Subgroups — #33103771

Order 18688.

916 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊C₄×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#22610648	C₂	1	1	yes	maximal, characteristic, complemented
3	#22610646	C₂	1	1	yes	maximal, characteristic, complemented
4	#22610490	C₂	1	1	yes	maximal, characteristic, complemented
5	#22610489	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610487	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609910	C₂	1	1	yes	maximal, characteristic
8	#22609910	C₂	1	1	yes	maximal, characteristic
9	#22609908	C₂	1	1	yes	maximal, characteristic
10	C₈×#11924007	C₂	1	1	yes	maximal, characteristic, complemented
11	#22609792	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#14556503	C₂	1	1	yes	maximal, characteristic
13	#22609688	C₂	1	1	yes	maximal, characteristic
14	#22609688	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊C₄×D₇₃	C₄	1	1	yes	characteristic
17	C₂×C₄⋊C₄×D₇₃	C₄	1	1	yes	characteristic
18	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
22	C₂×#14556520	C₂²	1	1	yes	characteristic
23	C₂×#14556520	C₂²	1	1	yes	characteristic
24	C₂×#14556520	C₂²	1	1	yes	characteristic
25	C₂×#14556520	C₂²	1	1	yes	characteristic
26	C₂×#14556503	C₂²	1	1	yes	characteristic
27	C₂×#14556503	C₂²	1	1	yes	characteristic
28	C₂×#14556503	C₂²	1	1	yes	characteristic
29	C₂×#14556503	C₂²	1	1	yes	characteristic
30	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
35	C₄⋊C₄×Dic₇₃	C₄	1	1	yes	characteristic
36	C₄⋊C₄×Dic₇₃	C₄	1	1	yes	characteristic
37	C₄×#11924007	C₂²	1	1	yes	characteristic
38	C₄×#11924007	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
40	#17988438	C₄	1	1	yes	characteristic
41	#17988438	C₄	1	1	yes	characteristic
42	#95×D₇₃	C₄	1	1	yes	characteristic
43	#95×D₇₃	C₄	1	1	yes	characteristic
44	#17988342	C₂²	1	1	yes	characteristic
45	#17988342	C₂²	1	1	yes	characteristic
46	#17988342	C₂²	1	1	yes	characteristic
47	#17988342	C₂²	1	1	yes	characteristic
48	#17988341	C₂²	1	1	yes	characteristic
49	#17988341	C₂²	1	1	yes	characteristic
50	#17988341	C₂²	1	1	yes	characteristic
51	#17988341	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
55	#336×C₇₃	C₂²	1	1	yes	characteristic
56	#336×C₇₃	C₂²	1	1	yes	characteristic
57	#336×C₇₃	C₂²	1	1	yes	characteristic
58	#336×C₇₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
66	C₂²×#10596831	C₂³	1	1	yes	characteristic
67	C₂²×#10596831	C₂³	1	1	yes	characteristic
68	C₂²×#10596831	C₂³	1	1	yes	characteristic
69	C₂²×#10596831	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
72	C₂×#11924007	C₂×C₄	1	1	yes	characteristic
