Subgroups — #33968306

Order 18688.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623541	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623526	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622941	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622804	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622625	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622589	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622548	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622533	C₂	1	2	yes	maximal, complemented
9	#22622271	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622180	C₂	1	2	yes	maximal, complemented
11	#22622164	C₂	1	1	yes	maximal, characteristic, complemented
12	#22622133	C₂	1	2	yes	maximal, complemented
13	#22621556	C₂	1	2	yes	maximal, complemented
14	#22621552	C₂	1	1	yes	maximal, characteristic, complemented
15	#22620669	C₂	1	1	yes	maximal, characteristic, complemented
16	#22620663	C₂	1	2	yes	maximal, complemented
17	#22620082	C₂	1	1	yes	maximal, characteristic, complemented
18	#22620073	C₂	1	2	yes	maximal, complemented
19	#22620053	C₂	1	1	yes	maximal, characteristic, complemented
20	#22620046	C₂	1	2	yes	maximal, complemented
21	#22618949	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618736	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556618	C₂²	1	2	yes	—
25	#17989322	—	2	1	no	—
26	#17989322	C₂²	1	1	yes	characteristic
27	#17989322	C₂²	1	1	yes	characteristic, complemented
28	#17989316	C₂²	1	1	yes	characteristic, complemented
29	#17989310	—	2	1	no	—
30	#17989310	C₂²	1	1	yes	characteristic
31	#17989297	C₂²	1	1	yes	characteristic
32	#17989294	C₂²	1	1	yes	characteristic
33	#17989285	—	2	2	no	—
34	#17989285	C₂²	1	2	yes	complemented
35	#17989283	—	2	1	no	—
36	#17989281	C₂²	1	2	yes	—
37	#17989261	—	2	2	no	—
38	#17989259	C₂²	1	1	yes	characteristic
39	#17989248	C₂²	1	2	yes	complemented
40	#17989233	—	2	1	no	—
41	#17989225	C₂²	1	2	yes	—
42	D₄×D₂₉₂	C₂²	1	1	yes	characteristic
43	#17989137	—	2	1	no	—
44	#17989137	C₂²	1	1	yes	characteristic
45	#17989137	C₂²	1	1	yes	characteristic, complemented
46	#17989124	—	2	2	no	—
47	#17989124	C₂²	1	2	yes	—
48	#17989124	C₂²	1	2	yes	complemented
49	#17989121	—	2	1	no	—
50	#17989096	—	2	2	no	—
51	C₄×#11924029	C₂²	1	2	yes	complemented
52	C₄×#11924028	—	2	1	no	—
53	C₄×#11924028	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₂₉₂	—	2	1	no	—
55	C₄×D₄×D₇₃	C₂²	1	2	yes	—
56	#17988987	C₂²	1	2	yes	complemented
57	#17988985	C₂²	1	1	yes	characteristic, complemented
58	#17988972	C₂²	1	2	yes	complemented
59	#17988964	C₂²	1	1	yes	characteristic
60	#17988943	C₂²	1	2	yes	complemented
61	#17988943	C₂²	1	2	yes	complemented
62	#17988934	C₂²	1	1	yes	characteristic
63	#17988934	C₂²	1	1	yes	characteristic, complemented
64	#17988926	C₂²	1	2	yes	complemented
65	#17988916	C₂²	1	2	yes	complemented
66	#17988913	C₂²	1	2	yes	—
67	#17988911	C₂²	1	2	yes	complemented
68	#17988902	C₂²	1	2	yes	complemented
69	#17988900	C₂²	1	2	yes	complemented
70	#17988892	C₂²	1	2	yes	complemented
71	#17988890	C₂²	1	2	yes	complemented
72	#17988889	C₂²	1	2	yes	—
73	#17988886	C₂²	1	2	yes	complemented
74	#17988882	C₂²	1	1	yes	characteristic, complemented
75	#17988882	C₂²	1	1	yes	characteristic, complemented
76	#17988872	C₂²	1	1	yes	characteristic, complemented
77	#17988867	C₂²	1	1	yes	characteristic
78	#17988842	C₂²	1	2	yes	complemented
79	#17988841	C₂²	1	2	yes	—
80	#17988840	C₂²	1	2	yes	complemented
81	#17988840	C₂²	1	2	yes	complemented
82	#17988836	C₂²	1	2	yes	—
83	#17988836	C₂²	1	2	yes	complemented
84	#17988811	C₂²	1	2	yes	complemented
85	#17988805	C₂²	1	2	yes	complemented
86	#17988805	C₂²	1	2	yes	complemented
87	#17988804	C₂²	1	2	yes	—
88	#17988787	C₂²	1	1	yes	characteristic
89	#17988787	C₂²	1	1	yes	characteristic
90	#17988787	C₂²	1	1	yes	characteristic, complemented
91	#17988782	C₂²	1	1	yes	characteristic
92	#17988748	C₂²	1	2	yes	complemented
93	#17988736	C₂²	1	2	yes	—
94	#17988735	C₂²	1	2	yes	—
95	#17988732	C₂²	1	2	yes	—
96	#17988726	C₂²	1	2	yes	complemented
97	#17988722	C₂²	1	2	yes	—
98	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
100	#17988700	C₂²	1	2	yes	complemented
101	#17988700	C₂²	1	2	yes	complemented
102	#17988697	C₂²	1	2	yes	—
103	#17988685	C₂²	1	2	yes	complemented
