Subgroups — #2170×D₇₃ #33239208

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504×D₇₃	C₂	1	2	yes	maximal, complemented
2	#443×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22611769	C₂	1	1	yes	maximal, characteristic, complemented
4	#22611768	C₂	1	1	yes	maximal, characteristic, complemented
5	#22611767	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611766	C₂	1	2	yes	maximal, complemented
7	#22611765	C₂	1	2	yes	maximal, complemented
8	#364×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	#350×D₇₃	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₇₃	C₄	1	1	yes	characteristic
13	#131×D₇₃	C₂²	1	2	yes	—
14	#17989005	—	2	2	no	—
15	#17989005	C₂²	1	2	yes	complemented
16	#17989004	C₂²	1	2	yes	complemented
17	#17989003	—	2	2	no	—
18	#17989003	C₂²	1	2	yes	complemented
19	M₃₂×D₇₃	—	2	2	no	—
20	M₃₂×D₇₃	C₂²	1	2	yes	—
21	C₂×C₁₆×D₇₃	—	2	2	no	—
22	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
24	#17988705	C₂²	1	1	yes	characteristic
25	#17988704	C₄	1	1	yes	characteristic
26	#17988703	C₄	1	1	yes	characteristic
27	#17988702	C₂²	1	2	yes	—
28	#17988701	C₄	1	2	yes	—
29	#108×D₇₃	C₄	1	1	yes	characteristic
30	#104×D₇₃	C₄	1	2	yes	—
31	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
32	#17988408	C₂²	1	1	yes	characteristic, complemented
33	#17988407	C₂²	1	2	yes	complemented
34	#17988372	C₂²	1	2	yes	complemented
35	#17988371	C₂²	1	2	yes	complemented
36	#17988370	C₂²	1	2	yes	complemented
37	C₄×#11924003	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic, complemented
40	#504×C₇₃	C₂²	1	2	yes	complemented
41	#443×C₇₃	C₂²	1	1	yes	characteristic
42	#364×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#350×C₇₃	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic, complemented
45	#41×D₇₃	C₂×C₄	1	2	yes	—
46	#14556614	C₈	1	1	yes	characteristic
47	#14556613	C₂×C₄	1	1	yes	characteristic
48	#14556612	C₈	1	2	yes	—
49	#14556611	C₂×C₄	1	2	yes	—
50	#14556610	C₈	1	1	yes	characteristic
51	Q₁₆×D₇₃	C₈	1	1	yes	characteristic
52	SD₁₆×D₇₃	C₈	1	2	yes	—
53	D₈×D₇₃	C₈	1	1	yes	characteristic
54	#14556599	—	2	2	no	—
55	#14556599	C₂×C₄	1	2	yes	—
56	#14556598	C₂×C₄	1	2	yes	—
57	#14556597	—	2	2	no	—
58	#14556597	C₂³	1	2	yes	—
59	M₁₆×D₇₃	—	2	2	no	—
60	M₁₆×D₇₃	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₇₃	—	2	2	no	—
62	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
64	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
65	#14556531	—	2	2	no	—
66	#14556531	C₂³	1	2	yes	—
67	#14556530	—	2	2	no	—
68	#14556530	—	2	2	no	—
69	#14556530	—	2	2	no	—
70	C₂×#11924003	—	2	2	no	—
71	C₂×#11924003	C₂³	1	1	yes	characteristic
72	C₂×#11924003	C₂³	1	1	yes	characteristic
73	C₁₆×D₇₃	—	2	2	no	—
74	C₁₆×D₇₃	—	2	1	no	—
75	C₁₆×D₇₃	—	2	1	no	—
76	C₁₆×D₇₃	—	2	2	no	—
77	C₁₆×D₇₃	—	2	2	no	—
78	C₁₆×D₇₃	D₄	1	1	yes	characteristic
