Subgroups — #33089506

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988634	C₂	1	2	yes	maximal
2	C₂×#17988609	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₃	C₂	1	1	yes	maximal, characteristic
4	C₄×M₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic
5	#22610707	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610706	C₂	1	1	yes	maximal, characteristic, complemented
7	#22610705	C₂	1	2	yes	maximal, complemented
8	#22610704	C₂	1	1	yes	maximal, characteristic, complemented
9	#22610703	C₂	1	2	yes	maximal, complemented
10	#22609656	C₂	1	2	yes	maximal
11	C₇₃×#1950	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	2	yes	—
13	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
14	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
15	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
17	#17988634	—	2	8	no	—
18	C₂×#14556527	C₂²	1	2	yes	—
19	C₂×#14556526	C₂²	1	2	yes	—
20	C₂×#14556526	C₂²	1	2	yes	—
21	#17988611	C₂²	1	1	yes	characteristic
22	#17988610	C₂²	1	2	yes	—
23	#17988609	—	2	1	no	—
24	#17988609	—	2	1	no	—
25	#17988609	C₄	1	2	yes	—
26	#17988609	C₄	1	2	yes	—
27	#17988609	C₄	1	2	yes	—
28	#17988609	C₄	1	2	yes	—
29	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
30	C₂×#14556520	C₂²	1	2	yes	—
31	C₄⋊C₈×D₇₃	—	2	1	no	—
32	C₄⋊C₈×D₇₃	—	2	1	no	—
33	C₄×#11924012	C₂²	1	1	yes	characteristic
34	#17988539	—	2	1	no	—
35	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
36	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
37	C₄×#11924011	—	2	1	no	—
38	#97×D₇₃	—	2	1	no	—
39	C₄×C₈×D₇₃	—	2	1	no	—
40	#17988352	C₂²	1	2	yes	—
41	#17988351	C₂²	1	2	yes	—
42	#17988351	C₂²	1	2	yes	—
43	C₂×#108×C₇₃	C₂²	1	2	yes	—
44	#423×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
47	#341×C₇₃	C₂²	1	2	yes	—
48	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
50	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
51	C₂×#11924012	C₂³	1	2	yes	—
52	C₂×#11924012	C₂³	1	1	yes	characteristic
53	C₂×#11924012	C₂³	1	1	yes	characteristic
54	C₂×#11924011	—	2	4	no	—
55	C₂×#11924011	—	2	1	no	—
56	C₂×#11924011	—	2	1	no	—
57	C₂×#11924011	—	2	4	no	—
58	C₂×#11924011	—	2	2	no	—
59	C₂×#11924011	C₂×C₄	1	4	yes	—
60	C₂×#11924011	C₂×C₄	1	4	yes	—
61	M₁₆×D₇₃	—	2	2	no	—
62	M₁₆×D₇₃	—	2	2	no	—
63	M₁₆×D₇₃	—	2	4	no	—
64	M₁₆×D₇₃	—	2	4	no	—
65	M₁₆×D₇₃	D₄	1	4	yes	—
66	M₁₆×D₇₃	Q₈	1	4	yes	—
67	C₂²×#10596831	C₂³	1	2	yes	—
68	C₂×C₈×D₇₃	—	2	1	no	—
69	C₂×C₈×D₇₃	—	2	1	no	—
70	C₂×C₈×D₇₃	—	2	2	no	—
71	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
72	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
73	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
74	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
77	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
