Subgroups — #33966859

Order 18688.

1690 conjugacy classes of subgroups.

The subgroup lattice has 1058 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623757	C₂	1	1	yes	maximal, characteristic
2	#22623736	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622898	C₂	1	2	yes	maximal, complemented
4	#22622893	C₂	1	2	yes	maximal, complemented
5	#22622880	C₂	1	2	yes	maximal, complemented
6	#22622869	C₂	1	2	yes	maximal, complemented
7	#22622858	C₂	1	2	yes	maximal, complemented
8	#22622836	C₂	1	2	yes	maximal, complemented
9	#22622817	C₂	1	2	yes	maximal, complemented
10	#22622801	C₂	1	2	yes	maximal, complemented
11	#22620484	C₂	1	1	yes	maximal, characteristic, complemented
12	#22620471	C₂	1	1	yes	maximal, characteristic, complemented
13	#22620463	C₂	1	1	yes	maximal, characteristic, complemented
14	#22619791	C₂	1	1	yes	maximal, characteristic
15	#22619780	C₂	1	1	yes	maximal, characteristic
16	#22619776	C₂	1	1	yes	maximal, characteristic, complemented
17	#22619776	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#17988895	C₂	1	1	yes	maximal, characteristic, complemented
19	#22618874	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618777	C₂	1	1	yes	maximal, characteristic
21	#22618777	C₂	1	1	yes	maximal, characteristic
22	C₄×#14556621	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3076	C₂	1	1	yes	maximal, characteristic
24	C₂×#14556621	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₄₆	—	2	1	no	—
26	#17989317	C₂²	1	2	yes	—
27	#17989315	—	2	1	no	—
28	#17989315	—	2	1	no	—
29	#17989315	—	2	1	no	—
30	#17989314	C₂²	1	2	yes	—
31	#17989314	C₂²	1	2	yes	—
32	#17989313	C₂²	1	2	yes	—
33	#17989313	C₂²	1	2	yes	—
34	#17989312	C₂²	1	2	yes	—
35	#17989296	—	2	2	no	—
36	#17989296	—	2	2	no	—
37	#17989296	C₂²	1	2	yes	—
38	#17989296	C₂²	1	2	yes	—
39	#17989216	—	2	2	no	—
40	#17989215	—	2	1	no	—
41	#17989215	—	2	1	no	—
42	#17989215	C₂²	1	1	yes	characteristic
43	#17989215	C₂²	1	1	yes	characteristic
44	#17989215	C₂²	1	1	yes	characteristic
45	#17989215	C₂²	1	1	yes	characteristic
46	#17989144	—	2	1	no	—
47	#17989144	C₂²	1	1	yes	characteristic
48	#17989139	—	2	2	no	—
49	C₂×#14556583	—	2	1	no	—
50	C₂×#14556583	C₂²	1	1	yes	characteristic
51	#17989070	C₂²	1	1	yes	characteristic
52	#17989070	C₂²	1	1	yes	characteristic
53	#17989064	C₂²	1	1	yes	characteristic
54	#17989064	C₂²	1	1	yes	characteristic
55	C₂×C₄×Dic₁₄₆	C₂²	1	1	yes	characteristic
56	#17988995	C₂²	1	2	yes	—
57	#17988995	C₂²	1	2	yes	—
58	#17988994	C₂²	1	2	yes	—
59	#17988994	C₂²	1	2	yes	—
60	#17988993	C₂²	1	2	yes	—
61	#17988993	C₂²	1	2	yes	—
62	#17988991	C₂²	1	2	yes	—
63	#17988988	C₂²	1	2	yes	—
64	#17988987	C₂²	1	2	yes	—
65	#17988986	C₂²	1	2	yes	—
66	#17988986	C₂²	1	2	yes	—
67	#17988984	C₂²	1	2	yes	—
68	#17988897	C₂²	1	2	yes	—
69	#17988897	C₂²	1	2	yes	—
70	#17988896	C₂²	1	2	yes	—
71	#17988895	C₂²	1	2	yes	—
72	#17988895	C₂²	1	2	yes	—
73	#17988895	C₂²	1	2	yes	—
74	#17988895	C₂²	1	2	yes	—
75	#17988893	C₂²	1	2	yes	—
76	#17988893	C₂²	1	2	yes	—
77	#17988892	C₂²	1	2	yes	—
78	#17988889	C₂²	1	2	yes	—
79	#17988885	C₂²	1	2	yes	—
80	#17988881	C₂²	1	2	yes	—
81	#17988881	C₂²	1	2	yes	—
82	#17988880	C₂²	1	2	yes	—
83	#17988875	C₂²	1	2	yes	—
84	#17988871	C₂²	1	2	yes	—
85	#17988871	C₂²	1	2	yes	—
86	#17988870	C₂²	1	2	yes	—
87	#17988865	C₂²	1	2	yes	—
88	#17988716	C₂²	1	2	yes	—
89	#17988716	C₂²	1	2	yes	—
90	#17988714	C₂²	1	2	yes	—
91	#17988711	C₂²	1	2	yes	—
92	#17988692	C₂²	1	2	yes	—
93	#17988691	C₂²	1	2	yes	—
94	#17988691	C₂²	1	2	yes	—
95	#17988687	C₂²	1	2	yes	—
96	#17988684	C₂²	1	2	yes	—
97	#17988684	C₂²	1	2	yes	—
98	C₄×#11924018	C₂²	1	2	yes	—
99	#17988679	C₂²	1	2	yes	—
100	#17988679	C₂²	1	2	yes	—
101	#17988678	C₂²	1	2	yes	—
102	#17988678	C₂²	1	2	yes	—
103	C₄×#11924016	C₂²	1	2	yes	—
104	#17988630	C₂²	1	1	yes	characteristic
105	#17988630	C₂²	1	1	yes	characteristic
106	#17988630	C₂²	1	1	yes	characteristic
107	#17988630	C₂²	1	1	yes	characteristic
