Subgroups — #33056884

Order 18688.

680 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619940	C₂	1	1	yes	maximal, characteristic
2	#22618878	C₂	1	1	yes	maximal, characteristic, complemented
3	M₁₆×D₂₉₂	C₂	1	1	yes	maximal, characteristic
4	#22608823	C₂	1	2	yes	maximal, complemented
5	#22608776	C₂	1	2	yes	maximal, complemented
6	#22608769	C₂	1	2	yes	maximal, complemented
7	C₈×#11924017	C₂	1	2	yes	maximal, complemented
8	#22608702	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608387	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#17988316	C₂	1	1	yes	maximal, characteristic
11	C₈×M₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₃	—	2	1	no	—
13	#17989144	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
15	#17988918	C₄	1	2	yes	—
16	#17988878	C₄	1	1	yes	characteristic
17	#17988878	C₄	1	1	yes	characteristic
18	#17988793	C₄	1	1	yes	characteristic
19	#17988793	C₄	1	1	yes	characteristic
20	#17988740	C₄	1	2	yes	—
21	#17988717	C₂²	1	2	yes	complemented
22	#17988715	—	2	2	no	—
23	C₈×Dic₁₄₆	C₂²	1	2	yes	complemented
24	C₄×#11924017	C₂²	1	2	yes	—
25	C₄×#11924017	C₂²	1	2	yes	—
26	#17988666	C₂²	1	2	yes	—
27	#17988660	—	2	2	no	—
28	C₈×D₂₉₂	C₂²	1	2	yes	—
29	#17988615	—	2	1	no	—
30	#17988611	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
32	#17988550	—	2	1	no	—
33	#17988545	—	2	1	no	—
34	#17988338	C₂²	1	2	yes	complemented
35	#17988338	C₂²	1	2	yes	complemented
36	#17988319	C₂²	1	2	yes	complemented
37	#17988319	C₂²	1	2	yes	complemented
38	#17988316	C₂²	1	1	yes	characteristic
39	#17988316	C₂²	1	1	yes	characteristic
40	#17988316	C₂²	1	1	yes	characteristic
41	#17988316	C₂²	1	1	yes	characteristic
42	#431×C₇₃	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
45	#322×C₇₃	C₂²	1	2	yes	complemented
46	C₈²×C₇₃	C₂²	1	2	yes	complemented
47	C₂²×D₂₉₂	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₇₃	—	2	1	no	—
49	C₂×#11924017	C₂×C₄	1	2	yes	—
50	C₂×#11924017	C₂×C₄	1	2	yes	—
51	C₂×#11924012	—	2	1	no	—
52	C₂×#11924011	—	2	2	no	—
53	M₁₆×D₇₃	—	4	4	no	—
54	C₂²×#10596831	—	2	1	no	—
55	C₂×C₈×D₇₃	—	2	2	no	—
56	#14556591	C₂×C₄	1	1	yes	characteristic
57	#14556591	C₂×C₄	1	1	yes	characteristic
58	#14556583	—	2	1	no	—
59	#14556570	—	2	1	no	—
60	#14556570	C₂×C₄	1	2	yes	—
61	C₄×Dic₁₄₆	—	2	1	no	—
62	C₄×Dic₁₄₆	C₂³	1	2	yes	—
63	C₄×D₂₉₂	—	2	1	no	—
64	C₄×D₂₉₂	—	2	1	no	—
65	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
66	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
67	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
68	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
69	#14556550	—	2	1	no	—
70	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×#11924005	—	2	1	no	—
72	#14556523	C₂×C₄	1	2	yes	—
73	#14556523	C₂×C₄	1	2	yes	—
74	C₄⋊#10596831	—	2	1	no	—
75	C₄⋊#10596831	—	2	1	no	—
76	C₄⋊#10596831	C₂³	1	1	yes	characteristic
