Subgroups — #33055791

Order 18688.

684 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619049	C₂	1	1	yes	maximal, characteristic, complemented
2	#22618971	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14556619	C₂	1	1	yes	maximal, characteristic
4	#22608844	C₂	1	2	yes	maximal, complemented
5	#22608832	C₂	1	2	yes	maximal, complemented
6	#22608820	C₂	1	2	yes	maximal, complemented
7	#22608815	C₂	1	2	yes	maximal, complemented
8	#22608311	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17988314	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#10596831	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₃×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556619	C₄	1	1	yes	characteristic
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₂₉₂	C₂²	1	1	yes	characteristic
15	#17988714	C₂²	1	2	yes	complemented
16	#17988700	C₄	1	2	yes	—
17	#17988689	C₄	1	2	yes	—
18	C₄×#11924017	C₂²	1	2	yes	—
19	C₄×D₅₈₄	C₂²	1	2	yes	—
20	#17988666	—	2	1	no	—
21	#17988666	—	2	1	no	—
22	#17988664	C₂²	1	2	yes	—
23	#17988664	C₂²	1	2	yes	—
24	#17988664	C₂²	1	2	yes	complemented
25	#17988658	—	2	2	no	—
26	#17988643	—	2	1	no	—
27	#17988640	C₂²	1	1	yes	characteristic
28	#17988629	C₄	1	1	yes	characteristic
29	#17988609	—	2	1	no	—
30	#17988593	C₄	1	1	yes	characteristic
31	#17988589	C₄	1	1	yes	characteristic
32	#17988549	—	2	2	no	—
33	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
34	#17988317	C₂²	1	1	yes	characteristic, complemented
35	#17988317	C₂²	1	1	yes	characteristic, complemented
36	#17988314	C₂²	1	2	yes	—
37	#17988314	C₂²	1	2	yes	—
38	#17988314	C₂²	1	1	yes	characteristic, complemented
39	#17988314	C₂²	1	1	yes	characteristic, complemented
40	#17988308	C₂²	1	2	yes	complemented
41	C₈×#10596831	C₂²	1	2	yes	complemented
42	#431×C₇₃	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	2	yes	complemented
46	#334×C₇₃	C₂²	1	2	yes	complemented
47	C₂×#11924028	C₂×C₄	1	1	yes	characteristic
48	C₂²×D₂₉₂	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₇₃	—	2	1	no	—
50	#14556619	—	2	4	no	—
51	C₂×#11924017	C₂×C₄	1	2	yes	—
52	C₂×D₅₈₄	C₂×C₄	1	2	yes	—
53	C₂×#11924011	—	2	2	no	—
54	C₂×#11924011	—	2	2	no	—
55	C₂×#11924011	—	2	2	no	—
56	C₂²×#10596831	—	2	1	no	—
57	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
58	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
59	C₄×D₂₉₂	—	2	1	no	—
60	C₄×D₂₉₂	—	2	1	no	—
61	C₄×D₂₉₂	C₂×C₄	1	2	yes	—
62	C₄×D₂₉₂	C₂×C₄	1	1	yes	characteristic
63	C₄×D₂₉₂	C₂³	1	2	yes	—
64	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₇₃	—	2	1	no	—
66	C₄×C₂²⋊D₇₃	—	2	1	no	—
67	#14556550	C₂×C₄	1	1	yes	characteristic
68	#14556548	—	2	1	no	—
69	C₂×C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
70	C₂×#11924005	—	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	D₄	1	1	yes	characteristic
75	C₄⋊#10596831	D₄	1	1	yes	characteristic
76	#14556520	—	2	2	no	—
77	#14556516	C₂×C₄	1	2	yes	—
78	#14556513	C₂×C₄	1	2	yes	—
