Subgroups — #3369×D₇₃ #33965701

Order 18688.

1842 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈²×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#556×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22622676	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622675	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622674	C₂	1	2	yes	maximal, complemented
6	#22622673	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622672	C₂	1	2	yes	maximal, complemented
8	#22622671	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622670	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622669	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622668	C₂	1	2	yes	maximal, complemented
12	#22622667	C₂	1	1	yes	maximal, characteristic, complemented
13	#22622666	C₂	1	2	yes	maximal, complemented
14	#489×D₇₃	C₂	1	2	yes	maximal
15	#487×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#475×D₇₃	C₂	1	2	yes	maximal, complemented
17	#476×D₇₃	C₂	1	1	yes	maximal, characteristic
18	#464×D₇₃	C₂	1	2	yes	maximal
19	#462×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#446×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#441×D₇₃	C₂	1	2	yes	maximal, complemented
22	C₄×SD₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3369	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	—
25	C₂×SD₁₆×D₇₃	C₂²	1	1	yes	characteristic
26	Q₈×Dic₁₄₆	—	2	1	no	—
27	Q₈×Dic₁₄₆	C₂²	1	2	yes	complemented
28	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
29	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
30	#17989317	—	2	2	no	—
31	#17989317	—	2	1	no	—
32	#17989317	C₂²	1	2	yes	complemented
33	#17989317	C₂²	1	1	yes	characteristic, complemented
34	#17989311	C₂²	1	1	yes	characteristic
35	#17989310	C₂²	1	1	yes	characteristic
36	#17989309	C₂²	1	2	yes	—
37	#17989308	—	2	1	no	—
38	#17989307	C₂²	1	1	yes	characteristic
39	#17989306	C₂²	1	2	yes	—
40	#17989305	—	2	1	no	—
41	#17989304	—	2	2	no	—
42	C₄⋊Q₈×D₇₃	—	2	1	no	—
43	C₄⋊Q₈×D₇₃	—	2	2	no	—
44	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
45	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
46	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
47	#126×D₇₃	—	2	2	no	—
48	#124×D₇₃	C₂²	1	2	yes	—
49	C₂²⋊Q₈×D₇₃	—	2	1	no	—
50	C₄×Q₈×D₇₃	—	2	1	no	—
51	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
52	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
53	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
54	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
56	#117×D₇₃	—	2	1	no	—
57	#17988949	C₂²	1	2	yes	—
58	#17988948	C₂²	1	2	yes	—
59	#17988948	C₂²	1	2	yes	—
60	#17988947	C₂²	1	2	yes	—
61	#17988946	C₂²	1	2	yes	—
62	#17988945	C₂²	1	2	yes	—
63	#17988945	C₂²	1	2	yes	—
64	#17988939	C₂²	1	1	yes	characteristic, complemented
65	#17988938	C₂²	1	1	yes	characteristic, complemented
66	#17988937	C₂²	1	1	yes	characteristic, complemented
67	#17988936	C₂²	1	2	yes	complemented
68	#17988936	C₂²	1	2	yes	complemented
69	#17988878	C₂²	1	1	yes	characteristic
70	#17988877	C₂²	1	1	yes	characteristic
71	#17988876	C₂²	1	2	yes	—
72	#17988875	C₂²	1	2	yes	—
73	#17988874	C₂²	1	1	yes	characteristic
74	#17988873	C₂²	1	2	yes	complemented
75	#17988872	C₂²	1	2	yes	complemented
76	#17988871	C₂²	1	2	yes	complemented
77	#17988871	C₂²	1	2	yes	complemented
78	#17988870	C₂²	1	2	yes	complemented
79	#17988870	C₂²	1	2	yes	complemented
80	#17988869	C₂²	1	2	yes	complemented
81	#17988812	C₂²	1	2	yes	—
82	#17988811	C₂²	1	2	yes	—
83	#17988810	C₂²	1	2	yes	—
84	#17988809	C₂²	1	2	yes	—
85	#17988808	C₂²	1	2	yes	—
86	#17988807	C₂²	1	2	yes	—
87	#17988806	C₂²	1	2	yes	—
88	#17988798	C₂²	1	1	yes	characteristic, complemented
89	#17988797	C₂²	1	1	yes	characteristic, complemented
90	#17988796	C₂²	1	2	yes	complemented
91	#17988795	C₂²	1	2	yes	complemented
92	#17988794	C₂²	1	1	yes	characteristic, complemented
93	#17988718	C₂²	1	1	yes	characteristic, complemented
94	#17988717	C₂²	1	1	yes	characteristic, complemented
95	#17988716	C₂²	1	2	yes	complemented
96	#17988715	C₂²	1	2	yes	complemented
97	#17988714	C₂²	1	1	yes	characteristic, complemented
98	#17988695	C₂²	1	2	yes	complemented
99	#17988694	C₂²	1	2	yes	complemented
100	#17988693	C₂²	1	2	yes	complemented
101	#17988692	C₂²	1	2	yes	complemented
102	#17988692	C₂²	1	2	yes	complemented
103	#17988691	C₂²	1	2	yes	complemented
104	#17988691	C₂²	1	2	yes	complemented
