Subgroups — #472×Dic₇₃ #33092865

Order 18688.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,ℤ/8)×Dic₇₃	C₂	1	2	yes	maximal, complemented
2	C₂×D₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#131×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610842	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610717	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610595	C₂	1	2	yes	maximal, complemented
7	#22610441	C₂	1	2	yes	maximal, complemented
8	#22609995	C₂	1	1	yes	maximal, characteristic, complemented
9	#108×Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#100×Dic₇₃	C₂	1	2	yes	maximal, complemented
11	C₂×#472×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂×#14556598	C₂²	1	1	yes	characteristic
13	#41×Dic₇₃	C₂²	1	1	yes	characteristic
14	C₂×D₄×Dic₇₃	C₂²	1	2	yes	—
15	#17988699	—	2	2	no	—
16	#17988688	—	2	2	no	—
17	SD₁₆×Dic₇₃	—	2	2	no	—
18	D₈×Dic₇₃	—	2	2	no	—
19	D₈×Dic₇₃	—	2	1	no	—
20	D₈×Dic₇₃	—	2	1	no	—
21	D₈×Dic₇₃	—	2	1	no	—
22	D₈×Dic₇₃	—	2	1	no	—
23	C₂×#14556527	C₂²	1	1	yes	characteristic
24	#17988629	C₂²	1	2	yes	—
25	C₂×#14556525	C₂²	1	1	yes	characteristic
26	#17988592	C₂²	1	2	yes	—
27	#17988588	C₂²	1	2	yes	—
28	C₂×#14556512	C₂²	1	2	yes	—
29	C₂×#14556508	C₂²	1	2	yes	—
30	#17988545	—	2	1	no	—
31	#17988545	C₂²	1	1	yes	characteristic
32	#17988542	—	2	1	no	—
33	#17988542	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₇₃	—	2	1	no	—
35	M₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
36	M₁₆×Dic₇₃	C₂²	1	2	yes	—
37	C₂×C₈×Dic₇₃	—	2	1	no	—
38	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
39	#17988355	C₂²	1	2	yes	—
40	#17988355	C₂²	1	2	yes	—
41	#17988351	C₂²	1	2	yes	—
42	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	2	yes	—
43	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
45	#472×C₇₃	C₄	1	8	yes	complemented
46	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#100×C₇₃	C₂²	1	2	yes	—
48	C₂³×Dic₇₃	—	2	2	no	—
49	#14556598	—	2	2	no	—
50	#14556598	—	2	2	no	—
51	C₂×#11924012	—	2	1	no	—
52	C₂×#11924012	C₂³	1	2	yes	—
53	C₂×#11924012	C₂³	1	1	yes	characteristic
54	C₂²×#10596831	—	2	1	no	—
55	C₂²×#10596831	C₂³	1	1	yes	characteristic
56	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
57	Q₈×Dic₇₃	D₄	1	1	yes	characteristic
58	D₄×Dic₇₃	—	2	1	no	—
59	D₄×Dic₇₃	—	2	1	no	—
60	D₄×Dic₇₃	—	2	2	no	—
61	D₄×Dic₇₃	—	2	2	no	—
62	D₄×Dic₇₃	—	2	2	no	—
63	D₄×Dic₇₃	—	2	2	no	—
64	D₄×Dic₇₃	D₄	1	1	yes	characteristic
65	D₄×Dic₇₃	D₄	1	1	yes	characteristic
66	#14556550	—	2	1	no	—
67	#14556550	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊Dic₇₃	—	2	2	no	—
70	C₂×C₄×Dic₇₃	—	2	1	no	—
