Subgroups — #33966120

Order 18688.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623827	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623750	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622778	C₂	1	2	yes	maximal, complemented
4	#22622763	C₂	1	2	yes	maximal, complemented
5	#22622746	C₂	1	2	yes	maximal, complemented
6	#22622724	C₂	1	2	yes	maximal, complemented
7	#22622704	C₂	1	2	yes	maximal, complemented
8	#22622689	C₂	1	2	yes	maximal, complemented
9	#22622672	C₂	1	2	yes	maximal, complemented
10	#22622650	C₂	1	2	yes	maximal, complemented
11	#22620300	C₂	1	1	yes	maximal, characteristic, complemented
12	#22620289	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17988947	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619776	C₂	1	1	yes	maximal, characteristic, complemented
15	#22619765	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619746	C₂	1	1	yes	maximal, characteristic, complemented
17	#22619479	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619468	C₂	1	1	yes	maximal, characteristic
19	#22619425	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618871	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618777	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618766	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556621	C₂²	1	1	yes	characteristic
25	C₂×#14556616	C₂²	1	1	yes	characteristic
26	#17989320	C₂²	1	2	yes	—
27	#17989320	C₂²	1	2	yes	—
28	Q₈×Dic₁₄₆	C₂²	1	2	yes	complemented
29	#17989316	C₂²	1	2	yes	complemented
30	#17989309	C₂²	1	2	yes	—
31	#17989309	C₂²	1	2	yes	—
32	#17989294	—	2	2	no	—
33	#17989294	C₂²	1	2	yes	complemented
34	#17989266	—	2	2	no	—
35	#17989266	—	2	2	no	—
36	D₄×Dic₁₄₆	—	2	2	no	—
37	D₄×Dic₁₄₆	C₂²	1	2	yes	complemented
38	#17989215	—	2	1	no	—
39	#17989215	—	2	1	no	—
40	#17989215	C₂²	1	1	yes	characteristic
41	#17989215	C₂²	1	1	yes	characteristic
42	#17989208	—	2	1	no	—
43	#17989208	—	2	1	no	—
44	#17989158	C₂²	1	1	yes	characteristic
45	#17989151	C₂²	1	1	yes	characteristic
46	#17989144	—	2	1	no	—
47	#17989144	C₂²	1	1	yes	characteristic
48	C₂×#14556591	—	2	1	no	—
49	C₂×#14556591	C₂²	1	1	yes	characteristic
50	#17989121	—	2	1	no	—
51	#17989121	—	2	1	no	—
52	C₂×#14556579	C₂²	1	1	yes	characteristic
53	#17989070	C₂²	1	1	yes	characteristic
54	#17989070	C₂²	1	1	yes	characteristic
55	#17989064	C₂²	1	1	yes	characteristic
56	#17989061	C₂²	1	1	yes	characteristic
57	#17988954	C₂²	1	2	yes	complemented
58	#17988950	C₂²	1	2	yes	—
59	#17988948	C₂²	1	2	yes	—
60	#17988947	C₂²	1	2	yes	—
61	#17988947	C₂²	1	2	yes	—
62	#17988947	C₂²	1	2	yes	—
63	#17988947	C₂²	1	2	yes	—
64	#17988945	C₂²	1	2	yes	complemented
65	#17988943	C₂²	1	2	yes	—
66	#17988940	C₂²	1	2	yes	complemented
67	#17988936	C₂²	1	2	yes	complemented
68	#17988932	C₂²	1	2	yes	—
69	#17988897	C₂²	1	2	yes	complemented
70	#17988893	C₂²	1	2	yes	complemented
71	#17988890	C₂²	1	2	yes	—
72	#17988886	C₂²	1	2	yes	—
73	#17988882	C₂²	1	2	yes	complemented
74	#17988881	C₂²	1	2	yes	complemented
75	#17988877	C₂²	1	2	yes	complemented
76	#17988876	C₂²	1	2	yes	—
77	#17988872	C₂²	1	2	yes	complemented
78	#17988871	C₂²	1	2	yes	complemented
79	#17988867	C₂²	1	2	yes	complemented
80	#17988866	C₂²	1	2	yes	—
81	#17988811	C₂²	1	2	yes	—
82	#17988809	C₂²	1	2	yes	—
83	#17988809	C₂²	1	2	yes	—
84	#17988807	C₂²	1	2	yes	complemented
85	#17988804	C₂²	1	2	yes	—
86	#17988802	C₂²	1	2	yes	—
87	#17988802	C₂²	1	2	yes	—
88	#17988800	C₂²	1	2	yes	complemented
89	#17988795	C₂²	1	2	yes	complemented
90	#17988790	C₂²	1	2	yes	complemented
91	#17988785	C₂²	1	2	yes	—
92	#17988780	C₂²	1	2	yes	—
93	#17988715	C₂²	1	2	yes	complemented
94	#17988715	C₂²	1	2	yes	complemented
95	#17988715	C₂²	1	2	yes	complemented
96	#17988715	C₂²	1	2	yes	complemented
97	#17988696	C₂²	1	2	yes	—
98	#17988691	C₂²	1	2	yes	complemented
99	#17988690	C₂²	1	2	yes	—
100	#17988684	C₂²	1	2	yes	complemented
101	#17988679	C₂²	1	2	yes	complemented
102	#17988678	C₂²	1	2	yes	complemented
103	#17988672	C₂²	1	2	yes	—
104	#17988667	C₂²	1	2	yes	—
105	#17988630	C₂²	1	1	yes	characteristic
106	#17988630	C₂²	1	1	yes	characteristic
107	#17988613	C₂²	1	1	yes	characteristic
