Subgroups — #3339×D₇₃ #33964448

Order 18688.

1994 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#553×D₇₃	C₂	1	2	yes	maximal, complemented
2	#22622336	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622335	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622334	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622333	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622332	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622331	C₂	1	2	yes	maximal, complemented
8	#22622330	C₂	1	2	yes	maximal, complemented
9	#22622329	C₂	1	1	yes	maximal, characteristic, complemented
10	#22622328	C₂	1	1	yes	maximal, characteristic, complemented
11	#22622327	C₂	1	2	yes	maximal, complemented
12	#22622326	C₂	1	2	yes	maximal, complemented
13	#499×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#481×D₇₃	C₂	1	2	yes	maximal, complemented
15	#482×D₇₃	C₂	1	2	yes	maximal, complemented
16	#478×D₇₃	C₂	1	2	yes	maximal, complemented
17	#466×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#466×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
20	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#427×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#107×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3339	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
27	#17989290	C₂²	1	2	yes	complemented
28	#17989289	C₂²	1	2	yes	complemented
29	#17989288	—	2	2	no	—
30	#17989287	C₂²	1	2	yes	complemented
31	#17989286	—	2	2	no	—
32	#17989285	C₂²	1	2	yes	complemented
33	#17989284	C₂²	1	2	yes	complemented
34	#17989283	C₂²	1	2	yes	complemented
35	#17989282	—	2	2	no	—
36	#17989281	C₂²	1	2	yes	complemented
37	#17989280	—	2	2	no	—
38	#126×D₇₃	—	2	2	no	—
39	#125×D₇₃	C₂²	1	2	yes	—
40	#123×D₇₃	—	2	2	no	—
41	#121×D₇₃	—	2	2	no	—
42	#121×D₇₃	C₂²	1	2	yes	—
43	#121×D₇₃	C₂²	1	2	yes	—
44	C₄×D₄×D₇₃	—	2	2	no	—
45	C₄×D₄×D₇₃	C₂²	1	2	yes	—
46	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
47	#117×D₇₃	C₂²	1	2	yes	—
48	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
49	#17988989	C₂²	1	1	yes	characteristic, complemented
50	#17988988	C₂²	1	1	yes	characteristic, complemented
51	#17988988	C₂²	1	1	yes	characteristic, complemented
52	#17988987	C₂²	1	2	yes	complemented
53	#17988986	C₂²	1	2	yes	complemented
54	#17988914	C₂²	1	2	yes	complemented
55	#17988913	C₂²	1	2	yes	complemented
56	#17988912	C₂²	1	2	yes	complemented
57	#17988911	C₂²	1	2	yes	complemented
58	#17988910	C₂²	1	2	yes	complemented
59	#17988909	C₂²	1	2	yes	complemented
60	#17988908	C₂²	1	2	yes	complemented
61	#17988907	C₂²	1	2	yes	complemented
62	#17988907	C₂²	1	2	yes	complemented
63	#17988906	C₂²	1	2	yes	complemented
64	#17988905	C₂²	1	2	yes	complemented
65	#17988904	C₂²	1	2	yes	complemented
66	#17988904	C₂²	1	2	yes	complemented
67	#17988903	C₂²	1	2	yes	complemented
68	#17988890	C₂²	1	2	yes	complemented
69	#17988889	C₂²	1	2	yes	complemented
70	#17988888	C₂²	1	2	yes	complemented
71	#17988887	C₂²	1	2	yes	complemented
72	#17988886	C₂²	1	2	yes	complemented
73	#17988885	C₂²	1	2	yes	complemented
74	#17988884	C₂²	1	2	yes	complemented
75	#17988824	C₂²	1	1	yes	characteristic, complemented
76	#17988824	C₂²	1	1	yes	characteristic, complemented
77	#17988823	C₂²	1	1	yes	characteristic, complemented
78	#17988823	C₂²	1	1	yes	characteristic, complemented
79	#17988822	C₂²	1	2	yes	complemented
80	#17988822	C₂²	1	2	yes	complemented
81	#17988821	C₂²	1	2	yes	complemented
82	#17988821	C₂²	1	2	yes	complemented
83	#17988820	C₂²	1	1	yes	characteristic, complemented
84	#17988820	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₅₈₄	C₂²	1	1	yes	characteristic, complemented
86	D₈×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
87	#17988669	C₂²	1	1	yes	characteristic, complemented
88	C₄×#11924013	C₂²	1	2	yes	complemented
89	#17988667	C₂²	1	2	yes	complemented
90	C₈×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
91	D₄×#10596831	C₂²	1	1	yes	characteristic, complemented
92	#17988652	C₂²	1	1	yes	characteristic, complemented
93	C₈×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
94	C₈×C₂²⋊D₇₃	C₂²	1	1	yes	characteristic, complemented
95	#17988650	C₂²	1	1	yes	characteristic, complemented
96	#17988650	C₂²	1	1	yes	characteristic, complemented
97	#17988625	C₂²	1	1	yes	characteristic, complemented
98	#17988624	C₂²	1	1	yes	characteristic, complemented
99	#17988624	C₂²	1	1	yes	characteristic, complemented
100	#17988623	C₂²	1	2	yes	complemented
101	#17988622	C₂²	1	2	yes	complemented
102	C₂×#14556525	C₂²	1	1	yes	characteristic, complemented
