Subgroups — #33089532

Order 18688.

874 conjugacy classes of subgroups.

The subgroup lattice has 470 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	#22618518	C₂	1	2	yes	maximal
3	C₂×#17988622	C₂	1	1	yes	maximal, characteristic
4	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
5	#22610715	C₂	1	2	yes	maximal, complemented
6	#22610713	C₂	1	2	yes	maximal, complemented
7	#22610712	C₂	1	1	yes	maximal, characteristic, complemented
8	#22610711	C₂	1	1	yes	maximal, characteristic, complemented
9	#22610709	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609668	C₂	1	2	yes	maximal
11	C₇₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₂×#14556549	C₂²	1	2	yes	—
16	#117×D₇₃	C₂²	1	1	yes	characteristic
17	C₂×#14556527	C₂²	1	1	yes	characteristic
18	C₂×#14556526	C₂²	1	2	yes	—
19	#108×D₇₃	C₄	1	8	yes	complemented
20	#17988630	C₂²	1	2	yes	—
21	#17988629	C₂²	1	2	yes	—
22	#17988628	—	2	2	no	—
23	#17988627	C₂²	1	2	yes	—
24	#17988626	—	2	2	no	—
25	#17988624	—	2	2	no	—
26	#17988622	—	2	1	no	—
27	#17988622	—	2	1	no	—
28	#17988622	—	2	1	no	—
29	#17988622	—	2	1	no	—
30	#17988622	—	2	2	no	—
31	C₂×#14556524	C₂²	1	2	yes	—
32	C₂×#14556523	C₂²	1	1	yes	characteristic
33	#17988545	C₂²	1	1	yes	characteristic
34	#17988544	—	2	1	no	—
35	#17988543	C₂²	1	1	yes	characteristic
36	#17988542	C₂²	1	1	yes	characteristic
37	#17988541	—	2	1	no	—
38	#97×D₇₃	—	2	1	no	—
39	C₄×C₈×D₇₃	—	2	1	no	—
40	#17988356	C₂²	1	2	yes	—
41	#17988355	C₂²	1	2	yes	—
42	#17988355	C₂²	1	2	yes	—
43	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
44	#428×C₇₃	C₂²	1	2	yes	—
45	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
46	#405×C₇₃	C₂²	1	1	yes	characteristic
47	#343×C₇₃	C₂²	1	2	yes	—
48	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
49	C₂×#11924012	C₂³	1	2	yes	—
50	C₂×#11924012	C₂³	1	1	yes	characteristic
51	C₂×#11924011	—	2	2	no	—
52	C₂×#11924011	—	2	1	no	—
53	M₁₆×D₇₃	—	2	4	no	—
54	M₁₆×D₇₃	—	2	2	no	—
55	M₁₆×D₇₃	C₂×C₄	1	8	yes	—
56	M₁₆×D₇₃	Q₈	1	4	yes	—
57	C₂²×#10596831	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₇₃	—	2	2	no	—
59	C₂×C₈×D₇₃	—	2	1	no	—
60	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
61	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
62	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₇₃	Q₈	1	4	yes	—
66	#14556550	C₂³	1	1	yes	characteristic
67	#14556549	—	2	2	no	—
68	#14556549	—	2	2	no	—
69	#14556549	—	2	2	no	—
70	#14556549	—	2	2	no	—
71	#14556549	D₄	1	2	yes	—
72	#14556548	—	2	1	no	—
73	#14556547	—	2	1	no	—
74	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
75	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
76	C₂×#11924005	—	2	2	no	—
77	C₂²⋊C₄×D₇₃	—	2	1	no	—
78	C₂×C₄×Dic₇₃	—	2	2	no	—
79	C₄²×D₇₃	—	2	1	no	—
80	#14556527	C₂×C₄	1	4	yes	complemented
81	#14556526	C₂×C₄	1	8	yes	complemented
82	#14556525	—	2	2	no	—
83	#14556524	—	2	2	no	—
84	#14556524	—	2	2	no	—
85	#14556524	—	2	2	no	—
