Subgroups — #25078940

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145024	C₂	1	1	yes	maximal, characteristic
2	#19144628	C₂	1	2	yes	maximal, complemented
3	C₈×Q₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#19133962	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133956	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133955	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133946	C₂	1	2	yes	maximal, complemented
8	#19133945	C₂	1	2	yes	maximal, complemented
9	#19133342	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133243	C₂	1	2	yes	maximal, complemented
11	C₄₃×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063348	—	2	1	no	—
13	C₂×#13063348	—	2	1	no	—
14	#14583450	C₂²	1	2	yes	—
15	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
16	#14583284	—	2	1	no	—
17	#14583284	—	2	1	no	—
18	#14583276	C₂²	1	1	yes	characteristic
19	#14583273	C₂²	1	2	yes	—
20	#14583219	—	2	2	no	—
21	#14583181	C₂²	1	2	yes	—
22	#14583100	C₂²	1	2	yes	—
23	#14583099	C₂²	1	2	yes	—
24	#14583039	—	2	2	no	—
25	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
26	C₈×Dic₈₆	—	2	1	no	—
27	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
28	#14583023	—	2	1	no	—
29	#14583023	C₂²	1	1	yes	characteristic
30	#14582986	—	2	2	no	—
31	#14582984	—	2	2	no	—
32	#14582951	C₂²	1	2	yes	—
33	C₄⋊C₈×D₄₃	—	2	1	no	—
34	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₄₃	—	2	1	no	—
36	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
37	#14582652	C₂²	1	1	yes	characteristic
38	#14582649	C₂²	1	2	yes	—
39	#14582645	C₂²	1	2	yes	—
40	#14582642	C₂²	1	2	yes	—
41	#14582642	C₂²	1	2	yes	—
42	C₄₃×#494	C₂²	1	1	yes	characteristic
43	C₄₃×#475	C₂²	1	2	yes	—
44	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#335	C₂²	1	1	yes	characteristic
46	C₄₃×#332	C₂²	1	2	yes	—
47	C₂×#10621902	—	2	2	no	—
48	C₂×Q₈×D₄₃	D₄	1	1	yes	characteristic
49	#13063348	—	4	4	no	—
50	#13063348	—	4	4	no	—
51	C₂×#10621873	—	2	2	no	—
52	C₂×#10621884	—	2	2	no	—
53	C₂×#10621884	—	2	2	no	—
54	C₂×#10621884	—	2	2	no	—
55	C₂×D₃₄₄	—	2	1	no	—
56	C₂×D₃₄₄	—	2	1	no	—
57	C₂×C₈×D₄₃	—	2	1	no	—
58	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
59	C₂×C₈×D₄₃	D₄	1	1	yes	characteristic
60	#13063322	C₂³	1	2	yes	—
61	#13063314	—	2	2	no	—
62	#13063300	—	2	2	no	—
63	#13063300	—	2	2	no	—
64	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
65	C₄×Dic₈₆	—	2	1	no	—
66	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
67	#13063290	—	2	1	no	—
68	#13063290	D₄	1	1	yes	characteristic
69	#13063287	—	2	2	no	—
70	#13063287	—	2	2	no	—
71	C₄⋊C₄×D₄₃	—	2	1	no	—
72	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
73	C₄²×D₄₃	—	2	1	no	—
