Subgroups — C₇₃×#18682 #32928086

Order 18688.

1134 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₃×#3543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇₃×#3217	C₂	1	2	yes	maximal, complemented
3	C₂×#493×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇₃×#1621	C₂	1	4	yes	maximal, complemented
5	C₇₃×#1620	C₂	1	2	yes	maximal, complemented
6	C₇₃×#1619	C₂	1	2	yes	maximal, complemented
7	C₇₃×#1555	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇₃×#1494	C₂	1	2	yes	maximal, complemented
9	C₂²×D₈×C₇₃	—	2	2	no	—
10	#560×C₇₃	—	2	2	no	—
11	#559×C₇₃	C₂²	1	1	yes	characteristic, complemented
12	#550×C₇₃	C₂²	1	2	yes	complemented
13	#546×C₇₃	—	2	2	no	—
14	D₄²×C₇₃	—	2	2	no	—
15	D₄²×C₇₃	C₂²	1	1	yes	characteristic, complemented
16	#540×C₇₃	—	2	2	no	—
17	#535×C₇₃	—	2	2	no	—
18	#534×C₇₃	—	2	2	no	—
19	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
20	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic, complemented
21	#529×C₇₃	C₂²	1	2	yes	—
22	#496×C₇₃	—	2	2	no	—
23	#493×C₇₃	—	2	2	no	—
24	#493×C₇₃	C₂²	1	2	yes	—
25	#493×C₇₃	C₂²	1	2	yes	complemented
26	#490×C₇₃	—	2	2	no	—
27	#460×C₇₃	C₂²	1	4	yes	complemented
28	#459×C₇₃	C₂²	1	4	yes	complemented
29	#450×C₇₃	—	2	2	no	—
30	#447×C₇₃	—	2	2	no	—
31	#432×C₇₃	C₂²	1	2	yes	complemented
32	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
33	#331×C₇₃	C₂²	1	2	yes	complemented
34	#331×C₇₃	C₂²	1	2	yes	complemented
35	Q₈⋊C₈×C₇₃	C₂²	1	4	yes	complemented
36	D₄⋊C₈×C₇₃	C₂²	1	4	yes	complemented
37	C₂×#41×C₇₃	—	2	2	no	—
38	C₂²×D₄×C₇₃	—	2	2	no	—
39	C₂²×D₄×C₇₃	—	2	2	no	—
40	C₂²×D₄×C₇₃	—	2	2	no	—
41	C₂²×D₄×C₇₃	—	2	1	no	—
42	C₂²×D₄×C₇₃	—	2	2	no	—
43	C₂²×D₄×C₇₃	D₄	1	2	yes	—
44	C₂×SD₁₆×C₇₃	—	2	4	no	—
45	C₂×D₈×C₇₃	—	2	4	no	—
46	C₂×D₈×C₇₃	—	2	4	no	—
47	C₂×D₈×C₇₃	—	2	4	no	—
48	C₂×D₈×C₇₃	—	4	8	no	—
49	C₂²×C₈×C₇₃	—	2	1	no	—
50	#127×C₇₃	—	2	2	no	—
51	#127×C₇₃	—	2	2	no	—
52	#127×C₇₃	—	2	2	no	—
53	#127×C₇₃	—	2	1	no	—
54	#127×C₇₃	D₄	1	2	yes	—
55	#127×C₇₃	C₂³	1	2	yes	—
56	#127×C₇₃	C₂³	1	1	yes	characteristic
57	#127×C₇₃	C₂³	1	1	yes	characteristic
58	#126×C₇₃	—	2	2	no	—
59	#125×C₇₃	D₄	1	2	yes	—
60	#124×C₇₃	—	2	2	no	—
61	#124×C₇₃	D₄	1	2	yes	—
62	#123×C₇₃	—	2	2	no	—
63	#123×C₇₃	—	2	4	no	—
64	#123×C₇₃	—	2	2	no	—
65	#123×C₇₃	—	2	2	no	—
66	C₂²⋊Q₈×C₇₃	D₄	1	2	yes	—
67	#121×C₇₃	—	2	4	no	—
68	#121×C₇₃	—	2	4	no	—
69	#121×C₇₃	—	2	4	no	—
70	#121×C₇₃	—	2	4	no	—
71	#121×C₇₃	—	2	2	no	—
72	#121×C₇₃	—	2	2	no	—
73	#121×C₇₃	D₄	1	2	yes	—
74	#120×C₇₃	—	2	2	no	—
75	#120×C₇₃	—	2	4	no	—
76	#120×C₇₃	—	2	4	no	—
77	#120×C₇₃	—	2	2	no	—
78	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
79	C₄×D₄×C₇₃	—	2	2	no	—
80	C₄×D₄×C₇₃	—	2	2	no	—
