Subgroups — #33084014

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#108×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#427×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22618347	C₂	1	2	yes	maximal
4	C₂×#17988541	C₂	1	1	yes	maximal, characteristic
5	#22609816	C₂	1	2	yes	maximal, complemented
6	#22609814	C₂	1	2	yes	maximal, complemented
7	#22609813	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609812	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609810	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609639	C₂	1	2	yes	maximal
11	C₇₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₂×#14556548	C₂²	1	1	yes	characteristic
16	#117×D₇₃	C₂²	1	2	yes	—
17	C₂×#14556527	C₂²	1	1	yes	characteristic
18	C₂×#14556526	C₂²	1	2	yes	—
19	#108×D₇₃	C₄	1	8	yes	complemented
20	#17988625	C₂²	1	1	yes	characteristic
21	#17988624	C₄	1	2	yes	complemented
22	#17988623	C₂²	1	2	yes	—
23	#17988622	C₄	1	2	yes	complemented
24	#107×D₇₃	C₄	1	2	yes	complemented
25	#106×D₇₃	C₄	1	2	yes	complemented
26	#17988545	C₂²	1	2	yes	—
27	#17988544	—	2	2	no	—
28	#17988543	C₂²	1	2	yes	—
29	#17988542	C₂²	1	2	yes	—
30	#17988541	—	2	2	no	—
31	#17988541	C₄	1	8	yes	complemented
32	#17988539	—	2	2	no	—
33	C₄×#11924011	—	2	2	no	—
34	C₂×#14556502	C₂²	1	1	yes	characteristic
35	C₂×#14556501	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
37	#17988348	C₂²	1	2	yes	—
38	#17988347	C₂²	1	2	yes	—
39	#17988346	C₂²	1	2	yes	—
40	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
41	#427×C₇₃	C₂²	1	1	yes	characteristic
42	#405×C₇₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
44	#339×C₇₃	C₂²	1	2	yes	—
45	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
46	C₂×#11924012	C₂³	1	2	yes	—
47	C₂×#11924011	—	2	2	no	—
48	C₂×#11924011	C₂×C₄	1	4	yes	—
49	C₂×#11924011	D₄	1	1	yes	characteristic
50	C₂×#11924011	D₄	1	1	yes	characteristic
51	C₂×#11924011	D₄	1	1	yes	characteristic
52	C₂×#11924011	D₄	1	1	yes	characteristic
53	C₂×#11924011	Q₈	1	4	yes	—
54	M₁₆×D₇₃	—	2	4	no	—
55	M₁₆×D₇₃	C₂×C₄	1	8	yes	—
56	C₂²×#10596831	C₂³	1	1	yes	characteristic
57	C₂²×#10596831	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₇₃	—	2	2	no	—
59	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
64	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
65	#14556550	C₂³	1	2	yes	—
66	#14556549	C₂×C₄	1	4	yes	—
67	#14556548	—	2	2	no	—
68	#14556548	—	2	2	no	—
69	#14556548	C₂×C₄	1	4	yes	—
70	#14556547	—	2	2	no	—
71	C₂×#11924007	—	2	1	no	—
72	C₄⋊C₄×D₇₃	C₂×C₄	1	4	yes	—
73	C₂×#11924005	—	2	1	no	—
74	C₂²⋊C₄×D₇₃	—	2	2	no	—
75	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
76	C₄²×D₇₃	—	2	2	no	—
77	#14556527	C₂×C₄	1	4	yes	complemented
78	#14556526	C₂×C₄	1	8	yes	complemented
79	#14556525	C₂×C₄	1	2	yes	—
80	#14556524	C₂×C₄	1	4	yes	—
81	#14556523	C₂×C₄	1	2	yes	—
82	#14556522	C₂×C₄	1	4	yes	—
83	#14556502	—	2	2	no	—
84	#14556502	C₂×C₄	1	4	yes	complemented
85	#14556501	—	2	2	no	—
86	#14556501	—	2	2	no	—
87	#14556501	C₂×C₄	1	4	yes	complemented
