Subgroups — #33966713

Order 18688.

1742 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623737	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623733	C₂	1	1	yes	maximal, characteristic
3	#22622883	C₂	1	2	yes	maximal, complemented
4	#22622879	C₂	1	2	yes	maximal, complemented
5	#22622874	C₂	1	2	yes	maximal, complemented
6	#22622874	C₂	1	2	yes	maximal, complemented
7	#22622855	C₂	1	2	yes	maximal, complemented
8	#22622851	C₂	1	2	yes	maximal, complemented
9	#22622844	C₂	1	2	yes	maximal, complemented
10	#22622840	C₂	1	2	yes	maximal, complemented
11	#22620469	C₂	1	1	yes	maximal, characteristic, complemented
12	#22620465	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620454	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619769	C₂	1	1	yes	maximal, characteristic, complemented
15	#22619765	C₂	1	1	yes	maximal, characteristic
16	#22619763	C₂	1	1	yes	maximal, characteristic
17	#22619733	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619727	C₂	1	1	yes	maximal, characteristic
19	#22618870	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618790	C₂	1	1	yes	maximal, characteristic
21	#22618786	C₂	1	1	yes	maximal, characteristic
22	C₂×#17988690	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3082	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#11924015	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₄₆	—	2	1	no	—
26	Q₈×Dic₁₄₆	C₂²	1	2	yes	complemented
27	#17989316	—	2	1	no	—
28	#17989316	C₂²	1	2	yes	complemented
29	#17989313	—	2	1	no	—
30	#17989313	—	2	1	no	—
31	#17989313	C₂²	1	2	yes	complemented
32	#17989313	C₂²	1	2	yes	complemented
33	#17989298	—	2	1	no	—
34	#17989298	C₂²	1	2	yes	—
35	#17989293	—	2	1	no	—
36	#17989293	—	2	1	no	—
37	#17989293	C₂²	1	2	yes	—
38	#17989293	C₂²	1	2	yes	—
39	#17989252	—	2	1	no	—
40	#17989252	C₂²	1	2	yes	—
41	#17989218	C₂²	1	1	yes	characteristic
42	#17989215	—	2	2	no	—
43	#17989215	C₂²	1	1	yes	characteristic
44	#17989215	C₂²	1	1	yes	characteristic
45	#17989212	—	2	2	no	—
46	#17989140	—	2	2	no	—
47	#17989140	C₂²	1	1	yes	characteristic
48	#17989140	C₂²	1	1	yes	characteristic
49	#17989140	C₂²	1	1	yes	characteristic
50	C₂²⋊Q₈×D₇₃	—	2	2	no	—
51	#17989065	C₂²	1	1	yes	characteristic
52	#17989061	C₂²	1	1	yes	characteristic
53	#17989061	C₂²	1	1	yes	characteristic
54	C₂×Q₈×Dic₇₃	C₂²	1	1	yes	characteristic
55	C₂×#14556553	C₂²	1	1	yes	characteristic
56	#17988997	C₂²	1	2	yes	complemented
57	#17988995	C₂²	1	1	yes	characteristic, complemented
58	#17988995	C₂²	1	1	yes	characteristic, complemented
59	#17988995	C₂²	1	1	yes	characteristic, complemented
60	#17988995	C₂²	1	1	yes	characteristic, complemented
61	#17988995	C₂²	1	2	yes	complemented
62	#17988994	C₂²	1	1	yes	characteristic, complemented
63	#17988994	C₂²	1	1	yes	characteristic, complemented
64	#17988994	C₂²	1	1	yes	characteristic, complemented
65	#17988994	C₂²	1	1	yes	characteristic, complemented
66	#17988994	C₂²	1	2	yes	complemented
67	#17988993	C₂²	1	2	yes	complemented
68	#17988991	C₂²	1	2	yes	complemented
69	#17988990	C₂²	1	2	yes	complemented
70	#17988987	C₂²	1	2	yes	complemented
71	#17988986	C₂²	1	2	yes	complemented
72	#17988896	C₂²	1	2	yes	complemented
73	#17988896	C₂²	1	2	yes	complemented
74	#17988892	C₂²	1	2	yes	complemented
75	#17988892	C₂²	1	2	yes	complemented
76	#17988890	C₂²	1	2	yes	—
77	#17988890	C₂²	1	2	yes	—
78	#17988888	C₂²	1	2	yes	—
79	#17988888	C₂²	1	2	yes	—
80	#17988886	C₂²	1	2	yes	—
81	#17988886	C₂²	1	2	yes	—
82	#17988880	C₂²	1	2	yes	complemented
83	#17988880	C₂²	1	2	yes	complemented
84	#17988878	C₂²	1	2	yes	—
85	#17988876	C₂²	1	2	yes	—
86	#17988876	C₂²	1	2	yes	—
87	#17988870	C₂²	1	2	yes	complemented
88	#17988870	C₂²	1	2	yes	complemented
89	#17988868	C₂²	1	2	yes	—
90	#17988866	C₂²	1	2	yes	—
91	#17988866	C₂²	1	2	yes	—
92	#17988716	C₂²	1	2	yes	complemented
93	#17988716	C₂²	1	2	yes	complemented
94	#17988714	C₂²	1	2	yes	complemented
95	#17988714	C₂²	1	2	yes	complemented
96	#17988690	C₂²	1	2	yes	—
97	#17988690	C₂²	1	2	yes	—
98	#17988690	C₂²	1	2	yes	—
99	#17988690	C₂²	1	2	yes	—
100	#17988690	C₂²	1	2	yes	—
101	#17988690	C₂²	1	2	yes	—
102	#17988685	C₂²	1	2	yes	—
103	#17988685	C₂²	1	2	yes	—
