Subgroups — #33069908

Order 18688.

702 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#22619413	C₂	1	2	yes	maximal
3	C₈×#11924027	C₂	1	1	yes	maximal, characteristic
4	#22609326	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609324	C₂	1	2	yes	maximal, complemented
6	#22609322	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609320	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609318	C₂	1	2	yes	maximal, complemented
9	#22608688	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608601	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1673	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556620	—	2	2	no	—
13	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
14	C₄×#11924027	C₂²	1	1	yes	characteristic
15	#17988992	C₂²	1	1	yes	characteristic
16	#17988991	—	2	1	no	—
17	#17988991	—	2	1	no	—
18	#17988990	C₂²	1	2	yes	—
19	#17988798	C₂²	1	2	yes	—
20	#17988796	—	2	2	no	—
21	#17988794	C₂²	1	2	yes	—
22	#17988792	C₂²	1	2	yes	—
23	#17988790	—	2	2	no	—
24	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
25	#17988711	C₂²	1	1	yes	characteristic
26	D₄×#10596831	C₂²	1	1	yes	characteristic
27	C₈×C₂²⋊D₇₃	—	2	1	no	—
28	#17988650	—	2	1	no	—
29	#17988639	C₂²	1	1	yes	characteristic
30	#17988637	—	2	1	no	—
31	#107×D₇₃	—	2	1	no	—
32	#107×D₇₃	—	2	1	no	—
33	#17988609	C₂²	1	2	yes	—
34	#17988594	—	2	2	no	—
35	C₂×C₈×Dic₇₃	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988340	C₂²	1	1	yes	characteristic
38	#17988339	C₂²	1	2	yes	—
39	#17988334	C₂²	1	2	yes	—
40	#17988333	C₂²	1	2	yes	—
41	#17988332	C₂²	1	2	yes	—
42	#500×C₇₃	C₂²	1	1	yes	characteristic
43	#461×C₇₃	C₂²	1	2	yes	—
44	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	1	yes	characteristic
46	#332×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924027	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₇₃	—	2	2	no	—
49	#14556620	—	4	8	no	—
50	C₂×Dic₂₉₂	—	2	2	no	—
51	C₂×#11924018	—	2	2	no	—
52	C₂×#11924016	—	2	2	no	—
53	C₂×#11924011	—	2	2	no	—
54	C₂²×#10596831	—	2	1	no	—
55	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
57	#14556591	C₂³	1	2	yes	—
58	#14556590	—	2	2	no	—
59	#14556590	—	2	2	no	—
60	#14556589	—	2	2	no	—
61	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
62	#14556556	D₄	1	1	yes	characteristic
63	D₄×Dic₇₃	D₄	1	1	yes	characteristic
64	C₄×C₂²⋊D₇₃	—	2	1	no	—
65	#14556551	—	2	1	no	—
66	#14556549	D₄	1	1	yes	characteristic
67	#14556547	—	2	1	no	—
68	C₄⋊C₄×D₇₃	—	2	2	no	—
69	C₄⋊C₄×D₇₃	—	2	2	no	—
70	C₂×C₄×Dic₇₃	—	2	1	no	—
71	C₄²×D₇₃	C₂³	1	1	yes	characteristic
72	#14556525	—	2	1	no	—
73	#14556525	—	2	1	no	—
74	#14556524	—	2	2	no	—
75	#14556524	—	2	2	no	—
76	C₄⋊#10596831	C₂³	1	2	yes	—
