Subgroups — #25966233

Order 11008.

1770 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147998	C₂	1	2	yes	maximal
2	#19145132	C₂	1	4	yes	maximal, complemented
3	#19145128	C₂	1	4	yes	maximal, complemented
4	#19145124	C₂	1	4	yes	maximal, complemented
5	#19145120	C₂	1	4	yes	maximal, complemented
6	#19145118	C₂	1	2	yes	maximal, complemented
7	#19145117	C₂	1	2	yes	maximal, complemented
8	#19145109	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145107	C₂	1	2	yes	maximal, complemented
10	#19143183	C₂	1	2	yes	maximal
11	#427×D₄₃	C₂	1	2	yes	maximal
12	C₂×#14582853	C₂	1	1	yes	maximal, characteristic
13	C₄₃×#3160	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#10621872	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
16	#14583529	C₂²	1	8	yes	—
17	#14583528	—	2	4	no	—
18	#14583526	C₂²	1	8	yes	—
19	#14583524	—	2	4	no	—
20	#14583456	C₂²	1	2	yes	—
21	#14583453	—	2	8	no	—
22	#14583452	C₂²	1	4	yes	—
23	C₂×#13063282	C₂²	1	1	yes	characteristic
24	#117×D₄₃	C₂²	1	4	yes	—
25	#14583309	C₂²	1	8	yes	complemented
26	#14583307	C₂²	1	8	yes	complemented
27	#14583306	C₂²	1	8	yes	complemented
28	#14583305	C₂²	1	8	yes	complemented
29	#14583304	C₂²	1	2	yes	complemented
30	#14583303	C₂²	1	4	yes	complemented
31	#14583301	C₂²	1	2	yes	complemented
32	#14583301	C₂²	1	2	yes	complemented
33	#14583300	C₂²	1	4	yes	complemented
34	#14583299	C₂²	1	4	yes	complemented
35	#14583297	C₂²	1	2	yes	complemented
36	#14583296	C₂²	1	4	yes	complemented
37	#14582940	C₂²	1	8	yes	—
38	#14582938	C₂²	1	8	yes	—
39	#14582937	C₂²	1	2	yes	—
40	#14582937	C₂²	1	2	yes	—
41	#14582936	C₂²	1	4	yes	—
42	#14582935	C₂²	1	4	yes	—
43	#14582935	C₂²	1	4	yes	—
44	#14582934	C₂²	1	4	yes	—
45	#107×D₄₃	C₂²	1	4	yes	—
46	#106×D₄₃	C₂²	1	4	yes	—
47	#14582853	C₂²	1	2	yes	—
48	#14582853	C₂²	1	2	yes	—
49	#14582853	C₂²	1	2	yes	—
50	#14582853	C₂²	1	2	yes	—
51	C₂×#13063236	C₂²	1	1	yes	characteristic
52	C₂×#13063235	C₂²	1	1	yes	characteristic
53	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
54	C₄₃×#533	C₂²	1	2	yes	—
55	C₄₃×#500	C₂²	1	2	yes	complemented
56	C₄₃×#499	C₂²	1	2	yes	complemented
57	C₄₃×#499	C₂²	1	2	yes	complemented
58	C₄₃×#498	C₂²	1	2	yes	complemented
59	C₄₃×#427	C₂²	1	2	yes	—
60	C₄₃×#427	C₂²	1	2	yes	—
61	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
62	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
63	C₂×#10621872	Q₈	1	8	yes	complemented
64	C₂×#10621872	C₂³	1	2	yes	—
65	C₂×#10621872	C₂³	1	2	yes	—
66	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
67	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