105	#17988678	C₂²	1	1	yes	characteristic
106	C₄×#11924017	C₂²	1	1	yes	characteristic
107	SD₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
108	C₄×#11924015	C₂²	1	1	yes	characteristic
109	#17988674	C₂²	1	1	yes	characteristic
110	C₄×#11924016	C₂²	1	1	yes	characteristic
111	#17988672	C₂²	1	1	yes	characteristic
112	#106×D₇₃	C₂²	1	2	yes	—
113	#106×D₇₃	C₂²	1	1	yes	characteristic
114	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
115	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
116	#103×D₇₃	C₂²	1	2	yes	—
117	#103×D₇₃	C₂²	1	2	yes	—
118	#103×D₇₃	C₂²	1	1	yes	characteristic
119	#103×D₇₃	C₂²	1	2	yes	—
120	#102×D₇₃	C₂²	1	2	yes	—
121	#102×D₇₃	C₂²	1	1	yes	characteristic
122	#97×D₇₃	C₂²	1	2	yes	—
123	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
124	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#556×C₇₃	C₂²	1	1	yes	characteristic
126	#489×C₇₃	C₂²	1	2	yes	—
127	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#476×C₇₃	C₂²	1	1	yes	characteristic
129	#475×C₇₃	C₂²	1	2	yes	complemented
130	#464×C₇₃	C₂²	1	2	yes	—
131	#462×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#441×C₇₃	C₂²	1	2	yes	complemented
134	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₇₃	—	2	2	no	—
136	C₂×Q₈×D₇₃	—	2	1	no	—
137	C₂×Q₈×D₇₃	D₄	1	1	yes	characteristic
138	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
139	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
140	C₂×D₄×D₇₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×D₇₃	—	2	1	no	—
142	C₂×Dic₂₉₂	C₂³	1	2	yes	—
143	C₂×#11924018	C₂³	1	2	yes	—
144	C₂×#11924018	C₂³	1	2	yes	—
145	Q₁₆×D₇₃	—	2	8	no	—
146	C₂×#11924017	C₂³	1	1	yes	characteristic
147	C₂×#11924016	C₂³	1	1	yes	characteristic
148	C₂×#11924015	C₂³	1	1	yes	characteristic
149	SD₁₆×D₇₃	—	2	4	no	—
150	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₇₃	C₂³	1	2	yes	—
152	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
153	#14556591	—	2	1	no	—
154	#14556591	—	2	2	no	—
155	#14556591	C₂³	1	1	yes	characteristic
156	#14556591	C₂³	1	2	yes	—
157	#14556591	C₂³	1	1	yes	characteristic
158	#14556590	—	2	1	no	—
159	#14556590	—	2	2	no	—
160	#14556590	—	2	2	no	—
161	#14556590	—	2	2	no	—
162	#14556590	—	2	2	no	—
163	#14556590	—	2	1	no	—
164	#14556590	—	2	1	no	—
165	#14556590	—	2	1	no	—
166	#14556590	—	2	2	no	—
167	#14556590	—	2	1	no	—
168	#14556590	—	2	2	no	—
169	#14556590	C₂³	1	2	yes	—
170	#14556590	C₂³	1	2	yes	—
171	#14556590	C₂³	1	2	yes	—
172	#14556589	—	2	2	no	—
173	#14556589	—	2	2	no	—
174	#14556589	—	2	2	no	—
175	#14556589	—	2	1	no	—
176	#14556589	—	2	2	no	—
177	#14556589	C₂³	1	2	yes	—
178	#14556586	—	2	2	no	—
179	#14556586	—	2	2	no	—
180	#14556586	—	2	2	no	—
181	#14556585	—	2	2	no	—
182	#14556584	—	2	2	no	—
183	#14556584	—	2	2	no	—
184	#14556584	—	2	2	no	—
185	#14556580	C₂³	1	2	yes	—
186	#14556579	C₂³	1	2	yes	—
187	#14556578	C₂³	1	2	yes	—
188	#14556577	—	2	2	no	—
189	#14556577	—	2	2	no	—
190	#14556571	—	2	1	no	—
191	#14556570	—	2	1	no	—
192	#14556569	—	2	2	no	—
193	#14556568	—	2	2	no	—
194	#14556567	—	2	1	no	—
195	Q₈×Dic₇₃	—	2	1	no	—
196	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
197	Q₈×Dic₇₃	C₂³	1	2	yes	—
198	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
199	Q₈×Dic₇₃	C₂³	1	2	yes	—
200	C₄×Dic₁₄₆	—	2	2	no	—
201	C₄×Dic₁₄₆	—	2	1	no	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	C₄×Dic₁₄₆	—	2	1	no	—
204	C₄×Dic₁₄₆	—	2	2	no	—
205	C₄×Dic₁₄₆	C₂³	1	2	yes	—
206	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
207	C₄×Dic₁₄₆	C₂³	1	2	yes	—
208	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
209	C₄×Dic₁₄₆	C₂³	1	2	yes	—
210	#14556556	—	2	2	no	—
211	#14556556	—	2	1	no	—
212	#14556556	—	2	2	no	—
213	#14556556	—	2	1	no	—
214	#14556556	—	2	2	no	—
215	#14556556	D₄	1	2	yes	—
216	#14556556	D₄	1	1	yes	characteristic
217	#14556556	C₂³	1	2	yes	—
218	#14556556	C₂³	1	1	yes	characteristic
219	#14556556	C₂³	1	2	yes	—
220	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
221	D₄×Dic₇₃	C₂³	1	1	yes	characteristic
222	#14556553	C₂³	1	1	yes	characteristic
223	C₄×C₂²⋊D₇₃	—	2	1	no	—
224	#14556551	—	2	1	no	—
225	#14556550	—	2	1	no	—
226	#14556549	—	2	1	no	—
227	#14556549	—	2	1	no	—
228	#14556548	—	2	2	no	—
229	#14556547	—	2	2	no	—
230	C₄⋊C₄×D₇₃	—	2	2	no	—
231	C₄⋊C₄×D₇₃	—	2	1	no	—
232	C₄⋊C₄×D₇₃	—	2	2	no	—
233	C₄⋊C₄×D₇₃	—	2	1	no	—
234	C₄⋊C₄×D₇₃	—	2	1	no	—
235	C₄⋊C₄×D₇₃	—	2	1	no	—
236	C₄⋊C₄×D₇₃	—	2	2	no	—
