Subgroups — #33966743

Order 18688.

1734 conjugacy classes of subgroups.

The subgroup lattice has 1086 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623757	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623750	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622899	C₂	1	2	yes	maximal, complemented
4	#22622890	C₂	1	2	yes	maximal, complemented
5	#22622881	C₂	1	2	yes	maximal, complemented
6	#22622877	C₂	1	2	yes	maximal, complemented
7	#22622864	C₂	1	2	yes	maximal, complemented
8	#22622853	C₂	1	2	yes	maximal, complemented
9	#22622842	C₂	1	2	yes	maximal, complemented
10	#22622831	C₂	1	2	yes	maximal, complemented
11	#22620471	C₂	1	1	yes	maximal, characteristic, complemented
12	#22620463	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#17988996	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619791	C₂	1	1	yes	maximal, characteristic, complemented
15	#22619791	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619780	C₂	1	1	yes	maximal, characteristic, complemented
17	#22619780	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619753	C₂	1	1	yes	maximal, characteristic, complemented
19	#22619746	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618871	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618815	C₂	1	1	yes	maximal, characteristic
22	#22618807	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#2943	C₂	1	1	yes	maximal, characteristic
24	Q₈×Dic₁₄₆	C₂²	1	2	yes	—
25	#17989316	C₂²	1	2	yes	—
26	#17989313	C₂²	1	2	yes	—
27	#17989313	C₂²	1	2	yes	—
28	#17989296	—	2	2	no	—
29	#17989296	—	2	2	no	—
30	#17989296	C₂²	1	2	yes	—
31	#17989296	C₂²	1	2	yes	—
32	#17989294	—	2	2	no	—
33	#17989294	C₂²	1	2	yes	—
34	D₄×Dic₁₄₆	—	2	2	no	—
35	D₄×Dic₁₄₆	C₂²	1	2	yes	—
36	#17989215	—	2	1	no	—
37	#17989215	—	2	1	no	—
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	#17989215	C₂²	1	1	yes	characteristic
43	#17989215	C₂²	1	1	yes	characteristic
44	#17989144	—	2	1	no	—
45	#17989144	—	2	1	no	—
46	#17989144	C₂²	1	1	yes	characteristic
47	C₂×#14556591	—	2	1	no	—
48	C₂×#14556591	C₂²	1	1	yes	characteristic
49	C₂×#14556583	—	2	1	no	—
50	C₂×#14556583	C₂²	1	1	yes	characteristic
51	#17989070	C₂²	1	1	yes	characteristic
52	#17989070	C₂²	1	1	yes	characteristic
53	#17989070	C₂²	1	1	yes	characteristic
54	#17989070	C₂²	1	1	yes	characteristic
55	#17988996	C₂²	1	2	yes	—
56	#17988996	C₂²	1	2	yes	—
57	#17988996	C₂²	1	2	yes	—
58	#17988996	C₂²	1	2	yes	—
59	#17988995	C₂²	1	2	yes	—
60	#17988995	C₂²	1	2	yes	—
61	#17988994	C₂²	1	2	yes	—
62	#17988994	C₂²	1	2	yes	—
63	#17988991	C₂²	1	2	yes	—
64	#17988988	C₂²	1	2	yes	—
65	#17988987	C₂²	1	2	yes	—
66	#17988984	C₂²	1	2	yes	—
67	#17988896	C₂²	1	2	yes	—
68	#17988896	C₂²	1	2	yes	—
69	#17988894	C₂²	1	2	yes	—
70	#17988894	C₂²	1	2	yes	—
71	#17988892	C₂²	1	2	yes	—
72	#17988892	C₂²	1	2	yes	—
73	#17988889	C₂²	1	2	yes	—
74	#17988889	C₂²	1	2	yes	—
75	#17988887	C₂²	1	2	yes	—
76	#17988887	C₂²	1	2	yes	—
77	#17988885	C₂²	1	2	yes	—
78	#17988885	C₂²	1	2	yes	—
79	#17988882	C₂²	1	2	yes	—
80	#17988880	C₂²	1	2	yes	—
81	#17988880	C₂²	1	2	yes	—
82	#17988877	C₂²	1	2	yes	—
83	#17988875	C₂²	1	2	yes	—
84	#17988875	C₂²	1	2	yes	—
85	#17988872	C₂²	1	2	yes	—
86	#17988870	C₂²	1	2	yes	—
87	#17988870	C₂²	1	2	yes	—
88	#17988867	C₂²	1	2	yes	—
89	#17988865	C₂²	1	2	yes	—
90	#17988865	C₂²	1	2	yes	—
91	#17988715	C₂²	1	2	yes	—
92	#17988715	C₂²	1	2	yes	—
93	#17988715	C₂²	1	2	yes	—
94	#17988715	C₂²	1	2	yes	—
95	#17988699	C₂²	1	2	yes	—
96	#17988694	C₂²	1	2	yes	—
97	#17988688	C₂²	1	2	yes	—
98	#17988688	C₂²	1	2	yes	—
99	Q₁₆×Dic₇₃	C₂²	1	2	yes	—
100	SD₁₆×Dic₇₃	C₂²	1	2	yes	—
101	SD₁₆×Dic₇₃	C₂²	1	2	yes	—
102	D₈×Dic₇₃	C₂²	1	2	yes	—
103	#17988630	C₂²	1	1	yes	characteristic
104	#17988630	C₂²	1	1	yes	characteristic
105	#17988630	C₂²	1	1	yes	characteristic
106	#17988630	C₂²	1	1	yes	characteristic
107	C₂×#14556525	C₂²	1	1	yes	characteristic
108	C₂×#14556525	C₂²	1	1	yes	characteristic
109	C₂×#14556523	C₂²	1	1	yes	characteristic
