Subgroups — #25066549

Order 11008.

626 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144609	C₂	1	1	yes	maximal, characteristic
2	#19143573	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×#10621900	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133471	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133468	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133452	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133419	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133413	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133404	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133404	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133372	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133026	C₂	1	1	yes	maximal, characteristic, complemented
13	#19133000	C₂	1	1	yes	maximal, characteristic, complemented
14	#19132886	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1586	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583431	C₂²	1	1	yes	characteristic
17	C₄×#10621900	C₂²	1	1	yes	characteristic
18	#14583242	C₄	1	1	yes	characteristic
19	#14583221	C₄	1	1	yes	characteristic
20	#14583205	C₄	1	1	yes	characteristic
21	#14583197	C₄	1	1	yes	characteristic
22	#14583120	C₄	1	1	yes	characteristic
23	#14583112	C₄	1	1	yes	characteristic
24	#14583062	C₄	1	1	yes	characteristic
25	#14583041	C₄	1	1	yes	characteristic
26	#14583029	C₂²	1	1	yes	characteristic
27	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
28	#14583023	C₂²	1	1	yes	characteristic
29	#14583023	C₂²	1	1	yes	characteristic
30	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic
31	C₄×#10621883	C₂²	1	1	yes	characteristic
32	C₄×#10621883	C₂²	1	1	yes	characteristic
33	#14582968	—	2	1	no	—
34	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
36	C₈×C₂²⋊D₄₃	—	2	1	no	—
37	(C₂²⋊D₄₃)⋊C₈	—	2	1	no	—
38	(C₂²⋊D₄₃)⋊C₈	—	2	1	no	—
39	#14582957	—	2	1	no	—
40	#14582955	C₂²	1	1	yes	characteristic
41	#14582951	C₂²	1	1	yes	characteristic
42	#14582950	C₂²	1	1	yes	characteristic
43	#14582950	C₂²	1	1	yes	characteristic
44	#14582949	—	2	1	no	—
45	#14582857	—	2	1	no	—
46	C₂×C₈×Dic₄₃	—	2	1	no	—
47	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
48	#14582651	C₂²	1	1	yes	characteristic
49	#14582651	C₂²	1	1	yes	characteristic
50	#14582650	C₂²	1	1	yes	characteristic
51	#14582631	C₂²	1	1	yes	characteristic
52	#14582631	C₂²	1	1	yes	characteristic
53	#14582629	C₂²	1	1	yes	characteristic
54	#14582629	C₂²	1	1	yes	characteristic
55	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
56	D₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
57	#14582621	C₂²	1	1	yes	characteristic
58	#14582621	C₂²	1	1	yes	characteristic
59	#14582620	C₂²	1	1	yes	characteristic
60	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
61	C₄₃×#436	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
63	C₄₃×#334	C₂²	1	1	yes	characteristic
