Subgroups — C₇₃×#60425 #32969829

Order 18688.

2750 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₇₃	C₂	1	2	yes	maximal, complemented
2	C₇₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#520×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#3046	C₂	1	8	yes	maximal, complemented
5	C₇₃×#3045	C₂	1	8	yes	maximal, complemented
6	C₇₃×#3037	C₂	1	4	yes	maximal, complemented
7	C₇₃×#3036	C₂	1	4	yes	maximal, complemented
8	C₇₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#417×C₇₃	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₇₃	C₂²	1	2	yes	—
11	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
12	#575×C₇₃	—	2	16	no	—
13	C₂×#137×C₇₃	C₂²	1	4	yes	complemented
14	C₂×#137×C₇₃	C₂²	1	4	yes	complemented
15	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	4	yes	complemented
16	C₂×AGL(1,ℤ/8)×C₇₃	C₂²	1	4	yes	complemented
17	C₂×#135×C₇₃	C₂²	1	8	yes	—
18	C₂²×M₁₆×C₇₃	C₂²	1	2	yes	—
19	#537×C₇₃	—	2	1	no	—
20	#537×C₇₃	—	2	1	no	—
21	#536×C₇₃	C₂²	1	4	yes	complemented
22	#535×C₇₃	C₂²	1	4	yes	complemented
23	#534×C₇₃	—	2	2	no	—
24	#532×C₇₃	C₂²	1	4	yes	—
25	#525×C₇₃	—	2	4	no	—
26	#520×C₇₃	—	2	4	no	—
27	#520×C₇₃	C₂²	1	8	yes	complemented
28	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	complemented
29	C₂×C₄×D₄×C₇₃	—	2	2	no	—
30	C₂×C₄×D₄×C₇₃	C₂²	1	2	yes	complemented
31	C₂×#117×C₇₃	—	2	1	no	—
32	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₇₃	—	2	1	no	—
34	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
35	#464×C₇₃	C₂²	1	16	yes	complemented
36	#463×C₇₃	C₂²	1	16	yes	complemented
37	#462×C₇₃	C₂²	1	8	yes	complemented
38	#461×C₇₃	C₂²	1	8	yes	complemented
39	#460×C₇₃	C₂²	1	8	yes	complemented
40	#459×C₇₃	C₂²	1	8	yes	complemented
41	#424×C₇₃	C₂²	1	8	yes	complemented
42	#423×C₇₃	C₂²	1	4	yes	complemented
43	#417×C₇₃	C₂²	1	8	yes	complemented
44	#417×C₇₃	C₂²	1	8	yes	complemented
45	C₂×#103×C₇₃	C₂²	1	4	yes	complemented
46	C₂×#102×C₇₃	C₂²	1	4	yes	complemented
47	C₂×#41×C₇₃	—	2	2	no	—
48	C₂×#41×C₇₃	—	2	2	no	—
49	C₂×#41×C₇₃	—	2	2	no	—
50	C₂×#41×C₇₃	—	2	4	no	—
51	C₂×#41×C₇₃	—	2	8	no	—
52	C₂×#41×C₇₃	—	2	8	no	—
53	C₂×#41×C₇₃	D₄	1	8	yes	complemented
54	C₂×#41×C₇₃	C₂³	1	4	yes	—
55	C₂×#41×C₇₃	C₂³	1	4	yes	—
56	C₂×#41×C₇₃	C₂³	1	4	yes	—
57	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₇₃	—	2	1	no	—
60	C₂²×D₄×C₇₃	—	2	2	no	—
61	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
62	C₂²×D₄×C₇₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₇₃	—	2	1	no	—
64	C₂³×C₄×C₇₃	—	2	1	no	—
65	C₂³×C₄×C₇₃	—	2	2	no	—
66	C₂³×C₄×C₇₃	—	2	2	no	—
67	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
68	#137×C₇₃	—	2	16	no	—
69	#137×C₇₃	—	2	16	no	—
70	AGL(1,ℤ/8)×C₇₃	—	2	16	no	—
71	AGL(1,ℤ/8)×C₇₃	—	2	16	no	—
