Subgroups — #25116297

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063345	C₂	1	1	yes	maximal, characteristic
2	#19143263	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143261	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135485	C₂	1	2	yes	maximal
5	#19135246	C₂	1	2	yes	maximal, complemented
6	#19135241	C₂	1	2	yes	maximal, complemented
7	#19134766	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134616	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134478	C₂	1	2	yes	maximal, complemented
10	#19134464	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1806	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₂²	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	C₄×#10621885	C₄	1	1	yes	characteristic, complemented
15	C₄×#10621885	C₄	1	1	yes	characteristic, complemented
16	C₄×#10621884	C₄	1	1	yes	characteristic, complemented
17	C₄×#10621884	C₄	1	1	yes	characteristic, complemented
18	C₄×#10621883	C₄	1	1	yes	characteristic, complemented
19	C₄×#10621883	C₄	1	1	yes	characteristic, complemented
20	C₄×#10621882	C₄	1	1	yes	characteristic, complemented
21	C₄×#10621882	C₄	1	1	yes	characteristic, complemented
22	#14582960	—	2	2	no	—
23	#14582959	—	2	2	no	—
24	#14582956	—	2	1	no	—
25	#14582955	—	2	1	no	—
26	#14582952	—	2	1	no	—
27	#14582951	—	2	1	no	—
28	C₂×#13063260	C₂²	1	2	yes	—
29	C₂×#13063260	C₂²	1	2	yes	—
30	#14582935	C₂²	1	1	yes	characteristic
31	#14582923	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×#13063253	C₂²	1	2	yes	—
34	#14582895	C₂²	1	1	yes	characteristic
35	#14582893	C₂²	1	1	yes	characteristic
36	#14582867	C₂²	1	2	yes	—
37	#14582866	C₂²	1	2	yes	—
38	#14582857	C₂²	1	2	yes	—
39	#14582855	C₂²	1	2	yes	—
40	C₂×#13063236	C₂²	1	2	yes	—
41	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
42	#14582659	C₂²	1	2	yes	—
43	#14582654	C₂²	1	2	yes	—
44	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#423	C₂²	1	1	yes	characteristic
46	C₂×#104×C₄₃	C₂²	1	2	yes	—
47	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
48	C₄₃×#339	C₂²	1	2	yes	—
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	#13063345	—	2	2	no	—
51	#13063345	—	2	2	no	—
52	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
55	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
56	C₂×#10621877	C₂³	1	2	yes	—
57	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
62	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
63	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₄₃	—	2	1	no	—
65	C₄×C₂²⋊D₄₃	—	2	1	no	—
66	#13063284	C₂³	1	1	yes	characteristic
67	#13063282	—	2	1	no	—
68	C₄²×D₄₃	—	2	1	no	—
69	#13063260	—	2	4	no	—
70	#13063260	—	4	2	no	—
71	#13063258	C₂×C₄	1	1	yes	characteristic
72	#13063258	C₂×C₄	1	1	yes	characteristic
73	#13063256	C₂×C₄	1	1	yes	characteristic
74	#13063256	C₂×C₄	1	1	yes	characteristic
75	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
76	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
77	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
78	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
79	C₄⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
80	#13063253	—	4	2	no	—
81	#13063249	C₂×C₄	1	1	yes	characteristic
82	#13063249	C₂×C₄	1	1	yes	characteristic
83	#13063248	C₂×C₄	1	1	yes	characteristic
84	#13063248	C₂×C₄	1	1	yes	characteristic
85	#13063246	C₂×C₄	1	1	yes	characteristic
86	#13063246	C₂×C₄	1	1	yes	characteristic
