Subgroups — #33981651

Order 18688.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22623911	C₂	1	1	yes	maximal, characteristic, complemented
2	#22623541	C₂	1	1	yes	maximal, characteristic, complemented
3	#22622804	C₂	1	1	yes	maximal, characteristic, complemented
4	#22622796	C₂	1	1	yes	maximal, characteristic, complemented
5	#22622625	C₂	1	1	yes	maximal, characteristic, complemented
6	#22622589	C₂	1	1	yes	maximal, characteristic, complemented
7	#22622326	C₂	1	2	yes	maximal, complemented
8	#22622325	C₂	1	1	yes	maximal, characteristic, complemented
9	#22622313	C₂	1	2	yes	maximal, complemented
10	#22622290	C₂	1	1	yes	maximal, characteristic, complemented
11	#22621774	C₂	1	2	yes	maximal, complemented
12	#22621759	C₂	1	2	yes	maximal, complemented
13	#22621757	C₂	1	1	yes	maximal, characteristic, complemented
14	#22621746	C₂	1	1	yes	maximal, characteristic, complemented
15	#22621281	C₂	1	2	yes	maximal, complemented
16	#22621257	C₂	1	1	yes	maximal, characteristic, complemented
17	#22621103	C₂	1	2	yes	maximal, complemented
18	#22621069	C₂	1	1	yes	maximal, characteristic, complemented
19	#22619977	C₂	1	2	yes	maximal, complemented
20	#22619719	C₂	1	1	yes	maximal, characteristic, complemented
21	#478×D₇₃	C₂	1	2	yes	maximal, complemented
22	#22619039	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
24	#17989322	C₂²	1	1	yes	characteristic
25	#17989316	C₂²	1	1	yes	characteristic, complemented
26	#17989297	C₂²	1	1	yes	characteristic
27	#17989297	C₂²	1	1	yes	characteristic
28	#17989294	C₂²	1	1	yes	characteristic
29	#17989294	C₂²	1	1	yes	characteristic, complemented
30	#17989284	C₂²	1	2	yes	complemented
31	#17989283	—	2	1	no	—
32	#17989281	C₂²	1	2	yes	—
33	#17989277	—	2	1	no	—
34	#17989273	—	2	2	no	—
35	#17989271	C₂²	1	2	yes	complemented
36	#17989261	—	2	2	no	—
37	#17989242	—	2	1	no	—
38	#17989242	C₂²	1	1	yes	characteristic
39	#17989233	—	2	1	no	—
40	#17989225	C₂²	1	2	yes	—
41	D₄×D₂₉₂	C₂²	1	1	yes	characteristic
42	#17989199	—	2	1	no	—
43	#17989180	—	2	2	no	—
44	#17989144	C₂²	1	1	yes	characteristic, complemented
45	#17989137	C₂²	1	1	yes	characteristic
46	#17989124	C₂²	1	2	yes	—
47	#17989121	—	2	1	no	—
48	#17989116	C₂²	1	2	yes	complemented
49	#125×D₇₃	C₂²	1	2	yes	complemented
50	#17989096	—	2	2	no	—
51	#17989067	—	2	1	no	—
52	C₄×#11924028	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₂₉₂	—	2	1	no	—
54	C₄×D₄×D₇₃	C₂²	1	2	yes	—
55	#17988992	C₂²	1	1	yes	characteristic, complemented
56	#17988988	C₂²	1	2	yes	complemented
57	#17988987	C₂²	1	2	yes	complemented
58	#17988985	C₂²	1	1	yes	characteristic, complemented
59	#17988943	C₂²	1	2	yes	complemented
60	#17988943	C₂²	1	2	yes	complemented
61	#17988934	C₂²	1	1	yes	characteristic
62	#17988934	C₂²	1	1	yes	characteristic
63	#17988921	C₂²	1	2	yes	complemented
64	#17988921	C₂²	1	2	yes	complemented
65	#17988916	C₂²	1	2	yes	complemented
66	#17988912	C₂²	1	2	yes	complemented
67	#17988912	C₂²	1	2	yes	complemented
68	#17988907	C₂²	1	2	yes	—
69	#17988904	C₂²	1	2	yes	complemented
70	#17988902	C₂²	1	2	yes	—
71	#17988894	C₂²	1	2	yes	complemented
72	#17988892	C₂²	1	2	yes	complemented
73	#17988890	C₂²	1	2	yes	complemented
74	#17988889	C₂²	1	2	yes	—
75	#17988888	C₂²	1	2	yes	complemented
76	#17988888	C₂²	1	2	yes	complemented
77	#17988887	C₂²	1	2	yes	—
78	#17988886	C₂²	1	2	yes	complemented
79	#17988885	C₂²	1	2	yes	—
80	#17988885	C₂²	1	2	yes	complemented
81	#17988884	C₂²	1	2	yes	complemented
82	#17988882	C₂²	1	1	yes	characteristic, complemented
83	#17988882	C₂²	1	1	yes	characteristic, complemented
84	#17988877	C₂²	1	1	yes	characteristic
85	#17988877	C₂²	1	1	yes	characteristic, complemented
86	#17988872	C₂²	1	1	yes	characteristic, complemented
87	#17988867	C₂²	1	1	yes	characteristic
88	#17988825	C₂²	1	2	yes	complemented
89	#17988822	C₂²	1	2	yes	—
90	#17988821	C₂²	1	2	yes	complemented
91	#17988819	C₂²	1	2	yes	—
92	#17988818	C₂²	1	2	yes	complemented
93	#17988813	C₂²	1	2	yes	complemented
94	#17988811	C₂²	1	2	yes	complemented
95	#17988804	C₂²	1	2	yes	complemented
96	#17988799	C₂²	1	2	yes	complemented
97	#17988787	C₂²	1	1	yes	characteristic
98	#17988782	C₂²	1	1	yes	characteristic
