Subgroups — #32981666

Order 18688.

612 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988609	C₂	1	1	yes	maximal, characteristic
2	#22618278	C₂	1	1	yes	maximal, characteristic
3	#22609908	C₂	1	1	yes	maximal, characteristic
4	C₂×#17988333	C₂	1	1	yes	maximal, characteristic, complemented
5	#22607815	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#332×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11924011	—	2	1	no	—
9	C₂×#14556567	—	2	1	no	—
10	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#17988609	—	2	2	no	—
12	#17988609	—	2	2	no	—
13	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
15	C₂×#14556520	—	2	1	no	—
16	C₂×#14556503	—	2	1	no	—
17	#17988494	—	2	1	no	—
18	#17988483	—	2	1	no	—
19	#17988483	C₄	1	2	yes	—
20	#17988457	C₂²	1	1	yes	characteristic
21	#17988444	—	2	1	no	—
22	#17988444	C₄	1	2	yes	—
23	#17988341	—	2	1	no	—
24	#17988333	—	2	2	no	—
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	#332×C₇₃	—	2	2	no	—
29	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
32	C₂×#11924011	—	2	4	no	—
33	C₂×#11924011	—	4	2	no	—
34	C₂×#11924011	—	4	2	no	—
35	C₂²×#10596831	—	2	1	no	—
36	C₂²×#10596831	—	2	1	no	—
37	#14556567	—	4	2	no	—
38	#14556567	—	4	2	no	—
39	C₂×C₄⋊Dic₇₃	—	2	1	no	—
40	C₂×C₄⋊Dic₇₃	—	2	1	no	—
41	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
42	C₂×#11924007	—	2	2	no	—
43	C₂×#11924005	—	2	2	no	—
44	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
47	C₄²×D₇₃	—	2	1	no	—
48	C₄²×D₇₃	—	2	1	no	—
49	C₄²×D₇₃	—	2	1	no	—
50	C₄²×D₇₃	—	2	1	no	—
51	C₄⋊#10596831	—	2	1	no	—
52	C₄⋊#10596831	—	2	1	no	—
53	C₄⋊#10596831	—	2	1	no	—
54	C₄⋊#10596831	D₄	1	2	yes	—
55	#14556520	—	2	4	no	—
56	#14556503	—	4	2	no	—
57	#14556498	—	2	2	no	—
58	#14556498	—	2	2	no	—
59	C₂²×Q₈×C₇₃	—	2	1	no	—
60	C₂²×C₈×C₇₃	—	2	1	no	—
61	C₂²×C₈×C₇₃	—	2	1	no	—
62	C₄⋊Q₈×C₇₃	—	2	1	no	—
63	C₄⋊Q₈×C₇₃	—	2	1	no	—
64	C₄⋊Q₈×C₇₃	—	2	1	no	—
65	C₄⋊Q₈×C₇₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₇₃	—	2	1	no	—
70	C₄⋊C₈×C₇₃	—	2	1	no	—
71	C₄⋊C₈×C₇₃	—	2	1	no	—
72	C₄⋊C₈×C₇₃	D₄	1	2	yes	—
73	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₇₃	—	2	2	no	—
75	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₇₃	—	2	1	no	—
79	C₂×C₄×D₇₃	—	2	1	no	—
80	C₂×C₄×D₇₃	—	2	1	no	—
81	C₂×C₄×D₇₃	—	2	1	no	—
82	C₂×C₄×D₇₃	—	2	1	no	—
83	C₂×C₄×D₇₃	—	2	1	no	—
84	C₂×C₄×D₇₃	—	2	1	no	—
85	C₂×C₄×D₇₃	—	2	1	no	—
86	C₂×C₄×D₇₃	—	2	1	no	—
87	C₂×C₄×D₇₃	—	2	1	no	—
88	C₂×C₄×D₇₃	—	2	1	no	—
89	C₂×C₄×D₇₃	—	2	1	no	—
90	C₂×C₄×D₇₃	—	2	2	no	—
91	C₂×C₄×D₇₃	—	4	1	no	—
92	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
93	C₂×C₄×D₇₃	Q₁₆	1	2	yes	—
