Subgroups — #33964498

Order 18688.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623484	C₂	1	2	yes	maximal, complemented
2	#22622358	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622351	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622337	C₂	1	2	yes	maximal, complemented
5	#22622334	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622332	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622320	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622310	C₂	1	2	yes	maximal, complemented
9	#22622307	C₂	1	2	yes	maximal, complemented
10	#22622301	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622281	C₂	1	2	yes	maximal, complemented
12	#22622276	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620444	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619849	C₂	1	2	yes	maximal, complemented
15	#22619845	C₂	1	2	yes	maximal, complemented
16	#22619718	C₂	1	2	yes	maximal, complemented
17	#22619514	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619514	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14556614	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#17988624	C₂	1	1	yes	maximal, characteristic, complemented
22	#427×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3336	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556614	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
27	#17989308	C₂²	1	2	yes	—
28	#17989300	C₂²	1	2	yes	—
29	#17989295	C₂²	1	2	yes	—
30	#17989290	C₂²	1	2	yes	—
31	#17989283	C₂²	1	2	yes	—
32	#17989278	C₂²	1	2	yes	—
33	#17989269	—	2	2	no	—
34	#17989262	—	2	2	no	—
35	#17989261	—	2	2	no	—
36	#17989238	C₂²	1	2	yes	—
37	#17989229	—	2	2	no	—
38	#17989143	C₂²	1	2	yes	—
39	#17989122	—	2	2	no	—
40	#17989120	—	2	2	no	—
41	#17989114	—	2	2	no	—
42	#17989100	C₂²	1	2	yes	—
43	#17989100	C₂²	1	2	yes	—
44	C₄×#11924029	C₂²	1	2	yes	—
45	#17989055	—	2	2	no	—
46	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
47	C₂×#14556549	C₂²	1	2	yes	—
48	#117×D₇₃	C₂²	1	2	yes	—
49	#17988991	C₂²	1	1	yes	characteristic, complemented
50	#17988991	C₂²	1	1	yes	characteristic, complemented
51	#17988989	C₂²	1	1	yes	characteristic, complemented
52	#17988986	C₂²	1	2	yes	complemented
53	#17988984	C₂²	1	2	yes	complemented
54	#17988926	C₂²	1	2	yes	complemented
55	#17988926	C₂²	1	2	yes	complemented
56	#17988925	C₂²	1	2	yes	complemented
57	#17988921	C₂²	1	2	yes	complemented
58	#17988920	C₂²	1	2	yes	complemented
59	#17988916	C₂²	1	2	yes	complemented
60	#17988913	C₂²	1	2	yes	complemented
61	#17988913	C₂²	1	2	yes	complemented
62	#17988912	C₂²	1	2	yes	complemented
63	#17988911	C₂²	1	2	yes	complemented
64	#17988907	C₂²	1	2	yes	complemented
65	#17988906	C₂²	1	2	yes	complemented
66	#17988902	C₂²	1	2	yes	complemented
67	#17988900	C₂²	1	2	yes	complemented
68	#17988894	C₂²	1	2	yes	complemented
69	#17988888	C₂²	1	2	yes	complemented
70	#17988884	C₂²	1	2	yes	complemented
71	#17988880	C₂²	1	2	yes	complemented
72	#17988876	C₂²	1	2	yes	complemented
73	#17988870	C₂²	1	2	yes	complemented
74	#17988866	C₂²	1	2	yes	complemented
75	#17988825	C₂²	1	1	yes	characteristic, complemented
76	#17988825	C₂²	1	1	yes	characteristic, complemented
77	#17988824	C₂²	1	1	yes	characteristic, complemented
78	#17988824	C₂²	1	1	yes	characteristic, complemented
79	#17988823	C₂²	1	1	yes	characteristic, complemented
80	#17988823	C₂²	1	1	yes	characteristic, complemented
81	#17988819	C₂²	1	2	yes	complemented
82	#17988819	C₂²	1	2	yes	complemented
83	#17988818	C₂²	1	2	yes	complemented
84	#17988818	C₂²	1	2	yes	complemented
85	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
86	C₄×#11924015	C₂²	1	2	yes	complemented
87	#17988672	C₂²	1	2	yes	complemented
88	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
89	#17988669	C₂²	1	1	yes	characteristic, complemented
90	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
91	D₄×#10596831	C₂²	1	1	yes	characteristic
92	#17988652	C₂²	1	1	yes	characteristic
93	C₈×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
94	C₈×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
95	#17988650	C₂²	1	1	yes	characteristic
96	#17988650	C₂²	1	1	yes	characteristic
97	#17988625	C₂²	1	1	yes	characteristic, complemented
98	#17988624	C₂²	1	1	yes	characteristic
99	#17988624	C₂²	1	1	yes	characteristic