87	#13063245	C₂×C₄	1	1	yes	characteristic
88	#13063245	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
90	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
91	(C₂×D₄₃)⋊C₈	—	2	2	no	—
92	(C₂×D₄₃)⋊C₈	—	2	2	no	—
93	#13063236	—	2	2	no	—
94	#13063236	—	2	4	no	—
95	#13063235	—	2	2	no	—
96	C₄×C₄₃⋊C₈	—	2	2	no	—
97	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
99	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
100	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
101	C₈×Dic₄₃	—	2	2	no	—
102	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
104	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
106	C₄×D₄×C₄₃	—	2	1	no	—
107	C₄×D₄×C₄₃	—	2	1	no	—
108	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
109	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
110	#117×C₄₃	—	2	1	no	—
111	#117×C₄₃	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
113	C₂×C₄²×C₄₃	—	2	1	no	—
114	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₈×C₄₃	—	2	1	no	—
117	C₄⋊C₈×C₄₃	—	2	1	no	—
118	#104×C₄₃	—	4	2	no	—
119	#95×C₄₃	—	2	1	no	—
120	#41×C₄₃	—	2	1	no	—
121	#41×C₄₃	—	2	1	no	—
122	#41×C₄₃	—	2	1	no	—
123	#41×C₄₃	—	2	1	no	—
124	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×D₄×C₄₃	—	2	1	no	—
126	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	—	2	1	no	—
128	C₂²×C₄×C₄₃	—	2	1	no	—
129	C₂²×C₄×C₄₃	—	2	1	no	—
130	C₂²×C₄×C₄₃	—	2	2	no	—
131	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
132	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
133	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
134	C₂×C₂²⋊D₄₃	—	2	1	no	—
135	#10621898	—	2	1	no	—
136	#10621898	—	2	1	no	—
137	#10621898	—	2	1	no	—
138	#10621898	—	2	1	no	—
139	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄×D₄₃	—	2	1	no	—
141	C₂×C₄×D₄₃	—	2	1	no	—
142	C₂×C₄×D₄₃	—	2	1	no	—
143	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
144	M₁₆×C₄₃	—	2	2	no	—
145	M₁₆×C₄₃	—	2	2	no	—
146	C₂×C₈×C₄₃	—	2	2	no	—
147	C₄⋊C₄×C₄₃	—	2	1	no	—
148	C₄⋊C₄×C₄₃	—	2	1	no	—
149	C₄⋊C₄×C₄₃	—	4	2	no	—
150	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
152	C₂²⋊C₄×C₄₃	—	2	1	no	—
153	C₂²⋊C₄×C₄₃	—	2	1	no	—
154	C₂²⋊C₄×C₄₃	—	2	1	no	—
155	C₄²×C₄₃	—	2	1	no	—
156	C₄²×C₄₃	—	2	1	no	—
157	C₄²×C₄₃	—	2	1	no	—
158	C₄²×C₄₃	—	2	2	no	—
159	C₄²×C₄₃	—	2	2	no	—
160	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
164	C₂²⋊Dic₄₃	—	2	1	no	—
165	#10621885	—	2	2	no	—
166	#10621884	—	2	2	no	—
167	#10621883	—	2	2	no	—
168	#10621882	—	2	2	no	—
169	(C₂×D₄₃)⋊C₄	—	2	1	no	—
170	(C₂×D₄₃)⋊C₄	—	2	1	no	—
171	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
172	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
173	Dic₄₃⋊C₄	—	2	1	no	—
174	Dic₄₃⋊C₄	—	2	1	no	—
175	C₄×Dic₄₃	—	2	1	no	—
176	C₄×Dic₄₃	—	2	1	no	—
177	C₄×Dic₄₃	—	2	1	no	—
178	#10621877	—	2	2	no	—
179	#10621877	—	2	2	no	—
180	C₂×C₄₃⋊C₈	—	2	2	no	—
181	C₂×C₄₃⋊C₈	—	2	1	no	—
182	C₂×C₄₃⋊C₈	—	2	1	no	—
183	C₂×C₄₃⋊C₈	—	2	2	no	—
184	C₂×C₄₃⋊C₈	—	2	2	no	—
185	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
186	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
187	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
188	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
189	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
190	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
191	C₂×C₄₃⋊C₈	#41	1	2	yes	—
192	C₂×C₄₃⋊C₈	#41	1	2	yes	—
193	C₂³×C₄₃	—	2	1	no	—