79	C₁₆×D₇₃	D₄	1	1	yes	characteristic
80	C₁₆×D₇₃	D₄	1	1	yes	characteristic
81	C₁₆×D₇₃	D₄	1	1	yes	characteristic
82	#14556527	C₂×C₄	1	1	yes	characteristic
83	#14556526	C₂×C₄	1	2	yes	—
84	#14556519	C₂×C₄	1	2	yes	—
85	#14556518	C₂×C₄	1	2	yes	—
86	#14556517	C₂×C₄	1	2	yes	—
87	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
90	#135×C₇₃	C₂×C₄	1	1	yes	characteristic
91	#131×C₇₃	C₂³	1	2	yes	—
92	M₃₂×C₇₃	—	2	2	no	—
93	M₃₂×C₇₃	C₂³	1	2	yes	—
94	C₂×C₁₆×C₇₃	—	2	2	no	—
95	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
97	#108×C₇₃	C₂×C₄	1	1	yes	characteristic
98	#104×C₇₃	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
100	#11924029	C₂×C₈	1	2	yes	—
101	#11924028	—	2	2	no	—
102	#11924028	C₂²×C₄	1	2	yes	—
103	#11924027	—	2	2	no	—
104	#11924027	C₂×C₈	1	2	yes	—
105	Q₈×D₇₃	C₂×C₈	1	2	yes	—
106	D₄×D₇₃	—	2	2	no	—
107	D₄×D₇₃	C₂×C₈	1	2	yes	—
108	C₂×C₄×D₇₃	—	2	1	no	—
109	C₂×C₄×D₇₃	—	2	2	no	—
110	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
111	Dic₂₉₂	C₂×C₈	1	1	yes	characteristic
112	#11924018	C₂×C₈	1	2	yes	—
113	#11924017	C₂×C₈	1	2	yes	—
114	#11924016	C₂×C₈	1	2	yes	—
115	#11924015	C₂×C₈	1	2	yes	—
116	D₅₈₄	C₂×C₈	1	1	yes	characteristic
117	#11924013	C₂×C₈	1	2	yes	—
118	#11924012	—	2	2	no	—
119	#11924012	C₂²×C₄	1	2	yes	—
120	#11924011	—	2	2	no	—
121	#11924011	—	2	2	no	—
122	#11924011	—	2	2	no	—
123	C₂×#10596831	—	2	2	no	—
124	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
125	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
126	C₈×D₇₃	—	2	2	no	—
127	C₈×D₇₃	—	2	2	no	—
128	C₈×D₇₃	—	2	2	no	—
129	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic
130	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic
131	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic
132	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic
133	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
134	C₈×D₇₃	C₂×D₄	1	1	yes	characteristic
135	C₈×D₇₃	#41	1	1	yes	characteristic
136	C₈×D₇₃	#41	1	1	yes	characteristic
137	C₄×Dic₇₃	—	2	1	no	—
138	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
139	#11924003	—	2	2	no	—
140	#11924003	—	2	1	no	—
141	#11924003	C₂×D₄	1	1	yes	characteristic
142	#11924003	C₂×D₄	1	1	yes	characteristic
143	#41×C₇₃	C₂²×C₄	1	2	yes	—
144	Q₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
145	SD₁₆×C₇₃	C₂×C₈	1	2	yes	—
146	D₈×C₇₃	C₂×C₈	1	1	yes	characteristic
147	M₁₆×C₇₃	—	2	2	no	—
148	M₁₆×C₇₃	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
152	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
153	C₁₆×C₇₃	—	2	2	no	—
154	C₁₆×C₇₃	—	2	1	no	—
155	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×D₇₃	—	2	2	no	—
158	C₂²×D₇₃	#131	1	1	yes	characteristic
159	Q₈×C₇₃	C₂²×C₈	1	2	yes	—
160	D₄×C₇₃	—	2	2	no	—
161	D₄×C₇₃	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₇₃	—	2	1	no	—
