Subgroups — #3375×D₇₃ #33965713

Order 18688.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#559×D₇₃	C₂	1	1	yes	maximal, characteristic
2	Q₈²×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622750	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622749	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622748	C₂	1	2	yes	maximal, complemented
6	#22622747	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622746	C₂	1	2	yes	maximal, complemented
8	#22622745	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622744	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622743	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622742	C₂	1	2	yes	maximal, complemented
12	#22622741	C₂	1	1	yes	maximal, characteristic, complemented
13	#22622740	C₂	1	2	yes	maximal, complemented
14	#489×D₇₃	C₂	1	2	yes	maximal, complemented
15	#486×D₇₃	C₂	1	1	yes	maximal, characteristic
16	#477×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#474×D₇₃	C₂	1	2	yes	maximal, complemented
18	#464×D₇₃	C₂	1	2	yes	maximal, complemented
19	#460×D₇₃	C₂	1	1	yes	maximal, characteristic
20	#446×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#440×D₇₃	C₂	1	2	yes	maximal, complemented
22	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3375	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
26	#17989323	C₂²	1	1	yes	characteristic
27	#17989322	C₂²	1	1	yes	characteristic
28	#17989322	C₂²	1	1	yes	characteristic
29	#17989321	—	2	2	no	—
30	#17989320	—	2	1	no	—
31	#17989320	C₂²	1	2	yes	—
32	#17989319	—	2	1	no	—
33	#17989319	C₂²	1	2	yes	—
34	Q₈×Dic₁₄₆	—	2	1	no	—
35	Q₈×Dic₁₄₆	C₂²	1	2	yes	complemented
36	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
37	Q₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
38	#17989317	—	2	1	no	—
39	#17989317	—	2	2	no	—
40	#17989317	C₂²	1	2	yes	complemented
41	#17989317	C₂²	1	1	yes	characteristic, complemented
42	C₄⋊Q₈×D₇₃	—	2	1	no	—
43	C₄⋊Q₈×D₇₃	—	2	2	no	—
44	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
45	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
46	#127×D₇₃	C₂²	1	1	yes	characteristic
47	#124×D₇₃	—	2	1	no	—
48	#124×D₇₃	C₂²	1	2	yes	—
49	#123×D₇₃	—	2	2	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	1	yes	characteristic
54	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₇₃	—	2	1	no	—
56	C₄×D₄×D₇₃	C₂²	1	2	yes	—
57	#17988949	C₂²	1	2	yes	complemented
58	#17988948	C₂²	1	2	yes	complemented
59	#17988948	C₂²	1	2	yes	complemented
60	#17988947	C₂²	1	2	yes	complemented
61	#17988946	C₂²	1	2	yes	complemented
62	#17988945	C₂²	1	2	yes	complemented
63	#17988945	C₂²	1	2	yes	complemented
64	#17988935	C₂²	1	1	yes	characteristic
65	#17988934	C₂²	1	1	yes	characteristic
66	#17988933	C₂²	1	1	yes	characteristic
67	#17988932	C₂²	1	2	yes	—
68	#17988932	C₂²	1	2	yes	—
69	#17988883	C₂²	1	1	yes	characteristic, complemented
70	#17988882	C₂²	1	1	yes	characteristic, complemented
71	#17988881	C₂²	1	2	yes	complemented
72	#17988880	C₂²	1	2	yes	complemented
73	#17988879	C₂²	1	1	yes	characteristic, complemented
74	#17988868	C₂²	1	2	yes	complemented
75	#17988867	C₂²	1	2	yes	complemented
76	#17988866	C₂²	1	2	yes	complemented
77	#17988866	C₂²	1	2	yes	complemented
78	#17988865	C₂²	1	2	yes	complemented
79	#17988865	C₂²	1	2	yes	complemented
80	#17988864	C₂²	1	2	yes	complemented
81	#17988812	C₂²	1	2	yes	complemented
82	#17988811	C₂²	1	2	yes	complemented
83	#17988810	C₂²	1	2	yes	complemented
84	#17988809	C₂²	1	2	yes	complemented
85	#17988808	C₂²	1	2	yes	complemented
86	#17988807	C₂²	1	2	yes	complemented
87	#17988806	C₂²	1	2	yes	complemented
88	#17988788	C₂²	1	1	yes	characteristic
89	#17988787	C₂²	1	1	yes	characteristic
90	#17988786	C₂²	1	2	yes	—
91	#17988785	C₂²	1	2	yes	—
92	#17988784	C₂²	1	1	yes	characteristic
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	#17988690	C₂²	1	2	yes	complemented
99	#17988689	C₂²	1	2	yes	complemented
100	#17988688	C₂²	1	2	yes	complemented
101	#17988687	C₂²	1	2	yes	complemented
102	#17988686	C₂²	1	2	yes	complemented
103	#17988685	C₂²	1	2	yes	complemented
104	#17988684	C₂²	1	2	yes	complemented
105	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
106	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
107	#17988681	C₂²	1	1	yes	characteristic, complemented