86	#14556524	—	2	2	no	—
87	#14556523	—	2	2	no	—
88	#14556523	—	2	1	no	—
89	#14556523	—	2	1	no	—
90	#14556522	—	2	2	no	—
91	#14556522	—	2	2	no	—
92	#14556502	—	2	1	no	—
93	#14556501	—	2	1	no	—
94	#14556501	—	2	1	no	—
95	C₄×#10596831	—	2	1	no	—
96	C₈×Dic₇₃	—	2	1	no	—
97	C₈×Dic₇₃	—	2	1	no	—
98	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
99	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	#117×C₇₃	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
103	#108×C₇₃	C₂×C₄	1	4	yes	complemented
104	#107×C₇₃	—	2	2	no	—
105	#106×C₇₃	—	2	1	no	—
106	#106×C₇₃	—	2	1	no	—
107	#106×C₇₃	—	2	2	no	—
108	#97×C₇₃	—	2	1	no	—
109	C₄×C₈×C₇₃	—	2	1	no	—
110	C₂³×D₇₃	#41	1	1	yes	characteristic
111	C₂²×Dic₇₃	—	2	2	no	—
112	C₂²×Dic₇₃	#41	1	1	yes	characteristic
113	C₂×C₄×D₇₃	—	2	2	no	—
114	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
115	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
120	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
121	C₂×C₄×D₇₃	#41	1	2	yes	—
122	#11924012	—	2	2	no	—
123	#11924012	—	2	1	no	—
124	#11924012	C₂²×C₄	1	4	yes	—
125	#11924012	C₂×Q₈	1	2	yes	—
126	#11924011	—	2	8	no	—
127	#11924011	—	2	4	no	—
128	C₂×#10596831	—	2	1	no	—
129	C₂×#10596831	—	2	2	no	—
130	C₂×#10596831	C₂²×C₄	1	2	yes	—
131	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
132	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
133	C₂×#10596831	C₂×Q₈	1	2	yes	—
134	C₈×D₇₃	—	2	8	no	—
135	C₈×D₇₃	—	2	4	no	—
136	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
137	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
138	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
139	C₈×D₇₃	C₄⋊C₄	1	4	yes	—
140	C₄⋊Dic₇₃	—	2	2	no	—
141	C₄⋊Dic₇₃	—	2	2	no	—
142	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
143	#11924007	—	2	2	no	—
144	C₂²⋊Dic₇₃	—	2	1	no	—
145	#11924005	—	2	2	no	—
146	#11924005	—	4	2	no	—
147	#11924005	—	4	2	no	—
148	C₄×Dic₇₃	—	2	1	no	—
149	C₄×Dic₇₃	—	2	2	no	—
150	C₄×Dic₇₃	—	4	2	no	—
151	C₄×Dic₇₃	—	4	2	no	—
152	C₂²×C₄×C₇₃	—	2	2	no	—
153	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
154	M₁₆×C₇₃	—	2	2	no	—
155	M₁₆×C₇₃	—	2	1	no	—
156	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
157	M₁₆×C₇₃	C₂×Q₈	1	2	yes	—
158	C₂×C₈×C₇₃	—	2	1	no	—
159	C₂×C₈×C₇₃	—	2	2	no	—
160	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
161	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
167	C₂²⋊C₄×C₇₃	—	2	1	no	—
168	C₄²×C₇₃	—	2	1	no	—
169	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
170	C₂²×D₇₃	—	4	2	no	—
171	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
172	C₂²×D₇₃	#121	1	1	yes	characteristic
173	C₂²×D₇₃	#121	1	1	yes	characteristic
174	C₂²×D₇₃	#125	1	2	yes	—
175	C₂×C₄×C₇₃	—	2	2	no	—
176	C₂×C₄×C₇₃	—	4	2	no	—
177	C₂×C₄×C₇₃	—	8	2	no	—
178	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₇₃	—	2	2	no	—
185	C₂×Dic₇₃	—	4	2	no	—
186	C₂×Dic₇₃	—	8	2	no	—
187	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
