Subgroups — #33968369

Order 18688.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623875	C₂	1	2	yes	maximal, complemented
2	#22622944	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622799	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622686	C₂	1	2	yes	maximal, complemented
5	#22622334	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622300	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622279	C₂	1	1	yes	maximal, characteristic, complemented
8	#22622134	C₂	1	2	yes	maximal, complemented
9	#22621954	C₂	1	2	yes	maximal, complemented
10	#22621894	C₂	1	2	yes	maximal, complemented
11	#22621618	C₂	1	1	yes	maximal, characteristic, complemented
12	#22621618	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
14	#22620581	C₂	1	1	yes	maximal, characteristic, complemented
15	#22620570	C₂	1	1	yes	maximal, characteristic, complemented
16	#22620501	C₂	1	1	yes	maximal, characteristic, complemented
17	#22620132	C₂	1	2	yes	maximal, complemented
18	#22620117	C₂	1	2	yes	maximal, complemented
19	#22620071	C₂	1	2	yes	maximal, complemented
20	#22618808	C₂	1	1	yes	maximal, characteristic, complemented
21	#22618784	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₄×D₅₈₄	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#14556613	C₂²	1	1	yes	characteristic
25	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic
26	C₂²×D₅₈₄	C₂²	1	1	yes	characteristic
27	#17989322	C₂²	1	2	yes	complemented
28	#17989297	C₂²	1	2	yes	complemented
29	#17989288	—	2	2	no	—
30	#17989283	C₂²	1	2	yes	complemented
31	#17989277	C₂²	1	2	yes	—
32	#17989264	—	2	2	no	—
33	#17989262	—	2	2	no	—
34	#17989241	C₂²	1	2	yes	complemented
35	#17989233	C₂²	1	2	yes	complemented
36	#17989233	C₂²	1	2	yes	complemented
37	#17989226	—	2	2	no	—
38	D₄×D₂₉₂	C₂²	1	2	yes	—
39	#17989208	C₂²	1	2	yes	complemented
40	#17989192	C₂²	1	2	yes	complemented
41	#17989185	—	2	2	no	—
42	#17989171	—	2	2	no	—
43	#17989121	C₂²	1	2	yes	complemented
44	#17989095	—	2	2	no	—
45	#123×D₇₃	—	2	2	no	—
46	#17989067	C₂²	1	2	yes	complemented
47	#17989061	C₂²	1	2	yes	complemented
48	C₂×C₄×D₂₉₂	C₂²	1	2	yes	complemented
49	#17988992	C₂²	1	1	yes	characteristic, complemented
50	#17988989	C₂²	1	1	yes	characteristic, complemented
51	#17988989	C₂²	1	1	yes	characteristic, complemented
52	#17988971	C₂²	1	1	yes	characteristic, complemented
53	#17988971	C₂²	1	1	yes	characteristic, complemented
54	#17988964	C₂²	1	1	yes	characteristic
55	#17988952	C₂²	1	2	yes	complemented
56	#17988947	C₂²	1	2	yes	complemented
57	#17988942	C₂²	1	2	yes	complemented
58	#17988929	C₂²	1	2	yes	complemented
59	#17988918	C₂²	1	2	yes	complemented
60	#17988912	C₂²	1	2	yes	complemented
61	#17988906	C₂²	1	2	yes	complemented
62	#17988901	C₂²	1	2	yes	complemented
63	#17988901	C₂²	1	2	yes	complemented
64	#17988895	C₂²	1	2	yes	complemented
65	#17988888	C₂²	1	2	yes	complemented
66	#17988888	C₂²	1	2	yes	complemented
67	#17988888	C₂²	1	2	yes	complemented
68	#17988878	C₂²	1	2	yes	complemented
69	#17988868	C₂²	1	2	yes	complemented
70	#17988840	C₂²	1	2	yes	complemented
71	#17988833	C₂²	1	2	yes	complemented
72	#17988828	C₂²	1	1	yes	characteristic, complemented
73	#17988828	C₂²	1	1	yes	characteristic, complemented
74	#17988823	C₂²	1	1	yes	characteristic
75	#17988823	C₂²	1	1	yes	characteristic
76	#17988823	C₂²	1	1	yes	characteristic, complemented
77	#17988823	C₂²	1	1	yes	characteristic, complemented
78	#17988816	C₂²	1	2	yes	complemented
79	#17988803	C₂²	1	2	yes	complemented
80	#17988803	C₂²	1	2	yes	complemented
81	#17988803	C₂²	1	2	yes	complemented
82	#17988803	C₂²	1	2	yes	complemented
83	#17988788	C₂²	1	2	yes	complemented
84	#17988783	C₂²	1	2	yes	—
85	#17988740	C₂²	1	2	yes	complemented
86	#17988740	C₂²	1	2	yes	complemented
87	#17988734	C₂²	1	2	yes	complemented
88	#17988734	C₂²	1	2	yes	complemented
89	#17988723	C₂²	1	2	yes	—
90	#17988723	C₂²	1	2	yes	—
91	#17988700	C₂²	1	2	yes	complemented
92	#17988700	C₂²	1	2	yes	complemented
93	#17988700	C₂²	1	2	yes	complemented
94	#17988689	C₂²	1	2	yes	complemented
95	#17988689	C₂²	1	2	yes	complemented
96	#17988689	C₂²	1	2	yes	complemented
97	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
98	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
99	C₄×#11924017	C₂²	1	2	yes	complemented
100	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
101	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
102	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
103	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
104	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