104	C₄×#11924015	C₂²	1	2	yes	—
105	C₄×#11924015	C₂²	1	2	yes	—
106	#17988672	C₂²	1	2	yes	—
107	#17988672	C₂²	1	2	yes	—
108	#17988630	C₂²	1	1	yes	characteristic
109	#17988629	C₂²	1	1	yes	characteristic
110	#17988627	C₂²	1	1	yes	characteristic
111	#17988625	C₂²	1	1	yes	characteristic
112	#17988623	C₂²	1	1	yes	characteristic
113	#17988623	C₂²	1	1	yes	characteristic
114	C₂×#14556524	C₂²	1	1	yes	characteristic
115	#17988613	C₂²	1	1	yes	characteristic
116	#17988610	C₂²	1	1	yes	characteristic
117	#17988596	C₂²	1	1	yes	characteristic
118	#17988593	C₂²	1	1	yes	characteristic
119	#17988591	C₂²	1	1	yes	characteristic
120	C₂×#14556513	C₂²	1	1	yes	characteristic
121	#17988545	C₂²	1	1	yes	characteristic
122	#17988543	C₂²	1	1	yes	characteristic
123	C₂×#14556501	C₂²	1	1	yes	characteristic
124	#544×C₇₃	C₂²	1	1	yes	characteristic
125	#519×C₇₃	C₂²	1	1	yes	characteristic
126	#479×C₇₃	C₂²	1	2	yes	complemented
127	#479×C₇₃	C₂²	1	2	yes	complemented
128	#477×C₇₃	C₂²	1	2	yes	complemented
129	#475×C₇₃	C₂²	1	2	yes	complemented
130	#428×C₇₃	C₂²	1	1	yes	characteristic
131	#427×C₇₃	C₂²	1	1	yes	characteristic
132	#424×C₇₃	C₂²	1	1	yes	characteristic
133	#419×C₇₃	C₂²	1	1	yes	characteristic
134	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₇₃	—	2	2	no	—
136	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₇₃	—	2	1	no	—
138	C₂×#11924015	Q₈	1	8	yes	complemented
139	C₂×#11924015	C₂³	1	2	yes	—
140	C₂×#11924015	C₂³	1	2	yes	—
141	C₂×#11924012	C₂³	1	1	yes	characteristic
142	C₂²×#10596831	C₂³	1	1	yes	characteristic
143	#14556591	—	2	2	no	—
144	#14556591	—	2	2	no	—
145	#14556591	—	2	1	no	—
146	#14556591	C₂³	1	2	yes	—
147	#14556590	—	2	2	no	—
148	#14556590	—	2	2	no	—
149	#14556590	—	2	1	no	—
150	#14556590	—	2	2	no	—
151	#14556590	—	2	2	no	—
152	#14556590	—	2	1	no	—
153	#14556590	D₄	1	1	yes	characteristic
154	#14556590	D₄	1	1	yes	characteristic
155	#14556590	C₂³	1	1	yes	characteristic
156	#14556590	C₂³	1	2	yes	—
157	#14556590	C₂³	1	1	yes	characteristic
158	#14556590	C₂³	1	2	yes	—
159	#14556590	C₂³	1	1	yes	characteristic
160	#14556590	C₂³	1	1	yes	characteristic
161	#14556583	—	2	1	no	—
162	#14556583	—	2	2	no	—
163	#14556583	—	2	2	no	—
164	#14556583	C₂³	1	2	yes	—
165	#14556582	—	2	2	no	—
166	#14556582	—	2	2	no	—
167	#14556582	—	2	1	no	—
168	#14556582	—	2	2	no	—
169	#14556582	—	2	2	no	—
170	#14556582	—	2	1	no	—
171	#14556582	D₄	1	1	yes	characteristic
172	#14556582	D₄	1	1	yes	characteristic
173	#14556582	C₂³	1	1	yes	characteristic
174	#14556582	C₂³	1	1	yes	characteristic
175	#14556582	C₂³	1	1	yes	characteristic
176	#14556582	C₂³	1	1	yes	characteristic
177	#14556582	C₂³	1	2	yes	—
178	#14556582	C₂³	1	2	yes	—
179	#14556571	—	2	2	no	—
180	#14556571	—	2	2	no	—
181	#14556571	—	2	2	no	—
182	#14556570	—	2	2	no	—
183	#14556569	—	2	2	no	—
184	#14556569	—	2	2	no	—
185	#14556569	—	2	2	no	—
186	#14556569	—	2	2	no	—
187	#14556569	—	2	2	no	—
188	#14556569	—	2	2	no	—
189	#14556568	—	2	1	no	—
190	#14556568	—	2	1	no	—
191	#14556568	—	2	1	no	—
192	#14556568	—	2	1	no	—
193	#14556568	—	2	2	no	—
194	#14556568	—	2	2	no	—
195	#14556568	D₄	1	2	yes	—
196	#14556568	D₄	1	2	yes	—
197	#14556567	—	2	2	no	—
198	#14556567	—	2	2	no	—
199	#14556567	—	2	2	no	—
200	Q₈×Dic₇₃	—	2	1	no	—
201	Q₈×Dic₇₃	—	2	1	no	—
202	Q₈×Dic₇₃	—	2	1	no	—
203	Q₈×Dic₇₃	—	2	1	no	—
204	Q₈×Dic₇₃	C₂³	1	2	yes	—
205	Q₈×Dic₇₃	C₂³	1	2	yes	—
206	Q₈×Dic₇₃	C₂³	1	2	yes	—
207	Q₈×Dic₇₃	C₂³	1	2	yes	—
208	C₄×Dic₁₄₆	—	2	2	no	—
209	C₄×Dic₁₄₆	—	2	2	no	—
210	C₄×Dic₁₄₆	—	2	2	no	—
211	C₄×Dic₁₄₆	—	2	2	no	—
212	C₄×Dic₁₄₆	—	2	1	no	—
213	C₄×Dic₁₄₆	—	2	1	no	—
214	C₄×Dic₁₄₆	—	2	1	no	—
215	C₄×Dic₁₄₆	—	2	1	no	—
216	C₄×Dic₁₄₆	C₂³	1	2	yes	—
217	C₄×Dic₁₄₆	C₂³	1	2	yes	—
218	C₄×D₂₉₂	—	2	1	no	—
219	C₄×D₂₉₂	—	2	1	no	—
220	C₄×D₂₉₂	C₂³	1	2	yes	—
221	C₄×D₂₉₂	C₂³	1	2	yes	—
222	#14556553	—	2	1	no	—
223	#14556553	—	2	1	no	—
224	#14556553	—	2	1	no	—
225	#14556553	—	2	1	no	—
226	#14556553	C₂³	1	2	yes	—
227	#14556553	C₂³	1	2	yes	—
228	#14556553	C₂³	1	2	yes	—
229	#14556553	C₂³	1	2	yes	—
230	#14556550	—	2	2	no	—
231	#14556550	C₂³	1	1	yes	characteristic
232	#14556550	C₂³	1	1	yes	characteristic
233	#14556550	C₂³	1	1	yes	characteristic
