Subgroups — #25065617

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143227	C₂	1	1	yes	maximal, characteristic
2	#19143225	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#19133363	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133362	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133361	C₂	1	2	yes	maximal, complemented
7	#19133360	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133359	C₂	1	2	yes	maximal, complemented
9	#19133342	C₂	1	2	yes	maximal, complemented
10	#19133340	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₄₃	C₄	1	2	yes	—
13	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
14	#14582956	C₂²	1	1	yes	characteristic
15	#14582955	—	2	1	no	—
16	#14582955	C₂²	1	2	yes	—
17	#14582954	—	2	1	no	—
18	#14582951	—	2	1	no	—
19	#14582951	C₂²	1	1	yes	characteristic
20	#14582951	C₂²	1	1	yes	characteristic
21	#14582951	C₂²	1	2	yes	—
22	#14582949	—	2	1	no	—
23	#14582923	C₂²	1	1	yes	characteristic
24	#14582921	C₂²	1	1	yes	characteristic
25	#14582921	C₂²	1	1	yes	characteristic
26	#14582862	—	2	1	no	—
27	#14582861	—	2	1	no	—
28	C₄×#10621877	C₂²	1	1	yes	characteristic
29	#14582851	—	2	1	no	—
30	#14582851	C₄	1	1	yes	characteristic
31	#14582851	C₄	1	1	yes	characteristic
32	M₁₆×Dic₄₃	—	2	1	no	—
33	M₁₆×Dic₄₃	C₄	1	2	yes	—
34	C₄×#10621872	C₂²	1	2	yes	—
35	#97×D₄₃	C₄	1	1	yes	characteristic
36	#97×D₄₃	C₄	1	1	yes	characteristic
37	C₄×C₈×D₄₃	C₂²	1	2	yes	—
38	#14582652	C₂²	1	2	yes	complemented
39	#14582651	C₂²	1	2	yes	complemented
40	#14582651	C₂²	1	2	yes	complemented
41	#14582650	C₂²	1	2	yes	complemented
42	#14582649	C₂²	1	2	yes	complemented
43	#14582649	C₂²	1	2	yes	complemented
44	C₄₃×#432	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#335	C₂²	1	2	yes	complemented
48	C₄₃×#334	C₂²	1	2	yes	complemented
49	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₃	D₄	1	1	yes	characteristic
51	C₂²×C₄×D₄₃	Q₈	1	1	yes	characteristic
52	C₂×#10621877	—	2	1	no	—
53	C₂×#10621877	C₂×C₄	1	2	yes	—
54	C₂×#10621872	—	2	1	no	—
55	C₂×#10621872	—	2	1	no	—
56	C₂×#10621872	C₂×C₄	1	2	yes	—
57	C₂×#10621872	C₂×C₄	1	2	yes	—
58	M₁₆×D₄₃	—	2	8	no	—
59	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
60	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
61	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₃	D₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₃	Q₈	1	1	yes	characteristic
64	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₄₃	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₄₃	D₄	1	1	yes	characteristic
67	C₄²×D₄₃	D₄	1	1	yes	characteristic
68	C₄²×D₄₃	Q₈	1	1	yes	characteristic
69	C₄²×D₄₃	Q₈	1	1	yes	characteristic
70	C₄²×D₄₃	C₂³	1	1	yes	characteristic
71	C₄²×D₄₃	C₂³	1	1	yes	characteristic
72	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
76	Dic₄₃⋊C₈	—	2	1	no	—
77	Dic₄₃⋊C₈	—	2	1	no	—
