Subgroups — #33104453

Order 18688.

862 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988702	C₂	1	1	yes	maximal, characteristic
2	#22618810	C₂	1	2	yes	maximal
3	#22618526	C₂	1	1	yes	maximal, characteristic, complemented
4	#22618522	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610710	C₂	1	2	yes	maximal, complemented
6	#22610160	C₂	1	2	yes	maximal, complemented
7	#22610155	C₂	1	2	yes	maximal, complemented
8	#22610086	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609987	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609813	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1815	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556611	C₂²	1	1	yes	characteristic
13	C₂×#14556597	C₂²	1	1	yes	characteristic
14	#17989070	C₂²	1	2	yes	—
15	#17989068	C₂²	1	2	yes	—
16	#17988702	C₄	1	8	yes	complemented
17	#17988696	—	2	2	no	—
18	#17988691	—	2	2	no	—
19	#17988678	—	2	2	no	—
20	#17988672	—	2	2	no	—
21	C₂×#14556526	C₂²	1	1	yes	characteristic
22	#17988629	—	2	2	no	—
23	#17988629	C₂²	1	2	yes	—
24	#17988627	C₂²	1	2	yes	—
25	#17988626	—	2	2	no	—
26	#17988625	—	2	1	no	—
27	#17988625	C₂²	1	1	yes	characteristic
28	#17988622	—	2	1	no	—
29	C₂×#14556523	—	2	1	no	—
30	C₂×#14556523	C₂²	1	1	yes	characteristic
31	C₂×#14556522	C₂²	1	2	yes	—
32	#106×D₇₃	—	2	1	no	—
33	C₂×#14556518	C₂²	1	1	yes	characteristic
34	C₂×#14556517	C₂²	1	1	yes	characteristic
35	#17988589	C₂²	1	2	yes	—
36	#17988545	C₂²	1	2	yes	—
37	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
38	#17988456	C₂²	1	2	yes	—
39	#17988355	C₂²	1	2	yes	—
40	#17988348	C₂²	1	2	yes	—
41	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
44	#417×C₇₃	C₂²	1	2	yes	—
45	#343×C₇₃	C₂²	1	2	yes	—
46	C₂×#11924028	C₂³	1	1	yes	characteristic
47	#14556611	C₂×C₄	1	4	yes	—
48	#14556611	Q₈	1	4	yes	—
49	C₂×#11924018	D₄	1	1	yes	characteristic
50	C₂×#11924016	D₄	1	1	yes	characteristic
51	C₂×#11924015	D₄	1	1	yes	characteristic
52	C₂×#11924013	D₄	1	1	yes	characteristic
53	#14556597	—	2	2	no	—
54	#14556597	C₂×C₄	1	4	yes	complemented
55	C₂×#11924012	C₂³	1	1	yes	characteristic
56	C₂×#11924011	—	2	1	no	—
57	C₂²×#10596831	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₇₃	—	2	1	no	—
59	Q₈×Dic₇₃	—	2	2	no	—
60	#14556556	—	2	2	no	—
61	D₄×Dic₇₃	—	2	2	no	—
62	D₄×Dic₇₃	—	4	2	no	—
63	#14556553	—	2	2	no	—
64	C₄×C₂²⋊D₇₃	—	4	2	no	—
65	#14556550	—	2	2	no	—
66	#14556550	C₂³	1	2	yes	—
67	#14556549	—	2	2	no	—
68	C₂×C₄⋊Dic₇₃	—	2	2	no	—
69	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
70	C₂×#11924007	—	4	2	no	—
71	C₄⋊C₄×D₇₃	—	2	2	no	—
72	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
73	#14556526	C₂×C₄	1	4	yes	complemented
74	#14556525	—	2	2	no	—
75	#14556525	D₄	1	2	yes	—
76	#14556524	—	2	2	no	—
77	#14556523	—	2	2	no	—
78	#14556523	—	2	1	no	—
79	#14556523	—	2	1	no	—
80	#14556523	D₄	1	1	yes	characteristic
81	#14556523	D₄	1	1	yes	characteristic
82	#14556522	—	2	2	no	—
83	#14556522	—	2	2	no	—
84	#14556522	—	2	2	no	—
85	#14556518	C₂×C₄	1	4	yes	complemented
