Subgroups — #25065732

Order 11008.

602 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143714	C₂	1	1	yes	maximal, characteristic
2	#19143704	C₂	1	1	yes	maximal, characteristic
3	#19143234	C₂	1	1	yes	maximal, characteristic
4	#19133385	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133384	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133377	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133376	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133372	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133369	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133368	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133346	C₂	1	1	yes	maximal, characteristic, complemented
12	#19133344	C₂	1	1	yes	maximal, characteristic, complemented
13	#19133340	C₂	1	1	yes	maximal, characteristic, complemented
14	#335×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1573	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#10621898	C₂²	1	1	yes	characteristic
17	#14583027	—	2	1	no	—
18	#14583023	—	2	1	no	—
19	#14582974	—	2	1	no	—
20	#14582973	—	2	1	no	—
21	#14582972	—	2	1	no	—
22	#14582964	—	2	1	no	—
23	C₈×C₂²⋊D₄₃	—	2	1	no	—
24	C₈×C₂²⋊D₄₃	—	2	1	no	—
25	#14582959	C₄	1	2	yes	—
26	#14582957	C₄	1	2	yes	—
27	#14582955	C₂²	1	1	yes	characteristic
28	#14582952	C₂²	1	1	yes	characteristic
29	#14582952	C₂²	1	1	yes	characteristic
30	#14582951	C₂²	1	1	yes	characteristic
31	#14582951	C₂²	1	1	yes	characteristic
32	#14582951	C₂²	1	1	yes	characteristic
33	#14582950	C₂²	1	1	yes	characteristic
34	#14582950	C₂²	1	1	yes	characteristic
35	#14582924	C₄	1	2	yes	—
36	#14582923	C₂²	1	1	yes	characteristic
37	#14582921	C₂²	1	1	yes	characteristic
38	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
39	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
41	#14582864	C₄	1	2	yes	—
42	C₄×#10621872	C₂²	1	1	yes	characteristic
43	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
44	#14582652	C₂²	1	1	yes	characteristic
45	#14582652	C₂²	1	1	yes	characteristic
46	#14582651	C₂²	1	1	yes	characteristic
47	#14582651	C₂²	1	1	yes	characteristic
48	#14582651	C₂²	1	1	yes	characteristic
49	#14582651	C₂²	1	1	yes	characteristic
50	#14582651	C₂²	1	1	yes	characteristic
51	#14582651	C₂²	1	1	yes	characteristic
52	#14582650	C₂²	1	1	yes	characteristic
53	#14582650	C₂²	1	1	yes	characteristic
54	#14582649	C₂²	1	1	yes	characteristic
55	#14582649	C₂²	1	1	yes	characteristic
56	C₄₃×#432	C₂²	1	1	yes	characteristic
57	C₄₃×#431	C₂²	1	1	yes	characteristic
58	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
59	C₄₃×#335	C₂²	1	1	yes	characteristic
60	C₄₃×#335	C₂²	1	1	yes	characteristic
61	C₄₃×#334	C₂²	1	1	yes	characteristic
62	C₄₃×#334	C₂²	1	1	yes	characteristic
63	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
64	C₂×#10621877	—	2	1	no	—
65	C₂×#10621872	—	2	1	no	—
66	C₂×#10621872	C₂×C₄	1	2	yes	—
67	C₂×C₈×D₄₃	—	2	1	no	—
68	C₂×C₈×D₄₃	—	2	1	no	—
69	C₂×C₈×D₄₃	—	2	1	no	—
70	C₂×C₈×D₄₃	C₂×C₄	1	2	yes	—
71	C₄×Dic₈₆	D₄	1	1	yes	characteristic
72	C₄×Dic₈₆	Q₈	1	1	yes	characteristic
73	C₄×D₁₇₂	D₄	1	1	yes	characteristic
74	C₄×D₁₇₂	Q₈	1	1	yes	characteristic
75	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
76	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₄₃	Q₈	1	1	yes	characteristic