71	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
72	#14556527	—	2	2	no	—
73	#14556525	—	2	2	no	—
74	#14556525	—	2	1	no	—
75	#14556525	—	2	1	no	—
76	#14556523	—	2	2	no	—
77	#14556515	—	2	2	no	—
78	#14556512	—	2	2	no	—
79	#14556512	—	2	2	no	—
80	#14556512	—	2	2	no	—
81	#14556512	—	2	2	no	—
82	#14556512	—	2	2	no	—
83	#14556508	—	2	4	no	—
84	#14556501	—	2	1	no	—
85	#14556501	—	2	2	no	—
86	#14556501	—	2	1	no	—
87	#14556501	—	2	1	no	—
88	C₈×Dic₇₃	—	2	1	no	—
89	C₈×Dic₇₃	—	2	2	no	—
90	C₈×Dic₇₃	—	2	1	no	—
91	C₈×Dic₇₃	—	2	1	no	—
92	C₈×Dic₇₃	D₄	1	1	yes	characteristic
93	C₈×Dic₇₃	D₄	1	1	yes	characteristic
94	C₈×Dic₇₃	D₄	1	1	yes	characteristic
95	C₈×Dic₇₃	D₄	1	1	yes	characteristic
96	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
98	AGL(1,ℤ/8)×C₇₃	—	2	4	no	—
99	AGL(1,ℤ/8)×C₇₃	C₂×C₄	1	8	yes	complemented
100	C₂×SD₁₆×C₇₃	—	2	2	no	—
101	C₂×D₈×C₇₃	—	2	2	no	—
102	C₂×D₈×C₇₃	—	2	1	no	—
103	C₂×D₈×C₇₃	—	2	1	no	—
104	C₂×D₈×C₇₃	—	2	2	no	—
105	C₂×D₈×C₇₃	C₂×C₄	1	4	yes	complemented
106	#131×C₇₃	—	2	2	no	—
107	#131×C₇₃	C₂×C₄	1	4	yes	complemented
108	C₂×M₁₆×C₇₃	—	2	1	no	—
109	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
111	C₂²×C₈×C₇₃	—	2	1	no	—
112	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
113	#108×C₇₃	C₂×C₄	1	4	yes	complemented
114	#100×C₇₃	C₂×C₄	1	8	yes	complemented
115	C₂²×Dic₇₃	—	2	1	no	—
116	C₂²×Dic₇₃	—	2	1	no	—
117	C₂²×Dic₇₃	—	2	2	no	—
118	C₂²×Dic₇₃	—	4	2	no	—
119	C₂²×Dic₇₃	—	4	2	no	—
120	C₂²×Dic₇₃	—	8	4	no	—
121	C₂²×Dic₇₃	#41	1	1	yes	characteristic
122	C₂²×Dic₇₃	#41	1	1	yes	characteristic
123	#11924012	—	2	4	no	—
124	#11924012	—	2	1	no	—
125	#11924012	—	2	2	no	—
126	#11924012	—	2	2	no	—
127	#11924012	#41	1	2	yes	—
128	C₂×#10596831	—	2	4	no	—
129	C₂×#10596831	—	2	1	no	—
130	C₂×#10596831	—	2	1	no	—
131	C₂×#10596831	—	2	1	no	—
132	C₂×#10596831	—	2	2	no	—
133	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
134	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
135	C₄⋊Dic₇₃	—	2	1	no	—
136	C₄⋊Dic₇₃	—	2	1	no	—
137	C₄⋊Dic₇₃	—	2	2	no	—
138	C₄⋊Dic₇₃	—	2	2	no	—
139	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
140	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊Dic₇₃	—	2	1	no	—
142	C₂²⋊Dic₇₃	—	2	1	no	—
143	C₂²⋊Dic₇₃	—	2	1	no	—
144	C₂²⋊Dic₇₃	—	4	2	no	—
145	C₂²⋊Dic₇₃	—	4	2	no	—
146	C₄×Dic₇₃	—	2	1	no	—
147	C₄×Dic₇₃	—	2	1	no	—
148	C₄×Dic₇₃	—	2	1	no	—
149	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
151	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×C₇₃	—	2	2	no	—
154	#41×C₇₃	—	2	1	no	—
155	#41×C₇₃	—	2	1	no	—
156	#41×C₇₃	C₂²×C₄	1	2	yes	—
157	#41×C₇₃	#41	1	2	yes	—
158	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₇₃	—	2	1	no	—
