Subgroups — C₄₃×#62166 #24982183

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#3559	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₃×#3520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#3384	C₂	1	2	yes	maximal, complemented
4	C₄₃×#3376	C₂	1	2	yes	maximal, complemented
5	C₄₃×#3346	C₂	1	2	yes	maximal, complemented
6	C₄₃×#3345	C₂	1	2	yes	maximal, complemented
7	C₄₃×#3335	C₂	1	2	yes	maximal, complemented
8	C₄₃×#3307	C₂	1	2	yes	maximal, complemented
9	C₄₃×#3306	C₂	1	2	yes	maximal, complemented
10	C₄₃×#3297	C₂	1	2	yes	maximal, complemented
11	C₄₃×#3257	C₂	1	2	yes	maximal, complemented
12	C₄₃×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄₃×#3244	C₂	1	2	yes	maximal, complemented
14	C₄₃×#3236	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#3119	C₂	1	2	yes	maximal, complemented
16	C₄₃×#3109	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄₃×#3084	C₂	1	2	yes	maximal, complemented
18	C₂×C₄₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₃×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄₃×#563	—	2	1	no	—
21	C₄₃×#562	—	2	1	no	—
22	C₄₃×#556	C₂²	1	1	yes	characteristic
23	C₄₃×#554	C₂²	1	2	yes	—
24	C₄₃×#554	C₂²	1	2	yes	complemented
25	C₄₃×#553	C₂²	1	2	yes	—
26	C₄₃×#553	C₂²	1	2	yes	complemented
27	C₄₃×#552	—	2	1	no	—
28	C₄₃×#551	—	2	2	no	—
29	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
30	C₄₃×#548	—	2	1	no	—
31	C₄₃×#547	—	2	2	no	—
32	C₄₃×#547	C₂²	1	1	yes	characteristic
33	C₄₃×#547	C₂²	1	1	yes	characteristic
34	C₄₃×#547	C₂²	1	2	yes	—
35	C₄₃×#546	C₂²	1	2	yes	—
36	C₄₃×#544	C₂²	1	2	yes	complemented
37	C₄₃×#542	C₂²	1	2	yes	—
38	C₄₃×#540	C₂²	1	2	yes	complemented
39	C₄₃×#539	—	2	2	no	—
40	C₄₃×#539	—	2	2	no	—
41	C₄₃×#539	—	2	1	no	—
42	C₄₃×#537	—	2	1	no	—
43	C₄₃×#533	C₂²	1	1	yes	characteristic
44	C₄₃×#532	C₂²	1	1	yes	characteristic
45	C₄₃×#529	C₂²	1	1	yes	characteristic
46	C₂×#125×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#525	—	2	1	no	—
48	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
49	C₄₃×#520	C₂²	1	2	yes	—
50	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
51	C₄₃×#501	C₂²	1	2	yes	complemented
52	C₄₃×#501	C₂²	1	2	yes	complemented
53	C₄₃×#498	C₂²	1	2	yes	complemented
54	C₄₃×#491	C₂²	1	2	yes	complemented
55	C₄₃×#489	C₂²	1	2	yes	—
56	C₄₃×#488	C₂²	1	2	yes	—
57	C₄₃×#485	C₂²	1	2	yes	complemented
58	C₄₃×#484	C₂²	1	2	yes	—
59	C₄₃×#483	C₂²	1	2	yes	—
60	C₄₃×#483	C₂²	1	2	yes	complemented
61	C₄₃×#482	C₂²	1	2	yes	—
62	C₄₃×#481	C₂²	1	2	yes	—
63	C₄₃×#481	C₂²	1	2	yes	—
64	C₄₃×#481	C₂²	1	2	yes	complemented
65	C₄₃×#480	C₂²	1	2	yes	complemented
66	C₄₃×#479	C₂²	1	2	yes	complemented
67	C₄₃×#479	C₂²	1	2	yes	complemented
68	C₄₃×#479	C₂²	1	2	yes	complemented
69	C₄₃×#478	C₂²	1	2	yes	—
70	C₄₃×#478	C₂²	1	2	yes	—
71	C₄₃×#478	C₂²	1	2	yes	—
72	C₄₃×#478	C₂²	1	2	yes	—
73	C₄₃×#478	C₂²	1	2	yes	—
74	C₄₃×#476	C₂²	1	1	yes	characteristic
75	C₄₃×#476	C₂²	1	1	yes	characteristic
76	C₄₃×#476	C₂²	1	2	yes	—
77	C₄₃×#476	C₂²	1	2	yes	complemented
78	C₄₃×#476	C₂²	1	2	yes	complemented
79	C₄₃×#475	C₂²	1	2	yes	complemented
80	C₄₃×#475	C₂²	1	2	yes	complemented
81	C₄₃×#474	C₂²	1	2	yes	complemented
82	C₄₃×#469	C₂²	1	2	yes	—
83	C₄₃×#468	C₂²	1	2	yes	complemented
84	C₄₃×#466	C₂²	1	2	yes	—
85	C₄₃×#465	C₂²	1	2	yes	—
86	C₄₃×#465	C₂²	1	2	yes	—
87	C₄₃×#465	C₂²	1	2	yes	complemented
88	C₄₃×#463	C₂²	1	2	yes	—
89	C₄₃×#463	C₂²	1	2	yes	—
90	C₄₃×#461	C₂²	1	2	yes	complemented
91	C₄₃×#460	C₂²	1	2	yes	complemented
92	C₄₃×#459	C₂²	1	1	yes	characteristic
93	C₄₃×#459	C₂²	1	1	yes	characteristic
94	C₄₃×#449	C₂²	1	2	yes	—
95	C₄₃×#449	C₂²	1	2	yes	—
96	C₄₃×#447	C₂²	1	2	yes	—
97	C₄₃×#446	C₂²	1	2	yes	complemented
98	C₄₃×#442	C₂²	1	2	yes	—
99	C₄₃×#442	C₂²	1	2	yes	—
100	C₄₃×#442	C₂²	1	2	yes	—
101	C₄₃×#440	C₂²	1	2	yes	complemented
102	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
103	C₄×D₈×C₄₃	C₂²	1	2	yes	—
104	C₄₃×#435	C₂²	1	2	yes	—
105	C₄₃×#435	C₂²	1	2	yes	complemented
106	C₈×D₄×C₄₃	C₂²	1	2	yes	—
107	C₄₃×#433	C₂²	1	2	yes	complemented
108	C₄₃×#432	C₂²	1	1	yes	characteristic
109	C₄₃×#428	C₂²	1	2	yes	complemented
110	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
111	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
112	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
113	C₄₃×#424	C₂²	1	2	yes	complemented
114	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
115	C₄₃×#417	C₂²	1	2	yes	—
116	C₄₃×#416	C₂²	1	2	yes	—
117	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