72	#135×C₇₃	—	2	32	no	—
73	C₂×Q₁₆×C₇₃	C₂³	1	8	yes	—
74	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
75	C₂×SD₁₆×C₇₃	C₂³	1	8	yes	—
76	C₂×D₈×C₇₃	C₂³	1	8	yes	—
77	C₂×M₁₆×C₇₃	—	2	8	no	—
78	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
79	C₂×M₁₆×C₇₃	C₂³	1	4	yes	—
80	C₂²×C₈×C₇₃	C₂³	1	4	yes	—
81	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
82	#127×C₇₃	C₂³	1	4	yes	—
83	#124×C₇₃	C₂³	1	8	yes	—
84	#123×C₇₃	—	2	8	no	—
85	C₂²⋊Q₈×C₇₃	—	2	4	no	—
86	C₂²⋊Q₈×C₇₃	—	2	4	no	—
87	#121×C₇₃	—	2	4	no	—
88	#121×C₇₃	—	2	4	no	—
89	#121×C₇₃	—	2	4	no	—
90	#121×C₇₃	—	2	4	no	—
91	#120×C₇₃	—	2	8	no	—
92	C₄×Q₈×C₇₃	—	2	4	no	—
93	C₄×Q₈×C₇₃	C₂³	1	8	yes	—
94	C₄×D₄×C₇₃	—	2	16	no	—
95	C₄×D₄×C₇₃	—	2	4	no	—
96	C₄×D₄×C₇₃	—	2	4	no	—
97	C₄×D₄×C₇₃	—	2	4	no	—
98	C₄×D₄×C₇₃	C₂³	1	8	yes	—
99	#117×C₇₃	—	2	8	no	—
100	#117×C₇₃	D₄	1	4	yes	—
101	#117×C₇₃	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
103	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
104	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
105	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
106	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
110	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
111	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
112	C₂×C₄²×C₇₃	—	2	2	no	—
113	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
114	C₄⋊C₈×C₇₃	C₂³	1	8	yes	—
115	C₄⋊C₈×C₇₃	C₂³	1	8	yes	—
116	#103×C₇₃	C₂³	1	16	yes	—
117	#102×C₇₃	C₂³	1	16	yes	—
118	C₂⁴×C₇₃	—	2	1	no	—
119	C₂⁴×C₇₃	—	2	2	no	—
120	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
121	#41×C₇₃	—	2	16	no	—
122	#41×C₇₃	—	2	8	no	—
123	#41×C₇₃	—	2	8	no	—
124	#41×C₇₃	—	2	8	no	—
125	#41×C₇₃	—	2	8	no	—
126	#41×C₇₃	—	2	8	no	—
127	#41×C₇₃	—	4	8	no	—
128	#41×C₇₃	—	4	8	no	—
129	#41×C₇₃	C₂×D₄	1	16	yes	—
130	C₂×Q₈×C₇₃	—	2	1	no	—
131	C₂×Q₈×C₇₃	—	2	2	no	—
132	C₂×Q₈×C₇₃	—	2	2	no	—
133	C₂×Q₈×C₇₃	—	2	4	no	—
134	C₂×Q₈×C₇₃	—	2	4	no	—
135	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
136	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
137	C₂×Q₈×C₇₃	C₂⁴	1	2	yes	—
138	C₂×D₄×C₇₃	—	2	8	no	—
139	C₂×D₄×C₇₃	—	2	4	no	—
140	C₂×D₄×C₇₃	—	2	4	no	—
141	C₂×D₄×C₇₃	—	2	4	no	—
142	C₂×D₄×C₇₃	—	2	1	no	—
143	C₂×D₄×C₇₃	—	2	4	no	—
144	C₂×D₄×C₇₃	—	2	2	no	—
145	C₂×D₄×C₇₃	—	2	4	no	—
146	C₂×D₄×C₇₃	—	2	4	no	—
147	C₂×D₄×C₇₃	—	2	2	no	—
148	C₂×D₄×C₇₃	—	2	4	no	—
149	C₂×D₄×C₇₃	—	4	8	no	—
150	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
151	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
152	C₂×D₄×C₇₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₇₃	—	2	1	no	—
154	C₂²×C₄×C₇₃	—	2	8	no	—
155	C₂²×C₄×C₇₃	—	2	4	no	—
156	C₂²×C₄×C₇₃	—	2	2	no	—
157	C₂²×C₄×C₇₃	—	2	2	no	—
158	C₂²×C₄×C₇₃	—	2	4	no	—