237	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
238	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
239	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
241	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
242	C₂²⋊C₄×D₇₃	—	2	2	no	—
243	C₂²⋊C₄×D₇₃	—	2	1	no	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₄²×D₇₃	—	2	2	no	—
246	C₄²×D₇₃	—	2	1	no	—
247	C₄²×D₇₃	—	2	2	no	—
248	C₄²×D₇₃	C₂³	1	1	yes	characteristic
249	C₄²×D₇₃	C₂³	1	2	yes	—
250	#14556523	C₂³	1	1	yes	characteristic
251	#14556523	C₂³	1	2	yes	—
252	#14556522	C₂³	1	1	yes	characteristic
253	#14556522	C₂³	1	2	yes	—
254	#14556522	C₂³	1	1	yes	characteristic
255	#14556522	C₂³	1	2	yes	—
256	C₄⋊#10596831	C₂³	1	2	yes	—
257	C₄⋊#10596831	C₂³	1	1	yes	characteristic
258	#14556520	C₂³	1	2	yes	—
259	#14556520	C₂³	1	2	yes	—
260	#14556520	C₂³	1	2	yes	—
261	#14556516	C₂³	1	2	yes	—
262	#14556516	C₂³	1	2	yes	—
263	#14556516	C₂³	1	1	yes	characteristic
264	#14556516	C₂³	1	2	yes	—
265	#14556515	C₂³	1	2	yes	—
266	#14556515	C₂³	1	2	yes	—
267	#14556515	C₂³	1	1	yes	characteristic
268	#14556515	C₂³	1	2	yes	—
269	#14556514	C₂³	1	2	yes	—
270	#14556514	C₂³	1	2	yes	—
271	#14556514	C₂³	1	1	yes	characteristic
272	#14556514	C₂³	1	2	yes	—
273	#14556513	C₂³	1	2	yes	—
274	#14556513	C₂³	1	1	yes	characteristic
275	#14556512	C₂³	1	2	yes	—
276	#14556512	C₂³	1	1	yes	characteristic
277	#14556511	C₂³	1	2	yes	—
278	#14556511	C₂³	1	1	yes	characteristic
279	#14556502	C₂³	1	2	yes	—
280	#14556501	C₂³	1	2	yes	—
281	#14556501	C₂³	1	2	yes	—
282	C₄×#10596831	C₂³	1	1	yes	characteristic
283	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
284	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
285	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
286	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
287	C₄⋊Q₈×C₇₃	—	2	1	no	—
288	C₄⋊Q₈×C₇₃	—	2	2	no	—
289	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
291	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
292	#126×C₇₃	—	2	2	no	—
293	#124×C₇₃	C₂³	1	2	yes	—
294	C₂²⋊Q₈×C₇₃	—	2	1	no	—
295	C₄×Q₈×C₇₃	—	2	1	no	—
296	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
297	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
299	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
301	#117×C₇₃	—	2	1	no	—
302	#106×C₇₃	C₂³	1	1	yes	characteristic
303	#106×C₇₃	C₂³	1	2	yes	—
304	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
305	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
306	#103×C₇₃	C₂³	1	2	yes	—
307	#103×C₇₃	C₂³	1	2	yes	—
308	#103×C₇₃	C₂³	1	1	yes	characteristic
309	#103×C₇₃	C₂³	1	2	yes	—
310	#102×C₇₃	C₂³	1	2	yes	—
311	#102×C₇₃	C₂³	1	1	yes	characteristic
312	#97×C₇₃	C₂³	1	2	yes	—
313	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₂³×D₇₃	—	2	1	no	—
315	C₂×Dic₁₄₆	—	2	1	no	—
316	C₂×Dic₁₄₆	—	2	2	no	—
317	C₂×Dic₁₄₆	—	2	2	no	—
318	C₂×Dic₁₄₆	—	2	1	no	—
319	C₂×Dic₁₄₆	—	2	2	no	—
320	C₂×Dic₁₄₆	—	2	2	no	—
321	C₂×Dic₁₄₆	—	2	2	no	—
322	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
323	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
324	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
325	C₂×Dic₁₄₆	C₂⁴	1	1	yes	characteristic
326	Q₈×D₇₃	—	2	4	no	—
327	Q₈×D₇₃	—	2	2	no	—
328	Q₈×D₇₃	—	2	4	no	—
329	Q₈×D₇₃	—	2	4	no	—
330	Q₈×D₇₃	—	8	4	no	—
331	Q₈×D₇₃	—	8	2	no	—
332	Q₈×D₇₃	#41	1	4	yes	—
333	C₂×D₂₉₂	C₂⁴	1	1	yes	characteristic
334	C₂×C₂²⋊D₇₃	—	2	1	no	—
335	D₄×D₇₃	—	2	2	no	—
336	D₄×D₇₃	—	2	2	no	—
337	C₂²×Dic₇₃	—	2	1	no	—
338	C₂×C₄×D₇₃	—	2	1	no	—
339	C₂×C₄×D₇₃	—	2	1	no	—
340	C₂×C₄×D₇₃	—	2	2	no	—
341	C₂×C₄×D₇₃	—	2	2	no	—
342	C₂×C₄×D₇₃	—	2	1	no	—
343	C₂×C₄×D₇₃	—	2	1	no	—
344	C₂×C₄×D₇₃	—	2	1	no	—
345	C₂×C₄×D₇₃	—	4	4	no	—
346	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
347	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
348	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
349	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
350	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
351	Dic₂₉₂	—	2	4	no	—
352	#11924018	—	2	4	no	—
353	#11924018	—	2	4	no	—
354	#11924017	—	2	2	no	—
355	#11924016	—	2	2	no	—
356	#11924015	—	2	2	no	—
357	C₂×#10596831	C₂⁴	1	1	yes	characteristic
358	C₂×#10596831	C₂⁴	1	1	yes	characteristic
359	C₂×#10596831	C₂⁴	1	2	yes	—
360	C₈×D₇₃	—	2	2	no	—
361	C₈×D₇₃	—	2	4	no	—
362	C₈×D₇₃	—	2	2	no	—
363	C₄⋊Dic₇₃	—	2	1	no	—
364	C₄⋊Dic₇₃	—	2	2	no	—
365	C₄⋊Dic₇₃	—	2	1	no	—
366	C₄⋊Dic₇₃	—	2	1	no	—
