Subgroups — #25066603

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#19143530	C₂	1	1	yes	maximal, characteristic, complemented
3	#19133467	C₂	1	2	yes	maximal, complemented
4	#19133453	C₂	1	2	yes	maximal, complemented
5	Q₁₆×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
6	SD₁₆×C₄₃⋊C₈	C₂	1	2	yes	maximal, complemented
7	#19133384	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133034	C₂	1	1	yes	maximal, characteristic
9	#19133016	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3107	C₂	1	1	yes	maximal, characteristic
12	#14583030	—	2	1	no	—
13	#14583030	C₂²	1	2	yes	—
14	Q₈×C₄₃⋊C₈	—	2	1	no	—
15	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	—
17	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	D₄×C₄₃⋊C₈	—	2	1	no	—
19	D₄×C₄₃⋊C₈	—	2	1	no	—
20	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
21	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
22	#14582952	—	2	1	no	—
23	#14582952	C₂²	1	1	yes	characteristic
24	#14582926	—	2	1	no	—
25	#14582923	C₂²	1	1	yes	characteristic
26	#14582855	—	2	1	no	—
27	C₄×#10621877	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
29	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	#14582652	C₂²	1	2	yes	—
31	#14582650	C₂²	1	2	yes	—
32	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
33	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
34	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
35	D₄⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
36	#14582621	C₂²	1	2	yes	—
37	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
38	C₄₃×#533	C₂²	1	1	yes	characteristic
39	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
40	C₄₃×#485	C₄	1	2	yes	—
41	C₄₃×#475	C₄	1	1	yes	characteristic
42	C₄₃×#474	C₄	1	1	yes	characteristic
43	C₄₃×#462	C₄	1	1	yes	characteristic
44	C₄₃×#461	C₄	1	1	yes	characteristic
45	C₄₃×#452	C₄	1	2	yes	—
46	C₄×Q₁₆×C₄₃	C₂²	1	2	yes	—
47	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
48	C₄₃×#431	C₂²	1	1	yes	characteristic
49	C₂×#10621877	—	2	1	no	—
50	C₂×#10621877	—	2	1	no	—
51	C₂²×C₄₃⋊C₈	—	2	1	no	—
52	C₂²×C₄₃⋊C₈	—	2	1	no	—
53	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
55	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
57	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
58	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
59	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
62	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
63	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
64	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
66	#13063236	—	2	1	no	—
67	#13063236	—	2	2	no	—
68	C₄×C₄₃⋊C₈	—	2	1	no	—
69	C₄×C₄₃⋊C₈	—	2	1	no	—
70	C₄×C₄₃⋊C₈	—	2	1	no	—
71	C₄×C₄₃⋊C₈	—	2	2	no	—
72	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
73	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
74	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
75	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
77	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₄₃	C₂×C₄	1	2	yes	—
79	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
80	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
82	#125×C₄₃	—	2	1	no	—
