Subgroups — #34020354

Order 18688.

906 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₃⋊#433	C₂	1	1	yes	maximal, characteristic
2	#22626393	C₂	1	1	yes	maximal, characteristic
3	#22625729	C₂	1	2	yes	maximal, complemented
4	#22625725	C₂	1	2	yes	maximal, complemented
5	#22625671	C₂	1	2	yes	maximal
6	#22625667	C₂	1	2	yes	maximal
7	#22625651	C₂	1	1	yes	maximal, characteristic, complemented
8	#22625647	C₂	1	1	yes	maximal, characteristic, complemented
9	#22625587	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#14556645	C₂	1	1	yes	maximal, characteristic, complemented
11	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
12	#17989612	C₄	1	4	yes	complemented
13	#17989611	C₄	1	4	yes	complemented
14	#17989588	C₂²	1	2	yes	—
15	#17989555	C₂²	1	2	yes	—
16	#17989546	C₂²	1	1	yes	characteristic
17	C₂×#14556645	C₂²	1	2	yes	—
18	C₂×#14556645	C₂²	1	2	yes	—
19	C₂×#14556645	C₂²	1	2	yes	—
20	C₄×#11924036	C₂²	1	1	yes	characteristic
21	C₂×C₈×#64408	C₂²	1	2	yes	—
22	#17989537	C₄	1	4	yes	—
23	#17989536	C₄	1	4	yes	—
24	C₄×C₄⋊#64408	C₂²	1	2	yes	—
25	C₄×C₂²⋊#64408	C₂²	1	2	yes	—
26	#17989523	C₂²	1	1	yes	characteristic
27	C₄²×#64408	C₂²	1	1	yes	characteristic
28	#17989452	C₂²	1	2	yes	—
29	#17989452	C₂²	1	2	yes	—
30	#17989452	C₂²	1	2	yes	—
31	#17989452	C₂²	1	2	yes	—
32	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
34	#117×D₇₃	C₂²	1	1	yes	characteristic
35	#17988545	C₄	1	1	yes	characteristic, complemented
36	#17988544	C₄	1	1	yes	characteristic, complemented
37	#17988544	C₄	1	1	yes	characteristic, complemented
38	#17988543	C₄	1	1	yes	characteristic, complemented
39	#17988542	C₄	1	1	yes	characteristic, complemented
40	#17988541	C₄	1	1	yes	characteristic, complemented
41	#17988541	C₄	1	1	yes	characteristic, complemented
42	#97×D₇₃	C₂²	1	1	yes	characteristic
43	#97×D₇₃	C₂²	1	1	yes	characteristic
44	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
47	C₂×#11924036	C₂³	1	2	yes	—
48	C₂×#11924036	C₂³	1	2	yes	—
49	C₂×C₄⋊#64408	C₂×C₄	1	4	yes	—
50	C₂×C₂²⋊#64408	C₂×C₄	1	4	yes	—
51	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
52	C₂×C₄×#64408	C₂³	1	2	yes	—
53	C₂×C₄×#64408	C₂³	1	2	yes	—
54	#14556658	C₂×C₄	1	4	yes	—
55	C₄⋊#10596833	C₂×C₄	1	4	yes	—
56	#14556648	C₂×C₄	1	4	yes	—
57	C₂²⋊#10596833	C₂×C₄	1	4	yes	—
58	#14556646	C₂×C₄	1	4	yes	—
59	#14556645	—	2	4	no	—
60	#14556645	—	2	4	no	—
61	#14556645	—	2	4	no	—
62	C₄×#10596833	C₂×C₄	1	4	yes	—
63	C₈×#64408	—	2	4	no	—
64	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
65	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
66	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
67	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
68	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
69	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
70	C₂×#11924011	C₂×C₄	1	1	yes	characteristic
71	M₁₆×D₇₃	—	2	4	no	—