77	C₄⋊#10596831	C₂³	1	1	yes	characteristic
78	#14556520	—	2	1	no	—
79	#14556520	—	2	2	no	—
80	#14556520	—	2	1	no	—
81	#14556516	—	2	2	no	—
82	#14556515	—	2	2	no	—
83	#14556514	—	2	2	no	—
84	C₂²⋊#10596831	—	2	1	no	—
85	#14556503	—	2	1	no	—
86	C₄×#10596831	C₂³	1	1	yes	characteristic
87	C₈×Dic₇₃	—	2	1	no	—
88	C₈×Dic₇₃	—	2	1	no	—
89	C₈×Dic₇₃	—	2	1	no	—
90	C₈×Dic₇₃	D₄	1	1	yes	characteristic
91	C₈×Dic₇₃	D₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₇₃	—	2	2	no	—
93	C₂²×C₈×C₇₃	—	2	1	no	—
94	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
95	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
96	#107×C₇₃	—	2	1	no	—
97	#107×C₇₃	—	2	1	no	—
98	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
99	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
100	#103×C₇₃	—	2	2	no	—
101	C₂²⋊C₈×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	#11924027	—	2	2	no	—
104	#11924027	D₈	1	4	yes	—
105	C₂×Dic₁₄₆	—	2	2	no	—
106	C₂×Dic₁₄₆	—	4	2	no	—
107	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₇₃	—	4	4	no	—
109	Q₈×D₇₃	—	4	4	no	—
110	C₂×C₂²⋊D₇₃	—	2	1	no	—
111	C₂²×Dic₇₃	—	2	1	no	—
112	C₂²×Dic₇₃	—	2	1	no	—
113	C₂×C₄×D₇₃	—	4	2	no	—
114	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
117	Dic₂₉₂	—	4	4	no	—
118	#11924018	—	4	4	no	—
119	#11924016	—	4	4	no	—
120	#11924011	—	4	4	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	2	no	—
123	C₂×#10596831	—	4	2	no	—
124	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
125	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
126	C₈×D₇₃	—	2	2	no	—
127	C₈×D₇₃	—	2	2	no	—
128	C₄⋊Dic₇₃	—	2	2	no	—
129	C₄⋊Dic₇₃	—	2	2	no	—
130	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
131	#11924007	—	2	1	no	—
132	#11924007	—	2	1	no	—
133	#11924007	—	4	2	no	—
134	#11924007	—	4	2	no	—
135	C₂²⋊Dic₇₃	—	2	1	no	—
136	#11924005	—	2	1	no	—
137	C₄×Dic₇₃	—	2	1	no	—
138	C₄×Dic₇₃	—	2	1	no	—
139	C₄×Dic₇₃	—	2	1	no	—
140	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
142	C₄×Dic₇₃	#41	1	1	yes	characteristic
143	C₂×Q₈×C₇₃	—	2	2	no	—
144	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	—	2	1	no	—
146	SD₁₆×C₇₃	—	4	4	no	—
147	C₂×C₈×C₇₃	—	2	1	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	4	2	no	—
150	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂²⋊C₄×C₇₃	—	2	1	no	—
156	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₃	—	2	1	no	—
158	C₂²×D₇₃	#121	1	1	yes	characteristic
159	Q₈×C₇₃	—	4	2	no	—
160	Q₈×C₇₃	—	4	2	no	—
161	D₄×C₇₃	—	2	1	no	—
162	D₄×C₇₃	C₂×D₈	1	2	yes	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	4	1	no	—
165	C₂×C₄×C₇₃	—	4	1	no	—
166	C₂×C₄×C₇₃	—	4	2	no	—
