Subgroups — C₇₃×#25774 #32935178

Order 18688.

1760 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×SD₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#492×C₇₃	C₂	1	2	yes	maximal, complemented
3	C₂×#465×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#448×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#450×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇₃×#2434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2433	C₂	1	1	yes	maximal, characteristic
8	C₇₃×#2014	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2013	C₂	1	2	yes	maximal, complemented
10	C₇₃×#1968	C₂	1	2	yes	maximal, complemented
11	C₈×C₂²⋊C₄×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₇₃	—	2	8	no	—
15	C₂²×SD₁₆×C₇₃	—	2	4	no	—
16	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
17	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
18	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	—
19	C₂²×SD₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
20	C₂²×SD₁₆×C₇₃	C₂²	1	2	yes	complemented
21	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
23	C₂×#127×C₇₃	C₂²	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
25	C₂×#121×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×#120×C₇₃	—	2	2	no	—
27	#492×C₇₃	—	2	8	no	—
28	#465×C₇₃	—	2	4	no	—
29	#450×C₇₃	—	2	4	no	—
30	#448×C₇₃	—	2	4	no	—
31	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic, complemented
32	C₂×#103×C₇₃	C₂²	1	2	yes	complemented
33	C₂×#103×C₇₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×#102×C₇₃	C₂²	1	2	yes	—
35	C₂×#102×C₇₃	C₂²	1	1	yes	characteristic, complemented
36	C₂×C₂²⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₇₃	C₂²	1	2	yes	complemented
38	#395×C₇₃	—	2	2	no	—
39	#392×C₇₃	—	2	2	no	—
40	#391×C₇₃	C₂²	1	2	yes	complemented
41	#390×C₇₃	C₂²	1	2	yes	—
42	#385×C₇₃	—	2	2	no	—
43	C₄×C₂²⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
44	#336×C₇₃	C₂²	1	2	yes	complemented
45	C₂⁵×C₇₃	—	2	1	no	—
46	C₂²×Q₈×C₇₃	—	2	1	no	—
47	C₂²×Q₈×C₇₃	—	2	4	no	—
48	C₂²×Q₈×C₇₃	—	2	2	no	—
49	C₂²×Q₈×C₇₃	—	2	2	no	—
50	C₂²×Q₈×C₇₃	—	4	2	no	—
51	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
52	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₇₃	—	2	4	no	—
54	C₂²×D₄×C₇₃	—	2	1	no	—
55	C₂²×D₄×C₇₃	—	2	2	no	—
56	C₂²×D₄×C₇₃	—	2	2	no	—
57	C₂²×D₄×C₇₃	—	2	1	no	—
58	C₂²×D₄×C₇₃	—	2	4	no	—
59	C₂²×D₄×C₇₃	—	4	2	no	—
60	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
62	C₂³×C₄×C₇₃	—	2	1	no	—
63	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
64	C₂×SD₁₆×C₇₃	—	2	32	no	—
