Subgroups — C₇₃×#35014 #32944418

Order 18688.

1978 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2848	C₂	1	2	yes	maximal
4	C₇₃×#2646	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2626	C₂	1	2	yes	maximal
6	C₇₃×#2589	C₂	1	4	yes	maximal, complemented
7	C₇₃×#2587	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2497	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2492	C₂	1	2	yes	maximal, complemented
10	C₇₃×#2429	C₂	1	2	yes	maximal, complemented
11	C₇₃×#2423	C₂	1	2	yes	maximal, complemented
12	C₇₃×#2329	C₂	1	2	yes	maximal, complemented
13	C₇₃×#2312	C₂	1	2	yes	maximal
14	C₄×C₂²⋊Q₈×C₇₃	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic
16	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
19	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
21	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
24	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
28	#400×C₇₃	C₂²	1	4	yes	complemented
29	#400×C₇₃	C₂²	1	4	yes	complemented
30	#399×C₇₃	C₂²	1	4	yes	—
31	#398×C₇₃	C₂²	1	4	yes	complemented
32	#398×C₇₃	C₂²	1	4	yes	complemented
33	#396×C₇₃	C₂²	1	4	yes	—
34	#396×C₇₃	C₂²	1	4	yes	—
35	#393×C₇₃	C₂²	1	4	yes	—
36	#391×C₇₃	C₂²	1	2	yes	complemented
37	#391×C₇₃	C₂²	1	4	yes	complemented
38	#391×C₇₃	C₂²	1	2	yes	complemented
39	#391×C₇₃	C₂²	1	2	yes	complemented
40	#389×C₇₃	C₂²	1	2	yes	complemented
41	#389×C₇₃	C₂²	1	2	yes	complemented
42	#389×C₇₃	C₂²	1	4	yes	complemented
43	#389×C₇₃	C₂²	1	2	yes	complemented
44	#389×C₇₃	C₂²	1	2	yes	complemented
45	#389×C₇₃	C₂²	1	2	yes	complemented
46	#388×C₇₃	C₂²	1	4	yes	—
47	#388×C₇₃	C₂²	1	4	yes	—
48	#388×C₇₃	C₂²	1	4	yes	—
49	#388×C₇₃	C₂²	1	4	yes	—
50	#387×C₇₃	C₂²	1	4	yes	complemented
51	#387×C₇₃	C₂²	1	4	yes	complemented
52	#387×C₇₃	C₂²	1	4	yes	complemented
53	#385×C₇₃	C₂²	1	4	yes	—
54	#385×C₇₃	C₂²	1	4	yes	—
55	#385×C₇₃	C₂²	1	4	yes	—
56	#385×C₇₃	C₂²	1	4	yes	—
57	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
58	#384×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	#380×C₇₃	C₂²	1	2	yes	—
60	#380×C₇₃	C₂²	1	2	yes	—
61	#380×C₇₃	C₂²	1	2	yes	—
62	#380×C₇₃	C₂²	1	2	yes	—
63	#380×C₇₃	C₂²	1	2	yes	—
64	#380×C₇₃	C₂²	1	2	yes	—
65	#379×C₇₃	C₂²	1	4	yes	—
66	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	complemented
67	C₄×C₄⋊C₄×C₇₃	C₂²	1	4	yes	complemented
68	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
69	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₇₃	C₂²	1	4	yes	—
73	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
74	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
75	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
76	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
77	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₇₃	—	2	4	no	—
79	C₂³×C₄×C₇₃	—	4	2	no	—
80	C₂³×C₄×C₇₃	—	4	2	no	—
81	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
82	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
88	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
