Subgroups — #32991135

Order 18688.

1046 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556501	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988433	C₂	1	1	yes	maximal, characteristic
4	C₂×#17988342	C₂	1	1	yes	maximal, characteristic
5	C₂×#17988341	C₂	1	1	yes	maximal, characteristic
6	C₂×#17988341	C₂	1	1	yes	maximal, characteristic
7	C₂×#336×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×#10596831	C₂²	1	1	yes	characteristic
9	C₂³×#10596831	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
12	C₂×#14556501	—	2	2	no	—
13	C₂×#14556501	—	2	2	no	—
14	C₂×#14556501	C₄	1	4	yes	complemented
15	C₂×C₈×Dic₇₃	—	2	2	no	—
16	C₂×C₈×Dic₇₃	—	2	2	no	—
17	C₂×C₈×Dic₇₃	C₄	1	4	yes	complemented
18	#17988433	—	2	2	no	—
19	#17988433	—	2	2	no	—
20	C₂×#14556498	C₄	1	4	yes	—
21	#17988342	C₄	1	4	yes	complemented
22	#17988341	C₄	1	4	yes	complemented
23	#17988341	C₄	1	4	yes	complemented
24	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
27	#336×C₇₃	C₄	1	4	yes	complemented
28	C₂³×Dic₇₃	C₂×C₄	1	2	yes	—
29	C₂³×Dic₇₃	C₂×C₄	1	2	yes	—
30	C₂²×#10596831	—	2	1	no	—
31	C₂²×#10596831	—	2	1	no	—
32	C₂²×#10596831	—	2	1	no	—
33	C₂²×#10596831	—	2	1	no	—
34	C₂²×#10596831	—	2	1	no	—
35	C₂²×#10596831	—	2	1	no	—
36	C₂²×#10596831	—	2	1	no	—
37	C₂²×#10596831	—	2	1	no	—
38	C₂²×#10596831	C₂×C₄	1	2	yes	—
39	C₂²×#10596831	C₂×C₄	1	2	yes	—
40	C₂²×#10596831	C₂×C₄	1	2	yes	—
41	C₂²×#10596831	C₂×C₄	1	2	yes	—
42	C₂²×#10596831	C₂×C₄	1	2	yes	—
43	C₂²×#10596831	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₇₃	—	2	1	no	—
45	C₂×C₄×Dic₇₃	—	2	1	no	—
46	C₂×C₄×Dic₇₃	—	2	1	no	—
47	C₂×C₄×Dic₇₃	—	2	1	no	—
48	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
50	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
52	C₂×C₄×Dic₇₃	D₄	1	2	yes	—
53	C₂×C₄×Dic₇₃	D₄	1	2	yes	—
54	C₂×C₄×Dic₇₃	D₄	1	2	yes	—
55	C₂×C₄×Dic₇₃	Q₈	1	2	yes	—
56	#14556501	—	2	8	no	—
57	C₈×Dic₇₃	—	2	8	no	—
58	#14556498	—	2	8	no	—
59	C₂³×C₄×C₇₃	C₂×C₄	1	2	yes	—
60	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₇₃	—	2	1	no	—
62	C₂²×C₈×C₇₃	—	2	1	no	—
63	C₂²×C₈×C₇₃	—	2	1	no	—
64	C₂²×C₈×C₇₃	—	2	1	no	—
65	C₂²×C₈×C₇₃	—	2	1	no	—
66	C₂²×C₈×C₇₃	—	2	1	no	—
67	C₂²×C₈×C₇₃	—	2	1	no	—
68	C₂²×C₈×C₇₃	—	2	1	no	—
69	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
73	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
74	C₂²×C₈×C₇₃	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₇₃	—	2	1	no	—
76	C₂×C₄²×C₇₃	—	2	1	no	—
77	C₂×C₄²×C₇₃	—	2	1	no	—
78	C₂×C₄²×C₇₃	—	2	1	no	—
79	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₇₃	C₂×C₄	1	2	yes	—
81	C₂²×Dic₇₃	—	2	4	no	—
82	C₂²×Dic₇₃	—	2	4	no	—
83	C₂²×Dic₇₃	—	2	2	no	—
84	C₂²×Dic₇₃	—	2	2	no	—
85	C₂²×Dic₇₃	—	2	4	no	—
86	C₂²×Dic₇₃	—	2	4	no	—
87	C₂²×Dic₇₃	C₄²	1	4	yes	—
88	C₂²×Dic₇₃	C₄²	1	4	yes	—
