Subgroups — #33069189

Order 18688.

774 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620871	C₂	1	2	yes	maximal, complemented
2	#493×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22618862	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	#22609412	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609290	C₂	1	2	yes	maximal, complemented
8	#22609289	C₂	1	2	yes	maximal, complemented
9	#22608676	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608597	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1688	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₇₃	—	2	1	no	—
13	C₂×D₈×D₇₃	—	2	1	no	—
14	#17989141	C₂²	1	1	yes	characteristic
15	#127×D₇₃	C₂²	1	2	yes	—
16	#17988964	C₂²	1	1	yes	characteristic
17	#17988963	C₂²	1	2	yes	—
18	#17988962	—	2	1	no	—
19	#17988962	—	2	1	no	—
20	#17988958	—	2	2	no	—
21	#17988932	—	2	2	no	—
22	#17988788	C₂²	1	2	yes	complemented
23	#17988787	C₂²	1	2	yes	complemented
24	#17988784	C₂²	1	2	yes	complemented
25	#17988739	—	2	2	no	—
26	#17988736	—	2	2	no	—
27	#17988717	C₂²	1	1	yes	characteristic, complemented
28	#17988715	—	2	1	no	—
29	Q₈×#10596831	C₂²	1	1	yes	characteristic, complemented
30	#17988711	—	2	1	no	—
31	#17988711	C₂²	1	1	yes	characteristic, complemented
32	#17988639	C₂²	1	2	yes	—
33	#17988612	—	2	1	no	—
34	#17988609	C₂²	1	1	yes	characteristic
35	#17988544	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988339	C₂²	1	2	yes	complemented
38	#17988338	C₂²	1	1	yes	characteristic, 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×D₄×D₇₃	—	2	2	no	—
48	C₂×D₄×D₇₃	—	2	2	no	—
49	C₂×D₄×D₇₃	—	2	2	no	—
50	C₂×#11924017	—	2	2	no	—
51	C₂×#11924016	—	2	2	no	—
52	C₂×#11924015	—	2	2	no	—
53	C₂×D₅₈₄	—	2	1	no	—
54	C₂×D₅₈₄	—	2	1	no	—
55	C₂×#11924013	—	2	2	no	—
56	C₂×#11924013	—	2	2	no	—
57	D₈×D₇₃	—	4	4	no	—
58	D₈×D₇₃	—	4	4	no	—
59	C₂×#11924011	—	2	1	no	—
60	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
62	#14556590	D₄	1	1	yes	characteristic
63	#14556589	D₄	1	1	yes	characteristic
64	#14556588	C₂³	1	2	yes	—
65	#14556587	—	2	2	no	—
66	#14556587	—	2	2	no	—
67	#14556587	—	2	2	no	—
68	#14556581	—	2	1	no	—
69	#14556571	D₄	1	1	yes	characteristic
70	#14556569	—	2	1	no	—
71	#14556567	D₄	1	1	yes	characteristic
72	C₄×Dic₁₄₆	—	2	1	no	—
73	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
74	#14556548	—	2	1	no	—
75	C₄²×D₇₃	C₂³	1	1	yes	characteristic
76	C₄⋊#10596831	—	2	1	no	—
77	C₄⋊#10596831	C₂³	1	1	yes	characteristic
78	C₄⋊#10596831	C₂³	1	2	yes	—
79	#14556520	—	2	1	no	—
80	#14556520	—	2	1	no	—
81	#14556520	—	2	1	no	—
82	#14556513	—	2	2	no	—
83	#14556512	—	2	2	no	—
84	#14556511	—	2	2	no	—
85	#14556503	—	2	2	no	—
86	#14556501	—	2	1	no	—
87	C₄×#10596831	—	2	1	no	—
88	C₄×#10596831	C₂³	1	1	yes	characteristic