367	C₄⋊Dic₇₃	—	2	2	no	—
368	C₄⋊Dic₇₃	—	2	2	no	—
369	C₄⋊Dic₇₃	—	2	1	no	—
370	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
371	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
372	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
373	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
374	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
375	#11924007	—	2	2	no	—
376	#11924007	—	2	2	no	—
377	#11924007	—	2	1	no	—
378	#11924007	—	2	2	no	—
379	#11924007	—	2	2	no	—
380	#11924007	—	2	2	no	—
381	#11924007	—	2	2	no	—
382	#11924007	—	2	2	no	—
383	#11924007	—	2	2	no	—
384	#11924007	—	2	1	no	—
385	#11924007	—	2	2	no	—
386	#11924007	—	2	1	no	—
387	#11924007	—	2	2	no	—
388	#11924007	—	2	1	no	—
389	#11924007	C₂×D₄	1	2	yes	—
390	#11924007	C₂×D₄	1	2	yes	—
391	#11924007	C₂×D₄	1	2	yes	—
392	C₂²⋊Dic₇₃	—	2	2	no	—
393	C₂²⋊Dic₇₃	—	2	1	no	—
394	C₂²⋊Dic₇₃	—	2	2	no	—
395	#11924005	—	2	2	no	—
396	#11924005	—	2	1	no	—
397	#11924005	—	2	2	no	—
398	#11924005	—	2	2	no	—
399	#11924005	—	2	1	no	—
400	#11924005	—	2	2	no	—
401	C₄×Dic₇₃	—	2	2	no	—
402	C₄×Dic₇₃	—	2	2	no	—
403	C₄×Dic₇₃	—	2	1	no	—
404	C₄×Dic₇₃	—	2	2	no	—
405	C₄×Dic₇₃	—	2	2	no	—
406	C₄×Dic₇₃	—	2	2	no	—
407	C₄×Dic₇₃	—	2	1	no	—
408	C₄×Dic₇₃	—	2	2	no	—
409	C₄×Dic₇₃	—	2	1	no	—
410	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
413	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
414	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
415	C₄×Dic₇₃	C₂⁴	1	2	yes	—
416	C₂×Q₈×C₇₃	—	2	2	no	—
417	C₂×Q₈×C₇₃	—	2	1	no	—
418	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
419	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
420	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₇₃	—	2	1	no	—
423	Q₁₆×C₇₃	—	2	4	no	—
424	SD₁₆×C₇₃	—	2	2	no	—
425	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
428	C₄⋊C₄×C₇₃	—	2	1	no	—
429	C₄⋊C₄×C₇₃	—	2	2	no	—
430	C₄⋊C₄×C₇₃	—	2	1	no	—
431	C₄⋊C₄×C₇₃	—	2	2	no	—
432	C₄⋊C₄×C₇₃	—	2	2	no	—
433	C₄⋊C₄×C₇₃	—	2	1	no	—
434	C₄⋊C₄×C₇₃	—	2	1	no	—
435	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
436	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
437	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₇₃	—	2	2	no	—
441	C₂²⋊C₄×C₇₃	—	2	1	no	—
442	C₂²⋊C₄×C₇₃	—	2	2	no	—
443	C₄²×C₇₃	—	2	2	no	—
444	C₄²×C₇₃	—	2	2	no	—
445	C₄²×C₇₃	—	2	1	no	—
446	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
447	C₄²×C₇₃	C₂⁴	1	2	yes	—
448	C₂³×C₇₃	—	2	1	no	—
449	C₂²×D₇₃	—	2	1	no	—
450	C₂²×D₇₃	—	4	2	no	—
451	C₂²×D₇₃	—	4	2	no	—
452	C₂²×D₇₃	—	4	2	no	—
453	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₇₃	—	2	2	no	—
455	Q₈×C₇₃	—	2	1	no	—
456	Q₈×C₇₃	—	2	2	no	—
457	Q₈×C₇₃	—	2	2	no	—
458	Q₈×C₇₃	—	8	2	no	—
459	Q₈×C₇₃	—	8	1	no	—
460	Q₈×C₇₃	C₂×#41	1	2	yes	—
461	D₄×C₇₃	—	2	1	no	—
462	D₄×C₇₃	—	2	1	no	—
463	C₂×C₄×C₇₃	—	2	1	no	—
464	C₂×C₄×C₇₃	—	2	1	no	—
465	C₂×C₄×C₇₃	—	2	2	no	—
466	C₂×C₄×C₇₃	—	2	2	no	—
467	C₂×C₄×C₇₃	—	2	1	no	—
468	C₂×C₄×C₇₃	—	4	2	no	—
469	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
474	C₂²⋊D₇₃	—	4	2	no	—
475	C₂×Dic₇₃	—	2	1	no	—
476	C₂×Dic₇₃	—	2	1	no	—
477	C₂×Dic₇₃	—	2	2	no	—
478	C₂×Dic₇₃	—	2	2	no	—
479	C₂×Dic₇₃	—	2	1	no	—
480	C₂×Dic₇₃	—	4	2	no	—
481	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
482	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
483	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
486	D₂₉₂	—	2	1	no	—
487	D₂₉₂	—	2	1	no	—
488	C₄×D₇₃	—	2	4	no	—
489	C₄×D₇₃	—	2	4	no	—
490	C₄×D₇₃	—	2	4	no	—
491	C₄×D₇₃	—	2	2	no	—
492	C₄×D₇₃	—	4	4	no	—
493	C₄×D₇₃	—	4	2	no	—
494	C₄×D₇₃	—	4	4	no	—
495	C₄×D₇₃	—	4	2	no	—
496	C₄×D₇₃	—	4	2	no	—
497	C₄×D₇₃	—	4	2	no	—
498	C₄×D₇₃	#137	1	4	yes	—
499	C₄×D₇₃	C₂×#41	1	2	yes	—
500	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
501	Dic₁₄₆	—	2	2	no	—
502	Dic₁₄₆	—	2	1	no	—
503	Dic₁₄₆	—	2	4	no	—
504	Dic₁₄₆	—	2	4	no	—
505	Dic₁₄₆	—	2	2	no	—
506	Dic₁₄₆	—	2	2	no	—
507	Dic₁₄₆	—	4	4	no	—
508	Dic₁₄₆	—	8	2	no	—
509	Dic₁₄₆	—	8	2	no	—
510	Dic₁₄₆	—	8	2	no	—
511	Dic₁₄₆	—	8	2	no	—
512	Dic₁₄₆	—	8	1	no	—
513	Dic₁₄₆	C₂×#41	1	2	yes	—
514	C₈×C₇₃	—	2	1	no	—
515	C₈×C₇₃	—	2	2	no	—
516	C₈×C₇₃	—	2	1	no	—
517	#10596831	—	2	1	no	—
518	#10596831	—	2	2	no	—
519	#10596831	—	2	1	no	—
520	C₂²×C₇₃	—	4	1	no	—
521	C₂²×C₇₃	—	4	1	no	—
522	C₂²×C₇₃	—	4	1	no	—
523	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
524	C₂×D₇₃	—	4	1	no	—
525	C₂×D₇₃	—	4	1	no	—
526	C₂×D₇₃	—	4	1	no	—
527	C₂×D₇₃	—	8	4	no	—
