Subgroups — #33968833

Order 18688.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623909	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623892	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622982	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622828	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622589	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622571	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622548	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622442	C₂	1	2	yes	maximal, complemented
9	#22621855	C₂	1	2	yes	maximal, complemented
10	#22621850	C₂	1	1	yes	maximal, characteristic, complemented
11	#22621767	C₂	1	2	yes	maximal, complemented
12	#22621757	C₂	1	1	yes	maximal, characteristic, complemented
13	#22621532	C₂	1	1	yes	maximal, characteristic, complemented
14	#22621456	C₂	1	2	yes	maximal, complemented
15	#22620603	C₂	1	2	yes	maximal, complemented
16	#22620490	C₂	1	1	yes	maximal, characteristic, complemented
17	#22620204	C₂	1	2	yes	maximal, complemented
18	#22620180	C₂	1	2	yes	maximal, complemented
19	#22620093	C₂	1	1	yes	maximal, characteristic, complemented
20	#22620082	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618906	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618756	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556615	C₂²	1	2	yes	—
25	#17989322	C₂²	1	1	yes	characteristic
26	#17989315	C₂²	1	1	yes	characteristic, complemented
27	#17989310	C₂²	1	1	yes	characteristic
28	#17989300	C₂²	1	2	yes	—
29	#17989297	C₂²	1	1	yes	characteristic
30	#17989294	C₂²	1	1	yes	characteristic, complemented
31	#17989283	—	2	1	no	—
32	#17989277	—	2	1	no	—
33	#17989276	C₂²	1	2	yes	complemented
34	#17989270	—	2	2	no	—
35	#17989261	—	2	2	no	—
36	D₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
37	#17989246	—	2	1	no	—
38	#17989241	C₂²	1	1	yes	characteristic
39	#17989236	C₂²	1	2	yes	complemented
40	#17989233	—	2	1	no	—
41	#17989225	C₂²	1	2	yes	—
42	D₄×D₂₉₂	C₂²	1	1	yes	characteristic
43	#17989209	C₂²	1	2	yes	—
44	#17989195	C₂²	1	2	yes	complemented
45	#17989179	—	2	2	no	—
46	#17989170	—	2	2	no	—
47	#17989144	C₂²	1	1	yes	characteristic, complemented
48	#17989137	C₂²	1	1	yes	characteristic
49	#17989121	—	2	1	no	—
50	#17989121	—	2	1	no	—
51	#17989121	C₂²	1	1	yes	characteristic
52	C₂×#14556583	—	2	1	no	—
53	C₂×#14556579	—	2	1	no	—
54	#17989066	C₂²	1	2	yes	complemented
55	#17989059	C₂²	1	2	yes	—
56	#17988995	C₂²	1	2	yes	complemented
57	#17988985	C₂²	1	1	yes	characteristic, complemented
58	#17988980	C₂²	1	2	yes	complemented
59	#17988960	C₂²	1	1	yes	characteristic
60	#17988943	C₂²	1	2	yes	complemented
61	#17988938	C₂²	1	1	yes	characteristic, complemented
62	#17988936	C₂²	1	2	yes	complemented
63	#17988934	C₂²	1	1	yes	characteristic
64	#17988931	C₂²	1	2	yes	complemented
65	#17988928	C₂²	1	2	yes	complemented
66	#17988926	C₂²	1	2	yes	complemented
67	#17988916	C₂²	1	2	yes	complemented
68	#17988911	C₂²	1	2	yes	complemented
69	#17988907	C₂²	1	2	yes	—
70	#17988889	C₂²	1	2	yes	—
71	#17988886	C₂²	1	2	yes	complemented
72	#17988882	C₂²	1	1	yes	characteristic, complemented
73	#17988877	C₂²	1	1	yes	characteristic
74	#17988875	C₂²	1	2	yes	complemented
75	#17988872	C₂²	1	1	yes	characteristic, complemented
76	#17988871	C₂²	1	2	yes	complemented
77	#17988867	C₂²	1	1	yes	characteristic, complemented
78	#17988842	C₂²	1	2	yes	complemented
79	#17988834	C₂²	1	2	yes	—
80	#17988827	C₂²	1	2	yes	complemented
81	#17988819	C₂²	1	2	yes	—
82	#17988816	C₂²	1	2	yes	complemented
83	#17988816	C₂²	1	2	yes	complemented
84	#17988812	C₂²	1	2	yes	complemented
85	#17988804	C₂²	1	2	yes	complemented
86	#17988797	C₂²	1	1	yes	characteristic, complemented
87	#17988792	C₂²	1	1	yes	characteristic
88	#17988791	C₂²	1	2	yes	complemented
89	#17988790	C₂²	1	2	yes	—
90	#17988787	C₂²	1	1	yes	characteristic
91	#17988782	C₂²	1	1	yes	characteristic
92	#17988749	C₂²	1	2	yes	—
93	#17988746	C₂²	1	2	yes	complemented
94	#17988739	C₂²	1	2	yes	—
95	#17988736	C₂²	1	2	yes	—
96	#17988733	C₂²	1	2	yes	—
97	#17988732	C₂²	1	2	yes	complemented
98	#17988717	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
100	#17988699	C₂²	1	2	yes	—
101	#17988697	C₂²	1	2	yes	complemented