72	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₇₃	—	2	4	no	—
74	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
78	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
80	#14556550	C₂×C₄	1	1	yes	characteristic
81	#14556549	C₂×C₄	1	2	yes	—
82	#14556548	C₂×C₄	1	1	yes	characteristic
83	#14556548	C₂×C₄	1	1	yes	characteristic
84	#14556547	C₂×C₄	1	2	yes	—
85	C₄⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
86	C₂²⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
87	C₄²×D₇₃	C₂³	1	1	yes	characteristic
88	C₄²×D₇₃	C₂³	1	1	yes	characteristic
89	#14556502	C₂×C₄	1	1	yes	characteristic
90	#14556502	C₂×C₄	1	1	yes	characteristic
91	#14556501	C₂×C₄	1	1	yes	characteristic
92	#14556501	C₂×C₄	1	1	yes	characteristic
93	#14556501	C₂×C₄	1	1	yes	characteristic
94	#14556501	C₂×C₄	1	1	yes	characteristic
95	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
96	C₄×#10596831	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
101	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
103	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
104	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
105	#97×C₇₃	C₂×C₄	1	1	yes	characteristic
106	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
108	C₂²×#64408	C₂²×C₄	1	4	yes	—
109	C₂²×#64408	C₂²×C₄	1	4	yes	—
110	#11924036	—	2	2	no	—
111	#11924036	—	2	2	no	—
112	#11924036	—	2	2	no	—
113	#11924036	—	2	2	no	—
114	C₂×#10596833	C₂²×C₄	1	4	yes	—
115	C₂×#10596833	C₂²×C₄	1	4	yes	—
116	C₄⋊#64408	—	4	4	no	—
117	C₂²⋊#64408	—	4	4	no	—
118	C₄×#64408	—	2	2	no	—
119	C₄×#64408	—	2	2	no	—
120	C₄×#64408	—	2	2	no	—
121	C₄×#64408	—	2	2	no	—
122	C₄×#64408	—	4	4	no	—
123	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₇₃	—	2	2	no	—
126	C₂×C₄×D₇₃	—	2	2	no	—
127	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
128	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
129	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
133	#11924012	—	2	2	no	—
134	#11924011	—	2	2	no	—
135	#11924011	—	2	2	no	—
136	C₂×#10596831	—	2	2	no	—
137	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
138	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
139	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
140	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
141	C₈×D₇₃	—	2	2	no	—
142	C₈×D₇₃	—	2	2	no	—
143	C₈×D₇₃	—	2	2	no	—
144	C₈×D₇₃	—	2	2	no	—
145	C₈×D₇₃	#41	1	4	yes	—
146	C₈×D₇₃	#41	1	4	yes	—
147	C₄⋊Dic₇₃	C₄²	1	2	yes	—
148	#11924007	C₄²	1	2	yes	—
149	#11924007	C₄²	1	2	yes	—
150	C₂²⋊Dic₇₃	C₄²	1	2	yes	—
151	#11924005	C₄²	1	2	yes	—
152	#11924005	C₄²	1	2	yes	—
153	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
156	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
158	M₁₆×C₇₃	—	2	2	no	—
159	C₂×C₈×C₇₃	—	2	2	no	—
160	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊C₄×C₇₃	C₄²	1	2	yes	—
165	C₂²⋊C₄×C₇₃	C₄²	1	2	yes	—
166	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
