Subgroups — #33068415

Order 18688.

726 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22619380	C₂	1	2	yes	maximal, complemented
2	C₈×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
3	#22609372	C₂	1	2	yes	maximal, complemented
4	#22609365	C₂	1	2	yes	maximal, complemented
5	#22609322	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609317	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609288	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609283	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#17988340	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608580	C₂	1	2	yes	maximal, complemented
11	C₇₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556611	—	2	2	no	—
13	C₄×#11924028	C₂²	1	1	yes	characteristic
14	#17988806	—	2	2	no	—
15	#17988799	—	2	2	no	—
16	#17988794	C₂²	1	2	yes	—
17	#17988789	C₂²	1	2	yes	—
18	#17988784	C₂²	1	2	yes	—
19	#17988779	C₂²	1	2	yes	—
20	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
22	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
23	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₇₃	—	2	1	no	—
25	C₈×C₂²⋊D₇₃	—	2	1	no	—
26	#17988640	C₂²	1	1	yes	characteristic
27	#17988638	—	2	1	no	—
28	C₂×C₄⋊#10596831	C₂²	1	2	yes	—
29	#17988583	—	2	2	no	—
30	C₄×C₈×D₇₃	—	2	1	no	—
31	#17988340	C₂²	1	1	yes	characteristic
32	#17988340	C₂²	1	1	yes	characteristic
33	#17988340	C₂²	1	2	yes	—
34	#17988333	C₂²	1	2	yes	—
35	#17988333	C₂²	1	2	yes	—
36	#17988331	C₂²	1	2	yes	—
37	#17988331	C₂²	1	2	yes	—
38	#532×C₇₃	C₂²	1	2	yes	—
39	#500×C₇₃	C₂²	1	1	yes	characteristic
40	#493×C₇₃	C₂²	1	1	yes	characteristic
41	#486×C₇₃	C₂²	1	2	yes	—
42	#466×C₇₃	—	2	1	no	—
43	#466×C₇₃	—	2	1	no	—
44	C₄×D₈×C₇₃	—	2	1	no	—
45	C₄×D₈×C₇₃	—	2	1	no	—
46	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
47	C₂×#11924028	D₄	1	1	yes	characteristic
48	#14556611	—	4	8	no	—
49	C₂×#11924018	—	2	2	no	—
50	C₂×#11924016	—	2	2	no	—
51	C₂×#11924015	—	2	2	no	—
52	C₂×#11924013	—	2	2	no	—
53	C₂²×#10596831	—	2	2	no	—
54	C₂×C₈×D₇₃	—	2	1	no	—
55	C₂×C₈×D₇₃	—	2	1	no	—
56	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
57	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
58	C₄×D₂₉₂	D₄	1	1	yes	characteristic
59	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
60	C₄×C₂²⋊D₇₃	—	2	1	no	—
61	C₄×C₂²⋊D₇₃	—	2	1	no	—
62	#14556550	D₄	1	1	yes	characteristic
63	#14556548	—	2	1	no	—
64	C₄²×D₇₃	—	2	1	no	—
65	C₄⋊#10596831	—	2	2	no	—
66	C₄⋊#10596831	C₂³	1	2	yes	—
67	C₄⋊#10596831	C₂³	1	2	yes	—
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	—	2	2	no	—
73	#14556515	—	2	2	no	—
74	#14556512	—	2	2	no	—
75	#14556512	—	2	2	no	—
76	C₂²⋊#10596831	—	2	1	no	—
77	#14556503	—	2	1	no	—
78	#14556503	—	2	1	no	—
79	C₄×#10596831	—	2	1	no	—