89	C₂²×Dic₇₃	C₂²⋊C₄	1	4	yes	—
90	C₂²×Dic₇₃	C₄⋊C₄	1	4	yes	—
91	C₂×#10596831	—	2	2	no	—
92	C₂×#10596831	—	2	2	no	—
93	C₂×#10596831	—	2	2	no	—
94	C₂×#10596831	—	2	2	no	—
95	C₂×#10596831	—	2	2	no	—
96	C₂×#10596831	—	2	2	no	—
97	C₂×#10596831	—	2	2	no	—
98	C₂×#10596831	—	2	2	no	—
99	C₂×#10596831	—	2	2	no	—
100	C₂×#10596831	—	2	2	no	—
101	C₂×#10596831	—	2	2	no	—
102	C₂×#10596831	—	2	2	no	—
103	C₂×#10596831	C₄²	1	4	yes	—
104	C₂×#10596831	C₄²	1	4	yes	—
105	C₄×Dic₇₃	—	2	2	no	—
106	C₄×Dic₇₃	—	2	2	no	—
107	C₄×Dic₇₃	—	2	2	no	—
108	C₄×Dic₇₃	—	2	2	no	—
109	C₄×Dic₇₃	C₂²⋊C₄	1	4	yes	—
110	C₄×Dic₇₃	C₂²⋊C₄	1	4	yes	—
111	C₄×Dic₇₃	C₄⋊C₄	1	4	yes	—
112	C₄×Dic₇₃	C₄⋊C₄	1	4	yes	—
113	C₂⁴×C₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	—	2	2	no	—
115	C₂²×C₄×C₇₃	—	2	2	no	—
116	C₂²×C₄×C₇₃	—	2	4	no	—
117	C₂²×C₄×C₇₃	—	2	4	no	—
118	C₂²×C₄×C₇₃	C₄²	1	4	yes	—
119	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	2	no	—
138	C₂×C₈×C₇₃	—	2	2	no	—
139	C₂×C₈×C₇₃	—	2	2	no	—
140	C₂×C₈×C₇₃	—	2	2	no	—
141	C₂×C₈×C₇₃	—	2	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	2	2	no	—
145	C₂×C₈×C₇₃	C₄²	1	4	yes	—
146	C₂×C₈×C₇₃	C₄²	1	4	yes	—
147	C₄²×C₇₃	—	2	2	no	—
148	C₄²×C₇₃	—	2	2	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
152	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
153	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
154	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂³×C₇₃	#117	1	1	yes	characteristic
157	C₂³×C₇₃	#117	1	1	yes	characteristic
158	C₂³×C₇₃	#131	1	4	yes	—
159	C₂³×C₇₃	#131	1	4	yes	—
160	C₂×C₄×C₇₃	—	2	4	no	—
161	C₂×C₄×C₇₃	—	2	4	no	—
162	C₂×C₄×C₇₃	—	2	4	no	—
163	C₂×C₄×C₇₃	—	4	4	no	—
164	C₂×C₄×C₇₃	—	4	4	no	—
165	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
174	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
175	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
176	C₂×C₄×C₇₃	#117	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
193	C₂×Dic₇₃	—	2	4	no	—
194	C₂×Dic₇₃	—	2	4	no	—
195	C₂×Dic₇₃	—	2	8	no	—
196	C₂×Dic₇₃	—	2	8	no	—
197	C₂×Dic₇₃	—	2	4	no	—
198	C₂×Dic₇₃	—	2	4	no	—
199	C₂×Dic₇₃	—	2	4	no	—
200	C₂×Dic₇₃	—	4	4	no	—
201	C₂×Dic₇₃	—	4	4	no	—
202	C₂×Dic₇₃	#95	1	8	yes	—
203	C₈×C₇₃	—	2	4	no	—
204	C₈×C₇₃	—	2	4	no	—
205	#10596831	—	2	4	no	—
206	#10596831	—	2	4	no	—
207	C₂²×C₇₃	C₄³	1	1	yes	characteristic
208	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
209	C₂²×C₇₃	#376	1	1	yes	characteristic
210	C₂²×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
213	C₂²×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₇₃	#405	1	2	yes	—
215	C₂²×C₇₃	#405	1	2	yes	—
216	C₂²×C₇₃	#405	1	2	yes	—
217	C₂²×C₇₃	#405	1	2	yes	—
218	C₂²×C₇₃	#405	1	2	yes	—
219	C₂²×C₇₃	#405	1	2	yes	—
220	C₂²×C₇₃	#408	1	4	yes	—
221	C₂²×C₇₃	#424	1	4	yes	—
