Subgroups — #33966646

Order 18688.

1682 conjugacy classes of subgroups.

The subgroup lattice has 990 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623738	C₂	1	2	yes	maximal
2	#22622898	C₂	1	2	yes	maximal, complemented
3	#22622894	C₂	1	2	yes	maximal, complemented
4	#22622866	C₂	1	2	yes	maximal, complemented
5	#22622858	C₂	1	2	yes	maximal, complemented
6	#22622823	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622822	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622822	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622819	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622819	C₂	1	1	yes	maximal, characteristic, complemented
11	Q₁₆×Dic₁₄₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#22622814	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620468	C₂	1	1	yes	maximal, characteristic
14	#22620464	C₂	1	1	yes	maximal, characteristic
15	#22620444	C₂	1	1	yes	maximal, characteristic
16	#22619770	C₂	1	2	yes	maximal
17	#22619766	C₂	1	2	yes	maximal
18	#22619734	C₂	1	2	yes	maximal
19	#22618860	C₂	1	1	yes	maximal, characteristic
20	#22618794	C₂	1	1	yes	maximal, characteristic
21	#22618794	C₂	1	1	yes	maximal, characteristic
22	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3383	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₄₆	C₂²	1	2	yes	—
26	#17989317	—	2	2	no	—
27	#17989317	C₂²	1	2	yes	—
28	#17989315	—	2	2	no	—
29	#17989315	C₂²	1	2	yes	—
30	#17989314	—	2	2	no	—
31	#17989314	—	2	2	no	—
32	#17989314	C₂²	1	2	yes	—
33	#17989314	C₂²	1	2	yes	—
34	#17989313	C₂²	1	2	yes	—
35	#17989313	C₂²	1	2	yes	—
36	#17989217	—	2	2	no	—
37	#17989217	C₂²	1	2	yes	—
38	#17989214	—	2	2	no	—
39	#17989214	C₂²	1	2	yes	—
40	#17989143	—	2	2	no	—
41	#17989143	C₂²	1	2	yes	—
42	#17989141	—	2	2	no	—
43	#17989141	C₂²	1	1	yes	characteristic
44	#17989063	C₂²	1	2	yes	—
45	#17989063	C₂²	1	2	yes	—
46	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
47	#17988997	C₂²	1	2	yes	—
48	#17988995	C₂²	1	2	yes	—
49	#17988994	C₂²	1	2	yes	—
50	#17988993	C₂²	1	2	yes	—
51	#17988992	C₂²	1	1	yes	characteristic
52	#17988991	C₂²	1	1	yes	characteristic
53	#17988991	C₂²	1	1	yes	characteristic
54	#17988991	C₂²	1	1	yes	characteristic
55	#17988991	C₂²	1	1	yes	characteristic
56	#17988989	C₂²	1	1	yes	characteristic
57	#17988989	C₂²	1	1	yes	characteristic
58	#17988988	C₂²	1	1	yes	characteristic
59	#17988988	C₂²	1	1	yes	characteristic
60	#17988986	C₂²	1	2	yes	—
61	#17988984	C₂²	1	2	yes	—
62	#17988897	C₂²	1	2	yes	—
63	#17988897	C₂²	1	2	yes	—
64	#17988895	C₂²	1	2	yes	—
65	#17988895	C₂²	1	2	yes	—
66	#17988894	C₂²	1	2	yes	—
67	#17988894	C₂²	1	2	yes	—
68	#17988892	C₂²	1	2	yes	—
69	#17988892	C₂²	1	2	yes	—
70	#17988891	C₂²	1	2	yes	—
71	#17988891	C₂²	1	2	yes	—
72	#17988882	C₂²	1	2	yes	—
73	#17988881	C₂²	1	2	yes	—
74	#17988881	C₂²	1	2	yes	—
75	#17988880	C₂²	1	2	yes	—
76	#17988880	C₂²	1	2	yes	—
77	#17988879	C₂²	1	2	yes	—
78	#17988873	C₂²	1	2	yes	—
79	#17988871	C₂²	1	2	yes	—
80	#17988871	C₂²	1	2	yes	—
81	#17988870	C₂²	1	2	yes	—
82	#17988870	C₂²	1	2	yes	—
83	#17988718	C₂²	1	1	yes	characteristic
84	#17988716	C₂²	1	1	yes	characteristic
85	#17988716	C₂²	1	1	yes	characteristic
86	#17988714	C₂²	1	1	yes	characteristic
87	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
88	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
89	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
90	#17988692	C₂²	1	2	yes	—
91	#17988692	C₂²	1	2	yes	—
92	#17988691	C₂²	1	2	yes	—
93	#17988691	C₂²	1	2	yes	—
94	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic
95	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic
96	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic
97	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
98	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