83	C₂²⋊Q₈×C₄₃	—	2	1	no	—
84	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₄₃	—	2	1	no	—
86	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
88	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
89	C₄×D₄×C₄₃	—	2	1	no	—
90	C₄×D₄×C₄₃	—	2	1	no	—
91	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
93	#117×C₄₃	—	2	1	no	—
94	#117×C₄₃	—	2	1	no	—
95	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₄₃	—	2	1	no	—
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#107×C₄₃	C₂×C₄	1	2	yes	—
99	#106×C₄₃	C₂×C₄	1	2	yes	—
100	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
102	#103×C₄₃	C₂×C₄	1	2	yes	—
103	#103×C₄₃	C₂×C₄	1	2	yes	—
104	#103×C₄₃	C₂×C₄	1	2	yes	—
105	#102×C₄₃	C₂×C₄	1	2	yes	—
106	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
107	C₄×C₈×C₄₃	C₂³	1	2	yes	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
112	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	Q₁₆×C₄₃	—	2	4	no	—
122	SD₁₆×C₄₃	—	2	4	no	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
125	C₄⋊C₄×C₄₃	—	2	1	no	—
126	C₄⋊C₄×C₄₃	—	2	1	no	—
127	C₄⋊C₄×C₄₃	—	2	1	no	—
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂²⋊C₄×C₄₃	—	2	1	no	—
136	C₂²⋊C₄×C₄₃	—	2	1	no	—
137	C₂²⋊C₄×C₄₃	—	2	2	no	—
138	C₂²⋊C₄×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	—	2	1	no	—
140	C₄²×C₄₃	—	2	1	no	—
141	C₄²×C₄₃	—	2	1	no	—
142	C₄²×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₃	#41	1	1	yes	characteristic
146	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
147	#10621877	—	2	4	no	—
148	#10621877	—	4	2	no	—
149	C₂×C₄₃⋊C₈	—	2	2	no	—
150	C₂×C₄₃⋊C₈	—	2	2	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	1	no	—
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	4	1	no	—
155	C₂×C₄₃⋊C₈	—	4	2	no	—
156	C₂×C₄₃⋊C₈	—	4	2	no	—
157	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂³×C₄₃	—	2	1	no	—
162	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
163	Q₈×C₄₃	—	2	1	no	—
164	Q₈×C₄₃	—	2	2	no	—
165	Q₈×C₄₃	—	2	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	#131	1	2	yes	—
168	D₄×C₄₃	—	2	4	no	—
169	D₄×C₄₃	—	2	1	no	—
170	D₄×C₄₃	#131	1	2	yes	—
171	C₂×C₄×C₄₃	—	2	4	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	1	no	—
180	C₂×C₄×C₄₃	—	2	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	1	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	2	2	no	—
193	C₄₃⋊C₈	—	2	4	no	—
194	C₄₃⋊C₈	—	2	1	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₄₃⋊C₈	—	2	1	no	—
197	C₄₃⋊C₈	—	4	1	no	—
198	C₄₃⋊C₈	—	4	1	no	—
199	C₄₃⋊C₈	—	4	2	no	—
200	C₄₃⋊C₈	#137	1	2	yes	—
201	#17913	—	43	1	no	maximal, Sylow
202	C₂²×C₄₃	—	2	2	no	—
203	C₂²×C₄₃	—	2	1	no	—
204	C₂²×C₄₃	—	2	1	no	—
205	C₂²×C₄₃	—	2	1	no	—
206	C₂²×C₄₃	—	4	1	no	—
207	C₂²×C₄₃	—	4	1	no	—
208	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	2	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	2	1	no	—
213	C₄×C₄₃	—	4	2	no	—
214	C₄×C₄₃	—	4	1	no	—
215	C₄×C₄₃	—	4	1	no	—
216	C₄×C₄₃	—	4	2	no	—
217	C₄×C₄₃	#443	1	2	yes	—
218	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
219	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
220	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
221	C₄×C₄₃	#575	1	1	yes	characteristic
