Subgroups — #25066599

Order 11008.

632 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144664	C₂	1	1	yes	maximal, characteristic
2	C₈×#10621902	C₂	1	1	yes	maximal, characteristic
3	#19143524	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133467	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133463	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133455	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133451	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×#10621885	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#10621873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133385	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133033	C₂	1	1	yes	maximal, characteristic
13	#19133014	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#10621872	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×Q₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583453	C₂²	1	1	yes	characteristic
17	C₄×#10621902	C₂²	1	1	yes	characteristic
18	#14583242	C₄	1	1	yes	characteristic
19	#14583238	C₄	1	1	yes	characteristic
20	#14583182	C₄	1	1	yes	characteristic
21	#14583178	C₄	1	1	yes	characteristic
22	#14583107	C₄	1	1	yes	characteristic
23	#14583103	C₄	1	1	yes	characteristic
24	#14583064	C₄	1	1	yes	characteristic
25	#14583060	C₄	1	1	yes	characteristic
26	#14583030	C₂²	1	1	yes	characteristic
27	#14583028	—	2	1	no	—
28	#14583026	C₂²	1	1	yes	characteristic
29	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
30	C₈×Dic₈₆	—	2	1	no	—
31	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
32	C₄×#10621885	C₂²	1	1	yes	characteristic
33	C₄×#10621873	C₂²	1	1	yes	characteristic
34	C₄×#10621884	C₂²	1	1	yes	characteristic
35	C₈×D₁₇₂	—	2	1	no	—
36	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
37	#14582964	—	2	1	no	—
38	#14582964	C₂²	1	1	yes	characteristic
39	#14582951	—	2	1	no	—
40	#14582951	C₂²	1	1	yes	characteristic
41	#14582950	C₂²	1	1	yes	characteristic
42	#14582924	—	2	1	no	—
43	#14582921	C₂²	1	1	yes	characteristic
44	#14582853	—	2	1	no	—
45	C₄×#10621872	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₄₃	—	2	1	no	—
47	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
48	#14582651	C₂²	1	1	yes	characteristic
49	#14582650	C₂²	1	1	yes	characteristic
50	#14582649	C₂²	1	1	yes	characteristic
51	#14582631	C₂²	1	1	yes	characteristic
52	Q₈⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
54	#14582629	C₂²	1	1	yes	characteristic
55	#14582628	C₂²	1	1	yes	characteristic
56	#14582626	C₂²	1	1	yes	characteristic
57	#14582621	C₂²	1	1	yes	characteristic
58	#14582620	C₂²	1	1	yes	characteristic
59	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
63	C₄₃×#335	C₂²	1	1	yes	characteristic
64	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₈²×C₄₃	C₂²	1	1	yes	characteristic
67	C₂×#10621902	C₂×C₄	1	1	yes	characteristic