108	#17988613	C₂²	1	1	yes	characteristic
109	#17988611	C₂²	1	1	yes	characteristic
110	#17988595	C₂²	1	1	yes	characteristic
111	#17988591	C₂²	1	1	yes	characteristic
112	#17988588	C₂²	1	1	yes	characteristic
113	#17988588	C₂²	1	1	yes	characteristic
114	C₂×#14556516	C₂²	1	1	yes	characteristic
115	C₂×#14556516	C₂²	1	1	yes	characteristic
116	C₂×#14556513	C₂²	1	1	yes	characteristic
117	C₂×#14556513	C₂²	1	1	yes	characteristic
118	#17988542	C₂²	1	1	yes	characteristic
119	#17988542	C₂²	1	1	yes	characteristic
120	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
123	#442×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#442×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	#427×C₇₃	C₂²	1	1	yes	characteristic
132	#416×C₇₃	C₂²	1	1	yes	characteristic
133	#416×C₇₃	C₂²	1	1	yes	characteristic
134	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
135	C₂²×Dic₁₄₆	—	2	2	no	—
136	C₂²×Dic₁₄₆	—	2	1	no	—
137	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
138	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
139	#14556621	—	2	4	no	—
140	#14556616	—	2	4	no	—
141	C₂×#11924018	C₂³	1	2	yes	—
142	C₂×#11924016	C₂³	1	2	yes	—
143	C₂×#11924015	C₂³	1	2	yes	—
144	C₂×#11924013	C₂³	1	2	yes	—
145	C₂×#11924012	C₂³	1	1	yes	characteristic
146	C₂×#11924012	C₂³	1	1	yes	characteristic
147	#14556591	—	2	2	no	—
148	#14556591	—	2	1	no	—
149	#14556591	—	2	1	no	—
150	#14556591	—	2	2	no	—
151	#14556591	—	2	1	no	—
152	#14556591	—	2	1	no	—
153	#14556591	D₄	1	1	yes	characteristic
154	#14556591	D₄	1	1	yes	characteristic
155	#14556591	C₂³	1	2	yes	—
156	#14556591	C₂³	1	2	yes	—
157	#14556590	—	2	2	no	—
158	#14556590	—	2	2	no	—
159	#14556590	C₂³	1	2	yes	—
160	#14556590	C₂³	1	2	yes	—
161	#14556589	C₂³	1	2	yes	—
162	#14556587	C₂³	1	2	yes	—
163	#14556586	—	2	2	no	—
164	#14556586	—	2	2	no	—
165	#14556585	—	2	2	no	—
166	#14556585	—	2	2	no	—
167	#14556583	—	2	1	no	—
168	#14556583	—	2	1	no	—
169	#14556583	D₄	1	1	yes	characteristic
170	#14556583	D₄	1	1	yes	characteristic
171	#14556582	—	2	2	no	—
172	#14556582	—	2	2	no	—
173	#14556582	C₂³	1	2	yes	—
174	#14556582	C₂³	1	2	yes	—
175	#14556580	C₂³	1	2	yes	—
176	#14556579	—	2	1	no	—
177	#14556579	—	2	1	no	—
178	#14556579	C₂³	1	2	yes	—
179	#14556579	C₂³	1	2	yes	—
180	#14556578	C₂³	1	2	yes	—
181	#14556577	—	2	2	no	—
182	#14556577	—	2	2	no	—
183	#14556574	—	2	2	no	—
184	#14556574	—	2	2	no	—
185	#14556573	—	2	2	no	—
186	#14556573	—	2	2	no	—
187	#14556572	—	2	2	no	—
188	#14556570	—	2	2	no	—
189	#14556570	—	2	1	no	—
190	#14556570	—	2	1	no	—
191	#14556570	—	2	2	no	—
192	#14556570	D₄	1	2	yes	—
193	#14556570	D₄	1	2	yes	—
194	#14556569	—	2	2	no	—
195	#14556569	—	2	2	no	—
196	#14556568	—	2	2	no	—
197	#14556568	—	2	2	no	—
198	#14556568	—	2	2	no	—
199	#14556568	—	2	2	no	—
200	#14556568	—	2	2	no	—
201	#14556568	—	2	2	no	—
202	#14556565	—	2	1	no	—
203	#14556565	—	2	1	no	—
204	#14556559	—	2	2	no	—
205	Q₈×Dic₇₃	C₂³	1	2	yes	—
206	Q₈×Dic₇₃	C₂³	1	2	yes	—
207	C₄×Dic₁₄₆	—	2	2	no	—
208	C₄×Dic₁₄₆	—	2	1	no	—
209	C₄×Dic₁₄₆	—	2	1	no	—
210	C₄×Dic₁₄₆	—	2	2	no	—
211	C₄×Dic₁₄₆	C₂³	1	2	yes	—
212	C₄×Dic₁₄₆	C₂³	1	2	yes	—
213	#14556556	C₂³	1	2	yes	—
214	#14556556	C₂³	1	2	yes	—
215	C₄×D₂₉₂	—	2	1	no	—
216	C₄×D₂₉₂	—	2	1	no	—
217	D₄×Dic₇₃	—	2	2	no	—
218	D₄×Dic₇₃	—	2	2	no	—
219	D₄×Dic₇₃	C₂³	1	2	yes	—
220	D₄×Dic₇₃	C₂³	1	2	yes	—
221	#14556553	C₂³	1	2	yes	—
222	#14556553	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₇₃	—	2	2	no	—
224	C₄×C₂²⋊D₇₃	—	2	2	no	—
225	#14556550	—	2	1	no	—
226	#14556550	—	2	1	no	—
227	#14556550	C₂³	1	1	yes	characteristic
228	#14556550	C₂³	1	1	yes	characteristic
229	#14556548	—	2	2	no	—
230	#14556548	—	2	2	no	—
231	#14556547	—	2	2	no	—
232	C₂×C₄⋊Dic₇₃	—	2	1	no	—
233	C₂×C₄⋊Dic₇₃	—	2	1	no	—
234	C₂×C₄⋊Dic₇₃	—	2	2	no	—
235	C₂×C₄⋊Dic₇₃	—	2	1	no	—
236	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
237	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
238	C₂×#11924005	—	2	1	no	—
239	C₂×#11924005	—	2	1	no	—
240	C₂²⋊C₄×D₇₃	—	2	2	no	—
241	#14556524	C₂³	1	2	yes	—
242	#14556524	C₂³	1	2	yes	—
243	#14556522	C₂³	1	2	yes	—
244	#14556522	C₂³	1	2	yes	—
245	C₄⋊#10596831	C₂³	1	2	yes	—