102	#17988692	C₂²	1	2	yes	complemented
103	#17988687	C₂²	1	2	yes	—
104	#17988686	C₂²	1	2	yes	complemented
105	#17988685	C₂²	1	2	yes	complemented
106	#17988678	C₂²	1	2	yes	—
107	C₄×#11924017	C₂²	1	2	yes	complemented
108	C₄×#11924017	C₂²	1	2	yes	complemented
109	#17988667	C₂²	1	2	yes	complemented
110	#17988666	C₂²	1	1	yes	characteristic
111	#17988658	C₂²	1	2	yes	complemented
112	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
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	#17988628	C₂²	1	2	yes	complemented
117	#17988580	C₂²	1	2	yes	complemented
118	#102×D₇₃	C₂²	1	2	yes	—
119	#17988541	C₂²	1	2	yes	complemented
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, complemented
123	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
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×D₈×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
131	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	#416×C₇₃	C₂²	1	1	yes	characteristic
133	#416×C₇₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924028	—	2	1	no	—
136	C₂×#11924027	C₂³	1	2	yes	—
137	C₂²×Dic₁₄₆	—	2	1	no	—
138	C₂²×D₂₉₂	—	2	1	no	—
139	C₂×D₄×D₇₃	C₂³	1	2	yes	—
140	#14556615	—	2	8	no	—
141	C₂×#11924018	C₂³	1	2	yes	—
142	C₂×#11924017	C₂³	1	2	yes	—
143	C₂×#11924017	C₂³	1	2	yes	—
144	C₂×#11924016	C₂³	1	2	yes	—
145	C₂×#11924015	C₂³	1	2	yes	—
146	C₂×#11924013	C₂³	1	2	yes	—
147	C₂×#11924011	C₂³	1	2	yes	—
148	C₂×C₈×D₇₃	C₂³	1	2	yes	—
149	#14556591	C₂³	1	1	yes	characteristic
150	#14556591	C₂³	1	1	yes	characteristic
151	#14556591	C₂³	1	1	yes	characteristic
152	#14556590	C₂³	1	2	yes	—
153	#14556589	C₂³	1	2	yes	—
154	#14556588	C₂³	1	1	yes	characteristic
155	#14556586	—	2	2	no	—
156	#14556586	—	2	2	no	—
157	#14556585	—	2	2	no	—
158	#14556585	—	2	2	no	—
159	#14556585	D₄	1	2	yes	—
160	#14556584	—	2	2	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	D₄	1	1	yes	characteristic
167	#14556582	C₂³	1	2	yes	—
168	#14556581	—	2	2	no	—
169	#14556581	—	2	2	no	—
170	#14556580	C₂³	1	2	yes	—
171	#14556579	—	2	1	no	—
172	#14556579	—	2	1	no	—
173	#14556579	—	2	2	no	—
174	#14556579	—	2	2	no	—
175	#14556579	—	2	1	no	—
176	#14556579	D₄	1	1	yes	characteristic
177	#14556577	—	2	2	no	—
178	#14556576	—	2	2	no	—
179	#14556576	—	2	2	no	—
180	#14556575	—	2	2	no	—
181	#14556574	—	2	2	no	—
182	#14556574	—	2	2	no	—
183	#14556574	D₄	1	2	yes	—
184	#14556573	—	2	2	no	—
185	#14556572	—	2	2	no	—
186	#14556571	C₂³	1	2	yes	—
187	#14556570	—	2	1	no	—
188	#14556570	—	2	1	no	—
189	#14556570	—	2	1	no	—
190	#14556570	D₄	1	1	yes	characteristic
191	#14556570	C₂³	1	2	yes	—
192	#14556569	—	2	2	no	—
193	#14556569	—	2	2	no	—
194	#14556568	—	2	2	no	—
195	#14556568	—	2	2	no	—
196	#14556567	C₂³	1	2	yes	—
197	#14556567	C₂³	1	2	yes	—
198	#14556566	C₂³	1	2	yes	—
199	#14556565	—	2	1	no	—
200	#14556565	—	2	1	no	—
201	#14556565	—	2	1	no	—
202	#14556565	D₄	1	1	yes	characteristic
203	#14556565	C₂³	1	2	yes	—
204	#14556564	—	2	2	no	—
205	#14556563	—	2	2	no	—
206	#14556563	—	2	2	no	—
207	#14556561	—	2	2	no	—
208	#14556559	—	2	2	no	—
209	C₄×Dic₁₄₆	—	2	1	no	—
210	C₄×Dic₁₄₆	—	2	1	no	—
211	C₄×Dic₁₄₆	—	2	1	no	—
212	C₄×Dic₁₄₆	C₂³	1	2	yes	—
213	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
214	#14556556	C₂³	1	2	yes	—
215	C₄×D₂₉₂	—	2	1	no	—
216	C₄×D₂₉₂	—	2	1	no	—
217	C₄×D₂₉₂	—	2	1	no	—
218	C₄×D₂₉₂	C₂³	1	2	yes	—
219	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
220	D₄×Dic₇₃	C₂³	1	2	yes	—
221	D₄×Dic₇₃	C₂³	1	2	yes	—
222	#14556553	C₂³	1	2	yes	—
223	C₄×C₂²⋊D₇₃	—	2	2	no	—
224	C₄×C₂²⋊D₇₃	—	2	2	no	—
225	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
226	#14556551	—	2	2	no	—
227	#14556551	—	2	2	no	—
228	#14556550	—	2	1	no	—
229	#14556549	C₂³	1	2	yes	—
230	#14556548	—	2	2	no	—
231	#14556548	—	2	2	no	—
232	#14556548	C₂³	1	2	yes	—
233	#14556547	—	2	2	no	—
234	C₂×C₄⋊Dic₇₃	—	2	1	no	—
235	C₂×C₄⋊Dic₇₃	—	2	1	no	—
236	C₂×#11924007	—	2	2	no	—
237	C₂×#11924007	—	2	2	no	—
238	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
239	C₂×#11924005	—	2	2	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	#14556523	C₂³	1	2	yes	—
245	#14556523	C₂³	1	2	yes	—
246	#14556522	C₂³	1	2	yes	—
247	#14556522	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	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
