Subgroups — #19143852

Order 5504.

754 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#13063357	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²⋊Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583063	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583061	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583059	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583056	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583053	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583051	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583048	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582899	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582897	C₂	1	1	yes	maximal, characteristic, complemented
14	#14582861	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10621902	C₂²	1	1	yes	characteristic
17	C₂×#10621898	—	2	1	no	—
18	C₂×#10621898	C₂²	1	1	yes	characteristic
19	C₂×#10621900	—	2	1	no	—
20	C₂×#10621900	C₂²	1	1	yes	characteristic
21	#41×D₄₃	—	2	4	no	—
22	#41×D₄₃	—	2	4	no	—
23	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic
24	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₄×D₄₃	—	2	1	no	—
26	C₂×D₄×D₄₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₄₃	—	2	1	no	—
28	C₂²×C₄×D₄₃	C₂²	1	1	yes	characteristic
29	#13063357	—	2	4	no	—
30	#13063354	—	2	4	no	—
31	C₂×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
32	C₂×#10621885	C₂²	1	1	yes	characteristic, complemented
33	C₂×#10621885	C₂²	1	1	yes	characteristic, complemented
34	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
35	C₂×#10621883	C₂²	1	1	yes	characteristic, complemented
36	C₂×#10621884	C₂²	1	1	yes	characteristic, complemented
37	C₂×#10621872	C₂²	1	1	yes	characteristic, complemented
38	C₂×#10621872	C₂²	1	1	yes	characteristic, complemented
39	#13063305	C₂²	1	1	yes	characteristic
40	#13063304	C₂²	1	1	yes	characteristic, complemented
41	#13063303	—	2	1	no	—
42	#13063302	—	2	1	no	—
43	#13063301	C₂²	1	1	yes	characteristic
44	C₄⋊C₄×D₄₃	—	2	1	no	—
45	C₄⋊C₄×D₄₃	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊C₄×D₄₃	—	2	1	no	—
47	#13063250	C₂²	1	1	yes	characteristic, complemented
48	#13063249	C₂²	1	1	yes	characteristic, complemented
49	#13063248	C₂²	1	1	yes	characteristic, complemented
50	#13063247	C₂²	1	1	yes	characteristic, complemented
51	#13063246	C₂²	1	1	yes	characteristic, complemented
52	#13063245	C₂²	1	1	yes	characteristic, complemented
53	C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
55	(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
56	C₂×#41×C₄₃	C₂²	1	1	yes	characteristic
57	C₂×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
58	C₂×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
59	C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
60	#103×C₄₃	C₂²	1	1	yes	characteristic, complemented
61	#102×C₄₃	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
63	C₂³×D₄₃	—	2	1	no	—
