Subgroups — #33950326

Order 18688.

2604 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22624704	C₂	1	1	yes	maximal, characteristic
2	#22624644	C₂	1	2	yes	maximal, complemented
3	#22618846	C₂	1	2	yes	maximal, complemented
4	#22618843	C₂	1	4	yes	maximal, complemented
5	#22618842	C₂	1	1	yes	maximal, characteristic, complemented
6	#22618839	C₂	1	4	yes	maximal, complemented
7	#22618834	C₂	1	1	yes	maximal, characteristic, complemented
8	#22618833	C₂	1	1	yes	maximal, characteristic, complemented
9	#22618829	C₂	1	4	yes	maximal, complemented
10	C₂×#17988706	C₂	1	2	yes	maximal, complemented
11	#444×D₇₃	C₂	1	4	yes	maximal, complemented
12	#22618541	C₂	1	1	yes	maximal, characteristic, complemented
13	#22618475	C₂	1	2	yes	maximal, complemented
14	#22618360	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#2956	C₂	1	1	yes	maximal, characteristic, complemented
16	#17989423	C₂²	1	2	yes	—
17	#17989403	C₄	1	4	yes	complemented
18	#17989397	C₄	1	4	yes	complemented
19	#17989396	C₄	1	4	yes	complemented
20	#17989391	C₄	1	4	yes	complemented
21	#17989387	C₂²	1	1	yes	characteristic
22	#17989384	C₂²	1	4	yes	—
23	C₂×#14556611	C₂²	1	2	yes	—
24	#135×D₇₃	C₂²	1	4	yes	—
25	#17989353	—	2	4	no	—
26	#17989353	C₂²	1	2	yes	—
27	#17989353	C₂²	1	2	yes	complemented
28	#17989352	—	2	4	no	—
29	#17989352	C₂²	1	8	yes	complemented
30	C₂×#14556599	—	2	4	no	—
31	C₂×#14556599	C₂²	1	1	yes	characteristic
32	C₂×#14556599	C₂²	1	1	yes	characteristic
33	C₂×#14556599	C₂²	1	2	yes	complemented
34	C₂×#14556598	C₂²	1	2	yes	complemented
35	#131×D₇₃	—	2	4	no	—
36	#131×D₇₃	C₂²	1	8	yes	complemented
37	C₄×#11924028	C₂²	1	1	yes	characteristic
38	#17988710	C₂²	1	4	yes	complemented
39	#17988709	C₂²	1	4	yes	complemented
40	#17988708	C₂²	1	4	yes	complemented
41	#17988707	C₂²	1	8	yes	complemented
42	#17988706	C₂²	1	4	yes	complemented
43	#17988706	C₂²	1	4	yes	complemented
44	#17988706	C₂²	1	4	yes	complemented
45	#17988706	C₂²	1	4	yes	complemented
46	#17988705	C₂²	1	4	yes	complemented
47	#17988704	C₂²	1	4	yes	complemented
48	#17988703	C₂²	1	4	yes	complemented
49	#17988702	C₂²	1	8	yes	complemented
50	#17988636	C₂²	1	1	yes	characteristic, complemented
51	#17988634	C₂²	1	4	yes	complemented
52	C₂×#14556526	C₂²	1	2	yes	complemented
53	#108×D₇₃	C₂²	1	4	yes	complemented
54	#17988604	C₂²	1	2	yes	complemented
55	#17988603	C₂²	1	2	yes	complemented
56	#17988602	C₂²	1	8	yes	complemented
57	C₂×#14556519	C₂²	1	2	yes	complemented
58	#104×D₇₃	C₂²	1	8	yes	complemented
59	#17988545	C₂²	1	1	yes	characteristic, complemented
60	#17988545	C₂²	1	1	yes	characteristic, complemented
61	#17988541	C₂²	1	2	yes	complemented
62	#17988541	C₂²	1	2	yes	complemented
63	#17988539	C₂²	1	2	yes	complemented
64	C₂×#14556502	C₂²	1	1	yes	characteristic, complemented
65	#97×D₇₃	C₂²	1	2	yes	complemented
66	#575×C₇₃	C₂²	1	1	yes	characteristic
67	#568×C₇₃	C₂²	1	2	yes	complemented
68	#444×C₇₃	C₂²	1	4	yes	complemented
69	#443×C₇₃	C₂²	1	4	yes	complemented
70	#430×C₇₃	C₂²	1	1	yes	characteristic, complemented
