Subgroups — C₇₃×#26255 #32935659

Order 18688.

814 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#494×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2446	C₂	1	2	yes	maximal
4	C₇₃×#2056	C₂	1	2	yes	maximal
5	C₇₃×#2043	C₂	1	2	yes	maximal
6	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic
7	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#1969	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#1942	C₂	1	1	yes	maximal, characteristic
10	C₇₃×#1878	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
17	#494×C₇₃	—	2	4	no	—
18	C₄×Q₁₆×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×#103×C₇₃	C₂²	1	2	yes	—
25	C₂×#103×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	#400×C₇₃	—	2	2	no	—
30	#398×C₇₃	—	2	2	no	—
31	#391×C₇₃	C₂²	1	2	yes	—
32	#391×C₇₃	C₂²	1	2	yes	—
33	#391×C₇₃	C₂²	1	2	yes	—
34	#389×C₇₃	C₂²	1	2	yes	—
35	#387×C₇₃	—	2	2	no	—
36	#387×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×Q₈×C₇₃	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₇₃	—	2	4	no	—
44	C₂×Q₁₆×C₇₃	—	2	2	no	—
45	C₂×Q₁₆×C₇₃	—	2	2	no	—
46	C₂×Q₁₆×C₇₃	—	2	2	no	—
47	C₂×Q₁₆×C₇₃	—	2	4	no	—
48	C₂×Q₁₆×C₇₃	—	2	2	no	—
49	C₂×Q₁₆×C₇₃	—	2	2	no	—
50	C₂×Q₁₆×C₇₃	—	4	2	no	—
51	C₂×Q₁₆×C₇₃	D₄	1	4	yes	—
52	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
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	C₄⋊Q₈×C₇₃	—	2	4	no	—
57	C₄⋊Q₈×C₇₃	—	4	2	no	—
58	C₄×Q₈×C₇₃	—	2	4	no	—
59	C₄×Q₈×C₇₃	—	4	2	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₇₃	—	2	2	no	—
69	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
72	#107×C₇₃	—	2	2	no	—
73	#107×C₇₃	—	2	2	no	—
74	C₄⋊C₈×C₇₃	—	2	2	no	—
75	#103×C₇₃	—	2	4	no	—
76	#103×C₇₃	—	4	2	no	—
77	#103×C₇₃	—	4	2	no	—
78	#103×C₇₃	—	4	2	no	—
79	C₄×C₈×C₇₃	—	2	2	no	—
80	C₄×C₈×C₇₃	—	2	2	no	—
81	C₄×C₈×C₇₃	—	2	2	no	—
82	#95×C₇₃	—	2	2	no	—
83	#95×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	C₂×Q₈×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×Q₈×C₇₃	—	2	2	no	—
99	C₂×Q₈×C₇₃	—	2	2	no	—
100	C₂×Q₈×C₇₃	—	2	2	no	—
101	C₂×Q₈×C₇₃	—	2	2	no	—
102	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₇₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₇₃	—	2	8	no	—
115	Q₁₆×C₇₃	—	4	8	no	—
116	Q₁₆×C₇₃	—	4	4	no	—
117	C₂×C₈×C₇₃	—	2	1	no	—
118	C₂×C₈×C₇₃	—	2	1	no	—
119	C₂×C₈×C₇₃	—	2	1	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	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₇₃	#41	1	2	yes	—
127	C₂×C₈×C₇₃	#41	1	2	yes	—
128	C₂×C₈×C₇₃	#41	1	2	yes	—
129	C₄⋊C₄×C₇₃	—	2	2	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	—	4	4	no	—
135	C₄⋊C₄×C₇₃	—	4	4	no	—
136	C₄⋊C₄×C₇₃	—	4	4	no	—
137	C₄⋊C₄×C₇₃	—	4	4	no	—
138	C₄⋊C₄×C₇₃	Q₁₆	1	4	yes	complemented
139	C₄²×C₇₃	—	2	1	no	—
140	C₄²×C₇₃	—	2	1	no	—
141	C₄²×C₇₃	—	2	1	no	—
142	C₄²×C₇₃	—	2	1	no	—
143	C₄²×C₇₃	—	2	1	no	—
144	C₄²×C₇₃	—	2	1	no	—
145	C₄²×C₇₃	—	4	4	no	—
146	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₇₃	—	2	4	no	—
148	Q₈×C₇₃	—	2	4	no	—
149	Q₈×C₇₃	—	4	2	no	—
150	Q₈×C₇₃	—	4	2	no	—
151	Q₈×C₇₃	—	4	2	no	—
152	Q₈×C₇₃	—	4	2	no	—
153	Q₈×C₇₃	—	4	2	no	—
154	Q₈×C₇₃	—	4	2	no	—
155	C₂×C₄×C₇₃	—	2	1	no	—
156	C₂×C₄×C₇₃	—	2	1	no	—
157	C₂×C₄×C₇₃	—	2	1	no	—
158	C₂×C₄×C₇₃	—	2	1	no	—
159	C₂×C₄×C₇₃	—	2	1	no	—
160	C₂×C₄×C₇₃	—	2	1	no	—
161	C₂×C₄×C₇₃	—	2	1	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	4	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	—	4	2	no	—
