Subgroups — #33055985

Order 18688.

632 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	#22619996	C₂	1	1	yes	maximal, characteristic
2	C₈×#11924028	C₂	1	1	yes	maximal, characteristic
3	#22608800	C₂	1	2	yes	maximal, complemented
4	#22608786	C₂	1	2	yes	maximal, complemented
5	C₈×#11924018	C₂	1	2	yes	maximal, complemented
6	C₈×#11924015	C₂	1	2	yes	maximal, complemented
7	#22608722	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608368	C₂	1	1	yes	maximal, characteristic
9	#22608352	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#11924012	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#11924028	C₂²	1	1	yes	characteristic
13	#17988925	C₄	1	2	yes	—
14	#17988869	C₄	1	1	yes	characteristic
15	#17988864	C₄	1	1	yes	characteristic
16	#17988794	C₄	1	1	yes	characteristic
17	#17988789	C₄	1	1	yes	characteristic
18	#17988747	C₄	1	2	yes	—
19	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
20	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
21	C₄×#11924018	C₂²	1	2	yes	—
22	C₄×#11924015	C₂²	1	2	yes	—
23	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
24	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₇₃	—	2	1	no	—
26	C₈×C₂²⋊D₇₃	—	2	1	no	—
27	#17988640	C₂²	1	1	yes	characteristic
28	#17988640	C₂²	1	1	yes	characteristic
29	#17988638	—	2	1	no	—
30	C₄×#11924012	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₇₃	—	2	1	no	—
32	#17988339	C₂²	1	2	yes	—
33	#17988337	C₂²	1	2	yes	—
34	Q₈⋊#10596831	C₂²	1	2	yes	—
35	Q₈⋊#10596831	C₂²	1	2	yes	—
36	#17988317	C₂²	1	2	yes	—
37	#17988314	C₂²	1	2	yes	—
38	#17988309	C₂²	1	2	yes	—
39	C₈×#10596831	C₂²	1	2	yes	—
40	#533×C₇₃	C₂²	1	1	yes	characteristic
41	#446×C₇₃	—	2	1	no	—
42	#446×C₇₃	C₂²	1	2	yes	—
43	C₈×Q₈×C₇₃	—	2	1	no	—
44	C₈×Q₈×C₇₃	C₂²	1	2	yes	—
45	#424×C₇₃	—	2	1	no	—
46	#423×C₇₃	C₂²	1	1	yes	characteristic
47	#405×C₇₃	—	2	1	no	—
48	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
49	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
50	C₂×#11924018	C₂×C₄	1	2	yes	—
51	C₂×#11924015	C₂×C₄	1	2	yes	—
52	C₂×#11924012	—	2	1	no	—
53	C₂×C₈×D₇₃	—	2	1	no	—
54	C₂×C₈×D₇₃	—	2	1	no	—
55	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
56	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
57	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
58	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
59	C₄×C₂²⋊D₇₃	—	2	1	no	—
60	C₄×C₂²⋊D₇₃	—	2	1	no	—
61	#14556550	C₂×C₄	1	1	yes	characteristic
62	#14556548	—	2	1	no	—
63	C₄²×D₇₃	—	2	1	no	—
64	#14556524	C₂×C₄	1	2	yes	—
65	#14556522	C₂×C₄	1	2	yes	—
66	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
68	C₄⋊#10596831	C₂³	1	1	yes	characteristic
69	C₄⋊#10596831	C₂³	1	1	yes	characteristic
70	#14556520	—	2	1	no	—
71	#14556520	—	2	1	no	—
72	#14556515	C₂×C₄	1	2	yes	—
73	#14556515	C₂×C₄	1	2	yes	—
74	#14556514	C₂×C₄	1	2	yes	—
75	#14556511	C₂×C₄	1	2	yes	—
76	C₂²⋊#10596831	—	2	1	no	—
77	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
78	#14556503	—	2	1	no	—
79	#14556503	—	2	1	no	—
80	#14556502	—	2	1	no	—
81	C₄×#10596831	—	2	1	no	—
82	C₄×#10596831	C₂³	1	2	yes	—
83	C₄×#10596831	C₂³	1	2	yes	—
84	C₈×Dic₇₃	—	2	1	no	—
85	C₈×Dic₇₃	—	2	1	no	—
86	C₂×M₁₆×C₇₃	—	2	1	no	—
87	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
88	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
89	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
90	C₄⋊Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