100	#17988624	C₂²	1	2	yes	—
101	#17988624	C₂²	1	1	yes	characteristic
102	#17988624	C₂²	1	1	yes	characteristic, complemented
103	#17988624	C₂²	1	2	yes	complemented
104	#17988624	C₂²	1	1	yes	characteristic, complemented
105	#17988623	C₂²	1	2	yes	complemented
106	#17988622	C₂²	1	2	yes	—
107	#17988622	C₂²	1	2	yes	—
108	C₂×#14556525	C₂²	1	1	yes	characteristic, complemented
109	#107×D₇₃	C₂²	1	1	yes	characteristic, complemented
110	#107×D₇₃	C₂²	1	1	yes	characteristic, complemented
111	C₂×#14556522	C₂²	1	2	yes	complemented
112	#106×D₇₃	C₂²	1	2	yes	complemented
113	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
114	#17988582	C₂²	1	2	yes	—
115	#17988582	C₂²	1	2	yes	—
116	#17988582	C₂²	1	2	yes	—
117	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
118	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
120	#552×C₇₃	C₂²	1	2	yes	—
121	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#485×C₇₃	C₂²	1	2	yes	complemented
123	#483×C₇₃	C₂²	1	2	yes	complemented
124	#479×C₇₃	C₂²	1	2	yes	complemented
125	#467×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#467×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
129	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11924029	C₂³	1	2	yes	—
132	C₂×#11924028	—	2	2	no	—
133	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
134	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
136	#14556614	—	2	4	no	—
137	C₂×#11924015	C₂³	1	2	yes	—
138	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
139	C₂²×#10596831	C₂³	1	1	yes	characteristic
140	C₂²×#10596831	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₇₃	—	2	4	no	—
142	C₂×C₈×D₇₃	—	2	4	no	—
143	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
151	#14556590	C₂³	1	2	yes	—
152	#14556590	C₂³	1	2	yes	—
153	#14556586	—	2	2	no	—
154	#14556586	—	2	2	no	—
155	#14556586	—	2	2	no	—
156	#14556585	—	2	2	no	—
157	#14556584	—	2	2	no	—
158	#14556583	C₂³	1	2	yes	—
159	#14556581	—	2	2	no	—
160	#14556581	—	2	2	no	—
161	#14556579	—	2	2	no	—
162	#14556577	—	2	2	no	—
163	#14556577	—	2	2	no	—
164	#14556576	—	2	2	no	—
165	#14556576	—	2	2	no	—
166	#14556576	—	2	2	no	—
167	#14556576	—	2	2	no	—
168	#14556576	—	2	2	no	—
169	#14556574	—	2	2	no	—
170	#14556573	—	2	2	no	—
171	#14556571	—	2	2	no	—
172	#14556569	—	2	2	no	—
173	#14556569	—	2	2	no	—
174	#14556569	—	2	2	no	—
175	#14556568	—	2	2	no	—
176	#14556567	C₂³	1	2	yes	—
177	#14556567	C₂³	1	2	yes	—
178	#14556566	—	2	2	no	—
179	#14556566	C₂³	1	2	yes	—
180	#14556566	C₂³	1	2	yes	—
181	#14556565	C₂³	1	2	yes	—
182	#14556565	C₂³	1	2	yes	—
183	#14556564	—	2	2	no	—
184	#14556563	—	2	2	no	—
185	#14556561	—	2	2	no	—
186	#14556561	—	2	2	no	—
187	Q₈×Dic₇₃	C₂³	1	2	yes	—
188	#14556556	—	2	2	no	—
189	#14556556	—	2	2	no	—
190	#14556556	—	2	2	no	—
191	C₄×D₂₉₂	—	2	2	no	—
192	C₄×D₂₉₂	C₂³	1	2	yes	—
193	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
194	D₄×Dic₇₃	D₄	1	1	yes	characteristic
195	#14556553	—	2	2	no	—
196	#14556553	—	2	2	no	—
197	#14556553	—	2	2	no	—
198	#14556553	—	2	2	no	—
199	#14556553	D₄	1	1	yes	characteristic
200	#14556553	C₂³	1	2	yes	—
201	C₄×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
202	C₄×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
203	#14556551	—	2	2	no	—
204	#14556551	—	2	2	no	—
205	#14556551	—	2	2	no	—
206	#14556551	—	2	2	no	—
207	#14556551	D₄	1	1	yes	characteristic
208	#14556551	D₄	1	1	yes	characteristic
209	#14556550	C₂³	1	2	yes	—
210	#14556549	—	2	2	no	—
211	#14556549	—	2	2	no	—
212	#14556549	—	2	2	no	—
213	#14556549	C₂³	1	2	yes	—
214	#14556549	C₂³	1	2	yes	—
215	#14556549	C₂³	1	2	yes	—
216	#14556549	C₂³	1	2	yes	—
217	#14556549	C₂³	1	2	yes	—
218	#14556548	—	2	2	no	—
219	#14556548	—	2	2	no	—
220	#14556548	—	2	2	no	—
221	#14556547	—	2	2	no	—
222	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
223	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
224	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
225	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
226	C₂×#11924005	—	2	2	no	—
227	C₂²⋊C₄×D₇₃	—	2	2	no	—
228	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
229	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
230	C₂×C₄×Dic₇₃	—	2	2	no	—
231	C₄²×D₇₃	—	2	2	no	—
232	C₄²×D₇₃	—	2	2	no	—
233	C₄²×D₇₃	C₂³	1	1	yes	characteristic
