Subgroups — #33968709

Order 18688.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623993	C₂	1	2	yes	maximal, complemented
2	#22622916	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622795	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622764	C₂	1	2	yes	maximal, complemented
5	#22622358	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622328	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622298	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622146	C₂	1	2	yes	maximal, complemented
9	#22621973	C₂	1	2	yes	maximal, complemented
10	#22621913	C₂	1	2	yes	maximal, complemented
11	#22621650	C₂	1	1	yes	maximal, characteristic, complemented
12	#22621619	C₂	1	1	yes	maximal, characteristic, complemented
13	#22621615	C₂	1	1	yes	maximal, characteristic, complemented
14	#22620586	C₂	1	1	yes	maximal, characteristic, complemented
15	#22620566	C₂	1	1	yes	maximal, characteristic, complemented
16	#22620214	C₂	1	2	yes	maximal, complemented
17	#22620180	C₂	1	2	yes	maximal, complemented
18	#22620034	C₂	1	2	yes	maximal, complemented
19	#22618906	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618806	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618778	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#14556613	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556614	C₂²	1	1	yes	characteristic
25	C₂×#14556613	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₇₃	C₂²	1	1	yes	characteristic
27	#17989308	C₂²	1	2	yes	—
28	#17989306	C₂²	1	2	yes	complemented
29	#17989293	C₂²	1	2	yes	complemented
30	#17989287	—	2	2	no	—
31	#17989284	C₂²	1	2	yes	complemented
32	#17989276	—	2	2	no	—
33	#17989275	C₂²	1	2	yes	—
34	#17989266	—	2	2	no	—
35	#17989261	—	2	2	no	—
36	#17989239	C₂²	1	2	yes	complemented
37	#17989234	C₂²	1	2	yes	—
38	#17989230	C₂²	1	2	yes	—
39	#17989202	C₂²	1	2	yes	complemented
40	#17989195	C₂²	1	2	yes	—
41	#17989180	—	2	2	no	—
42	#17989173	—	2	2	no	—
43	#17989121	C₂²	1	1	yes	characteristic
44	#17989120	—	2	2	no	—
45	#126×D₇₃	—	2	2	no	—
46	#17989069	C₂²	1	2	yes	complemented
47	#17989059	C₂²	1	2	yes	—
48	C₄×#11924028	C₂²	1	2	yes	complemented
49	#17988991	C₂²	1	1	yes	characteristic, complemented
50	#17988988	C₂²	1	1	yes	characteristic, complemented
51	#17988970	C₂²	1	1	yes	characteristic
52	#17988965	C₂²	1	1	yes	characteristic, complemented
53	#17988954	C₂²	1	2	yes	complemented
54	#17988945	C₂²	1	2	yes	complemented
55	#17988931	C₂²	1	2	yes	—
56	#17988926	C₂²	1	2	yes	—
57	#17988925	C₂²	1	2	yes	complemented
58	#17988919	C₂²	1	2	yes	complemented
59	#17988908	C₂²	1	2	yes	complemented
60	#17988904	C₂²	1	2	yes	complemented
61	#17988891	C₂²	1	2	yes	complemented
62	#17988889	C₂²	1	2	yes	complemented
63	#17988886	C₂²	1	2	yes	complemented
64	#17988884	C₂²	1	2	yes	complemented
65	#17988876	C₂²	1	2	yes	complemented
66	#17988870	C₂²	1	2	yes	complemented
67	#17988844	C₂²	1	2	yes	—
68	#17988832	C₂²	1	2	yes	complemented
69	#17988829	C₂²	1	1	yes	characteristic
70	#17988829	C₂²	1	1	yes	characteristic, complemented
71	#17988825	C₂²	1	1	yes	characteristic
72	#17988820	C₂²	1	1	yes	characteristic
73	#17988807	C₂²	1	2	yes	complemented
74	#17988806	C₂²	1	2	yes	complemented
75	#17988801	C₂²	1	2	yes	—
76	#17988799	C₂²	1	2	yes	—
77	#17988791	C₂²	1	2	yes	complemented
78	#17988790	C₂²	1	2	yes	complemented
79	#17988752	C₂²	1	2	yes	complemented
80	#17988747	C₂²	1	2	yes	complemented
81	#17988739	C₂²	1	2	yes	—
82	#17988736	C₂²	1	2	yes	—
83	#17988731	C₂²	1	2	yes	—
84	#17988730	C₂²	1	2	yes	—
85	#17988717	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
87	#17988697	C₂²	1	2	yes	—
88	#17988696	C₂²	1	2	yes	—
89	#17988692	C₂²	1	2	yes	complemented
90	#17988690	C₂²	1	2	yes	complemented
91	#17988687	C₂²	1	2	yes	complemented
92	#17988685	C₂²	1	2	yes	complemented
93	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
94	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
95	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×#11924017	C₂²	1	2	yes	complemented