108	#17988630	C₂²	1	1	yes	characteristic
109	C₂×#14556525	C₂²	1	1	yes	characteristic
110	C₂×#14556523	C₂²	1	1	yes	characteristic
111	#17988613	C₂²	1	1	yes	characteristic
112	#17988613	C₂²	1	1	yes	characteristic
113	#17988595	C₂²	1	1	yes	characteristic
114	#17988588	C₂²	1	1	yes	characteristic
115	C₂×#14556516	C₂²	1	1	yes	characteristic
116	C₂×#14556516	C₂²	1	1	yes	characteristic
117	#17988542	C₂²	1	1	yes	characteristic
118	#17988542	C₂²	1	1	yes	characteristic
119	C₄×#11924012	C₂²	1	1	yes	characteristic
120	#533×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	#479×C₇₃	C₂²	1	1	yes	characteristic
123	#479×C₇₃	C₂²	1	1	yes	characteristic
124	#478×C₇₃	C₂²	1	1	yes	characteristic
125	#478×C₇₃	C₂²	1	1	yes	characteristic
126	#477×C₇₃	C₂²	1	1	yes	characteristic
127	#476×C₇₃	C₂²	1	1	yes	characteristic
128	#475×C₇₃	C₂²	1	1	yes	characteristic
129	#474×C₇₃	C₂²	1	1	yes	characteristic
130	#427×C₇₃	C₂²	1	1	yes	characteristic
131	#427×C₇₃	C₂²	1	1	yes	characteristic
132	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
133	#416×C₇₃	C₂²	1	1	yes	characteristic
134	#416×C₇₃	C₂²	1	1	yes	characteristic
135	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
136	#14556621	Q₈	1	8	yes	complemented
137	C₂×#11924018	C₂³	1	2	yes	—
138	C₂×#11924016	C₂³	1	2	yes	—
139	C₂×#11924012	C₂³	1	1	yes	characteristic
140	C₂×#11924012	C₂³	1	1	yes	characteristic
141	#14556591	—	2	1	no	—
142	#14556591	—	2	1	no	—
143	#14556591	—	2	1	no	—
144	#14556591	—	2	1	no	—
145	#14556591	D₄	1	1	yes	characteristic
146	#14556591	D₄	1	1	yes	characteristic
147	#14556590	—	2	2	no	—
148	#14556590	—	2	2	no	—
149	#14556590	—	2	2	no	—
150	#14556590	—	2	2	no	—
151	#14556590	—	2	2	no	—
152	#14556590	C₂³	1	2	yes	—
153	#14556590	C₂³	1	2	yes	—
154	#14556590	C₂³	1	2	yes	—
155	#14556590	C₂³	1	2	yes	—
156	#14556589	—	2	2	no	—
157	#14556589	—	2	2	no	—
158	#14556589	—	2	2	no	—
159	#14556583	—	2	1	no	—
160	#14556583	—	2	1	no	—
161	#14556583	—	2	1	no	—
162	#14556583	—	2	1	no	—
163	#14556583	—	2	2	no	—
164	#14556583	—	2	2	no	—
165	#14556583	—	2	1	no	—
166	#14556583	—	2	1	no	—
167	#14556583	D₄	1	1	yes	characteristic
168	#14556583	D₄	1	1	yes	characteristic
169	#14556583	C₂³	1	2	yes	—
170	#14556583	C₂³	1	2	yes	—
171	#14556582	—	2	2	no	—
172	#14556582	—	2	2	no	—
173	#14556582	C₂³	1	2	yes	—
174	#14556582	C₂³	1	2	yes	—
175	#14556582	C₂³	1	2	yes	—
176	#14556582	C₂³	1	2	yes	—
177	#14556581	—	2	2	no	—
178	#14556581	—	2	2	no	—
179	#14556581	—	2	2	no	—
180	#14556581	—	2	2	no	—
181	#14556581	—	2	2	no	—
182	#14556581	—	2	2	no	—
183	#14556570	—	2	2	no	—
184	#14556570	—	2	2	no	—
185	#14556570	D₄	1	2	yes	—
186	#14556570	D₄	1	2	yes	—
187	#14556568	—	2	2	no	—
188	#14556568	—	2	2	no	—
189	#14556568	—	2	2	no	—
190	#14556568	—	2	2	no	—
191	#14556568	—	2	2	no	—
192	#14556568	—	2	2	no	—
193	#14556568	—	2	2	no	—
194	#14556568	—	2	2	no	—
195	Q₈×Dic₇₃	—	2	2	no	—
196	Q₈×Dic₇₃	C₂³	1	2	yes	—
197	Q₈×Dic₇₃	C₂³	1	2	yes	—
198	C₄×Dic₁₄₆	—	2	1	no	—
199	C₄×Dic₁₄₆	—	2	1	no	—
200	C₄×Dic₁₄₆	—	2	1	no	—
201	C₄×Dic₁₄₆	—	2	1	no	—
202	C₄×Dic₁₄₆	—	2	2	no	—
203	C₄×Dic₁₄₆	—	2	2	no	—
204	C₄×Dic₁₄₆	—	2	1	no	—
205	C₄×Dic₁₄₆	—	2	1	no	—
206	C₄×Dic₁₄₆	C₂³	1	2	yes	—
207	C₄×Dic₁₄₆	C₂³	1	2	yes	—
208	C₄×Dic₁₄₆	C₂³	1	2	yes	—
209	C₄×Dic₁₄₆	C₂³	1	2	yes	—
210	#14556556	—	2	2	no	—
211	#14556556	—	2	2	no	—
212	#14556556	—	2	2	no	—
213	#14556556	C₂³	1	2	yes	—
214	#14556556	C₂³	1	2	yes	—
215	#14556556	C₂³	1	2	yes	—
216	#14556556	C₂³	1	2	yes	—
217	D₄×Dic₇₃	—	2	2	no	—
218	D₄×Dic₇₃	—	2	2	no	—
219	D₄×Dic₇₃	C₂³	1	2	yes	—
220	D₄×Dic₇₃	C₂³	1	2	yes	—
221	#14556550	—	2	1	no	—
222	#14556550	—	2	1	no	—
223	#14556550	C₂³	1	1	yes	characteristic
224	#14556550	C₂³	1	1	yes	characteristic
225	#14556547	—	2	2	no	—
226	#14556547	—	2	2	no	—
227	C₂×C₄⋊Dic₇₃	—	2	1	no	—
228	C₂×C₄⋊Dic₇₃	—	2	1	no	—
229	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
230	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
