Subgroups — #3168×D₇₃ #33955702

Order 18688.

2070 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#529×D₇₃	C₂	1	2	yes	maximal, complemented
2	#22620504	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620503	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620502	C₂	1	1	yes	maximal, characteristic, complemented
5	#22620501	C₂	1	1	yes	maximal, characteristic, complemented
6	#22620500	C₂	1	2	yes	maximal, complemented
7	#22620499	C₂	1	1	yes	maximal, characteristic, complemented
8	#22620498	C₂	1	1	yes	maximal, characteristic, complemented
9	#22620497	C₂	1	2	yes	maximal, complemented
10	#22620496	C₂	1	1	yes	maximal, characteristic, complemented
11	#22620495	C₂	1	2	yes	maximal, complemented
12	#22620494	C₂	1	2	yes	maximal, complemented
13	#499×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#488×D₇₃	C₂	1	2	yes	maximal, complemented
16	#467×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#466×D₇₃	C₂	1	1	yes	maximal, characteristic
18	#465×D₇₃	C₂	1	2	yes	maximal, complemented
19	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×SD₁₆×D₇₃	C₂	1	2	yes	maximal, complemented
21	C₄×D₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
26	C₂×D₈×D₇₃	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
29	#17989124	C₂²	1	2	yes	complemented
30	#17989123	C₂²	1	2	yes	complemented
31	#17989122	C₂²	1	2	yes	complemented
32	#17989121	C₂²	1	2	yes	complemented
33	#17989120	—	2	2	no	—
34	#17989119	C₂²	1	2	yes	complemented
35	#17989118	C₂²	1	2	yes	complemented
36	#17989117	—	2	2	no	—
37	#17989116	C₂²	1	2	yes	complemented
38	#17989115	—	2	2	no	—
39	#17989114	—	2	2	no	—
40	#126×D₇₃	—	2	2	no	—
41	#125×D₇₃	C₂²	1	2	yes	—
42	#124×D₇₃	C₂²	1	2	yes	—
43	#123×D₇₃	—	2	2	no	—
44	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
45	#121×D₇₃	C₂²	1	2	yes	—
46	C₄×Q₈×D₇₃	C₂²	1	2	yes	—
47	C₄×D₄×D₇₃	—	2	2	no	—
48	C₄×D₄×D₇₃	C₂²	1	2	yes	—
49	#117×D₇₃	—	2	2	no	—
50	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
51	#17988989	C₂²	1	1	yes	characteristic, complemented
52	#17988988	C₂²	1	1	yes	characteristic, complemented
53	#17988988	C₂²	1	1	yes	characteristic, complemented
54	#17988987	C₂²	1	2	yes	complemented
55	#17988986	C₂²	1	2	yes	complemented
56	#17988972	C₂²	1	1	yes	characteristic, complemented
57	#17988971	C₂²	1	1	yes	characteristic, complemented
58	#17988970	C₂²	1	1	yes	characteristic, complemented
59	#17988969	C₂²	1	2	yes	complemented
60	#17988968	C₂²	1	2	yes	complemented
61	#17988944	C₂²	1	2	yes	complemented
62	#17988943	C₂²	1	2	yes	complemented
63	#17988943	C₂²	1	2	yes	complemented
64	#17988942	C₂²	1	2	yes	complemented
65	#17988941	C₂²	1	2	yes	complemented
66	#17988940	C₂²	1	2	yes	complemented
67	#17988940	C₂²	1	2	yes	complemented
68	#17988829	C₂²	1	1	yes	characteristic, complemented
69	#17988828	C₂²	1	1	yes	characteristic, complemented
70	#17988827	C₂²	1	2	yes	complemented
71	#17988826	C₂²	1	2	yes	complemented
72	#17988825	C₂²	1	1	yes	characteristic, complemented
73	#17988824	C₂²	1	1	yes	characteristic
74	#17988823	C₂²	1	1	yes	characteristic
75	#17988822	C₂²	1	2	yes	—
76	#17988821	C₂²	1	2	yes	—
77	#17988820	C₂²	1	1	yes	characteristic
78	#17988819	C₂²	1	2	yes	complemented
79	#17988818	C₂²	1	2	yes	complemented
80	#17988817	C₂²	1	2	yes	complemented
81	#17988816	C₂²	1	2	yes	complemented
82	#17988815	C₂²	1	2	yes	complemented
83	#17988814	C₂²	1	2	yes	complemented
84	#17988813	C₂²	1	2	yes	complemented
85	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
86	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
87	#17988681	C₂²	1	1	yes	characteristic, complemented
88	C₄×#11924018	C₂²	1	2	yes	complemented
89	#17988679	C₂²	1	2	yes	complemented
90	#17988678	C₂²	1	2	yes	complemented
91	C₄×#11924017	C₂²	1	2	yes	complemented
92	SD₁₆×Dic₇₃	C₂²	1	2	yes	complemented
93	C₄×#11924015	C₂²	1	2	yes	complemented
94	#17988674	C₂²	1	2	yes	complemented
95	C₄×#11924016	C₂²	1	2	yes	complemented
96	#17988672	C₂²	1	2	yes	complemented
97	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
98	D₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
99	#17988669	C₂²	1	1	yes	characteristic, complemented
100	C₄×#11924013	C₂²	1	2	yes	complemented
101	#17988667	C₂²	1	2	yes	complemented
102	#107×D₇₃	C₂²	1	1	yes	characteristic
103	#107×D₇₃	C₂²	1	1	yes	characteristic
