Subgroups — #1695×D₇₃ #33068515

Order 18688.

694 conjugacy classes of subgroups.

The subgroup lattice has 454 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	#476×D₇₃	C₂	1	2	yes	maximal
3	#436×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22609455	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609454	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609453	C₂	1	2	yes	maximal, complemented
7	#22609452	C₂	1	2	yes	maximal, complemented
8	#22609451	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#333×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1695	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₃	—	2	1	no	—
13	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
14	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
15	#17988992	C₂²	1	1	yes	characteristic, complemented
16	#17988991	—	2	1	no	—
17	#17988991	—	2	1	no	—
18	#17988990	C₂²	1	2	yes	complemented
19	#17988878	C₂²	1	2	yes	—
20	#17988877	C₂²	1	2	yes	—
21	#17988876	—	2	2	no	—
22	#17988875	—	2	2	no	—
23	#17988874	C₂²	1	2	yes	—
24	#17988666	C₂²	1	1	yes	characteristic
25	#17988665	C₂²	1	1	yes	characteristic
26	#17988664	C₂²	1	1	yes	characteristic
27	#17988663	—	2	1	no	—
28	#17988662	—	2	1	no	—
29	#107×D₇₃	—	2	1	no	—
30	#107×D₇₃	—	2	1	no	—
31	#106×D₇₃	—	2	2	no	—
32	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
33	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
34	#102×D₇₃	—	2	2	no	—
35	C₂²⋊C₈×D₇₃	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988338	C₂²	1	1	yes	characteristic, complemented
38	#17988337	C₂²	1	2	yes	complemented
39	#17988336	C₂²	1	2	yes	complemented
40	#17988335	C₂²	1	2	yes	complemented
41	#17988335	C₂²	1	2	yes	complemented
42	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#476×C₇₃	C₂²	1	2	yes	—
44	#436×C₇₃	C₂²	1	1	yes	characteristic
45	#334×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#333×C₇₃	C₂²	1	2	yes	complemented
47	C₂×Q₈×D₇₃	—	2	2	no	—
48	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	—	2	1	no	—
50	C₂×#11924012	—	2	1	no	—
51	C₂×#11924011	—	2	1	no	—
52	C₂×#11924011	—	2	1	no	—
53	M₁₆×D₇₃	—	4	4	no	—
54	C₂×C₈×D₇₃	—	2	2	no	—
55	C₂×C₈×D₇₃	—	2	1	no	—
56	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
57	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
58	#14556591	C₂³	1	2	yes	—
59	#14556590	—	2	2	no	—
60	#14556590	—	2	2	no	—
61	#14556589	—	2	2	no	—
62	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
63	D₄×Dic₇₃	D₄	1	1	yes	characteristic
64	#14556553	D₄	1	1	yes	characteristic
65	C₄×C₂²⋊D₇₃	—	2	1	no	—
66	#14556551	—	2	1	no	—
67	C₄⋊C₄×D₇₃	—	2	2	no	—
68	C₄⋊C₄×D₇₃	—	2	2	no	—
69	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
70	C₂²⋊C₄×D₇₃	—	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	#14556523	—	2	2	no	—
