Subgroups — #33964357

Order 18688.

2088 conjugacy classes of subgroups.

The subgroup lattice has 1236 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623842	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623724	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622122	C₂	1	2	yes	maximal, complemented
4	#22622092	C₂	1	2	yes	maximal, complemented
5	#22622047	C₂	1	2	yes	maximal, complemented
6	#22622017	C₂	1	2	yes	maximal, complemented
7	#22622002	C₂	1	2	yes	maximal, complemented
8	#22621972	C₂	1	2	yes	maximal, complemented
9	#22621927	C₂	1	2	yes	maximal, complemented
10	#22621897	C₂	1	2	yes	maximal, complemented
11	C₂×#17988947	C₂	1	1	yes	maximal, characteristic, complemented
12	#22619903	C₂	1	1	yes	maximal, characteristic, complemented
13	#22619892	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619746	C₂	1	1	yes	maximal, characteristic, complemented
15	#22619625	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619614	C₂	1	1	yes	maximal, characteristic, complemented
17	#22619425	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619242	C₂	1	1	yes	maximal, characteristic, complemented
19	#22619231	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618650	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618460	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618453	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2943	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556638	C₂²	1	1	yes	characteristic
25	C₂×#14556637	C₂²	1	1	yes	characteristic
26	C₂×#14556621	C₂²	1	1	yes	characteristic, complemented
27	C₂×#14556616	C₂²	1	1	yes	characteristic
28	C₂×#14556597	C₂²	1	1	yes	characteristic
29	C₂×#14556597	C₂²	1	1	yes	characteristic, complemented
30	#17989310	C₂²	1	2	yes	complemented
31	#17989302	C₂²	1	2	yes	complemented
32	#17989297	C₂²	1	2	yes	complemented
33	#17989283	—	2	2	no	—
34	#17989249	C₂²	1	2	yes	—
35	#17989249	C₂²	1	2	yes	—
36	#17989246	—	2	2	no	—
37	#17989242	C₂²	1	2	yes	complemented
38	#17989232	—	2	2	no	—
39	#17989232	—	2	2	no	—
40	#17989232	C₂²	1	2	yes	—
41	#17989232	C₂²	1	2	yes	—
42	#17989208	—	2	1	no	—
43	#17989208	—	2	1	no	—
44	#17989165	C₂²	1	1	yes	characteristic
45	#17989165	C₂²	1	1	yes	characteristic, complemented
46	#17989163	—	2	1	no	—
47	#17989163	C₂²	1	1	yes	characteristic
48	#17989156	—	2	1	no	—
49	#17989156	C₂²	1	1	yes	characteristic
50	#17989144	—	2	1	no	—
51	#17989137	—	2	1	no	—
52	#17989137	—	2	1	no	—
53	#17989137	C₂²	1	1	yes	characteristic
54	C₂×#14556591	C₂²	1	1	yes	characteristic, complemented
55	C₂×#14556579	—	2	1	no	—
56	C₂×#14556579	C₂²	1	1	yes	characteristic
57	#17989067	C₂²	1	1	yes	characteristic
58	#17989067	C₂²	1	1	yes	characteristic, complemented
59	#17988947	C₂²	1	2	yes	complemented
60	#17988947	C₂²	1	2	yes	complemented
61	#17988947	C₂²	1	2	yes	complemented
62	#17988947	C₂²	1	2	yes	complemented
63	#17988931	C₂²	1	2	yes	complemented
64	#17988930	C₂²	1	2	yes	complemented
65	#17988924	C₂²	1	2	yes	complemented
66	#17988919	C₂²	1	2	yes	complemented
67	#17988914	C₂²	1	2	yes	complemented
68	#17988913	C₂²	1	2	yes	complemented
69	#17988907	C₂²	1	2	yes	complemented
70	#17988902	C₂²	1	2	yes	complemented
71	#17988882	C₂²	1	2	yes	complemented
72	#17988877	C₂²	1	2	yes	complemented
73	#17988872	C₂²	1	2	yes	complemented
74	#17988867	C₂²	1	2	yes	complemented
75	#17988844	C₂²	1	2	yes	complemented
76	#17988839	C₂²	1	2	yes	complemented
77	#17988836	C₂²	1	2	yes	complemented
78	#17988832	C₂²	1	2	yes	complemented
79	#17988827	C₂²	1	2	yes	complemented
80	#17988822	C₂²	1	2	yes	complemented
81	#17988819	C₂²	1	2	yes	complemented
82	#17988815	C₂²	1	2	yes	complemented
83	#17988809	C₂²	1	2	yes	complemented
84	#17988809	C₂²	1	2	yes	complemented
85	#17988802	C₂²	1	2	yes	complemented
86	#17988802	C₂²	1	2	yes	complemented
87	#17988748	C₂²	1	2	yes	—
88	#17988746	C₂²	1	2	yes	complemented
89	#17988741	C₂²	1	2	yes	complemented
90	#17988736	C₂²	1	2	yes	—
91	#17988731	C₂²	1	2	yes	—
92	#17988729	C₂²	1	2	yes	complemented
93	#17988724	C₂²	1	2	yes	complemented
94	#17988719	C₂²	1	2	yes	—
95	#17988660	C₂²	1	2	yes	complemented
96	#17988660	C₂²	1	2	yes	complemented
97	#17988660	C₂²	1	2	yes	complemented
98	#17988660	C₂²	1	2	yes	complemented
99	#17988630	C₂²	1	1	yes	characteristic, complemented
100	#17988630	C₂²	1	1	yes	characteristic, complemented
101	#17988611	C₂²	1	1	yes	characteristic, complemented
102	#17988595	C₂²	1	1	yes	characteristic, complemented
103	#17988594	C₂²	1	2	yes	complemented
104	#17988591	C₂²	1	1	yes	characteristic
105	#17988590	C₂²	1	2	yes	—
106	#17988588	C₂²	1	1	yes	characteristic
107	#17988588	C₂²	1	1	yes	characteristic
108	#17988587	C₂²	1	2	yes	—
109	#17988585	C₂²	1	2	yes	complemented
110	#17988582	C₂²	1	2	yes	—
111	#17988580	C₂²	1	2	yes	complemented
112	C₂×#14556516	C₂²	1	1	yes	characteristic, complemented
113	C₂×#14556516	C₂²	1	1	yes	characteristic, complemented
114	#103×D₇₃	C₂²	1	2	yes	complemented
