Subgroups — #3387×D₇₃ #33966491

Order 18688.

1778 conjugacy classes of subgroups.

The subgroup lattice has 1074 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
2	#557×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22622868	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622867	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622866	C₂	1	2	yes	maximal, complemented
6	#22622865	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622864	C₂	1	2	yes	maximal, complemented
8	#22622863	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622862	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622861	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622860	C₂	1	2	yes	maximal, complemented
12	#22622859	C₂	1	1	yes	maximal, characteristic, complemented
13	#22622858	C₂	1	2	yes	maximal, complemented
14	#501×D₇₃	C₂	1	2	yes	maximal
15	#498×D₇₃	C₂	1	1	yes	maximal, characteristic
16	#479×D₇₃	C₂	1	2	yes	maximal
17	#477×D₇₃	C₂	1	1	yes	maximal, characteristic
18	#475×D₇₃	C₂	1	2	yes	maximal
19	#475×D₇₃	C₂	1	1	yes	maximal, characteristic
20	#446×D₇₃	C₂	1	1	yes	maximal, characteristic
21	#441×D₇₃	C₂	1	2	yes	maximal
22	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3387	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₄₆	—	2	1	no	—
26	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
27	Q₈×Dic₁₄₆	C₂²	1	2	yes	—
28	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
29	#17989317	—	2	2	no	—
30	#17989317	—	2	1	no	—
31	#17989317	C₂²	1	2	yes	—
32	#17989317	C₂²	1	1	yes	characteristic
33	#17989316	C₂²	1	1	yes	characteristic
34	#17989315	—	2	1	no	—
35	#17989315	C₂²	1	1	yes	characteristic
36	#17989314	—	2	2	no	—
37	#17989314	C₂²	1	2	yes	—
38	#17989313	C₂²	1	2	yes	—
39	#17989312	—	2	1	no	—
40	#17989312	C₂²	1	1	yes	characteristic
41	C₄⋊Q₈×D₇₃	—	2	1	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	#125×D₇₃	—	2	2	no	—
48	#125×D₇₃	C₂²	1	2	yes	—
49	C₄×Q₈×D₇₃	—	2	1	no	—
50	C₄×Q₈×D₇₃	—	2	1	no	—
51	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
52	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
53	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
54	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
55	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
56	#17988997	C₂²	1	2	yes	—
57	#17988996	C₂²	1	2	yes	—
58	#17988995	C₂²	1	2	yes	—
59	#17988995	C₂²	1	2	yes	—
60	#17988994	C₂²	1	2	yes	—
61	#17988994	C₂²	1	2	yes	—
62	#17988993	C₂²	1	2	yes	—
63	#17988985	C₂²	1	1	yes	characteristic
64	#17988984	C₂²	1	2	yes	—
65	#17988984	C₂²	1	2	yes	—
66	#17988983	C₂²	1	1	yes	characteristic
67	#17988983	C₂²	1	1	yes	characteristic
68	#17988897	C₂²	1	2	yes	—
69	#17988896	C₂²	1	2	yes	—
70	#17988895	C₂²	1	2	yes	—
71	#17988894	C₂²	1	2	yes	—
72	#17988893	C₂²	1	2	yes	—
73	#17988892	C₂²	1	2	yes	—
74	#17988891	C₂²	1	2	yes	—
75	#17988883	C₂²	1	1	yes	characteristic
76	#17988882	C₂²	1	1	yes	characteristic
77	#17988881	C₂²	1	2	yes	—
78	#17988880	C₂²	1	2	yes	—
79	#17988879	C₂²	1	1	yes	characteristic
80	#17988873	C₂²	1	2	yes	—
81	#17988873	C₂²	1	1	yes	characteristic
82	#17988872	C₂²	1	1	yes	characteristic
83	#17988872	C₂²	1	2	yes	—
84	#17988871	C₂²	1	2	yes	—
85	#17988871	C₂²	1	2	yes	—
86	#17988871	C₂²	1	2	yes	—
87	#17988870	C₂²	1	2	yes	—
88	#17988870	C₂²	1	2	yes	—
89	#17988870	C₂²	1	2	yes	—
90	#17988869	C₂²	1	2	yes	—
91	#17988869	C₂²	1	1	yes	characteristic
92	#17988718	C₂²	1	1	yes	characteristic
93	#17988717	C₂²	1	1	yes	characteristic
94	#17988716	C₂²	1	2	yes	—
95	#17988715	C₂²	1	2	yes	—
96	#17988714	C₂²	1	1	yes	characteristic
97	#17988695	C₂²	1	2	yes	—
98	#17988694	C₂²	1	2	yes	—
99	#17988693	C₂²	1	2	yes	—
100	#17988692	C₂²	1	2	yes	—
101	#17988692	C₂²	1	2	yes	—
102	#17988691	C₂²	1	2	yes	—
103	#17988691	C₂²	1	2	yes	—
104	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic
105	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
106	#17988681	C₂²	1	1	yes	characteristic
107	C₄×#11924018	C₂²	1	1	yes	characteristic
