Subgroups — C₇₃×#23472 #32932876

Order 18688.

1148 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#421×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#421×C₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#410×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₇₃×#2031	C₂	1	8	yes	maximal, complemented
6	C₂×#344×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1733	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×H(3,ℤ/4)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
12	#544×C₇₃	—	2	2	no	—
13	#544×C₇₃	—	2	2	no	—
14	#544×C₇₃	—	2	2	no	—
15	#543×C₇₃	—	2	2	no	—
16	#533×C₇₃	—	2	2	no	—
17	#533×C₇₃	—	2	2	no	—
18	#533×C₇₃	C₂²	1	4	yes	complemented
19	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
21	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
23	#421×C₇₃	—	2	2	no	—
24	#421×C₇₃	—	2	2	no	—
25	#421×C₇₃	—	2	2	no	—
26	#421×C₇₃	C₂²	1	4	yes	—
27	C₂×#104×C₇₃	—	2	2	no	—
28	C₂×#104×C₇₃	C₂²	1	4	yes	—
29	#410×C₇₃	—	2	2	no	—
30	#410×C₇₃	C₂²	1	4	yes	—
31	C₂×#99×C₇₃	—	2	2	no	—
32	#344×C₇₃	C₂²	1	4	yes	complemented
33	#339×C₇₃	C₂²	1	4	yes	complemented
34	H(3,ℤ/4)×C₇₃	C₂²	1	4	yes	complemented
35	C₂×#41×C₇₃	—	2	1	no	—
36	C₂×#41×C₇₃	—	2	1	no	—
37	C₂×#41×C₇₃	—	2	1	no	—
38	C₂×#41×C₇₃	—	2	1	no	—
39	C₂×#41×C₇₃	—	2	1	no	—
40	C₂×#41×C₇₃	—	2	1	no	—
41	C₂×#41×C₇₃	—	2	1	no	—
42	C₂×#41×C₇₃	—	2	1	no	—
43	C₂×#41×C₇₃	—	2	1	no	—
44	C₂×#41×C₇₃	—	2	1	no	—
45	C₂×#41×C₇₃	Q₈	1	2	yes	complemented
46	C₂×#41×C₇₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₇₃	Q₈	1	1	yes	characteristic, complemented
48	C₂²×D₄×C₇₃	—	2	1	no	—
49	C₂²×D₄×C₇₃	Q₈	1	1	yes	characteristic, complemented
50	C₂³×C₄×C₇₃	—	2	1	no	—
51	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₇₃	—	2	1	no	—
53	C₂×M₁₆×C₇₃	—	2	1	no	—
54	C₂×M₁₆×C₇₃	—	2	1	no	—
55	C₂×M₁₆×C₇₃	—	2	1	no	—
56	C₂×M₁₆×C₇₃	—	2	1	no	—
57	C₂×M₁₆×C₇₃	—	2	1	no	—
58	C₂×M₁₆×C₇₃	—	2	1	no	—
59	C₂×M₁₆×C₇₃	—	2	1	no	—
60	C₂×M₁₆×C₇₃	—	2	1	no	—
61	C₂×M₁₆×C₇₃	—	2	1	no	—
62	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
63	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
64	C₂²×C₈×C₇₃	—	2	1	no	—
65	C₂²×C₈×C₇₃	—	2	1	no	—
66	C₄⋊Q₈×C₇₃	—	2	4	no	—
67	C₄⋊Q₈×C₇₃	—	2	4	no	—
68	C₄⋊Q₈×C₇₃	—	2	4	no	—
69	#125×C₇₃	—	2	4	no	—
70	#125×C₇₃	—	2	4	no	—
71	#125×C₇₃	—	2	4	no	—
72	C₂²⋊Q₈×C₇₃	—	2	8	no	—
73	C₂²⋊Q₈×C₇₃	—	2	8	no	—
74	C₂²⋊Q₈×C₇₃	—	2	8	no	—
75	C₄×Q₈×C₇₃	—	2	8	no	—
76	#117×C₇₃	—	2	1	no	—
77	#117×C₇₃	—	2	1	no	—
78	#117×C₇₃	—	2	1	no	—
79	#117×C₇₃	—	2	1	no	—
80	#117×C₇₃	—	2	1	no	—
81	#117×C₇₃	—	2	1	no	—
82	#117×C₇₃	—	2	1	no	—
83	#117×C₇₃	—	2	1	no	—
84	#117×C₇₃	—	2	1	no	—
85	#117×C₇₃	D₄	1	2	yes	—
86	#117×C₇₃	D₄	1	2	yes	—
87	#117×C₇₃	D₄	1	2	yes	—
88	#117×C₇₃	D₄	1	2	yes	—
89	#117×C₇₃	C₂³	1	2	yes	—
90	#117×C₇₃	C₂³	1	2	yes	—
91	#117×C₇₃	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