171	C₂×C₄×C₇₃	—	4	2	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	—	4	2	no	—
175	C₂×C₄×C₇₃	—	4	2	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	—	4	2	no	—
179	C₂×C₄×C₇₃	—	4	2	no	—
180	C₂×C₄×C₇₃	—	4	2	no	—
181	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
182	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₇₃	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₇₃	#135	1	2	yes	—
185	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
190	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
191	C₈×C₇₃	—	2	2	no	—
192	C₈×C₇₃	—	4	1	no	—
193	C₈×C₇₃	—	4	1	no	—
194	C₈×C₇₃	#123	1	4	yes	—
195	C₂²×C₇₃	#532	1	1	yes	characteristic
196	C₂²×C₇₃	D₄²	1	1	yes	characteristic
197	C₂²×C₇₃	#550	1	1	yes	characteristic
198	C₂²×C₇₃	C₂²×Q₁₆	1	1	yes	characteristic
199	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
200	C₂²×C₇₃	#578	1	1	yes	characteristic
201	C₂²×C₇₃	#578	1	1	yes	characteristic
202	C₄×C₇₃	—	2	2	no	—
203	C₄×C₇₃	—	2	2	no	—
204	C₄×C₇₃	—	2	2	no	—
205	C₄×C₇₃	—	2	2	no	—
206	C₄×C₇₃	—	4	1	no	—
207	C₄×C₇₃	—	4	4	no	—
208	C₄×C₇₃	—	4	1	no	—
209	C₄×C₇₃	—	8	2	no	—
210	C₄×C₇₃	—	8	2	no	—
211	C₄×C₇₃	—	8	2	no	—
212	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
213	C₄×C₇₃	#540	1	1	yes	characteristic
214	C₄×C₇₃	#546	1	1	yes	characteristic
215	C₄×C₇₃	#559	1	1	yes	characteristic
216	#26255	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₇₃	#2445	1	1	yes	characteristic
218	C₂×C₇₃	#3170	1	1	yes	characteristic
219	C₂×C₇₃	#3177	1	1	yes	characteristic
220	C₂×C₇₃	#3285	1	1	yes	characteristic
221	C₂×C₇₃	D₄×Q₁₆	1	1	yes	characteristic
222	C₂×C₇₃	#3393	1	1	yes	characteristic
223	C₂×C₇₃	#3395	1	1	yes	characteristic
224	C₂×#494	C₂×C₇₃	1	1	yes	characteristic
225	C₂×C₄×Q₁₆	C₂×C₇₃	1	1	yes	characteristic
226	#2446	C₂×C₇₃	1	2	yes	—
227	#2056	C₂×C₇₃	1	2	yes	—
228	#2043	C₂×C₇₃	1	2	yes	—
229	#1969	C₂×C₇₃	1	1	yes	characteristic
230	#1969	C₂×C₇₃	1	1	yes	characteristic
231	#1969	C₂×C₇₃	1	1	yes	characteristic
232	#1942	C₂×C₇₃	1	1	yes	characteristic
233	#1878	C₂×C₇₃	1	2	yes	—
234	C₈×C₄⋊C₄	C₂×C₇₃	1	1	yes	characteristic
235	C₇₃	#26255	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
237	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
238	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
239	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	—
240	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
241	#494	—	2	4	no	—
242	C₄×Q₁₆	—	2	4	no	—
243	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
244	C₂×#107	C₂²×C₇₃	1	1	yes	characteristic
245	C₂×C₄⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
246	C₂×#103	C₂²×C₇₃	1	2	yes	—
247	C₂×#103	C₂²×C₇₃	1	2	yes	—
248	C₂×#103	C₂²×C₇₃	1	2	yes	—
249	C₂×#103	C₂²×C₇₃	1	2	yes	—
250	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
253	#400	—	2	2	no	—
254	#398	—	2	2	no	—
255	#391	C₂²×C₇₃	1	2	yes	—
256	#391	C₂²×C₇₃	1	2	yes	—
257	#391	C₂²×C₇₃	1	2	yes	—
258	#389	C₂²×C₇₃	1	2	yes	—
259	#387	—	2	2	no	—
260	#387	—	2	2	no	—
261	C₄×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
262	#340	C₂²×C₇₃	1	2	yes	—
263	#336	C₂²×C₇₃	1	1	yes	characteristic
264	#336	C₂²×C₇₃	1	1	yes	characteristic
265	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
266	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
267	C₂×Q₁₆	—	2	4	no	—
268	C₂×Q₁₆	—	2	2	no	—
269	C₂×Q₁₆	—	2	2	no	—
270	C₂×Q₁₆	—	2	2	no	—
271	C₂×Q₁₆	—	2	4	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	—	2	2	no	—