118	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
119	C₂×#41×C₄₃	—	2	1	no	—
120	C₂×#41×C₄₃	—	2	2	no	—
121	C₂×#41×C₄₃	—	2	1	no	—
122	C₂×#41×C₄₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₄₃	—	2	1	no	—
124	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₄₃	—	2	1	no	—
126	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
127	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
128	C₂×D₈×C₄₃	C₂³	1	2	yes	—
129	C₂×D₈×C₄₃	C₂³	1	2	yes	—
130	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
131	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
134	C₄⋊Q₈×C₄₃	—	2	2	no	—
135	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
136	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
137	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
138	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
139	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
140	#127×C₄₃	C₂³	1	1	yes	characteristic
141	#126×C₄₃	—	2	2	no	—
142	#126×C₄₃	—	2	2	no	—
143	#126×C₄₃	—	2	2	no	—
144	#126×C₄₃	—	2	2	no	—
145	#126×C₄₃	D₄	1	2	yes	—
146	#125×C₄₃	—	2	2	no	—
147	#125×C₄₃	—	2	2	no	—
148	#125×C₄₃	—	2	1	no	—
149	#125×C₄₃	—	2	1	no	—
150	#125×C₄₃	—	2	1	no	—
151	#125×C₄₃	D₄	1	1	yes	characteristic
152	#125×C₄₃	C₂³	1	2	yes	—
153	#125×C₄₃	C₂³	1	2	yes	—
154	#125×C₄₃	C₂³	1	2	yes	—
155	#124×C₄₃	—	2	2	no	—
156	#124×C₄₃	—	2	1	no	—
157	#124×C₄₃	D₄	1	1	yes	characteristic
158	#124×C₄₃	C₂³	1	2	yes	—
159	#123×C₄₃	—	2	2	no	—
160	#123×C₄₃	—	2	2	no	—
161	#123×C₄₃	—	2	2	no	—
162	#123×C₄₃	—	2	2	no	—
163	#123×C₄₃	—	2	2	no	—
164	#123×C₄₃	—	2	2	no	—
165	#123×C₄₃	—	2	2	no	—
166	#123×C₄₃	—	2	2	no	—
167	#123×C₄₃	—	2	2	no	—
168	#123×C₄₃	—	2	2	no	—
169	#123×C₄₃	D₄	1	2	yes	—
170	C₂²⋊Q₈×C₄₃	—	2	1	no	—
171	C₂²⋊Q₈×C₄₃	—	2	2	no	—
172	C₂²⋊Q₈×C₄₃	—	2	1	no	—
173	C₂²⋊Q₈×C₄₃	—	2	2	no	—
174	C₂²⋊Q₈×C₄₃	—	2	1	no	—
175	C₂²⋊Q₈×C₄₃	—	2	1	no	—
176	C₂²⋊Q₈×C₄₃	—	2	2	no	—
177	C₂²⋊Q₈×C₄₃	—	2	2	no	—
178	C₂²⋊Q₈×C₄₃	—	2	2	no	—
179	C₂²⋊Q₈×C₄₃	—	2	2	no	—
180	C₂²⋊Q₈×C₄₃	—	2	2	no	—
181	C₂²⋊Q₈×C₄₃	—	2	2	no	—
182	C₂²⋊Q₈×C₄₃	—	2	2	no	—
183	C₂²⋊Q₈×C₄₃	—	2	2	no	—
184	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
185	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
186	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
187	#121×C₄₃	—	2	1	no	—
188	#121×C₄₃	—	2	2	no	—
189	#121×C₄₃	—	2	2	no	—
190	#121×C₄₃	—	2	1	no	—
191	#121×C₄₃	—	2	2	no	—
192	#121×C₄₃	—	2	2	no	—
193	#121×C₄₃	—	2	2	no	—
194	#121×C₄₃	D₄	1	1	yes	characteristic
195	#121×C₄₃	C₂³	1	2	yes	—
196	#121×C₄₃	C₂³	1	2	yes	—
197	#121×C₄₃	C₂³	1	2	yes	—
198	#121×C₄₃	C₂³	1	2	yes	—
199	#120×C₄₃	—	2	2	no	—
200	C₄×Q₈×C₄₃	—	2	1	no	—
201	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
202	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
203	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
204	C₄×D₄×C₄₃	—	2	2	no	—
205	C₄×D₄×C₄₃	—	2	2	no	—
206	C₄×D₄×C₄₃	—	2	2	no	—
207	C₄×D₄×C₄₃	—	2	2	no	—
208	C₄×D₄×C₄₃	—	2	2	no	—
209	C₄×D₄×C₄₃	—	2	1	no	—
210	C₄×D₄×C₄₃	—	2	1	no	—
211	C₄×D₄×C₄₃	—	2	1	no	—
212	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
213	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
214	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
215	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
216	C₄×D₄×C₄₃	C₂³	1	2	yes	—
217	C₄×D₄×C₄₃	C₂³	1	2	yes	—
218	C₄×D₄×C₄₃	C₂³	1	2	yes	—
219	C₄×D₄×C₄₃	C₂³	1	2	yes	—
220	C₄×D₄×C₄₃	C₂³	1	2	yes	—
221	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
222	#117×C₄₃	—	2	1	no	—
223	#117×C₄₃	—	2	2	no	—
224	#117×C₄₃	—	2	1	no	—
225	#117×C₄₃	C₂³	1	2	yes	—
226	#117×C₄₃	C₂³	1	2	yes	—
227	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
228	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
229	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
230	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
231	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
232	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
234	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
235	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
236	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
237	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
238	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
239	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
240	#107×C₄₃	C₂³	1	2	yes	—
241	#107×C₄₃	C₂³	1	2	yes	—
242	#107×C₄₃	C₂³	1	2	yes	—
243	#107×C₄₃	C₂³	1	2	yes	—