71	C₂×#104×C₇₃	C₂²	1	2	yes	complemented
72	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
73	#14556639	C₂×C₄	1	4	yes	—
74	#14556638	—	2	2	no	—
75	#14556638	C₂×C₄	1	4	yes	—
76	#14556637	—	2	2	no	—
77	#14556637	C₂×C₄	1	4	yes	—
78	#14556636	—	2	4	no	—
79	#14556636	C₂×C₄	1	4	yes	—
80	C₂×#11924028	—	2	4	no	—
81	C₂×#11924028	C₂³	1	2	yes	—
82	C₂×#11924028	C₂³	1	1	yes	characteristic
83	#41×D₇₃	—	2	4	no	—
84	#41×D₇₃	C₂³	1	8	yes	—
85	#14556624	C₂×C₄	1	4	yes	complemented
86	#14556623	C₂×C₄	1	8	yes	complemented
87	#14556620	C₂×C₄	1	8	yes	complemented
88	#14556619	C₂×C₄	1	4	yes	complemented
89	#14556618	C₂×C₄	1	8	yes	complemented
90	#14556615	C₂×C₄	1	8	yes	complemented
91	#14556614	C₂×C₄	1	4	yes	complemented
92	#14556613	C₂³	1	4	yes	—
93	#14556612	C₂×C₄	1	8	yes	complemented
94	#14556611	C₂×C₄	1	4	yes	complemented
95	#14556611	C₂×C₄	1	4	yes	complemented
96	#14556611	C₂³	1	4	yes	—
97	#14556611	C₂³	1	4	yes	—
98	#14556610	C₂×C₄	1	4	yes	complemented
99	C₂×#11924018	C₂×C₄	1	2	yes	complemented
100	Q₁₆×D₇₃	C₂×C₄	1	4	yes	complemented
101	C₂×#11924016	C₂×C₄	1	2	yes	complemented
102	C₂×#11924015	C₂×C₄	1	2	yes	complemented
103	SD₁₆×D₇₃	C₂×C₄	1	8	yes	complemented
104	C₂×#11924013	C₂×C₄	1	2	yes	complemented
105	D₈×D₇₃	C₂×C₄	1	4	yes	complemented
106	#14556599	—	2	4	no	—
107	#14556599	—	2	8	no	—
108	#14556599	—	2	2	no	—
109	#14556599	—	2	2	no	—
110	#14556599	—	2	8	no	—
111	#14556599	—	2	4	no	—
112	#14556599	C₂×C₄	1	4	yes	—
113	#14556599	C₂×C₄	1	4	yes	—
114	#14556599	D₄	1	4	yes	—
115	#14556599	D₄	1	4	yes	—
116	#14556599	C₂³	1	4	yes	—
117	#14556599	C₂³	1	4	yes	—
118	#14556598	—	2	2	no	—
119	#14556598	—	2	2	no	—
120	#14556598	C₂³	1	4	yes	—
121	#14556598	C₂³	1	4	yes	—
122	#14556597	—	2	4	no	—
123	#14556597	—	2	8	no	—
124	#14556597	—	2	8	no	—
125	#14556597	C₂³	1	8	yes	—
126	C₂×#11924012	—	2	2	no	—
127	C₂×#11924012	C₂³	1	2	yes	—
128	C₂×#11924011	—	2	8	no	—
129	C₂×#11924011	—	2	2	no	—
130	C₂×#11924011	C₂³	1	2	yes	—
131	C₂×#11924011	C₂³	1	2	yes	—
132	M₁₆×D₇₃	—	2	8	no	—
133	M₁₆×D₇₃	—	2	8	no	—
134	M₁₆×D₇₃	—	2	4	no	—
135	M₁₆×D₇₃	C₂³	1	8	yes	—
136	C₂²×#10596831	—	2	2	no	—
137	C₂²×#10596831	C₂³	1	1	yes	characteristic
138	C₂²×#10596831	C₂³	1	1	yes	characteristic
139	C₂×C₈×D₇₃	—	2	2	no	—
140	C₂×C₈×D₇₃	—	2	8	no	—
141	C₂×C₈×D₇₃	C₂³	1	2	yes	—
142	C₂×C₈×D₇₃	C₂³	1	2	yes	—
143	C₄×Dic₁₄₆	—	2	1	no	—
144	C₄×D₂₉₂	—	2	1	no	—
145	C₄×C₂²⋊D₇₃	—	2	2	no	—
146	#14556550	C₂³	1	1	yes	characteristic
147	#14556548	C₂³	1	2	yes	—
148	C₄²×D₇₃	C₂³	1	2	yes	—
149	#14556527	C₂³	1	4	yes	—
150	#14556526	C₂³	1	4	yes	—
151	#14556526	C₂³	1	4	yes	—
152	#14556519	C₂³	1	4	yes	—
153	#14556519	C₂³	1	4	yes	—
154	#14556518	C₂³	1	8	yes	—
155	#14556517	C₂³	1	8	yes	—
156	#14556502	C₂³	1	1	yes	characteristic
157	#14556502	C₂³	1	1	yes	characteristic
158	#14556502	C₂³	1	1	yes	characteristic
159	#14556502	C₂³	1	1	yes	characteristic
160	#14556501	C₂³	1	2	yes	—
161	#14556501	C₂³	1	2	yes	—
162	C₈×Dic₇₃	C₂³	1	2	yes	—
163	C₈×Dic₇₃	C₂³	1	2	yes	—
164	C₂×#41×C₇₃	C₂³	1	2	yes	—
165	#137×C₇₃	C₂×C₄	1	4	yes	complemented
