Subgroups — #25000404

Order 11008.

522 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	C₂×#14583100	C₂	1	1	yes	maximal, characteristic
2	#19135530	C₂	1	1	yes	maximal, characteristic, complemented
3	#19135400	C₂	1	1	yes	maximal, characteristic
4	#19134597	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#14582651	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14582642	C₂	1	1	yes	maximal, characteristic
7	C₄₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10621873	—	2	1	no	—
9	C₂×#13063322	C₂²	1	1	yes	characteristic
10	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
11	#14583100	—	2	2	no	—
12	#14583100	—	2	2	no	—
13	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#13063248	—	2	1	no	—
15	C₂×#13063247	—	2	1	no	—
16	C₂×#13063245	—	2	1	no	—
17	C₂×#13063245	—	2	1	no	—
18	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
19	#14582661	—	2	1	no	—
20	#14582653	—	2	1	no	—
21	#14582653	—	2	1	no	—
22	#14582651	—	2	2	no	—
23	#14582642	—	2	2	no	—
24	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
26	C₄₃×#384	C₂²	1	1	yes	characteristic
27	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
28	C₂²×D₁₇₂	—	2	1	no	—
29	C₂²×D₁₇₂	—	2	1	no	—
30	C₂²×D₁₇₂	—	2	1	no	—
31	C₂×#10621873	—	2	4	no	—
32	C₂×#10621873	—	4	2	no	—
33	C₂×#10621873	—	4	2	no	—
34	C₂²×C₄₃⋊C₈	—	2	1	no	—
35	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
36	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
37	#13063322	—	2	1	no	—
38	#13063322	—	2	1	no	—
39	#13063322	—	2	1	no	—
40	#13063322	D₄	1	2	yes	—
41	C₄×Dic₈₆	—	2	1	no	—
42	C₄×Dic₈₆	—	2	1	no	—
43	C₄×Dic₈₆	—	2	1	no	—
44	C₄×Dic₈₆	—	2	1	no	—
45	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
46	C₂×Dic₄₃⋊C₄	—	2	1	no	—
47	C₂×C₄×Dic₄₃	—	2	1	no	—
48	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
49	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
50	#13063248	—	4	2	no	—
51	#13063247	—	2	4	no	—
52	#13063245	—	4	2	no	—
53	#13063245	—	4	2	no	—
54	C₄×C₄₃⋊C₈	—	2	1	no	—
55	C₄×C₄₃⋊C₈	—	2	1	no	—
56	C₂²×C₈×C₄₃	—	2	1	no	—
57	C₂²×C₈×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
62	C₄⋊C₈×C₄₃	—	2	1	no	—
63	C₄⋊C₈×C₄₃	—	2	1	no	—
64	C₄⋊C₈×C₄₃	—	2	1	no	—
65	C₄⋊C₈×C₄₃	D₄	1	2	yes	—
66	C₂³×D₄₃	—	4	1	no	—
67	C₂²×C₄×C₄₃	—	4	1	no	—
68	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
71	C₂²×Dic₄₃	—	2	1	no	—
72	C₂²×Dic₄₃	—	2	1	no	—
73	C₂×D₁₇₂	—	2	2	no	—
74	C₂×D₁₇₂	—	2	2	no	—
75	C₂×D₁₇₂	—	2	2	no	—
76	C₂×D₁₇₂	—	4	1	no	—
77	C₂×D₁₇₂	—	4	1	no	—
78	C₂×D₁₇₂	—	4	1	no	—
79	C₂×D₁₇₂	—	4	1	no	—
