Subgroups — #25080432

Order 11008.

656 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	#19145155	C₂	1	1	yes	maximal, characteristic
2	#19144067	C₂	1	1	yes	maximal, characteristic
3	C₂×Q₈×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#19134023	C₂	1	2	yes	maximal, complemented
5	#19134013	C₂	1	2	yes	maximal, complemented
6	#19133979	C₂	1	2	yes	maximal, complemented
7	#19133945	C₂	1	2	yes	maximal, complemented
8	#19133350	C₂	1	1	yes	maximal, characteristic, complemented
9	#19133285	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133273	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063356	—	2	1	no	—
13	#14583449	C₂²	1	1	yes	characteristic
14	#14583295	C₂²	1	1	yes	characteristic
15	#14583273	C₂²	1	1	yes	characteristic
16	#14583249	C₂²	1	1	yes	characteristic
17	#14583247	C₂²	1	1	yes	characteristic
18	#14583130	—	2	1	no	—
19	#14583130	—	2	1	no	—
20	#14583121	—	2	2	no	—
21	#14583109	C₂²	1	2	yes	—
22	#14583099	C₂²	1	2	yes	—
23	Q₈×C₄₃⋊C₈	—	2	1	no	—
24	Q₈×C₄₃⋊C₈	—	2	1	no	—
25	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	—
26	Q₈×C₄₃⋊C₈	C₂²	1	2	yes	—
27	C₄×#10621884	—	2	1	no	—
28	C₄×#10621884	—	2	1	no	—
29	#14582923	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
31	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
32	#14582898	—	2	1	no	—
33	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	#14582649	C₂²	1	2	yes	—
36	#14582649	C₂²	1	2	yes	—
37	#14582648	C₂²	1	2	yes	—
38	#14582646	C₂²	1	2	yes	—
39	#14582645	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	C₄₃×#533	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
43	C₄₃×#479	—	2	2	no	—
44	C₄₃×#477	C₂²	1	2	yes	—
45	C₄₃×#475	C₂²	1	2	yes	—
46	C₄₃×#428	—	2	1	no	—
47	C₄₃×#423	C₂²	1	1	yes	characteristic
48	C₄₃×#419	—	2	1	no	—
49	C₂×#10621898	—	2	1	no	—
50	#13063356	—	4	4	no	—
51	C₂×#10621885	—	2	2	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621884	—	2	1	no	—
54	C₂×#10621884	—	2	1	no	—
55	C₂×#10621877	—	2	1	no	—
56	C₂²×C₄₃⋊C₈	—	2	1	no	—
57	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
58	C₂²×C₄₃⋊C₈	D₄	1	1	yes	characteristic
59	#13063325	C₂³	1	1	yes	characteristic
60	#13063322	C₂³	1	1	yes	characteristic
61	#13063313	—	2	1	no	—
62	#13063299	—	2	1	no	—
63	#13063299	—	2	1	no	—
64	C₄×D₁₇₂	—	2	1	no	—
65	C₄×D₁₇₂	—	2	1	no	—
66	#13063256	—	2	1	no	—
67	#13063256	—	2	1	no	—
68	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
73	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
74	#13063249	—	2	1	no	—
75	#13063249	—	2	1	no	—
76	#13063248	—	2	2	no	—
77	#13063245	—	2	2	no	—
78	#13063245	—	2	1	no	—
79	#13063245	—	2	1	no	—
80	C₄×C₄₃⋊C₈	—	2	2	no	—
81	C₄×C₄₃⋊C₈	—	2	2	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×Q₈×C₄₃	D₄	1	1	yes	characteristic
87	C₂×M₁₆×C₄₃	—	2	1	no	—
88	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
90	#125×C₄₃	—	2	1	no	—
91	C₂²⋊Q₈×C₄₃	—	2	1	no	—
92	C₂²⋊Q₈×C₄₃	—	2	1	no	—
93	C₄×Q₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	—	2	1	no	—
95	C₄×Q₈×C₄₃	—	2	1	no	—
96	C₄×Q₈×C₄₃	—	2	1	no	—
97	C₄×Q₈×C₄₃	D₄	1	2	yes	—
98	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
99	#117×C₄₃	—	2	1	no	—
100	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
101	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	#107×C₄₃	—	2	2	no	—
105	#106×C₄₃	—	2	2	no	—
106	C₄⋊C₈×C₄₃	—	2	1	no	—