159	C₂²×C₄×C₇₃	—	2	4	no	—
160	C₂²×C₄×C₇₃	—	2	4	no	—
161	C₂²×C₄×C₇₃	—	2	8	no	—
162	C₂²×C₄×C₇₃	—	4	8	no	—
163	C₂²×C₄×C₇₃	—	8	4	no	—
164	C₂²×C₄×C₇₃	—	8	2	no	—
165	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₇₃	#41	1	4	yes	—
171	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
173	Q₁₆×C₇₃	—	2	16	no	—
174	SD₁₆×C₇₃	—	2	16	no	—
175	SD₁₆×C₇₃	—	2	16	no	—
176	D₈×C₇₃	—	2	16	no	—
177	M₁₆×C₇₃	—	2	8	no	—
178	M₁₆×C₇₃	—	2	8	no	—
179	C₂×C₈×C₇₃	—	2	8	no	—
180	C₂×C₈×C₇₃	C₂⁴	1	8	yes	—
181	C₄⋊C₄×C₇₃	—	2	4	no	—
182	C₄⋊C₄×C₇₃	—	2	8	no	—
183	C₄⋊C₄×C₇₃	—	2	2	no	—
184	C₄⋊C₄×C₇₃	—	2	4	no	—
185	C₄⋊C₄×C₇₃	—	2	4	no	—
186	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
187	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
188	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
189	C₂²⋊C₄×C₇₃	—	2	8	no	—
190	C₂²⋊C₄×C₇₃	—	2	8	no	—
191	C₂²⋊C₄×C₇₃	—	2	8	no	—
192	C₂²⋊C₄×C₇₃	C₂×D₄	1	8	yes	—
193	C₄²×C₇₃	—	2	8	no	—
194	C₄²×C₇₃	C₂×D₄	1	4	yes	—
195	C₄²×C₇₃	C₂⁴	1	4	yes	—
196	C₂³×C₇₃	—	2	4	no	—
197	C₂³×C₇₃	—	2	2	no	—
198	C₂³×C₇₃	—	2	4	no	—
199	C₂³×C₇₃	—	4	1	no	—
200	C₂³×C₇₃	—	4	1	no	—
201	C₂³×C₇₃	—	4	2	no	—
202	C₂³×C₇₃	—	4	2	no	—
203	C₂³×C₇₃	—	4	4	no	—
204	C₂³×C₇₃	—	8	2	no	—
205	C₂³×C₇₃	—	8	2	no	—
206	C₂³×C₇₃	#121	1	4	yes	—
207	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
208	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₇₃	—	2	4	no	—
210	Q₈×C₇₃	—	2	2	no	—
211	Q₈×C₇₃	—	2	4	no	—
212	Q₈×C₇₃	—	2	4	no	—
213	Q₈×C₇₃	—	4	4	no	—
214	Q₈×C₇₃	C₂²×D₄	1	4	yes	—
215	D₄×C₇₃	—	2	16	no	—
216	D₄×C₇₃	—	2	4	no	—
217	D₄×C₇₃	—	2	4	no	—
218	D₄×C₇₃	—	2	2	no	—
219	D₄×C₇₃	—	2	4	no	—
220	D₄×C₇₃	—	4	8	no	—
221	D₄×C₇₃	—	4	8	no	—
222	D₄×C₇₃	—	4	4	no	—
223	D₄×C₇₃	—	8	4	no	—
224	D₄×C₇₃	—	8	4	no	—
225	D₄×C₇₃	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₇₃	—	2	4	no	—
227	C₂×C₄×C₇₃	—	2	2	no	—
228	C₂×C₄×C₇₃	—	2	16	no	—
229	C₂×C₄×C₇₃	—	2	4	no	—
230	C₂×C₄×C₇₃	—	2	4	no	—
231	C₂×C₄×C₇₃	—	4	2	no	—
232	C₂×C₄×C₇₃	—	4	2	no	—
233	C₂×C₄×C₇₃	—	4	4	no	—
234	C₂×C₄×C₇₃	—	4	4	no	—
235	C₂×C₄×C₇₃	—	4	8	no	—
236	C₂×C₄×C₇₃	—	4	8	no	—
237	C₂×C₄×C₇₃	—	8	8	no	—
238	C₂×C₄×C₇₃	—	8	4	no	—
239	C₂×C₄×C₇₃	#121	1	4	yes	—
240	C₂×C₄×C₇₃	#121	1	8	yes	—
241	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
242	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
243	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
245	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
246	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₇₃	C₂×#41	1	4	yes	—
248	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
249	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
250	C₈×C₇₃	—	2	8	no	—
251	C₂²×C₇₃	—	2	1	no	—
252	C₂²×C₇₃	—	2	2	no	—
253	C₂²×C₇₃	—	2	1	no	—
