Subgroups — #25068054

Order 11008.

638 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143547	C₂	1	1	yes	maximal, characteristic
2	Q₈×#10621872	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#19133490	C₂	1	1	yes	maximal, characteristic, complemented
5	#19133489	C₂	1	1	yes	maximal, characteristic, complemented
6	#19133447	C₂	1	1	yes	maximal, characteristic, complemented
7	#19133446	C₂	1	1	yes	maximal, characteristic, complemented
8	#19133444	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#10621885	C₂	1	1	yes	maximal, characteristic, complemented
10	#19133399	C₂	1	1	yes	maximal, characteristic, complemented
11	#19133352	C₂	1	1	yes	maximal, characteristic
12	#19133022	C₂	1	1	yes	maximal, characteristic
13	#19133022	C₂	1	1	yes	maximal, characteristic
14	#19132874	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₄₃	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
19	#14583030	C₂²	1	1	yes	characteristic
20	#14583029	—	2	1	no	—
21	#14583029	C₂²	1	1	yes	characteristic
22	#14583028	—	2	1	no	—
23	#14583027	—	2	1	no	—
24	#14583026	—	2	1	no	—
25	#14583026	C₂²	1	1	yes	characteristic
26	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
27	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
28	#14583023	C₂²	1	1	yes	characteristic
29	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₄₃	C₄	1	1	yes	characteristic
31	#14582993	C₄	1	1	yes	characteristic
32	C₄×#10621885	C₂²	1	1	yes	characteristic
33	C₄×#10621885	C₂²	1	1	yes	characteristic
34	#14582991	C₄	1	1	yes	characteristic
35	#14582991	C₄	1	1	yes	characteristic
36	#14582950	C₂²	1	1	yes	characteristic
37	#107×D₄₃	C₄	1	1	yes	characteristic
38	#14582921	—	2	1	no	—
39	#14582921	—	2	1	no	—
40	#14582921	C₂²	1	1	yes	characteristic
41	#14582921	C₂²	1	1	yes	characteristic
42	#103×D₄₃	C₄	1	1	yes	characteristic
43	#103×D₄₃	C₄	1	1	yes	characteristic
44	#14582851	—	2	1	no	—
45	C₄×#10621872	—	2	1	no	—
46	C₄×#10621872	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
48	#14582652	C₂²	1	1	yes	characteristic
49	#14582651	C₂²	1	1	yes	characteristic
50	#14582651	C₂²	1	1	yes	characteristic
51	#14582631	C₂²	1	1	yes	characteristic
52	#14582631	C₂²	1	1	yes	characteristic
53	Q₈⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
54	Q₈⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
55	#14582629	C₂²	1	1	yes	characteristic
56	#14582629	C₂²	1	1	yes	characteristic
57	#14582621	C₂²	1	1	yes	characteristic
58	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
59	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
60	C₄₃×#446	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
63	C₄₃×#335	C₂²	1	1	yes	characteristic
64	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₄₃×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₄₃×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₄₃	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₄₃	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₁₇₂	C₂×C₄	1	1	yes	characteristic