99	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
100	#17988681	C₂²	1	1	yes	characteristic
101	#17988681	C₂²	1	1	yes	characteristic
102	#17988681	C₂²	1	1	yes	characteristic
103	C₄×#11924018	C₂²	1	2	yes	—
104	#17988679	C₂²	1	2	yes	—
105	#17988628	C₂²	1	2	yes	—
106	#17988626	C₂²	1	2	yes	—
107	#17988624	C₂²	1	1	yes	characteristic
108	#17988624	C₂²	1	1	yes	characteristic
109	#17988622	C₂²	1	2	yes	—
110	#107×D₇₃	C₂²	1	1	yes	characteristic
111	#17988612	C₂²	1	1	yes	characteristic
112	#17988612	C₂²	1	1	yes	characteristic
113	#17988609	C₂²	1	1	yes	characteristic
114	#17988594	C₂²	1	2	yes	—
115	#17988594	C₂²	1	2	yes	—
116	#103×D₇₃	C₂²	1	2	yes	—
117	#17988541	C₂²	1	1	yes	characteristic
118	#17988541	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
120	#557×C₇₃	C₂²	1	2	yes	—
121	#500×C₇₃	C₂²	1	1	yes	characteristic
122	#499×C₇₃	C₂²	1	1	yes	characteristic
123	#499×C₇₃	C₂²	1	1	yes	characteristic
124	#479×C₇₃	C₂²	1	2	yes	—
125	#479×C₇₃	C₂²	1	2	yes	—
126	#475×C₇₃	C₂²	1	2	yes	—
127	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
128	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
129	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
131	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
132	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
133	C₂×#11924018	C₂³	1	2	yes	—
134	Q₁₆×D₇₃	Q₈	1	8	yes	complemented
135	C₂×#11924011	C₂³	1	1	yes	characteristic
136	C₂×#11924011	C₂³	1	1	yes	characteristic
137	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
138	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
139	#14556591	—	2	2	no	—
140	#14556591	C₂³	1	2	yes	—
141	#14556590	—	2	2	no	—
142	#14556590	—	2	2	no	—
143	#14556590	—	2	2	no	—
144	#14556590	—	2	2	no	—
145	#14556590	—	2	2	no	—
146	#14556590	—	2	2	no	—
147	#14556590	—	2	2	no	—
148	#14556590	—	2	2	no	—
149	#14556590	D₄	1	1	yes	characteristic
150	#14556590	C₂³	1	2	yes	—
151	#14556590	C₂³	1	2	yes	—
152	#14556590	C₂³	1	2	yes	—
153	#14556590	C₂³	1	2	yes	—
154	#14556589	—	2	2	no	—
155	#14556589	—	2	2	no	—
156	#14556589	—	2	2	no	—
157	#14556589	—	2	2	no	—
158	#14556589	D₄	1	1	yes	characteristic
159	#14556583	—	2	2	no	—
160	#14556583	—	2	2	no	—
161	#14556583	C₂³	1	2	yes	—
162	#14556583	C₂³	1	2	yes	—
163	#14556582	—	2	2	no	—
164	#14556582	—	2	2	no	—
165	#14556582	C₂³	1	2	yes	—
166	#14556582	C₂³	1	2	yes	—
167	#14556581	—	2	2	no	—
168	#14556581	—	2	2	no	—
169	#14556581	—	2	2	no	—
170	#14556581	—	2	2	no	—
171	#14556581	—	2	2	no	—
172	#14556581	—	2	2	no	—
173	#14556581	—	2	2	no	—
174	#14556581	—	2	2	no	—
175	#14556581	D₄	1	1	yes	characteristic
176	#14556581	D₄	1	1	yes	characteristic
177	#14556571	—	2	2	no	—
178	#14556571	D₄	1	1	yes	characteristic
179	#14556569	—	2	2	no	—
180	#14556569	—	2	2	no	—
181	#14556569	—	2	2	no	—
182	#14556569	—	2	2	no	—
183	#14556569	D₄	1	1	yes	characteristic
184	#14556569	D₄	1	1	yes	characteristic
185	#14556567	—	2	2	no	—
186	#14556567	D₄	1	1	yes	characteristic
187	Q₈×Dic₇₃	C₂³	1	2	yes	—
188	Q₈×Dic₇₃	C₂³	1	2	yes	—
189	Q₈×Dic₇₃	C₂³	1	2	yes	—
190	C₄×Dic₁₄₆	—	2	2	no	—
191	C₄×Dic₁₄₆	—	2	2	no	—
192	C₄×Dic₁₄₆	—	2	2	no	—
193	C₄×Dic₁₄₆	—	2	2	no	—
194	C₄×Dic₁₄₆	—	2	2	no	—
195	C₄×Dic₁₄₆	—	2	2	no	—
196	C₄×Dic₁₄₆	C₂³	1	2	yes	—
197	C₄×Dic₁₄₆	C₂³	1	2	yes	—
198	C₄×Dic₁₄₆	C₂³	1	2	yes	—
199	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
200	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
201	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
202	#14556556	—	2	2	no	—
203	#14556556	—	2	2	no	—
204	#14556556	—	2	2	no	—
205	#14556556	—	2	2	no	—
206	#14556556	—	2	2	no	—
207	#14556556	—	2	2	no	—
208	#14556556	—	2	2	no	—
209	#14556556	—	2	2	no	—
210	#14556556	—	2	2	no	—
211	#14556556	C₂³	1	2	yes	—
212	#14556556	C₂³	1	2	yes	—
213	#14556556	C₂³	1	2	yes	—
214	#14556549	—	2	2	no	—
215	#14556549	—	2	2	no	—
