Subgroups — C₇₃×#25746 #32935150

Order 18688.

1470 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3499	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#3152	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#3039	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#456×C₇₃	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2005	C₂	1	4	yes	maximal, complemented
7	C₇₃×#1966	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1962	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#104×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×2₋¹⁺⁴×C₇₃	C₂²	1	2	yes	—
11	C₂×#137×C₇₃	C₂²	1	2	yes	—
12	C₂×#137×C₇₃	C₂²	1	4	yes	—
13	D₄×Q₈×C₇₃	—	2	2	no	—
14	#547×C₇₃	—	2	2	no	—
15	#547×C₇₃	—	2	4	no	—
16	#536×C₇₃	—	2	2	no	—
17	#536×C₇₃	C₂²	1	2	yes	—
18	#532×C₇₃	—	2	1	no	—
19	#532×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₇₃	—	2	1	no	—
21	C₂×C₄⋊Q₈×C₇₃	C₂²	1	4	yes	—
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
24	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
25	#497×C₇₃	—	2	2	no	—
26	#494×C₇₃	—	2	1	no	—
27	#492×C₇₃	—	2	1	no	—
28	#462×C₇₃	—	2	2	no	—
29	#461×C₇₃	—	2	2	no	—
30	#456×C₇₃	—	2	16	no	—
31	#423×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×#104×C₇₃	C₂²	1	4	yes	—
33	C₂×#104×C₇₃	C₂²	1	2	yes	—
34	#419×C₇₃	C₂²	1	2	yes	—
35	C₂×#101×C₇₃	C₂²	1	4	yes	—
36	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
37	#384×C₇₃	—	2	4	no	—
38	C₄³×C₇₃	C₂²	1	1	yes	characteristic
39	#339×C₇₃	C₂²	1	2	yes	—
40	2₋¹⁺⁴×C₇₃	—	2	8	no	—
41	2₋¹⁺⁴×C₇₃	—	4	4	no	—
42	C₂×#41×C₇₃	—	2	2	no	—
43	C₂×#41×C₇₃	—	2	2	no	—
44	C₂×#41×C₇₃	—	2	4	no	—
45	C₂×#41×C₇₃	C₂³	1	2	yes	—
46	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₇₃	—	2	2	no	—
48	C₂²×Q₈×C₇₃	—	2	2	no	—
49	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
50	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
51	#137×C₇₃	—	2	8	no	—
52	#137×C₇₃	—	2	8	no	—
53	#137×C₇₃	—	4	4	no	—
54	C₂×Q₁₆×C₇₃	—	2	2	no	—
55	C₂×Q₁₆×C₇₃	—	2	4	no	—
56	C₂×SD₁₆×C₇₃	—	2	2	no	—
57	C₂×SD₁₆×C₇₃	—	2	4	no	—
58	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
59	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₇₃	—	2	4	no	—
61	C₄⋊Q₈×C₇₃	—	2	2	no	—
62	C₄⋊Q₈×C₇₃	—	2	1	no	—
63	C₄⋊Q₈×C₇₃	—	2	1	no	—
64	C₄⋊Q₈×C₇₃	—	2	2	no	—
65	C₄⋊Q₈×C₇₃	—	2	8	no	—
66	C₄⋊Q₈×C₇₃	—	2	2	no	—
67	C₄⋊Q₈×C₇₃	—	2	1	no	—
68	C₄⋊Q₈×C₇₃	—	2	1	no	—
69	C₄⋊Q₈×C₇₃	—	4	4	no	—
70	C₄⋊Q₈×C₇₃	D₄	1	1	yes	characteristic
71	#127×C₇₃	D₄	1	1	yes	characteristic
72	#124×C₇₃	—	2	2	no	—
73	#124×C₇₃	D₄	1	2	yes	—
74	#123×C₇₃	—	2	8	no	—
75	#123×C₇₃	—	2	4	no	—
76	C₂²⋊Q₈×C₇₃	—	2	8	no	—
77	C₂²⋊Q₈×C₇₃	—	2	4	no	—
78	#121×C₇₃	—	2	4	no	—
79	#121×C₇₃	—	2	2	no	—
80	C₄×Q₈×C₇₃	D₄	1	2	yes	—
81	C₄×D₄×C₇₃	—	2	4	no	—
82	C₄×D₄×C₇₃	—	2	2	no	—