64	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₄₃×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₄₃×#322	C₂²	1	1	yes	characteristic
67	C₂×#10621900	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
69	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
70	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₄₃⋊C₈	—	2	1	no	—
72	C₂²×C₄₃⋊C₈	—	2	1	no	—
73	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
74	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
75	#13063318	—	2	1	no	—
76	#13063316	C₂×C₄	1	1	yes	characteristic
77	#13063312	C₂×C₄	1	1	yes	characteristic
78	#13063307	—	2	1	no	—
79	#13063305	C₂×C₄	1	1	yes	characteristic
80	#13063296	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
82	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
83	#13063290	C₂×C₄	1	1	yes	characteristic
84	D₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
85	C₄×C₂²⋊D₄₃	—	2	1	no	—
86	C₄×C₂²⋊D₄₃	—	2	1	no	—
87	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
88	#13063284	—	2	1	no	—
89	#13063283	C₂×C₄	1	1	yes	characteristic
90	#13063281	—	2	1	no	—
91	C₂×C₄×Dic₄₃	—	2	1	no	—
92	C₄²×D₄₃	C₂³	1	1	yes	characteristic
93	#13063259	C₂×C₄	1	1	yes	characteristic
94	#13063256	C₂×C₄	1	1	yes	characteristic
95	#13063256	C₂×C₄	1	1	yes	characteristic
96	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
97	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
98	Dic₄₃⋊C₈	—	2	1	no	—
99	Dic₄₃⋊C₈	—	2	1	no	—
100	Dic₄₃⋊C₈	—	2	1	no	—
101	Dic₄₃⋊C₈	—	2	1	no	—
102	Dic₄₃⋊C₈	—	2	1	no	—
103	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
104	Dic₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
105	#13063250	C₂×C₄	1	1	yes	characteristic
106	#13063250	C₂×C₄	1	1	yes	characteristic
107	#13063248	C₂×C₄	1	1	yes	characteristic
108	#13063248	C₂×C₄	1	1	yes	characteristic
109	#13063246	C₂×C₄	1	1	yes	characteristic
110	#13063246	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
112	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
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	#13063235	—	2	1	no	—
119	#13063235	—	2	1	no	—
120	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
121	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
123	C₈×Dic₄₃	—	2	1	no	—
124	C₈×Dic₄₃	—	2	1	no	—
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×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
130	C₂×M₁₆×C₄₃	—	2	1	no	—
131	C₂²×C₈×C₄₃	—	2	1	no	—
132	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
133	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
134	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
135	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
137	#102×C₄₃	C₂×C₄	1	1	yes	characteristic
138	#102×C₄₃	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₄₃	—	2	1	no	—
140	C₂²⋊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×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₃	—	2	1	no	—
