Subgroups — C₇₃×#33777 #32943181

Order 18688.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#495×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇₃×#2249	C₂	1	2	yes	maximal, complemented
4	C₇₃×#2242	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2211	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2210	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#2187	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2185	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2184	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₇₃	—	2	1	no	—
14	C₂²×D₈×C₇₃	C₂²	1	1	yes	characteristic
15	#529×C₇₃	—	2	1	no	—
16	C₂×#124×C₇₃	—	2	1	no	—
17	C₂×Q₃₂×C₇₃	C₂²	1	2	yes	complemented
18	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	—
19	C₂×SD₃₂×C₇₃	C₂²	1	2	yes	complemented
20	C₂×D₁₆×C₇₃	C₂²	1	2	yes	—
21	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
22	#495×C₇₃	—	2	1	no	—
23	#495×C₇₃	—	2	1	no	—
24	#495×C₇₃	C₂²	1	2	yes	—
25	#495×C₇₃	C₂²	1	2	yes	—
26	#495×C₇₃	C₂²	1	1	yes	characteristic, complemented
27	#488×C₇₃	—	2	1	no	—
28	#467×C₇₃	C₂²	1	1	yes	characteristic
29	#466×C₇₃	C₂²	1	1	yes	characteristic
30	#465×C₇₃	—	2	1	no	—
31	C₄×Q₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₄×SD₁₆×C₇₃	—	2	1	no	—
33	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
35	C₄⋊C₁₆×C₇₃	C₂²	1	2	yes	complemented
36	#358×C₇₃	C₂²	1	2	yes	complemented
37	#358×C₇₃	C₂²	1	2	yes	complemented
38	#357×C₇₃	C₂²	1	2	yes	—
39	#357×C₇₃	C₂²	1	2	yes	—
40	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
41	C₂²⋊C₁₆×C₇₃	C₂²	1	1	yes	characteristic
42	C₄×C₁₆×C₇₃	C₂²	1	2	yes	complemented
43	C₂²×Q₈×C₇₃	—	2	1	no	—
44	C₂²×D₄×C₇₃	—	2	1	no	—
45	C₂×Q₁₆×C₇₃	—	2	1	no	—
46	C₂×Q₁₆×C₇₃	—	4	2	no	—
47	C₂×Q₁₆×C₇₃	C₂³	1	1	yes	characteristic
48	C₂×Q₁₆×C₇₃	C₂³	1	2	yes	—
49	C₂×SD₁₆×C₇₃	—	2	1	no	—
50	C₂×SD₁₆×C₇₃	—	2	2	no	—
51	C₂×SD₁₆×C₇₃	—	2	2	no	—
52	C₂×SD₁₆×C₇₃	—	4	4	no	—
53	C₂×D₈×C₇₃	—	2	1	no	—
54	C₂×D₈×C₇₃	—	4	2	no	—
55	C₂×D₈×C₇₃	C₂³	1	1	yes	characteristic
56	C₂×D₈×C₇₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
59	#126×C₇₃	—	4	1	no	—
60	#125×C₇₃	—	2	1	no	—
61	#124×C₇₃	—	2	1	no	—
62	#124×C₇₃	—	2	2	no	—
63	#124×C₇₃	—	2	2	no	—
64	#124×C₇₃	—	4	1	no	—
65	#124×C₇₃	—	4	1	no	—
66	#123×C₇₃	—	4	1	no	—
67	C₂²⋊Q₈×C₇₃	—	2	1	no	—
68	#121×C₇₃	—	2	1	no	—
69	C₄×Q₈×C₇₃	—	2	1	no	—
70	C₄×D₄×C₇₃	—	2	1	no	—
71	C₄×D₄×C₇₃	—	4	1	no	—
72	#117×C₇₃	—	4	1	no	—
73	C₂×C₂²⋊C₄×C₇₃	—	4	1	no	—
74	C₂×C₂²⋊C₄×C₇₃	—	4	1	no	—
75	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
76	Q₃₂×C₇₃	—	4	2	no	—
77	SD₃₂×C₇₃	—	4	2	no	—
78	SD₃₂×C₇₃	—	4	2	no	—
79	D₁₆×C₇₃	—	4	2	no	—