222	#3107	D₄₃	1	1	yes	characteristic
223	C₈×#41	—	43	1	no	—
224	#2960	—	43	1	no	—
225	#1587	—	43	2	no	—
226	#1585	—	43	2	no	—
227	C₈×Q₁₆	—	43	2	no	—
228	C₈×SD₁₆	—	43	2	no	—
229	#1574	—	43	1	no	—
230	#1489	—	43	1	no	—
231	#1485	—	43	1	no	—
232	C₈×M₁₆	—	43	1	no	—
233	C₂×C₄₃	—	4	1	no	—
234	C₂×C₄₃	—	4	2	no	—
235	C₂×C₄₃	#2929	1	1	yes	characteristic
236	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
237	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
238	#533	C₂×D₄₃	1	1	yes	characteristic
239	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
240	#485	Dic₄₃	1	2	yes	—
241	#475	Dic₄₃	1	1	yes	characteristic
242	#474	Dic₄₃	1	1	yes	characteristic
243	#462	Dic₄₃	1	1	yes	characteristic
244	#461	Dic₄₃	1	1	yes	characteristic
245	#452	Dic₄₃	1	2	yes	—
246	#446	—	43	2	no	—
247	#446	—	86	1	no	—
248	C₈×Q₈	—	43	2	no	—
249	C₈×Q₈	—	43	1	no	—
250	C₈×Q₈	—	43	1	no	—
251	C₈×Q₈	—	86	1	no	—
252	C₄×Q₁₆	C₂×D₄₃	1	2	yes	—
253	C₄×SD₁₆	C₂×D₄₃	1	2	yes	—
254	C₈×D₄	—	43	1	no	—
255	C₈×D₄	—	43	1	no	—
256	C₈×D₄	—	86	1	no	—
257	C₈×D₄	—	86	1	no	—
258	#431	—	43	1	no	—
259	#431	—	86	1	no	—
260	#431	C₂×D₄₃	1	1	yes	characteristic
261	#424	—	86	1	no	—
262	#423	—	43	1	no	—
263	#405	—	86	1	no	—
264	C₄×M₁₆	—	43	1	no	—
265	C₂×C₄×C₈	—	43	1	no	—
266	C₂×C₄×C₈	—	86	1	no	—
267	#335	—	43	2	no	—
268	#334	—	43	2	no	—
269	Q₈⋊C₈	—	43	2	no	—
270	Q₈⋊C₈	—	43	2	no	—
271	Q₈⋊C₈	—	43	2	no	—
272	D₄⋊C₈	—	43	2	no	—
273	#322	—	43	2	no	—
274	C₈²	—	43	2	no	—
275	C₄₃	#17913	1	1	yes	characteristic, complemented, Sylow
276	C₂×#41	C₂×Dic₄₃	1	1	yes	characteristic
277	C₂×Q₁₆	C₂×Dic₄₃	1	2	yes	—
278	C₂×SD₁₆	C₂×Dic₄₃	1	2	yes	—
279	C₂×M₁₆	—	86	1	no	—
280	C₂×M₁₆	—	86	1	no	—
281	C₂²×C₈	—	43	1	no	—
282	C₂²×C₈	—	43	1	no	—
283	C₂²×C₈	—	86	1	no	—
284	C₂²×C₈	—	86	1	no	—
285	C₄⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
286	C₄⋊Q₈	C₂×Dic₄₃	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	C₂×Dic₄₃	1	2	yes	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	C₂×Dic₄₃	1	1	yes	characteristic
292	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
293	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
294	C₄×D₄	—	2	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	C₂×Dic₄₃	1	1	yes	characteristic
297	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
298	#117	—	2	1	no	—
299	#117	—	2	1	no	—
300	#117	C₂×Dic₄₃	1	1	yes	characteristic
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
303	#107	C₂×Dic₄₃	1	2	yes	—
304	#106	C₂×Dic₄₃	1	2	yes	—
305	C₄⋊C₈	—	43	2	no	—
306	C₄⋊C₈	—	43	1	no	—
307	C₄⋊C₈	—	43	1	no	—
308	C₄⋊C₈	—	86	2	no	—
309	C₄⋊C₈	—	86	2	no	—
310	C₄⋊C₈	—	86	1	no	—
311	C₄⋊C₈	—	86	1	no	—
312	C₄⋊C₈	—	86	1	no	—
313	C₄⋊C₈	C₂×Dic₄₃	1	1	yes	characteristic
314	C₄⋊C₈	C₂×Dic₄₃	1	1	yes	characteristic
315	#103	C₂×Dic₄₃	1	2	yes	—
316	#103	C₂×Dic₄₃	1	2	yes	—
317	#103	C₂×Dic₄₃	1	2	yes	—
318	#102	C₂×Dic₄₃	1	2	yes	—
319	C₂²⋊C₈	—	86	1	no	—
320	C₂²⋊C₈	—	86	1	no	—
321	C₂²⋊C₈	—	86	1	no	—
322	C₂²⋊C₈	C₂×Dic₄₃	1	2	yes	—
323	#97	—	86	2	no	—
324	#97	—	86	1	no	—
325	C₄×C₈	—	43	1	no	—
326	C₄×C₈	—	43	1	no	—
327	C₄×C₈	—	43	1	no	—
328	C₄×C₈	—	43	1	no	—
329	C₄×C₈	—	43	2	no	—
330	C₄×C₈	—	86	1	no	—
331	C₄×C₈	—	86	1	no	—