81	C₄×D₄×C₇₃	—	2	2	no	—
82	C₄×D₄×C₇₃	C₂³	1	2	yes	—
83	#117×C₇₃	—	2	2	no	—
84	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₇₃	C₂³	1	4	yes	—
87	#102×C₇₃	—	2	4	no	—
88	#102×C₇₃	—	2	4	no	—
89	C₂²⋊C₈×C₇₃	—	2	2	no	—
90	#97×C₇₃	—	2	2	no	—
91	C₄×C₈×C₇₃	—	2	1	no	—
92	C₄×C₈×C₇₃	C₂³	1	2	yes	—
93	C₂⁴×C₇₃	—	2	2	no	—
94	C₂⁴×C₇₃	—	2	2	no	—
95	C₂⁴×C₇₃	—	4	1	no	—
96	#41×C₇₃	—	8	4	no	—
97	C₂×Q₈×C₇₃	C₂×D₄	1	2	yes	—
98	C₂×D₄×C₇₃	—	2	2	no	—
99	C₂×D₄×C₇₃	—	2	4	no	—
100	C₂×D₄×C₇₃	—	2	4	no	—
101	C₂×D₄×C₇₃	—	2	4	no	—
102	C₂×D₄×C₇₃	—	2	2	no	—
103	C₂×D₄×C₇₃	—	2	4	no	—
104	C₂×D₄×C₇₃	—	2	2	no	—
105	C₂×D₄×C₇₃	—	2	2	no	—
106	C₂×D₄×C₇₃	—	2	4	no	—
107	C₂×D₄×C₇₃	—	2	2	no	—
108	C₂×D₄×C₇₃	—	4	4	no	—
109	C₂×D₄×C₇₃	—	4	4	no	—
110	C₂×D₄×C₇₃	—	4	1	no	—
111	C₂×D₄×C₇₃	—	4	2	no	—
112	C₂×D₄×C₇₃	—	8	4	no	—
113	C₂×D₄×C₇₃	—	8	4	no	—
114	C₂×D₄×C₇₃	—	8	4	no	—
115	C₂×D₄×C₇₃	—	8	4	no	—
116	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
117	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
118	C₂×D₄×C₇₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₇₃	—	2	4	no	—
120	C₂²×C₄×C₇₃	—	2	2	no	—
121	C₂²×C₄×C₇₃	—	2	2	no	—
122	C₂²×C₄×C₇₃	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
124	SD₁₆×C₇₃	—	8	4	no	—
125	D₈×C₇₃	—	4	8	no	—
126	D₈×C₇₃	—	4	8	no	—
127	D₈×C₇₃	—	8	4	no	—
128	C₂×C₈×C₇₃	—	2	4	no	—
129	C₂×C₈×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	4	no	—
131	C₄⋊C₄×C₇₃	—	2	2	no	—
132	C₄⋊C₄×C₇₃	—	2	2	no	—
133	C₄⋊C₄×C₇₃	—	2	2	no	—
134	C₄⋊C₄×C₇₃	—	2	2	no	—
135	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₇₃	—	2	2	no	—
138	C₂²⋊C₄×C₇₃	—	2	2	no	—
139	C₂²⋊C₄×C₇₃	—	2	4	no	—
140	C₂²⋊C₄×C₇₃	—	2	4	no	—
141	C₂²⋊C₄×C₇₃	—	2	2	no	—
142	C₂²⋊C₄×C₇₃	—	2	2	no	—
143	C₂²⋊C₄×C₇₃	—	2	2	no	—
144	C₂²⋊C₄×C₇₃	—	2	2	no	—
145	C₂²⋊C₄×C₇₃	—	2	2	no	—
146	C₄²×C₇₃	—	2	2	no	—
147	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₇₃	C₂×D₄	1	2	yes	—
149	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
150	C₂³×C₇₃	—	2	2	no	—
151	C₂³×C₇₃	—	2	2	no	—
152	C₂³×C₇₃	—	2	2	no	—
153	C₂³×C₇₃	—	4	4	no	—
154	C₂³×C₇₃	—	4	2	no	—
155	C₂³×C₇₃	—	8	4	no	—
156	C₂³×C₇₃	—	8	4	no	—
157	C₂³×C₇₃	—	8	4	no	—
158	C₂³×C₇₃	—	8	2	no	—
159	C₂³×C₇₃	—	8	2	no	—
160	C₂³×C₇₃	#120	1	1	yes	characteristic
161	Q₈×C₇₃	—	2	4	no	—
162	D₄×C₇₃	—	2	4	no	—
163	D₄×C₇₃	—	4	2	no	—
164	D₄×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	4	4	no	—
166	D₄×C₇₃	—	4	4	no	—
167	D₄×C₇₃	—	4	4	no	—
168	D₄×C₇₃	—	4	4	no	—
169	D₄×C₇₃	—	4	4	no	—
170	D₄×C₇₃	—	4	4	no	—
171	D₄×C₇₃	—	8	2	no	—
172	D₄×C₇₃	—	8	4	no	—
173	D₄×C₇₃	—	8	2	no	—
174	D₄×C₇₃	—	8	4	no	—
175	D₄×C₇₃	—	8	4	no	—
176	D₄×C₇₃	—	8	4	no	—
177	D₄×C₇₃	—	8	4	no	—
