Subgroups — C₇₃×#24400 #32933804

Order 18688.

1322 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#473×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₇₃×#3007	C₂	1	1	yes	maximal, characteristic
4	C₂×#451×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₃×#2880	C₂	1	1	yes	maximal, characteristic
6	C₇₃×#2052	C₂	1	2	yes	maximal, complemented
7	C₇₃×#2020	C₂	1	2	yes	maximal, complemented
8	C₇₃×#1908	C₂	1	2	yes	maximal, complemented
9	C₇₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1784	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×#137×C₇₃	—	2	1	no	—
15	C₂×#137×C₇₃	—	2	1	no	—
16	C₂×#137×C₇₃	—	2	8	no	—
17	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
18	C₂×#137×C₇₃	C₂²	1	2	yes	—
19	C₂×#137×C₇₃	C₂²	1	2	yes	—
20	C₂×#137×C₇₃	C₂²	1	1	yes	characteristic
21	C₂²×Q₁₆×C₇₃	—	2	1	no	—
22	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	complemented
23	C₂²×SD₁₆×C₇₃	—	2	1	no	—
24	C₂×#131×C₇₃	C₂²	1	2	yes	—
25	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
27	#473×C₇₃	—	2	8	no	—
28	#452×C₇₃	—	2	1	no	—
29	#452×C₇₃	—	2	1	no	—
30	#451×C₇₃	—	2	1	no	—
31	#451×C₇₃	—	2	1	no	—
32	#451×C₇₃	—	2	1	no	—
33	#451×C₇₃	—	2	2	no	—
34	#450×C₇₃	—	2	1	no	—
35	C₂×#108×C₇₃	C₂²	1	2	yes	complemented
36	#417×C₇₃	C₂²	1	1	yes	characteristic
37	#417×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
39	C₂×#101×C₇₃	C₂²	1	2	yes	complemented
40	C₂×#101×C₇₃	C₂²	1	2	yes	complemented
41	C₂×#101×C₇₃	C₂²	1	2	yes	complemented
42	#408×C₇₃	—	2	2	no	—
43	#408×C₇₃	C₂²	1	2	yes	—
44	#407×C₇₃	—	2	1	no	—
45	#407×C₇₃	C₂²	1	1	yes	characteristic
46	#407×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₇₃	—	2	1	no	—
48	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
49	#343×C₇₃	C₂²	1	2	yes	complemented
50	#341×C₇₃	C₂²	1	2	yes	complemented
51	C₂×#41×C₇₃	—	2	1	no	—
52	C₂×#41×C₇₃	—	2	1	no	—
53	C₂×#41×C₇₃	—	2	4	no	—
54	C₂×#41×C₇₃	—	4	2	no	—
55	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
56	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
57	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
58	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₇₃	—	2	1	no	—
60	C₂²×Q₈×C₇₃	—	2	4	no	—
61	C₂²×Q₈×C₇₃	—	2	1	no	—
62	C₂²×Q₈×C₇₃	—	2	1	no	—
63	C₂²×Q₈×C₇₃	—	2	1	no	—
64	C₂²×Q₈×C₇₃	—	2	1	no	—
65	C₂²×Q₈×C₇₃	—	4	2	no	—
66	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
67	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
68	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
69	C₂²×D₄×C₇₃	—	2	1	no	—