271	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
272	#135×C₇₃	—	2	4	no	—
273	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
274	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
276	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×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×Q₈×C₇₃	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
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	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
291	#117×C₇₃	—	2	1	no	—
292	#117×C₇₃	—	2	1	no	—
293	#117×C₇₃	C₂³	1	1	yes	characteristic
294	#117×C₇₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₇₃	—	2	1	no	—
296	C₂×C₄²×C₇₃	—	2	1	no	—
297	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
298	#107×C₇₃	C₂³	1	1	yes	characteristic
299	#107×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	#11924027	—	2	4	no	—
317	#11924027	—	4	2	no	—
318	C₂×Dic₁₄₆	—	2	1	no	—
319	C₂×Dic₁₄₆	—	2	1	no	—
320	C₂×Dic₁₄₆	—	2	2	no	—
321	C₂×Dic₁₄₆	—	8	2	no	—
322	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
323	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
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	C₂×D₄	1	2	yes	—
334	D₄×D₇₃	—	2	4	no	—
335	D₄×D₇₃	—	4	2	no	—
336	C₂²×Dic₇₃	—	2	2	no	—
337	C₂²×Dic₇₃	—	2	2	no	—
338	C₂²×Dic₇₃	—	2	2	no	—
339	C₂×C₄×D₇₃	—	2	2	no	—
340	C₂×C₄×D₇₃	—	2	2	no	—
341	C₂×C₄×D₇₃	—	2	2	no	—
342	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
343	#11924018	—	4	2	no	—
344	#11924017	—	2	4	no	—
345	#11924017	—	4	2	no	—
346	#11924016	—	2	4	no	—
347	#11924015	—	4	2	no	—
348	#11924013	—	2	4	no	—
349	#11924011	—	2	4	no	—
350	C₂×#10596831	C₂⁴	1	2	yes	—
351	C₂×#10596831	C₂⁴	1	2	yes	—
352	C₈×D₇₃	—	4	2	no	—
353	C₄⋊Dic₇₃	—	2	1	no	—
354	C₄⋊Dic₇₃	—	2	1	no	—
355	C₄⋊Dic₇₃	—	2	1	no	—
356	C₄⋊Dic₇₃	—	2	1	no	—
357	C₄⋊Dic₇₃	—	2	2	no	—
358	C₄⋊Dic₇₃	—	2	2	no	—
359	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
360	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
361	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
362	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
372	#11924007	—	2	2	no	—
373	#11924007	C₂×D₄	1	2	yes	—
374	#11924007	C₂×D₄	1	2	yes	—
375	#11924007	C₂×D₄	1	2	yes	—
376	#11924007	C₂×D₄	1	2	yes	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	—	2	2	no	—
379	C₂²⋊Dic₇₃	—	2	2	no	—
380	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
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	#11924005	C₂×D₄	1	2	yes	—
392	#11924005	C₂×D₄	1	2	yes	—
393	#11924005	C₂×D₄	1	2	yes	—
394	#11924005	C₂×D₄	1	2	yes	—
395	C₄×Dic₇₃	—	2	2	no	—
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	—	2	2	no	—
398	C₄×Dic₇₃	C₂⁴	1	2	yes	—
399	#41×C₇₃	—	2	2	no	—
400	#41×C₇₃	—	2	2	no	—
401	#41×C₇₃	—	4	1	no	—
402	#41×C₇₃	—	4	1	no	—
403	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
404	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×D₄×C₇₃	—	2	1	no	—
406	C₂×D₄×C₇₃	—	2	1	no	—
407	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₇₃	—	2	1	no	—
410	C₂²×C₄×C₇₃	—	2	1	no	—
411	C₂²×C₄×C₇₃	—	2	1	no	—
412	C₂²×C₄×C₇₃	—	2	1	no	—
413	C₂²×C₄×C₇₃	—	2	1	no	—
414	C₂²×C₄×C₇₃	—	2	1	no	—
415	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
418	Q₁₆×C₇₃	—	2	2	no	—
419	SD₁₆×C₇₃	—	2	2	no	—
420	SD₁₆×C₇₃	—	2	2	no	—
421	D₈×C₇₃	#41	1	4	yes	complemented
422	C₂×C₈×C₇₃	—	2	2	no	—
423	C₂×C₈×C₇₃	—	4	1	no	—
424	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
425	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₄⋊C₄×C₇₃	—	2	1	no	—
429	C₄⋊C₄×C₇₃	—	2	1	no	—
430	C₄⋊C₄×C₇₃	—	2	1	no	—
431	C₄⋊C₄×C₇₃	—	2	1	no	—
432	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
433	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
436	C₂²⋊C₄×C₇₃	—	2	1	no	—
437	C₂²⋊C₄×C₇₃	—	2	1	no	—
438	C₂²⋊C₄×C₇₃	—	2	1	no	—
439	C₂²⋊C₄×C₇₃	—	2	1	no	—
440	C₂²⋊C₄×C₇₃	—	2	1	no	—
441	C₂²⋊C₄×C₇₃	—	2	1	no	—
442	C₄²×C₇₃	—	2	1	no	—
443	C₄²×C₇₃	—	2	1	no	—
444	C₄²×C₇₃	—	2	1	no	—
445	C₄²×C₇₃	—	2	1	no	—
446	C₄²×C₇₃	—	2	1	no	—
447	C₄²×C₇₃	—	2	1	no	—
448	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
449	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
450	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