80	C₂×D₁₇₂	—	4	1	no	—
81	C₂×D₁₇₂	—	4	1	no	—
82	C₂×D₁₇₂	—	4	1	no	—
83	C₂×D₁₇₂	—	4	1	no	—
84	C₂×D₁₇₂	—	4	1	no	—
85	C₂×D₁₇₂	—	4	1	no	—
86	C₂×D₁₇₂	—	4	1	no	—
87	C₂×D₁₇₂	—	8	1	no	—
88	C₂×D₁₇₂	—	8	1	no	—
89	C₂×Dic₈₆	—	2	1	no	—
90	C₂×Dic₈₆	—	2	1	no	—
91	C₂×Dic₈₆	—	2	1	no	—
92	C₂×Dic₈₆	—	2	1	no	—
93	C₂×Dic₈₆	—	2	1	no	—
94	C₂×Dic₈₆	D₈	1	2	yes	—
95	C₂×C₈×C₄₃	—	2	2	no	—
96	C₂×C₈×C₄₃	—	4	1	no	—
97	C₂×C₈×C₄₃	—	4	1	no	—
98	C₂×C₈×C₄₃	—	4	1	no	—
99	C₂×C₈×C₄₃	—	4	1	no	—
100	C₂×C₈×C₄₃	—	4	1	no	—
101	C₄⋊C₄×C₄₃	—	4	1	no	—
102	C₄⋊C₄×C₄₃	—	4	1	no	—
103	C₄⋊C₄×C₄₃	—	4	1	no	—
104	C₄⋊C₄×C₄₃	—	4	1	no	—
105	C₄⋊C₄×C₄₃	—	8	1	no	—
106	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₃	#41	1	1	yes	characteristic
109	C₄²×C₄₃	#41	1	1	yes	characteristic
110	C₄⋊Dic₄₃	—	2	1	no	—
111	C₄⋊Dic₄₃	—	2	1	no	—
112	Dic₄₃⋊C₄	—	4	1	no	—
113	Dic₄₃⋊C₄	—	4	1	no	—
114	C₄×Dic₄₃	—	4	1	no	—
115	C₄×Dic₄₃	—	4	1	no	—
116	C₂×C₄₃⋊C₈	—	2	1	no	—
117	C₂×C₄₃⋊C₈	—	2	1	no	—
118	C₂×C₄₃⋊C₈	—	2	1	no	—
119	C₂×C₄₃⋊C₈	—	2	1	no	—
120	C₂×C₄₃⋊C₈	—	2	1	no	—
121	C₂×C₄₃⋊C₈	—	4	1	no	—
122	C₂×C₄₃⋊C₈	—	4	1	no	—
123	C₂×C₄₃⋊C₈	—	4	1	no	—
124	C₂×C₄₃⋊C₈	SD₁₆	1	2	yes	complemented
125	#10621873	—	4	8	no	—
126	C₂³×C₄₃	#121	1	1	yes	characteristic
127	C₂²×D₄₃	—	4	2	no	—
128	C₂²×D₄₃	—	8	1	no	—
129	C₂²×D₄₃	—	8	1	no	—
130	C₂²×D₄₃	—	8	1	no	—
131	C₂²×D₄₃	—	8	1	no	—
132	C₂²×D₄₃	—	8	1	no	—
133	C₂²×D₄₃	—	8	1	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	8	1	no	—
137	C₂×C₄×C₄₃	—	8	1	no	—
138	C₂×C₄×C₄₃	—	8	1	no	—
139	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
140	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
141	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
142	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
143	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
144	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
145	C₂×C₄×C₄₃	C₂×D₈	1	1	yes	characteristic
146	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
149	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
150	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
152	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
153	C₂×Dic₄₃	—	2	2	no	—
154	C₂×Dic₄₃	—	4	1	no	—
155	C₂×Dic₄₃	—	4	1	no	—
156	C₂×Dic₄₃	—	4	1	no	—
157	C₂×Dic₄₃	—	4	1	no	—
158	C₂×Dic₄₃	—	4	1	no	—
159	D₁₇₂	—	4	2	no	—
160	D₁₇₂	—	4	2	no	—
161	D₁₇₂	—	4	2	no	—
162	D₁₇₂	—	4	2	no	—
163	D₁₇₂	—	8	2	no	—
164	D₁₇₂	—	8	2	no	—
165	D₁₇₂	—	8	1	no	—
166	D₁₇₂	—	8	1	no	—
167	D₁₇₂	—	8	1	no	—
168	D₁₇₂	—	8	1	no	—
169	Dic₈₆	—	2	2	no	—
170	Dic₈₆	—	2	2	no	—
171	Dic₈₆	—	4	1	no	—