64	C₂³×D₄₃	D₄	1	1	yes	characteristic
65	#41×C₄₃	—	2	2	no	—
66	#41×C₄₃	—	2	2	no	—
67	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
68	C₂×Q₈×C₄₃	C₂³	1	1	yes	characteristic
69	C₂×D₄×C₄₃	—	2	1	no	—
70	C₂×D₄×C₄₃	C₂³	1	1	yes	characteristic
71	C₂²×C₄×C₄₃	—	2	1	no	—
72	C₂²×C₄×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊D₄₃	—	2	1	no	—
74	C₂×C₂²⋊D₄₃	—	2	1	no	—
75	C₂×C₂²⋊D₄₃	—	2	1	no	—
76	C₂²×Dic₄₃	—	2	1	no	—
77	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
78	#10621902	—	2	2	no	—
79	#10621902	D₄	1	4	yes	—
80	Q₈×D₄₃	—	2	2	no	—
81	Q₈×D₄₃	—	2	2	no	—
82	Q₈×D₄₃	—	2	2	no	—
83	Q₈×D₄₃	—	2	2	no	—
84	#10621900	—	2	8	no	—
85	#10621900	—	2	2	no	—
86	#10621900	D₄	1	4	yes	—
87	D₄×D₄₃	—	2	8	no	—
88	D₄×D₄₃	—	2	2	no	—
89	D₄×D₄₃	—	2	2	no	—
90	#10621898	—	2	8	no	—
91	#10621898	—	2	2	no	—
92	#10621898	—	2	2	no	—
93	C₂×D₁₇₂	—	2	1	no	—
94	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
95	C₂×C₄×D₄₃	—	2	8	no	—
96	C₂×C₄×D₄₃	—	2	1	no	—
97	C₂×C₄×D₄₃	—	2	1	no	—
98	C₂×C₄×D₄₃	—	2	2	no	—
99	C₂×C₄×D₄₃	—	2	2	no	—
100	C₂×C₄×D₄₃	—	2	1	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	C₂×C₄×D₄₃	—	2	1	no	—
103	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
104	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
105	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
107	C₂×Dic₈₆	—	2	1	no	—
108	C₂×Dic₈₆	—	2	1	no	—
109	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
110	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
111	Q₁₆×C₄₃	—	2	2	no	—
112	SD₁₆×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₄₃	—	2	1	no	—
116	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
117	C₂²⋊C₄×C₄₃	—	2	1	no	—
118	C₂²⋊Dic₄₃	—	2	1	no	—
119	#10621885	—	2	2	no	—
120	#10621885	—	2	2	no	—
121	#10621884	—	2	2	no	—
122	#10621883	—	2	2	no	—
123	(C₂×D₄₃)⋊C₄	—	2	1	no	—
124	(C₂×D₄₃)⋊C₄	—	2	1	no	—
125	C₄⋊Dic₄₃	—	2	1	no	—
126	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
127	Dic₄₃⋊C₄	—	2	1	no	—
128	Dic₄₃⋊C₄	—	2	1	no	—
129	Dic₄₃⋊C₄	—	2	1	no	—
130	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
132	Dic₁₇₂	—	2	2	no	—
133	#10621873	—	2	2	no	—
134	#10621872	—	2	2	no	—
135	#10621872	—	2	2	no	—
136	C₂³×C₄₃	—	2	1	no	—
137	C₂³×C₄₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×D₄₃	—	2	4	no	—
139	C₂²×D₄₃	—	2	1	no	—
140	C₂²×D₄₃	—	2	2	no	—
141	C₂²×D₄₃	—	2	2	no	—
142	C₂²×D₄₃	—	4	1	no	—
143	C₂²×D₄₃	—	4	2	no	—
144	C₂²×D₄₃	—	4	2	no	—
145	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
147	Q₈×C₄₃	—	2	1	no	—
148	Q₈×C₄₃	—	2	1	no	—
149	Q₈×C₄₃	—	2	1	no	—
150	Q₈×C₄₃	C₂×D₄	1	2	yes	—
151	D₄×C₄₃	—	2	4	no	—
152	D₄×C₄₃	—	2	1	no	—
153	D₄×C₄₃	C₂×D₄	1	2	yes	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
162	C₂²⋊D₄₃	—	2	4	no	—
163	C₂²⋊D₄₃	—	2	4	no	—
164	C₂²⋊D₄₃	—	2	4	no	—
165	C₂×Dic₄₃	—	2	1	no	—
166	C₂×Dic₄₃	—	2	2	no	—
167	C₂×Dic₄₃	—	2	4	no	—
168	C₂×Dic₄₃	—	2	1	no	—
169	C₂×Dic₄₃	—	2	1	no	—
170	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