97	C₄×#11924017	C₂²	1	2	yes	complemented
98	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
99	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
100	D₈×Dic₇₃	C₂²	1	1	yes	characteristic
101	#17988669	C₂²	1	1	yes	characteristic
102	#17988669	C₂²	1	1	yes	characteristic
103	#17988666	C₂²	1	1	yes	characteristic
104	#17988658	C₂²	1	1	yes	characteristic
105	#17988658	C₂²	1	1	yes	characteristic, complemented
106	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
107	C₈×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic
108	C₈×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
109	#17988646	C₂²	1	1	yes	characteristic
110	#17988646	C₂²	1	1	yes	characteristic, complemented
111	#17988644	C₂²	1	1	yes	characteristic, complemented
112	#17988625	C₂²	1	1	yes	characteristic, complemented
113	#17988624	C₂²	1	1	yes	characteristic
114	#107×D₇₃	C₂²	1	1	yes	characteristic, complemented
115	#17988590	C₂²	1	2	yes	—
116	#17988587	C₂²	1	2	yes	complemented
117	#17988584	C₂²	1	2	yes	complemented
118	#17988541	C₂²	1	1	yes	characteristic
119	#17988541	C₂²	1	1	yes	characteristic, complemented
120	#529×C₇₃	C₂²	1	2	yes	complemented
121	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#495×C₇₃	C₂²	1	1	yes	characteristic
123	#488×C₇₃	C₂²	1	2	yes	complemented
124	#467×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#466×C₇₃	C₂²	1	1	yes	characteristic
126	#465×C₇₃	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
129	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11924029	C₂³	1	2	yes	—
132	C₂×#11924028	C₂³	1	2	yes	—
133	C₂×D₄×D₇₃	C₂³	1	2	yes	—
134	#14556614	—	2	4	no	—
135	#14556613	—	2	4	no	—
136	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
137	C₂×#11924018	C₂³	1	2	yes	—
138	C₂×#11924017	C₂³	1	2	yes	—
139	C₂×#11924016	C₂³	1	2	yes	—
140	C₂×#11924015	C₂³	1	2	yes	—
141	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
142	C₂×#11924013	C₂³	1	2	yes	—
143	D₈×D₇₃	—	2	4	no	—
144	C₂×#11924011	C₂³	1	1	yes	characteristic
145	C₂×#11924011	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
148	#14556590	C₂³	1	2	yes	—
149	#14556589	C₂³	1	2	yes	—
150	#14556586	—	2	2	no	—
151	#14556586	—	2	2	no	—
152	#14556586	—	2	2	no	—
153	#14556585	—	2	2	no	—
154	#14556585	D₄	1	1	yes	characteristic
155	#14556585	D₄	1	1	yes	characteristic
156	#14556584	—	2	2	no	—
157	#14556584	—	2	2	no	—
158	#14556584	—	2	2	no	—
159	#14556584	—	2	2	no	—
160	#14556584	—	2	2	no	—
161	#14556583	—	2	2	no	—
162	#14556583	D₄	1	1	yes	characteristic
163	#14556582	—	2	2	no	—
164	#14556582	C₂³	1	2	yes	—
165	#14556581	—	2	2	no	—
166	#14556579	D₄	1	1	yes	characteristic
167	#14556578	C₂³	1	2	yes	—
168	#14556577	—	2	2	no	—
169	#14556577	—	2	2	no	—
170	#14556576	—	2	2	no	—
171	#14556576	—	2	2	no	—
172	#14556574	—	2	2	no	—
173	#14556574	D₄	1	1	yes	characteristic
174	#14556574	D₄	1	1	yes	characteristic
175	#14556573	—	2	2	no	—
176	#14556573	—	2	2	no	—
177	#14556573	—	2	2	no	—
178	#14556572	—	2	2	no	—
179	#14556571	—	2	2	no	—
180	#14556571	C₂³	1	2	yes	—
181	#14556571	C₂³	1	2	yes	—
182	#14556570	—	2	2	no	—
183	#14556570	D₄	1	1	yes	characteristic
184	#14556569	—	2	2	no	—
185	#14556569	—	2	2	no	—
186	#14556568	—	2	2	no	—
187	#14556567	C₂³	1	2	yes	—
188	#14556565	D₄	1	1	yes	characteristic
189	#14556564	—	2	2	no	—
190	#14556564	—	2	2	no	—
191	#14556562	—	2	2	no	—
192	#14556562	—	2	2	no	—
193	#14556562	C₂³	1	2	yes	—
194	#14556561	—	2	2	no	—
195	#14556559	—	2	2	no	—
196	Q₈×Dic₇₃	C₂³	1	2	yes	—
197	C₄×Dic₁₄₆	C₂³	1	2	yes	—
198	C₄×Dic₁₄₆	C₂³	1	2	yes	—
199	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
200	#14556556	—	2	2	no	—
201	C₄×D₂₉₂	—	2	2	no	—
202	C₄×D₂₉₂	C₂³	1	2	yes	—
203	C₄×D₂₉₂	C₂³	1	2	yes	—
204	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
205	D₄×Dic₇₃	C₂³	1	2	yes	—
206	#14556553	—	2	2	no	—
207	#14556553	C₂³	1	2	yes	—
208	#14556553	C₂³	1	2	yes	—
209	C₄×C₂²⋊D₇₃	—	2	2	no	—
210	C₄×C₂²⋊D₇₃	—	2	2	no	—
211	C₄×C₂²⋊D₇₃	—	2	2	no	—
212	C₄×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
213	C₄×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