172	Dic₈₆	—	4	1	no	—
173	C₈×C₄₃	—	4	2	no	—
174	C₈×C₄₃	—	8	1	no	—
175	C₄₃⋊C₈	—	2	2	no	—
176	C₄₃⋊C₈	—	4	1	no	—
177	C₄₃⋊C₈	—	8	1	no	—
178	#10474	—	43	1	no	maximal, Sylow
179	C₂²×C₄₃	#394	1	1	yes	characteristic
180	C₂²×C₄₃	#460	1	1	yes	characteristic
181	C₂²×C₄₃	#464	1	1	yes	characteristic
182	C₂²×C₄₃	#466	1	1	yes	characteristic
183	C₂²×C₄₃	#468	1	1	yes	characteristic
184	C₂²×C₄₃	#471	1	1	yes	characteristic
185	C₂²×C₄₃	#472	1	1	yes	characteristic
186	C₂×D₄₃	—	8	2	no	—
187	C₂×D₄₃	—	8	2	no	—
188	C₂×D₄₃	—	8	2	no	—
189	C₂×D₄₃	—	16	1	no	—
190	C₂×D₄₃	—	16	1	no	—
191	C₂×D₄₃	—	16	1	no	—
192	C₂×D₄₃	—	16	1	no	—
193	C₄×C₄₃	—	2	1	no	—
194	C₄×C₄₃	—	2	1	no	—
195	C₄×C₄₃	—	16	1	no	—
196	C₄×C₄₃	#447	1	1	yes	characteristic
197	C₄×C₄₃	#452	1	1	yes	characteristic
198	C₄×C₄₃	#461	1	1	yes	characteristic
199	C₄×C₄₃	#463	1	1	yes	characteristic
200	C₄×C₄₃	#465	1	1	yes	characteristic
201	C₄×C₄₃	#468	1	1	yes	characteristic
202	C₄×C₄₃	#480	1	1	yes	characteristic
203	C₄×C₄₃	#482	1	1	yes	characteristic
204	Dic₄₃	—	4	2	no	—
205	Dic₄₃	—	8	1	no	—
206	C₂×#460	—	43	1	no	—
207	#1984	—	43	1	no	—
208	#1957	—	43	1	no	—
209	#1803	—	43	1	no	—
210	C₂×#335	—	43	1	no	—
211	C₂×#331	—	43	1	no	—
212	#1296	D₄₃	1	1	yes	characteristic, complemented
213	C₂×C₄₃	#1668	1	1	yes	characteristic
214	C₂×C₄₃	#1682	1	1	yes	characteristic
215	C₂×C₄₃	#1686	1	1	yes	characteristic
216	C₂×C₄₃	#1698	1	1	yes	characteristic
217	C₂×C₄₃	#2033	1	1	yes	characteristic
218	C₂×C₄₃	#2051	1	1	yes	characteristic
219	C₂×C₄₃	#2055	1	1	yes	characteristic
220	D₄₃	—	16	2	no	—
221	C₂²×SD₁₆	—	86	1	no	—
222	C₂×#127	—	43	1	no	—
223	C₂×C₄×Q₈	—	43	1	no	—
224	#460	—	86	2	no	—
225	#460	—	86	2	no	—
226	C₂×C₄⋊C₈	—	43	1	no	—
227	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
228	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
229	C₂×#103	—	86	1	no	—
230	C₂×#102	—	86	1	no	—
231	C₂×#102	—	86	1	no	—
232	C₂×#102	—	86	1	no	—
233	C₂×C₄×C₈	—	43	1	no	—
234	#384	C₂×D₄₃	1	1	yes	characteristic
235	#340	—	86	1	no	—
236	#336	—	86	1	no	—
237	#336	—	86	1	no	—
238	#335	—	86	2	no	—
239	#331	—	86	2	no	—
240	C₄₃	#10474	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	—	43	1	no	—
242	C₂²×D₄	—	86	1	no	—
243	C₂²×D₄	—	86	1	no	—
244	C₂²×D₄	—	86	1	no	—
245	C₂×SD₁₆	—	86	4	no	—
246	C₂×SD₁₆	—	172	2	no	—
247	C₂×SD₁₆	—	172	2	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	43	1	no	—
251	C₂²×C₈	—	43	1	no	—
252	C₂²×C₈	—	86	1	no	—
253	#127	—	43	2	no	—
254	#127	—	86	1	no	—
255	#127	—	86	1	no	—
256	#127	—	86	1	no	—
257	C₄×Q₈	—	86	1	no	—