106	C₄×D₅₈₄	C₂²	1	2	yes	complemented
107	C₄×D₅₈₄	C₂²	1	2	yes	complemented
108	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
110	#17988625	C₂²	1	1	yes	characteristic, complemented
111	C₂×#14556525	C₂²	1	1	yes	characteristic, complemented
112	C₂×#14556525	C₂²	1	1	yes	characteristic, complemented
113	#17988593	C₂²	1	2	yes	complemented
114	#17988589	C₂²	1	2	yes	complemented
115	C₂×#14556513	C₂²	1	2	yes	complemented
116	#529×C₇₃	C₂²	1	1	yes	characteristic
117	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
118	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
119	#436×C₇₃	C₂²	1	1	yes	characteristic, complemented
120	#435×C₇₃	C₂²	1	1	yes	characteristic
121	#435×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#433×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#433×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#432×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	#405×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#405×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#11924028	C₂³	1	2	yes	—
132	C₂×#11924027	—	2	2	no	—
133	C₂²×D₂₉₂	C₂³	1	2	yes	—
134	C₂²×D₂₉₂	C₂³	1	2	yes	—
135	C₂×D₄×D₇₃	—	2	2	no	—
136	C₂²×C₄×D₇₃	—	2	2	no	—
137	#14556613	—	2	4	no	—
138	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
139	C₂×#11924017	C₂³	1	2	yes	—
140	C₂×#11924017	C₂³	1	2	yes	—
141	C₂×#11924017	C₂³	1	2	yes	—
142	C₂×D₅₈₄	—	2	4	no	—
143	C₂×D₅₈₄	—	2	4	no	—
144	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
145	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
146	C₂×D₅₈₄	C₂³	1	2	yes	—
147	C₂×D₅₈₄	C₂³	1	2	yes	—
148	C₂×D₅₈₄	C₂³	1	2	yes	—
149	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
150	#14556591	C₂³	1	2	yes	—
151	#14556588	C₂³	1	2	yes	—
152	#14556586	—	2	2	no	—
153	#14556586	—	2	2	no	—
154	#14556585	—	2	2	no	—
155	#14556584	—	2	2	no	—
156	#14556583	C₂³	1	2	yes	—
157	#14556583	C₂³	1	2	yes	—
158	#14556581	—	2	2	no	—
159	#14556580	—	2	2	no	—
160	#14556579	C₂³	1	2	yes	—
161	#14556579	C₂³	1	2	yes	—
162	#14556577	—	2	2	no	—
163	#14556576	—	2	2	no	—
164	#14556576	—	2	2	no	—
165	#14556576	—	2	2	no	—
166	#14556576	—	2	2	no	—
167	#14556576	—	2	2	no	—
168	#14556576	—	2	2	no	—
169	#14556575	—	2	2	no	—
170	#14556575	—	2	2	no	—
171	#14556574	—	2	2	no	—
172	#14556573	—	2	2	no	—
173	#14556573	—	2	2	no	—
174	#14556572	—	2	2	no	—
175	#14556571	—	2	2	no	—
176	#14556570	C₂³	1	2	yes	—
177	#14556570	C₂³	1	2	yes	—
178	#14556569	—	2	2	no	—
179	#14556569	—	2	2	no	—
180	#14556569	—	2	2	no	—
181	#14556567	—	2	2	no	—
182	#14556566	—	2	2	no	—
183	#14556565	C₂³	1	2	yes	—
184	#14556565	C₂³	1	2	yes	—
185	#14556565	C₂³	1	2	yes	—
186	#14556565	C₂³	1	2	yes	—
187	#14556564	—	2	2	no	—
188	#14556564	—	2	2	no	—
189	#14556564	—	2	2	no	—
190	#14556564	—	2	2	no	—
191	#14556563	—	2	2	no	—
192	#14556561	—	2	2	no	—
193	#14556561	—	2	2	no	—
194	#14556559	—	2	2	no	—
195	#14556559	—	2	2	no	—
196	C₄×Dic₁₄₆	C₂³	1	2	yes	—
197	C₄×Dic₁₄₆	C₂³	1	2	yes	—
198	C₄×D₂₉₂	—	2	2	no	—
199	C₄×D₂₉₂	—	2	2	no	—
200	C₄×D₂₉₂	C₂³	1	2	yes	—
201	C₄×D₂₉₂	C₂³	1	2	yes	—
202	C₄×D₂₉₂	C₂³	1	2	yes	—
203	C₄×D₂₉₂	C₂³	1	2	yes	—
204	C₄×D₂₉₂	C₂³	1	2	yes	—
205	C₄×D₂₉₂	C₂³	1	2	yes	—
206	C₄×D₂₉₂	C₂³	1	2	yes	—
207	C₄×D₂₉₂	C₂³	1	2	yes	—
208	#14556553	—	2	2	no	—
209	#14556553	—	2	2	no	—
210	#14556553	—	2	2	no	—
211	C₄×C₂²⋊D₇₃	—	2	2	no	—
212	#14556551	—	2	2	no	—
213	#14556551	—	2	2	no	—
214	#14556551	—	2	2	no	—
215	#14556550	C₂³	1	2	yes	—
216	#14556549	—	2	2	no	—
217	#14556548	—	2	2	no	—
218	#14556547	—	2	2	no	—
219	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
220	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
221	C₄⋊C₄×D₇₃	—	2	2	no	—
222	C₄⋊C₄×D₇₃	—	2	2	no	—
223	C₂×#11924005	—	2	2	no	—
224	C₂²⋊C₄×D₇₃	—	2	2	no	—
225	C₂²⋊C₄×D₇₃	—	2	2	no	—
226	C₂²⋊C₄×D₇₃	—	2	2	no	—
227	C₂²⋊C₄×D₇₃	—	2	2	no	—
228	#14556525	C₂³	1	2	yes	—
229	#14556525	C₂³	1	2	yes	—
230	#14556525	C₂³	1	1	yes	characteristic
231	#14556525	C₂³	1	1	yes	characteristic
232	#14556525	C₂³	1	1	yes	characteristic
233	#14556525	C₂³	1	1	yes	characteristic
234	#14556525	C₂³	1	2	yes	—
235	#14556523	C₂³	1	2	yes	—
236	#14556523	C₂³	1	2	yes	—
237	#14556523	C₂³	1	2	yes	—
238	#14556516	C₂³	1	2	yes	—
239	#14556516	C₂³	1	2	yes	—
240	#14556516	C₂³	1	2	yes	—
241	#14556516	C₂³	1	2	yes	—
242	#14556513	C₂³	1	2	yes	—
243	#14556513	C₂³	1	2	yes	—
244	#14556513	C₂³	1	2	yes	—
245	#14556513	C₂³	1	2	yes	—
246	#14556513	C₂³	1	2	yes	—
247	#14556513	C₂³	1	2	yes	—
248	#14556513	C₂³	1	2	yes	—
249	#14556513	C₂³	1	2	yes	—
250	#14556513	C₂³	1	2	yes	—
251	#14556513	C₂³	1	2	yes	—
252	#14556513	C₂³	1	2	yes	—
