Subgroups — C₇₃×#18721 #32928125

Order 18688.

870 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3544	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3248	C₂	1	2	yes	maximal, complemented
3	C₇₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1646	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1645	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1644	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1643	C₂	1	2	yes	maximal, complemented
8	C₂×#333×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1483	C₂	1	2	yes	maximal, complemented
10	#563×C₇₃	—	2	2	no	—
11	Q₈²×C₇₃	C₂²	1	1	yes	characteristic
12	#555×C₇₃	C₂²	1	1	yes	characteristic
13	#554×C₇₃	C₂²	1	2	yes	—
14	#552×C₇₃	—	2	2	no	—
15	#547×C₇₃	—	2	2	no	—
16	#544×C₇₃	—	2	2	no	—
17	#542×C₇₃	—	2	2	no	—
18	#536×C₇₃	—	2	2	no	—
19	#533×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
21	#529×C₇₃	C₂²	1	2	yes	—
22	#491×C₇₃	—	2	2	no	—
23	#487×C₇₃	C₂²	1	2	yes	—
24	#487×C₇₃	C₂²	1	2	yes	—
25	#479×C₇₃	—	2	2	no	—
26	#475×C₇₃	C₂²	1	2	yes	—
27	#474×C₇₃	C₂²	1	2	yes	—
28	#467×C₇₃	—	2	2	no	—
29	#465×C₇₃	—	2	2	no	—
30	#464×C₇₃	—	2	2	no	—
31	#462×C₇₃	C₂²	1	2	yes	—
32	#461×C₇₃	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
34	#419×C₇₃	—	2	2	no	—
35	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
36	#333×C₇₃	C₂²	1	1	yes	characteristic
37	#333×C₇₃	C₂²	1	1	yes	characteristic
38	#333×C₇₃	C₂²	1	2	yes	—
39	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
40	Q₈⋊C₈×C₇₃	C₂²	1	2	yes	—
41	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
42	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂²×Q₈×C₇₃	D₄	1	2	yes	—
45	C₂×Q₁₆×C₇₃	—	2	2	no	—
46	C₂×SD₁₆×C₇₃	—	2	2	no	—
47	C₂×M₁₆×C₇₃	—	2	1	no	—
48	C₂²×C₈×C₇₃	—	2	2	no	—
49	C₄⋊Q₈×C₇₃	—	2	2	no	—
50	C₄⋊Q₈×C₇₃	—	2	2	no	—
51	C₄⋊Q₈×C₇₃	—	2	2	no	—
52	C₄⋊Q₈×C₇₃	—	2	2	no	—
53	C₄⋊Q₈×C₇₃	D₄	1	2	yes	—
54	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
57	#126×C₇₃	—	2	4	no	—
58	#126×C₇₃	—	2	2	no	—
59	#125×C₇₃	—	2	4	no	—
60	#125×C₇₃	—	2	2	no	—
61	#125×C₇₃	—	2	1	no	—
62	#125×C₇₃	D₄	1	2	yes	—
63	#124×C₇₃	—	2	2	no	—
64	#124×C₇₃	—	2	2	no	—
65	#124×C₇₃	D₄	1	2	yes	—
66	#123×C₇₃	—	2	4	no	—
67	#123×C₇₃	—	2	4	no	—
68	#123×C₇₃	—	2	2	no	—
69	C₂²⋊Q₈×C₇₃	—	2	4	no	—
70	C₂²⋊Q₈×C₇₃	—	2	4	no	—
71	C₂²⋊Q₈×C₇₃	—	2	4	no	—
72	C₂²⋊Q₈×C₇₃	—	2	2	no	—
73	C₂²⋊Q₈×C₇₃	—	2	2	no	—
74	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
75	#121×C₇₃	—	2	2	no	—
76	#121×C₇₃	D₄	1	2	yes	—
77	C₄×Q₈×C₇₃	—	2	2	no	—
78	C₄×Q₈×C₇₃	—	2	2	no	—
79	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
80	C₄×D₄×C₇₃	—	2	2	no	—
81	C₄×D₄×C₇₃	—	2	2	no	—
82	C₄×D₄×C₇₃	C₂³	1	2	yes	—
83	#117×C₇₃	—	2	2	no	—
84	#117×C₇₃	—	2	2	no	—
85	#117×C₇₃	—	2	2	no	—
86	#117×C₇₃	—	2	1	no	—
87	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
88	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
89	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
90	#107×C₇₃	—	2	2	no	—
