Subgroups — #34020490

Order 18688.

1006 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#444	C₂	1	1	yes	maximal, characteristic
2	#22626685	C₂	1	1	yes	maximal, characteristic
3	#131×#64408	C₂	1	2	yes	maximal, complemented
4	#22625752	C₂	1	1	yes	maximal, characteristic, complemented
5	#22625740	C₂	1	1	yes	maximal, characteristic, complemented
6	#22625733	C₂	1	1	yes	maximal, characteristic, complemented
7	#22625711	C₂	1	2	yes	maximal, complemented
8	#22625705	C₂	1	2	yes	maximal, complemented
9	#22625696	C₂	1	2	yes	maximal, complemented
10	#22625587	C₂	1	1	yes	maximal, characteristic, complemented
11	#443×D₇₃	C₂	1	1	yes	maximal, characteristic
12	D₇₃⋊#131	C₂²	1	2	yes	—
13	#41×#64408	C₂²	1	2	yes	—
14	#17989634	C₄	1	2	yes	complemented
15	#17989633	C₄	1	2	yes	complemented
16	#17989632	C₄	1	4	yes	complemented
17	#17989628	C₄	1	2	yes	complemented
18	#17989627	C₄	1	2	yes	complemented
19	#17989626	C₄	1	4	yes	complemented
20	D₇₃⋊#108	C₂²	1	1	yes	characteristic
21	#17989597	C₂²	1	1	yes	characteristic
22	D₇₃⋊#104	C₂²	1	2	yes	—
23	#17989577	C₂²	1	2	yes	—
24	#17989553	—	2	2	no	—
25	#17989553	C₂²	1	2	yes	—
26	#17989550	—	2	2	no	—
27	#17989550	C₂²	1	2	yes	—
28	M₁₆×#64408	—	2	2	no	—
29	M₁₆×#64408	C₂²	1	2	yes	—
30	#17989546	C₂²	1	1	yes	characteristic
31	C₂×#14556645	C₂²	1	1	yes	characteristic
32	C₂×#14556645	C₂²	1	1	yes	characteristic
33	C₂×C₈×#64408	—	2	2	no	—
34	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
35	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
36	#17989523	C₂²	1	1	yes	characteristic
37	#17989462	C₂²	1	2	yes	—
38	#17989459	C₂²	1	2	yes	—
39	#17989458	C₂²	1	2	yes	—
40	#135×D₇₃	C₂²	1	1	yes	characteristic
41	#131×D₇₃	C₂²	1	2	yes	—
42	#17988705	C₄	1	1	yes	characteristic, complemented
43	#17988704	C₄	1	1	yes	characteristic, complemented
44	#17988703	C₄	1	1	yes	characteristic, complemented
45	#17988702	C₄	1	2	yes	complemented
46	#17988701	C₄	1	2	yes	complemented
47	#108×D₇₃	C₂²	1	1	yes	characteristic
48	#104×D₇₃	C₂²	1	2	yes	—
49	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
50	#443×C₇₃	C₄	1	1	yes	characteristic, complemented
51	#14556679	C₂×C₄	1	4	yes	complemented
52	#14556678	—	2	4	no	—
53	#14556678	C₂×C₄	1	4	yes	complemented
54	D₇₃⋊M₁₆	—	2	2	no	—
55	D₇₃⋊M₁₆	C₂³	1	2	yes	—
56	C₂×#11924036	—	2	2	no	—
57	C₂×#11924036	C₂³	1	1	yes	characteristic
58	C₂×#11924036	C₂³	1	1	yes	characteristic
59	Q₈×#64408	C₂×C₄	1	4	yes	—
60	D₄×#64408	—	2	4	no	—
61	D₄×#64408	C₂×C₄	1	4	yes	—
62	#14556670	—	2	2	no	—
63	#14556670	C₂³	1	2	yes	—
64	C₂×C₄×#64408	—	2	2	no	—
