Subgroups — #25074329

Order 11008.

912 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145907	C₂	1	1	yes	maximal, characteristic
2	#19145155	C₂	1	1	yes	maximal, characteristic
3	#19144067	C₂	1	1	yes	maximal, characteristic
4	#19133872	C₂	1	2	yes	maximal, complemented
5	#19133816	C₂	1	2	yes	maximal, complemented
6	#19133691	C₂	1	2	yes	maximal, complemented
7	#19133673	C₂	1	2	yes	maximal, complemented
8	#19133285	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133050	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×Q₈⋊(C₄₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3502	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583295	C₂²	1	1	yes	characteristic
15	#14583273	C₂²	1	1	yes	characteristic
16	#14583249	C₂²	1	1	yes	characteristic
17	#14583247	C₂²	1	1	yes	characteristic
18	#14583186	—	2	1	no	—
19	#14583184	C₂²	1	2	yes	—
20	#14583130	—	2	2	no	—
21	#14583130	—	2	2	no	—
22	#14583121	—	2	2	no	—
23	#14583109	C₂²	1	2	yes	—
24	#14583101	—	2	1	no	—
25	#14583099	C₂²	1	2	yes	—
26	#14583099	C₂²	1	2	yes	—
27	C₄×#10621884	—	2	2	no	—
28	#14582923	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	#14582898	—	2	1	no	—
31	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
32	#14582648	C₂²	1	2	yes	—
33	#14582645	C₂²	1	2	yes	—
34	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
35	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
36	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
37	Q₈⋊(C₄₃⋊C₈)	C₂²	1	2	yes	—
38	Q₈²×C₄₃	—	2	1	no	—
39	Q₈²×C₄₃	C₂²	1	2	yes	—
40	C₄₃×#557	—	2	1	no	—
41	C₄₃×#557	—	2	2	no	—
42	C₄₃×#557	—	2	2	no	—
43	C₄₃×#557	C₂²	1	2	yes	—
44	C₄₃×#544	—	2	2	no	—
45	C₄₃×#544	—	2	1	no	—
46	C₄₃×#533	—	2	2	no	—
47	C₄₃×#533	C₂²	1	1	yes	characteristic
48	C₄₃×#533	C₂²	1	1	yes	characteristic
49	C₄₃×#519	—	2	1	no	—
50	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×#10621898	—	2	1	no	—
52	#13063356	—	4	4	no	—
53	C₂×#10621885	—	2	2	no	—
54	C₂×#10621884	—	2	2	no	—
55	C₂×#10621884	—	2	2	no	—
56	C₂×#10621884	—	2	2	no	—
57	C₂×#10621877	—	2	1	no	—
58	C₂²×C₄₃⋊C₈	—	2	1	no	—
59	C₂²×C₄₃⋊C₈	—	2	1	no	—
60	#13063325	C₂³	1	1	yes	characteristic
61	#13063322	C₂³	1	1	yes	characteristic
62	#13063313	—	2	1	no	—
63	#13063299	—	2	1	no	—
64	#13063299	—	2	1	no	—
65	C₄×D₁₇₂	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	#13063256	—	2	2	no	—
68	#13063256	—	2	2	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
73	#13063249	—	2	2	no	—
74	#13063249	—	2	2	no	—
75	#13063248	—	2	2	no	—
76	#13063245	—	2	2	no	—
77	#13063245	—	2	2	no	—
78	#13063245	—	2	2	no	—
79	C₄×C₄₃⋊C₈	—	2	1	no	—
80	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₃	—	2	4	no	—
84	C₄⋊Q₈×C₄₃	—	2	2	no	—
85	C₄⋊Q₈×C₄₃	—	2	2	no	—
86	C₄⋊Q₈×C₄₃	—	2	4	no	—
87	C₄⋊Q₈×C₄₃	—	2	2	no	—
88	C₄⋊Q₈×C₄₃	—	2	2	no	—
89	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
92	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
93	#125×C₄₃	—	2	4	no	—
94	#125×C₄₃	—	2	4	no	—
95	#125×C₄₃	—	2	2	no	—
96	#125×C₄₃	—	2	4	no	—
