Subgroups — #33121927

Order 18688.

1290 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624705	C₂	1	1	yes	maximal, characteristic, complemented
2	#22619651	C₂	1	2	yes	maximal, complemented
3	#22619279	C₂	1	2	yes	maximal, complemented
4	#22611218	C₂	1	2	yes	maximal, complemented
5	#22611035	C₂	1	2	yes	maximal, complemented
6	#22610824	C₂	1	2	yes	maximal, complemented
7	#22609981	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609881	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2932	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989423	C₂²	1	2	yes	—
11	#17989404	—	2	2	no	—
12	#17989399	—	2	4	no	—
13	#17989392	—	2	2	no	—
14	#17989387	—	2	2	no	—
15	#17989387	C₂²	1	2	yes	—
16	#17989385	C₂²	1	4	yes	complemented
17	C₂×#14556613	—	2	2	no	—
18	C₂×#14556613	C₂²	1	2	yes	—
19	#17988862	—	2	2	no	—
20	#17988857	—	2	2	no	—
21	#17988850	—	2	4	no	—
22	#17988769	—	2	2	no	—
23	#17988764	—	2	2	no	—
24	#17988759	—	2	2	no	—
25	#17988754	—	2	2	no	—
26	C₂×#14556527	C₂²	1	2	yes	complemented
27	C₂×#14556519	C₂²	1	4	yes	complemented
28	#17988571	C₂²	1	2	yes	—
29	#17988569	C₂²	1	4	yes	complemented
30	#17988553	C₂²	1	4	yes	complemented
31	#17988345	C₂²	1	2	yes	complemented
32	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
33	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	#532×C₇₃	C₂²	1	1	yes	characteristic
35	#435×C₇₃	—	2	2	no	—
36	#435×C₇₃	—	2	2	no	—
37	#423×C₇₃	C₂²	1	1	yes	characteristic, complemented
38	#408×C₇₃	C₂²	1	1	yes	characteristic
39	#408×C₇₃	C₂²	1	1	yes	characteristic, complemented
40	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	#14556639	—	2	2	no	—
42	#14556638	—	2	4	no	—
43	#14556637	—	2	4	no	—
44	#14556636	—	2	2	no	—
45	#14556636	—	2	4	no	—
46	C₂×#11924028	—	2	4	no	—
47	C₂×#11924028	C₂³	1	4	yes	—
48	#41×D₇₃	—	4	4	no	—
49	#14556624	—	2	8	no	—
50	#14556624	—	2	4	no	—
51	#14556622	—	2	4	no	—
52	#14556621	—	2	4	no	—
53	#14556619	—	2	8	no	—
54	#14556619	—	2	4	no	—
55	#14556617	—	2	4	no	—
56	#14556616	—	2	4	no	—
57	#14556613	—	2	4	no	—
58	#14556613	—	2	4	no	—
59	#14556613	—	2	2	no	—
60	#14556613	—	2	4	no	—
61	#14556613	—	2	2	no	—
62	#14556613	—	2	2	no	—
63	#14556613	—	2	2	no	—
64	#14556611	—	4	4	no	—
65	C₂×Dic₂₉₂	—	2	2	no	—
66	C₂×Dic₂₉₂	D₄	1	2	yes	complemented
67	C₂×#11924017	—	2	4	no	—
68	C₂×#11924017	D₄	1	4	yes	complemented
69	C₂×D₅₈₄	—	2	2	no	—
70	C₂×D₅₈₄	D₄	1	2	yes	complemented
71	C₂×#11924012	C₂³	1	4	yes	—
72	#14556527	—	2	2	no	—
73	#14556527	—	2	2	no	—
74	#14556519	—	2	4	no	—
75	#14556519	—	2	4	no	—
76	#14556510	—	2	2	no	—
77	#14556509	—	2	4	no	—
78	#14556508	—	2	2	no	—
79	#14556507	—	2	4	no	—
80	#14556503	—	4	4	no	—
81	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
82	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
83	#131×C₇₃	—	2	2	no	—
84	#131×C₇₃	—	2	2	no	—
85	#131×C₇₃	—	2	2	no	—
86	#131×C₇₃	—	2	2	no	—
87	C₂×M₁₆×C₇₃	—	2	1	no	—
88	C₂×M₁₆×C₇₃	D₄	1	2	yes	—