253	#14556513	C₂³	1	2	yes	—
254	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
255	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
256	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
257	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
258	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
259	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
260	#126×C₇₃	D₄	1	1	yes	characteristic
261	#126×C₇₃	D₄	1	1	yes	characteristic
262	#125×C₇₃	D₄	1	1	yes	characteristic
263	#124×C₇₃	D₄	1	1	yes	characteristic
264	#123×C₇₃	D₄	1	1	yes	characteristic
265	#123×C₇₃	D₄	1	1	yes	characteristic
266	C₂²⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
267	#121×C₇₃	D₄	1	1	yes	characteristic
268	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
269	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
270	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
271	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
272	#117×C₇₃	C₂³	1	1	yes	characteristic
273	#117×C₇₃	C₂³	1	1	yes	characteristic
274	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
275	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
276	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
277	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
278	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
279	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
280	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
281	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
282	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
284	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
285	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
286	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
287	#97×C₇₃	C₂³	1	1	yes	characteristic
288	#97×C₇₃	C₂³	1	1	yes	characteristic
289	#97×C₇₃	C₂³	1	1	yes	characteristic
290	#97×C₇₃	C₂³	1	1	yes	characteristic
291	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
292	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
297	C₂³×D₇₃	—	2	2	no	—
298	C₂³×D₇₃	—	2	2	no	—
299	#11924028	—	2	4	no	—
300	#11924028	—	4	2	no	—
301	#11924027	—	8	4	no	—
302	C₂×Dic₁₄₆	—	2	2	no	—
303	C₂×Dic₁₄₆	C₂⁴	1	2	yes	—
304	C₂×D₂₉₂	—	2	4	no	—
305	C₂×D₂₉₂	—	2	4	no	—
306	C₂×D₂₉₂	—	2	2	no	—
307	C₂×D₂₉₂	—	2	2	no	—
308	C₂×D₂₉₂	—	2	2	no	—
309	C₂×D₂₉₂	—	2	2	no	—
310	C₂×D₂₉₂	—	4	2	no	—
311	C₂×D₂₉₂	—	4	2	no	—
312	C₂×D₂₉₂	C₂⁴	1	2	yes	—
313	C₂×D₂₉₂	C₂⁴	1	2	yes	—
314	C₂×D₂₉₂	C₂⁴	1	2	yes	—
315	C₂×C₂²⋊D₇₃	—	2	2	no	—
316	C₂×C₂²⋊D₇₃	—	2	2	no	—
317	C₂×C₂²⋊D₇₃	—	2	2	no	—
318	C₂×C₂²⋊D₇₃	—	2	2	no	—
319	C₂×C₂²⋊D₇₃	—	2	2	no	—
320	D₄×D₇₃	—	8	4	no	—
321	C₂²×Dic₇₃	—	2	2	no	—
322	C₂²×Dic₇₃	—	2	2	no	—
323	C₂×C₄×D₇₃	—	2	2	no	—
324	C₂×C₄×D₇₃	—	2	2	no	—
325	C₂×C₄×D₇₃	—	2	2	no	—
326	C₂×C₄×D₇₃	—	2	2	no	—
327	C₂×C₄×D₇₃	—	2	2	no	—
328	C₂×C₄×D₇₃	—	2	2	no	—
329	C₂×C₄×D₇₃	—	2	2	no	—
330	C₂×C₄×D₇₃	—	2	2	no	—
331	C₂×C₄×D₇₃	—	2	2	no	—
332	C₂×C₄×D₇₃	—	8	4	no	—
333	Dic₂₉₂	—	2	2	no	—
334	#11924017	—	2	4	no	—
335	#11924017	—	4	2	no	—
336	#11924017	—	4	2	no	—
337	D₅₈₄	—	2	4	no	—
338	D₅₈₄	—	2	4	no	—
339	D₅₈₄	—	2	2	no	—
340	D₅₈₄	—	2	2	no	—
341	D₅₈₄	—	4	2	no	—
342	D₅₈₄	#41	1	4	yes	complemented
343	C₄⋊Dic₇₃	—	2	2	no	—
344	C₄⋊Dic₇₃	—	2	2	no	—
345	C₄⋊Dic₇₃	—	2	2	no	—
346	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
347	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
348	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
349	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
350	#11924007	—	2	2	no	—
351	#11924007	—	2	2	no	—
352	#11924007	—	2	2	no	—
353	#11924007	—	2	2	no	—
354	#11924007	—	2	2	no	—
355	#11924007	—	2	2	no	—
356	#11924007	—	2	2	no	—
357	#11924007	—	2	2	no	—
358	C₂²⋊Dic₇₃	—	2	2	no	—
359	C₂²⋊Dic₇₃	—	2	2	no	—
360	C₂²⋊Dic₇₃	—	2	2	no	—
361	#11924005	—	2	2	no	—
362	#11924005	—	2	2	no	—
363	#11924005	—	2	2	no	—
364	#11924005	—	2	2	no	—
365	#11924005	—	2	2	no	—
366	#11924005	—	2	2	no	—
367	#11924005	—	2	2	no	—
368	#11924005	—	2	2	no	—
369	#11924005	—	2	2	no	—
370	#11924005	—	2	2	no	—
371	#11924005	—	2	2	no	—
372	#11924005	—	2	2	no	—
373	#11924005	—	2	2	no	—
374	#11924005	—	2	2	no	—
375	#11924005	—	2	2	no	—
376	#11924005	—	2	2	no	—
377	C₄×Dic₇₃	—	2	2	no	—
378	C₄×Dic₇₃	—	2	2	no	—
379	C₄×Dic₇₃	—	2	2	no	—
380	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
381	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
382	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
383	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
386	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
387	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