246	C₄⋊#10596831	C₂³	1	2	yes	—
247	#14556520	C₂³	1	2	yes	—
248	#14556520	C₂³	1	2	yes	—
249	#14556520	C₂³	1	2	yes	—
250	#14556520	C₂³	1	2	yes	—
251	#14556516	C₂³	1	2	yes	—
252	#14556516	C₂³	1	2	yes	—
253	#14556516	C₂³	1	2	yes	—
254	#14556516	C₂³	1	2	yes	—
255	#14556515	C₂³	1	2	yes	—
256	#14556515	C₂³	1	2	yes	—
257	#14556514	C₂³	1	2	yes	—
258	#14556514	C₂³	1	2	yes	—
259	#14556513	C₂³	1	2	yes	—
260	#14556513	C₂³	1	2	yes	—
261	#14556513	C₂³	1	2	yes	—
262	#14556513	C₂³	1	2	yes	—
263	#14556512	C₂³	1	2	yes	—
264	#14556512	C₂³	1	2	yes	—
265	#14556511	C₂³	1	2	yes	—
266	#14556511	C₂³	1	2	yes	—
267	#14556501	C₂³	1	2	yes	—
268	#14556501	C₂³	1	2	yes	—
269	C₈×Dic₇₃	C₂³	1	2	yes	—
270	C₈×Dic₇₃	C₂³	1	2	yes	—
271	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
272	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
273	#135×C₇₃	—	2	4	no	—
274	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₇₃	—	2	1	no	—
285	C₄×D₄×C₇₃	—	2	1	no	—
286	C₄×D₄×C₇₃	—	2	1	no	—
287	C₄×D₄×C₇₃	—	2	1	no	—
288	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
292	#117×C₇₃	—	2	1	no	—
293	#117×C₇₃	—	2	1	no	—
294	#117×C₇₃	C₂³	1	1	yes	characteristic
295	#117×C₇₃	C₂³	1	1	yes	characteristic
296	C₂×C₄²×C₇₃	—	2	1	no	—
297	C₂×C₄²×C₇₃	—	2	1	no	—
298	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
299	#107×C₇₃	C₂³	1	1	yes	characteristic
300	#107×C₇₃	C₂³	1	1	yes	characteristic
301	#106×C₇₃	C₂³	1	1	yes	characteristic
302	#106×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#103×C₇₃	C₂³	1	1	yes	characteristic
305	#103×C₇₃	C₂³	1	1	yes	characteristic
306	#103×C₇₃	C₂³	1	1	yes	characteristic
307	#102×C₇₃	C₂³	1	1	yes	characteristic
308	#102×C₇₃	C₂³	1	1	yes	characteristic
309	#102×C₇₃	C₂³	1	1	yes	characteristic
310	#102×C₇₃	C₂³	1	1	yes	characteristic
311	#97×C₇₃	C₂³	1	1	yes	characteristic
312	#97×C₇₃	C₂³	1	1	yes	characteristic
313	#97×C₇₃	C₂³	1	1	yes	characteristic
314	#97×C₇₃	C₂³	1	1	yes	characteristic
315	C₂³×D₇₃	—	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	—	2	2	no	—
323	C₂×Dic₁₄₆	—	8	4	no	—
324	C₂×Dic₁₄₆	—	8	2	no	—
325	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
326	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
327	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
328	C₂×D₂₉₂	—	2	2	no	—
329	C₂×D₂₉₂	—	2	2	no	—
330	C₂×D₂₉₂	—	2	1	no	—
331	C₂×D₂₉₂	C₂⁴	1	2	yes	—
332	C₂×C₂²⋊D₇₃	—	2	2	no	—
333	C₂×C₂²⋊D₇₃	—	2	2	no	—
334	C₂²×Dic₇₃	—	2	1	no	—
335	C₂²×Dic₇₃	—	2	1	no	—
336	C₂²×Dic₇₃	—	2	1	no	—
337	C₂²×Dic₇₃	—	2	2	no	—
338	C₂²×Dic₇₃	—	2	2	no	—
339	C₂×C₄×D₇₃	—	2	2	no	—
340	C₂×C₄×D₇₃	—	2	2	no	—
341	#11924018	—	2	4	no	—
342	#11924016	—	2	4	no	—
343	#11924015	—	2	4	no	—
344	#11924013	—	2	4	no	—
345	#11924012	—	2	2	no	—
346	#11924012	—	2	2	no	—
347	C₂×#10596831	C₂⁴	1	2	yes	—
348	C₂×#10596831	C₂⁴	1	2	yes	—
349	C₄⋊Dic₇₃	—	2	2	no	—
350	C₄⋊Dic₇₃	—	2	1	no	—
351	C₄⋊Dic₇₃	—	2	1	no	—
352	C₄⋊Dic₇₃	—	2	2	no	—
353	C₄⋊Dic₇₃	—	2	2	no	—
354	C₄⋊Dic₇₃	—	2	2	no	—
355	C₄⋊Dic₇₃	—	2	2	no	—
356	C₄⋊Dic₇₃	—	2	2	no	—
357	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
360	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
363	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
364	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
365	#11924007	—	2	2	no	—
366	#11924007	—	2	2	no	—
367	#11924007	—	2	2	no	—
368	#11924007	—	2	2	no	—
369	#11924007	—	2	2	no	—
370	#11924007	—	2	2	no	—
371	#11924007	—	2	2	no	—
372	#11924007	—	2	2	no	—
373	#11924007	C₂×D₄	1	2	yes	—
374	#11924007	C₂×D₄	1	2	yes	—
375	#11924007	C₂×D₄	1	2	yes	—
376	#11924007	C₂×D₄	1	2	yes	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	—	2	2	no	—
379	C₂²⋊Dic₇₃	—	2	2	no	—
380	C₂²⋊Dic₇₃	—	2	2	no	—
381	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
382	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
383	#11924005	—	2	2	no	—
384	#11924005	—	2	2	no	—
385	#11924005	—	2	2	no	—
386	#11924005	—	2	2	no	—
387	#11924005	—	2	2	no	—
388	#11924005	—	2	2	no	—
389	#11924005	—	2	2	no	—
390	#11924005	—	2	2	no	—
391	C₄×Dic₇₃	—	2	2	no	—
392	C₄×Dic₇₃	—	2	2	no	—
393	C₄×Dic₇₃	—	2	2	no	—
394	C₄×Dic₇₃	—	2	2	no	—
395	C₄×Dic₇₃	C₂⁴	1	2	yes	—
396	C₄×Dic₇₃	C₂⁴	1	2	yes	—
