Subgroups — #33962953

Order 18688.

2132 conjugacy classes of subgroups.

The subgroup lattice has 1210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623495	C₂	1	1	yes	maximal, characteristic, complemented
2	#41×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622271	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622260	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622249	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622238	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622227	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622216	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622204	C₂	1	2	yes	maximal, complemented
10	#22622189	C₂	1	2	yes	maximal, complemented
11	#22622175	C₂	1	1	yes	maximal, characteristic, complemented
12	#22622164	C₂	1	1	yes	maximal, characteristic, complemented
13	#22622152	C₂	1	2	yes	maximal, complemented
14	#22622137	C₂	1	2	yes	maximal, complemented
15	#22620254	C₂	1	1	yes	maximal, characteristic, complemented
16	#22619848	C₂	1	2	yes	maximal, complemented
17	#22619719	C₂	1	1	yes	maximal, characteristic, complemented
18	#22619539	C₂	1	2	yes	maximal, complemented
19	#22619386	C₂	1	1	yes	maximal, characteristic, complemented
20	#22619145	C₂	1	2	yes	maximal, complemented
21	C₂×#17988666	C₂	1	1	yes	maximal, characteristic, complemented
22	#22618446	C₂	1	2	yes	maximal, complemented
23	C₄×#135×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41×D₇₃	C₂²	1	2	yes	—
25	C₂×#14556611	C₂²	1	2	yes	complemented
26	C₂²×#11924011	C₂²	1	2	yes	complemented
27	#17989310	C₂²	1	1	yes	characteristic
28	#17989302	C₂²	1	1	yes	characteristic
29	#17989297	C₂²	1	1	yes	characteristic, complemented
30	#17989287	C₂²	1	2	yes	complemented
31	#17989278	C₂²	1	2	yes	complemented
32	#17989277	—	2	1	no	—
33	#17989266	—	2	2	no	—
34	#17989259	C₂²	1	1	yes	characteristic
35	Q₈×D₂₉₂	C₂²	1	1	yes	characteristic
36	#17989249	C₂²	1	2	yes	—
37	#17989242	C₂²	1	1	yes	characteristic, complemented
38	#17989241	—	2	1	no	—
39	#17989241	C₂²	1	1	yes	characteristic
40	#17989233	—	2	1	no	—
41	#17989232	—	2	2	no	—
42	#17989232	C₂²	1	2	yes	—
43	D₄×D₂₉₂	—	2	1	no	—
44	D₄×D₂₉₂	C₂²	1	1	yes	characteristic
45	#17989144	C₂²	1	1	yes	characteristic, complemented
46	#17989137	—	2	1	no	—
47	#17989137	C₂²	1	1	yes	characteristic
48	#17989121	—	2	1	no	—
49	#17989115	—	2	2	no	—
50	#17989099	—	2	2	no	—
51	#17989099	C₂²	1	2	yes	—
52	#17989094	C₂²	1	2	yes	complemented
53	C₄×#11924028	—	2	1	no	—
54	C₂×C₄×D₂₉₂	—	2	1	no	—
55	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
56	#117×D₇₃	C₂²	1	2	yes	complemented
57	#17988942	C₂²	1	2	yes	complemented
58	#17988942	C₂²	1	2	yes	complemented
59	#17988938	C₂²	1	1	yes	characteristic, complemented
60	#17988938	C₂²	1	1	yes	characteristic, complemented
61	#17988934	C₂²	1	1	yes	characteristic, complemented
62	#17988934	C₂²	1	1	yes	characteristic, complemented
63	#17988931	C₂²	1	2	yes	complemented
64	#17988930	C₂²	1	2	yes	complemented
65	#17988924	C₂²	1	2	yes	complemented
66	#17988919	C₂²	1	2	yes	complemented
67	#17988914	C₂²	1	2	yes	complemented
68	#17988913	C₂²	1	2	yes	complemented
69	#17988907	C₂²	1	2	yes	complemented
70	#17988902	C₂²	1	2	yes	complemented
71	#17988894	C₂²	1	2	yes	complemented
72	#17988887	C₂²	1	2	yes	complemented
73	#17988882	C₂²	1	1	yes	characteristic, complemented
74	#17988877	C₂²	1	1	yes	characteristic, complemented
75	#17988872	C₂²	1	1	yes	characteristic, complemented
76	#17988867	C₂²	1	1	yes	characteristic, complemented
77	#17988844	C₂²	1	2	yes	complemented
78	#17988844	C₂²	1	2	yes	complemented
79	#17988839	C₂²	1	2	yes	complemented
80	#17988839	C₂²	1	2	yes	complemented
81	#17988836	C₂²	1	2	yes	complemented
82	#17988836	C₂²	1	2	yes	complemented
83	#17988832	C₂²	1	2	yes	complemented
84	#17988832	C₂²	1	2	yes	complemented
85	#17988809	C₂²	1	2	yes	complemented
86	#17988802	C₂²	1	2	yes	complemented
87	#17988797	C₂²	1	1	yes	characteristic, complemented
88	#17988792	C₂²	1	1	yes	characteristic, complemented
89	#17988787	C₂²	1	1	yes	characteristic, complemented
90	#17988782	C₂²	1	1	yes	characteristic, complemented
91	#17988748	C₂²	1	2	yes	complemented
92	#17988746	C₂²	1	2	yes	complemented
93	#17988741	C₂²	1	2	yes	complemented
94	#17988736	C₂²	1	2	yes	complemented
95	#17988731	C₂²	1	2	yes	complemented
96	#17988729	C₂²	1	2	yes	complemented
97	#17988724	C₂²	1	2	yes	complemented
98	#17988719	C₂²	1	2	yes	complemented
99	#17988666	C₂²	1	1	yes	characteristic
100	#17988666	C₂²	1	1	yes	characteristic
101	#17988666	C₂²	1	1	yes	characteristic, complemented
102	#17988666	C₂²	1	1	yes	characteristic, complemented
103	#17988666	C₂²	1	2	yes	complemented
104	#17988666	C₂²	1	2	yes	complemented
105	#17988623	C₂²	1	2	yes	complemented
106	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic, complemented
107	#17988594	C₂²	1	2	yes	complemented
108	#17988594	C₂²	1	2	yes	complemented
