Subgroups — #25105207

Order 11008.

1046 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145019	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583017	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583014	C₂	1	2	yes	maximal, complemented
4	#19143305	C₂	1	2	yes	maximal, complemented
5	#19135484	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135481	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135480	C₂	1	2	yes	maximal, complemented
8	#19135421	C₂	1	2	yes	maximal, complemented
9	#19134765	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#443	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063347	C₂²	1	1	yes	characteristic
13	C₂×#13063345	C₂²	1	2	yes	—
14	C₂×#13063331	C₂²	1	2	yes	—
15	#14583445	C₂²	1	2	yes	—
16	#14583284	C₄	1	1	yes	characteristic, complemented
17	#14583282	C₄	1	1	yes	characteristic, complemented
18	#14583280	C₄	1	2	yes	complemented
19	#14583277	C₄	1	1	yes	characteristic, complemented
20	#14583274	C₄	1	1	yes	characteristic, complemented
21	#14583270	C₄	1	2	yes	complemented
22	#14583017	—	2	4	no	—
23	#14583014	—	2	8	no	—
24	#14582975	—	2	4	no	—
25	C₈×C₂²⋊D₄₃	—	2	4	no	—
26	C₂×#13063261	C₂²	1	1	yes	characteristic
27	C₂×#13063260	C₂²	1	2	yes	—
28	#14582922	C₂²	1	2	yes	—
29	C₂×#13063253	C₂²	1	2	yes	—
30	C₂×#13063252	C₂²	1	2	yes	—
31	C₂×#13063251	C₂²	1	2	yes	—
32	#14582867	C₂²	1	2	yes	—
33	#14582866	C₂²	1	2	yes	—
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
39	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
40	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#131×C₄₃	C₂²	1	2	yes	—
42	C₄₃×#443	—	2	4	no	—
43	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#104×C₄₃	C₂²	1	2	yes	—
45	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
46	C₂×#10621898	C₂³	1	2	yes	—
47	#13063347	—	2	2	no	—
48	#13063347	—	2	2	no	—
49	#13063345	—	2	4	no	—
50	#13063345	—	2	4	no	—
51	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
52	C₂×#10621885	C₂×C₄	1	2	yes	—
53	C₂×#10621873	C₂×C₄	1	2	yes	—
54	C₂×#10621883	C₂×C₄	1	2	yes	—
55	C₂×#10621884	C₂×C₄	1	2	yes	—
56	C₂×D₃₄₄	C₂×C₄	1	1	yes	characteristic
57	C₂×#10621882	C₂×C₄	1	2	yes	—
58	#13063331	—	2	4	no	—
59	#13063331	—	2	4	no	—
60	C₂×#10621877	C₂³	1	2	yes	—
61	C₂×#10621872	—	2	2	no	—
62	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
64	C₂×C₈×D₄₃	—	2	2	no	—
65	#13063323	C₂×C₄	1	2	yes	—
66	#13063321	C₂×C₄	1	2	yes	—
67	#13063314	C₂×C₄	1	2	yes	—
68	#13063312	C₂×C₄	1	2	yes	—
69	#13063297	—	2	4	no	—
70	C₄×C₂²⋊D₄₃	—	2	4	no	—
71	C₂×C₄×Dic₄₃	—	2	2	no	—
72	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
74	#13063261	—	2	2	no	—
75	#13063260	—	2	4	no	—
76	Dic₄₃⋊C₈	—	2	4	no	—
77	#13063253	—	2	4	no	—
78	#13063252	—	2	4	no	—
79	#13063251	—	2	4	no	—
80	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
81	(C₂×D₄₃)⋊C₈	—	2	4	no	—
82	C₄×C₄₃⋊C₈	—	2	2	no	—
83	C₈×Dic₄₃	—	2	2	no	—
