Subgroups — #3385×D₇₃ #33966467

Order 18688.

1854 conjugacy classes of subgroups.

The subgroup lattice has 1112 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	#554×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22622846	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622845	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622844	C₂	1	2	yes	maximal, complemented
6	#22622843	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622842	C₂	1	2	yes	maximal, complemented
8	#22622841	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622840	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622839	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622838	C₂	1	2	yes	maximal, complemented
12	#22622837	C₂	1	1	yes	maximal, characteristic, complemented
13	#22622836	C₂	1	2	yes	maximal, complemented
14	#501×D₇₃	C₂	1	2	yes	maximal, complemented
15	#500×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#479×D₇₃	C₂	1	2	yes	maximal, complemented
17	#477×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#476×D₇₃	C₂	1	1	yes	maximal, characteristic
19	#474×D₇₃	C₂	1	2	yes	maximal
20	#446×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#440×D₇₃	C₂	1	2	yes	maximal
22	C₄×SD₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₄₆	—	2	1	no	—
26	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
27	Q₈×Dic₁₄₆	C₂²	1	2	yes	complemented
28	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
29	#17989317	—	2	2	no	—
30	#17989317	—	2	1	no	—
31	#17989317	C₂²	1	2	yes	complemented
32	#17989317	C₂²	1	1	yes	characteristic, complemented
33	#17989298	C₂²	1	1	yes	characteristic
34	#17989297	C₂²	1	1	yes	characteristic
35	#17989296	C₂²	1	2	yes	—
36	#17989295	—	2	1	no	—
37	#17989294	C₂²	1	1	yes	characteristic
38	#17989293	C₂²	1	2	yes	—
39	#17989292	—	2	1	no	—
40	#17989291	—	2	2	no	—
41	C₄⋊Q₈×D₇₃	—	2	1	no	—
42	C₄⋊Q₈×D₇₃	—	2	2	no	—
43	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
44	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
45	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
46	#125×D₇₃	C₂²	1	2	yes	—
47	C₂²⋊Q₈×D₇₃	—	2	1	no	—
48	C₂²⋊Q₈×D₇₃	—	2	2	no	—
49	C₄×Q₈×D₇₃	—	2	1	no	—
50	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
51	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
52	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
53	C₄×D₄×D₇₃	C₂²	1	2	yes	—
54	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₇₃	—	2	1	no	—
56	#17988997	C₂²	1	2	yes	complemented
57	#17988996	C₂²	1	2	yes	complemented
58	#17988995	C₂²	1	2	yes	complemented
59	#17988995	C₂²	1	2	yes	complemented
60	#17988994	C₂²	1	2	yes	complemented
61	#17988994	C₂²	1	2	yes	complemented
62	#17988993	C₂²	1	2	yes	complemented
63	#17988992	C₂²	1	1	yes	characteristic, complemented
64	#17988991	C₂²	1	2	yes	complemented
65	#17988991	C₂²	1	2	yes	complemented
66	#17988990	C₂²	1	1	yes	characteristic, complemented
67	#17988990	C₂²	1	1	yes	characteristic, complemented
68	#17988897	C₂²	1	2	yes	complemented
69	#17988896	C₂²	1	2	yes	complemented
70	#17988895	C₂²	1	2	yes	complemented
71	#17988894	C₂²	1	2	yes	complemented
72	#17988893	C₂²	1	2	yes	complemented
73	#17988892	C₂²	1	2	yes	complemented
74	#17988891	C₂²	1	2	yes	complemented
75	#17988883	C₂²	1	1	yes	characteristic, complemented
76	#17988882	C₂²	1	1	yes	characteristic, complemented
77	#17988881	C₂²	1	2	yes	complemented
78	#17988880	C₂²	1	2	yes	complemented
79	#17988879	C₂²	1	1	yes	characteristic, complemented
80	#17988878	C₂²	1	1	yes	characteristic
81	#17988877	C₂²	1	1	yes	characteristic
82	#17988876	C₂²	1	2	yes	—
83	#17988875	C₂²	1	2	yes	—
84	#17988874	C₂²	1	1	yes	characteristic
85	#17988868	C₂²	1	2	yes	—
86	#17988867	C₂²	1	2	yes	—
87	#17988866	C₂²	1	2	yes	—
88	#17988866	C₂²	1	2	yes	—
89	#17988865	C₂²	1	2	yes	—
90	#17988865	C₂²	1	2	yes	—
91	#17988864	C₂²	1	2	yes	—
92	#17988718	C₂²	1	1	yes	characteristic, complemented
93	#17988717	C₂²	1	1	yes	characteristic, complemented
94	#17988716	C₂²	1	2	yes	complemented
95	#17988715	C₂²	1	2	yes	complemented
96	#17988714	C₂²	1	1	yes	characteristic, complemented
97	#17988690	C₂²	1	2	yes	—
98	#17988689	C₂²	1	2	yes	—
99	#17988688	C₂²	1	2	yes	—
100	#17988687	C₂²	1	2	yes	—