104	#17988685	C₂²	1	2	yes	complemented
105	#17988685	C₂²	1	2	yes	complemented
106	SD₁₆×Dic₇₃	C₂²	1	2	yes	—
107	#17988672	C₂²	1	2	yes	complemented
108	#17988669	C₂²	1	2	yes	complemented
109	#17988667	C₂²	1	2	yes	—
110	#17988666	C₂²	1	1	yes	characteristic
111	#17988666	C₂²	1	1	yes	characteristic
112	#17988663	C₂²	1	2	yes	complemented
113	#17988663	C₂²	1	2	yes	complemented
114	#17988644	C₂²	1	1	yes	characteristic, complemented
115	#17988642	C₂²	1	2	yes	complemented
116	#17988628	C₂²	1	2	yes	complemented
117	#17988590	C₂²	1	2	yes	—
118	#17988587	C₂²	1	2	yes	complemented
119	#17988539	C₂²	1	2	yes	complemented
120	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#441×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#440×C₇₃	C₂²	1	1	yes	characteristic
126	#440×C₇₃	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
131	#428×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	#419×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#417×C₇₃	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924029	C₂³	1	2	yes	—
136	C₂×#11924028	—	2	1	no	—
137	C₂×#11924028	—	2	1	no	—
138	C₂×#11924028	D₄	1	1	yes	characteristic
139	C₂²×D₂₉₂	—	2	1	no	—
140	C₂×D₄×D₇₃	C₂³	1	2	yes	—
141	C₂²×C₄×D₇₃	—	2	2	no	—
142	#14556618	—	2	8	no	—
143	C₂×#11924015	C₂³	1	2	yes	—
144	C₂×#11924015	C₂³	1	2	yes	—
145	C₂×#11924015	C₂³	1	2	yes	—
146	C₂×D₅₈₄	C₂³	1	2	yes	—
147	C₂×D₅₈₄	C₂³	1	2	yes	—
148	C₂×#11924013	C₂³	1	2	yes	—
149	C₂×#11924011	C₂³	1	2	yes	—
150	C₂×#11924011	C₂³	1	2	yes	—
151	#14556591	—	2	1	no	—
152	#14556591	C₂³	1	1	yes	characteristic
153	#14556591	C₂³	1	1	yes	characteristic
154	#14556588	—	2	1	no	—
155	#14556588	C₂³	1	1	yes	characteristic
156	#14556588	C₂³	1	1	yes	characteristic
157	#14556586	—	2	2	no	—
158	#14556586	—	2	2	no	—
159	#14556586	—	2	2	no	—
160	#14556586	—	2	2	no	—
161	#14556585	—	2	2	no	—
162	#14556583	—	2	1	no	—
163	#14556582	—	2	2	no	—
164	#14556582	C₂³	1	2	yes	—
165	#14556582	C₂³	1	2	yes	—
166	#14556580	—	2	2	no	—
167	#14556580	C₂³	1	2	yes	—
168	#14556580	C₂³	1	2	yes	—
169	#14556579	—	2	1	no	—
170	#14556579	—	2	1	no	—
171	#14556579	—	2	1	no	—
172	#14556579	—	2	1	no	—
173	#14556579	—	2	1	no	—
174	#14556576	—	2	2	no	—
175	#14556576	—	2	2	no	—
176	#14556576	—	2	2	no	—
177	#14556576	—	2	2	no	—
178	#14556576	—	2	2	no	—
179	#14556574	—	2	2	no	—
180	#14556573	—	2	2	no	—
181	#14556570	—	2	1	no	—
182	#14556569	—	2	2	no	—
183	#14556568	—	2	2	no	—
184	#14556567	—	2	2	no	—
185	#14556567	C₂³	1	2	yes	—
186	#14556567	C₂³	1	2	yes	—
187	#14556566	—	2	2	no	—
188	#14556566	C₂³	1	2	yes	—
189	#14556566	C₂³	1	2	yes	—
190	#14556565	—	2	2	no	—
191	#14556565	—	2	2	no	—
192	#14556565	—	2	1	no	—
193	#14556565	—	2	1	no	—
194	#14556565	—	2	1	no	—
195	#14556565	C₂³	1	2	yes	—
196	#14556565	C₂³	1	2	yes	—
197	#14556564	—	2	2	no	—
198	#14556563	—	2	2	no	—
199	#14556561	—	2	2	no	—
200	#14556559	—	2	2	no	—
201	Q₈×Dic₇₃	C₂³	1	2	yes	—
202	C₄×Dic₁₄₆	—	2	1	no	—
203	C₄×Dic₁₄₆	—	2	1	no	—
204	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
205	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
206	C₄×D₂₉₂	—	2	1	no	—
207	C₄×D₂₉₂	—	2	2	no	—
208	C₄×D₂₉₂	—	2	2	no	—
209	C₄×D₂₉₂	—	2	2	no	—
210	C₄×D₂₉₂	—	2	1	no	—
211	C₄×D₂₉₂	—	2	1	no	—
212	C₄×D₂₉₂	—	2	1	no	—
213	C₄×D₂₉₂	—	2	2	no	—
214	C₄×D₂₉₂	—	2	1	no	—
215	C₄×D₂₉₂	—	2	1	no	—
216	C₄×D₂₉₂	D₄	1	1	yes	characteristic
217	C₄×D₂₉₂	C₂³	1	2	yes	—
218	C₄×D₂₉₂	C₂³	1	2	yes	—
219	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
220	D₄×Dic₇₃	C₂³	1	2	yes	—
221	#14556553	—	2	2	no	—
222	#14556553	C₂³	1	2	yes	—
223	#14556553	C₂³	1	2	yes	—
224	C₄×C₂²⋊D₇₃	—	2	2	no	—
225	C₄×C₂²⋊D₇₃	—	2	2	no	—
226	C₄×C₂²⋊D₇₃	—	2	2	no	—
227	C₄×C₂²⋊D₇₃	D₄	1	2	yes	—
228	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
229	#14556551	—	2	2	no	—
230	#14556550	D₄	1	1	yes	characteristic
231	#14556549	—	2	2	no	—
232	#14556549	C₂³	1	2	yes	—
233	#14556548	—	2	2	no	—
234	#14556548	—	2	2	no	—
235	#14556548	D₄	1	2	yes	—
236	C₂×C₄⋊Dic₇₃	—	2	1	no	—
237	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
238	C₂×#11924005	—	2	2	no	—
239	C₂²⋊C₄×D₇₃	—	2	2	no	—
240	C₄²×D₇₃	—	2	2	no	—
241	C₄²×D₇₃	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	C₄⋊#10596831	C₂³	1	1	yes	characteristic
249	C₄⋊#10596831	C₂³	1	1	yes	characteristic