160	C₂×D₄×C₇₃	—	2	2	no	—
161	C₂×D₄×C₇₃	—	2	2	no	—
162	C₂×D₄×C₇₃	—	2	2	no	—
163	C₂×D₄×C₇₃	—	2	2	no	—
164	C₂×D₄×C₇₃	—	2	2	no	—
165	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
166	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	—	2	1	no	—
168	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
169	SD₁₆×C₇₃	—	2	8	no	—
170	D₈×C₇₃	—	2	8	no	—
171	D₈×C₇₃	—	2	4	no	—
172	D₈×C₇₃	—	2	4	no	—
173	M₁₆×C₇₃	—	2	1	no	—
174	M₁₆×C₇₃	—	2	2	no	—
175	M₁₆×C₇₃	—	2	4	no	—
176	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
177	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
178	C₂×C₈×C₇₃	—	2	1	no	—
179	C₂×C₈×C₇₃	—	2	2	no	—
180	C₂×C₈×C₇₃	—	2	4	no	—
181	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
182	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₇₃	#41	1	2	yes	—
185	C₂³×C₇₃	—	2	1	no	—
186	C₂³×C₇₃	—	2	4	no	—
187	C₂³×C₇₃	—	4	2	no	—
188	C₂³×C₇₃	—	4	2	no	—
189	C₂³×C₇₃	—	8	2	no	—
190	C₂³×C₇₃	—	8	2	no	—
191	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
192	Q₈×C₇₃	—	2	1	no	—
193	Q₈×C₇₃	C₄×D₄	1	2	yes	—
194	D₄×C₇₃	—	2	2	no	—
195	D₄×C₇₃	—	2	2	no	—
196	D₄×C₇₃	—	2	4	no	—
197	D₄×C₇₃	—	2	4	no	—
198	D₄×C₇₃	—	2	1	no	—
199	D₄×C₇₃	—	4	2	no	—
200	D₄×C₇₃	—	4	2	no	—
201	D₄×C₇₃	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₇₃	—	2	1	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
211	C₂×Dic₇₃	—	2	2	no	—
212	C₂×Dic₇₃	—	2	1	no	—
213	C₂×Dic₇₃	—	2	1	no	—
214	C₂×Dic₇₃	—	4	1	no	—
215	C₂×Dic₇₃	—	4	2	no	—
216	C₂×Dic₇₃	—	4	2	no	—
217	C₂×Dic₇₃	—	4	2	no	—
218	C₂×Dic₇₃	—	8	4	no	—
219	C₂×Dic₇₃	—	8	4	no	—
220	C₂×Dic₇₃	—	8	2	no	—
221	C₂×Dic₇₃	#121	1	1	yes	characteristic
222	C₂×Dic₇₃	#121	1	1	yes	characteristic
223	C₂×Dic₇₃	#121	1	1	yes	characteristic
224	C₂×Dic₇₃	#121	1	1	yes	characteristic
225	C₈×C₇₃	—	2	2	no	—
226	C₈×C₇₃	—	2	4	no	—
227	C₈×C₇₃	C₄×D₄	1	2	yes	—
228	C₈×C₇₃	C₄×D₄	1	2	yes	—
229	#10596831	—	2	1	no	—
230	#10596831	—	2	2	no	—
231	#10596831	—	2	1	no	—
232	#10596831	—	4	2	no	—
233	C₂²×C₇₃	—	2	1	no	—
234	C₂²×C₇₃	—	2	1	no	—
235	C₂²×C₇₃	—	2	2	no	—
236	C₂²×C₇₃	—	4	1	no	—
237	C₂²×C₇₃	—	4	1	no	—
238	C₂²×C₇₃	—	4	4	no	—
239	C₂²×C₇₃	—	8	4	no	—
240	C₂²×C₇₃	—	8	4	no	—
241	C₂²×C₇₃	—	8	2	no	—
242	C₂²×C₇₃	—	8	2	no	—
243	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
244	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₇₃	#529	1	1	yes	characteristic
246	C₄×C₇₃	—	2	2	no	—
247	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
248	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
249	C₄×C₇₃	#525	1	1	yes	characteristic
250	C₄×C₇₃	#532	1	1	yes	characteristic
251	Dic₇₃	—	2	1	no	—
252	Dic₇₃	—	2	1	no	—
253	Dic₇₃	—	2	1	no	—