110	C₂×#14556523	C₂²	1	1	yes	characteristic
111	#17988613	C₂²	1	1	yes	characteristic
112	#17988613	C₂²	1	1	yes	characteristic
113	#17988611	C₂²	1	1	yes	characteristic
114	#17988588	C₂²	1	1	yes	characteristic
115	#17988588	C₂²	1	1	yes	characteristic
116	#17988588	C₂²	1	1	yes	characteristic
117	#17988588	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
124	#442×C₇₃	C₂²	1	1	yes	characteristic
125	#441×C₇₃	C₂²	1	1	yes	characteristic
126	#441×C₇₃	C₂²	1	1	yes	characteristic
127	#440×C₇₃	C₂²	1	1	yes	characteristic
128	#440×C₇₃	C₂²	1	1	yes	characteristic
129	#440×C₇₃	C₂²	1	1	yes	characteristic
130	#440×C₇₃	C₂²	1	1	yes	characteristic
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	C₂×#11924012	C₂³	1	1	yes	characteristic
138	C₂×#11924012	C₂³	1	1	yes	characteristic
139	#14556591	—	2	2	no	—
140	#14556591	—	2	1	no	—
141	#14556591	—	2	1	no	—
142	#14556591	—	2	2	no	—
143	#14556591	—	2	1	no	—
144	#14556591	—	2	1	no	—
145	#14556591	—	2	1	no	—
146	#14556591	—	2	1	no	—
147	#14556591	D₄	1	1	yes	characteristic
148	#14556591	D₄	1	1	yes	characteristic
149	#14556591	C₂³	1	2	yes	—
150	#14556591	C₂³	1	2	yes	—
151	#14556590	—	2	2	no	—
152	#14556590	—	2	2	no	—
153	#14556590	—	2	2	no	—
154	#14556590	—	2	2	no	—
155	#14556590	C₂³	1	2	yes	—
156	#14556590	C₂³	1	2	yes	—
157	#14556590	C₂³	1	2	yes	—
158	#14556590	C₂³	1	2	yes	—
159	#14556583	—	2	1	no	—
160	#14556583	—	2	1	no	—
161	#14556583	—	2	1	no	—
162	#14556583	—	2	1	no	—
163	#14556583	—	2	2	no	—
164	#14556583	—	2	2	no	—
165	#14556583	—	2	1	no	—
166	#14556583	—	2	1	no	—
167	#14556583	D₄	1	1	yes	characteristic
168	#14556583	D₄	1	1	yes	characteristic
169	#14556583	C₂³	1	2	yes	—
170	#14556583	C₂³	1	2	yes	—
171	#14556582	—	2	2	no	—
172	#14556582	—	2	2	no	—
173	#14556582	—	2	2	no	—
174	#14556582	—	2	2	no	—
175	#14556582	C₂³	1	2	yes	—
176	#14556582	C₂³	1	2	yes	—
177	#14556582	C₂³	1	2	yes	—
178	#14556582	C₂³	1	2	yes	—
179	#14556570	—	2	2	no	—
180	#14556570	—	2	2	no	—
181	#14556570	—	2	2	no	—
182	#14556570	—	2	2	no	—
183	#14556570	D₄	1	2	yes	—
184	#14556570	D₄	1	2	yes	—
185	#14556568	—	2	2	no	—
186	#14556568	—	2	2	no	—
187	#14556568	—	2	2	no	—
188	#14556568	—	2	2	no	—
189	#14556568	—	2	2	no	—
190	#14556568	—	2	2	no	—
191	#14556568	—	2	2	no	—
192	#14556568	—	2	2	no	—
193	#14556568	—	2	2	no	—
194	#14556568	—	2	2	no	—
195	#14556568	—	2	2	no	—
196	#14556568	—	2	2	no	—
197	Q₈×Dic₇₃	C₂³	1	2	yes	—
198	Q₈×Dic₇₃	C₂³	1	2	yes	—
199	Q₈×Dic₇₃	C₂³	1	2	yes	—
200	Q₈×Dic₇₃	C₂³	1	2	yes	—
201	C₄×Dic₁₄₆	—	2	2	no	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	C₄×Dic₁₄₆	—	2	2	no	—
204	C₄×Dic₁₄₆	—	2	2	no	—
205	C₄×Dic₁₄₆	C₂³	1	2	yes	—
206	C₄×Dic₁₄₆	C₂³	1	2	yes	—
207	D₄×Dic₇₃	—	2	2	no	—
208	D₄×Dic₇₃	—	2	2	no	—
209	D₄×Dic₇₃	—	2	2	no	—
210	D₄×Dic₇₃	—	2	2	no	—
211	D₄×Dic₇₃	C₂³	1	2	yes	—
212	D₄×Dic₇₃	C₂³	1	2	yes	—
213	D₄×Dic₇₃	C₂³	1	2	yes	—
214	D₄×Dic₇₃	C₂³	1	2	yes	—
215	#14556550	—	2	1	no	—
216	#14556550	—	2	1	no	—
217	#14556550	—	2	1	no	—
218	#14556550	—	2	1	no	—
219	#14556550	C₂³	1	1	yes	characteristic
220	#14556550	C₂³	1	1	yes	characteristic
221	C₂×C₄⋊Dic₇₃	—	2	1	no	—
222	C₂×C₄⋊Dic₇₃	—	2	1	no	—
223	C₂×C₄⋊Dic₇₃	—	2	2	no	—
224	C₂×C₄⋊Dic₇₃	—	2	1	no	—
225	C₂×C₄⋊Dic₇₃	—	2	1	no	—
226	C₂×C₄⋊Dic₇₃	—	2	1	no	—
227	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
228	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
229	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
231	C₂×#11924007	—	2	2	no	—
232	C₂×#11924007	—	2	2	no	—
233	C₂×#11924007	—	2	1	no	—
234	C₂×#11924007	—	2	1	no	—
235	#14556525	C₂³	1	2	yes	—
236	#14556525	C₂³	1	2	yes	—
237	#14556525	C₂³	1	2	yes	—
238	#14556525	C₂³	1	2	yes	—
239	#14556524	C₂³	1	2	yes	—
240	#14556524	C₂³	1	2	yes	—
241	#14556524	C₂³	1	2	yes	—
242	#14556524	C₂³	1	2	yes	—
243	#14556523	C₂³	1	2	yes	—
244	#14556523	C₂³	1	2	yes	—
245	#14556523	C₂³	1	2	yes	—
246	#14556523	C₂³	1	2	yes	—
247	#14556522	C₂³	1	2	yes	—
248	#14556522	C₂³	1	2	yes	—
249	#14556522	C₂³	1	2	yes	—