171	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
172	D₁₇₂	—	2	4	no	—
173	D₁₇₂	—	2	1	no	—
174	D₁₇₂	C₂×D₄	1	2	yes	—
175	C₄×D₄₃	—	2	4	no	—
176	C₄×D₄₃	—	2	4	no	—
177	C₄×D₄₃	—	2	2	no	—
178	C₄×D₄₃	—	2	1	no	—
179	C₄×D₄₃	—	2	1	no	—
180	C₄×D₄₃	—	2	2	no	—
181	C₄×D₄₃	—	2	4	no	—
182	C₄×D₄₃	—	4	2	no	—
183	C₄×D₄₃	—	4	2	no	—
184	C₄×D₄₃	C₂×D₄	1	2	yes	—
185	C₄×D₄₃	C₂×D₄	1	2	yes	—
186	Dic₈₆	—	2	4	no	—
187	Dic₈₆	—	2	1	no	—
188	Dic₈₆	—	2	1	no	—
189	Dic₈₆	—	2	1	no	—
190	Dic₈₆	—	4	2	no	—
191	Dic₈₆	C₂×D₄	1	2	yes	—
192	C₈×C₄₃	—	2	1	no	—
193	C₈×C₄₃	—	2	1	no	—
194	C₄₃⋊C₈	—	2	1	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₂²×C₄₃	—	2	2	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	4	1	no	—
201	C₂²×C₄₃	—	4	1	no	—
202	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
203	C₂×D₄₃	—	2	1	no	—
204	C₂×D₄₃	—	2	1	no	—
205	C₂×D₄₃	—	2	1	no	—
206	C₂×D₄₃	—	2	1	no	—
207	C₂×D₄₃	—	2	2	no	—
208	C₂×D₄₃	—	4	4	no	—
209	C₂×D₄₃	—	4	8	no	—
210	C₂×D₄₃	—	4	1	no	—
211	C₂×D₄₃	—	4	1	no	—
212	C₂×D₄₃	#120	1	2	yes	—
213	C₂×D₄₃	#137	1	2	yes	complemented
214	C₄×C₄₃	—	2	2	no	—
215	C₄×C₄₃	—	2	1	no	—
216	C₄×C₄₃	—	4	1	no	—
217	C₄×C₄₃	—	4	1	no	—
218	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
219	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	Dic₄₃	—	2	1	no	—
221	Dic₄₃	—	2	2	no	—
222	Dic₄₃	—	4	1	no	—
223	Dic₄₃	—	4	1	no	—
224	Dic₄₃	#120	1	2	yes	—
225	#3007	—	43	1	no	maximal, Sylow
226	C₂×C₄₃	—	4	1	no	—
227	C₂×C₄₃	—	4	2	no	—
228	C₂×C₄₃	C₂×#120	1	1	yes	characteristic
229	C₂×C₄₃	C₂×#137	1	1	yes	characteristic
230	C₂×C₄₃	#575	1	1	yes	characteristic
231	D₄₃	—	2	2	no	—
232	D₄₃	—	2	2	no	—
233	D₄₃	—	4	2	no	—
234	C₂²×#41	—	43	1	no	—
235	C₂×#137	—	43	1	no	—
236	C₂×#137	—	43	1	no	—
237	C₂×C₂²⋊Q₈	—	43	1	no	—
238	#452	—	43	1	no	—
239	#452	—	43	1	no	—
240	#452	—	43	1	no	—
241	#452	D₄₃	1	1	yes	characteristic, complemented
242	#451	—	43	1	no	—
243	#451	—	43	1	no	—
244	#450	—	43	1	no	—
245	#450	—	43	1	no	—
246	#417	—	43	1	no	—
247	#417	—	43	1	no	—
248	#407	—	43	1	no	—
249	C₄₃	#3007	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	43	1	no	—
251	C₂×#41	—	43	1	no	—
252	C₂×#41	—	43	1	no	—
253	C₂×#41	—	86	1	no	—
254	C₂×#41	—	86	1	no	—
255	C₂×#41	—	86	4	no	—
256	C₂×#41	—	86	4	no	—
257	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
258	C₂²×Q₈	—	43	1	no	—
259	C₂²×Q₈	—	43	1	no	—
260	C₂²×D₄	—	43	1	no	—
261	C₂²×D₄	—	86	1	no	—
262	C₂³×C₄	—	43	1	no	—
263	C₂³×C₄	—	86	1	no	—
264	#137	—	86	4	no	—
265	#137	—	86	4	no	—
266	C₂×Q₁₆	—	43	1	no	—
267	C₂×Q₁₆	—	43	1	no	—
268	C₂×Q₁₆	—	43	1	no	—
269	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
270	C₂×SD₁₆	—	43	1	no	—
271	C₂×SD₁₆	—	43	1	no	—
272	C₂×SD₁₆	—	43	1	no	—
273	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
274	C₂×M₁₆	—	43	1	no	—
275	C₂×M₁₆	—	43	1	no	—
276	C₂²⋊Q₈	—	43	1	no	—
277	C₂²⋊Q₈	—	43	1	no	—
278	C₂²⋊Q₈	—	43	1	no	—
279	C₂²⋊Q₈	—	86	1	no	—
280	C₂²⋊Q₈	—	86	1	no	—
281	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
