Subgroups — #33056035

Order 18688.

692 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619992	C₂	1	1	yes	maximal, characteristic
2	C₈×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618644	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608776	C₂	1	2	yes	maximal, complemented
5	#22608762	C₂	1	2	yes	maximal, complemented
6	#22608756	C₂	1	2	yes	maximal, complemented
7	#22608745	C₂	1	2	yes	maximal, complemented
8	#22608720	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608371	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608349	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556597	—	2	1	no	—
13	#17989137	C₂²	1	1	yes	characteristic
14	C₄×#11924028	C₂²	1	1	yes	characteristic
15	#17988912	C₄	1	2	yes	—
16	#17988883	C₄	1	1	yes	characteristic
17	#17988878	C₄	1	1	yes	characteristic
18	#17988788	C₄	1	1	yes	characteristic
19	#17988783	C₄	1	1	yes	characteristic
20	#17988734	C₄	1	2	yes	—
21	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
22	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
23	C₄×#11924017	C₂²	1	2	yes	—
24	C₄×D₅₈₄	C₂²	1	2	yes	—
25	#17988666	—	2	1	no	—
26	#17988666	C₂²	1	2	yes	—
27	C₈×D₂₉₂	—	2	1	no	—
28	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
29	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
30	C₈×D₂₉₂	C₂²	1	2	yes	—
31	C₈×C₂²⋊D₇₃	—	2	1	no	—
32	C₈×C₂²⋊D₇₃	—	2	1	no	—
33	#17988640	C₂²	1	1	yes	characteristic
34	#17988638	—	2	1	no	—
35	#17988611	C₂²	1	1	yes	characteristic
36	#17988553	—	2	1	no	—
37	C₄×C₈×D₇₃	—	2	1	no	—
38	#17988340	C₂²	1	2	yes	—
39	#17988338	C₂²	1	2	yes	—
40	#17988319	C₂²	1	2	yes	—
41	#17988316	C₂²	1	2	yes	—
42	#17988316	C₂²	1	2	yes	—
43	#17988316	C₂²	1	2	yes	—
44	#431×C₇₃	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	#322×C₇₃	C₂²	1	2	yes	—
48	#322×C₇₃	C₂²	1	2	yes	—
49	C₂×#11924028	—	2	1	no	—
50	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
51	C₂×#11924017	C₂×C₄	1	2	yes	—
52	C₂×D₅₈₄	C₂×C₄	1	2	yes	—
53	#14556597	—	4	4	no	—
54	C₂×#11924012	—	2	1	no	—
55	C₂×#11924011	—	2	2	no	—
56	C₂×C₈×D₇₃	—	2	1	no	—
57	C₂×C₈×D₇₃	—	2	1	no	—
58	C₂×C₈×D₇₃	—	2	2	no	—
59	#14556591	C₂×C₄	1	1	yes	characteristic
60	#14556588	C₂×C₄	1	1	yes	characteristic
61	#14556579	—	2	1	no	—
62	#14556565	—	2	1	no	—
63	#14556565	C₂×C₄	1	2	yes	—
64	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
65	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
66	C₄×D₂₉₂	—	2	1	no	—
67	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
68	C₄×D₂₉₂	C₂³	1	2	yes	—
69	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
70	C₄×C₂²⋊D₇₃	—	2	1	no	—
71	C₄×C₂²⋊D₇₃	—	2	1	no	—
72	#14556550	C₂×C₄	1	1	yes	characteristic
73	#14556548	—	2	1	no	—
74	C₄²×D₇₃	—	2	1	no	—
75	#14556525	C₂×C₄	1	2	yes	—
76	#14556523	C₂×C₄	1	2	yes	—
77	C₄⋊#10596831	—	2	1	no	—
78	C₄⋊#10596831	C₂³	1	2	yes	—
79	C₄⋊#10596831	C₂³	1	1	yes	characteristic
