Subgroups — #2207×D₇₃ #33240224

Order 18688.

806 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₇₃	C₂	1	2	yes	maximal, complemented
2	#493×D₇₃	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22611972	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611971	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611970	C₂	1	2	yes	maximal, complemented
7	#22611969	C₂	1	2	yes	maximal, complemented
8	#22611968	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2207	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₃	C₂²	1	1	yes	characteristic
13	C₂×D₈×D₇₃	—	2	1	no	—
14	C₂×D₈×D₇₃	C₂²	1	2	yes	—
15	#127×D₇₃	—	2	1	no	—
16	C₄×Q₈×D₇₃	—	2	1	no	—
17	C₂×#14556536	C₂²	1	2	yes	complemented
18	C₂×#14556535	C₂²	1	2	yes	complemented
19	C₂×#14556534	C₂²	1	2	yes	complemented
20	SD₃₂×D₇₃	—	2	8	no	—
21	C₂×C₁₆×D₇₃	C₂²	1	2	yes	—
22	#17988964	C₂²	1	1	yes	characteristic
23	#17988963	—	2	1	no	—
24	#17988962	—	2	1	no	—
25	#17988962	C₂²	1	2	yes	—
26	C₄×Dic₂₉₂	C₂²	1	1	yes	characteristic, complemented
27	Q₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
28	#17988681	C₂²	1	1	yes	characteristic, complemented
29	C₄×#11924018	—	2	1	no	—
30	#17988679	—	2	1	no	—
31	#107×D₇₃	C₂²	1	1	yes	characteristic
32	#103×D₇₃	—	2	1	no	—
33	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
34	C₄⋊#11924003	C₂²	1	1	yes	characteristic, complemented
35	#17988405	C₂²	1	2	yes	complemented
36	#17988389	C₂²	1	2	yes	complemented
37	#17988388	C₂²	1	2	yes	complemented
38	#17988387	C₂²	1	2	yes	complemented
39	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	complemented
40	#493×C₇₃	C₂²	1	1	yes	characteristic
41	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	C₄⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#357×C₇₃	C₂²	1	2	yes	complemented
44	C₂×Q₈×D₇₃	—	2	1	no	—
45	C₂×D₄×D₇₃	—	2	2	no	—
46	C₂×D₄×D₇₃	—	4	1	no	—
47	C₂×D₄×D₇₃	—	4	1	no	—
48	C₂×Dic₂₉₂	C₂³	1	1	yes	characteristic
49	C₂×#11924018	—	2	1	no	—
50	Q₁₆×D₇₃	—	2	2	no	—
51	Q₁₆×D₇₃	D₄	1	4	yes	complemented
52	C₂×D₅₈₄	—	2	1	no	—
53	C₂×D₅₈₄	C₂³	1	2	yes	—
54	C₂×#11924013	—	2	2	no	—
55	C₂×#11924013	—	2	2	no	—
56	D₈×D₇₃	—	2	4	no	—
57	D₈×D₇₃	—	2	4	no	—
58	D₈×D₇₃	—	4	4	no	—
59	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
61	#14556588	—	2	1	no	—
62	#14556587	—	2	2	no	—
63	#14556587	—	4	1	no	—
64	#14556587	—	4	1	no	—
65	Q₈×Dic₇₃	—	2	1	no	—
66	C₄×Dic₁₄₆	—	2	1	no	—
67	C₄×Dic₁₄₆	—	4	1	no	—
68	#14556556	—	2	1	no	—