65	C₂×SD₁₆×C₇₃	—	2	4	no	—
66	C₂×SD₁₆×C₇₃	—	2	4	no	—
67	C₂×SD₁₆×C₇₃	—	2	4	no	—
68	C₂×SD₁₆×C₇₃	—	2	4	no	—
69	C₂×SD₁₆×C₇₃	—	2	4	no	—
70	C₂×SD₁₆×C₇₃	—	2	4	no	—
71	C₂×SD₁₆×C₇₃	—	2	4	no	—
72	C₂×SD₁₆×C₇₃	—	2	4	no	—
73	C₂×SD₁₆×C₇₃	—	2	4	no	—
74	C₂×SD₁₆×C₇₃	—	2	2	no	—
75	C₂×SD₁₆×C₇₃	—	2	4	no	—
76	C₂×SD₁₆×C₇₃	—	4	2	no	—
77	C₂×SD₁₆×C₇₃	—	4	2	no	—
78	C₂×SD₁₆×C₇₃	D₄	1	8	yes	complemented
79	C₂²×C₈×C₇₃	—	2	4	no	—
80	C₂²×C₈×C₇₃	D₄	1	4	yes	complemented
81	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
82	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₇₃	—	2	4	no	—
85	C₄⋊Q₈×C₇₃	—	4	2	no	—
86	#127×C₇₃	—	2	4	no	—
87	#127×C₇₃	—	4	2	no	—
88	C₂²⋊Q₈×C₇₃	—	2	2	no	—
89	C₂²⋊Q₈×C₇₃	—	2	2	no	—
90	#121×C₇₃	—	2	2	no	—
91	#121×C₇₃	—	2	2	no	—
92	#120×C₇₃	—	4	8	no	—
93	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
94	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₇₃	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
99	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
101	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
102	#106×C₇₃	—	2	2	no	—
103	#103×C₇₃	—	2	4	no	—
104	#103×C₇₃	—	2	2	no	—
105	#102×C₇₃	—	2	4	no	—
106	#102×C₇₃	—	2	2	no	—
107	C₂²⋊C₈×C₇₃	D₄	1	4	yes	complemented
108	C₄×C₈×C₇₃	—	2	4	no	—
109	#95×C₇₃	—	2	4	no	—
110	#95×C₇₃	D₄	1	2	yes	—
111	C₂⁴×C₇₃	—	2	2	no	—
112	C₂⁴×C₇₃	—	2	1	no	—
113	C₂⁴×C₇₃	—	4	4	no	—
114	C₂⁴×C₇₃	—	4	2	no	—
115	C₂⁴×C₇₃	—	4	4	no	—
116	C₂⁴×C₇₃	—	8	2	no	—
117	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₇₃	—	2	2	no	—
119	C₂×Q₈×C₇₃	—	2	8	no	—
120	C₂×Q₈×C₇₃	—	2	2	no	—
121	C₂×Q₈×C₇₃	—	2	2	no	—
122	C₂×Q₈×C₇₃	—	2	2	no	—
123	C₂×Q₈×C₇₃	—	2	1	no	—
124	C₂×Q₈×C₇₃	—	2	1	no	—
125	C₂×Q₈×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	2	no	—
128	C₂×Q₈×C₇₃	—	4	4	no	—
129	C₂×Q₈×C₇₃	—	4	8	no	—
130	C₂×Q₈×C₇₃	—	4	4	no	—
131	C₂×Q₈×C₇₃	—	4	2	no	—
132	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
133	C₂×D₄×C₇₃	—	2	8	no	—
134	C₂×D₄×C₇₃	—	2	2	no	—
135	C₂×D₄×C₇₃	—	2	2	no	—
136	C₂×D₄×C₇₃	—	2	2	no	—
137	C₂×D₄×C₇₃	—	2	1	no	—
138	C₂×D₄×C₇₃	—	2	1	no	—
139	C₂×D₄×C₇₃	—	2	2	no	—
140	C₂×D₄×C₇₃	—	2	2	no	—
141	C₂×D₄×C₇₃	—	2	2	no	—
142	C₂×D₄×C₇₃	—	2	2	no	—
143	C₂×D₄×C₇₃	—	4	8	no	—
144	C₂×D₄×C₇₃	—	4	4	no	—
145	C₂×D₄×C₇₃	—	4	4	no	—
146	C₂×D₄×C₇₃	—	4	8	no	—
147	C₂×D₄×C₇₃	—	4	2	no	—
148	C₂×D₄×C₇₃	—	4	4	no	—
149	C₂×D₄×C₇₃	—	4	2	no	—
150	C₂×D₄×C₇₃	—	4	8	no	—
151	C₂×D₄×C₇₃	—	8	4	no	—
152	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₇₃	—	2	2	no	—
154	C₂²×C₄×C₇₃	—	2	2	no	—
155	C₂²×C₄×C₇₃	—	2	2	no	—
156	C₂²×C₄×C₇₃	—	2	1	no	—
157	C₂²×C₄×C₇₃	—	2	1	no	—