68	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
69	C₂×#10621873	C₂×C₄	1	1	yes	characteristic
70	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
71	C₂×#10621872	—	2	1	no	—
72	C₂×#10621872	—	2	1	no	—
73	C₂×C₈×D₄₃	—	2	1	no	—
74	C₂×C₈×D₄₃	—	2	1	no	—
75	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
76	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
77	#13063324	C₂×C₄	1	1	yes	characteristic
78	#13063323	C₂×C₄	1	1	yes	characteristic
79	#13063315	—	2	1	no	—
80	#13063305	C₂×C₄	1	1	yes	characteristic
81	#13063303	—	2	1	no	—
82	#13063301	C₂×C₄	1	1	yes	characteristic
83	Q₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
84	C₄×Dic₈₆	—	2	1	no	—
85	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
86	C₄×D₁₇₂	—	2	1	no	—
87	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
88	#13063287	—	2	1	no	—
89	#13063287	C₂×C₄	1	1	yes	characteristic
90	#13063283	—	2	1	no	—
91	#13063283	C₂×C₄	1	1	yes	characteristic
92	#13063282	—	2	1	no	—
93	C₄²×D₄₃	—	2	1	no	—
94	C₄²×D₄₃	C₂³	1	1	yes	characteristic
95	#13063258	C₂×C₄	1	1	yes	characteristic
96	#13063257	C₂×C₄	1	1	yes	characteristic
97	#13063256	C₂×C₄	1	1	yes	characteristic
98	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
99	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
100	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
101	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
102	Dic₄₃⋊C₈	—	2	1	no	—
103	Dic₄₃⋊C₈	—	2	1	no	—
104	Dic₄₃⋊C₈	—	2	1	no	—
105	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
106	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
107	#13063250	C₂×C₄	1	1	yes	characteristic
108	#13063249	C₂×C₄	1	1	yes	characteristic
109	#13063249	C₂×C₄	1	1	yes	characteristic
110	#13063248	C₂×C₄	1	1	yes	characteristic
111	#13063247	C₂×C₄	1	1	yes	characteristic
112	#13063245	C₂×C₄	1	1	yes	characteristic
113	(C₂×D₄₃)⋊C₈	—	2	1	no	—
114	(C₂×D₄₃)⋊C₈	—	2	1	no	—
115	(C₂×D₄₃)⋊C₈	—	2	1	no	—
116	(C₂×D₄₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
117	(C₂×D₄₃)⋊C₈	C₂×C₄	1	1	yes	characteristic
118	#13063236	—	2	1	no	—
119	#13063235	—	2	1	no	—
120	#13063235	—	2	1	no	—
121	C₄×C₄₃⋊C₈	—	2	1	no	—
122	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₈×Dic₄₃	—	2	1	no	—
126	C₈×Dic₄₃	—	2	1	no	—
127	C₈×Dic₄₃	D₄	1	1	yes	characteristic
128	C₈×Dic₄₃	D₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
132	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₄₃	—	2	1	no	—
134	C₄⋊C₈×C₄₃	—	2	1	no	—
135	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
137	#103×C₄₃	C₂×C₄	1	1	yes	characteristic
138	#103×C₄₃	C₂×C₄	1	1	yes	characteristic
139	C₄×C₈×C₄₃	—	2	1	no	—
140	C₄×C₈×C₄₃	—	2	1	no	—
141	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	#10621902	—	2	2	no	—
147	#10621902	—	2	2	no	—
148	C₂×D₁₇₂	—	2	1	no	—
