Subgroups — #19143816

Order 5504.

764 conjugacy classes of subgroups.

The subgroup lattice has 476 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, complemented
2	C₂×#13063348	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#13063346	C₂	1	1	yes	maximal, characteristic, complemented
4	#14583412	C₂	1	1	yes	maximal, characteristic, complemented
5	#14583059	C₂	1	1	yes	maximal, characteristic, complemented
6	#14583053	C₂	1	1	yes	maximal, characteristic, complemented
7	#14583048	C₂	1	1	yes	maximal, characteristic, complemented
8	#14583046	C₂	1	1	yes	maximal, characteristic, complemented
9	#14583044	C₂	1	1	yes	maximal, characteristic, complemented
10	#14583039	C₂	1	1	yes	maximal, characteristic, complemented
11	#14583034	C₂	1	1	yes	maximal, characteristic, complemented
12	#14582894	C₂	1	1	yes	maximal, characteristic, complemented
13	#14582892	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₈×D₄₃	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×#10621902	C₂²	1	1	yes	characteristic, complemented
18	C₂×#10621898	—	2	1	no	—
19	C₂×#10621898	C₂²	1	1	yes	characteristic
20	C₂×#10621900	—	2	1	no	—
21	C₂×#10621900	C₂²	1	1	yes	characteristic
22	#41×D₄₃	—	2	4	no	—
23	#41×D₄₃	—	2	4	no	—
24	C₂×Q₈×D₄₃	C₂²	1	1	yes	characteristic
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	#13063348	—	2	4	no	—
30	#13063346	—	2	4	no	—
31	C₂×#10621885	C₂²	1	1	yes	characteristic, complemented
32	C₂×#10621873	C₂²	1	1	yes	characteristic, complemented
33	C₂×#10621884	C₂²	1	1	yes	characteristic, complemented
34	C₂×#10621884	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
36	C₂×#10621882	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
39	#13063310	—	2	1	no	—
40	#13063301	C₂²	1	1	yes	characteristic
41	#13063300	C₂²	1	1	yes	characteristic
42	#13063299	C₂²	1	1	yes	characteristic, complemented
43	#13063295	—	2	1	no	—
44	#13063287	—	2	1	no	—
45	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
46	#13063283	C₂²	1	1	yes	characteristic, complemented
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	C₂×C₂²⋊D₄₃	—	2	1	no	—
77	C₂²×Dic₄₃	—	2	1	no	—
78	C₂²×Dic₄₃	D₄	1	1	yes	characteristic
79	#10621902	—	2	2	no	—
80	#10621902	—	2	2	no	—
81	#10621902	—	2	2	no	—
82	#10621902	D₄	1	4	yes	complemented
83	Q₈×D₄₃	—	2	2	no	—
84	Q₈×D₄₃	—	2	2	no	—
85	#10621900	—	2	8	no	—
86	#10621900	—	2	2	no	—
87	#10621900	D₄	1	4	yes	complemented
88	D₄×D₄₃	—	2	8	no	—
89	D₄×D₄₃	—	2	2	no	—
90	D₄×D₄₃	—	2	2	no	—
91	#10621898	—	2	8	no	—
92	#10621898	—	2	2	no	—
93	#10621898	—	2	2	no	—
94	C₂×D₁₇₂	—	2	1	no	—
95	C₂×D₁₇₂	—	2	1	no	—
96	C₂×D₁₇₂	—	2	1	no	—
97	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
