Subgroups — #33968567

Order 18688.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624027	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623963	C₂	1	1	yes	maximal, characteristic
3	#22622910	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622804	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622710	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622658	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622346	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622306	C₂	1	2	yes	maximal, complemented
9	#22622227	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622164	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622098	C₂	1	2	yes	maximal, complemented
12	#22621948	C₂	1	2	yes	maximal, complemented
13	SD₁₆×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
14	SD₁₆×C₂²⋊D₇₃	C₂	1	2	yes	maximal, complemented
15	#22620555	C₂	1	2	yes	maximal, complemented
16	#22620490	C₂	1	1	yes	maximal, characteristic, complemented
17	#22620219	C₂	1	2	yes	maximal, complemented
18	#22620180	C₂	1	2	yes	maximal, complemented
19	#22620053	C₂	1	1	yes	maximal, characteristic, complemented
20	#22620030	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618906	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618785	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₇₃	C₂²	1	2	yes	—
25	#17989316	C₂²	1	1	yes	characteristic, complemented
26	#17989315	—	2	1	no	—
27	#17989315	C₂²	1	1	yes	characteristic, complemented
28	#17989310	—	2	1	no	—
29	#17989310	C₂²	1	1	yes	characteristic, complemented
30	#17989302	C₂²	1	1	yes	characteristic
31	#17989294	C₂²	1	1	yes	characteristic
32	#17989285	C₂²	1	2	yes	—
33	#17989283	—	2	1	no	—
34	#17989272	—	2	2	no	—
35	#17989272	C₂²	1	2	yes	complemented
36	#17989258	C₂²	1	1	yes	characteristic
37	Q₈×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
38	Q₈×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
39	#17989233	—	2	1	no	—
40	#17989227	—	2	2	no	—
41	D₄×D₂₉₂	C₂²	1	1	yes	characteristic
42	D₄×C₂²⋊D₇₃	C₂²	1	2	yes	—
43	#17989195	—	2	2	no	—
44	#17989195	C₂²	1	2	yes	complemented
45	#17989188	C₂²	1	2	yes	—
46	#17989170	—	2	2	no	—
47	#17989144	—	2	1	no	—
48	#17989144	C₂²	1	1	yes	characteristic, complemented
49	#17989137	C₂²	1	1	yes	characteristic
50	#17989121	—	2	1	no	—
51	#17989121	C₂²	1	1	yes	characteristic
52	#17989098	—	2	1	no	—
53	C₂×#14556565	—	2	1	no	—
54	#17989063	C₂²	1	2	yes	complemented
55	#17989059	C₂²	1	2	yes	—
56	#17988987	C₂²	1	2	yes	complemented
57	#17988985	C₂²	1	1	yes	characteristic, complemented
58	#17988960	C₂²	1	1	yes	characteristic, complemented
59	#17988958	C₂²	1	2	yes	complemented
60	#17988954	C₂²	1	2	yes	complemented
61	#17988950	C₂²	1	2	yes	complemented
62	#17988938	C₂²	1	1	yes	characteristic, complemented
63	#17988934	C₂²	1	1	yes	characteristic, complemented
64	#17988931	C₂²	1	2	yes	complemented
65	#17988926	C₂²	1	2	yes	complemented
66	#17988922	C₂²	1	2	yes	complemented
67	#17988913	C₂²	1	2	yes	complemented
68	#17988910	C₂²	1	2	yes	complemented
69	#17988900	C₂²	1	2	yes	complemented
70	#17988897	C₂²	1	2	yes	complemented
71	#17988892	C₂²	1	2	yes	complemented
72	#17988889	C₂²	1	2	yes	—
73	#17988886	C₂²	1	2	yes	complemented
74	#17988882	C₂²	1	1	yes	characteristic, complemented
75	#17988882	C₂²	1	1	yes	characteristic, complemented
76	#17988867	C₂²	1	1	yes	characteristic
77	#17988867	C₂²	1	1	yes	characteristic, complemented
78	#17988836	C₂²	1	2	yes	complemented
79	#17988832	C₂²	1	2	yes	complemented
80	#17988817	C₂²	1	2	yes	complemented
81	#17988816	C₂²	1	2	yes	complemented
82	#17988816	C₂²	1	2	yes	complemented
83	#17988813	C₂²	1	2	yes	complemented
84	#17988792	C₂²	1	1	yes	characteristic
85	#17988792	C₂²	1	1	yes	characteristic, complemented
86	#17988791	C₂²	1	2	yes	complemented
87	#17988790	C₂²	1	2	yes	—
88	#17988787	C₂²	1	1	yes	characteristic, complemented
89	#17988787	C₂²	1	1	yes	characteristic, complemented
90	#17988786	C₂²	1	2	yes	complemented
91	#17988785	C₂²	1	2	yes	complemented
92	#17988739	C₂²	1	2	yes	—
93	#17988738	C₂²	1	2	yes	—
94	#17988736	C₂²	1	2	yes	—
95	#17988727	C₂²	1	2	yes	complemented
96	#17988726	C₂²	1	2	yes	complemented
97	#17988724	C₂²	1	2	yes	complemented
98	#17988717	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
100	#17988690	C₂²	1	2	yes	complemented
101	#17988687	C₂²	1	2	yes	—