88	C₄×#10596831	—	2	2	no	—
89	C₈×Dic₇₃	—	2	2	no	—
90	C₈×Dic₇₃	—	2	2	no	—
91	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
92	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
93	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
95	#117×C₇₃	C₂³	1	2	yes	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	#108×C₇₃	C₂×C₄	1	4	yes	complemented
98	#107×C₇₃	C₂×C₄	1	2	yes	—
99	#106×C₇₃	C₂×C₄	1	2	yes	—
100	#97×C₇₃	—	2	2	no	—
101	C₄×C₈×C₇₃	—	2	2	no	—
102	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
103	C₂³×D₇₃	#41	1	1	yes	characteristic
104	C₂²×Dic₇₃	—	2	1	no	—
105	C₂²×Dic₇₃	#41	1	1	yes	characteristic
106	C₂×C₄×D₇₃	—	2	4	no	—
107	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
108	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
109	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
114	C₂×C₄×D₇₃	#41	1	2	yes	—
115	#11924012	—	2	2	no	—
116	#11924012	C₂²×C₄	1	4	yes	—
117	#11924011	—	2	8	no	—
118	#11924011	C₄⋊C₄	1	4	yes	—
119	#11924011	C₄⋊C₄	1	4	yes	—
120	#11924011	C₄⋊C₄	1	4	yes	—
121	#11924011	C₄⋊C₄	1	4	yes	—
122	C₂×#10596831	—	2	2	no	—
123	C₂×#10596831	C₂²×C₄	1	2	yes	—
124	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
125	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
126	C₂×#10596831	C₂²×C₄	1	2	yes	—
127	C₂×#10596831	C₂²×C₄	1	2	yes	—
128	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
129	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
130	C₂×#10596831	C₂×Q₈	1	2	yes	—
131	C₈×D₇₃	—	2	8	no	—
132	C₈×D₇₃	C₄²	1	4	yes	—
133	C₈×D₇₃	C₄²	1	4	yes	—
134	C₈×D₇₃	C₄²	1	4	yes	—
135	C₈×D₇₃	C₄²	1	4	yes	—
136	C₄⋊Dic₇₃	C₂²×C₄	1	4	yes	—
137	#11924007	—	2	4	no	—
138	#11924007	—	2	4	no	—
139	C₂²⋊Dic₇₃	—	2	2	no	—
140	#11924005	—	2	4	no	—
141	#11924005	—	2	4	no	—
142	C₄×Dic₇₃	—	2	2	no	—
143	C₄×Dic₇₃	—	2	1	no	—
144	C₄×Dic₇₃	—	2	4	no	—
145	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
146	C₂²×C₄×C₇₃	—	2	1	no	—
147	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₇₃	—	2	2	no	—
149	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
155	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
159	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
160	C₂²⋊C₄×C₇₃	—	2	2	no	—
161	C₄²×C₇₃	—	2	2	no	—
162	C₄²×C₇₃	—	2	1	no	—
163	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
164	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
165	C₂²×D₇₃	—	4	2	no	—
166	C₂²×D₇₃	#117	1	2	yes	—
167	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
168	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
169	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	4	no	—
172	C₂×C₄×C₇₃	—	4	2	no	—
173	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
179	C₂×Dic₇₃	—	2	2	no	—
180	C₂×Dic₇₃	—	2	4	no	—
181	C₂×Dic₇₃	—	4	2	no	—
182	C₂×Dic₇₃	#117	1	2	yes	—
183	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
184	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
185	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
186	C₄×D₇₃	—	8	4	no	—