99	#17988736	C₂²	1	2	yes	—
100	#17988719	C₂²	1	2	yes	—
101	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
102	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic, complemented
103	SD₁₆×Dic₇₃	C₂²	1	2	yes	—
104	#17988672	C₂²	1	2	yes	complemented
105	D₈×Dic₇₃	C₂²	1	2	yes	—
106	#17988667	C₂²	1	2	yes	complemented
107	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
108	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
109	#17988650	C₂²	1	2	yes	complemented
110	#17988650	C₂²	1	2	yes	complemented
111	#17988639	C₂²	1	2	yes	complemented
112	#17988623	C₂²	1	2	yes	complemented
113	#107×D₇₃	C₂²	1	2	yes	complemented
114	#106×D₇₃	C₂²	1	2	yes	complemented
115	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic, complemented
116	C₄⋊C₈×D₇₃	C₂²	1	2	yes	complemented
117	#17988583	C₂²	1	2	yes	—
118	#102×D₇₃	C₂²	1	2	yes	—
119	#102×D₇₃	C₂²	1	2	yes	—
120	#529×C₇₃	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
122	#485×C₇₃	C₂²	1	1	yes	characteristic, complemented
123	#482×C₇₃	C₂²	1	1	yes	characteristic, complemented
124	#479×C₇₃	C₂²	1	1	yes	characteristic, complemented
125	#478×C₇₃	C₂²	1	1	yes	characteristic
126	#464×C₇₃	C₂²	1	1	yes	characteristic, complemented
127	#463×C₇₃	C₂²	1	1	yes	characteristic
128	#452×C₇₃	C₂²	1	1	yes	characteristic
129	#449×C₇₃	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic
132	C₄×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
134	#431×C₇₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#11924028	—	2	1	no	—
136	C₂×#11924028	—	2	1	no	—
137	C₂×#11924028	D₄	1	1	yes	characteristic
138	C₂²×D₂₉₂	—	2	1	no	—
139	C₂×D₄×D₇₃	C₂³	1	2	yes	—
140	C₂²×C₄×D₇₃	—	2	2	no	—
141	C₂×#11924015	C₂³	1	2	yes	—
142	C₂×#11924013	C₂³	1	2	yes	—
143	C₂²×#10596831	C₂³	1	2	yes	—
144	C₂×C₈×D₇₃	C₂³	1	2	yes	—
145	C₂×C₈×D₇₃	C₂³	1	2	yes	—
146	#14556591	—	2	1	no	—
147	#14556591	C₂³	1	1	yes	characteristic
148	#14556591	C₂³	1	1	yes	characteristic
149	#14556591	C₂³	1	1	yes	characteristic
150	#14556588	C₂³	1	1	yes	characteristic
151	#14556586	—	2	2	no	—
152	#14556585	—	2	2	no	—
153	#14556584	—	2	2	no	—
154	#14556584	—	2	2	no	—
155	#14556584	—	2	2	no	—
156	#14556583	—	2	1	no	—
157	#14556583	—	2	1	no	—
158	#14556583	C₂³	1	2	yes	—
159	#14556582	—	2	2	no	—
160	#14556582	C₂³	1	2	yes	—
161	#14556582	C₂³	1	2	yes	—
162	#14556582	C₂³	1	2	yes	—
163	#14556581	—	2	2	no	—
164	#14556581	—	2	2	no	—
165	#14556581	—	2	2	no	—
166	#14556580	C₂³	1	2	yes	—
167	#14556579	—	2	1	no	—
168	#14556579	—	2	1	no	—
169	#14556576	—	2	2	no	—
170	#14556576	—	2	2	no	—
171	#14556574	—	2	2	no	—
172	#14556573	—	2	2	no	—
173	#14556573	—	2	2	no	—
174	#14556573	—	2	2	no	—
175	#14556573	—	2	2	no	—
176	#14556572	—	2	2	no	—
177	#14556570	—	2	1	no	—
178	#14556570	—	2	1	no	—
179	#14556570	—	2	1	no	—
180	#14556570	—	2	1	no	—
181	#14556570	—	2	1	no	—
182	#14556569	—	2	2	no	—
183	#14556569	—	2	2	no	—
184	#14556568	—	2	2	no	—
185	#14556568	—	2	2	no	—
186	#14556567	C₂³	1	2	yes	—
187	#14556567	C₂³	1	2	yes	—
188	#14556566	C₂³	1	2	yes	—
189	#14556565	—	2	1	no	—
190	#14556565	—	2	1	no	—
191	#14556565	C₂³	1	2	yes	—
192	#14556564	—	2	2	no	—
193	#14556563	—	2	2	no	—
194	#14556562	—	2	2	no	—
195	#14556562	C₂³	1	2	yes	—
196	#14556561	—	2	2	no	—
197	#14556559	—	2	2	no	—
198	Q₈×Dic₇₃	C₂³	1	2	yes	—
199	C₄×Dic₁₄₆	—	2	1	no	—
200	C₄×Dic₁₄₆	—	2	1	no	—
201	C₄×Dic₁₄₆	—	2	1	no	—
202	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
203	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
204	C₄×D₂₉₂	—	2	1	no	—
205	C₄×D₂₉₂	—	2	1	no	—
206	C₄×D₂₉₂	—	2	2	no	—
207	C₄×D₂₉₂	—	2	1	no	—
208	C₄×D₂₉₂	—	2	2	no	—
209	C₄×D₂₉₂	—	2	1	no	—
210	C₄×D₂₉₂	D₄	1	1	yes	characteristic
211	C₄×D₂₉₂	C₂³	1	2	yes	—
212	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
213	D₄×Dic₇₃	C₂³	1	2	yes	—
214	D₄×Dic₇₃	C₂³	1	2	yes	—
215	#14556553	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₇₃	—	2	2	no	—
217	C₄×C₂²⋊D₇₃	D₄	1	2	yes	—
218	C₄×C₂²⋊D₇₃	C₂³	1	2	yes	—
219	#14556551	—	2	2	no	—
220	#14556551	—	2	2	no	—
221	#14556551	—	2	2	no	—
222	#14556550	D₄	1	1	yes	characteristic
223	#14556550	C₂³	1	2	yes	—
224	#14556549	—	2	2	no	—
225	#14556548	—	2	2	no	—