103	C₂×#14556524	C₂²	1	2	yes	complemented
104	#107×D₇₃	C₂²	1	1	yes	characteristic
105	#107×D₇₃	C₂²	1	1	yes	characteristic
106	#107×D₇₃	C₂²	1	2	yes	—
107	#107×D₇₃	C₂²	1	1	yes	characteristic
108	#107×D₇₃	C₂²	1	2	yes	complemented
109	#107×D₇₃	C₂²	1	1	yes	characteristic, complemented
110	#107×D₇₃	C₂²	1	1	yes	characteristic, complemented
111	#106×D₇₃	C₂²	1	2	yes	—
112	#106×D₇₃	C₂²	1	2	yes	—
113	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
114	#102×D₇₃	C₂²	1	2	yes	—
115	#102×D₇₃	C₂²	1	2	yes	—
116	#102×D₇₃	C₂²	1	2	yes	—
117	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
118	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
120	#553×C₇₃	C₂²	1	2	yes	complemented
121	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
122	#482×C₇₃	C₂²	1	2	yes	complemented
123	#481×C₇₃	C₂²	1	2	yes	complemented
124	#478×C₇₃	C₂²	1	2	yes	complemented
125	#466×C₇₃	C₂²	1	1	yes	characteristic, complemented
126	#466×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
128	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
129	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×D₄×D₇₃	—	2	2	no	—
132	C₂×D₄×D₇₃	—	2	2	no	—
133	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
134	C₂×D₄×D₇₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₇₃	—	2	2	no	—
136	C₂²×C₄×D₇₃	—	2	2	no	—
137	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
139	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
140	C₂×#11924013	C₂³	1	2	yes	—
141	D₈×D₇₃	—	2	4	no	—
142	C₂²×#10596831	C₂³	1	1	yes	characteristic
143	C₂²×#10596831	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₇₃	—	2	4	no	—
145	C₂×C₈×D₇₃	—	2	4	no	—
146	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
154	#14556586	—	2	2	no	—
155	#14556586	—	2	2	no	—
156	#14556586	—	2	2	no	—
157	#14556585	—	2	2	no	—
158	#14556584	—	2	2	no	—
159	#14556584	—	2	2	no	—
160	#14556584	—	2	2	no	—
161	#14556583	C₂³	1	2	yes	—
162	#14556582	C₂³	1	2	yes	—
163	#14556582	C₂³	1	2	yes	—
164	#14556581	—	2	2	no	—
165	#14556581	—	2	2	no	—
166	#14556576	—	2	2	no	—
167	#14556576	—	2	2	no	—
168	#14556575	—	2	2	no	—
169	#14556574	—	2	2	no	—
170	#14556573	—	2	2	no	—
171	#14556573	—	2	2	no	—
172	#14556572	—	2	2	no	—
173	#14556566	—	2	2	no	—
174	#14556566	C₂³	1	2	yes	—
175	#14556566	C₂³	1	2	yes	—
176	#14556565	—	2	2	no	—
177	#14556565	C₂³	1	2	yes	—
178	#14556565	C₂³	1	2	yes	—
179	#14556564	—	2	2	no	—
180	#14556564	—	2	2	no	—
181	#14556564	—	2	2	no	—
182	#14556564	—	2	2	no	—
183	#14556563	—	2	2	no	—
184	#14556563	—	2	2	no	—
185	#14556563	—	2	2	no	—
186	#14556563	—	2	2	no	—
187	#14556562	—	2	2	no	—
188	#14556562	C₂³	1	2	yes	—
189	#14556562	C₂³	1	2	yes	—
190	C₄×D₂₉₂	—	2	2	no	—
191	C₄×D₂₉₂	C₂³	1	2	yes	—
192	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
193	D₄×Dic₇₃	—	2	2	no	—
194	D₄×Dic₇₃	D₄	1	1	yes	characteristic
195	D₄×Dic₇₃	C₂³	1	2	yes	—
196	#14556553	—	2	2	no	—
197	#14556553	D₄	1	1	yes	characteristic
198	#14556553	C₂³	1	2	yes	—
199	C₄×C₂²⋊D₇₃	—	2	2	no	—
200	C₄×C₂²⋊D₇₃	—	2	2	no	—
201	C₄×C₂²⋊D₇₃	—	2	2	no	—
202	C₄×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
203	C₄×C₂²⋊D₇₃	C₂³	1	1	yes	characteristic
204	#14556551	—	2	2	no	—
205	#14556551	—	2	2	no	—
206	#14556551	—	2	2	no	—
207	#14556551	D₄	1	1	yes	characteristic
208	#14556551	D₄	1	1	yes	characteristic
209	#14556550	C₂³	1	2	yes	—
210	#14556549	C₂³	1	2	yes	—
211	#14556549	C₂³	1	2	yes	—
212	#14556548	—	2	2	no	—
213	#14556547	—	2	2	no	—
214	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
215	C₂×#11924007	—	2	2	no	—
216	C₄⋊C₄×D₇₃	—	2	2	no	—
217	C₄⋊C₄×D₇₃	—	2	2	no	—
218	C₄⋊C₄×D₇₃	—	2	2	no	—
219	C₄⋊C₄×D₇₃	—	2	2	no	—
220	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
221	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
222	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
223	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
224	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
225	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×D₇₃	—	2	2	no	—
227	C₂²⋊C₄×D₇₃	—	2	2	no	—
228	C₂²⋊C₄×D₇₃	—	2	2	no	—
229	C₂²⋊C₄×D₇₃	—	2	2	no	—
230	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
231	C₂²⋊C₄×D₇₃	D₄	1	1	yes	characteristic
232	C₄²×D₇₃	—	2	2	no	—
233	C₄²×D₇₃	C₂³	1	1	yes	characteristic
234	#14556525	C₂³	1	1	yes	characteristic
235	#14556525	C₂³	1	2	yes	—
236	#14556525	C₂³	1	1	yes	characteristic
237	#14556525	C₂³	1	1	yes	characteristic
238	#14556524	C₂³	1	2	yes	—
239	#14556524	C₂³	1	2	yes	—
240	#14556524	C₂³	1	2	yes	—
