Subgroups — #25067769

Order 11008.

640 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144656	C₂	1	1	yes	maximal, characteristic
2	#19143716	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143661	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133487	C₂	1	2	yes	maximal, complemented
5	#19133461	C₂	1	2	yes	maximal, complemented
6	#19133454	C₂	1	2	yes	maximal, complemented
7	C₈×D₃₄₄	C₂	1	2	yes	maximal, complemented
8	#19133384	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133047	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132978	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583449	C₂²	1	1	yes	characteristic
13	C₄×#10621898	C₂²	1	1	yes	characteristic
14	#14583224	C₄	1	2	yes	—
15	#14583195	C₄	1	1	yes	characteristic
16	#14583190	C₄	1	1	yes	characteristic
17	#14583100	C₄	1	1	yes	characteristic
18	#14583095	C₄	1	1	yes	characteristic
19	#14583046	C₄	1	2	yes	—
20	#14583029	C₂²	1	2	yes	—
21	C₄×#10621873	C₂²	1	2	yes	—
22	C₄×D₃₄₄	C₂²	1	2	yes	—
23	#14582978	C₂²	1	2	yes	—
24	#14582976	—	2	1	no	—
25	#14582973	—	2	2	no	—
26	C₈×D₁₇₂	C₂²	1	2	yes	—
27	C₈×D₁₇₂	C₂²	1	2	yes	—
28	#14582964	—	2	1	no	—
29	#14582955	—	2	1	no	—
30	#14582952	C₂²	1	1	yes	characteristic
31	#14582923	C₂²	1	1	yes	characteristic
32	C₄⋊C₈×D₄₃	—	2	1	no	—
33	#14582864	—	2	2	no	—
34	#14582652	C₂²	1	2	yes	—
35	#14582650	C₂²	1	2	yes	—
36	#14582631	C₂²	1	1	yes	characteristic
37	#14582631	C₂²	1	1	yes	characteristic
38	#14582628	C₂²	1	2	yes	—
39	#14582628	C₂²	1	1	yes	characteristic
40	#14582628	C₂²	1	2	yes	—
41	#14582628	C₂²	1	1	yes	characteristic
42	C₄₃×#431	C₂²	1	1	yes	characteristic
43	C₄₃×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#322	C₂²	1	2	yes	—
46	C₈²×C₄₃	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
49	C₂×#10621873	C₂×C₄	1	2	yes	—
50	C₂×D₃₄₄	C₂×C₄	1	2	yes	—
51	C₂×#10621877	—	2	1	no	—
52	C₂×#10621872	—	2	2	no	—
53	C₂×C₈×D₄₃	—	2	2	no	—
54	C₂×C₈×D₄₃	—	2	2	no	—
55	#13063325	C₂×C₄	1	1	yes	characteristic
56	#13063322	C₂×C₄	1	1	yes	characteristic
57	#13063313	—	2	1	no	—
58	#13063299	—	2	1	no	—
59	#13063299	C₂×C₄	1	2	yes	—
60	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
62	C₄×D₁₇₂	—	2	1	no	—
63	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
64	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
65	C₄×D₁₇₂	C₂³	1	2	yes	—
66	C₄×C₂²⋊D₄₃	—	2	1	no	—
67	C₄×C₂²⋊D₄₃	—	2	1	no	—
68	#13063284	C₂×C₄	1	1	yes	characteristic
69	#13063282	—	2	1	no	—
70	C₄²×D₄₃	—	2	1	no	—
71	#13063259	C₂×C₄	1	2	yes	—
72	#13063257	C₂×C₄	1	2	yes	—
73	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
75	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₃⋊C₈	—	2	2	no	—
78	#13063250	C₂×C₄	1	2	yes	—
79	#13063247	C₂×C₄	1	2	yes	—
80	#13063247	C₂×C₄	1	2	yes	—
81	#13063247	C₂×C₄	1	2	yes	—
82	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
83	(C₂×D₄₃)⋊C₈	—	2	2	no	—
84	(C₂×D₄₃)⋊C₈	—	2	2	no	—
85	(C₂×D₄₃)⋊C₈	—	2	2	no	—
86	#13063235	—	2	2	no	—
87	C₄×C₄₃⋊C₈	—	2	1	no	—
88	C₂²×C₈×C₄₃	—	2	1	no	—
89	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
91	C₄⋊C₈×C₄₃	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₃	D₄	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
95	C₂²⋊C₈×C₄₃	D₄	1	2	yes	—
