Subgroups — C₂×C₇₃×#2042 #32932906

Order 18688.

1670 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	C₂²×#124×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#103×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#102×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×#102×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#389×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#2042	C₂	1	8	yes	maximal, direct product factor
8	C₂×#336×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×Q₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₂³×D₄×C₇₃	C₂²	1	1	yes	characteristic
11	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#124×C₇₃	—	2	4	no	—
14	C₂×#124×C₇₃	—	2	4	no	—
15	C₂×#124×C₇₃	—	2	2	no	—
16	C₂×#124×C₇₃	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₇₃	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₇₃	—	2	1	no	—
22	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
23	C₂×#103×C₇₃	—	2	4	no	—
24	C₂×#103×C₇₃	—	2	4	no	—
25	C₂×#103×C₇₃	C₂²	1	4	yes	complemented
26	C₂×#103×C₇₃	C₂²	1	4	yes	complemented
27	C₂×#102×C₇₃	—	2	4	no	—
28	C₂×#102×C₇₃	—	2	4	no	—
29	C₂×#102×C₇₃	C₂²	1	4	yes	—
30	C₂×#102×C₇₃	C₂²	1	4	yes	—
31	#389×C₇₃	—	2	2	no	—
32	#389×C₇₃	C₂²	1	4	yes	complemented
33	C₂×#95×C₇₃	—	2	1	no	—
34	#336×C₇₃	C₂²	1	4	yes	complemented
35	C₂⁵×C₇₃	—	2	1	no	—
36	C₂²×Q₈×C₇₃	—	2	2	no	—
37	C₂²×Q₈×C₇₃	—	2	1	no	—
38	C₂²×Q₈×C₇₃	—	2	2	no	—
39	C₂²×Q₈×C₇₃	—	2	2	no	—
40	C₂²×Q₈×C₇₃	—	2	2	no	—
41	C₂²×Q₈×C₇₃	—	2	2	no	—
42	C₂²×Q₈×C₇₃	D₄	1	4	yes	—
43	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₇₃	—	2	2	no	—
45	C₂²×D₄×C₇₃	—	2	1	no	—
46	C₂²×D₄×C₇₃	—	2	2	no	—
47	C₂²×D₄×C₇₃	—	2	2	no	—
48	C₂²×D₄×C₇₃	—	2	2	no	—
49	C₂²×D₄×C₇₃	—	2	2	no	—
50	C₂²×D₄×C₇₃	D₄	1	4	yes	—
51	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₇₃	—	2	1	no	—
53	C₂³×C₄×C₇₃	—	2	1	no	—
54	C₂³×C₄×C₇₃	—	2	1	no	—
55	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₇₃	—	2	2	no	—
59	C₂²×C₈×C₇₃	—	2	2	no	—
60	C₂²×C₈×C₇₃	—	2	2	no	—
61	C₂²×C₈×C₇₃	—	2	2	no	—
62	C₂²×C₈×C₇₃	—	2	2	no	—
63	C₂²×C₈×C₇₃	—	2	2	no	—
64	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
65	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
66	#124×C₇₃	—	2	16	no	—
67	#124×C₇₃	—	2	8	no	—
68	#124×C₇₃	—	2	8	no	—
69	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
70	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
71	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
72	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
73	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
74	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
75	C₂×C₄⋊C₄×C₇₃	—	4	4	no	—
76	C₂×C₄⋊C₄×C₇₃	D₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
79	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
