Subgroups — #33056024

Order 18688.

624 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	#22620003	C₂	1	1	yes	maximal, characteristic
2	C₈×#11924028	C₂	1	1	yes	maximal, characteristic
3	#22618865	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608783	C₂	1	2	yes	maximal, complemented
5	#22608769	C₂	1	2	yes	maximal, complemented
6	#22608751	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
10	#22608353	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989144	C₂²	1	1	yes	characteristic
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	#17988929	C₄	1	2	yes	—
15	#17988873	C₄	1	1	yes	characteristic
16	#17988868	C₄	1	1	yes	characteristic
17	#17988798	C₄	1	1	yes	characteristic
18	#17988793	C₄	1	1	yes	characteristic
19	#17988751	C₄	1	2	yes	—
20	#17988717	—	2	1	no	—
21	#17988717	C₂²	1	2	yes	—
22	C₈×Dic₁₄₆	—	2	1	no	—
23	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
24	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₄₆	C₂²	1	2	yes	—
26	C₄×Dic₂₉₂	C₂²	1	2	yes	—
27	C₄×#11924017	C₂²	1	2	yes	—
28	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
29	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₇₃	—	2	1	no	—
31	C₈×C₂²⋊D₇₃	—	2	1	no	—
32	#17988640	C₂²	1	1	yes	characteristic
33	#17988638	—	2	1	no	—
34	#17988613	—	2	1	no	—
35	#17988611	C₂²	1	1	yes	characteristic
36	#17988542	—	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	#17988319	C₂²	1	2	yes	—
42	#17988319	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	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₂₉₂	C₂×C₄	1	2	yes	—
51	C₂×#11924017	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	#14556591	C₂×C₄	1	1	yes	characteristic
56	#14556591	C₂×C₄	1	1	yes	characteristic
57	#14556583	—	2	1	no	—
58	#14556570	—	2	1	no	—
59	#14556570	C₂×C₄	1	2	yes	—
60	C₄×Dic₁₄₆	—	2	1	no	—
61	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₁₄₆	C₂³	1	2	yes	—
63	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
64	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
65	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₇₃	—	2	1	no	—
67	C₄×C₂²⋊D₇₃	—	2	1	no	—
68	#14556550	—	2	1	no	—
69	#14556550	C₂×C₄	1	1	yes	characteristic
70	#14556548	—	2	1	no	—
71	C₄²×D₇₃	—	2	1	no	—
72	#14556525	C₂×C₄	1	2	yes	—
73	#14556523	C₂×C₄	1	2	yes	—
74	C₄⋊#10596831	—	2	1	no	—
75	C₄⋊#10596831	C₂³	1	2	yes	—
76	C₄⋊#10596831	C₂³	1	1	yes	characteristic
77	C₄⋊#10596831	C₂³	1	1	yes	characteristic
78	#14556520	—	2	2	no	—
79	#14556520	—	2	2	no	—
80	#14556520	—	2	1	no	—
81	#14556520	—	2	1	no	—
82	#14556516	C₂×C₄	1	2	yes	—
83	#14556516	C₂×C₄	1	2	yes	—
84	#14556516	C₂×C₄	1	2	yes	—
85	#14556513	C₂×C₄	1	2	yes	—
86	C₂²⋊#10596831	—	2	1	no	—
87	#14556503	—	2	1	no	—
88	#14556503	—	2	1	no	—
89	#14556501	—	2	2	no	—
90	C₄×#10596831	—	2	1	no	—
91	C₈×Dic₇₃	—	2	1	no	—
92	C₈×Dic₇₃	—	2	1	no	—
93	C₈×Dic₇₃	—	2	2	no	—
94	C₂×M₁₆×C₇₃	—	2	1	no	—
95	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
99	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
101	#97×C₇₃	—	2	1	no	—
102	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
103	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
104	C₄×C₈×C₇₃	C₂³	1	2	yes	—
105	C₄×C₈×C₇₃	C₂³	1	2	yes	—
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	—	2	1	no	—
111	C₂×Dic₁₄₆	C₂²×C₄	1	2	yes	—
112	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
113	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	2	1	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	2	1	no	—
118	Dic₂₉₂	—	2	4	no	—
119	#11924017	—	2	4	no	—
120	#11924012	—	4	2	no	—
121	C₂×#10596831	—	2	1	no	—
122	C₂×#10596831	—	2	1	no	—
123	C₂×#10596831	—	2	2	no	—
124	C₈×D₇₃	—	4	2	no	—
125	C₈×D₇₃	—	4	2	no	—
126	C₄⋊Dic₇₃	—	2	1	no	—
127	C₄⋊Dic₇₃	—	2	1	no	—
128	C₄⋊Dic₇₃	—	2	1	no	—