91	#125×C₇₃	—	2	1	no	—
92	C₂²⋊Q₈×C₇₃	—	2	1	no	—
93	C₂²⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
94	C₄×Q₈×C₇₃	—	2	1	no	—
95	C₄×Q₈×C₇₃	C₂³	1	2	yes	—
96	#117×C₇₃	—	2	1	no	—
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₃	—	2	2	no	—
99	C₄⋊C₈×C₇₃	—	2	2	no	—
100	C₄⋊C₈×C₇₃	—	2	1	no	—
101	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
102	#97×C₇₃	—	2	2	no	—
103	C₄×C₈×C₇₃	—	2	2	no	—
104	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
105	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
106	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
108	#11924028	—	2	2	no	—
109	#11924028	—	2	2	no	—
110	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
111	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊D₇₃	—	2	1	no	—
113	C₂×C₄×D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	2	1	no	—
116	#11924018	—	2	4	no	—
117	#11924015	—	2	4	no	—
118	#11924012	—	2	4	no	—
119	C₂×#10596831	—	2	2	no	—
120	C₂×#10596831	—	2	1	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	C₂²×C₄	1	2	yes	—
123	C₂×#10596831	C₂²×C₄	1	2	yes	—
124	C₈×D₇₃	—	4	2	no	—
125	C₈×D₇₃	—	4	2	no	—
126	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	#11924007	—	2	1	no	—
129	#11924007	—	2	1	no	—
130	C₂²⋊Dic₇₃	—	2	1	no	—
131	#11924005	—	2	1	no	—
132	#11924005	—	2	1	no	—
133	C₄×Dic₇₃	—	2	1	no	—
134	C₄×Dic₇₃	—	2	1	no	—
135	C₄×Dic₇₃	—	2	1	no	—
136	C₂×Q₈×C₇₃	—	2	1	no	—
137	C₂×Q₈×C₇₃	C₂²×C₄	1	2	yes	—
138	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
141	M₁₆×C₇₃	—	4	2	no	—
142	C₂×C₈×C₇₃	—	2	2	no	—
143	C₂×C₈×C₇₃	—	2	2	no	—
144	C₂×C₈×C₇₃	—	4	1	no	—
145	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₄⋊C₄×C₇₃	—	2	1	no	—
150	C₄⋊C₄×C₇₃	—	2	1	no	—
151	C₄⋊C₄×C₇₃	—	2	1	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₄⋊C₄×C₇₃	—	2	2	no	—
154	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
155	C₂²⋊C₄×C₇₃	—	2	2	no	—
156	C₄²×C₇₃	—	2	2	no	—
157	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₇₃	#41	1	1	yes	characteristic
160	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
161	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₇₃	—	2	1	no	—
163	Q₈×C₇₃	—	2	2	no	—
164	Q₈×C₇₃	—	2	2	no	—
165	Q₈×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	1	no	—
168	C₂×C₄×C₇₃	—	2	1	no	—
169	C₂×C₄×C₇₃	—	2	1	no	—
170	C₂×C₄×C₇₃	—	2	2	no	—
171	C₂×C₄×C₇₃	—	2	2	no	—
172	C₂×C₄×C₇₃	—	2	2	no	—
173	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₇₃	—	2	4	no	—
180	C₂×Dic₇₃	—	2	1	no	—
181	C₂×Dic₇₃	—	2	1	no	—
182	C₂×Dic₇₃	—	2	1	no	—
183	D₂₉₂	—	2	1	no	—
184	D₂₉₂	#131	1	2	yes	—
185	C₄×D₇₃	—	2	4	no	—
186	C₄×D₇₃	—	4	1	no	—
187	C₄×D₇₃	—	4	1	no	—
188	C₄×D₇₃	—	4	2	no	—
189	Dic₁₄₆	—	2	1	no	—
190	Dic₁₄₆	#131	1	2	yes	—
191	C₈×C₇₃	—	2	1	no	—
192	C₈×C₇₃	—	2	1	no	—
193	C₈×C₇₃	—	2	1	no	—
194	C₈×C₇₃	—	4	2	no	—
195	C₈×C₇₃	#137	1	2	yes	—
196	#10596831	—	2	4	no	—
197	#10596831	—	2	2	no	—
198	#10596831	—	2	2	no	—
199	#10596831	—	4	1	no	—
200	#10596831	—	4	1	no	—
201	C₂²×C₇₃	—	2	1	no	—
202	C₂²×C₇₃	—	2	1	no	—
203	C₂²×C₇₃	—	2	1	no	—
204	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×D₇₃	—	2	2	no	—
206	C₂×D₇₃	—	4	1	no	—
207	C₂×D₇₃	—	4	1	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	—	4	2	no	—
212	C₄×C₇₃	—	4	2	no	—
213	C₄×C₇₃	#443	1	2	yes	—
214	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
215	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