214	#14556551	—	2	2	no	—
215	#14556551	—	2	2	no	—
216	#14556550	C₂³	1	2	yes	—
217	#14556549	—	2	2	no	—
218	#14556549	C₂³	1	2	yes	—
219	#14556548	—	2	2	no	—
220	#14556548	—	2	2	no	—
221	#14556548	C₂³	1	1	yes	characteristic
222	#14556548	C₂³	1	1	yes	characteristic
223	#14556547	—	2	2	no	—
224	C₄⋊C₄×D₇₃	—	2	2	no	—
225	C₄⋊C₄×D₇₃	—	2	2	no	—
226	C₄⋊C₄×D₇₃	—	2	2	no	—
227	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
228	C₂×#11924005	—	2	2	no	—
229	C₂²⋊C₄×D₇₃	—	2	2	no	—
230	C₂²⋊C₄×D₇₃	—	2	2	no	—
231	C₂²⋊C₄×D₇₃	—	2	2	no	—
232	C₄²×D₇₃	—	2	2	no	—
233	#14556525	C₂³	1	1	yes	characteristic
234	#14556525	C₂³	1	1	yes	characteristic
235	#14556524	C₂³	1	2	yes	—
236	#14556524	C₂³	1	2	yes	—
237	#14556523	C₂³	1	2	yes	—
238	#14556522	C₂³	1	2	yes	—
239	#14556522	C₂³	1	2	yes	—
240	C₄⋊#10596831	C₂³	1	1	yes	characteristic
241	C₄⋊#10596831	C₂³	1	1	yes	characteristic
242	#14556520	C₂³	1	1	yes	characteristic
243	#14556520	C₂³	1	1	yes	characteristic
244	#14556520	C₂³	1	1	yes	characteristic
245	#14556520	C₂³	1	1	yes	characteristic
246	#14556516	C₂³	1	2	yes	—
247	#14556516	C₂³	1	2	yes	—
248	#14556515	C₂³	1	2	yes	—
249	#14556515	C₂³	1	2	yes	—
250	#14556514	C₂³	1	2	yes	—
251	#14556514	C₂³	1	2	yes	—
252	#14556513	C₂³	1	2	yes	—
253	#14556513	C₂³	1	2	yes	—
254	#14556512	C₂³	1	2	yes	—
255	#14556512	C₂³	1	2	yes	—
256	#14556511	C₂³	1	2	yes	—
257	#14556511	C₂³	1	2	yes	—
258	C₂²⋊#10596831	C₂³	1	1	yes	characteristic
259	C₂²⋊#10596831	C₂³	1	1	yes	characteristic
260	#14556503	C₂³	1	1	yes	characteristic
261	#14556503	C₂³	1	1	yes	characteristic
262	#14556503	C₂³	1	1	yes	characteristic
263	#14556503	C₂³	1	1	yes	characteristic
264	#14556502	C₂³	1	1	yes	characteristic
265	#14556502	C₂³	1	1	yes	characteristic
266	#14556501	C₂³	1	1	yes	characteristic
267	#14556501	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	C₂×SD₁₆×C₇₃	C₂³	1	2	yes	—
272	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
275	#126×C₇₃	—	2	2	no	—
276	#125×C₇₃	C₂³	1	2	yes	—
277	#124×C₇₃	C₂³	1	2	yes	—
278	#123×C₇₃	—	2	2	no	—
279	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
280	#121×C₇₃	C₂³	1	2	yes	—
281	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
282	C₄×D₄×C₇₃	—	2	2	no	—
283	C₄×D₄×C₇₃	C₂³	1	2	yes	—
284	#117×C₇₃	—	2	2	no	—
285	C₂×C₄²×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	#103×C₇₃	C₂³	1	2	yes	—
290	#103×C₇₃	C₂³	1	2	yes	—
291	#102×C₇₃	C₂³	1	2	yes	—
292	#102×C₇₃	C₂³	1	2	yes	—
293	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
297	C₂³×D₇₃	—	2	2	no	—
298	#11924029	—	2	4	no	—
299	#11924029	—	4	2	no	—
300	#11924028	—	2	4	no	—
301	#11924028	—	4	2	no	—
302	C₂×Dic₁₄₆	—	2	2	no	—
303	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
304	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
305	C₂×D₂₉₂	—	2	2	no	—
306	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
307	C₂×D₂₉₂	C₂⁴	1	2	yes	—
308	C₂×C₂²⋊D₇₃	—	2	2	no	—
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	D₄×D₇₃	—	4	2	no	—
315	C₂²×Dic₇₃	—	2	2	no	—
316	C₂×C₄×D₇₃	—	2	2	no	—
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	C₂⁴	1	1	yes	characteristic
324	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
325	Dic₂₉₂	—	2	2	no	—
326	#11924018	—	4	2	no	—
327	#11924017	—	2	4	no	—
328	#11924016	—	4	2	no	—
329	#11924015	—	2	4	no	—
330	D₅₈₄	#41	1	4	yes	—
331	#11924013	—	2	4	no	—
332	#11924011	—	4	1	no	—
333	#11924011	—	4	1	no	—
334	C₂×#10596831	C₂⁴	1	1	yes	characteristic
335	C₂×#10596831	C₂⁴	1	1	yes	characteristic
336	C₂×#10596831	C₂⁴	1	1	yes	characteristic
337	C₂×#10596831	C₂⁴	1	1	yes	characteristic
338	C₈×D₇₃	—	2	2	no	—
339	C₈×D₇₃	—	2	2	no	—
340	C₄⋊Dic₇₃	—	2	2	no	—
341	C₄⋊Dic₇₃	—	2	2	no	—
342	C₄⋊Dic₇₃	—	2	2	no	—
343	C₄⋊Dic₇₃	—	2	2	no	—
344	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
345	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
346	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
347	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
348	#11924007	—	2	2	no	—
349	#11924007	—	2	2	no	—
