Subgroups — #25080127

Order 11008.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145510	C₂	1	1	yes	maximal, characteristic
2	#19144971	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	#19134130	C₂	1	2	yes	maximal, complemented
6	#19134034	C₂	1	2	yes	maximal, complemented
7	#19134006	C₂	1	2	yes	maximal, complemented
8	#19133345	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133252	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#14582642	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063332	—	2	1	no	—
13	C₂×#13063322	C₂²	1	1	yes	characteristic
14	#14583275	—	2	1	no	—
15	#14583265	—	2	2	no	—
16	#14583247	—	2	1	no	—
17	#14583247	C₂²	1	2	yes	—
18	#14583247	C₂²	1	2	yes	—
19	#14583094	C₂²	1	2	yes	—
20	#14583094	C₂²	1	2	yes	—
21	#14583032	—	2	2	no	—
22	#14582977	C₂²	1	2	yes	complemented
23	#14582971	—	2	2	no	—
24	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
25	#14582952	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
27	#14582903	—	2	1	no	—
28	#14582903	—	2	1	no	—
29	#14582866	—	2	1	no	—
30	C₄×#10621877	C₂²	1	1	yes	characteristic
31	#14582651	C₂²	1	2	yes	complemented
32	#14582649	C₂²	1	2	yes	complemented
33	#14582648	C₂²	1	1	yes	characteristic, complemented
34	#14582648	C₂²	1	1	yes	characteristic, complemented
35	#14582645	C₂²	1	1	yes	characteristic, complemented
36	#14582645	C₂²	1	1	yes	characteristic, complemented
37	#14582642	C₂²	1	2	yes	—
38	#14582642	C₂²	1	2	yes	—
39	C₄₃×#533	C₂²	1	1	yes	characteristic
40	C₄₃×#532	C₂²	1	1	yes	characteristic
41	C₄₃×#476	C₂²	1	2	yes	complemented
42	C₄₃×#475	—	2	1	no	—
43	C₄₃×#465	—	2	2	no	—
44	C₄₃×#461	C₂²	1	2	yes	complemented
45	C₄₃×#460	—	2	1	no	—
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₂²×D₁₇₂	—	2	1	no	—
48	C₂²×D₁₇₂	—	2	1	no	—
49	C₂²×D₁₇₂	—	2	1	no	—
50	C₂×#10621882	—	2	2	no	—
51	C₂×#10621882	—	2	2	no	—
52	#13063332	—	4	4	no	—
53	C₂×#10621877	—	2	2	no	—
54	C₂×#10621877	D₄	1	1	yes	characteristic
55	C₂×#10621877	D₄	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	C₂²×C₄₃⋊C₈	—	2	2	no	—
58	#13063322	—	2	1	no	—
59	#13063322	—	2	1	no	—
60	#13063322	—	2	1	no	—
61	#13063322	C₂³	1	2	yes	—
62	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
66	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
67	#13063245	—	2	2	no	—
68	#13063245	—	2	2	no	—
69	#13063245	—	2	2	no	—
70	#13063245	—	2	2	no	—
71	#13063245	—	2	2	no	—
72	#13063245	—	2	2	no	—
73	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
75	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
76	#13063236	D₄	1	2	yes	—
77	C₄×C₄₃⋊C₈	—	2	1	no	—
78	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
79	C₂×#41×C₄₃	—	2	1	no	—
80	C₂×SD₁₆×C₄₃	—	2	2	no	—
81	C₂²×C₈×C₄₃	—	2	1	no	—
82	C₄⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
85	#127×C₄₃	D₄	1	1	yes	characteristic
86	#125×C₄₃	—	2	1	no	—
87	#124×C₄₃	—	2	1	no	—
88	C₂²⋊Q₈×C₄₃	—	2	1	no	—
89	C₂²⋊Q₈×C₄₃	—	2	1	no	—
90	#121×C₄₃	—	2	1	no	—
91	#121×C₄₃	D₄	1	2	yes	—
92	C₄×Q₈×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×D₄×C₄₃	—	2	1	no	—
95	C₄×D₄×C₄₃	C₂³	1	2	yes	—
96	#117×C₄₃	—	2	1	no	—
97	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
98	#106×C₄₃	—	2	2	no	—
99	C₄⋊C₈×C₄₃	—	2	1	no	—
100	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
101	#103×C₄₃	—	2	2	no	—
102	#102×C₄₃	—	2	2	no	—
103	C₂³×D₄₃	—	4	1	no	—
104	#41×C₄₃	—	4	2	no	—
105	#41×C₄₃	—	4	2	no	—
106	C₂×Q₈×C₄₃	—	2	1	no	—
107	C₂×Q₈×C₄₃	—	2	1	no	—
108	C₂×Q₈×C₄₃	—	2	1	no	—
109	C₂×D₄×C₄₃	—	2	1	no	—
110	C₂×D₄×C₄₃	—	2	1	no	—
111	C₂×D₄×C₄₃	—	2	2	no	—
112	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₃	—	2	2	no	—
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
117	C₂×D₁₇₂	—	2	2	no	—
118	C₂×D₁₇₂	—	2	2	no	—
119	C₂×D₁₇₂	—	2	2	no	—
120	C₂×D₁₇₂	—	4	1	no	—
121	C₂×D₁₇₂	—	4	1	no	—
122	C₂×D₁₇₂	—	4	1	no	—
123	C₂×D₁₇₂	—	4	2	no	—
124	C₂×D₁₇₂	—	4	2	no	—
125	C₂×D₁₇₂	—	8	1	no	—
126	C₂×D₁₇₂	—	8	1	no	—
127	C₂×D₁₇₂	—	8	2	no	—
128	SD₁₆×C₄₃	—	8	2	no	—
129	C₂×C₈×C₄₃	—	2	2	no	—
130	C₂×C₈×C₄₃	—	8	1	no	—
131	C₄⋊C₄×C₄₃	—	2	1	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	—	2	1	no	—