166	AGL(1,ℤ/8)×C₇₃	C₂×C₄	1	4	yes	complemented
167	#135×C₇₃	C₂³	1	4	yes	—
168	#131×C₇₃	—	2	4	no	—
169	#131×C₇₃	C₂³	1	8	yes	—
170	C₂×M₁₆×C₇₃	—	2	4	no	—
171	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
172	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
173	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
175	#108×C₇₃	C₂³	1	4	yes	—
176	#104×C₇₃	C₂³	1	4	yes	—
177	#104×C₇₃	C₂³	1	4	yes	—
178	#97×C₇₃	C₂³	1	2	yes	—
179	C₄×C₈×C₇₃	C₂³	1	2	yes	—
180	#11924029	—	2	4	no	—
181	#11924029	C₂²×C₄	1	8	yes	—
182	#11924028	—	2	2	no	—
183	#11924028	—	2	2	no	—
184	#11924028	—	2	8	no	—
185	#11924028	—	2	4	no	—
186	#11924028	—	2	8	no	—
187	#11924028	—	2	4	no	—
188	#11924028	C₂²×C₄	1	4	yes	—
189	#11924028	C₂²×C₄	1	4	yes	—
190	#11924028	C₂×D₄	1	4	yes	—
191	#11924028	C₂⁴	1	4	yes	—
192	#11924027	—	2	8	no	—
193	#11924027	—	2	8	no	—
194	#11924027	—	2	4	no	—
195	#11924027	C₂²×C₄	1	8	yes	—
196	C₂×Dic₁₄₆	—	2	4	no	—
197	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
198	C₂×Dic₁₄₆	#41	1	1	yes	characteristic
199	Q₈×D₇₃	—	2	4	no	—
200	Q₈×D₇₃	C₂²×C₄	1	8	yes	—
201	C₂×D₂₉₂	—	2	4	no	—
202	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
203	C₂×D₂₉₂	#41	1	1	yes	characteristic
204	C₂×C₂²⋊D₇₃	—	2	2	no	—
205	C₂×C₂²⋊D₇₃	—	2	8	no	—
206	C₂×C₂²⋊D₇₃	#41	1	2	yes	—
207	D₄×D₇₃	—	2	8	no	—
208	D₄×D₇₃	—	2	8	no	—
209	D₄×D₇₃	—	2	4	no	—
210	D₄×D₇₃	C₂²×C₄	1	8	yes	—
211	C₂×C₄×D₇₃	—	2	2	no	—
212	C₂×C₄×D₇₃	—	2	8	no	—
213	C₂×C₄×D₇₃	—	2	2	no	—
214	C₂×C₄×D₇₃	C₂⁴	1	2	yes	—
215	Dic₂₉₂	C₂²×C₄	1	4	yes	—
216	#11924018	C₂²×C₄	1	4	yes	—
217	#11924018	C₂²×C₄	1	4	yes	—
218	#11924017	C₂²×C₄	1	8	yes	—
219	#11924016	C₂²×C₄	1	4	yes	—
220	#11924016	C₂²×C₄	1	4	yes	—
221	#11924015	C₂²×C₄	1	4	yes	—
222	#11924015	C₂²×C₄	1	4	yes	—
223	D₅₈₄	C₂²×C₄	1	4	yes	—
224	#11924013	C₂²×C₄	1	4	yes	—
225	#11924013	C₂²×C₄	1	4	yes	—
226	#11924012	—	2	2	no	—
227	#11924012	—	2	4	no	—
228	#11924012	—	2	4	no	—
229	#11924012	C₂⁴	1	4	yes	—
230	#11924011	—	2	8	no	—
231	#11924011	—	2	8	no	—
232	#11924011	—	2	4	no	—
233	#11924011	—	2	4	no	—
234	#11924011	C₂²×C₄	1	8	yes	—
235	#11924011	C₂×D₄	1	4	yes	—
236	#11924011	C₂×D₄	1	4	yes	—
237	C₂×#10596831	—	2	2	no	—
238	C₂×#10596831	—	2	4	no	—
239	C₂×#10596831	—	2	4	no	—
240	C₂×#10596831	C₂²×C₄	1	2	yes	—
241	C₂×#10596831	C₂²×C₄	1	2	yes	—
242	C₂×#10596831	C₂×D₄	1	2	yes	—
243	C₂×#10596831	C₂×D₄	1	2	yes	—
244	C₂×#10596831	C₂⁴	1	1	yes	characteristic
245	C₂×#10596831	C₂⁴	1	1	yes	characteristic
246	C₂×#10596831	C₂⁴	1	1	yes	characteristic
247	C₂×#10596831	C₂⁴	1	1	yes	characteristic
248	C₈×D₇₃	—	2	8	no	—
249	C₈×D₇₃	—	2	8	no	—
250	C₈×D₇₃	—	2	4	no	—
251	C₈×D₇₃	—	2	4	no	—
252	C₈×D₇₃	C₂²×C₄	1	4	yes	—
253	C₈×D₇₃	C₂²×C₄	1	4	yes	—
254	C₈×D₇₃	C₂×D₄	1	8	yes	—
255	C₄⋊Dic₇₃	—	2	1	no	—
256	#11924007	—	2	2	no	—
257	C₂²⋊Dic₇₃	—	2	1	no	—
258	#11924005	—	2	2	no	—
259	C₄×Dic₇₃	—	2	2	no	—
260	C₄×Dic₇₃	C₂⁴	1	2	yes	—
261	#41×C₇₃	—	2	2	no	—
262	#41×C₇₃	—	2	2	no	—
263	#41×C₇₃	C₂²×C₄	1	4	yes	—
264	#41×C₇₃	C₂⁴	1	4	yes	—
265	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
266	C₂×D₄×C₇₃	—	2	2	no	—