108	C₄×#11924018	C₂²	1	1	yes	characteristic, complemented
109	C₄×#11924018	C₂²	1	1	yes	characteristic, complemented
110	#17988679	C₂²	1	1	yes	characteristic, complemented
111	#17988679	C₂²	1	1	yes	characteristic, complemented
112	#107×D₇₃	C₂²	1	1	yes	characteristic
113	#107×D₇₃	C₂²	1	2	yes	—
114	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
115	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
116	#103×D₇₃	C₂²	1	2	yes	—
117	#103×D₇₃	C₂²	1	1	yes	characteristic
118	#103×D₇₃	C₂²	1	1	yes	characteristic
119	#102×D₇₃	C₂²	1	2	yes	—
120	#102×D₇₃	C₂²	1	2	yes	—
121	#102×D₇₃	C₂²	1	2	yes	—
122	#97×D₇₃	C₂²	1	2	yes	—
123	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
124	#559×C₇₃	C₂²	1	1	yes	characteristic
125	Q₈²×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#489×C₇₃	C₂²	1	2	yes	complemented
127	#486×C₇₃	C₂²	1	1	yes	characteristic
128	#477×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#474×C₇₃	C₂²	1	2	yes	complemented
130	#464×C₇₃	C₂²	1	2	yes	complemented
131	#460×C₇₃	C₂²	1	1	yes	characteristic
132	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#440×C₇₃	C₂²	1	2	yes	complemented
134	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
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	1	yes	characteristic
139	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
140	C₂×D₄×D₇₃	—	2	1	no	—
141	C₂×D₄×D₇₃	—	2	1	no	—
142	C₂×D₄×D₇₃	C₂³	1	2	yes	—
143	C₂²×C₄×D₇₃	—	2	2	no	—
144	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
145	C₂×#11924018	C₂³	1	1	yes	characteristic
146	C₂×#11924018	C₂³	1	1	yes	characteristic
147	Q₁₆×D₇₃	—	2	4	no	—
148	C₂×#11924017	C₂³	1	2	yes	—
149	C₂×#11924016	C₂³	1	2	yes	—
150	C₂×#11924015	C₂³	1	2	yes	—
151	SD₁₆×D₇₃	—	2	8	no	—
152	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₇₃	C₂³	1	2	yes	—
154	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
155	#14556591	—	2	1	no	—
156	#14556591	—	2	2	no	—
157	#14556591	C₂³	1	2	yes	—
158	#14556591	C₂³	1	1	yes	characteristic
159	#14556590	—	2	1	no	—
160	#14556590	—	2	2	no	—
161	#14556590	—	2	2	no	—
162	#14556590	—	2	2	no	—
163	#14556590	—	2	2	no	—
164	#14556590	—	2	2	no	—
165	#14556590	—	2	1	no	—
166	#14556590	—	2	1	no	—
167	#14556590	—	2	2	no	—
168	#14556590	C₂³	1	2	yes	—
169	#14556590	C₂³	1	2	yes	—
170	#14556590	C₂³	1	2	yes	—
171	#14556589	—	2	2	no	—
172	#14556589	—	2	2	no	—
173	#14556589	—	2	2	no	—
174	#14556589	—	2	2	no	—
175	#14556589	—	2	1	no	—
176	#14556588	C₂³	1	1	yes	characteristic
177	#14556587	—	2	1	no	—
178	#14556587	—	2	1	no	—
179	#14556587	C₂³	1	2	yes	—
180	#14556580	—	2	1	no	—
181	#14556580	C₂³	1	2	yes	—
182	#14556579	—	2	1	no	—
183	#14556579	C₂³	1	2	yes	—
184	#14556578	—	2	1	no	—
185	#14556578	C₂³	1	2	yes	—
186	#14556577	—	2	2	no	—
187	#14556577	—	2	2	no	—
188	#14556577	—	2	2	no	—
189	#14556577	—	2	2	no	—
190	#14556576	—	2	2	no	—
191	#14556576	—	2	2	no	—
192	#14556575	—	2	2	no	—
193	#14556574	—	2	2	no	—
194	#14556573	—	2	2	no	—
195	#14556573	—	2	2	no	—
196	#14556572	—	2	2	no	—
197	Q₈×Dic₇₃	—	2	1	no	—
198	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
199	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
200	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
201	Q₈×Dic₇₃	C₂³	1	2	yes	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	C₄×Dic₁₄₆	—	2	1	no	—
204	C₄×Dic₁₄₆	—	2	2	no	—
205	C₄×Dic₁₄₆	—	2	1	no	—
206	C₄×Dic₁₄₆	—	2	1	no	—
207	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
208	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
209	C₄×Dic₁₄₆	C₂³	1	2	yes	—
210	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
211	C₄×Dic₁₄₆	C₂³	1	2	yes	—
212	#14556556	—	2	2	no	—
213	#14556556	—	2	1	no	—
214	#14556556	—	2	2	no	—
215	#14556556	—	2	1	no	—
216	#14556556	—	2	1	no	—
217	#14556556	D₄	1	1	yes	characteristic
218	#14556556	D₄	1	2	yes	—
219	#14556556	C₂³	1	1	yes	characteristic
220	#14556556	C₂³	1	1	yes	characteristic
221	#14556556	C₂³	1	2	yes	—
222	C₄×D₂₉₂	—	2	1	no	—
223	C₄×D₂₉₂	C₂³	1	2	yes	—
224	D₄×Dic₇₃	—	2	1	no	—
225	D₄×Dic₇₃	C₂³	1	2	yes	—
226	#14556553	—	2	1	no	—
227	#14556553	C₂³	1	2	yes	—
228	C₄×C₂²⋊D₇₃	—	2	2	no	—
229	C₄×C₂²⋊D₇₃	—	2	2	no	—
230	#14556551	—	2	2	no	—
231	#14556551	—	2	2	no	—
232	C₄⋊C₄×D₇₃	—	2	2	no	—
233	C₄⋊C₄×D₇₃	—	2	1	no	—
234	C₄⋊C₄×D₇₃	—	2	2	no	—
