Subgroups — #25080160

Order 11008.

674 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145902	C₂	1	1	yes	maximal, characteristic
2	#19144991	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143339	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134158	C₂	1	2	yes	maximal, complemented
5	#19134144	C₂	1	2	yes	maximal, complemented
6	#19134034	C₂	1	2	yes	maximal, complemented
7	#19134020	C₂	1	2	yes	maximal, complemented
8	#19133348	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133242	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3206	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063332	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583261	—	2	2	no	—
15	#14583251	C₂²	1	2	yes	—
16	#14583247	C₂²	1	2	yes	—
17	#14583179	C₂²	1	2	yes	—
18	#14583176	—	2	1	no	—
19	#14583133	—	2	2	no	—
20	#14583094	C₂²	1	2	yes	—
21	#14583091	—	2	1	no	—
22	#14582977	C₂²	1	2	yes	—
23	#14582971	—	2	2	no	—
24	D₄×C₄₃⋊C₈	C₂²	1	2	yes	—
25	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	#14582898	—	2	1	no	—
28	#14582898	—	2	1	no	—
29	#14582866	—	2	1	no	—
30	C₄×#10621877	C₂²	1	1	yes	characteristic
31	#14582651	C₂²	1	2	yes	—
32	#14582649	C₂²	1	2	yes	—
33	#14582645	C₂²	1	2	yes	—
34	#14582645	C₂²	1	2	yes	—
35	#14582644	C₂²	1	1	yes	characteristic
36	#14582644	C₂²	1	1	yes	characteristic
37	#14582642	C₂²	1	1	yes	characteristic
38	#14582642	C₂²	1	1	yes	characteristic
39	C₄₃×#532	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
41	C₄₃×#492	—	2	1	no	—
42	C₄₃×#487	—	2	1	no	—
43	C₄₃×#461	C₂²	1	2	yes	—
44	C₄₃×#461	C₂²	1	2	yes	—
45	C₄₃×#448	—	2	2	no	—
46	C₄₃×#431	C₂²	1	1	yes	characteristic
47	C₂×#10621898	—	2	1	no	—
48	C₂×#10621882	—	2	2	no	—
49	#13063332	—	4	4	no	—
50	C₂×#10621877	—	2	2	no	—
51	C₂×#10621877	D₄	1	1	yes	characteristic
52	C₂×#10621877	D₄	1	1	yes	characteristic
53	C₂²×C₄₃⋊C₈	—	2	1	no	—
54	C₂²×C₄₃⋊C₈	—	2	1	no	—
55	C₂²×C₄₃⋊C₈	—	2	2	no	—
56	#13063325	C₂³	1	1	yes	characteristic
57	#13063322	C₂³	1	1	yes	characteristic
58	#13063313	—	2	1	no	—
59	#13063299	—	2	1	no	—
60	#13063299	—	2	1	no	—
61	C₄×D₁₇₂	—	2	1	no	—
62	C₄×D₁₇₂	—	2	1	no	—
63	#13063258	—	2	2	no	—
64	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
67	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
69	#13063248	—	2	2	no	—
70	#13063248	—	2	2	no	—
71	#13063246	—	2	2	no	—
72	#13063245	—	2	2	no	—
73	#13063245	—	2	2	no	—
74	#13063245	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
76	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
77	#13063236	D₄	1	2	yes	—
78	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
79	C₂×#41×C₄₃	—	2	1	no	—
80	C₂²×Q₈×C₄₃	—	2	1	no	—
81	C₂×SD₁₆×C₄₃	—	2	2	no	—
82	C₂×SD₁₆×C₄₃	—	2	2	no	—
83	C₄⋊Q₈×C₄₃	—	2	1	no	—
84	C₄⋊Q₈×C₄₃	—	2	1	no	—
85	C₄⋊Q₈×C₄₃	—	2	1	no	—
86	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
88	#127×C₄₃	D₄	1	1	yes	characteristic
89	#124×C₄₃	—	2	1	no	—
90	#121×C₄₃	—	2	1	no	—
91	#121×C₄₃	D₄	1	2	yes	—
92	C₄×D₄×C₄₃	—	2	1	no	—
93	C₄×D₄×C₄₃	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
99	#103×C₄₃	—	2	2	no	—
100	#103×C₄₃	—	2	2	no	—
101	C₂²⋊C₈×C₄₃	—	2	1	no	—
102	C₄×C₈×C₄₃	—	2	1	no	—
103	#41×C₄₃	—	4	2	no	—
104	#41×C₄₃	—	4	2	no	—
105	C₂×Q₈×C₄₃	—	2	1	no	—