73	C₂×#11924007	C₂×C₄	1	1	yes	characteristic
74	C₂×#11924007	C₂×C₄	1	1	yes	characteristic
75	C₂×#11924007	C₂×C₄	1	1	yes	characteristic
76	C₄⋊C₄×D₇₃	—	2	4	no	—
77	C₄⋊C₄×D₇₃	C₈	1	8	yes	complemented
78	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
85	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
87	C₄²×D₇₃	—	2	2	no	—
88	C₄²×D₇₃	—	2	2	no	—
89	C₄²×D₇₃	—	4	1	no	—
90	C₄²×D₇₃	—	4	1	no	—
91	C₄²×D₇₃	—	4	1	no	—
92	C₄²×D₇₃	—	4	1	no	—
93	C₄⋊#10596831	—	4	1	no	—
94	#14556520	—	2	2	no	—
95	#14556520	—	2	2	no	—
96	#14556520	—	4	1	no	—
97	#14556520	—	4	1	no	—
98	#14556503	—	2	2	no	—
99	#14556503	—	2	2	no	—
100	#14556503	—	2	2	no	—
101	#14556503	Q₈	1	4	yes	—
102	C₄×#10596831	—	4	1	no	—
103	C₈×Dic₇₃	—	2	2	no	—
104	C₈×Dic₇₃	—	2	2	no	—
105	C₈×Dic₇₃	—	4	1	no	—
106	C₈×Dic₇₃	—	4	1	no	—
107	#14556498	C₂×C₄	1	1	yes	characteristic
108	#14556498	C₂×C₄	1	1	yes	characteristic
109	#14556498	C₂×C₄	1	1	yes	characteristic
110	#14556498	C₂×C₄	1	1	yes	characteristic
111	#14556498	C₂×C₄	1	1	yes	characteristic
112	#14556498	C₂×C₄	1	1	yes	characteristic
113	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
117	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₇₃	—	4	1	no	—
123	C₄×C₈×C₇₃	—	4	1	no	—
124	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
125	#95×C₇₃	C₂×C₄	1	1	yes	characteristic
126	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×D₇₃	—	2	1	no	—
135	C₂×C₄×D₇₃	—	2	1	no	—
136	C₂×C₄×D₇₃	—	2	1	no	—
137	C₂×C₄×D₇₃	—	2	1	no	—
138	C₂×C₄×D₇₃	—	2	2	no	—
139	C₂×C₄×D₇₃	—	2	2	no	—
140	C₂×C₄×D₇₃	—	2	2	no	—
141	C₂×C₄×D₇₃	—	2	2	no	—
142	C₂×C₄×D₇₃	—	2	2	no	—
143	C₂×C₄×D₇₃	—	2	2	no	—
144	C₂×C₄×D₇₃	—	2	2	no	—
145	C₂×C₄×D₇₃	—	2	2	no	—
146	C₂×C₄×D₇₃	—	4	1	no	—
147	C₂×C₄×D₇₃	—	4	1	no	—
148	C₂×C₄×D₇₃	—	4	1	no	—
149	C₂×C₄×D₇₃	—	4	1	no	—
150	C₂×C₄×D₇₃	—	4	1	no	—
151	C₂×C₄×D₇₃	—	4	1	no	—
152	C₂×C₄×D₇₃	—	4	1	no	—
153	C₂×C₄×D₇₃	C₂×C₈	1	4	yes	—
154	C₂×C₄×D₇₃	C₂×C₈	1	4	yes	—
155	C₂×C₄×D₇₃	C₂×C₈	1	4	yes	—
156	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
157	C₂×C₄×D₇₃	#41	1	2	yes	—
158	C₂×#10596831	—	2	1	no	—
159	C₂×#10596831	—	2	1	no	—
160	C₂×#10596831	—	2	1	no	—
161	C₂×#10596831	—	2	1	no	—
162	C₂×#10596831	—	2	1	no	—
163	C₂×#10596831	—	2	1	no	—
164	C₂×#10596831	—	2	1	no	—
165	C₂×#10596831	—	2	1	no	—
166	C₂×#10596831	—	2	1	no	—
167	C₂×#10596831	—	2	1	no	—
168	C₂×#10596831	—	2	1	no	—
169	C₂×#10596831	C₂×Q₈	1	2	yes	—
170	C₄⋊Dic₇₃	—	2	2	no	—
171	C₄⋊Dic₇₃	C₂×C₈	1	4	yes	—
172	#11924007	—	2	2	no	—
173	#11924007	C₂×C₈	1	4	yes	—
174	#11924007	C₂×C₈	1	4	yes	—
175	#11924007	M₁₆	1	4	yes	—
176	C₄×Dic₇₃	—	2	1	no	—