65	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
66	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
67	#14556662	C₂×C₄	1	2	yes	complemented
68	#14556661	C₂×C₄	1	2	yes	complemented
69	#14556660	C₂×C₄	1	2	yes	—
70	#14556659	C₂×C₄	1	2	yes	—
71	#14556656	C₂×C₄	1	4	yes	complemented
72	#14556655	C₂×C₄	1	4	yes	complemented
73	#14556654	C₂×C₄	1	4	yes	—
74	#14556653	C₂×C₄	1	4	yes	—
75	#14556646	—	2	2	no	—
76	#14556645	—	2	2	no	—
77	#14556645	—	2	2	no	—
78	#14556645	—	2	2	no	—
79	#14556645	C₂×C₄	1	2	yes	—
80	#14556645	C₂×C₄	1	2	yes	—
81	#14556645	C₂×C₄	1	2	yes	complemented
82	#14556645	C₂×C₄	1	2	yes	complemented
83	C₈×#64408	—	2	2	no	—
84	C₈×#64408	—	2	2	no	—
85	C₈×#64408	—	2	2	no	—
86	C₈×#64408	—	2	1	no	—
87	C₈×#64408	—	2	1	no	—
88	C₈×#64408	D₄	1	2	yes	—
89	C₈×#64408	D₄	1	2	yes	—
90	(C₂×#64408)⋊C₄	—	2	2	no	—
91	#41×D₇₃	C₂³	1	2	yes	—
92	#14556614	C₂×C₄	1	1	yes	characteristic
93	#14556613	C₂×C₄	1	1	yes	characteristic
94	#14556612	C₂×C₄	1	2	yes	—
95	#14556611	C₂×C₄	1	2	yes	—
96	#14556610	C₂×C₄	1	1	yes	characteristic
97	Q₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
98	SD₁₆×D₇₃	C₂×C₄	1	2	yes	—
99	D₈×D₇₃	C₂×C₄	1	1	yes	characteristic
100	#14556599	—	2	2	no	—
101	#14556599	C₂×C₄	1	2	yes	complemented
102	#14556598	C₂×C₄	1	2	yes	complemented
103	#14556597	—	2	2	no	—
104	#14556597	C₂×C₄	1	2	yes	complemented
105	M₁₆×D₇₃	—	2	2	no	—
106	M₁₆×D₇₃	C₂³	1	2	yes	—
107	C₂×C₈×D₇₃	—	2	2	no	—
108	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
109	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
110	C₄²×D₇₃	C₂³	1	1	yes	characteristic
111	#14556527	C₂×C₄	1	1	yes	characteristic, complemented
112	#14556526	C₂×C₄	1	2	yes	complemented
113	#14556519	C₂×C₄	1	2	yes	complemented
114	#14556518	C₂×C₄	1	2	yes	complemented
115	#14556517	C₂×C₄	1	2	yes	complemented
116	C₄×#10596831	C₂×C₄	1	1	yes	characteristic, complemented
117	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
118	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic, complemented
119	#135×C₇₃	C₂×C₄	1	1	yes	characteristic
120	#131×C₇₃	C₂×C₄	1	2	yes	complemented
121	#108×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
122	#104×C₇₃	C₂×C₄	1	2	yes	complemented
123	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂²×#64408	—	2	1	no	—
125	C₂²×#64408	—	2	4	no	—
126	C₂²×#64408	#41	1	2	yes	—
127	#11924038	—	2	4	no	—
128	#11924038	C₂²×C₄	1	4	yes	—
129	#11924037	—	2	2	no	—
130	#11924037	—	2	4	no	—
131	#11924036	—	2	2	no	—
132	#11924036	—	2	1	no	—
133	#11924036	—	2	4	no	—
134	#11924036	C₂²×C₄	1	2	yes	—
135	#11924036	C₂²×C₄	1	2	yes	—