70	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
71	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₄₃	—	2	4	no	—
73	C₂×#10621872	—	2	1	no	—
74	C₂×#10621872	—	2	1	no	—
75	C₂×#10621872	D₄	1	1	yes	characteristic
76	C₂×#10621872	D₄	1	1	yes	characteristic
77	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₄₃	C₂×C₄	1	1	yes	characteristic
79	Q₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
80	Q₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
81	C₄×Dic₈₆	—	2	1	no	—
82	C₄×Dic₈₆	—	2	1	no	—
83	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
84	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
85	#13063290	—	2	1	no	—
86	#13063290	—	2	1	no	—
87	#13063290	C₂×C₄	1	1	yes	characteristic
88	#13063290	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₄₃	—	2	1	no	—
90	C₄⋊C₄×D₄₃	—	2	1	no	—
91	C₄⋊C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
93	C₄²×D₄₃	—	2	1	no	—
94	C₄²×D₄₃	—	2	1	no	—
95	C₄²×D₄₃	C₂³	1	1	yes	characteristic
96	#13063259	C₂×C₄	1	1	yes	characteristic
97	#13063258	C₂×C₄	1	1	yes	characteristic
98	#13063258	C₂×C₄	1	1	yes	characteristic
99	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
100	C₄⋊(C₄₃⋊C₈)	—	2	1	no	—
101	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
102	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
103	Dic₄₃⋊C₈	—	2	1	no	—
104	Dic₄₃⋊C₈	—	2	1	no	—
105	Dic₄₃⋊C₈	—	2	1	no	—
106	Dic₄₃⋊C₈	—	2	1	no	—
107	Dic₄₃⋊C₈	—	2	1	no	—
108	Dic₄₃⋊C₈	—	2	1	no	—
109	Dic₄₃⋊C₈	—	2	1	no	—
110	#13063250	C₂×C₄	1	1	yes	characteristic
111	#13063250	C₂×C₄	1	1	yes	characteristic
112	#13063249	C₂×C₄	1	1	yes	characteristic
113	#13063249	C₂×C₄	1	1	yes	characteristic
114	#13063248	C₂×C₄	1	1	yes	characteristic
115	#13063248	C₂×C₄	1	1	yes	characteristic
116	(C₂×D₄₃)⋊C₈	—	2	1	no	—
117	#13063236	—	2	1	no	—
118	#13063235	—	2	1	no	—
119	#13063235	—	2	1	no	—
120	#13063235	D₄	1	1	yes	characteristic
121	#13063235	D₄	1	1	yes	characteristic
122	C₄×C₄₃⋊C₈	—	2	1	no	—
123	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
124	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
125	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
126	C₈×Dic₄₃	—	2	1	no	—
127	C₈×Dic₄₃	—	2	1	no	—
128	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₄₃	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
133	#107×C₄₃	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₄₃	—	2	1	no	—
135	C₄⋊C₈×C₄₃	—	2	1	no	—
136	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
138	#103×C₄₃	C₂×C₄	1	1	yes	characteristic
139	#103×C₄₃	C₂×C₄	1	1	yes	characteristic
140	#97×C₄₃	—	2	1	no	—
141	C₄×C₈×C₄₃	—	2	1	no	—
142	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
145	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
147	Q₈×D₄₃	—	2	2	no	—
148	Q₈×D₄₃	—	2	2	no	—
149	Q₈×D₄₃	—	4	1	no	—
150	Q₈×D₄₃	—	4	1	no	—
151	C₂×C₄×D₄₃	—	2	1	no	—
152	C₂×C₄×D₄₃	—	2	1	no	—
153	C₂×C₄×D₄₃	—	2	1	no	—