102	#17988687	C₂²	1	2	yes	complemented
103	#17988685	C₂²	1	2	yes	complemented
104	#17988685	C₂²	1	2	yes	complemented
105	#17988684	C₂²	1	2	yes	—
106	C₄×#11924017	C₂²	1	2	yes	complemented
107	C₄×#11924017	C₂²	1	2	yes	complemented
108	SD₁₆×Dic₇₃	C₂²	1	2	yes	—
109	#17988674	C₂²	1	2	yes	complemented
110	#17988666	C₂²	1	1	yes	characteristic, complemented
111	#17988658	C₂²	1	2	yes	complemented
112	C₈×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
113	C₈×C₂²⋊D₇₃	C₂²	1	2	yes	complemented
114	#17988646	C₂²	1	2	yes	complemented
115	#17988644	C₂²	1	1	yes	characteristic, complemented
116	#17988622	C₂²	1	2	yes	complemented
117	#17988594	C₂²	1	2	yes	complemented
118	#17988590	C₂²	1	2	yes	—
119	#17988541	C₂²	1	2	yes	complemented
120	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄×D₄×C₇₃	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924028	—	2	1	no	—
136	C₂×#11924028	—	2	1	no	—
137	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
138	C₂²×D₂₉₂	—	2	1	no	—
139	C₂²×C₂²⋊D₇₃	—	2	2	no	—
140	C₂×D₄×D₇₃	C₂³	1	2	yes	—
141	C₂×#11924017	C₂³	1	2	yes	—
142	C₂×#11924017	C₂³	1	2	yes	—
143	C₂×#11924016	C₂³	1	2	yes	—
144	C₂×#11924016	C₂³	1	2	yes	—
145	C₂×#11924015	C₂³	1	2	yes	—
146	C₂×#11924015	C₂³	1	2	yes	—
147	SD₁₆×D₇₃	—	2	8	no	—
148	C₂×#11924011	C₂³	1	2	yes	—
149	C₂×C₈×D₇₃	C₂³	1	2	yes	—
150	#14556591	—	2	1	no	—
151	#14556591	—	2	1	no	—
152	#14556591	C₂³	1	1	yes	characteristic
153	#14556591	C₂³	1	1	yes	characteristic
154	#14556591	C₂³	1	1	yes	characteristic
155	#14556589	—	2	2	no	—
156	#14556589	C₂³	1	2	yes	—
157	#14556588	C₂³	1	1	yes	characteristic
158	#14556587	C₂³	1	2	yes	—
159	#14556586	—	2	2	no	—
160	#14556586	—	2	2	no	—
161	#14556586	—	2	2	no	—
162	#14556586	—	2	2	no	—
163	#14556585	—	2	2	no	—
164	#14556585	D₄	1	2	yes	—
165	#14556583	—	2	1	no	—
166	#14556583	—	2	2	no	—
167	#14556583	—	2	1	no	—
168	#14556583	D₄	1	1	yes	characteristic
169	#14556582	—	2	2	no	—
170	#14556582	C₂³	1	2	yes	—
171	#14556582	C₂³	1	2	yes	—
172	#14556581	—	2	2	no	—
173	#14556581	—	2	2	no	—
174	#14556581	—	2	2	no	—
175	#14556579	—	2	1	no	—
176	#14556579	—	2	1	no	—
177	#14556579	D₄	1	1	yes	characteristic
178	#14556577	—	2	2	no	—
179	#14556576	—	2	2	no	—
180	#14556574	—	2	2	no	—
181	#14556574	—	2	2	no	—
182	#14556574	D₄	1	2	yes	—
183	#14556573	—	2	2	no	—
184	#14556571	—	2	2	no	—
185	#14556571	C₂³	1	2	yes	—
186	#14556570	—	2	1	no	—
187	#14556570	—	2	2	no	—
188	#14556570	—	2	1	no	—
189	#14556570	D₄	1	1	yes	characteristic
190	#14556570	C₂³	1	2	yes	—
191	#14556568	—	2	2	no	—
192	#14556567	—	2	2	no	—
193	#14556567	C₂³	1	2	yes	—
194	#14556566	C₂³	1	2	yes	—
195	#14556565	—	2	1	no	—
196	#14556565	—	2	2	no	—
197	#14556565	—	2	1	no	—
198	#14556565	—	2	1	no	—
199	#14556565	—	2	2	no	—
200	#14556565	—	2	1	no	—
201	#14556565	D₄	1	1	yes	characteristic
202	#14556565	C₂³	1	2	yes	—
203	#14556564	—	2	2	no	—
204	#14556564	—	2	2	no	—
205	#14556563	—	2	2	no	—
206	#14556562	C₂³	1	2	yes	—
207	#14556561	—	2	2	no	—
208	#14556560	—	2	2	no	—
209	#14556559	—	2	2	no	—
210	Q₈×Dic₇₃	C₂³	1	2	yes	—
211	C₄×Dic₁₄₆	—	2	1	no	—
212	C₄×Dic₁₄₆	—	2	1	no	—
213	C₄×Dic₁₄₆	—	2	1	no	—
214	C₄×Dic₁₄₆	—	2	2	no	—
215	C₄×Dic₁₄₆	—	2	1	no	—
216	C₄×Dic₁₄₆	C₂³	1	2	yes	—
217	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
218	#14556556	—	2	2	no	—
219	#14556556	C₂³	1	2	yes	—
220	C₄×D₂₉₂	—	2	1	no	—
221	C₄×D₂₉₂	—	2	1	no	—
222	C₄×D₂₉₂	C₂³	1	2	yes	—
223	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
224	D₄×Dic₇₃	C₂³	1	2	yes	—
225	#14556553	C₂³	1	2	yes	—
226	C₄×C₂²⋊D₇₃	—	2	2	no	—
227	C₄×C₂²⋊D₇₃	—	2	2	no	—
228	C₄×C₂²⋊D₇₃	—	2	2	no	—
229	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
230	#14556551	—	2	2	no	—
231	#14556550	—	2	1	no	—
232	#14556550	—	2	2	no	—
233	#14556550	—	2	1	no	—
234	#14556549	—	2	2	no	—
235	#14556549	C₂³	1	2	yes	—
236	#14556549	C₂³	1	2	yes	—
237	#14556548	—	2	2	no	—
238	#14556548	C₂³	1	2	yes	—
239	C₂×C₄⋊Dic₇₃	—	2	1	no	—
240	C₂×#11924005	—	2	2	no	—
241	C₂²⋊C₄×D₇₃	—	2	2	no	—
242	#14556524	C₂³	1	2	yes	—
243	#14556524	C₂³	1	2	yes	—
244	#14556524	C₂³	1	2	yes	—
245	#14556524	C₂³	1	2	yes	—
246	#14556523	C₂³	1	2	yes	—
247	#14556523	C₂³	1	2	yes	—
248	C₄⋊#10596831	C₂³	1	1	yes	characteristic
249	C₄⋊#10596831	C₂³	1	1	yes	characteristic
250	#14556520	C₂³	1	2	yes	—
251	#14556520	C₂³	1	2	yes	—
252	#14556516	C₂³	1	2	yes	—