89	C₄⋊Q₈×C₇₃	—	4	2	no	—
90	C₄⋊Q₈×C₇₃	—	4	2	no	—
91	C₂²⋊Q₈×C₇₃	—	2	8	no	—
92	C₂²⋊Q₈×C₇₃	—	2	8	no	—
93	C₂²⋊Q₈×C₇₃	—	4	4	no	—
94	C₂²⋊Q₈×C₇₃	—	4	4	no	—
95	C₄×Q₈×C₇₃	—	4	4	no	—
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
111	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
112	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
113	C₂×C₂²⋊C₄×C₇₃	Q₈	1	8	yes	complemented
114	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
119	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₇₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₇₃	—	4	2	no	—
125	C₂×C₄²×C₇₃	—	4	2	no	—
126	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
130	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
133	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
134	#95×C₇₃	C₂³	1	2	yes	—
135	#95×C₇₃	C₂³	1	2	yes	—
136	#95×C₇₃	C₂³	1	2	yes	—
137	#95×C₇₃	C₂³	1	2	yes	—
138	#95×C₇₃	C₂³	1	4	yes	—
139	#95×C₇₃	C₂³	1	4	yes	—
140	#95×C₇₃	C₂³	1	4	yes	—
141	#95×C₇₃	C₂³	1	4	yes	—
142	#95×C₇₃	C₂³	1	4	yes	—
143	#95×C₇₃	C₂³	1	4	yes	—
144	#95×C₇₃	C₂³	1	4	yes	—
145	#95×C₇₃	C₂³	1	4	yes	—
146	#95×C₇₃	C₂³	1	4	yes	—
147	#95×C₇₃	C₂³	1	4	yes	—
148	C₂⁴×C₇₃	—	2	2	no	—
149	C₂⁴×C₇₃	—	2	2	no	—
150	C₂⁴×C₇₃	—	4	1	no	—
151	C₂⁴×C₇₃	—	4	1	no	—
152	C₂⁴×C₇₃	—	4	1	no	—
153	C₂⁴×C₇₃	—	4	1	no	—
154	C₂⁴×C₇₃	C₂×Q₈	1	4	yes	—
155	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
156	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
157	C₂×Q₈×C₇₃	—	2	4	no	—
158	C₂×Q₈×C₇₃	—	2	4	no	—
159	C₂×Q₈×C₇₃	—	2	4	no	—
160	C₂×Q₈×C₇₃	—	2	4	no	—
161	C₂×Q₈×C₇₃	—	4	2	no	—
162	C₂×Q₈×C₇₃	—	4	2	no	—
163	C₂²×C₄×C₇₃	—	2	2	no	—
164	C₂²×C₄×C₇₃	—	2	2	no	—
165	C₂²×C₄×C₇₃	—	2	2	no	—
166	C₂²×C₄×C₇₃	—	2	2	no	—
167	C₂²×C₄×C₇₃	—	2	4	no	—
168	C₂²×C₄×C₇₃	—	2	4	no	—
169	C₂²×C₄×C₇₃	—	2	4	no	—
170	C₂²×C₄×C₇₃	—	2	4	no	—
171	C₂²×C₄×C₇₃	—	4	1	no	—
172	C₂²×C₄×C₇₃	—	4	1	no	—
173	C₂²×C₄×C₇₃	—	4	1	no	—
174	C₂²×C₄×C₇₃	—	4	1	no	—
175	C₂²×C₄×C₇₃	—	4	2	no	—
176	C₂²×C₄×C₇₃	—	4	2	no	—
177	C₂²×C₄×C₇₃	—	4	1	no	—
178	C₂²×C₄×C₇₃	—	4	1	no	—
179	C₂²×C₄×C₇₃	—	4	1	no	—
180	C₂²×C₄×C₇₃	—	4	1	no	—
181	C₂²×C₄×C₇₃	—	4	1	no	—
182	C₂²×C₄×C₇₃	—	4	1	no	—
183	C₂²×C₄×C₇₃	—	4	16	no	—
184	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
185	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
186	C₂²×C₄×C₇₃	#41	1	4	yes	—
187	C₂²×C₄×C₇₃	#41	1	4	yes	—
188	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
192	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
193	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
195	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
196	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
197	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
200	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
201	C₄⋊C₄×C₇₃	—	2	4	no	—
202	C₄⋊C₄×C₇₃	—	2	4	no	—
203	C₄⋊C₄×C₇₃	—	2	8	no	—
204	C₄⋊C₄×C₇₃	—	2	8	no	—
205	C₄⋊C₄×C₇₃	—	2	4	no	—
206	C₄⋊C₄×C₇₃	—	2	4	no	—
207	C₄⋊C₄×C₇₃	—	4	2	no	—
208	C₄⋊C₄×C₇₃	—	4	2	no	—
209	C₄⋊C₄×C₇₃	—	4	2	no	—
