Subgroups — #25066027

Order 11008.

714 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₄₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#14583023	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063355	C₂	1	1	yes	maximal, characteristic
4	#19133411	C₂	1	2	yes	maximal, complemented
5	#19133404	C₂	1	2	yes	maximal, complemented
6	#19133399	C₂	1	2	yes	maximal, complemented
7	#19133398	C₂	1	2	yes	maximal, complemented
8	#19133345	C₂	1	1	yes	maximal, characteristic, complemented
9	#19132991	C₂	1	1	yes	maximal, characteristic, complemented
10	#19132876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1477	C₂	1	1	yes	maximal, characteristic
12	C₂×#13063355	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
14	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
15	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
16	#14583023	—	2	1	no	—
17	#14583023	—	2	1	no	—
18	#14583023	C₂²	1	2	yes	—
19	#14583023	C₂²	1	2	yes	—
20	#14583004	C₄	1	2	yes	—
21	#14582999	C₄	1	2	yes	—
22	C₄×#10621885	C₂²	1	2	yes	—
23	C₄×#10621883	C₂²	1	2	yes	—
24	D₄×C₄₃⋊C₈	—	2	1	no	—
25	D₄×C₄₃⋊C₈	—	2	1	no	—
26	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
28	#14582952	—	2	1	no	—
29	#14582952	C₂²	1	1	yes	characteristic
30	#14582942	C₄	1	1	yes	characteristic
31	C₂×Dic₄₃⋊C₈	—	2	1	no	—
32	#14582907	C₄	1	1	yes	characteristic
33	#14582900	C₄	1	1	yes	characteristic
34	C₄×#10621877	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₄₃⋊C₈	—	2	1	no	—
36	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₃	—	2	1	no	—
38	#14582651	C₂²	1	2	yes	—
39	#14582649	C₂²	1	2	yes	—
40	#14582631	C₂²	1	2	yes	—
41	#14582631	C₂²	1	2	yes	—
42	#14582621	C₂²	1	2	yes	—
43	C₈×C₄₃⋊C₈	C₂²	1	2	yes	—
44	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₄₃×D₄⋊C₈	C₂²	1	2	yes	—
49	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
50	#13063355	C₈	1	8	yes	complemented
51	C₂×#10621885	C₂×C₄	1	2	yes	—
52	C₂×#10621883	C₂×C₄	1	2	yes	—
53	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621877	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₄₃⋊C₈	—	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	C₄×Dic₈₆	—	2	1	no	—
60	C₄×Dic₈₆	—	2	1	no	—
61	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
62	C₄×Dic₈₆	C₂³	1	2	yes	—
63	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
64	C₂×Dic₄₃⋊C₄	—	2	1	no	—
65	C₂×C₄×Dic₄₃	—	2	1	no	—
66	#13063258	C₂×C₄	1	2	yes	—
67	#13063256	C₂×C₄	1	2	yes	—
68	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
69	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
71	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
72	Dic₄₃⋊C₈	—	2	2	no	—
73	Dic₄₃⋊C₈	—	2	2	no	—
74	#13063249	C₂×C₄	1	2	yes	—
75	#13063248	C₂×C₄	1	2	yes	—
76	#13063248	C₂×C₄	1	2	yes	—
77	#13063246	C₂×C₄	1	2	yes	—
78	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