70	C₂²×D₄×C₇₃	D₄	1	1	yes	characteristic
71	C₂³×C₄×C₇₃	—	2	1	no	—
72	C₂³×C₄×C₇₃	—	2	1	no	—
73	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
74	#137×C₇₃	—	2	8	no	—
75	#137×C₇₃	—	2	8	no	—
76	#137×C₇₃	—	2	4	no	—
77	#137×C₇₃	—	2	4	no	—
78	#137×C₇₃	—	2	4	no	—
79	#137×C₇₃	—	2	4	no	—
80	#137×C₇₃	—	4	2	no	—
81	#137×C₇₃	D₄	1	8	yes	—
82	C₂×Q₁₆×C₇₃	—	2	8	no	—
83	C₂×Q₁₆×C₇₃	—	2	2	no	—
84	C₂×Q₁₆×C₇₃	—	2	2	no	—
85	C₂×Q₁₆×C₇₃	—	2	1	no	—
86	C₂×Q₁₆×C₇₃	—	2	1	no	—
87	C₂×Q₁₆×C₇₃	—	2	4	no	—
88	C₂×Q₁₆×C₇₃	—	2	2	no	—
89	C₂×Q₁₆×C₇₃	—	2	2	no	—
90	C₂×Q₁₆×C₇₃	—	4	2	no	—
91	C₂×SD₁₆×C₇₃	—	2	8	no	—
92	C₂×SD₁₆×C₇₃	—	2	2	no	—
93	C₂×SD₁₆×C₇₃	—	2	2	no	—
94	C₂×SD₁₆×C₇₃	—	2	1	no	—
95	C₂×SD₁₆×C₇₃	—	2	1	no	—
96	#131×C₇₃	—	2	4	no	—
97	#131×C₇₃	—	4	2	no	—
98	C₂×M₁₆×C₇₃	—	2	1	no	—
99	C₂×M₁₆×C₇₃	—	2	4	no	—
100	C₂×M₁₆×C₇₃	—	2	2	no	—
101	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
102	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
104	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
105	C₂²×C₈×C₇₃	—	2	1	no	—
106	C₂²×C₈×C₇₃	—	2	2	no	—
107	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
108	C₂²⋊Q₈×C₇₃	—	2	1	no	—
109	C₂²⋊Q₈×C₇₃	—	2	1	no	—
110	C₂²⋊Q₈×C₇₃	—	2	1	no	—
111	C₂²⋊Q₈×C₇₃	—	2	1	no	—
112	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
113	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
115	#108×C₇₃	—	2	4	no	—
116	#103×C₇₃	—	2	1	no	—
117	#103×C₇₃	—	2	1	no	—
118	#103×C₇₃	—	2	2	no	—
119	#103×C₇₃	—	2	2	no	—
120	#102×C₇₃	—	2	1	no	—
121	#102×C₇₃	—	2	1	no	—
122	#101×C₇₃	—	2	4	no	—
123	#101×C₇₃	—	2	4	no	—
124	#101×C₇₃	—	4	2	no	—
125	C₂²⋊C₈×C₇₃	—	2	1	no	—
126	C₂²⋊C₈×C₇₃	—	2	1	no	—
127	C₂²⋊C₈×C₇₃	—	2	1	no	—
128	C₂²⋊C₈×C₇₃	—	2	1	no	—
129	C₂²⋊C₈×C₇₃	—	2	2	no	—
130	C₂²⋊C₈×C₇₃	—	2	2	no	—
131	C₂²⋊C₈×C₇₃	D₄	1	1	yes	characteristic
132	C₂²⋊C₈×C₇₃	D₄	1	1	yes	characteristic
133	C₂²⋊C₈×C₇₃	D₄	1	2	yes	—
134	C₂⁴×C₇₃	—	2	1	no	—
135	C₂⁴×C₇₃	#41	1	1	yes	characteristic
136	#41×C₇₃	—	2	2	no	—
137	#41×C₇₃	—	2	2	no	—
138	#41×C₇₃	—	2	2	no	—
139	#41×C₇₃	—	2	2	no	—
140	#41×C₇₃	—	2	2	no	—
141	#41×C₇₃	—	4	4	no	—
142	#41×C₇₃	—	4	1	no	—
143	#41×C₇₃	—	4	1	no	—
144	#41×C₇₃	—	4	4	no	—
145	#41×C₇₃	C₂×D₄	1	4	yes	—
146	C₂×Q₈×C₇₃	—	2	1	no	—
147	C₂×Q₈×C₇₃	—	2	2	no	—
148	C₂×Q₈×C₇₃	—	2	4	no	—
149	C₂×Q₈×C₇₃	—	2	4	no	—
150	C₂×Q₈×C₇₃	—	2	2	no	—
151	C₂×Q₈×C₇₃	—	2	2	no	—
152	C₂×Q₈×C₇₃	—	2	2	no	—
153	C₂×Q₈×C₇₃	—	2	2	no	—
154	C₂×Q₈×C₇₃	—	2	2	no	—
155	C₂×Q₈×C₇₃	—	2	1	no	—
156	C₂×Q₈×C₇₃	—	2	1	no	—
157	C₂×Q₈×C₇₃	—	2	2	no	—
158	C₂×Q₈×C₇₃	—	2	2	no	—