68	C₂×C₈×D₄₃	Q₈	1	8	yes	complemented
69	C₂×C₈×D₄₃	C₂³	1	2	yes	—
70	C₂×C₈×D₄₃	C₂³	1	2	yes	—
71	#13063325	C₂³	1	4	yes	—
72	#13063324	—	2	8	no	—
73	#13063324	C₂³	1	8	yes	—
74	#13063323	—	2	8	no	—
75	#13063317	C₂³	1	4	yes	—
76	#13063316	C₂³	1	8	yes	—
77	#13063315	—	2	8	no	—
78	#13063315	—	2	8	no	—
79	#13063305	—	2	8	no	—
80	#13063304	—	2	4	no	—
81	#13063303	—	2	8	no	—
82	#13063303	—	2	8	no	—
83	#13063302	—	2	8	no	—
84	#13063301	—	2	8	no	—
85	C₄×Dic₈₆	—	2	4	no	—
86	C₄×Dic₈₆	—	2	8	no	—
87	#13063284	C₂³	1	4	yes	—
88	#13063283	C₂³	1	8	yes	—
89	#13063282	—	2	4	no	—
90	#13063282	D₄	1	4	yes	—
91	#13063282	C₂³	1	2	yes	—
92	#13063282	C₂³	1	2	yes	—
93	#13063281	—	2	4	no	—
94	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
95	C₄⋊C₄×D₄₃	C₂³	1	8	yes	—
96	C₂×(C₂×D₄₃)⋊C₄	D₄	1	2	yes	—
97	C₂²⋊C₄×D₄₃	—	2	4	no	—
98	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
99	C₄²×D₄₃	—	2	4	no	—
100	#13063259	C₂³	1	4	yes	—
101	#13063259	C₂³	1	4	yes	—
102	#13063258	C₂³	1	8	yes	—
103	#13063258	C₂³	1	8	yes	—
104	#13063257	C₂³	1	4	yes	—
105	#13063257	C₂³	1	4	yes	—
106	#13063256	C₂³	1	8	yes	—
107	#13063256	C₂³	1	8	yes	—
108	#13063236	C₂³	1	2	yes	—
109	#13063236	C₂³	1	2	yes	—
110	#13063235	C₂³	1	2	yes	—
111	#13063235	C₂³	1	2	yes	—
112	C₈×Dic₄₃	C₂³	1	2	yes	—
113	C₈×Dic₄₃	C₂³	1	2	yes	—
114	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
116	C₄⋊Q₈×C₄₃	C₂³	1	4	yes	—
117	#125×C₄₃	C₂³	1	4	yes	—
118	C₂²⋊Q₈×C₄₃	—	2	4	no	—
119	C₄×Q₈×C₄₃	—	2	4	no	—
120	#117×C₄₃	C₂³	1	4	yes	—
121	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
122	#107×C₄₃	C₂³	1	4	yes	—
123	#107×C₄₃	C₂³	1	4	yes	—
124	#106×C₄₃	C₂³	1	4	yes	—
125	#106×C₄₃	C₂³	1	4	yes	—
126	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
130	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₄₃	—	2	4	no	—
132	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
134	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
135	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₄₃	—	2	8	no	—
137	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
138	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
139	C₂×C₄×D₄₃	C₂×Q₈	1	4	yes	—
140	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
141	C₂×Dic₈₆	—	2	4	no	—
142	C₂×Dic₈₆	—	2	8	no	—
143	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
144	C₂×C₈×C₄₃	C₂×Q₈	1	4	yes	—
145	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
147	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₄₃	—	2	8	no	—
150	C₄⋊C₄×C₄₃	—	2	4	no	—
151	C₄⋊C₄×C₄₃	C₂⁴	1	8	yes	—
152	C₂²⋊C₄×C₄₃	—	2	4	no	—