74	C₄²×D₄₃	C₂³	1	1	yes	characteristic
75	#13063256	—	2	2	no	—
76	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
77	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
78	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
79	Dic₄₃⋊C₈	—	2	1	no	—
80	Dic₄₃⋊C₈	—	2	1	no	—
81	Dic₄₃⋊C₈	—	2	1	no	—
82	#13063248	—	2	2	no	—
83	#13063247	—	2	2	no	—
84	#13063245	—	2	2	no	—
85	(C₂×D₄₃)⋊C₈	—	2	2	no	—
86	C₄×C₄₃⋊C₈	—	2	1	no	—
87	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₈×Dic₄₃	—	2	1	no	—
89	C₈×Dic₄₃	—	2	2	no	—
90	C₈×Dic₄₃	—	2	1	no	—
91	C₈×Dic₄₃	D₄	1	1	yes	characteristic
92	C₈×Dic₄₃	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₄₃	—	2	1	no	—
94	C₂×Q₁₆×C₄₃	—	2	1	no	—
95	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
96	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
97	#106×C₄₃	—	2	2	no	—
98	C₄⋊C₈×C₄₃	—	2	1	no	—
99	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
101	#103×C₄₃	—	2	2	no	—
102	C₄×C₈×C₄₃	—	2	1	no	—
103	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
106	#10621902	—	4	4	no	—
107	#10621902	—	4	4	no	—
108	Q₈×D₄₃	—	2	2	no	—
109	Q₈×D₄₃	—	2	2	no	—
110	C₂×D₁₇₂	—	2	2	no	—
111	C₂×D₁₇₂	—	2	2	no	—
112	C₂×D₁₇₂	—	2	2	no	—
113	C₂×D₁₇₂	—	4	2	no	—
114	C₂×C₄×D₄₃	—	2	1	no	—
115	C₂×C₄×D₄₃	—	2	1	no	—
116	C₂×C₄×D₄₃	—	4	2	no	—
117	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
120	C₂×Dic₈₆	—	2	1	no	—
121	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
122	Q₁₆×C₄₃	—	4	2	no	—
123	Q₁₆×C₄₃	—	4	2	no	—
124	C₂×C₈×C₄₃	—	2	1	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
128	C₄⋊C₄×C₄₃	—	2	1	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	2	2	no	—
131	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₄₃	—	2	1	no	—
133	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
134	#10621884	—	4	4	no	—
135	#10621884	—	4	4	no	—
136	#10621884	—	4	4	no	—
137	(C₂×D₄₃)⋊C₄	—	4	2	no	—
138	(C₂×D₄₃)⋊C₄	—	4	2	no	—
139	C₄⋊Dic₄₃	—	2	1	no	—
140	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
141	Dic₄₃⋊C₄	—	2	1	no	—
142	Dic₄₃⋊C₄	—	2	1	no	—
143	Dic₄₃⋊C₄	—	2	1	no	—
144	C₄×Dic₄₃	—	2	1	no	—
145	C₄×Dic₄₃	—	2	1	no	—
146	C₄×Dic₄₃	—	2	1	no	—
147	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₄₃	#41	1	1	yes	characteristic
150	C₂×C₄₃⋊C₈	—	2	1	no	—
151	C₂×C₄₃⋊C₈	—	2	2	no	—
152	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
154	D₃₄₄	—	4	2	no	—
155	D₃₄₄	—	4	2	no	—
156	#10621873	—	4	4	no	—
157	C₈×D₄₃	—	2	2	no	—
158	C₈×D₄₃	—	4	2	no	—
159	C₈×D₄₃	SD₁₆	1	4	yes	complemented
160	C₂²×D₄₃	—	4	2	no	—
161	C₂²×D₄₃	#121	1	1	yes	characteristic
162	Q₈×C₄₃	—	2	1	no	—
163	Q₈×C₄₃	—	4	2	no	—
164	Q₈×C₄₃	—	4	2	no	—
165	Q₈×C₄₃	#135	1	2	yes	complemented