154	C₂×C₄×D₄₃	—	2	1	no	—
155	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
156	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×D₄₃	#41	1	1	yes	characteristic
158	C₂×Dic₈₆	—	2	1	no	—
159	C₂×Dic₈₆	—	2	1	no	—
160	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
161	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
162	Q₁₆×C₄₃	—	2	2	no	—
163	C₂×C₈×C₄₃	—	2	1	no	—
164	C₂×C₈×C₄₃	—	2	1	no	—
165	C₂×C₈×C₄₃	—	2	1	no	—
166	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₄₃	—	2	1	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
173	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
174	C₄²×C₄₃	—	2	1	no	—
175	C₄²×C₄₃	—	2	1	no	—
176	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
177	#10621885	—	2	2	no	—
178	#10621885	M₁₆	1	4	yes	complemented
179	C₄⋊Dic₄₃	—	2	1	no	—
180	C₄⋊Dic₄₃	—	2	1	no	—
181	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
182	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
183	Dic₄₃⋊C₄	—	2	1	no	—
184	Dic₄₃⋊C₄	—	2	1	no	—
185	Dic₄₃⋊C₄	—	2	1	no	—
186	Dic₄₃⋊C₄	—	2	1	no	—
187	Dic₄₃⋊C₄	—	2	1	no	—
188	Dic₄₃⋊C₄	—	2	1	no	—
189	C₄×Dic₄₃	—	2	1	no	—
190	C₄×Dic₄₃	—	2	1	no	—
191	C₄×Dic₄₃	—	2	1	no	—
192	C₄×Dic₄₃	—	2	1	no	—
193	C₄×Dic₄₃	—	2	1	no	—
194	C₄×Dic₄₃	—	2	1	no	—
195	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
196	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
197	C₄×Dic₄₃	#41	1	1	yes	characteristic
198	C₂×C₄₃⋊C₈	—	2	1	no	—
199	C₂×C₄₃⋊C₈	—	2	1	no	—
200	C₂×C₄₃⋊C₈	—	2	1	no	—
201	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₄₃⋊C₈	C₂×D₄	1	1	yes	characteristic
205	Dic₁₇₂	—	2	2	no	—
206	#10621872	—	2	2	no	—
207	#10621872	—	4	2	no	—
208	#10621872	—	4	2	no	—
209	#10621872	Q₁₆	1	4	yes	complemented
210	C₈×D₄₃	—	2	2	no	—
211	C₈×D₄₃	—	4	1	no	—
212	C₂²×D₄₃	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₄₃	—	2	1	no	—
214	Q₈×C₄₃	—	2	1	no	—
215	Q₈×C₄₃	—	2	1	no	—
216	Q₈×C₄₃	C₂×M₁₆	1	2	yes	—
217	C₂×C₄×C₄₃	—	2	1	no	—
218	C₂×C₄×C₄₃	—	2	1	no	—
219	C₂×C₄×C₄₃	—	2	1	no	—
220	C₂×C₄×C₄₃	—	2	1	no	—
221	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
224	C₂×Dic₄₃	—	2	1	no	—
225	C₂×Dic₄₃	—	2	1	no	—
226	C₂×Dic₄₃	—	2	1	no	—
227	C₂×Dic₄₃	—	2	1	no	—
228	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
229	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₄₃	C₄×D₄	1	1	yes	characteristic
231	C₄×D₄₃	—	2	1	no	—
232	C₄×D₄₃	—	2	1	no	—
233	C₄×D₄₃	—	4	1	no	—
234	C₄×D₄₃	—	4	2	no	—
235	C₄×D₄₃	—	4	2	no	—
236	C₄×D₄₃	—	8	1	no	—
237	C₄×D₄₃	—	8	1	no	—
238	C₄×D₄₃	C₂×Q₁₆	1	2	yes	—
239	C₄×D₄₃	#135	1	2	yes	—
240	Dic₈₆	—	2	1	no	—
241	Dic₈₆	—	2	1	no	—
242	Dic₈₆	—	2	1	no	—
243	Dic₈₆	—	4	2	no	—
244	Dic₈₆	—	4	2	no	—
245	Dic₈₆	C₂×M₁₆	1	2	yes	—
246	C₈×C₄₃	—	2	1	no	—
247	C₈×C₄₃	—	2	1	no	—
248	C₈×C₄₃	—	2	1	no	—
249	C₈×C₄₃	—	4	1	no	—
250	C₈×C₄₃	—	4	1	no	—
251	C₈×C₄₃	—	4	1	no	—
252	C₈×C₄₃	C₂×Q₁₆	1	2	yes	complemented
253	C₄₃⋊C₈	—	2	1	no	—
254	C₄₃⋊C₈	—	2	1	no	—
255	C₄₃⋊C₈	—	4	1	no	—
