Subgroups — #25079182

Order 11008.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19144920	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144595	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582977	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134172	C₂	1	2	yes	maximal, complemented
5	#19134158	C₂	1	2	yes	maximal, complemented
6	#19134144	C₂	1	2	yes	maximal, complemented
7	#19134130	C₂	1	2	yes	maximal, complemented
8	#19133341	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133252	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133242	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621877	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583256	—	2	1	no	—
15	#14583256	—	2	1	no	—
16	#14583251	C₂²	1	1	yes	characteristic, complemented
17	#14583251	C₂²	1	1	yes	characteristic, complemented
18	#14583247	C₂²	1	1	yes	characteristic, complemented
19	#14583247	C₂²	1	1	yes	characteristic, complemented
20	#14583212	—	2	1	no	—
21	#14583179	C₂²	1	2	yes	—
22	#14583094	C₂²	1	2	yes	—
23	#14583033	—	2	1	no	—
24	C₄×#10621882	—	2	2	no	—
25	#14582977	—	2	1	no	—
26	#14582977	—	2	1	no	—
27	#14582977	C₂²	1	2	yes	—
28	#14582977	C₂²	1	2	yes	—
29	#14582952	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
31	#14582893	—	2	1	no	—
32	#14582893	—	2	1	no	—
33	C₂×C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	#14582651	C₂²	1	2	yes	complemented
36	#14582649	C₂²	1	2	yes	complemented
37	#14582648	C₂²	1	2	yes	complemented
38	#14582645	C₂²	1	2	yes	complemented
39	#14582644	C₂²	1	2	yes	complemented
40	#14582642	C₂²	1	2	yes	complemented
41	C₄₃×#533	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#483	—	2	1	no	—
44	C₄₃×#476	C₂²	1	2	yes	—
45	C₄₃×#461	C₂²	1	2	yes	—
46	C₄₃×#450	—	2	1	no	—
47	C₄×SD₁₆×C₄₃	—	2	2	no	—
48	C₄₃×#431	C₂²	1	1	yes	characteristic
49	C₂×#10621898	—	2	1	no	—
50	C₂×#10621882	—	2	2	no	—
51	C₂×#10621877	—	2	2	no	—
52	C₂×#10621877	—	2	2	no	—
53	C₂×#10621877	—	4	4	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
57	#13063325	C₂³	1	1	yes	characteristic
58	#13063322	C₂³	1	1	yes	characteristic
59	#13063313	—	2	1	no	—
60	#13063299	—	2	1	no	—
61	#13063299	—	2	1	no	—
62	C₄×D₁₇₂	—	2	1	no	—
63	C₄×D₁₇₂	—	2	1	no	—
64	#13063258	—	2	2	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
68	#13063248	—	2	1	no	—
69	#13063248	—	2	1	no	—
70	#13063248	—	2	1	no	—
71	#13063248	—	2	1	no	—
72	#13063246	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	#13063245	—	2	1	no	—
75	#13063245	—	2	1	no	—
76	#13063245	—	2	1	no	—
77	#13063245	—	2	1	no	—
78	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
79	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
81	C₄×C₄₃⋊C₈	—	2	1	no	—
82	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
87	C₂³×C₄×C₄₃	—	2	1	no	—
88	C₂×SD₁₆×C₄₃	—	2	2	no	—
89	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
90	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
91	#125×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	—	2	1	no	—
93	C₂²⋊Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×D₄×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	D₄	1	2	yes	—
99	C₄×D₄×C₄₃	C₂³	1	2	yes	—
100	#117×C₄₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#106×C₄₃	—	2	2	no	—
105	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
