Subgroups — #3328×D₇₃ #33962861

Order 18688.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#556×D₇₃	C₂	1	1	yes	maximal, characteristic
2	D₄×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22622217	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622216	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622215	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622214	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622213	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622212	C₂	1	2	yes	maximal, complemented
9	#22622211	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622210	C₂	1	2	yes	maximal, complemented
11	#22622209	C₂	1	2	yes	maximal, complemented
12	#22622208	C₂	1	1	yes	maximal, characteristic, complemented
13	#22622207	C₂	1	2	yes	maximal, complemented
14	#487×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#485×D₇₃	C₂	1	2	yes	maximal, complemented
16	#475×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#470×D₇₃	C₂	1	2	yes	maximal, complemented
18	#462×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#451×D₇₃	C₂	1	2	yes	maximal, complemented
20	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#436×D₇₃	C₂	1	1	yes	maximal, characteristic
22	#419×D₇₃	C₂	1	2	yes	maximal, complemented
23	C₇₃×#3328	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×Q₈×D₇₃	C₂²	1	2	yes	—
25	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
26	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	—
27	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
28	#17989311	C₂²	1	1	yes	characteristic
29	#17989310	C₂²	1	1	yes	characteristic
30	#17989309	—	2	1	no	—
31	#17989308	C₂²	1	2	yes	—
32	#17989307	C₂²	1	1	yes	characteristic
33	#17989306	—	2	1	no	—
34	#17989305	C₂²	1	2	yes	—
35	#17989304	—	2	2	no	—
36	Q₈×D₂₉₂	C₂²	1	1	yes	characteristic
37	D₄×Dic₁₄₆	—	2	1	no	—
38	D₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
39	#17989252	—	2	1	no	—
40	#17989252	C₂²	1	1	yes	characteristic
41	Q₈×C₂²⋊D₇₃	C₂²	1	2	yes	—
42	#17989250	—	2	2	no	—
43	#17989250	C₂²	1	2	yes	—
44	C₄⋊Q₈×D₇₃	—	2	1	no	—
45	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
46	C₄⋊Q₈×D₇₃	C₂²	1	1	yes	characteristic
47	#126×D₇₃	—	2	2	no	—
48	#124×D₇₃	—	2	1	no	—
49	C₂²⋊Q₈×D₇₃	—	2	2	no	—
50	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
51	C₂²⋊Q₈×D₇₃	C₂²	1	2	yes	—
52	C₄×Q₈×D₇₃	—	2	1	no	—
53	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
54	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₇₃	—	2	1	no	—
56	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
57	#117×D₇₃	C₂²	1	2	yes	—
58	#17988939	C₂²	1	1	yes	characteristic, complemented
59	#17988938	C₂²	1	1	yes	characteristic, complemented
60	#17988937	C₂²	1	1	yes	characteristic, complemented
61	#17988936	C₂²	1	2	yes	complemented
62	#17988936	C₂²	1	2	yes	complemented
63	#17988931	C₂²	1	2	yes	complemented
64	#17988930	C₂²	1	2	yes	complemented
65	#17988929	C₂²	1	2	yes	complemented
66	#17988928	C₂²	1	2	yes	complemented
67	#17988927	C₂²	1	2	yes	complemented
68	#17988926	C₂²	1	2	yes	complemented
69	#17988925	C₂²	1	2	yes	complemented
70	#17988873	C₂²	1	1	yes	characteristic, complemented
71	#17988872	C₂²	1	1	yes	characteristic, complemented
72	#17988871	C₂²	1	2	yes	complemented
73	#17988870	C₂²	1	2	yes	complemented
74	#17988869	C₂²	1	1	yes	characteristic, complemented
75	#17988846	C₂²	1	2	yes	complemented
76	#17988845	C₂²	1	2	yes	complemented
77	#17988844	C₂²	1	2	yes	complemented
78	#17988844	C₂²	1	2	yes	complemented
79	#17988843	C₂²	1	2	yes	complemented
80	#17988843	C₂²	1	2	yes	complemented
81	#17988842	C₂²	1	2	yes	complemented
82	#17988798	C₂²	1	1	yes	characteristic, complemented
83	#17988797	C₂²	1	1	yes	characteristic, complemented
84	#17988796	C₂²	1	2	yes	complemented
85	#17988795	C₂²	1	2	yes	complemented
86	#17988794	C₂²	1	1	yes	characteristic, complemented
87	#17988745	C₂²	1	2	yes	complemented
88	#17988744	C₂²	1	2	yes	complemented
89	#17988744	C₂²	1	2	yes	complemented
90	#17988743	C₂²	1	2	yes	complemented
91	#17988742	C₂²	1	2	yes	complemented
92	#17988741	C₂²	1	2	yes	complemented
93	#17988741	C₂²	1	2	yes	complemented
94	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
95	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
96	#17988681	C₂²	1	1	yes	characteristic, complemented
97	C₄×#11924018	C₂²	1	1	yes	characteristic, complemented
98	C₄×#11924018	C₂²	1	1	yes	characteristic, complemented
99	#17988679	C₂²	1	1	yes	characteristic, complemented
100	#17988679	C₂²	1	1	yes	characteristic, complemented
101	#17988666	C₂²	1	1	yes	characteristic
102	#17988665	C₂²	1	1	yes	characteristic
103	#17988664	C₂²	1	1	yes	characteristic
104	#17988663	C₂²	1	2	yes	—
105	#17988662	C₂²	1	2	yes	—
106	#107×D₇₃	C₂²	1	1	yes	characteristic