80	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
82	C₂×C₂²⋊C₄×C₇₃	—	2	4	no	—
83	C₂×C₄²×C₇₃	—	2	2	no	—
84	C₂×C₄²×C₇₃	—	2	2	no	—
85	C₂×C₄²×C₇₃	D₄	1	2	yes	—
86	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
87	#103×C₇₃	—	2	8	no	—
88	#103×C₇₃	—	2	8	no	—
89	#102×C₇₃	—	2	8	no	—
90	#102×C₇₃	—	2	8	no	—
91	#95×C₇₃	—	2	4	no	—
92	C₂⁴×C₇₃	—	2	4	no	—
93	C₂⁴×C₇₃	—	2	2	no	—
94	C₂⁴×C₇₃	—	4	2	no	—
95	C₂⁴×C₇₃	—	4	2	no	—
96	C₂⁴×C₇₃	—	4	2	no	—
97	C₂⁴×C₇₃	—	4	2	no	—
98	C₂⁴×C₇₃	—	4	2	no	—
99	C₂⁴×C₇₃	—	4	2	no	—
100	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₇₃	—	2	4	no	—
102	C₂×Q₈×C₇₃	—	2	2	no	—
103	C₂×Q₈×C₇₃	—	2	8	no	—
104	C₂×Q₈×C₇₃	—	2	8	no	—
105	C₂×Q₈×C₇₃	—	2	2	no	—
106	C₂×Q₈×C₇₃	—	2	2	no	—
107	C₂×Q₈×C₇₃	—	2	2	no	—
108	C₂×Q₈×C₇₃	—	2	2	no	—
109	C₂×Q₈×C₇₃	—	4	2	no	—
110	C₂×Q₈×C₇₃	—	4	4	no	—
111	C₂×Q₈×C₇₃	—	4	4	no	—
112	C₂×Q₈×C₇₃	—	4	2	no	—
113	C₂×Q₈×C₇₃	C₂×D₄	1	4	yes	—
114	C₂×D₄×C₇₃	—	2	4	no	—
115	C₂×D₄×C₇₃	—	2	8	no	—
116	C₂×D₄×C₇₃	—	2	8	no	—
117	C₂×D₄×C₇₃	—	2	2	no	—
118	C₂×D₄×C₇₃	—	2	2	no	—
119	C₂×D₄×C₇₃	—	2	2	no	—
120	C₂×D₄×C₇₃	—	2	2	no	—
121	C₂×D₄×C₇₃	—	2	2	no	—
122	C₂×D₄×C₇₃	—	4	4	no	—
123	C₂×D₄×C₇₃	—	4	2	no	—
124	C₂×D₄×C₇₃	—	4	4	no	—
125	C₂×D₄×C₇₃	—	4	2	no	—
126	C₂×D₄×C₇₃	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₇₃	—	2	2	no	—
128	C₂²×C₄×C₇₃	—	2	2	no	—
129	C₂²×C₄×C₇₃	—	2	4	no	—
130	C₂²×C₄×C₇₃	—	2	4	no	—
131	C₂²×C₄×C₇₃	—	2	2	no	—
132	C₂²×C₄×C₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	—	2	2	no	—
134	C₂²×C₄×C₇₃	—	2	2	no	—
135	C₂²×C₄×C₇₃	—	2	2	no	—
136	C₂²×C₄×C₇₃	—	2	2	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	—	4	2	no	—
139	C₂²×C₄×C₇₃	—	4	2	no	—
140	C₂²×C₄×C₇₃	—	4	2	no	—
141	C₂²×C₄×C₇₃	—	4	2	no	—
142	C₂²×C₄×C₇₃	—	4	2	no	—
143	C₂²×C₄×C₇₃	—	4	2	no	—
144	C₂²×C₄×C₇₃	—	4	2	no	—
145	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
149	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₇₃	#41	1	2	yes	—
152	C₂²×C₄×C₇₃	#41	1	2	yes	—
153	C₂²×C₄×C₇₃	#41	1	2	yes	—
154	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
155	C₂×C₈×C₇₃	—	2	2	no	—
156	C₂×C₈×C₇₃	—	2	2	no	—
157	C₂×C₈×C₇₃	—	2	2	no	—
158	C₂×C₈×C₇₃	—	2	2	no	—
159	C₂×C₈×C₇₃	—	2	2	no	—
160	C₂×C₈×C₇₃	—	2	2	no	—
161	C₂×C₈×C₇₃	—	4	4	no	—
162	C₂×C₈×C₇₃	—	4	4	no	—
163	C₄⋊C₄×C₇₃	—	2	4	no	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	—	2	2	no	—
167	C₄⋊C₄×C₇₃	—	4	8	no	—
168	C₄⋊C₄×C₇₃	—	4	2	no	—
169	C₄⋊C₄×C₇₃	C₂×D₄	1	4	yes	—
170	C₂²⋊C₄×C₇₃	—	2	16	no	—
171	C₂²⋊C₄×C₇₃	—	2	16	no	—
172	C₄²×C₇₃	—	2	4	no	—
173	C₄²×C₇₃	—	2	2	no	—
174	C₄²×C₇₃	—	2	2	no	—
175	C₂³×C₇₃	—	2	4	no	—
176	C₂³×C₇₃	—	4	2	no	—
177	C₂³×C₇₃	—	4	2	no	—
178	C₂³×C₇₃	—	4	2	no	—
179	C₂³×C₇₃	—	4	2	no	—
180	C₂³×C₇₃	—	4	2	no	—
181	C₂³×C₇₃	—	4	2	no	—
182	C₂³×C₇₃	—	4	8	no	—
183	C₂³×C₇₃	—	4	8	no	—