250	#14556522	C₂³	1	2	yes	—
251	C₄⋊#10596831	C₂³	1	2	yes	—
252	C₄⋊#10596831	C₂³	1	2	yes	—
253	#14556520	C₂³	1	2	yes	—
254	#14556520	C₂³	1	2	yes	—
255	#14556520	C₂³	1	2	yes	—
256	#14556520	C₂³	1	2	yes	—
257	#14556515	C₂³	1	2	yes	—
258	#14556515	C₂³	1	2	yes	—
259	#14556515	C₂³	1	2	yes	—
260	#14556515	C₂³	1	2	yes	—
261	#14556512	C₂³	1	2	yes	—
262	#14556512	C₂³	1	2	yes	—
263	#14556512	C₂³	1	2	yes	—
264	#14556512	C₂³	1	2	yes	—
265	#14556501	C₂³	1	2	yes	—
266	#14556501	C₂³	1	2	yes	—
267	C₈×Dic₇₃	C₂³	1	2	yes	—
268	C₈×Dic₇₃	C₂³	1	2	yes	—
269	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
270	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
271	#135×C₇₃	Q₈	1	8	yes	complemented
272	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₄×Q₈×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×D₄×C₇₃	—	2	1	no	—
283	C₄×D₄×C₇₃	—	2	1	no	—
284	C₄×D₄×C₇₃	—	2	1	no	—
285	C₄×D₄×C₇₃	—	2	1	no	—
286	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
290	#117×C₇₃	—	2	1	no	—
291	#117×C₇₃	—	2	1	no	—
292	#117×C₇₃	C₂³	1	1	yes	characteristic
293	#117×C₇₃	C₂³	1	1	yes	characteristic
294	C₂×C₄²×C₇₃	—	2	1	no	—
295	C₂×C₄²×C₇₃	—	2	1	no	—
296	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
297	#107×C₇₃	C₂³	1	1	yes	characteristic
298	#107×C₇₃	C₂³	1	1	yes	characteristic
299	#106×C₇₃	C₂³	1	1	yes	characteristic
300	#106×C₇₃	C₂³	1	1	yes	characteristic
301	#103×C₇₃	C₂³	1	1	yes	characteristic
302	#103×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#103×C₇₃	C₂³	1	1	yes	characteristic
305	#102×C₇₃	C₂³	1	1	yes	characteristic
306	#102×C₇₃	C₂³	1	1	yes	characteristic
307	#102×C₇₃	C₂³	1	1	yes	characteristic
308	#102×C₇₃	C₂³	1	1	yes	characteristic
309	#97×C₇₃	C₂³	1	1	yes	characteristic
310	#97×C₇₃	C₂³	1	1	yes	characteristic
311	#97×C₇₃	C₂³	1	1	yes	characteristic
312	#97×C₇₃	C₂³	1	1	yes	characteristic
313	C₂×Dic₁₄₆	—	2	2	no	—
314	C₂×Dic₁₄₆	—	2	2	no	—
315	C₂×Dic₁₄₆	—	2	2	no	—
316	C₂×Dic₁₄₆	—	2	2	no	—
317	C₂×Dic₁₄₆	—	2	2	no	—
318	C₂×Dic₁₄₆	—	2	2	no	—
319	C₂×Dic₁₄₆	—	8	4	no	—
320	C₂×Dic₁₄₆	—	8	2	no	—
321	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
322	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
323	C₂²×Dic₇₃	—	2	1	no	—
324	C₂²×Dic₇₃	—	2	1	no	—
325	C₂²×Dic₇₃	—	2	1	no	—
326	C₂²×Dic₇₃	—	2	1	no	—
327	C₂²×Dic₇₃	—	2	2	no	—
328	C₂²×Dic₇₃	—	2	2	no	—
329	C₂²×Dic₇₃	—	2	2	no	—
330	C₂²×Dic₇₃	—	2	2	no	—
331	#11924012	—	2	2	no	—
332	#11924012	—	2	2	no	—
333	C₂×#10596831	C₂⁴	1	2	yes	—
334	C₂×#10596831	C₂⁴	1	2	yes	—
335	C₄⋊Dic₇₃	—	2	2	no	—
336	C₄⋊Dic₇₃	—	2	1	no	—
337	C₄⋊Dic₇₃	—	2	1	no	—
338	C₄⋊Dic₇₃	—	2	1	no	—
339	C₄⋊Dic₇₃	—	2	1	no	—
340	C₄⋊Dic₇₃	—	2	2	no	—
341	C₄⋊Dic₇₃	—	2	2	no	—
342	C₄⋊Dic₇₃	—	2	2	no	—
343	C₄⋊Dic₇₃	—	2	2	no	—
344	C₄⋊Dic₇₃	—	2	2	no	—
345	C₄⋊Dic₇₃	—	2	2	no	—
346	C₄⋊Dic₇₃	—	2	2	no	—
347	C₄⋊Dic₇₃	—	2	2	no	—
348	C₄⋊Dic₇₃	—	2	2	no	—
349	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
350	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
351	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
352	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
353	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
355	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
356	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
357	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
358	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
359	#11924007	—	2	2	no	—
360	#11924007	—	2	2	no	—
361	#11924007	—	2	2	no	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
372	#11924007	C₂×D₄	1	2	yes	—
373	#11924007	C₂×D₄	1	2	yes	—
374	#11924007	C₂×D₄	1	2	yes	—
375	C₂²⋊Dic₇₃	—	2	2	no	—
376	C₂²⋊Dic₇₃	—	2	2	no	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	—	2	2	no	—
379	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
380	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
381	C₄×Dic₇₃	—	2	2	no	—
382	C₄×Dic₇₃	—	2	2	no	—
383	C₄×Dic₇₃	—	2	2	no	—
384	C₄×Dic₇₃	—	2	2	no	—
385	C₄×Dic₇₃	C₂⁴	1	2	yes	—
386	C₄×Dic₇₃	C₂⁴	1	2	yes	—
