Subgroups — #2213×D₇₃ #33240360

Order 18688.

790 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#509×D₇₃	C₂	1	2	yes	maximal, complemented
2	#493×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22612008	C₂	1	1	yes	maximal, characteristic, complemented
5	#22612007	C₂	1	1	yes	maximal, characteristic, complemented
6	#22612006	C₂	1	2	yes	maximal, complemented
7	#22612005	C₂	1	2	yes	maximal, complemented
8	#22612004	C₂	1	1	yes	maximal, characteristic, complemented
9	#364×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#361×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2213	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₃	C₂²	1	1	yes	characteristic
13	C₂×D₈×D₇₃	—	2	1	no	—
14	C₂×D₈×D₇₃	C₂²	1	2	yes	—
15	#131×D₇₃	—	2	1	no	—
16	#127×D₇₃	—	2	1	no	—
17	#17989025	C₂²	1	2	yes	complemented
18	#17989024	—	2	2	no	—
19	#17989023	C₂²	1	2	yes	complemented
20	#17989022	C₂²	1	2	yes	complemented
21	#17989021	—	2	2	no	—
22	SD₃₂×D₇₃	—	2	2	no	—
23	D₁₆×D₇₃	—	2	2	no	—
24	M₃₂×D₇₃	C₂²	1	2	yes	—
25	#17988964	C₂²	1	1	yes	characteristic, complemented
26	#17988963	—	2	1	no	—
27	#17988962	—	2	1	no	—
28	#17988962	C₂²	1	2	yes	complemented
29	#17988705	C₂²	1	1	yes	characteristic, complemented
30	#17988704	C₂²	1	1	yes	characteristic, complemented
31	#17988703	C₂²	1	1	yes	characteristic, complemented
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	#17988401	C₂²	1	2	yes	complemented
40	#17988400	C₂²	1	2	yes	complemented
41	#17988399	C₂²	1	2	yes	complemented
42	#509×C₇₃	C₂²	1	2	yes	complemented
43	#493×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	#443×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#364×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#361×C₇₃	C₂²	1	2	yes	complemented
47	#41×D₇₃	—	2	1	no	—
48	C₂×D₄×D₇₃	—	2	2	no	—
49	C₂×D₄×D₇₃	—	4	2	no	—
50	#14556614	D₄	1	1	yes	characteristic, complemented
51	#14556613	C₂³	1	1	yes	characteristic
52	#14556612	—	2	1	no	—
53	#14556611	—	2	1	no	—
54	#14556610	D₄	1	1	yes	characteristic, complemented
55	Q₁₆×D₇₃	D₄	1	1	yes	characteristic, complemented
56	SD₁₆×D₇₃	—	2	1	no	—
57	C₂×D₅₈₄	—	2	1	no	—
58	C₂×D₅₈₄	C₂³	1	2	yes	—
59	C₂×#11924013	—	2	2	no	—
60	C₂×#11924013	—	2	2	no	—
61	D₈×D₇₃	—	2	2	no	—
62	D₈×D₇₃	—	2	2	no	—
63	D₈×D₇₃	—	2	2	no	—
64	D₈×D₇₃	—	2	2	no	—
65	D₈×D₇₃	—	4	1	no	—
66	D₈×D₇₃	—	4	1	no	—
67	D₈×D₇₃	—	4	1	no	—
68	D₈×D₇₃	—	4	1	no	—
69	D₈×D₇₃	D₄	1	1	yes	characteristic, complemented
70	#14556599	—	2	1	no	—
71	#14556599	—	4	1	no	—
72	#14556598	—	2	1	no	—
73	#14556597	—	2	1	no	—
74	#14556597	—	4	1	no	—
75	M₁₆×D₇₃	—	2	1	no	—
76	M₁₆×D₇₃	—	4	1	no	—
77	C₂×C₈×D₇₃	—	4	1	no	—
78	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
79	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