83	C₄×D₄×C₇₃	—	2	2	no	—
84	C₄×D₄×C₇₃	D₄	1	2	yes	—
85	#117×C₇₃	—	2	1	no	—
86	#117×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
88	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
89	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
90	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
91	C₂×C₄²×C₇₃	—	2	2	no	—
92	C₂×C₄²×C₇₃	—	2	1	no	—
93	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
94	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₃	—	2	2	no	—
96	#104×C₇₃	—	2	8	no	—
97	#104×C₇₃	D₄	1	8	yes	complemented
98	#103×C₇₃	—	2	4	no	—
99	#101×C₇₃	—	2	8	no	—
100	#97×C₇₃	—	2	1	no	—
101	C₄×C₈×C₇₃	—	2	1	no	—
102	#41×C₇₃	—	2	2	no	—
103	#41×C₇₃	—	2	4	no	—
104	#41×C₇₃	—	2	4	no	—
105	#41×C₇₃	—	4	8	no	—
106	#41×C₇₃	—	4	16	no	—
107	#41×C₇₃	—	4	4	no	—
108	#41×C₇₃	—	4	4	no	—
109	#41×C₇₃	C₂×D₄	1	4	yes	—
110	C₂×Q₈×C₇₃	—	2	4	no	—
111	C₂×Q₈×C₇₃	—	2	4	no	—
112	C₂×Q₈×C₇₃	—	2	2	no	—
113	C₂×Q₈×C₇₃	—	2	2	no	—
114	C₂×Q₈×C₇₃	—	2	4	no	—
115	C₂×Q₈×C₇₃	—	2	2	no	—
116	C₂×Q₈×C₇₃	—	2	2	no	—
117	C₂×Q₈×C₇₃	—	2	4	no	—
118	C₂×Q₈×C₇₃	—	2	4	no	—
119	C₂×Q₈×C₇₃	—	4	8	no	—
120	C₂×Q₈×C₇₃	—	4	4	no	—
121	C₂×Q₈×C₇₃	—	4	4	no	—
122	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
123	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×D₄×C₇₃	—	2	1	no	—
125	C₂×D₄×C₇₃	—	2	4	no	—
126	C₂×D₄×C₇₃	—	2	2	no	—
127	C₂×D₄×C₇₃	—	2	2	no	—
128	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
129	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	—	2	2	no	—
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	—	2	4	no	—
133	C₂²×C₄×C₇₃	—	2	4	no	—
134	C₂²×C₄×C₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₇₃	—	4	8	no	—
141	Q₁₆×C₇₃	—	4	4	no	—
142	SD₁₆×C₇₃	—	4	8	no	—
143	SD₁₆×C₇₃	—	4	4	no	—
144	M₁₆×C₇₃	—	2	2	no	—
145	M₁₆×C₇₃	—	2	4	no	—
146	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
147	C₂×C₈×C₇₃	—	2	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₄⋊C₄×C₇₃	—	2	8	no	—
150	C₄⋊C₄×C₇₃	—	2	2	no	—
151	C₄⋊C₄×C₇₃	—	2	4	no	—
152	C₄⋊C₄×C₇₃	—	2	4	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	—	4	16	no	—
155	C₄⋊C₄×C₇₃	—	4	2	no	—
156	C₄⋊C₄×C₇₃	—	4	2	no	—
157	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
158	C₂²⋊C₄×C₇₃	—	2	8	no	—
159	C₂²⋊C₄×C₇₃	—	2	1	no	—
160	C₂²⋊C₄×C₇₃	—	2	2	no	—
161	C₂²⋊C₄×C₇₃	—	2	4	no	—
162	C₄²×C₇₃	—	2	8	no	—
163	C₄²×C₇₃	—	2	2	no	—
164	C₄²×C₇₃	—	2	1	no	—
165	C₄²×C₇₃	—	2	2	no	—
166	C₄²×C₇₃	C₂×D₄	1	4	yes	—
167	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₇₃	C₂×D₄	1	2	yes	—
170	C₂³×C₇₃	—	2	1	no	—
171	C₂³×C₇₃	—	2	2	no	—
172	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₇₃	—	2	1	no	—
174	Q₈×C₇₃	—	2	4	no	—
175	Q₈×C₇₃	—	4	8	no	—
176	Q₈×C₇₃	—	4	2	no	—
177	Q₈×C₇₃	—	4	2	no	—