387	#41×C₇₃	—	2	2	no	—
388	#41×C₇₃	—	2	2	no	—
389	#41×C₇₃	C₂×Q₈	1	4	yes	—
390	#41×C₇₃	C₂×Q₈	1	4	yes	complemented
391	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
392	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
393	C₂×D₄×C₇₃	—	2	1	no	—
394	C₂×D₄×C₇₃	—	2	1	no	—
395	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
396	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
397	C₂²×C₄×C₇₃	—	2	1	no	—
398	C₂²×C₄×C₇₃	—	2	1	no	—
399	C₂²×C₄×C₇₃	—	2	1	no	—
400	C₂²×C₄×C₇₃	—	2	1	no	—
401	C₂²×C₄×C₇₃	—	2	1	no	—
402	C₂²×C₄×C₇₃	—	2	1	no	—
403	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
404	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
405	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
406	Q₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
407	SD₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
408	SD₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
409	D₈×C₇₃	C₂×Q₈	1	4	yes	complemented
410	C₂×C₈×C₇₃	—	2	2	no	—
411	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	complemented
412	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
416	C₄⋊C₄×C₇₃	—	2	1	no	—
417	C₄⋊C₄×C₇₃	—	2	1	no	—
418	C₄⋊C₄×C₇₃	—	2	1	no	—
419	C₄⋊C₄×C₇₃	—	2	1	no	—
420	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
424	C₂²⋊C₄×C₇₃	—	2	1	no	—
425	C₂²⋊C₄×C₇₃	—	2	1	no	—
426	C₂²⋊C₄×C₇₃	—	2	1	no	—
427	C₂²⋊C₄×C₇₃	—	2	1	no	—
428	C₂²⋊C₄×C₇₃	—	2	1	no	—
429	C₂²⋊C₄×C₇₃	—	2	1	no	—
430	C₄²×C₇₃	—	2	1	no	—
431	C₄²×C₇₃	—	2	1	no	—
432	C₄²×C₇₃	—	2	1	no	—
433	C₄²×C₇₃	—	2	1	no	—
434	C₄²×C₇₃	—	2	1	no	—
435	C₄²×C₇₃	—	2	1	no	—
436	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
439	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₂³×C₇₃	—	2	1	no	—
441	C₂³×C₇₃	—	2	1	no	—
442	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₇₃	—	2	1	no	—
444	Q₈×C₇₃	—	2	1	no	—
445	Q₈×C₇₃	C₂²×Q₈	1	2	yes	—
446	Q₈×C₇₃	C₂²×Q₈	1	2	yes	—
447	D₄×C₇₃	—	2	4	no	—
448	D₄×C₇₃	—	2	4	no	—
449	D₄×C₇₃	—	2	1	no	—
450	D₄×C₇₃	—	2	1	no	—
451	D₄×C₇₃	C₂²×Q₈	1	2	yes	—
452	D₄×C₇₃	C₂²×Q₈	1	2	yes	—
453	C₂×C₄×C₇₃	—	2	1	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	4	no	—
456	C₂×C₄×C₇₃	—	2	4	no	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	2	1	no	—
459	C₂×C₄×C₇₃	—	2	1	no	—
460	C₂×C₄×C₇₃	—	2	1	no	—
461	C₂×C₄×C₇₃	—	4	1	no	—
462	C₂×C₄×C₇₃	—	4	1	no	—
463	C₂×C₄×C₇₃	—	4	2	no	—
464	C₂×C₄×C₇₃	—	4	2	no	—
465	C₂×C₄×C₇₃	—	8	1	no	—
466	C₂×C₄×C₇₃	—	8	1	no	—
467	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
473	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
474	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
475	C₂×Dic₇₃	—	2	2	no	—
476	C₂×Dic₇₃	—	2	2	no	—
477	C₂×Dic₇₃	—	2	2	no	—
478	C₂×Dic₇₃	—	2	2	no	—
479	C₂×Dic₇₃	—	8	2	no	—
480	C₂×Dic₇₃	—	8	2	no	—
481	C₂×Dic₇₃	—	8	2	no	—
482	C₂×Dic₇₃	—	8	2	no	—
483	C₂×Dic₇₃	—	8	1	no	—
484	C₂×Dic₇₃	—	8	1	no	—
485	C₂×Dic₇₃	—	8	1	no	—
486	C₂×Dic₇₃	—	8	1	no	—
487	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
488	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
489	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
490	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
491	Dic₁₄₆	—	4	2	no	—
492	Dic₁₄₆	—	4	2	no	—
493	Dic₁₄₆	—	4	4	no	—
494	Dic₁₄₆	—	8	2	no	—
495	Dic₁₄₆	—	8	2	no	—
496	Dic₁₄₆	—	8	2	no	—
497	Dic₁₄₆	—	8	2	no	—
498	Dic₁₄₆	—	8	2	no	—
499	C₈×C₇₃	—	2	1	no	—
500	C₈×C₇₃	—	2	1	no	—
501	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
502	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
503	#10596831	—	2	2	no	—
504	#10596831	—	2	2	no	—
505	C₂²×C₇₃	—	2	1	no	—
506	C₂²×C₇₃	—	2	1	no	—
507	C₂²×C₇₃	—	2	2	no	—
508	C₂²×C₇₃	—	2	2	no	—
509	C₂²×C₇₃	—	4	1	no	—
510	C₂²×C₇₃	—	4	1	no	—
511	C₂²×C₇₃	—	4	1	no	—
512	C₂²×C₇₃	—	4	1	no	—
513	C₂²×C₇₃	D₄×Q₈	1	2	yes	—
514	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
515	C₄×C₇₃	—	2	1	no	—
516	C₄×C₇₃	—	2	1	no	—
517	C₄×C₇₃	—	2	1	no	—
518	C₄×C₇₃	—	2	1	no	—
519	C₄×C₇₃	—	2	2	no	—
520	C₄×C₇₃	—	2	2	no	—