80	#14556588	—	2	1	no	—
81	#14556587	—	2	2	no	—
82	#14556587	—	4	2	no	—
83	C₄²×D₇₃	D₄	1	1	yes	characteristic
84	#14556536	—	2	2	no	—
85	#14556535	—	2	2	no	—
86	#14556534	—	2	2	no	—
87	D₁₁₆₈	—	2	2	no	—
88	#14556532	—	2	2	no	—
89	#14556532	—	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×D₈×C₇₃	—	2	1	no	—
103	C₂×D₈×C₇₃	C₂³	1	2	yes	—
104	#131×C₇₃	—	2	1	no	—
105	#127×C₇₃	—	2	1	no	—
106	SD₃₂×C₇₃	—	2	2	no	—
107	D₁₆×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	C₂³×D₇₃	—	4	2	no	—
113	#11924029	—	2	1	no	—
114	#11924028	—	2	1	no	—
115	#11924028	—	4	1	no	—
116	#11924027	—	2	1	no	—
117	#11924027	—	4	1	no	—
118	Q₈×D₇₃	—	2	1	no	—
119	C₂×D₂₉₂	—	2	2	no	—
120	C₂×D₂₉₂	—	4	2	no	—
121	C₂×C₂²⋊D₇₃	—	4	4	no	—
122	C₂×C₂²⋊D₇₃	—	4	2	no	—
123	D₄×D₇₃	—	2	1	no	—
124	D₄×D₇₃	—	4	1	no	—
125	D₄×D₇₃	—	4	2	no	—
126	D₄×D₇₃	—	4	2	no	—
127	D₄×D₇₃	—	4	2	no	—
128	D₄×D₇₃	—	4	2	no	—
129	D₄×D₇₃	—	8	8	no	—
130	C₂×C₄×D₇₃	—	2	1	no	—
131	C₂×C₄×D₇₃	—	4	1	no	—
132	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
133	Dic₂₉₂	C₂×D₄	1	1	yes	characteristic, complemented
134	#11924018	—	2	1	no	—
135	#11924017	—	2	1	no	—
136	#11924016	—	2	1	no	—
137	#11924015	—	2	1	no	—
138	D₅₈₄	—	2	2	no	—
139	D₅₈₄	—	2	2	no	—
140	D₅₈₄	—	4	1	no	—
141	D₅₈₄	—	4	1	no	—
142	D₅₈₄	C₂×D₄	1	1	yes	characteristic, complemented
143	#11924013	—	2	1	no	—
144	#11924013	—	4	2	no	—
145	#11924013	—	4	2	no	—
146	#11924013	—	4	2	no	—
147	#11924013	—	4	2	no	—
148	#11924012	—	2	1	no	—
149	#11924012	—	4	1	no	—
150	#11924011	—	4	1	no	—
151	#11924011	—	4	1	no	—
152	#11924011	—	4	1	no	—
153	C₂×#10596831	—	4	1	no	—
154	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
155	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
156	C₈×D₇₃	—	4	1	no	—
157	C₈×D₇₃	—	4	1	no	—
158	C₈×D₇₃	—	4	1	no	—
159	C₈×D₇₃	D₈	1	1	yes	characteristic
160	C₈×D₇₃	D₈	1	1	yes	characteristic
161	C₈×D₇₃	D₈	1	1	yes	characteristic
162	C₈×D₇₃	D₈	1	1	yes	characteristic
163	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
164	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
165	C₈×D₇₃	#41	1	1	yes	characteristic
166	C₈×D₇₃	#41	1	1	yes	characteristic
167	C₄×Dic₇₃	—	2	1	no	—
168	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
169	#11924003	—	2	2	no	—
170	#41×C₇₃	—	2	1	no	—
171	C₂×D₄×C₇₃	—	2	2	no	—
172	C₂×D₄×C₇₃	—	4	2	no	—
173	Q₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic, complemented
174	SD₁₆×C₇₃	—	2	1	no	—
175	D₈×C₇₃	—	2	2	no	—
176	D₈×C₇₃	—	2	2	no	—
177	D₈×C₇₃	—	4	1	no	—
178	D₈×C₇₃	—	4	1	no	—
179	D₈×C₇₃	C₂×D₄	1	1	yes	characteristic, complemented
180	M₁₆×C₇₃	—	2	1	no	—
181	M₁₆×C₇₃	—	4	1	no	—
182	C₂×C₈×C₇₃	—	4	1	no	—
183	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