188	C₂×Dic₇₃	#121	1	1	yes	characteristic
189	C₂×Dic₇₃	#121	1	1	yes	characteristic
190	C₂×Dic₇₃	#125	1	2	yes	—
191	C₄×D₇₃	—	4	4	no	—
192	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
193	C₄×D₇₃	C₂×C₄⋊C₄	1	2	yes	—
194	C₄×D₇₃	C₄×D₄	1	2	yes	—
195	C₄×D₇₃	C₄×D₄	1	2	yes	—
196	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
197	C₄×D₇₃	C₂²⋊Q₈	1	2	yes	—
198	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
199	C₄×D₇₃	C₄⋊Q₈	1	2	yes	—
200	C₈×C₇₃	—	2	4	no	—
201	C₈×C₇₃	—	2	2	no	—
202	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
203	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
204	#10596831	—	2	4	no	—
205	#10596831	—	2	2	no	—
206	#10596831	C₂×C₄⋊C₄	1	2	yes	—
207	#10596831	C₂×C₄⋊C₄	1	2	yes	—
208	C₂²×C₇₃	—	2	2	no	—
209	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
210	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
211	C₂²×C₇₃	C₂×#125	1	1	yes	characteristic
212	C₂×D₇₃	—	2	2	no	—
213	C₂×D₇₃	—	2	2	no	—
214	C₂×D₇₃	—	4	2	no	—
215	C₂×D₇₃	—	4	2	no	—
216	C₂×D₇₃	#389	1	2	yes	—
217	C₂×D₇₃	#389	1	2	yes	—
218	C₄×C₇₃	—	4	2	no	—
219	C₄×C₇₃	—	8	2	no	—
220	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
221	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
222	C₄×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
223	C₄×C₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
224	Dic₇₃	—	4	2	no	—
225	Dic₇₃	—	8	2	no	—
226	Dic₇₃	#389	1	2	yes	—
227	Dic₇₃	#389	1	2	yes	—
228	#21181	—	73	1	no	maximal, Sylow
229	C₂×C₇₃	—	2	1	no	—
230	C₂×C₇₃	—	2	1	no	—
231	C₂×C₇₃	C₂×#389	1	1	yes	characteristic
232	C₂×C₇₃	#3067	1	2	yes	—
233	D₇₃	—	2	2	no	—
234	D₇₃	—	2	2	no	—
235	C₂²×#108	—	73	1	no	—
236	#2911	—	73	2	no	—
237	C₂×#427	—	73	1	no	—
238	C₂×#405	—	73	1	no	—
239	#1952	—	73	2	no	—
240	#1952	—	73	2	no	—
241	#1951	—	73	1	no	—
242	#1951	—	73	1	no	—
243	#1951	—	73	1	no	—
244	#1951	D₇₃	1	1	yes	characteristic, complemented
245	#1742	—	73	2	no	—
246	C₇₃	#21181	1	1	yes	characteristic, complemented, Sylow
247	C₂²×M₁₆	—	73	1	no	—
248	C₂²×M₁₆	—	73	2	no	—
249	C₂³×C₈	—	73	1	no	—
250	C₂×#117	—	73	1	no	—
251	C₂×#117	—	73	2	no	—
252	C₂×#108	—	73	2	no	—
253	C₂×#108	—	73	1	no	—
254	C₂×#108	—	73	8	no	—
255	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
256	#428	—	73	2	no	—
257	#428	—	73	2	no	—
258	#428	—	73	2	no	—
259	#428	—	146	2	no	—
260	#428	—	146	2	no	—
261	#428	C₂×D₇₃	1	2	yes	—
262	#427	—	146	2	no	—
263	#427	—	146	1	no	—
264	#427	—	146	1	no	—
265	#427	—	146	1	no	—
266	#427	—	146	1	no	—
267	#427	—	146	2	no	—
268	C₂×#107	—	73	2	no	—
269	C₂×#106	—	73	1	no	—
270	C₂×#106	C₂×D₇₃	1	1	yes	characteristic
271	#405	—	73	1	no	—
272	#405	—	73	1	no	—
273	#405	—	73	1	no	—
274	#405	—	146	1	no	—
275	#405	—	146	1	no	—
276	#405	C₂×D₇₃	1	1	yes	characteristic
277	C₂×#97	—	146	1	no	—
278	C₂×C₄×C₈	—	146	1	no	—
279	#343	—	73	2	no	—
280	#343	—	73	2	no	—
281	#343	—	73	2	no	—
282	#343	C₂×D₇₃	1	2	yes	—