216	#14556549	C₂³	1	2	yes	—
217	#14556549	C₂³	1	2	yes	—
218	#14556548	—	2	2	no	—
219	#14556548	—	2	2	no	—
220	#14556548	C₂³	1	1	yes	characteristic
221	#14556548	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×D₇₃	—	2	2	no	—
223	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
224	C₄²×D₇₃	—	2	2	no	—
225	C₄²×D₇₃	C₂³	1	1	yes	characteristic
226	#14556525	C₂³	1	1	yes	characteristic
227	#14556525	C₂³	1	1	yes	characteristic
228	#14556525	C₂³	1	1	yes	characteristic
229	#14556525	C₂³	1	2	yes	—
230	#14556524	C₂³	1	2	yes	—
231	#14556524	C₂³	1	2	yes	—
232	#14556524	C₂³	1	2	yes	—
233	#14556524	C₂³	1	2	yes	—
234	#14556524	C₂³	1	2	yes	—
235	#14556523	C₂³	1	2	yes	—
236	#14556523	C₂³	1	2	yes	—
237	#14556522	C₂³	1	2	yes	—
238	#14556522	C₂³	1	2	yes	—
239	#14556522	C₂³	1	2	yes	—
240	#14556522	C₂³	1	2	yes	—
241	C₄⋊#10596831	C₂³	1	1	yes	characteristic
242	C₄⋊#10596831	C₂³	1	1	yes	characteristic
243	C₄⋊#10596831	C₂³	1	1	yes	characteristic
244	#14556520	C₂³	1	1	yes	characteristic
245	#14556520	C₂³	1	1	yes	characteristic
246	#14556520	C₂³	1	1	yes	characteristic
247	#14556520	C₂³	1	1	yes	characteristic
248	#14556520	C₂³	1	1	yes	characteristic
249	#14556520	C₂³	1	1	yes	characteristic
250	#14556516	C₂³	1	2	yes	—
251	#14556516	C₂³	1	2	yes	—
252	#14556516	C₂³	1	2	yes	—
253	#14556515	C₂³	1	2	yes	—
254	#14556515	C₂³	1	2	yes	—
255	#14556515	C₂³	1	2	yes	—
256	#14556514	C₂³	1	2	yes	—
257	#14556514	C₂³	1	2	yes	—
258	#14556514	C₂³	1	2	yes	—
259	#14556502	C₂³	1	1	yes	characteristic
260	#14556502	C₂³	1	1	yes	characteristic
261	#14556501	C₂³	1	1	yes	characteristic
262	#14556501	C₂³	1	1	yes	characteristic
263	C₄×#10596831	C₂³	1	1	yes	characteristic
264	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
268	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₇₃	—	2	2	no	—
270	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
271	#125×C₇₃	—	2	2	no	—
272	#125×C₇₃	—	2	2	no	—
273	#125×C₇₃	C₂³	1	2	yes	—
274	#125×C₇₃	C₂³	1	2	yes	—
275	C₄×Q₈×C₇₃	—	2	2	no	—
276	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
277	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
278	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
280	#107×C₇₃	C₂³	1	1	yes	characteristic
281	#107×C₇₃	C₂³	1	1	yes	characteristic
282	#107×C₇₃	C₂³	1	1	yes	characteristic
283	#107×C₇₃	C₂³	1	2	yes	—
284	#106×C₇₃	C₂³	1	2	yes	—
285	#106×C₇₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
289	#103×C₇₃	C₂³	1	2	yes	—
290	#103×C₇₃	C₂³	1	2	yes	—
291	#103×C₇₃	C₂³	1	2	yes	—
292	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₂×Dic₁₄₆	—	2	2	no	—
296	C₂×Dic₁₄₆	—	2	2	no	—
297	C₂×Dic₁₄₆	—	2	2	no	—
298	C₂×Dic₁₄₆	—	2	2	no	—
299	C₂×Dic₁₄₆	—	2	2	no	—
300	C₂×Dic₁₄₆	—	2	2	no	—
301	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
302	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
303	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
304	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
305	Q₈×D₇₃	—	2	4	no	—
306	Q₈×D₇₃	C₂×Q₈	1	8	yes	—
307	C₂×C₄×D₇₃	—	2	2	no	—
308	C₂×C₄×D₇₃	—	2	2	no	—
309	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
310	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
311	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
312	Dic₂₉₂	C₂×Q₈	1	4	yes	—
313	#11924018	C₂×Q₈	1	8	yes	—
314	#11924011	—	2	2	no	—
315	#11924011	—	2	2	no	—
316	C₂×#10596831	C₂⁴	1	1	yes	characteristic
317	C₂×#10596831	C₂⁴	1	1	yes	characteristic
318	C₂×#10596831	C₂⁴	1	1	yes	characteristic
319	C₂×#10596831	C₂⁴	1	1	yes	characteristic
320	C₈×D₇₃	—	2	2	no	—
321	C₈×D₇₃	C₂×Q₈	1	4	yes	—
322	C₄⋊Dic₇₃	—	2	2	no	—
323	C₄⋊Dic₇₃	—	2	2	no	—
324	C₄⋊Dic₇₃	—	2	2	no	—
325	C₄⋊Dic₇₃	—	2	2	no	—
326	C₄⋊Dic₇₃	—	2	2	no	—
327	C₄⋊Dic₇₃	—	2	2	no	—
328	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
