Subgroups — #33953595

Order 18688.

2178 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623335	C₂	1	1	yes	maximal, characteristic, complemented
2	#518×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22619765	C₂	1	1	yes	maximal, characteristic, complemented
4	#22619764	C₂	1	1	yes	maximal, characteristic, complemented
5	#22619763	C₂	1	1	yes	maximal, characteristic, complemented
6	#22619762	C₂	1	1	yes	maximal, characteristic, complemented
7	#22619761	C₂	1	2	yes	maximal, complemented
8	#22619760	C₂	1	1	yes	maximal, characteristic, complemented
9	#22619759	C₂	1	2	yes	maximal, complemented
10	#22619758	C₂	1	1	yes	maximal, characteristic, complemented
11	#22619757	C₂	1	2	yes	maximal, complemented
12	#22619756	C₂	1	1	yes	maximal, characteristic, complemented
13	#22619755	C₂	1	2	yes	maximal, complemented
14	#22619729	C₂	1	2	yes	maximal, complemented
15	#22619726	C₂	1	2	yes	maximal, complemented
16	#22619726	C₂	1	2	yes	maximal, complemented
17	#22619723	C₂	1	2	yes	maximal, complemented
18	#22618519	C₂	1	1	yes	maximal, characteristic, complemented
19	#22618518	C₂	1	1	yes	maximal, characteristic, complemented
20	#22618492	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#17988590	C₂	1	1	yes	maximal, characteristic
22	#418×D₇₃	C₂	1	1	yes	maximal, characteristic
23	C₇₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₄×D₇₃	C₂²	1	1	yes	characteristic
25	C₂²×#11924011	C₂²	1	1	yes	characteristic
26	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
27	#17989218	C₂²	1	1	yes	characteristic, complemented
28	#17989217	—	2	1	no	—
29	#17989217	C₂²	1	2	yes	complemented
30	#17989215	C₂²	1	1	yes	characteristic, complemented
31	#17989215	C₂²	1	1	yes	characteristic, complemented
32	#17989214	—	2	1	no	—
33	#17989214	C₂²	1	2	yes	complemented
34	#17989212	—	2	2	no	—
35	#17989143	—	2	1	no	—
36	#17989143	C₂²	1	2	yes	complemented
37	#17989142	—	2	1	no	—
38	#17989142	C₂²	1	2	yes	complemented
39	#17989139	—	2	2	no	—
40	#17989062	C₂²	1	1	yes	characteristic
41	#17989061	C₂²	1	1	yes	characteristic
42	#17989061	C₂²	1	1	yes	characteristic
43	#17989060	—	2	2	no	—
44	#17989059	—	2	1	no	—
45	#17989059	—	2	1	no	—
46	#17989059	C₂²	1	2	yes	—
47	#17989059	C₂²	1	2	yes	—
48	C₄×D₄×D₇₃	—	2	1	no	—
49	C₄×D₄×D₇₃	—	2	1	no	—
50	C₄×D₄×D₇₃	C₂²	1	2	yes	—
51	C₄×D₄×D₇₃	C₂²	1	2	yes	—
52	C₂×#14556549	C₂²	1	1	yes	characteristic
53	#117×D₇₃	C₂²	1	1	yes	characteristic
54	#117×D₇₃	C₂²	1	1	yes	characteristic
55	#117×D₇₃	C₂²	1	1	yes	characteristic
56	C₂×C₂²⋊C₄×D₇₃	—	2	2	no	—
57	#17988890	C₂²	1	2	yes	complemented
58	#17988890	C₂²	1	2	yes	complemented
59	#17988889	C₂²	1	2	yes	complemented
60	#17988889	C₂²	1	2	yes	complemented
61	#17988888	C₂²	1	2	yes	complemented
62	#17988888	C₂²	1	2	yes	complemented
63	#17988887	C₂²	1	2	yes	complemented
64	#17988887	C₂²	1	2	yes	complemented
65	#17988886	C₂²	1	2	yes	complemented
66	#17988886	C₂²	1	2	yes	complemented
67	#17988885	C₂²	1	2	yes	complemented
68	#17988885	C₂²	1	2	yes	complemented
69	#17988884	C₂²	1	2	yes	complemented
70	#17988884	C₂²	1	2	yes	complemented
71	#17988878	C₂²	1	2	yes	complemented
72	#17988877	C₂²	1	2	yes	complemented
73	#17988876	C₂²	1	2	yes	complemented
74	#17988876	C₂²	1	2	yes	complemented
75	#17988875	C₂²	1	2	yes	complemented
76	#17988875	C₂²	1	2	yes	complemented
77	#17988874	C₂²	1	2	yes	complemented
78	#17988868	C₂²	1	2	yes	complemented
79	#17988867	C₂²	1	2	yes	complemented
80	#17988866	C₂²	1	2	yes	complemented
81	#17988866	C₂²	1	2	yes	complemented
82	#17988865	C₂²	1	2	yes	complemented
83	#17988865	C₂²	1	2	yes	complemented
84	#17988864	C₂²	1	2	yes	complemented
85	#17988630	C₂²	1	1	yes	characteristic, complemented
86	#17988629	C₂²	1	1	yes	characteristic, complemented
87	#17988628	C₂²	1	1	yes	characteristic, complemented
88	#17988628	C₂²	1	2	yes	complemented
89	#17988628	C₂²	1	1	yes	characteristic, complemented
90	#17988628	C₂²	1	1	yes	characteristic, complemented
91	#17988628	C₂²	1	1	yes	characteristic, complemented
92	#17988627	C₂²	1	1	yes	characteristic, complemented
93	#17988626	C₂²	1	1	yes	characteristic, complemented
94	#17988626	C₂²	1	2	yes	complemented
95	#17988626	C₂²	1	1	yes	characteristic, complemented
96	#17988626	C₂²	1	1	yes	characteristic, complemented
97	#17988626	C₂²	1	1	yes	characteristic, complemented
98	#17988625	C₂²	1	1	yes	characteristic, complemented
99	#17988624	C₂²	1	2	yes	complemented
100	#17988623	C₂²	1	1	yes	characteristic, complemented
101	#17988623	C₂²	1	1	yes	characteristic, complemented
102	#17988622	C₂²	1	2	yes	complemented
103	#17988615	C₂²	1	1	yes	characteristic, complemented
104	#17988614	C₂²	1	1	yes	characteristic, complemented
105	#17988613	C₂²	1	1	yes	characteristic, complemented
106	#17988612	C₂²	1	2	yes	complemented
107	#17988612	C₂²	1	2	yes	complemented
108	#17988609	C₂²	1	2	yes	complemented
109	#17988609	C₂²	1	2	yes	complemented
110	#17988593	C₂²	1	1	yes	characteristic
111	#17988592	C₂²	1	1	yes	characteristic
112	#17988591	C₂²	1	1	yes	characteristic
113	#17988590	C₂²	1	2	yes	—
114	#17988590	C₂²	1	2	yes	—