149	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₄₃	—	2	1	no	—
151	C₂×C₄×D₄₃	—	2	1	no	—
152	C₂×C₄×D₄₃	—	2	1	no	—
153	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
156	C₂×Dic₈₆	—	2	1	no	—
157	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
158	Q₁₆×C₄₃	—	2	2	no	—
159	C₂×C₈×C₄₃	—	2	1	no	—
160	C₂×C₈×C₄₃	—	2	1	no	—
161	C₂×C₈×C₄₃	—	2	1	no	—
162	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₄₃	—	2	1	no	—
167	C₄⋊C₄×C₄₃	—	2	1	no	—
168	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₄₃	—	2	1	no	—
171	C₄²×C₄₃	—	2	1	no	—
172	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
173	#10621885	—	2	2	no	—
174	#10621884	—	2	2	no	—
175	(C₂×D₄₃)⋊C₄	—	2	1	no	—
176	(C₂×D₄₃)⋊C₄	—	2	1	no	—
177	(C₂×D₄₃)⋊C₄	—	2	1	no	—
178	(C₂×D₄₃)⋊C₄	—	2	1	no	—
179	(C₂×D₄₃)⋊C₄	—	2	1	no	—
180	C₄⋊Dic₄₃	—	2	1	no	—
181	C₄⋊Dic₄₃	—	2	1	no	—
182	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
184	Dic₄₃⋊C₄	—	2	1	no	—
185	Dic₄₃⋊C₄	—	2	1	no	—
186	Dic₄₃⋊C₄	—	2	1	no	—
187	Dic₄₃⋊C₄	—	2	1	no	—
188	Dic₄₃⋊C₄	—	2	1	no	—
189	C₄×Dic₄₃	—	2	1	no	—
190	C₄×Dic₄₃	—	2	1	no	—
191	C₄×Dic₄₃	—	2	1	no	—
192	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₄₃	#41	1	1	yes	characteristic
195	C₂×C₄₃⋊C₈	—	2	1	no	—
196	C₂×C₄₃⋊C₈	—	2	1	no	—
197	C₂×C₄₃⋊C₈	—	2	1	no	—
198	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
200	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
201	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
202	#10621873	—	2	2	no	—
203	#10621872	—	2	4	no	—
204	#10621872	—	4	2	no	—
205	C₈×D₄₃	—	2	2	no	—
206	C₈×D₄₃	—	4	1	no	—
207	C₈×D₄₃	—	4	2	no	—
208	C₈×D₄₃	—	4	2	no	—
209	C₂²×D₄₃	—	2	1	no	—
210	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
211	Q₈×C₄₃	—	2	1	no	—
212	Q₈×C₄₃	—	2	1	no	—
213	Q₈×C₄₃	—	2	1	no	—
214	Q₈×C₄₃	#131	1	2	yes	—
215	C₂×C₄×C₄₃	—	2	1	no	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
222	C₂×Dic₄₃	—	2	1	no	—
223	C₂×Dic₄₃	—	2	1	no	—
224	C₂×Dic₄₃	—	2	1	no	—
225	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
228	D₁₇₂	—	2	4	no	—
229	D₁₇₂	—	2	1	no	—
230	D₁₇₂	#131	1	2	yes	—
231	C₄×D₄₃	—	2	4	no	—
232	C₄×D₄₃	—	2	1	no	—
233	C₄×D₄₃	—	2	1	no	—
234	C₄×D₄₃	—	2	1	no	—
235	C₄×D₄₃	—	2	1	no	—
236	C₄×D₄₃	—	2	2	no	—
237	C₄×D₄₃	—	4	1	no	—
238	C₄×D₄₃	—	4	1	no	—
239	C₄×D₄₃	—	4	2	no	—
240	Dic₈₆	—	2	1	no	—
241	Dic₈₆	—	2	1	no	—
242	Dic₈₆	—	4	2	no	—
243	C₈×C₄₃	—	2	2	no	—
244	C₈×C₄₃	—	2	1	no	—
245	C₈×C₄₃	—	2	1	no	—
246	C₈×C₄₃	—	2	1	no	—
247	C₈×C₄₃	—	4	1	no	—
248	C₈×C₄₃	—	4	1	no	—
249	C₈×C₄₃	#137	1	2	yes	—
250	C₄₃⋊C₈	—	2	2	no	—
251	C₄₃⋊C₈	—	2	1	no	—
252	C₄₃⋊C₈	—	2	1	no	—
253	C₄₃⋊C₈	—	2	1	no	—
254	C₄₃⋊C₈	—	2	1	no	—
255	C₄₃⋊C₈	—	4	1	no	—
256	C₄₃⋊C₈	—	4	1	no	—
257	#17913	—	43	1	no	maximal, Sylow
258	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
259	C₂×D₄₃	—	2	2	no	—
260	C₂×D₄₃	—	2	1	no	—
261	C₂×D₄₃	—	2	1	no	—
262	C₂×D₄₃	—	2	1	no	—
263	C₂×D₄₃	—	4	1	no	—