78	C₄²×D₇₃	D₄	1	1	yes	characteristic
79	C₄²×D₇₃	D₄	1	1	yes	characteristic
80	C₄²×D₇₃	D₄	1	1	yes	characteristic
81	C₄²×D₇₃	D₄	1	1	yes	characteristic
82	#14556527	—	2	4	no	—
83	#14556526	—	2	4	no	—
84	#14556526	—	2	4	no	—
85	C₄⋊#10596831	—	2	1	no	—
86	C₄⋊#10596831	—	2	1	no	—
87	C₄⋊#10596831	C₂×C₄	1	2	yes	—
88	C₄⋊#10596831	C₂×C₄	1	2	yes	—
89	#14556520	—	2	2	no	—
90	#14556520	—	2	2	no	—
91	#14556520	C₂×C₄	1	4	yes	—
92	#14556520	C₂×C₄	1	4	yes	—
93	#14556502	—	2	1	no	—
94	#14556501	—	2	1	no	—
95	#14556501	—	2	1	no	—
96	C₄×#10596831	—	2	1	no	—
97	C₈×Dic₇₃	—	2	1	no	—
98	C₈×Dic₇₃	—	2	1	no	—
99	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
100	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
103	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
104	#108×C₇₃	—	2	4	no	—
105	C₄⋊C₈×C₇₃	—	2	1	no	—
106	C₄⋊C₈×C₇₃	—	2	1	no	—
107	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
108	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
109	#97×C₇₃	—	2	1	no	—
110	C₄×C₈×C₇₃	—	2	1	no	—
111	C₂³×D₇₃	C₂×Q₈	1	1	yes	characteristic
112	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
113	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
114	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₄×D₇₃	—	4	2	no	—
116	C₂×C₄×D₇₃	—	4	2	no	—
117	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
125	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
128	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
131	C₂×C₄×D₇₃	#41	1	2	yes	—
132	C₂×C₄×D₇₃	#41	1	2	yes	—
133	#11924012	—	2	1	no	—
134	#11924012	—	2	1	no	—
135	#11924012	—	2	2	no	—
136	#11924012	—	2	2	no	—
137	#11924012	C₂×D₄	1	2	yes	—
138	#11924012	C₂×Q₈	1	2	yes	—
139	#11924011	—	2	8	no	—
140	#11924011	—	2	8	no	—
141	#11924011	—	2	4	no	—
142	#11924011	—	2	4	no	—
143	#11924011	—	4	4	no	—
144	C₂×#10596831	—	2	1	no	—
145	C₂×#10596831	—	2	1	no	—
146	C₂×#10596831	—	2	2	no	—
147	C₂×#10596831	—	2	2	no	—
148	C₂×#10596831	—	2	2	no	—
149	C₂×#10596831	C₂²×C₄	1	4	yes	—
150	C₈×D₇₃	—	2	4	no	—
151	C₈×D₇₃	—	2	4	no	—
152	C₈×D₇₃	—	4	4	no	—
153	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
154	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
155	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
156	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
157	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
158	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
159	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
160	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
161	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
164	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
168	M₁₆×C₇₃	—	2	1	no	—
169	M₁₆×C₇₃	—	2	1	no	—
170	M₁₆×C₇₃	—	2	2	no	—
171	M₁₆×C₇₃	—	2	2	no	—