241	#14556524	C₂³	1	2	yes	—
242	#14556524	C₂³	1	2	yes	—
243	#14556523	C₂³	1	2	yes	—
244	#14556523	C₂³	1	2	yes	—
245	#14556522	C₂³	1	2	yes	—
246	#14556522	C₂³	1	2	yes	—
247	#14556522	C₂³	1	2	yes	—
248	#14556522	C₂³	1	2	yes	—
249	C₄⋊#10596831	C₂³	1	1	yes	characteristic
250	#14556520	C₂³	1	1	yes	characteristic
251	#14556520	C₂³	1	1	yes	characteristic
252	#14556513	C₂³	1	2	yes	—
253	#14556513	C₂³	1	2	yes	—
254	#14556513	C₂³	1	2	yes	—
255	#14556512	C₂³	1	2	yes	—
256	#14556512	C₂³	1	2	yes	—
257	#14556512	C₂³	1	2	yes	—
258	#14556511	C₂³	1	2	yes	—
259	#14556511	C₂³	1	2	yes	—
260	#14556511	C₂³	1	2	yes	—
261	C₂²⋊#10596831	C₂³	1	1	yes	characteristic
262	C₂²⋊#10596831	C₂³	1	1	yes	characteristic
263	#14556503	C₂³	1	1	yes	characteristic
264	#14556503	C₂³	1	1	yes	characteristic
265	#14556503	C₂³	1	1	yes	characteristic
266	#14556503	C₂³	1	1	yes	characteristic
267	C₄×#10596831	C₂³	1	1	yes	characteristic
268	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
270	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
273	#126×C₇₃	—	2	2	no	—
274	#125×C₇₃	C₂³	1	2	yes	—
275	#123×C₇₃	—	2	2	no	—
276	#121×C₇₃	—	2	2	no	—
277	#121×C₇₃	C₂³	1	2	yes	—
278	#121×C₇₃	C₂³	1	2	yes	—
279	C₄×D₄×C₇₃	—	2	2	no	—
280	C₄×D₄×C₇₃	C₂³	1	2	yes	—
281	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
282	#117×C₇₃	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
284	#107×C₇₃	C₂³	1	1	yes	characteristic
285	#107×C₇₃	C₂³	1	2	yes	—
286	#107×C₇₃	C₂³	1	1	yes	characteristic
287	#107×C₇₃	C₂³	1	1	yes	characteristic
288	#106×C₇₃	C₂³	1	2	yes	—
289	#106×C₇₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
291	#102×C₇₃	C₂³	1	2	yes	—
292	#102×C₇₃	C₂³	1	2	yes	—
293	#102×C₇₃	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
295	C₂²⋊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	C₂×D₄	1	1	yes	characteristic
299	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
300	C₂×D₂₉₂	—	2	2	no	—
301	C₂×D₂₉₂	—	2	2	no	—
302	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
303	C₂×D₂₉₂	C₂⁴	1	2	yes	—
304	C₂×C₂²⋊D₇₃	—	2	2	no	—
305	C₂×C₂²⋊D₇₃	—	2	2	no	—
306	C₂×C₂²⋊D₇₃	—	2	2	no	—
307	C₂×C₂²⋊D₇₃	—	2	2	no	—
308	C₂×C₂²⋊D₇₃	—	2	2	no	—
309	C₂×C₂²⋊D₇₃	C₂×D₄	1	1	yes	characteristic
310	C₂×C₂²⋊D₇₃	C₂×D₄	1	1	yes	characteristic
311	D₄×D₇₃	—	2	4	no	—
312	D₄×D₇₃	—	2	4	no	—
313	D₄×D₇₃	—	2	4	no	—
314	D₄×D₇₃	—	4	8	no	—
315	D₄×D₇₃	—	8	4	no	—
316	C₂²×Dic₇₃	—	2	2	no	—
317	C₂²×Dic₇₃	—	2	2	no	—
318	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
320	C₂×C₄×D₇₃	—	2	2	no	—
321	C₂×C₄×D₇₃	—	2	2	no	—
322	C₂×C₄×D₇₃	—	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	—	8	4	no	—
332	C₂×C₄×D₇₃	—	8	4	no	—
333	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
336	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
337	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
338	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
339	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
342	D₅₈₄	—	2	2	no	—
343	#11924013	—	2	4	no	—
344	C₂×#10596831	—	2	2	no	—
345	C₂×#10596831	—	2	2	no	—
346	C₂×#10596831	C₂⁴	1	1	yes	characteristic
347	C₂×#10596831	C₂⁴	1	1	yes	characteristic
348	C₂×#10596831	C₂⁴	1	1	yes	characteristic
349	C₂×#10596831	C₂⁴	1	1	yes	characteristic
350	C₈×D₇₃	—	2	2	no	—
351	C₈×D₇₃	—	2	2	no	—
352	C₈×D₇₃	—	2	2	no	—
353	C₈×D₇₃	—	2	2	no	—
354	C₈×D₇₃	—	2	2	no	—
355	C₈×D₇₃	—	2	2	no	—
356	C₈×D₇₃	—	2	2	no	—
357	C₈×D₇₃	#41	1	4	yes	—
358	C₄⋊Dic₇₃	—	2	2	no	—
359	C₄⋊Dic₇₃	—	2	2	no	—
360	C₄⋊Dic₇₃	—	2	2	no	—
361	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
362	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
363	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
364	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
365	#11924007	—	2	2	no	—
366	#11924007	—	2	2	no	—
367	#11924007	—	2	2	no	—
368	#11924007	—	2	2	no	—
369	#11924007	—	2	2	no	—
370	#11924007	—	2	2	no	—
371	#11924007	—	2	2	no	—
372	#11924007	—	2	2	no	—
373	#11924007	—	2	2	no	—
374	#11924007	C₂×D₄	1	1	yes	characteristic
375	#11924007	C₂×D₄	1	1	yes	characteristic
376	C₂²⋊Dic₇₃	—	2	2	no	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	—	2	2	no	—
379	C₂²⋊Dic₇₃	—	2	2	no	—
380	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
381	C₂²⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
391	#11924005	C₂×D₄	1	1	yes	characteristic
392	#11924005	C₂×D₄	1	1	yes	characteristic
393	#11924005	C₂×D₄	1	1	yes	characteristic
394	C₄×Dic₇₃	—	2	2	no	—
395	C₄×Dic₇₃	—	2	2	no	—
396	C₄×Dic₇₃	—	2	2	no	—
397	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