244	#106×C₄₃	C₂³	1	2	yes	—
245	#106×C₄₃	C₂³	1	2	yes	—
246	#106×C₄₃	C₂³	1	2	yes	—
247	#106×C₄₃	C₂³	1	2	yes	—
248	#106×C₄₃	C₂³	1	2	yes	—
249	#106×C₄₃	C₂³	1	2	yes	—
250	#106×C₄₃	C₂³	1	2	yes	—
251	#106×C₄₃	C₂³	1	2	yes	—
252	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
253	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
254	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
255	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
256	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
257	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
258	#103×C₄₃	C₂³	1	2	yes	—
259	#103×C₄₃	C₂³	1	2	yes	—
260	#103×C₄₃	C₂³	1	2	yes	—
261	#103×C₄₃	C₂³	1	2	yes	—
262	#103×C₄₃	C₂³	1	2	yes	—
263	#103×C₄₃	C₂³	1	2	yes	—
264	#102×C₄₃	C₂³	1	2	yes	—
265	#102×C₄₃	C₂³	1	2	yes	—
266	#102×C₄₃	C₂³	1	2	yes	—
267	#102×C₄₃	C₂³	1	2	yes	—
268	#102×C₄₃	C₂³	1	2	yes	—
269	#102×C₄₃	C₂³	1	2	yes	—
270	#102×C₄₃	C₂³	1	2	yes	—
271	#102×C₄₃	C₂³	1	2	yes	—
272	#102×C₄₃	C₂³	1	2	yes	—
273	#102×C₄₃	C₂³	1	2	yes	—
274	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
275	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
276	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
277	#97×C₄₃	C₂³	1	2	yes	—
278	#97×C₄₃	C₂³	1	2	yes	—
279	C₄×C₈×C₄₃	C₂³	1	2	yes	—
280	C₂⁴×C₄₃	—	2	1	no	—
281	#41×C₄₃	—	2	4	no	—
282	#41×C₄₃	—	4	2	no	—
283	#41×C₄₃	—	8	2	no	—
284	#41×C₄₃	—	8	4	no	—
285	#41×C₄₃	—	8	2	no	—
286	C₂×Q₈×C₄₃	—	2	1	no	—
287	C₂×Q₈×C₄₃	—	2	2	no	—
288	C₂×Q₈×C₄₃	—	2	2	no	—
289	C₂×Q₈×C₄₃	—	2	1	no	—
290	C₂×Q₈×C₄₃	—	8	2	no	—
291	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
292	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
293	C₂×D₄×C₄₃	—	2	1	no	—
294	C₂×D₄×C₄₃	—	2	1	no	—
295	C₂×D₄×C₄₃	—	2	1	no	—
296	C₂×D₄×C₄₃	—	2	2	no	—
297	C₂×D₄×C₄₃	—	2	2	no	—
298	C₂×D₄×C₄₃	—	2	2	no	—
299	C₂×D₄×C₄₃	—	2	2	no	—
300	C₂×D₄×C₄₃	—	2	2	no	—
301	C₂×D₄×C₄₃	—	2	2	no	—
302	C₂×D₄×C₄₃	—	4	1	no	—
303	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
304	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
305	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
306	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₄₃	—	2	2	no	—
309	C₂²×C₄×C₄₃	—	2	1	no	—
310	C₂²×C₄×C₄₃	—	2	1	no	—
311	C₂²×C₄×C₄₃	—	2	2	no	—
312	C₂²×C₄×C₄₃	—	2	1	no	—
313	C₂²×C₄×C₄₃	—	2	2	no	—
314	C₂²×C₄×C₄₃	—	2	2	no	—
315	C₂²×C₄×C₄₃	—	2	2	no	—
316	C₂²×C₄×C₄₃	—	2	1	no	—
317	C₂²×C₄×C₄₃	—	2	1	no	—
318	C₂²×C₄×C₄₃	—	2	1	no	—
319	C₂²×C₄×C₄₃	—	2	1	no	—
320	C₂²×C₄×C₄₃	—	2	2	no	—
321	C₂²×C₄×C₄₃	—	2	2	no	—
322	C₂²×C₄×C₄₃	—	8	2	no	—
323	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
327	SD₁₆×C₄₃	—	4	2	no	—
328	SD₁₆×C₄₃	—	4	2	no	—
329	D₈×C₄₃	—	2	4	no	—
330	D₈×C₄₃	—	4	2	no	—
331	M₁₆×C₄₃	—	4	2	no	—
332	C₂×C₈×C₄₃	—	4	1	no	—
333	C₂×C₈×C₄₃	—	4	2	no	—
334	C₂×C₈×C₄₃	—	4	1	no	—
335	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
336	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
337	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
338	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
339	C₄⋊C₄×C₄₃	—	2	2	no	—
340	C₄⋊C₄×C₄₃	—	2	2	no	—
341	C₄⋊C₄×C₄₃	—	2	1	no	—
342	C₄⋊C₄×C₄₃	—	2	2	no	—
343	C₄⋊C₄×C₄₃	—	2	2	no	—
344	C₄⋊C₄×C₄₃	—	2	2	no	—
345	C₄⋊C₄×C₄₃	—	2	2	no	—
346	C₄⋊C₄×C₄₃	—	2	2	no	—
347	C₄⋊C₄×C₄₃	—	2	2	no	—
348	C₄⋊C₄×C₄₃	—	2	2	no	—
349	C₄⋊C₄×C₄₃	—	2	2	no	—
350	C₄⋊C₄×C₄₃	—	2	1	no	—
351	C₄⋊C₄×C₄₃	—	2	1	no	—
352	C₄⋊C₄×C₄₃	—	2	2	no	—
353	C₄⋊C₄×C₄₃	—	2	1	no	—
354	C₄⋊C₄×C₄₃	—	2	1	no	—
355	C₄⋊C₄×C₄₃	—	2	1	no	—
356	C₄⋊C₄×C₄₃	—	2	1	no	—
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	—	2	2	no	—
359	C₄⋊C₄×C₄₃	—	2	2	no	—
360	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
361	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
363	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
366	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
367	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
369	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
372	C₂²⋊C₄×C₄₃	—	2	1	no	—
373	C₂²⋊C₄×C₄₃	—	2	1	no	—
374	C₂²⋊C₄×C₄₃	—	2	1	no	—
375	C₂²⋊C₄×C₄₃	—	2	1	no	—
376	C₂²⋊C₄×C₄₃	—	2	2	no	—
377	C₂²⋊C₄×C₄₃	—	2	2	no	—
378	C₂²⋊C₄×C₄₃	—	2	2	no	—
379	C₂²⋊C₄×C₄₃	—	2	2	no	—
380	C₂²⋊C₄×C₄₃	—	2	2	no	—
381	C₂²⋊C₄×C₄₃	—	2	2	no	—
382	C₂²⋊C₄×C₄₃	—	2	2	no	—
383	C₂²⋊C₄×C₄₃	—	2	2	no	—
384	C₂²⋊C₄×C₄₃	—	2	2	no	—
385	C₂²⋊C₄×C₄₃	—	2	2	no	—
386	C₂²⋊C₄×C₄₃	—	2	2	no	—
387	C₂²⋊C₄×C₄₃	—	2	2	no	—
388	C₂²⋊C₄×C₄₃	—	2	2	no	—
389	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