79	#14556513	C₂×C₄	1	2	yes	—
80	#14556513	C₂×C₄	1	2	yes	—
81	C₂²⋊#10596831	D₄	1	2	yes	—
82	#14556503	—	2	2	no	—
83	#14556503	—	2	2	no	—
84	#14556503	—	2	2	no	—
85	#14556501	—	2	2	no	—
86	C₄×#10596831	—	2	1	no	—
87	C₄×#10596831	C₂³	1	1	yes	characteristic
88	C₄×#10596831	C₂³	1	1	yes	characteristic
89	C₄×#10596831	C₂³	1	2	yes	—
90	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
91	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₈×C₇₃	—	2	1	no	—
93	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₇₃	—	2	1	no	—
95	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
96	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
98	C₂²⋊C₈×C₇₃	—	2	1	no	—
99	#97×C₇₃	C₂×C₄	1	2	yes	—
100	C₄×C₈×C₇₃	—	2	1	no	—
101	C₄×C₈×C₇₃	C₂³	1	2	yes	—
102	C₂³×D₇₃	—	2	1	no	—
103	#11924028	—	2	2	no	—
104	#11924028	—	2	2	no	—
105	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
106	C₂×D₂₉₂	—	2	2	no	—
107	C₂×D₂₉₂	—	2	2	no	—
108	C₂×D₂₉₂	—	2	1	no	—
109	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
110	C₂×D₂₉₂	C₂²×C₄	1	2	yes	—
111	C₂×C₂²⋊D₇₃	—	2	1	no	—
112	C₂²×Dic₇₃	—	2	1	no	—
113	C₂×C₄×D₇₃	—	2	1	no	—
114	C₂×C₄×D₇₃	—	2	1	no	—
115	C₂×C₄×D₇₃	—	2	2	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	2	2	no	—
118	C₂×C₄×D₇₃	—	8	1	no	—
119	C₂×C₄×D₇₃	—	8	1	no	—
120	#11924017	—	2	4	no	—
121	D₅₈₄	—	2	4	no	—
122	#11924011	—	8	2	no	—
123	#11924011	—	8	2	no	—
124	#11924011	—	8	2	no	—
125	C₂×#10596831	—	2	1	no	—
126	C₂×#10596831	—	2	1	no	—
127	C₂×#10596831	—	4	2	no	—
128	C₂×#10596831	C₂×D₄	1	2	yes	—
129	C₂×#10596831	C₂×D₄	1	2	yes	—
130	C₄⋊Dic₇₃	—	2	1	no	—
131	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
134	#11924007	—	2	1	no	—
135	#11924007	—	2	1	no	—
136	C₂²⋊Dic₇₃	—	2	1	no	—
137	#11924005	—	2	2	no	—
138	#11924005	—	2	1	no	—
139	#11924005	—	2	2	no	—
140	#11924005	—	2	1	no	—
141	C₄×Dic₇₃	—	2	1	no	—
142	C₄×Dic₇₃	—	2	1	no	—
143	C₄×Dic₇₃	—	2	1	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	—	2	2	no	—
148	M₁₆×C₇₃	M₁₆	1	4	yes	complemented
149	C₂×C₈×C₇₃	—	2	1	no	—
150	C₂×C₈×C₇₃	—	2	1	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	8	1	no	—
153	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
155	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₇₃	#41	1	1	yes	characteristic
158	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
159	C₂³×C₇₃	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₇₃	—	2	1	no	—
161	C₂²×D₇₃	—	2	2	no	—
162	C₂²×D₇₃	—	4	2	no	—
163	C₂²×D₇₃	—	8	1	no	—
164	C₂²×D₇₃	—	8	1	no	—
165	C₂×C₄×C₇₃	—	2	1	no	—
166	C₂×C₄×C₇₃	—	2	1	no	—
167	C₂×C₄×C₇₃	—	4	1	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	C₂×M₁₆	1	2	yes	—
172	C₂×C₄×C₇₃	#131	1	2	yes	—
173	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₇₃	—	4	2	no	—
177	C₂×Dic₇₃	—	2	1	no	—
178	C₂×Dic₇₃	—	2	1	no	—
179	C₂×Dic₇₃	—	2	1	no	—
180	C₂×Dic₇₃	—	2	2	no	—
181	C₂×Dic₇₃	—	8	1	no	—
182	D₂₉₂	—	2	1	no	—
183	D₂₉₂	—	2	2	no	—
184	D₂₉₂	—	2	2	no	—