253	#14556516	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	#14556513	C₂³	1	2	yes	—
259	#14556513	C₂³	1	2	yes	—
260	#14556512	C₂³	1	2	yes	—
261	#14556512	C₂³	1	2	yes	—
262	#14556511	C₂³	1	2	yes	—
263	#14556511	C₂³	1	2	yes	—
264	C₂²⋊#10596831	C₂³	1	2	yes	—
265	#14556503	C₂³	1	2	yes	—
266	#14556503	C₂³	1	2	yes	—
267	#14556502	C₂³	1	2	yes	—
268	#14556501	C₂³	1	2	yes	—
269	C₈×Dic₇₃	C₂³	1	2	yes	—
270	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
272	C₂³×C₄×C₇₃	—	2	1	no	—
273	C₂×SD₁₆×C₇₃	—	2	4	no	—
274	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
277	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₇₃	—	2	1	no	—
281	C₄×Q₈×C₇₃	—	2	1	no	—
282	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₇₃	—	2	1	no	—
287	C₄×D₄×C₇₃	—	2	1	no	—
288	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
296	C₂×C₄²×C₇₃	—	2	1	no	—
297	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
298	#106×C₇₃	C₂³	1	1	yes	characteristic
299	#106×C₇₃	C₂³	1	1	yes	characteristic
300	#106×C₇₃	C₂³	1	1	yes	characteristic
301	#106×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	#103×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	#102×C₇₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₂³×D₇₃	—	2	2	no	—
315	#11924028	—	8	2	no	—
316	#11924028	—	8	2	no	—
317	C₂×Dic₁₄₆	—	2	1	no	—
318	C₂×Dic₁₄₆	—	2	2	no	—
319	C₂×Dic₁₄₆	—	2	1	no	—
320	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
321	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
322	Q₈×D₇₃	—	2	4	no	—
323	Q₈×D₇₃	—	4	2	no	—
324	C₂×D₂₉₂	—	2	1	no	—
325	C₂×D₂₉₂	—	2	2	no	—
326	C₂×D₂₉₂	—	2	1	no	—
327	C₂×D₂₉₂	—	8	2	no	—
328	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
329	C₂×D₂₉₂	C₂⁴	1	2	yes	—
330	C₂×C₂²⋊D₇₃	—	2	2	no	—
331	C₂×C₂²⋊D₇₃	—	2	2	no	—
332	C₂×C₂²⋊D₇₃	—	2	2	no	—
333	C₂×C₂²⋊D₇₃	—	2	2	no	—
334	C₂×C₂²⋊D₇₃	—	2	2	no	—
335	C₂×C₂²⋊D₇₃	—	8	4	no	—
336	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
337	D₄×D₇₃	—	2	4	no	—
338	D₄×D₇₃	—	4	2	no	—
339	C₂²×Dic₇₃	—	2	2	no	—
340	C₂×C₄×D₇₃	—	2	2	no	—
341	C₂×C₄×D₇₃	—	2	2	no	—
342	C₂×C₄×D₇₃	—	2	2	no	—
343	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
344	#11924017	—	2	4	no	—
345	#11924017	—	4	2	no	—
346	#11924016	—	2	4	no	—
347	#11924016	—	4	2	no	—
348	#11924015	—	2	4	no	—
349	#11924015	—	4	2	no	—
350	#11924011	—	4	2	no	—
351	C₂×#10596831	C₂⁴	1	2	yes	—
352	C₂×#10596831	C₂⁴	1	2	yes	—
353	C₈×D₇₃	—	2	4	no	—
354	C₄⋊Dic₇₃	—	2	1	no	—
355	C₄⋊Dic₇₃	—	2	1	no	—
356	C₄⋊Dic₇₃	—	2	1	no	—
357	C₄⋊Dic₇₃	—	2	1	no	—
358	C₄⋊Dic₇₃	—	2	2	no	—
359	C₄⋊Dic₇₃	—	2	2	no	—
360	C₄⋊Dic₇₃	—	2	2	no	—
361	C₄⋊Dic₇₃	—	2	2	no	—
362	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
363	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	2	yes	—
375	#11924007	C₂×D₄	1	2	yes	—
376	#11924007	C₂×D₄	1	2	yes	—
377	#11924007	C₂×D₄	1	2	yes	—
378	C₂²⋊Dic₇₃	—	2	2	no	—
379	C₂²⋊Dic₇₃	—	2	2	no	—
380	C₂²⋊Dic₇₃	—	2	2	no	—
381	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
382	#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	C₂×D₄	1	2	yes	—
391	#11924005	C₂×D₄	1	2	yes	—
392	#11924005	C₂×D₄	1	2	yes	—
393	#11924005	C₂×D₄	1	2	yes	—
394	C₄×Dic₇₃	—	2	2	no	—
395	C₄×Dic₇₃	—	2	2	no	—
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	—	2	2	no	—
398	C₄×Dic₇₃	—	2	2	no	—
399	C₄×Dic₇₃	C₂⁴	1	2	yes	—
400	C₂⁴×C₇₃	—	2	1	no	—
401	C₂×Q₈×C₇₃	—	2	1	no	—
402	C₂×Q₈×C₇₃	—	2	2	no	—
403	C₂×Q₈×C₇₃	—	4	1	no	—
404	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×D₄×C₇₃	—	2	2	no	—
407	C₂×D₄×C₇₃	—	2	1	no	—
408	C₂×D₄×C₇₃	—	4	1	no	—
409	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
410	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₇₃	—	2	1	no	—
412	C₂²×C₄×C₇₃	—	2	1	no	—
413	C₂²×C₄×C₇₃	—	2	1	no	—
414	C₂²×C₄×C₇₃	—	2	1	no	—
415	C₂²×C₄×C₇₃	—	2	1	no	—
416	C₂²×C₄×C₇₃	—	2	1	no	—
417	C₂²×C₄×C₇₃	—	2	1	no	—
418	C₂²×C₄×C₇₃	—	8	2	no	—
419	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
420	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
422	SD₁₆×C₇₃	—	2	2	no	—
423	SD₁₆×C₇₃	—	2	2	no	—
424	SD₁₆×C₇₃	—	2	2	no	—
425	SD₁₆×C₇₃	#41	1	4	yes	complemented
426	C₂×C₈×C₇₃	—	2	2	no	—
427	C₂×C₈×C₇₃	—	4	1	no	—
428	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
429	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
431	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
432	C₄⋊C₄×C₇₃	—	2	1	no	—
433	C₄⋊C₄×C₇₃	—	2	1	no	—