101	#17988686	C₂²	1	2	yes	—
102	#17988685	C₂²	1	2	yes	—
103	#17988684	C₂²	1	2	yes	—
104	#17988678	C₂²	1	1	yes	characteristic
105	C₄×#11924017	C₂²	1	1	yes	characteristic
106	SD₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
107	C₄×#11924015	C₂²	1	1	yes	characteristic
108	#17988674	C₂²	1	1	yes	characteristic
109	C₄×#11924016	C₂²	1	1	yes	characteristic
110	#17988672	C₂²	1	1	yes	characteristic
111	#107×D₇₃	C₂²	1	2	yes	—
112	#107×D₇₃	C₂²	1	2	yes	—
113	#107×D₇₃	C₂²	1	2	yes	—
114	#106×D₇₃	C₂²	1	2	yes	—
115	#106×D₇₃	C₂²	1	1	yes	characteristic
116	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
117	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
118	#103×D₇₃	C₂²	1	2	yes	—
119	#103×D₇₃	C₂²	1	1	yes	characteristic
120	#102×D₇₃	C₂²	1	1	yes	characteristic
121	#102×D₇₃	C₂²	1	2	yes	—
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	#554×C₇₃	C₂²	1	1	yes	characteristic
126	#501×C₇₃	C₂²	1	2	yes	complemented
127	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#479×C₇₃	C₂²	1	2	yes	complemented
129	#477×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#476×C₇₃	C₂²	1	1	yes	characteristic
131	#474×C₇₃	C₂²	1	2	yes	—
132	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#440×C₇₃	C₂²	1	2	yes	—
134	C₄×SD₁₆×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×D₄×D₇₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×D₇₃	—	2	1	no	—
142	C₂²×C₄×D₇₃	—	2	2	no	—
143	C₂×#11924017	C₂³	1	1	yes	characteristic
144	C₂×#11924016	C₂³	1	1	yes	characteristic
145	C₂×#11924015	C₂³	1	1	yes	characteristic
146	SD₁₆×D₇₃	Q₈	1	8	yes	complemented
147	C₂×C₈×D₇₃	C₂³	1	2	yes	—
148	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
150	#14556591	—	2	1	no	—
151	#14556591	—	2	2	no	—
152	#14556591	C₂³	1	2	yes	—
153	#14556591	C₂³	1	1	yes	characteristic
154	#14556591	C₂³	1	1	yes	characteristic
155	#14556590	—	2	1	no	—
156	#14556590	—	2	2	no	—
157	#14556590	—	2	2	no	—
158	#14556590	—	2	2	no	—
159	#14556590	—	2	2	no	—
160	#14556590	—	2	1	no	—
161	#14556590	—	2	2	no	—
162	#14556590	—	2	1	no	—
163	#14556590	—	2	1	no	—
164	#14556590	—	2	2	no	—
165	#14556590	C₂³	1	2	yes	—
166	#14556590	C₂³	1	2	yes	—
167	#14556590	C₂³	1	2	yes	—
168	#14556590	C₂³	1	2	yes	—
169	#14556589	—	2	2	no	—
170	#14556589	—	2	2	no	—
171	#14556589	—	2	2	no	—
172	#14556589	—	2	1	no	—
173	#14556589	—	2	1	no	—
174	#14556589	—	2	2	no	—
175	#14556583	C₂³	1	2	yes	—
176	#14556582	C₂³	1	2	yes	—
177	#14556582	C₂³	1	2	yes	—
178	#14556581	—	2	2	no	—
179	#14556581	—	2	2	no	—
180	#14556571	—	2	1	no	—
181	#14556571	—	2	2	no	—
182	#14556570	—	2	1	no	—
183	#14556570	—	2	2	no	—
184	#14556569	—	2	2	no	—
185	#14556569	—	2	2	no	—
186	#14556569	—	2	2	no	—
187	#14556568	—	2	2	no	—
188	#14556568	—	2	2	no	—
189	#14556568	—	2	2	no	—
190	#14556567	—	2	2	no	—
191	#14556567	—	2	1	no	—
192	Q₈×Dic₇₃	—	2	1	no	—
193	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
194	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
195	Q₈×Dic₇₃	C₂³	1	2	yes	—
196	C₄×Dic₁₄₆	—	2	2	no	—
197	C₄×Dic₁₄₆	—	2	1	no	—
198	C₄×Dic₁₄₆	—	2	2	no	—
199	C₄×Dic₁₄₆	—	2	1	no	—
200	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₄₆	C₂³	1	2	yes	—
202	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
203	C₄×Dic₁₄₆	C₂³	1	2	yes	—
204	#14556556	—	2	2	no	—
205	#14556556	—	2	1	no	—
206	#14556556	—	2	1	no	—
207	#14556556	—	2	2	no	—
208	#14556556	D₄	1	2	yes	—
209	#14556556	D₄	1	1	yes	characteristic
210	#14556556	C₂³	1	1	yes	characteristic
211	#14556556	C₂³	1	2	yes	—
212	C₄×D₂₉₂	C₂³	1	2	yes	—
213	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
214	D₄×Dic₇₃	C₂³	1	2	yes	—
215	D₄×Dic₇₃	C₂³	1	1	yes	characteristic
216	#14556553	C₂³	1	2	yes	—
217	#14556553	C₂³	1	1	yes	characteristic
218	C₄×C₂²⋊D₇₃	—	2	2	no	—
219	C₄×C₂²⋊D₇₃	—	2	1	no	—
220	#14556551	—	2	1	no	—
221	#14556551	—	2	2	no	—
222	C₂×C₄⋊Dic₇₃	—	2	1	no	—
223	C₂×#11924007	—	2	2	no	—
224	C₄⋊C₄×D₇₃	—	2	1	no	—
225	C₄⋊C₄×D₇₃	—	2	2	no	—
226	C₄⋊C₄×D₇₃	—	2	2	no	—
227	C₄⋊C₄×D₇₃	—	2	1	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	1	yes	characteristic
237	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
238	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
240	C₂²⋊C₄×D₇₃	—	2	1	no	—
241	C₂²⋊C₄×D₇₃	—	2	2	no	—
242	C₄²×D₇₃	—	2	2	no	—
