Subgroups — #33964076

Order 18688.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623798	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623724	C₂	1	1	yes	maximal, characteristic
3	#22622196	C₂	1	2	yes	maximal, complemented
4	#22622144	C₂	1	2	yes	maximal, complemented
5	#22622039	C₂	1	2	yes	maximal, complemented
6	#22622009	C₂	1	2	yes	maximal, complemented
7	#22621994	C₂	1	2	yes	maximal, complemented
8	#22621964	C₂	1	2	yes	maximal, complemented
9	#22621815	C₂	1	2	yes	maximal, complemented
10	#22621763	C₂	1	2	yes	maximal, complemented
11	#22620320	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	#22619587	C₂	1	1	yes	maximal, characteristic, complemented
15	#22619571	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#17988810	C₂	1	1	yes	maximal, characteristic, complemented
17	#22619229	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619211	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#14556621	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618674	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×#3076	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
27	C₂²×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#11924017	C₂²	1	1	yes	characteristic
29	C₂×#14556597	C₂²	1	1	yes	characteristic
30	C₂×#14556597	C₂²	1	1	yes	characteristic, complemented
31	#17989322	—	2	1	no	—
32	#17989316	—	2	1	no	—
33	#17989311	C₂²	1	2	yes	complemented
34	#17989310	—	2	1	no	—
35	#17989310	—	2	1	no	—
36	#17989298	C₂²	1	2	yes	complemented
37	#17989275	C₂²	1	2	yes	complemented
38	#17989275	C₂²	1	2	yes	complemented
39	#17989249	C₂²	1	2	yes	—
40	#17989249	C₂²	1	2	yes	—
41	#17989232	—	2	2	no	—
42	#17989232	—	2	2	no	—
43	#17989232	C₂²	1	2	yes	—
44	#17989232	C₂²	1	2	yes	—
45	#17989186	—	2	2	no	—
46	#17989163	—	2	1	no	—
47	#17989163	C₂²	1	1	yes	characteristic
48	#17989163	C₂²	1	1	yes	characteristic
49	#17989163	C₂²	1	1	yes	characteristic, complemented
50	#17989156	—	2	1	no	—
51	#17989156	C₂²	1	1	yes	characteristic
52	#17989137	—	2	1	no	—
53	#17989137	C₂²	1	1	yes	characteristic
54	#17989123	—	2	2	no	—
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	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
60	#17988949	C₂²	1	2	yes	complemented
61	#17988949	C₂²	1	2	yes	complemented
62	#17988944	C₂²	1	2	yes	complemented
63	#17988944	C₂²	1	2	yes	complemented
64	#17988931	C₂²	1	2	yes	complemented
65	#17988930	C₂²	1	2	yes	complemented
66	#17988924	C₂²	1	2	yes	complemented
67	#17988919	C₂²	1	2	yes	complemented
68	#17988914	C₂²	1	2	yes	complemented
69	#17988913	C₂²	1	2	yes	complemented
70	#17988907	C₂²	1	2	yes	complemented
71	#17988902	C₂²	1	2	yes	complemented
72	#17988846	C₂²	1	2	yes	complemented
73	#17988846	C₂²	1	2	yes	complemented
74	#17988834	C₂²	1	2	yes	complemented
75	#17988834	C₂²	1	2	yes	complemented
76	#17988829	C₂²	1	2	yes	complemented
77	#17988829	C₂²	1	2	yes	complemented
78	#17988817	C₂²	1	2	yes	complemented
79	#17988817	C₂²	1	2	yes	complemented
80	#17988810	C₂²	1	2	yes	complemented
81	#17988810	C₂²	1	2	yes	complemented
82	#17988810	C₂²	1	2	yes	complemented
83	#17988810	C₂²	1	2	yes	complemented
84	#17988752	C₂²	1	2	yes	—
85	#17988752	C₂²	1	2	yes	—
86	#17988750	C₂²	1	2	yes	complemented
87	#17988750	C₂²	1	2	yes	complemented
88	#17988744	C₂²	1	2	yes	complemented
89	#17988744	C₂²	1	2	yes	complemented
90	#17988739	C₂²	1	2	yes	—
91	#17988739	C₂²	1	2	yes	—
92	#17988692	C₂²	1	2	yes	complemented
93	#17988687	C₂²	1	2	yes	complemented
94	C₄×#11924018	C₂²	1	2	yes	complemented
95	C₄×#11924016	C₂²	1	2	yes	complemented
96	#17988664	C₂²	1	2	yes	complemented
97	#17988657	C₂²	1	2	yes	complemented
98	#17988657	C₂²	1	2	yes	complemented
99	#17988652	C₂²	1	2	yes	complemented
100	#17988630	C₂²	1	1	yes	characteristic, complemented
101	#17988595	C₂²	1	1	yes	characteristic, complemented
102	#17988595	C₂²	1	1	yes	characteristic, complemented
103	#17988595	C₂²	1	1	yes	characteristic, complemented
104	#17988594	C₂²	1	2	yes	complemented
105	#17988591	C₂²	1	1	yes	characteristic
106	#17988591	C₂²	1	1	yes	characteristic
107	#17988590	C₂²	1	2	yes	—
108	#17988588	C₂²	1	1	yes	characteristic
109	#17988587	C₂²	1	2	yes	—
110	#17988585	C₂²	1	2	yes	complemented
111	#17988582	C₂²	1	2	yes	—
112	#17988580	C₂²	1	2	yes	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	#102×D₇₃	C₂²	1	2	yes	—
117	#17988553	C₂²	1	1	yes	characteristic
118	#17988553	C₂²	1	1	yes	characteristic, complemented