528	C₂×D₇₃	#548	1	2	yes	—
529	C₂×D₇₃	C₂×#137	1	2	yes	—
530	C₂×D₇₃	#577	1	2	yes	—
531	C₄×C₇₃	—	2	2	no	—
532	C₄×C₇₃	—	2	2	no	—
533	C₄×C₇₃	—	2	2	no	—
534	C₄×C₇₃	—	2	1	no	—
535	C₄×C₇₃	—	4	2	no	—
536	C₄×C₇₃	—	4	1	no	—
537	C₄×C₇₃	—	4	1	no	—
538	C₄×C₇₃	—	4	2	no	—
539	C₄×C₇₃	C₂×#137	1	2	yes	—
540	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
541	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
542	Dic₇₃	—	2	2	no	—
543	Dic₇₃	—	2	2	no	—
544	Dic₇₃	—	2	2	no	—
545	Dic₇₃	—	2	1	no	—
546	Dic₇₃	—	4	2	no	—
547	Dic₇₃	—	4	1	no	—
548	Dic₇₃	—	4	1	no	—
549	Dic₇₃	—	4	2	no	—
550	Dic₇₃	#548	1	2	yes	—
551	Dic₇₃	C₂×#137	1	2	yes	—
552	C₂×#3369	—	73	1	no	maximal, Sylow
553	C₂×C₇₃	—	8	1	no	—
554	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
555	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
556	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
557	D₇₃	—	8	1	no	—
558	D₇₃	#3369	1	4	yes	direct product factor
559	C₂×Q₈²	—	73	1	no	—
560	C₂×#556	—	73	1	no	—
561	#3369	—	73	2	no	—
562	#3369	—	73	1	no	—
563	#3369	—	73	1	no	—
564	#3369	—	73	2	no	—
565	#3369	—	73	2	no	—
566	#3369	—	73	1	no	—
567	#3369	—	73	1	no	—
568	#3369	—	73	2	no	—
569	#3369	—	73	1	no	—
570	#3369	—	73	1	no	—
571	#3369	—	73	1	no	—
572	#3369	D₇₃	1	1	yes	characteristic, direct product factor
573	C₂×#489	—	73	2	no	—
574	C₂×#487	—	73	1	no	—
575	C₂×#475	—	73	2	no	—
576	C₂×#476	—	73	1	no	—
577	C₂×#464	—	73	2	no	—
578	C₂×#462	—	73	1	no	—
579	C₂×#446	—	73	1	no	—
580	C₂×#441	—	73	2	no	—
581	C₂×C₄×SD₁₆	—	73	1	no	—
582	C₇₃	C₂×#3369	1	1	yes	characteristic, complemented, Sylow
583	C₂²×Q₁₆	—	73	2	no	—
584	C₂²×SD₁₆	—	73	1	no	—
585	Q₈²	—	73	2	no	—
586	Q₈²	—	73	1	no	—
587	Q₈²	—	73	2	no	—
588	Q₈²	—	73	1	no	—
589	Q₈²	—	73	1	no	—
590	Q₈²	—	146	1	no	—
591	Q₈²	—	146	2	no	—
592	Q₈²	—	146	1	no	—
593	Q₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
594	#556	—	73	1	no	—
595	#556	—	73	2	no	—
596	#556	—	73	2	no	—
597	#556	—	73	1	no	—
598	#556	—	73	1	no	—
599	#556	—	146	1	no	—
600	#556	—	146	1	no	—
601	#556	—	146	2	no	—
602	#556	C₂×D₇₃	1	1	yes	characteristic
603	C₂×C₄⋊Q₈	—	73	2	no	—
604	C₂×C₄⋊Q₈	—	73	1	no	—
605	C₂×C₄⋊Q₈	—	73	1	no	—
606	C₂×C₄⋊Q₈	—	146	1	no	—
607	C₂×C₄⋊Q₈	—	146	2	no	—
608	C₂×#126	—	146	2	no	—
609	C₂×#124	—	73	2	no	—
610	C₂×C₂²⋊Q₈	—	146	1	no	—
611	C₂×C₄×Q₈	—	73	1	no	—
612	C₂×C₄×Q₈	—	73	2	no	—
613	C₂×C₄×Q₈	—	73	1	no	—
614	C₂×C₄×Q₈	—	73	2	no	—
615	C₂×C₄×Q₈	—	146	1	no	—
616	C₂×C₄×D₄	—	73	1	no	—
617	C₂×#117	—	146	1	no	—
618	#489	—	73	2	no	—
619	#489	—	73	2	no	—
620	#489	—	73	2	no	—
621	#489	—	73	2	no	—
622	#489	—	73	2	no	—
623	#489	—	73	2	no	—
624	#489	—	73	2	no	—
625	#489	C₂×D₇₃	1	2	yes	—
626	#487	—	73	1	no	—
627	#487	—	73	1	no	—
628	#487	—	73	2	no	—
629	#487	—	73	2	no	—
630	#487	—	73	1	no	—
631	#487	C₂×D₇₃	1	1	yes	characteristic, complemented
632	#476	—	73	1	no	—
633	#476	—	73	1	no	—
634	#476	—	73	2	no	—
635	#476	—	73	1	no	—
636	#476	—	73	2	no	—
637	#476	C₂×D₇₃	1	1	yes	characteristic
638	#475	—	73	2	no	—
639	#475	—	73	2	no	—
640	#475	—	73	2	no	—
641	#475	—	73	2	no	—
642	#475	—	73	2	no	—
643	#475	—	73	2	no	—
644	#475	—	73	2	no	—
645	#475	C₂×D₇₃	1	2	yes	complemented
646	#464	—	73	2	no	—
647	#464	—	73	2	no	—
648	#464	—	73	2	no	—
649	#464	—	73	2	no	—
650	#464	—	73	2	no	—
651	#464	—	73	2	no	—
652	#464	—	73	2	no	—
653	#464	C₂×D₇₃	1	2	yes	—
654	#462	—	73	2	no	—
655	#462	—	73	1	no	—
656	#462	—	73	1	no	—
657	#462	—	73	1	no	—
658	#462	—	73	2	no	—
659	#462	C₂×D₇₃	1	1	yes	characteristic, complemented
660	#446	—	73	1	no	—
661	#446	—	73	1	no	—
662	#446	—	73	2	no	—
663	#446	—	73	2	no	—
664	#446	—	73	1	no	—
665	#446	C₂×D₇₃	1	1	yes	characteristic, complemented
666	#441	—	73	2	no	—
667	#441	—	73	2	no	—
668	#441	—	73	2	no	—
669	#441	—	73	2	no	—
670	#441	—	73	2	no	—
671	#441	—	73	2	no	—
672	#441	—	73	2	no	—
673	#441	C₂×D₇₃	1	2	yes	complemented
674	C₄×SD₁₆	—	73	1	no	—
675	C₄×SD₁₆	—	73	1	no	—
676	C₄×SD₁₆	—	73	1	no	—
677	C₄×SD₁₆	—	73	1	no	—
678	C₄×SD₁₆	—	73	1	no	—
679	C₄×SD₁₆	—	73	1	no	—
680	C₄×SD₁₆	—	73	1	no	—
681	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
682	C₂×#106	—	73	1	no	—
683	C₂×#106	—	73	2	no	—
684	C₂×C₄⋊C₈	—	73	2	no	—
685	C₂×C₄⋊C₈	—	73	1	no	—
686	C₂×#103	—	73	2	no	—
687	C₂×#103	—	73	2	no	—
688	C₂×#103	—	73	2	no	—
689	C₂×#103	—	73	1	no	—
690	C₂×#102	—	73	1	no	—
691	C₂×#102	—	73	2	no	—
692	C₂×#97	—	73	2	no	—
693	C₂×C₄×C₈	—	73	1	no	—
694	C₂²×Q₈	—	73	1	no	—
695	C₂²×Q₈	—	73	1	no	—