232	C₂×#11924007	—	2	2	no	—
233	C₂×#11924007	—	2	2	no	—
234	C₂×#11924007	—	2	1	no	—
235	C₂×#11924007	—	2	1	no	—
236	C₂×#11924007	—	2	1	no	—
237	C₂×C₄×Dic₇₃	—	2	1	no	—
238	#14556525	C₂³	1	2	yes	—
239	#14556525	C₂³	1	2	yes	—
240	#14556524	C₂³	1	2	yes	—
241	#14556524	C₂³	1	2	yes	—
242	#14556524	C₂³	1	2	yes	—
243	#14556524	C₂³	1	2	yes	—
244	#14556524	C₂³	1	2	yes	—
245	#14556523	C₂³	1	2	yes	—
246	#14556523	C₂³	1	2	yes	—
247	#14556522	C₂³	1	2	yes	—
248	#14556522	C₂³	1	2	yes	—
249	#14556522	C₂³	1	2	yes	—
250	#14556522	C₂³	1	2	yes	—
251	#14556522	C₂³	1	2	yes	—
252	#14556520	C₂³	1	2	yes	—
253	#14556520	C₂³	1	2	yes	—
254	#14556520	C₂³	1	2	yes	—
255	#14556520	C₂³	1	2	yes	—
256	#14556516	C₂³	1	2	yes	—
257	#14556516	C₂³	1	2	yes	—
258	#14556516	C₂³	1	2	yes	—
259	#14556516	C₂³	1	2	yes	—
260	#14556515	C₂³	1	2	yes	—
261	#14556514	C₂³	1	2	yes	—
262	#14556514	C₂³	1	2	yes	—
263	#14556512	C₂³	1	2	yes	—
264	#14556502	C₂³	1	2	yes	—
265	#14556501	C₂³	1	2	yes	—
266	#14556501	C₂³	1	2	yes	—
267	C₄×#10596831	C₂³	1	2	yes	—
268	C₈×Dic₇₃	C₂³	1	2	yes	—
269	C₈×Dic₇₃	C₂³	1	2	yes	—
270	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
274	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
275	#125×C₇₃	C₂³	1	1	yes	characteristic
276	#125×C₇₃	C₂³	1	1	yes	characteristic
277	C₂²⋊Q₈×C₇₃	—	2	1	no	—
278	C₂²⋊Q₈×C₇₃	—	2	1	no	—
279	C₄×Q₈×C₇₃	—	2	1	no	—
280	C₄×Q₈×C₇₃	—	2	1	no	—
281	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₇₃	—	2	1	no	—
284	C₄×D₄×C₇₃	—	2	1	no	—
285	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
287	#117×C₇₃	—	2	1	no	—
288	#117×C₇₃	C₂³	1	1	yes	characteristic
289	#117×C₇₃	C₂³	1	1	yes	characteristic
290	#117×C₇₃	C₂³	1	1	yes	characteristic
291	C₂×C₄²×C₇₃	—	2	1	no	—
292	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
293	#107×C₇₃	C₂³	1	1	yes	characteristic
294	#107×C₇₃	C₂³	1	1	yes	characteristic
295	#107×C₇₃	C₂³	1	1	yes	characteristic
296	#107×C₇₃	C₂³	1	1	yes	characteristic
297	#106×C₇₃	C₂³	1	1	yes	characteristic
298	#106×C₇₃	C₂³	1	1	yes	characteristic
299	#106×C₇₃	C₂³	1	1	yes	characteristic
300	#106×C₇₃	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
305	#103×C₇₃	C₂³	1	1	yes	characteristic
306	#103×C₇₃	C₂³	1	1	yes	characteristic
307	#103×C₇₃	C₂³	1	1	yes	characteristic
308	#103×C₇₃	C₂³	1	1	yes	characteristic
309	#102×C₇₃	C₂³	1	1	yes	characteristic
310	#102×C₇₃	C₂³	1	1	yes	characteristic
311	#102×C₇₃	C₂³	1	1	yes	characteristic
312	#102×C₇₃	C₂³	1	1	yes	characteristic
313	C₂×Dic₁₄₆	—	2	1	no	—
314	C₂×Dic₁₄₆	—	2	2	no	—
315	C₂×Dic₁₄₆	—	2	2	no	—
316	C₂×Dic₁₄₆	—	2	2	no	—
317	C₂×Dic₁₄₆	—	2	2	no	—
318	C₂×Dic₁₄₆	—	2	2	no	—
319	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
320	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
321	C₂×Dic₁₄₆	C₂×Q₈	1	4	yes	—
322	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
323	C₂²×Dic₇₃	—	2	1	no	—
324	C₂²×Dic₇₃	—	2	1	no	—
325	C₂²×Dic₇₃	—	2	1	no	—
326	C₂²×Dic₇₃	—	2	1	no	—
327	C₂²×Dic₇₃	—	2	2	no	—
328	C₂²×Dic₇₃	—	2	2	no	—
329	#11924018	C₂×Q₈	1	8	yes	—
330	#11924016	C₂×Q₈	1	8	yes	—
331	#11924012	—	2	2	no	—
332	#11924012	C₂×Q₈	1	4	yes	—
333	C₂×#10596831	C₂⁴	1	2	yes	—
334	C₂×#10596831	C₂⁴	1	2	yes	—
335	C₄⋊Dic₇₃	—	2	1	no	—
336	C₄⋊Dic₇₃	—	2	1	no	—
337	C₄⋊Dic₇₃	—	2	1	no	—
338	C₄⋊Dic₇₃	—	2	2	no	—
339	C₄⋊Dic₇₃	—	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	C₂×D₄	1	1	yes	characteristic
347	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
348	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
349	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
350	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
351	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
352	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
353	#11924007	—	2	2	no	—
354	#11924007	—	2	2	no	—
355	#11924007	—	2	2	no	—
356	#11924007	—	2	2	no	—
357	#11924007	—	2	2	no	—
358	#11924007	—	2	2	no	—
359	#11924007	—	2	2	no	—
