Subgroups — #25068631

Order 11008.

644 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145170	C₂	1	1	yes	maximal, characteristic
2	#19143662	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143661	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133506	C₂	1	2	yes	maximal, complemented
5	#19133427	C₂	1	2	yes	maximal, complemented
6	#19133421	C₂	1	2	yes	maximal, complemented
7	#19133416	C₂	1	2	yes	maximal, complemented
8	#19133341	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133013	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132882	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	#14583449	C₂²	1	1	yes	characteristic
13	#14583302	C₄	1	1	yes	characteristic
14	#14583275	C₄	1	1	yes	characteristic
15	#14583247	C₄	1	1	yes	characteristic
16	#14583245	C₄	1	1	yes	characteristic
17	#14583133	C₄	1	2	yes	—
18	#14583133	C₄	1	2	yes	—
19	C₄×#10621882	C₂²	1	2	yes	—
20	C₄×#10621882	C₂²	1	2	yes	—
21	#14582978	—	2	1	no	—
22	#14582977	—	2	1	no	—
23	#14582977	C₂²	1	2	yes	—
24	#14582976	C₂²	1	2	yes	—
25	C₈×D₁₇₂	—	2	1	no	—
26	D₄×C₄₃⋊C₈	—	2	1	no	—
27	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
28	#14582964	C₂²	1	2	yes	—
29	#14582952	C₂²	1	1	yes	characteristic
30	#14582952	C₂²	1	1	yes	characteristic
31	#14582866	—	2	2	no	—
32	#14582864	—	2	2	no	—
33	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
34	#14582651	C₂²	1	1	yes	characteristic
35	#14582651	C₂²	1	1	yes	characteristic
36	#14582649	C₂²	1	1	yes	characteristic
37	#14582649	C₂²	1	1	yes	characteristic
38	#14582628	C₂²	1	2	yes	—
39	#14582628	C₂²	1	2	yes	—
40	#14582621	C₂²	1	2	yes	—
41	#14582621	C₂²	1	2	yes	—
42	C₄₃×#532	C₂²	1	1	yes	characteristic
43	C₄₃×#431	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
46	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621882	C₂×C₄	1	2	yes	—
49	C₂×#10621882	C₂×C₄	1	2	yes	—
50	C₂×#10621877	—	2	2	no	—
51	C₂×#10621872	—	2	2	no	—
52	C₂²×C₄₃⋊C₈	—	2	2	no	—
53	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₄₃	—	2	2	no	—
56	#13063325	C₂×C₄	1	1	yes	characteristic
57	#13063322	C₂×C₄	1	1	yes	characteristic
58	#13063313	—	2	1	no	—
59	#13063299	—	2	1	no	—
60	#13063299	C₂×C₄	1	2	yes	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	C₂³	1	2	yes	—
63	#13063258	C₂×C₄	1	2	yes	—
64	#13063258	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	#13063246	C₂×C₄	1	2	yes	—
70	#13063246	C₂×C₄	1	2	yes	—
71	#13063245	C₂×C₄	1	2	yes	—
72	#13063245	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
77	(C₂×D₄₃)⋊C₈	—	2	2	no	—
78	(C₂×D₄₃)⋊C₈	—	2	2	no	—
79	C₄×C₄₃⋊C₈	—	2	1	no	—
80	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
85	C₂×#41×C₄₃	—	2	1	no	—
86	C₂×M₁₆×C₄₃	—	2	1	no	—
87	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
88	#127×C₄₃	C₂×C₄	1	1	yes	characteristic
89	#124×C₄₃	—	2	1	no	—
90	#121×C₄₃	—	2	1	no	—
91	#121×C₄₃	C₂×C₄	1	2	yes	—
92	C₄×D₄×C₄₃	—	2	1	no	—
93	C₄×D₄×C₄₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
97	C₂²⋊C₈×C₄₃	—	2	1	no	—
98	#97×C₄₃	—	2	1	no	—
99	C₄×C₈×C₄₃	—	2	1	no	—
100	C₄×C₈×C₄₃	C₂³	1	2	yes	—