89	C₈×Dic₇₃	—	2	1	no	—
90	C₈×Dic₇₃	—	2	2	no	—
91	C₈×Dic₇₃	D₄	1	1	yes	characteristic
92	C₈×Dic₇₃	D₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₇₃	—	2	2	no	—
94	C₂×D₈×C₇₃	—	2	1	no	—
95	C₂×D₈×C₇₃	—	2	1	no	—
96	#127×C₇₃	C₂³	1	2	yes	—
97	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₃	—	2	1	no	—
99	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
101	#102×C₇₃	—	2	2	no	—
102	#97×C₇₃	—	2	1	no	—
103	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
104	C₂³×D₇₃	—	4	2	no	—
105	C₂×Dic₁₄₆	—	2	1	no	—
106	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
107	C₂×D₂₉₂	—	2	2	no	—
108	C₂×D₂₉₂	—	2	2	no	—
109	C₂×D₂₉₂	—	2	2	no	—
110	C₂×C₂²⋊D₇₃	—	4	2	no	—
111	C₂×C₂²⋊D₇₃	—	4	2	no	—
112	C₂×C₂²⋊D₇₃	—	4	2	no	—
113	D₄×D₇₃	—	4	4	no	—
114	D₄×D₇₃	—	4	4	no	—
115	D₄×D₇₃	—	8	2	no	—
116	D₄×D₇₃	—	8	2	no	—
117	D₄×D₇₃	—	8	4	no	—
118	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
121	#11924017	—	8	2	no	—
122	#11924016	—	8	2	no	—
123	#11924015	—	8	2	no	—
124	D₅₈₄	—	4	2	no	—
125	D₅₈₄	—	4	2	no	—
126	#11924013	—	4	4	no	—
127	#11924013	—	4	4	no	—
128	#11924011	—	4	2	no	—
129	C₂×#10596831	—	2	2	no	—
130	C₂×#10596831	—	2	1	no	—
131	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
132	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
133	C₈×D₇₃	—	2	2	no	—
134	C₈×D₇₃	SD₁₆	1	4	yes	complemented
135	C₄⋊Dic₇₃	—	2	1	no	—
136	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
137	#11924007	—	2	1	no	—
138	#11924007	—	2	1	no	—
139	#11924007	—	2	1	no	—
140	#11924007	—	2	1	no	—
141	#11924007	—	2	1	no	—
142	#11924005	—	2	1	no	—
143	#11924005	—	2	1	no	—
144	C₄×Dic₇₃	—	2	1	no	—
145	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
146	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
147	C₄×Dic₇₃	#41	1	1	yes	characteristic
148	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₇₃	—	2	2	no	—
150	C₂×D₄×C₇₃	—	2	2	no	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	SD₁₆×C₇₃	—	8	2	no	—
153	D₈×C₇₃	—	4	2	no	—
154	D₈×C₇₃	—	4	2	no	—
155	C₂×C₈×C₇₃	—	2	1	no	—
156	C₂×C₈×C₇₃	—	2	2	no	—
157	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₇₃	—	2	1	no	—
160	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₇₃	—	2	1	no	—
162	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
163	C₂³×C₇₃	—	4	2	no	—
164	C₂²×D₇₃	—	4	2	no	—
165	C₂²×D₇₃	—	8	4	no	—
166	C₂²×D₇₃	—	8	4	no	—
167	C₂²×D₇₃	—	8	4	no	—
168	C₂²×D₇₃	#121	1	1	yes	characteristic
169	Q₈×C₇₃	—	2	2	no	—
170	D₄×C₇₃	—	4	2	no	—
171	D₄×C₇₃	—	4	2	no	—
172	D₄×C₇₃	—	4	2	no	—
173	D₄×C₇₃	—	4	2	no	—
174	D₄×C₇₃	—	8	2	no	—
175	C₂×C₄×C₇₃	—	2	1	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₇₃	—	8	4	no	—
181	C₂²⋊D₇₃	—	8	4	no	—
182	C₂²⋊D₇₃	—	8	4	no	—
183	C₂×Dic₇₃	—	2	1	no	—
184	C₂×Dic₇₃	—	2	1	no	—
185	C₂×Dic₇₃	#121	1	1	yes	characteristic