104	#106×D₇₃	C₂²	1	2	yes	—
105	#103×D₇₃	C₂²	1	2	yes	—
106	#103×D₇₃	C₂²	1	2	yes	—
107	#102×D₇₃	C₂²	1	2	yes	—
108	#102×D₇₃	C₂²	1	2	yes	—
109	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
112	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
113	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
114	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
115	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
116	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic, complemented
120	#529×C₇₃	C₂²	1	2	yes	complemented
121	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#495×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#488×C₇₃	C₂²	1	2	yes	complemented
124	#467×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#466×C₇₃	C₂²	1	1	yes	characteristic
126	#465×C₇₃	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
129	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
132	C₂×D₄×D₇₃	—	2	2	no	—
133	C₂×D₄×D₇₃	C₂³	1	2	yes	—
134	C₂²×C₄×D₇₃	—	2	2	no	—
135	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
136	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
137	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
138	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
139	C₂×#11924018	C₂³	1	2	yes	—
140	Q₁₆×D₇₃	—	2	4	no	—
141	C₂×#11924017	C₂³	1	2	yes	—
142	C₂×#11924016	C₂³	1	2	yes	—
143	C₂×#11924015	C₂³	1	2	yes	—
144	SD₁₆×D₇₃	—	2	8	no	—
145	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
146	C₂×#11924013	C₂³	1	2	yes	—
147	D₈×D₇₃	—	2	4	no	—
148	C₂²×#10596831	C₂³	1	1	yes	characteristic
149	C₂²×#10596831	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₇₃	—	2	4	no	—
151	C₂×C₈×D₇₃	—	2	4	no	—
152	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
158	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
159	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
160	#14556586	—	2	2	no	—
161	#14556586	—	2	2	no	—
162	#14556586	—	2	2	no	—
163	#14556585	—	2	2	no	—
164	#14556584	—	2	2	no	—
165	#14556584	—	2	2	no	—
166	#14556584	—	2	2	no	—
167	#14556583	C₂³	1	2	yes	—
168	#14556582	C₂³	1	2	yes	—
169	#14556582	C₂³	1	2	yes	—
170	#14556581	—	2	2	no	—
171	#14556581	—	2	2	no	—
172	#14556580	C₂³	1	2	yes	—
173	#14556579	C₂³	1	2	yes	—
174	#14556578	C₂³	1	2	yes	—
175	#14556577	—	2	2	no	—
176	#14556577	—	2	2	no	—
177	#14556576	—	2	2	no	—
178	#14556576	—	2	2	no	—
179	#14556575	—	2	2	no	—
180	#14556574	—	2	2	no	—
181	#14556573	—	2	2	no	—
182	#14556573	—	2	2	no	—
183	#14556572	—	2	2	no	—
184	#14556571	C₂³	1	2	yes	—
185	#14556570	C₂³	1	2	yes	—
186	#14556569	—	2	2	no	—
187	#14556568	—	2	2	no	—
188	#14556567	C₂³	1	2	yes	—
189	#14556566	C₂³	1	2	yes	—
190	#14556565	C₂³	1	2	yes	—
191	#14556564	—	2	2	no	—
192	#14556563	—	2	2	no	—
193	#14556562	C₂³	1	2	yes	—
194	Q₈×Dic₇₃	C₂³	1	2	yes	—
195	C₄×Dic₁₄₆	—	2	2	no	—
196	C₄×Dic₁₄₆	C₂³	1	2	yes	—
197	#14556556	—	2	2	no	—
198	#14556556	C₂³	1	2	yes	—
199	C₄×D₂₉₂	—	2	2	no	—
200	C₄×D₂₉₂	C₂³	1	2	yes	—
201	D₄×Dic₇₃	—	2	2	no	—
202	D₄×Dic₇₃	C₂³	1	2	yes	—
203	#14556553	—	2	2	no	—
204	#14556553	C₂³	1	2	yes	—
205	C₄×C₂²⋊D₇₃	—	2	2	no	—
206	C₄×C₂²⋊D₇₃	—	2	2	no	—
207	C₄×C₂²⋊D₇₃	—	2	2	no	—
208	#14556551	—	2	2	no	—
209	#14556551	—	2	2	no	—
210	#14556551	—	2	2	no	—
211	#14556550	—	2	2	no	—
212	#14556549	—	2	2	no	—
213	#14556549	—	2	2	no	—
214	#14556548	—	2	2	no	—
215	#14556548	—	2	2	no	—
216	#14556547	—	2	2	no	—
217	#14556547	—	2	2	no	—
218	C₄⋊C₄×D₇₃	—	2	2	no	—
219	C₄⋊C₄×D₇₃	—	2	2	no	—
220	C₄⋊C₄×D₇₃	—	2	2	no	—
221	C₄⋊C₄×D₇₃	—	2	2	no	—
222	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
223	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
224	C₂²⋊C₄×D₇₃	—	2	2	no	—
225	C₂²⋊C₄×D₇₃	—	2	2	no	—
226	C₂²⋊C₄×D₇₃	—	2	2	no	—
227	C₂²⋊C₄×D₇₃	—	2	2	no	—
228	C₂²⋊C₄×D₇₃	—	2	2	no	—
229	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
230	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
231	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
232	C₄²×D₇₃	—	2	2	no	—
233	C₄²×D₇₃	D₄	1	1	yes	characteristic
234	C₄²×D₇₃	D₄	1	1	yes	characteristic
235	C₄²×D₇₃	D₄	1	1	yes	characteristic
236	C₄²×D₇₃	D₄	1	1	yes	characteristic
237	C₄²×D₇₃	C₂³	1	1	yes	characteristic
238	C₄²×D₇₃	C₂³	1	1	yes	characteristic
239	C₄²×D₇₃	C₂³	1	1	yes	characteristic
240	C₄²×D₇₃	C₂³	1	1	yes	characteristic
241	#14556525	C₂³	1	1	yes	characteristic