80	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
81	C₂×C₁₆×C₇₃	C₂³	1	2	yes	—
82	#107×C₇₃	C₂³	1	1	yes	characteristic
83	#107×C₇₃	C₂³	1	1	yes	characteristic
84	#106×C₇₃	—	2	1	no	—
85	#103×C₇₃	—	2	1	no	—
86	#103×C₇₃	—	2	1	no	—
87	#102×C₇₃	—	2	1	no	—
88	#102×C₇₃	—	2	1	no	—
89	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
93	C₂⁴×C₇₃	—	4	1	no	—
94	C₂×Q₈×C₇₃	—	2	1	no	—
95	C₂×Q₈×C₇₃	—	2	2	no	—
96	C₂×Q₈×C₇₃	—	4	2	no	—
97	C₂×Q₈×C₇₃	—	4	2	no	—
98	C₂×Q₈×C₇₃	—	4	1	no	—
99	C₂×D₄×C₇₃	—	2	1	no	—
100	C₂×D₄×C₇₃	—	2	2	no	—
101	C₂×D₄×C₇₃	—	4	2	no	—
102	C₂×D₄×C₇₃	—	4	2	no	—
103	C₂×D₄×C₇₃	—	4	1	no	—
104	C₂×D₄×C₇₃	—	4	1	no	—
105	C₂²×C₄×C₇₃	—	4	1	no	—
106	C₂²×C₄×C₇₃	—	4	1	no	—
107	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
108	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
109	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
110	Q₁₆×C₇₃	—	2	2	no	—
111	Q₁₆×C₇₃	—	2	2	no	—
112	Q₁₆×C₇₃	—	2	2	no	—
113	Q₁₆×C₇₃	—	4	2	no	—
114	SD₁₆×C₇₃	—	4	4	no	—
115	SD₁₆×C₇₃	—	4	2	no	—
116	SD₁₆×C₇₃	—	4	4	no	—
117	D₈×C₇₃	—	2	2	no	—
118	D₈×C₇₃	—	2	2	no	—
119	D₈×C₇₃	—	2	2	no	—
120	D₈×C₇₃	—	4	2	no	—
121	C₂×C₈×C₇₃	—	2	2	no	—
122	C₂×C₈×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
126	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
127	C₄⋊C₄×C₇₃	—	2	1	no	—
128	C₄⋊C₄×C₇₃	—	2	1	no	—
129	C₄⋊C₄×C₇₃	—	4	1	no	—
130	C₄⋊C₄×C₇₃	—	4	1	no	—
131	C₄⋊C₄×C₇₃	—	4	1	no	—
132	C₄⋊C₄×C₇₃	—	4	1	no	—
133	C₂²⋊C₄×C₇₃	—	4	1	no	—
134	C₂²⋊C₄×C₇₃	—	4	2	no	—
135	C₂²⋊C₄×C₇₃	—	4	2	no	—
136	C₂²⋊C₄×C₇₃	—	4	2	no	—
137	C₂²⋊C₄×C₇₃	—	4	2	no	—
138	C₂²⋊C₄×C₇₃	—	4	1	no	—
139	C₂²⋊C₄×C₇₃	—	4	1	no	—
140	C₂²⋊C₄×C₇₃	—	4	1	no	—
141	C₂²⋊C₄×C₇₃	—	4	1	no	—
142	C₄²×C₇₃	—	4	1	no	—
143	C₄²×C₇₃	D₈	1	1	yes	characteristic
144	C₄²×C₇₃	D₈	1	1	yes	characteristic
145	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₁₆×C₇₃	—	2	2	no	—
148	C₁₆×C₇₃	—	2	2	no	—
149	C₂³×C₇₃	—	4	1	no	—
150	C₂³×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	8	2	no	—
152	C₂³×C₇₃	—	8	2	no	—
153	C₂³×C₇₃	—	8	2	no	—
154	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
155	Q₈×C₇₃	—	4	2	no	—
156	Q₈×C₇₃	—	4	1	no	—
157	Q₈×C₇₃	—	4	2	no	—
158	Q₈×C₇₃	—	4	1	no	—
159	Q₈×C₇₃	—	8	2	no	—
160	D₄×C₇₃	—	4	2	no	—
161	D₄×C₇₃	—	4	1	no	—
162	D₄×C₇₃	—	4	2	no	—
163	D₄×C₇₃	—	4	1	no	—
164	D₄×C₇₃	—	8	2	no	—
165	D₄×C₇₃	—	8	2	no	—
166	C₂×C₄×C₇₃	—	2	2	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	4	1	no	—
170	C₂×C₄×C₇₃	—	4	1	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	—	4	1	no	—
174	C₂×C₄×C₇₃	—	8	2	no	—
175	C₂×C₄×C₇₃	—	8	2	no	—
176	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