153	C₄²×C₄₃	—	2	4	no	—
154	C₄²×C₄₃	C₂×D₄	1	2	yes	—
155	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
156	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
157	C₂²⋊Dic₄₃	—	2	4	no	—
158	(C₂×D₄₃)⋊C₄	—	2	8	no	—
159	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
160	(C₂×D₄₃)⋊C₄	C₂×D₄	1	4	yes	—
161	C₄⋊Dic₄₃	—	2	4	no	—
162	C₄⋊Dic₄₃	—	2	8	no	—
163	C₄⋊Dic₄₃	C₂⁴	1	8	yes	—
164	Dic₄₃⋊C₄	—	2	8	no	—
165	Dic₄₃⋊C₄	—	2	8	no	—
166	Dic₄₃⋊C₄	—	2	8	no	—
167	Dic₄₃⋊C₄	—	2	8	no	—
168	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
169	Dic₄₃⋊C₄	C₂×D₄	1	4	yes	—
170	C₄×Dic₄₃	—	2	4	no	—
171	C₄×Dic₄₃	—	2	8	no	—
172	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
173	C₄×Dic₄₃	C₂⁴	1	2	yes	—
174	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
175	C₂×C₄₃⋊C₈	C₂×Q₈	1	4	yes	—
176	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
177	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
178	#10621872	C₂×Q₈	1	8	yes	—
179	#10621872	C₂×Q₈	1	8	yes	—
180	C₈×D₄₃	C₂×Q₈	1	8	yes	—
181	C₈×D₄₃	C₂×Q₈	1	8	yes	—
182	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
183	C₂²×D₄₃	—	4	2	no	—
184	C₂²×D₄₃	C₄⋊Q₈	1	4	yes	—
185	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
186	Q₈×C₄₃	—	8	4	no	—
187	C₂×C₄×C₄₃	—	2	8	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
191	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
193	C₂×C₄×C₄₃	C₂²×Q₈	1	2	yes	—
194	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
195	C₂×Dic₄₃	—	2	8	no	—
196	C₂×Dic₄₃	—	4	2	no	—
197	C₂×Dic₄₃	C₄⋊Q₈	1	4	yes	—
198	C₂×Dic₄₃	C₂²×D₄	1	4	yes	—
199	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
200	C₄×D₄₃	—	8	8	no	—
201	C₄×D₄₃	C₄⋊Q₈	1	8	yes	—
202	C₄×D₄₃	C₂²×Q₈	1	4	yes	—
203	C₄×D₄₃	C₂²×Q₈	1	4	yes	—
204	Dic₈₆	—	8	8	no	—
205	Dic₈₆	—	8	4	no	—
206	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
207	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
208	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
209	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
210	C₄₃⋊C₈	C₂²×Q₈	1	4	yes	—
211	C₄₃⋊C₈	C₂²×Q₈	1	4	yes	—
212	#60660	—	43	1	no	maximal, Sylow
213	C₂²×C₄₃	—	2	2	no	—
214	C₂²×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
215	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
216	C₂×D₄₃	—	2	4	no	—
217	C₂×D₄₃	—	4	4	no	—
218	C₂×D₄₃	C₂×C₄⋊Q₈	1	4	yes	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	2	2	no	—
221	C₄×C₄₃	—	4	8	no	—
222	C₄×C₄₃	C₂×C₄⋊Q₈	1	2	yes	—
223	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
224	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