136	#11924036	C₂×D₄	1	2	yes	—
137	C₂×#10596833	—	2	1	no	—
138	C₂×#10596833	—	2	4	no	—
139	C₂×#10596833	#41	1	2	yes	—
140	C₄⋊#64408	—	2	4	no	—
141	C₄⋊#64408	C₂²×C₄	1	4	yes	—
142	C₂²⋊#64408	—	2	2	no	—
143	C₂²⋊#64408	—	2	4	no	—
144	C₄×#64408	—	2	4	no	—
145	C₄×#64408	—	2	2	no	—
146	C₄×#64408	—	2	1	no	—
147	C₄×#64408	C₂²×C₄	1	2	yes	—
148	C₄×#64408	C₂²×C₄	1	2	yes	—
149	C₄×#64408	C₂×D₄	1	2	yes	—
150	#11924029	C₂²×C₄	1	2	yes	—
151	#11924028	—	2	2	no	—
152	#11924028	C₂²×C₄	1	2	yes	—
153	#11924027	—	2	2	no	—
154	#11924027	C₂²×C₄	1	2	yes	—
155	Q₈×D₇₃	C₂²×C₄	1	2	yes	—
156	D₄×D₇₃	—	2	2	no	—
157	D₄×D₇₃	C₂²×C₄	1	2	yes	—
158	C₂×C₄×D₇₃	—	2	2	no	—
159	C₂×C₄×D₇₃	—	2	1	no	—
160	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
161	Dic₂₉₂	C₄²	1	1	yes	characteristic
162	#11924018	C₄²	1	2	yes	—
163	#11924017	C₄²	1	2	yes	—
164	#11924016	C₄²	1	2	yes	—
165	#11924015	C₄²	1	2	yes	—
166	D₅₈₄	C₄²	1	1	yes	characteristic
167	#11924013	C₄²	1	2	yes	—
168	#11924012	—	2	2	no	—
169	#11924012	C₂²×C₄	1	2	yes	—
170	#11924011	—	2	2	no	—
171	#11924011	—	2	2	no	—
172	#11924011	—	2	2	no	—
173	C₂×#10596831	—	2	2	no	—
174	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
175	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
176	C₈×D₇₃	—	2	2	no	—
177	C₈×D₇₃	—	2	2	no	—
178	C₈×D₇₃	—	2	2	no	—
179	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
180	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
181	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
183	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
184	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
185	C₈×D₇₃	#41	1	1	yes	characteristic
186	C₈×D₇₃	#41	1	1	yes	characteristic
187	C₄×Dic₇₃	—	2	1	no	—
188	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
189	#41×C₇₃	C₂²×C₄	1	2	yes	—
190	Q₁₆×C₇₃	C₄²	1	1	yes	characteristic
191	SD₁₆×C₇₃	C₄²	1	2	yes	—
192	D₈×C₇₃	C₄²	1	1	yes	characteristic
193	M₁₆×C₇₃	—	2	2	no	—
194	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
195	C₂×C₈×C₇₃	—	2	2	no	—
196	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
198	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
199	C₂²×D₇₃	—	2	2	no	—
200	C₂²×D₇₃	C₂×#41	1	1	yes	characteristic
201	C₂×#64408	—	2	4	no	—
202	C₂×#64408	—	2	2	no	—
203	C₂×#64408	—	4	2	no	—
204	C₂×#64408	—	4	8	no	—
205	C₂×#64408	—	4	2	no	—
206	C₂×#64408	C₄×D₄	1	4	yes	—
207	Q₈×C₇₃	C₂×C₄²	1	2	yes	—
208	D₄×C₇₃	—	2	2	no	—
209	D₄×C₇₃	C₂×C₄²	1	2	yes	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	1	no	—
212	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
213	C₂²⋊D₇₃	—	2	2	no	—
214	C₂²⋊D₇₃	—	2	2	no	—