158	C₂²×C₄×C₇₃	—	2	1	no	—
159	C₂²×C₄×C₇₃	—	4	4	no	—
160	C₂²×C₄×C₇₃	—	4	2	no	—
161	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
165	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
166	SD₁₆×C₇₃	—	2	16	no	—
167	SD₁₆×C₇₃	—	2	16	no	—
168	SD₁₆×C₇₃	—	4	8	no	—
169	SD₁₆×C₇₃	—	4	8	no	—
170	SD₁₆×C₇₃	—	4	4	no	—
171	C₂×C₈×C₇₃	—	2	2	no	—
172	C₂×C₈×C₇₃	—	2	2	no	—
173	C₂×C₈×C₇₃	—	2	2	no	—
174	C₂×C₈×C₇₃	—	2	8	no	—
175	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
176	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
178	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₇₃	—	2	1	no	—
180	C₄⋊C₄×C₇₃	—	2	1	no	—
181	C₄⋊C₄×C₇₃	—	2	1	no	—
182	C₄⋊C₄×C₇₃	—	2	1	no	—
183	C₄⋊C₄×C₇₃	—	4	8	no	—
184	C₄⋊C₄×C₇₃	—	4	2	no	—
185	C₂²⋊C₄×C₇₃	—	4	2	no	—
186	C₂²⋊C₄×C₇₃	—	4	2	no	—
187	C₂²⋊C₄×C₇₃	—	4	8	no	—
188	C₂²⋊C₄×C₇₃	SD₁₆	1	8	yes	complemented
189	C₄²×C₇₃	—	2	2	no	—
190	C₄²×C₇₃	—	2	2	no	—
191	C₂³×C₇₃	—	2	2	no	—
192	C₂³×C₇₃	—	2	2	no	—
193	C₂³×C₇₃	—	2	4	no	—
194	C₂³×C₇₃	—	4	8	no	—
195	C₂³×C₇₃	—	4	2	no	—
196	C₂³×C₇₃	—	4	2	no	—
197	C₂³×C₇₃	—	4	4	no	—
198	C₂³×C₇₃	—	4	4	no	—
199	C₂³×C₇₃	—	4	1	no	—
200	C₂³×C₇₃	—	4	2	no	—
201	C₂³×C₇₃	—	4	2	no	—
202	C₂³×C₇₃	—	4	2	no	—
203	C₂³×C₇₃	—	8	16	no	—
204	C₂³×C₇₃	—	8	4	no	—
205	C₂³×C₇₃	—	8	4	no	—
206	C₂³×C₇₃	#127	1	2	yes	—
207	C₂³×C₇₃	C₂×SD₁₆	1	4	yes	—
208	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₇₃	—	2	4	no	—
210	Q₈×C₇₃	—	2	4	no	—
211	Q₈×C₇₃	—	4	8	no	—
212	Q₈×C₇₃	—	4	2	no	—
213	Q₈×C₇₃	—	4	2	no	—
214	Q₈×C₇₃	—	4	1	no	—
215	Q₈×C₇₃	—	4	1	no	—
216	Q₈×C₇₃	—	4	2	no	—
217	D₄×C₇₃	—	2	4	no	—
218	D₄×C₇₃	—	2	4	no	—
219	D₄×C₇₃	—	4	8	no	—
220	D₄×C₇₃	—	4	1	no	—
221	D₄×C₇₃	—	4	2	no	—
222	D₄×C₇₃	—	4	1	no	—
223	D₄×C₇₃	—	4	2	no	—
224	D₄×C₇₃	—	4	2	no	—
225	D₄×C₇₃	—	8	16	no	—
226	D₄×C₇₃	—	8	4	no	—
227	C₂×C₄×C₇₃	—	2	4	no	—
228	C₂×C₄×C₇₃	—	2	2	no	—
229	C₂×C₄×C₇₃	—	2	4	no	—
230	C₂×C₄×C₇₃	—	2	2	no	—
231	C₂×C₄×C₇₃	—	2	2	no	—
232	C₂×C₄×C₇₃	—	2	4	no	—
233	C₂×C₄×C₇₃	—	2	4	no	—
234	C₂×C₄×C₇₃	—	4	8	no	—
235	C₂×C₄×C₇₃	—	4	2	no	—
236	C₂×C₄×C₇₃	—	4	2	no	—
237	C₂×C₄×C₇₃	—	4	1	no	—
238	C₂×C₄×C₇₃	—	4	1	no	—
239	C₂×C₄×C₇₃	—	4	1	no	—
240	C₂×C₄×C₇₃	—	4	2	no	—
241	C₂×C₄×C₇₃	—	4	2	no	—
242	C₂×C₄×C₇₃	—	4	2	no	—
243	C₂×C₄×C₇₃	#127	1	2	yes	—
244	C₂×C₄×C₇₃	C₂×SD₁₆	1	8	yes	complemented
245	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
249	C₈×C₇₃	—	2	2	no	—
250	C₈×C₇₃	—	2	4	no	—
251	C₈×C₇₃	#120	1	4	yes	complemented
252	C₂²×C₇₃	—	2	2	no	—
253	C₂²×C₇₃	—	2	2	no	—
254	C₂²×C₇₃	—	2	8	no	—
255	C₂²×C₇₃	—	4	4	no	—
256	C₂²×C₇₃	—	4	8	no	—
257	C₂²×C₇₃	—	8	16	no	—
258	C₂²×C₇₃	—	8	2	no	—