391	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
394	C₄²×C₄₃	—	2	2	no	—
395	C₄²×C₄₃	—	2	2	no	—
396	C₄²×C₄₃	—	2	2	no	—
397	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
398	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₄₃	C₂⁴	1	2	yes	—
400	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
401	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
402	C₂³×C₄₃	—	2	1	no	—
403	C₂³×C₄₃	—	2	1	no	—
404	C₂³×C₄₃	—	2	2	no	—
405	C₂³×C₄₃	—	4	2	no	—
406	C₂³×C₄₃	—	4	2	no	—
407	C₂³×C₄₃	—	8	1	no	—
408	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
409	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
410	Q₈×C₄₃	—	2	2	no	—
411	Q₈×C₄₃	—	2	2	no	—
412	Q₈×C₄₃	—	4	1	no	—
413	Q₈×C₄₃	—	4	2	no	—
414	Q₈×C₄₃	—	8	2	no	—
415	Q₈×C₄₃	—	8	1	no	—
416	Q₈×C₄₃	—	8	2	no	—
417	D₄×C₄₃	—	2	4	no	—
418	D₄×C₄₃	—	2	2	no	—
419	D₄×C₄₃	—	2	1	no	—
420	D₄×C₄₃	—	2	1	no	—
421	D₄×C₄₃	—	2	1	no	—
422	D₄×C₄₃	—	2	2	no	—
423	D₄×C₄₃	—	4	1	no	—
424	D₄×C₄₃	—	4	2	no	—
425	D₄×C₄₃	—	4	4	no	—
426	D₄×C₄₃	—	4	4	no	—
427	D₄×C₄₃	—	8	1	no	—
428	D₄×C₄₃	—	8	1	no	—
429	D₄×C₄₃	—	8	2	no	—
430	D₄×C₄₃	—	8	2	no	—
431	D₄×C₄₃	—	8	2	no	—
432	D₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
433	C₂×C₄×C₄₃	—	2	2	no	—
434	C₂×C₄×C₄₃	—	2	1	no	—
435	C₂×C₄×C₄₃	—	2	2	no	—
436	C₂×C₄×C₄₃	—	2	1	no	—
437	C₂×C₄×C₄₃	—	2	2	no	—
438	C₂×C₄×C₄₃	—	2	2	no	—
439	C₂×C₄×C₄₃	—	2	1	no	—
440	C₂×C₄×C₄₃	—	2	2	no	—
441	C₂×C₄×C₄₃	—	2	2	no	—
442	C₂×C₄×C₄₃	—	2	2	no	—
443	C₂×C₄×C₄₃	—	2	1	no	—
444	C₂×C₄×C₄₃	—	2	2	no	—
445	C₂×C₄×C₄₃	—	4	1	no	—
446	C₂×C₄×C₄₃	—	4	4	no	—
447	C₂×C₄×C₄₃	—	4	2	no	—
448	C₂×C₄×C₄₃	—	4	2	no	—
449	C₂×C₄×C₄₃	—	4	2	no	—
450	C₂×C₄×C₄₃	—	8	2	no	—
451	C₂×C₄×C₄₃	—	8	1	no	—
452	C₂×C₄×C₄₃	—	8	1	no	—
453	C₂×C₄×C₄₃	—	8	2	no	—
454	C₂×C₄×C₄₃	—	8	2	no	—
455	C₂×C₄×C₄₃	—	8	2	no	—
456	C₂×C₄×C₄₃	—	8	1	no	—
457	C₂×C₄×C₄₃	—	8	1	no	—
458	C₂×C₄×C₄₃	—	8	2	no	—
459	C₂×C₄×C₄₃	—	8	2	no	—
460	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
462	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
468	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
469	C₈×C₄₃	—	2	2	no	—
470	C₈×C₄₃	—	2	2	no	—
471	C₈×C₄₃	—	2	2	no	—
472	C₈×C₄₃	—	2	2	no	—
473	#62166	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
474	C₂²×C₄₃	—	2	1	no	—
475	C₂²×C₄₃	—	2	1	no	—
476	C₂²×C₄₃	—	2	2	no	—
477	C₂²×C₄₃	—	2	2	no	—
478	C₂²×C₄₃	—	2	2	no	—
479	C₂²×C₄₃	—	2	2	no	—
480	C₂²×C₄₃	—	4	1	no	—
481	C₂²×C₄₃	—	4	1	no	—
482	C₂²×C₄₃	—	4	1	no	—
483	C₂²×C₄₃	—	4	2	no	—
484	C₂²×C₄₃	—	4	1	no	—
485	C₂²×C₄₃	—	4	2	no	—
486	C₂²×C₄₃	—	4	1	no	—
487	C₂²×C₄₃	—	4	2	no	—
488	C₂²×C₄₃	—	8	4	no	—
489	C₂²×C₄₃	#577	1	2	yes	—
490	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
491	C₄×C₄₃	—	2	1	no	—
492	C₄×C₄₃	—	2	1	no	—
493	C₄×C₄₃	—	2	2	no	—
494	C₄×C₄₃	—	2	2	no	—
495	C₄×C₄₃	—	2	1	no	—
496	C₄×C₄₃	—	2	1	no	—
497	C₄×C₄₃	—	2	1	no	—
498	C₄×C₄₃	—	2	2	no	—
499	C₄×C₄₃	—	4	1	no	—
500	C₄×C₄₃	—	4	1	no	—
501	C₄×C₄₃	—	4	2	no	—
502	C₄×C₄₃	—	4	2	no	—
503	C₄×C₄₃	—	4	2	no	—
504	C₄×C₄₃	—	4	2	no	—
505	C₄×C₄₃	—	4	2	no	—
506	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
507	C₄×C₄₃	#585	1	1	yes	characteristic
508	#3559	C₂×C₄₃	1	1	yes	characteristic, complemented
509	#3520	C₂×C₄₃	1	1	yes	characteristic, complemented
510	#3384	C₂×C₄₃	1	2	yes	complemented
511	#3376	C₂×C₄₃	1	2	yes	complemented
512	#3346	C₂×C₄₃	1	2	yes	complemented
513	#3345	C₂×C₄₃	1	2	yes	complemented
514	#3335	C₂×C₄₃	1	2	yes	complemented
515	#3307	C₂×C₄₃	1	2	yes	complemented
516	#3306	C₂×C₄₃	1	2	yes	complemented
517	#3297	C₂×C₄₃	1	2	yes	complemented
518	#3257	C₂×C₄₃	1	2	yes	complemented
519	#3246	C₂×C₄₃	1	1	yes	characteristic, complemented
520	#3244	C₂×C₄₃	1	2	yes	complemented
521	#3236	C₂×C₄₃	1	1	yes	characteristic, complemented
522	#3119	C₂×C₄₃	1	2	yes	complemented
523	#3109	C₂×C₄₃	1	1	yes	characteristic, complemented
524	#3084	C₂×C₄₃	1	2	yes	complemented
525	C₂×#478	C₂×C₄₃	1	1	yes	characteristic, complemented
526	#2992	C₂×C₄₃	1	1	yes	characteristic, complemented
527	C₂×C₄₃	—	2	2	no	—
528	C₂×C₄₃	—	4	2	no	—
529	C₂×C₄₃	—	4	2	no	—
530	C₂×C₄₃	—	8	2	no	—
531	C₂×C₄₃	—	8	1	no	—
532	C₂×C₄₃	#3489	1	1	yes	characteristic
533	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
534	C₂×C₄₃	#3585	1	1	yes	characteristic
535	#563	—	2	1	no	—
536	#562	—	2	1	no	—
537	#556	C₂²×C₄₃	1	1	yes	characteristic
538	#554	C₂²×C₄₃	1	2	yes	—
539	#554	C₂²×C₄₃	1	2	yes	complemented
540	#553	C₂²×C₄₃	1	2	yes	—
541	#553	C₂²×C₄₃	1	2	yes	complemented