107	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
108	#103×C₄₃	—	2	2	no	—
109	#103×C₄₃	—	2	2	no	—
110	C₂×Q₈×C₄₃	—	2	1	no	—
111	C₂×Q₈×C₄₃	—	2	2	no	—
112	C₂×Q₈×C₄₃	—	2	1	no	—
113	C₂×Q₈×C₄₃	—	2	1	no	—
114	C₂×Q₈×C₄₃	SD₁₆	1	4	yes	complemented
115	C₂×Q₈×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	—	2	1	no	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
121	C₂×C₂²⋊D₄₃	—	4	1	no	—
122	#10621898	—	4	2	no	—
123	#10621898	—	4	2	no	—
124	C₂×D₁₇₂	—	2	1	no	—
125	C₂×D₁₇₂	—	2	1	no	—
126	C₂×D₁₇₂	—	2	1	no	—
127	C₂×C₄×D₄₃	—	4	1	no	—
128	C₂×Dic₈₆	—	2	1	no	—
129	M₁₆×C₄₃	—	4	2	no	—
130	C₂×C₈×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	—	2	2	no	—
132	C₄⋊C₄×C₄₃	—	2	1	no	—
133	C₄⋊C₄×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	—	4	1	no	—
139	C₄⋊C₄×C₄₃	—	4	1	no	—
140	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₄₃	—	4	1	no	—
142	C₄²×C₄₃	—	2	2	no	—
143	C₄²×C₄₃	—	2	2	no	—
144	C₄²×C₄₃	—	4	1	no	—
145	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
147	C₄²×C₄₃	#41	1	1	yes	characteristic
148	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
149	#10621885	—	4	4	no	—
150	#10621884	—	4	2	no	—
151	#10621884	—	4	4	no	—
152	#10621884	—	4	2	no	—
153	(C₂×D₄₃)⋊C₄	—	4	1	no	—
154	(C₂×D₄₃)⋊C₄	—	4	1	no	—
155	C₄⋊Dic₄₃	—	2	1	no	—
156	C₄⋊Dic₄₃	—	2	1	no	—
157	#10621877	—	4	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	1	no	—
162	C₂×C₄₃⋊C₈	—	4	2	no	—
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	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₄₃	#121	1	1	yes	characteristic
168	C₂²×D₄₃	—	4	1	no	—
169	Q₈×C₄₃	—	2	2	no	—
170	Q₈×C₄₃	—	2	4	no	—
171	Q₈×C₄₃	—	4	1	no	—
172	Q₈×C₄₃	—	4	1	no	—
173	Q₈×C₄₃	—	8	1	no	—
174	Q₈×C₄₃	C₂×SD₁₆	1	4	yes	—
175	C₂×C₄×C₄₃	—	2	2	no	—
176	C₂×C₄×C₄₃	—	2	4	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	2	1	no	—
179	C₂×C₄×C₄₃	—	2	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	1	no	—
183	C₂×C₄×C₄₃	—	4	1	no	—
184	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
185	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₃	#121	1	1	yes	characteristic
187	C₂×C₄×C₄₃	C₂×SD₁₆	1	2	yes	—
188	C₂×C₄×C₄₃	#135	1	2	yes	—
189	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
192	C₂²⋊D₄₃	—	8	2	no	—
193	C₂×Dic₄₃	—	4	1	no	—
194	D₁₇₂	—	4	1	no	—
195	D₁₇₂	—	4	1	no	—
196	D₁₇₂	—	4	1	no	—
197	D₁₇₂	—	4	1	no	—
198	D₁₇₂	—	8	1	no	—
199	C₄×D₄₃	—	8	2	no	—
200	Dic₈₆	—	4	1	no	—
201	Dic₈₆	—	4	1	no	—
202	C₈×C₄₃	—	4	2	no	—
203	C₄₃⋊C₈	—	2	1	no	—
204	C₄₃⋊C₈	—	2	1	no	—
205	C₄₃⋊C₈	—	2	1	no	—
206	C₄₃⋊C₈	—	4	2	no	—
207	C₄₃⋊C₈	—	4	2	no	—
208	C₄₃⋊C₈	#137	1	2	yes	complemented
209	#19260	—	43	1	no	maximal, Sylow
210	C₂²×C₄₃	—	2	1	no	—
211	C₂²×C₄₃	—	2	1	no	—
212	C₂²×C₄₃	#465	1	2	yes	—
213	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
214	C₂×D₄₃	—	8	1	no	—
215	C₂×D₄₃	—	8	1	no	—
216	C₂×D₄₃	—	8	1	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	4	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	#465	1	2	yes	—
225	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
226	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
227	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
228	C₄×C₄₃	#575	1	1	yes	characteristic
229	Dic₄₃	—	8	1	no	—
230	#3167	—	43	1	no	—
231	#3078	D₄₃	1	1	yes	characteristic, complemented
232	#3037	—	43	1	no	—
233	C₂×C₈×Q₈	—	43	1	no	—
234	#1680	—	43	2	no	—
235	#1678	—	43	2	no	—