80	C₈×Dic₇₃	—	2	1	no	—
81	C₈×Dic₇₃	—	2	1	no	—
82	C₂×#41×C₇₃	—	2	2	no	—
83	C₂×D₈×C₇₃	—	2	1	no	—
84	C₂×D₈×C₇₃	—	2	1	no	—
85	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
87	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
88	#127×C₇₃	C₂³	1	2	yes	—
89	#124×C₇₃	—	2	2	no	—
90	#121×C₇₃	—	2	2	no	—
91	#121×C₇₃	—	2	2	no	—
92	C₄×D₄×C₇₃	—	2	2	no	—
93	C₄×D₄×C₇₃	—	2	2	no	—
94	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
95	#107×C₇₃	—	2	1	no	—
96	#107×C₇₃	—	2	1	no	—
97	#102×C₇₃	—	2	2	no	—
98	#102×C₇₃	—	2	2	no	—
99	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
100	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	#11924028	—	2	2	no	—
104	#11924028	D₈	1	4	yes	complemented
105	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
106	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
107	C₂×C₂²⋊D₇₃	—	2	1	no	—
108	C₂×C₄×D₇₃	—	2	1	no	—
109	C₂×C₄×D₇₃	—	2	1	no	—
110	C₂×C₄×D₇₃	—	2	1	no	—
111	#11924018	—	4	4	no	—
112	#11924016	—	4	4	no	—
113	#11924015	—	4	4	no	—
114	#11924013	—	4	4	no	—
115	C₂×#10596831	—	2	1	no	—
116	C₂×#10596831	—	2	1	no	—
117	C₂×#10596831	—	2	2	no	—
118	C₂×#10596831	—	2	2	no	—
119	C₂×#10596831	—	4	4	no	—
120	C₈×D₇₃	—	4	2	no	—
121	C₈×D₇₃	—	4	2	no	—
122	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
123	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
124	#11924007	—	2	1	no	—
125	#11924007	—	2	1	no	—
126	C₂²⋊Dic₇₃	—	2	1	no	—
127	#11924005	—	2	1	no	—
128	#11924005	—	2	1	no	—
129	C₄×Dic₇₃	—	2	1	no	—
130	C₄×Dic₇₃	—	2	1	no	—
131	C₄×Dic₇₃	—	2	1	no	—
132	#41×C₇₃	—	4	4	no	—
133	#41×C₇₃	—	4	4	no	—
134	C₂×Q₈×C₇₃	—	2	2	no	—
135	C₂×D₄×C₇₃	—	2	2	no	—
136	C₂×D₄×C₇₃	—	2	2	no	—
137	C₂×D₄×C₇₃	—	2	2	no	—
138	C₂×D₄×C₇₃	—	4	2	no	—
139	C₂²×C₄×C₇₃	—	4	2	no	—
140	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
143	D₈×C₇₃	—	4	2	no	—
144	D₈×C₇₃	—	4	2	no	—
145	C₂×C₈×C₇₃	—	2	2	no	—
146	C₂×C₈×C₇₃	—	4	1	no	—
147	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
151	C₄⋊C₄×C₇₃	—	2	2	no	—
152	C₄⋊C₄×C₇₃	—	2	2	no	—
153	C₂²⋊C₄×C₇₃	—	4	2	no	—
154	C₂²⋊C₄×C₇₃	—	4	2	no	—
155	C₄²×C₇₃	C₂×D₄	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	—	4	2	no	—
160	C₂³×C₇₃	#121	1	1	yes	characteristic
161	C₂²×D₇₃	—	2	1	no	—
162	Q₈×C₇₃	—	4	2	no	—
163	Q₈×C₇₃	—	4	2	no	—
164	D₄×C₇₃	—	4	2	no	—
165	D₄×C₇₃	—	4	2	no	—
166	D₄×C₇₃	—	4	2	no	—
167	D₄×C₇₃	—	4	2	no	—
168	D₄×C₇₃	—	8	2	no	—
169	D₄×C₇₃	—	8	4	no	—
170	C₂×C₄×C₇₃	—	2	1	no	—
171	C₂×C₄×C₇₃	—	2	1	no	—
172	C₂×C₄×C₇₃	—	4	1	no	—
173	C₂×C₄×C₇₃	—	4	2	no	—
174	C₂×C₄×C₇₃	—	8	4	no	—
175	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
176	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
177	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
178	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