360	#11924007	—	2	2	no	—
361	#11924007	—	2	2	no	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
365	#11924007	—	2	2	no	—
366	#11924007	—	2	2	no	—
367	#11924007	—	2	2	no	—
368	#11924007	—	2	2	no	—
369	#11924007	—	2	2	no	—
370	#11924007	—	2	2	no	—
371	#11924007	C₂×D₄	1	2	yes	—
372	#11924007	C₂×D₄	1	2	yes	—
373	#11924007	C₂×D₄	1	2	yes	—
374	#11924007	C₂×D₄	1	2	yes	—
375	C₂²⋊Dic₇₃	—	2	2	no	—
376	C₂²⋊Dic₇₃	—	2	2	no	—
377	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
378	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
379	C₄×Dic₇₃	—	2	2	no	—
380	C₄×Dic₇₃	—	2	2	no	—
381	C₄×Dic₇₃	—	2	2	no	—
382	C₄×Dic₇₃	—	2	2	no	—
383	C₄×Dic₇₃	—	2	2	no	—
384	C₄×Dic₇₃	—	2	2	no	—
385	C₄×Dic₇₃	—	2	2	no	—
386	C₄×Dic₇₃	—	2	2	no	—
387	C₄×Dic₇₃	C₂⁴	1	2	yes	—
388	C₄×Dic₇₃	C₂⁴	1	2	yes	—
389	#41×C₇₃	—	2	2	no	—
390	#41×C₇₃	C₂×Q₈	1	4	yes	—
391	C₂×Q₈×C₇₃	—	2	1	no	—
392	C₂×Q₈×C₇₃	—	2	1	no	—
393	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
394	C₂×D₄×C₇₃	—	2	1	no	—
395	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
396	C₂²×C₄×C₇₃	—	2	1	no	—
397	C₂²×C₄×C₇₃	—	2	1	no	—
398	C₂²×C₄×C₇₃	—	2	1	no	—
399	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
400	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
401	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₇₃	—	2	2	no	—
403	C₂×C₈×C₇₃	—	2	2	no	—
404	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
406	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₇₃	—	2	1	no	—
409	C₄⋊C₄×C₇₃	—	2	1	no	—
410	C₄⋊C₄×C₇₃	—	2	1	no	—
411	C₄⋊C₄×C₇₃	—	2	1	no	—
412	C₄⋊C₄×C₇₃	—	2	1	no	—
413	C₄⋊C₄×C₇₃	—	2	1	no	—
414	C₄⋊C₄×C₇₃	—	2	1	no	—
415	C₄⋊C₄×C₇₃	—	2	1	no	—
416	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
418	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
419	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
422	C₂²⋊C₄×C₇₃	—	2	1	no	—
423	C₂²⋊C₄×C₇₃	—	2	1	no	—
424	C₂²⋊C₄×C₇₃	—	2	1	no	—
425	C₂²⋊C₄×C₇₃	—	2	1	no	—
426	C₂²⋊C₄×C₇₃	—	2	1	no	—
427	C₄²×C₇₃	—	2	1	no	—
428	C₄²×C₇₃	—	2	1	no	—
429	C₄²×C₇₃	—	2	1	no	—
430	C₄²×C₇₃	—	2	1	no	—
431	C₄²×C₇₃	—	2	1	no	—
432	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
433	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
434	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
435	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
436	C₂³×C₇₃	—	2	1	no	—
437	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
438	Q₈×C₇₃	—	2	1	no	—
439	Q₈×C₇₃	—	4	2	no	—
440	Q₈×C₇₃	—	8	1	no	—
441	Q₈×C₇₃	C₂²×Q₈	1	2	yes	—
442	D₄×C₇₃	—	2	4	no	—
443	D₄×C₇₃	—	2	1	no	—
444	D₄×C₇₃	C₂²×Q₈	1	2	yes	—
445	C₂×C₄×C₇₃	—	2	1	no	—
446	C₂×C₄×C₇₃	—	2	4	no	—
447	C₂×C₄×C₇₃	—	2	1	no	—
448	C₂×C₄×C₇₃	—	2	1	no	—
449	C₂×C₄×C₇₃	—	2	1	no	—
450	C₂×C₄×C₇₃	—	2	1	no	—
451	C₂×C₄×C₇₃	—	2	1	no	—
452	C₂×C₄×C₇₃	—	2	1	no	—
453	C₂×C₄×C₇₃	—	4	1	no	—
454	C₂×C₄×C₇₃	—	4	1	no	—
455	C₂×C₄×C₇₃	—	8	1	no	—
456	C₂×C₄×C₇₃	—	8	1	no	—
457	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
463	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
464	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
465	C₂×Dic₇₃	—	2	4	no	—
466	C₂×Dic₇₃	—	2	2	no	—
467	C₂×Dic₇₃	—	2	2	no	—
468	C₂×Dic₇₃	—	2	2	no	—
469	C₂×Dic₇₃	—	2	2	no	—
470	C₂×Dic₇₃	—	8	2	no	—
471	C₂×Dic₇₃	—	8	2	no	—
472	C₂×Dic₇₃	—	8	1	no	—
473	C₂×Dic₇₃	—	8	1	no	—
474	C₂×Dic₇₃	—	8	1	no	—
475	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
476	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
477	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
478	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
479	Dic₁₄₆	—	2	4	no	—
480	Dic₁₄₆	—	2	2	no	—
481	Dic₁₄₆	—	4	2	no	—
482	Dic₁₄₆	—	4	2	no	—
483	Dic₁₄₆	—	8	2	no	—
484	Dic₁₄₆	—	8	2	no	—
485	Dic₁₄₆	—	8	2	no	—
486	Dic₁₄₆	—	8	2	no	—
487	Dic₁₄₆	C₂²×Q₈	1	4	yes	—
488	C₈×C₇₃	—	2	1	no	—
489	C₈×C₇₃	—	2	1	no	—
490	C₈×C₇₃	—	2	1	no	—
491	C₈×C₇₃	—	2	1	no	—
492	#10596831	—	2	2	no	—
493	#10596831	C₂²×Q₈	1	4	yes	—
494	C₂²×C₇₃	—	2	1	no	—