108	C₄×#11924018	C₂²	1	1	yes	characteristic
109	#17988679	C₂²	1	1	yes	characteristic
110	#17988679	C₂²	1	1	yes	characteristic
111	#107×D₇₃	C₂²	1	1	yes	characteristic
112	#107×D₇₃	C₂²	1	2	yes	—
113	#106×D₇₃	C₂²	1	2	yes	—
114	#106×D₇₃	C₂²	1	2	yes	—
115	#106×D₇₃	C₂²	1	2	yes	—
116	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
117	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
118	#103×D₇₃	C₂²	1	1	yes	characteristic
119	#103×D₇₃	C₂²	1	2	yes	—
120	#103×D₇₃	C₂²	1	2	yes	—
121	#103×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
125	#557×C₇₃	C₂²	1	1	yes	characteristic
126	#501×C₇₃	C₂²	1	2	yes	—
127	#498×C₇₃	C₂²	1	1	yes	characteristic
128	#479×C₇₃	C₂²	1	2	yes	—
129	#477×C₇₃	C₂²	1	1	yes	characteristic
130	#475×C₇₃	C₂²	1	2	yes	—
131	#475×C₇₃	C₂²	1	1	yes	characteristic
132	#446×C₇₃	C₂²	1	1	yes	characteristic
133	#441×C₇₃	C₂²	1	2	yes	—
134	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₇₃	—	2	1	no	—
136	C₂×Q₈×D₇₃	—	2	2	no	—
137	C₂×Q₈×D₇₃	—	2	1	no	—
138	C₂×Q₈×D₇₃	D₄	1	1	yes	characteristic
139	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
140	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
141	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
142	C₂×#11924018	C₂³	1	1	yes	characteristic
143	C₂×#11924018	C₂³	1	1	yes	characteristic
144	Q₁₆×D₇₃	Q₈	1	8	yes	complemented
145	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₇₃	C₂³	1	2	yes	—
147	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
148	#14556591	—	2	1	no	—
149	#14556591	—	2	1	no	—
150	#14556591	—	2	2	no	—
151	#14556591	C₂³	1	1	yes	characteristic
152	#14556591	C₂³	1	2	yes	—
153	#14556591	C₂³	1	1	yes	characteristic
154	#14556590	—	2	2	no	—
155	#14556590	—	2	2	no	—
156	#14556590	—	2	1	no	—
157	#14556590	—	2	2	no	—
158	#14556590	—	2	2	no	—
159	#14556590	—	2	2	no	—
160	#14556590	—	2	2	no	—
161	#14556590	—	2	1	no	—
162	#14556590	—	2	2	no	—
163	#14556590	—	2	1	no	—
164	#14556590	—	2	1	no	—
165	#14556590	—	2	2	no	—
166	#14556590	C₂³	1	2	yes	—
167	#14556590	C₂³	1	2	yes	—
168	#14556590	C₂³	1	2	yes	—
169	#14556590	C₂³	1	2	yes	—
170	#14556589	—	2	1	no	—
171	#14556589	—	2	2	no	—
172	#14556589	—	2	2	no	—
173	#14556589	—	2	2	no	—
174	#14556589	—	2	1	no	—
175	#14556589	—	2	1	no	—
176	#14556589	—	2	2	no	—
177	#14556589	—	2	1	no	—
178	#14556583	—	2	2	no	—
179	#14556583	C₂³	1	2	yes	—
180	#14556582	—	2	2	no	—
181	#14556582	—	2	2	no	—
182	#14556582	C₂³	1	2	yes	—
183	#14556582	C₂³	1	2	yes	—
184	#14556581	—	2	2	no	—
185	#14556581	—	2	2	no	—
186	#14556581	—	2	2	no	—
187	#14556581	—	2	2	no	—
188	#14556581	—	2	2	no	—
189	#14556581	—	2	2	no	—
190	Q₈×Dic₇₃	—	2	1	no	—
191	Q₈×Dic₇₃	—	2	1	no	—
192	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
193	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
194	Q₈×Dic₇₃	C₂³	1	2	yes	—
195	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
196	Q₈×Dic₇₃	C₂³	1	2	yes	—
197	C₄×Dic₁₄₆	—	2	1	no	—
198	C₄×Dic₁₄₆	—	2	2	no	—
199	C₄×Dic₁₄₆	—	2	1	no	—
200	C₄×Dic₁₄₆	—	2	2	no	—
201	C₄×Dic₁₄₆	—	2	1	no	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	C₄×Dic₁₄₆	—	2	2	no	—
204	C₄×Dic₁₄₆	—	2	1	no	—
205	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
206	C₄×Dic₁₄₆	C₂³	1	2	yes	—
207	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
208	C₄×Dic₁₄₆	C₂³	1	2	yes	—
209	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
210	C₄×Dic₁₄₆	C₂³	1	2	yes	—
211	#14556556	—	2	1	no	—
212	#14556556	—	2	2	no	—
213	#14556556	—	2	2	no	—
214	#14556556	—	2	2	no	—
215	#14556556	—	2	1	no	—
216	#14556556	—	2	1	no	—
217	#14556556	—	2	2	no	—
218	#14556556	—	2	1	no	—
219	#14556556	D₄	1	2	yes	—
220	#14556556	D₄	1	1	yes	characteristic
221	#14556556	C₂³	1	1	yes	characteristic
222	#14556556	C₂³	1	2	yes	—
223	#14556556	C₂³	1	1	yes	characteristic
224	#14556556	C₂³	1	2	yes	—
225	C₄⋊C₄×D₇₃	—	2	2	no	—
226	C₄⋊C₄×D₇₃	—	2	1	no	—
227	C₄⋊C₄×D₇₃	—	2	2	no	—
228	C₄⋊C₄×D₇₃	—	2	1	no	—