101	#41×C₄₃	—	8	1	no	—
102	#41×C₄₃	—	8	1	no	—
103	C₂×Q₈×C₄₃	—	2	1	no	—
104	C₂×D₄×C₄₃	—	2	1	no	—
105	C₂×D₄×C₄₃	—	2	1	no	—
106	C₂×D₄×C₄₃	—	2	2	no	—
107	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
112	C₂×C₂²⋊D₄₃	—	2	2	no	—
113	#10621898	—	8	1	no	—
114	#10621898	—	8	1	no	—
115	C₂×D₁₇₂	—	2	1	no	—
116	C₂×D₁₇₂	—	2	1	no	—
117	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₄₃	—	2	2	no	—
119	C₂×Dic₈₆	—	2	1	no	—
120	M₁₆×C₄₃	—	4	2	no	—
121	C₂×C₈×C₄₃	—	2	1	no	—
122	C₂×C₈×C₄₃	—	2	1	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	2	1	no	—
125	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
126	C₂²⋊C₄×C₄₃	—	2	2	no	—
127	C₂²⋊C₄×C₄₃	—	2	2	no	—
128	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₃	#41	1	1	yes	characteristic
131	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
132	#10621882	—	2	4	no	—
133	#10621882	—	4	2	no	—
134	(C₂×D₄₃)⋊C₄	—	2	2	no	—
135	(C₂×D₄₃)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₃	—	2	1	no	—
137	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
138	#10621877	—	8	2	no	—
139	C₂×C₄₃⋊C₈	—	2	2	no	—
140	C₂×C₄₃⋊C₈	—	2	1	no	—
141	C₂×C₄₃⋊C₈	—	2	1	no	—
142	C₂×C₄₃⋊C₈	—	4	1	no	—
143	C₂×C₄₃⋊C₈	—	8	2	no	—
144	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
149	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
150	#10621872	—	8	2	no	—
151	C₈×D₄₃	—	8	2	no	—
152	C₂³×C₄₃	—	2	2	no	—
153	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
154	C₂²×D₄₃	—	2	2	no	—
155	Q₈×C₄₃	—	8	1	no	—
156	D₄×C₄₃	—	2	2	no	—
157	D₄×C₄₃	—	2	2	no	—
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	8	1	no	—
160	D₄×C₄₃	—	8	2	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	1	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	1	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₄₃	—	8	2	no	—
176	C₂×Dic₄₃	—	2	2	no	—
177	D₁₇₂	—	2	2	no	—
178	D₁₇₂	—	2	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	8	1	no	—
181	C₄×D₄₃	—	4	2	no	—
182	C₄×D₄₃	—	4	2	no	—
183	Dic₈₆	—	8	1	no	—
184	C₈×C₄₃	—	4	2	no	—
185	C₈×C₄₃	—	4	1	no	—
186	C₈×C₄₃	—	4	1	no	—
187	C₄₃⋊C₈	—	2	1	no	—
188	C₄₃⋊C₈	—	2	1	no	—
189	C₄₃⋊C₈	—	2	1	no	—
190	C₄₃⋊C₈	—	2	2	no	—
191	C₄₃⋊C₈	—	2	2	no	—
192	C₄₃⋊C₈	—	4	1	no	—
193	C₄₃⋊C₈	—	4	1	no	—
194	C₄₃⋊C₈	#131	1	2	yes	—
195	#18091	—	43	1	no	maximal, Sylow
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	—	4	2	no	—
200	C₂²×C₄₃	—	4	2	no	—
201	C₂²×C₄₃	—	4	2	no	—
202	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₂×D₄₃	—	4	2	no	—
204	C₂×D₄₃	—	4	2	no	—
205	C₂×D₄₃	—	4	2	no	—
206	C₄×C₄₃	—	2	1	no	—
207	C₄×C₄₃	—	2	1	no	—
208	C₄×C₄₃	—	2	1	no	—
209	C₄×C₄₃	—	4	2	no	—
210	C₄×C₄₃	#444	1	2	yes	—
211	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
212	C₄×C₄₃	#568	1	1	yes	characteristic
213	C₄×C₄₃	#576	1	1	yes	characteristic
214	C₄×C₄₃	#576	1	1	yes	characteristic
215	Dic₄₃	—	4	2	no	—
216	#3169	—	43	1	no	—
217	#2979	—	43	1	no	—
218	#2979	—	43	1	no	—
219	#1594	—	43	2	no	—
220	#1581	—	43	2	no	—
221	#1581	—	43	2	no	—
222	#1580	—	43	2	no	—
223	#1564	—	43	1	no	—
224	#1484	—	43	1	no	—
225	#1484	D₄₃	1	1	yes	characteristic, complemented