226	#14556548	D₄	1	2	yes	—
227	#14556547	—	2	2	no	—
228	C₂×C₄⋊Dic₇₃	—	2	1	no	—
229	C₂×C₄⋊Dic₇₃	—	2	1	no	—
230	C₄⋊C₄×D₇₃	—	2	2	no	—
231	C₄⋊C₄×D₇₃	—	2	2	no	—
232	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
233	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
234	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
235	C₂×#11924005	—	2	2	no	—
236	C₂²⋊C₄×D₇₃	—	2	2	no	—
237	C₄²×D₇₃	C₂³	1	2	yes	—
238	#14556525	C₂³	1	2	yes	—
239	#14556525	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	C₄⋊#10596831	C₂³	1	1	yes	characteristic
249	C₄⋊#10596831	C₂³	1	1	yes	characteristic
250	C₄⋊#10596831	C₂³	1	2	yes	—
251	#14556520	C₂³	1	2	yes	—
252	#14556520	C₂³	1	2	yes	—
253	#14556515	C₂³	1	2	yes	—
254	#14556515	C₂³	1	2	yes	—
255	#14556515	C₂³	1	2	yes	—
256	#14556513	C₂³	1	2	yes	—
257	#14556513	C₂³	1	2	yes	—
258	#14556513	C₂³	1	2	yes	—
259	#14556513	C₂³	1	2	yes	—
260	#14556512	C₂³	1	2	yes	—
261	#14556512	C₂³	1	2	yes	—
262	#14556512	C₂³	1	2	yes	—
263	#14556511	C₂³	1	2	yes	—
264	#14556511	C₂³	1	2	yes	—
265	#14556503	C₂³	1	2	yes	—
266	#14556503	C₂³	1	2	yes	—
267	C₈×Dic₇₃	C₂³	1	2	yes	—
268	C₈×Dic₇₃	C₂³	1	2	yes	—
269	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₇₃	C₂³	1	1	yes	characteristic
273	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
274	#126×C₇₃	—	2	1	no	—
275	#125×C₇₃	C₂³	1	1	yes	characteristic
276	#124×C₇₃	C₂³	1	1	yes	characteristic
277	#123×C₇₃	—	2	1	no	—
278	C₂²⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
279	#121×C₇₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₇₃	—	2	1	no	—
284	C₄×D₄×C₇₃	—	2	1	no	—
285	C₄×D₄×C₇₃	—	2	1	no	—
286	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
289	#117×C₇₃	—	2	1	no	—
290	#117×C₇₃	—	2	1	no	—
291	#117×C₇₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₇₃	—	2	1	no	—
293	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
294	#107×C₇₃	C₂³	1	1	yes	characteristic
295	#107×C₇₃	C₂³	1	1	yes	characteristic
296	#106×C₇₃	C₂³	1	1	yes	characteristic
297	#106×C₇₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
300	#103×C₇₃	C₂³	1	1	yes	characteristic
301	#103×C₇₃	C₂³	1	1	yes	characteristic
302	#103×C₇₃	C₂³	1	1	yes	characteristic
303	#103×C₇₃	C₂³	1	1	yes	characteristic
304	#102×C₇₃	C₂³	1	1	yes	characteristic
305	#102×C₇₃	C₂³	1	1	yes	characteristic
306	#102×C₇₃	C₂³	1	1	yes	characteristic
307	#102×C₇₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
312	C₂³×D₇₃	—	2	2	no	—
313	#11924028	—	2	4	no	—
314	#11924028	—	4	4	no	—
315	#11924028	—	8	2	no	—
316	C₂×Dic₁₄₆	—	2	1	no	—
317	C₂×Dic₁₄₆	—	2	1	no	—
318	C₂×Dic₁₄₆	—	2	1	no	—
319	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
320	C₂×D₂₉₂	—	2	2	no	—
321	C₂×D₂₉₂	—	2	1	no	—
322	C₂×D₂₉₂	—	2	1	no	—
323	C₂×D₂₉₂	—	4	4	no	—
324	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
325	C₂×D₂₉₂	C₂⁴	1	2	yes	—
326	C₂×C₂²⋊D₇₃	—	2	2	no	—
327	C₂×C₂²⋊D₇₃	—	2	2	no	—
328	C₂×C₂²⋊D₇₃	—	2	2	no	—
329	C₂×C₂²⋊D₇₃	C₂×D₄	1	2	yes	—
330	D₄×D₇₃	—	2	4	no	—
331	D₄×D₇₃	—	4	2	no	—
332	C₂²×Dic₇₃	—	2	2	no	—
333	C₂²×Dic₇₃	—	2	2	no	—
334	C₂×C₄×D₇₃	—	2	2	no	—
335	C₂×C₄×D₇₃	—	2	2	no	—
336	C₂×C₄×D₇₃	—	2	2	no	—
337	C₂×C₄×D₇₃	—	2	2	no	—
338	C₂×C₄×D₇₃	—	2	2	no	—
339	C₂×C₄×D₇₃	—	8	4	no	—
340	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
341	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
342	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
343	#11924015	—	4	2	no	—
344	#11924013	—	4	2	no	—
345	C₂×#10596831	—	4	2	no	—
346	C₂×#10596831	C₂⁴	1	2	yes	—
347	C₂×#10596831	C₂⁴	1	2	yes	—
348	C₈×D₇₃	—	4	2	no	—
349	C₈×D₇₃	—	4	2	no	—
350	C₄⋊Dic₇₃	—	2	1	no	—
351	C₄⋊Dic₇₃	—	2	1	no	—
352	C₄⋊Dic₇₃	—	2	1	no	—
353	C₄⋊Dic₇₃	—	2	2	no	—
354	C₄⋊Dic₇₃	—	2	2	no	—
355	C₄⋊Dic₇₃	—	2	2	no	—
356	C₄⋊Dic₇₃	—	2	2	no	—
357	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
358	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
360	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
361	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
362	#11924007	—	2	2	no	—
363	#11924007	—	2	2	no	—
364	#11924007	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
373	#11924007	C₂×D₄	1	2	yes	—
374	C₂²⋊Dic₇₃	—	2	2	no	—
375	C₂²⋊Dic₇₃	—	2	2	no	—