542	#552	—	2	1	no	—
543	#551	—	2	2	no	—
544	D₄×Q₈	C₂²×C₄₃	1	1	yes	characteristic
545	#548	—	2	1	no	—
546	#547	—	2	2	no	—
547	#547	C₂²×C₄₃	1	1	yes	characteristic
548	#547	C₂²×C₄₃	1	2	yes	—
549	#547	C₂²×C₄₃	1	1	yes	characteristic
550	#546	C₂²×C₄₃	1	2	yes	—
551	#544	C₂²×C₄₃	1	2	yes	complemented
552	#542	C₂²×C₄₃	1	2	yes	—
553	#540	C₂²×C₄₃	1	2	yes	complemented
554	#539	—	2	2	no	—
555	#539	—	2	2	no	—
556	#539	—	2	1	no	—
557	#537	—	2	1	no	—
558	#533	C₂²×C₄₃	1	1	yes	characteristic
559	#532	C₂²×C₄₃	1	1	yes	characteristic
560	#529	C₂²×C₄₃	1	1	yes	characteristic
561	C₂×#125	C₂²×C₄₃	1	1	yes	characteristic
562	#525	—	2	1	no	—
563	C₂×C₂²⋊Q₈	—	2	1	no	—
564	#520	C₂²×C₄₃	1	2	yes	—
565	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
566	#501	C₂²×C₄₃	1	2	yes	complemented
567	#501	C₂²×C₄₃	1	2	yes	complemented
568	#498	C₂²×C₄₃	1	2	yes	complemented
569	#491	C₂²×C₄₃	1	2	yes	complemented
570	#489	C₂²×C₄₃	1	2	yes	—
571	#488	C₂²×C₄₃	1	2	yes	—
572	#485	C₂²×C₄₃	1	2	yes	complemented
573	#484	C₂²×C₄₃	1	2	yes	—
574	#483	C₂²×C₄₃	1	2	yes	—
575	#483	C₂²×C₄₃	1	2	yes	complemented
576	#482	C₂²×C₄₃	1	2	yes	—
577	#481	C₂²×C₄₃	1	2	yes	—
578	#481	C₂²×C₄₃	1	2	yes	—
579	#481	C₂²×C₄₃	1	2	yes	complemented
580	#480	C₂²×C₄₃	1	2	yes	complemented
581	#479	C₂²×C₄₃	1	2	yes	complemented
582	#479	C₂²×C₄₃	1	2	yes	complemented
583	#479	C₂²×C₄₃	1	2	yes	complemented
584	#478	C₂²×C₄₃	1	2	yes	—
585	#478	C₂²×C₄₃	1	2	yes	—
586	#478	C₂²×C₄₃	1	2	yes	—
587	#478	C₂²×C₄₃	1	2	yes	—
588	#478	C₂²×C₄₃	1	2	yes	—
589	#476	C₂²×C₄₃	1	1	yes	characteristic
590	#476	C₂²×C₄₃	1	2	yes	—
591	#476	C₂²×C₄₃	1	1	yes	characteristic
592	#476	C₂²×C₄₃	1	2	yes	complemented
593	#476	C₂²×C₄₃	1	2	yes	complemented
594	#475	C₂²×C₄₃	1	2	yes	complemented
595	#475	C₂²×C₄₃	1	2	yes	complemented
596	#474	C₂²×C₄₃	1	2	yes	complemented
597	#469	C₂²×C₄₃	1	2	yes	—
598	#468	C₂²×C₄₃	1	2	yes	complemented
599	#466	C₂²×C₄₃	1	2	yes	—
600	#465	C₂²×C₄₃	1	2	yes	—
601	#465	C₂²×C₄₃	1	2	yes	—
602	#465	C₂²×C₄₃	1	2	yes	complemented
603	#463	C₂²×C₄₃	1	2	yes	—
604	#463	C₂²×C₄₃	1	2	yes	—
605	#461	C₂²×C₄₃	1	2	yes	complemented
606	#460	C₂²×C₄₃	1	2	yes	complemented
607	#459	C₂²×C₄₃	1	1	yes	characteristic
608	#459	C₂²×C₄₃	1	1	yes	characteristic
609	#449	C₂²×C₄₃	1	2	yes	—
610	#449	C₂²×C₄₃	1	2	yes	—
611	#447	C₂²×C₄₃	1	2	yes	—
612	#446	C₂²×C₄₃	1	2	yes	complemented
613	#442	C₂²×C₄₃	1	2	yes	—
614	#442	C₂²×C₄₃	1	2	yes	—
615	#442	C₂²×C₄₃	1	2	yes	—
616	#440	C₂²×C₄₃	1	2	yes	complemented
617	C₄×SD₁₆	C₂²×C₄₃	1	2	yes	complemented
618	C₄×D₈	C₂²×C₄₃	1	2	yes	—
619	#435	C₂²×C₄₃	1	2	yes	—
620	#435	C₂²×C₄₃	1	2	yes	complemented
621	C₈×D₄	C₂²×C₄₃	1	2	yes	—
622	#433	C₂²×C₄₃	1	2	yes	complemented
623	#432	C₂²×C₄₃	1	1	yes	characteristic
624	#428	C₂²×C₄₃	1	2	yes	complemented
625	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
626	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
627	C₂×#106	C₂²×C₄₃	1	2	yes	complemented
628	#424	C₂²×C₄₃	1	2	yes	complemented
629	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
630	#417	C₂²×C₄₃	1	2	yes	—
631	#416	C₂²×C₄₃	1	2	yes	—
632	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
633	C₂×#102	C₂²×C₄₃	1	1	yes	characteristic
634	C₄₃	#62166	1	1	yes	characteristic, direct product factor, Sylow
635	C₂×#41	—	2	1	no	—
636	C₂×#41	—	2	2	no	—
637	C₂×#41	—	2	1	no	—
638	C₂×#41	C₂³×C₄₃	1	2	yes	—
639	C₂²×Q₈	—	2	1	no	—
640	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
641	C₂³×C₄	—	2	1	no	—
642	C₂×SD₁₆	C₂³×C₄₃	1	2	yes	—
643	C₂×SD₁₆	C₂³×C₄₃	1	2	yes	—
644	C₂×D₈	C₂³×C₄₃	1	2	yes	—
645	C₂×D₈	C₂³×C₄₃	1	2	yes	—
646	C₂×M₁₆	C₂³×C₄₃	1	2	yes	—
647	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
648	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
649	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
650	C₄⋊Q₈	—	2	2	no	—
651	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
652	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
653	C₄⋊Q₈	C₂³×C₄₃	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
655	C₄⋊Q₈	C₂³×C₄₃	1	2	yes	—
656	#127	C₂³×C₄₃	1	1	yes	characteristic
657	#126	—	2	2	no	—
658	#126	—	2	2	no	—
659	#126	—	2	2	no	—
660	#126	—	2	2	no	—
661	#126	D₄×C₄₃	1	2	yes	—
662	#125	—	2	2	no	—
663	#125	—	2	2	no	—
664	#125	—	2	1	no	—
665	#125	—	2	1	no	—
666	#125	—	2	1	no	—
667	#125	D₄×C₄₃	1	1	yes	characteristic
668	#125	C₂³×C₄₃	1	2	yes	—
669	#125	C₂³×C₄₃	1	2	yes	—
670	#125	C₂³×C₄₃	1	2	yes	—
671	#124	—	2	2	no	—
672	#124	—	2	1	no	—