243	C₄²×D₇₃	—	2	1	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	2	yes	—
248	#14556525	C₂³	1	2	yes	—
249	#14556524	C₂³	1	2	yes	—
250	#14556524	C₂³	1	2	yes	—
251	#14556524	C₂³	1	2	yes	—
252	#14556524	C₂³	1	2	yes	—
253	#14556524	C₂³	1	2	yes	—
254	#14556524	C₂³	1	2	yes	—
255	#14556523	C₂³	1	2	yes	—
256	#14556523	C₂³	1	1	yes	characteristic
257	#14556522	C₂³	1	2	yes	—
258	#14556522	C₂³	1	2	yes	—
259	#14556522	C₂³	1	1	yes	characteristic
260	#14556522	C₂³	1	1	yes	characteristic
261	C₄⋊#10596831	C₂³	1	2	yes	—
262	C₄⋊#10596831	C₂³	1	1	yes	characteristic
263	#14556520	C₂³	1	2	yes	—
264	#14556520	C₂³	1	2	yes	—
265	#14556520	C₂³	1	2	yes	—
266	#14556516	C₂³	1	2	yes	—
267	#14556516	C₂³	1	1	yes	characteristic
268	#14556515	C₂³	1	2	yes	—
269	#14556515	C₂³	1	1	yes	characteristic
270	#14556514	C₂³	1	2	yes	—
271	#14556514	C₂³	1	1	yes	characteristic
272	#14556513	C₂³	1	1	yes	characteristic
273	#14556513	C₂³	1	2	yes	—
274	#14556512	C₂³	1	1	yes	characteristic
275	#14556512	C₂³	1	2	yes	—
276	#14556511	C₂³	1	1	yes	characteristic
277	#14556511	C₂³	1	2	yes	—
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×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₇₃	—	2	1	no	—
286	C₄⋊Q₈×C₇₃	—	2	2	no	—
287	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
288	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
289	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
290	#125×C₇₃	C₂³	1	2	yes	—
291	C₂²⋊Q₈×C₇₃	—	2	1	no	—
292	C₂²⋊Q₈×C₇₃	—	2	2	no	—
293	C₄×Q₈×C₇₃	—	2	1	no	—
294	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
296	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₇₃	C₂³	1	2	yes	—
298	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
300	#107×C₇₃	C₂³	1	2	yes	—
301	#107×C₇₃	C₂³	1	2	yes	—
302	#107×C₇₃	C₂³	1	2	yes	—
303	#106×C₇₃	C₂³	1	2	yes	—
304	#106×C₇₃	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
306	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
307	#103×C₇₃	C₂³	1	2	yes	—
308	#103×C₇₃	C₂³	1	1	yes	characteristic
309	#102×C₇₃	C₂³	1	1	yes	characteristic
310	#102×C₇₃	C₂³	1	2	yes	—
311	#97×C₇₃	C₂³	1	2	yes	—
312	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
313	C₂³×D₇₃	—	2	1	no	—
314	C₂×Dic₁₄₆	—	2	1	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	—	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	1	yes	characteristic
325	Q₈×D₇₃	—	2	4	no	—
326	Q₈×D₇₃	—	2	2	no	—
327	Q₈×D₇₃	—	8	4	no	—
328	Q₈×D₇₃	—	8	2	no	—
329	Q₈×D₇₃	—	8	2	no	—
330	Q₈×D₇₃	C₂×Q₈	1	4	yes	—
331	C₂×D₂₉₂	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₇₃	—	2	1	no	—
333	D₄×D₇₃	—	2	2	no	—
334	D₄×D₇₃	C₂×Q₈	1	4	yes	—
335	C₂²×Dic₇₃	—	2	1	no	—
336	C₂²×Dic₇₃	—	2	2	no	—
337	C₂×C₄×D₇₃	—	2	1	no	—
338	C₂×C₄×D₇₃	—	2	2	no	—
339	C₂×C₄×D₇₃	—	2	1	no	—
340	C₂×C₄×D₇₃	—	2	1	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	2	no	—
345	C₂×C₄×D₇₃	—	2	2	no	—
346	C₂×C₄×D₇₃	—	4	4	no	—
347	C₂×C₄×D₇₃	—	8	4	no	—
348	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
349	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
350	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
351	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
352	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
353	#11924017	C₂×Q₈	1	4	yes	complemented
354	#11924016	C₂×Q₈	1	4	yes	complemented
355	#11924015	C₂×Q₈	1	4	yes	complemented
356	C₂×#10596831	C₂⁴	1	1	yes	characteristic
357	C₂×#10596831	C₂⁴	1	2	yes	—
358	C₂×#10596831	C₂⁴	1	1	yes	characteristic
359	C₈×D₇₃	—	2	4	no	—
360	C₈×D₇₃	—	2	2	no	—
361	C₈×D₇₃	C₂×Q₈	1	4	yes	—
362	C₄⋊Dic₇₃	—	2	1	no	—
363	C₄⋊Dic₇₃	—	2	2	no	—
364	C₄⋊Dic₇₃	—	2	1	no	—
365	C₄⋊Dic₇₃	—	2	2	no	—
366	C₄⋊Dic₇₃	—	2	1	no	—
367	C₄⋊Dic₇₃	—	2	2	no	—
368	C₄⋊Dic₇₃	—	2	2	no	—
369	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
370	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
371	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
372	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
373	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
374	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
375	#11924007	—	2	2	no	—
376	#11924007	—	2	1	no	—
377	#11924007	—	2	2	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	2	no	—
387	#11924007	—	2	1	no	—