236	#1672	—	43	2	no	—
237	#1666	—	43	2	no	—
238	#1566	—	43	1	no	—
239	#1550	—	43	1	no	—
240	#1547	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	#3037	1	1	yes	characteristic
243	C₂×C₄₃	C₂×#465	1	1	yes	characteristic
244	C₂×C₄₃	#3067	1	1	yes	characteristic
245	D₄₃	—	16	1	no	—
246	C₂×#137	—	86	1	no	—
247	#533	C₂×D₄₃	1	1	yes	characteristic
248	#532	—	43	1	no	—
249	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
250	#498	—	43	1	no	—
251	#492	—	43	1	no	—
252	#487	—	43	1	no	—
253	#486	—	43	1	no	—
254	#479	—	2	2	no	—
255	#477	C₂×D₄₃	1	2	yes	—
256	#475	C₂×D₄₃	1	2	yes	—
257	#465	—	86	1	no	—
258	#465	—	86	1	no	—
259	#464	—	86	2	no	—
260	#462	—	43	2	no	—
261	#460	—	43	2	no	—
262	C₈×Q₈	—	43	2	no	—
263	C₈×Q₈	—	43	2	no	—
264	C₈×Q₈	—	86	1	no	—
265	C₈×Q₈	—	86	1	no	—
266	C₄×SD₁₆	—	86	1	no	—
267	C₄×SD₁₆	—	86	1	no	—
268	#428	—	2	1	no	—
269	#423	—	43	1	no	—
270	#423	C₂×D₄₃	1	1	yes	characteristic
271	C₂×C₄⋊C₈	—	43	1	no	—
272	C₂×C₄⋊C₈	—	86	1	no	—
273	#419	—	2	1	no	—
274	#417	—	86	1	no	—
275	C₂×C₄×C₈	—	43	1	no	—
276	C₂×C₄×C₈	—	86	1	no	—
277	#334	—	43	2	no	—
278	#334	—	43	2	no	—
279	#333	—	43	2	no	—
280	#332	—	43	2	no	—
281	#332	—	43	2	no	—
282	#331	—	43	2	no	—
283	C₄₃	#19260	1	1	yes	characteristic, complemented, Sylow
284	C₂×#41	—	86	1	no	—
285	C₂²×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
286	#137	—	172	4	no	—
287	C₂×Q₁₆	—	86	2	no	—
288	C₂×SD₁₆	—	86	1	no	—
289	C₂×SD₁₆	—	86	1	no	—
290	C₂×SD₁₆	—	86	2	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	86	1	no	—
293	C₂²×C₈	—	43	1	no	—
294	C₂²×C₈	—	43	1	no	—
295	C₂²×C₈	—	86	1	no	—
296	C₄⋊Q₈	—	43	1	no	—
297	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
298	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
299	#127	—	43	1	no	—
300	#125	—	2	1	no	—
301	#124	—	86	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	#121	—	86	1	no	—
305	#121	—	86	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	—	2	1	no	—
309	C₄×Q₈	—	2	1	no	—
310	C₄×Q₈	C₂²⋊D₄₃	1	2	yes	—
311	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
312	C₄×D₄	—	86	1	no	—
313	C₄×D₄	—	86	1	no	—
314	#117	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	C₂²⋊D₄₃	1	1	yes	characteristic
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
319	#107	—	2	2	no	—
320	#106	—	2	2	no	—
321	#106	—	86	1	no	—
322	#106	—	86	1	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	43	2	no	—
325	C₄⋊C₈	—	43	2	no	—
326	C₄⋊C₈	—	86	2	no	—
327	C₄⋊C₈	—	86	2	no	—
328	C₄⋊C₈	—	86	1	no	—
329	C₄⋊C₈	—	86	1	no	—
330	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
331	#103	—	2	2	no	—
332	#103	—	2	2	no	—
333	#103	—	86	1	no	—
334	#103	—	86	1	no	—
335	#103	—	86	2	no	—
336	#102	—	86	1	no	—
337	#102	—	86	1	no	—
338	#102	—	86	2	no	—
339	C₄×C₈	—	43	1	no	—
340	C₄×C₈	—	43	1	no	—
341	C₄×C₈	—	43	1	no	—
342	C₄×C₈	—	43	1	no	—
343	C₄×C₈	—	86	2	no	—
344	C₄×C₈	—	86	2	no	—
345	#41	—	172	2	no	—
346	#41	—	172	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	—	86	1	no	—
352	C₂×Q₈	#10621884	1	4	yes	complemented
353	C₂×Q₈	C₂×C₂²⋊D₄₃	1	2	yes	—
354	C₂×D₄	—	86	1	no	—
355	C₂×D₄	—	86	1	no	—
356	C₂×D₄	—	86	1	no	—
357	C₂×D₄	—	172	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	172	1	no	—
361	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
362	C₂²×C₄	#10621900	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
364	Q₁₆	—	172	4	no	—