234	#14556525	C₂³	1	1	yes	characteristic
235	#14556525	C₂³	1	1	yes	characteristic
236	#14556525	C₂³	1	2	yes	—
237	#14556525	C₂³	1	1	yes	characteristic
238	#14556524	C₂³	1	2	yes	—
239	#14556524	C₂³	1	2	yes	—
240	#14556524	C₂³	1	2	yes	—
241	#14556524	C₂³	1	2	yes	—
242	#14556523	C₂³	1	2	yes	—
243	#14556523	C₂³	1	2	yes	—
244	#14556522	C₂³	1	2	yes	—
245	#14556522	C₂³	1	2	yes	—
246	#14556522	C₂³	1	2	yes	—
247	#14556522	C₂³	1	2	yes	—
248	#14556522	C₂³	1	2	yes	—
249	C₄⋊#10596831	C₂³	1	1	yes	characteristic
250	#14556520	C₂³	1	1	yes	characteristic
251	#14556520	C₂³	1	1	yes	characteristic
252	#14556515	C₂³	1	2	yes	—
253	#14556515	C₂³	1	2	yes	—
254	#14556515	C₂³	1	2	yes	—
255	#14556513	C₂³	1	2	yes	—
256	#14556513	C₂³	1	2	yes	—
257	#14556513	C₂³	1	2	yes	—
258	#14556511	C₂³	1	2	yes	—
259	#14556511	C₂³	1	2	yes	—
260	#14556511	C₂³	1	2	yes	—
261	C₂²⋊#10596831	C₂³	1	1	yes	characteristic
262	C₂²⋊#10596831	C₂³	1	1	yes	characteristic
263	#14556503	C₂³	1	1	yes	characteristic
264	#14556503	C₂³	1	1	yes	characteristic
265	#14556503	C₂³	1	1	yes	characteristic
266	#14556503	C₂³	1	1	yes	characteristic
267	C₄×#10596831	C₂³	1	1	yes	characteristic
268	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
273	#126×C₇₃	—	2	2	no	—
274	#125×C₇₃	—	2	2	no	—
275	#125×C₇₃	C₂³	1	2	yes	—
276	#123×C₇₃	—	2	2	no	—
277	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
280	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
281	#117×C₇₃	—	2	2	no	—
282	#117×C₇₃	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
284	#107×C₇₃	C₂³	1	2	yes	—
285	#107×C₇₃	C₂³	1	1	yes	characteristic
286	#107×C₇₃	C₂³	1	1	yes	characteristic
287	#107×C₇₃	C₂³	1	1	yes	characteristic
288	#106×C₇₃	C₂³	1	2	yes	—
289	#106×C₇₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
291	#103×C₇₃	C₂³	1	2	yes	—
292	#103×C₇₃	C₂³	1	2	yes	—
293	#103×C₇₃	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
297	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
298	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
299	#11924029	—	2	4	no	—
300	#11924029	—	2	4	no	—
301	#11924028	—	4	8	no	—
302	C₂×Dic₁₄₆	—	2	2	no	—
303	C₂×Dic₁₄₆	—	2	2	no	—
304	C₂×D₂₉₂	—	2	2	no	—
305	C₂×D₂₉₂	—	2	2	no	—
306	C₂×D₂₉₂	—	2	2	no	—
307	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
308	C₂×D₂₉₂	C₂⁴	1	2	yes	—
309	C₂×C₂²⋊D₇₃	—	2	2	no	—
310	C₂×C₂²⋊D₇₃	—	2	2	no	—
311	C₂×C₂²⋊D₇₃	C₂×D₄	1	1	yes	characteristic
312	C₂×C₂²⋊D₇₃	C₂×D₄	1	1	yes	characteristic
313	D₄×D₇₃	—	2	4	no	—
314	C₂²×Dic₇₃	—	2	2	no	—
315	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
316	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
317	C₂×C₄×D₇₃	—	2	2	no	—
318	C₂×C₄×D₇₃	—	2	2	no	—
319	C₂×C₄×D₇₃	—	2	2	no	—
320	C₂×C₄×D₇₃	—	2	2	no	—
321	C₂×C₄×D₇₃	—	2	2	no	—
322	C₂×C₄×D₇₃	—	2	2	no	—
323	C₂×C₄×D₇₃	—	2	2	no	—
324	C₂×C₄×D₇₃	—	2	2	no	—
325	C₂×C₄×D₇₃	—	2	2	no	—
326	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
335	#11924015	—	2	4	no	—
336	D₅₈₄	—	2	2	no	—
337	C₂×#10596831	—	2	2	no	—
338	C₂×#10596831	—	2	2	no	—
339	C₂×#10596831	C₂⁴	1	1	yes	characteristic
340	C₂×#10596831	C₂⁴	1	1	yes	characteristic
341	C₂×#10596831	C₂⁴	1	1	yes	characteristic
342	C₂×#10596831	C₂⁴	1	1	yes	characteristic
343	C₈×D₇₃	—	2	2	no	—
344	C₈×D₇₃	—	2	2	no	—
345	C₈×D₇₃	—	2	2	no	—
346	C₈×D₇₃	—	2	2	no	—
347	C₈×D₇₃	—	2	2	no	—
348	C₈×D₇₃	—	2	2	no	—
349	C₈×D₇₃	—	2	2	no	—
350	C₈×D₇₃	#41	1	4	yes	complemented
351	C₄⋊Dic₇₃	—	2	2	no	—
352	C₄⋊Dic₇₃	—	2	2	no	—
353	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
355	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
356	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
357	#11924007	—	2	2	no	—
358	#11924007	—	2	2	no	—
359	#11924007	—	2	2	no	—
360	#11924007	—	2	2	no	—
361	#11924007	—	2	2	no	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
365	#11924007	C₂×D₄	1	1	yes	characteristic
366	#11924007	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊Dic₇₃	—	2	2	no	—
368	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
369	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
370	#11924005	—	2	2	no	—
371	#11924005	—	2	2	no	—
372	#11924005	—	2	2	no	—
373	#11924005	—	2	2	no	—
374	#11924005	—	2	2	no	—
375	#11924005	—	2	2	no	—
376	#11924005	—	2	2	no	—
377	#11924005	—	2	2	no	—
378	#11924005	—	2	2	no	—
379	#11924005	—	2	2	no	—
