Subgroups — #33084000

Order 18688.

1018 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988634	C₂	1	1	yes	maximal, characteristic
2	#22618519	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988541	C₂	1	1	yes	maximal, characteristic
4	#405×D₇₃	C₂	1	2	yes	maximal
5	#22609818	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609817	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609814	C₂	1	2	yes	maximal, complemented
8	#22609811	C₂	1	2	yes	maximal, complemented
9	#22609810	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609639	C₂	1	2	yes	maximal
11	C₇₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924011	C₂²	1	1	yes	characteristic
13	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
14	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
15	C₂×#14556548	C₂²	1	1	yes	characteristic
16	#117×D₇₃	C₂²	1	2	yes	—
17	#17988634	C₄	1	8	yes	complemented
18	C₂×#14556527	C₂²	1	1	yes	characteristic
19	C₂×#14556526	C₂²	1	2	yes	—
20	#17988628	C₄	1	4	yes	complemented
21	#17988626	C₄	1	4	yes	complemented
22	#17988625	C₂²	1	1	yes	characteristic
23	#17988623	C₂²	1	2	yes	—
24	#17988545	C₂²	1	2	yes	—
25	#17988544	—	2	2	no	—
26	#17988543	C₂²	1	2	yes	—
27	#17988542	C₂²	1	2	yes	—
28	#17988541	—	2	2	no	—
29	#17988541	C₄	1	8	yes	complemented
30	C₂×#14556502	C₂²	1	1	yes	characteristic
31	C₂×#14556501	C₂²	1	1	yes	characteristic
32	#97×D₇₃	—	2	2	no	—
33	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₇₃	—	2	2	no	—
35	#17988348	C₂²	1	2	yes	—
36	#17988347	C₂²	1	2	yes	—
37	#17988346	C₂²	1	2	yes	—
38	C₂×#108×C₇₃	C₂²	1	1	yes	characteristic
39	#427×C₇₃	C₂²	1	1	yes	characteristic
40	#405×C₇₃	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
42	#339×C₇₃	C₂²	1	2	yes	—
43	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
44	C₂×#11924012	C₂³	1	2	yes	—
45	C₂×#11924011	—	2	2	no	—
46	C₂×#11924011	C₂×C₄	1	2	yes	—
47	C₂×#11924011	C₂×C₄	1	2	yes	—
48	C₂×#11924011	C₂×C₄	1	4	yes	—
49	C₂×#11924011	C₂×C₄	1	4	yes	—
50	M₁₆×D₇₃	—	2	4	no	—
51	M₁₆×D₇₃	C₂×C₄	1	8	yes	—
52	C₂²×#10596831	C₂³	1	1	yes	characteristic
53	C₂²×#10596831	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₇₃	—	2	2	no	—
55	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
56	C₂×C₈×D₇₃	D₄	1	2	yes	—
57	C₂×C₈×D₇₃	D₄	1	2	yes	—
58	C₂×C₈×D₇₃	Q₈	1	4	yes	—
59	#14556550	C₂³	1	2	yes	—
60	#14556549	C₂×C₄	1	4	yes	—
61	#14556548	—	2	2	no	—
62	#14556548	—	2	2	no	—
63	#14556548	C₂×C₄	1	4	yes	—
64	#14556547	—	2	2	no	—
65	C₂×#11924007	—	2	1	no	—
66	C₄⋊C₄×D₇₃	C₂×C₄	1	4	yes	—
67	C₂×#11924005	—	2	1	no	—
68	C₂²⋊C₄×D₇₃	—	2	2	no	—
69	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
70	C₄²×D₇₃	—	2	2	no	—
71	#14556527	C₂×C₄	1	4	yes	complemented