235	C₄⋊C₄×D₇₃	—	2	1	no	—
236	C₄⋊C₄×D₇₃	—	2	1	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	2	no	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₄²×D₇₃	—	2	2	no	—
246	C₄²×D₇₃	—	2	1	no	—
247	C₄²×D₇₃	—	2	1	no	—
248	C₄²×D₇₃	C₂³	1	1	yes	characteristic
249	C₄²×D₇₃	C₂³	1	2	yes	—
250	#14556525	C₂³	1	1	yes	characteristic
251	#14556525	C₂³	1	2	yes	—
252	#14556524	C₂³	1	1	yes	characteristic
253	#14556524	C₂³	1	2	yes	—
254	#14556524	C₂³	1	1	yes	characteristic
255	#14556524	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	1	yes	characteristic
263	#14556516	C₂³	1	1	yes	characteristic
264	#14556515	C₂³	1	2	yes	—
265	#14556515	C₂³	1	1	yes	characteristic
266	#14556515	C₂³	1	1	yes	characteristic
267	#14556514	C₂³	1	2	yes	—
268	#14556514	C₂³	1	1	yes	characteristic
269	#14556514	C₂³	1	1	yes	characteristic
270	#14556513	C₂³	1	2	yes	—
271	#14556513	C₂³	1	2	yes	—
272	#14556513	C₂³	1	2	yes	—
273	#14556512	C₂³	1	2	yes	—
274	#14556512	C₂³	1	2	yes	—
275	#14556512	C₂³	1	2	yes	—
276	#14556511	C₂³	1	2	yes	—
277	#14556511	C₂³	1	2	yes	—
278	#14556511	C₂³	1	2	yes	—
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	1	yes	characteristic
286	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
287	C₄⋊Q₈×C₇₃	—	2	1	no	—
288	C₄⋊Q₈×C₇₃	—	2	2	no	—
289	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
290	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
291	#127×C₇₃	C₂³	1	1	yes	characteristic
292	#124×C₇₃	—	2	1	no	—
293	#124×C₇₃	C₂³	1	2	yes	—
294	#123×C₇₃	—	2	2	no	—
295	C₄×Q₈×C₇₃	—	2	1	no	—
296	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
301	C₄×D₄×C₇₃	C₂³	1	2	yes	—
302	#107×C₇₃	C₂³	1	1	yes	characteristic
303	#107×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	1	yes	characteristic
308	#103×C₇₃	C₂³	1	1	yes	characteristic
309	#102×C₇₃	C₂³	1	2	yes	—
310	#102×C₇₃	C₂³	1	2	yes	—
311	#102×C₇₃	C₂³	1	2	yes	—
312	#97×C₇₃	C₂³	1	2	yes	—
313	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₂³×D₇₃	—	2	2	no	—
315	C₂×Dic₁₄₆	—	2	1	no	—
316	C₂×Dic₁₄₆	—	2	1	no	—
317	C₂×Dic₁₄₆	—	2	2	no	—
318	C₂×Dic₁₄₆	—	2	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	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	—	2	2	no	—
330	Q₈×D₇₃	—	8	4	no	—
331	Q₈×D₇₃	—	8	2	no	—
332	Q₈×D₇₃	#41	1	4	yes	—
333	C₂×D₂₉₂	—	2	1	no	—
334	C₂×D₂₉₂	—	2	1	no	—
335	C₂×D₂₉₂	C₂⁴	1	2	yes	—
336	C₂×C₂²⋊D₇₃	—	2	2	no	—
337	C₂×C₂²⋊D₇₃	—	2	2	no	—
338	C₂×C₂²⋊D₇₃	—	2	2	no	—
339	D₄×D₇₃	—	2	4	no	—
340	D₄×D₇₃	—	2	4	no	—
341	D₄×D₇₃	—	4	4	no	—
342	D₄×D₇₃	—	8	2	no	—
343	C₂²×Dic₇₃	—	2	2	no	—
344	C₂×C₄×D₇₃	—	2	1	no	—
345	C₂×C₄×D₇₃	—	2	1	no	—
346	C₂×C₄×D₇₃	—	2	1	no	—
347	C₂×C₄×D₇₃	—	2	2	no	—
348	C₂×C₄×D₇₃	—	2	1	no	—
349	C₂×C₄×D₇₃	—	2	2	no	—
350	C₂×C₄×D₇₃	—	2	2	no	—
351	C₂×C₄×D₇₃	—	8	4	no	—
352	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
353	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
354	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
355	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
356	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
357	Dic₂₉₂	—	2	2	no	—
358	#11924018	—	2	2	no	—
359	#11924018	—	2	2	no	—
360	#11924017	—	2	4	no	—
361	#11924016	—	2	4	no	—
362	#11924015	—	2	4	no	—
363	C₂×#10596831	C₂⁴	1	1	yes	characteristic
364	C₂×#10596831	C₂⁴	1	1	yes	characteristic
365	C₂×#10596831	C₂⁴	1	2	yes	—
366	C₈×D₇₃	—	2	4	no	—
367	C₈×D₇₃	—	2	2	no	—
368	C₈×D₇₃	—	2	2	no	—
369	C₄⋊Dic₇₃	—	2	2	no	—
370	C₄⋊Dic₇₃	—	2	1	no	—
371	C₄⋊Dic₇₃	—	2	1	no	—
372	C₄⋊Dic₇₃	—	2	2	no	—
373	C₄⋊Dic₇₃	—	2	1	no	—
374	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
375	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
376	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
377	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
378	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
379	#11924007	—	2	1	no	—
380	#11924007	—	2	2	no	—
381	#11924007	—	2	1	no	—
382	#11924007	—	2	2	no	—
383	#11924007	—	2	2	no	—
384	#11924007	—	2	2	no	—
385	#11924007	—	2	1	no	—
386	#11924007	—	2	2	no	—
387	#11924007	—	2	1	no	—
388	#11924007	—	2	1	no	—
389	#11924007	—	2	1	no	—
390	#11924007	—	2	2	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	2	no	—
395	C₂²⋊Dic₇₃	—	2	2	no	—
396	C₂²⋊Dic₇₃	—	2	2	no	—
397	#11924005	—	2	2	no	—
398	#11924005	—	2	2	no	—
399	#11924005	—	2	2	no	—