216	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
217	C₄×C₇₃	#575	1	1	yes	characteristic
218	Dic₇₃	—	2	2	no	—
219	Dic₇₃	—	4	1	no	—
220	Dic₇₃	—	4	1	no	—
221	#17913	—	73	1	no	maximal, Sylow
222	C₂×C₇₃	—	4	1	no	—
223	C₂×C₇₃	#2929	1	1	yes	characteristic
224	C₂×C₇₃	C₄×#137	1	1	yes	characteristic
225	C₂×C₇₃	C₂×#443	1	1	yes	characteristic
226	D₇₃	—	4	2	no	—
227	#3107	—	73	1	no	—
228	C₈×#41	—	73	1	no	—
229	#2960	D₇₃	1	1	yes	characteristic, complemented
230	#1587	—	73	2	no	—
231	#1585	—	73	2	no	—
232	C₈×Q₁₆	—	73	2	no	—
233	C₈×SD₁₆	—	73	2	no	—
234	#1574	—	73	1	no	—
235	#1489	—	73	1	no	—
236	#1485	—	73	1	no	—
237	C₈×M₁₆	—	73	1	no	—
238	C₇₃	#17913	1	1	yes	characteristic, complemented, Sylow
239	#533	C₂×D₇₃	1	1	yes	characteristic
240	C₄×#41	—	73	1	no	—
241	#485	—	73	2	no	—
242	#475	—	73	1	no	—
243	#474	—	73	1	no	—
244	#462	—	73	1	no	—
245	#461	—	73	1	no	—
246	#452	—	73	2	no	—
247	#446	—	2	1	no	—
248	#446	C₂×D₇₃	1	2	yes	—
249	C₈×Q₈	—	2	1	no	—
250	C₈×Q₈	—	73	1	no	—
251	C₈×Q₈	—	73	1	no	—
252	C₈×Q₈	C₂×D₇₃	1	2	yes	—
253	C₄×Q₁₆	—	73	2	no	—
254	C₄×SD₁₆	—	73	2	no	—
255	C₈×D₄	—	73	1	no	—
256	C₈×D₄	—	73	1	no	—
257	C₈×D₄	—	146	1	no	—
258	C₈×D₄	—	146	1	no	—
259	#431	—	73	1	no	—
260	#431	—	73	1	no	—
261	#431	—	146	1	no	—
262	#424	—	2	1	no	—
263	#423	C₂×D₇₃	1	1	yes	characteristic
264	#405	—	2	1	no	—
265	C₄×M₁₆	—	73	1	no	—
266	C₂×C₄×C₈	—	146	1	no	—
267	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
268	#335	—	73	2	no	—
269	#334	—	73	2	no	—
270	Q₈⋊C₈	—	73	2	no	—
271	Q₈⋊C₈	—	73	2	no	—
272	Q₈⋊C₈	—	73	2	no	—
273	D₄⋊C₈	—	73	2	no	—
274	#322	—	73	2	no	—
275	C₈²	—	73	2	no	—
276	C₂×#41	—	73	1	no	—
277	C₂×Q₁₆	—	73	2	no	—
278	C₂×SD₁₆	—	73	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	146	1	no	—
281	C₂²×C₈	—	146	1	no	—
282	C₂²×C₈	—	146	1	no	—
283	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
284	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
285	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
286	C₄⋊Q₈	C₄×D₇₃	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	C₂²⋊Q₈	—	2	1	no	—
289	C₂²⋊Q₈	C₄×D₇₃	1	2	yes	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	73	1	no	—
292	C₄×Q₈	—	73	1	no	—
293	C₄×Q₈	C₂²×D₇₃	1	2	yes	—
294	C₄×D₄	—	73	1	no	—
295	C₄×D₄	—	73	1	no	—
296	C₄×D₄	—	146	1	no	—
297	C₄×D₄	—	146	1	no	—
298	#117	—	2	1	no	—
299	#117	—	73	1	no	—
300	#117	—	146	1	no	—
301	C₂×C₄²	—	146	1	no	—
302	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
303	#107	—	73	2	no	—
304	#106	—	73	2	no	—
305	C₄⋊C₈	—	2	2	no	—
306	C₄⋊C₈	—	2	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	73	1	no	—
309	C₄⋊C₈	—	73	1	no	—
310	C₄⋊C₈	—	73	1	no	—
311	C₄⋊C₈	—	73	1	no	—
312	C₄⋊C₈	—	146	1	no	—
313	C₄⋊C₈	—	146	1	no	—
314	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
315	#103	—	73	2	no	—
316	#103	—	73	2	no	—
317	#103	—	73	2	no	—
318	#102	—	73	2	no	—
319	C₂²⋊C₈	—	73	2	no	—
320	C₂²⋊C₈	—	146	1	no	—
321	C₂²⋊C₈	—	146	1	no	—
322	C₂²⋊C₈	—	146	1	no	—
323	#97	—	2	2	no	—
324	#97	—	146	1	no	—
325	C₄×C₈	—	2	2	no	—
326	C₄×C₈	—	73	2	no	—
327	C₄×C₈	—	73	2	no	—
328	C₄×C₈	—	146	1	no	—
329	C₄×C₈	—	146	1	no	—
330	C₄×C₈	—	146	1	no	—
331	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
332	C₄×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
335	#41	—	146	2	no	—
336	#41	—	146	2	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	73	1	no	—
339	C₂×Q₈	C₂×C₄×D₇₃	1	2	yes	—
340	C₂×D₄	—	73	1	no	—