115	C₂×#14556513	C₂²	1	1	yes	characteristic
116	C₂×#14556513	C₂²	1	1	yes	characteristic
117	#102×D₇₃	C₂²	1	2	yes	—
118	#17988553	C₂²	1	1	yes	characteristic
119	#17988553	C₂²	1	1	yes	characteristic, 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	#442×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#442×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#440×C₇₃	C₂²	1	1	yes	characteristic, complemented
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×#97×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	#14556638	—	2	4	no	—
136	#14556638	—	4	2	no	—
137	#14556637	—	2	4	no	—
138	#14556637	—	4	2	no	—
139	C₂×#11924029	C₂³	1	2	yes	—
140	C₂×#11924028	—	2	1	no	—
141	C₂×#11924028	—	2	1	no	—
142	C₂×#11924028	—	2	2	no	—
143	C₂×#11924028	C₂³	1	1	yes	characteristic
144	C₂×#11924028	C₂³	1	1	yes	characteristic
145	C₂×#11924027	—	2	2	no	—
146	C₂×#11924027	C₂³	1	2	yes	—
147	C₂²×Dic₁₄₆	—	2	1	no	—
148	C₂²×Dic₁₄₆	—	2	1	no	—
149	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
150	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
151	C₂²×D₂₉₂	—	2	1	no	—
152	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
153	C₂×D₄×D₇₃	—	2	2	no	—
154	C₂×D₄×D₇₃	C₂³	1	2	yes	—
155	#14556621	—	4	2	no	—
156	#14556616	—	4	2	no	—
157	C₂×#11924018	C₂³	1	2	yes	—
158	C₂×#11924016	C₂³	1	2	yes	—
159	C₂×#11924015	C₂³	1	2	yes	—
160	C₂×#11924013	C₂³	1	2	yes	—
161	#14556597	—	4	2	no	—
162	#14556597	—	4	2	no	—
163	C₂×#11924012	C₂³	1	1	yes	characteristic
164	C₂×#11924012	C₂³	1	1	yes	characteristic
165	C₂×#11924011	C₂³	1	2	yes	—
166	C₂×#11924011	C₂³	1	2	yes	—
167	C₂×C₈×D₇₃	C₂³	1	2	yes	—
168	C₂×C₈×D₇₃	C₂³	1	2	yes	—
169	#14556591	—	2	1	no	—
170	#14556591	—	2	1	no	—
171	#14556591	—	2	1	no	—
172	#14556591	D₄	1	1	yes	characteristic
173	#14556591	C₂³	1	2	yes	—
174	#14556591	C₂³	1	2	yes	—
175	#14556588	—	2	1	no	—
176	#14556588	D₄	1	1	yes	characteristic
177	#14556586	—	2	2	no	—
178	#14556586	—	2	2	no	—
179	#14556583	—	2	2	no	—
180	#14556579	—	2	1	no	—
181	#14556579	—	2	2	no	—
182	#14556579	—	2	1	no	—
183	#14556579	—	2	2	no	—
184	#14556579	—	2	2	no	—
185	#14556579	—	2	1	no	—
186	#14556579	—	2	1	no	—
187	#14556579	D₄	1	1	yes	characteristic
188	#14556579	D₄	1	1	yes	characteristic
189	#14556579	C₂³	1	2	yes	—
190	#14556579	C₂³	1	2	yes	—
191	#14556577	—	2	2	no	—
192	#14556577	—	2	2	no	—
193	#14556575	—	2	2	no	—
194	#14556575	—	2	2	no	—
195	#14556575	—	2	2	no	—
196	#14556573	—	2	2	no	—
197	#14556573	—	2	2	no	—
198	#14556571	—	2	2	no	—
199	#14556571	—	2	2	no	—
200	#14556571	C₂³	1	2	yes	—
201	#14556571	C₂³	1	2	yes	—
202	#14556570	—	2	1	no	—
203	#14556570	—	2	1	no	—
204	#14556570	—	2	2	no	—
205	#14556569	—	2	2	no	—
206	#14556569	—	2	2	no	—
207	#14556567	C₂³	1	2	yes	—
208	#14556567	C₂³	1	2	yes	—
209	#14556566	—	2	2	no	—
210	#14556566	—	2	2	no	—
211	#14556566	C₂³	1	2	yes	—
212	#14556566	C₂³	1	2	yes	—
213	#14556565	—	2	1	no	—
214	#14556565	—	2	1	no	—
215	#14556565	—	2	2	no	—
216	#14556565	—	2	2	no	—
217	#14556565	—	2	2	no	—
218	#14556565	D₄	1	2	yes	—
219	#14556565	D₄	1	2	yes	—
220	#14556563	—	2	2	no	—
221	#14556563	—	2	2	no	—
222	#14556562	C₂³	1	2	yes	—
223	#14556562	C₂³	1	2	yes	—
224	#14556561	—	2	2	no	—
225	#14556561	—	2	2	no	—
226	#14556561	—	2	2	no	—
227	C₄×Dic₁₄₆	—	2	1	no	—
228	C₄×Dic₁₄₆	—	2	1	no	—
229	C₄×Dic₁₄₆	—	2	2	no	—
230	C₄×D₂₉₂	—	2	1	no	—
231	C₄×D₂₉₂	—	2	1	no	—
232	C₄×D₂₉₂	—	2	2	no	—
233	C₄×D₂₉₂	—	2	2	no	—
234	C₄×D₂₉₂	—	2	2	no	—
235	C₄×D₂₉₂	C₂³	1	2	yes	—
236	C₄×D₂₉₂	C₂³	1	2	yes	—
237	#14556551	—	2	2	no	—
238	#14556551	—	2	2	no	—
239	#14556550	—	2	2	no	—
240	#14556549	C₂³	1	2	yes	—
241	#14556549	C₂³	1	2	yes	—
242	C₂×C₄⋊Dic₇₃	—	2	1	no	—
243	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
244	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
246	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
247	C₂×#11924005	—	2	2	no	—
248	C₂×#11924005	—	2	2	no	—
249	C₂×#11924005	—	2	1	no	—
250	C₂×#11924005	—	2	1	no	—
251	#14556524	C₂³	1	2	yes	—
252	#14556524	C₂³	1	2	yes	—
253	#14556522	C₂³	1	2	yes	—
254	#14556522	C₂³	1	2	yes	—
255	C₄⋊#10596831	C₂³	1	2	yes	—
256	C₄⋊#10596831	C₂³	1	2	yes	—
257	#14556516	C₂³	1	2	yes	—
258	#14556516	C₂³	1	2	yes	—
259	#14556516	C₂³	1	2	yes	—
260	#14556516	C₂³	1	2	yes	—
261	#14556515	C₂³	1	2	yes	—
262	#14556515	C₂³	1	2	yes	—
263	#14556514	C₂³	1	2	yes	—
264	#14556514	C₂³	1	2	yes	—
265	#14556513	C₂³	1	2	yes	—
266	#14556513	C₂³	1	2	yes	—
267	#14556513	C₂³	1	2	yes	—
268	#14556513	C₂³	1	2	yes	—
269	#14556512	C₂³	1	2	yes	—
270	#14556512	C₂³	1	2	yes	—
271	#14556511	C₂³	1	2	yes	—
272	#14556511	C₂³	1	2	yes	—
273	#14556503	C₂³	1	2	yes	—
274	#14556503	C₂³	1	2	yes	—
275	#14556503	C₂³	1	2	yes	—
276	#14556503	C₂³	1	2	yes	—
277	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
278	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
279	#135×C₇₃	—	2	4	no	—
280	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
281	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