242	#14556525	C₂³	1	1	yes	characteristic
243	#14556524	C₂³	1	2	yes	—
244	#14556524	C₂³	1	2	yes	—
245	#14556523	C₂³	1	2	yes	—
246	#14556522	C₂³	1	2	yes	—
247	#14556522	C₂³	1	2	yes	—
248	#14556516	C₂³	1	2	yes	—
249	#14556516	C₂³	1	2	yes	—
250	#14556515	C₂³	1	2	yes	—
251	#14556515	C₂³	1	2	yes	—
252	#14556514	C₂³	1	2	yes	—
253	#14556514	C₂³	1	2	yes	—
254	#14556513	C₂³	1	2	yes	—
255	#14556513	C₂³	1	2	yes	—
256	#14556512	C₂³	1	2	yes	—
257	#14556512	C₂³	1	2	yes	—
258	#14556511	C₂³	1	2	yes	—
259	#14556511	C₂³	1	2	yes	—
260	C₄×#10596831	C₂³	1	1	yes	characteristic
261	C₄×#10596831	C₂³	1	1	yes	characteristic
262	C₄×#10596831	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	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
270	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
271	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
274	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
277	#126×C₇₃	—	2	2	no	—
278	#125×C₇₃	C₂³	1	2	yes	—
279	#124×C₇₃	C₂³	1	2	yes	—
280	#123×C₇₃	—	2	2	no	—
281	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
282	#121×C₇₃	C₂³	1	2	yes	—
283	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
284	C₄×D₄×C₇₃	—	2	2	no	—
285	C₄×D₄×C₇₃	C₂³	1	2	yes	—
286	#117×C₇₃	—	2	2	no	—
287	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
288	#107×C₇₃	C₂³	1	1	yes	characteristic
289	#107×C₇₃	C₂³	1	1	yes	characteristic
290	#106×C₇₃	C₂³	1	2	yes	—
291	#103×C₇₃	C₂³	1	2	yes	—
292	#103×C₇₃	C₂³	1	2	yes	—
293	#102×C₇₃	C₂³	1	2	yes	—
294	#102×C₇₃	C₂³	1	2	yes	—
295	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
299	C₂³×D₇₃	—	2	2	no	—
300	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
301	C₂×Dic₁₄₆	—	2	2	no	—
302	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
303	Q₈×D₇₃	—	2	4	no	—
304	Q₈×D₇₃	—	2	4	no	—
305	C₂×D₂₉₂	—	2	2	no	—
306	C₂×D₂₉₂	C₂⁴	1	2	yes	—
307	C₂×C₂²⋊D₇₃	—	2	2	no	—
308	C₂×C₂²⋊D₇₃	—	2	2	no	—
309	C₂×C₂²⋊D₇₃	—	2	2	no	—
310	D₄×D₇₃	—	2	4	no	—
311	D₄×D₇₃	—	2	4	no	—
312	D₄×D₇₃	—	4	8	no	—
313	C₂²×Dic₇₃	—	2	2	no	—
314	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
315	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
317	C₂×C₄×D₇₃	—	2	4	no	—
318	C₂×C₄×D₇₃	—	2	4	no	—
319	C₂×C₄×D₇₃	—	2	2	no	—
320	C₂×C₄×D₇₃	—	2	2	no	—
321	C₂×C₄×D₇₃	—	2	2	no	—
322	C₂×C₄×D₇₃	—	2	2	no	—
323	C₂×C₄×D₇₃	—	2	2	no	—
324	C₂×C₄×D₇₃	—	2	2	no	—
325	C₂×C₄×D₇₃	—	2	2	no	—
326	C₂×C₄×D₇₃	—	4	8	no	—
327	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
336	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
337	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
339	Dic₂₉₂	—	2	2	no	—
340	#11924018	—	2	4	no	—
341	#11924017	—	2	4	no	—
342	#11924016	—	2	4	no	—
343	#11924015	—	2	4	no	—
344	D₅₈₄	—	2	2	no	—
345	#11924013	—	2	4	no	—
346	C₂×#10596831	—	2	2	no	—
347	C₂×#10596831	—	2	2	no	—
348	C₂×#10596831	C₂⁴	1	1	yes	characteristic
349	C₂×#10596831	C₂⁴	1	1	yes	characteristic
350	C₂×#10596831	C₂⁴	1	1	yes	characteristic
351	C₂×#10596831	C₂⁴	1	1	yes	characteristic
352	C₈×D₇₃	—	2	2	no	—
353	C₈×D₇₃	—	2	2	no	—
354	C₈×D₇₃	—	2	2	no	—
355	C₈×D₇₃	—	2	2	no	—
356	C₈×D₇₃	—	2	2	no	—
357	C₈×D₇₃	—	2	2	no	—
358	C₈×D₇₃	#41	1	4	yes	—
359	C₈×D₇₃	#41	1	4	yes	—
360	C₄⋊Dic₇₃	—	2	2	no	—
361	C₄⋊Dic₇₃	—	2	2	no	—
362	C₄⋊Dic₇₃	—	2	2	no	—
363	C₄⋊Dic₇₃	—	2	2	no	—
364	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
365	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
374	#11924007	—	2	2	no	—
375	#11924007	—	2	2	no	—
376	C₂²⋊Dic₇₃	—	2	2	no	—
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	#11924005	—	2	2	no	—
382	#11924005	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
395	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
396	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
397	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
398	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
399	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
400	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
401	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
402	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
403	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
404	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
405	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
407	C₂×D₄×C₇₃	—	2	2	no	—
408	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₇₃	—	2	2	no	—