136	C₄⋊C₄×C₄₃	—	4	1	no	—
137	C₄⋊C₄×C₄₃	—	4	1	no	—
138	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
139	C₂²⋊C₄×C₄₃	—	2	2	no	—
140	C₂²⋊C₄×C₄₃	—	2	2	no	—
141	C₂²⋊C₄×C₄₃	—	4	1	no	—
142	C₄²×C₄₃	—	4	1	no	—
143	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
145	C₄²×C₄₃	#41	1	1	yes	characteristic
146	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
147	#10621882	—	8	2	no	—
148	#10621882	—	8	2	no	—
149	#10621877	—	2	2	no	—
150	#10621877	—	2	2	no	—
151	#10621877	—	4	4	no	—
152	C₂×C₄₃⋊C₈	—	2	1	no	—
153	C₂×C₄₃⋊C₈	—	2	1	no	—
154	C₂×C₄₃⋊C₈	—	2	1	no	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	4	4	no	—
157	C₂×C₄₃⋊C₈	—	4	2	no	—
158	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
159	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
160	C₂³×C₄₃	—	2	2	no	—
161	C₂³×C₄₃	#121	1	1	yes	characteristic
162	C₂²×D₄₃	—	4	2	no	—
163	C₂²×D₄₃	—	8	2	no	—
164	C₂²×D₄₃	—	8	2	no	—
165	C₂²×D₄₃	—	8	2	no	—
166	Q₈×C₄₃	—	4	2	no	—
167	Q₈×C₄₃	—	4	1	no	—
168	Q₈×C₄₃	—	4	1	no	—
169	Q₈×C₄₃	—	8	1	no	—
170	D₄×C₄₃	—	2	2	no	—
171	D₄×C₄₃	—	2	2	no	—
172	D₄×C₄₃	—	4	4	no	—
173	D₄×C₄₃	—	4	2	no	—
174	D₄×C₄₃	—	8	1	no	—
175	C₂×C₄×C₄₃	—	2	1	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	2	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	—	4	1	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	D₁₇₂	—	4	2	no	—
192	D₁₇₂	—	4	2	no	—
193	D₁₇₂	—	4	2	no	—
194	D₁₇₂	—	4	2	no	—
195	D₁₇₂	—	8	2	no	—
196	D₁₇₂	—	8	2	no	—
197	D₁₇₂	—	8	2	no	—
198	D₁₇₂	—	8	2	no	—
199	C₈×C₄₃	—	4	2	no	—
200	C₄₃⋊C₈	—	2	2	no	—
201	C₄₃⋊C₈	—	2	2	no	—
202	C₄₃⋊C₈	—	4	1	no	—
203	C₄₃⋊C₈	—	4	1	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	C₄₃⋊C₈	—	4	1	no	—
206	#19234	—	43	1	no	maximal, Sylow
207	C₂²×C₄₃	—	2	1	no	—
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	4	2	no	—
210	C₂²×C₄₃	—	4	2	no	—
211	C₂²×C₄₃	—	4	2	no	—
212	C₂²×C₄₃	#463	1	2	yes	—
213	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
214	C₂×D₄₃	—	8	2	no	—
215	C₂×D₄₃	—	8	2	no	—
216	C₂×D₄₃	—	8	2	no	—
217	C₂×D₄₃	—	16	4	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	2	1	no	—
221	C₄×C₄₃	—	4	2	no	—
222	C₄×C₄₃	—	8	1	no	—
223	C₄×C₄₃	—	8	1	no	—
224	C₄×C₄₃	#463	1	2	yes	—
225	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
226	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₄×C₄₃	#576	1	1	yes	characteristic
228	C₄×C₄₃	#577	1	1	yes	characteristic
229	#3246	D₄₃	1	1	yes	characteristic, complemented
230	#3205	—	43	1	no	—
231	#3138	—	43	1	no	—
232	#2935	—	43	1	no	—
233	#1701	—	43	2	no	—
234	#1697	—	43	2	no	—
235	#1681	—	43	2	no	—
236	#1677	—	43	2	no	—
237	#1565	—	43	1	no	—
238	#1542	—	43	1	no	—
239	C₂×#331	—	43	1	no	—
240	C₂×C₄₃	—	2	2	no	—
241	C₂×C₄₃	—	8	2	no	—
242	C₂×C₄₃	C₂×#463	1	1	yes	characteristic
243	C₂×C₄₃	#3062	1	1	yes	characteristic
244	C₂×C₄₃	#3068	1	1	yes	characteristic
245	D₄₃	—	16	2	no	—
246	C₂×#131	—	86	1	no	—
247	#533	C₂×D₄₃	1	1	yes	characteristic
248	#532	C₂×D₄₃	1	1	yes	characteristic
249	C₂×#127	—	43	1	no	—
250	#493	—	86	1	no	—
251	#490	—	86	2	no	—
252	#486	—	43	2	no	—
253	#486	—	43	2	no	—
254	#486	—	86	1	no	—
255	#476	C₂×D₄₃	1	2	yes	complemented
256	#475	—	2	1	no	—
257	#465	—	2	2	no	—
258	#461	C₂×D₄₃	1	2	yes	complemented
259	#460	—	2	1	no	—
260	#459	—	43	2	no	—
261	#459	—	43	2	no	—
262	#447	—	86	2	no	—
263	#436	—	43	2	no	—
264	#435	—	86	2	no	—
265	C₈×D₄	—	43	2	no	—
266	#431	—	43	1	no	—
267	C₂×C₄⋊C₈	—	43	1	no	—
268	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
269	#418	—	86	1	no	—
270	#418	—	86	1	no	—
271	#408	—	86	1	no	—
272	C₄×M₁₆	—	43	1	no	—
273	#335	—	43	2	no	—
274	#334	—	43	2	no	—
275	#333	—	43	1	no	—
276	#333	—	43	1	no	—
277	#332	—	43	1	no	—
278	#332	—	43	1	no	—
279	#331	—	43	2	no	—
280	#331	—	43	2	no	—
281	C₄₃	#19234	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	—	2	1	no	—
283	C₂²×D₄	—	86	1	no	—
284	C₂²×D₄	—	86	1	no	—
285	C₂²×D₄	—	86	1	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	86	2	no	—
288	C₂×D₈	—	86	2	no	—
289	#131	—	172	4	no	—
290	C₂×M₁₆	—	43	1	no	—
291	C₂×M₁₆	—	43	1	no	—