178	C₂×C₄×C₇₃	—	2	2	no	—
179	C₂×C₄×C₇₃	—	2	4	no	—
180	C₂×C₄×C₇₃	—	2	2	no	—
181	C₂×C₄×C₇₃	—	2	2	no	—
182	C₂×C₄×C₇₃	—	2	2	no	—
183	C₂×C₄×C₇₃	—	4	4	no	—
184	C₂×C₄×C₇₃	—	8	2	no	—
185	C₂×C₄×C₇₃	—	8	4	no	—
186	C₂×C₄×C₇₃	#120	1	2	yes	—
187	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
188	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
190	C₈×C₇₃	—	2	4	no	—
191	C₈×C₇₃	—	4	4	no	—
192	C₂²×C₇₃	—	2	2	no	—
193	C₂²×C₇₃	—	4	2	no	—
194	C₂²×C₇₃	—	4	4	no	—
195	C₂²×C₇₃	—	4	2	no	—
196	C₂²×C₇₃	—	4	4	no	—
197	C₂²×C₇₃	—	4	2	no	—
198	C₂²×C₇₃	—	4	2	no	—
199	C₂²×C₇₃	—	4	2	no	—
200	C₂²×C₇₃	—	8	4	no	—
201	C₂²×C₇₃	—	8	2	no	—
202	C₂²×C₇₃	—	16	4	no	—
203	C₂²×C₇₃	—	16	4	no	—
204	C₂²×C₇₃	—	16	4	no	—
205	C₂²×C₇₃	#453	1	2	yes	—
206	C₂²×C₇₃	C₂×#120	1	1	yes	characteristic
207	C₄×C₇₃	—	2	2	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	4	2	no	—
211	C₄×C₇₃	—	4	2	no	—
212	C₄×C₇₃	—	4	2	no	—
213	C₄×C₇₃	#576	1	4	yes	—
214	#18682	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂×C₇₃	—	2	2	no	—
216	C₂×C₇₃	—	8	2	no	—
217	C₂×C₇₃	—	8	2	no	—
218	C₂×C₇₃	—	8	2	no	—
219	C₂×C₇₃	—	16	2	no	—
220	C₂×C₇₃	#3008	1	2	yes	—
221	C₂×C₇₃	C₂×#453	1	1	yes	characteristic
222	#3543	C₂×C₇₃	1	1	yes	characteristic, complemented
223	#3217	C₂×C₇₃	1	2	yes	complemented
224	C₂×#493	C₂×C₇₃	1	1	yes	characteristic, complemented
225	#1621	C₂×C₇₃	1	4	yes	complemented
226	#1620	C₂×C₇₃	1	2	yes	complemented
227	#1619	C₂×C₇₃	1	2	yes	complemented
228	#1555	C₂×C₇₃	1	1	yes	characteristic, complemented
229	#1494	C₂×C₇₃	1	2	yes	complemented
230	C₇₃	#18682	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×D₈	—	2	2	no	—
232	#560	—	2	2	no	—
233	#559	C₂²×C₇₃	1	1	yes	characteristic, complemented
234	#550	C₂²×C₇₃	1	2	yes	complemented
235	#546	—	2	2	no	—
236	D₄²	—	2	2	no	—
237	D₄²	C₂²×C₇₃	1	1	yes	characteristic, complemented
238	#540	—	2	2	no	—
239	#535	—	2	2	no	—
240	#534	—	2	2	no	—
241	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic
242	C₂×#127	C₂²×C₇₃	1	1	yes	characteristic, complemented
243	#529	C₂²×C₇₃	1	2	yes	—
244	#496	—	2	2	no	—
245	#493	—	2	2	no	—
246	#493	C₂²×C₇₃	1	2	yes	—
247	#493	C₂²×C₇₃	1	2	yes	complemented
248	#490	—	2	2	no	—
249	#460	C₂²×C₇₃	1	4	yes	complemented
250	#459	C₂²×C₇₃	1	4	yes	complemented
251	#450	—	2	2	no	—
252	#447	—	2	2	no	—
253	#432	C₂²×C₇₃	1	2	yes	complemented
254	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic, complemented
255	#331	C₂²×C₇₃	1	2	yes	complemented
256	#331	C₂²×C₇₃	1	2	yes	complemented
257	Q₈⋊C₈	C₂²×C₇₃	1	4	yes	complemented
258	D₄⋊C₈	C₂²×C₇₃	1	4	yes	complemented
259	C₂×#41	—	2	2	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	—	2	2	no	—
