Subgroups — #25105224

Order 11008.

998 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145021	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583018	C₂	1	2	yes	maximal, complemented
3	C₂×#14583013	C₂	1	2	yes	maximal, complemented
4	#19143313	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143312	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135485	C₂	1	2	yes	maximal, complemented
7	#19135480	C₂	1	2	yes	maximal, complemented
8	#19135427	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134766	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134282	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1963	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₂²	1	2	yes	—
13	C₂×#13063345	C₂²	1	2	yes	—
14	C₂×#13063333	C₂²	1	2	yes	—
15	C₂×#13063332	C₂²	1	2	yes	—
16	#14583449	C₂²	1	1	yes	characteristic
17	#14583281	C₄	1	2	yes	complemented
18	#14583281	C₄	1	2	yes	complemented
19	#14583278	C₄	1	1	yes	characteristic, complemented
20	#14583275	C₄	1	1	yes	characteristic, complemented
21	#14583273	C₄	1	1	yes	characteristic, complemented
22	#14583271	C₄	1	1	yes	characteristic, complemented
23	#14583018	—	2	8	no	—
24	#14583013	—	2	8	no	—
25	#14582971	—	2	4	no	—
26	#14582969	—	2	4	no	—
27	C₂×#13063260	C₂²	1	2	yes	—
28	C₂×#13063260	C₂²	1	2	yes	—
29	#14582923	C₂²	1	1	yes	characteristic
30	C₂×#13063253	C₂²	1	2	yes	—
31	C₂×#13063253	C₂²	1	2	yes	—
32	#14582867	C₂²	1	2	yes	—
33	#14582866	C₂²	1	2	yes	—
34	C₂×#13063236	C₂²	1	1	yes	characteristic
35	C₂×#13063236	C₂²	1	1	yes	characteristic
36	C₂×#13063236	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₄₃×#532	C₂²	1	1	yes	characteristic
41	C₄₃×#423	C₂²	1	1	yes	characteristic
42	C₂×#104×C₄₃	C₂²	1	2	yes	—
43	C₂×#104×C₄₃	C₂²	1	2	yes	—
44	C₄₃×#376	C₂²	1	1	yes	characteristic
45	C₂×#10621898	C₂³	1	2	yes	—
46	#13063345	—	2	4	no	—
47	#13063345	—	2	4	no	—
48	#13063345	—	2	4	no	—
49	#13063345	—	2	4	no	—
50	C₂×#10621885	C₂×C₄	1	2	yes	—
51	C₂×#10621885	C₂×C₄	1	2	yes	—
52	C₂×#10621883	C₂×C₄	1	2	yes	—
53	C₂×#10621883	C₂×C₄	1	2	yes	—
54	C₂×#10621884	C₂×C₄	1	2	yes	—
55	C₂×#10621884	C₂×C₄	1	2	yes	—
56	C₂×#10621882	C₂×C₄	1	2	yes	—
57	C₂×#10621882	C₂×C₄	1	2	yes	—
58	#13063333	—	2	4	no	—
59	#13063333	—	2	4	no	—
60	#13063332	—	2	4	no	—
61	#13063332	—	2	4	no	—
62	C₂×#10621877	—	2	2	no	—
63	C₂×#10621877	C₂³	1	2	yes	—
64	C₂×#10621872	—	2	2	no	—
65	C₂²×C₄₃⋊C₈	—	2	2	no	—
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	C₂×C₈×D₄₃	—	2	2	no	—
71	#13063325	C₂×C₄	1	1	yes	characteristic
72	#13063322	C₂×C₄	1	1	yes	characteristic
73	#13063313	C₂×C₄	1	2	yes	—
74	#13063299	—	2	2	no	—
75	C₄×D₁₇₂	—	2	2	no	—
76	#13063260	—	2	4	no	—
77	#13063260	—	2	4	no	—
78	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
79	#13063253	—	2	4	no	—
80	#13063253	—	2	4	no	—
81	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
82	(C₂×D₄₃)⋊C₈	—	2	4	no	—
83	#13063236	—	2	2	no	—
84	#13063236	D₄	1	4	yes	—
85	#13063236	D₄	1	4	yes	complemented
86	C₄×C₄₃⋊C₈	—	2	2	no	—
87	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
88	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
89	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
90	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
91	C₄×C₄₃⋊C₈	D₄	1	4	yes	complemented
92	C₂×#41×C₄₃	C₂³	1	2	yes	—
93	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
95	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
96	#124×C₄₃	C₂×C₄	1	2	yes	—
97	#121×C₄₃	—	2	2	no	—
98	C₄×D₄×C₄₃	—	2	2	no	—
99	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₃	—	2	2	no	—
