Subgroups — #1688×D₇₃ #33068580

Order 18688.

850 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#493×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#460×D₇₃	C₂	1	2	yes	maximal, complemented
3	#446×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22609416	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609415	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609414	C₂	1	2	yes	maximal, complemented
7	#22609413	C₂	1	2	yes	maximal, complemented
8	#22609412	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#331×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1688	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×SD₁₆×D₇₃	—	2	2	no	—
13	C₂×D₈×D₇₃	—	2	1	no	—
14	C₂×D₈×D₇₃	—	2	1	no	—
15	#127×D₇₃	C₂²	1	2	yes	—
16	C₄×Q₈×D₇₃	C₂²	1	1	yes	characteristic
17	#17988964	C₂²	1	1	yes	characteristic
18	#17988963	C₂²	1	2	yes	—
19	#17988962	—	2	1	no	—
20	#17988962	—	2	1	no	—
21	#17988788	C₂²	1	2	yes	complemented
22	#17988787	C₂²	1	2	yes	complemented
23	#17988786	—	2	2	no	—
24	#17988785	—	2	2	no	—
25	#17988784	C₂²	1	2	yes	complemented
26	#17988718	C₂²	1	1	yes	characteristic, complemented
27	#17988717	C₂²	1	1	yes	characteristic, complemented
28	#17988716	—	2	1	no	—
29	#17988715	—	2	1	no	—
30	#17988714	C₂²	1	1	yes	characteristic, complemented
31	C₄⋊C₈×D₇₃	—	2	1	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	#97×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	#17988331	C₂²	1	2	yes	complemented
40	#17988330	C₂²	1	2	yes	complemented
41	#17988330	C₂²	1	2	yes	complemented
42	#493×C₇₃	C₂²	1	1	yes	characteristic
43	#460×C₇₃	C₂²	1	2	yes	complemented
44	#446×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#334×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#331×C₇₃	C₂²	1	2	yes	complemented
47	C₂×Q₈×D₇₃	D₄	1	1	yes	characteristic
48	C₂×D₄×D₇₃	—	2	2	no	—
49	C₂×D₄×D₇₃	—	2	2	no	—
50	C₂×D₄×D₇₃	—	2	2	no	—
51	C₂×#11924017	—	2	2	no	—
52	C₂×#11924016	—	2	2	no	—
53	C₂×#11924015	—	2	2	no	—
54	SD₁₆×D₇₃	—	4	8	no	—
55	C₂×D₅₈₄	—	2	1	no	—
56	C₂×D₅₈₄	—	2	1	no	—
57	C₂×#11924013	—	2	2	no	—
58	C₂×#11924013	—	2	2	no	—
59	D₈×D₇₃	—	4	4	no	—
60	D₈×D₇₃	—	4	4	no	—
61	C₂×C₈×D₇₃	—	2	1	no	—
62	C₂×C₈×D₇₃	—	2	2	no	—
63	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
65	#14556588	C₂³	1	2	yes	—
66	#14556587	—	2	2	no	—
67	#14556587	—	2	2	no	—
68	#14556587	—	2	2	no	—
69	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
70	C₄×Dic₁₄₆	—	2	1	no	—