400	#11924005	—	2	2	no	—
401	#11924005	—	2	2	no	—
402	#11924005	—	2	2	no	—
403	C₄×Dic₇₃	—	2	1	no	—
404	C₄×Dic₇₃	—	2	2	no	—
405	C₄×Dic₇₃	—	2	1	no	—
406	C₄×Dic₇₃	—	2	1	no	—
407	C₄×Dic₇₃	—	2	1	no	—
408	C₄×Dic₇₃	—	2	2	no	—
409	C₄×Dic₇₃	—	2	1	no	—
410	C₄×Dic₇₃	—	2	2	no	—
411	C₄×Dic₇₃	—	2	1	no	—
412	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
413	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
414	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₇₃	C₂⁴	1	2	yes	—
418	C₂×Q₈×C₇₃	—	2	2	no	—
419	C₂×Q₈×C₇₃	—	2	1	no	—
420	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
421	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
423	C₂×D₄×C₇₃	—	2	1	no	—
424	C₂×D₄×C₇₃	—	2	1	no	—
425	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
426	C₂²×C₄×C₇₃	—	2	2	no	—
427	Q₁₆×C₇₃	—	2	2	no	—
428	SD₁₆×C₇₃	—	2	4	no	—
429	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
436	C₄⋊C₄×C₇₃	—	2	1	no	—
437	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
438	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
439	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
440	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₇₃	—	2	2	no	—
443	C₂²⋊C₄×C₇₃	—	2	2	no	—
444	C₂²⋊C₄×C₇₃	—	2	2	no	—
445	C₄²×C₇₃	—	2	1	no	—
446	C₄²×C₇₃	—	2	2	no	—
447	C₄²×C₇₃	—	2	1	no	—
448	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
449	C₄²×C₇₃	C₂⁴	1	2	yes	—
450	C₂³×C₇₃	—	2	2	no	—
451	C₂²×D₇₃	—	2	2	no	—
452	C₂²×D₇₃	—	4	4	no	—
453	C₂²×D₇₃	—	4	4	no	—
454	C₂²×D₇₃	—	4	4	no	—
455	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
456	Q₈×C₇₃	—	2	2	no	—
457	Q₈×C₇₃	—	2	1	no	—
458	Q₈×C₇₃	—	2	1	no	—
459	Q₈×C₇₃	—	2	1	no	—
460	Q₈×C₇₃	—	8	2	no	—
461	Q₈×C₇₃	—	8	1	no	—
462	Q₈×C₇₃	C₂×#41	1	2	yes	—
463	D₄×C₇₃	—	2	2	no	—
464	D₄×C₇₃	—	2	2	no	—
465	D₄×C₇₃	—	4	2	no	—
466	D₄×C₇₃	—	8	1	no	—
467	C₂×C₄×C₇₃	—	2	1	no	—
468	C₂×C₄×C₇₃	—	2	1	no	—
469	C₂×C₄×C₇₃	—	2	1	no	—
470	C₂×C₄×C₇₃	—	2	2	no	—
471	C₂×C₄×C₇₃	—	2	1	no	—
472	C₂×C₄×C₇₃	—	8	2	no	—
473	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
475	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
478	C₂²⋊D₇₃	—	4	4	no	—
479	C₂²⋊D₇₃	—	4	4	no	—
480	C₂²⋊D₇₃	—	8	2	no	—
481	C₂×Dic₇₃	—	2	1	no	—
482	C₂×Dic₇₃	—	2	1	no	—
483	C₂×Dic₇₃	—	2	1	no	—
484	C₂×Dic₇₃	—	2	2	no	—
485	C₂×Dic₇₃	—	2	1	no	—
486	C₂×Dic₇₃	—	8	2	no	—
487	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
488	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
489	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
492	D₂₉₂	—	2	2	no	—
493	D₂₉₂	—	2	2	no	—
494	D₂₉₂	—	4	2	no	—
495	D₂₉₂	—	8	1	no	—
496	C₄×D₇₃	—	2	4	no	—
497	C₄×D₇₃	—	2	4	no	—
498	C₄×D₇₃	—	2	4	no	—
499	C₄×D₇₃	—	2	2	no	—
500	C₄×D₇₃	—	4	2	no	—
501	C₄×D₇₃	—	4	2	no	—
502	C₄×D₇₃	—	4	2	no	—
503	C₄×D₇₃	—	4	4	no	—
504	C₄×D₇₃	—	8	2	no	—
505	C₄×D₇₃	—	8	2	no	—
506	C₄×D₇₃	#137	1	4	yes	—
507	C₄×D₇₃	C₂×#41	1	2	yes	—
508	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
509	Dic₁₄₆	—	2	2	no	—
510	Dic₁₄₆	—	2	1	no	—
511	Dic₁₄₆	—	2	4	no	—
512	Dic₁₄₆	—	2	4	no	—
513	Dic₁₄₆	—	2	1	no	—
514	Dic₁₄₆	—	2	1	no	—
515	Dic₁₄₆	—	4	2	no	—
516	Dic₁₄₆	—	8	2	no	—
517	Dic₁₄₆	—	8	2	no	—
518	Dic₁₄₆	—	8	2	no	—
519	Dic₁₄₆	—	8	2	no	—
520	Dic₁₄₆	—	8	1	no	—
521	Dic₁₄₆	C₂×#41	1	2	yes	—
522	C₈×C₇₃	—	2	2	no	—
523	C₈×C₇₃	—	2	1	no	—
524	C₈×C₇₃	—	2	1	no	—
525	#10596831	—	2	2	no	—
526	#10596831	—	2	1	no	—
527	#10596831	—	2	1	no	—
528	C₂²×C₇₃	—	4	2	no	—
529	C₂²×C₇₃	—	4	2	no	—
530	C₂²×C₇₃	—	4	2	no	—
531	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
532	C₂×D₇₃	—	4	2	no	—
533	C₂×D₇₃	—	4	2	no	—
534	C₂×D₇₃	—	4	2	no	—
535	C₂×D₇₃	—	8	8	no	—
536	C₂×D₇₃	#548	1	2	yes	—
537	C₂×D₇₃	C₂×#137	1	2	yes	—
538	C₂×D₇₃	#576	1	2	yes	—
539	C₄×C₇₃	—	2	2	no	—
540	C₄×C₇₃	—	2	2	no	—
541	C₄×C₇₃	—	2	2	no	—
542	C₄×C₇₃	—	2	1	no	—
543	C₄×C₇₃	—	4	1	no	—
544	C₄×C₇₃	—	4	1	no	—
545	C₄×C₇₃	—	4	2	no	—
546	C₄×C₇₃	—	4	1	no	—
547	C₄×C₇₃	C₂×#137	1	2	yes	—
548	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
549	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	Dic₇₃	—	2	2	no	—
551	Dic₇₃	—	2	2	no	—
552	Dic₇₃	—	2	2	no	—
553	Dic₇₃	—	2	1	no	—
554	Dic₇₃	—	4	1	no	—
555	Dic₇₃	—	4	1	no	—
556	Dic₇₃	—	4	2	no	—
557	Dic₇₃	—	4	1	no	—
558	Dic₇₃	#548	1	2	yes	—
559	Dic₇₃	C₂×#137	1	2	yes	—
560	C₂×#3375	—	73	1	no	maximal, Sylow
561	C₂×C₇₃	—	8	2	no	—