282	C₂×C₄⋊C₄	—	43	1	no	—
283	C₂×C₄⋊C₄	—	86	1	no	—
284	C₂×C₂²⋊C₄	—	86	1	no	—
285	#103	—	43	1	no	—
286	#103	—	43	1	no	—
287	#103	—	43	1	no	—
288	#103	C₂×D₄₃	1	1	yes	characteristic, complemented
289	#102	—	43	1	no	—
290	#102	—	43	1	no	—
291	#102	—	43	1	no	—
292	#102	C₂×D₄₃	1	1	yes	characteristic, complemented
293	C₂²⋊C₈	—	43	1	no	—
294	C₂²⋊C₈	—	43	1	no	—
295	C₂²⋊C₈	—	43	1	no	—
296	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
297	C₂⁴	—	43	1	no	—
298	C₂⁴	—	86	1	no	—
299	#41	—	2	2	no	—
300	#41	—	2	2	no	—
301	#41	—	43	4	no	—
302	#41	—	43	4	no	—
303	#41	—	86	2	no	—
304	#41	—	86	2	no	—
305	#41	—	86	8	no	—
306	#41	—	86	2	no	—
307	#41	—	86	2	no	—
308	#41	—	86	8	no	—
309	C₂×Q₈	—	43	1	no	—
310	C₂×Q₈	—	43	1	no	—
311	C₂×Q₈	—	86	1	no	—
312	C₂×Q₈	—	86	1	no	—
313	C₂×Q₈	—	86	2	no	—
314	C₂×Q₈	—	86	2	no	—
315	C₂×Q₈	—	86	2	no	—
316	C₂×Q₈	—	86	2	no	—
317	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
318	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	43	1	no	—
321	C₂×D₄	—	86	1	no	—
322	C₂×D₄	—	86	1	no	—
323	C₂×D₄	—	86	2	no	—
324	C₂×D₄	—	86	8	no	—
325	C₂×D₄	—	86	1	no	—
326	C₂×D₄	—	86	1	no	—
327	C₂×D₄	—	86	2	no	—
328	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	43	1	no	—
331	C₂²×C₄	—	43	1	no	—
332	C₂²×C₄	—	43	1	no	—
333	C₂²×C₄	—	43	1	no	—
334	C₂²×C₄	—	43	1	no	—
335	C₂²×C₄	—	86	2	no	—
336	C₂²×C₄	—	86	2	no	—
337	C₂²×C₄	—	86	1	no	—
338	C₂²×C₄	—	86	1	no	—
339	C₂²×C₄	—	86	8	no	—
340	C₂²×C₄	—	86	1	no	—
341	C₂²×C₄	—	86	1	no	—
342	C₂²×C₄	—	86	1	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
345	Q₁₆	—	2	2	no	—
346	Q₁₆	—	86	2	no	—
347	Q₁₆	—	86	2	no	—
348	Q₁₆	—	86	2	no	—
349	SD₁₆	—	2	2	no	—
350	SD₁₆	—	86	2	no	—
351	SD₁₆	—	86	2	no	—
352	SD₁₆	—	86	2	no	—
353	M₁₆	—	86	2	no	—
354	M₁₆	—	86	2	no	—
355	C₂×C₈	—	43	1	no	—
356	C₂×C₈	—	43	1	no	—
357	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
358	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	43	1	no	—
361	C₄⋊C₄	—	86	1	no	—
362	C₄⋊C₄	—	86	1	no	—
363	C₄⋊C₄	—	86	1	no	—
364	C₄⋊C₄	—	86	1	no	—
365	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	86	1	no	—
368	C₂²⋊C₄	—	86	1	no	—
369	C₂²⋊C₄	—	86	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	43	1	no	—
372	C₂³	—	43	1	no	—
373	C₂³	—	86	2	no	—
374	C₂³	—	86	2	no	—
375	C₂³	—	86	4	no	—
376	C₂³	—	86	1	no	—
377	C₂³	—	172	1	no	—
378	C₂³	—	172	2	no	—
379	C₂³	—	172	2	no	—
380	C₂³	D₄×D₄₃	1	1	yes	characteristic
381	Q₈	—	2	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	—	2	1	no	—
384	Q₈	—	43	2	no	—
385	Q₈	—	86	4	no	—
386	Q₈	—	86	1	no	—
387	Q₈	—	86	1	no	—
388	Q₈	—	86	1	no	—
389	Q₈	—	172	2	no	—
390	Q₈	D₄×D₄₃	1	2	yes	—
391	D₄	—	2	4	no	—
392	D₄	—	2	1	no	—
393	D₄	—	43	2	no	—
394	D₄	—	86	4	no	—
395	D₄	—	86	4	no	—
396	D₄	—	86	4	no	—
397	D₄	—	86	4	no	—
398	D₄	—	86	1	no	—
399	D₄	D₄×D₄₃	1	2	yes	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	43	1	no	—
407	C₂×C₄	—	43	2	no	—
408	C₂×C₄	—	43	2	no	—