185	D₂₉₂	—	2	1	no	—
186	D₂₉₂	—	4	2	no	—
187	C₄×D₇₃	—	4	1	no	—
188	C₄×D₇₃	—	4	2	no	—
189	C₄×D₇₃	—	4	2	no	—
190	C₄×D₇₃	—	4	1	no	—
191	C₄×D₇₃	—	4	2	no	—
192	C₄×D₇₃	—	8	1	no	—
193	C₄×D₇₃	—	8	2	no	—
194	Dic₁₄₆	—	2	1	no	—
195	Dic₁₄₆	—	2	1	no	—
196	C₈×C₇₃	—	2	2	no	—
197	C₈×C₇₃	—	4	2	no	—
198	C₈×C₇₃	—	4	1	no	—
199	C₈×C₇₃	—	4	1	no	—
200	C₈×C₇₃	C₂×M₁₆	1	4	yes	—
201	#10596831	—	2	2	no	—
202	#10596831	—	2	2	no	—
203	#10596831	—	2	2	no	—
204	#10596831	—	4	1	no	—
205	C₂²×C₇₃	—	2	1	no	—
206	C₂²×C₇₃	—	2	1	no	—
207	C₂²×C₇₃	#436	1	2	yes	—
208	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
209	C₂×D₇₃	—	4	1	no	—
210	C₂×D₇₃	—	4	2	no	—
211	C₂×D₇₃	—	4	2	no	—
212	C₂×D₇₃	—	4	1	no	—
213	C₂×D₇₃	—	4	1	no	—
214	C₂×D₇₃	—	4	2	no	—
215	C₂×D₇₃	—	8	4	no	—
216	C₄×C₇₃	—	2	1	no	—
217	C₄×C₇₃	—	2	1	no	—
218	C₄×C₇₃	—	2	1	no	—
219	C₄×C₇₃	#436	1	2	yes	—
220	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
221	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
222	C₄×C₇₃	#576	1	1	yes	characteristic
223	C₄×C₇₃	#577	1	1	yes	characteristic
224	Dic₇₃	—	4	1	no	—
225	Dic₇₃	—	4	2	no	—
226	Dic₇₃	—	4	1	no	—
227	Dic₇₃	—	4	1	no	—
228	#17893	—	73	1	no	maximal, Sylow
229	C₂×C₇₃	—	2	2	no	—
230	C₂×C₇₃	C₂×#436	1	1	yes	characteristic
231	C₂×C₇₃	#2946	1	1	yes	characteristic
232	C₂×C₇₃	#2956	1	1	yes	characteristic
233	D₇₃	—	8	1	no	—
234	D₇₃	—	8	2	no	—
235	#2989	—	73	1	no	—
236	#2975	—	73	1	no	—
237	C₄×AGL(1,ℤ/8)	—	73	1	no	—
238	#1594	—	73	2	no	—
239	#1592	—	73	2	no	—
240	#1590	—	73	2	no	—
241	#1589	—	73	2	no	—
242	#1565	D₇₃	1	1	yes	characteristic, complemented
243	#1476	—	73	1	no	—
244	C₂×D₄⋊C₈	—	73	1	no	—
245	C₈×M₁₆	—	73	1	no	—
246	C₇₃	#17893	1	1	yes	characteristic, complemented, Sylow
247	C₂×AGL(1,ℤ/8)	—	73	1	no	—
248	C₄×#41	—	73	1	no	—
249	C₂×C₄×D₄	—	73	1	no	—
250	#446	—	73	2	no	—
251	#442	—	73	2	no	—
252	#440	—	73	2	no	—
253	C₄×SD₁₆	—	73	2	no	—
254	C₄×D₈	—	73	2	no	—
255	#436	—	73	2	no	—
256	#436	—	73	2	no	—
257	#436	—	73	2	no	—
258	#436	—	146	1	no	—
259	#436	—	146	1	no	—
260	#435	—	146	2	no	—
261	#432	—	146	1	no	—
262	#431	—	73	1	no	—
263	#431	C₂×D₇₃	1	1	yes	characteristic
264	#428	—	73	1	no	—
265	#423	—	146	1	no	—
266	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
267	#418	—	73	1	no	—
268	#417	—	73	1	no	—
269	#407	—	146	2	no	—
270	C₄×M₁₆	C₂×D₇₃	1	1	yes	characteristic
271	C₂×C₄×C₈	—	73	1	no	—
272	#335	C₂×D₇₃	1	2	yes	complemented
273	#334	C₂×D₇₃	1	2	yes	complemented
274	Q₈⋊C₈	—	73	1	no	—
275	Q₈⋊C₈	—	73	1	no	—
276	D₄⋊C₈	—	73	1	no	—
277	D₄⋊C₈	—	73	2	no	—
278	D₄⋊C₈	—	73	2	no	—
279	D₄⋊C₈	—	73	1	no	—
280	#322	—	73	2	no	—
281	C₈²	—	73	2	no	—
282	C₂×#41	—	73	1	no	—
283	C₂²×D₄	—	73	1	no	—
284	C₂³×C₄	—	146	1	no	—
285	AGL(1,ℤ/8)	—	146	4	no	—
286	C₂×SD₁₆	—	73	2	no	—
287	C₂×D₈	—	73	2	no	—
288	C₂×M₁₆	—	146	2	no	—
289	C₂×M₁₆	—	146	2	no	—
290	C₂×M₁₆	—	146	2	no	—
291	C₂×M₁₆	C₄×D₇₃	1	1	yes	characteristic
292	C₂×M₁₆	C₄×D₇₃	1	1	yes	characteristic
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	146	1	no	—