119	C₄×#11924012	C₂²	1	1	yes	characteristic, complemented
120	#533×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#478×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#478×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#477×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#476×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#475×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#474×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#416×C₇₃	C₂²	1	1	yes	characteristic
134	#416×C₇₃	C₂²	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
143	C₂×#11924028	C₂³	1	1	yes	characteristic
144	C₂×#11924027	—	2	2	no	—
145	C₂×#11924027	C₂³	1	2	yes	—
146	C₂²×Dic₁₄₆	—	2	1	no	—
147	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
148	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
149	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
150	C₂²×D₂₉₂	—	2	1	no	—
151	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
152	C₂×D₄×D₇₃	—	2	2	no	—
153	C₂×D₄×D₇₃	C₂³	1	2	yes	—
154	#14556621	—	2	4	no	—
155	C₂×Dic₂₉₂	—	4	2	no	—
156	C₂×Dic₂₉₂	C₂³	1	2	yes	—
157	C₂×Dic₂₉₂	C₂³	1	2	yes	—
158	C₂×#11924018	C₂³	1	2	yes	—
159	C₂×#11924017	—	4	2	no	—
160	C₂×#11924017	C₂³	1	2	yes	—
161	C₂×#11924017	C₂³	1	2	yes	—
162	C₂×#11924016	C₂³	1	2	yes	—
163	#14556597	—	4	2	no	—
164	#14556597	—	4	2	no	—
165	C₂×#11924012	C₂³	1	1	yes	characteristic
166	C₂×#11924012	C₂³	1	1	yes	characteristic
167	C₂×#11924011	C₂³	1	2	yes	—
168	C₂×#11924011	C₂³	1	2	yes	—
169	C₂×C₈×D₇₃	C₂³	1	2	yes	—
170	C₂×C₈×D₇₃	C₂³	1	2	yes	—
171	#14556591	—	2	1	no	—
172	#14556591	—	2	1	no	—
173	#14556591	—	2	1	no	—
174	#14556591	D₄	1	1	yes	characteristic
175	#14556588	—	2	1	no	—
176	#14556588	D₄	1	1	yes	characteristic
177	#14556586	—	2	2	no	—
178	#14556586	—	2	2	no	—
179	#14556586	—	2	2	no	—
180	#14556586	—	2	2	no	—
181	#14556582	—	2	2	no	—
182	#14556582	—	2	2	no	—
183	#14556582	—	2	2	no	—
184	#14556580	—	2	2	no	—
185	#14556579	—	2	1	no	—
186	#14556579	—	2	1	no	—
187	#14556579	—	2	1	no	—
188	#14556579	—	2	1	no	—
189	#14556579	—	2	2	no	—
190	#14556579	—	2	2	no	—
191	#14556579	—	2	1	no	—
192	#14556579	—	2	1	no	—
193	#14556579	D₄	1	1	yes	characteristic
194	#14556579	D₄	1	1	yes	characteristic
195	#14556579	C₂³	1	2	yes	—
196	#14556579	C₂³	1	2	yes	—
197	#14556576	—	2	2	no	—
198	#14556576	—	2	2	no	—
199	#14556575	—	2	2	no	—
200	#14556575	—	2	2	no	—
201	#14556575	—	2	2	no	—
202	#14556575	—	2	2	no	—
203	#14556575	—	2	2	no	—
204	#14556571	—	2	2	no	—
205	#14556571	—	2	2	no	—
206	#14556571	C₂³	1	2	yes	—
207	#14556571	C₂³	1	2	yes	—
208	#14556571	C₂³	1	2	yes	—
209	#14556571	C₂³	1	2	yes	—
210	#14556571	C₂³	1	2	yes	—
211	#14556571	C₂³	1	2	yes	—
212	#14556567	—	2	2	no	—
213	#14556567	—	2	2	no	—
214	#14556566	—	2	2	no	—
215	#14556566	—	2	2	no	—
216	#14556566	C₂³	1	2	yes	—
217	#14556566	C₂³	1	2	yes	—
218	#14556565	—	2	2	no	—
219	#14556565	—	2	2	no	—
220	#14556565	D₄	1	2	yes	—
221	#14556565	D₄	1	2	yes	—
222	#14556561	—	2	2	no	—
223	#14556561	—	2	2	no	—
224	#14556561	—	2	2	no	—
225	Q₈×Dic₇₃	—	2	2	no	—
226	C₄×Dic₁₄₆	—	2	1	no	—
227	C₄×Dic₁₄₆	—	2	1	no	—
228	C₄×Dic₁₄₆	—	2	1	no	—
229	C₄×Dic₁₄₆	—	2	1	no	—
230	C₄×Dic₁₄₆	C₂³	1	2	yes	—
231	C₄×Dic₁₄₆	C₂³	1	2	yes	—
232	C₄×D₂₉₂	—	2	1	no	—
233	C₄×D₂₉₂	—	2	1	no	—
234	C₄×D₂₉₂	—	2	2	no	—
235	C₄×D₂₉₂	—	2	2	no	—
236	C₄×D₂₉₂	C₂³	1	2	yes	—
237	C₄×D₂₉₂	C₂³	1	2	yes	—
238	#14556553	—	2	2	no	—
239	#14556551	—	2	2	no	—
240	#14556551	—	2	2	no	—
241	#14556549	—	2	2	no	—
242	#14556549	—	2	2	no	—
243	#14556549	C₂³	1	2	yes	—
244	#14556549	C₂³	1	2	yes	—
245	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
246	C₂×#11924007	—	2	1	no	—
247	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
248	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
249	C₂×#11924005	—	2	2	no	—
250	C₂×#11924005	—	2	2	no	—
251	C₂×#11924005	—	2	1	no	—
252	C₂×#11924005	—	2	1	no	—
253	C₂×C₄×Dic₇₃	—	2	1	no	—
254	#14556524	C₂³	1	2	yes	—
255	#14556522	C₂³	1	2	yes	—
256	#14556516	C₂³	1	2	yes	—
257	#14556516	C₂³	1	2	yes	—
258	#14556515	C₂³	1	2	yes	—
259	#14556514	C₂³	1	2	yes	—
260	#14556514	C₂³	1	2	yes	—
261	#14556514	C₂³	1	2	yes	—
262	#14556514	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	#14556512	C₂³	1	2	yes	—
268	#14556511	C₂³	1	2	yes	—
269	#14556511	C₂³	1	2	yes	—
270	#14556511	C₂³	1	2	yes	—
271	#14556511	C₂³	1	2	yes	—
272	#14556503	C₂³	1	2	yes	—
273	#14556503	C₂³	1	2	yes	—
274	#14556503	C₂³	1	2	yes	—
