Subgroups — #25104430

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144377	C₂	1	1	yes	maximal, characteristic
2	#19143530	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063333	C₂	1	1	yes	maximal, characteristic
4	#19135370	C₂	1	1	yes	maximal, characteristic, complemented
5	#19135197	C₂	1	2	yes	maximal, complemented
6	#19134871	C₂	1	2	yes	maximal
7	#19134616	C₂	1	1	yes	maximal, characteristic
8	#19134473	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₄×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134429	C₂	1	2	yes	maximal
11	C₄₃×#1986	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063333	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	1	yes	characteristic
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	#14583203	C₄	1	2	yes	complemented
16	#14583196	C₄	1	2	yes	complemented
17	#14583191	C₄	1	1	yes	characteristic, complemented
18	#14583186	C₄	1	1	yes	characteristic, complemented
19	#14583181	C₄	1	1	yes	characteristic, complemented
20	#14583176	C₄	1	1	yes	characteristic, complemented
21	#14583030	—	2	1	no	—
22	#14583030	—	2	1	no	—
23	Q₈×C₄₃⋊C₈	—	2	1	no	—
24	Q₈×C₄₃⋊C₈	—	2	1	no	—
25	C₂×#13063260	C₂²	1	2	yes	—
26	#14582935	C₂²	1	2	yes	—
27	#14582926	C₂²	1	2	yes	—
28	#14582923	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×#13063253	C₂²	1	2	yes	—
31	#14582893	C₂²	1	2	yes	—
32	#14582857	C₂²	1	1	yes	characteristic
33	#14582857	C₂²	1	1	yes	characteristic
34	#14582856	—	2	1	no	—
35	#14582856	—	2	1	no	—
36	#14582855	C₂²	1	2	yes	—
37	C₄×#10621872	—	2	1	no	—
38	C₂×C₄×C₄₃⋊C₈	C₂²	1	2	yes	—
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₄₃	—	2	1	no	—
41	#14582663	C₂²	1	2	yes	—
42	#14582659	C₂²	1	2	yes	—
43	#14582654	C₂²	1	2	yes	—
44	C₄₃×#533	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#339	C₂²	1	2	yes	—
48	C₄₃×#339	C₂²	1	2	yes	—
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	#13063333	—	2	2	no	—
51	#13063333	—	2	2	no	—
52	#13063333	—	2	2	no	—
53	#13063333	Q₈	1	4	yes	complemented
54	C₂×#10621877	C₂³	1	2	yes	—
55	C₂×#10621872	—	2	1	no	—
56	C₂×#10621872	—	2	1	no	—
57	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
58	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂×C₈×D₄₃	—	2	1	no	—
61	C₂×C₈×D₄₃	—	2	1	no	—
62	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
64	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₃	—	2	1	no	—
67	C₄×C₂²⋊D₄₃	—	2	1	no	—
68	#13063284	C₂³	1	1	yes	characteristic
69	#13063282	—	2	1	no	—
70	C₄²×D₄₃	—	2	1	no	—
71	#13063260	—	2	4	no	—
72	#13063258	C₂×C₄	1	2	yes	—
73	#13063258	C₂×C₄	1	2	yes	—
74	#13063256	C₂×C₄	1	2	yes	—
75	#13063256	C₂×C₄	1	2	yes	—
76	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
77	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
78	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
79	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
80	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
81	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	2	yes	—
83	#13063253	—	2	4	no	—
84	#13063248	C₂×C₄	1	2	yes	—