91	#106×C₇₃	—	2	2	no	—
92	C₄⋊C₈×C₇₃	—	2	2	no	—
93	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
94	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
95	#103×C₇₃	—	2	4	no	—
96	#103×C₇₃	—	2	4	no	—
97	#103×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	2	no	—
99	#103×C₇₃	—	2	2	no	—
100	#102×C₇₃	—	2	2	no	—
101	#97×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	C₂³	1	2	yes	—
103	#41×C₇₃	—	8	4	no	—
104	C₂×Q₈×C₇₃	—	2	2	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	—	2	2	no	—
107	C₂×Q₈×C₇₃	—	4	4	no	—
108	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
110	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
111	C₂×D₄×C₇₃	—	2	2	no	—
112	C₂×D₄×C₇₃	—	2	2	no	—
113	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₇₃	—	2	2	no	—
115	C₂²×C₄×C₇₃	—	2	4	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
119	Q₁₆×C₇₃	—	8	2	no	—
120	SD₁₆×C₇₃	—	8	2	no	—
121	M₁₆×C₇₃	—	4	2	no	—
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	—	2	2	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	8	2	no	—
126	C₄⋊C₄×C₇₃	—	2	4	no	—
127	C₄⋊C₄×C₇₃	—	2	4	no	—
128	C₄⋊C₄×C₇₃	—	2	4	no	—
129	C₄⋊C₄×C₇₃	—	2	4	no	—
130	C₄⋊C₄×C₇₃	—	2	2	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	—	2	2	no	—
136	C₄⋊C₄×C₇₃	—	2	2	no	—
137	C₄⋊C₄×C₇₃	—	2	2	no	—
138	C₄⋊C₄×C₇₃	—	4	2	no	—
139	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
141	C₂²⋊C₄×C₇₃	—	2	4	no	—
142	C₂²⋊C₄×C₇₃	—	2	4	no	—
143	C₂²⋊C₄×C₇₃	—	2	2	no	—
144	C₂²⋊C₄×C₇₃	—	2	2	no	—
145	C₂²⋊C₄×C₇₃	—	2	2	no	—
146	C₂²⋊C₄×C₇₃	—	2	2	no	—
147	C₂²⋊C₄×C₇₃	—	2	2	no	—
148	C₂²⋊C₄×C₇₃	—	4	1	no	—
149	C₄²×C₇₃	—	2	2	no	—
150	C₄²×C₇₃	—	2	2	no	—
151	C₄²×C₇₃	—	2	2	no	—
152	C₄²×C₇₃	—	4	1	no	—
153	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₇₃	C₂×D₄	1	2	yes	—
155	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
156	C₂³×C₇₃	—	2	2	no	—
157	C₂³×C₇₃	#120	1	1	yes	characteristic
158	Q₈×C₇₃	—	2	2	no	—
159	Q₈×C₇₃	—	2	2	no	—
160	Q₈×C₇₃	—	4	2	no	—
161	Q₈×C₇₃	—	4	2	no	—
162	Q₈×C₇₃	—	4	2	no	—
163	Q₈×C₇₃	—	4	2	no	—
164	Q₈×C₇₃	—	8	2	no	—
165	Q₈×C₇₃	—	8	2	no	—
166	D₄×C₇₃	—	2	2	no	—
167	D₄×C₇₃	—	2	2	no	—
168	D₄×C₇₃	—	4	4	no	—
169	D₄×C₇₃	—	8	2	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	2	2	no	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	2	2	no	—
177	C₂×C₄×C₇₃	—	2	2	no	—
178	C₂×C₄×C₇₃	—	4	4	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	—	4	2	no	—
182	C₂×C₄×C₇₃	—	8	4	no	—
183	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
184	C₂×C₄×C₇₃	#120	1	2	yes	—
185	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
187	C₈×C₇₃	—	4	2	no	—
188	C₈×C₇₃	—	4	2	no	—
189	C₈×C₇₃	—	4	2	no	—
190	C₂²×C₇₃	—	2	2	no	—
191	C₂²×C₇₃	—	4	2	no	—
192	C₂²×C₇₃	—	4	2	no	—
193	C₂²×C₇₃	—	4	2	no	—
194	C₂²×C₇₃	#455	1	2	yes	—
195	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
196	C₄×C₇₃	—	2	2	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	4	2	no	—
200	C₄×C₇₃	—	4	2	no	—
