Subgroups — #33976298

Order 18688.

1664 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623736	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic
3	#22622861	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622858	C₂	1	2	yes	maximal, complemented
5	#22622839	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622836	C₂	1	2	yes	maximal, complemented
7	Q₁₆×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622732	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622729	C₂	1	2	yes	maximal, complemented
11	#22622710	C₂	1	1	yes	maximal, characteristic, complemented
12	#22622707	C₂	1	2	yes	maximal, complemented
13	#22622607	C₂	1	1	yes	maximal, characteristic, complemented
14	#22622571	C₂	1	1	yes	maximal, characteristic, complemented
15	#22621142	C₂	1	2	yes	maximal, complemented
16	#22621141	C₂	1	1	yes	maximal, characteristic, complemented
17	#22621092	C₂	1	1	yes	maximal, characteristic, complemented
18	#22621088	C₂	1	2	yes	maximal, complemented
19	#22620093	C₂	1	1	yes	maximal, characteristic
20	#22620086	C₂	1	2	yes	maximal
21	#22619995	C₂	1	2	yes	maximal
22	#22619018	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3107	C₂	1	1	yes	maximal, characteristic
24	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
26	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
27	#17989317	C₂²	1	2	yes	—
28	#17989316	C₂²	1	1	yes	characteristic
29	#17989315	—	2	1	no	—
30	#17989315	—	2	1	no	—
31	#17989315	C₂²	1	1	yes	characteristic
32	#17989315	C₂²	1	1	yes	characteristic
33	#17989314	—	2	2	no	—
34	#17989313	C₂²	1	2	yes	—
35	#17989312	C₂²	1	2	yes	—
36	#17989296	—	2	2	no	—
37	#17989296	C₂²	1	2	yes	—
38	#17989294	—	2	1	no	—
39	#17989294	C₂²	1	1	yes	characteristic
40	D₄×Dic₁₄₆	—	2	1	no	—
41	D₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
42	#17989216	—	2	2	no	—
43	#17989215	—	2	1	no	—
44	#17989144	—	2	1	no	—
45	#17989144	C₂²	1	1	yes	characteristic
46	#17989144	C₂²	1	1	yes	characteristic
47	#17989140	—	2	2	no	—
48	#17989140	C₂²	1	2	yes	—
49	#17989139	C₂²	1	2	yes	—
50	#17989139	C₂²	1	2	yes	—
51	#17989064	—	2	1	no	—
52	#41×Dic₇₃	C₂²	1	2	yes	—
53	C₂×C₄×Dic₁₄₆	—	2	1	no	—
54	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
55	#17988995	C₂²	1	2	yes	—
56	#17988994	C₂²	1	2	yes	—
57	#17988993	C₂²	1	2	yes	—
58	#17988992	C₂²	1	1	yes	characteristic
59	#17988991	C₂²	1	2	yes	—
60	#17988985	C₂²	1	1	yes	characteristic
61	#17988984	C₂²	1	2	yes	—
62	#17988955	C₂²	1	2	yes	—
63	#17988954	C₂²	1	2	yes	—
64	#17988954	C₂²	1	2	yes	—
65	#17988938	C₂²	1	1	yes	characteristic
66	#17988938	C₂²	1	1	yes	characteristic
67	#17988936	C₂²	1	2	yes	—
68	#17988936	C₂²	1	2	yes	—
69	#17988929	C₂²	1	2	yes	—
70	#17988929	C₂²	1	2	yes	—
71	#17988928	C₂²	1	2	yes	—
72	#17988925	C₂²	1	2	yes	—
73	#17988925	C₂²	1	2	yes	—
74	#17988897	C₂²	1	2	yes	—
75	#17988896	C₂²	1	2	yes	—
76	#17988895	C₂²	1	2	yes	—
77	#17988895	C₂²	1	2	yes	—
78	#17988893	C₂²	1	2	yes	—
79	#17988892	C₂²	1	2	yes	—
80	#17988882	C₂²	1	1	yes	characteristic
81	#17988882	C₂²	1	1	yes	characteristic
82	#17988882	C₂²	1	1	yes	characteristic
83	#17988881	C₂²	1	2	yes	—
84	#17988880	C₂²	1	2	yes	—
85	#17988880	C₂²	1	2	yes	—
86	#17988877	C₂²	1	1	yes	characteristic
87	#17988875	C₂²	1	2	yes	—
88	#17988872	C₂²	1	1	yes	characteristic
89	#17988872	C₂²	1	1	yes	characteristic
90	#17988871	C₂²	1	2	yes	—
91	#17988870	C₂²	1	2	yes	—
92	#17988870	C₂²	1	2	yes	—
93	#17988865	C₂²	1	2	yes	—
94	#17988797	C₂²	1	1	yes	characteristic
95	#17988795	C₂²	1	2	yes	—
96	#17988795	C₂²	1	2	yes	—
97	#17988792	C₂²	1	1	yes	characteristic
98	#17988790	C₂²	1	2	yes	—
99	#17988790	C₂²	1	2	yes	—
100	#17988749	C₂²	1	2	yes	—
101	#17988717	C₂²	1	1	yes	characteristic
102	#17988717	C₂²	1	1	yes	characteristic
103	#17988716	C₂²	1	2	yes	—
104	#17988716	C₂²	1	2	yes	—
105	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