185	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
186	C₁₆×C₇₃	—	2	2	no	—
187	C₂³×C₇₃	—	4	2	no	—
188	C₂²×D₇₃	—	4	1	no	—
189	C₂²×D₇₃	—	4	2	no	—
190	C₂²×D₇₃	—	8	8	no	—
191	C₂²×D₇₃	—	8	2	no	—
192	C₂²×D₇₃	—	8	2	no	—
193	C₂²×D₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
194	Q₈×C₇₃	—	2	1	no	—
195	D₄×C₇₃	—	2	1	no	—
196	D₄×C₇₃	—	4	1	no	—
197	D₄×C₇₃	—	4	2	no	—
198	D₄×C₇₃	—	4	2	no	—
199	D₄×C₇₃	—	8	4	no	—
200	C₂×C₄×C₇₃	—	2	1	no	—
201	C₂×C₄×C₇₃	—	4	1	no	—
202	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
203	C₂²⋊D₇₃	—	4	1	no	—
204	C₂²⋊D₇₃	—	4	1	no	—
205	C₂²⋊D₇₃	—	4	1	no	—
206	C₂²⋊D₇₃	—	8	8	no	—
207	C₂²⋊D₇₃	—	8	2	no	—
208	C₂²⋊D₇₃	—	8	2	no	—
209	C₂×Dic₇₃	—	2	1	no	—
210	C₂×Dic₇₃	—	4	1	no	—
211	C₂×Dic₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
212	D₂₉₂	—	2	1	no	—
213	D₂₉₂	—	4	1	no	—
214	D₂₉₂	—	4	2	no	—
215	D₂₉₂	—	4	2	no	—
216	D₂₉₂	—	8	4	no	—
217	C₄×D₇₃	—	2	4	no	—
218	C₄×D₇₃	—	4	1	no	—
219	C₄×D₇₃	—	4	1	no	—
220	C₄×D₇₃	—	4	1	no	—
221	C₄×D₇₃	#121	1	1	yes	characteristic
222	C₄×D₇₃	#121	1	1	yes	characteristic
223	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
224	C₄×D₇₃	C₂×D₈	1	1	yes	characteristic
225	Dic₁₄₆	—	2	1	no	—
226	Dic₁₄₆	—	4	1	no	—
227	C₈×C₇₃	—	4	1	no	—
228	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
229	C₈×C₇₃	C₂×D₈	1	1	yes	characteristic
230	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
231	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
232	#10596831	—	4	1	no	—
233	#10596831	#121	1	1	yes	characteristic
234	#10596831	#121	1	1	yes	characteristic
235	#10596831	C₂×D₈	1	1	yes	characteristic
236	#10596831	C₂×D₈	1	1	yes	characteristic
237	C₂²×C₇₃	—	4	1	no	—
238	C₂²×C₇₃	—	8	4	no	—
239	C₂²×C₇₃	—	8	2	no	—
240	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
241	C₂×D₇₃	—	2	2	no	—
242	C₂×D₇₃	—	4	1	no	—
243	C₂×D₇₃	—	8	2	no	—
244	C₂×D₇₃	—	8	4	no	—
245	C₂×D₇₃	—	8	2	no	—
246	C₂×D₇₃	—	16	4	no	—
247	C₂×D₇₃	—	16	4	no	—
248	C₂×D₇₃	#459	1	1	yes	characteristic
249	C₂×D₇₃	#459	1	1	yes	characteristic
250	C₄×C₇₃	—	2	2	no	—
251	C₄×C₇₃	—	4	1	no	—
252	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
253	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
254	Dic₇₃	—	2	2	no	—
255	Dic₇₃	—	4	1	no	—
256	Dic₇₃	#459	1	1	yes	characteristic
257	Dic₇₃	#459	1	1	yes	characteristic
258	C₂×#2213	—	73	1	no	maximal, Sylow
259	C₂×C₇₃	—	2	1	no	—
260	C₂×C₇₃	—	8	1	no	—
261	C₂×C₇₃	—	16	2	no	—
262	C₂×C₇₃	C₂×#459	1	1	yes	characteristic
263	D₇₃	—	2	1	no	—
264	D₇₃	—	8	1	no	—
265	D₇₃	—	16	2	no	—
266	D₇₃	#2213	1	2	yes	direct product factor
267	C₂×#509	—	73	2	no	—
268	C₂×#493	—	73	1	no	—
269	C₂×#443	—	73	1	no	—
270	#2213	—	73	2	no	—
271	#2213	—	73	1	no	—
272	#2213	—	73	1	no	—
273	#2213	—	73	1	no	—
274	#2213	—	73	2	no	—