210	C₄⋊C₄×C₇₃	—	4	4	no	—
211	C₄⋊C₄×C₇₃	—	4	4	no	—
212	C₄⋊C₄×C₇₃	—	4	4	no	—
213	C₄⋊C₄×C₇₃	—	4	4	no	—
214	C₄⋊C₄×C₇₃	—	4	2	no	—
215	C₄⋊C₄×C₇₃	—	4	2	no	—
216	C₄⋊C₄×C₇₃	—	4	2	no	—
217	C₂²⋊C₄×C₇₃	—	2	8	no	—
218	C₂²⋊C₄×C₇₃	—	2	8	no	—
219	C₂²⋊C₄×C₇₃	—	2	4	no	—
220	C₂²⋊C₄×C₇₃	—	2	4	no	—
221	C₂²⋊C₄×C₇₃	—	4	4	no	—
222	C₂²⋊C₄×C₇₃	—	4	4	no	—
223	C₂²⋊C₄×C₇₃	—	4	4	no	—
224	C₂²⋊C₄×C₇₃	—	4	4	no	—
225	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
226	C₂²⋊C₄×C₇₃	C₂×Q₈	1	8	yes	—
227	C₄²×C₇₃	—	2	4	no	—
228	C₄²×C₇₃	—	2	2	no	—
229	C₄²×C₇₃	—	2	2	no	—
230	C₄²×C₇₃	—	4	2	no	—
231	C₄²×C₇₃	—	4	1	no	—
232	C₄²×C₇₃	—	4	1	no	—
233	C₄²×C₇₃	—	4	4	no	—
234	C₄²×C₇₃	—	4	4	no	—
235	C₂³×C₇₃	—	2	1	no	—
236	C₂³×C₇₃	—	2	1	no	—
237	C₂³×C₇₃	—	2	1	no	—
238	C₂³×C₇₃	—	2	1	no	—
239	C₂³×C₇₃	—	2	8	no	—
240	C₂³×C₇₃	—	2	2	no	—
241	C₂³×C₇₃	—	2	2	no	—
242	C₂³×C₇₃	—	2	2	no	—
243	C₂³×C₇₃	—	2	2	no	—
244	C₂³×C₇₃	—	2	2	no	—
245	C₂³×C₇₃	—	2	2	no	—
246	C₂³×C₇₃	—	4	4	no	—
247	C₂³×C₇₃	—	4	4	no	—
248	C₂³×C₇₃	—	4	4	no	—
249	C₂³×C₇₃	—	4	4	no	—
250	C₂³×C₇₃	—	4	4	no	—
251	C₂³×C₇₃	—	4	4	no	—
252	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
253	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
254	C₂³×C₇₃	C₂×#41	1	2	yes	—
255	C₂³×C₇₃	C₂×#41	1	2	yes	—
256	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
257	Q₈×C₇₃	—	4	8	no	—
258	Q₈×C₇₃	—	8	4	no	—
259	C₂×C₄×C₇₃	—	2	2	no	—
260	C₂×C₄×C₇₃	—	2	1	no	—
261	C₂×C₄×C₇₃	—	2	1	no	—
262	C₂×C₄×C₇₃	—	2	1	no	—
263	C₂×C₄×C₇₃	—	2	1	no	—
264	C₂×C₄×C₇₃	—	2	1	no	—
265	C₂×C₄×C₇₃	—	2	1	no	—
266	C₂×C₄×C₇₃	—	2	2	no	—
267	C₂×C₄×C₇₃	—	2	1	no	—
268	C₂×C₄×C₇₃	—	2	1	no	—
269	C₂×C₄×C₇₃	—	2	1	no	—
270	C₂×C₄×C₇₃	—	2	1	no	—
271	C₂×C₄×C₇₃	—	2	8	no	—
272	C₂×C₄×C₇₃	—	2	2	no	—
273	C₂×C₄×C₇₃	—	2	4	no	—
274	C₂×C₄×C₇₃	—	2	4	no	—
275	C₂×C₄×C₇₃	—	2	4	no	—
276	C₂×C₄×C₇₃	—	2	4	no	—
277	C₂×C₄×C₇₃	—	2	2	no	—
278	C₂×C₄×C₇₃	—	2	2	no	—
279	C₂×C₄×C₇₃	—	2	4	no	—
280	C₂×C₄×C₇₃	—	2	4	no	—
281	C₂×C₄×C₇₃	—	2	4	no	—
282	C₂×C₄×C₇₃	—	2	4	no	—
283	C₂×C₄×C₇₃	—	2	2	no	—
284	C₂×C₄×C₇₃	—	2	2	no	—
285	C₂×C₄×C₇₃	—	2	4	no	—
286	C₂×C₄×C₇₃	—	2	4	no	—
287	C₂×C₄×C₇₃	—	2	4	no	—
288	C₂×C₄×C₇₃	—	2	4	no	—
289	C₂×C₄×C₇₃	—	2	2	no	—
290	C₂×C₄×C₇₃	—	4	4	no	—
291	C₂×C₄×C₇₃	—	4	4	no	—
292	C₂×C₄×C₇₃	—	4	4	no	—
293	C₂×C₄×C₇₃	—	4	8	no	—
294	C₂×C₄×C₇₃	—	4	4	no	—
295	C₂×C₄×C₇₃	—	4	4	no	—
296	C₂×C₄×C₇₃	—	4	8	no	—
297	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
298	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
299	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
300	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
301	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
302	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
303	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
304	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
305	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
306	C₂²×C₇₃	—	2	2	no	—
307	C₂²×C₇₃	—	2	2	no	—
308	C₂²×C₇₃	—	2	2	no	—
309	C₂²×C₇₃	—	2	2	no	—
310	C₂²×C₇₃	—	2	2	no	—