262	C₂²×D₄	—	2	2	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	2	no	—
265	C₂²×D₄	D₄×C₇₃	1	2	yes	—
266	C₂×SD₁₆	—	2	4	no	—
267	C₂×D₈	—	2	4	no	—
268	C₂×D₈	—	2	4	no	—
269	C₂×D₈	—	2	4	no	—
270	C₂×D₈	—	4	8	no	—
271	C₂²×C₈	—	2	1	no	—
272	#127	—	2	2	no	—
273	#127	—	2	2	no	—
274	#127	—	2	2	no	—
275	#127	—	2	1	no	—
276	#127	D₄×C₇₃	1	2	yes	—
277	#127	C₂³×C₇₃	1	2	yes	—
278	#127	C₂³×C₇₃	1	1	yes	characteristic
279	#127	C₂³×C₇₃	1	1	yes	characteristic
280	#126	—	2	2	no	—
281	#125	D₄×C₇₃	1	2	yes	—
282	#124	—	2	2	no	—
283	#124	D₄×C₇₃	1	2	yes	—
284	#123	—	2	2	no	—
285	#123	—	2	4	no	—
286	#123	—	2	2	no	—
287	#123	—	2	2	no	—
288	C₂²⋊Q₈	D₄×C₇₃	1	2	yes	—
289	#121	—	2	4	no	—
290	#121	—	2	4	no	—
291	#121	—	2	4	no	—
292	#121	—	2	4	no	—
293	#121	—	2	2	no	—
294	#121	—	2	2	no	—
295	#121	D₄×C₇₃	1	2	yes	—
296	#120	—	2	2	no	—
297	#120	—	2	4	no	—
298	#120	—	2	4	no	—
299	#120	—	2	2	no	—
300	C₄×Q₈	C₂³×C₇₃	1	2	yes	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	—	2	2	no	—
304	C₄×D₄	C₂³×C₇₃	1	2	yes	—
305	#117	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₄²	C₂³×C₇₃	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₇₃	1	4	yes	—
309	#102	—	2	4	no	—
310	#102	—	2	4	no	—
311	C₂²⋊C₈	—	2	2	no	—
312	#97	—	2	2	no	—
313	C₄×C₈	—	2	1	no	—
314	C₄×C₈	C₂³×C₇₃	1	2	yes	—
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	4	1	no	—
318	#41	—	8	4	no	—
319	C₂×Q₈	C₂×D₄×C₇₃	1	2	yes	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	4	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	4	no	—
331	C₂×D₄	—	4	4	no	—
332	C₂×D₄	—	4	1	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	8	4	no	—
335	C₂×D₄	—	8	4	no	—
336	C₂×D₄	—	8	4	no	—
337	C₂×D₄	—	8	4	no	—
338	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
339	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
340	C₂×D₄	C₂×D₄×C₇₃	1	2	yes	—
341	C₂²×C₄	—	2	4	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂×D₄×C₇₃	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
346	SD₁₆	—	8	4	no	—
347	D₈	—	4	8	no	—
348	D₈	—	4	8	no	—
349	D₈	—	8	4	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
358	C₄⋊C₄	C₂×D₄×C₇₃	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	2	4	no	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	C₂×D₄×C₇₃	1	1	yes	characteristic
370	C₄²	C₂×D₄×C₇₃	1	2	yes	—
371	C₄²	C₂⁴×C₇₃	1	1	yes	characteristic
372	C₂³	—	2	2	no	—
373	C₂³	—	2	2	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	4	2	no	—
377	C₂³	—	8	4	no	—
378	C₂³	—	8	4	no	—
379	C₂³	—	8	4	no	—
380	C₂³	—	8	2	no	—
381	C₂³	—	8	2	no	—
382	C₂³	#120×C₇₃	1	1	yes	characteristic
383	Q₈	—	2	4	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	4	no	—