106	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
107	#17988694	C₂²	1	2	yes	—
108	#17988692	C₂²	1	2	yes	—
109	#17988691	C₂²	1	2	yes	—
110	#17988688	C₂²	1	2	yes	—
111	#17988687	C₂²	1	2	yes	—
112	#17988684	C₂²	1	2	yes	—
113	Q₁₆×Dic₇₃	C₂²	1	2	yes	—
114	#17988679	C₂²	1	2	yes	—
115	#17988678	C₂²	1	2	yes	—
116	SD₁₆×Dic₇₃	C₂²	1	2	yes	—
117	#17988644	C₂²	1	1	yes	characteristic
118	#17988641	C₂²	1	2	yes	—
119	#17988637	C₂²	1	2	yes	—
120	#533×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	#485×C₇₃	C₂²	1	1	yes	characteristic
123	#485×C₇₃	C₂²	1	1	yes	characteristic
124	#475×C₇₃	C₂²	1	1	yes	characteristic
125	#474×C₇₃	C₂²	1	1	yes	characteristic
126	#462×C₇₃	C₂²	1	1	yes	characteristic
127	#461×C₇₃	C₂²	1	1	yes	characteristic
128	#452×C₇₃	C₂²	1	1	yes	characteristic
129	#452×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
131	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
132	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
134	#431×C₇₃	C₂²	1	1	yes	characteristic
135	C₂²×Dic₁₄₆	—	2	1	no	—
136	C₂²×Dic₁₄₆	D₄	1	1	yes	characteristic
137	C₂×#11924018	C₂³	1	2	yes	—
138	C₂×#11924016	C₂³	1	2	yes	—
139	#14556591	—	2	1	no	—
140	#14556591	—	2	1	no	—
141	#14556591	—	2	1	no	—
142	#14556591	—	2	1	no	—
143	#14556591	C₂³	1	1	yes	characteristic
144	#14556591	C₂³	1	1	yes	characteristic
145	#14556591	C₂³	1	1	yes	characteristic
146	#14556591	C₂³	1	1	yes	characteristic
147	#14556590	—	2	2	no	—
148	#14556590	—	2	2	no	—
149	#14556590	—	2	2	no	—
150	#14556590	—	2	2	no	—
151	#14556590	—	2	2	no	—
152	#14556590	C₂³	1	2	yes	—
153	#14556590	C₂³	1	2	yes	—
154	#14556590	C₂³	1	2	yes	—
155	#14556590	C₂³	1	2	yes	—
156	#14556589	—	2	2	no	—
157	#14556589	—	2	2	no	—
158	#14556589	C₂³	1	2	yes	—
159	#14556589	C₂³	1	2	yes	—
160	#14556583	—	2	1	no	—
161	#14556583	—	2	1	no	—
162	#14556583	—	2	2	no	—
163	#14556583	—	2	1	no	—
164	#14556583	C₂³	1	2	yes	—
165	#14556582	—	2	2	no	—
166	#14556582	—	2	2	no	—
167	#14556582	—	2	2	no	—
168	#14556582	C₂³	1	2	yes	—
169	#14556582	C₂³	1	2	yes	—
170	#14556581	—	2	2	no	—
171	#14556581	—	2	2	no	—
172	#14556581	—	2	2	no	—
173	#14556581	—	2	2	no	—
174	#14556581	—	2	2	no	—
175	#14556581	—	2	2	no	—
176	#14556570	—	2	1	no	—
177	#14556570	—	2	1	no	—
178	#14556570	—	2	2	no	—
179	#14556570	—	2	1	no	—
180	#14556570	—	2	1	no	—
181	#14556570	—	2	1	no	—
182	#14556570	C₂³	1	2	yes	—
183	#14556568	—	2	2	no	—
184	#14556568	—	2	2	no	—
185	#14556568	—	2	2	no	—
186	#14556568	—	2	2	no	—
187	#14556568	—	2	2	no	—
188	#14556568	—	2	2	no	—
189	#14556568	—	2	2	no	—
190	#14556568	—	2	2	no	—
191	Q₈×Dic₇₃	C₂³	1	2	yes	—
192	Q₈×Dic₇₃	C₂³	1	2	yes	—
193	Q₈×Dic₇₃	C₂³	1	2	yes	—
194	Q₈×Dic₇₃	C₂³	1	2	yes	—
195	C₄×Dic₁₄₆	—	2	1	no	—
196	C₄×Dic₁₄₆	—	2	1	no	—
197	C₄×Dic₁₄₆	—	2	1	no	—
198	C₄×Dic₁₄₆	—	2	1	no	—
199	C₄×Dic₁₄₆	—	2	1	no	—
200	C₄×Dic₁₄₆	—	2	1	no	—
201	C₄×Dic₁₄₆	—	2	2	no	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	C₄×Dic₁₄₆	—	2	2	no	—
204	C₄×Dic₁₄₆	—	2	1	no	—
205	C₄×Dic₁₄₆	—	2	1	no	—
206	C₄×Dic₁₄₆	—	2	1	no	—
207	C₄×Dic₁₄₆	D₄	1	2	yes	—
208	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
209	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
210	C₄×Dic₁₄₆	C₂³	1	2	yes	—
211	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₄₆	C₂³	1	2	yes	—
213	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
214	#14556556	—	2	2	no	—
215	#14556556	—	2	2	no	—
216	#14556556	—	2	2	no	—
217	#14556556	—	2	2	no	—
218	#14556556	C₂³	1	2	yes	—
219	#14556556	C₂³	1	2	yes	—
220	D₄×Dic₇₃	—	2	2	no	—
221	D₄×Dic₇₃	—	2	2	no	—
222	D₄×Dic₇₃	C₂³	1	2	yes	—
223	D₄×Dic₇₃	C₂³	1	2	yes	—
224	#14556550	—	2	2	no	—
225	#14556550	—	2	1	no	—
226	#14556550	C₂³	1	2	yes	—
227	#14556547	—	2	2	no	—
228	#14556547	—	2	2	no	—
229	C₂×C₄⋊Dic₇₃	—	2	1	no	—
230	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
231	C₂×#11924007	—	2	2	no	—