79	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
81	#13063236	C₂×C₄	1	2	yes	—
82	C₄×C₄₃⋊C₈	—	2	1	no	—
83	C₄×C₄₃⋊C₈	—	2	1	no	—
84	C₄×C₄₃⋊C₈	—	2	1	no	—
85	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
86	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
87	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
88	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₈×Dic₄₃	—	2	2	no	—
91	C₈×Dic₄₃	—	2	2	no	—
92	C₂×#41×C₄₃	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₃	—	2	1	no	—
94	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
95	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₄₃	—	2	1	no	—
97	C₄×D₄×C₄₃	—	2	1	no	—
98	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
99	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
100	#117×C₄₃	—	2	1	no	—
101	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₃	—	2	1	no	—
103	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₃	—	2	1	no	—
105	C₄⋊C₈×C₄₃	—	2	1	no	—
106	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
107	C₂²⋊C₈×C₄₃	—	2	1	no	—
108	C₄×C₈×C₄₃	C₂³	1	2	yes	—
109	#41×C₄₃	—	2	2	no	—
110	#41×C₄₃	C₂×C₈	1	4	yes	—
111	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₄₃	—	2	1	no	—
113	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	—	2	1	no	—
115	C₂²×C₄×C₄₃	—	2	1	no	—
116	C₂²×C₄×C₄₃	—	2	1	no	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
120	C₂²×Dic₄₃	—	2	1	no	—
121	C₂²×Dic₄₃	—	2	1	no	—
122	C₂×Dic₈₆	—	2	1	no	—
123	C₂×Dic₈₆	—	2	2	no	—
124	C₂×Dic₈₆	C₂×C₈	1	4	yes	complemented
125	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₃	—	2	2	no	—
127	C₂×C₈×C₄₃	—	2	2	no	—
128	C₂×C₈×C₄₃	—	4	2	no	—
129	C₄⋊C₄×C₄₃	—	2	1	no	—
130	C₄⋊C₄×C₄₃	—	2	1	no	—
131	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²⋊C₄×C₄₃	—	2	1	no	—
134	C₂²⋊C₄×C₄₃	—	2	1	no	—
135	C₂²⋊C₄×C₄₃	—	2	1	no	—
136	C₄²×C₄₃	—	2	1	no	—
137	C₄²×C₄₃	—	2	1	no	—
138	C₄²×C₄₃	—	2	1	no	—
139	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₃	#41	1	1	yes	characteristic
142	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
143	#10621885	C₂×C₈	1	8	yes	complemented
144	#10621883	C₂×C₈	1	8	yes	complemented
145	C₄⋊Dic₄₃	—	2	1	no	—
146	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
147	Dic₄₃⋊C₄	—	2	2	no	—
148	Dic₄₃⋊C₄	—	2	2	no	—
149	C₄×Dic₄₃	—	2	2	no	—
150	C₄×Dic₄₃	—	2	2	no	—
151	#10621877	—	2	2	no	—
152	#10621877	C₂×C₈	1	4	yes	complemented
153	C₂×C₄₃⋊C₈	—	2	2	no	—
154	C₂×C₄₃⋊C₈	—	2	1	no	—
155	C₂×C₄₃⋊C₈	—	2	1	no	—
156	C₂×C₄₃⋊C₈	—	4	1	no	—
157	C₂×C₄₃⋊C₈	—	4	2	no	—
158	C₂×C₄₃⋊C₈	—	4	2	no	—
159	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
160	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
161	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂³×C₄₃	—	2	1	no	—
166	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