167	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₇₃	—	2	4	no	—
171	C₂×Dic₇₃	—	2	1	no	—
172	C₂×Dic₇₃	—	2	4	no	—
173	C₂×Dic₇₃	—	2	1	no	—
174	C₂×Dic₇₃	—	4	2	no	—
175	C₂×Dic₇₃	—	4	2	no	—
176	C₂×Dic₇₃	#121	1	1	yes	characteristic
177	C₂×Dic₇₃	#121	1	1	yes	characteristic
178	C₂×Dic₇₃	#121	1	1	yes	characteristic
179	C₄×D₇₃	—	2	1	no	—
180	C₄×D₇₃	—	2	1	no	—
181	C₄×D₇₃	—	2	2	no	—
182	C₄×D₇₃	—	8	4	no	—
183	C₄×D₇₃	C₂×D₈	1	2	yes	—
184	C₄×D₇₃	#135	1	2	yes	—
185	Dic₁₄₆	—	2	1	no	—
186	Dic₁₄₆	—	4	2	no	—
187	Dic₁₄₆	—	4	2	no	—
188	Dic₁₄₆	—	8	4	no	—
189	Dic₁₄₆	C₂×D₈	1	2	yes	—
190	C₈×C₇₃	—	2	1	no	—
191	C₈×C₇₃	—	4	2	no	—
192	C₈×C₇₃	—	4	1	no	—
193	C₈×C₇₃	#137	1	2	yes	complemented
194	#10596831	—	2	1	no	—
195	#10596831	—	4	2	no	—
196	#10596831	—	4	1	no	—
197	#10596831	#137	1	2	yes	complemented
198	C₂²×C₇₃	—	2	2	no	—
199	C₂²×C₇₃	—	4	1	no	—
200	C₂²×C₇₃	—	4	1	no	—
201	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
202	C₂×D₇₃	—	2	1	no	—
203	C₂×D₇₃	—	2	1	no	—
204	C₂×D₇₃	#466	1	2	yes	—
205	C₄×C₇₃	—	2	1	no	—
206	C₄×C₇₃	—	4	1	no	—
207	C₄×C₇₃	—	8	2	no	—
208	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
209	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
210	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
211	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
212	Dic₇₃	—	2	1	no	—
213	Dic₇₃	—	2	2	no	—
214	Dic₇₃	—	4	1	no	—
215	Dic₇₃	—	8	2	no	—
216	Dic₇₃	#466	1	2	yes	—
217	Dic₇₃	#473	1	2	yes	—
218	#19271	—	73	1	no	maximal, Sylow
219	C₂×C₇₃	—	4	2	no	—
220	C₂×C₇₃	#3039	1	1	yes	characteristic
221	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
222	C₂×C₇₃	C₂×#473	1	1	yes	characteristic
223	D₇₃	—	2	2	no	—
224	C₂×#500	—	73	1	no	—
225	#3039	—	73	2	no	—
226	C₈×#41	—	73	1	no	—
227	#1674	—	73	1	no	—
228	#1674	—	73	1	no	—
229	#1674	—	73	2	no	—
230	#1673	—	73	2	no	—
231	#1673	—	73	1	no	—
232	#1673	D₇₃	1	1	yes	characteristic, complemented
233	#1567	—	73	1	no	—
234	#1546	—	73	2	no	—
235	C₇₃	#19271	1	1	yes	characteristic, complemented, Sylow
236	C₂×#137	—	146	2	no	—
237	C₂×C₄⋊Q₈	—	73	2	no	—
238	C₄×#41	—	73	1	no	—
239	#500	—	73	2	no	—
240	#500	—	73	1	no	—
241	#500	—	146	1	no	—
242	#500	—	146	1	no	—
243	#500	C₂×D₇₃	1	1	yes	characteristic
244	#462	—	73	2	no	—
245	#462	—	73	2	no	—
246	#462	—	146	2	no	—
247	#461	—	73	2	no	—
248	#461	—	146	2	no	—
249	#461	C₂×D₇₃	1	2	yes	—
250	C₈×Q₈	—	73	1	no	—
251	C₈×Q₈	—	73	1	no	—
252	C₈×D₄	—	73	1	no	—
253	C₈×D₄	—	146	1	no	—
254	C₈×D₄	—	146	1	no	—
255	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic
256	#431	—	73	1	no	—
257	#431	—	146	1	no	—
258	C₂×#107	—	146	1	no	—
259	C₂×#107	—	146	1	no	—
260	#423	—	73	2	no	—
261	#419	—	146	2	no	—
262	C₂×C₄×C₈	—	73	1	no	—
263	C₂×C₄×C₈	—	146	1	no	—