78	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
79	(C₂×D₄₃)⋊C₈	—	2	1	no	—
80	(C₂×D₄₃)⋊C₈	—	2	1	no	—
81	(C₂×D₄₃)⋊C₈	—	2	2	no	—
82	(C₂×D₄₃)⋊C₈	—	2	2	no	—
83	#13063236	—	2	1	no	—
84	#13063236	C₂×C₄	1	1	yes	characteristic
85	#13063236	C₂×C₄	1	1	yes	characteristic
86	#13063235	—	2	2	no	—
87	#13063235	C₂×C₄	1	2	yes	—
88	#13063235	C₂×C₄	1	2	yes	—
89	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
90	C₈×Dic₄₃	—	2	2	no	—
91	C₈×Dic₄₃	—	2	1	no	—
92	C₈×Dic₄₃	—	2	1	no	—
93	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
94	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
95	C₂×M₁₆×C₄₃	—	2	1	no	—
96	C₂×M₁₆×C₄₃	C₂×C₄	1	2	yes	—
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	—	2	1	no	—
99	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
101	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²⋊C₈×C₄₃	—	2	1	no	—
103	#97×C₄₃	—	2	1	no	—
104	#97×C₄₃	C₂×C₄	1	1	yes	characteristic
105	#97×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₄₃	C₂³	1	2	yes	—
107	C₂³×D₄₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
111	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
113	C₂²×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₃	—	2	4	no	—
115	C₂×C₄×D₄₃	—	4	2	no	—
116	C₂×C₄×D₄₃	—	4	1	no	—
117	C₂×C₄×D₄₃	—	4	1	no	—
118	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₃	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
130	M₁₆×C₄₃	—	2	4	no	—
131	M₁₆×C₄₃	—	4	2	no	—
132	C₂×C₈×C₄₃	—	2	1	no	—
133	C₂×C₈×C₄₃	—	2	1	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
137	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
140	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
141	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
142	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
143	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
152	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
153	#10621877	—	2	4	no	—
154	#10621877	—	4	2	no	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	2	1	no	—
157	C₂×C₄₃⋊C₈	—	2	1	no	—
158	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
159	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
160	#10621872	—	2	4	no	—
161	#10621872	—	2	4	no	—
162	#10621872	—	4	2	no	—
163	#10621872	—	4	2	no	—
164	C₈×D₄₃	—	2	4	no	—
165	C₈×D₄₃	M₁₆	1	8	yes	complemented
166	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₂²×D₄₃	—	2	2	no	—
168	C₂²×D₄₃	—	4	1	no	—
169	C₂²×D₄₃	—	4	1	no	—
170	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	—	2	2	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
177	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
180	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×Dic₄₃	—	2	2	no	—
183	C₂×Dic₄₃	—	2	2	no	—
184	C₂×Dic₄₃	—	4	1	no	—
185	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₄×D₄₃	—	2	2	no	—
192	C₄×D₄₃	—	2	2	no	—
193	C₄×D₄₃	—	2	1	no	—