159	C₂×Q₈×C₇₃	—	4	4	no	—
160	C₂×Q₈×C₇₃	—	4	1	no	—
161	C₂×Q₈×C₇₃	—	4	4	no	—
162	C₂×Q₈×C₇₃	—	4	4	no	—
163	C₂×Q₈×C₇₃	—	4	2	no	—
164	C₂×Q₈×C₇₃	—	4	2	no	—
165	C₂×Q₈×C₇₃	—	4	1	no	—
166	C₂×Q₈×C₇₃	—	4	1	no	—
167	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
168	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
169	C₂×Q₈×C₇₃	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₇₃	—	2	1	no	—
171	C₂×D₄×C₇₃	—	2	2	no	—
172	C₂×D₄×C₇₃	—	2	1	no	—
173	C₂×D₄×C₇₃	—	2	1	no	—
174	C₂×D₄×C₇₃	—	2	1	no	—
175	C₂×D₄×C₇₃	—	2	1	no	—
176	C₂×D₄×C₇₃	—	4	1	no	—
177	C₂×D₄×C₇₃	—	4	4	no	—
178	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
179	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₇₃	—	2	1	no	—
181	C₂²×C₄×C₇₃	—	2	2	no	—
182	C₂²×C₄×C₇₃	—	2	2	no	—
183	C₂²×C₄×C₇₃	—	2	1	no	—
184	C₂²×C₄×C₇₃	—	2	2	no	—
185	C₂²×C₄×C₇₃	—	2	1	no	—
186	C₂²×C₄×C₇₃	—	2	1	no	—
187	C₂²×C₄×C₇₃	—	2	1	no	—
188	C₂²×C₄×C₇₃	—	2	1	no	—
189	C₂²×C₄×C₇₃	—	2	1	no	—
190	C₂²×C₄×C₇₃	—	4	4	no	—
191	C₂²×C₄×C₇₃	—	4	4	no	—
192	C₂²×C₄×C₇₃	—	4	1	no	—
193	C₂²×C₄×C₇₃	—	4	1	no	—
194	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
198	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
199	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
200	Q₁₆×C₇₃	—	2	8	no	—
201	Q₁₆×C₇₃	—	2	8	no	—
202	Q₁₆×C₇₃	—	4	4	no	—
203	Q₁₆×C₇₃	—	4	4	no	—
204	Q₁₆×C₇₃	—	4	2	no	—
205	Q₁₆×C₇₃	—	4	2	no	—
206	SD₁₆×C₇₃	—	2	8	no	—
207	SD₁₆×C₇₃	—	2	8	no	—
208	SD₁₆×C₇₃	—	4	2	no	—
209	SD₁₆×C₇₃	—	4	2	no	—
210	M₁₆×C₇₃	—	2	4	no	—
211	M₁₆×C₇₃	—	2	2	no	—
212	M₁₆×C₇₃	—	2	2	no	—
213	M₁₆×C₇₃	—	2	2	no	—
214	M₁₆×C₇₃	—	2	2	no	—
215	M₁₆×C₇₃	—	2	2	no	—
216	M₁₆×C₇₃	—	4	4	no	—
217	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
218	C₂×C₈×C₇₃	—	2	4	no	—
219	C₂×C₈×C₇₃	—	2	2	no	—
220	C₂×C₈×C₇₃	—	2	2	no	—
221	C₂×C₈×C₇₃	—	2	2	no	—
222	C₂×C₈×C₇₃	—	2	2	no	—
223	C₂×C₈×C₇₃	—	2	1	no	—
224	C₂×C₈×C₇₃	—	2	1	no	—
225	C₂×C₈×C₇₃	—	4	4	no	—
226	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
227	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₇₃	—	2	1	no	—
229	C₄⋊C₄×C₇₃	—	2	1	no	—
230	C₄⋊C₄×C₇₃	—	4	1	no	—
231	C₄⋊C₄×C₇₃	—	4	1	no	—
232	C₂²⋊C₄×C₇₃	—	4	1	no	—
233	C₂²⋊C₄×C₇₃	—	4	1	no	—
234	C₂³×C₇₃	—	2	1	no	—
235	C₂³×C₇₃	—	2	2	no	—
236	C₂³×C₇₃	—	2	2	no	—
237	C₂³×C₇₃	—	2	1	no	—
238	C₂³×C₇₃	—	4	1	no	—
239	C₂³×C₇₃	—	4	2	no	—
240	C₂³×C₇₃	—	4	2	no	—
241	C₂³×C₇₃	—	8	1	no	—
242	C₂³×C₇₃	#121	1	1	yes	characteristic
243	C₂³×C₇₃	#121	1	1	yes	characteristic
244	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