350	#11924007	—	2	2	no	—
351	#11924007	—	2	2	no	—
352	#11924007	—	2	2	no	—
353	#11924007	—	2	2	no	—
354	#11924007	—	2	2	no	—
355	#11924007	—	2	2	no	—
356	#11924007	C₂×D₄	1	1	yes	characteristic
357	#11924007	C₂×D₄	1	1	yes	characteristic
358	#11924007	C₂×D₄	1	1	yes	characteristic
359	#11924007	C₂×D₄	1	1	yes	characteristic
360	#11924007	C₂×D₄	1	1	yes	characteristic
361	#11924007	C₂×D₄	1	1	yes	characteristic
362	#11924007	C₂×D₄	1	1	yes	characteristic
363	#11924007	C₂×D₄	1	1	yes	characteristic
364	C₂²⋊Dic₇₃	—	2	2	no	—
365	C₂²⋊Dic₇₃	—	2	2	no	—
366	C₂²⋊Dic₇₃	—	2	2	no	—
367	C₂²⋊Dic₇₃	—	2	2	no	—
368	C₂²⋊Dic₇₃	—	2	2	no	—
369	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
380	#11924005	C₂×D₄	1	1	yes	characteristic
381	#11924005	C₂×D₄	1	1	yes	characteristic
382	#11924005	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
393	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
394	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
395	C₂×D₄×C₇₃	—	2	2	no	—
396	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
397	C₂²×C₄×C₇₃	—	2	2	no	—
398	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
399	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
401	Q₁₆×C₇₃	—	2	2	no	—
402	SD₁₆×C₇₃	—	4	2	no	—
403	D₈×C₇₃	—	2	2	no	—
404	C₂×C₈×C₇₃	—	2	2	no	—
405	C₂×C₈×C₇₃	—	4	1	no	—
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	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
415	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
416	C₂²⋊C₄×C₇₃	—	2	2	no	—
417	C₂²⋊C₄×C₇₃	—	2	2	no	—
418	C₂²⋊C₄×C₇₃	—	2	2	no	—
419	C₂²⋊C₄×C₇₃	—	2	2	no	—
420	C₂²⋊C₄×C₇₃	—	2	2	no	—
421	C₄²×C₇₃	—	2	2	no	—
422	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
423	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
425	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₂³×C₇₃	—	2	2	no	—
427	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
428	C₂²×D₇₃	—	2	2	no	—
429	C₂²×D₇₃	—	4	4	no	—
430	C₂²×D₇₃	—	8	2	no	—
431	C₂²×D₇₃	—	8	2	no	—
432	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
434	Q₈×C₇₃	—	2	2	no	—
435	Q₈×C₇₃	—	2	2	no	—
436	D₄×C₇₃	—	2	2	no	—
437	D₄×C₇₃	—	2	2	no	—
438	D₄×C₇₃	—	8	2	no	—
439	C₂×C₄×C₇₃	—	2	1	no	—
440	C₂×C₄×C₇₃	—	2	1	no	—
441	C₂×C₄×C₇₃	—	2	2	no	—
442	C₂×C₄×C₇₃	—	2	2	no	—
443	C₂×C₄×C₇₃	—	2	2	no	—
444	C₂×C₄×C₇₃	—	4	1	no	—
445	C₂×C₄×C₇₃	—	4	1	no	—
446	C₂×C₄×C₇₃	—	8	2	no	—
447	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
453	C₂²⋊D₇₃	—	4	1	no	—
454	C₂²⋊D₇₃	—	4	1	no	—
455	C₂²⋊D₇₃	—	4	4	no	—
456	C₂²⋊D₇₃	—	4	4	no	—
457	C₂²⋊D₇₃	—	8	2	no	—
458	C₂×Dic₇₃	—	2	2	no	—
459	C₂×Dic₇₃	—	2	2	no	—
460	C₂×Dic₇₃	—	2	2	no	—
461	C₂×Dic₇₃	—	8	2	no	—
462	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
468	D₂₉₂	—	2	2	no	—
469	D₂₉₂	—	4	1	no	—
470	D₂₉₂	—	4	4	no	—
471	D₂₉₂	C₂×#41	1	4	yes	—
472	C₄×D₇₃	—	2	1	no	—
473	C₄×D₇₃	—	2	1	no	—
474	C₄×D₇₃	—	2	1	no	—
475	C₄×D₇₃	—	2	1	no	—
476	C₄×D₇₃	—	4	4	no	—
477	C₄×D₇₃	—	4	4	no	—
478	C₄×D₇₃	—	8	2	no	—
479	C₄×D₇₃	—	8	2	no	—
480	C₄×D₇₃	—	8	2	no	—
481	C₄×D₇₃	—	8	2	no	—
482	C₄×D₇₃	—	8	2	no	—
483	Dic₁₄₆	—	2	2	no	—
484	Dic₁₄₆	—	2	2	no	—
485	Dic₁₄₆	—	4	1	no	—
486	Dic₁₄₆	—	8	2	no	—
487	C₈×C₇₃	—	2	1	no	—
488	C₈×C₇₃	—	2	1	no	—
489	C₈×C₇₃	—	2	1	no	—
490	C₈×C₇₃	C₂×#41	1	2	yes	—
491	#10596831	—	2	1	no	—
492	#10596831	—	2	1	no	—
493	#10596831	—	2	1	no	—
494	#10596831	—	2	1	no	—
495	C₂²×C₇₃	—	2	1	no	—
496	C₂²×C₇₃	—	2	1	no	—
497	C₂²×C₇₃	—	2	1	no	—
498	C₂²×C₇₃	—	4	2	no	—
499	C₂²×C₇₃	—	4	2	no	—
500	C₂²×C₇₃	—	4	2	no	—
501	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
502	C₂×D₇₃	—	2	1	no	—
503	C₂×D₇₃	—	2	1	no	—
504	C₂×D₇₃	—	2	1	no	—
505	C₂×D₇₃	—	2	1	no	—
506	C₂×D₇₃	—	2	1	no	—
507	C₂×D₇₃	—	2	1	no	—
508	C₂×D₇₃	—	2	4	no	—
509	C₂×D₇₃	—	4	2	no	—
510	C₂×D₇₃	—	4	2	no	—
511	C₂×D₇₃	—	16	4	no	—
512	C₄×C₇₃	—	2	1	no	—
513	C₄×C₇₃	—	2	1	no	—
514	C₄×C₇₃	—	2	1	no	—
515	C₄×C₇₃	—	2	1	no	—
516	C₄×C₇₃	—	2	1	no	—
517	C₄×C₇₃	—	4	2	no	—
518	C₄×C₇₃	—	4	2	no	—
519	C₄×C₇₃	—	4	2	no	—
520	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
521	C₄×C₇₃	#585	1	1	yes	characteristic