451	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
452	C₂³×C₇₃	—	2	1	no	—
453	C₂³×C₇₃	—	2	1	no	—
454	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
455	C₂²×D₇₃	—	2	2	no	—
456	C₂²×D₇₃	—	4	4	no	—
457	C₂²×D₇₃	—	8	2	no	—
458	C₂²×D₇₃	—	8	2	no	—
459	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
460	Q₈×C₇₃	—	2	1	no	—
461	Q₈×C₇₃	—	2	1	no	—
462	Q₈×C₇₃	—	2	1	no	—
463	Q₈×C₇₃	—	2	1	no	—
464	D₄×C₇₃	—	2	1	no	—
465	D₄×C₇₃	—	2	1	no	—
466	D₄×C₇₃	—	4	2	no	—
467	D₄×C₇₃	—	4	2	no	—
468	D₄×C₇₃	C₂×#41	1	2	yes	—
469	D₄×C₇₃	C₂×#41	1	2	yes	—
470	C₂×C₄×C₇₃	—	2	2	no	—
471	C₂×C₄×C₇₃	—	2	1	no	—
472	C₂×C₄×C₇₃	—	2	1	no	—
473	C₂×C₄×C₇₃	—	2	1	no	—
474	C₂×C₄×C₇₃	—	2	1	no	—
475	C₂×C₄×C₇₃	—	2	1	no	—
476	C₂×C₄×C₇₃	—	2	1	no	—
477	C₂×C₄×C₇₃	—	2	1	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	4	1	no	—
480	C₂×C₄×C₇₃	—	4	2	no	—
481	C₂×C₄×C₇₃	—	4	2	no	—
482	C₂×C₄×C₇₃	—	4	2	no	—
483	C₂×C₄×C₇₃	—	4	2	no	—
484	C₂×C₄×C₇₃	—	8	1	no	—
485	C₂×C₄×C₇₃	—	8	1	no	—
486	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
492	C₂²⋊D₇₃	—	4	2	no	—
493	C₂²⋊D₇₃	—	4	4	no	—
494	C₂²⋊D₇₃	—	4	4	no	—
495	C₂²⋊D₇₃	—	8	2	no	—
496	C₂×Dic₇₃	—	2	2	no	—
497	C₂×Dic₇₃	—	2	2	no	—
498	C₂×Dic₇₃	—	2	2	no	—
499	C₂×Dic₇₃	—	4	4	no	—
500	C₂×Dic₇₃	—	8	2	no	—
501	C₂×Dic₇₃	—	8	2	no	—
502	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
503	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
504	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
505	D₂₉₂	—	2	2	no	—
506	D₂₉₂	—	2	2	no	—
507	D₂₉₂	—	2	2	no	—
508	D₂₉₂	—	4	2	no	—
509	D₂₉₂	—	8	1	no	—
510	D₂₉₂	—	8	2	no	—
511	C₄×D₇₃	—	2	2	no	—
512	C₄×D₇₃	—	2	2	no	—
513	C₄×D₇₃	—	8	2	no	—
514	C₄×D₇₃	—	8	2	no	—
515	C₄×D₇₃	—	8	2	no	—
516	Dic₁₄₆	—	2	2	no	—
517	Dic₁₄₆	—	2	2	no	—
518	Dic₁₄₆	—	2	2	no	—
519	Dic₁₄₆	—	4	2	no	—
520	Dic₁₄₆	—	8	2	no	—
521	Dic₁₄₆	—	8	1	no	—
522	C₈×C₇₃	—	2	1	no	—
523	C₈×C₇₃	—	2	1	no	—
524	C₈×C₇₃	—	2	1	no	—
525	C₈×C₇₃	C₂×#41	1	2	yes	—
526	#10596831	—	2	2	no	—
527	#10596831	—	2	2	no	—
528	C₂²×C₇₃	—	2	1	no	—
529	C₂²×C₇₃	—	2	2	no	—
530	C₂²×C₇₃	—	2	2	no	—
531	C₂²×C₇₃	—	2	1	no	—
532	C₂²×C₇₃	—	2	1	no	—
533	C₂²×C₇₃	—	4	1	no	—
534	C₂²×C₇₃	—	4	1	no	—
535	C₂²×C₇₃	—	4	1	no	—
536	C₂²×C₇₃	—	4	1	no	—
537	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
538	C₂×D₇₃	—	2	2	no	—
539	C₂×D₇₃	—	2	2	no	—
540	C₂×D₇₃	—	2	2	no	—
541	C₂×D₇₃	—	4	2	no	—
542	C₂×D₇₃	—	4	2	no	—
543	C₂×D₇₃	—	4	2	no	—
544	C₂×D₇₃	—	16	4	no	—
545	C₄×C₇₃	—	2	1	no	—
546	C₄×C₇₃	—	2	1	no	—
547	C₄×C₇₃	—	2	1	no	—
548	C₄×C₇₃	—	2	1	no	—
549	C₄×C₇₃	—	4	1	no	—
550	C₄×C₇₃	—	4	1	no	—
551	C₄×C₇₃	—	4	1	no	—
552	C₄×C₇₃	—	4	1	no	—
553	C₄×C₇₃	—	4	1	no	—
554	C₄×C₇₃	—	4	1	no	—
555	C₄×C₇₃	#577	1	2	yes	—
556	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
557	C₄×C₇₃	#585	1	1	yes	characteristic
558	Dic₇₃	—	2	2	no	—
559	Dic₇₃	—	2	2	no	—
560	Dic₇₃	—	2	2	no	—
561	Dic₇₃	—	4	2	no	—
562	Dic₇₃	—	4	2	no	—
563	Dic₇₃	—	4	2	no	—
564	#61493	—	73	1	no	maximal, Sylow
565	C₂×C₇₃	—	4	2	no	—
566	C₂×C₇₃	—	4	1	no	—
567	C₂×C₇₃	—	4	2	no	—
568	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
569	C₂×C₇₃	C₂×#577	1	1	yes	characteristic
570	C₂×C₇₃	#3584	1	1	yes	characteristic
571	D₇₃	—	4	2	no	—
572	D₇₃	—	8	2	no	—
573	#3515	—	73	1	no	—
574	#3514	—	73	1	no	—
575	#3400	—	73	1	no	—
576	#3384	—	73	1	no	—
577	#3361	—	73	1	no	—
578	#3359	—	73	1	no	—
579	#3356	—	73	1	no	—
580	#3348	—	73	2	no	—
581	#3303	—	73	2	no	—
582	#3302	—	73	1	no	—
583	#3296	—	73	2	no	—
584	#3295	—	73	1	no	—
585	#3272	—	73	1	no	—
586	#3267	—	73	2	no	—
587	#3178	—	73	2	no	—
588	#3167	—	73	1	no	—
589	#3125	—	73	2	no	—
590	#3123	—	73	2	no	—
591	#3116	—	73	1	no	—
592	#3115	—	73	1	no	—
593	#2966	—	73	1	no	—
594	#2946	—	73	2	no	—
595	C₄×#135	D₇₃	1	1	yes	characteristic, complemented
596	C₇₃	#61493	1	1	yes	characteristic, complemented, Sylow
597	C₂×AGL(1,ℤ/8)	—	73	2	no	—
598	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
599	#559	—	73	1	no	—
600	#557	—	73	1	no	—
601	#556	—	73	1	no	—
602	#555	—	73	2	no	—
603	#554	—	73	1	no	—
604	#554	—	73	1	no	—
605	#553	—	146	1	no	—
606	#552	—	73	2	no	—
607	#552	—	146	2	no	—
608	#552	—	146	1	no	—
609	#551	—	146	2	no	—
610	D₄×Q₈	—	73	1	no	—
611	#548	—	146	1	no	—
612	#547	—	73	2	no	—
613	#547	—	73	1	no	—
614	#546	—	73	2	no	—