103	#104×C₄₃	—	2	4	no	—
104	#104×C₄₃	—	2	4	no	—
105	#95×C₄₃	—	2	2	no	—
106	#41×C₄₃	—	2	2	no	—
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	#41	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₃	—	2	2	no	—
120	#10621898	—	2	2	no	—
121	#10621898	—	2	2	no	—
122	#10621898	—	2	2	no	—
123	#10621898	—	2	2	no	—
124	C₂×D₁₇₂	—	2	2	no	—
125	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
126	C₂×C₄×D₄₃	—	2	2	no	—
127	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
128	M₁₆×C₄₃	—	2	2	no	—
129	M₁₆×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₂²⋊C₄×C₄₃	—	2	4	no	—
133	C₄²×C₄₃	—	2	1	no	—
134	C₄²×C₄₃	—	2	1	no	—
135	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₄²×C₄₃	C₂×D₄	1	2	yes	—
138	C₄²×C₄₃	C₂×D₄	1	2	yes	—
139	C₄²×C₄₃	C₂×D₄	1	2	yes	—
140	#10621885	—	2	4	no	—
141	#10621885	—	2	4	no	—
142	#10621884	—	2	4	no	—
143	#10621884	—	2	4	no	—
144	#10621883	—	2	4	no	—
145	#10621883	—	2	4	no	—
146	#10621882	—	2	4	no	—
147	#10621882	—	2	4	no	—
148	(C₂×D₄₃)⋊C₄	—	2	4	no	—
149	C₄⋊Dic₄₃	—	2	2	no	—
150	#10621877	—	2	2	no	—
151	#10621877	—	2	2	no	—
152	#10621877	—	4	4	no	—
153	C₂×C₄₃⋊C₈	—	2	1	no	—
154	C₂×C₄₃⋊C₈	—	2	1	no	—
155	C₂×C₄₃⋊C₈	—	2	2	no	—
156	C₂×C₄₃⋊C₈	—	4	4	no	—
157	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
162	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
163	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
164	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
165	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
166	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
167	C₂×C₄₃⋊C₈	#41	1	2	yes	—
168	C₂×C₄₃⋊C₈	#41	1	2	yes	—
169	#10621872	—	4	4	no	—
170	C₈×D₄₃	—	4	4	no	—
171	C₂³×C₄₃	—	2	2	no	—
172	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
173	C₂²×D₄₃	—	2	2	no	—
174	Q₈×C₄₃	—	2	2	no	—
175	Q₈×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	2	2	no	—
177	D₄×C₄₃	—	2	2	no	—
178	D₄×C₄₃	—	4	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	8	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	2	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	2	no	—
187	C₂×C₄×C₄₃	—	4	2	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
191	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
197	C₂²⋊D₄₃	—	4	2	no	—
198	C₂²⋊D₄₃	—	4	2	no	—
199	C₂×Dic₄₃	—	2	2	no	—
200	D₁₇₂	—	2	2	no	—
201	D₁₇₂	—	2	2	no	—
202	D₁₇₂	—	8	2	no	—
203	C₄×D₄₃	—	4	2	no	—
204	C₄×D₄₃	—	4	2	no	—
205	Dic₈₆	—	2	2	no	—
206	Dic₈₆	—	2	2	no	—
207	C₈×C₄₃	—	4	2	no	—
208	C₄₃⋊C₈	—	2	2	no	—
209	C₄₃⋊C₈	—	4	2	no	—
210	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
211	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
212	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
213	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
214	C₄₃⋊C₈	#127	1	4	yes	—
215	#21707	—	43	1	no	maximal, Sylow
216	C₂²×C₄₃	—	2	2	no	—
217	C₂²×C₄₃	—	4	2	no	—
218	C₂²×C₄₃	—	4	4	no	—
219	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₃	#532	1	1	yes	characteristic
221	C₂²×C₄₃	#532	1	1	yes	characteristic
222	C₂×D₄₃	—	4	2	no	—
223	C₂×D₄₃	—	4	4	no	—
224	C₄×C₄₃	—	2	2	no	—
225	C₄×C₄₃	—	2	2	no	—
226	C₄×C₄₃	—	4	2	no	—
227	C₄×C₄₃	—	4	2	no	—
228	C₄×C₄₃	—	4	2	no	—
229	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
230	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
231	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
232	C₄×C₄₃	#532	1	1	yes	characteristic
233	Dic₄₃	—	4	2	no	—
234	#3147	—	43	1	no	—
235	C₂×#444	—	43	2	no	—
236	C₂×#443	—	43	2	no	—
237	#2932	—	43	1	no	—