187	C₄×D₇₃	C₂×C₄²	1	2	yes	—
188	C₄×D₇₃	C₂×C₄²	1	2	yes	—
189	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
190	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
191	C₄×D₇₃	C₄×D₄	1	2	yes	—
192	C₄×D₇₃	C₄×D₄	1	2	yes	—
193	C₄×D₇₃	C₄×Q₈	1	2	yes	—
194	C₄×D₇₃	C₄×Q₈	1	2	yes	—
195	C₈×C₇₃	—	2	4	no	—
196	C₈×C₇₃	C₂×C₄²	1	2	yes	—
197	C₈×C₇₃	C₂×C₄²	1	2	yes	—
198	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
199	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
200	#10596831	—	2	4	no	—
201	#10596831	C₂×C₄²	1	2	yes	—
202	#10596831	C₂×C₄²	1	2	yes	—
203	#10596831	C₂×C₄⋊C₄	1	2	yes	—
204	#10596831	C₂×C₄⋊C₄	1	2	yes	—
205	C₂²×C₇₃	—	2	2	no	—
206	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
207	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
209	C₂×D₇₃	—	2	2	no	—
210	C₂×D₇₃	—	2	2	no	—
211	C₂×D₇₃	—	4	2	no	—
212	C₂×D₇₃	—	4	2	no	—
213	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
214	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
215	C₄×C₇₃	—	4	2	no	—
216	C₄×C₇₃	—	4	4	no	—
217	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
218	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
219	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
220	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
221	Dic₇₃	—	4	2	no	—
222	Dic₇₃	—	4	4	no	—
223	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
224	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
225	#20446	—	73	1	no	maximal, Sylow
226	C₂×C₇₃	—	2	1	no	—
227	C₂×C₇₃	—	2	1	no	—
228	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
229	C₂×C₇₃	#2957	1	2	yes	—
230	D₇₃	—	2	2	no	—
231	D₇₃	—	2	2	no	—
232	C₂²×#108	—	73	1	no	—
233	C₂×#427	—	73	1	no	—
234	#2873	—	73	2	no	—
235	C₂×#405	—	73	1	no	—
236	#1773	—	73	2	no	—
237	#1773	—	73	2	no	—
238	#1772	—	73	1	no	—
239	#1772	—	73	1	no	—
240	#1772	—	73	1	no	—
241	#1772	D₇₃	1	1	yes	characteristic, complemented
242	#1733	—	73	2	no	—
243	C₇₃	#20446	1	1	yes	characteristic, complemented, Sylow
244	C₂²×M₁₆	—	73	1	no	—
245	C₂²×M₁₆	—	73	2	no	—
246	C₂³×C₈	—	73	1	no	—
247	C₂×#117	—	73	1	no	—
248	C₂×#117	—	73	2	no	—
249	C₂×#108	—	73	2	no	—
250	C₂×#108	—	73	1	no	—
251	C₂×#108	—	73	8	no	—
252	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
253	#427	—	73	1	no	—
254	#427	—	73	2	no	—
255	#427	—	73	2	no	—
256	#427	—	73	2	no	—
257	#427	C₂×D₇₃	1	1	yes	characteristic
258	C₂×#107	—	73	2	no	—
259	C₂×#106	—	73	2	no	—
260	#405	—	73	8	no	—
261	#405	—	73	2	no	—
262	#405	—	73	2	no	—
263	#405	—	73	2	no	—
264	#405	—	146	2	no	—
265	#405	—	146	2	no	—
266	#405	C₂×D₇₃	1	2	yes	—
267	C₄×M₁₆	—	146	2	no	—
268	C₄×M₁₆	—	146	2	no	—
269	C₂×#97	—	73	1	no	—
270	C₂×#97	—	73	1	no	—
271	C₂×C₄×C₈	—	73	1	no	—
272	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
273	#339	—	73	2	no	—
274	#339	—	73	2	no	—
275	#339	—	73	2	no	—
276	#339	C₂×D₇₃	1	2	yes	—
277	C₂³×C₄	—	73	1	no	—
278	C₂×M₁₆	—	73	4	no	—
279	C₂×M₁₆	—	73	1	no	—
280	C₂×M₁₆	—	73	1	no	—
281	C₂×M₁₆	—	73	1	no	—
282	C₂×M₁₆	—	73	1	no	—
283	C₂×M₁₆	—	73	4	no	—