80	C₄⋊#10596831	C₂³	1	1	yes	characteristic
81	#14556520	—	2	1	no	—
82	#14556520	—	2	1	no	—
83	#14556516	C₂×C₄	1	2	yes	—
84	#14556513	C₂×C₄	1	2	yes	—
85	#14556513	C₂×C₄	1	2	yes	—
86	#14556513	C₂×C₄	1	2	yes	—
87	C₂²⋊#10596831	—	2	1	no	—
88	#14556503	—	2	1	no	—
89	#14556503	—	2	1	no	—
90	#14556503	—	2	2	no	—
91	#14556503	—	2	2	no	—
92	C₄×#10596831	—	2	1	no	—
93	C₈×Dic₇₃	—	2	1	no	—
94	C₈×Dic₇₃	—	2	1	no	—
95	C₂×M₁₆×C₇₃	—	2	1	no	—
96	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
102	#97×C₇₃	—	2	1	no	—
103	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₇₃	C₂³	1	2	yes	—
106	C₄×C₈×C₇₃	C₂³	1	2	yes	—
107	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
109	#11924028	—	2	2	no	—
110	#11924028	—	2	2	no	—
111	#11924028	—	4	2	no	—
112	#11924028	—	4	2	no	—
113	C₂×Dic₁₄₆	—	2	1	no	—
114	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
115	C₂×D₂₉₂	—	2	1	no	—
116	C₂×D₂₉₂	—	2	1	no	—
117	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
118	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊D₇₃	—	2	1	no	—
120	C₂×C₂²⋊D₇₃	—	2	2	no	—
121	C₂×C₄×D₇₃	—	2	1	no	—
122	C₂×C₄×D₇₃	—	2	1	no	—
123	C₂×C₄×D₇₃	—	2	1	no	—
124	C₂×C₄×D₇₃	—	2	2	no	—
125	#11924017	—	2	4	no	—
126	D₅₈₄	—	2	4	no	—
127	#11924012	—	4	2	no	—
128	#11924011	—	4	4	no	—
129	C₂×#10596831	—	2	1	no	—
130	C₂×#10596831	—	2	1	no	—
131	C₂×#10596831	—	2	2	no	—
132	C₈×D₇₃	—	4	2	no	—
133	C₈×D₇₃	—	4	4	no	—
134	C₈×D₇₃	—	4	2	no	—
135	C₄⋊Dic₇₃	—	2	1	no	—
136	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
138	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
139	#11924007	—	2	1	no	—
140	#11924007	—	2	1	no	—
141	C₂²⋊Dic₇₃	—	2	1	no	—
142	#11924005	—	2	1	no	—
143	#11924005	—	2	2	no	—
144	#11924005	—	2	1	no	—
145	#11924005	—	2	2	no	—
146	C₄×Dic₇₃	—	2	1	no	—
147	C₄×Dic₇₃	—	2	1	no	—
148	C₄×Dic₇₃	—	2	1	no	—
149	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
152	M₁₆×C₇₃	—	4	2	no	—
153	C₂×C₈×C₇₃	—	2	2	no	—
154	C₂×C₈×C₇₃	—	2	2	no	—
155	C₂×C₈×C₇₃	—	4	1	no	—
156	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₇₃	#41	1	1	yes	characteristic
165	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
166	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
167	C₂²×D₇₃	—	2	1	no	—
168	C₂²×D₇₃	—	2	2	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	1	no	—
172	C₂×C₄×C₇₃	—	2	1	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₇₃	—	2	4	no	—
181	C₂²⋊D₇₃	—	4	4	no	—
182	C₂×Dic₇₃	—	2	1	no	—
183	C₂×Dic₇₃	—	2	1	no	—
184	C₂×Dic₇₃	—	2	1	no	—
185	C₂×Dic₇₃	—	2	2	no	—
186	D₂₉₂	—	2	1	no	—
187	D₂₉₂	—	2	2	no	—
188	D₂₉₂	—	2	2	no	—
189	D₂₉₂	—	4	2	no	—
190	D₂₉₂	—	4	2	no	—
191	D₂₉₂	#131	1	2	yes	complemented
192	C₄×D₇₃	—	2	4	no	—
193	C₄×D₇₃	—	4	2	no	—
194	C₄×D₇₃	—	4	1	no	—
195	C₄×D₇₃	—	4	1	no	—
196	C₄×D₇₃	—	4	2	no	—
197	C₄×D₇₃	—	4	2	no	—
198	Dic₁₄₆	—	2	1	no	—
199	Dic₁₄₆	—	4	2	no	—
200	Dic₁₄₆	#131	1	2	yes	complemented