398	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
399	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
400	C₂×D₄×C₇₃	—	2	2	no	—
401	C₂×D₄×C₇₃	—	2	2	no	—
402	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
403	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
404	C₂²×C₄×C₇₃	—	2	2	no	—
405	C₂²×C₄×C₇₃	—	2	2	no	—
406	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
407	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
408	D₈×C₇₃	—	2	2	no	—
409	C₂×C₈×C₇₃	—	2	2	no	—
410	C₂×C₈×C₇₃	—	2	2	no	—
411	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
413	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
415	C₄⋊C₄×C₇₃	—	2	2	no	—
416	C₄⋊C₄×C₇₃	—	2	2	no	—
417	C₄⋊C₄×C₇₃	—	2	2	no	—
418	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
420	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
421	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
422	C₂²⋊C₄×C₇₃	—	2	2	no	—
423	C₂²⋊C₄×C₇₃	—	2	2	no	—
424	C₂²⋊C₄×C₇₃	—	2	2	no	—
425	C₂²⋊C₄×C₇₃	—	2	2	no	—
426	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
427	C₂²⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
428	C₄²×C₇₃	—	2	2	no	—
429	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
430	C₂³×C₇₃	—	2	2	no	—
431	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₇₃	—	2	2	no	—
434	C₂²×D₇₃	—	2	2	no	—
435	C₂²×D₇₃	—	2	2	no	—
436	C₂²×D₇₃	—	2	2	no	—
437	C₂²×D₇₃	—	2	2	no	—
438	C₂²×D₇₃	—	2	2	no	—
439	C₂²×D₇₃	—	4	4	no	—
440	C₂²×D₇₃	—	4	4	no	—
441	C₂²×D₇₃	—	4	4	no	—
442	C₂²×D₇₃	#135	1	4	yes	—
443	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
444	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
445	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
446	D₄×C₇₃	—	2	2	no	—
447	D₄×C₇₃	—	2	2	no	—
448	D₄×C₇₃	—	2	2	no	—
449	D₄×C₇₃	—	4	4	no	—
450	D₄×C₇₃	—	8	2	no	—
451	C₂×C₄×C₇₃	—	2	1	no	—
452	C₂×C₄×C₇₃	—	2	1	no	—
453	C₂×C₄×C₇₃	—	2	1	no	—
454	C₂×C₄×C₇₃	—	2	1	no	—
455	C₂×C₄×C₇₃	—	2	2	no	—
456	C₂×C₄×C₇₃	—	2	2	no	—
457	C₂×C₄×C₇₃	—	2	2	no	—
458	C₂×C₄×C₇₃	—	8	2	no	—
459	C₂×C₄×C₇₃	—	8	2	no	—
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	—	2	2	no	—
466	C₂²⋊D₇₃	—	2	2	no	—
467	C₂²⋊D₇₃	—	4	4	no	—
468	C₂²⋊D₇₃	—	4	4	no	—
469	C₂²⋊D₇₃	—	4	4	no	—
470	C₂²⋊D₇₃	—	8	2	no	—
471	C₂²⋊D₇₃	—	8	2	no	—
472	C₂×Dic₇₃	—	2	2	no	—
473	C₂×Dic₇₃	—	2	2	no	—
474	C₂×Dic₇₃	—	2	2	no	—
475	C₂×Dic₇₃	—	2	2	no	—
476	C₂×Dic₇₃	—	2	2	no	—
477	C₂×Dic₇₃	—	8	2	no	—
478	C₂×Dic₇₃	—	8	2	no	—
479	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
484	D₂₉₂	—	2	2	no	—
485	D₂₉₂	—	2	2	no	—
486	D₂₉₂	—	2	2	no	—
487	D₂₉₂	—	4	4	no	—
488	D₂₉₂	—	8	2	no	—
489	C₄×D₇₃	—	2	2	no	—
490	C₄×D₇₃	—	2	2	no	—
491	C₄×D₇₃	—	2	2	no	—
492	C₄×D₇₃	—	2	2	no	—
493	C₄×D₇₃	—	2	1	no	—
494	C₄×D₇₃	—	2	1	no	—
495	C₄×D₇₃	—	2	1	no	—
496	C₄×D₇₃	—	2	1	no	—
497	C₄×D₇₃	—	2	2	no	—
498	C₄×D₇₃	—	2	2	no	—
499	C₄×D₇₃	—	4	4	no	—
500	C₄×D₇₃	—	4	4	no	—
501	C₄×D₇₃	—	4	4	no	—
502	C₄×D₇₃	—	8	2	no	—
503	C₄×D₇₃	—	8	2	no	—
504	C₄×D₇₃	—	8	2	no	—
505	C₄×D₇₃	—	8	2	no	—
506	C₄×D₇₃	C₂×#41	1	2	yes	—
507	C₄×D₇₃	2₋¹⁺⁴	1	2	yes	—
508	C₈×C₇₃	—	2	1	no	—
509	C₈×C₇₃	—	2	1	no	—
510	C₈×C₇₃	—	2	1	no	—
511	C₈×C₇₃	C₂×#41	1	2	yes	—
512	#10596831	—	2	1	no	—
513	#10596831	—	2	1	no	—
514	#10596831	—	2	1	no	—
515	#10596831	C₂×#41	1	2	yes	—
516	C₂²×C₇₃	—	2	1	no	—
517	C₂²×C₇₃	—	2	1	no	—
518	C₂²×C₇₃	—	2	1	no	—
519	C₂²×C₇₃	—	2	1	no	—
520	C₂²×C₇₃	—	2	1	no	—
521	C₂²×C₇₃	—	4	2	no	—
522	C₂²×C₇₃	—	4	2	no	—
523	C₂²×C₇₃	—	4	2	no	—
524	C₂²×C₇₃	C₂×#135	1	2	yes	—
525	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
526	C₂×D₇₃	—	2	1	no	—
527	C₂×D₇₃	—	2	1	no	—
528	C₂×D₇₃	—	2	8	no	—
529	C₂×D₇₃	—	2	1	no	—
530	C₂×D₇₃	—	2	1	no	—
531	C₂×D₇₃	—	2	1	no	—
532	C₂×D₇₃	—	4	4	no	—
533	C₂×D₇₃	—	4	2	no	—
534	C₂×D₇₃	—	4	2	no	—
535	C₂×D₇₃	—	4	2	no	—
536	C₂×D₇₃	—	8	8	no	—
537	C₂×D₇₃	#547	1	2	yes	—
538	C₂×D₇₃	C₂×#135	1	2	yes	—
539	C₂×D₇₃	C₂×#135	1	2	yes	—
540	C₂×D₇₃	#576	1	2	yes	—
541	C₄×C₇₃	—	2	1	no	—
542	C₄×C₇₃	—	2	1	no	—
543	C₄×C₇₃	—	2	1	no	—
544	C₄×C₇₃	—	2	1	no	—
545	C₄×C₇₃	—	4	2	no	—
546	C₄×C₇₃	—	4	2	no	—
547	C₄×C₇₃	—	4	2	no	—
548	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
549	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
550	Dic₇₃	—	2	1	no	—
551	Dic₇₃	—	2	1	no	—
552	Dic₇₃	—	2	1	no	—
553	Dic₇₃	—	2	1	no	—
554	Dic₇₃	—	4	2	no	—
555	Dic₇₃	—	4	2	no	—
556	Dic₇₃	—	4	2	no	—
557	Dic₇₃	#547	1	2	yes	—
558	C₂×#3339	—	73	1	no	maximal, Sylow
559	C₂×C₇₃	—	2	2	no	—
560	C₂×C₇₃	—	4	1	no	—
561	C₂×C₇₃	—	8	2	no	—
562	C₂×C₇₃	C₂×#547	1	1	yes	characteristic
563	C₂×C₇₃	C₂²×#135	1	1	yes	characteristic
