Subgroups — #25105225

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	#19145019	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583022	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#14583014	C₂	1	2	yes	maximal, complemented
4	#19143311	C₂	1	2	yes	maximal, complemented
5	#19135489	C₂	1	1	yes	maximal, characteristic, complemented
6	#19135486	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135480	C₂	1	2	yes	maximal, complemented
8	#19135425	C₂	1	2	yes	maximal, complemented
9	#19134765	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134283	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₃×#444	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	#14583022	—	2	4	no	—
23	#14583014	—	2	8	no	—
24	#14582970	—	2	4	no	—
25	#14582968	—	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×#13063235	C₂²	1	1	yes	characteristic
35	C₂×#13063235	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
39	#14582745	C₂²	1	1	yes	characteristic
40	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
41	C₂×#131×C₄₃	C₂²	1	2	yes	—
42	C₄₃×#444	—	2	4	no	—
43	C₂×#108×C₄₃	C₂²	1	1	yes	characteristic
44	C₂×#104×C₄₃	C₂²	1	2	yes	—
45	C₂×#97×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	C₂³	1	1	yes	characteristic
72	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
73	#13063261	—	2	2	no	—
74	#13063260	—	2	4	no	—
75	Dic₄₃⋊C₈	—	2	4	no	—
76	#13063253	—	2	4	no	—
77	#13063252	—	2	4	no	—
78	#13063251	—	2	4	no	—
79	C₂²⋊(C₄₃⋊C₈)	—	2	4	no	—
80	(C₂×D₄₃)⋊C₈	—	2	4	no	—
81	#13063235	—	2	2	no	—
82	#13063235	D₄	1	4	yes	—
83	C₄×C₄₃⋊C₈	—	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	4	yes	complemented
89	C₄₃⋊#95	—	2	2	no	—
90	C₂×#41×C₄₃	C₂³	1	2	yes	—
91	#135×C₄₃	—	2	2	no	—
92	#135×C₄₃	—	2	2	no	—
93	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
94	C₂×SD₁₆×C₄₃	C₂×C₄	1	2	yes	—
95	C₂×D₈×C₄₃	C₂×C₄	1	1	yes	characteristic
96	#131×C₄₃	—	2	4	no	—
97	#131×C₄₃	—	2	4	no	—
98	C₂×M₁₆×C₄₃	—	2	2	no	—
99	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
100	C₂²×C₈×C₄₃	—	2	2	no	—
101	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#108×C₄₃	—	2	2	no	—
105	#104×C₄₃	—	2	4	no	—
106	#97×C₄₃	D₄	1	4	yes	complemented
107	#41×C₄₃	—	2	2	no	—
108	#41×C₄₃	—	2	2	no	—
109	#41×C₄₃	—	2	2	no	—
110	#41×C₄₃	—	2	2	no	—
111	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
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	C₂⁴	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₃	—	2	4	no	—
118	C₂×C₂²⋊D₄₃	—	2	2	no	—
119	C₂²×Dic₄₃	—	2	1	no	—
120	C₂²×Dic₄₃	#41	1	2	yes	—
121	#10621898	—	2	2	no	—
122	#10621898	—	2	2	no	—
123	#10621898	—	2	2	no	—
124	#10621898	—	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	Q₁₆×C₄₃	—	2	2	no	—
129	SD₁₆×C₄₃	—	2	4	no	—
130	D₈×C₄₃	—	2	2	no	—
131	M₁₆×C₄₃	—	2	2	no	—
132	M₁₆×C₄₃	—	2	2	no	—
133	M₁₆×C₄₃	—	4	4	no	—
134	C₂×C₈×C₄₃	—	2	2	no	—
135	C₂×C₈×C₄₃	—	4	4	no	—
136	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₄₃	#41	1	2	yes	—