85	#13063248	C₂×C₄	1	2	yes	—
86	#13063245	C₂×C₄	1	2	yes	—
87	#13063245	C₂×C₄	1	2	yes	—
88	#13063236	—	2	2	no	—
89	#13063235	—	2	1	no	—
90	#13063235	—	2	1	no	—
91	C₄×C₄₃⋊C₈	—	2	2	no	—
92	C₄×C₄₃⋊C₈	—	2	4	no	—
93	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
95	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
96	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
97	C₈×Dic₄₃	—	2	1	no	—
98	C₈×Dic₄₃	—	2	1	no	—
99	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
101	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
102	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
103	#125×C₄₃	C₂×C₄	1	2	yes	—
104	C₂²⋊Q₈×C₄₃	—	2	1	no	—
105	C₂²⋊Q₈×C₄₃	—	2	1	no	—
106	C₄×Q₈×C₄₃	—	2	1	no	—
107	C₄×Q₈×C₄₃	—	2	1	no	—
108	#117×C₄₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
110	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
111	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
112	#97×C₄₃	—	2	1	no	—
113	C₄×C₈×C₄₃	—	2	1	no	—
114	#95×C₄₃	—	2	1	no	—
115	C₂×Q₈×C₄₃	—	2	1	no	—
116	C₂×Q₈×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₃	—	2	1	no	—
122	#10621898	—	2	1	no	—
123	#10621898	—	2	1	no	—
124	#10621898	C₂×Q₈	1	2	yes	—
125	#10621898	#41	1	2	yes	—
126	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₄₃	—	2	1	no	—
128	C₂×C₄×D₄₃	—	2	1	no	—
129	C₂×C₄×D₄₃	—	2	1	no	—
130	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
131	M₁₆×C₄₃	—	2	1	no	—
132	M₁₆×C₄₃	—	2	1	no	—
133	M₁₆×C₄₃	C₂×Q₈	1	2	yes	—
134	M₁₆×C₄₃	#41	1	2	yes	—
135	C₂×C₈×C₄₃	—	2	1	no	—
136	C₂×C₈×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	4	no	—
138	C₄⋊C₄×C₄₃	—	2	2	no	—
139	C₄⋊C₄×C₄₃	—	2	2	no	—
140	C₄⋊C₄×C₄₃	—	2	1	no	—
141	C₄⋊C₄×C₄₃	—	2	1	no	—
142	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₄₃	—	2	2	no	—
145	C₄²×C₄₃	—	2	2	no	—
146	C₄²×C₄₃	—	2	2	no	—
147	C₄²×C₄₃	—	2	2	no	—
148	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
150	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
152	C₂²⋊Dic₄₃	—	2	1	no	—
153	(C₂×D₄₃)⋊C₄	—	2	1	no	—
154	(C₂×D₄₃)⋊C₄	—	2	1	no	—
155	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
157	Dic₄₃⋊C₄	—	2	1	no	—
158	Dic₄₃⋊C₄	—	2	1	no	—
159	C₄×Dic₄₃	—	2	1	no	—
160	C₄×Dic₄₃	—	2	1	no	—
161	C₄×Dic₄₃	—	2	1	no	—
162	#10621877	—	2	2	no	—
163	#10621877	—	2	2	no	—
164	C₂×C₄₃⋊C₈	—	2	2	no	—
165	C₂×C₄₃⋊C₈	—	2	2	no	—
166	C₂×C₄₃⋊C₈	—	2	1	no	—
167	C₂×C₄₃⋊C₈	—	2	1	no	—
168	C₂×C₄₃⋊C₈	—	2	2	no	—
169	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
170	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
171	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
172	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
173	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
174	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
175	C₂×C₄₃⋊C₈	C₂×Q₈	1	2	yes	—
176	C₂×C₄₃⋊C₈	#41	1	2	yes	—
177	#10621872	—	2	4	no	—
178	#10621872	—	2	4	no	—
179	C₈×D₄₃	—	2	4	no	—
180	C₈×D₄₃	—	2	4	no	—
181	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂²×D₄₃	—	2	1	no	—
183	Q₈×C₄₃	—	4	2	no	—