77	#14556522	—	2	2	no	—
78	#14556522	—	2	2	no	—
79	C₄⋊#10596831	C₂³	1	2	yes	—
80	C₄⋊#10596831	C₂³	1	1	yes	characteristic
81	#14556520	—	2	2	no	—
82	#14556520	—	2	1	no	—
83	#14556513	—	2	2	no	—
84	#14556512	—	2	2	no	—
85	#14556511	—	2	2	no	—
86	C₂²⋊#10596831	—	2	1	no	—
87	#14556503	—	2	1	no	—
88	#14556503	—	2	1	no	—
89	C₄×#10596831	C₂³	1	1	yes	characteristic
90	C₈×Dic₇₃	D₄	1	1	yes	characteristic
91	C₈×Dic₇₃	D₄	1	1	yes	characteristic
92	C₂×M₁₆×C₇₃	—	2	1	no	—
93	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
94	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
95	#107×C₇₃	—	2	1	no	—
96	#107×C₇₃	—	2	1	no	—
97	#106×C₇₃	—	2	2	no	—
98	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
99	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
100	#102×C₇₃	—	2	2	no	—
101	C₂²⋊C₈×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	C₂³×D₇₃	—	2	1	no	—
104	C₂×Dic₁₄₆	—	2	2	no	—
105	C₂×Dic₁₄₆	—	4	2	no	—
106	Q₈×D₇₃	—	8	4	no	—
107	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
108	C₂×C₂²⋊D₇₃	—	2	1	no	—
109	D₄×D₇₃	—	2	4	no	—
110	C₂²×Dic₇₃	—	2	1	no	—
111	C₂×C₄×D₇₃	—	2	1	no	—
112	C₂×C₄×D₇₃	—	2	1	no	—
113	C₂×C₄×D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	4	2	no	—
115	C₂×C₄×D₇₃	—	4	2	no	—
116	C₂×C₄×D₇₃	—	4	2	no	—
117	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
120	#11924012	—	4	2	no	—
121	#11924011	—	4	2	no	—
122	#11924011	—	4	2	no	—
123	C₂×#10596831	—	2	1	no	—
124	C₂×#10596831	—	2	2	no	—
125	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
126	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
127	C₈×D₇₃	—	2	2	no	—
128	C₈×D₇₃	—	4	2	no	—
129	C₈×D₇₃	—	4	4	no	—
130	C₈×D₇₃	SD₁₆	1	4	yes	—
131	C₄⋊Dic₇₃	—	2	2	no	—
132	C₄⋊Dic₇₃	—	2	2	no	—
133	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
134	#11924007	—	2	1	no	—
135	#11924007	—	4	2	no	—
136	#11924007	—	4	2	no	—
137	C₂²⋊Dic₇₃	—	2	1	no	—
138	#11924005	—	2	1	no	—
139	#11924005	—	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	M₁₆×C₇₃	—	4	2	no	—
147	C₂×C₈×C₇₃	—	2	1	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₄⋊C₄×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₇₃	—	2	1	no	—
155	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
156	C₂³×C₇₃	—	2	1	no	—
157	C₂²×D₇₃	—	2	1	no	—
158	C₂²×D₇₃	—	4	2	no	—
159	C₂²×D₇₃	—	4	2	no	—
160	C₂²×D₇₃	—	4	2	no	—
161	C₂²×D₇₃	#121	1	1	yes	characteristic
162	Q₈×C₇₃	—	8	2	no	—
163	D₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	4	1	no	—
166	C₂×C₄×C₇₃	—	4	1	no	—
167	C₂×C₄×C₇₃	—	4	2	no	—
168	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
171	C₂²⋊D₇₃	—	4	2	no	—
172	C₂×Dic₇₃	—	2	1	no	—
173	C₂×Dic₇₃	—	4	2	no	—
174	C₂×Dic₇₃	—	4	2	no	—
175	C₂×Dic₇₃	#121	1	1	yes	characteristic
176	C₂×Dic₇₃	#121	1	1	yes	characteristic
177	C₂×Dic₇₃	#121	1	1	yes	characteristic
