Subgroups — C₇₃×#21398 #32930802

Order 18688.

1086 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#541×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#433×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#2274	C₂	1	1	yes	maximal, characteristic
4	C₇₃×#1989	C₂	1	2	yes	maximal, complemented
5	C₇₃×#1981	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1873	C₂	1	2	yes	maximal
7	C₇₃×#1872	C₂	1	2	yes	maximal
8	C₇₃×#1763	C₂	1	2	yes	maximal, complemented
9	C₄×#103×C₇₃	C₂	1	2	yes	maximal, complemented
10	#541×C₇₃	—	2	4	no	—
11	#541×C₇₃	C₄	1	8	yes	complemented
12	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×#126×C₇₃	—	2	2	no	—
14	C₂×#125×C₇₃	—	2	2	no	—
15	C₂×#125×C₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₇₃	C₂²	1	2	yes	—
18	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
21	#433×C₇₃	—	2	4	no	—
22	C₂×C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
23	C₂×#103×C₇₃	C₂²	1	2	yes	—
24	C₂×#103×C₇₃	C₂²	1	2	yes	—
25	C₂×#103×C₇₃	C₂²	1	2	yes	—
26	C₂×#103×C₇₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₇₃	C₂²	1	2	yes	—
28	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₇₃	—	2	2	no	—
31	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₇₃	C₂²	1	2	yes	—
33	C₄×C₂²⋊C₄×C₇₃	—	2	2	no	—
34	#340×C₇₃	C₂²	1	2	yes	—
35	#340×C₇₃	C₂²	1	2	yes	—
36	#340×C₇₃	C₂²	1	2	yes	—
37	#340×C₇₃	C₂²	1	2	yes	—
38	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₇₃	—	2	1	no	—
40	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
41	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
42	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
43	C₄⋊Q₈×C₇₃	—	2	2	no	—
44	C₄⋊Q₈×C₇₃	C₂×C₄	1	4	yes	complemented
45	#126×C₇₃	—	2	16	no	—
46	#125×C₇₃	—	2	16	no	—
47	#125×C₇₃	—	2	2	no	—
48	#125×C₇₃	C₂×C₄	1	4	yes	complemented
49	C₂²⋊Q₈×C₇₃	—	2	4	no	—
50	C₂²⋊Q₈×C₇₃	C₂×C₄	1	8	yes	—
51	C₄×Q₈×C₇₃	—	2	4	no	—
52	C₄×Q₈×C₇₃	C₂×C₄	1	8	yes	complemented
53	#117×C₇₃	—	2	4	no	—
54	#117×C₇₃	C₂×C₄	1	4	yes	—
55	#117×C₇₃	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₇₃	—	2	4	no	—
62	C₂×C₄⋊C₄×C₇₃	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₇₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₇₃	D₄	1	2	yes	—
69	C₂×C₄²×C₇₃	—	2	1	no	—
70	C₂×C₄²×C₇₃	—	2	2	no	—
71	C₂×C₄²×C₇₃	—	2	2	no	—
72	C₂×C₄²×C₇₃	—	2	2	no	—
73	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₇₃	—	2	4	no	—
76	#103×C₇₃	—	2	4	no	—
77	#103×C₇₃	—	2	4	no	—
78	#103×C₇₃	—	2	4	no	—
79	#103×C₇₃	—	2	4	no	—
80	C₂²⋊C₈×C₇₃	—	2	4	no	—
81	#97×C₇₃	—	2	2	no	—
82	C₄×C₈×C₇₃	—	2	2	no	—
83	#95×C₇₃	—	2	2	no	—
84	#95×C₇₃	—	2	2	no	—
85	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
86	C₂×Q₈×C₇₃	—	2	2	no	—
87	C₂×Q₈×C₇₃	—	2	2	no	—
88	C₂×Q₈×C₇₃	—	2	2	no	—
89	C₂×Q₈×C₇₃	—	2	2	no	—
90	C₂×Q₈×C₇₃	—	2	2	no	—