109	#17988590	C₂²	1	2	yes	complemented
110	#17988590	C₂²	1	2	yes	complemented
111	#17988587	C₂²	1	2	yes	complemented
112	#17988587	C₂²	1	2	yes	complemented
113	#17988585	C₂²	1	2	yes	complemented
114	#17988585	C₂²	1	2	yes	complemented
115	#17988584	C₂²	1	2	yes	complemented
116	#17988584	C₂²	1	2	yes	complemented
117	#17988583	C₂²	1	2	yes	—
118	#17988581	C₂²	1	2	yes	complemented
119	C₂×#14556503	C₂²	1	2	yes	complemented
120	C₂×#135×C₇₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	#416×C₇₃	C₂²	1	1	yes	characteristic
133	#416×C₇₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924029	C₂³	1	2	yes	—
136	C₂×#11924028	—	2	1	no	—
137	C₂×#11924028	—	2	2	no	—
138	C₂×#11924028	C₂³	1	2	yes	—
139	C₂×#11924027	—	2	2	no	—
140	C₂×#11924027	C₂³	1	2	yes	—
141	#41×D₇₃	—	2	8	no	—
142	#41×D₇₃	—	4	4	no	—
143	C₂×Q₈×D₇₃	C₂³	1	2	yes	—
144	C₂²×D₂₉₂	—	2	1	no	—
145	C₂²×D₂₉₂	D₄	1	1	yes	characteristic
146	C₂×D₄×D₇₃	—	2	2	no	—
147	C₂×D₄×D₇₃	C₂³	1	2	yes	—
148	C₂²×C₄×D₇₃	—	2	2	no	—
149	C₂²×C₄×D₇₃	C₂³	1	2	yes	—
150	#14556611	—	4	4	no	—
151	C₂×#11924018	C₂³	1	2	yes	—
152	C₂×#11924016	C₂³	1	2	yes	—
153	C₂×#11924015	C₂³	1	2	yes	—
154	C₂×#11924013	C₂³	1	2	yes	—
155	C₂×#11924011	—	4	4	no	—
156	C₂×#11924011	C₂³	1	2	yes	—
157	C₂×#11924011	C₂³	1	2	yes	—
158	C₂×#11924011	C₂³	1	2	yes	—
159	C₂×#11924011	C₂³	1	2	yes	—
160	C₂²×#10596831	C₂³	1	2	yes	—
161	#14556591	—	2	1	no	—
162	#14556591	C₂³	1	1	yes	characteristic
163	#14556591	C₂³	1	1	yes	characteristic
164	#14556591	C₂³	1	1	yes	characteristic
165	#14556588	—	2	1	no	—
166	#14556588	C₂³	1	1	yes	characteristic
167	#14556586	—	2	2	no	—
168	#14556585	—	2	2	no	—
169	#14556584	—	2	2	no	—
170	#14556583	—	2	1	no	—
171	#14556583	C₂³	1	2	yes	—
172	#14556581	—	2	2	no	—
173	#14556579	—	2	1	no	—
174	#14556579	—	2	2	no	—
175	#14556579	C₂³	1	2	yes	—
176	#14556577	—	2	2	no	—
177	#14556576	—	2	2	no	—
178	#14556575	—	2	2	no	—
179	#14556575	—	2	2	no	—
180	#14556575	—	2	2	no	—
181	#14556574	—	2	2	no	—
182	#14556573	—	2	2	no	—
183	#14556572	—	2	2	no	—
184	#14556571	—	2	2	no	—
185	#14556571	—	2	2	no	—
186	#14556571	C₂³	1	2	yes	—
187	#14556571	C₂³	1	2	yes	—
188	#14556570	—	2	1	no	—
189	#14556570	—	2	1	no	—
190	#14556570	—	2	1	no	—
191	#14556569	—	2	2	no	—
192	#14556567	C₂³	1	2	yes	—
193	#14556567	C₂³	1	2	yes	—
194	#14556566	—	2	2	no	—
195	#14556566	—	2	2	no	—
196	#14556566	C₂³	1	2	yes	—
197	#14556566	C₂³	1	2	yes	—
198	#14556565	—	2	1	no	—
199	#14556565	—	2	1	no	—
200	#14556565	—	2	1	no	—
201	#14556565	—	2	2	no	—
202	#14556565	—	2	1	no	—
203	#14556565	—	2	1	no	—
204	#14556564	—	2	2	no	—
205	#14556562	C₂³	1	2	yes	—
206	#14556562	C₂³	1	2	yes	—
207	#14556561	—	2	2	no	—
208	#14556561	—	2	2	no	—
209	#14556561	—	2	2	no	—
210	#14556559	—	2	2	no	—
211	C₄×Dic₁₄₆	—	2	1	no	—
212	C₄×Dic₁₄₆	—	2	1	no	—
213	C₄×Dic₁₄₆	—	2	1	no	—
214	C₄×D₂₉₂	—	2	1	no	—
215	C₄×D₂₉₂	—	2	1	no	—
216	C₄×D₂₉₂	—	2	2	no	—
217	C₄×D₂₉₂	—	2	2	no	—
218	C₄×D₂₉₂	—	2	1	no	—
219	C₄×D₂₉₂	—	2	2	no	—
220	C₄×D₂₉₂	—	2	1	no	—
221	C₄×D₂₉₂	—	2	1	no	—
222	C₄×D₂₉₂	D₄	1	1	yes	characteristic
223	C₄×D₂₉₂	D₄	1	1	yes	characteristic
224	C₄×D₂₉₂	D₄	1	2	yes	—
225	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
226	C₄×D₂₉₂	C₂³	1	2	yes	—
227	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
228	C₄×C₂²⋊D₇₃	—	2	2	no	—
229	C₄×C₂²⋊D₇₃	—	2	2	no	—
230	C₄×C₂²⋊D₇₃	—	2	2	no	—
231	#14556550	—	2	1	no	—
232	#14556550	C₂³	1	2	yes	—
233	#14556549	C₂³	1	2	yes	—
234	#14556549	C₂³	1	2	yes	—
235	#14556548	—	2	2	no	—
236	#14556548	—	2	2	no	—
237	#14556547	—	2	2	no	—
238	C₂×C₄⋊Dic₇₃	—	2	1	no	—
239	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
240	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
241	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
242	C₂×#11924005	—	2	2	no	—
243	C₂×#11924005	D₄	1	2	yes	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₄²×D₇₃	—	2	2	no	—
246	#14556524	C₂³	1	2	yes	—
247	#14556524	C₂³	1	2	yes	—
248	#14556522	C₂³	1	2	yes	—
249	#14556522	C₂³	1	2	yes	—
250	C₄⋊#10596831	C₂³	1	1	yes	characteristic
251	C₄⋊#10596831	C₂³	1	1	yes	characteristic
252	C₄⋊#10596831	C₂³	1	2	yes	—
253	#14556516	C₂³	1	2	yes	—
254	#14556516	C₂³	1	2	yes	—
255	#14556516	C₂³	1	2	yes	—
256	#14556516	C₂³	1	2	yes	—
257	#14556515	C₂³	1	2	yes	—
258	#14556515	C₂³	1	2	yes	—
259	#14556514	C₂³	1	2	yes	—
260	#14556514	C₂³	1	2	yes	—
261	#14556513	C₂³	1	2	yes	—
262	#14556513	C₂³	1	2	yes	—
263	#14556513	C₂³	1	2	yes	—
264	#14556513	C₂³	1	2	yes	—
265	#14556512	C₂³	1	2	yes	—
266	#14556512	C₂³	1	2	yes	—
267	#14556511	C₂³	1	2	yes	—
268	#14556511	C₂³	1	2	yes	—
269	#14556503	C₂³	1	2	yes	—
270	#14556503	C₂³	1	2	yes	—
271	#14556503	C₂³	1	2	yes	—
272	#14556503	C₂³	1	2	yes	—
273	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
274	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
275	#135×C₇₃	—	2	4	no	—
276	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
277	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
