Subgroups — C₇₃×#19889 #32929293

Order 18688.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3391	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3278	C₂	1	2	yes	maximal, complemented
4	C₇₃×#1706	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#1685	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1668	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1641	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1627	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1589	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₇₃	—	2	2	no	—
13	#550×C₇₃	C₂²	1	2	yes	—
14	D₄×Q₈×C₇₃	C₂²	1	2	yes	—
15	#500×C₇₃	—	2	1	no	—
16	#500×C₇₃	C₂²	1	1	yes	characteristic
17	#493×C₇₃	—	2	1	no	—
18	#493×C₇₃	C₂²	1	1	yes	characteristic
19	#492×C₇₃	C₂²	1	2	yes	—
20	#486×C₇₃	C₂²	1	2	yes	—
21	#474×C₇₃	—	2	2	no	—
22	#474×C₇₃	C₂²	1	2	yes	—
23	#468×C₇₃	—	2	2	no	—
24	#462×C₇₃	C₂²	1	2	yes	—
25	#460×C₇₃	C₂²	1	2	yes	—
26	#459×C₇₃	—	2	2	no	—
27	#459×C₇₃	C₂²	1	2	yes	—
28	#452×C₇₃	—	2	2	no	—
29	#448×C₇₃	—	2	2	no	—
30	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₇₃	C₂²	1	1	yes	characteristic
32	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
33	C₄×D₈×C₇₃	—	2	1	no	—
34	C₄×D₈×C₇₃	—	2	1	no	—
35	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
36	#436×C₇₃	C₂²	1	2	yes	—
37	#335×C₇₃	C₂²	1	1	yes	characteristic
38	#335×C₇₃	C₂²	1	1	yes	characteristic
39	#332×C₇₃	C₂²	1	2	yes	—
40	#331×C₇₃	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₇₃	C₂²	1	2	yes	—
44	C₈²×C₇₃	C₂²	1	1	yes	characteristic
45	C₂×#41×C₇₃	—	2	2	no	—
46	C₂²×Q₈×C₇₃	—	2	2	no	—
47	#137×C₇₃	—	4	8	no	—
48	C₂×Q₁₆×C₇₃	—	2	2	no	—
49	C₂×Q₁₆×C₇₃	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₇₃	—	2	2	no	—
51	C₂×SD₁₆×C₇₃	—	2	2	no	—
52	C₂×SD₁₆×C₇₃	—	2	2	no	—
53	C₂×D₈×C₇₃	—	2	2	no	—
54	C₂×D₈×C₇₃	—	2	1	no	—
55	C₂×D₈×C₇₃	—	2	1	no	—
56	C₂×D₈×C₇₃	D₄	1	1	yes	characteristic
57	C₂×M₁₆×C₇₃	—	2	2	no	—
58	C₄⋊Q₈×C₇₃	—	2	2	no	—
59	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
60	#127×C₇₃	—	2	2	no	—
61	#127×C₇₃	C₂³	1	2	yes	—
62	C₂²⋊Q₈×C₇₃	—	2	2	no	—
63	C₂²⋊Q₈×C₇₃	—	4	2	no	—
64	#121×C₇₃	—	2	2	no	—
65	#121×C₇₃	—	4	2	no	—
66	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
67	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₇₃	—	2	2	no	—
69	C₄×D₄×C₇₃	—	2	2	no	—
70	C₄×D₄×C₇₃	C₂³	1	2	yes	—
71	#107×C₇₃	—	2	1	no	—
72	#107×C₇₃	—	2	1	no	—
73	#107×C₇₃	—	2	2	no	—
74	#107×C₇₃	D₄	1	1	yes	characteristic
75	#107×C₇₃	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₇₃	—	2	1	no	—
77	C₄⋊C₈×C₇₃	—	2	1	no	—
78	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
79	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
81	#103×C₇₃	—	2	2	no	—
82	#103×C₇₃	D₄	1	1	yes	characteristic
83	#103×C₇₃	D₄	1	1	yes	characteristic
84	#102×C₇₃	—	2	2	no	—
85	#102×C₇₃	—	2	2	no	—
86	#102×C₇₃	—	2	2	no	—
87	#102×C₇₃	—	4	2	no	—
88	#102×C₇₃	D₄	1	2	yes	—
89	C₂²⋊C₈×C₇₃	—	2	2	no	—
90	C₄×C₈×C₇₃	—	2	1	no	—
91	C₄×C₈×C₇₃	—	2	1	no	—
92	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
95	#41×C₇₃	—	4	4	no	—
96	#41×C₇₃	—	8	2	no	—
97	C₂×Q₈×C₇₃	—	2	2	no	—
98	C₂×Q₈×C₇₃	—	4	2	no	—