562	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
563	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
564	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
565	D₇₃	—	8	2	no	—
566	D₇₃	#3375	1	4	yes	direct product factor
567	C₂×#559	—	73	1	no	—
568	C₂×Q₈²	—	73	1	no	—
569	#3375	—	73	2	no	—
570	#3375	—	73	1	no	—
571	#3375	—	73	1	no	—
572	#3375	—	73	2	no	—
573	#3375	—	73	2	no	—
574	#3375	—	73	1	no	—
575	#3375	—	73	1	no	—
576	#3375	—	73	2	no	—
577	#3375	—	73	1	no	—
578	#3375	—	73	1	no	—
579	#3375	—	73	1	no	—
580	#3375	D₇₃	1	1	yes	characteristic, direct product factor
581	C₂×#489	—	73	2	no	—
582	C₂×#486	—	73	1	no	—
583	C₂×#477	—	73	1	no	—
584	C₂×#474	—	73	2	no	—
585	C₂×#464	—	73	2	no	—
586	C₂×#460	—	73	1	no	—
587	C₂×#446	—	73	1	no	—
588	C₂×#440	—	73	2	no	—
589	C₂×C₄×Q₁₆	—	73	1	no	—
590	C₇₃	C₂×#3375	1	1	yes	characteristic, complemented, Sylow
591	C₂²×Q₁₆	—	73	1	no	—
592	C₂²×SD₁₆	—	73	2	no	—
593	#559	—	73	1	no	—
594	#559	—	73	2	no	—
595	#559	—	73	1	no	—
596	#559	—	73	1	no	—
597	#559	—	73	2	no	—
598	#559	—	146	1	no	—
599	#559	—	146	2	no	—
600	#559	—	146	1	no	—
601	#559	C₂×D₇₃	1	1	yes	characteristic
602	Q₈²	—	73	2	no	—
603	Q₈²	—	73	1	no	—
604	Q₈²	—	73	2	no	—
605	Q₈²	—	73	1	no	—
606	Q₈²	—	73	1	no	—
607	Q₈²	—	146	1	no	—
608	Q₈²	—	146	2	no	—
609	Q₈²	—	146	1	no	—
610	Q₈²	C₂×D₇₃	1	1	yes	characteristic, complemented
611	C₂×C₄⋊Q₈	—	73	1	no	—
612	C₂×C₄⋊Q₈	—	73	2	no	—
613	C₂×C₄⋊Q₈	—	146	1	no	—
614	C₂×C₄⋊Q₈	—	146	2	no	—
615	C₂×#127	—	73	1	no	—
616	C₂×#124	—	73	2	no	—
617	C₂×#124	—	146	1	no	—
618	C₂×#123	—	146	2	no	—
619	C₂×C₄×Q₈	—	73	1	no	—
620	C₂×C₄×Q₈	—	73	1	no	—
621	C₂×C₄×Q₈	—	73	1	no	—
622	C₂×C₄×Q₈	—	73	2	no	—
623	C₂×C₄×Q₈	—	146	1	no	—
624	C₂×C₄×D₄	—	73	2	no	—
625	C₂×C₄×D₄	—	146	1	no	—
626	#489	—	73	2	no	—
627	#489	—	73	2	no	—
628	#489	—	73	2	no	—
629	#489	—	73	2	no	—
630	#489	—	73	2	no	—
631	#489	—	73	2	no	—
632	#489	—	73	2	no	—
633	#489	C₂×D₇₃	1	2	yes	complemented
634	#486	—	73	1	no	—
635	#486	—	73	1	no	—
636	#486	—	73	2	no	—
637	#486	—	73	2	no	—
638	#486	—	73	1	no	—
639	#486	C₂×D₇₃	1	1	yes	characteristic
640	#477	—	73	1	no	—
641	#477	—	73	1	no	—
642	#477	—	73	2	no	—
643	#477	—	73	1	no	—
644	#477	—	73	2	no	—
645	#477	C₂×D₇₃	1	1	yes	characteristic, complemented
646	#474	—	73	2	no	—
647	#474	—	73	2	no	—
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	C₂×D₇₃	1	2	yes	complemented
654	#464	—	73	2	no	—
655	#464	—	73	2	no	—
656	#464	—	73	2	no	—
657	#464	—	73	2	no	—
658	#464	—	73	2	no	—
659	#464	—	73	2	no	—
660	#464	—	73	2	no	—
661	#464	C₂×D₇₃	1	2	yes	complemented
662	#460	—	73	2	no	—
663	#460	—	73	1	no	—
664	#460	—	73	1	no	—
665	#460	—	73	1	no	—
666	#460	—	73	2	no	—
667	#460	C₂×D₇₃	1	1	yes	characteristic
668	#446	—	73	1	no	—
669	#446	—	73	1	no	—
670	#446	—	73	2	no	—
671	#446	—	73	2	no	—
672	#446	—	73	1	no	—
673	#446	C₂×D₇₃	1	1	yes	characteristic, complemented
674	#440	—	73	2	no	—
675	#440	—	73	2	no	—
676	#440	—	73	2	no	—
677	#440	—	73	2	no	—
678	#440	—	73	2	no	—
679	#440	—	73	2	no	—
680	#440	—	73	2	no	—
681	#440	C₂×D₇₃	1	2	yes	complemented
682	C₄×Q₁₆	—	73	1	no	—
683	C₄×Q₁₆	—	73	1	no	—
684	C₄×Q₁₆	—	73	1	no	—
685	C₄×Q₁₆	—	73	1	no	—
686	C₄×Q₁₆	—	73	1	no	—
687	C₄×Q₁₆	—	73	1	no	—
688	C₄×Q₁₆	—	73	1	no	—
689	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
690	C₂×#107	—	73	2	no	—
691	C₂×#107	—	73	1	no	—
692	C₂×C₄⋊C₈	—	73	1	no	—
693	C₂×C₄⋊C₈	—	73	2	no	—
694	C₂×#103	—	73	2	no	—
695	C₂×#103	—	73	1	no	—
696	C₂×#103	—	73	1	no	—
697	C₂×#102	—	73	2	no	—
698	C₂×#102	—	73	2	no	—
699	C₂×#102	—	73	2	no	—
700	C₂×#97	—	73	2	no	—
701	C₂×C₄×C₈	—	73	1	no	—
702	C₂²×Q₈	—	73	1	no	—
703	C₂²×Q₈	—	73	1	no	—
704	C₂²×Q₈	—	73	1	no	—
705	C₂²×Q₈	—	146	2	no	—
706	C₂²×Q₈	—	146	1	no	—
707	C₂²×D₄	—	73	2	no	—
708	C₂²×D₄	—	146	1	no	—
709	C₂²×D₄	—	146	1	no	—
710	C₂³×C₄	—	146	2	no	—
711	C₂×Q₁₆	—	73	1	no	—
712	C₂×Q₁₆	—	73	1	no	—
713	C₂×Q₁₆	—	73	1	no	—
714	C₂×Q₁₆	—	146	4	no	—
715	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
716	C₂×SD₁₆	—	73	2	no	—
717	C₂×SD₁₆	—	73	2	no	—
718	C₂×SD₁₆	—	73	2	no	—
719	C₂×SD₁₆	—	146	8	no	—
720	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
721	C₂²×C₈	—	73	2	no	—
722	C₂²×C₈	—	73	1	no	—
723	C₂²×C₈	—	73	1	no	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	73	2	no	—
727	C₄⋊Q₈	—	73	2	no	—