245	Q₈×C₇₃	—	2	1	no	—
246	Q₈×C₇₃	—	2	4	no	—
247	Q₈×C₇₃	—	2	1	no	—
248	Q₈×C₇₃	—	2	1	no	—
249	Q₈×C₇₃	—	2	4	no	—
250	Q₈×C₇₃	—	4	2	no	—
251	Q₈×C₇₃	—	4	4	no	—
252	Q₈×C₇₃	—	4	4	no	—
253	Q₈×C₇₃	—	4	2	no	—
254	Q₈×C₇₃	—	4	2	no	—
255	Q₈×C₇₃	—	4	1	no	—
256	Q₈×C₇₃	—	4	1	no	—
257	Q₈×C₇₃	—	4	2	no	—
258	Q₈×C₇₃	#120	1	2	yes	—
259	D₄×C₇₃	—	2	4	no	—
260	D₄×C₇₃	—	2	1	no	—
261	D₄×C₇₃	—	2	1	no	—
262	D₄×C₇₃	—	2	1	no	—
263	D₄×C₇₃	—	4	2	no	—
264	D₄×C₇₃	—	4	2	no	—
265	D₄×C₇₃	—	4	2	no	—
266	D₄×C₇₃	—	4	2	no	—
267	D₄×C₇₃	#120	1	2	yes	—
268	C₂×C₄×C₇₃	—	2	1	no	—
269	C₂×C₄×C₇₃	—	2	2	no	—
270	C₂×C₄×C₇₃	—	2	1	no	—
271	C₂×C₄×C₇₃	—	2	1	no	—
272	C₂×C₄×C₇₃	—	2	1	no	—
273	C₂×C₄×C₇₃	—	2	1	no	—
274	C₂×C₄×C₇₃	—	2	4	no	—
275	C₂×C₄×C₇₃	—	2	2	no	—
276	C₂×C₄×C₇₃	—	2	2	no	—
277	C₂×C₄×C₇₃	—	2	1	no	—
278	C₂×C₄×C₇₃	—	2	4	no	—
279	C₂×C₄×C₇₃	—	4	2	no	—
280	C₂×C₄×C₇₃	—	4	2	no	—
281	C₂×C₄×C₇₃	—	4	2	no	—
282	C₂×C₄×C₇₃	—	4	4	no	—
283	C₂×C₄×C₇₃	—	4	4	no	—
284	C₂×C₄×C₇₃	—	4	2	no	—
285	C₂×C₄×C₇₃	—	4	2	no	—
286	C₂×C₄×C₇₃	—	4	2	no	—
287	C₂×C₄×C₇₃	—	4	1	no	—
288	C₂×C₄×C₇₃	—	4	1	no	—
289	C₂×C₄×C₇₃	—	4	2	no	—
290	C₂×C₄×C₇₃	—	8	1	no	—
291	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
292	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
293	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
297	C₈×C₇₃	—	2	4	no	—
298	C₈×C₇₃	—	2	2	no	—
299	C₈×C₇₃	—	2	2	no	—
300	C₈×C₇₃	—	4	1	no	—
301	C₈×C₇₃	—	4	1	no	—
302	C₈×C₇₃	—	4	2	no	—
303	C₂²×C₇₃	—	2	1	no	—
304	C₂²×C₇₃	—	2	1	no	—
305	C₂²×C₇₃	—	2	1	no	—
306	C₂²×C₇₃	—	2	1	no	—
307	C₂²×C₇₃	—	2	1	no	—
308	C₂²×C₇₃	—	2	2	no	—
309	C₂²×C₇₃	—	2	1	no	—
310	C₂²×C₇₃	—	2	1	no	—
311	C₂²×C₇₃	—	4	4	no	—
312	C₂²×C₇₃	—	4	1	no	—
313	C₂²×C₇₃	—	4	1	no	—
314	C₂²×C₇₃	—	4	1	no	—
315	C₂²×C₇₃	—	4	1	no	—
316	C₂²×C₇₃	—	4	1	no	—
317	C₂²×C₇₃	—	8	4	no	—
318	C₂²×C₇₃	#473	1	2	yes	complemented
319	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
320	C₂²×C₇₃	#546	1	2	yes	—
321	C₄×C₇₃	—	2	1	no	—
322	C₄×C₇₃	—	2	1	no	—
323	C₄×C₇₃	—	2	2	no	—
324	C₄×C₇₃	—	4	1	no	—
325	C₄×C₇₃	—	4	4	no	—
326	C₄×C₇₃	—	8	1	no	—
327	C₄×C₇₃	—	8	1	no	—
328	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
329	C₄×C₇₃	#534	1	1	yes	characteristic
330	C₄×C₇₃	D₄²	1	2	yes	—
331	#24400	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
332	C₂×C₇₃	—	2	2	no	—
333	C₂×C₇₃	—	2	2	no	—
334	C₂×C₇₃	—	4	1	no	—
335	C₂×C₇₃	—	4	2	no	—
336	C₂×C₇₃	—	8	1	no	—
337	C₂×C₇₃	#2410	1	1	yes	characteristic
338	C₂×C₇₃	C₂×#473	1	1	yes	characteristic
339	C₂×C₇₃	#3069	1	1	yes	characteristic
