Subgroups — C₇₃×#34634 #32944038

Order 18688.

2374 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#117×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2629	C₂	1	4	yes	maximal, complemented
4	C₇₃×#2628	C₂	1	4	yes	maximal, complemented
5	C₇₃×#2627	C₂	1	4	yes	maximal, complemented
6	C₇₃×#2626	C₂	1	4	yes	maximal
7	C₇₃×#2396	C₂	1	8	yes	maximal, complemented
8	C₇₃×#2296	C₂	1	2	yes	maximal, complemented
9	C₇₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇₃×#2280	C₂	1	2	yes	maximal
11	C₂⁴×C₄×C₇₃	C₂²	1	1	yes	characteristic
12	#533×C₇₃	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₇₃	C₂²	1	2	yes	complemented
14	C₂×#125×C₇₃	C₂²	1	2	yes	complemented
15	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	4	yes	—
16	C₂×C₄×Q₈×C₇₃	C₂²	1	4	yes	complemented
17	C₂×#117×C₇₃	—	2	8	no	—
18	C₂×#117×C₇₃	C₂²	1	2	yes	—
19	C₂×#117×C₇₃	C₂²	1	2	yes	—
20	C₂×#117×C₇₃	C₂²	1	2	yes	—
21	C₂×#117×C₇₃	C₂²	1	2	yes	—
22	C₂×#117×C₇₃	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₇₃	C₂²	1	2	yes	—
25	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
26	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
27	#400×C₇₃	C₂²	1	8	yes	complemented
28	#399×C₇₃	C₂²	1	8	yes	—
29	#398×C₇₃	C₂²	1	16	yes	complemented
30	#396×C₇₃	C₂²	1	16	yes	—
31	#395×C₇₃	C₂²	1	8	yes	complemented
32	#393×C₇₃	C₂²	1	8	yes	—
33	#389×C₇₃	C₂²	1	8	yes	complemented
34	#385×C₇₃	C₂²	1	8	yes	—
35	#384×C₇₃	C₂²	1	2	yes	complemented
36	#382×C₇₃	C₂²	1	2	yes	complemented
37	#381×C₇₃	C₂²	1	4	yes	—
38	#380×C₇₃	C₂²	1	8	yes	—
39	#380×C₇₃	C₂²	1	4	yes	—
40	#379×C₇₃	C₂²	1	4	yes	—
41	C₄×C₄⋊C₄×C₇₃	C₂²	1	4	yes	complemented
42	C₄×C₄⋊C₄×C₇₃	C₂²	1	8	yes	complemented
43	C₄×C₂²⋊C₄×C₇₃	C₂²	1	8	yes	—
44	C₂⁵×C₇₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₇₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₇₃	—	2	4	no	—
47	C₂³×C₄×C₇₃	—	2	4	no	—
48	C₂³×C₄×C₇₃	Q₈	1	8	yes	complemented
49	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
50	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₇₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
55	C₄⋊Q₈×C₇₃	—	2	8	no	—
56	#125×C₇₃	—	2	8	no	—
57	C₂²⋊Q₈×C₇₃	—	2	16	no	—
58	C₄×Q₈×C₇₃	—	2	16	no	—
59	#117×C₇₃	—	2	8	no	—
60	#117×C₇₃	—	2	8	no	—
61	#117×C₇₃	—	2	16	no	—
62	#117×C₇₃	—	2	8	no	—
63	#117×C₇₃	—	2	8	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	8	no	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₇₃	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₇₃	C₂³	1	8	yes	—
72	C₂×C₄⋊C₄×C₇₃	C₂³	1	16	yes	—
73	C₂×C₂²⋊C₄×C₇₃	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
75	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₇₃	C₂³	1	16	yes	—
79	C₂×C₄²×C₇₃	—	2	4	no	—
80	C₂×C₄²×C₇₃	D₄	1	8	yes	—
81	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
82	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
83	C₂×C₄²×C₇₃	C₂³	1	4	yes	—
84	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₇₃	C₂³	1	2	yes	—
88	#95×C₇₃	C₂³	1	16	yes	—