115	#17988590	C₂²	1	2	yes	—
116	#17988590	C₂²	1	2	yes	—
117	#17988590	C₂²	1	2	yes	—
118	#17988590	C₂²	1	2	yes	—
119	C₂×#14556513	C₂²	1	1	yes	characteristic
120	C₂×#14556512	C₂²	1	1	yes	characteristic
121	C₂×#14556511	C₂²	1	1	yes	characteristic
122	#102×D₇₃	C₂²	1	2	yes	—
123	#102×D₇₃	C₂²	1	2	yes	—
124	#544×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#518×C₇₃	C₂²	1	1	yes	characteristic
126	#478×C₇₃	C₂²	1	2	yes	complemented
127	#478×C₇₃	C₂²	1	2	yes	complemented
128	#476×C₇₃	C₂²	1	2	yes	complemented
129	#474×C₇₃	C₂²	1	2	yes	complemented
130	#428×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	#427×C₇₃	C₂²	1	1	yes	characteristic, complemented
132	#424×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	#418×C₇₃	C₂²	1	1	yes	characteristic
134	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic
135	C₂⁴×D₇₃	—	2	1	no	—
136	C₂²×D₂₉₂	C₂³	1	1	yes	characteristic
137	C₂²×C₂²⋊D₇₃	—	2	1	no	—
138	C₂×D₄×D₇₃	—	2	1	no	—
139	C₂×D₄×D₇₃	—	2	1	no	—
140	C₂×D₄×D₇₃	—	2	4	no	—
141	C₂×D₄×D₇₃	Q₈	1	8	yes	complemented
142	C₂×D₄×D₇₃	C₂³	1	2	yes	—
143	C₂×D₄×D₇₃	C₂³	1	2	yes	—
144	C₂²×C₄×D₇₃	—	2	2	no	—
145	C₂²×C₄×D₇₃	—	2	2	no	—
146	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
147	C₂×#11924012	C₂³	1	1	yes	characteristic
148	C₂×#11924011	—	2	4	no	—
149	C₂×#11924011	C₂³	1	1	yes	characteristic
150	C₂×#11924011	C₂³	1	2	yes	—
151	C₂×#11924011	C₂³	1	1	yes	characteristic
152	C₂×#11924011	C₂³	1	1	yes	characteristic
153	C₂×#11924011	C₂³	1	1	yes	characteristic
154	M₁₆×D₇₃	—	2	4	no	—
155	C₂²×#10596831	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₇₃	C₂³	1	2	yes	—
157	#14556591	—	2	1	no	—
158	#14556591	C₂³	1	2	yes	complemented
159	#14556590	—	2	1	no	—
160	#14556590	—	2	2	no	—
161	#14556590	—	2	1	no	—
162	#14556590	C₂³	1	2	yes	complemented
163	#14556590	C₂³	1	2	yes	complemented
164	#14556589	—	2	2	no	—
165	#14556583	—	2	1	no	—
166	#14556583	C₂³	1	2	yes	complemented
167	#14556582	—	2	1	no	—
168	#14556582	—	2	1	no	—
169	#14556582	C₂³	1	2	yes	complemented
170	#14556582	C₂³	1	2	yes	complemented
171	#14556581	—	2	2	no	—
172	#14556581	—	2	2	no	—
173	#14556571	—	2	2	no	—
174	#14556571	—	2	2	no	—
175	#14556570	—	2	2	no	—
176	#14556569	—	2	2	no	—
177	#14556569	—	2	2	no	—
178	#14556569	—	2	2	no	—
179	#14556569	—	2	2	no	—
180	#14556568	—	2	2	no	—
181	#14556568	—	2	2	no	—
182	#14556567	—	2	2	no	—
183	#14556567	—	2	2	no	—
184	Q₈×Dic₇₃	—	2	2	no	—
185	#14556556	—	2	2	no	—
186	#14556556	—	2	2	no	—
187	#14556556	—	2	2	no	—
188	C₄×D₂₉₂	—	2	1	no	—
189	C₄×D₂₉₂	—	2	1	no	—
190	C₄×D₂₉₂	C₂³	1	2	yes	—
191	C₄×D₂₉₂	C₂³	1	2	yes	—
192	D₄×Dic₇₃	—	2	1	no	—
193	D₄×Dic₇₃	—	2	1	no	—
194	D₄×Dic₇₃	C₂³	1	2	yes	—
195	D₄×Dic₇₃	C₂³	1	2	yes	—
196	#14556553	—	2	1	no	—
197	#14556553	—	2	1	no	—
198	#14556553	C₂³	1	2	yes	—
199	#14556553	C₂³	1	2	yes	—
200	C₄×C₂²⋊D₇₃	—	2	2	no	—
201	C₄×C₂²⋊D₇₃	—	2	2	no	—
202	C₄×C₂²⋊D₇₃	—	2	2	no	—
203	C₄×C₂²⋊D₇₃	—	2	2	no	—
204	#14556551	—	2	2	no	—
205	#14556551	—	2	2	no	—
206	#14556551	—	2	2	no	—
207	#14556551	—	2	2	no	—
208	#14556550	C₂³	1	1	yes	characteristic
209	#14556550	C₂³	1	1	yes	characteristic
210	#14556550	C₂³	1	1	yes	characteristic
211	#14556549	—	2	1	no	—
212	#14556549	—	2	1	no	—
213	#14556549	D₄	1	1	yes	characteristic
214	#14556549	D₄	1	1	yes	characteristic
215	#14556549	C₂³	1	1	yes	characteristic
216	#14556549	C₂³	1	2	yes	—
217	#14556549	C₂³	1	1	yes	characteristic
218	#14556549	C₂³	1	1	yes	characteristic
219	#14556549	C₂³	1	2	yes	—
220	#14556549	C₂³	1	1	yes	characteristic
221	#14556548	—	2	1	no	—
222	#14556548	—	2	1	no	—
223	#14556548	C₂³	1	2	yes	—
224	#14556547	—	2	1	no	—
225	#14556547	—	2	1	no	—
226	#14556547	D₄	1	2	yes	—
227	C₂×C₄⋊Dic₇₃	C₂³	1	1	yes	characteristic
228	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
229	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
230	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
231	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
232	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
233	C₄⋊C₄×D₇₃	C₂³	1	1	yes	characteristic
234	C₂×C₂²⋊Dic₇₃	—	2	2	no	—
235	C₂×#11924005	—	2	1	no	—
236	C₂×#11924005	—	2	2	no	—
237	C₂×#11924005	—	2	2	no	—
238	C₂²⋊C₄×D₇₃	—	2	1	no	—
239	C₂²⋊C₄×D₇₃	—	2	1	no	—
240	C₂²⋊C₄×D₇₃	—	2	2	no	—
241	C₂²⋊C₄×D₇₃	—	2	2	no	—
242	C₂²⋊C₄×D₇₃	—	2	2	no	—
243	C₂²⋊C₄×D₇₃	—	2	2	no	—
244	C₂²⋊C₄×D₇₃	—	2	2	no	—
245	C₂²⋊C₄×D₇₃	—	2	2	no	—
246	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
247	C₂×C₄×Dic₇₃	—	2	1	no	—
248	C₄²×D₇₃	—	2	1	no	—
249	C₄²×D₇₃	—	2	1	no	—
250	C₄²×D₇₃	C₂³	1	2	yes	—
251	#14556525	C₂³	1	1	yes	characteristic, complemented
252	#14556525	C₂³	1	2	yes	complemented
253	#14556525	C₂³	1	1	yes	characteristic, complemented
254	#14556524	C₂³	1	1	yes	characteristic, complemented
255	#14556524	C₂³	1	2	yes	complemented
256	#14556524	C₂³	1	1	yes	characteristic, complemented
257	#14556524	C₂³	1	1	yes	characteristic, complemented
258	#14556524	C₂³	1	2	yes	complemented
259	#14556524	C₂³	1	1	yes	characteristic, complemented
260	#14556523	C₂³	1	1	yes	characteristic, complemented
