Subgroups — #33055169

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618563	C₂	1	1	yes	maximal, characteristic
2	#22618562	C₂	1	1	yes	maximal, characteristic
3	#432×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22608715	C₂	1	2	yes	maximal, complemented
5	#22608713	C₂	1	2	yes	maximal, complemented
6	#22608710	C₂	1	2	yes	maximal, complemented
7	#22608708	C₂	1	2	yes	maximal, complemented
8	#22608699	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608698	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608696	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	#17988644	C₂²	1	1	yes	characteristic
14	#17988643	—	2	1	no	—
15	#17988643	C₂²	1	1	yes	characteristic
16	#17988643	C₂²	1	1	yes	characteristic
17	#17988643	C₂²	1	2	yes	—
18	#17988642	—	2	1	no	—
19	#17988642	C₄	1	2	yes	—
20	#17988642	C₄	1	2	yes	—
21	#17988641	—	2	1	no	—
22	#17988639	—	2	1	no	—
23	#17988639	C₂²	1	2	yes	—
24	#17988638	C₂²	1	2	yes	—
25	#17988638	C₂²	1	2	yes	—
26	#17988611	C₂²	1	1	yes	characteristic
27	#17988610	C₄	1	2	yes	—
28	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
29	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
30	#17988550	—	2	1	no	—
31	#17988550	C₄	1	2	yes	—
32	C₂²⋊C₈×D₇₃	—	2	1	no	—
33	C₄×#11924012	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₇₃	—	2	1	no	—
35	#97×D₇₃	—	2	1	no	—
36	#17988340	C₂²	1	2	yes	complemented
37	#17988339	C₂²	1	2	yes	complemented
38	#17988339	C₂²	1	2	yes	complemented
39	#17988338	C₂²	1	2	yes	complemented
40	#17988337	C₂²	1	2	yes	complemented
41	#17988337	C₂²	1	2	yes	complemented
42	#432×C₇₃	C₂²	1	1	yes	characteristic
43	#423×C₇₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	2	yes	complemented
46	#334×C₇₃	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
50	C₂×#11924012	—	2	1	no	—
51	C₂×#11924012	C₂×C₄	1	2	yes	—
52	C₂×C₈×D₇₃	—	2	1	no	—
53	C₂×C₈×D₇₃	—	2	1	no	—
54	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
56	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
57	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₇₃	D₄	1	1	yes	characteristic
60	C₄²×D₇₃	D₄	1	1	yes	characteristic
61	C₄²×D₇₃	Q₈	1	1	yes	characteristic
62	C₄²×D₇₃	Q₈	1	1	yes	characteristic
63	C₄²×D₇₃	C₂³	1	1	yes	characteristic
64	C₄²×D₇₃	C₂³	1	1	yes	characteristic
65	C₄⋊#10596831	—	2	1	no	—
66	C₄⋊#10596831	C₂³	1	2	yes	—
67	C₄⋊#10596831	C₂³	1	1	yes	characteristic
68	C₄⋊#10596831	C₂³	1	1	yes	characteristic
69	#14556520	—	2	1	no	—
70	#14556520	—	2	1	no	—
71	#14556520	C₂×C₄	1	4	yes	—
72	#14556520	C₂×C₄	1	4	yes	—
73	C₂²⋊#10596831	—	2	1	no	—
74	#14556503	—	2	2	no	—
75	#14556503	—	2	2	no	—
76	#14556503	—	2	1	no	—
77	#14556503	—	2	1	no	—
78	#14556503	C₂×C₄	1	4	yes	—
79	#14556503	C₂×C₄	1	4	yes	—
80	#14556502	—	2	1	no	—
81	#14556502	C₂×C₄	1	2	yes	—
82	#14556501	—	2	1	no	—
83	#14556501	—	2	1	no	—
84	#14556501	—	2	2	no	—
85	C₄×#10596831	C₂³	1	2	yes	—
86	C₈×Dic₇₃	—	2	2	no	—
87	C₂×M₁₆×C₇₃	—	2	1	no	—
88	C₂×M₁₆×C₇₃	C₂×C₄	1	2	yes	—
89	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₇₃	—	2	1	no	—
91	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
92	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₇₃	—	2	1	no	—