365	SD₁₆	—	172	2	no	—
366	SD₁₆	—	172	2	no	—
367	SD₁₆	—	172	4	no	—
368	M₁₆	—	4	2	no	—
369	M₁₆	—	172	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	43	1	no	—
372	C₂×C₈	—	43	1	no	—
373	C₂×C₈	—	43	1	no	—
374	C₂×C₈	—	43	1	no	—
375	C₂×C₈	—	86	2	no	—
376	C₂×C₈	—	86	2	no	—
377	C₂×C₈	—	86	2	no	—
378	C₂×C₈	—	172	1	no	—
379	C₂×C₈	—	172	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	4	1	no	—
388	C₄⋊C₄	—	4	1	no	—
389	C₄⋊C₄	—	86	1	no	—
390	C₄⋊C₄	—	86	1	no	—
391	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
392	C₂²⋊C₄	—	4	1	no	—
393	C₂²⋊C₄	—	172	1	no	—
394	C₂²⋊C₄	—	172	1	no	—
395	C₄²	—	2	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	4	1	no	—
398	C₄²	D₄×D₄₃	1	1	yes	characteristic
399	C₄²	#10621900	1	1	yes	characteristic
400	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
401	C₄²	C₂³×D₄₃	1	1	yes	characteristic
402	C₂³	—	172	1	no	—
403	C₂³	#13063297	1	1	yes	characteristic
404	Q₈	—	2	4	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	4	1	no	—
407	Q₈	—	4	1	no	—
408	Q₈	—	8	1	no	—
409	Q₈	—	172	1	no	—
410	Q₈	—	172	1	no	—
411	Q₈	C₂×#10621884	1	4	yes	—
412	D₄	—	344	1	no	—
413	D₄	—	344	2	no	—
414	D₄	—	172	1	no	—
415	D₄	—	172	1	no	—
416	D₄	—	172	1	no	—
417	D₄	—	172	1	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	344	2	no	—
428	C₂×C₄	—	172	1	no	—
429	C₂×C₄	#13063297	1	1	yes	characteristic
430	C₂×C₄	#13063297	1	1	yes	characteristic
431	C₂×C₄	#13063297	1	1	yes	characteristic
432	C₂×C₄	C₂×#10621884	1	2	yes	—
433	C₂×C₄	#13063345	1	2	yes	—
434	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
436	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
437	C₈	—	4	2	no	—
438	C₈	—	43	2	no	—
439	C₈	—	86	1	no	—
440	C₈	—	86	1	no	—
441	C₈	—	86	1	no	—
442	C₈	—	172	2	no	—
443	C₈	—	172	2	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	344	1	no	—
447	C₂²	—	344	1	no	—
448	C₂²	—	344	1	no	—
449	C₂²	#14583130	1	2	yes	—
450	C₂²	C₂×#13063297	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	8	1	no	—
457	C₄	—	8	1	no	—
458	C₄	—	344	1	no	—
459	C₄	#14583130	1	2	yes	—
460	C₄	C₂²×#10621884	1	1	yes	characteristic
461	C₄	C₂×#13063345	1	1	yes	characteristic
462	C₄	#137×D₄₃	1	1	yes	characteristic
463	C₄	#14583698	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	688	1	no	—
466	C₂	#19144064	1	1	yes	characteristic
467	C₂	C₂×#14583130	1	1	yes	characteristic
468	C₂	#19144312	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13063297
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#3078	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#14583449	C₂²
hypercenter	#3078	D₄₃
hypocenter	C₄₃	#19260
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3078

Complements

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

N	H ≅ G/N	type
3. C₂×Q₈×C₄₃⋊C₈	C₂	semidirect
4. #19134023	C₂	semidirect
5. #19134013	C₂	semidirect
6. #19133979	C₂	semidirect
7. #19133945	C₂	semidirect
8. #19133350	C₂	semidirect
9. #19133285	C₂	semidirect
11. C₄₃×#3078	C₂	semidirect
114. C₂×Q₈×C₄₃	SD₁₆	semidirect
208. C₄₃⋊C₈	#137	semidirect
231. #3078	D₄₃	semidirect
283. C₄₃	#19260	semidirect
352. C₂×Q₈	#10621884	semidirect

Maximal subgroups

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

subgroup	index
#19145155	2
#19144067	2
C₂×Q₈×C₄₃⋊C₈	2
#19134023	2
#19134013	2
#19133979	2
#19133945	2
#19133350	2
#19133285	2
#19133273	2
C₄₃×#3078	2
#19260	43