275	#14556503	C₂³	1	2	yes	—
276	#14556502	C₂³	1	2	yes	—
277	C₄×#10596831	C₂³	1	2	yes	—
278	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
280	C₂²×C₈×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	#125×C₇₃	C₂³	1	1	yes	characteristic
284	#125×C₇₃	C₂³	1	1	yes	characteristic
285	C₂²⋊Q₈×C₇₃	—	2	1	no	—
286	C₂²⋊Q₈×C₇₃	—	2	1	no	—
287	C₄×Q₈×C₇₃	—	2	1	no	—
288	C₄×Q₈×C₇₃	—	2	1	no	—
289	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₇₃	—	2	1	no	—
292	C₄×D₄×C₇₃	—	2	1	no	—
293	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
295	#117×C₇₃	—	2	1	no	—
296	#117×C₇₃	C₂³	1	1	yes	characteristic
297	#117×C₇₃	C₂³	1	1	yes	characteristic
298	#117×C₇₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₇₃	—	2	1	no	—
300	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
301	#107×C₇₃	C₂³	1	1	yes	characteristic
302	#107×C₇₃	C₂³	1	1	yes	characteristic
303	#107×C₇₃	C₂³	1	1	yes	characteristic
304	#107×C₇₃	C₂³	1	1	yes	characteristic
305	#106×C₇₃	C₂³	1	1	yes	characteristic
306	#106×C₇₃	C₂³	1	1	yes	characteristic
307	#106×C₇₃	C₂³	1	1	yes	characteristic
308	#106×C₇₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×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	#103×C₇₃	C₂³	1	1	yes	characteristic
314	#103×C₇₃	C₂³	1	1	yes	characteristic
315	#103×C₇₃	C₂³	1	1	yes	characteristic
316	#103×C₇₃	C₂³	1	1	yes	characteristic
317	#102×C₇₃	C₂³	1	1	yes	characteristic
318	#102×C₇₃	C₂³	1	1	yes	characteristic
319	#102×C₇₃	C₂³	1	1	yes	characteristic
320	#102×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	#11924027	—	2	4	no	—
332	#11924027	—	4	2	no	—
333	#11924027	—	4	8	no	—
334	C₂×Dic₁₄₆	—	2	2	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	1	no	—
340	C₂×Dic₁₄₆	—	2	2	no	—
341	C₂×Dic₁₄₆	—	4	4	no	—
342	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
343	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
344	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
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	C₂×D₄	1	2	yes	—
363	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
364	D₄×D₇₃	—	2	4	no	—
365	D₄×D₇₃	—	4	2	no	—
366	D₄×D₇₃	—	4	8	no	—
367	C₂²×Dic₇₃	—	2	1	no	—
368	C₂²×Dic₇₃	—	2	1	no	—
369	C₂²×Dic₇₃	—	2	1	no	—
370	C₂²×Dic₇₃	—	2	2	no	—
371	C₂×C₄×D₇₃	—	2	2	no	—
372	C₂×C₄×D₇₃	—	2	2	no	—
373	C₂×C₄×D₇₃	—	2	2	no	—
374	C₂×C₄×D₇₃	—	2	2	no	—
375	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
376	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
377	Dic₂₉₂	—	4	2	no	—
378	Dic₂₉₂	—	4	2	no	—
379	#11924018	—	2	4	no	—
380	#11924017	—	4	2	no	—
381	#11924017	—	4	2	no	—
382	#11924016	—	2	4	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	1	no	—
392	C₄⋊Dic₇₃	—	2	2	no	—
393	C₄⋊Dic₇₃	—	2	2	no	—
394	C₄⋊Dic₇₃	—	2	2	no	—
395	C₄⋊Dic₇₃	—	2	2	no	—
396	C₄⋊Dic₇₃	—	2	2	no	—
397	C₄⋊Dic₇₃	—	2	2	no	—
398	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
399	C₄⋊Dic₇₃	C₂×D₄	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	#11924005	—	2	2	no	—
406	#11924005	—	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	C₄×Dic₇₃	—	2	2	no	—
426	C₄×Dic₇₃	—	2	2	no	—
427	#41×C₇₃	—	2	2	no	—
428	#41×C₇₃	#41	1	4	yes	—
429	C₂×Q₈×C₇₃	—	2	1	no	—
430	C₂×Q₈×C₇₃	—	2	1	no	—
431	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
432	C₂×D₄×C₇₃	—	2	1	no	—
433	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₇₃	—	2	1	no	—
435	C₂²×C₄×C₇₃	—	2	1	no	—
436	C₂²×C₄×C₇₃	—	2	1	no	—
437	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
438	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
439	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₂×C₈×C₇₃	—	2	2	no	—
441	C₂×C₈×C₇₃	—	2	2	no	—
442	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
443	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
444	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
445	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₇₃	—	2	1	no	—
447	C₄⋊C₄×C₇₃	—	2	1	no	—
448	C₄⋊C₄×C₇₃	—	2	1	no	—
449	C₄⋊C₄×C₇₃	—	2	1	no	—
450	C₄⋊C₄×C₇₃	—	2	1	no	—
451	C₄⋊C₄×C₇₃	—	2	1	no	—
452	C₄⋊C₄×C₇₃	—	2	1	no	—
453	C₄⋊C₄×C₇₃	—	2	1	no	—
454	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
455	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
457	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
459	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
460	C₂²⋊C₄×C₇₃	—	2	1	no	—
461	C₂²⋊C₄×C₇₃	—	2	1	no	—
462	C₂²⋊C₄×C₇₃	—	2	1	no	—
463	C₂²⋊C₄×C₇₃	—	2	1	no	—
464	C₂²⋊C₄×C₇₃	—	2	1	no	—
465	C₄²×C₇₃	—	2	1	no	—
