Subgroups — #1689×D₇₃ #33068487

Order 18688.

758 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#474×D₇₃	C₂	1	2	yes	maximal
3	#436×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22609421	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609420	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609419	C₂	1	2	yes	maximal, complemented
7	#22609418	C₂	1	2	yes	maximal, complemented
8	#22609417	C₂	1	1	yes	maximal, characteristic, complemented
9	#334×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#332×D₇₃	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1689	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₇₃	—	2	1	no	—
13	C₂×Q₁₆×D₇₃	—	2	1	no	—
14	C₂×M₁₆×D₇₃	—	2	1	no	—
15	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
16	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
17	#17988967	C₂²	1	1	yes	characteristic, complemented
18	#17988966	C₂²	1	2	yes	complemented
19	#17988965	—	2	1	no	—
20	#17988965	—	2	1	no	—
21	#17988868	C₂²	1	2	yes	—
22	#17988867	C₂²	1	2	yes	—
23	#17988866	—	2	2	no	—
24	#17988865	—	2	2	no	—
25	#17988864	C₂²	1	2	yes	—
26	#17988666	C₂²	1	1	yes	characteristic
27	#17988665	C₂²	1	1	yes	characteristic
28	#17988664	C₂²	1	1	yes	characteristic
29	#17988663	—	2	1	no	—
30	#17988662	—	2	1	no	—
31	#107×D₇₃	—	2	2	no	—
32	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
33	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
34	#102×D₇₃	—	2	2	no	—
35	C₂²⋊C₈×D₇₃	—	2	1	no	—
36	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
37	#17988338	C₂²	1	1	yes	characteristic, complemented
38	#17988337	C₂²	1	2	yes	complemented
39	#17988334	C₂²	1	2	yes	complemented
40	#17988333	C₂²	1	2	yes	complemented
41	#17988332	C₂²	1	2	yes	complemented
42	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#474×C₇₃	C₂²	1	2	yes	—
44	#436×C₇₃	C₂²	1	1	yes	characteristic
45	#334×C₇₃	C₂²	1	1	yes	characteristic, complemented
46	#332×C₇₃	C₂²	1	2	yes	complemented
47	C₂×Q₈×D₇₃	—	2	2	no	—
48	C₂×D₄×D₇₃	D₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	—	2	1	no	—
50	C₂×Dic₂₉₂	—	2	1	no	—
51	C₂×Dic₂₉₂	—	2	1	no	—
52	C₂×#11924018	—	2	2	no	—
53	C₂×#11924018	—	2	2	no	—
54	Q₁₆×D₇₃	—	4	4	no	—
55	Q₁₆×D₇₃	—	4	4	no	—
56	C₂×#11924012	—	2	1	no	—
57	C₂×#11924011	—	2	1	no	—
58	C₂×#11924011	—	2	1	no	—
59	M₁₆×D₇₃	—	4	4	no	—
60	C₂×C₈×D₇₃	—	2	2	no	—
61	C₂×C₈×D₇₃	—	2	1	no	—
62	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
64	#14556591	C₂³	1	2	yes	—
65	#14556590	—	2	2	no	—
66	#14556590	—	2	2	no	—
67	#14556589	—	2	2	no	—