172	M₁₆×C₇₃	C₂×D₄	1	2	yes	—
173	M₁₆×C₇₃	C₂×Q₈	1	2	yes	—
174	C₂×C₈×C₇₃	—	2	1	no	—
175	C₂×C₈×C₇₃	—	2	1	no	—
176	C₂×C₈×C₇₃	—	2	2	no	—
177	C₂×C₈×C₇₃	—	2	2	no	—
178	C₂×C₈×C₇₃	—	2	2	no	—
179	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
180	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₂³×C₇₃	C₂²×Q₈	1	1	yes	characteristic
185	C₂²×D₇₃	—	4	1	no	—
186	C₂²×D₇₃	—	4	1	no	—
187	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×D₇₃	#125	1	2	yes	—
190	C₂²×D₇₃	C₄⋊Q₈	1	2	yes	—
191	C₂×C₄×C₇₃	—	2	2	no	—
192	C₂×C₄×C₇₃	—	4	1	no	—
193	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
201	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
203	C₂×Dic₇₃	—	2	2	no	—
204	C₂×Dic₇₃	—	4	1	no	—
205	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
206	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
207	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
208	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
209	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
210	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
211	C₂×Dic₇₃	#125	1	2	yes	—
212	C₂×Dic₇₃	C₄⋊Q₈	1	2	yes	—
213	C₄×D₇₃	—	2	2	no	—
214	C₄×D₇₃	—	2	2	no	—
215	C₄×D₇₃	—	2	2	no	—
216	C₄×D₇₃	—	2	2	no	—
217	C₄×D₇₃	—	4	1	no	—
218	C₄×D₇₃	—	4	1	no	—
219	C₄×D₇₃	—	4	1	no	—
220	C₄×D₇₃	—	4	1	no	—
221	C₄×D₇₃	C₄×D₄	1	2	yes	—
222	C₄×D₇₃	C₄×D₄	1	2	yes	—
223	C₄×D₇₃	C₄×Q₈	1	2	yes	—
224	C₄×D₇₃	C₄×Q₈	1	2	yes	—
225	C₄×D₇₃	#121	1	2	yes	—
226	C₄×D₇₃	#121	1	2	yes	—
227	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
228	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
229	C₈×C₇₃	—	2	4	no	—
230	C₈×C₇₃	—	2	2	no	—
231	C₈×C₇₃	—	2	2	no	—
232	C₈×C₇₃	—	4	2	no	—
233	#10596831	—	2	4	no	—
234	#10596831	—	2	2	no	—
235	#10596831	—	2	2	no	—
236	#10596831	—	4	2	no	—
237	C₂²×C₇₃	—	2	1	no	—
238	C₂²×C₇₃	—	2	1	no	—
239	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×C₇₃	C₂×#125	1	1	yes	characteristic
241	C₂²×C₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
242	C₂×D₇₃	—	2	1	no	—
243	C₂×D₇₃	—	2	1	no	—
244	C₂×D₇₃	—	2	1	no	—
245	C₂×D₇₃	—	2	1	no	—
246	C₂×D₇₃	—	4	2	no	—
247	C₂×D₇₃	—	4	2	no	—
248	C₂×D₇₃	#389	1	2	yes	—
249	C₂×D₇₃	#389	1	2	yes	—
250	C₄×C₇₃	—	2	1	no	—
251	C₄×C₇₃	—	2	1	no	—
252	C₄×C₇₃	—	2	1	no	—
253	C₄×C₇₃	#430	1	2	yes	complemented
254	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
255	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
256	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
257	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
258	Dic₇₃	—	2	1	no	—
259	Dic₇₃	—	2	1	no	—
260	Dic₇₃	—	2	1	no	—
261	Dic₇₃	#389	1	2	yes	—
262	Dic₇₃	#389	1	2	yes	—
263	Dic₇₃	#430	1	2	yes	complemented
264	#21177	—	73	1	no	maximal, Sylow
265	C₂×C₇₃	—	2	1	no	—
266	C₂×C₇₃	—	2	1	no	—
