Subgroups — #25079178

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	#19144917	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144604	C₂	1	1	yes	maximal, characteristic, complemented
3	#19144591	C₂	1	1	yes	maximal, characteristic
4	C₂×#14582976	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134169	C₂	1	2	yes	maximal, complemented
6	#19134155	C₂	1	2	yes	maximal, complemented
7	#19134141	C₂	1	2	yes	maximal, complemented
8	#19134127	C₂	1	2	yes	maximal, complemented
9	#19133341	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133253	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10621872	—	2	1	no	—
13	#14583456	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
15	#14583253	—	2	1	no	—
16	#14583253	—	2	1	no	—
17	#14583249	C₂²	1	1	yes	characteristic, complemented
18	#14583249	C₂²	1	1	yes	characteristic, complemented
19	#14583245	C₂²	1	1	yes	characteristic, complemented
20	#14583245	C₂²	1	1	yes	characteristic, complemented
21	#14583230	—	2	1	no	—
22	#14583210	—	2	1	no	—
23	#14583190	C₂²	1	2	yes	—
24	#14583176	C₂²	1	2	yes	—
25	#14583105	C₂²	1	2	yes	—
26	#14583091	C₂²	1	2	yes	—
27	#14583052	—	2	1	no	—
28	#14583032	—	2	1	no	—
29	C₄×#10621873	—	2	2	no	—
30	C₄×#10621882	—	2	2	no	—
31	#14582976	—	2	1	no	—
32	#14582976	—	2	1	no	—
33	#14582976	C₂²	1	2	yes	—
34	#14582976	C₂²	1	2	yes	—
35	#14582952	C₂²	1	1	yes	characteristic
36	#14582895	—	2	1	no	—
37	#14582895	—	2	1	no	—
38	C₂×(C₂×D₄₃)⋊C₈	—	2	1	no	—
39	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
40	#14582651	C₂²	1	2	yes	complemented
41	#14582649	C₂²	1	2	yes	complemented
42	#14582647	C₂²	1	2	yes	complemented
43	#14582644	C₂²	1	2	yes	complemented
44	C₄₃×#532	C₂²	1	1	yes	characteristic
45	C₄₃×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#332	C₂²	1	2	yes	complemented
48	C₄₃×#331	C₂²	1	2	yes	complemented
49	C₂²×D₁₇₂	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₄₃	—	2	1	no	—
51	C₂×#10621873	—	2	2	no	—
52	C₂×#10621882	—	2	2	no	—
53	C₂×#10621872	—	2	2	no	—
54	C₂×#10621872	—	2	2	no	—
55	C₂×#10621872	—	4	4	no	—
56	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
58	#13063325	C₂³	1	1	yes	characteristic
59	#13063325	C₂³	1	1	yes	characteristic
60	#13063317	—	2	1	no	—
61	#13063304	—	2	1	no	—
62	#13063304	—	2	1	no	—
63	C₄×Dic₈₆	—	2	1	no	—
64	C₄×Dic₈₆	—	2	1	no	—
65	C₄×D₁₇₂	—	2	1	no	—
66	C₄×D₁₇₂	—	2	1	no	—
67	C₄×D₁₇₂	D₄	1	2	yes	—
68	C₄×D₁₇₂	C₂³	1	2	yes	—
69	#13063284	—	2	1	no	—
70	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
71	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
72	#13063258	—	2	2	no	—
73	#13063257	—	2	2	no	—
74	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
75	#13063250	—	2	2	no	—
76	#13063249	—	2	1	no	—
77	#13063249	—	2	1	no	—
78	#13063249	—	2	1	no	—
79	#13063249	—	2	1	no	—
80	#13063247	—	2	2	no	—
81	#13063246	—	2	2	no	—
82	#13063246	—	2	1	no	—
83	#13063246	—	2	1	no	—
84	#13063246	—	2	1	no	—
85	#13063246	—	2	1	no	—
86	#13063245	—	2	2	no	—
87	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
88	(C₂×D₄₃)⋊C₈	—	2	2	no	—
89	(C₂×D₄₃)⋊C₈	—	2	2	no	—
90	C₄×C₄₃⋊C₈	—	2	1	no	—
91	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
95	C₂×#41×C₄₃	—	2	1	no	—
96	C₂²×C₈×C₄₃	—	2	1	no	—
97	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
98	#127×C₄₃	C₂³	1	1	yes	characteristic