95	#97×C₇₃	—	2	1	no	—
96	#97×C₇₃	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₇₃	C₂³	1	2	yes	—
98	C₂³×D₇₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₃	—	4	2	no	—
103	C₂×C₄×D₇₃	—	4	1	no	—
104	C₂×C₄×D₇₃	—	4	1	no	—
105	C₂×C₄×D₇₃	—	4	2	no	—
106	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
107	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
118	#11924012	—	4	2	no	—
119	#11924012	—	4	2	no	—
120	C₂×#10596831	—	2	2	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	1	no	—
123	C₂×#10596831	C₂²×C₄	1	4	yes	—
124	C₈×D₇₃	—	4	2	no	—
125	C₈×D₇₃	—	4	2	no	—
126	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
141	M₁₆×C₇₃	—	4	2	no	—
142	M₁₆×C₇₃	—	4	2	no	—
143	C₂×C₈×C₇₃	—	2	1	no	—
144	C₂×C₈×C₇₃	—	2	1	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
147	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₇₃	C₂×Q₈	1	1	yes	characteristic
150	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
151	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂²×D₇₃	—	2	2	no	—
153	C₂²×D₇₃	—	4	1	no	—
154	C₂²×D₇₃	—	4	1	no	—
155	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₃	—	2	2	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	2	1	no	—
160	C₂×C₄×C₇₃	—	4	1	no	—
161	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
167	C₂×Dic₇₃	—	4	1	no	—
168	C₂×Dic₇₃	—	4	1	no	—
169	C₂×Dic₇₃	—	4	1	no	—
170	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₄×D₇₃	—	2	2	no	—
177	C₄×D₇₃	—	2	2	no	—
178	C₄×D₇₃	—	2	2	no	—
179	C₄×D₇₃	—	2	2	no	—
180	C₄×D₇₃	—	2	1	no	—
181	C₄×D₇₃	—	2	1	no	—
182	C₄×D₇₃	—	2	1	no	—
183	C₄×D₇₃	—	2	1	no	—
184	C₄×D₇₃	—	4	1	no	—
185	C₄×D₇₃	—	4	1	no	—
186	C₄×D₇₃	—	4	1	no	—
187	C₄×D₇₃	—	4	1	no	—
188	C₄×D₇₃	—	4	1	no	—
189	C₄×D₇₃	—	4	1	no	—
190	C₈×C₇₃	—	2	4	no	—
191	C₈×C₇₃	—	4	2	no	—
192	C₈×C₇₃	—	4	1	no	—
193	C₈×C₇₃	—	4	1	no	—
194	#10596831	—	2	4	no	—
195	#10596831	—	4	1	no	—
196	#10596831	—	4	1	no	—
197	#10596831	—	4	2	no	—
198	C₂²×C₇₃	—	2	1	no	—
199	C₂²×C₇₃	—	2	1	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
202	C₂×D₇₃	—	2	1	no	—
203	C₂×D₇₃	—	2	1	no	—
204	C₂×D₇₃	—	2	1	no	—
205	C₂×D₇₃	—	2	1	no	—
206	C₂×D₇₃	—	2	1	no	—
207	C₂×D₇₃	—	4	4	no	—
208	C₂×D₇₃	#430	1	2	yes	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	—	2	1	no	—
212	C₄×C₇₃	—	2	1	no	—
213	C₄×C₇₃	#568	1	2	yes	—
214	C₄×C₇₃	#575	1	1	yes	characteristic
215	C₄×C₇₃	#575	1	1	yes	characteristic
216	Dic₇₃	—	2	1	no	—
217	Dic₇₃	—	2	1	no	—
218	Dic₇₃	—	2	1	no	—
219	Dic₇₃	—	2	1	no	—
220	Dic₇₃	—	2	1	no	—
221	Dic₇₃	—	2	1	no	—
222	#17821	—	73	1	no	maximal, Sylow
223	C₂×C₇₃	—	4	1	no	—
224	C₂×C₇₃	#2905	1	1	yes	characteristic
225	C₂×C₇₃	#2911	1	1	yes	characteristic
226	C₂×C₇₃	C₂×#430	1	1	yes	characteristic
227	D₇₃	—	2	2	no	—
228	D₇₃	—	4	1	no	—
229	#2920	—	73	1	no	—
230	#2920	—	73	1	no	—
231	C₂×#432	—	73	1	no	—
232	#1573	—	73	2	no	—
233	#1573	—	73	2	no	—
234	#1572	—	73	2	no	—
235	#1572	—	73	2	no	—
236	#1569	—	73	1	no	—
237	#1569	—	73	1	no	—
238	#1569	—	73	1	no	—
239	#1569	D₇₃	1	1	yes	characteristic, complemented
240	C₇₃	#17821	1	1	yes	characteristic, complemented, Sylow
241	C₂²×C₄²	—	73	1	no	—
242	#432	—	73	2	no	—
243	#432	—	73	2	no	—