410	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
413	Q₁₆×C₇₃	—	2	2	no	—
414	SD₁₆×C₇₃	—	2	4	no	—
415	D₈×C₇₃	—	2	2	no	—
416	C₂×C₈×C₇₃	—	2	2	no	—
417	C₂×C₈×C₇₃	—	2	2	no	—
418	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
419	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₄⋊C₄×C₇₃	—	2	2	no	—
423	C₄⋊C₄×C₇₃	—	2	2	no	—
424	C₄⋊C₄×C₇₃	—	2	2	no	—
425	C₄⋊C₄×C₇₃	—	2	2	no	—
426	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
427	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
428	C₂²⋊C₄×C₇₃	—	2	2	no	—
429	C₂²⋊C₄×C₇₃	—	2	2	no	—
430	C₂²⋊C₄×C₇₃	—	2	2	no	—
431	C₂²⋊C₄×C₇₃	—	2	2	no	—
432	C₂²⋊C₄×C₇₃	—	2	2	no	—
433	C₄²×C₇₃	—	2	2	no	—
434	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
437	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
438	C₂³×C₇₃	—	2	2	no	—
439	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₇₃	—	2	2	no	—
441	C₂²×D₇₃	—	2	2	no	—
442	C₂²×D₇₃	—	2	2	no	—
443	C₂²×D₇₃	—	4	4	no	—
444	C₂²×D₇₃	—	4	4	no	—
445	C₂²×D₇₃	—	4	4	no	—
446	C₂²×D₇₃	#135	1	4	yes	—
447	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
448	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₇₃	—	2	2	no	—
450	Q₈×C₇₃	—	2	2	no	—
451	D₄×C₇₃	—	2	2	no	—
452	D₄×C₇₃	—	2	2	no	—
453	D₄×C₇₃	—	4	4	no	—
454	C₂×C₄×C₇₃	—	2	2	no	—
455	C₂×C₄×C₇₃	—	2	2	no	—
456	C₂×C₄×C₇₃	—	2	1	no	—
457	C₂×C₄×C₇₃	—	2	1	no	—
458	C₂×C₄×C₇₃	—	2	2	no	—
459	C₂×C₄×C₇₃	—	2	2	no	—
460	C₂×C₄×C₇₃	—	2	2	no	—
461	C₂×C₄×C₇₃	—	4	4	no	—
462	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
468	C₂²⋊D₇₃	—	4	4	no	—
469	C₂²⋊D₇₃	—	4	4	no	—
470	C₂²⋊D₇₃	—	4	4	no	—
471	C₂×Dic₇₃	—	2	2	no	—
472	C₂×Dic₇₃	—	2	2	no	—
473	C₂×Dic₇₃	—	2	2	no	—
474	C₂×Dic₇₃	—	2	2	no	—
475	C₂×Dic₇₃	—	2	2	no	—
476	C₂×Dic₇₃	—	2	2	no	—
477	C₂×Dic₇₃	—	4	4	no	—
478	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
484	D₂₉₂	—	2	2	no	—
485	D₂₉₂	—	2	2	no	—
486	D₂₉₂	—	4	4	no	—
487	C₄×D₇₃	—	2	2	no	—
488	C₄×D₇₃	—	2	2	no	—
489	C₄×D₇₃	—	2	2	no	—
490	C₄×D₇₃	—	2	2	no	—
491	C₄×D₇₃	—	2	2	no	—
492	C₄×D₇₃	—	2	2	no	—
493	C₄×D₇₃	—	2	2	no	—
494	C₄×D₇₃	—	2	1	no	—
495	C₄×D₇₃	—	2	1	no	—
496	C₄×D₇₃	—	2	2	no	—
497	C₄×D₇₃	—	2	2	no	—
498	C₄×D₇₃	—	4	4	no	—
499	C₄×D₇₃	—	4	4	no	—
500	C₄×D₇₃	—	4	4	no	—
501	C₄×D₇₃	—	4	4	no	—
502	C₄×D₇₃	—	4	4	no	—
503	C₄×D₇₃	#135	1	4	yes	—
504	C₄×D₇₃	C₂×#41	1	2	yes	—
505	C₄×D₇₃	C₂×#41	1	2	yes	—
506	Dic₁₄₆	—	2	2	no	—
507	Dic₁₄₆	—	2	2	no	—
508	Dic₁₄₆	—	4	4	no	—
509	C₈×C₇₃	—	2	1	no	—
510	C₈×C₇₃	—	2	1	no	—
511	C₈×C₇₃	C₂×#41	1	2	yes	—
512	C₈×C₇₃	C₂×#41	1	2	yes	—
513	#10596831	—	2	1	no	—
514	#10596831	—	2	1	no	—
515	#10596831	C₂×#41	1	2	yes	—
516	#10596831	C₂×#41	1	2	yes	—
517	C₂²×C₇₃	—	2	1	no	—
518	C₂²×C₇₃	—	2	1	no	—
519	C₂²×C₇₃	—	4	2	no	—
520	C₂²×C₇₃	—	4	2	no	—
521	C₂²×C₇₃	—	4	2	no	—
522	C₂²×C₇₃	C₂×#135	1	2	yes	—
523	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
524	C₂×D₇₃	—	2	1	no	—
525	C₂×D₇₃	—	2	1	no	—
526	C₂×D₇₃	—	2	8	no	—
527	C₂×D₇₃	—	4	2	no	—
528	C₂×D₇₃	—	4	2	no	—
529	C₂×D₇₃	—	4	2	no	—
530	C₂×D₇₃	—	8	8	no	—
531	C₂×D₇₃	#532	1	2	yes	—
532	C₂×D₇₃	C₂×#135	1	2	yes	—
533	C₂×D₇₃	C₂×#135	1	2	yes	—
534	C₂×D₇₃	C₂×#135	1	2	yes	—
535	C₄×C₇₃	—	2	1	no	—
536	C₄×C₇₃	—	2	1	no	—
537	C₄×C₇₃	—	2	1	no	—
538	C₄×C₇₃	—	2	1	no	—
539	C₄×C₇₃	—	4	2	no	—
540	C₄×C₇₃	—	4	2	no	—
541	C₄×C₇₃	—	4	2	no	—
542	C₄×C₇₃	C₂×#135	1	2	yes	—
543	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
544	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
545	Dic₇₃	—	2	1	no	—
546	Dic₇₃	—	2	1	no	—
547	Dic₇₃	—	2	1	no	—
548	Dic₇₃	—	2	1	no	—
549	Dic₇₃	—	4	2	no	—
550	Dic₇₃	—	4	2	no	—
551	Dic₇₃	—	4	2	no	—
552	Dic₇₃	#532	1	2	yes	—
553	Dic₇₃	C₂×#135	1	2	yes	—
554	C₂×#3168	—	73	1	no	maximal, Sylow
555	C₂×C₇₃	—	2	2	no	—
556	C₂×C₇₃	—	8	2	no	—
557	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
558	C₂×C₇₃	C₂²×#135	1	1	yes	characteristic
559	C₂×C₇₃	C₂²×#135	1	1	yes	characteristic
560	D₇₃	—	2	2	no	—
561	D₇₃	—	8	2	no	—
562	D₇₃	#3168	1	4	yes	direct product factor
563	C₂×#529	—	73	2	no	—
564	#3168	—	73	1	no	—
565	#3168	—	73	1	no	—
566	#3168	—	73	2	no	—
567	#3168	—	73	1	no	—
568	#3168	—	73	1	no	—
569	#3168	—	73	2	no	—
570	#3168	—	73	1	no	—
571	#3168	—	73	2	no	—
572	#3168	—	73	1	no	—
573	#3168	—	73	1	no	—
574	#3168	—	73	2	no	—
575	#3168	D₇₃	1	1	yes	characteristic, direct product factor
576	C₂×#499	—	73	1	no	—
577	C₂×#495	—	73	1	no	—