278	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
279	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
281	C₂²×C₈×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×D₄×C₇₃	—	2	1	no	—
287	C₄×D₄×C₇₃	—	2	1	no	—
288	C₄×D₄×C₇₃	—	2	1	no	—
289	C₄×D₄×C₇₃	—	2	1	no	—
290	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
294	#117×C₇₃	—	2	1	no	—
295	#117×C₇₃	—	2	1	no	—
296	#117×C₇₃	C₂³	1	1	yes	characteristic
297	#117×C₇₃	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₇₃	—	2	1	no	—
299	C₂×C₄²×C₇₃	—	2	1	no	—
300	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
301	#107×C₇₃	C₂³	1	1	yes	characteristic
302	#107×C₇₃	C₂³	1	1	yes	characteristic
303	#106×C₇₃	C₂³	1	1	yes	characteristic
304	#106×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	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
317	C₂³×D₇₃	—	2	2	no	—
318	C₂³×D₇₃	C₂×D₄	1	2	yes	—
319	#11924029	—	2	4	no	—
320	#11924029	—	4	2	no	—
321	#11924028	—	2	4	no	—
322	#11924028	—	2	4	no	—
323	#11924028	—	4	8	no	—
324	#11924028	—	4	4	no	—
325	#11924027	—	2	4	no	—
326	#11924027	—	4	2	no	—
327	#11924027	—	4	8	no	—
328	C₂×Dic₁₄₆	—	2	1	no	—
329	C₂×Dic₁₄₆	—	2	2	no	—
330	C₂×Dic₁₄₆	—	2	1	no	—
331	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
332	Q₈×D₇₃	—	2	4	no	—
333	Q₈×D₇₃	—	4	2	no	—
334	C₂×D₂₉₂	—	2	2	no	—
335	C₂×D₂₉₂	—	2	2	no	—
336	C₂×D₂₉₂	—	2	1	no	—
337	C₂×D₂₉₂	—	2	2	no	—
338	C₂×D₂₉₂	—	2	1	no	—
339	C₂×D₂₉₂	—	4	2	no	—
340	C₂×D₂₉₂	—	4	4	no	—
341	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
342	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
343	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
344	C₂×D₂₉₂	C₂⁴	1	2	yes	—
345	C₂×C₂²⋊D₇₃	—	2	2	no	—
346	C₂×C₂²⋊D₇₃	—	2	2	no	—
347	C₂×C₂²⋊D₇₃	—	2	2	no	—
348	C₂×C₂²⋊D₇₃	—	2	2	no	—
349	C₂×C₂²⋊D₇₃	—	2	2	no	—
350	D₄×D₇₃	—	2	4	no	—
351	D₄×D₇₃	—	4	2	no	—
352	D₄×D₇₃	—	4	8	no	—
353	C₂²×Dic₇₃	—	2	2	no	—
354	C₂²×Dic₇₃	C₂×D₄	1	2	yes	—
355	C₂×C₄×D₇₃	—	2	4	no	—
356	C₂×C₄×D₇₃	—	2	4	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	—	2	2	no	—
361	C₂×C₄×D₇₃	—	2	2	no	—
362	C₂×C₄×D₇₃	—	4	8	no	—
363	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
364	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
365	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
366	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
367	#11924018	—	4	2	no	—
368	#11924016	—	4	2	no	—
369	#11924015	—	4	2	no	—
370	#11924013	—	4	2	no	—
371	#11924011	—	4	2	no	—
372	#11924011	—	4	2	no	—
373	#11924011	—	4	2	no	—
374	#11924011	—	4	2	no	—
375	C₂×#10596831	—	2	4	no	—
376	C₂×#10596831	C₂⁴	1	2	yes	—
377	C₂×#10596831	C₂⁴	1	2	yes	—
378	C₄⋊Dic₇₃	—	2	1	no	—
379	C₄⋊Dic₇₃	—	2	1	no	—
380	C₄⋊Dic₇₃	—	2	1	no	—
381	C₄⋊Dic₇₃	—	2	1	no	—
382	C₄⋊Dic₇₃	—	2	2	no	—
383	C₄⋊Dic₇₃	—	2	2	no	—
384	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
385	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
386	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
387	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
388	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
389	#11924007	—	2	2	no	—
390	#11924007	—	2	2	no	—
391	#11924007	—	2	2	no	—
392	#11924007	—	2	2	no	—
393	#11924007	—	2	2	no	—
394	#11924007	—	2	2	no	—
395	C₂²⋊Dic₇₃	—	2	2	no	—
396	C₂²⋊Dic₇₃	—	2	2	no	—
397	C₂²⋊Dic₇₃	—	2	2	no	—
398	#11924005	—	2	2	no	—
399	#11924005	—	2	2	no	—
400	#11924005	—	2	2	no	—
401	#11924005	—	2	2	no	—
402	#11924005	—	2	2	no	—
403	#11924005	—	2	2	no	—
404	#11924005	—	2	2	no	—
405	#11924005	—	2	2	no	—
406	#11924005	—	2	2	no	—
407	#11924005	—	2	2	no	—
408	#11924005	C₂×D₄	1	2	yes	—
409	#11924005	C₂×D₄	1	2	yes	—
410	#11924005	C₂×D₄	1	2	yes	—
411	#11924005	C₂×D₄	1	2	yes	—
412	C₄×Dic₇₃	—	2	2	no	—
413	C₄×Dic₇₃	—	2	2	no	—
414	C₄×Dic₇₃	—	2	2	no	—
415	#41×C₇₃	—	2	2	no	—
416	#41×C₇₃	—	2	2	no	—
417	#41×C₇₃	—	2	2	no	—
418	#41×C₇₃	#41	1	4	yes	complemented
419	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
420	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
421	C₂×D₄×C₇₃	—	2	1	no	—
422	C₂×D₄×C₇₃	—	2	1	no	—
423	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
424	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₇₃	—	2	1	no	—
426	C₂²×C₄×C₇₃	—	2	1	no	—
427	C₂²×C₄×C₇₃	—	2	1	no	—
428	C₂²×C₄×C₇₃	—	2	1	no	—
429	C₂²×C₄×C₇₃	—	2	1	no	—
430	C₂²×C₄×C₇₃	—	2	1	no	—
431	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
434	Q₁₆×C₇₃	—	2	2	no	—
435	SD₁₆×C₇₃	—	2	2	no	—
436	SD₁₆×C₇₃	—	2	2	no	—
437	D₈×C₇₃	—	2	2	no	—
438	C₂×C₈×C₇₃	—	2	2	no	—
439	C₂×C₈×C₇₃	—	2	2	no	—
440	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
441	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
443	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
444	C₄⋊C₄×C₇₃	—	2	1	no	—
445	C₄⋊C₄×C₇₃	—	2	1	no	—
446	C₄⋊C₄×C₇₃	—	2	1	no	—
447	C₄⋊C₄×C₇₃	—	2	1	no	—
448	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
449	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
450	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