194	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
195	C₂²×D₄₃	—	2	1	no	—
196	Q₈×C₄₃	—	2	1	no	—
197	Q₈×C₄₃	—	2	1	no	—
198	D₄×C₄₃	—	2	1	no	—
199	D₄×C₄₃	—	2	1	no	—
200	D₄×C₄₃	—	4	1	no	—
201	D₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	2	2	no	—
203	C₂×C₄×C₄₃	—	2	1	no	—
204	C₂×C₄×C₄₃	—	2	1	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	—	4	2	no	—
210	C₂×C₄×C₄₃	—	4	2	no	—
211	C₂×C₄×C₄₃	—	4	2	no	—
212	C₂×C₄×C₄₃	—	4	2	no	—
213	C₂×C₄×C₄₃	—	8	1	no	—
214	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
216	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
217	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
218	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
223	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
224	C₂²⋊D₄₃	—	4	1	no	—
225	C₂²⋊D₄₃	—	4	1	no	—
226	C₂×Dic₄₃	—	2	1	no	—
227	C₂×Dic₄₃	—	2	1	no	—
228	C₂×Dic₄₃	—	2	1	no	—
229	D₁₇₂	—	2	1	no	—
230	D₁₇₂	—	2	1	no	—
231	C₄×D₄₃	—	4	1	no	—
232	C₄×D₄₃	—	4	1	no	—
233	C₄×D₄₃	—	4	2	no	—
234	C₄×D₄₃	—	8	1	no	—
235	Dic₈₆	—	2	1	no	—
236	Dic₈₆	—	2	1	no	—
237	C₈×C₄₃	—	4	2	no	—
238	C₄₃⋊C₈	—	2	1	no	—
239	C₄₃⋊C₈	—	2	1	no	—
240	C₄₃⋊C₈	—	2	2	no	—
241	C₄₃⋊C₈	—	2	2	no	—
242	C₄₃⋊C₈	—	4	2	no	—
243	C₄₃⋊C₈	#117	1	2	yes	—
244	C₄₃⋊C₈	#117	1	2	yes	—
245	#22803	—	43	1	no	maximal, Sylow
246	C₂²×C₄₃	—	2	1	no	—
247	C₂²×C₄₃	—	2	1	no	—
248	C₂²×C₄₃	—	4	1	no	—
249	C₂²×C₄₃	—	4	1	no	—
250	C₂²×C₄₃	—	4	1	no	—
251	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₄₃	#555	1	1	yes	characteristic
253	C₂²×C₄₃	#556	1	1	yes	characteristic
254	C₂×D₄₃	—	4	1	no	—
255	C₂×D₄₃	—	4	1	no	—
256	C₂×D₄₃	—	4	1	no	—
257	C₄×C₄₃	—	2	1	no	—
258	C₄×C₄₃	—	2	1	no	—
259	C₄×C₄₃	—	2	1	no	—
260	C₄×C₄₃	—	4	1	no	—
261	C₄×C₄₃	—	4	1	no	—
262	C₄×C₄₃	—	4	1	no	—
263	C₄×C₄₃	—	8	2	no	—
264	C₄×C₄₃	#444	1	2	yes	—
265	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
266	C₄×C₄₃	#520	1	1	yes	characteristic
267	C₄×C₄₃	#547	1	1	yes	characteristic
268	C₄×C₄₃	#550	1	1	yes	characteristic
269	Dic₄₃	—	4	1	no	—
270	Dic₄₃	—	4	1	no	—
271	Dic₄₃	—	4	1	no	—
272	C₄×#135	—	43	1	no	—
273	#2925	—	43	1	no	—
274	#2925	—	43	1	no	—
275	#1975	—	43	2	no	—
276	#1929	—	43	2	no	—
277	#1929	—	43	2	no	—
278	#1848	—	43	1	no	—
279	#1806	—	43	1	no	—
280	#1806	D₄₃	1	1	yes	characteristic, complemented
281	#1773	—	43	2	no	—
282	#1770	—	43	1	no	—
283	C₂×C₄₃	—	2	1	no	—
284	C₂×C₄₃	—	2	1	no	—
285	C₂×C₄₃	—	8	1	no	—
286	C₂×C₄₃	#2354	1	1	yes	characteristic
287	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
288	C₂×C₄₃	#2957	1	1	yes	characteristic
289	D₄₃	—	8	1	no	—
290	C₂×#135	—	43	1	no	—
291	C₄×#41	—	43	1	no	—
292	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
293	C₄×Q₁₆	—	43	1	no	—
294	C₄×Q₁₆	—	43	1	no	—
295	C₄×SD₁₆	—	43	1	no	—
296	C₄×SD₁₆	—	43	1	no	—
297	C₄×SD₁₆	—	43	1	no	—
298	C₄×SD₁₆	—	43	1	no	—
299	C₄×D₈	—	43	1	no	—
300	C₄×D₈	—	43	1	no	—
301	#433	—	86	2	no	—
302	#433	—	86	2	no	—
303	#432	—	86	1	no	—
304	#432	—	86	1	no	—
305	#431	—	86	1	no	—
306	#431	—	86	1	no	—
307	C₂×#108	—	43	2	no	—
308	C₂×#108	—	43	2	no	—
309	#427	—	43	1	no	—
310	#423	—	43	1	no	—
311	#423	C₂×D₄₃	1	1	yes	characteristic
312	C₂×C₄⋊C₈	—	43	1	no	—
313	C₂×#104	—	43	2	no	—
314	C₂×#104	C₂×D₄₃	1	2	yes	—
315	#416	—	43	1	no	—
316	#416	—	43	1	no	—
317	#408	—	43	2	no	—
318	#408	—	43	2	no	—
319	#405	—	43	2	no	—
320	#405	—	43	2	no	—
321	C₂×#97	—	43	2	no	—
322	C₂×C₄×C₈	—	43	1	no	—
323	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
324	#339	—	43	2	no	—