261	#14556523	C₂³	1	2	yes	complemented
262	#14556523	C₂³	1	1	yes	characteristic, complemented
263	#14556522	C₂³	1	1	yes	characteristic, complemented
264	#14556522	C₂³	1	2	yes	complemented
265	#14556522	C₂³	1	1	yes	characteristic, complemented
266	#14556522	C₂³	1	1	yes	characteristic, complemented
267	#14556522	C₂³	1	2	yes	complemented
268	#14556522	C₂³	1	1	yes	characteristic, complemented
269	C₄⋊#10596831	C₂³	1	2	yes	complemented
270	C₄⋊#10596831	C₂³	1	2	yes	complemented
271	#14556520	C₂³	1	2	yes	complemented
272	#14556520	C₂³	1	2	yes	complemented
273	#14556520	C₂³	1	2	yes	complemented
274	#14556520	C₂³	1	2	yes	complemented
275	#14556513	C₂³	1	2	yes	—
276	#14556513	C₂³	1	2	yes	—
277	#14556513	C₂³	1	2	yes	—
278	#14556513	C₂³	1	2	yes	—
279	#14556512	C₂³	1	2	yes	—
280	#14556512	C₂³	1	2	yes	—
281	#14556512	C₂³	1	2	yes	—
282	#14556512	C₂³	1	2	yes	—
283	#14556511	C₂³	1	2	yes	—
284	#14556511	C₂³	1	2	yes	—
285	#14556511	C₂³	1	2	yes	—
286	#14556511	C₂³	1	2	yes	—
287	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
288	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
289	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
290	C₄⋊Q₈×C₇₃	—	2	1	no	—
291	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	complemented
292	#125×C₇₃	—	2	1	no	—
293	#125×C₇₃	C₂³	1	2	yes	complemented
294	C₂²⋊Q₈×C₇₃	—	2	2	no	—
295	C₄×D₄×C₇₃	—	2	1	no	—
296	C₄×D₄×C₇₃	—	2	1	no	—
297	C₄×D₄×C₇₃	C₂³	1	2	yes	—
298	C₄×D₄×C₇₃	C₂³	1	2	yes	—
299	#117×C₇₃	C₂³	1	1	yes	characteristic
300	#117×C₇₃	C₂³	1	1	yes	characteristic
301	#117×C₇₃	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
303	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
304	#107×C₇₃	C₂³	1	1	yes	characteristic, complemented
305	#107×C₇₃	C₂³	1	2	yes	complemented
306	#107×C₇₃	C₂³	1	1	yes	characteristic, complemented
307	#106×C₇₃	C₂³	1	1	yes	characteristic, complemented
308	#106×C₇₃	C₂³	1	2	yes	complemented
309	#106×C₇₃	C₂³	1	1	yes	characteristic, complemented
310	C₄⋊C₈×C₇₃	C₂³	1	2	yes	complemented
311	C₄⋊C₈×C₇₃	C₂³	1	2	yes	complemented
312	#102×C₇₃	C₂³	1	2	yes	—
313	#102×C₇₃	C₂³	1	2	yes	—
314	#102×C₇₃	C₂³	1	2	yes	—
315	#102×C₇₃	C₂³	1	2	yes	—
316	C₂³×D₇₃	—	2	1	no	—
317	C₂³×D₇₃	—	2	2	no	—
318	C₂³×D₇₃	—	2	8	no	—
319	C₂³×D₇₃	—	2	2	no	—
320	C₂³×D₇₃	—	8	2	no	—
321	C₂³×D₇₃	—	8	2	no	—
322	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Dic₁₄₆	—	2	2	no	—
324	C₂×Dic₁₄₆	—	2	2	no	—
325	C₂×Dic₁₄₆	—	2	2	no	—
326	C₂×D₂₉₂	—	2	1	no	—
327	C₂×D₂₉₂	—	2	2	no	—
328	C₂×D₂₉₂	C₂×Q₈	1	4	yes	—
329	C₂×D₂₉₂	C₂⁴	1	2	yes	—
330	C₂×C₂²⋊D₇₃	—	2	8	no	—
331	C₂×C₂²⋊D₇₃	—	2	2	no	—
332	C₂×C₂²⋊D₇₃	—	2	2	no	—
333	D₄×D₇₃	—	2	8	no	—
334	D₄×D₇₃	—	2	8	no	—
335	D₄×D₇₃	—	2	4	no	—
336	D₄×D₇₃	—	2	4	no	—
337	D₄×D₇₃	C₂×Q₈	1	8	yes	—
338	D₄×D₇₃	C₂×Q₈	1	8	yes	—
339	C₂²×Dic₇₃	—	2	1	no	—
340	C₂²×Dic₇₃	—	2	2	no	—
341	C₂²×Dic₇₃	—	2	2	no	—
342	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₇₃	—	2	1	no	—
344	C₂×C₄×D₇₃	—	2	1	no	—
345	C₂×C₄×D₇₃	—	2	1	no	—
346	C₂×C₄×D₇₃	—	2	1	no	—
347	C₂×C₄×D₇₃	—	2	2	no	—
348	C₂×C₄×D₇₃	—	2	2	no	—
349	C₂×C₄×D₇₃	—	2	2	no	—
350	C₂×C₄×D₇₃	—	2	2	no	—
351	C₂×C₄×D₇₃	—	8	4	no	—
352	C₂×C₄×D₇₃	—	8	4	no	—
353	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
354	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
355	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
356	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
357	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
358	C₂×C₄×D₇₃	#41	1	4	yes	—
359	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
360	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
361	#11924012	—	2	2	no	—
362	#11924011	—	2	4	no	—
363	#11924011	—	2	2	no	—
364	#11924011	—	2	2	no	—
365	#11924011	—	2	2	no	—
366	#11924011	—	2	2	no	—
367	C₂×#10596831	—	2	2	no	—
368	C₂×#10596831	C₂⁴	1	2	yes	—
369	C₂×#10596831	C₂⁴	1	1	yes	characteristic
370	C₂×#10596831	C₂⁴	1	1	yes	characteristic
371	C₈×D₇₃	—	2	4	no	—
372	C₄⋊Dic₇₃	—	2	1	no	—
373	C₄⋊Dic₇₃	—	2	2	no	—
374	C₄⋊Dic₇₃	—	2	2	no	—
375	C₄⋊Dic₇₃	—	2	2	no	—
376	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
377	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
378	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
379	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
380	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
381	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
382	C₄⋊Dic₇₃	C₂⁴	1	1	yes	characteristic
383	#11924007	—	2	2	no	—
384	#11924007	—	2	2	no	—
385	#11924007	—	2	1	no	—
386	#11924007	—	2	1	no	—
387	#11924007	—	2	1	no	—
388	#11924007	—	2	1	no	—
389	#11924007	—	2	2	no	—
390	#11924007	—	2	2	no	—
391	#11924007	—	2	2	no	—
392	#11924007	—	2	2	no	—
393	#11924007	C₂×D₄	1	2	yes	—
394	#11924007	C₂×D₄	1	2	yes	—
395	C₂²⋊Dic₇₃	—	2	1	no	—
396	C₂²⋊Dic₇₃	—	2	1	no	—
397	C₂²⋊Dic₇₃	—	2	2	no	—
398	C₂²⋊Dic₇₃	—	2	2	no	—
399	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
400	#11924005	—	2	1	no	—
401	#11924005	—	2	1	no	—
402	#11924005	—	2	1	no	—
403	#11924005	—	2	1	no	—
404	#11924005	—	2	2	no	—
405	#11924005	—	2	2	no	—
406	#11924005	—	2	2	no	—
