Subgroups — #25013459

Order 11008.

494 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#19143287	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582683	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×(C₂×D₄₃)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19132685	C₂	1	1	yes	maximal, characteristic, complemented
6	#19132683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₃×#350	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
9	#14583406	C₄	1	1	yes	characteristic
10	C₂×#13063265	C₂²	1	1	yes	characteristic
11	C₂×#13063264	—	2	1	no	—
12	M₃₂×D₄₃	—	2	2	no	—
13	M₃₂×D₄₃	—	2	2	no	—
14	C₂²×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₆×D₄₃	—	2	1	no	—
16	#14582968	—	2	1	no	—
17	#14582968	—	2	1	no	—
18	C₈×C₂²⋊D₄₃	—	2	1	no	—
19	C₈×C₂²⋊D₄₃	—	2	1	no	—
20	#14582927	C₄	1	1	yes	characteristic
21	#14582866	C₄	1	1	yes	characteristic
22	#14582862	C₄	1	1	yes	characteristic
23	#14582854	C₂²	1	1	yes	characteristic
24	#14582683	—	2	2	no	—
25	(C₂×D₄₃)⋊C₁₆	—	2	1	no	—
26	(C₂×D₄₃)⋊C₁₆	—	2	1	no	—
27	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×M₃₂×C₄₃	C₂²	1	1	yes	characteristic
29	C₂²×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#350	—	2	2	no	—
31	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
32	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
34	C₂×C₈×D₄₃	—	2	1	no	—
35	C₂×C₈×D₄₃	—	2	1	no	—
36	C₂×C₈×D₄₃	—	2	1	no	—
37	C₂×C₈×D₄₃	—	2	1	no	—
38	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
39	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
40	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
41	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
42	#13063306	—	2	1	no	—
43	#13063301	C₈	1	1	yes	characteristic
44	#13063301	C₈	1	1	yes	characteristic
45	#13063296	C₈	1	1	yes	characteristic
46	#13063296	C₈	1	1	yes	characteristic
47	#13063293	—	2	1	no	—
48	C₄×C₂²⋊D₄₃	—	2	1	no	—
49	C₄×C₂²⋊D₄₃	—	2	1	no	—
50	#13063284	C₂×C₄	1	1	yes	characteristic
51	#13063265	—	2	1	no	—
52	#13063265	D₄	1	2	yes	complemented
53	#13063264	—	2	4	no	—
54	C₂×C₄₃⋊C₁₆	—	2	1	no	—
55	C₂×C₄₃⋊C₁₆	—	2	1	no	—
56	C₂×C₄₃⋊C₁₆	—	2	1	no	—
57	C₂×C₄₃⋊C₁₆	—	2	1	no	—
58	C₁₆×D₄₃	—	2	4	no	—
59	Dic₄₃⋊C₈	—	2	1	no	—
60	Dic₄₃⋊C₈	—	2	1	no	—
61	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
62	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
63	(C₂×D₄₃)⋊C₈	—	2	1	no	—
64	(C₂×D₄₃)⋊C₈	—	2	1	no	—
65	#13063235	—	2	1	no	—
66	C₈×Dic₄₃	—	2	1	no	—
67	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
68	#131×C₄₃	—	2	1	no	—
69	#131×C₄₃	—	2	1	no	—
70	#131×C₄₃	—	2	1	no	—
71	#131×C₄₃	—	2	1	no	—
72	C₂×M₁₆×C₄₃	—	2	1	no	—
