Subgroups — #33069764

Order 18688.

744 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620490	C₂	1	1	yes	maximal, characteristic, complemented
2	#22619730	C₂	1	1	yes	maximal, characteristic, complemented
3	#22619397	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×D₂₉₂	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609355	C₂	1	2	yes	maximal, complemented
6	#22609341	C₂	1	2	yes	maximal, complemented
7	#22609307	C₂	1	2	yes	maximal, complemented
8	#22609273	C₂	1	2	yes	maximal, complemented
9	#22608622	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608609	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1566	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556619	—	2	1	no	—
13	C₂²×C₈×D₇₃	—	2	1	no	—
14	#17989144	C₂²	1	1	yes	characteristic
15	#17989137	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
17	#17988985	C₂²	1	1	yes	characteristic, complemented
18	#17988960	C₂²	1	1	yes	characteristic, complemented
19	#17988938	C₂²	1	1	yes	characteristic, complemented
20	#17988934	C₂²	1	1	yes	characteristic, complemented
21	#17988888	—	2	2	no	—
22	#17988878	C₂²	1	2	yes	—
23	#17988868	C₂²	1	2	yes	—
24	#17988816	—	2	1	no	—
25	#17988816	—	2	1	no	—
26	#17988803	—	2	2	no	—
27	#17988793	C₂²	1	2	yes	—
28	#17988783	C₂²	1	2	yes	—
29	C₄×#11924017	—	2	1	no	—
30	C₄×#11924017	—	2	1	no	—
31	C₈×D₂₉₂	—	2	1	no	—
32	C₈×D₂₉₂	—	2	1	no	—
33	C₈×D₂₉₂	C₂²	1	2	yes	—
34	C₈×D₂₉₂	C₂²	1	2	yes	—
35	#17988629	—	2	1	no	—
36	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
37	#17988593	—	2	1	no	—
38	#17988589	—	2	1	no	—
39	C₂×#14556503	—	2	1	no	—
40	#17988335	C₂²	1	2	yes	complemented
41	#17988334	C₂²	1	2	yes	complemented
42	#17988332	C₂²	1	2	yes	complemented
43	#17988330	C₂²	1	2	yes	complemented
44	#423×C₇₃	C₂²	1	1	yes	characteristic
45	#423×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	#334×C₇₃	C₂²	1	2	yes	complemented
48	#334×C₇₃	C₂²	1	2	yes	complemented
49	C₂×#11924028	—	2	1	no	—
50	C₂²×D₂₉₂	D₄	1	1	yes	characteristic
51	C₂²×C₄×D₇₃	—	2	1	no	—
52	#14556619	—	4	4	no	—
53	C₂×#11924017	—	2	2	no	—
54	C₂×#11924017	—	2	1	no	—
55	C₂×#11924017	—	2	1	no	—
56	C₂×D₅₈₄	—	2	2	no	—
57	C₂²×#10596831	—	2	1	no	—
58	C₂×C₈×D₇₃	—	2	2	no	—
59	C₂×C₈×D₇₃	—	2	2	no	—
60	C₂×C₈×D₇₃	—	4	4	no	—
61	#14556591	C₂³	1	1	yes	characteristic
62	#14556591	C₂³	1	1	yes	characteristic
63	#14556591	C₂³	1	1	yes	characteristic
64	#14556588	C₂³	1	1	yes	characteristic
65	#14556583	—	2	1	no	—
66	#14556579	—	2	1	no	—
67	#14556570	—	2	1	no	—
68	#14556570	—	2	1	no	—
69	#14556565	—	2	1	no	—