194	C₄×D₄₃	—	2	1	no	—
195	C₄×D₄₃	—	2	1	no	—
196	C₄×D₄₃	—	2	1	no	—
197	C₄×D₄₃	—	2	2	no	—
198	C₄×D₄₃	—	2	2	no	—
199	C₄×D₄₃	—	2	2	no	—
200	C₄×D₄₃	—	4	1	no	—
201	C₄×D₄₃	—	4	1	no	—
202	C₄×D₄₃	—	4	1	no	—
203	C₄×D₄₃	—	4	1	no	—
204	C₄×D₄₃	C₂×M₁₆	1	4	yes	—
205	C₈×C₄₃	—	2	2	no	—
206	C₈×C₄₃	—	4	1	no	—
207	C₈×C₄₃	—	4	1	no	—
208	C₈×C₄₃	—	4	2	no	—
209	C₈×C₄₃	C₂×M₁₆	1	4	yes	—
210	C₄₃⋊C₈	—	2	2	no	—
211	C₄₃⋊C₈	—	4	1	no	—
212	C₄₃⋊C₈	—	4	1	no	—
213	C₄₃⋊C₈	—	4	2	no	—
214	C₄₃⋊C₈	C₂×M₁₆	1	4	yes	—
215	#17795	—	43	1	no	maximal, Sylow
216	C₂²×C₄₃	—	2	1	no	—
217	C₂²×C₄₃	—	2	1	no	—
218	C₂²×C₄₃	—	2	1	no	—
219	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
220	C₂×D₄₃	—	2	1	no	—
221	C₂×D₄₃	—	2	1	no	—
222	C₂×D₄₃	—	2	1	no	—
223	C₂×D₄₃	—	2	1	no	—
224	C₂×D₄₃	—	2	1	no	—
225	C₂×D₄₃	—	4	4	no	—
226	C₂×D₄₃	#423	1	2	yes	—
227	C₄×C₄₃	—	2	1	no	—
228	C₄×C₄₃	—	2	1	no	—
229	C₄×C₄₃	—	2	1	no	—
230	C₄×C₄₃	—	2	1	no	—
231	C₄×C₄₃	C₂²×M₁₆	1	2	yes	—
232	C₄×C₄₃	#575	1	1	yes	characteristic
233	C₄×C₄₃	#575	1	1	yes	characteristic
234	Dic₄₃	—	2	1	no	—
235	Dic₄₃	—	2	1	no	—
236	Dic₄₃	—	2	1	no	—
237	Dic₄₃	—	2	1	no	—
238	Dic₄₃	#423	1	2	yes	—
239	Dic₄₃	#430	1	2	yes	—
240	#2920	—	43	1	no	—
241	#2920	—	43	1	no	—
242	C₂×C₄×M₁₆	—	43	1	no	—
243	#1569	—	43	1	no	—
244	#1569	—	43	1	no	—
245	#1569	—	43	1	no	—
246	#1569	—	43	2	no	—
247	#1569	—	43	2	no	—
248	#1569	D₄₃	1	1	yes	characteristic, complemented
249	#1564	—	43	2	no	—
250	#1564	—	43	2	no	—
251	C₂×C₄₃	—	4	1	no	—
252	C₂×C₄₃	C₂×#423	1	1	yes	characteristic
253	C₂×C₄₃	#2911	1	1	yes	characteristic
254	C₂×C₄₃	C₂×#430	1	1	yes	characteristic
255	D₄₃	—	2	2	no	—
256	D₄₃	—	4	1	no	—
257	C₂²×M₁₆	—	43	2	no	—
258	C₂²×C₄²	—	43	1	no	—
259	#432	—	43	1	no	—
260	#432	—	43	2	no	—
261	#432	—	86	1	no	—
262	#432	—	86	1	no	—
263	#432	C₂×D₄₃	1	1	yes	characteristic
264	#431	—	43	1	no	—
265	#431	—	43	2	no	—
266	#431	—	43	1	no	—
267	#431	—	86	1	no	—
268	#431	—	86	1	no	—
269	#423	—	43	1	no	—
270	#423	—	43	1	no	—
271	#423	—	43	1	no	—
272	#423	C₂×D₄₃	1	1	yes	characteristic
273	#407	—	86	1	no	—
274	#407	—	86	1	no	—
275	C₄×M₁₆	—	43	2	no	—
276	C₄×M₁₆	—	43	1	no	—
277	C₄×M₁₆	—	43	1	no	—
278	C₄×M₁₆	—	43	1	no	—
279	C₄×M₁₆	—	43	2	no	—
280	C₄×M₁₆	—	86	1	no	—
281	C₄×M₁₆	—	86	1	no	—
282	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
283	C₂×#97	—	43	1	no	—
284	C₂×#97	—	43	1	no	—
285	C₂×C₄×C₈	—	43	2	no	—
286	#335	—	43	2	no	—
287	#335	—	43	2	no	—
288	#335	—	43	2	no	—
289	#335	C₂×D₄₃	1	2	yes	complemented
290	#334	—	43	2	no	—
291	#334	—	43	2	no	—
292	#334	—	43	2	no	—
293	#334	C₂×D₄₃	1	2	yes	complemented
294	C₄₃	#17795	1	1	yes	characteristic, complemented, Sylow
295	C₂³×C₄	—	43	1	no	—
296	C₂³×C₄	—	43	1	no	—
297	C₂³×C₄	—	43	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	43	2	no	—
300	C₂×M₁₆	—	43	2	no	—
301	C₂×M₁₆	—	43	2	no	—
302	C₂×M₁₆	—	86	1	no	—
303	C₂×M₁₆	—	86	1	no	—
304	C₂×M₁₆	—	86	8	no	—