380	#11924005	—	2	2	no	—
381	#11924005	—	2	2	no	—
382	#11924005	—	2	2	no	—
383	#11924005	C₂×D₄	1	1	yes	characteristic
384	#11924005	C₂×D₄	1	1	yes	characteristic
385	#11924005	C₂×D₄	1	1	yes	characteristic
386	#11924005	C₂×D₄	1	1	yes	characteristic
387	C₄×Dic₇₃	—	2	2	no	—
388	C₄×Dic₇₃	—	2	2	no	—
389	C₄×Dic₇₃	—	2	2	no	—
390	C₄×Dic₇₃	—	2	2	no	—
391	C₄×Dic₇₃	—	2	2	no	—
392	C₄×Dic₇₃	—	2	2	no	—
393	C₄×Dic₇₃	—	2	2	no	—
394	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
395	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
396	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
397	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
398	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₇₃	—	2	2	no	—
400	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
401	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
402	Q₁₆×C₇₃	—	2	2	no	—
403	C₂×C₈×C₇₃	—	2	2	no	—
404	C₂×C₈×C₇₃	—	2	2	no	—
405	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₇₃	—	2	2	no	—
410	C₄⋊C₄×C₇₃	—	2	2	no	—
411	C₄⋊C₄×C₇₃	—	2	2	no	—
412	C₄⋊C₄×C₇₃	—	2	2	no	—
413	C₄⋊C₄×C₇₃	—	2	2	no	—
414	C₄⋊C₄×C₇₃	—	2	2	no	—
415	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
416	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
417	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
418	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
419	C₂²⋊C₄×C₇₃	—	2	2	no	—
420	C₂²⋊C₄×C₇₃	—	2	2	no	—
421	C₂²⋊C₄×C₇₃	—	2	2	no	—
422	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
423	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₇₃	—	2	2	no	—
425	C₄²×C₇₃	—	2	2	no	—
426	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
429	C₂²×D₇₃	—	2	2	no	—
430	C₂²×D₇₃	—	2	2	no	—
431	C₂²×D₇₃	—	2	2	no	—
432	C₂²×D₇₃	—	2	2	no	—
433	C₂²×D₇₃	—	2	2	no	—
434	C₂²×D₇₃	—	4	1	no	—
435	C₂²×D₇₃	—	4	1	no	—
436	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
438	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
439	Q₈×C₇₃	—	2	2	no	—
440	Q₈×C₇₃	—	2	2	no	—
441	D₄×C₇₃	—	2	2	no	—
442	C₂×C₄×C₇₃	—	2	1	no	—
443	C₂×C₄×C₇₃	—	2	1	no	—
444	C₂×C₄×C₇₃	—	2	1	no	—
445	C₂×C₄×C₇₃	—	2	1	no	—
446	C₂×C₄×C₇₃	—	2	2	no	—
447	C₂×C₄×C₇₃	—	2	2	no	—
448	C₂×C₄×C₇₃	—	2	2	no	—
449	C₂×C₄×C₇₃	—	2	2	no	—
450	C₂×C₄×C₇₃	—	4	4	no	—
451	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
456	C₂²⋊D₇₃	—	2	2	no	—
457	C₂²⋊D₇₃	—	4	4	no	—
458	C₂²⋊D₇₃	—	8	2	no	—
459	C₂²⋊D₇₃	#135	1	4	yes	complemented
460	C₂×Dic₇₃	—	2	2	no	—
461	C₂×Dic₇₃	—	2	2	no	—
462	C₂×Dic₇₃	—	2	2	no	—
463	C₂×Dic₇₃	—	2	2	no	—
464	C₂×Dic₇₃	—	2	2	no	—
465	C₂×Dic₇₃	—	8	2	no	—
466	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
471	D₂₉₂	—	2	2	no	—
472	D₂₉₂	—	2	2	no	—
473	D₂₉₂	—	2	2	no	—
474	D₂₉₂	—	4	4	no	—
475	D₂₉₂	—	4	4	no	—
476	D₂₉₂	—	8	2	no	—
477	C₄×D₇₃	—	2	2	no	—
478	C₄×D₇₃	—	2	2	no	—
479	C₄×D₇₃	—	2	1	no	—
480	C₄×D₇₃	—	2	1	no	—
481	C₄×D₇₃	—	2	1	no	—
482	C₄×D₇₃	—	2	1	no	—
483	C₄×D₇₃	—	2	2	no	—
484	C₄×D₇₃	—	2	2	no	—
485	C₄×D₇₃	—	2	2	no	—
486	C₄×D₇₃	—	4	1	no	—
487	C₄×D₇₃	—	4	4	no	—
488	C₄×D₇₃	—	4	4	no	—
489	C₄×D₇₃	—	4	4	no	—
490	C₄×D₇₃	—	8	2	no	—
491	C₄×D₇₃	—	8	2	no	—
492	C₄×D₇₃	C₂×#41	1	2	yes	—
493	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
494	Dic₁₄₆	—	4	4	no	—
495	Dic₁₄₆	—	8	2	no	—
496	C₈×C₇₃	—	2	1	no	—
497	C₈×C₇₃	—	2	1	no	—
498	C₈×C₇₃	—	2	1	no	—
499	C₈×C₇₃	C₂×#41	1	2	yes	—
500	#10596831	—	2	1	no	—
501	#10596831	—	2	1	no	—
502	#10596831	—	2	1	no	—
503	#10596831	C₂×#41	1	2	yes	—
504	C₂²×C₇₃	—	2	1	no	—
505	C₂²×C₇₃	—	2	1	no	—
506	C₂²×C₇₃	—	2	1	no	—
507	C₂²×C₇₃	—	2	1	no	—
508	C₂²×C₇₃	—	2	1	no	—
509	C₂²×C₇₃	C₂×#135	1	2	yes	—
510	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
511	C₂×D₇₃	—	2	1	no	—
512	C₂×D₇₃	—	2	1	no	—
513	C₂×D₇₃	—	2	1	no	—
514	C₂×D₇₃	—	2	1	no	—
515	C₂×D₇₃	—	2	1	no	—
516	C₂×D₇₃	—	2	1	no	—
517	C₂×D₇₃	—	2	1	no	—
518	C₂×D₇₃	—	4	4	no	—
519	C₂×D₇₃	—	4	4	no	—
520	C₂×D₇₃	—	4	2	no	—
521	C₂×D₇₃	—	4	2	no	—
522	C₂×D₇₃	—	4	2	no	—
523	C₂×D₇₃	#547	1	2	yes	—
524	C₂×D₇₃	C₂×#135	1	2	yes	—
525	C₄×C₇₃	—	2	1	no	—
526	C₄×C₇₃	—	2	1	no	—
527	C₄×C₇₃	—	2	1	no	—
528	C₄×C₇₃	—	2	1	no	—
529	C₄×C₇₃	—	4	2	no	—
530	C₄×C₇₃	—	4	2	no	—
531	C₄×C₇₃	—	4	2	no	—
532	C₄×C₇₃	—	4	2	no	—
533	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
534	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	Dic₇₃	—	2	1	no	—
536	Dic₇₃	—	2	1	no	—
537	Dic₇₃	—	2	1	no	—
