Subgroups — #2214×D₇₃ #33240366

Order 18688.

686 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#510×D₇₃	C₂	1	2	yes	maximal
2	#494×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22612013	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612012	C₂	1	1	yes	maximal, characteristic, complemented
6	#22612011	C₂	1	2	yes	maximal, complemented
7	#22612010	C₂	1	2	yes	maximal, complemented
8	#22612009	C₂	1	1	yes	maximal, characteristic, complemented
9	#364×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#362×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2214	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₃	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×D₇₃	—	2	1	no	—
14	C₂×Q₁₆×D₇₃	C₂²	1	2	yes	—
15	#131×D₇₃	—	2	1	no	—
16	C₄⋊Q₈×D₇₃	—	2	1	no	—
17	#17989030	C₂²	1	2	yes	—
18	#17989029	—	2	2	no	—
19	#17989028	C₂²	1	2	yes	—
20	#17989027	C₂²	1	2	yes	—
21	#17989026	—	2	2	no	—
22	Q₃₂×D₇₃	—	2	2	no	—
23	SD₃₂×D₇₃	—	2	2	no	—
24	M₃₂×D₇₃	C₂²	1	2	yes	—
25	#17988967	C₂²	1	1	yes	characteristic, complemented
26	#17988966	—	2	1	no	—
27	#17988965	—	2	1	no	—
28	#17988965	C₂²	1	2	yes	complemented
29	#17988705	C₂²	1	1	yes	characteristic
30	#17988704	C₂²	1	1	yes	characteristic
31	#17988703	C₂²	1	1	yes	characteristic
32	#17988702	—	2	1	no	—
33	#17988701	—	2	1	no	—
34	#108×D₇₃	C₂²	1	1	yes	characteristic
35	#104×D₇₃	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988408	C₂²	1	1	yes	characteristic, complemented
38	#17988407	C₂²	1	2	yes	complemented
39	#17988404	C₂²	1	2	yes	complemented
40	#17988403	C₂²	1	2	yes	complemented
41	#17988402	C₂²	1	2	yes	complemented
42	#510×C₇₃	C₂²	1	2	yes	—
43	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	#443×C₇₃	C₂²	1	1	yes	characteristic
45	#364×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#362×C₇₃	C₂²	1	2	yes	complemented
47	#41×D₇₃	—	2	1	no	—
48	C₂×Q₈×D₇₃	—	2	2	no	—
49	#14556614	D₄	1	1	yes	characteristic
50	#14556613	C₂³	1	1	yes	characteristic
51	#14556612	—	2	1	no	—
52	#14556611	—	2	1	no	—
53	#14556610	D₄	1	1	yes	characteristic
54	C₂×Dic₂₉₂	—	2	1	no	—
55	C₂×Dic₂₉₂	C₂³	1	2	yes	—
56	C₂×#11924018	—	2	2	no	—
57	C₂×#11924018	—	2	2	no	—
58	Q₁₆×D₇₃	—	2	2	no	—
59	Q₁₆×D₇₃	—	2	2	no	—
60	Q₁₆×D₇₃	—	2	2	no	—
61	Q₁₆×D₇₃	—	2	2	no	—
62	Q₁₆×D₇₃	—	4	1	no	—
63	Q₁₆×D₇₃	—	4	1	no	—
64	Q₁₆×D₇₃	—	4	1	no	—
65	Q₁₆×D₇₃	—	4	1	no	—
66	Q₁₆×D₇₃	D₄	1	1	yes	characteristic
67	SD₁₆×D₇₃	—	2	1	no	—
68	D₈×D₇₃	D₄	1	1	yes	characteristic
69	#14556599	—	2	1	no	—
70	#14556599	—	4	1	no	—
71	#14556598	—	2	1	no	—
72	#14556597	—	2	1	no	—
73	#14556597	—	4	1	no	—
74	M₁₆×D₇₃	—	2	1	no	—
75	M₁₆×D₇₃	—	4	1	no	—
76	C₂×C₈×D₇₃	—	4	1	no	—