86	#14556517	C₂×C₄	1	4	yes	complemented
87	#14556516	—	2	2	no	—
88	#14556513	—	2	2	no	—
89	#14556501	—	2	2	no	—
90	C₈×Dic₇₃	—	2	2	no	—
91	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
92	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
93	#131×C₇₃	—	2	2	no	—
94	#131×C₇₃	C₂×C₄	1	4	yes	complemented
95	C₂×M₁₆×C₇₃	—	2	1	no	—
96	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
97	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₇₃	—	2	1	no	—
99	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
101	#108×C₇₃	—	2	2	no	—
102	#106×C₇₃	—	2	1	no	—
103	#106×C₇₃	—	2	1	no	—
104	#103×C₇₃	—	2	2	no	—
105	#102×C₇₃	—	2	2	no	—
106	#11924028	—	2	1	no	—
107	#11924028	—	2	1	no	—
108	#11924028	C₂²×C₄	1	2	yes	—
109	#11924028	C₂×Q₈	1	2	yes	—
110	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
111	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₇₃	—	2	1	no	—
113	C₂²×Dic₇₃	—	2	1	no	—
114	C₂²×Dic₇₃	—	2	2	no	—
115	C₂²×Dic₇₃	—	4	2	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	4	2	no	—
118	#11924018	C₄⋊C₄	1	4	yes	complemented
119	#11924016	C₄⋊C₄	1	4	yes	complemented
120	#11924015	C₄⋊C₄	1	4	yes	complemented
121	#11924013	C₄⋊C₄	1	4	yes	complemented
122	#11924012	—	2	1	no	—
123	#11924012	C₂²×C₄	1	2	yes	—
124	#11924011	—	2	4	no	—
125	C₂×#10596831	—	2	1	no	—
126	C₂×#10596831	C₂²×C₄	1	2	yes	—
127	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
128	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
129	C₂×#10596831	C₂×Q₈	1	2	yes	—
130	C₈×D₇₃	—	2	4	no	—
131	C₄⋊Dic₇₃	—	2	2	no	—
132	C₄⋊Dic₇₃	—	2	2	no	—
133	C₄⋊Dic₇₃	—	4	2	no	—
134	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
135	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
136	#11924007	—	4	2	no	—
137	#11924007	—	8	4	no	—
138	C₂²⋊Dic₇₃	—	2	2	no	—
139	C₂²⋊Dic₇₃	—	4	2	no	—
140	#11924005	—	4	2	no	—
141	C₄×Dic₇₃	—	2	2	no	—
142	C₄×Dic₇₃	—	2	1	no	—
143	C₄×Dic₇₃	—	4	2	no	—
144	C₄×Dic₇₃	—	4	2	no	—
145	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
146	#41×C₇₃	—	2	1	no	—
147	#41×C₇₃	—	2	1	no	—
148	#41×C₇₃	C₂²×C₄	1	2	yes	—
149	#41×C₇₃	C₂×Q₈	1	2	yes	—
150	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂×D₄×C₇₃	—	2	1	no	—
152	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	—	2	1	no	—
154	C₂²×C₄×C₇₃	—	2	2	no	—
155	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
156	M₁₆×C₇₃	—	2	1	no	—
157	M₁₆×C₇₃	—	2	4	no	—
158	M₁₆×C₇₃	—	2	2	no	—
159	M₁₆×C₇₃	—	2	2	no	—
160	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₇₃	—	2	1	no	—
162	C₂×C₈×C₇₃	—	2	4	no	—
163	C₂×C₈×C₇₃	—	2	2	no	—
164	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₇₃	#41	1	2	yes	—
168	C₄⋊C₄×C₇₃	—	2	2	no	—
169	C₄⋊C₄×C₇₃	—	2	2	no	—
170	C₂³×C₇₃	—	2	1	no	—
171	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂²×D₇₃	—	2	1	no	—
173	Q₈×C₇₃	—	2	1	no	—
174	Q₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
175	D₄×C₇₃	—	2	2	no	—
176	D₄×C₇₃	—	2	2	no	—
177	D₄×C₇₃	—	2	1	no	—
178	D₄×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	4	2	no	—