177	C₄×Dic₇₃	—	2	1	no	—
178	C₄×Dic₇₃	—	2	1	no	—
179	C₄×Dic₇₃	—	2	1	no	—
180	C₄×Dic₇₃	—	2	2	no	—
181	C₄×Dic₇₃	—	2	2	no	—
182	C₄×Dic₇₃	—	4	1	no	—
183	C₄×Dic₇₃	—	4	1	no	—
184	C₄×Dic₇₃	—	4	1	no	—
185	C₄×Dic₇₃	—	4	1	no	—
186	C₄×Dic₇₃	#41	1	2	yes	—
187	C₄×Dic₇₃	#41	1	2	yes	—
188	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
189	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₇₃	—	2	1	no	—
196	C₂×C₈×C₇₃	—	2	1	no	—
197	C₂×C₈×C₇₃	—	2	1	no	—
198	C₂×C₈×C₇₃	—	2	1	no	—
199	C₂×C₈×C₇₃	—	2	1	no	—
200	C₂×C₈×C₇₃	—	2	1	no	—
201	C₂×C₈×C₇₃	—	2	1	no	—
202	C₂×C₈×C₇₃	—	2	1	no	—
203	C₂×C₈×C₇₃	—	2	1	no	—
204	C₂×C₈×C₇₃	—	2	1	no	—
205	C₂×C₈×C₇₃	—	2	1	no	—
206	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
207	C₄⋊C₄×C₇₃	—	2	2	no	—
208	C₄⋊C₄×C₇₃	C₂×C₈	1	4	yes	—
209	C₄²×C₇₃	—	2	1	no	—
210	C₄²×C₇₃	—	2	1	no	—
211	C₄²×C₇₃	—	2	1	no	—
212	C₄²×C₇₃	—	2	1	no	—
213	C₄²×C₇₃	—	2	1	no	—
214	C₄²×C₇₃	—	2	1	no	—
215	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
216	C₂²×D₇₃	—	2	1	no	—
217	C₂²×D₇₃	—	2	1	no	—
218	C₂²×D₇₃	—	2	1	no	—
219	C₂²×D₇₃	—	2	1	no	—
220	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
221	C₂²×D₇₃	C₂²×C₈	1	2	yes	—
222	C₂²×D₇₃	#131	1	2	yes	—
223	C₂×C₄×C₇₃	—	2	1	no	—
224	C₂×C₄×C₇₃	—	2	1	no	—
225	C₂×C₄×C₇₃	—	2	1	no	—
226	C₂×C₄×C₇₃	—	2	1	no	—
227	C₂×C₄×C₇₃	—	2	1	no	—
228	C₂×C₄×C₇₃	—	2	1	no	—
229	C₂×C₄×C₇₃	—	2	1	no	—
230	C₂×C₄×C₇₃	—	2	1	no	—
231	C₂×C₄×C₇₃	—	2	1	no	—
232	C₂×C₄×C₇₃	—	2	1	no	—
233	C₂×C₄×C₇₃	—	2	1	no	—
234	C₂×C₄×C₇₃	—	2	1	no	—
235	C₂×C₄×C₇₃	—	2	1	no	—
236	C₂×C₄×C₇₃	—	2	1	no	—
237	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
238	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
239	C₂×C₄×C₇₃	C₂²×C₈	1	2	yes	—
240	C₂×C₄×C₇₃	C₂×M₁₆	1	2	yes	—
241	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
242	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
243	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×Dic₇₃	—	2	1	no	—
248	C₂×Dic₇₃	—	2	1	no	—
249	C₂×Dic₇₃	—	2	1	no	—
250	C₂×Dic₇₃	—	2	1	no	—
251	C₂×Dic₇₃	—	2	1	no	—
252	C₂×Dic₇₃	—	2	1	no	—
253	C₂×Dic₇₃	—	2	1	no	—
254	C₂×Dic₇₃	—	2	1	no	—
255	C₂×Dic₇₃	—	2	1	no	—
256	C₂×Dic₇₃	—	2	1	no	—
257	C₂×Dic₇₃	—	2	1	no	—
258	C₂×Dic₇₃	—	2	1	no	—
259	C₂×Dic₇₃	—	2	1	no	—
260	C₂×Dic₇₃	#117	1	2	yes	—
261	C₂×Dic₇₃	#117	1	2	yes	—
262	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
263	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
264	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
265	C₂×Dic₇₃	C₂²×C₈	1	2	yes	—
266	C₂×Dic₇₃	C₂×M₁₆	1	2	yes	—
267	C₂×Dic₇₃	C₂×M₁₆	1	2	yes	—
268	C₄×D₇₃	—	2	2	no	—
269	C₄×D₇₃	—	2	2	no	—