696	C₂²×Q₈	—	73	2	no	—
697	C₂²×Q₈	—	146	2	no	—
698	C₂²×Q₈	—	146	1	no	—
699	C₂²×D₄	—	73	1	no	—
700	C₂³×C₄	—	146	1	no	—
701	C₂×Q₁₆	—	73	2	no	—
702	C₂×Q₁₆	—	73	2	no	—
703	C₂×Q₁₆	—	73	2	no	—
704	C₂×Q₁₆	—	146	8	no	—
705	C₂×Q₁₆	C₂²×D₇₃	1	2	yes	—
706	C₂×SD₁₆	—	73	1	no	—
707	C₂×SD₁₆	—	73	1	no	—
708	C₂×SD₁₆	—	73	1	no	—
709	C₂×SD₁₆	—	146	4	no	—
710	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
711	C₂²×C₈	—	73	1	no	—
712	C₂²×C₈	—	73	2	no	—
713	C₂²×C₈	—	73	1	no	—
714	C₄⋊Q₈	—	2	1	no	—
715	C₄⋊Q₈	—	2	2	no	—
716	C₄⋊Q₈	—	73	2	no	—
717	C₄⋊Q₈	—	73	2	no	—
718	C₄⋊Q₈	—	73	2	no	—
719	C₄⋊Q₈	—	73	2	no	—
720	C₄⋊Q₈	—	73	2	no	—
721	C₄⋊Q₈	—	73	1	no	—
722	C₄⋊Q₈	—	73	1	no	—
723	C₄⋊Q₈	—	146	1	no	—
724	C₄⋊Q₈	—	146	2	no	—
725	C₄⋊Q₈	—	146	1	no	—
726	C₄⋊Q₈	—	146	1	no	—
727	C₄⋊Q₈	—	146	1	no	—
728	C₄⋊Q₈	—	146	2	no	—
729	C₄⋊Q₈	—	146	1	no	—
730	C₄⋊Q₈	—	146	2	no	—
731	C₄⋊Q₈	—	146	2	no	—
732	C₄⋊Q₈	—	146	2	no	—
733	C₄⋊Q₈	—	146	2	no	—
734	C₄⋊Q₈	—	146	1	no	—
735	C₄⋊Q₈	—	146	2	no	—
736	C₄⋊Q₈	—	146	2	no	—
737	C₄⋊Q₈	—	146	2	no	—
738	C₄⋊Q₈	—	146	2	no	—
739	C₄⋊Q₈	—	146	1	no	—
740	C₄⋊Q₈	—	146	2	no	—
741	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
742	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
743	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
744	#126	—	2	2	no	—
745	#126	—	146	2	no	—
746	#126	—	146	2	no	—
747	#126	—	146	2	no	—
748	#126	—	146	2	no	—
749	#126	—	146	2	no	—
750	#126	—	146	2	no	—
751	#126	—	146	2	no	—
752	#124	—	73	2	no	—
753	#124	—	73	2	no	—
754	#124	—	73	2	no	—
755	#124	—	146	2	no	—
756	#124	—	146	2	no	—
757	#124	C₂²×D₇₃	1	2	yes	—
758	C₂²⋊Q₈	—	2	1	no	—
759	C₂²⋊Q₈	—	146	2	no	—
760	C₂²⋊Q₈	—	146	2	no	—
761	C₂²⋊Q₈	—	146	1	no	—
762	C₂²⋊Q₈	—	146	1	no	—
763	C₂²⋊Q₈	—	146	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	73	1	no	—
766	C₄×Q₈	—	73	2	no	—
767	C₄×Q₈	—	73	1	no	—
768	C₄×Q₈	—	73	2	no	—
769	C₄×Q₈	—	73	1	no	—
770	C₄×Q₈	—	73	2	no	—
771	C₄×Q₈	—	73	1	no	—
772	C₄×Q₈	—	73	2	no	—
773	C₄×Q₈	—	73	2	no	—
774	C₄×Q₈	—	73	1	no	—
775	C₄×Q₈	—	73	2	no	—
776	C₄×Q₈	—	73	2	no	—
777	C₄×Q₈	—	73	1	no	—
778	C₄×Q₈	—	73	2	no	—
779	C₄×Q₈	—	146	2	no	—
780	C₄×Q₈	—	146	1	no	—
781	C₄×Q₈	—	146	2	no	—
782	C₄×Q₈	—	146	2	no	—
783	C₄×Q₈	—	146	1	no	—
784	C₄×Q₈	—	146	2	no	—
785	C₄×Q₈	—	146	1	no	—
786	C₄×Q₈	—	146	2	no	—
787	C₄×Q₈	—	146	2	no	—
788	C₄×Q₈	—	146	1	no	—
789	C₄×Q₈	—	146	1	no	—
790	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
791	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
792	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
793	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
794	C₄×D₄	—	73	1	no	—
795	C₄×D₄	—	73	1	no	—
796	C₄×D₄	—	73	1	no	—
797	C₄×D₄	—	146	1	no	—
798	C₄×D₄	—	146	1	no	—
799	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
800	#117	—	2	1	no	—
801	#117	—	146	2	no	—
802	#117	—	146	2	no	—
803	#117	—	146	1	no	—
804	#117	—	146	1	no	—
805	#117	—	146	1	no	—
806	C₂×C₄⋊C₄	—	73	1	no	—
807	C₂×C₄⋊C₄	—	73	2	no	—
808	C₂×C₄⋊C₄	—	73	1	no	—
809	C₂×C₄⋊C₄	—	73	1	no	—
810	C₂×C₄⋊C₄	—	73	2	no	—
811	C₂×C₄⋊C₄	—	146	1	no	—
812	C₂×C₄⋊C₄	—	146	2	no	—
813	C₂×C₄⋊C₄	—	146	2	no	—
814	C₂×C₄⋊C₄	—	146	1	no	—
815	C₂×C₄⋊C₄	—	146	1	no	—
816	C₂×C₄⋊C₄	—	146	2	no	—
817	C₂×C₄⋊C₄	—	146	1	no	—
818	C₂×C₂²⋊C₄	—	146	2	no	—
819	C₂×C₂²⋊C₄	—	146	1	no	—
820	C₂×C₂²⋊C₄	—	146	2	no	—
821	C₂×C₄²	—	73	1	no	—
822	C₂×C₄²	—	73	2	no	—
823	C₂×C₄²	—	146	2	no	—
824	C₂×C₄²	—	146	1	no	—
825	C₂×C₄²	—	146	2	no	—
826	#106	—	73	1	no	—
827	#106	—	73	2	no	—
828	#106	—	73	1	no	—
829	#106	—	73	1	no	—
830	#106	—	73	2	no	—
831	#106	—	73	2	no	—
832	#106	C₂²×D₇₃	1	1	yes	characteristic
833	#106	C₂²×D₇₃	1	2	yes	—
834	C₄⋊C₈	—	73	2	no	—
835	C₄⋊C₈	—	73	2	no	—
836	C₄⋊C₈	—	73	2	no	—
837	C₄⋊C₈	—	73	1	no	—
838	C₄⋊C₈	—	73	2	no	—
839	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
840	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
841	#103	—	73	1	no	—
842	#103	—	73	2	no	—
843	#103	—	73	2	no	—
844	#103	—	73	2	no	—
845	#103	—	73	1	no	—
846	#103	—	73	2	no	—
847	#103	—	73	2	no	—
848	#103	—	73	2	no	—
849	#103	—	73	1	no	—
850	#103	—	73	2	no	—
851	#103	—	73	2	no	—
852	#103	—	73	2	no	—
853	#103	C₂²×D₇₃	1	1	yes	characteristic
854	#103	C₂²×D₇₃	1	2	yes	—
855	#103	C₂²×D₇₃	1	2	yes	—
856	#103	C₂²×D₇₃	1	2	yes	—
857	#102	—	73	1	no	—
858	#102	—	73	2	no	—
859	#102	—	73	1	no	—
860	#102	—	73	2	no	—
861	#102	—	73	1	no	—
862	#102	—	73	2	no	—
863	#102	C₂²×D₇₃	1	1	yes	characteristic