284	C₂×M₁₆	—	73	2	no	—
285	C₂×M₁₆	—	73	8	no	—
286	C₂×M₁₆	—	146	2	no	—
287	C₂×M₁₆	—	146	4	no	—
288	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
289	C₂²×C₈	—	73	1	no	—
290	C₂²×C₈	—	73	1	no	—
291	C₂²×C₈	—	73	4	no	—
292	C₂²×C₈	—	73	1	no	—
293	C₂²×C₈	—	73	1	no	—
294	C₂²×C₈	—	73	1	no	—
295	C₂²×C₈	—	73	1	no	—
296	C₂²×C₈	—	73	4	no	—
297	C₂²×C₈	—	146	2	no	—
298	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
299	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
300	#117	—	73	4	no	—
301	#117	—	73	2	no	—
302	#117	—	73	4	no	—
303	#117	—	146	2	no	—
304	#117	—	146	2	no	—
305	#117	—	146	2	no	—
306	#117	C₂²×D₇₃	1	2	yes	—
307	C₂×C₄⋊C₄	—	73	4	no	—
308	C₂×C₄⋊C₄	—	146	1	no	—
309	C₂×C₂²⋊C₄	—	146	2	no	—
310	C₂×C₂²⋊C₄	—	146	1	no	—
311	C₂×C₄²	—	73	1	no	—
312	C₂×C₄²	—	146	2	no	—
313	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
314	#108	—	73	8	no	—
315	#108	—	73	4	no	—
316	#108	C₄×D₇₃	1	4	yes	complemented
317	#107	—	73	2	no	—
318	#107	—	73	4	no	—
319	#107	C₄×D₇₃	1	2	yes	—
320	#106	—	73	2	no	—
321	#106	—	73	4	no	—
322	#106	C₄×D₇₃	1	2	yes	—
323	#97	—	2	2	no	—
324	#97	—	73	4	no	—
325	#97	—	73	4	no	—
326	#97	—	146	2	no	—
327	#97	—	146	2	no	—
328	#97	—	146	2	no	—
329	C₄×C₈	—	2	2	no	—
330	C₄×C₈	—	73	4	no	—
331	C₄×C₈	—	146	2	no	—
332	C₄×C₈	—	146	2	no	—
333	C₄×C₈	—	146	2	no	—
334	C₄×C₈	C₄×D₇₃	1	4	yes	complemented
335	C₂⁴	—	73	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	73	1	no	—
338	C₂²×C₄	—	73	1	no	—
339	C₂²×C₄	—	73	1	no	—
340	C₂²×C₄	—	73	2	no	—
341	C₂²×C₄	—	73	2	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	2	no	—
345	C₂²×C₄	—	73	2	no	—
346	C₂²×C₄	—	146	4	no	—
347	C₂²×C₄	—	146	1	no	—
348	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
349	M₁₆	—	2	2	no	—
350	M₁₆	—	73	4	no	—
351	M₁₆	—	73	4	no	—
352	M₁₆	—	73	4	no	—
353	M₁₆	—	73	4	no	—
354	M₁₆	—	73	4	no	—
355	M₁₆	—	146	8	no	—
356	M₁₆	—	146	2	no	—
357	M₁₆	C₂×C₄×D₇₃	1	4	yes	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	73	2	no	—
360	C₂×C₈	—	73	2	no	—
361	C₂×C₈	—	73	1	no	—
362	C₂×C₈	—	73	1	no	—
363	C₂×C₈	—	73	2	no	—
364	C₂×C₈	—	73	1	no	—
365	C₂×C₈	—	73	1	no	—
366	C₂×C₈	—	73	2	no	—
367	C₂×C₈	—	73	4	no	—
368	C₂×C₈	—	73	4	no	—
369	C₂×C₈	—	73	4	no	—
370	C₂×C₈	—	73	4	no	—
371	C₂×C₈	—	146	8	no	—
372	C₂×C₈	—	146	2	no	—
373	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
374	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
375	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
376	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
377	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
378	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
379	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
380	C₂×C₈	Q₈×D₇₃	1	2	yes	—
381	C₄⋊C₄	—	73	4	no	—
382	C₄⋊C₄	—	146	4	no	—
383	C₄⋊C₄	—	146	4	no	—
384	C₄⋊C₄	C₂×C₄×D₇₃	1	4	yes	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	146	4	no	—
387	C₂²⋊C₄	—	146	4	no	—
388	C₂²⋊C₄	—	146	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	73	2	no	—