270	C₄×D₇₃	—	2	2	no	—
271	C₄×D₇₃	—	2	2	no	—
272	C₄×D₇₃	—	2	8	no	—
273	C₄×D₇₃	—	4	4	no	—
274	C₄×D₇₃	—	4	4	no	—
275	C₄×D₇₃	—	4	4	no	—
276	C₄×D₇₃	—	4	4	no	—
277	C₄×D₇₃	—	4	4	no	—
278	C₈×C₇₃	—	2	2	no	—
279	C₈×C₇₃	—	4	1	no	—
280	C₈×C₇₃	—	4	1	no	—
281	C₈×C₇₃	—	4	1	no	—
282	#10596831	—	2	2	no	—
283	#10596831	—	4	1	no	—
284	#10596831	—	4	1	no	—
285	#10596831	—	4	1	no	—
286	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
287	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
288	C₂²×C₇₃	#518	1	1	yes	characteristic
289	C₂²×C₇₃	C₂³×C₈	1	1	yes	characteristic
290	C₂²×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
291	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
292	C₂²×C₇₃	#568	1	1	yes	characteristic
293	C₂×D₇₃	—	2	2	no	—
294	C₂×D₇₃	—	2	2	no	—
295	C₂×D₇₃	—	2	2	no	—
296	C₂×D₇₃	—	2	2	no	—
297	C₂×D₇₃	—	2	2	no	—
298	C₂×D₇₃	—	2	2	no	—
299	C₂×D₇₃	C₈×Q₈	1	4	yes	—
300	C₄×C₇₃	—	2	2	no	—
301	C₄×C₇₃	—	2	2	no	—
302	C₄×C₇₃	—	2	2	no	—
303	C₄×C₇₃	—	2	2	no	—
304	C₄×C₇₃	—	4	1	no	—
305	C₄×C₇₃	—	4	1	no	—
306	C₄×C₇₃	#553	1	1	yes	characteristic
307	C₄×C₇₃	#553	1	1	yes	characteristic
308	C₄×C₇₃	#554	1	1	yes	characteristic
309	C₄×C₇₃	#554	1	1	yes	characteristic
310	Dic₇₃	—	2	2	no	—
311	Dic₇₃	—	2	2	no	—
312	Dic₇₃	—	2	2	no	—
313	Dic₇₃	—	2	2	no	—
314	Dic₇₃	—	2	2	no	—
315	Dic₇₃	—	4	1	no	—
316	Dic₇₃	#431	1	4	yes	—
317	#22625	—	73	1	no	maximal, Sylow
318	C₂×C₇₃	#2345	1	1	yes	characteristic
319	C₂×C₇₃	C₂×#431	1	1	yes	characteristic
320	C₂×C₇₃	#2924	1	1	yes	characteristic
321	C₂×C₇₃	C₂×C₈×Q₈	1	1	yes	characteristic
322	C₂×C₇₃	Q₈×M₁₆	1	1	yes	characteristic
323	C₂×C₇₃	#2972	1	1	yes	characteristic
324	C₂×C₇₃	#2974	1	1	yes	characteristic
325	D₇₃	—	2	4	no	—
326	C₂×C₄×C₄⋊C₄	—	73	1	no	—
327	#1939	—	73	1	no	—
328	#1939	—	73	1	no	—
329	#1916	—	73	1	no	—
330	#1916	—	73	1	no	—
331	#1916	—	73	1	no	—
332	#1916	D₇₃	1	1	yes	characteristic, complemented
333	#1797	—	73	1	no	—
334	#1797	—	73	1	no	—
335	#1797	—	73	1	no	—
336	C₈×C₄⋊C₄	—	73	1	no	—
337	C₈×C₄⋊C₄	—	73	1	no	—
338	C₄×C₂²⋊C₈	—	73	1	no	—
339	C₄×C₂²⋊C₈	—	73	1	no	—
340	C₄×C₂²⋊C₈	—	73	1	no	—
341	C₇₃	#22625	1	1	yes	characteristic, complemented, Sylow
342	C₂²×C₄⋊C₄	—	73	1	no	—
343	C₂²×C₄⋊C₄	—	73	1	no	—
344	C₂²×C₄²	—	73	1	no	—
345	C₂²×C₄²	—	73	1	no	—
346	C₂²×C₄²	—	73	1	no	—
347	C₂×C₄⋊C₈	—	73	1	no	—
348	C₂×C₄⋊C₈	—	73	1	no	—
349	C₂×C₄⋊C₈	—	73	1	no	—
350	C₂×C₄⋊C₈	—	73	1	no	—
351	C₂×C₄⋊C₈	—	73	1	no	—
352	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
353	C₂×C₂²⋊C₈	—	73	1	no	—
354	C₂×C₂²⋊C₈	—	73	1	no	—
355	C₂×C₂²⋊C₈	—	73	1	no	—
356	C₂×C₂²⋊C₈	—	73	1	no	—
357	C₂×C₄×C₈	—	73	1	no	—