388	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
389	M₁₆×C₇₃	—	4	1	no	—
390	M₁₆×C₇₃	—	4	1	no	—
391	C₂×C₈×C₇₃	—	2	2	no	—
392	C₂×C₈×C₇₃	—	2	2	no	—
393	C₂×C₈×C₇₃	—	2	2	no	—
394	C₂×C₈×C₇₃	—	4	1	no	—
395	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
398	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
404	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
405	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
406	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
407	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
411	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
412	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
413	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
414	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
415	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
416	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
417	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
418	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
419	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
420	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
421	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
422	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
423	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
424	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
425	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
428	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
429	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
430	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
431	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
432	C₂²×D₇₃	—	2	2	no	—
433	C₂²×D₇₃	—	2	2	no	—
434	C₂²×D₇₃	—	2	2	no	—
435	C₂²×D₇₃	—	4	4	no	—
436	C₂²×D₇₃	—	4	4	no	—
437	C₂²×D₇₃	—	4	4	no	—
438	C₂²×D₇₃	—	8	2	no	—
439	C₂²×D₇₃	—	8	2	no	—
440	C₂²×D₇₃	—	8	2	no	—
441	Q₈×C₇₃	—	4	1	no	—
442	D₄×C₇₃	—	2	2	no	—
443	D₄×C₇₃	—	2	2	no	—
444	D₄×C₇₃	—	4	1	no	—
445	C₂×C₄×C₇₃	—	2	2	no	—
446	C₂×C₄×C₇₃	—	2	1	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	—	4	1	no	—
453	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
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×D₄	1	1	yes	characteristic
463	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
465	C₂²⋊D₇₃	—	4	4	no	—
466	C₂²⋊D₇₃	—	4	4	no	—
467	C₂²⋊D₇₃	—	8	2	no	—
468	C₂²⋊D₇₃	—	8	2	no	—
469	C₂²⋊D₇₃	—	8	2	no	—
470	C₂×Dic₇₃	—	2	2	no	—
471	C₂×Dic₇₃	—	2	2	no	—
472	C₂×Dic₇₃	—	2	2	no	—
473	C₂×Dic₇₃	—	2	2	no	—
474	C₂×Dic₇₃	—	2	2	no	—
475	C₂×Dic₇₃	—	4	4	no	—
476	C₂×Dic₇₃	—	8	2	no	—
477	D₂₉₂	—	2	2	no	—
478	D₂₉₂	—	2	2	no	—
479	D₂₉₂	—	2	2	no	—
480	D₂₉₂	—	2	2	no	—
481	D₂₉₂	—	2	2	no	—
482	D₂₉₂	—	4	4	no	—
483	D₂₉₂	—	4	4	no	—
484	D₂₉₂	—	8	2	no	—
485	D₂₉₂	—	8	2	no	—
486	D₂₉₂	C₂×#41	1	4	yes	—
487	C₄×D₇₃	—	4	4	no	—
488	C₄×D₇₃	—	8	2	no	—
489	C₄×D₇₃	—	8	2	no	—
490	C₄×D₇₃	—	8	2	no	—
491	C₄×D₇₃	—	8	2	no	—
492	C₄×D₇₃	—	8	2	no	—
493	C₄×D₇₃	—	8	2	no	—
494	C₄×D₇₃	—	8	2	no	—
495	C₄×D₇₃	—	8	2	no	—
496	Dic₁₄₆	—	2	2	no	—
497	Dic₁₄₆	—	2	2	no	—
498	Dic₁₄₆	—	8	2	no	—
499	C₈×C₇₃	—	2	1	no	—
500	C₈×C₇₃	—	2	1	no	—
501	C₈×C₇₃	—	2	1	no	—
502	C₈×C₇₃	—	2	1	no	—
503	C₈×C₇₃	—	2	1	no	—
504	C₈×C₇₃	—	2	1	no	—
505	C₈×C₇₃	—	2	1	no	—
506	C₈×C₇₃	C₂×#41	1	2	yes	—
507	C₂²×C₇₃	—	2	1	no	—
508	C₂²×C₇₃	—	2	1	no	—
509	C₂²×C₇₃	—	2	1	no	—
510	C₂²×C₇₃	—	2	1	no	—
511	C₂²×C₇₃	—	2	1	no	—
512	C₂²×C₇₃	—	2	1	no	—
513	C₂²×C₇₃	—	2	1	no	—
514	C₂²×C₇₃	—	2	1	no	—
515	C₂²×C₇₃	#576	1	2	yes	—
516	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
517	C₂×D₇₃	—	2	4	no	—
518	C₂×D₇₃	—	4	2	no	—
519	C₂×D₇₃	—	4	2	no	—
520	C₂×D₇₃	—	4	2	no	—
521	C₂×D₇₃	—	4	2	no	—
522	C₂×D₇₃	—	4	2	no	—
523	C₂×D₇₃	—	4	2	no	—
524	C₂×D₇₃	—	4	2	no	—
525	C₂×D₇₃	—	4	2	no	—
526	C₂×D₇₃	—	8	8	no	—
527	C₂×D₇₃	—	16	4	no	—
528	C₄×C₇₃	—	2	1	no	—
529	C₄×C₇₃	—	2	1	no	—
530	C₄×C₇₃	—	2	1	no	—
531	C₄×C₇₃	—	2	1	no	—
532	C₄×C₇₃	—	2	1	no	—
533	C₄×C₇₃	—	2	1	no	—
534	C₄×C₇₃	—	2	1	no	—
535	C₄×C₇₃	—	2	1	no	—
536	C₄×C₇₃	—	2	1	no	—
537	C₄×C₇₃	—	2	1	no	—
538	C₄×C₇₃	—	2	1	no	—
539	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
540	C₄×C₇₃	#585	1	1	yes	characteristic
541	Dic₇₃	—	4	2	no	—
542	Dic₇₃	—	4	2	no	—
543	Dic₇₃	—	4	2	no	—
544	Dic₇₃	—	4	2	no	—
545	Dic₇₃	—	4	2	no	—
546	#61471	—	73	1	no	maximal, Sylow
547	C₂×C₇₃	—	2	2	no	—
548	C₂×C₇₃	—	4	1	no	—
549	C₂×C₇₃	—	4	1	no	—
550	C₂×C₇₃	D₄×#41	1	1	yes	characteristic
551	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
552	C₂×C₇₃	#3584	1	1	yes	characteristic
553	D₇₃	—	4	4	no	—
554	D₇₃	—	8	2	no	—
555	D₇₃	—	8	2	no	—
556	#3513	—	73	2	no	—