70	#14556565	—	2	1	no	—
71	C₄×Dic₁₄₆	—	2	1	no	—
72	C₄×Dic₁₄₆	—	2	1	no	—
73	C₄×D₂₉₂	—	2	1	no	—
74	C₄×D₂₉₂	—	2	1	no	—
75	C₄×D₂₉₂	—	2	1	no	—
76	C₄×D₂₉₂	—	2	1	no	—
77	C₄×D₂₉₂	D₄	1	2	yes	—
78	C₄×D₂₉₂	C₂³	1	2	yes	—
79	#14556550	—	2	1	no	—
80	C₂×C₄⋊Dic₇₃	D₄	1	1	yes	characteristic
81	C₂×#11924005	—	2	1	no	—
82	#14556525	—	2	2	no	—
83	#14556523	—	2	2	no	—
84	#14556523	—	2	1	no	—
85	#14556523	—	2	1	no	—
86	C₄⋊#10596831	—	2	1	no	—
87	C₄⋊#10596831	C₂³	1	2	yes	—
88	#14556516	—	2	2	no	—
89	#14556516	—	2	1	no	—
90	#14556516	—	2	1	no	—
91	#14556513	—	2	2	no	—
92	#14556513	—	2	2	no	—
93	#14556513	—	2	2	no	—
94	#14556513	—	2	1	no	—
95	#14556513	—	2	1	no	—
96	#14556503	—	2	2	no	—
97	#14556503	—	2	2	no	—
98	C₂×M₁₆×C₇₃	—	2	1	no	—
99	C₂×M₁₆×C₇₃	—	2	1	no	—
100	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
101	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₇₃	—	2	1	no	—
104	C₄⋊C₈×C₇₃	—	2	1	no	—
105	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
106	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
107	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
108	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
109	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
111	C₂³×D₇₃	—	2	1	no	—
112	#11924028	—	4	2	no	—
113	#11924028	—	4	2	no	—
114	C₂×Dic₁₄₆	—	2	1	no	—
115	C₂×Dic₁₄₆	—	2	1	no	—
116	C₂×Dic₁₄₆	—	2	1	no	—
117	C₂×D₂₉₂	—	2	1	no	—
118	C₂×D₂₉₂	—	2	2	no	—
119	C₂×D₂₉₂	—	2	1	no	—
120	C₂×D₂₉₂	—	2	1	no	—
121	C₂×D₂₉₂	—	2	1	no	—
122	C₂×D₂₉₂	SD₁₆	1	4	yes	complemented
123	C₂×D₂₉₂	C₂×D₄	1	2	yes	—
124	C₂×C₂²⋊D₇₃	—	4	1	no	—
125	C₂²×Dic₇₃	—	2	1	no	—
126	C₂×C₄×D₇₃	—	2	2	no	—
127	C₂×C₄×D₇₃	—	2	2	no	—
128	C₂×C₄×D₇₃	—	4	2	no	—
129	C₂×C₄×D₇₃	—	4	2	no	—
130	C₂×C₄×D₇₃	—	4	1	no	—
131	#11924017	—	4	2	no	—
132	#11924017	—	4	4	no	—
133	#11924017	—	4	2	no	—
134	D₅₈₄	—	4	4	no	—
135	C₂×#10596831	—	2	2	no	—
136	C₂×#10596831	—	4	2	no	—
137	C₈×D₇₃	—	4	4	no	—
138	C₈×D₇₃	—	4	4	no	—
139	C₄⋊Dic₇₃	—	2	1	no	—
140	C₄⋊Dic₇₃	—	2	1	no	—
141	C₄⋊Dic₇₃	—	2	1	no	—
142	C₄⋊Dic₇₃	—	2	1	no	—
143	C₄⋊Dic₇₃	—	2	1	no	—
144	C₄⋊Dic₇₃	—	2	1	no	—
145	C₄⋊Dic₇₃	—	2	1	no	—
146	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
147	#11924007	—	4	1	no	—
148	#11924007	—	4	1	no	—
149	C₂²⋊Dic₇₃	—	4	1	no	—
150	#11924005	—	2	2	no	—
151	#11924005	—	2	2	no	—
152	#11924005	—	4	1	no	—
153	#11924005	—	4	1	no	—
154	C₄×Dic₇₃	—	4	1	no	—
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
158	M₁₆×C₇₃	—	4	2	no	—
159	M₁₆×C₇₃	—	4	2	no	—
160	C₂×C₈×C₇₃	—	2	2	no	—
161	C₂×C₈×C₇₃	—	2	2	no	—
162	C₂×C₈×C₇₃	—	2	2	no	—
163	C₂×C₈×C₇₃	—	4	1	no	—