325	#339	C₂×D₄₃	1	2	yes	—
326	#336	—	43	2	no	—
327	C₄₃	#22803	1	1	yes	characteristic, complemented, Sylow
328	C₂×#41	—	43	1	no	—
329	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
330	#135	—	86	2	no	—
331	#135	—	86	2	no	—
332	C₂×Q₁₆	—	43	1	no	—
333	C₂×SD₁₆	—	43	1	no	—
334	C₂×SD₁₆	—	43	1	no	—
335	C₂×D₈	—	43	1	no	—
336	C₂×M₁₆	—	43	2	no	—
337	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
338	C₂²×C₈	—	43	1	no	—
339	C₂²×C₈	—	43	1	no	—
340	C₂²×C₈	—	43	2	no	—
341	C₄×Q₈	—	43	1	no	—
342	C₄×Q₈	—	43	1	no	—
343	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
344	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	—	2	1	no	—
347	C₄×D₄	—	43	1	no	—
348	C₄×D₄	—	43	1	no	—
349	C₄×D₄	—	86	1	no	—
350	C₄×D₄	—	86	1	no	—
351	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
352	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
353	#117	—	2	1	no	—
354	#117	—	43	1	no	—
355	#117	—	86	1	no	—
356	#117	C₂²×D₄₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	86	1	no	—
360	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
361	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
362	#108	—	86	4	no	—
363	#108	—	172	2	no	—
364	#107	—	43	1	no	—
365	#107	—	43	1	no	—
366	#106	—	43	1	no	—
367	#106	—	43	1	no	—
368	C₄⋊C₈	—	2	1	no	—
369	C₄⋊C₈	—	2	1	no	—
370	C₄⋊C₈	—	43	1	no	—
371	C₄⋊C₈	—	43	1	no	—
372	C₄⋊C₈	—	43	2	no	—
373	C₄⋊C₈	—	86	1	no	—
374	C₄⋊C₈	—	86	1	no	—
375	#104	—	4	2	no	—
376	#104	—	172	2	no	—
377	#103	—	43	1	no	—
378	#103	—	43	1	no	—
379	#103	—	43	1	no	—
380	#103	—	43	1	no	—
381	#102	—	43	1	no	—
382	#102	—	43	1	no	—
383	#102	—	43	1	no	—
384	#102	—	43	1	no	—
385	C₂²⋊C₈	—	86	2	no	—
386	C₂²⋊C₈	—	86	2	no	—
387	C₂²⋊C₈	—	86	2	no	—
388	C₂²⋊C₈	—	86	2	no	—
389	#97	—	86	4	no	—
390	#97	—	86	2	no	—
391	#97	—	86	2	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	2	no	—
397	C₄×C₈	—	86	2	no	—
398	#95	—	2	1	no	—
399	#41	—	2	1	no	—
400	#41	—	2	1	no	—
401	#41	—	2	1	no	—
402	#41	—	2	1	no	—
403	#41	—	86	1	no	—
404	#41	—	86	1	no	—
405	#41	—	86	1	no	—
406	#41	—	86	1	no	—
407	C₂×Q₈	—	43	1	no	—
408	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	43	1	no	—
411	C₂×D₄	—	86	1	no	—
412	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
413	C₂²×C₄	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	86	1	no	—
418	C₂²×C₄	—	86	1	no	—
419	C₂²×C₄	—	86	1	no	—
420	C₂²×C₄	#10621900	1	1	yes	characteristic
421	C₂²×C₄	#10621900	1	1	yes	characteristic
422	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
423	Q₁₆	—	86	2	no	—
424	SD₁₆	—	86	2	no	—
425	SD₁₆	—	86	2	no	—
426	D₈	—	86	2	no	—
427	M₁₆	—	2	2	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	86	2	no	—
430	M₁₆	—	86	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	43	1	no	—
433	C₂×C₈	—	43	1	no	—
434	C₂×C₈	—	43	2	no	—
435	C₂×C₈	—	43	2	no	—
436	C₂×C₈	—	43	1	no	—
437	C₂×C₈	—	43	1	no	—
438	C₂×C₈	—	43	2	no	—
439	C₂×C₈	—	43	2	no	—
440	C₂×C₈	—	86	2	no	—
441	C₂×C₈	—	86	1	no	—
442	C₂×C₈	—	86	1	no	—
443	C₂×C₈	—	86	2	no	—
444	C₂×C₈	—	86	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	—	43	1	no	—
449	C₄⋊C₄	—	43	1	no	—
450	C₄⋊C₄	—	86	1	no	—
451	C₄⋊C₄	—	86	1	no	—
452	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
453	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	2	1	no	—
456	C₂²⋊C₄	—	2	1	no	—
457	C₂²⋊C₄	—	86	1	no	—
458	C₂²⋊C₄	—	86	1	no	—
459	C₂²⋊C₄	—	86	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	86	1	no	—