340	C₂²×#137	C₂×C₇₃	1	1	yes	characteristic
341	C₂×#473	C₂×C₇₃	1	2	yes	complemented
342	#3007	C₂×C₇₃	1	1	yes	characteristic
343	C₂×#451	C₂×C₇₃	1	1	yes	characteristic, complemented
344	#2880	C₂×C₇₃	1	1	yes	characteristic
345	#2052	C₂×C₇₃	1	2	yes	complemented
346	#2020	C₂×C₇₃	1	2	yes	complemented
347	#1908	C₂×C₇₃	1	2	yes	complemented
348	#1901	C₂×C₇₃	1	1	yes	characteristic, complemented
349	#1855	C₂×C₇₃	1	1	yes	characteristic, complemented
350	#1784	C₂×C₇₃	1	1	yes	characteristic, complemented
351	C₇₃	#24400	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
353	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
354	C₂×#137	—	2	1	no	—
355	C₂×#137	—	2	1	no	—
356	C₂×#137	—	2	8	no	—
357	C₂×#137	C₂²×C₇₃	1	2	yes	—
358	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
359	C₂×#137	C₂²×C₇₃	1	2	yes	—
360	C₂×#137	C₂²×C₇₃	1	1	yes	characteristic
361	C₂²×Q₁₆	—	2	1	no	—
362	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	complemented
363	C₂²×SD₁₆	—	2	1	no	—
364	C₂×#131	C₂²×C₇₃	1	2	yes	—
365	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
366	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
367	#473	—	2	8	no	—
368	#452	—	2	1	no	—
369	#452	—	2	1	no	—
370	#451	—	2	1	no	—
371	#451	—	2	1	no	—
372	#451	—	2	1	no	—
373	#451	—	2	2	no	—
374	#450	—	2	1	no	—
375	C₂×#108	C₂²×C₇₃	1	2	yes	complemented
376	#417	C₂²×C₇₃	1	1	yes	characteristic
377	#417	C₂²×C₇₃	1	1	yes	characteristic
378	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
379	C₂×#101	C₂²×C₇₃	1	2	yes	complemented
380	C₂×#101	C₂²×C₇₃	1	2	yes	complemented
381	C₂×#101	C₂²×C₇₃	1	2	yes	complemented
382	#408	—	2	2	no	—
383	#408	C₂²×C₇₃	1	2	yes	—
384	#407	—	2	1	no	—
385	#407	C₂²×C₇₃	1	1	yes	characteristic
386	#407	C₂²×C₇₃	1	1	yes	characteristic
387	C₂×C₂²⋊C₈	—	2	1	no	—
388	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
389	#343	C₂²×C₇₃	1	2	yes	complemented
390	#341	C₂²×C₇₃	1	2	yes	complemented
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	—	2	4	no	—
394	C₂×#41	—	4	2	no	—
395	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
396	C₂×#41	D₄×C₇₃	1	1	yes	characteristic
397	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
398	C₂×#41	C₂³×C₇₃	1	1	yes	characteristic
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×Q₈	—	2	4	no	—
401	C₂²×Q₈	—	2	1	no	—
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×Q₈	—	2	1	no	—
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	—	4	2	no	—
406	C₂²×Q₈	D₄×C₇₃	1	1	yes	characteristic