341	C₂×D₄	—	146	1	no	—
342	C₂²×C₄	—	146	1	no	—
343	C₂²×C₄	—	146	1	no	—
344	C₂²×C₄	—	146	1	no	—
345	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
347	C₂²×C₄	#11924028	1	1	yes	characteristic
348	Q₁₆	—	146	4	no	—
349	SD₁₆	—	146	4	no	—
350	M₁₆	—	4	2	no	—
351	M₁₆	—	146	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	292	2	no	—
356	C₂×C₈	—	292	2	no	—
357	C₂×C₈	—	73	2	no	—
358	C₂×C₈	—	73	2	no	—
359	C₂×C₈	—	146	1	no	—
360	C₂×C₈	—	146	1	no	—
361	C₂×C₈	—	146	2	no	—
362	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
363	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
364	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
365	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	73	1	no	—
372	C₄⋊C₄	—	73	1	no	—
373	C₄⋊C₄	—	146	1	no	—
374	C₄⋊C₄	—	146	1	no	—
375	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	146	1	no	—
378	C₂²⋊C₄	—	146	1	no	—
379	C₂²⋊C₄	—	146	1	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	146	1	no	—
382	C₄²	—	146	1	no	—
383	C₄²	—	146	1	no	—
384	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
385	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
386	C₄²	#11924028	1	1	yes	characteristic
387	C₄²	C₂³×D₇₃	1	1	yes	characteristic
388	C₂³	—	146	1	no	—
389	C₂³	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	73	2	no	—
394	Q₈	—	146	1	no	—
395	D₄	—	73	2	no	—
396	D₄	—	146	4	no	—
397	D₄	—	146	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	292	1	no	—
406	C₂×C₄	—	292	1	no	—
407	C₂×C₄	—	292	2	no	—
408	C₂×C₄	—	146	4	no	—
409	C₂×C₄	—	146	1	no	—
410	C₂×C₄	—	146	1	no	—
411	C₂×C₄	—	146	1	no	—
412	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
413	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
414	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
417	C₂×C₄	C₂×#11924028	1	1	yes	characteristic
418	C₈	—	2	1	no	—
419	C₈	—	2	1	no	—
420	C₈	—	2	1	no	—
421	C₈	—	4	2	no	—
422	C₈	—	292	1	no	—
423	C₈	—	292	1	no	—
424	C₈	—	146	4	no	—
425	C₈	—	146	2	no	—
426	C₈	—	146	2	no	—
427	C₈	#14556622	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	292	1	no	—
432	C₂²	—	292	1	no	—
433	C₂²	—	146	2	no	—
434	C₂²	C₂×C₄×C₂²⋊D₇₃	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	2	no	—
440	C₄	—	292	1	no	—
441	C₄	—	292	1	no	—
442	C₄	—	146	2	no	—
443	C₄	#17988702	1	2	yes	—
444	C₄	#131×D₇₃	1	1	yes	characteristic
445	C₄	#131×D₇₃	1	1	yes	characteristic
446	C₄	C₂×#14556622	1	1	yes	characteristic
447	C₄	#17989385	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	292	2	no	—
450	C₂	#22618623	1	1	yes	characteristic
451	C₂	C₄×#14556622	1	1	yes	characteristic
452	C₂	C₂×#17988702	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#2960	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#11924028	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#2960	D₇₃
hypocenter	C₇₃	#17913
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #22608800	C₂	semidirect
4. #22608786	C₂	semidirect
5. C₈×#11924018	C₂	semidirect
6. C₈×#11924015	C₂	semidirect
7. #22608722	C₂	semidirect
9. #22608352	C₂	semidirect
10. C₈×#11924012	C₂	semidirect
11. C₇₃×#2960	C₂	semidirect
229. #2960	D₇₃	semidirect
238. C₇₃	#17913	semidirect

Maximal subgroups

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

subgroup	index
#22619996	2
C₈×#11924028	2
#22608800	2
#22608786	2
C₈×#11924018	2
C₈×#11924015	2
#22608722	2
#22608368	2
#22608352	2
C₈×#11924012	2
C₇₃×#2960	2
#17913	73