222	C₂²×C₇₃	#433	1	4	yes	—
223	C₂²×C₇₃	#433	1	4	yes	—
224	C₄×C₇₃	—	4	4	no	—
225	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
226	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
227	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
228	C₄×C₇₃	C₄×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
230	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
231	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₄×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
233	Dic₇₃	—	2	8	no	—
234	Dic₇₃	—	4	4	no	—
235	#10694	—	73	1	no	maximal, Sylow
236	C₂×C₇₃	C₄×#95	1	1	yes	characteristic
237	C₂×C₇₃	#1726	1	1	yes	characteristic
238	C₂×C₇₃	#1726	1	1	yes	characteristic
239	C₂×C₇₃	#1729	1	2	yes	—
240	C₂×C₇₃	#1746	1	2	yes	—
241	C₂×C₇₃	#1750	1	2	yes	—
242	C₂×C₇₃	#1750	1	2	yes	—
243	C₂×C₇₃	#1768	1	2	yes	—
244	C₂×C₇₃	#1768	1	2	yes	—
245	C₂²×#97	—	73	1	no	—
246	C₂²×C₄×C₈	—	73	1	no	—
247	C₂×#376	—	73	1	no	—
248	C₂×#336	—	73	1	no	—
249	C₂×#336	—	73	1	no	—
250	C₂×#336	—	73	1	no	—
251	C₂×#336	D₇₃	1	1	yes	characteristic
252	C₇₃	#10694	1	1	yes	characteristic, complemented, Sylow
253	C₂³×C₈	—	73	1	no	—
254	C₂³×C₈	—	73	1	no	—
255	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
256	C₂³×C₈	C₂×D₇₃	1	1	yes	characteristic
257	C₂²×C₄²	—	73	1	no	—
258	C₂²×C₄²	—	73	1	no	—
259	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
260	C₂×#97	—	73	4	no	—
261	C₂×#97	—	146	2	no	—
262	C₂×#97	—	146	2	no	—
263	C₂×C₄×C₈	—	73	4	no	—
264	C₂×C₄×C₈	—	146	2	no	—
265	C₂×C₄×C₈	—	146	2	no	—
266	#376	—	146	2	no	—
267	#376	—	146	2	no	—
268	C₂×#95	—	73	4	no	—
269	#336	—	73	4	no	—
270	#336	—	73	4	no	—
271	#336	—	73	4	no	—
272	#336	Dic₇₃	1	4	yes	complemented
273	C₂³×C₄	—	73	2	no	—
274	C₂³×C₄	—	73	2	no	—
275	C₂³×C₄	C₄×D₇₃	1	2	yes	—
276	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	73	2	no	—
286	C₂²×C₈	—	73	2	no	—
287	C₂²×C₈	—	73	2	no	—
288	C₂²×C₈	—	73	2	no	—
289	C₂²×C₈	—	73	2	no	—
290	C₂²×C₈	—	73	2	no	—
291	C₂²×C₈	—	146	1	no	—
292	C₂²×C₈	—	146	1	no	—
293	C₂²×C₈	—	146	1	no	—
294	C₂²×C₈	—	146	1	no	—
295	C₂²×C₈	—	146	1	no	—
296	C₂²×C₈	—	146	1	no	—
297	C₂²×C₈	—	146	1	no	—
298	C₂²×C₈	—	146	1	no	—
299	C₂²×C₈	C₄×D₇₃	1	2	yes	—
300	C₂²×C₈	C₄×D₇₃	1	2	yes	—
301	C₂²×C₈	C₄×D₇₃	1	2	yes	—
302	C₂²×C₈	C₄×D₇₃	1	2	yes	—
303	C₂²×C₈	C₂×Dic₇₃	1	2	yes	—
304	C₂²×C₈	C₂×Dic₇₃	1	2	yes	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	73	2	no	—
310	C₂×C₄²	—	73	2	no	—
311	C₂×C₄²	—	73	2	no	—
312	C₂×C₄²	—	73	2	no	—
313	C₂×C₄²	—	73	2	no	—
314	C₂×C₄²	—	73	2	no	—
315	C₂×C₄²	—	73	2	no	—
316	C₂×C₄²	—	73	2	no	—
317	C₂×C₄²	—	146	1	no	—
318	C₂×C₄²	—	146	1	no	—
319	C₂×C₄²	—	146	1	no	—
320	C₂×C₄²	—	146	1	no	—
321	C₂×C₄²	C₄×D₇₃	1	2	yes	—
322	C₂×C₄²	C₂×Dic₇₃	1	2	yes	—
323	#97	—	146	8	no	—
324	C₄×C₈	—	146	8	no	—