329	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
330	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
331	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
332	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
333	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
334	#11924007	—	2	2	no	—
335	#11924007	—	2	2	no	—
336	#11924007	—	2	2	no	—
337	#11924007	—	2	2	no	—
338	#11924007	—	2	2	no	—
339	#11924007	—	2	2	no	—
340	#11924007	—	2	2	no	—
341	#11924007	—	2	2	no	—
342	#11924007	—	2	2	no	—
343	#11924007	—	2	2	no	—
344	#11924007	—	2	2	no	—
345	#11924007	—	2	2	no	—
346	#11924007	—	2	2	no	—
347	#11924007	—	2	2	no	—
348	#11924007	—	2	2	no	—
349	#11924007	—	2	2	no	—
350	#11924007	—	2	2	no	—
351	#11924007	C₂×D₄	1	1	yes	characteristic
352	#11924007	C₂×D₄	1	1	yes	characteristic
353	#11924007	C₂×D₄	1	1	yes	characteristic
354	#11924007	C₂×D₄	1	1	yes	characteristic
355	#11924007	C₂×D₄	1	1	yes	characteristic
356	#11924007	C₂×D₄	1	1	yes	characteristic
357	#11924007	C₂×D₄	1	1	yes	characteristic
358	#11924007	C₂×D₄	1	1	yes	characteristic
359	#11924007	C₂×D₄	1	1	yes	characteristic
360	#11924007	C₂×D₄	1	1	yes	characteristic
361	#11924005	—	2	2	no	—
362	#11924005	—	2	2	no	—
363	#11924005	C₂×D₄	1	1	yes	characteristic
364	#11924005	C₂×D₄	1	1	yes	characteristic
365	#11924005	C₂×D₄	1	1	yes	characteristic
366	#11924005	C₂×D₄	1	1	yes	characteristic
367	C₄×Dic₇₃	—	2	2	no	—
368	C₄×Dic₇₃	—	2	2	no	—
369	C₄×Dic₇₃	—	2	2	no	—
370	C₄×Dic₇₃	—	2	2	no	—
371	C₄×Dic₇₃	—	2	2	no	—
372	C₄×Dic₇₃	—	2	2	no	—
373	C₄×Dic₇₃	—	2	2	no	—
374	C₄×Dic₇₃	—	2	2	no	—
375	C₄×Dic₇₃	—	2	2	no	—
376	C₄×Dic₇₃	—	2	2	no	—
377	C₄×Dic₇₃	—	2	2	no	—
378	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
379	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
380	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
381	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
382	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
383	C₂×Q₈×C₇₃	—	2	2	no	—
384	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
385	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
386	Q₁₆×C₇₃	C₂×Q₈	1	4	yes	—
387	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
388	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
389	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
390	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₇₃	—	2	2	no	—
392	C₄⋊C₄×C₇₃	—	2	2	no	—
393	C₄⋊C₄×C₇₃	—	2	2	no	—
394	C₄⋊C₄×C₇₃	—	2	2	no	—
395	C₄⋊C₄×C₇₃	—	2	2	no	—
396	C₄⋊C₄×C₇₃	—	2	2	no	—
397	C₄⋊C₄×C₇₃	—	2	2	no	—
398	C₄⋊C₄×C₇₃	—	2	2	no	—
399	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
402	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
405	C₄²×C₇₃	—	2	2	no	—
406	C₄²×C₇₃	—	2	2	no	—
407	C₄²×C₇₃	—	2	2	no	—
408	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
410	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
411	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
412	Q₈×C₇₃	—	2	2	no	—
413	Q₈×C₇₃	—	4	1	no	—
414	Q₈×C₇₃	—	8	2	no	—
415	Q₈×C₇₃	C₂²×Q₈	1	4	yes	—
416	C₂×C₄×C₇₃	—	2	2	no	—
417	C₂×C₄×C₇₃	—	2	2	no	—
418	C₂×C₄×C₇₃	—	2	2	no	—
419	C₂×C₄×C₇₃	—	2	2	no	—
420	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
421	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
422	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
423	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
424	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
425	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
426	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
427	C₂×Dic₇₃	—	2	2	no	—
428	C₂×Dic₇₃	—	2	2	no	—
429	C₂×Dic₇₃	—	2	2	no	—
430	C₂×Dic₇₃	—	2	2	no	—
431	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
437	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
438	C₄×D₇₃	—	2	8	no	—
439	C₄×D₇₃	—	2	2	no	—
440	C₄×D₇₃	—	4	1	no	—