376	C₂²⋊Dic₇₃	—	2	2	no	—
377	C₂²⋊Dic₇₃	—	2	2	no	—
378	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
379	#11924005	—	2	2	no	—
380	#11924005	—	2	2	no	—
381	#11924005	—	2	2	no	—
382	#11924005	—	2	2	no	—
383	#11924005	—	2	2	no	—
384	#11924005	—	2	2	no	—
385	#11924005	—	2	2	no	—
386	#11924005	—	2	2	no	—
387	#11924005	C₂×D₄	1	2	yes	—
388	#11924005	C₂×D₄	1	2	yes	—
389	C₄×Dic₇₃	—	2	2	no	—
390	C₄×Dic₇₃	—	2	2	no	—
391	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
392	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
393	C₄×Dic₇₃	C₂⁴	1	2	yes	—
394	#41×C₇₃	—	2	2	no	—
395	#41×C₇₃	—	4	1	no	—
396	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
397	C₂×Q₈×C₇₃	C₂⁴	1	1	yes	characteristic
398	C₂×D₄×C₇₃	—	2	1	no	—
399	C₂×D₄×C₇₃	—	2	1	no	—
400	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
401	C₂×D₄×C₇₃	C₂⁴	1	1	yes	characteristic
402	C₂²×C₄×C₇₃	—	2	1	no	—
403	C₂²×C₄×C₇₃	—	2	1	no	—
404	C₂²×C₄×C₇₃	—	2	1	no	—
405	C₂²×C₄×C₇₃	—	2	1	no	—
406	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
407	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
408	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
409	Q₁₆×C₇₃	—	4	1	no	—
410	SD₁₆×C₇₃	—	2	2	no	—
411	SD₁₆×C₇₃	—	4	1	no	—
412	D₈×C₇₃	—	2	2	no	—
413	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
416	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
417	C₄⋊C₄×C₇₃	—	2	1	no	—
418	C₄⋊C₄×C₇₃	—	2	1	no	—
419	C₄⋊C₄×C₇₃	—	2	1	no	—
420	C₄⋊C₄×C₇₃	—	2	1	no	—
421	C₄⋊C₄×C₇₃	—	2	1	no	—
422	C₄⋊C₄×C₇₃	—	2	1	no	—
423	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
426	C₄⋊C₄×C₇₃	C₂⁴	1	1	yes	characteristic
427	C₂²⋊C₄×C₇₃	—	2	1	no	—
428	C₂²⋊C₄×C₇₃	—	2	1	no	—
429	C₂²⋊C₄×C₇₃	—	2	1	no	—
430	C₂²⋊C₄×C₇₃	—	2	1	no	—
431	C₂²⋊C₄×C₇₃	—	2	1	no	—
432	C₂²⋊C₄×C₇₃	—	2	1	no	—
433	C₂²⋊C₄×C₇₃	—	2	1	no	—
434	C₂²⋊C₄×C₇₃	—	2	1	no	—
435	C₄²×C₇₃	—	2	1	no	—
436	C₄²×C₇₃	—	2	1	no	—
437	C₄²×C₇₃	—	2	1	no	—
438	C₄²×C₇₃	—	2	1	no	—
439	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
440	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
441	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
442	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
443	C₂³×C₇₃	—	2	1	no	—
444	C₂³×C₇₃	—	2	1	no	—
445	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
446	C₂²×D₇₃	—	2	2	no	—
447	C₂²×D₇₃	—	4	4	no	—
448	C₂²×D₇₃	—	4	4	no	—
449	C₂²×D₇₃	—	8	2	no	—
450	C₂²×D₇₃	C₂²×D₄	1	2	yes	—
451	Q₈×C₇₃	—	2	1	no	—
452	Q₈×C₇₃	—	2	1	no	—
453	Q₈×C₇₃	—	2	1	no	—
454	Q₈×C₇₃	—	2	1	no	—
455	D₄×C₇₃	—	2	1	no	—
456	D₄×C₇₃	—	2	1	no	—
457	D₄×C₇₃	—	2	1	no	—
458	D₄×C₇₃	—	4	2	no	—
459	D₄×C₇₃	—	8	1	no	—
460	D₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
461	C₂×C₄×C₇₃	—	2	2	no	—
462	C₂×C₄×C₇₃	—	2	1	no	—
463	C₂×C₄×C₇₃	—	2	1	no	—
464	C₂×C₄×C₇₃	—	2	1	no	—
465	C₂×C₄×C₇₃	—	2	1	no	—
466	C₂×C₄×C₇₃	—	2	1	no	—
467	C₂×C₄×C₇₃	—	2	1	no	—
468	C₂×C₄×C₇₃	—	2	1	no	—
469	C₂×C₄×C₇₃	—	2	1	no	—
470	C₂×C₄×C₇₃	—	4	1	no	—
471	C₂×C₄×C₇₃	—	4	2	no	—
472	C₂×C₄×C₇₃	—	4	2	no	—
473	C₂×C₄×C₇₃	—	4	2	no	—
474	C₂×C₄×C₇₃	—	4	2	no	—
475	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
481	C₂²⋊D₇₃	—	2	4	no	—
482	C₂²⋊D₇₃	—	4	4	no	—
483	C₂²⋊D₇₃	—	4	4	no	—
484	C₂²⋊D₇₃	—	8	2	no	—
485	C₂×Dic₇₃	—	2	2	no	—
486	C₂×Dic₇₃	—	2	2	no	—
487	C₂×Dic₇₃	—	2	2	no	—
488	C₂×Dic₇₃	—	8	2	no	—
489	C₂×Dic₇₃	—	8	2	no	—
490	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
491	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
492	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
493	D₂₉₂	—	2	2	no	—
494	D₂₉₂	—	2	2	no	—
495	D₂₉₂	—	4	4	no	—
496	D₂₉₂	—	4	2	no	—
497	D₂₉₂	—	8	1	no	—
498	D₂₉₂	#135	1	4	yes	—
499	C₄×D₇₃	—	2	4	no	—
500	C₄×D₇₃	—	2	2	no	—
501	C₄×D₇₃	—	2	2	no	—
502	C₄×D₇₃	—	4	2	no	—
503	C₄×D₇₃	—	4	4	no	—
504	C₄×D₇₃	—	4	4	no	—
505	C₄×D₇₃	—	8	2	no	—
506	C₄×D₇₃	—	8	2	no	—
507	C₄×D₇₃	—	8	2	no	—
508	Dic₁₄₆	—	2	2	no	—
509	Dic₁₄₆	—	4	2	no	—
510	Dic₁₄₆	—	8	1	no	—
511	Dic₁₄₆	—	8	1	no	—
512	C₈×C₇₃	—	2	1	no	—
513	C₈×C₇₃	—	2	1	no	—
514	C₈×C₇₃	—	2	1	no	—
515	C₈×C₇₃	—	2	1	no	—
516	#10596831	—	2	2	no	—
517	#10596831	—	2	2	no	—
518	C₂²×C₇₃	—	2	1	no	—
519	C₂²×C₇₃	—	2	2	no	—
520	C₂²×C₇₃	—	2	1	no	—
521	C₂²×C₇₃	—	2	1	no	—
