Subgroups — C₇₃×#32807 #32942211

Order 18688.

856 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#2858	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2055	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2024	C₂	1	2	yes	maximal, complemented
5	C₇₃×#2023	C₂	1	2	yes	maximal, complemented
6	C₇₃×#2014	C₂	1	2	yes	maximal
7	C₇₃×#2013	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1831	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	—
10	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#124×C₇₃	—	2	1	no	—
15	C₂×#124×C₇₃	—	2	1	no	—
16	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
17	C₂×#103×C₇₃	C₂²	1	4	yes	—
18	C₂×#102×C₇₃	C₂²	1	4	yes	—
19	#391×C₇₃	—	2	1	no	—
20	#391×C₇₃	—	2	1	no	—
21	#391×C₇₃	C₂²	1	2	yes	—
22	#391×C₇₃	C₂²	1	2	yes	—
23	#390×C₇₃	—	2	1	no	—
24	#390×C₇₃	—	2	1	no	—
25	#390×C₇₃	C₂²	1	2	yes	—
26	#390×C₇₃	C₂²	1	2	yes	—
27	#382×C₇₃	—	2	1	no	—
28	#382×C₇₃	—	2	1	no	—
29	C₄³×C₇₃	C₂²	1	1	yes	characteristic
30	#340×C₇₃	C₂²	1	4	yes	—
31	#336×C₇₃	C₂²	1	2	yes	—
32	#336×C₇₃	C₂²	1	2	yes	—
33	C₂²×Q₈×C₇₃	—	2	1	no	—
34	C₂²×Q₈×C₇₃	—	2	1	no	—
35	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
36	C₂²×D₄×C₇₃	—	2	1	no	—
37	C₂²×D₄×C₇₃	—	2	1	no	—
38	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
39	C₂×SD₁₆×C₇₃	—	4	4	no	—
40	C₂×SD₁₆×C₇₃	—	4	4	no	—
41	C₂×SD₁₆×C₇₃	—	4	4	no	—
42	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
43	C₄⋊Q₈×C₇₃	—	4	2	no	—
44	C₄⋊Q₈×C₇₃	—	4	2	no	—
45	C₄⋊Q₈×C₇₃	—	4	2	no	—
46	#127×C₇₃	—	4	2	no	—
47	#124×C₇₃	—	4	4	no	—
48	#124×C₇₃	—	4	4	no	—
49	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
50	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
51	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
52	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
53	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₇₃	—	4	2	no	—
67	#103×C₇₃	—	4	4	no	—
68	#102×C₇₃	—	4	4	no	—
69	#95×C₇₃	—	2	2	no	—
70	#95×C₇₃	—	2	2	no	—
71	#95×C₇₃	—	2	2	no	—
72	#95×C₇₃	—	2	2	no	—
73	C₂⁴×C₇₃	—	2	2	no	—
74	C₂×Q₈×C₇₃	—	2	4	no	—
75	C₂×Q₈×C₇₃	—	2	4	no	—
76	C₂×Q₈×C₇₃	—	2	2	no	—
77	C₂×Q₈×C₇₃	—	2	2	no	—
78	C₂×Q₈×C₇₃	—	4	2	no	—
79	C₂×Q₈×C₇₃	—	4	2	no	—
80	C₂×Q₈×C₇₃	—	4	2	no	—
81	C₂×Q₈×C₇₃	—	4	2	no	—
82	C₂×Q₈×C₇₃	—	4	2	no	—
83	C₂×Q₈×C₇₃	—	4	2	no	—
84	C₂×D₄×C₇₃	—	2	4	no	—
85	C₂×D₄×C₇₃	—	2	4	no	—
86	C₂×D₄×C₇₃	—	2	2	no	—
87	C₂×D₄×C₇₃	—	2	2	no	—
88	C₂×D₄×C₇₃	—	4	2	no	—
89	C₂×D₄×C₇₃	—	4	2	no	—
90	C₂×D₄×C₇₃	—	4	2	no	—
91	C₂×D₄×C₇₃	—	4	2	no	—
92	C₂×D₄×C₇₃	—	4	2	no	—
93	C₂×D₄×C₇₃	—	4	2	no	—
94	C₂²×C₄×C₇₃	—	2	2	no	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
104	SD₁₆×C₇₃	—	4	16	no	—
105	C₂×C₈×C₇₃	—	2	4	no	—