99	C₂×Q₈×C₇₃	—	4	4	no	—
100	C₂×Q₈×C₇₃	—	8	2	no	—
101	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
103	C₂×D₄×C₇₃	—	2	2	no	—
104	C₂×D₄×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	4	2	no	—
107	C₂×D₄×C₇₃	—	4	2	no	—
108	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₇₃	—	2	2	no	—
110	C₂²×C₄×C₇₃	—	4	2	no	—
111	C₂²×C₄×C₇₃	—	4	2	no	—
112	Q₁₆×C₇₃	—	4	4	no	—
113	Q₁₆×C₇₃	D₈	1	4	yes	complemented
114	SD₁₆×C₇₃	—	4	4	no	—
115	SD₁₆×C₇₃	—	4	4	no	—
116	SD₁₆×C₇₃	—	8	2	no	—
117	D₈×C₇₃	—	2	2	no	—
118	D₈×C₇₃	—	4	2	no	—
119	D₈×C₇₃	—	8	1	no	—
120	D₈×C₇₃	—	8	2	no	—
121	M₁₆×C₇₃	—	4	4	no	—
122	C₂×C₈×C₇₃	—	2	1	no	—
123	C₂×C₈×C₇₃	—	2	1	no	—
124	C₂×C₈×C₇₃	—	2	2	no	—
125	C₂×C₈×C₇₃	—	2	1	no	—
126	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₇₃	—	2	1	no	—
131	C₄⋊C₄×C₇₃	—	2	1	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	4	2	no	—
135	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
136	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
137	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂²⋊C₄×C₇₃	—	2	2	no	—
139	C₂²⋊C₄×C₇₃	—	4	2	no	—
140	C₂²⋊C₄×C₇₃	—	4	2	no	—
141	C₄²×C₇₃	—	2	1	no	—
142	C₄²×C₇₃	—	2	1	no	—
143	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
144	C₂³×C₇₃	—	2	2	no	—
145	C₂³×C₇₃	—	4	2	no	—
146	Q₈×C₇₃	—	2	1	no	—
147	Q₈×C₇₃	—	2	1	no	—
148	Q₈×C₇₃	—	4	2	no	—
149	Q₈×C₇₃	—	4	2	no	—
150	Q₈×C₇₃	—	8	4	no	—
151	Q₈×C₇₃	C₂×D₈	1	2	yes	—
152	Q₈×C₇₃	C₂×D₈	1	2	yes	—
153	D₄×C₇₃	—	2	2	no	—
154	D₄×C₇₃	—	2	2	no	—
155	D₄×C₇₃	—	4	2	no	—
156	D₄×C₇₃	—	4	2	no	—
157	D₄×C₇₃	—	4	2	no	—
158	D₄×C₇₃	—	4	2	no	—
159	D₄×C₇₃	—	8	4	no	—
160	D₄×C₇₃	—	8	2	no	—
161	D₄×C₇₃	—	16	2	no	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	4	2	no	—
168	C₂×C₄×C₇₃	—	4	2	no	—
169	C₂×C₄×C₇₃	—	4	2	no	—
170	C₂×C₄×C₇₃	—	8	4	no	—
171	C₂×C₄×C₇₃	—	8	4	no	—
172	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
175	C₈×C₇₃	—	2	1	no	—
176	C₈×C₇₃	—	2	1	no	—
177	C₈×C₇₃	—	4	1	no	—
178	C₈×C₇₃	—	4	2	no	—
179	C₈×C₇₃	—	4	1	no	—
180	C₈×C₇₃	—	4	1	no	—
181	C₈×C₇₃	C₂×D₈	1	2	yes	—
182	C₈×C₇₃	#137	1	2	yes	complemented
183	C₂²×C₇₃	—	4	2	no	—
184	C₂²×C₇₃	—	4	2	no	—
185	C₂²×C₇₃	—	4	2	no	—
186	C₂²×C₇₃	—	8	2	no	—
187	C₂²×C₇₃	—	8	2	no	—
188	C₂²×C₇₃	—	8	2	no	—
189	C₂²×C₇₃	D₄²	1	1	yes	characteristic
190	C₄×C₇₃	—	2	2	no	—
191	C₄×C₇₃	—	2	2	no	—
192	C₄×C₇₃	—	2	1	no	—
193	C₄×C₇₃	—	4	2	no	—
194	C₄×C₇₃	—	4	1	no	—
195	C₄×C₇₃	—	4	1	no	—
196	C₄×C₇₃	—	8	2	no	—
197	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
198	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
199	C₄×C₇₃	#576	1	1	yes	characteristic
200	C₄×C₇₃	#577	1	1	yes	characteristic
201	#19889	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂×C₇₃	—	8	2	no	—
203	C₂×C₇₃	—	16	2	no	—
204	C₂×C₇₃	#3278	1	1	yes	characteristic
205	C₂×C₇₃	D₄×D₈	1	1	yes	characteristic
206	C₂×C₇₃	#3290	1	1	yes	characteristic
207	#3391	C₂×C₇₃	1	1	yes	characteristic
208	Q₈×D₈	C₂×C₇₃	1	1	yes	characteristic, complemented
209	#3278	C₂×C₇₃	1	2	yes	complemented
210	#1706	C₂×C₇₃	1	1	yes	characteristic, complemented
211	#1685	C₂×C₇₃	1	2	yes	complemented