107	#106×D₇₃	C₂²	1	2	yes	—
108	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
109	#17988597	C₂²	1	2	yes	complemented
110	#17988596	C₂²	1	2	yes	complemented
111	#17988595	C₂²	1	2	yes	complemented
112	#17988594	C₂²	1	2	yes	complemented
113	#17988594	C₂²	1	2	yes	complemented
114	#17988594	C₂²	1	2	yes	complemented
115	#17988594	C₂²	1	2	yes	complemented
116	#103×D₇₃	C₂²	1	2	yes	—
117	#103×D₇₃	C₂²	1	1	yes	characteristic
118	#103×D₇₃	C₂²	1	2	yes	—
119	#103×D₇₃	C₂²	1	2	yes	—
120	#103×D₇₃	C₂²	1	1	yes	characteristic
121	#103×D₇₃	C₂²	1	2	yes	—
122	C₂²⋊C₈×D₇₃	C₂²	1	2	yes	—
123	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
124	#556×C₇₃	C₂²	1	1	yes	characteristic
125	D₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic
126	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#485×C₇₃	C₂²	1	2	yes	complemented
128	#475×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#470×C₇₃	C₂²	1	2	yes	complemented
130	#462×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	#451×C₇₃	C₂²	1	2	yes	complemented
132	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#436×C₇₃	C₂²	1	1	yes	characteristic
134	#419×C₇₃	C₂²	1	2	yes	complemented
135	C₂²×Dic₁₄₆	—	2	2	no	—
136	C₂²×Dic₁₄₆	C₂³	1	2	yes	—
137	C₂×Q₈×D₇₃	—	2	2	no	—
138	C₂×Q₈×D₇₃	—	2	1	no	—
139	C₂×Q₈×D₇₃	—	2	2	no	—
140	C₂×Q₈×D₇₃	—	2	8	no	—
141	C₂×Q₈×D₇₃	—	4	4	no	—
142	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
143	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
144	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
145	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
146	C₂×Q₈×D₇₃	C₂³	1	1	yes	characteristic
147	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
148	C₂²×C₄×D₇₃	—	2	2	no	—
149	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
150	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
151	C₂×Dic₂₉₂	C₂³	1	2	yes	—
152	C₂×#11924018	C₂³	1	1	yes	characteristic
153	C₂×#11924018	C₂³	1	1	yes	characteristic
154	C₂×#11924018	C₂³	1	2	yes	—
155	C₂×#11924018	C₂³	1	2	yes	—
156	Q₁₆×D₇₃	—	2	4	no	—
157	Q₁₆×D₇₃	—	4	4	no	—
158	C₂×#11924012	C₂³	1	2	yes	—
159	C₂×#11924011	C₂³	1	2	yes	—
160	C₂×#11924011	C₂³	1	2	yes	—
161	M₁₆×D₇₃	—	4	4	no	—
162	C₂×C₈×D₇₃	C₂³	1	2	yes	—
163	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
164	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
165	#14556591	—	2	1	no	—
166	#14556591	C₂³	1	1	yes	characteristic
167	#14556591	C₂³	1	1	yes	characteristic
168	#14556590	—	2	1	no	—
169	#14556590	—	2	2	no	—
170	#14556590	—	2	1	no	—
171	#14556590	—	2	1	no	—
172	#14556590	—	2	1	no	—
173	#14556590	—	2	1	no	—
174	#14556590	C₂³	1	2	yes	—
175	#14556589	—	2	2	no	—
176	#14556589	—	2	1	no	—
177	#14556589	C₂³	1	2	yes	—
178	#14556586	—	2	2	no	—
179	#14556586	—	2	2	no	—
180	#14556586	—	2	2	no	—
181	#14556585	—	2	2	no	—
182	#14556584	—	2	2	no	—
183	#14556584	—	2	2	no	—
184	#14556584	—	2	2	no	—
185	#14556580	—	2	1	no	—
186	#14556579	—	2	1	no	—
187	#14556578	—	2	1	no	—
188	#14556577	—	2	2	no	—
189	#14556577	—	2	2	no	—
190	#14556571	—	2	2	no	—
191	#14556571	C₂³	1	2	yes	—
192	#14556571	C₂³	1	2	yes	—
193	#14556570	—	2	2	no	—
194	#14556570	C₂³	1	2	yes	—
195	#14556570	C₂³	1	2	yes	—
196	#14556569	—	2	2	no	—
197	#14556569	—	2	2	no	—
198	#14556569	—	2	2	no	—
199	#14556569	—	2	2	no	—
200	#14556568	—	2	2	no	—
201	#14556568	—	2	2	no	—
202	#14556568	—	2	2	no	—
203	#14556568	—	2	2	no	—
204	#14556567	—	2	2	no	—
205	#14556567	C₂³	1	2	yes	—
206	#14556567	C₂³	1	2	yes	—
207	Q₈×Dic₇₃	—	2	1	no	—
208	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
209	Q₈×Dic₇₃	C₂³	1	1	yes	characteristic
210	C₄×Dic₁₄₆	—	2	1	no	—
211	C₄×Dic₁₄₆	—	2	2	no	—
212	C₄×Dic₁₄₆	—	2	1	no	—
213	C₄×Dic₁₄₆	—	2	1	no	—
214	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
216	#14556556	—	2	2	no	—
217	#14556556	—	2	1	no	—
218	#14556556	—	2	1	no	—
219	#14556556	—	2	1	no	—
220	#14556556	C₂³	1	1	yes	characteristic
221	#14556556	C₂³	1	1	yes	characteristic
222	C₄×D₂₉₂	—	2	1	no	—
223	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
224	D₄×Dic₇₃	—	2	1	no	—
225	D₄×Dic₇₃	D₄	1	1	yes	characteristic
226	#14556553	—	2	1	no	—
227	#14556553	D₄	1	1	yes	characteristic
228	C₄×C₂²⋊D₇₃	—	2	2	no	—
229	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
230	#14556551	—	2	2	no	—
231	#14556551	D₄	1	2	yes	—
232	#14556550	C₂³	1	2	yes	—
233	#14556549	C₂³	1	2	yes	—
234	#14556549	C₂³	1	2	yes	—
235	#14556548	—	2	2	no	—
236	#14556547	—	2	2	no	—
237	C₄⋊C₄×D₇₃	—	2	1	no	—
238	C₄⋊C₄×D₇₃	—	2	2	no	—
239	C₄⋊C₄×D₇₃	—	2	1	no	—
240	C₄⋊C₄×D₇₃	—	2	1	no	—
241	C₄⋊C₄×D₇₃	—	2	2	no	—
242	C₄⋊C₄×D₇₃	—	2	1	no	—
243	C₄⋊C₄×D₇₃	—	2	1	no	—
244	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
245	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
247	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