522	Dic₇₃	—	2	1	no	—
523	Dic₇₃	—	2	1	no	—
524	Dic₇₃	—	2	1	no	—
525	Dic₇₃	—	2	1	no	—
526	Dic₇₃	—	2	1	no	—
527	Dic₇₃	—	2	1	no	—
528	Dic₇₃	—	4	2	no	—
529	Dic₇₃	—	4	2	no	—
530	Dic₇₃	—	4	2	no	—
531	#61487	—	73	1	no	maximal, Sylow
532	C₂×C₇₃	—	4	1	no	—
533	C₂×C₇₃	—	8	2	no	—
534	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
535	C₂×C₇₃	#3584	1	1	yes	characteristic
536	C₂×C₇₃	#3584	1	1	yes	characteristic
537	D₇₃	—	4	1	no	—
538	D₇₃	—	4	1	no	—
539	D₇₃	—	4	4	no	—
540	#3521	—	73	2	no	—
541	#3393	—	73	1	no	—
542	#3380	—	73	1	no	—
543	#3376	—	73	2	no	—
544	#3342	—	73	1	no	—
545	#3339	—	73	1	no	—
546	#3336	—	73	1	no	—
547	#3323	—	73	2	no	—
548	#3311	—	73	2	no	—
549	#3307	—	73	2	no	—
550	#3283	—	73	1	no	—
551	#3280	—	73	1	no	—
552	#3280	—	73	1	no	—
553	#3177	—	73	1	no	—
554	#3175	—	73	1	no	—
555	#3168	D₇₃	1	1	yes	characteristic, complemented
556	#3125	—	73	2	no	—
557	#3123	—	73	2	no	—
558	#3111	—	73	2	no	—
559	#2966	—	73	1	no	—
560	#2951	—	73	1	no	—
561	#2948	—	73	1	no	—
562	C₄×#135	—	73	1	no	—
563	C₇₃	#61487	1	1	yes	characteristic, complemented, Sylow
564	C₂×#135	—	73	1	no	—
565	C₂×#135	—	73	1	no	—
566	C₂²×D₈	—	73	1	no	—
567	#556	—	73	2	no	—
568	#556	—	73	2	no	—
569	#554	—	73	2	no	—
570	#553	—	73	2	no	—
571	#553	—	146	2	no	—
572	#552	—	73	2	no	—
573	#552	—	146	2	no	—
574	#551	—	146	2	no	—
575	#551	—	146	2	no	—
576	#547	—	73	2	no	—
577	#546	—	73	2	no	—
578	#546	—	73	2	no	—
579	#542	—	73	2	no	—
580	#541	—	73	2	no	—
581	#539	—	146	2	no	—
582	#538	—	146	2	no	—
583	#529	—	73	1	no	—
584	#529	—	146	2	no	—
585	#529	C₂×D₇₃	1	2	yes	complemented
586	C₂×#126	—	146	2	no	—
587	#520	—	73	2	no	—
588	#518	—	73	2	no	—
589	C₄×#41	—	73	2	no	—
590	#500	—	73	1	no	—
591	#499	—	73	1	no	—
592	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
593	#495	—	73	1	no	—
594	#495	C₂×D₇₃	1	1	yes	characteristic
595	#494	—	73	1	no	—
596	#491	—	73	2	no	—
597	#489	—	73	2	no	—
598	#488	C₂×D₇₃	1	2	yes	complemented
599	#485	—	73	2	no	—
600	#485	—	73	2	no	—
601	#485	—	73	2	no	—
602	#483	—	73	2	no	—
603	#482	—	73	2	no	—
604	#481	—	73	2	no	—
605	#479	—	73	2	no	—
606	#478	—	73	2	no	—
607	#478	—	73	2	no	—
608	#478	—	73	2	no	—
609	#476	—	73	2	no	—
610	#475	—	73	2	no	—
611	#470	—	73	2	no	—
612	#468	—	73	2	no	—
613	#467	—	73	1	no	—
614	#467	—	73	1	no	—
615	#467	—	73	1	no	—
616	#467	C₂×D₇₃	1	1	yes	characteristic, complemented
617	#466	—	73	1	no	—
618	#466	C₂×D₇₃	1	1	yes	characteristic
619	#465	C₂×D₇₃	1	2	yes	complemented
620	#464	—	73	2	no	—
621	#464	—	73	2	no	—
622	#463	—	73	2	no	—
623	#463	—	73	2	no	—
624	#461	—	73	2	no	—
625	#461	—	73	2	no	—
626	#452	—	73	2	no	—
627	#452	—	73	2	no	—
628	#450	—	73	2	no	—
629	#450	—	73	2	no	—
630	#449	—	73	2	no	—
631	#449	—	73	2	no	—
632	#446	—	73	1	no	—
633	C₈×Q₈	—	73	1	no	—
634	#442	—	73	2	no	—
635	#442	—	73	2	no	—
636	#441	—	73	2	no	—
637	#440	—	73	2	no	—
638	#440	—	73	2	no	—
639	#440	—	73	2	no	—
640	C₄×Q₁₆	—	73	1	no	—
641	C₄×Q₁₆	—	73	1	no	—
642	C₄×Q₁₆	—	73	1	no	—
643	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
644	C₄×SD₁₆	—	73	2	no	—
645	C₄×SD₁₆	—	73	2	no	—
646	C₄×SD₁₆	C₂×D₇₃	1	2	yes	complemented
647	C₄×D₈	—	73	1	no	—
648	C₄×D₈	—	73	1	no	—
649	C₄×D₈	—	73	1	no	—
650	C₄×D₈	—	73	1	no	—
651	C₄×D₈	—	73	1	no	—
652	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
653	#436	—	73	1	no	—
654	#435	—	73	1	no	—
655	#435	—	73	1	no	—
656	C₈×D₄	—	73	1	no	—
657	C₈×D₄	—	73	1	no	—
658	C₈×D₄	—	73	1	no	—
659	#433	—	73	1	no	—
660	#433	—	73	1	no	—
661	#432	—	73	1	no	—
662	#427	—	73	1	no	—
663	#427	—	73	1	no	—
664	C₂×#107	—	73	1	no	—
665	#418	—	73	2	no	—
666	#417	—	73	2	no	—
667	#416	—	73	2	no	—
668	#405	—	73	1	no	—
669	#405	—	73	1	no	—
670	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
671	C₂×#41	—	73	2	no	—
672	C₂×#41	—	73	2	no	—
673	C₂²×D₄	—	73	2	no	—
674	#135	—	146	4	no	—
675	#135	—	146	4	no	—
676	C₂×Q₁₆	—	73	2	no	—
677	C₂×Q₁₆	—	73	1	no	—
678	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
679	C₂×SD₁₆	—	73	2	no	—
680	C₂×SD₁₆	—	73	2	no	—
681	C₂×SD₁₆	—	73	2	no	—
682	C₂×SD₁₆	C₂²×D₇₃	1	2	yes	—