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
172	C₂×Dic₄₃	—	2	1	no	—
173	C₂×Dic₄₃	—	2	1	no	—
174	C₂×Dic₄₃	#121	1	1	yes	characteristic
175	C₂×Dic₄₃	#121	1	1	yes	characteristic
176	C₂×Dic₄₃	#121	1	1	yes	characteristic
177	D₁₇₂	—	4	2	no	—
178	D₁₇₂	—	4	2	no	—
179	D₁₇₂	—	4	2	no	—
180	D₁₇₂	—	4	2	no	—
181	D₁₇₂	—	8	2	no	—
182	D₁₇₂	—	8	4	no	—
183	C₄×D₄₃	—	2	4	no	—
184	C₄×D₄₃	—	2	1	no	—
185	C₄×D₄₃	—	2	1	no	—
186	C₄×D₄₃	—	4	1	no	—
187	C₄×D₄₃	—	4	2	no	—
188	C₄×D₄₃	—	8	4	no	—
189	C₄×D₄₃	C₂×SD₁₆	1	2	yes	—
190	C₄×D₄₃	AGL(1,ℤ/8)	1	2	yes	—
191	Dic₈₆	—	2	4	no	—
192	Dic₈₆	—	2	1	no	—
193	Dic₈₆	#135	1	2	yes	complemented
194	C₈×C₄₃	—	2	1	no	—
195	C₈×C₄₃	—	4	2	no	—
196	C₈×C₄₃	—	4	1	no	—
197	C₈×C₄₃	C₂×SD₁₆	1	2	yes	—
198	C₄₃⋊C₈	—	2	1	no	—
199	C₄₃⋊C₈	—	4	2	no	—
200	C₄₃⋊C₈	—	4	1	no	—
201	C₄₃⋊C₈	C₂×SD₁₆	1	2	yes	—
202	#19114	—	43	1	no	maximal, Sylow
203	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
204	C₂×D₄₃	—	2	1	no	—
205	C₂×D₄₃	—	2	1	no	—
206	C₂×D₄₃	—	8	2	no	—
207	C₂×D₄₃	—	8	2	no	—
208	C₂×D₄₃	—	8	2	no	—
209	C₂×D₄₃	#460	1	2	yes	—
210	C₄×C₄₃	—	2	2	no	—
211	C₄×C₄₃	—	2	1	no	—
212	C₄×C₄₃	—	4	1	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	C₂²×SD₁₆	1	1	yes	characteristic
215	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
216	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
217	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	Dic₄₃	—	2	1	no	—
219	Dic₄₃	—	2	2	no	—
220	Dic₄₃	—	2	1	no	—
221	Dic₄₃	—	4	1	no	—
222	Dic₄₃	#460	1	2	yes	—
223	#3147	—	43	1	no	—
224	#3103	—	43	2	no	—
225	C₂×C₈×Q₈	—	43	1	no	—
226	#1670	—	43	1	no	—
227	#1670	D₄₃	1	1	yes	characteristic, complemented
228	#1668	—	43	1	no	—
229	#1668	—	43	1	no	—
230	#1666	—	43	2	no	—
231	#1666	—	43	2	no	—
232	#1564	—	43	1	no	—
233	#1540	—	43	2	no	—
234	C₂×C₄₃	C₂×#460	1	1	yes	characteristic
235	C₂×C₄₃	#3050	1	1	yes	characteristic
236	C₂×C₄₃	#3067	1	1	yes	characteristic
237	D₄₃	—	2	2	no	—
238	D₄₃	—	16	2	no	—
239	C₂×#135	—	86	1	no	—
240	C₂×#135	—	86	1	no	—
241	#532	—	43	2	no	—
242	C₂×C₄×Q₈	—	43	1	no	—
243	#495	—	86	1	no	—
244	#495	—	86	1	no	—
245	#494	C₂×D₄₃	1	1	yes	characteristic
246	#493	—	43	1	no	—
247	#492	—	43	2	no	—
248	#481	—	86	2	no	—
249	#475	—	43	2	no	—
250	#475	C₂×D₄₃	1	2	yes	—
251	#460	—	43	2	no	—
252	#460	—	43	2	no	—
253	#448	—	86	2	no	—
254	C₈×Q₈	—	43	1	no	—
255	C₈×Q₈	—	43	1	no	—
256	C₈×Q₈	—	43	1	no	—
257	C₈×Q₈	—	86	1	no	—
258	C₈×Q₈	—	86	1	no	—
259	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
260	C₄×SD₁₆	—	86	2	no	—
261	C₄×SD₁₆	—	86	2	no	—
262	#431	—	43	2	no	—
263	C₂×C₄⋊C₈	—	43	1	no	—
264	C₂×C₄⋊C₈	—	86	1	no	—
265	C₂×C₄×C₈	—	43	1	no	—
266	C₂×C₄×C₈	—	86	1	no	—
267	#335	—	43	1	no	—
268	#335	C₂×D₄₃	1	1	yes	characteristic