147	C₂²×C₄×C₄₃	—	2	1	no	—
148	C₂×C₂²⋊D₄₃	—	2	1	no	—
149	C₂×C₂²⋊D₄₃	—	2	1	no	—
150	C₂²×Dic₄₃	—	2	1	no	—
151	C₂²×Dic₄₃	—	2	1	no	—
152	#10621900	—	2	2	no	—
153	#10621900	—	2	2	no	—
154	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
157	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
159	D₈×C₄₃	—	2	2	no	—
160	M₁₆×C₄₃	—	4	2	no	—
161	C₂×C₈×C₄₃	—	2	1	no	—
162	C₂×C₈×C₄₃	—	2	1	no	—
163	C₂×C₈×C₄₃	—	2	1	no	—
164	C₂×C₈×C₄₃	—	4	2	no	—
165	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
171	C₂²⋊C₄×C₄₃	—	2	1	no	—
172	C₂²⋊C₄×C₄₃	—	2	1	no	—
173	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊Dic₄₃	—	2	1	no	—
175	C₂²⋊Dic₄₃	—	2	1	no	—
176	C₂²⋊Dic₄₃	—	2	1	no	—
177	C₂²⋊Dic₄₃	—	2	1	no	—
178	#10621883	—	2	2	no	—
179	#10621883	—	2	2	no	—
180	(C₂×D₄₃)⋊C₄	—	2	1	no	—
181	(C₂×D₄₃)⋊C₄	—	2	1	no	—
182	C₄⋊Dic₄₃	—	2	1	no	—
183	C₄⋊Dic₄₃	—	2	1	no	—
184	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
185	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
186	Dic₄₃⋊C₄	—	2	1	no	—
187	Dic₄₃⋊C₄	—	2	1	no	—
188	Dic₄₃⋊C₄	—	2	1	no	—
189	Dic₄₃⋊C₄	—	2	1	no	—
190	C₄×Dic₄₃	—	2	1	no	—
191	C₄×Dic₄₃	—	2	1	no	—
192	C₄×Dic₄₃	—	2	1	no	—
193	C₄×Dic₄₃	—	2	1	no	—
194	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
195	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
196	C₄×Dic₄₃	#41	1	1	yes	characteristic
197	C₂×C₄₃⋊C₈	—	2	1	no	—
198	C₂×C₄₃⋊C₈	—	2	1	no	—
199	C₂×C₄₃⋊C₈	—	2	1	no	—
200	C₂×C₄₃⋊C₈	—	4	2	no	—
201	C₂×C₄₃⋊C₈	—	4	2	no	—
202	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
206	Dic₁₇₂	—	2	2	no	—
207	C₈×D₄₃	—	4	1	no	—
208	C₈×D₄₃	—	4	1	no	—
209	C₂³×C₄₃	—	2	1	no	—
210	C₂³×C₄₃	—	2	1	no	—
211	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
212	D₄×C₄₃	—	2	1	no	—
213	D₄×C₄₃	—	2	1	no	—
214	D₄×C₄₃	—	2	1	no	—
215	D₄×C₄₃	#131	1	2	yes	—
216	C₂×C₄×C₄₃	—	2	1	no	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	—	4	1	no	—
220	C₂×C₄×C₄₃	—	4	1	no	—
221	C₂×C₄×C₄₃	—	4	1	no	—
222	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
225	C₂²⋊D₄₃	—	2	4	no	—
226	C₂²⋊D₄₃	—	4	2	no	—
227	C₂×Dic₄₃	—	2	4	no	—
228	C₂×Dic₄₃	—	2	1	no	—
229	C₂×Dic₄₃	—	2	1	no	—
230	C₂×Dic₄₃	—	2	1	no	—
231	C₂×Dic₄₃	—	2	1	no	—
232	C₂×Dic₄₃	—	4	2	no	—
233	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
234	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
235	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
236	C₄×D₄₃	—	2	1	no	—
237	C₄×D₄₃	—	2	1	no	—
238	C₄×D₄₃	—	2	1	no	—
239	C₄×D₄₃	—	2	1	no	—
240	C₄×D₄₃	—	4	1	no	—
241	Dic₈₆	—	2	1	no	—
242	Dic₈₆	—	2	1	no	—
243	Dic₈₆	—	2	1	no	—
244	Dic₈₆	#131	1	2	yes	—
245	C₈×C₄₃	—	2	1	no	—
246	C₈×C₄₃	—	2	1	no	—
247	C₈×C₄₃	—	2	1	no	—
248	C₈×C₄₃	—	2	1	no	—
249	C₈×C₄₃	—	4	1	no	—
250	C₈×C₄₃	—	4	1	no	—
251	C₈×C₄₃	—	4	1	no	—
252	C₄₃⋊C₈	—	2	1	no	—
253	C₄₃⋊C₈	—	2	1	no	—
254	C₄₃⋊C₈	—	2	1	no	—
255	C₄₃⋊C₈	—	2	1	no	—
256	C₄₃⋊C₈	—	4	1	no	—
257	C₄₃⋊C₈	—	4	1	no	—