212	#1674	C₂×C₇₃	1	1	yes	characteristic, complemented
213	#1668	C₂×C₇₃	1	1	yes	characteristic, complemented
214	#1641	C₂×C₇₃	1	2	yes	complemented
215	#1627	C₂×C₇₃	1	2	yes	complemented
216	#1589	C₂×C₇₃	1	1	yes	characteristic, complemented
217	C₈×Q₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
218	C₇₃	#19889	1	1	yes	characteristic, direct product factor, Sylow
219	C₂×#137	—	2	2	no	—
220	#550	C₂²×C₇₃	1	2	yes	—
221	D₄×Q₈	C₂²×C₇₃	1	2	yes	—
222	#500	—	2	1	no	—
223	#500	C₂²×C₇₃	1	1	yes	characteristic
224	#493	—	2	1	no	—
225	#493	C₂²×C₇₃	1	1	yes	characteristic
226	#492	C₂²×C₇₃	1	2	yes	—
227	#486	C₂²×C₇₃	1	2	yes	—
228	#474	—	2	2	no	—
229	#474	C₂²×C₇₃	1	2	yes	—
230	#468	—	2	2	no	—
231	#462	C₂²×C₇₃	1	2	yes	—
232	#460	C₂²×C₇₃	1	2	yes	—
233	#459	—	2	2	no	—
234	#459	C₂²×C₇₃	1	2	yes	—
235	#452	—	2	2	no	—
236	#448	—	2	2	no	—
237	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic
238	C₈×Q₈	C₂²×C₇₃	1	1	yes	characteristic
239	C₄×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
240	C₄×D₈	—	2	1	no	—
241	C₄×D₈	—	2	1	no	—
242	C₄×D₈	C₂²×C₇₃	1	1	yes	characteristic
243	#436	C₂²×C₇₃	1	2	yes	—
244	#335	C₂²×C₇₃	1	1	yes	characteristic
245	#335	C₂²×C₇₃	1	1	yes	characteristic
246	#332	C₂²×C₇₃	1	2	yes	—
247	#331	C₂²×C₇₃	1	2	yes	—
248	Q₈⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
249	Q₈⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
250	D₄⋊C₈	C₂²×C₇₃	1	2	yes	—
251	C₈²	C₂²×C₇₃	1	1	yes	characteristic
252	C₂×#41	—	2	2	no	—
253	C₂²×Q₈	—	2	2	no	—
254	#137	—	4	8	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	D₄×C₇₃	1	1	yes	characteristic
257	C₂×SD₁₆	—	2	2	no	—
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×SD₁₆	—	2	2	no	—
260	C₂×D₈	—	2	2	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	1	no	—
263	C₂×D₈	D₄×C₇₃	1	1	yes	characteristic
264	C₂×M₁₆	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	C₂³×C₇₃	1	2	yes	—
267	#127	—	2	2	no	—
268	#127	C₂³×C₇₃	1	2	yes	—
269	C₂²⋊Q₈	—	2	2	no	—
270	C₂²⋊Q₈	—	4	2	no	—
271	#121	—	2	2	no	—
272	#121	—	4	2	no	—
273	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
274	C₄×Q₈	C₂³×C₇₃	1	1	yes	characteristic
275	C₄×D₄	—	2	2	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	C₂³×C₇₃	1	2	yes	—
278	#107	—	2	1	no	—
279	#107	—	2	1	no	—
280	#107	—	2	2	no	—
281	#107	D₄×C₇₃	1	1	yes	characteristic
282	#107	D₄×C₇₃	1	1	yes	characteristic
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	C₂³×C₇₃	1	2	yes	—
286	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
287	C₄⋊C₈	C₂³×C₇₃	1	1	yes	characteristic
288	#103	—	2	2	no	—
289	#103	D₄×C₇₃	1	1	yes	characteristic
290	#103	D₄×C₇₃	1	1	yes	characteristic
291	#102	—	2	2	no	—
292	#102	—	2	2	no	—
293	#102	—	2	2	no	—
294	#102	—	4	2	no	—
295	#102	D₄×C₇₃	1	2	yes	—
296	C₂²⋊C₈	—	2	2	no	—
297	C₄×C₈	—	2	1	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
300	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
301	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
302	#41	—	4	4	no	—
303	#41	—	8	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	—	4	4	no	—
307	C₂×Q₈	—	8	2	no	—
308	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