259	C₂²×C₇₃	—	8	2	no	—
260	C₂²×C₇₃	—	8	4	no	—
261	C₂²×C₇₃	—	8	1	no	—
262	C₂²×C₇₃	—	8	1	no	—
263	C₂²×C₇₃	—	8	1	no	—
264	C₂²×C₇₃	—	8	4	no	—
265	C₂²×C₇₃	#492	1	4	yes	complemented
266	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
267	C₂²×C₇₃	D₄²	1	2	yes	—
268	C₂²×C₇₃	C₂²×SD₁₆	1	2	yes	—
269	C₂²×C₇₃	#577	1	2	yes	—
270	C₄×C₇₃	—	2	2	no	—
271	C₄×C₇₃	—	2	8	no	—
272	C₄×C₇₃	—	4	4	no	—
273	C₄×C₇₃	—	8	1	no	—
274	C₄×C₇₃	—	8	1	no	—
275	C₄×C₇₃	—	8	1	no	—
276	C₄×C₇₃	C₂×#120	1	1	yes	characteristic
277	C₄×C₇₃	#535	1	1	yes	characteristic
278	C₄×C₇₃	D₄²	1	2	yes	—
279	#25774	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂×C₇₃	—	2	4	no	—
281	C₂×C₇₃	—	8	4	no	—
282	C₂×C₇₃	—	16	1	no	—
283	C₂×C₇₃	#2433	1	1	yes	characteristic
284	C₂×C₇₃	C₂×#492	1	1	yes	characteristic
285	C₂×C₇₃	#3154	1	1	yes	characteristic
286	C₂×C₇₃	D₄×SD₁₆	1	4	yes	—
287	C₂³×SD₁₆	C₂×C₇₃	1	1	yes	characteristic, complemented
288	C₂×#492	C₂×C₇₃	1	2	yes	complemented
289	C₂×#465	C₂×C₇₃	1	1	yes	characteristic, complemented
290	C₂×#448	C₂×C₇₃	1	1	yes	characteristic, complemented
291	C₂×#450	C₂×C₇₃	1	1	yes	characteristic, complemented
292	#2434	C₂×C₇₃	1	1	yes	characteristic, complemented
293	#2433	C₂×C₇₃	1	1	yes	characteristic
294	#2014	C₂×C₇₃	1	2	yes	complemented
295	#2013	C₂×C₇₃	1	2	yes	complemented
296	#1968	C₂×C₇₃	1	2	yes	complemented
297	C₈×C₂²⋊C₄	C₂×C₇₃	1	1	yes	characteristic, complemented
298	C₇₃	#25774	1	1	yes	characteristic, direct product factor, Sylow
299	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
300	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
301	C₂²×SD₁₆	—	2	8	no	—
302	C₂²×SD₁₆	—	2	4	no	—
303	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
304	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
305	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	—
306	C₂²×SD₁₆	C₂²×C₇₃	1	1	yes	characteristic, complemented
307	C₂²×SD₁₆	C₂²×C₇₃	1	2	yes	complemented
308	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	complemented
310	C₂×#127	C₂²×C₇₃	1	2	yes	—
311	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
312	C₂×#121	C₂²×C₇₃	1	1	yes	characteristic
313	C₂×#120	—	2	2	no	—
314	#492	—	2	8	no	—
315	#465	—	2	4	no	—
316	#450	—	2	4	no	—
317	#448	—	2	4	no	—
318	C₂×#106	C₂²×C₇₃	1	1	yes	characteristic, complemented
319	C₂×#103	C₂²×C₇₃	1	2	yes	complemented
320	C₂×#103	C₂²×C₇₃	1	1	yes	characteristic, complemented
321	C₂×#102	C₂²×C₇₃	1	2	yes	—
322	C₂×#102	C₂²×C₇₃	1	1	yes	characteristic, complemented
323	C₂×C₂²⋊C₈	C₂²×C₇₃	1	1	yes	characteristic
324	C₂×C₄×C₈	C₂²×C₇₃	1	2	yes	complemented
325	#395	—	2	2	no	—