179	C₂×C₄×C₇₃	#135	1	2	yes	—
180	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
183	C₂²⋊D₇₃	—	2	4	no	—
184	C₂×Dic₇₃	—	2	1	no	—
185	C₂×Dic₇₃	—	2	1	no	—
186	C₂×Dic₇₃	—	2	1	no	—
187	D₂₉₂	—	2	1	no	—
188	D₂₉₂	C₂×D₈	1	2	yes	—
189	C₄×D₇₃	—	2	4	no	—
190	C₄×D₇₃	—	4	2	no	—
191	C₄×D₇₃	—	4	1	no	—
192	C₄×D₇₃	—	4	1	no	—
193	Dic₁₄₆	—	2	1	no	—
194	Dic₁₄₆	C₂×D₈	1	2	yes	—
195	C₈×C₇₃	—	2	1	no	—
196	C₈×C₇₃	—	2	1	no	—
197	C₈×C₇₃	—	2	1	no	—
198	C₈×C₇₃	#135	1	2	yes	complemented
199	#10596831	—	4	2	no	—
200	#10596831	—	4	2	no	—
201	#10596831	—	4	1	no	—
202	#10596831	—	4	1	no	—
203	C₂²×C₇₃	—	2	1	no	—
204	C₂²×C₇₃	—	2	1	no	—
205	C₂²×C₇₃	—	8	2	no	—
206	C₂²×C₇₃	—	8	2	no	—
207	C₂²×C₇₃	—	8	2	no	—
208	C₂²×C₇₃	#466	1	2	yes	—
209	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
210	C₂×D₇₃	—	2	2	no	—
211	C₂×D₇₃	—	4	1	no	—
212	C₂×D₇₃	—	4	1	no	—
213	C₄×C₇₃	—	2	1	no	—
214	C₄×C₇₃	—	2	1	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	—	8	2	no	—
217	C₄×C₇₃	#466	1	2	yes	—
218	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
220	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
221	C₄×C₇₃	#575	1	1	yes	characteristic
222	Dic₇₃	—	2	2	no	—
223	Dic₇₃	—	4	1	no	—
224	Dic₇₃	—	4	1	no	—
225	#19125	—	73	1	no	maximal, Sylow
226	C₂×C₇₃	—	2	2	no	—
227	C₂×C₇₃	—	16	2	no	—
228	C₂×C₇₃	#3035	1	1	yes	characteristic
229	C₂×C₇₃	C₂×#466	1	1	yes	characteristic
230	C₂×C₇₃	#3067	1	1	yes	characteristic
231	D₇₃	—	4	2	no	—
232	#3169	D₇₃	1	1	yes	characteristic, complemented
233	#3035	—	73	2	no	—
234	C₈×#41	—	73	1	no	—
235	#1682	—	73	2	no	—
236	#1681	—	73	2	no	—
237	#1674	—	73	1	no	—
238	#1673	—	73	1	no	—
239	#1668	—	73	1	no	—
240	#1667	—	73	1	no	—
241	C₂×#335	—	73	1	no	—
242	#1540	—	73	2	no	—
243	C₇₃	#19125	1	1	yes	characteristic, complemented, Sylow
244	C₂×#135	—	146	2	no	—
245	#532	C₂×D₇₃	1	2	yes	—
246	C₄×#41	—	73	1	no	—
247	#500	C₂×D₇₃	1	1	yes	characteristic
248	#493	C₂×D₇₃	1	1	yes	characteristic
249	#486	C₂×D₇₃	1	2	yes	—
250	#466	—	2	1	no	—
251	#466	—	2	1	no	—
252	#464	—	146	2	no	—
253	#463	—	146	2	no	—
254	#462	—	73	2	no	—
255	#461	—	73	2	no	—
256	#460	—	73	2	no	—
257	#459	—	73	2	no	—
258	C₈×Q₈	—	73	1	no	—
259	C₈×Q₈	—	73	1	no	—
260	C₄×D₈	—	2	1	no	—
261	C₄×D₈	—	2	1	no	—
262	C₈×D₄	—	73	1	no	—
263	C₈×D₄	—	73	1	no	—
264	C₈×D₄	—	146	1	no	—
265	C₈×D₄	—	146	1	no	—
266	#431	—	73	1	no	—
267	#431	—	146	1	no	—
268	C₂×C₄⋊C₈	—	73	2	no	—
269	#416	—	146	2	no	—
270	C₂×C₄×C₈	—	146	1	no	—
271	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
272	#335	—	73	1	no	—
273	#335	—	73	1	no	—
274	#335	—	73	2	no	—
275	#332	—	73	2	no	—
276	#332	—	73	2	no	—
277	#331	—	73	2	no	—
278	#331	—	73	2	no	—
279	C₂×#41	—	2	2	no	—
280	C₂×#41	—	73	1	no	—
281	#135	—	292	8	no	—