254	C₂²×C₇₃	—	2	2	no	—
255	C₂²×C₇₃	—	2	4	no	—
256	C₂²×C₇₃	—	4	4	no	—
257	C₂²×C₇₃	—	4	8	no	—
258	C₂²×C₇₃	—	4	2	no	—
259	C₂²×C₇₃	—	4	2	no	—
260	C₂²×C₇₃	—	4	4	no	—
261	C₂²×C₇₃	—	4	4	no	—
262	C₂²×C₇₃	—	4	4	no	—
263	C₂²×C₇₃	—	8	8	no	—
264	C₂²×C₇₃	C₂×#121	1	2	yes	—
265	C₂²×C₇₃	C₂×#121	1	4	yes	—
266	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
267	C₄×C₇₃	—	2	4	no	—
268	C₄×C₇₃	—	2	4	no	—
269	C₄×C₇₃	—	2	4	no	—
270	C₄×C₇₃	—	4	4	no	—
271	C₄×C₇₃	—	4	4	no	—
272	C₄×C₇₃	C₂×#121	1	4	yes	—
273	C₄×C₇₃	C₂×#121	1	2	yes	—
274	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
275	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
276	#60425	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
277	C₂×C₇₃	—	2	2	no	—
278	C₂×C₇₃	—	2	4	no	—
279	C₂×C₇₃	—	4	4	no	—
280	C₂×C₇₃	—	8	4	no	—
281	C₂×C₇₃	C₂²×#121	1	1	yes	characteristic
282	C₂×C₇₃	#3585	1	1	yes	characteristic
283	C₂×C₇₃	#3586	1	1	yes	characteristic
284	C₂×#575	C₂×C₇₃	1	2	yes	complemented
285	#3449	C₂×C₇₃	1	1	yes	characteristic, complemented
286	C₂×#520	C₂×C₇₃	1	1	yes	characteristic, complemented
287	#3046	C₂×C₇₃	1	8	yes	complemented
288	#3045	C₂×C₇₃	1	8	yes	complemented
289	#3037	C₂×C₇₃	1	4	yes	complemented
290	#3036	C₂×C₇₃	1	4	yes	complemented
291	#2905	C₂×C₇₃	1	1	yes	characteristic, complemented
292	C₂×#417	C₂×C₇₃	1	2	yes	complemented
293	C₇₃	#60425	1	1	yes	characteristic, direct product factor, Sylow
294	C₂²×#41	C₂²×C₇₃	1	2	yes	—
295	C₂²×#41	C₂²×C₇₃	1	1	yes	characteristic
296	#575	—	2	16	no	—
297	C₂×#137	C₂²×C₇₃	1	4	yes	complemented
298	C₂×#137	C₂²×C₇₃	1	4	yes	complemented
299	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	4	yes	complemented
300	C₂×AGL(1,ℤ/8)	C₂²×C₇₃	1	4	yes	complemented
301	C₂×#135	C₂²×C₇₃	1	8	yes	—
302	C₂²×M₁₆	C₂²×C₇₃	1	2	yes	—
303	#537	—	2	1	no	—
304	#537	—	2	1	no	—
305	#536	C₂²×C₇₃	1	4	yes	complemented
306	#535	C₂²×C₇₃	1	4	yes	complemented
307	#534	—	2	2	no	—
308	#532	C₂²×C₇₃	1	4	yes	—
309	#525	—	2	4	no	—
310	#520	—	2	4	no	—
311	#520	C₂²×C₇₃	1	8	yes	complemented
312	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	complemented
313	C₂×C₄×D₄	—	2	2	no	—
314	C₂×C₄×D₄	C₂²×C₇₃	1	2	yes	complemented
315	C₂×#117	—	2	1	no	—
316	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
317	C₂²×C₄⋊C₄	—	2	1	no	—
318	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
319	#464	C₂²×C₇₃	1	16	yes	complemented
320	#463	C₂²×C₇₃	1	16	yes	complemented
321	#462	C₂²×C₇₃	1	8	yes	complemented
322	#461	C₂²×C₇₃	1	8	yes	complemented
323	#460	C₂²×C₇₃	1	8	yes	complemented
324	#459	C₂²×C₇₃	1	8	yes	complemented
325	#424	C₂²×C₇₃	1	8	yes	complemented
326	#423	C₂²×C₇₃	1	4	yes	complemented
327	#417	C₂²×C₇₃	1	8	yes	complemented
328	#417	C₂²×C₇₃	1	8	yes	complemented