325	#95	—	146	8	no	—
326	C₂⁴	C₂×C₄×D₇₃	1	1	yes	characteristic
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	73	4	no	—
332	C₂²×C₄	—	73	4	no	—
333	C₂²×C₄	—	73	4	no	—
334	C₂²×C₄	—	73	4	no	—
335	C₂²×C₄	—	146	2	no	—
336	C₂²×C₄	—	146	2	no	—
337	C₂²×C₄	—	146	4	no	—
338	C₂²×C₄	—	146	4	no	—
339	C₂²×C₄	—	146	4	no	—
340	C₂²×C₄	—	146	4	no	—
341	C₂²×C₄	C₄×Dic₇₃	1	4	yes	—
342	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
343	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
344	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
347	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
350	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
351	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
352	C₂²×C₄	#11924027	1	1	yes	characteristic
353	C₂²×C₄	#11924027	1	1	yes	characteristic
354	C₂²×C₄	#11924027	1	1	yes	characteristic
355	C₂²×C₄	#11924029	1	1	yes	characteristic
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	73	4	no	—
369	C₂×C₈	—	73	4	no	—
370	C₂×C₈	—	146	2	no	—
371	C₂×C₈	—	146	2	no	—
372	C₂×C₈	—	146	2	no	—
373	C₂×C₈	—	146	2	no	—
374	C₂×C₈	—	146	2	no	—
375	C₂×C₈	—	146	2	no	—
376	C₂×C₈	—	146	2	no	—
377	C₂×C₈	—	146	2	no	—
378	C₂×C₈	—	146	2	no	—
379	C₂×C₈	—	146	2	no	—
380	C₂×C₈	—	146	2	no	—
381	C₂×C₈	—	146	2	no	—
382	C₂×C₈	C₄×Dic₇₃	1	4	yes	—
383	C₂×C₈	C₄×Dic₇₃	1	4	yes	—
384	C₄²	—	2	2	no	—
385	C₄²	—	2	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	73	4	no	—
389	C₄²	—	73	4	no	—
390	C₄²	—	73	4	no	—
391	C₄²	—	73	4	no	—
392	C₄²	—	146	2	no	—
393	C₄²	—	146	2	no	—
394	C₄²	—	146	2	no	—
395	C₄²	—	146	2	no	—
396	C₂³	C₄²×D₇₃	1	1	yes	characteristic
397	C₂³	C₄²×D₇₃	1	1	yes	characteristic
398	C₂³	C₂×C₄×Dic₇₃	1	1	yes	characteristic
399	C₂³	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
400	C₂³	C₄⋊C₄×D₇₃	1	1	yes	characteristic
401	C₂³	#14556547	1	1	yes	characteristic
402	C₂³	#14556549	1	1	yes	characteristic
403	C₂³	#14556597	1	4	yes	—
404	C₂³	#14556599	1	4	yes	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	292	4	no	—
411	C₂×C₄	—	292	4	no	—
412	C₂×C₄	—	73	8	no	—
413	C₂×C₄	—	146	4	no	—
414	C₂×C₄	—	146	4	no	—
415	C₂×C₄	—	146	4	no	—
416	C₂×C₄	—	146	8	no	—
417	C₂×C₄	—	146	4	no	—
418	C₂×C₄	—	146	4	no	—
419	C₂×C₄	—	146	8	no	—
420	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
421	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
422	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂×C₄×Dic₇₃	1	1	yes	characteristic
424	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
427	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
428	C₂×C₄	#14556547	1	1	yes	characteristic
429	C₂×C₄	#14556547	1	1	yes	characteristic
430	C₂×C₄	#14556549	1	1	yes	characteristic
431	C₂×C₄	#14556549	1	1	yes	characteristic