164	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
165	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₇₃	#41	1	1	yes	characteristic
171	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
172	C₂³×C₇₃	#121	1	1	yes	characteristic
173	C₂²×D₇₃	—	2	2	no	—
174	C₂²×D₇₃	—	2	4	no	—
175	C₂²×D₇₃	—	4	2	no	—
176	C₂²×D₇₃	—	4	2	no	—
177	C₂²×D₇₃	—	4	1	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	4	1	no	—
181	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
182	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
183	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
185	C₂×C₄×C₇₃	#135	1	2	yes	—
186	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
189	C₂²⋊D₇₃	—	8	2	no	—
190	C₂×Dic₇₃	—	2	2	no	—
191	C₂×Dic₇₃	—	4	2	no	—
192	C₂×Dic₇₃	—	4	1	no	—
193	C₂×Dic₇₃	—	4	1	no	—
194	C₂×Dic₇₃	—	4	1	no	—
195	D₂₉₂	—	2	2	no	—
196	D₂₉₂	—	2	4	no	—
197	D₂₉₂	—	4	1	no	—
198	D₂₉₂	—	4	1	no	—
199	D₂₉₂	—	4	1	no	—
200	D₂₉₂	—	4	1	no	—
201	D₂₉₂	—	8	1	no	—
202	D₂₉₂	C₂×SD₁₆	1	4	yes	—
203	C₄×D₇₃	—	4	4	no	—
204	C₄×D₇₃	—	4	2	no	—
205	C₄×D₇₃	—	4	2	no	—
206	C₄×D₇₃	—	8	2	no	—
207	Dic₁₄₆	—	4	1	no	—
208	Dic₁₄₆	—	4	1	no	—
209	Dic₁₄₆	—	4	1	no	—
210	Dic₁₄₆	—	4	1	no	—
211	Dic₁₄₆	—	8	1	no	—
212	C₈×C₇₃	—	2	1	no	—
213	C₈×C₇₃	—	2	1	no	—
214	C₈×C₇₃	—	2	1	no	—
215	C₈×C₇₃	—	4	2	no	—
216	C₈×C₇₃	—	4	2	no	—
217	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	complemented
218	#10596831	—	4	2	no	—
219	C₂²×C₇₃	—	2	1	no	—
220	C₂²×C₇₃	—	2	1	no	—
221	C₂²×C₇₃	#465	1	2	yes	—
222	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
223	C₂×D₇₃	—	2	4	no	—
224	C₂×D₇₃	—	4	8	no	—
225	C₂×D₇₃	—	4	2	no	—
226	C₂×D₇₃	—	4	2	no	—
227	C₂×D₇₃	—	8	1	no	—
228	C₂×D₇₃	—	8	1	no	—
229	C₂×D₇₃	—	8	1	no	—
230	C₄×C₇₃	—	2	1	no	—
231	C₄×C₇₃	—	2	1	no	—
232	C₄×C₇₃	—	2	1	no	—
233	C₄×C₇₃	#465	1	2	yes	—
234	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
235	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
236	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₄×C₇₃	#575	1	1	yes	characteristic
238	Dic₇₃	—	4	2	no	—
239	Dic₇₃	—	8	1	no	—
240	Dic₇₃	—	8	1	no	—
241	Dic₇₃	—	8	1	no	—
242	#19254	—	73	1	no	maximal, Sylow
243	C₂×C₇₃	—	2	2	no	—
244	C₂×C₇₃	#3036	1	1	yes	characteristic
245	C₂×C₇₃	C₂×#465	1	1	yes	characteristic
246	C₂×C₇₃	#3067	1	1	yes	characteristic
247	D₇₃	—	4	4	no	—
248	D₇₃	—	16	1	no	—
249	#3167	—	73	1	no	—
250	#3077	—	73	1	no	—
251	#3036	—	73	1	no	—
252	C₂×C₈×D₄	—	73	1	no	—
253	#1679	—	73	2	no	—
254	#1677	—	73	2	no	—
255	#1671	—	73	2	no	—
256	#1665	—	73	2	no	—
257	#1566	D₇₃	1	1	yes	characteristic, complemented