564	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
565	D₇₃	—	2	2	no	—
566	D₇₃	—	4	1	no	—
567	D₇₃	—	8	2	no	—
568	D₇₃	#3339	1	4	yes	direct product factor
569	C₂×#553	—	73	2	no	—
570	#3339	—	73	1	no	—
571	#3339	—	73	2	no	—
572	#3339	—	73	2	no	—
573	#3339	—	73	2	no	—
574	#3339	—	73	1	no	—
575	#3339	—	73	1	no	—
576	#3339	—	73	1	no	—
577	#3339	—	73	1	no	—
578	#3339	—	73	1	no	—
579	#3339	—	73	1	no	—
580	#3339	—	73	2	no	—
581	#3339	D₇₃	1	1	yes	characteristic, direct product factor
582	C₂×#499	—	73	1	no	—
583	C₂×#481	—	73	2	no	—
584	C₂×#482	—	73	2	no	—
585	C₂×#478	—	73	2	no	—
586	C₂×#466	—	73	1	no	—
587	C₂×#466	—	73	1	no	—
588	C₂×C₄×D₈	—	73	1	no	—
589	C₂×C₈×D₄	—	73	1	no	—
590	C₂×#427	—	73	1	no	—
591	C₂²×#107	—	73	1	no	—
592	C₇₃	C₂×#3339	1	1	yes	characteristic, complemented, Sylow
593	C₂²×D₈	—	73	1	no	—
594	C₂³×C₈	—	73	1	no	—
595	C₂³×C₈	—	73	1	no	—
596	#553	—	73	2	no	—
597	#553	—	73	2	no	—
598	#553	—	73	2	no	—
599	#553	—	73	2	no	—
600	#553	—	73	2	no	—
601	#553	—	73	2	no	—
602	#553	—	73	2	no	—
603	#553	—	146	2	no	—
604	#553	—	146	2	no	—
605	#553	—	146	2	no	—
606	#553	—	146	2	no	—
607	#553	C₂×D₇₃	1	2	yes	complemented
608	C₂×#126	—	146	2	no	—
609	C₂×#125	—	73	2	no	—
610	C₂×#123	—	146	2	no	—
611	C₂×#121	—	73	2	no	—
612	C₂×#121	—	73	2	no	—
613	C₂×#121	—	146	2	no	—
614	C₂×C₄×D₄	—	73	1	no	—
615	C₂×C₄×D₄	—	73	2	no	—
616	C₂×C₄×D₄	—	146	2	no	—
617	C₂×#117	—	73	2	no	—
618	C₂²×C₄⋊C₄	—	73	2	no	—
619	#499	—	73	2	no	—
620	#499	—	73	1	no	—
621	#499	—	73	1	no	—
622	#499	—	73	2	no	—
623	#499	—	73	1	no	—
624	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
625	#482	—	73	2	no	—
626	#482	—	73	2	no	—
627	#482	—	73	2	no	—
628	#482	—	73	2	no	—
629	#482	—	73	2	no	—
630	#482	—	73	2	no	—
631	#482	—	73	2	no	—
632	#482	C₂×D₇₃	1	2	yes	complemented
633	#481	—	73	2	no	—
634	#481	—	73	2	no	—
635	#481	—	73	2	no	—
636	#481	—	73	2	no	—
637	#481	—	73	2	no	—
638	#481	—	73	2	no	—
639	#481	—	73	2	no	—
640	#481	C₂×D₇₃	1	2	yes	complemented
641	#478	—	73	2	no	—
642	#478	—	73	2	no	—
643	#478	—	73	2	no	—
644	#478	—	73	2	no	—
645	#478	—	73	2	no	—
646	#478	—	73	2	no	—
647	#478	—	73	2	no	—
648	#478	C₂×D₇₃	1	2	yes	complemented
649	#466	—	73	1	no	—
650	#466	—	73	1	no	—
651	#466	—	73	1	no	—
652	#466	—	73	1	no	—
653	#466	—	73	2	no	—
654	#466	—	73	2	no	—
655	#466	—	73	1	no	—
656	#466	—	73	1	no	—
657	#466	—	73	2	no	—
658	#466	—	73	2	no	—
659	#466	C₂×D₇₃	1	1	yes	characteristic, complemented
660	#466	C₂×D₇₃	1	1	yes	characteristic, complemented
661	C₄×D₈	—	73	1	no	—
662	C₄×D₈	—	73	2	no	—
663	C₄×D₈	—	73	1	no	—
664	C₄×D₈	—	73	2	no	—
665	C₄×D₈	—	73	1	no	—
666	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic, complemented
667	C₈×D₄	—	73	1	no	—
668	C₈×D₄	—	73	1	no	—
669	C₈×D₄	—	73	1	no	—
670	C₈×D₄	—	73	1	no	—
671	C₈×D₄	—	73	1	no	—
672	C₈×D₄	—	73	1	no	—
673	C₈×D₄	—	73	1	no	—
674	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
675	#427	—	73	1	no	—
676	#427	—	73	2	no	—
677	#427	—	73	1	no	—
678	#427	—	73	1	no	—
679	#427	—	73	2	no	—
680	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
681	C₂×#107	—	73	1	no	—
682	C₂×#107	—	73	2	no	—
683	C₂×#107	—	73	2	no	—
684	C₂×#107	—	73	1	no	—
685	C₂×#107	—	73	1	no	—
686	C₂×#107	—	73	2	no	—
687	C₂×#107	—	73	1	no	—
688	C₂×#107	—	73	1	no	—
689	C₂×#107	—	73	1	no	—
690	C₂×#107	C₂×D₇₃	1	1	yes	characteristic, complemented
691	C₂×#106	—	73	2	no	—
692	C₂×#106	—	73	2	no	—
693	C₂×C₄⋊C₈	—	73	1	no	—
694	C₂×#102	—	73	2	no	—
695	C₂×#102	—	73	2	no	—
696	C₂×#102	—	73	2	no	—
697	C₂×C₂²⋊C₈	—	73	1	no	—
698	C₂×C₂²⋊C₈	—	73	1	no	—
699	C₂×C₄×C₈	—	73	1	no	—
700	C₂²×D₄	—	73	1	no	—
701	C₂²×D₄	—	73	2	no	—
702	C₂²×D₄	—	146	2	no	—
703	C₂²×D₄	—	146	2	no	—
704	C₂³×C₄	—	73	1	no	—
705	C₂³×C₄	—	73	1	no	—
706	C₂³×C₄	—	146	2	no	—
707	C₂³×C₄	—	146	2	no	—
708	C₂×D₈	—	73	2	no	—
709	C₂×D₈	—	73	1	no	—
710	C₂×D₈	—	146	4	no	—
711	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
712	C₂²×C₈	—	73	1	no	—
713	C₂²×C₈	—	73	1	no	—
714	C₂²×C₈	—	73	1	no	—
715	C₂²×C₈	—	73	1	no	—
716	C₂²×C₈	—	73	1	no	—
717	C₂²×C₈	—	73	1	no	—
718	C₂²×C₈	—	73	1	no	—
719	C₂²×C₈	—	73	1	no	—
720	C₂²×C₈	—	73	1	no	—
721	C₂²×C₈	—	73	1	no	—
722	C₂²×C₈	—	146	4	no	—
723	C₂²×C₈	—	146	4	no	—
724	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
725	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
726	#126	—	2	2	no	—
727	#126	—	146	2	no	—
728	#126	—	146	2	no	—
729	#126	—	146	2	no	—
730	#126	—	146	2	no	—
731	#126	—	146	2	no	—
732	#126	—	146	2	no	—
733	#126	—	146	2	no	—
734	#125	—	73	2	no	—
735	#125	—	73	2	no	—
736	#125	—	73	2	no	—