248	C₂²⋊C₄×D₇₃	—	2	2	no	—
249	C₂²⋊C₄×D₇₃	—	2	2	no	—
250	C₂²⋊C₄×D₇₃	—	2	2	no	—
251	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
252	C₄²×D₇₃	—	2	1	no	—
253	C₄²×D₇₃	—	2	2	no	—
254	C₄²×D₇₃	—	2	1	no	—
255	C₄²×D₇₃	C₂³	1	1	yes	characteristic
256	#14556525	C₂³	1	1	yes	characteristic
257	#14556524	C₂³	1	1	yes	characteristic
258	#14556524	C₂³	1	1	yes	characteristic
259	#14556523	C₂³	1	2	yes	—
260	#14556522	C₂³	1	2	yes	—
261	#14556522	C₂³	1	2	yes	—
262	C₄⋊#10596831	C₂³	1	1	yes	characteristic
263	#14556520	C₂³	1	2	yes	—
264	#14556516	C₂³	1	2	yes	—
265	#14556516	C₂³	1	2	yes	—
266	#14556516	C₂³	1	2	yes	—
267	#14556516	C₂³	1	1	yes	characteristic
268	#14556516	C₂³	1	1	yes	characteristic
269	#14556516	C₂³	1	2	yes	—
270	#14556515	C₂³	1	2	yes	—
271	#14556515	C₂³	1	2	yes	—
272	#14556515	C₂³	1	2	yes	—
273	#14556515	C₂³	1	1	yes	characteristic
274	#14556515	C₂³	1	1	yes	characteristic
275	#14556515	C₂³	1	2	yes	—
276	#14556514	C₂³	1	2	yes	—
277	#14556514	C₂³	1	2	yes	—
278	#14556514	C₂³	1	2	yes	—
279	#14556514	C₂³	1	1	yes	characteristic
280	#14556514	C₂³	1	1	yes	characteristic
281	#14556514	C₂³	1	2	yes	—
282	C₂²⋊#10596831	C₂³	1	2	yes	—
283	#14556503	C₂³	1	2	yes	—
284	#14556503	C₂³	1	2	yes	—
285	C₄×#10596831	C₂³	1	1	yes	characteristic
286	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
287	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
288	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
289	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
290	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
291	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
292	C₄⋊Q₈×C₇₃	—	2	1	no	—
293	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
295	#126×C₇₃	—	2	2	no	—
296	#124×C₇₃	—	2	1	no	—
297	C₂²⋊Q₈×C₇₃	—	2	2	no	—
298	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
299	C₂²⋊Q₈×C₇₃	C₂³	1	2	yes	—
300	C₄×Q₈×C₇₃	—	2	1	no	—
301	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
302	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
303	C₄×D₄×C₇₃	—	2	1	no	—
304	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
305	#117×C₇₃	C₂³	1	2	yes	—
306	#107×C₇₃	C₂³	1	1	yes	characteristic
307	#106×C₇₃	C₂³	1	2	yes	—
308	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
309	#103×C₇₃	C₂³	1	2	yes	—
310	#103×C₇₃	C₂³	1	1	yes	characteristic
311	#103×C₇₃	C₂³	1	2	yes	—
312	#103×C₇₃	C₂³	1	2	yes	—
313	#103×C₇₃	C₂³	1	1	yes	characteristic
314	#103×C₇₃	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₇₃	C₂³	1	2	yes	—
316	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
317	C₂³×D₇₃	C₂×D₄	1	2	yes	—
318	C₂×Dic₁₄₆	—	2	1	no	—
319	C₂×Dic₁₄₆	—	2	4	no	—
320	C₂×Dic₁₄₆	—	2	1	no	—
321	C₂×Dic₁₄₆	—	2	2	no	—
322	C₂×Dic₁₄₆	—	2	1	no	—
323	C₂×Dic₁₄₆	—	2	2	no	—
324	C₂×Dic₁₄₆	—	2	2	no	—
325	C₂×Dic₁₄₆	—	2	2	no	—
326	C₂×Dic₁₄₆	—	2	2	no	—
327	C₂×Dic₁₄₆	—	4	2	no	—
328	C₂×Dic₁₄₆	—	4	8	no	—
329	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
330	C₂×Dic₁₄₆	C₂⁴	1	1	yes	characteristic
331	C₂×Dic₁₄₆	C₂⁴	1	1	yes	characteristic
332	Q₈×D₇₃	—	2	2	no	—
333	Q₈×D₇₃	—	2	4	no	—
334	Q₈×D₇₃	—	2	2	no	—
335	Q₈×D₇₃	—	2	4	no	—
336	Q₈×D₇₃	—	2	2	no	—
337	Q₈×D₇₃	—	2	4	no	—
338	Q₈×D₇₃	—	2	4	no	—
339	Q₈×D₇₃	—	4	2	no	—
340	Q₈×D₇₃	—	4	2	no	—
341	Q₈×D₇₃	—	4	8	no	—
342	Q₈×D₇₃	—	4	8	no	—
343	Q₈×D₇₃	—	4	4	no	—
344	Q₈×D₇₃	#41	1	4	yes	—
345	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
346	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
347	D₄×D₇₃	—	2	4	no	—
348	C₂²×Dic₇₃	—	2	2	no	—
349	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
350	C₂×C₄×D₇₃	—	2	1	no	—
351	C₂×C₄×D₇₃	—	2	4	no	—
352	C₂×C₄×D₇₃	—	2	4	no	—
353	C₂×C₄×D₇₃	—	2	1	no	—
354	C₂×C₄×D₇₃	—	2	1	no	—
355	C₂×C₄×D₇₃	—	2	1	no	—
356	C₂×C₄×D₇₃	—	2	2	no	—
357	C₂×C₄×D₇₃	—	2	2	no	—
358	C₂×C₄×D₇₃	—	2	2	no	—
359	C₂×C₄×D₇₃	—	2	2	no	—
360	C₂×C₄×D₇₃	—	4	8	no	—
361	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
362	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
363	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
364	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
365	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
366	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
367	Dic₂₉₂	—	2	2	no	—
368	Dic₂₉₂	—	4	2	no	—
369	#11924018	—	2	2	no	—
370	#11924018	—	2	2	no	—
371	#11924018	—	4	2	no	—
372	#11924018	—	4	2	no	—
373	#11924012	—	4	2	no	—
374	#11924011	—	4	2	no	—
375	#11924011	—	4	2	no	—
376	C₂×#10596831	C₂⁴	1	1	yes	characteristic
377	C₂×#10596831	C₂⁴	1	1	yes	characteristic
378	C₂×#10596831	C₂⁴	1	2	yes	—
379	C₈×D₇₃	—	2	2	no	—
380	C₈×D₇₃	—	2	2	no	—
381	C₈×D₇₃	—	2	4	no	—
382	C₄⋊Dic₇₃	—	2	1	no	—
383	C₄⋊Dic₇₃	—	2	1	no	—
384	C₄⋊Dic₇₃	—	2	1	no	—
385	C₄⋊Dic₇₃	—	2	2	no	—
386	C₄⋊Dic₇₃	—	2	1	no	—
387	C₄⋊Dic₇₃	—	2	1	no	—