93	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
94	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
100	C₂×C₄²×C₇₃	—	2	1	no	—
101	C₂×C₄²×C₇₃	—	2	1	no	—
102	C₂×C₄²×C₇₃	D₄	1	2	yes	—
103	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
104	#104×C₇₃	—	2	8	no	—
105	#104×C₇₃	—	2	8	no	—
106	#99×C₇₃	—	2	8	no	—
107	C₂⁴×C₇₃	—	2	1	no	—
108	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
109	#41×C₇₃	—	2	2	no	—
110	#41×C₇₃	—	2	2	no	—
111	#41×C₇₃	—	2	2	no	—
112	#41×C₇₃	—	2	2	no	—
113	#41×C₇₃	—	2	2	no	—
114	#41×C₇₃	—	2	2	no	—
115	#41×C₇₃	—	2	2	no	—
116	#41×C₇₃	—	2	2	no	—
117	#41×C₇₃	—	4	1	no	—
118	#41×C₇₃	—	4	1	no	—
119	#41×C₇₃	—	4	1	no	—
120	#41×C₇₃	—	4	1	no	—
121	#41×C₇₃	—	4	1	no	—
122	#41×C₇₃	—	4	1	no	—
123	#41×C₇₃	—	4	1	no	—
124	#41×C₇₃	—	4	1	no	—
125	C₂×Q₈×C₇₃	—	2	8	no	—
126	C₂×Q₈×C₇₃	—	2	1	no	—
127	C₂×Q₈×C₇₃	—	2	1	no	—
128	C₂×Q₈×C₇₃	—	2	1	no	—
129	C₂×Q₈×C₇₃	—	2	1	no	—
130	C₂×Q₈×C₇₃	—	2	1	no	—
131	C₂×Q₈×C₇₃	C₂×Q₈	1	2	yes	—
132	C₂×D₄×C₇₃	—	2	2	no	—
133	C₂×D₄×C₇₃	—	2	2	no	—
134	C₂×D₄×C₇₃	—	2	1	no	—
135	C₂×D₄×C₇₃	—	2	1	no	—
136	C₂×D₄×C₇₃	—	2	1	no	—
137	C₂×D₄×C₇₃	—	2	1	no	—
138	C₂×D₄×C₇₃	—	2	1	no	—
139	C₂×D₄×C₇₃	—	4	1	no	—
140	C₂×D₄×C₇₃	—	4	1	no	—
141	C₂×D₄×C₇₃	—	4	1	no	—
142	C₂×D₄×C₇₃	—	4	1	no	—
143	C₂×D₄×C₇₃	C₂×Q₈	1	2	yes	—
144	C₂²×C₄×C₇₃	—	2	1	no	—
145	C₂²×C₄×C₇₃	—	2	2	no	—
146	C₂²×C₄×C₇₃	—	2	2	no	—
147	C₂²×C₄×C₇₃	—	2	2	no	—
148	C₂²×C₄×C₇₃	—	2	2	no	—
149	C₂²×C₄×C₇₃	—	2	2	no	—
150	C₂²×C₄×C₇₃	—	4	1	no	—
151	C₂²×C₄×C₇₃	—	4	1	no	—
152	C₂²×C₄×C₇₃	—	4	1	no	—
153	C₂²×C₄×C₇₃	—	4	1	no	—
154	C₂²×C₄×C₇₃	—	4	1	no	—
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
161	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
163	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
164	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
165	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
166	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
167	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
169	M₁₆×C₇₃	—	2	2	no	—
170	M₁₆×C₇₃	—	2	2	no	—
171	M₁₆×C₇₃	—	2	2	no	—
172	M₁₆×C₇₃	—	2	2	no	—
173	M₁₆×C₇₃	—	4	1	no	—
174	M₁₆×C₇₃	—	4	1	no	—
175	M₁₆×C₇₃	—	4	1	no	—
176	M₁₆×C₇₃	—	4	1	no	—
177	C₂×C₈×C₇₃	—	2	2	no	—
178	C₂×C₈×C₇₃	—	2	2	no	—
179	C₂×C₈×C₇₃	—	4	1	no	—
180	C₂×C₈×C₇₃	—	4	1	no	—
181	C₂×C₈×C₇₃	—	4	1	no	—
182	C₂×C₈×C₇₃	—	4	1	no	—
183	C₄⋊C₄×C₇₃	—	2	8	no	—
184	C₄⋊C₄×C₇₃	—	2	8	no	—
185	C₄⋊C₄×C₇₃	—	2	8	no	—
186	C₄⋊C₄×C₇₃	—	2	2	no	—
187	C₄⋊C₄×C₇₃	—	2	2	no	—
188	C₄⋊C₄×C₇₃	—	2	2	no	—
189	C₄⋊C₄×C₇₃	—	2	2	no	—
190	C₄⋊C₄×C₇₃	—	2	2	no	—
191	C₄⋊C₄×C₇₃	—	2	2	no	—
192	C₄⋊C₄×C₇₃	—	2	2	no	—
193	C₄⋊C₄×C₇₃	—	4	1	no	—
194	C₂²⋊C₄×C₇₃	—	2	2	no	—
195	C₂²⋊C₄×C₇₃	—	2	2	no	—
196	C₂²⋊C₄×C₇₃	—	2	2	no	—
197	C₂²⋊C₄×C₇₃	—	2	2	no	—
198	C₂²⋊C₄×C₇₃	—	2	2	no	—
199	C₂²⋊C₄×C₇₃	—	2	2	no	—