234	C₂×C₄⋊Dic₇₃	—	2	1	no	—
235	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
236	C₄⋊C₄×D₇₃	—	2	2	no	—
237	C₄⋊C₄×D₇₃	—	2	2	no	—
238	C₄⋊C₄×D₇₃	—	2	2	no	—
239	C₂×#11924005	—	2	1	no	—
240	C₂²⋊C₄×D₇₃	—	2	2	no	—
241	C₂²⋊C₄×D₇₃	—	2	2	no	—
242	C₂×C₄×Dic₇₃	—	2	1	no	—
243	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
244	#14556525	C₂³	1	1	yes	characteristic
245	#14556525	C₂³	1	2	yes	—
246	#14556525	C₂³	1	1	yes	characteristic
247	#14556524	C₂³	1	2	yes	—
248	#14556524	C₂³	1	2	yes	—
249	#14556524	C₂³	1	2	yes	—
250	#14556524	C₂³	1	2	yes	—
251	#14556524	C₂³	1	1	yes	characteristic
252	#14556524	C₂³	1	1	yes	characteristic
253	#14556524	C₂³	1	1	yes	characteristic
254	#14556524	C₂³	1	1	yes	characteristic
255	#14556523	C₂³	1	1	yes	characteristic
256	#14556523	C₂³	1	2	yes	—
257	#14556523	C₂³	1	1	yes	characteristic
258	#14556522	C₂³	1	2	yes	—
259	#14556522	C₂³	1	2	yes	—
260	#14556522	C₂³	1	1	yes	characteristic
261	#14556522	C₂³	1	1	yes	characteristic
262	#14556522	C₂³	1	1	yes	characteristic
263	#14556522	C₂³	1	1	yes	characteristic
264	#14556520	C₂³	1	2	yes	—
265	#14556520	C₂³	1	2	yes	—
266	#14556520	C₂³	1	2	yes	—
267	#14556520	C₂³	1	2	yes	—
268	#14556515	C₂³	1	2	yes	—
269	#14556515	C₂³	1	2	yes	—
270	#14556513	C₂³	1	2	yes	—
271	#14556513	C₂³	1	2	yes	—
272	#14556513	C₂³	1	2	yes	—
273	#14556513	C₂³	1	2	yes	—
274	#14556511	C₂³	1	2	yes	—
275	#14556511	C₂³	1	2	yes	—
276	#14556502	C₂³	1	2	yes	—
277	#14556501	C₂³	1	1	yes	characteristic
278	#14556501	C₂³	1	2	yes	—
279	#14556501	C₂³	1	1	yes	characteristic
280	#14556501	C₂³	1	1	yes	characteristic
281	#14556501	C₂³	1	1	yes	characteristic
282	C₄×#10596831	C₂³	1	2	yes	—
283	C₈×Dic₇₃	C₂³	1	2	yes	—
284	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
285	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
286	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄⋊Q₈×C₇₃	—	2	1	no	—
288	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
289	#125×C₇₃	—	2	1	no	—
290	#125×C₇₃	C₂³	1	2	yes	—
291	C₂²⋊Q₈×C₇₃	—	2	2	no	—
292	C₄×Q₈×C₇₃	—	2	1	no	—
293	C₄×Q₈×C₇₃	—	2	1	no	—
294	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
295	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
296	#117×C₇₃	—	2	2	no	—
297	#117×C₇₃	C₂³	1	1	yes	characteristic
298	#117×C₇₃	C₂³	1	1	yes	characteristic
299	#117×C₇₃	C₂³	1	1	yes	characteristic
300	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
301	#107×C₇₃	C₂³	1	1	yes	characteristic
302	#107×C₇₃	C₂³	1	2	yes	—
303	#107×C₇₃	C₂³	1	1	yes	characteristic
304	#106×C₇₃	C₂³	1	1	yes	characteristic
305	#106×C₇₃	C₂³	1	2	yes	—
306	#106×C₇₃	C₂³	1	1	yes	characteristic
307	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
308	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
309	#103×C₇₃	C₂³	1	2	yes	—
310	#103×C₇₃	C₂³	1	2	yes	—
311	#103×C₇₃	C₂³	1	2	yes	—
312	#103×C₇₃	C₂³	1	2	yes	—
313	C₂³×D₇₃	—	2	1	no	—
314	C₂×Dic₁₄₆	—	2	1	no	—
315	C₂×Dic₁₄₆	—	2	1	no	—
316	C₂×Dic₁₄₆	—	2	2	no	—
317	C₂×Dic₁₄₆	—	2	1	no	—
318	C₂×Dic₁₄₆	—	2	1	no	—
319	C₂×Dic₁₄₆	—	2	2	no	—
320	C₂×Dic₁₄₆	—	2	2	no	—
321	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
322	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
323	Q₈×D₇₃	—	8	4	no	—
324	C₂×D₂₉₂	—	2	1	no	—
325	C₂×D₂₉₂	—	2	2	no	—
326	C₂×D₂₉₂	C₂×Q₈	1	4	yes	—
327	C₂×D₂₉₂	C₂⁴	1	2	yes	—
328	C₂²×Dic₇₃	—	2	1	no	—
329	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
330	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₇₃	—	2	2	no	—
332	C₂×C₄×D₇₃	—	2	2	no	—
333	C₂×C₄×D₇₃	—	2	2	no	—
334	C₂×C₄×D₇₃	—	2	2	no	—
335	C₂×C₄×D₇₃	—	2	2	no	—
336	C₂×C₄×D₇₃	—	2	2	no	—
337	C₂×C₄×D₇₃	—	8	2	no	—
338	#11924015	C₂×Q₈	1	8	yes	complemented
339	#11924015	C₂×Q₈	1	8	yes	complemented
340	#11924012	—	2	2	no	—
341	C₂×#10596831	C₂×Q₈	1	4	yes	complemented
342	C₂×#10596831	C₂⁴	1	2	yes	—
343	C₂×#10596831	C₂⁴	1	1	yes	characteristic
344	C₂×#10596831	C₂⁴	1	1	yes	characteristic
345	C₄⋊Dic₇₃	—	2	1	no	—
346	C₄⋊Dic₇₃	—	2	2	no	—
347	C₄⋊Dic₇₃	—	2	1	no	—
348	C₄⋊Dic₇₃	—	2	2	no	—
349	C₄⋊Dic₇₃	—	2	2	no	—
350	C₄⋊Dic₇₃	—	2	2	no	—
351	C₄⋊Dic₇₃	—	2	2	no	—
352	C₄⋊Dic₇₃	—	2	2	no	—
353	C₄⋊Dic₇₃	—	2	1	no	—
354	C₄⋊Dic₇₃	—	2	1	no	—
355	C₄⋊Dic₇₃	—	2	1	no	—
356	C₄⋊Dic₇₃	—	2	2	no	—