232	C₂×#11924007	D₄	1	2	yes	—
233	C₂×C₄×Dic₇₃	—	2	2	no	—
234	C₂×C₄×Dic₇₃	C₂³	1	2	yes	—
235	#14556525	C₂³	1	2	yes	—
236	#14556525	C₂³	1	2	yes	—
237	#14556524	C₂³	1	2	yes	—
238	#14556524	C₂³	1	2	yes	—
239	#14556524	C₂³	1	2	yes	—
240	#14556523	C₂³	1	2	yes	—
241	#14556523	C₂³	1	2	yes	—
242	#14556522	C₂³	1	2	yes	—
243	#14556522	C₂³	1	2	yes	—
244	#14556522	C₂³	1	2	yes	—
245	C₄⋊#10596831	C₂³	1	1	yes	characteristic
246	C₄⋊#10596831	C₂³	1	1	yes	characteristic
247	#14556520	C₂³	1	2	yes	—
248	#14556520	C₂³	1	2	yes	—
249	#14556520	C₂³	1	2	yes	—
250	#14556520	C₂³	1	2	yes	—
251	#14556516	C₂³	1	2	yes	—
252	#14556516	C₂³	1	2	yes	—
253	#14556516	C₂³	1	2	yes	—
254	#14556516	C₂³	1	2	yes	—
255	#14556515	C₂³	1	2	yes	—
256	#14556515	C₂³	1	2	yes	—
257	#14556515	C₂³	1	2	yes	—
258	#14556515	C₂³	1	2	yes	—
259	#14556515	C₂³	1	2	yes	—
260	#14556514	C₂³	1	2	yes	—
261	#14556514	C₂³	1	2	yes	—
262	#14556512	C₂³	1	2	yes	—
263	C₂²⋊#10596831	C₂³	1	2	yes	—
264	#14556502	C₂³	1	2	yes	—
265	#14556501	C₂³	1	2	yes	—
266	#14556501	C₂³	1	2	yes	—
267	C₈×Dic₇₃	C₂³	1	2	yes	—
268	C₈×Dic₇₃	C₂³	1	2	yes	—
269	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
271	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
274	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
276	#125×C₇₃	—	2	1	no	—
277	C₂²⋊Q₈×C₇₃	—	2	1	no	—
278	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₇₃	—	2	1	no	—
281	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₇₃	—	2	1	no	—
286	C₄×D₄×C₇₃	—	2	1	no	—
287	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
289	#117×C₇₃	—	2	1	no	—
290	#117×C₇₃	—	2	1	no	—
291	#117×C₇₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₇₃	—	2	1	no	—
293	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
294	#107×C₇₃	C₂³	1	1	yes	characteristic
295	#107×C₇₃	C₂³	1	1	yes	characteristic
296	#106×C₇₃	C₂³	1	1	yes	characteristic
297	#106×C₇₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
300	#103×C₇₃	C₂³	1	1	yes	characteristic
301	#103×C₇₃	C₂³	1	1	yes	characteristic
302	#103×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#103×C₇₃	C₂³	1	1	yes	characteristic
305	#103×C₇₃	C₂³	1	1	yes	characteristic
306	#102×C₇₃	C₂³	1	1	yes	characteristic
307	#102×C₇₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
312	C₂×Dic₁₄₆	—	2	4	no	—
313	C₂×Dic₁₄₆	—	2	1	no	—
314	C₂×Dic₁₄₆	—	2	2	no	—
315	C₂×Dic₁₄₆	—	2	1	no	—
316	C₂×Dic₁₄₆	—	2	1	no	—
317	C₂×Dic₁₄₆	—	2	2	no	—
318	C₂×Dic₁₄₆	—	2	2	no	—
319	C₂×Dic₁₄₆	—	2	2	no	—
320	C₂×Dic₁₄₆	—	4	4	no	—
321	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
322	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
323	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
324	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
325	C₂²×Dic₇₃	—	2	2	no	—
326	C₂²×Dic₇₃	—	2	2	no	—
327	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
328	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
329	#11924018	—	2	4	no	—
330	#11924016	—	2	4	no	—
331	C₂×#10596831	C₂⁴	1	2	yes	—
332	C₂×#10596831	C₂⁴	1	2	yes	—
333	C₄⋊Dic₇₃	—	2	1	no	—
334	C₄⋊Dic₇₃	—	2	1	no	—
335	C₄⋊Dic₇₃	—	2	1	no	—
336	C₄⋊Dic₇₃	—	2	1	no	—
337	C₄⋊Dic₇₃	—	2	1	no	—
338	C₄⋊Dic₇₃	—	2	2	no	—
339	C₄⋊Dic₇₃	—	2	2	no	—
340	C₄⋊Dic₇₃	—	2	2	no	—
341	C₄⋊Dic₇₃	—	2	2	no	—
342	C₄⋊Dic₇₃	—	2	2	no	—
343	C₄⋊Dic₇₃	—	2	2	no	—
344	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
345	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
346	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
347	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
348	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
349	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
350	#11924007	—	2	2	no	—
351	#11924007	—	2	2	no	—
352	#11924007	—	2	2	no	—
353	#11924007	—	2	2	no	—
354	#11924007	—	2	2	no	—
355	#11924007	—	2	2	no	—
356	#11924007	—	2	2	no	—
357	#11924007	—	2	2	no	—