250	#14556520	C₂³	1	2	yes	—
251	#14556520	C₂³	1	2	yes	—
252	#14556515	C₂³	1	2	yes	—
253	#14556515	C₂³	1	2	yes	—
254	#14556515	C₂³	1	2	yes	—
255	#14556513	C₂³	1	2	yes	—
256	#14556513	C₂³	1	2	yes	—
257	#14556513	C₂³	1	2	yes	—
258	#14556513	C₂³	1	2	yes	—
259	#14556512	C₂³	1	2	yes	—
260	#14556511	C₂³	1	2	yes	—
261	#14556511	C₂³	1	2	yes	—
262	#14556511	C₂³	1	2	yes	—
263	#14556511	C₂³	1	2	yes	—
264	C₂²⋊#10596831	C₂³	1	2	yes	—
265	#14556503	C₂³	1	2	yes	—
266	#14556503	C₂³	1	2	yes	—
267	#14556502	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×Q₈×C₇₃	C₂³	1	1	yes	characteristic
272	#137×C₇₃	—	2	4	no	—
273	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
277	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
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×Q₈×C₇₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₇₃	—	2	1	no	—
288	C₄×D₄×C₇₃	—	2	1	no	—
289	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
291	#117×C₇₃	—	2	1	no	—
292	#117×C₇₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₇₃	—	2	1	no	—
296	C₂×C₄²×C₇₃	—	2	1	no	—
297	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
298	#107×C₇₃	C₂³	1	1	yes	characteristic
299	#107×C₇₃	C₂³	1	1	yes	characteristic
300	#106×C₇₃	C₂³	1	1	yes	characteristic
301	#106×C₇₃	C₂³	1	1	yes	characteristic
302	#103×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#103×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	#102×C₇₃	C₂³	1	1	yes	characteristic
309	#102×C₇₃	C₂³	1	1	yes	characteristic
310	#97×C₇₃	C₂³	1	1	yes	characteristic
311	#97×C₇₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₂³×D₇₃	—	2	2	no	—
315	#11924029	—	2	4	no	—
316	#11924029	—	4	2	no	—
317	#11924028	—	4	2	no	—
318	#11924028	—	4	4	no	—
319	#11924028	—	8	2	no	—
320	C₂×Dic₁₄₆	—	2	1	no	—
321	C₂×Dic₁₄₆	—	2	1	no	—
322	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
323	C₂×D₂₉₂	—	2	2	no	—
324	C₂×D₂₉₂	—	2	2	no	—
325	C₂×D₂₉₂	—	2	1	no	—
326	C₂×D₂₉₂	—	2	1	no	—
327	C₂×D₂₉₂	—	2	2	no	—
328	C₂×D₂₉₂	—	2	1	no	—
329	C₂×D₂₉₂	—	2	1	no	—
330	C₂×D₂₉₂	—	4	4	no	—
331	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
332	C₂×D₂₉₂	C₂⁴	1	2	yes	—
333	C₂×D₂₉₂	C₂⁴	1	2	yes	—
334	C₂×C₂²⋊D₇₃	—	2	2	no	—
335	C₂×C₂²⋊D₇₃	—	2	2	no	—
336	C₂×C₂²⋊D₇₃	—	2	2	no	—
337	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
338	D₄×D₇₃	—	2	4	no	—
339	D₄×D₇₃	—	4	2	no	—
340	C₂²×Dic₇₃	—	2	2	no	—
341	C₂×C₄×D₇₃	—	2	2	no	—
342	C₂×C₄×D₇₃	—	2	2	no	—
343	C₂×C₄×D₇₃	—	2	2	no	—
344	C₂×C₄×D₇₃	—	2	2	no	—
345	C₂×C₄×D₇₃	—	2	2	no	—
346	C₂×C₄×D₇₃	—	2	2	no	—
347	C₂×C₄×D₇₃	—	8	4	no	—
348	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
349	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
350	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
351	#11924015	—	2	4	no	—
352	#11924015	—	4	2	no	—
353	#11924015	—	4	2	no	—
354	D₅₈₄	—	2	4	no	—
355	D₅₈₄	—	4	2	no	—
356	#11924013	—	2	4	no	—
357	#11924011	—	2	4	no	—
358	#11924011	—	4	2	no	—
359	C₂×#10596831	C₂⁴	1	2	yes	—
360	C₂×#10596831	C₂⁴	1	2	yes	—
361	C₄⋊Dic₇₃	—	2	1	no	—
362	C₄⋊Dic₇₃	—	2	1	no	—
363	C₄⋊Dic₇₃	—	2	2	no	—
364	C₄⋊Dic₇₃	—	2	2	no	—
365	C₄⋊Dic₇₃	—	2	2	no	—
366	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
367	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
368	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
369	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
370	#11924007	—	2	2	no	—
371	#11924007	—	2	2	no	—
372	#11924007	—	2	2	no	—
373	#11924007	—	2	2	no	—
374	#11924007	—	2	2	no	—
375	#11924007	C₂×D₄	1	2	yes	—
376	#11924007	C₂×D₄	1	2	yes	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
379	#11924005	—	2	2	no	—
380	#11924005	—	2	2	no	—
381	#11924005	—	2	2	no	—
382	#11924005	—	2	2	no	—
383	#11924005	—	2	2	no	—
384	#11924005	—	2	2	no	—
385	#11924005	—	2	2	no	—
386	#11924005	—	2	2	no	—
387	#11924005	—	2	2	no	—
388	#11924005	—	2	2	no	—
389	#11924005	—	2	2	no	—
390	#11924005	—	2	2	no	—
391	#11924005	—	2	2	no	—
392	#11924005	—	2	2	no	—
393	#11924005	—	2	2	no	—
394	#11924005	C₂×D₄	1	2	yes	—
395	#11924005	C₂×D₄	1	2	yes	—
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	—	2	2	no	—
398	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
399	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
400	C₄×Dic₇₃	C₂⁴	1	2	yes	—
401	#41×C₇₃	—	2	2	no	—