106	C₂×C₈×C₇₃	—	2	4	no	—
107	C₂×C₈×C₇₃	—	2	4	no	—
108	C₄⋊C₄×C₇₃	—	2	4	no	—
109	C₄⋊C₄×C₇₃	—	2	4	no	—
110	C₄⋊C₄×C₇₃	—	4	2	no	—
111	C₄⋊C₄×C₇₃	—	4	2	no	—
112	C₄⋊C₄×C₇₃	—	4	2	no	—
113	C₄⋊C₄×C₇₃	—	4	2	no	—
114	C₂²⋊C₄×C₇₃	—	4	4	no	—
115	C₂²⋊C₄×C₇₃	—	4	4	no	—
116	C₂²⋊C₄×C₇₃	—	4	4	no	—
117	C₂²⋊C₄×C₇₃	—	4	4	no	—
118	C₄²×C₇₃	—	2	2	no	—
119	C₄²×C₇₃	—	2	2	no	—
120	C₄²×C₇₃	—	2	1	no	—
121	C₄²×C₇₃	—	2	2	no	—
122	C₄²×C₇₃	—	2	2	no	—
123	C₄²×C₇₃	—	2	1	no	—
124	C₄²×C₇₃	—	4	1	no	—
125	C₄²×C₇₃	SD₁₆	1	4	yes	complemented
126	C₂³×C₇₃	—	4	2	no	—
127	C₂³×C₇₃	—	4	2	no	—
128	C₂³×C₇₃	—	4	2	no	—
129	C₂³×C₇₃	—	4	2	no	—
130	C₂³×C₇₃	—	4	2	no	—
131	C₂³×C₇₃	—	4	2	no	—
132	C₂³×C₇₃	—	4	2	no	—
133	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
134	Q₈×C₇₃	—	4	4	no	—
135	Q₈×C₇₃	—	4	4	no	—
136	Q₈×C₇₃	—	8	4	no	—
137	Q₈×C₇₃	—	8	4	no	—
138	D₄×C₇₃	—	4	4	no	—
139	D₄×C₇₃	—	4	4	no	—
140	D₄×C₇₃	—	8	4	no	—
141	D₄×C₇₃	—	8	4	no	—
142	C₂×C₄×C₇₃	—	2	1	no	—
143	C₂×C₄×C₇₃	—	2	1	no	—
144	C₂×C₄×C₇₃	—	2	1	no	—
145	C₂×C₄×C₇₃	—	2	1	no	—
146	C₂×C₄×C₇₃	—	2	1	no	—
147	C₂×C₄×C₇₃	—	2	1	no	—
148	C₂×C₄×C₇₃	—	2	1	no	—
149	C₂×C₄×C₇₃	—	2	1	no	—
150	C₂×C₄×C₇₃	—	2	1	no	—
151	C₂×C₄×C₇₃	—	2	1	no	—
152	C₂×C₄×C₇₃	—	2	1	no	—
153	C₂×C₄×C₇₃	—	2	1	no	—
154	C₂×C₄×C₇₃	—	2	1	no	—
155	C₂×C₄×C₇₃	—	4	2	no	—
156	C₂×C₄×C₇₃	—	4	2	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	—	4	2	no	—
159	C₂×C₄×C₇₃	—	4	2	no	—
160	C₂×C₄×C₇₃	—	4	2	no	—
161	C₂×C₄×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	—	4	2	no	—
163	C₂×C₄×C₇₃	—	4	2	no	—
164	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
165	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
168	C₂×C₄×C₇₃	#137	1	2	yes	—
169	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
172	C₂×C₄×C₇₃	2₋¹⁺⁴	1	1	yes	characteristic
173	C₈×C₇₃	—	4	4	no	—
174	C₂²×C₇₃	—	8	2	no	—
175	C₂²×C₇₃	—	8	2	no	—
176	C₂²×C₇₃	—	8	2	no	—
177	C₂²×C₇₃	—	8	2	no	—
178	C₂²×C₇₃	—	8	2	no	—
179	C₂²×C₇₃	—	8	2	no	—
180	C₂²×C₇₃	—	8	2	no	—
181	C₂²×C₇₃	#535	1	1	yes	characteristic
182	C₂²×C₇₃	#535	1	1	yes	characteristic
183	C₂²×C₇₃	#537	1	1	yes	characteristic
184	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
185	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
186	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
187	C₂²×C₇₃	#575	1	1	yes	characteristic
188	C₄×C₇₃	—	2	2	no	—
189	C₄×C₇₃	—	2	2	no	—
190	C₄×C₇₃	—	2	2	no	—
191	C₄×C₇₃	—	2	2	no	—
192	C₄×C₇₃	—	2	2	no	—
193	C₄×C₇₃	—	4	1	no	—
194	C₄×C₇₃	—	8	2	no	—
195	C₄×C₇₃	—	8	2	no	—
196	C₄×C₇₃	—	8	2	no	—
197	C₄×C₇₃	H(3,𝔽₄)	1	2	yes	—
198	C₄×C₇₃	#562	1	2	yes	—
199	#32807	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₇₃	—	16	2	no	—