673	#124	D₄×C₄₃	1	1	yes	characteristic
674	#124	C₂³×C₄₃	1	2	yes	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	D₄×C₄₃	1	2	yes	—
686	C₂²⋊Q₈	—	2	1	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	D₄×C₄₃	1	1	yes	characteristic
701	C₂²⋊Q₈	C₂³×C₄₃	1	2	yes	—
702	C₂²⋊Q₈	C₂³×C₄₃	1	2	yes	—
703	#121	—	2	1	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	1	no	—
707	#121	—	2	2	no	—
708	#121	—	2	2	no	—
709	#121	—	2	2	no	—
710	#121	D₄×C₄₃	1	1	yes	characteristic
711	#121	C₂³×C₄₃	1	2	yes	—
712	#121	C₂³×C₄₃	1	2	yes	—
713	#121	C₂³×C₄₃	1	2	yes	—
714	#121	C₂³×C₄₃	1	2	yes	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
718	C₄×Q₈	C₂³×C₄₃	1	2	yes	—
719	C₄×Q₈	C₂³×C₄₃	1	1	yes	characteristic
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	2	no	—
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	2	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	1	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
729	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
732	C₄×D₄	C₂³×C₄₃	1	2	yes	—
733	C₄×D₄	C₂³×C₄₃	1	2	yes	—
734	C₄×D₄	C₂³×C₄₃	1	2	yes	—
735	C₄×D₄	C₂³×C₄₃	1	2	yes	—
736	C₄×D₄	C₂³×C₄₃	1	2	yes	—
737	C₄×D₄	C₂³×C₄₃	1	1	yes	characteristic
738	#117	—	2	1	no	—
739	#117	—	2	2	no	—
740	#117	—	2	1	no	—
741	#117	C₂³×C₄₃	1	2	yes	—
742	#117	C₂³×C₄₃	1	2	yes	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	—	2	2	no	—
746	C₂×C₄⋊C₄	—	2	1	no	—
747	C₂×C₄⋊C₄	—	2	2	no	—
748	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
750	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
751	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
752	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
753	C₂×C₂²⋊C₄	—	2	1	no	—
754	C₂×C₂²⋊C₄	—	2	2	no	—
755	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
756	#107	C₂³×C₄₃	1	2	yes	—
757	#107	C₂³×C₄₃	1	2	yes	—
758	#107	C₂³×C₄₃	1	2	yes	—
759	#107	C₂³×C₄₃	1	2	yes	—
760	#106	C₂³×C₄₃	1	2	yes	—
761	#106	C₂³×C₄₃	1	2	yes	—
762	#106	C₂³×C₄₃	1	2	yes	—
763	#106	C₂³×C₄₃	1	2	yes	—
764	#106	C₂³×C₄₃	1	2	yes	—
765	#106	C₂³×C₄₃	1	2	yes	—
766	#106	C₂³×C₄₃	1	2	yes	—
767	#106	C₂³×C₄₃	1	2	yes	—
768	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
769	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
770	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
771	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
772	C₄⋊C₈	C₂³×C₄₃	1	2	yes	—
773	C₄⋊C₈	C₂³×C₄₃	1	1	yes	characteristic
774	#103	C₂³×C₄₃	1	2	yes	—
775	#103	C₂³×C₄₃	1	2	yes	—
776	#103	C₂³×C₄₃	1	2	yes	—
777	#103	C₂³×C₄₃	1	2	yes	—
778	#103	C₂³×C₄₃	1	2	yes	—
779	#103	C₂³×C₄₃	1	2	yes	—
780	#102	C₂³×C₄₃	1	2	yes	—
781	#102	C₂³×C₄₃	1	2	yes	—
782	#102	C₂³×C₄₃	1	2	yes	—
783	#102	C₂³×C₄₃	1	2	yes	—
784	#102	C₂³×C₄₃	1	2	yes	—
785	#102	C₂³×C₄₃	1	2	yes	—
786	#102	C₂³×C₄₃	1	2	yes	—
787	#102	C₂³×C₄₃	1	2	yes	—
788	#102	C₂³×C₄₃	1	2	yes	—
789	#102	C₂³×C₄₃	1	2	yes	—
790	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
791	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
792	C₂²⋊C₈	C₂³×C₄₃	1	2	yes	—
793	#97	C₂³×C₄₃	1	2	yes	—
794	#97	C₂³×C₄₃	1	2	yes	—
795	C₄×C₈	C₂³×C₄₃	1	2	yes	—
796	C₂⁴	—	2	1	no	—
797	#41	—	2	4	no	—
798	#41	—	4	2	no	—
799	#41	—	8	2	no	—
800	#41	—	8	4	no	—
801	#41	—	8	2	no	—
802	C₂×Q₈	—	2	1	no	—
803	C₂×Q₈	—	2	2	no	—
804	C₂×Q₈	—	2	2	no	—
805	C₂×Q₈	—	2	1	no	—
806	C₂×Q₈	—	8	2	no	—
807	C₂×Q₈	C₂×D₄×C₄₃	1	1	yes	characteristic
808	C₂×Q₈	C₂⁴×C₄₃	1	2	yes	—
809	C₂×D₄	—	2	2	no	—
810	C₂×D₄	—	2	2	no	—
811	C₂×D₄	—	2	2	no	—
812	C₂×D₄	—	2	2	no	—
813	C₂×D₄	—	2	2	no	—
814	C₂×D₄	—	2	2	no	—
815	C₂×D₄	—	2	1	no	—
816	C₂×D₄	—	2	1	no	—
817	C₂×D₄	—	2	1	no	—
818	C₂×D₄	—	4	1	no	—
819	C₂×D₄	C₂×D₄×C₄₃	1	2	yes	—
820	C₂×D₄	C₂×D₄×C₄₃	1	1	yes	characteristic
821	C₂×D₄	C₂⁴×C₄₃	1	1	yes	characteristic
822	C₂×D₄	C₂⁴×C₄₃	1	2	yes	—
823	C₂×D₄	C₂⁴×C₄₃	1	1	yes	characteristic
824	C₂²×C₄	—	2	1	no	—
825	C₂²×C₄	—	2	1	no	—
826	C₂²×C₄	—	2	1	no	—
827	C₂²×C₄	—	2	2	no	—
828	C₂²×C₄	—	2	2	no	—
829	C₂²×C₄	—	2	2	no	—
830	C₂²×C₄	—	2	1	no	—
831	C₂²×C₄	—	2	1	no	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	1	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	2	2	no	—
836	C₂²×C₄	—	2	2	no	—
837	C₂²×C₄	—	2	1	no	—
838	C₂²×C₄	—	8	2	no	—
839	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
840	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
841	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
842	C₂²×C₄	C₂⁴×C₄₃	1	2	yes	—
843	SD₁₆	—	4	2	no	—
844	SD₁₆	—	4	2	no	—
845	D₈	—	2	4	no	—
846	D₈	—	4	2	no	—
