Subgroups — C₇₃×#26252 #32935656

Order 18688.

894 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₈×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2447	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2055	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2042	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1970	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1877	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×#124×C₇₃	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	—
17	#495×C₇₃	—	2	4	no	—
18	C₄×D₈×C₇₃	—	2	4	no	—
19	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#107×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#103×C₇₃	C₂²	1	2	yes	—
23	C₂×#103×C₇₃	C₂²	1	2	yes	—
24	C₂×#102×C₇₃	C₂²	1	2	yes	—
25	C₂×#102×C₇₃	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
29	#397×C₇₃	—	2	2	no	—
30	#397×C₇₃	—	2	2	no	—
31	#391×C₇₃	C₂²	1	2	yes	—
32	#391×C₇₃	C₂²	1	2	yes	—
33	#390×C₇₃	C₂²	1	2	yes	—
34	#389×C₇₃	C₂²	1	2	yes	—
35	#385×C₇₃	—	2	2	no	—
36	#381×C₇₃	—	2	2	no	—
37	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
38	#340×C₇₃	C₂²	1	2	yes	—
39	#336×C₇₃	C₂²	1	1	yes	characteristic
40	#336×C₇₃	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
42	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₇₃	—	2	2	no	—
44	C₂×Q₁₆×C₇₃	—	2	2	no	—
45	C₂×Q₁₆×C₇₃	—	2	2	no	—
46	C₂×Q₁₆×C₇₃	—	2	2	no	—
47	C₂×SD₁₆×C₇₃	—	2	4	no	—
48	C₂×SD₁₆×C₇₃	—	2	4	no	—
49	C₂×SD₁₆×C₇₃	—	4	2	no	—
50	C₂×D₈×C₇₃	—	2	2	no	—
51	C₂×D₈×C₇₃	—	2	2	no	—
52	C₂×D₈×C₇₃	D₄	1	4	yes	—
53	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
57	#124×C₇₃	—	2	4	no	—
58	#124×C₇₃	—	4	2	no	—
59	C₄×D₄×C₇₃	—	2	4	no	—
60	C₄×D₄×C₇₃	—	4	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
74	#107×C₇₃	—	2	2	no	—
75	#107×C₇₃	—	2	2	no	—
76	C₄⋊C₈×C₇₃	—	2	2	no	—
77	#103×C₇₃	—	4	2	no	—
78	#103×C₇₃	—	4	2	no	—
79	#102×C₇₃	—	2	4	no	—
80	#102×C₇₃	—	4	2	no	—
81	C₄×C₈×C₇₃	—	2	2	no	—
82	C₄×C₈×C₇₃	—	2	2	no	—
83	C₄×C₈×C₇₃	—	2	2	no	—
84	#95×C₇₃	—	2	2	no	—
85	#95×C₇₃	—	2	2	no	—
86	#95×C₇₃	—	2	2	no	—
87	#95×C₇₃	—	2	2	no	—
88	#95×C₇₃	—	2	2	no	—
89	#95×C₇₃	D₄	1	1	yes	characteristic
90	#95×C₇₃	D₄	1	1	yes	characteristic
91	C₂⁴×C₇₃	—	2	2	no	—
92	C₂×Q₈×C₇₃	—	2	2	no	—
93	C₂×Q₈×C₇₃	—	2	2	no	—
94	C₂×Q₈×C₇₃	—	2	2	no	—
95	C₂×Q₈×C₇₃	—	2	2	no	—
96	C₂×Q₈×C₇₃	—	2	2	no	—
97	C₂×Q₈×C₇₃	—	2	2	no	—
98	C₂×D₄×C₇₃	—	2	2	no	—
99	C₂×D₄×C₇₃	—	2	2	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	2	2	no	—
102	C₂×D₄×C₇₃	—	2	2	no	—
103	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₇₃	—	2	2	no	—
105	C₂²×C₄×C₇₃	—	2	2	no	—
106	C₂²×C₄×C₇₃	—	2	2	no	—
107	C₂²×C₄×C₇₃	—	4	4	no	—
108	C₂²×C₄×C₇₃	—	4	4	no	—
109	C₂²×C₄×C₇₃	—	8	2	no	—
110	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₇₃	—	4	4	no	—
118	SD₁₆×C₇₃	—	4	8	no	—
119	D₈×C₇₃	—	2	8	no	—
120	C₂×C₈×C₇₃	—	2	1	no	—
121	C₂×C₈×C₇₃	—	2	1	no	—
122	C₂×C₈×C₇₃	—	2	1	no	—
123	C₂×C₈×C₇₃	—	2	1	no	—
124	C₂×C₈×C₇₃	—	2	1	no	—
125	C₂×C₈×C₇₃	—	2	1	no	—
