Subgroups — #33073873

Order 18688.

836 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22621079	C₂	1	1	yes	maximal, characteristic, complemented
2	#22620846	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988960	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620324	C₂	1	1	yes	maximal, characteristic, complemented
5	#22620307	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609586	C₂	1	2	yes	maximal, complemented
7	#22609572	C₂	1	2	yes	maximal, complemented
8	#22609533	C₂	1	2	yes	maximal, complemented
9	#22609521	C₂	1	2	yes	maximal, complemented
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#11924017	—	2	2	no	—
13	C₂×#14556591	C₂²	1	1	yes	characteristic
14	C₂×#14556588	C₂²	1	1	yes	characteristic
15	#17988990	C₂²	1	2	yes	complemented
16	#17988963	C₂²	1	2	yes	—
17	#17988960	—	2	2	no	—
18	#17988960	C₂²	1	2	yes	—
19	#17988960	C₂²	1	2	yes	—
20	#17988953	—	2	2	no	—
21	#17988946	—	2	2	no	—
22	#17988937	C₂²	1	2	yes	complemented
23	#17988937	C₂²	1	2	yes	complemented
24	#17988935	C₂²	1	2	yes	—
25	#17988935	C₂²	1	2	yes	—
26	#17988935	C₂²	1	2	yes	—
27	#17988933	C₂²	1	2	yes	complemented
28	#17988920	—	2	2	no	—
29	#17988882	—	2	2	no	—
30	#17988782	—	2	2	no	—
31	#17988720	—	2	2	no	—
32	#17988640	C₂²	1	1	yes	characteristic
33	#17988591	—	2	2	no	—
34	#17988588	—	2	2	no	—
35	C₄×#11924012	C₂²	1	1	yes	characteristic
36	#17988309	C₂²	1	2	yes	complemented
37	C₈×#10596831	C₂²	1	2	yes	complemented
38	#533×C₇₃	C₂²	1	1	yes	characteristic
39	#532×C₇₃	C₂²	1	1	yes	characteristic
40	#498×C₇₃	C₂²	1	1	yes	characteristic, complemented
41	#492×C₇₃	C₂²	1	1	yes	characteristic, complemented
42	#487×C₇₃	C₂²	1	1	yes	characteristic, complemented
43	#486×C₇₃	C₂²	1	1	yes	characteristic, complemented
44	#465×C₇₃	—	2	2	no	—
45	C₄×SD₁₆×C₇₃	—	2	2	no	—
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂²×Dic₁₄₆	—	2	1	no	—
48	C₂²×D₂₉₂	—	2	1	no	—
49	C₂²×D₂₉₂	—	2	1	no	—
50	C₂²×D₂₉₂	—	2	1	no	—
51	C₂×#11924017	—	2	4	no	—
52	C₂×#11924017	—	2	4	no	—
53	C₂×#11924017	—	4	8	no	—
54	C₂×#11924013	—	2	4	no	—
55	C₂×#11924012	D₄	1	2	yes	—
56	#14556591	—	2	1	no	—
57	#14556591	—	2	1	no	—
58	#14556591	—	2	1	no	—
59	#14556591	C₂³	1	2	yes	—
60	#14556588	—	2	1	no	—
61	#14556588	—	2	1	no	—
62	#14556588	—	2	1	no	—
63	#14556588	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₇₃	—	2	1	no	—
65	C₂×C₄⋊Dic₇₃	—	2	1	no	—
66	#14556524	—	2	4	no	—
67	C₄⋊#10596831	D₄	1	2	yes	—
68	#14556515	—	2	4	no	—
69	#14556515	—	2	4	no	—
70	#14556512	—	2	4	no	—
71	#14556511	—	2	4	no	—
72	#14556511	—	2	4	no	—
73	#14556511	—	2	4	no	—
74	C₂²⋊#10596831	D₄	1	2	yes	—
75	#14556502	D₄	1	2	yes	—
76	C₄×#10596831	C₂³	1	2	yes	—
77	C₄×#10596831	C₂³	1	2	yes	—