434	C₄⋊C₄×C₇₃	—	2	1	no	—
435	C₄⋊C₄×C₇₃	—	2	1	no	—
436	C₄⋊C₄×C₇₃	—	2	1	no	—
437	C₄⋊C₄×C₇₃	—	2	1	no	—
438	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
441	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₂²⋊C₄×C₇₃	—	2	1	no	—
443	C₂²⋊C₄×C₇₃	—	2	1	no	—
444	C₂²⋊C₄×C₇₃	—	2	1	no	—
445	C₂²⋊C₄×C₇₃	—	2	1	no	—
446	C₄²×C₇₃	—	2	1	no	—
447	C₄²×C₇₃	—	2	1	no	—
448	C₄²×C₇₃	—	2	1	no	—
449	C₄²×C₇₃	—	2	1	no	—
450	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
454	C₂³×C₇₃	—	2	1	no	—
455	C₂³×C₇₃	—	2	1	no	—
456	C₂³×C₇₃	—	4	2	no	—
457	C₂³×C₇₃	—	4	2	no	—
458	C₂³×C₇₃	—	8	1	no	—
459	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
460	C₂²×D₇₃	—	2	2	no	—
461	C₂²×D₇₃	—	4	4	no	—
462	C₂²×D₇₃	—	8	2	no	—
463	C₂²×D₇₃	—	8	2	no	—
464	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
465	Q₈×C₇₃	—	2	1	no	—
466	Q₈×C₇₃	—	2	1	no	—
467	Q₈×C₇₃	—	2	1	no	—
468	Q₈×C₇₃	—	4	2	no	—
469	Q₈×C₇₃	C₂×#41	1	2	yes	—
470	D₄×C₇₃	—	2	1	no	—
471	D₄×C₇₃	—	2	1	no	—
472	D₄×C₇₃	—	2	1	no	—
473	D₄×C₇₃	—	4	2	no	—
474	D₄×C₇₃	C₂×#41	1	2	yes	—
475	C₂×C₄×C₇₃	—	2	2	no	—
476	C₂×C₄×C₇₃	—	2	1	no	—
477	C₂×C₄×C₇₃	—	2	2	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	2	1	no	—
480	C₂×C₄×C₇₃	—	2	1	no	—
481	C₂×C₄×C₇₃	—	2	1	no	—
482	C₂×C₄×C₇₃	—	2	1	no	—
483	C₂×C₄×C₇₃	—	2	1	no	—
484	C₂×C₄×C₇₃	—	2	1	no	—
485	C₂×C₄×C₇₃	—	4	2	no	—
486	C₂×C₄×C₇₃	—	4	2	no	—
487	C₂×C₄×C₇₃	—	4	2	no	—
488	C₂×C₄×C₇₃	—	4	2	no	—
489	C₂×C₄×C₇₃	—	8	1	no	—
490	C₂×C₄×C₇₃	—	8	1	no	—
491	C₂×C₄×C₇₃	—	8	1	no	—
492	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
498	C₂²⋊D₇₃	—	2	4	no	—
499	C₂²⋊D₇₃	—	4	4	no	—
500	C₂²⋊D₇₃	—	4	4	no	—
501	C₂²⋊D₇₃	—	8	2	no	—
502	C₂²⋊D₇₃	—	8	2	no	—
503	C₂²⋊D₇₃	—	8	2	no	—
504	C₂×Dic₇₃	—	2	2	no	—
505	C₂×Dic₇₃	—	2	2	no	—
506	C₂×Dic₇₃	—	2	2	no	—
507	C₂×Dic₇₃	—	8	2	no	—
508	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
509	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
510	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
511	D₂₉₂	—	2	2	no	—
512	D₂₉₂	—	2	2	no	—
513	D₂₉₂	—	2	2	no	—
514	D₂₉₂	—	4	2	no	—
515	D₂₉₂	—	8	1	no	—
516	D₂₉₂	—	8	2	no	—
517	C₄×D₇₃	—	2	2	no	—
518	C₄×D₇₃	—	2	2	no	—
519	C₄×D₇₃	—	4	4	no	—
520	C₄×D₇₃	—	8	2	no	—
521	C₄×D₇₃	—	8	2	no	—
522	Dic₁₄₆	—	2	2	no	—
523	Dic₁₄₆	—	2	2	no	—
524	Dic₁₄₆	—	2	2	no	—
525	Dic₁₄₆	—	4	4	no	—
526	Dic₁₄₆	—	4	2	no	—
527	Dic₁₄₆	—	8	1	no	—
528	C₈×C₇₃	—	2	1	no	—
529	C₈×C₇₃	—	2	1	no	—
530	C₈×C₇₃	—	2	1	no	—
531	C₈×C₇₃	C₂×#41	1	2	yes	—
532	#10596831	—	2	2	no	—
533	#10596831	—	2	2	no	—
534	C₂²×C₇₃	—	2	1	no	—
535	C₂²×C₇₃	—	2	1	no	—
536	C₂²×C₇₃	—	2	2	no	—
537	C₂²×C₇₃	—	4	1	no	—
538	C₂²×C₇₃	—	4	1	no	—
539	C₂²×C₇₃	—	4	1	no	—
540	C₂²×C₇₃	—	4	1	no	—
541	C₂²×C₇₃	—	4	1	no	—
542	C₂²×C₇₃	—	8	4	no	—
543	C₂²×C₇₃	#577	1	2	yes	—
544	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
545	C₂×D₇₃	—	2	2	no	—
546	C₂×D₇₃	—	2	2	no	—
547	C₂×D₇₃	—	2	2	no	—
548	C₂×D₇₃	—	4	2	no	—
549	C₂×D₇₃	—	4	2	no	—
550	C₂×D₇₃	—	4	2	no	—
551	C₂×D₇₃	—	16	4	no	—
552	C₄×C₇₃	—	2	2	no	—
553	C₄×C₇₃	—	2	1	no	—
554	C₄×C₇₃	—	2	1	no	—
555	C₄×C₇₃	—	2	1	no	—
556	C₄×C₇₃	—	2	1	no	—
557	C₄×C₇₃	—	4	1	no	—
558	C₄×C₇₃	—	4	1	no	—
559	C₄×C₇₃	—	4	1	no	—
560	C₄×C₇₃	—	4	1	no	—
561	C₄×C₇₃	—	4	1	no	—
562	C₄×C₇₃	#577	1	2	yes	—
563	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
564	C₄×C₇₃	#585	1	1	yes	characteristic
565	Dic₇₃	—	2	2	no	—
566	Dic₇₃	—	2	2	no	—
567	Dic₇₃	—	2	2	no	—
568	Dic₇₃	—	4	2	no	—
569	Dic₇₃	—	4	2	no	—
570	Dic₇₃	—	4	2	no	—
571	#61481	—	73	1	no	maximal, Sylow
572	C₂×C₇₃	—	2	2	no	—
573	C₂×C₇₃	—	4	2	no	—
574	C₂×C₇₃	—	8	1	no	—
575	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
576	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
577	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
578	D₇₃	—	4	2	no	—
579	D₇₃	—	8	2	no	—
580	#3523	—	73	1	no	—
581	#3519	—	73	1	no	—
582	#3392	—	73	1	no	—
583	#3381	—	73	1	no	—
584	#3372	—	73	1	no	—
585	#3368	—	73	1	no	—
586	#3340	—	73	1	no	—
587	#3337	—	73	2	no	—
588	#3329	—	73	1	no	—
589	#3324	—	73	1	no	—
590	#3320	—	73	2	no	—
591	#3310	—	73	2	no	—
592	D₄×SD₁₆	—	73	1	no	—
593	D₄×SD₁₆	—	73	2	no	—
594	#3174	—	73	2	no	—
595	#3167	—	73	1	no	—
596	#3126	—	73	2	no	—
597	#3123	—	73	2	no	—
598	#3112	—	73	1	no	—
599	#3110	—	73	1	no	—
600	#2966	—	73	1	no	—
601	#2949	—	73	2	no	—
602	C₂×C₄×SD₁₆	D₇₃	1	1	yes	characteristic, complemented
603	C₇₃	#61481	1	1	yes	characteristic, complemented, Sylow