178	D₂₉₂	—	2	2	no	—
179	C₄×D₇₃	—	2	2	no	—
180	C₄×D₇₃	—	4	2	no	—
181	C₄×D₇₃	—	4	1	no	—
182	C₄×D₇₃	—	4	1	no	—
183	C₄×D₇₃	—	4	2	no	—
184	C₄×D₇₃	—	8	4	no	—
185	C₄×D₇₃	C₂×SD₁₆	1	2	yes	—
186	C₄×D₇₃	#137	1	2	yes	—
187	C₄×D₇₃	#137	1	4	yes	—
188	Dic₁₄₆	—	8	4	no	—
189	Dic₁₄₆	—	8	2	no	—
190	C₈×C₇₃	—	2	1	no	—
191	C₈×C₇₃	—	4	1	no	—
192	C₈×C₇₃	—	4	2	no	—
193	C₈×C₇₃	C₂×SD₁₆	1	2	yes	—
194	#10596831	—	2	1	no	—
195	#10596831	—	4	1	no	—
196	#10596831	—	4	2	no	—
197	#10596831	C₂×SD₁₆	1	2	yes	—
198	C₂²×C₇₃	—	4	1	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	—	4	1	no	—
203	C₂×D₇₃	—	4	1	no	—
204	C₂×D₇₃	—	4	1	no	—
205	C₂×D₇₃	—	8	4	no	—
206	C₂×D₇₃	#461	1	2	yes	—
207	C₂×D₇₃	#470	1	2	yes	—
208	C₂×D₇₃	#472	1	2	yes	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	4	1	no	—
211	C₄×C₇₃	—	8	2	no	—
212	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
213	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
214	C₄×C₇₃	C₂×#137	1	2	yes	—
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	—	4	1	no	—
217	Dic₇₃	—	8	2	no	—
218	Dic₇₃	#461	1	2	yes	—
219	Dic₇₃	#470	1	2	yes	—
220	C₂×#1695	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	8	1	no	—
222	C₂×C₇₃	C₂×#461	1	1	yes	characteristic
223	C₂×C₇₃	C₂×#470	1	1	yes	characteristic
224	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
225	D₇₃	—	8	1	no	—
226	D₇₃	#1695	1	4	yes	direct product factor
227	C₂×#500	—	73	1	no	—
228	C₂×#476	—	73	2	no	—
229	C₂×#436	—	73	1	no	—
230	#1695	—	73	1	no	—
231	#1695	—	73	2	no	—
232	#1695	—	73	1	no	—
233	#1695	—	73	1	no	—
234	#1695	—	73	2	no	—
235	#1695	D₇₃	1	1	yes	characteristic, direct product factor
236	C₂×#334	—	73	1	no	—
237	C₂×#333	—	73	2	no	—
238	C₇₃	C₂×#1695	1	1	yes	characteristic, complemented, Sylow
239	C₂²×M₁₆	—	146	1	no	—
240	C₂×C₄⋊Q₈	—	73	2	no	—
241	C₂×C₄×D₄	—	73	1	no	—
242	#500	—	73	2	no	—
243	#500	—	73	1	no	—
244	#500	—	146	1	no	—
245	#500	—	146	1	no	—
246	#500	C₂×D₇₃	1	1	yes	characteristic, complemented
247	#476	—	73	2	no	—
248	#476	—	73	2	no	—
249	#476	—	73	2	no	—
250	#476	—	146	2	no	—
251	#476	—	146	2	no	—
252	#476	C₂×D₇₃	1	2	yes	—
253	#436	—	73	1	no	—
254	#436	—	73	1	no	—
255	#436	—	73	1	no	—
256	#436	—	146	1	no	—
257	#436	—	146	1	no	—
258	#436	C₂×D₇₃	1	1	yes	characteristic
259	C₂×#107	—	146	1	no	—
260	C₂×#107	—	146	1	no	—
261	C₂×#106	—	146	2	no	—
262	C₂×C₄⋊C₈	—	73	1	no	—
263	C₂×C₄⋊C₈	—	73	2	no	—
264	C₂×#102	—	146	2	no	—
265	C₂×C₂²⋊C₈	—	146	1	no	—
266	C₂×C₄×C₈	—	73	1	no	—
267	#334	—	73	2	no	—
268	#334	—	73	1	no	—
269	#334	C₂×D₇₃	1	1	yes	characteristic, complemented
270	#333	—	73	2	no	—
271	#333	—	73	2	no	—
272	#333	—	73	2	no	—
273	#333	C₂×D₇₃	1	2	yes	complemented
274	C₂²×Q₈	—	146	2	no	—
275	C₂²×D₄	—	73	1	no	—
276	C₂³×C₄	—	146	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	292	4	no	—