69	#14556556	—	4	1	no	—
70	C₄⋊C₄×D₇₃	—	2	1	no	—
71	C₄⋊C₄×D₇₃	—	4	1	no	—
72	C₄²×D₇₃	—	4	1	no	—
73	C₄²×D₇₃	D₄	1	1	yes	characteristic
74	#14556536	—	2	4	no	—
75	#14556535	—	2	4	no	—
76	#14556534	—	2	4	no	—
77	C₂×#11924003	C₂³	1	2	yes	—
78	C₁₆×D₇₃	—	2	4	no	—
79	#14556525	C₂³	1	1	yes	characteristic
80	#14556524	—	2	1	no	—
81	#14556516	—	2	1	no	—
82	#14556515	—	2	1	no	—
83	#14556514	—	2	1	no	—
84	C₄×#10596831	D₄	1	1	yes	characteristic
85	C₈×Dic₇₃	D₄	1	1	yes	characteristic
86	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
87	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
88	C₂×D₈×C₇₃	—	2	1	no	—
89	C₂×D₈×C₇₃	C₂³	1	2	yes	—
90	#127×C₇₃	—	2	1	no	—
91	C₄×Q₈×C₇₃	—	2	1	no	—
92	SD₃₂×C₇₃	—	2	4	no	—
93	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
94	#107×C₇₃	C₂³	1	1	yes	characteristic
95	#103×C₇₃	—	2	1	no	—
96	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₂³×D₇₃	—	4	2	no	—
98	C₂×Dic₁₄₆	—	2	1	no	—
99	C₂×Dic₁₄₆	—	4	1	no	—
100	Q₈×D₇₃	—	2	4	no	—
101	Q₈×D₇₃	—	4	2	no	—
102	C₂×D₂₉₂	—	2	2	no	—
103	C₂×D₂₉₂	—	4	1	no	—
104	C₂×D₂₉₂	—	4	1	no	—
105	C₂×C₂²⋊D₇₃	—	4	2	no	—
106	C₂×C₂²⋊D₇₃	—	4	2	no	—
107	C₂×C₂²⋊D₇₃	—	4	2	no	—
108	D₄×D₇₃	—	4	4	no	—
109	D₄×D₇₃	—	4	4	no	—
110	D₄×D₇₃	—	8	4	no	—
111	D₄×D₇₃	—	8	4	no	—
112	C₂×C₄×D₇₃	—	4	1	no	—
113	C₂×C₄×D₇₃	—	4	1	no	—
114	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
115	C₂×C₄×D₇₃	D₈	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
117	Dic₂₉₂	—	2	1	no	—
118	Dic₂₉₂	C₂×D₄	1	2	yes	complemented
119	#11924018	—	2	4	no	—
120	D₅₈₄	—	2	2	no	—
121	D₅₈₄	—	2	2	no	—
122	D₅₈₄	—	4	2	no	—
123	#11924013	—	4	4	no	—
124	#11924013	—	4	4	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	C₂×D₄	1	2	yes	—
129	C₈×D₇₃	#41	1	2	yes	—
130	C₄⋊Dic₇₃	—	2	1	no	—
131	C₄⋊Dic₇₃	—	4	1	no	—
132	#11924007	—	4	1	no	—
133	#11924007	—	4	1	no	—
134	#11924007	—	4	1	no	—
135	C₄×Dic₇₃	—	4	1	no	—
136	C₄×Dic₇₃	—	4	1	no	—
137	C₄×Dic₇₃	—	4	1	no	—
138	C₄×Dic₇₃	D₈	1	1	yes	characteristic
139	C₄×Dic₇₃	D₈	1	1	yes	characteristic
140	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	#11924003	—	2	2	no	—
142	C₂×Q₈×C₇₃	—	2	1	no	—
143	C₂×D₄×C₇₃	—	2	2	no	—
144	C₂×D₄×C₇₃	—	4	1	no	—
145	C₂×D₄×C₇₃	—	4	1	no	—
146	Q₁₆×C₇₃	—	2	1	no	—
147	Q₁₆×C₇₃	C₂×D₄	1	2	yes	complemented
148	D₈×C₇₃	—	2	2	no	—
149	D₈×C₇₃	—	2	2	no	—
150	D₈×C₇₃	—	4	2	no	—
151	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
153	C₄⋊C₄×C₇₃	—	2	1	no	—
154	C₄⋊C₄×C₇₃	—	4	1	no	—