71	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
72	#14556556	—	2	1	no	—
73	#14556556	D₄	1	1	yes	characteristic
74	C₄⋊C₄×D₇₃	—	2	1	no	—
75	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
76	C₄²×D₇₃	—	2	1	no	—
77	C₄²×D₇₃	C₂³	1	1	yes	characteristic
78	C₄⋊#10596831	—	2	1	no	—
79	C₄⋊#10596831	C₂³	1	1	yes	characteristic
80	C₄⋊#10596831	C₂³	1	2	yes	—
81	#14556520	—	2	1	no	—
82	#14556520	—	2	1	no	—
83	#14556520	—	2	2	no	—
84	#14556520	—	2	1	no	—
85	#14556513	—	2	2	no	—
86	#14556512	—	2	2	no	—
87	#14556511	—	2	2	no	—
88	#14556502	—	2	1	no	—
89	#14556501	—	2	1	no	—
90	#14556501	—	2	1	no	—
91	C₄×#10596831	C₂³	1	1	yes	characteristic
92	C₈×Dic₇₃	D₄	1	1	yes	characteristic
93	C₈×Dic₇₃	D₄	1	1	yes	characteristic
94	C₂×SD₁₆×C₇₃	—	2	2	no	—
95	C₂×D₈×C₇₃	—	2	1	no	—
96	C₂×D₈×C₇₃	—	2	1	no	—
97	#127×C₇₃	C₂³	1	2	yes	—
98	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₃	—	2	1	no	—
100	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
102	#102×C₇₃	—	2	2	no	—
103	#97×C₇₃	—	2	1	no	—
104	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
105	C₂³×D₇₃	—	4	2	no	—
106	C₂×Dic₁₄₆	—	2	1	no	—
107	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₇₃	—	2	4	no	—
109	C₂×D₂₉₂	—	2	2	no	—
110	C₂×D₂₉₂	—	2	2	no	—
111	C₂×D₂₉₂	—	2	2	no	—
112	C₂×C₂²⋊D₇₃	—	4	2	no	—
113	C₂×C₂²⋊D₇₃	—	4	2	no	—
114	C₂×C₂²⋊D₇₃	—	4	2	no	—
115	D₄×D₇₃	—	4	4	no	—
116	D₄×D₇₃	—	4	4	no	—
117	D₄×D₇₃	—	4	4	no	—
118	D₄×D₇₃	—	4	4	no	—
119	D₄×D₇₃	—	8	4	no	—
120	C₂×C₄×D₇₃	—	2	1	no	—
121	C₂×C₄×D₇₃	—	2	1	no	—
122	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
125	#11924017	—	4	4	no	—
126	#11924016	—	4	4	no	—
127	#11924015	—	4	4	no	—
128	D₅₈₄	—	4	2	no	—
129	D₅₈₄	—	4	2	no	—
130	#11924013	—	4	4	no	—
131	#11924013	—	4	4	no	—
132	C₂×#10596831	—	2	1	no	—
133	C₂×#10596831	—	2	2	no	—
134	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
135	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
136	C₈×D₇₃	—	2	2	no	—
137	C₈×D₇₃	—	4	2	no	—
138	C₈×D₇₃	—	4	4	no	—
139	C₈×D₇₃	SD₁₆	1	4	yes	complemented
140	C₄⋊Dic₇₃	—	2	1	no	—
141	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
142	#11924007	—	2	1	no	—
143	#11924007	—	2	1	no	—
144	#11924007	—	2	1	no	—
145	C₄×Dic₇₃	—	2	1	no	—
146	C₄×Dic₇₃	—	2	1	no	—
147	C₄×Dic₇₃	—	2	1	no	—
148	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₇₃	#41	1	1	yes	characteristic
151	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₇₃	—	2	2	no	—
153	C₂×D₄×C₇₃	—	2	2	no	—
154	C₂×D₄×C₇₃	—	2	2	no	—