388	#11924007	—	2	2	no	—
389	#11924007	—	2	2	no	—
390	#11924007	—	2	1	no	—
391	#11924007	C₂×D₄	1	2	yes	—
392	#11924007	C₂×D₄	1	2	yes	—
393	#11924007	C₂×D₄	1	2	yes	—
394	C₂²⋊Dic₇₃	—	2	1	no	—
395	C₂²⋊Dic₇₃	—	2	2	no	—
396	#11924005	—	2	1	no	—
397	#11924005	—	2	2	no	—
398	#11924005	—	2	2	no	—
399	#11924005	—	2	1	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	—	2	2	no	—
405	C₄×Dic₇₃	—	2	1	no	—
406	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
407	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
408	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
409	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
410	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
411	C₄×Dic₇₃	C₂⁴	1	2	yes	—
412	C₂×Q₈×C₇₃	—	2	1	no	—
413	C₂×Q₈×C₇₃	—	2	1	no	—
414	C₂×Q₈×C₇₃	—	2	2	no	—
415	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
416	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₂²×C₄×C₇₃	—	2	1	no	—
419	C₂²×C₄×C₇₃	—	2	2	no	—
420	SD₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
421	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
423	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₇₃	—	2	2	no	—
425	C₄⋊C₄×C₇₃	—	2	1	no	—
426	C₄⋊C₄×C₇₃	—	2	2	no	—
427	C₄⋊C₄×C₇₃	—	2	1	no	—
428	C₄⋊C₄×C₇₃	—	2	1	no	—
429	C₄⋊C₄×C₇₃	—	2	2	no	—
430	C₄⋊C₄×C₇₃	—	2	2	no	—
431	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
432	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
435	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
437	C₂²⋊C₄×C₇₃	—	2	1	no	—
438	C₂²⋊C₄×C₇₃	—	2	2	no	—
439	C₄²×C₇₃	—	2	2	no	—
440	C₄²×C₇₃	—	2	1	no	—
441	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₇₃	C₂⁴	1	2	yes	—
443	C₂³×C₇₃	—	2	1	no	—
444	C₂²×D₇₃	—	2	1	no	—
445	C₂²×D₇₃	—	2	4	no	—
446	C₂²×D₇₃	—	4	2	no	—
447	C₂²×D₇₃	—	4	2	no	—
448	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₇₃	—	2	2	no	—
450	Q₈×C₇₃	—	2	1	no	—
451	Q₈×C₇₃	—	8	1	no	—
452	Q₈×C₇₃	—	8	1	no	—
453	Q₈×C₇₃	—	8	2	no	—
454	Q₈×C₇₃	C₂²×Q₈	1	2	yes	—
455	D₄×C₇₃	—	2	1	no	—
456	D₄×C₇₃	C₂²×Q₈	1	2	yes	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	2	2	no	—
459	C₂×C₄×C₇₃	—	2	1	no	—
460	C₂×C₄×C₇₃	—	2	1	no	—
461	C₂×C₄×C₇₃	—	2	2	no	—
462	C₂×C₄×C₇₃	—	4	2	no	—
463	C₂×C₄×C₇₃	—	8	2	no	—
464	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
467	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₇₃	—	2	4	no	—
470	C₂×Dic₇₃	—	2	1	no	—
471	C₂×Dic₇₃	—	2	2	no	—
472	C₂×Dic₇₃	—	2	1	no	—
473	C₂×Dic₇₃	—	2	1	no	—
474	C₂×Dic₇₃	—	2	2	no	—
475	C₂×Dic₇₃	—	4	2	no	—
476	C₂×Dic₇₃	—	8	2	no	—
477	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
478	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
480	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
482	D₂₉₂	—	2	1	no	—
483	D₂₉₂	C₂²×Q₈	1	2	yes	—
484	C₄×D₇₃	—	2	4	no	—
485	C₄×D₇₃	—	2	4	no	—
486	C₄×D₇₃	—	2	4	no	—
487	C₄×D₇₃	—	2	2	no	—
488	C₄×D₇₃	—	4	2	no	—
489	C₄×D₇₃	—	4	4	no	—
490	C₄×D₇₃	—	4	2	no	—
491	C₄×D₇₃	—	4	4	no	—
492	C₄×D₇₃	—	4	2	no	—
493	C₄×D₇₃	—	4	2	no	—
494	C₄×D₇₃	—	8	2	no	—
495	C₄×D₇₃	—	8	2	no	—
496	C₄×D₇₃	#137	1	4	yes	—
497	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
498	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
499	Dic₁₄₆	—	2	2	no	—
500	Dic₁₄₆	—	2	1	no	—
501	Dic₁₄₆	—	2	4	no	—
502	Dic₁₄₆	—	2	4	no	—
503	Dic₁₄₆	—	8	2	no	—
504	Dic₁₄₆	—	8	2	no	—
505	Dic₁₄₆	—	8	2	no	—
506	Dic₁₄₆	—	8	2	no	—
507	Dic₁₄₆	—	8	1	no	—
508	Dic₁₄₆	—	8	2	no	—
509	Dic₁₄₆	—	8	1	no	—
510	Dic₁₄₆	C₂²×Q₈	1	2	yes	—
511	C₈×C₇₃	—	2	1	no	—
512	C₈×C₇₃	—	2	2	no	—
513	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
514	#10596831	—	2	1	no	—
515	#10596831	—	2	2	no	—
516	#10596831	C₂²×Q₈	1	2	yes	—
517	C₂²×C₇₃	—	2	2	no	—
518	C₂²×C₇₃	—	4	1	no	—
519	C₂²×C₇₃	—	4	1	no	—
520	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
521	C₂×D₇₃	—	2	2	no	—
522	C₂×D₇₃	—	4	1	no	—
523	C₂×D₇₃	—	4	1	no	—
524	C₂×D₇₃	—	4	8	no	—
525	C₂×D₇₃	D₄×Q₈	1	2	yes	—
526	C₂×D₇₃	C₂×#137	1	2	yes	—
527	C₂×D₇₃	#576	1	2	yes	—
528	C₄×C₇₃	—	2	2	no	—
529	C₄×C₇₃	—	2	2	no	—
530	C₄×C₇₃	—	2	1	no	—
531	C₄×C₇₃	—	2	2	no	—
532	C₄×C₇₃	—	4	1	no	—
533	C₄×C₇₃	—	4	2	no	—
534	C₄×C₇₃	—	4	1	no	—
535	C₄×C₇₃	—	4	2	no	—
536	C₄×C₇₃	C₂×#137	1	2	yes	—
537	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