264	#335	—	73	2	no	—
265	#335	—	73	1	no	—
266	#335	C₂×D₇₃	1	1	yes	characteristic
267	#332	—	73	2	no	—
268	#332	—	73	2	no	—
269	#332	—	73	2	no	—
270	#332	C₂×D₇₃	1	2	yes	—
271	C₂×#41	—	73	1	no	—
272	C₂²×Q₈	—	146	2	no	—
273	#137	—	292	8	no	—
274	C₂×Q₁₆	—	146	2	no	—
275	C₂×Q₁₆	—	146	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	146	2	no	—
278	C₂×M₁₆	—	146	2	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	73	1	no	—
281	C₂²×C₈	—	73	1	no	—
282	C₂²×C₈	—	146	1	no	—
283	C₄⋊Q₈	—	73	2	no	—
284	C₄⋊Q₈	—	146	2	no	—
285	C₄⋊Q₈	—	146	2	no	—
286	C₄⋊Q₈	—	146	2	no	—
287	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
288	C₄×Q₈	—	73	1	no	—
289	C₄×Q₈	—	73	1	no	—
290	C₄×D₄	—	73	1	no	—
291	C₄×D₄	—	146	1	no	—
292	C₄×D₄	—	146	1	no	—
293	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
294	#117	—	73	1	no	—
295	#117	—	146	1	no	—
296	C₂×C₄⋊C₄	—	146	2	no	—
297	C₂×C₄⋊C₄	—	146	2	no	—
298	C₂×C₄²	—	73	1	no	—
299	C₂×C₄²	—	146	1	no	—
300	#107	—	2	1	no	—
301	#107	—	2	1	no	—
302	#107	—	146	2	no	—
303	#107	—	146	2	no	—
304	#107	—	146	1	no	—
305	#107	—	146	1	no	—
306	C₄⋊C₈	—	73	1	no	—
307	C₄⋊C₈	—	73	2	no	—
308	C₄⋊C₈	—	146	2	no	—
309	C₄⋊C₈	—	146	1	no	—
310	C₄⋊C₈	—	146	1	no	—
311	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	146	2	no	—
315	#103	—	146	2	no	—
316	#103	—	146	2	no	—
317	C₂²⋊C₈	—	2	1	no	—
318	C₂²⋊C₈	—	146	1	no	—
319	C₂²⋊C₈	—	146	1	no	—
320	C₄×C₈	—	73	1	no	—
321	C₄×C₈	—	73	1	no	—
322	C₄×C₈	—	73	1	no	—
323	C₄×C₈	—	146	1	no	—
324	C₄×C₈	—	146	1	no	—
325	C₄×C₈	—	146	1	no	—
326	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
327	#41	—	73	4	no	—
328	#41	—	146	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	292	2	no	—
331	C₂×Q₈	—	292	4	no	—
332	C₂×Q₈	—	292	4	no	—
333	C₂×Q₈	—	73	1	no	—
334	C₂×Q₈	—	146	2	no	—
335	C₂×D₄	—	146	1	no	—
336	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	292	2	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	146	1	no	—
343	C₂²×C₄	—	146	1	no	—
344	Q₁₆	—	292	4	no	—
345	Q₁₆	—	292	4	no	—
346	SD₁₆	—	4	4	no	—
347	SD₁₆	—	292	4	no	—
348	M₁₆	—	292	4	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	4	2	no	—
352	C₂×C₈	—	292	2	no	—
353	C₂×C₈	—	73	1	no	—
354	C₂×C₈	—	73	1	no	—
355	C₂×C₈	—	146	2	no	—
356	C₂×C₈	—	146	1	no	—
357	C₂×C₈	—	146	2	no	—
358	C₂×C₈	—	146	2	no	—
359	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
360	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	292	2	no	—
364	C₄⋊C₄	—	292	2	no	—
365	C₄⋊C₄	—	73	1	no	—
366	C₄⋊C₄	—	146	1	no	—
367	C₄⋊C₄	—	146	2	no	—
368	C₄⋊C₄	—	146	2	no	—
369	C₄⋊C₄	—	146	1	no	—
370	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	146	1	no	—
373	C₂²⋊C₄	—	146	1	no	—