538	Dic₇₃	—	4	2	no	—
539	Dic₇₃	—	4	2	no	—
540	Dic₇₃	—	4	2	no	—
541	Dic₇₃	#547	1	2	yes	—
542	Dic₇₃	C₂×#135	1	2	yes	—
543	#61234	—	73	1	no	maximal, Sylow
544	C₂×C₇₃	—	2	2	no	—
545	C₂×C₇₃	—	4	1	no	—
546	C₂×C₇₃	C₂×#547	1	1	yes	characteristic
547	C₂×C₇₃	C₂²×#135	1	1	yes	characteristic
548	C₂×C₇₃	#3584	1	1	yes	characteristic
549	D₇₃	—	2	2	no	—
550	D₇₃	—	2	2	no	—
551	D₇₃	—	4	1	no	—
552	D₇₃	—	8	2	no	—
553	#3475	—	73	2	no	—
554	#3342	—	73	1	no	—
555	#3341	—	73	1	no	—
556	#3340	—	73	2	no	—
557	#3339	—	73	1	no	—
558	#3339	—	73	1	no	—
559	#3338	—	73	1	no	—
560	#3337	—	73	2	no	—
561	#3337	—	73	2	no	—
562	#3336	—	73	1	no	—
563	#3336	D₇₃	1	1	yes	characteristic, complemented
564	#3335	—	73	2	no	—
565	#3334	—	73	1	no	—
566	#3160	—	73	1	no	—
567	#3091	—	73	2	no	—
568	#3091	—	73	2	no	—
569	#3076	—	73	2	no	—
570	#3050	—	73	1	no	—
571	#3050	—	73	1	no	—
572	C₄×#135	—	73	1	no	—
573	C₂×C₈×D₄	—	73	1	no	—
574	C₂×#427	—	73	1	no	—
575	C₂×#427	—	73	1	no	—
576	C₇₃	#61234	1	1	yes	characteristic, complemented, Sylow
577	C₂×#135	—	73	1	no	—
578	C₂³×C₈	—	73	1	no	—
579	C₂³×C₈	—	73	1	no	—
580	#556	—	73	2	no	—
581	#555	—	73	2	no	—
582	#554	—	73	2	no	—
583	#553	—	73	2	no	—
584	#553	—	73	2	no	—
585	#552	—	73	2	no	—
586	#552	—	146	2	no	—
587	#552	C₂×D₇₃	1	2	yes	—
588	#551	—	146	2	no	—
589	#551	—	146	2	no	—
590	#547	—	73	2	no	—
591	#546	—	146	2	no	—
592	#533	—	73	2	no	—
593	#529	—	146	2	no	—
594	#529	—	146	2	no	—
595	#529	—	146	2	no	—
596	#525	—	73	2	no	—
597	#525	—	73	2	no	—
598	C₄×#41	—	73	2	no	—
599	C₄×#41	—	146	2	no	—
600	C₂×C₄×D₄	—	73	1	no	—
601	C₂×#117	—	73	2	no	—
602	C₂×#117	—	73	2	no	—
603	#500	—	73	1	no	—
604	#500	—	73	1	no	—
605	#499	—	73	2	no	—
606	#499	—	73	1	no	—
607	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
608	#498	—	73	2	no	—
609	#485	—	73	2	no	—
610	#485	—	73	2	no	—
611	#485	—	73	2	no	—
612	#485	C₂×D₇₃	1	2	yes	complemented
613	#484	—	73	2	no	—
614	#484	—	73	2	no	—
615	#483	—	73	2	no	—
616	#483	C₂×D₇₃	1	2	yes	complemented
617	#482	—	73	2	no	—
618	#482	—	73	2	no	—
619	#482	—	73	2	no	—
620	#482	—	73	2	no	—
621	#481	—	73	2	no	—
622	#481	—	73	2	no	—
623	#480	—	73	2	no	—
624	#480	—	73	2	no	—
625	#479	—	73	2	no	—
626	#479	C₂×D₇₃	1	2	yes	complemented
627	#478	—	73	2	no	—
628	#478	—	73	2	no	—
629	#477	—	73	2	no	—
630	#476	—	73	2	no	—
631	#475	—	73	2	no	—
632	#474	—	73	2	no	—
633	#467	—	73	1	no	—
634	#467	—	73	1	no	—
635	#467	C₂×D₇₃	1	1	yes	characteristic, complemented
636	#467	C₂×D₇₃	1	1	yes	characteristic, complemented
637	#466	—	73	1	no	—
638	#466	—	73	1	no	—
639	#466	—	73	1	no	—
640	#466	—	73	1	no	—
641	#465	—	73	2	no	—
642	#465	—	73	2	no	—
643	#465	—	73	2	no	—
644	#465	—	73	2	no	—
645	C₄×Q₁₆	—	73	1	no	—
646	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
647	C₄×SD₁₆	—	73	2	no	—
648	C₄×SD₁₆	—	73	2	no	—
649	C₄×D₈	—	73	1	no	—
650	C₄×D₈	—	73	1	no	—
651	C₈×D₄	—	73	1	no	—
652	C₈×D₄	—	73	1	no	—
653	C₈×D₄	—	73	1	no	—
654	C₈×D₄	—	73	1	no	—
655	C₈×D₄	—	73	1	no	—
656	C₈×D₄	—	73	1	no	—
657	C₈×D₄	—	73	1	no	—
658	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic
659	#427	—	73	1	no	—
660	#427	—	73	2	no	—
661	#427	—	73	2	no	—
662	#427	—	73	1	no	—
663	#427	—	73	2	no	—
664	#427	—	73	1	no	—
665	#427	—	73	1	no	—
666	#427	—	73	1	no	—
667	#427	—	73	1	no	—
668	#427	—	73	2	no	—
669	#427	—	73	2	no	—
670	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
671	C₂×#107	—	73	1	no	—
672	C₂×#107	—	73	1	no	—
673	C₂×#107	—	73	1	no	—
674	C₂×#107	C₂×D₇₃	1	1	yes	characteristic, complemented
675	C₂×#106	—	73	2	no	—
676	C₂×#106	—	73	2	no	—
677	C₂×C₄⋊C₈	—	73	1	no	—
678	#416	—	73	2	no	—
679	#416	—	73	2	no	—
680	#416	—	73	2	no	—
681	C₂×C₂²⋊C₈	—	73	1	no	—
682	C₂×C₂²⋊C₈	—	73	1	no	—
683	C₂×C₄×C₈	—	73	1	no	—
684	C₂×#41	—	73	2	no	—
685	C₂×#41	—	146	2	no	—
686	C₂²×D₄	—	73	1	no	—
687	C₂³×C₄	—	73	1	no	—
688	C₂³×C₄	—	73	1	no	—
689	#135	—	146	4	no	—
690	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
691	C₂×SD₁₆	—	73	2	no	—
692	C₂×D₈	—	73	1	no	—
693	C₂²×C₈	—	73	1	no	—
694	C₂²×C₈	—	73	1	no	—
695	C₂²×C₈	—	73	1	no	—
696	C₂²×C₈	—	73	1	no	—
697	C₂²×C₈	—	73	1	no	—
698	C₂²×C₈	—	73	1	no	—
699	C₂²×C₈	—	73	1	no	—
700	C₂²×C₈	—	73	1	no	—
701	C₂²×C₈	—	73	1	no	—
702	C₂²×C₈	—	73	1	no	—
703	C₂²×C₈	—	146	4	no	—
704	C₂²×C₈	—	146	4	no	—
705	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