397	#41×C₇₃	—	2	2	no	—
398	#41×C₇₃	—	2	2	no	—
399	#41×C₇₃	—	2	2	no	—
400	#41×C₇₃	#41	1	4	yes	—
401	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₂×D₄×C₇₃	—	2	1	no	—
404	C₂×D₄×C₇₃	—	2	1	no	—
405	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₇₃	—	2	1	no	—
408	C₂²×C₄×C₇₃	—	2	1	no	—
409	C₂²×C₄×C₇₃	—	2	1	no	—
410	C₂²×C₄×C₇₃	—	2	1	no	—
411	C₂²×C₄×C₇₃	—	2	1	no	—
412	C₂²×C₄×C₇₃	—	2	1	no	—
413	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
416	Q₁₆×C₇₃	—	2	2	no	—
417	SD₁₆×C₇₃	—	2	2	no	—
418	SD₁₆×C₇₃	—	2	2	no	—
419	D₈×C₇₃	—	2	2	no	—
420	C₂×C₈×C₇₃	—	2	2	no	—
421	C₂×C₈×C₇₃	—	2	2	no	—
422	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
423	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
424	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₇₃	—	2	1	no	—
427	C₄⋊C₄×C₇₃	—	2	1	no	—
428	C₄⋊C₄×C₇₃	—	2	1	no	—
429	C₄⋊C₄×C₇₃	—	2	1	no	—
430	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
431	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₂²⋊C₄×C₇₃	—	2	1	no	—
435	C₂²⋊C₄×C₇₃	—	2	1	no	—
436	C₂²⋊C₄×C₇₃	—	2	1	no	—
437	C₂²⋊C₄×C₇₃	—	2	1	no	—
438	C₂²⋊C₄×C₇₃	—	2	1	no	—
439	C₂²⋊C₄×C₇₃	—	2	1	no	—
440	C₄²×C₇₃	—	2	1	no	—
441	C₄²×C₇₃	—	2	1	no	—
442	C₄²×C₇₃	—	2	1	no	—
443	C₄²×C₇₃	—	2	1	no	—
444	C₄²×C₇₃	—	2	1	no	—
445	C₄²×C₇₃	—	2	1	no	—
446	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
447	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
448	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
449	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
450	C₂³×C₇₃	—	2	1	no	—
451	C₂³×C₇₃	—	2	1	no	—
452	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
453	C₂²×D₇₃	—	2	2	no	—
454	C₂²×D₇₃	—	4	2	no	—
455	C₂²×D₇₃	—	8	1	no	—
456	C₂²×D₇₃	—	8	1	no	—
457	Q₈×C₇₃	—	2	1	no	—
458	Q₈×C₇₃	—	2	1	no	—
459	Q₈×C₇₃	—	2	1	no	—
460	Q₈×C₇₃	C₂×#41	1	2	yes	—
461	D₄×C₇₃	—	2	4	no	—
462	D₄×C₇₃	—	2	1	no	—
463	D₄×C₇₃	—	2	1	no	—
464	D₄×C₇₃	—	2	1	no	—
465	D₄×C₇₃	—	4	2	no	—
466	D₄×C₇₃	C₂×#41	1	2	yes	—
467	C₂×C₄×C₇₃	—	2	1	no	—
468	C₂×C₄×C₇₃	—	2	4	no	—
469	C₂×C₄×C₇₃	—	2	1	no	—
470	C₂×C₄×C₇₃	—	2	1	no	—
471	C₂×C₄×C₇₃	—	2	1	no	—
472	C₂×C₄×C₇₃	—	2	1	no	—
473	C₂×C₄×C₇₃	—	2	1	no	—
474	C₂×C₄×C₇₃	—	4	1	no	—
475	C₂×C₄×C₇₃	—	4	1	no	—
476	C₂×C₄×C₇₃	—	4	2	no	—
477	C₂×C₄×C₇₃	—	4	2	no	—
478	C₂×C₄×C₇₃	—	4	2	no	—
479	C₂×C₄×C₇₃	—	8	1	no	—
480	C₂×C₄×C₇₃	—	8	1	no	—
481	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
487	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
489	C₂²⋊D₇₃	—	8	2	no	—
490	C₂²⋊D₇₃	—	8	2	no	—
491	C₂×Dic₇₃	—	2	2	no	—
492	C₂×Dic₇₃	—	2	2	no	—
493	C₂×Dic₇₃	—	2	2	no	—
494	C₂×Dic₇₃	—	4	2	no	—
495	C₂×Dic₇₃	—	8	2	no	—
496	C₂×Dic₇₃	—	8	2	no	—
497	C₂×Dic₇₃	—	8	1	no	—
498	C₂×Dic₇₃	—	8	1	no	—
499	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
500	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
501	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
502	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
503	D₂₉₂	—	2	2	no	—
504	D₂₉₂	—	2	2	no	—
505	D₂₉₂	—	4	2	no	—
506	C₄×D₇₃	—	8	2	no	—
507	C₄×D₇₃	—	8	2	no	—
508	Dic₁₄₆	—	2	2	no	—
509	Dic₁₄₆	—	2	2	no	—
510	Dic₁₄₆	—	4	2	no	—
511	Dic₁₄₆	—	4	2	no	—
512	Dic₁₄₆	—	4	4	no	—
513	Dic₁₄₆	—	4	2	no	—
514	Dic₁₄₆	—	8	2	no	—
515	Dic₁₄₆	—	8	2	no	—
516	Dic₁₄₆	—	8	2	no	—
517	C₈×C₇₃	—	2	1	no	—
518	C₈×C₇₃	—	2	1	no	—
519	C₈×C₇₃	—	2	1	no	—
520	C₈×C₇₃	—	2	1	no	—
521	#10596831	—	2	2	no	—
522	#10596831	—	2	2	no	—
523	C₂²×C₇₃	—	2	1	no	—
524	C₂²×C₇₃	—	2	1	no	—
525	C₂²×C₇₃	—	2	2	no	—
526	C₂²×C₇₃	—	4	1	no	—
527	C₂²×C₇₃	—	4	1	no	—
528	C₂²×C₇₃	—	4	1	no	—
529	C₂²×C₇₃	—	4	1	no	—
530	C₂²×C₇₃	—	4	1	no	—
531	C₂²×C₇₃	#548	1	2	yes	—
532	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
533	C₂×D₇₃	—	4	2	no	—
534	C₂×D₇₃	—	4	2	no	—
535	C₂×D₇₃	—	4	2	no	—
536	C₂×D₇₃	—	16	2	no	—
537	C₄×C₇₃	—	2	1	no	—
538	C₄×C₇₃	—	2	1	no	—
539	C₄×C₇₃	—	2	1	no	—
540	C₄×C₇₃	—	2	1	no	—
541	C₄×C₇₃	—	2	2	no	—
542	C₄×C₇₃	—	4	1	no	—
543	C₄×C₇₃	—	4	1	no	—
544	C₄×C₇₃	—	4	1	no	—
545	C₄×C₇₃	—	4	1	no	—
546	C₄×C₇₃	—	4	1	no	—
547	C₄×C₇₃	#548	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	2	no	—
554	Dic₇₃	—	4	2	no	—
555	Dic₇₃	—	4	2	no	—
556	Dic₇₃	—	4	2	no	—