244	#432	—	73	1	no	—
245	#432	—	73	1	no	—
246	#432	—	73	1	no	—
247	#432	—	73	2	no	—
248	#432	—	146	1	no	—
249	#432	—	146	1	no	—
250	#432	—	146	1	no	—
251	#432	C₂×D₇₃	1	1	yes	characteristic
252	#431	—	73	2	no	—
253	#431	—	73	2	no	—
254	#431	—	73	2	no	—
255	#431	—	146	1	no	—
256	#423	—	73	2	no	—
257	#423	—	73	1	no	—
258	#423	C₂×D₇₃	1	1	yes	characteristic
259	C₂×C₄⋊C₈	—	73	1	no	—
260	C₂×C₄⋊C₈	—	73	1	no	—
261	#407	—	73	2	no	—
262	#407	—	146	1	no	—
263	C₂×C₂²⋊C₈	—	146	1	no	—
264	C₄×M₁₆	—	73	1	no	—
265	C₄×M₁₆	—	146	1	no	—
266	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
267	C₂×#97	—	146	1	no	—
268	#335	—	73	2	no	—
269	#335	—	73	2	no	—
270	#335	—	73	2	no	—
271	#335	C₂×D₇₃	1	2	yes	complemented
272	#334	—	73	2	no	—
273	#334	—	73	2	no	—
274	#334	—	73	2	no	—
275	#334	C₂×D₇₃	1	2	yes	complemented
276	C₂³×C₄	—	73	1	no	—
277	C₂³×C₄	—	73	1	no	—
278	C₂³×C₄	—	73	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	73	2	no	—
281	C₂×M₁₆	—	146	1	no	—
282	C₂×M₁₆	C₄×D₇₃	1	2	yes	—
283	C₂²×C₈	—	146	1	no	—
284	C₂²×C₈	—	146	1	no	—
285	C₂×C₄²	—	73	1	no	—
286	C₂×C₄²	—	73	1	no	—
287	C₂×C₄²	—	73	1	no	—
288	C₂×C₄²	—	73	1	no	—
289	C₂×C₄²	—	73	1	no	—
290	C₂×C₄²	—	73	1	no	—
291	C₂×C₄²	—	73	1	no	—
292	C₂×C₄²	—	73	1	no	—
293	C₂×C₄²	—	73	1	no	—
294	C₂×C₄²	—	73	1	no	—
295	C₂×C₄²	—	73	1	no	—
296	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	73	4	no	—
299	C₄⋊C₈	—	73	4	no	—
300	C₄⋊C₈	—	73	1	no	—
301	C₄⋊C₈	—	73	1	no	—
302	C₄⋊C₈	—	73	2	no	—
303	C₄⋊C₈	—	146	1	no	—
304	C₄⋊C₈	—	146	1	no	—
305	C₄⋊C₈	—	146	1	no	—
306	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
307	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
308	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
309	C₂²⋊C₈	—	2	1	no	—
310	C₂²⋊C₈	—	73	4	no	—
311	C₂²⋊C₈	—	73	4	no	—
312	C₂²⋊C₈	—	146	1	no	—
313	C₂²⋊C₈	—	146	1	no	—
314	C₂²⋊C₈	—	146	2	no	—
315	C₂²⋊C₈	—	146	2	no	—
316	C₂²⋊C₈	—	146	1	no	—
317	#97	—	2	1	no	—
318	#97	—	73	2	no	—
319	#97	—	146	1	no	—
320	#97	—	146	1	no	—
321	#97	—	146	2	no	—
322	#97	—	146	1	no	—
323	#97	C₄×D₇₃	1	2	yes	—
324	C₄×C₈	—	73	2	no	—
325	C₄×C₈	—	146	2	no	—
326	C₄×C₈	C₂²×D₇₃	1	2	yes	—
327	C₂⁴	—	73	1	no	—
328	C₂²×C₄	—	292	1	no	—
329	C₂²×C₄	—	292	1	no	—
330	C₂²×C₄	—	292	2	no	—
331	C₂²×C₄	—	292	2	no	—
332	C₂²×C₄	—	73	1	no	—
333	C₂²×C₄	—	73	1	no	—
334	C₂²×C₄	—	73	1	no	—
335	C₂²×C₄	—	73	1	no	—
336	C₂²×C₄	—	73	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	—	73	1	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	1	no	—
341	C₂²×C₄	—	73	1	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	73	1	no	—
346	C₂²×C₄	—	73	1	no	—
347	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
349	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
350	M₁₆	—	4	2	no	—
351	M₁₆	—	4	2	no	—
352	M₁₆	—	292	2	no	—
353	M₁₆	—	292	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	292	2	no	—
358	C₂×C₈	—	292	2	no	—
359	C₂×C₈	—	73	4	no	—
360	C₂×C₈	—	146	2	no	—
361	C₂×C₈	—	146	1	no	—
362	C₂×C₈	—	146	1	no	—
363	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
364	C₄²	—	73	1	no	—
365	C₄²	—	73	1	no	—
366	C₄²	—	73	1	no	—
367	C₄²	—	73	1	no	—
368	C₄²	—	73	1	no	—