129	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
130	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	#11924007	—	2	1	no	—
133	#11924007	—	2	2	no	—
134	#11924007	—	2	1	no	—
135	#11924007	—	2	2	no	—
136	C₂²⋊Dic₇₃	—	2	2	no	—
137	C₂²⋊Dic₇₃	—	2	1	no	—
138	#11924005	—	2	1	no	—
139	#11924005	—	2	1	no	—
140	C₄×Dic₇₃	—	2	1	no	—
141	C₄×Dic₇₃	—	2	1	no	—
142	C₄×Dic₇₃	—	2	1	no	—
143	C₄×Dic₇₃	—	2	2	no	—
144	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
147	M₁₆×C₇₃	—	4	2	no	—
148	C₂×C₈×C₇₃	—	2	2	no	—
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	—	4	1	no	—
151	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
153	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
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	C₂×C₄×C₇₃	—	2	1	no	—
164	C₂×C₄×C₇₃	—	2	1	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	2	2	no	—
168	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
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	C₂²⋊D₇₃	—	2	4	no	—
175	C₂×Dic₇₃	—	2	1	no	—
176	C₂×Dic₇₃	—	2	1	no	—
177	C₂×Dic₇₃	—	2	1	no	—
178	C₂×Dic₇₃	—	2	2	no	—
179	C₂×Dic₇₃	—	2	2	no	—
180	D₂₉₂	—	2	1	no	—
181	D₂₉₂	#131	1	2	yes	—
182	C₄×D₇₃	—	2	4	no	—
183	C₄×D₇₃	—	4	1	no	—
184	C₄×D₇₃	—	4	1	no	—
185	C₄×D₇₃	—	4	2	no	—
186	Dic₁₄₆	—	2	1	no	—
187	Dic₁₄₆	—	2	2	no	—
188	Dic₁₄₆	—	2	2	no	—
189	Dic₁₄₆	—	4	2	no	—
190	Dic₁₄₆	#131	1	2	yes	—
191	C₈×C₇₃	—	2	2	no	—
192	C₈×C₇₃	—	2	2	no	—
193	C₈×C₇₃	—	2	1	no	—
194	C₈×C₇₃	—	2	1	no	—
195	C₈×C₇₃	—	2	1	no	—
196	C₈×C₇₃	—	4	2	no	—
197	C₈×C₇₃	#137	1	2	yes	—
198	#10596831	—	4	1	no	—
199	#10596831	—	4	1	no	—
200	#10596831	—	4	2	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	#444	1	2	yes	—
212	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
213	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
214	C₄×C₇₃	C₂×#137	1	1	yes	characteristic
215	C₄×C₇₃	#575	1	1	yes	characteristic
216	Dic₇₃	—	2	2	no	—
217	Dic₇₃	—	4	2	no	—
218	Dic₇₃	—	4	1	no	—
219	Dic₇₃	—	4	2	no	—
220	Dic₇₃	—	4	1	no	—
221	#17916	—	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×#444	1	1	yes	characteristic
226	D₇₃	—	4	2	no	—
227	#3107	—	73	1	no	—
228	C₈×#41	—	73	1	no	—
229	#2960	—	73	1	no	—
230	#1584	—	73	2	no	—
231	#1582	—	73	2	no	—
232	#1579	—	73	2	no	—
233	SD₁₆⋊C₈	—	73	2	no	—
234	#1574	—	73	1	no	—
235	#1489	—	73	1	no	—
236	#1485	—	73	1	no	—
237	#1451	D₇₃	1	1	yes	characteristic, complemented
238	C₇₃	#17916	1	1	yes	characteristic, complemented, Sylow
239	#533	—	73	1	no	—
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	—	73	2	no	—
248	#446	—	146	1	no	—
249	C₈×Q₈	—	73	2	no	—
250	C₈×Q₈	—	73	1	no	—
251	C₈×Q₈	—	73	1	no	—
252	C₈×Q₈	—	146	1	no	—
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	—	146	1	no	—
261	#431	C₂×D₇₃	1	1	yes	characteristic
262	#424	—	146	1	no	—
263	#423	—	73	1	no	—
264	#405	—	146	1	no	—
265	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
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	C₂×D₇₃	1	2	yes	—
275	#322	C₂×D₇₃	1	2	yes	—
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	D₂₉₂	1	1	yes	characteristic
284	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
285	C₄⋊Q₈	—	73	1	no	—
286	C₄⋊Q₈	—	73	1	no	—
287	#125	—	146	1	no	—
288	C₂²⋊Q₈	—	73	2	no	—
289	C₂²⋊Q₈	—	146	1	no	—
290	C₄×Q₈	—	73	1	no	—
291	C₄×Q₈	—	73	1	no	—
292	C₄×Q₈	—	73	2	no	—
293	C₄×Q₈	—	146	1	no	—
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	—	73	1	no	—
299	#117	—	146	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	—	73	2	no	—
306	C₄⋊C₈	—	73	1	no	—
307	C₄⋊C₈	—	73	1	no	—
308	C₄⋊C₈	—	146	2	no	—
309	C₄⋊C₈	—	146	2	no	—
310	C₄⋊C₈	—	146	1	no	—
311	C₄⋊C₈	—	146	1	no	—
312	C₄⋊C₈	—	146	1	no	—
313	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
314	C₄⋊C₈	C₄×D₇₃	1	1	yes	characteristic
315	#103	—	73	2	no	—