466	C₄²	—	86	1	no	—
467	C₄²	—	86	1	no	—
468	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
469	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
470	C₄²	D₄×D₄₃	1	1	yes	characteristic
471	C₄²	D₄×D₄₃	1	1	yes	characteristic
472	C₂³	—	2	1	no	—
473	C₂³	—	86	1	no	—
474	C₂³	C₂×#10621900	1	1	yes	characteristic
475	Q₈	—	2	1	no	—
476	Q₈	—	2	1	no	—
477	Q₈	—	86	1	no	—
478	Q₈	—	86	1	no	—
479	D₄	—	2	1	no	—
480	D₄	—	2	1	no	—
481	D₄	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	86	1	no	—
484	D₄	—	86	1	no	—
485	D₄	—	172	1	no	—
486	D₄	—	172	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	2	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	8	1	no	—
499	C₂×C₄	—	86	1	no	—
500	C₂×C₄	—	86	1	no	—
501	C₂×C₄	—	86	1	no	—
502	C₂×C₄	—	344	1	no	—
503	C₂×C₄	—	172	1	no	—
504	C₂×C₄	—	172	2	no	—
505	C₂×C₄	—	172	1	no	—
506	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
507	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
508	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
509	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
512	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
513	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
514	C₂×C₄	#13063370	1	1	yes	characteristic
515	C₂×C₄	#13063373	1	1	yes	characteristic
516	C₈	—	4	2	no	—
517	C₈	—	43	2	no	—
518	C₈	—	43	2	no	—
519	C₈	—	86	1	no	—
520	C₈	—	86	1	no	—
521	C₈	—	86	2	no	—
522	C₈	—	86	2	no	—
523	C₈	—	172	2	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	1	no	—
527	C₂²	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	172	1	no	—
530	C₂²	—	172	1	no	—
531	C₂²	—	172	1	no	—
532	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
533	C₂²	#14583613	1	1	yes	characteristic
534	C₂²	#14583620	1	1	yes	characteristic
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	2	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	1	no	—
541	C₄	—	8	2	no	—
542	C₄	—	172	1	no	—
543	C₄	—	172	1	no	—
544	C₄	—	172	1	no	—
545	C₄	#14583018	1	2	yes	—
546	C₄	#117×D₄₃	1	1	yes	characteristic
547	C₄	#14583380	1	1	yes	characteristic
548	C₄	#14583551	1	1	yes	characteristic
549	C₄	#14583567	1	1	yes	characteristic
550	C₂	—	2	1	no	—
551	C₂	—	2	1	no	—
552	C₂	—	8	1	no	—
553	C₂	—	344	1	no	—
554	C₂	#19137539	1	1	yes	characteristic
555	C₂	C₂×#14583018	1	1	yes	characteristic
556	C₂	#19143508	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×#1806	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063345	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1806	D₄₃
hypocenter	C₄₃	#22803
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1806

Complements

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

N	H ≅ G/N	type
2. #19143263	C₂	semidirect
3. #19143261	C₂	semidirect
5. #19135246	C₂	semidirect
6. #19135241	C₂	semidirect
7. #19134766	C₂	semidirect
8. #19134616	C₂	semidirect
9. #19134478	C₂	semidirect
10. #19134464	C₂	semidirect
11. C₄₃×#1806	C₂	semidirect
14. C₄×#10621885	C₄	semidirect
15. C₄×#10621885	C₄	semidirect
16. C₄×#10621884	C₄	semidirect
17. C₄×#10621884	C₄	semidirect
18. C₄×#10621883	C₄	semidirect
19. C₄×#10621883	C₄	semidirect
20. C₄×#10621882	C₄	semidirect
21. C₄×#10621882	C₄	semidirect
280. #1806	D₄₃	semidirect
327. C₄₃	#22803	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063345	2
#19143263	2
#19143261	2
#19135485	2
#19135246	2
#19135241	2
#19134766	2
#19134616	2
#19134478	2
#19134464	2
C₄₃×#1806	2
#22803	43