522	C₂²×C₇₃	—	4	1	no	—
523	C₂²×C₇₃	—	4	1	no	—
524	C₂²×C₇₃	—	4	1	no	—
525	C₂²×C₇₃	—	4	1	no	—
526	C₂²×C₇₃	—	4	1	no	—
527	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₇₃	—	2	2	no	—
529	C₂×D₇₃	—	2	2	no	—
530	C₂×D₇₃	—	4	2	no	—
531	C₂×D₇₃	—	4	2	no	—
532	C₂×D₇₃	—	4	2	no	—
533	C₂×D₇₃	—	8	8	no	—
534	C₂×D₇₃	C₂×#135	1	4	yes	—
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	—	4	1	no	—
540	C₄×C₇₃	—	4	1	no	—
541	C₄×C₇₃	—	4	1	no	—
542	C₄×C₇₃	—	4	1	no	—
543	C₄×C₇₃	—	4	1	no	—
544	C₄×C₇₃	—	4	1	no	—
545	C₄×C₇₃	C₂×#135	1	2	yes	—
546	C₄×C₇₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
547	C₄×C₇₃	#585	1	1	yes	characteristic
548	Dic₇₃	—	2	2	no	—
549	Dic₇₃	—	2	2	no	—
550	Dic₇₃	—	2	2	no	—
551	Dic₇₃	—	4	2	no	—
552	Dic₇₃	—	4	2	no	—
553	Dic₇₃	—	4	2	no	—
554	#62103	—	73	1	no	maximal, Sylow
555	C₂×C₇₃	—	4	2	no	—
556	C₂×C₇₃	—	4	1	no	—
557	C₂×C₇₃	—	8	1	no	—
558	C₂×C₇₃	#3489	1	1	yes	characteristic
559	C₂×C₇₃	C₂²×#135	1	1	yes	characteristic
560	C₂×C₇₃	#3585	1	1	yes	characteristic
561	D₇₃	—	2	4	no	—
562	D₇₃	—	8	2	no	—
563	#3515	—	73	1	no	—
564	#3481	—	73	1	no	—
565	#3381	—	73	1	no	—
566	#3380	—	73	1	no	—
567	#3365	—	73	1	no	—
568	#3361	—	73	1	no	—
569	#3339	—	73	2	no	—
570	#3338	—	73	1	no	—
571	#3337	—	73	2	no	—
572	#3335	—	73	1	no	—
573	#3297	—	73	2	no	—
574	#3296	—	73	2	no	—
575	#3295	—	73	1	no	—
576	#3294	—	73	1	no	—
577	#3250	—	73	2	no	—
578	#3247	—	73	1	no	—
579	#3232	—	73	2	no	—
580	#3228	—	73	1	no	—
581	#3105	—	73	2	no	—
582	#3102	D₇₃	1	1	yes	characteristic, complemented
583	#3076	—	73	1	no	—
584	C₂×#478	—	73	2	no	—
585	#2988	—	73	1	no	—
586	C₇₃	#62103	1	1	yes	characteristic, complemented, Sylow
587	#559	—	73	1	no	—
588	#557	—	73	1	no	—
589	#554	—	73	1	no	—
590	#554	—	73	1	no	—
591	#554	—	73	1	no	—
592	#554	—	73	1	no	—
593	#553	—	73	2	no	—
594	#553	—	73	2	no	—
595	#553	—	146	1	no	—
596	#552	—	73	2	no	—
597	#552	—	146	1	no	—
598	#552	—	146	2	no	—
599	#551	—	146	2	no	—
600	#547	—	73	1	no	—
601	#547	—	146	1	no	—
602	#546	—	73	2	no	—
603	#546	—	146	1	no	—
604	D₄²	—	73	1	no	—
605	#541	—	146	1	no	—
606	#539	—	146	2	no	—
607	#533	—	73	1	no	—
608	#532	—	73	1	no	—
609	#529	—	73	2	no	—
610	#529	—	73	2	no	—
611	#529	—	146	1	no	—
612	#529	C₂×D₇₃	1	1	yes	characteristic, complemented
613	C₂×#125	—	73	2	no	—
614	#525	—	146	2	no	—
615	#520	—	146	1	no	—
616	C₄×#41	—	73	1	no	—
617	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
618	C₂×C₄×D₄	—	73	2	no	—
619	C₂×C₄×D₄	—	146	1	no	—
620	#500	—	73	1	no	—
621	#499	—	73	2	no	—
622	#499	—	73	2	no	—
623	#498	—	73	1	no	—
624	#488	—	73	2	no	—
625	#488	—	73	2	no	—
626	#486	—	73	1	no	—
627	#486	—	73	1	no	—
628	#485	C₂×D₇₃	1	1	yes	characteristic, complemented
629	#484	—	73	2	no	—
630	#484	—	73	2	no	—
631	#483	—	73	2	no	—
632	#482	—	73	2	no	—
633	#482	—	73	2	no	—
634	#482	C₂×D₇₃	1	1	yes	characteristic, complemented
635	#481	—	73	2	no	—
636	#481	—	73	2	no	—
637	#480	—	73	2	no	—
638	#479	—	73	2	no	—
639	#479	—	73	2	no	—
640	#479	C₂×D₇₃	1	1	yes	characteristic, 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	—	73	2	no	—
649	#478	—	73	2	no	—
650	#478	C₂×D₇₃	1	1	yes	characteristic
651	#477	—	73	1	no	—
652	#477	—	73	1	no	—
653	#476	—	73	1	no	—
654	#476	—	73	1	no	—
655	#475	—	73	1	no	—
656	#474	—	73	1	no	—
657	#467	—	73	2	no	—
658	#466	—	73	2	no	—
659	#466	—	73	2	no	—
660	#465	—	73	2	no	—
661	#465	—	73	2	no	—
662	#465	—	73	2	no	—
663	#464	—	73	2	no	—
664	#464	C₂×D₇₃	1	1	yes	characteristic, complemented
665	#463	—	73	2	no	—
666	#463	—	73	2	no	—
667	#463	C₂×D₇₃	1	1	yes	characteristic
668	#460	—	73	1	no	—
669	#459	—	73	1	no	—
670	#452	C₂×D₇₃	1	1	yes	characteristic
671	#450	—	73	2	no	—
672	#449	C₂×D₇₃	1	1	yes	characteristic
673	#447	—	73	2	no	—
674	C₈×Q₈	—	73	1	no	—
675	C₈×Q₈	—	73	1	no	—
676	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
677	C₄×SD₁₆	—	73	2	no	—
678	C₄×SD₁₆	—	73	2	no	—
679	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
681	C₄×D₈	—	73	2	no	—
682	C₄×D₈	—	73	2	no	—
683	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
684	C₈×D₄	—	73	2	no	—
685	C₈×D₄	—	73	2	no	—
686	C₈×D₄	—	73	1	no	—
687	C₈×D₄	—	73	1	no	—
688	#431	—	73	2	no	—