295	C₄×Q₈	—	73	1	no	—
296	C₄×Q₈	—	73	1	no	—
297	C₄×D₄	—	73	2	no	—
298	C₄×D₄	—	73	1	no	—
299	C₄×D₄	—	73	2	no	—
300	C₄×D₄	—	73	1	no	—
301	C₄×D₄	—	146	1	no	—
302	C₄×D₄	—	146	1	no	—
303	C₄×D₄	—	146	1	no	—
304	C₄×D₄	—	146	1	no	—
305	#117	—	73	1	no	—
306	#117	—	146	1	no	—
307	C₂×C₄⋊C₄	—	73	1	no	—
308	C₂×C₂²⋊C₄	—	146	1	no	—
309	C₂×C₄²	—	146	1	no	—
310	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
311	#107	—	73	2	no	—
312	#106	—	73	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	—	73	1	no	—
315	C₄⋊C₈	—	73	1	no	—
316	C₄⋊C₈	—	146	2	no	—
317	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
318	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
319	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
320	#103	—	73	2	no	—
321	#102	—	73	2	no	—
322	#102	—	73	2	no	—
323	#102	—	73	2	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	C₂²⋊C₈	—	73	2	no	—
326	C₂²⋊C₈	—	146	2	no	—
327	C₂²⋊C₈	—	146	2	no	—
328	C₂²⋊C₈	—	146	2	no	—
329	#97	—	146	2	no	—
330	#97	C₄×D₇₃	1	2	yes	—
331	C₄×C₈	—	2	1	no	—
332	C₄×C₈	—	73	2	no	—
333	C₄×C₈	—	73	1	no	—
334	C₄×C₈	—	73	1	no	—
335	C₄×C₈	—	146	1	no	—
336	C₄×C₈	C₂²×D₇₃	1	2	yes	—
337	C₂⁴	—	146	1	no	—
338	#41	—	146	2	no	—
339	#41	—	146	2	no	—
340	C₂×Q₈	—	73	1	no	—
341	C₂×D₄	—	73	1	no	—
342	C₂×D₄	—	73	2	no	—
343	C₂×D₄	—	146	1	no	—
344	C₂×D₄	—	146	1	no	—
345	C₂×D₄	—	146	2	no	—
346	C₂×D₄	—	146	2	no	—
347	C₂²×C₄	—	584	1	no	—
348	C₂²×C₄	—	584	1	no	—
349	C₂²×C₄	—	146	1	no	—
350	C₂²×C₄	—	146	1	no	—
351	C₂²×C₄	—	146	2	no	—
352	C₂²×C₄	—	146	1	no	—
353	C₂²×C₄	—	146	1	no	—
354	C₂²×C₄	—	146	2	no	—
355	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
356	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
357	C₂²×C₄	#11924029	1	1	yes	characteristic
358	SD₁₆	—	146	4	no	—
359	D₈	—	146	4	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	584	2	no	—
362	M₁₆	—	584	2	no	—
363	M₁₆	—	584	2	no	—
364	M₁₆	#11924011	1	4	yes	complemented
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	8	1	no	—
369	C₂×C₈	—	292	2	no	—
370	C₂×C₈	—	73	2	no	—
371	C₂×C₈	—	73	2	no	—
372	C₂×C₈	—	146	1	no	—
373	C₂×C₈	—	146	1	no	—
374	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
375	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
376	C₄⋊C₄	—	73	1	no	—
377	C₄⋊C₄	—	73	1	no	—
378	C₄⋊C₄	—	73	2	no	—
379	C₄⋊C₄	—	146	1	no	—
380	C₄⋊C₄	—	146	1	no	—
381	C₄⋊C₄	—	146	1	no	—
382	C₂²⋊C₄	—	146	1	no	—
383	C₂²⋊C₄	—	146	2	no	—
384	C₂²⋊C₄	—	146	1	no	—
385	C₂²⋊C₄	—	146	2	no	—
386	C₂²⋊C₄	—	146	1	no	—
387	C₄²	—	146	1	no	—
388	C₄²	—	146	1	no	—
389	C₄²	—	146	1	no	—
390	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
391	C₄²	D₄×D₇₃	1	1	yes	characteristic
392	C₄²	#11924029	1	1	yes	characteristic
393	C₄²	C₂³×D₇₃	1	1	yes	characteristic
394	C₂³	—	292	2	no	—
395	C₂³	—	584	1	no	—
396	C₂³	—	584	1	no	—
397	C₂³	—	146	1	no	—
398	C₂³	—	146	2	no	—
399	C₂³	#14556553	1	1	yes	characteristic
400	Q₈	—	146	1	no	—
401	Q₈	—	146	1	no	—