229	C₄⋊C₄×D₇₃	—	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	D₄	1	1	yes	characteristic
235	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
236	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
237	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
238	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
240	C₄²×D₇₃	—	2	1	no	—
241	C₄²×D₇₃	—	2	2	no	—
242	C₄²×D₇₃	—	2	1	no	—
243	C₄²×D₇₃	—	2	2	no	—
244	C₄²×D₇₃	C₂³	1	1	yes	characteristic
245	C₄²×D₇₃	C₂³	1	2	yes	—
246	#14556525	C₂³	1	2	yes	—
247	#14556525	C₂³	1	1	yes	characteristic
248	#14556524	C₂³	1	2	yes	—
249	#14556524	C₂³	1	2	yes	—
250	#14556524	C₂³	1	1	yes	characteristic
251	#14556524	C₂³	1	1	yes	characteristic
252	#14556523	C₂³	1	2	yes	—
253	#14556523	C₂³	1	2	yes	—
254	#14556523	C₂³	1	2	yes	—
255	#14556522	C₂³	1	2	yes	—
256	#14556522	C₂³	1	2	yes	—
257	#14556522	C₂³	1	2	yes	—
258	#14556522	C₂³	1	2	yes	—
259	#14556522	C₂³	1	2	yes	—
260	#14556522	C₂³	1	2	yes	—
261	C₄⋊#10596831	C₂³	1	1	yes	characteristic
262	C₄⋊#10596831	C₂³	1	2	yes	—
263	#14556520	C₂³	1	2	yes	—
264	#14556520	C₂³	1	2	yes	—
265	#14556520	C₂³	1	2	yes	—
266	#14556516	C₂³	1	1	yes	characteristic
267	#14556516	C₂³	1	2	yes	—
268	#14556516	C₂³	1	2	yes	—
269	#14556516	C₂³	1	1	yes	characteristic
270	#14556515	C₂³	1	1	yes	characteristic
271	#14556515	C₂³	1	2	yes	—
272	#14556515	C₂³	1	2	yes	—
273	#14556515	C₂³	1	1	yes	characteristic
274	#14556514	C₂³	1	1	yes	characteristic
275	#14556514	C₂³	1	2	yes	—
276	#14556514	C₂³	1	2	yes	—
277	#14556514	C₂³	1	1	yes	characteristic
278	#14556502	C₂³	1	2	yes	—
279	#14556501	C₂³	1	2	yes	—
280	#14556501	C₂³	1	2	yes	—
281	C₄×#10596831	C₂³	1	1	yes	characteristic
282	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
283	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
284	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₇₃	—	2	1	no	—
286	C₄⋊Q₈×C₇₃	—	2	1	no	—
287	C₄⋊Q₈×C₇₃	—	2	2	no	—
288	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
289	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
290	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
291	#125×C₇₃	—	2	2	no	—
292	#125×C₇₃	C₂³	1	2	yes	—
293	C₄×Q₈×C₇₃	—	2	1	no	—
294	C₄×Q₈×C₇₃	—	2	1	no	—
295	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
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	#107×C₇₃	C₂³	1	2	yes	—
301	#107×C₇₃	C₂³	1	1	yes	characteristic
302	#106×C₇₃	C₂³	1	2	yes	—
303	#106×C₇₃	C₂³	1	2	yes	—
304	#106×C₇₃	C₂³	1	2	yes	—
305	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
307	#103×C₇₃	C₂³	1	1	yes	characteristic
308	#103×C₇₃	C₂³	1	2	yes	—
309	#103×C₇₃	C₂³	1	2	yes	—
310	#103×C₇₃	C₂³	1	1	yes	characteristic
311	#97×C₇₃	C₂³	1	2	yes	—
312	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
313	C₂×Dic₁₄₆	—	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	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	1	yes	characteristic
323	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
324	C₂×Dic₁₄₆	C₂⁴	1	1	yes	characteristic
325	C₂×Dic₁₄₆	C₂⁴	1	1	yes	characteristic
326	Q₈×D₇₃	—	2	4	no	—
327	Q₈×D₇₃	—	2	2	no	—
328	Q₈×D₇₃	—	2	2	no	—
329	Q₈×D₇₃	—	4	4	no	—
330	Q₈×D₇₃	—	8	4	no	—
331	Q₈×D₇₃	—	8	2	no	—
332	Q₈×D₇₃	C₂×Q₈	1	4	yes	—
333	Q₈×D₇₃	C₂×Q₈	1	4	yes	—
334	C₂×C₄×D₇₃	—	2	1	no	—
335	C₂×C₄×D₇₃	—	2	1	no	—
336	C₂×C₄×D₇₃	—	2	1	no	—
337	C₂×C₄×D₇₃	—	2	2	no	—
338	C₂×C₄×D₇₃	—	2	2	no	—
339	C₂×C₄×D₇₃	—	2	1	no	—
340	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
341	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
342	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
344	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
345	Dic₂₉₂	C₂×Q₈	1	4	yes	complemented
346	#11924018	C₂×Q₈	1	4	yes	complemented
347	#11924018	C₂×Q₈	1	4	yes	complemented
348	C₂×#10596831	C₂⁴	1	1	yes	characteristic
349	C₂×#10596831	C₂⁴	1	2	yes	—
350	C₂×#10596831	C₂⁴	1	1	yes	characteristic
351	C₈×D₇₃	—	2	2	no	—
352	C₈×D₇₃	—	2	4	no	—
353	C₈×D₇₃	C₂×Q₈	1	4	yes	—
354	C₄⋊Dic₇₃	—	2	2	no	—
355	C₄⋊Dic₇₃	—	2	1	no	—
356	C₄⋊Dic₇₃	—	2	1	no	—