369	C₄²	—	73	1	no	—
370	C₄²	—	73	1	no	—
371	C₄²	—	73	1	no	—
372	C₄²	—	73	1	no	—
373	C₄²	—	73	1	no	—
374	C₄²	—	73	1	no	—
375	C₄²	—	73	1	no	—
376	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
377	C₄²	D₄×D₇₃	1	1	yes	characteristic
378	C₄²	Q₈×D₇₃	1	1	yes	characteristic
379	C₄²	C₂³×D₇₃	1	1	yes	characteristic
380	C₂³	—	292	1	no	—
381	C₂³	—	292	1	no	—
382	C₂³	—	73	1	no	—
383	C₂³	—	73	1	no	—
384	C₂³	—	146	2	no	—
385	C₂³	C₄⋊C₄×D₇₃	1	1	yes	characteristic
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	292	1	no	—
391	C₂×C₄	—	292	1	no	—
392	C₂×C₄	—	292	1	no	—
393	C₂×C₄	—	292	1	no	—
394	C₂×C₄	—	292	1	no	—
395	C₂×C₄	—	292	1	no	—
396	C₂×C₄	—	292	1	no	—
397	C₂×C₄	—	292	1	no	—
398	C₂×C₄	—	292	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	73	1	no	—
401	C₂×C₄	—	73	1	no	—
402	C₂×C₄	—	73	1	no	—
403	C₂×C₄	—	73	1	no	—
404	C₂×C₄	—	73	1	no	—
405	C₂×C₄	—	146	2	no	—
406	C₂×C₄	—	146	2	no	—
407	C₂×C₄	—	146	1	no	—
408	C₂×C₄	—	146	1	no	—
409	C₂×C₄	—	146	1	no	—
410	C₂×C₄	—	146	1	no	—
411	C₂×C₄	—	146	2	no	—
412	C₂×C₄	—	146	2	no	—
413	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
414	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
415	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
417	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
418	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
419	C₈	—	2	4	no	—
420	C₈	—	4	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	292	1	no	—
424	C₈	—	292	1	no	—
425	C₈	—	292	2	no	—
426	C₈	—	146	4	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	292	4	no	—
431	C₂²	—	73	2	no	—
432	C₂²	—	146	1	no	—
433	C₂²	—	146	1	no	—
434	C₂²	—	146	1	no	—
435	C₂²	—	146	1	no	—
436	C₂²	—	146	1	no	—
437	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	146	1	no	—
443	C₄	—	146	1	no	—
444	C₄	—	146	1	no	—
445	C₄	—	146	1	no	—
446	C₄	—	146	1	no	—
447	C₄	—	146	1	no	—
448	C₄	#17989353	1	2	yes	—
449	C₄	#17989383	1	1	yes	characteristic
450	C₄	#17989386	1	1	yes	characteristic
451	C₂	—	4	1	no	—
452	C₂	—	292	1	no	—
453	C₂	—	146	2	no	—
454	C₂	#22618493	1	1	yes	characteristic
455	C₂	#22618518	1	1	yes	characteristic
456	C₂	#430×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1569	C₂
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₄⋊C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1569	D₇₃
hypocenter	C₇₃	#17821
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #22608715	C₂	semidirect
5. #22608713	C₂	semidirect
6. #22608710	C₂	semidirect
7. #22608708	C₂	semidirect
8. #22608699	C₂	semidirect
9. #22608698	C₂	semidirect
10. #22608696	C₂	semidirect
11. C₇₃×#1569	C₂	semidirect
36. #17988340	C₂²	semidirect
37. #17988339	C₂²	semidirect
38. #17988339	C₂²	semidirect
39. #17988338	C₂²	semidirect
40. #17988337	C₂²	semidirect
41. #17988337	C₂²	semidirect
45. #335×C₇₃	C₂²	semidirect
46. #334×C₇₃	C₂²	semidirect
239. #1569	D₇₃	semidirect
240. C₇₃	#17821	semidirect
271. #335	C₂×D₇₃	semidirect
275. #334	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22618563	2
#22618562	2
#432×D₇₃	2
#22608715	2
#22608713	2
#22608710	2
#22608708	2
#22608699	2
#22608698	2
#22608696	2
C₇₃×#1569	2
#17821	73