106	C₂×Q₈×C₄₃	—	2	2	no	—
107	C₂×Q₈×C₄₃	—	4	1	no	—
108	C₂×Q₈×C₄₃	—	8	1	no	—
109	C₂×Q₈×C₄₃	—	8	1	no	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	1	no	—
112	C₂×D₄×C₄₃	—	2	2	no	—
113	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₃	—	2	2	no	—
115	C₂²×C₄×C₄₃	—	4	1	no	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
119	C₂×C₂²⋊D₄₃	—	4	1	no	—
120	#10621898	—	4	2	no	—
121	#10621898	—	4	2	no	—
122	C₂×D₁₇₂	—	2	1	no	—
123	C₂×D₁₇₂	—	2	1	no	—
124	C₂×D₁₇₂	—	2	1	no	—
125	C₂×C₄×D₄₃	—	4	1	no	—
126	C₂×Dic₈₆	—	2	1	no	—
127	SD₁₆×C₄₃	—	8	2	no	—
128	SD₁₆×C₄₃	—	8	2	no	—
129	C₂×C₈×C₄₃	—	2	1	no	—
130	C₂×C₈×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	2	no	—
134	C₄⋊C₄×C₄₃	—	4	1	no	—
135	C₄⋊C₄×C₄₃	—	4	1	no	—
136	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₄₃	—	2	2	no	—
138	C₂²⋊C₄×C₄₃	—	2	2	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	#10621882	—	8	2	no	—
144	(C₂×D₄₃)⋊C₄	—	4	1	no	—
145	(C₂×D₄₃)⋊C₄	—	4	1	no	—
146	C₄⋊Dic₄₃	—	2	1	no	—
147	C₄⋊Dic₄₃	—	2	1	no	—
148	#10621877	—	2	2	no	—
149	#10621877	—	2	2	no	—
150	#10621877	—	4	4	no	—
151	C₂×C₄₃⋊C₈	—	2	1	no	—
152	C₂×C₄₃⋊C₈	—	2	1	no	—
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	4	4	no	—
155	C₂×C₄₃⋊C₈	—	4	2	no	—
156	C₂×C₄₃⋊C₈	—	8	1	no	—
157	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
158	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
159	C₂³×C₄₃	—	2	2	no	—
160	C₂³×C₄₃	#121	1	1	yes	characteristic
161	C₂²×D₄₃	—	4	1	no	—
162	Q₈×C₄₃	—	4	2	no	—
163	Q₈×C₄₃	—	4	2	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	—	8	2	no	—
166	D₄×C₄₃	—	2	2	no	—
167	D₄×C₄₃	—	2	2	no	—
168	D₄×C₄₃	—	4	4	no	—
169	D₄×C₄₃	—	4	2	no	—
170	D₄×C₄₃	—	8	1	no	—
171	C₂×C₄×C₄₃	—	2	1	no	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	2	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	8	2	no	—
179	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
180	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
181	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₄₃	#135	1	2	yes	—
183	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
184	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₄₃	—	8	2	no	—
188	C₂×Dic₄₃	—	4	1	no	—
189	D₁₇₂	—	4	1	no	—
190	D₁₇₂	—	4	1	no	—
191	D₁₇₂	—	4	1	no	—
192	D₁₇₂	—	4	1	no	—
193	D₁₇₂	—	8	1	no	—
194	C₄×D₄₃	—	8	2	no	—
195	Dic₈₆	—	4	1	no	—
196	Dic₈₆	—	4	1	no	—
197	C₈×C₄₃	—	4	1	no	—
198	C₈×C₄₃	—	4	1	no	—
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	4	1	no	—
202	C₄₃⋊C₈	—	4	1	no	—
203	C₄₃⋊C₈	—	4	2	no	—
204	#19237	—	43	1	no	maximal, Sylow
205	C₂²×C₄₃	—	2	1	no	—
206	C₂²×C₄₃	—	2	1	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	2	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	#463	1	2	yes	—
211	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
212	C₂×D₄₃	—	8	1	no	—
213	C₂×D₄₃	—	8	1	no	—
214	C₂×D₄₃	—	8	1	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	4	2	no	—
219	C₄×C₄₃	—	8	2	no	—
220	C₄×C₄₃	#463	1	2	yes	—
221	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
222	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₄₃	#576	1	1	yes	characteristic
224	C₄×C₄₃	#577	1	1	yes	characteristic
225	Dic₄₃	—	8	1	no	—
226	#3245	—	43	1	no	—