728	C₄⋊Q₈	—	73	2	no	—
729	C₄⋊Q₈	—	73	2	no	—
730	C₄⋊Q₈	—	73	1	no	—
731	C₄⋊Q₈	—	146	1	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	1	no	—
737	C₄⋊Q₈	—	146	2	no	—
738	C₄⋊Q₈	—	146	2	no	—
739	C₄⋊Q₈	—	146	2	no	—
740	C₄⋊Q₈	—	146	1	no	—
741	C₄⋊Q₈	—	146	2	no	—
742	C₄⋊Q₈	—	146	2	no	—
743	C₄⋊Q₈	—	146	2	no	—
744	C₄⋊Q₈	—	146	2	no	—
745	C₄⋊Q₈	—	146	1	no	—
746	C₄⋊Q₈	—	146	2	no	—
747	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
748	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
749	#127	—	73	2	no	—
750	#127	—	73	1	no	—
751	#127	—	146	1	no	—
752	#127	—	146	1	no	—
753	#127	C₂²×D₇₃	1	1	yes	characteristic
754	#124	—	2	1	no	—
755	#124	—	73	2	no	—
756	#124	—	73	2	no	—
757	#124	—	73	2	no	—
758	#124	—	146	1	no	—
759	#124	—	146	2	no	—
760	#124	—	146	2	no	—
761	#124	—	146	2	no	—
762	#124	—	146	2	no	—
763	#124	—	146	1	no	—
764	#124	—	146	1	no	—
765	#124	C₂²×D₇₃	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	146	2	no	—
768	#123	—	146	2	no	—
769	#123	—	146	2	no	—
770	#123	—	146	2	no	—
771	#123	—	146	2	no	—
772	#123	—	146	2	no	—
773	#123	—	146	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	73	1	no	—
776	C₄×Q₈	—	73	2	no	—
777	C₄×Q₈	—	73	1	no	—
778	C₄×Q₈	—	73	2	no	—
779	C₄×Q₈	—	73	1	no	—
780	C₄×Q₈	—	73	1	no	—
781	C₄×Q₈	—	73	2	no	—
782	C₄×Q₈	—	73	1	no	—
783	C₄×Q₈	—	73	1	no	—
784	C₄×Q₈	—	73	2	no	—
785	C₄×Q₈	—	73	1	no	—
786	C₄×Q₈	—	73	1	no	—
787	C₄×Q₈	—	73	2	no	—
788	C₄×Q₈	—	73	1	no	—
789	C₄×Q₈	—	146	2	no	—
790	C₄×Q₈	—	146	1	no	—
791	C₄×Q₈	—	146	1	no	—
792	C₄×Q₈	—	146	2	no	—
793	C₄×Q₈	—	146	1	no	—
794	C₄×Q₈	—	146	2	no	—
795	C₄×Q₈	—	146	1	no	—
796	C₄×Q₈	—	146	1	no	—
797	C₄×Q₈	—	146	2	no	—
798	C₄×Q₈	—	146	1	no	—
799	C₄×Q₈	—	146	1	no	—
800	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
802	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	73	2	no	—
806	C₄×D₄	—	73	2	no	—
807	C₄×D₄	—	73	2	no	—
808	C₄×D₄	—	146	1	no	—
809	C₄×D₄	—	146	2	no	—
810	C₄×D₄	—	146	2	no	—
811	C₄×D₄	—	146	2	no	—
812	C₄×D₄	—	146	2	no	—
813	C₄×D₄	—	146	1	no	—
814	C₄×D₄	—	146	1	no	—
815	C₄×D₄	C₂²×D₇₃	1	2	yes	—
816	C₂×C₄⋊C₄	—	73	1	no	—
817	C₂×C₄⋊C₄	—	73	2	no	—
818	C₂×C₄⋊C₄	—	73	1	no	—
819	C₂×C₄⋊C₄	—	73	1	no	—
820	C₂×C₄⋊C₄	—	73	2	no	—
821	C₂×C₄⋊C₄	—	146	1	no	—
822	C₂×C₄⋊C₄	—	146	2	no	—
823	C₂×C₄⋊C₄	—	146	1	no	—
824	C₂×C₄⋊C₄	—	146	1	no	—
825	C₂×C₄⋊C₄	—	146	2	no	—
826	C₂×C₂²⋊C₄	—	146	2	no	—
827	C₂×C₂²⋊C₄	—	146	2	no	—
828	C₂×C₂²⋊C₄	—	146	2	no	—
829	C₂×C₄²	—	73	2	no	—
830	C₂×C₄²	—	73	1	no	—
831	C₂×C₄²	—	146	1	no	—
832	C₂×C₄²	—	146	1	no	—
833	C₂×C₄²	—	146	2	no	—
834	#107	—	73	1	no	—
835	#107	—	73	2	no	—
836	#107	—	73	1	no	—
837	#107	—	73	1	no	—
838	#107	—	73	2	no	—
839	#107	—	73	2	no	—
840	#107	C₂²×D₇₃	1	1	yes	characteristic
841	#107	C₂²×D₇₃	1	2	yes	—
842	C₄⋊C₈	—	73	2	no	—
843	C₄⋊C₈	—	73	2	no	—
844	C₄⋊C₈	—	73	2	no	—
845	C₄⋊C₈	—	73	1	no	—
846	C₄⋊C₈	—	73	2	no	—
847	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
849	#103	—	73	1	no	—
850	#103	—	73	1	no	—
851	#103	—	73	2	no	—
852	#103	—	73	1	no	—
853	#103	—	73	1	no	—
854	#103	—	73	2	no	—
855	#103	—	73	1	no	—
856	#103	—	73	1	no	—
857	#103	—	73	2	no	—
858	#103	C₂²×D₇₃	1	1	yes	characteristic
859	#103	C₂²×D₇₃	1	1	yes	characteristic
860	#103	C₂²×D₇₃	1	2	yes	—
861	#102	—	73	2	no	—
862	#102	—	73	2	no	—
863	#102	—	73	2	no	—
864	#102	—	73	2	no	—
865	#102	—	73	2	no	—
866	#102	—	73	2	no	—
867	#102	—	73	2	no	—
868	#102	—	73	2	no	—
869	#102	—	73	2	no	—
870	#102	C₂²×D₇₃	1	2	yes	—
871	#102	C₂²×D₇₃	1	2	yes	—
872	#102	C₂²×D₇₃	1	2	yes	—
873	#97	—	73	2	no	—
874	#97	—	73	2	no	—
875	#97	—	73	2	no	—
876	#97	C₂²×D₇₃	1	2	yes	—
877	C₄×C₈	—	73	1	no	—
878	C₄×C₈	—	73	1	no	—
879	C₄×C₈	—	73	1	no	—
880	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
881	C₂⁴	—	146	2	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	584	4	no	—
885	C₂×Q₈	—	584	2	no	—
886	C₂×Q₈	—	73	2	no	—
887	C₂×Q₈	—	73	1	no	—
888	C₂×Q₈	—	73	4	no	—
889	C₂×Q₈	—	73	1	no	—
890	C₂×Q₈	—	73	1	no	—
891	C₂×Q₈	—	146	1	no	—
892	C₂×Q₈	—	146	2	no	—
893	C₂×Q₈	—	146	2	no	—
894	C₂×Q₈	—	146	2	no	—
895	C₂×Q₈	—	146	1	no	—
896	C₂×Q₈	—	146	2	no	—
897	C₂×Q₈	—	146	2	no	—
898	C₂×Q₈	—	146	4	no	—
899	C₂×Q₈	—	146	2	no	—
900	C₂×Q₈	—	146	2	no	—
901	C₂×Q₈	—	146	1	no	—
902	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
903	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