98	C₂×D₁₇₂	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₄₃	—	2	8	no	—
100	C₂×C₄×D₄₃	—	2	1	no	—
101	C₂×C₄×D₄₃	—	2	1	no	—
102	C₂×C₄×D₄₃	—	2	2	no	—
103	C₂×C₄×D₄₃	—	2	2	no	—
104	C₂×C₄×D₄₃	—	2	1	no	—
105	C₂×C₄×D₄₃	—	2	1	no	—
106	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
107	C₂×C₄×D₄₃	D₄	1	1	yes	characteristic
108	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₄₃	C₂³	1	1	yes	characteristic
110	C₂×Dic₈₆	—	2	1	no	—
111	C₂×Dic₈₆	C₂³	1	1	yes	characteristic
112	Q₁₆×C₄₃	—	2	2	no	—
113	SD₁₆×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₄⋊C₄×C₄₃	—	2	1	no	—
117	C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₄₃	—	2	1	no	—
119	#10621885	—	2	2	no	—
120	#10621884	—	2	2	no	—
121	#10621884	—	2	2	no	—
122	#10621882	—	2	2	no	—
123	(C₂×D₄₃)⋊C₄	—	2	1	no	—
124	(C₂×D₄₃)⋊C₄	—	2	1	no	—
125	(C₂×D₄₃)⋊C₄	—	2	1	no	—
126	(C₂×D₄₃)⋊C₄	—	2	1	no	—
127	C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
128	Dic₄₃⋊C₄	—	2	1	no	—
129	C₄×Dic₄₃	—	2	1	no	—
130	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
131	C₂×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
132	D₃₄₄	—	2	2	no	—
133	#10621873	—	2	2	no	—
134	C₈×D₄₃	—	2	2	no	—
135	C₈×D₄₃	—	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	—	2	1	no	—
143	C₂²×D₄₃	—	4	1	no	—
144	C₂²×D₄₃	—	4	2	no	—
145	C₂²×D₄₃	—	4	2	no	—
146	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×D₄₃	C₂×D₄	1	1	yes	characteristic
148	Q₈×C₄₃	—	2	1	no	—
149	Q₈×C₄₃	—	2	1	no	—
150	Q₈×C₄₃	—	2	1	no	—
151	Q₈×C₄₃	C₂×D₄	1	2	yes	—
152	D₄×C₄₃	—	2	4	no	—
153	D₄×C₄₃	—	2	1	no	—
154	D₄×C₄₃	C₂×D₄	1	2	yes	—
155	C₂×C₄×C₄₃	—	2	4	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	—	2	1	no	—
161	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
163	C₂²⋊D₄₃	—	2	4	no	—
164	C₂²⋊D₄₃	—	2	4	no	—
165	C₂²⋊D₄₃	—	2	4	no	—
166	C₂²⋊D₄₃	—	4	2	no	—
167	C₂×Dic₄₃	—	2	1	no	—
168	C₂×Dic₄₃	—	2	2	no	—
169	C₂×Dic₄₃	—	2	4	no	—
170	C₂×Dic₄₃	—	2	1	no	—
171	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
172	C₂×Dic₄₃	C₂×D₄	1	1	yes	characteristic
173	D₁₇₂	—	2	4	no	—
174	D₁₇₂	—	2	1	no	—
175	D₁₇₂	—	2	1	no	—
176	D₁₇₂	—	2	1	no	—
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	C₂×D₄	1	2	yes	—
180	C₄×D₄₃	—	2	4	no	—
181	C₄×D₄₃	—	2	4	no	—
182	C₄×D₄₃	—	2	2	no	—
183	C₄×D₄₃	—	2	1	no	—
184	C₄×D₄₃	—	2	1	no	—
185	C₄×D₄₃	—	2	2	no	—
186	C₄×D₄₃	—	2	4	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	C₂×D₄	1	2	yes	—
189	C₄×D₄₃	C₂×D₄	1	2	yes	—
190	Dic₈₆	—	2	4	no	—
191	Dic₈₆	—	2	1	no	—
192	Dic₈₆	C₂×D₄	1	2	yes	—
193	C₈×C₄₃	—	2	1	no	—
194	C₈×C₄₃	—	2	1	no	—
195	C₄₃⋊C₈	—	2	1	no	—
196	C₄₃⋊C₈	—	2	1	no	—