155	SD₁₆×C₇₃	—	4	4	no	—
156	D₈×C₇₃	—	4	2	no	—
157	D₈×C₇₃	—	4	2	no	—
158	C₂×C₈×C₇₃	—	2	1	no	—
159	C₂×C₈×C₇₃	—	2	2	no	—
160	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₇₃	—	2	1	no	—
163	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇₃	—	2	1	no	—
165	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
166	C₂³×C₇₃	—	4	2	no	—
167	C₂²×D₇₃	—	4	2	no	—
168	C₂²×D₇₃	—	8	4	no	—
169	C₂²×D₇₃	—	8	4	no	—
170	C₂²×D₇₃	—	8	4	no	—
171	C₂²×D₇₃	#121	1	1	yes	characteristic
172	Q₈×C₇₃	—	2	2	no	—
173	D₄×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	4	2	no	—
175	D₄×C₇₃	—	4	2	no	—
176	D₄×C₇₃	—	4	2	no	—
177	D₄×C₇₃	—	8	2	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
183	C₂²⋊D₇₃	—	8	4	no	—
184	C₂²⋊D₇₃	—	8	4	no	—
185	C₂²⋊D₇₃	—	8	4	no	—
186	C₂×Dic₇₃	—	2	1	no	—
187	C₂×Dic₇₃	—	2	1	no	—
188	C₂×Dic₇₃	#121	1	1	yes	characteristic
189	C₂×Dic₇₃	#121	1	1	yes	characteristic
190	C₂×Dic₇₃	#121	1	1	yes	characteristic
191	D₂₉₂	—	4	2	no	—
192	D₂₉₂	—	4	2	no	—
193	D₂₉₂	—	4	2	no	—
194	D₂₉₂	—	4	2	no	—
195	D₂₉₂	—	8	2	no	—
196	C₄×D₇₃	—	2	2	no	—
197	C₄×D₇₃	—	4	2	no	—
198	C₄×D₇₃	—	4	2	no	—
199	C₄×D₇₃	C₂×SD₁₆	1	2	yes	—
200	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
201	C₄×D₇₃	AGL(1,ℤ/8)	1	4	yes	—
202	Dic₁₄₆	—	2	2	no	—
203	Dic₁₄₆	—	4	2	no	—
204	C₈×C₇₃	—	2	1	no	—
205	C₈×C₇₃	—	4	2	no	—
206	C₈×C₇₃	—	4	1	no	—
207	C₈×C₇₃	C₂×SD₁₆	1	2	yes	complemented
208	#10596831	—	2	1	no	—
209	#10596831	—	4	1	no	—
210	#10596831	—	4	2	no	—
211	#10596831	C₂×SD₁₆	1	2	yes	complemented
212	C₂²×C₇₃	—	8	2	no	—
213	C₂²×C₇₃	—	8	2	no	—
214	C₂²×C₇₃	—	8	2	no	—
215	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
216	C₂×D₇₃	—	8	2	no	—
217	C₂×D₇₃	—	8	2	no	—
218	C₂×D₇₃	—	8	2	no	—
219	C₂×D₇₃	—	16	8	no	—
220	C₂×D₇₃	#460	1	2	yes	—
221	C₂×D₇₃	#469	1	2	yes	—
222	C₂×D₇₃	#472	1	2	yes	—
223	C₄×C₇₃	—	2	1	no	—
224	C₄×C₇₃	—	4	1	no	—
225	C₄×C₇₃	—	4	1	no	—
226	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
227	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
229	Dic₇₃	—	2	1	no	—
230	Dic₇₃	—	4	1	no	—
231	Dic₇₃	—	4	1	no	—
232	Dic₇₃	#460	1	2	yes	—
233	Dic₇₃	#469	1	2	yes	—
234	C₂×#1688	—	73	1	no	maximal, Sylow
235	C₂×C₇₃	—	16	2	no	—
236	C₂×C₇₃	C₂×#460	1	1	yes	characteristic
237	C₂×C₇₃	C₂×#469	1	1	yes	characteristic
238	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
239	D₇₃	—	16	2	no	—
240	D₇₃	#1688	1	4	yes	direct product factor
241	C₂×#493	—	73	1	no	—
242	C₂×#460	—	73	2	no	—
243	C₂×#446	—	73	1	no	—
244	#1688	—	73	1	no	—