155	C₄²×C₇₃	—	4	1	no	—
156	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₁₆×C₇₃	—	2	2	no	—
158	C₂³×C₇₃	—	4	2	no	—
159	C₂²×D₇₃	—	4	2	no	—
160	C₂²×D₇₃	—	8	4	no	—
161	C₂²×D₇₃	—	8	4	no	—
162	C₂²×D₇₃	—	8	4	no	—
163	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
164	Q₈×C₇₃	—	2	2	no	—
165	Q₈×C₇₃	—	4	1	no	—
166	D₄×C₇₃	—	4	2	no	—
167	D₄×C₇₃	—	4	2	no	—
168	D₄×C₇₃	—	8	2	no	—
169	D₄×C₇₃	—	8	2	no	—
170	C₂×C₄×C₇₃	—	4	1	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
175	C₂²⋊D₇₃	—	8	4	no	—
176	C₂²⋊D₇₃	—	8	4	no	—
177	C₂²⋊D₇₃	—	8	4	no	—
178	C₂×Dic₇₃	—	4	1	no	—
179	C₂×Dic₇₃	—	4	1	no	—
180	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
181	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
182	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
183	D₂₉₂	—	4	2	no	—
184	D₂₉₂	—	4	2	no	—
185	D₂₉₂	—	8	2	no	—
186	D₂₉₂	—	8	2	no	—
187	C₄×D₇₃	—	2	2	no	—
188	C₄×D₇₃	—	4	4	no	—
189	C₄×D₇₃	—	8	2	no	—
190	C₄×D₇₃	SD₃₂	1	4	yes	complemented
191	C₄×D₇₃	#121	1	2	yes	—
192	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
193	Dic₁₄₆	—	2	2	no	—
194	Dic₁₄₆	—	4	1	no	—
195	Dic₁₄₆	—	4	4	no	—
196	C₈×C₇₃	—	2	1	no	—
197	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
198	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
199	#10596831	—	2	1	no	—
200	#10596831	#121	1	2	yes	—
201	C₂²×C₇₃	—	8	2	no	—
202	C₂²×C₇₃	—	8	2	no	—
203	C₂²×C₇₃	—	8	2	no	—
204	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
205	C₂×D₇₃	—	8	2	no	—
206	C₂×D₇₃	—	8	2	no	—
207	C₂×D₇₃	—	8	2	no	—
208	C₂×D₇₃	—	16	8	no	—
209	C₂×D₇₃	#459	1	2	yes	—
210	C₂×D₇₃	C₂×SD₃₂	1	2	yes	—
211	C₂×D₇₃	#509	1	2	yes	—
212	C₄×C₇₃	—	2	1	no	—
213	C₄×C₇₃	—	4	2	no	—
214	C₄×C₇₃	—	8	1	no	—
215	C₄×C₇₃	C₂×SD₃₂	1	2	yes	complemented
216	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
217	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	Dic₇₃	—	2	1	no	—
219	Dic₇₃	—	4	2	no	—
220	Dic₇₃	—	8	1	no	—
221	Dic₇₃	#459	1	2	yes	—
222	Dic₇₃	C₂×SD₃₂	1	2	yes	complemented
223	C₂×#2207	—	73	1	no	maximal, Sylow
224	C₂×C₇₃	—	16	2	no	—
225	C₂×C₇₃	C₂×#459	1	1	yes	characteristic
226	C₂×C₇₃	C₂²×SD₃₂	1	1	yes	characteristic
227	C₂×C₇₃	C₂×#509	1	1	yes	characteristic
228	D₇₃	—	16	2	no	—
229	D₇₃	#2207	1	4	yes	direct product factor
230	C₂²×SD₃₂	—	73	2	no	—
231	C₂×#493	—	73	1	no	—
232	C₂×C₄×Q₁₆	—	73	1	no	—
233	#2207	—	73	2	no	—
234	#2207	—	73	1	no	—
235	#2207	—	73	1	no	—
236	#2207	—	73	1	no	—
237	#2207	—	73	2	no	—