557	#61336	—	73	1	no	maximal, Sylow
558	C₂×C₇₃	—	2	2	no	—
559	C₂×C₇₃	—	4	2	no	—
560	C₂×C₇₃	—	8	1	no	—
561	C₂×C₇₃	C₂×#548	1	1	yes	characteristic
562	C₂×C₇₃	#3585	1	1	yes	characteristic
563	C₂×C₇₃	#3586	1	1	yes	characteristic
564	D₇₃	—	8	2	no	—
565	#3510	—	73	1	no	—
566	#3503	—	73	1	no	—
567	#3377	—	73	2	no	—
568	#3376	—	73	2	no	—
569	#3375	—	73	2	no	—
570	#3373	—	73	2	no	—
571	#3371	—	73	2	no	—
572	#3370	—	73	2	no	—
573	#3369	—	73	2	no	—
574	#3367	—	73	2	no	—
575	#3137	—	73	1	no	—
576	#3136	—	73	1	no	—
577	C₂×#489	—	73	1	no	—
578	#3082	—	73	1	no	—
579	#3081	—	73	1	no	—
580	#3079	—	73	1	no	—
581	#3046	—	73	1	no	—
582	#3045	—	73	1	no	—
583	#3040	—	73	1	no	—
584	#2961	—	73	1	no	—
585	#2947	—	73	1	no	—
586	#2946	—	73	1	no	—
587	#2943	D₇₃	1	1	yes	characteristic, complemented
588	C₇₃	#61336	1	1	yes	characteristic, complemented, Sylow
589	C₂×#137	—	73	1	no	—
590	C₂×AGL(1,ℤ/8)	—	73	1	no	—
591	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
592	#559	—	73	2	no	—
593	#559	—	73	2	no	—
594	Q₈²	—	73	2	no	—
595	#557	—	73	2	no	—
596	#556	—	73	2	no	—
597	#556	—	73	2	no	—
598	#554	—	73	2	no	—
599	#554	—	146	2	no	—
600	#551	—	146	2	no	—
601	#551	—	146	2	no	—
602	D₄×Q₈	—	73	2	no	—
603	D₄×Q₈	—	146	2	no	—
604	#544	—	73	1	no	—
605	#544	—	73	1	no	—
606	#544	—	146	1	no	—
607	#544	—	146	1	no	—
608	#542	—	146	1	no	—
609	#542	—	146	1	no	—
610	#536	—	73	1	no	—
611	#535	—	73	1	no	—
612	#533	—	73	1	no	—
613	#533	—	146	1	no	—
614	C₂×C₄⋊Q₈	—	73	1	no	—
615	C₂×C₄⋊Q₈	—	146	1	no	—
616	#529	—	146	1	no	—
617	#529	—	146	1	no	—
618	C₂×#124	—	73	1	no	—
619	#520	—	73	1	no	—
620	#520	—	73	1	no	—
621	#519	—	73	1	no	—
622	#518	—	73	1	no	—
623	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
624	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
625	#491	—	73	2	no	—
626	#490	—	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	#488	—	73	2	no	—
634	#488	—	73	2	no	—
635	#487	—	73	2	no	—
636	#486	—	73	2	no	—
637	#479	—	73	2	no	—
638	#479	—	73	2	no	—
639	#478	—	73	2	no	—
640	#478	—	73	2	no	—
641	#477	—	73	2	no	—
642	#477	—	73	2	no	—
643	#476	—	73	2	no	—
644	#476	—	73	2	no	—
645	#475	—	73	2	no	—
646	#475	—	73	2	no	—
647	#474	—	73	2	no	—
648	#474	—	73	2	no	—
649	#464	—	73	2	no	—
650	#464	—	73	2	no	—
651	#464	—	73	2	no	—
652	#464	—	73	2	no	—
653	#463	—	73	2	no	—
654	#463	—	73	2	no	—
655	#463	—	73	2	no	—
656	#463	—	73	2	no	—
657	#462	—	73	2	no	—
658	#461	—	73	2	no	—
659	#460	—	73	2	no	—
660	#459	—	73	2	no	—
661	#446	—	73	2	no	—
662	#446	—	73	2	no	—
663	#446	—	73	2	no	—
664	#446	—	73	2	no	—
665	#442	—	73	2	no	—
666	#442	C₂×D₇₃	1	1	yes	characteristic, complemented
667	#442	C₂×D₇₃	1	1	yes	characteristic, complemented
668	#441	—	73	2	no	—
669	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
670	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
671	#440	—	73	2	no	—
672	#440	—	73	2	no	—
673	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
674	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
675	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
676	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
677	C₄×Q₁₆	—	73	2	no	—
678	C₄×SD₁₆	—	73	2	no	—
679	C₄×SD₁₆	—	73	2	no	—
680	C₄×D₈	—	73	2	no	—
681	#428	—	73	1	no	—
682	#428	—	73	1	no	—
683	#427	C₂×D₇₃	1	1	yes	characteristic
684	#424	—	73	1	no	—
685	#424	—	73	1	no	—
686	#423	—	73	1	no	—
687	#419	—	73	1	no	—
688	#418	—	73	1	no	—
689	#417	—	73	1	no	—
690	#417	—	73	1	no	—
691	#416	C₂×D₇₃	1	1	yes	characteristic
692	#416	C₂×D₇₃	1	1	yes	characteristic
693	C₂×#103	—	73	1	no	—
694	C₂×#103	—	73	1	no	—
695	C₂×#102	—	73	1	no	—
696	C₂×#102	—	73	1	no	—
697	#405	—	73	1	no	—
698	#405	—	73	1	no	—
699	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
700	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
701	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
702	C₂²×Q₈	—	73	1	no	—
703	C₂²×Q₈	—	146	2	no	—
704	C₂²×Q₈	—	146	1	no	—
705	C₂²×D₄	—	73	1	no	—
706	#137	—	146	4	no	—
707	AGL(1,ℤ/8)	—	146	4	no	—
708	#135	—	2	4	no	—
709	C₂×Q₁₆	—	73	2	no	—
710	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
711	C₂×SD₁₆	—	73	2	no	—
712	C₂×SD₁₆	—	73	2	no	—