184	C₂³×C₇₃	—	4	8	no	—
185	C₂³×C₇₃	—	8	4	no	—
186	C₂³×C₇₃	—	8	4	no	—
187	C₂³×C₇₃	—	8	4	no	—
188	C₂³×C₇₃	—	8	4	no	—
189	C₂³×C₇₃	#120	1	2	yes	—
190	C₂³×C₇₃	#121	1	2	yes	—
191	C₂³×C₇₃	#124	1	2	yes	—
192	C₂³×C₇₃	#135	1	2	yes	—
193	C₂³×C₇₃	#135	1	2	yes	—
194	C₂³×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
195	C₂³×C₇₃	#137	1	2	yes	—
196	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₇₃	—	2	4	no	—
198	Q₈×C₇₃	—	2	4	no	—
199	Q₈×C₇₃	—	4	2	no	—
200	Q₈×C₇₃	—	4	2	no	—
201	Q₈×C₇₃	—	4	8	no	—
202	D₄×C₇₃	—	2	4	no	—
203	D₄×C₇₃	—	2	4	no	—
204	D₄×C₇₃	—	4	2	no	—
205	D₄×C₇₃	—	4	2	no	—
206	D₄×C₇₃	—	4	8	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	2	4	no	—
210	C₂×C₄×C₇₃	—	2	4	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	2	no	—
215	C₂×C₄×C₇₃	—	4	2	no	—
216	C₂×C₄×C₇₃	—	4	2	no	—
217	C₂×C₄×C₇₃	—	4	2	no	—
218	C₂×C₄×C₇₃	—	4	2	no	—
219	C₂×C₄×C₇₃	—	4	8	no	—
220	C₂×C₄×C₇₃	—	4	4	no	—
221	C₂×C₄×C₇₃	—	4	4	no	—
222	C₂×C₄×C₇₃	—	4	8	no	—
223	C₂×C₄×C₇₃	—	4	2	no	—
224	C₂×C₄×C₇₃	—	4	2	no	—
225	C₂×C₄×C₇₃	—	4	2	no	—
226	C₂×C₄×C₇₃	—	8	4	no	—
227	C₂×C₄×C₇₃	#120	1	2	yes	—
228	C₂×C₄×C₇₃	#121	1	4	yes	—
229	C₂×C₄×C₇₃	#121	1	4	yes	—
230	C₂×C₄×C₇₃	#121	1	2	yes	—
231	C₂×C₄×C₇₃	#123	1	4	yes	—
232	C₂×C₄×C₇₃	#123	1	4	yes	—
233	C₂×C₄×C₇₃	#124	1	2	yes	—
234	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
240	C₈×C₇₃	—	4	2	no	—
241	C₈×C₇₃	—	4	2	no	—
242	C₂²×C₇₃	—	4	4	no	—
243	C₂²×C₇₃	—	4	4	no	—
244	C₂²×C₇₃	—	4	4	no	—
245	C₂²×C₇₃	—	8	2	no	—
246	C₂²×C₇₃	—	8	2	no	—
247	C₂²×C₇₃	—	8	2	no	—
248	C₂²×C₇₃	—	8	2	no	—
249	C₂²×C₇₃	—	8	16	no	—
250	C₂²×C₇₃	#394	1	4	yes	—
251	C₂²×C₇₃	#449	1	4	yes	—
252	C₂²×C₇₃	#452	1	4	yes	—
253	C₂²×C₇₃	#463	1	4	yes	—
254	C₂²×C₇₃	#464	1	4	yes	—
255	C₂²×C₇₃	#488	1	4	yes	—
256	C₂²×C₇₃	#489	1	4	yes	—
257	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
258	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
259	C₂²×C₇₃	C₂×#124	1	1	yes	characteristic
260	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
261	C₂²×C₇₃	C₂×#135	1	1	yes	characteristic
262	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
263	C₂²×C₇₃	C₂×#137	1	1	yes	characteristic
264	C₄×C₇₃	—	4	4	no	—
265	C₄×C₇₃	—	4	2	no	—
266	C₄×C₇₃	—	4	2	no	—
267	C₄×C₇₃	—	4	4	no	—
268	C₄×C₇₃	—	8	2	no	—
269	C₄×C₇₃	#394	1	4	yes	—
270	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
271	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
272	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
273	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
274	C₂×#2042	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
275	C₂×C₇₃	—	8	4	no	—
276	C₂×C₇₃	#2042	1	8	yes	direct product factor
277	C₂×C₇₃	C₂×#394	1	1	yes	characteristic
278	C₂×C₇₃	C₂×#449	1	1	yes	characteristic
279	C₂×C₇₃	C₂×#452	1	1	yes	characteristic