604	C₂²×SD₁₆	—	73	2	no	—
605	C₂²×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
606	#557	—	73	1	no	—
607	#557	—	73	1	no	—
608	#557	—	146	1	no	—
609	#556	—	73	1	no	—
610	#556	—	146	1	no	—
611	#555	—	73	1	no	—
612	#554	—	73	1	no	—
613	#553	—	73	2	no	—
614	#553	—	146	1	no	—
615	#552	—	73	2	no	—
616	#552	—	146	2	no	—
617	#550	—	73	1	no	—
618	D₄×Q₈	—	73	2	no	—
619	D₄×Q₈	—	73	1	no	—
620	#546	—	146	2	no	—
621	#546	—	146	1	no	—
622	D₄²	—	73	2	no	—
623	D₄²	—	73	1	no	—
624	#541	—	73	2	no	—
625	#541	—	146	2	no	—
626	#540	—	73	2	no	—
627	#538	—	146	2	no	—
628	#533	—	73	1	no	—
629	#533	—	146	1	no	—
630	#532	—	73	1	no	—
631	#529	—	73	1	no	—
632	#529	—	146	1	no	—
633	#525	—	146	1	no	—
634	C₂×#121	—	146	1	no	—
635	#519	—	73	2	no	—
636	#518	—	73	2	no	—
637	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
638	C₂×C₄×D₄	C₂×D₇₃	1	1	yes	characteristic
639	#499	—	73	2	no	—
640	#498	—	73	1	no	—
641	#492	—	73	2	no	—
642	#492	—	73	1	no	—
643	#491	—	73	2	no	—
644	#490	—	73	2	no	—
645	#487	—	73	1	no	—
646	#486	—	73	1	no	—
647	#485	—	73	2	no	—
648	#485	—	73	2	no	—
649	#484	—	73	2	no	—
650	#482	—	73	2	no	—
651	#482	—	73	2	no	—
652	#480	—	73	2	no	—
653	#479	—	73	2	no	—
654	#479	—	73	2	no	—
655	#478	—	73	2	no	—
656	#478	—	73	2	no	—
657	#477	—	73	1	no	—
658	#477	—	73	1	no	—
659	#474	—	73	1	no	—
660	#474	—	73	1	no	—
661	#468	—	73	2	no	—
662	#468	—	73	2	no	—
663	#465	—	73	2	no	—
664	#465	—	73	2	no	—
665	#465	—	73	2	no	—
666	#465	—	73	2	no	—
667	#461	—	73	2	no	—
668	#461	—	73	1	no	—
669	#461	—	73	1	no	—
670	#461	—	73	2	no	—
671	#460	—	73	2	no	—
672	#460	—	73	1	no	—
673	#460	—	73	1	no	—
674	#460	—	73	2	no	—
675	#450	—	73	2	no	—
676	#450	—	73	2	no	—
677	#450	—	73	2	no	—
678	#448	—	73	2	no	—
679	#448	—	73	2	no	—
680	#448	—	73	2	no	—
681	#446	—	73	1	no	—
682	C₈×Q₈	—	73	1	no	—
683	#440	—	73	2	no	—
684	#440	—	73	2	no	—
685	#440	—	73	2	no	—
686	#440	—	73	2	no	—
687	#440	—	73	2	no	—
688	#440	—	73	2	no	—
689	C₄×SD₁₆	—	73	2	no	—
690	C₄×SD₁₆	—	73	2	no	—
691	C₄×SD₁₆	—	73	2	no	—
692	C₄×SD₁₆	—	73	2	no	—
693	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
694	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
695	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
696	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
697	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
698	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
699	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
700	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
701	#436	—	73	1	no	—
702	#435	—	73	2	no	—
703	C₈×D₄	—	73	2	no	—
704	C₈×D₄	—	73	1	no	—
705	#433	—	73	2	no	—
706	#432	—	73	1	no	—
707	#427	—	73	2	no	—
708	C₂×#106	C₂×D₇₃	1	1	yes	characteristic, complemented
709	#419	—	73	2	no	—
710	#418	—	73	2	no	—
711	C₂×#103	C₂×D₇₃	1	1	yes	characteristic, complemented
712	C₂×#102	C₂×D₇₃	1	1	yes	characteristic
713	#405	—	73	2	no	—
714	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
715	C₂×#41	—	146	1	no	—
716	C₂×#41	—	146	1	no	—
717	C₂²×Q₈	—	73	2	no	—
718	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
719	C₂²×D₄	—	73	2	no	—
720	C₂²×D₄	—	146	1	no	—
721	C₂²×D₄	—	146	2	no	—
722	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
723	C₂³×C₄	—	2	1	no	—
724	C₂×SD₁₆	—	2	4	no	—
725	C₂×SD₁₆	—	73	2	no	—
726	C₂×SD₁₆	—	73	2	no	—
727	C₂×SD₁₆	—	73	2	no	—
728	C₂×SD₁₆	—	73	2	no	—
729	C₂×SD₁₆	—	73	2	no	—
730	C₂×SD₁₆	—	73	2	no	—
731	C₂×SD₁₆	—	146	8	no	—
732	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
733	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
734	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
735	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
736	C₂×M₁₆	—	73	2	no	—
737	C₂²×C₈	—	73	2	no	—
738	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
739	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
740	C₄⋊Q₈	—	73	2	no	—
741	C₄⋊Q₈	—	73	1	no	—
742	C₄⋊Q₈	—	73	1	no	—
743	C₄⋊Q₈	—	73	1	no	—
744	C₄⋊Q₈	—	146	1	no	—
745	C₄⋊Q₈	—	146	1	no	—
746	C₄⋊Q₈	—	146	2	no	—
747	#127	—	73	2	no	—
748	#127	—	73	1	no	—
749	#126	—	73	2	no	—
750	#126	—	146	2	no	—
751	#126	—	146	2	no	—
752	#126	—	146	2	no	—
753	#126	—	146	2	no	—
754	#126	—	146	2	no	—
755	#125	—	73	2	no	—
756	#125	—	73	2	no	—
757	#125	—	73	1	no	—
758	#125	—	146	1	no	—
759	#125	—	146	2	no	—
760	#125	—	146	2	no	—
761	#125	—	146	2	no	—