143	C₄²×C₄₃	—	2	1	no	—
144	C₄²×C₄₃	C₂×D₄	1	2	yes	—
145	C₂²⋊Dic₄₃	—	2	4	no	—
146	#10621885	—	2	4	no	—
147	#10621884	—	2	4	no	—
148	#10621883	—	2	4	no	—
149	#10621882	—	2	4	no	—
150	(C₂×D₄₃)⋊C₄	—	2	4	no	—
151	Dic₄₃⋊C₄	—	2	4	no	—
152	C₄×Dic₄₃	—	2	1	no	—
153	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
156	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
157	#10621877	—	2	2	no	—
158	#10621877	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	1	no	—
160	C₂×C₄₃⋊C₈	—	2	1	no	—
161	C₂×C₄₃⋊C₈	—	2	2	no	—
162	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
165	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
166	C₂×C₄₃⋊C₈	#41	1	2	yes	—
167	Dic₁₇₂	—	2	2	no	—
168	D₃₄₄	—	2	2	no	—
169	#10621873	—	2	4	no	—
170	#10621872	—	4	4	no	—
171	C₈×D₄₃	—	4	4	no	—
172	C₂³×C₄₃	—	2	2	no	—
173	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
174	C₂²×D₄₃	—	2	2	no	—
175	Q₈×C₄₃	—	2	2	no	—
176	Q₈×C₄₃	—	2	2	no	—
177	D₄×C₄₃	—	2	2	no	—
178	D₄×C₄₃	—	2	2	no	—
179	D₄×C₄₃	—	4	2	no	—
180	D₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	2	2	no	—
182	C₂×C₄×C₄₃	—	2	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₄₃	—	4	2	no	—
193	C₂²⋊D₄₃	—	4	2	no	—
194	C₂²⋊D₄₃	—	8	4	no	—
195	C₂×Dic₄₃	—	2	2	no	—
196	C₂×Dic₄₃	—	2	2	no	—
197	C₂×Dic₄₃	—	4	2	no	—
198	C₂×Dic₄₃	—	4	2	no	—
199	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
200	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
201	D₁₇₂	—	2	2	no	—
202	D₁₇₂	—	2	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	C₈×C₄₃	C₄×D₄	1	2	yes	—
209	C₈×C₄₃	C₄×D₄	1	2	yes	—
210	C₈×C₄₃	#127	1	4	yes	—
211	C₄₃⋊C₈	—	2	2	no	—
212	C₄₃⋊C₈	—	4	2	no	—
213	C₄₃⋊C₈	C₄×D₄	1	2	yes	—
214	C₄₃⋊C₈	C₄×D₄	1	2	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	—	4	2	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
227	C₄×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
228	C₄×C₄₃	C₂×#127	1	1	yes	characteristic
229	C₄×C₄₃	#532	1	1	yes	characteristic
230	Dic₄₃	—	2	2	no	—
231	Dic₄₃	—	2	2	no	—
232	Dic₄₃	—	4	2	no	—
233	Dic₄₃	—	4	2	no	—
234	#3147	—	43	1	no	—
235	C₂×#444	—	43	1	no	—
236	C₂×#444	D₄₃	1	1	yes	characteristic, complemented
237	C₂×#443	—	43	2	no	—
238	#2932	—	43	2	no	—
239	#1975	—	43	1	no	—
240	#1975	—	43	1	no	—
241	#1974	—	43	2	no	—
242	#1963	—	43	2	no	—
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	1	no	—
253	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
254	C₂×#131	—	43	2	no	—
255	C₂×#131	C₂×D₄₃	1	2	yes	—
256	#532	—	43	2	no	—
257	#495	—	43	1	no	—
258	#495	—	43	2	no	—
259	#495	—	43	1	no	—
260	#494	—	43	1	no	—
261	#493	—	43	1	no	—
262	#492	—	43	2	no	—
263	#444	—	2	4	no	—
264	#444	—	86	4	no	—
265	#443	—	86	8	no	—
266	#435	—	86	4	no	—
267	#435	—	86	4	no	—
268	C₂×#108	—	43	2	no	—
269	C₂×#108	—	43	1	no	—
270	C₂×#108	C₂×D₄₃	1	1	yes	characteristic
271	#423	—	43	2	no	—
272	C₂×#104	—	43	2	no	—
273	C₂×#104	—	43	2	no	—
274	C₂×#104	—	43	2	no	—
275	C₂×#104	C₂×D₄₃	1	2	yes	—
276	#408	—	43	2	no	—
277	#408	—	43	2	no	—