441	C₄×D₇₃	—	8	2	no	—
442	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
443	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
444	Dic₁₄₆	—	2	2	no	—
445	Dic₁₄₆	—	2	8	no	—
446	Dic₁₄₆	—	2	2	no	—
447	Dic₁₄₆	—	2	2	no	—
448	Dic₁₄₆	—	4	1	no	—
449	Dic₁₄₆	—	4	4	no	—
450	Dic₁₄₆	—	8	2	no	—
451	Dic₁₄₆	—	8	2	no	—
452	Dic₁₄₆	—	8	2	no	—
453	Dic₁₄₆	—	8	2	no	—
454	Dic₁₄₆	C₂²×Q₈	1	4	yes	—
455	C₈×C₇₃	—	2	1	no	—
456	C₈×C₇₃	—	2	1	no	—
457	C₈×C₇₃	—	2	1	no	—
458	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
459	#10596831	—	2	1	no	—
460	#10596831	—	2	1	no	—
461	#10596831	—	2	1	no	—
462	#10596831	C₂²×Q₈	1	2	yes	—
463	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
464	C₂×D₇₃	—	2	1	no	—
465	C₂×D₇₃	—	2	1	no	—
466	C₂×D₇₃	D₄×Q₈	1	2	yes	—
467	C₄×C₇₃	—	2	1	no	—
468	C₄×C₇₃	—	2	1	no	—
469	C₄×C₇₃	—	2	1	no	—
470	C₄×C₇₃	—	2	4	no	—
471	C₄×C₇₃	—	2	1	no	—
472	C₄×C₇₃	—	2	1	no	—
473	C₄×C₇₃	—	2	1	no	—
474	C₄×C₇₃	—	4	2	no	—
475	C₄×C₇₃	—	4	2	no	—
476	C₄×C₇₃	—	4	2	no	—
477	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
478	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
479	Dic₇₃	—	2	1	no	—
480	Dic₇₃	—	2	1	no	—
481	Dic₇₃	—	2	1	no	—
482	Dic₇₃	—	2	4	no	—
483	Dic₇₃	—	2	1	no	—
484	Dic₇₃	—	2	1	no	—
485	Dic₇₃	—	4	2	no	—
486	Dic₇₃	—	4	2	no	—
487	Dic₇₃	—	4	2	no	—
488	Dic₇₃	D₄×Q₈	1	2	yes	—
489	Dic₇₃	#578	1	2	yes	—
490	#61372	—	73	1	no	maximal, Sylow
491	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
492	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
493	C₂×C₇₃	#3584	1	1	yes	characteristic
494	D₇₃	—	2	2	no	—
495	#3502	—	73	2	no	—
496	#3390	—	73	2	no	—
497	#3390	—	73	2	no	—
498	#3387	—	73	2	no	—
499	#3387	—	73	2	no	—
500	#3383	—	73	1	no	—
501	#3383	—	73	1	no	—
502	#3383	—	73	1	no	—
503	#3383	—	73	1	no	—
504	#3383	—	73	1	no	—
505	#3383	D₇₃	1	1	yes	characteristic, complemented
506	Q₈×Q₁₆	—	73	1	no	—
507	Q₈×Q₁₆	—	73	1	no	—
508	#3164	—	73	1	no	—
509	#3164	—	73	1	no	—
510	#3160	—	73	1	no	—
511	#3082	—	73	2	no	—
512	#3082	—	73	2	no	—
513	#3078	—	73	2	no	—
514	#2960	—	73	1	no	—
515	#2950	—	73	1	no	—
516	#2950	—	73	1	no	—
517	C₂×C₄×Q₁₆	—	73	1	no	—
518	C₇₃	#61372	1	1	yes	characteristic, complemented, Sylow
519	C₂²×Q₁₆	—	73	1	no	—
520	Q₈²	—	73	2	no	—
521	Q₈²	—	73	2	no	—
522	Q₈²	—	146	2	no	—
523	#557	—	73	2	no	—
524	#557	—	73	2	no	—
525	#557	—	73	2	no	—
526	#557	—	73	2	no	—
527	#557	—	73	2	no	—
528	#557	—	146	2	no	—
529	#557	—	146	2	no	—
530	#557	—	146	2	no	—
531	#557	C₂×D₇₃	1	2	yes	—
532	#544	—	73	2	no	—
533	#544	—	73	2	no	—
534	#544	—	146	2	no	—
535	#544	—	146	2	no	—
536	#533	—	73	1	no	—
537	#533	—	73	2	no	—
538	#533	—	146	2	no	—
539	#533	—	146	2	no	—
540	#519	—	73	2	no	—
541	#519	—	73	2	no	—
542	C₂×C₄×Q₈	—	73	2	no	—
543	#501	—	73	2	no	—
544	#501	—	73	2	no	—
545	#501	—	73	2	no	—
546	#501	—	73	2	no	—
547	#500	—	73	1	no	—
548	#500	—	73	1	no	—
549	#500	—	73	1	no	—
550	#500	—	73	1	no	—
551	#500	—	73	1	no	—
552	#500	C₂×D₇₃	1	1	yes	characteristic
553	#499	—	73	2	no	—
554	#499	—	73	1	no	—
555	#499	—	73	1	no	—
556	#499	—	73	1	no	—
557	#499	—	73	1	no	—
558	#499	C₂×D₇₃	1	1	yes	characteristic
559	#499	C₂×D₇₃	1	1	yes	characteristic
560	#498	—	73	2	no	—
561	#479	—	73	2	no	—
562	#479	—	73	2	no	—
563	#479	—	73	2	no	—
564	#479	—	73	2	no	—
565	#479	—	73	2	no	—
566	#479	—	73	2	no	—
567	#479	—	73	2	no	—
568	#479	—	73	2	no	—
569	#479	—	73	2	no	—
570	#479	—	73	2	no	—
571	#479	C₂×D₇₃	1	2	yes	—
572	#479	C₂×D₇₃	1	2	yes	—
573	#477	—	73	2	no	—
574	#477	—	73	2	no	—
575	#477	—	73	2	no	—
576	#477	—	73	2	no	—
577	#477	—	73	2	no	—
578	#477	—	73	2	no	—
579	#475	—	73	2	no	—
580	#475	—	73	2	no	—
581	#475	—	73	2	no	—
582	#475	—	73	2	no	—
583	#475	—	73	2	no	—
584	#475	C₂×D₇₃	1	2	yes	—
585	#446	—	73	1	no	—
586	#446	—	73	1	no	—
587	#446	—	73	1	no	—
588	#446	—	73	1	no	—
589	C₈×Q₈	—	73	1	no	—
590	C₈×Q₈	—	73	1	no	—