538	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
539	Dic₇₃	—	2	2	no	—
540	Dic₇₃	—	2	2	no	—
541	Dic₇₃	—	2	1	no	—
542	Dic₇₃	—	2	2	no	—
543	Dic₇₃	—	4	1	no	—
544	Dic₇₃	—	4	2	no	—
545	Dic₇₃	—	4	1	no	—
546	Dic₇₃	—	4	2	no	—
547	Dic₇₃	D₄×Q₈	1	2	yes	—
548	Dic₇₃	C₂×#137	1	2	yes	—
549	C₂×#3385	—	73	1	no	maximal, Sylow
550	C₂×C₇₃	—	4	2	no	—
551	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
552	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
553	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
554	D₇₃	—	4	2	no	—
555	D₇₃	#3385	1	4	yes	direct product factor
556	C₂×Q₈²	—	73	1	no	—
557	C₂×#554	—	73	1	no	—
558	#3385	—	73	2	no	—
559	#3385	—	73	1	no	—
560	#3385	—	73	2	no	—
561	#3385	—	73	1	no	—
562	#3385	—	73	1	no	—
563	#3385	—	73	2	no	—
564	#3385	—	73	1	no	—
565	#3385	—	73	2	no	—
566	#3385	—	73	1	no	—
567	#3385	—	73	1	no	—
568	#3385	—	73	1	no	—
569	#3385	D₇₃	1	1	yes	characteristic, direct product factor
570	C₂×#501	—	73	2	no	—
571	C₂×#500	—	73	1	no	—
572	C₂×#479	—	73	2	no	—
573	C₂×#477	—	73	1	no	—
574	C₂×#476	—	73	1	no	—
575	C₂×#474	—	73	2	no	—
576	C₂×#446	—	73	1	no	—
577	C₂×#440	—	73	2	no	—
578	C₂×C₄×SD₁₆	—	73	1	no	—
579	C₇₃	C₂×#3385	1	1	yes	characteristic, complemented, Sylow
580	C₂²×SD₁₆	—	73	1	no	—
581	Q₈²	—	73	2	no	—
582	Q₈²	—	73	1	no	—
583	Q₈²	—	73	2	no	—
584	Q₈²	—	73	1	no	—
585	Q₈²	—	73	1	no	—
586	Q₈²	—	146	1	no	—
587	Q₈²	—	146	2	no	—
588	Q₈²	—	146	1	no	—
589	Q₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
590	#554	—	73	1	no	—
591	#554	—	73	2	no	—
592	#554	—	73	1	no	—
593	#554	—	73	1	no	—
594	#554	—	73	2	no	—
595	#554	—	146	1	no	—
596	#554	—	146	2	no	—
597	#554	—	146	1	no	—
598	#554	C₂×D₇₃	1	1	yes	characteristic
599	C₂×C₄⋊Q₈	—	73	1	no	—
600	C₂×C₄⋊Q₈	—	73	1	no	—
601	C₂×C₄⋊Q₈	—	73	2	no	—
602	C₂×C₄⋊Q₈	—	146	1	no	—
603	C₂×C₄⋊Q₈	—	146	2	no	—
604	C₂×#125	—	73	2	no	—
605	C₂×C₂²⋊Q₈	—	146	2	no	—
606	C₂×C₂²⋊Q₈	—	146	1	no	—
607	C₂×C₄×Q₈	—	73	1	no	—
608	C₂×C₄×Q₈	—	73	1	no	—
609	C₂×C₄×Q₈	—	73	2	no	—
610	C₂×C₄×Q₈	—	146	1	no	—
611	C₂×C₄×D₄	—	73	1	no	—
612	C₂×C₄×D₄	—	73	2	no	—
613	C₂²×C₄⋊C₄	—	146	1	no	—
614	#501	—	73	2	no	—
615	#501	—	73	2	no	—
616	#501	—	73	2	no	—
617	#501	—	73	2	no	—
618	#501	—	73	2	no	—
619	#501	—	73	2	no	—
620	#501	—	73	2	no	—
621	#501	C₂×D₇₃	1	2	yes	complemented
622	#500	—	73	1	no	—
623	#500	—	73	1	no	—
624	#500	—	73	2	no	—
625	#500	—	73	2	no	—
626	#500	—	73	1	no	—
627	#500	C₂×D₇₃	1	1	yes	characteristic, complemented
628	#479	—	73	2	no	—
629	#479	—	73	2	no	—
630	#479	—	73	2	no	—
631	#479	—	73	2	no	—
632	#479	—	73	2	no	—
633	#479	—	73	2	no	—
634	#479	—	73	2	no	—
635	#479	C₂×D₇₃	1	2	yes	complemented
636	#477	—	73	1	no	—
637	#477	—	73	1	no	—
638	#477	—	73	2	no	—
639	#477	—	73	1	no	—
640	#477	—	73	2	no	—
641	#477	C₂×D₇₃	1	1	yes	characteristic, complemented
642	#476	—	73	1	no	—
643	#476	—	73	1	no	—
644	#476	—	73	2	no	—
645	#476	—	73	1	no	—
646	#476	—	73	2	no	—
647	#476	C₂×D₇₃	1	1	yes	characteristic
648	#474	—	73	2	no	—
649	#474	—	73	2	no	—
650	#474	—	73	2	no	—
651	#474	—	73	2	no	—
652	#474	—	73	2	no	—
653	#474	—	73	2	no	—
654	#474	—	73	2	no	—
655	#474	C₂×D₇₃	1	2	yes	—
656	#446	—	73	1	no	—
657	#446	—	73	1	no	—
658	#446	—	73	2	no	—
659	#446	—	73	2	no	—
660	#446	—	73	1	no	—
661	#446	C₂×D₇₃	1	1	yes	characteristic, complemented
662	#440	—	73	2	no	—
663	#440	—	73	2	no	—
664	#440	—	73	2	no	—
665	#440	—	73	2	no	—
666	#440	—	73	2	no	—
667	#440	—	73	2	no	—
668	#440	—	73	2	no	—
669	#440	C₂×D₇₃	1	2	yes	—
670	C₄×SD₁₆	—	73	1	no	—
671	C₄×SD₁₆	—	73	1	no	—
672	C₄×SD₁₆	—	73	1	no	—
673	C₄×SD₁₆	—	73	1	no	—
674	C₄×SD₁₆	—	73	1	no	—
675	C₄×SD₁₆	—	73	1	no	—
676	C₄×SD₁₆	—	73	1	no	—
677	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
678	C₂×#107	—	73	2	no	—
679	C₂×#107	—	73	2	no	—
680	C₂×#107	—	73	2	no	—
681	C₂×#106	—	73	2	no	—
682	C₂×#106	—	73	1	no	—
683	C₂×C₄⋊C₈	—	73	1	no	—
684	C₂×C₄⋊C₈	—	73	2	no	—
685	C₂×#103	—	73	2	no	—
686	C₂×#103	—	73	1	no	—
687	C₂×#102	—	73	1	no	—
688	C₂×#102	—	73	2	no	—
689	C₂×#97	—	73	2	no	—
690	C₂×C₄×C₈	—	73	1	no	—
691	C₂²×Q₈	—	73	1	no	—
692	C₂²×Q₈	—	73	1	no	—
693	C₂²×Q₈	—	146	1	no	—
694	C₂²×Q₈	—	146	1	no	—
695	C₂²×Q₈	—	146	2	no	—
696	C₂²×D₄	—	73	1	no	—
697	C₂³×C₄	—	146	1	no	—
698	C₂³×C₄	—	146	2	no	—
699	C₂×SD₁₆	—	73	1	no	—
700	C₂×SD₁₆	—	73	1	no	—