256	C₄₃⋊C₈	—	4	1	no	—
257	C₄₃⋊C₈	—	4	1	no	—
258	C₄₃⋊C₈	C₂×M₁₆	1	2	yes	—
259	C₄₃⋊C₈	C₂×Q₁₆	1	2	yes	complemented
260	M₁₆×Q₁₆	—	43	1	no	maximal, Sylow
261	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂×D₄₃	—	2	1	no	—
263	C₂×D₄₃	—	2	1	no	—
264	C₂×D₄₃	C₄×Q₁₆	1	2	yes	—
265	C₄×C₄₃	—	2	2	no	—
266	C₄×C₄₃	—	2	1	no	—
267	C₄×C₄₃	—	4	1	no	—
268	C₄×C₄₃	—	4	1	no	—
269	C₄×C₄₃	—	4	1	no	—
270	C₄×C₄₃	C₂²×M₁₆	1	1	yes	characteristic
271	C₄×C₄₃	#568	1	1	yes	characteristic
272	C₄×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
273	C₄×C₄₃	C₂×#135	1	1	yes	characteristic
274	Dic₄₃	—	2	2	no	—
275	Dic₄₃	—	2	1	no	—
276	Dic₄₃	—	2	1	no	—
277	Dic₄₃	—	4	1	no	—
278	Dic₄₃	—	4	1	no	—
279	Dic₄₃	—	4	1	no	—
280	Dic₄₃	C₄×Q₁₆	1	2	yes	—
281	Q₈×M₁₆	—	43	1	no	—
282	Q₈×M₁₆	—	43	1	no	—
283	C₂×C₄×Q₁₆	—	43	1	no	—
284	#1591	—	43	1	no	—
285	#1591	—	43	1	no	—
286	#1584	—	43	1	no	—
287	#1584	—	43	1	no	—
288	#1584	—	43	1	no	—
289	#1584	D₄₃	1	1	yes	characteristic, complemented
290	C₈×Q₁₆	—	43	1	no	—
291	C₈×Q₁₆	—	43	1	no	—
292	#1567	—	43	1	no	—
293	#1487	—	43	1	no	—
294	#1487	—	43	1	no	—
295	C₈×M₁₆	—	43	1	no	—
296	C₂×C₄₃	D₄×M₁₆	1	1	yes	characteristic
297	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
298	C₂×C₄₃	#2957	1	1	yes	characteristic
299	D₄₃	—	2	2	no	—
300	C₂²×Q₁₆	—	43	1	no	—
301	C₂×C₄×Q₈	—	43	1	no	—
302	C₂×C₄×Q₈	—	43	1	no	—
303	#446	—	43	1	no	—
304	#446	—	43	1	no	—
305	#446	—	43	1	no	—
306	#446	—	86	1	no	—
307	#446	—	86	1	no	—
308	#446	—	86	1	no	—
309	#446	—	86	1	no	—
310	#446	C₂×D₄₃	1	1	yes	characteristic
311	C₈×Q₈	—	43	1	no	—
312	C₈×Q₈	—	43	1	no	—
313	C₈×Q₈	—	43	1	no	—
314	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
315	C₄×Q₁₆	—	43	1	no	—
316	C₄×Q₁₆	—	43	1	no	—
317	C₄×Q₁₆	—	43	1	no	—
318	C₄×Q₁₆	—	43	1	no	—
319	C₄×Q₁₆	—	43	1	no	—
320	C₄×Q₁₆	—	43	1	no	—
321	C₄×Q₁₆	—	43	1	no	—
322	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
323	#431	—	43	1	no	—
324	C₂×#107	—	43	1	no	—
325	#423	—	43	1	no	—
326	#423	—	43	1	no	—
327	#423	—	86	1	no	—
328	#423	—	86	1	no	—
329	C₂×#103	—	43	1	no	—
330	C₂×#103	—	43	1	no	—
331	C₄×M₁₆	—	43	1	no	—
332	C₄×M₁₆	—	86	1	no	—
333	C₄×M₁₆	—	86	1	no	—
334	C₂×C₄×C₈	—	43	1	no	—
335	#335	—	43	1	no	—
336	#335	—	43	1	no	—
337	#335	—	43	1	no	—
338	#335	C₂×D₄₃	1	1	yes	characteristic
339	Q₈⋊C₈	—	43	1	no	—
340	Q₈⋊C₈	—	43	1	no	—
341	Q₈⋊C₈	—	43	1	no	—
342	Q₈⋊C₈	—	43	1	no	—
343	Q₈⋊C₈	—	43	1	no	—
344	Q₈⋊C₈	—	43	1	no	—
345	Q₈⋊C₈	C₂×D₄₃	1	1	yes	characteristic
346	Q₈⋊C₈	C₂×D₄₃	1	1	yes	characteristic
347	#322	—	43	1	no	—
348	#322	C₂×D₄₃	1	1	yes	characteristic
349	C₈²	—	43	1	no	—
350	C₈²	—	43	1	no	—
351	C₄₃	M₁₆×Q₁₆	1	1	yes	characteristic, complemented, Sylow
352	C₂²×Q₈	—	43	1	no	—
353	C₂²×Q₈	—	43	1	no	—
354	C₂×Q₁₆	—	43	1	no	—
355	C₂×Q₁₆	—	43	1	no	—
356	C₂×Q₁₆	—	43	1	no	—
357	C₂×Q₁₆	—	86	4	no	—
358	C₂×Q₁₆	C₄×D₄₃	1	1	yes	characteristic
359	C₂×M₁₆	—	43	1	no	—
360	C₂×M₁₆	—	43	1	no	—
361	C₂×M₁₆	—	86	1	no	—
362	C₂×M₁₆	—	86	1	no	—
363	C₂²×C₈	—	43	1	no	—