683	C₂×D₈	—	73	2	no	—
684	C₂×D₈	—	73	1	no	—
685	C₂×D₈	—	146	4	no	—
686	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
687	C₂×M₁₆	—	73	1	no	—
688	C₂×M₁₆	—	73	1	no	—
689	C₂²×C₈	—	73	1	no	—
690	C₂²×C₈	—	73	1	no	—
691	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
692	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
693	C₄⋊Q₈	—	73	2	no	—
694	C₄⋊Q₈	—	73	2	no	—
695	#126	—	2	2	no	—
696	#126	—	73	1	no	—
697	#126	—	73	1	no	—
698	#126	—	146	2	no	—
699	#126	—	146	2	no	—
700	#126	—	146	2	no	—
701	#126	—	146	2	no	—
702	#126	—	146	2	no	—
703	#126	—	146	2	no	—
704	#126	—	146	2	no	—
705	#126	—	146	2	no	—
706	#126	—	146	2	no	—
707	#125	—	73	2	no	—
708	#125	—	73	1	no	—
709	#125	—	146	2	no	—
710	#125	—	146	2	no	—
711	#125	—	146	2	no	—
712	#125	C₂²×D₇₃	1	2	yes	—
713	#124	—	73	2	no	—
714	#124	—	73	1	no	—
715	#124	—	146	2	no	—
716	#124	—	146	2	no	—
717	#124	C₂²×D₇₃	1	2	yes	—
718	#123	—	2	2	no	—
719	#123	—	73	1	no	—
720	#123	—	73	1	no	—
721	#123	—	146	2	no	—
722	#123	—	146	2	no	—
723	#123	—	146	2	no	—
724	#123	—	146	2	no	—
725	#123	—	146	2	no	—
726	#123	—	146	2	no	—
727	#123	—	146	2	no	—
728	C₂²⋊Q₈	—	73	1	no	—
729	C₂²⋊Q₈	—	73	2	no	—
730	C₂²⋊Q₈	—	73	2	no	—
731	C₂²⋊Q₈	—	73	2	no	—
732	C₂²⋊Q₈	—	146	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	C₂²×D₇₃	1	2	yes	—
738	#121	—	73	1	no	—
739	#121	—	73	2	no	—
740	#121	—	146	2	no	—
741	#121	—	146	2	no	—
742	#121	—	146	2	no	—
743	#121	—	146	2	no	—
744	#121	C₂²×D₇₃	1	2	yes	—
745	#120	—	146	2	no	—
746	#120	—	146	2	no	—
747	C₄×Q₈	—	73	1	no	—
748	C₄×Q₈	—	73	2	no	—
749	C₄×Q₈	—	73	2	no	—
750	C₄×Q₈	—	73	2	no	—
751	C₄×Q₈	—	146	2	no	—
752	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	73	1	no	—
755	C₄×D₄	—	73	1	no	—
756	C₄×D₄	—	73	2	no	—
757	C₄×D₄	—	73	2	no	—
758	C₄×D₄	—	73	2	no	—
759	C₄×D₄	—	73	1	no	—
760	C₄×D₄	—	73	2	no	—
761	C₄×D₄	—	73	2	no	—
762	C₄×D₄	—	146	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	C₂²×D₇₃	1	2	yes	—
770	#117	—	2	2	no	—
771	#117	—	73	1	no	—
772	#117	—	73	1	no	—
773	#117	—	73	2	no	—
774	#117	—	73	2	no	—
775	#117	—	146	2	no	—
776	#117	—	146	2	no	—
777	#117	—	146	2	no	—
778	#117	—	146	2	no	—
779	C₂×C₄⋊C₄	—	73	2	no	—
780	C₂×C₄⋊C₄	—	146	2	no	—
781	C₂×C₄⋊C₄	—	146	2	no	—
782	C₂×C₄⋊C₄	—	146	2	no	—
783	C₂×C₂²⋊C₄	—	146	2	no	—
784	C₂×C₂²⋊C₄	—	146	2	no	—
785	C₂×C₂²⋊C₄	—	146	2	no	—
786	C₂×C₂²⋊C₄	—	146	2	no	—
787	C₂×C₄²	—	146	2	no	—
788	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
789	#107	—	73	1	no	—
790	#107	—	73	1	no	—
791	#107	—	73	2	no	—
792	#107	—	73	2	no	—
793	#107	C₂²×D₇₃	1	1	yes	characteristic
794	#107	C₂²×D₇₃	1	1	yes	characteristic
795	#106	—	73	2	no	—
796	#106	—	73	2	no	—
797	#106	—	73	2	no	—
798	#106	C₂²×D₇₃	1	2	yes	—
799	C₄⋊C₈	—	73	1	no	—
800	C₄⋊C₈	—	73	1	no	—
801	C₄⋊C₈	—	73	1	no	—
802	C₄⋊C₈	—	73	1	no	—
803	C₄⋊C₈	—	73	1	no	—
804	C₄⋊C₈	—	73	1	no	—
805	#103	—	73	2	no	—
806	#103	—	73	2	no	—
807	#103	—	73	2	no	—
808	#103	—	73	2	no	—
809	#103	—	73	2	no	—
810	#103	—	73	2	no	—
811	#103	C₂²×D₇₃	1	2	yes	—
812	#103	C₂²×D₇₃	1	2	yes	—
813	#102	—	73	2	no	—
814	#102	—	73	2	no	—
815	#102	—	73	2	no	—
816	#102	—	73	2	no	—
817	#102	—	73	2	no	—
818	#102	—	73	2	no	—
819	#102	C₂²×D₇₃	1	2	yes	—
820	#102	C₂²×D₇₃	1	2	yes	—
821	C₂²⋊C₈	—	73	1	no	—
822	C₂²⋊C₈	—	73	1	no	—
823	C₂²⋊C₈	—	73	1	no	—
824	C₂²⋊C₈	—	73	1	no	—
825	C₂²⋊C₈	—	73	1	no	—
826	C₂²⋊C₈	—	73	1	no	—
827	#97	—	73	1	no	—
828	#97	—	73	1	no	—
829	#97	—	73	1	no	—
830	#97	—	73	1	no	—
831	C₄×C₈	—	73	1	no	—
832	C₄×C₈	—	73	1	no	—
833	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
834	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
835	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
836	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
837	C₂⁴	—	146	2	no	—
838	#41	—	292	2	no	—
839	#41	—	292	2	no	—
840	#41	—	146	4	no	—
841	#41	—	146	4	no	—
842	C₂×Q₈	—	73	1	no	—
843	C₂×Q₈	—	73	2	no	—
844	C₂×Q₈	—	146	2	no	—
845	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	292	2	no	—
848	C₂×D₄	—	73	1	no	—
849	C₂×D₄	—	73	1	no	—
850	C₂×D₄	—	73	1	no	—