357	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
358	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
361	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
362	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
363	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
364	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
366	#11924007	—	2	2	no	—
367	#11924007	—	2	2	no	—
368	#11924007	—	2	1	no	—
369	#11924007	—	2	1	no	—
370	#11924007	—	2	2	no	—
371	#11924007	—	2	2	no	—
372	#11924007	—	2	1	no	—
373	#11924007	—	2	1	no	—
374	#11924007	—	2	1	no	—
375	#11924007	—	2	1	no	—
376	#11924007	—	2	1	no	—
377	#11924007	—	2	2	no	—
378	#11924007	—	2	2	no	—
379	#11924007	—	2	1	no	—
380	#11924007	C₂×D₄	1	2	yes	—
381	#11924007	C₂×D₄	1	2	yes	—
382	#11924007	C₂×D₄	1	2	yes	—
383	#11924007	C₂×D₄	1	2	yes	—
384	C₂²⋊Dic₇₃	—	2	1	no	—
385	C₂²⋊Dic₇₃	—	2	1	no	—
386	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
387	#11924005	—	2	2	no	—
388	#11924005	—	2	2	no	—
389	#11924005	—	2	2	no	—
390	#11924005	—	2	2	no	—
391	#11924005	—	2	2	no	—
392	#11924005	—	2	2	no	—
393	C₄×Dic₇₃	—	2	1	no	—
394	C₄×Dic₇₃	—	2	1	no	—
395	C₄×Dic₇₃	—	2	2	no	—
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	—	2	2	no	—
398	C₄×Dic₇₃	—	2	2	no	—
399	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
401	C₄×Dic₇₃	C₂⁴	1	2	yes	—
402	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
403	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
404	C₂×Q₈×C₇₃	—	2	1	no	—
405	C₂×Q₈×C₇₃	—	2	2	no	—
406	C₂×Q₈×C₇₃	—	2	2	no	—
407	C₂×Q₈×C₇₃	C₂×Q₈	1	4	yes	complemented
408	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₇₃	—	2	1	no	—
410	C₂²×C₄×C₇₃	—	2	1	no	—
411	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
412	M₁₆×C₇₃	—	2	2	no	—
413	C₂×C₈×C₇₃	—	2	2	no	—
414	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
416	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₃	—	2	1	no	—
418	C₄⋊C₄×C₇₃	—	2	2	no	—
419	C₄⋊C₄×C₇₃	—	2	2	no	—
420	C₄⋊C₄×C₇₃	—	2	2	no	—
421	C₄⋊C₄×C₇₃	—	2	2	no	—
422	C₄⋊C₄×C₇₃	—	2	2	no	—
423	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
425	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
426	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂²⋊C₄×C₇₃	—	2	1	no	—
431	C₂²⋊C₄×C₇₃	—	2	1	no	—
432	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
433	C₄²×C₇₃	—	2	2	no	—
434	C₄²×C₇₃	—	2	2	no	—
435	C₄²×C₇₃	—	2	1	no	—
436	C₄²×C₇₃	—	2	1	no	—
437	C₄²×C₇₃	C₂⁴	1	2	yes	—
438	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₇₃	—	2	2	no	—
440	C₂²×D₇₃	—	2	4	no	—
441	C₂²×D₇₃	—	8	1	no	—
442	C₂²×D₇₃	—	8	1	no	—
443	Q₈×C₇₃	—	2	4	no	—
444	Q₈×C₇₃	—	2	2	no	—
445	Q₈×C₇₃	—	8	2	no	—
446	Q₈×C₇₃	C₂²×Q₈	1	4	yes	—
447	C₂×C₄×C₇₃	—	2	4	no	—
448	C₂×C₄×C₇₃	—	2	2	no	—
449	C₂×C₄×C₇₃	—	2	1	no	—
450	C₂×C₄×C₇₃	—	2	1	no	—
451	C₂×C₄×C₇₃	—	2	1	no	—
452	C₂×C₄×C₇₃	—	2	1	no	—
453	C₂×C₄×C₇₃	—	2	2	no	—
454	C₂×C₄×C₇₃	—	8	1	no	—
455	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
456	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
459	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
460	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
461	C₂×Dic₇₃	—	2	1	no	—
462	C₂×Dic₇₃	—	2	1	no	—
463	C₂×Dic₇₃	—	2	2	no	—
464	C₂×Dic₇₃	—	2	1	no	—
465	C₂×Dic₇₃	—	2	1	no	—
466	C₂×Dic₇₃	—	4	1	no	—
467	C₂×Dic₇₃	—	4	1	no	—
468	C₂×Dic₇₃	—	8	1	no	—
469	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
472	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
473	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
475	D₂₉₂	—	2	4	no	—
476	D₂₉₂	—	2	2	no	—
477	D₂₉₂	C₂²×Q₈	1	4	yes	—
478	C₄×D₇₃	—	4	4	no	—
479	C₄×D₇₃	—	8	2	no	—
480	C₄×D₇₃	—	8	2	no	—
481	C₄×D₇₃	—	8	2	no	—
482	C₄×D₇₃	—	8	2	no	—
483	C₄×D₇₃	—	8	2	no	—
484	Dic₁₄₆	—	4	2	no	—
485	Dic₁₄₆	—	4	2	no	—
486	Dic₁₄₆	—	4	2	no	—
487	Dic₁₄₆	—	4	2	no	—
488	Dic₁₄₆	—	8	2	no	—
489	Dic₁₄₆	—	8	2	no	—
490	Dic₁₄₆	—	8	1	no	—
491	Dic₁₄₆	—	8	1	no	—
492	Dic₁₄₆	—	8	2	no	—
493	C₈×C₇₃	—	2	1	no	—
494	C₈×C₇₃	—	2	1	no	—
495	C₈×C₇₃	—	2	2	no	—
496	#10596831	—	2	2	no	—
497	#10596831	C₂²×Q₈	1	2	yes	—
498	#10596831	C₂²×Q₈	1	2	yes	—
499	C₂²×C₇₃	—	2	1	no	—
500	C₂²×C₇₃	—	2	1	no	—
501	C₂²×C₇₃	D₄×Q₈	1	2	yes	—