275	#2213	D₇₃	1	1	yes	characteristic, direct product factor
276	C₂×#364	—	73	1	no	—
277	C₂×#361	—	73	2	no	—
278	C₇₃	C₂×#2213	1	1	yes	characteristic, complemented, Sylow
279	C₂×#135	—	73	1	no	—
280	C₂²×D₈	—	73	2	no	—
281	C₂²×D₈	—	146	1	no	—
282	C₂×#131	—	146	1	no	—
283	C₂×#127	—	146	1	no	—
284	#509	—	73	2	no	—
285	#509	—	73	2	no	—
286	#509	—	73	2	no	—
287	#509	—	146	2	no	—
288	#509	—	146	2	no	—
289	#509	C₂×D₇₃	1	2	yes	complemented
290	C₂×SD₃₂	—	146	2	no	—
291	C₂×D₁₆	—	146	2	no	—
292	C₂×M₃₂	—	73	2	no	—
293	#493	—	73	2	no	—
294	#493	—	73	1	no	—
295	#493	—	146	1	no	—
296	#493	—	146	1	no	—
297	#493	C₂×D₇₃	1	1	yes	characteristic, complemented
298	#443	—	73	1	no	—
299	#443	—	73	1	no	—
300	#443	—	73	1	no	—
301	#443	—	146	1	no	—
302	#443	—	146	1	no	—
303	#443	C₂×D₇₃	1	1	yes	characteristic, complemented
304	C₂×#108	—	73	1	no	—
305	C₂×#104	—	146	1	no	—
306	C₂×C₄×C₈	—	73	1	no	—
307	#364	—	73	2	no	—
308	#364	—	73	1	no	—
309	#364	C₂×D₇₃	1	1	yes	characteristic, complemented
310	#361	—	73	2	no	—
311	#361	—	73	2	no	—
312	#361	—	73	2	no	—
313	#361	C₂×D₇₃	1	2	yes	complemented
314	C₂×#41	—	146	1	no	—
315	C₂²×D₄	—	292	2	no	—
316	C₂²×D₄	—	146	2	no	—
317	#135	—	73	1	no	—
318	#135	—	73	1	no	—
319	#135	—	73	1	no	—
320	#135	—	146	1	no	—
321	#135	—	146	1	no	—
322	#135	C₂²×D₇₃	1	1	yes	characteristic
323	C₂×Q₁₆	—	73	1	no	—
324	C₂×SD₁₆	—	146	1	no	—
325	C₂×D₈	—	2	1	no	—
326	C₂×D₈	—	292	1	no	—
327	C₂×D₈	—	292	1	no	—
328	C₂×D₈	—	292	1	no	—
329	C₂×D₈	—	292	1	no	—
330	C₂×D₈	—	73	1	no	—
331	C₂×D₈	—	73	2	no	—
332	C₂×D₈	—	146	2	no	—
333	C₂×D₈	—	146	2	no	—
334	C₂×D₈	—	146	2	no	—
335	C₂×D₈	—	146	2	no	—
336	C₂×D₈	—	146	2	no	—
337	C₂×D₈	—	146	2	no	—
338	C₂×D₈	—	146	1	no	—
339	C₂×D₈	C₂²×D₇₃	1	2	yes	—
340	#131	—	2	1	no	—
341	#131	—	292	1	no	—
342	#131	—	292	1	no	—
343	#131	—	146	1	no	—
344	#131	—	146	1	no	—
345	#131	—	146	1	no	—
346	C₂×M₁₆	—	292	1	no	—
347	C₂×M₁₆	—	146	1	no	—
348	C₂²×C₈	—	292	1	no	—
349	C₂²×C₈	—	73	1	no	—
350	C₂²×C₈	—	73	1	no	—
351	#127	—	2	1	no	—
352	#127	—	292	2	no	—
353	#127	—	146	2	no	—
354	#127	—	146	1	no	—
355	C₂×C₄²	—	73	1	no	—
356	SD₃₂	—	2	2	no	—
357	SD₃₂	—	146	2	no	—
358	SD₃₂	—	146	2	no	—
359	SD₃₂	—	146	2	no	—
360	D₁₆	—	2	2	no	—
361	D₁₆	—	146	2	no	—
362	D₁₆	—	146	2	no	—
363	D₁₆	—	146	2	no	—
364	M₃₂	—	73	2	no	—
365	M₃₂	—	146	2	no	—
366	M₃₂	C₂²×D₇₃	1	2	yes	—
367	C₂×C₁₆	—	146	2	no	—
368	#108	—	73	1	no	—
369	#108	—	146	1	no	—
370	#108	C₂²×D₇₃	1	1	yes	characteristic
371	#104	—	2	1	no	—
372	#104	—	146	1	no	—
373	#104	—	146	1	no	—
374	#104	—	146	1	no	—
375	C₄×C₈	—	73	1	no	—
376	C₄×C₈	—	73	1	no	—
377	C₄×C₈	—	73	1	no	—
378	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
379	C₂⁴	—	292	2	no	—
380	#41	—	2	1	no	—
381	#41	—	292	1	no	—