201	C₈×C₇₃	—	2	2	no	—
202	C₈×C₇₃	—	2	2	no	—
203	C₈×C₇₃	—	2	1	no	—
204	C₈×C₇₃	—	2	1	no	—
205	C₈×C₇₃	—	2	1	no	—
206	C₈×C₇₃	—	4	2	no	—
207	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
208	#10596831	—	4	1	no	—
209	#10596831	—	4	2	no	—
210	#10596831	—	4	1	no	—
211	C₂²×C₇₃	—	2	1	no	—
212	C₂²×C₇₃	—	2	1	no	—
213	C₂²×C₇₃	—	2	1	no	—
214	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
215	C₂×D₇₃	—	2	2	no	—
216	C₂×D₇₃	—	4	1	no	—
217	C₂×D₇₃	—	4	1	no	—
218	C₂×D₇₃	—	4	2	no	—
219	C₂×D₇₃	—	4	2	no	—
220	C₂×D₇₃	—	4	2	no	—
221	C₄×C₇₃	—	2	1	no	—
222	C₄×C₇₃	—	2	1	no	—
223	C₄×C₇₃	—	2	1	no	—
224	C₄×C₇₃	#444	1	2	yes	—
225	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
226	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
227	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₄×C₇₃	#575	1	1	yes	characteristic
229	Dic₇₃	—	2	2	no	—
230	Dic₇₃	—	4	2	no	—
231	Dic₇₃	—	4	1	no	—
232	Dic₇₃	—	4	1	no	—
233	#17917	—	73	1	no	maximal, Sylow
234	C₂×C₇₃	—	4	1	no	—
235	C₂×C₇₃	#2929	1	1	yes	characteristic
236	C₂×C₇₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂×C₇₃	C₂×#444	1	1	yes	characteristic
238	D₇₃	—	4	2	no	—
239	D₇₃	—	8	2	no	—
240	#3106	—	73	1	no	—
241	C₈×#41	—	73	1	no	—
242	#2931	—	73	1	no	—
243	#1583	—	73	2	no	—
244	#1581	—	73	2	no	—
245	#1580	—	73	2	no	—
246	SD₁₆⋊C₈	—	73	2	no	—
247	#1574	—	73	1	no	—
248	#1489	—	73	1	no	—
249	#1484	—	73	1	no	—
250	#1451	D₇₃	1	1	yes	characteristic, complemented
251	C₇₃	#17917	1	1	yes	characteristic, complemented, Sylow
252	C₂×#131	—	146	1	no	—
253	#532	—	73	1	no	—
254	C₄×#41	—	73	1	no	—
255	#482	—	73	2	no	—
256	#477	—	73	1	no	—
257	#476	—	73	1	no	—
258	#460	—	73	1	no	—
259	#459	—	73	1	no	—
260	#449	—	73	2	no	—
261	C₈×Q₈	—	73	1	no	—
262	C₈×Q₈	—	73	1	no	—
263	C₄×SD₁₆	—	73	2	no	—
264	C₄×D₈	—	73	2	no	—
265	#436	—	73	2	no	—
266	#436	—	146	1	no	—
267	C₈×D₄	—	73	2	no	—
268	C₈×D₄	—	73	1	no	—
269	C₈×D₄	—	73	1	no	—
270	C₈×D₄	—	146	1	no	—
271	C₈×D₄	—	146	1	no	—
272	C₈×D₄	—	146	1	no	—
273	#431	—	73	1	no	—
274	#431	—	146	1	no	—
275	#431	C₂×D₇₃	1	1	yes	characteristic
276	#423	—	73	1	no	—
277	#408	—	146	1	no	—
278	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
279	C₂×C₄×C₈	—	146	1	no	—
280	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
281	#335	—	73	2	no	—
282	#334	—	73	2	no	—
283	Q₈⋊C₈	—	73	2	no	—
284	D₄⋊C₈	—	73	2	no	—
285	D₄⋊C₈	—	73	2	no	—
286	D₄⋊C₈	—	73	2	no	—
287	#322	C₂×D₇₃	1	2	yes	—
288	#322	C₂×D₇₃	1	2	yes	—
289	C₂×#41	—	73	1	no	—
290	C₂×#41	—	146	1	no	—
291	C₂×SD₁₆	—	73	2	no	—
292	C₂×D₈	—	73	2	no	—
293	#131	—	292	4	no	—
294	C₂×M₁₆	—	2	1	no	—
295	C₂×M₁₆	—	146	1	no	—
296	C₂×M₁₆	—	146	2	no	—
297	C₂²×C₈	—	146	2	no	—
298	C₂²×C₈	—	146	1	no	—
299	C₂²×C₈	—	146	1	no	—
300	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
301	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
302	C₄⋊Q₈	—	73	1	no	—