178	Q₈×C₇₃	—	4	4	no	—
179	Q₈×C₇₃	—	4	2	no	—
180	Q₈×C₇₃	—	4	2	no	—
181	Q₈×C₇₃	—	4	4	no	—
182	Q₈×C₇₃	#127	1	2	yes	—
183	D₄×C₇₃	—	2	4	no	—
184	D₄×C₇₃	—	2	1	no	—
185	D₄×C₇₃	—	2	4	no	—
186	D₄×C₇₃	—	4	8	no	—
187	D₄×C₇₃	—	4	4	no	—
188	D₄×C₇₃	—	4	4	no	—
189	D₄×C₇₃	#127	1	2	yes	—
190	C₂×C₄×C₇₃	—	2	8	no	—
191	C₂×C₄×C₇₃	—	2	1	no	—
192	C₂×C₄×C₇₃	—	2	4	no	—
193	C₂×C₄×C₇₃	—	2	4	no	—
194	C₂×C₄×C₇₃	—	2	4	no	—
195	C₂×C₄×C₇₃	—	2	2	no	—
196	C₂×C₄×C₇₃	—	2	2	no	—
197	C₂×C₄×C₇₃	—	2	4	no	—
198	C₂×C₄×C₇₃	—	2	8	no	—
199	C₂×C₄×C₇₃	—	4	8	no	—
200	C₂×C₄×C₇₃	—	4	8	no	—
201	C₂×C₄×C₇₃	—	4	2	no	—
202	C₂×C₄×C₇₃	—	4	2	no	—
203	C₂×C₄×C₇₃	—	4	4	no	—
204	C₂×C₄×C₇₃	—	4	2	no	—
205	C₂×C₄×C₇₃	—	4	4	no	—
206	C₂×C₄×C₇₃	#120	1	2	yes	—
207	C₂×C₄×C₇₃	#120	1	2	yes	—
208	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
212	C₈×C₇₃	—	2	4	no	—
213	C₈×C₇₃	—	4	2	no	—
214	C₂²×C₇₃	—	2	2	no	—
215	C₂²×C₇₃	—	2	2	no	—
216	C₂²×C₇₃	—	4	2	no	—
217	C₂²×C₇₃	—	4	2	no	—
218	C₂²×C₇₃	—	4	4	no	—
219	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
220	C₂²×C₇₃	D₄²	1	2	yes	—
221	C₄×C₇₃	—	2	8	no	—
222	C₄×C₇₃	—	2	2	no	—
223	C₄×C₇₃	—	2	2	no	—
224	C₄×C₇₃	—	4	4	no	—
225	C₄×C₇₃	—	4	2	no	—
226	C₄×C₇₃	—	4	2	no	—
227	C₄×C₇₃	—	8	2	no	—
228	C₄×C₇₃	#456	1	4	yes	complemented
229	C₄×C₇₃	C₂×#127	1	1	yes	characteristic
230	C₄×C₇₃	#535	1	1	yes	characteristic
231	C₄×C₇₃	D₄²	1	2	yes	—
232	#25746	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂×C₇₃	—	2	2	no	—
234	C₂×C₇₃	—	4	2	no	—
235	C₂×C₇₃	—	8	2	no	—
236	C₂×C₇₃	#2433	1	1	yes	characteristic
237	C₂×C₇₃	C₂×#456	1	2	yes	—
238	#3499	C₂×C₇₃	1	1	yes	characteristic
239	#3152	C₂×C₇₃	1	1	yes	characteristic, complemented
240	#3039	C₂×C₇₃	1	1	yes	characteristic, complemented
241	C₂×#456	C₂×C₇₃	1	4	yes	complemented
242	#2868	C₂×C₇₃	1	1	yes	characteristic, complemented
243	#2005	C₂×C₇₃	1	4	yes	complemented
244	#1966	C₂×C₇₃	1	1	yes	characteristic, complemented
245	#1962	C₂×C₇₃	1	1	yes	characteristic, complemented
246	C₄×#104	C₂×C₇₃	1	1	yes	characteristic, complemented
247	C₇₃	#25746	1	1	yes	characteristic, direct product factor, Sylow
248	C₂×2₋¹⁺⁴	C₂²×C₇₃	1	2	yes	—
249	C₂×#137	C₂²×C₇₃	1	2	yes	—
250	C₂×#137	C₂²×C₇₃	1	4	yes	—
251	D₄×Q₈	—	2	2	no	—
252	#547	—	2	2	no	—
253	#547	—	2	4	no	—
254	#536	—	2	2	no	—
255	#536	C₂²×C₇₃	1	2	yes	—
256	#532	—	2	1	no	—
257	#532	C₂²×C₇₃	1	1	yes	characteristic
258	C₂×C₄⋊Q₈	—	2	1	no	—
259	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
260	C₂×C₄⋊Q₈	C₂²×C₇₃	1	4	yes	—
261	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
262	C₄×#41	C₂²×C₇₃	1	1	yes	characteristic
263	#497	—	2	2	no	—
264	#494	—	2	1	no	—
265	#492	—	2	1	no	—
266	#462	—	2	2	no	—
267	#461	—	2	2	no	—
268	#456	—	2	16	no	—
269	#423	C₂²×C₇₃	1	1	yes	characteristic