305	C₂×M₁₆	—	86	1	no	—
306	C₂×M₁₆	C₄×D₄₃	1	2	yes	—
307	C₂²×C₈	—	43	2	no	—
308	C₂²×C₈	—	43	2	no	—
309	C₂×C₄²	—	43	1	no	—
310	C₂×C₄²	—	43	1	no	—
311	C₂×C₄²	—	43	1	no	—
312	C₂×C₄²	—	43	1	no	—
313	C₂×C₄²	—	43	1	no	—
314	C₂×C₄²	—	43	1	no	—
315	C₂×C₄²	—	43	1	no	—
316	C₂×C₄²	—	43	1	no	—
317	C₂×C₄²	—	43	1	no	—
318	C₂×C₄²	—	43	1	no	—
319	C₂×C₄²	—	43	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	C₄⋊C₈	—	2	1	no	—
322	C₄⋊C₈	—	43	1	no	—
323	C₄⋊C₈	—	43	2	no	—
324	C₄⋊C₈	—	43	1	no	—
325	C₄⋊C₈	—	86	1	no	—
326	C₄⋊C₈	—	86	1	no	—
327	C₄⋊C₈	—	86	1	no	—
328	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
329	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
330	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
331	C₂²⋊C₈	—	2	1	no	—
332	C₂²⋊C₈	—	86	1	no	—
333	C₂²⋊C₈	—	86	1	no	—
334	C₂²⋊C₈	—	86	2	no	—
335	C₂²⋊C₈	—	86	2	no	—
336	C₂²⋊C₈	—	86	1	no	—
337	#97	—	2	1	no	—
338	#97	—	43	2	no	—
339	#97	—	43	2	no	—
340	#97	—	43	1	no	—
341	#97	—	43	1	no	—
342	#97	—	86	2	no	—
343	#97	—	86	1	no	—
344	#97	C₄×D₄₃	1	1	yes	characteristic
345	#97	C₄×D₄₃	1	1	yes	characteristic
346	C₄×C₈	—	43	2	no	—
347	C₄×C₈	—	43	2	no	—
348	C₄×C₈	—	43	2	no	—
349	C₄×C₈	—	86	1	no	—
350	C₄×C₈	—	86	1	no	—
351	C₄×C₈	—	86	2	no	—
352	C₄×C₈	C₂²×D₄₃	1	2	yes	—
353	C₂⁴	—	43	1	no	—
354	C₂²×C₄	—	43	1	no	—
355	C₂²×C₄	—	43	1	no	—
356	C₂²×C₄	—	43	1	no	—
357	C₂²×C₄	—	43	1	no	—
358	C₂²×C₄	—	43	1	no	—
359	C₂²×C₄	—	43	1	no	—
360	C₂²×C₄	—	43	1	no	—
361	C₂²×C₄	—	43	1	no	—
362	C₂²×C₄	—	43	1	no	—
363	C₂²×C₄	—	43	1	no	—
364	C₂²×C₄	—	43	1	no	—
365	C₂²×C₄	—	43	1	no	—
366	C₂²×C₄	—	43	1	no	—
367	C₂²×C₄	—	43	1	no	—
368	C₂²×C₄	—	43	1	no	—
369	C₂²×C₄	—	86	4	no	—
370	C₂²×C₄	—	172	1	no	—
371	C₂²×C₄	—	172	1	no	—
372	C₂²×C₄	—	172	2	no	—
373	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
374	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
375	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
376	M₁₆	—	2	4	no	—
377	M₁₆	—	4	2	no	—
378	M₁₆	—	86	4	no	—
379	M₁₆	—	86	4	no	—
380	M₁₆	—	86	4	no	—
381	M₁₆	—	172	2	no	—
382	M₁₆	—	172	2	no	—
383	M₁₆	—	172	2	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	43	2	no	—
388	C₂×C₈	—	43	8	no	—
389	C₂×C₈	—	43	2	no	—
390	C₂×C₈	—	86	4	no	—
391	C₂×C₈	—	86	1	no	—
392	C₂×C₈	—	86	2	no	—
393	C₂×C₈	—	86	1	no	—
394	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
395	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
396	C₄²	—	43	1	no	—
397	C₄²	—	43	1	no	—
398	C₄²	—	43	1	no	—
399	C₄²	—	43	1	no	—
400	C₄²	—	43	1	no	—
401	C₄²	—	43	1	no	—
402	C₄²	—	43	1	no	—
403	C₄²	—	43	1	no	—
404	C₄²	—	43	1	no	—
405	C₄²	—	43	1	no	—
406	C₄²	—	43	1	no	—
407	C₄²	—	43	1	no	—
408	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
409	C₄²	D₄×D₄₃	1	1	yes	characteristic
410	C₄²	Q₈×D₄₃	1	1	yes	characteristic
411	C₄²	C₂³×D₄₃	1	1	yes	characteristic
412	C₂³	—	43	1	no	—
413	C₂³	—	43	1	no	—
