Subgroups — #33057234

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	#22619991	C₂	1	1	yes	maximal, characteristic
2	#22619056	C₂	1	1	yes	maximal, characteristic, complemented
3	#22618997	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608836	C₂	1	2	yes	maximal, complemented
5	#22608770	C₂	1	2	yes	maximal, complemented
6	#22608757	C₂	1	2	yes	maximal, complemented
7	#22608752	C₂	1	2	yes	maximal, complemented
8	#22608719	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608383	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608223	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	#17989137	C₂²	1	1	yes	characteristic
13	#17988911	C₄	1	2	yes	—
14	#17988882	C₄	1	1	yes	characteristic
15	#17988877	C₄	1	1	yes	characteristic
16	#17988787	C₄	1	1	yes	characteristic
17	#17988782	C₄	1	1	yes	characteristic
18	#17988732	C₄	1	2	yes	—
19	#17988718	C₂²	1	2	yes	—
20	C₄×#11924015	C₂²	1	2	yes	—
21	C₄×#11924013	C₂²	1	2	yes	—
22	#17988666	—	2	1	no	—
23	#17988664	C₂²	1	2	yes	—
24	#17988659	—	2	2	no	—
25	C₈×D₂₉₂	—	2	1	no	—
26	D₄×#10596831	C₂²	1	2	yes	—
27	#17988652	C₂²	1	2	yes	—
28	#17988644	—	2	1	no	—
29	#17988640	C₂²	1	1	yes	characteristic
30	#17988640	C₂²	1	1	yes	characteristic
31	#17988611	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊#10596831	—	2	1	no	—
33	#17988552	—	2	2	no	—
34	#17988339	C₂²	1	2	yes	—
35	#17988337	C₂²	1	2	yes	—
36	#17988316	C₂²	1	2	yes	—
37	#17988316	C₂²	1	2	yes	—
38	#17988309	C₂²	1	2	yes	—
39	#17988309	C₂²	1	2	yes	—
40	C₄×#41×C₇₃	C₂²	1	1	yes	characteristic
41	#431×C₇₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
43	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
44	Q₈⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
45	D₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
46	D₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	—	2	1	no	—
48	C₂×#11924015	C₂×C₄	1	2	yes	—
49	C₂×#11924013	C₂×C₄	1	2	yes	—
50	C₂×#11924012	—	2	1	no	—
51	C₂×#11924011	—	2	2	no	—
52	C₂²×#10596831	—	2	2	no	—
53	C₂×C₈×D₇₃	—	2	2	no	—
54	#14556591	C₂×C₄	1	1	yes	characteristic
55	#14556588	C₂×C₄	1	1	yes	characteristic
56	#14556579	—	2	1	no	—
57	#14556565	—	2	1	no	—
58	#14556565	C₂×C₄	1	2	yes	—
59	C₄×D₂₉₂	—	2	1	no	—
60	C₄×D₂₉₂	C₂³	1	2	yes	—
61	#14556524	C₂×C₄	1	2	yes	—
62	#14556522	C₂×C₄	1	2	yes	—
63	C₄⋊#10596831	—	2	2	no	—
64	C₄⋊#10596831	—	2	1	no	—
65	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
67	C₄⋊#10596831	D₄	1	1	yes	characteristic
68	C₄⋊#10596831	D₄	1	1	yes	characteristic
69	C₄⋊#10596831	C₂³	1	2	yes	—
70	#14556515	C₂×C₄	1	2	yes	—
71	#14556512	C₂×C₄	1	2	yes	—
72	#14556511	C₂×C₄	1	2	yes	—
73	#14556511	C₂×C₄	1	2	yes	—
74	C₂²⋊#10596831	—	2	2	no	—
75	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
76	C₂²⋊#10596831	D₄	1	2	yes	—
77	#14556503	—	2	2	no	—
78	#14556503	—	2	2	no	—
79	#14556502	—	2	2	no	—
80	C₄×#10596831	C₂³	1	2	yes	—
81	C₄×#10596831	C₂³	1	2	yes	—
82	C₂×#41×C₇₃	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₈×C₇₃	—	2	1	no	—
84	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
85	C₄×Q₈×C₇₃	C₂³	1	1	yes	characteristic
86	C₄×D₄×C₇₃	—	2	1	no	—
87	C₄×D₄×C₇₃	—	2	1	no	—
88	C₄×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
90	#117×C₇₃	—	2	1	no	—
91	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₇₃	—	2	1	no	—