292	C₂×M₁₆	—	86	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	86	2	no	—
295	C₂²×C₈	—	86	1	no	—
296	C₄⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
297	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
299	#127	—	43	2	no	—
300	#127	—	86	1	no	—
301	#127	—	86	1	no	—
302	#127	—	86	1	no	—
303	#127	C₂²⋊D₄₃	1	1	yes	characteristic
304	#125	—	2	1	no	—
305	#124	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	#121	—	2	1	no	—
309	#121	C₂²⋊D₄₃	1	2	yes	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	C₂²×D₄₃	1	2	yes	—
314	#117	—	2	1	no	—
315	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
316	#106	—	2	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	43	1	no	—
319	C₄⋊C₈	—	43	1	no	—
320	C₄⋊C₈	—	43	1	no	—
321	C₄⋊C₈	—	43	1	no	—
322	C₄⋊C₈	—	86	1	no	—
323	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
324	#103	—	2	2	no	—
325	#102	—	2	2	no	—
326	#102	—	86	2	no	—
327	#102	—	86	2	no	—
328	#102	—	86	2	no	—
329	#102	—	86	2	no	—
330	#102	—	86	2	no	—
331	#102	—	86	2	no	—
332	C₂²⋊C₈	—	86	2	no	—
333	C₂²⋊C₈	—	86	2	no	—
334	C₂²⋊C₈	—	86	1	no	—
335	#97	—	43	2	no	—
336	C₄×C₈	—	43	2	no	—
337	C₄×C₈	—	86	1	no	—
338	C₂⁴	—	172	1	no	—
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	86	2	no	—
348	C₂×D₄	—	86	2	no	—
349	C₂×D₄	—	86	2	no	—
350	C₂×D₄	—	344	1	no	—
351	C₂×D₄	—	344	1	no	—
352	C₂×D₄	—	344	2	no	—
353	C₂×D₄	—	172	1	no	—
354	C₂×D₄	—	172	1	no	—
355	C₂×D₄	—	172	1	no	—
356	C₂×D₄	—	172	2	no	—
357	C₂×D₄	—	172	2	no	—
358	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
361	C₂²×C₄	#10621900	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
363	SD₁₆	—	8	2	no	—
364	D₈	—	344	2	no	—
365	D₈	—	344	2	no	—
366	M₁₆	—	86	2	no	—
367	M₁₆	—	86	2	no	—
368	M₁₆	—	172	4	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	8	1	no	—
371	C₂×C₈	—	43	2	no	—
372	C₂×C₈	—	43	2	no	—
373	C₂×C₈	—	86	1	no	—
374	C₂×C₈	—	86	1	no	—
375	C₂×C₈	—	86	1	no	—
376	C₂×C₈	—	86	1	no	—
377	C₂×C₈	—	172	4	no	—
378	C₂×C₈	—	172	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	4	1	no	—
390	C₄²	—	4	1	no	—
391	C₄²	D₄×D₄₃	1	1	yes	characteristic
392	C₄²	#10621900	1	1	yes	characteristic
393	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
394	C₄²	C₂³×D₄₃	1	1	yes	characteristic
395	C₂³	—	2	2	no	—
396	C₂³	—	344	2	no	—
397	C₂³	—	344	2	no	—
398	C₂³	—	344	2	no	—
399	C₂³	—	172	2	no	—
400	C₂³	#13063297	1	1	yes	characteristic
401	Q₈	—	4	2	no	—
402	Q₈	—	4	1	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	8	1	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	8	1	no	—
410	D₄	—	344	2	no	—
411	D₄	—	344	2	no	—
412	D₄	—	344	2	no	—
413	D₄	—	344	2	no	—
414	D₄	—	172	2	no	—
415	D₄	—	172	2	no	—
416	D₄	—	172	2	no	—
417	D₄	—	172	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	#13063297	1	1	yes	characteristic
427	C₂×C₄	#13063297	1	1	yes	characteristic
428	C₂×C₄	#13063297	1	1	yes	characteristic
429	C₂×C₄	#13063346	1	2	yes	—
430	C₂×C₄	#13063352	1	2	yes	—
431	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
432	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
433	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
434	C₈	—	4	2	no	—
435	C₈	—	86	2	no	—
436	C₈	—	86	2	no	—
437	C₈	—	172	1	no	—
438	C₈	—	172	1	no	—
439	C₈	—	172	1	no	—
440	C₈	—	172	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	344	2	no	—
447	C₂²	—	344	2	no	—
448	C₂²	—	344	2	no	—
449	C₂²	—	688	4	no	—
450	C₂²	#14583116	1	2	yes	—
451	C₂²	C₂×#13063297	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	#14583116	1	2	yes	—
459	C₄	C₂×#13063346	1	1	yes	characteristic
460	C₄	C₂×#13063352	1	1	yes	characteristic
461	C₄	#14583702	1	1	yes	characteristic
462	C₄	#14583707	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	2	no	—
465	C₂	—	688	2	no	—
466	C₂	C₂×#14583116	1	1	yes	characteristic
467	C₂	#19144277	1	1	yes	characteristic
468	C₂	#19144325	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3246	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145510	C₂
hypercenter	#3246	D₄₃
hypocenter	C₄₃	#19234
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3246