358	C₂×C₄×C₈	—	73	1	no	—
359	C₂×C₄×C₈	—	73	1	no	—
360	C₂×C₄×C₈	—	73	1	no	—
361	C₂×C₄×C₈	—	73	1	no	—
362	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
363	C₄×C₄⋊C₄	—	73	1	no	—
364	C₄×C₄⋊C₄	—	73	1	no	—
365	C₄×C₄⋊C₄	—	73	1	no	—
366	C₄×C₄⋊C₄	—	73	1	no	—
367	C₄×C₄⋊C₄	—	73	1	no	—
368	C₄×C₄⋊C₄	—	73	1	no	—
369	C₄×C₄⋊C₄	—	73	1	no	—
370	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
371	C₂×#95	—	73	1	no	—
372	C₂×#95	—	73	1	no	—
373	#336	—	73	1	no	—
374	#336	—	73	1	no	—
375	#336	—	73	1	no	—
376	#336	—	73	1	no	—
377	#336	—	73	1	no	—
378	#336	—	73	1	no	—
379	#336	—	73	1	no	—
380	#336	—	73	1	no	—
381	#336	C₂×D₇₃	1	1	yes	characteristic
382	#336	C₂×D₇₃	1	1	yes	characteristic
383	#336	C₂×D₇₃	1	1	yes	characteristic
384	#336	C₂×D₇₃	1	1	yes	characteristic
385	C₂³×C₄	—	73	1	no	—
386	C₂³×C₄	—	73	1	no	—
387	C₂³×C₄	—	73	1	no	—
388	C₂³×C₄	—	73	1	no	—
389	C₂³×C₄	—	73	1	no	—
390	C₂³×C₄	—	73	1	no	—
391	C₂³×C₄	—	73	1	no	—
392	C₂²×C₈	—	73	1	no	—
393	C₂²×C₈	—	73	1	no	—
394	C₂²×C₈	—	73	1	no	—
395	C₂²×C₈	—	73	1	no	—
396	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
397	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
398	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	—	73	1	no	—
401	C₂×C₄⋊C₄	—	73	1	no	—
402	C₂×C₄⋊C₄	—	73	1	no	—
403	C₂×C₄⋊C₄	—	73	1	no	—
404	C₂×C₄⋊C₄	—	73	8	no	—
405	C₂×C₄⋊C₄	—	73	1	no	—
406	C₂×C₄⋊C₄	—	73	1	no	—
407	C₂×C₄⋊C₄	—	146	4	no	—
408	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₄×D₇₃	1	1	yes	characteristic
410	C₂×C₄²	—	292	1	no	—
411	C₂×C₄²	—	292	1	no	—
412	C₂×C₄²	—	292	1	no	—
413	C₂×C₄²	—	292	1	no	—
414	C₂×C₄²	—	73	1	no	—
415	C₂×C₄²	—	73	1	no	—
416	C₂×C₄²	—	73	1	no	—
417	C₂×C₄²	—	73	1	no	—
418	C₂×C₄²	—	73	1	no	—
419	C₂×C₄²	—	73	1	no	—
420	C₂×C₄²	—	73	1	no	—
421	C₂×C₄²	—	73	1	no	—
422	C₂×C₄²	—	73	1	no	—
423	C₂×C₄²	—	146	2	no	—
424	C₂×C₄²	—	146	2	no	—
425	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
426	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
427	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
428	C₄⋊C₈	—	4	1	no	—
429	C₄⋊C₈	—	292	1	no	—
430	C₄⋊C₈	—	292	1	no	—
431	C₄⋊C₈	—	292	1	no	—
432	C₄⋊C₈	—	146	2	no	—
433	C₄⋊C₈	—	146	2	no	—
434	C₂²⋊C₈	—	73	4	no	—
435	C₂²⋊C₈	—	146	2	no	—
436	C₂²⋊C₈	—	146	2	no	—
437	C₂²⋊C₈	—	146	2	no	—
438	C₄×C₈	—	4	1	no	—
439	C₄×C₈	—	292	1	no	—
440	C₄×C₈	—	292	1	no	—
441	C₄×C₈	—	292	1	no	—
442	C₄×C₈	—	146	2	no	—
443	C₄×C₈	—	146	2	no	—
444	#95	—	73	1	no	—
445	#95	—	73	1	no	—
446	#95	—	73	1	no	—
447	#95	—	73	1	no	—
448	#95	—	73	1	no	—
449	#95	—	73	1	no	—
450	#95	C₄×D₇₃	1	1	yes	characteristic
451	#95	C₄×D₇₃	1	1	yes	characteristic