182	C₈×C₇₃	—	2	1	no	—
183	C₈×C₇₃	—	2	1	no	—
184	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
185	C₈×C₇₃	H(5,𝔽₂)	1	2	yes	—
186	C₂²×C₇₃	—	2	1	no	—
187	C₂²×C₇₃	—	2	1	no	—
188	C₂²×C₇₃	—	8	1	no	—
189	C₂²×C₇₃	—	8	2	no	—
190	C₂²×C₇₃	—	8	1	no	—
191	C₂²×C₇₃	—	8	2	no	—
192	C₂²×C₇₃	—	8	2	no	—
193	C₂²×C₇₃	—	8	1	no	—
194	C₂²×C₇₃	—	16	4	no	—
195	C₂²×C₇₃	#508	1	2	yes	—
196	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	—	2	1	no	—
201	C₄×C₇₃	—	2	1	no	—
202	C₄×C₇₃	—	8	1	no	—
203	C₄×C₇₃	—	8	1	no	—
204	C₄×C₇₃	—	8	2	no	—
205	C₄×C₇₃	—	8	1	no	—
206	C₄×C₇₃	#535	1	1	yes	characteristic
207	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
208	#33777	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂×C₇₃	—	2	2	no	—
210	C₂×C₇₃	—	16	1	no	—
211	C₂×C₇₃	—	16	2	no	—
212	C₂×C₇₃	#3205	1	1	yes	characteristic
213	C₂×C₇₃	C₂×#508	1	1	yes	characteristic
214	C₂×C₇₃	#3414	1	1	yes	characteristic
215	#3168	C₂×C₇₃	1	1	yes	characteristic, complemented
216	C₂×#495	C₂×C₇₃	1	1	yes	characteristic, complemented
217	#2249	C₂×C₇₃	1	2	yes	complemented
218	#2242	C₂×C₇₃	1	2	yes	complemented
219	#2211	C₂×C₇₃	1	2	yes	complemented
220	#2210	C₂×C₇₃	1	2	yes	complemented
221	#2188	C₂×C₇₃	1	1	yes	characteristic, complemented
222	#2187	C₂×C₇₃	1	1	yes	characteristic, complemented
223	#2185	C₂×C₇₃	1	1	yes	characteristic, complemented
224	#2184	C₂×C₇₃	1	1	yes	characteristic
225	#2162	C₂×C₇₃	1	1	yes	characteristic, complemented
226	C₇₃	#33777	1	1	yes	characteristic, direct product factor, Sylow
227	C₂²×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic
228	C₂²×SD₁₆	—	2	1	no	—
229	C₂²×D₈	C₂²×C₇₃	1	1	yes	characteristic
230	#529	—	2	1	no	—
231	C₂×#124	—	2	1	no	—
232	C₂×Q₃₂	C₂²×C₇₃	1	2	yes	complemented
233	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	—
234	C₂×SD₃₂	C₂²×C₇₃	1	2	yes	complemented
235	C₂×D₁₆	C₂²×C₇₃	1	2	yes	—
236	#499	C₂²×C₇₃	1	1	yes	characteristic, complemented
237	#495	—	2	1	no	—
238	#495	—	2	1	no	—
239	#495	C₂²×C₇₃	1	2	yes	—
240	#495	C₂²×C₇₃	1	2	yes	—
241	#495	C₂²×C₇₃	1	1	yes	characteristic, complemented
242	#488	—	2	1	no	—
243	#467	C₂²×C₇₃	1	1	yes	characteristic
244	#466	C₂²×C₇₃	1	1	yes	characteristic
245	#465	—	2	1	no	—
246	C₄×Q₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
247	C₄×SD₁₆	—	2	1	no	—
248	C₄×D₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
249	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
250	C₄⋊C₁₆	C₂²×C₇₃	1	2	yes	complemented
251	#358	C₂²×C₇₃	1	2	yes	complemented
252	#358	C₂²×C₇₃	1	2	yes	complemented
253	#357	C₂²×C₇₃	1	2	yes	—
254	#357	C₂²×C₇₃	1	2	yes	—
255	C₂²⋊C₁₆	C₂²×C₇₃	1	1	yes	characteristic