183	C₂×C₄×C₇₃	—	8	2	no	—
184	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂²⋊D₇₃	—	2	2	no	—
191	C₂²⋊D₇₃	—	2	2	no	—
192	C₂×Dic₇₃	—	2	4	no	—
193	C₂×Dic₇₃	—	2	2	no	—
194	C₂×Dic₇₃	—	2	1	no	—
195	C₂×Dic₇₃	—	2	2	no	—
196	C₂×Dic₇₃	—	2	2	no	—
197	C₂×Dic₇₃	—	4	2	no	—
198	C₂×Dic₇₃	—	8	2	no	—
199	C₂×Dic₇₃	—	16	2	no	—
200	D₂₉₂	—	2	1	no	—
201	D₂₉₂	C₂×C₄⋊C₄	1	2	yes	—
202	C₄×D₇₃	—	2	2	no	—
203	C₄×D₇₃	—	2	2	no	—
204	C₄×D₇₃	—	16	2	no	—
205	Dic₁₄₆	—	2	1	no	—
206	Dic₁₄₆	C₂×C₄⋊C₄	1	2	yes	—
207	C₈×C₇₃	—	2	2	no	—
208	C₈×C₇₃	—	4	2	no	—
209	C₈×C₇₃	C₄×D₄	1	2	yes	—
210	C₈×C₇₃	C₄×D₄	1	2	yes	—
211	#10596831	—	2	2	no	—
212	#10596831	C₂×C₄⋊C₄	1	2	yes	—
213	#10596831	C₂×C₄⋊C₄	1	2	yes	—
214	C₂²×C₇₃	—	2	2	no	—
215	C₂²×C₇₃	—	2	2	no	—
216	C₂²×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	#520	1	1	yes	characteristic
218	C₂²×C₇₃	D₄²	1	1	yes	characteristic
219	C₂²×C₇₃	#554	1	1	yes	characteristic
220	C₂×D₇₃	—	2	2	no	—
221	C₂×D₇₃	—	4	2	no	—
222	C₄×C₇₃	—	2	2	no	—
223	C₄×C₇₃	—	8	2	no	—
224	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
225	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₇₃	#547	1	1	yes	characteristic
227	C₄×C₇₃	D₄×Q₈	1	1	yes	characteristic
228	Dic₇₃	—	2	4	no	—
229	Dic₇₃	—	2	2	no	—
230	Dic₇₃	—	4	2	no	—
231	Dic₇₃	—	4	2	no	—
232	Dic₇₃	—	8	2	no	—
233	#22689	—	73	1	no	maximal, Sylow
234	C₂×C₇₃	—	2	1	no	—
235	C₂×C₇₃	—	2	1	no	—
236	C₂×C₇₃	—	4	2	no	—
237	C₂×C₇₃	D₄×C₄⋊C₄	1	1	yes	characteristic
238	C₂×C₇₃	#3291	1	2	yes	—
239	D₇₃	—	4	2	no	—
240	C₂×#443	—	73	1	no	—
241	#2952	—	73	2	no	—
242	#2912	—	73	1	no	—
243	#2912	—	73	1	no	—
244	#1951	—	73	2	no	—
245	#1859	—	73	2	no	—
246	#1859	—	73	2	no	—
247	#1844	—	73	1	no	—
248	#1815	—	73	1	no	—
249	#1815	D₇₃	1	1	yes	characteristic, complemented
250	#1772	—	73	1	no	—
251	C₇₃	#22689	1	1	yes	characteristic, complemented, Sylow
252	C₂×#135	—	73	1	no	—
253	C₂×#131	—	73	1	no	—
254	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
255	#520	—	73	2	no	—
256	#520	—	73	2	no	—
257	#443	—	73	8	no	—
258	#442	—	146	2	no	—
259	#441	—	146	2	no	—
260	C₄×SD₁₆	—	146	2	no	—
261	C₄×SD₁₆	—	146	2	no	—
262	C₂×#108	—	73	1	no	—
263	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
264	#428	—	73	2	no	—
265	#428	—	73	2	no	—
266	#428	—	146	2	no	—
267	#428	—	146	2	no	—
268	#427	—	73	1	no	—
269	#427	—	146	1	no	—
270	#427	—	146	1	no	—
271	C₂×#106	—	73	1	no	—
272	C₂×#106	—	73	2	no	—
273	C₂×#106	—	146	1	no	—
274	C₂×#106	—	146	1	no	—
275	C₂×#106	C₂×D₇₃	1	1	yes	characteristic
276	C₂×#104	—	73	1	no	—
277	C₂×#104	—	73	1	no	—
278	#417	—	73	2	no	—
279	#417	C₂×D₇₃	1	2	yes	—
280	#405	—	73	2	no	—
281	C₂×C₄×C₈	—	73	1	no	—
282	#384	—	73	2	no	—
283	#343	—	73	2	no	—
284	#343	C₂×D₇₃	1	2	yes	—
285	#339	—	73	2	no	—
286	C₂×#41	—	73	1	no	—
287	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
288	#135	—	73	4	no	—
289	#135	—	73	4	no	—
290	C₂×Q₁₆	—	73	1	no	—
291	C₂×SD₁₆	—	73	1	no	—
292	C₂×SD₁₆	—	73	1	no	—
293	C₂×D₈	—	73	1	no	—
294	#131	—	2	2	no	—
295	#131	—	73	4	no	—
296	#131	—	146	2	no	—