578	C₂×#488	—	73	2	no	—
579	C₂×#467	—	73	1	no	—
580	C₂×#466	—	73	1	no	—
581	C₂×#465	—	73	2	no	—
582	C₂×C₄×Q₁₆	—	73	1	no	—
583	C₂×C₄×SD₁₆	—	73	2	no	—
584	C₂×C₄×D₈	—	73	1	no	—
585	C₂²×C₄×C₈	—	73	1	no	—
586	C₇₃	C₂×#3168	1	1	yes	characteristic, complemented, Sylow
587	C₂²×Q₁₆	—	73	1	no	—
588	C₂²×SD₁₆	—	73	2	no	—
589	C₂²×D₈	—	73	1	no	—
590	C₂³×C₈	—	73	1	no	—
591	C₂³×C₈	—	73	1	no	—
592	#529	—	73	2	no	—
593	#529	—	73	2	no	—
594	#529	—	73	2	no	—
595	#529	—	73	2	no	—
596	#529	—	73	2	no	—
597	#529	—	73	2	no	—
598	#529	—	73	2	no	—
599	#529	—	146	2	no	—
600	#529	—	146	2	no	—
601	#529	—	146	2	no	—
602	#529	—	146	2	no	—
603	#529	C₂×D₇₃	1	2	yes	complemented
604	C₂×#126	—	146	2	no	—
605	C₂×#125	—	73	2	no	—
606	C₂×#124	—	73	2	no	—
607	C₂×#123	—	146	2	no	—
608	C₂×C₂²⋊Q₈	—	73	2	no	—
609	C₂×#121	—	73	2	no	—
610	C₂×C₄×Q₈	—	73	2	no	—
611	C₂×C₄×D₄	—	73	2	no	—
612	C₂×C₄×D₄	—	146	2	no	—
613	C₂×#117	—	146	2	no	—
614	C₂²×C₄²	—	73	1	no	—
615	#499	—	73	2	no	—
616	#499	—	73	1	no	—
617	#499	—	73	1	no	—
618	#499	—	73	2	no	—
619	#499	—	73	1	no	—
620	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
621	#495	—	73	1	no	—
622	#495	—	73	2	no	—
623	#495	—	73	1	no	—
624	#495	—	73	2	no	—
625	#495	—	73	1	no	—
626	#495	C₂×D₇₃	1	1	yes	characteristic, complemented
627	#488	—	73	2	no	—
628	#488	—	73	2	no	—
629	#488	—	73	2	no	—
630	#488	—	73	2	no	—
631	#488	—	73	2	no	—
632	#488	—	73	2	no	—
633	#488	—	73	2	no	—
634	#488	C₂×D₇₃	1	2	yes	complemented
635	#467	—	73	1	no	—
636	#467	—	73	1	no	—
637	#467	—	73	2	no	—
638	#467	—	73	1	no	—
639	#467	—	73	2	no	—
640	#467	C₂×D₇₃	1	1	yes	characteristic, complemented
641	#466	—	73	1	no	—
642	#466	—	73	1	no	—
643	#466	—	73	2	no	—
644	#466	—	73	1	no	—
645	#466	—	73	2	no	—
646	#466	C₂×D₇₃	1	1	yes	characteristic
647	#465	—	73	2	no	—
648	#465	—	73	2	no	—
649	#465	—	73	2	no	—
650	#465	—	73	2	no	—
651	#465	—	73	2	no	—
652	#465	—	73	2	no	—
653	#465	—	73	2	no	—
654	#465	C₂×D₇₃	1	2	yes	complemented
655	C₄×Q₁₆	—	73	1	no	—
656	C₄×Q₁₆	—	73	2	no	—
657	C₄×Q₁₆	—	73	1	no	—
658	C₄×Q₁₆	—	73	2	no	—
659	C₄×Q₁₆	—	73	1	no	—
660	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
661	C₄×SD₁₆	—	73	2	no	—
662	C₄×SD₁₆	—	73	2	no	—
663	C₄×SD₁₆	—	73	2	no	—
664	C₄×SD₁₆	—	73	2	no	—
665	C₄×SD₁₆	—	73	2	no	—
666	C₄×SD₁₆	—	73	2	no	—
667	C₄×SD₁₆	—	73	2	no	—
668	C₄×SD₁₆	C₂×D₇₃	1	2	yes	complemented
669	C₄×D₈	—	73	1	no	—
670	C₄×D₈	—	73	2	no	—
671	C₄×D₈	—	73	1	no	—
672	C₄×D₈	—	73	2	no	—
673	C₄×D₈	—	73	1	no	—
674	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
675	C₂×#107	—	73	1	no	—
676	C₂×#107	—	73	1	no	—
677	C₂×#106	—	73	2	no	—
678	C₂×#103	—	73	2	no	—
679	C₂×#103	—	73	2	no	—
680	C₂×#102	—	73	2	no	—
681	C₂×#102	—	73	2	no	—
682	C₂×C₄×C₈	—	73	1	no	—
683	C₂×C₄×C₈	—	73	1	no	—
684	C₂×C₄×C₈	—	73	1	no	—
685	C₂×C₄×C₈	—	73	1	no	—
686	C₂×C₄×C₈	—	73	1	no	—
687	C₂×C₄×C₈	—	73	1	no	—
688	C₂×C₄×C₈	—	73	1	no	—
689	C₂×C₄×C₈	—	73	1	no	—
690	C₂×C₄×C₈	—	73	1	no	—
691	C₂×C₄×C₈	—	73	1	no	—
692	C₂×C₄×C₈	—	73	1	no	—
693	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
694	C₂²×Q₈	—	73	2	no	—
695	C₂²×D₄	—	73	2	no	—
696	C₂²×D₄	—	146	2	no	—
697	C₂³×C₄	—	73	1	no	—
698	C₂³×C₄	—	73	1	no	—
699	C₂³×C₄	—	73	1	no	—
700	C₂³×C₄	—	146	2	no	—
701	C₂×Q₁₆	—	73	2	no	—
702	C₂×Q₁₆	—	73	1	no	—
703	C₂×Q₁₆	—	146	4	no	—
704	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
705	C₂×SD₁₆	—	73	2	no	—
706	C₂×SD₁₆	—	73	2	no	—
707	C₂×SD₁₆	—	73	2	no	—
708	C₂×SD₁₆	—	146	8	no	—
709	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
710	C₂×D₈	—	73	2	no	—
711	C₂×D₈	—	73	1	no	—
712	C₂×D₈	—	146	4	no	—
713	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
714	C₂²×C₈	—	73	1	no	—
715	C₂²×C₈	—	73	1	no	—
716	C₂²×C₈	—	73	1	no	—
717	C₂²×C₈	—	73	1	no	—
718	C₂²×C₈	—	73	1	no	—
719	C₂²×C₈	—	73	1	no	—
720	C₂²×C₈	—	73	1	no	—
721	C₂²×C₈	—	73	1	no	—
722	C₂²×C₈	—	73	1	no	—
723	C₂²×C₈	—	73	1	no	—
724	C₂²×C₈	—	146	4	no	—
725	C₂²×C₈	—	146	4	no	—
726	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
727	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
728	#126	—	2	2	no	—
729	#126	—	146	2	no	—
730	#126	—	146	2	no	—
731	#126	—	146	2	no	—
732	#126	—	146	2	no	—
733	#126	—	146	2	no	—
734	#126	—	146	2	no	—
735	#126	—	146	2	no	—
736	#125	—	73	2	no	—
737	#125	—	73	2	no	—
738	#125	—	73	2	no	—
739	#125	—	146	2	no	—
740	#125	—	146	2	no	—