77	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
78	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
79	#14556591	—	2	1	no	—
80	#14556590	—	4	2	no	—
81	#14556589	—	2	2	no	—
82	C₄⋊C₄×D₇₃	—	4	2	no	—
83	C₄²×D₇₃	D₄	1	1	yes	characteristic
84	Dic₅₈₄	—	2	2	no	—
85	#14556537	—	2	2	no	—
86	#14556537	—	2	2	no	—
87	#14556536	—	2	2	no	—
88	#14556535	—	2	2	no	—
89	#14556534	—	2	2	no	—
90	#14556531	C₂³	1	2	yes	—
91	#14556530	—	2	2	no	—
92	C₁₆×D₇₃	—	2	2	no	—
93	#14556527	C₂³	1	1	yes	characteristic
94	#14556526	—	2	1	no	—
95	#14556519	—	2	1	no	—
96	#14556518	—	2	1	no	—
97	#14556517	—	2	1	no	—
98	C₄×#10596831	D₄	1	1	yes	characteristic
99	C₈×Dic₇₃	D₄	1	1	yes	characteristic
100	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
101	#135×C₇₃	C₂³	1	1	yes	characteristic
102	C₂×Q₁₆×C₇₃	—	2	1	no	—
103	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
104	#131×C₇₃	—	2	1	no	—
105	C₄⋊Q₈×C₇₃	—	2	1	no	—
106	Q₃₂×C₇₃	—	2	2	no	—
107	SD₃₂×C₇₃	—	2	2	no	—
108	M₃₂×C₇₃	C₂³	1	2	yes	—
109	#108×C₇₃	C₂³	1	1	yes	characteristic
110	#104×C₇₃	—	2	1	no	—
111	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
112	#11924029	—	2	1	no	—
113	#11924028	—	2	1	no	—
114	#11924028	—	4	1	no	—
115	#11924027	—	2	1	no	—
116	#11924027	—	4	1	no	—
117	C₂×Dic₁₄₆	—	2	2	no	—
118	C₂×Dic₁₄₆	—	4	2	no	—
119	Q₈×D₇₃	—	2	1	no	—
120	Q₈×D₇₃	—	4	2	no	—
121	Q₈×D₇₃	—	4	2	no	—
122	Q₈×D₇₃	—	4	2	no	—
123	Q₈×D₇₃	—	4	2	no	—
124	D₄×D₇₃	—	2	1	no	—
125	D₄×D₇₃	—	4	1	no	—
126	C₂×C₄×D₇₃	—	2	1	no	—
127	C₂×C₄×D₇₃	—	4	1	no	—
128	C₂×C₄×D₇₃	—	4	2	no	—
129	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
130	Dic₂₉₂	—	2	2	no	—
131	Dic₂₉₂	—	2	2	no	—
132	Dic₂₉₂	—	4	1	no	—
133	Dic₂₉₂	—	4	1	no	—
134	Dic₂₉₂	C₂×D₄	1	1	yes	characteristic
135	#11924018	—	2	1	no	—
136	#11924018	—	4	2	no	—
137	#11924018	—	4	2	no	—
138	#11924018	—	4	2	no	—
139	#11924018	—	4	2	no	—
140	#11924017	—	2	1	no	—
141	#11924016	—	2	1	no	—
142	#11924015	—	2	1	no	—
143	D₅₈₄	C₂×D₄	1	1	yes	characteristic
144	#11924013	—	2	1	no	—
145	#11924012	—	2	1	no	—
146	#11924012	—	4	1	no	—
147	#11924011	—	4	1	no	—
148	#11924011	—	4	1	no	—
149	#11924011	—	4	1	no	—
150	C₂×#10596831	—	4	1	no	—
151	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
152	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
153	C₈×D₇₃	—	4	1	no	—
154	C₈×D₇₃	—	4	1	no	—
155	C₈×D₇₃	—	4	1	no	—
156	C₈×D₇₃	D₈	1	1	yes	characteristic
157	C₈×D₇₃	D₈	1	1	yes	characteristic
158	C₈×D₇₃	D₈	1	1	yes	characteristic
159	C₈×D₇₃	D₈	1	1	yes	characteristic
160	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
161	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
162	C₈×D₇₃	#41	1	1	yes	characteristic