451	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
452	C₂²⋊C₄×C₇₃	—	2	1	no	—
453	C₂²⋊C₄×C₇₃	—	2	1	no	—
454	C₂²⋊C₄×C₇₃	—	2	1	no	—
455	C₂²⋊C₄×C₇₃	—	2	1	no	—
456	C₂²⋊C₄×C₇₃	—	2	1	no	—
457	C₂²⋊C₄×C₇₃	—	2	1	no	—
458	C₄²×C₇₃	—	2	1	no	—
459	C₄²×C₇₃	—	2	1	no	—
460	C₄²×C₇₃	—	2	1	no	—
461	C₄²×C₇₃	—	2	1	no	—
462	C₄²×C₇₃	—	2	1	no	—
463	C₄²×C₇₃	—	2	1	no	—
464	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
465	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
466	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
467	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
468	C₂³×C₇₃	—	2	1	no	—
469	C₂³×C₇₃	—	2	1	no	—
470	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
471	C₂²×D₇₃	—	2	4	no	—
472	C₂²×D₇₃	—	2	2	no	—
473	C₂²×D₇₃	—	4	2	no	—
474	C₂²×D₇₃	—	4	2	no	—
475	C₂²×D₇₃	—	4	4	no	—
476	C₂²×D₇₃	—	4	4	no	—
477	C₂²×D₇₃	—	8	2	no	—
478	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
479	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
480	Q₈×C₇₃	—	2	1	no	—
481	Q₈×C₇₃	—	2	1	no	—
482	Q₈×C₇₃	—	2	1	no	—
483	Q₈×C₇₃	C₂×#41	1	2	yes	—
484	D₄×C₇₃	—	2	4	no	—
485	D₄×C₇₃	—	2	1	no	—
486	D₄×C₇₃	—	2	1	no	—
487	D₄×C₇₃	—	2	1	no	—
488	D₄×C₇₃	—	4	2	no	—
489	D₄×C₇₃	C₂×#41	1	2	yes	—
490	C₂×C₄×C₇₃	—	2	1	no	—
491	C₂×C₄×C₇₃	—	2	4	no	—
492	C₂×C₄×C₇₃	—	2	2	no	—
493	C₂×C₄×C₇₃	—	2	1	no	—
494	C₂×C₄×C₇₃	—	2	1	no	—
495	C₂×C₄×C₇₃	—	2	1	no	—
496	C₂×C₄×C₇₃	—	2	1	no	—
497	C₂×C₄×C₇₃	—	2	1	no	—
498	C₂×C₄×C₇₃	—	4	1	no	—
499	C₂×C₄×C₇₃	—	4	2	no	—
500	C₂×C₄×C₇₃	—	4	2	no	—
501	C₂×C₄×C₇₃	—	4	2	no	—
502	C₂×C₄×C₇₃	—	8	1	no	—
503	C₂×C₄×C₇₃	—	8	1	no	—
504	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
510	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
511	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
512	C₂²⋊D₇₃	—	4	4	no	—
513	C₂²⋊D₇₃	—	4	4	no	—
514	C₂²⋊D₇₃	—	4	4	no	—
515	C₂²⋊D₇₃	—	4	4	no	—
516	C₂²⋊D₇₃	—	8	2	no	—
517	C₂×Dic₇₃	—	2	4	no	—
518	C₂×Dic₇₃	—	2	2	no	—
519	C₂×Dic₇₃	—	2	2	no	—
520	C₂×Dic₇₃	—	2	2	no	—
521	C₂×Dic₇₃	—	4	4	no	—
522	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
523	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
524	D₂₉₂	—	2	2	no	—
525	D₂₉₂	—	2	2	no	—
526	D₂₉₂	—	2	2	no	—
527	D₂₉₂	—	2	2	no	—
528	D₂₉₂	—	4	2	no	—
529	D₂₉₂	—	4	4	no	—
530	D₂₉₂	—	4	4	no	—
531	D₂₉₂	—	4	2	no	—
532	D₂₉₂	—	8	1	no	—
533	D₂₉₂	—	8	2	no	—
534	C₄×D₇₃	—	2	4	no	—
535	C₄×D₇₃	—	2	4	no	—
536	C₄×D₇₃	—	2	2	no	—
537	C₄×D₇₃	—	2	2	no	—
538	C₄×D₇₃	—	2	2	no	—
539	C₄×D₇₃	—	2	2	no	—
540	C₄×D₇₃	—	4	4	no	—
541	C₄×D₇₃	—	4	4	no	—
542	C₄×D₇₃	—	4	4	no	—
543	C₄×D₇₃	—	4	4	no	—
544	C₄×D₇₃	—	8	2	no	—
545	Dic₁₄₆	—	2	2	no	—
546	Dic₁₄₆	—	2	2	no	—
547	Dic₁₄₆	—	4	4	no	—
548	Dic₁₄₆	—	4	2	no	—
549	Dic₁₄₆	—	8	1	no	—
550	C₈×C₇₃	—	2	1	no	—
551	C₈×C₇₃	—	2	1	no	—
552	C₈×C₇₃	—	2	1	no	—
553	C₈×C₇₃	—	2	1	no	—
554	#10596831	—	2	2	no	—
555	#10596831	—	2	2	no	—
556	C₂²×C₇₃	—	2	1	no	—
557	C₂²×C₇₃	—	2	1	no	—
558	C₂²×C₇₃	—	2	2	no	—
559	C₂²×C₇₃	—	4	1	no	—
560	C₂²×C₇₃	—	4	1	no	—
561	C₂²×C₇₃	—	4	1	no	—
562	C₂²×C₇₃	—	4	1	no	—
563	C₂²×C₇₃	—	4	1	no	—
564	C₂²×C₇₃	#546	1	2	yes	—
565	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
566	C₂×D₇₃	—	2	2	no	—
567	C₂×D₇₃	—	2	2	no	—
568	C₂×D₇₃	—	2	2	no	—
569	C₂×D₇₃	—	2	2	no	—
570	C₂×D₇₃	—	2	2	no	—
571	C₂×D₇₃	—	2	2	no	—
572	C₂×D₇₃	—	4	2	no	—
573	C₂×D₇₃	—	4	2	no	—
574	C₂×D₇₃	—	4	2	no	—
575	C₂×D₇₃	—	8	4	no	—
576	C₂×D₇₃	—	8	8	no	—
577	C₄×C₇₃	—	2	1	no	—
578	C₄×C₇₃	—	2	1	no	—
579	C₄×C₇₃	—	2	2	no	—
580	C₄×C₇₃	—	2	1	no	—
581	C₄×C₇₃	—	4	1	no	—
582	C₄×C₇₃	—	4	1	no	—
583	C₄×C₇₃	—	4	1	no	—
584	C₄×C₇₃	—	4	1	no	—
585	C₄×C₇₃	—	4	1	no	—
586	C₄×C₇₃	#546	1	2	yes	—
587	C₄×C₇₃	#575	1	2	yes	—
588	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
589	C₄×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
590	Dic₇₃	—	2	2	no	—
591	Dic₇₃	—	2	2	no	—
592	Dic₇₃	—	4	2	no	—
593	Dic₇₃	—	4	2	no	—
594	Dic₇₃	—	4	2	no	—
595	#61154	—	73	1	no	maximal, Sylow
596	C₂×C₇₃	—	2	2	no	—
597	C₂×C₇₃	—	4	2	no	—
598	C₂×C₇₃	—	8	1	no	—
599	C₂×C₇₃	C₂×#546	1	1	yes	characteristic
600	C₂×C₇₃	C₂×#575	1	1	yes	characteristic
601	C₂×C₇₃	#3584	1	1	yes	characteristic
602	D₇₃	—	4	2	no	—
603	D₇₃	—	4	2	no	—
604	D₇₃	—	8	2	no	—
605	#3475	—	73	1	no	—
606	D₄×#41	—	73	1	no	—
607	#3333	—	73	1	no	—
608	#3332	—	73	1	no	—
609	#3331	—	73	1	no	—
610	#3330	—	73	1	no	—
611	#3329	—	73	1	no	—
612	#3328	—	73	1	no	—
613	#3327	—	73	2	no	—
614	#3326	—	73	2	no	—
615	#3325	—	73	1	no	—
616	#3324	—	73	1	no	—
617	#3323	—	73	2	no	—
618	#3322	—	73	2	no	—
619	#3131	—	73	1	no	—
620	#3091	—	73	2	no	—
621	#3076	—	73	1	no	—
622	#3054	—	73	2	no	—
623	#3035	—	73	1	no	—
624	#3002	—	73	2	no	—
625	C₄×#135	D₇₃	1	1	yes	characteristic, complemented
626	C₂×#436	—	73	1	no	—
627	#2896	—	73	2	no	—
628	C₇₃	#61154	1	1	yes	characteristic, complemented, Sylow
629	C₂²×#41	—	73	2	no	—
630	C₂×#135	—	73	2	no	—
631	C₂×#135	C₂×D₇₃	1	1	yes	characteristic
632	C₂²×M₁₆	—	73	2	no	—
633	#556	—	73	1	no	—
634	#555	—	73	1	no	—
635	#554	—	73	1	no	—