270	C₂×#104	C₂²×C₇₃	1	4	yes	—
271	C₂×#104	C₂²×C₇₃	1	2	yes	—
272	#419	C₂²×C₇₃	1	2	yes	—
273	C₂×#101	C₂²×C₇₃	1	4	yes	—
274	C₄×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
275	#384	—	2	4	no	—
276	C₄³	C₂²×C₇₃	1	1	yes	characteristic
277	#339	C₂²×C₇₃	1	2	yes	—
278	2₋¹⁺⁴	—	2	8	no	—
279	2₋¹⁺⁴	—	4	4	no	—
280	C₂×#41	—	2	2	no	—
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	C₂³×C₇₃	1	2	yes	—
284	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	—	2	2	no	—
287	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
288	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
289	#137	—	2	8	no	—
290	#137	—	2	8	no	—
291	#137	—	4	4	no	—
292	C₂×Q₁₆	—	2	2	no	—
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×SD₁₆	—	2	4	no	—
296	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
297	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
298	C₄⋊Q₈	—	2	4	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	8	no	—
304	C₄⋊Q₈	—	2	2	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	4	4	no	—
308	C₄⋊Q₈	D₄×C₇₃	1	1	yes	characteristic
309	#127	D₄×C₇₃	1	1	yes	characteristic
310	#124	—	2	2	no	—
311	#124	D₄×C₇₃	1	2	yes	—
312	#123	—	2	8	no	—
313	#123	—	2	4	no	—
314	C₂²⋊Q₈	—	2	8	no	—
315	C₂²⋊Q₈	—	2	4	no	—
316	#121	—	2	4	no	—
317	#121	—	2	2	no	—
318	C₄×Q₈	D₄×C₇₃	1	2	yes	—
319	C₄×D₄	—	2	4	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	D₄×C₇₃	1	2	yes	—
323	#117	—	2	1	no	—
324	#117	C₂³×C₇₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	—	2	4	no	—
326	C₂×C₄⋊C₄	—	2	8	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	1	no	—
331	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
332	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
333	C₄⋊C₈	—	2	2	no	—
334	#104	—	2	8	no	—
335	#104	D₄×C₇₃	1	8	yes	complemented
336	#103	—	2	4	no	—
337	#101	—	2	8	no	—
338	#97	—	2	1	no	—
339	C₄×C₈	—	2	1	no	—
340	#41	—	2	2	no	—
341	#41	—	2	4	no	—
342	#41	—	2	4	no	—
343	#41	—	4	8	no	—
344	#41	—	4	16	no	—
345	#41	—	4	4	no	—
346	#41	—	4	4	no	—
347	#41	C₂×D₄×C₇₃	1	4	yes	—
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	4	8	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	—	4	4	no	—
360	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
367	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
376	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
377	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
378	Q₁₆	—	4	8	no	—
379	Q₁₆	—	4	4	no	—
380	SD₁₆	—	4	8	no	—
381	SD₁₆	—	4	4	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
385	C₂×C₈	—	2	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	16	no	—
393	C₄⋊C₄	—	4	2	no	—
394	C₄⋊C₄	—	4	2	no	—
395	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