84	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₄₃	D₄	1	2	yes	—
89	C₈×Dic₄₃	D₄	1	2	yes	—
90	C₈×Dic₄₃	D₄	1	4	yes	complemented
91	C₂×#41×C₄₃	C₂³	1	2	yes	—
92	#135×C₄₃	—	2	2	no	—
93	#135×C₄₃	—	2	2	no	—
94	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
96	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
97	#131×C₄₃	—	2	4	no	—
98	#131×C₄₃	—	2	4	no	—
99	C₂×M₁₆×C₄₃	—	2	2	no	—
100	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
101	C₂²×C₈×C₄₃	—	2	2	no	—
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	#108×C₄₃	—	2	2	no	—
106	#104×C₄₃	—	2	4	no	—
107	C₄×C₈×C₄₃	D₄	1	4	yes	complemented
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	#41×C₄₃	—	2	2	no	—
111	#41×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
113	C₂×D₄×C₄₃	—	2	2	no	—
114	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₄₃	—	2	2	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
118	C₂×C₂²⋊D₄₃	—	2	4	no	—
119	C₂×C₂²⋊D₄₃	—	2	2	no	—
120	C₂²×Dic₄₃	—	2	1	no	—
121	C₂²×Dic₄₃	#41	1	2	yes	—
122	#10621898	—	2	2	no	—
123	#10621898	—	2	2	no	—
124	#10621898	—	2	2	no	—
125	#10621898	—	2	2	no	—
126	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
127	C₂×C₄×D₄₃	—	2	2	no	—
128	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
129	Q₁₆×C₄₃	—	2	2	no	—
130	SD₁₆×C₄₃	—	2	4	no	—
131	D₈×C₄₃	—	2	2	no	—
132	M₁₆×C₄₃	—	2	2	no	—
133	M₁₆×C₄₃	—	2	2	no	—
134	M₁₆×C₄₃	—	4	4	no	—
135	C₂×C₈×C₄₃	—	2	2	no	—
136	C₂×C₈×C₄₃	—	4	4	no	—
137	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₄₃	#41	1	2	yes	—
145	C₄²×C₄₃	—	2	1	no	—
146	C₄²×C₄₃	C₂×D₄	1	2	yes	—
147	C₂²⋊Dic₄₃	—	2	4	no	—
148	#10621885	—	2	4	no	—
149	#10621884	—	2	4	no	—
150	#10621883	—	2	4	no	—
151	#10621882	—	2	4	no	—
152	(C₂×D₄₃)⋊C₄	—	2	4	no	—
153	Dic₄₃⋊C₄	—	2	4	no	—
154	C₄×Dic₄₃	—	2	8	no	—
155	C₄×Dic₄₃	—	2	1	no	—
156	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
159	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
160	#10621877	—	2	2	no	—
161	#10621877	—	2	2	no	—
162	C₂×C₄₃⋊C₈	—	2	1	no	—
163	C₂×C₄₃⋊C₈	—	2	1	no	—
164	C₂×C₄₃⋊C₈	—	2	2	no	—
165	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
168	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
169	C₂×C₄₃⋊C₈	#41	1	2	yes	—
170	Dic₁₇₂	—	2	2	no	—
171	D₃₄₄	—	2	2	no	—
172	#10621873	—	2	4	no	—
173	#10621872	—	4	4	no	—
174	C₈×D₄₃	—	4	4	no	—
175	C₂³×C₄₃	—	2	2	no	—
176	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
177	C₂²×D₄₃	—	2	2	no	—
178	Q₈×C₄₃	—	2	2	no	—
179	Q₈×C₄₃	—	2	2	no	—
180	D₄×C₄₃	—	2	2	no	—
181	D₄×C₄₃	—	2	2	no	—
182	D₄×C₄₃	—	4	2	no	—
183	D₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	2	4	no	—
185	C₂×C₄×C₄₃	—	2	2	no	—
186	C₂×C₄×C₄₃	—	2	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
195	C₂²⋊D₄₃	—	4	2	no	—
196	C₂²⋊D₄₃	—	4	2	no	—
197	C₂²⋊D₄₃	—	4	8	no	—
198	C₂×Dic₄₃	—	2	4	no	—
199	C₂×Dic₄₃	—	2	2	no	—
200	C₂×Dic₄₃	—	2	4	no	—
201	C₂×Dic₄₃	—	2	2	no	—