97	#125×C₄₃	—	2	2	no	—
98	#125×C₄₃	—	2	1	no	—
99	#125×C₄₃	—	2	1	no	—
100	C₂²⋊Q₈×C₄₃	—	2	4	no	—
101	C₂²⋊Q₈×C₄₃	—	2	1	no	—
102	C₂²⋊Q₈×C₄₃	—	2	1	no	—
103	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
104	C₂²⋊Q₈×C₄₃	D₄	1	2	yes	—
105	C₄×Q₈×C₄₃	—	2	2	no	—
106	C₄×Q₈×C₄₃	—	2	2	no	—
107	C₄×Q₈×C₄₃	—	2	4	no	—
108	C₄×Q₈×C₄₃	—	2	2	no	—
109	C₄×Q₈×C₄₃	—	2	2	no	—
110	C₄×Q₈×C₄₃	—	2	2	no	—
111	C₄×Q₈×C₄₃	—	2	2	no	—
112	C₄×Q₈×C₄₃	—	2	1	no	—
113	C₄×Q₈×C₄₃	—	2	1	no	—
114	C₄×Q₈×C₄₃	—	2	1	no	—
115	C₄×Q₈×C₄₃	—	2	1	no	—
116	C₄×Q₈×C₄₃	D₄	1	2	yes	—
117	C₄×Q₈×C₄₃	D₄	1	2	yes	—
118	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
119	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
120	#117×C₄₃	—	2	4	no	—
121	#117×C₄₃	—	2	1	no	—
122	#117×C₄₃	—	2	1	no	—
123	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₃	—	2	1	no	—
126	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₄₃	—	2	4	no	—
128	C₂×Q₈×C₄₃	—	2	1	no	—
129	C₂×Q₈×C₄₃	—	2	1	no	—
130	C₂×Q₈×C₄₃	—	2	2	no	—
131	C₂×Q₈×C₄₃	—	2	1	no	—
132	C₂×Q₈×C₄₃	SD₁₆	1	4	yes	complemented
133	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₄₃	—	2	1	no	—
137	C₂²×C₄×C₄₃	—	2	1	no	—
138	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₂×C₂²⋊D₄₃	—	4	1	no	—
142	#10621898	—	4	2	no	—
143	#10621898	—	4	2	no	—
144	C₂×D₁₇₂	—	2	1	no	—
145	C₂×D₁₇₂	—	2	1	no	—
146	C₂×D₁₇₂	—	2	1	no	—
147	C₂×C₄×D₄₃	—	4	1	no	—
148	C₂×Dic₈₆	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	2	4	no	—
150	C₄⋊C₄×C₄₃	—	2	4	no	—
151	C₄⋊C₄×C₄₃	—	2	4	no	—
152	C₄⋊C₄×C₄₃	—	2	4	no	—
153	C₄⋊C₄×C₄₃	—	2	4	no	—
154	C₄⋊C₄×C₄₃	—	2	2	no	—
155	C₄⋊C₄×C₄₃	—	2	1	no	—
156	C₄⋊C₄×C₄₃	—	2	1	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	2	no	—
159	C₄⋊C₄×C₄₃	—	2	2	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	2	no	—
162	C₄⋊C₄×C₄₃	—	2	2	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	1	no	—
165	C₄⋊C₄×C₄₃	—	2	1	no	—
166	C₄⋊C₄×C₄₃	—	2	2	no	—
167	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
169	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
170	C₂²⋊C₄×C₄₃	—	2	2	no	—
171	C₂²⋊C₄×C₄₃	—	2	2	no	—
172	C₄²×C₄₃	—	2	4	no	—
173	C₄²×C₄₃	—	2	4	no	—
174	C₄²×C₄₃	—	2	2	no	—
175	C₄²×C₄₃	—	2	2	no	—
176	C₄²×C₄₃	—	2	2	no	—
177	C₄²×C₄₃	—	2	2	no	—
178	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
182	#10621885	—	4	4	no	—
183	#10621884	—	4	4	no	—
184	#10621884	—	4	4	no	—
185	#10621884	—	8	2	no	—
186	(C₂×D₄₃)⋊C₄	—	4	1	no	—
187	(C₂×D₄₃)⋊C₄	—	4	1	no	—
188	C₄⋊Dic₄₃	—	2	1	no	—
189	C₄⋊Dic₄₃	—	2	1	no	—
190	#10621877	—	4	2	no	—
191	C₂×C₄₃⋊C₈	—	2	1	no	—
192	C₂×C₄₃⋊C₈	—	2	1	no	—
193	C₂×C₄₃⋊C₈	—	2	2	no	—
194	C₂×C₄₃⋊C₈	—	2	2	no	—
195	C₂×C₄₃⋊C₈	—	4	2	no	—
196	C₂×C₄₃⋊C₈	—	8	1	no	—
197	C₂³×C₄₃	#120	1	1	yes	characteristic
198	C₂²×D₄₃	—	4	1	no	—
199	Q₈×C₄₃	—	2	2	no	—
200	Q₈×C₄₃	—	2	4	no	—
201	Q₈×C₄₃	—	2	2	no	—
202	Q₈×C₄₃	—	2	2	no	—
203	Q₈×C₄₃	—	4	2	no	—
204	Q₈×C₄₃	—	4	1	no	—
205	Q₈×C₄₃	—	4	1	no	—
206	Q₈×C₄₃	—	8	1	no	—
207	Q₈×C₄₃	—	8	4	no	—
208	Q₈×C₄₃	C₂×SD₁₆	1	4	yes	—
209	C₂×C₄×C₄₃	—	2	2	no	—