407	#11924005	—	2	2	no	—
408	#11924005	—	2	2	no	—
409	#11924005	—	2	2	no	—
410	#11924005	C₂×D₄	1	2	yes	—
411	#11924005	C₂×D₄	1	2	yes	—
412	C₄×Dic₇₃	—	2	1	no	—
413	C₄×Dic₇₃	—	2	1	no	—
414	C₄×Dic₇₃	—	2	1	no	—
415	C₄×Dic₇₃	—	2	1	no	—
416	C₄×Dic₇₃	—	2	1	no	—
417	C₄×Dic₇₃	—	2	1	no	—
418	C₄×Dic₇₃	—	2	2	no	—
419	C₄×Dic₇₃	—	2	2	no	—
420	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
421	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
422	C₄×Dic₇₃	C₂⁴	1	2	yes	—
423	C₂⁴×C₇₃	—	2	1	no	—
424	C₂×Q₈×C₇₃	—	2	2	no	—
425	C₂×D₄×C₇₃	—	2	1	no	—
426	C₂×D₄×C₇₃	—	2	2	no	—
427	C₂×D₄×C₇₃	C₂×Q₈	1	4	yes	—
428	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
429	C₂²×C₄×C₇₃	—	2	1	no	—
430	C₂²×C₄×C₇₃	—	2	2	no	—
431	C₂²×C₄×C₇₃	—	2	2	no	—
432	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
433	M₁₆×C₇₃	—	2	2	no	—
434	C₂×C₈×C₇₃	—	2	2	no	—
435	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
436	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
437	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
438	C₄⋊C₄×C₇₃	—	2	1	no	—
439	C₄⋊C₄×C₇₃	—	2	2	no	—
440	C₄⋊C₄×C₇₃	—	2	2	no	—
441	C₄⋊C₄×C₇₃	—	2	2	no	—
442	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
443	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
444	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
445	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
446	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
447	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
448	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
449	C₂²⋊C₄×C₇₃	—	2	1	no	—
450	C₂²⋊C₄×C₇₃	—	2	1	no	—
451	C₂²⋊C₄×C₇₃	—	2	2	no	—
452	C₂²⋊C₄×C₇₃	—	2	2	no	—
453	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
454	C₄²×C₇₃	—	2	1	no	—
455	C₄²×C₇₃	—	2	1	no	—
456	C₄²×C₇₃	C₂⁴	1	2	yes	—
457	C₂³×C₇₃	—	2	2	no	—
458	C₂³×C₇₃	—	2	4	no	—
459	C₂³×C₇₃	—	8	1	no	—
460	C₂³×C₇₃	—	8	1	no	—
461	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
462	C₂²×D₇₃	—	2	2	no	—
463	C₂²×D₇₃	—	2	4	no	—
464	C₂²×D₇₃	—	2	8	no	—
465	C₂²×D₇₃	—	2	8	no	—
466	C₂²×D₇₃	—	4	1	no	—
467	C₂²×D₇₃	—	4	1	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	C₂²×D₇₃	—	8	16	no	—
473	C₂²×D₇₃	—	8	1	no	—
474	C₂²×D₇₃	—	8	1	no	—
475	C₂²×D₇₃	C₂²⋊Q₈	1	4	yes	—
476	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
477	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
478	Q₈×C₇₃	—	8	2	no	—
479	D₄×C₇₃	—	2	4	no	—
480	D₄×C₇₃	—	2	2	no	—
481	D₄×C₇₃	C₂²×Q₈	1	4	yes	—
482	C₂×C₄×C₇₃	—	2	1	no	—
483	C₂×C₄×C₇₃	—	2	1	no	—
484	C₂×C₄×C₇₃	—	2	1	no	—
485	C₂×C₄×C₇₃	—	2	1	no	—
486	C₂×C₄×C₇₃	—	2	2	no	—
487	C₂×C₄×C₇₃	—	8	2	no	—
488	C₂×C₄×C₇₃	—	8	2	no	—
489	C₂×C₄×C₇₃	—	8	1	no	—
490	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
494	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
495	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
496	C₂²⋊D₇₃	—	2	8	no	—
497	C₂²⋊D₇₃	—	2	8	no	—
498	C₂×Dic₇₃	—	2	1	no	—
499	C₂×Dic₇₃	—	2	1	no	—
500	C₂×Dic₇₃	—	2	2	no	—
501	C₂×Dic₇₃	—	2	1	no	—
502	C₂×Dic₇₃	—	2	1	no	—
503	C₂×Dic₇₃	—	8	2	no	—
504	C₂×Dic₇₃	—	8	2	no	—
505	C₂×Dic₇₃	—	8	1	no	—
506	C₂×Dic₇₃	C₂²⋊Q₈	1	4	yes	—
507	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
508	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
509	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
511	D₂₉₂	—	2	4	no	—
512	D₂₉₂	—	2	2	no	—
513	D₂₉₂	C₂²×Q₈	1	4	yes	—
514	C₄×D₇₃	—	4	2	no	—
515	C₄×D₇₃	—	4	2	no	—
516	C₄×D₇₃	—	4	2	no	—
517	C₄×D₇₃	—	4	2	no	—
518	C₄×D₇₃	—	8	2	no	—
519	C₄×D₇₃	—	8	2	no	—
520	C₄×D₇₃	—	8	2	no	—
521	C₄×D₇₃	—	8	2	no	—
522	C₄×D₇₃	—	8	1	no	—
523	C₄×D₇₃	—	8	1	no	—
524	C₄×D₇₃	C₂²⋊Q₈	1	4	yes	—
525	C₄×D₇₃	C₂²⋊Q₈	1	4	yes	—
526	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
527	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
528	C₄×D₇₃	C₂×#41	1	2	yes	—
529	C₄×D₇₃	C₂×#41	1	2	yes	—
530	Dic₁₄₆	—	8	2	no	—
531	Dic₁₄₆	—	8	2	no	—
532	Dic₁₄₆	—	8	2	no	—
533	C₈×C₇₃	—	2	1	no	—
534	C₈×C₇₃	—	2	1	no	—
535	C₈×C₇₃	—	2	2	no	—
536	#10596831	—	2	2	no	—
537	#10596831	—	2	1	no	—
538	#10596831	—	2	1	no	—
539	C₂²×C₇₃	—	2	1	no	—
540	C₂²×C₇₃	—	2	1	no	—
541	C₂²×C₇₃	—	2	4	no	—
542	C₂²×C₇₃	—	4	2	no	—
543	C₂²×C₇₃	—	4	2	no	—
544	C₂²×C₇₃	—	8	4	no	—
545	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	2	yes	—
546	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
547	C₂×D₇₃	—	2	1	no	—
548	C₂×D₇₃	—	2	1	no	—
549	C₂×D₇₃	—	2	1	no	—
550	C₂×D₇₃	—	2	1	no	—
551	C₂×D₇₃	—	2	4	no	—
552	C₂×D₇₃	—	4	4	no	—
553	C₂×D₇₃	—	4	16	no	—
554	C₂×D₇₃	—	4	2	no	—
555	C₂×D₇₃	—	4	2	no	—
556	C₂×D₇₃	—	8	8	no	—
557	C₂×D₇₃	—	8	4	no	—
558	C₂×D₇₃	C₂×C₂²⋊Q₈	1	2	yes	—
559	C₂×D₇₃	C₂×C₂²⋊Q₈	1	2	yes	—
560	C₄×C₇₃	—	2	2	no	—
561	C₄×C₇₃	—	2	2	no	—
562	C₄×C₇₃	—	4	1	no	—
563	C₄×C₇₃	—	4	2	no	—
564	C₄×C₇₃	—	4	1	no	—
565	C₄×C₇₃	—	4	1	no	—
566	C₄×C₇₃	—	4	1	no	—
567	C₄×C₇₃	C₂×C₂²⋊Q₈	1	2	yes	—
568	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
569	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
570	Dic₇₃	—	2	2	no	—
571	Dic₇₃	—	2	2	no	—
572	Dic₇₃	—	4	1	no	—
573	Dic₇₃	—	4	1	no	—
574	Dic₇₃	—	4	2	no	—
575	Dic₇₃	—	4	1	no	—