279	C₂×M₁₆	—	146	1	no	—
280	C₂×M₁₆	—	146	1	no	—
281	C₂×M₁₆	—	146	1	no	—
282	C₂²×C₈	—	73	1	no	—
283	C₂²×C₈	—	73	1	no	—
284	C₂²×C₈	—	146	1	no	—
285	C₂²×C₈	—	146	2	no	—
286	C₄⋊Q₈	—	73	2	no	—
287	C₄⋊Q₈	—	146	2	no	—
288	C₄⋊Q₈	—	146	2	no	—
289	C₄⋊Q₈	—	146	2	no	—
290	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
291	C₄×D₄	—	73	1	no	—
292	C₄×D₄	—	73	1	no	—
293	C₄×D₄	—	73	1	no	—
294	C₄×D₄	—	146	1	no	—
295	C₄×D₄	—	146	1	no	—
296	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	73	1	no	—
298	C₂×C₄⋊C₄	—	146	2	no	—
299	C₂×C₄⋊C₄	—	146	2	no	—
300	C₂×C₂²⋊C₄	—	146	1	no	—
301	C₂×C₄²	—	73	1	no	—
302	#107	—	2	1	no	—
303	#107	—	2	1	no	—
304	#107	—	146	2	no	—
305	#107	—	146	2	no	—
306	#107	—	146	1	no	—
307	#107	—	146	1	no	—
308	#106	—	2	2	no	—
309	#106	—	146	2	no	—
310	#106	—	146	2	no	—
311	#106	—	146	2	no	—
312	C₄⋊C₈	—	73	1	no	—
313	C₄⋊C₈	—	73	2	no	—
314	C₄⋊C₈	—	146	1	no	—
315	C₄⋊C₈	—	146	2	no	—
316	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
317	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
318	#102	—	2	2	no	—
319	#102	—	146	2	no	—
320	#102	—	146	2	no	—
321	#102	—	146	2	no	—
322	C₂²⋊C₈	—	2	1	no	—
323	C₂²⋊C₈	—	146	1	no	—
324	C₂²⋊C₈	—	146	1	no	—
325	C₂²⋊C₈	—	146	1	no	—
326	C₄×C₈	—	73	1	no	—
327	C₄×C₈	—	73	1	no	—
328	C₄×C₈	—	73	1	no	—
329	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
330	C₂⁴	—	146	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	292	2	no	—
333	C₂×Q₈	—	584	4	no	—
334	C₂×Q₈	—	146	2	no	—
335	C₂×D₄	—	73	1	no	—
336	C₂×D₄	—	146	4	no	—
337	C₂×D₄	—	146	1	no	—
338	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	292	2	no	—
341	C₂²×C₄	—	292	2	no	—
342	C₂²×C₄	—	292	2	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	73	1	no	—
346	C₂²×C₄	—	146	1	no	—
347	C₂²×C₄	—	146	1	no	—
348	C₂²×C₄	—	146	1	no	—
349	C₂²×C₄	—	146	1	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	292	2	no	—
352	M₁₆	—	292	2	no	—
353	M₁₆	—	292	2	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	292	4	no	—
357	C₂×C₈	—	292	2	no	—
358	C₂×C₈	—	73	1	no	—
359	C₂×C₈	—	73	4	no	—
360	C₂×C₈	—	73	1	no	—
361	C₂×C₈	—	146	2	no	—
362	C₂×C₈	—	146	1	no	—
363	C₂×C₈	—	146	2	no	—
364	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
365	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	292	2	no	—
369	C₄⋊C₄	—	292	2	no	—
370	C₄⋊C₄	—	73	1	no	—
371	C₄⋊C₄	—	146	1	no	—
372	C₄⋊C₄	—	146	2	no	—
373	C₄⋊C₄	—	146	2	no	—
374	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	146	1	no	—
377	C₂²⋊C₄	—	146	1	no	—
378	C₂²⋊C₄	—	146	1	no	—
379	C₄²	—	73	1	no	—
380	C₄²	—	73	1	no	—
381	C₄²	—	73	1	no	—
382	C₄²	C₂³×D₇₃	1	1	yes	characteristic
383	C₂³	—	2	1	no	—
384	C₂³	—	292	2	no	—
385	C₂³	—	292	2	no	—
386	C₂³	—	292	2	no	—
387	C₂³	—	73	1	no	—
388	C₂³	—	146	1	no	—
389	Q₈	—	8	2	no	—