215	C₂²⋊D₇₃	—	2	2	no	—
216	C₂×Dic₇₃	—	2	2	no	—
217	C₂×Dic₇₃	—	2	1	no	—
218	C₂×Dic₇₃	C₂×#41	1	1	yes	characteristic
219	D₂₉₂	—	2	2	no	—
220	D₂₉₂	C₂×C₄²	1	2	yes	—
221	C₄×D₇₃	—	2	2	no	—
222	C₄×D₇₃	—	2	2	no	—
223	C₄×D₇₃	—	2	2	no	—
224	C₄×D₇₃	—	4	2	no	—
225	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
226	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
227	C₄×D₇₃	C₂²×D₄	1	1	yes	characteristic
228	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
229	Dic₁₄₆	—	2	2	no	—
230	Dic₁₄₆	C₂×C₄²	1	2	yes	—
231	#10596833	—	2	4	no	—
232	#10596833	—	2	2	no	—
233	#10596833	C₄×D₄	1	4	yes	—
234	C₈×C₇₃	—	2	2	no	—
235	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
236	C₈×C₇₃	C₂×C₄²	1	1	yes	characteristic
237	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
238	C₈×C₇₃	C₄×D₄	1	1	yes	characteristic
239	#10596831	—	2	2	no	—
240	#10596831	C₂×C₄²	1	1	yes	characteristic
241	#10596831	C₂×C₄²	1	1	yes	characteristic
242	#10596831	C₄×D₄	1	1	yes	characteristic
243	#10596831	C₄×D₄	1	1	yes	characteristic
244	C₂²×C₇₃	—	2	2	no	—
245	C₂²×C₇₃	C₄×#41	1	1	yes	characteristic
246	C₂×D₇₃	—	2	2	no	—
247	C₂×D₇₃	—	2	2	no	—
248	C₂×D₇₃	—	4	4	no	—
249	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
250	C₂×D₇₃	C₄×#41	1	1	yes	characteristic
251	#64408	—	2	4	no	—
252	#64408	—	4	2	no	—
253	#64408	—	4	4	no	—
254	C₄×C₇₃	—	2	2	no	—
255	C₄×C₇₃	—	4	1	no	—
256	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
257	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
258	Dic₇₃	—	2	2	no	—
259	Dic₇₃	—	4	1	no	—
260	Dic₇₃	C₂×C₄×D₄	1	1	yes	characteristic
261	Dic₇₃	C₄×#41	1	1	yes	characteristic
262	#20510	—	73	1	no	maximal, Sylow
263	C₂×C₇₃	—	2	1	no	—
264	C₂×C₇₃	—	4	2	no	—
265	C₂×C₇₃	C₄²×D₄	1	1	yes	characteristic
266	D₇₃	—	2	1	no	—
267	D₇₃	—	4	2	no	—
268	D₇₃	#2955	1	2	yes	—
269	C₂×#444	—	73	1	no	—
270	C₂×#443	—	73	1	no	—
271	#2943	—	73	1	no	—
272	C₄×#131	—	73	2	no	—
273	#1778	—	73	1	no	—
274	#1773	—	73	1	no	—
275	#1772	—	73	1	no	—
276	#1765	—	73	2	no	—
277	#1764	—	73	2	no	—
278	#1759	—	73	2	no	—
279	#1726	—	73	1	no	—
280	C₇₃	#20510	1	1	yes	characteristic, complemented, Sylow
281	C₂×#135	—	73	1	no	—
282	C₂×#131	—	73	2	no	—
283	C₂×#131	—	73	2	no	—
284	C₄×#41	—	73	2	no	—
285	#444	—	73	4	no	—
286	#444	—	73	2	no	—
287	#444	—	73	2	no	—
288	#443	—	73	1	no	—
289	#443	—	73	2	no	—
290	#443	—	73	1	no	—
291	#443	—	73	2	no	—
292	#443	—	73	1	no	—
293	#443	#64408	1	1	yes	characteristic, complemented
294	#442	—	73	2	no	—
295	#441	—	73	2	no	—
296	#440	—	73	4	no	—
297	C₂×#108	—	73	1	no	—
298	C₂×#108	—	73	1	no	—
299	#427	—	73	1	no	—