200	C₂²⋊C₄×C₇₃	—	4	1	no	—
201	C₂²⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
202	C₄²×C₇₃	—	2	2	no	—
203	C₄²×C₇₃	—	2	2	no	—
204	C₄²×C₇₃	—	2	2	no	—
205	C₄²×C₇₃	—	2	2	no	—
206	C₄²×C₇₃	—	2	2	no	—
207	C₄²×C₇₃	—	4	1	no	—
208	C₄²×C₇₃	C₂×D₄	1	4	yes	—
209	C₄²×C₇₃	C₂×D₄	1	4	yes	—
210	C₂³×C₇₃	—	2	2	no	—
211	C₂³×C₇₃	—	4	1	no	—
212	C₂³×C₇₃	—	4	1	no	—
213	C₂³×C₇₃	—	8	1	no	—
214	C₂³×C₇₃	—	8	2	no	—
215	C₂³×C₇₃	#120	1	1	yes	characteristic
216	C₂³×C₇₃	#120	1	1	yes	characteristic
217	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
218	C₂³×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
219	C₂³×C₇₃	#124	1	1	yes	characteristic
220	C₂³×C₇₃	#124	1	1	yes	characteristic
221	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
222	Q₈×C₇₃	—	2	2	no	—
223	Q₈×C₇₃	—	2	2	no	—
224	Q₈×C₇₃	—	4	1	no	—
225	Q₈×C₇₃	—	4	1	no	—
226	Q₈×C₇₃	—	8	8	no	—
227	D₄×C₇₃	—	2	2	no	—
228	D₄×C₇₃	—	2	2	no	—
229	D₄×C₇₃	—	4	2	no	—
230	D₄×C₇₃	—	4	2	no	—
231	D₄×C₇₃	—	4	2	no	—
232	D₄×C₇₃	—	4	2	no	—
233	D₄×C₇₃	—	4	1	no	—
234	D₄×C₇₃	—	4	1	no	—
235	C₂×C₄×C₇₃	—	2	4	no	—
236	C₂×C₄×C₇₃	—	2	4	no	—
237	C₂×C₄×C₇₃	—	2	4	no	—
238	C₂×C₄×C₇₃	—	2	2	no	—
239	C₂×C₄×C₇₃	—	4	1	no	—
240	C₂×C₄×C₇₃	—	4	1	no	—
241	C₂×C₄×C₇₃	—	4	2	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	—	4	2	no	—
244	C₂×C₄×C₇₃	—	4	2	no	—
245	C₂×C₄×C₇₃	—	4	2	no	—
246	C₂×C₄×C₇₃	—	8	2	no	—
247	C₂×C₄×C₇₃	—	8	2	no	—
248	C₂×C₄×C₇₃	—	8	2	no	—
249	C₂×C₄×C₇₃	—	8	2	no	—
250	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
251	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
252	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
256	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
257	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
258	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
259	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
260	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
261	C₂×C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
263	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
264	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
265	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
266	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
267	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
268	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
269	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
270	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
271	C₂×C₄×C₇₃	#124	1	1	yes	characteristic
272	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
275	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
276	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
277	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
278	C₈×C₇₃	—	4	2	no	—
279	C₈×C₇₃	—	4	2	no	—
280	C₂²×C₇₃	—	4	1	no	—
281	C₂²×C₇₃	—	4	1	no	—
