no	—
300	#106	—	86	2	no	—
301	#106	—	86	2	no	—
302	#106	—	86	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	43	1	no	—
305	C₄⋊C₈	—	43	1	no	—
306	C₄⋊C₈	—	86	1	no	—
307	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
309	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
310	#103	—	86	2	no	—
311	#102	—	86	2	no	—
312	#102	—	86	2	no	—
313	#102	—	86	2	no	—
314	C₂²⋊C₈	—	2	1	no	—
315	C₂²⋊C₈	—	86	2	no	—
316	C₂²⋊C₈	—	86	2	no	—
317	#97	D₁₇₂	1	2	yes	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	C₂²×D₄₃	1	2	yes	—
320	#41	—	172	2	no	—
321	#41	—	172	2	no	—
322	C₂×Q₈	—	86	1	no	—
323	C₂×Q₈	—	86	1	no	—
324	C₂×Q₈	—	86	1	no	—
325	C₂×Q₈	—	86	2	no	—
326	C₂×Q₈	—	344	2	no	—
327	C₂×Q₈	—	172	1	no	—
328	C₂×D₄	—	43	2	no	—
329	C₂×D₄	—	86	2	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂²×C₄	—	86	2	no	—
333	C₂²×C₄	—	172	1	no	—
334	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
336	C₂²×C₄	#10621902	1	1	yes	characteristic
337	SD₁₆	—	344	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	172	4	no	—
340	M₁₆	#10621873	1	4	yes	complemented
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	8	1	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	—	86	1	no	—
347	C₂×C₈	—	172	2	no	—
348	C₂×C₈	—	172	4	no	—
349	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
350	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
351	C₄⋊C₄	—	43	2	no	—
352	C₄⋊C₄	—	86	1	no	—
353	C₄⋊C₄	—	86	2	no	—
354	C₄⋊C₄	—	86	1	no	—
355	C₄⋊C₄	—	86	1	no	—
356	C₄⋊C₄	—	86	2	no	—
357	C₄⋊C₄	—	86	1	no	—
358	C₄⋊C₄	—	86	1	no	—
359	C₄⋊C₄	—	172	1	no	—
360	C₄⋊C₄	—	172	1	no	—
361	C₄⋊C₄	—	172	1	no	—
362	C₄⋊C₄	—	172	1	no	—
363	C₂²⋊C₄	—	86	2	no	—
364	C₂²⋊C₄	—	86	2	no	—
365	C₂²⋊C₄	—	172	1	no	—
366	C₄²	—	172	1	no	—
367	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
368	C₄²	D₄×D₄₃	1	1	yes	characteristic
369	C₄²	#10621902	1	1	yes	characteristic
370	C₄²	C₂³×D₄₃	1	1	yes	characteristic
371	C₂³	—	86	2	no	—
372	C₂³	#13063300	1	1	yes	characteristic
373	Q₈	—	344	2	no	—
374	Q₈	—	344	1	no	—
375	Q₈	—	344	2	no	—
376	Q₈	—	172	1	no	—
377	Q₈	—	172	1	no	—
378	Q₈	—	172	2	no	—
379	D₄	—	86	2	no	—
380	D₄	—	86	2	no	—
381	D₄	—	344	1	no	—
382	D₄	—	172	4	no	—
383	D₄	—	172	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	86	2	no	—
388	C₂×C₄	—	344	2	no	—
389	C₂×C₄	—	172	1	no	—
390	C₂×C₄	—	172	1	no	—
391	C₂×C₄	—	172	2	no	—
392	C₂×C₄	—	172	2	no	—
393	C₂×C₄	—	172	2	no	—
394	C₂×C₄	#13063300	1	1	yes	characteristic
395	C₂×C₄	#13063300	1	1	yes	characteristic
396	C₂×C₄	#13063300	1	1	yes	characteristic
397	C₂×C₄	C₂×#10621873	1	2	yes	—
398	C₂×C₄	#13063358	1	2	yes	—
399	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
401	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	172	1	no	—
407	C₈	—	172	1	no	—
408	C₈	C₂×#10621873	1	4	yes	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	172	2	no	—
412	C₂²	—	172	2	no	—
413	C₂²	—	172	2	no	—
414	C₂²	#14583105	1	2	yes	—
415	C₂²	C₂×#13063300	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	344	1	no	—
420	C₄	—	344	2	no	—
421	C₄	—	344	1	no	—
422	C₄	—	172	2	no	—
423	C₄	#14583105	1	2	yes	—
424	C₄	C₂²×#10621873	1	1	yes	characteristic
425	C₄	C₂×#13063358	1	1	yes	characteristic
426	C₄	#14583709	1	1	yes	characteristic
427	C₄	#14583715	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	344	2	no	—
430	C₂	C₂×#14583105	1	1	yes	characteristic
431	C₂	#19144287	1	1	yes	characteristic
432	C₂	#19144324	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063300
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1565	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#1565	D₄₃
hypocenter	C₄₃	#19233
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
3. #19145141	C₂	semidirect
5. #19134119	C₂	semidirect
6. #19134095	C₂	semidirect
7. #19133995	C₂	semidirect
8. #19133971	C₂	semidirect
9. #19133250	C₂	semidirect
10. C₂×#14582647	C₂	semidirect
11. C₄₃×#1565	C₂	semidirect
121. M₁₆×C₄₃	SD₁₆	semidirect
220. #1565	D₄₃	semidirect
263. C₄₃	#19233	semidirect
340. M₁₆	#10621873	semidirect

Maximal subgroups

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

subgroup	index
#19145912	2
#19145725	2
#19145141	2
#19143341	2
#19134119	2
#19134095	2
#19133995	2
#19133971	2
#19133250	2
C₂×#14582647	2
C₄₃×#1565	2
#19233	43