89	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₇₃	—	2	1	no	—
92	C₂²×C₈×C₇₃	D₄	1	2	yes	—
93	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
96	#127×C₇₃	D₄	1	1	yes	characteristic
97	#124×C₇₃	D₄	1	1	yes	characteristic
98	#124×C₇₃	D₄	1	1	yes	characteristic
99	#121×C₇₃	—	2	2	no	—
100	C₄×D₄×C₇₃	—	2	2	no	—
101	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₇₃	—	2	2	no	—
103	C₂²⋊C₈×C₇₃	—	2	2	no	—
104	C₂²⋊C₈×C₇₃	—	2	2	no	—
105	#97×C₇₃	—	2	1	no	—
106	#97×C₇₃	—	2	1	no	—
107	#11924029	—	4	4	no	—
108	#11924028	—	2	8	no	—
109	#11924028	—	2	4	no	—
110	#11924028	—	2	4	no	—
111	#11924028	—	2	4	no	—
112	#11924028	—	2	4	no	—
113	#11924028	—	4	4	no	—
114	#11924028	—	4	4	no	—
115	#11924027	—	4	4	no	—
116	#11924027	—	4	8	no	—
117	C₂×Dic₁₄₆	—	2	4	no	—
118	C₂×Dic₁₄₆	C₂×D₄	1	4	yes	—
119	Q₈×D₇₃	—	4	4	no	—
120	C₂×D₂₉₂	—	2	4	no	—
121	C₂×D₂₉₂	C₂×D₄	1	4	yes	—
122	C₂×C₂²⋊D₇₃	—	2	4	no	—
123	C₂×C₂²⋊D₇₃	—	4	4	no	—
124	D₄×D₇₃	—	4	4	no	—
125	D₄×D₇₃	—	4	8	no	—
126	C₂×C₄×D₇₃	—	2	4	no	—
127	C₂×C₄×D₇₃	—	4	4	no	—
128	Dic₂₉₂	—	2	4	no	—
129	Dic₂₉₂	—	2	2	no	—
130	Dic₂₉₂	—	2	2	no	—
131	#11924018	—	4	4	no	—
132	#11924017	—	2	8	no	—
133	#11924017	—	2	4	no	—
134	#11924017	—	2	4	no	—
135	#11924016	—	4	4	no	—
136	#11924015	—	4	4	no	—
137	D₅₈₄	—	2	4	no	—
138	D₅₈₄	—	2	2	no	—
139	D₅₈₄	—	2	2	no	—
140	#11924013	—	4	4	no	—
141	#11924012	—	2	4	no	—
142	#11924012	—	2	4	no	—
143	C₂×#10596831	—	2	4	no	—
144	#41×C₇₃	—	2	2	no	—
145	#41×C₇₃	—	2	2	no	—
146	#41×C₇₃	—	2	2	no	—
147	#41×C₇₃	—	2	2	no	—
148	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂×D₄×C₇₃	—	2	1	no	—
151	C₂×D₄×C₇₃	—	2	2	no	—
152	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₇₃	#41	1	2	yes	—
155	C₂²×C₄×C₇₃	—	2	1	no	—
156	C₂²×C₄×C₇₃	—	2	1	no	—
157	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
159	M₁₆×C₇₃	—	2	2	no	—
160	M₁₆×C₇₃	—	2	4	no	—
161	M₁₆×C₇₃	—	2	2	no	—
162	M₁₆×C₇₃	—	4	1	no	—
163	M₁₆×C₇₃	—	4	1	no	—
164	C₂×C₈×C₇₃	—	2	2	no	—
165	C₂×C₈×C₇₃	—	2	2	no	—
166	C₂×C₈×C₇₃	—	2	1	no	—
167	C₂×C₈×C₇₃	—	2	1	no	—
168	C₂×C₈×C₇₃	—	2	2	no	—
169	C₂×C₈×C₇₃	—	4	2	no	—
170	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
172	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₇₃	—	2	2	no	—
176	C₂²⋊C₄×C₇₃	—	2	2	no	—
177	C₂²⋊C₄×C₇₃	—	2	2	no	—
178	C₄²×C₇₃	—	2	1	no	—
179	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
181	C₂³×C₇₃	—	2	1	no	—
182	C₂³×C₇₃	#121	1	2	yes	—
183	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
184	C₂²×D₇₃	—	2	4	no	—
185	C₂²×D₇₃	—	4	4	no	—
186	Q₈×C₇₃	—	2	2	no	—
187	Q₈×C₇₃	—	2	2	no	—
188	D₄×C₇₃	—	2	4	no	—
189	D₄×C₇₃	—	2	2	no	—
190	D₄×C₇₃	—	2	2	no	—
191	D₄×C₇₃	—	4	2	no	—
192	D₄×C₇₃	—	8	2	no	—
193	C₂×C₄×C₇₃	—	2	2	no	—
194	C₂×C₄×C₇₃	—	2	2	no	—
195	C₂×C₄×C₇₃	—	2	1	no	—
196	C₂×C₄×C₇₃	—	2	1	no	—
197	C₂×C₄×C₇₃	—	2	1	no	—
198	C₂×C₄×C₇₃	—	4	1	no	—
199	C₂×C₄×C₇₃	—	4	1	no	—
200	C₂×C₄×C₇₃	—	8	1	no	—
201	C₂×C₄×C₇₃	#121	1	2	yes	—
202	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