258	#1550	—	73	1	no	—
259	#1547	—	73	1	no	—
260	C₇₃	#19254	1	1	yes	characteristic, complemented, Sylow
261	C₂×AGL(1,ℤ/8)	—	146	1	no	—
262	C₂³×C₈	—	146	1	no	—
263	#533	—	73	1	no	—
264	#532	—	73	1	no	—
265	C₂×C₄×D₄	—	73	1	no	—
266	#498	—	73	1	no	—
267	#492	—	73	1	no	—
268	#487	—	73	1	no	—
269	#486	—	73	1	no	—
270	#478	—	146	2	no	—
271	#476	—	73	2	no	—
272	#474	—	73	2	no	—
273	#465	—	146	1	no	—
274	#465	—	146	1	no	—
275	#463	—	146	2	no	—
276	#461	—	73	2	no	—
277	#459	—	73	2	no	—
278	C₄×SD₁₆	—	146	1	no	—
279	C₄×SD₁₆	—	146	1	no	—
280	C₈×D₄	—	73	2	no	—
281	C₈×D₄	—	73	2	no	—
282	C₈×D₄	—	146	1	no	—
283	C₈×D₄	—	146	1	no	—
284	#428	—	146	1	no	—
285	#423	C₂×D₇₃	1	1	yes	characteristic
286	#423	C₂×D₇₃	1	1	yes	characteristic
287	C₂×C₄⋊C₈	—	73	1	no	—
288	#418	—	146	1	no	—
289	#417	—	146	1	no	—
290	C₂×C₂²⋊C₈	—	146	1	no	—
291	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
292	#334	C₂×D₇₃	1	2	yes	complemented
293	#334	C₂×D₇₃	1	2	yes	complemented
294	#333	—	73	2	no	—
295	#332	—	73	2	no	—
296	#332	—	73	2	no	—
297	#331	—	73	2	no	—
298	C₂×#41	—	146	1	no	—
299	C₂²×D₄	—	73	1	no	—
300	C₂³×C₄	—	146	1	no	—
301	AGL(1,ℤ/8)	—	292	4	no	—
302	C₂×SD₁₆	—	146	2	no	—
303	C₂×SD₁₆	—	146	1	no	—
304	C₂×SD₁₆	—	146	1	no	—
305	C₂×D₈	—	146	2	no	—
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂²×C₈	—	292	4	no	—
309	C₂²×C₈	—	146	1	no	—
310	C₂²×C₈	—	146	2	no	—
311	C₂²×C₈	—	146	2	no	—
312	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
313	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
314	C₄⋊Q₈	—	73	1	no	—
315	C₄⋊Q₈	—	73	1	no	—
316	C₄⋊Q₈	—	73	1	no	—
317	#127	—	73	1	no	—
318	#125	—	146	1	no	—
319	#124	—	146	1	no	—
320	C₂²⋊Q₈	—	146	1	no	—
321	C₂²⋊Q₈	—	146	1	no	—
322	#121	—	146	1	no	—
323	#121	—	146	1	no	—
324	C₄×Q₈	—	146	1	no	—
325	C₄×Q₈	—	146	1	no	—
326	C₄×D₄	—	73	2	no	—
327	C₄×D₄	—	73	2	no	—
328	C₄×D₄	—	146	1	no	—
329	C₄×D₄	—	146	1	no	—
330	C₄×D₄	—	146	1	no	—
331	C₄×D₄	—	146	1	no	—
332	#117	—	146	1	no	—
333	C₂×C₄⋊C₄	—	73	1	no	—
334	C₂×C₂²⋊C₄	—	146	1	no	—
335	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
336	#107	—	146	2	no	—
337	#106	—	146	2	no	—
338	#106	—	146	1	no	—
339	#106	—	146	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	2	1	no	—
342	C₄⋊C₈	—	73	2	no	—
343	C₄⋊C₈	—	146	1	no	—
344	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
345	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
346	#103	—	146	2	no	—
347	#103	—	146	1	no	—
348	#103	—	146	1	no	—
349	#102	—	146	2	no	—
350	#102	—	146	2	no	—
351	#102	—	146	2	no	—
352	#102	—	146	1	no	—
