Subgroups — C₂×C₇₃×#2586 #32944239

Order 18688.

2182 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2586	C₂	1	16	yes	maximal, direct product factor
2	C₂×#398×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#395×C₇₃	C₂	1	2	yes	maximal
4	C₂×#395×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#391×C₇₃	C₂	1	2	yes	maximal
6	C₂×#391×C₇₃	C₂	1	1	yes	maximal, characteristic
7	C₂×#389×C₇₃	C₂	1	2	yes	maximal
8	C₂×#387×C₇₃	C₂	1	2	yes	maximal
9	C₂×#387×C₇₃	C₂	1	2	yes	maximal
10	C₂×C₄×C₄⋊C₄×C₇₃	C₂	1	2	yes	maximal
11	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
14	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₇₃	C₂²	1	2	yes	—
21	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₇₃	C₂²	1	2	yes	—
23	#398×C₇₃	C₂²	1	8	yes	—
24	#395×C₇₃	C₂²	1	8	yes	—
25	#395×C₇₃	C₂²	1	16	yes	—
26	#391×C₇₃	C₂²	1	16	yes	—
27	#391×C₇₃	C₂²	1	8	yes	—
28	#389×C₇₃	C₂²	1	16	yes	—
29	#387×C₇₃	C₂²	1	16	yes	—
30	#387×C₇₃	C₂²	1	16	yes	—
31	C₄×C₄⋊C₄×C₇₃	C₂²	1	16	yes	—
32	C₂×#95×C₇₃	C₂²	1	2	yes	—
33	C₂×#95×C₇₃	C₂²	1	2	yes	—
34	C₂×#95×C₇₃	C₂²	1	2	yes	—
35	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
36	C₂×#95×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×#95×C₇₃	C₂²	1	2	yes	—
38	C₂×#95×C₇₃	C₂²	1	2	yes	—
39	C₂×#95×C₇₃	C₂²	1	2	yes	—
40	C₂×#95×C₇₃	C₂²	1	2	yes	—
41	C₂²×Q₈×C₇₃	—	2	8	no	—
42	C₂²×Q₈×C₇₃	—	2	4	no	—
43	C₂²×Q₈×C₇₃	—	4	2	no	—
44	C₂²×Q₈×C₇₃	—	4	2	no	—
45	C₂²×Q₈×C₇₃	—	4	2	no	—
46	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
47	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
48	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
58	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
59	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
60	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
61	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
62	C₂×C₄⋊C₄×C₇₃	—	4	2	no	—
63	C₂×C₄⋊C₄×C₇₃	Q₈	1	16	yes	complemented
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
71	C₂×C₄²×C₇₃	—	2	8	no	—
72	C₂×C₄²×C₇₃	—	4	2	no	—
73	C₂×C₄²×C₇₃	—	4	4	no	—
74	C₂×C₄²×C₇₃	C₂³	1	8	yes	—
75	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
76	C₂×C₄²×C₇₃	C₂³	1	8	yes	—
77	#95×C₇₃	C₂³	1	8	yes	—
78	#95×C₇₃	C₂³	1	8	yes	—
79	#95×C₇₃	C₂³	1	4	yes	—
80	#95×C₇₃	C₂³	1	8	yes	—
81	#95×C₇₃	C₂³	1	4	yes	—
82	#95×C₇₃	C₂³	1	8	yes	—
83	#95×C₇₃	C₂³	1	8	yes	—
84	#95×C₇₃	C₂³	1	8	yes	—
85	#95×C₇₃	C₂³	1	8	yes	—
86	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
87	C₂×Q₈×C₇₃	—	2	16	no	—
88	C₂×Q₈×C₇₃	—	2	8	no	—
89	C₂×Q₈×C₇₃	—	4	4	no	—
90	C₂×Q₈×C₇₃	—	4	4	no	—
91	C₂×Q₈×C₇₃	—	4	4	no	—
92	C₂×Q₈×C₇₃	—	4	16	no	—
93	C₂×Q₈×C₇₃	—	4	16	no	—
94	C₂²×C₄×C₇₃	—	2	4	no	—
95	C₂²×C₄×C₇₃	—	2	4	no	—
96	C₂²×C₄×C₇₃	—	2	4	no	—
97	C₂²×C₄×C₇₃	—	2	4	no	—
98	C₂²×C₄×C₇₃	—	2	4	no	—
99	C₂²×C₄×C₇₃	—	2	4	no	—
100	C₂²×C₄×C₇₃	—	2	4	no	—
101	C₂²×C₄×C₇₃	—	2	2	no	—
102	C₂²×C₄×C₇₃	—	2	2	no	—
103	C₂²×C₄×C₇₃	—	2	4	no	—
104	C₂²×C₄×C₇₃	—	2	4	no	—
105	C₂²×C₄×C₇₃	—	2	4	no	—
106	C₂²×C₄×C₇₃	—	2	4	no	—
107	C₂²×C₄×C₇₃	—	2	4	no	—
108	C₂²×C₄×C₇₃	—	2	4	no	—
109	C₂²×C₄×C₇₃	—	2	4	no	—