402	#41×C₇₃	—	4	1	no	—
403	C₂×Q₈×C₇₃	—	2	1	no	—
404	C₂×Q₈×C₇₃	—	2	2	no	—
405	C₂×Q₈×C₇₃	—	4	1	no	—
406	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
408	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
409	C₂×D₄×C₇₃	—	2	1	no	—
410	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₇₃	—	2	1	no	—
412	C₂²×C₄×C₇₃	—	2	1	no	—
413	C₂²×C₄×C₇₃	—	2	1	no	—
414	C₂²×C₄×C₇₃	—	2	1	no	—
415	C₂²×C₄×C₇₃	—	2	1	no	—
416	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
419	Q₁₆×C₇₃	—	2	2	no	—
420	Q₁₆×C₇₃	—	2	2	no	—
421	SD₁₆×C₇₃	—	2	2	no	—
422	SD₁₆×C₇₃	#41	1	4	yes	complemented
423	M₁₆×C₇₃	—	2	2	no	—
424	M₁₆×C₇₃	—	4	1	no	—
425	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
429	C₄⋊C₄×C₇₃	—	2	1	no	—
430	C₄⋊C₄×C₇₃	—	2	1	no	—
431	C₄⋊C₄×C₇₃	—	2	1	no	—
432	C₄⋊C₄×C₇₃	—	2	1	no	—
433	C₄⋊C₄×C₇₃	—	2	1	no	—
434	C₄⋊C₄×C₇₃	—	2	1	no	—
435	C₄⋊C₄×C₇₃	—	2	1	no	—
436	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
437	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₇₃	—	2	1	no	—
441	C₂²⋊C₄×C₇₃	—	2	1	no	—
442	C₂²⋊C₄×C₇₃	—	2	1	no	—
443	C₄²×C₇₃	—	2	1	no	—
444	C₄²×C₇₃	—	2	1	no	—
445	C₄²×C₇₃	—	2	1	no	—
446	C₄²×C₇₃	—	2	1	no	—
447	C₄²×C₇₃	—	2	1	no	—
448	C₄²×C₇₃	—	2	1	no	—
449	C₄²×C₇₃	—	2	1	no	—
450	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
451	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
452	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
453	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
454	C₂³×C₇₃	—	2	1	no	—
455	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
456	C₂²×D₇₃	—	2	2	no	—
457	C₂²×D₇₃	—	2	2	no	—
458	C₂²×D₇₃	—	4	4	no	—
459	C₂²×D₇₃	—	4	4	no	—
460	C₂²×D₇₃	—	8	2	no	—
461	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
462	Q₈×C₇₃	—	2	1	no	—
463	Q₈×C₇₃	—	2	1	no	—
464	Q₈×C₇₃	—	2	1	no	—
465	Q₈×C₇₃	—	2	1	no	—
466	Q₈×C₇₃	—	2	1	no	—
467	Q₈×C₇₃	—	4	2	no	—
468	Q₈×C₇₃	C₂×#41	1	2	yes	—
469	D₄×C₇₃	—	2	1	no	—
470	D₄×C₇₃	—	4	2	no	—
471	D₄×C₇₃	C₂×#41	1	2	yes	—
472	C₂×C₄×C₇₃	—	2	1	no	—
473	C₂×C₄×C₇₃	—	2	2	no	—
474	C₂×C₄×C₇₃	—	2	1	no	—
475	C₂×C₄×C₇₃	—	2	1	no	—
476	C₂×C₄×C₇₃	—	2	1	no	—
477	C₂×C₄×C₇₃	—	2	1	no	—
478	C₂×C₄×C₇₃	—	2	1	no	—
479	C₂×C₄×C₇₃	—	2	1	no	—
480	C₂×C₄×C₇₃	—	2	1	no	—
481	C₂×C₄×C₇₃	—	2	1	no	—
482	C₂×C₄×C₇₃	—	4	1	no	—
483	C₂×C₄×C₇₃	—	4	2	no	—
484	C₂×C₄×C₇₃	—	4	2	no	—
485	C₂×C₄×C₇₃	—	4	2	no	—
486	C₂×C₄×C₇₃	—	4	2	no	—
487	C₂×C₄×C₇₃	—	8	1	no	—
488	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₇₃	—	4	2	no	—
495	C₂²⋊D₇₃	—	4	4	no	—
496	C₂²⋊D₇₃	—	4	4	no	—
497	C₂²⋊D₇₃	—	8	2	no	—
498	C₂×Dic₇₃	—	2	2	no	—
499	C₂×Dic₇₃	—	2	2	no	—
500	C₂×Dic₇₃	—	8	2	no	—
501	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
502	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
503	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
504	D₂₉₂	—	2	2	no	—
505	D₂₉₂	—	2	2	no	—
506	D₂₉₂	—	2	2	no	—
507	D₂₉₂	—	2	2	no	—
508	D₂₉₂	—	2	2	no	—
509	D₂₉₂	—	4	4	no	—
510	D₂₉₂	—	4	4	no	—
511	D₂₉₂	—	4	2	no	—
512	D₂₉₂	—	4	2	no	—
513	D₂₉₂	—	8	1	no	—
514	D₂₉₂	—	8	1	no	—
515	D₂₉₂	—	8	2	no	—
516	C₄×D₇₃	—	2	2	no	—
517	C₄×D₇₃	—	2	2	no	—
518	C₄×D₇₃	—	4	2	no	—
519	C₄×D₇₃	—	4	2	no	—
520	C₄×D₇₃	—	4	4	no	—
521	C₄×D₇₃	—	4	4	no	—
522	C₄×D₇₃	—	4	4	no	—
523	C₄×D₇₃	—	8	2	no	—
524	C₄×D₇₃	—	8	2	no	—
525	C₄×D₇₃	—	8	2	no	—
526	Dic₁₄₆	—	2	2	no	—
527	Dic₁₄₆	—	4	2	no	—
528	Dic₁₄₆	—	8	1	no	—
529	C₈×C₇₃	—	2	1	no	—
530	C₈×C₇₃	—	2	1	no	—
531	C₈×C₇₃	—	2	1	no	—
532	C₈×C₇₃	C₂×#41	1	2	yes	—
533	#10596831	—	2	2	no	—
534	#10596831	—	2	2	no	—
535	C₂²×C₇₃	—	2	1	no	—
536	C₂²×C₇₃	—	2	2	no	—
537	C₂²×C₇₃	—	2	1	no	—
538	C₂²×C₇₃	—	2	1	no	—
539	C₂²×C₇₃	—	4	1	no	—
540	C₂²×C₇₃	—	4	1	no	—
541	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
542	C₂×D₇₃	—	2	2	no	—
543	C₂×D₇₃	—	2	2	no	—
544	C₂×D₇₃	—	2	2	no	—
545	C₂×D₇₃	—	4	2	no	—
546	C₂×D₇₃	—	4	2	no	—
547	C₂×D₇₃	—	4	2	no	—
548	C₂×D₇₃	—	4	2	no	—
549	C₂×D₇₃	—	4	2	no	—
550	C₂×D₇₃	—	4	2	no	—
551	C₂×D₇₃	—	8	8	no	—
552	C₄×C₇₃	—	2	1	no	—
553	C₄×C₇₃	—	2	1	no	—
554	C₄×C₇₃	—	2	2	no	—
555	C₄×C₇₃	—	2	1	no	—
556	C₄×C₇₃	—	2	1	no	—
557	C₄×C₇₃	—	4	1	no	—
558	C₄×C₇₃	—	4	1	no	—
559	C₄×C₇₃	—	4	1	no	—
560	C₄×C₇₃	—	4	1	no	—
561	C₄×C₇₃	—	4	1	no	—
562	C₄×C₇₃	—	4	1	no	—
563	C₄×C₇₃	#575	1	2	yes	—
564	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
565	C₄×C₇₃	#585	1	1	yes	characteristic
566	Dic₇₃	—	2	2	no	—
567	Dic₇₃	—	2	2	no	—