78	C₂×#41×C₇₃	—	2	1	no	—
79	C₂×SD₁₆×C₇₃	—	2	2	no	—
80	C₂²×C₈×C₇₃	D₄	1	2	yes	—
81	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₇₃	C₂³	1	1	yes	characteristic
84	#127×C₇₃	C₂³	1	1	yes	characteristic
85	#125×C₇₃	—	2	1	no	—
86	#124×C₇₃	—	2	1	no	—
87	C₂²⋊Q₈×C₇₃	—	2	1	no	—
88	C₂²⋊Q₈×C₇₃	—	2	1	no	—
89	#121×C₇₃	—	2	1	no	—
90	#121×C₇₃	—	2	1	no	—
91	C₄×Q₈×C₇₃	—	2	1	no	—
92	C₄×Q₈×C₇₃	—	2	1	no	—
93	C₄×D₄×C₇₃	—	2	1	no	—
94	C₄×D₄×C₇₃	—	2	1	no	—
95	#117×C₇₃	—	2	1	no	—
96	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
97	#106×C₇₃	—	2	2	no	—
98	#103×C₇₃	—	2	2	no	—
99	#102×C₇₃	—	2	2	no	—
100	C₄×C₈×C₇₃	D₄	1	2	yes	—
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	C₂³×D₇₃	—	4	1	no	—
104	C₂×Dic₁₄₆	—	2	2	no	—
105	C₂×Dic₁₄₆	—	4	4	no	—
106	C₂×Dic₁₄₆	—	4	1	no	—
107	C₂×D₂₉₂	—	2	2	no	—
108	C₂×D₂₉₂	—	2	2	no	—
109	C₂×D₂₉₂	—	2	2	no	—
110	C₂×D₂₉₂	—	4	4	no	—
111	C₂×D₂₉₂	—	4	4	no	—
112	C₂×D₂₉₂	—	4	1	no	—
113	C₂×D₂₉₂	—	4	1	no	—
114	C₂×D₂₉₂	—	4	1	no	—
115	C₂×D₂₉₂	—	8	2	no	—
116	C₂²×Dic₇₃	—	4	1	no	—
117	#11924017	—	4	8	no	—
118	#11924017	—	4	8	no	—
119	#11924013	—	8	4	no	—
120	#11924012	—	2	4	no	—
121	C₂×#10596831	C₂×D₄	1	4	yes	—
122	C₂×#10596831	C₂×D₄	1	4	yes	—
123	C₄⋊Dic₇₃	—	2	2	no	—
124	C₄⋊Dic₇₃	—	2	2	no	—
125	C₄⋊Dic₇₃	—	4	1	no	—
126	C₄⋊Dic₇₃	—	4	1	no	—
127	#41×C₇₃	—	4	4	no	—
128	C₂×Q₈×C₇₃	—	2	1	no	—
129	C₂×Q₈×C₇₃	—	2	1	no	—
130	C₂×Q₈×C₇₃	—	2	1	no	—
131	C₂×D₄×C₇₃	—	2	1	no	—
132	C₂×D₄×C₇₃	—	2	1	no	—
133	C₂×D₄×C₇₃	—	2	1	no	—
134	C₂×D₄×C₇₃	—	4	1	no	—
135	C₂²×C₄×C₇₃	—	4	1	no	—
136	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
139	SD₁₆×C₇₃	—	4	4	no	—
140	C₂×C₈×C₇₃	—	2	4	no	—
141	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₇₃	—	2	1	no	—
144	C₄⋊C₄×C₇₃	—	2	1	no	—
145	C₄⋊C₄×C₇₃	—	2	1	no	—
146	C₄⋊C₄×C₇₃	—	2	1	no	—
147	C₄⋊C₄×C₇₃	—	2	1	no	—
148	C₄⋊C₄×C₇₃	—	2	1	no	—
149	C₄⋊C₄×C₇₃	—	4	1	no	—
150	C₄⋊C₄×C₇₃	—	4	1	no	—
151	C₂²⋊C₄×C₇₃	—	4	1	no	—
152	C₂²⋊C₄×C₇₃	—	4	1	no	—
153	C₂²⋊C₄×C₇₃	—	4	1	no	—
154	C₄²×C₇₃	—	4	1	no	—
155	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₇₃	—	4	1	no	—
160	C₂³×C₇₃	#127	1	1	yes	characteristic
161	C₂²×D₇₃	—	4	2	no	—
162	C₂²×D₇₃	—	8	2	no	—
163	C₂²×D₇₃	—	8	2	no	—
164	C₂²×D₇₃	—	8	2	no	—
165	Q₈×C₇₃	—	4	2	no	—
166	Q₈×C₇₃	—	4	2	no	—
167	Q₈×C₇₃	—	4	2	no	—
168	D₄×C₇₃	—	4	2	no	—
169	D₄×C₇₃	—	4	2	no	—
170	D₄×C₇₃	—	4	2	no	—
171	D₄×C₇₃	—	8	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	—	2	2	no	—
174	C₂×C₄×C₇₃	—	4	1	no	—
175	C₂×C₄×C₇₃	—	4	1	no	—
176	C₂×C₄×C₇₃	—	4	1	no	—
177	C₂×C₄×C₇₃	—	8	2	no	—
178	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
179	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
180	C₂×C₄×C₇₃	#127	1	1	yes	characteristic