300	C₂×#104	—	73	2	no	—
301	C₂×#104	—	73	2	no	—
302	#416	—	73	2	no	—
303	#405	—	73	2	no	—
304	#405	—	73	2	no	—
305	#405	—	146	2	no	—
306	#405	—	146	2	no	—
307	C₄×M₁₆	—	73	2	no	—
308	C₄×M₁₆	—	146	2	no	—
309	C₂×#97	—	73	1	no	—
310	C₂×#97	—	73	1	no	—
311	C₂×#97	—	73	1	no	—
312	C₂×C₄×C₈	—	73	1	no	—
313	C₂×C₄×C₈	—	73	1	no	—
314	C₂×C₄×C₈	—	73	1	no	—
315	C₂×C₄×C₈	—	146	2	no	—
316	#376	—	73	1	no	—
317	#341	—	73	2	no	—
318	#339	—	73	2	no	—
319	#339	—	73	2	no	—
320	C₂×#41	—	73	2	no	—
321	#135	—	73	2	no	—
322	#135	—	73	1	no	—
323	#135	—	73	2	no	—
324	#135	—	73	1	no	—
325	#135	—	73	1	no	—
326	#135	C₂×#64408	1	1	yes	characteristic
327	C₂×Q₁₆	—	73	1	no	—
328	C₂×SD₁₆	—	73	2	no	—
329	C₂×D₈	—	73	1	no	—
330	#131	—	73	4	no	—
331	#131	—	73	4	no	—
332	#131	—	73	2	no	—
333	#131	—	73	2	no	—
334	#131	—	73	2	no	—
335	#131	—	146	2	no	—
336	#131	—	146	2	no	—
337	#131	—	146	4	no	—
338	#131	C₂×#64408	1	2	yes	complemented
339	C₂×M₁₆	—	73	2	no	—
340	C₂×M₁₆	—	73	2	no	—
341	C₂×M₁₆	—	146	2	no	—
342	C₂×M₁₆	—	146	2	no	—
343	C₂²×C₈	—	73	1	no	—
344	C₂²×C₈	—	73	1	no	—
345	C₂²×C₈	—	73	1	no	—
346	C₂²×C₈	—	73	1	no	—
347	C₂²×C₈	—	146	2	no	—
348	C₂²×C₈	—	146	2	no	—
349	C₄×Q₈	—	73	4	no	—
350	C₄×D₄	—	73	4	no	—
351	C₄×D₄	—	146	4	no	—
352	#117	—	73	2	no	—
353	#117	—	146	2	no	—
354	C₂×C₄²	—	73	1	no	—
355	C₂×C₄²	—	73	1	no	—
356	C₂×C₄²	—	73	1	no	—
357	C₂×C₄²	—	146	2	no	—
358	#108	—	73	2	no	—
359	#108	—	73	2	no	—
360	#108	—	73	2	no	—
361	#108	—	73	1	no	—
362	#108	C₂×#64408	1	1	yes	characteristic, complemented
363	#107	—	73	2	no	—
364	#106	—	73	2	no	—
365	#104	—	73	4	no	—
366	#104	—	73	4	no	—
367	#104	—	73	2	no	—
368	#104	—	73	2	no	—
369	#104	—	73	2	no	—
370	#104	C₂×#64408	1	2	yes	complemented
371	#103	—	73	4	no	—
372	#102	—	73	4	no	—
373	#97	—	73	2	no	—
374	#97	—	73	2	no	—
375	#97	—	73	2	no	—
376	#97	—	73	2	no	—
377	#97	—	146	2	no	—
378	#97	—	146	2	no	—
379	#97	—	146	2	no	—
380	#97	—	146	2	no	—
381	C₄×C₈	—	73	2	no	—
382	C₄×C₈	—	73	2	no	—
383	C₄×C₈	—	73	1	no	—
384	C₄×C₈	—	73	1	no	—
385	C₄×C₈	—	73	1	no	—
386	C₄×C₈	—	146	2	no	—
387	C₄×C₈	—	146	1	no	—
388	C₄×C₈	—	146	1	no	—
389	C₄×C₈	—	146	2	no	—
390	C₄×C₈	—	146	2	no	—
391	C₄×C₈	C₂×#64408	1	1	yes	characteristic, complemented
392	#95	—	146	2	no	—
393	#41	—	73	2	no	—
394	#41	—	73	2	no	—
395	#41	—	73	2	no	—
396	#41	—	146	2	no	—
397	#41	—	146	2	no	—
398	#41	C₂²×#64408	1	2	yes	—
399	C₂×Q₈	—	73	2	no	—
400	C₂×D₄	—	73	2	no	—
401	C₂×D₄	—	146	2	no	—
402	C₂²×C₄	—	73	2	no	—
403	C₂²×C₄	—	73	1	no	—
404	C₂²×C₄	—	146	1	no	—
405	C₂²×C₄	—	146	2	no	—
406	C₂²×C₄	—	146	4	no	—
407	C₂²×C₄	—	146	1	no	—