358	#11924007	—	2	2	no	—
359	#11924007	—	2	2	no	—
360	#11924007	—	2	2	no	—
361	#11924007	—	2	2	no	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
365	#11924007	—	2	2	no	—
366	#11924007	C₂×D₄	1	2	yes	—
367	#11924007	C₂×D₄	1	2	yes	—
368	#11924007	C₂×D₄	1	2	yes	—
369	#11924007	C₂×D₄	1	2	yes	—
370	C₂²⋊Dic₇₃	—	2	2	no	—
371	C₂²⋊Dic₇₃	—	2	2	no	—
372	C₂²⋊Dic₇₃	—	2	2	no	—
373	C₂²⋊Dic₇₃	—	2	2	no	—
374	C₄×Dic₇₃	—	2	2	no	—
375	C₄×Dic₇₃	—	2	2	no	—
376	C₄×Dic₇₃	—	2	2	no	—
377	C₄×Dic₇₃	—	2	2	no	—
378	C₄×Dic₇₃	—	2	2	no	—
379	C₄×Dic₇₃	—	2	2	no	—
380	C₄×Dic₇₃	—	2	2	no	—
381	C₄×Dic₇₃	—	2	2	no	—
382	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
383	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
384	C₄×Dic₇₃	C₂⁴	1	2	yes	—
385	C₄×Dic₇₃	C₂⁴	1	2	yes	—
386	#41×C₇₃	—	2	2	no	—
387	#41×C₇₃	—	2	2	no	—
388	C₂×Q₈×C₇₃	—	2	1	no	—
389	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
390	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
391	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
392	C₂×D₄×C₇₃	—	2	1	no	—
393	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
394	C₂²×C₄×C₇₃	—	2	1	no	—
395	C₂²×C₄×C₇₃	—	2	1	no	—
396	C₂²×C₄×C₇₃	—	2	1	no	—
397	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
398	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
400	Q₁₆×C₇₃	—	2	2	no	—
401	Q₁₆×C₇₃	—	2	2	no	—
402	SD₁₆×C₇₃	—	2	2	no	—
403	SD₁₆×C₇₃	—	2	2	no	—
404	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₇₃	—	2	1	no	—
409	C₄⋊C₄×C₇₃	—	2	1	no	—
410	C₄⋊C₄×C₇₃	—	2	1	no	—
411	C₄⋊C₄×C₇₃	—	2	1	no	—
412	C₄⋊C₄×C₇₃	—	2	1	no	—
413	C₄⋊C₄×C₇₃	—	2	1	no	—
414	C₄⋊C₄×C₇₃	—	2	1	no	—
415	C₄⋊C₄×C₇₃	—	2	1	no	—
416	C₄⋊C₄×C₇₃	—	2	1	no	—
417	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂²⋊C₄×C₇₃	—	2	1	no	—
422	C₂²⋊C₄×C₇₃	—	2	1	no	—
423	C₂²⋊C₄×C₇₃	—	2	1	no	—
424	C₂²⋊C₄×C₇₃	—	2	1	no	—
425	C₂²⋊C₄×C₇₃	—	2	1	no	—
426	C₄²×C₇₃	—	2	1	no	—
427	C₄²×C₇₃	—	2	1	no	—
428	C₄²×C₇₃	—	2	1	no	—
429	C₄²×C₇₃	—	2	1	no	—
430	C₄²×C₇₃	—	2	1	no	—
431	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
435	C₂³×C₇₃	—	2	1	no	—
436	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
437	Q₈×C₇₃	—	2	1	no	—
438	Q₈×C₇₃	—	2	1	no	—
439	Q₈×C₇₃	—	2	1	no	—
440	Q₈×C₇₃	—	2	1	no	—
441	Q₈×C₇₃	—	2	1	no	—
442	Q₈×C₇₃	—	8	1	no	—
443	Q₈×C₇₃	2₋¹⁺⁴	1	2	yes	—
444	D₄×C₇₃	—	2	4	no	—
445	D₄×C₇₃	—	2	1	no	—
446	D₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
447	C₂×C₄×C₇₃	—	2	4	no	—
448	C₂×C₄×C₇₃	—	2	1	no	—
449	C₂×C₄×C₇₃	—	2	2	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	1	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	—	2	1	no	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	4	1	no	—
459	C₂×C₄×C₇₃	—	4	2	no	—
460	C₂×C₄×C₇₃	—	8	1	no	—
461	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
467	C₂×Dic₇₃	—	2	4	no	—
468	C₂×Dic₇₃	—	2	2	no	—
469	C₂×Dic₇₃	—	2	2	no	—
470	C₂×Dic₇₃	—	2	2	no	—
471	C₂×Dic₇₃	—	2	2	no	—
472	C₂×Dic₇₃	—	4	2	no	—
473	C₂×Dic₇₃	—	4	4	no	—
474	C₂×Dic₇₃	—	8	2	no	—
475	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
476	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
477	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
478	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
479	Dic₁₄₆	—	2	2	no	—
480	Dic₁₄₆	—	2	4	no	—
481	Dic₁₄₆	—	2	2	no	—
482	Dic₁₄₆	—	2	2	no	—
483	Dic₁₄₆	—	4	2	no	—
484	Dic₁₄₆	—	4	4	no	—
485	Dic₁₄₆	—	8	2	no	—
486	Dic₁₄₆	—	8	2	no	—
487	Dic₁₄₆	—	8	2	no	—
488	Dic₁₄₆	—	8	1	no	—
489	Dic₁₄₆	—	8	1	no	—
490	Dic₁₄₆	#137	1	4	yes	—
491	C₈×C₇₃	—	2	1	no	—
492	C₈×C₇₃	—	2	1	no	—
493	C₈×C₇₃	—	2	1	no	—
494	C₈×C₇₃	—	2	1	no	—
495	#10596831	—	2	2	no	—
496	#10596831	—	2	2	no	—
497	C₂²×C₇₃	—	2	1	no	—
498	C₂²×C₇₃	—	2	1	no	—
499	C₂²×C₇₃	—	2	2	no	—
500	C₂²×C₇₃	—	2	1	no	—
501	C₂²×C₇₃	—	4	1	no	—
502	C₂²×C₇₃	—	4	1	no	—
503	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₇₃	—	2	1	no	—
505	C₄×C₇₃	—	2	1	no	—