68	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
69	D₄×Dic₇₃	D₄	1	1	yes	characteristic
70	#14556553	D₄	1	1	yes	characteristic
71	C₄×C₂²⋊D₇₃	—	2	1	no	—
72	#14556551	—	2	1	no	—
73	C₄⋊C₄×D₇₃	—	2	2	no	—
74	C₄⋊C₄×D₇₃	—	2	2	no	—
75	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
76	C₂²⋊C₄×D₇₃	—	2	1	no	—
77	C₄²×D₇₃	C₂³	1	1	yes	characteristic
78	#14556525	—	2	2	no	—
79	#14556524	—	2	2	no	—
80	#14556524	—	2	2	no	—
81	C₄⋊#10596831	C₂³	1	2	yes	—
82	C₄⋊#10596831	C₂³	1	1	yes	characteristic
83	#14556520	—	2	2	no	—
84	#14556520	—	2	1	no	—
85	#14556513	—	2	2	no	—
86	#14556512	—	2	2	no	—
87	#14556511	—	2	2	no	—
88	C₂²⋊#10596831	—	2	1	no	—
89	#14556503	—	2	1	no	—
90	#14556503	—	2	1	no	—
91	C₄×#10596831	C₂³	1	1	yes	characteristic
92	C₈×Dic₇₃	D₄	1	1	yes	characteristic
93	C₈×Dic₇₃	D₄	1	1	yes	characteristic
94	C₂×Q₁₆×C₇₃	—	2	1	no	—
95	C₂×Q₁₆×C₇₃	—	2	1	no	—
96	C₂×M₁₆×C₇₃	—	2	1	no	—
97	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
98	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
99	#107×C₇₃	—	2	2	no	—
100	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
101	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
102	#102×C₇₃	—	2	2	no	—
103	C₂²⋊C₈×C₇₃	—	2	1	no	—
104	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
105	C₂³×D₇₃	—	2	1	no	—
106	C₂×Dic₁₄₆	—	2	2	no	—
107	C₂×Dic₁₄₆	—	4	2	no	—
108	Q₈×D₇₃	—	4	4	no	—
109	Q₈×D₇₃	—	4	4	no	—
110	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
111	C₂×C₂²⋊D₇₃	—	2	1	no	—
112	D₄×D₇₃	—	2	4	no	—
113	C₂²×Dic₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	2	1	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	4	2	no	—
118	C₂×C₄×D₇₃	—	4	2	no	—
119	C₂×C₄×D₇₃	—	4	2	no	—
120	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
121	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
122	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
123	Dic₂₉₂	—	4	2	no	—
124	Dic₂₉₂	—	4	2	no	—
125	#11924018	—	4	4	no	—
126	#11924018	—	4	4	no	—
127	#11924012	—	4	2	no	—
128	#11924011	—	4	2	no	—
129	#11924011	—	4	2	no	—
130	C₂×#10596831	—	2	1	no	—
131	C₂×#10596831	—	2	2	no	—
132	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
133	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
134	C₈×D₇₃	—	2	2	no	—
135	C₈×D₇₃	—	4	2	no	—
136	C₈×D₇₃	—	4	4	no	—
137	C₈×D₇₃	D₈	1	4	yes	—
138	C₄⋊Dic₇₃	—	2	2	no	—
139	C₄⋊Dic₇₃	—	2	2	no	—
140	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
141	#11924007	—	2	1	no	—
142	#11924007	—	4	2	no	—
143	#11924007	—	4	2	no	—
144	C₂²⋊Dic₇₃	—	2	1	no	—