73	C₂×M₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₄₃	—	2	1	no	—
75	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
76	M₃₂×C₄₃	—	2	1	no	—
77	M₃₂×C₄₃	D₄	1	2	yes	complemented
78	C₂×C₁₆×C₄₃	—	2	1	no	—
79	C₂×C₁₆×C₄₃	—	2	1	no	—
80	C₂×C₁₆×C₄₃	—	2	1	no	—
81	C₂×C₁₆×C₄₃	—	2	1	no	—
82	C₂³×D₄₃	M₁₆	1	1	yes	characteristic
83	#41×C₄₃	—	2	1	no	—
84	#41×C₄₃	—	2	1	no	—
85	#41×C₄₃	—	2	1	no	—
86	#41×C₄₃	—	2	1	no	—
87	C₂×Q₈×C₄₃	C₂×C₈	1	1	yes	characteristic
88	C₂×D₄×C₄₃	—	2	1	no	—
89	C₂×D₄×C₄₃	C₂×C₈	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	—	2	1	no	—
91	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊D₄₃	—	2	1	no	—
93	C₂×C₂²⋊D₄₃	—	2	1	no	—
94	C₂²×Dic₄₃	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₄₃	—	2	1	no	—
96	C₂×C₄×D₄₃	—	2	1	no	—
97	C₂×C₄×D₄₃	—	2	1	no	—
98	C₂×C₄×D₄₃	—	2	1	no	—
99	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₃	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₄₃	C₂×C₈	1	1	yes	characteristic
103	M₁₆×C₄₃	—	2	1	no	—
104	M₁₆×C₄₃	—	2	1	no	—
105	M₁₆×C₄₃	—	4	1	no	—
106	M₁₆×C₄₃	—	4	1	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	4	1	no	—
109	C₂×C₈×C₄₃	—	4	1	no	—
110	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
115	C₂×C₈×C₄₃	#41	1	1	yes	characteristic
116	C₂²⋊Dic₄₃	—	2	1	no	—
117	C₂²⋊Dic₄₃	—	2	1	no	—
118	C₂²⋊Dic₄₃	—	2	1	no	—
119	(C₂×D₄₃)⋊C₄	—	2	1	no	—
120	(C₂×D₄₃)⋊C₄	—	2	1	no	—
121	C₄⋊Dic₄₃	C₂×C₈	1	1	yes	characteristic
122	C₄⋊Dic₄₃	C₂×C₈	1	1	yes	characteristic
123	Dic₄₃⋊C₄	—	2	1	no	—
124	Dic₄₃⋊C₄	—	2	1	no	—
125	C₄×Dic₄₃	—	2	1	no	—
126	#10621877	—	2	1	no	—
127	#10621877	—	2	1	no	—
128	C₂×C₄₃⋊C₈	—	2	1	no	—
129	C₂×C₄₃⋊C₈	—	2	1	no	—
130	C₂×C₄₃⋊C₈	—	2	1	no	—
131	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
133	C₈×D₄₃	—	2	1	no	—
134	C₈×D₄₃	—	2	1	no	—
135	C₈×D₄₃	—	2	1	no	—
136	C₈×D₄₃	—	2	1	no	—
137	C₈×D₄₃	—	2	1	no	—
138	C₈×D₄₃	—	2	1	no	—
139	C₈×D₄₃	—	2	1	no	—
140	C₈×D₄₃	—	2	1	no	—
141	C₁₆×C₄₃	—	2	2	no	—
142	C₁₆×C₄₃	—	4	1	no	—
143	C₄₃⋊C₁₆	—	2	2	no	—
144	C₄₃⋊C₁₆	—	4	1	no	—
145	C₂³×C₄₃	—	2	1	no	—
146	C₂³×C₄₃	C₂×M₁₆	1	1	yes	characteristic
147	C₂²×D₄₃	—	2	1	no	—
148	C₂²×D₄₃	—	2	1	no	—
149	C₂²×D₄₃	—	2	2	no	—
150	C₂²×D₄₃	—	4	1	no	—
151	C₂²×D₄₃	C₂²⋊C₈	1	1	yes	characteristic
152	C₂²×D₄₃	C₂²⋊C₈	1	1	yes	characteristic
153	Q₈×C₄₃	—	2	1	no	—
154	Q₈×C₄₃	—	2	1	no	—
155	D₄×C₄₃	—	2	1	no	—
156	D₄×C₄₃	—	2	1	no	—
157	D₄×C₄₃	—	4	1	no	—
158	D₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
167	C₂×C₄×C₄₃	#131	1	1	yes	characteristic
168	C₂²⋊D₄₃	—	4	2	no	—
169	C₂²⋊D₄₃	—	4	2	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	C₂²⋊C₈	1	1	yes	characteristic
175	C₂×Dic₄₃	C₂²⋊C₈	1	1	yes	characteristic
176	C₄×D₄₃	—	2	1	no	—
177	C₄×D₄₃	—	2	1	no	—