521	C₄×C₇₃	—	4	1	no	—
522	C₄×C₇₃	—	4	1	no	—
523	C₄×C₇₃	—	4	1	no	—
524	C₄×C₇₃	—	4	1	no	—
525	C₄×C₇₃	D₄×Q₈	1	2	yes	—
526	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
527	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
528	Dic₇₃	—	2	2	no	—
529	Dic₇₃	—	2	2	no	—
530	Dic₇₃	—	2	2	no	—
531	Dic₇₃	—	2	2	no	—
532	Dic₇₃	—	4	2	no	—
533	Dic₇₃	—	4	2	no	—
534	Dic₇₃	—	4	2	no	—
535	Dic₇₃	—	4	2	no	—
536	#61380	—	73	1	no	maximal, Sylow
537	C₂×C₇₃	—	2	2	no	—
538	C₂×C₇₃	—	4	2	no	—
539	C₂×C₇₃	—	4	2	no	—
540	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
541	C₂×C₇₃	#3585	1	1	yes	characteristic
542	C₂×C₇₃	#3586	1	1	yes	characteristic
543	#3504	—	73	1	no	—
544	#3503	—	73	1	no	—
545	#3390	—	73	2	no	—
546	#3389	—	73	2	no	—
547	#3388	—	73	2	no	—
548	#3388	—	73	2	no	—
549	#3387	—	73	2	no	—
550	#3386	—	73	2	no	—
551	#3385	—	73	2	no	—
552	#3384	—	73	2	no	—
553	#3164	—	73	1	no	—
554	#3163	—	73	1	no	—
555	C₂×#501	—	73	1	no	—
556	#3084	—	73	1	no	—
557	#3084	—	73	1	no	—
558	#3083	—	73	1	no	—
559	#3083	—	73	1	no	—
560	#3080	—	73	1	no	—
561	#3079	—	73	1	no	—
562	#2961	—	73	1	no	—
563	#2952	—	73	1	no	—
564	#2951	—	73	1	no	—
565	#2943	D₇₃	1	1	yes	characteristic
566	C₇₃	#61380	1	1	yes	characteristic, complemented, Sylow
567	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
568	Q₈²	—	73	2	no	—
569	#557	—	73	2	no	—
570	#557	—	73	2	no	—
571	#557	—	73	2	no	—
572	#554	—	73	2	no	—
573	#554	—	73	2	no	—
574	#554	—	73	2	no	—
575	#554	—	146	2	no	—
576	#554	—	146	2	no	—
577	#554	—	146	2	no	—
578	D₄×Q₈	—	73	2	no	—
579	D₄×Q₈	—	146	2	no	—
580	#544	—	73	1	no	—
581	#544	—	73	1	no	—
582	#544	—	73	1	no	—
583	#544	—	73	1	no	—
584	#544	—	146	1	no	—
585	#544	—	146	1	no	—
586	#544	—	146	1	no	—
587	#544	—	146	1	no	—
588	#533	—	73	1	no	—
589	#533	—	146	1	no	—
590	#533	—	146	1	no	—
591	C₂×C₄⋊Q₈	—	73	1	no	—
592	C₂×C₄⋊Q₈	—	146	1	no	—
593	C₂×#125	—	73	1	no	—
594	C₂×#125	—	146	1	no	—
595	#520	—	73	1	no	—
596	#520	—	73	1	no	—
597	#520	—	73	1	no	—
598	#520	—	73	1	no	—
599	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
600	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
601	#501	—	73	2	no	—
602	#501	—	73	2	no	—
603	#501	—	73	2	no	—
604	#501	—	73	2	no	—
605	#501	—	73	2	no	—
606	#501	—	73	2	no	—
607	#501	—	73	2	no	—
608	#501	—	73	2	no	—
609	#500	—	73	2	no	—
610	#499	—	73	2	no	—
611	#499	—	73	2	no	—
612	#498	—	73	2	no	—
613	#479	—	73	2	no	—
614	#479	—	73	2	no	—
615	#479	—	73	2	no	—
616	#479	—	73	2	no	—
617	#479	—	73	2	no	—
618	#479	—	73	2	no	—
619	#478	—	73	2	no	—
620	#478	—	73	2	no	—
621	#478	—	73	2	no	—
622	#478	—	73	2	no	—
623	#478	—	73	2	no	—
624	#478	—	73	2	no	—
625	#477	—	73	2	no	—
626	#477	—	73	2	no	—
627	#477	—	73	2	no	—
628	#476	—	73	2	no	—
629	#476	—	73	2	no	—
630	#476	—	73	2	no	—
631	#475	—	73	2	no	—
632	#475	—	73	2	no	—
633	#475	—	73	2	no	—
634	#474	—	73	2	no	—
635	#474	—	73	2	no	—
636	#474	—	73	2	no	—
637	#446	—	73	2	no	—
638	#446	—	73	2	no	—
639	#446	—	73	2	no	—
640	#446	—	73	2	no	—
641	#442	—	73	2	no	—
642	#442	C₂×D₇₃	1	1	yes	characteristic
643	#442	C₂×D₇₃	1	1	yes	characteristic
644	#441	—	73	2	no	—
645	#441	C₂×D₇₃	1	1	yes	characteristic
646	#441	C₂×D₇₃	1	1	yes	characteristic
647	#440	—	73	2	no	—
648	#440	—	73	2	no	—
649	#440	C₂×D₇₃	1	1	yes	characteristic
650	#440	C₂×D₇₃	1	1	yes	characteristic
651	#440	C₂×D₇₃	1	1	yes	characteristic
652	#440	C₂×D₇₃	1	1	yes	characteristic
653	C₄×Q₁₆	—	73	2	no	—
654	C₄×SD₁₆	—	73	2	no	—
655	C₄×SD₁₆	—	73	2	no	—
656	C₄×D₈	—	73	2	no	—
657	#428	—	73	1	no	—
658	#428	—	73	1	no	—
659	#428	—	73	1	no	—
660	#428	—	73	1	no	—
661	#427	C₂×D₇₃	1	1	yes	characteristic
662	C₂×#107	—	73	1	no	—
663	C₂×#107	—	73	1	no	—
664	C₂×#106	—	73	1	no	—
665	C₂×#106	—	73	1	no	—
666	#424	—	73	1	no	—
667	#424	—	73	1	no	—
668	#423	—	73	1	no	—
669	#417	—	73	1	no	—
670	#417	—	73	1	no	—
671	#417	—	73	1	no	—
672	#417	—	73	1	no	—
673	#416	C₂×D₇₃	1	1	yes	characteristic
674	#416	C₂×D₇₃	1	1	yes	characteristic
675	#405	—	73	1	no	—
676	#405	—	73	1	no	—