636	#553	—	73	2	no	—
637	#552	—	73	2	no	—
638	#552	—	146	1	no	—
639	#551	—	146	2	no	—
640	#550	—	73	1	no	—
641	D₄×Q₈	—	73	1	no	—
642	#548	—	73	2	no	—
643	#547	—	73	1	no	—
644	#547	—	73	1	no	—
645	#547	—	146	1	no	—
646	#546	—	73	2	no	—
647	#546	—	146	2	no	—
648	#546	—	146	1	no	—
649	D₄²	—	73	1	no	—
650	D₄²	—	146	1	no	—
651	#533	—	73	1	no	—
652	#532	—	73	1	no	—
653	#532	—	146	1	no	—
654	#529	—	146	1	no	—
655	#529	—	146	2	no	—
656	#525	—	73	2	no	—
657	#525	—	73	2	no	—
658	#525	—	146	2	no	—
659	C₄×#41	—	146	1	no	—
660	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
661	C₄×#41	C₂×D₇₃	1	1	yes	characteristic, complemented
662	C₂×C₄×D₄	—	73	1	no	—
663	C₂×C₄×D₄	—	146	1	no	—
664	C₂×#117	—	73	2	no	—
665	#488	—	73	2	no	—
666	#488	—	73	2	no	—
667	#487	—	73	1	no	—
668	#487	—	73	1	no	—
669	#486	—	73	1	no	—
670	#486	—	73	1	no	—
671	#485	—	73	2	no	—
672	#485	—	73	2	no	—
673	#484	—	73	2	no	—
674	#483	—	73	2	no	—
675	#482	—	73	2	no	—
676	#482	—	73	2	no	—
677	#481	—	73	2	no	—
678	#480	—	73	2	no	—
679	#479	—	73	2	no	—
680	#478	—	73	2	no	—
681	#477	—	73	1	no	—
682	#476	—	73	1	no	—
683	#475	—	73	1	no	—
684	#474	—	73	1	no	—
685	#470	—	73	2	no	—
686	#470	—	73	2	no	—
687	#469	—	73	2	no	—
688	#469	—	73	2	no	—
689	#468	—	73	2	no	—
690	#468	—	73	2	no	—
691	#468	—	73	2	no	—
692	#468	—	73	2	no	—
693	#464	—	73	2	no	—
694	#463	—	73	2	no	—
695	#462	—	73	1	no	—
696	#461	—	73	1	no	—
697	#460	—	73	1	no	—
698	#459	—	73	1	no	—
699	#452	—	73	2	no	—
700	#452	—	73	2	no	—
701	#451	—	73	2	no	—
702	#450	—	73	2	no	—
703	#449	—	73	2	no	—
704	#449	—	73	2	no	—
705	#448	—	73	2	no	—
706	#447	—	73	2	no	—
707	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
708	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
709	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
710	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
711	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
712	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
713	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
714	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
715	#436	—	73	1	no	—
716	#436	—	73	1	no	—
717	#436	—	73	1	no	—
718	#436	—	73	1	no	—
719	#436	—	73	2	no	—
720	#436	—	73	2	no	—
721	#427	—	73	2	no	—
722	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
723	C₂×C₄⋊C₈	—	73	1	no	—
724	#419	—	73	2	no	—
725	#419	—	73	2	no	—
726	#418	—	73	2	no	—
727	#418	—	73	2	no	—
728	#417	—	73	2	no	—
729	#417	—	73	2	no	—
730	#417	—	73	2	no	—
731	#417	—	73	2	no	—
732	#416	—	73	2	no	—
733	#416	—	73	2	no	—
734	#416	—	73	2	no	—
735	#416	—	73	2	no	—
736	#416	C₂×D₇₃	1	1	yes	characteristic
737	#416	C₂×D₇₃	1	1	yes	characteristic, complemented
738	C₂×C₂²⋊C₈	—	73	2	no	—
739	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
740	C₂×#41	—	292	4	no	—
741	C₂×#41	—	73	2	no	—
742	C₂×#41	—	73	2	no	—
743	C₂×#41	—	73	2	no	—
744	C₂×#41	—	146	2	no	—
745	C₂×#41	—	146	1	no	—
746	C₂×#41	—	146	8	no	—
747	C₂×#41	—	146	2	no	—
748	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
749	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
750	C₂²×Q₈	—	73	2	no	—
751	C₂²×D₄	—	73	2	no	—
752	C₂²×D₄	—	73	1	no	—
753	C₂²×D₄	—	146	1	no	—
754	C₂²×D₄	—	146	2	no	—
755	C₂³×C₄	—	73	2	no	—
756	C₂³×C₄	—	146	2	no	—
757	#135	—	2	4	no	—
758	#135	—	292	4	no	—
759	C₂×Q₁₆	—	73	2	no	—
760	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
761	C₂×SD₁₆	—	73	2	no	—
762	C₂×SD₁₆	—	73	2	no	—
763	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
764	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
765	C₂×D₈	—	73	2	no	—
766	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
767	C₂×M₁₆	—	292	4	no	—
768	C₂×M₁₆	—	73	2	no	—
769	C₂×M₁₆	—	73	2	no	—
770	C₂×M₁₆	—	73	2	no	—
771	C₂×M₁₆	—	73	2	no	—
772	C₂²×C₈	—	73	2	no	—
773	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
774	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
775	C₄⋊Q₈	—	73	1	no	—
776	C₄⋊Q₈	—	73	1	no	—
777	C₄⋊Q₈	—	73	1	no	—
778	C₄⋊Q₈	—	146	1	no	—
779	#127	—	73	1	no	—
780	#127	—	146	1	no	—
781	#126	—	146	2	no	—
782	#126	—	146	2	no	—
783	#126	—	146	2	no	—
784	#125	—	73	2	no	—
785	#125	—	146	1	no	—
786	#125	—	146	2	no	—
787	#124	—	73	2	no	—
788	#124	—	146	2	no	—
789	#124	—	146	1	no	—
790	#124	—	146	2	no	—
791	#123	—	146	2	no	—
792	#123	—	146	2	no	—
793	#123	—	146	2	no	—
794	#123	—	146	2	no	—
795	#123	—	146	2	no	—
796	#123	—	146	2	no	—
797	#123	—	146	2	no	—
798	C₂²⋊Q₈	—	73	2	no	—
799	C₂²⋊Q₈	—	73	2	no	—
800	C₂²⋊Q₈	—	73	2	no	—
801	C₂²⋊Q₈	—	73	2	no	—
802	C₂²⋊Q₈	—	146	2	no	—
803	C₂²⋊Q₈	—	146	2	no	—
804	C₂²⋊Q₈	—	146	2	no	—
805	C₂²⋊Q₈	—	146	1	no	—
806	C₂²⋊Q₈	—	146	1	no	—
807	C₂²⋊Q₈	—	146	1	no	—
808	#121	—	73	2	no	—
809	#121	—	73	2	no	—
810	#121	—	73	2	no	—
811	#121	—	73	2	no	—
812	#121	—	146	2	no	—
813	#121	—	146	2	no	—
814	#121	—	146	2	no	—
815	#121	—	146	2	no	—
816	#121	—	146	1	no	—
817	#121	—	146	1	no	—
818	#121	—	146	1	no	—
819	#121	—	146	1	no	—
820	#121	—	146	1	no	—