264	C₂×D₄₃	—	4	1	no	—
265	C₄×C₄₃	—	2	2	no	—
266	C₄×C₄₃	—	2	1	no	—
267	C₄×C₄₃	—	4	1	no	—
268	C₄×C₄₃	—	4	1	no	—
269	C₄×C₄₃	—	4	1	no	—
270	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
271	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
272	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
273	C₄×C₄₃	#575	1	1	yes	characteristic
274	Dic₄₃	—	2	1	no	—
275	Dic₄₃	—	2	1	no	—
276	Dic₄₃	—	4	1	no	—
277	Dic₄₃	—	4	1	no	—
278	Dic₄₃	—	4	1	no	—
279	Dic₄₃	#443	1	2	yes	—
280	#3107	—	43	1	no	—
281	C₈×#41	—	43	1	no	—
282	#2960	—	43	1	no	—
283	#1587	—	43	1	no	—
284	#1587	—	43	1	no	—
285	#1585	—	43	1	no	—
286	#1585	—	43	1	no	—
287	C₈×Q₁₆	—	43	1	no	—
288	C₈×Q₁₆	D₄₃	1	1	yes	characteristic, complemented
289	C₈×SD₁₆	—	43	1	no	—
290	C₈×SD₁₆	—	43	1	no	—
291	#1574	—	43	1	no	—
292	#1489	—	43	1	no	—
293	#1485	—	43	1	no	—
294	C₈×M₁₆	—	43	1	no	—
295	C₂×C₄₃	#2929	1	1	yes	characteristic
296	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
297	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
298	D₄₃	—	4	1	no	—
299	D₄₃	—	4	2	no	—
300	#533	—	43	1	no	—
301	C₄×#41	—	43	1	no	—
302	#485	—	43	1	no	—
303	#485	—	43	1	no	—
304	#475	—	43	1	no	—
305	#474	—	43	1	no	—
306	#462	—	43	1	no	—
307	#461	—	43	1	no	—
308	#452	—	43	1	no	—
309	#452	—	43	1	no	—
310	#446	—	43	1	no	—
311	#446	—	43	1	no	—
312	#446	—	86	1	no	—
313	C₈×Q₈	—	43	1	no	—
314	C₈×Q₈	—	43	1	no	—
315	C₈×Q₈	—	86	1	no	—
316	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
317	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
318	C₄×Q₁₆	—	43	1	no	—
319	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
320	C₄×SD₁₆	—	43	1	no	—
321	C₄×SD₁₆	—	43	1	no	—
322	C₈×D₄	—	43	1	no	—
323	C₈×D₄	—	43	1	no	—
324	C₈×D₄	—	86	1	no	—
325	C₈×D₄	—	86	1	no	—
326	#431	—	43	1	no	—
327	#431	—	43	1	no	—
328	#431	—	86	1	no	—
329	#424	—	86	1	no	—
330	#423	—	43	1	no	—
331	#405	—	86	1	no	—
332	C₄×M₁₆	—	43	1	no	—
333	C₂×C₄×C₈	—	43	1	no	—
334	C₂×C₄×C₈	—	86	1	no	—
335	#335	—	43	1	no	—
336	#335	C₂×D₄₃	1	1	yes	characteristic
337	#334	—	43	1	no	—
338	#334	—	43	1	no	—
339	Q₈⋊C₈	—	43	1	no	—
340	Q₈⋊C₈	—	43	1	no	—
341	Q₈⋊C₈	—	43	1	no	—
342	Q₈⋊C₈	—	43	1	no	—
343	Q₈⋊C₈	C₂×D₄₃	1	1	yes	characteristic
344	Q₈⋊C₈	C₂×D₄₃	1	1	yes	characteristic
345	D₄⋊C₈	—	43	1	no	—
346	D₄⋊C₈	—	43	1	no	—
347	#322	—	43	1	no	—
348	#322	—	43	1	no	—
349	C₈²	—	43	1	no	—
350	C₈²	C₂×D₄₃	1	1	yes	characteristic
351	C₄₃	#17913	1	1	yes	characteristic, complemented, Sylow
352	C₂×#41	—	43	1	no	—
353	C₂×Q₁₆	—	43	1	no	—
354	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic
355	C₂×SD₁₆	—	43	1	no	—
356	C₂×SD₁₆	—	43	1	no	—
357	C₂×M₁₆	—	86	1	no	—
358	C₂×M₁₆	—	86	1	no	—
359	C₂²×C₈	—	43	1	no	—
360	C₂²×C₈	—	43	1	no	—
361	C₂²×C₈	—	86	1	no	—
362	C₂²×C₈	—	86	1	no	—
363	C₄⋊Q₈	—	43	1	no	—
364	C₄⋊Q₈	—	43	1	no	—
365	#125	—	86	1	no	—
366	C₂²⋊Q₈	—	43	1	no	—