167	Q₈×C₄₃	—	2	1	no	—
168	Q₈×C₄₃	C₂²×C₈	1	2	yes	—
169	D₄×C₄₃	—	2	4	no	—
170	D₄×C₄₃	—	2	1	no	—
171	D₄×C₄₃	C₂²×C₈	1	2	yes	—
172	C₂×C₄×C₄₃	—	2	1	no	—
173	C₂×C₄×C₄₃	—	2	1	no	—
174	C₂×C₄×C₄₃	—	2	1	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	2	1	no	—
177	C₂×C₄×C₄₃	—	2	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	1	no	—
181	C₂×C₄×C₄₃	—	4	1	no	—
182	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₃	C₂²×C₈	1	2	yes	—
186	C₂×C₄×C₄₃	#131	1	2	yes	—
187	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
190	C₂×Dic₄₃	—	2	2	no	—
191	C₂×Dic₄₃	—	2	4	no	—
192	C₂×Dic₄₃	—	2	2	no	—
193	C₂×Dic₄₃	—	4	2	no	—
194	Dic₈₆	—	2	2	no	—
195	Dic₈₆	—	2	4	no	—
196	Dic₈₆	C₂²×C₈	1	4	yes	—
197	C₈×C₄₃	—	4	2	no	—
198	C₈×C₄₃	—	4	2	no	—
199	C₄₃⋊C₈	—	2	2	no	—
200	C₄₃⋊C₈	—	2	1	no	—
201	C₄₃⋊C₈	—	2	1	no	—
202	C₄₃⋊C₈	—	2	1	no	—
203	C₄₃⋊C₈	—	4	1	no	—
204	C₄₃⋊C₈	—	4	1	no	—
205	C₄₃⋊C₈	C₂²×C₈	1	4	yes	—
206	C₄₃⋊C₈	#137	1	2	yes	complemented
207	C₈×#137	—	43	1	no	maximal, Sylow
208	C₂²×C₄₃	—	2	1	no	—
209	C₂²×C₄₃	—	2	1	no	—
210	C₂²×C₄₃	—	2	2	no	—
211	C₂²×C₄₃	—	4	1	no	—
212	C₂²×C₄₃	—	4	1	no	—
213	C₂²×C₄₃	C₈×D₄	1	2	yes	—
214	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₄×C₄₃	—	2	2	no	—
216	C₄×C₄₃	—	2	1	no	—
217	C₄×C₄₃	—	2	1	no	—
218	C₄×C₄₃	—	2	1	no	—
219	C₄×C₄₃	—	4	1	no	—
220	C₄×C₄₃	—	4	1	no	—
221	C₄×C₄₃	C₈×D₄	1	2	yes	—
222	C₄×C₄₃	C₂³×C₈	1	1	yes	characteristic
223	C₄×C₄₃	C₂×#131	1	1	yes	characteristic
224	C₄×C₄₃	C₂×#137	1	1	yes	characteristic
225	C₄×C₄₃	#575	1	1	yes	characteristic
226	Dic₄₃	—	2	4	no	—
227	Dic₄₃	—	4	2	no	—
228	C₈×#41	—	43	1	no	—
229	C₂×C₈×Q₈	—	43	1	no	—
230	C₄×#137	—	43	1	no	—
231	#1579	—	43	2	no	—
232	SD₁₆⋊C₈	—	43	2	no	—
233	C₈×Q₁₆	—	43	2	no	—
234	C₈×SD₁₆	—	43	2	no	—
235	#1565	—	43	1	no	—
236	#1479	—	43	1	no	—
237	#1477	D₄₃	1	1	yes	characteristic
238	C₈×M₁₆	—	43	1	no	—
239	C₂×C₄₃	—	2	2	no	—
240	C₂×C₄₃	—	4	2	no	—
241	C₂×C₄₃	C₂×C₈×D₄	1	1	yes	characteristic
242	C₂×C₄₃	C₄×#137	1	1	yes	characteristic
243	C₂×C₄₃	#2955	1	1	yes	characteristic
244	C₂×#137	—	43	1	no	—
245	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
246	C₂×C₄×Q₈	—	43	1	no	—
247	C₈×Q₈	—	43	1	no	—
248	C₈×Q₈	—	43	1	no	—
249	C₈×Q₈	—	43	2	no	—
250	C₈×Q₈	—	43	2	no	—
251	C₈×Q₈	—	86	1	no	—
252	C₈×Q₈	—	86	1	no	—
253	#441	—	43	2	no	—
254	#440	—	43	2	no	—
255	C₄×Q₁₆	—	43	2	no	—
256	C₄×SD₁₆	—	43	2	no	—
257	C₈×D₄	—	43	1	no	—
258	C₈×D₄	—	43	1	no	—
259	C₈×D₄	—	86	1	no	—
260	C₈×D₄	—	86	1	no	—
261	#431	—	43	1	no	—
262	#431	—	86	1	no	—
263	#431	C₂×D₄₃	1	1	yes	characteristic
264	#428	—	43	1	no	—
265	C₂×C₄⋊C₈	—	86	1	no	—
266	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
267	#419	—	43	1	no	—
268	#417	—	43	1	no	—
269	C₄×M₁₆	—	43	1	no	—
270	C₂×C₄×C₈	—	43	1	no	—
271	C₂×C₄×C₈	—	86	1	no	—
272	C₂×C₄×C₈	—	86	1	no	—
273	#335	—	43	2	no	—
274	#334	—	43	2	no	—
275	Q₈⋊C₈	—	43	2	no	—