96	C₄×C₈×C₄₃	—	2	1	no	—
97	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₃	C₂³	1	2	yes	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₃	—	2	1	no	—
105	C₂×C₂²⋊D₄₃	—	2	2	no	—
106	#10621898	—	2	2	no	—
107	#10621898	—	4	1	no	—
108	#10621898	—	8	1	no	—
109	#10621898	—	8	1	no	—
110	C₂×D₁₇₂	—	2	1	no	—
111	C₂×D₁₇₂	—	2	1	no	—
112	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
113	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₃	—	2	1	no	—
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	2	1	no	—
117	C₂×C₄×D₄₃	—	2	2	no	—
118	C₂×Dic₈₆	—	2	1	no	—
119	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
127	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₃	#41	1	1	yes	characteristic
130	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₄₃	—	2	1	no	—
132	(C₂×D₄₃)⋊C₄	—	2	1	no	—
133	(C₂×D₄₃)⋊C₄	—	2	2	no	—
134	(C₂×D₄₃)⋊C₄	—	2	1	no	—
135	(C₂×D₄₃)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	1	no	—
137	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
140	Dic₄₃⋊C₄	—	2	1	no	—
141	Dic₄₃⋊C₄	—	2	1	no	—
142	C₄×Dic₄₃	—	2	1	no	—
143	C₄×Dic₄₃	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	#10621877	—	8	1	no	—
146	C₂×C₄₃⋊C₈	—	2	1	no	—
147	C₂×C₄₃⋊C₈	—	2	1	no	—
148	C₂×C₄₃⋊C₈	—	2	2	no	—
149	D₃₄₄	—	2	4	no	—
150	#10621873	—	4	2	no	—
151	#10621872	—	8	2	no	—
152	C₈×D₄₃	—	8	2	no	—
153	C₈×D₄₃	—	8	2	no	—
154	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂²×D₄₃	—	2	1	no	—
156	C₂²×D₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₄₃	—	4	2	no	—
169	C₂²⋊D₄₃	—	8	2	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	—	2	1	no	—
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	2	no	—
174	D₁₇₂	—	2	2	no	—
175	D₁₇₂	—	2	1	no	—
176	D₁₇₂	—	2	2	no	—
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	8	1	no	—
179	D₁₇₂	#131	1	2	yes	—
180	C₄×D₄₃	—	4	2	no	—
181	C₄×D₄₃	—	4	1	no	—
182	C₄×D₄₃	—	4	2	no	—
183	C₄×D₄₃	—	4	2	no	—
184	C₄×D₄₃	—	4	1	no	—
185	C₄×D₄₃	—	4	2	no	—
186	Dic₈₆	—	2	1	no	—
187	Dic₈₆	—	2	1	no	—
188	Dic₈₆	—	8	1	no	—
189	C₈×C₄₃	—	2	2	no	—
190	C₈×C₄₃	—	2	2	no	—
191	C₈×C₄₃	—	2	2	no	—
192	C₈×C₄₃	—	2	2	no	—
193	C₈×C₄₃	—	2	2	no	—
194	C₈×C₄₃	—	2	2	no	—
195	C₄₃⋊C₈	—	4	1	no	—
196	C₄₃⋊C₈	—	4	2	no	—
197	C₄₃⋊C₈	—	4	1	no	—
198	#18015	—	43	1	no	maximal, Sylow
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₄₃	—	2	2	no	—
204	C₂×D₄₃	—	4	1	no	—
205	C₂×D₄₃	—	4	1	no	—
206	C₂×D₄₃	—	4	2	no	—
207	C₂×D₄₃	—	4	2	no	—
208	C₂×D₄₃	—	4	2	no	—
209	C₄×C₄₃	—	2	1	no	—
210	C₄×C₄₃	—	2	1	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	#443	1	2	yes	—
213	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
214	C₄×C₄₃	#568	1	1	yes	characteristic
215	C₄×C₄₃	#576	1	1	yes	characteristic
216	C₄×C₄₃	#577	1	1	yes	characteristic
217	Dic₄₃	—	4	1	no	—
218	Dic₄₃	—	4	2	no	—
219	Dic₄₃	—	4	1	no	—
220	Dic₄₃	—	4	1	no	—
221	#3106	—	43	1	no	—
222	#2990	—	43	1	no	—
223	#2979	—	43	1	no	—
224	#1590	—	43	2	no	—
225	#1586	—	43	2	no	—
226	#1585	—	43	2	no	—
227	C₈×D₈	—	43	2	no	—
228	#1574	—	43	1	no	—
229	#1492	—	43	1	no	—
230	#1476	—	43	1	no	—
231	#1450	D₄₃	1	1	yes	characteristic, complemented
232	C₂×C₄₃	—	4	1	no	—
233	C₂×C₄₃	#2933	1	1	yes	characteristic
234	C₂×C₄₃	#2946	1	1	yes	characteristic