186	C₂×Dic₇₃	#121	1	1	yes	characteristic
187	C₂×Dic₇₃	#121	1	1	yes	characteristic
188	D₂₉₂	—	4	2	no	—
189	D₂₉₂	—	4	2	no	—
190	D₂₉₂	—	4	2	no	—
191	D₂₉₂	—	4	2	no	—
192	D₂₉₂	—	8	2	no	—
193	C₄×D₇₃	—	2	2	no	—
194	C₄×D₇₃	—	2	2	no	—
195	C₄×D₇₃	C₂×SD₁₆	1	2	yes	—
196	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
197	Dic₁₄₆	—	2	2	no	—
198	Dic₁₄₆	—	4	2	no	—
199	C₈×C₇₃	—	2	1	no	—
200	C₈×C₇₃	—	4	1	no	—
201	C₈×C₇₃	—	4	2	no	—
202	C₈×C₇₃	C₂×SD₁₆	1	2	yes	—
203	#10596831	—	2	1	no	—
204	#10596831	—	4	1	no	—
205	#10596831	—	4	2	no	—
206	#10596831	C₂×SD₁₆	1	2	yes	—
207	C₂²×C₇₃	—	8	2	no	—
208	C₂²×C₇₃	—	8	2	no	—
209	C₂²×C₇₃	—	8	2	no	—
210	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
211	C₂×D₇₃	—	2	1	no	—
212	C₂×D₇₃	—	2	1	no	—
213	C₂×D₇₃	—	8	2	no	—
214	C₂×D₇₃	—	8	2	no	—
215	C₂×D₇₃	—	8	2	no	—
216	C₂×D₇₃	—	16	8	no	—
217	C₂×D₇₃	#460	1	2	yes	—
218	C₄×C₇₃	—	2	1	no	—
219	C₄×C₇₃	—	4	1	no	—
220	C₄×C₇₃	—	4	1	no	—
221	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
222	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	C₄×C₇₃	#576	1	2	yes	—
224	Dic₇₃	—	2	1	no	—
225	Dic₇₃	—	4	1	no	—
226	Dic₇₃	—	4	1	no	—
227	Dic₇₃	#460	1	2	yes	—
228	Dic₇₃	#472	1	2	yes	—
229	#19203	—	73	1	no	maximal, Sylow
230	C₂×C₇₃	—	16	2	no	—
231	C₂×C₇₃	C₂×#460	1	1	yes	characteristic
232	C₂×C₇₃	#3058	1	1	yes	characteristic
233	C₂×C₇₃	C₂×#472	1	1	yes	characteristic
234	D₇₃	—	2	2	no	—
235	D₇₃	—	16	2	no	—
236	#3208	—	73	2	no	—
237	C₂×#493	—	73	1	no	—
238	#2960	—	73	1	no	—
239	#1688	—	73	1	no	—
240	#1688	—	73	1	no	—
241	#1688	—	73	1	no	—
242	#1688	D₇₃	1	1	yes	characteristic, complemented
243	#1668	—	73	2	no	—
244	#1668	—	73	2	no	—
245	#1564	—	73	1	no	—
246	#1545	—	73	2	no	—
247	C₇₃	#19203	1	1	yes	characteristic, complemented, Sylow
248	C₂²×D₈	—	146	1	no	—
249	C₂²×D₈	—	146	1	no	—
250	#533	—	73	1	no	—
251	C₂×#127	—	73	2	no	—
252	#493	—	73	2	no	—
253	#493	—	73	1	no	—
254	#493	—	146	1	no	—
255	#493	—	146	1	no	—
256	#493	C₂×D₇₃	1	1	yes	characteristic
257	#492	—	146	2	no	—
258	#486	—	146	2	no	—
259	#460	—	73	2	no	—
260	#460	—	73	2	no	—
261	#460	—	73	2	no	—
262	#460	C₂×D₇₃	1	2	yes	complemented
263	#450	—	146	2	no	—
264	#450	—	146	2	no	—
265	#446	—	73	1	no	—
266	#446	—	146	1	no	—
267	#446	C₂×D₇₃	1	1	yes	characteristic, complemented
268	C₈×Q₈	—	73	1	no	—
269	C₈×Q₈	—	73	1	no	—
270	C₈×Q₈	—	146	1	no	—
271	#431	—	73	2	no	—
272	#424	—	146	1	no	—
273	#423	—	73	1	no	—
274	#405	—	146	1	no	—
275	C₂×C₄×C₈	—	73	1	no	—
276	#335	—	73	2	no	—
277	#334	—	73	1	no	—
278	#334	C₂×D₇₃	1	1	yes	characteristic, complemented
279	#331	—	73	2	no	—
280	#331	—	73	2	no	—
281	#331	—	73	2	no	—
282	#331	C₂×D₇₃	1	2	yes	complemented
283	C₂²×D₄	—	146	2	no	—
284	C₂²×D₄	—	146	2	no	—
285	C₂²×D₄	—	146	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	146	2	no	—