184	Q₈×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	4	no	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	4	1	no	—
190	C₂×C₄×C₄₃	—	4	2	no	—
191	C₂×C₄×C₄₃	—	4	2	no	—
192	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
202	C₂²⋊D₄₃	—	2	2	no	—
203	C₂²⋊D₄₃	—	2	2	no	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	1	no	—
206	C₂×Dic₄₃	—	2	1	no	—
207	D₁₇₂	—	2	1	no	—
208	D₁₇₂	C₄×Q₈	1	2	yes	—
209	C₄×D₄₃	—	2	2	no	—
210	C₄×D₄₃	—	2	2	no	—
211	C₄×D₄₃	—	4	2	no	—
212	C₄×D₄₃	—	4	2	no	—
213	Dic₈₆	—	2	1	no	—
214	Dic₈₆	C₄×Q₈	1	2	yes	—
215	C₈×C₄₃	—	2	2	no	—
216	C₈×C₄₃	—	2	2	no	—
217	C₄₃⋊C₈	—	2	2	no	—
218	C₄₃⋊C₈	—	2	2	no	—
219	C₄₃⋊C₈	—	2	1	no	—
220	C₄₃⋊C₈	—	2	1	no	—
221	C₄₃⋊C₈	—	4	2	no	—
222	C₄₃⋊C₈	C₂²⋊Q₈	1	2	yes	—
223	C₄₃⋊C₈	C₂²⋊Q₈	1	2	yes	—
224	#21627	—	43	1	no	maximal, Sylow
225	C₂²×C₄₃	—	2	1	no	—
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
228	C₂²×C₄₃	#529	1	1	yes	characteristic
229	C₂²×C₄₃	#533	1	1	yes	characteristic
230	C₂×D₄₃	—	2	2	no	—
231	C₂×D₄₃	—	4	1	no	—
232	C₂×D₄₃	—	4	1	no	—
233	C₄×C₄₃	—	2	1	no	—
234	C₄×C₄₃	—	2	1	no	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	4	4	no	—
237	C₄×C₄₃	—	4	2	no	—
238	C₄×C₄₃	—	4	2	no	—
239	C₄×C₄₃	#443	1	2	yes	—
240	C₄×C₄₃	C₂×C₄×Q₈	1	1	yes	characteristic
241	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
242	C₄×C₄₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₄₃	#525	1	1	yes	characteristic
244	Dic₄₃	—	2	2	no	—
245	Dic₄₃	—	4	1	no	—
246	Dic₄₃	—	4	1	no	—
247	#3076	—	43	1	no	—
248	#2960	—	43	1	no	—
249	C₄×#131	—	43	1	no	—
250	#1986	D₄₃	1	1	yes	characteristic, complemented
251	#1950	—	43	1	no	—
252	#1922	—	43	2	no	—
253	#1866	—	43	2	no	—
254	#1806	—	43	1	no	—
255	#1772	—	43	2	no	—
256	C₈×C₄⋊C₄	—	43	1	no	—
257	#1764	—	43	2	no	—
258	C₂×C₄₃	—	2	1	no	—
259	C₂×C₄₃	—	2	1	no	—
260	C₂×C₄₃	C₄×C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
262	C₂×C₄₃	#2955	1	1	yes	characteristic
263	D₄₃	—	4	2	no	—
264	C₂×#131	—	43	1	no	—
265	C₂×#131	—	43	1	no	—
266	#533	C₂×D₄₃	1	1	yes	characteristic
267	C₄×#41	—	43	1	no	—
268	#479	—	43	2	no	—
269	#478	—	43	2	no	—
270	#477	—	43	1	no	—
271	#476	—	43	1	no	—
272	#475	—	43	1	no	—
273	#474	—	43	1	no	—
274	#446	—	86	1	no	—
275	#446	—	86	1	no	—
276	C₈×Q₈	—	86	1	no	—
277	C₈×Q₈	—	86	1	no	—
278	C₂×#108	—	43	2	no	—
279	#427	—	43	2	no	—
280	#424	—	43	2	no	—
281	#423	—	43	1	no	—
282	C₂×C₄⋊C₈	—	43	1	no	—
283	C₂×#104	—	43	2	no	—
284	#416	—	43	2	no	—
285	#405	—	43	1	no	—
286	#405	—	43	1	no	—
287	#405	—	43	2	no	—
288	#405	—	86	1	no	—
289	#405	—	86	1	no	—
290	C₄×M₁₆	—	86	1	no	—
291	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
292	C₂×C₄×C₈	—	43	1	no	—
293	C₂×C₄×C₈	—	43	2	no	—
294	C₂×C₄×C₈	—	86	1	no	—
295	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
296	#341	—	43	2	no	—
297	#339	—	43	2	no	—
298	#339	C₂×D₄₃	1	2	yes	—
299	#339	C₂×D₄₃	1	2	yes	—
300	#336	—	43	2	no	—
301	C₄₃	#21627	1	1	yes	characteristic, complemented, Sylow
302	C₂×#41	—	43	1	no	—
303	#131	—	43	4	no	—
304	#131	—	86	2	no	—
305	#131	—	86	2	no	—
306	#131	—	86	2	no	—
307	C₂×M₁₆	—	43	2	no	—
308	C₂×M₁₆	—	86	1	no	—