353	#102	—	146	1	no	—
354	C₂²⋊C₈	—	146	2	no	—
355	C₂²⋊C₈	—	146	2	no	—
356	C₄×C₈	D₂₉₂	1	1	yes	characteristic
357	C₄×C₈	D₂₉₂	1	1	yes	characteristic
358	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
360	C₂⁴	—	146	1	no	—
361	#41	—	292	2	no	—
362	#41	—	292	2	no	—
363	C₂×Q₈	—	146	1	no	—
364	C₂×Q₈	—	146	1	no	—
365	C₂×Q₈	—	146	1	no	—
366	C₂×D₄	—	292	1	no	—
367	C₂×D₄	—	73	4	no	—
368	C₂×D₄	—	73	2	no	—
369	C₂×D₄	—	146	1	no	—
370	C₂×D₄	—	146	2	no	—
371	C₂×D₄	—	146	1	no	—
372	C₂×D₄	—	146	1	no	—
373	C₂×D₄	—	146	1	no	—
374	C₂²×C₄	—	292	2	no	—
375	C₂²×C₄	—	292	2	no	—
376	C₂²×C₄	—	292	1	no	—
377	C₂²×C₄	—	146	1	no	—
378	C₂²×C₄	—	146	2	no	—
379	C₂²×C₄	—	146	2	no	—
380	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
381	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
382	C₂²×C₄	#11924029	1	1	yes	characteristic
383	SD₁₆	—	292	2	no	—
384	SD₁₆	—	292	4	no	—
385	SD₁₆	—	292	2	no	—
386	D₈	—	292	4	no	—
387	M₁₆	—	4	2	no	—
388	M₁₆	—	4	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	1	no	—
393	C₂×C₈	—	292	4	no	—
394	C₂×C₈	—	292	2	no	—
395	C₂×C₈	—	292	4	no	—
396	C₂×C₈	—	146	2	no	—
397	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
398	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
399	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
400	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
401	C₄⋊C₄	—	292	1	no	—
402	C₄⋊C₄	—	292	1	no	—
403	C₄⋊C₄	—	73	2	no	—
404	C₄⋊C₄	—	146	1	no	—
405	C₄⋊C₄	—	146	1	no	—
406	C₄⋊C₄	—	146	1	no	—
407	C₄⋊C₄	—	146	1	no	—
408	C₄⋊C₄	—	146	1	no	—
409	C₄⋊C₄	—	146	1	no	—
410	C₄⋊C₄	—	146	1	no	—
411	C₂²⋊C₄	—	292	1	no	—
412	C₂²⋊C₄	—	292	1	no	—
413	C₂²⋊C₄	—	292	1	no	—
414	C₂²⋊C₄	—	146	2	no	—
415	C₂²⋊C₄	—	146	2	no	—
416	C₄²	—	292	1	no	—
417	C₄²	D₄×D₇₃	1	1	yes	characteristic
418	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
419	C₄²	#11924029	1	1	yes	characteristic
420	C₄²	C₂³×D₇₃	1	1	yes	characteristic
421	C₂³	—	292	2	no	—
422	C₂³	—	292	2	no	—
423	C₂³	—	292	1	no	—
424	C₂³	—	146	4	no	—
425	C₂³	—	146	2	no	—
426	C₂³	#14556566	1	1	yes	characteristic
427	Q₈	—	292	1	no	—
428	Q₈	—	292	1	no	—
429	Q₈	—	292	1	no	—
430	Q₈	—	292	1	no	—
431	Q₈	—	584	1	no	—
432	D₄	—	292	1	no	—
433	D₄	—	292	1	no	—
434	D₄	—	292	1	no	—
435	D₄	—	292	1	no	—
436	D₄	—	584	1	no	—
437	D₄	—	584	2	no	—
438	D₄	—	73	4	no	—
439	D₄	—	146	4	no	—
440	D₄	—	146	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	292	4	no	—
445	C₂×C₄	—	292	2	no	—
446	C₂×C₄	—	292	2	no	—
447	C₂×C₄	—	292	2	no	—
448	C₂×C₄	—	292	1	no	—
449	C₂×C₄	—	292	1	no	—
450	C₂×C₄	—	292	1	no	—
451	C₂×C₄	—	584	2	no	—