364	C₂²×C₈	—	43	1	no	—
365	C₄×Q₈	—	43	1	no	—
366	C₄×Q₈	—	43	1	no	—
367	C₄×Q₈	—	43	1	no	—
368	C₄×Q₈	—	43	1	no	—
369	C₄×Q₈	—	43	1	no	—
370	C₄×Q₈	—	43	1	no	—
371	C₄×Q₈	—	86	1	no	—
372	C₄×Q₈	—	86	1	no	—
373	C₄×Q₈	—	86	1	no	—
374	C₄×Q₈	—	86	1	no	—
375	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
376	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	—	43	1	no	—
378	C₂×C₄⋊C₄	—	43	1	no	—
379	C₂×C₄⋊C₄	—	86	1	no	—
380	C₂×C₄⋊C₄	—	86	1	no	—
381	C₂×C₄²	—	43	1	no	—
382	C₂×C₄²	—	86	1	no	—
383	C₂×C₄²	—	86	1	no	—
384	#107	—	43	1	no	—
385	#107	—	43	1	no	—
386	#107	—	43	1	no	—
387	#107	C₄×D₄₃	1	1	yes	characteristic
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	43	1	no	—
391	C₄⋊C₈	—	43	1	no	—
392	C₄⋊C₈	—	86	1	no	—
393	C₄⋊C₈	—	86	1	no	—
394	C₄⋊C₈	—	86	1	no	—
395	C₄⋊C₈	—	86	1	no	—
396	C₄⋊C₈	—	86	1	no	—
397	C₄⋊C₈	—	86	1	no	—
398	C₄⋊C₈	—	86	1	no	—
399	C₄⋊C₈	—	86	1	no	—
400	C₄⋊C₈	—	86	1	no	—
401	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
403	#103	—	43	1	no	—
404	#103	—	43	1	no	—
405	#103	—	43	1	no	—
406	#103	—	43	1	no	—
407	#103	—	43	1	no	—
408	#103	—	43	1	no	—
409	#103	C₄×D₄₃	1	1	yes	characteristic
410	#103	C₄×D₄₃	1	1	yes	characteristic
411	C₂²⋊C₈	—	86	1	no	—
412	#97	—	2	1	no	—
413	#97	—	43	1	no	—
414	#97	—	43	1	no	—
415	#97	—	86	1	no	—
416	#97	—	86	1	no	—
417	#97	—	86	1	no	—
418	C₄×C₈	—	2	1	no	—
419	C₄×C₈	—	43	1	no	—
420	C₄×C₈	—	43	1	no	—
421	C₄×C₈	—	43	1	no	—
422	C₄×C₈	—	43	1	no	—
423	C₄×C₈	—	43	1	no	—
424	C₄×C₈	—	86	1	no	—
425	C₄×C₈	—	86	1	no	—
426	C₄×C₈	—	86	1	no	—
427	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
428	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
429	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
430	C₂×Q₈	—	43	1	no	—
431	C₂×Q₈	—	43	1	no	—
432	C₂×Q₈	—	86	1	no	—
433	C₂×Q₈	—	86	1	no	—
434	C₂×Q₈	—	86	2	no	—
435	C₂×Q₈	—	86	2	no	—
436	C₂×Q₈	—	172	1	no	—
437	C₂×Q₈	—	172	1	no	—
438	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
439	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
440	C₂²×C₄	—	43	1	no	—
441	C₂²×C₄	—	43	1	no	—
442	C₂²×C₄	—	43	1	no	—
443	C₂²×C₄	—	86	1	no	—
444	C₂²×C₄	—	86	1	no	—
445	C₂²×C₄	—	86	1	no	—
446	C₂²×C₄	—	86	1	no	—
447	Q₁₆	—	2	2	no	—
448	Q₁₆	—	43	4	no	—
449	Q₁₆	—	86	2	no	—
450	Q₁₆	—	86	2	no	—
451	M₁₆	—	43	4	no	—
452	M₁₆	—	86	2	no	—
453	M₁₆	—	172	2	no	—
454	M₁₆	—	172	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	43	1	no	—
459	C₂×C₈	—	43	1	no	—
460	C₂×C₈	—	43	1	no	—
461	C₂×C₈	—	43	1	no	—
462	C₂×C₈	—	86	2	no	—
463	C₂×C₈	—	86	1	no	—
464	C₂×C₈	—	86	1	no	—
465	C₂×C₈	—	86	1	no	—
466	C₂×C₈	—	172	1	no	—
467	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₄₃	1	1	yes	characteristic
469	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
470	C₂×C₈	D₄×D₄₃	1	1	yes	characteristic
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	43	1	no	—
474	C₄⋊C₄	—	43	1	no	—
475	C₄⋊C₄	—	86	1	no	—
476	C₄⋊C₄	—	86	1	no	—
477	C₄⋊C₄	—	86	1	no	—
478	C₄⋊C₄	—	86	1	no	—