576	Dic₇₃	—	4	1	no	—
577	Dic₇₃	C₂×C₂²⋊Q₈	1	2	yes	—
578	Dic₇₃	C₂×C₂²⋊Q₈	1	2	yes	—
579	#60490	—	73	1	no	maximal, Sylow
580	C₂×C₇₃	—	2	2	no	—
581	C₂×C₇₃	—	4	4	no	—
582	C₂×C₇₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
583	C₂×C₇₃	#3585	1	1	yes	characteristic
584	C₂×C₇₃	#3585	1	1	yes	characteristic
585	D₇₃	—	2	2	no	—
586	D₇₃	—	2	2	no	—
587	D₇₃	—	4	4	no	—
588	#3458	—	73	1	no	—
589	C₂×#518	—	73	1	no	—
590	#3081	—	73	2	no	—
591	#3081	—	73	2	no	—
592	#3081	—	73	2	no	—
593	#3081	—	73	2	no	—
594	#3081	—	73	1	no	—
595	#3081	—	73	1	no	—
596	#3081	—	73	1	no	—
597	#3081	—	73	1	no	—
598	#3081	—	73	1	no	—
599	#3081	—	73	1	no	—
600	#3081	—	73	1	no	—
601	#3081	D₇₃	1	1	yes	characteristic, complemented
602	#3077	—	73	2	no	—
603	#3077	—	73	2	no	—
604	#3077	—	73	2	no	—
605	#3077	—	73	2	no	—
606	#2911	—	73	1	no	—
607	#2911	—	73	1	no	—
608	#2905	—	73	1	no	—
609	C₂×#418	—	73	1	no	—
610	C₂×#418	—	73	1	no	—
611	C₇₃	#60490	1	1	yes	characteristic, complemented, Sylow
612	C₂³×D₄	—	73	1	no	—
613	C₂²×M₁₆	—	73	1	no	—
614	C₂²×M₁₆	—	73	1	no	—
615	#544	—	73	2	no	—
616	#544	—	73	2	no	—
617	#544	—	73	1	no	—
618	#544	—	73	1	no	—
619	#544	—	73	1	no	—
620	#544	—	146	1	no	—
621	#544	—	146	1	no	—
622	#544	C₂×D₇₃	1	1	yes	characteristic, complemented
623	#543	—	146	2	no	—
624	#533	—	73	2	no	—
625	#533	—	73	2	no	—
626	#533	—	146	2	no	—
627	#533	—	146	1	no	—
628	#533	—	146	1	no	—
629	#518	—	73	1	no	—
630	#518	—	73	2	no	—
631	#518	—	73	2	no	—
632	#518	—	73	1	no	—
633	#518	—	73	1	no	—
634	#518	—	146	2	no	—
635	#518	—	146	1	no	—
636	#518	—	146	1	no	—
637	#518	C₂×D₇₃	1	1	yes	characteristic
638	C₂×C₄×D₄	—	73	2	no	—
639	C₂×C₄×D₄	—	73	2	no	—
640	C₂×C₄×D₄	—	146	1	no	—
641	C₂×C₄×D₄	—	146	1	no	—
642	C₂×#117	—	73	1	no	—
643	C₂×#117	—	73	1	no	—
644	C₂×#117	—	73	1	no	—
645	C₂×#117	—	73	1	no	—
646	C₂²×C₂²⋊C₄	—	146	2	no	—
647	#478	—	73	2	no	—
648	#478	—	73	2	no	—
649	#478	—	73	2	no	—
650	#478	—	73	2	no	—
651	#478	—	73	2	no	—
652	#478	—	73	2	no	—
653	#478	—	73	2	no	—
654	#478	—	73	2	no	—
655	#478	—	73	2	no	—
656	#478	—	73	2	no	—
657	#478	—	73	2	no	—
658	#478	—	73	2	no	—
659	#478	—	73	2	no	—
660	#478	—	73	2	no	—
661	#478	C₂×D₇₃	1	2	yes	complemented
662	#478	C₂×D₇₃	1	2	yes	complemented
663	#476	—	73	2	no	—
664	#476	—	73	2	no	—
665	#476	—	73	2	no	—
666	#476	—	73	2	no	—
667	#476	—	73	2	no	—
668	#476	—	73	2	no	—
669	#476	—	73	2	no	—
670	#476	C₂×D₇₃	1	2	yes	complemented
671	#474	—	73	2	no	—
672	#474	—	73	2	no	—
673	#474	—	73	2	no	—
674	#474	—	73	2	no	—
675	#474	—	73	2	no	—
676	#474	—	73	2	no	—
677	#474	—	73	2	no	—
678	#474	C₂×D₇₃	1	2	yes	complemented
679	#428	—	73	1	no	—
680	#428	—	73	1	no	—
681	#428	—	73	1	no	—
682	#428	—	73	2	no	—
683	#428	—	73	1	no	—
684	#428	—	73	1	no	—
685	#428	—	73	1	no	—
686	#428	—	73	1	no	—
687	#428	—	73	2	no	—
688	#428	—	73	1	no	—
689	#428	—	73	1	no	—
690	#428	—	73	1	no	—
691	#428	—	73	1	no	—
692	#428	C₂×D₇₃	1	1	yes	characteristic, complemented
693	#427	—	73	1	no	—
694	#427	—	73	1	no	—
695	#427	—	73	1	no	—
696	#427	—	73	2	no	—
697	#427	—	73	2	no	—
698	#427	C₂×D₇₃	1	1	yes	characteristic, complemented
699	#424	—	73	1	no	—
700	#424	—	73	1	no	—
701	#424	—	73	1	no	—
702	#424	—	73	2	no	—
703	#424	—	73	2	no	—
704	#424	C₂×D₇₃	1	1	yes	characteristic, complemented
705	#423	—	73	2	no	—
706	#423	—	73	2	no	—
707	#418	—	73	1	no	—
708	#418	—	73	1	no	—
709	#418	—	73	1	no	—
710	#418	—	73	2	no	—
711	#418	—	73	2	no	—
712	#418	—	73	2	no	—
713	#418	—	73	2	no	—
714	#418	—	73	2	no	—
715	#418	—	73	2	no	—
716	#418	C₂×D₇₃	1	1	yes	characteristic
717	C₂×#102	—	73	1	no	—
718	C₂×#102	—	73	1	no	—
719	C₂×#102	—	73	1	no	—
720	C₂×#102	—	73	2	no	—
721	C₂×#102	—	73	2	no	—
722	C₂×#102	C₂×D₇₃	1	1	yes	characteristic
723	C₂⁵	—	146	1	no	—
724	C₂²×D₄	—	73	8	no	—
725	C₂²×D₄	—	73	2	no	—
726	C₂²×D₄	—	73	2	no	—
727	C₂²×D₄	—	73	1	no	—
728	C₂²×D₄	—	146	1	no	—
729	C₂²×D₄	—	146	1	no	—
730	C₂²×D₄	—	146	4	no	—
731	C₂²×D₄	—	146	1	no	—
732	C₂²×D₄	C₂²×D₇₃	1	1	yes	characteristic
733	C₂³×C₄	—	73	1	no	—
734	C₂³×C₄	—	146	2	no	—
735	C₂³×C₄	—	146	2	no	—
736	C₂×M₁₆	—	73	1	no	—
737	C₂×M₁₆	—	73	1	no	—
738	C₂×M₁₆	—	73	2	no	—
739	C₂×M₁₆	—	73	1	no	—
740	C₂×M₁₆	—	73	1	no	—
741	C₂×M₁₆	—	73	1	no	—
742	C₂×M₁₆	—	146	4	no	—
743	C₂×M₁₆	—	146	4	no	—
744	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
745	C₂²×C₈	—	73	1	no	—
746	C₂²×C₈	—	73	2	no	—
747	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
748	C₄⋊Q₈	—	2	1	no	—
749	C₄⋊Q₈	—	73	2	no	—
750	C₄⋊Q₈	—	73	2	no	—
751	C₄⋊Q₈	—	73	2	no	—
752	C₄⋊Q₈	—	146	1	no	—
753	C₄⋊Q₈	—	146	2	no	—
754	C₄⋊Q₈	—	146	1	no	—
755	C₄⋊Q₈	—	146	2	no	—
756	C₄⋊Q₈	—	146	1	no	—
757	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	complemented
758	#125	—	2	1	no	—
759	#125	—	73	2	no	—
760	#125	—	73	2	no	—
761	#125	—	73	2	no	—
762	#125	—	146	1	no	—
763	#125	—	146	2	no	—
764	#125	—	146	2	no	—
765	#125	—	146	1	no	—
766	#125	—	146	1	no	—
767	#125	C₂²×D₇₃	1	2	yes	complemented
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	146	2	no	—
770	C₂²⋊Q₈	—	146	2	no	—
771	C₂²⋊Q₈	—	146	2	no	—
772	C₂²⋊Q₈	—	146	2	no	—
773	C₂²⋊Q₈	—	146	2	no	—