701	C₂×SD₁₆	—	73	8	no	—
702	C₂×SD₁₆	—	73	1	no	—
703	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
704	C₂²×C₈	—	73	1	no	—
705	C₂²×C₈	—	73	1	no	—
706	C₂²×C₈	—	73	2	no	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	—	73	2	no	—
710	C₄⋊Q₈	—	73	2	no	—
711	C₄⋊Q₈	—	73	2	no	—
712	C₄⋊Q₈	—	73	2	no	—
713	C₄⋊Q₈	—	73	1	no	—
714	C₄⋊Q₈	—	73	2	no	—
715	C₄⋊Q₈	—	73	1	no	—
716	C₄⋊Q₈	—	146	1	no	—
717	C₄⋊Q₈	—	146	2	no	—
718	C₄⋊Q₈	—	146	1	no	—
719	C₄⋊Q₈	—	146	2	no	—
720	C₄⋊Q₈	—	146	1	no	—
721	C₄⋊Q₈	—	146	1	no	—
722	C₄⋊Q₈	—	146	2	no	—
723	C₄⋊Q₈	—	146	1	no	—
724	C₄⋊Q₈	—	146	2	no	—
725	C₄⋊Q₈	—	146	2	no	—
726	C₄⋊Q₈	—	146	2	no	—
727	C₄⋊Q₈	—	146	1	no	—
728	C₄⋊Q₈	—	146	2	no	—
729	C₄⋊Q₈	—	146	2	no	—
730	C₄⋊Q₈	—	146	2	no	—
731	C₄⋊Q₈	—	146	2	no	—
732	C₄⋊Q₈	—	146	1	no	—
733	C₄⋊Q₈	—	146	2	no	—
734	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
736	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
737	#125	—	73	2	no	—
738	#125	—	73	2	no	—
739	#125	—	73	2	no	—
740	#125	—	146	2	no	—
741	#125	—	146	2	no	—
742	#125	C₂²×D₇₃	1	2	yes	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	146	2	no	—
746	C₂²⋊Q₈	—	146	2	no	—
747	C₂²⋊Q₈	—	146	2	no	—
748	C₂²⋊Q₈	—	146	2	no	—
749	C₂²⋊Q₈	—	146	2	no	—
750	C₂²⋊Q₈	—	146	2	no	—
751	C₂²⋊Q₈	—	146	1	no	—
752	C₂²⋊Q₈	—	146	2	no	—
753	C₂²⋊Q₈	—	146	2	no	—
754	C₂²⋊Q₈	—	146	1	no	—
755	C₂²⋊Q₈	—	146	1	no	—
756	C₂²⋊Q₈	—	146	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	73	1	no	—
759	C₄×Q₈	—	73	2	no	—
760	C₄×Q₈	—	73	1	no	—
761	C₄×Q₈	—	73	2	no	—
762	C₄×Q₈	—	73	1	no	—
763	C₄×Q₈	—	73	1	no	—
764	C₄×Q₈	—	73	2	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	—	146	2	no	—
770	C₄×Q₈	—	146	1	no	—
771	C₄×Q₈	—	146	2	no	—
772	C₄×Q₈	—	146	1	no	—
773	C₄×Q₈	—	146	2	no	—
774	C₄×Q₈	—	146	1	no	—
775	C₄×Q₈	—	146	2	no	—
776	C₄×Q₈	—	146	1	no	—
777	C₄×Q₈	—	146	1	no	—
778	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
780	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
781	C₄×D₄	—	73	1	no	—
782	C₄×D₄	—	73	2	no	—
783	C₄×D₄	—	73	1	no	—
784	C₄×D₄	—	73	2	no	—
785	C₄×D₄	—	73	1	no	—
786	C₄×D₄	—	73	2	no	—
787	C₄×D₄	—	146	2	no	—
788	C₄×D₄	—	146	1	no	—
789	C₄×D₄	—	146	2	no	—
790	C₄×D₄	—	146	1	no	—
791	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
792	C₄×D₄	C₂²×D₇₃	1	2	yes	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	—	73	1	no	—
795	C₂×C₄⋊C₄	—	73	2	no	—
796	C₂×C₄⋊C₄	—	73	1	no	—
797	C₂×C₄⋊C₄	—	73	2	no	—
798	C₂×C₄⋊C₄	—	73	1	no	—
799	C₂×C₄⋊C₄	—	73	2	no	—
800	C₂×C₄⋊C₄	—	146	2	no	—
801	C₂×C₄⋊C₄	—	146	1	no	—
802	C₂×C₄⋊C₄	—	146	2	no	—
803	C₂×C₄⋊C₄	—	146	1	no	—
804	C₂×C₄⋊C₄	—	146	1	no	—
805	C₂×C₄⋊C₄	—	146	2	no	—
806	C₂×C₄⋊C₄	—	146	1	no	—
807	C₂×C₄⋊C₄	—	146	2	no	—
808	C₂×C₄⋊C₄	—	146	2	no	—
809	C₂×C₄⋊C₄	—	146	2	no	—
810	C₂×C₄⋊C₄	—	146	1	no	—
811	C₂×C₄⋊C₄	—	146	1	no	—
812	C₂×C₂²⋊C₄	—	146	2	no	—
813	C₂×C₂²⋊C₄	—	146	1	no	—
814	C₂×C₄²	—	73	2	no	—
815	C₂×C₄²	—	73	1	no	—
816	C₂×C₄²	—	146	1	no	—
817	C₂×C₄²	—	146	2	no	—
818	#107	—	73	2	no	—
819	#107	—	73	2	no	—
820	#107	—	73	2	no	—
821	#107	—	73	2	no	—
822	#107	—	73	2	no	—
823	#107	—	73	2	no	—
824	#107	—	73	2	no	—
825	#107	—	73	2	no	—
826	#107	—	73	2	no	—
827	#107	C₂²×D₇₃	1	2	yes	—
828	#107	C₂²×D₇₃	1	2	yes	—
829	#107	C₂²×D₇₃	1	2	yes	—
830	#106	—	73	1	no	—
831	#106	—	73	2	no	—
832	#106	—	73	1	no	—
833	#106	—	73	1	no	—
834	#106	—	73	2	no	—
835	#106	—	73	2	no	—
836	#106	C₂²×D₇₃	1	1	yes	characteristic
837	#106	C₂²×D₇₃	1	2	yes	—
838	C₄⋊C₈	—	73	2	no	—
839	C₄⋊C₈	—	73	2	no	—
840	C₄⋊C₈	—	73	2	no	—
841	C₄⋊C₈	—	73	2	no	—
842	C₄⋊C₈	—	73	1	no	—
843	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
844	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
845	#103	—	73	1	no	—
846	#103	—	73	2	no	—
847	#103	—	73	1	no	—
848	#103	—	73	2	no	—
849	#103	—	73	1	no	—
850	#103	—	73	2	no	—
851	#103	C₂²×D₇₃	1	1	yes	characteristic
852	#103	C₂²×D₇₃	1	2	yes	—
853	#102	—	73	1	no	—
854	#102	—	73	2	no	—
855	#102	—	73	1	no	—
856	#102	—	73	2	no	—
857	#102	—	73	1	no	—
858	#102	—	73	2	no	—
859	#102	C₂²×D₇₃	1	1	yes	characteristic
860	#102	C₂²×D₇₃	1	2	yes	—
861	#97	—	73	2	no	—
862	#97	—	73	2	no	—
863	#97	—	73	2	no	—
864	#97	C₂²×D₇₃	1	2	yes	—
865	C₄×C₈	—	73	1	no	—
866	C₄×C₈	—	73	1	no	—
867	C₄×C₈	—	73	1	no	—
868	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