202	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
203	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
204	D₁₇₂	—	2	2	no	—
205	D₁₇₂	—	2	2	no	—
206	C₄×D₄₃	—	4	2	no	—
207	C₄×D₄₃	—	4	2	no	—
208	Dic₈₆	—	2	2	no	—
209	Dic₈₆	—	2	2	no	—
210	C₈×C₄₃	—	4	2	no	—
211	C₈×C₄₃	C₄×D₄	1	2	yes	—
212	C₈×C₄₃	C₄×D₄	1	2	yes	—
213	C₈×C₄₃	#127	1	2	yes	—
214	C₈×C₄₃	#127	1	2	yes	—
215	C₄₃⋊C₈	—	2	2	no	—
216	C₄₃⋊C₈	—	4	2	no	—
217	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
218	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
219	#21705	—	43	1	no	maximal, Sylow
220	C₂²×C₄₃	—	2	2	no	—
221	C₂²×C₄₃	—	4	2	no	—
222	C₂²×C₄₃	—	4	4	no	—
223	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂²×C₄₃	#532	1	1	yes	characteristic
225	C₂²×C₄₃	#532	1	1	yes	characteristic
226	C₂×D₄₃	—	4	2	no	—
227	C₂×D₄₃	—	4	4	no	—
228	C₄×C₄₃	—	2	4	no	—
229	C₄×C₄₃	—	4	2	no	—
230	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
231	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
232	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
233	C₄×C₄₃	#532	1	1	yes	characteristic
234	Dic₄₃	—	2	4	no	—
235	Dic₄₃	—	2	2	no	—
236	Dic₄₃	—	4	2	no	—
237	Dic₄₃	#443	1	4	yes	complemented
238	#3147	—	43	1	no	—
239	C₂×#443	—	43	1	no	—
240	C₂×#443	—	43	2	no	—
241	C₂×#443	D₄₃	1	1	yes	characteristic, complemented
242	#2931	—	43	2	no	—
243	#1974	—	43	1	no	—
244	#1974	—	43	2	no	—
245	#1974	—	43	1	no	—
246	#1962	—	43	2	no	—
247	#1848	—	43	1	no	—
248	C₄²×C₈	—	43	1	no	—
249	C₂×C₄₃	—	2	1	no	—
250	C₂×C₄₃	—	2	1	no	—
251	C₂×C₄₃	—	8	2	no	—
252	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
253	C₂×C₄₃	C₂×#443	1	2	yes	—
254	D₄₃	—	8	2	no	—
255	C₂×#135	—	43	2	no	—
256	C₂×#135	—	43	1	no	—
257	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
258	C₂×#131	—	43	2	no	—
259	C₂×#131	C₂×D₄₃	1	2	yes	—
260	#532	—	43	2	no	—
261	#495	—	43	1	no	—
262	#495	—	43	2	no	—
263	#495	—	43	1	no	—
264	#494	—	43	1	no	—
265	#493	—	43	1	no	—
266	#492	—	43	2	no	—
267	#443	—	2	4	no	—
268	#443	—	86	8	no	—
269	#443	—	86	4	no	—
270	#436	—	86	4	no	—
271	C₈×D₄	—	86	4	no	—
272	C₂×#108	—	43	2	no	—
273	C₂×#108	—	43	1	no	—
274	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
275	#423	—	43	2	no	—
276	C₂×#104	—	43	2	no	—
277	C₂×#104	—	43	2	no	—
278	C₂×#104	—	43	2	no	—
279	C₂×#104	C₂×D₄₃	1	2	yes	—
280	#408	—	43	2	no	—
281	#408	—	43	2	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	C₂×C₄×C₈	—	43	1	no	—
284	C₂×C₄×C₈	—	43	1	no	—
285	C₂×C₄×C₈	—	43	1	no	—
286	C₂×C₄×C₈	—	43	1	no	—
287	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
288	C₄³	—	43	1	no	—
289	C₄₃	#21705	1	1	yes	characteristic, complemented, Sylow
290	C₂×#41	—	43	2	no	—
291	C₂×#41	C₂²×D₄₃	1	2	yes	—
292	#135	—	2	2	no	—
293	#135	—	2	2	no	—
294	#135	—	86	4	no	—
295	#135	—	86	4	no	—
296	#135	—	86	2	no	—
297	#135	—	86	2	no	—
298	C₂×Q₁₆	—	43	2	no	—
299	C₂×Q₁₆	—	43	1	no	—
300	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic
301	C₂×SD₁₆	—	43	2	no	—
302	C₂×SD₁₆	—	43	2	no	—
303	C₂×SD₁₆	—	43	2	no	—
304	C₂×SD₁₆	C₄×D₄₃	1	2	yes	—
305	C₂×D₈	—	43	2	no	—
306	C₂×D₈	—	43	1	no	—
307	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic
308	#131	—	2	4	no	—
309	#131	—	2	4	no	—
310	#131	—	86	4	no	—
311	#131	—	86	4	no	—
312	C₂×M₁₆	—	2	2	no	—
313	C₂×M₁₆	—	43	2	no	—
314	C₂×M₁₆	—	86	2	no	—
315	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
316	C₂²×C₈	—	2	2	no	—
317	C₂²×C₈	—	43	1	no	—
318	C₂²×C₈	—	43	1	no	—
319	C₂²×C₈	—	86	2	no	—
320	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
321	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
322	C₄⋊Q₈	—	43	2	no	—
323	#127	—	43	2	no	—
324	#124	—	43	2	no	—
325	#124	—	43	2	no	—
326	#121	—	86	4	no	—
327	C₄×D₄	—	86	4	no	—
328	C₂×C₄²	—	43	1	no	—
329	C₂×C₄²	—	43	1	no	—
330	C₂×C₄²	—	86	2	no	—
331	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
332	#108	—	2	2	no	—
333	#108	—	86	4	no	—
334	#108	—	86	2	no	—
335	C₄⋊C₈	—	86	4	no	—
336	#104	—	2	4	no	—
337	#104	—	86	4	no	—
338	#104	—	86	4	no	—
339	#104	—	86	4	no	—
340	C₂²⋊C₈	—	86	4	no	—
341	C₂²⋊C₈	—	86	4	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	43	1	no	—
344	C₄×C₈	—	43	1	no	—
345	C₄×C₈	—	43	1	no	—
346	C₄×C₈	—	43	2	no	—
347	C₄×C₈	—	43	4	no	—
348	C₄×C₈	—	43	2	no	—
349	C₄×C₈	—	86	2	no	—
350	C₄×C₈	—	86	2	no	—
351	C₄×C₈	C₂²⋊D₄₃	1	4	yes	complemented
352	#41	—	2	2	no	—
353	#41	—	2	2	no	—
354	#41	—	2	2	no	—
355	#41	—	2	2	no	—
356	#41	—	86	2	no	—
357	#41	—	86	2	no	—
358	#41	—	86	2	no	—
359	#41	—	86	2	no	—
360	C₂×Q₈	—	43	2	no	—
361	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	43	2	no	—
364	C₂×D₄	—	86	4	no	—
365	C₂×D₄	—	86	2	no	—
366	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	43	2	no	—
370	C₂²×C₄	—	86	1	no	—
371	C₂²×C₄	—	86	2	no	—
372	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
373	Q₁₆	—	2	2	no	—
374	Q₁₆	—	86	4	no	—
375	Q₁₆	—	86	2	no	—
376	SD₁₆	—	2	4	no	—
377	SD₁₆	—	86	4	no	—
378	SD₁₆	—	86	4	no	—
379	SD₁₆	—	86	4	no	—
380	D₈	—	2	2	no	—
381	D₈	—	86	4	no	—
382	D₈	—	86	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	4	4	no	—
386	M₁₆	—	86	2	no	—
387	M₁₆	—	86	2	no	—
388	M₁₆	—	172	4	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	4	4	no	—
391	C₂×C₈	—	43	1	no	—
392	C₂×C₈	—	43	1	no	—
393	C₂×C₈	—	43	2	no	—
394	C₂×C₈	—	43	2	no	—
395	C₂×C₈	—	43	2	no	—
396	C₂×C₈	—	86	1	no	—
397	C₂×C₈	—	86	1	no	—
398	C₂×C₈	—	86	2	no	—
399	C₂×C₈	—	172	4	no	—
400	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
401	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
402	C₂×C₈	#10621898	1	2	yes	—
403	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
404	C₂×C₈	D₄×D₄₃	1	2	yes	—
405	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
407	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
408	C₄⋊C₄	—	86	4	no	—
409	C₂²⋊C₄	—	86	4	no	—
410	C₂²⋊C₄	—	86	4	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	43	1	no	—