851	C₂×D₄	—	73	2	no	—
852	C₂×D₄	—	146	2	no	—
853	C₂×D₄	—	146	2	no	—
854	C₂×D₄	—	146	4	no	—
855	C₂×D₄	—	146	2	no	—
856	C₂×D₄	—	146	2	no	—
857	C₂×D₄	C₂³×D₇₃	1	2	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	73	1	no	—
860	C₂²×C₄	—	73	1	no	—
861	C₂²×C₄	—	146	2	no	—
862	C₂²×C₄	—	146	2	no	—
863	C₂²×C₄	—	146	2	no	—
864	C₂²×C₄	—	146	2	no	—
865	C₂²×C₄	—	146	2	no	—
866	C₂²×C₄	—	146	2	no	—
867	C₂²×C₄	—	146	2	no	—
868	C₂²×C₄	—	146	2	no	—
869	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
870	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	292	2	no	—
874	Q₁₆	—	146	2	no	—
875	SD₁₆	—	4	2	no	—
876	SD₁₆	—	292	2	no	—
877	SD₁₆	—	146	4	no	—
878	SD₁₆	—	146	4	no	—
879	D₈	—	2	2	no	—
880	D₈	—	73	4	no	—
881	D₈	—	146	4	no	—
882	M₁₆	—	292	1	no	—
883	M₁₆	—	292	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	4	1	no	—
886	C₂×C₈	—	73	1	no	—
887	C₂×C₈	—	73	1	no	—
888	C₂×C₈	—	73	1	no	—
889	C₂×C₈	—	73	1	no	—
890	C₂×C₈	—	146	2	no	—
891	C₂×C₈	—	146	2	no	—
892	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	73	1	no	—
901	C₄⋊C₄	—	73	1	no	—
902	C₄⋊C₄	—	73	1	no	—
903	C₄⋊C₄	—	73	1	no	—
904	C₄⋊C₄	—	73	1	no	—
905	C₄⋊C₄	—	73	1	no	—
906	C₄⋊C₄	—	73	1	no	—
907	C₄⋊C₄	—	73	1	no	—
908	C₄⋊C₄	—	73	1	no	—
909	C₄⋊C₄	—	73	1	no	—
910	C₄⋊C₄	—	73	2	no	—
911	C₄⋊C₄	—	73	2	no	—
912	C₄⋊C₄	—	146	2	no	—
913	C₄⋊C₄	—	146	2	no	—
914	C₄⋊C₄	—	146	2	no	—
915	C₄⋊C₄	—	146	2	no	—
916	C₄⋊C₄	—	146	2	no	—
917	C₄⋊C₄	—	146	2	no	—
918	C₄⋊C₄	—	146	2	no	—
919	C₄⋊C₄	—	146	2	no	—
920	C₄⋊C₄	—	146	2	no	—
921	C₄⋊C₄	—	146	2	no	—
922	C₄⋊C₄	—	146	2	no	—
923	C₄⋊C₄	—	146	2	no	—
924	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
925	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	73	1	no	—
932	C₂²⋊C₄	—	73	1	no	—
933	C₂²⋊C₄	—	73	1	no	—
934	C₂²⋊C₄	—	73	1	no	—
935	C₂²⋊C₄	—	73	1	no	—
936	C₂²⋊C₄	—	73	1	no	—
937	C₂²⋊C₄	—	73	1	no	—
938	C₂²⋊C₄	—	73	1	no	—
939	C₂²⋊C₄	—	73	1	no	—
940	C₂²⋊C₄	—	73	1	no	—
941	C₂²⋊C₄	—	146	2	no	—
942	C₂²⋊C₄	—	146	2	no	—
943	C₂²⋊C₄	—	146	2	no	—
944	C₂²⋊C₄	—	146	2	no	—
945	C₂²⋊C₄	—	146	2	no	—
946	C₂²⋊C₄	—	146	2	no	—
947	C₂²⋊C₄	—	146	2	no	—
948	C₂²⋊C₄	—	146	2	no	—
949	C₂²⋊C₄	—	146	2	no	—
950	C₂²⋊C₄	—	146	2	no	—
951	C₂²⋊C₄	—	146	2	no	—
952	C₂²⋊C₄	—	146	2	no	—
953	C₂²⋊C₄	—	146	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	73	1	no	—
956	C₄²	—	73	1	no	—
957	C₄²	—	146	2	no	—
958	C₄²	—	146	2	no	—
959	C₄²	—	146	2	no	—
960	C₄²	—	146	2	no	—
961	C₄²	—	146	2	no	—
962	C₄²	D₄×D₇₃	1	1	yes	characteristic
963	C₄²	D₄×D₇₃	1	1	yes	characteristic
964	C₄²	C₂³×D₇₃	1	1	yes	characteristic
965	C₄²	C₂³×D₇₃	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	292	4	no	—
968	C₂³	—	584	2	no	—
969	C₂³	—	584	2	no	—
970	C₂³	—	73	1	no	—
971	C₂³	—	73	1	no	—
972	C₂³	—	146	2	no	—
973	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	292	1	no	—
977	Q₈	—	584	2	no	—
978	Q₈	—	146	2	no	—
979	Q₈	—	146	2	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	8	2	no	—
983	D₄	—	292	1	no	—
984	D₄	—	292	4	no	—
985	D₄	—	292	4	no	—
986	D₄	—	292	1	no	—
987	D₄	—	292	1	no	—
988	D₄	—	292	4	no	—
989	D₄	—	584	2	no	—
990	D₄	—	73	4	no	—
991	D₄	—	146	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	292	4	no	—
1001	C₂×C₄	—	292	4	no	—
1002	C₂×C₄	—	584	2	no	—
1003	C₂×C₄	—	584	2	no	—
1004	C₂×C₄	—	584	2	no	—
1005	C₂×C₄	—	584	2	no	—
1006	C₂×C₄	—	584	2	no	—
1007	C₂×C₄	—	584	2	no	—
1008	C₂×C₄	—	73	1	no	—
1009	C₂×C₄	—	73	1	no	—
1010	C₂×C₄	—	73	1	no	—
1011	C₂×C₄	—	73	1	no	—
1012	C₂×C₄	—	73	1	no	—
1013	C₂×C₄	—	73	1	no	—
1014	C₂×C₄	—	146	2	no	—
1015	C₂×C₄	—	146	2	no	—
1016	C₂×C₄	—	146	2	no	—
1017	C₂×C₄	—	146	1	no	—
1018	C₂×C₄	—	146	1	no	—
1019	C₂×C₄	—	146	1	no	—
1020	C₂×C₄	—	146	1	no	—
1021	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1022	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1023	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1024	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1025	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	146	1	no	—
1031	C₈	—	146	1	no	—
1032	C₈	—	146	1	no	—
1033	C₈	—	146	1	no	—