452	C₂⁴	—	73	1	no	—
453	C₂²×C₄	—	292	1	no	—
454	C₂²×C₄	—	292	1	no	—
455	C₂²×C₄	—	292	1	no	—
456	C₂²×C₄	—	292	1	no	—
457	C₂²×C₄	—	292	1	no	—
458	C₂²×C₄	—	292	1	no	—
459	C₂²×C₄	—	292	1	no	—
460	C₂²×C₄	—	73	4	no	—
461	C₂²×C₄	—	73	4	no	—
462	C₂²×C₄	—	73	1	no	—
463	C₂²×C₄	—	73	1	no	—
464	C₂²×C₄	—	73	1	no	—
465	C₂²×C₄	—	73	1	no	—
466	C₂²×C₄	—	73	1	no	—
467	C₂²×C₄	—	73	1	no	—
468	C₂²×C₄	—	73	4	no	—
469	C₂²×C₄	—	73	2	no	—
470	C₂²×C₄	—	73	2	no	—
471	C₂²×C₄	—	73	1	no	—
472	C₂²×C₄	—	146	2	no	—
473	C₂²×C₄	—	146	2	no	—
474	C₂²×C₄	—	146	2	no	—
475	C₂²×C₄	—	146	2	no	—
476	C₂²×C₄	—	146	2	no	—
477	C₂²×C₄	—	146	2	no	—
478	C₂²×C₄	—	146	2	no	—
479	C₂²×C₄	—	146	2	no	—
480	C₂²×C₄	—	146	1	no	—
481	C₂²×C₄	—	146	1	no	—
482	C₂²×C₄	—	146	1	no	—
483	C₂²×C₄	—	146	1	no	—
484	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
490	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	73	2	no	—
503	C₂×C₈	—	146	1	no	—
504	C₂×C₈	—	146	1	no	—
505	C₂×C₈	—	146	1	no	—
506	C₂×C₈	—	146	1	no	—
507	C₂×C₈	—	146	1	no	—
508	C₂×C₈	—	146	1	no	—
509	C₂×C₈	—	146	1	no	—
510	C₂×C₈	—	146	1	no	—
511	C₂×C₈	—	146	1	no	—
512	C₂×C₈	—	146	1	no	—
513	C₂×C₈	—	146	1	no	—
514	C₂×C₈	Q₈×D₇₃	1	2	yes	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	73	4	no	—
517	C₄⋊C₄	—	73	4	no	—
518	C₄⋊C₄	—	73	4	no	—
519	C₄⋊C₄	—	73	4	no	—
520	C₄⋊C₄	—	146	2	no	—
521	C₄⋊C₄	—	146	2	no	—
522	C₄⋊C₄	C₈×D₇₃	1	4	yes	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	292	1	no	—
530	C₄²	—	292	1	no	—
531	C₄²	—	292	1	no	—
532	C₄²	—	292	1	no	—
533	C₄²	—	73	2	no	—
534	C₄²	—	73	2	no	—
535	C₄²	—	146	2	no	—
536	C₄²	—	146	2	no	—
537	C₄²	—	146	1	no	—
538	C₄²	—	146	1	no	—
539	C₄²	—	146	1	no	—
540	C₄²	—	146	1	no	—
541	C₂³	—	73	2	no	—
542	C₂³	—	73	2	no	—
543	C₂³	—	73	2	no	—
544	C₂³	—	146	1	no	—
545	C₂³	—	146	1	no	—
546	C₂³	—	146	1	no	—
547	C₂³	—	146	1	no	—
548	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	292	4	no	—
564	C₂×C₄	—	292	4	no	—
565	C₂×C₄	—	292	4	no	—
566	C₂×C₄	—	292	4	no	—
567	C₂×C₄	—	292	4	no	—
568	C₂×C₄	—	73	2	no	—
569	C₂×C₄	—	73	2	no	—
570	C₂×C₄	—	73	2	no	—
571	C₂×C₄	—	73	2	no	—
572	C₂×C₄	—	73	2	no	—
573	C₂×C₄	—	73	2	no	—
574	C₂×C₄	—	73	2	no	—
575	C₂×C₄	—	73	2	no	—
576	C₂×C₄	—	146	8	no	—
577	C₂×C₄	—	146	1	no	—
578	C₂×C₄	—	146	1	no	—
579	C₂×C₄	—	146	1	no	—
580	C₂×C₄	—	146	1	no	—
581	C₂×C₄	—	146	1	no	—
582	C₂×C₄	—	146	1	no	—
583	C₂×C₄	—	146	1	no	—
584	C₂×C₄	—	146	1	no	—
585	C₂×C₄	—	146	1	no	—
586	C₂×C₄	—	146	1	no	—
587	C₂×C₄	—	146	1	no	—
588	C₂×C₄	—	146	1	no	—
589	C₂×C₄	—	146	1	no	—
590	C₂×C₄	—	146	2	no	—
591	C₂×C₄	—	146	2	no	—
592	C₂×C₄	—	146	2	no	—