201	C₄×C₇₃	—	4	2	no	—
202	C₄×C₇₃	—	4	2	no	—
203	C₄×C₇₃	—	4	2	no	—
204	C₄×C₇₃	—	8	2	no	—
205	C₄×C₇₃	#577	1	2	yes	—
206	C₄×C₇₃	#578	1	2	yes	—
207	#18721	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂×C₇₃	—	2	2	no	—
209	C₂×C₇₃	—	8	2	no	—
210	C₂×C₇₃	#3013	1	2	yes	—
211	C₂×C₇₃	C₂×#455	1	1	yes	characteristic
212	#3544	C₂×C₇₃	1	1	yes	characteristic
213	#3248	C₂×C₇₃	1	2	yes	complemented
214	#3139	C₂×C₇₃	1	1	yes	characteristic, complemented
215	#1646	C₂×C₇₃	1	2	yes	complemented
216	#1645	C₂×C₇₃	1	2	yes	complemented
217	#1644	C₂×C₇₃	1	2	yes	complemented
218	#1643	C₂×C₇₃	1	2	yes	complemented
219	C₂×#333	C₂×C₇₃	1	1	yes	characteristic, complemented
220	#1483	C₂×C₇₃	1	2	yes	complemented
221	C₇₃	#18721	1	1	yes	characteristic, direct product factor, Sylow
222	#563	—	2	2	no	—
223	Q₈²	C₂²×C₇₃	1	1	yes	characteristic
224	#555	C₂²×C₇₃	1	1	yes	characteristic
225	#554	C₂²×C₇₃	1	2	yes	—
226	#552	—	2	2	no	—
227	#547	—	2	2	no	—
228	#544	—	2	2	no	—
229	#542	—	2	2	no	—
230	#536	—	2	2	no	—
231	#533	C₂²×C₇₃	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
233	#529	C₂²×C₇₃	1	2	yes	—
234	#491	—	2	2	no	—
235	#487	C₂²×C₇₃	1	2	yes	—
236	#487	C₂²×C₇₃	1	2	yes	—
237	#479	—	2	2	no	—
238	#475	C₂²×C₇₃	1	2	yes	—
239	#474	C₂²×C₇₃	1	2	yes	—
240	#467	—	2	2	no	—
241	#465	—	2	2	no	—
242	#464	—	2	2	no	—
243	#462	C₂²×C₇₃	1	2	yes	—
244	#461	C₂²×C₇₃	1	2	yes	—
245	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
246	#419	—	2	2	no	—
247	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
248	#333	C₂²×C₇₃	1	1	yes	characteristic
249	#333	C₂²×C₇₃	1	1	yes	characteristic
250	#333	C₂²×C₇₃	1	2	yes	—
251	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
252	Q₈⋊C₈	C₂²×C₇₃	1	2	yes	—
253	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
254	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
255	C₂×#41	—	2	2	no	—
256	C₂²×Q₈	D₄×C₇₃	1	2	yes	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂²×C₈	—	2	2	no	—
261	C₄⋊Q₈	—	2	2	no	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	D₄×C₇₃	1	2	yes	—
266	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
267	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
268	C₄⋊Q₈	C₂³×C₇₃	1	1	yes	characteristic
269	#126	—	2	4	no	—
270	#126	—	2	2	no	—
271	#125	—	2	4	no	—
272	#125	—	2	2	no	—
273	#125	—	2	1	no	—
274	#125	D₄×C₇₃	1	2	yes	—
275	#124	—	2	2	no	—
276	#124	—	2	2	no	—
277	#124	D₄×C₇₃	1	2	yes	—
278	#123	—	2	4	no	—
279	#123	—	2	4	no	—
280	#123	—	2	2	no	—
281	C₂²⋊Q₈	—	2	4	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	4	no	—
284	C₂²⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	—	2	2	no	—
286	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
287	#121	—	2	2	no	—
288	#121	D₄×C₇₃	1	2	yes	—
289	C₄×Q₈	—	2	2	no	—
290	C₄×Q₈	—	2	2	no	—
291	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
292	C₄×D₄	—	2	2	no	—
293	C₄×D₄	—	2	2	no	—
294	C₄×D₄	C₂³×C₇₃	1	2	yes	—
295	#117	—	2	2	no	—