741	#125	C₂²×D₇₃	1	2	yes	—
742	#124	—	73	2	no	—
743	#124	—	73	2	no	—
744	#124	—	73	2	no	—
745	#124	—	146	2	no	—
746	#124	—	146	2	no	—
747	#124	C₂²×D₇₃	1	2	yes	—
748	#123	—	2	2	no	—
749	#123	—	146	2	no	—
750	#123	—	146	2	no	—
751	#123	—	146	2	no	—
752	#123	—	146	2	no	—
753	#123	—	146	2	no	—
754	#123	—	146	2	no	—
755	#123	—	146	2	no	—
756	C₂²⋊Q₈	—	73	2	no	—
757	C₂²⋊Q₈	—	73	2	no	—
758	C₂²⋊Q₈	—	73	2	no	—
759	C₂²⋊Q₈	—	146	2	no	—
760	C₂²⋊Q₈	—	146	2	no	—
761	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
762	#121	—	73	2	no	—
763	#121	—	73	2	no	—
764	#121	—	73	2	no	—
765	#121	—	146	2	no	—
766	#121	—	146	2	no	—
767	#121	C₂²×D₇₃	1	2	yes	—
768	C₄×Q₈	—	73	2	no	—
769	C₄×Q₈	—	73	2	no	—
770	C₄×Q₈	—	73	2	no	—
771	C₄×Q₈	—	146	2	no	—
772	C₄×Q₈	—	146	2	no	—
773	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	73	2	no	—
776	C₄×D₄	—	73	2	no	—
777	C₄×D₄	—	73	2	no	—
778	C₄×D₄	—	146	2	no	—
779	C₄×D₄	—	146	2	no	—
780	C₄×D₄	—	146	2	no	—
781	C₄×D₄	—	146	2	no	—
782	C₄×D₄	—	146	2	no	—
783	C₄×D₄	—	146	2	no	—
784	C₄×D₄	—	146	2	no	—
785	C₄×D₄	—	146	2	no	—
786	C₄×D₄	—	146	2	no	—
787	C₄×D₄	C₂²×D₇₃	1	2	yes	—
788	#117	—	2	2	no	—
789	#117	—	146	2	no	—
790	#117	—	146	2	no	—
791	#117	—	146	2	no	—
792	#117	—	146	2	no	—
793	#117	—	146	2	no	—
794	#117	—	146	2	no	—
795	#117	—	146	2	no	—
796	C₂×C₄⋊C₄	—	73	2	no	—
797	C₂×C₄⋊C₄	—	73	2	no	—
798	C₂×C₄⋊C₄	—	146	2	no	—
799	C₂×C₄⋊C₄	—	146	2	no	—
800	C₂×C₄⋊C₄	—	146	2	no	—
801	C₂×C₄⋊C₄	—	146	2	no	—
802	C₂×C₂²⋊C₄	—	146	2	no	—
803	C₂×C₂²⋊C₄	—	146	2	no	—
804	C₂×C₂²⋊C₄	—	146	2	no	—
805	C₂×C₂²⋊C₄	—	146	2	no	—
806	C₂×C₂²⋊C₄	—	146	2	no	—
807	C₂×C₄²	—	73	1	no	—
808	C₂×C₄²	—	73	1	no	—
809	C₂×C₄²	—	73	1	no	—
810	C₂×C₄²	—	73	1	no	—
811	C₂×C₄²	—	73	1	no	—
812	C₂×C₄²	—	73	1	no	—
813	C₂×C₄²	—	73	1	no	—
814	C₂×C₄²	—	73	1	no	—
815	C₂×C₄²	—	73	1	no	—
816	C₂×C₄²	—	73	1	no	—
817	C₂×C₄²	—	73	1	no	—
818	C₂×C₄²	—	146	2	no	—
819	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
820	#107	—	73	1	no	—
821	#107	—	73	1	no	—
822	#107	—	73	2	no	—
823	#107	—	73	2	no	—
824	#107	C₂²×D₇₃	1	1	yes	characteristic
825	#107	C₂²×D₇₃	1	1	yes	characteristic
826	#106	—	73	2	no	—
827	#106	—	73	2	no	—
828	#106	—	73	2	no	—
829	#106	C₂²×D₇₃	1	2	yes	—
830	#103	—	73	2	no	—
831	#103	—	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	2	yes	—
837	#103	C₂²×D₇₃	1	2	yes	—
838	#102	—	73	2	no	—
839	#102	—	73	2	no	—
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	2	yes	—
845	#102	C₂²×D₇₃	1	2	yes	—
846	C₄×C₈	—	73	1	no	—
847	C₄×C₈	—	73	1	no	—
848	C₄×C₈	—	73	1	no	—
849	C₄×C₈	—	73	1	no	—
850	C₄×C₈	—	73	1	no	—
851	C₄×C₈	—	73	1	no	—
852	C₄×C₈	—	73	1	no	—
853	C₄×C₈	—	73	1	no	—
854	C₄×C₈	—	73	1	no	—
855	C₄×C₈	—	73	1	no	—
856	C₄×C₈	—	73	1	no	—
857	C₄×C₈	—	73	1	no	—
858	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
859	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
860	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
861	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
862	C₂⁴	—	73	1	no	—
863	C₂⁴	—	146	2	no	—
864	C₂×Q₈	—	73	2	no	—
865	C₂×Q₈	—	146	2	no	—
866	C₂×Q₈	—	146	4	no	—
867	C₂×Q₈	—	146	4	no	—
868	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	292	8	no	—
871	C₂×D₄	—	73	2	no	—
872	C₂×D₄	—	146	2	no	—
873	C₂×D₄	—	146	4	no	—
874	C₂×D₄	—	146	4	no	—
875	C₂×D₄	—	146	2	no	—
876	C₂×D₄	—	146	2	no	—
877	C₂×D₄	—	146	2	no	—
878	C₂×D₄	C₂³×D₇₃	1	2	yes	—
879	C₂²×C₄	—	2	2	no	—
880	C₂²×C₄	—	292	8	no	—
881	C₂²×C₄	—	73	1	no	—
882	C₂²×C₄	—	73	1	no	—
883	C₂²×C₄	—	73	1	no	—
884	C₂²×C₄	—	73	1	no	—
885	C₂²×C₄	—	73	1	no	—
886	C₂²×C₄	—	73	1	no	—
887	C₂²×C₄	—	73	1	no	—
888	C₂²×C₄	—	73	1	no	—
889	C₂²×C₄	—	73	1	no	—
890	C₂²×C₄	—	73	1	no	—
891	C₂²×C₄	—	73	1	no	—
892	C₂²×C₄	—	73	1	no	—
893	C₂²×C₄	—	73	1	no	—
894	C₂²×C₄	—	73	1	no	—
895	C₂²×C₄	—	73	1	no	—
896	C₂²×C₄	—	146	2	no	—
897	C₂²×C₄	—	146	2	no	—
898	C₂²×C₄	—	146	2	no	—
899	C₂²×C₄	—	146	2	no	—
900	C₂²×C₄	—	146	2	no	—
901	C₂²×C₄	—	146	2	no	—
902	C₂²×C₄	—	146	4	no	—
903	C₂²×C₄	—	146	4	no	—
904	C₂²×C₄	—	146	2	no	—
905	C₂²×C₄	—	146	2	no	—
906	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
907	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
908	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
909	Q₁₆	—	2	2	no	—
910	Q₁₆	—	146	4	no	—
911	Q₁₆	—	146	2	no	—
912	SD₁₆	—	2	4	no	—
913	SD₁₆	—	146	4	no	—
914	SD₁₆	—	146	4	no	—