269	#334	—	43	2	no	—
270	#332	—	43	2	no	—
271	#332	C₂×D₄₃	1	2	yes	—
272	#331	—	43	2	no	—
273	#331	—	43	2	no	—
274	C₄₃	#19114	1	1	yes	characteristic, complemented, Sylow
275	C₂×#41	—	86	2	no	—
276	C₂²×Q₈	—	43	1	no	—
277	#135	—	172	4	no	—
278	#135	—	172	4	no	—
279	C₂×Q₁₆	—	2	1	no	—
280	C₂×Q₁₆	—	2	1	no	—
281	C₂×SD₁₆	—	86	2	no	—
282	C₂×SD₁₆	—	86	2	no	—
283	C₂×SD₁₆	—	86	2	no	—
284	C₂×SD₁₆	—	86	2	no	—
285	C₂×D₈	—	86	1	no	—
286	C₂×D₈	—	86	1	no	—
287	C₂²×C₈	—	43	1	no	—
288	C₂²×C₈	—	43	1	no	—
289	C₂²×C₈	—	86	1	no	—
290	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
291	#127	—	43	2	no	—
292	#124	—	86	2	no	—
293	#121	—	86	2	no	—
294	#121	—	86	2	no	—
295	C₄×Q₈	—	43	1	no	—
296	C₄×Q₈	—	43	1	no	—
297	C₄×Q₈	—	43	1	no	—
298	C₄×Q₈	—	86	1	no	—
299	C₄×Q₈	—	86	1	no	—
300	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
301	C₄×D₄	—	86	2	no	—
302	C₄×D₄	—	86	2	no	—
303	C₂×C₄⋊C₄	—	43	1	no	—
304	C₂×C₄⋊C₄	—	86	1	no	—
305	C₂×C₄²	—	43	1	no	—
306	C₂×C₄²	—	86	1	no	—
307	#106	—	2	2	no	—
308	#106	—	86	2	no	—
309	C₄⋊C₈	—	2	1	no	—
310	C₄⋊C₈	—	43	1	no	—
311	C₄⋊C₈	—	43	2	no	—
312	C₄⋊C₈	—	86	1	no	—
313	C₄⋊C₈	—	86	1	no	—
314	C₄⋊C₈	—	86	1	no	—
315	C₄⋊C₈	—	86	1	no	—
316	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
318	#103	—	2	2	no	—
319	#103	—	86	2	no	—
320	#102	—	86	2	no	—
321	#102	—	86	2	no	—
322	C₂²⋊C₈	—	86	2	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	43	1	no	—
325	C₄×C₈	—	43	1	no	—
326	C₄×C₈	—	43	1	no	—
327	C₄×C₈	—	86	1	no	—
328	C₄×C₈	—	86	2	no	—
329	C₄×C₈	—	86	1	no	—
330	C₄×C₈	—	86	1	no	—
331	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
332	#41	—	172	4	no	—
333	#41	—	172	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	43	1	no	—
336	C₂×Q₈	—	86	1	no	—
337	C₂×Q₈	—	86	2	no	—
338	C₂×Q₈	—	86	2	no	—
339	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
340	C₂×D₄	—	86	2	no	—
341	C₂×D₄	—	86	2	no	—
342	C₂×D₄	—	86	2	no	—
343	C₂×D₄	—	172	2	no	—
344	C₂²×C₄	—	43	1	no	—
345	C₂²×C₄	—	43	1	no	—
346	C₂²×C₄	—	43	1	no	—
347	C₂²×C₄	—	86	1	no	—
348	C₂²×C₄	—	86	1	no	—
349	C₂²×C₄	—	172	2	no	—
350	Q₁₆	—	4	2	no	—
351	Q₁₆	—	4	2	no	—
352	SD₁₆	—	172	4	no	—
353	SD₁₆	—	172	4	no	—
354	SD₁₆	—	172	4	no	—
355	SD₁₆	—	172	4	no	—
356	D₈	—	172	2	no	—
357	D₈	—	172	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	43	1	no	—
361	C₂×C₈	—	43	4	no	—
362	C₂×C₈	—	43	1	no	—
363	C₂×C₈	—	86	2	no	—
364	C₂×C₈	—	86	1	no	—
365	C₂×C₈	—	86	2	no	—
366	C₂×C₈	—	172	2	no	—
367	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
368	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	43	1	no	—
373	C₄⋊C₄	—	86	1	no	—
374	C₄⋊C₄	—	86	1	no	—
375	C₄⋊C₄	—	86	1	no	—
376	C₄⋊C₄	—	86	1	no	—
377	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