238	#2207	D₇₃	1	1	yes	characteristic, direct product factor
239	C₂×C₄⋊C₁₆	—	73	1	no	—
240	C₂×#357	—	73	2	no	—
241	C₇₃	C₂×#2207	1	1	yes	characteristic, complemented, Sylow
242	C₂²×Q₁₆	—	73	1	no	—
243	C₂²×D₈	—	73	2	no	—
244	C₂²×D₈	—	146	1	no	—
245	C₂×#127	—	146	1	no	—
246	C₂×C₄×Q₈	—	146	1	no	—
247	C₂×SD₃₂	—	73	2	no	—
248	C₂×SD₃₂	—	73	2	no	—
249	C₂×SD₃₂	—	73	2	no	—
250	C₂×SD₃₂	—	146	8	no	—
251	C₂×SD₃₂	C₂×D₇₃	1	2	yes	complemented
252	C₂²×C₁₆	—	73	2	no	—
253	#493	—	73	2	no	—
254	#493	—	73	1	no	—
255	#493	—	146	1	no	—
256	#493	—	146	1	no	—
257	#493	C₂×D₇₃	1	1	yes	characteristic
258	C₄×Q₁₆	—	73	1	no	—
259	C₄×Q₁₆	—	73	1	no	—
260	C₄×Q₁₆	—	73	1	no	—
261	C₄×Q₁₆	—	146	1	no	—
262	C₄×Q₁₆	—	146	1	no	—
263	C₄×Q₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
264	C₂×#107	—	73	1	no	—
265	C₂×#103	—	146	1	no	—
266	C₂×C₄×C₈	—	73	1	no	—
267	C₄⋊C₁₆	—	73	2	no	—
268	C₄⋊C₁₆	—	73	1	no	—
269	C₄⋊C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
270	#357	—	73	2	no	—
271	#357	—	73	2	no	—
272	#357	—	73	2	no	—
273	#357	C₂×D₇₃	1	2	yes	complemented
274	C₂²×Q₈	—	146	1	no	—
275	C₂²×D₄	—	292	1	no	—
276	C₂²×D₄	—	292	1	no	—
277	C₂²×D₄	—	146	2	no	—
278	C₂×Q₁₆	—	73	4	no	—
279	C₂×Q₁₆	—	73	1	no	—
280	C₂×Q₁₆	—	146	2	no	—
281	C₂×Q₁₆	—	146	1	no	—
282	C₂×Q₁₆	C₂²×D₇₃	1	1	yes	characteristic
283	C₂×D₈	—	2	1	no	—
284	C₂×D₈	—	292	4	no	—
285	C₂×D₈	—	73	2	no	—
286	C₂×D₈	—	146	4	no	—
287	C₂×D₈	—	146	4	no	—
288	C₂×D₈	—	146	2	no	—
289	C₂×D₈	—	146	2	no	—
290	C₂×D₈	—	146	1	no	—
291	C₂×D₈	C₂²×D₇₃	1	2	yes	—
292	C₂²×C₈	—	73	1	no	—
293	C₂²×C₈	—	73	1	no	—
294	#127	—	2	1	no	—
295	#127	—	292	1	no	—
296	#127	—	292	1	no	—
297	#127	—	146	2	no	—
298	#127	—	146	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	292	1	no	—
301	C₄×Q₈	—	292	1	no	—
302	C₄×Q₈	—	146	1	no	—
303	C₄×Q₈	—	146	1	no	—
304	C₄×Q₈	—	146	1	no	—
305	C₂×C₄⋊C₄	—	292	1	no	—
306	C₂×C₄⋊C₄	—	146	1	no	—
307	C₂×C₄²	—	292	1	no	—
308	C₂×C₄²	—	73	1	no	—
309	SD₃₂	—	2	4	no	—
310	SD₃₂	—	146	4	no	—
311	SD₃₂	—	146	4	no	—
312	SD₃₂	—	146	4	no	—
313	C₂×C₁₆	—	73	2	no	—
314	C₂×C₁₆	—	146	4	no	—
315	C₂×C₁₆	C₂²×D₇₃	1	2	yes	—
316	#107	—	73	1	no	—
317	#107	—	146	1	no	—
318	#107	C₂²×D₇₃	1	1	yes	characteristic
319	#103	—	2	1	no	—
320	#103	—	146	1	no	—
321	#103	—	146	1	no	—
322	#103	—	146	1	no	—
323	C₄×C₈	—	73	1	no	—
324	C₄×C₈	—	73	1	no	—
325	C₄×C₈	—	73	1	no	—
326	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
327	C₂⁴	—	292	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	292	1	no	—