568	Dic₇₃	—	2	2	no	—
569	Dic₇₃	—	4	2	no	—
570	Dic₇₃	—	4	2	no	—
571	#61468	—	73	1	no	maximal, Sylow
572	C₂×C₇₃	—	4	2	no	—
573	C₂×C₇₃	—	4	1	no	—
574	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
575	C₂×C₇₃	C₂×#575	1	1	yes	characteristic
576	C₂×C₇₃	#3585	1	1	yes	characteristic
577	D₇₃	—	4	2	no	—
578	D₇₃	—	8	2	no	—
579	D₇₃	—	8	2	no	—
580	#3481	—	73	1	no	—
581	#3480	—	73	1	no	—
582	#3396	—	73	1	no	—
583	#3381	—	73	1	no	—
584	#3365	—	73	1	no	—
585	#3361	—	73	1	no	—
586	#3356	—	73	1	no	—
587	#3355	—	73	2	no	—
588	#3333	—	73	1	no	—
589	#3326	—	73	2	no	—
590	#3324	—	73	1	no	—
591	#3322	—	73	2	no	—
592	#3275	—	73	2	no	—
593	#3274	—	73	1	no	—
594	#3184	—	73	1	no	—
595	#3183	—	73	2	no	—
596	#3115	—	73	1	no	—
597	#3114	—	73	2	no	—
598	#3112	—	73	1	no	—
599	#3111	—	73	2	no	—
600	#2971	—	73	1	no	—
601	C₄×#137	D₇₃	1	1	yes	characteristic, complemented
602	C₄×AGL(1,ℤ/8)	—	73	2	no	—
603	C₇₃	#61468	1	1	yes	characteristic, complemented, Sylow
604	C₂×#137	C₂×D₇₃	1	1	yes	characteristic
605	C₂×AGL(1,ℤ/8)	—	73	2	no	—
606	#559	—	73	1	no	—
607	#559	—	73	1	no	—
608	#559	—	146	1	no	—
609	#557	—	73	1	no	—
610	#556	—	73	1	no	—
611	#556	—	146	1	no	—
612	#554	—	73	1	no	—
613	#554	—	73	1	no	—
614	#553	—	73	2	no	—
615	#553	—	73	2	no	—
616	#553	—	146	2	no	—
617	#553	—	146	1	no	—
618	#551	—	146	2	no	—
619	#550	—	73	1	no	—
620	#548	—	73	2	no	—
621	#546	—	73	2	no	—
622	#546	—	146	1	no	—
623	D₄²	—	73	1	no	—
624	#532	—	73	1	no	—
625	#532	—	73	1	no	—
626	#532	—	146	1	no	—
627	#529	—	73	2	no	—
628	#529	—	73	2	no	—
629	#529	—	146	1	no	—
630	#529	—	146	2	no	—
631	#525	—	146	2	no	—
632	C₄×#41	—	73	1	no	—
633	C₄×#41	—	73	2	no	—
634	C₄×#41	—	146	1	no	—
635	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
636	C₂×C₄×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
637	C₂×C₄×D₄	—	73	2	no	—
638	C₂×C₄×D₄	—	146	1	no	—
639	#499	—	73	2	no	—
640	#498	—	73	1	no	—
641	#495	—	73	2	no	—
642	#493	—	73	1	no	—
643	#488	—	73	2	no	—
644	#488	—	73	2	no	—
645	#486	—	73	1	no	—
646	#486	—	73	1	no	—
647	#485	—	73	2	no	—
648	#483	—	73	2	no	—
649	#482	—	73	2	no	—
650	#482	—	73	2	no	—
651	#480	—	73	2	no	—
652	#480	—	73	2	no	—
653	#479	—	73	2	no	—
654	#478	—	73	2	no	—
655	#478	—	73	2	no	—
656	#478	—	73	2	no	—
657	#477	—	73	1	no	—
658	#477	—	73	1	no	—
659	#475	—	73	1	no	—
660	#474	—	73	1	no	—
661	#470	—	73	2	no	—
662	#469	—	73	2	no	—
663	#469	—	73	2	no	—
664	#469	—	73	2	no	—
665	#468	—	73	2	no	—
666	#468	—	73	2	no	—
667	#464	—	73	2	no	—
668	#463	—	73	2	no	—
669	#463	—	73	2	no	—
670	#463	—	73	2	no	—
671	#460	—	73	1	no	—
672	#460	—	73	1	no	—
673	#460	—	73	1	no	—
674	#459	—	73	1	no	—
675	#452	—	73	2	no	—
676	#450	—	73	2	no	—
677	#449	—	73	2	no	—
678	#449	—	73	2	no	—
679	#448	—	73	2	no	—
680	#447	—	73	2	no	—
681	C₈×Q₈	—	73	1	no	—
682	C₈×Q₈	—	73	1	no	—
683	#442	—	73	2	no	—
684	#442	—	73	2	no	—
685	#442	—	73	2	no	—
686	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
687	#441	C₂×D₇₃	1	1	yes	characteristic, complemented
688	#440	—	73	2	no	—
689	#440	—	73	2	no	—
690	#440	—	73	2	no	—
691	#440	C₂×D₇₃	1	1	yes	characteristic
692	#440	C₂×D₇₃	1	1	yes	characteristic
693	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
694	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
695	C₄×SD₁₆	—	73	2	no	—
696	C₄×SD₁₆	—	73	2	no	—
697	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
698	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
699	C₄×D₈	—	73	2	no	—
700	C₄×D₈	—	73	2	no	—
701	#436	—	73	2	no	—
702	#436	—	73	2	no	—
703	#436	—	73	1	no	—
704	#436	—	73	1	no	—
705	#432	—	73	1	no	—
706	#432	—	73	2	no	—
707	#428	—	73	2	no	—
708	#428	C₂×D₇₃	1	1	yes	characteristic, complemented
709	#419	C₂×D₇₃	1	1	yes	characteristic, complemented
710	#418	—	73	2	no	—
711	#417	—	73	2	no	—
712	#417	C₂×D₇₃	1	1	yes	characteristic
713	C₄×M₁₆	—	73	2	no	—
714	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
715	C₂×#41	—	73	1	no	—
716	C₂×#41	—	73	2	no	—
717	C₂×#41	—	146	1	no	—
718	C₂×#41	—	146	1	no	—
719	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
720	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
721	C₂²×D₄	—	73	2	no	—
722	C₂²×D₄	—	146	1	no	—
723	C₂³×C₄	—	146	2	no	—
724	#137	—	2	4	no	—
725	AGL(1,ℤ/8)	—	146	8	no	—
726	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