762	#125	—	146	2	no	—
763	#125	—	146	2	no	—
764	#125	—	146	1	no	—
765	#124	—	73	1	no	—
766	#124	—	146	1	no	—
767	#124	—	146	2	no	—
768	#124	—	146	1	no	—
769	#123	—	73	2	no	—
770	#123	—	146	2	no	—
771	#123	—	146	2	no	—
772	#123	—	146	2	no	—
773	#123	—	146	2	no	—
774	C₂²⋊Q₈	—	73	1	no	—
775	C₂²⋊Q₈	—	73	2	no	—
776	C₂²⋊Q₈	—	73	2	no	—
777	C₂²⋊Q₈	—	73	2	no	—
778	C₂²⋊Q₈	—	146	2	no	—
779	C₂²⋊Q₈	—	146	2	no	—
780	C₂²⋊Q₈	—	146	2	no	—
781	C₂²⋊Q₈	—	146	2	no	—
782	C₂²⋊Q₈	—	146	1	no	—
783	C₂²⋊Q₈	—	146	1	no	—
784	#121	—	73	1	no	—
785	#121	—	73	2	no	—
786	#121	—	73	2	no	—
787	#121	—	73	2	no	—
788	#121	—	146	2	no	—
789	#121	—	146	2	no	—
790	#121	—	146	2	no	—
791	#121	—	146	1	no	—
792	#121	—	146	1	no	—
793	#121	—	146	2	no	—
794	#121	—	146	2	no	—
795	#121	—	146	1	no	—
796	#121	—	146	1	no	—
797	#120	—	146	2	no	—
798	#120	—	146	2	no	—
799	#120	—	146	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	1	no	—
802	C₄×Q₈	—	73	1	no	—
803	C₄×Q₈	—	73	2	no	—
804	C₄×Q₈	—	73	2	no	—
805	C₄×Q₈	—	73	2	no	—
806	C₄×Q₈	—	146	2	no	—
807	C₄×Q₈	—	146	1	no	—
808	C₄×Q₈	—	146	1	no	—
809	C₄×Q₈	—	146	1	no	—
810	C₄×Q₈	—	146	2	no	—
811	C₄×Q₈	—	146	1	no	—
812	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
815	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
816	C₄×D₄	—	2	1	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	73	2	no	—
819	C₄×D₄	—	73	2	no	—
820	C₄×D₄	—	73	2	no	—
821	C₄×D₄	—	73	1	no	—
822	C₄×D₄	—	73	2	no	—
823	C₄×D₄	—	146	1	no	—
824	C₄×D₄	—	146	2	no	—
825	C₄×D₄	—	146	2	no	—
826	C₄×D₄	—	146	2	no	—
827	C₄×D₄	—	146	2	no	—
828	C₄×D₄	—	146	1	no	—
829	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
830	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
831	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
832	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
833	#117	—	73	2	no	—
834	#117	—	73	2	no	—
835	#117	—	73	2	no	—
836	#117	—	146	2	no	—
837	#117	—	146	2	no	—
838	#117	—	146	2	no	—
839	#117	—	146	1	no	—
840	#117	—	146	1	no	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	—	146	1	no	—
843	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
844	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	—	2	1	no	—
846	C₂×C₂²⋊C₄	—	146	2	no	—
847	C₂×C₂²⋊C₄	—	146	2	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
850	#107	—	73	2	no	—
851	#107	—	73	2	no	—
852	#107	—	73	2	no	—
853	#107	—	73	2	no	—
854	#106	—	73	2	no	—
855	#106	—	73	2	no	—
856	#106	C₂²×D₇₃	1	1	yes	characteristic
857	#106	C₂²×D₇₃	1	1	yes	characteristic
858	#106	C₂²×D₇₃	1	1	yes	characteristic
859	#106	C₂²×D₇₃	1	1	yes	characteristic
860	C₄⋊C₈	—	73	2	no	—
861	C₄⋊C₈	—	73	2	no	—
862	C₄⋊C₈	—	73	1	no	—
863	C₄⋊C₈	—	73	1	no	—
864	#103	—	73	2	no	—
865	#103	—	73	2	no	—
866	#103	—	73	2	no	—
867	#103	—	73	2	no	—
868	#103	—	73	2	no	—
869	#103	—	73	2	no	—
870	#103	C₂²×D₇₃	1	1	yes	characteristic
871	#103	C₂²×D₇₃	1	1	yes	characteristic
872	#103	C₂²×D₇₃	1	1	yes	characteristic
873	#103	C₂²×D₇₃	1	1	yes	characteristic
874	#102	—	73	2	no	—
875	#102	—	73	2	no	—
876	#102	—	73	2	no	—
877	#102	—	73	2	no	—
878	#102	—	73	2	no	—
879	#102	—	73	2	no	—
880	#102	C₂²×D₇₃	1	1	yes	characteristic
881	#102	C₂²×D₇₃	1	1	yes	characteristic
882	#102	C₂²×D₇₃	1	1	yes	characteristic
883	#102	C₂²×D₇₃	1	1	yes	characteristic
884	C₂²⋊C₈	—	73	2	no	—
885	C₂²⋊C₈	—	73	2	no	—
886	C₂²⋊C₈	—	73	2	no	—
887	#97	—	73	2	no	—
888	#97	—	73	2	no	—
889	C₄×C₈	—	73	2	no	—
890	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
891	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
892	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
894	C₂⁴	—	2	1	no	—
895	C₂⁴	—	146	2	no	—
896	#41	—	584	2	no	—
897	#41	—	584	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	4	1	no	—
901	C₂×Q₈	—	292	2	no	—
902	C₂×Q₈	—	73	1	no	—
903	C₂×Q₈	—	73	2	no	—
904	C₂×Q₈	—	146	2	no	—
905	C₂×Q₈	—	146	4	no	—
906	C₂×Q₈	—	146	1	no	—
907	C₂×Q₈	—	146	1	no	—
908	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
909	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
910	C₂×D₄	—	2	2	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	4	1	no	—
913	C₂×D₄	—	292	2	no	—
914	C₂×D₄	—	584	2	no	—
915	C₂×D₄	—	584	4	no	—
916	C₂×D₄	—	73	2	no	—
917	C₂×D₄	—	73	1	no	—
918	C₂×D₄	—	73	2	no	—
919	C₂×D₄	—	146	2	no	—
920	C₂×D₄	—	146	2	no	—
921	C₂×D₄	—	146	2	no	—
922	C₂×D₄	—	146	2	no	—
923	C₂×D₄	—	146	2	no	—