254	Dic₇₃	—	4	1	no	—
255	Dic₇₃	—	4	1	no	—
256	Dic₇₃	—	8	2	no	—
257	Dic₇₃	#472	1	2	yes	direct product factor
258	C₄×#472	—	73	1	no	maximal, Sylow
259	C₂×C₇₃	—	2	1	no	—
260	C₂×C₇₃	—	2	1	no	—
261	C₂×C₇₃	—	4	2	no	—
262	C₂×C₇₃	—	8	4	no	—
263	C₂×C₇₃	C₄×#121	1	1	yes	characteristic
264	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
265	C₂×C₇₃	#3067	1	1	yes	characteristic
266	C₂×#472	D₇₃	1	1	yes	characteristic
267	C₄×AGL(1,ℤ/8)	—	73	2	no	—
268	C₂×C₄×D₈	—	73	1	no	—
269	C₄×#131	—	73	1	no	—
270	#1978	—	73	1	no	—
271	#1952	—	73	1	no	—
272	#1931	—	73	2	no	—
273	#1907	—	73	2	no	—
274	#1816	—	73	1	no	—
275	C₄×#108	—	73	1	no	—
276	C₄×#100	—	73	2	no	—
277	C₇₃	C₄×#472	1	1	yes	characteristic, complemented, Sylow
278	C₂×AGL(1,ℤ/8)	C₂×D₇₃	1	2	yes	—
279	C₂²×D₈	C₂×D₇₃	1	1	yes	characteristic
280	C₂×#131	—	73	1	no	—
281	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
282	C₄×#41	—	73	1	no	—
283	C₂×C₄×D₄	—	73	2	no	—
284	#472	Dic₇₃	1	8	yes	direct product factor
285	#442	—	146	2	no	—
286	#440	—	146	2	no	—
287	C₄×SD₁₆	—	146	2	no	—
288	C₄×D₈	—	146	1	no	—
289	C₄×D₈	—	146	1	no	—
290	C₄×D₈	—	146	1	no	—
291	C₄×D₈	—	146	1	no	—
292	C₄×D₈	—	146	2	no	—
293	C₂×#108	—	73	1	no	—
294	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
295	#428	—	73	2	no	—
296	C₂×#107	—	73	1	no	—
297	#418	—	73	2	no	—
298	#417	—	73	2	no	—
299	C₂×#102	—	73	2	no	—
300	C₂×#100	—	73	2	no	—
301	C₂×#100	C₂×D₇₃	1	2	yes	—
302	#405	—	73	1	no	—
303	#405	—	73	1	no	—
304	#405	—	146	1	no	—
305	#405	—	146	1	no	—
306	C₄×M₁₆	—	73	1	no	—
307	C₄×M₁₆	—	73	2	no	—
308	C₄×M₁₆	—	146	1	no	—
309	C₂×C₄×C₈	—	73	1	no	—
310	C₂×C₄×C₈	—	146	1	no	—
311	#343	—	73	2	no	—
312	#343	—	73	2	no	—
313	#341	—	73	2	no	—
314	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
315	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
316	C₂³×C₄	—	146	2	no	—
317	AGL(1,ℤ/8)	—	2	4	no	—
318	AGL(1,ℤ/8)	C₂×Dic₇₃	1	8	yes	complemented
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	2	1	no	—
322	C₂×D₈	—	2	1	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	C₂×Dic₇₃	1	4	yes	complemented
325	#131	—	2	2	no	—
326	#131	—	146	2	no	—
327	#131	—	146	2	no	—
328	#131	C₂×Dic₇₃	1	4	yes	complemented
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	73	1	no	—
331	C₂×M₁₆	—	73	2	no	—
332	C₂×M₁₆	—	146	1	no	—
333	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	—	73	1	no	—
337	C₂²×C₈	—	146	1	no	—
338	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
339	C₄×Q₈	—	73	1	no	—
340	C₄×Q₈	—	73	1	no	—
341	C₄×D₄	—	73	1	no	—
342	C₄×D₄	—	73	1	no	—
343	C₄×D₄	—	146	2	no	—
344	C₄×D₄	—	146	2	no	—
345	C₄×D₄	—	146	2	no	—
346	C₄×D₄	—	146	2	no	—
347	C₄×D₄	—	146	1	no	—