288	C₂×SD₁₆	—	146	2	no	—
289	C₂×SD₁₆	—	146	2	no	—
290	C₂×D₈	—	2	1	no	—
291	C₂×D₈	—	2	1	no	—
292	C₂×D₈	—	292	4	no	—
293	C₂×D₈	—	292	4	no	—
294	C₂×D₈	—	146	2	no	—
295	C₂×D₈	—	146	2	no	—
296	C₂×D₈	—	146	1	no	—
297	C₂×D₈	—	146	1	no	—
298	C₂×M₁₆	—	146	1	no	—
299	C₂²×C₈	—	73	1	no	—
300	C₂²×C₈	—	73	1	no	—
301	C₄⋊Q₈	—	73	1	no	—
302	C₄⋊Q₈	—	73	1	no	—
303	#127	—	73	2	no	—
304	#127	—	146	2	no	—
305	#127	—	146	2	no	—
306	#127	—	146	2	no	—
307	#127	C₂²×D₇₃	1	2	yes	—
308	#125	—	146	1	no	—
309	C₂²⋊Q₈	—	73	1	no	—
310	C₂²⋊Q₈	—	73	1	no	—
311	C₂²⋊Q₈	—	146	1	no	—
312	C₄×Q₈	—	73	1	no	—
313	C₄×Q₈	—	146	1	no	—
314	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
315	#117	—	146	1	no	—
316	C₂×C₄²	—	73	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	73	1	no	—
319	C₄⋊C₈	—	73	2	no	—
320	C₄⋊C₈	—	146	1	no	—
321	C₄⋊C₈	—	146	1	no	—
322	C₄⋊C₈	—	146	1	no	—
323	C₄⋊C₈	—	146	1	no	—
324	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
325	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
326	#102	—	2	2	no	—
327	#102	—	146	2	no	—
328	#102	—	146	2	no	—
329	#102	—	146	2	no	—
330	C₂²⋊C₈	—	146	2	no	—
331	#97	—	2	1	no	—
332	#97	—	146	1	no	—
333	C₄×C₈	—	73	1	no	—
334	C₄×C₈	—	73	1	no	—
335	C₄×C₈	—	73	1	no	—
336	C₄×C₈	—	146	1	no	—
337	C₄×C₈	—	146	2	no	—
338	C₄×C₈	—	146	1	no	—
339	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
340	C₂⁴	—	292	2	no	—
341	C₂×Q₈	—	73	1	no	—
342	C₂×Q₈	—	146	1	no	—
343	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	292	4	no	—
348	C₂×D₄	—	292	4	no	—
349	C₂×D₄	—	292	2	no	—
350	C₂×D₄	—	292	2	no	—
351	C₂×D₄	—	292	2	no	—
352	C₂×D₄	—	584	2	no	—
353	C₂×D₄	—	584	2	no	—
354	C₂×D₄	—	584	4	no	—
355	C₂×D₄	—	146	2	no	—
356	C₂×D₄	—	146	2	no	—
357	C₂×D₄	—	146	2	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	1	no	—
360	C₂²×C₄	—	73	1	no	—
361	SD₁₆	—	8	2	no	—
362	SD₁₆	—	584	2	no	—
363	SD₁₆	—	584	2	no	—
364	SD₁₆	—	584	2	no	—
365	D₈	—	4	2	no	—
366	D₈	—	4	2	no	—
367	D₈	—	292	2	no	—
368	D₈	—	292	4	no	—
369	D₈	—	292	4	no	—
370	D₈	—	292	2	no	—
371	M₁₆	—	292	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	73	1	no	—
375	C₂×C₈	—	73	4	no	—
376	C₂×C₈	—	73	1	no	—
377	C₂×C₈	—	146	2	no	—
378	C₂×C₈	—	146	1	no	—
379	C₂×C₈	—	146	2	no	—
380	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
381	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	73	1	no	—
384	C₄⋊C₄	—	146	1	no	—
385	C₄⋊C₄	—	146	1	no	—
386	C₄⋊C₄	—	146	1	no	—
387	C₄⋊C₄	—	146	1	no	—
388	C₄⋊C₄	—	146	1	no	—
389	C₄⋊C₄	—	146	1	no	—
390	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
391	C₂²⋊C₄	—	146	1	no	—
392	C₂²⋊C₄	—	146	1	no	—
393	C₄²	—	2	1	no	—
394	C₄²	—	73	1	no	—
395	C₄²	—	73	1	no	—
396	C₄²	—	73	1	no	—
397	C₄²	—	146	1	no	—
398	C₄²	C₂³×D₇₃	1	1	yes	characteristic