276	Q₈⋊C₈	—	43	2	no	—
277	Q₈⋊C₈	C₂×D₄₃	1	2	yes	—
278	D₄⋊C₈	C₂×D₄₃	1	2	yes	—
279	#322	—	43	2	no	—
280	C₈²	—	43	2	no	—
281	C₄₃	C₈×#137	1	1	yes	characteristic, complemented, Sylow
282	C₂×#41	C₄×D₄₃	1	1	yes	characteristic
283	C₂²×Q₈	—	43	1	no	—
284	#137	—	43	8	no	—
285	C₂×Q₁₆	—	43	2	no	—
286	C₂×SD₁₆	—	43	2	no	—
287	C₂×M₁₆	—	43	1	no	—
288	C₂×M₁₆	—	43	1	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	43	1	no	—
291	C₂²×C₈	—	43	1	no	—
292	C₂²×C₈	—	86	1	no	—
293	C₂²×C₈	—	86	1	no	—
294	C₄×Q₈	—	43	2	no	—
295	C₄×Q₈	—	43	2	no	—
296	C₄×Q₈	—	86	1	no	—
297	C₄×Q₈	—	86	1	no	—
298	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
299	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
303	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
304	#117	—	2	1	no	—
305	#117	C₄×D₄₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	—	43	1	no	—
307	C₂×C₄⋊C₄	—	86	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	86	1	no	—
310	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
311	#107	—	43	2	no	—
312	#106	—	43	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	2	1	no	—
315	C₄⋊C₈	—	43	1	no	—
316	C₄⋊C₈	—	43	1	no	—
317	C₄⋊C₈	—	86	1	no	—
318	C₄⋊C₈	—	86	1	no	—
319	C₄⋊C₈	—	86	2	no	—
320	C₄⋊C₈	—	86	2	no	—
321	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
322	#103	—	43	2	no	—
323	#103	—	43	2	no	—
324	#103	—	43	2	no	—
325	#102	—	43	2	no	—
326	C₂²⋊C₈	—	2	1	no	—
327	C₂²⋊C₈	—	86	1	no	—
328	C₂²⋊C₈	—	86	1	no	—
329	C₂²⋊C₈	—	86	1	no	—
330	#97	—	43	2	no	—
331	C₄×C₈	—	43	1	no	—
332	C₄×C₈	—	43	1	no	—
333	C₄×C₈	—	43	1	no	—
334	C₄×C₈	—	43	2	no	—
335	C₄×C₈	—	43	1	no	—
336	C₄×C₈	—	86	1	no	—
337	C₄×C₈	—	86	1	no	—
338	C₄×C₈	—	86	2	no	—
339	C₄×C₈	—	86	2	no	—
340	C₄×C₈	—	86	1	no	—
341	C₄×C₈	C₂²×D₄₃	1	2	yes	—
342	#41	—	2	2	no	—
343	#41	C₈×D₄₃	1	4	yes	—
344	C₂×Q₈	—	43	4	no	—
345	C₂×Q₈	—	43	2	no	—
346	C₂×Q₈	—	86	1	no	—
347	C₂×Q₈	—	86	2	no	—
348	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	86	1	no	—
355	C₂²×C₄	—	86	1	no	—
356	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
357	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
358	C₂²×C₄	#10621900	1	1	yes	characteristic
359	Q₁₆	—	43	8	no	—
360	SD₁₆	—	43	8	no	—
361	M₁₆	—	43	4	no	—
362	M₁₆	—	86	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	4	2	no	—
366	C₂×C₈	—	43	2	no	—
367	C₂×C₈	—	43	1	no	—
368	C₂×C₈	—	43	2	no	—
369	C₂×C₈	—	43	1	no	—
370	C₂×C₈	—	43	1	no	—
371	C₂×C₈	—	43	1	no	—
372	C₂×C₈	—	86	2	no	—
373	C₂×C₈	—	86	1	no	—
374	C₂×C₈	—	86	1	no	—
375	C₂×C₈	—	172	2	no	—
376	C₂×C₈	—	172	1	no	—
377	C₂×C₈	—	172	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	43	2	no	—
381	C₄⋊C₄	—	86	1	no	—
382	C₄⋊C₄	—	86	2	no	—
383	C₄⋊C₄	—	86	2	no	—
384	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
385	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
386	C₂²⋊C₄	—	2	1	no	—