163	C₂×C₄×C₇₃	—	2	2	no	—
164	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₇₃	—	2	2	no	—
166	C₂²⋊D₇₃	—	2	2	no	—
167	C₂²⋊D₇₃	—	2	2	no	—
168	C₂×Dic₇₃	—	2	1	no	—
169	C₂×Dic₇₃	—	2	2	no	—
170	C₂×Dic₇₃	#131	1	1	yes	characteristic
171	D₂₉₂	—	2	2	no	—
172	D₂₉₂	C₂²×C₈	1	2	yes	—
173	C₄×D₇₃	—	2	4	no	—
174	C₄×D₇₃	—	2	2	no	—
175	C₄×D₇₃	—	2	2	no	—
176	C₄×D₇₃	—	2	2	no	—
177	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
178	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
179	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
181	Dic₁₄₆	—	2	2	no	—
182	Dic₁₄₆	C₂²×C₈	1	2	yes	—
183	C₈×C₇₃	—	2	2	no	—
184	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
185	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
186	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
188	#10596831	—	2	2	no	—
189	#10596831	C₄×D₄	1	1	yes	characteristic
190	#10596831	C₄×D₄	1	1	yes	characteristic
191	#10596831	C₂²×C₈	1	1	yes	characteristic
192	#10596831	C₂²×C₈	1	1	yes	characteristic
193	C₂²×C₇₃	—	2	2	no	—
194	C₂²×C₇₃	C₂×#131	1	1	yes	characteristic
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	—	4	4	no	—
198	C₂×D₇₃	C₈×D₄	1	1	yes	characteristic
199	C₂×D₇₃	C₈×D₄	1	1	yes	characteristic
200	C₄×C₇₃	—	2	2	no	—
201	C₄×C₇₃	—	2	2	no	—
202	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
204	Dic₇₃	—	2	2	no	—
205	Dic₇₃	—	2	2	no	—
206	Dic₇₃	C₈×D₄	1	1	yes	characteristic
207	Dic₇₃	C₈×D₄	1	1	yes	characteristic
208	C₂×#2170	—	73	1	no	maximal, Sylow
209	C₂×C₇₃	—	2	1	no	—
210	C₂×C₇₃	—	4	2	no	—
211	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
212	D₇₃	—	2	1	no	—
213	D₇₃	—	4	2	no	—
214	D₇₃	#2170	1	2	yes	direct product factor
215	C₂×#504	—	73	2	no	—
216	C₂×#443	—	73	1	no	—
217	#2170	—	73	2	no	—
218	#2170	—	73	1	no	—
219	#2170	—	73	1	no	—
220	#2170	—	73	2	no	—
221	#2170	—	73	1	no	—
222	#2170	D₇₃	1	1	yes	characteristic, direct product factor
223	C₂×#364	—	73	1	no	—
224	C₂×#350	—	73	2	no	—
225	C₂×C₄×C₁₆	—	73	1	no	—
226	C₇₃	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
227	C₂×#135	—	73	1	no	—
228	C₂×#131	—	73	2	no	—
229	#504	—	73	2	no	—
230	#504	—	73	2	no	—
231	#504	—	73	2	no	—
232	#504	—	146	2	no	—
233	#504	—	146	2	no	—
234	#504	C₂×D₇₃	1	2	yes	complemented
235	C₂×M₃₂	—	73	2	no	—
236	C₂×M₃₂	—	146	2	no	—
237	C₂²×C₁₆	—	73	1	no	—
238	C₂²×C₁₆	—	73	1	no	—
239	C₂²×C₁₆	—	146	2	no	—
240	#443	—	73	1	no	—
241	#443	—	73	2	no	—
242	#443	—	73	1	no	—
243	#443	—	73	2	no	—
244	#443	—	73	1	no	—
245	#443	C₂×D₇₃	1	1	yes	characteristic
246	C₂×#108	—	73	1	no	—
247	C₂×#104	—	73	2	no	—
248	C₂×C₄×C₈	—	73	1	no	—
249	#364	—	73	2	no	—
250	#364	—	73	1	no	—
251	#364	C₂×D₇₃	1	1	yes	characteristic, complemented
252	#350	—	73	2	no	—
253	#350	—	73	2	no	—
254	#350	—	73	2	no	—
255	#350	C₂×D₇₃	1	2	yes	complemented
256	C₄×C₁₆	—	73	1	no	—