466	C₄²×C₇₃	—	2	1	no	—
467	C₄²×C₇₃	—	2	1	no	—
468	C₄²×C₇₃	—	2	1	no	—
469	C₄²×C₇₃	—	2	1	no	—
470	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
471	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
472	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
473	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
474	C₂³×C₇₃	—	2	1	no	—
475	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
476	C₂²×D₇₃	—	2	2	no	—
477	C₂²×D₇₃	—	4	4	no	—
478	C₂²×D₇₃	—	4	2	no	—
479	C₂²×D₇₃	—	8	2	no	—
480	C₂²×D₇₃	—	8	2	no	—
481	C₂²×D₇₃	—	8	1	no	—
482	C₂²×D₇₃	—	8	1	no	—
483	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
484	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
485	Q₈×C₇₃	—	2	1	no	—
486	Q₈×C₇₃	—	4	2	no	—
487	Q₈×C₇₃	—	8	1	no	—
488	Q₈×C₇₃	C₂×#41	1	2	yes	—
489	D₄×C₇₃	—	2	4	no	—
490	D₄×C₇₃	—	2	1	no	—
491	D₄×C₇₃	C₂×#41	1	2	yes	—
492	C₂×C₄×C₇₃	—	2	1	no	—
493	C₂×C₄×C₇₃	—	2	4	no	—
494	C₂×C₄×C₇₃	—	2	1	no	—
495	C₂×C₄×C₇₃	—	2	1	no	—
496	C₂×C₄×C₇₃	—	2	1	no	—
497	C₂×C₄×C₇₃	—	2	1	no	—
498	C₂×C₄×C₇₃	—	2	1	no	—
499	C₂×C₄×C₇₃	—	2	1	no	—
500	C₂×C₄×C₇₃	—	4	1	no	—
501	C₂×C₄×C₇₃	—	4	1	no	—
502	C₂×C₄×C₇₃	—	8	1	no	—
503	C₂×C₄×C₇₃	—	8	1	no	—
504	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
511	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
512	C₂²⋊D₇₃	—	2	4	no	—
513	C₂²⋊D₇₃	—	2	4	no	—
514	C₂²⋊D₇₃	—	4	4	no	—
515	C₂²⋊D₇₃	—	4	4	no	—
516	C₂×Dic₇₃	—	2	2	no	—
517	C₂×Dic₇₃	—	2	2	no	—
518	C₂×Dic₇₃	—	2	2	no	—
519	C₂×Dic₇₃	—	4	4	no	—
520	C₂×Dic₇₃	—	4	2	no	—
521	C₂×Dic₇₃	—	4	2	no	—
522	C₂×Dic₇₃	—	8	1	no	—
523	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
524	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
525	D₂₉₂	—	2	2	no	—
526	D₂₉₂	—	2	2	no	—
527	D₂₉₂	—	2	2	no	—
528	D₂₉₂	—	2	2	no	—
529	D₂₉₂	—	4	2	no	—
530	D₂₉₂	—	4	2	no	—
531	D₂₉₂	—	4	4	no	—
532	D₂₉₂	—	4	2	no	—
533	D₂₉₂	—	8	2	no	—
534	D₂₉₂	—	8	2	no	—
535	C₄×D₇₃	—	2	2	no	—
536	C₄×D₇₃	—	2	2	no	—
537	C₄×D₇₃	—	2	2	no	—
538	C₄×D₇₃	—	2	2	no	—
539	C₄×D₇₃	—	4	4	no	—
540	C₄×D₇₃	—	4	4	no	—
541	C₄×D₇₃	—	8	2	no	—
542	C₄×D₇₃	—	8	2	no	—
543	Dic₁₄₆	—	2	2	no	—
544	Dic₁₄₆	—	2	2	no	—
545	Dic₁₄₆	—	2	2	no	—
546	Dic₁₄₆	—	2	2	no	—
547	Dic₁₄₆	—	2	2	no	—
548	Dic₁₄₆	—	2	2	no	—
549	Dic₁₄₆	—	4	4	no	—
550	Dic₁₄₆	—	4	2	no	—
551	Dic₁₄₆	—	4	2	no	—
552	C₈×C₇₃	—	2	1	no	—
553	C₈×C₇₃	—	2	1	no	—
554	C₈×C₇₃	—	2	1	no	—
555	C₈×C₇₃	—	2	1	no	—
556	#10596831	—	2	2	no	—
557	#10596831	—	2	2	no	—
558	C₂²×C₇₃	—	2	1	no	—
559	C₂²×C₇₃	—	2	1	no	—
560	C₂²×C₇₃	—	2	2	no	—
561	C₂²×C₇₃	—	4	1	no	—
562	C₂²×C₇₃	—	4	1	no	—
563	C₂²×C₇₃	#546	1	2	yes	—
564	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
565	C₂×D₇₃	—	2	2	no	—
566	C₂×D₇₃	—	2	2	no	—
567	C₂×D₇₃	—	2	2	no	—
568	C₂×D₇₃	—	2	2	no	—
569	C₂×D₇₃	—	2	2	no	—
570	C₂×D₇₃	—	2	2	no	—
571	C₂×D₇₃	—	4	2	no	—
572	C₂×D₇₃	—	4	2	no	—
573	C₂×D₇₃	—	4	2	no	—
574	C₂×D₇₃	—	16	4	no	—
575	C₂×D₇₃	—	16	2	no	—
576	C₄×C₇₃	—	2	1	no	—
577	C₄×C₇₃	—	2	1	no	—
578	C₄×C₇₃	—	2	1	no	—
579	C₄×C₇₃	—	2	1	no	—
580	C₄×C₇₃	—	2	2	no	—
581	C₄×C₇₃	—	4	1	no	—
582	C₄×C₇₃	—	4	1	no	—
583	C₄×C₇₃	—	4	1	no	—
584	C₄×C₇₃	—	4	1	no	—
585	C₄×C₇₃	—	4	1	no	—
586	C₄×C₇₃	—	4	1	no	—
587	C₄×C₇₃	#546	1	2	yes	—
588	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
589	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	Dic₇₃	—	2	2	no	—
591	Dic₇₃	—	2	2	no	—
592	Dic₇₃	—	4	2	no	—
593	Dic₇₃	—	4	2	no	—
594	Dic₇₃	—	4	2	no	—
595	#61207	—	73	1	no	maximal, Sylow
596	C₂×C₇₃	—	2	2	no	—
597	C₂×C₇₃	—	4	2	no	—
598	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
599	C₂×C₇₃	#3584	1	1	yes	characteristic
600	C₂×C₇₃	#3586	1	1	yes	characteristic
601	D₇₃	—	4	2	no	—
602	D₇₃	—	4	2	no	—
603	D₇₃	—	8	2	no	—
604	#3507	—	73	1	no	—
605	#3500	—	73	1	no	—
606	#3327	—	73	2	no	—
607	#3323	—	73	2	no	—
608	#3316	—	73	2	no	—
609	#3314	—	73	2	no	—
610	#3313	—	73	2	no	—
611	#3311	—	73	2	no	—
612	#3300	—	73	2	no	—
613	#3296	—	73	2	no	—
614	#3140	—	73	1	no	—
615	#3097	—	73	1	no	—
616	#3096	—	73	1	no	—
617	#3076	D₇₃	1	1	yes	characteristic, complemented
618	#3059	—	73	1	no	—
619	#3057	—	73	1	no	—
620	C₂×#464	—	73	1	no	—
621	#3011	—	73	1	no	—
622	#3009	—	73	1	no	—
623	C₄×#137	—	73	1	no	—
624	#2935	—	73	1	no	—
625	#2898	—	73	1	no	—
626	#2897	—	73	1	no	—
627	C₇₃	#61207	1	1	yes	characteristic, complemented, Sylow
628	C₂×2₋¹⁺⁴	—	73	1	no	—
629	C₂×H(5,𝔽₂)	—	73	1	no	—
630	C₂×#137	—	73	1	no	—
631	C₂²×Q₁₆	—	73	1	no	—
632	C₂²×SD₁₆	—	73	1	no	—
633	C₂×#131	—	73	1	no	—
634	C₂×#131	—	73	1	no	—
635	#559	—	146	1	no	—