329	C₂×#103	C₂²×C₇₃	1	4	yes	complemented
330	C₂×#102	C₂²×C₇₃	1	4	yes	complemented
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	4	no	—
335	C₂×#41	—	2	8	no	—
336	C₂×#41	—	2	8	no	—
337	C₂×#41	D₄×C₇₃	1	8	yes	complemented
338	C₂×#41	C₂³×C₇₃	1	4	yes	—
339	C₂×#41	C₂³×C₇₃	1	4	yes	—
340	C₂×#41	C₂³×C₇₃	1	4	yes	—
341	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
342	C₂²×Q₈	C₂³×C₇₃	1	1	yes	characteristic
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
346	C₂²×D₄	C₂³×C₇₃	1	1	yes	characteristic
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	1	no	—
349	C₂³×C₄	—	2	2	no	—
350	C₂³×C₄	—	2	2	no	—
351	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
352	#137	—	2	16	no	—
353	#137	—	2	16	no	—
354	AGL(1,ℤ/8)	—	2	16	no	—
355	AGL(1,ℤ/8)	—	2	16	no	—
356	#135	—	2	32	no	—
357	C₂×Q₁₆	C₂³×C₇₃	1	8	yes	—
358	C₂×SD₁₆	C₂³×C₇₃	1	8	yes	—
359	C₂×SD₁₆	C₂³×C₇₃	1	8	yes	—
360	C₂×D₈	C₂³×C₇₃	1	8	yes	—
361	C₂×M₁₆	—	2	8	no	—
362	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
363	C₂×M₁₆	C₂³×C₇₃	1	4	yes	—
364	C₂²×C₈	C₂³×C₇₃	1	4	yes	—
365	C₄⋊Q₈	C₂³×C₇₃	1	4	yes	—
366	#127	C₂³×C₇₃	1	4	yes	—
367	#124	C₂³×C₇₃	1	8	yes	—
368	#123	—	2	8	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	2	4	no	—
371	#121	—	2	4	no	—
372	#121	—	2	4	no	—
373	#121	—	2	4	no	—
374	#121	—	2	4	no	—
375	#120	—	2	8	no	—
376	C₄×Q₈	—	2	4	no	—
377	C₄×Q₈	C₂³×C₇₃	1	8	yes	—
378	C₄×D₄	—	2	16	no	—
379	C₄×D₄	—	2	4	no	—
380	C₄×D₄	—	2	4	no	—
381	C₄×D₄	—	2	4	no	—
382	C₄×D₄	C₂³×C₇₃	1	8	yes	—
383	#117	—	2	8	no	—
384	#117	D₄×C₇₃	1	4	yes	—
385	#117	C₂³×C₇₃	1	4	yes	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	8	no	—
390	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
391	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
394	C₂×C₂²⋊C₄	—	2	2	no	—
395	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
396	C₂×C₄²	—	2	2	no	—
397	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
398	C₄⋊C₈	C₂³×C₇₃	1	8	yes	—
399	C₄⋊C₈	C₂³×C₇₃	1	8	yes	—
400	#103	C₂³×C₇₃	1	16	yes	—
401	#102	C₂³×C₇₃	1	16	yes	—
402	C₂⁴	—	2	1	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
405	#41	—	2	16	no	—
406	#41	—	2	8	no	—
407	#41	—	2	8	no	—
408	#41	—	2	8	no	—
409	#41	—	2	8	no	—
410	#41	—	2	8	no	—
411	#41	—	4	8	no	—
412	#41	—	4	8	no	—
413	#41	C₂×D₄×C₇₃	1	16	yes	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	—	2	4	no	—
418	C₂×Q₈	—	2	4	no	—
419	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
420	C₂×Q₈	C₂⁴×C₇₃	1	4	yes	—
421	C₂×Q₈	C₂⁴×C₇₃	1	2	yes	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	4	no	—
424	C₂×D₄	—	2	4	no	—
425	C₂×D₄	—	2	4	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	4	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	4	no	—