396	C₂²⋊C₄	—	2	8	no	—
397	C₂²⋊C₄	—	2	1	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	2	4	no	—
400	C₄²	—	2	8	no	—
401	C₄²	—	2	2	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	2	no	—
404	C₄²	C₂×D₄×C₇₃	1	4	yes	—
405	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
406	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
407	C₄²	C₂×D₄×C₇₃	1	2	yes	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	2	no	—
410	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
411	Q₈	—	2	1	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	8	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	4	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	4	no	—
420	Q₈	#127×C₇₃	1	2	yes	—
421	D₄	—	2	4	no	—
422	D₄	—	2	1	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	8	no	—
425	D₄	—	4	4	no	—
426	D₄	—	4	4	no	—
427	D₄	#127×C₇₃	1	2	yes	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	8	no	—
437	C₂×C₄	—	4	8	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	#120×C₇₃	1	2	yes	—
445	C₂×C₄	#120×C₇₃	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
448	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
449	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
450	C₈	—	2	4	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	2	no	—
457	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
458	C₂²	D₄²×C₇₃	1	2	yes	—
459	C₄	—	2	8	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	2	no	—
466	C₄	#456×C₇₃	1	4	yes	complemented
467	C₄	C₂×#127×C₇₃	1	1	yes	characteristic
468	C₄	#535×C₇₃	1	1	yes	characteristic
469	C₄	D₄²×C₇₃	1	2	yes	—
470	C₂	—	2	2	no	—
471	C₂	—	4	2	no	—
472	C₂	—	8	2	no	—
473	C₂	C₇₃×#2433	1	1	yes	characteristic
474	C₂	C₂×#456×C₇₃	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#3499	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3152	C₂	semidirect
3. C₇₃×#3039	C₂	semidirect
4. C₂×#456×C₇₃	C₂	semidirect
5. C₇₃×#2868	C₂	semidirect
6. C₇₃×#2005	C₂	semidirect
7. C₇₃×#1966	C₂	semidirect
8. C₇₃×#1962	C₂	semidirect
9. C₄×#104×C₇₃	C₂	semidirect
97. #104×C₇₃	D₄	semidirect
228. C₄×C₇₃	#456	semidirect
232. #25746	C₇₃	direct (N × H)
239. #3152	C₂×C₇₃	semidirect
240. #3039	C₂×C₇₃	semidirect
241. C₂×#456	C₂×C₇₃	semidirect
242. #2868	C₂×C₇₃	semidirect
243. #2005	C₂×C₇₃	semidirect
244. #1966	C₂×C₇₃	semidirect
245. #1962	C₂×C₇₃	semidirect
246. C₄×#104	C₂×C₇₃	semidirect
247. C₇₃	#25746	direct (N × H)
335. #104	D₄×C₇₃	semidirect
466. C₄	#456×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3499	2
C₇₃×#3152	2
C₇₃×#3039	2
C₂×#456×C₇₃	2
C₇₃×#2868	2
C₇₃×#2005	2
C₇₃×#1966	2
C₇₃×#1962	2
C₄×#104×C₇₃	2
#25746	73

Subgroups — C73×#25746 #32935150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25746 #32935150