348	C₄×D₄	—	146	1	no	—
349	#117	—	73	1	no	—
350	#117	—	146	1	no	—
351	C₂×C₄⋊C₄	—	73	2	no	—
352	C₂×C₂²⋊C₄	—	146	2	no	—
353	C₂×C₄²	—	73	1	no	—
354	C₂×C₄²	—	146	1	no	—
355	#108	—	146	2	no	—
356	#108	C₂×Dic₇₃	1	4	yes	complemented
357	#107	—	146	2	no	—
358	#107	—	146	1	no	—
359	#107	—	146	1	no	—
360	#106	—	146	2	no	—
361	#103	—	146	2	no	—
362	#102	—	146	2	no	—
363	#102	—	146	2	no	—
364	#102	—	146	2	no	—
365	#102	—	146	2	no	—
366	#102	—	146	2	no	—
367	#100	—	146	4	no	—
368	#100	C₂×Dic₇₃	1	8	yes	complemented
369	#97	—	146	1	no	—
370	#97	—	146	2	no	—
371	#97	—	146	1	no	—
372	#97	—	146	1	no	—
373	C₄×C₈	—	73	1	no	—
374	C₄×C₈	—	73	1	no	—
375	C₄×C₈	—	73	1	no	—
376	C₄×C₈	—	73	1	no	—
377	C₄×C₈	—	146	1	no	—
378	C₄×C₈	—	146	2	no	—
379	C₄×C₈	—	146	1	no	—
380	C₄×C₈	—	146	1	no	—
381	C₂⁴	—	2	2	no	—
382	#41	—	2	1	no	—
383	#41	—	2	1	no	—
384	#41	C₂²×Dic₇₃	1	2	yes	—
385	#41	#11924027	1	2	yes	—
386	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	C₂²×Dic₇₃	1	4	yes	—
394	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	292	2	no	—
397	C₂²×C₄	—	292	2	no	—
398	C₂²×C₄	—	584	4	no	—
399	C₂²×C₄	—	73	1	no	—
400	C₂²×C₄	—	73	1	no	—
401	C₂²×C₄	—	146	1	no	—
402	C₂²×C₄	—	146	1	no	—
403	C₂²×C₄	—	146	2	no	—
404	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
405	SD₁₆	—	2	8	no	—
406	D₈	—	2	8	no	—
407	D₈	—	2	4	no	—
408	D₈	—	2	4	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	73	2	no	—
413	M₁₆	—	146	2	no	—
414	M₁₆	—	146	2	no	—
415	M₁₆	—	146	4	no	—
416	M₁₆	—	146	1	no	—
417	M₁₆	C₂²×Dic₇₃	1	2	yes	—
418	M₁₆	C₂²×Dic₇₃	1	4	yes	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	—	73	1	no	—
423	C₂×C₈	—	73	1	no	—
424	C₂×C₈	—	146	2	no	—
425	C₂×C₈	—	146	4	no	—
426	C₂×C₈	—	146	1	no	—
427	C₂×C₈	—	146	1	no	—
428	C₂×C₈	—	146	1	no	—
429	C₂×C₈	C₂²×Dic₇₃	1	2	yes	—
430	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
431	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
432	C₂×C₈	#11924027	1	2	yes	—
433	C₄⋊C₄	—	73	1	no	—
434	C₄⋊C₄	—	73	1	no	—
435	C₄⋊C₄	—	146	1	no	—
436	C₄⋊C₄	—	146	1	no	—
437	C₄⋊C₄	—	146	2	no	—
438	C₄⋊C₄	—	146	2	no	—
439	C₂²⋊C₄	—	292	2	no	—
440	C₂²⋊C₄	—	292	2	no	—
441	C₂²⋊C₄	—	146	1	no	—
442	C₂²⋊C₄	—	146	1	no	—
443	C₂²⋊C₄	—	146	1	no	—
444	C₄²	—	73	1	no	—
445	C₄²	—	73	1	no	—
446	C₄²	—	73	1	no	—
447	C₄²	—	73	1	no	—
448	C₄²	—	146	1	no	—
449	C₄²	—	146	1	no	—
450	C₄²	—	146	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	#41×D₇₃	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	D₄×Dic₇₃	1	2	yes	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	4	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	D₄×Dic₇₃	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	292	2	no	—