245	#1688	—	73	2	no	—
246	#1688	—	73	1	no	—
247	#1688	—	73	1	no	—
248	#1688	—	73	2	no	—
249	#1688	D₇₃	1	1	yes	characteristic, direct product factor
250	C₂×#334	—	73	1	no	—
251	C₂×#331	—	73	2	no	—
252	C₇₃	C₂×#1688	1	1	yes	characteristic, complemented, Sylow
253	C₂²×SD₁₆	—	146	2	no	—
254	C₂²×D₈	—	146	1	no	—
255	C₂²×D₈	—	146	1	no	—
256	C₂×#127	—	73	2	no	—
257	C₂×C₄×Q₈	—	73	1	no	—
258	#493	—	73	2	no	—
259	#493	—	73	1	no	—
260	#493	—	146	1	no	—
261	#493	—	146	1	no	—
262	#493	C₂×D₇₃	1	1	yes	characteristic
263	#460	—	73	2	no	—
264	#460	—	73	2	no	—
265	#460	—	73	2	no	—
266	#460	—	146	2	no	—
267	#460	—	146	2	no	—
268	#460	C₂×D₇₃	1	2	yes	complemented
269	#446	—	73	1	no	—
270	#446	—	73	1	no	—
271	#446	—	73	1	no	—
272	#446	—	146	1	no	—
273	#446	—	146	1	no	—
274	#446	C₂×D₇₃	1	1	yes	characteristic, complemented
275	C₂×C₄⋊C₈	—	73	1	no	—
276	C₂×C₄⋊C₈	—	73	2	no	—
277	C₂×C₄⋊C₈	—	146	1	no	—
278	C₂×#102	—	146	2	no	—
279	C₂×#97	—	146	1	no	—
280	C₂×C₄×C₈	—	73	1	no	—
281	#334	—	73	2	no	—
282	#334	—	73	1	no	—
283	#334	C₂×D₇₃	1	1	yes	characteristic, complemented
284	#331	—	73	2	no	—
285	#331	—	73	2	no	—
286	#331	—	73	2	no	—
287	#331	C₂×D₇₃	1	2	yes	complemented
288	C₂²×Q₈	—	73	1	no	—
289	C₂²×D₄	—	146	2	no	—
290	C₂²×D₄	—	146	2	no	—
291	C₂²×D₄	—	146	2	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	292	8	no	—
294	C₂×SD₁₆	—	146	2	no	—
295	C₂×SD₁₆	—	146	2	no	—
296	C₂×SD₁₆	—	146	2	no	—
297	C₂×D₈	—	2	1	no	—
298	C₂×D₈	—	2	1	no	—
299	C₂×D₈	—	292	4	no	—
300	C₂×D₈	—	292	4	no	—
301	C₂×D₈	—	146	2	no	—
302	C₂×D₈	—	146	2	no	—
303	C₂×D₈	—	146	1	no	—
304	C₂×D₈	—	146	1	no	—
305	C₂²×C₈	—	73	1	no	—
306	C₂²×C₈	—	73	1	no	—
307	C₂²×C₈	—	146	2	no	—
308	C₂²×C₈	—	146	1	no	—
309	#127	—	73	2	no	—
310	#127	—	146	2	no	—
311	#127	—	146	2	no	—
312	#127	—	146	2	no	—
313	#127	C₂²×D₇₃	1	2	yes	—
314	C₄×Q₈	—	73	1	no	—
315	C₄×Q₈	—	73	1	no	—
316	C₄×Q₈	—	73	1	no	—
317	C₄×Q₈	—	146	1	no	—
318	C₄×Q₈	—	146	1	no	—
319	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	—	73	1	no	—
321	C₂×C₄⋊C₄	—	146	1	no	—
322	C₂×C₄²	—	73	1	no	—
323	C₂×C₄²	—	146	1	no	—
324	C₄⋊C₈	—	2	1	no	—
325	C₄⋊C₈	—	73	1	no	—
326	C₄⋊C₈	—	73	2	no	—
327	C₄⋊C₈	—	146	1	no	—
328	C₄⋊C₈	—	146	1	no	—
329	C₄⋊C₈	—	146	2	no	—
330	C₄⋊C₈	—	146	1	no	—
331	C₄⋊C₈	—	146	1	no	—
332	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
333	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
334	#102	—	2	2	no	—
335	#102	—	146	2	no	—
336	#102	—	146	2	no	—