409	C₂×C₄	—	43	1	no	—
410	C₂×C₄	—	86	2	no	—
411	C₂×C₄	—	86	4	no	—
412	C₂×C₄	—	86	2	no	—
413	C₂×C₄	—	86	4	no	—
414	C₂×C₄	—	86	4	no	—
415	C₂×C₄	—	86	2	no	—
416	C₂×C₄	—	86	4	no	—
417	C₂×C₄	—	86	1	no	—
418	C₂×C₄	—	86	1	no	—
419	C₂×C₄	—	86	1	no	—
420	C₂×C₄	—	86	1	no	—
421	C₂×C₄	—	86	1	no	—
422	C₂×C₄	—	172	2	no	—
423	C₂×C₄	—	172	2	no	—
424	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
425	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	2	1	no	—
428	C₈	—	86	1	no	—
429	C₈	—	86	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	43	2	no	—
437	C₂²	—	43	2	no	—
438	C₂²	—	86	1	no	—
439	C₂²	—	86	1	no	—
440	C₂²	—	86	1	no	—
441	C₂²	—	86	1	no	—
442	C₂²	—	86	2	no	—
443	C₂²	—	172	4	no	—
444	C₂²	—	172	8	no	—
445	C₂²	—	172	1	no	—
446	C₂²	—	172	1	no	—
447	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	43	2	no	—
453	C₄	—	86	1	no	—
454	C₄	—	86	2	no	—
455	C₄	—	172	1	no	—
456	C₄	—	172	1	no	—
457	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
458	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
459	C₂	—	4	1	no	—
460	C₂	—	4	2	no	—
461	C₂	—	86	2	no	—
462	C₂	—	86	2	no	—
463	C₂	—	172	2	no	—
464	C₂	#120×D₄₃	1	1	yes	characteristic
465	C₂	#137×D₄₃	1	1	yes	characteristic
466	C₂	#14583696	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂⁴
Frattini	C₂×C₄	C₂³×D₄₃
Fitting	C₄₃×#452	C₂
socle	C₂²×C₄₃	C₂²×D₄
hypercenter	#452	D₄₃
hypocenter	C₄₃	#3007
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #452

Complements

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

N	H ≅ G/N	type
2. C₂×#13063357	C₂	semidirect
3. C₂×#13063354	C₂	semidirect
4. C₂²⋊Q₈×D₄₃	C₂	semidirect
5. #14583063	C₂	semidirect
6. #14583061	C₂	semidirect
7. #14583059	C₂	semidirect
8. #14583056	C₂	semidirect
9. #14583053	C₂	semidirect
10. #14583051	C₂	semidirect
11. #14583048	C₂	semidirect
12. #14582899	C₂	semidirect
13. #14582897	C₂	semidirect
14. #14582861	C₂	semidirect
15. C₄₃×#452	C₂	semidirect
24. C₂×Q₈×D₄₃	C₂²	semidirect
31. C₂×Dic₁₇₂	C₂²	semidirect
32. C₂×#10621885	C₂²	semidirect
33. C₂×#10621885	C₂²	semidirect
34. C₂×#10621873	C₂²	semidirect
35. C₂×#10621883	C₂²	semidirect
36. C₂×#10621884	C₂²	semidirect
37. C₂×#10621872	C₂²	semidirect
38. C₂×#10621872	C₂²	semidirect
40. #13063304	C₂²	semidirect
45. C₄⋊C₄×D₄₃	C₂²	semidirect
47. #13063250	C₂²	semidirect
48. #13063249	C₂²	semidirect
49. #13063248	C₂²	semidirect
50. #13063247	C₂²	semidirect
51. #13063246	C₂²	semidirect
52. #13063245	C₂²	semidirect
53. C₂²⋊(C₄₃⋊C₈)	C₂²	semidirect
57. C₂×Q₁₆×C₄₃	C₂²	semidirect
58. C₂×SD₁₆×C₄₃	C₂²	semidirect
59. C₂²⋊Q₈×C₄₃	C₂²	semidirect
60. #103×C₄₃	C₂²	semidirect
61. #102×C₄₃	C₂²	semidirect
62. C₂²⋊C₈×C₄₃	C₂²	semidirect
213. C₂×D₄₃	#137	semidirect
241. #452	D₄₃	semidirect
249. C₄₃	#3007	semidirect
269. C₂×Q₁₆	C₂×D₄₃	semidirect
273. C₂×SD₁₆	C₂×D₄₃	semidirect
281. C₂²⋊Q₈	C₂×D₄₃	semidirect
288. #103	C₂×D₄₃	semidirect
292. #102	C₂×D₄₃	semidirect
296. C₂²⋊C₈	C₂×D₄₃	semidirect