267	C₂×C₇₃	C₂×#389	1	1	yes	characteristic
268	C₂×C₇₃	C₂×#430	1	1	yes	characteristic
269	C₂×C₇₃	C₂×#430	1	1	yes	characteristic
270	D₇₃	—	2	2	no	—
271	D₇₃	—	2	2	no	—
272	C₂×#430	—	73	2	no	—
273	C₂×#423	—	73	1	no	—
274	C₂×#423	—	73	1	no	—
275	C₂×C₄×M₁₆	—	73	1	no	—
276	#1950	—	73	2	no	—
277	#1950	—	73	1	no	—
278	#1950	—	73	1	no	—
279	#1950	—	73	1	no	—
280	#1950	—	73	2	no	—
281	#1950	D₇₃	1	1	yes	characteristic, complemented
282	#1738	—	73	2	no	—
283	C₇₃	#21177	1	1	yes	characteristic, complemented, Sylow
284	C₂²×M₁₆	—	73	2	no	—
285	C₂²×M₁₆	—	73	1	no	—
286	C₂²×M₁₆	—	73	1	no	—
287	C₂²×M₁₆	—	73	2	no	—
288	C₂²×C₄²	—	73	1	no	—
289	#430	—	146	8	no	—
290	C₂×#108	—	73	2	no	—
291	C₂×#108	—	73	2	no	—
292	C₂×#108	—	73	2	no	—
293	C₂×#108	C₂×D₇₃	1	2	yes	—
294	#423	—	73	2	no	—
295	#423	—	73	2	no	—
296	#423	—	73	2	no	—
297	#423	—	73	2	no	—
298	#423	—	73	2	no	—
299	#423	—	73	1	no	—
300	#423	—	146	1	no	—
301	#423	—	146	1	no	—
302	#423	C₂×D₇₃	1	1	yes	characteristic
303	C₂×C₄⋊C₈	—	73	2	no	—
304	C₂×C₄⋊C₈	—	73	1	no	—
305	C₂×C₄⋊C₈	—	146	1	no	—
306	C₂×C₄⋊C₈	—	146	1	no	—
307	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
308	C₄×M₁₆	—	73	1	no	—
309	C₄×M₁₆	—	73	1	no	—
310	C₄×M₁₆	—	73	1	no	—
311	C₄×M₁₆	—	146	1	no	—
312	C₄×M₁₆	—	146	1	no	—
313	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
314	C₂×#97	—	146	1	no	—
315	C₂×C₄×C₈	—	146	1	no	—
316	#341	—	73	2	no	—
317	#341	—	73	2	no	—
318	#341	—	73	2	no	—
319	#341	C₂×D₇₃	1	2	yes	—
320	C₂³×C₄	—	73	1	no	—
321	C₂³×C₄	—	73	1	no	—
322	C₂³×C₄	—	73	1	no	—
323	C₂×M₁₆	—	73	4	no	—
324	C₂×M₁₆	—	73	4	no	—
325	C₂×M₁₆	—	73	1	no	—
326	C₂×M₁₆	—	73	1	no	—
327	C₂×M₁₆	—	73	4	no	—
328	C₂×M₁₆	—	73	4	no	—
329	C₂×M₁₆	—	73	2	no	—
330	C₂×M₁₆	—	146	2	no	—
331	C₂×M₁₆	—	146	1	no	—
332	C₂×M₁₆	—	146	1	no	—
333	C₂×M₁₆	—	146	4	no	—
334	C₂×M₁₆	—	146	4	no	—
335	C₂×M₁₆	—	146	4	no	—
336	C₂×M₁₆	—	146	4	no	—
337	C₂×M₁₆	—	146	2	no	—
338	C₂×M₁₆	—	146	2	no	—
339	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
340	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
341	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
342	C₂²×C₈	—	73	2	no	—
343	C₂²×C₈	—	146	2	no	—
344	C₂²×C₈	—	146	1	no	—
345	C₂²×C₈	—	146	1	no	—
346	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
347	C₂×C₄²	—	73	1	no	—
348	C₂×C₄²	—	73	1	no	—
349	C₂×C₄²	—	73	1	no	—
350	C₂×C₄²	—	73	1	no	—
351	C₂×C₄²	—	73	1	no	—
352	C₂×C₄²	—	73	1	no	—
353	C₂×C₄²	—	73	1	no	—
354	C₂×C₄²	—	73	1	no	—
355	C₂×C₄²	—	73	1	no	—
356	C₂×C₄²	—	73	1	no	—
357	C₂×C₄²	—	73	1	no	—
358	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
359	#108	—	2	4	no	—
360	#108	—	146	4	no	—
361	#108	—	146	4	no	—
362	#108	—	146	4	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	—	73	4	no	—
366	C₄⋊C₈	—	73	4	no	—
367	C₄⋊C₈	—	73	2	no	—