178	C₄×D₄₃	—	2	1	no	—
179	C₄×D₄₃	—	2	1	no	—
180	C₄×D₄₃	—	2	1	no	—
181	C₄×D₄₃	—	2	1	no	—
182	C₄×D₄₃	—	2	1	no	—
183	C₄×D₄₃	—	2	1	no	—
184	C₈×C₄₃	—	4	1	no	—
185	C₈×C₄₃	#120	1	1	yes	characteristic
186	C₈×C₄₃	#121	1	1	yes	characteristic
187	C₈×C₄₃	#121	1	1	yes	characteristic
188	C₈×C₄₃	#123	1	1	yes	characteristic
189	C₄₃⋊C₈	—	2	1	no	—
190	C₄₃⋊C₈	—	2	1	no	—
191	C₄₃⋊C₈	—	4	1	no	—
192	#12978	—	43	1	no	maximal, Sylow
193	C₂²×C₄₃	—	2	1	no	—
194	C₂²×C₄₃	—	2	1	no	—
195	C₂²×C₄₃	—	4	1	no	—
196	C₂²×C₄₃	—	4	1	no	—
197	C₂²×C₄₃	—	4	1	no	—
198	C₂²×C₄₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
199	C₂²×C₄₃	#435	1	1	yes	characteristic
200	C₂²×C₄₃	#435	1	1	yes	characteristic
201	C₂×D₄₃	—	2	1	no	—
202	C₂×D₄₃	—	2	1	no	—
203	C₂×D₄₃	—	2	1	no	—
204	C₂×D₄₃	—	2	1	no	—
205	C₂×D₄₃	—	2	1	no	—
206	C₂×D₄₃	—	4	2	no	—
207	C₂×D₄₃	—	4	2	no	—
208	C₂×D₄₃	#350	1	2	yes	complemented
209	C₄×C₄₃	—	4	1	no	—
210	C₄×C₄₃	#386	1	1	yes	characteristic
211	C₄×C₄₃	#408	1	1	yes	characteristic
212	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
213	C₄×C₄₃	C₈×D₄	1	1	yes	characteristic
214	Dic₄₃	—	2	1	no	—
215	Dic₄₃	—	2	1	no	—
216	Dic₄₃	—	4	1	no	—
217	Dic₄₃	—	4	1	no	—
218	C₂²×M₃₂	—	43	1	no	—
219	#2929	—	43	1	no	—
220	C₂×#350	—	43	1	no	—
221	C₂×#350	D₄₃	1	1	yes	characteristic, complemented
222	C₂×C₂²⋊C₁₆	—	43	1	no	—
223	#1379	—	43	1	no	—
224	#1379	—	43	1	no	—
225	C₂×C₄₃	—	2	1	no	—
226	C₂×C₄₃	—	2	1	no	—
227	C₂×C₄₃	—	8	1	no	—
228	C₂×C₄₃	#1869	1	1	yes	characteristic
229	C₂×C₄₃	C₂×#350	1	1	yes	characteristic
230	C₂×C₄₃	#2117	1	1	yes	characteristic
231	D₄₃	—	2	2	no	—
232	D₄₃	—	4	1	no	—
233	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
234	C₂³×C₈	—	43	1	no	—
235	#525	—	43	1	no	—
236	C₂×M₃₂	—	43	1	no	—
237	C₂×M₃₂	—	86	1	no	—
238	C₂×M₃₂	—	86	2	no	—
239	C₂×M₃₂	—	86	2	no	—
240	C₂×M₃₂	C₂×D₄₃	1	1	yes	characteristic
241	C₂²×C₁₆	—	43	1	no	—
242	C₂²×C₁₆	—	86	1	no	—
243	C₂²×C₁₆	C₂×D₄₃	1	1	yes	characteristic
244	#435	—	86	1	no	—
245	#435	—	86	1	no	—
246	C₈×D₄	—	86	1	no	—
247	C₈×D₄	—	86	1	no	—
248	#424	—	43	1	no	—
249	#408	—	43	1	no	—
250	#407	—	43	1	no	—
251	#405	—	43	1	no	—
252	#350	—	2	2	no	—
253	#350	—	86	2	no	—
254	C₂²⋊C₁₆	—	86	1	no	—
255	C₂²⋊C₁₆	—	86	1	no	—
256	C₄₃	#12978	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
258	C₂³×C₄	—	43	1	no	—
259	#131	—	2	1	no	—
260	#131	—	2	1	no	—
261	#131	—	2	1	no	—
262	#131	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	43	1	no	—
265	C₂×M₁₆	C₄×D₄₃	1	1	yes	characteristic
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	43	1	no	—
268	C₂²×C₈	—	43	1	no	—
269	C₂²×C₈	—	43	1	no	—
270	C₂²×C₈	—	43	1	no	—
271	C₂²×C₈	—	43	1	no	—
272	C₂²×C₈	—	86	1	no	—
273	C₂²×C₈	—	86	1	no	—