267	C₂×D₄×C₇₃	C₂²×C₄	1	2	yes	—
268	C₂²×C₄×C₇₃	—	2	2	no	—
269	C₂²×C₄×C₇₃	—	2	1	no	—
270	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
271	Q₁₆×C₇₃	C₂²×C₄	1	4	yes	—
272	SD₁₆×C₇₃	C₂²×C₄	1	8	yes	—
273	D₈×C₇₃	C₂²×C₄	1	4	yes	—
274	M₁₆×C₇₃	—	2	2	no	—
275	M₁₆×C₇₃	—	2	8	no	—
276	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
277	M₁₆×C₇₃	C₂×D₄	1	4	yes	—
278	M₁₆×C₇₃	C₂⁴	1	4	yes	—
279	C₂×C₈×C₇₃	—	2	2	no	—
280	C₂×C₈×C₇₃	—	2	8	no	—
281	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
282	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
283	C₄²×C₇₃	—	2	1	no	—
284	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
285	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
286	C₂³×C₇₃	—	2	2	no	—
287	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
288	C₂²×D₇₃	—	2	2	no	—
289	C₂²×D₇₃	—	2	8	no	—
290	C₂²×D₇₃	C₂×#41	1	2	yes	—
291	Q₈×C₇₃	—	2	2	no	—
292	Q₈×C₇₃	C₂³×C₄	1	4	yes	—
293	D₄×C₇₃	—	2	4	no	—
294	D₄×C₇₃	—	2	4	no	—
295	D₄×C₇₃	—	2	2	no	—
296	D₄×C₇₃	C₂³×C₄	1	4	yes	—
297	C₂×C₄×C₇₃	—	2	2	no	—
298	C₂×C₄×C₇₃	—	2	4	no	—
299	C₂×C₄×C₇₃	—	2	4	no	—
300	C₂×C₄×C₇₃	—	2	1	no	—
301	C₂×C₄×C₇₃	—	2	1	no	—
302	C₂×C₄×C₇₃	—	8	1	no	—
303	C₂×C₄×C₇₃	C₂³×C₄	1	2	yes	—
304	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
305	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
306	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
307	C₂²⋊D₇₃	—	2	4	no	—
308	C₂²⋊D₇₃	—	2	4	no	—
309	C₂²⋊D₇₃	—	2	8	no	—
310	C₂²⋊D₇₃	—	2	8	no	—
311	C₂²⋊D₇₃	C₄×D₄	1	8	yes	—
312	C₂×Dic₇₃	—	2	2	no	—
313	C₂×Dic₇₃	—	2	8	no	—
314	C₂×Dic₇₃	—	2	2	no	—
315	C₂×Dic₇₃	C₂×#41	1	2	yes	—
316	D₂₉₂	—	2	8	no	—
317	D₂₉₂	—	2	2	no	—
318	D₂₉₂	C₄×D₄	1	4	yes	—
319	D₂₉₂	C₂³×C₄	1	4	yes	—
320	C₄×D₇₃	—	2	8	no	—
321	C₄×D₇₃	—	2	4	no	—
322	C₄×D₇₃	—	2	4	no	—
323	C₄×D₇₃	—	2	8	no	—
324	C₄×D₇₃	—	8	2	no	—
325	C₄×D₇₃	C₂³×C₄	1	4	yes	—
326	C₄×D₇₃	C₂²×D₄	1	4	yes	—
327	Dic₁₄₆	—	2	2	no	—
328	Dic₁₄₆	—	2	8	no	—
329	Dic₁₄₆	C₄×D₄	1	4	yes	—
330	Dic₁₄₆	C₂³×C₄	1	4	yes	—
331	C₈×C₇₃	—	2	4	no	—
332	C₈×C₇₃	C₂³×C₄	1	4	yes	—
333	C₈×C₇₃	C₂²×D₄	1	4	yes	—
334	#10596831	—	2	4	no	—
335	#10596831	C₂³×C₄	1	1	yes	characteristic
336	#10596831	C₂³×C₄	1	1	yes	characteristic
337	#10596831	C₂³×C₄	1	2	yes	—
338	#10596831	C₂²×D₄	1	1	yes	characteristic
339	#10596831	C₂²×D₄	1	2	yes	—
340	#10596831	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₇₃	—	2	4	no	—
342	C₂²×C₇₃	—	4	1	no	—
343	C₂²×C₇₃	—	8	2	no	—
344	C₂²×C₇₃	C₂×C₄×D₄	1	2	yes	—
345	C₂²×C₇₃	C₂²×#41	1	1	yes	characteristic
346	C₂×D₇₃	—	2	4	no	—
347	C₂×D₇₃	—	4	2	no	—
348	C₂×D₇₃	—	8	8	no	—
349	C₂×D₇₃	—	8	2	no	—
350	C₂×D₇₃	C₂×C₄×D₄	1	4	yes	—
351	C₄×C₇₃	—	2	4	no	—
352	C₄×C₇₃	—	4	1	no	—
353	C₄×C₇₃	—	4	1	no	—
354	C₄×C₇₃	C₂×C₄×D₄	1	2	yes	—
355	C₄×C₇₃	C₂⁴×C₄	1	1	yes	characteristic
356	C₄×C₇₃	C₂³×D₄	1	1	yes	characteristic
357	Dic₇₃	—	2	4	no	—
358	Dic₇₃	—	4	2	no	—
359	Dic₇₃	C₂×C₄×D₄	1	4	yes	—
360	#60184	—	73	1	no	maximal, Sylow
361	C₂×C₇₃	—	2	1	no	—
362	C₂×C₇₃	—	2	2	no	—
363	C₂×C₇₃	—	4	4	no	—
364	C₂×C₇₃	C₂²×C₄×D₄	1	1	yes	characteristic
365	D₇₃	—	2	4	no	—
366	D₇₃	—	4	4	no	—