311	C₂²×C₇₃	—	2	2	no	—
312	C₂²×C₇₃	—	2	4	no	—
313	C₂²×C₇₃	—	2	4	no	—
314	C₂²×C₇₃	—	2	4	no	—
315	C₂²×C₇₃	—	4	16	no	—
316	C₂²×C₇₃	—	4	2	no	—
317	C₂²×C₇₃	—	4	2	no	—
318	C₂²×C₇₃	—	4	2	no	—
319	C₂²×C₇₃	—	4	2	no	—
320	C₂²×C₇₃	#533	1	4	yes	—
321	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
322	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
323	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
324	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
326	C₂²×C₇₃	#585	1	1	yes	characteristic
327	C₂²×C₇₃	#585	1	1	yes	characteristic
328	C₄×C₇₃	—	2	2	no	—
329	C₄×C₇₃	—	2	4	no	—
330	C₄×C₇₃	—	2	2	no	—
331	C₄×C₇₃	—	2	2	no	—
332	C₄×C₇₃	—	2	2	no	—
333	C₄×C₇₃	—	2	2	no	—
334	C₄×C₇₃	—	4	2	no	—
335	C₄×C₇₃	—	4	4	no	—
336	C₄×C₇₃	—	4	4	no	—
337	C₄×C₇₃	—	4	4	no	—
338	C₄×C₇₃	—	4	4	no	—
339	C₄×C₇₃	—	4	2	no	—
340	C₄×C₇₃	#538	1	4	yes	—
341	#35014	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
342	C₂×C₇₃	—	2	4	no	—
343	C₂×C₇₃	—	4	4	no	—
344	C₂×C₇₃	C₂×#533	1	1	yes	characteristic
345	C₂×C₇₃	C₂×#538	1	1	yes	characteristic
346	C₂×C₇₃	#3455	1	1	yes	characteristic
347	C₂×C₇₃	#3501	1	1	yes	characteristic
348	C₂×C₇₃	#3501	1	1	yes	characteristic
349	C₂×C₇₃	#3505	1	1	yes	characteristic
350	C₂×C₇₃	#3506	1	1	yes	characteristic
351	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
352	#2857	C₂×C₇₃	1	1	yes	characteristic, complemented
353	#2848	C₂×C₇₃	1	2	yes	—
354	#2646	C₂×C₇₃	1	2	yes	complemented
355	#2626	C₂×C₇₃	1	2	yes	—
356	#2589	C₂×C₇₃	1	4	yes	complemented
357	#2587	C₂×C₇₃	1	4	yes	complemented
358	#2497	C₂×C₇₃	1	2	yes	complemented
359	#2492	C₂×C₇₃	1	2	yes	complemented
360	#2429	C₂×C₇₃	1	2	yes	complemented
361	#2423	C₂×C₇₃	1	2	yes	complemented
362	#2329	C₂×C₇₃	1	2	yes	complemented
363	#2312	C₂×C₇₃	1	2	yes	—
364	C₄×C₂²⋊Q₈	C₂×C₇₃	1	2	yes	complemented
365	C₂×C₄×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic
366	C₇₃	#35014	1	1	yes	characteristic, direct product factor, Sylow
367	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
368	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
369	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
370	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
371	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
372	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
373	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
374	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
375	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
376	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
378	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
379	#400	C₂²×C₇₃	1	4	yes	complemented
380	#400	C₂²×C₇₃	1	4	yes	complemented
381	#399	C₂²×C₇₃	1	4	yes	—
382	#398	C₂²×C₇₃	1	4	yes	complemented
383	#398	C₂²×C₇₃	1	4	yes	complemented
384	#396	C₂²×C₇₃	1	4	yes	—
385	#396	C₂²×C₇₃	1	4	yes	—
386	#393	C₂²×C₇₃	1	4	yes	—
387	#391	C₂²×C₇₃	1	4	yes	complemented
388	#391	C₂²×C₇₃	1	2	yes	complemented
389	#391	C₂²×C₇₃	1	2	yes	complemented