201	C₂×C₇₃	#2819	1	1	yes	characteristic
202	C₂×C₇₃	#3206	1	1	yes	characteristic
203	C₂×C₇₃	#3208	1	1	yes	characteristic
204	C₂×C₇₃	#3213	1	1	yes	characteristic
205	C₂×C₇₃	#3215	1	1	yes	characteristic
206	C₂×C₇₃	#3246	1	1	yes	characteristic
207	C₂×C₇₃	#3254	1	1	yes	characteristic
208	#2862	C₂×C₇₃	1	1	yes	characteristic, complemented
209	#2858	C₂×C₇₃	1	1	yes	characteristic
210	#2055	C₂×C₇₃	1	4	yes	complemented
211	#2024	C₂×C₇₃	1	2	yes	complemented
212	#2023	C₂×C₇₃	1	2	yes	complemented
213	#2014	C₂×C₇₃	1	2	yes	—
214	#2013	C₂×C₇₃	1	2	yes	complemented
215	#1831	C₂×C₇₃	1	1	yes	characteristic, complemented
216	C₇₃	#32807	1	1	yes	characteristic, direct product factor, Sylow
217	C₂²×SD₁₆	C₂²×C₇₃	1	4	yes	—
218	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
219	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
221	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
222	C₂×#124	—	2	1	no	—
223	C₂×#124	—	2	1	no	—
224	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
225	C₂×#103	C₂²×C₇₃	1	4	yes	—
226	C₂×#102	C₂²×C₇₃	1	4	yes	—
227	#391	—	2	1	no	—
228	#391	—	2	1	no	—
229	#391	C₂²×C₇₃	1	2	yes	—
230	#391	C₂²×C₇₃	1	2	yes	—
231	#390	—	2	1	no	—
232	#390	—	2	1	no	—
233	#390	C₂²×C₇₃	1	2	yes	—
234	#390	C₂²×C₇₃	1	2	yes	—
235	#382	—	2	1	no	—
236	#382	—	2	1	no	—
237	C₄³	C₂²×C₇₃	1	1	yes	characteristic
238	#340	C₂²×C₇₃	1	4	yes	—
239	#336	C₂²×C₇₃	1	2	yes	—
240	#336	C₂²×C₇₃	1	2	yes	—
241	C₂²×Q₈	—	2	1	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
247	C₂×SD₁₆	—	4	4	no	—
248	C₂×SD₁₆	—	4	4	no	—
249	C₂×SD₁₆	—	4	4	no	—
250	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
251	C₄⋊Q₈	—	4	2	no	—
252	C₄⋊Q₈	—	4	2	no	—
253	C₄⋊Q₈	—	4	2	no	—
254	#127	—	4	2	no	—
255	#124	—	4	4	no	—
256	#124	—	4	4	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
263	C₂×C₂²⋊C₄	—	2	2	no	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
268	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
273	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
274	C₄⋊C₈	—	4	2	no	—
275	#103	—	4	4	no	—
276	#102	—	4	4	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	C₂⁴	—	2	2	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	2	no	—
288	C₂×Q₈	—	4	2	no	—
289	C₂×Q₈	—	4	2	no	—
290	C₂×Q₈	—	4	2	no	—
291	C₂×Q₈	—	4	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
306	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
307	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
311	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
312	SD₁₆	—	4	16	no	—
313	C₂×C₈	—	2	4	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	4	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₄⋊C₄	—	4	2	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₂²⋊C₄	—	4	4	no	—