593	C₂×C₄	—	146	2	no	—
594	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
595	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
596	C₂×C₄	C₂×C₈×D₇₃	1	2	yes	—
597	C₂×C₄	M₁₆×D₇₃	1	2	yes	—
598	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
599	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
600	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
601	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
602	C₂×C₄	#14556636	1	1	yes	characteristic
603	C₂×C₄	#14556637	1	1	yes	characteristic
604	C₈	—	2	2	no	—
605	C₈	—	4	1	no	—
606	C₈	—	4	1	no	—
607	C₈	—	4	1	no	—
608	C₈	—	292	1	no	—
609	C₈	—	292	1	no	—
610	C₈	—	292	1	no	—
611	C₈	—	146	2	no	—
612	C₂²	—	73	4	no	—
613	C₂²	—	146	2	no	—
614	C₂²	—	146	2	no	—
615	C₂²	—	146	2	no	—
616	C₂²	—	146	2	no	—
617	C₂²	—	146	2	no	—
618	C₂²	—	146	2	no	—
619	C₂²	#117×D₇₃	1	1	yes	characteristic
620	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
621	C₂²	#17989059	1	1	yes	characteristic
622	C₂²	C₂²×C₈×D₇₃	1	1	yes	characteristic
623	C₂²	C₂×M₁₆×D₇₃	1	1	yes	characteristic
624	C₂²	#131×D₇₃	1	1	yes	characteristic
625	C₂²	#17989352	1	1	yes	characteristic
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	2	no	—
629	C₄	—	2	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	292	1	no	—
633	C₄	—	73	4	no	—
634	C₄	—	146	2	no	—
635	C₄	—	146	2	no	—
636	C₄	—	146	2	no	—
637	C₄	—	146	2	no	—
638	C₄	—	146	2	no	—
639	C₄	#17989282	1	1	yes	characteristic
640	C₄	#17989288	1	1	yes	characteristic
641	C₄	#17989291	1	1	yes	characteristic
642	C₄	#17989293	1	1	yes	characteristic
643	C₂	—	146	4	no	—
644	C₂	#22612805	1	1	yes	characteristic
645	C₂	#431×D₇₃	1	1	yes	characteristic
646	C₂	#22618587	1	1	yes	characteristic
647	C₂	C₈×Q₈×D₇₃	1	1	yes	characteristic
648	C₂	#22618883	1	1	yes	characteristic
649	C₂	#22618952	1	1	yes	characteristic
650	C₂	#22618961	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂³×C₈
Fitting	C₇₃×#1916	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1916	D₇₃
hypocenter	C₇₃	#22625
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
2. #22610648	C₂	semidirect
3. #22610646	C₂	semidirect
4. #22610490	C₂	semidirect
5. #22610489	C₂	semidirect
6. #22610487	C₂	semidirect
10. C₈×#11924007	C₂	semidirect
11. #22609792	C₂	semidirect
15. C₇₃×#1916	C₂	semidirect
77. C₄⋊C₄×D₇₃	C₈	semidirect
332. #1916	D₇₃	semidirect
341. C₇₃	#22625	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊C₄×D₇₃	2
#22610648	2
#22610646	2
#22610490	2
#22610489	2
#22610487	2
#22609910	2
#22609908	2
C₈×#11924007	2
#22609792	2
C₄×#14556503	2
#22609688	2
C₇₃×#1916	2
#22625	73