864	#102	C₂²×D₇₃	1	2	yes	—
865	#97	—	73	2	no	—
866	#97	—	73	2	no	—
867	#97	—	73	2	no	—
868	#97	C₂²×D₇₃	1	2	yes	—
869	C₄×C₈	—	73	1	no	—
870	C₄×C₈	—	73	1	no	—
871	C₄×C₈	—	73	1	no	—
872	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
873	C₂⁴	—	146	1	no	—
874	C₂×Q₈	—	2	2	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	584	4	no	—
877	C₂×Q₈	—	584	2	no	—
878	C₂×Q₈	—	73	2	no	—
879	C₂×Q₈	—	73	1	no	—
880	C₂×Q₈	—	73	4	no	—
881	C₂×Q₈	—	73	1	no	—
882	C₂×Q₈	—	73	2	no	—
883	C₂×Q₈	—	146	2	no	—
884	C₂×Q₈	—	146	2	no	—
885	C₂×Q₈	—	146	2	no	—
886	C₂×Q₈	—	146	2	no	—
887	C₂×Q₈	—	146	1	no	—
888	C₂×Q₈	—	146	4	no	—
889	C₂×Q₈	—	146	4	no	—
890	C₂×Q₈	—	146	4	no	—
891	C₂×Q₈	—	146	2	no	—
892	C₂×Q₈	—	146	2	no	—
893	C₂×Q₈	—	146	1	no	—
894	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
895	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
896	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
897	C₂×D₄	—	73	1	no	—
898	C₂×D₄	—	146	2	no	—
899	C₂×D₄	—	146	2	no	—
900	C₂×D₄	—	146	1	no	—
901	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	292	4	no	—
904	C₂²×C₄	—	73	1	no	—
905	C₂²×C₄	—	73	1	no	—
906	C₂²×C₄	—	73	2	no	—
907	C₂²×C₄	—	73	2	no	—
908	C₂²×C₄	—	73	1	no	—
909	C₂²×C₄	—	146	1	no	—
910	C₂²×C₄	—	146	1	no	—
911	C₂²×C₄	—	146	2	no	—
912	C₂²×C₄	—	146	1	no	—
913	C₂²×C₄	—	146	2	no	—
914	C₂²×C₄	—	146	1	no	—
915	C₂²×C₄	—	146	1	no	—
916	C₂²×C₄	—	146	1	no	—
917	Q₁₆	—	2	4	no	—
918	Q₁₆	—	146	4	no	—
919	Q₁₆	—	146	4	no	—
920	Q₁₆	—	146	4	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	146	2	no	—
923	SD₁₆	—	146	2	no	—
924	SD₁₆	—	146	2	no	—
925	C₂×C₈	—	73	1	no	—
926	C₂×C₈	—	73	1	no	—
927	C₂×C₈	—	73	2	no	—
928	C₂×C₈	—	146	2	no	—
929	C₂×C₈	—	146	2	no	—
930	C₂×C₈	—	146	4	no	—
931	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
932	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₇₃	1	2	yes	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	73	2	no	—
942	C₄⋊C₄	—	73	2	no	—
943	C₄⋊C₄	—	73	2	no	—
944	C₄⋊C₄	—	73	1	no	—
945	C₄⋊C₄	—	73	2	no	—
946	C₄⋊C₄	—	73	1	no	—
947	C₄⋊C₄	—	73	2	no	—
948	C₄⋊C₄	—	73	1	no	—
949	C₄⋊C₄	—	146	1	no	—
950	C₄⋊C₄	—	146	1	no	—
951	C₄⋊C₄	—	146	2	no	—
952	C₄⋊C₄	—	146	2	no	—
953	C₄⋊C₄	—	146	2	no	—
954	C₄⋊C₄	—	146	2	no	—
955	C₄⋊C₄	—	146	1	no	—
956	C₄⋊C₄	—	146	2	no	—
957	C₄⋊C₄	—	146	2	no	—
958	C₄⋊C₄	—	146	2	no	—
959	C₄⋊C₄	—	146	2	no	—
960	C₄⋊C₄	—	146	2	no	—
961	C₄⋊C₄	—	146	2	no	—
962	C₄⋊C₄	—	146	1	no	—
963	C₄⋊C₄	—	146	2	no	—
964	C₄⋊C₄	—	146	2	no	—
965	C₄⋊C₄	—	146	1	no	—
966	C₄⋊C₄	—	146	1	no	—
967	C₄⋊C₄	—	146	2	no	—
968	C₄⋊C₄	—	146	1	no	—
969	C₄⋊C₄	—	146	1	no	—
970	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
971	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
972	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
974	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	146	2	no	—
979	C₂²⋊C₄	—	146	1	no	—
980	C₂²⋊C₄	—	146	2	no	—
981	C₂²⋊C₄	—	146	2	no	—
982	C₂²⋊C₄	—	146	1	no	—
983	C₂²⋊C₄	—	146	2	no	—
984	C₂²⋊C₄	—	146	2	no	—
985	C₂²⋊C₄	—	146	1	no	—
986	C₂²⋊C₄	—	146	2	no	—
987	C₄²	—	2	2	no	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	73	1	no	—
991	C₄²	—	73	1	no	—
992	C₄²	—	73	2	no	—
993	C₄²	—	73	2	no	—
994	C₄²	—	73	1	no	—
995	C₄²	—	73	2	no	—
996	C₄²	—	146	2	no	—
997	C₄²	—	146	2	no	—
998	C₄²	—	146	1	no	—
999	C₄²	—	146	2	no	—
1000	C₄²	—	146	1	no	—
1001	C₄²	—	146	2	no	—
1002	C₄²	—	146	2	no	—
1003	C₄²	—	146	2	no	—
1004	C₄²	—	146	1	no	—
1005	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1006	C₄²	C₂³×D₇₃	1	2	yes	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	292	2	no	—
1009	C₂³	—	292	2	no	—
1010	C₂³	—	292	2	no	—
1011	C₂³	—	73	1	no	—
1012	C₂³	—	146	1	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	2	no	—
1017	Q₈	—	8	2	no	—
1018	Q₈	—	8	1	no	—
1019	Q₈	—	292	4	no	—
1020	Q₈	—	584	2	no	—
1021	Q₈	—	584	1	no	—
1022	Q₈	—	584	2	no	—
1023	Q₈	—	584	2	no	—
1024	Q₈	—	584	2	no	—
1025	Q₈	—	73	2	no	—
1026	Q₈	—	146	4	no	—
1027	Q₈	—	146	4	no	—
1028	Q₈	—	146	2	no	—
1029	Q₈	—	146	2	no	—
1030	Q₈	—	146	2	no	—
1031	Q₈	—	146	1	no	—
1032	Q₈	#41×D₇₃	1	2	yes	—
1033	D₄	—	2	1	no	—
1034	D₄	—	2	1	no	—
1035	D₄	—	292	2	no	—
1036	D₄	—	146	1	no	—
1037	D₄	—	146	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	4	2	no	—
1044	C₂×C₄	—	292	2	no	—
1045	C₂×C₄	—	292	2	no	—
1046	C₂×C₄	—	292	4	no	—
1047	C₂×C₄	—	292	4	no	—
1048	C₂×C₄	—	292	2	no	—
1049	C₂×C₄	—	292	2	no	—
1050	C₂×C₄	—	292	2	no	—
1051	C₂×C₄	—	73	1	no	—