91	C₂×Q₈×C₇₃	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₇₃	—	2	2	no	—
93	C₂²×C₄×C₇₃	—	2	2	no	—
94	C₂²×C₄×C₇₃	—	2	2	no	—
95	C₂²×C₄×C₇₃	—	2	2	no	—
96	C₂²×C₄×C₇₃	—	2	2	no	—
97	C₂²×C₄×C₇₃	—	2	2	no	—
98	C₂²×C₄×C₇₃	—	2	4	no	—
99	C₂²×C₄×C₇₃	—	8	2	no	—
100	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
106	C₂×C₈×C₇₃	—	2	2	no	—
107	C₂×C₈×C₇₃	—	2	2	no	—
108	C₂×C₈×C₇₃	—	2	2	no	—
109	C₂×C₈×C₇₃	—	2	2	no	—
110	C₂×C₈×C₇₃	—	2	2	no	—
111	C₂×C₈×C₇₃	—	2	2	no	—
112	C₄⋊C₄×C₇₃	—	2	4	no	—
113	C₄⋊C₄×C₇₃	—	2	8	no	—
114	C₄⋊C₄×C₇₃	—	2	8	no	—
115	C₄⋊C₄×C₇₃	—	2	8	no	—
116	C₄⋊C₄×C₇₃	—	2	8	no	—
117	C₄⋊C₄×C₇₃	—	2	2	no	—
118	C₄⋊C₄×C₇₃	—	2	2	no	—
119	C₄⋊C₄×C₇₃	—	2	2	no	—
120	C₄⋊C₄×C₇₃	C₂²⋊C₄	1	8	yes	—
121	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
122	C₄⋊C₄×C₇₃	#41	1	4	yes	—
123	C₄⋊C₄×C₇₃	#41	1	4	yes	—
124	C₂²⋊C₄×C₇₃	—	2	4	no	—
125	C₂²⋊C₄×C₇₃	—	2	8	no	—
126	C₂²⋊C₄×C₇₃	C₂²⋊C₄	1	8	yes	—
127	C₄²×C₇₃	—	2	4	no	—
128	C₄²×C₇₃	—	2	8	no	—
129	C₄²×C₇₃	—	8	2	no	—
130	C₄²×C₇₃	—	8	2	no	—
131	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
132	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
133	C₄²×C₇₃	C₂×D₄	1	2	yes	—
134	C₄²×C₇₃	C₂×D₄	1	2	yes	—
135	C₂³×C₇₃	—	2	1	no	—
136	C₂³×C₇₃	—	2	1	no	—
137	C₂³×C₇₃	—	2	2	no	—
138	C₂³×C₇₃	—	2	2	no	—
139	C₂³×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
141	Q₈×C₇₃	—	2	4	no	—
142	Q₈×C₇₃	—	2	4	no	—
143	Q₈×C₇₃	—	4	2	no	—
144	Q₈×C₇₃	—	4	2	no	—
145	C₂×C₄×C₇₃	—	2	1	no	—
146	C₂×C₄×C₇₃	—	2	1	no	—
147	C₂×C₄×C₇₃	—	2	2	no	—
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	4	no	—
152	C₂×C₄×C₇₃	—	2	4	no	—
153	C₂×C₄×C₇₃	—	2	4	no	—
154	C₂×C₄×C₇₃	—	2	4	no	—
155	C₂×C₄×C₇₃	—	2	4	no	—
156	C₂×C₄×C₇₃	—	2	4	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	—	4	2	no	—
159	C₂×C₄×C₇₃	—	4	2	no	—
160	C₂×C₄×C₇₃	—	4	2	no	—
161	C₂×C₄×C₇₃	—	4	2	no	—
162	C₂×C₄×C₇₃	—	4	2	no	—
163	C₂×C₄×C₇₃	—	4	2	no	—
164	C₂×C₄×C₇₃	—	4	2	no	—
165	C₂×C₄×C₇₃	—	8	4	no	—
166	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
167	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	2	yes	—
169	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
172	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
173	C₈×C₇₃	—	4	2	no	—
174	C₈×C₇₃	—	4	2	no	—
175	C₂²×C₇₃	—	2	4	no	—
176	C₂²×C₇₃	—	2	2	no	—
177	C₂²×C₇₃	—	4	2	no	—
178	C₂²×C₇₃	—	4	1	no	—
179	C₂²×C₇₃	—	4	1	no	—
180	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₇₃	#525	1	1	yes	characteristic
182	C₂²×C₇₃	#525	1	1	yes	characteristic
183	C₂²×C₇₃	#577	1	2	yes	—
184	C₂²×C₇₃	#578	1	2	yes	—
185	C₄×C₇₃	—	2	4	no	—
186	C₄×C₇₃	—	2	4	no	—
187	C₄×C₇₃	—	2	2	no	—
188	C₄×C₇₃	—	4	4	no	—
189	C₄×C₇₃	—	4	4	no	—
190	C₄×C₇₃	—	4	4	no	—
191	C₄×C₇₃	—	4	4	no	—
192	C₄×C₇₃	C₄×#41	1	2	yes	—
193	C₄×C₇₃	#532	1	2	yes	—
194	#21398	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂×C₇₃	—	4	2	no	—