282	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
283	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
285	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₇₃	—	2	1	no	—
291	C₄×D₄×C₇₃	—	2	1	no	—
292	C₄×D₄×C₇₃	—	2	1	no	—
293	C₄×D₄×C₇₃	—	2	1	no	—
294	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
296	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
298	#117×C₇₃	—	2	1	no	—
299	#117×C₇₃	—	2	1	no	—
300	#117×C₇₃	C₂³	1	1	yes	characteristic
301	#117×C₇₃	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₇₃	—	2	1	no	—
303	C₂×C₄²×C₇₃	—	2	1	no	—
304	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
305	#107×C₇₃	C₂³	1	1	yes	characteristic
306	#107×C₇₃	C₂³	1	1	yes	characteristic
307	#106×C₇₃	C₂³	1	1	yes	characteristic
308	#106×C₇₃	C₂³	1	1	yes	characteristic
309	#103×C₇₃	C₂³	1	1	yes	characteristic
310	#103×C₇₃	C₂³	1	1	yes	characteristic
311	#103×C₇₃	C₂³	1	1	yes	characteristic
312	#103×C₇₃	C₂³	1	1	yes	characteristic
313	#102×C₇₃	C₂³	1	1	yes	characteristic
314	#102×C₇₃	C₂³	1	1	yes	characteristic
315	#102×C₇₃	C₂³	1	1	yes	characteristic
316	#102×C₇₃	C₂³	1	1	yes	characteristic
317	#97×C₇₃	C₂³	1	1	yes	characteristic
318	#97×C₇₃	C₂³	1	1	yes	characteristic
319	#97×C₇₃	C₂³	1	1	yes	characteristic
320	#97×C₇₃	C₂³	1	1	yes	characteristic
321	C₂³×D₇₃	—	2	1	no	—
322	C₂³×D₇₃	—	2	2	no	—
323	#11924029	—	2	4	no	—
324	#11924029	—	4	2	no	—
325	#11924028	—	2	2	no	—
326	#11924028	—	2	2	no	—
327	#11924028	—	2	2	no	—
328	#11924028	—	2	2	no	—
329	#11924028	—	4	4	no	—
330	#11924028	—	4	4	no	—
331	#11924028	—	8	4	no	—
332	#11924027	—	2	4	no	—
333	#11924027	—	4	2	no	—
334	#11924027	—	4	8	no	—
335	C₂×Dic₁₄₆	—	2	2	no	—
336	C₂×Dic₁₄₆	—	2	2	no	—
337	C₂×Dic₁₄₆	—	2	2	no	—
338	C₂×Dic₁₄₆	—	2	1	no	—
339	C₂×Dic₁₄₆	—	2	2	no	—
340	C₂×Dic₁₄₆	—	2	2	no	—
341	C₂×Dic₁₄₆	—	4	4	no	—
342	C₂×Dic₁₄₆	—	8	2	no	—
343	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
344	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
345	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
346	Q₈×D₇₃	—	2	4	no	—
347	Q₈×D₇₃	—	4	2	no	—
348	C₂×D₂₉₂	—	2	2	no	—
349	C₂×D₂₉₂	—	2	2	no	—
350	C₂×D₂₉₂	—	2	2	no	—
351	C₂×D₂₉₂	—	2	1	no	—
352	C₂×D₂₉₂	—	2	2	no	—
353	C₂×D₂₉₂	—	2	2	no	—
354	C₂×D₂₉₂	—	4	4	no	—
355	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
356	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
357	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
358	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
359	C₂×D₂₉₂	C₂⁴	1	2	yes	—
360	C₂×C₂²⋊D₇₃	—	2	2	no	—
361	C₂×C₂²⋊D₇₃	—	2	2	no	—
362	C₂×C₂²⋊D₇₃	—	2	2	no	—
363	C₂×C₂²⋊D₇₃	—	2	2	no	—
364	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
365	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
366	D₄×D₇₃	—	2	4	no	—
367	D₄×D₇₃	—	4	2	no	—
368	D₄×D₇₃	—	4	8	no	—
369	C₂²×Dic₇₃	—	2	1	no	—
370	C₂²×Dic₇₃	—	2	1	no	—
371	C₂²×Dic₇₃	—	2	1	no	—
372	C₂²×Dic₇₃	—	2	2	no	—
373	C₂×C₄×D₇₃	—	2	2	no	—
374	C₂×C₄×D₇₃	—	2	2	no	—
375	C₂×C₄×D₇₃	—	2	2	no	—
376	C₂×C₄×D₇₃	—	2	2	no	—
377	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
378	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
379	#11924018	—	4	2	no	—
380	#11924016	—	4	2	no	—
381	#11924015	—	4	2	no	—
382	#11924013	—	4	2	no	—
383	#11924012	—	2	2	no	—
384	#11924012	—	2	2	no	—
385	#11924011	—	4	2	no	—
386	#11924011	—	4	2	no	—
387	C₂×#10596831	C₂⁴	1	2	yes	—
388	C₂×#10596831	C₂⁴	1	2	yes	—
389	C₈×D₇₃	—	4	2	no	—
390	C₈×D₇₃	—	4	2	no	—
391	C₄⋊Dic₇₃	—	2	2	no	—
392	C₄⋊Dic₇₃	—	2	2	no	—
393	C₄⋊Dic₇₃	—	2	1	no	—
394	C₄⋊Dic₇₃	—	2	1	no	—
395	C₄⋊Dic₇₃	—	2	2	no	—
396	C₄⋊Dic₇₃	—	2	2	no	—
397	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
398	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
399	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
400	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
401	#11924007	—	2	2	no	—
402	#11924007	—	2	2	no	—
403	#11924007	—	2	2	no	—
404	#11924007	—	2	2	no	—
405	C₂²⋊Dic₇₃	—	2	2	no	—
406	C₂²⋊Dic₇₃	—	2	2	no	—
407	#11924005	—	2	2	no	—
408	#11924005	—	2	2	no	—
409	#11924005	—	2	2	no	—
410	#11924005	—	2	2	no	—
411	#11924005	—	2	2	no	—
412	#11924005	—	2	2	no	—
413	#11924005	—	2	2	no	—
414	#11924005	—	2	2	no	—
415	#11924005	—	2	2	no	—
416	#11924005	—	2	2	no	—
417	#11924005	—	2	2	no	—
418	#11924005	—	2	2	no	—
419	#11924005	C₂×D₄	1	2	yes	—
420	#11924005	C₂×D₄	1	2	yes	—
421	#11924005	C₂×D₄	1	2	yes	—
422	#11924005	C₂×D₄	1	2	yes	—
423	C₄×Dic₇₃	—	2	2	no	—
424	C₄×Dic₇₃	—	2	2	no	—
425	#41×C₇₃	—	2	2	no	—
426	#41×C₇₃	—	2	2	no	—
427	#41×C₇₃	—	2	2	no	—
428	#41×C₇₃	#41	1	4	yes	complemented
429	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
431	C₂×D₄×C₇₃	—	2	1	no	—
432	C₂×D₄×C₇₃	—	2	1	no	—
433	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₇₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
442	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
443	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
444	Q₁₆×C₇₃	—	2	2	no	—
445	SD₁₆×C₇₃	—	2	2	no	—
446	SD₁₆×C₇₃	—	2	2	no	—
447	D₈×C₇₃	—	2	2	no	—