677	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
678	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
679	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
680	C₂²×Q₈	—	146	2	no	—
681	C₂²×Q₈	—	146	1	no	—
682	#135	Dic₁₄₆	1	8	yes	complemented
683	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
684	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
685	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
686	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
687	C₂×M₁₆	—	73	1	no	—
688	C₂×M₁₆	—	73	1	no	—
689	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
690	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
691	C₄⋊Q₈	—	73	2	no	—
692	C₄⋊Q₈	—	73	2	no	—
693	C₄⋊Q₈	—	73	2	no	—
694	C₄⋊Q₈	—	73	2	no	—
695	C₄⋊Q₈	—	73	1	no	—
696	C₄⋊Q₈	—	73	1	no	—
697	C₄⋊Q₈	—	73	2	no	—
698	C₄⋊Q₈	—	73	2	no	—
699	C₄⋊Q₈	—	146	1	no	—
700	C₄⋊Q₈	—	146	1	no	—
701	C₄⋊Q₈	—	146	2	no	—
702	C₄⋊Q₈	—	146	1	no	—
703	C₄⋊Q₈	—	146	1	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	1	no	—
710	C₄⋊Q₈	—	146	1	no	—
711	#125	—	73	2	no	—
712	#125	—	73	2	no	—
713	#125	—	73	2	no	—
714	#125	—	73	2	no	—
715	#125	—	73	1	no	—
716	#125	—	73	1	no	—
717	#125	—	73	2	no	—
718	#125	—	73	2	no	—
719	#125	—	146	1	no	—
720	#125	—	146	1	no	—
721	#125	—	146	2	no	—
722	#125	—	146	2	no	—
723	#125	—	146	1	no	—
724	#125	—	146	1	no	—
725	#125	—	146	2	no	—
726	#125	—	146	2	no	—
727	#125	—	146	2	no	—
728	#125	—	146	2	no	—
729	#125	—	146	1	no	—
730	#125	—	146	1	no	—
731	C₂²⋊Q₈	—	73	2	no	—
732	C₂²⋊Q₈	—	73	2	no	—
733	C₂²⋊Q₈	—	146	2	no	—
734	C₂²⋊Q₈	—	146	2	no	—
735	C₂²⋊Q₈	—	146	2	no	—
736	C₂²⋊Q₈	—	146	2	no	—
737	C₂²⋊Q₈	—	146	2	no	—
738	C₂²⋊Q₈	—	146	2	no	—
739	C₂²⋊Q₈	—	146	2	no	—
740	C₂²⋊Q₈	—	146	2	no	—
741	C₂²⋊Q₈	—	146	2	no	—
742	C₂²⋊Q₈	—	146	2	no	—
743	C₂²⋊Q₈	—	146	2	no	—
744	C₂²⋊Q₈	—	146	2	no	—
745	C₂²⋊Q₈	—	146	2	no	—
746	C₂²⋊Q₈	—	146	2	no	—
747	C₂²⋊Q₈	—	146	2	no	—
748	C₂²⋊Q₈	—	146	2	no	—
749	C₄×Q₈	—	73	2	no	—
750	C₄×Q₈	—	73	2	no	—
751	C₄×Q₈	—	73	2	no	—
752	C₄×Q₈	—	73	2	no	—
753	C₄×Q₈	—	73	2	no	—
754	C₄×Q₈	—	73	2	no	—
755	C₄×Q₈	—	146	2	no	—
756	C₄×Q₈	—	146	2	no	—
757	C₄×Q₈	—	146	2	no	—
758	C₄×Q₈	—	146	2	no	—
759	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
760	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
761	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
762	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
763	C₄×D₄	—	2	1	no	—
764	C₄×D₄	—	2	1	no	—
765	C₄×D₄	—	2	1	no	—
766	C₄×D₄	—	2	1	no	—
767	C₄×D₄	—	73	2	no	—
768	C₄×D₄	—	73	2	no	—
769	C₄×D₄	—	73	2	no	—
770	C₄×D₄	—	73	2	no	—
771	C₄×D₄	—	146	2	no	—
772	C₄×D₄	—	146	2	no	—
773	C₄×D₄	—	146	2	no	—
774	C₄×D₄	—	146	2	no	—
775	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
776	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
777	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
778	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
779	#117	—	2	1	no	—
780	#117	—	2	1	no	—
781	#117	—	73	1	no	—
782	#117	—	73	1	no	—
783	#117	—	146	1	no	—
784	#117	—	146	1	no	—
785	#117	—	146	1	no	—
786	#117	—	146	1	no	—
787	#117	C₂²×D₇₃	1	1	yes	characteristic
788	#117	C₂²×D₇₃	1	1	yes	characteristic
789	C₂×C₄⋊C₄	—	73	1	no	—
790	C₂×C₄⋊C₄	—	73	1	no	—
791	C₂×C₄⋊C₄	—	73	1	no	—
792	C₂×C₄⋊C₄	—	73	1	no	—
793	C₂×C₄⋊C₄	—	146	1	no	—
794	C₂×C₄⋊C₄	—	146	1	no	—
795	C₂×C₄⋊C₄	—	146	1	no	—
796	C₂×C₄⋊C₄	—	146	1	no	—
797	C₂×C₄⋊C₄	—	146	2	no	—
798	C₂×C₄⋊C₄	—	146	2	no	—
799	C₂×C₄⋊C₄	—	146	2	no	—
800	C₂×C₄⋊C₄	—	146	1	no	—
801	C₂×C₄⋊C₄	—	146	1	no	—
802	C₂×C₄⋊C₄	—	146	1	no	—
803	C₂×C₄²	—	2	1	no	—
804	C₂×C₄²	—	2	1	no	—
805	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
806	#107	—	73	2	no	—
807	#107	—	73	2	no	—
808	#107	—	73	2	no	—
809	#107	—	73	2	no	—
810	#107	—	73	2	no	—
811	#107	—	73	2	no	—
812	#107	—	73	2	no	—
813	#107	—	73	2	no	—
814	#107	C₂²×D₇₃	1	1	yes	characteristic
815	#107	C₂²×D₇₃	1	1	yes	characteristic
816	#106	—	73	2	no	—
817	#106	—	73	2	no	—
818	#106	—	73	2	no	—