727	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
728	C₂×SD₁₆	—	73	2	no	—
729	C₂×SD₁₆	—	73	2	no	—
730	C₂×SD₁₆	—	73	2	no	—
731	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
732	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
733	C₂×D₈	—	73	2	no	—
734	C₂×D₈	—	73	2	no	—
735	C₂×D₈	—	73	2	no	—
736	C₂×M₁₆	—	73	2	no	—
737	C₂×M₁₆	—	73	2	no	—
738	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
739	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
740	C₄⋊Q₈	—	73	1	no	—
741	C₄⋊Q₈	—	73	1	no	—
742	C₄⋊Q₈	—	146	1	no	—
743	#127	—	73	1	no	—
744	#127	—	73	1	no	—
745	#127	—	146	1	no	—
746	#126	—	146	2	no	—
747	#126	—	146	2	no	—
748	#126	—	146	2	no	—
749	#126	—	146	2	no	—
750	#126	—	146	2	no	—
751	#125	—	73	2	no	—
752	#125	—	73	2	no	—
753	#125	—	146	1	no	—
754	#125	—	146	2	no	—
755	#124	—	73	2	no	—
756	#124	—	73	2	no	—
757	#124	—	146	1	no	—
758	#124	—	146	1	no	—
759	#124	—	146	1	no	—
760	#124	—	146	2	no	—
761	#124	—	146	1	no	—
762	#124	—	146	1	no	—
763	#123	—	146	2	no	—
764	#123	—	146	2	no	—
765	#123	—	146	2	no	—
766	#123	—	146	2	no	—
767	#123	—	146	2	no	—
768	#123	—	146	2	no	—
769	#123	—	146	2	no	—
770	C₂²⋊Q₈	—	73	2	no	—
771	C₂²⋊Q₈	—	73	2	no	—
772	C₂²⋊Q₈	—	146	2	no	—
773	C₂²⋊Q₈	—	146	2	no	—
774	C₂²⋊Q₈	—	146	2	no	—
775	C₂²⋊Q₈	—	146	1	no	—
776	#121	—	73	2	no	—
777	#121	—	73	2	no	—
778	#121	—	73	2	no	—
779	#121	—	73	2	no	—
780	#121	—	146	2	no	—
781	#121	—	146	2	no	—
782	#121	—	146	2	no	—
783	#121	—	146	1	no	—
784	#121	—	146	2	no	—
785	#121	—	146	2	no	—
786	#121	—	146	1	no	—
787	#121	—	146	1	no	—
788	#120	—	146	2	no	—
789	#120	—	146	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	73	1	no	—
793	C₄×Q₈	—	73	1	no	—
794	C₄×Q₈	—	73	2	no	—
795	C₄×Q₈	—	146	1	no	—
796	C₄×Q₈	—	146	1	no	—
797	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
798	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	73	2	no	—
806	C₄×D₄	—	73	2	no	—
807	C₄×D₄	—	73	2	no	—
808	C₄×D₄	—	73	2	no	—
809	C₄×D₄	—	73	2	no	—
810	C₄×D₄	—	73	1	no	—
811	C₄×D₄	—	73	1	no	—
812	C₄×D₄	—	73	2	no	—
813	C₄×D₄	—	73	2	no	—
814	C₄×D₄	—	146	2	no	—
815	C₄×D₄	—	146	1	no	—
816	C₄×D₄	—	146	1	no	—
817	C₄×D₄	—	146	1	no	—
818	C₄×D₄	—	146	2	no	—
819	C₄×D₄	—	146	2	no	—
820	C₄×D₄	—	146	2	no	—
821	C₄×D₄	—	146	1	no	—
822	C₄×D₄	—	146	2	no	—
823	C₄×D₄	—	146	2	no	—
824	C₄×D₄	—	146	2	no	—
825	C₄×D₄	—	146	2	no	—
826	C₄×D₄	—	146	2	no	—
827	C₄×D₄	—	146	1	no	—
828	C₄×D₄	—	146	1	no	—
829	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
830	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
831	#117	—	2	1	no	—
832	#117	—	73	1	no	—
833	#117	—	73	2	no	—
834	#117	—	73	2	no	—
835	#117	—	146	2	no	—
836	#117	—	146	2	no	—
837	#117	—	146	2	no	—
838	#117	C₂²×D₇₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	73	2	no	—
841	C₂×C₄⋊C₄	—	146	1	no	—
842	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	—	146	2	no	—
844	C₂×C₂²⋊C₄	—	146	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	—	73	2	no	—
848	C₂×C₄²	—	146	2	no	—
849	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
850	#107	—	73	2	no	—
851	#107	—	73	2	no	—
852	#107	—	73	2	no	—
853	#107	C₂²×D₇₃	1	1	yes	characteristic
854	#107	C₂²×D₇₃	1	1	yes	characteristic
855	#106	—	73	2	no	—
856	#106	—	73	2	no	—
857	#106	—	73	2	no	—
858	#106	C₂²×D₇₃	1	1	yes	characteristic
859	#106	C₂²×D₇₃	1	1	yes	characteristic
860	C₄⋊C₈	—	73	2	no	—
861	C₄⋊C₈	—	73	2	no	—
862	C₄⋊C₈	—	73	1	no	—
863	C₄⋊C₈	—	73	1	no	—
864	#103	—	73	2	no	—
865	#103	—	73	2	no	—
866	#103	—	73	2	no	—
867	#103	C₂²×D₇₃	1	1	yes	characteristic
868	#103	C₂²×D₇₃	1	1	yes	characteristic
869	#103	C₂²×D₇₃	1	1	yes	characteristic
870	#103	C₂²×D₇₃	1	1	yes	characteristic
871	#103	C₂²×D₇₃	1	1	yes	characteristic
872	#103	C₂²×D₇₃	1	1	yes	characteristic
873	#102	—	73	2	no	—
874	#102	—	73	2	no	—
875	#102	—	73	2	no	—
876	#102	—	73	2	no	—
877	#102	—	73	2	no	—
878	#102	—	73	2	no	—
879	#102	—	73	2	no	—
880	#102	—	73	2	no	—
881	#102	—	73	2	no	—
882	#102	C₂²×D₇₃	1	1	yes	characteristic
883	#102	C₂²×D₇₃	1	1	yes	characteristic
884	C₂²⋊C₈	—	73	2	no	—
885	C₂²⋊C₈	—	73	2	no	—
886	C₂²⋊C₈	—	73	2	no	—
887	#97	—	73	2	no	—
888	#97	C₂²×D₇₃	1	1	yes	characteristic
889	#97	C₂²×D₇₃	1	1	yes	characteristic
890	C₄×C₈	—	73	2	no	—
891	C₄×C₈	—	73	2	no	—
892	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