368	C₄⋊C₈	—	73	2	no	—
369	C₄⋊C₈	—	146	2	no	—
370	C₄⋊C₈	—	146	2	no	—
371	C₄⋊C₈	—	146	1	no	—
372	C₄⋊C₈	—	146	1	no	—
373	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
374	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
375	#97	—	2	1	no	—
376	#97	—	146	1	no	—
377	#97	—	146	1	no	—
378	#97	—	146	1	no	—
379	C₄×C₈	—	2	1	no	—
380	C₄×C₈	—	146	1	no	—
381	C₄×C₈	—	146	1	no	—
382	C₄×C₈	—	146	1	no	—
383	C₂⁴	—	73	1	no	—
384	C₂²×C₄	—	292	2	no	—
385	C₂²×C₄	—	292	2	no	—
386	C₂²×C₄	—	73	1	no	—
387	C₂²×C₄	—	73	1	no	—
388	C₂²×C₄	—	73	1	no	—
389	C₂²×C₄	—	73	1	no	—
390	C₂²×C₄	—	73	1	no	—
391	C₂²×C₄	—	73	1	no	—
392	C₂²×C₄	—	73	1	no	—
393	C₂²×C₄	—	73	1	no	—
394	C₂²×C₄	—	73	2	no	—
395	C₂²×C₄	—	73	1	no	—
396	C₂²×C₄	—	73	1	no	—
397	C₂²×C₄	—	73	2	no	—
398	C₂²×C₄	—	73	2	no	—
399	C₂²×C₄	—	73	2	no	—
400	C₂²×C₄	—	73	1	no	—
401	C₂²×C₄	—	73	1	no	—
402	C₂²×C₄	—	73	1	no	—
403	C₂²×C₄	—	73	1	no	—
404	C₂²×C₄	—	73	1	no	—
405	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
406	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
407	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	2	no	—
412	M₁₆	—	292	4	no	—
413	M₁₆	—	73	2	no	—
414	M₁₆	—	73	2	no	—
415	M₁₆	—	146	8	no	—
416	M₁₆	—	146	8	no	—
417	M₁₆	—	146	4	no	—
418	M₁₆	—	146	4	no	—
419	M₁₆	—	146	2	no	—
420	M₁₆	—	146	2	no	—
421	M₁₆	—	146	1	no	—
422	M₁₆	—	146	1	no	—
423	M₁₆	D₄×D₇₃	1	2	yes	—
424	M₁₆	Q₈×D₇₃	1	2	yes	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	292	4	no	—
431	C₂×C₈	—	73	4	no	—
432	C₂×C₈	—	146	4	no	—
433	C₂×C₈	—	146	4	no	—
434	C₂×C₈	—	146	2	no	—
435	C₂×C₈	—	146	2	no	—
436	C₂×C₈	—	146	1	no	—
437	C₂×C₈	—	146	1	no	—
438	C₂×C₈	—	146	2	no	—
439	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
440	C₄²	—	73	1	no	—
441	C₄²	—	73	1	no	—
442	C₄²	—	73	1	no	—
443	C₄²	—	73	1	no	—
444	C₄²	—	73	1	no	—
445	C₄²	—	73	1	no	—
446	C₄²	—	73	1	no	—
447	C₄²	—	73	1	no	—
448	C₄²	—	73	1	no	—
449	C₄²	—	73	1	no	—
450	C₄²	—	73	1	no	—
451	C₄²	—	73	1	no	—
452	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
453	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
454	C₄²	D₄×D₇₃	1	1	yes	characteristic
455	C₄²	D₄×D₇₃	1	1	yes	characteristic
456	C₂³	—	292	1	no	—
457	C₂³	—	292	1	no	—
458	C₂³	—	73	2	no	—
459	C₂³	—	73	2	no	—
460	C₂³	—	73	1	no	—
461	C₂³	—	73	1	no	—
462	C₂³	C₂×Q₈×D₇₃	1	1	yes	characteristic
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	292	1	no	—
466	C₂×C₄	—	292	1	no	—
467	C₂×C₄	—	292	1	no	—
468	C₂×C₄	—	292	1	no	—
469	C₂×C₄	—	292	1	no	—
470	C₂×C₄	—	73	2	no	—
471	C₂×C₄	—	73	1	no	—
472	C₂×C₄	—	73	1	no	—
473	C₂×C₄	—	73	1	no	—
474	C₂×C₄	—	73	2	no	—
475	C₂×C₄	—	73	2	no	—
476	C₂×C₄	—	73	2	no	—
477	C₂×C₄	—	73	2	no	—
478	C₂×C₄	—	73	2	no	—
479	C₂×C₄	—	73	2	no	—
480	C₂×C₄	—	73	2	no	—
481	C₂×C₄	—	73	2	no	—