904	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	292	4	no	—
908	C₂×D₄	—	584	2	no	—
909	C₂×D₄	—	73	2	no	—
910	C₂×D₄	—	146	4	no	—
911	C₂×D₄	—	146	4	no	—
912	C₂×D₄	—	146	2	no	—
913	C₂×D₄	—	146	2	no	—
914	C₂×D₄	—	146	2	no	—
915	C₂×D₄	—	146	1	no	—
916	C₂×D₄	—	146	1	no	—
917	C₂×D₄	C₂³×D₇₃	1	2	yes	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	584	4	no	—
920	C₂²×C₄	—	73	1	no	—
921	C₂²×C₄	—	73	1	no	—
922	C₂²×C₄	—	73	2	no	—
923	C₂²×C₄	—	73	2	no	—
924	C₂²×C₄	—	73	1	no	—
925	C₂²×C₄	—	146	1	no	—
926	C₂²×C₄	—	146	1	no	—
927	C₂²×C₄	—	146	1	no	—
928	C₂²×C₄	—	146	2	no	—
929	C₂²×C₄	—	146	2	no	—
930	C₂²×C₄	—	146	1	no	—
931	C₂²×C₄	—	146	2	no	—
932	C₂²×C₄	—	146	2	no	—
933	Q₁₆	—	2	2	no	—
934	Q₁₆	—	146	2	no	—
935	Q₁₆	—	146	2	no	—
936	Q₁₆	—	146	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	146	4	no	—
939	SD₁₆	—	146	4	no	—
940	SD₁₆	—	146	4	no	—
941	C₂×C₈	—	73	1	no	—
942	C₂×C₈	—	73	1	no	—
943	C₂×C₈	—	73	2	no	—
944	C₂×C₈	—	146	2	no	—
945	C₂×C₈	—	146	4	no	—
946	C₂×C₈	—	146	2	no	—
947	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
948	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
949	C₂×C₈	C₂³×D₇₃	1	2	yes	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	73	2	no	—
956	C₄⋊C₄	—	73	2	no	—
957	C₄⋊C₄	—	73	2	no	—
958	C₄⋊C₄	—	73	1	no	—
959	C₄⋊C₄	—	73	2	no	—
960	C₄⋊C₄	—	73	2	no	—
961	C₄⋊C₄	—	73	1	no	—
962	C₄⋊C₄	—	73	1	no	—
963	C₄⋊C₄	—	146	1	no	—
964	C₄⋊C₄	—	146	1	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	—	146	2	no	—
970	C₄⋊C₄	—	146	2	no	—
971	C₄⋊C₄	—	146	2	no	—
972	C₄⋊C₄	—	146	1	no	—
973	C₄⋊C₄	—	146	2	no	—
974	C₄⋊C₄	—	146	1	no	—
975	C₄⋊C₄	—	146	1	no	—
976	C₄⋊C₄	—	146	2	no	—
977	C₄⋊C₄	—	146	1	no	—
978	C₄⋊C₄	—	146	2	no	—
979	C₄⋊C₄	—	146	1	no	—
980	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
981	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
982	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
983	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	146	2	no	—
989	C₂²⋊C₄	—	146	2	no	—
990	C₂²⋊C₄	—	146	2	no	—
991	C₂²⋊C₄	—	146	2	no	—
992	C₂²⋊C₄	—	146	2	no	—
993	C₂²⋊C₄	—	146	2	no	—
994	C₂²⋊C₄	—	146	2	no	—
995	C₂²⋊C₄	—	146	2	no	—
996	C₂²⋊C₄	—	146	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	73	2	no	—
1001	C₄²	—	73	2	no	—
1002	C₄²	—	73	1	no	—
1003	C₄²	—	73	1	no	—
1004	C₄²	—	73	1	no	—
1005	C₄²	—	73	2	no	—
1006	C₄²	—	146	1	no	—
1007	C₄²	—	146	1	no	—
1008	C₄²	—	146	1	no	—
1009	C₄²	—	146	2	no	—
1010	C₄²	—	146	1	no	—
1011	C₄²	—	146	2	no	—
1012	C₄²	—	146	1	no	—
1013	C₄²	—	146	2	no	—
1014	C₄²	—	146	1	no	—
1015	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1016	C₄²	C₂³×D₇₃	1	2	yes	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	292	4	no	—
1019	C₂³	—	292	4	no	—
1020	C₂³	—	292	4	no	—
1021	C₂³	—	73	1	no	—
1022	C₂³	—	146	2	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	8	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	292	2	no	—
1030	Q₈	—	584	2	no	—
1031	Q₈	—	584	1	no	—
1032	Q₈	—	584	2	no	—
1033	Q₈	—	584	2	no	—
1034	Q₈	—	584	2	no	—
1035	Q₈	—	73	2	no	—
1036	Q₈	—	146	4	no	—
1037	Q₈	—	146	4	no	—
1038	Q₈	—	146	1	no	—
1039	Q₈	—	146	1	no	—
1040	Q₈	—	146	2	no	—
1041	Q₈	—	146	1	no	—
1042	Q₈	#41×D₇₃	1	2	yes	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	292	4	no	—
1048	D₄	—	292	4	no	—
1049	D₄	—	292	2	no	—
1050	D₄	—	584	1	no	—
1051	D₄	—	584	2	no	—
1052	D₄	—	146	2	no	—
1053	D₄	—	146	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	292	2	no	—
1061	C₂×C₄	—	292	2	no	—
1062	C₂×C₄	—	292	4	no	—
1063	C₂×C₄	—	292	2	no	—
1064	C₂×C₄	—	584	2	no	—
1065	C₂×C₄	—	584	2	no	—
1066	C₂×C₄	—	584	2	no	—
1067	C₂×C₄	—	73	1	no	—
1068	C₂×C₄	—	73	1	no	—
1069	C₂×C₄	—	73	4	no	—
1070	C₂×C₄	—	73	2	no	—
1071	C₂×C₄	—	73	2	no	—
1072	C₂×C₄	—	73	2	no	—
1073	C₂×C₄	—	73	2	no	—
1074	C₂×C₄	—	73	1	no	—
1075	C₂×C₄	—	146	4	no	—
1076	C₂×C₄	—	146	2	no	—
1077	C₂×C₄	—	146	4	no	—
1078	C₂×C₄	—	146	4	no	—
1079	C₂×C₄	—	146	1	no	—
1080	C₂×C₄	—	146	1	no	—
1081	C₂×C₄	—	146	1	no	—
1082	C₂×C₄	—	146	2	no	—
1083	C₂×C₄	—	146	1	no	—
1084	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1085	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1086	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1087	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1088	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1089	C₈	—	2	2	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	146	2	no	—