557	#3396	—	73	1	no	—
558	#3380	—	73	1	no	—
559	#3370	—	73	2	no	—
560	#3339	—	73	1	no	—
561	#3336	—	73	1	no	—
562	#3334	—	73	1	no	—
563	#3322	—	73	2	no	—
564	#3310	—	73	2	no	—
565	#3306	—	73	2	no	—
566	#3280	—	73	1	no	—
567	#3280	—	73	1	no	—
568	D₄×D₈	—	73	1	no	—
569	#3176	—	73	1	no	—
570	#3175	—	73	1	no	—
571	#3168	—	73	1	no	—
572	#3119	—	73	2	no	—
573	#3118	—	73	2	no	—
574	#3114	—	73	2	no	—
575	#2966	D₇₃	1	1	yes	characteristic, complemented
576	#2951	—	73	1	no	—
577	#2948	—	73	1	no	—
578	C₂×C₄×D₈	—	73	1	no	—
579	C₇₃	#61471	1	1	yes	characteristic, complemented, Sylow
580	C₂×#135	—	73	1	no	—
581	C₂²×D₈	—	73	1	no	—
582	C₂²×D₈	—	73	1	no	—
583	#559	—	73	2	no	—
584	#554	—	73	2	no	—
585	#553	—	73	2	no	—
586	#553	—	146	2	no	—
587	#552	—	73	2	no	—
588	#551	—	146	2	no	—
589	#551	—	146	2	no	—
590	#547	—	73	2	no	—
591	#546	—	73	2	no	—
592	#546	—	73	2	no	—
593	#546	—	146	2	no	—
594	D₄²	—	73	2	no	—
595	#542	—	73	2	no	—
596	#540	—	73	2	no	—
597	#539	—	146	2	no	—
598	#538	—	146	2	no	—
599	#529	—	73	2	no	—
600	#529	C₂×D₇₃	1	1	yes	characteristic
601	#525	—	146	2	no	—
602	C₂×#123	—	146	2	no	—
603	#520	—	73	2	no	—
604	#518	—	73	2	no	—
605	C₂×C₄×D₄	—	73	2	no	—
606	#500	—	73	1	no	—
607	#499	—	73	1	no	—
608	#499	—	73	1	no	—
609	#495	—	73	1	no	—
610	#495	—	73	1	no	—
611	#493	—	73	1	no	—
612	#490	—	73	2	no	—
613	#489	—	73	2	no	—
614	#488	—	73	2	no	—
615	#485	—	73	2	no	—
616	#483	—	73	2	no	—
617	#482	—	73	2	no	—
618	#481	—	73	2	no	—
619	#480	—	73	2	no	—
620	#480	—	73	2	no	—
621	#479	—	73	2	no	—
622	#478	—	73	2	no	—
623	#478	—	73	2	no	—
624	#478	—	73	2	no	—
625	#476	—	73	2	no	—
626	#474	—	73	2	no	—
627	#469	—	73	2	no	—
628	#468	—	73	2	no	—
629	#467	—	73	1	no	—
630	#467	—	73	1	no	—
631	#466	—	73	1	no	—
632	#466	—	73	1	no	—
633	#466	—	73	1	no	—
634	#466	—	73	1	no	—
635	#465	—	73	2	no	—
636	#463	—	73	2	no	—
637	#463	—	73	2	no	—
638	#463	—	73	2	no	—
639	#463	—	73	2	no	—
640	#460	—	73	2	no	—
641	#459	—	73	2	no	—
642	#450	—	73	2	no	—
643	#450	—	73	2	no	—
644	#449	—	73	2	no	—
645	#449	—	73	2	no	—
646	#447	—	73	2	no	—
647	#447	—	73	2	no	—
648	#446	C₂×D₇₃	1	1	yes	characteristic, complemented
649	C₈×Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
650	#442	—	73	2	no	—
651	#442	—	73	2	no	—
652	#442	—	73	2	no	—
653	#440	—	73	2	no	—
654	#440	—	73	2	no	—
655	#440	—	73	2	no	—
656	C₄×Q₁₆	—	73	1	no	—
657	C₄×Q₁₆	—	73	1	no	—
658	C₄×SD₁₆	—	73	2	no	—
659	C₄×D₈	—	73	1	no	—
660	C₄×D₈	—	73	1	no	—
661	C₄×D₈	—	73	2	no	—
662	C₄×D₈	—	73	2	no	—
663	C₄×D₈	—	73	1	no	—
664	C₄×D₈	—	73	1	no	—
665	C₄×D₈	—	73	1	no	—
666	C₄×D₈	—	73	1	no	—
667	C₄×D₈	—	73	1	no	—
668	C₄×D₈	—	73	1	no	—
669	#436	C₂×D₇₃	1	1	yes	characteristic, complemented
670	#435	C₂×D₇₃	1	1	yes	characteristic
671	#435	C₂×D₇₃	1	1	yes	characteristic, complemented
672	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic
673	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
674	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
675	#433	C₂×D₇₃	1	1	yes	characteristic, complemented
676	#433	C₂×D₇₃	1	1	yes	characteristic, complemented
677	#432	C₂×D₇₃	1	1	yes	characteristic, complemented
678	#427	—	73	1	no	—
679	C₂×#107	—	73	1	no	—
680	C₂×#107	—	73	1	no	—
681	#418	—	73	2	no	—
682	#417	—	73	2	no	—
683	C₂×#102	—	73	2	no	—
684	#405	C₂×D₇₃	1	1	yes	characteristic, complemented
685	#405	C₂×D₇₃	1	1	yes	characteristic, complemented
686	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
687	C₂×#41	—	73	2	no	—
688	C₂×#41	—	146	2	no	—
689	C₂²×D₄	—	73	2	no	—
690	C₂²×D₄	—	73	2	no	—
691	C₂²×D₄	—	146	2	no	—
692	C₂³×C₄	—	146	2	no	—
693	#135	—	146	4	no	—
694	C₂×Q₁₆	—	73	1	no	—
695	C₂×SD₁₆	—	73	2	no	—
696	C₂×SD₁₆	—	73	2	no	—
697	C₂×SD₁₆	—	73	2	no	—
698	C₂×D₈	—	73	2	no	—
699	C₂×D₈	—	73	1	no	—
700	C₂×D₈	—	73	2	no	—
701	C₂×D₈	—	73	1	no	—
702	C₂×D₈	—	73	1	no	—
703	C₂×D₈	—	73	2	no	—
704	C₂×D₈	—	146	4	no	—
705	C₂×D₈	—	146	4	no	—
706	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
707	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
708	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
709	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
710	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
711	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
712	C₄⋊Q₈	—	73	2	no	—
713	#127	—	73	2	no	—
714	#126	—	146	2	no	—
715	#126	—	146	2	no	—
716	#126	—	146	2	no	—
717	#126	—	146	2	no	—
718	#126	D₂₉₂	1	1	yes	characteristic
719	#126	D₂₉₂	1	1	yes	characteristic
720	#125	—	73	2	no	—
721	#125	—	73	2	no	—
722	#125	—	146	2	no	—
723	#125	D₂₉₂	1	1	yes	characteristic
724	#124	—	73	2	no	—
725	#124	—	73	2	no	—