506	C₄×C₇₃	—	2	1	no	—
507	C₄×C₇₃	—	2	2	no	—
508	C₄×C₇₃	—	2	1	no	—
509	C₄×C₇₃	—	4	1	no	—
510	C₄×C₇₃	—	4	1	no	—
511	C₄×C₇₃	—	4	1	no	—
512	C₄×C₇₃	—	4	1	no	—
513	C₄×C₇₃	—	4	1	no	—
514	C₄×C₇₃	—	4	1	no	—
515	C₄×C₇₃	C₂×#137	1	2	yes	—
516	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
517	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
518	Dic₇₃	—	2	2	no	—
519	Dic₇₃	—	2	2	no	—
520	Dic₇₃	—	2	2	no	—
521	Dic₇₃	—	4	2	no	—
522	Dic₇₃	—	4	2	no	—
523	Dic₇₃	—	4	2	no	—
524	Dic₇₃	—	4	2	no	—
525	Dic₇₃	C₂×#137	1	4	yes	—
526	#61846	—	73	1	no	maximal, Sylow
527	C₂×C₇₃	—	4	1	no	—
528	C₂×C₇₃	—	4	2	no	—
529	C₂×C₇₃	#3486	1	1	yes	characteristic
530	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
531	C₂×C₇₃	#3584	1	1	yes	characteristic
532	#3502	—	73	1	no	—
533	Q₈×#41	—	73	1	no	—
534	#3387	—	73	2	no	—
535	#3387	—	73	1	no	—
536	#3385	—	73	2	no	—
537	#3385	—	73	1	no	—
538	Q₈×Q₁₆	—	73	1	no	—
539	Q₈×SD₁₆	—	73	1	no	—
540	#3374	—	73	2	no	—
541	#3374	—	73	1	no	—
542	#3372	—	73	2	no	—
543	#3372	—	73	1	no	—
544	#3363	—	73	1	no	—
545	#3359	—	73	1	no	—
546	#3237	—	73	2	no	—
547	#3237	—	73	1	no	—
548	#3231	—	73	2	no	—
549	#3231	—	73	1	no	—
550	#3116	—	73	2	no	—
551	#3116	—	73	1	no	—
552	#3107	—	73	2	no	—
553	#3107	D₇₃	1	1	yes	characteristic
554	#2984	—	73	1	no	—
555	C₇₃	#61846	1	1	yes	characteristic, complemented, Sylow
556	Q₈²	—	73	2	no	—
557	Q₈²	—	73	1	no	—
558	Q₈²	—	73	1	no	—
559	Q₈²	—	73	1	no	—
560	#557	—	73	2	no	—
561	#557	—	73	2	no	—
562	#557	—	73	1	no	—
563	#557	—	73	1	no	—
564	#557	—	73	1	no	—
565	#557	—	146	1	no	—
566	#557	—	146	1	no	—
567	#557	—	146	2	no	—
568	#554	—	73	1	no	—
569	#554	—	73	2	no	—
570	#554	—	146	1	no	—
571	#554	—	146	2	no	—
572	D₄×Q₈	—	73	1	no	—
573	D₄×Q₈	—	146	1	no	—
574	#544	—	146	1	no	—
575	#544	—	146	2	no	—
576	#533	—	73	2	no	—
577	#533	—	73	2	no	—
578	#533	—	73	2	no	—
579	#533	—	73	1	no	—
580	#533	—	73	1	no	—
581	#533	—	146	1	no	—
582	#533	—	146	2	no	—
583	#533	C₂×D₇₃	1	1	yes	characteristic
584	#519	—	146	1	no	—
585	C₄×#41	—	73	2	no	—
586	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
587	C₂×C₄×Q₈	—	73	1	no	—
588	C₂×C₄×Q₈	—	146	1	no	—
589	#501	—	73	2	no	—
590	#501	—	73	2	no	—
591	#501	—	73	2	no	—
592	#500	—	73	2	no	—
593	#500	—	73	1	no	—
594	#498	—	73	2	no	—
595	#498	—	73	1	no	—
596	#491	—	73	2	no	—
597	#491	—	73	2	no	—
598	#491	—	73	2	no	—
599	#487	—	73	2	no	—
600	#487	—	73	2	no	—
601	#487	—	73	1	no	—
602	#487	—	73	1	no	—
603	#485	—	73	2	no	—
604	#485	—	73	2	no	—
605	#485	—	73	2	no	—
606	#485	—	73	2	no	—
607	#485	—	73	2	no	—
608	#485	C₂×D₇₃	1	1	yes	characteristic
609	#485	C₂×D₇₃	1	1	yes	characteristic
610	#479	—	73	2	no	—
611	#479	—	73	2	no	—
612	#479	—	73	2	no	—
613	#479	—	73	2	no	—
614	#479	—	73	2	no	—
615	#479	—	73	2	no	—
616	#477	—	73	1	no	—
617	#477	—	73	1	no	—
618	#477	—	73	1	no	—
619	#477	—	73	2	no	—
620	#477	—	73	2	no	—
621	#477	—	73	2	no	—
622	#476	—	73	1	no	—
623	#476	—	73	2	no	—
624	#475	—	73	1	no	—
625	#475	—	73	1	no	—
626	#475	—	73	2	no	—
627	#475	—	73	2	no	—
628	#475	—	73	2	no	—
629	#475	C₂×D₇₃	1	1	yes	characteristic
630	#474	—	73	2	no	—
631	#474	C₂×D₇₃	1	1	yes	characteristic
632	#462	—	73	2	no	—
633	#462	—	73	2	no	—
634	#462	—	73	1	no	—
635	#462	C₂×D₇₃	1	1	yes	characteristic
636	#461	—	73	2	no	—
637	#461	—	73	2	no	—
638	#461	—	73	1	no	—
639	#461	C₂×D₇₃	1	1	yes	characteristic
640	#452	—	73	2	no	—
641	#452	C₂×D₇₃	1	1	yes	characteristic
642	#452	C₂×D₇₃	1	1	yes	characteristic
643	#446	—	73	2	no	—
644	#446	—	73	2	no	—
645	#446	—	73	1	no	—
646	#446	—	73	1	no	—
647	C₈×Q₈	—	73	1	no	—
648	C₈×Q₈	—	73	1	no	—
649	#441	—	73	2	no	—
650	#441	—	73	2	no	—
651	#441	—	73	2	no	—
652	#440	—	73	2	no	—
653	#440	—	73	2	no	—
654	#440	—	73	2	no	—
655	C₄×Q₁₆	—	73	2	no	—
656	C₄×Q₁₆	—	73	2	no	—
657	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