225	Dic₄₃	—	2	4	no	—
226	Dic₄₃	—	4	8	no	—
227	Dic₄₃	C₂×C₄⋊Q₈	1	4	yes	—
228	#3458	—	43	2	no	—
229	#3164	—	43	4	no	—
230	#3164	—	43	4	no	—
231	#3163	—	43	4	no	—
232	#3163	—	43	4	no	—
233	#3162	—	43	2	no	—
234	#3162	—	43	2	no	—
235	#3160	—	43	2	no	—
236	#3160	—	43	1	no	—
237	#3160	D₄₃	1	1	yes	characteristic, complemented
238	#2911	—	43	2	no	—
239	C₂×#427	—	43	2	no	—
240	C₂×#405	—	43	1	no	—
241	C₂×C₄₃	—	2	2	no	—
242	C₂×C₄₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
243	C₂×C₄₃	#3584	1	2	yes	—
244	D₄₃	—	2	4	no	—
245	C₂²×M₁₆	—	43	1	no	—
246	C₂³×C₈	—	43	1	no	—
247	#544	—	43	8	no	—
248	#544	—	43	8	no	—
249	#544	—	86	4	no	—
250	#543	—	86	4	no	—
251	#533	—	43	4	no	—
252	#533	—	43	2	no	—
253	#533	—	86	8	no	—
254	#533	C₂×D₄₃	1	2	yes	—
255	C₂×#117	—	43	1	no	—
256	C₂×#117	—	43	4	no	—
257	#501	—	43	8	no	—
258	#501	—	43	8	no	—
259	#501	—	43	8	no	—
260	#501	—	43	8	no	—
261	#500	—	43	4	no	—
262	#500	—	43	2	no	—
263	#500	C₂×D₄₃	1	2	yes	complemented
264	#499	—	43	4	no	—
265	#499	—	43	4	no	—
266	#499	—	43	2	no	—
267	#499	—	43	2	no	—
268	#499	C₂×D₄₃	1	2	yes	complemented
269	#499	C₂×D₄₃	1	2	yes	complemented
270	#498	—	43	4	no	—
271	#498	—	43	2	no	—
272	#498	C₂×D₄₃	1	2	yes	complemented
273	#428	—	43	8	no	—
274	#428	—	43	8	no	—
275	#427	—	43	2	no	—
276	#427	—	43	2	no	—
277	#427	—	43	4	no	—
278	#427	—	43	4	no	—
279	#427	—	43	4	no	—
280	#427	—	43	4	no	—
281	#427	C₂×D₄₃	1	2	yes	—
282	#427	C₂×D₄₃	1	2	yes	—
283	C₂×#107	—	43	4	no	—
284	C₂×#106	—	43	4	no	—
285	#405	—	43	2	no	—
286	#405	—	43	2	no	—
287	#405	—	43	2	no	—
288	#405	—	43	2	no	—
289	C₂×#97	—	43	1	no	—
290	C₂×#97	—	43	1	no	—
291	C₂×C₄×C₈	—	43	1	no	—
292	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
293	C₄₃	#60660	1	1	yes	characteristic, complemented, Sylow
294	C₂³×C₄	—	43	1	no	—
295	C₂×M₁₆	—	43	8	no	—
296	C₂×M₁₆	—	43	2	no	—
297	C₂×M₁₆	—	43	2	no	—
298	C₂²×C₈	—	43	1	no	—
299	C₂²×C₈	—	43	1	no	—
300	C₂²×C₈	—	43	8	no	—
301	C₂²×C₈	—	43	2	no	—
302	C₂²×C₈	—	43	2	no	—
303	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
305	C₄⋊Q₈	—	43	8	no	—
306	C₄⋊Q₈	—	43	4	no	—
307	C₄⋊Q₈	—	86	8	no	—
308	C₄⋊Q₈	—	86	8	no	—
309	C₄⋊Q₈	C₂²×D₄₃	1	4	yes	—
310	#125	—	43	8	no	—
311	#125	—	43	4	no	—
312	#125	—	86	8	no	—
313	#125	—	86	8	no	—
314	#125	C₂²×D₄₃	1	4	yes	—
315	C₂²⋊Q₈	—	2	4	no	—
316	C₂²⋊Q₈	—	86	8	no	—
317	C₂²⋊Q₈	—	86	8	no	—
318	C₂²⋊Q₈	—	86	8	no	—
319	C₂²⋊Q₈	—	86	8	no	—
320	C₂²⋊Q₈	—	86	8	no	—
321	C₂²⋊Q₈	—	86	4	no	—
322	C₄×Q₈	—	2	4	no	—
323	C₄×Q₈	—	86	8	no	—
324	C₄×Q₈	—	86	4	no	—
325	#117	—	43	4	no	—
326	#117	—	43	2	no	—
327	#117	—	43	2	no	—