126	C₂×C₈×C₇₃	—	2	1	no	—
127	C₂×C₈×C₇₃	—	2	1	no	—
128	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₇₃	#41	1	2	yes	—
130	C₂×C₈×C₇₃	#41	1	2	yes	—
131	C₂×C₈×C₇₃	#41	1	2	yes	—
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	—	8	2	no	—
139	C₂²⋊C₄×C₇₃	—	4	4	no	—
140	C₂²⋊C₄×C₇₃	—	4	4	no	—
141	C₂²⋊C₄×C₇₃	—	4	4	no	—
142	C₂²⋊C₄×C₇₃	—	4	4	no	—
143	C₂²⋊C₄×C₇₃	—	8	2	no	—
144	C₄²×C₇₃	—	2	1	no	—
145	C₄²×C₇₃	—	2	1	no	—
146	C₄²×C₇₃	—	2	1	no	—
147	C₄²×C₇₃	—	2	1	no	—
148	C₄²×C₇₃	—	2	1	no	—
149	C₄²×C₇₃	—	2	1	no	—
150	C₂³×C₇₃	—	2	4	no	—
151	C₂³×C₇₃	—	4	2	no	—
152	C₂³×C₇₃	—	4	2	no	—
153	C₂³×C₇₃	—	4	2	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	4	2	no	—
156	C₂³×C₇₃	—	4	2	no	—
157	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₇₃	—	4	2	no	—
159	Q₈×C₇₃	—	4	2	no	—
160	Q₈×C₇₃	—	4	2	no	—
161	Q₈×C₇₃	—	4	2	no	—
162	D₄×C₇₃	—	2	4	no	—
163	D₄×C₇₃	—	2	4	no	—
164	D₄×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	1	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	1	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	—	2	1	no	—
176	C₂×C₄×C₇₃	—	2	1	no	—
177	C₂×C₄×C₇₃	—	2	1	no	—
178	C₂×C₄×C₇₃	—	2	1	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	1	no	—
181	C₂×C₄×C₇₃	—	2	1	no	—
182	C₂×C₄×C₇₃	—	4	2	no	—
183	C₂×C₄×C₇₃	—	4	2	no	—
184	C₂×C₄×C₇₃	—	4	2	no	—
185	C₂×C₄×C₇₃	—	4	2	no	—
186	C₂×C₄×C₇₃	—	4	2	no	—
187	C₂×C₄×C₇₃	—	4	2	no	—
188	C₂×C₄×C₇₃	—	4	2	no	—
189	C₂×C₄×C₇₃	—	4	2	no	—
190	C₂×C₄×C₇₃	—	4	2	no	—
191	C₂×C₄×C₇₃	—	8	8	no	—
192	C₂×C₄×C₇₃	#135	1	2	yes	—
193	C₂×C₄×C₇₃	#135	1	2	yes	—
194	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
199	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₈×C₇₃	—	2	2	no	—
201	C₈×C₇₃	—	4	1	no	—
202	C₈×C₇₃	—	4	1	no	—
203	C₈×C₇₃	#123	1	4	yes	—
204	C₂²×C₇₃	—	4	4	no	—
205	C₂²×C₇₃	—	4	4	no	—
206	C₂²×C₇₃	—	4	4	no	—
207	C₂²×C₇₃	—	8	2	no	—
208	C₂²×C₇₃	—	8	2	no	—
209	C₂²×C₇₃	—	8	2	no	—
210	C₂²×C₇₃	—	8	2	no	—
211	C₂²×C₇₃	#532	1	1	yes	characteristic
212	C₂²×C₇₃	D₄²	1	1	yes	characteristic
213	C₂²×C₇₃	#550	1	1	yes	characteristic
214	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
215	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
216	C₂²×C₇₃	#576	1	1	yes	characteristic
217	C₂²×C₇₃	#578	1	1	yes	characteristic
218	C₄×C₇₃	—	2	2	no	—
219	C₄×C₇₃	—	2	2	no	—
220	C₄×C₇₃	—	4	1	no	—
221	C₄×C₇₃	—	4	1	no	—
222	C₄×C₇₃	—	4	1	no	—
223	C₄×C₇₃	—	4	1	no	—
224	C₄×C₇₃	—	8	2	no	—
225	C₄×C₇₃	—	8	2	no	—
226	C₄×C₇₃	—	8	2	no	—
227	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
228	C₄×C₇₃	#540	1	1	yes	characteristic
229	C₄×C₇₃	#546	1	1	yes	characteristic
230	C₄×C₇₃	#559	1	1	yes	characteristic
231	#26252	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂×C₇₃	—	8	4	no	—
233	C₂×C₇₃	#2445	1	1	yes	characteristic
234	C₂×C₇₃	#3168	1	1	yes	characteristic
235	C₂×C₇₃	#3175	1	1	yes	characteristic
236	C₂×C₇₃	#3280	1	1	yes	characteristic
237	C₂×C₇₃	#3283	1	1	yes	characteristic
238	C₂×C₇₃	#3393	1	1	yes	characteristic