774	C₂²⋊Q₈	—	146	2	no	—
775	C₂²⋊Q₈	—	146	2	no	—
776	C₂²⋊Q₈	—	146	2	no	—
777	C₂²⋊Q₈	—	146	2	no	—
778	C₂²⋊Q₈	—	146	2	no	—
779	C₂²⋊Q₈	—	146	2	no	—
780	C₄×Q₈	—	146	2	no	—
781	C₄×Q₈	—	146	2	no	—
782	C₄×Q₈	—	146	2	no	—
783	C₄×Q₈	—	146	2	no	—
784	C₄×D₄	—	2	1	no	—
785	C₄×D₄	—	2	1	no	—
786	C₄×D₄	—	73	2	no	—
787	C₄×D₄	—	73	2	no	—
788	C₄×D₄	—	73	2	no	—
789	C₄×D₄	—	73	2	no	—
790	C₄×D₄	—	73	2	no	—
791	C₄×D₄	—	73	2	no	—
792	C₄×D₄	—	146	1	no	—
793	C₄×D₄	—	146	1	no	—
794	C₄×D₄	—	146	2	no	—
795	C₄×D₄	—	146	2	no	—
796	C₄×D₄	—	146	2	no	—
797	C₄×D₄	—	146	2	no	—
798	C₄×D₄	—	146	2	no	—
799	C₄×D₄	—	146	2	no	—
800	C₄×D₄	—	146	2	no	—
801	C₄×D₄	—	146	2	no	—
802	C₄×D₄	—	146	1	no	—
803	C₄×D₄	—	146	1	no	—
804	C₄×D₄	—	146	1	no	—
805	C₄×D₄	—	146	1	no	—
806	C₄×D₄	C₂²×D₇₃	1	2	yes	—
807	C₄×D₄	C₂²×D₇₃	1	2	yes	—
808	#117	—	73	1	no	—
809	#117	—	73	1	no	—
810	#117	—	73	1	no	—
811	#117	—	73	2	no	—
812	#117	—	73	2	no	—
813	#117	—	73	1	no	—
814	#117	—	73	1	no	—
815	#117	—	73	1	no	—
816	#117	—	73	1	no	—
817	#117	—	73	1	no	—
818	#117	—	73	1	no	—
819	#117	—	73	2	no	—
820	#117	—	73	2	no	—
821	#117	—	146	1	no	—
822	#117	—	146	1	no	—
823	#117	—	146	1	no	—
824	#117	—	146	1	no	—
825	#117	—	146	1	no	—
826	#117	—	146	1	no	—
827	#117	C₂²×D₇₃	1	1	yes	characteristic
828	#117	C₂²×D₇₃	1	1	yes	characteristic
829	#117	C₂²×D₇₃	1	1	yes	characteristic
830	C₂×C₄⋊C₄	—	73	1	no	—
831	C₂×C₄⋊C₄	—	73	1	no	—
832	C₂×C₄⋊C₄	—	73	1	no	—
833	C₂×C₄⋊C₄	—	73	1	no	—
834	C₂×C₄⋊C₄	—	73	1	no	—
835	C₂×C₄⋊C₄	—	73	1	no	—
836	C₂×C₄⋊C₄	—	73	1	no	—
837	C₂×C₄⋊C₄	C₂²×D₇₃	1	1	yes	characteristic
838	C₂×C₂²⋊C₄	—	2	2	no	—
839	C₂×C₂²⋊C₄	—	73	2	no	—
840	C₂×C₂²⋊C₄	—	146	2	no	—
841	C₂×C₂²⋊C₄	—	146	2	no	—
842	C₂×C₂²⋊C₄	—	146	2	no	—
843	C₂×C₂²⋊C₄	—	146	2	no	—
844	C₂×C₂²⋊C₄	—	146	2	no	—
845	C₂×C₂²⋊C₄	—	146	1	no	—
846	C₂×C₂²⋊C₄	—	146	1	no	—
847	C₂×C₂²⋊C₄	—	146	2	no	—
848	C₂×C₂²⋊C₄	—	146	2	no	—
849	C₂×C₂²⋊C₄	—	146	2	no	—
850	C₂×C₂²⋊C₄	—	146	1	no	—
851	C₂×C₂²⋊C₄	—	146	2	no	—
852	C₂×C₄²	—	73	2	no	—
853	C₂×C₄²	—	146	1	no	—
854	C₂×C₄²	—	146	1	no	—
855	C₂×C₄²	—	146	1	no	—
856	#107	—	73	2	no	—
857	#107	—	73	1	no	—
858	#107	—	73	1	no	—
859	#107	—	73	1	no	—
860	#107	—	73	2	no	—
861	#107	—	73	1	no	—
862	#107	—	73	1	no	—
863	#107	—	73	1	no	—
864	#107	—	73	2	no	—
865	#107	C₂²×D₇₃	1	2	yes	complemented
866	#107	C₂²×D₇₃	1	1	yes	characteristic, complemented
867	#107	C₂²×D₇₃	1	1	yes	characteristic, complemented
868	#106	—	73	1	no	—
869	#106	—	73	1	no	—
870	#106	—	73	2	no	—
871	#106	—	73	2	no	—
872	#106	—	73	1	no	—
873	#106	—	73	1	no	—
874	#106	—	73	1	no	—
875	#106	—	73	1	no	—
876	#106	—	73	2	no	—
877	#106	C₂²×D₇₃	1	2	yes	complemented
878	#106	C₂²×D₇₃	1	1	yes	characteristic, complemented
879	#106	C₂²×D₇₃	1	1	yes	characteristic, complemented
880	C₄⋊C₈	—	73	2	no	—
881	C₄⋊C₈	—	73	2	no	—
882	C₄⋊C₈	—	73	2	no	—
883	C₄⋊C₈	—	73	2	no	—
884	C₄⋊C₈	—	73	2	no	—
885	C₄⋊C₈	—	73	2	no	—
886	C₄⋊C₈	C₂²×D₇₃	1	2	yes	complemented
887	C₄⋊C₈	C₂²×D₇₃	1	2	yes	complemented
888	#102	—	73	2	no	—
889	#102	—	73	2	no	—
890	#102	—	73	2	no	—
891	#102	—	73	2	no	—
892	#102	—	73	2	no	—
893	#102	—	73	2	no	—
894	#102	—	73	2	no	—
895	#102	—	73	2	no	—
896	#102	—	73	2	no	—
897	#102	—	73	2	no	—
898	#102	—	73	2	no	—
899	#102	—	73	2	no	—
900	#102	C₂²×D₇₃	1	2	yes	—
901	#102	C₂²×D₇₃	1	2	yes	—
902	#102	C₂²×D₇₃	1	2	yes	—
903	#102	C₂²×D₇₃	1	2	yes	—
904	C₂⁴	—	2	1	no	—
905	C₂⁴	—	584	2	no	—
906	C₂⁴	—	584	2	no	—
907	C₂⁴	—	73	1	no	—
908	C₂⁴	—	146	2	no	—
909	C₂⁴	—	146	2	no	—
910	C₂⁴	—	146	8	no	—
911	C₂⁴	—	146	1	no	—
912	C₂×Q₈	—	2	2	no	—
913	C₂×Q₈	—	146	2	no	—
914	C₂×Q₈	—	146	2	no	—
915	C₂×Q₈	—	146	2	no	—
916	C₂×D₄	—	2	1	no	—
917	C₂×D₄	—	2	2	no	—
918	C₂×D₄	—	73	8	no	—
919	C₂×D₄	—	73	8	no	—
920	C₂×D₄	—	73	4	no	—
921	C₂×D₄	—	73	2	no	—
922	C₂×D₄	—	146	4	no	—
923	C₂×D₄	—	146	4	no	—
924	C₂×D₄	—	146	8	no	—
925	C₂×D₄	—	146	8	no	—
926	C₂×D₄	—	146	2	no	—
927	C₂×D₄	—	146	2	no	—
928	C₂×D₄	—	146	8	no	—
929	C₂×D₄	—	146	1	no	—
930	C₂×D₄	—	146	2	no	—
931	C₂×D₄	Q₈×D₇₃	1	4	yes	—
932	C₂×D₄	C₂³×D₇₃	1	2	yes	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	2	no	—
935	C₂²×C₄	—	2	2	no	—
936	C₂²×C₄	—	584	4	no	—
937	C₂²×C₄	—	584	4	no	—
938	C₂²×C₄	—	73	2	no	—
939	C₂²×C₄	—	73	2	no	—
940	C₂²×C₄	—	73	1	no	—
941	C₂²×C₄	—	73	1	no	—
942	C₂²×C₄	—	73	1	no	—
943	C₂²×C₄	—	73	4	no	—
944	C₂²×C₄	—	73	4	no	—
945	C₂²×C₄	—	73	1	no	—
946	C₂²×C₄	—	73	1	no	—
947	C₂²×C₄	—	146	1	no	—
948	C₂²×C₄	—	146	1	no	—
949	C₂²×C₄	—	146	2	no	—
950	C₂²×C₄	—	146	2	no	—
951	C₂²×C₄	—	146	1	no	—
952	C₂²×C₄	—	146	1	no	—
953	C₂²×C₄	—	146	2	no	—
954	C₂²×C₄	—	146	2	no	—
955	C₂²×C₄	—	146	1	no	—
956	C₂²×C₄	—	146	2	no	—
957	C₂²×C₄	—	146	2	no	—
958	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
959	M₁₆	—	2	2	no	—
960	M₁₆	—	146	2	no	—
961	M₁₆	—	146	2	no	—
962	M₁₆	—	146	2	no	—
963	M₁₆	—	146	2	no	—
964	M₁₆	—	146	4	no	—
965	M₁₆	—	146	2	no	—
966	C₂×C₈	—	2	2	no	—
967	C₂×C₈	—	73	2	no	—
968	C₂×C₈	—	73	1	no	—
969	C₂×C₈	—	73	1	no	—
970	C₂×C₈	—	146	4	no	—
971	C₂×C₈	—	146	2	no	—
972	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
973	C₂×C₈	C₂³×D₇₃	1	2	yes	—