430	C₂×D₄	—	2	4	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
435	C₂×D₄	C₂⁴×C₇₃	1	4	yes	—
436	C₂×D₄	C₂⁴×C₇₃	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	8	no	—
446	C₂²×C₄	—	4	8	no	—
447	C₂²×C₄	—	8	4	no	—
448	C₂²×C₄	—	8	2	no	—
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	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
453	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
454	C₂²×C₄	#41×C₇₃	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
457	Q₁₆	—	2	16	no	—
458	SD₁₆	—	2	16	no	—
459	SD₁₆	—	2	16	no	—
460	D₈	—	2	16	no	—
461	M₁₆	—	2	8	no	—
462	M₁₆	—	2	8	no	—
463	C₂×C₈	—	2	8	no	—
464	C₂×C₈	C₂⁴×C₇₃	1	8	yes	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
471	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
472	C₄⋊C₄	C₂⁴×C₇₃	1	4	yes	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	C₂×D₄×C₇₃	1	8	yes	—
477	C₄²	—	2	8	no	—
478	C₄²	C₂×D₄×C₇₃	1	4	yes	—
479	C₄²	C₂⁴×C₇₃	1	4	yes	—
480	C₂³	—	2	4	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	4	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	4	no	—
488	C₂³	—	8	2	no	—
489	C₂³	—	8	2	no	—
490	C₂³	#121×C₇₃	1	4	yes	—
491	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
492	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
493	Q₈	—	2	4	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	2	4	no	—
496	Q₈	—	2	4	no	—
497	Q₈	—	4	4	no	—
498	Q₈	C₂²×D₄×C₇₃	1	4	yes	—
499	D₄	—	2	16	no	—
500	D₄	—	2	4	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	2	no	—
503	D₄	—	2	4	no	—
504	D₄	—	4	8	no	—
505	D₄	—	4	8	no	—
506	D₄	—	4	4	no	—
507	D₄	—	8	4	no	—
508	D₄	—	8	4	no	—
509	D₄	C₂²×D₄×C₇₃	1	4	yes	—
510	C₂×C₄	—	2	4	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	16	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	8	8	no	—
522	C₂×C₄	—	8	4	no	—
523	C₂×C₄	#121×C₇₃	1	4	yes	—
524	C₂×C₄	#121×C₇₃	1	8	yes	—
525	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
526	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
527	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
529	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
530	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
531	C₂×C₄	C₂×#41×C₇₃	1	4	yes	—
532	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
533	C₂×C₄	C₂⁵×C₇₃	1	1	yes	characteristic
534	C₈	—	2	8	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	1	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	4	no	—
541	C₂²	—	4	8	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	8	8	no	—
548	C₂²	C₂×#121×C₇₃	1	2	yes	—
549	C₂²	C₂×#121×C₇₃	1	4	yes	—
550	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
551	C₄	—	2	4	no	—
552	C₄	—	2	4	no	—