390	#391	C₂²×C₇₃	1	2	yes	complemented
391	#389	C₂²×C₇₃	1	4	yes	complemented
392	#389	C₂²×C₇₃	1	2	yes	complemented
393	#389	C₂²×C₇₃	1	2	yes	complemented
394	#389	C₂²×C₇₃	1	2	yes	complemented
395	#389	C₂²×C₇₃	1	2	yes	complemented
396	#389	C₂²×C₇₃	1	2	yes	complemented
397	#388	C₂²×C₇₃	1	4	yes	—
398	#388	C₂²×C₇₃	1	4	yes	—
399	#388	C₂²×C₇₃	1	4	yes	—
400	#388	C₂²×C₇₃	1	4	yes	—
401	#387	C₂²×C₇₃	1	4	yes	complemented
402	#387	C₂²×C₇₃	1	4	yes	complemented
403	#387	C₂²×C₇₃	1	4	yes	complemented
404	#385	C₂²×C₇₃	1	4	yes	—
405	#385	C₂²×C₇₃	1	4	yes	—
406	#385	C₂²×C₇₃	1	4	yes	—
407	#385	C₂²×C₇₃	1	4	yes	—
408	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
409	#384	C₂²×C₇₃	1	1	yes	characteristic, complemented
410	#380	C₂²×C₇₃	1	2	yes	—
411	#380	C₂²×C₇₃	1	2	yes	—
412	#380	C₂²×C₇₃	1	2	yes	—
413	#380	C₂²×C₇₃	1	2	yes	—
414	#380	C₂²×C₇₃	1	2	yes	—
415	#380	C₂²×C₇₃	1	2	yes	—
416	#379	C₂²×C₇₃	1	4	yes	—
417	C₄×C₄⋊C₄	C₂²×C₇₃	1	4	yes	complemented
418	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	complemented
419	C₄×C₂²⋊C₄	C₂²×C₇₃	1	4	yes	—
420	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
421	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
422	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
423	C₄×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
424	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
425	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
426	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
427	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
428	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
429	C₂³×C₄	—	2	4	no	—
430	C₂³×C₄	—	4	2	no	—
431	C₂³×C₄	—	4	2	no	—
432	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
433	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
434	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
435	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
436	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
437	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
438	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
439	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
440	C₄⋊Q₈	—	4	2	no	—
441	C₄⋊Q₈	—	4	2	no	—
442	C₂²⋊Q₈	—	2	8	no	—
443	C₂²⋊Q₈	—	2	8	no	—
444	C₂²⋊Q₈	—	4	4	no	—
445	C₂²⋊Q₈	—	4	4	no	—
446	C₄×Q₈	—	4	4	no	—
447	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
448	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
451	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
452	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
456	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
457	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
458	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
459	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
460	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
461	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
462	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