227	#3206	D₄₃	1	1	yes	characteristic, complemented
228	#3141	—	43	1	no	—
229	#2935	—	43	1	no	—
230	#1701	—	43	2	no	—
231	#1699	—	43	2	no	—
232	#1681	—	43	2	no	—
233	#1679	—	43	2	no	—
234	#1565	—	43	1	no	—
235	#1540	—	43	1	no	—
236	C₂×#332	—	43	1	no	—
237	C₂×C₄₃	—	2	2	no	—
238	C₂×C₄₃	—	8	2	no	—
239	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
240	C₂×C₄₃	#3062	1	1	yes	characteristic
241	C₂×C₄₃	#3069	1	1	yes	characteristic
242	D₄₃	—	16	1	no	—
243	C₂×#131	—	86	1	no	—
244	#532	—	43	1	no	—
245	#532	C₂×D₄₃	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
247	#492	—	2	1	no	—
248	#489	—	86	2	no	—
249	#487	—	2	1	no	—
250	#487	—	43	2	no	—
251	#486	—	43	2	no	—
252	#474	—	43	2	no	—
253	#474	—	86	1	no	—
254	#466	—	86	2	no	—
255	#461	C₂×D₄₃	1	2	yes	—
256	#461	C₂×D₄₃	1	2	yes	—
257	#459	—	43	2	no	—
258	#459	—	86	1	no	—
259	#448	—	2	2	no	—
260	#436	—	43	2	no	—
261	#435	—	86	2	no	—
262	C₈×D₄	—	43	2	no	—
263	#431	C₂×D₄₃	1	1	yes	characteristic
264	C₂×C₄⋊C₈	—	43	1	no	—
265	C₂×C₄⋊C₈	—	43	1	no	—
266	#417	—	86	1	no	—
267	#417	—	86	1	no	—
268	#408	—	86	1	no	—
269	C₄×M₁₆	—	43	1	no	—
270	#335	—	43	2	no	—
271	#334	—	43	2	no	—
272	#332	—	43	2	no	—
273	#332	—	43	2	no	—
274	#332	—	43	1	no	—
275	#332	—	43	1	no	—
276	#331	—	43	1	no	—
277	#331	—	43	1	no	—
278	C₄₃	#19237	1	1	yes	characteristic, complemented, Sylow
279	C₂×#41	—	2	1	no	—
280	C₂×#41	—	86	1	no	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×D₈	—	86	2	no	—
285	#131	—	172	4	no	—
286	C₂×M₁₆	—	43	1	no	—
287	C₂×M₁₆	—	43	1	no	—
288	C₂×M₁₆	—	86	2	no	—
289	C₂²×C₈	—	86	2	no	—
290	C₂²×C₈	—	86	1	no	—
291	C₂²×C₈	—	86	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	43	1	no	—
296	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
297	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
298	#127	—	43	1	no	—
299	#127	C₂²⋊D₄₃	1	1	yes	characteristic
300	#124	—	2	1	no	—
301	#124	—	86	1	no	—
302	#121	—	2	1	no	—
303	#121	—	86	1	no	—
304	#121	—	86	1	no	—
305	#121	C₂²⋊D₄₃	1	2	yes	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	86	1	no	—
308	C₄×D₄	—	86	1	no	—
309	C₄×D₄	C₂²×D₄₃	1	2	yes	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
313	#107	—	86	2	no	—
314	C₄⋊C₈	—	43	1	no	—
315	C₄⋊C₈	—	43	1	no	—
316	C₄⋊C₈	—	43	2	no	—
317	C₄⋊C₈	—	86	1	no	—
318	C₄⋊C₈	—	86	1	no	—
319	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
321	#103	—	2	2	no	—
322	#103	—	2	2	no	—
323	#103	—	86	2	no	—
324	#103	—	86	2	no	—
325	#102	—	86	2	no	—
326	#102	—	86	2	no	—
327	#102	—	86	2	no	—
328	#102	—	86	2	no	—
329	C₂²⋊C₈	—	2	1	no	—
330	C₂²⋊C₈	—	86	2	no	—
331	C₂²⋊C₈	—	86	2	no	—
332	#97	—	43	2	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	—	43	2	no	—
335	#41	—	4	2	no	—
336	#41	—	4	2	no	—
337	#41	—	172	2	no	—
338	#41	—	172	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	1	no	—
342	C₂×Q₈	—	8	1	no	—
343	C₂×Q₈	—	8	1	no	—
344	C₂×Q₈	—	86	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	86	1	no	—
349	C₂×D₄	—	86	1	no	—
350	C₂×D₄	—	86	1	no	—
351	C₂×D₄	—	172	1	no	—
352	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	1	no	—
355	C₂²×C₄	—	172	1	no	—
356	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
357	C₂²×C₄	#10621900	1	1	yes	characteristic