407	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
408	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
409	C₂²×D₄	—	2	1	no	—
410	C₂²×D₄	D₄×C₇₃	1	1	yes	characteristic
411	C₂³×C₄	—	2	1	no	—
412	C₂³×C₄	—	2	1	no	—
413	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
414	#137	—	2	8	no	—
415	#137	—	2	8	no	—
416	#137	—	2	4	no	—
417	#137	—	2	4	no	—
418	#137	—	2	4	no	—
419	#137	—	2	4	no	—
420	#137	—	4	2	no	—
421	#137	D₄×C₇₃	1	8	yes	—
422	C₂×Q₁₆	—	2	8	no	—
423	C₂×Q₁₆	—	2	2	no	—
424	C₂×Q₁₆	—	2	2	no	—
425	C₂×Q₁₆	—	2	4	no	—
426	C₂×Q₁₆	—	2	1	no	—
427	C₂×Q₁₆	—	2	1	no	—
428	C₂×Q₁₆	—	2	2	no	—
429	C₂×Q₁₆	—	2	2	no	—
430	C₂×Q₁₆	—	4	2	no	—
431	C₂×SD₁₆	—	2	8	no	—
432	C₂×SD₁₆	—	2	2	no	—
433	C₂×SD₁₆	—	2	2	no	—
434	C₂×SD₁₆	—	2	1	no	—
435	C₂×SD₁₆	—	2	1	no	—
436	#131	—	2	4	no	—
437	#131	—	4	2	no	—
438	C₂×M₁₆	—	2	1	no	—
439	C₂×M₁₆	—	2	4	no	—
440	C₂×M₁₆	—	2	2	no	—
441	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
442	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
443	C₂×M₁₆	C₂³×C₇₃	1	1	yes	characteristic
444	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
445	C₂²×C₈	—	2	1	no	—
446	C₂²×C₈	—	2	2	no	—
447	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
448	C₂²⋊Q₈	—	2	1	no	—
449	C₂²⋊Q₈	—	2	1	no	—
450	C₂²⋊Q₈	—	2	1	no	—
451	C₂²⋊Q₈	—	2	1	no	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	#108	—	2	4	no	—
456	#103	—	2	1	no	—
457	#103	—	2	1	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#102	—	2	1	no	—
461	#102	—	2	1	no	—
462	#101	—	2	4	no	—
463	#101	—	2	4	no	—
464	#101	—	4	2	no	—
465	C₂²⋊C₈	—	2	1	no	—
466	C₂²⋊C₈	—	2	1	no	—
467	C₂²⋊C₈	—	2	1	no	—
468	C₂²⋊C₈	—	2	1	no	—
469	C₂²⋊C₈	—	2	2	no	—
470	C₂²⋊C₈	—	2	2	no	—
471	C₂²⋊C₈	D₄×C₇₃	1	1	yes	characteristic
472	C₂²⋊C₈	D₄×C₇₃	1	1	yes	characteristic
473	C₂²⋊C₈	D₄×C₇₃	1	2	yes	—
474	C₂⁴	—	2	1	no	—
475	C₂⁴	#41×C₇₃	1	1	yes	characteristic
476	#41	—	2	2	no	—
477	#41	—	2	2	no	—
478	#41	—	2	2	no	—
479	#41	—	2	2	no	—
480	#41	—	2	2	no	—
481	#41	—	4	4	no	—
482	#41	—	4	1	no	—
483	#41	—	4	1	no	—
484	#41	—	4	4	no	—
485	#41	C₂×D₄×C₇₃	1	4	yes	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	2	no	—
488	C₂×Q₈	—	2	4	no	—
489	C₂×Q₈	—	2	4	no	—
490	C₂×Q₈	—	2	2	no	—
491	C₂×Q₈	—	2	2	no	—
492	C₂×Q₈	—	2	2	no	—
493	C₂×Q₈	—	2	2	no	—
494	C₂×Q₈	—	2	2	no	—
495	C₂×Q₈	—	2	1	no	—
496	C₂×Q₈	—	2	1	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	4	4	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	4	4	no	—
502	C₂×Q₈	—	4	4	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	—	4	2	no	—