726	#124	—	146	2	no	—
727	#124	—	146	2	no	—
728	#124	D₂₉₂	1	1	yes	characteristic
729	#123	—	146	2	no	—
730	#123	—	146	2	no	—
731	#123	—	146	2	no	—
732	#123	—	146	2	no	—
733	#123	—	146	2	no	—
734	#123	—	146	2	no	—
735	#123	—	146	2	no	—
736	#123	—	146	2	no	—
737	#123	—	146	2	no	—
738	#123	—	146	2	no	—
739	#123	—	146	2	no	—
740	#123	—	146	2	no	—
741	#123	D₂₉₂	1	1	yes	characteristic
742	#123	D₂₉₂	1	1	yes	characteristic
743	C₂²⋊Q₈	—	73	2	no	—
744	C₂²⋊Q₈	—	73	2	no	—
745	C₂²⋊Q₈	—	146	2	no	—
746	C₂²⋊Q₈	—	146	2	no	—
747	C₂²⋊Q₈	—	146	2	no	—
748	C₂²⋊Q₈	—	146	2	no	—
749	C₂²⋊Q₈	—	146	2	no	—
750	C₂²⋊Q₈	D₂₉₂	1	1	yes	characteristic
751	#121	—	73	2	no	—
752	#121	—	73	2	no	—
753	#121	—	73	2	no	—
754	#121	—	73	2	no	—
755	#121	—	146	2	no	—
756	#121	—	146	2	no	—
757	#121	—	146	2	no	—
758	#121	—	146	2	no	—
759	#121	—	146	2	no	—
760	#121	—	146	2	no	—
761	#121	D₂₉₂	1	1	yes	characteristic
762	#120	—	146	2	no	—
763	#120	—	146	2	no	—
764	#120	—	146	2	no	—
765	#120	—	146	2	no	—
766	C₄×Q₈	—	73	2	no	—
767	C₄×Q₈	—	73	2	no	—
768	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
769	C₄×D₄	—	73	2	no	—
770	C₄×D₄	—	73	2	no	—
771	C₄×D₄	—	73	2	no	—
772	C₄×D₄	—	73	2	no	—
773	C₄×D₄	—	73	2	no	—
774	C₄×D₄	—	73	2	no	—
775	C₄×D₄	—	73	2	no	—
776	C₄×D₄	—	73	2	no	—
777	C₄×D₄	—	146	2	no	—
778	C₄×D₄	—	146	2	no	—
779	C₄×D₄	—	146	2	no	—
780	C₄×D₄	—	146	2	no	—
781	C₄×D₄	—	146	2	no	—
782	C₄×D₄	—	146	2	no	—
783	C₄×D₄	—	146	2	no	—
784	C₄×D₄	—	146	2	no	—
785	C₄×D₄	—	146	2	no	—
786	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
787	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
788	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
789	#117	—	73	2	no	—
790	#117	—	146	2	no	—
791	#117	—	146	2	no	—
792	#117	—	146	2	no	—
793	#117	C₂²×D₇₃	1	1	yes	characteristic
794	#117	C₂²×D₇₃	1	1	yes	characteristic
795	C₂×C₄⋊C₄	—	73	2	no	—
796	C₂×C₄⋊C₄	—	73	2	no	—
797	C₂×C₄⋊C₄	—	146	2	no	—
798	C₂×C₄⋊C₄	—	146	2	no	—
799	C₂×C₂²⋊C₄	—	146	2	no	—
800	C₂×C₂²⋊C₄	—	146	2	no	—
801	C₂×C₂²⋊C₄	—	146	2	no	—
802	C₂×C₂²⋊C₄	—	146	2	no	—
803	C₂×C₂²⋊C₄	—	146	2	no	—
804	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
805	#107	—	73	1	no	—
806	#107	—	73	1	no	—
807	#107	—	73	2	no	—
808	#107	—	73	1	no	—
809	#107	—	73	2	no	—
810	#107	—	73	1	no	—
811	#107	—	73	2	no	—
812	#106	—	73	2	no	—
813	#106	—	73	2	no	—
814	#106	—	73	2	no	—
815	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
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	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
821	#103	—	73	2	no	—
822	#103	—	73	2	no	—
823	#103	—	73	2	no	—
824	#103	—	73	2	no	—
825	#102	—	73	2	no	—
826	#102	—	73	2	no	—
827	#102	—	73	2	no	—
828	#102	—	73	2	no	—
829	#102	—	73	2	no	—
830	#102	—	73	2	no	—
831	#102	—	73	2	no	—
832	#102	—	73	2	no	—
833	#102	—	73	2	no	—
834	#102	—	73	2	no	—
835	#102	—	73	2	no	—
836	#102	—	73	2	no	—
837	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
838	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
839	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
840	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
841	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
842	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
843	#97	C₂²×D₇₃	1	1	yes	characteristic
844	#97	C₂²×D₇₃	1	1	yes	characteristic
845	#97	C₂²×D₇₃	1	1	yes	characteristic
846	#97	C₂²×D₇₃	1	1	yes	characteristic
847	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
848	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
849	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
850	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
852	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
853	C₂⁴	—	146	2	no	—
854	C₂⁴	—	146	2	no	—
855	#41	—	292	2	no	—
856	#41	—	584	4	no	—
857	#41	—	146	4	no	—
858	C₂×Q₈	—	73	2	no	—
859	C₂×Q₈	—	146	2	no	—
860	C₂×Q₈	C₂×D₂₉₂	1	1	yes	characteristic
861	C₂×D₄	—	292	2	no	—
862	C₂×D₄	—	292	2	no	—
863	C₂×D₄	—	584	4	no	—
864	C₂×D₄	—	73	2	no	—
865	C₂×D₄	—	73	2	no	—
866	C₂×D₄	—	73	2	no	—
867	C₂×D₄	—	146	4	no	—
868	C₂×D₄	—	146	4	no	—
869	C₂×D₄	—	146	2	no	—
870	C₂×D₄	—	146	2	no	—
871	C₂×D₄	—	146	2	no	—
872	C₂×D₄	—	146	2	no	—
873	C₂×D₄	—	146	2	no	—
874	C₂×D₄	—	146	2	no	—
875	C₂×D₄	—	146	2	no	—
876	C₂×D₄	—	146	2	no	—
877	C₂×D₄	—	146	2	no	—
878	C₂×D₄	C₂×D₂₉₂	1	1	yes	characteristic
879	C₂×D₄	C₂×D₂₉₂	1	1	yes	characteristic
880	C₂×D₄	C₂×D₂₉₂	1	1	yes	characteristic
881	C₂²×C₄	—	584	4	no	—
882	C₂²×C₄	—	146	2	no	—
883	C₂²×C₄	—	146	2	no	—
884	C₂²×C₄	—	146	2	no	—
885	C₂²×C₄	—	146	2	no	—
886	C₂²×C₄	—	146	2	no	—
887	C₂²×C₄	—	146	2	no	—
888	C₂²×C₄	—	146	2	no	—