636	#557	—	146	1	no	—
637	#556	—	73	2	no	—
638	#556	—	146	1	no	—
639	#556	—	146	1	no	—
640	#554	—	73	2	no	—
641	#552	—	73	2	no	—
642	#552	—	73	2	no	—
643	#548	—	73	2	no	—
644	#548	—	73	2	no	—
645	#546	—	73	2	no	—
646	#546	—	73	2	no	—
647	#546	—	146	2	no	—
648	#546	—	146	2	no	—
649	#539	—	146	2	no	—
650	#536	—	73	1	no	—
651	#536	—	73	1	no	—
652	#536	—	73	1	no	—
653	#536	—	146	1	no	—
654	#535	—	73	1	no	—
655	#535	—	146	1	no	—
656	#533	C₂×D₇₃	1	1	yes	characteristic, complemented
657	#532	—	73	1	no	—
658	#532	—	146	1	no	—
659	#529	—	146	2	no	—
660	C₂×#124	—	73	1	no	—
661	C₂×#124	—	146	1	no	—
662	#520	—	73	1	no	—
663	#520	—	73	1	no	—
664	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
665	C₂×C₄×Q₈	—	73	1	no	—
666	#489	—	73	2	no	—
667	#489	—	73	2	no	—
668	#488	—	73	2	no	—
669	#488	—	73	2	no	—
670	#485	—	73	2	no	—
671	#485	—	73	2	no	—
672	#484	—	73	2	no	—
673	#483	—	73	2	no	—
674	#482	—	73	2	no	—
675	#482	—	73	2	no	—
676	#481	—	73	2	no	—
677	#480	—	73	2	no	—
678	#479	C₂×D₇₃	1	1	yes	characteristic, complemented
679	#479	C₂×D₇₃	1	1	yes	characteristic, complemented
680	#478	C₂×D₇₃	1	1	yes	characteristic, complemented
681	#478	C₂×D₇₃	1	1	yes	characteristic, complemented
682	#477	C₂×D₇₃	1	1	yes	characteristic, complemented
683	#476	C₂×D₇₃	1	1	yes	characteristic, complemented
684	#475	C₂×D₇₃	1	1	yes	characteristic, complemented
685	#474	C₂×D₇₃	1	1	yes	characteristic, complemented
686	#470	—	73	2	no	—
687	#470	—	73	2	no	—
688	#468	—	73	2	no	—
689	#468	—	73	2	no	—
690	#467	—	73	2	no	—
691	#467	—	73	2	no	—
692	#465	—	73	2	no	—
693	#465	—	73	2	no	—
694	#464	—	73	2	no	—
695	#464	—	73	2	no	—
696	#464	—	73	2	no	—
697	#464	—	73	2	no	—
698	#452	—	73	2	no	—
699	#452	—	73	2	no	—
700	#452	—	73	2	no	—
701	#452	—	73	2	no	—
702	#451	—	73	2	no	—
703	#451	—	73	2	no	—
704	#450	—	73	2	no	—
705	#450	—	73	2	no	—
706	#441	—	73	2	no	—
707	#440	—	73	2	no	—
708	C₄×Q₁₆	—	73	2	no	—
709	C₄×SD₁₆	—	73	2	no	—
710	#436	—	73	2	no	—
711	#435	—	73	2	no	—
712	#435	—	73	2	no	—
713	C₈×D₄	—	73	2	no	—
714	#428	—	73	1	no	—
715	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
716	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
717	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
718	#419	—	73	1	no	—
719	#419	—	73	1	no	—
720	#419	—	73	1	no	—
721	#419	—	73	2	no	—
722	#418	—	73	1	no	—
723	#418	—	73	1	no	—
724	#418	—	73	2	no	—
725	#417	—	73	1	no	—
726	#417	—	73	2	no	—
727	#417	—	73	2	no	—
728	#416	—	73	2	no	—
729	#416	—	73	2	no	—
730	#416	C₂×D₇₃	1	1	yes	characteristic
731	#416	C₂×D₇₃	1	1	yes	characteristic
732	C₂×#103	—	73	1	no	—
733	C₂×#103	—	73	2	no	—
734	C₂×#102	—	73	1	no	—
735	C₂×#102	—	73	2	no	—
736	#408	—	73	1	no	—
737	#408	—	73	1	no	—
738	C₄×M₁₆	—	73	1	no	—
739	2₋¹⁺⁴	—	292	2	no	—
740	2₋¹⁺⁴	—	146	4	no	—
741	H(5,𝔽₂)	—	292	2	no	—
742	H(5,𝔽₂)	—	146	4	no	—
743	C₂×#41	—	73	1	no	—
744	C₂×#41	—	73	1	no	—
745	C₂×#41	—	73	2	no	—
746	C₂×#41	—	73	2	no	—
747	C₂×#41	—	146	1	no	—
748	C₂×#41	—	146	1	no	—
749	C₂×#41	—	146	2	no	—
750	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
751	C₂²×Q₈	—	73	2	no	—
752	C₂²×Q₈	—	73	1	no	—
753	C₂²×Q₈	—	73	1	no	—
754	C₂²×Q₈	—	146	1	no	—
755	C₂²×D₄	—	73	2	no	—
756	C₂²×D₄	—	73	1	no	—
757	C₂²×D₄	—	146	1	no	—
758	C₂²×D₄	—	146	2	no	—
759	#137	—	146	4	no	—
760	C₂×Q₁₆	—	292	2	no	—
761	C₂×Q₁₆	—	73	2	no	—
762	C₂×Q₁₆	—	73	2	no	—
763	C₂×Q₁₆	—	73	2	no	—
764	C₂×SD₁₆	—	292	2	no	—
765	C₂×SD₁₆	—	73	2	no	—
766	C₂×SD₁₆	—	73	2	no	—
767	C₂×SD₁₆	—	73	2	no	—
768	#131	—	292	2	no	—
769	#131	—	292	2	no	—
770	C₂×M₁₆	—	73	1	no	—
771	C₂×M₁₆	—	73	1	no	—
772	C₂×M₁₆	—	73	2	no	—
773	C₂×M₁₆	—	73	2	no	—
774	C₂²×C₈	—	73	2	no	—
775	C₂²×C₈	—	73	2	no	—
776	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
777	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
778	C₄⋊Q₈	—	73	1	no	—
779	C₄⋊Q₈	—	146	1	no	—
780	C₄⋊Q₈	—	146	1	no	—
781	C₄⋊Q₈	—	146	1	no	—
782	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
783	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
784	#127	—	73	1	no	—
785	#127	—	146	1	no	—
786	#126	—	146	2	no	—
787	#126	—	146	2	no	—
788	#126	—	146	2	no	—
789	#126	—	146	2	no	—
790	#125	—	146	2	no	—
791	#125	—	146	2	no	—
792	#125	—	146	2	no	—
793	#125	C₂²×D₇₃	1	1	yes	characteristic
794	#125	C₂²×D₇₃	1	1	yes	characteristic
795	#124	—	73	1	no	—
796	#124	—	73	1	no	—
797	#124	—	73	2	no	—
798	#124	—	73	2	no	—
799	#124	—	146	2	no	—
800	#124	—	146	2	no	—
801	#124	—	146	1	no	—
802	#124	—	146	1	no	—