408	Q₁₆	—	73	2	no	—
409	Q₁₆	—	73	1	no	—
410	Q₁₆	C₄×#64408	1	1	yes	characteristic
411	SD₁₆	—	73	2	no	—
412	SD₁₆	—	73	2	no	—
413	SD₁₆	—	73	2	no	—
414	SD₁₆	C₄×#64408	1	2	yes	—
415	D₈	—	73	2	no	—
416	D₈	—	73	1	no	—
417	D₈	C₄×#64408	1	1	yes	characteristic
418	M₁₆	—	2	2	no	—
419	M₁₆	—	73	4	no	—
420	M₁₆	—	73	2	no	—
421	M₁₆	—	146	2	no	—
422	M₁₆	—	146	2	no	—
423	M₁₆	—	146	2	no	—
424	M₁₆	—	146	4	no	—
425	M₁₆	—	146	4	no	—
426	M₁₆	—	146	2	no	—
427	M₁₆	—	146	2	no	—
428	M₁₆	C₂²×#64408	1	2	yes	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	73	2	no	—
431	C₂×C₈	—	73	2	no	—
432	C₂×C₈	—	73	2	no	—
433	C₂×C₈	—	73	1	no	—
434	C₂×C₈	—	73	1	no	—
435	C₂×C₈	—	73	1	no	—
436	C₂×C₈	—	73	1	no	—
437	C₂×C₈	—	73	1	no	—
438	C₂×C₈	—	73	1	no	—
439	C₂×C₈	—	73	1	no	—
440	C₂×C₈	—	73	1	no	—
441	C₂×C₈	—	73	1	no	—
442	C₂×C₈	—	73	1	no	—
443	C₂×C₈	—	73	2	no	—
444	C₂×C₈	—	146	2	no	—
445	C₂×C₈	—	146	2	no	—
446	C₂×C₈	—	146	2	no	—
447	C₂×C₈	—	146	4	no	—
448	C₂×C₈	—	146	4	no	—
449	C₂×C₈	—	146	1	no	—
450	C₂×C₈	—	146	2	no	—
451	C₂×C₈	—	146	1	no	—
452	C₂×C₈	—	146	2	no	—
453	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
454	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
455	C₄⋊C₄	—	73	4	no	—
456	C₄⋊C₄	—	146	4	no	—
457	C₂²⋊C₄	—	146	4	no	—
458	C₂²⋊C₄	—	146	2	no	—
459	C₄²	—	73	2	no	—
460	C₄²	—	73	2	no	—
461	C₄²	—	73	2	no	—
462	C₄²	—	73	1	no	—
463	C₄²	—	146	1	no	—
464	C₄²	—	146	2	no	—
465	C₄²	—	146	1	no	—
466	C₄²	—	146	4	no	—
467	C₄²	C₂²×#64408	1	1	yes	characteristic
468	C₂³	—	73	1	no	—
469	C₂³	—	146	2	no	—
470	Q₈	—	73	2	no	—
471	Q₈	—	146	2	no	—
472	Q₈	C₂×C₄×#64408	1	2	yes	—
473	D₄	—	2	2	no	—
474	D₄	—	73	2	no	—
475	D₄	—	146	2	no	—
476	D₄	—	146	2	no	—
477	D₄	—	146	2	no	—
478	D₄	—	146	2	no	—
479	D₄	C₂×C₄×#64408	1	2	yes	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	292	2	no	—
483	C₂×C₄	—	292	2	no	—
484	C₂×C₄	—	292	8	no	—
485	C₂×C₄	—	292	2	no	—
486	C₂×C₄	—	73	1	no	—
487	C₂×C₄	—	73	1	no	—
488	C₂×C₄	—	73	1	no	—
489	C₂×C₄	—	73	1	no	—
490	C₂×C₄	—	73	1	no	—
491	C₂×C₄	—	73	4	no	—
492	C₂×C₄	—	146	2	no	—
493	C₂×C₄	—	146	2	no	—
494	C₂×C₄	—	146	2	no	—
495	C₂×C₄	—	146	4	no	—
496	C₂×C₄	—	146	1	no	—
497	C₂×C₄	—	146	2	no	—
498	C₂×C₄	—	146	2	no	—
499	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	73	4	no	—
502	C₈	—	73	1	no	—
503	C₈	—	73	1	no	—
504	C₈	—	73	1	no	—
505	C₈	—	73	1	no	—
506	C₈	—	146	2	no	—
507	C₈	—	146	4	no	—
508	C₈	—	146	2	no	—
509	C₈	C₂×C₄×#64408	1	1	yes	characteristic
510	C₈	C₂×C₄×#64408	1	1	yes	characteristic
511	C₈	D₄×#64408	1	1	yes	characteristic
512	C₈	D₄×#64408	1	1	yes	characteristic
513	C₂²	—	2	2	no	—