282	C₂×Q₁₆	—	146	2	no	—
283	C₂×SD₁₆	—	146	2	no	—
284	C₂×SD₁₆	—	146	2	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×D₈	—	146	2	no	—
288	C₂²×C₈	—	146	2	no	—
289	C₂²×C₈	—	146	1	no	—
290	C₂²×C₈	—	146	1	no	—
291	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
292	C₂²×C₈	C₂²⋊D₇₃	1	1	yes	characteristic
293	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
294	#127	C₂²×D₇₃	1	2	yes	—
295	#124	—	2	2	no	—
296	#121	—	2	2	no	—
297	#121	—	2	2	no	—
298	C₄×Q₈	—	73	1	no	—
299	C₄×Q₈	—	73	1	no	—
300	C₄×D₄	—	2	2	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	73	1	no	—
303	C₄×D₄	—	73	1	no	—
304	C₄×D₄	—	146	1	no	—
305	C₄×D₄	—	146	1	no	—
306	#117	—	73	1	no	—
307	#117	—	146	1	no	—
308	C₂×C₄²	—	146	1	no	—
309	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
310	#107	—	2	1	no	—
311	#107	—	2	1	no	—
312	C₄⋊C₈	—	73	1	no	—
313	C₄⋊C₈	—	73	1	no	—
314	C₄⋊C₈	—	73	2	no	—
315	C₄⋊C₈	—	73	2	no	—
316	C₄⋊C₈	—	146	1	no	—
317	C₄⋊C₈	—	146	1	no	—
318	C₄⋊C₈	—	146	2	no	—
319	#103	—	146	2	no	—
320	#103	—	146	2	no	—
321	#102	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	146	2	no	—
324	#102	—	146	2	no	—
325	C₂²⋊C₈	—	146	1	no	—
326	C₂²⋊C₈	—	146	1	no	—
327	C₂²⋊C₈	—	146	1	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	—	4	4	no	—
336	#41	—	4	4	no	—
337	#41	—	73	4	no	—
338	#41	—	146	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	73	1	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	4	2	no	—
345	C₂×D₄	—	73	1	no	—
346	C₂×D₄	—	146	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	146	1	no	—
349	C₂²×C₄	—	146	1	no	—
350	C₂²×C₄	—	146	1	no	—
351	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
352	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
353	C₂²×C₄	#11924027	1	1	yes	characteristic
354	Q₁₆	—	292	4	no	—
355	SD₁₆	—	292	4	no	—
356	SD₁₆	—	292	4	no	—
357	D₈	—	4	2	no	—
358	D₈	—	4	2	no	—
359	D₈	—	292	4	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	4	1	no	—
362	C₂×C₈	—	292	2	no	—
363	C₂×C₈	—	292	4	no	—
364	C₂×C₈	—	292	2	no	—
365	C₂×C₈	—	146	2	no	—
366	C₂×C₈	—	146	2	no	—
367	C₂×C₈	—	146	1	no	—
368	C₂×C₈	—	146	1	no	—
369	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
370	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
371	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
372	C₂×C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	73	1	no	—
376	C₄⋊C₄	—	73	1	no	—
377	C₄⋊C₄	—	146	1	no	—
378	C₄⋊C₄	—	146	1	no	—
379	C₂²⋊C₄	—	4	2	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	146	1	no	—
382	C₂²⋊C₄	—	146	1	no	—
383	C₂²⋊C₄	—	146	1	no	—
384	C₄²	—	146	1	no	—
385	C₄²	—	146	1	no	—
386	C₄²	—	146	1	no	—
387	C₄²	D₄×D₇₃	1	1	yes	characteristic
388	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