502	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
503	C₂×D₇₃	—	2	4	no	—
504	C₂×D₇₃	—	4	2	no	—
505	C₂×D₇₃	—	4	2	no	—
506	C₂×D₇₃	—	8	4	no	—
507	C₄×C₇₃	—	2	2	no	—
508	C₄×C₇₃	—	2	2	no	—
509	C₄×C₇₃	—	2	4	no	—
510	C₄×C₇₃	—	4	1	no	—
511	C₄×C₇₃	—	4	1	no	—
512	C₄×C₇₃	—	4	2	no	—
513	C₄×C₇₃	—	4	1	no	—
514	C₄×C₇₃	—	4	1	no	—
515	C₄×C₇₃	D₄×Q₈	1	2	yes	—
516	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
517	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
518	Dic₇₃	—	2	1	no	—
519	Dic₇₃	—	2	2	no	—
520	Dic₇₃	—	2	1	no	—
521	Dic₇₃	—	2	1	no	—
522	Dic₇₃	—	2	2	no	—
523	Dic₇₃	—	2	1	no	—
524	Dic₇₃	—	4	1	no	—
525	Dic₇₃	—	4	1	no	—
526	Dic₇₃	—	4	2	no	—
527	Dic₇₃	—	4	1	no	—
528	Dic₇₃	—	4	1	no	—
529	#61377	—	73	1	no	maximal, Sylow
530	C₂×C₇₃	—	2	2	no	—
531	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
532	C₂×C₇₃	#3585	1	1	yes	characteristic
533	C₂×C₇₃	#3586	1	1	yes	characteristic
534	D₇₃	—	4	4	no	—
535	#3502	—	73	1	no	—
536	#3501	—	73	1	no	—
537	#3388	—	73	2	no	—
538	#3388	—	73	2	no	—
539	#3388	—	73	2	no	—
540	#3388	—	73	2	no	—
541	#3386	—	73	2	no	—
542	#3386	—	73	2	no	—
543	#3385	—	73	2	no	—
544	#3385	—	73	2	no	—
545	#3164	—	73	1	no	—
546	#3164	—	73	1	no	—
547	#3162	—	73	1	no	—
548	#3082	—	73	1	no	—
549	#3082	D₇₃	1	1	yes	characteristic, complemented
550	#3081	—	73	1	no	—
551	#3081	—	73	1	no	—
552	#3078	—	73	1	no	—
553	#3077	—	73	1	no	—
554	#2961	—	73	1	no	—
555	#2949	—	73	1	no	—
556	#2949	—	73	1	no	—
557	C₂×#440	—	73	1	no	—
558	C₇₃	#61377	1	1	yes	characteristic, complemented, Sylow
559	C₂²×SD₁₆	—	73	1	no	—
560	Q₈²	—	73	2	no	—
561	Q₈²	—	146	1	no	—
562	#557	—	73	2	no	—
563	#557	—	73	2	no	—
564	#557	—	73	2	no	—
565	#557	—	146	1	no	—
566	#557	—	146	1	no	—
567	#557	—	146	1	no	—
568	#554	—	73	2	no	—
569	#554	—	73	2	no	—
570	#554	—	73	2	no	—
571	#554	—	146	1	no	—
572	#554	—	146	1	no	—
573	#554	—	146	1	no	—
574	D₄×Q₈	—	73	2	no	—
575	D₄×Q₈	—	146	1	no	—
576	#544	—	73	1	no	—
577	#544	—	73	1	no	—
578	#544	—	73	1	no	—
579	#544	—	146	2	no	—
580	#544	C₂×D₇₃	1	1	yes	characteristic
581	#543	—	146	2	no	—
582	#533	—	73	1	no	—
583	#533	—	73	1	no	—
584	#533	—	73	1	no	—
585	#533	—	146	2	no	—
586	C₂×C₂²⋊Q₈	—	146	2	no	—
587	#519	—	73	1	no	—
588	#519	C₂×D₇₃	1	1	yes	characteristic
589	#518	—	73	1	no	—
590	#518	—	73	1	no	—
591	C₂×C₄×Q₈	—	73	1	no	—
592	C₂×C₄×D₄	—	73	1	no	—
593	#501	—	73	2	no	—
594	#501	—	73	2	no	—
595	#501	—	73	1	no	—
596	#501	—	73	2	no	—
597	#501	—	73	1	no	—
598	#501	—	73	1	no	—
599	#501	—	73	1	no	—
600	#501	—	73	1	no	—
601	#501	—	73	1	no	—
602	#501	—	73	2	no	—
603	#501	—	73	1	no	—
604	#501	—	73	1	no	—
605	#500	—	73	2	no	—
606	#500	—	73	2	no	—
607	#499	—	73	2	no	—
608	#499	—	73	2	no	—
609	#479	—	73	2	no	—
610	#479	—	73	2	no	—
611	#479	—	73	2	no	—
612	#479	—	73	2	no	—
613	#479	C₂×D₇₃	1	2	yes	complemented
614	#479	C₂×D₇₃	1	2	yes	complemented
615	#478	—	73	2	no	—
616	#478	—	73	2	no	—
617	#478	—	73	2	no	—
618	#478	—	73	2	no	—
619	#478	—	73	2	no	—
620	#478	—	73	2	no	—
621	#477	—	73	2	no	—
622	#477	—	73	2	no	—
623	#477	C₂×D₇₃	1	2	yes	complemented
624	#476	—	73	2	no	—
625	#476	—	73	2	no	—
626	#476	—	73	2	no	—
627	#475	—	73	2	no	—
628	#475	—	73	2	no	—
629	#475	C₂×D₇₃	1	2	yes	complemented
630	#474	—	73	2	no	—
631	#474	—	73	2	no	—
632	#474	—	73	2	no	—
633	#446	—	73	2	no	—
634	#446	—	73	2	no	—
635	#446	—	73	2	no	—
636	#446	—	73	2	no	—
637	#440	—	73	2	no	—
638	#440	—	73	2	no	—
639	#440	—	73	2	no	—
640	#440	—	73	2	no	—
641	#440	—	73	2	no	—
642	#440	—	73	2	no	—
643	#440	—	73	2	no	—
644	#440	—	73	2	no	—
645	C₄×SD₁₆	—	73	2	no	—
646	C₄×SD₁₆	—	73	2	no	—
647	C₄×SD₁₆	—	73	2	no	—
648	C₄×SD₁₆	—	73	2	no	—
649	#428	—	73	1	no	—
650	#428	—	73	1	no	—
651	#428	—	73	1	no	—
652	#428	C₂×D₇₃	1	1	yes	characteristic
653	#427	—	73	1	no	—
654	#427	—	73	1	no	—
655	#427	—	73	1	no	—
656	#427	C₂×D₇₃	1	1	yes	characteristic
657	C₂×#107	—	73	1	no	—
658	#424	—	73	1	no	—
659	#424	C₂×D₇₃	1	1	yes	characteristic
660	#423	—	73	1	no	—
661	#419	—	73	1	no	—
662	#419	C₂×D₇₃	1	1	yes	characteristic
663	#418	—	73	1	no	—
664	#418	—	73	1	no	—
665	C₂×#103	C₂×D₇₃	1	1	yes	characteristic
666	C₂×#102	—	73	1	no	—
667	#405	—	73	1	no	—
668	#405	—	73	1	no	—
669	C₂×#97	—	73	1	no	—