915	SD₁₆	—	146	4	no	—
916	D₈	—	2	2	no	—
917	D₈	—	146	4	no	—
918	D₈	—	146	2	no	—
919	C₂×C₈	—	2	2	no	—
920	C₂×C₈	—	2	2	no	—
921	C₂×C₈	—	73	1	no	—
922	C₂×C₈	—	73	1	no	—
923	C₂×C₈	—	73	4	no	—
924	C₂×C₈	—	73	4	no	—
925	C₂×C₈	—	73	1	no	—
926	C₂×C₈	—	73	1	no	—
927	C₂×C₈	—	146	2	no	—
928	C₂×C₈	—	146	2	no	—
929	C₂×C₈	—	146	2	no	—
930	C₂×C₈	—	146	2	no	—
931	C₂×C₈	—	146	2	no	—
932	C₂×C₈	—	146	2	no	—
933	C₂×C₈	—	146	2	no	—
934	C₂×C₈	—	146	2	no	—
935	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
936	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
937	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
938	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	73	2	no	—
944	C₄⋊C₄	—	73	2	no	—
945	C₄⋊C₄	—	146	2	no	—
946	C₄⋊C₄	—	146	2	no	—
947	C₄⋊C₄	—	146	2	no	—
948	C₄⋊C₄	—	146	2	no	—
949	C₄⋊C₄	—	146	2	no	—
950	C₄⋊C₄	—	146	2	no	—
951	C₄⋊C₄	—	146	2	no	—
952	C₄⋊C₄	—	146	2	no	—
953	C₄⋊C₄	—	146	2	no	—
954	C₄⋊C₄	—	146	2	no	—
955	C₄⋊C₄	—	146	2	no	—
956	C₄⋊C₄	—	146	2	no	—
957	C₄⋊C₄	—	146	2	no	—
958	C₄⋊C₄	—	146	2	no	—
959	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
960	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	146	2	no	—
967	C₂²⋊C₄	—	146	2	no	—
968	C₂²⋊C₄	—	146	2	no	—
969	C₂²⋊C₄	—	146	2	no	—
970	C₂²⋊C₄	—	146	2	no	—
971	C₂²⋊C₄	—	146	2	no	—
972	C₂²⋊C₄	—	146	2	no	—
973	C₂²⋊C₄	—	146	2	no	—
974	C₂²⋊C₄	—	146	2	no	—
975	C₂²⋊C₄	—	146	2	no	—
976	C₂²⋊C₄	—	146	2	no	—
977	C₂²⋊C₄	—	146	2	no	—
978	C₂²⋊C₄	—	146	2	no	—
979	C₂²⋊C₄	—	146	2	no	—
980	C₂²⋊C₄	—	146	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	—	73	1	no	—
983	C₄²	—	73	1	no	—
984	C₄²	—	73	1	no	—
985	C₄²	—	73	1	no	—
986	C₄²	—	73	1	no	—
987	C₄²	—	73	1	no	—
988	C₄²	—	73	1	no	—
989	C₄²	—	73	1	no	—
990	C₄²	—	73	1	no	—
991	C₄²	—	73	1	no	—
992	C₄²	—	73	1	no	—
993	C₄²	—	73	1	no	—
994	C₄²	—	146	2	no	—
995	C₄²	—	146	2	no	—
996	C₄²	—	146	2	no	—
997	C₄²	D₄×D₇₃	1	1	yes	characteristic
998	C₄²	D₄×D₇₃	1	1	yes	characteristic
999	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1000	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1001	C₂³	—	2	2	no	—
1002	C₂³	—	292	4	no	—
1003	C₂³	—	292	4	no	—
1004	C₂³	—	292	4	no	—
1005	C₂³	—	73	1	no	—
1006	C₂³	—	73	1	no	—
1007	C₂³	—	73	4	no	—
1008	C₂³	—	146	2	no	—
1009	C₂³	—	146	2	no	—
1010	C₂³	—	146	2	no	—
1011	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1012	Q₈	—	2	2	no	—
1013	Q₈	—	2	2	no	—
1014	Q₈	—	292	4	no	—
1015	Q₈	—	146	2	no	—
1016	Q₈	—	146	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	292	4	no	—
1021	D₄	—	292	4	no	—
1022	D₄	—	292	4	no	—
1023	D₄	—	292	4	no	—
1024	D₄	—	146	2	no	—
1025	D₄	—	146	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	4	no	—
1034	C₂×C₄	—	292	4	no	—
1035	C₂×C₄	—	292	4	no	—
1036	C₂×C₄	—	292	4	no	—
1037	C₂×C₄	—	292	4	no	—
1038	C₂×C₄	—	292	4	no	—
1039	C₂×C₄	—	292	4	no	—
1040	C₂×C₄	—	73	1	no	—
1041	C₂×C₄	—	73	1	no	—
1042	C₂×C₄	—	73	2	no	—
1043	C₂×C₄	—	73	2	no	—
1044	C₂×C₄	—	73	4	no	—
1045	C₂×C₄	—	73	1	no	—
1046	C₂×C₄	—	73	1	no	—
1047	C₂×C₄	—	73	1	no	—
1048	C₂×C₄	—	73	1	no	—
1049	C₂×C₄	—	146	2	no	—
1050	C₂×C₄	—	146	2	no	—
1051	C₂×C₄	—	146	2	no	—
1052	C₂×C₄	—	146	2	no	—
1053	C₂×C₄	—	146	2	no	—
1054	C₂×C₄	—	146	2	no	—
1055	C₂×C₄	—	146	2	no	—
1056	C₂×C₄	—	146	2	no	—
1057	C₂×C₄	—	146	2	no	—
1058	C₂×C₄	—	146	2	no	—
1059	C₂×C₄	—	146	2	no	—
1060	C₂×C₄	—	146	2	no	—
1061	C₂×C₄	—	146	2	no	—
1062	C₂×C₄	—	146	2	no	—
1063	C₂×C₄	—	146	1	no	—
1064	C₂×C₄	—	146	1	no	—
1065	C₂×C₄	—	146	2	no	—
1066	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1067	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1068	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1069	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1071	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	73	2	no	—
1075	C₈	—	73	2	no	—
1076	C₈	—	146	1	no	—
1077	C₈	—	146	1	no	—
1078	C₈	#41×D₇₃	1	2	yes	—
1079	C₈	#41×D₇₃	1	2	yes	—
1080	C₂²	—	2	1	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	292	2	no	—
1086	C₂²	—	292	2	no	—
1087	C₂²	—	292	2	no	—
1088	C₂²	—	584	8	no	—
1089	C₂²	—	73	2	no	—
1090	C₂²	—	73	2	no	—
1091	C₂²	—	73	2	no	—
1092	C₂²	—	73	2	no	—
1093	C₂²	—	146	8	no	—
1094	C₂²	—	146	1	no	—
1095	C₂²	—	146	1	no	—
1096	C₂²	#135×D₇₃	1	2	yes	—
1097	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	4	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	292	2	no	—