163	C₈×D₇₃	#41	1	1	yes	characteristic
164	C₄⋊Dic₇₃	—	4	2	no	—
165	#11924007	—	4	4	no	—
166	C₄×Dic₇₃	—	2	1	no	—
167	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
168	#11924003	—	2	2	no	—
169	#41×C₇₃	—	2	1	no	—
170	C₂×Q₈×C₇₃	—	2	2	no	—
171	Q₁₆×C₇₃	—	2	2	no	—
172	Q₁₆×C₇₃	—	2	2	no	—
173	Q₁₆×C₇₃	—	4	1	no	—
174	Q₁₆×C₇₃	—	4	1	no	—
175	Q₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
176	SD₁₆×C₇₃	—	2	1	no	—
177	D₈×C₇₃	C₂×D₄	1	1	yes	characteristic
178	M₁₆×C₇₃	—	2	1	no	—
179	M₁₆×C₇₃	—	4	1	no	—
180	C₂×C₈×C₇₃	—	4	1	no	—
181	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
183	C₄⋊C₄×C₇₃	—	4	2	no	—
184	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
185	C₁₆×C₇₃	—	2	2	no	—
186	C₂²×D₇₃	—	4	1	no	—
187	C₂²×D₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
188	Q₈×C₇₃	—	2	1	no	—
189	Q₈×C₇₃	—	4	2	no	—
190	Q₈×C₇₃	—	4	2	no	—
191	D₄×C₇₃	—	2	1	no	—
192	D₄×C₇₃	—	4	1	no	—
193	C₂×C₄×C₇₃	—	2	1	no	—
194	C₂×C₄×C₇₃	—	4	1	no	—
195	C₂×C₄×C₇₃	—	4	2	no	—
196	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
197	C₂²⋊D₇₃	—	4	1	no	—
198	C₂²⋊D₇₃	—	4	1	no	—
199	C₂²⋊D₇₃	—	4	1	no	—
200	C₂×Dic₇₃	—	2	1	no	—
201	C₂×Dic₇₃	—	4	1	no	—
202	C₂×Dic₇₃	—	4	2	no	—
203	C₂×Dic₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
204	D₂₉₂	—	2	1	no	—
205	D₂₉₂	—	4	1	no	—
206	C₄×D₇₃	—	2	4	no	—
207	C₄×D₇₃	—	4	1	no	—
208	C₄×D₇₃	—	4	1	no	—
209	C₄×D₇₃	—	4	1	no	—
210	C₄×D₇₃	—	8	2	no	—
211	C₄×D₇₃	—	8	2	no	—
212	C₄×D₇₃	#121	1	1	yes	characteristic
213	C₄×D₇₃	#121	1	1	yes	characteristic
214	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
215	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
216	Dic₁₄₆	—	2	1	no	—
217	Dic₁₄₆	—	4	1	no	—
218	Dic₁₄₆	—	4	2	no	—
219	Dic₁₄₆	—	4	2	no	—
220	Dic₁₄₆	—	8	2	no	—
221	Dic₁₄₆	—	8	2	no	—
222	C₈×C₇₃	—	4	1	no	—
223	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
224	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
225	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
226	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
227	#10596831	—	4	1	no	—
228	#10596831	#121	1	1	yes	characteristic
229	#10596831	#121	1	1	yes	characteristic
230	#10596831	C₂×D₈	1	1	yes	characteristic
231	#10596831	C₂×D₈	1	1	yes	characteristic
232	C₂²×C₇₃	—	4	1	no	—
233	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×D₇₃	—	2	2	no	—
235	C₂×D₇₃	—	4	1	no	—
236	C₂×D₇₃	—	8	2	no	—
237	C₂×D₇₃	#459	1	1	yes	characteristic
238	C₂×D₇₃	#459	1	1	yes	characteristic
239	C₄×C₇₃	—	2	2	no	—
240	C₄×C₇₃	—	4	1	no	—
241	C₄×C₇₃	—	8	2	no	—
242	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
243	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