1093	C₈	—	146	1	no	—
1094	C₈	—	146	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	292	2	no	—
1099	C₂²	—	292	2	no	—
1100	C₂²	—	292	2	no	—
1101	C₂²	—	584	8	no	—
1102	C₂²	—	73	2	no	—
1103	C₂²	—	73	2	no	—
1104	C₂²	—	73	2	no	—
1105	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	292	1	no	—
1115	C₄	—	292	1	no	—
1116	C₄	—	292	1	no	—
1117	C₄	—	292	2	no	—
1118	C₄	—	73	2	no	—
1119	C₄	—	73	2	no	—
1120	C₄	—	146	2	no	—
1121	C₄	—	146	2	no	—
1122	C₄	—	146	2	no	—
1123	C₄	—	146	1	no	—
1124	C₄	#137×D₇₃	1	2	yes	—
1125	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1126	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1127	C₂	—	8	2	no	—
1128	C₂	—	584	2	no	—
1129	C₂	—	73	4	no	—
1130	C₂	#548×D₇₃	1	1	yes	characteristic
1131	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1132	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×#3375	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#127×D₇₃	C₂²
hypercenter	#3375	D₇₃
hypocenter	C₇₃	C₂×#3375
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3375

Complements

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

N	H ≅ G/N	type
2. Q₈²×D₇₃	C₂	semidirect
3. #22622750	C₂	semidirect
4. #22622749	C₂	semidirect
5. #22622748	C₂	semidirect
6. #22622747	C₂	semidirect
7. #22622746	C₂	semidirect
8. #22622745	C₂	semidirect
9. #22622744	C₂	semidirect
10. #22622743	C₂	semidirect
11. #22622742	C₂	semidirect
12. #22622741	C₂	semidirect
13. #22622740	C₂	semidirect
14. #489×D₇₃	C₂	semidirect
16. #477×D₇₃	C₂	semidirect
17. #474×D₇₃	C₂	semidirect
18. #464×D₇₃	C₂	semidirect
20. #446×D₇₃	C₂	semidirect
21. #440×D₇₃	C₂	semidirect
22. C₄×Q₁₆×D₇₃	C₂	semidirect
23. C₇₃×#3375	C₂	semidirect
35. Q₈×Dic₁₄₆	C₂²	semidirect
36. Q₈×Dic₁₄₆	C₂²	semidirect
37. Q₈×Dic₁₄₆	C₂²	semidirect
40. #17989317	C₂²	semidirect
41. #17989317	C₂²	semidirect
57. #17988949	C₂²	semidirect
58. #17988948	C₂²	semidirect
59. #17988948	C₂²	semidirect
60. #17988947	C₂²	semidirect
61. #17988946	C₂²	semidirect
62. #17988945	C₂²	semidirect
63. #17988945	C₂²	semidirect
69. #17988883	C₂²	semidirect
70. #17988882	C₂²	semidirect
71. #17988881	C₂²	semidirect
72. #17988880	C₂²	semidirect
73. #17988879	C₂²	semidirect
74. #17988868	C₂²	semidirect
75. #17988867	C₂²	semidirect
76. #17988866	C₂²	semidirect
77. #17988866	C₂²	semidirect
78. #17988865	C₂²	semidirect
79. #17988865	C₂²	semidirect
80. #17988864	C₂²	semidirect
81. #17988812	C₂²	semidirect
82. #17988811	C₂²	semidirect
83. #17988810	C₂²	semidirect
84. #17988809	C₂²	semidirect
85. #17988808	C₂²	semidirect
86. #17988807	C₂²	semidirect
87. #17988806	C₂²	semidirect
93. #17988718	C₂²	semidirect
94. #17988717	C₂²	semidirect
95. #17988716	C₂²	semidirect
96. #17988715	C₂²	semidirect
97. #17988714	C₂²	semidirect
98. #17988690	C₂²	semidirect
99. #17988689	C₂²	semidirect
100. #17988688	C₂²	semidirect
101. #17988687	C₂²	semidirect
102. #17988686	C₂²	semidirect
103. #17988685	C₂²	semidirect
104. #17988684	C₂²	semidirect
105. C₄×Dic₂₉₂	C₂²	semidirect
106. Q₁₆×Dic₇₃	C₂²	semidirect
107. #17988681	C₂²	semidirect
108. C₄×#11924018	C₂²	semidirect
109. C₄×#11924018	C₂²	semidirect
110. #17988679	C₂²	semidirect
111. #17988679	C₂²	semidirect
125. Q₈²×C₇₃	C₂²	semidirect
126. #489×C₇₃	C₂²	semidirect
128. #477×C₇₃	C₂²	semidirect
129. #474×C₇₃	C₂²	semidirect
130. #464×C₇₃	C₂²	semidirect
132. #446×C₇₃	C₂²	semidirect
133. #440×C₇₃	C₂²	semidirect
134. C₄×Q₁₆×C₇₃	C₂²	semidirect
566. D₇₃	#3375	direct (N × H)
580. #3375	D₇₃	direct (N × H)
590. C₇₃	C₂×#3375	semidirect
610. Q₈²	C₂×D₇₃	semidirect
633. #489	C₂×D₇₃	semidirect
645. #477	C₂×D₇₃	semidirect
653. #474	C₂×D₇₃	semidirect
661. #464	C₂×D₇₃	semidirect
673. #446	C₂×D₇₃	semidirect
681. #440	C₂×D₇₃	semidirect
689. C₄×Q₁₆	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#559×D₇₃	2
Q₈²×D₇₃	2
#22622750	2
#22622749	2
#22622748	2
#22622747	2
#22622746	2
#22622745	2
#22622744	2
#22622743	2
#22622742	2
#22622741	2
#22622740	2
#489×D₇₃	2
#486×D₇₃	2
#477×D₇₃	2
#474×D₇₃	2
#464×D₇₃	2
#460×D₇₃	2
#446×D₇₃	2
#440×D₇₃	2
C₄×Q₁₆×D₇₃	2
C₇₃×#3375	2
C₂×#3375	73

Subgroups — #3375×D73 #33965713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3375×D₇₃ #33965713