77	C₄⋊#10596831	C₂³	1	1	yes	characteristic
78	C₄⋊#10596831	C₂³	1	2	yes	—
79	#14556520	—	2	2	no	—
80	#14556520	—	2	2	no	—
81	#14556516	C₂×C₄	1	2	yes	—
82	#14556516	C₂×C₄	1	2	yes	—
83	#14556513	C₂×C₄	1	2	yes	—
84	#14556513	C₂×C₄	1	2	yes	—
85	#14556503	—	2	2	no	—
86	#14556503	—	2	2	no	—
87	#14556501	—	2	2	no	—
88	C₈×Dic₇₃	—	2	2	no	—
89	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
90	C₂×M₁₆×C₇₃	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₇₃	—	2	1	no	—
92	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
94	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
96	#97×C₇₃	D₄	1	2	yes	—
97	C₄×C₈×C₇₃	—	2	1	no	—
98	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₇₃	C₂³	1	2	yes	—
101	C₄×C₈×C₇₃	C₂³	1	2	yes	—
102	C₂³×D₇₃	—	2	1	no	—
103	C₂×Dic₁₄₆	—	2	1	no	—
104	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
105	C₂×D₂₉₂	—	2	2	no	—
106	C₂×D₂₉₂	—	2	1	no	—
107	C₂×D₂₉₂	—	4	1	no	—
108	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
110	C₂²×Dic₇₃	—	2	1	no	—
111	C₂×C₄×D₇₃	—	2	1	no	—
112	C₂×C₄×D₇₃	—	2	1	no	—
113	C₂×C₄×D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	4	2	no	—
116	C₂×C₄×D₇₃	—	4	2	no	—
117	#11924017	—	2	4	no	—
118	#11924017	—	4	2	no	—
119	#11924012	—	4	2	no	—
120	#11924011	—	4	4	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	1	no	—
123	C₂×#10596831	—	2	2	no	—
124	C₂×#10596831	—	4	2	no	—
125	C₈×D₇₃	—	4	4	no	—
126	C₄⋊Dic₇₃	—	2	1	no	—
127	C₄⋊Dic₇₃	—	2	1	no	—
128	C₄⋊Dic₇₃	—	2	1	no	—
129	C₄⋊Dic₇₃	—	2	1	no	—
130	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
131	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
133	#11924007	—	2	2	no	—
134	#11924007	—	2	2	no	—
135	C₂²⋊Dic₇₃	—	2	2	no	—
136	#11924005	—	2	1	no	—
137	#11924005	—	2	1	no	—
138	#11924005	—	2	1	no	—
139	#11924005	—	2	1	no	—
140	C₄×Dic₇₃	—	2	2	no	—
141	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
144	M₁₆×C₇₃	—	2	2	no	—
145	M₁₆×C₇₃	SD₁₆	1	4	yes	complemented
146	C₂×C₈×C₇₃	—	2	1	no	—
147	C₂×C₈×C₇₃	—	2	1	no	—
148	C₂×C₈×C₇₃	—	4	2	no	—
149	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
151	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
153	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₇₃	#41	1	1	yes	characteristic
156	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
157	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
158	C₂²×D₇₃	—	2	1	no	—
159	C₂²×D₇₃	—	2	1	no	—
160	C₂²×D₇₃	—	4	2	no	—
161	C₂²×D₇₃	—	4	2	no	—
162	C₂²×D₇₃	—	8	1	no	—
163	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	4	1	no	—
166	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₇₃	#135	1	2	yes	—
171	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
174	C₂×Dic₇₃	—	2	2	no	—
175	C₂×Dic₇₃	—	2	2	no	—
176	C₂×Dic₇₃	—	2	1	no	—
177	C₂×Dic₇₃	—	2	1	no	—
178	C₂×Dic₇₃	—	4	2	no	—
179	D₂₉₂	—	2	1	no	—
180	D₂₉₂	—	2	1	no	—
181	D₂₉₂	—	2	1	no	—
182	D₂₉₂	—	4	2	no	—