615	#546	—	146	1	no	—
616	D₄²	—	73	1	no	—
617	#542	—	73	2	no	—
618	#541	—	73	2	no	—
619	#539	—	146	2	no	—
620	#538	—	146	2	no	—
621	#533	—	73	1	no	—
622	#532	—	73	1	no	—
623	#529	—	73	1	no	—
624	#529	—	146	1	no	—
625	#529	—	146	1	no	—
626	C₂×#125	—	146	1	no	—
627	C₂×#124	—	146	1	no	—
628	#520	—	73	2	no	—
629	#518	—	73	2	no	—
630	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
631	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
632	#501	—	73	2	no	—
633	#498	—	73	1	no	—
634	#497	—	73	2	no	—
635	#492	—	73	1	no	—
636	#488	—	73	2	no	—
637	#487	—	73	2	no	—
638	#487	—	73	1	no	—
639	#486	—	73	1	no	—
640	#485	—	73	2	no	—
641	#485	—	73	2	no	—
642	#485	—	73	2	no	—
643	#483	—	73	2	no	—
644	#482	—	73	2	no	—
645	#481	—	73	2	no	—
646	#478	—	73	2	no	—
647	#478	—	73	2	no	—
648	#477	—	73	1	no	—
649	#476	—	73	1	no	—
650	#476	—	73	2	no	—
651	#475	—	73	1	no	—
652	#475	—	73	2	no	—
653	#474	—	73	1	no	—
654	#470	—	73	2	no	—
655	#468	—	73	2	no	—
656	#467	—	73	2	no	—
657	#465	—	73	2	no	—
658	#465	—	73	2	no	—
659	#465	—	73	2	no	—
660	#464	—	73	2	no	—
661	#463	—	73	2	no	—
662	#462	—	73	1	no	—
663	#461	—	73	2	no	—
664	#461	—	73	1	no	—
665	#461	—	73	2	no	—
666	#460	—	73	1	no	—
667	#459	—	73	1	no	—
668	#452	—	73	2	no	—
669	#452	—	73	2	no	—
670	#450	—	73	2	no	—
671	#450	—	73	2	no	—
672	#449	—	73	2	no	—
673	#449	—	73	2	no	—
674	#446	—	73	1	no	—
675	C₈×Q₈	—	73	1	no	—
676	#442	—	73	2	no	—
677	#442	—	73	2	no	—
678	#441	—	73	2	no	—
679	#440	—	73	2	no	—
680	#440	—	73	2	no	—
681	#440	—	73	2	no	—
682	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
683	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
684	C₄×SD₁₆	—	73	2	no	—
685	C₄×SD₁₆	—	73	2	no	—
686	C₄×SD₁₆	—	73	2	no	—
687	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
688	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
689	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
690	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
691	C₄×D₈	—	73	2	no	—
692	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
693	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
694	#436	—	73	1	no	—
695	#435	—	73	2	no	—
696	C₈×D₄	—	73	2	no	—
697	C₈×D₄	—	73	1	no	—
698	#433	—	73	2	no	—
699	#432	—	73	1	no	—
700	#428	—	73	2	no	—
701	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
702	#416	—	73	2	no	—
703	#416	C₂×D₇₃	1	1	yes	characteristic
704	#416	C₂×D₇₃	1	1	yes	characteristic, complemented
705	C₂×#102	—	73	2	no	—
706	#405	—	73	2	no	—
707	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
708	C₂×#41	—	73	2	no	—
709	C₂×#41	—	146	1	no	—
710	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
711	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
712	C₂²×Q₈	—	146	1	no	—
713	C₂²×D₄	—	73	2	no	—
714	C₂²×D₄	—	146	1	no	—
715	AGL(1,ℤ/8)	—	146	8	no	—
716	#135	—	2	4	no	—
717	C₂×Q₁₆	—	73	2	no	—
718	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
719	C₂×SD₁₆	—	73	2	no	—
720	C₂×SD₁₆	—	73	2	no	—
721	C₂×SD₁₆	—	73	2	no	—
722	C₂×SD₁₆	—	73	2	no	—
723	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
724	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
725	C₂×D₈	—	73	2	no	—
726	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
727	C₂×M₁₆	—	73	2	no	—
728	C₂²×C₈	—	73	2	no	—
729	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
730	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
731	C₄⋊Q₈	—	73	2	no	—
732	C₄⋊Q₈	—	73	2	no	—
733	C₄⋊Q₈	—	73	1	no	—
734	C₄⋊Q₈	—	73	1	no	—
735	C₄⋊Q₈	—	73	1	no	—
736	#127	—	73	1	no	—
737	#126	—	73	2	no	—
738	#126	—	146	2	no	—
739	#126	—	146	2	no	—
740	#126	—	146	2	no	—
741	#126	—	146	2	no	—
742	#126	—	146	2	no	—
743	#125	—	73	2	no	—
744	#125	—	73	1	no	—
745	#125	—	146	2	no	—
746	#125	—	146	2	no	—
747	#125	—	146	1	no	—
748	#125	—	146	1	no	—
749	#125	—	146	2	no	—
750	#125	—	146	2	no	—
751	#125	—	146	1	no	—
752	#124	—	73	2	no	—
753	#124	—	73	1	no	—
754	#124	—	146	2	no	—
755	#124	—	146	2	no	—
756	#124	—	146	1	no	—
757	#124	—	146	1	no	—
758	#124	—	146	2	no	—
759	#124	—	146	1	no	—
760	#123	—	73	2	no	—
761	#123	—	146	2	no	—
762	#123	—	146	2	no	—
763	#123	—	146	2	no	—
764	#123	—	146	2	no	—
765	#123	—	146	2	no	—
766	#123	—	146	2	no	—
767	#123	—	146	2	no	—
768	C₂²⋊Q₈	—	73	1	no	—