337	#102	—	146	2	no	—
338	#97	—	2	1	no	—
339	#97	—	146	1	no	—
340	#97	—	146	1	no	—
341	#97	—	146	1	no	—
342	C₄×C₈	—	73	1	no	—
343	C₄×C₈	—	73	1	no	—
344	C₄×C₈	—	73	1	no	—
345	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
346	C₂⁴	—	292	2	no	—
347	C₂×Q₈	—	73	1	no	—
348	C₂×Q₈	—	146	1	no	—
349	C₂×Q₈	—	146	4	no	—
350	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	292	4	no	—
355	C₂×D₄	—	292	4	no	—
356	C₂×D₄	—	292	4	no	—
357	C₂×D₄	—	292	4	no	—
358	C₂×D₄	—	292	2	no	—
359	C₂×D₄	—	292	2	no	—
360	C₂×D₄	—	292	2	no	—
361	C₂×D₄	—	584	4	no	—
362	C₂×D₄	—	146	2	no	—
363	C₂×D₄	—	146	2	no	—
364	C₂×D₄	—	146	2	no	—
365	C₂²×C₄	—	73	1	no	—
366	C₂²×C₄	—	73	1	no	—
367	C₂²×C₄	—	73	1	no	—
368	C₂²×C₄	—	146	1	no	—
369	C₂²×C₄	—	146	1	no	—
370	SD₁₆	—	4	4	no	—
371	SD₁₆	—	292	4	no	—
372	SD₁₆	—	292	4	no	—
373	SD₁₆	—	292	4	no	—
374	D₈	—	4	2	no	—
375	D₈	—	4	2	no	—
376	D₈	—	292	2	no	—
377	D₈	—	292	4	no	—
378	D₈	—	292	4	no	—
379	D₈	—	292	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	292	2	no	—
383	C₂×C₈	—	292	4	no	—
384	C₂×C₈	—	73	1	no	—
385	C₂×C₈	—	73	4	no	—
386	C₂×C₈	—	73	1	no	—
387	C₂×C₈	—	146	2	no	—
388	C₂×C₈	—	146	1	no	—
389	C₂×C₈	—	146	2	no	—
390	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
391	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	73	1	no	—
394	C₄⋊C₄	—	146	1	no	—
395	C₄⋊C₄	—	146	1	no	—
396	C₄⋊C₄	—	146	1	no	—
397	C₄⋊C₄	—	146	1	no	—
398	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
399	C₄²	—	2	1	no	—
400	C₄²	—	73	1	no	—
401	C₄²	—	73	1	no	—
402	C₄²	—	73	1	no	—
403	C₄²	—	146	1	no	—
404	C₄²	—	146	1	no	—
405	C₄²	—	146	1	no	—
406	C₄²	C₂³×D₇₃	1	1	yes	characteristic
407	C₂³	—	4	2	no	—
408	C₂³	—	292	2	no	—
409	C₂³	—	584	4	no	—
410	C₂³	—	584	4	no	—
411	C₂³	—	584	4	no	—
412	C₂³	—	73	1	no	—
413	Q₈	—	2	2	no	—
414	Q₈	—	292	2	no	—
415	Q₈	—	146	2	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	8	2	no	—
421	D₄	—	292	2	no	—
422	D₄	—	292	2	no	—
423	D₄	—	292	2	no	—
424	D₄	—	292	2	no	—
425	D₄	—	584	2	no	—
426	D₄	—	584	4	no	—
427	D₄	—	584	4	no	—
428	D₄	—	584	4	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	292	2	no	—
432	C₂×C₄	—	292	2	no	—
433	C₂×C₄	—	73	1	no	—
434	C₂×C₄	—	73	1	no	—
435	C₂×C₄	—	73	2	no	—
436	C₂×C₄	—	73	2	no	—
437	C₂×C₄	—	73	4	no	—
438	C₂×C₄	—	73	1	no	—
439	C₂×C₄	—	146	2	no	—
440	C₂×C₄	—	146	1	no	—
441	C₂×C₄	—	146	1	no	—
442	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
444	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