99	#124×C₄₃	—	2	1	no	—
100	#121×C₄₃	—	2	1	no	—
101	#121×C₄₃	—	2	1	no	—
102	C₄×D₄×C₄₃	—	2	1	no	—
103	C₄×D₄×C₄₃	—	2	1	no	—
104	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₃	—	2	1	no	—
106	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
107	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
108	C₂²⋊C₈×C₄₃	—	2	1	no	—
109	C₄×C₈×C₄₃	—	2	1	no	—
110	C₂³×D₄₃	—	2	1	no	—
111	#41×C₄₃	—	4	2	no	—
112	#41×C₄₃	—	4	2	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×D₄×C₄₃	—	2	1	no	—
115	C₂×D₄×C₄₃	—	2	1	no	—
116	C₂×D₄×C₄₃	—	2	1	no	—
117	C₂×D₄×C₄₃	—	4	1	no	—
118	C₂²×C₄×C₄₃	—	4	1	no	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
122	C₂²×Dic₄₃	—	2	1	no	—
123	C₂×D₁₇₂	—	2	1	no	—
124	C₂×D₁₇₂	—	4	2	no	—
125	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
126	C₂×C₄×D₄₃	—	2	2	no	—
127	C₂×C₄×D₄₃	—	2	2	no	—
128	C₂×C₄×D₄₃	—	4	2	no	—
129	C₂×C₄×D₄₃	—	4	2	no	—
130	C₂×Dic₈₆	—	2	1	no	—
131	C₂×Dic₈₆	—	2	1	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₂×C₈×C₄₃	—	2	2	no	—
134	C₂×C₈×C₄₃	—	4	2	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	2	1	no	—
137	C₂²⋊C₄×C₄₃	—	4	1	no	—
138	C₂²⋊C₄×C₄₃	—	4	1	no	—
139	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	#41	1	1	yes	characteristic
142	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₃	—	4	1	no	—
144	#10621882	—	4	4	no	—
145	(C₂×D₄₃)⋊C₄	—	2	2	no	—
146	(C₂×D₄₃)⋊C₄	—	2	2	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	C₄⋊Dic₄₃	—	2	1	no	—
149	C₄⋊Dic₄₃	—	2	1	no	—
150	C₄⋊Dic₄₃	—	2	1	no	—
151	C₄⋊Dic₄₃	—	2	1	no	—
152	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
153	Dic₄₃⋊C₄	—	4	1	no	—
154	Dic₄₃⋊C₄	—	4	1	no	—
155	C₄×Dic₄₃	—	4	1	no	—
156	C₂×C₄₃⋊C₈	—	2	2	no	—
157	C₂×C₄₃⋊C₈	—	2	2	no	—
158	C₂×C₄₃⋊C₈	—	2	2	no	—
159	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
160	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	#10621873	—	4	4	no	—
164	#10621872	—	4	4	no	—
165	#10621872	—	4	4	no	—
166	C₂³×C₄₃	—	4	1	no	—
167	C₂³×C₄₃	#121	1	1	yes	characteristic
168	C₂²×D₄₃	—	2	2	no	—
169	C₂²×D₄₃	—	4	2	no	—
170	C₂²×D₄₃	—	4	2	no	—
171	C₂²×D₄₃	—	4	2	no	—
172	Q₈×C₄₃	—	4	1	no	—
173	Q₈×C₄₃	—	4	1	no	—
174	D₄×C₄₃	—	4	1	no	—
175	D₄×C₄₃	—	4	1	no	—
176	D₄×C₄₃	—	4	2	no	—
177	D₄×C₄₃	—	8	1	no	—
178	D₄×C₄₃	—	8	2	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	8	2	no	—
183	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#135	1	2	yes	—
187	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
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×Dic₄₃	—	2	2	no	—
192	C₂×Dic₄₃	—	4	2	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	C₂×Dic₄₃	—	4	1	no	—
195	D₁₇₂	—	2	2	no	—
196	D₁₇₂	—	2	2	no	—
197	D₁₇₂	—	4	2	no	—
198	C₄×D₄₃	—	4	2	no	—
199	C₄×D₄₃	—	4	2	no	—
200	C₄×D₄₃	—	4	4	no	—
201	Dic₈₆	—	4	2	no	—
202	Dic₈₆	—	8	1	no	—
203	C₈×C₄₃	—	4	2	no	—
204	C₈×C₄₃	—	4	2	no	—
205	C₄₃⋊C₈	—	2	1	no	—
206	C₄₃⋊C₈	—	2	1	no	—
207	C₄₃⋊C₈	—	2	1	no	—
208	C₄₃⋊C₈	—	2	1	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	—	8	1	no	—
214	C₂²×C₄₃	—	8	1	no	—
215	C₂²×C₄₃	—	8	1	no	—
216	C₂²×C₄₃	#463	1	2	yes	—
217	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
218	C₂×D₄₃	—	4	2	no	—
219	C₂×D₄₃	—	4	2	no	—
220	C₂×D₄₃	—	4	2	no	—
221	C₂×D₄₃	—	8	4	no	—
222	C₄×C₄₃	—	2	1	no	—
223	C₄×C₄₃	—	2	1	no	—
224	C₄×C₄₃	—	2	1	no	—
225	C₄×C₄₃	—	8	1	no	—