181	C₂×C₄×C₇₃	#135	1	4	yes	—
182	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
185	C₂×Dic₇₃	—	4	2	no	—
186	C₂×Dic₇₃	—	8	2	no	—
187	D₂₉₂	—	4	4	no	—
188	D₂₉₂	—	4	4	no	—
189	D₂₉₂	—	4	4	no	—
190	D₂₉₂	—	8	2	no	—
191	D₂₉₂	—	8	2	no	—
192	D₂₉₂	—	8	2	no	—
193	Dic₁₄₆	—	4	4	no	—
194	Dic₁₄₆	—	8	2	no	—
195	C₈×C₇₃	—	2	2	no	—
196	C₈×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
197	#10596831	—	2	4	no	—
198	#10596831	—	2	4	no	—
199	C₂²×C₇₃	—	2	1	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	—	8	1	no	—
202	C₂²×C₇₃	—	8	1	no	—
203	C₂²×C₇₃	—	8	1	no	—
204	C₂²×C₇₃	#495	1	2	yes	—
205	C₂²×C₇₃	C₂×#127	1	1	yes	characteristic
206	C₂×D₇₃	—	8	2	no	—
207	C₂×D₇₃	—	8	2	no	—
208	C₂×D₇₃	—	8	2	no	—
209	C₂×D₇₃	—	16	4	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	—	2	1	no	—
212	C₄×C₇₃	—	8	1	no	—
213	C₄×C₇₃	—	8	1	no	—
214	C₄×C₇₃	—	8	1	no	—
215	C₄×C₇₃	#495	1	2	yes	—
216	C₄×C₇₃	C₂×#135	1	2	yes	—
217	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₄×C₇₃	#577	1	2	yes	—
219	Dic₇₃	—	8	2	no	—
220	#19625	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	2	2	no	—
222	C₂×C₇₃	—	16	1	no	—
223	C₂×C₇₃	C₂×#495	1	1	yes	characteristic
224	C₂×C₇₃	#3151	1	1	yes	characteristic
225	C₂×C₇₃	#3154	1	1	yes	characteristic
226	D₇₃	—	16	2	no	—
227	#3230	—	73	1	no	—
228	#3205	—	73	1	no	—
229	#3167	D₇₃	1	1	yes	characteristic, complemented
230	C₂×#492	—	73	1	no	—
231	#3141	—	73	1	no	—
232	#3138	—	73	1	no	—
233	#1719	—	73	2	no	—
234	#1717	—	73	2	no	—
235	#1708	—	73	2	no	—
236	#1706	—	73	2	no	—
237	C₈×M₁₆	—	73	1	no	—
238	C₇₃	#19625	1	1	yes	characteristic, complemented, Sylow
239	C₂²×SD₁₆	—	146	2	no	—
240	#533	C₂×D₇₃	1	1	yes	characteristic
241	#532	C₂×D₇₃	1	1	yes	characteristic
242	C₂×C₄⋊Q₈	—	73	1	no	—
243	C₂×#127	—	73	1	no	—
244	#500	—	73	2	no	—
245	#498	C₂×D₇₃	1	1	yes	characteristic, complemented
246	#493	—	73	2	no	—
247	#492	—	73	2	no	—
248	#492	—	73	2	no	—
249	#492	—	146	2	no	—
250	#492	C₂×D₇₃	1	1	yes	characteristic, complemented
251	#490	—	146	2	no	—
252	#489	—	146	2	no	—
253	#487	—	73	2	no	—
254	#487	—	73	2	no	—
255	#487	C₂×D₇₃	1	1	yes	characteristic, complemented
256	#486	—	73	2	no	—
257	#486	—	73	2	no	—
258	#486	—	73	2	no	—
259	#486	—	73	2	no	—
260	#486	C₂×D₇₃	1	1	yes	characteristic, complemented
261	#484	—	146	2	no	—
262	#477	—	146	2	no	—
263	#465	—	2	2	no	—
264	#459	—	146	2	no	—
265	#447	—	146	2	no	—
266	C₄×SD₁₆	—	2	2	no	—
267	#431	—	73	1	no	—
268	#418	—	146	2	no	—
269	#417	—	146	2	no	—
270	C₄×M₁₆	—	73	1	no	—
271	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
272	#322	—	73	2	no	—
273	C₈²	—	73	2	no	—
274	C₂×#41	—	2	1	no	—
275	C₂²×Q₈	—	146	1	no	—
276	C₂²×D₄	—	146	1	no	—
277	C₂²×D₄	—	146	1	no	—