388	C₄⋊Dic₇₃	—	2	2	no	—
389	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
390	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
391	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
392	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
393	#11924007	—	2	2	no	—
394	#11924007	—	2	1	no	—
395	#11924007	—	2	1	no	—
396	#11924007	—	2	2	no	—
397	#11924007	—	2	2	no	—
398	#11924007	—	2	2	no	—
399	#11924007	—	2	1	no	—
400	#11924007	—	2	1	no	—
401	#11924007	—	2	2	no	—
402	#11924007	—	2	2	no	—
403	#11924007	—	2	2	no	—
404	#11924007	—	2	1	no	—
405	#11924007	—	2	2	no	—
406	#11924007	—	2	1	no	—
407	#11924007	C₂×D₄	1	2	yes	—
408	C₂²⋊Dic₇₃	—	2	2	no	—
409	C₂²⋊Dic₇₃	—	2	2	no	—
410	C₂²⋊Dic₇₃	—	2	2	no	—
411	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
419	#11924005	C₂×D₄	1	2	yes	—
420	C₄×Dic₇₃	—	2	2	no	—
421	C₄×Dic₇₃	—	2	1	no	—
422	C₄×Dic₇₃	—	2	1	no	—
423	C₄×Dic₇₃	—	2	2	no	—
424	C₄×Dic₇₃	—	2	2	no	—
425	C₄×Dic₇₃	—	2	1	no	—
426	C₄×Dic₇₃	—	2	1	no	—
427	C₄×Dic₇₃	—	2	1	no	—
428	C₄×Dic₇₃	—	2	1	no	—
429	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
430	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
431	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
432	C₂×Q₈×C₇₃	—	2	1	no	—
433	C₂×Q₈×C₇₃	—	2	2	no	—
434	C₂×Q₈×C₇₃	—	2	4	no	—
435	C₂×Q₈×C₇₃	—	4	2	no	—
436	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
437	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
438	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
439	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
440	C₂²×C₄×C₇₃	—	2	2	no	—
441	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
442	Q₁₆×C₇₃	—	2	2	no	—
443	Q₁₆×C₇₃	—	4	2	no	—
444	M₁₆×C₇₃	—	4	2	no	—
445	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
446	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
447	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
448	C₄⋊C₄×C₇₃	—	2	1	no	—
449	C₄⋊C₄×C₇₃	—	2	2	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	2	no	—
454	C₄⋊C₄×C₇₃	—	2	1	no	—
455	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
456	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
457	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
458	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
459	C₂²⋊C₄×C₇₃	—	2	2	no	—
460	C₂²⋊C₄×C₇₃	—	2	2	no	—
461	C₂²⋊C₄×C₇₃	—	2	2	no	—
462	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
463	C₄²×C₇₃	—	2	2	no	—
464	C₄²×C₇₃	—	2	1	no	—
465	C₄²×C₇₃	—	2	1	no	—
466	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
467	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
468	C₂²×D₇₃	—	2	4	no	—
469	C₂²×D₇₃	—	2	4	no	—
470	C₂²×D₇₃	—	2	4	no	—
471	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
472	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
473	Q₈×C₇₃	—	2	1	no	—
474	Q₈×C₇₃	—	2	1	no	—
475	Q₈×C₇₃	—	2	2	no	—
476	Q₈×C₇₃	—	2	1	no	—
477	Q₈×C₇₃	—	2	2	no	—
478	Q₈×C₇₃	—	4	4	no	—
479	Q₈×C₇₃	—	4	2	no	—
480	Q₈×C₇₃	C₂×#41	1	2	yes	—
481	D₄×C₇₃	—	2	2	no	—
482	C₂×C₄×C₇₃	—	2	1	no	—
483	C₂×C₄×C₇₃	—	2	2	no	—
484	C₂×C₄×C₇₃	—	2	2	no	—
485	C₂×C₄×C₇₃	—	2	1	no	—
486	C₂×C₄×C₇₃	—	2	1	no	—
487	C₂×C₄×C₇₃	—	2	1	no	—
488	C₂×C₄×C₇₃	—	2	2	no	—
489	C₂×C₄×C₇₃	—	2	2	no	—
490	C₂×C₄×C₇₃	—	4	4	no	—
491	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
495	C₂²⋊D₇₃	—	2	4	no	—
496	C₂×Dic₇₃	—	2	1	no	—
497	C₂×Dic₇₃	—	2	4	no	—
498	C₂×Dic₇₃	—	2	1	no	—
499	C₂×Dic₇₃	—	2	1	no	—
500	C₂×Dic₇₃	—	2	1	no	—
501	C₂×Dic₇₃	—	2	2	no	—
502	C₂×Dic₇₃	—	2	2	no	—
503	C₂×Dic₇₃	—	4	4	no	—
504	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
505	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
508	D₂₉₂	—	2	2	no	—
509	C₄×D₇₃	—	2	4	no	—
510	C₄×D₇₃	—	2	4	no	—
511	C₄×D₇₃	—	2	2	no	—
512	C₄×D₇₃	—	2	2	no	—
513	C₄×D₇₃	—	2	2	no	—
514	C₄×D₇₃	—	2	4	no	—
515	C₄×D₇₃	—	4	4	no	—
516	C₄×D₇₃	—	4	4	no	—
517	C₄×D₇₃	—	4	4	no	—
518	C₄×D₇₃	—	4	2	no	—
519	C₄×D₇₃	—	4	4	no	—
520	C₄×D₇₃	—	4	2	no	—
521	C₄×D₇₃	—	4	2	no	—
522	C₄×D₇₃	#137	1	4	yes	—
523	C₄×D₇₃	C₂×#41	1	2	yes	—
524	C₄×D₇₃	H(5,𝔽₂)	1	2	yes	—
525	Dic₁₄₆	—	2	1	no	—
526	Dic₁₄₆	—	2	4	no	—
527	Dic₁₄₆	—	2	1	no	—
528	Dic₁₄₆	—	2	2	no	—
529	Dic₁₄₆	—	2	1	no	—
530	Dic₁₄₆	—	2	2	no	—
531	Dic₁₄₆	—	4	4	no	—
532	Dic₁₄₆	—	4	4	no	—
533	Dic₁₄₆	—	4	4	no	—
534	Dic₁₄₆	—	4	2	no	—
535	Dic₁₄₆	—	4	4	no	—
536	Dic₁₄₆	—	4	2	no	—
537	Dic₁₄₆	—	4	4	no	—
538	Dic₁₄₆	C₂×#41	1	2	yes	—
539	C₈×C₇₃	—	2	1	no	—
540	C₈×C₇₃	—	2	1	no	—
541	C₈×C₇₃	—	2	2	no	—
542	#10596831	—	2	1	no	—
543	#10596831	—	2	1	no	—
544	#10596831	—	2	2	no	—
545	C₂²×C₇₃	—	2	2	no	—
546	C₂²×C₇₃	—	2	2	no	—
547	C₂²×C₇₃	—	2	2	no	—
548	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
549	C₂×D₇₃	—	2	2	no	—
550	C₂×D₇₃	—	2	2	no	—
551	C₂×D₇₃	—	2	2	no	—
552	C₂×D₇₃	—	4	8	no	—
553	C₂×D₇₃	#546	1	2	yes	—
554	C₂×D₇₃	C₂×#137	1	2	yes	—