297	#131	C₄×D₇₃	1	4	yes	complemented
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	73	1	no	—
300	C₂×M₁₆	—	146	1	no	—
301	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
302	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
303	C₂²×C₈	—	2	1	no	—
304	C₂²×C₈	—	73	1	no	—
305	C₂²×C₈	—	146	1	no	—
306	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
307	C₄×Q₈	—	146	2	no	—
308	C₄×Q₈	—	146	2	no	—
309	C₄×D₄	—	292	2	no	—
310	C₄×D₄	—	292	2	no	—
311	C₄×D₄	—	146	2	no	—
312	C₄×D₄	—	146	2	no	—
313	#117	—	73	2	no	—
314	#117	—	146	2	no	—
315	#117	—	146	2	no	—
316	C₂×C₄⋊C₄	—	292	2	no	—
317	C₂×C₄⋊C₄	—	73	2	no	—
318	C₂×C₄⋊C₄	—	146	2	no	—
319	C₂×C₄⋊C₄	—	146	2	no	—
320	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
321	C₂×C₄²	—	73	1	no	—
322	#108	—	2	2	no	—
323	#108	—	73	4	no	—
324	#107	—	73	2	no	—
325	#107	—	146	2	no	—
326	#107	—	146	2	no	—
327	#106	—	2	1	no	—
328	#106	—	2	1	no	—
329	#106	—	73	1	no	—
330	#106	—	73	1	no	—
331	#106	—	146	2	no	—
332	#106	—	146	2	no	—
333	#106	—	146	2	no	—
334	#106	—	146	2	no	—
335	#106	—	146	1	no	—
336	#106	—	146	1	no	—
337	#104	—	73	4	no	—
338	#104	—	73	4	no	—
339	#103	—	2	2	no	—
340	#103	—	146	2	no	—
341	#102	—	2	2	no	—
342	#102	—	146	2	no	—
343	#97	—	146	2	no	—
344	C₄×C₈	—	73	4	no	—
345	C₄×C₈	—	146	2	no	—
346	#41	—	2	1	no	—
347	#41	—	2	1	no	—
348	#41	—	73	2	no	—
349	#41	—	73	2	no	—
350	#41	—	146	1	no	—
351	#41	—	146	1	no	—
352	#41	C₂×C₄×D₇₃	1	2	yes	—
353	#41	Q₈×D₇₃	1	2	yes	—
354	C₂×Q₈	—	73	1	no	—
355	C₂×Q₈	D₄×D₇₃	1	1	yes	characteristic
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	73	1	no	—
358	C₂×D₄	—	146	1	no	—
359	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	292	2	no	—
363	C₂²×C₄	—	292	2	no	—
364	C₂²×C₄	—	146	2	no	—
365	C₂²×C₄	—	146	1	no	—
366	C₂²×C₄	—	146	1	no	—
367	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
368	Q₁₆	—	73	4	no	—
369	SD₁₆	—	73	4	no	—
370	SD₁₆	—	73	4	no	—
371	D₈	—	73	4	no	—
372	M₁₆	—	2	1	no	—
373	M₁₆	—	2	4	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	73	2	no	—
377	M₁₆	—	146	1	no	—
378	M₁₆	—	146	4	no	—
379	M₁₆	C₂×C₄×D₇₃	1	2	yes	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	4	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	73	2	no	—
384	C₂×C₈	—	73	1	no	—
385	C₂×C₈	—	73	1	no	—
386	C₂×C₈	—	73	2	no	—
387	C₂×C₈	—	146	1	no	—
388	C₂×C₈	—	146	4	no	—
389	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
390	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
391	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
392	C₂×C₈	#11924027	1	2	yes	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	292	2	no	—
396	C₄⋊C₄	—	292	2	no	—
397	C₄⋊C₄	—	584	4	no	—
398	C₄⋊C₄	—	73	2	no	—
399	C₄⋊C₄	—	73	2	no	—
400	C₄⋊C₄	—	146	2	no	—
401	C₄⋊C₄	—	146	2	no	—
402	C₂²⋊C₄	—	292	2	no	—
403	C₂²⋊C₄	—	292	2	no	—
404	C₂²⋊C₄	—	146	2	no	—
405	C₄²	—	292	2	no	—
406	C₄²	—	292	2	no	—
407	C₄²	—	73	2	no	—
408	C₄²	—	146	2	no	—
409	C₄²	—	146	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	146	1	no	—
412	C₂³	#14556637	1	1	yes	characteristic