367	C₂²⋊Q₈	—	43	1	no	—
368	C₂²⋊Q₈	—	86	1	no	—
369	C₄×Q₈	—	43	1	no	—
370	C₄×Q₈	—	43	1	no	—
371	C₄×Q₈	—	86	1	no	—
372	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
373	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
374	C₄×D₄	—	43	1	no	—
375	C₄×D₄	—	43	1	no	—
376	C₄×D₄	—	86	1	no	—
377	C₄×D₄	—	86	1	no	—
378	#117	—	43	1	no	—
379	#117	—	86	1	no	—
380	#117	—	86	1	no	—
381	C₂×C₄²	—	43	1	no	—
382	C₂×C₄²	—	86	1	no	—
383	#107	—	43	1	no	—
384	#107	C₄×D₄₃	1	1	yes	characteristic
385	#106	—	43	1	no	—
386	#106	—	43	1	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	43	1	no	—
390	C₄⋊C₈	—	43	1	no	—
391	C₄⋊C₈	—	43	1	no	—
392	C₄⋊C₈	—	43	1	no	—
393	C₄⋊C₈	—	86	1	no	—
394	C₄⋊C₈	—	86	1	no	—
395	C₄⋊C₈	—	86	1	no	—
396	C₄⋊C₈	—	86	1	no	—
397	C₄⋊C₈	—	86	1	no	—
398	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
399	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
400	#103	—	43	1	no	—
401	#103	—	43	1	no	—
402	#103	—	43	1	no	—
403	#103	—	43	1	no	—
404	#103	C₄×D₄₃	1	1	yes	characteristic
405	#103	C₄×D₄₃	1	1	yes	characteristic
406	#102	—	43	1	no	—
407	#102	—	43	1	no	—
408	C₂²⋊C₈	—	43	1	no	—
409	C₂²⋊C₈	—	43	1	no	—
410	C₂²⋊C₈	—	86	1	no	—
411	C₂²⋊C₈	—	86	1	no	—
412	C₂²⋊C₈	—	86	1	no	—
413	#97	—	86	1	no	—
414	#97	—	86	1	no	—
415	#97	—	86	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	2	1	no	—
418	C₄×C₈	—	43	1	no	—
419	C₄×C₈	—	43	1	no	—
420	C₄×C₈	—	43	1	no	—
421	C₄×C₈	—	43	1	no	—
422	C₄×C₈	—	43	1	no	—
423	C₄×C₈	—	86	1	no	—
424	C₄×C₈	—	86	1	no	—
425	C₄×C₈	—	86	1	no	—
426	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
429	#41	—	86	2	no	—
430	#41	—	86	2	no	—
431	C₂×Q₈	—	43	1	no	—
432	C₂×Q₈	—	86	1	no	—
433	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
434	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
435	C₂×D₄	—	43	1	no	—
436	C₂×D₄	—	86	1	no	—
437	C₂²×C₄	—	43	1	no	—
438	C₂²×C₄	—	43	1	no	—
439	C₂²×C₄	—	43	1	no	—
440	C₂²×C₄	—	86	1	no	—
441	C₂²×C₄	—	86	1	no	—
442	C₂²×C₄	—	86	1	no	—
443	Q₁₆	—	2	2	no	—
444	Q₁₆	—	86	2	no	—
445	SD₁₆	—	86	2	no	—
446	SD₁₆	—	86	2	no	—
447	M₁₆	—	86	4	no	—
448	M₁₆	—	172	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	43	1	no	—
453	C₂×C₈	—	43	1	no	—
454	C₂×C₈	—	43	1	no	—
455	C₂×C₈	—	43	1	no	—
456	C₂×C₈	—	86	1	no	—
457	C₂×C₈	—	86	2	no	—
458	C₂×C₈	—	86	1	no	—
459	C₂×C₈	—	86	1	no	—
460	C₂×C₈	—	172	1	no	—
461	C₂×C₈	—	172	2	no	—
462	C₂×C₈	—	172	2	no	—
463	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
465	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
466	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	43	1	no	—
470	C₄⋊C₄	—	43	1	no	—
471	C₄⋊C₄	—	86	1	no	—
472	C₄⋊C₄	—	86	1	no	—
473	C₄⋊C₄	—	86	1	no	—
474	C₄⋊C₄	—	86	1	no	—
475	C₄⋊C₄	—	86	1	no	—
476	C₄⋊C₄	—	86	1	no	—
477	C₄⋊C₄	—	86	1	no	—
478	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
480	C₂²⋊C₄	—	86	1	no	—
481	C₂²⋊C₄	—	86	1	no	—