1106	C₄	—	292	2	no	—
1107	C₄	—	292	2	no	—
1108	C₄	—	73	2	no	—
1109	C₄	—	73	2	no	—
1110	C₄	—	146	1	no	—
1111	C₄	—	146	1	no	—
1112	C₄	—	146	1	no	—
1113	C₄	—	146	1	no	—
1114	C₄	#135×D₇₃	1	2	yes	—
1115	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1116	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1117	C₂	—	2	2	no	—
1118	C₂	—	8	2	no	—
1119	C₂	—	584	2	no	—
1120	C₂	—	73	4	no	—
1121	C₂	—	146	2	no	—
1122	C₂	#532×D₇₃	1	1	yes	characteristic
1123	C₂	C₂×#135×D₇₃	1	1	yes	characteristic
1124	C₂	C₂×#135×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3168	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#466×D₇₃	C₂
hypercenter	#3168	D₇₃
hypocenter	C₇₃	C₂×#3168
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #529×D₇₃	C₂	semidirect
2. #22620504	C₂	semidirect
3. #22620503	C₂	semidirect
4. #22620502	C₂	semidirect
5. #22620501	C₂	semidirect
6. #22620500	C₂	semidirect
7. #22620499	C₂	semidirect
8. #22620498	C₂	semidirect
9. #22620497	C₂	semidirect
10. #22620496	C₂	semidirect
11. #22620495	C₂	semidirect
12. #22620494	C₂	semidirect
13. #499×D₇₃	C₂	semidirect
14. #495×D₇₃	C₂	semidirect
15. #488×D₇₃	C₂	semidirect
16. #467×D₇₃	C₂	semidirect
18. #465×D₇₃	C₂	semidirect
19. C₄×Q₁₆×D₇₃	C₂	semidirect
20. C₄×SD₁₆×D₇₃	C₂	semidirect
21. C₄×D₈×D₇₃	C₂	semidirect
22. C₂×C₄×C₈×D₇₃	C₂	semidirect
23. C₇₃×#3168	C₂	semidirect
29. #17989124	C₂²	semidirect
30. #17989123	C₂²	semidirect
31. #17989122	C₂²	semidirect
32. #17989121	C₂²	semidirect
34. #17989119	C₂²	semidirect
35. #17989118	C₂²	semidirect
37. #17989116	C₂²	semidirect
51. #17988989	C₂²	semidirect
52. #17988988	C₂²	semidirect
53. #17988988	C₂²	semidirect
54. #17988987	C₂²	semidirect
55. #17988986	C₂²	semidirect
56. #17988972	C₂²	semidirect
57. #17988971	C₂²	semidirect
58. #17988970	C₂²	semidirect
59. #17988969	C₂²	semidirect
60. #17988968	C₂²	semidirect
61. #17988944	C₂²	semidirect
62. #17988943	C₂²	semidirect
63. #17988943	C₂²	semidirect
64. #17988942	C₂²	semidirect
65. #17988941	C₂²	semidirect
66. #17988940	C₂²	semidirect
67. #17988940	C₂²	semidirect
68. #17988829	C₂²	semidirect
69. #17988828	C₂²	semidirect
70. #17988827	C₂²	semidirect
71. #17988826	C₂²	semidirect
72. #17988825	C₂²	semidirect
78. #17988819	C₂²	semidirect
79. #17988818	C₂²	semidirect
80. #17988817	C₂²	semidirect
81. #17988816	C₂²	semidirect
82. #17988815	C₂²	semidirect
83. #17988814	C₂²	semidirect
84. #17988813	C₂²	semidirect
85. C₄×Dic₂₉₂	C₂²	semidirect
86. Q₁₆×Dic₇₃	C₂²	semidirect
87. #17988681	C₂²	semidirect
88. C₄×#11924018	C₂²	semidirect
89. #17988679	C₂²	semidirect
90. #17988678	C₂²	semidirect
91. C₄×#11924017	C₂²	semidirect
92. SD₁₆×Dic₇₃	C₂²	semidirect
93. C₄×#11924015	C₂²	semidirect
94. #17988674	C₂²	semidirect
95. C₄×#11924016	C₂²	semidirect
96. #17988672	C₂²	semidirect
97. C₄×D₅₈₄	C₂²	semidirect
98. D₈×Dic₇₃	C₂²	semidirect
99. #17988669	C₂²	semidirect
100. C₄×#11924013	C₂²	semidirect
101. #17988667	C₂²	semidirect
109. C₂×C₄×#10596831	C₂²	semidirect
110. C₂×C₈×Dic₇₃	C₂²	semidirect
111. C₂×C₈×Dic₇₃	C₂²	semidirect
116. C₄×C₈×D₇₃	C₂²	semidirect
117. C₄×C₈×D₇₃	C₂²	semidirect
118. C₄×C₈×D₇₃	C₂²	semidirect
119. C₄×C₈×D₇₃	C₂²	semidirect
120. #529×C₇₃	C₂²	semidirect
121. #499×C₇₃	C₂²	semidirect
122. #495×C₇₃	C₂²	semidirect
123. #488×C₇₃	C₂²	semidirect
124. #467×C₇₃	C₂²	semidirect
126. #465×C₇₃	C₂²	semidirect
127. C₄×Q₁₆×C₇₃	C₂²	semidirect
128. C₄×SD₁₆×C₇₃	C₂²	semidirect
129. C₄×D₈×C₇₃	C₂²	semidirect
130. C₂×C₄×C₈×C₇₃	C₂²	semidirect
562. D₇₃	#3168	direct (N × H)
575. #3168	D₇₃	direct (N × H)
586. C₇₃	C₂×#3168	semidirect
603. #529	C₂×D₇₃	semidirect
620. #499	C₂×D₇₃	semidirect
626. #495	C₂×D₇₃	semidirect
634. #488	C₂×D₇₃	semidirect
640. #467	C₂×D₇₃	semidirect
654. #465	C₂×D₇₃	semidirect
660. C₄×Q₁₆	C₂×D₇₃	semidirect
668. C₄×SD₁₆	C₂×D₇₃	semidirect
674. C₄×D₈	C₂×D₇₃	semidirect
693. C₂×C₄×C₈	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#529×D₇₃	2
#22620504	2
#22620503	2
#22620502	2
#22620501	2
#22620500	2
#22620499	2
#22620498	2
#22620497	2
#22620496	2
#22620495	2
#22620494	2
#499×D₇₃	2
#495×D₇₃	2
#488×D₇₃	2
#467×D₇₃	2
#466×D₇₃	2
#465×D₇₃	2
C₄×Q₁₆×D₇₃	2
C₄×SD₁₆×D₇₃	2
C₄×D₈×D₇₃	2
C₂×C₄×C₈×D₇₃	2
C₇₃×#3168	2
C₂×#3168	73

Subgroups — #3168×D73 #33955702

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3168×D₇₃ #33955702