309	C₂×M₁₆	—	86	1	no	—
310	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
311	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
312	C₂²×C₈	—	43	1	no	—
313	C₂²×C₈	—	43	1	no	—
314	C₂²×C₈	—	43	2	no	—
315	C₂²×C₈	—	86	1	no	—
316	C₂²×C₈	—	86	1	no	—
317	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
318	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
319	#125	C₄×D₄₃	1	2	yes	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₄×Q₈	—	2	1	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	43	1	no	—
325	C₄×Q₈	—	43	1	no	—
326	C₄×D₄	—	43	1	no	—
327	C₄×D₄	—	43	1	no	—
328	C₄×D₄	—	86	1	no	—
329	C₄×D₄	—	86	1	no	—
330	#117	—	43	1	no	—
331	#117	—	86	1	no	—
332	#117	C₂²×D₄₃	1	2	yes	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄²	—	86	1	no	—
335	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
336	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
337	#108	—	86	4	no	—
338	#107	—	43	2	no	—
339	#107	—	43	2	no	—
340	#106	—	43	2	no	—
341	#106	—	43	2	no	—
342	C₄⋊C₈	—	43	1	no	—
343	C₄⋊C₈	—	43	1	no	—
344	C₄⋊C₈	—	43	2	no	—
345	C₄⋊C₈	—	86	2	no	—
346	C₄⋊C₈	—	86	2	no	—
347	C₄⋊C₈	—	86	1	no	—
348	C₄⋊C₈	—	86	1	no	—
349	#104	—	86	4	no	—
350	#103	—	43	2	no	—
351	#103	—	43	2	no	—
352	#102	—	43	2	no	—
353	#102	—	43	2	no	—
354	#97	—	2	1	no	—
355	#97	—	86	2	no	—
356	#97	—	86	1	no	—
357	#97	—	86	1	no	—
358	C₄×C₈	—	2	1	no	—
359	C₄×C₈	—	43	1	no	—
360	C₄×C₈	—	43	1	no	—
361	C₄×C₈	—	43	1	no	—
362	C₄×C₈	—	43	1	no	—
363	C₄×C₈	—	86	4	no	—
364	C₄×C₈	—	86	2	no	—
365	C₄×C₈	—	86	1	no	—
366	C₄×C₈	—	86	1	no	—
367	#95	—	2	1	no	—
368	#41	—	43	2	no	—
369	#41	—	43	2	no	—
370	#41	—	86	1	no	—
371	#41	—	86	1	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	43	1	no	—
375	C₂×D₄	—	43	1	no	—
376	C₂×D₄	—	86	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	86	1	no	—
379	C₂²×C₄	—	86	1	no	—
380	C₂²×C₄	—	86	1	no	—
381	C₂²×C₄	#10621900	1	1	yes	characteristic
382	C₂²×C₄	#10621900	1	1	yes	characteristic
383	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	86	4	no	—
387	M₁₆	—	86	4	no	—
388	M₁₆	—	86	2	no	—
389	M₁₆	—	86	2	no	—
390	M₁₆	Q₈×D₄₃	1	2	yes	—
391	M₁₆	#10621902	1	2	yes	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	43	1	no	—
395	C₂×C₈	—	43	1	no	—
396	C₂×C₈	—	43	2	no	—
397	C₂×C₈	—	43	2	no	—
398	C₂×C₈	—	43	2	no	—
399	C₂×C₈	—	43	2	no	—
400	C₂×C₈	—	43	1	no	—
401	C₂×C₈	—	43	1	no	—
402	C₂×C₈	—	86	4	no	—
403	C₂×C₈	—	86	4	no	—
404	C₂×C₈	—	86	2	no	—
405	C₂×C₈	—	86	1	no	—
406	C₂×C₈	—	86	2	no	—
407	C₂×C₈	—	86	1	no	—
408	C₂×C₈	—	86	2	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	43	1	no	—
415	C₄⋊C₄	—	43	1	no	—
416	C₄⋊C₄	—	86	1	no	—
417	C₄⋊C₄	—	86	1	no	—
418	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
419	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	86	1	no	—
422	C₂²⋊C₄	—	86	1	no	—
423	C₂²⋊C₄	—	86	1	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	86	1	no	—
428	C₄²	—	86	1	no	—
429	C₄²	—	86	1	no	—
430	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
431	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