445	C₈	—	2	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	292	2	no	—
449	C₈	—	292	1	no	—
450	C₈	—	73	2	no	—
451	C₈	—	146	1	no	—
452	C₈	SD₁₆×D₇₃	1	2	yes	complemented
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	584	2	no	—
457	C₂²	—	584	2	no	—
458	C₂²	—	584	2	no	—
459	C₂²	—	73	2	no	—
460	C₂²	—	73	2	no	—
461	C₂²	—	73	2	no	—
462	C₂²	—	1168	8	no	—
463	C₂²	#121×D₇₃	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	292	1	no	—
468	C₄	—	292	1	no	—
469	C₄	—	73	2	no	—
470	C₄	—	73	2	no	—
471	C₄	—	146	1	no	—
472	C₄	C₂×SD₁₆×D₇₃	1	1	yes	characteristic
473	C₄	AGL(1,ℤ/8)×D₇₃	1	2	yes	—
474	C₄	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
475	C₂	—	16	2	no	—
476	C₂	—	73	4	no	—
477	C₂	—	1168	2	no	—
478	C₂	#460×D₇₃	1	1	yes	characteristic
479	C₂	#469×D₇₃	1	1	yes	characteristic
480	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×#1688	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	#493×D₇₃	C₂
hypercenter	#1688	D₇₃
hypocenter	C₇₃	C₂×#1688
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1688

Complements

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

N	H ≅ G/N	type
2. #460×D₇₃	C₂	semidirect
3. #446×D₇₃	C₂	semidirect
4. #22609416	C₂	semidirect
5. #22609415	C₂	semidirect
6. #22609414	C₂	semidirect
7. #22609413	C₂	semidirect
8. #22609412	C₂	semidirect
9. #334×D₇₃	C₂	semidirect
10. #331×D₇₃	C₂	semidirect
11. C₇₃×#1688	C₂	semidirect
21. #17988788	C₂²	semidirect
22. #17988787	C₂²	semidirect
25. #17988784	C₂²	semidirect
26. #17988718	C₂²	semidirect
27. #17988717	C₂²	semidirect
30. #17988714	C₂²	semidirect
37. #17988338	C₂²	semidirect
38. #17988337	C₂²	semidirect
39. #17988331	C₂²	semidirect
40. #17988330	C₂²	semidirect
41. #17988330	C₂²	semidirect
43. #460×C₇₃	C₂²	semidirect
44. #446×C₇₃	C₂²	semidirect
45. #334×C₇₃	C₂²	semidirect
46. #331×C₇₃	C₂²	semidirect
139. C₈×D₇₃	SD₁₆	semidirect
207. C₈×C₇₃	C₂×SD₁₆	semidirect
211. #10596831	C₂×SD₁₆	semidirect
240. D₇₃	#1688	direct (N × H)
249. #1688	D₇₃	direct (N × H)
252. C₇₃	C₂×#1688	semidirect
268. #460	C₂×D₇₃	semidirect
274. #446	C₂×D₇₃	semidirect
283. #334	C₂×D₇₃	semidirect
287. #331	C₂×D₇₃	semidirect
452. C₈	SD₁₆×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#493×D₇₃	2
#460×D₇₃	2
#446×D₇₃	2
#22609416	2
#22609415	2
#22609414	2
#22609413	2
#22609412	2
#334×D₇₃	2
#331×D₇₃	2
C₇₃×#1688	2
C₂×#1688	73

Subgroups — #1688×D73 #33068580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1688×D₇₃ #33068580