226	#1451	—	43	1	no	—
227	C₂×C₄₃	—	4	1	no	—
228	C₂×C₄₃	—	8	2	no	—
229	C₂×C₄₃	#2935	1	1	yes	characteristic
230	C₂×C₄₃	#2948	1	1	yes	characteristic
231	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
232	D₄₃	—	8	2	no	—
233	#532	—	43	1	no	—
234	#532	C₂×D₄₃	1	1	yes	characteristic
235	#500	—	43	1	no	—
236	#493	—	43	1	no	—
237	#486	—	43	1	no	—
238	#486	—	43	1	no	—
239	#466	—	43	2	no	—
240	#466	—	43	2	no	—
241	C₄×D₈	—	43	2	no	—
242	C₄×D₈	—	43	2	no	—
243	#436	—	43	2	no	—
244	#436	—	43	2	no	—
245	#436	—	86	1	no	—
246	#436	—	86	1	no	—
247	C₈×D₄	—	43	2	no	—
248	C₈×D₄	—	43	2	no	—
249	C₈×D₄	—	86	1	no	—
250	C₈×D₄	—	86	1	no	—
251	#431	—	43	1	no	—
252	#431	—	43	1	no	—
253	#431	C₂×D₄₃	1	1	yes	characteristic
254	#408	—	86	2	no	—
255	#408	—	86	2	no	—
256	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
257	C₂×C₄×C₈	—	43	1	no	—
258	#335	—	43	1	no	—
259	#335	—	43	1	no	—
260	#334	—	43	1	no	—
261	#334	—	43	1	no	—
262	D₄⋊C₈	—	43	2	no	—
263	D₄⋊C₈	—	43	2	no	—
264	D₄⋊C₈	C₂×D₄₃	1	2	yes	—
265	D₄⋊C₈	C₂×D₄₃	1	2	yes	—
266	#322	—	43	2	no	—
267	#322	—	43	2	no	—
268	C₄₃	#18091	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	86	1	no	—
271	C₂×D₈	—	43	2	no	—
272	C₂×D₈	—	43	2	no	—
273	C₂×M₁₆	—	2	1	no	—
274	C₂×M₁₆	—	86	2	no	—
275	C₂×M₁₆	—	86	2	no	—
276	C₂²×C₈	—	43	1	no	—
277	C₂²×C₈	—	43	1	no	—
278	C₂²×C₈	—	86	2	no	—
279	C₂²×C₈	—	86	2	no	—
280	C₄⋊Q₈	—	43	1	no	—
281	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
282	#127	—	43	1	no	—
283	#127	C₄×D₄₃	1	1	yes	characteristic
284	#124	—	2	1	no	—
285	#124	—	86	1	no	—
286	#121	—	2	1	no	—
287	#121	—	43	2	no	—
288	#121	—	86	1	no	—
289	#121	C₄×D₄₃	1	2	yes	—
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	43	2	no	—
292	C₄×D₄	—	86	1	no	—
293	C₄×D₄	C₂²×D₄₃	1	2	yes	—
294	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
295	#107	—	43	2	no	—
296	#107	—	43	2	no	—
297	C₄⋊C₈	—	43	1	no	—
298	C₄⋊C₈	—	43	1	no	—
299	C₄⋊C₈	—	43	1	no	—
300	C₄⋊C₈	—	43	1	no	—
301	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
302	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
303	#102	—	43	2	no	—
304	#102	—	43	2	no	—
305	#102	—	43	2	no	—
306	#102	—	43	2	no	—
307	C₂²⋊C₈	—	2	1	no	—
308	C₂²⋊C₈	—	43	2	no	—
309	C₂²⋊C₈	—	86	2	no	—
310	C₂²⋊C₈	—	86	2	no	—
311	C₂²⋊C₈	—	86	2	no	—
312	C₂²⋊C₈	—	86	2	no	—
313	C₂²⋊C₈	—	86	1	no	—
314	#97	—	2	1	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	43	1	no	—
317	C₄×C₈	—	43	1	no	—
318	C₄×C₈	—	43	1	no	—
319	C₄×C₈	—	43	1	no	—
320	C₄×C₈	—	43	2	no	—
321	C₄×C₈	—	86	1	no	—
322	C₄×C₈	C₂²×D₄₃	1	2	yes	—
323	#41	—	8	1	no	—
324	#41	—	8	1	no	—
325	#41	—	344	1	no	—
326	#41	—	344	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	86	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	43	2	no	—
333	C₂×D₄	—	86	2	no	—
334	C₂×D₄	—	86	1	no	—
335	C₂×D₄	—	86	1	no	—
336	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	86	2	no	—
339	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
341	C₂²×C₄	#10621900	1	1	yes	characteristic
342	D₈	—	86	4	no	—
