Subgroups — #33057788

Order 18688.

646 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620490	C₂	1	1	yes	maximal, characteristic
2	#22618874	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618674	C₂	1	1	yes	maximal, characteristic
4	#22608832	C₂	1	2	yes	maximal, complemented
5	#22608808	C₂	1	2	yes	maximal, complemented
6	#22608787	C₂	1	2	yes	maximal, complemented
7	#22608742	C₂	1	2	yes	maximal, complemented
8	#22608333	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608329	C₂	1	1	yes	maximal, characteristic
10	#22608220	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#335×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556597	—	2	1	no	—
13	#17989144	C₂²	1	1	yes	characteristic
14	#17989137	C₂²	1	1	yes	characteristic
15	#17988985	C₄	1	1	yes	characteristic
16	#17988960	C₄	1	1	yes	characteristic
17	#17988938	C₄	1	1	yes	characteristic
18	#17988934	C₄	1	1	yes	characteristic
19	#17988816	C₄	1	2	yes	—
20	#17988816	C₄	1	2	yes	—
21	#17988716	—	2	2	no	—
22	#17988714	C₂²	1	2	yes	—
23	#17988711	C₂²	1	2	yes	—
24	C₄×#11924017	C₂²	1	2	yes	—
25	C₄×#11924017	C₂²	1	2	yes	—
26	#17988664	C₂²	1	2	yes	—
27	#17988657	—	2	2	no	—
28	#17988652	C₂²	1	2	yes	—
29	#17988640	C₂²	1	1	yes	characteristic
30	#17988613	—	2	1	no	—
31	#17988553	—	2	1	no	—
32	#17988542	—	2	1	no	—
33	C₄×#11924012	C₂²	1	1	yes	characteristic
34	#17988317	C₂²	1	2	yes	—
35	#17988317	C₂²	1	2	yes	—
36	#17988314	C₂²	1	2	yes	—
37	#17988314	C₂²	1	2	yes	—
38	#17988309	C₂²	1	2	yes	—
39	#17988308	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
43	#335×C₇₃	C₂²	1	1	yes	characteristic
44	#335×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	1	yes	characteristic
46	#335×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	—	2	1	no	—
48	C₂×#11924017	C₂×C₄	1	2	yes	—
49	C₂×#11924017	C₂×C₄	1	2	yes	—
50	#14556597	—	4	4	no	—
51	C₂×#11924012	D₄	1	1	yes	characteristic
52	C₂×#11924012	D₄	1	1	yes	characteristic
53	C₂×#11924011	—	2	2	no	—
54	C₂×C₈×D₇₃	—	2	2	no	—
55	#14556591	C₂×C₄	1	1	yes	characteristic
56	#14556591	C₂×C₄	1	1	yes	characteristic
57	#14556591	C₂×C₄	1	1	yes	characteristic
58	#14556588	C₂×C₄	1	1	yes	characteristic
59	#14556583	—	2	1	no	—
60	#14556579	—	2	1	no	—
61	#14556570	—	2	1	no	—
62	#14556570	C₂×C₄	1	2	yes	—
63	#14556565	—	2	1	no	—
64	#14556565	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₄₆	—	2	1	no	—
66	C₄×Dic₁₄₆	C₂³	1	2	yes	—
67	C₄×D₂₉₂	—	2	1	no	—
68	C₄×D₂₉₂	C₂³	1	2	yes	—
69	#14556550	—	2	1	no	—
70	#14556523	C₂×C₄	1	2	yes	—
71	#14556523	C₂×C₄	1	2	yes	—
72	C₄⋊#10596831	—	2	1	no	—
73	#14556520	—	2	2	no	—
74	#14556520	—	2	2	no	—
75	#14556516	C₂×C₄	1	2	yes	—
76	#14556516	C₂×C₄	1	2	yes	—
77	#14556513	C₂×C₄	1	2	yes	—
78	#14556513	C₂×C₄	1	2	yes	—
79	C₂²⋊#10596831	—	2	1	no	—
80	#14556503	—	2	2	no	—
81	#14556503	—	2	2	no	—
82	#14556502	D₄	1	2	yes	—
83	#14556501	—	2	2	no	—
84	C₄×#10596831	C₂³	1	2	yes	—
85	C₄×#10596831	C₂³	1	2	yes	—
86	C₈×Dic₇₃	—	2	2	no	—
87	C₂²×C₈×C₇₃	—	2	1	no	—