448	C₂×C₈×C₇₃	—	2	2	no	—
449	C₂×C₈×C₇₃	—	2	2	no	—
450	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
451	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
452	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
453	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
454	C₄⋊C₄×C₇₃	—	2	1	no	—
455	C₄⋊C₄×C₇₃	—	2	1	no	—
456	C₄⋊C₄×C₇₃	—	2	1	no	—
457	C₄⋊C₄×C₇₃	—	2	1	no	—
458	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
460	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
461	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
462	C₂²⋊C₄×C₇₃	—	2	1	no	—
463	C₂²⋊C₄×C₇₃	—	2	1	no	—
464	C₂²⋊C₄×C₇₃	—	2	1	no	—
465	C₂²⋊C₄×C₇₃	—	2	1	no	—
466	C₂²⋊C₄×C₇₃	—	2	1	no	—
467	C₂²⋊C₄×C₇₃	—	2	1	no	—
468	C₄²×C₇₃	—	2	1	no	—
469	C₄²×C₇₃	—	2	1	no	—
470	C₄²×C₇₃	—	2	1	no	—
471	C₄²×C₇₃	—	2	1	no	—
472	C₄²×C₇₃	—	2	1	no	—
473	C₄²×C₇₃	—	2	1	no	—
474	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
475	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
476	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
477	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
478	C₂³×C₇₃	—	2	1	no	—
479	C₂³×C₇₃	—	2	1	no	—
480	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
481	C₂²×D₇₃	—	2	2	no	—
482	C₂²×D₇₃	—	4	4	no	—
483	C₂²×D₇₃	—	4	2	no	—
484	C₂²×D₇₃	—	8	2	no	—
485	C₂²×D₇₃	—	8	2	no	—
486	C₂²×D₇₃	—	8	1	no	—
487	C₂²×D₇₃	—	8	1	no	—
488	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
489	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
490	Q₈×C₇₃	—	2	1	no	—
491	Q₈×C₇₃	—	2	1	no	—
492	Q₈×C₇₃	—	2	1	no	—
493	Q₈×C₇₃	C₂×#41	1	2	yes	—
494	D₄×C₇₃	—	2	4	no	—
495	D₄×C₇₃	—	2	1	no	—
496	D₄×C₇₃	—	2	1	no	—
497	D₄×C₇₃	—	2	1	no	—
498	D₄×C₇₃	—	4	2	no	—
499	D₄×C₇₃	C₂×#41	1	2	yes	—
500	C₂×C₄×C₇₃	—	2	1	no	—
501	C₂×C₄×C₇₃	—	2	4	no	—
502	C₂×C₄×C₇₃	—	2	1	no	—
503	C₂×C₄×C₇₃	—	2	1	no	—
504	C₂×C₄×C₇₃	—	2	1	no	—
505	C₂×C₄×C₇₃	—	2	1	no	—
506	C₂×C₄×C₇₃	—	2	1	no	—
507	C₂×C₄×C₇₃	—	4	1	no	—
508	C₂×C₄×C₇₃	—	4	1	no	—
509	C₂×C₄×C₇₃	—	4	2	no	—
510	C₂×C₄×C₇₃	—	4	2	no	—
511	C₂×C₄×C₇₃	—	4	2	no	—
512	C₂×C₄×C₇₃	—	8	1	no	—
513	C₂×C₄×C₇₃	—	8	1	no	—
514	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
515	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
520	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
521	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
522	C₂²⋊D₇₃	—	2	4	no	—
523	C₂²⋊D₇₃	—	2	4	no	—
524	C₂²⋊D₇₃	—	4	4	no	—
525	C₂²⋊D₇₃	—	4	4	no	—
526	C₂²⋊D₇₃	—	8	2	no	—
527	C₂²⋊D₇₃	—	8	2	no	—
528	C₂×Dic₇₃	—	2	2	no	—
529	C₂×Dic₇₃	—	2	2	no	—
530	C₂×Dic₇₃	—	2	2	no	—
531	C₂×Dic₇₃	—	4	4	no	—
532	C₂×Dic₇₃	—	4	2	no	—
533	C₂×Dic₇₃	—	8	1	no	—
534	C₂×Dic₇₃	—	8	1	no	—
535	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
536	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
537	D₂₉₂	—	2	2	no	—
538	D₂₉₂	—	2	2	no	—
539	D₂₉₂	—	2	2	no	—
540	D₂₉₂	—	2	2	no	—
541	D₂₉₂	—	4	2	no	—
542	D₂₉₂	—	4	2	no	—
543	D₂₉₂	—	4	4	no	—
544	D₂₉₂	—	4	2	no	—
545	D₂₉₂	—	8	2	no	—
546	D₂₉₂	—	8	2	no	—
547	C₄×D₇₃	—	2	2	no	—
548	C₄×D₇₃	—	2	2	no	—
549	C₄×D₇₃	—	2	2	no	—
550	C₄×D₇₃	—	2	2	no	—
551	C₄×D₇₃	—	4	4	no	—
552	C₄×D₇₃	—	4	4	no	—
553	C₄×D₇₃	—	8	2	no	—
554	C₄×D₇₃	—	8	2	no	—
555	Dic₁₄₆	—	2	2	no	—
556	Dic₁₄₆	—	2	2	no	—
557	Dic₁₄₆	—	2	2	no	—
558	Dic₁₄₆	—	2	2	no	—
559	Dic₁₄₆	—	4	4	no	—
560	Dic₁₄₆	—	4	4	no	—
561	Dic₁₄₆	—	4	2	no	—
562	Dic₁₄₆	—	8	2	no	—
563	C₈×C₇₃	—	2	1	no	—
564	C₈×C₇₃	—	2	1	no	—
565	C₈×C₇₃	—	2	1	no	—
566	C₈×C₇₃	—	2	1	no	—
567	#10596831	—	2	2	no	—
568	#10596831	—	2	2	no	—
569	C₂²×C₇₃	—	2	1	no	—
570	C₂²×C₇₃	—	2	1	no	—
571	C₂²×C₇₃	—	2	2	no	—
572	C₂²×C₇₃	—	4	1	no	—
573	C₂²×C₇₃	—	4	1	no	—
574	C₂²×C₇₃	—	4	1	no	—
575	C₂²×C₇₃	—	4	1	no	—
576	C₂²×C₇₃	—	4	1	no	—
577	C₂²×C₇₃	#546	1	2	yes	—
578	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
579	C₂×D₇₃	—	2	2	no	—
580	C₂×D₇₃	—	2	2	no	—
581	C₂×D₇₃	—	2	2	no	—
582	C₂×D₇₃	—	2	2	no	—
583	C₂×D₇₃	—	2	2	no	—
584	C₂×D₇₃	—	2	2	no	—
585	C₂×D₇₃	—	4	2	no	—
586	C₂×D₇₃	—	4	2	no	—
587	C₂×D₇₃	—	4	2	no	—
588	C₂×D₇₃	—	16	4	no	—
589	C₂×D₇₃	—	16	2	no	—
590	C₄×C₇₃	—	2	1	no	—
591	C₄×C₇₃	—	2	1	no	—
592	C₄×C₇₃	—	2	1	no	—
593	C₄×C₇₃	—	2	1	no	—
594	C₄×C₇₃	—	2	2	no	—
595	C₄×C₇₃	—	4	1	no	—
596	C₄×C₇₃	—	4	1	no	—
597	C₄×C₇₃	—	4	1	no	—
598	C₄×C₇₃	—	4	1	no	—
599	C₄×C₇₃	—	4	1	no	—
600	C₄×C₇₃	#546	1	2	yes	—
601	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
602	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
603	Dic₇₃	—	2	2	no	—
604	Dic₇₃	—	2	2	no	—
605	Dic₇₃	—	4	2	no	—
606	Dic₇₃	—	4	2	no	—
607	Dic₇₃	—	4	2	no	—
608	#61222	—	73	1	no	maximal, Sylow
609	C₂×C₇₃	—	2	2	no	—
610	C₂×C₇₃	—	4	2	no	—
611	C₂×C₇₃	—	8	1	no	—
612	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
613	C₂×C₇₃	#3585	1	1	yes	characteristic
614	C₂×C₇₃	#3586	1	1	yes	characteristic
615	D₇₃	—	4	2	no	—
616	D₇₃	—	4	2	no	—
617	D₇₃	—	8	2	no	—
618	#3511	—	73	1	no	—
619	#3500	—	73	1	no	—
620	#3321	—	73	2	no	—
621	#3319	—	73	2	no	—
622	#3316	—	73	2	no	—
623	#3314	—	73	2	no	—
624	#3313	—	73	2	no	—
625	#3311	—	73	2	no	—