316	#103	—	73	2	no	—
317	#103	—	73	2	no	—
318	#102	—	73	2	no	—
319	C₂²⋊C₈	—	146	1	no	—
320	C₂²⋊C₈	—	146	1	no	—
321	C₂²⋊C₈	—	146	1	no	—
322	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
323	#97	—	2	1	no	—
324	#97	—	146	2	no	—
325	C₄×C₈	—	146	1	no	—
326	C₄×C₈	—	146	1	no	—
327	C₄×C₈	—	146	2	no	—
328	C₄×C₈	—	146	1	no	—
329	C₄×C₈	D₂₉₂	1	1	yes	characteristic
330	C₄×C₈	D₂₉₂	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₇₃	1	2	yes	—
332	C₄×C₈	C₂²×D₇₃	1	2	yes	—
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	—	73	1	no	—
338	C₂×Q₈	—	73	2	no	—
339	C₂×Q₈	—	146	1	no	—
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×D₂₉₂	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	—	292	2	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	—	146	1	no	—
358	C₂×C₈	—	146	1	no	—
359	C₂×C₈	—	146	2	no	—
360	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
361	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
362	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
363	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
364	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
365	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
366	C₄⋊C₄	—	73	2	no	—
367	C₄⋊C₄	—	73	1	no	—
368	C₄⋊C₄	—	73	1	no	—
369	C₄⋊C₄	—	146	1	no	—
370	C₄⋊C₄	—	146	2	no	—
371	C₄⋊C₄	—	146	1	no	—
372	C₄⋊C₄	—	146	1	no	—
373	C₄⋊C₄	—	146	1	no	—
374	C₄⋊C₄	—	146	1	no	—
375	C₄⋊C₄	—	146	2	no	—
376	C₂²⋊C₄	—	146	1	no	—
377	C₂²⋊C₄	—	146	2	no	—
378	C₂²⋊C₄	—	146	1	no	—
379	C₂²⋊C₄	—	146	1	no	—
380	C₄²	—	146	1	no	—
381	C₄²	—	146	1	no	—
382	C₄²	—	146	1	no	—
383	C₄²	—	146	2	no	—
384	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
385	C₄²	C₂×D₂₉₂	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×D₂₉₂	1	1	yes	characteristic
390	Q₈	—	292	2	no	—
391	Q₈	—	73	2	no	—
392	Q₈	—	146	2	no	—
393	Q₈	—	146	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	—	292	1	no	—
404	C₂×C₄	—	292	1	no	—
405	C₂×C₄	—	292	2	no	—
406	C₂×C₄	—	146	4	no	—
407	C₂×C₄	—	146	1	no	—
408	C₂×C₄	—	146	1	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	—	146	2	no	—
411	C₂×C₄	—	146	1	no	—
412	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
413	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
414	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₂₉₂	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	—	2	2	no	—
422	C₈	—	2	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	292	1	no	—
425	C₈	—	292	1	no	—
426	C₈	—	292	2	no	—
427	C₈	#14556624	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×D₂₉₂	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	292	2	no	—
439	C₄	—	292	1	no	—
440	C₄	—	292	1	no	—
441	C₄	—	292	2	no	—
442	C₄	—	146	2	no	—
443	C₄	#17988710	1	2	yes	—
444	C₄	#131×D₇₃	1	1	yes	characteristic
445	C₄	#131×D₇₃	1	1	yes	characteristic
446	C₄	C₂×#14556624	1	1	yes	characteristic
447	C₄	#17989387	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	292	2	no	—
450	C₂	#22618627	1	1	yes	characteristic
451	C₂	C₄×#14556624	1	1	yes	characteristic
452	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	C₂×#11924028	C₂×C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1451	D₇₃
hypocenter	C₇₃	#17916
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
3. #22618865	C₂	semidirect
4. #22608783	C₂	semidirect
5. #22608769	C₂	semidirect
6. #22608751	C₂	semidirect
7. #22608745	C₂	semidirect
8. #22608720	C₂	semidirect
10. #22608353	C₂	semidirect
11. C₇₃×#1451	C₂	semidirect
237. #1451	D₇₃	semidirect
238. C₇₃	#17916	semidirect

Maximal subgroups

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

subgroup	index
#22620003	2
C₈×#11924028	2
#22618865	2
#22608783	2
#22608769	2
#22608751	2
#22608745	2
#22608720	2
#22608371	2
#22608353	2
C₇₃×#1451	2
#17916	73