393	D₄	—	8	2	no	—
394	D₄	—	8	4	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	4	no	—
397	D₄	—	8	4	no	—
398	D₄	—	8	4	no	—
399	D₄	—	8	4	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	8	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	#120×C₇₃	1	2	yes	—
409	C₂×C₄	#120×C₇₃	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₇₃	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₇₃	1	2	yes	—
412	C₈	—	2	4	no	—
413	C₈	—	4	4	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	4	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	16	4	no	—
425	C₂²	—	16	4	no	—
426	C₂²	—	16	4	no	—
427	C₂²	#453×C₇₃	1	2	yes	—
428	C₂²	C₂×#120×C₇₃	1	1	yes	characteristic
429	C₄	—	2	2	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	#576×C₇₃	1	4	yes	—
436	C₂	—	2	2	no	—
437	C₂	—	8	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	8	2	no	—
440	C₂	—	16	2	no	—
441	C₂	C₇₃×#3008	1	2	yes	—
442	C₂	C₂×#453×C₇₃	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₇₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇₃×#3543	C₂	semidirect
2. C₇₃×#3217	C₂	semidirect
3. C₂×#493×C₇₃	C₂	semidirect
4. C₇₃×#1621	C₂	semidirect
5. C₇₃×#1620	C₂	semidirect
6. C₇₃×#1619	C₂	semidirect
7. C₇₃×#1555	C₂	semidirect
8. C₇₃×#1494	C₂	semidirect
11. #559×C₇₃	C₂²	semidirect
12. #550×C₇₃	C₂²	semidirect
15. D₄²×C₇₃	C₂²	semidirect
20. C₂×#127×C₇₃	C₂²	semidirect
25. #493×C₇₃	C₂²	semidirect
27. #460×C₇₃	C₂²	semidirect
28. #459×C₇₃	C₂²	semidirect
31. #432×C₇₃	C₂²	semidirect
32. C₂×C₄×C₈×C₇₃	C₂²	semidirect
33. #331×C₇₃	C₂²	semidirect
34. #331×C₇₃	C₂²	semidirect
35. Q₈⋊C₈×C₇₃	C₂²	semidirect
36. D₄⋊C₈×C₇₃	C₂²	semidirect
214. #18682	C₇₃	direct (N × H)
222. #3543	C₂×C₇₃	semidirect
223. #3217	C₂×C₇₃	semidirect
224. C₂×#493	C₂×C₇₃	semidirect
225. #1621	C₂×C₇₃	semidirect
226. #1620	C₂×C₇₃	semidirect
227. #1619	C₂×C₇₃	semidirect
228. #1555	C₂×C₇₃	semidirect
229. #1494	C₂×C₇₃	semidirect
230. C₇₃	#18682	direct (N × H)
233. #559	C₂²×C₇₃	semidirect
234. #550	C₂²×C₇₃	semidirect
237. D₄²	C₂²×C₇₃	semidirect
242. C₂×#127	C₂²×C₇₃	semidirect
247. #493	C₂²×C₇₃	semidirect
249. #460	C₂²×C₇₃	semidirect
250. #459	C₂²×C₇₃	semidirect
253. #432	C₂²×C₇₃	semidirect
254. C₂×C₄×C₈	C₂²×C₇₃	semidirect
255. #331	C₂²×C₇₃	semidirect
256. #331	C₂²×C₇₃	semidirect
257. Q₈⋊C₈	C₂²×C₇₃	semidirect
258. D₄⋊C₈	C₂²×C₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₇₃×#3543	2
C₇₃×#3217	2
C₂×#493×C₇₃	2
C₇₃×#1621	2
C₇₃×#1620	2
C₇₃×#1619	2
C₇₃×#1555	2
C₇₃×#1494	2
#18682	73

Subgroups — C73×#18682 #32928086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#18682 #32928086