670	C₂²×Q₈	—	146	2	no	—
671	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
672	C₂²×D₄	—	73	1	no	—
673	C₂³×C₄	—	146	1	no	—
674	C₂×SD₁₆	—	73	8	no	—
675	C₂×SD₁₆	—	73	2	no	—
676	C₂×SD₁₆	—	73	2	no	—
677	C₂×M₁₆	—	73	1	no	—
678	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
679	C₂²×C₈	—	73	1	no	—
680	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
681	C₄⋊Q₈	—	2	1	no	—
682	C₄⋊Q₈	—	73	1	no	—
683	C₄⋊Q₈	—	73	1	no	—
684	C₄⋊Q₈	—	73	1	no	—
685	C₄⋊Q₈	—	73	1	no	—
686	C₄⋊Q₈	—	73	1	no	—
687	C₄⋊Q₈	—	73	1	no	—
688	C₄⋊Q₈	—	73	2	no	—
689	C₄⋊Q₈	—	73	2	no	—
690	C₄⋊Q₈	—	73	2	no	—
691	C₄⋊Q₈	—	146	1	no	—
692	C₄⋊Q₈	—	146	2	no	—
693	C₄⋊Q₈	—	146	2	no	—
694	C₄⋊Q₈	—	146	2	no	—
695	C₄⋊Q₈	—	146	1	no	—
696	C₄⋊Q₈	—	146	2	no	—
697	C₄⋊Q₈	—	146	2	no	—
698	C₄⋊Q₈	—	146	2	no	—
699	C₄⋊Q₈	—	146	1	no	—
700	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
701	#125	—	2	1	no	—
702	#125	—	73	1	no	—
703	#125	—	73	1	no	—
704	#125	—	73	1	no	—
705	#125	—	73	1	no	—
706	#125	—	73	1	no	—
707	#125	—	73	1	no	—
708	#125	—	73	2	no	—
709	#125	—	73	2	no	—
710	#125	—	73	2	no	—
711	#125	—	146	1	no	—
712	#125	—	146	2	no	—
713	#125	—	146	2	no	—
714	#125	—	146	2	no	—
715	#125	—	146	2	no	—
716	#125	—	146	1	no	—
717	#125	—	146	2	no	—
718	#125	—	146	2	no	—
719	#125	—	146	1	no	—
720	#125	C₂²×D₇₃	1	2	yes	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	73	2	no	—
723	C₂²⋊Q₈	—	73	2	no	—
724	C₂²⋊Q₈	—	146	2	no	—
725	C₂²⋊Q₈	—	146	1	no	—
726	C₂²⋊Q₈	—	146	1	no	—
727	C₂²⋊Q₈	—	146	1	no	—
728	C₂²⋊Q₈	—	146	1	no	—
729	C₂²⋊Q₈	—	146	2	no	—
730	C₂²⋊Q₈	—	146	2	no	—
731	C₂²⋊Q₈	—	146	2	no	—
732	C₂²⋊Q₈	—	146	2	no	—
733	C₂²⋊Q₈	—	146	2	no	—
734	C₂²⋊Q₈	—	146	2	no	—
735	C₂²⋊Q₈	—	146	2	no	—
736	C₂²⋊Q₈	—	146	2	no	—
737	C₂²⋊Q₈	—	146	2	no	—
738	C₂²⋊Q₈	—	146	2	no	—
739	C₂²⋊Q₈	—	146	2	no	—
740	C₂²⋊Q₈	—	146	2	no	—
741	C₂²⋊Q₈	—	146	2	no	—
742	C₂²⋊Q₈	—	146	2	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	2	1	no	—
745	C₄×Q₈	—	73	2	no	—
746	C₄×Q₈	—	73	2	no	—
747	C₄×Q₈	—	73	2	no	—
748	C₄×Q₈	—	73	2	no	—
749	C₄×Q₈	—	73	2	no	—
750	C₄×Q₈	—	73	2	no	—
751	C₄×Q₈	—	146	1	no	—
752	C₄×Q₈	—	146	1	no	—
753	C₄×Q₈	—	146	1	no	—
754	C₄×Q₈	—	146	1	no	—
755	C₄×Q₈	—	146	2	no	—
756	C₄×Q₈	—	146	2	no	—
757	C₄×Q₈	—	146	2	no	—
758	C₄×Q₈	—	146	2	no	—
759	C₄×Q₈	—	146	1	no	—
760	C₄×Q₈	—	146	1	no	—
761	C₄×Q₈	—	146	1	no	—
762	C₄×Q₈	—	146	1	no	—
763	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
764	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
765	C₄×D₄	—	73	2	no	—
766	C₄×D₄	—	73	2	no	—
767	C₄×D₄	—	73	2	no	—
768	C₄×D₄	—	73	2	no	—
769	C₄×D₄	—	73	2	no	—
770	C₄×D₄	—	73	2	no	—
771	C₄×D₄	—	146	1	no	—
772	C₄×D₄	—	146	1	no	—
773	C₄×D₄	—	146	1	no	—
774	C₄×D₄	—	146	1	no	—
775	C₄×D₄	—	146	1	no	—
776	C₄×D₄	—	146	1	no	—
777	#117	—	2	2	no	—
778	#117	—	73	1	no	—
779	#117	—	73	1	no	—
780	#117	—	73	1	no	—
781	#117	—	146	2	no	—
782	#117	C₂²×D₇₃	1	1	yes	characteristic
783	#117	C₂²×D₇₃	1	1	yes	characteristic
784	#117	C₂²×D₇₃	1	1	yes	characteristic
785	C₂×C₄⋊C₄	—	73	1	no	—
786	C₂×C₄⋊C₄	—	146	2	no	—
787	C₂×C₄⋊C₄	—	146	2	no	—
788	C₂×C₄⋊C₄	—	146	2	no	—
789	C₂×C₄⋊C₄	—	146	1	no	—
790	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
791	C₂×C₂²⋊C₄	—	146	2	no	—
792	C₂×C₂²⋊C₄	—	146	1	no	—
793	C₂×C₂²⋊C₄	—	146	2	no	—
794	C₂×C₄²	—	73	1	no	—
795	C₂×C₄²	—	146	1	no	—
796	#107	—	73	1	no	—
797	#107	—	73	1	no	—
798	#107	—	73	2	no	—
799	#107	—	73	2	no	—
800	#107	—	73	2	no	—
801	#107	—	73	1	no	—
802	#107	—	73	1	no	—
803	#107	—	73	1	no	—
804	#107	—	73	1	no	—
805	#107	—	73	2	no	—
806	#107	—	73	2	no	—
807	#107	C₂²×D₇₃	1	1	yes	characteristic
808	#107	C₂²×D₇₃	1	1	yes	characteristic
809	#107	C₂²×D₇₃	1	2	yes	—
810	#106	—	73	1	no	—
811	#106	—	73	1	no	—
812	#106	—	73	2	no	—
813	#106	—	73	1	no	—
814	#106	—	73	1	no	—
815	#106	—	73	1	no	—
816	#106	—	73	1	no	—
817	#106	—	73	2	no	—
818	#106	—	73	2	no	—
819	#106	C₂²×D₇₃	1	1	yes	characteristic
820	#106	C₂²×D₇₃	1	1	yes	characteristic
821	#106	C₂²×D₇₃	1	2	yes	—
822	C₄⋊C₈	—	73	2	no	—
823	C₄⋊C₈	—	73	2	no	—
824	C₄⋊C₈	—	73	2	no	—
825	C₄⋊C₈	—	73	2	no	—
826	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
827	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
828	#103	—	73	2	no	—