210	C₂×C₄×C₄₃	—	2	4	no	—
211	C₂×C₄×C₄₃	—	2	1	no	—
212	C₂×C₄×C₄₃	—	2	1	no	—
213	C₂×C₄×C₄₃	—	2	2	no	—
214	C₂×C₄×C₄₃	—	2	2	no	—
215	C₂×C₄×C₄₃	—	2	2	no	—
216	C₂×C₄×C₄₃	—	2	2	no	—
217	C₂×C₄×C₄₃	—	2	2	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	8	1	no	—
220	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
221	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
224	C₂×C₄×C₄₃	#137	1	2	yes	—
225	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
228	C₂²⋊D₄₃	—	8	2	no	—
229	C₂×Dic₄₃	—	4	1	no	—
230	D₁₇₂	—	4	2	no	—
231	D₁₇₂	—	4	1	no	—
232	D₁₇₂	—	4	1	no	—
233	D₁₇₂	—	4	1	no	—
234	D₁₇₂	—	4	1	no	—
235	C₄×D₄₃	—	8	2	no	—
236	Dic₈₆	—	4	1	no	—
237	Dic₈₆	—	4	1	no	—
238	C₄₃⋊C₈	—	2	2	no	—
239	C₄₃⋊C₈	—	4	1	no	—
240	C₄₃⋊C₈	—	4	2	no	—
241	C₄₃⋊C₈	—	4	2	no	—
242	#18676	—	43	1	no	maximal, Sylow
243	C₂²×C₄₃	—	2	1	no	—
244	C₂²×C₄₃	—	2	1	no	—
245	C₂²×C₄₃	#448	1	2	yes	—
246	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
247	C₂×D₄₃	—	8	1	no	—
248	C₂×D₄₃	—	8	1	no	—
249	C₂×D₄₃	—	8	1	no	—
250	C₄×C₄₃	—	2	4	no	—
251	C₄×C₄₃	—	2	1	no	—
252	C₄×C₄₃	—	2	1	no	—
253	C₄×C₄₃	—	2	1	no	—
254	C₄×C₄₃	—	4	2	no	—
255	C₄×C₄₃	—	4	2	no	—
256	C₄×C₄₃	—	4	2	no	—
257	C₄×C₄₃	—	4	2	no	—
258	C₄×C₄₃	—	4	2	no	—
259	C₄×C₄₃	#448	1	2	yes	—
260	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
261	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
262	C₄×C₄₃	#577	1	1	yes	characteristic
263	C₄×C₄₃	#578	1	1	yes	characteristic
264	Dic₄₃	—	8	1	no	—
265	#3502	D₄₃	1	1	yes	characteristic, complemented
266	#3246	—	43	1	no	—
267	#3167	—	43	1	no	—
268	#3037	—	43	1	no	—
269	#1653	—	43	2	no	—
270	#1645	—	43	2	no	—
271	#1626	—	43	2	no	—
272	#1623	—	43	2	no	—
273	#1550	—	43	1	no	—
274	#1493	—	43	1	no	—
275	C₂×Q₈⋊C₈	—	43	1	no	—
276	C₂×C₄₃	—	2	2	no	—
277	C₂×C₄₃	C₂×#448	1	1	yes	characteristic
278	C₂×C₄₃	#3013	1	1	yes	characteristic
279	C₂×C₄₃	#3018	1	1	yes	characteristic
280	D₄₃	—	16	1	no	—
281	C₂×#137	—	86	1	no	—
282	Q₈²	—	2	1	no	—
283	Q₈²	C₂×D₄₃	1	2	yes	—
284	#557	—	2	1	no	—
285	#557	—	2	2	no	—
286	#557	—	2	2	no	—
287	#557	C₂×D₄₃	1	2	yes	—
288	#544	—	2	2	no	—
289	#544	—	2	1	no	—
290	#533	—	2	2	no	—
291	#533	C₂×D₄₃	1	1	yes	characteristic
292	#533	C₂×D₄₃	1	1	yes	characteristic
293	#532	—	43	1	no	—
294	#519	—	2	1	no	—
295	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
296	#498	—	43	1	no	—
297	#492	—	43	1	no	—
298	#487	—	43	1	no	—
299	#486	—	43	1	no	—
300	#476	—	86	1	no	—
301	#475	—	43	2	no	—
302	#465	—	86	2	no	—
303	#465	—	86	2	no	—
304	#464	—	86	2	no	—
305	#462	—	43	2	no	—
306	#461	—	86	1	no	—
307	#460	—	43	2	no	—
308	#460	—	43	2	no	—
309	C₄×SD₁₆	—	86	2	no	—
310	#423	—	43	1	no	—
311	C₂×C₄⋊C₈	—	43	1	no	—
312	#417	—	86	1	no	—
313	C₂×C₄×C₈	—	43	1	no	—
314	#333	—	43	2	no	—
315	#332	—	43	2	no	—
316	Q₈⋊C₈	—	43	2	no	—
317	Q₈⋊C₈	—	43	2	no	—
318	Q₈⋊C₈	—	43	2	no	—
319	Q₈⋊C₈	—	43	2	no	—
320	C₄₃	#18676	1	1	yes	characteristic, complemented, Sylow
321	C₂×#41	—	86	1	no	—
322	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