78	C₄×C₂²⋊D₄₃	Q₈	1	1	yes	characteristic
79	#13063284	C₂×C₄	1	1	yes	characteristic
80	#13063282	C₂×C₄	1	1	yes	characteristic
81	#13063282	C₂×C₄	1	1	yes	characteristic
82	C₄²×D₄₃	C₂³	1	1	yes	characteristic
83	C₄²×D₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
85	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
86	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
87	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
88	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
89	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
90	Dic₄₃⋊C₈	—	2	1	no	—
91	Dic₄₃⋊C₈	—	2	1	no	—
92	Dic₄₃⋊C₈	—	2	1	no	—
93	Dic₄₃⋊C₈	—	2	1	no	—
94	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
95	Dic₄₃⋊C₈	C₂×C₄	1	2	yes	—
96	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
97	C₂²⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
98	(C₂×D₄₃)⋊C₈	—	2	1	no	—
99	(C₂×D₄₃)⋊C₈	—	2	1	no	—
100	(C₂×D₄₃)⋊C₈	—	2	1	no	—
101	(C₂×D₄₃)⋊C₈	—	2	1	no	—
102	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
103	(C₂×D₄₃)⋊C₈	C₂×C₄	1	2	yes	—
104	#13063235	—	2	1	no	—
105	#13063235	C₂×C₄	1	2	yes	—
106	C₄×C₄₃⋊C₈	—	2	1	no	—
107	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
108	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
109	C₈×Dic₄₃	—	2	1	no	—
110	C₈×Dic₄₃	—	2	1	no	—
111	C₈×Dic₄₃	—	2	1	no	—
112	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
113	C₂²×C₈×C₄₃	—	2	1	no	—
114	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₈×C₄₃	—	2	1	no	—
116	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
117	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
120	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
121	C₂²⋊C₈×C₄₃	—	2	1	no	—
122	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
123	#97×C₄₃	—	2	1	no	—
124	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₃	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₂²⋊D₄₃	C₄⋊C₄	1	1	yes	characteristic
131	#10621898	—	2	4	no	—
132	C₂×D₁₇₂	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
138	C₂×C₄×D₄₃	C₂×Q₈	1	1	yes	characteristic
139	C₂×Dic₈₆	C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₈×C₄₃	—	2	1	no	—
141	C₂×C₈×C₄₃	—	2	1	no	—
142	C₂×C₈×C₄₃	—	2	1	no	—
143	C₂×C₈×C₄₃	—	2	1	no	—
144	C₂×C₈×C₄₃	—	8	1	no	—
145	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
147	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
150	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
151	C₂²⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
152	C₂²⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
153	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
154	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
155	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
156	(C₂×D₄₃)⋊C₄	C₄⋊C₄	1	1	yes	characteristic
157	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
158	C₄⋊Dic₄₃	C₄⋊C₄	1	1	yes	characteristic
159	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
160	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
161	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
162	Dic₄₃⋊C₄	C₄⋊C₄	1	1	yes	characteristic
163	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
164	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