829	#103	—	73	2	no	—
830	#103	C₂²×D₇₃	1	2	yes	—
831	#103	C₂²×D₇₃	1	2	yes	—
832	#103	C₂²×D₇₃	1	2	yes	—
833	#103	C₂²×D₇₃	1	2	yes	—
834	#102	—	73	2	no	—
835	#102	—	73	2	no	—
836	#102	—	73	2	no	—
837	#102	—	73	2	no	—
838	#102	—	73	2	no	—
839	#102	—	73	2	no	—
840	#97	—	73	1	no	—
841	#97	—	73	1	no	—
842	#97	—	73	1	no	—
843	#97	—	73	1	no	—
844	#97	—	73	2	no	—
845	#97	—	73	2	no	—
846	C₄×C₈	—	73	2	no	—
847	C₄×C₈	—	73	2	no	—
848	C₂⁴	—	146	1	no	—
849	C₂×Q₈	—	2	1	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	584	4	no	—
853	C₂×Q₈	—	73	2	no	—
854	C₂×Q₈	—	73	2	no	—
855	C₂×Q₈	—	146	1	no	—
856	C₂×Q₈	—	146	1	no	—
857	C₂×Q₈	—	146	1	no	—
858	C₂×Q₈	—	146	1	no	—
859	C₂×Q₈	—	146	2	no	—
860	C₂×Q₈	—	146	2	no	—
861	C₂×Q₈	—	146	2	no	—
862	C₂×Q₈	Q₈×D₇₃	1	4	yes	complemented
863	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
864	C₂×D₄	—	73	4	no	—
865	C₂×D₄	—	73	2	no	—
866	C₂×D₄	—	146	1	no	—
867	C₂×D₄	—	146	2	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	584	2	no	—
871	C₂²×C₄	—	73	1	no	—
872	C₂²×C₄	—	73	1	no	—
873	C₂²×C₄	—	146	2	no	—
874	C₂²×C₄	—	146	2	no	—
875	C₂²×C₄	—	146	2	no	—
876	C₂²×C₄	—	146	2	no	—
877	C₂²×C₄	—	146	1	no	—
878	C₂²×C₄	—	146	2	no	—
879	C₂²×C₄	—	146	2	no	—
880	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
881	SD₁₆	—	73	8	no	—
882	SD₁₆	—	73	8	no	—
883	M₁₆	—	2	2	no	—
884	M₁₆	—	146	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	73	4	no	—
887	C₂×C₈	—	73	1	no	—
888	C₂×C₈	—	73	1	no	—
889	C₂×C₈	—	73	2	no	—
890	C₂×C₈	C₂³×D₇₃	1	2	yes	—
891	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
892	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	1	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	73	2	no	—
900	C₄⋊C₄	—	73	2	no	—
901	C₄⋊C₄	—	73	2	no	—
902	C₄⋊C₄	—	73	2	no	—
903	C₄⋊C₄	—	73	2	no	—
904	C₄⋊C₄	—	73	1	no	—
905	C₄⋊C₄	—	73	1	no	—
906	C₄⋊C₄	—	73	2	no	—
907	C₄⋊C₄	—	73	1	no	—
908	C₄⋊C₄	—	73	2	no	—
909	C₄⋊C₄	—	73	1	no	—
910	C₄⋊C₄	—	73	1	no	—
911	C₄⋊C₄	—	73	1	no	—
912	C₄⋊C₄	—	146	1	no	—
913	C₄⋊C₄	—	146	1	no	—
914	C₄⋊C₄	—	146	2	no	—
915	C₄⋊C₄	—	146	2	no	—
916	C₄⋊C₄	—	146	1	no	—
917	C₄⋊C₄	—	146	1	no	—
918	C₄⋊C₄	—	146	1	no	—
919	C₄⋊C₄	—	146	1	no	—
920	C₄⋊C₄	—	146	2	no	—
921	C₄⋊C₄	—	146	1	no	—
922	C₄⋊C₄	—	146	1	no	—
923	C₄⋊C₄	—	146	2	no	—
924	C₄⋊C₄	—	146	1	no	—
925	C₄⋊C₄	—	146	2	no	—
926	C₄⋊C₄	—	146	2	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	2	no	—
929	C₄⋊C₄	—	146	2	no	—
930	C₄⋊C₄	—	146	1	no	—
931	C₄⋊C₄	—	146	1	no	—
932	C₄⋊C₄	—	146	1	no	—
933	C₄⋊C₄	—	146	2	no	—
934	C₄⋊C₄	—	146	2	no	—
935	C₄⋊C₄	—	146	2	no	—
936	C₄⋊C₄	—	146	1	no	—
937	C₄⋊C₄	—	146	2	no	—
938	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
939	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
943	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
944	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	73	2	no	—
948	C₂²⋊C₄	—	146	2	no	—
949	C₂²⋊C₄	—	146	2	no	—
950	C₂²⋊C₄	—	146	2	no	—
951	C₂²⋊C₄	—	146	2	no	—
952	C₂²⋊C₄	—	146	1	no	—
953	C₂²⋊C₄	—	146	1	no	—
954	C₂²⋊C₄	—	146	2	no	—
955	C₂²⋊C₄	—	146	2	no	—
956	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
957	C₄²	—	2	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	73	1	no	—
962	C₄²	—	73	1	no	—
963	C₄²	—	73	2	no	—
964	C₄²	—	73	1	no	—
965	C₄²	—	73	1	no	—
966	C₄²	—	146	2	no	—
967	C₄²	—	146	2	no	—
968	C₄²	—	146	2	no	—
969	C₄²	—	146	2	no	—
970	C₄²	—	146	1	no	—
971	C₄²	—	146	1	no	—
972	C₄²	C₂³×D₇₃	1	2	yes	—
973	C₂³	—	584	1	no	—
974	C₂³	—	584	1	no	—
975	C₂³	—	146	2	no	—
976	C₂³	—	146	4	no	—
977	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
978	Q₈	—	2	2	no	—
979	Q₈	—	2	4	no	—
980	Q₈	—	8	2	no	—
981	Q₈	—	292	2	no	—
982	Q₈	—	292	2	no	—
983	Q₈	—	292	2	no	—
984	Q₈	—	292	2	no	—
985	Q₈	—	584	2	no	—
986	Q₈	—	584	2	no	—
987	Q₈	—	584	2	no	—
988	Q₈	—	584	1	no	—
989	Q₈	—	584	1	no	—
990	Q₈	C₂×Q₈×D₇₃	1	4	yes	—
991	D₄	—	73	4	no	—
992	D₄	—	146	2	no	—
993	D₄	—	146	4	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	4	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	8	1	no	—
1002	C₂×C₄	—	292	4	no	—
1003	C₂×C₄	—	292	1	no	—
1004	C₂×C₄	—	292	1	no	—
1005	C₂×C₄	—	584	2	no	—
1006	C₂×C₄	—	584	2	no	—
1007	C₂×C₄	—	584	2	no	—
1008	C₂×C₄	—	584	2	no	—