238	#2932	—	43	1	no	—
239	#1975	—	43	2	no	—
240	#1974	—	43	2	no	—
241	#1963	—	43	1	no	—
242	#1963	D₄₃	1	1	yes	characteristic, complemented
243	#1848	—	43	1	no	—
244	#1726	—	43	1	no	—
245	C₂×C₄₃	—	2	1	no	—
246	C₂×C₄₃	—	2	1	no	—
247	C₂×C₄₃	—	8	2	no	—
248	C₂×C₄₃	C₄×#127	1	1	yes	characteristic
249	C₂×C₄₃	#2957	1	2	yes	—
250	D₄₃	—	8	2	no	—
251	C₂×#135	—	43	2	no	—
252	C₂×#135	—	43	2	no	—
253	C₂×#131	—	43	2	no	—
254	C₂×#131	—	43	2	no	—
255	#532	—	43	1	no	—
256	#532	C₂×D₄₃	1	1	yes	characteristic
257	#495	—	43	2	no	—
258	#495	—	43	2	no	—
259	#494	—	43	1	no	—
260	#493	—	43	1	no	—
261	#492	—	43	1	no	—
262	#492	—	43	1	no	—
263	#444	—	86	8	no	—
264	#443	—	86	8	no	—
265	#435	—	86	4	no	—
266	#435	—	86	4	no	—
267	C₂×#108	—	43	2	no	—
268	C₂×#108	—	43	2	no	—
269	#423	—	43	1	no	—
270	#423	C₂×D₄₃	1	1	yes	characteristic
271	C₂×#104	—	43	2	no	—
272	C₂×#104	—	43	2	no	—
273	C₂×#104	C₂×D₄₃	1	2	yes	—
274	C₂×#104	C₂×D₄₃	1	2	yes	—
275	#408	—	43	2	no	—
276	#408	—	43	2	no	—
277	C₂×#97	—	43	1	no	—
278	C₂×#97	—	43	1	no	—
279	C₂×#97	—	43	1	no	—
280	C₂×C₄×C₈	—	43	1	no	—
281	C₂×C₄×C₈	—	43	1	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	#376	C₂×D₄₃	1	1	yes	characteristic
284	C₄₃	#21707	1	1	yes	characteristic, complemented, Sylow
285	C₂×#41	—	43	2	no	—
286	C₂×#41	C₂²×D₄₃	1	2	yes	—
287	#135	—	86	4	no	—
288	#135	—	86	4	no	—
289	#135	—	86	4	no	—
290	#135	—	86	4	no	—
291	C₂×Q₁₆	—	43	2	no	—
292	C₂×Q₁₆	—	43	2	no	—
293	C₂×SD₁₆	—	43	2	no	—
294	C₂×SD₁₆	—	43	2	no	—
295	C₂×SD₁₆	—	43	2	no	—
296	C₂×SD₁₆	—	43	2	no	—
297	C₂×D₈	—	43	2	no	—
298	C₂×D₈	—	43	2	no	—
299	#131	—	86	4	no	—
300	#131	—	86	4	no	—
301	#131	—	86	4	no	—
302	#131	—	86	4	no	—
303	C₂×M₁₆	—	43	2	no	—
304	C₂×M₁₆	—	86	2	no	—
305	C₂×M₁₆	—	86	2	no	—
306	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
307	C₂²×C₈	—	43	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	43	1	no	—
311	C₂²×C₈	—	86	2	no	—
312	C₂²×C₈	—	86	2	no	—
313	C₄⋊Q₈	—	43	1	no	—
314	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
315	#127	—	43	1	no	—
316	#127	C₄×D₄₃	1	1	yes	characteristic
317	#124	—	43	2	no	—
318	#124	C₄×D₄₃	1	2	yes	—
319	#121	—	2	2	no	—
320	#121	—	86	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	86	2	no	—
323	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
325	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
326	#108	—	86	4	no	—
327	#108	—	86	4	no	—
328	C₄⋊C₈	—	2	2	no	—
329	C₄⋊C₈	—	86	2	no	—
330	#104	—	2	4	no	—
331	#104	—	2	4	no	—
332	#104	—	86	4	no	—
333	#104	—	86	4	no	—
334	C₂²⋊C₈	—	86	4	no	—
335	C₂²⋊C₈	—	86	4	no	—
336	#97	—	43	4	no	—
337	#97	—	43	4	no	—
338	#97	—	86	2	no	—
339	C₄×C₈	—	43	1	no	—
340	C₄×C₈	—	43	1	no	—
341	C₄×C₈	—	43	1	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	43	4	no	—
344	C₄×C₈	—	86	2	no	—
345	#95	—	2	2	no	—
346	#41	—	2	2	no	—
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	86	2	no	—
351	#41	—	86	2	no	—
352	#41	—	86	2	no	—
353	#41	—	86	2	no	—
354	C₂×Q₈	—	43	2	no	—
355	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
356	C₂×D₄	—	2	2	no	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	43	2	no	—
359	C₂×D₄	—	86	2	no	—
360	C₂×D₄	—	86	2	no	—
361	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	86	2	no	—
366	C₂²×C₄	#10621900	1	2	yes	—
367	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
368	Q₁₆	—	86	4	no	—
369	Q₁₆	—	86	4	no	—
370	SD₁₆	—	86	4	no	—
371	SD₁₆	—	86	4	no	—
372	SD₁₆	—	86	4	no	—
373	SD₁₆	—	86	4	no	—
374	D₈	—	86	4	no	—
375	D₈	—	86	4	no	—
376	M₁₆	—	2	2	no	—
377	M₁₆	—	2	2	no	—
378	M₁₆	—	86	2	no	—
379	M₁₆	—	86	2	no	—