737	#125	—	146	2	no	—
738	#125	—	146	2	no	—
739	#125	C₂²×D₇₃	1	2	yes	—
740	#123	—	2	2	no	—
741	#123	—	146	2	no	—
742	#123	—	146	2	no	—
743	#123	—	146	2	no	—
744	#123	—	146	2	no	—
745	#123	—	146	2	no	—
746	#123	—	146	2	no	—
747	#123	—	146	2	no	—
748	#121	—	2	2	no	—
749	#121	—	73	2	no	—
750	#121	—	73	2	no	—
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	—	146	2	no	—
762	#121	—	146	2	no	—
763	#121	—	146	2	no	—
764	#121	—	146	2	no	—
765	#121	—	146	2	no	—
766	#121	C₂²×D₇₃	1	2	yes	—
767	#121	C₂²×D₇₃	1	2	yes	—
768	C₄×D₄	—	2	2	no	—
769	C₄×D₄	—	73	1	no	—
770	C₄×D₄	—	73	1	no	—
771	C₄×D₄	—	73	1	no	—
772	C₄×D₄	—	73	1	no	—
773	C₄×D₄	—	73	1	no	—
774	C₄×D₄	—	73	1	no	—
775	C₄×D₄	—	73	2	no	—
776	C₄×D₄	—	73	2	no	—
777	C₄×D₄	—	73	1	no	—
778	C₄×D₄	—	73	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	—	146	2	no	—
787	C₄×D₄	—	146	2	no	—
788	C₄×D₄	C₂²×D₇₃	1	2	yes	—
789	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
790	#117	—	73	2	no	—
791	#117	—	73	2	no	—
792	#117	—	73	2	no	—
793	#117	—	146	2	no	—
794	#117	—	146	2	no	—
795	#117	C₂²×D₇₃	1	2	yes	—
796	C₂×C₄⋊C₄	—	73	1	no	—
797	C₂×C₄⋊C₄	—	73	2	no	—
798	C₂×C₄⋊C₄	—	73	2	no	—
799	C₂×C₄⋊C₄	—	73	2	no	—
800	C₂×C₄⋊C₄	—	73	2	no	—
801	C₂×C₄⋊C₄	—	73	2	no	—
802	C₂×C₄⋊C₄	—	73	2	no	—
803	C₂×C₄⋊C₄	—	146	2	no	—
804	C₂×C₄⋊C₄	—	146	2	no	—
805	C₂×C₄⋊C₄	—	146	2	no	—
806	C₂×C₄⋊C₄	—	146	2	no	—
807	C₂×C₄⋊C₄	—	146	2	no	—
808	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
809	C₂×C₂²⋊C₄	—	73	1	no	—
810	C₂×C₂²⋊C₄	—	73	1	no	—
811	C₂×C₂²⋊C₄	—	146	2	no	—
812	C₂×C₂²⋊C₄	—	146	2	no	—
813	C₂×C₂²⋊C₄	—	146	2	no	—
814	C₂×C₂²⋊C₄	—	146	2	no	—
815	C₂×C₄²	—	73	1	no	—
816	C₂×C₄²	—	146	2	no	—
817	#107	—	73	1	no	—
818	#107	—	73	1	no	—
819	#107	—	73	2	no	—
820	#107	—	73	1	no	—
821	#107	—	73	2	no	—
822	#107	—	73	2	no	—
823	#107	—	73	2	no	—
824	#107	—	73	2	no	—
825	#107	—	73	2	no	—
826	#107	C₂²×D₇₃	1	1	yes	characteristic
827	#107	C₂²×D₇₃	1	1	yes	characteristic
828	#107	C₂²×D₇₃	1	2	yes	—
829	#107	C₂²×D₇₃	1	1	yes	characteristic
830	#106	—	73	2	no	—
831	#106	—	73	2	no	—
832	#106	—	73	2	no	—
833	#106	—	73	2	no	—
834	#106	—	73	2	no	—
835	#106	—	73	2	no	—
836	#106	C₂²×D₇₃	1	2	yes	—
837	#106	C₂²×D₇₃	1	2	yes	—
838	C₄⋊C₈	—	73	1	no	—
839	C₄⋊C₈	—	73	1	no	—
840	C₄⋊C₈	—	73	1	no	—
841	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
842	#102	—	73	2	no	—
843	#102	—	73	2	no	—
844	#102	—	73	2	no	—
845	#102	—	73	2	no	—
846	#102	—	73	2	no	—
847	#102	—	73	2	no	—
848	#102	—	73	2	no	—
849	#102	—	73	2	no	—
850	#102	—	73	2	no	—
851	#102	C₂²×D₇₃	1	2	yes	—
852	#102	C₂²×D₇₃	1	2	yes	—
853	#102	C₂²×D₇₃	1	2	yes	—
854	C₂²⋊C₈	—	73	1	no	—
855	C₂²⋊C₈	—	73	1	no	—
856	C₂²⋊C₈	—	73	1	no	—
857	C₂²⋊C₈	—	73	1	no	—
858	C₂²⋊C₈	—	73	1	no	—
859	C₂²⋊C₈	—	73	1	no	—
860	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
861	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
862	C₄×C₈	—	73	1	no	—
863	C₄×C₈	—	73	1	no	—
864	C₄×C₈	—	73	1	no	—
865	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
866	C₂⁴	—	73	1	no	—
867	C₂⁴	—	73	1	no	—
868	C₂⁴	—	146	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	292	8	no	—
872	C₂×D₄	—	584	4	no	—
873	C₂×D₄	—	73	1	no	—
874	C₂×D₄	—	73	1	no	—
875	C₂×D₄	—	73	1	no	—
876	C₂×D₄	—	73	2	no	—
877	C₂×D₄	—	146	2	no	—
878	C₂×D₄	—	146	2	no	—
879	C₂×D₄	—	146	4	no	—
880	C₂×D₄	—	146	4	no	—
881	C₂×D₄	—	146	2	no	—
882	C₂×D₄	—	146	4	no	—
883	C₂×D₄	—	146	2	no	—
884	C₂×D₄	—	146	2	no	—
885	C₂×D₄	—	146	2	no	—
886	C₂×D₄	—	146	2	no	—
887	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
888	C₂×D₄	C₂³×D₇₃	1	2	yes	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	2	2	no	—
891	C₂²×C₄	—	584	4	no	—
892	C₂²×C₄	—	584	4	no	—
893	C₂²×C₄	—	73	1	no	—
894	C₂²×C₄	—	73	1	no	—
895	C₂²×C₄	—	73	1	no	—
896	C₂²×C₄	—	73	1	no	—
897	C₂²×C₄	—	73	1	no	—
898	C₂²×C₄	—	73	1	no	—
899	C₂²×C₄	—	73	1	no	—
900	C₂²×C₄	—	73	1	no	—
901	C₂²×C₄	—	73	1	no	—
902	C₂²×C₄	—	73	1	no	—
903	C₂²×C₄	—	73	1	no	—
904	C₂²×C₄	—	146	2	no	—
905	C₂²×C₄	—	146	2	no	—
906	C₂²×C₄	—	146	2	no	—
907	C₂²×C₄	—	146	2	no	—
908	C₂²×C₄	—	146	2	no	—
909	C₂²×C₄	—	146	2	no	—
910	C₂²×C₄	—	146	2	no	—
911	C₂²×C₄	—	146	2	no	—
912	C₂²×C₄	—	146	2	no	—
913	C₂²×C₄	—	146	2	no	—
914	C₂²×C₄	—	146	2	no	—
915	C₂²×C₄	—	146	2	no	—
916	C₂²×C₄	—	146	2	no	—
917	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
918	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
919	D₈	—	2	2	no	—
920	D₈	—	146	4	no	—
921	D₈	—	146	2	no	—
922	C₂×C₈	—	2	2	no	—
923	C₂×C₈	—	2	2	no	—
924	C₂×C₈	—	73	1	no	—
925	C₂×C₈	—	73	4	no	—
926	C₂×C₈	—	73	1	no	—