94	#11924011	—	4	8	no	—
95	C₂×#10596831	—	2	2	no	—
96	C₂×#10596831	—	4	1	no	—
97	C₂×#10596831	—	4	1	no	—
98	C₂×#10596831	—	4	1	no	—
99	C₂×#10596831	—	4	1	no	—
100	C₂×#10596831	—	4	1	no	—
101	C₄⋊Dic₇₃	—	4	1	no	—
102	C₄⋊Dic₇₃	—	4	1	no	—
103	C₄⋊Dic₇₃	—	4	1	no	—
104	C₄⋊Dic₇₃	—	4	1	no	—
105	C₄⋊Dic₇₃	—	4	2	no	—
106	#11924007	—	4	4	no	—
107	#11924005	—	4	4	no	—
108	C₄×Dic₇₃	—	2	1	no	—
109	C₄×Dic₇₃	—	2	1	no	—
110	C₄×Dic₇₃	—	2	1	no	—
111	C₄×Dic₇₃	—	2	1	no	—
112	C₄×Dic₇₃	—	2	1	no	—
113	C₄×Dic₇₃	—	2	1	no	—
114	C₂×Q₈×C₇₃	—	4	1	no	—
115	C₂×Q₈×C₇₃	—	4	1	no	—
116	C₂×Q₈×C₇₃	—	4	1	no	—
117	C₂×Q₈×C₇₃	—	4	1	no	—
118	C₂×Q₈×C₇₃	—	4	1	no	—
119	C₂×Q₈×C₇₃	—	4	1	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	4	1	no	—
126	C₂×C₈×C₇₃	—	4	1	no	—
127	C₂×C₈×C₇₃	—	4	1	no	—
128	C₂×C₈×C₇₃	—	4	1	no	—
129	C₂×C₈×C₇₃	—	4	1	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	4	1	no	—
133	C₄⋊C₄×C₇₃	—	4	1	no	—
134	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₇₃	#41	1	1	yes	characteristic
137	C₄²×C₇₃	#41	1	1	yes	characteristic
138	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂²×D₇₃	—	2	1	no	—
140	C₂²×D₇₃	—	2	1	no	—
141	C₂²×D₇₃	—	2	1	no	—
142	C₂²×D₇₃	—	2	1	no	—
143	C₂²×D₇₃	—	2	1	no	—
144	C₂²×D₇₃	—	2	1	no	—
145	C₂²×D₇₃	#103	1	2	yes	—
146	Q₈×C₇₃	—	8	1	no	—
147	Q₈×C₇₃	—	8	1	no	—
148	Q₈×C₇₃	—	8	1	no	—
149	Q₈×C₇₃	—	8	1	no	—
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	2	1	no	—
152	C₂×C₄×C₇₃	—	4	2	no	—
153	C₂×C₄×C₇₃	—	4	2	no	—
154	C₂×C₄×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
158	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
159	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
160	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
163	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
168	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
169	C₂×Dic₇₃	—	2	1	no	—
170	C₂×Dic₇₃	—	2	1	no	—
171	C₂×Dic₇₃	—	2	1	no	—
172	C₂×Dic₇₃	—	2	1	no	—
173	C₂×Dic₇₃	—	2	1	no	—
174	C₂×Dic₇₃	—	2	1	no	—
175	C₂×Dic₇₃	—	2	1	no	—
176	C₂×Dic₇₃	—	4	2	no	—
177	C₂×Dic₇₃	—	4	2	no	—
178	C₂×Dic₇₃	—	4	2	no	—
179	C₂×Dic₇₃	#101	1	2	yes	—
180	C₂×Dic₇₃	#103	1	2	yes	—
181	C₄×D₇₃	—	2	2	no	—
182	C₄×D₇₃	—	2	2	no	—
183	C₄×D₇₃	—	2	2	no	—
184	C₄×D₇₃	—	2	2	no	—
185	C₄×D₇₃	—	4	2	no	—
186	C₄×D₇₃	—	4	2	no	—
187	C₄×D₇₃	—	4	1	no	—
188	C₄×D₇₃	—	4	1	no	—
189	C₄×D₇₃	—	4	1	no	—
190	C₄×D₇₃	—	4	1	no	—
191	C₈×C₇₃	—	4	2	no	—
192	C₈×C₇₃	—	8	1	no	—
193	#10596831	—	4	2	no	—
194	#10596831	—	8	1	no	—
195	C₂²×C₇₃	#386	1	1	yes	characteristic
196	C₂²×C₇₃	C₂×#101	1	1	yes	characteristic
197	C₂²×C₇₃	#413	1	1	yes	characteristic