282	C₂²×C₇₃	—	4	1	no	—
283	C₂²×C₇₃	—	4	1	no	—
284	C₂²×C₇₃	—	4	1	no	—
285	C₂²×C₇₃	—	4	1	no	—
286	C₂²×C₇₃	—	4	1	no	—
287	C₂²×C₇₃	—	4	2	no	—
288	C₂²×C₇₃	—	8	2	no	—
289	C₂²×C₇₃	—	8	2	no	—
290	C₂²×C₇₃	—	8	2	no	—
291	C₂²×C₇₃	#393	1	1	yes	characteristic
292	C₂²×C₇₃	#393	1	1	yes	characteristic
293	C₂²×C₇₃	#393	1	1	yes	characteristic
294	C₂²×C₇₃	#393	1	1	yes	characteristic
295	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
296	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
297	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
298	C₄×C₇₃	—	4	4	no	—
299	C₄×C₇₃	—	4	4	no	—
300	C₄×C₇₃	—	4	4	no	—
301	C₄×C₇₃	—	4	2	no	—
302	C₄×C₇₃	—	8	2	no	—
303	C₄×C₇₃	#393	1	1	yes	characteristic
304	C₄×C₇₃	#393	1	1	yes	characteristic
305	C₄×C₇₃	#393	1	1	yes	characteristic
306	C₄×C₇₃	#393	1	1	yes	characteristic
307	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
308	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
309	C₄×C₇₃	C₂×#124	1	1	yes	characteristic
310	C₄×C₇₃	C₂×#124	1	1	yes	characteristic
311	#23472	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
312	C₂×C₇₃	—	2	1	no	—
313	C₂×C₇₃	—	2	1	no	—
314	C₂×C₇₃	—	2	1	no	—
315	C₂×C₇₃	—	2	1	no	—
316	C₂×C₇₃	—	2	1	no	—
317	C₂×C₇₃	—	2	1	no	—
318	C₂×C₇₃	—	2	1	no	—
319	C₂×C₇₃	—	8	2	no	—
320	C₂×C₇₃	C₂×#393	1	1	yes	characteristic
321	#3458	C₂×C₇₃	1	1	yes	characteristic, complemented
322	C₂×#421	C₂×C₇₃	1	1	yes	characteristic
323	C₂×#421	C₂×C₇₃	1	1	yes	characteristic
324	C₂×#410	C₂×C₇₃	1	1	yes	characteristic
325	#2031	C₂×C₇₃	1	8	yes	complemented
326	C₂×#344	C₂×C₇₃	1	1	yes	characteristic, complemented
327	#1733	C₂×C₇₃	1	1	yes	characteristic, complemented
328	C₂×H(3,ℤ/4)	C₂×C₇₃	1	1	yes	characteristic, complemented
329	C₇₃	#23472	1	1	yes	characteristic, direct product factor, Sylow
330	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
331	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
332	C₂²×M₁₆	C₂²×C₇₃	1	1	yes	characteristic
333	#544	—	2	2	no	—
334	#544	—	2	2	no	—
335	#544	—	2	2	no	—
336	#543	—	2	2	no	—
337	#533	—	2	2	no	—
338	#533	—	2	2	no	—
339	#533	C₂²×C₇₃	1	4	yes	complemented
340	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
341	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
342	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
343	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
344	#421	—	2	2	no	—
345	#421	—	2	2	no	—
346	#421	—	2	2	no	—
347	#421	C₂²×C₇₃	1	4	yes	—
348	C₂×#104	—	2	2	no	—
349	C₂×#104	C₂²×C₇₃	1	4	yes	—
350	#410	—	2	2	no	—
351	#410	C₂²×C₇₃	1	4	yes	—
352	C₂×#99	—	2	2	no	—
353	#344	C₂²×C₇₃	1	4	yes	complemented
354	#339	C₂²×C₇₃	1	4	yes	complemented
355	H(3,ℤ/4)	C₂²×C₇₃	1	4	yes	complemented
356	C₂×#41	—	2	1	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	—	2	1	no	—