258	C₄×Q₈	—	86	1	no	—
259	C₄×Q₈	—	86	1	no	—
260	C₄×Q₈	—	86	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	43	1	no	—
265	C₂×C₄⋊C₄	—	86	1	no	—
266	C₂×C₄²	—	86	1	no	—
267	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	86	1	no	—
272	C₄⋊C₈	—	86	1	no	—
273	C₄⋊C₈	D₁₇₂	1	2	yes	—
274	#103	—	172	2	no	—
275	#102	—	86	4	no	—
276	#102	—	172	2	no	—
277	#102	—	172	2	no	—
278	C₄×C₈	—	86	1	no	—
279	C₄×C₈	—	86	1	no	—
280	C₂⁴	—	172	1	no	—
281	C₂×Q₈	—	43	2	no	—
282	C₂×Q₈	—	86	1	no	—
283	C₂×Q₈	—	86	1	no	—
284	C₂×Q₈	—	86	1	no	—
285	C₂×Q₈	—	86	1	no	—
286	C₂×Q₈	—	86	1	no	—
287	C₂×D₄	—	86	2	no	—
288	C₂×D₄	—	86	2	no	—
289	C₂×D₄	—	86	2	no	—
290	C₂×D₄	—	344	1	no	—
291	C₂×D₄	—	344	1	no	—
292	C₂×D₄	—	172	1	no	—
293	C₂×D₄	—	172	1	no	—
294	C₂×D₄	—	172	1	no	—
295	C₂×D₄	—	172	1	no	—
296	C₂×D₄	—	172	1	no	—
297	C₂×D₄	—	172	1	no	—
298	C₂×D₄	—	172	1	no	—
299	C₂×D₄	—	172	1	no	—
300	C₂×D₄	—	172	1	no	—
301	C₂×D₄	—	172	1	no	—
302	C₂×D₄	—	172	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	86	1	no	—
305	C₂²×C₄	—	86	1	no	—
306	C₂²×C₄	#10621898	1	1	yes	characteristic
307	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
309	SD₁₆	—	172	8	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	4	1	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	43	2	no	—
317	C₂×C₈	—	86	1	no	—
318	C₂×C₈	—	86	1	no	—
319	C₂×C₈	—	86	1	no	—
320	C₂×C₈	—	86	1	no	—
321	C₂×C₈	—	86	1	no	—
322	C₂×C₈	—	172	1	no	—
323	C₂×C₈	—	172	1	no	—
324	C₂×C₈	—	172	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	8	1	no	—
330	C₄⋊C₄	—	86	1	no	—
331	C₄⋊C₄	—	86	1	no	—
332	C₄⋊C₄	—	172	1	no	—
333	C₄⋊C₄	—	172	1	no	—
334	C₄²	—	172	1	no	—
335	C₄²	—	172	1	no	—
336	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
337	C₄²	#10621898	1	1	yes	characteristic
338	C₄²	D₄×D₄₃	1	1	yes	characteristic
339	C₄²	#10621902	1	1	yes	characteristic
340	C₂³	—	344	1	no	—
341	C₂³	—	344	1	no	—
342	C₂³	—	344	1	no	—
343	C₂³	—	344	1	no	—
344	C₂³	—	344	1	no	—
345	C₂³	—	344	1	no	—
346	C₂³	—	172	2	no	—
347	C₂³	#13063298	1	1	yes	characteristic
348	Q₈	—	86	2	no	—
349	Q₈	—	86	2	no	—
350	Q₈	—	172	1	no	—
351	Q₈	—	172	1	no	—
352	D₄	—	344	2	no	—
353	D₄	—	344	2	no	—
354	D₄	—	344	1	no	—
355	D₄	—	344	1	no	—
356	D₄	—	344	1	no	—
357	D₄	—	344	1	no	—
358	D₄	—	172	2	no	—
359	D₄	—	172	2	no	—
360	D₄	—	172	2	no	—
361	D₄	—	172	2	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	8	1	no	—
365	C₂×C₄	—	8	1	no	—
366	C₂×C₄	—	8	1	no	—
367	C₂×C₄	—	86	2	no	—
368	C₂×C₄	—	172	1	no	—
369	C₂×C₄	—	172	1	no	—
370	C₂×C₄	—	172	1	no	—
371	C₂×C₄	—	172	1	no	—