482	C₂×C₄	—	73	2	no	—
483	C₂×C₄	—	73	1	no	—
484	C₂×C₄	—	73	1	no	—
485	C₂×C₄	—	73	1	no	—
486	C₂×C₄	—	146	2	no	—
487	C₂×C₄	—	146	2	no	—
488	C₂×C₄	—	146	2	no	—
489	C₂×C₄	—	146	2	no	—
490	C₂×C₄	—	146	2	no	—
491	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
492	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
493	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
494	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
495	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
496	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
497	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
498	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
499	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
500	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
501	C₈	—	2	4	no	—
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	4	2	no	—
505	C₈	—	292	2	no	—
506	C₈	—	146	4	no	—
507	C₈	—	146	2	no	—
508	C₈	—	146	2	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	292	2	no	—
512	C₂²	—	292	2	no	—
513	C₂²	—	73	2	no	—
514	C₂²	—	73	2	no	—
515	C₂²	—	146	1	no	—
516	C₂²	—	146	1	no	—
517	C₂²	—	146	1	no	—
518	C₂²	—	146	1	no	—
519	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
520	C₂²	#125×D₇₃	1	1	yes	characteristic
521	C₂²	C₄⋊Q₈×D₇₃	1	1	yes	characteristic
522	C₄	—	2	1	no	—
523	C₄	—	2	1	no	—
524	C₄	—	2	1	no	—
525	C₄	—	73	2	no	—
526	C₄	—	73	2	no	—
527	C₄	—	73	2	no	—
528	C₄	—	146	1	no	—
529	C₄	—	146	1	no	—
530	C₄	—	146	1	no	—
531	C₄	#17988634	1	2	yes	complemented
532	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
533	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
534	C₄	#121×D₇₃	1	1	yes	characteristic
535	C₄	C₂²⋊Q₈×D₇₃	1	1	yes	characteristic
536	C₂	—	2	1	no	—
537	C₂	—	2	1	no	—
538	C₂	—	146	2	no	—
539	C₂	—	146	2	no	—
540	C₂	#389×D₇₃	1	1	yes	characteristic
541	C₂	#430×D₇₃	1	1	yes	characteristic
542	C₂	C₂×#17988634	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1950	C₂
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×Q₈
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1950	D₇₃
hypocenter	C₇₃	#21177
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1950

Complements

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

N	H ≅ G/N	type
5. #22610707	C₂	semidirect
6. #22610706	C₂	semidirect
7. #22610705	C₂	semidirect
8. #22610704	C₂	semidirect
9. #22610703	C₂	semidirect
11. C₇₃×#1950	C₂	semidirect
253. C₄×C₇₃	#430	semidirect
263. Dic₇₃	#430	semidirect
281. #1950	D₇₃	semidirect
283. C₇₃	#21177	semidirect
531. C₄	#17988634	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988634	2
C₂×#17988609	2
#423×D₇₃	2
C₄×M₁₆×D₇₃	2
#22610707	2
#22610706	2
#22610705	2
#22610704	2
#22610703	2
#22609656	2
C₇₃×#1950	2
#21177	73