378	C₂²⋊C₄	—	172	2	no	—
379	C₂²⋊C₄	—	172	2	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	43	1	no	—
382	C₄²	—	43	1	no	—
383	C₄²	—	43	1	no	—
384	C₄²	—	86	1	no	—
385	C₄²	—	86	1	no	—
386	C₄²	—	86	1	no	—
387	C₄²	C₂³×D₄₃	1	1	yes	characteristic
388	C₂³	—	43	1	no	—
389	C₂³	—	172	2	no	—
390	Q₈	—	2	1	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	43	2	no	—
394	Q₈	—	86	4	no	—
395	Q₈	—	86	1	no	—
396	Q₈	#13063348	1	2	yes	complemented
397	D₄	—	344	2	no	—
398	D₄	—	344	4	no	—
399	D₄	—	172	2	no	—
400	D₄	—	172	2	no	—
401	D₄	—	172	2	no	—
402	D₄	—	172	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	2	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	—	43	1	no	—
411	C₂×C₄	—	86	4	no	—
412	C₂×C₄	—	86	1	no	—
413	C₂×C₄	—	86	1	no	—
414	C₂×C₄	—	86	1	no	—
415	C₂×C₄	—	86	1	no	—
416	C₂×C₄	—	344	4	no	—
417	C₂×C₄	—	172	1	no	—
418	C₂×C₄	—	172	2	no	—
419	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
421	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₈	—	43	2	no	—
426	C₈	—	86	1	no	—
427	C₈	—	172	2	no	—
428	C₈	—	172	1	no	—
429	C₈	SD₁₆×D₄₃	1	2	yes	—
430	C₂²	—	43	2	no	—
431	C₂²	—	86	1	no	—
432	C₂²	—	86	1	no	—
433	C₂²	—	344	2	no	—
434	C₂²	—	344	2	no	—
435	C₂²	—	344	2	no	—
436	C₂²	#121×D₄₃	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	2	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	43	2	no	—
442	C₄	—	86	1	no	—
443	C₄	—	86	1	no	—
444	C₄	—	86	2	no	—
445	C₄	—	172	1	no	—
446	C₄	C₂×SD₁₆×D₄₃	1	1	yes	characteristic
447	C₄	#135×D₄₃	1	1	yes	characteristic
448	C₄	C₂×#13063348	1	1	yes	characteristic
449	C₄	AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
450	C₂	—	86	2	no	—
451	C₂	—	688	2	no	—
452	C₂	#460×D₄₃	1	1	yes	characteristic
453	C₂	#19144178	1	1	yes	characteristic
454	C₂	#19144317	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1670	C₂
socle	C₂²×C₄₃	C₂×#121
prime radical	#19145024	C₂
hypercenter	#1670	D₄₃
hypocenter	C₄₃	#19114
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
2. #19144628	C₂	semidirect
3. C₈×Q₈×D₄₃	C₂	semidirect
4. #19133962	C₂	semidirect
5. #19133956	C₂	semidirect
6. #19133955	C₂	semidirect
7. #19133946	C₂	semidirect
8. #19133945	C₂	semidirect
9. #19133342	C₂	semidirect
10. #19133243	C₂	semidirect
11. C₄₃×#1670	C₂	semidirect
159. C₈×D₄₃	SD₁₆	semidirect
165. Q₈×C₄₃	#135	semidirect
193. Dic₈₆	#135	semidirect
227. #1670	D₄₃	semidirect
274. C₄₃	#19114	semidirect
396. Q₈	#13063348	semidirect

Maximal subgroups

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

subgroup	index
#19145024	2
#19144628	2
C₈×Q₈×D₄₃	2
#19133962	2
#19133956	2
#19133955	2
#19133946	2
#19133945	2
#19133342	2
#19133243	2
C₄₃×#1670	2
#19114	43