165	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
167	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
168	C₄×Dic₄₃	C₂×Q₈	1	1	yes	characteristic
169	#10621877	—	8	1	no	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	C₂×C₄₃⋊C₈	—	2	1	no	—
172	C₂×C₄₃⋊C₈	—	2	1	no	—
173	C₂×C₄₃⋊C₈	—	2	1	no	—
174	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
175	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
176	#10621872	—	2	4	no	—
177	#10621872	—	8	1	no	—
178	C₈×D₄₃	—	2	4	no	—
179	C₈×D₄₃	—	8	1	no	—
180	C₈×D₄₃	—	8	1	no	—
181	C₈×D₄₃	—	8	1	no	—
182	C₂³×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×D₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	1	no	—
187	C₂×C₄×C₄₃	—	2	1	no	—
188	C₂×C₄×C₄₃	—	4	1	no	—
189	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
195	C₂²⋊D₄₃	—	2	2	no	—
196	C₂²⋊D₄₃	—	2	2	no	—
197	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
201	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
202	C₂×Dic₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	D₁₇₂	—	2	2	no	—
204	C₄×D₄₃	—	2	2	no	—
205	C₄×D₄₃	—	2	1	no	—
206	C₄×D₄₃	—	2	1	no	—
207	C₄×D₄₃	—	2	1	no	—
208	C₄×D₄₃	—	2	1	no	—
209	C₄×D₄₃	—	4	1	no	—
210	C₄×D₄₃	—	4	1	no	—
211	C₄×D₄₃	#131	1	4	yes	—
212	Dic₈₆	—	2	2	no	—
213	C₈×C₄₃	—	2	2	no	—
214	C₈×C₄₃	—	2	2	no	—
215	C₈×C₄₃	—	4	1	no	—
216	C₈×C₄₃	—	4	1	no	—
217	C₈×C₄₃	—	4	1	no	—
218	C₈×C₄₃	—	4	1	no	—
219	C₄₃⋊C₈	—	2	2	no	—
220	C₄₃⋊C₈	—	2	2	no	—
221	C₄₃⋊C₈	—	4	1	no	—
222	C₄₃⋊C₈	—	4	1	no	—
223	C₄₃⋊C₈	—	4	1	no	—
224	C₄₃⋊C₈	—	4	1	no	—
225	#17812	—	43	1	no	maximal, Sylow
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	—	2	1	no	—
228	C₂²×C₄₃	—	2	1	no	—
229	C₂²×C₄₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
230	C₂×D₄₃	—	2	1	no	—
231	C₂×D₄₃	—	2	1	no	—
232	C₂×D₄₃	—	2	1	no	—
233	C₂×D₄₃	—	2	1	no	—
234	C₂×D₄₃	—	2	1	no	—
235	C₂×D₄₃	#424	1	2	yes	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	2	1	no	—
238	C₄×C₄₃	—	2	1	no	—
239	C₄×C₄₃	—	2	1	no	—
240	C₄×C₄₃	C₂×#131	1	2	yes	—
241	C₄×C₄₃	#576	1	1	yes	characteristic
242	C₄×C₄₃	#578	1	1	yes	characteristic
243	Dic₄₃	—	2	1	no	—
244	Dic₄₃	—	2	1	no	—
245	Dic₄₃	—	2	1	no	—
246	Dic₄₃	—	2	1	no	—
247	Dic₄₃	—	2	1	no	—
248	Dic₄₃	#424	1	2	yes	—
249	#2989	—	43	1	no	—
250	#2988	—	43	1	no	—
251	#2922	—	43	1	no	—
252	#1574	—	43	1	no	—
253	#1574	—	43	1	no	—
254	#1573	—	43	1	no	—
255	#1573	D₄₃	1	1	yes	characteristic, complemented
256	#1572	—	43	1	no	—
257	#1572	—	43	1	no	—
258	#1571	—	43	1	no	—
259	#1571	—	43	1	no	—
260	#1565	—	43	1	no	—
261	#1565	—	43	1	no	—
262	#1564	—	43	1	no	—
263	C₂×#335	—	43	1	no	—
264	C₂×C₄₃	—	4	1	no	—
265	C₂×C₄₃	C₂×#424	1	1	yes	characteristic
266	C₂×C₄₃	#2913	1	1	yes	characteristic
267	C₂×C₄₃	#2916	1	1	yes	characteristic
268	D₄₃	—	2	2	no	—
269	D₄₃	—	4	1	no	—
270	C₄×#41	—	43	1	no	—
271	#446	—	86	1	no	—
272	C₈×Q₈	—	86	1	no	—
273	#436	—	86	1	no	—
274	#435	—	86	1	no	—
275	#435	—	86	1	no	—
276	C₈×D₄	—	86	1	no	—
277	C₈×D₄	—	86	1	no	—
278	C₈×D₄	—	86	1	no	—
279	#433	—	43	2	no	—
280	#433	—	43	2	no	—
281	#432	—	43	1	no	—
282	#432	C₂×D₄₃	1	1	yes	characteristic
283	#431	—	43	1	no	—
284	#431	—	43	1	no	—
285	#431	—	43	1	no	—
286	#431	—	43	1	no	—
287	#431	—	43	1	no	—
288	#431	—	43	1	no	—
289	#431	—	43	1	no	—