183	D₂₉₂	#131	1	2	yes	—
184	C₄×D₇₃	—	4	1	no	—
185	C₄×D₇₃	—	4	1	no	—
186	C₄×D₇₃	—	4	1	no	—
187	C₄×D₇₃	—	4	1	no	—
188	C₄×D₇₃	—	4	2	no	—
189	C₄×D₇₃	—	4	2	no	—
190	Dic₁₄₆	—	2	2	no	—
191	Dic₁₄₆	—	2	2	no	—
192	Dic₁₄₆	—	8	1	no	—
193	C₈×C₇₃	—	2	2	no	—
194	C₈×C₇₃	—	2	2	no	—
195	C₈×C₇₃	—	2	2	no	—
196	C₈×C₇₃	—	2	2	no	—
197	C₈×C₇₃	—	4	1	no	—
198	C₈×C₇₃	C₂×SD₁₆	1	4	yes	—
199	#10596831	—	4	2	no	—
200	#10596831	—	4	1	no	—
201	#10596831	—	4	1	no	—
202	C₂²×C₇₃	—	2	1	no	—
203	C₂²×C₇₃	—	2	1	no	—
204	C₂²×C₇₃	C₄×SD₁₆	1	2	yes	—
205	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂×D₇₃	—	2	2	no	—
207	C₂×D₇₃	—	4	1	no	—
208	C₂×D₇₃	—	4	1	no	—
209	C₂×D₇₃	—	4	1	no	—
210	C₂×D₇₃	—	4	1	no	—
211	C₂×D₇₃	—	4	1	no	—
212	C₂×D₇₃	—	8	4	no	—
213	C₄×C₇₃	—	2	1	no	—
214	C₄×C₇₃	—	2	1	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	C₄×SD₁₆	1	2	yes	—
217	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
218	C₄×C₇₃	#568	1	1	yes	characteristic
219	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
220	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
221	Dic₇₃	—	4	2	no	—
222	Dic₇₃	—	4	1	no	—
223	Dic₇₃	—	4	1	no	—
224	Dic₇₃	—	4	2	no	—
225	#17995	—	73	1	no	maximal, Sylow
226	C₂×C₇₃	—	2	2	no	—
227	C₂×C₇₃	#2933	1	1	yes	characteristic
228	C₂×C₇₃	C₂×C₄×SD₁₆	1	1	yes	characteristic
229	C₂×C₇₃	#2956	1	1	yes	characteristic
230	D₇₃	—	4	2	no	—
231	D₇₃	—	8	1	no	—
232	#3101	—	73	1	no	—
233	#2962	—	73	1	no	—
234	D₄×M₁₆	—	73	1	no	—
235	#1590	—	73	2	no	—
236	#1583	—	73	2	no	—
237	#1582	—	73	2	no	—
238	C₈×SD₁₆	—	73	2	no	—
239	#1570	—	73	1	no	—
240	#1493	—	73	1	no	—
241	C₂×D₄⋊C₈	—	73	1	no	—
242	C₈×M₁₆	D₇₃	1	1	yes	characteristic, complemented
243	C₇₃	#17995	1	1	yes	characteristic, complemented, Sylow
244	C₂²×M₁₆	—	146	1	no	—
245	#533	—	73	1	no	—
246	C₂×C₄×D₄	—	73	1	no	—
247	#483	—	73	2	no	—
248	#476	—	73	1	no	—
249	#476	—	73	1	no	—
250	#461	—	73	1	no	—
251	#461	—	73	1	no	—
252	#450	—	73	2	no	—
253	#446	—	73	2	no	—
254	#446	—	146	2	no	—
255	C₈×Q₈	—	73	2	no	—
256	C₄×SD₁₆	—	73	2	no	—
257	C₄×SD₁₆	—	73	2	no	—
258	#436	—	73	2	no	—
259	#435	—	146	2	no	—
260	C₈×D₄	—	73	2	no	—
261	#431	C₂×D₇₃	1	1	yes	characteristic
262	#424	—	146	1	no	—
263	#423	—	73	1	no	—
264	C₂×C₄⋊C₈	—	73	1	no	—
265	#407	—	146	1	no	—
266	#405	—	146	1	no	—
267	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
269	#334	—	73	2	no	—
270	#334	—	73	2	no	—
271	Q₈⋊C₈	—	73	2	no	—
272	Q₈⋊C₈	—	73	2	no	—
273	D₄⋊C₈	—	73	1	no	—
274	D₄⋊C₈	—	73	1	no	—
275	D₄⋊C₈	—	73	1	no	—
276	D₄⋊C₈	—	73	1	no	—
277	#322	C₂×D₇₃	1	2	yes	complemented
278	C₈²	C₂×D₇₃	1	2	yes	complemented
279	C₂²×D₄	—	73	1	no	—
280	C₂³×C₄	—	146	1	no	—
281	C₂×SD₁₆	—	73	2	no	—
282	C₂×SD₁₆	—	73	2	no	—
283	C₂×M₁₆	—	292	4	no	—
284	C₂×M₁₆	—	146	1	no	—
285	C₂×M₁₆	—	146	2	no	—
286	C₂×M₁₆	D₂₉₂	1	1	yes	characteristic
287	C₂×M₁₆	D₂₉₂	1	1	yes	characteristic
288	C₂²×C₈	—	2	1	no	—