257	C₄×C₁₆	—	73	1	no	—
258	C₄×C₁₆	—	73	1	no	—
259	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic, complemented
260	C₂×#41	—	73	2	no	—
261	#135	—	73	2	no	—
262	#135	—	73	1	no	—
263	#135	—	73	2	no	—
264	#135	—	73	1	no	—
265	#135	—	73	1	no	—
266	#135	C₄×D₇₃	1	1	yes	characteristic
267	C₂×Q₁₆	—	73	1	no	—
268	C₂×SD₁₆	—	73	2	no	—
269	C₂×D₈	—	73	1	no	—
270	#131	—	73	2	no	—
271	#131	—	73	2	no	—
272	#131	—	73	2	no	—
273	#131	—	146	2	no	—
274	#131	—	146	2	no	—
275	#131	C₂²×D₇₃	1	2	yes	—
276	C₂×M₁₆	—	73	2	no	—
277	C₂×M₁₆	—	146	2	no	—
278	C₂²×C₈	—	73	1	no	—
279	C₂²×C₈	—	73	1	no	—
280	C₂²×C₈	—	146	2	no	—
281	C₂×C₄²	—	73	1	no	—
282	M₃₂	—	2	2	no	—
283	M₃₂	—	73	2	no	—
284	M₃₂	—	146	2	no	—
285	M₃₂	—	146	2	no	—
286	M₃₂	—	146	2	no	—
287	M₃₂	—	146	2	no	—
288	M₃₂	C₂²×D₇₃	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	73	1	no	—
291	C₂×C₁₆	—	73	1	no	—
292	C₂×C₁₆	—	73	1	no	—
293	C₂×C₁₆	—	73	1	no	—
294	C₂×C₁₆	—	73	1	no	—
295	C₂×C₁₆	—	73	1	no	—
296	C₂×C₁₆	—	146	2	no	—
297	C₂×C₁₆	—	146	1	no	—
298	C₂×C₁₆	—	146	1	no	—
299	C₂×C₁₆	—	146	2	no	—
300	C₂×C₁₆	—	146	2	no	—
301	C₂×C₁₆	—	146	2	no	—
302	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
304	#108	—	73	2	no	—
305	#108	—	73	1	no	—
306	#108	C₄×D₇₃	1	1	yes	characteristic
307	#104	—	73	2	no	—
308	#104	—	73	2	no	—
309	#104	—	73	2	no	—
310	#104	C₄×D₇₃	1	2	yes	—
311	C₄×C₈	—	73	1	no	—
312	C₄×C₈	—	73	1	no	—
313	C₄×C₈	—	73	1	no	—
314	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
315	#41	—	73	2	no	—
316	#41	—	73	2	no	—
317	#41	—	73	2	no	—
318	#41	—	146	2	no	—
319	#41	—	146	2	no	—
320	#41	C₂×C₄×D₇₃	1	2	yes	—
321	C₂×Q₈	—	73	2	no	—
322	C₂×D₄	—	73	2	no	—
323	C₂×D₄	—	146	2	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	146	2	no	—
326	C₂²×C₄	—	146	1	no	—
327	Q₁₆	—	73	2	no	—
328	Q₁₆	—	73	1	no	—
329	Q₁₆	C₈×D₇₃	1	1	yes	characteristic
330	SD₁₆	—	73	2	no	—
331	SD₁₆	—	73	2	no	—
332	SD₁₆	—	73	2	no	—
333	SD₁₆	C₈×D₇₃	1	2	yes	—
334	D₈	—	73	2	no	—
335	D₈	—	73	1	no	—
336	D₈	C₈×D₇₃	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	73	2	no	—
339	M₁₆	—	146	2	no	—
340	M₁₆	—	146	2	no	—
341	M₁₆	—	146	2	no	—
342	M₁₆	—	146	2	no	—
343	M₁₆	C₂×C₄×D₇₃	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	73	1	no	—
346	C₂×C₈	—	73	1	no	—
347	C₂×C₈	—	73	1	no	—
348	C₂×C₈	—	73	1	no	—
349	C₂×C₈	—	73	1	no	—
350	C₂×C₈	—	73	1	no	—
351	C₂×C₈	—	73	1	no	—
352	C₂×C₈	—	73	1	no	—
353	C₂×C₈	—	73	1	no	—
354	C₂×C₈	—	73	1	no	—
355	C₂×C₈	—	146	2	no	—
356	C₂×C₈	—	146	2	no	—
357	C₂×C₈	—	146	2	no	—
358	C₂×C₈	—	146	2	no	—
359	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
361	C₄²	—	73	1	no	—
362	C₄²	—	146	1	no	—
363	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	1	no	—
366	C₁₆	—	73	1	no	—
367	C₁₆	—	73	1	no	—
368	C₁₆	—	146	2	no	—
369	C₁₆	—	146	1	no	—
370	C₁₆	D₄×D₇₃	1	1	yes	characteristic