894	C₂⁴	—	146	2	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	292	4	no	—
898	#41	—	292	2	no	—
899	#41	—	292	2	no	—
900	#41	—	584	2	no	—
901	#41	—	146	4	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	73	1	no	—
906	C₂×Q₈	—	146	1	no	—
907	C₂×Q₈	—	146	1	no	—
908	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
909	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
910	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	292	4	no	—
913	C₂×D₄	—	292	2	no	—
914	C₂×D₄	—	73	2	no	—
915	C₂×D₄	—	73	1	no	—
916	C₂×D₄	—	73	2	no	—
917	C₂×D₄	—	73	2	no	—
918	C₂×D₄	—	146	2	no	—
919	C₂×D₄	—	146	2	no	—
920	C₂×D₄	—	146	2	no	—
921	C₂×D₄	—	146	2	no	—
922	C₂×D₄	—	146	2	no	—
923	C₂×D₄	—	146	4	no	—
924	C₂×D₄	—	146	2	no	—
925	C₂×D₄	—	146	1	no	—
926	C₂×D₄	—	146	1	no	—
927	C₂×D₄	—	146	1	no	—
928	C₂×D₄	—	146	1	no	—
929	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	584	4	no	—
936	C₂²×C₄	—	73	2	no	—
937	C₂²×C₄	—	73	2	no	—
938	C₂²×C₄	—	73	2	no	—
939	C₂²×C₄	—	146	2	no	—
940	C₂²×C₄	—	146	2	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	D₄×D₇₃	1	1	yes	characteristic
947	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
948	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	292	2	no	—
953	SD₁₆	—	292	2	no	—
954	SD₁₆	—	146	4	no	—
955	SD₁₆	#11924028	1	4	yes	complemented
956	D₈	—	292	2	no	—
957	D₈	—	146	4	no	—
958	D₈	—	146	4	no	—
959	M₁₆	—	2	2	no	—
960	M₁₆	—	4	1	no	—
961	M₁₆	—	292	2	no	—
962	M₁₆	—	146	4	no	—
963	C₂×C₈	—	73	2	no	—
964	C₂×C₈	—	73	2	no	—
965	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
967	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
968	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	73	2	no	—
977	C₄⋊C₄	—	73	2	no	—
978	C₄⋊C₄	—	73	1	no	—
979	C₄⋊C₄	—	73	1	no	—
980	C₄⋊C₄	—	73	2	no	—
981	C₄⋊C₄	—	73	2	no	—
982	C₄⋊C₄	—	146	2	no	—
983	C₄⋊C₄	—	146	2	no	—
984	C₄⋊C₄	—	146	2	no	—
985	C₄⋊C₄	—	146	2	no	—
986	C₄⋊C₄	—	146	2	no	—
987	C₄⋊C₄	—	146	2	no	—
988	C₄⋊C₄	—	146	2	no	—
989	C₄⋊C₄	—	146	2	no	—
990	C₄⋊C₄	—	146	1	no	—
991	C₄⋊C₄	—	146	1	no	—
992	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	73	2	no	—
1000	C₂²⋊C₄	—	73	2	no	—
1001	C₂²⋊C₄	—	73	2	no	—
1002	C₂²⋊C₄	—	146	2	no	—
1003	C₂²⋊C₄	—	146	2	no	—
1004	C₂²⋊C₄	—	146	2	no	—
1005	C₂²⋊C₄	—	146	2	no	—
1006	C₂²⋊C₄	—	146	2	no	—
1007	C₂²⋊C₄	—	146	2	no	—
1008	C₂²⋊C₄	—	146	2	no	—
1009	C₂²⋊C₄	—	146	2	no	—
1010	C₂²⋊C₄	—	146	2	no	—
1011	C₂²⋊C₄	—	146	2	no	—
1012	C₂²⋊C₄	—	146	2	no	—
1013	C₂²⋊C₄	—	146	2	no	—
1014	C₂²⋊C₄	—	146	2	no	—
1015	C₂²⋊C₄	—	146	2	no	—
1016	C₂²⋊C₄	—	146	2	no	—
1017	C₂²⋊C₄	—	146	2	no	—
1018	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	73	2	no	—
1026	C₄²	—	73	2	no	—
1027	C₄²	—	73	2	no	—
1028	C₄²	—	146	2	no	—
1029	C₄²	—	146	2	no	—
1030	C₄²	D₄×D₇₃	1	1	yes	characteristic
1031	C₄²	D₄×D₇₃	1	1	yes	characteristic
1032	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1033	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	292	4	no	—
1036	C₂³	—	292	4	no	—
1037	C₂³	—	584	2	no	—
1038	C₂³	—	73	2	no	—
1039	C₂³	—	146	2	no	—
1040	C₂³	—	146	2	no	—
1041	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	292	2	no	—
1049	Q₈	—	584	1	no	—
1050	Q₈	—	146	2	no	—
1051	Q₈	C₂×#11924028	1	2	yes	—
1052	D₄	—	2	1	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	292	4	no	—
1055	D₄	—	292	4	no	—
1056	D₄	—	292	4	no	—
1057	D₄	—	292	4	no	—
1058	D₄	—	292	2	no	—
1059	D₄	—	292	2	no	—
1060	D₄	—	292	2	no	—
1061	D₄	—	584	1	no	—
1062	D₄	—	584	1	no	—
1063	D₄	—	584	2	no	—
1064	D₄	—	584	2	no	—
1065	D₄	—	146	2	no	—
1066	D₄	—	146	2	no	—
1067	D₄	—	146	2	no	—
1068	D₄	—	146	2	no	—
1069	D₄	—	146	2	no	—
1070	D₄	C₂×#11924028	1	2	yes	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	292	4	no	—
1088	C₂×C₄	—	292	4	no	—
1089	C₂×C₄	—	292	4	no	—
1090	C₂×C₄	—	292	2	no	—
1091	C₂×C₄	—	292	2	no	—
1092	C₂×C₄	—	584	2	no	—
1093	C₂×C₄	—	584	2	no	—
1094	C₂×C₄	—	584	2	no	—
1095	C₂×C₄	—	584	2	no	—
1096	C₂×C₄	—	73	2	no	—
1097	C₂×C₄	—	73	2	no	—
1098	C₂×C₄	—	73	2	no	—
1099	C₂×C₄	—	146	2	no	—
1100	C₂×C₄	—	146	2	no	—
1101	C₂×C₄	—	146	2	no	—
1102	C₂×C₄	—	146	2	no	—
1103	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1104	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1105	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1106	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1107	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	146	2	no	—