821	#120	—	146	2	no	—
822	#120	—	146	2	no	—
823	#120	—	146	2	no	—
824	#120	—	146	2	no	—
825	C₄×Q₈	—	146	1	no	—
826	C₄×Q₈	—	146	1	no	—
827	C₄×Q₈	—	146	1	no	—
828	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
829	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
830	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
831	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	73	1	no	—
837	C₄×D₄	—	73	1	no	—
838	C₄×D₄	—	73	2	no	—
839	C₄×D₄	—	73	1	no	—
840	C₄×D₄	—	73	2	no	—
841	C₄×D₄	—	73	1	no	—
842	C₄×D₄	—	146	2	no	—
843	C₄×D₄	—	146	1	no	—
844	C₄×D₄	—	146	2	no	—
845	C₄×D₄	—	146	2	no	—
846	C₄×D₄	—	146	1	no	—
847	C₄×D₄	—	146	1	no	—
848	C₄×D₄	—	146	2	no	—
849	C₄×D₄	—	146	2	no	—
850	C₄×D₄	—	146	2	no	—
851	C₄×D₄	—	146	1	no	—
852	C₄×D₄	—	146	1	no	—
853	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
854	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
855	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
856	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
857	#117	—	2	1	no	—
858	#117	—	2	1	no	—
859	#117	—	73	2	no	—
860	#117	—	73	2	no	—
861	#117	—	73	2	no	—
862	#117	—	146	2	no	—
863	#117	—	146	2	no	—
864	#117	—	146	2	no	—
865	#117	—	146	1	no	—
866	#117	C₂²×D₇₃	1	1	yes	characteristic
867	#117	C₂²×D₇₃	1	1	yes	characteristic
868	C₂×C₄⋊C₄	—	73	1	no	—
869	C₂×C₄⋊C₄	—	73	2	no	—
870	C₂×C₄⋊C₄	—	73	2	no	—
871	C₂×C₄⋊C₄	—	146	1	no	—
872	C₂×C₂²⋊C₄	—	73	2	no	—
873	C₂×C₂²⋊C₄	—	146	2	no	—
874	C₂×C₂²⋊C₄	—	146	2	no	—
875	C₂×C₄²	—	2	1	no	—
876	C₂×C₄²	—	2	1	no	—
877	C₂×C₄²	—	146	2	no	—
878	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
879	#107	—	73	2	no	—
880	#107	—	73	2	no	—
881	#107	C₂²×D₇₃	1	1	yes	characteristic
882	#107	C₂²×D₇₃	1	1	yes	characteristic
883	#106	—	73	2	no	—
884	#106	—	73	2	no	—
885	#106	C₂²×D₇₃	1	1	yes	characteristic
886	#106	C₂²×D₇₃	1	1	yes	characteristic
887	C₄⋊C₈	—	73	1	no	—
888	C₄⋊C₈	—	73	1	no	—
889	C₄⋊C₈	—	73	2	no	—
890	#103	—	73	2	no	—
891	#103	—	73	2	no	—
892	#103	—	73	2	no	—
893	#103	—	73	2	no	—
894	#103	—	73	2	no	—
895	#103	—	73	2	no	—
896	#103	—	73	2	no	—
897	#103	—	73	2	no	—
898	#103	C₂²×D₇₃	1	1	yes	characteristic
899	#103	C₂²×D₇₃	1	1	yes	characteristic
900	#103	C₂²×D₇₃	1	1	yes	characteristic
901	#103	C₂²×D₇₃	1	1	yes	characteristic
902	#102	—	73	2	no	—
903	#102	—	73	2	no	—
904	#102	—	73	2	no	—
905	#102	—	73	2	no	—
906	#102	—	73	2	no	—
907	#102	—	73	2	no	—
908	#102	—	73	2	no	—
909	#102	—	73	2	no	—
910	#102	C₂²×D₇₃	1	1	yes	characteristic
911	#102	C₂²×D₇₃	1	1	yes	characteristic
912	#102	C₂²×D₇₃	1	1	yes	characteristic
913	#102	C₂²×D₇₃	1	1	yes	characteristic
914	C₂²⋊C₈	—	73	2	no	—
915	C₂²⋊C₈	—	73	2	no	—
916	C₂²⋊C₈	—	73	2	no	—
917	C₂²⋊C₈	—	73	2	no	—
918	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
919	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
920	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
921	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
922	C₂⁴	—	73	2	no	—
923	C₂⁴	—	146	2	no	—
924	#41	—	2	2	no	—
925	#41	—	2	2	no	—
926	#41	—	2	2	no	—
927	#41	—	292	8	no	—
928	#41	—	292	4	no	—
929	#41	—	292	8	no	—
930	#41	—	292	2	no	—
931	#41	—	292	2	no	—
932	#41	—	146	4	no	—
933	#41	—	146	4	no	—
934	#41	—	146	4	no	—
935	#41	—	146	4	no	—
936	#41	#11924028	1	4	yes	complemented
937	C₂×Q₈	—	292	2	no	—
938	C₂×Q₈	—	73	2	no	—
939	C₂×Q₈	—	146	2	no	—
940	C₂×Q₈	—	146	4	no	—
941	C₂×Q₈	—	146	1	no	—
942	C₂×Q₈	—	146	1	no	—
943	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
944	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
945	C₂×D₄	—	2	1	no	—
946	C₂×D₄	—	2	1	no	—
947	C₂×D₄	—	292	2	no	—
948	C₂×D₄	—	292	4	no	—
949	C₂×D₄	—	292	8	no	—
950	C₂×D₄	—	292	2	no	—
951	C₂×D₄	—	73	2	no	—
952	C₂×D₄	—	73	1	no	—
953	C₂×D₄	—	73	1	no	—
954	C₂×D₄	—	73	2	no	—
955	C₂×D₄	—	146	2	no	—
956	C₂×D₄	—	146	2	no	—
957	C₂×D₄	—	146	2	no	—
958	C₂×D₄	—	146	2	no	—
959	C₂×D₄	—	146	2	no	—
960	C₂×D₄	—	146	2	no	—
961	C₂×D₄	—	146	2	no	—
962	C₂×D₄	—	146	4	no	—
963	C₂×D₄	—	146	2	no	—
964	C₂×D₄	—	146	1	no	—
965	C₂×D₄	—	146	1	no	—
966	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
967	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
968	C₂²×C₄	—	2	1	no	—
969	C₂²×C₄	—	2	1	no	—
970	C₂²×C₄	—	2	1	no	—
971	C₂²×C₄	—	2	1	no	—
972	C₂²×C₄	—	2	1	no	—
973	C₂²×C₄	—	2	1	no	—
974	C₂²×C₄	—	292	8	no	—
975	C₂²×C₄	—	73	2	no	—
976	C₂²×C₄	—	73	2	no	—
977	C₂²×C₄	—	73	2	no	—
978	C₂²×C₄	—	73	2	no	—
979	C₂²×C₄	—	73	2	no	—
980	C₂²×C₄	—	146	2	no	—
981	C₂²×C₄	—	146	2	no	—
982	C₂²×C₄	—	146	2	no	—
983	C₂²×C₄	—	146	2	no	—
984	C₂²×C₄	—	146	2	no	—
985	C₂²×C₄	—	146	2	no	—
986	C₂²×C₄	—	146	4	no	—
987	C₂²×C₄	—	146	4	no	—
988	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
989	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
990	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
991	Q₁₆	—	2	2	no	—
992	Q₁₆	—	292	2	no	—
993	SD₁₆	—	2	2	no	—
994	SD₁₆	—	2	2	no	—
995	SD₁₆	—	292	2	no	—
996	SD₁₆	—	292	2	no	—
997	D₈	—	2	2	no	—