326	#392	—	2	2	no	—
327	#391	C₂²×C₇₃	1	2	yes	complemented
328	#390	C₂²×C₇₃	1	2	yes	—
329	#385	—	2	2	no	—
330	C₄×C₂²⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
331	#336	C₂²×C₇₃	1	2	yes	complemented
332	C₂⁵	—	2	1	no	—
333	C₂²×Q₈	—	2	1	no	—
334	C₂²×Q₈	—	2	4	no	—
335	C₂²×Q₈	—	2	2	no	—
336	C₂²×Q₈	—	2	2	no	—
337	C₂²×Q₈	—	4	2	no	—
338	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
339	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
340	C₂²×D₄	—	2	4	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	2	no	—
343	C₂²×D₄	—	2	2	no	—
344	C₂²×D₄	—	2	1	no	—
345	C₂²×D₄	—	2	4	no	—
346	C₂²×D₄	—	4	2	no	—
347	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
348	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
351	C₂×SD₁₆	—	2	32	no	—
352	C₂×SD₁₆	—	2	4	no	—
353	C₂×SD₁₆	—	2	4	no	—
354	C₂×SD₁₆	—	2	4	no	—
355	C₂×SD₁₆	—	2	4	no	—
356	C₂×SD₁₆	—	2	4	no	—
357	C₂×SD₁₆	—	2	4	no	—
358	C₂×SD₁₆	—	2	4	no	—
359	C₂×SD₁₆	—	2	4	no	—
360	C₂×SD₁₆	—	2	4	no	—
361	C₂×SD₁₆	—	2	2	no	—
362	C₂×SD₁₆	—	2	4	no	—
363	C₂×SD₁₆	—	4	2	no	—
364	C₂×SD₁₆	—	4	2	no	—
365	C₂×SD₁₆	D₄×C₇₃	1	8	yes	complemented
366	C₂²×C₈	—	2	4	no	—
367	C₂²×C₈	D₄×C₇₃	1	4	yes	complemented
368	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
370	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
371	C₄⋊Q₈	—	2	4	no	—
372	C₄⋊Q₈	—	4	2	no	—
373	#127	—	2	4	no	—
374	#127	—	4	2	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	#121	—	2	2	no	—
378	#121	—	2	2	no	—
379	#120	—	4	8	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
383	C₂×C₄⋊C₄	C₂³×C₇₃	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	4	no	—
386	C₂×C₂²⋊C₄	—	2	1	no	—
387	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
388	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
389	#106	—	2	2	no	—
390	#103	—	2	4	no	—
391	#103	—	2	2	no	—
392	#102	—	2	4	no	—
393	#102	—	2	2	no	—
394	C₂²⋊C₈	D₄×C₇₃	1	4	yes	complemented
395	C₄×C₈	—	2	4	no	—
396	#95	—	2	4	no	—
397	#95	D₄×C₇₃	1	2	yes	—
398	C₂⁴	—	2	2	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	—	4	4	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	4	no	—
403	C₂⁴	—	8	2	no	—
404	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	8	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	—	4	4	no	—
416	C₂×Q₈	—	4	8	no	—
417	C₂×Q₈	—	4	4	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	4	8	no	—
431	C₂×D₄	—	4	4	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	—	4	2	no	—
435	C₂×D₄	—	4	4	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	8	4	no	—