198	C₂²×C₇₃	C₂×#103	1	1	yes	characteristic
199	C₂²×C₇₃	#417	1	1	yes	characteristic
200	C₂²×C₇₃	#417	1	1	yes	characteristic
201	C₂²×C₇₃	#418	1	1	yes	characteristic
202	C₂×D₇₃	—	2	2	no	—
203	C₂×D₇₃	—	2	2	no	—
204	C₂×D₇₃	—	2	2	no	—
205	C₂×D₇₃	—	4	1	no	—
206	C₂×D₇₃	—	4	1	no	—
207	C₂×D₇₃	—	4	1	no	—
208	C₂×D₇₃	—	4	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	—	8	2	no	—
212	C₄×C₇₃	#450	1	1	yes	characteristic
213	C₄×C₇₃	#451	1	1	yes	characteristic
214	C₄×C₇₃	#468	1	1	yes	characteristic
215	C₄×C₇₃	#468	1	1	yes	characteristic
216	C₄×C₇₃	#469	1	1	yes	characteristic
217	C₄×C₇₃	#469	1	1	yes	characteristic
218	C₄×C₇₃	#483	1	1	yes	characteristic
219	C₄×C₇₃	#484	1	1	yes	characteristic
220	Dic₇₃	—	2	2	no	—
221	Dic₇₃	—	2	2	no	—
222	Dic₇₃	—	4	1	no	—
223	Dic₇₃	—	8	2	no	—
224	#9137	—	73	1	no	maximal, Sylow
225	C₂×C₇₃	#1549	1	1	yes	characteristic
226	C₂×C₇₃	#1550	1	1	yes	characteristic
227	C₂×C₇₃	#1557	1	1	yes	characteristic
228	C₂×C₇₃	#1561	1	1	yes	characteristic
229	C₂×C₇₃	#1872	1	1	yes	characteristic
230	C₂×C₇₃	#1895	1	1	yes	characteristic
231	C₂×C₇₃	#1901	1	1	yes	characteristic
232	D₇₃	—	4	2	no	—
233	C₂×#423	—	73	1	no	—
234	#2857	—	73	1	no	—
235	#1797	—	73	1	no	—
236	C₂×#332	—	73	1	no	—
237	C₂×#332	D₇₃	1	1	yes	characteristic, complemented
238	#1296	—	73	1	no	—
239	#1296	—	73	1	no	—
240	C₇₃	#9137	1	1	yes	characteristic, complemented, Sylow
241	C₂²×M₁₆	—	146	1	no	—
242	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
243	C₂×C₂²⋊Q₈	—	146	1	no	—
244	C₂²×C₄²	—	73	1	no	—
245	#423	—	146	2	no	—
246	#423	—	146	2	no	—
247	C₂×C₄⋊C₈	—	73	1	no	—
248	C₂×C₄⋊C₈	—	73	1	no	—
249	C₂×C₄⋊C₈	—	146	1	no	—
250	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	—	146	1	no	—
253	#391	—	146	1	no	—
254	#389	—	73	2	no	—
255	#389	—	146	1	no	—
256	#384	—	73	1	no	—
257	#380	—	73	2	no	—
258	#380	—	146	1	no	—
259	#336	—	146	1	no	—
260	#332	—	2	2	no	—
261	#332	—	146	2	no	—
262	C₂²×Q₈	—	2	1	no	—
263	C₂³×C₄	—	73	1	no	—
264	C₂³×C₄	—	73	1	no	—
265	C₂³×C₄	—	73	1	no	—
266	C₂×M₁₆	—	292	2	no	—
267	C₂×M₁₆	—	292	2	no	—
268	C₂×M₁₆	—	146	4	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	—	146	1	no	—
272	C₂²×C₈	—	146	1	no	—
273	C₄⋊Q₈	—	2	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	292	2	no	—
278	C₂²⋊Q₈	—	292	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	73	2	no	—
281	C₂×C₄⋊C₄	—	146	2	no	—
282	C₂×C₄⋊C₄	—	146	1	no	—
283	C₂×C₄⋊C₄	—	146	1	no	—
284	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	146	2	no	—
286	C₂×C₄²	—	73	1	no	—
287	C₂×C₄²	—	73	1	no	—
288	C₂×C₄²	—	73	1	no	—
289	C₂×C₄²	—	146	1	no	—
290	C₂×C₄²	—	146	1	no	—
291	C₂×C₄²	—	146	1	no	—