555	C₂×D₇₃	#578	1	2	yes	—
556	C₄×C₇₃	—	2	2	no	—
557	C₄×C₇₃	—	2	2	no	—
558	C₄×C₇₃	—	2	1	no	—
559	C₄×C₇₃	—	4	2	no	—
560	C₄×C₇₃	—	4	1	no	—
561	C₄×C₇₃	—	4	2	no	—
562	C₄×C₇₃	—	4	1	no	—
563	C₄×C₇₃	—	4	1	no	—
564	C₄×C₇₃	C₂×#137	1	2	yes	—
565	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
566	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
567	Dic₇₃	—	2	2	no	—
568	Dic₇₃	—	2	2	no	—
569	Dic₇₃	—	2	1	no	—
570	Dic₇₃	—	4	2	no	—
571	Dic₇₃	—	4	1	no	—
572	Dic₇₃	—	4	2	no	—
573	Dic₇₃	—	4	1	no	—
574	Dic₇₃	—	4	1	no	—
575	Dic₇₃	#546	1	2	yes	—
576	Dic₇₃	C₂×#137	1	2	yes	—
577	C₂×#3328	—	73	1	no	maximal, Sylow
578	C₂×C₇₃	—	4	2	no	—
579	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
580	C₂×C₇₃	C₂²×#137	1	1	yes	characteristic
581	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
582	D₇₃	—	4	2	no	—
583	D₇₃	#3328	1	4	yes	direct product factor
584	C₂×#556	—	73	1	no	—
585	C₂×D₄×Q₈	—	73	1	no	—
586	#3328	—	73	1	no	—
587	#3328	—	73	2	no	—
588	#3328	—	73	1	no	—
589	#3328	—	73	2	no	—
590	#3328	—	73	1	no	—
591	#3328	—	73	2	no	—
592	#3328	—	73	1	no	—
593	#3328	—	73	1	no	—
594	#3328	—	73	2	no	—
595	#3328	—	73	1	no	—
596	#3328	—	73	1	no	—
597	#3328	D₇₃	1	1	yes	characteristic, direct product factor
598	C₂×#487	—	73	1	no	—
599	C₂×#485	—	73	2	no	—
600	C₂×#475	—	73	1	no	—
601	C₂×#470	—	73	2	no	—
602	C₂×#462	—	73	1	no	—
603	C₂×#451	—	73	2	no	—
604	C₂×C₄×Q₁₆	—	73	1	no	—
605	C₂×#436	—	73	1	no	—
606	C₂×#419	—	73	2	no	—
607	C₇₃	C₂×#3328	1	1	yes	characteristic, complemented, Sylow
608	C₂³×Q₈	—	73	2	no	—
609	C₂²×Q₁₆	—	73	2	no	—
610	C₂²×Q₁₆	—	73	1	no	—
611	C₂²×M₁₆	—	73	2	no	—
612	#556	—	73	1	no	—
613	#556	—	73	2	no	—
614	#556	—	73	1	no	—
615	#556	—	73	1	no	—
616	#556	—	73	2	no	—
617	#556	—	146	1	no	—
618	#556	—	146	1	no	—
619	#556	—	146	2	no	—
620	#556	C₂×D₇₃	1	1	yes	characteristic
621	D₄×Q₈	—	73	2	no	—
622	D₄×Q₈	—	73	1	no	—
623	D₄×Q₈	—	73	2	no	—
624	D₄×Q₈	—	73	1	no	—
625	D₄×Q₈	—	73	1	no	—
626	D₄×Q₈	—	146	1	no	—
627	D₄×Q₈	—	146	2	no	—
628	D₄×Q₈	—	146	1	no	—
629	D₄×Q₈	C₂×D₇₃	1	1	yes	characteristic
630	C₂×C₄⋊Q₈	—	73	1	no	—
631	C₂×C₄⋊Q₈	—	73	1	no	—
632	C₂×C₄⋊Q₈	—	146	1	no	—
633	C₂×#126	—	146	2	no	—
634	C₂×#124	—	146	1	no	—
635	C₂×C₂²⋊Q₈	—	73	2	no	—
636	C₂×C₂²⋊Q₈	—	73	2	no	—
637	C₂×C₂²⋊Q₈	—	146	2	no	—
638	C₂×C₄×Q₈	—	73	1	no	—
639	C₂×C₄×Q₈	—	73	1	no	—
640	C₂×C₄×Q₈	—	146	1	no	—
641	C₂×C₄×D₄	—	73	1	no	—
642	C₂×C₄×D₄	—	146	1	no	—
643	C₂×#117	—	73	2	no	—
644	#487	—	73	1	no	—
645	#487	—	73	1	no	—
646	#487	—	73	2	no	—
647	#487	—	73	2	no	—
648	#487	—	73	1	no	—
649	#487	C₂×D₇₃	1	1	yes	characteristic, complemented
650	#485	—	73	2	no	—
651	#485	—	73	2	no	—
652	#485	—	73	2	no	—
653	#485	—	73	2	no	—
654	#485	—	73	2	no	—
655	#485	—	73	2	no	—
656	#485	—	73	2	no	—
657	#485	C₂×D₇₃	1	2	yes	complemented
658	#475	—	73	1	no	—
659	#475	—	73	1	no	—
660	#475	—	73	2	no	—
661	#475	—	73	1	no	—
662	#475	—	73	2	no	—
663	#475	C₂×D₇₃	1	1	yes	characteristic, complemented
664	#470	—	73	2	no	—
665	#470	—	73	2	no	—
666	#470	—	73	2	no	—
667	#470	—	73	2	no	—
668	#470	—	73	2	no	—
669	#470	—	73	2	no	—
670	#470	—	73	2	no	—
671	#470	C₂×D₇₃	1	2	yes	complemented
672	#462	—	73	2	no	—
673	#462	—	73	1	no	—
674	#462	—	73	1	no	—
675	#462	—	73	1	no	—
676	#462	—	73	2	no	—
677	#462	C₂×D₇₃	1	1	yes	characteristic, complemented
678	#451	—	73	2	no	—
679	#451	—	73	2	no	—
680	#451	—	73	2	no	—
681	#451	—	73	2	no	—
682	#451	—	73	2	no	—
683	#451	—	73	2	no	—
684	#451	—	73	2	no	—
685	#451	C₂×D₇₃	1	2	yes	complemented
686	C₄×Q₁₆	—	73	1	no	—
687	C₄×Q₁₆	—	73	1	no	—
688	C₄×Q₁₆	—	73	1	no	—
689	C₄×Q₁₆	—	73	1	no	—
690	C₄×Q₁₆	—	73	1	no	—
691	C₄×Q₁₆	—	73	1	no	—
692	C₄×Q₁₆	—	73	1	no	—
693	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
694	#436	—	73	2	no	—
695	#436	—	73	1	no	—
696	#436	—	73	1	no	—
697	#436	—	73	2	no	—
698	#436	—	73	1	no	—
699	#436	C₂×D₇₃	1	1	yes	characteristic
700	C₂×#107	—	73	1	no	—
701	C₂×#106	—	73	2	no	—
702	C₂×C₄⋊C₈	—	73	1	no	—
703	#419	—	73	2	no	—
704	#419	—	73	2	no	—
705	#419	—	73	2	no	—
706	#419	—	73	2	no	—
707	#419	—	73	2	no	—
708	#419	—	73	2	no	—
709	#419	—	73	2	no	—
710	#419	C₂×D₇₃	1	2	yes	complemented
711	C₂×#103	—	73	2	no	—
712	C₂×#103	—	73	2	no	—
713	C₂×#103	—	73	2	no	—
714	C₂×#103	—	73	2	no	—
715	C₂×#103	—	73	1	no	—
716	C₂×#103	—	73	1	no	—
717	C₂×C₂²⋊C₈	—	73	2	no	—
718	C₂×C₄×C₈	—	73	1	no	—
719	C₂²×Q₈	—	292	4	no	—
720	C₂²×Q₈	—	73	2	no	—
721	C₂²×Q₈	—	73	2	no	—
722	C₂²×Q₈	—	73	1	no	—
723	C₂²×Q₈	—	73	1	no	—
724	C₂²×Q₈	—	73	2	no	—
725	C₂²×Q₈	—	73	2	no	—
726	C₂²×Q₈	—	146	2	no	—
727	C₂²×Q₈	—	146	8	no	—
728	C₂²×Q₈	—	146	1	no	—
729	C₂²×Q₈	—	146	2	no	—
730	C₂²×Q₈	—	146	2	no	—
731	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
732	C₂²×D₄	—	73	1	no	—
733	C₂³×C₄	—	73	2	no	—
734	C₂³×C₄	—	146	2	no	—
735	C₂×Q₁₆	—	292	4	no	—
736	C₂×Q₁₆	—	73	2	no	—