626	#3308	—	73	2	no	—
627	#3306	—	73	2	no	—
628	C₂×#489	—	73	1	no	—
629	#3097	—	73	1	no	—
630	#3096	—	73	1	no	—
631	#3079	—	73	1	no	—
632	#3063	—	73	1	no	—
633	#3062	—	73	1	no	—
634	#3040	—	73	1	no	—
635	#3013	—	73	1	no	—
636	#3012	—	73	1	no	—
637	#2943	D₇₃	1	1	yes	characteristic, complemented
638	#2932	—	73	1	no	—
639	#2898	—	73	1	no	—
640	#2897	—	73	1	no	—
641	C₇₃	#61222	1	1	yes	characteristic, complemented, Sylow
642	C₂×2₋¹⁺⁴	—	73	1	no	—
643	C₂×H(5,𝔽₂)	—	73	1	no	—
644	C₂×#137	—	73	1	no	—
645	C₂×AGL(1,ℤ/8)	—	73	1	no	—
646	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
647	C₂×#131	—	73	1	no	—
648	C₂×#131	—	73	1	no	—
649	#556	—	73	2	no	—
650	#555	—	73	2	no	—
651	#554	—	73	2	no	—
652	#553	—	146	2	no	—
653	#548	—	73	2	no	—
654	#548	—	73	2	no	—
655	#548	—	146	2	no	—
656	#547	—	73	2	no	—
657	#546	—	73	2	no	—
658	#546	—	73	2	no	—
659	#546	—	146	2	no	—
660	#546	—	146	2	no	—
661	#542	—	146	1	no	—
662	#542	—	146	1	no	—
663	#537	—	73	1	no	—
664	#537	—	73	1	no	—
665	#536	—	73	1	no	—
666	#536	—	146	1	no	—
667	#535	—	73	1	no	—
668	#535	—	146	1	no	—
669	#533	—	146	1	no	—
670	#532	—	73	1	no	—
671	#532	—	146	1	no	—
672	#532	—	146	1	no	—
673	C₂×C₄⋊Q₈	—	73	1	no	—
674	C₂×#124	—	73	1	no	—
675	C₂×#124	—	146	1	no	—
676	#520	—	73	1	no	—
677	#520	—	73	1	no	—
678	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
679	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
680	#489	—	73	2	no	—
681	#489	—	73	2	no	—
682	#489	—	73	2	no	—
683	#489	—	73	2	no	—
684	#485	—	73	2	no	—
685	#485	—	73	2	no	—
686	#484	—	73	2	no	—
687	#483	—	73	2	no	—
688	#482	—	73	2	no	—
689	#482	—	73	2	no	—
690	#481	—	73	2	no	—
691	#480	—	73	2	no	—
692	#477	—	73	2	no	—
693	#476	—	73	2	no	—
694	#475	—	73	2	no	—
695	#474	—	73	2	no	—
696	#470	—	73	2	no	—
697	#469	—	73	2	no	—
698	#468	—	73	2	no	—
699	#468	—	73	2	no	—
700	#467	—	73	2	no	—
701	#466	—	73	2	no	—
702	#465	—	73	2	no	—
703	#465	—	73	2	no	—
704	#464	—	73	2	no	—
705	#464	—	73	2	no	—
706	#463	—	73	2	no	—
707	#463	—	73	2	no	—
708	#452	—	73	2	no	—
709	#452	—	73	2	no	—
710	#451	—	73	2	no	—
711	#450	—	73	2	no	—
712	#449	—	73	2	no	—
713	#449	—	73	2	no	—
714	#448	—	73	2	no	—
715	#447	—	73	2	no	—
716	#442	C₂×D₇₃	1	1	yes	characteristic, complemented
717	#442	C₂×D₇₃	1	1	yes	characteristic, complemented
718	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
719	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
720	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
721	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
722	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
723	#440	C₂×D₇₃	1	1	yes	characteristic, complemented
724	#435	—	73	2	no	—
725	#435	—	73	2	no	—
726	#435	—	73	2	no	—
727	#435	—	73	2	no	—
728	#428	—	73	1	no	—
729	#428	—	73	1	no	—
730	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
731	#423	—	73	1	no	—
732	#419	—	73	1	no	—
733	#419	—	73	2	no	—
734	#418	—	73	1	no	—
735	#418	—	73	2	no	—
736	#417	—	73	1	no	—
737	#417	—	73	1	no	—
738	#417	—	73	2	no	—
739	#417	—	73	2	no	—
740	#416	—	73	2	no	—
741	#416	—	73	2	no	—
742	#416	C₂×D₇₃	1	1	yes	characteristic
743	#416	C₂×D₇₃	1	1	yes	characteristic, complemented
744	C₂×#103	—	73	1	no	—
745	C₂×#103	—	73	1	no	—
746	C₂×#103	—	73	2	no	—
747	C₂×#102	—	73	1	no	—
748	C₂×#102	—	73	1	no	—
749	C₂×#102	—	73	2	no	—
750	#408	—	73	1	no	—
751	#408	—	73	1	no	—
752	C₂×#97	C₂×D₇₃	1	1	yes	characteristic, complemented
753	2₋¹⁺⁴	—	292	2	no	—
754	2₋¹⁺⁴	—	146	4	no	—
755	H(5,𝔽₂)	—	292	2	no	—
756	H(5,𝔽₂)	—	146	4	no	—
757	C₂×#41	—	73	1	no	—
758	C₂×#41	—	73	1	no	—
759	C₂×#41	—	73	2	no	—
760	C₂×#41	—	73	2	no	—
761	C₂×#41	—	146	1	no	—
762	C₂×#41	—	146	2	no	—
763	C₂×#41	—	146	1	no	—
764	C₂×#41	—	146	2	no	—
765	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
766	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
767	C₂²×Q₈	—	73	2	no	—
768	C₂²×Q₈	—	73	1	no	—
769	C₂²×Q₈	—	146	1	no	—
770	C₂²×Q₈	—	146	1	no	—
771	C₂²×D₄	—	73	2	no	—
772	C₂²×D₄	—	73	1	no	—
773	C₂²×D₄	—	146	1	no	—
774	C₂²×D₄	—	146	2	no	—
775	#137	—	292	2	no	—
776	AGL(1,ℤ/8)	—	292	2	no	—
777	#135	—	2	4	no	—
778	C₂×Q₁₆	—	73	2	no	—
779	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
780	C₂×SD₁₆	—	73	2	no	—
781	C₂×SD₁₆	—	73	2	no	—
782	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
783	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
784	C₂×D₈	—	73	2	no	—
785	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
786	#131	—	292	2	no	—
787	#131	—	292	2	no	—
788	C₂×M₁₆	—	73	1	no	—
789	C₂×M₁₆	—	73	1	no	—
790	C₂×M₁₆	—	73	2	no	—
791	C₂×M₁₆	—	73	2	no	—
792	C₂²×C₈	—	73	2	no	—
793	C₂²×C₈	—	73	2	no	—
794	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
795	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
796	C₄⋊Q₈	—	73	1	no	—
797	C₄⋊Q₈	—	73	2	no	—
798	C₄⋊Q₈	—	73	2	no	—
799	C₄⋊Q₈	—	146	1	no	—
800	C₄⋊Q₈	—	146	1	no	—
801	C₄⋊Q₈	—	146	1	no	—
802	#127	—	73	1	no	—
803	#127	—	146	1	no	—
804	#126	—	146	2	no	—
805	#126	—	146	2	no	—
806	#125	—	146	2	no	—