495	C₂²×C₇₃	—	2	1	no	—
496	C₂²×C₇₃	—	2	2	no	—
497	C₂²×C₇₃	—	4	1	no	—
498	C₂²×C₇₃	—	4	1	no	—
499	C₂²×C₇₃	D₄×Q₈	1	2	yes	—
500	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
501	C₄×C₇₃	—	2	1	no	—
502	C₄×C₇₃	—	2	1	no	—
503	C₄×C₇₃	—	2	1	no	—
504	C₄×C₇₃	—	2	1	no	—
505	C₄×C₇₃	—	2	2	no	—
506	C₄×C₇₃	—	4	1	no	—
507	C₄×C₇₃	—	4	1	no	—
508	C₄×C₇₃	—	4	1	no	—
509	C₄×C₇₃	—	4	1	no	—
510	C₄×C₇₃	—	4	1	no	—
511	C₄×C₇₃	—	4	1	no	—
512	C₄×C₇₃	D₄×Q₈	1	2	yes	—
513	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
514	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
515	Dic₇₃	—	2	2	no	—
516	Dic₇₃	—	2	2	no	—
517	Dic₇₃	—	2	2	no	—
518	Dic₇₃	—	2	2	no	—
519	Dic₇₃	—	2	4	no	—
520	Dic₇₃	—	4	2	no	—
521	Dic₇₃	—	4	2	no	—
522	Dic₇₃	—	4	2	no	—
523	#61386	—	73	1	no	maximal, Sylow
524	C₂×C₇₃	—	2	2	no	—
525	C₂×C₇₃	—	4	2	no	—
526	C₂×C₇₃	C₂×D₄×Q₈	1	1	yes	characteristic
527	C₂×C₇₃	#3584	1	1	yes	characteristic
528	C₂×C₇₃	#3586	1	1	yes	characteristic
529	#3504	—	73	1	no	—
530	#3502	—	73	1	no	—
531	#3390	—	73	2	no	—
532	#3390	—	73	2	no	—
533	#3388	—	73	2	no	—
534	#3388	—	73	2	no	—
535	#3387	—	73	2	no	—
536	#3385	—	73	2	no	—
537	#3383	—	73	2	no	—
538	#3381	—	73	2	no	—
539	#3166	—	73	1	no	—
540	#3164	—	73	1	no	—
541	#3163	—	73	1	no	—
542	#3084	—	73	1	no	—
543	#3083	—	73	1	no	—
544	#3082	—	73	1	no	—
545	#3082	—	73	1	no	—
546	#3076	D₇₃	1	1	yes	characteristic
547	C₂×#479	—	73	1	no	—
548	#2962	—	73	1	no	—
549	#2947	—	73	1	no	—
550	#2947	—	73	1	no	—
551	C₄×#137	—	73	1	no	—
552	C₇₃	#61386	1	1	yes	characteristic, complemented, Sylow
553	C₂×#137	—	73	1	no	—
554	Q₈²	—	73	2	no	—
555	Q₈²	—	146	1	no	—
556	#557	—	73	2	no	—
557	#557	—	73	2	no	—
558	#557	—	73	2	no	—
559	#557	—	73	2	no	—
560	#557	—	73	2	no	—
561	#557	—	146	1	no	—
562	#557	—	146	1	no	—
563	#557	—	146	1	no	—
564	#554	—	73	2	no	—
565	#554	—	73	2	no	—
566	#554	—	146	2	no	—
567	#554	—	146	2	no	—
568	#544	—	73	1	no	—
569	#544	—	73	1	no	—
570	#544	—	73	1	no	—
571	#544	—	73	1	no	—
572	#544	—	146	1	no	—
573	#544	—	146	1	no	—
574	#544	—	146	2	no	—
575	#533	—	73	1	no	—
576	#533	—	146	1	no	—
577	#533	—	146	2	no	—
578	#533	C₂×D₇₃	1	1	yes	characteristic
579	C₂×#125	—	73	1	no	—
580	C₂×#125	—	146	1	no	—
581	#520	—	73	1	no	—
582	#520	—	73	1	no	—
583	#519	—	73	1	no	—
584	#519	—	73	1	no	—
585	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
586	C₂×C₄×Q₈	—	73	1	no	—
587	#501	—	73	2	no	—
588	#501	—	73	2	no	—
589	#501	—	73	2	no	—
590	#501	—	73	2	no	—
591	#501	—	73	2	no	—
592	#501	—	73	2	no	—
593	#500	—	73	2	no	—
594	#499	—	73	2	no	—
595	#499	—	73	2	no	—
596	#499	—	73	2	no	—
597	#499	—	73	2	no	—
598	#498	—	73	2	no	—
599	#479	—	73	2	no	—
600	#479	—	73	2	no	—
601	#479	—	73	2	no	—
602	#479	—	73	2	no	—
603	#479	—	73	2	no	—
604	#479	—	73	2	no	—
605	#479	—	73	2	no	—
606	#479	—	73	2	no	—
607	#479	—	73	2	no	—
608	#479	—	73	2	no	—
609	#479	C₂×D₇₃	1	1	yes	characteristic
610	#479	C₂×D₇₃	1	1	yes	characteristic
611	#478	—	73	2	no	—
612	#478	—	73	2	no	—
613	#478	C₂×D₇₃	1	1	yes	characteristic
614	#478	C₂×D₇₃	1	1	yes	characteristic
615	#477	—	73	2	no	—
616	#477	—	73	2	no	—
617	#477	—	73	2	no	—
618	#477	C₂×D₇₃	1	1	yes	characteristic
619	#476	—	73	2	no	—
620	#476	C₂×D₇₃	1	1	yes	characteristic
621	#475	—	73	2	no	—
622	#475	—	73	2	no	—
623	#475	—	73	2	no	—
624	#475	C₂×D₇₃	1	1	yes	characteristic
625	#474	—	73	2	no	—
626	#474	C₂×D₇₃	1	1	yes	characteristic
627	#446	—	73	2	no	—
628	#446	—	73	2	no	—
629	#446	—	73	2	no	—
630	C₈×Q₈	—	73	2	no	—
631	#441	—	73	2	no	—
632	#441	—	73	2	no	—
633	#441	—	73	2	no	—
634	#440	—	73	2	no	—
635	#440	—	73	2	no	—
636	#440	—	73	2	no	—
637	C₄×Q₁₆	—	73	2	no	—
638	C₄×Q₁₆	—	73	2	no	—
639	C₄×Q₁₆	—	73	2	no	—
640	C₄×SD₁₆	—	73	2	no	—
641	C₄×SD₁₆	—	73	2	no	—
642	C₄×SD₁₆	—	73	2	no	—
643	#428	—	73	1	no	—
644	#428	—	73	1	no	—
645	#428	—	73	1	no	—
646	#428	—	73	1	no	—
647	#428	—	73	1	no	—
648	#427	C₂×D₇₃	1	1	yes	characteristic
649	#427	C₂×D₇₃	1	1	yes	characteristic