924	C₂×D₄	—	146	4	no	—
925	C₂×D₄	—	146	2	no	—
926	C₂×D₄	—	146	1	no	—
927	C₂×D₄	—	146	1	no	—
928	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
929	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	2	1	no	—
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	8	2	no	—
938	C₂²×C₄	—	73	2	no	—
939	C₂²×C₄	—	146	2	no	—
940	C₂²×C₄	—	146	2	no	—
941	C₂²×C₄	—	146	2	no	—
942	C₂²×C₄	—	146	2	no	—
943	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
944	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
946	SD₁₆	—	2	2	no	—
947	SD₁₆	—	2	2	no	—
948	SD₁₆	—	2	2	no	—
949	SD₁₆	—	292	2	no	—
950	SD₁₆	—	292	2	no	—
951	SD₁₆	—	292	2	no	—
952	SD₁₆	—	146	4	no	—
953	SD₁₆	—	146	4	no	—
954	SD₁₆	—	146	4	no	—
955	SD₁₆	#11924028	1	4	yes	complemented
956	M₁₆	—	292	2	no	—
957	C₂×C₈	—	2	2	no	—
958	C₂×C₈	—	4	1	no	—
959	C₂×C₈	—	73	2	no	—
960	C₂×C₈	—	73	2	no	—
961	C₂×C₈	—	146	4	no	—
962	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
964	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
965	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	73	2	no	—
973	C₄⋊C₄	—	73	2	no	—
974	C₄⋊C₄	—	73	2	no	—
975	C₄⋊C₄	—	73	2	no	—
976	C₄⋊C₄	—	73	1	no	—
977	C₄⋊C₄	—	73	1	no	—
978	C₄⋊C₄	—	73	2	no	—
979	C₄⋊C₄	—	73	2	no	—
980	C₄⋊C₄	—	146	2	no	—
981	C₄⋊C₄	—	146	2	no	—
982	C₄⋊C₄	—	146	2	no	—
983	C₄⋊C₄	—	146	2	no	—
984	C₄⋊C₄	—	146	2	no	—
985	C₄⋊C₄	—	146	2	no	—
986	C₄⋊C₄	—	146	2	no	—
987	C₄⋊C₄	—	146	2	no	—
988	C₄⋊C₄	—	146	2	no	—
989	C₄⋊C₄	—	146	2	no	—
990	C₄⋊C₄	—	146	2	no	—
991	C₄⋊C₄	—	146	2	no	—
992	C₄⋊C₄	—	146	1	no	—
993	C₄⋊C₄	—	146	1	no	—
994	C₄⋊C₄	—	146	1	no	—
995	C₄⋊C₄	—	146	1	no	—
996	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
997	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	73	2	no	—
1005	C₂²⋊C₄	—	73	2	no	—
1006	C₂²⋊C₄	—	73	2	no	—
1007	C₂²⋊C₄	—	73	2	no	—
1008	C₂²⋊C₄	—	73	2	no	—
1009	C₂²⋊C₄	—	146	2	no	—
1010	C₂²⋊C₄	—	146	2	no	—
1011	C₂²⋊C₄	—	146	2	no	—
1012	C₂²⋊C₄	—	146	2	no	—
1013	C₂²⋊C₄	—	146	2	no	—
1014	C₂²⋊C₄	—	146	2	no	—
1015	C₂²⋊C₄	—	146	2	no	—
1016	C₂²⋊C₄	—	146	2	no	—
1017	C₂²⋊C₄	—	146	2	no	—
1018	C₂²⋊C₄	—	146	2	no	—
1019	C₂²⋊C₄	—	146	2	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	73	2	no	—
1025	C₄²	—	146	2	no	—
1026	C₄²	—	146	2	no	—
1027	C₄²	—	146	2	no	—
1028	C₄²	—	146	2	no	—
1029	C₄²	—	146	2	no	—
1030	C₄²	D₄×D₇₃	1	1	yes	characteristic
1031	C₄²	D₄×D₇₃	1	1	yes	characteristic
1032	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1033	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	2	1	no	—
1036	C₂³	—	4	2	no	—
1037	C₂³	—	4	2	no	—
1038	C₂³	—	8	1	no	—
1039	C₂³	—	292	4	no	—
1040	C₂³	—	584	2	no	—
1041	C₂³	—	584	2	no	—
1042	C₂³	—	73	2	no	—
1043	C₂³	—	146	2	no	—
1044	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	4	2	no	—
1049	Q₈	—	292	4	no	—
1050	Q₈	—	292	2	no	—
1051	Q₈	—	584	1	no	—
1052	Q₈	—	146	2	no	—
1053	Q₈	—	146	2	no	—
1054	Q₈	—	146	2	no	—
1055	Q₈	C₂×#11924028	1	2	yes	—
1056	D₄	—	2	1	no	—
1057	D₄	—	2	1	no	—
1058	D₄	—	2	1	no	—
1059	D₄	—	4	2	no	—
1060	D₄	—	292	4	no	—
1061	D₄	—	292	4	no	—
1062	D₄	—	292	2	no	—
1063	D₄	—	584	1	no	—
1064	D₄	—	584	2	no	—
1065	D₄	—	584	2	no	—
1066	D₄	—	584	2	no	—
1067	D₄	—	584	2	no	—
1068	D₄	—	146	4	no	—
1069	D₄	—	146	2	no	—
1070	D₄	—	146	2	no	—
1071	D₄	—	146	2	no	—
1072	D₄	C₂×#11924028	1	2	yes	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	8	1	no	—
1088	C₂×C₄	—	8	1	no	—
1089	C₂×C₄	—	8	1	no	—
1090	C₂×C₄	—	292	4	no	—
1091	C₂×C₄	—	584	2	no	—
1092	C₂×C₄	—	584	2	no	—
1093	C₂×C₄	—	584	2	no	—
1094	C₂×C₄	—	73	2	no	—
1095	C₂×C₄	—	73	2	no	—
1096	C₂×C₄	—	73	2	no	—
1097	C₂×C₄	—	146	2	no	—
1098	C₂×C₄	—	146	2	no	—
1099	C₂×C₄	—	146	2	no	—
1100	C₂×C₄	—	146	2	no	—
1101	C₂×C₄	—	146	2	no	—
1102	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1103	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1104	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1105	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1106	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1107	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1108	C₈	—	2	1	no	—
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	146	2	no	—
1112	C₈	—	146	2	no	—
1113	C₈	C₂×#11924028	1	2	yes	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	8	4	no	—
1123	C₂²	—	292	2	no	—
1124	C₂²	—	292	2	no	—
1125	C₂²	—	292	2	no	—
1126	C₂²	—	1168	4	no	—
1127	C₂²	—	146	2	no	—