658	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
659	C₄×SD₁₆	—	73	2	no	—
660	C₄×SD₁₆	—	73	2	no	—
661	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
662	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
663	#432	—	73	1	no	—
664	#432	—	73	2	no	—
665	#431	—	73	2	no	—
666	#431	C₂×D₇₃	1	1	yes	characteristic
667	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
668	C₂²×Q₈	—	73	1	no	—
669	C₂²×Q₈	—	146	1	no	—
670	C₂×Q₁₆	—	73	2	no	—
671	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
672	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
673	C₂×SD₁₆	—	73	2	no	—
674	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
675	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
676	C₄⋊Q₈	—	73	2	no	—
677	C₄⋊Q₈	—	73	2	no	—
678	C₄⋊Q₈	—	73	2	no	—
679	C₄⋊Q₈	—	73	2	no	—
680	C₄⋊Q₈	—	73	2	no	—
681	C₄⋊Q₈	—	73	2	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	—	146	1	no	—
687	C₄⋊Q₈	—	146	1	no	—
688	C₄⋊Q₈	—	146	1	no	—
689	C₄⋊Q₈	—	146	1	no	—
690	C₄⋊Q₈	—	146	2	no	—
691	C₄⋊Q₈	—	146	2	no	—
692	C₄⋊Q₈	—	146	2	no	—
693	C₄⋊Q₈	—	146	2	no	—
694	C₄⋊Q₈	—	146	2	no	—
695	C₄⋊Q₈	—	146	2	no	—
696	C₄⋊Q₈	—	146	2	no	—
697	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
698	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
699	#125	—	2	1	no	—
700	#125	—	73	2	no	—
701	#125	—	73	2	no	—
702	#125	—	73	2	no	—
703	#125	—	146	2	no	—
704	#125	—	146	1	no	—
705	#125	—	146	1	no	—
706	#125	—	146	2	no	—
707	#125	—	146	2	no	—
708	#125	—	146	2	no	—
709	#125	—	146	2	no	—
710	#125	—	146	2	no	—
711	#125	—	146	2	no	—
712	#125	—	146	2	no	—
713	#125	—	146	2	no	—
714	#125	—	146	2	no	—
715	#125	—	146	1	no	—
716	C₂²⋊Q₈	—	2	1	no	—
717	C₂²⋊Q₈	—	73	2	no	—
718	C₂²⋊Q₈	—	146	2	no	—
719	C₂²⋊Q₈	—	146	2	no	—
720	C₂²⋊Q₈	—	146	2	no	—
721	C₂²⋊Q₈	—	146	2	no	—
722	C₂²⋊Q₈	—	146	2	no	—
723	C₂²⋊Q₈	—	146	2	no	—
724	C₂²⋊Q₈	—	146	2	no	—
725	C₂²⋊Q₈	—	146	2	no	—
726	C₂²⋊Q₈	—	146	1	no	—
727	C₂²⋊Q₈	—	146	2	no	—
728	C₂²⋊Q₈	—	146	1	no	—
729	C₂²⋊Q₈	—	146	1	no	—
730	C₂²⋊Q₈	—	146	1	no	—
731	C₂²⋊Q₈	—	146	1	no	—
732	C₂²⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
733	C₂²⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	73	1	no	—
736	C₄×Q₈	—	73	2	no	—
737	C₄×Q₈	—	73	1	no	—
738	C₄×Q₈	—	73	1	no	—
739	C₄×Q₈	—	73	2	no	—
740	C₄×Q₈	—	73	1	no	—
741	C₄×Q₈	—	73	2	no	—
742	C₄×Q₈	—	73	2	no	—
743	C₄×Q₈	—	73	2	no	—
744	C₄×Q₈	—	73	2	no	—
745	C₄×Q₈	—	73	2	no	—
746	C₄×Q₈	—	73	2	no	—
747	C₄×Q₈	—	73	2	no	—
748	C₄×Q₈	—	146	2	no	—
749	C₄×Q₈	—	146	2	no	—
750	C₄×Q₈	—	146	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	1	no	—
756	C₄×Q₈	—	146	1	no	—
757	C₄×Q₈	—	146	2	no	—
758	C₄×Q₈	—	146	2	no	—
759	C₄×Q₈	—	146	2	no	—
760	C₄×Q₈	—	146	2	no	—
761	C₄×Q₈	—	146	1	no	—
762	C₄×Q₈	—	146	1	no	—
763	C₄×Q₈	—	146	1	no	—
764	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
765	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
766	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
767	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	73	2	no	—
771	C₄×D₄	—	73	2	no	—
772	C₄×D₄	—	146	2	no	—
773	C₄×D₄	—	146	2	no	—
774	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
775	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
776	#117	—	2	1	no	—
777	#117	—	2	1	no	—
778	#117	—	73	2	no	—
779	#117	—	146	2	no	—
780	#117	—	146	2	no	—
781	#117	—	146	2	no	—
782	#117	—	146	1	no	—
783	#117	C₂²×D₇₃	1	1	yes	characteristic
784	C₂×C₄⋊C₄	—	73	2	no	—
785	C₂×C₄⋊C₄	—	73	1	no	—
786	C₂×C₄⋊C₄	—	146	2	no	—
787	C₂×C₄⋊C₄	—	146	1	no	—
788	C₂×C₄²	—	2	1	no	—
789	C₂×C₄²	—	73	2	no	—
790	C₂×C₄²	—	146	2	no	—
791	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
792	#107	—	73	2	no	—
793	#107	—	73	2	no	—
794	#107	—	73	2	no	—
795	#107	—	73	2	no	—
796	#107	—	73	2	no	—
797	#107	C₂²×D₇₃	1	1	yes	characteristic
798	#107	C₂²×D₇₃	1	1	yes	characteristic
799	#106	—	73	2	no	—
800	#106	—	73	2	no	—
801	#106	—	73	2	no	—