706	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
707	C₄⋊Q₈	—	73	2	no	—
708	C₄⋊Q₈	—	73	2	no	—
709	#126	—	2	2	no	—
710	#126	—	146	2	no	—
711	#126	—	146	2	no	—
712	#126	—	146	2	no	—
713	#126	—	146	2	no	—
714	#126	—	146	2	no	—
715	#125	—	2	2	no	—
716	#125	—	73	2	no	—
717	#125	—	146	2	no	—
718	#125	—	146	2	no	—
719	#125	C₂²×D₇₃	1	2	yes	—
720	#124	—	146	2	no	—
721	#124	—	146	2	no	—
722	#124	—	146	2	no	—
723	#123	—	2	2	no	—
724	#123	—	146	2	no	—
725	#123	—	146	2	no	—
726	#123	—	146	2	no	—
727	#123	—	146	2	no	—
728	#123	—	146	2	no	—
729	#123	—	146	2	no	—
730	#123	—	146	2	no	—
731	C₂²⋊Q₈	—	73	2	no	—
732	C₂²⋊Q₈	—	73	2	no	—
733	C₂²⋊Q₈	—	146	2	no	—
734	C₂²⋊Q₈	—	146	2	no	—
735	C₂²⋊Q₈	—	146	2	no	—
736	C₂²⋊Q₈	—	146	2	no	—
737	C₂²⋊Q₈	—	146	2	no	—
738	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
739	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
740	#121	—	73	2	no	—
741	#121	—	73	2	no	—
742	#121	—	73	2	no	—
743	#121	—	73	2	no	—
744	#121	—	146	2	no	—
745	#121	—	146	2	no	—
746	#121	—	146	2	no	—
747	#120	—	146	2	no	—
748	#120	—	146	2	no	—
749	C₄×Q₈	—	73	2	no	—
750	C₄×Q₈	—	146	2	no	—
751	C₄×Q₈	—	146	2	no	—
752	C₄×Q₈	—	146	2	no	—
753	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
754	C₄×D₄	—	73	1	no	—
755	C₄×D₄	—	73	1	no	—
756	C₄×D₄	—	73	1	no	—
757	C₄×D₄	—	73	1	no	—
758	C₄×D₄	—	73	1	no	—
759	C₄×D₄	—	73	1	no	—
760	C₄×D₄	—	73	2	no	—
761	C₄×D₄	—	73	1	no	—
762	C₄×D₄	—	73	2	no	—
763	C₄×D₄	—	146	2	no	—
764	C₄×D₄	—	146	2	no	—
765	C₄×D₄	—	146	2	no	—
766	C₄×D₄	—	146	2	no	—
767	C₄×D₄	—	146	2	no	—
768	C₄×D₄	—	146	2	no	—
769	C₄×D₄	—	146	2	no	—
770	C₄×D₄	—	146	2	no	—
771	C₄×D₄	—	146	2	no	—
772	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
773	#117	—	2	2	no	—
774	#117	—	73	2	no	—
775	#117	—	73	2	no	—
776	#117	—	73	2	no	—
777	#117	—	73	2	no	—
778	#117	—	73	2	no	—
779	#117	—	73	2	no	—
780	#117	—	146	2	no	—
781	#117	—	146	2	no	—
782	#117	—	146	2	no	—
783	#117	—	146	2	no	—
784	#117	—	146	2	no	—
785	#117	—	146	2	no	—
786	#117	—	146	2	no	—
787	#117	C₂²×D₇₃	1	2	yes	—
788	C₂×C₄⋊C₄	—	73	1	no	—
789	C₂×C₄⋊C₄	—	73	2	no	—
790	C₂×C₄⋊C₄	—	73	2	no	—
791	C₂×C₄⋊C₄	—	73	2	no	—
792	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
793	C₂×C₂²⋊C₄	—	73	1	no	—
794	C₂×C₂²⋊C₄	—	73	1	no	—
795	C₂×C₂²⋊C₄	—	146	2	no	—
796	C₂×C₂²⋊C₄	—	146	2	no	—
797	C₂×C₄²	—	73	1	no	—
798	C₂×C₄²	—	146	2	no	—
799	C₂×C₄²	—	146	2	no	—
800	C₂×C₄²	—	146	2	no	—
801	#107	—	73	1	no	—
802	#107	—	73	1	no	—
803	#107	—	73	1	no	—
804	#107	—	73	2	no	—
805	#107	—	73	2	no	—
806	#107	—	73	2	no	—
807	#107	—	73	2	no	—
808	#107	—	73	2	no	—
809	#107	C₂²×D₇₃	1	1	yes	characteristic
810	#107	C₂²×D₇₃	1	1	yes	characteristic
811	#107	C₂²×D₇₃	1	1	yes	characteristic
812	#107	C₂²×D₇₃	1	2	yes	—
813	#106	—	73	2	no	—
814	#106	—	73	2	no	—
815	#106	—	73	2	no	—
816	#106	—	73	2	no	—
817	#106	—	73	2	no	—
818	#106	—	73	2	no	—
819	#106	—	73	2	no	—
820	#106	C₂²×D₇₃	1	2	yes	—
821	#106	C₂²×D₇₃	1	2	yes	—
822	C₄⋊C₈	—	73	1	no	—
823	C₄⋊C₈	—	73	1	no	—
824	C₄⋊C₈	—	73	1	no	—
825	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
826	#103	—	73	2	no	—
827	#103	—	73	2	no	—
828	#103	—	73	2	no	—
829	#103	C₂²×D₇₃	1	2	yes	—
830	#103	C₂²×D₇₃	1	2	yes	—
831	#103	C₂²×D₇₃	1	2	yes	—
832	#102	—	73	2	no	—
833	#102	—	73	2	no	—
834	#102	—	73	2	no	—
835	#102	—	73	2	no	—
836	#102	—	73	2	no	—
837	#102	—	73	2	no	—
838	C₂²⋊C₈	—	73	1	no	—
839	C₂²⋊C₈	—	73	1	no	—
840	C₂²⋊C₈	—	73	1	no	—
841	C₂²⋊C₈	—	73	1	no	—
842	C₂²⋊C₈	—	73	1	no	—
843	C₂²⋊C₈	—	73	1	no	—
844	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
845	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
846	C₄×C₈	—	73	1	no	—
847	C₄×C₈	—	73	1	no	—
848	C₄×C₈	—	73	1	no	—
849	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
850	C₂⁴	—	73	1	no	—
851	C₂⁴	—	73	1	no	—
852	#41	—	292	8	no	—
853	#41	—	146	4	no	—
854	#41	—	146	4	no	—
855	C₂×Q₈	—	146	2	no	—
856	C₂×Q₈	—	146	2	no	—
857	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
858	C₂×D₄	—	73	1	no	—
859	C₂×D₄	—	73	1	no	—
860	C₂×D₄	—	73	1	no	—
861	C₂×D₄	—	73	2	no	—
862	C₂×D₄	—	146	2	no	—
863	C₂×D₄	—	146	2	no	—
864	C₂×D₄	—	146	2	no	—
865	C₂×D₄	—	146	4	no	—
866	C₂×D₄	—	146	2	no	—
867	C₂×D₄	—	146	2	no	—
868	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	73	1	no	—
871	C₂²×C₄	—	73	1	no	—