Complements

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

N	H ≅ G/N	type
2. #19144971	C₂	semidirect
3. #19143339	C₂	semidirect
4. #19134158	C₂	semidirect
5. #19134130	C₂	semidirect
6. #19134034	C₂	semidirect
7. #19134006	C₂	semidirect
8. #19133345	C₂	semidirect
9. #19133252	C₂	semidirect
10. C₂×#14582642	C₂	semidirect
11. C₄₃×#3246	C₂	semidirect
22. #14582977	C₂²	semidirect
24. D₄×C₄₃⋊C₈	C₂²	semidirect
31. #14582651	C₂²	semidirect
32. #14582649	C₂²	semidirect
33. #14582648	C₂²	semidirect
34. #14582648	C₂²	semidirect
35. #14582645	C₂²	semidirect
36. #14582645	C₂²	semidirect
41. C₄₃×#476	C₂²	semidirect
44. C₄₃×#461	C₂²	semidirect
229. #3246	D₄₃	semidirect
255. #476	C₂×D₄₃	semidirect
258. #461	C₂×D₄₃	semidirect
281. C₄₃	#19234	semidirect

Maximal subgroups

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

subgroup	index
#19145510	2
#19144971	2
#19143339	2
#19134158	2
#19134130	2
#19134034	2
#19134006	2
#19133345	2
#19133252	2
C₂×#14582642	2
C₄₃×#3246	2
#19234	43