197	C₂²×C₄₃	—	2	2	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	—	2	1	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	4	1	no	—
202	C₂²×C₄₃	—	4	1	no	—
203	C₂²×C₄₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×D₄₃	—	2	1	no	—
205	C₂×D₄₃	—	2	1	no	—
206	C₂×D₄₃	—	2	1	no	—
207	C₂×D₄₃	—	2	1	no	—
208	C₂×D₄₃	—	2	2	no	—
209	C₂×D₄₃	—	4	4	no	—
210	C₂×D₄₃	—	4	8	no	—
211	C₂×D₄₃	—	4	1	no	—
212	C₂×D₄₃	—	4	1	no	—
213	C₂×D₄₃	—	4	1	no	—
214	C₂×D₄₃	—	4	1	no	—
215	C₂×D₄₃	—	4	1	no	—
216	C₂×D₄₃	#120	1	2	yes	—
217	C₂×D₄₃	#135	1	2	yes	complemented
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	1	no	—
220	C₄×C₄₃	—	4	1	no	—
221	C₄×C₄₃	—	4	1	no	—
222	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
224	Dic₄₃	—	2	1	no	—
225	Dic₄₃	—	2	2	no	—
226	Dic₄₃	—	4	1	no	—
227	Dic₄₃	#120	1	2	yes	—
228	#3002	—	43	1	no	maximal, Sylow
229	C₂×C₄₃	—	4	1	no	—
230	C₂×C₄₃	—	4	2	no	—
231	C₂×C₄₃	C₂×#120	1	1	yes	characteristic
232	C₂×C₄₃	C₂×#135	1	1	yes	characteristic
233	C₂×C₄₃	#575	1	1	yes	characteristic
234	D₄₃	—	2	2	no	—
235	D₄₃	—	2	2	no	—
236	D₄₃	—	4	2	no	—
237	D₄₃	—	8	1	no	—
238	C₂²×#41	—	43	1	no	—
239	C₂×#135	—	43	1	no	—
240	C₂×#135	—	43	1	no	—
241	#525	—	43	1	no	—
242	#452	—	43	1	no	—
243	#452	D₄₃	1	1	yes	characteristic, complemented
244	#451	—	43	1	no	—
245	#450	—	43	1	no	—
246	#449	—	43	1	no	—
247	#449	—	43	1	no	—
248	#448	—	43	1	no	—
249	#447	—	43	1	no	—
250	#416	—	43	1	no	—
251	#416	—	43	1	no	—
252	C₂×C₂²⋊C₈	—	43	1	no	—
253	C₄₃	#3002	1	1	yes	characteristic, complemented, Sylow
254	C₂×#41	—	43	1	no	—
255	C₂×#41	—	43	1	no	—
256	C₂×#41	—	43	1	no	—
257	C₂×#41	—	43	1	no	—
258	C₂×#41	—	86	1	no	—
259	C₂×#41	—	86	1	no	—
260	C₂×#41	—	86	4	no	—
261	C₂×#41	—	86	4	no	—
262	C₂×#41	C₂×D₄₃	1	1	yes	characteristic
263	C₂²×Q₈	—	43	1	no	—
264	C₂²×D₄	—	43	1	no	—
265	C₂²×D₄	—	86	1	no	—
266	C₂³×C₄	—	43	1	no	—
267	C₂³×C₄	—	86	1	no	—
268	#135	—	86	4	no	—
269	#135	—	86	4	no	—
270	C₂×Q₁₆	—	43	1	no	—
271	C₂×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
272	C₂×SD₁₆	—	43	1	no	—
273	C₂×SD₁₆	—	43	1	no	—
274	C₂×SD₁₆	—	43	1	no	—
275	C₂×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
276	C₂×D₈	—	43	1	no	—
277	C₂×D₈	—	43	1	no	—
278	C₂²×C₈	—	43	1	no	—
279	C₂²×C₈	—	43	1	no	—
280	#123	—	86	1	no	—
281	C₂²⋊Q₈	—	43	1	no	—
282	C₂²⋊Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
283	#121	—	43	1	no	—
284	#121	—	43	1	no	—
285	#120	—	86	1	no	—
286	C₄×D₄	—	86	1	no	—
287	C₄×D₄	—	86	1	no	—
288	#117	—	43	1	no	—
289	#103	—	43	1	no	—
290	#103	—	43	1	no	—
291	#103	—	43	1	no	—
292	#103	C₂×D₄₃	1	1	yes	characteristic, complemented
293	#102	—	43	1	no	—
294	#102	—	43	1	no	—
295	#102	—	43	1	no	—
296	#102	C₂×D₄₃	1	1	yes	characteristic, complemented