802	#106	—	73	2	no	—
803	#106	—	73	2	no	—
804	#106	C₂²×D₇₃	1	1	yes	characteristic
805	#106	C₂²×D₇₃	1	1	yes	characteristic
806	C₄⋊C₈	—	73	2	no	—
807	C₄⋊C₈	—	73	2	no	—
808	C₄⋊C₈	—	73	2	no	—
809	C₄⋊C₈	—	73	2	no	—
810	C₄⋊C₈	—	73	1	no	—
811	C₄⋊C₈	—	73	1	no	—
812	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
813	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
814	#103	—	73	2	no	—
815	#103	—	73	2	no	—
816	#103	—	73	2	no	—
817	#103	—	73	2	no	—
818	#103	—	73	2	no	—
819	#103	—	73	2	no	—
820	#103	—	73	2	no	—
821	#103	—	73	2	no	—
822	#103	—	73	2	no	—
823	#103	—	73	2	no	—
824	#103	—	73	2	no	—
825	#103	C₂²×D₇₃	1	1	yes	characteristic
826	#103	C₂²×D₇₃	1	1	yes	characteristic
827	#103	C₂²×D₇₃	1	1	yes	characteristic
828	#103	C₂²×D₇₃	1	1	yes	characteristic
829	#103	C₂²×D₇₃	1	1	yes	characteristic
830	#103	C₂²×D₇₃	1	1	yes	characteristic
831	#102	—	73	2	no	—
832	#102	C₂²×D₇₃	1	1	yes	characteristic
833	#102	C₂²×D₇₃	1	1	yes	characteristic
834	C₂²⋊C₈	—	73	2	no	—
835	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
836	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
837	#97	—	73	2	no	—
838	#97	—	73	2	no	—
839	#97	—	73	2	no	—
840	C₄×C₈	—	73	2	no	—
841	C₄×C₈	—	73	2	no	—
842	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
843	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
844	#41	—	2	2	no	—
845	#41	—	2	2	no	—
846	C₂×Q₈	—	2	1	no	—
847	C₂×Q₈	—	292	4	no	—
848	C₂×Q₈	—	73	1	no	—
849	C₂×Q₈	—	73	2	no	—
850	C₂×Q₈	—	73	1	no	—
851	C₂×Q₈	—	73	2	no	—
852	C₂×Q₈	—	146	2	no	—
853	C₂×Q₈	—	146	2	no	—
854	C₂×Q₈	—	146	2	no	—
855	C₂×Q₈	—	146	2	no	—
856	C₂×Q₈	—	146	4	no	—
857	C₂×Q₈	—	146	1	no	—
858	C₂×Q₈	—	146	1	no	—
859	C₂×Q₈	—	146	1	no	—
860	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
861	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
862	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
863	C₂×D₄	—	2	1	no	—
864	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	73	2	no	—
869	C₂²×C₄	—	73	2	no	—
870	C₂²×C₄	—	146	2	no	—
871	C₂²×C₄	—	146	2	no	—
872	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
873	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
874	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
875	Q₁₆	—	2	2	no	—
876	Q₁₆	—	2	2	no	—
877	Q₁₆	—	146	4	no	—
878	SD₁₆	—	2	2	no	—
879	SD₁₆	—	2	2	no	—
880	SD₁₆	—	146	4	no	—
881	C₂×C₈	—	73	2	no	—
882	C₂×C₈	—	73	2	no	—
883	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
884	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
885	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
886	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	1	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	1	no	—
895	C₄⋊C₄	—	2	1	no	—
896	C₄⋊C₄	—	73	2	no	—
897	C₄⋊C₄	—	73	2	no	—
898	C₄⋊C₄	—	73	2	no	—
899	C₄⋊C₄	—	73	2	no	—
900	C₄⋊C₄	—	73	1	no	—
901	C₄⋊C₄	—	73	2	no	—
902	C₄⋊C₄	—	73	1	no	—
903	C₄⋊C₄	—	73	2	no	—
904	C₄⋊C₄	—	73	2	no	—
905	C₄⋊C₄	—	73	2	no	—
906	C₄⋊C₄	—	146	2	no	—
907	C₄⋊C₄	—	146	2	no	—
908	C₄⋊C₄	—	146	2	no	—
909	C₄⋊C₄	—	146	2	no	—
910	C₄⋊C₄	—	146	2	no	—
911	C₄⋊C₄	—	146	2	no	—
912	C₄⋊C₄	—	146	2	no	—
913	C₄⋊C₄	—	146	2	no	—
914	C₄⋊C₄	—	146	2	no	—
915	C₄⋊C₄	—	146	2	no	—
916	C₄⋊C₄	—	146	2	no	—
917	C₄⋊C₄	—	146	2	no	—
918	C₄⋊C₄	—	146	2	no	—
919	C₄⋊C₄	—	146	2	no	—
920	C₄⋊C₄	—	146	2	no	—
921	C₄⋊C₄	—	146	2	no	—
922	C₄⋊C₄	—	146	2	no	—
923	C₄⋊C₄	—	146	2	no	—
924	C₄⋊C₄	—	146	2	no	—
925	C₄⋊C₄	—	146	2	no	—
926	C₄⋊C₄	—	146	2	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	1	no	—
929	C₄⋊C₄	—	146	1	no	—
930	C₄⋊C₄	—	146	1	no	—
931	C₄⋊C₄	—	146	1	no	—
932	C₄⋊C₄	—	146	1	no	—
933	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	146	2	no	—
943	C₂²⋊C₄	—	146	2	no	—
944	C₂²⋊C₄	—	146	2	no	—
945	C₂²⋊C₄	—	146	2	no	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	73	2	no	—
952	C₄²	—	73	2	no	—
953	C₄²	—	73	2	no	—
954	C₄²	—	73	2	no	—