196	C₂×C₇₃	#2297	1	1	yes	characteristic
197	C₂×C₇₃	#2898	1	2	yes	—
198	C₂×C₇₃	#3120	1	2	yes	—
199	C₂×C₇₃	#3123	1	1	yes	characteristic
200	C₂×C₇₃	#3127	1	1	yes	characteristic
201	C₂×#541	C₂×C₇₃	1	1	yes	characteristic
202	C₂×#433	C₂×C₇₃	1	1	yes	characteristic
203	#2274	C₂×C₇₃	1	1	yes	characteristic
204	#1989	C₂×C₇₃	1	2	yes	complemented
205	#1981	C₂×C₇₃	1	2	yes	complemented
206	#1873	C₂×C₇₃	1	2	yes	—
207	#1872	C₂×C₇₃	1	2	yes	—
208	#1763	C₂×C₇₃	1	2	yes	complemented
209	C₄×#103	C₂×C₇₃	1	2	yes	complemented
210	C₇₃	#21398	1	1	yes	characteristic, direct product factor, Sylow
211	#541	—	2	4	no	—
212	#541	C₄×C₇₃	1	8	yes	complemented
213	C₂×C₄⋊Q₈	C₂²×C₇₃	1	1	yes	characteristic
214	C₂×#126	—	2	2	no	—
215	C₂×#125	—	2	2	no	—
216	C₂×#125	C₂²×C₇₃	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂²×C₇₃	1	2	yes	—
218	C₂×C₄×Q₈	C₂²×C₇₃	1	2	yes	—
219	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
220	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
221	C₂²×C₄⋊C₄	C₂²×C₇₃	1	1	yes	characteristic
222	#433	—	2	4	no	—
223	C₂×C₄⋊C₈	C₂²×C₇₃	1	2	yes	—
224	C₂×#103	C₂²×C₇₃	1	2	yes	—
225	C₂×#103	C₂²×C₇₃	1	2	yes	—
226	C₂×#103	C₂²×C₇₃	1	2	yes	—
227	C₂×#103	C₂²×C₇₃	1	2	yes	—
228	C₂×C₂²⋊C₈	C₂²×C₇₃	1	2	yes	—
229	C₂×#97	C₂²×C₇₃	1	1	yes	characteristic
230	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
231	C₄×C₄⋊C₄	—	2	2	no	—
232	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
233	C₄×C₄⋊C₄	C₂²×C₇₃	1	2	yes	—
234	C₄×C₂²⋊C₄	—	2	2	no	—
235	#340	C₂²×C₇₃	1	2	yes	—
236	#340	C₂²×C₇₃	1	2	yes	—
237	#340	C₂²×C₇₃	1	2	yes	—
238	#340	C₂²×C₇₃	1	2	yes	—
239	C₂²×Q₈	C₂³×C₇₃	1	2	yes	—
240	C₂³×C₄	—	2	1	no	—
241	C₂³×C₄	C₂³×C₇₃	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
243	C₂²×C₈	C₂³×C₇₃	1	2	yes	—
244	C₄⋊Q₈	—	2	2	no	—
245	C₄⋊Q₈	C₂×C₄×C₇₃	1	4	yes	complemented
246	#126	—	2	16	no	—
247	#125	—	2	16	no	—
248	#125	—	2	2	no	—
249	#125	C₂×C₄×C₇₃	1	4	yes	complemented
250	C₂²⋊Q₈	—	2	4	no	—
251	C₂²⋊Q₈	C₂×C₄×C₇₃	1	8	yes	—
252	C₄×Q₈	—	2	4	no	—
253	C₄×Q₈	C₂×C₄×C₇₃	1	8	yes	complemented
254	#117	—	2	4	no	—
255	#117	C₂×C₄×C₇₃	1	4	yes	—
256	#117	D₄×C₇₃	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	—	2	2	no	—
262	C₂×C₄⋊C₄	—	2	4	no	—
263	C₂×C₄⋊C₄	D₄×C₇₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
265	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
266	C₂×C₄⋊C₄	C₂³×C₇₃	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₇₃	1	2	yes	—
270	C₂×C₄²	—	2	1	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
276	C₄⋊C₈	—	2	4	no	—
277	#103	—	2	4	no	—
278	#103	—	2	4	no	—
279	#103	—	2	4	no	—
280	#103	—	2	4	no	—
281	C₂²⋊C₈	—	2	4	no	—
282	#97	—	2	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	C₂⁴	C₂×D₄×C₇₃	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	C₂²×C₄×C₇₃	1	4	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	8	2	no	—