650	C₂×#107	—	73	1	no	—
651	C₂×#106	—	73	1	no	—
652	#424	—	73	1	no	—
653	#424	—	73	1	no	—
654	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
655	#419	—	73	1	no	—
656	#417	—	73	1	no	—
657	#416	C₂×D₇₃	1	1	yes	characteristic
658	#416	C₂×D₇₃	1	1	yes	characteristic
659	C₂×#103	—	73	1	no	—
660	C₂×#103	—	73	1	no	—
661	#405	—	73	1	no	—
662	#405	—	73	1	no	—
663	C₄×M₁₆	—	73	1	no	—
664	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
665	C₂²×Q₈	—	73	1	no	—
666	#137	—	73	8	no	—
667	C₂×Q₁₆	—	73	2	no	—
668	C₂×SD₁₆	—	73	2	no	—
669	C₂×M₁₆	—	73	1	no	—
670	C₂×M₁₆	—	73	1	no	—
671	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
672	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
673	C₄⋊Q₈	—	73	2	no	—
674	C₄⋊Q₈	—	73	2	no	—
675	C₄⋊Q₈	—	73	2	no	—
676	C₄⋊Q₈	—	73	2	no	—
677	C₄⋊Q₈	—	73	1	no	—
678	C₄⋊Q₈	—	73	1	no	—
679	C₄⋊Q₈	—	146	1	no	—
680	C₄⋊Q₈	—	146	1	no	—
681	C₄⋊Q₈	—	146	1	no	—
682	C₄⋊Q₈	—	146	1	no	—
683	C₄⋊Q₈	—	146	2	no	—
684	C₄⋊Q₈	—	146	2	no	—
685	C₄⋊Q₈	—	146	2	no	—
686	C₄⋊Q₈	—	146	2	no	—
687	C₄⋊Q₈	—	146	2	no	—
688	C₄⋊Q₈	—	146	2	no	—
689	C₄⋊Q₈	—	146	2	no	—
690	C₄⋊Q₈	—	146	2	no	—
691	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
692	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
693	#125	—	73	2	no	—
694	#125	—	73	2	no	—
695	#125	—	73	2	no	—
696	#125	—	73	2	no	—
697	#125	—	73	1	no	—
698	#125	—	73	1	no	—
699	#125	—	73	2	no	—
700	#125	—	73	2	no	—
701	#125	—	146	1	no	—
702	#125	—	146	1	no	—
703	#125	—	146	2	no	—
704	#125	—	146	2	no	—
705	#125	—	146	1	no	—
706	#125	—	146	1	no	—
707	#125	—	146	2	no	—
708	#125	—	146	2	no	—
709	#125	—	146	2	no	—
710	#125	—	146	2	no	—
711	#125	—	146	2	no	—
712	#125	—	146	2	no	—
713	#125	—	146	2	no	—
714	#125	—	146	2	no	—
715	#125	—	146	1	no	—
716	#125	—	146	1	no	—
717	#125	C₂²×D₇₃	1	1	yes	characteristic
718	#125	C₂²×D₇₃	1	1	yes	characteristic
719	C₂²⋊Q₈	—	2	1	no	—
720	C₂²⋊Q₈	—	2	1	no	—
721	C₂²⋊Q₈	—	73	2	no	—
722	C₂²⋊Q₈	—	73	2	no	—
723	C₂²⋊Q₈	—	146	2	no	—
724	C₂²⋊Q₈	—	146	2	no	—
725	C₂²⋊Q₈	—	146	2	no	—
726	C₂²⋊Q₈	—	146	2	no	—
727	C₂²⋊Q₈	—	146	2	no	—
728	C₂²⋊Q₈	—	146	2	no	—
729	C₂²⋊Q₈	—	146	2	no	—
730	C₂²⋊Q₈	—	146	2	no	—
731	C₂²⋊Q₈	—	146	2	no	—
732	C₂²⋊Q₈	—	146	2	no	—
733	C₄×Q₈	—	2	1	no	—
734	C₄×Q₈	—	2	1	no	—
735	C₄×Q₈	—	73	2	no	—
736	C₄×Q₈	—	73	2	no	—
737	C₄×Q₈	—	73	2	no	—
738	C₄×Q₈	—	73	2	no	—
739	C₄×Q₈	—	73	2	no	—
740	C₄×Q₈	—	73	2	no	—
741	C₄×Q₈	—	73	2	no	—
742	C₄×Q₈	—	73	2	no	—
743	C₄×Q₈	—	73	2	no	—
744	C₄×Q₈	—	73	2	no	—
745	C₄×Q₈	—	146	1	no	—
746	C₄×Q₈	—	146	1	no	—
747	C₄×Q₈	—	146	1	no	—
748	C₄×Q₈	—	146	1	no	—
749	C₄×Q₈	—	146	2	no	—
750	C₄×Q₈	—	146	2	no	—
751	C₄×Q₈	—	146	2	no	—
752	C₄×Q₈	—	146	2	no	—
753	C₄×Q₈	—	146	2	no	—
754	C₄×Q₈	—	146	2	no	—
755	C₄×Q₈	—	146	1	no	—
756	C₄×Q₈	—	146	1	no	—
757	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
758	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	—	2	1	no	—
761	C₄×D₄	—	73	2	no	—
762	C₄×D₄	—	73	2	no	—
763	C₄×D₄	—	146	2	no	—
764	C₄×D₄	—	146	2	no	—
765	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
766	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
767	#117	—	2	1	no	—
768	#117	—	73	1	no	—
769	#117	—	73	1	no	—
770	#117	—	146	2	no	—
771	#117	—	146	2	no	—
772	#117	—	146	1	no	—
773	#117	—	146	1	no	—
774	#117	C₂²×D₇₃	1	1	yes	characteristic
775	#117	C₂²×D₇₃	1	1	yes	characteristic
776	#117	C₂²×D₇₃	1	1	yes	characteristic
777	C₂×C₄⋊C₄	—	73	1	no	—
778	C₂×C₄⋊C₄	—	73	1	no	—
779	C₂×C₄⋊C₄	—	73	1	no	—
780	C₂×C₄⋊C₄	—	146	1	no	—
781	C₂×C₄⋊C₄	—	146	1	no	—
782	C₂×C₄⋊C₄	—	146	2	no	—
783	C₂×C₄⋊C₄	—	146	2	no	—
784	C₂×C₄⋊C₄	—	146	1	no	—
785	C₂×C₄⋊C₄	—	146	1	no	—
786	C₂×C₄⋊C₄	—	146	1	no	—
787	C₂×C₄²	—	2	1	no	—
788	C₂×C₄²	—	146	1	no	—
789	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
790	#107	—	73	2	no	—
791	#107	—	73	2	no	—
792	#107	—	73	2	no	—
793	#107	—	73	2	no	—
794	#107	—	73	2	no	—
795	#107	—	73	2	no	—
796	#107	—	73	2	no	—