206	C₂²⋊D₇₃	—	4	8	no	—
207	C₂²⋊D₇₃	—	4	4	no	—
208	C₂²⋊D₇₃	—	4	4	no	—
209	C₂×Dic₇₃	—	2	4	no	—
210	C₂×Dic₇₃	—	4	4	no	—
211	D₂₉₂	—	2	4	no	—
212	D₂₉₂	—	2	4	no	—
213	D₂₉₂	—	4	4	no	—
214	C₄×D₇₃	—	4	8	no	—
215	C₄×D₇₃	—	4	4	no	—
216	C₄×D₇₃	—	4	4	no	—
217	Dic₁₄₆	—	2	4	no	—
218	Dic₁₄₆	—	2	4	no	—
219	Dic₁₄₆	—	4	4	no	—
220	C₈×C₇₃	—	2	2	no	—
221	C₈×C₇₃	—	4	1	no	—
222	C₈×C₇₃	—	4	1	no	—
223	C₈×C₇₃	#120	1	1	yes	characteristic
224	C₈×C₇₃	#120	1	1	yes	characteristic
225	C₈×C₇₃	#120	1	2	yes	—
226	#10596831	—	4	4	no	—
227	C₂²×C₇₃	—	2	2	no	—
228	C₂²×C₇₃	—	4	1	no	—
229	C₂²×C₇₃	—	4	2	no	—
230	C₂²×C₇₃	—	4	2	no	—
231	C₂²×C₇₃	—	4	1	no	—
232	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
233	C₂²×C₇₃	#546	1	2	yes	—
234	C₂×D₇₃	—	4	4	no	—
235	C₂×D₇₃	—	8	4	no	—
236	C₂×D₇₃	—	16	4	no	—
237	C₄×C₇₃	—	2	2	no	—
238	C₄×C₇₃	—	4	1	no	—
239	C₄×C₇₃	—	4	1	no	—
240	C₄×C₇₃	—	4	1	no	—
241	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
242	C₄×C₇₃	#535	1	1	yes	characteristic
243	C₄×C₇₃	D₄²	1	2	yes	—
244	Dic₇₃	—	4	4	no	—
245	#24288	—	73	1	no	maximal, Sylow
246	C₂×C₇₃	—	2	1	no	—
247	C₂×C₇₃	—	2	2	no	—
248	C₂×C₇₃	—	4	2	no	—
249	C₂×C₇₃	—	8	1	no	—
250	C₂×C₇₃	#2408	1	1	yes	characteristic
251	D₇₃	—	8	4	no	—
252	#3584	—	73	1	no	—
253	#3067	—	73	2	no	—
254	#3018	—	73	2	no	—
255	#2932	D₇₃	1	1	yes	characteristic, complemented
256	#2050	—	73	2	no	—
257	#2017	—	73	2	no	—
258	#1975	—	73	2	no	—
259	#1813	—	73	1	no	—
260	#1791	—	73	2	no	—
261	C₇₃	#24288	1	1	yes	characteristic, complemented, Sylow
262	#585	—	73	2	no	—
263	#578	—	146	2	no	—
264	#577	—	146	4	no	—
265	#576	—	146	2	no	—
266	#575	—	73	4	no	—
267	#575	—	73	2	no	—
268	#575	—	146	2	no	—
269	C₂×#135	—	73	2	no	—
270	C₂×#135	—	146	2	no	—
271	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
272	C₂×#131	C₂×D₇₃	1	1	yes	characteristic, complemented
273	#532	C₂×D₇₃	1	1	yes	characteristic
274	#473	—	146	2	no	—
275	#472	—	146	2	no	—
276	#471	—	146	4	no	—
277	#456	—	146	2	no	—
278	#455	—	146	2	no	—
279	#454	—	146	2	no	—
280	#453	—	146	2	no	—
281	#435	—	2	2	no	—
282	#435	—	2	2	no	—
283	C₂×#108	—	73	2	no	—
284	#423	C₂×D₇₃	1	1	yes	characteristic, complemented
285	C₂×#104	—	73	4	no	—
286	#413	—	73	2	no	—
287	#413	—	73	4	no	—
288	#408	—	73	4	no	—
289	#408	C₂×D₇₃	1	1	yes	characteristic
290	#408	C₂×D₇₃	1	1	yes	characteristic, complemented
291	C₂×#97	C₂×D₇₃	1	1	yes	characteristic, complemented
292	#338	—	73	2	no	—
293	2₋¹⁺⁴	—	146	2	no	—
294	2₋¹⁺⁴	—	146	4	no	—
295	H(5,𝔽₂)	—	146	2	no	—
296	H(5,𝔽₂)	—	146	4	no	—
297	H(5,𝔽₂)	—	146	4	no	—
298	C₂×#41	—	292	4	no	—
299	C₂×#41	—	73	4	no	—
300	C₂×#41	—	146	4	no	—
301	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
302	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
303	#137	—	146	4	no	—
304	#137	—	146	8	no	—
305	#137	—	146	4	no	—
306	#137	—	146	4	no	—
307	AGL(1,ℤ/8)	—	146	4	no	—
308	AGL(1,ℤ/8)	—	146	8	no	—
309	AGL(1,ℤ/8)	—	146	4	no	—