296	#117	—	2	2	no	—
297	#117	—	2	2	no	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
302	#107	—	2	2	no	—
303	#106	—	2	2	no	—
304	C₄⋊C₈	—	2	2	no	—
305	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
306	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
307	#103	—	2	4	no	—
308	#103	—	2	4	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#102	—	2	2	no	—
313	#97	—	2	1	no	—
314	C₄×C₈	C₂³×C₇₃	1	2	yes	—
315	#41	—	8	4	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	4	4	no	—
320	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
321	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
322	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
331	Q₁₆	—	8	2	no	—
332	SD₁₆	—	8	2	no	—
333	M₁₆	—	4	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	8	2	no	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	4	no	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
352	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
353	C₂²⋊C₄	—	2	4	no	—
354	C₂²⋊C₄	—	2	4	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₂²⋊C₄	—	2	2	no	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	4	1	no	—
365	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
366	C₄²	C₂×D₄×C₇₃	1	2	yes	—
367	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
368	C₂³	—	2	2	no	—
369	C₂³	#120×C₇₃	1	1	yes	characteristic
370	Q₈	—	2	2	no	—
371	Q₈	—	2	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	8	2	no	—
377	Q₈	—	8	2	no	—
378	D₄	—	2	2	no	—
379	D₄	—	2	2	no	—
380	D₄	—	4	4	no	—
381	D₄	—	8	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	4	4	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	4	no	—
395	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
396	C₂×C₄	#120×C₇₃	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	#455×C₇₃	1	2	yes	—
407	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	8	2	no	—
417	C₄	#577×C₇₃	1	2	yes	—
418	C₄	#578×C₇₃	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	8	2	no	—
421	C₂	C₇₃×#3013	1	2	yes	—
422	C₂	C₂×#455×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	C₇₃×#3544	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₇₃×#3248	C₂	semidirect
3. C₇₃×#3139	C₂	semidirect
4. C₇₃×#1646	C₂	semidirect
5. C₇₃×#1645	C₂	semidirect
6. C₇₃×#1644	C₂	semidirect
7. C₇₃×#1643	C₂	semidirect
8. C₂×#333×C₇₃	C₂	semidirect
9. C₇₃×#1483	C₂	semidirect
207. #18721	C₇₃	direct (N × H)
213. #3248	C₂×C₇₃	semidirect
214. #3139	C₂×C₇₃	semidirect
215. #1646	C₂×C₇₃	semidirect
216. #1645	C₂×C₇₃	semidirect
217. #1644	C₂×C₇₃	semidirect
218. #1643	C₂×C₇₃	semidirect
219. C₂×#333	C₂×C₇₃	semidirect
220. #1483	C₂×C₇₃	semidirect
221. C₇₃	#18721	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#3544	2
C₇₃×#3248	2
C₇₃×#3139	2
C₇₃×#1646	2
C₇₃×#1645	2
C₇₃×#1644	2
C₇₃×#1643	2
C₂×#333×C₇₃	2
C₇₃×#1483	2
#18721	73

Subgroups — C73×#18721 #32928125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18721 #32928125