280	C₂×C₇₃	C₂×#463	1	1	yes	characteristic
281	C₂×C₇₃	C₂×#464	1	1	yes	characteristic
282	C₂×C₇₃	C₂×#488	1	1	yes	characteristic
283	C₂×C₇₃	C₂×#489	1	1	yes	characteristic
284	C₂²×#124	C₂×C₇₃	1	1	yes	characteristic
285	C₂²×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
286	C₂²×#103	C₂×C₇₃	1	1	yes	characteristic, complemented
287	C₂²×#102	C₂×C₇₃	1	1	yes	characteristic
288	C₂²×#102	C₂×C₇₃	1	1	yes	characteristic
289	C₂×#389	C₂×C₇₃	1	1	yes	characteristic, complemented
290	#2042	C₂×C₇₃	1	8	yes	direct product factor
291	C₂×#336	C₂×C₇₃	1	1	yes	characteristic, complemented
292	C₇₃	C₂×#2042	1	1	yes	characteristic, direct product factor, Sylow
293	C₂³×Q₈	C₂²×C₇₃	1	1	yes	characteristic
294	C₂³×D₄	C₂²×C₇₃	1	1	yes	characteristic
295	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
296	C₂³×C₈	C₂²×C₇₃	1	1	yes	characteristic
297	C₂×#124	—	2	4	no	—
298	C₂×#124	—	2	4	no	—
299	C₂×#124	—	2	2	no	—
300	C₂×#124	C₂²×C₇₃	1	4	yes	—
301	C₂²×C₄⋊C₄	—	2	1	no	—
302	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
304	C₂²×C₂²⋊C₄	—	2	1	no	—
305	C₂²×C₂²⋊C₄	—	2	1	no	—
306	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
307	C₂×#103	—	2	4	no	—
308	C₂×#103	—	2	4	no	—
309	C₂×#103	C₂²×C₇₃	1	4	yes	complemented
310	C₂×#103	C₂²×C₇₃	1	4	yes	complemented
311	C₂×#102	—	2	4	no	—
312	C₂×#102	—	2	4	no	—
313	C₂×#102	C₂²×C₇₃	1	4	yes	—
314	C₂×#102	C₂²×C₇₃	1	4	yes	—
315	#389	—	2	2	no	—
316	#389	C₂²×C₇₃	1	4	yes	complemented
317	C₂×#95	—	2	1	no	—
318	#336	C₂²×C₇₃	1	4	yes	complemented
319	C₂⁵	—	2	1	no	—
320	C₂²×Q₈	—	2	2	no	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	D₄×C₇₃	1	4	yes	—
327	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	2	no	—
332	C₂²×D₄	—	2	2	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	D₄×C₇₃	1	4	yes	—
335	C₂²×D₄	C₂³×C₇₃	1	2	yes	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
340	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
341	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	—	2	2	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	2	no	—
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
349	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
350	#124	—	2	16	no	—
351	#124	—	2	8	no	—
352	#124	—	2	8	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	2	no	—
355	C₂×C₄⋊C₄	—	2	2	no	—
356	C₂×C₄⋊C₄	—	2	2	no	—
357	C₂×C₄⋊C₄	—	2	4	no	—
358	C₂×C₄⋊C₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	4	4	no	—
360	C₂×C₄⋊C₄	D₄×C₇₃	1	4	yes	—
361	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
362	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
363	C₂×C₂²⋊C₄	—	2	8	no	—
364	C₂×C₂²⋊C₄	—	2	8	no	—
365	C₂×C₂²⋊C₄	—	2	4	no	—
366	C₂×C₂²⋊C₄	—	2	4	no	—
367	C₂×C₄²	—	2	2	no	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	D₄×C₇₃	1	2	yes	—