399	C₂³	—	4	2	no	—
400	C₂³	—	292	2	no	—
401	C₂³	—	584	4	no	—
402	C₂³	—	584	4	no	—
403	C₂³	—	584	4	no	—
404	C₂³	—	73	1	no	—
405	Q₈	—	2	2	no	—
406	Q₈	—	292	2	no	—
407	Q₈	—	146	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	2	no	—
412	D₄	—	8	2	no	—
413	D₄	—	292	2	no	—
414	D₄	—	292	2	no	—
415	D₄	—	292	2	no	—
416	D₄	—	292	2	no	—
417	D₄	—	584	2	no	—
418	D₄	—	584	4	no	—
419	D₄	—	584	4	no	—
420	D₄	—	584	4	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	73	1	no	—
424	C₂×C₄	—	73	1	no	—
425	C₂×C₄	—	73	2	no	—
426	C₂×C₄	—	73	2	no	—
427	C₂×C₄	—	73	1	no	—
428	C₂×C₄	—	146	2	no	—
429	C₂×C₄	—	146	1	no	—
430	C₂×C₄	—	146	1	no	—
431	C₂×C₄	—	146	2	no	—
432	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
433	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
434	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
435	C₈	—	2	1	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	292	2	no	—
439	C₈	—	292	1	no	—
440	C₈	—	73	2	no	—
441	C₈	—	146	1	no	—
442	C₈	SD₁₆×D₇₃	1	2	yes	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	584	2	no	—
447	C₂²	—	584	2	no	—
448	C₂²	—	584	2	no	—
449	C₂²	—	73	2	no	—
450	C₂²	—	1168	8	no	—
451	C₂²	—	146	1	no	—
452	C₂²	—	146	1	no	—
453	C₂²	#121×D₇₃	1	1	yes	characteristic
454	C₄	—	2	1	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	1	no	—
457	C₄	—	292	1	no	—
458	C₄	—	292	1	no	—
459	C₄	—	73	2	no	—
460	C₄	—	73	2	no	—
461	C₄	—	146	1	no	—
462	C₄	C₂×SD₁₆×D₇₃	1	1	yes	characteristic
463	C₄	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
464	C₄	#17989391	1	2	yes	—
465	C₂	—	16	2	no	—
466	C₂	—	1168	2	no	—
467	C₂	—	146	2	no	—
468	C₂	#460×D₇₃	1	1	yes	characteristic
469	C₂	#22619577	1	1	yes	characteristic
470	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	#19203
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
1. #22620871	C₂	semidirect
3. #22618862	C₂	semidirect
4. #22609416	C₂	semidirect
5. #22609415	C₂	semidirect
6. #22609412	C₂	semidirect
7. #22609290	C₂	semidirect
8. #22609289	C₂	semidirect
9. #22608676	C₂	semidirect
10. #22608597	C₂	semidirect
11. C₇₃×#1688	C₂	semidirect
22. #17988788	C₂²	semidirect
23. #17988787	C₂²	semidirect
24. #17988784	C₂²	semidirect
27. #17988717	C₂²	semidirect
29. Q₈×#10596831	C₂²	semidirect
31. #17988711	C₂²	semidirect
37. #17988339	C₂²	semidirect
38. #17988338	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
134. C₈×D₇₃	SD₁₆	semidirect
242. #1688	D₇₃	semidirect
247. C₇₃	#19203	semidirect
262. #460	C₂×D₇₃	semidirect
267. #446	C₂×D₇₃	semidirect
278. #334	C₂×D₇₃	semidirect
282. #331	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22620871	2
#493×D₇₃	2
#22618862	2
#22609416	2
#22609415	2
#22609412	2
#22609290	2
#22609289	2
#22608676	2
#22608597	2
C₇₃×#1688	2
#19203	73