168	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
169	C₂²×D₇₃	—	2	2	no	—
170	C₂²×D₇₃	—	2	4	no	—
171	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
172	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
173	C₂×#64408	—	2	4	no	—
174	C₂×#64408	—	2	4	no	—
175	C₂×#64408	—	2	4	no	—
176	C₂×#64408	—	2	4	no	—
177	C₂×#64408	—	2	4	no	—
178	C₂×#64408	—	2	4	no	—
179	C₂×C₄×C₇₃	—	2	1	no	—
180	C₂×C₄×C₇₃	—	2	1	no	—
181	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
182	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
183	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
185	C₂×Dic₇₃	—	2	2	no	—
186	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
187	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
188	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
190	C₄×D₇₃	—	2	2	no	—
191	C₄×D₇₃	—	2	4	no	—
192	C₄×D₇₃	—	2	4	no	—
193	C₄×D₇₃	—	2	1	no	—
194	C₄×D₇₃	—	2	1	no	—
195	C₄×D₇₃	—	2	2	no	—
196	C₄×D₇₃	C₂×#41	1	2	yes	—
197	C₄×D₇₃	C₂×#41	1	2	yes	—
198	#10596833	—	2	4	no	—
199	#10596833	—	2	4	no	—
200	C₈×C₇₃	—	2	1	no	—
201	C₈×C₇₃	—	2	1	no	—
202	C₈×C₇₃	#117	1	2	yes	—
203	C₈×C₇₃	#117	1	2	yes	—
204	#10596831	—	2	1	no	—
205	#10596831	—	2	1	no	—
206	#10596831	#117	1	2	yes	—
207	#10596831	#117	1	2	yes	—
208	C₂²×C₇₃	—	2	2	no	—
209	C₂²×C₇₃	—	2	1	no	—
210	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
211	C₂×D₇₃	—	2	2	no	—
212	C₂×D₇₃	—	2	1	no	—
213	C₂×D₇₃	—	4	4	no	—
214	C₂×D₇₃	C₄×#41	1	2	yes	—
215	C₂×D₇₃	#568	1	4	yes	—
216	#64408	—	4	4	no	—
217	#64408	—	4	4	no	—
218	C₄×C₇₃	—	2	2	no	—
219	C₄×C₇₃	—	2	2	no	—
220	C₄×C₇₃	—	2	1	no	—
221	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
222	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
223	Dic₇₃	—	2	2	no	—
224	Dic₇₃	—	2	2	no	—
225	Dic₇₃	—	2	1	no	—
226	Dic₇₃	C₄×#41	1	2	yes	—
227	#20475	—	73	1	no	maximal, Sylow
228	C₂×C₇₃	—	4	1	no	—
229	C₂×C₇₃	C₄×#117	1	1	yes	characteristic
230	C₂×C₇₃	#2875	1	2	yes	—
231	D₇₃	—	4	1	no	—
232	D₇₃	#2967	1	4	yes	—
233	C₂×#433	—	73	1	no	—
234	C₂×#405	—	73	1	no	—
235	#2298	—	73	1	no	—
236	#1771	—	73	2	no	—
237	#1770	—	73	2	no	—
238	#1753	—	73	2	no	—
239	#1752	—	73	2	no	—
240	#1746	—	73	1	no	—
241	#1745	—	73	1	no	—
242	#1726	—	73	1	no	—
243	C₄×#97	—	73	1	no	—
244	C₇₃	#20475	1	1	yes	characteristic, complemented, Sylow
245	C₂²×M₁₆	—	73	1	no	—
246	C₂³×C₈	—	73	1	no	—
247	C₂×#117	—	73	1	no	—
248	#433	—	73	4	no	—
249	#433	—	73	4	no	—
250	C₂×C₄⋊C₈	—	73	2	no	—
251	C₂×C₂²⋊C₈	—	73	2	no	—
252	#405	—	73	1	no	—
253	#405	—	73	1	no	—
254	#405	—	73	1	no	—
255	#405	—	73	1	no	—
256	#405	—	73	1	no	—
257	#405	—	73	1	no	—
258	#405	—	73	1	no	—
259	#405	#64408	1	1	yes	characteristic, complemented
260	C₂×#97	—	73	1	no	—
261	C₂×#97	—	73	1	no	—
262	C₂×#97	—	73	1	no	—
263	C₂×#97	—	73	2	no	—
264	C₂×#97	—	73	2	no	—
265	C₂×#97	—	73	2	no	—
266	C₂×C₄×C₈	—	73	1	no	—
267	C₂×C₄×C₈	—	73	1	no	—
268	C₂×C₄×C₈	—	73	1	no	—