328	#117	—	43	4	no	—
329	#117	—	43	8	no	—
330	#117	—	86	4	no	—
331	#117	—	86	4	no	—
332	#117	C₂²×D₄₃	1	4	yes	—
333	C₂×C₄⋊C₄	—	43	2	no	—
334	C₂×C₄⋊C₄	—	43	8	no	—
335	C₂×C₂²⋊C₄	—	43	2	no	—
336	C₂×C₂²⋊C₄	—	86	4	no	—
337	C₂×C₄²	—	43	1	no	—
338	C₂×C₄²	—	86	4	no	—
339	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
340	#107	—	43	4	no	—
341	#107	—	43	4	no	—
342	#107	—	43	8	no	—
343	#107	—	43	8	no	—
344	#107	C₂²×D₄₃	1	4	yes	—
345	#107	C₂²×D₄₃	1	4	yes	—
346	#106	—	43	4	no	—
347	#106	—	43	4	no	—
348	#106	—	43	8	no	—
349	#106	—	43	8	no	—
350	#106	C₂²×D₄₃	1	4	yes	—
351	#106	C₂²×D₄₃	1	4	yes	—
352	#97	—	43	2	no	—
353	#97	—	43	2	no	—
354	#97	—	43	2	no	—
355	#97	—	43	2	no	—
356	C₄×C₈	—	43	2	no	—
357	C₄×C₈	—	43	2	no	—
358	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
360	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
361	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
362	C₂⁴	—	43	1	no	—
363	C₂×Q₈	—	2	4	no	—
364	C₂×Q₈	—	86	8	no	—
365	C₂×Q₈	—	86	4	no	—
366	C₂²×C₄	—	43	1	no	—
367	C₂²×C₄	—	43	2	no	—
368	C₂²×C₄	—	43	4	no	—
369	C₂²×C₄	—	43	4	no	—
370	C₂²×C₄	—	43	2	no	—
371	C₂²×C₄	—	43	2	no	—
372	C₂²×C₄	—	86	8	no	—
373	C₂²×C₄	D₄×D₄₃	1	2	yes	—
374	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
375	M₁₆	—	43	8	no	—
376	M₁₆	—	43	8	no	—
377	C₂×C₈	—	43	4	no	—
378	C₂×C₈	—	43	4	no	—
379	C₂×C₈	—	43	2	no	—
380	C₂×C₈	—	43	2	no	—
381	C₂×C₈	—	43	8	no	—
382	C₂×C₈	—	43	8	no	—
383	C₂×C₈	Q₈×D₄₃	1	4	yes	—
384	C₂×C₈	Q₈×D₄₃	1	4	yes	—
385	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
386	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
387	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
388	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	8	no	—
391	C₄⋊C₄	—	43	4	no	—
392	C₄⋊C₄	—	43	4	no	—
393	C₄⋊C₄	—	43	8	no	—
394	C₄⋊C₄	—	86	8	no	—
395	C₄⋊C₄	—	86	8	no	—
396	C₄⋊C₄	—	86	8	no	—
397	C₄⋊C₄	—	86	8	no	—
398	C₄⋊C₄	—	86	8	no	—
399	C₄⋊C₄	—	86	4	no	—
400	C₄⋊C₄	C₂³×D₄₃	1	8	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	43	4	no	—
403	C₂²⋊C₄	—	43	4	no	—
404	C₂²⋊C₄	—	86	8	no	—
405	C₂²⋊C₄	—	86	4	no	—
406	C₄²	—	2	4	no	—
407	C₄²	—	43	2	no	—
408	C₄²	—	43	2	no	—
409	C₄²	—	86	8	no	—
410	C₄²	—	86	4	no	—
411	C₄²	D₄×D₄₃	1	2	yes	—
412	C₄²	C₂³×D₄₃	1	1	yes	characteristic
413	C₄²	C₂³×D₄₃	1	1	yes	characteristic
414	C₂³	—	43	2	no	—
415	C₂³	—	43	4	no	—
416	C₂³	—	172	2	no	—
417	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
418	Q₈	—	8	4	no	—
419	Q₈	—	344	4	no	—
420	Q₈	—	344	8	no	—
421	C₂×C₄	—	2	8	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	43	4	no	—
424	C₂×C₄	—	43	2	no	—