872	C₂²×C₄	—	73	1	no	—
873	C₂²×C₄	—	73	1	no	—
874	C₂²×C₄	—	73	1	no	—
875	C₂²×C₄	—	73	1	no	—
876	C₂²×C₄	—	73	1	no	—
877	C₂²×C₄	—	73	1	no	—
878	C₂²×C₄	—	73	1	no	—
879	C₂²×C₄	—	73	1	no	—
880	C₂²×C₄	—	73	1	no	—
881	C₂²×C₄	—	146	2	no	—
882	C₂²×C₄	—	146	2	no	—
883	C₂²×C₄	—	146	2	no	—
884	C₂²×C₄	—	146	2	no	—
885	C₂²×C₄	—	146	2	no	—
886	C₂²×C₄	—	146	2	no	—
887	C₂²×C₄	—	146	2	no	—
888	C₂²×C₄	—	146	2	no	—
889	C₂²×C₄	—	146	2	no	—
890	C₂²×C₄	—	146	2	no	—
891	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
893	Q₁₆	—	2	2	no	—
894	SD₁₆	—	146	4	no	—
895	D₈	—	146	2	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	73	1	no	—
899	C₂×C₈	—	73	4	no	—
900	C₂×C₈	—	73	1	no	—
901	C₂×C₈	—	73	1	no	—
902	C₂×C₈	—	73	1	no	—
903	C₂×C₈	—	146	2	no	—
904	C₂×C₈	—	146	2	no	—
905	C₂×C₈	—	146	2	no	—
906	C₂×C₈	—	146	2	no	—
907	C₂×C₈	—	146	2	no	—
908	C₂×C₈	—	146	2	no	—
909	C₂×C₈	—	146	2	no	—
910	C₂×C₈	—	146	2	no	—
911	C₂×C₈	—	146	2	no	—
912	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	73	1	no	—
923	C₄⋊C₄	—	73	1	no	—
924	C₄⋊C₄	—	73	1	no	—
925	C₄⋊C₄	—	73	2	no	—
926	C₄⋊C₄	—	73	2	no	—
927	C₄⋊C₄	—	73	2	no	—
928	C₄⋊C₄	—	146	2	no	—
929	C₄⋊C₄	—	146	2	no	—
930	C₄⋊C₄	—	146	2	no	—
931	C₄⋊C₄	—	146	2	no	—
932	C₄⋊C₄	—	146	2	no	—
933	C₄⋊C₄	—	146	2	no	—
934	C₄⋊C₄	—	146	2	no	—
935	C₄⋊C₄	—	146	2	no	—
936	C₄⋊C₄	—	146	2	no	—
937	C₄⋊C₄	—	146	2	no	—
938	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
940	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
941	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	73	1	no	—
946	C₂²⋊C₄	—	73	1	no	—
947	C₂²⋊C₄	—	73	1	no	—
948	C₂²⋊C₄	—	73	1	no	—
949	C₂²⋊C₄	—	73	1	no	—
950	C₂²⋊C₄	—	73	1	no	—
951	C₂²⋊C₄	—	146	2	no	—
952	C₂²⋊C₄	—	146	2	no	—
953	C₂²⋊C₄	—	146	2	no	—
954	C₂²⋊C₄	—	146	2	no	—
955	C₂²⋊C₄	—	146	2	no	—
956	C₂²⋊C₄	—	146	2	no	—
957	C₂²⋊C₄	—	146	2	no	—
958	C₂²⋊C₄	—	146	2	no	—
959	C₂²⋊C₄	—	146	2	no	—
960	C₂²⋊C₄	—	146	2	no	—
961	C₂²⋊C₄	—	146	2	no	—
962	C₂²⋊C₄	—	146	2	no	—
963	C₂²⋊C₄	—	146	2	no	—
964	C₂²⋊C₄	—	146	2	no	—
965	C₂²⋊C₄	D₄×D₇₃	1	1	yes	characteristic
966	C₂²⋊C₄	D₄×D₇₃	1	1	yes	characteristic
967	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	73	1	no	—
970	C₄²	—	73	1	no	—
971	C₄²	—	73	1	no	—
972	C₄²	—	146	2	no	—
973	C₄²	—	146	2	no	—
974	C₄²	—	146	2	no	—
975	C₄²	—	146	2	no	—
976	C₄²	—	146	2	no	—
977	C₄²	—	146	2	no	—
978	C₄²	—	146	2	no	—
979	C₄²	C₂³×D₇₃	1	1	yes	characteristic
980	C₂³	—	292	1	no	—
981	C₂³	—	292	1	no	—
982	C₂³	—	73	1	no	—
983	C₂³	—	73	1	no	—
984	C₂³	—	73	1	no	—
985	C₂³	—	146	2	no	—
986	C₂³	—	146	2	no	—
987	C₂³	—	146	2	no	—
988	C₂³	—	146	2	no	—
989	C₂³	—	146	2	no	—
990	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
991	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	292	4	no	—
995	Q₈	—	584	2	no	—
996	D₄	—	2	2	no	—
997	D₄	—	292	4	no	—
998	D₄	—	292	4	no	—
999	D₄	—	292	4	no	—
1000	D₄	—	584	2	no	—
1001	D₄	—	584	2	no	—
1002	D₄	—	73	4	no	—
1003	D₄	—	146	2	no	—
1004	D₄	—	146	2	no	—
1005	D₄	—	146	2	no	—
1006	D₄	—	146	2	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	4	4	no	—
1016	C₂×C₄	—	292	1	no	—
1017	C₂×C₄	—	292	4	no	—
1018	C₂×C₄	—	292	4	no	—
1019	C₂×C₄	—	292	4	no	—
1020	C₂×C₄	—	584	2	no	—
1021	C₂×C₄	—	584	2	no	—
1022	C₂×C₄	—	584	2	no	—
1023	C₂×C₄	—	73	1	no	—
1024	C₂×C₄	—	73	1	no	—
1025	C₂×C₄	—	73	2	no	—
1026	C₂×C₄	—	73	2	no	—
1027	C₂×C₄	—	73	1	no	—
1028	C₂×C₄	—	73	1	no	—
1029	C₂×C₄	—	73	1	no	—
1030	C₂×C₄	—	146	2	no	—
1031	C₂×C₄	—	146	2	no	—
1032	C₂×C₄	—	146	2	no	—
1033	C₂×C₄	—	146	2	no	—
1034	C₂×C₄	—	146	2	no	—
1035	C₂×C₄	—	146	2	no	—
1036	C₂×C₄	—	146	2	no	—
1037	C₂×C₄	—	146	2	no	—
1038	C₂×C₄	—	146	2	no	—
1039	C₂×C₄	—	146	2	no	—
1040	C₂×C₄	—	146	1	no	—
1041	C₂×C₄	—	146	1	no	—
1042	C₂×C₄	—	146	1	no	—
1043	C₂×C₄	—	146	1	no	—
1044	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1046	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1047	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1048	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₈	—	73	2	no	—
1053	C₈	—	146	1	no	—
1054	C₈	—	146	1	no	—
1055	C₈	—	146	1	no	—
1056	C₈	#41×D₇₃	1	2	yes	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	292	4	no	—
1063	C₂²	—	292	4	no	—
1064	C₂²	—	292	2	no	—
1065	C₂²	—	292	2	no	—
1066	C₂²	—	292	2	no	—
1067	C₂²	—	73	2	no	—
1068	C₂²	—	73	2	no	—
1069	C₂²	—	146	1	no	—
1070	C₂²	—	146	1	no	—