310	AGL(1,ℤ/8)	—	146	4	no	—
311	#135	—	292	4	no	—
312	#135	—	146	4	no	—
313	#135	—	146	4	no	—
314	#135	—	146	2	no	—
315	#135	—	146	2	no	—
316	#135	—	146	2	no	—
317	#135	—	146	2	no	—
318	#135	—	146	4	no	—
319	C₂×Q₁₆	—	73	2	no	—
320	C₂×Q₁₆	—	146	2	no	—
321	C₂×SD₁₆	—	73	4	no	—
322	C₂×SD₁₆	—	146	4	no	—
323	C₂×D₈	—	73	2	no	—
324	C₂×D₈	—	146	2	no	—
325	#131	—	2	2	no	—
326	#131	—	2	2	no	—
327	#131	—	2	2	no	—
328	#131	—	2	2	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	73	4	no	—
331	C₂×M₁₆	C₂²⋊D₇₃	1	2	yes	—
332	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
333	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
336	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
337	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
338	C₄⋊Q₈	D₂₉₂	1	1	yes	characteristic
339	#127	D₂₉₂	1	1	yes	characteristic
340	#124	D₂₉₂	1	1	yes	characteristic
341	#124	D₂₉₂	1	1	yes	characteristic
342	#121	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
345	#108	—	146	2	no	—
346	#108	—	146	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	#104	—	146	4	no	—
349	#104	—	146	4	no	—
350	#101	—	146	4	no	—
351	#101	—	146	2	no	—
352	#100	—	146	4	no	—
353	#100	—	146	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₂²⋊C₈	—	292	4	no	—
357	#97	—	2	1	no	—
358	#97	—	2	1	no	—
359	#41	—	2	2	no	—
360	#41	—	2	2	no	—
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	292	4	no	—
364	#41	—	292	4	no	—
365	#41	—	292	4	no	—
366	#41	—	292	8	no	—
367	#41	—	292	4	no	—
368	#41	—	146	8	no	—
369	#41	—	146	4	no	—
370	#41	—	146	4	no	—
371	#41	—	146	4	no	—
372	#41	—	146	4	no	—
373	C₂×Q₈	—	292	4	no	—
374	C₂×Q₈	—	73	4	no	—
375	C₂×Q₈	—	146	4	no	—
376	C₂×Q₈	C₂×D₂₉₂	1	1	yes	characteristic
377	C₂×Q₈	C₂×D₂₉₂	1	1	yes	characteristic
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	292	8	no	—
381	C₂×D₄	—	292	4	no	—
382	C₂×D₄	—	292	4	no	—
383	C₂×D₄	—	73	4	no	—
384	C₂×D₄	—	146	4	no	—
385	C₂×D₄	—	146	4	no	—
386	C₂×D₄	C₂×D₂₉₂	1	1	yes	characteristic
387	C₂×D₄	C₂×D₂₉₂	1	1	yes	characteristic
388	C₂×D₄	#11924028	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	292	4	no	—
392	C₂²×C₄	—	146	4	no	—
393	C₂²×C₄	C₂×C₂²⋊D₇₃	1	2	yes	—
394	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
395	Q₁₆	—	292	4	no	—
396	Q₁₆	—	146	4	no	—
397	Q₁₆	—	146	2	no	—
398	Q₁₆	—	146	2	no	—
399	SD₁₆	—	292	4	no	—
400	SD₁₆	—	292	4	no	—
401	SD₁₆	—	146	8	no	—
402	SD₁₆	—	146	4	no	—
403	SD₁₆	—	146	4	no	—
404	D₈	—	292	4	no	—
405	D₈	—	146	4	no	—
406	D₈	—	146	2	no	—
407	D₈	—	146	2	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	4	1	no	—
413	M₁₆	—	146	4	no	—
414	M₁₆	—	146	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	146	4	no	—
422	C₂×C₈	D₄×D₇₃	1	2	yes	—
423	C₂×C₈	D₄×D₇₃	1	2	yes	—
424	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
425	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
426	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