372	C₂×C₄	—	172	1	no	—
373	C₂×C₄	#13063295	1	1	yes	characteristic
374	C₂×C₄	#13063298	1	1	yes	characteristic
375	C₂×C₄	#13063300	1	1	yes	characteristic
376	C₂×C₄	#13063310	1	1	yes	characteristic
377	C₂×C₄	#13063310	1	1	yes	characteristic
378	C₂×C₄	#13063313	1	1	yes	characteristic
379	C₂×C₄	D₈×D₄₃	1	1	yes	characteristic
380	C₂×C₄	SD₁₆×D₄₃	1	1	yes	characteristic
381	C₂×C₄	#13063346	1	1	yes	characteristic
382	C₂×C₄	#13063346	1	1	yes	characteristic
383	C₂×C₄	#13063349	1	1	yes	characteristic
384	C₂×C₄	#13063352	1	1	yes	characteristic
385	C₂×C₄	#13063357	1	1	yes	characteristic
386	C₂×C₄	#13063357	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	8	1	no	—
389	C₈	—	86	2	no	—
390	C₈	—	344	1	no	—
391	C₈	—	172	1	no	—
392	C₂²	—	344	2	no	—
393	C₂²	—	344	2	no	—
394	C₂²	—	344	2	no	—
395	C₂²	—	688	1	no	—
396	C₂²	—	688	1	no	—
397	C₂²	—	688	1	no	—
398	C₂²	—	688	1	no	—
399	C₂²	#14582817	1	1	yes	characteristic
400	C₂²	#14583098	1	1	yes	characteristic
401	C₂²	#14583124	1	1	yes	characteristic
402	C₂²	#14583134	1	1	yes	characteristic
403	C₂²	#14583148	1	1	yes	characteristic
404	C₂²	#14583165	1	1	yes	characteristic
405	C₂²	#14583168	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	16	1	no	—
409	C₄	—	344	1	no	—
410	C₄	—	172	2	no	—
411	C₄	#14583034	1	1	yes	characteristic
412	C₄	#14583064	1	1	yes	characteristic
413	C₄	#14583103	1	1	yes	characteristic
414	C₄	#14583113	1	1	yes	characteristic
415	C₄	#14583129	1	1	yes	characteristic
416	C₄	#14583146	1	1	yes	characteristic
417	C₄	#14583214	1	1	yes	characteristic
418	C₄	#14583225	1	1	yes	characteristic
419	C₂	—	688	2	no	—
420	C₂	#19133954	1	1	yes	characteristic
421	C₂	#19134042	1	1	yes	characteristic
422	C₂	#19134070	1	1	yes	characteristic
423	C₂	#19134138	1	1	yes	characteristic
424	C₂	#19135780	1	1	yes	characteristic
425	C₂	#19135890	1	1	yes	characteristic
426	C₂	#19135914	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13063298
commutator, cosocle	C₂×C₄²×C₄₃	C₂³
Frattini	C₂×C₄²	C₂²×D₄₃
Fitting	C₄₃×#1296	C₂
socle	C₂³×C₄₃	#121
prime radical	C₂×#13063322	C₂²
hypercenter	#1296	D₄₃
hypocenter	C₄₃	#10474
LCS	G ▷ C₂×C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #19135530	C₂	semidirect
4. #19134597	C₂	semidirect
5. C₂×#14582651	C₂	semidirect
7. C₄₃×#1296	C₂	semidirect
124. C₂×C₄₃⋊C₈	SD₁₆	semidirect
212. #1296	D₄₃	semidirect
240. C₄₃	#10474	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583100	2
#19135530	2
#19135400	2
#19134597	2
C₂×#14582651	2
C₂×#14582642	2
C₄₃×#1296	2
#10474	43