869	C₂⁴	—	146	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	584	2	no	—
874	C₂×Q₈	—	584	4	no	—
875	C₂×Q₈	—	584	2	no	—
876	C₂×Q₈	—	73	2	no	—
877	C₂×Q₈	—	73	1	no	—
878	C₂×Q₈	—	73	4	no	—
879	C₂×Q₈	—	73	1	no	—
880	C₂×Q₈	—	146	2	no	—
881	C₂×Q₈	—	146	2	no	—
882	C₂×Q₈	—	146	2	no	—
883	C₂×Q₈	—	146	2	no	—
884	C₂×Q₈	—	146	1	no	—
885	C₂×Q₈	—	146	4	no	—
886	C₂×Q₈	—	146	2	no	—
887	C₂×Q₈	—	146	1	no	—
888	C₂×Q₈	—	146	1	no	—
889	C₂×Q₈	—	146	2	no	—
890	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
891	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
892	C₂×D₄	—	73	4	no	—
893	C₂×D₄	—	73	1	no	—
894	C₂×D₄	—	146	2	no	—
895	C₂×D₄	—	146	1	no	—
896	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	292	4	no	—
900	C₂²×C₄	—	584	4	no	—
901	C₂²×C₄	—	73	1	no	—
902	C₂²×C₄	—	73	1	no	—
903	C₂²×C₄	—	73	2	no	—
904	C₂²×C₄	—	73	1	no	—
905	C₂²×C₄	—	73	2	no	—
906	C₂²×C₄	—	146	1	no	—
907	C₂²×C₄	—	146	1	no	—
908	C₂²×C₄	—	146	2	no	—
909	C₂²×C₄	—	146	1	no	—
910	C₂²×C₄	—	146	2	no	—
911	C₂²×C₄	—	146	2	no	—
912	C₂²×C₄	—	146	1	no	—
913	C₂²×C₄	—	146	1	no	—
914	C₂²×C₄	—	146	1	no	—
915	C₂²×C₄	—	146	2	no	—
916	C₂²×C₄	—	146	2	no	—
917	SD₁₆	—	73	4	no	—
918	SD₁₆	—	73	4	no	—
919	SD₁₆	—	73	4	no	—
920	SD₁₆	Q₈×D₇₃	1	4	yes	complemented
921	C₂×C₈	—	73	1	no	—
922	C₂×C₈	—	73	4	no	—
923	C₂×C₈	—	73	1	no	—
924	C₂×C₈	—	73	2	no	—
925	C₂×C₈	—	146	2	no	—
926	C₂×C₈	—	146	4	no	—
927	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
928	C₂×C₈	C₂³×D₇₃	1	2	yes	—
929	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	73	2	no	—
938	C₄⋊C₄	—	73	2	no	—
939	C₄⋊C₄	—	73	2	no	—
940	C₄⋊C₄	—	73	1	no	—
941	C₄⋊C₄	—	73	2	no	—
942	C₄⋊C₄	—	73	1	no	—
943	C₄⋊C₄	—	73	2	no	—
944	C₄⋊C₄	—	73	1	no	—
945	C₄⋊C₄	—	73	2	no	—
946	C₄⋊C₄	—	146	1	no	—
947	C₄⋊C₄	—	146	2	no	—
948	C₄⋊C₄	—	146	1	no	—
949	C₄⋊C₄	—	146	2	no	—
950	C₄⋊C₄	—	146	2	no	—
951	C₄⋊C₄	—	146	2	no	—
952	C₄⋊C₄	—	146	1	no	—
953	C₄⋊C₄	—	146	2	no	—
954	C₄⋊C₄	—	146	2	no	—
955	C₄⋊C₄	—	146	2	no	—
956	C₄⋊C₄	—	146	2	no	—
957	C₄⋊C₄	—	146	2	no	—
958	C₄⋊C₄	—	146	2	no	—
959	C₄⋊C₄	—	146	1	no	—
960	C₄⋊C₄	—	146	2	no	—
961	C₄⋊C₄	—	146	2	no	—
962	C₄⋊C₄	—	146	2	no	—
963	C₄⋊C₄	—	146	1	no	—
964	C₄⋊C₄	—	146	2	no	—
965	C₄⋊C₄	—	146	2	no	—
966	C₄⋊C₄	—	146	1	no	—
967	C₄⋊C₄	—	146	2	no	—
968	C₄⋊C₄	—	146	1	no	—
969	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
970	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
971	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
973	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	146	1	no	—
978	C₂²⋊C₄	—	146	2	no	—
979	C₂²⋊C₄	—	146	2	no	—
980	C₂²⋊C₄	—	146	1	no	—
981	C₂²⋊C₄	—	146	1	no	—
982	C₂²⋊C₄	—	146	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	73	2	no	—
986	C₄²	—	73	2	no	—
987	C₄²	—	73	1	no	—
988	C₄²	—	73	1	no	—
989	C₄²	—	73	1	no	—
990	C₄²	—	73	2	no	—
991	C₄²	—	146	1	no	—
992	C₄²	—	146	2	no	—
993	C₄²	—	146	1	no	—
994	C₄²	—	146	2	no	—
995	C₄²	—	146	2	no	—
996	C₄²	—	146	1	no	—
997	C₄²	C₂³×D₇₃	1	1	yes	characteristic
998	C₄²	C₂³×D₇₃	1	2	yes	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	292	2	no	—
1001	C₂³	—	292	2	no	—
1002	C₂³	—	73	1	no	—
1003	C₂³	—	146	4	no	—
1004	C₂³	—	146	1	no	—
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	8	1	no	—
1009	Q₈	—	8	1	no	—
1010	Q₈	—	584	2	no	—
1011	Q₈	—	584	1	no	—
1012	Q₈	—	584	1	no	—
1013	Q₈	—	584	2	no	—
1014	Q₈	—	584	2	no	—
1015	Q₈	—	584	2	no	—
1016	Q₈	—	584	2	no	—
1017	Q₈	—	73	2	no	—
1018	Q₈	—	146	4	no	—
1019	Q₈	—	146	4	no	—
1020	Q₈	—	146	2	no	—
1021	Q₈	—	146	1	no	—
1022	Q₈	C₂×Q₈×D₇₃	1	2	yes	—
1023	D₄	—	2	1	no	—
1024	D₄	—	73	2	no	—
1025	D₄	—	146	4	no	—
1026	D₄	—	146	1	no	—
1027	D₄	C₂×Q₈×D₇₃	1	2	yes	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	292	2	no	—
1036	C₂×C₄	—	292	4	no	—
1037	C₂×C₄	—	292	2	no	—
1038	C₂×C₄	—	292	4	no	—
1039	C₂×C₄	—	292	2	no	—
1040	C₂×C₄	—	292	2	no	—
1041	C₂×C₄	—	292	2	no	—
1042	C₂×C₄	—	584	2	no	—
1043	C₂×C₄	—	584	2	no	—
1044	C₂×C₄	—	584	2	no	—
1045	C₂×C₄	—	73	1	no	—
1046	C₂×C₄	—	73	1	no	—
1047	C₂×C₄	—	73	4	no	—
1048	C₂×C₄	—	73	2	no	—
1049	C₂×C₄	—	73	2	no	—
1050	C₂×C₄	—	73	2	no	—
1051	C₂×C₄	—	73	1	no	—
1052	C₂×C₄	—	73	2	no	—
1053	C₂×C₄	—	146	4	no	—
1054	C₂×C₄	—	146	2	no	—
1055	C₂×C₄	—	146	4	no	—
1056	C₂×C₄	—	146	4	no	—