258	C₄₃⋊C₈	—	4	1	no	—
259	#17909	—	43	1	no	maximal, Sylow
260	C₂²×C₄₃	—	2	2	no	—
261	C₂²×C₄₃	—	4	1	no	—
262	C₂²×C₄₃	—	4	1	no	—
263	C₂²×C₄₃	—	4	1	no	—
264	C₂²×C₄₃	—	4	1	no	—
265	C₂²×C₄₃	—	4	1	no	—
266	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂×D₄₃	—	2	1	no	—
268	C₂×D₄₃	—	2	1	no	—
269	C₂×D₄₃	—	2	1	no	—
270	C₄×C₄₃	—	2	1	no	—
271	C₄×C₄₃	—	4	1	no	—
272	C₄×C₄₃	—	4	1	no	—
273	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
274	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
275	C₄×C₄₃	#575	1	1	yes	characteristic
276	C₄×C₄₃	#575	1	1	yes	characteristic
277	Dic₄₃	—	2	2	no	—
278	Dic₄₃	—	2	1	no	—
279	Dic₄₃	—	2	1	no	—
280	Dic₄₃	—	2	1	no	—
281	Dic₄₃	—	4	1	no	—
282	Dic₄₃	—	4	1	no	—
283	Dic₄₃	—	4	1	no	—
284	#3102	—	43	1	no	—
285	#2966	—	43	1	no	—
286	C₈×#41	—	43	1	no	—
287	#1588	—	43	1	no	—
288	#1587	—	43	1	no	—
289	#1586	D₄₃	1	1	yes	characteristic, complemented
290	#1585	—	43	1	no	—
291	#1580	—	43	1	no	—
292	#1579	—	43	1	no	—
293	SD₁₆⋊C₈	—	43	1	no	—
294	SD₁₆⋊C₈	—	43	1	no	—
295	#1572	—	43	1	no	—
296	#1488	—	43	1	no	—
297	#1482	—	43	1	no	—
298	#1452	—	43	1	no	—
299	C₂×C₄₃	—	4	2	no	—
300	C₂×C₄₃	—	8	1	no	—
301	C₂×C₄₃	#2929	1	1	yes	characteristic
302	C₂×C₄₃	#2943	1	1	yes	characteristic
303	C₂×C₄₃	#2955	1	1	yes	characteristic
304	D₄₃	—	4	1	no	—
305	#529	—	43	1	no	—
306	C₄×#41	—	43	1	no	—
307	#485	—	43	1	no	—
308	#482	—	43	1	no	—
309	#479	—	43	1	no	—
310	#478	—	43	1	no	—
311	#464	—	43	1	no	—
312	#463	—	43	1	no	—
313	#452	—	43	1	no	—
314	#449	—	43	1	no	—
315	#446	—	43	1	no	—
316	C₈×Q₈	—	43	1	no	—
317	C₈×Q₈	—	43	1	no	—
318	C₈×Q₈	—	43	1	no	—
319	C₄×Q₁₆	—	43	1	no	—
320	C₄×SD₁₆	—	43	1	no	—
321	C₄×SD₁₆	—	43	1	no	—
322	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
323	#436	C₂×D₄₃	1	1	yes	characteristic
324	#435	—	86	1	no	—
325	C₈×D₄	—	43	1	no	—
326	C₈×D₄	—	43	1	no	—
327	C₈×D₄	—	86	1	no	—
328	C₈×D₄	—	86	1	no	—
329	C₈×D₄	—	86	1	no	—
330	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
331	#433	—	86	1	no	—
332	#432	—	43	1	no	—
333	#431	—	43	1	no	—
334	#431	—	43	1	no	—
335	#431	—	43	1	no	—
336	#431	—	86	1	no	—
337	#405	—	86	1	no	—
338	C₂×C₄×C₈	—	43	1	no	—
339	C₂×C₄×C₈	—	86	1	no	—
340	#335	—	43	1	no	—
341	#335	—	43	1	no	—
342	#334	—	43	1	no	—
343	#334	C₂×D₄₃	1	1	yes	characteristic
344	Q₈⋊C₈	—	43	1	no	—
345	Q₈⋊C₈	—	43	1	no	—
346	Q₈⋊C₈	—	43	1	no	—
347	Q₈⋊C₈	—	43	1	no	—
348	D₄⋊C₈	—	43	1	no	—
349	D₄⋊C₈	—	43	1	no	—
350	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
351	D₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
352	#322	—	43	1	no	—
353	#322	—	43	1	no	—
354	#322	—	43	1	no	—
355	#322	C₂×D₄₃	1	1	yes	characteristic
356	C₄₃	#17909	1	1	yes	characteristic, complemented, Sylow
357	C₂×#41	—	43	1	no	—
358	C₂×Q₁₆	—	43	1	no	—
359	C₂×SD₁₆	—	43	1	no	—
360	C₂×SD₁₆	—	43	1	no	—
361	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic
362	C₂×M₁₆	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	43	1	no	—