382	#41	—	292	1	no	—
383	#41	—	146	1	no	—
384	#41	—	146	1	no	—
385	#41	—	146	1	no	—
386	C₂×Q₈	—	146	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	292	2	no	—
390	C₂×D₄	—	292	1	no	—
391	C₂×D₄	—	292	2	no	—
392	C₂×D₄	—	292	2	no	—
393	C₂×D₄	—	292	2	no	—
394	C₂×D₄	—	292	2	no	—
395	C₂×D₄	—	292	2	no	—
396	C₂×D₄	—	292	4	no	—
397	C₂×D₄	—	584	8	no	—
398	C₂×D₄	—	146	1	no	—
399	C₂×D₄	—	146	2	no	—
400	C₂²×C₄	—	292	1	no	—
401	C₂²×C₄	—	73	1	no	—
402	C₂²×C₄	—	146	1	no	—
403	Q₁₆	—	73	1	no	—
404	Q₁₆	—	146	1	no	—
405	Q₁₆	D₄×D₇₃	1	1	yes	characteristic, complemented
406	SD₁₆	—	2	1	no	—
407	SD₁₆	—	146	1	no	—
408	SD₁₆	—	146	1	no	—
409	SD₁₆	—	146	1	no	—
410	D₈	—	2	2	no	—
411	D₈	—	2	2	no	—
412	D₈	—	4	1	no	—
413	D₈	—	4	1	no	—
414	D₈	—	292	2	no	—
415	D₈	—	292	2	no	—
416	D₈	—	292	2	no	—
417	D₈	—	292	2	no	—
418	D₈	—	292	1	no	—
419	D₈	—	292	1	no	—
420	D₈	—	73	1	no	—
421	D₈	—	146	1	no	—
422	D₈	—	146	2	no	—
423	D₈	—	146	2	no	—
424	D₈	D₄×D₇₃	1	1	yes	characteristic, complemented
425	M₁₆	—	2	1	no	—
426	M₁₆	—	4	1	no	—
427	M₁₆	—	292	1	no	—
428	M₁₆	—	292	1	no	—
429	M₁₆	—	292	1	no	—
430	M₁₆	—	292	1	no	—
431	M₁₆	—	146	1	no	—
432	C₂×C₈	—	4	1	no	—
433	C₂×C₈	—	292	1	no	—
434	C₂×C₈	—	292	1	no	—
435	C₂×C₈	—	292	1	no	—
436	C₂×C₈	—	292	1	no	—
437	C₂×C₈	—	73	1	no	—
438	C₂×C₈	—	73	1	no	—
439	C₂×C₈	—	73	1	no	—
440	C₂×C₈	—	73	1	no	—
441	C₂×C₈	—	73	1	no	—
442	C₂×C₈	—	73	1	no	—
443	C₂×C₈	—	73	1	no	—
444	C₂×C₈	—	73	1	no	—
445	C₂×C₈	—	73	1	no	—
446	C₂×C₈	—	73	1	no	—
447	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
448	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
449	C₄²	—	73	1	no	—
450	C₄²	—	146	1	no	—
451	C₄²	D₄×D₇₃	1	1	yes	characteristic
452	C₁₆	—	2	2	no	—
453	C₁₆	—	146	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	292	1	no	—
456	C₂³	—	292	2	no	—
457	C₂³	—	584	2	no	—
458	C₂³	—	584	2	no	—
459	C₂³	—	584	8	no	—
460	C₂³	—	73	1	no	—
461	Q₈	—	2	1	no	—
462	Q₈	—	292	1	no	—
463	Q₈	—	146	1	no	—
464	D₄	—	2	1	no	—
465	D₄	—	4	1	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	2	no	—
468	D₄	—	8	4	no	—
469	D₄	—	292	1	no	—
470	D₄	—	292	1	no	—
471	D₄	—	292	1	no	—
472	D₄	—	292	1	no	—
473	D₄	—	292	2	no	—
474	D₄	—	292	2	no	—
475	D₄	—	584	4	no	—
476	D₄	—	584	2	no	—
477	D₄	—	584	2	no	—
478	D₄	—	584	8	no	—
479	D₄	—	146	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	292	1	no	—
483	C₂×C₄	—	292	1	no	—
484	C₂×C₄	—	292	1	no	—
485	C₂×C₄	—	292	1	no	—
486	C₂×C₄	—	73	1	no	—
487	C₂×C₄	—	73	1	no	—
488	C₂×C₄	—	73	1	no	—
489	C₂×C₄	—	73	1	no	—
490	C₂×C₄	—	73	1	no	—
491	C₂×C₄	—	146	4	no	—
492	C₂×C₄	—	146	1	no	—
493	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
494	C₈	—	4	1	no	—
495	C₈	—	292	1	no	—
496	C₈	—	73	1	no	—
497	C₈	—	73	1	no	—
498	C₈	—	73	1	no	—