402	D₄	—	292	2	no	—
403	D₄	—	292	2	no	—
404	D₄	—	146	1	no	—
405	D₄	—	146	2	no	—
406	D₄	—	146	2	no	—
407	D₄	—	146	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	292	1	no	—
412	C₂×C₄	—	292	2	no	—
413	C₂×C₄	—	292	2	no	—
414	C₂×C₄	—	292	1	no	—
415	C₂×C₄	—	292	2	no	—
416	C₂×C₄	—	584	2	no	—
417	C₂×C₄	—	584	1	no	—
418	C₂×C₄	—	584	1	no	—
419	C₂×C₄	—	146	1	no	—
420	C₂×C₄	—	146	1	no	—
421	C₂×C₄	—	146	1	no	—
422	C₂×C₄	—	146	2	no	—
423	C₂×C₄	#14556553	1	1	yes	characteristic
424	C₂×C₄	#14556553	1	1	yes	characteristic
425	C₂×C₄	#14556553	1	1	yes	characteristic
426	C₂×C₄	C₂×#11924011	1	2	yes	—
427	C₂×C₄	#14556599	1	2	yes	—
428	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
430	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	2	no	—
433	C₈	—	4	1	no	—
434	C₈	—	4	1	no	—
435	C₈	—	292	1	no	—
436	C₈	—	146	2	no	—
437	C₈	—	146	2	no	—
438	C₈	—	146	2	no	—
439	C₈	C₂×#11924011	1	4	yes	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	292	2	no	—
443	C₂²	—	292	1	no	—
444	C₂²	—	292	1	no	—
445	C₂²	—	292	2	no	—
446	C₂²	—	292	1	no	—
447	C₂²	—	292	2	no	—
448	C₂²	—	584	4	no	—
449	C₂²	#17988664	1	2	yes	—
450	C₂²	C₂×#14556553	1	1	yes	characteristic
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	292	2	no	—
455	C₄	—	292	1	no	—
456	C₄	—	292	1	no	—
457	C₄	—	292	1	no	—
458	C₄	#17988664	1	2	yes	—
459	C₄	C₂²×#11924011	1	1	yes	characteristic
460	C₄	C₂×#14556599	1	1	yes	characteristic
461	C₄	#17989391	1	1	yes	characteristic
462	C₄	#17989396	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	584	2	no	—
465	C₂	—	584	1	no	—
466	C₂	C₂×#17988664	1	1	yes	characteristic
467	C₂	#22618761	1	1	yes	characteristic
468	C₂	#22618840	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×#1565	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#14556619	C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1565	D₇₃
hypocenter	C₇₃	#17893
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
1. #22619049	C₂	semidirect
2. #22618971	C₂	semidirect
4. #22608844	C₂	semidirect
5. #22608832	C₂	semidirect
6. #22608820	C₂	semidirect
7. #22608815	C₂	semidirect
8. #22608311	C₂	semidirect
9. C₂×#17988314	C₂	semidirect
10. M₁₆×#10596831	C₂	semidirect
11. C₇₃×#1565	C₂	semidirect
15. #17988714	C₂²	semidirect
24. #17988664	C₂²	semidirect
34. #17988317	C₂²	semidirect
35. #17988317	C₂²	semidirect
38. #17988314	C₂²	semidirect
39. #17988314	C₂²	semidirect
40. #17988308	C₂²	semidirect
41. C₈×#10596831	C₂²	semidirect
45. #335×C₇₃	C₂²	semidirect
46. #334×C₇₃	C₂²	semidirect
148. M₁₆×C₇₃	M₁₆	semidirect
242. #1565	D₇₃	semidirect
246. C₇₃	#17893	semidirect
272. #335	C₂×D₇₃	semidirect
273. #334	C₂×D₇₃	semidirect
364. M₁₆	#11924011	semidirect

Maximal subgroups

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

subgroup	index
#22619049	2
#22618971	2
C₄×#14556619	2
#22608844	2
#22608832	2
#22608820	2
#22608815	2
#22608311	2
C₂×#17988314	2
M₁₆×#10596831	2
C₇₃×#1565	2
#17893	73