591	C₈×Q₈	—	73	1	no	—
592	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic
593	#441	—	73	2	no	—
594	#441	—	73	2	no	—
595	#441	—	73	2	no	—
596	#441	—	73	2	no	—
597	C₄×Q₁₆	—	73	1	no	—
598	C₄×Q₁₆	—	73	1	no	—
599	C₄×Q₁₆	—	73	1	no	—
600	C₄×Q₁₆	—	73	2	no	—
601	C₄×Q₁₆	—	73	1	no	—
602	C₄×Q₁₆	—	73	1	no	—
603	C₄×Q₁₆	—	73	1	no	—
604	C₄×Q₁₆	—	73	2	no	—
605	C₄×Q₁₆	—	73	1	no	—
606	C₄×Q₁₆	—	73	1	no	—
607	C₄×Q₁₆	—	73	1	no	—
608	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
609	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
610	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic
611	#428	—	73	2	no	—
612	#428	—	73	2	no	—
613	#427	—	73	1	no	—
614	#427	—	73	1	no	—
615	#427	—	73	2	no	—
616	C₂×#107	—	73	1	no	—
617	#424	—	73	1	no	—
618	#424	—	73	1	no	—
619	#423	—	73	1	no	—
620	#419	—	73	2	no	—
621	#419	—	73	2	no	—
622	C₂×#103	—	73	2	no	—
623	#405	—	73	1	no	—
624	#405	—	73	1	no	—
625	C₂×C₄×C₈	—	73	1	no	—
626	C₂²×Q₈	—	73	2	no	—
627	C₂×Q₁₆	—	73	2	no	—
628	C₂×Q₁₆	—	73	8	no	—
629	C₂×Q₁₆	—	73	1	no	—
630	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
631	C₂×M₁₆	—	73	1	no	—
632	C₂×M₁₆	—	73	1	no	—
633	C₂²×C₈	—	73	1	no	—
634	C₂²×C₈	—	73	1	no	—
635	C₄⋊Q₈	—	2	2	no	—
636	C₄⋊Q₈	—	73	1	no	—
637	C₄⋊Q₈	—	73	1	no	—
638	C₄⋊Q₈	—	73	2	no	—
639	C₄⋊Q₈	—	73	2	no	—
640	C₄⋊Q₈	—	73	2	no	—
641	C₄⋊Q₈	—	73	2	no	—
642	C₄⋊Q₈	—	73	2	no	—
643	C₄⋊Q₈	—	146	2	no	—
644	C₄⋊Q₈	—	146	2	no	—
645	C₄⋊Q₈	—	146	2	no	—
646	C₄⋊Q₈	—	146	2	no	—
647	C₄⋊Q₈	—	146	2	no	—
648	C₄⋊Q₈	—	146	2	no	—
649	C₄⋊Q₈	—	146	2	no	—
650	C₄⋊Q₈	—	146	2	no	—
651	C₄⋊Q₈	—	146	2	no	—
652	C₄⋊Q₈	—	146	2	no	—
653	C₄⋊Q₈	—	146	2	no	—
654	C₄⋊Q₈	—	146	2	no	—
655	C₄⋊Q₈	—	146	2	no	—
656	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	73	1	no	—
660	#125	—	73	1	no	—
661	#125	—	73	2	no	—
662	#125	—	73	2	no	—
663	#125	—	73	2	no	—
664	#125	—	73	2	no	—
665	#125	—	146	2	no	—
666	#125	—	146	2	no	—
667	#125	—	146	2	no	—
668	#125	—	146	2	no	—
669	#125	—	146	2	no	—
670	#125	—	146	2	no	—
671	#125	—	146	2	no	—
672	#125	—	146	2	no	—
673	#125	—	146	2	no	—
674	#125	—	146	2	no	—
675	#125	—	146	2	no	—
676	#125	—	146	2	no	—
677	#125	C₂²×D₇₃	1	2	yes	—
678	#125	C₂²×D₇₃	1	2	yes	—
679	C₂²⋊Q₈	—	73	1	no	—
680	C₂²⋊Q₈	—	73	1	no	—
681	C₂²⋊Q₈	—	73	1	no	—
682	C₂²⋊Q₈	—	73	1	no	—
683	C₂²⋊Q₈	—	146	2	no	—
684	C₂²⋊Q₈	—	146	2	no	—
685	C₂²⋊Q₈	—	146	2	no	—
686	C₂²⋊Q₈	—	146	2	no	—
687	C₂²⋊Q₈	—	146	2	no	—
688	C₂²⋊Q₈	—	146	2	no	—
689	C₄×Q₈	—	2	2	no	—
690	C₄×Q₈	—	73	1	no	—
691	C₄×Q₈	—	73	1	no	—
692	C₄×Q₈	—	73	1	no	—
693	C₄×Q₈	—	73	2	no	—
694	C₄×Q₈	—	73	2	no	—
695	C₄×Q₈	—	73	2	no	—
696	C₄×Q₈	—	73	2	no	—
697	C₄×Q₈	—	73	2	no	—
698	C₄×Q₈	—	73	2	no	—
699	C₄×Q₈	—	73	2	no	—
700	C₄×Q₈	—	73	2	no	—
701	C₄×Q₈	—	73	2	no	—
702	C₄×Q₈	—	146	2	no	—
703	C₄×Q₈	—	146	2	no	—
704	C₄×Q₈	—	146	2	no	—
705	C₄×Q₈	—	146	2	no	—
706	C₄×Q₈	—	146	2	no	—
707	C₄×Q₈	—	146	2	no	—
708	C₄×Q₈	—	146	2	no	—
709	C₄×Q₈	—	146	2	no	—
710	C₄×Q₈	—	146	2	no	—
711	C₄×Q₈	—	146	2	no	—
712	C₄×Q₈	—	146	2	no	—
713	C₄×Q₈	—	146	2	no	—
714	C₄×Q₈	—	146	2	no	—
715	C₄×Q₈	—	146	2	no	—
716	C₄×Q₈	—	146	2	no	—
717	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
718	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
719	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
720	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
721	#117	—	73	1	no	—
722	#117	—	73	1	no	—
723	#117	—	73	2	no	—
724	#117	—	73	2	no	—
725	#117	—	146	2	no	—
726	#117	—	146	2	no	—
727	#117	—	146	2	no	—
728	#117	—	146	2	no	—
729	C₂×C₄⋊C₄	—	73	2	no	—
730	C₂×C₄⋊C₄	—	146	2	no	—
731	C₂×C₄²	—	73	1	no	—
732	C₂×C₄²	—	146	2	no	—
733	#107	—	73	1	no	—
734	#107	—	73	1	no	—
735	#107	—	73	1	no	—
736	#107	—	73	2	no	—
737	#107	—	73	2	no	—
738	#107	—	73	2	no	—
739	#107	—	73	2	no	—
740	#107	—	73	2	no	—
741	#107	—	73	2	no	—
742	#107	C₂²×D₇₃	1	1	yes	characteristic