380	M₁₆	—	172	4	no	—
381	M₁₆	—	172	4	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	43	1	no	—
384	C₂×C₈	—	43	1	no	—
385	C₂×C₈	—	43	1	no	—
386	C₂×C₈	—	43	1	no	—
387	C₂×C₈	—	43	2	no	—
388	C₂×C₈	—	43	2	no	—
389	C₂×C₈	—	43	2	no	—
390	C₂×C₈	—	43	2	no	—
391	C₂×C₈	—	43	2	no	—
392	C₂×C₈	—	43	2	no	—
393	C₂×C₈	—	43	2	no	—
394	C₂×C₈	—	43	2	no	—
395	C₂×C₈	—	86	1	no	—
396	C₂×C₈	—	86	1	no	—
397	C₂×C₈	—	86	2	no	—
398	C₂×C₈	—	172	4	no	—
399	C₂×C₈	—	172	4	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	86	2	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	86	4	no	—
404	C₄²	—	2	1	no	—
405	C₄²	—	2	1	no	—
406	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
407	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
408	C₄²	D₄×D₄₃	1	2	yes	—
409	C₄²	D₄×D₄₃	1	2	yes	—
410	C₄²	D₄×D₄₃	1	2	yes	—
411	C₂³	—	2	2	no	—
412	C₂³	—	86	2	no	—
413	C₂³	C₂×#10621900	1	1	yes	characteristic
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	86	2	no	—
417	Q₈	—	86	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	8	2	no	—
423	D₄	—	86	2	no	—
424	D₄	—	86	2	no	—
425	D₄	—	344	2	no	—
426	D₄	—	172	2	no	—
427	D₄	—	172	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
440	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	2	yes	—
441	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
442	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
444	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
445	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
446	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
447	C₈	—	4	2	no	—
448	C₈	—	43	2	no	—
449	C₈	—	43	2	no	—
450	C₈	—	43	2	no	—
451	C₈	—	43	2	no	—
452	C₈	—	43	4	no	—
453	C₈	—	86	2	no	—
454	C₈	—	172	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	172	4	no	—
459	C₂²	—	172	2	no	—
460	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
461	C₂²	#14583444	1	1	yes	characteristic
462	C₂²	#14583444	1	1	yes	characteristic
463	C₄	—	2	2	no	—
464	C₄	—	2	2	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	172	2	no	—
469	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
470	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
471	C₄	#127×D₄₃	1	1	yes	characteristic
472	C₄	#14583448	1	1	yes	characteristic
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	8	2	no	—
476	C₂	—	344	2	no	—
477	C₂	#19137159	1	1	yes	characteristic
478	C₂	#19143508	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1963	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19145021	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1963	D₄₃
hypocenter	C₄₃	#21707
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1963

Complements

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

N	H ≅ G/N	type
2. C₂×#14583018	C₂	semidirect
3. C₂×#14583013	C₂	semidirect
4. #19143313	C₂	semidirect
5. #19143312	C₂	semidirect
6. #19135485	C₂	semidirect
7. #19135480	C₂	semidirect
8. #19135427	C₂	semidirect
9. #19134766	C₂	semidirect
10. #19134282	C₂	semidirect
11. C₄₃×#1963	C₂	semidirect
17. #14583281	C₄	semidirect
18. #14583281	C₄	semidirect
19. #14583278	C₄	semidirect
20. #14583275	C₄	semidirect
21. #14583273	C₄	semidirect
22. #14583271	C₄	semidirect
85. #13063236	D₄	semidirect
91. C₄×C₄₃⋊C₈	D₄	semidirect
242. #1963	D₄₃	semidirect
284. C₄₃	#21707	semidirect

Maximal subgroups

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

subgroup	index
#19145021	2
C₂×#14583018	2
C₂×#14583013	2
#19143313	2
#19143312	2
#19135485	2
#19135480	2
#19135427	2
#19134766	2
#19134282	2
C₄₃×#1963	2
#21707	43