452	C₂×C₄	—	146	2	no	—
453	C₂×C₄	#14556566	1	1	yes	characteristic
454	C₂×C₄	#14556566	1	1	yes	characteristic
455	C₂×C₄	#14556566	1	1	yes	characteristic
456	C₂×C₄	SD₁₆×D₇₃	1	2	yes	—
457	C₂×C₄	#14556612	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
460	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	4	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	292	2	no	—
467	C₈	#14556619	1	2	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	292	8	no	—
471	C₂²	—	292	2	no	—
472	C₂²	—	292	2	no	—
473	C₂²	—	584	1	no	—
474	C₂²	—	584	1	no	—
475	C₂²	—	584	1	no	—
476	C₂²	—	146	4	no	—
477	C₂²	#17988817	1	2	yes	—
478	C₂²	C₂×#14556566	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	292	2	no	—
483	C₄	—	584	1	no	—
484	C₄	—	584	1	no	—
485	C₄	—	584	1	no	—
486	C₄	#17988817	1	2	yes	—
487	C₄	C₂×SD₁₆×D₇₃	1	1	yes	characteristic
488	C₄	C₂×#14556612	1	1	yes	characteristic
489	C₄	C₂×#14556619	1	1	yes	characteristic
490	C₄	#17989387	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	292	4	no	—
493	C₂	—	1168	1	no	—
494	C₂	#22619397	1	1	yes	characteristic
495	C₂	C₂×#17988817	1	1	yes	characteristic
496	C₂	#22619652	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14556566
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1566	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	#22619397	C₂
hypercenter	#1566	D₇₃
hypocenter	C₇₃	#19254
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1566

Complements

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

N	H ≅ G/N	type
1. #22620490	C₂	semidirect
2. #22619730	C₂	semidirect
4. C₂×C₈×D₂₉₂	C₂	semidirect
5. #22609355	C₂	semidirect
6. #22609341	C₂	semidirect
7. #22609307	C₂	semidirect
8. #22609273	C₂	semidirect
9. #22608622	C₂	semidirect
10. #22608609	C₂	semidirect
11. C₇₃×#1566	C₂	semidirect
17. #17988985	C₂²	semidirect
18. #17988960	C₂²	semidirect
19. #17988938	C₂²	semidirect
20. #17988934	C₂²	semidirect
40. #17988335	C₂²	semidirect
41. #17988334	C₂²	semidirect
42. #17988332	C₂²	semidirect
43. #17988330	C₂²	semidirect
47. #334×C₇₃	C₂²	semidirect
48. #334×C₇₃	C₂²	semidirect
122. C₂×D₂₉₂	SD₁₆	semidirect
217. C₈×C₇₃	AGL(1,ℤ/8)	semidirect
257. #1566	D₇₃	semidirect
260. C₇₃	#19254	semidirect
292. #334	C₂×D₇₃	semidirect
293. #334	C₂×D₇₃	semidirect
467. C₈	#14556619	semidirect

Maximal subgroups

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

subgroup	index
#22620490	2
#22619730	2
#22619397	2
C₂×C₈×D₂₉₂	2
#22609355	2
#22609341	2
#22609307	2
#22609273	2
#22608622	2
#22608609	2
C₇₃×#1566	2
#19254	73