1128	C₂²	—	146	2	no	—
1129	C₂²	—	146	2	no	—
1130	C₂²	#17989394	1	2	yes	—
1131	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	292	2	no	—
1143	C₄	—	292	2	no	—
1144	C₄	—	292	2	no	—
1145	C₄	—	146	2	no	—
1146	C₄	—	146	2	no	—
1147	C₄	—	146	2	no	—
1148	C₄	#17989393	1	2	yes	—
1149	C₄	C₂²×#11924028	1	1	yes	characteristic
1150	C₄	#17989423	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	8	1	no	—
1154	C₂	—	292	2	no	—
1155	C₂	—	584	2	no	—
1156	C₂	D₄×#11924028	1	1	yes	characteristic
1157	C₂	C₂×#17989393	1	1	yes	characteristic
1158	C₂	C₂×#17989394	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×C₄×SD₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#22623963	C₂
hypercenter	C₂×C₄×SD₁₆	D₇₃
hypocenter	C₇₃	#61481
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #22624027	C₂	semidirect
3. #22622910	C₂	semidirect
4. #22622804	C₂	semidirect
5. #22622710	C₂	semidirect
6. #22622658	C₂	semidirect
7. #22622346	C₂	semidirect
8. #22622306	C₂	semidirect
9. #22622227	C₂	semidirect
10. #22622164	C₂	semidirect
11. #22622098	C₂	semidirect
12. #22621948	C₂	semidirect
13. SD₁₆×D₂₉₂	C₂	semidirect
14. SD₁₆×C₂²⋊D₇₃	C₂	semidirect
15. #22620555	C₂	semidirect
16. #22620490	C₂	semidirect
17. #22620219	C₂	semidirect
18. #22620180	C₂	semidirect
19. #22620053	C₂	semidirect
20. #22620030	C₂	semidirect
21. #22618906	C₂	semidirect
22. #22618785	C₂	semidirect
23. C₂×C₄×SD₁₆×C₇₃	C₂	semidirect
25. #17989316	C₂²	semidirect
27. #17989315	C₂²	semidirect
29. #17989310	C₂²	semidirect
35. #17989272	C₂²	semidirect
37. Q₈×D₂₉₂	C₂²	semidirect
38. Q₈×C₂²⋊D₇₃	C₂²	semidirect
44. #17989195	C₂²	semidirect
48. #17989144	C₂²	semidirect
54. #17989063	C₂²	semidirect
56. #17988987	C₂²	semidirect
57. #17988985	C₂²	semidirect
58. #17988960	C₂²	semidirect
59. #17988958	C₂²	semidirect
60. #17988954	C₂²	semidirect
61. #17988950	C₂²	semidirect
62. #17988938	C₂²	semidirect
63. #17988934	C₂²	semidirect
64. #17988931	C₂²	semidirect
65. #17988926	C₂²	semidirect
66. #17988922	C₂²	semidirect
67. #17988913	C₂²	semidirect
68. #17988910	C₂²	semidirect
69. #17988900	C₂²	semidirect
70. #17988897	C₂²	semidirect
71. #17988892	C₂²	semidirect
73. #17988886	C₂²	semidirect
74. #17988882	C₂²	semidirect
75. #17988882	C₂²	semidirect
77. #17988867	C₂²	semidirect
78. #17988836	C₂²	semidirect
79. #17988832	C₂²	semidirect
80. #17988817	C₂²	semidirect
81. #17988816	C₂²	semidirect
82. #17988816	C₂²	semidirect
83. #17988813	C₂²	semidirect
85. #17988792	C₂²	semidirect
86. #17988791	C₂²	semidirect
88. #17988787	C₂²	semidirect
89. #17988787	C₂²	semidirect
90. #17988786	C₂²	semidirect
91. #17988785	C₂²	semidirect
95. #17988727	C₂²	semidirect
96. #17988726	C₂²	semidirect
97. #17988724	C₂²	semidirect
98. #17988717	C₂²	semidirect
99. C₈×Dic₁₄₆	C₂²	semidirect
100. #17988690	C₂²	semidirect
102. #17988687	C₂²	semidirect
103. #17988685	C₂²	semidirect
104. #17988685	C₂²	semidirect
106. C₄×#11924017	C₂²	semidirect
107. C₄×#11924017	C₂²	semidirect
109. #17988674	C₂²	semidirect
110. #17988666	C₂²	semidirect
111. #17988658	C₂²	semidirect
112. C₈×D₂₉₂	C₂²	semidirect
113. C₈×C₂²⋊D₇₃	C₂²	semidirect
114. #17988646	C₂²	semidirect
115. #17988644	C₂²	semidirect
116. #17988622	C₂²	semidirect
117. #17988594	C₂²	semidirect
119. #17988541	C₂²	semidirect
121. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
127. C₄×SD₁₆×C₇₃	C₂²	semidirect
128. C₄×SD₁₆×C₇₃	C₂²	semidirect
129. C₄×SD₁₆×C₇₃	C₂²	semidirect
130. C₄×SD₁₆×C₇₃	C₂²	semidirect
131. C₂×#106×C₇₃	C₂²	semidirect
132. C₂×#103×C₇₃	C₂²	semidirect
134. C₂×C₄×C₈×C₇₃	C₂²	semidirect
425. SD₁₆×C₇₃	#41	semidirect
602. C₂×C₄×SD₁₆	D₇₃	semidirect
603. C₇₃	#61481	semidirect
637. C₂×C₄×Q₈	C₂×D₇₃	semidirect
697. C₄×SD₁₆	C₂×D₇₃	semidirect
698. C₄×SD₁₆	C₂×D₇₃	semidirect
699. C₄×SD₁₆	C₂×D₇₃	semidirect
700. C₄×SD₁₆	C₂×D₇₃	semidirect
708. C₂×#106	C₂×D₇₃	semidirect
711. C₂×#103	C₂×D₇₃	semidirect
714. C₂×C₄×C₈	C₂×D₇₃	semidirect
955. SD₁₆	#11924028	semidirect

Maximal subgroups

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

subgroup	index
#22624027	2
#22623963	2
#22622910	2
#22622804	2
#22622710	2
#22622658	2
#22622346	2
#22622306	2
#22622227	2
#22622164	2
#22622098	2
#22621948	2
SD₁₆×D₂₉₂	2
SD₁₆×C₂²⋊D₇₃	2
#22620555	2
#22620490	2
#22620219	2
#22620180	2
#22620053	2
#22620030	2
#22618906	2
#22618785	2
C₂×C₄×SD₁₆×C₇₃	2
#61481	73