1052	C₂×C₄	—	73	1	no	—
1053	C₂×C₄	—	73	4	no	—
1054	C₂×C₄	—	73	2	no	—
1055	C₂×C₄	—	73	2	no	—
1056	C₂×C₄	—	73	2	no	—
1057	C₂×C₄	—	73	2	no	—
1058	C₂×C₄	—	73	1	no	—
1059	C₂×C₄	—	146	4	no	—
1060	C₂×C₄	—	146	2	no	—
1061	C₂×C₄	—	146	4	no	—
1062	C₂×C₄	—	146	4	no	—
1063	C₂×C₄	—	146	1	no	—
1064	C₂×C₄	—	146	2	no	—
1065	C₂×C₄	—	146	1	no	—
1066	C₂×C₄	—	146	2	no	—
1067	C₂×C₄	—	146	1	no	—
1068	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1069	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1070	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1072	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1073	C₈	—	2	1	no	—
1074	C₈	—	2	2	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	146	1	no	—
1077	C₈	—	146	2	no	—
1078	C₈	—	146	1	no	—
1079	C₂²	—	4	1	no	—
1080	C₂²	—	4	1	no	—
1081	C₂²	—	4	1	no	—
1082	C₂²	—	292	1	no	—
1083	C₂²	—	292	1	no	—
1084	C₂²	—	292	1	no	—
1085	C₂²	—	584	4	no	—
1086	C₂²	—	73	2	no	—
1087	C₂²	—	73	2	no	—
1088	C₂²	—	73	2	no	—
1089	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1090	C₄	—	2	2	no	—
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	2	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	292	1	no	—
1099	C₄	—	292	2	no	—
1100	C₄	—	292	1	no	—
1101	C₄	—	292	2	no	—
1102	C₄	—	73	2	no	—
1103	C₄	—	73	2	no	—
1104	C₄	—	146	2	no	—
1105	C₄	—	146	2	no	—
1106	C₄	—	146	2	no	—
1107	C₄	—	146	1	no	—
1108	C₄	#137×D₇₃	1	2	yes	—
1109	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1110	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1111	C₂	—	8	1	no	—
1112	C₂	—	584	1	no	—
1113	C₂	—	73	4	no	—
1114	C₂	#548×D₇₃	1	1	yes	characteristic
1115	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1116	C₂	#577×D₇₃	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×#3369	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂×D₄×D₇₃	C₂³
hypercenter	#3369	D₇₃
hypocenter	C₇₃	C₂×#3369
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3369

Complements

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

N	H ≅ G/N	type
1. Q₈²×D₇₃	C₂	semidirect
3. #22622676	C₂	semidirect
4. #22622675	C₂	semidirect
5. #22622674	C₂	semidirect
6. #22622673	C₂	semidirect
7. #22622672	C₂	semidirect
8. #22622671	C₂	semidirect
9. #22622670	C₂	semidirect
10. #22622669	C₂	semidirect
11. #22622668	C₂	semidirect
12. #22622667	C₂	semidirect
13. #22622666	C₂	semidirect
15. #487×D₇₃	C₂	semidirect
16. #475×D₇₃	C₂	semidirect
19. #462×D₇₃	C₂	semidirect
20. #446×D₇₃	C₂	semidirect
21. #441×D₇₃	C₂	semidirect
23. C₇₃×#3369	C₂	semidirect
27. Q₈×Dic₁₄₆	C₂²	semidirect
28. Q₈×Dic₁₄₆	C₂²	semidirect
29. Q₈×Dic₁₄₆	C₂²	semidirect
32. #17989317	C₂²	semidirect
33. #17989317	C₂²	semidirect
64. #17988939	C₂²	semidirect
65. #17988938	C₂²	semidirect
66. #17988937	C₂²	semidirect
67. #17988936	C₂²	semidirect
68. #17988936	C₂²	semidirect
74. #17988873	C₂²	semidirect
75. #17988872	C₂²	semidirect
76. #17988871	C₂²	semidirect
77. #17988871	C₂²	semidirect
78. #17988870	C₂²	semidirect
79. #17988870	C₂²	semidirect
80. #17988869	C₂²	semidirect
88. #17988798	C₂²	semidirect
89. #17988797	C₂²	semidirect
90. #17988796	C₂²	semidirect
91. #17988795	C₂²	semidirect
92. #17988794	C₂²	semidirect
93. #17988718	C₂²	semidirect
94. #17988717	C₂²	semidirect
95. #17988716	C₂²	semidirect
96. #17988715	C₂²	semidirect
97. #17988714	C₂²	semidirect
98. #17988695	C₂²	semidirect
99. #17988694	C₂²	semidirect
100. #17988693	C₂²	semidirect
101. #17988692	C₂²	semidirect
102. #17988692	C₂²	semidirect
103. #17988691	C₂²	semidirect
104. #17988691	C₂²	semidirect
124. Q₈²×C₇₃	C₂²	semidirect
127. #487×C₇₃	C₂²	semidirect
129. #475×C₇₃	C₂²	semidirect
131. #462×C₇₃	C₂²	semidirect
132. #446×C₇₃	C₂²	semidirect
133. #441×C₇₃	C₂²	semidirect
558. D₇₃	#3369	direct (N × H)
572. #3369	D₇₃	direct (N × H)
582. C₇₃	C₂×#3369	semidirect
593. Q₈²	C₂×D₇₃	semidirect
631. #487	C₂×D₇₃	semidirect
645. #475	C₂×D₇₃	semidirect
659. #462	C₂×D₇₃	semidirect
665. #446	C₂×D₇₃	semidirect
673. #441	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈²×D₇₃	2
#556×D₇₃	2
#22622676	2
#22622675	2
#22622674	2
#22622673	2
#22622672	2
#22622671	2
#22622670	2
#22622669	2
#22622668	2
#22622667	2
#22622666	2
#489×D₇₃	2
#487×D₇₃	2
#475×D₇₃	2
#476×D₇₃	2
#464×D₇₃	2
#462×D₇₃	2
#446×D₇₃	2
#441×D₇₃	2
C₄×SD₁₆×D₇₃	2
C₇₃×#3369	2
C₂×#3369	73

Subgroups — #3369×D73 #33965701

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3369×D₇₃ #33965701