797	#107	C₂²×D₇₃	1	1	yes	characteristic
798	#107	C₂²×D₇₃	1	1	yes	characteristic
799	#107	C₂²×D₇₃	1	1	yes	characteristic
800	#107	C₂²×D₇₃	1	1	yes	characteristic
801	#106	—	73	2	no	—
802	#106	—	73	2	no	—
803	#106	—	73	2	no	—
804	#106	—	73	2	no	—
805	#106	—	73	2	no	—
806	#106	—	73	2	no	—
807	#106	—	73	2	no	—
808	#106	C₂²×D₇₃	1	1	yes	characteristic
809	#106	C₂²×D₇₃	1	1	yes	characteristic
810	#106	C₂²×D₇₃	1	1	yes	characteristic
811	#106	C₂²×D₇₃	1	1	yes	characteristic
812	C₄⋊C₈	—	73	2	no	—
813	C₄⋊C₈	—	73	2	no	—
814	C₄⋊C₈	—	73	2	no	—
815	C₄⋊C₈	—	73	2	no	—
816	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
817	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
820	#103	—	73	2	no	—
821	#103	—	73	2	no	—
822	#103	—	73	2	no	—
823	#103	—	73	2	no	—
824	#103	—	73	2	no	—
825	#103	—	73	2	no	—
826	#103	—	73	2	no	—
827	#103	C₂²×D₇₃	1	1	yes	characteristic
828	#103	C₂²×D₇₃	1	1	yes	characteristic
829	#103	C₂²×D₇₃	1	1	yes	characteristic
830	#103	C₂²×D₇₃	1	1	yes	characteristic
831	#102	—	73	2	no	—
832	#102	C₂²×D₇₃	1	1	yes	characteristic
833	#102	C₂²×D₇₃	1	1	yes	characteristic
834	#102	C₂²×D₇₃	1	1	yes	characteristic
835	#102	C₂²×D₇₃	1	1	yes	characteristic
836	#97	—	73	2	no	—
837	#97	—	73	2	no	—
838	#97	—	73	2	no	—
839	C₄×C₈	—	73	2	no	—
840	C₄×C₈	—	73	2	no	—
841	C₄×C₈	—	73	2	no	—
842	#41	—	2	2	no	—
843	#41	Q₈×D₇₃	1	4	yes	—
844	C₂×Q₈	—	2	1	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	73	2	no	—
847	C₂×Q₈	—	73	2	no	—
848	C₂×Q₈	—	73	4	no	—
849	C₂×Q₈	—	73	2	no	—
850	C₂×Q₈	—	146	2	no	—
851	C₂×Q₈	—	146	2	no	—
852	C₂×Q₈	—	146	2	no	—
853	C₂×Q₈	—	146	2	no	—
854	C₂×Q₈	—	146	1	no	—
855	C₂×Q₈	—	146	2	no	—
856	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
857	C₂×D₄	—	2	1	no	—
858	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
859	C₂²×C₄	—	2	1	no	—
860	C₂²×C₄	—	2	1	no	—
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	146	2	no	—
863	C₂²×C₄	—	146	2	no	—
864	C₂²×C₄	—	146	1	no	—
865	C₂²×C₄	—	146	1	no	—
866	C₂²×C₄	—	146	1	no	—
867	C₂²×C₄	—	146	1	no	—
868	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
869	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
870	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
871	Q₁₆	—	73	8	no	—
872	SD₁₆	—	73	8	no	—
873	M₁₆	—	73	4	no	—
874	M₁₆	—	146	2	no	—
875	C₂×C₈	—	2	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	—	73	2	no	—
878	C₂×C₈	—	73	2	no	—
879	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
880	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
881	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
882	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	1	no	—
885	C₄⋊C₄	—	2	1	no	—
886	C₄⋊C₄	—	2	1	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	1	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	1	no	—
891	C₄⋊C₄	—	73	2	no	—
892	C₄⋊C₄	—	73	2	no	—
893	C₄⋊C₄	—	73	2	no	—
894	C₄⋊C₄	—	73	2	no	—
895	C₄⋊C₄	—	73	1	no	—
896	C₄⋊C₄	—	73	1	no	—
897	C₄⋊C₄	—	73	1	no	—
898	C₄⋊C₄	—	73	1	no	—
899	C₄⋊C₄	—	73	2	no	—
900	C₄⋊C₄	—	73	2	no	—
901	C₄⋊C₄	—	73	2	no	—
902	C₄⋊C₄	—	73	2	no	—
903	C₄⋊C₄	—	73	2	no	—
904	C₄⋊C₄	—	146	2	no	—
905	C₄⋊C₄	—	146	2	no	—
906	C₄⋊C₄	—	146	2	no	—
907	C₄⋊C₄	—	146	2	no	—
908	C₄⋊C₄	—	146	2	no	—
909	C₄⋊C₄	—	146	2	no	—
910	C₄⋊C₄	—	146	2	no	—
911	C₄⋊C₄	—	146	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	—	146	2	no	—
925	C₄⋊C₄	—	146	2	no	—
926	C₄⋊C₄	—	146	2	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	1	no	—
929	C₄⋊C₄	—	146	1	no	—
930	C₄⋊C₄	—	146	1	no	—
931	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
932	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
933	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
934	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
935	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
936	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	1	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	73	2	no	—
943	C₂²⋊C₄	—	73	2	no	—