106	#103×C₄₃	—	2	2	no	—
107	#102×C₄₃	—	2	2	no	—
108	C₂²⋊C₈×C₄₃	—	2	1	no	—
109	C₄×C₈×C₄₃	—	2	1	no	—
110	C₂⁴×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	1	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	4	2	no	—
115	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	2	no	—
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	1	no	—
119	C₂²×C₄×C₄₃	—	4	2	no	—
120	C₂²×C₄×C₄₃	—	4	2	no	—
121	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₃	—	4	1	no	—
125	#10621898	—	4	2	no	—
126	#10621898	—	4	2	no	—
127	C₂×D₁₇₂	—	2	1	no	—
128	C₂×D₁₇₂	—	2	1	no	—
129	C₂×D₁₇₂	—	2	1	no	—
130	C₂×C₄×D₄₃	—	4	1	no	—
131	C₂×Dic₈₆	—	2	1	no	—
132	SD₁₆×C₄₃	—	4	4	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₄⋊C₄×C₄₃	—	2	1	no	—
138	C₄⋊C₄×C₄₃	—	2	1	no	—
139	C₄⋊C₄×C₄₃	—	4	1	no	—
140	C₄⋊C₄×C₄₃	—	4	1	no	—
141	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₄₃	—	2	2	no	—
143	C₂²⋊C₄×C₄₃	—	2	2	no	—
144	C₂²⋊C₄×C₄₃	—	4	1	no	—
145	C₄²×C₄₃	—	4	1	no	—
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₃	#41	1	1	yes	characteristic
149	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
150	#10621882	—	4	4	no	—
151	(C₂×D₄₃)⋊C₄	—	4	1	no	—
152	(C₂×D₄₃)⋊C₄	—	4	1	no	—
153	C₄⋊Dic₄₃	—	2	1	no	—
154	C₄⋊Dic₄₃	—	2	1	no	—
155	#10621877	—	4	4	no	—
156	#10621877	—	4	4	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	—	2	2	no	—
160	C₂×C₄₃⋊C₈	—	2	2	no	—
161	C₂×C₄₃⋊C₈	—	4	2	no	—
162	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂³×C₄₃	—	2	2	no	—
167	C₂³×C₄₃	—	4	2	no	—
168	C₂³×C₄₃	—	4	2	no	—
169	C₂³×C₄₃	—	4	2	no	—
170	C₂³×C₄₃	#121	1	1	yes	characteristic
171	C₂²×D₄₃	—	4	1	no	—
172	Q₈×C₄₃	—	4	2	no	—
173	Q₈×C₄₃	—	8	1	no	—
174	D₄×C₄₃	—	2	2	no	—
175	D₄×C₄₃	—	2	2	no	—
176	D₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	2	2	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	4	no	—
184	C₂×C₄×C₄₃	—	4	1	no	—
185	C₂×C₄×C₄₃	—	4	1	no	—
186	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
188	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₃	#135	1	2	yes	—
190	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
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	C₂²⋊D₄₃	—	8	2	no	—
195	C₂×Dic₄₃	—	4	1	no	—
196	D₁₇₂	—	4	1	no	—
197	D₁₇₂	—	4	1	no	—
198	D₁₇₂	—	4	2	no	—
199	D₁₇₂	—	8	1	no	—
200	C₄×D₄₃	—	8	2	no	—
201	Dic₈₆	—	4	1	no	—
202	Dic₈₆	—	4	1	no	—
203	C₈×C₄₃	—	4	2	no	—
204	C₄₃⋊C₈	—	2	1	no	—
205	C₄₃⋊C₈	—	2	1	no	—
206	C₄₃⋊C₈	—	2	1	no	—
207	C₄₃⋊C₈	—	2	1	no	—
208	C₄₃⋊C₈	—	4	2	no	—
209	C₄₃⋊C₈	—	4	2	no	—
210	#19142	—	43	1	no	maximal, Sylow
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	—	2	1	no	—
213	C₂²×C₄₃	—	4	2	no	—
214	C₂²×C₄₃	—	4	2	no	—
215	C₂²×C₄₃	—	4	2	no	—
216	C₂²×C₄₃	—	8	4	no	—
217	C₂²×C₄₃	#463	1	2	yes	—
218	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
219	C₂×D₄₃	—	8	1	no	—
220	C₂×D₄₃	—	8	1	no	—
221	C₂×D₄₃	—	8	1	no	—
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	4	2	no	—
226	C₄×C₄₃	—	8	1	no	—
227	C₄×C₄₃	—	8	1	no	—
228	C₄×C₄₃	#463	1	2	yes	—
229	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
230	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₄₃	#575	1	2	yes	—
232	Dic₄₃	—	8	1	no	—
233	#3131	—	43	1	no	—
234	#3101	D₄₃	1	1	yes	characteristic, complemented
235	#3100	—	43	1	no	—
236	C₂×#436	—	43	1	no	—