1057	C₂×C₄	—	146	1	no	—
1058	C₂×C₄	—	146	2	no	—
1059	C₂×C₄	—	146	1	no	—
1060	C₂×C₄	—	146	2	no	—
1061	C₂×C₄	—	146	1	no	—
1062	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1063	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1064	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1065	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1066	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1067	C₈	—	2	1	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	73	2	no	—
1070	C₈	—	146	1	no	—
1071	C₈	—	146	2	no	—
1072	C₈	C₂×Q₈×D₇₃	1	2	yes	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	292	8	no	—
1077	C₂²	—	292	1	no	—
1078	C₂²	—	292	1	no	—
1079	C₂²	—	73	2	no	—
1080	C₂²	—	73	2	no	—
1081	C₂²	—	73	2	no	—
1082	C₂²	—	146	2	no	—
1083	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	292	1	no	—
1093	C₄	—	292	2	no	—
1094	C₄	—	292	1	no	—
1095	C₄	—	292	2	no	—
1096	C₄	—	73	2	no	—
1097	C₄	—	73	2	no	—
1098	C₄	—	146	2	no	—
1099	C₄	—	146	2	no	—
1100	C₄	—	146	1	no	—
1101	C₄	—	146	2	no	—
1102	C₄	#137×D₇₃	1	2	yes	—
1103	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
1104	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1105	C₂	—	4	2	no	—
1106	C₂	—	292	2	no	—
1107	C₂	—	73	4	no	—
1108	C₂	D₄×Q₈×D₇₃	1	1	yes	characteristic
1109	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1110	C₂	#576×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×#3385	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂×D₄×D₇₃	C₂³
hypercenter	#3385	D₇₃
hypocenter	C₇₃	C₂×#3385
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3385

Complements

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

N	H ≅ G/N	type
1. Q₈²×D₇₃	C₂	semidirect
3. #22622846	C₂	semidirect
4. #22622845	C₂	semidirect
5. #22622844	C₂	semidirect
6. #22622843	C₂	semidirect
7. #22622842	C₂	semidirect
8. #22622841	C₂	semidirect
9. #22622840	C₂	semidirect
10. #22622839	C₂	semidirect
11. #22622838	C₂	semidirect
12. #22622837	C₂	semidirect
13. #22622836	C₂	semidirect
14. #501×D₇₃	C₂	semidirect
15. #500×D₇₃	C₂	semidirect
16. #479×D₇₃	C₂	semidirect
17. #477×D₇₃	C₂	semidirect
20. #446×D₇₃	C₂	semidirect
23. C₇₃×#3385	C₂	semidirect
26. Q₈×Dic₁₄₆	C₂²	semidirect
27. Q₈×Dic₁₄₆	C₂²	semidirect
28. Q₈×Dic₁₄₆	C₂²	semidirect
31. #17989317	C₂²	semidirect
32. #17989317	C₂²	semidirect
56. #17988997	C₂²	semidirect
57. #17988996	C₂²	semidirect
58. #17988995	C₂²	semidirect
59. #17988995	C₂²	semidirect
60. #17988994	C₂²	semidirect
61. #17988994	C₂²	semidirect
62. #17988993	C₂²	semidirect
63. #17988992	C₂²	semidirect
64. #17988991	C₂²	semidirect
65. #17988991	C₂²	semidirect
66. #17988990	C₂²	semidirect
67. #17988990	C₂²	semidirect
68. #17988897	C₂²	semidirect
69. #17988896	C₂²	semidirect
70. #17988895	C₂²	semidirect
71. #17988894	C₂²	semidirect
72. #17988893	C₂²	semidirect
73. #17988892	C₂²	semidirect
74. #17988891	C₂²	semidirect
75. #17988883	C₂²	semidirect
76. #17988882	C₂²	semidirect
77. #17988881	C₂²	semidirect
78. #17988880	C₂²	semidirect
79. #17988879	C₂²	semidirect
92. #17988718	C₂²	semidirect
93. #17988717	C₂²	semidirect
94. #17988716	C₂²	semidirect
95. #17988715	C₂²	semidirect
96. #17988714	C₂²	semidirect
124. Q₈²×C₇₃	C₂²	semidirect
126. #501×C₇₃	C₂²	semidirect
127. #500×C₇₃	C₂²	semidirect
128. #479×C₇₃	C₂²	semidirect
129. #477×C₇₃	C₂²	semidirect
132. #446×C₇₃	C₂²	semidirect
146. SD₁₆×D₇₃	Q₈	semidirect
353. #11924017	C₂×Q₈	semidirect
354. #11924016	C₂×Q₈	semidirect
355. #11924015	C₂×Q₈	semidirect
420. SD₁₆×C₇₃	C₂×Q₈	semidirect
555. D₇₃	#3385	direct (N × H)
569. #3385	D₇₃	direct (N × H)
579. C₇₃	C₂×#3385	semidirect
589. Q₈²	C₂×D₇₃	semidirect
621. #501	C₂×D₇₃	semidirect
627. #500	C₂×D₇₃	semidirect
635. #479	C₂×D₇₃	semidirect
641. #477	C₂×D₇₃	semidirect
661. #446	C₂×D₇₃	semidirect
920. SD₁₆	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
#554×D₇₃	2
#22622846	2
#22622845	2
#22622844	2
#22622843	2
#22622842	2
#22622841	2
#22622840	2
#22622839	2
#22622838	2
#22622837	2
#22622836	2
#501×D₇₃	2
#500×D₇₃	2
#479×D₇₃	2
#477×D₇₃	2
#476×D₇₃	2
#474×D₇₃	2
#446×D₇₃	2
#440×D₇₃	2
C₄×SD₁₆×D₇₃	2
C₇₃×#3385	2
C₂×#3385	73

Subgroups — #3385×D73 #33966467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3385×D₇₃ #33966467