769	C₂²⋊Q₈	—	73	2	no	—
770	C₂²⋊Q₈	—	73	2	no	—
771	C₂²⋊Q₈	—	73	2	no	—
772	C₂²⋊Q₈	—	73	2	no	—
773	C₂²⋊Q₈	—	146	2	no	—
774	C₂²⋊Q₈	—	146	2	no	—
775	C₂²⋊Q₈	—	146	2	no	—
776	C₂²⋊Q₈	—	146	2	no	—
777	C₂²⋊Q₈	—	146	1	no	—
778	C₂²⋊Q₈	—	146	1	no	—
779	C₂²⋊Q₈	—	146	1	no	—
780	#121	—	73	1	no	—
781	#121	—	73	2	no	—
782	#121	—	73	2	no	—
783	#121	—	146	2	no	—
784	#121	—	146	2	no	—
785	#121	—	146	1	no	—
786	#121	—	146	1	no	—
787	#121	—	146	2	no	—
788	#121	—	146	1	no	—
789	#120	—	146	2	no	—
790	#120	—	146	2	no	—
791	C₄×Q₈	—	73	1	no	—
792	C₄×Q₈	—	73	2	no	—
793	C₄×Q₈	—	73	2	no	—
794	C₄×Q₈	—	146	1	no	—
795	C₄×Q₈	—	146	1	no	—
796	C₄×Q₈	—	146	1	no	—
797	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
798	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	73	2	no	—
806	C₄×D₄	—	73	2	no	—
807	C₄×D₄	—	73	2	no	—
808	C₄×D₄	—	73	2	no	—
809	C₄×D₄	—	73	1	no	—
810	C₄×D₄	—	73	2	no	—
811	C₄×D₄	—	146	1	no	—
812	C₄×D₄	—	146	1	no	—
813	C₄×D₄	—	146	2	no	—
814	C₄×D₄	—	146	2	no	—
815	C₄×D₄	—	146	2	no	—
816	C₄×D₄	—	146	2	no	—
817	C₄×D₄	—	146	1	no	—
818	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
819	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
820	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
822	#117	—	2	1	no	—
823	#117	—	2	1	no	—
824	#117	—	73	2	no	—
825	#117	—	73	2	no	—
826	#117	—	146	2	no	—
827	#117	—	146	2	no	—
828	#117	—	146	2	no	—
829	#117	—	146	1	no	—
830	#117	C₂²×D₇₃	1	1	yes	characteristic
831	#117	C₂²×D₇₃	1	1	yes	characteristic
832	C₂×C₄⋊C₄	—	73	2	no	—
833	C₂×C₄⋊C₄	—	146	2	no	—
834	C₂×C₄⋊C₄	—	146	2	no	—
835	C₂×C₄⋊C₄	—	146	1	no	—
836	C₂×C₄⋊C₄	—	146	1	no	—
837	C₂×C₂²⋊C₄	—	146	2	no	—
838	C₂×C₂²⋊C₄	—	146	2	no	—
839	C₂×C₂²⋊C₄	—	146	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	2	1	no	—
842	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
843	#107	—	73	2	no	—
844	#107	—	73	2	no	—
845	#107	C₂²×D₇₃	1	1	yes	characteristic
846	#107	C₂²×D₇₃	1	1	yes	characteristic
847	#106	—	73	2	no	—
848	#106	—	73	2	no	—
849	#106	—	73	2	no	—
850	#106	—	73	2	no	—
851	#106	C₂²×D₇₃	1	1	yes	characteristic
852	#106	C₂²×D₇₃	1	1	yes	characteristic
853	C₄⋊C₈	—	73	2	no	—
854	C₄⋊C₈	—	73	2	no	—
855	C₄⋊C₈	—	73	1	no	—
856	C₄⋊C₈	—	73	1	no	—
857	#103	—	73	2	no	—
858	#103	—	73	2	no	—
859	#103	—	73	2	no	—
860	#103	—	73	2	no	—
861	#103	—	73	2	no	—
862	#103	—	73	2	no	—
863	#103	C₂²×D₇₃	1	1	yes	characteristic
864	#103	C₂²×D₇₃	1	1	yes	characteristic
865	#103	C₂²×D₇₃	1	1	yes	characteristic
866	#103	C₂²×D₇₃	1	1	yes	characteristic
867	#102	—	73	2	no	—
868	#102	—	73	2	no	—
869	#102	—	73	2	no	—
870	#102	—	73	2	no	—
871	#102	—	73	2	no	—
872	#102	—	73	2	no	—
873	#102	C₂²×D₇₃	1	1	yes	characteristic
874	#102	C₂²×D₇₃	1	1	yes	characteristic
875	#102	C₂²×D₇₃	1	1	yes	characteristic
876	#102	C₂²×D₇₃	1	1	yes	characteristic
877	C₂²⋊C₈	—	73	2	no	—
878	C₂²⋊C₈	—	73	2	no	—
879	C₂²⋊C₈	—	73	2	no	—
880	#97	—	73	2	no	—
881	#97	—	73	2	no	—
882	C₄×C₈	—	73	2	no	—
883	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
884	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
885	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
886	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
887	C₂⁴	—	146	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	2	no	—
890	#41	—	4	1	no	—
891	#41	—	4	1	no	—
892	#41	—	292	2	no	—
893	#41	—	584	2	no	—
894	#41	—	146	4	no	—
895	C₂×Q₈	—	584	2	no	—
896	C₂×Q₈	—	73	1	no	—
897	C₂×Q₈	—	73	2	no	—
898	C₂×Q₈	—	146	2	no	—
899	C₂×Q₈	—	146	1	no	—
900	C₂×Q₈	—	146	1	no	—
901	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
902	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	1	no	—
905	C₂×D₄	—	292	2	no	—
906	C₂×D₄	—	584	2	no	—
907	C₂×D₄	—	73	2	no	—
908	C₂×D₄	—	73	1	no	—
909	C₂×D₄	—	73	2	no	—
910	C₂×D₄	—	146	2	no	—
911	C₂×D₄	—	146	2	no	—
912	C₂×D₄	—	146	2	no	—
913	C₂×D₄	—	146	4	no	—
914	C₂×D₄	—	146	2	no	—
915	C₂×D₄	—	146	1	no	—
916	C₂×D₄	—	146	1	no	—
917	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
918	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
919	C₂²×C₄	—	2	1	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	73	2	no	—
926	C₂²×C₄	—	146	2	no	—
927	C₂²×C₄	—	146	2	no	—
928	C₂²×C₄	—	146	2	no	—
929	C₂²×C₄	—	146	2	no	—
930	C₂²×C₄	—	146	2	no	—
931	C₂²×C₄	—	146	2	no	—