89	#95×C₇₃	C₂³	1	8	yes	—
90	#95×C₇₃	C₂³	1	16	yes	—
91	C₂⁴×C₇₃	—	2	2	no	—
92	C₂⁴×C₇₃	—	2	2	no	—
93	C₂⁴×C₇₃	—	4	4	no	—
94	C₂⁴×C₇₃	C₂×Q₈	1	4	yes	—
95	C₂⁴×C₇₃	C₂⁴	1	2	yes	—
96	C₂⁴×C₇₃	C₂⁴	1	1	yes	characteristic
97	C₂×Q₈×C₇₃	—	2	8	no	—
98	C₂×Q₈×C₇₃	—	4	8	no	—
99	C₂²×C₄×C₇₃	—	2	2	no	—
100	C₂²×C₄×C₇₃	—	2	2	no	—
101	C₂²×C₄×C₇₃	—	2	32	no	—
102	C₂²×C₄×C₇₃	—	2	4	no	—
103	C₂²×C₄×C₇₃	—	2	4	no	—
104	C₂²×C₄×C₇₃	—	2	4	no	—
105	C₂²×C₄×C₇₃	—	2	4	no	—
106	C₂²×C₄×C₇₃	—	2	4	no	—
107	C₂²×C₄×C₇₃	—	4	4	no	—
108	C₂²×C₄×C₇₃	—	4	4	no	—
109	C₂²×C₄×C₇₃	C₂×D₄	1	8	yes	—
110	C₂²×C₄×C₇₃	C₂×D₄	1	4	yes	—
111	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₇₃	C₂×Q₈	1	8	yes	—
113	C₂²×C₄×C₇₃	C₂×Q₈	1	8	yes	—
114	C₂²×C₄×C₇₃	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₇₃	#41	1	4	yes	—
116	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
117	C₂²×C₄×C₇₃	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₇₃	C₂⁴	1	8	yes	—
119	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₇₃	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
123	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
124	C₄⋊C₄×C₇₃	—	2	8	no	—
125	C₄⋊C₄×C₇₃	—	2	8	no	—
126	C₄⋊C₄×C₇₃	—	2	8	no	—
127	C₄⋊C₄×C₇₃	—	2	16	no	—
128	C₄⋊C₄×C₇₃	—	2	8	no	—
129	C₄⋊C₄×C₇₃	—	2	8	no	—
130	C₄⋊C₄×C₇₃	—	4	8	no	—
131	C₄⋊C₄×C₇₃	—	4	16	no	—
132	C₂²⋊C₄×C₇₃	—	2	8	no	—
133	C₂²⋊C₄×C₇₃	—	2	8	no	—
134	C₂²⋊C₄×C₇₃	—	2	8	no	—
135	C₂²⋊C₄×C₇₃	—	2	8	no	—
136	C₂²⋊C₄×C₇₃	—	4	16	no	—
137	C₄²×C₇₃	—	2	4	no	—
138	C₄²×C₇₃	—	2	4	no	—
139	C₄²×C₇₃	—	2	8	no	—
140	C₄²×C₇₃	—	2	8	no	—
141	C₄²×C₇₃	C₂×D₄	1	8	yes	—
142	C₄²×C₇₃	C₂×D₄	1	4	yes	—
143	C₄²×C₇₃	C₂×D₄	1	4	yes	—
144	C₂³×C₇₃	—	2	4	no	—
145	C₂³×C₇₃	—	2	8	no	—
146	C₂³×C₇₃	—	2	2	no	—
147	C₂³×C₇₃	—	2	2	no	—
148	C₂³×C₇₃	—	2	8	no	—
149	C₂³×C₇₃	—	4	8	no	—
150	C₂³×C₇₃	—	4	8	no	—
151	C₂³×C₇₃	—	4	8	no	—
152	C₂³×C₇₃	C₂²×D₄	1	2	yes	—
153	C₂³×C₇₃	C₂²×Q₈	1	4	yes	—
154	C₂³×C₇₃	C₂²×Q₈	1	2	yes	—
155	C₂³×C₇₃	C₂×#41	1	2	yes	—
156	C₂³×C₇₃	C₂⁵	1	1	yes	characteristic
157	Q₈×C₇₃	—	4	16	no	—
158	C₂×C₄×C₇₃	—	2	8	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	2	2	no	—
161	C₂×C₄×C₇₃	—	2	4	no	—
162	C₂×C₄×C₇₃	—	2	4	no	—
163	C₂×C₄×C₇₃	—	2	16	no	—
164	C₂×C₄×C₇₃	—	2	16	no	—
165	C₂×C₄×C₇₃	—	2	4	no	—
166	C₂×C₄×C₇₃	—	2	8	no	—
167	C₂×C₄×C₇₃	—	2	8	no	—
168	C₂×C₄×C₇₃	—	2	16	no	—
169	C₂×C₄×C₇₃	—	2	16	no	—
170	C₂×C₄×C₇₃	—	2	8	no	—
171	C₂×C₄×C₇₃	—	4	8	no	—
172	C₂×C₄×C₇₃	—	4	8	no	—
173	C₂×C₄×C₇₃	C₂²⋊Q₈	1	16	yes	—
174	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
175	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
176	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
177	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
178	C₂×C₄×C₇₃	C₂²×Q₈	1	4	yes	—
179	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
180	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
181	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
182	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
183	C₂²×C₇₃	—	2	4	no	—
184	C₂²×C₇₃	—	2	4	no	—