367	#3584	—	73	1	no	—
368	#3573	—	73	2	no	—
369	#2957	—	73	4	no	—
370	#2957	—	73	2	no	—
371	#2956	—	73	4	no	—
372	#2956	—	73	1	no	—
373	#2956	D₇₃	1	1	yes	characteristic, complemented
374	#2955	—	73	4	no	—
375	#2955	—	73	1	no	—
376	#2955	—	73	1	no	—
377	C₂×#444	—	73	4	no	—
378	C₂×#444	—	73	2	no	—
379	#2916	—	73	1	no	—
380	#2901	—	73	2	no	—
381	#2875	—	73	1	no	—
382	C₇₃	#60184	1	1	yes	characteristic, complemented, Sylow
383	#585	—	73	2	no	—
384	#578	—	73	4	no	—
385	#577	—	73	4	no	—
386	#577	—	73	4	no	—
387	#576	—	73	4	no	—
388	#575	—	73	4	no	—
389	#575	—	73	1	no	—
390	#575	C₂×D₇₃	1	1	yes	characteristic
391	C₂×#135	—	73	2	no	—
392	C₂×#135	—	73	4	no	—
393	#568	—	73	2	no	—
394	#568	—	73	8	no	—
395	#568	—	73	2	no	—
396	#568	—	146	4	no	—
397	#568	—	146	4	no	—
398	#568	C₂×D₇₃	1	2	yes	complemented
399	C₂×#131	—	73	1	no	—
400	C₂×#131	—	73	1	no	—
401	C₂×#131	—	73	2	no	—
402	C₂×#131	—	73	8	no	—
403	C₂×#131	—	73	2	no	—
404	C₂×#131	—	146	4	no	—
405	C₂×#131	—	146	4	no	—
406	C₄×#41	—	73	1	no	—
407	#444	—	73	4	no	—
408	#444	—	73	8	no	—
409	#444	—	73	4	no	—
410	#444	—	73	4	no	—
411	#444	—	73	4	no	—
412	#444	—	73	4	no	—
413	#444	—	73	4	no	—
414	#444	—	73	4	no	—
415	#444	C₂×D₇₃	1	4	yes	complemented
416	#443	—	73	4	no	—
417	#443	—	73	8	no	—
418	#443	—	73	4	no	—
419	#443	—	73	4	no	—
420	#443	C₂×D₇₃	1	4	yes	complemented
421	#430	—	73	1	no	—
422	#430	—	73	4	no	—
423	#430	C₂×D₇₃	1	1	yes	characteristic, complemented
424	C₂×#108	—	73	2	no	—
425	C₂×#108	—	73	4	no	—
426	#421	—	73	2	no	—
427	#421	—	73	2	no	—
428	#421	—	73	8	no	—
429	C₂×#104	—	73	2	no	—
430	C₂×#104	—	73	8	no	—
431	C₂×#104	C₂×D₇₃	1	2	yes	complemented
432	#405	—	73	1	no	—
433	#405	—	73	1	no	—
434	#405	—	73	2	no	—
435	#405	—	73	2	no	—
436	C₄×M₁₆	—	73	2	no	—
437	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
438	C₂×#97	—	73	1	no	—
439	C₂×#97	—	73	2	no	—
440	2₋¹⁺⁴	—	73	4	no	—
441	2₋¹⁺⁴	—	73	4	no	—
442	2₋¹⁺⁴	—	146	2	no	—
443	H(5,𝔽₂)	—	73	4	no	—
444	H(5,𝔽₂)	—	73	4	no	—
445	H(5,𝔽₂)	—	146	4	no	—
446	H(5,𝔽₂)	—	146	2	no	—
447	C₂×#41	—	73	1	no	—
448	C₂×#41	—	73	8	no	—
449	C₂×#41	—	73	2	no	—
450	C₂×#41	—	146	4	no	—
451	C₂×#41	—	146	4	no	—
452	C₂×#41	C₂²×D₇₃	1	2	yes	—
453	#137	—	73	8	no	—
454	#137	—	73	8	no	—
455	#137	—	73	4	no	—
456	#137	C₄×D₇₃	1	4	yes	complemented
457	AGL(1,ℤ/8)	—	73	8	no	—
458	AGL(1,ℤ/8)	—	73	8	no	—
459	AGL(1,ℤ/8)	—	73	4	no	—
460	AGL(1,ℤ/8)	C₄×D₇₃	1	4	yes	complemented
461	#135	—	73	4	no	—
462	#135	—	73	4	no	—
463	#135	—	73	4	no	—
464	#135	—	73	4	no	—
465	#135	—	73	4	no	—
466	#135	—	73	8	no	—
467	#135	—	73	4	no	—
468	#135	—	73	4	no	—
469	#135	C₂²×D₇₃	1	4	yes	—
470	C₂×Q₁₆	—	73	2	no	—
471	C₂×Q₁₆	—	73	4	no	—
472	C₂×SD₁₆	—	73	2	no	—
473	C₂×SD₁₆	—	73	2	no	—
474	C₂×SD₁₆	—	73	8	no	—
475	C₂×D₈	—	73	2	no	—
476	C₂×D₈	—	73	4	no	—
477	#131	—	2	4	no	—
478	#131	—	73	4	no	—
479	#131	—	73	4	no	—
480	#131	—	73	4	no	—
481	#131	—	73	4	no	—
482	#131	—	73	4	no	—
483	#131	—	73	4	no	—
484	#131	—	73	4	no	—
485	#131	—	73	4	no	—
486	#131	—	73	8	no	—
487	#131	—	146	8	no	—
488	#131	—	146	8	no	—