244	Dic₇₃	—	2	2	no	—
245	Dic₇₃	—	4	1	no	—
246	Dic₇₃	—	8	2	no	—
247	Dic₇₃	#459	1	1	yes	characteristic
248	Dic₇₃	#459	1	1	yes	characteristic
249	C₂×#2214	—	73	1	no	maximal, Sylow
250	C₂×C₇₃	—	2	1	no	—
251	C₂×C₇₃	—	8	1	no	—
252	C₂×C₇₃	C₂×#459	1	1	yes	characteristic
253	D₇₃	—	2	1	no	—
254	D₇₃	—	8	1	no	—
255	D₇₃	#2214	1	2	yes	direct product factor
256	C₂×#510	—	73	2	no	—
257	C₂×#494	—	73	1	no	—
258	C₂×#443	—	73	1	no	—
259	#2214	—	73	2	no	—
260	#2214	—	73	1	no	—
261	#2214	—	73	1	no	—
262	#2214	—	73	1	no	—
263	#2214	—	73	2	no	—
264	#2214	D₇₃	1	1	yes	characteristic, direct product factor
265	C₂×#364	—	73	1	no	—
266	C₂×#362	—	73	2	no	—
267	C₇₃	C₂×#2214	1	1	yes	characteristic, complemented, Sylow
268	C₂×#135	—	73	1	no	—
269	C₂²×Q₁₆	—	73	2	no	—
270	C₂²×Q₁₆	—	146	1	no	—
271	C₂×#131	—	146	1	no	—
272	C₂×C₄⋊Q₈	—	146	1	no	—
273	#510	—	73	2	no	—
274	#510	—	73	2	no	—
275	#510	—	73	2	no	—
276	#510	—	146	2	no	—
277	#510	—	146	2	no	—
278	#510	C₂×D₇₃	1	2	yes	—
279	C₂×Q₃₂	—	146	2	no	—
280	C₂×SD₃₂	—	146	2	no	—
281	C₂×M₃₂	—	73	2	no	—
282	#494	—	73	2	no	—
283	#494	—	73	1	no	—
284	#494	—	146	1	no	—
285	#494	—	146	1	no	—
286	#494	C₂×D₇₃	1	1	yes	characteristic, complemented
287	#443	—	73	1	no	—
288	#443	—	73	1	no	—
289	#443	—	73	1	no	—
290	#443	—	146	1	no	—
291	#443	—	146	1	no	—
292	#443	C₂×D₇₃	1	1	yes	characteristic
293	C₂×#108	—	73	1	no	—
294	C₂×#104	—	146	1	no	—
295	C₂×C₄×C₈	—	73	1	no	—
296	#364	—	73	2	no	—
297	#364	—	73	1	no	—
298	#364	C₂×D₇₃	1	1	yes	characteristic, complemented
299	#362	—	73	2	no	—
300	#362	—	73	2	no	—
301	#362	—	73	2	no	—
302	#362	C₂×D₇₃	1	2	yes	complemented
303	C₂×#41	—	146	1	no	—
304	C₂²×Q₈	—	146	2	no	—
305	#135	—	73	1	no	—
306	#135	—	73	1	no	—
307	#135	—	73	1	no	—
308	#135	—	146	1	no	—
309	#135	—	146	1	no	—
310	#135	C₂²×D₇₃	1	1	yes	characteristic
311	C₂×Q₁₆	—	2	1	no	—
312	C₂×Q₁₆	—	292	1	no	—
313	C₂×Q₁₆	—	292	1	no	—
314	C₂×Q₁₆	—	292	1	no	—
315	C₂×Q₁₆	—	292	1	no	—
316	C₂×Q₁₆	—	73	1	no	—
317	C₂×Q₁₆	—	73	2	no	—
318	C₂×Q₁₆	—	146	2	no	—
319	C₂×Q₁₆	—	146	2	no	—
320	C₂×Q₁₆	—	146	2	no	—
321	C₂×Q₁₆	—	146	2	no	—
322	C₂×Q₁₆	—	146	2	no	—
323	C₂×Q₁₆	—	146	2	no	—
324	C₂×Q₁₆	—	146	1	no	—
325	C₂×Q₁₆	C₂²×D₇₃	1	2	yes	—
326	C₂×SD₁₆	—	146	1	no	—
327	C₂×D₈	—	73	1	no	—
328	#131	—	2	1	no	—
329	#131	—	292	1	no	—
330	#131	—	292	1	no	—
331	#131	—	146	1	no	—
332	#131	—	146	1	no	—
333	#131	—	146	1	no	—
334	C₂×M₁₆	—	292	1	no	—
335	C₂×M₁₆	—	146	1	no	—
336	C₂²×C₈	—	292	1	no	—
337	C₂²×C₈	—	73	1	no	—
338	C₂²×C₈	—	73	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	292	2	no	—
341	C₄⋊Q₈	—	146	2	no	—
342	C₄⋊Q₈	—	146	1	no	—
343	C₂×C₄⋊C₄	—	292	2	no	—