689	#431	C₂×D₇₃	1	1	yes	characteristic, complemented
690	#427	—	73	2	no	—
691	C₂×#107	—	73	2	no	—
692	C₂×#106	—	73	2	no	—
693	C₂×C₄⋊C₈	—	73	1	no	—
694	C₂×C₄⋊C₈	—	73	2	no	—
695	#416	—	73	2	no	—
696	C₂×#102	—	73	2	no	—
697	C₂×#102	—	73	2	no	—
698	C₂×#41	—	73	1	no	—
699	C₂×#41	—	146	1	no	—
700	C₂×#41	—	146	1	no	—
701	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
702	C₂²×D₄	—	73	2	no	—
703	C₂²×D₄	—	146	1	no	—
704	C₂³×C₄	—	146	2	no	—
705	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
706	C₂×SD₁₆	—	73	2	no	—
707	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂²×D₇₃	1	1	yes	characteristic
709	C₂×D₈	—	73	2	no	—
710	C₂×D₈	C₂²×D₇₃	1	1	yes	characteristic
711	C₂²×C₈	—	73	2	no	—
712	C₂²×C₈	—	73	2	no	—
713	C₂²×C₈	—	73	2	no	—
714	C₄⋊Q₈	—	73	1	no	—
715	C₄⋊Q₈	—	73	1	no	—
716	C₄⋊Q₈	—	73	1	no	—
717	C₄⋊Q₈	—	146	1	no	—
718	#127	—	73	1	no	—
719	#126	—	2	1	no	—
720	#126	—	146	2	no	—
721	#126	—	146	2	no	—
722	#126	—	146	2	no	—
723	#126	—	146	2	no	—
724	#126	—	146	2	no	—
725	#125	—	73	2	no	—
726	#125	—	73	2	no	—
727	#125	—	73	2	no	—
728	#125	—	73	2	no	—
729	#125	—	146	1	no	—
730	#125	—	146	1	no	—
731	#125	—	146	2	no	—
732	#125	—	146	2	no	—
733	#125	—	146	2	no	—
734	#125	—	146	2	no	—
735	#125	C₂²×D₇₃	1	1	yes	characteristic
736	#124	—	73	2	no	—
737	#124	—	146	1	no	—
738	#124	—	146	1	no	—
739	#124	C₂²×D₇₃	1	1	yes	characteristic
740	#123	—	2	1	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	#123	—	146	2	no	—
749	C₂²⋊Q₈	—	73	2	no	—
750	C₂²⋊Q₈	—	73	2	no	—
751	C₂²⋊Q₈	—	146	2	no	—
752	C₂²⋊Q₈	—	146	2	no	—
753	C₂²⋊Q₈	—	146	2	no	—
754	C₂²⋊Q₈	—	146	2	no	—
755	C₂²⋊Q₈	—	146	1	no	—
756	C₂²⋊Q₈	—	146	1	no	—
757	C₂²⋊Q₈	—	146	1	no	—
758	C₂²⋊Q₈	—	146	1	no	—
759	C₂²⋊Q₈	—	146	1	no	—
760	C₂²⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
761	#121	—	73	2	no	—
762	#121	—	73	2	no	—
763	#121	—	73	2	no	—
764	#121	—	146	2	no	—
765	#121	—	146	2	no	—
766	#121	—	146	1	no	—
767	#121	—	146	2	no	—
768	#121	—	146	1	no	—
769	#121	C₂²×D₇₃	1	1	yes	characteristic
770	#120	—	146	2	no	—
771	#120	—	146	2	no	—
772	C₄×Q₈	—	73	1	no	—
773	C₄×Q₈	—	73	1	no	—
774	C₄×Q₈	—	73	2	no	—
775	C₄×Q₈	—	146	1	no	—
776	C₄×Q₈	—	146	1	no	—
777	C₄×Q₈	—	146	1	no	—
778	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
780	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	73	2	no	—
785	C₄×D₄	—	73	2	no	—
786	C₄×D₄	—	73	2	no	—
787	C₄×D₄	—	73	2	no	—
788	C₄×D₄	—	73	2	no	—
789	C₄×D₄	—	73	1	no	—
790	C₄×D₄	—	73	1	no	—
791	C₄×D₄	—	73	2	no	—
792	C₄×D₄	—	146	2	no	—
793	C₄×D₄	—	146	1	no	—
794	C₄×D₄	—	146	2	no	—
795	C₄×D₄	—	146	1	no	—
796	C₄×D₄	—	146	1	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	1	no	—
802	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
803	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
804	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	73	1	no	—
808	#117	—	73	2	no	—
809	#117	—	73	2	no	—
810	#117	—	146	2	no	—
811	#117	—	146	2	no	—
812	#117	—	146	2	no	—
813	#117	C₂²×D₇₃	1	1	yes	characteristic
814	C₂×C₄⋊C₄	—	73	2	no	—
815	C₂×C₄⋊C₄	—	73	2	no	—
816	C₂×C₄⋊C₄	—	73	2	no	—
817	C₂×C₄⋊C₄	—	146	2	no	—
818	C₂×C₄⋊C₄	—	146	2	no	—
819	C₂×C₄⋊C₄	—	146	1	no	—
820	C₂×C₄⋊C₄	—	146	1	no	—
821	C₂×C₂²⋊C₄	—	146	2	no	—
822	C₂×C₂²⋊C₄	—	146	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	—	73	2	no	—
825	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
826	#107	—	73	2	no	—
827	#107	—	73	2	no	—
828	#107	—	73	2	no	—
829	#107	—	73	2	no	—
830	#107	—	73	2	no	—
831	#107	C₂²×D₇₃	1	1	yes	characteristic
832	#107	C₂²×D₇₃	1	1	yes	characteristic
833	#106	—	73	2	no	—
834	#106	—	73	2	no	—
835	#106	—	73	2	no	—
836	#106	—	73	2	no	—
837	#106	—	73	2	no	—
838	#106	C₂²×D₇₃	1	1	yes	characteristic
839	#106	C₂²×D₇₃	1	1	yes	characteristic
840	C₄⋊C₈	—	73	2	no	—
841	C₄⋊C₈	—	73	2	no	—
842	C₄⋊C₈	—	73	2	no	—
843	C₄⋊C₈	—	73	1	no	—
844	C₄⋊C₈	—	73	1	no	—
845	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
847	#103	—	73	2	no	—
848	#103	—	73	2	no	—
849	#103	—	73	2	no	—
850	#103	C₂²×D₇₃	1	1	yes	characteristic
851	#103	C₂²×D₇₃	1	1	yes	characteristic
852	#103	C₂²×D₇₃	1	1	yes	characteristic
853	#103	C₂²×D₇₃	1	1	yes	characteristic
854	#102	—	73	2	no	—
855	#102	—	73	2	no	—