944	C₂²⋊C₄	—	146	2	no	—
945	C₂²⋊C₄	—	146	2	no	—
946	C₄²	—	2	1	no	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	73	2	no	—
952	C₄²	—	73	2	no	—
953	C₄²	—	146	2	no	—
954	C₄²	—	146	2	no	—
955	C₄²	—	146	2	no	—
956	C₄²	—	146	2	no	—
957	C₄²	—	146	2	no	—
958	C₄²	—	146	2	no	—
959	C₄²	—	146	2	no	—
960	C₄²	—	146	2	no	—
961	C₄²	D₄×D₇₃	1	1	yes	characteristic
962	C₄²	D₄×D₇₃	1	1	yes	characteristic
963	C₄²	C₂³×D₇₃	1	1	yes	characteristic
964	C₄²	C₂³×D₇₃	1	1	yes	characteristic
965	C₂³	—	2	1	no	—
966	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
967	Q₈	—	2	1	no	—
968	Q₈	—	4	2	no	—
969	Q₈	—	8	1	no	—
970	Q₈	—	292	2	no	—
971	Q₈	—	292	2	no	—
972	Q₈	—	584	2	no	—
973	Q₈	—	584	2	no	—
974	Q₈	—	584	2	no	—
975	Q₈	—	584	2	no	—
976	Q₈	—	73	4	no	—
977	Q₈	—	146	2	no	—
978	Q₈	—	146	4	no	—
979	Q₈	C₂×Q₈×D₇₃	1	2	yes	—
980	D₄	—	2	4	no	—
981	D₄	—	2	1	no	—
982	D₄	C₂×Q₈×D₇₃	1	2	yes	—
983	C₂×C₄	—	2	1	no	—
984	C₂×C₄	—	2	4	no	—
985	C₂×C₄	—	2	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	4	1	no	—
992	C₂×C₄	—	4	1	no	—
993	C₂×C₄	—	8	1	no	—
994	C₂×C₄	—	8	1	no	—
995	C₂×C₄	—	584	1	no	—
996	C₂×C₄	—	584	1	no	—
997	C₂×C₄	—	584	1	no	—
998	C₂×C₄	—	584	2	no	—
999	C₂×C₄	—	584	2	no	—
1000	C₂×C₄	—	73	2	no	—
1001	C₂×C₄	—	73	2	no	—
1002	C₂×C₄	—	73	2	no	—
1003	C₂×C₄	—	73	2	no	—
1004	C₂×C₄	—	146	2	no	—
1005	C₂×C₄	—	146	2	no	—
1006	C₂×C₄	—	146	2	no	—
1007	C₂×C₄	—	146	2	no	—
1008	C₂×C₄	—	146	4	no	—
1009	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1010	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1011	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1012	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1013	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1014	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
1015	C₂×C₄	#14556638	1	2	yes	—
1016	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1017	C₈	—	2	1	no	—
1018	C₈	—	2	1	no	—
1019	C₈	—	2	1	no	—
1020	C₈	—	2	1	no	—
1021	C₈	—	73	4	no	—
1022	C₈	—	146	2	no	—
1023	C₂²	—	2	1	no	—
1024	C₂²	—	2	1	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	4	1	no	—
1027	C₂²	—	4	1	no	—
1028	C₂²	#17989250	1	2	yes	—
1029	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1030	C₄	—	2	2	no	—
1031	C₄	—	2	1	no	—
1032	C₄	—	2	1	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	2	1	no	—
1035	C₄	—	4	1	no	—
1036	C₄	—	4	1	no	—
1037	C₄	—	4	1	no	—
1038	C₄	—	4	1	no	—
1039	C₄	—	4	1	no	—
1040	C₄	—	4	1	no	—
1041	C₄	—	292	2	no	—
1042	C₄	—	292	2	no	—
1043	C₄	—	292	2	no	—
1044	C₄	—	146	4	no	—
1045	C₄	—	146	2	no	—
1046	C₄	—	146	2	no	—
1047	C₄	—	146	2	no	—
1048	C₄	—	146	2	no	—
1049	C₄	#17989250	1	2	yes	—
1050	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
1051	C₄	C₂×#14556638	1	1	yes	characteristic
1052	C₂	—	2	2	no	—
1053	C₂	—	4	2	no	—
1054	C₂	C₂×#17989250	1	1	yes	characteristic
1055	C₂	#22624700	1	1	yes	characteristic
1056	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	C₂×#41×C₇₃	C₂³
hypercenter	#3076	D₇₃
hypocenter	C₇₃	#61386
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
2. #22623736	C₂	semidirect
3. #22622898	C₂	semidirect
4. #22622893	C₂	semidirect
5. #22622880	C₂	semidirect
6. #22622869	C₂	semidirect
7. #22622858	C₂	semidirect
8. #22622836	C₂	semidirect
9. #22622817	C₂	semidirect
10. #22622801	C₂	semidirect
11. #22620484	C₂	semidirect
12. #22620471	C₂	semidirect
13. #22620463	C₂	semidirect
16. #22619776	C₂	semidirect
17. #22619776	C₂	semidirect
18. C₂×#17988895	C₂	semidirect
19. #22618874	C₂	semidirect
136. #14556621	Q₈	semidirect
552. C₇₃	#61386	semidirect

Maximal subgroups

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

subgroup	index
#22623757	2
#22623736	2
#22622898	2
#22622893	2
#22622880	2
#22622869	2
#22622858	2
#22622836	2
#22622817	2
#22622801	2
#22620484	2
#22620471	2
#22620463	2
#22619791	2
#22619780	2
#22619776	2
C₂×#17988895	2
#22618874	2
#22618777	2
C₄×#14556621	2
C₇₃×#3076	2
#61386	73