330	C₂×Q₈	—	292	2	no	—
331	C₂×Q₈	—	146	4	no	—
332	C₂×Q₈	—	146	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	4	1	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	292	4	no	—
337	C₂×D₄	—	292	4	no	—
338	C₂×D₄	—	292	2	no	—
339	C₂×D₄	—	292	2	no	—
340	C₂×D₄	—	292	2	no	—
341	C₂×D₄	—	292	1	no	—
342	C₂×D₄	—	292	1	no	—
343	C₂×D₄	—	584	4	no	—
344	C₂×D₄	—	584	4	no	—
345	C₂×D₄	—	146	2	no	—
346	C₂²×C₄	—	292	1	no	—
347	C₂²×C₄	—	292	1	no	—
348	C₂²×C₄	—	73	1	no	—
349	C₂²×C₄	—	73	1	no	—
350	C₂²×C₄	—	73	1	no	—
351	Q₁₆	—	2	1	no	—
352	Q₁₆	—	73	2	no	—
353	Q₁₆	—	146	4	no	—
354	Q₁₆	—	146	1	no	—
355	Q₁₆	D₄×D₇₃	1	2	yes	complemented
356	D₈	—	2	2	no	—
357	D₈	—	2	2	no	—
358	D₈	—	4	2	no	—
359	D₈	—	292	2	no	—
360	D₈	—	292	4	no	—
361	D₈	—	292	4	no	—
362	D₈	—	146	2	no	—
363	D₈	—	146	2	no	—
364	C₂×C₈	—	73	1	no	—
365	C₂×C₈	—	73	2	no	—
366	C₂×C₈	—	73	2	no	—
367	C₂×C₈	—	73	1	no	—
368	C₂×C₈	—	146	2	no	—
369	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
370	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	292	1	no	—
374	C₄⋊C₄	—	292	1	no	—
375	C₄⋊C₄	—	292	1	no	—
376	C₄⋊C₄	—	292	1	no	—
377	C₄⋊C₄	—	146	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	292	1	no	—
380	C₄²	—	292	1	no	—
381	C₄²	—	292	1	no	—
382	C₄²	—	73	1	no	—
383	C₄²	—	73	1	no	—
384	C₄²	—	73	1	no	—
385	C₄²	D₄×D₇₃	1	1	yes	characteristic
386	C₁₆	—	2	2	no	—
387	C₁₆	—	146	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	292	2	no	—
390	C₂³	—	584	4	no	—
391	C₂³	—	584	4	no	—
392	C₂³	—	584	4	no	—
393	C₂³	—	73	1	no	—
394	Q₈	—	2	2	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	292	4	no	—
397	Q₈	—	292	1	no	—
398	Q₈	—	146	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	292	2	no	—
404	D₄	—	292	2	no	—
405	D₄	—	584	2	no	—
406	D₄	—	584	4	no	—
407	D₄	—	584	4	no	—
408	D₄	—	584	4	no	—
409	D₄	—	584	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	292	4	no	—
413	C₂×C₄	—	292	1	no	—
414	C₂×C₄	—	292	1	no	—
415	C₂×C₄	—	584	2	no	—
416	C₂×C₄	—	73	1	no	—
417	C₂×C₄	—	73	1	no	—
418	C₂×C₄	—	73	4	no	—
419	C₂×C₄	—	73	2	no	—
420	C₂×C₄	—	73	2	no	—
421	C₂×C₄	—	73	1	no	—
422	C₂×C₄	—	146	2	no	—
423	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
424	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
426	C₈	—	2	1	no	—
427	C₈	—	73	2	no	—
428	C₈	—	146	1	no	—
429	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
430	C₈	#41×D₇₃	1	1	yes	characteristic
431	C₂²	—	8	2	no	—