803	#124	—	146	1	no	—
804	#124	—	146	1	no	—
805	#124	—	146	2	no	—
806	#124	—	146	1	no	—
807	#124	—	146	1	no	—
808	#123	—	146	2	no	—
809	#123	—	146	2	no	—
810	#123	—	146	2	no	—
811	#123	—	146	2	no	—
812	#123	—	146	2	no	—
813	#123	—	146	2	no	—
814	#123	—	146	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	73	2	no	—
818	C₂²⋊Q₈	—	73	2	no	—
819	C₂²⋊Q₈	—	73	2	no	—
820	C₂²⋊Q₈	—	73	2	no	—
821	C₂²⋊Q₈	—	73	2	no	—
822	C₂²⋊Q₈	—	73	2	no	—
823	C₂²⋊Q₈	—	146	2	no	—
824	C₂²⋊Q₈	—	146	2	no	—
825	C₂²⋊Q₈	—	146	2	no	—
826	C₂²⋊Q₈	—	146	2	no	—
827	#121	—	73	2	no	—
828	#121	—	73	2	no	—
829	#121	—	73	2	no	—
830	#121	—	73	2	no	—
831	#121	—	146	2	no	—
832	#121	—	146	2	no	—
833	#121	—	146	2	no	—
834	#121	—	146	2	no	—
835	#120	—	146	2	no	—
836	#120	—	146	2	no	—
837	#120	—	146	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	73	2	no	—
841	C₄×Q₈	—	73	2	no	—
842	C₄×Q₈	—	146	1	no	—
843	C₄×Q₈	—	146	1	no	—
844	C₄×Q₈	—	146	2	no	—
845	C₄×Q₈	—	146	1	no	—
846	C₄×Q₈	—	146	1	no	—
847	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
848	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	73	2	no	—
852	C₄×D₄	—	73	2	no	—
853	C₄×D₄	—	146	2	no	—
854	C₄×D₄	—	146	2	no	—
855	C₄×D₄	—	146	1	no	—
856	C₄×D₄	—	146	1	no	—
857	C₄×D₄	—	146	2	no	—
858	C₄×D₄	—	146	2	no	—
859	C₄×D₄	—	146	2	no	—
860	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
861	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
862	#117	—	2	1	no	—
863	#117	—	73	2	no	—
864	#117	—	73	2	no	—
865	#117	—	146	2	no	—
866	#117	—	146	2	no	—
867	#117	C₂²×D₇₃	1	1	yes	characteristic
868	#117	C₂²×D₇₃	1	1	yes	characteristic
869	#117	C₂²×D₇₃	1	1	yes	characteristic
870	C₂×C₄⋊C₄	—	73	1	no	—
871	C₂×C₄⋊C₄	—	73	2	no	—
872	C₂×C₄⋊C₄	—	73	2	no	—
873	C₂×C₄⋊C₄	—	146	1	no	—
874	C₂×C₂²⋊C₄	—	146	2	no	—
875	C₂×C₂²⋊C₄	—	146	2	no	—
876	C₂×C₂²⋊C₄	—	146	1	no	—
877	C₂×C₂²⋊C₄	—	146	1	no	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	—	146	1	no	—
880	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
881	#107	—	73	2	no	—
882	#107	C₂²×D₇₃	1	1	yes	characteristic
883	#107	C₂²×D₇₃	1	1	yes	characteristic
884	#107	C₂²×D₇₃	1	1	yes	characteristic
885	#107	C₂²×D₇₃	1	1	yes	characteristic
886	#106	—	73	2	no	—
887	#106	C₂²×D₇₃	1	1	yes	characteristic
888	#106	C₂²×D₇₃	1	1	yes	characteristic
889	#106	C₂²×D₇₃	1	1	yes	characteristic
890	#106	C₂²×D₇₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
892	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
893	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
894	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
895	#103	—	73	2	no	—
896	#103	—	73	2	no	—
897	#103	—	73	2	no	—
898	#103	—	73	2	no	—
899	#103	—	73	2	no	—
900	#103	—	73	2	no	—
901	#103	—	73	2	no	—
902	#103	—	73	2	no	—
903	#103	—	73	2	no	—
904	#103	C₂²×D₇₃	1	1	yes	characteristic
905	#103	C₂²×D₇₃	1	1	yes	characteristic
906	#103	C₂²×D₇₃	1	1	yes	characteristic
907	#103	C₂²×D₇₃	1	1	yes	characteristic
908	#102	—	73	2	no	—
909	#102	—	73	2	no	—
910	#102	—	73	2	no	—
911	#102	—	73	2	no	—
912	#102	—	73	2	no	—
913	#102	—	73	2	no	—
914	#102	—	73	2	no	—
915	#102	C₂²×D₇₃	1	1	yes	characteristic
916	#102	C₂²×D₇₃	1	1	yes	characteristic
917	#102	C₂²×D₇₃	1	1	yes	characteristic
918	#102	C₂²×D₇₃	1	1	yes	characteristic
919	C₂²⋊C₈	—	73	2	no	—
920	C₂²⋊C₈	—	73	2	no	—
921	C₂²⋊C₈	—	73	2	no	—
922	C₂²⋊C₈	—	73	2	no	—
923	#97	—	73	2	no	—
924	C₄×C₈	—	73	2	no	—
925	C₂⁴	—	146	2	no	—
926	C₂⁴	—	146	1	no	—
927	#41	—	2	2	no	—
928	#41	—	292	4	no	—
929	#41	—	292	4	no	—
930	#41	—	292	8	no	—
931	#41	—	292	2	no	—
932	#41	—	292	2	no	—
933	#41	—	146	4	no	—
934	#41	—	146	4	no	—
935	#41	—	146	2	no	—
936	#41	—	146	2	no	—
937	#41	—	146	2	no	—
938	#41	—	146	2	no	—
939	#41	#11924029	1	4	yes	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	292	4	no	—
943	C₂×Q₈	—	292	2	no	—
944	C₂×Q₈	—	73	1	no	—
945	C₂×Q₈	—	73	1	no	—
946	C₂×Q₈	—	73	2	no	—
947	C₂×Q₈	—	73	2	no	—
948	C₂×Q₈	—	146	2	no	—
949	C₂×Q₈	—	146	4	no	—
950	C₂×Q₈	—	146	2	no	—
951	C₂×Q₈	—	146	2	no	—
952	C₂×Q₈	—	146	2	no	—
953	C₂×Q₈	—	146	2	no	—
954	C₂×Q₈	—	146	1	no	—
955	C₂×Q₈	—	146	1	no	—
956	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	292	4	no	—
959	C₂×D₄	—	292	8	no	—
960	C₂×D₄	—	292	2	no	—
961	C₂×D₄	—	73	2	no	—
962	C₂×D₄	—	73	2	no	—
963	C₂×D₄	—	73	2	no	—
964	C₂×D₄	—	73	2	no	—
965	C₂×D₄	—	73	1	no	—
966	C₂×D₄	—	73	1	no	—
967	C₂×D₄	—	73	2	no	—
968	C₂×D₄	—	146	2	no	—
969	C₂×D₄	—	146	2	no	—
970	C₂×D₄	—	146	2	no	—