998	D₈	—	292	2	no	—
999	M₁₆	—	292	2	no	—
1000	M₁₆	—	292	2	no	—
1001	M₁₆	—	292	2	no	—
1002	M₁₆	—	292	2	no	—
1003	C₂×C₈	—	2	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	73	2	no	—
1006	C₂×C₈	—	73	2	no	—
1007	C₂×C₈	—	146	4	no	—
1008	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1009	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1010	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1011	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
1012	C₄⋊C₄	—	2	1	no	—
1013	C₄⋊C₄	—	2	1	no	—
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	73	1	no	—
1017	C₄⋊C₄	—	73	1	no	—
1018	C₄⋊C₄	—	73	2	no	—
1019	C₄⋊C₄	—	73	2	no	—
1020	C₄⋊C₄	—	73	2	no	—
1021	C₄⋊C₄	—	146	2	no	—
1022	C₄⋊C₄	—	146	2	no	—
1023	C₄⋊C₄	—	146	2	no	—
1024	C₄⋊C₄	—	146	2	no	—
1025	C₄⋊C₄	—	146	2	no	—
1026	C₄⋊C₄	—	146	2	no	—
1027	C₄⋊C₄	—	146	2	no	—
1028	C₄⋊C₄	—	146	2	no	—
1029	C₄⋊C₄	—	146	1	no	—
1030	C₄⋊C₄	—	146	1	no	—
1031	C₄⋊C₄	—	146	1	no	—
1032	C₄⋊C₄	—	146	1	no	—
1033	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1034	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1035	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1036	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1037	C₂²⋊C₄	—	2	1	no	—
1038	C₂²⋊C₄	—	2	1	no	—
1039	C₂²⋊C₄	—	2	1	no	—
1040	C₂²⋊C₄	—	2	1	no	—
1041	C₂²⋊C₄	—	2	1	no	—
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	73	2	no	—
1044	C₂²⋊C₄	—	73	2	no	—
1045	C₂²⋊C₄	—	73	2	no	—
1046	C₂²⋊C₄	—	73	2	no	—
1047	C₂²⋊C₄	—	146	2	no	—
1048	C₂²⋊C₄	—	146	2	no	—
1049	C₂²⋊C₄	—	146	2	no	—
1050	C₂²⋊C₄	—	146	2	no	—
1051	C₂²⋊C₄	—	146	2	no	—
1052	C₂²⋊C₄	—	146	2	no	—
1053	C₂²⋊C₄	—	146	2	no	—
1054	C₂²⋊C₄	—	146	2	no	—
1055	C₂²⋊C₄	—	146	2	no	—
1056	C₂²⋊C₄	—	146	2	no	—
1057	C₂²⋊C₄	—	146	2	no	—
1058	C₂²⋊C₄	—	146	2	no	—
1059	C₂²⋊C₄	—	146	2	no	—
1060	C₄²	—	2	1	no	—
1061	C₄²	—	2	1	no	—
1062	C₄²	—	2	1	no	—
1063	C₄²	—	2	1	no	—
1064	C₄²	—	2	1	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	146	2	no	—
1067	C₄²	—	146	2	no	—
1068	C₄²	—	146	2	no	—
1069	C₄²	D₄×D₇₃	1	1	yes	characteristic
1070	C₄²	D₄×D₇₃	1	1	yes	characteristic
1071	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1072	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1073	C₂³	—	2	1	no	—
1074	C₂³	—	2	1	no	—
1075	C₂³	—	292	4	no	—
1076	C₂³	—	292	2	no	—
1077	C₂³	—	292	2	no	—
1078	C₂³	—	292	4	no	—
1079	C₂³	—	584	2	no	—
1080	C₂³	—	73	2	no	—
1081	C₂³	—	73	2	no	—
1082	C₂³	—	146	2	no	—
1083	C₂³	—	146	4	no	—
1084	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1085	Q₈	—	2	1	no	—
1086	Q₈	—	2	1	no	—
1087	Q₈	—	2	1	no	—
1088	Q₈	—	292	4	no	—
1089	Q₈	—	292	2	no	—
1090	Q₈	—	584	1	no	—
1091	Q₈	—	146	2	no	—
1092	Q₈	—	146	2	no	—
1093	Q₈	C₂×#11924028	1	2	yes	—
1094	D₄	—	2	4	no	—
1095	D₄	—	2	1	no	—
1096	D₄	—	2	1	no	—
1097	D₄	—	2	1	no	—
1098	D₄	—	4	2	no	—
1099	D₄	—	292	4	no	—
1100	D₄	—	292	2	no	—
1101	D₄	—	292	4	no	—
1102	D₄	—	292	4	no	—
1103	D₄	—	292	4	no	—
1104	D₄	—	292	4	no	—
1105	D₄	—	292	4	no	—
1106	D₄	—	292	2	no	—
1107	D₄	—	584	1	no	—
1108	D₄	—	584	2	no	—
1109	D₄	—	584	2	no	—
1110	D₄	—	146	2	no	—
1111	D₄	—	146	2	no	—
1112	D₄	—	146	2	no	—
1113	D₄	—	146	2	no	—
1114	D₄	C₂×#11924028	1	2	yes	—
1115	C₂×C₄	—	2	1	no	—
1116	C₂×C₄	—	2	2	no	—
1117	C₂×C₄	—	2	4	no	—
1118	C₂×C₄	—	2	1	no	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	1	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	4	1	no	—
1124	C₂×C₄	—	4	2	no	—
1125	C₂×C₄	—	4	2	no	—
1126	C₂×C₄	—	4	2	no	—
1127	C₂×C₄	—	8	1	no	—
1128	C₂×C₄	—	8	1	no	—
1129	C₂×C₄	—	292	4	no	—
1130	C₂×C₄	—	292	4	no	—
1131	C₂×C₄	—	292	4	no	—
1132	C₂×C₄	—	292	4	no	—
1133	C₂×C₄	—	292	4	no	—
1134	C₂×C₄	—	584	2	no	—
1135	C₂×C₄	—	73	2	no	—
1136	C₂×C₄	—	73	2	no	—
1137	C₂×C₄	—	146	2	no	—
1138	C₂×C₄	—	146	2	no	—
1139	C₂×C₄	—	146	2	no	—
1140	C₂×C₄	—	146	4	no	—
1141	C₂×C₄	—	146	2	no	—
1142	C₂×C₄	—	146	2	no	—
1143	C₂×C₄	—	146	2	no	—
1144	C₂×C₄	—	146	2	no	—
1145	C₂×C₄	—	146	4	no	—
1146	C₂×C₄	—	146	4	no	—
1147	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1148	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1149	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1150	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1151	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1152	C₂×C₄	C₂×#11924028	1	2	yes	—
1153	C₂×C₄	#14556637	1	2	yes	—
1154	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1155	C₈	—	2	1	no	—
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	146	2	no	—
1160	C₈	—	146	2	no	—
1161	C₂²	—	2	1	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	2	no	—
1164	C₂²	—	4	1	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	4	1	no	—
1168	C₂²	—	4	1	no	—
1169	C₂²	—	292	2	no	—
1170	C₂²	—	292	2	no	—
1171	C₂²	—	292	2	no	—
1172	C₂²	—	584	4	no	—
1173	C₂²	—	584	8	no	—
1174	C₂²	—	146	2	no	—
1175	C₂²	—	146	2	no	—
1176	C₂²	—	146	2	no	—
1177	C₂²	—	146	2	no	—
1178	C₂²	—	146	2	no	—
1179	C₂²	—	146	2	no	—
1180	C₂²	#17989233	1	2	yes	—