713	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
714	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
715	C₂×D₈	—	73	2	no	—
716	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
717	C₂×M₁₆	—	73	1	no	—
718	C₂×M₁₆	—	73	1	no	—
719	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
720	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
721	C₄⋊Q₈	—	73	2	no	—
722	C₄⋊Q₈	—	73	2	no	—
723	C₄⋊Q₈	—	73	2	no	—
724	C₄⋊Q₈	—	73	1	no	—
725	C₄⋊Q₈	—	73	1	no	—
726	C₄⋊Q₈	—	73	2	no	—
727	C₄⋊Q₈	—	73	2	no	—
728	C₄⋊Q₈	—	146	1	no	—
729	C₄⋊Q₈	—	146	1	no	—
730	C₄⋊Q₈	—	146	2	no	—
731	C₄⋊Q₈	—	146	2	no	—
732	C₄⋊Q₈	—	146	2	no	—
733	C₄⋊Q₈	—	146	2	no	—
734	C₄⋊Q₈	—	146	1	no	—
735	C₄⋊Q₈	—	146	1	no	—
736	#127	—	73	2	no	—
737	#126	—	146	2	no	—
738	#126	—	146	2	no	—
739	#126	—	146	2	no	—
740	#126	—	146	2	no	—
741	#125	—	73	2	no	—
742	#125	—	73	2	no	—
743	#125	—	73	1	no	—
744	#125	—	73	1	no	—
745	#125	—	146	1	no	—
746	#125	—	146	1	no	—
747	#125	—	146	2	no	—
748	#125	—	146	2	no	—
749	#124	—	73	2	no	—
750	#124	—	73	2	no	—
751	#124	—	73	2	no	—
752	#124	—	73	2	no	—
753	#124	—	146	2	no	—
754	#124	—	146	2	no	—
755	#124	—	146	1	no	—
756	#124	—	146	1	no	—
757	#123	—	146	2	no	—
758	#123	—	146	2	no	—
759	#123	—	146	2	no	—
760	#123	—	146	2	no	—
761	#123	—	146	2	no	—
762	C₂²⋊Q₈	—	73	2	no	—
763	C₂²⋊Q₈	—	73	2	no	—
764	C₂²⋊Q₈	—	146	2	no	—
765	C₂²⋊Q₈	—	146	2	no	—
766	C₂²⋊Q₈	—	146	2	no	—
767	C₂²⋊Q₈	—	146	2	no	—
768	C₂²⋊Q₈	—	146	2	no	—
769	C₂²⋊Q₈	—	146	2	no	—
770	C₂²⋊Q₈	—	146	2	no	—
771	C₂²⋊Q₈	—	146	2	no	—
772	C₂²⋊Q₈	—	146	1	no	—
773	C₂²⋊Q₈	—	146	1	no	—
774	C₂²⋊Q₈	—	146	2	no	—
775	C₂²⋊Q₈	—	146	2	no	—
776	#121	—	146	1	no	—
777	#121	—	146	1	no	—
778	#120	—	146	2	no	—
779	C₄×Q₈	—	73	2	no	—
780	C₄×Q₈	—	73	2	no	—
781	C₄×Q₈	—	73	2	no	—
782	C₄×Q₈	—	73	2	no	—
783	C₄×Q₈	—	73	2	no	—
784	C₄×Q₈	—	73	2	no	—
785	C₄×Q₈	—	146	1	no	—
786	C₄×Q₈	—	146	1	no	—
787	C₄×Q₈	—	146	2	no	—
788	C₄×Q₈	—	146	2	no	—
789	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
790	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
791	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
792	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	1	no	—
797	C₄×D₄	—	73	2	no	—
798	C₄×D₄	—	73	2	no	—
799	C₄×D₄	—	73	2	no	—
800	C₄×D₄	—	73	2	no	—
801	C₄×D₄	—	146	1	no	—
802	C₄×D₄	—	146	1	no	—
803	C₄×D₄	—	146	2	no	—
804	C₄×D₄	—	146	2	no	—
805	C₄×D₄	—	146	2	no	—
806	C₄×D₄	—	146	2	no	—
807	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
808	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
809	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
810	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	73	1	no	—
814	#117	—	73	1	no	—
815	#117	—	146	2	no	—
816	#117	—	146	2	no	—
817	#117	—	146	2	no	—
818	#117	—	146	1	no	—
819	#117	—	146	1	no	—
820	#117	C₂²×D₇₃	1	1	yes	characteristic
821	#117	C₂²×D₇₃	1	1	yes	characteristic
822	C₂×C₄⋊C₄	—	73	1	no	—
823	C₂×C₄⋊C₄	—	73	1	no	—
824	C₂×C₄⋊C₄	—	146	1	no	—
825	C₂×C₄⋊C₄	—	146	1	no	—
826	C₂×C₄⋊C₄	—	146	2	no	—
827	C₂×C₄⋊C₄	—	146	1	no	—
828	C₂×C₂²⋊C₄	—	146	2	no	—
829	C₂×C₂²⋊C₄	—	146	1	no	—
830	C₂×C₂²⋊C₄	—	146	1	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
834	#107	—	73	2	no	—
835	#107	—	73	2	no	—
836	#107	C₂²×D₇₃	1	1	yes	characteristic
837	#107	C₂²×D₇₃	1	1	yes	characteristic
838	#106	—	73	2	no	—
839	#106	—	73	2	no	—
840	#106	C₂²×D₇₃	1	1	yes	characteristic
841	#106	C₂²×D₇₃	1	1	yes	characteristic
842	C₄⋊C₈	—	73	2	no	—
843	C₄⋊C₈	—	73	2	no	—
844	C₄⋊C₈	—	73	2	no	—
845	C₄⋊C₈	—	73	2	no	—
846	C₄⋊C₈	—	73	2	no	—
847	C₄⋊C₈	—	73	2	no	—
848	#103	—	73	2	no	—
849	#103	—	73	2	no	—
850	#103	—	73	2	no	—
851	#103	—	73	2	no	—
852	#103	—	73	2	no	—
853	#103	—	73	2	no	—
854	#103	—	73	2	no	—
855	#103	—	73	2	no	—
856	#103	C₂²×D₇₃	1	1	yes	characteristic
857	#103	C₂²×D₇₃	1	1	yes	characteristic
858	#103	C₂²×D₇₃	1	1	yes	characteristic
859	#103	C₂²×D₇₃	1	1	yes	characteristic
860	#102	—	73	2	no	—
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	C₂²×D₇₃	1	1	yes	characteristic
869	#102	C₂²×D₇₃	1	1	yes	characteristic
870	#102	C₂²×D₇₃	1	1	yes	characteristic
871	#102	C₂²×D₇₃	1	1	yes	characteristic
872	#97	—	73	2	no	—
873	#97	—	73	2	no	—