489	#131	—	146	4	no	—
490	#131	—	146	2	no	—
491	#131	—	146	8	no	—
492	#131	—	146	2	no	—
493	#131	—	146	2	no	—
494	#131	—	146	2	no	—
495	#131	—	146	8	no	—
496	#131	—	146	4	no	—
497	#131	—	146	4	no	—
498	#131	C₂²×D₇₃	1	8	yes	—
499	C₂×M₁₆	—	2	4	no	—
500	C₂×M₁₆	—	73	2	no	—
501	C₂×M₁₆	—	73	2	no	—
502	C₂×M₁₆	—	73	2	no	—
503	C₂×M₁₆	—	73	8	no	—
504	C₂×M₁₆	—	146	2	no	—
505	C₂×M₁₆	—	146	8	no	—
506	C₂×M₁₆	—	146	8	no	—
507	C₂×M₁₆	—	146	2	no	—
508	C₂×M₁₆	—	146	8	no	—
509	C₂×M₁₆	—	146	4	no	—
510	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
511	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
512	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
513	C₂²×C₈	—	73	1	no	—
514	C₂²×C₈	—	73	1	no	—
515	C₂²×C₈	—	73	2	no	—
516	C₂²×C₈	—	73	2	no	—
517	C₂²×C₈	—	146	2	no	—
518	C₂²×C₈	—	146	8	no	—
519	C₂²×C₈	—	146	2	no	—
520	C₄×Q₈	—	146	1	no	—
521	C₄×D₄	—	146	1	no	—
522	C₄×D₄	—	146	2	no	—
523	#117	—	73	1	no	—
524	#117	—	73	2	no	—
525	C₂×C₄²	—	73	2	no	—
526	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
527	#108	—	73	4	no	—
528	#108	—	73	4	no	—
529	#108	—	73	4	no	—
530	#108	C₂²×D₇₃	1	4	yes	—
531	#104	—	73	8	no	—
532	#104	—	73	8	no	—
533	#104	—	73	4	no	—
534	#104	—	73	4	no	—
535	#104	C₂²×D₇₃	1	4	yes	—
536	#104	C₂²×D₇₃	1	4	yes	—
537	#97	—	73	2	no	—
538	#97	—	73	2	no	—
539	#97	—	73	1	no	—
540	#97	—	73	1	no	—
541	#97	—	73	1	no	—
542	#97	—	73	1	no	—
543	#97	C₂²×D₇₃	1	2	yes	—
544	C₄×C₈	—	73	2	no	—
545	C₄×C₈	—	73	2	no	—
546	C₄×C₈	C₂²×D₇₃	1	2	yes	—
547	#41	—	2	2	no	—
548	#41	—	2	2	no	—
549	#41	—	73	4	no	—
550	#41	—	73	4	no	—
551	#41	—	73	8	no	—
552	#41	—	73	8	no	—
553	#41	—	73	4	no	—
554	#41	—	73	4	no	—
555	#41	—	146	8	no	—
556	#41	—	146	8	no	—
557	#41	—	146	4	no	—
558	#41	—	146	4	no	—
559	#41	—	146	8	no	—
560	#41	—	146	8	no	—
561	#41	—	146	4	no	—
562	#41	—	146	4	no	—
563	#41	—	146	2	no	—
564	#41	—	146	2	no	—
565	#41	C₂×C₄×D₇₃	1	4	yes	—
566	#41	C₂³×D₇₃	1	4	yes	—
567	C₂×Q₈	—	73	1	no	—
568	C₂×Q₈	—	73	8	no	—
569	C₂×Q₈	—	73	2	no	—
570	C₂×Q₈	—	146	4	no	—
571	C₂×Q₈	—	146	4	no	—
572	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	73	2	no	—
575	C₂×D₄	—	73	8	no	—
576	C₂×D₄	—	73	2	no	—
577	C₂×D₄	—	73	1	no	—
578	C₂×D₄	—	146	4	no	—
579	C₂×D₄	—	146	8	no	—
580	C₂×D₄	—	146	4	no	—
581	C₂×D₄	—	146	8	no	—
582	C₂×D₄	—	146	8	no	—
583	C₂×D₄	—	146	2	no	—
584	C₂×D₄	C₂×C₄×D₇₃	1	2	yes	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	73	2	no	—
588	C₂²×C₄	—	146	2	no	—
589	C₂²×C₄	—	146	8	no	—
590	C₂²×C₄	—	146	2	no	—
591	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
592	Q₁₆	—	73	4	no	—
593	Q₁₆	—	73	4	no	—
594	Q₁₆	—	73	4	no	—
595	Q₁₆	C₂×C₄×D₇₃	1	4	yes	—
596	SD₁₆	—	73	4	no	—
597	SD₁₆	—	73	4	no	—
598	SD₁₆	—	73	4	no	—
599	SD₁₆	—	73	4	no	—
600	SD₁₆	—	73	8	no	—
601	SD₁₆	C₂×C₄×D₇₃	1	8	yes	—
602	D₈	—	73	4	no	—
603	D₈	—	73	4	no	—
604	D₈	—	73	4	no	—
605	D₈	C₂×C₄×D₇₃	1	4	yes	—
606	M₁₆	—	2	2	no	—
607	M₁₆	—	2	8	no	—
608	M₁₆	—	73	8	no	—
609	M₁₆	—	73	4	no	—
610	M₁₆	—	73	4	no	—
611	M₁₆	—	73	4	no	—
612	M₁₆	—	146	4	no	—
613	M₁₆	—	146	4	no	—
614	M₁₆	—	146	8	no	—