374	C₄²	—	73	1	no	—
375	C₄²	—	73	1	no	—
376	C₄²	—	73	1	no	—
377	C₄²	—	146	1	no	—
378	C₄²	—	146	1	no	—
379	C₄²	—	146	1	no	—
380	C₄²	C₂³×D₇₃	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	73	1	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	292	2	no	—
386	Q₈	—	292	2	no	—
387	Q₈	—	584	4	no	—
388	Q₈	—	73	2	no	—
389	Q₈	—	146	1	no	—
390	D₄	—	2	1	no	—
391	D₄	—	146	4	no	—
392	D₄	D₈×D₇₃	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	292	2	no	—
398	C₂×C₄	—	292	2	no	—
399	C₂×C₄	—	584	4	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	2	no	—
403	C₂×C₄	—	73	2	no	—
404	C₂×C₄	—	73	1	no	—
405	C₂×C₄	—	146	2	no	—
406	C₂×C₄	—	146	1	no	—
407	C₂×C₄	—	146	4	no	—
408	C₂×C₄	—	146	1	no	—
409	C₂×C₄	—	146	1	no	—
410	C₂×C₄	—	146	1	no	—
411	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
412	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
413	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	2	no	—
417	C₈	—	292	1	no	—
418	C₈	—	292	2	no	—
419	C₈	—	73	2	no	—
420	C₈	—	146	1	no	—
421	C₈	#14556620	1	2	yes	complemented
422	C₂²	—	2	2	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	—	73	2	no	—
426	C₂²	—	146	1	no	—
427	C₂²	—	146	1	no	—
428	C₂²	#121×D₇₃	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	4	1	no	—
431	C₄	—	8	2	no	—
432	C₄	—	292	1	no	—
433	C₄	—	584	2	no	—
434	C₄	—	73	2	no	—
435	C₄	—	73	2	no	—
436	C₄	—	146	1	no	—
437	C₄	—	146	2	no	—
438	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
439	C₄	#135×D₇₃	1	1	yes	characteristic
440	C₄	#137×D₇₃	1	1	yes	characteristic
441	C₄	C₂×#14556620	1	1	yes	characteristic
442	C₂	—	4	2	no	—
443	C₂	—	146	2	no	—
444	C₂	#22619413	1	1	yes	characteristic
445	C₂	#466×D₇₃	1	1	yes	characteristic
446	C₂	#473×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1673	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×#11924027	D₄
hypercenter	#1673	D₇₃
hypocenter	C₇₃	#19271
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1673

Complements

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

N	H ≅ G/N	type
1. #500×D₇₃	C₂	semidirect
4. #22609326	C₂	semidirect
5. #22609324	C₂	semidirect
6. #22609322	C₂	semidirect
7. #22609320	C₂	semidirect
8. #22609318	C₂	semidirect
9. #22608688	C₂	semidirect
10. #22608601	C₂	semidirect
11. C₇₃×#1673	C₂	semidirect
193. C₈×C₇₃	#137	semidirect
197. #10596831	#137	semidirect
232. #1673	D₇₃	semidirect
235. C₇₃	#19271	semidirect
421. C₈	#14556620	semidirect

Maximal subgroups

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

subgroup	index
#500×D₇₃	2
#22619413	2
C₈×#11924027	2
#22609326	2
#22609324	2
#22609322	2
#22609320	2
#22609318	2
#22608688	2
#22608601	2
C₇₃×#1673	2
#19271	73