389	C₄²	#11924027	1	1	yes	characteristic
390	C₄²	C₂³×D₇₃	1	1	yes	characteristic
391	C₂³	—	4	2	no	—
392	C₂³	—	146	1	no	—
393	C₂³	#14556562	1	1	yes	characteristic
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	73	2	no	—
397	Q₈	—	146	1	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	8	4	no	—
404	D₄	—	73	2	no	—
405	D₄	—	146	4	no	—
406	D₄	—	146	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	8	4	no	—
412	C₂×C₄	—	292	2	no	—
413	C₂×C₄	—	292	1	no	—
414	C₂×C₄	—	292	1	no	—
415	C₂×C₄	—	146	1	no	—
416	C₂×C₄	—	146	1	no	—
417	C₂×C₄	—	146	1	no	—
418	C₂×C₄	—	146	4	no	—
419	C₂×C₄	#14556562	1	1	yes	characteristic
420	C₂×C₄	#14556562	1	1	yes	characteristic
421	C₂×C₄	#14556562	1	1	yes	characteristic
422	C₂×C₄	D₈×D₇₃	1	2	yes	—
423	C₂×C₄	#14556610	1	2	yes	—
424	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
425	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
426	C₂×C₄	C₂×#11924027	1	1	yes	characteristic
427	C₈	—	2	1	no	—
428	C₈	—	2	1	no	—
429	C₈	—	2	1	no	—
430	C₈	—	292	1	no	—
431	C₈	—	292	2	no	—
432	C₈	—	292	2	no	—
433	C₈	—	292	1	no	—
434	C₈	#14556611	1	2	yes	complemented
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	292	1	no	—
441	C₂²	—	292	1	no	—
442	C₂²	—	146	2	no	—
443	C₂²	#17988820	1	2	yes	—
444	C₂²	C₂×#14556562	1	1	yes	characteristic
445	C₄	—	2	1	no	—
446	C₄	—	2	1	no	—
447	C₄	—	2	1	no	—
448	C₄	—	8	2	no	—
449	C₄	—	292	1	no	—
450	C₄	—	292	1	no	—
451	C₄	—	146	2	no	—
452	C₄	#17988820	1	2	yes	—
453	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
454	C₄	C₂×#14556610	1	1	yes	characteristic
455	C₄	C₂×#14556611	1	1	yes	characteristic
456	C₄	#17989385	1	1	yes	characteristic
457	C₂	—	2	2	no	—
458	C₂	—	16	2	no	—
459	C₂	—	292	2	no	—
460	C₂	#22619380	1	1	yes	characteristic
461	C₂	C₂×#17988820	1	1	yes	characteristic
462	C₂	#22619647	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14556562
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#3169	C₂
socle	C₂²×C₇₃	C₂×#121
hypercenter	#3169	D₇₃
hypocenter	C₇₃	#19125
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #22619380	C₂	semidirect
2. C₈×#11924028	C₂	semidirect
3. #22609372	C₂	semidirect
4. #22609365	C₂	semidirect
5. #22609322	C₂	semidirect
6. #22609317	C₂	semidirect
7. #22609288	C₂	semidirect
8. #22609283	C₂	semidirect
9. C₂×#17988340	C₂	semidirect
10. #22608580	C₂	semidirect
11. C₇₃×#3169	C₂	semidirect
104. #11924028	D₈	semidirect
198. C₈×C₇₃	#135	semidirect
232. #3169	D₇₃	semidirect
243. C₇₃	#19125	semidirect
434. C₈	#14556611	semidirect

Maximal subgroups

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

subgroup	index
#22619380	2
C₈×#11924028	2
#22609372	2
#22609365	2
#22609322	2
#22609317	2
#22609288	2
#22609283	2
C₂×#17988340	2
#22608580	2
C₇₃×#3169	2
#19125	73