737	C₂×Q₁₆	—	73	2	no	—
738	C₂×Q₁₆	—	73	1	no	—
739	C₂×Q₁₆	—	73	1	no	—
740	C₂×Q₁₆	—	73	2	no	—
741	C₂×Q₁₆	—	73	1	no	—
742	C₂×Q₁₆	—	146	4	no	—
743	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
744	C₂×Q₁₆	C₂²×D₇₃	1	2	yes	—
745	C₂×M₁₆	—	292	4	no	—
746	C₂×M₁₆	—	73	2	no	—
747	C₂×M₁₆	—	73	2	no	—
748	C₂×M₁₆	—	73	2	no	—
749	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
750	C₂²×C₈	—	73	1	no	—
751	C₂²×C₈	—	73	2	no	—
752	C₂²×C₈	—	73	1	no	—
753	C₄⋊Q₈	—	2	1	no	—
754	C₄⋊Q₈	—	73	2	no	—
755	C₄⋊Q₈	—	73	2	no	—
756	C₄⋊Q₈	—	73	1	no	—
757	C₄⋊Q₈	—	73	1	no	—
758	C₄⋊Q₈	—	146	1	no	—
759	C₄⋊Q₈	—	146	1	no	—
760	C₄⋊Q₈	—	146	1	no	—
761	C₄⋊Q₈	—	146	1	no	—
762	C₄⋊Q₈	—	146	1	no	—
763	C₄⋊Q₈	—	146	2	no	—
764	C₄⋊Q₈	—	146	1	no	—
765	C₄⋊Q₈	—	146	2	no	—
766	C₄⋊Q₈	—	146	1	no	—
767	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
768	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
769	#126	—	2	2	no	—
770	#126	—	146	2	no	—
771	#126	—	146	2	no	—
772	#126	—	146	2	no	—
773	#126	—	146	2	no	—
774	#126	—	146	2	no	—
775	#126	—	146	2	no	—
776	#126	—	146	2	no	—
777	#124	—	2	1	no	—
778	#124	—	146	1	no	—
779	#124	—	146	2	no	—
780	#124	—	146	2	no	—
781	#124	—	146	1	no	—
782	#124	—	146	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	73	2	no	—
785	C₂²⋊Q₈	—	73	2	no	—
786	C₂²⋊Q₈	—	73	2	no	—
787	C₂²⋊Q₈	—	73	2	no	—
788	C₂²⋊Q₈	—	73	2	no	—
789	C₂²⋊Q₈	—	73	2	no	—
790	C₂²⋊Q₈	—	146	2	no	—
791	C₂²⋊Q₈	—	146	2	no	—
792	C₂²⋊Q₈	—	146	2	no	—
793	C₂²⋊Q₈	—	146	2	no	—
794	C₂²⋊Q₈	—	146	2	no	—
795	C₂²⋊Q₈	—	146	2	no	—
796	C₂²⋊Q₈	—	146	2	no	—
797	C₂²⋊Q₈	—	146	2	no	—
798	C₂²⋊Q₈	—	146	2	no	—
799	C₂²⋊Q₈	—	146	2	no	—
800	C₂²⋊Q₈	—	146	2	no	—
801	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
802	C₂²⋊Q₈	C₂²×D₇₃	1	2	yes	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	73	1	no	—
805	C₄×Q₈	—	73	1	no	—
806	C₄×Q₈	—	73	1	no	—
807	C₄×Q₈	—	73	1	no	—
808	C₄×Q₈	—	73	1	no	—
809	C₄×Q₈	—	73	1	no	—
810	C₄×Q₈	—	146	1	no	—
811	C₄×Q₈	—	146	1	no	—
812	C₄×Q₈	—	146	2	no	—
813	C₄×Q₈	—	146	1	no	—
814	C₄×Q₈	—	146	1	no	—
815	C₄×Q₈	—	146	1	no	—
816	C₄×Q₈	—	146	2	no	—
817	C₄×Q₈	—	146	1	no	—
818	C₄×Q₈	—	146	1	no	—
819	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
820	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	73	1	no	—
823	C₄×D₄	—	73	2	no	—
824	C₄×D₄	—	73	1	no	—
825	C₄×D₄	—	73	2	no	—
826	C₄×D₄	—	73	1	no	—
827	C₄×D₄	—	146	1	no	—
828	C₄×D₄	—	146	2	no	—
829	C₄×D₄	—	146	1	no	—
830	C₄×D₄	—	146	2	no	—
831	C₄×D₄	—	146	1	no	—
832	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
833	#117	—	73	2	no	—
834	#117	—	73	2	no	—
835	#117	—	73	2	no	—
836	#117	—	146	2	no	—
837	#117	—	146	2	no	—
838	#117	C₂²×D₇₃	1	2	yes	—
839	C₂×C₄⋊C₄	—	73	1	no	—
840	C₂×C₄⋊C₄	—	73	1	no	—
841	C₂×C₄⋊C₄	—	73	2	no	—
842	C₂×C₄⋊C₄	—	73	1	no	—
843	C₂×C₄⋊C₄	—	146	1	no	—
844	C₂×C₄⋊C₄	—	146	1	no	—
845	C₂×C₄⋊C₄	—	146	1	no	—
846	C₂×C₄⋊C₄	—	146	2	no	—
847	C₂×C₄⋊C₄	—	146	2	no	—
848	C₂×C₄⋊C₄	—	146	1	no	—
849	C₂×C₄⋊C₄	—	146	1	no	—
850	C₂×C₂²⋊C₄	—	73	2	no	—
851	C₂×C₂²⋊C₄	—	146	2	no	—
852	C₂×C₂²⋊C₄	—	146	2	no	—
853	C₂×C₂²⋊C₄	—	146	2	no	—
854	C₂×C₄²	—	73	1	no	—
855	C₂×C₄²	—	146	2	no	—
856	C₂×C₄²	—	146	1	no	—
857	C₂×C₄²	—	146	1	no	—
858	#107	—	73	1	no	—
859	#107	—	73	1	no	—
860	#107	—	73	1	no	—
861	#107	C₂²×D₇₃	1	1	yes	characteristic
862	#106	—	73	2	no	—
863	#106	—	73	2	no	—
864	#106	—	73	2	no	—
865	#106	C₂²×D₇₃	1	2	yes	—
866	C₄⋊C₈	—	73	2	no	—
867	C₄⋊C₈	—	73	1	no	—
868	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
869	#103	—	73	1	no	—
870	#103	—	73	2	no	—
871	#103	—	73	2	no	—
872	#103	—	73	2	no	—
873	#103	—	73	1	no	—
874	#103	—	73	2	no	—
875	#103	—	73	1	no	—
876	#103	—	73	2	no	—
877	#103	—	73	2	no	—
878	#103	—	73	2	no	—
879	#103	—	73	1	no	—
880	#103	—	73	2	no	—
881	#103	—	73	1	no	—
882	#103	—	73	2	no	—
883	#103	—	73	2	no	—
884	#103	—	73	2	no	—
885	#103	—	73	1	no	—
886	#103	—	73	2	no	—
887	#103	C₂²×D₇₃	1	1	yes	characteristic
888	#103	C₂²×D₇₃	1	2	yes	—
889	#103	C₂²×D₇₃	1	2	yes	—
890	#103	C₂²×D₇₃	1	2	yes	—
891	#103	C₂²×D₇₃	1	1	yes	characteristic
892	#103	C₂²×D₇₃	1	2	yes	—
893	C₂²⋊C₈	—	73	2	no	—
894	C₂²⋊C₈	—	73	2	no	—
895	C₂²⋊C₈	—	73	2	no	—
896	C₂²⋊C₈	C₂²×D₇₃	1	2	yes	—
897	C₄×C₈	—	73	1	no	—
898	C₄×C₈	—	73	1	no	—
899	C₄×C₈	—	73	1	no	—
900	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
901	C₂⁴	—	73	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	2	4	no	—
905	C₂×Q₈	—	4	2	no	—
906	C₂×Q₈	—	292	2	no	—
907	C₂×Q₈	—	292	8	no	—
908	C₂×Q₈	—	292	4	no	—
909	C₂×Q₈	—	292	2	no	—
910	C₂×Q₈	—	292	2	no	—
911	C₂×Q₈	—	292	8	no	—
912	C₂×Q₈	—	292	8	no	—
913	C₂×Q₈	—	73	4	no	—
914	C₂×Q₈	—	73	1	no	—
915	C₂×Q₈	—	73	2	no	—
916	C₂×Q₈	—	73	1	no	—
917	C₂×Q₈	—	146	4	no	—
918	C₂×Q₈	—	146	1	no	—
919	C₂×Q₈	—	146	2	no	—
920	C₂×Q₈	—	146	2	no	—
921	C₂×Q₈	—	146	2	no	—
922	C₂×Q₈	—	146	2	no	—