1034	C₈	#41×D₇₃	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	292	2	no	—
1042	C₂²	—	292	2	no	—
1043	C₂²	—	1168	4	no	—
1044	C₂²	—	146	4	no	—
1045	C₂²	—	146	1	no	—
1046	C₂²	—	146	1	no	—
1047	C₂²	—	146	1	no	—
1048	C₂²	—	146	1	no	—
1049	C₂²	—	146	1	no	—
1050	C₂²	—	146	1	no	—
1051	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	292	2	no	—
1061	C₄	—	292	2	no	—
1062	C₄	—	292	2	no	—
1063	C₄	—	146	1	no	—
1064	C₄	—	146	1	no	—
1065	C₄	—	146	1	no	—
1066	C₄	—	146	1	no	—
1067	C₄	—	146	1	no	—
1068	C₄	—	146	1	no	—
1069	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1070	C₄	#17989423	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	292	4	no	—
1074	C₂	—	292	1	no	—
1075	C₂	—	292	1	no	—
1076	C₂	#22623417	1	1	yes	characteristic
1077	C₂	#22624700	1	1	yes	characteristic
1078	C₂	#22624700	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3168	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#3168	D₇₃
hypocenter	C₇₃	#61487
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #22623993	C₂	semidirect
2. #22622916	C₂	semidirect
3. #22622795	C₂	semidirect
4. #22622764	C₂	semidirect
5. #22622358	C₂	semidirect
6. #22622328	C₂	semidirect
7. #22622298	C₂	semidirect
8. #22622146	C₂	semidirect
9. #22621973	C₂	semidirect
10. #22621913	C₂	semidirect
11. #22621650	C₂	semidirect
12. #22621619	C₂	semidirect
13. #22621615	C₂	semidirect
14. #22620586	C₂	semidirect
15. #22620566	C₂	semidirect
16. #22620214	C₂	semidirect
17. #22620180	C₂	semidirect
18. #22620034	C₂	semidirect
19. #22618906	C₂	semidirect
20. #22618806	C₂	semidirect
21. #22618778	C₂	semidirect
22. C₄×#14556613	C₂	semidirect
23. C₇₃×#3168	C₂	semidirect
28. #17989306	C₂²	semidirect
29. #17989293	C₂²	semidirect
31. #17989284	C₂²	semidirect
36. #17989239	C₂²	semidirect
39. #17989202	C₂²	semidirect
46. #17989069	C₂²	semidirect
48. C₄×#11924028	C₂²	semidirect
49. #17988991	C₂²	semidirect
50. #17988988	C₂²	semidirect
52. #17988965	C₂²	semidirect
53. #17988954	C₂²	semidirect
54. #17988945	C₂²	semidirect
57. #17988925	C₂²	semidirect
58. #17988919	C₂²	semidirect
59. #17988908	C₂²	semidirect
60. #17988904	C₂²	semidirect
61. #17988891	C₂²	semidirect
62. #17988889	C₂²	semidirect
63. #17988886	C₂²	semidirect
64. #17988884	C₂²	semidirect
65. #17988876	C₂²	semidirect
66. #17988870	C₂²	semidirect
68. #17988832	C₂²	semidirect
70. #17988829	C₂²	semidirect
73. #17988807	C₂²	semidirect
74. #17988806	C₂²	semidirect
77. #17988791	C₂²	semidirect
78. #17988790	C₂²	semidirect
79. #17988752	C₂²	semidirect
80. #17988747	C₂²	semidirect
85. #17988717	C₂²	semidirect
86. C₈×Dic₁₄₆	C₂²	semidirect
89. #17988692	C₂²	semidirect
90. #17988690	C₂²	semidirect
91. #17988687	C₂²	semidirect
92. #17988685	C₂²	semidirect
93. C₄×Dic₂₉₂	C₂²	semidirect
94. C₄×Dic₂₉₂	C₂²	semidirect
95. Q₁₆×Dic₇₃	C₂²	semidirect
96. C₄×#11924017	C₂²	semidirect
97. C₄×#11924017	C₂²	semidirect
105. #17988658	C₂²	semidirect
108. C₈×C₂²⋊D₇₃	C₂²	semidirect
110. #17988646	C₂²	semidirect
111. #17988644	C₂²	semidirect
112. #17988625	C₂²	semidirect
114. #107×D₇₃	C₂²	semidirect
116. #17988587	C₂²	semidirect
117. #17988584	C₂²	semidirect
119. #17988541	C₂²	semidirect
120. #529×C₇₃	C₂²	semidirect
121. #499×C₇₃	C₂²	semidirect
123. #488×C₇₃	C₂²	semidirect
124. #467×C₇₃	C₂²	semidirect
126. #465×C₇₃	C₂²	semidirect
127. C₄×Q₁₆×C₇₃	C₂²	semidirect
128. C₄×SD₁₆×C₇₃	C₂²	semidirect
130. C₂×C₄×C₈×C₇₃	C₂²	semidirect
555. #3168	D₇₃	semidirect
563. C₇₃	#61487	semidirect
585. #529	C₂×D₇₃	semidirect
592. #499	C₂×D₇₃	semidirect
598. #488	C₂×D₇₃	semidirect
616. #467	C₂×D₇₃	semidirect
619. #465	C₂×D₇₃	semidirect
643. C₄×Q₁₆	C₂×D₇₃	semidirect
646. C₄×SD₁₆	C₂×D₇₃	semidirect
670. 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
#22623993	2
#22622916	2
#22622795	2
#22622764	2
#22622358	2
#22622328	2
#22622298	2
#22622146	2
#22621973	2
#22621913	2
#22621650	2
#22621619	2
#22621615	2
#22620586	2
#22620566	2
#22620214	2
#22620180	2
#22620034	2
#22618906	2
#22618806	2
#22618778	2
C₄×#14556613	2
C₇₃×#3168	2
#61487	73