332	C₄×C₈	—	86	2	no	—
333	C₄×C₈	—	86	1	no	—
334	C₄×C₈	C₂²×D₄₃	1	2	yes	—
335	#41	—	2	2	no	—
336	#41	—	2	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	C₂²×Dic₄₃	1	2	yes	—
339	C₂×Q₈	C₂²×Dic₄₃	1	1	yes	characteristic
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	C₂²×Dic₄₃	1	1	yes	characteristic
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
346	C₂²×C₄	#10621900	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₄₃	1	1	yes	characteristic
348	Q₁₆	—	2	4	no	—
349	SD₁₆	—	2	4	no	—
350	M₁₆	—	86	4	no	—
351	M₁₆	—	172	2	no	—
352	C₂×C₈	—	43	1	no	—
353	C₂×C₈	—	43	1	no	—
354	C₂×C₈	—	43	1	no	—
355	C₂×C₈	—	43	1	no	—
356	C₂×C₈	—	86	2	no	—
357	C₂×C₈	—	86	2	no	—
358	C₂×C₈	—	86	1	no	—
359	C₂×C₈	—	86	1	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	172	2	no	—
362	C₂×C₈	—	172	1	no	—
363	C₂×C₈	—	172	2	no	—
364	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
365	C₂×C₈	C₂²×Dic₄₃	1	2	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	C₂²×Dic₄₃	1	2	yes	—
374	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
375	C₄⋊C₄	C₂²×Dic₄₃	1	1	yes	characteristic
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	2	no	—
384	C₄²	D₄×D₄₃	1	1	yes	characteristic
385	C₄²	#10621900	1	1	yes	characteristic
386	C₄²	C₂²×Dic₄₃	1	1	yes	characteristic
387	C₄²	C₂³×D₄₃	1	1	yes	characteristic
388	C₂³	—	2	1	no	—
389	C₂³	D₄×Dic₄₃	1	1	yes	characteristic
390	Q₈	—	2	1	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	#13063332	1	2	yes	—
395	D₄	—	2	4	no	—
396	D₄	—	2	1	no	—
397	D₄	#13063332	1	2	yes	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
413	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
414	C₂×C₄	D₄×Dic₄₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×Dic₄₃	1	1	yes	characteristic
416	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	43	2	no	—
421	C₈	—	86	4	no	—
422	C₈	—	86	1	no	—
423	C₈	—	86	1	no	—
424	C₈	—	86	1	no	—
425	C₈	—	172	1	no	—
426	C₈	—	172	1	no	—
427	C₈	—	172	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	C₂×D₄×Dic₄₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	1	no	—
443	C₄	#14583016	1	2	yes	—
444	C₄	C₂×#13063332	1	1	yes	characteristic
445	C₄	C₂×#13063332	1	1	yes	characteristic
446	C₄	#137×D₄₃	1	1	yes	characteristic
447	C₄	#14583698	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	4	2	no	—
450	C₂	#19143290	1	1	yes	characteristic
451	C₂	#137×Dic₄₃	1	1	yes	characteristic
452	C₂	C₂×#14583016	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×#3107	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#41×C₄₃	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#3107	D₄₃
hypocenter	C₄₃	#17913
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
2. #19143530	C₂	semidirect
3. #19133467	C₂	semidirect
4. #19133453	C₂	semidirect
5. Q₁₆×C₄₃⋊C₈	C₂	semidirect
6. SD₁₆×C₄₃⋊C₈	C₂	semidirect
7. #19133384	C₂	semidirect
9. #19133016	C₂	semidirect
10. #19132876	C₂	semidirect
275. C₄₃	#17913	semidirect

Maximal subgroups

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

subgroup	index
#41×C₄₃⋊C₈	2
#19143530	2
#19133467	2
#19133453	2
Q₁₆×C₄₃⋊C₈	2
SD₁₆×C₄₃⋊C₈	2
#19133384	2
#19133034	2
#19133016	2
#19132876	2
C₄₃×#3107	2
#17913	43