1181	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1182	C₄	—	2	2	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	2	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	292	2	no	—
1192	C₄	—	292	2	no	—
1193	C₄	—	292	2	no	—
1194	C₄	—	146	2	no	—
1195	C₄	—	146	2	no	—
1196	C₄	#17989233	1	2	yes	—
1197	C₄	#17989384	1	2	yes	—
1198	C₄	C₂²×#11924028	1	1	yes	characteristic
1199	C₄	C₂×#14556637	1	1	yes	characteristic
1200	C₂	—	2	2	no	—
1201	C₂	—	4	2	no	—
1202	C₂	—	8	1	no	—
1203	C₂	—	292	2	no	—
1204	C₂	—	292	2	no	—
1205	C₂	—	584	2	no	—
1206	C₂	C₂×#17989233	1	1	yes	characteristic
1207	C₂	C₂×#17989384	1	1	yes	characteristic
1208	C₂	#22624700	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₄×#135×C₇₃	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	C₄×#135	D₇₃
hypocenter	C₇₃	#61154
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄×#135

Complements

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

N	H ≅ G/N	type
1. #22623495	C₂	semidirect
2. #41×D₂₉₂	C₂	semidirect
3. #22622271	C₂	semidirect
4. #22622260	C₂	semidirect
5. #22622249	C₂	semidirect
6. #22622238	C₂	semidirect
7. #22622227	C₂	semidirect
8. #22622216	C₂	semidirect
9. #22622204	C₂	semidirect
10. #22622189	C₂	semidirect
11. #22622175	C₂	semidirect
12. #22622164	C₂	semidirect
13. #22622152	C₂	semidirect
14. #22622137	C₂	semidirect
15. #22620254	C₂	semidirect
16. #22619848	C₂	semidirect
17. #22619719	C₂	semidirect
18. #22619539	C₂	semidirect
19. #22619386	C₂	semidirect
20. #22619145	C₂	semidirect
21. C₂×#17988666	C₂	semidirect
22. #22618446	C₂	semidirect
23. C₄×#135×C₇₃	C₂	semidirect
25. C₂×#14556611	C₂²	semidirect
26. C₂²×#11924011	C₂²	semidirect
29. #17989297	C₂²	semidirect
30. #17989287	C₂²	semidirect
31. #17989278	C₂²	semidirect
37. #17989242	C₂²	semidirect
45. #17989144	C₂²	semidirect
52. #17989094	C₂²	semidirect
56. #117×D₇₃	C₂²	semidirect
57. #17988942	C₂²	semidirect
58. #17988942	C₂²	semidirect
59. #17988938	C₂²	semidirect
60. #17988938	C₂²	semidirect
61. #17988934	C₂²	semidirect
62. #17988934	C₂²	semidirect
63. #17988931	C₂²	semidirect
64. #17988930	C₂²	semidirect
65. #17988924	C₂²	semidirect
66. #17988919	C₂²	semidirect
67. #17988914	C₂²	semidirect
68. #17988913	C₂²	semidirect
69. #17988907	C₂²	semidirect
70. #17988902	C₂²	semidirect
71. #17988894	C₂²	semidirect
72. #17988887	C₂²	semidirect
73. #17988882	C₂²	semidirect
74. #17988877	C₂²	semidirect
75. #17988872	C₂²	semidirect
76. #17988867	C₂²	semidirect
77. #17988844	C₂²	semidirect
78. #17988844	C₂²	semidirect
79. #17988839	C₂²	semidirect
80. #17988839	C₂²	semidirect
81. #17988836	C₂²	semidirect
82. #17988836	C₂²	semidirect
83. #17988832	C₂²	semidirect
84. #17988832	C₂²	semidirect
85. #17988809	C₂²	semidirect
86. #17988802	C₂²	semidirect
87. #17988797	C₂²	semidirect
88. #17988792	C₂²	semidirect
89. #17988787	C₂²	semidirect
90. #17988782	C₂²	semidirect
91. #17988748	C₂²	semidirect
92. #17988746	C₂²	semidirect
93. #17988741	C₂²	semidirect
94. #17988736	C₂²	semidirect
95. #17988731	C₂²	semidirect
96. #17988729	C₂²	semidirect
97. #17988724	C₂²	semidirect
98. #17988719	C₂²	semidirect
101. #17988666	C₂²	semidirect
102. #17988666	C₂²	semidirect
103. #17988666	C₂²	semidirect
104. #17988666	C₂²	semidirect
105. #17988623	C₂²	semidirect
106. C₂×C₄⋊#10596831	C₂²	semidirect
107. #17988594	C₂²	semidirect
108. #17988594	C₂²	semidirect
109. #17988590	C₂²	semidirect
110. #17988590	C₂²	semidirect
111. #17988587	C₂²	semidirect
112. #17988587	C₂²	semidirect
113. #17988585	C₂²	semidirect
114. #17988585	C₂²	semidirect
115. #17988584	C₂²	semidirect
116. #17988584	C₂²	semidirect
118. #17988581	C₂²	semidirect
119. C₂×#14556503	C₂²	semidirect
122. C₄×#41×C₇₃	C₂²	semidirect
123. C₄×Q₁₆×C₇₃	C₂²	semidirect
124. C₄×Q₁₆×C₇₃	C₂²	semidirect
125. C₄×SD₁₆×C₇₃	C₂²	semidirect
126. C₄×SD₁₆×C₇₃	C₂²	semidirect
127. C₄×SD₁₆×C₇₃	C₂²	semidirect
128. C₄×SD₁₆×C₇₃	C₂²	semidirect
129. C₄×D₈×C₇₃	C₂²	semidirect
130. C₄×D₈×C₇₃	C₂²	semidirect
131. #427×C₇₃	C₂²	semidirect
133. #416×C₇₃	C₂²	semidirect
134. C₂×C₄×C₈×C₇₃	C₂²	semidirect
418. #41×C₇₃	#41	semidirect
625. C₄×#135	D₇₃	semidirect
628. C₇₃	#61154	semidirect
661. C₄×#41	C₂×D₇₃	semidirect
707. C₄×Q₁₆	C₂×D₇₃	semidirect
708. C₄×Q₁₆	C₂×D₇₃	semidirect
709. C₄×SD₁₆	C₂×D₇₃	semidirect
710. C₄×SD₁₆	C₂×D₇₃	semidirect
711. C₄×SD₁₆	C₂×D₇₃	semidirect
712. C₄×SD₁₆	C₂×D₇₃	semidirect
713. C₄×D₈	C₂×D₇₃	semidirect
714. C₄×D₈	C₂×D₇₃	semidirect
722. #427	C₂×D₇₃	semidirect
737. #416	C₂×D₇₃	semidirect
739. C₂×C₄×C₈	C₂×D₇₃	semidirect
936. #41	#11924028	semidirect

Maximal subgroups

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

subgroup	index
#22623495	2
#41×D₂₉₂	2
#22622271	2
#22622260	2
#22622249	2
#22622238	2
#22622227	2
#22622216	2
#22622204	2
#22622189	2
#22622175	2
#22622164	2
#22622152	2
#22622137	2
#22620254	2
#22619848	2
#22619719	2
#22619539	2
#22619386	2
#22619145	2
C₂×#17988666	2
#22618446	2
C₄×#135×C₇₃	2
#61154	73