472	C₂×C₄	—	292	2	no	—
473	C₂×C₄	—	292	2	no	—
474	C₂×C₄	—	292	1	no	—
475	C₂×C₄	—	584	4	no	—
476	C₂×C₄	—	584	4	no	—
477	C₂×C₄	—	584	2	no	—
478	C₂×C₄	—	73	1	no	—
479	C₂×C₄	—	73	1	no	—
480	C₂×C₄	—	73	1	no	—
481	C₂×C₄	—	73	1	no	—
482	C₂×C₄	—	146	1	no	—
483	C₂×C₄	—	146	1	no	—
484	C₂×C₄	—	146	2	no	—
485	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
488	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
489	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
490	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	4	no	—
493	C₈	—	292	2	no	—
494	C₈	—	146	1	no	—
495	C₈	—	146	1	no	—
496	C₈	—	146	2	no	—
497	C₈	D₄×Dic₇₃	1	2	yes	—
498	C₈	D₄×Dic₇₃	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	#41×Dic₇₃	1	1	yes	characteristic
510	C₂²	#121×D₇₃	1	1	yes	characteristic
511	C₂²	#17989118	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	292	1	no	—
514	C₄	—	292	1	no	—
515	C₄	—	584	2	no	—
516	C₄	—	73	2	no	—
517	C₄	—	146	1	no	—
518	C₄	—	146	1	no	—
519	C₄	—	146	1	no	—
520	C₄	C₂×D₄×Dic₇₃	1	1	yes	characteristic
521	C₄	C₂×D₄×Dic₇₃	1	1	yes	characteristic
522	C₄	#17989097	1	1	yes	characteristic
523	C₄	#17989132	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	4	no	—
528	C₂	#121×Dic₇₃	1	1	yes	characteristic
529	C₂	#472×D₇₃	1	1	yes	characteristic
530	C₂	#22619649	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting, prime radical	C₂×#472×C₇₃	C₂
socle	C₂²×C₇₃	C₂×#121
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#472	D₇₃
hypocenter	C₇₃	C₄×#472
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. AGL(1,ℤ/8)×Dic₇₃	C₂	semidirect
2. C₂×D₈×Dic₇₃	C₂	semidirect
3. #131×Dic₇₃	C₂	semidirect
4. #22610842	C₂	semidirect
5. #22610717	C₂	semidirect
6. #22610595	C₂	semidirect
7. #22610441	C₂	semidirect
8. #22609995	C₂	semidirect
9. #108×Dic₇₃	C₂	semidirect
10. #100×Dic₇₃	C₂	semidirect
45. #472×C₇₃	C₄	semidirect
99. AGL(1,ℤ/8)×C₇₃	C₂×C₄	semidirect
105. C₂×D₈×C₇₃	C₂×C₄	semidirect
107. #131×C₇₃	C₂×C₄	semidirect
113. #108×C₇₃	C₂×C₄	semidirect
114. #100×C₇₃	C₂×C₄	semidirect
257. Dic₇₃	#472	direct (N × H)
277. C₇₃	C₄×#472	semidirect
284. #472	Dic₇₃	direct (N × H)
318. AGL(1,ℤ/8)	C₂×Dic₇₃	semidirect
324. C₂×D₈	C₂×Dic₇₃	semidirect
328. #131	C₂×Dic₇₃	semidirect
356. #108	C₂×Dic₇₃	semidirect
368. #100	C₂×Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
AGL(1,ℤ/8)×Dic₇₃	2
C₂×D₈×Dic₇₃	2
#131×Dic₇₃	2
#22610842	2
#22610717	2
#22610595	2
#22610441	2
#22609995	2
#108×Dic₇₃	2
#100×Dic₇₃	2
C₂×#472×C₇₃	2
C₄×#472	73

Subgroups — #472×Dic73 #33092865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #472×Dic₇₃ #33092865