235	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
236	D₄₃	—	4	2	no	—
237	D₄₃	—	8	2	no	—
238	#532	—	43	1	no	—
239	C₄×#41	—	43	1	no	—
240	#482	—	43	2	no	—
241	#477	—	43	1	no	—
242	#476	—	43	1	no	—
243	#460	—	43	1	no	—
244	#459	—	43	1	no	—
245	#449	—	43	2	no	—
246	#446	—	43	2	no	—
247	C₄×SD₁₆	—	43	2	no	—
248	C₄×D₈	—	43	2	no	—
249	#436	—	43	2	no	—
250	#436	—	86	1	no	—
251	#435	—	86	2	no	—
252	C₈×D₄	—	43	2	no	—
253	C₈×D₄	—	43	2	no	—
254	C₈×D₄	—	86	1	no	—
255	#432	—	86	1	no	—
256	#431	—	43	1	no	—
257	#431	C₂×D₄₃	1	1	yes	characteristic
258	#431	C₂×D₄₃	1	1	yes	characteristic
259	#423	—	43	1	no	—
260	C₂×C₄⋊C₈	—	86	1	no	—
261	#408	—	86	2	no	—
262	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
263	#335	—	43	2	no	—
264	#334	—	43	2	no	—
265	Q₈⋊C₈	—	43	1	no	—
266	Q₈⋊C₈	—	43	1	no	—
267	D₄⋊C₈	—	43	1	no	—
268	D₄⋊C₈	—	43	2	no	—
269	D₄⋊C₈	—	43	2	no	—
270	D₄⋊C₈	—	43	1	no	—
271	#322	C₂×D₄₃	1	2	yes	—
272	C₈²	C₂×D₄₃	1	2	yes	—
273	C₄₃	#18015	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	43	1	no	—
275	C₂×#41	—	86	1	no	—
276	C₂×SD₁₆	—	43	2	no	—
277	C₂×D₈	—	43	2	no	—
278	C₂×M₁₆	—	86	1	no	—
279	C₂×M₁₆	—	86	2	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	86	2	no	—
282	C₂²×C₈	—	86	2	no	—
283	C₄⋊Q₈	—	43	1	no	—
284	#127	—	43	1	no	—
285	#124	—	86	1	no	—
286	#121	—	43	2	no	—
287	#121	—	86	1	no	—
288	C₄×Q₈	—	43	1	no	—
289	C₄×Q₈	—	43	1	no	—
290	C₄×D₄	—	43	1	no	—
291	C₄×D₄	—	43	1	no	—
292	C₄×D₄	—	43	2	no	—
293	C₄×D₄	—	86	1	no	—
294	C₄×D₄	—	86	1	no	—
295	C₄×D₄	—	86	1	no	—
296	#117	—	43	1	no	—
297	#117	—	86	1	no	—
298	C₂×C₄²	—	86	1	no	—
299	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
300	#107	—	43	2	no	—
301	#106	—	43	2	no	—
302	C₄⋊C₈	—	43	2	no	—
303	C₄⋊C₈	—	43	1	no	—
304	C₄⋊C₈	—	43	1	no	—
305	C₄⋊C₈	—	86	2	no	—
306	C₄⋊C₈	—	86	1	no	—
307	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
308	C₄⋊C₈	C₄×D₄₃	1	1	yes	characteristic
309	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
310	C₄⋊C₈	D₁₇₂	1	1	yes	characteristic
311	#103	—	43	2	no	—
312	#102	—	43	2	no	—
313	#102	—	43	2	no	—
314	#102	—	43	2	no	—
315	C₂²⋊C₈	—	86	1	no	—
316	C₂²⋊C₈	—	86	2	no	—
317	C₂²⋊C₈	—	86	2	no	—
318	C₂²⋊C₈	—	86	2	no	—
319	C₂²⋊C₈	C₄×D₄₃	1	2	yes	—
320	C₂²⋊C₈	D₁₇₂	1	2	yes	—
321	#97	—	86	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	86	1	no	—
324	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
325	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₄₃	1	2	yes	—
327	C₄×C₈	C₂²×D₄₃	1	2	yes	—
328	#41	—	86	2	no	—
329	#41	—	344	1	no	—
330	#41	—	344	1	no	—
331	#41	—	172	1	no	—
332	C₂×Q₈	—	43	1	no	—
333	C₂×Q₈	—	86	1	no	—
334	C₂×D₄	—	43	1	no	—
335	C₂×D₄	—	43	2	no	—
336	C₂×D₄	—	86	2	no	—
337	C₂×D₄	—	86	1	no	—
338	C₂×D₄	—	86	1	no	—
339	C₂×D₄	—	86	1	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	2	no	—
344	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₁₇₂	1	1	yes	characteristic
346	C₂²×C₄	#10621898	1	1	yes	characteristic
347	SD₁₆	—	172	2	no	—
348	D₈	—	86	4	no	—
349	M₁₆	—	344	2	no	—
350	M₁₆	—	344	1	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	86	1	no	—
355	C₂×C₈	—	86	1	no	—
356	C₂×C₈	—	86	2	no	—
357	C₂×C₈	—	344	2	no	—
358	C₂×C₈	—	344	2	no	—
359	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