819	#106	—	73	2	no	—
820	#106	—	73	2	no	—
821	#106	—	73	2	no	—
822	#106	—	73	2	no	—
823	#106	—	73	2	no	—
824	#106	C₂²×D₇₃	1	1	yes	characteristic
825	#106	C₂²×D₇₃	1	1	yes	characteristic
826	C₄⋊C₈	—	73	2	no	—
827	C₄⋊C₈	—	73	2	no	—
828	C₄⋊C₈	—	73	2	no	—
829	C₄⋊C₈	—	73	2	no	—
830	C₄⋊C₈	—	73	2	no	—
831	C₄⋊C₈	—	73	2	no	—
832	#103	—	73	2	no	—
833	#103	—	73	2	no	—
834	#103	—	73	2	no	—
835	#103	—	73	2	no	—
836	#103	C₂²×D₇₃	1	1	yes	characteristic
837	#103	C₂²×D₇₃	1	1	yes	characteristic
838	#103	C₂²×D₇₃	1	1	yes	characteristic
839	#103	C₂²×D₇₃	1	1	yes	characteristic
840	#102	—	73	2	no	—
841	#102	—	73	2	no	—
842	#102	—	73	2	no	—
843	#102	—	73	2	no	—
844	#102	C₂²×D₇₃	1	1	yes	characteristic
845	#102	C₂²×D₇₃	1	1	yes	characteristic
846	#102	C₂²×D₇₃	1	1	yes	characteristic
847	#102	C₂²×D₇₃	1	1	yes	characteristic
848	#97	—	73	2	no	—
849	#97	—	73	2	no	—
850	#97	C₂²×D₇₃	1	1	yes	characteristic
851	#97	C₂²×D₇₃	1	1	yes	characteristic
852	#97	C₂²×D₇₃	1	1	yes	characteristic
853	#97	C₂²×D₇₃	1	1	yes	characteristic
854	C₄×C₈	—	73	2	no	—
855	C₄×C₈	—	73	2	no	—
856	#41	—	2	2	no	—
857	#41	—	2	2	no	—
858	#41	C₂×Dic₁₄₆	1	4	yes	—
859	#41	C₂×Dic₁₄₆	1	4	yes	complemented
860	C₂×Q₈	—	584	2	no	—
861	C₂×Q₈	—	584	4	no	—
862	C₂×Q₈	—	73	2	no	—
863	C₂×Q₈	—	73	2	no	—
864	C₂×Q₈	—	146	2	no	—
865	C₂×Q₈	—	146	2	no	—
866	C₂×Q₈	—	146	2	no	—
867	C₂×Q₈	—	146	2	no	—
868	C₂×Q₈	—	146	2	no	—
869	C₂×Q₈	—	146	2	no	—
870	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
871	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	2	1	no	—
874	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
875	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	146	2	no	—
883	C₂²×C₄	—	146	2	no	—
884	C₂²×C₄	—	146	2	no	—
885	C₂²×C₄	—	146	2	no	—
886	C₂²×C₄	—	146	1	no	—
887	C₂²×C₄	—	146	1	no	—
888	C₂²×C₄	—	146	1	no	—
889	C₂²×C₄	—	146	1	no	—
890	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
891	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
893	Q₁₆	C₂×Dic₁₄₆	1	4	yes	complemented
894	SD₁₆	C₂×Dic₁₄₆	1	4	yes	complemented
895	SD₁₆	C₂×Dic₁₄₆	1	4	yes	complemented
896	D₈	C₂×Dic₁₄₆	1	4	yes	complemented
897	M₁₆	—	146	2	no	—
898	M₁₆	—	146	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	73	2	no	—
901	C₂×C₈	—	73	2	no	—
902	C₂×C₈	C₂×Dic₁₄₆	1	4	yes	complemented
903	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
904	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
905	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
906	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	73	2	no	—
912	C₄⋊C₄	—	73	2	no	—
913	C₄⋊C₄	—	73	2	no	—
914	C₄⋊C₄	—	73	2	no	—
915	C₄⋊C₄	—	73	1	no	—
916	C₄⋊C₄	—	73	1	no	—
917	C₄⋊C₄	—	73	1	no	—
918	C₄⋊C₄	—	73	2	no	—
919	C₄⋊C₄	—	73	1	no	—
920	C₄⋊C₄	—	73	2	no	—
921	C₄⋊C₄	—	73	2	no	—
922	C₄⋊C₄	—	73	2	no	—
923	C₄⋊C₄	—	73	2	no	—
924	C₄⋊C₄	—	73	2	no	—
925	C₄⋊C₄	—	146	2	no	—
926	C₄⋊C₄	—	146	2	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	2	no	—
929	C₄⋊C₄	—	146	2	no	—
930	C₄⋊C₄	—	146	2	no	—
931	C₄⋊C₄	—	146	2	no	—
932	C₄⋊C₄	—	146	2	no	—
933	C₄⋊C₄	—	146	2	no	—
934	C₄⋊C₄	—	146	2	no	—
935	C₄⋊C₄	—	146	2	no	—
936	C₄⋊C₄	—	146	2	no	—
937	C₄⋊C₄	—	146	2	no	—
938	C₄⋊C₄	—	146	2	no	—
939	C₄⋊C₄	—	146	2	no	—
940	C₄⋊C₄	—	146	2	no	—
941	C₄⋊C₄	—	146	2	no	—
942	C₄⋊C₄	—	146	2	no	—
943	C₄⋊C₄	—	146	2	no	—
944	C₄⋊C₄	—	146	2	no	—
945	C₄⋊C₄	—	146	1	no	—
946	C₄⋊C₄	—	146	1	no	—
947	C₄⋊C₄	—	146	1	no	—
948	C₄⋊C₄	—	146	1	no	—
949	C₄⋊C₄	—	146	2	no	—
950	C₄⋊C₄	—	146	2	no	—
951	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
954	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	73	2	no	—
962	C₂²⋊C₄	—	73	2	no	—
963	C₂²⋊C₄	—	146	2	no	—
964	C₂²⋊C₄	—	146	2	no	—
965	C₂²⋊C₄	—	146	2	no	—
966	C₂²⋊C₄	—	146	2	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	73	2	no	—
974	C₄²	—	73	2	no	—
975	C₄²	—	146	2	no	—
976	C₄²	—	146	2	no	—
977	C₄²	—	146	2	no	—
978	C₄²	—	146	2	no	—
979	C₄²	D₄×D₇₃	1	1	yes	characteristic
980	C₄²	D₄×D₇₃	1	1	yes	characteristic
981	C₄²	C₂³×D₇₃	1	1	yes	characteristic