278	C₂²×D₄	—	146	1	no	—
279	C₂×SD₁₆	—	2	2	no	—
280	C₂×SD₁₆	—	292	8	no	—
281	C₂×SD₁₆	—	146	4	no	—
282	C₂×SD₁₆	—	146	4	no	—
283	C₂×D₈	—	146	4	no	—
284	C₂×M₁₆	—	73	2	no	—
285	C₂²×C₈	C₂²⋊D₇₃	1	2	yes	—
286	C₄⋊Q₈	—	73	2	no	—
287	C₄⋊Q₈	—	146	1	no	—
288	C₄⋊Q₈	—	146	1	no	—
289	C₄⋊Q₈	—	146	1	no	—
290	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
291	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
292	C₄⋊Q₈	C₂²×D₇₃	1	1	yes	characteristic
293	#127	—	73	2	no	—
294	#127	—	146	1	no	—
295	#127	—	146	1	no	—
296	#127	—	146	1	no	—
297	#127	C₂²×D₇₃	1	1	yes	characteristic
298	#125	—	2	1	no	—
299	#124	—	2	1	no	—
300	C₂²⋊Q₈	—	2	1	no	—
301	C₂²⋊Q₈	—	2	1	no	—
302	#121	—	2	1	no	—
303	#121	—	2	1	no	—
304	C₄×Q₈	—	2	1	no	—
305	C₄×Q₈	—	2	1	no	—
306	C₄×D₄	—	2	1	no	—
307	C₄×D₄	—	2	1	no	—
308	#117	—	2	1	no	—
309	C₂×C₄⋊C₄	—	146	1	no	—
310	C₂×C₄⋊C₄	—	146	1	no	—
311	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
312	#107	—	146	4	no	—
313	#106	—	2	2	no	—
314	C₄⋊C₈	—	73	2	no	—
315	#103	—	2	2	no	—
316	#103	—	146	4	no	—
317	#103	—	146	4	no	—
318	#102	—	2	2	no	—
319	#102	—	146	4	no	—
320	#102	—	146	4	no	—
321	#102	—	146	4	no	—
322	#102	—	146	4	no	—
323	C₂²⋊C₈	—	73	2	no	—
324	#97	—	73	2	no	—
325	C₄×C₈	—	73	2	no	—
326	C₄×C₈	—	73	2	no	—
327	C₄×C₈	C₂²⋊D₇₃	1	2	yes	—
328	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
329	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
330	C₂⁴	—	292	1	no	—
331	#41	—	4	4	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	292	4	no	—
336	C₂×Q₈	—	292	1	no	—
337	C₂×Q₈	—	146	2	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	292	4	no	—
343	C₂×D₄	—	292	1	no	—
344	C₂×D₄	—	292	1	no	—
345	C₂×D₄	—	292	1	no	—
346	C₂×D₄	—	292	4	no	—
347	C₂×D₄	—	584	2	no	—
348	C₂×D₄	—	146	2	no	—
349	C₂×D₄	—	146	2	no	—
350	C₂×D₄	—	146	2	no	—
351	C₂²×C₄	—	4	1	no	—
352	C₂²×C₄	—	292	1	no	—
353	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
354	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
356	SD₁₆	—	4	4	no	—
357	SD₁₆	—	292	8	no	—
358	SD₁₆	—	292	8	no	—
359	D₈	—	584	4	no	—
360	M₁₆	—	146	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	73	4	no	—
363	C₂×C₈	—	73	4	no	—
364	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
365	C₂×C₈	C₂×C₂²⋊D₇₃	1	2	yes	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	292	1	no	—
375	C₄⋊C₄	—	292	1	no	—
376	C₄⋊C₄	—	146	2	no	—
377	C₄⋊C₄	—	146	2	no	—
378	C₂²⋊C₄	—	4	1	no	—
379	C₂²⋊C₄	—	4	1	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₄²	—	4	1	no	—
382	C₄²	D₄×D₇₃	1	1	yes	characteristic
383	C₄²	D₄×D₇₃	1	1	yes	characteristic
384	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
385	C₄²	C₂³×D₇₃	1	1	yes	characteristic
386	C₂³	—	4	1	no	—