269	C₂×C₄×C₈	—	73	2	no	—
270	#388	—	73	4	no	—
271	#387	—	73	4	no	—
272	C₄×C₄⋊C₄	—	73	2	no	—
273	C₄×C₂²⋊C₄	—	73	2	no	—
274	#376	—	73	1	no	—
275	C₄³	—	73	1	no	—
276	#336	—	73	2	no	—
277	#336	—	73	2	no	—
278	#336	—	73	2	no	—
279	#336	—	73	2	no	—
280	C₂³×C₄	—	73	1	no	—
281	C₂×M₁₆	—	73	1	no	—
282	C₂×M₁₆	—	73	1	no	—
283	C₂×M₁₆	—	73	1	no	—
284	C₂×M₁₆	—	146	4	no	—
285	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
286	C₂²×C₈	—	73	1	no	—
287	C₂²×C₈	—	73	1	no	—
288	C₂²×C₈	—	73	2	no	—
289	C₂²×C₈	—	73	2	no	—
290	C₂²×C₈	—	73	1	no	—
291	C₂²×C₈	—	73	1	no	—
292	C₂²×C₈	—	73	1	no	—
293	C₂²×C₈	—	73	1	no	—
294	C₂²×C₈	—	73	1	no	—
295	C₂²×C₈	—	146	4	no	—
296	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
297	#117	—	73	1	no	—
298	#117	—	73	2	no	—
299	#117	—	73	2	no	—
300	#117	—	73	1	no	—
301	#117	—	73	1	no	—
302	#117	C₂×#64408	1	1	yes	characteristic
303	C₂×C₄⋊C₄	—	73	4	no	—
304	C₂×C₄⋊C₄	—	73	2	no	—
305	C₂×C₂²⋊C₄	—	73	4	no	—
306	C₂×C₂²⋊C₄	—	73	2	no	—
307	C₂×C₄²	—	73	4	no	—
308	C₂×C₄²	—	73	1	no	—
309	C₂×C₄²	—	73	1	no	—
310	C₂×C₄²	—	73	2	no	—
311	C₂×C₄²	—	73	2	no	—
312	C₄⋊C₈	—	73	4	no	—
313	C₄⋊C₈	—	73	4	no	—
314	C₂²⋊C₈	—	73	4	no	—
315	C₂²⋊C₈	—	73	4	no	—
316	#97	—	73	4	no	—
317	#97	—	73	1	no	—
318	#97	—	73	1	no	—
319	#97	—	73	1	no	—
320	#97	—	73	1	no	—
321	#97	—	73	1	no	—
322	#97	—	73	1	no	—
323	#97	—	146	4	no	—
324	#97	—	146	4	no	—
325	#97	—	146	4	no	—
326	#97	C₂×#64408	1	1	yes	characteristic
327	#97	C₂×#64408	1	1	yes	characteristic
328	C₄×C₈	—	73	4	no	—
329	C₄×C₈	—	73	1	no	—
330	C₄×C₈	—	73	1	no	—
331	C₄×C₈	—	73	1	no	—
332	C₄×C₈	—	73	1	no	—
333	C₄×C₈	—	73	1	no	—
334	C₄×C₈	—	73	1	no	—
335	C₄×C₈	—	146	4	no	—
336	C₄×C₈	C₂×#64408	1	1	yes	characteristic
337	C₄×C₈	C₂×#64408	1	1	yes	characteristic
338	#95	—	73	4	no	—
339	#95	—	73	4	no	—
340	#95	—	73	4	no	—
341	C₂⁴	—	73	1	no	—
342	C₂²×C₄	—	73	1	no	—
343	C₂²×C₄	—	73	1	no	—
344	C₂²×C₄	—	73	1	no	—
345	C₂²×C₄	—	73	1	no	—
346	C₂²×C₄	—	73	2	no	—
347	C₂²×C₄	—	73	2	no	—
348	C₂²×C₄	—	73	1	no	—
349	C₂²×C₄	—	73	4	no	—
350	C₂²×C₄	—	73	4	no	—
351	C₂²×C₄	—	146	2	no	—
352	C₂²×C₄	—	146	2	no	—
353	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
354	M₁₆	—	2	2	no	—
355	M₁₆	—	146	2	no	—
356	M₁₆	—	146	2	no	—
357	M₁₆	—	146	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	73	1	no	—
360	C₂×C₈	—	73	1	no	—
361	C₂×C₈	—	73	4	no	—
362	C₂×C₈	—	73	4	no	—
363	C₂×C₈	—	73	4	no	—
364	C₂×C₈	—	73	4	no	—
365	C₂×C₈	—	73	1	no	—
366	C₂×C₈	—	73	1	no	—
367	C₂×C₈	—	146	2	no	—
368	C₂×C₈	—	146	2	no	—
369	C₂×C₈	—	146	2	no	—
370	C₂×C₈	—	146	2	no	—
371	C₂×C₈	—	146	2	no	—
372	C₂×C₈	—	146	2	no	—
373	C₂×C₈	—	146	2	no	—
374	C₂×C₈	—	146	2	no	—
375	C₂×C₈	—	146	2	no	—
376	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
377	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
378	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
379	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