344	C₂×C₄²	—	73	1	no	—
345	Q₃₂	—	2	2	no	—
346	Q₃₂	—	146	2	no	—
347	Q₃₂	—	146	2	no	—
348	Q₃₂	—	146	2	no	—
349	SD₃₂	—	2	2	no	—
350	SD₃₂	—	146	2	no	—
351	SD₃₂	—	146	2	no	—
352	SD₃₂	—	146	2	no	—
353	M₃₂	—	73	2	no	—
354	M₃₂	—	146	2	no	—
355	M₃₂	C₂²×D₇₃	1	2	yes	—
356	C₂×C₁₆	—	146	2	no	—
357	#108	—	73	1	no	—
358	#108	—	146	1	no	—
359	#108	C₂²×D₇₃	1	1	yes	characteristic
360	#104	—	2	1	no	—
361	#104	—	146	1	no	—
362	#104	—	146	1	no	—
363	#104	—	146	1	no	—
364	C₄×C₈	—	73	1	no	—
365	C₄×C₈	—	73	1	no	—
366	C₄×C₈	—	73	1	no	—
367	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
368	#41	—	2	1	no	—
369	#41	—	292	1	no	—
370	#41	—	292	1	no	—
371	#41	—	146	1	no	—
372	#41	—	146	1	no	—
373	#41	—	146	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	292	2	no	—
376	C₂×Q₈	—	292	2	no	—
377	C₂×Q₈	—	292	2	no	—
378	C₂×Q₈	—	292	2	no	—
379	C₂×Q₈	—	292	2	no	—
380	C₂×Q₈	—	146	1	no	—
381	C₂×Q₈	—	146	2	no	—
382	C₂×D₄	—	292	1	no	—
383	C₂×D₄	—	146	1	no	—
384	C₂²×C₄	—	292	1	no	—
385	C₂²×C₄	—	292	2	no	—
386	C₂²×C₄	—	73	1	no	—
387	C₂²×C₄	—	146	1	no	—
388	Q₁₆	—	2	2	no	—
389	Q₁₆	—	2	2	no	—
390	Q₁₆	—	4	1	no	—
391	Q₁₆	—	4	1	no	—
392	Q₁₆	—	292	2	no	—
393	Q₁₆	—	292	2	no	—
394	Q₁₆	—	292	2	no	—
395	Q₁₆	—	292	2	no	—
396	Q₁₆	—	292	1	no	—
397	Q₁₆	—	292	1	no	—
398	Q₁₆	—	73	1	no	—
399	Q₁₆	—	146	1	no	—
400	Q₁₆	—	146	2	no	—
401	Q₁₆	—	146	2	no	—
402	Q₁₆	D₄×D₇₃	1	1	yes	characteristic
403	SD₁₆	—	2	1	no	—
404	SD₁₆	—	146	1	no	—
405	SD₁₆	—	146	1	no	—
406	SD₁₆	—	146	1	no	—
407	D₈	—	73	1	no	—
408	D₈	—	146	1	no	—
409	D₈	D₄×D₇₃	1	1	yes	characteristic
410	M₁₆	—	2	1	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	292	1	no	—
413	M₁₆	—	292	1	no	—
414	M₁₆	—	292	1	no	—
415	M₁₆	—	292	1	no	—
416	M₁₆	—	146	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	292	1	no	—
419	C₂×C₈	—	292	1	no	—
420	C₂×C₈	—	292	1	no	—
421	C₂×C₈	—	292	1	no	—
422	C₂×C₈	—	73	1	no	—
423	C₂×C₈	—	73	1	no	—
424	C₂×C₈	—	73	1	no	—
425	C₂×C₈	—	73	1	no	—
426	C₂×C₈	—	73	1	no	—
427	C₂×C₈	—	73	1	no	—
428	C₂×C₈	—	73	1	no	—
429	C₂×C₈	—	73	1	no	—
430	C₂×C₈	—	73	1	no	—
431	C₂×C₈	—	73	1	no	—
432	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
433	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	—	292	2	no	—
436	C₄⋊C₄	—	292	4	no	—
437	C₄²	—	73	1	no	—
438	C₄²	—	146	1	no	—
439	C₄²	D₄×D₇₃	1	1	yes	characteristic
440	C₁₆	—	2	2	no	—
441	C₁₆	—	146	2	no	—
442	C₂³	—	292	1	no	—
443	C₂³	—	73	1	no	—
444	Q₈	—	2	1	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	292	1	no	—
448	Q₈	—	292	2	no	—
449	Q₈	—	292	2	no	—
450	Q₈	—	584	2	no	—
451	Q₈	—	584	2	no	—
452	Q₈	—	146	1	no	—
453	D₄	—	2	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	292	1	no	—