145	#11924005	—	2	1	no	—
146	#11924005	—	2	1	no	—
147	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
148	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄×Dic₇₃	#41	1	1	yes	characteristic
150	C₂×Q₈×C₇₃	—	2	2	no	—
151	C₂×D₄×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	—	2	1	no	—
153	Q₁₆×C₇₃	—	4	2	no	—
154	Q₁₆×C₇₃	—	4	2	no	—
155	M₁₆×C₇₃	—	4	2	no	—
156	C₂×C₈×C₇₃	—	2	1	no	—
157	C₂×C₈×C₇₃	—	2	2	no	—
158	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₄⋊C₄×C₇₃	—	2	2	no	—
161	C₄⋊C₄×C₇₃	—	2	2	no	—
162	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
163	C₂²⋊C₄×C₇₃	—	2	1	no	—
164	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
165	C₂³×C₇₃	—	2	1	no	—
166	C₂²×D₇₃	—	2	1	no	—
167	C₂²×D₇₃	—	4	2	no	—
168	C₂²×D₇₃	—	4	2	no	—
169	C₂²×D₇₃	—	4	2	no	—
170	C₂²×D₇₃	#121	1	1	yes	characteristic
171	Q₈×C₇₃	—	4	2	no	—
172	Q₈×C₇₃	—	4	2	no	—
173	D₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	2	1	no	—
175	C₂×C₄×C₇₃	—	4	1	no	—
176	C₂×C₄×C₇₃	—	4	1	no	—
177	C₂×C₄×C₇₃	—	4	2	no	—
178	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
181	C₂²⋊D₇₃	—	4	2	no	—
182	C₂×Dic₇₃	—	2	1	no	—
183	C₂×Dic₇₃	—	4	2	no	—
184	C₂×Dic₇₃	—	4	2	no	—
185	C₂×Dic₇₃	#121	1	1	yes	characteristic
186	C₂×Dic₇₃	#121	1	1	yes	characteristic
187	C₂×Dic₇₃	#121	1	1	yes	characteristic
188	D₂₉₂	—	2	2	no	—
189	C₄×D₇₃	—	2	2	no	—
190	C₄×D₇₃	—	4	2	no	—
191	C₄×D₇₃	—	4	1	no	—
192	C₄×D₇₃	—	4	1	no	—
193	C₄×D₇₃	—	4	2	no	—
194	C₄×D₇₃	—	8	4	no	—
195	C₄×D₇₃	C₂×D₈	1	2	yes	—
196	C₄×D₇₃	AGL(1,ℤ/8)	1	2	yes	—
197	C₄×D₇₃	#137	1	4	yes	—
198	Dic₁₄₆	—	4	2	no	—
199	Dic₁₄₆	—	4	2	no	—
200	Dic₁₄₆	—	8	4	no	—
201	C₈×C₇₃	—	2	1	no	—
202	C₈×C₇₃	—	4	1	no	—
203	C₈×C₇₃	—	4	2	no	—
204	C₈×C₇₃	C₂×D₈	1	2	yes	—
205	#10596831	—	2	1	no	—
206	#10596831	—	4	1	no	—
207	#10596831	—	4	2	no	—
208	#10596831	C₂×D₈	1	2	yes	—
209	C₂²×C₇₃	—	4	1	no	—
210	C₂²×C₇₃	—	4	1	no	—
211	C₂²×C₇₃	—	4	1	no	—
212	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
213	C₂×D₇₃	—	4	1	no	—
214	C₂×D₇₃	—	4	1	no	—
215	C₂×D₇₃	—	4	1	no	—
216	C₂×D₇₃	—	8	4	no	—
217	C₂×D₇₃	#459	1	2	yes	—
218	C₂×D₇₃	#470	1	2	yes	—
219	C₂×D₇₃	#473	1	2	yes	—
220	C₄×C₇₃	—	2	1	no	—
221	C₄×C₇₃	—	4	1	no	—
222	C₄×C₇₃	—	8	2	no	—
223	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
224	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
225	C₄×C₇₃	C₂×#137	1	2	yes	—
226	Dic₇₃	—	2	1	no	—
227	Dic₇₃	—	4	1	no	—
228	Dic₇₃	—	8	2	no	—
229	Dic₇₃	#459	1	2	yes	—
230	Dic₇₃	#470	1	2	yes	—
231	C₂×#1689	—	73	1	no	maximal, Sylow
232	C₂×C₇₃	—	8	1	no	—