274	C₂²×C₈	—	86	1	no	—
275	C₂²×C₈	—	86	1	no	—
276	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
277	#123	—	86	1	no	—
278	C₂²⋊Q₈	—	43	1	no	—
279	C₂²⋊Q₈	—	43	1	no	—
280	#121	—	43	1	no	—
281	#121	—	43	1	no	—
282	#120	—	86	1	no	—
283	C₄×D₄	—	86	1	no	—
284	C₄×D₄	—	86	1	no	—
285	#117	—	43	1	no	—
286	M₃₂	—	2	1	no	—
287	M₃₂	—	43	2	no	—
288	M₃₂	—	86	4	no	—
289	M₃₂	—	86	1	no	—
290	M₃₂	C₂²⋊D₄₃	1	2	yes	complemented
291	C₂×C₁₆	—	2	1	no	—
292	C₂×C₁₆	—	2	1	no	—
293	C₂×C₁₆	—	2	1	no	—
294	C₂×C₁₆	—	2	1	no	—
295	C₂×C₁₆	—	86	4	no	—
296	C₂×C₁₆	—	86	1	no	—
297	C₂×C₁₆	—	86	1	no	—
298	C₂×C₁₆	—	86	1	no	—
299	C₂×C₁₆	—	86	1	no	—
300	C₄⋊C₈	—	86	1	no	—
301	C₄⋊C₈	—	86	1	no	—
302	C₂²⋊C₈	—	86	1	no	—
303	C₂²⋊C₈	—	86	1	no	—
304	C₂²⋊C₈	—	86	1	no	—
305	C₂²⋊C₈	—	86	1	no	—
306	#97	—	86	1	no	—
307	C₄×C₈	—	86	1	no	—
308	C₂⁴	—	43	1	no	—
309	#41	—	2	1	no	—
310	#41	—	2	1	no	—
311	#41	—	2	1	no	—
312	#41	—	2	1	no	—
313	C₂×Q₈	C₈×D₄₃	1	1	yes	characteristic
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	86	1	no	—
316	C₂×D₄	—	86	1	no	—
317	C₂×D₄	C₈×D₄₃	1	1	yes	characteristic
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	43	1	no	—
320	C₂²×C₄	—	43	1	no	—
321	C₂²×C₄	—	43	1	no	—
322	C₂²×C₄	—	43	1	no	—
323	C₂²×C₄	—	43	1	no	—
324	C₂²×C₄	—	86	1	no	—
325	C₂²×C₄	—	86	1	no	—
326	C₂²×C₄	—	86	1	no	—
327	C₂²×C₄	—	86	1	no	—
328	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
329	M₁₆	—	2	1	no	—
330	M₁₆	—	2	1	no	—
331	M₁₆	—	4	1	no	—
332	M₁₆	—	4	1	no	—
333	M₁₆	—	86	1	no	—
334	M₁₆	—	86	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	43	1	no	—
339	C₂×C₈	—	43	1	no	—
340	C₂×C₈	—	86	1	no	—
341	C₂×C₈	—	86	1	no	—
342	C₂×C₈	—	86	1	no	—
343	C₂×C₈	—	86	1	no	—
344	C₂×C₈	—	86	1	no	—
345	C₂×C₈	—	86	1	no	—
346	C₂×C₈	—	86	1	no	—
347	C₂×C₈	—	86	1	no	—
348	C₂×C₈	—	86	1	no	—
349	C₂×C₈	—	86	1	no	—
350	C₂×C₈	—	86	1	no	—
351	C₂×C₈	#10621898	1	1	yes	characteristic
352	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
353	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
354	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
355	C₂×C₈	#10621900	1	1	yes	characteristic
356	C₂×C₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
357	C₄⋊C₄	—	43	1	no	—
358	C₄⋊C₄	—	43	1	no	—
359	C₄⋊C₄	—	86	1	no	—
360	C₄⋊C₄	—	86	1	no	—
361	C₂²⋊C₄	—	86	1	no	—
362	C₂²⋊C₄	—	86	1	no	—
363	C₂²⋊C₄	—	86	1	no	—
364	C₂²⋊C₄	—	86	1	no	—
365	C₂²⋊C₄	—	86	1	no	—
366	C₄²	—	86	1	no	—
367	C₁₆	—	2	2	no	—
368	C₁₆	—	4	1	no	—
369	C₁₆	—	86	2	no	—
370	C₁₆	—	172	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	43	1	no	—
373	C₂³	—	43	1	no	—
374	C₂³	—	86	2	no	—
375	C₂³	—	86	1	no	—
376	C₂³	—	86	1	no	—
377	C₂³	—	172	1	no	—