955	C₄²	—	146	2	no	—
956	C₄²	—	146	2	no	—
957	C₄²	—	146	2	no	—
958	C₄²	—	146	2	no	—
959	C₄²	—	146	2	no	—
960	C₄²	—	146	2	no	—
961	C₄²	—	146	2	no	—
962	C₄²	—	146	2	no	—
963	C₄²	D₄×D₇₃	1	1	yes	characteristic
964	C₄²	D₄×D₇₃	1	1	yes	characteristic
965	C₄²	C₂³×D₇₃	1	1	yes	characteristic
966	C₄²	C₂³×D₇₃	1	1	yes	characteristic
967	C₂³	—	2	1	no	—
968	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
969	Q₈	—	2	1	no	—
970	Q₈	—	2	1	no	—
971	Q₈	—	2	1	no	—
972	Q₈	—	2	1	no	—
973	Q₈	—	2	1	no	—
974	Q₈	—	8	1	no	—
975	Q₈	—	292	4	no	—
976	Q₈	—	292	2	no	—
977	Q₈	—	584	1	no	—
978	Q₈	—	584	1	no	—
979	Q₈	—	584	2	no	—
980	Q₈	—	584	2	no	—
981	Q₈	—	584	2	no	—
982	Q₈	—	73	4	no	—
983	Q₈	—	146	4	no	—
984	Q₈	—	146	2	no	—
985	Q₈	—	146	2	no	—
986	Q₈	—	146	2	no	—
987	Q₈	#14556638	1	2	yes	—
988	D₄	—	2	4	no	—
989	D₄	—	2	1	no	—
990	D₄	#14556638	1	2	yes	—
991	C₂×C₄	—	2	4	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	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	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	4	1	no	—
1003	C₂×C₄	—	4	2	no	—
1004	C₂×C₄	—	8	1	no	—
1005	C₂×C₄	—	292	4	no	—
1006	C₂×C₄	—	292	2	no	—
1007	C₂×C₄	—	584	2	no	—
1008	C₂×C₄	—	73	2	no	—
1009	C₂×C₄	—	73	2	no	—
1010	C₂×C₄	—	73	2	no	—
1011	C₂×C₄	—	73	2	no	—
1012	C₂×C₄	—	146	2	no	—
1013	C₂×C₄	—	146	2	no	—
1014	C₂×C₄	—	146	2	no	—
1015	C₂×C₄	—	146	2	no	—
1016	C₂×C₄	—	146	4	no	—
1017	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1018	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1019	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1020	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1021	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1022	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1023	C₈	—	2	1	no	—
1024	C₈	—	2	1	no	—
1025	C₈	—	2	1	no	—
1026	C₈	—	2	1	no	—
1027	C₈	—	146	2	no	—
1028	C₈	—	146	2	no	—
1029	C₂²	—	2	1	no	—
1030	C₂²	—	2	2	no	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	1	no	—
1035	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1036	C₄	—	2	1	no	—
1037	C₄	—	2	2	no	—
1038	C₄	—	2	1	no	—
1039	C₄	—	2	1	no	—
1040	C₄	—	2	1	no	—
1041	C₄	—	4	1	no	—
1042	C₄	—	4	1	no	—
1043	C₄	—	4	1	no	—
1044	C₄	—	4	1	no	—
1045	C₄	—	4	1	no	—
1046	C₄	—	4	1	no	—
1047	C₄	—	292	2	no	—
1048	C₄	—	292	2	no	—
1049	C₄	—	292	2	no	—
1050	C₄	—	292	2	no	—
1051	C₄	—	73	4	no	—
1052	C₄	—	146	2	no	—
1053	C₄	—	146	2	no	—
1054	C₄	—	146	2	no	—
1055	C₄	#137×D₇₃	1	2	yes	—
1056	C₄	C₂×#14556638	1	1	yes	characteristic
1057	C₄	C₂×#14556638	1	1	yes	characteristic
1058	C₂	—	4	1	no	—
1059	C₂	—	4	2	no	—
1060	C₂	#22623578	1	1	yes	characteristic
1061	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1062	C₂	#22624700	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×#3107	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂×#41×C₇₃	C₂³
hypercenter	#3107	D₇₃
hypocenter	C₇₃	#61846
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
1. #22623736	C₂	semidirect
3. #22622861	C₂	semidirect
4. #22622858	C₂	semidirect
5. #22622839	C₂	semidirect
6. #22622836	C₂	semidirect
7. Q₁₆×Dic₁₄₆	C₂	semidirect
8. SD₁₆×Dic₁₄₆	C₂	semidirect
9. #22622732	C₂	semidirect
10. #22622729	C₂	semidirect
11. #22622710	C₂	semidirect
12. #22622707	C₂	semidirect
13. #22622607	C₂	semidirect
14. #22622571	C₂	semidirect
15. #22621142	C₂	semidirect
16. #22621141	C₂	semidirect
17. #22621092	C₂	semidirect
18. #22621088	C₂	semidirect
22. #22619018	C₂	semidirect
555. C₇₃	#61846	semidirect

Maximal subgroups

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

subgroup	index
#22623736	2
#41×Dic₁₄₆	2
#22622861	2
#22622858	2
#22622839	2
#22622836	2
Q₁₆×Dic₁₄₆	2
SD₁₆×Dic₁₄₆	2
#22622732	2
#22622729	2
#22622710	2
#22622707	2
#22622607	2
#22622571	2
#22621142	2
#22621141	2
#22621092	2
#22621088	2
#22620093	2
#22620086	2
#22619995	2
#22619018	2
C₇₃×#3107	2
#61846	73