290	#431	C₂×D₄₃	1	1	yes	characteristic
291	#424	—	43	2	no	—
292	#423	—	43	1	no	—
293	#423	—	43	1	no	—
294	C₂×C₄⋊C₈	—	43	1	no	—
295	C₂×C₄⋊C₈	—	43	1	no	—
296	C₂×C₄⋊C₈	—	43	1	no	—
297	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
298	#408	—	43	2	no	—
299	C₄×M₁₆	—	43	1	no	—
300	C₂×C₄×C₈	—	43	1	no	—
301	#335	—	43	1	no	—
302	#335	—	43	1	no	—
303	#335	—	43	1	no	—
304	#335	—	43	1	no	—
305	#335	—	43	1	no	—
306	#335	—	43	1	no	—
307	#335	—	43	1	no	—
308	#335	—	43	1	no	—
309	#335	C₂×D₄₃	1	1	yes	characteristic
310	#335	C₂×D₄₃	1	1	yes	characteristic
311	#334	—	43	1	no	—
312	#334	—	43	1	no	—
313	#334	—	43	1	no	—
314	#334	—	43	1	no	—
315	#334	C₂×D₄₃	1	1	yes	characteristic
316	#334	C₂×D₄₃	1	1	yes	characteristic
317	C₄₃	#17812	1	1	yes	characteristic, complemented, Sylow
318	C₂×#41	—	43	1	no	—
319	C₂×M₁₆	—	43	2	no	—
320	C₂×M₁₆	—	86	1	no	—
321	C₂×M₁₆	—	86	1	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	43	2	no	—
324	C₂²×C₈	—	86	1	no	—
325	C₂²×C₈	—	86	1	no	—
326	C₂²×C₈	—	86	1	no	—
327	C₄×Q₈	—	43	1	no	—
328	C₄×Q₈	—	43	1	no	—
329	C₄×D₄	—	43	1	no	—
330	C₄×D₄	—	43	1	no	—
331	C₄×D₄	—	43	1	no	—
332	C₄×D₄	—	43	1	no	—
333	C₄×D₄	—	43	1	no	—
334	C₄×D₄	—	43	1	no	—
335	#117	—	43	1	no	—
336	#117	—	43	1	no	—
337	#117	—	43	1	no	—
338	C₂×C₄²	—	43	1	no	—
339	C₂×C₄²	—	43	1	no	—
340	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	43	2	no	—
343	C₄⋊C₈	—	43	2	no	—
344	C₄⋊C₈	—	43	2	no	—
345	C₄⋊C₈	—	43	1	no	—
346	C₄⋊C₈	—	43	1	no	—
347	C₄⋊C₈	—	43	1	no	—
348	C₄⋊C₈	—	43	1	no	—
349	C₄⋊C₈	—	86	1	no	—
350	C₄⋊C₈	—	86	1	no	—
351	C₄⋊C₈	—	86	1	no	—
352	C₄⋊C₈	—	86	1	no	—
353	C₄⋊C₈	—	86	1	no	—
354	C₄⋊C₈	C₄×D₄₃	1	2	yes	—
355	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
356	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
357	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	43	2	no	—
361	C₂²⋊C₈	—	43	2	no	—
362	C₂²⋊C₈	—	43	2	no	—
363	C₂²⋊C₈	—	86	1	no	—
364	C₂²⋊C₈	—	86	1	no	—
365	C₂²⋊C₈	—	86	1	no	—
366	C₂²⋊C₈	—	86	1	no	—
367	C₂²⋊C₈	—	86	1	no	—
368	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
369	#97	—	2	1	no	—
370	#97	—	43	2	no	—
371	#97	—	86	1	no	—
372	C₄×C₈	—	43	2	no	—
373	C₄×C₈	—	43	1	no	—
374	C₄×C₈	—	43	1	no	—
375	C₄×C₈	—	86	1	no	—
376	C₄×C₈	—	86	1	no	—
377	C₄×C₈	—	86	1	no	—
378	C₄×C₈	—	86	1	no	—
379	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
380	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
381	#41	—	86	4	no	—
382	C₂×Q₈	—	43	1	no	—
383	C₂×D₄	—	43	1	no	—
384	C₂×D₄	—	43	1	no	—
385	C₂×D₄	—	43	1	no	—
386	C₂²×C₄	—	43	1	no	—
387	C₂²×C₄	—	43	1	no	—
388	C₂²×C₄	—	43	1	no	—
389	C₂²×C₄	—	43	1	no	—
390	C₂²×C₄	—	43	1	no	—
391	C₂²×C₄	—	43	1	no	—
392	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
393	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
394	C₂²×C₄	Q₈×D₄₃	1	1	yes	characteristic
395	M₁₆	—	86	4	no	—
396	M₁₆	—	344	1	no	—
397	M₁₆	—	344	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	8	1	no	—
403	C₂×C₈	—	43	2	no	—
404	C₂×C₈	—	43	2	no	—
405	C₂×C₈	—	86	4	no	—
406	C₂×C₈	—	86	1	no	—
407	C₂×C₈	—	86	1	no	—
408	C₂×C₈	—	86	1	no	—
409	C₂×C₈	—	86	1	no	—
410	C₂×C₈	—	344	1	no	—
411	C₂×C₈	—	344	1	no	—
412	C₂×C₈	—	344	1	no	—
413	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