289	C₂²×C₈	—	146	1	no	—
290	C₂²×C₈	—	146	2	no	—
291	C₄⋊Q₈	—	73	1	no	—
292	C₄⋊Q₈	—	73	1	no	—
293	#125	—	146	1	no	—
294	C₂²⋊Q₈	—	73	2	no	—
295	C₂²⋊Q₈	—	146	1	no	—
296	C₄×Q₈	—	73	2	no	—
297	C₄×Q₈	—	146	1	no	—
298	C₄×D₄	—	73	1	no	—
299	C₄×D₄	—	73	1	no	—
300	C₄×D₄	—	73	1	no	—
301	C₄×D₄	—	73	1	no	—
302	C₄×D₄	—	146	1	no	—
303	C₄×D₄	—	146	1	no	—
304	#117	—	146	1	no	—
305	C₂×C₄⋊C₄	—	73	1	no	—
306	C₂×C₂²⋊C₄	—	146	1	no	—
307	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
308	#106	—	73	2	no	—
309	#106	—	73	2	no	—
310	C₄⋊C₈	—	73	1	no	—
311	C₄⋊C₈	—	73	1	no	—
312	C₄⋊C₈	—	73	2	no	—
313	C₄⋊C₈	—	146	2	no	—
314	C₄⋊C₈	—	146	2	no	—
315	C₄⋊C₈	—	146	1	no	—
316	C₄⋊C₈	—	146	1	no	—
317	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
318	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
319	#103	—	73	2	no	—
320	#103	—	73	2	no	—
321	#102	—	73	2	no	—
322	#102	—	73	2	no	—
323	C₂²⋊C₈	—	146	2	no	—
324	C₂²⋊C₈	—	146	2	no	—
325	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
326	#97	—	146	2	no	—
327	#97	D₂₉₂	1	2	yes	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	—	146	2	no	—
330	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
332	C₄×C₈	C₂²×D₇₃	1	2	yes	—
333	C₄×C₈	C₂²×D₇₃	1	2	yes	—
334	C₂⁴	—	146	1	no	—
335	C₂×Q₈	—	73	2	no	—
336	C₂×Q₈	—	146	1	no	—
337	C₂×D₄	—	292	1	no	—
338	C₂×D₄	—	73	1	no	—
339	C₂×D₄	—	73	1	no	—
340	C₂×D₄	—	146	2	no	—
341	C₂×D₄	—	146	1	no	—
342	C₂²×C₄	—	292	2	no	—
343	C₂²×C₄	—	292	2	no	—
344	C₂²×C₄	—	146	1	no	—
345	C₂²×C₄	—	146	1	no	—
346	C₂²×C₄	—	146	1	no	—
347	C₂²×C₄	—	146	1	no	—
348	C₂²×C₄	—	146	1	no	—
349	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
351	C₂²×C₄	#11924028	1	1	yes	characteristic
352	SD₁₆	—	292	2	no	—
353	SD₁₆	—	146	4	no	—
354	M₁₆	—	2	2	no	—
355	M₁₆	—	292	2	no	—
356	M₁₆	—	292	4	no	—
357	M₁₆	#11924017	1	4	yes	complemented
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	4	2	no	—
361	C₂×C₈	—	292	2	no	—
362	C₂×C₈	—	292	4	no	—
363	C₂×C₈	—	146	1	no	—
364	C₂×C₈	—	146	1	no	—
365	C₂×C₈	—	146	2	no	—
366	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
367	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
368	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
369	C₂×C₈	C₂×D₂₉₂	1	2	yes	—
370	C₄⋊C₄	—	73	2	no	—
371	C₄⋊C₄	—	73	1	no	—
372	C₄⋊C₄	—	73	1	no	—
373	C₄⋊C₄	—	146	2	no	—
374	C₄⋊C₄	—	146	1	no	—
375	C₄⋊C₄	—	146	1	no	—
376	C₄⋊C₄	—	146	1	no	—
377	C₄⋊C₄	—	146	1	no	—
378	C₄⋊C₄	—	146	2	no	—
379	C₂²⋊C₄	—	146	2	no	—
380	C₂²⋊C₄	—	146	1	no	—
381	C₂²⋊C₄	—	146	1	no	—
382	C₂²⋊C₄	—	146	1	no	—
383	C₂²⋊C₄	—	146	1	no	—
384	C₄²	—	146	2	no	—
385	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
386	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
387	C₄²	#11924028	1	1	yes	characteristic
388	C₄²	C₂³×D₇₃	1	1	yes	characteristic
389	C₂³	—	292	2	no	—
390	C₂³	—	292	2	no	—
391	C₂³	—	584	1	no	—
392	C₂³	—	146	1	no	—