499	C₈	—	73	1	no	—
500	C₈	D₈×D₇₃	1	1	yes	characteristic
501	C₈	D₈×D₇₃	1	1	yes	characteristic
502	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
503	C₈	#41×D₇₃	1	1	yes	characteristic
504	C₂²	—	4	1	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	292	1	no	—
508	C₂²	—	584	4	no	—
509	C₂²	—	584	2	no	—
510	C₂²	—	584	2	no	—
511	C₂²	—	73	1	no	—
512	C₂²	—	73	1	no	—
513	C₂²	—	1168	4	no	—
514	C₂²	—	1168	4	no	—
515	C₂²	—	146	2	no	—
516	C₂²	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	292	1	no	—
520	C₄	—	73	1	no	—
521	C₄	—	73	1	no	—
522	C₄	—	146	2	no	—
523	C₄	#121×D₇₃	1	1	yes	characteristic
524	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
525	C₂	—	2	1	no	—
526	C₂	—	8	1	no	—
527	C₂	—	16	2	no	—
528	C₂	—	584	1	no	—
529	C₂	—	73	2	no	—
530	C₂	—	1168	2	no	—
531	C₂	—	146	1	no	—
532	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×#2213	C₂
socle	C₂×C₇₃	C₂×#459
hypercenter	#2213	D₇₃
hypocenter	C₇₃	C₂×#2213
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2213

Complements

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

N	H ≅ G/N	type
1. #509×D₇₃	C₂	semidirect
2. #493×D₇₃	C₂	semidirect
3. #443×D₇₃	C₂	semidirect
4. #22612008	C₂	semidirect
5. #22612007	C₂	semidirect
6. #22612006	C₂	semidirect
7. #22612005	C₂	semidirect
8. #22612004	C₂	semidirect
9. #364×D₇₃	C₂	semidirect
10. #361×D₇₃	C₂	semidirect
11. C₇₃×#2213	C₂	semidirect
17. #17989025	C₂²	semidirect
19. #17989023	C₂²	semidirect
20. #17989022	C₂²	semidirect
25. #17988964	C₂²	semidirect
28. #17988962	C₂²	semidirect
29. #17988705	C₂²	semidirect
30. #17988704	C₂²	semidirect
31. #17988703	C₂²	semidirect
37. #17988408	C₂²	semidirect
38. #17988407	C₂²	semidirect
39. #17988401	C₂²	semidirect
40. #17988400	C₂²	semidirect
41. #17988399	C₂²	semidirect
42. #509×C₇₃	C₂²	semidirect
43. #493×C₇₃	C₂²	semidirect
44. #443×C₇₃	C₂²	semidirect
45. #364×C₇₃	C₂²	semidirect
46. #361×C₇₃	C₂²	semidirect
50. #14556614	D₄	semidirect
54. #14556610	D₄	semidirect
55. Q₁₆×D₇₃	D₄	semidirect
69. D₈×D₇₃	D₄	semidirect
133. Dic₂₉₂	C₂×D₄	semidirect
142. D₅₈₄	C₂×D₄	semidirect
173. Q₁₆×C₇₃	C₂×D₄	semidirect
179. D₈×C₇₃	C₂×D₄	semidirect
266. D₇₃	#2213	direct (N × H)
275. #2213	D₇₃	direct (N × H)
278. C₇₃	C₂×#2213	semidirect
289. #509	C₂×D₇₃	semidirect
297. #493	C₂×D₇₃	semidirect
303. #443	C₂×D₇₃	semidirect
309. #364	C₂×D₇₃	semidirect
313. #361	C₂×D₇₃	semidirect
405. Q₁₆	D₄×D₇₃	semidirect
424. D₈	D₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#509×D₇₃	2
#493×D₇₃	2
#443×D₇₃	2
#22612008	2
#22612007	2
#22612006	2
#22612005	2
#22612004	2
#364×D₇₃	2
#361×D₇₃	2
C₇₃×#2213	2
C₂×#2213	73

Subgroups — #2213×D73 #33240360

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2213×D₇₃ #33240360