274	C₂×Q₁₆	—	4	2	no	—
275	C₂×Q₁₆	D₄×C₇₃	1	4	yes	—
276	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
278	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
279	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
280	C₄⋊Q₈	—	2	4	no	—
281	C₄⋊Q₈	—	4	2	no	—
282	C₄×Q₈	—	2	4	no	—
283	C₄×Q₈	—	4	2	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	—	2	2	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
289	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
290	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
291	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
292	C₂×C₄²	—	2	2	no	—
293	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#107	—	2	2	no	—
298	C₄⋊C₈	—	2	2	no	—
299	#103	—	2	4	no	—
300	#103	—	4	2	no	—
301	#103	—	4	2	no	—
302	#103	—	4	2	no	—
303	C₄×C₈	—	2	2	no	—
304	C₄×C₈	—	2	2	no	—
305	C₄×C₈	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	D₄×C₇₃	1	1	yes	characteristic
314	#95	D₄×C₇₃	1	1	yes	characteristic
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
338	Q₁₆	—	2	8	no	—
339	Q₁₆	—	4	8	no	—
340	Q₁₆	—	4	4	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
350	C₂×C₈	#41×C₇₃	1	2	yes	—
351	C₂×C₈	#41×C₇₃	1	2	yes	—
352	C₂×C₈	#41×C₇₃	1	2	yes	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	Q₁₆×C₇₃	1	4	yes	complemented
363	C₄²	—	2	1	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	2	1	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	1	no	—
368	C₄²	—	2	1	no	—
369	C₄²	—	4	4	no	—
370	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
371	Q₈	—	2	4	no	—
372	Q₈	—	2	4	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	C₂×Q₁₆×C₇₃	1	2	yes	—
406	C₂×C₄	C₂×Q₁₆×C₇₃	1	2	yes	—
407	C₂×C₄	C₂×Q₁₆×C₇₃	1	2	yes	—
408	C₂×C₄	#135×C₇₃	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
413	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
414	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
415	C₈	—	2	2	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	#123×C₇₃	1	4	yes	—
419	C₂²	#532×C₇₃	1	1	yes	characteristic
420	C₂²	D₄²×C₇₃	1	1	yes	characteristic
421	C₂²	#550×C₇₃	1	1	yes	characteristic
422	C₂²	C₂²×Q₁₆×C₇₃	1	1	yes	characteristic
423	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
424	C₂²	#578×C₇₃	1	1	yes	characteristic
425	C₂²	#578×C₇₃	1	1	yes	characteristic
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	1	no	—
432	C₄	—	4	1	no	—
433	C₄	—	8	2	no	—
434	C₄	—	8	2	no	—
435	C₄	—	8	2	no	—
436	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
437	C₄	#540×C₇₃	1	1	yes	characteristic
438	C₄	#546×C₇₃	1	1	yes	characteristic
439	C₄	#559×C₇₃	1	1	yes	characteristic
440	C₂	C₇₃×#2445	1	1	yes	characteristic
441	C₂	C₇₃×#3170	1	1	yes	characteristic
442	C₂	C₇₃×#3177	1	1	yes	characteristic
443	C₂	C₇₃×#3285	1	1	yes	characteristic
444	C₂	D₄×Q₁₆×C₇₃	1	1	yes	characteristic
445	C₂	C₇₃×#3393	1	1	yes	characteristic
446	C₂	C₇₃×#3395	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
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
138. C₄⋊C₄×C₇₃	Q₁₆	semidirect
216. #26255	C₇₃	direct (N × H)
235. C₇₃	#26255	direct (N × H)
362. C₄⋊C₄	Q₁₆×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#494×C₇₃	2
C₂×C₄×Q₁₆×C₇₃	2
C₇₃×#2446	2
C₇₃×#2056	2
C₇₃×#2043	2
C₇₃×#1969	2
C₇₃×#1942	2
C₇₃×#1878	2
C₈×C₄⋊C₄×C₇₃	2
#26255	73

Subgroups — C73×#26255 #32935659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#26255 #32935659