927	C₂×C₈	—	73	1	no	—
928	C₂×C₈	—	73	1	no	—
929	C₂×C₈	—	146	2	no	—
930	C₂×C₈	—	146	2	no	—
931	C₂×C₈	—	146	2	no	—
932	C₂×C₈	—	146	2	no	—
933	C₂×C₈	—	146	2	no	—
934	C₂×C₈	—	146	2	no	—
935	C₂×C₈	—	146	2	no	—
936	C₂×C₈	—	146	2	no	—
937	C₂×C₈	—	146	2	no	—
938	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
939	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
940	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
941	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	73	1	no	—
946	C₄⋊C₄	—	73	1	no	—
947	C₄⋊C₄	—	73	1	no	—
948	C₄⋊C₄	—	73	2	no	—
949	C₄⋊C₄	—	73	2	no	—
950	C₄⋊C₄	—	73	2	no	—
951	C₄⋊C₄	—	146	2	no	—
952	C₄⋊C₄	—	146	2	no	—
953	C₄⋊C₄	—	146	2	no	—
954	C₄⋊C₄	—	146	2	no	—
955	C₄⋊C₄	—	146	2	no	—
956	C₄⋊C₄	—	146	2	no	—
957	C₄⋊C₄	—	146	2	no	—
958	C₄⋊C₄	—	146	2	no	—
959	C₄⋊C₄	—	146	2	no	—
960	C₄⋊C₄	—	146	2	no	—
961	C₄⋊C₄	—	146	2	no	—
962	C₄⋊C₄	—	146	2	no	—
963	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
964	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
965	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
966	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	73	1	no	—
972	C₂²⋊C₄	—	73	1	no	—
973	C₂²⋊C₄	—	73	1	no	—
974	C₂²⋊C₄	—	73	1	no	—
975	C₂²⋊C₄	—	73	1	no	—
976	C₂²⋊C₄	—	73	1	no	—
977	C₂²⋊C₄	—	146	2	no	—
978	C₂²⋊C₄	—	146	2	no	—
979	C₂²⋊C₄	—	146	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	2	no	—
987	C₂²⋊C₄	—	146	2	no	—
988	C₂²⋊C₄	—	146	2	no	—
989	C₂²⋊C₄	D₄×D₇₃	1	1	yes	characteristic
990	C₂²⋊C₄	D₄×D₇₃	1	1	yes	characteristic
991	C₄²	—	2	2	no	—
992	C₄²	—	73	1	no	—
993	C₄²	—	73	1	no	—
994	C₄²	—	73	1	no	—
995	C₄²	—	146	2	no	—
996	C₄²	—	146	2	no	—
997	C₄²	—	146	2	no	—
998	C₄²	C₂³×D₇₃	1	1	yes	characteristic
999	C₂³	—	2	2	no	—
1000	C₂³	—	292	4	no	—
1001	C₂³	—	292	4	no	—
1002	C₂³	—	292	4	no	—
1003	C₂³	—	73	1	no	—
1004	C₂³	—	73	1	no	—
1005	C₂³	—	73	4	no	—
1006	C₂³	—	73	1	no	—
1007	C₂³	—	146	2	no	—
1008	C₂³	—	146	2	no	—
1009	C₂³	—	146	2	no	—
1010	C₂³	—	146	2	no	—
1011	C₂³	—	146	2	no	—
1012	C₂³	—	146	2	no	—
1013	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1014	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1015	D₄	—	2	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	4	4	no	—
1019	D₄	—	8	2	no	—
1020	D₄	—	292	4	no	—
1021	D₄	—	292	4	no	—
1022	D₄	—	292	4	no	—
1023	D₄	—	292	4	no	—
1024	D₄	—	584	2	no	—
1025	D₄	—	584	2	no	—
1026	D₄	—	584	2	no	—
1027	D₄	—	146	2	no	—
1028	D₄	—	146	2	no	—
1029	D₄	—	146	2	no	—
1030	D₄	—	146	2	no	—
1031	D₄	—	146	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	8	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	292	4	no	—
1042	C₂×C₄	—	292	4	no	—
1043	C₂×C₄	—	292	4	no	—
1044	C₂×C₄	—	584	2	no	—
1045	C₂×C₄	—	584	2	no	—
1046	C₂×C₄	—	584	2	no	—
1047	C₂×C₄	—	584	2	no	—
1048	C₂×C₄	—	584	2	no	—
1049	C₂×C₄	—	584	2	no	—
1050	C₂×C₄	—	73	1	no	—
1051	C₂×C₄	—	73	2	no	—
1052	C₂×C₄	—	73	2	no	—
1053	C₂×C₄	—	73	1	no	—
1054	C₂×C₄	—	73	1	no	—
1055	C₂×C₄	—	73	1	no	—
1056	C₂×C₄	—	73	1	no	—
1057	C₂×C₄	—	146	2	no	—
1058	C₂×C₄	—	146	2	no	—
1059	C₂×C₄	—	146	2	no	—
1060	C₂×C₄	—	146	2	no	—
1061	C₂×C₄	—	146	2	no	—
1062	C₂×C₄	—	146	2	no	—
1063	C₂×C₄	—	146	2	no	—
1064	C₂×C₄	—	146	2	no	—
1065	C₂×C₄	—	146	2	no	—
1066	C₂×C₄	—	146	2	no	—
1067	C₂×C₄	—	146	2	no	—
1068	C₂×C₄	—	146	1	no	—
1069	C₂×C₄	—	146	1	no	—
1070	C₂×C₄	—	146	1	no	—
1071	C₂×C₄	—	146	1	no	—
1072	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1073	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1074	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1075	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1076	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	2	1	no	—
1080	C₈	—	73	2	no	—
1081	C₈	—	146	1	no	—
1082	C₈	—	146	1	no	—
1083	C₈	—	146	1	no	—
1084	C₈	#41×D₇₃	1	2	yes	—
1085	C₂²	—	2	1	no	—
1086	C₂²	—	2	1	no	—
1087	C₂²	—	2	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	4	2	no	—
1092	C₂²	—	4	2	no	—
1093	C₂²	—	292	4	no	—
1094	C₂²	—	292	2	no	—
1095	C₂²	—	292	2	no	—
1096	C₂²	—	292	2	no	—
1097	C₂²	—	584	8	no	—
1098	C₂²	—	73	2	no	—
1099	C₂²	—	73	2	no	—
1100	C₂²	—	73	2	no	—
1101	C₂²	—	73	2	no	—
1102	C₂²	—	146	8	no	—
1103	C₂²	—	146	1	no	—
1104	C₂²	—	146	1	no	—
1105	C₂²	—	146	1	no	—
1106	C₂²	—	146	1	no	—
1107	C₂²	—	146	1	no	—
1108	C₂²	#135×D₇₃	1	2	yes	—
1109	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1110	C₄	—	2	1	no	—
1111	C₄	—	2	1	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	2	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	2	no	—
1116	C₄	—	4	2	no	—
1117	C₄	—	292	2	no	—