303	#127	—	73	1	no	—
304	#124	—	146	1	no	—
305	#121	—	73	2	no	—
306	#121	—	146	1	no	—
307	C₄×Q₈	—	73	1	no	—
308	C₄×Q₈	—	73	1	no	—
309	C₄×D₄	—	73	1	no	—
310	C₄×D₄	—	73	1	no	—
311	C₄×D₄	—	73	2	no	—
312	C₄×D₄	—	146	1	no	—
313	C₄×D₄	—	146	1	no	—
314	C₄×D₄	—	146	1	no	—
315	#117	—	73	1	no	—
316	#117	—	146	1	no	—
317	C₂×C₄²	—	146	1	no	—
318	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
319	#107	—	73	2	no	—
320	#106	—	73	2	no	—
321	C₄⋊C₈	—	73	1	no	—
322	C₄⋊C₈	—	73	1	no	—
323	C₄⋊C₈	—	73	2	no	—
324	C₄⋊C₈	—	146	1	no	—
325	C₄⋊C₈	—	146	1	no	—
326	C₄⋊C₈	—	146	1	no	—
327	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
328	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
329	#103	—	73	2	no	—
330	#102	—	73	2	no	—
331	#102	—	73	2	no	—
332	#102	—	73	2	no	—
333	C₂²⋊C₈	—	146	1	no	—
334	C₂²⋊C₈	—	146	2	no	—
335	C₂²⋊C₈	—	146	2	no	—
336	C₂²⋊C₈	—	146	1	no	—
337	C₂²⋊C₈	—	146	1	no	—
338	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
339	#97	—	2	1	no	—
340	C₄×C₈	—	146	1	no	—
341	C₄×C₈	—	146	1	no	—
342	C₄×C₈	—	146	1	no	—
343	C₄×C₈	D₂₉₂	1	1	yes	characteristic
344	C₄×C₈	D₂₉₂	1	1	yes	characteristic
345	C₄×C₈	C₂²×D₇₃	1	2	yes	—
346	C₄×C₈	C₂²×D₇₃	1	2	yes	—
347	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
349	#41	—	292	2	no	—
350	#41	—	292	2	no	—
351	#41	—	146	2	no	—
352	#41	—	146	2	no	—
353	C₂×Q₈	—	73	1	no	—
354	C₂×Q₈	—	146	1	no	—
355	C₂×D₄	—	73	1	no	—
356	C₂×D₄	—	73	2	no	—
357	C₂×D₄	—	146	2	no	—
358	C₂×D₄	—	146	1	no	—
359	C₂×D₄	—	146	1	no	—
360	C₂×D₄	—	146	1	no	—
361	C₂²×C₄	—	146	1	no	—
362	C₂²×C₄	—	146	1	no	—
363	C₂²×C₄	—	146	2	no	—
364	C₂²×C₄	—	146	1	no	—
365	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
367	C₂²×C₄	#11924028	1	1	yes	characteristic
368	SD₁₆	—	146	4	no	—
369	D₈	—	146	4	no	—
370	M₁₆	—	4	2	no	—
371	M₁₆	—	292	2	no	—
372	M₁₆	—	292	4	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	1	no	—
376	C₂×C₈	—	292	2	no	—
377	C₂×C₈	—	292	4	no	—
378	C₂×C₈	—	292	2	no	—
379	C₂×C₈	—	146	1	no	—
380	C₂×C₈	—	146	1	no	—
381	C₂×C₈	—	146	2	no	—
382	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
383	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
384	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
385	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
386	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
387	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
388	C₄⋊C₄	—	73	1	no	—
389	C₄⋊C₄	—	73	1	no	—
390	C₄⋊C₄	—	73	2	no	—
391	C₄⋊C₄	—	146	1	no	—
392	C₄⋊C₄	—	146	1	no	—
393	C₄⋊C₄	—	146	1	no	—
394	C₂²⋊C₄	—	146	1	no	—
395	C₂²⋊C₄	—	146	1	no	—
396	C₂²⋊C₄	—	146	2	no	—
397	C₂²⋊C₄	—	146	1	no	—
398	C₂²⋊C₄	—	146	2	no	—
399	C₄²	—	146	1	no	—
400	C₄²	—	146	1	no	—
401	C₄²	—	146	1	no	—
402	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
403	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
404	C₄²	#11924028	1	1	yes	characteristic