456	D₄	—	292	1	no	—
457	D₄	—	292	1	no	—
458	D₄	—	292	1	no	—
459	D₄	—	146	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	292	1	no	—
464	C₂×C₄	—	292	1	no	—
465	C₂×C₄	—	292	1	no	—
466	C₂×C₄	—	292	1	no	—
467	C₂×C₄	—	292	2	no	—
468	C₂×C₄	—	584	2	no	—
469	C₂×C₄	—	584	2	no	—
470	C₂×C₄	—	73	1	no	—
471	C₂×C₄	—	73	1	no	—
472	C₂×C₄	—	73	1	no	—
473	C₂×C₄	—	73	1	no	—
474	C₂×C₄	—	73	1	no	—
475	C₂×C₄	—	146	4	no	—
476	C₂×C₄	—	146	1	no	—
477	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
478	C₈	—	4	1	no	—
479	C₈	—	292	1	no	—
480	C₈	—	73	1	no	—
481	C₈	—	73	1	no	—
482	C₈	—	73	1	no	—
483	C₈	—	73	1	no	—
484	C₈	D₈×D₇₃	1	1	yes	characteristic
485	C₈	D₈×D₇₃	1	1	yes	characteristic
486	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
487	C₈	#41×D₇₃	1	1	yes	characteristic
488	C₂²	—	4	1	no	—
489	C₂²	—	292	1	no	—
490	C₂²	—	584	2	no	—
491	C₂²	—	73	1	no	—
492	C₂²	—	73	1	no	—
493	C₂²	—	146	2	no	—
494	C₂²	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	2	no	—
498	C₄	—	292	1	no	—
499	C₄	—	584	2	no	—
500	C₄	—	73	1	no	—
501	C₄	—	73	1	no	—
502	C₄	—	146	2	no	—
503	C₄	#121×D₇₃	1	1	yes	characteristic
504	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	8	1	no	—
507	C₂	—	584	1	no	—
508	C₂	—	73	2	no	—
509	C₂	—	146	1	no	—
510	C₂	#459×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#459×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2214	C₂
socle	C₂×C₇₃	C₂×#459
prime radical	#135×D₇₃	C₂²
hypercenter	#2214	D₇₃
hypocenter	C₇₃	C₂×#2214
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2214

Complements

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

N	H ≅ G/N	type
2. #494×D₇₃	C₂	semidirect
4. #22612013	C₂	semidirect
5. #22612012	C₂	semidirect
6. #22612011	C₂	semidirect
7. #22612010	C₂	semidirect
8. #22612009	C₂	semidirect
9. #364×D₇₃	C₂	semidirect
10. #362×D₇₃	C₂	semidirect
11. C₇₃×#2214	C₂	semidirect
25. #17988967	C₂²	semidirect
28. #17988965	C₂²	semidirect
37. #17988408	C₂²	semidirect
38. #17988407	C₂²	semidirect
39. #17988404	C₂²	semidirect
40. #17988403	C₂²	semidirect
41. #17988402	C₂²	semidirect
43. #494×C₇₃	C₂²	semidirect
45. #364×C₇₃	C₂²	semidirect
46. #362×C₇₃	C₂²	semidirect
255. D₇₃	#2214	direct (N × H)
264. #2214	D₇₃	direct (N × H)
267. C₇₃	C₂×#2214	semidirect
286. #494	C₂×D₇₃	semidirect
298. #364	C₂×D₇₃	semidirect
302. #362	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#510×D₇₃	2
#494×D₇₃	2
#443×D₇₃	2
#22612013	2
#22612012	2
#22612011	2
#22612010	2
#22612009	2
#364×D₇₃	2
#362×D₇₃	2
C₇₃×#2214	2
C₂×#2214	73

Subgroups — #2214×D73 #33240366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2214×D₇₃ #33240366