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
96	C₂²⋊C₈×C₇₃	—	2	1	no	—
97	C₄×C₈×C₇₃	—	2	1	no	—
98	C₄×C₈×C₇₃	—	2	1	no	—
99	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
101	#11924028	—	8	1	no	—
102	#11924028	—	8	1	no	—
103	C₂×Dic₁₄₆	—	2	1	no	—
104	C₂×D₂₉₂	—	2	1	no	—
105	C₂×D₂₉₂	—	2	1	no	—
106	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
107	C₂×C₂²⋊D₇₃	—	2	2	no	—
108	C₂×C₄×D₇₃	—	2	2	no	—
109	#11924015	—	4	2	no	—
110	#11924013	—	2	4	no	—
111	#11924012	—	8	1	no	—
112	#11924011	—	8	2	no	—
113	C₂×#10596831	—	2	2	no	—
114	C₂×#10596831	—	8	2	no	—
115	C₂×#10596831	C₂²×C₄	1	2	yes	—
116	C₂×#10596831	C₂²×C₄	1	2	yes	—
117	C₂×#10596831	C₂×D₄	1	2	yes	—
118	C₂×#10596831	C₂×D₄	1	2	yes	—
119	C₈×D₇₃	—	8	2	no	—
120	C₄⋊Dic₇₃	—	2	1	no	—
121	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
122	#11924005	—	2	2	no	—
123	#11924005	—	2	2	no	—
124	#41×C₇₃	—	2	2	no	—
125	#41×C₇₃	—	4	1	no	—
126	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₇₃	—	2	1	no	—
128	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	—	2	1	no	—
130	C₂²×C₄×C₇₃	—	2	1	no	—
131	C₂²×C₄×C₇₃	—	2	1	no	—
132	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
135	C₂×C₈×C₇₃	—	2	1	no	—
136	C₂×C₈×C₇₃	—	2	1	no	—
137	C₂×C₈×C₇₃	—	2	1	no	—
138	C₂×C₈×C₇₃	—	2	1	no	—
139	C₂×C₈×C₇₃	—	4	2	no	—
140	C₄⋊C₄×C₇₃	—	2	1	no	—
141	C₄⋊C₄×C₇₃	—	2	1	no	—
142	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
143	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₂²⋊C₄×C₇₃	—	2	1	no	—
145	C₂²⋊C₄×C₇₃	—	2	1	no	—
146	C₂²⋊C₄×C₇₃	—	2	1	no	—
147	C₄²×C₇₃	—	2	1	no	—
148	C₄²×C₇₃	—	2	1	no	—
149	C₄²×C₇₃	—	2	1	no	—
150	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₇₃	#41	1	1	yes	characteristic
153	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
154	C₂³×C₇₃	—	2	1	no	—
155	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
156	C₂²×D₇₃	—	2	2	no	—
157	Q₈×C₇₃	—	2	1	no	—
158	Q₈×C₇₃	—	2	1	no	—
159	D₄×C₇₃	—	2	1	no	—
160	D₄×C₇₃	—	4	2	no	—
161	D₄×C₇₃	#131	1	2	yes	—
162	C₂×C₄×C₇₃	—	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	2	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	—	4	2	no	—
171	C₂×C₄×C₇₃	—	4	1	no	—
172	C₂×C₄×C₇₃	—	4	1	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
176	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
177	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₇₃	—	8	2	no	—
181	C₂×Dic₇₃	—	2	2	no	—
182	D₂₉₂	—	2	2	no	—
183	D₂₉₂	—	2	2	no	—
184	D₂₉₂	—	4	2	no	—
185	D₂₉₂	—	8	1	no	—
186	C₄×D₇₃	—	4	2	no	—
187	C₄×D₇₃	—	4	2	no	—
188	Dic₁₄₆	—	8	1	no	—
189	C₈×C₇₃	—	4	1	no	—
190	C₈×C₇₃	—	4	1	no	—
191	C₈×C₇₃	—	4	1	no	—
192	C₈×C₇₃	—	4	1	no	—
193	#10596831	—	2	2	no	—
194	#10596831	—	2	2	no	—
195	#10596831	—	2	2	no	—
196	#10596831	—	2	2	no	—
197	#10596831	—	4	2	no	—
198	C₂²×C₇₃	—	2	1	no	—
199	C₂²×C₇₃	—	2	2	no	—
200	C₂²×C₇₃	—	2	1	no	—
201	C₂²×C₇₃	—	2	1	no	—
202	C₂²×C₇₃	—	4	1	no	—
203	C₂²×C₇₃	—	4	1	no	—
204	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
205	C₂×D₇₃	—	4	2	no	—
206	C₂×D₇₃	—	4	2	no	—
207	C₂×D₇₃	—	4	2	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	—	4	1	no	—
212	C₄×C₇₃	—	4	1	no	—
213	C₄×C₇₃	—	4	1	no	—
214	C₄×C₇₃	#444	1	2	yes	—
215	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
216	C₄×C₇₃	#568	1	1	yes	characteristic
217	C₄×C₇₃	#576	1	1	yes	characteristic