432	C₄²	D₄×D₄₃	1	1	yes	characteristic
433	C₄²	D₄×D₄₃	1	1	yes	characteristic
434	C₂³	—	86	1	no	—
435	C₂³	C₂×#10621900	1	1	yes	characteristic
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	43	2	no	—
439	Q₈	—	86	1	no	—
440	D₄	—	43	2	no	—
441	D₄	—	86	2	no	—
442	D₄	—	86	2	no	—
443	D₄	—	86	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	86	1	no	—
452	C₂×C₄	—	86	2	no	—
453	C₂×C₄	—	86	2	no	—
454	C₂×C₄	—	86	1	no	—
455	C₂×C₄	—	86	1	no	—
456	C₂×C₄	—	172	2	no	—
457	C₂×C₄	—	172	2	no	—
458	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
459	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
460	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
461	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
462	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
463	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
464	C₂×C₄	C₂×Q₈×D₄₃	1	1	yes	characteristic
465	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
466	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
467	C₂×C₄	C₂×#10621902	1	1	yes	characteristic
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	—	43	2	no	—
471	C₈	—	43	2	no	—
472	C₈	—	86	2	no	—
473	C₈	—	86	2	no	—
474	C₈	—	86	1	no	—
475	C₈	—	86	1	no	—
476	C₈	—	172	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	86	2	no	—
480	C₂²	—	172	1	no	—
481	C₂²	—	172	1	no	—
482	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
483	C₂²	#14583428	1	1	yes	characteristic
484	C₂²	#14583454	1	1	yes	characteristic
485	C₄	—	2	1	no	—
486	C₄	—	2	1	no	—
487	C₄	—	2	1	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	2	no	—
491	C₄	—	86	2	no	—
492	C₄	—	172	1	no	—
493	C₄	—	172	1	no	—
494	C₄	#14583013	1	2	yes	—
495	C₄	C₄×Q₈×D₄₃	1	1	yes	characteristic
496	C₄	C₄×#10621902	1	1	yes	characteristic
497	C₄	C₂²⋊Q₈×D₄₃	1	1	yes	characteristic
498	C₄	#14583412	1	1	yes	characteristic
499	C₂	—	2	1	no	—
500	C₂	—	2	1	no	—
501	C₂	—	172	2	no	—
502	C₂	#19137133	1	1	yes	characteristic
503	C₂	C₂×#14583013	1	1	yes	characteristic
504	C₂	#19143494	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1986	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#10621898	C₂³
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1986	D₄₃
hypocenter	C₄₃	#21627
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1986

Complements

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

N	H ≅ G/N	type
2. #19143530	C₂	semidirect
4. #19135370	C₂	semidirect
5. #19135197	C₂	semidirect
8. #19134473	C₂	semidirect
9. C₄⋊C₄×C₄₃⋊C₈	C₂	semidirect
11. C₄₃×#1986	C₂	semidirect
15. #14583203	C₄	semidirect
16. #14583196	C₄	semidirect
17. #14583191	C₄	semidirect
18. #14583186	C₄	semidirect
19. #14583181	C₄	semidirect
20. #14583176	C₄	semidirect
53. #13063333	Q₈	semidirect
250. #1986	D₄₃	semidirect
301. C₄₃	#21627	semidirect

Maximal subgroups

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

subgroup	index
#19144377	2
#19143530	2
C₄×#13063333	2
#19135370	2
#19135197	2
#19134871	2
#19134616	2
#19134473	2
C₄⋊C₄×C₄₃⋊C₈	2
#19134429	2
C₄₃×#1986	2
#21627	43