553	C₄	—	2	4	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	4	no	—
556	C₄	C₂×#121×C₇₃	1	4	yes	—
557	C₄	C₂×#121×C₇₃	1	2	yes	—
558	C₄	C₂³×D₄×C₇₃	1	1	yes	characteristic
559	C₄	C₂²×#41×C₇₃	1	1	yes	characteristic
560	C₂	—	2	2	no	—
561	C₂	—	2	4	no	—
562	C₂	—	4	4	no	—
563	C₂	—	8	4	no	—
564	C₂	C₂²×#121×C₇₃	1	1	yes	characteristic
565	C₂	C₇₃×#3585	1	1	yes	characteristic
566	C₂	C₇₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#575×C₇₃	C₂	semidirect
2. C₇₃×#3449	C₂	semidirect
3. C₂×#520×C₇₃	C₂	semidirect
4. C₇₃×#3046	C₂	semidirect
5. C₇₃×#3045	C₂	semidirect
6. C₇₃×#3037	C₂	semidirect
7. C₇₃×#3036	C₂	semidirect
8. C₇₃×#2905	C₂	semidirect
9. C₂×#417×C₇₃	C₂	semidirect
13. C₂×#137×C₇₃	C₂²	semidirect
14. C₂×#137×C₇₃	C₂²	semidirect
15. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
16. C₂×AGL(1,ℤ/8)×C₇₃	C₂²	semidirect
21. #536×C₇₃	C₂²	semidirect
22. #535×C₇₃	C₂²	semidirect
27. #520×C₇₃	C₂²	semidirect
28. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
30. C₂×C₄×D₄×C₇₃	C₂²	semidirect
35. #464×C₇₃	C₂²	semidirect
36. #463×C₇₃	C₂²	semidirect
37. #462×C₇₃	C₂²	semidirect
38. #461×C₇₃	C₂²	semidirect
39. #460×C₇₃	C₂²	semidirect
40. #459×C₇₃	C₂²	semidirect
41. #424×C₇₃	C₂²	semidirect
42. #423×C₇₃	C₂²	semidirect
43. #417×C₇₃	C₂²	semidirect
44. #417×C₇₃	C₂²	semidirect
45. C₂×#103×C₇₃	C₂²	semidirect
46. C₂×#102×C₇₃	C₂²	semidirect
53. C₂×#41×C₇₃	D₄	semidirect
276. #60425	C₇₃	direct (N × H)
284. C₂×#575	C₂×C₇₃	semidirect
285. #3449	C₂×C₇₃	semidirect
286. C₂×#520	C₂×C₇₃	semidirect
287. #3046	C₂×C₇₃	semidirect
288. #3045	C₂×C₇₃	semidirect
289. #3037	C₂×C₇₃	semidirect
290. #3036	C₂×C₇₃	semidirect
291. #2905	C₂×C₇₃	semidirect
292. C₂×#417	C₂×C₇₃	semidirect
293. C₇₃	#60425	direct (N × H)
297. C₂×#137	C₂²×C₇₃	semidirect
298. C₂×#137	C₂²×C₇₃	semidirect
299. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
300. C₂×AGL(1,ℤ/8)	C₂²×C₇₃	semidirect
305. #536	C₂²×C₇₃	semidirect
306. #535	C₂²×C₇₃	semidirect
311. #520	C₂²×C₇₃	semidirect
312. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
314. C₂×C₄×D₄	C₂²×C₇₃	semidirect
319. #464	C₂²×C₇₃	semidirect
320. #463	C₂²×C₇₃	semidirect
321. #462	C₂²×C₇₃	semidirect
322. #461	C₂²×C₇₃	semidirect
323. #460	C₂²×C₇₃	semidirect
324. #459	C₂²×C₇₃	semidirect
325. #424	C₂²×C₇₃	semidirect
326. #423	C₂²×C₇₃	semidirect
327. #417	C₂²×C₇₃	semidirect
328. #417	C₂²×C₇₃	semidirect
329. C₂×#103	C₂²×C₇₃	semidirect
330. C₂×#102	C₂²×C₇₃	semidirect
337. C₂×#41	D₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₇₃	2
C₇₃×#3449	2
C₂×#520×C₇₃	2
C₇₃×#3046	2
C₇₃×#3045	2
C₇₃×#3037	2
C₇₃×#3036	2
C₇₃×#2905	2
C₂×#417×C₇₃	2
#60425	73

Subgroups — C73×#60425 #32969829

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#60425 #32969829