427	C₄⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₄²	—	2	1	no	—
431	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
432	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
433	C₂³	—	2	1	no	—
434	C₂³	—	292	4	no	—
435	C₂³	—	146	4	no	—
436	C₂³	#14556565	1	2	yes	—
437	C₂³	C₂×#11924028	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	292	4	no	—
441	Q₈	—	146	4	no	—
442	Q₈	—	146	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	8	2	no	—
448	D₄	—	292	4	no	—
449	D₄	—	292	8	no	—
450	D₄	—	292	4	no	—
451	D₄	—	292	4	no	—
452	D₄	—	146	4	no	—
453	D₄	—	146	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	8	1	no	—
462	C₂×C₄	—	292	8	no	—
463	C₂×C₄	—	292	4	no	—
464	C₂×C₄	—	292	4	no	—
465	C₂×C₄	—	292	4	no	—
466	C₂×C₄	—	146	4	no	—
467	C₂×C₄	#14556565	1	2	yes	—
468	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
469	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
471	C₂×C₄	#14556637	1	2	yes	—
472	C₈	—	2	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	—	292	4	no	—
476	C₈	#14556559	1	1	yes	characteristic
477	C₈	#14556559	1	1	yes	characteristic
478	C₈	#14556559	1	2	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	292	4	no	—
485	C₂²	—	584	4	no	—
486	C₂²	—	1168	4	no	—
487	C₂²	C₂×#14556565	1	1	yes	characteristic
488	C₂²	#17989233	1	2	yes	—
489	C₄	—	2	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	292	4	no	—
494	C₄	C₂×#14556559	1	1	yes	characteristic
495	C₄	#17989151	1	1	yes	characteristic
496	C₄	D₄×D₂₉₂	1	2	yes	—
497	C₂	—	2	1	no	—
498	C₂	—	2	2	no	—
499	C₂	—	4	2	no	—
500	C₂	—	8	1	no	—
501	C₂	—	584	4	no	—
502	C₂	#22613287	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17989151
commutator, cosocle	C₂²×C₄×C₇₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#2932	C₂
socle	C₂×C₇₃	#2408
hypercenter	#2932	D₇₃
hypocenter	C₇₃	#24288
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2932

Complements

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

N	H ≅ G/N	type
1. #22624705	C₂	semidirect
2. #22619651	C₂	semidirect
3. #22619279	C₂	semidirect
4. #22611218	C₂	semidirect
5. #22611035	C₂	semidirect
6. #22610824	C₂	semidirect
7. #22609981	C₂	semidirect
8. #22609881	C₂	semidirect
9. C₇₃×#2932	C₂	semidirect
16. #17989385	C₂²	semidirect
26. C₂×#14556527	C₂²	semidirect
27. C₂×#14556519	C₂²	semidirect
29. #17988569	C₂²	semidirect
30. #17988553	C₂²	semidirect
31. #17988345	C₂²	semidirect
33. C₂×#131×C₇₃	C₂²	semidirect
37. #423×C₇₃	C₂²	semidirect
39. #408×C₇₃	C₂²	semidirect
40. C₂×#97×C₇₃	C₂²	semidirect
66. C₂×Dic₂₉₂	D₄	semidirect
68. C₂×#11924017	D₄	semidirect
70. C₂×D₅₈₄	D₄	semidirect
255. #2932	D₇₃	semidirect
261. C₇₃	#24288	semidirect
272. C₂×#131	C₂×D₇₃	semidirect
284. #423	C₂×D₇₃	semidirect
290. #408	C₂×D₇₃	semidirect
291. C₂×#97	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22624705	2
#22619651	2
#22619279	2
#22611218	2
#22611035	2
#22610824	2
#22609981	2
#22609881	2
C₇₃×#2932	2
#24288	73