432	C₂²	—	8	2	no	—
433	C₂²	—	8	2	no	—
434	C₂²	—	584	2	no	—
435	C₂²	—	584	2	no	—
436	C₂²	—	584	2	no	—
437	C₂²	—	73	2	no	—
438	C₂²	—	73	2	no	—
439	C₂²	—	73	2	no	—
440	C₂²	—	1168	8	no	—
441	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	8	1	no	—
445	C₄	—	292	2	no	—
446	C₄	—	584	1	no	—
447	C₄	—	73	2	no	—
448	C₄	—	73	2	no	—
449	C₄	—	146	1	no	—
450	C₄	SD₃₂×D₇₃	1	2	yes	complemented
451	C₄	#121×D₇₃	1	1	yes	characteristic
452	C₄	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
453	C₂	—	16	2	no	—
454	C₂	—	73	4	no	—
455	C₂	—	1168	2	no	—
456	C₂	#459×D₇₃	1	1	yes	characteristic
457	C₂	C₂×SD₃₂×D₇₃	1	1	yes	characteristic
458	C₂	#509×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2207	C₂
socle	C₂²×C₇₃	C₂²×D₈
prime radical	#493×D₇₃	C₂
hypercenter	#2207	D₇₃
hypocenter	C₇₃	C₂×#2207
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2207

Complements

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

N	H ≅ G/N	type
1. C₂×SD₃₂×D₇₃	C₂	semidirect
3. C₄×Q₁₆×D₇₃	C₂	semidirect
4. #22611972	C₂	semidirect
5. #22611971	C₂	semidirect
6. #22611970	C₂	semidirect
7. #22611969	C₂	semidirect
8. #22611968	C₂	semidirect
9. C₄⋊C₁₆×D₇₃	C₂	semidirect
10. #357×D₇₃	C₂	semidirect
11. C₇₃×#2207	C₂	semidirect
17. C₂×#14556536	C₂²	semidirect
18. C₂×#14556535	C₂²	semidirect
19. C₂×#14556534	C₂²	semidirect
26. C₄×Dic₂₉₂	C₂²	semidirect
27. Q₁₆×Dic₇₃	C₂²	semidirect
28. #17988681	C₂²	semidirect
34. C₄⋊#11924003	C₂²	semidirect
35. #17988405	C₂²	semidirect
36. #17988389	C₂²	semidirect
37. #17988388	C₂²	semidirect
38. #17988387	C₂²	semidirect
39. C₂×SD₃₂×C₇₃	C₂²	semidirect
41. C₄×Q₁₆×C₇₃	C₂²	semidirect
42. C₄⋊C₁₆×C₇₃	C₂²	semidirect
43. #357×C₇₃	C₂²	semidirect
51. Q₁₆×D₇₃	D₄	semidirect
118. Dic₂₉₂	C₂×D₄	semidirect
147. Q₁₆×C₇₃	C₂×D₄	semidirect
190. C₄×D₇₃	SD₃₂	semidirect
215. C₄×C₇₃	C₂×SD₃₂	semidirect
222. Dic₇₃	C₂×SD₃₂	semidirect
229. D₇₃	#2207	direct (N × H)
238. #2207	D₇₃	direct (N × H)
241. C₇₃	C₂×#2207	semidirect
251. C₂×SD₃₂	C₂×D₇₃	semidirect
263. C₄×Q₁₆	C₂×D₇₃	semidirect
269. C₄⋊C₁₆	C₂×D₇₃	semidirect
273. #357	C₂×D₇₃	semidirect
355. Q₁₆	D₄×D₇₃	semidirect
450. C₄	SD₃₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₇₃	2
#493×D₇₃	2
C₄×Q₁₆×D₇₃	2
#22611972	2
#22611971	2
#22611970	2
#22611969	2
#22611968	2
C₄⋊C₁₆×D₇₃	2
#357×D₇₃	2
C₇₃×#2207	2
C₂×#2207	73

Subgroups — #2207×D73 #33240224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2207×D₇₃ #33240224