357	C₄⋊Dic₇₃	—	2	2	no	—
358	C₄⋊Dic₇₃	—	2	1	no	—
359	C₄⋊Dic₇₃	—	2	2	no	—
360	C₄⋊Dic₇₃	—	2	2	no	—
361	C₄⋊Dic₇₃	—	2	1	no	—
362	C₄⋊Dic₇₃	—	2	2	no	—
363	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
364	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
365	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
366	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
368	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
369	#11924007	—	2	2	no	—
370	#11924007	—	2	1	no	—
371	#11924007	—	2	2	no	—
372	#11924007	—	2	2	no	—
373	#11924007	—	2	1	no	—
374	#11924007	—	2	2	no	—
375	#11924007	—	2	2	no	—
376	#11924007	—	2	2	no	—
377	#11924007	—	2	2	no	—
378	#11924007	—	2	2	no	—
379	#11924007	—	2	1	no	—
380	#11924007	—	2	2	no	—
381	#11924007	—	2	2	no	—
382	#11924007	—	2	1	no	—
383	#11924007	—	2	2	no	—
384	#11924007	—	2	2	no	—
385	#11924007	—	2	1	no	—
386	#11924007	—	2	2	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	C₄×Dic₇₃	—	2	2	no	—
393	C₄×Dic₇₃	—	2	1	no	—
394	C₄×Dic₇₃	—	2	2	no	—
395	C₄×Dic₇₃	—	2	1	no	—
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	—	2	1	no	—
398	C₄×Dic₇₃	—	2	1	no	—
399	C₄×Dic₇₃	—	2	2	no	—
400	C₄×Dic₇₃	—	2	2	no	—
401	C₄×Dic₇₃	—	2	1	no	—
402	C₄×Dic₇₃	—	2	2	no	—
403	C₄×Dic₇₃	—	2	1	no	—
404	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
405	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
406	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
407	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
408	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
409	C₄×Dic₇₃	C₂⁴	1	2	yes	—
410	C₂×Q₈×C₇₃	—	2	1	no	—
411	C₂×Q₈×C₇₃	—	2	2	no	—
412	C₂×Q₈×C₇₃	—	2	1	no	—
413	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
414	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
415	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
416	Q₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
417	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
419	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₃	—	2	2	no	—
421	C₄⋊C₄×C₇₃	—	2	2	no	—
422	C₄⋊C₄×C₇₃	—	2	1	no	—
423	C₄⋊C₄×C₇₃	—	2	1	no	—
424	C₄⋊C₄×C₇₃	—	2	2	no	—
425	C₄⋊C₄×C₇₃	—	2	2	no	—
426	C₄⋊C₄×C₇₃	—	2	1	no	—
427	C₄⋊C₄×C₇₃	—	2	1	no	—
428	C₄⋊C₄×C₇₃	—	2	2	no	—
429	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
430	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
431	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
432	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
434	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₇₃	—	2	2	no	—
436	C₄²×C₇₃	—	2	1	no	—
437	C₄²×C₇₃	—	2	2	no	—
438	C₄²×C₇₃	—	2	1	no	—
439	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₄²×C₇₃	C₂⁴	1	2	yes	—
441	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₇₃	—	2	2	no	—
443	Q₈×C₇₃	—	2	1	no	—
444	Q₈×C₇₃	—	2	1	no	—
445	Q₈×C₇₃	—	4	2	no	—
446	Q₈×C₇₃	—	8	2	no	—
447	Q₈×C₇₃	—	8	1	no	—
448	Q₈×C₇₃	C₂²×Q₈	1	2	yes	—
449	Q₈×C₇₃	C₂²×Q₈	1	2	yes	—
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	—	2	2	no	—
455	C₂×C₄×C₇₃	—	2	1	no	—
456	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
457	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
458	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
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	1	no	—
464	C₂×Dic₇₃	—	2	2	no	—
465	C₂×Dic₇₃	—	2	2	no	—
466	C₂×Dic₇₃	—	2	1	no	—
467	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
468	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
469	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
472	C₄×D₇₃	—	2	4	no	—
473	C₄×D₇₃	—	2	4	no	—
474	C₄×D₇₃	—	2	4	no	—
475	C₄×D₇₃	—	2	4	no	—
476	C₄×D₇₃	—	2	2	no	—
477	C₄×D₇₃	—	4	4	no	—
478	C₄×D₇₃	—	4	2	no	—
479	C₄×D₇₃	—	4	4	no	—
480	C₄×D₇₃	—	4	2	no	—
481	C₄×D₇₃	#137	1	4	yes	—
482	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
483	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
484	Dic₁₄₆	—	2	2	no	—
485	Dic₁₄₆	—	2	1	no	—
486	Dic₁₄₆	—	2	1	no	—