856	#102	—	73	2	no	—
857	#102	—	73	2	no	—
858	#102	—	73	2	no	—
859	#102	—	73	2	no	—
860	#102	—	73	2	no	—
861	#102	—	73	2	no	—
862	#102	—	73	2	no	—
863	#102	C₂²×D₇₃	1	1	yes	characteristic
864	#102	C₂²×D₇₃	1	1	yes	characteristic
865	#102	C₂²×D₇₃	1	1	yes	characteristic
866	#102	C₂²×D₇₃	1	1	yes	characteristic
867	C₂²⋊C₈	—	73	2	no	—
868	C₂²⋊C₈	—	73	2	no	—
869	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
870	C₂²⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
871	C₄×C₈	—	73	2	no	—
872	C₄×C₈	—	73	2	no	—
873	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
874	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
875	C₂⁴	—	146	2	no	—
876	#41	—	2	2	no	—
877	#41	—	4	1	no	—
878	#41	—	292	4	no	—
879	#41	—	584	2	no	—
880	#41	—	146	4	no	—
881	C₂×Q₈	—	73	1	no	—
882	C₂×Q₈	—	146	1	no	—
883	C₂×Q₈	—	146	1	no	—
884	C₂×Q₈	—	146	1	no	—
885	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
886	C₂×Q₈	C₂³×D₇₃	1	1	yes	characteristic
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	292	4	no	—
890	C₂×D₄	—	292	2	no	—
891	C₂×D₄	—	73	2	no	—
892	C₂×D₄	—	73	1	no	—
893	C₂×D₄	—	73	2	no	—
894	C₂×D₄	—	146	2	no	—
895	C₂×D₄	—	146	2	no	—
896	C₂×D₄	—	146	2	no	—
897	C₂×D₄	—	146	4	no	—
898	C₂×D₄	—	146	2	no	—
899	C₂×D₄	—	146	1	no	—
900	C₂×D₄	—	146	1	no	—
901	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
902	C₂×D₄	C₂³×D₇₃	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	584	4	no	—
908	C₂²×C₄	—	73	2	no	—
909	C₂²×C₄	—	73	2	no	—
910	C₂²×C₄	—	73	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	—	146	2	no	—
918	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
919	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
920	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
921	Q₁₆	—	4	1	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	292	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	292	2	no	—
927	C₂×C₈	—	292	2	no	—
928	C₂×C₈	—	292	2	no	—
929	C₂×C₈	—	292	2	no	—
930	C₂×C₈	—	73	2	no	—
931	C₂×C₈	—	73	2	no	—
932	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
934	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
935	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	73	2	no	—
943	C₄⋊C₄	—	73	2	no	—
944	C₄⋊C₄	—	73	1	no	—
945	C₄⋊C₄	—	73	1	no	—
946	C₄⋊C₄	—	73	2	no	—
947	C₄⋊C₄	—	73	2	no	—
948	C₄⋊C₄	—	73	2	no	—
949	C₄⋊C₄	—	146	2	no	—
950	C₄⋊C₄	—	146	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	—	146	1	no	—
964	C₄⋊C₄	—	146	1	no	—
965	C₄⋊C₄	—	146	1	no	—
966	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂³×D₇₃	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	73	2	no	—
979	C₂²⋊C₄	—	73	2	no	—
980	C₂²⋊C₄	—	73	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	—	146	2	no	—
990	C₂²⋊C₄	—	146	2	no	—
991	C₂²⋊C₄	—	146	2	no	—
992	C₂²⋊C₄	—	146	2	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	73	2	no	—
998	C₄²	—	73	2	no	—
999	C₄²	—	73	2	no	—
1000	C₄²	—	146	2	no	—
1001	C₄²	—	146	2	no	—
1002	C₄²	D₄×D₇₃	1	1	yes	characteristic
1003	C₄²	D₄×D₇₃	1	1	yes	characteristic
1004	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1005	C₄²	C₂³×D₇₃	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	292	4	no	—
1009	C₂³	—	292	4	no	—
1010	C₂³	—	584	2	no	—
1011	C₂³	—	73	2	no	—
1012	C₂³	—	146	2	no	—
1013	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	292	2	no	—
1019	Q₈	—	584	1	no	—
1020	Q₈	—	584	1	no	—
1021	Q₈	—	146	2	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	4	2	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	292	4	no	—
1028	D₄	—	292	4	no	—
1029	D₄	—	292	4	no	—
1030	D₄	—	292	2	no	—
1031	D₄	—	584	1	no	—
1032	D₄	—	584	2	no	—
1033	D₄	—	73	4	no	—
1034	D₄	—	146	4	no	—
1035	D₄	—	146	2	no	—
1036	D₄	—	146	2	no	—
1037	D₄	#14556638	1	2	yes	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	292	4	no	—
1053	C₂×C₄	—	292	2	no	—
1054	C₂×C₄	—	292	4	no	—
1055	C₂×C₄	—	584	2	no	—
1056	C₂×C₄	—	584	2	no	—
1057	C₂×C₄	—	584	2	no	—
1058	C₂×C₄	—	584	2	no	—
1059	C₂×C₄	—	584	2	no	—
1060	C₂×C₄	—	73	2	no	—
1061	C₂×C₄	—	73	2	no	—
1062	C₂×C₄	—	73	2	no	—
1063	C₂×C₄	—	146	4	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	2	no	—