432	C₂×C₄	#14556551	1	1	yes	characteristic
433	C₂×C₄	#14556551	1	1	yes	characteristic
434	C₂×C₄	#14556551	1	1	yes	characteristic
435	C₂×C₄	#14556551	1	1	yes	characteristic
436	C₂×C₄	#14556551	1	1	yes	characteristic
437	C₂×C₄	#14556551	1	1	yes	characteristic
438	C₂×C₄	#14556553	1	1	yes	characteristic
439	C₂×C₄	#14556553	1	1	yes	characteristic
440	C₂×C₄	#14556553	1	1	yes	characteristic
441	C₂×C₄	D₄×Dic₇₃	1	1	yes	characteristic
442	C₂×C₄	D₄×Dic₇₃	1	1	yes	characteristic
443	C₂×C₄	D₄×Dic₇₃	1	1	yes	characteristic
444	C₂×C₄	#14556556	1	1	yes	characteristic
445	C₂×C₄	#14556556	1	1	yes	characteristic
446	C₂×C₄	#14556556	1	1	yes	characteristic
447	C₂×C₄	Q₈×Dic₇₃	1	1	yes	characteristic
448	C₈	—	2	4	no	—
449	C₈	—	2	4	no	—
450	C₈	—	146	4	no	—
451	C₈	—	146	4	no	—
452	C₂²	C₄²×Dic₇₃	1	1	yes	characteristic
453	C₂²	#95×D₇₃	1	1	yes	characteristic
454	C₂²	#17988432	1	1	yes	characteristic
455	C₂²	#17988434	1	1	yes	characteristic
456	C₂²	C₂²⋊C₄×Dic₇₃	1	1	yes	characteristic
457	C₂²	#17988438	1	1	yes	characteristic
458	C₂²	C₄⋊C₄×Dic₇₃	1	1	yes	characteristic
459	C₂²	#17988541	1	2	yes	—
460	C₂²	#17988541	1	2	yes	—
461	C₂²	#17988542	1	2	yes	—
462	C₂²	#17988544	1	2	yes	—
463	C₂²	#17988544	1	2	yes	—
464	C₂²	#17988545	1	2	yes	—
465	C₂²	#17988552	1	4	yes	—
466	C₂²	#17988612	1	4	yes	—
467	C₂²	#17988645	1	4	yes	—
468	C₂²	#17988647	1	4	yes	—
469	C₄	—	4	4	no	—
470	C₄	—	292	4	no	—
471	C₄	—	146	8	no	—
472	C₄	#17988434	1	1	yes	characteristic
473	C₄	#17988434	1	1	yes	characteristic
474	C₄	C₂²⋊C₄×Dic₇₃	1	1	yes	characteristic
475	C₄	C₂²⋊C₄×Dic₇₃	1	1	yes	characteristic
476	C₄	#17988438	1	1	yes	characteristic
477	C₄	#17988438	1	1	yes	characteristic
478	C₄	C₄⋊C₄×Dic₇₃	1	1	yes	characteristic
479	C₄	C₄⋊C₄×Dic₇₃	1	1	yes	characteristic
480	C₂	#95×Dic₇₃	1	1	yes	characteristic
481	C₂	#22609617	1	1	yes	characteristic
482	C₂	#22609619	1	1	yes	characteristic
483	C₂	#22609626	1	2	yes	—
484	C₂	#22609681	1	2	yes	—
485	C₂	#22609696	1	2	yes	—
486	C₂	#22609699	1	2	yes	—
487	C₂	#22609787	1	2	yes	—
488	C₂	#22609790	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₇₃
commutator	C₂²×C₇₃	C₄³
Fitting	C₂×#336×C₇₃	C₂
socle, prime radical	C₂⁴×C₇₃	C₂²×C₄
cosocle	C₂³×C₄×C₇₃	C₂³
hypercenter	C₂×#336	D₇₃
hypocenter	C₇₃	#10694
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³×C₄ ◁ C₂×#336

Complements

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

N	H ≅ G/N	type
14. C₂×#14556501	C₄	semidirect
17. C₂×C₈×Dic₇₃	C₄	semidirect
21. #17988342	C₄	semidirect
22. #17988341	C₄	semidirect
23. #17988341	C₄	semidirect
27. #336×C₇₃	C₄	semidirect
252. C₇₃	#10694	semidirect
272. #336	Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14556501	2
C₂²×C₈×Dic₇₃	2
C₂×#17988433	2
C₂×#17988342	2
C₂×#17988341	2
C₂×#336×C₇₃	2
#10694	73