278	C₂×#97	—	43	1	no	—
279	C₂×#97	—	43	1	no	—
280	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
281	C₂×C₄×C₈	—	43	1	no	—
282	C₂×C₄×C₈	—	43	1	no	—
283	C₂×C₄×C₈	—	43	1	no	—
284	#376	—	43	1	no	—
285	C₄₃	#21707	1	1	yes	characteristic, complemented, Sylow
286	C₂×#41	—	43	2	no	—
287	C₂×#41	C₂²×D₄₃	1	2	yes	—
288	#135	—	2	2	no	—
289	#135	—	2	2	no	—
290	#135	—	86	4	no	—
291	#135	—	86	4	no	—
292	#135	—	86	2	no	—
293	#135	—	86	2	no	—
294	C₂×Q₁₆	—	43	2	no	—
295	C₂×Q₁₆	—	43	1	no	—
296	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic
297	C₂×SD₁₆	—	43	2	no	—
298	C₂×SD₁₆	—	43	2	no	—
299	C₂×SD₁₆	—	43	2	no	—
300	C₂×SD₁₆	C₄×D₄₃	1	2	yes	—
301	C₂×D₈	—	43	2	no	—
302	C₂×D₈	—	43	1	no	—
303	C₂×D₈	C₄×D₄₃	1	1	yes	characteristic
304	#131	—	2	4	no	—
305	#131	—	2	4	no	—
306	#131	—	86	4	no	—
307	#131	—	86	4	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂×M₁₆	—	43	2	no	—
310	C₂×M₁₆	—	86	2	no	—
311	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	43	1	no	—
314	C₂²×C₈	—	43	1	no	—
315	C₂²×C₈	—	86	2	no	—
316	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₄⋊Q₈	—	43	2	no	—
319	#127	—	43	2	no	—
320	#124	—	43	2	no	—
321	#124	—	43	2	no	—
322	#121	—	86	4	no	—
323	C₄×D₄	—	86	4	no	—
324	C₂×C₄²	—	43	1	no	—
325	C₂×C₄²	—	43	1	no	—
326	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
327	#108	—	2	2	no	—
328	#108	—	86	4	no	—
329	#108	—	86	2	no	—
330	C₄⋊C₈	—	86	4	no	—
331	#104	—	2	4	no	—
332	#104	—	86	4	no	—
333	#104	—	86	4	no	—
334	#104	—	86	4	no	—
335	C₂²⋊C₈	—	86	4	no	—
336	C₂²⋊C₈	—	86	4	no	—
337	#97	—	43	4	no	—
338	#97	—	86	2	no	—
339	#97	C₂²⋊D₄₃	1	4	yes	complemented
340	C₄×C₈	—	43	1	no	—
341	C₄×C₈	—	43	1	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	43	1	no	—
344	C₄×C₈	—	43	4	no	—
345	C₄×C₈	—	86	2	no	—
346	#95	—	86	2	no	—
347	#41	—	2	2	no	—
348	#41	—	2	2	no	—
349	#41	—	2	2	no	—
350	#41	—	2	2	no	—
351	#41	—	86	2	no	—
352	#41	—	86	2	no	—
353	#41	—	86	2	no	—
354	#41	—	86	2	no	—
355	C₂×Q₈	—	43	2	no	—
356	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
357	C₂×D₄	—	2	2	no	—
358	C₂×D₄	—	43	2	no	—
359	C₂×D₄	—	86	4	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	2	no	—
364	C₂²×C₄	—	43	2	no	—
365	C₂²×C₄	—	86	1	no	—
366	C₂²×C₄	—	86	2	no	—
367	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
368	Q₁₆	—	2	2	no	—
369	Q₁₆	—	86	4	no	—
370	Q₁₆	—	86	2	no	—
371	SD₁₆	—	2	4	no	—
372	SD₁₆	—	86	4	no	—
373	SD₁₆	—	86	4	no	—
374	SD₁₆	—	86	4	no	—
375	D₈	—	2	2	no	—
376	D₈	—	86	4	no	—
377	D₈	—	86	2	no	—
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	4	4	no	—
381	M₁₆	—	86	2	no	—
382	M₁₆	—	86	2	no	—
383	M₁₆	—	172	4	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	4	4	no	—
386	C₂×C₈	—	43	1	no	—
387	C₂×C₈	—	43	1	no	—
388	C₂×C₈	—	43	2	no	—
389	C₂×C₈	—	43	2	no	—
390	C₂×C₈	—	43	2	no	—
391	C₂×C₈	—	86	1	no	—
392	C₂×C₈	—	86	1	no	—
393	C₂×C₈	—	86	2	no	—
394	C₂×C₈	—	172	4	no	—
395	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
396	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