413	Q₈	—	2	1	no	—
414	Q₈	—	73	2	no	—
415	Q₈	—	146	1	no	—
416	Q₈	C₄⋊C₄×D₇₃	1	2	yes	—
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	1	no	—
420	D₄	—	73	2	no	—
421	D₄	—	146	2	no	—
422	D₄	—	146	2	no	—
423	D₄	—	146	1	no	—
424	D₄	C₄⋊C₄×D₇₃	1	2	yes	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	292	2	no	—
431	C₂×C₄	—	584	2	no	—
432	C₂×C₄	—	1168	2	no	—
433	C₂×C₄	—	1168	2	no	—
434	C₂×C₄	—	146	2	no	—
435	C₂×C₄	—	146	2	no	—
436	C₂×C₄	—	146	4	no	—
437	C₂×C₄	—	146	1	no	—
438	C₂×C₄	—	146	2	no	—
439	C₂×C₄	—	146	2	no	—
440	C₂×C₄	—	146	2	no	—
441	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
442	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
443	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
444	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
445	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
446	C₂×C₄	#14556638	1	1	yes	characteristic
447	C₈	—	2	2	no	—
448	C₈	—	4	2	no	—
449	C₈	—	73	2	no	—
450	C₈	—	73	2	no	—
451	C₈	—	146	2	no	—
452	C₈	#14556551	1	2	yes	—
453	C₈	#14556551	1	2	yes	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	292	2	no	—
458	C₂²	—	146	2	no	—
459	C₂²	#17989067	1	1	yes	characteristic
460	C₂²	#17989221	1	1	yes	characteristic
461	C₂²	#17989295	1	1	yes	characteristic
462	C₄	—	2	2	no	—
463	C₄	—	8	2	no	—
464	C₄	—	292	2	no	—
465	C₄	—	292	2	no	—
466	C₄	—	584	2	no	—
467	C₄	—	146	4	no	—
468	C₄	—	146	2	no	—
469	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
470	C₄	C₂×#14556551	1	1	yes	characteristic
471	C₄	#17989237	1	1	yes	characteristic
472	C₄	#17989250	1	1	yes	characteristic
473	C₂	—	2	1	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	2	no	—
476	C₂	—	292	2	no	—
477	C₂	#22612827	1	1	yes	characteristic
478	C₂	#22621723	1	2	yes	—

	subgroup	G/H
center	C₂²	#17989221
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1815	C₂
socle	C₂²×C₇₃	D₄²
prime radical	C₂×#14556611	C₂²
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1815	D₇₃
hypocenter	C₇₃	#22689
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1815

Complements

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

N	H ≅ G/N	type
3. #22618526	C₂	semidirect
4. #22618522	C₂	semidirect
5. #22610710	C₂	semidirect
6. #22610160	C₂	semidirect
7. #22610155	C₂	semidirect
8. #22610086	C₂	semidirect
9. #22609987	C₂	semidirect
10. #22609813	C₂	semidirect
11. C₇₃×#1815	C₂	semidirect
16. #17988702	C₄	semidirect
54. #14556597	C₂×C₄	semidirect
73. #14556526	C₂×C₄	semidirect
85. #14556518	C₂×C₄	semidirect
86. #14556517	C₂×C₄	semidirect
91. C₈×Dic₇₃	C₂×C₄	semidirect
94. #131×C₇₃	C₂×C₄	semidirect
118. #11924018	C₄⋊C₄	semidirect
119. #11924016	C₄⋊C₄	semidirect
120. #11924015	C₄⋊C₄	semidirect
121. #11924013	C₄⋊C₄	semidirect
249. #1815	D₇₃	semidirect
251. C₇₃	#22689	semidirect
297. #131	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988702	2
#22618810	2
#22618526	2
#22618522	2
#22610710	2
#22610160	2
#22610155	2
#22610086	2
#22609987	2
#22609813	2
C₇₃×#1815	2
#22689	73