233	C₂×C₇₃	C₂×#459	1	1	yes	characteristic
234	C₂×C₇₃	C₂×#470	1	1	yes	characteristic
235	C₂×C₇₃	C₂×#473	1	1	yes	characteristic
236	D₇₃	—	8	1	no	—
237	D₇₃	#1689	1	4	yes	direct product factor
238	C₂×#494	—	73	1	no	—
239	C₂×#474	—	73	2	no	—
240	C₂×#436	—	73	1	no	—
241	#1689	—	73	1	no	—
242	#1689	—	73	2	no	—
243	#1689	—	73	1	no	—
244	#1689	—	73	1	no	—
245	#1689	—	73	2	no	—
246	#1689	D₇₃	1	1	yes	characteristic, direct product factor
247	C₂×#334	—	73	1	no	—
248	C₂×#332	—	73	2	no	—
249	C₇₃	C₂×#1689	1	1	yes	characteristic, complemented, Sylow
250	C₂²×Q₁₆	—	146	1	no	—
251	C₂²×Q₁₆	—	146	1	no	—
252	C₂²×M₁₆	—	146	1	no	—
253	C₂×C₄⋊Q₈	—	73	2	no	—
254	C₂×C₄×D₄	—	73	1	no	—
255	#494	—	73	2	no	—
256	#494	—	73	1	no	—
257	#494	—	146	1	no	—
258	#494	—	146	1	no	—
259	#494	C₂×D₇₃	1	1	yes	characteristic, complemented
260	#474	—	73	2	no	—
261	#474	—	73	2	no	—
262	#474	—	73	2	no	—
263	#474	—	146	2	no	—
264	#474	—	146	2	no	—
265	#474	C₂×D₇₃	1	2	yes	—
266	#436	—	73	1	no	—
267	#436	—	73	1	no	—
268	#436	—	73	1	no	—
269	#436	—	146	1	no	—
270	#436	—	146	1	no	—
271	#436	C₂×D₇₃	1	1	yes	characteristic
272	C₂×#107	—	146	2	no	—
273	C₂×C₄⋊C₈	—	73	1	no	—
274	C₂×C₄⋊C₈	—	73	2	no	—
275	C₂×#102	—	146	2	no	—
276	C₂×C₂²⋊C₈	—	146	1	no	—
277	C₂×C₄×C₈	—	73	1	no	—
278	#334	—	73	2	no	—
279	#334	—	73	1	no	—
280	#334	C₂×D₇₃	1	1	yes	characteristic, complemented
281	#332	—	73	2	no	—
282	#332	—	73	2	no	—
283	#332	—	73	2	no	—
284	#332	C₂×D₇₃	1	2	yes	complemented
285	C₂²×Q₈	—	146	2	no	—
286	C₂²×D₄	—	73	1	no	—
287	C₂³×C₄	—	146	1	no	—
288	C₂×Q₁₆	—	2	1	no	—
289	C₂×Q₁₆	—	2	1	no	—
290	C₂×Q₁₆	—	292	4	no	—
291	C₂×Q₁₆	—	292	4	no	—
292	C₂×Q₁₆	—	146	2	no	—
293	C₂×Q₁₆	—	146	2	no	—
294	C₂×Q₁₆	—	146	1	no	—
295	C₂×Q₁₆	—	146	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	292	4	no	—
298	C₂×M₁₆	—	146	1	no	—
299	C₂×M₁₆	—	146	1	no	—
300	C₂×M₁₆	—	146	1	no	—
301	C₂²×C₈	—	73	1	no	—
302	C₂²×C₈	—	73	1	no	—
303	C₂²×C₈	—	146	1	no	—
304	C₂²×C₈	—	146	2	no	—
305	C₄⋊Q₈	—	73	2	no	—
306	C₄⋊Q₈	—	146	2	no	—
307	C₄⋊Q₈	—	146	2	no	—
308	C₄⋊Q₈	—	146	2	no	—
309	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
310	C₄×D₄	—	73	1	no	—
311	C₄×D₄	—	73	1	no	—
312	C₄×D₄	—	73	1	no	—
313	C₄×D₄	—	146	1	no	—
314	C₄×D₄	—	146	1	no	—
315	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	—	73	1	no	—
317	C₂×C₄⋊C₄	—	146	2	no	—
318	C₂×C₄⋊C₄	—	146	2	no	—
319	C₂×C₂²⋊C₄	—	146	1	no	—
320	C₂×C₄²	—	73	1	no	—
321	#107	—	2	2	no	—
322	#107	—	146	2	no	—
323	#107	—	146	2	no	—
324	#107	—	146	2	no	—
325	C₄⋊C₈	—	73	1	no	—
326	C₄⋊C₈	—	73	2	no	—