397	C₂×C₈	#10621898	1	2	yes	—
398	C₂×C₈	D₄×D₄₃	1	2	yes	—
399	C₂×C₈	D₄×D₄₃	1	2	yes	—
400	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
401	C₂×C₈	C₂×C₂²⋊D₄₃	1	2	yes	—
402	C₄⋊C₄	—	86	4	no	—
403	C₂²⋊C₄	—	86	4	no	—
404	C₂²⋊C₄	—	86	4	no	—
405	C₄²	—	2	1	no	—
406	C₄²	—	43	1	no	—
407	C₄²	—	43	1	no	—
408	C₄²	—	43	2	no	—
409	C₄²	—	43	2	no	—
410	C₄²	—	86	1	no	—
411	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
412	C₂³	—	2	2	no	—
413	C₂³	—	86	2	no	—
414	C₂³	#41×D₄₃	1	1	yes	characteristic
415	Q₈	—	2	2	no	—
416	Q₈	—	2	2	no	—
417	Q₈	—	86	2	no	—
418	Q₈	—	86	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	2	2	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	86	2	no	—
424	D₄	—	86	2	no	—
425	D₄	—	344	4	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	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	43	2	no	—
434	C₂×C₄	—	43	2	no	—
435	C₂×C₄	—	86	2	no	—
436	C₂×C₄	—	86	2	no	—
437	C₂×C₄	—	172	2	no	—
438	C₂×C₄	—	172	2	no	—
439	C₂×C₄	—	172	2	no	—
440	C₂×C₄	—	172	2	no	—
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	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
445	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
446	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
447	C₈	—	4	2	no	—
448	C₈	—	43	2	no	—
449	C₈	—	43	2	no	—
450	C₈	—	86	2	no	—
451	C₈	—	172	2	no	—
452	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
453	C₈	C₄×C₂²⋊D₄₃	1	2	yes	—
454	C₈	#13063321	1	4	yes	—
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	C₄×D₄×D₄₃	1	1	yes	characteristic
461	C₂²	#14583445	1	1	yes	characteristic
462	C₂²	#14583446	1	1	yes	characteristic
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	86	2	no	—
466	C₄	—	86	2	no	—
467	C₄	—	172	2	no	—
468	C₄	—	172	2	no	—
469	C₄	C₄×D₄×D₄₃	1	1	yes	characteristic
470	C₄	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
471	C₄	C₂×#13063321	1	1	yes	characteristic
472	C₄	#14583446	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	C₄×#13063321	1	1	yes	characteristic
478	C₂	#19143509	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₂×C₄₃×#444	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19145019	C₂
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₂×#444	D₄₃
hypocenter	C₄₃	#21707
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
2. C₂×#14583022	C₂	semidirect
3. C₂×#14583014	C₂	semidirect
4. #19143311	C₂	semidirect
5. #19135489	C₂	semidirect
6. #19135486	C₂	semidirect
7. #19135480	C₂	semidirect
8. #19135425	C₂	semidirect
9. #19134765	C₂	semidirect
10. #19134283	C₂	semidirect
11. C₂×C₄₃×#444	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
88. C₈×Dic₄₃	D₄	semidirect
106. #97×C₄₃	D₄	semidirect
236. C₂×#444	D₄₃	semidirect
285. C₄₃	#21707	semidirect
339. #97	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×#14583022	2
C₂×#14583014	2
#19143311	2
#19135489	2
#19135486	2
#19135480	2
#19135425	2
#19134765	2
#19134283	2
C₂×C₄₃×#444	2
#21707	43