378	C₂³	M₁₆×D₄₃	1	1	yes	characteristic
379	Q₈	—	2	1	no	—
380	Q₈	—	2	1	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	172	2	no	—
386	D₄	—	172	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	43	1	no	—
391	C₂×C₄	—	43	1	no	—
392	C₂×C₄	—	86	1	no	—
393	C₂×C₄	—	86	1	no	—
394	C₂×C₄	—	86	1	no	—
395	C₂×C₄	—	86	1	no	—
396	C₂×C₄	—	86	1	no	—
397	C₂×C₄	—	86	1	no	—
398	C₂×C₄	—	86	1	no	—
399	C₂×C₄	—	86	1	no	—
400	C₂×C₄	—	86	1	no	—
401	C₂×C₄	—	86	1	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	86	1	no	—
404	C₂×C₄	C₂²⋊C₄×D₄₃	1	1	yes	characteristic
405	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
406	C₂×C₄	C₄×C₂²⋊D₄₃	1	1	yes	characteristic
407	C₂×C₄	C₂×C₈×D₄₃	1	1	yes	characteristic
408	C₂×C₄	#13063331	1	1	yes	characteristic
409	C₂×C₄	#13063333	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	86	1	no	—
412	C₈	—	86	1	no	—
413	C₈	—	172	1	no	—
414	C₈	#13063293	1	1	yes	characteristic
415	C₈	#13063296	1	1	yes	characteristic
416	C₈	#13063298	1	1	yes	characteristic
417	C₈	#13063307	1	1	yes	characteristic
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	1	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	43	2	no	—
424	C₂²	—	86	1	no	—
425	C₂²	—	86	1	no	—
426	C₂²	—	86	1	no	—
427	C₂²	—	86	1	no	—
428	C₂²	—	86	1	no	—
429	C₂²	—	172	2	no	—
430	C₂²	—	172	2	no	—
431	C₂²	C₂²⋊C₈×D₄₃	1	1	yes	characteristic
432	C₂²	#14582968	1	1	yes	characteristic
433	C₂²	#14582973	1	1	yes	characteristic
434	C₄	—	4	1	no	—
435	C₄	—	86	1	no	—
436	C₄	—	86	1	no	—
437	C₄	—	172	1	no	—
438	C₄	—	172	1	no	—
439	C₄	#14582775	1	1	yes	characteristic
440	C₄	#14582864	1	1	yes	characteristic
441	C₄	(C₂²⋊D₄₃)⋊C₈	1	1	yes	characteristic
442	C₄	C₈×C₂²⋊D₄₃	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	8	1	no	—
446	C₂	—	86	2	no	—
447	C₂	—	172	1	no	—
448	C₂	#19134884	1	1	yes	characteristic
449	C₂	#350×D₄₃	1	1	yes	characteristic
450	C₂	#19136221	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₄₃
Fitting	C₂×C₄₃×#350	C₂
socle	C₂²×C₄₃	C₂×C₂²⋊C₈
prime radical	#14583406	C₄
cosocle	C₂²×C₈×C₄₃	C₂³
hypercenter	C₂×#350	D₄₃
hypocenter	C₄₃	#12978
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#350

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₄₃	C₂	semidirect
3. C₂×#14582683	C₂	semidirect
4. C₂×(C₂×D₄₃)⋊C₁₆	C₂	semidirect
5. #19132685	C₂	semidirect
6. #19132683	C₂	semidirect
7. C₂×C₄₃×#350	C₂	semidirect
52. #13063265	D₄	semidirect
77. M₃₂×C₄₃	D₄	semidirect
208. C₂×D₄₃	#350	semidirect
221. C₂×#350	D₄₃	semidirect
256. C₄₃	#12978	semidirect
290. M₃₂	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₃	2
#19143287	2
C₂×#14582683	2
C₂×(C₂×D₄₃)⋊C₁₆	2
#19132685	2
#19132683	2
C₂×C₄₃×#350	2
#12978	43