889	C₂²×C₄	—	146	2	no	—
890	C₂²×C₄	—	146	2	no	—
891	C₂²×C₄	—	146	2	no	—
892	C₂²×C₄	—	146	2	no	—
893	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
895	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
896	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
897	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
898	Q₁₆	—	146	2	no	—
899	SD₁₆	—	292	2	no	—
900	SD₁₆	—	292	2	no	—
901	SD₁₆	—	146	4	no	—
902	D₈	—	292	2	no	—
903	D₈	—	73	4	no	—
904	D₈	—	146	4	no	—
905	D₈	—	146	4	no	—
906	D₈	—	146	2	no	—
907	D₈	—	146	2	no	—
908	M₁₆	—	4	1	no	—
909	M₁₆	—	4	1	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	—	4	1	no	—
914	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
916	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
917	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
918	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
920	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
922	C₄⋊C₄	—	73	2	no	—
923	C₄⋊C₄	—	73	2	no	—
924	C₄⋊C₄	—	73	2	no	—
925	C₄⋊C₄	—	73	2	no	—
926	C₄⋊C₄	—	146	2	no	—
927	C₄⋊C₄	—	146	2	no	—
928	C₄⋊C₄	—	146	2	no	—
929	C₄⋊C₄	—	146	2	no	—
930	C₄⋊C₄	—	146	2	no	—
931	C₄⋊C₄	—	146	2	no	—
932	C₄⋊C₄	—	146	2	no	—
933	C₄⋊C₄	—	146	2	no	—
934	C₄⋊C₄	—	146	2	no	—
935	C₄⋊C₄	—	146	2	no	—
936	C₄⋊C₄	—	146	2	no	—
937	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
938	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
945	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
947	C₂²⋊C₄	—	146	2	no	—
948	C₂²⋊C₄	—	146	2	no	—
949	C₂²⋊C₄	—	146	2	no	—
950	C₂²⋊C₄	—	146	2	no	—
951	C₂²⋊C₄	—	146	2	no	—
952	C₂²⋊C₄	—	146	2	no	—
953	C₂²⋊C₄	—	146	2	no	—
954	C₂²⋊C₄	—	146	2	no	—
955	C₂²⋊C₄	—	146	2	no	—
956	C₂²⋊C₄	—	146	2	no	—
957	C₂²⋊C₄	—	146	2	no	—
958	C₂²⋊C₄	—	146	2	no	—
959	C₂²⋊C₄	—	146	2	no	—
960	C₂²⋊C₄	—	146	2	no	—
961	C₂²⋊C₄	—	146	2	no	—
962	C₂²⋊C₄	—	146	2	no	—
963	C₂²⋊C₄	—	146	2	no	—
964	C₂²⋊C₄	—	146	2	no	—
965	C₂²⋊C₄	—	146	2	no	—
966	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
967	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
968	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
969	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
970	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
971	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
972	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
973	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
974	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
975	C₂²⋊C₄	C₂×D₂₉₂	1	1	yes	characteristic
976	C₄²	—	146	2	no	—
977	C₄²	—	146	2	no	—
978	C₄²	—	146	2	no	—
979	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
980	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
981	C₄²	C₂³×D₇₃	1	1	yes	characteristic
982	C₄²	C₂³×D₇₃	1	1	yes	characteristic
983	C₄²	C₂³×D₇₃	1	1	yes	characteristic
984	C₄²	C₂³×D₇₃	1	1	yes	characteristic
985	C₂³	—	292	4	no	—
986	C₂³	—	292	4	no	—
987	C₂³	—	292	4	no	—
988	C₂³	—	584	2	no	—
989	C₂³	—	584	2	no	—
990	C₂³	—	584	2	no	—
991	C₂³	—	146	2	no	—
992	C₂³	—	146	2	no	—
993	C₂³	—	146	2	no	—
994	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
995	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
996	C₂³	C₂²×D₂₉₂	1	1	yes	characteristic
997	Q₈	—	4	1	no	—
998	Q₈	—	584	2	no	—
999	Q₈	—	146	2	no	—
1000	Q₈	—	146	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	4	1	no	—
1004	D₄	—	292	4	no	—
1005	D₄	—	292	4	no	—
1006	D₄	—	292	4	no	—
1007	D₄	—	292	4	no	—
1008	D₄	—	584	2	no	—
1009	D₄	—	584	2	no	—
1010	D₄	—	584	2	no	—
1011	D₄	—	584	2	no	—
1012	D₄	—	584	2	no	—
1013	D₄	—	73	4	no	—
1014	D₄	—	146	2	no	—
1015	D₄	—	146	2	no	—
1016	D₄	—	146	2	no	—
1017	D₄	—	146	2	no	—
1018	D₄	—	146	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	4	1	no	—
1027	C₂×C₄	—	292	4	no	—
1028	C₂×C₄	—	292	4	no	—
1029	C₂×C₄	—	584	2	no	—
1030	C₂×C₄	—	584	2	no	—
1031	C₂×C₄	—	584	2	no	—
1032	C₂×C₄	—	584	2	no	—
1033	C₂×C₄	—	584	2	no	—
1034	C₂×C₄	—	584	2	no	—
1035	C₂×C₄	—	584	2	no	—
1036	C₂×C₄	—	584	2	no	—
1037	C₂×C₄	—	584	2	no	—
1038	C₂×C₄	—	146	2	no	—
1039	C₂×C₄	—	146	2	no	—
1040	C₂×C₄	—	146	2	no	—
1041	C₂×C₄	—	146	2	no	—
1042	C₂×C₄	—	146	2	no	—
1043	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
1054	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	1	no	—
1062	C₈	#41×D₇₃	1	2	yes	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	292	2	no	—
1072	C₂²	—	292	2	no	—
1073	C₂²	—	292	2	no	—
1074	C₂²	—	292	2	no	—
1075	C₂²	—	292	2	no	—
1076	C₂²	—	292	2	no	—
1077	C₂²	—	292	2	no	—
1078	C₂²	—	292	2	no	—
1079	C₂²	—	584	8	no	—
1080	C₂²	—	1168	4	no	—
1081	C₂²	—	146	4	no	—