971	C₂×D₄	—	146	2	no	—
972	C₂×D₄	—	146	2	no	—
973	C₂×D₄	—	146	4	no	—
974	C₂×D₄	—	146	1	no	—
975	C₂×D₄	—	146	2	no	—
976	C₂×D₄	—	146	2	no	—
977	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	73	2	no	—
982	C₂²×C₄	—	73	2	no	—
983	C₂²×C₄	—	146	2	no	—
984	C₂²×C₄	—	146	2	no	—
985	C₂²×C₄	—	146	2	no	—
986	C₂²×C₄	—	146	2	no	—
987	C₂²×C₄	—	146	2	no	—
988	C₂²×C₄	—	146	1	no	—
989	C₂²×C₄	—	146	1	no	—
990	C₂²×C₄	—	146	1	no	—
991	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
992	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
993	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
994	Q₁₆	—	292	2	no	—
995	Q₁₆	—	292	2	no	—
996	Q₁₆	—	146	4	no	—
997	SD₁₆	—	292	2	no	—
998	SD₁₆	—	292	2	no	—
999	SD₁₆	—	146	4	no	—
1000	M₁₆	—	292	2	no	—
1001	M₁₆	—	292	2	no	—
1002	M₁₆	—	146	2	no	—
1003	M₁₆	—	146	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	292	2	no	—
1007	C₂×C₈	—	292	2	no	—
1008	C₂×C₈	—	73	2	no	—
1009	C₂×C₈	—	73	2	no	—
1010	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1011	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1012	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1013	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	73	2	no	—
1023	C₄⋊C₄	—	73	2	no	—
1024	C₄⋊C₄	—	73	2	no	—
1025	C₄⋊C₄	—	146	2	no	—
1026	C₄⋊C₄	—	146	2	no	—
1027	C₄⋊C₄	—	146	2	no	—
1028	C₄⋊C₄	—	146	2	no	—
1029	C₄⋊C₄	—	146	2	no	—
1030	C₄⋊C₄	—	146	2	no	—
1031	C₄⋊C₄	—	146	2	no	—
1032	C₄⋊C₄	—	146	2	no	—
1033	C₄⋊C₄	—	146	2	no	—
1034	C₄⋊C₄	—	146	2	no	—
1035	C₄⋊C₄	—	146	1	no	—
1036	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1037	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1038	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1039	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1040	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1041	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	73	2	no	—
1048	C₂²⋊C₄	—	73	2	no	—
1049	C₂²⋊C₄	—	73	2	no	—
1050	C₂²⋊C₄	—	73	2	no	—
1051	C₂²⋊C₄	—	146	2	no	—
1052	C₂²⋊C₄	—	146	2	no	—
1053	C₂²⋊C₄	—	146	2	no	—
1054	C₂²⋊C₄	—	146	2	no	—
1055	C₂²⋊C₄	—	146	2	no	—
1056	C₂²⋊C₄	—	146	2	no	—
1057	C₂²⋊C₄	—	146	2	no	—
1058	C₂²⋊C₄	—	146	2	no	—
1059	C₂²⋊C₄	—	146	2	no	—
1060	C₂²⋊C₄	—	146	2	no	—
1061	C₂²⋊C₄	—	146	2	no	—
1062	C₂²⋊C₄	—	146	2	no	—
1063	C₂²⋊C₄	—	146	2	no	—
1064	C₂²⋊C₄	—	146	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	1	no	—
1070	C₄²	—	146	2	no	—
1071	C₄²	—	146	2	no	—
1072	C₄²	—	146	2	no	—
1073	C₄²	—	146	2	no	—
1074	C₄²	D₄×D₇₃	1	1	yes	characteristic
1075	C₄²	D₄×D₇₃	1	1	yes	characteristic
1076	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1077	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	292	4	no	—
1080	C₂³	—	292	2	no	—
1081	C₂³	—	584	1	no	—
1082	C₂³	—	584	1	no	—
1083	C₂³	—	584	2	no	—
1084	C₂³	—	584	2	no	—
1085	C₂³	—	73	2	no	—
1086	C₂³	—	73	2	no	—
1087	C₂³	—	146	2	no	—
1088	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1089	Q₈	—	2	1	no	—
1090	Q₈	—	4	2	no	—
1091	Q₈	—	8	1	no	—
1092	Q₈	—	292	4	no	—
1093	Q₈	—	292	2	no	—
1094	Q₈	—	292	2	no	—
1095	Q₈	—	146	2	no	—
1096	Q₈	—	146	2	no	—
1097	Q₈	—	146	2	no	—
1098	Q₈	—	146	2	no	—
1099	Q₈	—	146	2	no	—
1100	Q₈	—	146	2	no	—
1101	Q₈	C₂×#11924029	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	292	4	no	—
1105	D₄	—	292	2	no	—
1106	D₄	—	292	2	no	—
1107	D₄	—	292	4	no	—
1108	D₄	—	292	4	no	—
1109	D₄	—	292	2	no	—
1110	D₄	—	584	2	no	—
1111	D₄	—	584	2	no	—
1112	D₄	—	146	4	no	—
1113	D₄	—	146	4	no	—
1114	D₄	—	146	2	no	—
1115	D₄	—	146	2	no	—
1116	D₄	—	146	2	no	—
1117	D₄	—	146	2	no	—
1118	D₄	C₂×#11924029	1	2	yes	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	292	4	no	—
1132	C₂×C₄	—	292	4	no	—
1133	C₂×C₄	—	292	2	no	—
1134	C₂×C₄	—	292	2	no	—
1135	C₂×C₄	—	292	4	no	—
1136	C₂×C₄	—	584	2	no	—
1137	C₂×C₄	—	584	2	no	—
1138	C₂×C₄	—	584	1	no	—
1139	C₂×C₄	—	73	2	no	—
1140	C₂×C₄	—	73	2	no	—
1141	C₂×C₄	—	146	2	no	—
1142	C₂×C₄	—	146	2	no	—
1143	C₂×C₄	—	146	2	no	—
1144	C₂×C₄	—	146	2	no	—
1145	C₂×C₄	—	146	2	no	—
1146	C₂×C₄	—	146	2	no	—
1147	C₂×C₄	—	146	2	no	—
1148	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1149	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1150	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1151	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1152	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1153	C₂×C₄	C₂×#11924029	1	2	yes	—
1154	C₂×C₄	#14556637	1	2	yes	—
1155	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	146	2	no	—