72	#14556526	C₂×C₄	1	8	yes	complemented
73	#14556525	C₂×C₄	1	2	yes	—
74	#14556524	C₂×C₄	1	4	yes	—
75	#14556523	C₂×C₄	1	2	yes	—
76	#14556522	C₂×C₄	1	4	yes	—
77	#14556502	—	2	2	no	—
78	#14556502	C₂×C₄	1	4	yes	complemented
79	#14556501	—	2	2	no	—
80	#14556501	—	2	2	no	—
81	#14556501	C₂×C₄	1	4	yes	complemented
82	C₄×#10596831	—	2	2	no	—
83	C₈×Dic₇₃	—	2	2	no	—
84	C₈×Dic₇₃	—	2	2	no	—
85	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
86	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
87	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
89	#117×C₇₃	C₂³	1	2	yes	—
90	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
91	#108×C₇₃	C₂×C₄	1	4	yes	complemented
92	#107×C₇₃	C₂×C₄	1	2	yes	—
93	#106×C₇₃	C₂×C₄	1	2	yes	—
94	#97×C₇₃	—	2	2	no	—
95	C₄×C₈×C₇₃	—	2	2	no	—
96	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
97	C₂³×D₇₃	#41	1	1	yes	characteristic
98	C₂²×Dic₇₃	—	2	1	no	—
99	C₂²×Dic₇₃	#41	1	1	yes	characteristic
100	C₂×C₄×D₇₃	—	2	4	no	—
101	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
102	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
106	C₂×C₄×D₇₃	#41	1	2	yes	—
107	#11924012	—	2	2	no	—
108	#11924012	C₂²×C₄	1	4	yes	—
109	#11924011	—	2	8	no	—
110	#11924011	C₄²	1	8	yes	—
111	#11924011	C₄²	1	8	yes	—
112	C₂×#10596831	—	2	2	no	—
113	C₂×#10596831	C₂²×C₄	1	2	yes	—
114	C₂×#10596831	C₂²×C₄	1	2	yes	—
115	C₂×#10596831	C₂²×C₄	1	2	yes	—
116	C₂×#10596831	C₂²×C₄	1	2	yes	—
117	C₂×#10596831	C₂×D₄	1	2	yes	—
118	C₂×#10596831	C₂×Q₈	1	2	yes	—
119	C₈×D₇₃	—	2	8	no	—
120	C₈×D₇₃	C₄⋊C₄	1	8	yes	—
121	C₈×D₇₃	C₄⋊C₄	1	8	yes	—
122	C₄⋊Dic₇₃	C₂²×C₄	1	4	yes	—
123	#11924007	—	2	4	no	—
124	#11924007	—	2	4	no	—
125	C₂²⋊Dic₇₃	—	2	2	no	—
126	#11924005	—	2	4	no	—
127	#11924005	—	2	4	no	—
128	C₄×Dic₇₃	—	2	2	no	—
129	C₄×Dic₇₃	—	2	1	no	—
130	C₄×Dic₇₃	—	2	4	no	—
131	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₇₃	—	2	1	no	—
133	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
134	M₁₆×C₇₃	—	2	2	no	—
135	M₁₆×C₇₃	C₂²×C₄	1	4	yes	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
145	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₇₃	—	2	2	no	—
147	C₄²×C₇₃	—	2	2	no	—
148	C₄²×C₇₃	—	2	1	no	—
149	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
150	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
151	C₂²×D₇₃	—	4	2	no	—
152	C₂²×D₇₃	#117	1	2	yes	—
153	C₂²×D₇₃	C₄×D₄	1	2	yes	—
154	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₇₃	—	2	2	no	—
156	C₂×C₄×C₇₃	—	2	4	no	—
157	C₂×C₄×C₇₃	—	4	2	no	—
158	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
164	C₂×Dic₇₃	—	2	2	no	—
165	C₂×Dic₇₃	—	2	4	no	—
166	C₂×Dic₇₃	—	4	2	no	—
167	C₂×Dic₇₃	#117	1	2	yes	—
168	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