292	C₂×C₄²	—	146	1	no	—
293	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	—	73	2	no	—
298	C₄⋊C₈	—	146	4	no	—
299	C₄⋊C₈	—	146	1	no	—
300	C₄⋊C₈	—	146	1	no	—
301	C₄⋊C₈	—	146	1	no	—
302	C₄⋊C₈	C₂²⋊D₇₃	1	2	yes	—
303	C₂²⋊C₈	—	292	2	no	—
304	#95	—	146	2	no	—
305	#95	—	146	2	no	—
306	C₂⁴	—	73	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×Q₈	—	4	1	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	292	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	2	no	—
318	C₂²×C₄	—	73	2	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	146	2	no	—
321	C₂²×C₄	—	146	2	no	—
322	C₂²×C₄	—	146	1	no	—
323	C₂²×C₄	—	146	1	no	—
324	C₂²×C₄	—	146	1	no	—
325	C₂²×C₄	—	146	1	no	—
326	C₂²×C₄	—	146	1	no	—
327	C₂²×C₄	—	146	1	no	—
328	C₂²×C₄	—	146	1	no	—
329	C₂²×C₄	—	146	1	no	—
330	C₂²×C₄	—	146	1	no	—
331	C₂²×C₄	—	146	1	no	—
332	C₂²×C₄	—	146	1	no	—
333	C₂²×C₄	—	146	1	no	—
334	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
335	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
336	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
337	M₁₆	—	292	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	1	no	—
341	C₂×C₈	—	4	1	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	1	no	—
344	C₂×C₈	—	292	1	no	—
345	C₂×C₈	—	292	1	no	—
346	C₂×C₈	—	292	1	no	—
347	C₂×C₈	—	292	1	no	—
348	C₂×C₈	—	292	1	no	—
349	C₂×C₈	—	146	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	292	2	no	—
355	C₄⋊C₄	—	292	4	no	—
356	C₄⋊C₄	—	292	1	no	—
357	C₄⋊C₄	—	292	1	no	—
358	C₄⋊C₄	—	292	1	no	—
359	C₄⋊C₄	—	292	1	no	—
360	C₂²⋊C₄	—	292	4	no	—
361	C₄²	—	146	1	no	—
362	C₄²	—	146	1	no	—
363	C₄²	—	146	1	no	—
364	C₄²	—	146	1	no	—
365	C₄²	—	146	1	no	—
366	C₄²	—	146	1	no	—
367	C₄²	D₄×D₇₃	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
369	C₄²	#11924027	1	1	yes	characteristic
370	C₄²	#11924028	1	1	yes	characteristic
371	C₂³	—	73	2	no	—
372	C₂³	—	146	1	no	—
373	C₂³	—	146	1	no	—
374	C₂³	—	146	1	no	—
375	C₂³	—	146	1	no	—
376	C₂³	—	146	1	no	—
377	C₂³	—	146	1	no	—
378	C₂³	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
379	Q₈	—	8	1	no	—
380	Q₈	—	8	1	no	—
381	Q₈	—	8	1	no	—
382	Q₈	—	8	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	292	2	no	—
389	C₂×C₄	—	292	2	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	2	no	—
395	C₂×C₄	—	292	2	no	—
396	C₂×C₄	—	292	2	no	—
397	C₂×C₄	—	73	2	no	—
398	C₂×C₄	—	73	2	no	—
399	C₂×C₄	—	146	1	no	—
400	C₂×C₄	—	146	1	no	—
401	C₂×C₄	—	146	1	no	—
402	C₂×C₄	—	146	1	no	—
403	C₂×C₄	—	146	1	no	—
404	C₂×C₄	—	146	1	no	—
405	C₂×C₄	—	146	1	no	—
406	C₂×C₄	—	146	2	no	—
407	C₂×C₄	—	146	2	no	—