743	#107	C₂²×D₇₃	1	1	yes	characteristic
744	#107	C₂²×D₇₃	1	1	yes	characteristic
745	#107	C₂²×D₇₃	1	2	yes	—
746	#106	—	73	2	no	—
747	#106	—	73	2	no	—
748	#106	—	73	2	no	—
749	#106	—	73	2	no	—
750	#106	—	73	2	no	—
751	#106	—	73	2	no	—
752	#106	C₂²×D₇₃	1	2	yes	—
753	#106	C₂²×D₇₃	1	2	yes	—
754	C₄⋊C₈	—	73	1	no	—
755	C₄⋊C₈	—	73	1	no	—
756	C₄⋊C₈	—	73	1	no	—
757	C₄⋊C₈	—	73	1	no	—
758	C₄⋊C₈	—	73	1	no	—
759	C₄⋊C₈	—	73	1	no	—
760	C₄⋊C₈	—	73	1	no	—
761	C₄⋊C₈	—	73	1	no	—
762	C₄⋊C₈	—	73	1	no	—
763	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
764	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
765	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
766	#103	—	73	2	no	—
767	#103	—	73	2	no	—
768	#103	—	73	2	no	—
769	#103	—	73	2	no	—
770	#103	—	73	2	no	—
771	#103	—	73	2	no	—
772	#103	—	73	2	no	—
773	#103	—	73	2	no	—
774	#103	—	73	2	no	—
775	#103	C₂²×D₇₃	1	2	yes	—
776	#103	C₂²×D₇₃	1	2	yes	—
777	#103	C₂²×D₇₃	1	2	yes	—
778	#97	—	73	1	no	—
779	#97	—	73	1	no	—
780	#97	—	73	1	no	—
781	#97	—	73	1	no	—
782	C₄×C₈	—	73	1	no	—
783	C₄×C₈	—	73	1	no	—
784	C₄×C₈	—	73	1	no	—
785	C₄×C₈	—	73	1	no	—
786	C₄×C₈	—	73	1	no	—
787	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
788	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
789	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
790	C₂×Q₈	—	2	2	no	—
791	C₂×Q₈	—	73	1	no	—
792	C₂×Q₈	—	73	1	no	—
793	C₂×Q₈	—	73	1	no	—
794	C₂×Q₈	—	73	8	no	—
795	C₂×Q₈	—	73	2	no	—
796	C₂×Q₈	—	146	2	no	—
797	C₂×Q₈	—	146	2	no	—
798	C₂×Q₈	—	146	2	no	—
799	C₂×Q₈	—	146	2	no	—
800	C₂×Q₈	—	146	2	no	—
801	C₂×Q₈	—	146	4	no	—
802	C₂×Q₈	—	146	2	no	—
803	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
804	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
805	C₂²×C₄	—	73	1	no	—
806	C₂²×C₄	—	73	1	no	—
807	C₂²×C₄	—	73	1	no	—
808	C₂²×C₄	—	146	2	no	—
809	C₂²×C₄	—	146	2	no	—
810	Q₁₆	—	73	8	no	—
811	Q₁₆	—	73	4	no	—
812	Q₁₆	Q₈×D₇₃	1	4	yes	—
813	M₁₆	—	146	2	no	—
814	M₁₆	—	146	2	no	—
815	C₂×C₈	—	73	1	no	—
816	C₂×C₈	—	73	4	no	—
817	C₂×C₈	—	73	1	no	—
818	C₂×C₈	—	73	1	no	—
819	C₂×C₈	—	73	1	no	—
820	C₂×C₈	—	146	2	no	—
821	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
822	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
823	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
824	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
825	C₄⋊C₄	—	2	2	no	—
826	C₄⋊C₄	—	2	2	no	—
827	C₄⋊C₄	—	2	2	no	—
828	C₄⋊C₄	—	2	2	no	—
829	C₄⋊C₄	—	2	2	no	—
830	C₄⋊C₄	—	2	2	no	—
831	C₄⋊C₄	—	2	2	no	—
832	C₄⋊C₄	—	2	2	no	—
833	C₄⋊C₄	—	73	1	no	—
834	C₄⋊C₄	—	73	1	no	—
835	C₄⋊C₄	—	73	1	no	—
836	C₄⋊C₄	—	73	1	no	—
837	C₄⋊C₄	—	73	1	no	—
838	C₄⋊C₄	—	73	1	no	—
839	C₄⋊C₄	—	73	1	no	—
840	C₄⋊C₄	—	73	1	no	—
841	C₄⋊C₄	—	73	1	no	—
842	C₄⋊C₄	—	73	1	no	—
843	C₄⋊C₄	—	73	1	no	—
844	C₄⋊C₄	—	73	1	no	—
845	C₄⋊C₄	—	73	1	no	—
846	C₄⋊C₄	—	73	2	no	—
847	C₄⋊C₄	—	73	2	no	—
848	C₄⋊C₄	—	73	2	no	—
849	C₄⋊C₄	—	146	2	no	—
850	C₄⋊C₄	—	146	2	no	—
851	C₄⋊C₄	—	146	2	no	—
852	C₄⋊C₄	—	146	2	no	—
853	C₄⋊C₄	—	146	2	no	—
854	C₄⋊C₄	—	146	2	no	—
855	C₄⋊C₄	—	146	2	no	—
856	C₄⋊C₄	—	146	2	no	—
857	C₄⋊C₄	—	146	2	no	—
858	C₄⋊C₄	—	146	2	no	—
859	C₄⋊C₄	—	146	2	no	—
860	C₄⋊C₄	—	146	2	no	—
861	C₄⋊C₄	—	146	2	no	—
862	C₄⋊C₄	—	146	2	no	—
863	C₄⋊C₄	—	146	2	no	—
864	C₄⋊C₄	—	146	2	no	—
865	C₄⋊C₄	—	146	2	no	—
866	C₄⋊C₄	—	146	2	no	—
867	C₄⋊C₄	—	146	2	no	—
868	C₄⋊C₄	—	146	2	no	—
869	C₄⋊C₄	—	146	2	no	—
870	C₄⋊C₄	—	146	2	no	—
871	C₄⋊C₄	—	146	2	no	—
872	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
873	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
874	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
875	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
876	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
877	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
878	C₂²⋊C₄	—	73	1	no	—
879	C₂²⋊C₄	—	73	1	no	—