414	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
415	C₄⋊C₄	—	43	1	no	—
416	C₄⋊C₄	—	43	1	no	—
417	C₄⋊C₄	—	43	1	no	—
418	C₄⋊C₄	—	43	1	no	—
419	C₄⋊C₄	—	43	1	no	—
420	C₄⋊C₄	—	43	1	no	—
421	C₂²⋊C₄	—	43	1	no	—
422	C₂²⋊C₄	—	43	1	no	—
423	C₂²⋊C₄	—	43	1	no	—
424	C₂²⋊C₄	—	43	1	no	—
425	C₂²⋊C₄	—	43	1	no	—
426	C₂²⋊C₄	—	43	1	no	—
427	C₄²	—	43	1	no	—
428	C₄²	—	43	1	no	—
429	C₄²	—	43	1	no	—
430	C₄²	—	43	1	no	—
431	C₄²	—	43	1	no	—
432	C₄²	—	43	1	no	—
433	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
434	C₄²	D₄×D₄₃	1	1	yes	characteristic
435	C₄²	Q₈×D₄₃	1	1	yes	characteristic
436	C₄²	C₂³×D₄₃	1	1	yes	characteristic
437	C₂³	—	43	1	no	—
438	C₂³	—	43	1	no	—
439	C₂³	C₄⋊C₄×D₄₃	1	1	yes	characteristic
440	Q₈	—	86	2	no	—
441	D₄	—	86	2	no	—
442	D₄	—	86	2	no	—
443	D₄	—	86	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	43	1	no	—
449	C₂×C₄	—	43	4	no	—
450	C₂×C₄	—	43	1	no	—
451	C₂×C₄	—	43	1	no	—
452	C₂×C₄	—	43	1	no	—
453	C₂×C₄	—	43	1	no	—
454	C₂×C₄	—	43	1	no	—
455	C₂×C₄	—	86	2	no	—
456	C₂×C₄	—	86	1	no	—
457	C₂×C₄	—	86	1	no	—
458	C₂×C₄	—	86	1	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	172	1	no	—
461	C₂×C₄	—	172	1	no	—
462	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
463	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
464	C₂×C₄	C₄⋊C₄×D₄₃	1	1	yes	characteristic
465	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
467	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	1	no	—
473	C₈	—	4	1	no	—
474	C₈	—	86	2	no	—
475	C₈	—	86	2	no	—
476	C₈	—	172	1	no	—
477	C₈	—	172	1	no	—
478	C₈	—	172	1	no	—
479	C₈	—	172	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	43	2	no	—
484	C₂²	—	86	1	no	—
485	C₂²	—	86	1	no	—
486	C₂²	—	86	1	no	—
487	C₂²	—	86	1	no	—
488	C₂²	—	86	1	no	—
489	C₂²	C₂×C₄⋊C₄×D₄₃	1	1	yes	characteristic
490	C₄	—	2	1	no	—
491	C₄	—	2	1	no	—
492	C₄	—	2	1	no	—
493	C₄	—	2	1	no	—
494	C₄	—	43	2	no	—
495	C₄	—	86	1	no	—
496	C₄	—	86	1	no	—
497	C₄	—	86	1	no	—
498	C₄	—	86	1	no	—
499	C₄	—	86	1	no	—
500	C₄	#131×D₄₃	1	2	yes	—
501	C₄	#14583703	1	1	yes	characteristic
502	C₄	#14583715	1	1	yes	characteristic
503	C₂	—	4	1	no	—
504	C₂	—	86	2	no	—
505	C₂	—	172	1	no	—
506	C₂	#424×D₄₃	1	1	yes	characteristic
507	C₂	#19143194	1	1	yes	characteristic
508	C₂	#19143203	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×#1573	C₂
socle	C₂²×C₄₃	C₂²×C₄⋊C₄
prime radical	C₂×#10621898	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1573	D₄₃
hypocenter	C₄₃	#17812
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1573

Complements

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

N	H ≅ G/N	type
4. #19133385	C₂	semidirect
5. #19133384	C₂	semidirect
6. #19133377	C₂	semidirect
7. #19133376	C₂	semidirect
8. #19133372	C₂	semidirect
9. #19133369	C₂	semidirect
10. #19133368	C₂	semidirect
11. #19133346	C₂	semidirect
12. #19133344	C₂	semidirect
13. #19133340	C₂	semidirect
14. #335×D₄₃	C₂	semidirect
15. C₄₃×#1573	C₂	semidirect
255. #1573	D₄₃	semidirect
317. C₄₃	#17812	semidirect

Maximal subgroups

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

subgroup	index
#19143714	2
#19143704	2
#19143234	2
#19133385	2
#19133384	2
#19133377	2
#19133376	2
#19133372	2
#19133369	2
#19133368	2
#19133346	2
#19133344	2
#19133340	2
#335×D₄₃	2
C₄₃×#1573	2
#17812	43