923	C₂×Q₈	—	146	1	no	—
924	C₂×Q₈	—	146	2	no	—
925	C₂×Q₈	—	146	4	no	—
926	C₂×Q₈	—	146	2	no	—
927	C₂×Q₈	—	146	4	no	—
928	C₂×Q₈	—	146	4	no	—
929	C₂×Q₈	—	146	4	no	—
930	C₂×Q₈	—	146	2	no	—
931	C₂×Q₈	—	146	1	no	—
932	C₂×Q₈	—	146	2	no	—
933	C₂×Q₈	C₂³×D₇₃	1	2	yes	—
934	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
935	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
936	C₂×D₄	—	73	2	no	—
937	C₂×D₄	—	73	1	no	—
938	C₂×D₄	—	146	4	no	—
939	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
940	C₂²×C₄	—	2	2	no	—
941	C₂²×C₄	—	292	8	no	—
942	C₂²×C₄	—	73	1	no	—
943	C₂²×C₄	—	73	1	no	—
944	C₂²×C₄	—	73	2	no	—
945	C₂²×C₄	—	73	1	no	—
946	C₂²×C₄	—	73	2	no	—
947	C₂²×C₄	—	73	2	no	—
948	C₂²×C₄	—	73	2	no	—
949	C₂²×C₄	—	146	1	no	—
950	C₂²×C₄	—	146	1	no	—
951	C₂²×C₄	—	146	2	no	—
952	C₂²×C₄	—	146	1	no	—
953	C₂²×C₄	—	146	2	no	—
954	C₂²×C₄	—	146	2	no	—
955	C₂²×C₄	—	146	2	no	—
956	C₂²×C₄	—	146	4	no	—
957	C₂²×C₄	—	146	4	no	—
958	C₂²×C₄	—	146	1	no	—
959	C₂²×C₄	—	146	2	no	—
960	C₂²×C₄	C₂³×D₇₃	1	2	yes	—
961	Q₁₆	—	2	2	no	—
962	Q₁₆	—	4	2	no	—
963	Q₁₆	—	292	2	no	—
964	Q₁₆	—	292	2	no	—
965	Q₁₆	—	292	2	no	—
966	Q₁₆	—	146	2	no	—
967	Q₁₆	—	146	2	no	—
968	Q₁₆	—	146	2	no	—
969	M₁₆	—	4	2	no	—
970	M₁₆	—	292	2	no	—
971	M₁₆	—	292	2	no	—
972	M₁₆	—	292	2	no	—
973	C₂×C₈	—	73	1	no	—
974	C₂×C₈	—	73	1	no	—
975	C₂×C₈	—	73	2	no	—
976	C₂×C₈	—	146	2	no	—
977	C₂×C₈	—	146	4	no	—
978	C₂×C₈	—	146	2	no	—
979	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
980	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
981	C₂×C₈	C₂³×D₇₃	1	2	yes	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	1	no	—
986	C₄⋊C₄	—	2	1	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	73	2	no	—
990	C₄⋊C₄	—	73	1	no	—
991	C₄⋊C₄	—	73	2	no	—
992	C₄⋊C₄	—	73	1	no	—
993	C₄⋊C₄	—	73	1	no	—
994	C₄⋊C₄	—	146	1	no	—
995	C₄⋊C₄	—	146	2	no	—
996	C₄⋊C₄	—	146	1	no	—
997	C₄⋊C₄	—	146	2	no	—
998	C₄⋊C₄	—	146	1	no	—
999	C₄⋊C₄	—	146	1	no	—
1000	C₄⋊C₄	—	146	2	no	—
1001	C₄⋊C₄	—	146	2	no	—
1002	C₄⋊C₄	—	146	2	no	—
1003	C₄⋊C₄	—	146	2	no	—
1004	C₄⋊C₄	—	146	1	no	—
1005	C₄⋊C₄	—	146	1	no	—
1006	C₄⋊C₄	—	146	2	no	—
1007	C₄⋊C₄	—	146	2	no	—
1008	C₄⋊C₄	—	146	1	no	—
1009	C₄⋊C₄	—	146	1	no	—
1010	C₄⋊C₄	—	146	2	no	—
1011	C₄⋊C₄	—	146	2	no	—
1012	C₄⋊C₄	—	146	1	no	—
1013	C₄⋊C₄	—	146	1	no	—
1014	C₄⋊C₄	—	146	1	no	—
1015	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
1016	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
1017	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1018	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	73	2	no	—
1023	C₂²⋊C₄	—	73	2	no	—
1024	C₂²⋊C₄	—	73	2	no	—
1025	C₂²⋊C₄	—	146	2	no	—
1026	C₂²⋊C₄	—	146	2	no	—
1027	C₂²⋊C₄	—	146	2	no	—
1028	C₂²⋊C₄	—	146	2	no	—
1029	C₂²⋊C₄	—	146	2	no	—
1030	C₂²⋊C₄	—	146	2	no	—
1031	C₂²⋊C₄	—	146	2	no	—
1032	C₂²⋊C₄	—	146	2	no	—
1033	C₂²⋊C₄	—	146	2	no	—
1034	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	1	no	—
1037	C₄²	—	2	1	no	—
1038	C₄²	—	73	1	no	—
1039	C₄²	—	73	1	no	—
1040	C₄²	—	73	1	no	—
1041	C₄²	—	146	2	no	—
1042	C₄²	—	146	2	no	—
1043	C₄²	—	146	1	no	—
1044	C₄²	—	146	1	no	—
1045	C₄²	—	146	1	no	—
1046	C₄²	—	146	1	no	—
1047	C₄²	—	146	2	no	—
1048	C₄²	—	146	1	no	—
1049	C₄²	—	146	1	no	—
1050	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1051	C₂³	—	73	1	no	—
1052	C₂³	—	73	2	no	—
1053	C₂³	—	146	4	no	—
1054	C₂³	—	146	4	no	—
1055	C₂³	—	146	4	no	—
1056	C₂³	C₂×D₄×D₇₃	1	2	yes	—
1057	Q₈	—	2	1	no	—
1058	Q₈	—	2	1	no	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	1	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	4	4	no	—
1063	Q₈	—	4	2	no	—
1064	Q₈	—	292	4	no	—
1065	Q₈	—	292	4	no	—
1066	Q₈	—	292	4	no	—
1067	Q₈	—	292	4	no	—
1068	Q₈	—	292	2	no	—
1069	Q₈	—	292	4	no	—
1070	Q₈	—	292	2	no	—
1071	Q₈	—	73	2	no	—
1072	Q₈	—	146	4	no	—
1073	Q₈	—	146	1	no	—
1074	Q₈	—	146	2	no	—
1075	Q₈	—	146	1	no	—
1076	Q₈	—	146	2	no	—
1077	Q₈	—	146	1	no	—
1078	Q₈	#41×D₇₃	1	2	yes	—
1079	D₄	—	2	2	no	—
1080	D₄	—	146	4	no	—
1081	D₄	—	146	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	2	no	—
1084	C₂×C₄	—	2	2	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	2	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	4	4	no	—
1091	C₂×C₄	—	292	4	no	—
1092	C₂×C₄	—	292	4	no	—
1093	C₂×C₄	—	292	4	no	—
1094	C₂×C₄	—	292	2	no	—
1095	C₂×C₄	—	292	2	no	—
1096	C₂×C₄	—	292	2	no	—
1097	C₂×C₄	—	292	4	no	—
1098	C₂×C₄	—	292	4	no	—
1099	C₂×C₄	—	73	1	no	—
1100	C₂×C₄	—	73	1	no	—
1101	C₂×C₄	—	73	4	no	—
1102	C₂×C₄	—	73	2	no	—
1103	C₂×C₄	—	73	2	no	—
1104	C₂×C₄	—	73	1	no	—
1105	C₂×C₄	—	73	2	no	—
1106	C₂×C₄	—	146	4	no	—
1107	C₂×C₄	—	146	4	no	—
1108	C₂×C₄	—	146	4	no	—
1109	C₂×C₄	—	146	2	no	—
1110	C₂×C₄	—	146	1	no	—
1111	C₂×C₄	—	146	1	no	—
1112	C₂×C₄	—	146	2	no	—
1113	C₂×C₄	—	146	1	no	—
1114	C₂×C₄	—	146	2	no	—
1115	C₂×C₄	—	146	4	no	—
1116	C₂×C₄	—	146	1	no	—