226	C₄×C₄₃	#463	1	2	yes	—
227	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
228	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
229	C₄×C₄₃	#575	1	2	yes	—
230	Dic₄₃	—	4	2	no	—
231	Dic₄₃	—	8	1	no	—
232	Dic₄₃	—	8	1	no	—
233	#3131	—	43	1	no	—
234	#3101	—	43	1	no	—
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	D₄₃	1	1	yes	characteristic, complemented
244	C₂×C₄₃	—	2	2	no	—
245	C₂×C₄₃	—	16	1	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	—	8	2	no	—
250	C₂²×M₁₆	—	86	1	no	—
251	#533	—	43	1	no	—
252	#532	C₂×D₄₃	1	1	yes	characteristic
253	C₂×C₄×D₄	—	43	1	no	—
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	—	86	1	no	—
261	#480	—	86	1	no	—
262	#476	—	43	2	no	—
263	#474	—	43	2	no	—
264	#461	—	43	2	no	—
265	#459	—	43	2	no	—
266	#450	—	86	1	no	—
267	#447	—	86	1	no	—
268	C₄×SD₁₆	—	86	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	C₂×D₄₃	1	1	yes	characteristic
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	C₂×D₄₃	1	2	yes	complemented
286	#331	C₂×D₄₃	1	2	yes	complemented
287	C₄₃	#19142	1	1	yes	characteristic, complemented, Sylow
288	C₂×#41	—	2	1	no	—
289	C₂²×D₄	—	43	1	no	—
290	C₂³×C₄	—	86	1	no	—
291	C₂×SD₁₆	—	86	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	—	2	1	no	—
297	C₂²×C₈	—	43	1	no	—
298	C₂²×C₈	—	43	1	no	—
299	C₄⋊Q₈	—	43	1	no	—
300	C₄⋊Q₈	—	43	1	no	—
301	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
302	#127	C₂²×D₄₃	1	1	yes	characteristic
303	#125	—	86	1	no	—
304	#124	—	2	1	no	—
305	C₂²⋊Q₈	—	86	1	no	—
306	C₂²⋊Q₈	—	86	1	no	—
307	#121	—	2	1	no	—
308	#121	—	2	1	no	—
309	C₄×Q₈	—	86	1	no	—
310	C₄×Q₈	—	86	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	43	2	no	—
314	C₄×D₄	—	43	2	no	—
315	C₄×D₄	—	86	1	no	—
316	C₄×D₄	—	86	1	no	—
317	#117	—	86	1	no	—
318	C₂×C₄⋊C₄	—	43	1	no	—
319	C₂×C₂²⋊C₄	—	86	1	no	—
320	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
321	#107	—	86	2	no	—
322	#106	—	86	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	43	2	no	—
325	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
326	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
327	#103	—	86	2	no	—
328	#103	—	86	1	no	—
329	#103	—	86	1	no	—
330	#103	—	86	1	no	—
331	#103	—	86	1	no	—
332	#102	—	86	2	no	—
333	#102	—	86	2	no	—
334	#102	—	86	2	no	—
335	#102	—	86	1	no	—
336	#102	—	86	1	no	—
337	#102	—	86	1	no	—
338	#102	—	86	1	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	—	86	1	no	—
350	#41	—	4	2	no	—
351	#41	—	4	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	86	1	no	—
354	C₂×Q₈	—	86	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	43	2	no	—
360	C₂×D₄	—	86	1	no	—
361	C₂×D₄	—	172	2	no	—
362	C₂²×C₄	—	4	1	no	—
363	C₂²×C₄	—	86	1	no	—
364	C₂²×C₄	—	86	2	no	—
365	C₂²×C₄	—	86	2	no	—
366	C₂²×C₄	—	172	2	no	—
367	C₂²×C₄	—	172	2	no	—
368	C₂²×C₄	#10621898	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
371	SD₁₆	—	172	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	—	2	2	no	—
377	C₂×C₈	—	4	2	no	—
378	C₂×C₈	—	43	1	no	—
379	C₂×C₈	—	43	1	no	—
380	C₂×C₈	—	43	1	no	—
381	C₂×C₈	—	43	1	no	—
382	C₂×C₈	—	86	2	no	—
383	C₂×C₈	—	86	2	no	—
384	C₂×C₈	—	86	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	43	2	no	—
388	C₄⋊C₄	—	86	1	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	86	1	no	—
391	C₄⋊C₄	—	86	1	no	—
392	C₄⋊C₄	—	86	1	no	—