393	C₂³	—	146	1	no	—
394	C₂³	C₄×D₂₉₂	1	1	yes	characteristic
395	Q₈	—	584	1	no	—
396	Q₈	—	146	2	no	—
397	Q₈	—	146	2	no	—
398	D₄	—	292	2	no	—
399	D₄	—	73	2	no	—
400	D₄	—	146	1	no	—
401	D₄	—	146	1	no	—
402	D₄	—	146	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	292	2	no	—
407	C₂×C₄	—	292	2	no	—
408	C₂×C₄	—	292	2	no	—
409	C₂×C₄	—	292	1	no	—
410	C₂×C₄	—	292	1	no	—
411	C₂×C₄	—	292	1	no	—
412	C₂×C₄	—	292	1	no	—
413	C₂×C₄	—	146	2	no	—
414	C₂×C₄	—	146	2	no	—
415	C₂×C₄	—	146	1	no	—
416	C₂×C₄	—	146	1	no	—
417	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
418	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
419	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
420	C₂×C₄	C₂×#11924017	1	2	yes	—
421	C₂×C₄	#14556613	1	2	yes	—
422	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
424	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	—	4	1	no	—
430	C₈	—	292	2	no	—
431	C₈	—	292	1	no	—
432	C₈	—	292	1	no	—
433	C₈	C₂×#11924017	1	4	yes	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	292	1	no	—
437	C₂²	—	292	1	no	—
438	C₂²	—	292	1	no	—
439	C₂²	—	292	1	no	—
440	C₂²	—	292	1	no	—
441	C₂²	—	584	4	no	—
442	C₂²	—	146	2	no	—
443	C₂²	C₄×#11924017	1	2	yes	—
444	C₂²	C₂×C₄×D₂₉₂	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	292	2	no	—
449	C₄	—	292	1	no	—
450	C₄	—	292	1	no	—
451	C₄	—	292	2	no	—
452	C₄	C₄×#11924017	1	2	yes	—
453	C₄	#131×D₇₃	1	1	yes	characteristic
454	C₄	#17989352	1	1	yes	characteristic
455	C₄	C₂²×#11924017	1	1	yes	characteristic
456	C₄	C₂×#14556613	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	292	2	no	—
459	C₂	—	584	1	no	—
460	C₂	#22618659	1	1	yes	characteristic
461	C₂	C₂×C₄×#11924017	1	1	yes	characteristic
462	C₂	#22618842	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₈×M₁₆×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂²×D₂₉₂	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	C₈×M₁₆	D₇₃
hypocenter	C₇₃	#17995
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
2. #22618878	C₂	semidirect
4. #22608823	C₂	semidirect
5. #22608776	C₂	semidirect
6. #22608769	C₂	semidirect
7. C₈×#11924017	C₂	semidirect
8. #22608702	C₂	semidirect
9. #22608387	C₂	semidirect
11. C₈×M₁₆×C₇₃	C₂	semidirect
21. #17988717	C₂²	semidirect
23. C₈×Dic₁₄₆	C₂²	semidirect
34. #17988338	C₂²	semidirect
35. #17988338	C₂²	semidirect
36. #17988319	C₂²	semidirect
37. #17988319	C₂²	semidirect
45. #322×C₇₃	C₂²	semidirect
46. C₈²×C₇₃	C₂²	semidirect
145. M₁₆×C₇₃	SD₁₆	semidirect
242. C₈×M₁₆	D₇₃	semidirect
243. C₇₃	#17995	semidirect
277. #322	C₂×D₇₃	semidirect
278. C₈²	C₂×D₇₃	semidirect
357. M₁₆	#11924017	semidirect

Maximal subgroups

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

subgroup	index
#22619940	2
#22618878	2
M₁₆×D₂₉₂	2
#22608823	2
#22608776	2
#22608769	2
C₈×#11924017	2
#22608702	2
#22608387	2
C₂×#17988316	2
C₈×M₁₆×C₇₃	2
#17995	73