370	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
371	#103	—	2	8	no	—
372	#103	—	2	8	no	—
373	#102	—	2	8	no	—
374	#102	—	2	8	no	—
375	#95	—	2	4	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	4	2	no	—
379	C₂⁴	—	4	2	no	—
380	C₂⁴	—	4	2	no	—
381	C₂⁴	—	4	2	no	—
382	C₂⁴	—	4	2	no	—
383	C₂⁴	—	4	2	no	—
384	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
385	C₂×Q₈	—	2	4	no	—
386	C₂×Q₈	—	2	2	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	8	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	4	4	no	—
394	C₂×Q₈	—	4	2	no	—
395	C₂×Q₈	—	4	4	no	—
396	C₂×Q₈	—	4	2	no	—
397	C₂×Q₈	C₂×D₄×C₇₃	1	4	yes	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	8	no	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	4	2	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	2	no	—
410	C₂×D₄	C₂×D₄×C₇₃	1	4	yes	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	2	no	—
423	C₂²×C₄	—	4	2	no	—
424	C₂²×C₄	—	4	2	no	—
425	C₂²×C₄	—	4	2	no	—
426	C₂²×C₄	—	4	2	no	—
427	C₂²×C₄	—	4	2	no	—
428	C₂²×C₄	—	4	2	no	—
429	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
430	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
431	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
434	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
435	C₂²×C₄	#41×C₇₃	1	2	yes	—
436	C₂²×C₄	#41×C₇₃	1	2	yes	—
437	C₂²×C₄	#41×C₇₃	1	2	yes	—
438	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	4	no	—
446	C₂×C₈	—	4	4	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	4	8	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	C₂×D₄×C₇₃	1	4	yes	—
454	C₂²⋊C₄	—	2	16	no	—
455	C₂²⋊C₄	—	2	16	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	2	2	no	—
458	C₄²	—	2	2	no	—
459	C₂³	—	2	4	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	8	no	—
462	C₂³	—	4	8	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	8	4	no	—
470	C₂³	—	8	4	no	—
471	C₂³	—	8	4	no	—
472	C₂³	—	8	4	no	—
473	C₂³	#120×C₇₃	1	2	yes	—
474	C₂³	#121×C₇₃	1	2	yes	—
475	C₂³	#124×C₇₃	1	2	yes	—
476	C₂³	#135×C₇₃	1	2	yes	—
477	C₂³	#135×C₇₃	1	2	yes	—
478	C₂³	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
479	C₂³	#137×C₇₃	1	2	yes	—
480	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
481	Q₈	—	2	4	no	—
482	Q₈	—	2	4	no	—
483	Q₈	—	4	8	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	4	2	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	4	no	—
488	D₄	—	4	8	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	4	8	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#120×C₇₃	1	2	yes	—
512	C₂×C₄	#121×C₇₃	1	2	yes	—
513	C₂×C₄	#121×C₇₃	1	4	yes	—
514	C₂×C₄	#121×C₇₃	1	4	yes	—
515	C₂×C₄	#123×C₇₃	1	4	yes	—
516	C₂×C₄	#123×C₇₃	1	4	yes	—
517	C₂×C₄	#124×C₇₃	1	2	yes	—
518	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