487	Dic₁₄₆	—	2	4	no	—
488	Dic₁₄₆	—	2	4	no	—
489	Dic₁₄₆	—	2	4	no	—
490	Dic₁₄₆	—	4	2	no	—
491	Dic₁₄₆	—	4	4	no	—
492	Dic₁₄₆	—	8	2	no	—
493	Dic₁₄₆	—	8	2	no	—
494	Dic₁₄₆	—	8	2	no	—
495	Dic₁₄₆	—	8	2	no	—
496	Dic₁₄₆	—	8	1	no	—
497	Dic₁₄₆	C₂²×Q₈	1	2	yes	—
498	Dic₁₄₆	C₂²×Q₈	1	2	yes	—
499	C₈×C₇₃	—	2	1	no	—
500	C₈×C₇₃	—	2	2	no	—
501	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
502	#10596831	—	2	1	no	—
503	#10596831	—	2	2	no	—
504	#10596831	C₂²×Q₈	1	2	yes	—
505	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
506	C₂×D₇₃	D₄×Q₈	1	2	yes	—
507	C₂×D₇₃	C₂×#137	1	2	yes	—
508	C₂×D₇₃	#577	1	2	yes	—
509	C₄×C₇₃	—	2	2	no	—
510	C₄×C₇₃	—	2	2	no	—
511	C₄×C₇₃	—	2	2	no	—
512	C₄×C₇₃	—	2	2	no	—
513	C₄×C₇₃	—	2	1	no	—
514	C₄×C₇₃	—	4	2	no	—
515	C₄×C₇₃	—	4	1	no	—
516	C₄×C₇₃	—	4	2	no	—
517	C₄×C₇₃	—	4	1	no	—
518	C₄×C₇₃	C₂×#137	1	2	yes	—
519	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
520	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	Dic₇₃	—	2	2	no	—
522	Dic₇₃	—	2	2	no	—
523	Dic₇₃	—	2	2	no	—
524	Dic₇₃	—	2	2	no	—
525	Dic₇₃	—	2	1	no	—
526	Dic₇₃	—	4	2	no	—
527	Dic₇₃	—	4	1	no	—
528	Dic₇₃	—	4	2	no	—
529	Dic₇₃	—	4	1	no	—
530	Dic₇₃	D₄×Q₈	1	2	yes	—
531	Dic₇₃	C₂×#137	1	2	yes	—
532	C₂×#3387	—	73	1	no	maximal, Sylow
533	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
534	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
535	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
536	D₇₃	#3387	1	4	yes	direct product factor
537	C₂×Q₈²	—	73	1	no	—
538	C₂×#557	—	73	1	no	—
539	#3387	—	73	2	no	—
540	#3387	—	73	1	no	—
541	#3387	—	73	2	no	—
542	#3387	—	73	1	no	—
543	#3387	—	73	2	no	—
544	#3387	—	73	1	no	—
545	#3387	—	73	1	no	—
546	#3387	—	73	2	no	—
547	#3387	—	73	1	no	—
548	#3387	—	73	1	no	—
549	#3387	—	73	1	no	—
550	#3387	D₇₃	1	1	yes	characteristic, direct product factor
551	C₂×#501	—	73	2	no	—
552	C₂×#498	—	73	1	no	—
553	C₂×#479	—	73	2	no	—
554	C₂×#477	—	73	1	no	—
555	C₂×#475	—	73	1	no	—
556	C₂×#475	—	73	2	no	—
557	C₂×#446	—	73	1	no	—
558	C₂×#441	—	73	2	no	—
559	C₂×C₄×Q₁₆	—	73	1	no	—
560	C₇₃	C₂×#3387	1	1	yes	characteristic, complemented, Sylow
561	C₂²×Q₁₆	—	73	1	no	—
562	Q₈²	—	73	2	no	—
563	Q₈²	—	73	1	no	—
564	Q₈²	—	73	2	no	—
565	Q₈²	—	73	1	no	—
566	Q₈²	—	73	1	no	—
567	Q₈²	—	146	1	no	—
568	Q₈²	—	146	2	no	—
569	Q₈²	—	146	1	no	—
570	Q₈²	C₂×D₇₃	1	1	yes	characteristic
571	#557	—	73	1	no	—
572	#557	—	73	2	no	—
573	#557	—	73	2	no	—
574	#557	—	73	1	no	—
575	#557	—	73	1	no	—
576	#557	—	146	1	no	—
577	#557	—	146	2	no	—
578	#557	—	146	1	no	—
579	#557	C₂×D₇₃	1	1	yes	characteristic
580	C₂×C₄⋊Q₈	—	73	1	no	—
581	C₂×C₄⋊Q₈	—	73	2	no	—
582	C₂×C₄⋊Q₈	—	73	1	no	—
583	C₂×C₄⋊Q₈	—	146	1	no	—
584	C₂×C₄⋊Q₈	—	146	2	no	—
585	C₂×C₄⋊Q₈	—	146	1	no	—
586	C₂×#125	—	73	2	no	—
587	C₂×#125	—	146	2	no	—
588	C₂×C₄×Q₈	—	73	1	no	—
589	C₂×C₄×Q₈	—	73	1	no	—
590	C₂×C₄×Q₈	—	73	2	no	—
591	C₂×C₄×Q₈	—	73	1	no	—
592	C₂×C₄×Q₈	—	73	2	no	—
593	C₂×C₄×Q₈	—	146	1	no	—
594	C₂×C₄×Q₈	—	146	1	no	—
595	#501	—	73	2	no	—
596	#501	—	73	2	no	—
597	#501	—	73	2	no	—
598	#501	—	73	2	no	—
599	#501	—	73	2	no	—
600	#501	—	73	2	no	—
601	#501	—	73	2	no	—
602	#501	C₂×D₇₃	1	2	yes	—
603	#498	—	73	1	no	—
604	#498	—	73	1	no	—
605	#498	—	73	2	no	—
606	#498	—	73	2	no	—
607	#498	—	73	1	no	—
608	#498	C₂×D₇₃	1	1	yes	characteristic
609	#479	—	73	2	no	—
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	#479	C₂×D₇₃	1	2	yes	—
617	#477	—	73	1	no	—
618	#477	—	73	1	no	—
619	#477	—	73	2	no	—
620	#477	—	73	1	no	—
621	#477	—	73	2	no	—
622	#477	C₂×D₇₃	1	1	yes	characteristic
623	#475	—	73	2	no	—
624	#475	—	73	1	no	—
625	#475	—	73	2	no	—
626	#475	—	73	1	no	—
627	#475	—	73	2	no	—
628	#475	—	73	2	no	—
629	#475	—	73	2	no	—
630	#475	—	73	2	no	—
631	#475	—	73	1	no	—
632	#475	—	73	2	no	—
633	#475	—	73	2	no	—
634	#475	—	73	2	no	—
635	#475	C₂×D₇₃	1	2	yes	—
636	#475	C₂×D₇₃	1	1	yes	characteristic
637	#446	—	73	1	no	—
638	#446	—	73	1	no	—
639	#446	—	73	2	no	—
640	#446	—	73	2	no	—
641	#446	—	73	1	no	—
642	#446	C₂×D₇₃	1	1	yes	characteristic