807	#124	—	73	1	no	—
808	#124	—	73	1	no	—
809	#124	—	73	2	no	—
810	#124	—	73	2	no	—
811	#124	—	146	2	no	—
812	#124	—	146	2	no	—
813	#124	—	146	1	no	—
814	#124	—	146	2	no	—
815	#124	—	146	1	no	—
816	#124	—	146	2	no	—
817	#124	—	146	2	no	—
818	#124	—	146	1	no	—
819	#124	—	146	1	no	—
820	#123	—	146	2	no	—
821	#123	—	146	2	no	—
822	#123	—	146	2	no	—
823	#123	—	146	2	no	—
824	#123	—	146	2	no	—
825	C₂²⋊Q₈	—	73	2	no	—
826	C₂²⋊Q₈	—	73	2	no	—
827	C₂²⋊Q₈	—	73	2	no	—
828	C₂²⋊Q₈	—	73	2	no	—
829	C₂²⋊Q₈	—	146	2	no	—
830	C₂²⋊Q₈	—	146	2	no	—
831	C₂²⋊Q₈	—	146	2	no	—
832	C₂²⋊Q₈	—	146	2	no	—
833	C₂²⋊Q₈	—	146	2	no	—
834	C₂²⋊Q₈	—	146	1	no	—
835	C₂²⋊Q₈	—	146	1	no	—
836	#121	—	73	2	no	—
837	#121	—	73	2	no	—
838	#121	—	73	2	no	—
839	#121	—	73	2	no	—
840	#121	—	73	2	no	—
841	#121	—	73	2	no	—
842	#121	—	146	2	no	—
843	#121	—	146	2	no	—
844	#121	—	146	2	no	—
845	#121	—	146	2	no	—
846	#121	—	146	1	no	—
847	#121	—	146	1	no	—
848	#121	—	146	2	no	—
849	#121	—	146	2	no	—
850	#121	—	146	2	no	—
851	#120	—	146	2	no	—
852	#120	—	146	2	no	—
853	#120	—	146	2	no	—
854	C₄×Q₈	—	146	2	no	—
855	C₄×Q₈	—	146	1	no	—
856	C₄×Q₈	—	146	1	no	—
857	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
858	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
859	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
860	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	1	no	—
863	C₄×D₄	—	2	1	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	73	2	no	—
866	C₄×D₄	—	73	2	no	—
867	C₄×D₄	—	146	2	no	—
868	C₄×D₄	—	146	2	no	—
869	C₄×D₄	—	146	1	no	—
870	C₄×D₄	—	146	1	no	—
871	C₄×D₄	—	146	2	no	—
872	C₄×D₄	—	146	2	no	—
873	C₄×D₄	—	146	2	no	—
874	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
875	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
876	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
877	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
878	#117	—	2	1	no	—
879	#117	—	2	1	no	—
880	#117	—	73	2	no	—
881	#117	—	73	2	no	—
882	#117	—	146	2	no	—
883	#117	C₂²×D₇₃	1	1	yes	characteristic
884	#117	C₂²×D₇₃	1	1	yes	characteristic
885	C₂×C₄⋊C₄	—	73	1	no	—
886	C₂×C₄⋊C₄	—	73	1	no	—
887	C₂×C₄⋊C₄	—	73	2	no	—
888	C₂×C₄⋊C₄	—	73	2	no	—
889	C₂×C₄⋊C₄	—	146	1	no	—
890	C₂×C₂²⋊C₄	—	146	2	no	—
891	C₂×C₂²⋊C₄	—	146	2	no	—
892	C₂×C₂²⋊C₄	—	146	1	no	—
893	C₂×C₂²⋊C₄	—	146	1	no	—
894	C₂×C₄²	—	2	1	no	—
895	C₂×C₄²	—	2	1	no	—
896	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
897	#107	—	73	2	no	—
898	#107	—	73	2	no	—
899	#107	C₂²×D₇₃	1	1	yes	characteristic
900	#107	C₂²×D₇₃	1	1	yes	characteristic
901	#106	—	73	2	no	—
902	#106	—	73	2	no	—
903	#106	C₂²×D₇₃	1	1	yes	characteristic
904	#106	C₂²×D₇₃	1	1	yes	characteristic
905	C₄⋊C₈	—	73	2	no	—
906	C₄⋊C₈	—	73	2	no	—
907	#103	—	73	2	no	—
908	#103	—	73	2	no	—
909	#103	—	73	2	no	—
910	#103	—	73	2	no	—
911	#103	—	73	2	no	—
912	#103	—	73	2	no	—
913	#103	—	73	2	no	—
914	#103	—	73	2	no	—
915	#103	C₂²×D₇₃	1	1	yes	characteristic
916	#103	C₂²×D₇₃	1	1	yes	characteristic
917	#103	C₂²×D₇₃	1	1	yes	characteristic
918	#103	C₂²×D₇₃	1	1	yes	characteristic
919	#102	—	73	2	no	—
920	#102	—	73	2	no	—
921	#102	—	73	2	no	—
922	#102	—	73	2	no	—
923	#102	—	73	2	no	—
924	#102	—	73	2	no	—
925	#102	—	73	2	no	—
926	#102	—	73	2	no	—
927	#102	C₂²×D₇₃	1	1	yes	characteristic
928	#102	C₂²×D₇₃	1	1	yes	characteristic
929	#102	C₂²×D₇₃	1	1	yes	characteristic
930	#102	C₂²×D₇₃	1	1	yes	characteristic
931	C₂²⋊C₈	—	73	2	no	—
932	C₂²⋊C₈	—	73	2	no	—
933	C₂²⋊C₈	—	73	2	no	—
934	C₂²⋊C₈	—	73	2	no	—
935	#97	C₂²×D₇₃	1	1	yes	characteristic
936	#97	C₂²×D₇₃	1	1	yes	characteristic
937	#97	C₂²×D₇₃	1	1	yes	characteristic
938	#97	C₂²×D₇₃	1	1	yes	characteristic
939	C₂⁴	—	146	2	no	—
940	C₂⁴	—	146	1	no	—
941	#41	—	2	2	no	—
942	#41	—	2	2	no	—
943	#41	—	2	2	no	—
944	#41	—	292	4	no	—
945	#41	—	292	4	no	—
946	#41	—	292	8	no	—
947	#41	—	292	2	no	—
948	#41	—	292	2	no	—
949	#41	—	584	4	no	—
950	#41	—	146	4	no	—
951	#41	—	146	4	no	—
952	#41	—	146	2	no	—
953	#41	—	146	2	no	—
954	#41	—	146	2	no	—
955	#41	—	146	2	no	—
956	#41	#11924028	1	4	yes	complemented
957	C₂×Q₈	—	292	4	no	—
958	C₂×Q₈	—	292	2	no	—
959	C₂×Q₈	—	584	2	no	—
960	C₂×Q₈	—	73	1	no	—
961	C₂×Q₈	—	73	1	no	—
962	C₂×Q₈	—	73	2	no	—
963	C₂×Q₈	—	146	2	no	—
964	C₂×Q₈	—	146	4	no	—
965	C₂×Q₈	—	146	2	no	—
966	C₂×Q₈	—	146	2	no	—
967	C₂×Q₈	—	146	2	no	—
968	C₂×Q₈	—	146	1	no	—
969	C₂×Q₈	—	146	2	no	—
970	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
971	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
972	C₂×D₄	—	2	1	no	—
973	C₂×D₄	—	2	1	no	—
974	C₂×D₄	—	292	4	no	—
975	C₂×D₄	—	292	8	no	—
976	C₂×D₄	—	292	2	no	—
977	C₂×D₄	—	73	2	no	—
978	C₂×D₄	—	73	2	no	—
979	C₂×D₄	—	73	2	no	—
980	C₂×D₄	—	73	2	no	—
981	C₂×D₄	—	73	1	no	—
982	C₂×D₄	—	73	1	no	—
983	C₂×D₄	—	73	2	no	—
984	C₂×D₄	—	146	2	no	—
985	C₂×D₄	—	146	2	no	—
986	C₂×D₄	—	146	2	no	—
987	C₂×D₄	—	146	2	no	—
988	C₂×D₄	—	146	2	no	—
989	C₂×D₄	—	146	4	no	—
990	C₂×D₄	—	146	2	no	—
991	C₂×D₄	—	146	2	no	—
992	C₂×D₄	—	146	1	no	—
993	C₂×D₄	—	146	2	no	—