283	C₂³×C₄	—	73	1	no	—
284	C₂×M₁₆	—	73	1	no	—
285	C₂×M₁₆	—	73	2	no	—
286	C₂×M₁₆	—	73	8	no	—
287	C₂×M₁₆	—	73	4	no	—
288	C₂×M₁₆	—	146	1	no	—
289	C₂×M₁₆	—	146	2	no	—
290	C₂×M₁₆	—	146	2	no	—
291	C₂×M₁₆	—	146	4	no	—
292	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
293	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
294	C₂²×C₈	—	73	1	no	—
295	C₂²×C₈	—	73	4	no	—
296	C₂²×C₈	—	73	1	no	—
297	C₂²×C₈	—	73	1	no	—
298	C₂²×C₈	—	73	1	no	—
299	C₂²×C₈	—	73	1	no	—
300	C₂²×C₈	—	73	4	no	—
301	C₂²×C₈	—	146	1	no	—
302	C₂²×C₈	—	146	2	no	—
303	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
304	#117	—	73	1	no	—
305	#117	—	73	2	no	—
306	#117	—	146	1	no	—
307	#117	—	146	2	no	—
308	#117	—	146	2	no	—
309	#117	—	146	2	no	—
310	#117	—	146	2	no	—
311	#117	—	146	1	no	—
312	#117	C₂²×D₇₃	1	1	yes	characteristic
313	C₂×C₄⋊C₄	—	73	2	no	—
314	C₂×C₄⋊C₄	—	73	2	no	—
315	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
316	C₂×C₂²⋊C₄	—	146	1	no	—
317	C₂×C₂²⋊C₄	—	146	2	no	—
318	C₂×C₄²	—	146	1	no	—
319	C₂×C₄²	—	146	2	no	—
320	#108	—	73	8	no	—
321	#108	—	73	4	no	—
322	#108	C₄×D₇₃	1	4	yes	complemented
323	#107	—	2	2	no	—
324	#107	—	146	2	no	—
325	#107	—	146	2	no	—
326	#107	—	146	2	no	—
327	#107	—	146	2	no	—
328	#107	—	146	2	no	—
329	#106	—	2	1	no	—
330	#106	—	2	1	no	—
331	#106	—	2	2	no	—
332	#106	—	146	2	no	—
333	#106	—	146	2	no	—
334	#106	—	146	1	no	—
335	#106	—	146	1	no	—
336	#106	—	146	2	no	—
337	#97	—	2	1	no	—
338	#97	—	146	1	no	—
339	#97	—	146	1	no	—
340	#97	—	146	1	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	—	146	1	no	—
343	C₄×C₈	—	146	1	no	—
344	C₄×C₈	—	146	1	no	—
345	C₂⁴	—	73	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	73	1	no	—
348	C₂²×C₄	—	73	2	no	—
349	C₂²×C₄	—	73	1	no	—
350	C₂²×C₄	—	73	1	no	—
351	C₂²×C₄	—	73	1	no	—
352	C₂²×C₄	—	73	1	no	—
353	C₂²×C₄	—	73	2	no	—
354	C₂²×C₄	—	73	2	no	—
355	C₂²×C₄	—	73	2	no	—
356	C₂²×C₄	—	146	2	no	—
357	C₂²×C₄	—	146	2	no	—
358	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
359	M₁₆	—	2	2	no	—
360	M₁₆	—	2	1	no	—
361	M₁₆	—	73	4	no	—
362	M₁₆	—	73	2	no	—
363	M₁₆	—	146	8	no	—
364	M₁₆	—	146	4	no	—
365	M₁₆	—	146	2	no	—
366	M₁₆	—	146	1	no	—
367	M₁₆	C₂×C₄×D₇₃	1	4	yes	—
368	M₁₆	Q₈×D₇₃	1	2	yes	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	73	2	no	—
372	C₂×C₈	—	73	1	no	—
373	C₂×C₈	—	73	1	no	—
374	C₂×C₈	—	73	2	no	—
375	C₂×C₈	—	73	4	no	—
376	C₂×C₈	—	73	4	no	—
377	C₂×C₈	—	73	4	no	—
378	C₂×C₈	—	73	4	no	—
379	C₂×C₈	—	146	8	no	—
380	C₂×C₈	—	146	4	no	—
381	C₂×C₈	—	146	1	no	—
382	C₂×C₈	—	146	2	no	—
383	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
384	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
386	C₂×C₈	Q₈×D₇₃	1	2	yes	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	73	2	no	—
390	C₄⋊C₄	—	146	2	no	—
391	C₄⋊C₄	—	146	2	no	—
392	C₄⋊C₄	—	146	2	no	—
393	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₂²⋊C₄	—	292	2	no	—
396	C₂²⋊C₄	—	292	2	no	—