932	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
933	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
935	Q₁₆	—	2	2	no	—
936	Q₁₆	—	292	2	no	—
937	SD₁₆	—	2	2	no	—
938	SD₁₆	—	2	2	no	—
939	SD₁₆	—	292	2	no	—
940	SD₁₆	—	292	2	no	—
941	SD₁₆	—	146	4	no	—
942	SD₁₆	—	146	4	no	—
943	D₈	—	146	4	no	—
944	D₈	#11924028	1	4	yes	complemented
945	M₁₆	—	146	4	no	—
946	C₂×C₈	—	2	2	no	—
947	C₂×C₈	—	4	1	no	—
948	C₂×C₈	—	292	2	no	—
949	C₂×C₈	—	73	2	no	—
950	C₂×C₈	—	73	2	no	—
951	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
952	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
953	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
954	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	73	2	no	—
960	C₄⋊C₄	—	73	2	no	—
961	C₄⋊C₄	—	73	2	no	—
962	C₄⋊C₄	—	73	2	no	—
963	C₄⋊C₄	—	73	1	no	—
964	C₄⋊C₄	—	73	1	no	—
965	C₄⋊C₄	—	73	2	no	—
966	C₄⋊C₄	—	73	2	no	—
967	C₄⋊C₄	—	146	2	no	—
968	C₄⋊C₄	—	146	2	no	—
969	C₄⋊C₄	—	146	2	no	—
970	C₄⋊C₄	—	146	2	no	—
971	C₄⋊C₄	—	146	2	no	—
972	C₄⋊C₄	—	146	2	no	—
973	C₄⋊C₄	—	146	2	no	—
974	C₄⋊C₄	—	146	2	no	—
975	C₄⋊C₄	—	146	2	no	—
976	C₄⋊C₄	—	146	2	no	—
977	C₄⋊C₄	—	146	2	no	—
978	C₄⋊C₄	—	146	2	no	—
979	C₄⋊C₄	—	146	1	no	—
980	C₄⋊C₄	—	146	1	no	—
981	C₄⋊C₄	—	146	1	no	—
982	C₄⋊C₄	—	146	1	no	—
983	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
985	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
986	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	1	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	73	2	no	—
994	C₂²⋊C₄	—	73	2	no	—
995	C₂²⋊C₄	—	73	2	no	—
996	C₂²⋊C₄	—	73	2	no	—
997	C₂²⋊C₄	—	73	2	no	—
998	C₂²⋊C₄	—	146	2	no	—
999	C₂²⋊C₄	—	146	2	no	—
1000	C₂²⋊C₄	—	146	2	no	—
1001	C₂²⋊C₄	—	146	2	no	—
1002	C₂²⋊C₄	—	146	2	no	—
1003	C₂²⋊C₄	—	146	2	no	—
1004	C₂²⋊C₄	—	146	2	no	—
1005	C₂²⋊C₄	—	146	2	no	—
1006	C₂²⋊C₄	—	146	2	no	—
1007	C₂²⋊C₄	—	146	2	no	—
1008	C₂²⋊C₄	—	146	2	no	—
1009	C₂²⋊C₄	—	146	2	no	—
1010	C₂²⋊C₄	—	146	2	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	1	no	—
1015	C₄²	—	2	1	no	—
1016	C₄²	—	2	1	no	—
1017	C₄²	—	73	2	no	—
1018	C₄²	—	146	2	no	—
1019	C₄²	—	146	2	no	—
1020	C₄²	—	146	2	no	—
1021	C₄²	D₄×D₇₃	1	1	yes	characteristic
1022	C₄²	D₄×D₇₃	1	1	yes	characteristic
1023	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1024	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1025	C₂³	—	2	1	no	—
1026	C₂³	—	2	1	no	—
1027	C₂³	—	292	4	no	—
1028	C₂³	—	584	2	no	—
1029	C₂³	—	584	2	no	—
1030	C₂³	—	73	2	no	—
1031	C₂³	—	146	2	no	—
1032	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1033	Q₈	—	2	1	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	292	2	no	—
1038	Q₈	—	584	1	no	—
1039	Q₈	—	584	2	no	—
1040	Q₈	—	146	2	no	—
1041	Q₈	—	146	2	no	—
1042	Q₈	—	146	2	no	—
1043	D₄	—	2	1	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	292	4	no	—
1048	D₄	—	292	4	no	—
1049	D₄	—	292	2	no	—
1050	D₄	—	292	2	no	—
1051	D₄	—	584	1	no	—
1052	D₄	—	584	2	no	—
1053	D₄	—	584	2	no	—
1054	D₄	—	146	2	no	—
1055	D₄	—	146	2	no	—
1056	D₄	—	146	2	no	—
1057	D₄	C₂×#11924028	1	2	yes	—
1058	D₄	C₂×#11924028	1	2	yes	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	1	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	4	1	no	—
1069	C₂×C₄	—	4	2	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	2	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	1	no	—
1075	C₂×C₄	—	292	4	no	—
1076	C₂×C₄	—	584	2	no	—
1077	C₂×C₄	—	584	2	no	—
1078	C₂×C₄	—	584	2	no	—
1079	C₂×C₄	—	584	2	no	—
1080	C₂×C₄	—	584	2	no	—
1081	C₂×C₄	—	73	2	no	—
1082	C₂×C₄	—	73	2	no	—
1083	C₂×C₄	—	73	2	no	—
1084	C₂×C₄	—	146	2	no	—
1085	C₂×C₄	—	146	2	no	—
1086	C₂×C₄	—	146	2	no	—
1087	C₂×C₄	—	146	2	no	—
1088	C₂×C₄	—	146	2	no	—
1089	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1090	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1091	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1092	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1093	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1094	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1095	C₈	—	2	1	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	146	2	no	—
1099	C₈	—	146	2	no	—