371	C₁₆	D₄×D₇₃	1	1	yes	characteristic
372	C₂³	—	73	1	no	—
373	C₂³	—	146	2	no	—
374	Q₈	—	73	2	no	—
375	Q₈	—	146	2	no	—
376	Q₈	C₂×C₈×D₇₃	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	73	2	no	—
379	D₄	—	146	2	no	—
380	D₄	—	146	2	no	—
381	D₄	—	146	2	no	—
382	D₄	—	146	2	no	—
383	D₄	C₂×C₈×D₇₃	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	146	2	no	—
392	C₂×C₄	—	146	2	no	—
393	C₂×C₄	—	146	4	no	—
394	C₂×C₄	—	146	2	no	—
395	C₂×C₄	—	146	1	no	—
396	C₂×C₄	—	146	2	no	—
397	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	73	1	no	—
400	C₈	—	73	1	no	—
401	C₈	—	73	1	no	—
402	C₈	—	73	1	no	—
403	C₈	—	146	2	no	—
404	C₈	C₂×C₈×D₇₃	1	1	yes	characteristic
405	C₈	C₂×C₈×D₇₃	1	1	yes	characteristic
406	C₈	C₂×D₄×D₇₃	1	1	yes	characteristic
407	C₈	#41×D₇₃	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	292	4	no	—
410	C₂²	—	73	1	no	—
411	C₂²	—	73	1	no	—
412	C₂²	—	146	2	no	—
413	C₂²	—	146	2	no	—
414	C₂²	#131×D₇₃	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	73	1	no	—
418	C₄	—	73	1	no	—
419	C₄	—	146	2	no	—
420	C₄	—	146	2	no	—
421	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₇₃	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	292	2	no	—
426	C₂	—	73	2	no	—
427	C₂	—	146	1	no	—
428	C₂	C₈×D₄×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₇₃
commutator	C₄×C₇₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2170	C₂
socle	C₂×C₇₃	C₂×C₈×D₄
prime radical	#135×D₇₃	C₄
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	#2170	D₇₃
hypocenter	C₇₃	C₂×#2170
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #504×D₇₃	C₂	semidirect
3. #22611769	C₂	semidirect
4. #22611768	C₂	semidirect
5. #22611767	C₂	semidirect
6. #22611766	C₂	semidirect
7. #22611765	C₂	semidirect
8. #364×D₇₃	C₂	semidirect
9. #350×D₇₃	C₂	semidirect
10. C₄×C₁₆×D₇₃	C₂	semidirect
11. C₇₃×#2170	C₂	semidirect
15. #17989005	C₂²	semidirect
16. #17989004	C₂²	semidirect
18. #17989003	C₂²	semidirect
32. #17988408	C₂²	semidirect
33. #17988407	C₂²	semidirect
34. #17988372	C₂²	semidirect
35. #17988371	C₂²	semidirect
36. #17988370	C₂²	semidirect
37. C₄×#11924003	C₂²	semidirect
38. C₁₆×Dic₇₃	C₂²	semidirect
39. C₁₆×Dic₇₃	C₂²	semidirect
40. #504×C₇₃	C₂²	semidirect
42. #364×C₇₃	C₂²	semidirect
43. #350×C₇₃	C₂²	semidirect
44. C₄×C₁₆×C₇₃	C₂²	semidirect
214. D₇₃	#2170	direct (N × H)
222. #2170	D₇₃	direct (N × H)
226. C₇₃	C₂×#2170	semidirect
234. #504	C₂×D₇₃	semidirect
251. #364	C₂×D₇₃	semidirect
255. #350	C₂×D₇₃	semidirect
259. C₄×C₁₆	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#504×D₇₃	2
#443×D₇₃	2
#22611769	2
#22611768	2
#22611767	2
#22611766	2
#22611765	2
#364×D₇₃	2
#350×D₇₃	2
C₄×C₁₆×D₇₃	2
C₇₃×#2170	2
C₂×#2170	73

Subgroups — #2170×D73 #33239208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2170×D₇₃ #33239208