1009	C₂×C₄	—	584	2	no	—
1010	C₂×C₄	—	584	1	no	—
1011	C₂×C₄	—	73	1	no	—
1012	C₂×C₄	—	73	1	no	—
1013	C₂×C₄	—	73	1	no	—
1014	C₂×C₄	—	73	1	no	—
1015	C₂×C₄	—	73	2	no	—
1016	C₂×C₄	—	73	2	no	—
1017	C₂×C₄	—	146	1	no	—
1018	C₂×C₄	—	146	1	no	—
1019	C₂×C₄	—	146	2	no	—
1020	C₂×C₄	—	146	1	no	—
1021	C₂×C₄	—	146	1	no	—
1022	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1023	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1024	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1025	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
1026	C₂×C₄	#14556638	1	2	yes	—
1027	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	2	no	—
1031	C₈	—	73	2	no	—
1032	C₈	—	73	2	no	—
1033	C₈	—	146	2	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	292	2	no	—
1037	C₂²	—	292	2	no	—
1038	C₂²	—	584	4	no	—
1039	C₂²	—	146	4	no	—
1040	C₂²	#17989250	1	2	yes	—
1041	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1042	C₄	—	2	4	no	—
1043	C₄	—	2	2	no	—
1044	C₄	—	2	2	no	—
1045	C₄	—	4	2	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	4	1	no	—
1048	C₄	—	4	1	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	292	1	no	—
1051	C₄	—	292	2	no	—
1052	C₄	—	292	1	no	—
1053	C₄	—	292	1	no	—
1054	C₄	—	292	1	no	—
1055	C₄	—	146	1	no	—
1056	C₄	—	146	1	no	—
1057	C₄	—	146	2	no	—
1058	C₄	—	146	1	no	—
1059	C₄	—	146	1	no	—
1060	C₄	—	146	2	no	—
1061	C₄	#17989250	1	2	yes	—
1062	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
1063	C₄	C₂×#14556638	1	1	yes	characteristic
1064	C₂	—	2	2	no	—
1065	C₂	—	292	4	no	—
1066	C₂	C₂×#17989250	1	1	yes	characteristic
1067	C₂	#22624709	1	1	yes	characteristic
1068	C₂	#22624716	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3082	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂²×D₂₉₂	C₂³
hypercenter	#3082	D₇₃
hypocenter	C₇₃	#61377
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3082

Complements

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

N	H ≅ G/N	type
1. #22623737	C₂	semidirect
3. #22622883	C₂	semidirect
4. #22622879	C₂	semidirect
5. #22622874	C₂	semidirect
6. #22622874	C₂	semidirect
7. #22622855	C₂	semidirect
8. #22622851	C₂	semidirect
9. #22622844	C₂	semidirect
10. #22622840	C₂	semidirect
11. #22620469	C₂	semidirect
12. #22620465	C₂	semidirect
13. #22620454	C₂	semidirect
14. #22619769	C₂	semidirect
17. #22619733	C₂	semidirect
19. #22618870	C₂	semidirect
23. C₇₃×#3082	C₂	semidirect
26. Q₈×Dic₁₄₆	C₂²	semidirect
28. #17989316	C₂²	semidirect
31. #17989313	C₂²	semidirect
32. #17989313	C₂²	semidirect
56. #17988997	C₂²	semidirect
57. #17988995	C₂²	semidirect
58. #17988995	C₂²	semidirect
59. #17988995	C₂²	semidirect
60. #17988995	C₂²	semidirect
61. #17988995	C₂²	semidirect
62. #17988994	C₂²	semidirect
63. #17988994	C₂²	semidirect
64. #17988994	C₂²	semidirect
65. #17988994	C₂²	semidirect
66. #17988994	C₂²	semidirect
67. #17988993	C₂²	semidirect
68. #17988991	C₂²	semidirect
69. #17988990	C₂²	semidirect
70. #17988987	C₂²	semidirect
71. #17988986	C₂²	semidirect
72. #17988896	C₂²	semidirect
73. #17988896	C₂²	semidirect
74. #17988892	C₂²	semidirect
75. #17988892	C₂²	semidirect
82. #17988880	C₂²	semidirect
83. #17988880	C₂²	semidirect
87. #17988870	C₂²	semidirect
88. #17988870	C₂²	semidirect
92. #17988716	C₂²	semidirect
93. #17988716	C₂²	semidirect
94. #17988714	C₂²	semidirect
95. #17988714	C₂²	semidirect
126. #479×C₇₃	C₂²	semidirect
127. #479×C₇₃	C₂²	semidirect
128. #477×C₇₃	C₂²	semidirect
129. #475×C₇₃	C₂²	semidirect
138. C₂×#11924015	Q₈	semidirect
338. #11924015	C₂×Q₈	semidirect
339. #11924015	C₂×Q₈	semidirect
341. C₂×#10596831	C₂×Q₈	semidirect
407. C₂×Q₈×C₇₃	C₂×Q₈	semidirect
549. #3082	D₇₃	semidirect
558. C₇₃	#61377	semidirect
613. #479	C₂×D₇₃	semidirect
614. #479	C₂×D₇₃	semidirect
623. #477	C₂×D₇₃	semidirect
629. #475	C₂×D₇₃	semidirect
862. C₂×Q₈	Q₈×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623737	2
#22623733	2
#22622883	2
#22622879	2
#22622874	2
#22622855	2
#22622851	2
#22622844	2
#22622840	2
#22620469	2
#22620465	2
#22620454	2
#22619769	2
#22619765	2
#22619763	2
#22619733	2
#22619727	2
#22618870	2
#22618790	2
#22618786	2
C₂×#17988690	2
C₇₃×#3082	2
#61377	73