482	C₂²⋊C₄	—	86	1	no	—
483	C₂²⋊C₄	—	86	1	no	—
484	C₂²⋊C₄	—	86	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	43	1	no	—
488	C₄²	—	43	1	no	—
489	C₄²	—	43	1	no	—
490	C₄²	—	86	1	no	—
491	C₄²	—	86	1	no	—
492	C₄²	—	86	1	no	—
493	C₄²	C₂³×D₄₃	1	1	yes	characteristic
494	C₂³	—	43	1	no	—
495	C₂³	—	86	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	2	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	86	1	no	—
500	Q₈	—	86	1	no	—
501	Q₈	—	172	2	no	—
502	Q₈	#13063331	1	2	yes	—
503	D₄	—	43	2	no	—
504	D₄	—	86	4	no	—
505	D₄	—	86	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	43	1	no	—
511	C₂×C₄	—	43	1	no	—
512	C₂×C₄	—	43	1	no	—
513	C₂×C₄	—	86	2	no	—
514	C₂×C₄	—	86	4	no	—
515	C₂×C₄	—	86	1	no	—
516	C₂×C₄	—	86	1	no	—
517	C₂×C₄	—	86	1	no	—
518	C₂×C₄	—	86	1	no	—
519	C₂×C₄	—	86	1	no	—
520	C₂×C₄	—	86	1	no	—
521	C₂×C₄	—	86	1	no	—
522	C₂×C₄	—	172	2	no	—
523	C₂×C₄	—	172	1	no	—
524	C₂×C₄	—	172	1	no	—
525	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
527	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	4	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	86	2	no	—
535	C₈	—	86	1	no	—
536	C₈	—	86	1	no	—
537	C₈	—	86	1	no	—
538	C₈	—	86	1	no	—
539	C₈	—	172	1	no	—
540	C₈	—	172	1	no	—
541	C₈	#13063357	1	2	yes	—
542	C₂²	—	86	1	no	—
543	C₂²	—	86	2	no	—
544	C₂²	—	86	1	no	—
545	C₂²	—	86	1	no	—
546	C₂²	—	172	1	no	—
547	C₂²	—	172	1	no	—
548	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	43	2	no	—
555	C₄	—	86	1	no	—
556	C₄	—	86	1	no	—
557	C₄	—	172	1	no	—
558	C₄	—	172	1	no	—
559	C₄	—	172	1	no	—
560	C₄	#131×D₄₃	1	1	yes	characteristic
561	C₄	C₂×#13063331	1	1	yes	characteristic
562	C₄	C₂×#13063357	1	1	yes	characteristic
563	C₄	#14583696	1	1	yes	characteristic
564	C₂	—	172	1	no	—
565	C₂	—	172	2	no	—
566	C₂	#19143284	1	1	yes	characteristic
567	C₂	C₄×#13063357	1	1	yes	characteristic
568	C₂	#443×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₈×Q₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621902	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	C₈×Q₁₆	D₄₃
hypocenter	C₄₃	#17913
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
3. #19143524	C₂	semidirect
4. #19133467	C₂	semidirect
5. #19133463	C₂	semidirect
6. #19133455	C₂	semidirect
7. #19133451	C₂	semidirect
8. C₈×#10621885	C₂	semidirect
9. C₈×#10621873	C₂	semidirect
10. C₈×#10621884	C₂	semidirect
11. #19133385	C₂	semidirect
13. #19133014	C₂	semidirect
14. C₈×#10621872	C₂	semidirect
15. C₈×Q₁₆×C₄₃	C₂	semidirect
288. C₈×Q₁₆	D₄₃	semidirect
351. C₄₃	#17913	semidirect

Maximal subgroups

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

subgroup	index
#19144664	2
C₈×#10621902	2
#19143524	2
#19133467	2
#19133463	2
#19133455	2
#19133451	2
C₈×#10621885	2
C₈×#10621873	2
C₈×#10621884	2
#19133385	2
#19133033	2
#19133014	2
C₈×#10621872	2
C₈×Q₁₆×C₄₃	2
#17913	43