439	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	4	4	no	—
447	C₂²×C₄	—	4	2	no	—
448	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
451	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
452	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
453	SD₁₆	—	2	16	no	—
454	SD₁₆	—	2	16	no	—
455	SD₁₆	—	4	8	no	—
456	SD₁₆	—	4	8	no	—
457	SD₁₆	—	4	4	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	8	no	—
462	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
463	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
464	C₂×C₈	C₂×D₄×C₇₃	1	4	yes	—
465	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	4	8	no	—
471	C₄⋊C₄	—	4	2	no	—
472	C₂²⋊C₄	—	4	2	no	—
473	C₂²⋊C₄	—	4	2	no	—
474	C₂²⋊C₄	—	4	8	no	—
475	C₂²⋊C₄	SD₁₆×C₇₃	1	8	yes	complemented
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	4	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	4	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	4	2	no	—
489	C₂³	—	4	2	no	—
490	C₂³	—	8	16	no	—
491	C₂³	—	8	4	no	—
492	C₂³	—	8	4	no	—
493	C₂³	#127×C₇₃	1	2	yes	—
494	C₂³	C₂×SD₁₆×C₇₃	1	4	yes	—
495	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
496	Q₈	—	2	4	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	4	8	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	4	2	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	2	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	4	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	1	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	8	16	no	—
513	D₄	—	8	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	4	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	4	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	8	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	#127×C₇₃	1	2	yes	—
531	C₂×C₄	C₂×SD₁₆×C₇₃	1	8	yes	complemented
532	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
534	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
535	C₂×C₄	H(5,𝔽₂)×C₇₃	1	2	yes	—
536	C₈	—	2	2	no	—
537	C₈	—	2	4	no	—
538	C₈	#120×C₇₃	1	4	yes	complemented
539	C₂²	—	2	8	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	4	8	no	—
543	C₂²	—	4	4	no	—
544	C₂²	—	8	16	no	—
545	C₂²	—	8	4	no	—
546	C₂²	—	8	2	no	—
547	C₂²	—	8	2	no	—
548	C₂²	—	8	4	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	#492×C₇₃	1	4	yes	complemented
553	C₂²	C₂×#127×C₇₃	1	1	yes	characteristic
554	C₂²	D₄²×C₇₃	1	2	yes	—
555	C₂²	C₂²×SD₁₆×C₇₃	1	2	yes	—
556	C₂²	#577×C₇₃	1	2	yes	—
557	C₄	—	2	8	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	4	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	C₂×#120×C₇₃	1	1	yes	characteristic