1118	C₄	—	292	2	no	—
1119	C₄	—	292	2	no	—
1120	C₄	—	73	2	no	—
1121	C₄	—	146	1	no	—
1122	C₄	—	146	1	no	—
1123	C₄	—	146	1	no	—
1124	C₄	—	146	1	no	—
1125	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1126	C₄	2₋¹⁺⁴×D₇₃	1	1	yes	characteristic
1127	C₂	—	2	2	no	—
1128	C₂	—	4	1	no	—
1129	C₂	—	8	2	no	—
1130	C₂	—	292	1	no	—
1131	C₂	—	584	2	no	—
1132	C₂	—	73	4	no	—
1133	C₂	—	146	2	no	—
1134	C₂	#547×D₇₃	1	1	yes	characteristic
1135	C₂	C₂×#135×D₇₃	1	1	yes	characteristic
1136	C₂	#576×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3339	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#3339	D₇₃
hypocenter	C₇₃	C₂×#3339
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3339

Complements

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

N	H ≅ G/N	type
1. #553×D₇₃	C₂	semidirect
2. #22622336	C₂	semidirect
3. #22622335	C₂	semidirect
4. #22622334	C₂	semidirect
5. #22622333	C₂	semidirect
6. #22622332	C₂	semidirect
7. #22622331	C₂	semidirect
8. #22622330	C₂	semidirect
9. #22622329	C₂	semidirect
10. #22622328	C₂	semidirect
11. #22622327	C₂	semidirect
12. #22622326	C₂	semidirect
13. #499×D₇₃	C₂	semidirect
14. #481×D₇₃	C₂	semidirect
15. #482×D₇₃	C₂	semidirect
16. #478×D₇₃	C₂	semidirect
17. #466×D₇₃	C₂	semidirect
18. #466×D₇₃	C₂	semidirect
19. C₄×D₈×D₇₃	C₂	semidirect
20. C₈×D₄×D₇₃	C₂	semidirect
21. #427×D₇₃	C₂	semidirect
22. C₂×#107×D₇₃	C₂	semidirect
23. C₇₃×#3339	C₂	semidirect
27. #17989290	C₂²	semidirect
28. #17989289	C₂²	semidirect
30. #17989287	C₂²	semidirect
32. #17989285	C₂²	semidirect
33. #17989284	C₂²	semidirect
34. #17989283	C₂²	semidirect
36. #17989281	C₂²	semidirect
49. #17988989	C₂²	semidirect
50. #17988988	C₂²	semidirect
51. #17988988	C₂²	semidirect
52. #17988987	C₂²	semidirect
53. #17988986	C₂²	semidirect
54. #17988914	C₂²	semidirect
55. #17988913	C₂²	semidirect
56. #17988912	C₂²	semidirect
57. #17988911	C₂²	semidirect
58. #17988910	C₂²	semidirect
59. #17988909	C₂²	semidirect
60. #17988908	C₂²	semidirect
61. #17988907	C₂²	semidirect
62. #17988907	C₂²	semidirect
63. #17988906	C₂²	semidirect
64. #17988905	C₂²	semidirect
65. #17988904	C₂²	semidirect
66. #17988904	C₂²	semidirect
67. #17988903	C₂²	semidirect
68. #17988890	C₂²	semidirect
69. #17988889	C₂²	semidirect
70. #17988888	C₂²	semidirect
71. #17988887	C₂²	semidirect
72. #17988886	C₂²	semidirect
73. #17988885	C₂²	semidirect
74. #17988884	C₂²	semidirect
75. #17988824	C₂²	semidirect
76. #17988824	C₂²	semidirect
77. #17988823	C₂²	semidirect
78. #17988823	C₂²	semidirect
79. #17988822	C₂²	semidirect
80. #17988822	C₂²	semidirect
81. #17988821	C₂²	semidirect
82. #17988821	C₂²	semidirect
83. #17988820	C₂²	semidirect
84. #17988820	C₂²	semidirect
85. C₄×D₅₈₄	C₂²	semidirect
86. D₈×Dic₇₃	C₂²	semidirect
87. #17988669	C₂²	semidirect
88. C₄×#11924013	C₂²	semidirect
89. #17988667	C₂²	semidirect
90. C₈×D₂₉₂	C₂²	semidirect
91. D₄×#10596831	C₂²	semidirect
92. #17988652	C₂²	semidirect
93. C₈×C₂²⋊D₇₃	C₂²	semidirect
94. C₈×C₂²⋊D₇₃	C₂²	semidirect
95. #17988650	C₂²	semidirect
96. #17988650	C₂²	semidirect
97. #17988625	C₂²	semidirect
98. #17988624	C₂²	semidirect
99. #17988624	C₂²	semidirect
100. #17988623	C₂²	semidirect
101. #17988622	C₂²	semidirect
102. C₂×#14556525	C₂²	semidirect
103. C₂×#14556524	C₂²	semidirect
108. #107×D₇₃	C₂²	semidirect
109. #107×D₇₃	C₂²	semidirect
110. #107×D₇₃	C₂²	semidirect
120. #553×C₇₃	C₂²	semidirect
121. #499×C₇₃	C₂²	semidirect
122. #482×C₇₃	C₂²	semidirect
123. #481×C₇₃	C₂²	semidirect
124. #478×C₇₃	C₂²	semidirect
125. #466×C₇₃	C₂²	semidirect
126. #466×C₇₃	C₂²	semidirect
127. C₄×D₈×C₇₃	C₂²	semidirect
128. C₈×D₄×C₇₃	C₂²	semidirect
129. #427×C₇₃	C₂²	semidirect
130. C₂×#107×C₇₃	C₂²	semidirect
568. D₇₃	#3339	direct (N × H)
581. #3339	D₇₃	direct (N × H)
592. C₇₃	C₂×#3339	semidirect
607. #553	C₂×D₇₃	semidirect
624. #499	C₂×D₇₃	semidirect
632. #482	C₂×D₇₃	semidirect
640. #481	C₂×D₇₃	semidirect
648. #478	C₂×D₇₃	semidirect
659. #466	C₂×D₇₃	semidirect
660. #466	C₂×D₇₃	semidirect
666. C₄×D₈	C₂×D₇₃	semidirect
674. C₈×D₄	C₂×D₇₃	semidirect
680. #427	C₂×D₇₃	semidirect
690. C₂×#107	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#553×D₇₃	2
#22622336	2
#22622335	2
#22622334	2
#22622333	2
#22622332	2
#22622331	2
#22622330	2
#22622329	2
#22622328	2
#22622327	2
#22622326	2
#499×D₇₃	2
#481×D₇₃	2
#482×D₇₃	2
#478×D₇₃	2
#466×D₇₃	2
C₄×D₈×D₇₃	2
C₈×D₄×D₇₃	2
#427×D₇₃	2
C₂×#107×D₇₃	2
C₇₃×#3339	2
C₂×#3339	73

Subgroups — #3339×D73 #33964448

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3339×D₇₃ #33964448