359	C₂×#41	—	2	1	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂×#41	—	2	1	no	—
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	1	no	—
366	C₂×#41	Q₈×C₇₃	1	2	yes	complemented
367	C₂×#41	C₂³×C₇₃	1	2	yes	—
368	C₂²×Q₈	Q₈×C₇₃	1	1	yes	characteristic, complemented
369	C₂²×D₄	—	2	1	no	—
370	C₂²×D₄	Q₈×C₇₃	1	1	yes	characteristic, complemented
371	C₂³×C₄	—	2	1	no	—
372	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
373	C₂×M₁₆	—	2	1	no	—
374	C₂×M₁₆	—	2	1	no	—
375	C₂×M₁₆	—	2	1	no	—
376	C₂×M₁₆	—	2	1	no	—
377	C₂×M₁₆	—	2	1	no	—
378	C₂×M₁₆	—	2	1	no	—
379	C₂×M₁₆	—	2	1	no	—
380	C₂×M₁₆	—	2	1	no	—
381	C₂×M₁₆	—	2	1	no	—
382	C₂×M₁₆	—	2	1	no	—
383	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
384	C₂×M₁₆	C₂³×C₇₃	1	2	yes	—
385	C₂²×C₈	—	2	1	no	—
386	C₂²×C₈	—	2	1	no	—
387	C₄⋊Q₈	—	2	4	no	—
388	C₄⋊Q₈	—	2	4	no	—
389	C₄⋊Q₈	—	2	4	no	—
390	#125	—	2	4	no	—
391	#125	—	2	4	no	—
392	#125	—	2	4	no	—
393	C₂²⋊Q₈	—	2	8	no	—
394	C₂²⋊Q₈	—	2	8	no	—
395	C₂²⋊Q₈	—	2	8	no	—
396	C₄×Q₈	—	2	8	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	—	2	1	no	—
400	#117	—	2	1	no	—
401	#117	—	2	1	no	—
402	#117	—	2	1	no	—
403	#117	—	2	1	no	—
404	#117	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	D₄×C₇₃	1	2	yes	—
407	#117	D₄×C₇₃	1	2	yes	—
408	#117	D₄×C₇₃	1	2	yes	—
409	#117	D₄×C₇₃	1	2	yes	—
410	#117	C₂³×C₇₃	1	2	yes	—
411	#117	C₂³×C₇₃	1	2	yes	—
412	#117	C₂³×C₇₃	1	2	yes	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	—	2	1	no	—
416	C₂×C₄⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	D₄×C₇₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
425	#104	—	2	8	no	—
426	#104	—	2	8	no	—
427	#99	—	2	8	no	—
428	C₂⁴	—	2	1	no	—
429	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	4	1	no	—
439	#41	—	4	1	no	—
440	#41	—	4	1	no	—
441	#41	—	4	1	no	—
442	#41	—	4	1	no	—
443	#41	—	4	1	no	—
444	#41	—	4	1	no	—
445	#41	—	4	1	no	—
446	C₂×Q₈	—	2	8	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	C₂×Q₈×C₇₃	1	2	yes	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	4	1	no	—
461	C₂×D₄	—	4	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	C₂×Q₈×C₇₃	1	2	yes	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	4	1	no	—
472	C₂²×C₄	—	4	1	no	—
473	C₂²×C₄	—	4	1	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	—	4	1	no	—
476	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
480	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
481	C₂²×C₄	C₂×Q₈×C₇₃	1	1	yes	characteristic
482	C₂²×C₄	C₂×Q₈×C₇₃	1	1	yes	characteristic
483	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
484	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
485	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
486	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
487	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