256	C₂²⋊C₁₆	C₂²×C₇₃	1	1	yes	characteristic
257	C₄×C₁₆	C₂²×C₇₃	1	2	yes	complemented
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂×Q₁₆	—	2	1	no	—
261	C₂×Q₁₆	—	4	2	no	—
262	C₂×Q₁₆	C₂³×C₇₃	1	2	yes	—
263	C₂×Q₁₆	C₂³×C₇₃	1	1	yes	characteristic
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×SD₁₆	—	2	2	no	—
266	C₂×SD₁₆	—	2	1	no	—
267	C₂×SD₁₆	—	4	4	no	—
268	C₂×D₈	—	2	1	no	—
269	C₂×D₈	—	4	2	no	—
270	C₂×D₈	C₂³×C₇₃	1	2	yes	—
271	C₂×D₈	C₂³×C₇₃	1	1	yes	characteristic
272	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
273	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
274	#126	—	4	1	no	—
275	#125	—	2	1	no	—
276	#124	—	2	2	no	—
277	#124	—	2	2	no	—
278	#124	—	2	1	no	—
279	#124	—	4	1	no	—
280	#124	—	4	1	no	—
281	#123	—	4	1	no	—
282	C₂²⋊Q₈	—	2	1	no	—
283	#121	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	—	4	1	no	—
287	#117	—	4	1	no	—
288	C₂×C₂²⋊C₄	—	4	1	no	—
289	C₂×C₂²⋊C₄	—	4	1	no	—
290	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
291	Q₃₂	—	4	2	no	—
292	SD₃₂	—	4	2	no	—
293	SD₃₂	—	4	2	no	—
294	D₁₆	—	4	2	no	—
295	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
296	C₂×C₁₆	C₂³×C₇₃	1	2	yes	—
297	#107	C₂³×C₇₃	1	1	yes	characteristic
298	#107	C₂³×C₇₃	1	1	yes	characteristic
299	#106	—	2	1	no	—
300	#103	—	2	1	no	—
301	#103	—	2	1	no	—
302	#102	—	2	1	no	—
303	#102	—	2	1	no	—
304	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
305	C₄×C₈	D₄×C₇₃	1	1	yes	characteristic
306	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
307	C₄×C₈	C₂³×C₇₃	1	1	yes	characteristic
308	C₂⁴	—	4	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	4	1	no	—
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	1	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
323	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
325	Q₁₆	—	2	2	no	—
326	Q₁₆	—	2	2	no	—
327	Q₁₆	—	2	2	no	—
328	Q₁₆	—	4	2	no	—
329	SD₁₆	—	4	4	no	—
330	SD₁₆	—	4	2	no	—
331	SD₁₆	—	4	4	no	—
332	D₈	—	2	2	no	—
333	D₈	—	2	2	no	—
334	D₈	—	2	2	no	—
335	D₈	—	4	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
339	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
340	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
341	C₂×C₈	C₂⁴×C₇₃	1	1	yes	characteristic
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	4	1	no	—
355	C₂²⋊C₄	—	4	1	no	—
356	C₂²⋊C₄	—	4	1	no	—
357	C₄²	—	4	1	no	—
358	C₄²	D₈×C₇₃	1	1	yes	characteristic
359	C₄²	D₈×C₇₃	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
362	C₁₆	—	2	2	no	—
363	C₁₆	—	2	2	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	—	8	2	no	—
368	C₂³	—	8	2	no	—