387	C₂³	—	292	2	no	—
388	C₂³	—	584	2	no	—
389	C₂³	—	584	2	no	—
390	C₂³	—	584	2	no	—
391	C₂³	#14556587	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	292	4	no	—
396	Q₈	—	584	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	2	no	—
401	D₄	—	292	4	no	—
402	D₄	—	292	4	no	—
403	D₄	—	292	4	no	—
404	D₄	—	584	2	no	—
405	D₄	—	584	2	no	—
406	D₄	—	584	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	8	2	no	—
413	C₂×C₄	—	292	2	no	—
414	C₂×C₄	—	584	2	no	—
415	C₂×C₄	#14556587	1	1	yes	characteristic
416	C₂×C₄	#14556587	1	1	yes	characteristic
417	C₂×C₄	#14556587	1	1	yes	characteristic
418	C₂×C₄	#14556612	1	4	yes	—
419	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
420	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
421	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
422	C₈	—	2	2	no	—
423	C₈	—	146	4	no	—
424	C₈	—	146	4	no	—
425	C₈	#14556616	1	4	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	8	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	584	2	no	—
432	C₂²	—	584	2	no	—
433	C₂²	—	584	2	no	—
434	C₂²	—	1168	4	no	—
435	C₂²	#17988968	1	2	yes	—
436	C₂²	C₂×#14556587	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	584	2	no	—
443	C₄	#17988968	1	2	yes	—
444	C₄	C₂×#14556612	1	2	yes	—
445	C₄	C₂×#14556616	1	2	yes	—
446	C₄	#17989394	1	2	yes	—
447	C₂	—	2	2	no	—
448	C₂	—	16	1	no	—
449	C₂	—	1168	2	no	—
450	C₂	C₂×#17988968	1	1	yes	characteristic
451	C₂	#22620384	1	1	yes	characteristic
452	C₂	#22620408	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14556587
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#3167	C₂
socle	C₂²×C₇₃	C₂×#127
prime radical	#22620846	C₂
hypercenter	#3167	D₇₃
hypocenter	C₇₃	#19625
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #22621079	C₂	semidirect
3. C₂×#17988960	C₂	semidirect
4. #22620324	C₂	semidirect
5. #22620307	C₂	semidirect
6. #22609586	C₂	semidirect
7. #22609572	C₂	semidirect
8. #22609533	C₂	semidirect
9. #22609521	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₇₃×#3167	C₂	semidirect
15. #17988990	C₂²	semidirect
22. #17988937	C₂²	semidirect
23. #17988937	C₂²	semidirect
27. #17988933	C₂²	semidirect
36. #17988309	C₂²	semidirect
37. C₈×#10596831	C₂²	semidirect
40. #498×C₇₃	C₂²	semidirect
41. #492×C₇₃	C₂²	semidirect
42. #487×C₇₃	C₂²	semidirect
43. #486×C₇₃	C₂²	semidirect
229. #3167	D₇₃	semidirect
238. C₇₃	#19625	semidirect
245. #498	C₂×D₇₃	semidirect
250. #492	C₂×D₇₃	semidirect
255. #487	C₂×D₇₃	semidirect
260. #486	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22621079	2
#22620846	2
C₂×#17988960	2
#22620324	2
#22620307	2
#22609586	2
#22609572	2
#22609533	2
#22609521	2
C₈×#11924012	2
C₇₃×#3167	2
#19625	73