297	C₂²⋊C₈	—	43	1	no	—
298	C₂²⋊C₈	—	43	1	no	—
299	C₂²⋊C₈	—	43	1	no	—
300	C₂²⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
301	C₂⁴	—	43	1	no	—
302	C₂⁴	—	86	1	no	—
303	#41	—	2	2	no	—
304	#41	—	2	2	no	—
305	#41	—	43	4	no	—
306	#41	—	43	4	no	—
307	#41	—	86	2	no	—
308	#41	—	86	2	no	—
309	#41	—	86	8	no	—
310	#41	—	86	2	no	—
311	#41	—	86	2	no	—
312	#41	—	86	2	no	—
313	#41	—	86	2	no	—
314	#41	—	86	8	no	—
315	C₂×Q₈	—	43	1	no	—
316	C₂×Q₈	—	86	1	no	—
317	C₂×Q₈	—	86	2	no	—
318	C₂×Q₈	—	86	2	no	—
319	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
320	C₂×Q₈	C₂²×D₄₃	1	1	yes	characteristic
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	43	1	no	—
323	C₂×D₄	—	43	1	no	—
324	C₂×D₄	—	86	1	no	—
325	C₂×D₄	—	86	1	no	—
326	C₂×D₄	—	86	1	no	—
327	C₂×D₄	—	86	1	no	—
328	C₂×D₄	—	86	2	no	—
329	C₂×D₄	—	86	8	no	—
330	C₂×D₄	—	86	1	no	—
331	C₂×D₄	—	86	1	no	—
332	C₂×D₄	—	86	2	no	—
333	C₂×D₄	—	86	1	no	—
334	C₂×D₄	C₂²×D₄₃	1	1	yes	characteristic
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	43	1	no	—
337	C₂²×C₄	—	43	1	no	—
338	C₂²×C₄	—	43	1	no	—
339	C₂²×C₄	—	43	1	no	—
340	C₂²×C₄	—	43	1	no	—
341	C₂²×C₄	—	86	2	no	—
342	C₂²×C₄	—	86	2	no	—
343	C₂²×C₄	—	86	1	no	—
344	C₂²×C₄	—	86	1	no	—
345	C₂²×C₄	—	86	1	no	—
346	C₂²×C₄	—	86	8	no	—
347	C₂²×C₄	—	86	1	no	—
348	C₂²×C₄	—	86	1	no	—
349	C₂²×C₄	C₂²×D₄₃	1	1	yes	characteristic
350	Q₁₆	—	2	2	no	—
351	Q₁₆	—	86	2	no	—
352	SD₁₆	—	2	2	no	—
353	SD₁₆	—	86	2	no	—
354	SD₁₆	—	86	2	no	—
355	SD₁₆	—	86	2	no	—
356	D₈	—	86	2	no	—
357	D₈	—	86	2	no	—
358	C₂×C₈	—	43	1	no	—
359	C₂×C₈	—	43	1	no	—
360	C₂×C₈	—	86	2	no	—
361	C₂×C₈	—	86	2	no	—
362	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
363	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	43	1	no	—
366	C₄⋊C₄	—	86	1	no	—
367	C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
368	C₂²⋊C₄	—	2	1	no	—
369	C₂²⋊C₄	—	86	1	no	—
370	C₂²⋊C₄	—	86	1	no	—
371	C₂²⋊C₄	—	86	1	no	—
372	C₂²⋊C₄	—	86	1	no	—
373	C₄²	—	86	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	43	1	no	—
376	C₂³	—	43	1	no	—
377	C₂³	—	86	2	no	—
378	C₂³	—	86	2	no	—
379	C₂³	—	86	4	no	—
380	C₂³	—	86	1	no	—
381	C₂³	—	86	1	no	—
382	C₂³	—	172	1	no	—
383	C₂³	—	172	2	no	—
384	C₂³	—	172	2	no	—
385	C₂³	D₄×D₄₃	1	1	yes	characteristic
386	Q₈	—	2	1	no	—
387	Q₈	—	2	1	no	—
388	Q₈	—	2	1	no	—
389	Q₈	—	43	2	no	—
390	Q₈	—	86	4	no	—
391	Q₈	—	86	1	no	—
392	Q₈	D₄×D₄₃	1	2	yes	—
393	D₄	—	2	4	no	—
394	D₄	—	2	1	no	—
395	D₄	—	43	2	no	—
396	D₄	—	86	4	no	—
397	D₄	—	86	4	no	—
398	D₄	—	86	4	no	—
399	D₄	—	86	4	no	—
400	D₄	—	86	1	no	—
401	D₄	—	86	1	no	—
402	D₄	—	86	1	no	—
403	D₄	—	172	2	no	—
404	D₄	—	172	2	no	—
405	D₄	—	172	2	no	—