185	C₂²×C₇₃	—	2	4	no	—
186	C₂²×C₇₃	—	2	4	no	—
187	C₂²×C₇₃	—	2	8	no	—
188	C₂²×C₇₃	—	4	16	no	—
189	C₂²×C₇₃	—	4	4	no	—
190	C₂²×C₇₃	—	4	4	no	—
191	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	4	yes	—
192	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
193	C₂²×C₇₃	C₂³×Q₈	1	1	yes	characteristic
194	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
195	C₂²×C₇₃	#585	1	4	yes	—
196	C₄×C₇₃	—	2	4	no	—
197	C₄×C₇₃	—	2	4	no	—
198	C₄×C₇₃	—	2	4	no	—
199	C₄×C₇₃	—	4	4	no	—
200	C₄×C₇₃	—	4	8	no	—
201	C₄×C₇₃	—	4	8	no	—
202	C₄×C₇₃	C₂×C₂²⋊Q₈	1	4	yes	—
203	C₄×C₇₃	C₂×C₂²⋊Q₈	1	4	yes	—
204	#34634	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂×C₇₃	—	2	4	no	—
206	C₂×C₇₃	—	4	4	no	—
207	C₂×C₇₃	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
208	C₂×C₇₃	#3449	1	2	yes	—
209	C₂×C₇₃	#3455	1	2	yes	—
210	C₂×C₇₃	#3458	1	2	yes	—
211	C₂×#533	C₂×C₇₃	1	1	yes	characteristic, complemented
212	C₂²×#117	C₂×C₇₃	1	1	yes	characteristic
213	#2629	C₂×C₇₃	1	4	yes	complemented
214	#2628	C₂×C₇₃	1	4	yes	complemented
215	#2627	C₂×C₇₃	1	4	yes	complemented
216	#2626	C₂×C₇₃	1	4	yes	—
217	#2396	C₂×C₇₃	1	8	yes	complemented
218	#2296	C₂×C₇₃	1	2	yes	complemented
219	#2285	C₂×C₇₃	1	1	yes	characteristic, complemented
220	#2280	C₂×C₇₃	1	2	yes	—
221	C₇₃	#34634	1	1	yes	characteristic, direct product factor, Sylow
222	C₂⁴×C₄	C₂²×C₇₃	1	1	yes	characteristic
223	#533	—	2	8	no	—
224	C₂×C₄⋊Q₈	C₂²×C₇₃	1	2	yes	complemented
225	C₂×#125	C₂²×C₇₃	1	2	yes	complemented
226	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	4	yes	—
227	C₂×C₄×Q₈	C₂²×C₇₃	1	4	yes	complemented
228	C₂×#117	—	2	8	no	—
229	C₂×#117	C₂²×C₇₃	1	2	yes	—
230	C₂×#117	C₂²×C₇₃	1	2	yes	—
231	C₂×#117	C₂²×C₇₃	1	4	yes	—
232	C₂×#117	C₂²×C₇₃	1	2	yes	—
233	C₂×#117	C₂²×C₇₃	1	2	yes	—
234	C₂²×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
235	C₂²×C₂²⋊C₄	C₂²×C₇₃	1	2	yes	—
236	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₇₃	1	1	yes	characteristic
238	#400	C₂²×C₇₃	1	8	yes	complemented
239	#399	C₂²×C₇₃	1	8	yes	—
240	#398	C₂²×C₇₃	1	16	yes	complemented
241	#396	C₂²×C₇₃	1	16	yes	—
242	#395	C₂²×C₇₃	1	8	yes	complemented
243	#393	C₂²×C₇₃	1	8	yes	—
244	#389	C₂²×C₇₃	1	8	yes	complemented
245	#385	C₂²×C₇₃	1	8	yes	—
246	#384	C₂²×C₇₃	1	2	yes	complemented
247	#382	C₂²×C₇₃	1	2	yes	complemented
248	#381	C₂²×C₇₃	1	4	yes	—
249	#380	C₂²×C₇₃	1	4	yes	—
250	#380	C₂²×C₇₃	1	8	yes	—
251	#379	C₂²×C₇₃	1	4	yes	—
252	C₄×C₄⋊C₄	C₂²×C₇₃	1	4	yes	complemented
253	C₄×C₄⋊C₄	C₂²×C₇₃	1	8	yes	complemented
254	C₄×C₂²⋊C₄	C₂²×C₇₃	1	8	yes	—
255	C₂⁵	C₂³×C₇₃	1	1	yes	characteristic
256	C₂²×Q₈	C₂³×C₇₃	1	4	yes	—
257	C₂³×C₄	—	2	4	no	—
258	C₂³×C₄	—	2	4	no	—
259	C₂³×C₄	Q₈×C₇₃	1	8	yes	complemented
260	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
261	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
262	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
263	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
264	C₂³×C₄	C₂³×C₇₃	1	2	yes	—