414	C₂³	—	86	2	no	—
415	C₂³	—	172	1	no	—
416	C₂³	—	172	1	no	—
417	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	43	1	no	—
423	C₂×C₄	—	43	1	no	—
424	C₂×C₄	—	43	4	no	—
425	C₂×C₄	—	43	1	no	—
426	C₂×C₄	—	43	1	no	—
427	C₂×C₄	—	43	1	no	—
428	C₂×C₄	—	43	1	no	—
429	C₂×C₄	—	86	2	no	—
430	C₂×C₄	—	86	2	no	—
431	C₂×C₄	—	86	2	no	—
432	C₂×C₄	—	86	2	no	—
433	C₂×C₄	—	86	2	no	—
434	C₂×C₄	—	86	2	no	—
435	C₂×C₄	—	86	2	no	—
436	C₂×C₄	—	86	1	no	—
437	C₂×C₄	—	86	1	no	—
438	C₂×C₄	—	86	1	no	—
439	C₂×C₄	—	86	1	no	—
440	C₂×C₄	—	172	1	no	—
441	C₂×C₄	—	172	1	no	—
442	C₂×C₄	—	172	1	no	—
443	C₂×C₄	—	172	1	no	—
444	C₂×C₄	—	172	1	no	—
445	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
446	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
447	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
448	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
449	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
450	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	4	1	no	—
454	C₈	—	4	1	no	—
455	C₈	—	43	4	no	—
456	C₈	—	86	2	no	—
457	C₈	—	172	1	no	—
458	C₈	—	172	1	no	—
459	C₈	—	172	2	no	—
460	C₈	M₁₆×D₄₃	1	4	yes	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	43	2	no	—
465	C₂²	—	86	1	no	—
466	C₂²	—	86	1	no	—
467	C₂²	—	86	1	no	—
468	C₂²	—	86	1	no	—
469	C₂²	—	86	1	no	—
470	C₂²	—	172	4	no	—
471	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	43	2	no	—
477	C₄	—	43	2	no	—
478	C₄	—	86	1	no	—
479	C₄	—	86	1	no	—
480	C₄	—	86	1	no	—
481	C₄	—	86	1	no	—
482	C₄	C₂×M₁₆×D₄₃	1	2	yes	—
483	C₄	#14583695	1	1	yes	characteristic
484	C₄	#14583698	1	1	yes	characteristic
485	C₂	—	4	1	no	—
486	C₂	—	86	2	no	—
487	C₂	—	172	1	no	—
488	C₂	#423×D₄₃	1	1	yes	characteristic
489	C₂	#19143182	1	1	yes	characteristic
490	C₂	#430×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1569	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₄₃	C₄⋊C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1569	D₄₃
hypocenter	C₄₃	#17795
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #19133363	C₂	semidirect
5. #19133362	C₂	semidirect
6. #19133361	C₂	semidirect
7. #19133360	C₂	semidirect
8. #19133359	C₂	semidirect
9. #19133342	C₂	semidirect
10. #19133340	C₂	semidirect
11. C₄₃×#1569	C₂	semidirect
38. #14582652	C₂²	semidirect
39. #14582651	C₂²	semidirect
40. #14582651	C₂²	semidirect
41. #14582650	C₂²	semidirect
42. #14582649	C₂²	semidirect
43. #14582649	C₂²	semidirect
47. C₄₃×#335	C₂²	semidirect
48. C₄₃×#334	C₂²	semidirect
165. C₈×D₄₃	M₁₆	semidirect
248. #1569	D₄₃	semidirect
289. #335	C₂×D₄₃	semidirect
293. #334	C₂×D₄₃	semidirect
294. C₄₃	#17795	semidirect

Maximal subgroups

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

subgroup	index
#19143227	2
#19143225	2
C₄×M₁₆×D₄₃	2
#19133363	2
#19133362	2
#19133361	2
#19133360	2
#19133359	2
#19133342	2
#19133340	2
C₄₃×#1569	2
#17795	43