365	C₂²×C₈	—	43	1	no	—
366	C₂²×C₈	—	86	1	no	—
367	C₂²×C₈	—	86	1	no	—
368	#126	—	86	1	no	—
369	#125	—	43	1	no	—
370	#124	—	43	1	no	—
371	#123	—	86	1	no	—
372	C₂²⋊Q₈	—	43	1	no	—
373	#121	—	43	1	no	—
374	C₄×Q₈	—	43	1	no	—
375	C₄×Q₈	—	43	1	no	—
376	C₄×Q₈	—	43	1	no	—
377	C₄×D₄	—	43	1	no	—
378	C₄×D₄	—	86	1	no	—
379	C₄×D₄	—	86	1	no	—
380	C₄×D₄	—	86	1	no	—
381	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
382	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
383	#117	—	43	1	no	—
384	#117	—	86	1	no	—
385	#117	—	86	1	no	—
386	C₂×C₄²	—	43	1	no	—
387	C₂×C₄²	—	86	1	no	—
388	#107	—	43	1	no	—
389	#107	C₄×D₄₃	1	1	yes	characteristic
390	#106	—	43	1	no	—
391	#106	—	43	1	no	—
392	C₄⋊C₈	—	43	1	no	—
393	C₄⋊C₈	—	43	1	no	—
394	C₄⋊C₈	—	43	1	no	—
395	C₄⋊C₈	—	43	1	no	—
396	C₄⋊C₈	—	86	1	no	—
397	C₄⋊C₈	—	86	1	no	—
398	C₄⋊C₈	—	86	1	no	—
399	C₄⋊C₈	—	86	1	no	—
400	C₄⋊C₈	—	86	1	no	—
401	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
403	#103	—	43	1	no	—
404	#103	—	43	1	no	—
405	#103	—	43	1	no	—
406	#103	—	43	1	no	—
407	#102	—	43	1	no	—
408	#102	—	43	1	no	—
409	#102	C₄×D₄₃	1	1	yes	characteristic
410	#102	C₄×D₄₃	1	1	yes	characteristic
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	43	1	no	—
414	C₂²⋊C₈	—	43	1	no	—
415	C₂²⋊C₈	—	86	1	no	—
416	C₂²⋊C₈	—	86	1	no	—
417	C₂²⋊C₈	—	86	1	no	—
418	C₂²⋊C₈	—	86	1	no	—
419	C₂²⋊C₈	—	86	1	no	—
420	#97	—	86	1	no	—
421	#97	—	86	1	no	—
422	C₄×C₈	—	43	1	no	—
423	C₄×C₈	—	43	1	no	—
424	C₄×C₈	—	43	1	no	—
425	C₄×C₈	—	43	1	no	—
426	C₄×C₈	—	43	1	no	—
427	C₄×C₈	—	86	1	no	—
428	C₄×C₈	—	86	1	no	—
429	C₄×C₈	—	86	1	no	—
430	C₄×C₈	—	86	1	no	—
431	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
434	#41	—	86	2	no	—
435	#41	—	86	2	no	—
436	C₂×Q₈	—	43	1	no	—
437	C₂×Q₈	—	43	1	no	—
438	C₂×D₄	—	86	1	no	—
439	C₂×D₄	—	86	1	no	—
440	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
441	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	43	1	no	—
445	C₂²×C₄	—	43	1	no	—
446	C₂²×C₄	—	43	1	no	—
447	C₂²×C₄	—	86	1	no	—
448	C₂²×C₄	—	86	1	no	—
449	Q₁₆	—	86	2	no	—
450	SD₁₆	—	86	2	no	—
451	SD₁₆	—	86	2	no	—
452	D₈	—	2	2	no	—
453	M₁₆	—	4	2	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	4	2	no	—
458	C₂×C₈	—	43	1	no	—
459	C₂×C₈	—	43	1	no	—
460	C₂×C₈	—	43	1	no	—
461	C₂×C₈	—	43	1	no	—
462	C₂×C₈	—	86	1	no	—
463	C₂×C₈	—	86	1	no	—
464	C₂×C₈	—	86	1	no	—
465	C₂×C₈	—	172	1	no	—
466	C₂×C₈	—	172	1	no	—
467	C₂×C₈	—	172	2	no	—
468	C₂×C₈	—	172	2	no	—
469	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
471	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
472	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
473	C₄⋊C₄	—	43	1	no	—
474	C₄⋊C₄	—	43	1	no	—
475	C₄⋊C₄	—	86	1	no	—
476	C₄⋊C₄	—	86	1	no	—
477	C₄⋊C₄	—	86	1	no	—
478	C₄⋊C₄	—	86	1	no	—
479	C₄⋊C₄	—	86	1	no	—
480	C₄⋊C₄	—	86	1	no	—
481	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	86	1	no	—
486	C₂²⋊C₄	—	86	1	no	—
487	C₂²⋊C₄	—	86	1	no	—