169	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
170	C₄×D₇₃	—	4	8	no	—
171	C₄×D₇₃	C₂×C₄²	1	4	yes	—
172	C₄×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
173	C₄×D₇₃	C₄×D₄	1	4	yes	—
174	C₄×D₇₃	C₄×Q₈	1	4	yes	—
175	C₈×C₇₃	—	2	4	no	—
176	C₈×C₇₃	C₂×C₄²	1	2	yes	—
177	C₈×C₇₃	C₂×C₄²	1	2	yes	—
178	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
179	C₈×C₇₃	C₂×C₄⋊C₄	1	2	yes	—
180	#10596831	—	2	4	no	—
181	#10596831	C₂×C₄²	1	4	yes	—
182	#10596831	C₂×C₄⋊C₄	1	4	yes	—
183	C₂²×C₇₃	—	2	2	no	—
184	C₂²×C₇₃	C₂×#117	1	1	yes	characteristic
185	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
187	C₂×D₇₃	—	2	4	no	—
188	C₂×D₇₃	—	4	2	no	—
189	C₂×D₇₃	—	4	2	no	—
190	C₂×D₇₃	C₄×C₄⋊C₄	1	4	yes	—
191	C₄×C₇₃	—	4	2	no	—
192	C₄×C₇₃	—	4	4	no	—
193	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
194	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
195	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
196	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
197	Dic₇₃	—	4	2	no	—
198	Dic₇₃	—	4	4	no	—
199	Dic₇₃	C₄×C₄⋊C₄	1	4	yes	—
200	#20444	—	73	1	no	maximal, Sylow
201	C₂×C₇₃	—	2	1	no	—
202	C₂×C₇₃	—	2	1	no	—
203	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
204	C₂×C₇₃	#2955	1	2	yes	—
205	D₇₃	—	2	4	no	—
206	C₂×#430	—	73	1	no	—
207	#2911	—	73	1	no	—
208	C₂×#405	—	73	1	no	—
209	C₂×#405	—	73	2	no	—
210	#1773	—	73	1	no	—
211	#1773	—	73	1	no	—
212	#1773	—	73	2	no	—
213	#1772	—	73	2	no	—
214	#1772	—	73	1	no	—
215	#1772	D₇₃	1	1	yes	characteristic, complemented
216	#1733	—	73	2	no	—
217	C₇₃	#20444	1	1	yes	characteristic, complemented, Sylow
218	C₂²×M₁₆	—	73	1	no	—
219	C₂²×M₁₆	—	73	2	no	—
220	C₂³×C₈	—	73	1	no	—
221	C₂×#117	—	73	1	no	—
222	C₂×#117	—	73	2	no	—
223	#430	—	73	8	no	—
224	C₂×#108	—	73	2	no	—
225	C₂×#108	—	73	1	no	—
226	C₂×#108	C₂×D₇₃	1	1	yes	characteristic
227	#428	—	73	4	no	—
228	#428	—	73	4	no	—
229	#427	—	73	1	no	—
230	#427	—	73	2	no	—
231	#427	C₂×D₇₃	1	1	yes	characteristic
232	#405	—	73	8	no	—
233	#405	—	73	2	no	—
234	#405	—	73	2	no	—
235	#405	—	73	2	no	—
236	#405	—	146	2	no	—
237	#405	—	146	2	no	—
238	#405	C₂×D₇₃	1	2	yes	—
239	C₂×#97	—	73	1	no	—
240	C₂×#97	—	73	1	no	—
241	C₂×#97	—	146	2	no	—
242	C₂×C₄×C₈	—	73	1	no	—
243	C₂×C₄×C₈	—	146	2	no	—
244	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
245	#339	—	73	2	no	—
246	#339	—	73	2	no	—
247	#339	—	73	2	no	—
248	#339	C₂×D₇₃	1	2	yes	—
249	C₂³×C₄	—	73	1	no	—
250	C₂×M₁₆	—	73	4	no	—
251	C₂×M₁₆	—	73	2	no	—
252	C₂×M₁₆	—	73	2	no	—
253	C₂×M₁₆	—	73	4	no	—
254	C₂×M₁₆	—	73	2	no	—
255	C₂×M₁₆	—	73	8	no	—
256	C₂×M₁₆	—	146	2	no	—
257	C₂×M₁₆	—	146	4	no	—
258	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
259	C₂²×C₈	—	73	1	no	—