643	#441	—	73	2	no	—
644	#441	—	73	2	no	—
645	#441	—	73	2	no	—
646	#441	—	73	2	no	—
647	#441	—	73	2	no	—
648	#441	—	73	2	no	—
649	#441	—	73	2	no	—
650	#441	C₂×D₇₃	1	2	yes	—
651	C₄×Q₁₆	—	73	1	no	—
652	C₄×Q₁₆	—	73	1	no	—
653	C₄×Q₁₆	—	73	1	no	—
654	C₄×Q₁₆	—	73	1	no	—
655	C₄×Q₁₆	—	73	1	no	—
656	C₄×Q₁₆	—	73	1	no	—
657	C₄×Q₁₆	—	73	1	no	—
658	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
659	C₂×#107	—	73	2	no	—
660	C₂×#107	—	73	1	no	—
661	C₂×#106	—	73	2	no	—
662	C₂×#106	—	73	2	no	—
663	C₂×#106	—	73	2	no	—
664	C₂×C₄⋊C₈	—	73	1	no	—
665	C₂×C₄⋊C₈	—	73	2	no	—
666	C₂×#103	—	73	1	no	—
667	C₂×#103	—	73	2	no	—
668	C₂×#103	—	73	2	no	—
669	C₂×#103	—	73	1	no	—
670	C₂×#97	—	73	2	no	—
671	C₂×C₄×C₈	—	73	1	no	—
672	C₂²×Q₈	—	73	1	no	—
673	C₂²×Q₈	—	73	1	no	—
674	C₂²×Q₈	—	73	1	no	—
675	C₂²×Q₈	—	146	1	no	—
676	C₂²×Q₈	—	146	2	no	—
677	C₂²×Q₈	—	146	1	no	—
678	C₂×Q₁₆	—	73	1	no	—
679	C₂×Q₁₆	—	73	1	no	—
680	C₂×Q₁₆	—	73	8	no	—
681	C₂×Q₁₆	—	73	1	no	—
682	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
683	C₂²×C₈	—	73	1	no	—
684	C₂²×C₈	—	73	1	no	—
685	C₂²×C₈	—	73	2	no	—
686	C₄⋊Q₈	—	2	1	no	—
687	C₄⋊Q₈	—	2	1	no	—
688	C₄⋊Q₈	—	2	2	no	—
689	C₄⋊Q₈	—	73	2	no	—
690	C₄⋊Q₈	—	73	2	no	—
691	C₄⋊Q₈	—	73	2	no	—
692	C₄⋊Q₈	—	73	2	no	—
693	C₄⋊Q₈	—	73	1	no	—
694	C₄⋊Q₈	—	73	2	no	—
695	C₄⋊Q₈	—	73	1	no	—
696	C₄⋊Q₈	—	146	1	no	—
697	C₄⋊Q₈	—	146	2	no	—
698	C₄⋊Q₈	—	146	1	no	—
699	C₄⋊Q₈	—	146	1	no	—
700	C₄⋊Q₈	—	146	2	no	—
701	C₄⋊Q₈	—	146	1	no	—
702	C₄⋊Q₈	—	146	1	no	—
703	C₄⋊Q₈	—	146	2	no	—
704	C₄⋊Q₈	—	146	1	no	—
705	C₄⋊Q₈	—	146	2	no	—
706	C₄⋊Q₈	—	146	2	no	—
707	C₄⋊Q₈	—	146	2	no	—
708	C₄⋊Q₈	—	146	1	no	—
709	C₄⋊Q₈	—	146	2	no	—
710	C₄⋊Q₈	—	146	2	no	—
711	C₄⋊Q₈	—	146	2	no	—
712	C₄⋊Q₈	—	146	2	no	—
713	C₄⋊Q₈	—	146	2	no	—
714	C₄⋊Q₈	—	146	2	no	—
715	C₄⋊Q₈	—	146	1	no	—
716	C₄⋊Q₈	—	146	1	no	—
717	C₄⋊Q₈	—	146	1	no	—
718	C₄⋊Q₈	—	146	2	no	—
719	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
720	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
721	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
722	#125	—	2	2	no	—
723	#125	—	73	2	no	—
724	#125	—	73	2	no	—
725	#125	—	73	2	no	—
726	#125	—	146	2	no	—
727	#125	—	146	2	no	—
728	#125	—	146	2	no	—
729	#125	—	146	2	no	—
730	#125	—	146	2	no	—
731	#125	—	146	2	no	—
732	#125	—	146	2	no	—
733	#125	—	146	2	no	—
734	#125	—	146	2	no	—
735	#125	C₂²×D₇₃	1	2	yes	—
736	C₄×Q₈	—	2	1	no	—
737	C₄×Q₈	—	2	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	1	no	—
743	C₄×Q₈	—	73	1	no	—
744	C₄×Q₈	—	73	2	no	—
745	C₄×Q₈	—	73	1	no	—
746	C₄×Q₈	—	73	2	no	—
747	C₄×Q₈	—	73	1	no	—
748	C₄×Q₈	—	73	2	no	—
749	C₄×Q₈	—	73	1	no	—
750	C₄×Q₈	—	73	2	no	—
751	C₄×Q₈	—	73	1	no	—
752	C₄×Q₈	—	73	2	no	—
753	C₄×Q₈	—	73	1	no	—
754	C₄×Q₈	—	73	2	no	—
755	C₄×Q₈	—	146	2	no	—
756	C₄×Q₈	—	146	1	no	—
757	C₄×Q₈	—	146	2	no	—
758	C₄×Q₈	—	146	1	no	—
759	C₄×Q₈	—	146	2	no	—
760	C₄×Q₈	—	146	1	no	—
761	C₄×Q₈	—	146	2	no	—
762	C₄×Q₈	—	146	1	no	—
763	C₄×Q₈	—	146	2	no	—
764	C₄×Q₈	—	146	1	no	—
765	C₄×Q₈	—	146	2	no	—
766	C₄×Q₈	—	146	1	no	—
767	C₄×Q₈	—	146	2	no	—
768	C₄×Q₈	—	146	2	no	—
769	C₄×Q₈	—	146	1	no	—
770	C₄×Q₈	—	146	1	no	—
771	C₄×Q₈	—	146	1	no	—
772	C₄×Q₈	—	146	1	no	—
773	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
774	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
775	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
776	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
777	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
778	C₂×C₄⋊C₄	—	73	1	no	—
779	C₂×C₄⋊C₄	—	73	2	no	—
780	C₂×C₄⋊C₄	—	73	1	no	—
781	C₂×C₄⋊C₄	—	73	2	no	—
782	C₂×C₄⋊C₄	—	73	1	no	—
783	C₂×C₄⋊C₄	—	73	2	no	—
784	C₂×C₄⋊C₄	—	146	1	no	—
785	C₂×C₄⋊C₄	—	146	2	no	—
786	C₂×C₄⋊C₄	—	146	2	no	—
787	C₂×C₄⋊C₄	—	146	1	no	—
788	C₂×C₄⋊C₄	—	146	2	no	—
789	C₂×C₄⋊C₄	—	146	1	no	—
790	C₂×C₄⋊C₄	—	146	2	no	—
791	C₂×C₄⋊C₄	—	146	2	no	—
792	C₂×C₄⋊C₄	—	146	1	no	—
793	C₂×C₄²	—	73	2	no	—
794	C₂×C₄²	—	73	1	no	—
795	C₂×C₄²	—	146	2	no	—
796	C₂×C₄²	—	146	1	no	—
797	C₂×C₄²	—	146	1	no	—