615	M₁₆	—	146	4	no	—
616	M₁₆	—	146	4	no	—
617	M₁₆	—	146	2	no	—
618	M₁₆	—	146	8	no	—
619	M₁₆	C₂×C₄×D₇₃	1	4	yes	—
620	M₁₆	D₄×D₇₃	1	4	yes	—
621	M₁₆	C₂³×D₇₃	1	4	yes	—
622	C₂×C₈	—	2	2	no	—
623	C₂×C₈	—	2	8	no	—
624	C₂×C₈	—	73	2	no	—
625	C₂×C₈	—	73	2	no	—
626	C₂×C₈	—	73	2	no	—
627	C₂×C₈	—	73	2	no	—
628	C₂×C₈	—	73	1	no	—
629	C₂×C₈	—	73	1	no	—
630	C₂×C₈	—	73	1	no	—
631	C₂×C₈	—	73	1	no	—
632	C₂×C₈	—	73	4	no	—
633	C₂×C₈	—	73	4	no	—
634	C₂×C₈	—	73	8	no	—
635	C₂×C₈	—	146	4	no	—
636	C₂×C₈	—	146	4	no	—
637	C₂×C₈	—	146	8	no	—
638	C₂×C₈	—	146	4	no	—
639	C₂×C₈	—	146	4	no	—
640	C₂×C₈	—	146	2	no	—
641	C₂×C₈	—	146	8	no	—
642	C₂×C₈	C₂³×D₇₃	1	2	yes	—
643	C₂×C₈	C₂³×D₇₃	1	2	yes	—
644	C₄⋊C₄	—	146	2	no	—
645	C₄⋊C₄	—	146	1	no	—
646	C₂²⋊C₄	—	146	2	no	—
647	C₂²⋊C₄	—	146	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	73	2	no	—
650	C₄²	—	146	2	no	—
651	C₄²	C₂³×D₇₃	1	1	yes	characteristic
652	C₄²	C₂³×D₇₃	1	1	yes	characteristic
653	C₂³	—	2	2	no	—
654	C₂³	—	73	2	no	—
655	C₂³	—	146	8	no	—
656	C₂³	—	146	2	no	—
657	C₂³	#41×D₇₃	1	1	yes	characteristic
658	Q₈	—	2	2	no	—
659	Q₈	—	73	4	no	—
660	Q₈	—	73	4	no	—
661	Q₈	—	146	8	no	—
662	Q₈	—	146	2	no	—
663	Q₈	C₂²×C₄×D₇₃	1	4	yes	—
664	D₄	—	2	4	no	—
665	D₄	—	2	4	no	—
666	D₄	—	2	2	no	—
667	D₄	—	73	8	no	—
668	D₄	—	73	4	no	—
669	D₄	—	73	4	no	—
670	D₄	—	146	8	no	—
671	D₄	—	146	8	no	—
672	D₄	—	146	8	no	—
673	D₄	—	146	4	no	—
674	D₄	—	146	4	no	—
675	D₄	—	146	2	no	—
676	D₄	C₂²×C₄×D₇₃	1	4	yes	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	4	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	8	1	no	—
683	C₂×C₄	—	584	2	no	—
684	C₂×C₄	—	73	2	no	—
685	C₂×C₄	—	73	4	no	—
686	C₂×C₄	—	73	4	no	—
687	C₂×C₄	—	146	8	no	—
688	C₂×C₄	—	146	8	no	—
689	C₂×C₄	—	146	2	no	—
690	C₂×C₄	—	146	8	no	—
691	C₂×C₄	—	146	2	no	—
692	C₂×C₄	—	146	4	no	—
693	C₂×C₄	—	146	4	no	—
694	C₂×C₄	C₂²×C₄×D₇₃	1	2	yes	—
695	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
696	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
697	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
698	C₈	—	2	4	no	—
699	C₈	—	73	1	no	—
700	C₈	—	73	1	no	—
701	C₈	—	73	2	no	—
702	C₈	—	73	2	no	—
703	C₈	—	73	1	no	—
704	C₈	—	73	1	no	—
705	C₈	—	146	4	no	—
706	C₈	C₂²×C₄×D₇₃	1	4	yes	—
707	C₈	C₂×D₄×D₇₃	1	4	yes	—
708	C₂²	—	2	4	no	—
709	C₂²	—	4	1	no	—
710	C₂²	—	8	2	no	—
711	C₂²	—	292	2	no	—
712	C₂²	—	584	2	no	—
713	C₂²	—	584	8	no	—
714	C₂²	—	73	4	no	—
715	C₂²	—	146	4	no	—
716	C₂²	C₄×D₄×D₇₃	1	2	yes	—
717	C₂²	C₂×#41×D₇₃	1	1	yes	characteristic
718	C₄	—	2	4	no	—
719	C₄	—	4	1	no	—
720	C₄	—	4	1	no	—
721	C₄	—	292	2	no	—
722	C₄	—	73	4	no	—
723	C₄	—	146	4	no	—
724	C₄	C₄×D₄×D₇₃	1	2	yes	—
725	C₄	C₂³×C₄×D₇₃	1	1	yes	characteristic
726	C₄	C₂²×D₄×D₇₃	1	1	yes	characteristic
727	C₂	—	2	1	no	—
728	C₂	—	2	2	no	—
729	C₂	—	4	4	no	—
730	C₂	—	292	4	no	—
731	C₂	—	146	4	no	—
732	C₂	C₂×C₄×D₄×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₇₃
commutator	C₄×C₇₃	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#2956	C₂
socle	C₂×C₇₃	C₂²×C₄×D₄
prime radical	#22624704	C₂
cosocle	C₂×C₄×C₇₃	C₂⁵