488	C₂²×C₄	#41×C₇₃	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
490	M₁₆	—	2	2	no	—
491	M₁₆	—	2	2	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	4	1	no	—
495	M₁₆	—	4	1	no	—
496	M₁₆	—	4	1	no	—
497	M₁₆	—	4	1	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	2	2	no	—
500	C₂×C₈	—	4	1	no	—
501	C₂×C₈	—	4	1	no	—
502	C₂×C₈	—	4	1	no	—
503	C₂×C₈	—	4	1	no	—
504	C₄⋊C₄	—	2	8	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	2	2	no	—
516	C₂²⋊C₄	—	2	2	no	—
517	C₂²⋊C₄	—	2	2	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	4	1	no	—
522	C₂²⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	2	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	4	1	no	—
529	C₄²	C₂×D₄×C₇₃	1	4	yes	—
530	C₄²	C₂×D₄×C₇₃	1	4	yes	—
531	C₂³	—	2	2	no	—
532	C₂³	—	4	1	no	—
533	C₂³	—	4	1	no	—
534	C₂³	—	8	1	no	—
535	C₂³	—	8	2	no	—
536	C₂³	#120×C₇₃	1	1	yes	characteristic
537	C₂³	#120×C₇₃	1	1	yes	characteristic
538	C₂³	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
539	C₂³	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
540	C₂³	#124×C₇₃	1	1	yes	characteristic
541	C₂³	#124×C₇₃	1	1	yes	characteristic
542	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
543	Q₈	—	2	2	no	—
544	Q₈	—	2	2	no	—
545	Q₈	—	4	1	no	—
546	Q₈	—	4	1	no	—
547	Q₈	—	8	8	no	—
548	D₄	—	2	2	no	—
549	D₄	—	2	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	D₄	—	4	2	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	1	no	—
555	D₄	—	4	1	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	8	2	no	—
568	C₂×C₄	—	8	2	no	—
569	C₂×C₄	—	8	2	no	—
570	C₂×C₄	—	8	2	no	—
571	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
572	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
573	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
574	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
575	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
576	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
577	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
578	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
579	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
580	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
581	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
582	C₂×C₄	C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
583	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
584	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
585	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
586	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
587	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
588	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
589	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
590	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
591	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