110	C₂²×C₄×C₇₃	—	2	2	no	—
111	C₂²×C₄×C₇₃	—	2	4	no	—
112	C₂²×C₄×C₇₃	—	2	4	no	—
113	C₂²×C₄×C₇₃	—	2	2	no	—
114	C₂²×C₄×C₇₃	C₂×Q₈	1	8	yes	—
115	C₂²×C₄×C₇₃	C₂×Q₈	1	8	yes	—
116	C₂²×C₄×C₇₃	C₂×Q₈	1	8	yes	—
117	C₂²×C₄×C₇₃	#41	1	8	yes	—
118	C₂²×C₄×C₇₃	#41	1	4	yes	—
119	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
125	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
126	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
127	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
128	C₄⋊C₄×C₇₃	—	2	16	no	—
129	C₄⋊C₄×C₇₃	—	2	16	no	—
130	C₄⋊C₄×C₇₃	—	4	8	no	—
131	C₄⋊C₄×C₇₃	—	4	8	no	—
132	C₄⋊C₄×C₇₃	—	4	4	no	—
133	C₄⋊C₄×C₇₃	—	4	4	no	—
134	C₄⋊C₄×C₇₃	C₂×Q₈	1	32	yes	complemented
135	C₄²×C₇₃	—	2	16	no	—
136	C₄²×C₇₃	—	4	4	no	—
137	C₄²×C₇₃	—	4	8	no	—
138	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
139	C₂³×C₇₃	C₂×#41	1	2	yes	—
140	C₂³×C₇₃	C₂×#41	1	4	yes	—
141	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
142	C₂³×C₇₃	H(5,𝔽₂)	1	2	yes	—
143	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
144	Q₈×C₇₃	—	4	16	no	—
145	Q₈×C₇₃	—	4	16	no	—
146	C₂×C₄×C₇₃	—	2	16	no	—
147	C₂×C₄×C₇₃	—	2	8	no	—
148	C₂×C₄×C₇₃	—	2	16	no	—
149	C₂×C₄×C₇₃	—	2	16	no	—
150	C₂×C₄×C₇₃	—	2	16	no	—
151	C₂×C₄×C₇₃	—	2	4	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	4	no	—
154	C₂×C₄×C₇₃	—	2	4	no	—
155	C₂×C₄×C₇₃	—	2	4	no	—
156	C₂×C₄×C₇₃	—	2	4	no	—
157	C₂×C₄×C₇₃	—	2	4	no	—
158	C₂×C₄×C₇₃	—	2	2	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	4	no	—
161	C₂×C₄×C₇₃	—	2	4	no	—
162	C₂×C₄×C₇₃	—	2	4	no	—
163	C₂×C₄×C₇₃	—	2	4	no	—
164	C₂×C₄×C₇₃	—	2	4	no	—
165	C₂×C₄×C₇₃	—	2	4	no	—
166	C₂×C₄×C₇₃	—	2	4	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	—	2	4	no	—
169	C₂×C₄×C₇₃	—	2	4	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	4	8	no	—
172	C₂×C₄×C₇₃	—	4	8	no	—
173	C₂×C₄×C₇₃	—	4	4	no	—
174	C₂×C₄×C₇₃	—	4	4	no	—
175	C₂×C₄×C₇₃	C₂²×Q₈	1	8	yes	—
176	C₂×C₄×C₇₃	C₂²×Q₈	1	8	yes	—
177	C₂×C₄×C₇₃	C₂²×Q₈	1	8	yes	—
178	C₂×C₄×C₇₃	C₂×#41	1	8	yes	—
179	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
180	C₂²×C₇₃	#533	1	8	yes	—
181	C₂²×C₇₃	#538	1	4	yes	—
182	C₂²×C₇₃	#551	1	4	yes	—
183	C₂²×C₇₃	#554	1	8	yes	—
184	C₂²×C₇₃	Q₈²	1	4	yes	—
185	C₂²×C₇₃	C₂³×Q₈	1	2	yes	—
186	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
187	C₂²×C₇₃	C₂²×#41	1	2	yes	—
188	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
189	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
190	C₄×C₇₃	—	2	8	no	—
191	C₄×C₇₃	—	2	4	no	—
192	C₄×C₇₃	—	2	8	no	—
193	C₄×C₇₃	—	2	8	no	—
194	C₄×C₇₃	—	2	8	no	—
195	C₄×C₇₃	—	4	4	no	—
196	C₄×C₇₃	—	4	4	no	—
197	C₄×C₇₃	—	4	2	no	—
198	C₄×C₇₃	—	4	2	no	—
199	C₂×#2586	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₇₃	#2586	1	8	yes	direct product factor
201	C₂×C₇₃	C₂×#533	1	2	yes	—
202	C₂×C₇₃	C₂×#538	1	1	yes	characteristic
203	C₂×C₇₃	C₂×#551	1	1	yes	characteristic
204	C₂×C₇₃	C₂×#554	1	2	yes	—
205	C₂×C₇₃	C₂×Q₈²	1	1	yes	characteristic
206	#2586	C₂×C₇₃	1	16	yes	direct product factor
207	C₂×#398	C₂×C₇₃	1	1	yes	characteristic
208	C₂×#395	C₂×C₇₃	1	2	yes	—