564	C₄	#535×C₇₃	1	1	yes	characteristic
565	C₄	D₄²×C₇₃	1	2	yes	—
566	C₂	—	2	4	no	—
567	C₂	—	8	4	no	—
568	C₂	—	16	1	no	—
569	C₂	C₇₃×#2433	1	1	yes	characteristic
570	C₂	C₂×#492×C₇₃	1	1	yes	characteristic
571	C₂	C₇₃×#3154	1	1	yes	characteristic
572	C₂	D₄×SD₁₆×C₇₃	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₇₃×#2433	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₄×C₂²⋊C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂³×SD₁₆×C₇₃	C₂	semidirect
2. C₂×#492×C₇₃	C₂	semidirect
3. C₂×#465×C₇₃	C₂	semidirect
4. C₂×#448×C₇₃	C₂	semidirect
5. C₂×#450×C₇₃	C₂	semidirect
6. C₇₃×#2434	C₂	semidirect
8. C₇₃×#2014	C₂	semidirect
9. C₇₃×#2013	C₂	semidirect
10. C₇₃×#1968	C₂	semidirect
11. C₈×C₂²⋊C₄×C₇₃	C₂	semidirect
19. C₂²×SD₁₆×C₇₃	C₂²	semidirect
20. C₂²×SD₁₆×C₇₃	C₂²	semidirect
22. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
31. C₂×#106×C₇₃	C₂²	semidirect
32. C₂×#103×C₇₃	C₂²	semidirect
33. C₂×#103×C₇₃	C₂²	semidirect
35. C₂×#102×C₇₃	C₂²	semidirect
37. C₂×C₄×C₈×C₇₃	C₂²	semidirect
40. #391×C₇₃	C₂²	semidirect
44. #336×C₇₃	C₂²	semidirect
78. C₂×SD₁₆×C₇₃	D₄	semidirect
80. C₂²×C₈×C₇₃	D₄	semidirect
107. C₂²⋊C₈×C₇₃	D₄	semidirect
188. C₂²⋊C₄×C₇₃	SD₁₆	semidirect
244. C₂×C₄×C₇₃	C₂×SD₁₆	semidirect
251. C₈×C₇₃	#120	semidirect
265. C₂²×C₇₃	#492	semidirect
279. #25774	C₇₃	direct (N × H)
287. C₂³×SD₁₆	C₂×C₇₃	semidirect
288. C₂×#492	C₂×C₇₃	semidirect
289. C₂×#465	C₂×C₇₃	semidirect
290. C₂×#448	C₂×C₇₃	semidirect
291. C₂×#450	C₂×C₇₃	semidirect
292. #2434	C₂×C₇₃	semidirect
294. #2014	C₂×C₇₃	semidirect
295. #2013	C₂×C₇₃	semidirect
296. #1968	C₂×C₇₃	semidirect
297. C₈×C₂²⋊C₄	C₂×C₇₃	semidirect
298. C₇₃	#25774	direct (N × H)
306. C₂²×SD₁₆	C₂²×C₇₃	semidirect
307. C₂²×SD₁₆	C₂²×C₇₃	semidirect
309. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
318. C₂×#106	C₂²×C₇₃	semidirect
319. C₂×#103	C₂²×C₇₃	semidirect
320. C₂×#103	C₂²×C₇₃	semidirect
322. C₂×#102	C₂²×C₇₃	semidirect
324. C₂×C₄×C₈	C₂²×C₇₃	semidirect
327. #391	C₂²×C₇₃	semidirect
331. #336	C₂²×C₇₃	semidirect
365. C₂×SD₁₆	D₄×C₇₃	semidirect
367. C₂²×C₈	D₄×C₇₃	semidirect
394. C₂²⋊C₈	D₄×C₇₃	semidirect
475. C₂²⋊C₄	SD₁₆×C₇₃	semidirect
531. C₂×C₄	C₂×SD₁₆×C₇₃	semidirect
538. C₈	#120×C₇₃	semidirect
552. C₂²	#492×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂³×SD₁₆×C₇₃	2
C₂×#492×C₇₃	2
C₂×#465×C₇₃	2
C₂×#448×C₇₃	2
C₂×#450×C₇₃	2
C₇₃×#2434	2
C₇₃×#2433	2
C₇₃×#2014	2
C₇₃×#2013	2
C₇₃×#1968	2
C₈×C₂²⋊C₄×C₇₃	2
#25774	73

Subgroups — C73×#25774 #32935178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#25774 #32935178