425	C₂×C₄	—	43	8	no	—
426	C₂×C₄	—	43	4	no	—
427	C₂×C₄	—	43	4	no	—
428	C₂×C₄	—	43	4	no	—
429	C₂×C₄	—	86	8	no	—
430	C₂×C₄	—	344	8	no	—
431	C₂×C₄	—	172	2	no	—
432	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
433	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
434	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
435	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
436	C₂×C₄	C₂×Q₈×D₄₃	1	2	yes	—
437	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
438	C₈	—	43	4	no	—
439	C₈	—	43	4	no	—
440	C₈	C₂×Q₈×D₄₃	1	2	yes	—
441	C₈	C₂×Q₈×D₄₃	1	2	yes	—
442	C₈	C₂×Q₈×D₄₃	1	2	yes	—
443	C₈	C₂×Q₈×D₄₃	1	2	yes	—
444	C₂²	—	2	2	no	—
445	C₂²	—	43	4	no	—
446	C₂²	—	86	4	no	—
447	C₂²	—	172	4	no	—
448	C₂²	C₄⋊Q₈×D₄₃	1	2	yes	—
449	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	8	no	—
453	C₄	—	43	4	no	—
454	C₄	—	86	4	no	—
455	C₄	—	172	8	no	—
456	C₄	C₄⋊Q₈×D₄₃	1	2	yes	—
457	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
458	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
459	C₂	—	2	2	no	—
460	C₂	—	86	4	no	—
461	C₂	C₂×C₄⋊Q₈×D₄₃	1	1	yes	characteristic
462	C₂	#19149364	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3160	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂³×D₄₃	C₂×D₄
hypercenter	#3160	D₄₃
hypocenter	C₄₃	#60660
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
2. #19145132	C₂	semidirect
3. #19145128	C₂	semidirect
4. #19145124	C₂	semidirect
5. #19145120	C₂	semidirect
6. #19145118	C₂	semidirect
7. #19145117	C₂	semidirect
8. #19145109	C₂	semidirect
9. #19145107	C₂	semidirect
13. C₄₃×#3160	C₂	semidirect
25. #14583309	C₂²	semidirect
26. #14583307	C₂²	semidirect
27. #14583306	C₂²	semidirect
28. #14583305	C₂²	semidirect
29. #14583304	C₂²	semidirect
30. #14583303	C₂²	semidirect
31. #14583301	C₂²	semidirect
32. #14583301	C₂²	semidirect
33. #14583300	C₂²	semidirect
34. #14583299	C₂²	semidirect
35. #14583297	C₂²	semidirect
36. #14583296	C₂²	semidirect
55. C₄₃×#500	C₂²	semidirect
56. C₄₃×#499	C₂²	semidirect
57. C₄₃×#499	C₂²	semidirect
58. C₄₃×#498	C₂²	semidirect
63. C₂×#10621872	Q₈	semidirect
68. C₂×C₈×D₄₃	Q₈	semidirect
237. #3160	D₄₃	semidirect
263. #500	C₂×D₄₃	semidirect
268. #499	C₂×D₄₃	semidirect
269. #499	C₂×D₄₃	semidirect
272. #498	C₂×D₄₃	semidirect
293. C₄₃	#60660	semidirect

Maximal subgroups

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

subgroup	index
#19147998	2
#19145132	2
#19145128	2
#19145124	2
#19145120	2
#19145118	2
#19145117	2
#19145109	2
#19145107	2
#19143183	2
#427×D₄₃	2
C₂×#14582853	2
C₄₃×#3160	2
#60660	43