209	C₂×#395	C₂×C₇₃	1	1	yes	characteristic
210	C₂×#391	C₂×C₇₃	1	1	yes	characteristic
211	C₂×#391	C₂×C₇₃	1	2	yes	—
212	C₂×#389	C₂×C₇₃	1	2	yes	—
213	C₂×#387	C₂×C₇₃	1	2	yes	—
214	C₂×#387	C₂×C₇₃	1	2	yes	—
215	C₂×C₄×C₄⋊C₄	C₂×C₇₃	1	2	yes	—
216	C₇₃	C₂×#2586	1	1	yes	characteristic, direct product factor, Sylow
217	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
218	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
219	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
223	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
224	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
225	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
226	C₂²×C₄²	C₂²×C₇₃	1	2	yes	—
227	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
228	C₂²×C₄²	C₂²×C₇₃	1	2	yes	—
229	#398	C₂²×C₇₃	1	8	yes	—
230	#395	C₂²×C₇₃	1	8	yes	—
231	#395	C₂²×C₇₃	1	16	yes	—
232	#391	C₂²×C₇₃	1	16	yes	—
233	#391	C₂²×C₇₃	1	8	yes	—
234	#389	C₂²×C₇₃	1	16	yes	—
235	#387	C₂²×C₇₃	1	16	yes	—
236	#387	C₂²×C₇₃	1	16	yes	—
237	C₄×C₄⋊C₄	C₂²×C₇₃	1	16	yes	—
238	C₂×#95	C₂²×C₇₃	1	2	yes	—
239	C₂×#95	C₂²×C₇₃	1	2	yes	—
240	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
241	C₂×#95	C₂²×C₇₃	1	2	yes	—
242	C₂×#95	C₂²×C₇₃	1	1	yes	characteristic
243	C₂×#95	C₂²×C₇₃	1	2	yes	—
244	C₂×#95	C₂²×C₇₃	1	2	yes	—
245	C₂×#95	C₂²×C₇₃	1	2	yes	—
246	C₂×#95	C₂²×C₇₃	1	2	yes	—
247	C₂²×Q₈	—	2	8	no	—
248	C₂²×Q₈	—	2	4	no	—
249	C₂²×Q₈	—	4	2	no	—
250	C₂²×Q₈	—	4	2	no	—
251	C₂²×Q₈	—	4	2	no	—
252	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
253	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
254	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
255	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
256	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
257	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
258	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
259	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
260	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
261	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
263	C₂×C₄⋊C₄	—	2	8	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	4	4	no	—
266	C₂×C₄⋊C₄	—	4	2	no	—
267	C₂×C₄⋊C₄	—	4	4	no	—
268	C₂×C₄⋊C₄	—	4	2	no	—
269	C₂×C₄⋊C₄	Q₈×C₇₃	1	16	yes	complemented
270	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
271	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
272	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
273	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
275	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
277	C₂×C₄²	—	2	8	no	—
278	C₂×C₄²	—	4	2	no	—
279	C₂×C₄²	—	4	4	no	—
280	C₂×C₄²	C₂³×C₇₃	1	8	yes	—
281	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
282	C₂×C₄²	C₂³×C₇₃	1	8	yes	—
283	#95	C₂³×C₇₃	1	8	yes	—
284	#95	C₂³×C₇₃	1	8	yes	—
285	#95	C₂³×C₇₃	1	4	yes	—
286	#95	C₂³×C₇₃	1	8	yes	—
287	#95	C₂³×C₇₃	1	4	yes	—
288	#95	C₂³×C₇₃	1	8	yes	—
289	#95	C₂³×C₇₃	1	8	yes	—
290	#95	C₂³×C₇₃	1	8	yes	—
291	#95	C₂³×C₇₃	1	8	yes	—
292	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