327	C₄⋊C₈	—	146	1	no	—
328	C₄⋊C₈	—	146	2	no	—
329	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
330	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
331	#102	—	2	2	no	—
332	#102	—	146	2	no	—
333	#102	—	146	2	no	—
334	#102	—	146	2	no	—
335	C₂²⋊C₈	—	2	1	no	—
336	C₂²⋊C₈	—	146	1	no	—
337	C₂²⋊C₈	—	146	1	no	—
338	C₂²⋊C₈	—	146	1	no	—
339	C₄×C₈	—	73	1	no	—
340	C₄×C₈	—	73	1	no	—
341	C₄×C₈	—	73	1	no	—
342	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
343	C₂⁴	—	146	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	292	2	no	—
346	C₂×Q₈	—	292	4	no	—
347	C₂×Q₈	—	292	4	no	—
348	C₂×Q₈	—	146	2	no	—
349	C₂×D₄	—	73	1	no	—
350	C₂×D₄	—	146	4	no	—
351	C₂×D₄	—	146	1	no	—
352	C₂×D₄	D₄×D₇₃	1	1	yes	characteristic
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	292	2	no	—
355	C₂²×C₄	—	292	2	no	—
356	C₂²×C₄	—	292	2	no	—
357	C₂²×C₄	—	73	1	no	—
358	C₂²×C₄	—	73	1	no	—
359	C₂²×C₄	—	73	1	no	—
360	C₂²×C₄	—	146	1	no	—
361	C₂²×C₄	—	146	1	no	—
362	C₂²×C₄	—	146	1	no	—
363	C₂²×C₄	—	146	1	no	—
364	Q₁₆	—	4	2	no	—
365	Q₁₆	—	4	2	no	—
366	Q₁₆	—	292	2	no	—
367	Q₁₆	—	292	4	no	—
368	Q₁₆	—	292	4	no	—
369	Q₁₆	—	292	2	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	—	292	2	no	—
372	M₁₆	—	292	2	no	—
373	M₁₆	—	292	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	292	4	no	—
377	C₂×C₈	—	292	2	no	—
378	C₂×C₈	—	73	1	no	—
379	C₂×C₈	—	73	4	no	—
380	C₂×C₈	—	73	1	no	—
381	C₂×C₈	—	146	2	no	—
382	C₂×C₈	—	146	1	no	—
383	C₂×C₈	—	146	2	no	—
384	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
385	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	292	2	no	—
389	C₄⋊C₄	—	292	2	no	—
390	C₄⋊C₄	—	73	1	no	—
391	C₄⋊C₄	—	146	1	no	—
392	C₄⋊C₄	—	146	2	no	—
393	C₄⋊C₄	—	146	2	no	—
394	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
395	C₂²⋊C₄	—	2	1	no	—
396	C₂²⋊C₄	—	146	1	no	—
397	C₂²⋊C₄	—	146	1	no	—
398	C₂²⋊C₄	—	146	1	no	—
399	C₄²	—	73	1	no	—
400	C₄²	—	73	1	no	—
401	C₄²	—	73	1	no	—
402	C₄²	C₂³×D₇₃	1	1	yes	characteristic
403	C₂³	—	2	1	no	—
404	C₂³	—	292	2	no	—
405	C₂³	—	292	2	no	—
406	C₂³	—	292	2	no	—
407	C₂³	—	73	1	no	—
408	C₂³	—	146	1	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	292	2	no	—
412	Q₈	—	292	2	no	—
413	Q₈	—	584	4	no	—
414	D₄	—	2	2	no	—
415	D₄	—	292	2	no	—
416	D₄	—	146	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	292	2	no	—
422	C₂×C₄	—	292	2	no	—
423	C₂×C₄	—	292	2	no	—
424	C₂×C₄	—	292	1	no	—
425	C₂×C₄	—	292	1	no	—
426	C₂×C₄	—	292	2	no	—
427	C₂×C₄	—	584	4	no	—
428	C₂×C₄	—	73	1	no	—
429	C₂×C₄	—	73	1	no	—