847	M₁₆	—	4	2	no	—
848	C₂×C₈	—	4	1	no	—
849	C₂×C₈	—	4	2	no	—
850	C₂×C₈	—	4	1	no	—
851	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
852	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
853	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
854	C₂×C₈	C₂⁴×C₄₃	1	2	yes	—
855	C₄⋊C₄	—	2	2	no	—
856	C₄⋊C₄	—	2	2	no	—
857	C₄⋊C₄	—	2	1	no	—
858	C₄⋊C₄	—	2	2	no	—
859	C₄⋊C₄	—	2	2	no	—
860	C₄⋊C₄	—	2	2	no	—
861	C₄⋊C₄	—	2	2	no	—
862	C₄⋊C₄	—	2	2	no	—
863	C₄⋊C₄	—	2	2	no	—
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	1	no	—
867	C₄⋊C₄	—	2	1	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	2	1	no	—
870	C₄⋊C₄	—	2	1	no	—
871	C₄⋊C₄	—	2	1	no	—
872	C₄⋊C₄	—	2	1	no	—
873	C₄⋊C₄	—	2	2	no	—
874	C₄⋊C₄	—	2	2	no	—
875	C₄⋊C₄	—	2	2	no	—
876	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
877	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
878	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
879	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
880	C₄⋊C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
881	C₄⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
882	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
883	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
884	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
885	C₄⋊C₄	C₂⁴×C₄₃	1	1	yes	characteristic
886	C₄⋊C₄	C₂⁴×C₄₃	1	1	yes	characteristic
887	C₄⋊C₄	C₂⁴×C₄₃	1	2	yes	—
888	C₂²⋊C₄	—	2	2	no	—
889	C₂²⋊C₄	—	2	2	no	—
890	C₂²⋊C₄	—	2	2	no	—
891	C₂²⋊C₄	—	2	1	no	—
892	C₂²⋊C₄	—	2	1	no	—
893	C₂²⋊C₄	—	2	1	no	—
894	C₂²⋊C₄	—	2	1	no	—
895	C₂²⋊C₄	—	2	2	no	—
896	C₂²⋊C₄	—	2	2	no	—
897	C₂²⋊C₄	—	2	2	no	—
898	C₂²⋊C₄	—	2	2	no	—
899	C₂²⋊C₄	—	2	2	no	—
900	C₂²⋊C₄	—	2	2	no	—
901	C₂²⋊C₄	—	2	2	no	—
902	C₂²⋊C₄	—	2	2	no	—
903	C₂²⋊C₄	—	2	2	no	—
904	C₂²⋊C₄	—	2	2	no	—
905	C₂²⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
906	C₂²⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
907	C₂²⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
908	C₂²⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
909	C₂²⋊C₄	C₂×D₄×C₄₃	1	2	yes	—
910	C₄²	—	2	2	no	—
911	C₄²	—	2	2	no	—
912	C₄²	—	2	2	no	—
913	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
914	C₄²	C₂×D₄×C₄₃	1	1	yes	characteristic
915	C₄²	C₂⁴×C₄₃	1	2	yes	—
916	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
917	C₄²	C₂⁴×C₄₃	1	1	yes	characteristic
918	C₂³	—	2	1	no	—
919	C₂³	—	2	1	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	4	2	no	—
922	C₂³	—	4	2	no	—
923	C₂³	—	8	1	no	—
924	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
925	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
926	Q₈	—	2	2	no	—
927	Q₈	—	2	2	no	—
928	Q₈	—	4	1	no	—
929	Q₈	—	4	2	no	—
930	Q₈	—	8	2	no	—
931	Q₈	—	8	1	no	—
932	Q₈	—	8	2	no	—
933	D₄	—	2	4	no	—
934	D₄	—	2	2	no	—
935	D₄	—	2	1	no	—
936	D₄	—	2	1	no	—
937	D₄	—	2	1	no	—
938	D₄	—	2	2	no	—
939	D₄	—	4	1	no	—
940	D₄	—	4	2	no	—
941	D₄	—	4	4	no	—
942	D₄	—	4	4	no	—
943	D₄	—	8	1	no	—
944	D₄	—	8	1	no	—
945	D₄	—	8	2	no	—
946	D₄	—	8	2	no	—
947	D₄	—	8	2	no	—
948	D₄	2₋¹⁺⁴×C₄₃	1	2	yes	—
949	C₂×C₄	—	2	2	no	—
950	C₂×C₄	—	2	1	no	—
951	C₂×C₄	—	2	2	no	—
952	C₂×C₄	—	2	1	no	—
953	C₂×C₄	—	2	2	no	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	1	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	2	2	no	—
958	C₂×C₄	—	2	2	no	—
959	C₂×C₄	—	2	1	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	4	1	no	—
962	C₂×C₄	—	4	4	no	—
963	C₂×C₄	—	4	2	no	—
964	C₂×C₄	—	4	2	no	—
965	C₂×C₄	—	4	2	no	—
966	C₂×C₄	—	8	1	no	—
967	C₂×C₄	—	8	1	no	—
968	C₂×C₄	—	8	2	no	—
969	C₂×C₄	—	8	2	no	—
970	C₂×C₄	—	8	2	no	—
971	C₂×C₄	—	8	2	no	—
972	C₂×C₄	—	8	1	no	—
973	C₂×C₄	—	8	2	no	—
974	C₂×C₄	—	8	2	no	—
975	C₂×C₄	—	8	1	no	—
976	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
977	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
978	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
979	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
980	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
981	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
982	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
983	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
984	C₂×C₄	C₂⁵×C₄₃	1	1	yes	characteristic
985	C₈	—	2	2	no	—
986	C₈	—	2	2	no	—
987	C₈	—	2	2	no	—
988	C₈	—	2	2	no	—
989	C₂²	—	2	1	no	—
990	C₂²	—	2	1	no	—
991	C₂²	—	2	2	no	—
992	C₂²	—	2	2	no	—
993	C₂²	—	2	2	no	—
994	C₂²	—	2	2	no	—
995	C₂²	—	4	1	no	—
996	C₂²	—	4	1	no	—
997	C₂²	—	4	1	no	—