397	C₂²⋊C₄	—	146	2	no	—
398	C₂²⋊C₄	—	146	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	292	2	no	—
401	C₄²	—	292	2	no	—
402	C₄²	—	146	2	no	—
403	C₄²	—	146	1	no	—
404	C₂³	—	292	2	no	—
405	C₂³	—	73	2	no	—
406	C₂³	—	73	2	no	—
407	C₂³	—	73	1	no	—
408	C₂³	—	73	1	no	—
409	C₂³	#41×D₇₃	1	1	yes	characteristic
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	292	4	no	—
414	C₂×C₄	—	292	2	no	—
415	C₂×C₄	—	584	2	no	—
416	C₂×C₄	—	73	2	no	—
417	C₂×C₄	—	73	1	no	—
418	C₂×C₄	—	73	1	no	—
419	C₂×C₄	—	73	2	no	—
420	C₂×C₄	—	73	2	no	—
421	C₂×C₄	—	73	2	no	—
422	C₂×C₄	—	73	2	no	—
423	C₂×C₄	—	73	2	no	—
424	C₂×C₄	—	73	2	no	—
425	C₂×C₄	—	73	2	no	—
426	C₂×C₄	—	73	2	no	—
427	C₂×C₄	—	73	2	no	—
428	C₂×C₄	—	146	2	no	—
429	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
430	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
431	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
432	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
433	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
434	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
435	C₈	—	2	4	no	—
436	C₈	—	2	2	no	—
437	C₈	—	73	2	no	—
438	C₈	—	73	2	no	—
439	C₈	—	146	4	no	—
440	C₈	—	146	2	no	—
441	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
442	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
443	C₂²	—	2	2	no	—
444	C₂²	—	292	2	no	—
445	C₂²	—	292	2	no	—
446	C₂²	—	73	2	no	—
447	C₂²	—	73	2	no	—
448	C₂²	—	146	2	no	—
449	C₂²	—	146	2	no	—
450	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
451	C₂²	#121×D₇₃	1	1	yes	characteristic
452	C₂²	#125×D₇₃	1	1	yes	characteristic
453	C₄	—	4	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	292	2	no	—
456	C₄	—	584	2	no	—
457	C₄	—	73	2	no	—
458	C₄	—	73	2	no	—
459	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
460	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
461	C₄	C₂²⋊Q₈×D₇₃	1	1	yes	characteristic
462	C₄	C₄⋊Q₈×D₇₃	1	1	yes	characteristic
463	C₂	—	2	1	no	—
464	C₂	—	2	1	no	—
465	C₂	—	146	2	no	—
466	C₂	—	146	2	no	—
467	C₂	#389×D₇₃	1	1	yes	characteristic
468	C₂	#22619646	1	2	yes	—

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1951	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1951	D₇₃
hypocenter	C₇₃	#21181
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #1951

Complements

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

N	H ≅ G/N	type
5. #22610715	C₂	semidirect
6. #22610713	C₂	semidirect
7. #22610712	C₂	semidirect
8. #22610711	C₂	semidirect
9. #22610709	C₂	semidirect
11. C₇₃×#1951	C₂	semidirect
19. #108×D₇₃	C₄	semidirect
80. #14556527	C₂×C₄	semidirect
81. #14556526	C₂×C₄	semidirect
103. #108×C₇₃	C₂×C₄	semidirect
244. #1951	D₇₃	semidirect
246. C₇₃	#21181	semidirect
322. #108	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
#22618518	2
C₂×#17988622	2
#405×D₇₃	2
#22610715	2
#22610713	2
#22610712	2
#22610711	2
#22610709	2
#22609668	2
C₇₃×#1951	2
#21181	73