265	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
266	C₄⋊Q₈	—	2	8	no	—
267	#125	—	2	8	no	—
268	C₂²⋊Q₈	—	2	16	no	—
269	C₄×Q₈	—	2	16	no	—
270	#117	—	2	8	no	—
271	#117	—	2	8	no	—
272	#117	—	2	16	no	—
273	#117	—	2	8	no	—
274	#117	—	2	8	no	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₇₃	1	4	yes	—
282	C₂×C₄⋊C₄	C₂³×C₇₃	1	8	yes	—
283	C₂×C₄⋊C₄	C₂³×C₇₃	1	16	yes	—
284	C₂×C₂²⋊C₄	—	2	8	no	—
285	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
287	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
288	C₂×C₂²⋊C₄	C₂³×C₇₃	1	4	yes	—
289	C₂×C₂²⋊C₄	C₂³×C₇₃	1	16	yes	—
290	C₂×C₄²	—	2	4	no	—
291	C₂×C₄²	D₄×C₇₃	1	8	yes	—
292	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
293	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
294	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
295	C₂×C₄²	C₂³×C₇₃	1	4	yes	—
296	C₂×C₄²	C₂³×C₇₃	1	2	yes	—
297	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
298	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
299	#95	C₂³×C₇₃	1	16	yes	—
300	#95	C₂³×C₇₃	1	8	yes	—
301	#95	C₂³×C₇₃	1	16	yes	—
302	C₂⁴	—	2	2	no	—
303	C₂⁴	—	2	2	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	C₂×Q₈×C₇₃	1	4	yes	—
306	C₂⁴	C₂⁴×C₇₃	1	2	yes	—
307	C₂⁴	C₂⁴×C₇₃	1	1	yes	characteristic
308	C₂×Q₈	—	2	8	no	—
309	C₂×Q₈	—	4	8	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	32	no	—
313	C₂²×C₄	—	2	4	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	4	no	—
318	C₂²×C₄	—	4	4	no	—
319	C₂²×C₄	—	4	4	no	—
320	C₂²×C₄	C₂×D₄×C₇₃	1	8	yes	—
321	C₂²×C₄	C₂×D₄×C₇₃	1	4	yes	—
322	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
323	C₂²×C₄	C₂×Q₈×C₇₃	1	8	yes	—
324	C₂²×C₄	C₂×Q₈×C₇₃	1	8	yes	—
325	C₂²×C₄	C₂×Q₈×C₇₃	1	4	yes	—
326	C₂²×C₄	#41×C₇₃	1	4	yes	—
327	C₂²×C₄	C₂⁴×C₇₃	1	8	yes	—
328	C₂²×C₄	C₂⁴×C₇₃	1	4	yes	—
329	C₂²×C₄	C₂⁴×C₇₃	1	8	yes	—
330	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
331	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
332	C₂²×C₄	C₂⁴×C₇₃	1	2	yes	—
333	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
334	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	16	no	—
339	C₄⋊C₄	—	2	8	no	—
340	C₄⋊C₄	—	2	8	no	—
341	C₄⋊C₄	—	4	8	no	—
342	C₄⋊C₄	—	4	16	no	—
343	C₂²⋊C₄	—	2	8	no	—
344	C₂²⋊C₄	—	2	8	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	4	16	no	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	8	no	—
351	C₄²	—	2	8	no	—
352	C₄²	C₂×D₄×C₇₃	1	8	yes	—
353	C₄²	C₂×D₄×C₇₃	1	4	yes	—
354	C₄²	C₂×D₄×C₇₃	1	4	yes	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	8	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	8	no	—
360	C₂³	—	4	8	no	—
361	C₂³	—	4	8	no	—
362	C₂³	—	4	8	no	—
363	C₂³	C₂²×D₄×C₇₃	1	2	yes	—
364	C₂³	C₂²×Q₈×C₇₃	1	4	yes	—
365	C₂³	C₂²×Q₈×C₇₃	1	2	yes	—
366	C₂³	C₂×#41×C₇₃	1	2	yes	—
367	C₂³	C₂⁵×C₇₃	1	1	yes	characteristic
368	Q₈	—	4	16	no	—
369	C₂×C₄	—	2	8	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	16	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	16	no	—