998	C₂²	—	4	2	no	—
999	C₂²	—	4	2	no	—
1000	C₂²	—	4	1	no	—
1001	C₂²	—	4	1	no	—
1002	C₂²	—	4	2	no	—
1003	C₂²	—	8	4	no	—
1004	C₂²	C₄₃×#577	1	2	yes	—
1005	C₂²	C₂³×D₄×C₄₃	1	1	yes	characteristic
1006	C₄	—	2	2	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	2	1	no	—
1009	C₄	—	2	1	no	—
1010	C₄	—	2	2	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	2	no	—
1014	C₄	—	4	2	no	—
1015	C₄	—	4	2	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	1	no	—
1018	C₄	—	4	1	no	—
1019	C₄	—	4	2	no	—
1020	C₄	—	4	2	no	—
1021	C₄	C₂×2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
1022	C₄	C₄₃×#585	1	1	yes	characteristic
1023	C₂	—	2	2	no	—
1024	C₂	—	4	2	no	—
1025	C₂	—	4	2	no	—
1026	C₂	—	8	1	no	—
1027	C₂	—	8	2	no	—
1028	C₂	C₄₃×#3489	1	1	yes	characteristic
1029	C₂	C₂×C₄₃×#577	1	1	yes	characteristic
1030	C₂	C₄₃×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₄₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₄₃×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₃×#3559	C₂	semidirect
2. C₄₃×#3520	C₂	semidirect
3. C₄₃×#3384	C₂	semidirect
4. C₄₃×#3376	C₂	semidirect
5. C₄₃×#3346	C₂	semidirect
6. C₄₃×#3345	C₂	semidirect
7. C₄₃×#3335	C₂	semidirect
8. C₄₃×#3307	C₂	semidirect
9. C₄₃×#3306	C₂	semidirect
10. C₄₃×#3297	C₂	semidirect
11. C₄₃×#3257	C₂	semidirect
12. C₄₃×#3246	C₂	semidirect
13. C₄₃×#3244	C₂	semidirect
14. C₄₃×#3236	C₂	semidirect
15. C₄₃×#3119	C₂	semidirect
16. C₄₃×#3109	C₂	semidirect
17. C₄₃×#3084	C₂	semidirect
18. C₂×C₄₃×#478	C₂	semidirect
19. C₄₃×#2992	C₂	semidirect
24. C₄₃×#554	C₂²	semidirect
26. C₄₃×#553	C₂²	semidirect
36. C₄₃×#544	C₂²	semidirect
38. C₄₃×#540	C₂²	semidirect
51. C₄₃×#501	C₂²	semidirect
52. C₄₃×#501	C₂²	semidirect
53. C₄₃×#498	C₂²	semidirect
54. C₄₃×#491	C₂²	semidirect
57. C₄₃×#485	C₂²	semidirect
60. C₄₃×#483	C₂²	semidirect
64. C₄₃×#481	C₂²	semidirect
65. C₄₃×#480	C₂²	semidirect
66. C₄₃×#479	C₂²	semidirect
67. C₄₃×#479	C₂²	semidirect
68. C₄₃×#479	C₂²	semidirect
77. C₄₃×#476	C₂²	semidirect
78. C₄₃×#476	C₂²	semidirect
79. C₄₃×#475	C₂²	semidirect
80. C₄₃×#475	C₂²	semidirect
81. C₄₃×#474	C₂²	semidirect
83. C₄₃×#468	C₂²	semidirect
87. C₄₃×#465	C₂²	semidirect
90. C₄₃×#461	C₂²	semidirect
91. C₄₃×#460	C₂²	semidirect
97. C₄₃×#446	C₂²	semidirect
101. C₄₃×#440	C₂²	semidirect
102. C₄×SD₁₆×C₄₃	C₂²	semidirect
105. C₄₃×#435	C₂²	semidirect
107. C₄₃×#433	C₂²	semidirect
109. C₄₃×#428	C₂²	semidirect
112. C₂×#106×C₄₃	C₂²	semidirect
113. C₄₃×#424	C₂²	semidirect
473. #62166	C₄₃	direct (N × H)
508. #3559	C₂×C₄₃	semidirect
509. #3520	C₂×C₄₃	semidirect
510. #3384	C₂×C₄₃	semidirect
511. #3376	C₂×C₄₃	semidirect
512. #3346	C₂×C₄₃	semidirect
513. #3345	C₂×C₄₃	semidirect
514. #3335	C₂×C₄₃	semidirect
515. #3307	C₂×C₄₃	semidirect
516. #3306	C₂×C₄₃	semidirect
517. #3297	C₂×C₄₃	semidirect
518. #3257	C₂×C₄₃	semidirect
519. #3246	C₂×C₄₃	semidirect
520. #3244	C₂×C₄₃	semidirect
521. #3236	C₂×C₄₃	semidirect
522. #3119	C₂×C₄₃	semidirect
523. #3109	C₂×C₄₃	semidirect
524. #3084	C₂×C₄₃	semidirect
525. C₂×#478	C₂×C₄₃	semidirect
526. #2992	C₂×C₄₃	semidirect
539. #554	C₂²×C₄₃	semidirect
541. #553	C₂²×C₄₃	semidirect
551. #544	C₂²×C₄₃	semidirect
553. #540	C₂²×C₄₃	semidirect
566. #501	C₂²×C₄₃	semidirect
567. #501	C₂²×C₄₃	semidirect
568. #498	C₂²×C₄₃	semidirect
569. #491	C₂²×C₄₃	semidirect
572. #485	C₂²×C₄₃	semidirect
575. #483	C₂²×C₄₃	semidirect
579. #481	C₂²×C₄₃	semidirect
580. #480	C₂²×C₄₃	semidirect
581. #479	C₂²×C₄₃	semidirect
582. #479	C₂²×C₄₃	semidirect
583. #479	C₂²×C₄₃	semidirect
592. #476	C₂²×C₄₃	semidirect
593. #476	C₂²×C₄₃	semidirect
594. #475	C₂²×C₄₃	semidirect
595. #475	C₂²×C₄₃	semidirect
596. #474	C₂²×C₄₃	semidirect
598. #468	C₂²×C₄₃	semidirect
602. #465	C₂²×C₄₃	semidirect
605. #461	C₂²×C₄₃	semidirect
606. #460	C₂²×C₄₃	semidirect
612. #446	C₂²×C₄₃	semidirect
616. #440	C₂²×C₄₃	semidirect
617. C₄×SD₁₆	C₂²×C₄₃	semidirect
620. #435	C₂²×C₄₃	semidirect
622. #433	C₂²×C₄₃	semidirect
624. #428	C₂²×C₄₃	semidirect
627. C₂×#106	C₂²×C₄₃	semidirect
628. #424	C₂²×C₄₃	semidirect
634. C₄₃	#62166	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#3559	2
C₄₃×#3520	2
C₄₃×#3384	2
C₄₃×#3376	2
C₄₃×#3346	2
C₄₃×#3345	2
C₄₃×#3335	2
C₄₃×#3307	2
C₄₃×#3306	2
C₄₃×#3297	2
C₄₃×#3257	2
C₄₃×#3246	2
C₄₃×#3244	2
C₄₃×#3236	2
C₄₃×#3119	2
C₄₃×#3109	2
C₄₃×#3084	2
C₂×C₄₃×#478	2
C₄₃×#2992	2
#62166	43

Subgroups — C43×#62166 #24982183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#62166 #24982183