88	C₂²×C₈×C₇₃	—	2	1	no	—
89	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₇₃	—	2	1	no	—
93	C₄⋊C₈×C₇₃	—	2	1	no	—
94	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	#11924028	—	4	2	no	—
103	#11924028	—	4	2	no	—
104	C₂×Dic₁₄₆	—	2	1	no	—
105	C₂×Dic₁₄₆	—	2	1	no	—
106	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
107	C₂×D₂₉₂	—	2	1	no	—
108	C₂×D₂₉₂	—	2	1	no	—
109	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
110	C₂×C₂²⋊D₇₃	—	2	2	no	—
111	C₂×C₄×D₇₃	—	2	2	no	—
112	#11924017	—	2	4	no	—
113	#11924017	—	4	2	no	—
114	#11924012	—	2	2	no	—
115	#11924012	—	2	2	no	—
116	#11924011	—	4	4	no	—
117	C₂×#10596831	—	2	2	no	—
118	C₂×#10596831	C₂×D₄	1	2	yes	—
119	C₂×#10596831	C₂×D₄	1	2	yes	—
120	C₈×D₇₃	—	4	4	no	—
121	C₄⋊Dic₇₃	—	2	1	no	—
122	C₄⋊Dic₇₃	—	2	1	no	—
123	C₄⋊Dic₇₃	—	2	1	no	—
124	C₄⋊Dic₇₃	—	2	1	no	—
125	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
126	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
127	#11924007	—	2	2	no	—
128	#11924007	—	2	2	no	—
129	C₂²⋊Dic₇₃	—	2	2	no	—
130	#11924005	—	2	2	no	—
131	#11924005	—	2	2	no	—
132	C₄×Dic₇₃	—	2	2	no	—
133	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	—	2	1	no	—
138	C₂×C₈×C₇₃	—	2	1	no	—
139	C₂×C₈×C₇₃	—	2	1	no	—
140	C₂×C₈×C₇₃	—	2	1	no	—
141	C₂×C₈×C₇₃	—	4	1	no	—
142	C₂×C₈×C₇₃	—	4	2	no	—
143	C₂×C₈×C₇₃	—	4	2	no	—
144	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₇₃	#41	1	1	yes	characteristic
151	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
152	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₇₃	—	2	2	no	—
154	C₂×C₄×C₇₃	—	2	1	no	—
155	C₂×C₄×C₇₃	—	2	1	no	—
156	C₂×C₄×C₇₃	—	4	1	no	—
157	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₇₃	#137	1	2	yes	—
162	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
165	C₂²⋊D₇₃	—	4	4	no	—
166	C₂×Dic₇₃	—	2	2	no	—
167	C₂×Dic₇₃	—	2	2	no	—
168	C₂×Dic₇₃	—	2	2	no	—
169	D₂₉₂	—	2	2	no	—
170	D₂₉₂	—	2	2	no	—
171	D₂₉₂	—	4	2	no	—
172	D₂₉₂	—	8	1	no	—
173	C₄×D₇₃	—	4	2	no	—
174	C₄×D₇₃	—	4	2	no	—
175	Dic₁₄₆	—	2	2	no	—
176	Dic₁₄₆	—	2	2	no	—
177	Dic₁₄₆	—	4	2	no	—
178	Dic₁₄₆	—	8	1	no	—
179	C₈×C₇₃	—	2	1	no	—
180	C₈×C₇₃	—	2	1	no	—
181	C₈×C₇₃	—	2	1	no	—
182	C₈×C₇₃	—	4	1	no	—
183	C₈×C₇₃	—	4	1	no	—
184	C₈×C₇₃	—	4	1	no	—
185	C₈×C₇₃	—	4	1	no	—
186	C₈×C₇₃	#131	1	2	yes	complemented
187	#10596831	—	2	2	no	—
188	#10596831	—	2	2	no	—
189	#10596831	—	4	2	no	—
190	C₂²×C₇₃	—	2	1	no	—
191	C₂²×C₇₃	—	2	1	no	—
192	C₂²×C₇₃	#440	1	2	yes	—
193	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₇₃	—	4	2	no	—
195	C₂×D₇₃	—	4	2	no	—
196	C₂×D₇₃	—	4	2	no	—
197	C₄×C₇₃	—	2	1	no	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	#440	1	2	yes	—
201	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
202	C₄×C₇₃	#568	1	1	yes	characteristic
203	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
205	Dic₇₃	—	4	2	no	—
206	Dic₇₃	—	4	2	no	—
207	Dic₇₃	—	4	2	no	—
208	#18071	—	73	1	no	maximal, Sylow
209	C₂×C₇₃	—	2	2	no	—
210	C₂×C₇₃	#2935	1	1	yes	characteristic
211	C₂×C₇₃	C₂×#440	1	1	yes	characteristic