479	C₄⋊C₄	—	86	1	no	—
480	C₄⋊C₄	—	86	1	no	—
481	C₄⋊C₄	—	86	1	no	—
482	C₄⋊C₄	—	86	1	no	—
483	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
484	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	43	1	no	—
488	C₄²	—	43	1	no	—
489	C₄²	—	43	1	no	—
490	C₄²	—	86	1	no	—
491	C₄²	—	86	1	no	—
492	C₄²	—	86	1	no	—
493	C₄²	—	86	1	no	—
494	C₄²	—	86	1	no	—
495	C₄²	—	86	1	no	—
496	C₄²	C₂³×D₄₃	1	1	yes	characteristic
497	C₂³	—	43	1	no	—
498	Q₈	—	2	1	no	—
499	Q₈	—	2	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	43	2	no	—
502	Q₈	—	86	1	no	—
503	Q₈	—	86	1	no	—
504	Q₈	—	86	1	no	—
505	Q₈	—	172	2	no	—
506	Q₈	—	172	2	no	—
507	Q₈	M₁₆×D₄₃	1	2	yes	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	43	1	no	—
513	C₂×C₄	—	43	2	no	—
514	C₂×C₄	—	43	2	no	—
515	C₂×C₄	—	43	1	no	—
516	C₂×C₄	—	43	1	no	—
517	C₂×C₄	—	86	1	no	—
518	C₂×C₄	—	86	1	no	—
519	C₂×C₄	—	86	1	no	—
520	C₂×C₄	—	86	1	no	—
521	C₂×C₄	—	86	1	no	—
522	C₂×C₄	—	86	1	no	—
523	C₂×C₄	—	344	1	no	—
524	C₂×C₄	—	344	1	no	—
525	C₂×C₄	—	172	1	no	—
526	C₂×C₄	—	172	2	no	—
527	C₂×C₄	—	172	2	no	—
528	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
529	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
530	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	43	2	no	—
538	C₈	—	43	2	no	—
539	C₈	—	86	1	no	—
540	C₈	—	86	1	no	—
541	C₈	—	172	1	no	—
542	C₈	—	172	1	no	—
543	C₈	—	172	1	no	—
544	C₈	Q₁₆×D₄₃	1	2	yes	complemented
545	C₂²	—	43	2	no	—
546	C₂²	—	86	1	no	—
547	C₂²	—	86	1	no	—
548	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
549	C₄	—	2	1	no	—
550	C₄	—	2	2	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	43	2	no	—
555	C₄	—	86	1	no	—
556	C₄	—	86	1	no	—
557	C₄	—	86	2	no	—
558	C₄	—	172	1	no	—
559	C₄	—	172	1	no	—
560	C₄	—	172	1	no	—
561	C₄	C₂×M₁₆×D₄₃	1	1	yes	characteristic
562	C₄	#14583664	1	1	yes	characteristic
563	C₄	C₂×Q₁₆×D₄₃	1	1	yes	characteristic
564	C₄	#135×D₄₃	1	1	yes	characteristic
565	C₂	—	86	2	no	—
566	C₂	#19143328	1	1	yes	characteristic
567	C₂	C₄×Q₁₆×D₄₃	1	1	yes	characteristic
568	C₂	#19143509	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1584	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂²×D₄₃	C₄×D₄
cosocle	C₄²×C₄₃	C₂⁴
hypercenter	#1584	D₄₃
hypocenter	C₄₃	M₁₆×Q₁₆
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #19133490	C₂	semidirect
5. #19133489	C₂	semidirect
6. #19133447	C₂	semidirect
7. #19133446	C₂	semidirect
8. #19133444	C₂	semidirect
9. C₈×#10621885	C₂	semidirect
10. #19133399	C₂	semidirect
15. C₄₃×#1584	C₂	semidirect
178. #10621885	M₁₆	semidirect
209. #10621872	Q₁₆	semidirect
252. C₈×C₄₃	C₂×Q₁₆	semidirect
259. C₄₃⋊C₈	C₂×Q₁₆	semidirect
289. #1584	D₄₃	semidirect
351. C₄₃	M₁₆×Q₁₆	semidirect
544. C₈	Q₁₆×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19143547	2
Q₈×#10621872	2
C₄×Q₁₆×D₄₃	2
#19133490	2
#19133489	2
#19133447	2
#19133446	2
#19133444	2
C₈×#10621885	2
#19133399	2
#19133352	2
#19133022	2
#19132874	2
C₄₃×#1584	2
M₁₆×Q₁₆	43