358	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
359	SD₁₆	—	8	2	no	—
360	SD₁₆	—	8	2	no	—
361	D₈	—	344	2	no	—
362	M₁₆	—	86	2	no	—
363	M₁₆	—	86	2	no	—
364	M₁₆	—	172	4	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	43	2	no	—
368	C₂×C₈	—	43	2	no	—
369	C₂×C₈	—	86	1	no	—
370	C₂×C₈	—	86	1	no	—
371	C₂×C₈	—	86	2	no	—
372	C₂×C₈	—	344	1	no	—
373	C₂×C₈	—	172	4	no	—
374	C₂×C₈	—	172	2	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	86	1	no	—
381	C₄⋊C₄	—	86	1	no	—
382	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	172	1	no	—
386	C₂²⋊C₄	—	172	1	no	—
387	C₄²	D₄×D₄₃	1	1	yes	characteristic
388	C₄²	#10621900	1	1	yes	characteristic
389	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
390	C₄²	C₂³×D₄₃	1	1	yes	characteristic
391	C₂³	—	2	2	no	—
392	C₂³	—	172	1	no	—
393	C₂³	#13063297	1	1	yes	characteristic
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	8	2	no	—
398	Q₈	—	172	1	no	—
399	Q₈	—	172	1	no	—
400	D₄	—	2	2	no	—
401	D₄	—	2	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	2	no	—
404	D₄	—	8	1	no	—
405	D₄	—	344	1	no	—
406	D₄	—	344	2	no	—
407	D₄	—	172	1	no	—
408	D₄	—	172	1	no	—
409	D₄	—	172	1	no	—
410	D₄	—	172	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	344	2	no	—
420	C₂×C₄	—	172	1	no	—
421	C₂×C₄	#13063297	1	1	yes	characteristic
422	C₂×C₄	#13063297	1	1	yes	characteristic
423	C₂×C₄	#13063297	1	1	yes	characteristic
424	C₂×C₄	#13063346	1	2	yes	—
425	C₂×C₄	#13063352	1	2	yes	—
426	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
428	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
429	C₈	—	4	1	no	—
430	C₈	—	4	1	no	—
431	C₈	—	86	2	no	—
432	C₈	—	86	2	no	—
433	C₈	—	172	1	no	—
434	C₈	—	172	1	no	—
435	C₈	—	172	2	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	344	1	no	—
442	C₂²	—	344	1	no	—
443	C₂²	—	344	1	no	—
444	C₂²	#14583116	1	2	yes	—
445	C₂²	C₂×#13063297	1	1	yes	characteristic
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	2	no	—
451	C₄	—	344	1	no	—
452	C₄	#14583116	1	2	yes	—
453	C₄	C₂×#13063346	1	1	yes	characteristic
454	C₄	C₂×#13063352	1	1	yes	characteristic
455	C₄	#14583702	1	1	yes	characteristic
456	C₄	#14583710	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	8	2	no	—
459	C₂	—	688	1	no	—
460	C₂	C₂×#14583116	1	1	yes	characteristic
461	C₂	#19144271	1	1	yes	characteristic
462	C₂	#19144329	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3206	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145902	C₂
hypercenter	#3206	D₄₃
hypocenter	C₄₃	#19237
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3206

Complements

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

N	H ≅ G/N	type
2. #19144991	C₂	semidirect
3. #19143339	C₂	semidirect
4. #19134158	C₂	semidirect
5. #19134144	C₂	semidirect
6. #19134034	C₂	semidirect
7. #19134020	C₂	semidirect
8. #19133348	C₂	semidirect
9. #19133242	C₂	semidirect
10. C₂×#14582645	C₂	semidirect
11. C₄₃×#3206	C₂	semidirect
227. #3206	D₄₃	semidirect
278. C₄₃	#19237	semidirect

Maximal subgroups

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

subgroup	index
#19145902	2
#19144991	2
#19143339	2
#19134158	2
#19134144	2
#19134034	2
#19134020	2
#19133348	2
#19133242	2
C₂×#14582645	2
C₄₃×#3206	2
#19237	43