974	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	2	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	2	no	—
979	C₄⋊C₄	—	73	2	no	—
980	C₄⋊C₄	—	73	2	no	—
981	C₄⋊C₄	—	73	1	no	—
982	C₄⋊C₄	—	73	1	no	—
983	C₄⋊C₄	—	73	1	no	—
984	C₄⋊C₄	—	73	1	no	—
985	C₄⋊C₄	—	73	2	no	—
986	C₄⋊C₄	—	73	1	no	—
987	C₄⋊C₄	—	73	1	no	—
988	C₄⋊C₄	—	146	1	no	—
989	C₄⋊C₄	—	146	1	no	—
990	C₄⋊C₄	—	146	1	no	—
991	C₄⋊C₄	—	146	1	no	—
992	C₄⋊C₄	—	146	2	no	—
993	C₄⋊C₄	—	146	2	no	—
994	C₄⋊C₄	—	146	2	no	—
995	C₄⋊C₄	—	146	2	no	—
996	C₄⋊C₄	—	146	2	no	—
997	C₄⋊C₄	—	146	2	no	—
998	C₄⋊C₄	—	146	2	no	—
999	C₄⋊C₄	—	146	2	no	—
1000	C₄⋊C₄	—	146	1	no	—
1001	C₄⋊C₄	—	146	2	no	—
1002	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
1003	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
1004	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
1007	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1008	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
1009	C₂²⋊C₄	—	2	1	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	73	2	no	—
1014	C₂²⋊C₄	—	73	2	no	—
1015	C₂²⋊C₄	—	73	2	no	—
1016	C₂²⋊C₄	—	146	2	no	—
1017	C₂²⋊C₄	—	146	2	no	—
1018	C₂²⋊C₄	—	146	1	no	—
1019	C₂²⋊C₄	—	146	1	no	—
1020	C₂²⋊C₄	—	146	1	no	—
1021	C₂²⋊C₄	—	146	1	no	—
1022	C₂²⋊C₄	—	146	2	no	—
1023	C₂²⋊C₄	—	146	2	no	—
1024	C₂²⋊C₄	—	146	2	no	—
1025	C₂²⋊C₄	—	146	2	no	—
1026	C₂²⋊C₄	—	146	1	no	—
1027	C₂²⋊C₄	—	146	1	no	—
1028	C₂²⋊C₄	—	146	2	no	—
1029	C₂²⋊C₄	—	146	2	no	—
1030	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
1031	C₄²	—	2	1	no	—
1032	C₄²	—	2	1	no	—
1033	C₄²	—	73	2	no	—
1034	C₄²	—	73	2	no	—
1035	C₄²	—	73	2	no	—
1036	C₄²	—	146	1	no	—
1037	C₄²	—	146	1	no	—
1038	C₄²	—	146	1	no	—
1039	C₄²	—	146	1	no	—
1040	C₄²	—	146	2	no	—
1041	C₄²	—	146	2	no	—
1042	C₄²	—	146	1	no	—
1043	C₄²	—	146	1	no	—
1044	C₄²	C₂³×D₇₃	1	2	yes	—
1045	C₂³	—	2	2	no	—
1046	C₂³	—	2	4	no	—
1047	C₂³	—	8	1	no	—
1048	C₂³	—	8	1	no	—
1049	C₂³	—	292	1	no	—
1050	C₂³	—	292	1	no	—
1051	C₂³	—	292	4	no	—
1052	C₂³	—	292	4	no	—
1053	C₂³	—	584	1	no	—
1054	C₂³	—	584	1	no	—
1055	C₂³	—	584	2	no	—
1056	C₂³	—	584	2	no	—
1057	C₂³	—	584	16	no	—
1058	C₂³	—	73	4	no	—
1059	C₂³	—	73	1	no	—
1060	C₂³	—	73	1	no	—
1061	C₂³	—	146	8	no	—
1062	C₂³	—	146	8	no	—
1063	C₂³	—	146	2	no	—
1064	C₂³	—	146	4	no	—
1065	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1066	Q₈	—	8	2	no	—
1067	Q₈	—	584	2	no	—
1068	Q₈	—	584	2	no	—
1069	Q₈	—	584	2	no	—
1070	D₄	—	2	2	no	—
1071	D₄	—	2	4	no	—
1072	D₄	—	73	4	no	—
1073	D₄	—	146	8	no	—
1074	D₄	—	146	8	no	—
1075	D₄	—	146	2	no	—
1076	D₄	—	146	4	no	—
1077	D₄	C₂×Q₈×D₇₃	1	4	yes	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	1	no	—
1082	C₂×C₄	—	2	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	1	no	—
1086	C₂×C₄	—	292	2	no	—
1087	C₂×C₄	—	292	2	no	—
1088	C₂×C₄	—	292	2	no	—
1089	C₂×C₄	—	292	2	no	—
1090	C₂×C₄	—	584	2	no	—
1091	C₂×C₄	—	584	2	no	—
1092	C₂×C₄	—	584	1	no	—
1093	C₂×C₄	—	584	1	no	—
1094	C₂×C₄	—	584	2	no	—
1095	C₂×C₄	—	584	2	no	—
1096	C₂×C₄	—	584	1	no	—
1097	C₂×C₄	—	584	2	no	—
1098	C₂×C₄	—	584	2	no	—
1099	C₂×C₄	—	73	1	no	—
1100	C₂×C₄	—	73	1	no	—
1101	C₂×C₄	—	73	4	no	—
1102	C₂×C₄	—	73	2	no	—
1103	C₂×C₄	—	73	2	no	—
1104	C₂×C₄	—	73	2	no	—
1105	C₂×C₄	—	73	2	no	—
1106	C₂×C₄	—	73	4	no	—
1107	C₂×C₄	—	73	4	no	—
1108	C₂×C₄	—	73	2	no	—
1109	C₂×C₄	—	73	2	no	—
1110	C₂×C₄	—	146	1	no	—
1111	C₂×C₄	—	146	1	no	—
1112	C₂×C₄	—	146	1	no	—
1113	C₂×C₄	—	146	2	no	—
1114	C₂×C₄	—	146	1	no	—
1115	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1116	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
1117	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1118	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
1119	C₂×C₄	#41×D₇₃	1	2	yes	—
1120	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1121	C₈	—	2	1	no	—
1122	C₈	—	2	1	no	—
1123	C₈	—	2	2	no	—
1124	C₈	—	146	2	no	—
1125	C₈	—	146	1	no	—
1126	C₈	—	146	1	no	—
1127	C₂²	—	2	1	no	—
1128	C₂²	—	2	1	no	—
1129	C₂²	—	2	4	no	—
1130	C₂²	—	4	2	no	—
1131	C₂²	—	4	2	no	—
1132	C₂²	—	8	4	no	—
1133	C₂²	—	292	4	no	—
1134	C₂²	—	292	16	no	—
1135	C₂²	—	292	2	no	—
1136	C₂²	—	292	2	no	—
1137	C₂²	—	584	4	no	—
1138	C₂²	—	584	8	no	—
1139	C₂²	—	73	2	no	—
1140	C₂²	—	73	2	no	—
1141	C₂²	—	146	4	no	—
1142	C₂²	—	146	1	no	—
1143	C₂²	—	146	1	no	—
1144	C₂²	—	146	1	no	—
1145	C₂²	—	146	1	no	—
1146	C₂²	C₂²⋊Q₈×D₇₃	1	2	yes	—
1147	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1148	C₄	—	2	2	no	—
1149	C₄	—	2	2	no	—
1150	C₄	—	4	1	no	—
1151	C₄	—	4	2	no	—
1152	C₄	—	4	1	no	—
1153	C₄	—	4	1	no	—
1154	C₄	—	4	1	no	—
1155	C₄	—	292	1	no	—
1156	C₄	—	292	1	no	—
1157	C₄	—	292	1	no	—
1158	C₄	—	292	1	no	—
1159	C₄	—	292	2	no	—
1160	C₄	—	73	2	no	—
1161	C₄	—	73	2	no	—
1162	C₄	—	146	2	no	—
1163	C₄	—	146	2	no	—
1164	C₄	C₂²⋊Q₈×D₇₃	1	2	yes	—
1165	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
1166	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
1167	C₂	—	2	2	no	—
1168	C₂	—	4	4	no	—
1169	C₂	—	292	4	no	—
1170	C₂	—	146	2	no	—
1171	C₂	—	146	2	no	—
1172	C₂	C₂×C₂²⋊Q₈×D₇₃	1	1	yes	characteristic
1173	C₂	#22624706	1	1	yes	characteristic