237	#1703	—	43	2	no	—
238	#1701	—	43	2	no	—
239	#1699	—	43	2	no	—
240	#1697	—	43	2	no	—
241	#1564	—	43	1	no	—
242	#1542	—	43	1	no	—
243	#1540	—	43	1	no	—
244	C₂×C₄₃	—	2	2	no	—
245	C₂×C₄₃	—	8	2	no	—
246	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
247	C₂×C₄₃	#3054	1	1	yes	characteristic
248	C₂×C₄₃	#3067	1	1	yes	characteristic
249	D₄₃	—	16	1	no	—
250	C₂²×M₁₆	—	86	1	no	—
251	#533	C₂×D₄₃	1	1	yes	characteristic
252	#532	—	43	1	no	—
253	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
254	#488	—	86	1	no	—
255	#488	—	86	1	no	—
256	#487	—	43	1	no	—
257	#487	—	43	1	no	—
258	#486	—	43	1	no	—
259	#486	—	43	1	no	—
260	#483	—	2	1	no	—
261	#480	—	86	1	no	—
262	#476	C₂×D₄₃	1	2	yes	—
263	#474	—	43	2	no	—
264	#461	C₂×D₄₃	1	2	yes	—
265	#459	—	43	2	no	—
266	#450	—	2	1	no	—
267	#447	—	86	1	no	—
268	C₄×SD₁₆	—	2	2	no	—
269	C₄×D₈	—	86	2	no	—
270	#436	—	43	2	no	—
271	#436	—	43	2	no	—
272	#436	—	86	1	no	—
273	#436	—	86	1	no	—
274	#431	—	43	1	no	—
275	#431	C₂×D₄₃	1	1	yes	characteristic
276	C₂×C₄⋊C₈	—	43	1	no	—
277	#416	—	86	1	no	—
278	#416	—	86	1	no	—
279	C₂×C₂²⋊C₈	—	86	1	no	—
280	C₂×C₄×C₈	—	43	1	no	—
281	#335	—	43	2	no	—
282	#334	—	43	2	no	—
283	#333	—	43	2	no	—
284	#332	—	43	2	no	—
285	#332	—	43	2	no	—
286	#331	—	43	2	no	—
287	C₄₃	#19142	1	1	yes	characteristic, complemented, Sylow
288	C₂×#41	—	86	1	no	—
289	C₂²×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂×SD₁₆	—	2	2	no	—
292	C₂×D₈	—	86	2	no	—
293	C₂×M₁₆	—	86	2	no	—
294	C₂×M₁₆	—	86	2	no	—
295	C₂×M₁₆	—	172	4	no	—
296	C₂²×C₈	—	43	1	no	—
297	C₂²×C₈	—	43	1	no	—
298	C₂²×C₈	—	86	1	no	—
299	C₄⋊Q₈	—	43	1	no	—
300	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
301	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
302	#127	—	43	1	no	—
303	#125	—	2	1	no	—
304	#124	—	86	1	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	#121	—	86	1	no	—
308	#121	—	86	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	86	1	no	—
314	C₄×D₄	—	86	1	no	—
315	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
316	C₄×D₄	C₂²×D₄₃	1	2	yes	—
317	#117	—	2	1	no	—
318	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#107	—	86	2	no	—
322	#106	—	2	2	no	—
323	C₄⋊C₈	—	43	2	no	—
324	C₄⋊C₈	—	43	2	no	—
325	C₄⋊C₈	—	86	1	no	—
326	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
327	#103	—	2	2	no	—
328	#103	—	86	1	no	—
329	#103	—	86	1	no	—
330	#103	—	86	1	no	—
331	#103	—	86	1	no	—
332	#102	—	2	2	no	—
333	#102	—	86	1	no	—
334	#102	—	86	1	no	—
335	#102	—	86	1	no	—
336	#102	—	86	1	no	—
337	#102	—	86	2	no	—
338	#102	—	86	2	no	—
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	86	2	no	—
341	C₂²⋊C₈	—	86	2	no	—
342	C₂²⋊C₈	—	86	1	no	—
343	C₄×C₈	—	2	1	no	—
344	C₄×C₈	—	43	1	no	—
345	C₄×C₈	—	43	1	no	—
346	C₄×C₈	—	43	1	no	—
347	C₄×C₈	—	43	1	no	—
348	C₄×C₈	—	86	1	no	—
349	C₂⁴	—	2	1	no	—
350	#41	—	172	2	no	—
351	#41	—	172	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	86	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	86	1	no	—
358	C₂×D₄	—	86	1	no	—
359	C₂×D₄	—	86	1	no	—
360	C₂×D₄	—	172	1	no	—
361	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	172	1	no	—
368	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
369	C₂²×C₄	#10621900	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
371	SD₁₆	—	4	4	no	—
372	D₈	—	172	4	no	—