1113	C₈	—	146	2	no	—
1114	C₈	C₂×#11924028	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	292	2	no	—
1122	C₂²	—	292	2	no	—
1123	C₂²	—	292	2	no	—
1124	C₂²	—	292	2	no	—
1125	C₂²	—	292	2	no	—
1126	C₂²	—	292	2	no	—
1127	C₂²	—	584	8	no	—
1128	C₂²	—	146	2	no	—
1129	C₂²	—	146	2	no	—
1130	C₂²	—	146	2	no	—
1131	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	292	2	no	—
1144	C₄	—	292	2	no	—
1145	C₄	—	146	2	no	—
1146	C₄	—	146	2	no	—
1147	C₄	—	146	2	no	—
1148	C₄	#17989386	1	2	yes	—
1149	C₄	C₂²×#11924028	1	1	yes	characteristic
1150	C₄	#17989423	1	1	yes	characteristic
1151	C₂	—	4	1	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	292	2	no	—
1154	C₂	—	584	2	no	—
1155	C₂	—	584	2	no	—
1156	C₂	D₄×#11924028	1	1	yes	characteristic
1157	C₂	C₂×#17989386	1	1	yes	characteristic
1158	C₂	#22624708	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₄×#137×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	C₄×#137	D₇₃
hypocenter	C₇₃	#61468
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
1. #22623541	C₂	semidirect
2. #22623526	C₂	semidirect
3. #22622941	C₂	semidirect
4. #22622804	C₂	semidirect
5. #22622625	C₂	semidirect
6. #22622589	C₂	semidirect
7. #22622548	C₂	semidirect
8. #22622533	C₂	semidirect
9. #22622271	C₂	semidirect
10. #22622180	C₂	semidirect
11. #22622164	C₂	semidirect
12. #22622133	C₂	semidirect
13. #22621556	C₂	semidirect
14. #22621552	C₂	semidirect
15. #22620669	C₂	semidirect
16. #22620663	C₂	semidirect
17. #22620082	C₂	semidirect
18. #22620073	C₂	semidirect
19. #22620053	C₂	semidirect
20. #22620046	C₂	semidirect
21. #22618949	C₂	semidirect
22. #22618736	C₂	semidirect
23. C₄×#137×C₇₃	C₂	semidirect
27. #17989322	C₂²	semidirect
28. #17989316	C₂²	semidirect
34. #17989285	C₂²	semidirect
39. #17989248	C₂²	semidirect
45. #17989137	C₂²	semidirect
48. #17989124	C₂²	semidirect
51. C₄×#11924029	C₂²	semidirect
56. #17988987	C₂²	semidirect
57. #17988985	C₂²	semidirect
58. #17988972	C₂²	semidirect
60. #17988943	C₂²	semidirect
61. #17988943	C₂²	semidirect
63. #17988934	C₂²	semidirect
64. #17988926	C₂²	semidirect
65. #17988916	C₂²	semidirect
67. #17988911	C₂²	semidirect
68. #17988902	C₂²	semidirect
69. #17988900	C₂²	semidirect
70. #17988892	C₂²	semidirect
71. #17988890	C₂²	semidirect
73. #17988886	C₂²	semidirect
74. #17988882	C₂²	semidirect
75. #17988882	C₂²	semidirect
76. #17988872	C₂²	semidirect
78. #17988842	C₂²	semidirect
80. #17988840	C₂²	semidirect
81. #17988840	C₂²	semidirect
83. #17988836	C₂²	semidirect
84. #17988811	C₂²	semidirect
85. #17988805	C₂²	semidirect
86. #17988805	C₂²	semidirect
90. #17988787	C₂²	semidirect
92. #17988748	C₂²	semidirect
96. #17988726	C₂²	semidirect
98. C₈×Dic₁₄₆	C₂²	semidirect
99. C₈×Dic₁₄₆	C₂²	semidirect
100. #17988700	C₂²	semidirect
101. #17988700	C₂²	semidirect
103. #17988685	C₂²	semidirect
104. #17988685	C₂²	semidirect
105. #17988685	C₂²	semidirect
107. #17988672	C₂²	semidirect
108. #17988669	C₂²	semidirect
112. #17988663	C₂²	semidirect
113. #17988663	C₂²	semidirect
114. #17988644	C₂²	semidirect
115. #17988642	C₂²	semidirect
116. #17988628	C₂²	semidirect
118. #17988587	C₂²	semidirect
119. #17988539	C₂²	semidirect
122. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
123. #441×C₇₃	C₂²	semidirect
124. #441×C₇₃	C₂²	semidirect
127. C₄×Q₁₆×C₇₃	C₂²	semidirect
128. C₄×Q₁₆×C₇₃	C₂²	semidirect
131. #428×C₇₃	C₂²	semidirect
132. #419×C₇₃	C₂²	semidirect
134. C₄×M₁₆×C₇₃	C₂²	semidirect
422. SD₁₆×C₇₃	#41	semidirect
601. C₄×#137	D₇₃	semidirect
603. C₇₃	#61468	semidirect
636. C₂×C₄×Q₈	C₂×D₇₃	semidirect
686. #441	C₂×D₇₃	semidirect
687. #441	C₂×D₇₃	semidirect
693. C₄×Q₁₆	C₂×D₇₃	semidirect
694. C₄×Q₁₆	C₂×D₇₃	semidirect
708. #428	C₂×D₇₃	semidirect
709. #419	C₂×D₇₃	semidirect
714. C₄×M₁₆	C₂×D₇₃	semidirect
955. SD₁₆	#11924028	semidirect

Maximal subgroups

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

subgroup	index
#22623541	2
#22623526	2
#22622941	2
#22622804	2
#22622625	2
#22622589	2
#22622548	2
#22622533	2
#22622271	2
#22622180	2
#22622164	2
#22622133	2
#22621556	2
#22621552	2
#22620669	2
#22620663	2
#22620082	2
#22620073	2
#22620053	2
#22620046	2
#22618949	2
#22618736	2
C₄×#137×C₇₃	2
#61468	73