360	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
361	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
362	C₂×C₈	C₂×D₁₇₂	1	2	yes	—
363	C₄⋊C₄	—	43	1	no	—
364	C₄⋊C₄	—	43	1	no	—
365	C₄⋊C₄	—	43	2	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	—	86	1	no	—
368	C₄⋊C₄	—	86	1	no	—
369	C₂²⋊C₄	—	86	1	no	—
370	C₂²⋊C₄	—	86	1	no	—
371	C₂²⋊C₄	—	86	2	no	—
372	C₂²⋊C₄	—	86	1	no	—
373	C₂²⋊C₄	—	86	2	no	—
374	C₄²	—	86	1	no	—
375	C₄²	—	86	1	no	—
376	C₄²	—	86	1	no	—
377	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
378	C₄²	C₂×D₁₇₂	1	1	yes	characteristic
379	C₄²	#10621898	1	1	yes	characteristic
380	C₄²	C₂³×D₄₃	1	1	yes	characteristic
381	C₂³	—	86	1	no	—
382	C₂³	—	86	2	no	—
383	C₂³	C₄×D₁₇₂	1	1	yes	characteristic
384	Q₈	—	86	1	no	—
385	Q₈	—	86	1	no	—
386	Q₈	—	344	1	no	—
387	D₄	—	43	2	no	—
388	D₄	—	86	2	no	—
389	D₄	—	86	1	no	—
390	D₄	—	86	2	no	—
391	D₄	—	344	1	no	—
392	D₄	—	344	2	no	—
393	D₄	—	172	2	no	—
394	D₄	—	172	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	86	1	no	—
401	C₂×C₄	—	86	1	no	—
402	C₂×C₄	—	86	1	no	—
403	C₂×C₄	—	86	2	no	—
404	C₂×C₄	—	172	2	no	—
405	C₂×C₄	—	172	1	no	—
406	C₂×C₄	—	172	2	no	—
407	C₂×C₄	—	172	2	no	—
408	C₂×C₄	—	172	1	no	—
409	C₂×C₄	—	172	2	no	—
410	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
411	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
412	C₂×C₄	C₄×D₁₇₂	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₁₇₂	1	1	yes	characteristic
415	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	172	1	no	—
423	C₈	—	172	2	no	—
424	C₈	—	172	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	86	2	no	—
429	C₂²	—	172	2	no	—
430	C₂²	—	172	2	no	—
431	C₂²	—	172	2	no	—
432	C₂²	—	172	1	no	—
433	C₂²	—	172	1	no	—
434	C₂²	C₂×C₄×D₁₇₂	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	172	2	no	—
439	C₄	—	172	1	no	—
440	C₄	—	172	1	no	—
441	C₄	—	172	1	no	—
442	C₄	#14583017	1	2	yes	—
443	C₄	#131×D₄₃	1	1	yes	characteristic
444	C₄	#14583664	1	1	yes	characteristic
445	C₄	#14583704	1	1	yes	characteristic
446	C₄	#14583711	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	344	2	no	—
449	C₂	—	172	2	no	—
450	C₂	#19143323	1	1	yes	characteristic
451	C₂	#19143429	1	1	yes	characteristic
452	C₂	C₂×#14583017	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₇₂
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1450	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19144656	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1450	D₄₃
hypocenter	C₄₃	#18015
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1450

Complements

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

N	H ≅ G/N	type
2. #19143716	C₂	semidirect
3. #19143661	C₂	semidirect
4. #19133487	C₂	semidirect
5. #19133461	C₂	semidirect
6. #19133454	C₂	semidirect
7. C₈×D₃₄₄	C₂	semidirect
8. #19133384	C₂	semidirect
9. #19133047	C₂	semidirect
10. #19132978	C₂	semidirect
11. C₄₃×#1450	C₂	semidirect
231. #1450	D₄₃	semidirect
273. C₄₃	#18015	semidirect

Maximal subgroups

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

subgroup	index
#19144656	2
#19143716	2
#19143661	2
#19133487	2
#19133461	2
#19133454	2
C₈×D₃₄₄	2
#19133384	2
#19133047	2
#19132978	2
C₄₃×#1450	2
#18015	43