212	C₂×C₇₃	#2957	1	1	yes	characteristic
213	D₇₃	—	8	2	no	—
214	#3167	—	73	1	no	—
215	#2962	—	73	1	no	—
216	#2935	—	73	1	no	—
217	#1592	—	73	2	no	—
218	#1588	—	73	2	no	—
219	#1585	—	73	2	no	—
220	SD₁₆⋊C₈	—	73	2	no	—
221	C₂×#335	D₇₃	1	1	yes	characteristic, complemented
222	#1481	—	73	1	no	—
223	#1480	—	73	1	no	—
224	#1451	—	73	1	no	—
225	C₇₃	#18071	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	146	1	no	—
227	#533	—	73	1	no	—
228	#532	—	73	1	no	—
229	#498	—	73	1	no	—
230	#492	—	73	1	no	—
231	#487	—	73	1	no	—
232	#486	—	73	1	no	—
233	#465	—	73	2	no	—
234	#465	—	73	2	no	—
235	#446	—	73	2	no	—
236	#446	—	146	2	no	—
237	C₈×Q₈	—	73	2	no	—
238	C₄×SD₁₆	—	73	2	no	—
239	C₄×SD₁₆	—	73	2	no	—
240	#436	—	73	2	no	—
241	#435	—	146	2	no	—
242	C₈×D₄	—	73	2	no	—
243	#431	—	73	1	no	—
244	#424	—	146	1	no	—
245	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
247	#408	—	146	1	no	—
248	#405	—	146	1	no	—
249	C₄×M₁₆	—	73	1	no	—
250	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
251	#335	C₂×D₇₃	1	1	yes	characteristic
252	#335	C₂×D₇₃	1	1	yes	characteristic
253	#335	C₂×D₇₃	1	1	yes	characteristic
254	#335	C₂×D₇₃	1	1	yes	characteristic
255	Q₈⋊C₈	—	73	2	no	—
256	Q₈⋊C₈	—	73	2	no	—
257	D₄⋊C₈	—	73	2	no	—
258	D₄⋊C₈	—	73	2	no	—
259	#322	—	73	2	no	—
260	#322	—	73	2	no	—
261	C₂×#41	—	146	1	no	—
262	C₂×SD₁₆	—	73	2	no	—
263	C₂×SD₁₆	—	73	2	no	—
264	#131	—	292	4	no	—
265	C₂×M₁₆	—	73	1	no	—
266	C₂×M₁₆	—	73	1	no	—
267	C₂×M₁₆	—	146	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	—	146	2	no	—
271	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
272	C₂²×C₈	C₄×D₇₃	1	1	yes	characteristic
273	C₄⋊Q₈	—	73	1	no	—
274	C₄⋊Q₈	—	73	1	no	—
275	C₄⋊Q₈	—	73	1	no	—
276	#127	—	73	1	no	—
277	#125	—	146	1	no	—
278	#124	—	146	1	no	—
279	C₂²⋊Q₈	—	73	2	no	—
280	C₂²⋊Q₈	—	146	1	no	—
281	#121	—	73	2	no	—
282	#121	—	146	1	no	—
283	C₄×Q₈	—	73	2	no	—
284	C₄×Q₈	—	146	1	no	—
285	C₄×D₄	—	73	2	no	—
286	C₄×D₄	—	146	1	no	—
287	#117	—	146	1	no	—
288	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
289	#106	—	73	2	no	—
290	#106	—	73	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	146	2	no	—
294	C₄⋊C₈	—	146	2	no	—
295	C₄⋊C₈	—	146	1	no	—
296	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
300	#103	—	73	2	no	—
301	#103	—	73	2	no	—
302	#102	—	73	2	no	—
303	#102	—	73	2	no	—
304	C₂²⋊C₈	—	146	2	no	—
305	C₂²⋊C₈	—	146	2	no	—
306	C₂²⋊C₈	—	146	1	no	—
307	#97	—	73	2	no	—
308	#97	—	146	2	no	—
309	C₄×C₈	—	73	2	no	—
310	C₄×C₈	—	73	2	no	—
311	C₄×C₈	—	146	2	no	—
312	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
313	C₄×C₈	C₄×D₇₃	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
316	#41	—	292	2	no	—
317	#41	—	292	2	no	—
318	C₂×Q₈	—	73	2	no	—
319	C₂×Q₈	—	146	1	no	—
320	C₂×Q₈	—	146	1	no	—
321	C₂×D₄	—	73	2	no	—
322	C₂×D₄	—	146	2	no	—
323	C₂×D₄	—	146	1	no	—
324	C₂×D₄	—	146	1	no	—
325	C₂²×C₄	—	146	2	no	—
326	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
328	C₂²×C₄	#11924029	1	1	yes	characteristic