260	C₂²×C₈	—	73	1	no	—
261	C₂²×C₈	—	73	4	no	—
262	C₂²×C₈	—	73	2	no	—
263	C₂²×C₈	—	73	2	no	—
264	C₂²×C₈	—	73	4	no	—
265	C₂²×C₈	—	146	2	no	—
266	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
268	#117	—	73	4	no	—
269	#117	—	73	2	no	—
270	#117	—	73	4	no	—
271	#117	—	146	2	no	—
272	#117	—	146	2	no	—
273	#117	—	146	2	no	—
274	#117	C₂²×D₇₃	1	2	yes	—
275	C₂×C₄⋊C₄	—	73	4	no	—
276	C₂×C₄⋊C₄	—	146	1	no	—
277	C₂×C₂²⋊C₄	—	146	2	no	—
278	C₂×C₂²⋊C₄	—	146	1	no	—
279	C₂×C₄²	—	73	1	no	—
280	C₂×C₄²	—	146	2	no	—
281	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
282	#108	—	73	8	no	—
283	#108	—	73	4	no	—
284	#108	C₄×D₇₃	1	4	yes	complemented
285	#107	—	73	2	no	—
286	#107	—	73	4	no	—
287	#107	C₄×D₇₃	1	2	yes	—
288	#106	—	73	2	no	—
289	#106	—	73	4	no	—
290	#106	C₄×D₇₃	1	2	yes	—
291	#97	—	2	2	no	—
292	#97	—	73	4	no	—
293	#97	—	73	4	no	—
294	#97	—	146	2	no	—
295	#97	—	146	2	no	—
296	#97	—	146	2	no	—
297	C₄×C₈	—	2	2	no	—
298	C₄×C₈	—	73	4	no	—
299	C₄×C₈	—	146	2	no	—
300	C₄×C₈	—	146	2	no	—
301	C₄×C₈	—	146	2	no	—
302	C₄×C₈	C₄×D₇₃	1	4	yes	complemented
303	C₂⁴	—	73	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	73	1	no	—
306	C₂²×C₄	—	73	2	no	—
307	C₂²×C₄	—	73	2	no	—
308	C₂²×C₄	—	73	2	no	—
309	C₂²×C₄	—	73	2	no	—
310	C₂²×C₄	—	73	2	no	—
311	C₂²×C₄	—	73	2	no	—
312	C₂²×C₄	—	146	4	no	—
313	C₂²×C₄	—	146	1	no	—
314	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
315	M₁₆	—	2	2	no	—
316	M₁₆	—	73	8	no	—
317	M₁₆	—	73	8	no	—
318	M₁₆	—	73	4	no	—
319	M₁₆	—	146	8	no	—
320	M₁₆	—	146	2	no	—
321	M₁₆	C₂×C₄×D₇₃	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	73	2	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	73	2	no	—
326	C₂×C₈	—	73	2	no	—
327	C₂×C₈	—	73	2	no	—
328	C₂×C₈	—	73	2	no	—
329	C₂×C₈	—	73	8	no	—
330	C₂×C₈	—	73	8	no	—
331	C₂×C₈	—	146	8	no	—
332	C₂×C₈	—	146	2	no	—
333	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
334	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
335	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
336	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
337	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
338	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
339	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
340	C₂×C₈	Q₈×D₇₃	1	2	yes	—
341	C₄⋊C₄	—	73	4	no	—
342	C₄⋊C₄	—	146	4	no	—
343	C₄⋊C₄	—	146	4	no	—
344	C₄⋊C₄	C₂×C₄×D₇₃	1	4	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	146	4	no	—
347	C₂²⋊C₄	—	146	4	no	—
348	C₂²⋊C₄	—	146	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	73	2	no	—
352	C₄²	—	146	4	no	—
353	C₄²	—	146	2	no	—
354	C₄²	—	146	1	no	—
355	C₄²	C₂×C₄×D₇₃	1	2	yes	—
356	C₂³	—	292	2	no	—
357	C₂³	—	73	2	no	—
358	C₂³	—	73	2	no	—