982	C₄²	C₂³×D₇₃	1	1	yes	characteristic
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
986	Q₈	—	2	1	no	—
987	Q₈	—	2	1	no	—
988	Q₈	—	292	4	no	—
989	Q₈	—	292	2	no	—
990	Q₈	—	292	2	no	—
991	Q₈	—	584	2	no	—
992	Q₈	—	584	2	no	—
993	Q₈	—	584	2	no	—
994	Q₈	—	584	2	no	—
995	Q₈	—	584	2	no	—
996	Q₈	C₂²×Dic₁₄₆	1	2	yes	—
997	Q₈	C₂²×Dic₁₄₆	1	2	yes	—
998	D₄	—	2	4	no	—
999	D₄	—	2	4	no	—
1000	D₄	—	2	1	no	—
1001	D₄	—	2	1	no	—
1002	D₄	C₂²×Dic₁₄₆	1	2	yes	—
1003	D₄	C₂²×Dic₁₄₆	1	2	yes	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	4	no	—
1007	C₂×C₄	—	2	4	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	4	1	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	4	2	no	—
1016	C₂×C₄	—	8	1	no	—
1017	C₂×C₄	—	8	1	no	—
1018	C₂×C₄	—	584	1	no	—
1019	C₂×C₄	—	584	1	no	—
1020	C₂×C₄	—	584	1	no	—
1021	C₂×C₄	—	584	1	no	—
1022	C₂×C₄	—	584	2	no	—
1023	C₂×C₄	—	584	2	no	—
1024	C₂×C₄	—	584	2	no	—
1025	C₂×C₄	—	584	2	no	—
1026	C₂×C₄	—	73	2	no	—
1027	C₂×C₄	—	73	2	no	—
1028	C₂×C₄	—	73	2	no	—
1029	C₂×C₄	—	73	2	no	—
1030	C₂×C₄	—	146	2	no	—
1031	C₂×C₄	—	146	2	no	—
1032	C₂×C₄	—	146	2	no	—
1033	C₂×C₄	—	146	2	no	—
1034	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1035	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1036	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1038	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1039	C₂×C₄	C₂²×Dic₁₄₆	1	2	yes	—
1040	C₂×C₄	#14556638	1	2	yes	—
1041	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1042	C₈	—	2	1	no	—
1043	C₈	—	2	1	no	—
1044	C₈	—	146	2	no	—
1045	C₈	—	146	2	no	—
1046	C₈	C₂²×Dic₁₄₆	1	2	yes	—
1047	C₈	C₂²×Dic₁₄₆	1	2	yes	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	4	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	D₄×Dic₁₄₆	1	2	yes	—
1057	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1058	C₄	—	2	2	no	—
1059	C₄	—	2	2	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	4	1	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	292	2	no	—
1069	C₄	—	292	2	no	—
1070	C₄	—	292	2	no	—
1071	C₄	—	292	2	no	—
1072	C₄	—	146	2	no	—
1073	C₄	—	146	2	no	—
1074	C₄	—	146	2	no	—
1075	C₄	—	146	2	no	—
1076	C₄	D₄×Dic₁₄₆	1	2	yes	—
1077	C₄	C₂³×Dic₁₄₆	1	1	yes	characteristic
1078	C₄	C₂×#14556638	1	1	yes	characteristic
1079	C₂	—	2	2	no	—
1080	C₂	—	4	2	no	—
1081	C₂	—	4	2	no	—
1082	C₂	C₂×D₄×Dic₁₄₆	1	1	yes	characteristic
1083	C₂	#22624708	1	1	yes	characteristic
1084	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	C₂×#135×C₇₃	C₂²
hypercenter	#2943	D₇₃
hypocenter	C₇₃	#61380
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. #22623757	C₂	semidirect
2. #22623750	C₂	semidirect
3. #22622899	C₂	semidirect
4. #22622890	C₂	semidirect
5. #22622881	C₂	semidirect
6. #22622877	C₂	semidirect
7. #22622864	C₂	semidirect
8. #22622853	C₂	semidirect
9. #22622842	C₂	semidirect
10. #22622831	C₂	semidirect
11. #22620471	C₂	semidirect
12. #22620463	C₂	semidirect
13. C₂×#17988996	C₂	semidirect
14. #22619791	C₂	semidirect
15. #22619791	C₂	semidirect
16. #22619780	C₂	semidirect
17. #22619780	C₂	semidirect
18. #22619753	C₂	semidirect
19. #22619746	C₂	semidirect
20. #22618871	C₂	semidirect
271. #135×C₇₃	Q₈	semidirect
390. #41×C₇₃	C₂×Q₈	semidirect
406. Q₁₆×C₇₃	C₂×Q₈	semidirect
407. SD₁₆×C₇₃	C₂×Q₈	semidirect
408. SD₁₆×C₇₃	C₂×Q₈	semidirect
409. D₈×C₇₃	C₂×Q₈	semidirect
411. C₂×C₈×C₇₃	C₂×Q₈	semidirect
566. C₇₃	#61380	semidirect
682. #135	Dic₁₄₆	semidirect
859. #41	C₂×Dic₁₄₆	semidirect
893. Q₁₆	C₂×Dic₁₄₆	semidirect
894. SD₁₆	C₂×Dic₁₄₆	semidirect
895. SD₁₆	C₂×Dic₁₄₆	semidirect
896. D₈	C₂×Dic₁₄₆	semidirect
902. C₂×C₈	C₂×Dic₁₄₆	semidirect

Maximal subgroups

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

subgroup	index
#22623757	2
#22623750	2
#22622899	2
#22622890	2
#22622881	2
#22622877	2
#22622864	2
#22622853	2
#22622842	2
#22622831	2
#22620471	2
#22620463	2
C₂×#17988996	2
#22619791	2
#22619780	2
#22619753	2
#22619746	2
#22618871	2
#22618815	2
#22618807	2
C₇₃×#2943	2
#61380	73