373	M₁₆	—	172	4	no	—
374	M₁₆	—	172	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	43	1	no	—
377	C₂×C₈	—	43	1	no	—
378	C₂×C₈	—	43	1	no	—
379	C₂×C₈	—	43	1	no	—
380	C₂×C₈	—	86	2	no	—
381	C₂×C₈	—	86	2	no	—
382	C₂×C₈	—	86	2	no	—
383	C₂×C₈	—	86	2	no	—
384	C₂×C₈	—	172	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	4	1	no	—
391	C₄⋊C₄	—	4	1	no	—
392	C₄⋊C₄	—	86	1	no	—
393	C₄⋊C₄	—	86	1	no	—
394	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	4	1	no	—
398	C₂²⋊C₄	—	172	1	no	—
399	C₂²⋊C₄	—	172	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	D₄×D₄₃	1	1	yes	characteristic
402	C₄²	#10621900	1	1	yes	characteristic
403	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
404	C₄²	C₂³×D₄₃	1	1	yes	characteristic
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	172	1	no	—
410	C₂³	#13063297	1	1	yes	characteristic
411	Q₈	—	4	2	no	—
412	Q₈	—	8	1	no	—
413	Q₈	—	172	1	no	—
414	Q₈	—	172	1	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	344	1	no	—
419	D₄	—	344	2	no	—
420	D₄	—	172	1	no	—
421	D₄	—	172	1	no	—
422	D₄	—	172	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	344	2	no	—
433	C₂×C₄	—	172	1	no	—
434	C₂×C₄	#13063297	1	1	yes	characteristic
435	C₂×C₄	#13063297	1	1	yes	characteristic
436	C₂×C₄	#13063297	1	1	yes	characteristic
437	C₂×C₄	#13063346	1	2	yes	—
438	C₂×C₄	#13063352	1	2	yes	—
439	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	86	1	no	—
444	C₈	—	86	1	no	—
445	C₈	—	86	1	no	—
446	C₈	—	86	1	no	—
447	C₈	—	172	2	no	—
448	C₈	—	172	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	8	4	no	—
455	C₂²	—	344	1	no	—
456	C₂²	—	344	1	no	—
457	C₂²	—	344	1	no	—
458	C₂²	#14583116	1	2	yes	—
459	C₂²	C₂×#13063297	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	8	1	no	—
465	C₄	—	8	1	no	—
466	C₄	—	344	1	no	—
467	C₄	#14583116	1	2	yes	—
468	C₄	C₂×#13063346	1	1	yes	characteristic
469	C₄	C₂×#13063352	1	1	yes	characteristic
470	C₄	#14583697	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	8	2	no	—
473	C₂	—	688	1	no	—
474	C₂	C₂×#14583116	1	1	yes	characteristic
475	C₂	#19144201	1	1	yes	characteristic
476	C₂	#19144312	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3101	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19144595	C₂
hypercenter	#3101	D₄₃
hypocenter	C₄₃	#19142
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3101

Complements

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

N	H ≅ G/N	type
1. #19144920	C₂	semidirect
3. C₂×#14582977	C₂	semidirect
4. #19134172	C₂	semidirect
5. #19134158	C₂	semidirect
6. #19134144	C₂	semidirect
7. #19134130	C₂	semidirect
8. #19133341	C₂	semidirect
9. #19133252	C₂	semidirect
10. #19133242	C₂	semidirect
11. C₄₃×#3101	C₂	semidirect
16. #14583251	C₂²	semidirect
17. #14583251	C₂²	semidirect
18. #14583247	C₂²	semidirect
19. #14583247	C₂²	semidirect
35. #14582651	C₂²	semidirect
36. #14582649	C₂²	semidirect
37. #14582648	C₂²	semidirect
38. #14582645	C₂²	semidirect
39. #14582644	C₂²	semidirect
40. #14582642	C₂²	semidirect
234. #3101	D₄₃	semidirect
287. C₄₃	#19142	semidirect

Maximal subgroups

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

subgroup	index
#19144920	2
#19144595	2
C₂×#14582977	2
#19134172	2
#19134158	2
#19134144	2
#19134130	2
#19133341	2
#19133252	2
#19133242	2
C₄₃×#3101	2
#19142	43