359	C₂³	—	73	2	no	—
360	C₂³	#41×D₇₃	1	1	yes	characteristic
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	292	8	no	—
365	C₂×C₄	—	292	2	no	—
366	C₂×C₄	—	73	2	no	—
367	C₂×C₄	—	73	2	no	—
368	C₂×C₄	—	73	2	no	—
369	C₂×C₄	—	73	4	no	—
370	C₂×C₄	—	73	4	no	—
371	C₂×C₄	—	73	4	no	—
372	C₂×C₄	—	73	4	no	—
373	C₂×C₄	—	146	2	no	—
374	C₂×C₄	—	146	4	no	—
375	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
376	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
378	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
379	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
380	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
381	C₈	—	2	4	no	—
382	C₈	—	73	4	no	—
383	C₈	—	73	4	no	—
384	C₈	—	146	4	no	—
385	C₈	C₄²×D₇₃	1	2	yes	—
386	C₈	C₄²×D₇₃	1	2	yes	—
387	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
388	C₈	C₄⋊C₄×D₇₃	1	2	yes	—
389	C₂²	—	2	2	no	—
390	C₂²	—	292	2	no	—
391	C₂²	—	292	2	no	—
392	C₂²	—	73	4	no	—
393	C₂²	—	146	4	no	—
394	C₂²	#117×D₇₃	1	1	yes	characteristic
395	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
396	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
397	C₄	—	4	2	no	—
398	C₄	—	4	4	no	—
399	C₄	—	292	2	no	—
400	C₄	—	292	4	no	—
401	C₄	—	73	4	no	—
402	C₄	C₂×C₄²×D₇₃	1	1	yes	characteristic
403	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
404	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
405	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
406	C₂	—	2	1	no	—
407	C₂	—	2	1	no	—
408	C₂	—	146	4	no	—
409	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
410	C₂	#22618829	1	2	yes	—

	subgroup	G/H
center	C₂×C₈	D₄×D₇₃
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1772	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂³×D₇₃	#41
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1772	D₇₃
hypocenter	C₇₃	#20444
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
5. #22609818	C₂	semidirect
6. #22609817	C₂	semidirect
7. #22609814	C₂	semidirect
8. #22609811	C₂	semidirect
9. #22609810	C₂	semidirect
11. C₇₃×#1772	C₂	semidirect
17. #17988634	C₄	semidirect
20. #17988628	C₄	semidirect
21. #17988626	C₄	semidirect
29. #17988541	C₄	semidirect
71. #14556527	C₂×C₄	semidirect
72. #14556526	C₂×C₄	semidirect
78. #14556502	C₂×C₄	semidirect
81. #14556501	C₂×C₄	semidirect
85. C₈×Dic₇₃	C₂×C₄	semidirect
91. #108×C₇₃	C₂×C₄	semidirect
96. C₄×C₈×C₇₃	C₂×C₄	semidirect
215. #1772	D₇₃	semidirect
217. C₇₃	#20444	semidirect
284. #108	C₄×D₇₃	semidirect
302. C₄×C₈	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×#17988634	2
#22618519	2
C₂×#17988541	2
#405×D₇₃	2
#22609818	2
#22609817	2
#22609814	2
#22609811	2
#22609810	2
#22609639	2
C₇₃×#1772	2
#20444	73