514	C₂²	—	292	4	no	—
515	C₂²	—	73	1	no	—
516	C₂²	—	73	1	no	—
517	C₂²	—	146	2	no	—
518	C₂²	—	146	2	no	—
519	C₂²	#41×#64408	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	4	1	no	—
522	C₄	—	292	1	no	—
523	C₄	—	292	4	no	—
524	C₄	—	292	2	no	—
525	C₄	—	73	1	no	—
526	C₄	—	73	1	no	—
527	C₄	—	146	4	no	—
528	C₄	—	146	2	no	—
529	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
530	C₄	C₂×D₄×#64408	1	1	yes	characteristic
531	C₂	—	2	1	no	—
532	C₂	—	4	2	no	—
533	C₂	—	292	2	no	—
534	C₂	—	73	2	no	—
535	C₂	—	146	1	no	—
536	C₂	C₄×D₄×#64408	1	1	yes	characteristic

	subgroup	G/H
center	C₈	D₄×#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#443×C₇₃	C₄
socle	C₂×C₇₃	C₄²×D₄
prime radical	#135×D₇₃	C₂²
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#443	#64408
hypocenter	C₇₃	#20510
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₈ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #131×#64408	C₂	semidirect
4. #22625752	C₂	semidirect
5. #22625740	C₂	semidirect
6. #22625733	C₂	semidirect
7. #22625711	C₂	semidirect
8. #22625705	C₂	semidirect
9. #22625696	C₂	semidirect
10. #22625587	C₂	semidirect
14. #17989634	C₄	semidirect
15. #17989633	C₄	semidirect
16. #17989632	C₄	semidirect
17. #17989628	C₄	semidirect
18. #17989627	C₄	semidirect
19. #17989626	C₄	semidirect
42. #17988705	C₄	semidirect
43. #17988704	C₄	semidirect
44. #17988703	C₄	semidirect
45. #17988702	C₄	semidirect
46. #17988701	C₄	semidirect
50. #443×C₇₃	C₄	semidirect
51. #14556679	C₂×C₄	semidirect
53. #14556678	C₂×C₄	semidirect
67. #14556662	C₂×C₄	semidirect
68. #14556661	C₂×C₄	semidirect
71. #14556656	C₂×C₄	semidirect
72. #14556655	C₂×C₄	semidirect
81. #14556645	C₂×C₄	semidirect
82. #14556645	C₂×C₄	semidirect
101. #14556599	C₂×C₄	semidirect
102. #14556598	C₂×C₄	semidirect
104. #14556597	C₂×C₄	semidirect
111. #14556527	C₂×C₄	semidirect
112. #14556526	C₂×C₄	semidirect
113. #14556519	C₂×C₄	semidirect
114. #14556518	C₂×C₄	semidirect
115. #14556517	C₂×C₄	semidirect
116. C₄×#10596831	C₂×C₄	semidirect
117. C₈×Dic₇₃	C₂×C₄	semidirect
118. C₈×Dic₇₃	C₂×C₄	semidirect
120. #131×C₇₃	C₂×C₄	semidirect
121. #108×C₇₃	C₂×C₄	semidirect
122. #104×C₇₃	C₂×C₄	semidirect
123. C₄×C₈×C₇₃	C₂×C₄	semidirect
280. C₇₃	#20510	semidirect
293. #443	#64408	semidirect
338. #131	C₂×#64408	semidirect
362. #108	C₂×#64408	semidirect
370. #104	C₂×#64408	semidirect
391. C₄×C₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#444	2
#22626685	2
#131×#64408	2
#22625752	2
#22625740	2
#22625733	2
#22625711	2
#22625705	2
#22625696	2
#22625587	2
#443×D₇₃	2
#20510	73