343	D₈	—	172	2	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	344	2	no	—
346	M₁₆	—	344	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	43	1	no	—
351	C₂×C₈	—	43	1	no	—
352	C₂×C₈	—	43	1	no	—
353	C₂×C₈	—	43	1	no	—
354	C₂×C₈	—	43	2	no	—
355	C₂×C₈	—	43	2	no	—
356	C₂×C₈	—	86	2	no	—
357	C₂×C₈	—	86	1	no	—
358	C₂×C₈	—	86	1	no	—
359	C₂×C₈	—	344	2	no	—
360	C₂×C₈	—	344	2	no	—
361	C₂×C₈	—	172	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	43	2	no	—
364	C₄⋊C₄	—	86	1	no	—
365	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	86	2	no	—
369	C₂²⋊C₄	—	86	2	no	—
370	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
371	C₄²	D₄×D₄₃	1	1	yes	characteristic
372	C₄²	#10621900	1	1	yes	characteristic
373	C₄²	C₂³×D₄₃	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	—	86	2	no	—
376	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
377	Q₈	—	8	1	no	—
378	Q₈	—	344	1	no	—
379	D₄	—	2	2	no	—
380	D₄	—	2	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	8	1	no	—
383	D₄	—	8	2	no	—
384	D₄	—	86	2	no	—
385	D₄	—	86	2	no	—
386	D₄	—	344	1	no	—
387	D₄	—	344	2	no	—
388	D₄	—	172	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	86	2	no	—
398	C₂×C₄	—	172	2	no	—
399	C₂×C₄	—	172	2	no	—
400	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
401	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
402	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
404	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	43	2	no	—
410	C₈	—	86	1	no	—
411	C₈	—	86	1	no	—
412	C₈	—	86	1	no	—
413	C₈	—	86	2	no	—
414	C₈	—	86	2	no	—
415	C₈	—	172	1	no	—
416	C₈	—	172	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	4	2	no	—
423	C₂²	—	172	2	no	—
424	C₂²	—	172	2	no	—
425	C₂²	—	172	2	no	—
426	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	4	2	no	—
431	C₄	—	172	2	no	—
432	C₄	#14583018	1	2	yes	—
433	C₄	#131×D₄₃	1	1	yes	characteristic
434	C₄	#14583664	1	1	yes	characteristic
435	C₄	#14583703	1	1	yes	characteristic
436	C₄	#14583703	1	1	yes	characteristic
437	C₂	—	4	1	no	—
438	C₂	—	8	2	no	—
439	C₂	—	344	2	no	—
440	C₂	#19143335	1	1	yes	characteristic
441	C₂	#19143443	1	1	yes	characteristic
442	C₂	C₂×#14583018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1484	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	#19145170	C₂
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1484	D₄₃
hypocenter	C₄₃	#18091
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1484

Complements

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

N	H ≅ G/N	type
2. #19143662	C₂	semidirect
3. #19143661	C₂	semidirect
4. #19133506	C₂	semidirect
5. #19133427	C₂	semidirect
6. #19133421	C₂	semidirect
7. #19133416	C₂	semidirect
8. #19133341	C₂	semidirect
9. #19133013	C₂	semidirect
10. #19132882	C₂	semidirect
11. C₄₃×#1484	C₂	semidirect
225. #1484	D₄₃	semidirect
268. C₄₃	#18091	semidirect

Maximal subgroups

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

subgroup	index
#19145170	2
#19143662	2
#19143661	2
#19133506	2
#19133427	2
#19133421	2
#19133416	2
#19133341	2
#19133013	2
#19132882	2
C₄₃×#1484	2
#18091	43