488	C₂²⋊C₄	—	86	1	no	—
489	C₂²⋊C₄	—	86	1	no	—
490	C₂²⋊C₄	—	86	1	no	—
491	C₄²	—	43	1	no	—
492	C₄²	—	43	1	no	—
493	C₄²	—	43	1	no	—
494	C₄²	—	86	1	no	—
495	C₄²	—	86	1	no	—
496	C₄²	—	86	1	no	—
497	C₄²	—	86	1	no	—
498	C₄²	C₂³×D₄₃	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	43	1	no	—
502	Q₈	—	43	2	no	—
503	Q₈	—	86	1	no	—
504	Q₈	—	86	1	no	—
505	Q₈	—	86	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	86	4	no	—
510	D₄	—	172	2	no	—
511	D₄	#13063333	1	2	yes	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	43	1	no	—
519	C₂×C₄	—	43	1	no	—
520	C₂×C₄	—	43	1	no	—
521	C₂×C₄	—	86	4	no	—
522	C₂×C₄	—	86	1	no	—
523	C₂×C₄	—	86	1	no	—
524	C₂×C₄	—	86	1	no	—
525	C₂×C₄	—	86	1	no	—
526	C₂×C₄	—	86	1	no	—
527	C₂×C₄	—	86	1	no	—
528	C₂×C₄	—	86	1	no	—
529	C₂×C₄	—	86	1	no	—
530	C₂×C₄	—	172	1	no	—
531	C₂×C₄	—	172	2	no	—
532	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
533	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
534	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	86	1	no	—
543	C₈	—	86	1	no	—
544	C₈	—	86	1	no	—
545	C₈	—	86	1	no	—
546	C₈	—	172	1	no	—
547	C₈	—	172	1	no	—
548	C₈	—	172	1	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	4	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	86	1	no	—
556	C₂²	—	86	1	no	—
557	C₂²	—	86	1	no	—
558	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	86	1	no	—
563	C₄	—	86	1	no	—
564	C₄	—	86	2	no	—
565	C₄	—	86	1	no	—
566	C₄	—	172	1	no	—
567	C₄	—	172	1	no	—
568	C₄	—	172	1	no	—
569	C₄	#131×D₄₃	1	1	yes	characteristic
570	C₄	C₂×#13063333	1	1	yes	characteristic
571	C₄	#14583695	1	1	yes	characteristic
572	C₄	#14583695	1	1	yes	characteristic
573	C₂	—	4	2	no	—
574	C₂	—	8	1	no	—
575	C₂	—	172	1	no	—
576	C₂	#19143286	1	1	yes	characteristic
577	C₂	#19143392	1	1	yes	characteristic
578	C₂	#19143493	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×#1586	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#14583041	C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1586	D₄₃
hypocenter	C₄₃	#17909
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1586

Complements

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

N	H ≅ G/N	type
2. #19143573	C₂	semidirect
3. C₈×#10621900	C₂	semidirect
4. #19133471	C₂	semidirect
5. #19133468	C₂	semidirect
6. #19133452	C₂	semidirect
7. #19133419	C₂	semidirect
8. #19133413	C₂	semidirect
9. #19133404	C₂	semidirect
10. #19133404	C₂	semidirect
11. #19133372	C₂	semidirect
12. #19133026	C₂	semidirect
13. #19133000	C₂	semidirect
14. #19132886	C₂	semidirect
15. C₄₃×#1586	C₂	semidirect
289. #1586	D₄₃	semidirect
356. C₄₃	#17909	semidirect

Maximal subgroups

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

subgroup	index
#19144609	2
#19143573	2
C₈×#10621900	2
#19133471	2
#19133468	2
#19133452	2
#19133419	2
#19133413	2
#19133404	2
#19133372	2
#19133026	2
#19133000	2
#19132886	2
C₄₃×#1586	2
#17909	43