390	Q₈	—	584	2	no	—
391	Q₈	—	584	4	no	—
392	D₄	—	2	2	no	—
393	D₄	—	292	2	no	—
394	D₄	—	146	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	292	2	no	—
400	C₂×C₄	—	292	2	no	—
401	C₂×C₄	—	292	2	no	—
402	C₂×C₄	—	292	1	no	—
403	C₂×C₄	—	292	1	no	—
404	C₂×C₄	—	292	2	no	—
405	C₂×C₄	—	584	4	no	—
406	C₂×C₄	—	73	1	no	—
407	C₂×C₄	—	73	1	no	—
408	C₂×C₄	—	73	4	no	—
409	C₂×C₄	—	73	2	no	—
410	C₂×C₄	—	73	2	no	—
411	C₂×C₄	—	73	1	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	—	146	1	no	—
414	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
415	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
416	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
417	C₈	—	2	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	292	2	no	—
421	C₈	—	292	1	no	—
422	C₈	—	73	2	no	—
423	C₈	—	146	1	no	—
424	C₈	SD₁₆×D₇₃	1	2	yes	—
425	C₂²	—	4	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	292	1	no	—
429	C₂²	—	292	1	no	—
430	C₂²	—	292	1	no	—
431	C₂²	—	584	4	no	—
432	C₂²	—	73	2	no	—
433	C₂²	—	73	2	no	—
434	C₂²	—	73	2	no	—
435	C₂²	#121×D₇₃	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	292	1	no	—
440	C₄	—	584	2	no	—
441	C₄	—	73	2	no	—
442	C₄	—	73	2	no	—
443	C₄	—	146	1	no	—
444	C₄	C₂×SD₁₆×D₇₃	1	1	yes	characteristic
445	C₄	#137×D₇₃	1	2	yes	—
446	C₄	#137×D₇₃	1	1	yes	characteristic
447	C₂	—	8	1	no	—
448	C₂	—	584	1	no	—
449	C₂	—	73	4	no	—
450	C₂	#461×D₇₃	1	1	yes	characteristic
451	C₂	#470×D₇₃	1	1	yes	characteristic
452	C₂	#472×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1695	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×D₄×D₇₃	D₄
hypercenter	#1695	D₇₃
hypocenter	C₇₃	C₂×#1695
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1695

Complements

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

N	H ≅ G/N	type
1. #500×D₇₃	C₂	semidirect
4. #22609455	C₂	semidirect
5. #22609454	C₂	semidirect
6. #22609453	C₂	semidirect
7. #22609452	C₂	semidirect
8. #22609451	C₂	semidirect
9. #334×D₇₃	C₂	semidirect
10. #333×D₇₃	C₂	semidirect
11. C₇₃×#1695	C₂	semidirect
15. #17988992	C₂²	semidirect
18. #17988990	C₂²	semidirect
37. #17988338	C₂²	semidirect
38. #17988337	C₂²	semidirect
39. #17988336	C₂²	semidirect
40. #17988335	C₂²	semidirect
41. #17988335	C₂²	semidirect
42. #500×C₇₃	C₂²	semidirect
45. #334×C₇₃	C₂²	semidirect
46. #333×C₇₃	C₂²	semidirect
226. D₇₃	#1695	direct (N × H)
235. #1695	D₇₃	direct (N × H)
238. C₇₃	C₂×#1695	semidirect
246. #500	C₂×D₇₃	semidirect
269. #334	C₂×D₇₃	semidirect
273. #333	C₂×D₇₃	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
#476×D₇₃	2
#436×D₇₃	2
#22609455	2
#22609454	2
#22609453	2
#22609452	2
#22609451	2
#334×D₇₃	2
#333×D₇₃	2
C₇₃×#1695	2
C₂×#1695	73

Subgroups — #1695×D73 #33068515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1695×D₇₃ #33068515