325	C₂²⋊C₄	—	4	4	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	SD₁₆×C₇₃	1	4	yes	complemented
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	—	4	2	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	2	no	—
341	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
342	Q₈	—	4	4	no	—
343	Q₈	—	4	4	no	—
344	Q₈	—	8	4	no	—
345	Q₈	—	8	4	no	—
346	D₄	—	4	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	8	4	no	—
349	D₄	—	8	4	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
373	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
374	C₂×C₄	C₂×SD₁₆×C₇₃	1	2	yes	—
375	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
376	C₂×C₄	#137×C₇₃	1	2	yes	—
377	C₂×C₄	H(5,𝔽₂)×C₇₃	1	1	yes	characteristic
378	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
379	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
380	C₂×C₄	2₋¹⁺⁴×C₇₃	1	1	yes	characteristic
381	C₈	—	4	4	no	—
382	C₂²	—	8	2	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	#535×C₇₃	1	1	yes	characteristic
390	C₂²	#535×C₇₃	1	1	yes	characteristic
391	C₂²	#537×C₇₃	1	1	yes	characteristic
392	C₂²	C₂²×SD₁₆×C₇₃	1	1	yes	characteristic
393	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
394	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
395	C₂²	#575×C₇₃	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	H(3,𝔽₄)×C₇₃	1	2	yes	—
406	C₄	#562×C₇₃	1	2	yes	—
407	C₂	—	16	2	no	—
408	C₂	C₇₃×#2819	1	1	yes	characteristic
409	C₂	C₇₃×#3206	1	1	yes	characteristic
410	C₂	C₇₃×#3208	1	1	yes	characteristic
411	C₂	C₇₃×#3213	1	1	yes	characteristic
412	C₂	C₇₃×#3215	1	1	yes	characteristic
413	C₂	C₇₃×#3246	1	1	yes	characteristic
414	C₂	C₇₃×#3254	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂×#127×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄³×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#2862	C₂	semidirect
3. C₇₃×#2055	C₂	semidirect
4. C₇₃×#2024	C₂	semidirect
5. C₇₃×#2023	C₂	semidirect
7. C₇₃×#2013	C₂	semidirect
8. C₇₃×#1831	C₂	semidirect
125. C₄²×C₇₃	SD₁₆	semidirect
199. #32807	C₇₃	direct (N × H)
208. #2862	C₂×C₇₃	semidirect
210. #2055	C₂×C₇₃	semidirect
211. #2024	C₂×C₇₃	semidirect
212. #2023	C₂×C₇₃	semidirect
214. #2013	C₂×C₇₃	semidirect
215. #1831	C₂×C₇₃	semidirect
216. C₇₃	#32807	direct (N × H)
333. C₄²	SD₁₆×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#2862	2
C₇₃×#2858	2
C₇₃×#2055	2
C₇₃×#2024	2
C₇₃×#2023	2
C₇₃×#2014	2
C₇₃×#2013	2
C₇₃×#1831	2
#32807	73

Subgroups — C73×#32807 #32942211

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#32807 #32942211