239	C₂×C₇₃	#3396	1	1	yes	characteristic
240	C₂×#495	C₂×C₇₃	1	1	yes	characteristic
241	C₂×C₄×D₈	C₂×C₇₃	1	1	yes	characteristic
242	#2447	C₂×C₇₃	1	2	yes	complemented
243	#2055	C₂×C₇₃	1	2	yes	complemented
244	#2042	C₂×C₇₃	1	2	yes	complemented
245	#1970	C₂×C₇₃	1	1	yes	characteristic
246	#1969	C₂×C₇₃	1	1	yes	characteristic, complemented
247	#1969	C₂×C₇₃	1	1	yes	characteristic, complemented
248	#1942	C₂×C₇₃	1	1	yes	characteristic, complemented
249	#1877	C₂×C₇₃	1	2	yes	complemented
250	C₈×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
251	C₇₃	#26252	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
253	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
254	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
255	C₂×#124	C₂²×C₇₃	1	2	yes	—
256	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	—
257	#495	—	2	4	no	—
258	C₄×D₈	—	2	4	no	—
259	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
260	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
261	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
262	C₂×#103	C₂²×C₇₃	1	2	yes	—
263	C₂×#103	C₂²×C₇₃	1	2	yes	—
264	C₂×#102	C₂²×C₇₃	1	2	yes	—
265	C₂×#102	C₂²×C₇₃	1	2	yes	—
266	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
269	#397	—	2	2	no	—
270	#397	—	2	2	no	—
271	#391	C₂²×C₇₃	1	2	yes	—
272	#391	C₂²×C₇₃	1	2	yes	—
273	#390	C₂²×C₇₃	1	2	yes	—
274	#389	C₂²×C₇₃	1	2	yes	—
275	#385	—	2	2	no	—
276	#381	—	2	2	no	—
277	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
278	#340	C₂²×C₇₃	1	2	yes	—
279	#336	C₂²×C₇₃	1	1	yes	characteristic
280	#336	C₂²×C₇₃	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
282	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂×Q₁₆	—	2	2	no	—
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×Q₁₆	—	2	2	no	—
287	C₂×SD₁₆	—	2	4	no	—
288	C₂×SD₁₆	—	2	4	no	—
289	C₂×SD₁₆	—	4	2	no	—
290	C₂×D₈	—	2	2	no	—
291	C₂×D₈	—	2	2	no	—
292	C₂×D₈	D₄×C₇₃	1	4	yes	—
293	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
297	#124	—	2	4	no	—
298	#124	—	4	2	no	—
299	C₄×D₄	—	2	4	no	—
300	C₄×D₄	—	4	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
305	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
313	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
314	#107	—	2	2	no	—
315	#107	—	2	2	no	—
316	C₄⋊C₈	—	2	2	no	—
317	#103	—	4	2	no	—
318	#103	—	4	2	no	—
319	#102	—	2	4	no	—
320	#102	—	4	2	no	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	2	no	—
323	C₄×C₈	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	D₄×C₇₃	1	1	yes	characteristic
330	#95	D₄×C₇₃	1	1	yes	characteristic
331	C₂⁴	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	4	4	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	8	2	no	—
350	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
356	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
357	Q₁₆	—	4	4	no	—
358	SD₁₆	—	4	8	no	—
359	D₈	—	2	8	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
369	C₂×C₈	#41×C₇₃	1	2	yes	—
370	C₂×C₈	#41×C₇₃	1	2	yes	—