463	C₂×C₂²⋊C₄	—	2	4	no	—
464	C₂×C₂²⋊C₄	Q₈×C₇₃	1	8	yes	complemented
465	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₇₃	1	2	yes	—
475	C₂×C₄²	—	4	2	no	—
476	C₂×C₄²	—	4	2	no	—
477	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
478	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
479	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
480	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
481	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
482	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
483	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
484	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
485	#95	C₂³×C₇₃	1	2	yes	—
486	#95	C₂³×C₇₃	1	2	yes	—
487	#95	C₂³×C₇₃	1	2	yes	—
488	#95	C₂³×C₇₃	1	2	yes	—
489	#95	C₂³×C₇₃	1	4	yes	—
490	#95	C₂³×C₇₃	1	4	yes	—
491	#95	C₂³×C₇₃	1	4	yes	—
492	#95	C₂³×C₇₃	1	4	yes	—
493	#95	C₂³×C₇₃	1	4	yes	—
494	#95	C₂³×C₇₃	1	4	yes	—
495	#95	C₂³×C₇₃	1	4	yes	—
496	#95	C₂³×C₇₃	1	4	yes	—
497	#95	C₂³×C₇₃	1	4	yes	—
498	#95	C₂³×C₇₃	1	4	yes	—
499	C₂⁴	—	2	2	no	—
500	C₂⁴	—	2	2	no	—
501	C₂⁴	—	4	1	no	—
502	C₂⁴	—	4	1	no	—
503	C₂⁴	—	4	1	no	—
504	C₂⁴	—	4	1	no	—
505	C₂⁴	C₂×Q₈×C₇₃	1	4	yes	—
506	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
507	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
508	C₂×Q₈	—	2	4	no	—
509	C₂×Q₈	—	2	4	no	—
510	C₂×Q₈	—	2	4	no	—
511	C₂×Q₈	—	2	4	no	—
512	C₂×Q₈	—	4	2	no	—
513	C₂×Q₈	—	4	2	no	—
514	C₂²×C₄	—	2	2	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	4	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	—	4	1	no	—
524	C₂²×C₄	—	4	1	no	—
525	C₂²×C₄	—	4	1	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	4	2	no	—
528	C₂²×C₄	—	4	1	no	—
529	C₂²×C₄	—	4	1	no	—
530	C₂²×C₄	—	4	1	no	—
531	C₂²×C₄	—	4	1	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	—	4	16	no	—
535	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
536	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
537	C₂²×C₄	#41×C₇₃	1	4	yes	—
538	C₂²×C₄	#41×C₇₃	1	4	yes	—
539	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
542	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
543	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
544	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
545	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
546	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
547	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
548	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
549	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
551	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
552	C₄⋊C₄	—	2	4	no	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	8	no	—
555	C₄⋊C₄	—	2	8	no	—
556	C₄⋊C₄	—	2	4	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	4	2	no	—
559	C₄⋊C₄	—	4	2	no	—
560	C₄⋊C₄	—	4	2	no	—
561	C₄⋊C₄	—	4	4	no	—
562	C₄⋊C₄	—	4	4	no	—
563	C₄⋊C₄	—	4	4	no	—
564	C₄⋊C₄	—	4	4	no	—
565	C₄⋊C₄	—	4	2	no	—
566	C₄⋊C₄	—	4	2	no	—
567	C₄⋊C₄	—	4	2	no	—