1082	C₂²	#17989392	1	2	yes	—
1083	C₂²	C₂³×D₂₉₂	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	292	2	no	—
1096	C₄	—	292	2	no	—
1097	C₄	—	292	2	no	—
1098	C₄	—	292	2	no	—
1099	C₄	—	292	2	no	—
1100	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1101	C₄	#17989423	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	1	no	—
1104	C₂	—	4	1	no	—
1105	C₂	—	292	4	no	—
1106	C₂	—	584	2	no	—
1107	C₂	—	584	2	no	—
1108	C₂	#41×D₂₉₂	1	1	yes	characteristic
1109	C₂	C₂×#17989392	1	1	yes	characteristic
1110	C₂	#22624705	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₂₉₂
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#2966	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#2966	D₇₃
hypocenter	C₇₃	#61471
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #22623875	C₂	semidirect
2. #22622944	C₂	semidirect
3. #22622799	C₂	semidirect
4. #22622686	C₂	semidirect
5. #22622334	C₂	semidirect
6. #22622300	C₂	semidirect
7. #22622279	C₂	semidirect
8. #22622134	C₂	semidirect
9. #22621954	C₂	semidirect
10. #22621894	C₂	semidirect
11. #22621618	C₂	semidirect
12. #22621618	C₂	semidirect
13. D₄×D₅₈₄	C₂	semidirect
14. #22620581	C₂	semidirect
15. #22620570	C₂	semidirect
16. #22620501	C₂	semidirect
17. #22620132	C₂	semidirect
18. #22620117	C₂	semidirect
19. #22620071	C₂	semidirect
20. #22618808	C₂	semidirect
21. #22618784	C₂	semidirect
22. C₂×C₄×D₅₈₄	C₂	semidirect
23. C₇₃×#2966	C₂	semidirect
27. #17989322	C₂²	semidirect
28. #17989297	C₂²	semidirect
30. #17989283	C₂²	semidirect
34. #17989241	C₂²	semidirect
35. #17989233	C₂²	semidirect
36. #17989233	C₂²	semidirect
39. #17989208	C₂²	semidirect
40. #17989192	C₂²	semidirect
43. #17989121	C₂²	semidirect
46. #17989067	C₂²	semidirect
47. #17989061	C₂²	semidirect
48. C₂×C₄×D₂₉₂	C₂²	semidirect
49. #17988992	C₂²	semidirect
50. #17988989	C₂²	semidirect
51. #17988989	C₂²	semidirect
52. #17988971	C₂²	semidirect
53. #17988971	C₂²	semidirect
55. #17988952	C₂²	semidirect
56. #17988947	C₂²	semidirect
57. #17988942	C₂²	semidirect
58. #17988929	C₂²	semidirect
59. #17988918	C₂²	semidirect
60. #17988912	C₂²	semidirect
61. #17988906	C₂²	semidirect
62. #17988901	C₂²	semidirect
63. #17988901	C₂²	semidirect
64. #17988895	C₂²	semidirect
65. #17988888	C₂²	semidirect
66. #17988888	C₂²	semidirect
67. #17988888	C₂²	semidirect
68. #17988878	C₂²	semidirect
69. #17988868	C₂²	semidirect
70. #17988840	C₂²	semidirect
71. #17988833	C₂²	semidirect
72. #17988828	C₂²	semidirect
73. #17988828	C₂²	semidirect
76. #17988823	C₂²	semidirect
77. #17988823	C₂²	semidirect
78. #17988816	C₂²	semidirect
79. #17988803	C₂²	semidirect
80. #17988803	C₂²	semidirect
81. #17988803	C₂²	semidirect
82. #17988803	C₂²	semidirect
83. #17988788	C₂²	semidirect
85. #17988740	C₂²	semidirect
86. #17988740	C₂²	semidirect
87. #17988734	C₂²	semidirect
88. #17988734	C₂²	semidirect
91. #17988700	C₂²	semidirect
92. #17988700	C₂²	semidirect
93. #17988700	C₂²	semidirect
94. #17988689	C₂²	semidirect
95. #17988689	C₂²	semidirect
96. #17988689	C₂²	semidirect
97. C₄×Dic₂₉₂	C₂²	semidirect
98. C₄×Dic₂₉₂	C₂²	semidirect
99. C₄×#11924017	C₂²	semidirect
104. C₄×D₅₈₄	C₂²	semidirect
105. C₄×D₅₈₄	C₂²	semidirect
106. C₄×D₅₈₄	C₂²	semidirect
107. C₄×D₅₈₄	C₂²	semidirect
108. C₄×D₅₈₄	C₂²	semidirect
109. C₄×D₅₈₄	C₂²	semidirect
110. #17988625	C₂²	semidirect
111. C₂×#14556525	C₂²	semidirect
112. C₂×#14556525	C₂²	semidirect
113. #17988593	C₂²	semidirect
114. #17988589	C₂²	semidirect
115. C₂×#14556513	C₂²	semidirect
117. #446×C₇₃	C₂²	semidirect
118. C₈×Q₈×C₇₃	C₂²	semidirect
119. #436×C₇₃	C₂²	semidirect
121. #435×C₇₃	C₂²	semidirect
123. C₈×D₄×C₇₃	C₂²	semidirect
124. C₈×D₄×C₇₃	C₂²	semidirect
125. #433×C₇₃	C₂²	semidirect
126. #433×C₇₃	C₂²	semidirect
127. #432×C₇₃	C₂²	semidirect
128. #405×C₇₃	C₂²	semidirect
129. #405×C₇₃	C₂²	semidirect
130. C₂×C₄×C₈×C₇₃	C₂²	semidirect
342. D₅₈₄	#41	semidirect
575. #2966	D₇₃	semidirect
579. C₇₃	#61471	semidirect
648. #446	C₂×D₇₃	semidirect
649. C₈×Q₈	C₂×D₇₃	semidirect
669. #436	C₂×D₇₃	semidirect
671. #435	C₂×D₇₃	semidirect
673. C₈×D₄	C₂×D₇₃	semidirect
674. C₈×D₄	C₂×D₇₃	semidirect
675. #433	C₂×D₇₃	semidirect
676. #433	C₂×D₇₃	semidirect
677. #432	C₂×D₇₃	semidirect
684. #405	C₂×D₇₃	semidirect
685. #405	C₂×D₇₃	semidirect
686. C₂×C₄×C₈	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623875	2
#22622944	2
#22622799	2
#22622686	2
#22622334	2
#22622300	2
#22622279	2
#22622134	2
#22621954	2
#22621894	2
#22621618	2
D₄×D₅₈₄	2
#22620581	2
#22620570	2
#22620501	2
#22620132	2
#22620117	2
#22620071	2
#22618808	2
#22618784	2
C₂×C₄×D₅₈₄	2
C₇₃×#2966	2
#61471	73