309	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	4	2	no	—
319	Q₁₆	—	4	4	no	—
320	Q₁₆	D₈×C₇₃	1	4	yes	complemented
321	SD₁₆	—	4	4	no	—
322	SD₁₆	—	4	4	no	—
323	SD₁₆	—	8	2	no	—
324	D₈	—	2	2	no	—
325	D₈	—	4	2	no	—
326	D₈	—	8	1	no	—
327	D₈	—	8	2	no	—
328	M₁₆	—	4	4	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
334	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
335	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
336	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
343	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
344	C₄⋊C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₄²	—	2	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
351	C₂³	—	2	2	no	—
352	C₂³	—	4	2	no	—
353	Q₈	—	2	1	no	—
354	Q₈	—	2	1	no	—
355	Q₈	—	4	2	no	—
356	Q₈	—	4	2	no	—
357	Q₈	—	8	4	no	—
358	Q₈	C₂×D₈×C₇₃	1	2	yes	—
359	Q₈	C₂×D₈×C₇₃	1	2	yes	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	4	2	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	2	no	—
368	D₄	—	16	2	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	4	no	—
378	C₂×C₄	—	8	4	no	—
379	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
380	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	2	1	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	1	no	—
387	C₈	—	4	1	no	—
388	C₈	C₂×D₈×C₇₃	1	2	yes	—
389	C₈	#137×C₇₃	1	2	yes	complemented
390	C₂²	—	4	2	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	D₄²×C₇₃	1	1	yes	characteristic
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	1	no	—
400	C₄	—	4	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	1	no	—
403	C₄	—	8	2	no	—
404	C₄	C₂²×D₈×C₇₃	1	1	yes	characteristic
405	C₄	C₂×#137×C₇₃	1	1	yes	characteristic
406	C₄	#576×C₇₃	1	1	yes	characteristic
407	C₄	#577×C₇₃	1	1	yes	characteristic
408	C₂	—	8	2	no	—
409	C₂	—	16	2	no	—
410	C₂	C₇₃×#3278	1	1	yes	characteristic
411	C₂	D₄×D₈×C₇₃	1	1	yes	characteristic
412	C₂	C₇₃×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
prime radical	C₇₃×#3391	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×D₈×C₇₃	C₂	semidirect
3. C₇₃×#3278	C₂	semidirect
4. C₇₃×#1706	C₂	semidirect
5. C₇₃×#1685	C₂	semidirect
6. C₇₃×#1674	C₂	semidirect
7. C₇₃×#1668	C₂	semidirect
8. C₇₃×#1641	C₂	semidirect
9. C₇₃×#1627	C₂	semidirect
10. C₇₃×#1589	C₂	semidirect
11. C₈×Q₁₆×C₇₃	C₂	semidirect
113. Q₁₆×C₇₃	D₈	semidirect
182. C₈×C₇₃	#137	semidirect
201. #19889	C₇₃	direct (N × H)
208. Q₈×D₈	C₂×C₇₃	semidirect
209. #3278	C₂×C₇₃	semidirect
210. #1706	C₂×C₇₃	semidirect
211. #1685	C₂×C₇₃	semidirect
212. #1674	C₂×C₇₃	semidirect
213. #1668	C₂×C₇₃	semidirect
214. #1641	C₂×C₇₃	semidirect
215. #1627	C₂×C₇₃	semidirect
216. #1589	C₂×C₇₃	semidirect
217. C₈×Q₁₆	C₂×C₇₃	semidirect
218. C₇₃	#19889	direct (N × H)
320. Q₁₆	D₈×C₇₃	semidirect
389. C₈	#137×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3391	2
Q₈×D₈×C₇₃	2
C₇₃×#3278	2
C₇₃×#1706	2
C₇₃×#1685	2
C₇₃×#1674	2
C₇₃×#1668	2
C₇₃×#1641	2
C₇₃×#1627	2
C₇₃×#1589	2
C₈×Q₁₆×C₇₃	2
#19889	73

Subgroups — C73×#19889 #32929293

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#19889 #32929293