874	#97	C₂²×D₇₃	1	1	yes	characteristic
875	#97	C₂²×D₇₃	1	1	yes	characteristic
876	#97	C₂²×D₇₃	1	1	yes	characteristic
877	#97	C₂²×D₇₃	1	1	yes	characteristic
878	C₄×C₈	—	73	2	no	—
879	C₄×C₈	—	73	2	no	—
880	C₂⁴	—	146	1	no	—
881	#41	—	2	2	no	—
882	#41	—	2	2	no	—
883	#41	—	2	2	no	—
884	#41	#11924028	1	4	yes	—
885	C₂×Q₈	—	584	2	no	—
886	C₂×Q₈	—	584	4	no	—
887	C₂×Q₈	—	73	2	no	—
888	C₂×Q₈	—	73	2	no	—
889	C₂×Q₈	—	73	2	no	—
890	C₂×Q₈	—	146	2	no	—
891	C₂×Q₈	—	146	2	no	—
892	C₂×Q₈	—	146	2	no	—
893	C₂×Q₈	—	146	2	no	—
894	C₂×Q₈	—	146	1	no	—
895	C₂×Q₈	—	146	2	no	—
896	C₂×Q₈	—	146	2	no	—
897	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
898	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	73	2	no	—
902	C₂×D₄	—	146	2	no	—
903	C₂×D₄	—	146	2	no	—
904	C₂×D₄	—	146	1	no	—
905	C₂×D₄	—	146	2	no	—
906	C₂×D₄	—	146	2	no	—
907	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
908	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	146	2	no	—
916	C₂²×C₄	—	146	2	no	—
917	C₂²×C₄	—	146	1	no	—
918	C₂²×C₄	—	146	2	no	—
919	C₂²×C₄	—	146	2	no	—
920	C₂²×C₄	—	146	1	no	—
921	C₂²×C₄	—	146	1	no	—
922	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
923	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
924	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
925	Q₁₆	—	2	2	no	—
926	Q₁₆	—	146	4	no	—
927	SD₁₆	—	2	2	no	—
928	SD₁₆	—	2	2	no	—
929	SD₁₆	—	146	4	no	—
930	SD₁₆	—	146	4	no	—
931	D₈	—	2	2	no	—
932	D₈	—	146	4	no	—
933	M₁₆	—	146	2	no	—
934	M₁₆	—	146	2	no	—
935	C₂×C₈	—	2	2	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	73	2	no	—
938	C₂×C₈	—	73	2	no	—
939	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
940	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
941	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
942	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
943	C₄⋊C₄	—	2	1	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	73	2	no	—
948	C₄⋊C₄	—	73	2	no	—
949	C₄⋊C₄	—	73	2	no	—
950	C₄⋊C₄	—	73	2	no	—
951	C₄⋊C₄	—	73	1	no	—
952	C₄⋊C₄	—	73	1	no	—
953	C₄⋊C₄	—	73	2	no	—
954	C₄⋊C₄	—	73	1	no	—
955	C₄⋊C₄	—	73	1	no	—
956	C₄⋊C₄	—	73	2	no	—
957	C₄⋊C₄	—	73	2	no	—
958	C₄⋊C₄	—	73	2	no	—
959	C₄⋊C₄	—	146	2	no	—
960	C₄⋊C₄	—	146	2	no	—
961	C₄⋊C₄	—	146	2	no	—
962	C₄⋊C₄	—	146	2	no	—
963	C₄⋊C₄	—	146	2	no	—
964	C₄⋊C₄	—	146	2	no	—
965	C₄⋊C₄	—	146	2	no	—
966	C₄⋊C₄	—	146	2	no	—
967	C₄⋊C₄	—	146	2	no	—
968	C₄⋊C₄	—	146	2	no	—
969	C₄⋊C₄	—	146	2	no	—
970	C₄⋊C₄	—	146	2	no	—
971	C₄⋊C₄	—	146	1	no	—
972	C₄⋊C₄	—	146	1	no	—
973	C₄⋊C₄	—	146	2	no	—
974	C₄⋊C₄	—	146	2	no	—
975	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
977	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	73	2	no	—
986	C₂²⋊C₄	—	73	2	no	—
987	C₂²⋊C₄	—	146	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	C₂²⋊C₄	—	146	2	no	—
998	C₂²⋊C₄	—	146	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	73	2	no	—
1006	C₄²	—	73	2	no	—
1007	C₄²	—	146	2	no	—
1008	C₄²	—	146	2	no	—
1009	C₄²	—	146	2	no	—
1010	C₄²	—	146	2	no	—
1011	C₄²	D₄×D₇₃	1	1	yes	characteristic
1012	C₄²	D₄×D₇₃	1	1	yes	characteristic
1013	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1014	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	2	1	no	—
1017	C₂³	—	292	2	no	—
1018	C₂³	—	584	1	no	—
1019	C₂³	—	584	1	no	—
1020	C₂³	—	146	2	no	—
1021	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1022	Q₈	—	2	1	no	—
1023	Q₈	—	2	1	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	292	4	no	—
1026	Q₈	—	292	2	no	—
1027	Q₈	—	292	2	no	—
1028	Q₈	—	292	2	no	—
1029	Q₈	—	584	2	no	—
1030	Q₈	—	584	2	no	—
1031	Q₈	—	584	2	no	—
1032	Q₈	—	146	2	no	—
1033	Q₈	—	146	2	no	—
1034	Q₈	C₂×#11924028	1	2	yes	—
1035	D₄	—	2	4	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	2	1	no	—
1038	D₄	—	2	1	no	—
1039	D₄	—	4	2	no	—
1040	D₄	—	292	2	no	—
1041	D₄	—	584	2	no	—
1042	D₄	—	584	2	no	—
1043	D₄	—	146	2	no	—
1044	D₄	—	146	2	no	—
1045	D₄	C₂×#11924028	1	2	yes	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	4	1	no	—
1054	C₂×C₄	—	4	1	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	4	2	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	292	2	no	—
1061	C₂×C₄	—	584	2	no	—
1062	C₂×C₄	—	584	2	no	—