329	SD₁₆	—	292	2	no	—
330	SD₁₆	—	146	4	no	—
331	M₁₆	—	292	4	no	—
332	M₁₆	—	146	2	no	—
333	M₁₆	—	146	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	292	4	no	—
343	C₂×C₈	—	73	2	no	—
344	C₂×C₈	—	73	2	no	—
345	C₂×C₈	—	146	2	no	—
346	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
350	C₄⋊C₄	—	73	2	no	—
351	C₄⋊C₄	—	73	2	no	—
352	C₄⋊C₄	—	146	2	no	—
353	C₄⋊C₄	—	146	1	no	—
354	C₄⋊C₄	—	146	1	no	—
355	C₄⋊C₄	—	146	1	no	—
356	C₄⋊C₄	—	146	1	no	—
357	C₄⋊C₄	—	146	2	no	—
358	C₂²⋊C₄	—	146	2	no	—
359	C₂²⋊C₄	—	146	2	no	—
360	C₂²⋊C₄	—	146	2	no	—
361	C₄²	—	146	2	no	—
362	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
363	C₄²	D₄×D₇₃	1	1	yes	characteristic
364	C₄²	#11924029	1	1	yes	characteristic
365	C₄²	C₂³×D₇₃	1	1	yes	characteristic
366	C₂³	—	146	2	no	—
367	C₂³	#14556553	1	1	yes	characteristic
368	Q₈	—	292	2	no	—
369	Q₈	—	584	1	no	—
370	Q₈	—	146	2	no	—
371	Q₈	—	146	2	no	—
372	D₄	—	292	4	no	—
373	D₄	—	292	2	no	—
374	D₄	—	584	1	no	—
375	D₄	—	146	2	no	—
376	D₄	—	146	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	292	2	no	—
381	C₂×C₄	—	292	2	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	2	no	—
385	C₂×C₄	#14556553	1	1	yes	characteristic
386	C₂×C₄	#14556553	1	1	yes	characteristic
387	C₂×C₄	#14556553	1	1	yes	characteristic
388	C₂×C₄	#14556615	1	2	yes	—
389	C₂×C₄	#14556623	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
392	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	292	2	no	—
401	C₈	—	146	2	no	—
402	C₈	—	146	2	no	—
403	C₈	#14556597	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	292	2	no	—
407	C₂²	—	292	2	no	—
408	C₂²	—	292	2	no	—
409	C₂²	#17988686	1	2	yes	—
410	C₂²	C₂×#14556553	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	292	2	no	—
415	C₄	—	292	2	no	—
416	C₄	—	292	2	no	—
417	C₄	#17988686	1	2	yes	—
418	C₄	C₂×#14556597	1	1	yes	characteristic
419	C₄	#17989353	1	1	yes	characteristic
420	C₄	C₂×#14556615	1	1	yes	characteristic
421	C₄	C₂×#14556623	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	584	2	no	—
424	C₂	#22618674	1	1	yes	characteristic
425	C₂	C₂×#17988686	1	1	yes	characteristic
426	C₂	#22618847	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₂×#335×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#17989137	C₂²
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₂×#335	D₇₃
hypocenter	C₇₃	#18071
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
2. #22618874	C₂	semidirect
4. #22608832	C₂	semidirect
5. #22608808	C₂	semidirect
6. #22608787	C₂	semidirect
7. #22608742	C₂	semidirect
8. #22608333	C₂	semidirect
10. #22608220	C₂	semidirect
11. C₂×#335×C₇₃	C₂	semidirect
186. C₈×C₇₃	#131	semidirect
221. C₂×#335	D₇₃	semidirect
225. C₇₃	#18071	semidirect
403. C₈	#14556597	semidirect

Maximal subgroups

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

subgroup	index
#22620490	2
#22618874	2
#22618674	2
#22608832	2
#22608808	2
#22608787	2
#22608742	2
#22608333	2
#22608329	2
#22608220	2
C₂×#335×C₇₃	2
#18071	73