301	C₂²×C₄	C₂²×C₄×C₇₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
306	C₂²×C₄	C₂⁴×C₇₃	1	1	yes	characteristic
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	C₂²⋊C₄×C₇₃	1	8	yes	—
322	C₄⋊C₄	C₂²×C₄×C₇₃	1	4	yes	—
323	C₄⋊C₄	#41×C₇₃	1	4	yes	—
324	C₄⋊C₄	#41×C₇₃	1	4	yes	—
325	C₂²⋊C₄	—	2	4	no	—
326	C₂²⋊C₄	—	2	8	no	—
327	C₂²⋊C₄	C₂²⋊C₄×C₇₃	1	8	yes	—
328	C₄²	—	2	4	no	—
329	C₄²	—	2	8	no	—
330	C₄²	—	8	2	no	—
331	C₄²	—	8	2	no	—
332	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
333	C₄²	C₂²×C₄×C₇₃	1	2	yes	—
334	C₄²	C₂×D₄×C₇₃	1	2	yes	—
335	C₄²	C₂×D₄×C₇₃	1	2	yes	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	2	no	—
340	C₂³	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
341	C₂³	C₂²×D₄×C₇₃	1	1	yes	characteristic
342	Q₈	—	2	4	no	—
343	Q₈	—	2	4	no	—
344	Q₈	—	4	2	no	—
345	Q₈	—	4	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	8	4	no	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	4	yes	—
368	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	4	yes	—
369	C₂×C₄	C₂×C₂²⋊C₄×C₇₃	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₇₃	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
373	C₂×C₄	C₂×#41×C₇₃	1	2	yes	—
374	C₈	—	4	2	no	—
375	C₈	—	4	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	C₂²×C₂²⋊C₄×C₇₃	1	1	yes	characteristic
382	C₂²	#525×C₇₃	1	1	yes	characteristic
383	C₂²	#525×C₇₃	1	1	yes	characteristic
384	C₂²	#577×C₇₃	1	2	yes	—
385	C₂²	#578×C₇₃	1	2	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	2	4	no	—
388	C₄	—	2	4	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	4	no	—
391	C₄	—	4	4	no	—
392	C₄	—	4	4	no	—
393	C₄	C₄×#41×C₇₃	1	2	yes	—
394	C₄	#532×C₇₃	1	2	yes	—
395	C₂	—	4	2	no	—
396	C₂	C₇₃×#2297	1	1	yes	characteristic
397	C₂	C₇₃×#2898	1	2	yes	—
398	C₂	C₇₃×#3120	1	2	yes	—
399	C₂	C₇₃×#3123	1	1	yes	characteristic
400	C₂	C₇₃×#3127	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇₃
prime radical	C₂⁴×C₇₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₇₃×#1989	C₂	semidirect
5. C₇₃×#1981	C₂	semidirect
8. C₇₃×#1763	C₂	semidirect
9. C₄×#103×C₇₃	C₂	semidirect
11. #541×C₇₃	C₄	semidirect
44. C₄⋊Q₈×C₇₃	C₂×C₄	semidirect
48. #125×C₇₃	C₂×C₄	semidirect
52. C₄×Q₈×C₇₃	C₂×C₄	semidirect
194. #21398	C₇₃	direct (N × H)
204. #1989	C₂×C₇₃	semidirect
205. #1981	C₂×C₇₃	semidirect
208. #1763	C₂×C₇₃	semidirect
209. C₄×#103	C₂×C₇₃	semidirect
210. C₇₃	#21398	direct (N × H)
212. #541	C₄×C₇₃	semidirect
245. C₄⋊Q₈	C₂×C₄×C₇₃	semidirect
249. #125	C₂×C₄×C₇₃	semidirect
253. C₄×Q₈	C₂×C₄×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#541×C₇₃	2
C₂×#433×C₇₃	2
C₇₃×#2274	2
C₇₃×#1989	2
C₇₃×#1981	2
C₇₃×#1873	2
C₇₃×#1872	2
C₇₃×#1763	2
C₄×#103×C₇₃	2
#21398	73

Subgroups — C73×#21398 #32930802

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#21398 #32930802