1100	C₈	C₂×#11924028	1	2	yes	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	1	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	4	1	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	292	2	no	—
1111	C₂²	—	292	2	no	—
1112	C₂²	—	292	2	no	—
1113	C₂²	—	1168	4	no	—
1114	C₂²	—	146	2	no	—
1115	C₂²	—	146	2	no	—
1116	C₂²	—	146	2	no	—
1117	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	1	no	—
1122	C₄	—	4	1	no	—
1123	C₄	—	4	1	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	292	2	no	—
1129	C₄	—	292	2	no	—
1130	C₄	—	292	2	no	—
1131	C₄	—	146	2	no	—
1132	C₄	—	146	2	no	—
1133	C₄	—	146	2	no	—
1134	C₄	#17989394	1	2	yes	—
1135	C₄	C₂²×#11924028	1	1	yes	characteristic
1136	C₄	#17989423	1	1	yes	characteristic
1137	C₂	—	4	1	no	—
1138	C₂	—	4	2	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	292	2	no	—
1141	C₂	—	584	2	no	—
1142	C₂	D₄×#11924028	1	1	yes	characteristic
1143	C₂	C₂×#17989394	1	1	yes	characteristic
1144	C₂	#22624700	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₄×#135×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	C₄×#135	D₇₃
hypocenter	C₇₃	#61493
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22623909	C₂	semidirect
2. #22623892	C₂	semidirect
3. #22622982	C₂	semidirect
4. #22622828	C₂	semidirect
5. #22622589	C₂	semidirect
6. #22622571	C₂	semidirect
7. #22622548	C₂	semidirect
8. #22622442	C₂	semidirect
9. #22621855	C₂	semidirect
10. #22621850	C₂	semidirect
11. #22621767	C₂	semidirect
12. #22621757	C₂	semidirect
13. #22621532	C₂	semidirect
14. #22621456	C₂	semidirect
15. #22620603	C₂	semidirect
16. #22620490	C₂	semidirect
17. #22620204	C₂	semidirect
18. #22620180	C₂	semidirect
19. #22620093	C₂	semidirect
20. #22620082	C₂	semidirect
21. #22618906	C₂	semidirect
22. #22618756	C₂	semidirect
23. C₄×#135×C₇₃	C₂	semidirect
26. #17989315	C₂²	semidirect
30. #17989294	C₂²	semidirect
33. #17989276	C₂²	semidirect
39. #17989236	C₂²	semidirect
44. #17989195	C₂²	semidirect
47. #17989144	C₂²	semidirect
54. #17989066	C₂²	semidirect
56. #17988995	C₂²	semidirect
57. #17988985	C₂²	semidirect
58. #17988980	C₂²	semidirect
60. #17988943	C₂²	semidirect
61. #17988938	C₂²	semidirect
62. #17988936	C₂²	semidirect
64. #17988931	C₂²	semidirect
65. #17988928	C₂²	semidirect
66. #17988926	C₂²	semidirect
67. #17988916	C₂²	semidirect
68. #17988911	C₂²	semidirect
71. #17988886	C₂²	semidirect
72. #17988882	C₂²	semidirect
74. #17988875	C₂²	semidirect
75. #17988872	C₂²	semidirect
76. #17988871	C₂²	semidirect
77. #17988867	C₂²	semidirect
78. #17988842	C₂²	semidirect
80. #17988827	C₂²	semidirect
82. #17988816	C₂²	semidirect
83. #17988816	C₂²	semidirect
84. #17988812	C₂²	semidirect
85. #17988804	C₂²	semidirect
86. #17988797	C₂²	semidirect
88. #17988791	C₂²	semidirect
93. #17988746	C₂²	semidirect
97. #17988732	C₂²	semidirect
98. #17988717	C₂²	semidirect
99. C₈×Dic₁₄₆	C₂²	semidirect
101. #17988697	C₂²	semidirect
102. #17988692	C₂²	semidirect
104. #17988686	C₂²	semidirect
105. #17988685	C₂²	semidirect
107. C₄×#11924017	C₂²	semidirect
108. C₄×#11924017	C₂²	semidirect
109. #17988667	C₂²	semidirect
111. #17988658	C₂²	semidirect
113. C₈×C₂²⋊D₇₃	C₂²	semidirect
114. #17988646	C₂²	semidirect
115. #17988644	C₂²	semidirect
116. #17988628	C₂²	semidirect
117. #17988580	C₂²	semidirect
119. #17988541	C₂²	semidirect
122. C₄×#41×C₇₃	C₂²	semidirect
123. C₄×Q₁₆×C₇₃	C₂²	semidirect
124. C₄×Q₁₆×C₇₃	C₂²	semidirect
127. C₄×SD₁₆×C₇₃	C₂²	semidirect
128. C₄×SD₁₆×C₇₃	C₂²	semidirect
131. #427×C₇₃	C₂²	semidirect
133. #416×C₇₃	C₂²	semidirect
134. C₂×C₄×C₈×C₇₃	C₂²	semidirect
421. D₈×C₇₃	#41	semidirect
595. C₄×#135	D₇₃	semidirect
596. C₇₃	#61493	semidirect
631. C₄×#41	C₂×D₇₃	semidirect
682. C₄×Q₁₆	C₂×D₇₃	semidirect
683. C₄×Q₁₆	C₂×D₇₃	semidirect
689. C₄×SD₁₆	C₂×D₇₃	semidirect
690. C₄×SD₁₆	C₂×D₇₃	semidirect
701. #427	C₂×D₇₃	semidirect
704. #416	C₂×D₇₃	semidirect
707. C₂×C₄×C₈	C₂×D₇₃	semidirect
944. D₈	#11924028	semidirect

Maximal subgroups

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

subgroup	index
#22623909	2
#22623892	2
#22622982	2
#22622828	2
#22622589	2
#22622571	2
#22622548	2
#22622442	2
#22621855	2
#22621850	2
#22621767	2
#22621757	2
#22621532	2
#22621456	2
#22620603	2
#22620490	2
#22620204	2
#22620180	2
#22620093	2
#22620082	2
#22618906	2
#22618756	2
C₄×#135×C₇₃	2
#61493	73