798	C₂×C₄²	—	146	2	no	—
799	#107	—	73	1	no	—
800	#107	—	73	2	no	—
801	#107	—	73	1	no	—
802	#107	—	73	1	no	—
803	#107	—	73	2	no	—
804	#107	—	73	2	no	—
805	#107	C₂²×D₇₃	1	1	yes	characteristic
806	#107	C₂²×D₇₃	1	2	yes	—
807	#106	—	73	2	no	—
808	#106	—	73	2	no	—
809	#106	—	73	2	no	—
810	#106	—	73	2	no	—
811	#106	—	73	2	no	—
812	#106	—	73	2	no	—
813	#106	—	73	2	no	—
814	#106	—	73	2	no	—
815	#106	—	73	2	no	—
816	#106	C₂²×D₇₃	1	2	yes	—
817	#106	C₂²×D₇₃	1	2	yes	—
818	#106	C₂²×D₇₃	1	2	yes	—
819	C₄⋊C₈	—	73	2	no	—
820	C₄⋊C₈	—	73	2	no	—
821	C₄⋊C₈	—	73	2	no	—
822	C₄⋊C₈	—	73	1	no	—
823	C₄⋊C₈	—	73	2	no	—
824	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
825	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
826	#103	—	73	1	no	—
827	#103	—	73	1	no	—
828	#103	—	73	2	no	—
829	#103	—	73	2	no	—
830	#103	—	73	1	no	—
831	#103	—	73	1	no	—
832	#103	—	73	2	no	—
833	#103	—	73	2	no	—
834	#103	—	73	1	no	—
835	#103	—	73	1	no	—
836	#103	—	73	2	no	—
837	#103	—	73	2	no	—
838	#103	C₂²×D₇₃	1	1	yes	characteristic
839	#103	C₂²×D₇₃	1	1	yes	characteristic
840	#103	C₂²×D₇₃	1	2	yes	—
841	#103	C₂²×D₇₃	1	2	yes	—
842	#97	—	73	2	no	—
843	#97	—	73	2	no	—
844	#97	—	73	2	no	—
845	#97	C₂²×D₇₃	1	2	yes	—
846	C₄×C₈	—	73	1	no	—
847	C₄×C₈	—	73	1	no	—
848	C₄×C₈	—	73	1	no	—
849	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
850	C₂×Q₈	—	2	1	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	1	no	—
853	C₂×Q₈	—	292	4	no	—
854	C₂×Q₈	—	584	4	no	—
855	C₂×Q₈	—	584	2	no	—
856	C₂×Q₈	—	73	2	no	—
857	C₂×Q₈	—	73	1	no	—
858	C₂×Q₈	—	73	4	no	—
859	C₂×Q₈	—	73	4	no	—
860	C₂×Q₈	—	73	1	no	—
861	C₂×Q₈	—	73	1	no	—
862	C₂×Q₈	—	146	2	no	—
863	C₂×Q₈	—	146	2	no	—
864	C₂×Q₈	—	146	2	no	—
865	C₂×Q₈	—	146	2	no	—
866	C₂×Q₈	—	146	1	no	—
867	C₂×Q₈	—	146	1	no	—
868	C₂×Q₈	—	146	4	no	—
869	C₂×Q₈	—	146	2	no	—
870	C₂×Q₈	—	146	2	no	—
871	C₂×Q₈	—	146	1	no	—
872	C₂×Q₈	—	146	2	no	—
873	C₂×Q₈	—	146	1	no	—
874	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
875	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
876	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
877	C₂²×C₄	—	73	1	no	—
878	C₂²×C₄	—	73	1	no	—
879	C₂²×C₄	—	73	2	no	—
880	C₂²×C₄	—	73	2	no	—
881	C₂²×C₄	—	73	1	no	—
882	C₂²×C₄	—	146	1	no	—
883	C₂²×C₄	—	146	2	no	—
884	C₂²×C₄	—	146	1	no	—
885	C₂²×C₄	—	146	2	no	—
886	C₂²×C₄	—	146	1	no	—
887	C₂²×C₄	—	146	1	no	—
888	Q₁₆	—	73	4	no	—
889	Q₁₆	—	73	4	no	—
890	Q₁₆	—	73	4	no	—
891	Q₁₆	Q₈×D₇₃	1	4	yes	complemented
892	C₂×C₈	—	73	1	no	—
893	C₂×C₈	—	73	4	no	—
894	C₂×C₈	—	73	1	no	—
895	C₂×C₈	—	73	2	no	—
896	C₂×C₈	—	146	2	no	—
897	C₂×C₈	—	146	4	no	—
898	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
899	C₂×C₈	C₂³×D₇₃	1	2	yes	—
900	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	73	2	no	—
911	C₄⋊C₄	—	73	2	no	—
912	C₄⋊C₄	—	73	2	no	—
913	C₄⋊C₄	—	73	1	no	—
914	C₄⋊C₄	—	73	2	no	—
915	C₄⋊C₄	—	73	2	no	—
916	C₄⋊C₄	—	73	1	no	—
917	C₄⋊C₄	—	73	2	no	—
918	C₄⋊C₄	—	73	1	no	—
919	C₄⋊C₄	—	146	1	no	—
920	C₄⋊C₄	—	146	2	no	—
921	C₄⋊C₄	—	146	1	no	—
922	C₄⋊C₄	—	146	2	no	—
923	C₄⋊C₄	—	146	1	no	—
924	C₄⋊C₄	—	146	2	no	—
925	C₄⋊C₄	—	146	2	no	—
926	C₄⋊C₄	—	146	1	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	2	no	—
929	C₄⋊C₄	—	146	2	no	—
930	C₄⋊C₄	—	146	2	no	—
931	C₄⋊C₄	—	146	2	no	—
932	C₄⋊C₄	—	146	2	no	—
933	C₄⋊C₄	—	146	1	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	—	146	2	no	—
939	C₄⋊C₄	—	146	1	no	—
940	C₄⋊C₄	—	146	2	no	—
941	C₄⋊C₄	—	146	2	no	—
942	C₄⋊C₄	—	146	1	no	—
943	C₄⋊C₄	—	146	2	no	—
944	C₄⋊C₄	—	146	2	no	—
945	C₄⋊C₄	—	146	2	no	—
946	C₄⋊C₄	—	146	1	no	—
947	C₄⋊C₄	—	146	1	no	—
948	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
949	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
950	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
951	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
953	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
954	C₄²	—	2	2	no	—
955	C₄²	—	2	1	no	—
956	C₄²	—	2	2	no	—
957	C₄²	—	2	1	no	—
958	C₄²	—	73	2	no	—