406	D₄	D₄×D₄₃	1	2	yes	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	43	1	no	—
414	C₂×C₄	—	43	2	no	—
415	C₂×C₄	—	43	2	no	—
416	C₂×C₄	—	43	1	no	—
417	C₂×C₄	—	86	2	no	—
418	C₂×C₄	—	86	4	no	—
419	C₂×C₄	—	86	2	no	—
420	C₂×C₄	—	86	4	no	—
421	C₂×C₄	—	86	4	no	—
422	C₂×C₄	—	86	2	no	—
423	C₂×C₄	—	86	4	no	—
424	C₂×C₄	—	86	1	no	—
425	C₂×C₄	—	86	1	no	—
426	C₂×C₄	—	86	1	no	—
427	C₂×C₄	—	86	1	no	—
428	C₂×C₄	—	172	2	no	—
429	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₄₃	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	86	1	no	—
434	C₈	—	86	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	43	2	no	—
442	C₂²	—	43	2	no	—
443	C₂²	—	86	1	no	—
444	C₂²	—	86	1	no	—
445	C₂²	—	86	1	no	—
446	C₂²	—	86	1	no	—
447	C₂²	—	86	2	no	—
448	C₂²	—	172	4	no	—
449	C₂²	—	172	8	no	—
450	C₂²	—	172	1	no	—
451	C₂²	—	172	1	no	—
452	C₂²	—	172	1	no	—
453	C₂²	—	172	1	no	—
454	C₂²	—	172	1	no	—
455	C₂²	C₂×D₄×D₄₃	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	2	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	43	2	no	—
461	C₄	—	86	1	no	—
462	C₄	—	86	2	no	—
463	C₄	—	172	1	no	—
464	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
465	C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
466	C₂	—	4	1	no	—
467	C₂	—	4	2	no	—
468	C₂	—	86	2	no	—
469	C₂	—	86	2	no	—
470	C₂	—	344	1	no	—
471	C₂	—	172	2	no	—
472	C₂	#120×D₄₃	1	1	yes	characteristic
473	C₂	#135×D₄₃	1	1	yes	characteristic
474	C₂	#14583698	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	#3002
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
1. C₂×#41×D₄₃	C₂	semidirect
2. C₂×#13063348	C₂	semidirect
3. C₂×#13063346	C₂	semidirect
4. #14583412	C₂	semidirect
5. #14583059	C₂	semidirect
6. #14583053	C₂	semidirect
7. #14583048	C₂	semidirect
8. #14583046	C₂	semidirect
9. #14583044	C₂	semidirect
10. #14583039	C₂	semidirect
11. #14583034	C₂	semidirect
12. #14582894	C₂	semidirect
13. #14582892	C₂	semidirect
14. C₂²⋊C₈×D₄₃	C₂	semidirect
15. C₄₃×#452	C₂	semidirect
17. C₂×#10621902	C₂²	semidirect
31. C₂×#10621885	C₂²	semidirect
32. C₂×#10621873	C₂²	semidirect
33. C₂×#10621884	C₂²	semidirect
34. C₂×#10621884	C₂²	semidirect
35. C₂×D₃₄₄	C₂²	semidirect
36. C₂×#10621882	C₂²	semidirect
37. C₂×C₈×D₄₃	C₂²	semidirect
38. C₂×C₈×D₄₃	C₂²	semidirect
42. #13063299	C₂²	semidirect
46. #13063283	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
82. #10621902	D₄	semidirect
87. #10621900	D₄	semidirect
217. C₂×D₄₃	#135	semidirect
243. #452	D₄₃	semidirect
253. C₄₃	#3002	semidirect
271. C₂×Q₁₆	C₂×D₄₃	semidirect
275. C₂×SD₁₆	C₂×D₄₃	semidirect
282. C₂²⋊Q₈	C₂×D₄₃	semidirect
292. #103	C₂×D₄₃	semidirect
296. #102	C₂×D₄₃	semidirect
300. C₂²⋊C₈	C₂×D₄₃	semidirect