323	#137	—	172	4	no	—
324	C₂×Q₁₆	—	86	2	no	—
325	C₂×SD₁₆	—	86	2	no	—
326	C₂×SD₁₆	—	86	2	no	—
327	C₂×SD₁₆	—	86	2	no	—
328	C₂×M₁₆	—	86	1	no	—
329	C₂²×C₈	—	86	1	no	—
330	C₂²×C₈	—	86	1	no	—
331	C₄⋊Q₈	—	2	4	no	—
332	C₄⋊Q₈	—	2	2	no	—
333	C₄⋊Q₈	—	2	2	no	—
334	C₄⋊Q₈	—	2	4	no	—
335	C₄⋊Q₈	—	2	2	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	43	1	no	—
338	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
339	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
340	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
341	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
342	#127	—	43	1	no	—
343	#125	—	2	4	no	—
344	#125	—	2	4	no	—
345	#125	—	2	2	no	—
346	#125	—	2	4	no	—
347	#125	—	2	2	no	—
348	#125	—	2	1	no	—
349	#125	—	2	1	no	—
350	#124	—	86	1	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	1	no	—
354	C₂²⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
355	C₂²⋊Q₈	C₂²⋊D₄₃	1	2	yes	—
356	#121	—	86	1	no	—
357	#121	—	86	1	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	4	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	C₂²⋊D₄₃	1	2	yes	—
370	C₄×Q₈	C₂²⋊D₄₃	1	2	yes	—
371	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
372	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
373	C₄×D₄	—	86	1	no	—
374	C₄×D₄	—	86	1	no	—
375	#117	—	2	4	no	—
376	#117	—	2	1	no	—
377	#117	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
380	C₂×C₄²	—	2	1	no	—
381	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
382	#106	—	86	2	no	—
383	#106	—	86	2	no	—
384	C₄⋊C₈	—	43	2	no	—
385	C₄⋊C₈	—	43	2	no	—
386	C₄⋊C₈	—	86	1	no	—
387	C₄⋊C₈	—	86	1	no	—
388	#103	—	86	2	no	—
389	#103	—	86	2	no	—
390	#103	—	86	2	no	—
391	#102	—	86	2	no	—
392	#102	—	86	2	no	—
393	#102	—	86	2	no	—
394	C₄×C₈	—	43	1	no	—
395	C₄×C₈	—	43	1	no	—
396	C₄×C₈	—	86	1	no	—
397	#41	—	172	2	no	—
398	#41	—	172	2	no	—
399	C₂×Q₈	—	2	4	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	—	86	1	no	—
405	C₂×Q₈	#10621884	1	4	yes	complemented
406	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
407	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
408	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
409	C₂×D₄	—	86	1	no	—
410	C₂×D₄	—	86	1	no	—
411	C₂×D₄	—	86	1	no	—
412	C₂×D₄	—	172	1	no	—
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	172	1	no	—
416	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
419	Q₁₆	—	172	4	no	—
420	SD₁₆	—	344	2	no	—
421	SD₁₆	—	172	4	no	—
422	SD₁₆	—	172	4	no	—
423	M₁₆	—	172	2	no	—
424	C₂×C₈	—	86	1	no	—
425	C₂×C₈	—	86	1	no	—
426	C₂×C₈	—	86	2	no	—
427	C₂×C₈	—	86	2	no	—
428	C₂×C₈	—	344	1	no	—
429	C₂×C₈	—	172	2	no	—
430	C₄⋊C₄	—	2	4	no	—
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	4	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	2	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	86	1	no	—
449	C₄⋊C₄	—	86	1	no	—
450	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
451	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
452	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	172	1	no	—