293	C₂×Q₈	—	2	16	no	—
294	C₂×Q₈	—	2	8	no	—
295	C₂×Q₈	—	4	4	no	—
296	C₂×Q₈	—	4	4	no	—
297	C₂×Q₈	—	4	4	no	—
298	C₂×Q₈	—	4	16	no	—
299	C₂×Q₈	—	4	16	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	4	no	—
312	C₂²×C₄	—	2	4	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	C₂×Q₈×C₇₃	1	8	yes	—
321	C₂²×C₄	C₂×Q₈×C₇₃	1	8	yes	—
322	C₂²×C₄	C₂×Q₈×C₇₃	1	8	yes	—
323	C₂²×C₄	#41×C₇₃	1	8	yes	—
324	C₂²×C₄	#41×C₇₃	1	4	yes	—
325	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
330	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
331	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
332	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
333	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
334	C₄⋊C₄	—	2	16	no	—
335	C₄⋊C₄	—	2	16	no	—
336	C₄⋊C₄	—	4	8	no	—
337	C₄⋊C₄	—	4	8	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	C₂×Q₈×C₇₃	1	32	yes	complemented
341	C₄²	—	2	16	no	—
342	C₄²	—	4	4	no	—
343	C₄²	—	4	8	no	—
344	C₂³	C₂²×Q₈×C₇₃	1	4	yes	—
345	C₂³	C₂×#41×C₇₃	1	2	yes	—
346	C₂³	C₂×#41×C₇₃	1	4	yes	—
347	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
348	C₂³	H(5,𝔽₂)×C₇₃	1	2	yes	—
349	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
350	Q₈	—	4	16	no	—
351	Q₈	—	4	16	no	—
352	C₂×C₄	—	2	16	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	16	no	—
355	C₂×C₄	—	2	16	no	—
356	C₂×C₄	—	2	16	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	4	no	—
380	C₂×C₄	—	4	4	no	—
381	C₂×C₄	C₂²×Q₈×C₇₃	1	8	yes	—
382	C₂×C₄	C₂²×Q₈×C₇₃	1	8	yes	—
383	C₂×C₄	C₂²×Q₈×C₇₃	1	8	yes	—
384	C₂×C₄	C₂×#41×C₇₃	1	8	yes	—
385	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
386	C₂²	#533×C₇₃	1	8	yes	—
387	C₂²	#538×C₇₃	1	4	yes	—
388	C₂²	#551×C₇₃	1	4	yes	—
389	C₂²	#554×C₇₃	1	8	yes	—
390	C₂²	Q₈²×C₇₃	1	4	yes	—
391	C₂²	C₂³×Q₈×C₇₃	1	2	yes	—
392	C₂²	C₂²×#41×C₇₃	1	2	yes	—
393	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
394	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
395	C₂²	C₂×H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
396	C₄	—	2	8	no	—
397	C₄	—	2	8	no	—
398	C₄	—	2	8	no	—
399	C₄	—	2	8	no	—
400	C₄	—	2	4	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	4	no	—
405	C₂	C₇₃×#2586	1	8	yes	direct product factor
406	C₂	C₂×#533×C₇₃	1	2	yes	—
407	C₂	C₂×#538×C₇₃	1	1	yes	characteristic
408	C₂	C₂×#551×C₇₃	1	1	yes	characteristic
409	C₂	C₂×#554×C₇₃	1	2	yes	—
410	C₂	C₂×Q₈²×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₇₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2586	C₂	direct (N × H)
63. C₂×C₄⋊C₄×C₇₃	Q₈	semidirect
134. C₄⋊C₄×C₇₃	C₂×Q₈	semidirect
199. C₂×#2586	C₇₃	direct (N × H)
200. C₂×C₇₃	#2586	direct (N × H)
206. #2586	C₂×C₇₃	direct (N × H)
216. C₇₃	C₂×#2586	direct (N × H)
269. C₂×C₄⋊C₄	Q₈×C₇₃	semidirect
340. C₄⋊C₄	C₂×Q₈×C₇₃	semidirect
405. C₂	C₇₃×#2586	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇₃×#2586	2
C₂×#398×C₇₃	2
C₂×#395×C₇₃	2
C₂×#391×C₇₃	2
C₂×#389×C₇₃	2
C₂×#387×C₇₃	2
C₂×C₄×C₄⋊C₄×C₇₃	2
C₂×#2586	73

Subgroups — C2×C73×#2586 #32944239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#2586 #32944239