380	C₂×C₄	—	2	16	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	4	8	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	C₂²⋊Q₈×C₇₃	1	16	yes	—
385	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
386	C₂×C₄	C₂²×D₄×C₇₃	1	4	yes	—
387	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
388	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
389	C₂×C₄	C₂²×Q₈×C₇₃	1	4	yes	—
390	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
391	C₂×C₄	C₂²×Q₈×C₇₃	1	2	yes	—
392	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
393	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
394	C₂²	—	2	4	no	—
395	C₂²	—	2	4	no	—
396	C₂²	—	2	4	no	—
397	C₂²	—	2	4	no	—
398	C₂²	—	2	8	no	—
399	C₂²	—	4	16	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	4	no	—
402	C₂²	C₂×C₂²⋊Q₈×C₇₃	1	4	yes	—
403	C₂²	C₂³×D₄×C₇₃	1	1	yes	characteristic
404	C₂²	C₂³×Q₈×C₇₃	1	1	yes	characteristic
405	C₂²	C₂²×#41×C₇₃	1	1	yes	characteristic
406	C₂²	#585×C₇₃	1	4	yes	—
407	C₄	—	2	4	no	—
408	C₄	—	2	4	no	—
409	C₄	—	2	4	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	8	no	—
412	C₄	—	4	8	no	—
413	C₄	C₂×C₂²⋊Q₈×C₇₃	1	4	yes	—
414	C₄	C₂×C₂²⋊Q₈×C₇₃	1	4	yes	—
415	C₂	—	2	4	no	—
416	C₂	—	4	4	no	—
417	C₂	C₂²×C₂²⋊Q₈×C₇₃	1	1	yes	characteristic
418	C₂	C₇₃×#3449	1	2	yes	—
419	C₂	C₇₃×#3455	1	2	yes	—
420	C₂	C₇₃×#3458	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇₃
socle	C₂³×C₇₃	C₂⁵
prime radical	C₂⁵×C₇₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₇₃	C₂	semidirect
3. C₇₃×#2629	C₂	semidirect
4. C₇₃×#2628	C₂	semidirect
5. C₇₃×#2627	C₂	semidirect
7. C₇₃×#2396	C₂	semidirect
8. C₇₃×#2296	C₂	semidirect
9. C₇₃×#2285	C₂	semidirect
13. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
14. C₂×#125×C₇₃	C₂²	semidirect
16. C₂×C₄×Q₈×C₇₃	C₂²	semidirect
27. #400×C₇₃	C₂²	semidirect
29. #398×C₇₃	C₂²	semidirect
31. #395×C₇₃	C₂²	semidirect
33. #389×C₇₃	C₂²	semidirect
35. #384×C₇₃	C₂²	semidirect
36. #382×C₇₃	C₂²	semidirect
41. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
42. C₄×C₄⋊C₄×C₇₃	C₂²	semidirect
48. C₂³×C₄×C₇₃	Q₈	semidirect
204. #34634	C₇₃	direct (N × H)
211. C₂×#533	C₂×C₇₃	semidirect
213. #2629	C₂×C₇₃	semidirect
214. #2628	C₂×C₇₃	semidirect
215. #2627	C₂×C₇₃	semidirect
217. #2396	C₂×C₇₃	semidirect
218. #2296	C₂×C₇₃	semidirect
219. #2285	C₂×C₇₃	semidirect
221. C₇₃	#34634	direct (N × H)
224. C₂×C₄⋊Q₈	C₂²×C₇₃	semidirect
225. C₂×#125	C₂²×C₇₃	semidirect
227. C₂×C₄×Q₈	C₂²×C₇₃	semidirect
238. #400	C₂²×C₇₃	semidirect
240. #398	C₂²×C₇₃	semidirect
242. #395	C₂²×C₇₃	semidirect
244. #389	C₂²×C₇₃	semidirect
246. #384	C₂²×C₇₃	semidirect
247. #382	C₂²×C₇₃	semidirect
252. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
253. C₄×C₄⋊C₄	C₂²×C₇₃	semidirect
259. C₂³×C₄	Q₈×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₇₃	2
C₂²×#117×C₇₃	2
C₇₃×#2629	2
C₇₃×#2628	2
C₇₃×#2627	2
C₇₃×#2626	2
C₇₃×#2396	2
C₇₃×#2296	2
C₇₃×#2285	2
C₇₃×#2280	2
#34634	73

Subgroups — C73×#34634 #32944038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#34634 #32944038