994	C₂×D₄	—	146	2	no	—
995	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
996	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
997	C₂²×C₄	—	2	1	no	—
998	C₂²×C₄	—	2	1	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	73	2	no	—
1004	C₂²×C₄	—	73	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	1	no	—
1011	C₂²×C₄	—	146	1	no	—
1012	C₂²×C₄	—	146	1	no	—
1013	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
1014	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
1015	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
1016	Q₁₆	—	2	2	no	—
1017	Q₁₆	—	292	2	no	—
1018	SD₁₆	—	2	2	no	—
1019	SD₁₆	—	2	2	no	—
1020	SD₁₆	—	292	2	no	—
1021	SD₁₆	—	292	2	no	—
1022	D₈	—	2	2	no	—
1023	D₈	—	292	2	no	—
1024	M₁₆	—	292	2	no	—
1025	M₁₆	—	292	2	no	—
1026	M₁₆	—	146	2	no	—
1027	M₁₆	—	146	2	no	—
1028	C₂×C₈	—	2	2	no	—
1029	C₂×C₈	—	2	2	no	—
1030	C₂×C₈	—	292	2	no	—
1031	C₂×C₈	—	292	2	no	—
1032	C₂×C₈	—	73	2	no	—
1033	C₂×C₈	—	73	2	no	—
1034	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1035	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1036	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1037	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	73	2	no	—
1043	C₄⋊C₄	—	73	2	no	—
1044	C₄⋊C₄	—	73	2	no	—
1045	C₄⋊C₄	—	73	2	no	—
1046	C₄⋊C₄	—	146	2	no	—
1047	C₄⋊C₄	—	146	2	no	—
1048	C₄⋊C₄	—	146	2	no	—
1049	C₄⋊C₄	—	146	2	no	—
1050	C₄⋊C₄	—	146	2	no	—
1051	C₄⋊C₄	—	146	2	no	—
1052	C₄⋊C₄	—	146	1	no	—
1053	C₄⋊C₄	—	146	1	no	—
1054	C₄⋊C₄	—	146	2	no	—
1055	C₄⋊C₄	—	146	2	no	—
1056	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1057	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1058	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1059	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	2	1	no	—
1062	C₂²⋊C₄	—	2	1	no	—
1063	C₂²⋊C₄	—	2	1	no	—
1064	C₂²⋊C₄	—	2	1	no	—
1065	C₂²⋊C₄	—	2	1	no	—
1066	C₂²⋊C₄	—	73	2	no	—
1067	C₂²⋊C₄	—	73	2	no	—
1068	C₂²⋊C₄	—	73	2	no	—
1069	C₂²⋊C₄	—	73	2	no	—
1070	C₂²⋊C₄	—	146	2	no	—
1071	C₂²⋊C₄	—	146	2	no	—
1072	C₂²⋊C₄	—	146	2	no	—
1073	C₂²⋊C₄	—	146	2	no	—
1074	C₂²⋊C₄	—	146	2	no	—
1075	C₂²⋊C₄	—	146	2	no	—
1076	C₂²⋊C₄	—	146	2	no	—
1077	C₂²⋊C₄	—	146	2	no	—
1078	C₂²⋊C₄	—	146	2	no	—
1079	C₂²⋊C₄	—	146	2	no	—
1080	C₂²⋊C₄	—	146	2	no	—
1081	C₂²⋊C₄	—	146	2	no	—
1082	C₂²⋊C₄	—	146	2	no	—
1083	C₂²⋊C₄	—	146	2	no	—
1084	C₄²	—	2	1	no	—
1085	C₄²	—	2	1	no	—
1086	C₄²	—	2	1	no	—
1087	C₄²	—	2	1	no	—
1088	C₄²	—	2	1	no	—
1089	C₄²	—	2	1	no	—
1090	C₄²	—	146	2	no	—
1091	C₄²	—	146	2	no	—
1092	C₄²	D₄×D₇₃	1	1	yes	characteristic
1093	C₄²	D₄×D₇₃	1	1	yes	characteristic
1094	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1095	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1096	C₂³	—	2	1	no	—
1097	C₂³	—	2	1	no	—
1098	C₂³	—	292	4	no	—
1099	C₂³	—	292	2	no	—
1100	C₂³	—	584	1	no	—
1101	C₂³	—	584	1	no	—
1102	C₂³	—	584	2	no	—
1103	C₂³	—	584	2	no	—
1104	C₂³	—	73	2	no	—
1105	C₂³	—	73	2	no	—
1106	C₂³	—	146	2	no	—
1107	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1108	Q₈	—	2	1	no	—
1109	Q₈	—	2	1	no	—
1110	Q₈	—	2	1	no	—
1111	Q₈	—	292	4	no	—
1112	Q₈	—	292	4	no	—
1113	Q₈	—	292	2	no	—
1114	Q₈	—	584	2	no	—
1115	Q₈	—	146	2	no	—
1116	Q₈	—	146	2	no	—
1117	Q₈	—	146	2	no	—
1118	Q₈	—	146	2	no	—
1119	Q₈	C₂×#11924028	1	2	yes	—
1120	D₄	—	2	4	no	—
1121	D₄	—	2	1	no	—
1122	D₄	—	2	1	no	—
1123	D₄	—	2	1	no	—
1124	D₄	—	4	2	no	—
1125	D₄	—	292	4	no	—
1126	D₄	—	292	2	no	—
1127	D₄	—	292	2	no	—
1128	D₄	—	292	4	no	—
1129	D₄	—	292	4	no	—
1130	D₄	—	292	2	no	—
1131	D₄	—	584	2	no	—
1132	D₄	—	584	2	no	—
1133	D₄	—	584	2	no	—
1134	D₄	—	584	2	no	—
1135	D₄	—	146	4	no	—
1136	D₄	—	146	4	no	—
1137	D₄	—	146	2	no	—
1138	D₄	—	146	2	no	—
1139	D₄	—	146	2	no	—
1140	D₄	—	146	2	no	—
1141	D₄	C₂×#11924028	1	2	yes	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	4	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	1	no	—
1151	C₂×C₄	—	4	2	no	—
1152	C₂×C₄	—	4	2	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	8	1	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	292	4	no	—
1157	C₂×C₄	—	292	4	no	—
1158	C₂×C₄	—	292	2	no	—
1159	C₂×C₄	—	292	4	no	—
1160	C₂×C₄	—	584	2	no	—
1161	C₂×C₄	—	584	2	no	—
1162	C₂×C₄	—	584	1	no	—
1163	C₂×C₄	—	584	1	no	—
1164	C₂×C₄	—	73	2	no	—
1165	C₂×C₄	—	73	2	no	—
1166	C₂×C₄	—	146	2	no	—
1167	C₂×C₄	—	146	2	no	—
1168	C₂×C₄	—	146	2	no	—
1169	C₂×C₄	—	146	2	no	—
1170	C₂×C₄	—	146	2	no	—
1171	C₂×C₄	—	146	2	no	—
1172	C₂×C₄	—	146	2	no	—
1173	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1174	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1175	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1176	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1177	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1178	C₂×C₄	C₂×#11924028	1	2	yes	—
1179	C₂×C₄	#14556637	1	2	yes	—
1180	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1181	C₈	—	2	1	no	—
1182	C₈	—	2	1	no	—
1183	C₈	—	2	1	no	—
1184	C₈	—	2	1	no	—
1185	C₈	—	146	2	no	—
1186	C₈	—	146	2	no	—
1187	C₂²	—	2	1	no	—