408	C₂×C₄	—	146	2	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	#14556551	1	1	yes	characteristic
411	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
412	C₂×C₄	#14556559	1	1	yes	characteristic
413	C₂×C₄	#14556562	1	1	yes	characteristic
414	C₂×C₄	#14556564	1	1	yes	characteristic
415	C₂×C₄	#14556573	1	1	yes	characteristic
416	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
417	C₂×C₄	Q₁₆×D₇₃	1	1	yes	characteristic
418	C₂×C₄	#14556615	1	1	yes	characteristic
419	C₂×C₄	#14556615	1	1	yes	characteristic
420	C₂×C₄	#14556618	1	1	yes	characteristic
421	C₂×C₄	#14556618	1	1	yes	characteristic
422	C₂×C₄	#14556620	1	1	yes	characteristic
423	C₂×C₄	#14556623	1	1	yes	characteristic
424	C₈	—	4	2	no	—
425	C₈	—	8	1	no	—
426	C₈	—	292	2	no	—
427	C₈	—	584	1	no	—
428	C₂²	—	292	1	no	—
429	C₂²	—	292	1	no	—
430	C₂²	—	292	1	no	—
431	C₂²	—	292	1	no	—
432	C₂²	—	146	2	no	—
433	C₂²	—	146	2	no	—
434	C₂²	—	146	2	no	—
435	C₂²	#17988463	1	1	yes	characteristic
436	C₂²	#101×D₇₃	1	1	yes	characteristic
437	C₂²	#17988570	1	1	yes	characteristic
438	C₂²	#103×D₇₃	1	1	yes	characteristic
439	C₂²	#17988585	1	1	yes	characteristic
440	C₂²	#17988587	1	1	yes	characteristic
441	C₂²	#17988590	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	8	2	no	—
445	C₄	—	292	1	no	—
446	C₄	—	584	2	no	—
447	C₄	—	146	2	no	—
448	C₄	—	146	2	no	—
449	C₄	#17988736	1	1	yes	characteristic
450	C₄	#17988741	1	1	yes	characteristic
451	C₄	#17988830	1	1	yes	characteristic
452	C₄	#17988832	1	1	yes	characteristic
453	C₄	#17988837	1	1	yes	characteristic
454	C₄	#17988839	1	1	yes	characteristic
455	C₄	#17988916	1	1	yes	characteristic
456	C₄	#17988921	1	1	yes	characteristic
457	C₂	—	292	2	no	—
458	C₂	#22608614	1	1	yes	characteristic
459	C₂	#22608620	1	1	yes	characteristic
460	C₂	#22608652	1	1	yes	characteristic
461	C₂	#22608667	1	1	yes	characteristic
462	C₂	#22610235	1	1	yes	characteristic
463	C₂	#22610366	1	1	yes	characteristic
464	C₂	#22610396	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₇₃
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₂×#332×C₇₃	C₂
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	C₂×#332	D₇₃
hypocenter	C₇₃	#9137
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#332

Complements

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

N	H ≅ G/N	type
4. C₂×#17988333	C₂	semidirect
5. #22607815	C₂	semidirect
6. #22607815	C₂	semidirect
7. C₂×#332×C₇₃	C₂	semidirect
237. C₂×#332	D₇₃	semidirect
240. C₇₃	#9137	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988609	2
#22618278	2
#22609908	2
C₂×#17988333	2
#22607815	2
C₂×#332×C₇₃	2
#9137	73