456	C₂²⋊C₄	—	172	1	no	—
457	C₄²	—	2	4	no	—
458	C₄²	—	2	4	no	—
459	C₄²	—	2	2	no	—
460	C₄²	—	2	2	no	—
461	C₄²	—	2	2	no	—
462	C₄²	—	2	2	no	—
463	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
464	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
465	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
466	C₄²	C₂³×D₄₃	1	1	yes	characteristic
467	C₂³	—	172	1	no	—
468	C₂³	#13063294	1	1	yes	characteristic
469	Q₈	—	2	2	no	—
470	Q₈	—	2	4	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	2	2	no	—
473	Q₈	—	4	2	no	—
474	Q₈	—	4	1	no	—
475	Q₈	—	4	1	no	—
476	Q₈	—	8	1	no	—
477	Q₈	—	8	4	no	—
478	Q₈	—	172	1	no	—
479	Q₈	—	172	1	no	—
480	Q₈	C₂×#10621884	1	4	yes	—
481	D₄	—	344	2	no	—
482	D₄	—	172	2	no	—
483	D₄	—	172	1	no	—
484	D₄	—	172	1	no	—
485	D₄	—	172	1	no	—
486	D₄	—	172	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	8	1	no	—
498	C₂×C₄	—	344	2	no	—
499	C₂×C₄	—	172	1	no	—
500	C₂×C₄	#13063294	1	1	yes	characteristic
501	C₂×C₄	#13063294	1	1	yes	characteristic
502	C₂×C₄	#13063294	1	1	yes	characteristic
503	C₂×C₄	C₂×#10621884	1	2	yes	—
504	C₂×C₄	#13063356	1	2	yes	—
505	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
506	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
507	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
508	C₈	—	86	2	no	—
509	C₈	—	172	1	no	—
510	C₈	—	172	2	no	—
511	C₈	—	172	2	no	—
512	C₂²	—	2	1	no	—
513	C₂²	—	2	1	no	—
514	C₂²	—	344	1	no	—
515	C₂²	—	344	1	no	—
516	C₂²	—	344	1	no	—
517	C₂²	#14583038	1	2	yes	—
518	C₂²	C₂×#13063294	1	1	yes	characteristic
519	C₄	—	2	1	no	—
520	C₄	—	2	1	no	—
521	C₄	—	2	4	no	—
522	C₄	—	2	1	no	—
523	C₄	—	4	2	no	—
524	C₄	—	4	2	no	—
525	C₄	—	4	2	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	344	1	no	—
529	C₄	#14583038	1	2	yes	—
530	C₄	C₂²×#10621884	1	1	yes	characteristic
531	C₄	C₂×#13063356	1	1	yes	characteristic
532	C₄	#14583707	1	1	yes	characteristic
533	C₄	#14583714	1	1	yes	characteristic
534	C₂	—	2	2	no	—
535	C₂	—	688	1	no	—
536	C₂	C₂×#14583038	1	1	yes	characteristic
537	C₂	#19143910	1	1	yes	characteristic
538	C₂	#19143944	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063294
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3502	C₂
socle	C₂²×C₄₃	C₂×#120
prime radical	#14583449	C₂²
hypercenter	#3502	D₄₃
hypocenter	C₄₃	#18676
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3502

Complements

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

N	H ≅ G/N	type
4. #19133872	C₂	semidirect
5. #19133816	C₂	semidirect
6. #19133691	C₂	semidirect
7. #19133673	C₂	semidirect
8. #19133285	C₂	semidirect
9. #19133050	C₂	semidirect
10. C₂×Q₈⋊(C₄₃⋊C₈)	C₂	semidirect
11. C₄₃×#3502	C₂	semidirect
132. C₂×Q₈×C₄₃	SD₁₆	semidirect
265. #3502	D₄₃	semidirect
320. C₄₃	#18676	semidirect
405. C₂×Q₈	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145907	2
#19145155	2
#19144067	2
#19133872	2
#19133816	2
#19133691	2
#19133673	2
#19133285	2
#19133050	2
C₂×Q₈⋊(C₄₃⋊C₈)	2
C₄₃×#3502	2
#18676	43