959	C₄²	—	73	2	no	—
960	C₄²	—	73	1	no	—
961	C₄²	—	73	1	no	—
962	C₄²	—	73	1	no	—
963	C₄²	—	73	2	no	—
964	C₄²	—	146	2	no	—
965	C₄²	—	146	2	no	—
966	C₄²	—	146	1	no	—
967	C₄²	—	146	1	no	—
968	C₄²	—	146	2	no	—
969	C₄²	—	146	1	no	—
970	C₄²	—	146	1	no	—
971	C₄²	—	146	2	no	—
972	C₄²	—	146	2	no	—
973	C₄²	—	146	1	no	—
974	C₄²	—	146	2	no	—
975	C₄²	—	146	1	no	—
976	C₄²	C₂³×D₇₃	1	1	yes	characteristic
977	C₄²	C₂³×D₇₃	1	2	yes	—
978	C₂³	—	73	1	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	4	2	no	—
983	Q₈	—	8	2	no	—
984	Q₈	—	8	1	no	—
985	Q₈	—	292	4	no	—
986	Q₈	—	292	2	no	—
987	Q₈	—	584	2	no	—
988	Q₈	—	584	1	no	—
989	Q₈	—	584	2	no	—
990	Q₈	—	584	2	no	—
991	Q₈	—	584	2	no	—
992	Q₈	—	73	2	no	—
993	Q₈	—	73	2	no	—
994	Q₈	—	146	4	no	—
995	Q₈	—	146	4	no	—
996	Q₈	—	146	4	no	—
997	Q₈	—	146	2	no	—
998	Q₈	—	146	1	no	—
999	Q₈	—	146	1	no	—
1000	Q₈	C₂×Q₈×D₇₃	1	2	yes	—
1001	Q₈	C₂×Q₈×D₇₃	1	2	yes	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	292	4	no	—
1009	C₂×C₄	—	292	2	no	—
1010	C₂×C₄	—	292	4	no	—
1011	C₂×C₄	—	292	2	no	—
1012	C₂×C₄	—	73	1	no	—
1013	C₂×C₄	—	73	1	no	—
1014	C₂×C₄	—	73	4	no	—
1015	C₂×C₄	—	73	2	no	—
1016	C₂×C₄	—	73	2	no	—
1017	C₂×C₄	—	73	2	no	—
1018	C₂×C₄	—	73	2	no	—
1019	C₂×C₄	—	73	1	no	—
1020	C₂×C₄	—	146	4	no	—
1021	C₂×C₄	—	146	2	no	—
1022	C₂×C₄	—	146	4	no	—
1023	C₂×C₄	—	146	4	no	—
1024	C₂×C₄	—	146	4	no	—
1025	C₂×C₄	—	146	1	no	—
1026	C₂×C₄	—	146	2	no	—
1027	C₂×C₄	—	146	1	no	—
1028	C₂×C₄	—	146	2	no	—
1029	C₂×C₄	—	146	1	no	—
1030	C₂×C₄	—	146	1	no	—
1031	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1032	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1033	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1035	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1036	C₈	—	2	1	no	—
1037	C₈	—	2	2	no	—
1038	C₈	—	73	2	no	—
1039	C₈	—	146	1	no	—
1040	C₈	—	146	2	no	—
1041	C₈	C₂×Q₈×D₇₃	1	2	yes	—
1042	C₂²	—	73	2	no	—
1043	C₂²	—	73	2	no	—
1044	C₂²	—	73	2	no	—
1045	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1046	C₄	—	2	2	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	1	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	292	2	no	—
1056	C₄	—	292	1	no	—
1057	C₄	—	292	2	no	—
1058	C₄	—	292	1	no	—
1059	C₄	—	73	2	no	—
1060	C₄	—	73	2	no	—
1061	C₄	—	146	2	no	—
1062	C₄	—	146	2	no	—
1063	C₄	—	146	2	no	—
1064	C₄	—	146	2	no	—
1065	C₄	—	146	1	no	—
1066	C₄	#137×D₇₃	1	2	yes	—
1067	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
1068	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1069	C₂	—	73	4	no	—
1070	C₂	D₄×Q₈×D₇₃	1	1	yes	characteristic
1071	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1072	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×#3387	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂²×D₇₃	C₂²×D₄
hypercenter	#3387	D₇₃
hypocenter	C₇₃	C₂×#3387
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3387

Complements

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

N	H ≅ G/N	type
3. #22622868	C₂	semidirect
4. #22622867	C₂	semidirect
5. #22622866	C₂	semidirect
6. #22622865	C₂	semidirect
7. #22622864	C₂	semidirect
8. #22622863	C₂	semidirect
9. #22622862	C₂	semidirect
10. #22622861	C₂	semidirect
11. #22622860	C₂	semidirect
12. #22622859	C₂	semidirect
13. #22622858	C₂	semidirect
23. C₇₃×#3387	C₂	semidirect
144. Q₁₆×D₇₃	Q₈	semidirect
345. Dic₂₉₂	C₂×Q₈	semidirect
346. #11924018	C₂×Q₈	semidirect
347. #11924018	C₂×Q₈	semidirect
416. Q₁₆×C₇₃	C₂×Q₈	semidirect
536. D₇₃	#3387	direct (N × H)
550. #3387	D₇₃	direct (N × H)
560. C₇₃	C₂×#3387	semidirect
891. Q₁₆	Q₈×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
#557×D₇₃	2
#22622868	2
#22622867	2
#22622866	2
#22622865	2
#22622864	2
#22622863	2
#22622862	2
#22622861	2
#22622860	2
#22622859	2
#22622858	2
#501×D₇₃	2
#498×D₇₃	2
#479×D₇₃	2
#477×D₇₃	2
#475×D₇₃	2
#446×D₇₃	2
#441×D₇₃	2
C₄×Q₁₆×D₇₃	2
C₇₃×#3387	2
C₂×#3387	73

Subgroups — #3387×D73 #33966491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3387×D₇₃ #33966491