505	C₂×Q₈	—	4	1	no	—
506	C₂×Q₈	—	4	1	no	—
507	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
508	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
509	C₂×Q₈	C₂×D₄×C₇₃	1	1	yes	characteristic
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	4	no	—
518	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
519	C₂×D₄	C₂×D₄×C₇₃	1	1	yes	characteristic
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	2	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	4	4	no	—
531	C₂²×C₄	—	4	4	no	—
532	C₂²×C₄	—	4	1	no	—
533	C₂²×C₄	—	4	1	no	—
534	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
538	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
540	Q₁₆	—	2	8	no	—
541	Q₁₆	—	2	8	no	—
542	Q₁₆	—	4	4	no	—
543	Q₁₆	—	4	4	no	—
544	Q₁₆	—	4	2	no	—
545	Q₁₆	—	4	2	no	—
546	SD₁₆	—	2	8	no	—
547	SD₁₆	—	2	8	no	—
548	SD₁₆	—	4	2	no	—
549	SD₁₆	—	4	2	no	—
550	M₁₆	—	2	4	no	—
551	M₁₆	—	2	2	no	—
552	M₁₆	—	2	2	no	—
553	M₁₆	—	2	2	no	—
554	M₁₆	—	2	2	no	—
555	M₁₆	—	2	2	no	—
556	M₁₆	—	4	4	no	—
557	M₁₆	C₂×D₄×C₇₃	1	4	yes	—
558	C₂×C₈	—	2	4	no	—
559	C₂×C₈	—	2	2	no	—
560	C₂×C₈	—	2	2	no	—
561	C₂×C₈	—	2	2	no	—
562	C₂×C₈	—	2	2	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	4	4	no	—
566	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
567	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	4	1	no	—
571	C₄⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂³	—	2	2	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	1	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	4	2	no	—
580	C₂³	—	4	2	no	—
581	C₂³	—	8	1	no	—
582	C₂³	#121×C₇₃	1	1	yes	characteristic
583	C₂³	#121×C₇₃	1	1	yes	characteristic
584	C₂³	C₂×#41×C₇₃	1	1	yes	characteristic
585	Q₈	—	2	1	no	—
586	Q₈	—	2	4	no	—
587	Q₈	—	2	1	no	—
588	Q₈	—	2	1	no	—
589	Q₈	—	2	4	no	—
590	Q₈	—	4	2	no	—
591	Q₈	—	4	4	no	—
592	Q₈	—	4	4	no	—
593	Q₈	—	4	2	no	—
594	Q₈	—	4	2	no	—
595	Q₈	—	4	1	no	—
596	Q₈	—	4	1	no	—
597	Q₈	—	4	2	no	—
598	Q₈	#120×C₇₃	1	2	yes	—
599	D₄	—	2	4	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	1	no	—
602	D₄	—	2	1	no	—
603	D₄	—	4	2	no	—
604	D₄	—	4	2	no	—
605	D₄	—	4	2	no	—
606	D₄	—	4	2	no	—
607	D₄	#120×C₇₃	1	2	yes	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	4	2	no	—
620	C₂×C₄	—	4	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	—	4	2	no	—
626	C₂×C₄	—	4	2	no	—
627	C₂×C₄	—	4	1	no	—
628	C₂×C₄	—	4	1	no	—
629	C₂×C₄	—	4	2	no	—
630	C₂×C₄	—	8	1	no	—
631	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