218	C₄×C₇₃	#577	1	1	yes	characteristic
219	Dic₇₃	—	4	2	no	—
220	#18022	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	4	1	no	—
222	C₂×C₇₃	—	4	2	no	—
223	C₂×C₇₃	#2933	1	1	yes	characteristic
224	C₂×C₇₃	#2946	1	1	yes	characteristic
225	C₂×C₇₃	C₂×#444	1	1	yes	characteristic
226	D₇₃	—	8	2	no	—
227	#3106	—	73	1	no	—
228	#2990	—	73	1	no	—
229	#2979	—	73	1	no	—
230	#1592	—	73	2	no	—
231	#1582	—	73	2	no	—
232	#1581	—	73	2	no	—
233	#1580	—	73	2	no	—
234	#1574	—	73	1	no	—
235	#1492	—	73	1	no	—
236	#1476	D₇₃	1	1	yes	characteristic, complemented
237	#1452	—	73	1	no	—
238	C₇₃	#18022	1	1	yes	characteristic, complemented, Sylow
239	#532	—	73	1	no	—
240	C₄×#41	C₂×D₇₃	1	1	yes	characteristic
241	#482	—	73	2	no	—
242	#477	—	73	1	no	—
243	#476	—	73	1	no	—
244	#460	—	73	1	no	—
245	#459	—	73	1	no	—
246	#449	—	73	2	no	—
247	#446	—	73	2	no	—
248	C₄×SD₁₆	—	73	2	no	—
249	C₄×D₈	—	73	2	no	—
250	#436	—	73	2	no	—
251	#436	—	146	1	no	—
252	#435	—	146	2	no	—
253	C₈×D₄	—	73	2	no	—
254	C₈×D₄	—	73	2	no	—
255	C₈×D₄	—	146	1	no	—
256	#432	—	146	1	no	—
257	#431	—	73	1	no	—
258	#431	—	73	1	no	—
259	#431	C₂×D₇₃	1	1	yes	characteristic
260	#423	—	73	1	no	—
261	C₂×C₄⋊C₈	—	146	1	no	—
262	#408	—	146	2	no	—
263	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
264	#335	—	73	2	no	—
265	#334	—	73	2	no	—
266	Q₈⋊C₈	C₂×D₇₃	1	1	yes	characteristic
267	Q₈⋊C₈	C₂×D₇₃	1	1	yes	characteristic
268	D₄⋊C₈	—	73	2	no	—
269	D₄⋊C₈	—	73	2	no	—
270	D₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
271	D₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
272	#322	—	73	2	no	—
273	#322	—	73	2	no	—
274	C₂×#41	—	146	1	no	—
275	C₂×#41	C₄×D₇₃	1	1	yes	characteristic
276	C₂×SD₁₆	—	73	2	no	—
277	C₂×D₈	—	73	2	no	—
278	C₂×M₁₆	—	146	2	no	—
279	C₂×M₁₆	—	146	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	146	2	no	—
282	C₂²×C₈	—	146	2	no	—
283	C₄⋊Q₈	—	73	1	no	—
284	#127	—	73	1	no	—
285	#124	—	146	1	no	—
286	#121	—	73	2	no	—
287	#121	—	146	1	no	—
288	C₄×Q₈	C₄×D₇₃	1	1	yes	characteristic
289	C₄×Q₈	C₂²×D₇₃	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	73	2	no	—
293	C₄×D₄	—	146	1	no	—
294	C₄×D₄	C₄×D₇₃	1	1	yes	characteristic
295	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
296	#117	—	2	1	no	—
297	#117	C₄×D₇₃	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
300	#107	—	73	2	no	—
301	#106	—	73	2	no	—
302	C₄⋊C₈	—	73	1	no	—
303	C₄⋊C₈	—	73	1	no	—
304	C₄⋊C₈	—	73	1	no	—
305	C₄⋊C₈	—	73	1	no	—
306	C₄⋊C₈	—	73	2	no	—
307	C₄⋊C₈	—	146	2	no	—
308	C₄⋊C₈	—	146	1	no	—
309	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
310	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
311	#103	—	73	2	no	—
312	#102	—	73	2	no	—
313	#102	—	73	2	no	—
314	#102	—	73	2	no	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	73	2	no	—
317	C₂²⋊C₈	—	73	2	no	—
318	C₂²⋊C₈	—	146	2	no	—
319	C₂²⋊C₈	—	146	2	no	—
320	C₂²⋊C₈	—	146	2	no	—
321	#97	—	146	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	—	73	2	no	—
325	C₄×C₈	—	73	2	no	—
326	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
327	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
328	#41	—	2	2	no	—
329	#41	—	4	1	no	—
330	#41	—	584	1	no	—
331	#41	—	584	1	no	—
332	C₂×Q₈	—	146	1	no	—
333	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	73	2	no	—
336	C₂×D₄	—	146	2	no	—