1161	C₈	—	146	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	292	2	no	—
1168	C₂²	—	292	2	no	—
1169	C₂²	—	292	2	no	—
1170	C₂²	—	1168	2	no	—
1171	C₂²	—	1168	4	no	—
1172	C₂²	—	146	2	no	—
1173	C₂²	—	146	2	no	—
1174	C₂²	—	146	2	no	—
1175	C₂²	—	146	2	no	—
1176	C₂²	—	146	2	no	—
1177	C₂²	—	146	2	no	—
1178	C₂²	#17989228	1	2	yes	—
1179	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	292	2	no	—
1192	C₄	—	292	2	no	—
1193	C₄	—	292	2	no	—
1194	C₄	—	146	2	no	—
1195	C₄	—	146	2	no	—
1196	C₄	#17989228	1	2	yes	—
1197	C₄	C₂²×#11924029	1	1	yes	characteristic
1198	C₄	C₂×#14556637	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	292	2	no	—
1202	C₂	—	292	2	no	—
1203	C₂	—	584	2	no	—
1204	C₂	C₂×#17989228	1	1	yes	characteristic
1205	C₂	#22624700	1	1	yes	characteristic
1206	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×#3076	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	#22623724	C₂
hypercenter	#3076	D₇₃
hypocenter	C₇₃	#61207
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #22623798	C₂	semidirect
3. #22622196	C₂	semidirect
4. #22622144	C₂	semidirect
5. #22622039	C₂	semidirect
6. #22622009	C₂	semidirect
7. #22621994	C₂	semidirect
8. #22621964	C₂	semidirect
9. #22621815	C₂	semidirect
10. #22621763	C₂	semidirect
11. #22620320	C₂	semidirect
12. #22619903	C₂	semidirect
13. #22619892	C₂	semidirect
14. #22619587	C₂	semidirect
15. #22619571	C₂	semidirect
16. C₂×#17988810	C₂	semidirect
17. #22619229	C₂	semidirect
18. #22619211	C₂	semidirect
19. C₄×#14556621	C₂	semidirect
20. #22618674	C₂	semidirect
21. #22618460	C₂	semidirect
22. #22618453	C₂	semidirect
23. C₇₃×#3076	C₂	semidirect
27. C₂²×Dic₂₉₂	C₂²	semidirect
30. C₂×#14556597	C₂²	semidirect
33. #17989311	C₂²	semidirect
36. #17989298	C₂²	semidirect
37. #17989275	C₂²	semidirect
38. #17989275	C₂²	semidirect
49. #17989163	C₂²	semidirect
58. #17989067	C₂²	semidirect
59. C₂×C₄×Dic₁₄₆	C₂²	semidirect
60. #17988949	C₂²	semidirect
61. #17988949	C₂²	semidirect
62. #17988944	C₂²	semidirect
63. #17988944	C₂²	semidirect
64. #17988931	C₂²	semidirect
65. #17988930	C₂²	semidirect
66. #17988924	C₂²	semidirect
67. #17988919	C₂²	semidirect
68. #17988914	C₂²	semidirect
69. #17988913	C₂²	semidirect
70. #17988907	C₂²	semidirect
71. #17988902	C₂²	semidirect
72. #17988846	C₂²	semidirect
73. #17988846	C₂²	semidirect
74. #17988834	C₂²	semidirect
75. #17988834	C₂²	semidirect
76. #17988829	C₂²	semidirect
77. #17988829	C₂²	semidirect
78. #17988817	C₂²	semidirect
79. #17988817	C₂²	semidirect
80. #17988810	C₂²	semidirect
81. #17988810	C₂²	semidirect
82. #17988810	C₂²	semidirect
83. #17988810	C₂²	semidirect
86. #17988750	C₂²	semidirect
87. #17988750	C₂²	semidirect
88. #17988744	C₂²	semidirect
89. #17988744	C₂²	semidirect
92. #17988692	C₂²	semidirect
93. #17988687	C₂²	semidirect
94. C₄×#11924018	C₂²	semidirect
95. C₄×#11924016	C₂²	semidirect
96. #17988664	C₂²	semidirect
97. #17988657	C₂²	semidirect
98. #17988657	C₂²	semidirect
99. #17988652	C₂²	semidirect
100. #17988630	C₂²	semidirect
101. #17988595	C₂²	semidirect
102. #17988595	C₂²	semidirect
103. #17988595	C₂²	semidirect
104. #17988594	C₂²	semidirect
110. #17988585	C₂²	semidirect
112. #17988580	C₂²	semidirect
113. C₂×#14556516	C₂²	semidirect
114. #103×D₇₃	C₂²	semidirect
118. #17988553	C₂²	semidirect
119. C₄×#11924012	C₂²	semidirect
120. #533×C₇₃	C₂²	semidirect
122. #479×C₇₃	C₂²	semidirect
123. #479×C₇₃	C₂²	semidirect
124. #478×C₇₃	C₂²	semidirect
125. #478×C₇₃	C₂²	semidirect
126. #477×C₇₃	C₂²	semidirect
127. #476×C₇₃	C₂²	semidirect
128. #475×C₇₃	C₂²	semidirect
129. #474×C₇₃	C₂²	semidirect
130. #427×C₇₃	C₂²	semidirect
131. #427×C₇₃	C₂²	semidirect
132. C₂×C₄⋊C₈×C₇₃	C₂²	semidirect
617. #3076	D₇₃	semidirect
627. C₇₃	#61207	semidirect
656. #533	C₂×D₇₃	semidirect
678. #479	C₂×D₇₃	semidirect
679. #479	C₂×D₇₃	semidirect
680. #478	C₂×D₇₃	semidirect
681. #478	C₂×D₇₃	semidirect
682. #477	C₂×D₇₃	semidirect
683. #476	C₂×D₇₃	semidirect
684. #475	C₂×D₇₃	semidirect
685. #474	C₂×D₇₃	semidirect
715. #427	C₂×D₇₃	semidirect
716. #427	C₂×D₇₃	semidirect
717. C₂×C₄⋊C₈	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623798	2
#22623724	2
#22622196	2
#22622144	2
#22622039	2
#22622009	2
#22621994	2
#22621964	2
#22621815	2
#22621763	2
#22620320	2
#22619903	2
#22619892	2
#22619587	2
#22619571	2
C₂×#17988810	2
#22619229	2
#22619211	2
C₄×#14556621	2
#22618674	2
#22618460	2
#22618453	2
C₇₃×#3076	2
#61207	73