405	C₄²	C₂³×D₇₃	1	1	yes	characteristic
406	C₂³	—	146	2	no	—
407	C₂³	—	146	1	no	—
408	C₂³	C₄×D₂₉₂	1	1	yes	characteristic
409	Q₈	—	292	2	no	—
410	Q₈	—	73	2	no	—
411	Q₈	—	146	1	no	—
412	D₄	—	292	2	no	—
413	D₄	—	292	4	no	—
414	D₄	—	292	2	no	—
415	D₄	—	73	2	no	—
416	D₄	—	146	4	no	—
417	D₄	—	146	2	no	—
418	D₄	—	146	2	no	—
419	D₄	—	146	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	292	2	no	—
426	C₂×C₄	—	292	1	no	—
427	C₂×C₄	—	292	1	no	—
428	C₂×C₄	—	292	2	no	—
429	C₂×C₄	—	292	2	no	—
430	C₂×C₄	—	146	4	no	—
431	C₂×C₄	—	146	1	no	—
432	C₂×C₄	—	146	1	no	—
433	C₂×C₄	—	146	2	no	—
434	C₂×C₄	—	146	1	no	—
435	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
436	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
437	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
438	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
439	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
440	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
441	C₈	—	2	1	no	—
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	2	2	no	—
445	C₈	—	2	2	no	—
446	C₈	—	4	2	no	—
447	C₈	—	292	2	no	—
448	C₈	—	292	1	no	—
449	C₈	—	292	1	no	—
450	C₈	#14556619	1	2	yes	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	292	1	no	—
455	C₂²	—	292	1	no	—
456	C₂²	—	292	2	no	—
457	C₂²	—	292	2	no	—
458	C₂²	—	292	2	no	—
459	C₂²	—	146	2	no	—
460	C₂²	C₂×C₄×D₂₉₂	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	292	2	no	—
465	C₄	—	292	1	no	—
466	C₄	—	292	1	no	—
467	C₄	—	146	2	no	—
468	C₄	#17988710	1	2	yes	—
469	C₄	#131×D₇₃	1	1	yes	characteristic
470	C₄	#131×D₇₃	1	1	yes	characteristic
471	C₄	C₂×#14556619	1	1	yes	characteristic
472	C₄	#17989387	1	1	yes	characteristic
473	C₂	—	4	1	no	—
474	C₂	—	292	2	no	—
475	C₂	—	584	2	no	—
476	C₂	#22618627	1	1	yes	characteristic
477	C₂	C₄×#14556619	1	1	yes	characteristic
478	C₂	C₂×#17988710	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1451	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#22619992	C₂
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1451	D₇₃
hypocenter	C₇₃	#17917
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1451

Complements

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

N	H ≅ G/N	type
2. C₈×#11924028	C₂	semidirect
3. #22618644	C₂	semidirect
4. #22608776	C₂	semidirect
5. #22608762	C₂	semidirect
6. #22608756	C₂	semidirect
7. #22608745	C₂	semidirect
8. #22608720	C₂	semidirect
9. #22608371	C₂	semidirect
10. #22608349	C₂	semidirect
11. C₇₃×#1451	C₂	semidirect
191. D₂₉₂	#131	semidirect
200. Dic₁₄₆	#131	semidirect
250. #1451	D₇₃	semidirect
251. C₇₃	#17917	semidirect

Maximal subgroups

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

subgroup	index
#22619992	2
C₈×#11924028	2
#22618644	2
#22608776	2
#22608762	2
#22608756	2
#22608745	2
#22608720	2
#22608371	2
#22608349	2
C₇₃×#1451	2
#17917	73