337	C₂×D₄	—	146	1	no	—
338	C₂×D₄	—	146	1	no	—
339	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	146	2	no	—
344	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
345	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
346	C₂²×C₄	#11924027	1	1	yes	characteristic
347	SD₁₆	—	292	2	no	—
348	D₈	—	146	4	no	—
349	M₁₆	—	584	2	no	—
350	M₁₆	—	584	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	4	2	no	—
356	C₂×C₈	—	584	2	no	—
357	C₂×C₈	—	584	2	no	—
358	C₂×C₈	—	73	2	no	—
359	C₂×C₈	—	73	2	no	—
360	C₂×C₈	—	73	2	no	—
361	C₂×C₈	—	73	2	no	—
362	C₂×C₈	—	146	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	73	2	no	—
366	C₄⋊C₄	—	146	1	no	—
367	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	1	no	—
372	C₂²⋊C₄	—	146	2	no	—
373	C₂²⋊C₄	—	146	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
378	C₄²	D₄×D₇₃	1	1	yes	characteristic
379	C₄²	#11924027	1	1	yes	characteristic
380	C₄²	C₂³×D₇₃	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	146	2	no	—
383	C₂³	#14556551	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	2	1	no	—
386	Q₈	—	584	1	no	—
387	D₄	—	2	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	292	2	no	—
390	D₄	—	584	1	no	—
391	D₄	—	584	2	no	—
392	D₄	—	146	2	no	—
393	D₄	—	146	2	no	—
394	D₄	#14556597	1	2	yes	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	292	2	no	—
408	C₂×C₄	—	292	2	no	—
409	C₂×C₄	—	146	2	no	—
410	C₂×C₄	#14556551	1	1	yes	characteristic
411	C₂×C₄	#14556551	1	1	yes	characteristic
412	C₂×C₄	#14556551	1	1	yes	characteristic
413	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
414	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
415	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	1	no	—
420	C₈	—	292	2	no	—
421	C₈	—	146	2	no	—
422	C₈	—	146	2	no	—
423	C₈	—	146	2	no	—
424	C₈	—	146	2	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	292	2	no	—
432	C₂²	—	292	2	no	—
433	C₂²	—	292	2	no	—
434	C₂²	C₂×#14556551	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	292	2	no	—
442	C₄	#17988706	1	2	yes	—
443	C₄	C₂×#14556597	1	1	yes	characteristic
444	C₄	#17989353	1	1	yes	characteristic
445	C₄	#17989389	1	1	yes	characteristic
446	C₄	#17989394	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	4	2	no	—
449	C₂	—	584	2	no	—
450	C₂	#22618652	1	1	yes	characteristic
451	C₂	#22618766	1	1	yes	characteristic
452	C₂	C₂×#17988706	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1476	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	#22619991	C₂
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1476	D₇₃
hypocenter	C₇₃	#18022
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1476

Complements

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

N	H ≅ G/N	type
2. #22619056	C₂	semidirect
3. #22618997	C₂	semidirect
4. #22608836	C₂	semidirect
5. #22608770	C₂	semidirect
6. #22608757	C₂	semidirect
7. #22608752	C₂	semidirect
8. #22608719	C₂	semidirect
9. #22608383	C₂	semidirect
10. #22608223	C₂	semidirect
11. C₇₃×#1476	C₂	semidirect
236. #1476	D₇₃	semidirect
238. C₇₃	#18022	semidirect

Maximal subgroups

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

subgroup	index
#22619991	2
#22619056	2
#22618997	2
#22608836	2
#22608770	2
#22608757	2
#22608752	2
#22608719	2
#22608383	2
#22608223	2
C₇₃×#1476	2
#18022	73