371	C₂×C₈	#41×C₇₃	1	2	yes	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	8	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	—	4	4	no	—
381	C₂²⋊C₄	—	4	4	no	—
382	C₂²⋊C₄	—	4	4	no	—
383	C₂²⋊C₄	—	8	2	no	—
384	C₄²	—	2	1	no	—
385	C₄²	—	2	1	no	—
386	C₄²	—	2	1	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₂³	—	2	4	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	4	2	no	—
397	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	4	2	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	4	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	#135×C₇₃	1	2	yes	—
433	C₂×C₄	#135×C₇₃	1	2	yes	—
434	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
438	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
439	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
440	C₈	—	2	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	4	1	no	—
443	C₈	#123×C₇₃	1	4	yes	—
444	C₂²	—	4	4	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	4	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	8	2	no	—
449	C₂²	—	8	2	no	—
450	C₂²	—	8	2	no	—
451	C₂²	#532×C₇₃	1	1	yes	characteristic
452	C₂²	D₄²×C₇₃	1	1	yes	characteristic
453	C₂²	#550×C₇₃	1	1	yes	characteristic
454	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
455	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
456	C₂²	#576×C₇₃	1	1	yes	characteristic
457	C₂²	#578×C₇₃	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	4	1	no	—
461	C₄	—	4	1	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	—	8	2	no	—
467	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
468	C₄	#540×C₇₃	1	1	yes	characteristic
469	C₄	#546×C₇₃	1	1	yes	characteristic
470	C₄	#559×C₇₃	1	1	yes	characteristic
471	C₂	—	8	4	no	—
472	C₂	C₇₃×#2445	1	1	yes	characteristic
473	C₂	C₇₃×#3168	1	1	yes	characteristic
474	C₂	C₇₃×#3175	1	1	yes	characteristic
475	C₂	C₇₃×#3280	1	1	yes	characteristic
476	C₂	C₇₃×#3283	1	1	yes	characteristic
477	C₂	C₇₃×#3393	1	1	yes	characteristic
478	C₂	C₇₃×#3396	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×D₈×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₄⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₇₃×#2447	C₂	semidirect
4. C₇₃×#2055	C₂	semidirect
5. C₇₃×#2042	C₂	semidirect
7. C₇₃×#1969	C₂	semidirect
8. C₇₃×#1969	C₂	semidirect
9. C₇₃×#1942	C₂	semidirect
10. C₇₃×#1877	C₂	semidirect
11. C₈×C₄⋊C₄×C₇₃	C₂	semidirect
231. #26252	C₇₃	direct (N × H)
242. #2447	C₂×C₇₃	semidirect
243. #2055	C₂×C₇₃	semidirect
244. #2042	C₂×C₇₃	semidirect
246. #1969	C₂×C₇₃	semidirect
247. #1969	C₂×C₇₃	semidirect
248. #1942	C₂×C₇₃	semidirect
249. #1877	C₂×C₇₃	semidirect
250. C₈×C₄⋊C₄	C₂×C₇₃	semidirect
251. C₇₃	#26252	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#495×C₇₃	2
C₂×C₄×D₈×C₇₃	2
C₇₃×#2447	2
C₇₃×#2055	2
C₇₃×#2042	2
C₇₃×#1970	2
C₇₃×#1969	2
C₇₃×#1942	2
C₇₃×#1877	2
C₈×C₄⋊C₄×C₇₃	2
#26252	73

Subgroups — C73×#26252 #32935656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#26252 #32935656