1069	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1072	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1073	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
1074	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	146	2	no	—
1080	C₈	—	146	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	2	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	292	2	no	—
1091	C₂²	—	292	2	no	—
1092	C₂²	—	292	2	no	—
1093	C₂²	—	584	8	no	—
1094	C₂²	—	73	4	no	—
1095	C₂²	—	146	2	no	—
1096	C₂²	—	146	2	no	—
1097	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	292	2	no	—
1109	C₄	—	292	2	no	—
1110	C₄	—	292	2	no	—
1111	C₄	—	146	2	no	—
1112	C₄	—	146	2	no	—
1113	C₄	—	146	2	no	—
1114	C₄	#135×D₇₃	1	2	yes	—
1115	C₄	C₂×#14556638	1	1	yes	characteristic
1116	C₄	#17989423	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	—	584	2	no	—
1121	C₂	—	146	4	no	—
1122	C₂	#22623603	1	1	yes	characteristic
1123	C₂	C₂×#135×D₇₃	1	1	yes	characteristic
1124	C₂	#22624708	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3102	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#3102	D₇₃
hypocenter	C₇₃	#62103
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #22623911	C₂	semidirect
2. #22623541	C₂	semidirect
3. #22622804	C₂	semidirect
4. #22622796	C₂	semidirect
5. #22622625	C₂	semidirect
6. #22622589	C₂	semidirect
7. #22622326	C₂	semidirect
8. #22622325	C₂	semidirect
9. #22622313	C₂	semidirect
10. #22622290	C₂	semidirect
11. #22621774	C₂	semidirect
12. #22621759	C₂	semidirect
13. #22621757	C₂	semidirect
14. #22621746	C₂	semidirect
15. #22621281	C₂	semidirect
16. #22621257	C₂	semidirect
17. #22621103	C₂	semidirect
18. #22621069	C₂	semidirect
19. #22619977	C₂	semidirect
20. #22619719	C₂	semidirect
21. #478×D₇₃	C₂	semidirect
22. #22619039	C₂	semidirect
23. C₇₃×#3102	C₂	semidirect
25. #17989316	C₂²	semidirect
29. #17989294	C₂²	semidirect
30. #17989284	C₂²	semidirect
35. #17989271	C₂²	semidirect
44. #17989144	C₂²	semidirect
48. #17989116	C₂²	semidirect
49. #125×D₇₃	C₂²	semidirect
55. #17988992	C₂²	semidirect
56. #17988988	C₂²	semidirect
57. #17988987	C₂²	semidirect
58. #17988985	C₂²	semidirect
59. #17988943	C₂²	semidirect
60. #17988943	C₂²	semidirect
63. #17988921	C₂²	semidirect
64. #17988921	C₂²	semidirect
65. #17988916	C₂²	semidirect
66. #17988912	C₂²	semidirect
67. #17988912	C₂²	semidirect
69. #17988904	C₂²	semidirect
71. #17988894	C₂²	semidirect
72. #17988892	C₂²	semidirect
73. #17988890	C₂²	semidirect
75. #17988888	C₂²	semidirect
76. #17988888	C₂²	semidirect
78. #17988886	C₂²	semidirect
80. #17988885	C₂²	semidirect
81. #17988884	C₂²	semidirect
82. #17988882	C₂²	semidirect
83. #17988882	C₂²	semidirect
85. #17988877	C₂²	semidirect
86. #17988872	C₂²	semidirect
88. #17988825	C₂²	semidirect
90. #17988821	C₂²	semidirect
92. #17988818	C₂²	semidirect
93. #17988813	C₂²	semidirect
94. #17988811	C₂²	semidirect
95. #17988804	C₂²	semidirect
96. #17988799	C₂²	semidirect
101. C₈×Dic₁₄₆	C₂²	semidirect
102. C₈×Dic₁₄₆	C₂²	semidirect
104. #17988672	C₂²	semidirect
106. #17988667	C₂²	semidirect
109. #17988650	C₂²	semidirect
110. #17988650	C₂²	semidirect
111. #17988639	C₂²	semidirect
112. #17988623	C₂²	semidirect
113. #107×D₇₃	C₂²	semidirect
114. #106×D₇₃	C₂²	semidirect
115. C₂×C₄⋊#10596831	C₂²	semidirect
116. C₄⋊C₈×D₇₃	C₂²	semidirect
120. #529×C₇₃	C₂²	semidirect
122. #485×C₇₃	C₂²	semidirect
123. #482×C₇₃	C₂²	semidirect
124. #479×C₇₃	C₂²	semidirect
126. #464×C₇₃	C₂²	semidirect
130. C₄×Q₁₆×C₇₃	C₂²	semidirect
132. C₄×SD₁₆×C₇₃	C₂²	semidirect
134. #431×C₇₃	C₂²	semidirect
582. #3102	D₇₃	semidirect
586. C₇₃	#62103	semidirect
612. #529	C₂×D₇₃	semidirect
628. #485	C₂×D₇₃	semidirect
634. #482	C₂×D₇₃	semidirect
640. #479	C₂×D₇₃	semidirect
664. #464	C₂×D₇₃	semidirect
676. C₄×Q₁₆	C₂×D₇₃	semidirect
680. C₄×SD₁₆	C₂×D₇₃	semidirect
689. #431	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22623911	2
#22623541	2
#22622804	2
#22622796	2
#22622625	2
#22622589	2
#22622326	2
#22622325	2
#22622313	2
#22622290	2
#22621774	2
#22621759	2
#22621757	2
#22621746	2
#22621281	2
#22621257	2
#22621103	2
#22621069	2
#22619977	2
#22619719	2
#478×D₇₃	2
#22619039	2
C₇₃×#3102	2
#62103	73