568	C₂²⋊C₄	—	2	8	no	—
569	C₂²⋊C₄	—	2	8	no	—
570	C₂²⋊C₄	—	2	4	no	—
571	C₂²⋊C₄	—	2	4	no	—
572	C₂²⋊C₄	—	4	4	no	—
573	C₂²⋊C₄	—	4	4	no	—
574	C₂²⋊C₄	—	4	4	no	—
575	C₂²⋊C₄	—	4	4	no	—
576	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
577	C₂²⋊C₄	C₂×Q₈×C₇₃	1	8	yes	—
578	C₄²	—	2	4	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	2	2	no	—
581	C₄²	—	4	2	no	—
582	C₄²	—	4	1	no	—
583	C₄²	—	4	1	no	—
584	C₄²	—	4	4	no	—
585	C₄²	—	4	4	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	8	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	2	no	—
596	C₂³	—	2	2	no	—
597	C₂³	—	4	4	no	—
598	C₂³	—	4	4	no	—
599	C₂³	—	4	4	no	—
600	C₂³	—	4	4	no	—
601	C₂³	—	4	4	no	—
602	C₂³	—	4	4	no	—
603	C₂³	C₂²×Q₈×C₇₃	1	4	yes	—
604	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
605	C₂³	C₂×#41×C₇₃	1	2	yes	—
606	C₂³	C₂×#41×C₇₃	1	2	yes	—
607	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
608	Q₈	—	4	8	no	—
609	Q₈	—	8	4	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	4	no	—
626	C₂×C₄	—	2	4	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	2	4	no	—
633	C₂×C₄	—	2	4	no	—
634	C₂×C₄	—	2	2	no	—
635	C₂×C₄	—	2	2	no	—
636	C₂×C₄	—	2	4	no	—
637	C₂×C₄	—	2	4	no	—
638	C₂×C₄	—	2	4	no	—
639	C₂×C₄	—	2	4	no	—
640	C₂×C₄	—	2	2	no	—
641	C₂×C₄	—	4	4	no	—
642	C₂×C₄	—	4	4	no	—
643	C₂×C₄	—	4	4	no	—
644	C₂×C₄	—	4	8	no	—
645	C₂×C₄	—	4	4	no	—
646	C₂×C₄	—	4	4	no	—
647	C₂×C₄	—	4	8	no	—
648	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
649	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
650	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
651	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
652	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
653	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
654	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
655	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
656	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	4	no	—
664	C₂²	—	2	4	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	4	16	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	#533×C₇₃	1	4	yes	—
672	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
673	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
674	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
675	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
676	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
677	C₂²	#585×C₇₃	1	1	yes	characteristic
678	C₂²	#585×C₇₃	1	1	yes	characteristic
679	C₄	—	2	4	no	—
680	C₄	—	2	2	no	—
681	C₄	—	2	2	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	4	4	no	—
686	C₄	—	4	2	no	—
687	C₄	—	4	4	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	4	no	—
690	C₄	—	4	4	no	—
691	C₄	#538×C₇₃	1	4	yes	—
692	C₂	—	2	4	no	—
693	C₂	—	4	4	no	—
694	C₂	C₂×#533×C₇₃	1	1	yes	characteristic
695	C₂	C₂×#538×C₇₃	1	1	yes	characteristic
696	C₂	C₇₃×#3455	1	1	yes	characteristic
697	C₂	C₇₃×#3501	1	1	yes	characteristic
698	C₂	C₇₃×#3501	1	1	yes	characteristic