387	C₂²⋊C₄	—	2	1	no	—
388	C₂²⋊C₄	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	86	2	no	—
393	C₄²	—	86	2	no	—
394	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
395	C₄²	D₄×D₄₃	1	1	yes	characteristic
396	C₄²	#10621900	1	1	yes	characteristic
397	C₄²	C₂³×D₄₃	1	1	yes	characteristic
398	C₂³	—	2	1	no	—
399	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
400	Q₈	—	2	1	no	—
401	Q₈	—	43	4	no	—
402	Q₈	—	86	2	no	—
403	Q₈	—	86	4	no	—
404	Q₈	C₂×C₈×D₄₃	1	2	yes	—
405	D₄	—	2	4	no	—
406	D₄	—	2	1	no	—
407	D₄	C₂×C₈×D₄₃	1	2	yes	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	86	2	no	—
419	C₂×C₄	—	86	4	no	—
420	C₂×C₄	—	86	2	no	—
421	C₂×C₄	—	172	2	no	—
422	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
423	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
424	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
425	C₂×C₄	C₂×C₈×D₄₃	1	2	yes	—
426	C₂×C₄	#13063333	1	2	yes	—
427	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
429	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
430	C₈	—	4	2	no	—
431	C₈	—	4	2	no	—
432	C₈	—	43	4	no	—
433	C₈	—	43	2	no	—
434	C₈	—	86	2	no	—
435	C₈	—	86	1	no	—
436	C₈	—	86	1	no	—
437	C₈	—	86	1	no	—
438	C₈	—	172	1	no	—
439	C₈	—	172	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	(C₂²⋊D₄₃)⋊C₈	1	2	yes	—
446	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	2	no	—
450	C₄	—	2	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	86	4	no	—
454	C₄	—	172	2	no	—
455	C₄	(C₂²⋊D₄₃)⋊C₈	1	2	yes	—
456	C₄	C₂²×C₈×D₄₃	1	1	yes	characteristic
457	C₄	C₂×#13063333	1	1	yes	characteristic
458	C₄	#137×D₄₃	1	1	yes	characteristic
459	C₄	#14583695	1	1	yes	characteristic
460	C₂	—	2	2	no	—
461	C₂	—	4	2	no	—
462	C₂	C₂×(C₂²⋊D₄₃)⋊C₈	1	1	yes	characteristic
463	C₂	#19143419	1	1	yes	characteristic
464	C₂	#19143494	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₄×C₄₃	C₂³×C₈
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1477	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#41×C₄₃	C₂×C₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1477	D₄₃
hypocenter	C₄₃	C₈×#137
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
2. C₂×#14583023	C₂	semidirect
4. #19133411	C₂	semidirect
5. #19133404	C₂	semidirect
6. #19133399	C₂	semidirect
7. #19133398	C₂	semidirect
8. #19133345	C₂	semidirect
9. #19132991	C₂	semidirect
10. #19132876	C₂	semidirect
50. #13063355	C₈	semidirect
124. C₂×Dic₈₆	C₂×C₈	semidirect
143. #10621885	C₂×C₈	semidirect
144. #10621883	C₂×C₈	semidirect
152. #10621877	C₂×C₈	semidirect
206. C₄₃⋊C₈	#137	semidirect
281. C₄₃	C₈×#137	semidirect

Maximal subgroups

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

subgroup	index
#41×C₄₃⋊C₈	2
C₂×#14583023	2
C₄×#13063355	2
#19133411	2
#19133404	2
#19133399	2
#19133398	2
#19133345	2
#19132991	2
#19132876	2
C₄₃×#1477	2
C₈×#137	43