1188	C₂²	—	2	1	no	—
1189	C₂²	—	2	2	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	1	no	—
1193	C₂²	—	4	1	no	—
1194	C₂²	—	4	1	no	—
1195	C₂²	—	292	2	no	—
1196	C₂²	—	292	2	no	—
1197	C₂²	—	292	2	no	—
1198	C₂²	—	1168	2	no	—
1199	C₂²	—	1168	4	no	—
1200	C₂²	—	146	2	no	—
1201	C₂²	—	146	2	no	—
1202	C₂²	—	146	2	no	—
1203	C₂²	—	146	2	no	—
1204	C₂²	—	146	2	no	—
1205	C₂²	—	146	2	no	—
1206	C₂²	#17989233	1	2	yes	—
1207	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1208	C₄	—	2	2	no	—
1209	C₄	—	2	1	no	—
1210	C₄	—	2	1	no	—
1211	C₄	—	2	1	no	—
1212	C₄	—	2	1	no	—
1213	C₄	—	4	1	no	—
1214	C₄	—	4	1	no	—
1215	C₄	—	4	1	no	—
1216	C₄	—	4	1	no	—
1217	C₄	—	4	1	no	—
1218	C₄	—	292	2	no	—
1219	C₄	—	292	2	no	—
1220	C₄	—	292	2	no	—
1221	C₄	—	146	2	no	—
1222	C₄	—	146	2	no	—
1223	C₄	#17989233	1	2	yes	—
1224	C₄	C₂²×#11924028	1	1	yes	characteristic
1225	C₄	C₂×#14556637	1	1	yes	characteristic
1226	C₂	—	2	2	no	—
1227	C₂	—	4	2	no	—
1228	C₂	—	8	1	no	—
1229	C₂	—	292	2	no	—
1230	C₂	—	292	2	no	—
1231	C₂	—	584	2	no	—
1232	C₂	C₂×#17989233	1	1	yes	characteristic
1233	C₂	#22624708	1	1	yes	characteristic
1234	C₂	#22624715	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#2943	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#2943	D₇₃
hypocenter	C₇₃	#61222
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2943

Complements

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

N	H ≅ G/N	type
1. #22623842	C₂	semidirect
2. #22623724	C₂	semidirect
3. #22622122	C₂	semidirect
4. #22622092	C₂	semidirect
5. #22622047	C₂	semidirect
6. #22622017	C₂	semidirect
7. #22622002	C₂	semidirect
8. #22621972	C₂	semidirect
9. #22621927	C₂	semidirect
10. #22621897	C₂	semidirect
11. C₂×#17988947	C₂	semidirect
12. #22619903	C₂	semidirect
13. #22619892	C₂	semidirect
14. #22619746	C₂	semidirect
15. #22619625	C₂	semidirect
16. #22619614	C₂	semidirect
17. #22619425	C₂	semidirect
18. #22619242	C₂	semidirect
19. #22619231	C₂	semidirect
20. #22618650	C₂	semidirect
21. #22618460	C₂	semidirect
22. #22618453	C₂	semidirect
23. C₇₃×#2943	C₂	semidirect
26. C₂×#14556621	C₂²	semidirect
29. C₂×#14556597	C₂²	semidirect
30. #17989310	C₂²	semidirect
31. #17989302	C₂²	semidirect
32. #17989297	C₂²	semidirect
37. #17989242	C₂²	semidirect
45. #17989165	C₂²	semidirect
54. C₂×#14556591	C₂²	semidirect
58. #17989067	C₂²	semidirect
59. #17988947	C₂²	semidirect
60. #17988947	C₂²	semidirect
61. #17988947	C₂²	semidirect
62. #17988947	C₂²	semidirect
63. #17988931	C₂²	semidirect
64. #17988930	C₂²	semidirect
65. #17988924	C₂²	semidirect
66. #17988919	C₂²	semidirect
67. #17988914	C₂²	semidirect
68. #17988913	C₂²	semidirect
69. #17988907	C₂²	semidirect
70. #17988902	C₂²	semidirect
71. #17988882	C₂²	semidirect
72. #17988877	C₂²	semidirect
73. #17988872	C₂²	semidirect
74. #17988867	C₂²	semidirect
75. #17988844	C₂²	semidirect
76. #17988839	C₂²	semidirect
77. #17988836	C₂²	semidirect
78. #17988832	C₂²	semidirect
79. #17988827	C₂²	semidirect
80. #17988822	C₂²	semidirect
81. #17988819	C₂²	semidirect
82. #17988815	C₂²	semidirect
83. #17988809	C₂²	semidirect
84. #17988809	C₂²	semidirect
85. #17988802	C₂²	semidirect
86. #17988802	C₂²	semidirect
88. #17988746	C₂²	semidirect
89. #17988741	C₂²	semidirect
92. #17988729	C₂²	semidirect
93. #17988724	C₂²	semidirect
95. #17988660	C₂²	semidirect
96. #17988660	C₂²	semidirect
97. #17988660	C₂²	semidirect
98. #17988660	C₂²	semidirect
99. #17988630	C₂²	semidirect
100. #17988630	C₂²	semidirect
101. #17988611	C₂²	semidirect
102. #17988595	C₂²	semidirect
103. #17988594	C₂²	semidirect
109. #17988585	C₂²	semidirect
111. #17988580	C₂²	semidirect
112. C₂×#14556516	C₂²	semidirect
113. C₂×#14556516	C₂²	semidirect
114. #103×D₇₃	C₂²	semidirect
119. #17988553	C₂²	semidirect
122. C₄×#41×C₇₃	C₂²	semidirect
123. #442×C₇₃	C₂²	semidirect
124. #442×C₇₃	C₂²	semidirect
125. #441×C₇₃	C₂²	semidirect
126. #441×C₇₃	C₂²	semidirect
127. #440×C₇₃	C₂²	semidirect
128. #440×C₇₃	C₂²	semidirect
129. #440×C₇₃	C₂²	semidirect
130. #440×C₇₃	C₂²	semidirect
131. #427×C₇₃	C₂²	semidirect
133. #416×C₇₃	C₂²	semidirect
134. C₂×#97×C₇₃	C₂²	semidirect
428. #41×C₇₃	#41	semidirect
637. #2943	D₇₃	semidirect
641. C₇₃	#61222	semidirect
679. C₄×#41	C₂×D₇₃	semidirect
716. #442	C₂×D₇₃	semidirect
717. #442	C₂×D₇₃	semidirect
718. #441	C₂×D₇₃	semidirect
719. #441	C₂×D₇₃	semidirect
720. #440	C₂×D₇₃	semidirect
721. #440	C₂×D₇₃	semidirect
722. #440	C₂×D₇₃	semidirect
723. #440	C₂×D₇₃	semidirect
730. #427	C₂×D₇₃	semidirect
743. #416	C₂×D₇₃	semidirect
752. C₂×#97	C₂×D₇₃	semidirect
956. #41	#11924028	semidirect

Maximal subgroups

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

subgroup	index
#22623842	2
#22623724	2
#22622122	2
#22622092	2
#22622047	2
#22622017	2
#22622002	2
#22621972	2
#22621927	2
#22621897	2
C₂×#17988947	2
#22619903	2
#22619892	2
#22619746	2
#22619625	2
#22619614	2
#22619425	2
#22619242	2
#22619231	2
#22618650	2
#22618460	2
#22618453	2
C₇₃×#2943	2
#61222	73