392	C₄²	—	146	4	no	—
393	C₄²	—	146	2	no	—
394	C₄²	—	146	1	no	—
395	C₄²	C₂×C₄×D₇₃	1	2	yes	—
396	C₂³	—	292	2	no	—
397	C₂³	—	73	2	no	—
398	C₂³	—	73	2	no	—
399	C₂³	—	73	1	no	—
400	C₂³	—	73	1	no	—
401	C₂³	#41×D₇₃	1	1	yes	characteristic
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	292	2	no	—
406	C₂×C₄	—	584	4	no	—
407	C₂×C₄	—	73	2	no	—
408	C₂×C₄	—	73	1	no	—
409	C₂×C₄	—	73	1	no	—
410	C₂×C₄	—	73	2	no	—
411	C₂×C₄	—	73	2	no	—
412	C₂×C₄	—	73	2	no	—
413	C₂×C₄	—	73	2	no	—
414	C₂×C₄	—	73	2	no	—
415	C₂×C₄	—	73	2	no	—
416	C₂×C₄	—	73	2	no	—
417	C₂×C₄	—	73	2	no	—
418	C₂×C₄	—	73	2	no	—
419	C₂×C₄	—	146	2	no	—
420	C₂×C₄	—	146	4	no	—
421	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
422	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
424	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
426	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	—	73	2	no	—
429	C₈	—	73	2	no	—
430	C₈	—	73	2	no	—
431	C₈	—	73	2	no	—
432	C₈	—	146	4	no	—
433	C₈	C₄²×D₇₃	1	2	yes	—
434	C₈	C₄²×D₇₃	1	2	yes	—
435	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
436	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
437	C₂²	—	2	2	no	—
438	C₂²	—	292	2	no	—
439	C₂²	—	292	2	no	—
440	C₂²	—	73	2	no	—
441	C₂²	—	73	2	no	—
442	C₂²	—	146	2	no	—
443	C₂²	—	146	2	no	—
444	C₂²	#117×D₇₃	1	1	yes	characteristic
445	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
446	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
447	C₄	—	4	2	no	—
448	C₄	—	4	4	no	—
449	C₄	—	292	2	no	—
450	C₄	—	292	4	no	—
451	C₄	—	73	2	no	—
452	C₄	—	73	2	no	—
453	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
454	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
455	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
456	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
457	C₂	—	2	1	no	—
458	C₂	—	2	1	no	—
459	C₂	—	146	2	no	—
460	C₂	—	146	2	no	—
461	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
462	C₂	#22618843	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1772	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1772	D₇₃
hypocenter	C₇₃	#20446
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #22609816	C₂	semidirect
6. #22609814	C₂	semidirect
7. #22609813	C₂	semidirect
8. #22609812	C₂	semidirect
9. #22609810	C₂	semidirect
11. C₇₃×#1772	C₂	semidirect
19. #108×D₇₃	C₄	semidirect
21. #17988624	C₄	semidirect
23. #17988622	C₄	semidirect
24. #107×D₇₃	C₄	semidirect
25. #106×D₇₃	C₄	semidirect
31. #17988541	C₄	semidirect
77. #14556527	C₂×C₄	semidirect
78. #14556526	C₂×C₄	semidirect
84. #14556502	C₂×C₄	semidirect
87. #14556501	C₂×C₄	semidirect
91. C₈×Dic₇₃	C₂×C₄	semidirect
97. #108×C₇₃	C₂×C₄	semidirect
102. C₄×C₈×C₇₃	C₂×C₄	semidirect
241. #1772	D₇₃	semidirect
243. C₇₃	#20446	semidirect
316. #108	C₄×D₇₃	semidirect
334. C₄×C₈	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#108×D₇₃	2
#427×D₇₃	2
#22618347	2
C₂×#17988541	2
#22609816	2
#22609814	2
#22609813	2
#22609812	2
#22609810	2
#22609639	2
C₇₃×#1772	2
#20446	73