hypercenter	#2956	D₇₃
hypocenter	C₇₃	#60184
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2956

Complements

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

N	H ≅ G/N	type
2. #22624644	C₂	semidirect
3. #22618846	C₂	semidirect
4. #22618843	C₂	semidirect
5. #22618842	C₂	semidirect
6. #22618839	C₂	semidirect
7. #22618834	C₂	semidirect
8. #22618833	C₂	semidirect
9. #22618829	C₂	semidirect
10. C₂×#17988706	C₂	semidirect
11. #444×D₇₃	C₂	semidirect
12. #22618541	C₂	semidirect
13. #22618475	C₂	semidirect
14. #22618360	C₂	semidirect
15. C₇₃×#2956	C₂	semidirect
17. #17989403	C₄	semidirect
18. #17989397	C₄	semidirect
19. #17989396	C₄	semidirect
20. #17989391	C₄	semidirect
27. #17989353	C₂²	semidirect
29. #17989352	C₂²	semidirect
33. C₂×#14556599	C₂²	semidirect
34. C₂×#14556598	C₂²	semidirect
36. #131×D₇₃	C₂²	semidirect
38. #17988710	C₂²	semidirect
39. #17988709	C₂²	semidirect
40. #17988708	C₂²	semidirect
41. #17988707	C₂²	semidirect
42. #17988706	C₂²	semidirect
43. #17988706	C₂²	semidirect
44. #17988706	C₂²	semidirect
45. #17988706	C₂²	semidirect
46. #17988705	C₂²	semidirect
47. #17988704	C₂²	semidirect
48. #17988703	C₂²	semidirect
49. #17988702	C₂²	semidirect
50. #17988636	C₂²	semidirect
51. #17988634	C₂²	semidirect
52. C₂×#14556526	C₂²	semidirect
53. #108×D₇₃	C₂²	semidirect
54. #17988604	C₂²	semidirect
55. #17988603	C₂²	semidirect
56. #17988602	C₂²	semidirect
57. C₂×#14556519	C₂²	semidirect
58. #104×D₇₃	C₂²	semidirect
59. #17988545	C₂²	semidirect
60. #17988545	C₂²	semidirect
61. #17988541	C₂²	semidirect
62. #17988541	C₂²	semidirect
63. #17988539	C₂²	semidirect
64. C₂×#14556502	C₂²	semidirect
65. #97×D₇₃	C₂²	semidirect
67. #568×C₇₃	C₂²	semidirect
68. #444×C₇₃	C₂²	semidirect
69. #443×C₇₃	C₂²	semidirect
70. #430×C₇₃	C₂²	semidirect
71. C₂×#104×C₇₃	C₂²	semidirect
72. C₄×M₁₆×C₇₃	C₂²	semidirect
85. #14556624	C₂×C₄	semidirect
86. #14556623	C₂×C₄	semidirect
87. #14556620	C₂×C₄	semidirect
88. #14556619	C₂×C₄	semidirect
89. #14556618	C₂×C₄	semidirect
90. #14556615	C₂×C₄	semidirect
91. #14556614	C₂×C₄	semidirect
93. #14556612	C₂×C₄	semidirect
94. #14556611	C₂×C₄	semidirect
95. #14556611	C₂×C₄	semidirect
98. #14556610	C₂×C₄	semidirect
99. C₂×#11924018	C₂×C₄	semidirect
100. Q₁₆×D₇₃	C₂×C₄	semidirect
101. C₂×#11924016	C₂×C₄	semidirect
102. C₂×#11924015	C₂×C₄	semidirect
103. SD₁₆×D₇₃	C₂×C₄	semidirect
104. C₂×#11924013	C₂×C₄	semidirect
105. D₈×D₇₃	C₂×C₄	semidirect
165. #137×C₇₃	C₂×C₄	semidirect
166. AGL(1,ℤ/8)×C₇₃	C₂×C₄	semidirect
373. #2956	D₇₃	semidirect
382. C₇₃	#60184	semidirect
398. #568	C₂×D₇₃	semidirect
415. #444	C₂×D₇₃	semidirect
420. #443	C₂×D₇₃	semidirect
423. #430	C₂×D₇₃	semidirect
431. C₂×#104	C₂×D₇₃	semidirect
437. C₄×M₁₆	C₂×D₇₃	semidirect
456. #137	C₄×D₇₃	semidirect
460. AGL(1,ℤ/8)	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22624704	2
#22624644	2
#22618846	2
#22618843	2
#22618842	2
#22618839	2
#22618834	2
#22618833	2
#22618829	2
C₂×#17988706	2
#444×D₇₃	2
#22618541	2
#22618475	2
#22618360	2
C₇₃×#2956	2
#60184	73