393	C₄⋊C₄	—	172	1	no	—
394	C₄⋊C₄	—	172	1	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₂²⋊C₄	—	86	2	no	—
398	C₂²⋊C₄	—	86	2	no	—
399	C₂²⋊C₄	—	172	1	no	—
400	C₄²	—	172	1	no	—
401	C₄²	#10621898	1	1	yes	characteristic
402	C₄²	D₄×D₄₃	1	1	yes	characteristic
403	C₄²	D₄×D₄₃	1	1	yes	characteristic
404	C₄²	C₂³×D₄₃	1	1	yes	characteristic
405	C₂³	—	4	1	no	—
406	C₂³	—	86	2	no	—
407	C₂³	—	172	2	no	—
408	C₂³	—	172	2	no	—
409	C₂³	—	172	2	no	—
410	C₂³	#13063298	1	1	yes	characteristic
411	Q₈	—	4	1	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	344	1	no	—
414	Q₈	—	172	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	2	no	—
418	D₄	—	8	1	no	—
419	D₄	—	8	2	no	—
420	D₄	—	86	2	no	—
421	D₄	—	86	2	no	—
422	D₄	—	172	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	8	2	no	—
427	C₂×C₄	—	86	2	no	—
428	C₂×C₄	—	172	1	no	—
429	C₂×C₄	—	172	1	no	—
430	C₂×C₄	—	172	2	no	—
431	C₂×C₄	—	172	4	no	—
432	C₂×C₄	—	172	2	no	—
433	C₂×C₄	—	172	2	no	—
434	C₂×C₄	#13063298	1	1	yes	characteristic
435	C₂×C₄	#13063298	1	1	yes	characteristic
436	C₂×C₄	#13063298	1	1	yes	characteristic
437	C₂×C₄	#13063346	1	2	yes	—
438	C₂×C₄	#13063349	1	2	yes	—
439	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
440	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
441	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
442	C₈	—	4	2	no	—
443	C₈	—	4	2	no	—
444	C₈	—	86	1	no	—
445	C₈	—	86	1	no	—
446	C₈	—	86	1	no	—
447	C₈	—	86	1	no	—
448	C₈	—	172	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	344	4	no	—
455	C₂²	—	172	2	no	—
456	C₂²	—	172	2	no	—
457	C₂²	—	172	2	no	—
458	C₂²	#14583113	1	2	yes	—
459	C₂²	C₂×#13063298	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	8	1	no	—
464	C₄	—	344	1	no	—
465	C₄	—	344	1	no	—
466	C₄	—	172	2	no	—
467	C₄	#14583113	1	2	yes	—
468	C₄	C₂×#13063346	1	1	yes	characteristic
469	C₄	C₂×#13063349	1	1	yes	characteristic
470	C₄	#14583696	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	16	1	no	—
473	C₂	—	344	2	no	—
474	C₂	C₂×#14583113	1	1	yes	characteristic
475	C₂	#19144203	1	1	yes	characteristic
476	C₂	#19144314	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#13063298
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1540	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19144591	C₂
hypercenter	#1540	D₄₃
hypocenter	C₄₃	#19142
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1540

Complements

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

N	H ≅ G/N	type
1. #19144917	C₂	semidirect
2. #19144604	C₂	semidirect
4. C₂×#14582976	C₂	semidirect
5. #19134169	C₂	semidirect
6. #19134155	C₂	semidirect
7. #19134141	C₂	semidirect
8. #19134127	C₂	semidirect
9. #19133341	C₂	semidirect
10. #19133253	C₂	semidirect
11. C₄₃×#1540	C₂	semidirect
17. #14583249	C₂²	semidirect
18. #14583249	C₂²	semidirect
19. #14583245	C₂²	semidirect
20. #14583245	C₂²	semidirect
40. #14582651	C₂²	semidirect
41. #14582649	C₂²	semidirect
42. #14582647	C₂²	semidirect
43. #14582644	C₂²	semidirect
47. C₄₃×#332	C₂²	semidirect
48. C₄₃×#331	C₂²	semidirect
243. #1540	D₄₃	semidirect
285. #332	C₂×D₄₃	semidirect
286. #331	C₂×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
#19144917	2
#19144604	2
#19144591	2
C₂×#14582976	2
#19134169	2
#19134155	2
#19134141	2
#19134127	2
#19133341	2
#19133253	2
C₄₃×#1540	2
#19142	43