413	C₄²	—	43	1	no	—
414	C₄²	—	43	2	no	—
415	C₄²	—	43	2	no	—
416	C₄²	—	86	8	no	—
417	C₄²	—	86	1	no	—
418	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
419	C₂³	—	2	2	no	—
420	C₂³	—	86	2	no	—
421	C₂³	#41×D₄₃	1	1	yes	characteristic
422	Q₈	—	2	2	no	—
423	Q₈	—	2	2	no	—
424	Q₈	—	86	2	no	—
425	Q₈	—	86	2	no	—
426	D₄	—	2	2	no	—
427	D₄	—	2	2	no	—
428	D₄	—	4	2	no	—
429	D₄	—	4	2	no	—
430	D₄	—	86	2	no	—
431	D₄	—	86	2	no	—
432	D₄	—	172	8	no	—
433	D₄	—	172	2	no	—
434	D₄	—	172	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	43	2	no	—
441	C₂×C₄	—	43	2	no	—
442	C₂×C₄	—	86	4	no	—
443	C₂×C₄	—	86	4	no	—
444	C₂×C₄	—	86	2	no	—
445	C₂×C₄	—	86	2	no	—
446	C₂×C₄	—	172	2	no	—
447	C₂×C₄	—	172	2	no	—
448	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
449	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
453	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	43	2	no	—
456	C₈	—	43	2	no	—
457	C₈	—	86	2	no	—
458	C₈	—	172	2	no	—
459	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
460	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
461	C₈	#13063321	1	2	yes	—
462	C₈	#13063321	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	172	4	no	—
467	C₂²	—	172	2	no	—
468	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
469	C₂²	#14583445	1	1	yes	characteristic
470	C₂²	#14583446	1	1	yes	characteristic
471	C₄	—	2	4	no	—
472	C₄	—	4	2	no	—
473	C₄	—	43	4	no	—
474	C₄	—	86	4	no	—
475	C₄	—	86	2	no	—
476	C₄	—	172	2	no	—
477	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
478	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
479	C₄	C₂×#13063321	1	1	yes	characteristic
480	C₄	#14583446	1	1	yes	characteristic
481	C₂	—	2	1	no	—
482	C₂	—	2	1	no	—
483	C₂	—	8	2	no	—
484	C₂	—	344	2	no	—
485	C₂	C₄×#13063321	1	1	yes	characteristic
486	C₂	#443×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#443	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19145019	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#443	D₄₃
hypocenter	C₄₃	#21705
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#14583017	C₂	semidirect
3. C₂×#14583014	C₂	semidirect
4. #19143305	C₂	semidirect
5. #19135484	C₂	semidirect
6. #19135481	C₂	semidirect
7. #19135480	C₂	semidirect
8. #19135421	C₂	semidirect
9. #19134765	C₂	semidirect
10. C₄×C₈×Dic₄₃	C₂	semidirect
11. C₂×C₄₃×#443	C₂	semidirect
16. #14583284	C₄	semidirect
17. #14583282	C₄	semidirect
18. #14583280	C₄	semidirect
19. #14583277	C₄	semidirect
20. #14583274	C₄	semidirect
21. #14583270	C₄	semidirect
90. C₈×Dic₄₃	D₄	semidirect
107. C₄×C₈×C₄₃	D₄	semidirect
237. Dic₄₃	#443	semidirect
241. C₂×#443	D₄₃	semidirect
289. C₄₃	#21705	semidirect
351. C₄×C₈	C₂²⋊D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19145019	2
C₂×#14583017	2
C₂×#14583014	2
#19143305	2
#19135484	2
#19135481	2
#19135480	2
#19135421	2
#19134765	2
C₄×C₈×Dic₄₃	2
C₂×C₄₃×#443	2
#21705	43