632	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
633	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
634	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
635	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
636	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
637	C₈	—	2	4	no	—
638	C₈	—	2	2	no	—
639	C₈	—	2	2	no	—
640	C₈	—	4	1	no	—
641	C₈	—	4	1	no	—
642	C₈	—	4	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	4	4	no	—
652	C₂²	—	4	1	no	—
653	C₂²	—	4	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	8	4	no	—
658	C₂²	#473×C₇₃	1	2	yes	complemented
659	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
660	C₂²	#546×C₇₃	1	2	yes	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	4	no	—
666	C₄	—	8	1	no	—
667	C₄	—	8	1	no	—
668	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
669	C₄	#534×C₇₃	1	1	yes	characteristic
670	C₄	D₄²×C₇₃	1	2	yes	—
671	C₂	—	2	2	no	—
672	C₂	—	2	2	no	—
673	C₂	—	4	1	no	—
674	C₂	—	4	2	no	—
675	C₂	—	8	1	no	—
676	C₂	C₇₃×#2410	1	1	yes	characteristic
677	C₂	C₂×#473×C₇₃	1	1	yes	characteristic
678	C₂	C₇₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#473×C₇₃	C₂	semidirect
4. C₂×#451×C₇₃	C₂	semidirect
6. C₇₃×#2052	C₂	semidirect
7. C₇₃×#2020	C₂	semidirect
8. C₇₃×#1908	C₂	semidirect
9. C₇₃×#1901	C₂	semidirect
10. C₇₃×#1855	C₂	semidirect
11. C₇₃×#1784	C₂	semidirect
22. C₂²×Q₁₆×C₇₃	C₂²	semidirect
35. C₂×#108×C₇₃	C₂²	semidirect
38. C₂×#103×C₇₃	C₂²	semidirect
39. C₂×#101×C₇₃	C₂²	semidirect
40. C₂×#101×C₇₃	C₂²	semidirect
41. C₂×#101×C₇₃	C₂²	semidirect
49. #343×C₇₃	C₂²	semidirect
50. #341×C₇₃	C₂²	semidirect
318. C₂²×C₇₃	#473	semidirect
331. #24400	C₇₃	direct (N × H)
341. C₂×#473	C₂×C₇₃	semidirect
343. C₂×#451	C₂×C₇₃	semidirect
345. #2052	C₂×C₇₃	semidirect
346. #2020	C₂×C₇₃	semidirect
347. #1908	C₂×C₇₃	semidirect
348. #1901	C₂×C₇₃	semidirect
349. #1855	C₂×C₇₃	semidirect
350. #1784	C₂×C₇₃	semidirect
351. C₇₃	#24400	direct (N × H)
362. C₂²×Q₁₆	C₂²×C₇₃	semidirect
375. C₂×#108	C₂²×C₇₃	semidirect
378. C₂×#103	C₂²×C₇₃	semidirect
379. C₂×#101	C₂²×C₇₃	semidirect
380. C₂×#101	C₂²×C₇₃	semidirect
381. C₂×#101	C₂²×C₇₃	semidirect
389. #343	C₂²×C₇₃	semidirect
390. #341	C₂²×C₇₃	semidirect
658. C₂²	#473×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#137×C₇₃	2
C₂×#473×C₇₃	2
C₇₃×#3007	2
C₂×#451×C₇₃	2
C₇₃×#2880	2
C₇₃×#2052	2
C₇₃×#2020	2
C₇₃×#1908	2
C₇₃×#1901	2
C₇₃×#1855	2
C₇₃×#1784	2
#24400	73

Subgroups — C73×#24400 #32933804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#24400 #32933804