430	C₂×C₄	—	73	4	no	—
431	C₂×C₄	—	73	2	no	—
432	C₂×C₄	—	73	2	no	—
433	C₂×C₄	—	73	1	no	—
434	C₂×C₄	—	146	2	no	—
435	C₂×C₄	—	146	1	no	—
436	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
437	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
438	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
439	C₈	—	2	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	—	292	2	no	—
443	C₈	—	292	1	no	—
444	C₈	—	73	2	no	—
445	C₈	—	146	1	no	—
446	C₈	D₈×D₇₃	1	2	yes	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	292	1	no	—
451	C₂²	—	292	1	no	—
452	C₂²	—	292	1	no	—
453	C₂²	—	584	4	no	—
454	C₂²	—	73	2	no	—
455	C₂²	—	73	2	no	—
456	C₂²	—	73	2	no	—
457	C₂²	#121×D₇₃	1	1	yes	characteristic
458	C₄	—	2	1	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	292	1	no	—
462	C₄	—	584	2	no	—
463	C₄	—	73	2	no	—
464	C₄	—	73	2	no	—
465	C₄	—	146	1	no	—
466	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
467	C₄	AGL(1,ℤ/8)×D₇₃	1	1	yes	characteristic
468	C₄	#137×D₇₃	1	2	yes	—
469	C₂	—	8	1	no	—
470	C₂	—	584	1	no	—
471	C₂	—	73	4	no	—
472	C₂	#459×D₇₃	1	1	yes	characteristic
473	C₂	#470×D₇₃	1	1	yes	characteristic
474	C₂	#473×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₇₃
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1689	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×D₄×D₇₃	D₄
hypercenter	#1689	D₇₃
hypocenter	C₇₃	C₂×#1689
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1689

Complements

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

N	H ≅ G/N	type
1. #494×D₇₃	C₂	semidirect
4. #22609421	C₂	semidirect
5. #22609420	C₂	semidirect
6. #22609419	C₂	semidirect
7. #22609418	C₂	semidirect
8. #22609417	C₂	semidirect
9. #334×D₇₃	C₂	semidirect
10. #332×D₇₃	C₂	semidirect
11. C₇₃×#1689	C₂	semidirect
17. #17988967	C₂²	semidirect
18. #17988966	C₂²	semidirect
37. #17988338	C₂²	semidirect
38. #17988337	C₂²	semidirect
39. #17988334	C₂²	semidirect
40. #17988333	C₂²	semidirect
41. #17988332	C₂²	semidirect
42. #494×C₇₃	C₂²	semidirect
45. #334×C₇₃	C₂²	semidirect
46. #332×C₇₃	C₂²	semidirect
237. D₇₃	#1689	direct (N × H)
246. #1689	D₇₃	direct (N × H)
249. C₇₃	C₂×#1689	semidirect
259. #494	C₂×D₇₃	semidirect
280. #334	C₂×D₇₃	semidirect
284. #332	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#494×D₇₃	2
#474×D₇₃	2
#436×D₇₃	2
#22609421	2
#22609420	2
#22609419	2
#22609418	2
#22609417	2
#334×D₇₃	2
#332×D₇₃	2
C₇₃×#1689	2
C₂×#1689	73

Subgroups — #1689×D73 #33068487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1689×D₇₃ #33068487