1117	C₂×C₄	—	146	2	no	—
1118	C₂×C₄	—	146	2	no	—
1119	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1120	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1121	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1122	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1123	C₈	—	2	1	no	—
1124	C₈	—	2	1	no	—
1125	C₈	—	2	2	no	—
1126	C₈	—	146	1	no	—
1127	C₈	—	146	1	no	—
1128	C₈	—	146	2	no	—
1129	C₂²	—	2	2	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	292	8	no	—
1133	C₂²	—	73	2	no	—
1134	C₂²	—	73	2	no	—
1135	C₂²	—	73	2	no	—
1136	C₂²	—	146	2	no	—
1137	C₂²	—	146	2	no	—
1138	C₂²	—	146	2	no	—
1139	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1140	C₄	—	2	2	no	—
1141	C₄	—	2	2	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	4	2	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	2	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	292	2	no	—
1149	C₄	—	292	1	no	—
1150	C₄	—	292	2	no	—
1151	C₄	—	292	1	no	—
1152	C₄	—	292	1	no	—
1153	C₄	—	73	2	no	—
1154	C₄	—	73	2	no	—
1155	C₄	—	146	2	no	—
1156	C₄	—	146	2	no	—
1157	C₄	—	146	1	no	—
1158	C₄	#137×D₇₃	1	2	yes	—
1159	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1160	C₄	H(5,𝔽₂)×D₇₃	1	1	yes	characteristic
1161	C₂	—	4	2	no	—
1162	C₂	—	292	2	no	—
1163	C₂	—	73	4	no	—
1164	C₂	#546×D₇₃	1	1	yes	characteristic
1165	C₂	C₂×#137×D₇₃	1	1	yes	characteristic
1166	C₂	#578×D₇₃	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×#3328	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂×D₄×D₇₃	D₄
hypercenter	#3328	D₇₃
hypocenter	C₇₃	C₂×#3328
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3328

Complements

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

N	H ≅ G/N	type
3. #22622217	C₂	semidirect
4. #22622216	C₂	semidirect
5. #22622215	C₂	semidirect
6. #22622214	C₂	semidirect
7. #22622213	C₂	semidirect
8. #22622212	C₂	semidirect
9. #22622211	C₂	semidirect
10. #22622210	C₂	semidirect
11. #22622209	C₂	semidirect
12. #22622208	C₂	semidirect
13. #22622207	C₂	semidirect
14. #487×D₇₃	C₂	semidirect
15. #485×D₇₃	C₂	semidirect
16. #475×D₇₃	C₂	semidirect
17. #470×D₇₃	C₂	semidirect
18. #462×D₇₃	C₂	semidirect
19. #451×D₇₃	C₂	semidirect
20. C₄×Q₁₆×D₇₃	C₂	semidirect
22. #419×D₇₃	C₂	semidirect
23. C₇₃×#3328	C₂	semidirect
58. #17988939	C₂²	semidirect
59. #17988938	C₂²	semidirect
60. #17988937	C₂²	semidirect
61. #17988936	C₂²	semidirect
62. #17988936	C₂²	semidirect
63. #17988931	C₂²	semidirect
64. #17988930	C₂²	semidirect
65. #17988929	C₂²	semidirect
66. #17988928	C₂²	semidirect
67. #17988927	C₂²	semidirect
68. #17988926	C₂²	semidirect
69. #17988925	C₂²	semidirect
70. #17988873	C₂²	semidirect
71. #17988872	C₂²	semidirect
72. #17988871	C₂²	semidirect
73. #17988870	C₂²	semidirect
74. #17988869	C₂²	semidirect
75. #17988846	C₂²	semidirect
76. #17988845	C₂²	semidirect
77. #17988844	C₂²	semidirect
78. #17988844	C₂²	semidirect
79. #17988843	C₂²	semidirect
80. #17988843	C₂²	semidirect
81. #17988842	C₂²	semidirect
82. #17988798	C₂²	semidirect
83. #17988797	C₂²	semidirect
84. #17988796	C₂²	semidirect
85. #17988795	C₂²	semidirect
86. #17988794	C₂²	semidirect
87. #17988745	C₂²	semidirect
88. #17988744	C₂²	semidirect
89. #17988744	C₂²	semidirect
90. #17988743	C₂²	semidirect
91. #17988742	C₂²	semidirect
92. #17988741	C₂²	semidirect
93. #17988741	C₂²	semidirect
94. C₄×Dic₂₉₂	C₂²	semidirect
95. Q₁₆×Dic₇₃	C₂²	semidirect
96. #17988681	C₂²	semidirect
97. C₄×#11924018	C₂²	semidirect
98. C₄×#11924018	C₂²	semidirect
99. #17988679	C₂²	semidirect
100. #17988679	C₂²	semidirect
109. #17988597	C₂²	semidirect
110. #17988596	C₂²	semidirect
111. #17988595	C₂²	semidirect
112. #17988594	C₂²	semidirect
113. #17988594	C₂²	semidirect
114. #17988594	C₂²	semidirect
115. #17988594	C₂²	semidirect
126. #487×C₇₃	C₂²	semidirect
127. #485×C₇₃	C₂²	semidirect
128. #475×C₇₃	C₂²	semidirect
129. #470×C₇₃	C₂²	semidirect
130. #462×C₇₃	C₂²	semidirect
131. #451×C₇₃	C₂²	semidirect
132. C₄×Q₁₆×C₇₃	C₂²	semidirect
134. #419×C₇₃	C₂²	semidirect
583. D₇₃	#3328	direct (N × H)
597. #3328	D₇₃	direct (N × H)
607. C₇₃	C₂×#3328	semidirect
649. #487	C₂×D₇₃	semidirect
657. #485	C₂×D₇₃	semidirect
663. #475	C₂×D₇₃	semidirect
671. #470	C₂×D₇₃	semidirect
677. #462	C₂×D₇₃	semidirect
685. #451	C₂×D₇₃	semidirect
693. C₄×Q₁₆	C₂×D₇₃	semidirect
710. #419	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#556×D₇₃	2
D₄×Q₈×D₇₃	2
#22622217	2
#22622216	2
#22622215	2
#22622214	2
#22622213	2
#22622212	2
#22622211	2
#22622210	2
#22622209	2
#22622208	2
#22622207	2
#487×D₇₃	2
#485×D₇₃	2
#475×D₇₃	2
#470×D₇₃	2
#462×D₇₃	2
#451×D₇₃	2
C₄×Q₁₆×D₇₃	2
#436×D₇₃	2
#419×D₇₃	2
C₇₃×#3328	2
C₂×#3328	73

Subgroups — #3328×D73 #33962861

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3328×D₇₃ #33962861