592	C₂×C₄	#124×C₇₃	1	1	yes	characteristic
593	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
595	C₂×C₄	C₂²×Q₈×C₇₃	1	1	yes	characteristic
596	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
597	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
598	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
599	C₈	—	4	2	no	—
600	C₈	—	4	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	—	4	1	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	8	2	no	—
610	C₂²	—	8	2	no	—
611	C₂²	—	8	2	no	—
612	C₂²	#393×C₇₃	1	1	yes	characteristic
613	C₂²	#393×C₇₃	1	1	yes	characteristic
614	C₂²	#393×C₇₃	1	1	yes	characteristic
615	C₂²	#393×C₇₃	1	1	yes	characteristic
616	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
617	C₂²	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
618	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
619	C₄	—	4	4	no	—
620	C₄	—	4	4	no	—
621	C₄	—	4	4	no	—
622	C₄	—	4	2	no	—
623	C₄	—	8	2	no	—
624	C₄	#393×C₇₃	1	1	yes	characteristic
625	C₄	#393×C₇₃	1	1	yes	characteristic
626	C₄	#393×C₇₃	1	1	yes	characteristic
627	C₄	#393×C₇₃	1	1	yes	characteristic
628	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
629	C₄	C₂×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
630	C₄	C₂×#124×C₇₃	1	1	yes	characteristic
631	C₄	C₂×#124×C₇₃	1	1	yes	characteristic
632	C₂	—	2	1	no	—
633	C₂	—	2	1	no	—
634	C₂	—	2	1	no	—
635	C₂	—	2	1	no	—
636	C₂	—	2	1	no	—
637	C₂	—	2	1	no	—
638	C₂	—	2	1	no	—
639	C₂	—	8	2	no	—
640	C₂	C₂×#393×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₇₃	C₂×#124
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
socle	C₂×C₇₃	C₂×#393
prime radical	C₂²×#41×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₃ ◁ C₂³×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3458	C₂	semidirect
5. C₇₃×#2031	C₂	semidirect
6. C₂×#344×C₇₃	C₂	semidirect
7. C₇₃×#1733	C₂	semidirect
8. C₂×H(3,ℤ/4)×C₇₃	C₂	semidirect
18. #533×C₇₃	C₂²	semidirect
32. #344×C₇₃	C₂²	semidirect
33. #339×C₇₃	C₂²	semidirect
34. H(3,ℤ/4)×C₇₃	C₂²	semidirect
45. C₂×#41×C₇₃	Q₈	semidirect
47. C₂²×Q₈×C₇₃	Q₈	semidirect
49. C₂²×D₄×C₇₃	Q₈	semidirect
311. #23472	C₇₃	direct (N × H)
321. #3458	C₂×C₇₃	semidirect
325. #2031	C₂×C₇₃	semidirect
326. C₂×#344	C₂×C₇₃	semidirect
327. #1733	C₂×C₇₃	semidirect
328. C₂×H(3,ℤ/4)	C₂×C₇₃	semidirect
329. C₇₃	#23472	direct (N × H)
339. #533	C₂²×C₇₃	semidirect
353. #344	C₂²×C₇₃	semidirect
354. #339	C₂²×C₇₃	semidirect
355. H(3,ℤ/4)	C₂²×C₇₃	semidirect
366. C₂×#41	Q₈×C₇₃	semidirect
368. C₂²×Q₈	Q₈×C₇₃	semidirect
370. C₂²×D₄	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×#3458	2
C₂×#421×C₇₃	2
C₂×#410×C₇₃	2
C₇₃×#2031	2
C₂×#344×C₇₃	2
C₇₃×#1733	2
C₂×H(3,ℤ/4)×C₇₃	2
#23472	73

Subgroups — C73×#23472 #32932876

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#23472 #32932876