380	C₄⋊C₄	—	292	4	no	—
381	C₄⋊C₄	—	73	2	no	—
382	C₄⋊C₄	—	73	2	no	—
383	C₄⋊C₄	—	73	2	no	—
384	C₄⋊C₄	C₄×#64408	1	2	yes	—
385	C₂²⋊C₄	—	292	4	no	—
386	C₂²⋊C₄	—	73	2	no	—
387	C₂²⋊C₄	—	73	2	no	—
388	C₂²⋊C₄	—	73	2	no	—
389	C₂²⋊C₄	C₄×#64408	1	2	yes	—
390	C₄²	—	292	4	no	—
391	C₄²	—	73	1	no	—
392	C₄²	—	73	1	no	—
393	C₄²	—	73	2	no	—
394	C₄²	—	73	2	no	—
395	C₄²	—	146	2	no	—
396	C₄²	—	146	2	no	—
397	C₄²	—	146	2	no	—
398	C₄²	—	146	2	no	—
399	C₄²	C₂²×#64408	1	1	yes	characteristic
400	C₄²	C₂²×#64408	1	1	yes	characteristic
401	C₂³	—	73	1	no	—
402	C₂³	—	73	1	no	—
403	C₂³	—	146	4	no	—
404	C₂³	—	146	2	no	—
405	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	73	1	no	—
409	C₂×C₄	—	73	2	no	—
410	C₂×C₄	—	73	2	no	—
411	C₂×C₄	—	73	2	no	—
412	C₂×C₄	—	73	2	no	—
413	C₂×C₄	—	73	1	no	—
414	C₂×C₄	—	146	2	no	—
415	C₂×C₄	—	146	4	no	—
416	C₂×C₄	—	146	4	no	—
417	C₂×C₄	—	146	2	no	—
418	C₂×C₄	—	146	4	no	—
419	C₂×C₄	—	146	4	no	—
420	C₂×C₄	—	146	4	no	—
421	C₂×C₄	—	146	4	no	—
422	C₂×C₄	—	146	4	no	—
423	C₂×C₄	—	146	4	no	—
424	C₂×C₄	—	146	2	no	—
425	C₂×C₄	—	146	1	no	—
426	C₂×C₄	—	146	1	no	—
427	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
428	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
429	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
430	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	73	2	no	—
434	C₈	—	73	2	no	—
435	C₈	—	146	4	no	—
436	C₈	—	146	4	no	—
437	C₈	—	146	1	no	—
438	C₈	—	146	1	no	—
439	C₈	#14556670	1	2	yes	—
440	C₈	#14556670	1	2	yes	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	292	4	no	—
444	C₂²	—	73	2	no	—
445	C₂²	—	73	4	no	—
446	C₂²	—	146	1	no	—
447	C₂²	—	146	2	no	—
448	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	292	4	no	—
453	C₄	—	292	4	no	—
454	C₄	—	73	2	no	—
455	C₄	—	146	1	no	—
456	C₄	—	146	2	no	—
457	C₄	—	146	2	no	—
458	C₄	C₂×#14556670	1	1	yes	characteristic
459	C₄	C₂×#14556670	1	1	yes	characteristic
460	C₂	—	4	1	no	—
461	C₂	—	292	1	no	—
462	C₂	—	73	4	no	—
463	C₂	C₄×#14556670	1	1	yes	characteristic
464	C₂	#22626501	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#405×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20475
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #22625729	C₂	semidirect
4. #22625725	C₂	semidirect
7. #22625651	C₂	semidirect
8. #22625647	C₂	semidirect
9. #22625587	C₂	semidirect
10. C₄×#14556645	C₂	semidirect
12. #17989612	C₄	semidirect
13. #17989611	C₄	semidirect
35. #17988545	C₄	semidirect
36. #17988544	C₄	semidirect
37. #17988544	C₄	semidirect
38. #17988543	C₄	semidirect
39. #17988542	C₄	semidirect
40. #17988541	C₄	semidirect
41. #17988541	C₄	semidirect
46. #405×C₇₃	C₄	semidirect
244. C₇₃	#20475	semidirect
259. #405	#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#433	2
#22626393	2
#22625729	2
#22625725	2
#22625671	2
#22625667	2
#22625651	2
#22625647	2
#22625587	2
C₄×#14556645	2
#405×D₇₃	2
#20475	73