1071	C₂²	—	146	1	no	—
1072	C₂²	—	146	1	no	—
1073	C₂²	—	146	1	no	—
1074	C₂²	—	146	1	no	—
1075	C₂²	—	146	1	no	—
1076	C₂²	#135×D₇₃	1	2	yes	—
1077	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	2	1	no	—
1081	C₄	—	2	1	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	2	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	292	2	no	—
1087	C₄	—	292	2	no	—
1088	C₄	—	292	2	no	—
1089	C₄	—	73	2	no	—
1090	C₄	—	73	2	no	—
1091	C₄	—	146	1	no	—
1092	C₄	—	146	1	no	—
1093	C₄	—	146	1	no	—
1094	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1095	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1096	C₂	—	2	2	no	—
1097	C₂	—	4	1	no	—
1098	C₂	—	292	1	no	—
1099	C₂	—	584	2	no	—
1100	C₂	—	146	2	no	—
1101	C₂	—	146	2	no	—
1102	C₂	#547×D₇₃	1	1	yes	characteristic
1103	C₂	C₂×#135×D₇₃	1	1	yes	characteristic
1104	C₂	#22624701	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×#3336	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#3336	D₇₃
hypocenter	C₇₃	#61234
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3336

Complements

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

N	H ≅ G/N	type
1. #22623484	C₂	semidirect
2. #22622358	C₂	semidirect
3. #22622351	C₂	semidirect
4. #22622337	C₂	semidirect
5. #22622334	C₂	semidirect
6. #22622332	C₂	semidirect
7. #22622320	C₂	semidirect
8. #22622310	C₂	semidirect
9. #22622307	C₂	semidirect
10. #22622301	C₂	semidirect
11. #22622281	C₂	semidirect
12. #22622276	C₂	semidirect
13. #22620444	C₂	semidirect
14. #22619849	C₂	semidirect
15. #22619845	C₂	semidirect
16. #22619718	C₂	semidirect
17. #22619514	C₂	semidirect
18. #22619514	C₂	semidirect
19. C₄×#14556614	C₂	semidirect
20. C₈×D₄×D₇₃	C₂	semidirect
21. C₂×#17988624	C₂	semidirect
22. #427×D₇₃	C₂	semidirect
23. C₇₃×#3336	C₂	semidirect
49. #17988991	C₂²	semidirect
50. #17988991	C₂²	semidirect
51. #17988989	C₂²	semidirect
52. #17988986	C₂²	semidirect
53. #17988984	C₂²	semidirect
54. #17988926	C₂²	semidirect
55. #17988926	C₂²	semidirect
56. #17988925	C₂²	semidirect
57. #17988921	C₂²	semidirect
58. #17988920	C₂²	semidirect
59. #17988916	C₂²	semidirect
60. #17988913	C₂²	semidirect
61. #17988913	C₂²	semidirect
62. #17988912	C₂²	semidirect
63. #17988911	C₂²	semidirect
64. #17988907	C₂²	semidirect
65. #17988906	C₂²	semidirect
66. #17988902	C₂²	semidirect
67. #17988900	C₂²	semidirect
68. #17988894	C₂²	semidirect
69. #17988888	C₂²	semidirect
70. #17988884	C₂²	semidirect
71. #17988880	C₂²	semidirect
72. #17988876	C₂²	semidirect
73. #17988870	C₂²	semidirect
74. #17988866	C₂²	semidirect
75. #17988825	C₂²	semidirect
76. #17988825	C₂²	semidirect
77. #17988824	C₂²	semidirect
78. #17988824	C₂²	semidirect
79. #17988823	C₂²	semidirect
80. #17988823	C₂²	semidirect
81. #17988819	C₂²	semidirect
82. #17988819	C₂²	semidirect
83. #17988818	C₂²	semidirect
84. #17988818	C₂²	semidirect
85. Q₁₆×Dic₇₃	C₂²	semidirect
86. C₄×#11924015	C₂²	semidirect
87. #17988672	C₂²	semidirect
88. C₄×D₅₈₄	C₂²	semidirect
89. #17988669	C₂²	semidirect
97. #17988625	C₂²	semidirect
102. #17988624	C₂²	semidirect
103. #17988624	C₂²	semidirect
104. #17988624	C₂²	semidirect
105. #17988623	C₂²	semidirect
108. C₂×#14556525	C₂²	semidirect
109. #107×D₇₃	C₂²	semidirect
110. #107×D₇₃	C₂²	semidirect
111. C₂×#14556522	C₂²	semidirect
112. #106×D₇₃	C₂²	semidirect
121. #499×C₇₃	C₂²	semidirect
122. #485×C₇₃	C₂²	semidirect
123. #483×C₇₃	C₂²	semidirect
124. #479×C₇₃	C₂²	semidirect
125. #467×C₇₃	C₂²	semidirect
126. #467×C₇₃	C₂²	semidirect
127. C₄×Q₁₆×C₇₃	C₂²	semidirect
129. #427×C₇₃	C₂²	semidirect
130. C₂×#107×C₇₃	C₂²	semidirect
350. C₈×D₇₃	#41	semidirect
459. C₂²⋊D₇₃	#135	semidirect
563. #3336	D₇₃	semidirect
576. C₇₃	#61234	semidirect
607. #499	C₂×D₇₃	semidirect
612. #485	C₂×D₇₃	semidirect
616. #483	C₂×D₇₃	semidirect
626. #479	C₂×D₇₃	semidirect
635. #467	C₂×D₇₃	semidirect
636. #467	C₂×D₇₃	semidirect
646. C₄×Q₁₆	C₂×D₇₃	semidirect
670. #427	C₂×D₇₃	semidirect
674. C₂×#107	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623484	2
#22622358	2
#22622351	2
#22622337	2
#22622334	2
#22622332	2
#22622320	2
#22622310	2
#22622307	2
#22622301	2
#22622281	2
#22622276	2
#22620444	2
#22619849	2
#22619845	2
#22619718	2
#22619514	2
C₄×#14556614	2
C₈×D₄×D₇₃	2
C₂×#17988624	2
#427×D₇₃	2
C₇₃×#3336	2
#61234	73