699	C₂	C₇₃×#3505	1	1	yes	characteristic
700	C₂	C₇₃×#3506	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
prime radical	C₂⁵×C₇₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2857	C₂	semidirect
2. C₇₃×#2857	C₂	semidirect
4. C₇₃×#2646	C₂	semidirect
6. C₇₃×#2589	C₂	semidirect
7. C₇₃×#2587	C₂	semidirect
8. C₇₃×#2497	C₂	semidirect
9. C₇₃×#2492	C₂	semidirect
10. C₇₃×#2429	C₂	semidirect
11. C₇₃×#2423	C₂	semidirect
12. C₇₃×#2329	C₂	semidirect
14. C₄×C₂²⋊Q₈×C₇₃	C₂	semidirect
17. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
18. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
23. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
28. #400×C₇₃	C₂²	semidirect
29. #400×C₇₃	C₂²	semidirect
31. #398×C₇₃	C₂²	semidirect
32. #398×C₇₃	C₂²	semidirect
36. #391×C₇₃	C₂²	semidirect
37. #391×C₇₃	C₂²	semidirect
38. #391×C₇₃	C₂²	semidirect
39. #391×C₇₃	C₂²	semidirect
40. #389×C₇₃	C₂²	semidirect
41. #389×C₇₃	C₂²	semidirect
42. #389×C₇₃	C₂²	semidirect
43. #389×C₇₃	C₂²	semidirect
44. #389×C₇₃	C₂²	semidirect
45. #389×C₇₃	C₂²	semidirect
50. #387×C₇₃	C₂²	semidirect
51. #387×C₇₃	C₂²	semidirect
52. #387×C₇₃	C₂²	semidirect
57. #384×C₇₃	C₂²	semidirect
58. #384×C₇₃	C₂²	semidirect
66. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
67. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
113. C₂×C₂²⋊C₄×C₇₃	Q₈	semidirect
341. #35014	C₇₃	direct (N × H)
351. #2857	C₂×C₇₃	semidirect
352. #2857	C₂×C₇₃	semidirect
354. #2646	C₂×C₇₃	semidirect
356. #2589	C₂×C₇₃	semidirect
357. #2587	C₂×C₇₃	semidirect
358. #2497	C₂×C₇₃	semidirect
359. #2492	C₂×C₇₃	semidirect
360. #2429	C₂×C₇₃	semidirect
361. #2423	C₂×C₇₃	semidirect
362. #2329	C₂×C₇₃	semidirect
364. C₄×C₂²⋊Q₈	C₂×C₇₃	semidirect
366. C₇₃	#35014	direct (N × H)
368. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
369. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
374. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
379. #400	C₂²×C₇₃	semidirect
380. #400	C₂²×C₇₃	semidirect
382. #398	C₂²×C₇₃	semidirect
383. #398	C₂²×C₇₃	semidirect
387. #391	C₂²×C₇₃	semidirect
388. #391	C₂²×C₇₃	semidirect
389. #391	C₂²×C₇₃	semidirect
390. #391	C₂²×C₇₃	semidirect
391. #389	C₂²×C₇₃	semidirect
392. #389	C₂²×C₇₃	semidirect
393. #389	C₂²×C₇₃	semidirect
394. #389	C₂²×C₇₃	semidirect
395. #389	C₂²×C₇₃	semidirect
396. #389	C₂²×C₇₃	semidirect
401. #387	C₂²×C₇₃	semidirect
402. #387	C₂²×C₇₃	semidirect
403. #387	C₂²×C₇₃	semidirect
408. #384	C₂²×C₇₃	semidirect
409. #384	C₂²×C₇₃	semidirect
417. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
418. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
464. C₂×C₂²⋊C₄	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2857	2
C₇₃×#2848	2
C₇₃×#2646	2
C₇₃×#2626	2
C₇₃×#2589	2
C₇₃×#2587	2
C₇₃×#2497	2
C₇₃×#2492	2
C₇₃×#2429	2
C₇₃×#2423	2
C₇₃×#2329	2
C₇₃×#2312	2
C₄×C₂²⋊Q₈×C₇₃	2
C₂×C₄×C₂²⋊C₄×C₇₃	2
#35014	73

Subgroups — C73×#35014 #32944418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#35014 #32944418