519	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
521	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
522	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
523	C₂×C₄	C₂×#41×C₇₃	1	1	yes	characteristic
524	C₈	—	4	2	no	—
525	C₈	—	4	2	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	4	4	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	16	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	#394×C₇₃	1	4	yes	—
535	C₂²	#449×C₇₃	1	4	yes	—
536	C₂²	#452×C₇₃	1	4	yes	—
537	C₂²	#463×C₇₃	1	4	yes	—
538	C₂²	#464×C₇₃	1	4	yes	—
539	C₂²	#488×C₇₃	1	4	yes	—
540	C₂²	#489×C₇₃	1	4	yes	—
541	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
542	C₂²	C₂×#121×C₇₃	1	1	yes	characteristic
543	C₂²	C₂×#124×C₇₃	1	1	yes	characteristic
544	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
545	C₂²	C₂×#135×C₇₃	1	1	yes	characteristic
546	C₂²	C₂×AGL(1,ℤ/8)×C₇₃	1	1	yes	characteristic
547	C₂²	C₂×#137×C₇₃	1	1	yes	characteristic
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	4	no	—
552	C₄	—	8	2	no	—
553	C₄	#394×C₇₃	1	4	yes	—
554	C₄	C₂×#121×C₇₃	1	1	yes	characteristic
555	C₄	C₂×#121×C₇₃	1	1	yes	characteristic
556	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
557	C₄	C₂×#123×C₇₃	1	1	yes	characteristic
558	C₂	—	8	4	no	—
559	C₂	C₇₃×#2042	1	8	yes	direct product factor
560	C₂	C₂×#394×C₇₃	1	1	yes	characteristic
561	C₂	C₂×#449×C₇₃	1	1	yes	characteristic
562	C₂	C₂×#452×C₇₃	1	1	yes	characteristic
563	C₂	C₂×#463×C₇₃	1	1	yes	characteristic
564	C₂	C₂×#464×C₇₃	1	1	yes	characteristic
565	C₂	C₂×#488×C₇₃	1	1	yes	characteristic
566	C₂	C₂×#489×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₇₃	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂³×D₄×C₇₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₇₃ ◁ C₂²×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#103×C₇₃	C₂	semidirect
3. C₂²×#103×C₇₃	C₂	semidirect
6. C₂×#389×C₇₃	C₂	semidirect
7. C₇₃×#2042	C₂	direct (N × H)
8. C₂×#336×C₇₃	C₂	semidirect
25. C₂×#103×C₇₃	C₂²	semidirect
26. C₂×#103×C₇₃	C₂²	semidirect
32. #389×C₇₃	C₂²	semidirect
34. #336×C₇₃	C₂²	semidirect
274. C₂×#2042	C₇₃	direct (N × H)
276. C₂×C₇₃	#2042	direct (N × H)
285. C₂²×#103	C₂×C₇₃	semidirect
286. C₂²×#103	C₂×C₇₃	semidirect
289. C₂×#389	C₂×C₇₃	semidirect
290. #2042	C₂×C₇₃	direct (N × H)
291. C₂×#336	C₂×C₇₃	semidirect
292. C₇₃	C₂×#2042	direct (N × H)
309. C₂×#103	C₂²×C₇₃	semidirect
310. C₂×#103	C₂²×C₇₃	semidirect
316. #389	C₂²×C₇₃	semidirect
318. #336	C₂²×C₇₃	semidirect
559. C₂	C₇₃×#2042	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#124×C₇₃	2
C₂²×#103×C₇₃	2
C₂²×#102×C₇₃	2
C₂×#389×C₇₃	2
C₇₃×#2042	2
C₂×#336×C₇₃	2
C₂×#2042	73

Subgroups — C2×C73×#2042 #32932906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₇₃×#2042 #32932906