1174	C₂	#22624709	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×#3081	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂²×D₄×D₇₃	C₂²
hypercenter	#3081	D₇₃
hypocenter	C₇₃	#60490
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3081

Complements

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

N	H ≅ G/N	type
1. #22623335	C₂	semidirect
3. #22619765	C₂	semidirect
4. #22619764	C₂	semidirect
5. #22619763	C₂	semidirect
6. #22619762	C₂	semidirect
7. #22619761	C₂	semidirect
8. #22619760	C₂	semidirect
9. #22619759	C₂	semidirect
10. #22619758	C₂	semidirect
11. #22619757	C₂	semidirect
12. #22619756	C₂	semidirect
13. #22619755	C₂	semidirect
14. #22619729	C₂	semidirect
15. #22619726	C₂	semidirect
16. #22619726	C₂	semidirect
17. #22619723	C₂	semidirect
18. #22618519	C₂	semidirect
19. #22618518	C₂	semidirect
20. #22618492	C₂	semidirect
23. C₇₃×#3081	C₂	semidirect
27. #17989218	C₂²	semidirect
29. #17989217	C₂²	semidirect
30. #17989215	C₂²	semidirect
31. #17989215	C₂²	semidirect
33. #17989214	C₂²	semidirect
36. #17989143	C₂²	semidirect
38. #17989142	C₂²	semidirect
57. #17988890	C₂²	semidirect
58. #17988890	C₂²	semidirect
59. #17988889	C₂²	semidirect
60. #17988889	C₂²	semidirect
61. #17988888	C₂²	semidirect
62. #17988888	C₂²	semidirect
63. #17988887	C₂²	semidirect
64. #17988887	C₂²	semidirect
65. #17988886	C₂²	semidirect
66. #17988886	C₂²	semidirect
67. #17988885	C₂²	semidirect
68. #17988885	C₂²	semidirect
69. #17988884	C₂²	semidirect
70. #17988884	C₂²	semidirect
71. #17988878	C₂²	semidirect
72. #17988877	C₂²	semidirect
73. #17988876	C₂²	semidirect
74. #17988876	C₂²	semidirect
75. #17988875	C₂²	semidirect
76. #17988875	C₂²	semidirect
77. #17988874	C₂²	semidirect
78. #17988868	C₂²	semidirect
79. #17988867	C₂²	semidirect
80. #17988866	C₂²	semidirect
81. #17988866	C₂²	semidirect
82. #17988865	C₂²	semidirect
83. #17988865	C₂²	semidirect
84. #17988864	C₂²	semidirect
85. #17988630	C₂²	semidirect
86. #17988629	C₂²	semidirect
87. #17988628	C₂²	semidirect
88. #17988628	C₂²	semidirect
89. #17988628	C₂²	semidirect
90. #17988628	C₂²	semidirect
91. #17988628	C₂²	semidirect
92. #17988627	C₂²	semidirect
93. #17988626	C₂²	semidirect
94. #17988626	C₂²	semidirect
95. #17988626	C₂²	semidirect
96. #17988626	C₂²	semidirect
97. #17988626	C₂²	semidirect
98. #17988625	C₂²	semidirect
99. #17988624	C₂²	semidirect
100. #17988623	C₂²	semidirect
101. #17988623	C₂²	semidirect
102. #17988622	C₂²	semidirect
103. #17988615	C₂²	semidirect
104. #17988614	C₂²	semidirect
105. #17988613	C₂²	semidirect
106. #17988612	C₂²	semidirect
107. #17988612	C₂²	semidirect
108. #17988609	C₂²	semidirect
109. #17988609	C₂²	semidirect
124. #544×C₇₃	C₂²	semidirect
126. #478×C₇₃	C₂²	semidirect
127. #478×C₇₃	C₂²	semidirect
128. #476×C₇₃	C₂²	semidirect
129. #474×C₇₃	C₂²	semidirect
130. #428×C₇₃	C₂²	semidirect
131. #427×C₇₃	C₂²	semidirect
132. #424×C₇₃	C₂²	semidirect
141. C₂×D₄×D₇₃	Q₈	semidirect
158. #14556591	C₂³	semidirect
162. #14556590	C₂³	semidirect
163. #14556590	C₂³	semidirect
166. #14556583	C₂³	semidirect
169. #14556582	C₂³	semidirect
170. #14556582	C₂³	semidirect
251. #14556525	C₂³	semidirect
252. #14556525	C₂³	semidirect
253. #14556525	C₂³	semidirect
254. #14556524	C₂³	semidirect
255. #14556524	C₂³	semidirect
256. #14556524	C₂³	semidirect
257. #14556524	C₂³	semidirect
258. #14556524	C₂³	semidirect
259. #14556524	C₂³	semidirect
260. #14556523	C₂³	semidirect
261. #14556523	C₂³	semidirect
262. #14556523	C₂³	semidirect
263. #14556522	C₂³	semidirect
264. #14556522	C₂³	semidirect
265. #14556522	C₂³	semidirect
266. #14556522	C₂³	semidirect
267. #14556522	C₂³	semidirect
268. #14556522	C₂³	semidirect
269. C₄⋊#10596831	C₂³	semidirect
270. C₄⋊#10596831	C₂³	semidirect
271. #14556520	C₂³	semidirect
272. #14556520	C₂³	semidirect
273. #14556520	C₂³	semidirect
274. #14556520	C₂³	semidirect
291. C₄⋊Q₈×C₇₃	C₂³	semidirect
293. #125×C₇₃	C₂³	semidirect
304. #107×C₇₃	C₂³	semidirect
305. #107×C₇₃	C₂³	semidirect
306. #107×C₇₃	C₂³	semidirect
307. #106×C₇₃	C₂³	semidirect
308. #106×C₇₃	C₂³	semidirect
309. #106×C₇₃	C₂³	semidirect
310. C₄⋊C₈×C₇₃	C₂³	semidirect
311. C₄⋊C₈×C₇₃	C₂³	semidirect
601. #3081	D₇₃	semidirect
611. C₇₃	#60490	semidirect
622. #544	C₂×D₇₃	semidirect
661. #478	C₂×D₇₃	semidirect
662. #478	C₂×D₇₃	semidirect
670. #476	C₂×D₇₃	semidirect
678. #474	C₂×D₇₃	semidirect
692. #428	C₂×D₇₃	semidirect
698. #427	C₂×D₇₃	semidirect
704. #424	C₂×D₇₃	semidirect
757. C₄⋊Q₈	C₂²×D₇₃	semidirect
767. #125	C₂²×D₇₃	semidirect
865. #107	C₂²×D₇₃	semidirect
866. #107	C₂²×D₇₃	semidirect
867. #107	C₂²×D₇₃	semidirect
877. #106	C₂²×D₇₃	semidirect
878. #106	C₂²×D₇₃	semidirect
879. #106	C₂²×D₇₃	semidirect
886. C₄⋊C₈	C₂²×D₇₃	semidirect
887. C₄⋊C₈	C₂²×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623335	2
#518×D₇₃	2
#22619765	2
#22619764	2
#22619763	2
#22619762	2
#22619761	2
#22619760	2
#22619759	2
#22619758	2
#22619757	2
#22619756	2
#22619755	2
#22619729	2
#22619726	2
#22619723	2
#22618519	2
#22618518	2
#22618492	2
C₂×#17988590	2
#418×D₇₃	2
C₇₃×#3081	2
#60490	73