369	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	1	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	1	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	1	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
392	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
393	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
394	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
395	C₂×C₄	C₂×D₈×C₇₃	1	1	yes	characteristic
396	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
400	C₈	H(5,𝔽₂)×C₇₃	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	16	4	no	—
410	C₂²	#508×C₇₃	1	2	yes	—
411	C₂²	C₂²×D₈×C₇₃	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₄	#535×C₇₃	1	1	yes	characteristic
422	C₄	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
423	C₂	—	2	2	no	—
424	C₂	—	16	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₇₃×#3205	1	1	yes	characteristic
427	C₂	C₂×#508×C₇₃	1	1	yes	characteristic
428	C₂	C₇₃×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₇₃
prime radical	C₇₃×#2184	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3168	C₂	semidirect
2. C₂×#495×C₇₃	C₂	semidirect
3. C₇₃×#2249	C₂	semidirect
4. C₇₃×#2242	C₂	semidirect
5. C₇₃×#2211	C₂	semidirect
6. C₇₃×#2210	C₂	semidirect
7. C₇₃×#2188	C₂	semidirect
8. C₇₃×#2187	C₂	semidirect
9. C₇₃×#2185	C₂	semidirect
11. C₇₃×#2162	C₂	semidirect
17. C₂×Q₃₂×C₇₃	C₂²	semidirect
19. C₂×SD₃₂×C₇₃	C₂²	semidirect
21. #499×C₇₃	C₂²	semidirect
26. #495×C₇₃	C₂²	semidirect
31. C₄×Q₁₆×C₇₃	C₂²	semidirect
33. C₄×D₈×C₇₃	C₂²	semidirect
35. C₄⋊C₁₆×C₇₃	C₂²	semidirect
36. #358×C₇₃	C₂²	semidirect
37. #358×C₇₃	C₂²	semidirect
42. C₄×C₁₆×C₇₃	C₂²	semidirect
208. #33777	C₇₃	direct (N × H)
215. #3168	C₂×C₇₃	semidirect
216. C₂×#495	C₂×C₇₃	semidirect
217. #2249	C₂×C₇₃	semidirect
218. #2242	C₂×C₇₃	semidirect
219. #2211	C₂×C₇₃	semidirect
220. #2210	C₂×C₇₃	semidirect
221. #2188	C₂×C₇₃	semidirect
222. #2187	C₂×C₇₃	semidirect
223. #2185	C₂×C₇₃	semidirect
225. #2162	C₂×C₇₃	semidirect
226. C₇₃	#33777	direct (N × H)
232. C₂×Q₃₂	C₂²×C₇₃	semidirect
234. C₂×SD₃₂	C₂²×C₇₃	semidirect
236. #499	C₂²×C₇₃	semidirect
241. #495	C₂²×C₇₃	semidirect
246. C₄×Q₁₆	C₂²×C₇₃	semidirect
248. C₄×D₈	C₂²×C₇₃	semidirect
250. C₄⋊C₁₆	C₂²×C₇₃	semidirect
251. #358	C₂²×C₇₃	semidirect
252. #358	C₂²×C₇₃	semidirect
257. C₄×C₁₆	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3168	2
C₂×#495×C₇₃	2
C₇₃×#2249	2
C₇₃×#2242	2
C₇₃×#2211	2
C₇₃×#2210	2
C₇₃×#2188	2
C₇₃×#2187	2
C₇₃×#2185	2
C₇₃×#2184	2
C₇₃×#2162	2
#33777	73

Subgroups — C73×#33777 #32943181

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#33777 #32943181