1063	C₂×C₄	—	584	1	no	—
1064	C₂×C₄	—	584	1	no	—
1065	C₂×C₄	—	584	2	no	—
1066	C₂×C₄	—	584	2	no	—
1067	C₂×C₄	—	73	2	no	—
1068	C₂×C₄	—	73	2	no	—
1069	C₂×C₄	—	73	2	no	—
1070	C₂×C₄	—	73	2	no	—
1071	C₂×C₄	—	146	2	no	—
1072	C₂×C₄	—	146	2	no	—
1073	C₂×C₄	—	146	2	no	—
1074	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1075	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1076	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1077	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1078	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1079	C₂×C₄	C₂×#11924028	1	2	yes	—
1080	C₂×C₄	#14556638	1	2	yes	—
1081	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1082	C₈	—	2	1	no	—
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	146	2	no	—
1087	C₈	—	146	2	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	4	1	no	—
1094	C₂²	—	4	1	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	292	2	no	—
1097	C₂²	—	292	2	no	—
1098	C₂²	—	292	2	no	—
1099	C₂²	—	1168	2	no	—
1100	C₂²	#17989246	1	2	yes	—
1101	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	2	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	292	2	no	—
1113	C₄	—	292	2	no	—
1114	C₄	—	292	2	no	—
1115	C₄	—	146	2	no	—
1116	C₄	—	146	2	no	—
1117	C₄	—	146	2	no	—
1118	C₄	—	146	2	no	—
1119	C₄	#17989246	1	2	yes	—
1120	C₄	C₂²×#11924028	1	1	yes	characteristic
1121	C₄	C₂×#14556638	1	1	yes	characteristic
1122	C₂	—	2	2	no	—
1123	C₂	—	4	2	no	—
1124	C₂	—	8	1	no	—
1125	C₂	—	584	2	no	—
1126	C₂	C₂×#17989246	1	1	yes	characteristic
1127	C₂	#22624708	1	1	yes	characteristic
1128	C₂	#22624715	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×#2943	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#22619468	C₂
hypercenter	#2943	D₇₃
hypocenter	C₇₃	#61336
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #22623827	C₂	semidirect
2. #22623750	C₂	semidirect
3. #22622778	C₂	semidirect
4. #22622763	C₂	semidirect
5. #22622746	C₂	semidirect
6. #22622724	C₂	semidirect
7. #22622704	C₂	semidirect
8. #22622689	C₂	semidirect
9. #22622672	C₂	semidirect
10. #22622650	C₂	semidirect
11. #22620300	C₂	semidirect
12. #22620289	C₂	semidirect
13. C₂×#17988947	C₂	semidirect
14. #22619776	C₂	semidirect
15. #22619765	C₂	semidirect
16. #22619746	C₂	semidirect
17. #22619479	C₂	semidirect
19. #22619425	C₂	semidirect
20. #22618871	C₂	semidirect
21. #22618777	C₂	semidirect
22. #22618766	C₂	semidirect
23. C₇₃×#2943	C₂	semidirect
28. Q₈×Dic₁₄₆	C₂²	semidirect
29. #17989316	C₂²	semidirect
33. #17989294	C₂²	semidirect
37. D₄×Dic₁₄₆	C₂²	semidirect
57. #17988954	C₂²	semidirect
64. #17988945	C₂²	semidirect
66. #17988940	C₂²	semidirect
67. #17988936	C₂²	semidirect
69. #17988897	C₂²	semidirect
70. #17988893	C₂²	semidirect
73. #17988882	C₂²	semidirect
74. #17988881	C₂²	semidirect
75. #17988877	C₂²	semidirect
77. #17988872	C₂²	semidirect
78. #17988871	C₂²	semidirect
79. #17988867	C₂²	semidirect
84. #17988807	C₂²	semidirect
88. #17988800	C₂²	semidirect
89. #17988795	C₂²	semidirect
90. #17988790	C₂²	semidirect
93. #17988715	C₂²	semidirect
94. #17988715	C₂²	semidirect
95. #17988715	C₂²	semidirect
96. #17988715	C₂²	semidirect
98. #17988691	C₂²	semidirect
100. #17988684	C₂²	semidirect
101. #17988679	C₂²	semidirect
102. #17988678	C₂²	semidirect
123. #442×C₇₃	C₂²	semidirect
124. #442×C₇₃	C₂²	semidirect
125. #441×C₇₃	C₂²	semidirect
126. #441×C₇₃	C₂²	semidirect
127. #440×C₇₃	C₂²	semidirect
128. #440×C₇₃	C₂²	semidirect
129. #440×C₇₃	C₂²	semidirect
130. #440×C₇₃	C₂²	semidirect
587. #2943	D₇₃	semidirect
588. C₇₃	#61336	semidirect
666. #442	C₂×D₇₃	semidirect
667. #442	C₂×D₇₃	semidirect
669. #441	C₂×D₇₃	semidirect
670. #441	C₂×D₇₃	semidirect
673. #440	C₂×D₇₃	semidirect
674. #440	C₂×D₇₃	semidirect
675. #440	C₂×D₇₃	semidirect
676. #440	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623827	2
#22623750	2
#22622778	2
#22622763	2
#22622746	2
#22622724	2
#22622704	2
#22622689	2
#22622672	2
#22622650	2
#22620300	2
#22620289	2
C₂×#17988947	2
#22619776	2
#22619765	2
#22619746	2
#22619479	2
#22619468	2
#22619425	2
#22618871	2
#22618777	2
#22618766	2
C₇₃×#2943	2
#61336	73