880	C₂²⋊C₄	—	73	1	no	—
881	C₂²⋊C₄	—	73	1	no	—
882	C₂²⋊C₄	—	146	2	no	—
883	C₂²⋊C₄	—	146	2	no	—
884	C₄²	—	2	2	no	—
885	C₄²	—	2	2	no	—
886	C₄²	—	2	2	no	—
887	C₄²	—	73	1	no	—
888	C₄²	—	73	1	no	—
889	C₄²	—	73	1	no	—
890	C₄²	—	73	1	no	—
891	C₄²	—	73	1	no	—
892	C₄²	—	146	2	no	—
893	C₄²	—	146	2	no	—
894	C₄²	—	146	2	no	—
895	C₄²	—	146	2	no	—
896	C₄²	—	146	2	no	—
897	C₄²	—	146	2	no	—
898	C₄²	—	146	2	no	—
899	C₄²	—	146	2	no	—
900	C₄²	—	146	2	no	—
901	C₄²	—	146	2	no	—
902	C₄²	—	146	2	no	—
903	C₄²	C₂³×D₇₃	1	1	yes	characteristic
904	C₄²	C₂³×D₇₃	1	1	yes	characteristic
905	C₄²	C₂³×D₇₃	1	1	yes	characteristic
906	C₂³	—	73	1	no	—
907	Q₈	—	2	2	no	—
908	Q₈	—	4	1	no	—
909	Q₈	—	8	2	no	—
910	Q₈	—	292	1	no	—
911	Q₈	—	292	4	no	—
912	Q₈	—	584	2	no	—
913	Q₈	—	584	2	no	—
914	Q₈	—	584	2	no	—
915	Q₈	—	584	2	no	—
916	Q₈	—	73	4	no	—
917	Q₈	—	146	8	no	—
918	Q₈	—	146	2	no	—
919	Q₈	—	146	2	no	—
920	Q₈	—	146	2	no	—
921	Q₈	C₂×Q₈×D₇₃	1	4	yes	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	292	1	no	—
927	C₂×C₄	—	584	2	no	—
928	C₂×C₄	—	73	1	no	—
929	C₂×C₄	—	73	1	no	—
930	C₂×C₄	—	73	2	no	—
931	C₂×C₄	—	73	2	no	—
932	C₂×C₄	—	73	1	no	—
933	C₂×C₄	—	73	1	no	—
934	C₂×C₄	—	73	1	no	—
935	C₂×C₄	—	73	1	no	—
936	C₂×C₄	—	73	1	no	—
937	C₂×C₄	—	146	2	no	—
938	C₂×C₄	—	146	8	no	—
939	C₂×C₄	—	146	2	no	—
940	C₂×C₄	—	146	2	no	—
941	C₂×C₄	—	146	2	no	—
942	C₂×C₄	—	146	2	no	—
943	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
944	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
945	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
946	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
947	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
948	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
949	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
950	C₈	—	2	1	no	—
951	C₈	—	2	1	no	—
952	C₈	—	2	1	no	—
953	C₈	—	73	2	no	—
954	C₈	—	146	1	no	—
955	C₈	—	146	1	no	—
956	C₈	—	146	1	no	—
957	C₈	C₂×Q₈×D₇₃	1	2	yes	—
958	C₂²	—	73	2	no	—
959	C₂²	—	146	1	no	—
960	C₂²	—	146	1	no	—
961	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
962	C₄	—	2	4	no	—
963	C₄	—	2	1	no	—
964	C₄	—	2	1	no	—
965	C₄	—	2	1	no	—
966	C₄	—	2	1	no	—
967	C₄	—	2	1	no	—
968	C₄	—	2	1	no	—
969	C₄	—	4	2	no	—
970	C₄	—	4	2	no	—
971	C₄	—	4	2	no	—
972	C₄	—	292	2	no	—
973	C₄	—	292	2	no	—
974	C₄	—	292	2	no	—
975	C₄	—	73	2	no	—
976	C₄	—	73	2	no	—
977	C₄	—	146	4	no	—
978	C₄	—	146	1	no	—
979	C₄	—	146	1	no	—
980	C₄	—	146	1	no	—
981	C₄	—	146	1	no	—
982	C₄	—	146	1	no	—
983	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
984	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
985	C₂	—	146	2	no	—
986	C₂	D₄×Q₈×D₇₃	1	1	yes	characteristic
987	C₂	#578×D₇₃	1	1	yes	characteristic
988	C₂	#22624700	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×#3383	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂²×D₇₃	C₂²×D₄
hypercenter	#3383	D₇₃
hypocenter	C₇₃	#61372
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3383

Complements

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

N	H ≅ G/N	type
2. #22622898	C₂	semidirect
3. #22622894	C₂	semidirect
4. #22622866	C₂	semidirect
5. #22622858	C₂	semidirect
6. #22622823	C₂	semidirect
7. #22622822	C₂	semidirect
8. #22622822	C₂	semidirect
9. #22622819	C₂	semidirect
10. #22622819	C₂	semidirect
11. Q₁₆×Dic₁₄₆	C₂	semidirect
12. #22622814	C₂	semidirect
23. C₇₃×#3383	C₂	semidirect
134. Q₁₆×D₇₃	Q₈	semidirect
505. #3383	D₇₃	semidirect
518. C₇₃	#61372	semidirect

Maximal subgroups

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

subgroup	index
#22623738	2
#22622898	2
#22622894	2
#22622866	2
#22622858	2
#22622823	2
#22622822	2
#22622819	2
Q₁₆×Dic₁₄₆	2
#22622814	2
#22620468	2
#22620464	2
#22620444	2
#22619770	2
#22619766	2
#22619734	2
#22618860	2
#22618794	2
C₄×Q₁₆×D₇₃	2
C₇₃×#3383	2
#61372	73