Subgroups — #33069896

Order 18688.

716 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22620359	C₂	1	1	yes	maximal, characteristic, complemented
2	#22620083	C₂	1	2	yes	maximal, complemented
3	C₈×#11924028	C₂	1	1	yes	maximal, characteristic, complemented
4	#22609302	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609297	C₂	1	1	yes	maximal, characteristic, complemented
6	#22609292	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609287	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609280	C₂	1	2	yes	maximal, complemented
9	#22609273	C₂	1	2	yes	maximal, complemented
10	#22608637	C₂	1	2	yes	maximal, complemented
11	C₇₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556613	—	2	1	no	—
13	C₂×#14556613	—	2	1	no	—
14	#17989137	C₂²	1	2	yes	—
15	C₄×#11924028	C₂²	1	1	yes	characteristic
16	#17988971	—	2	1	no	—
17	#17988971	—	2	1	no	—
18	#17988967	C₂²	1	1	yes	characteristic
19	#17988964	C₂²	1	1	yes	characteristic
20	#17988960	C₂²	1	2	yes	—
21	#17988912	—	2	2	no	—
22	#17988873	C₂²	1	2	yes	—
23	#17988868	C₂²	1	2	yes	—
24	#17988788	C₂²	1	2	yes	—
25	#17988783	C₂²	1	2	yes	—
26	#17988734	—	2	2	no	—
27	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₄₆	C₂²	1	1	yes	characteristic
29	#17988700	—	2	2	no	—
30	#17988689	—	2	2	no	—
31	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
32	C₈×D₂₉₂	C₂²	1	1	yes	characteristic
33	C₈×C₂²⋊D₇₃	—	2	1	no	—
34	C₈×C₂²⋊D₇₃	—	2	1	no	—
35	#17988640	C₂²	1	1	yes	characteristic
36	#17988638	—	2	1	no	—
37	C₄×C₈×D₇₃	—	2	1	no	—
38	#17988332	C₂²	1	2	yes	—
39	#17988332	C₂²	1	2	yes	—
40	#17988330	C₂²	1	2	yes	—
41	#17988330	C₂²	1	2	yes	—
42	#432×C₇₃	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
44	#335×C₇₃	C₂²	1	1	yes	characteristic
45	#335×C₇₃	C₂²	1	1	yes	characteristic
46	#334×C₇₃	C₂²	1	2	yes	—
47	C₂×#11924028	—	2	2	no	—
48	C₂×#11924028	D₄	1	1	yes	characteristic
49	#14556613	—	4	4	no	—
50	#14556613	—	4	4	no	—
51	C₂×Dic₂₉₂	—	2	1	no	—
52	C₂×Dic₂₉₂	—	2	1	no	—
53	C₂×#11924017	—	2	2	no	—
54	C₂×#11924017	—	2	2	no	—
55	C₂×#11924017	—	2	2	no	—
56	C₂×D₅₈₄	—	2	2	no	—
57	C₂×D₅₈₄	—	2	1	no	—
58	C₂×D₅₈₄	—	2	1	no	—
59	C₂×C₈×D₇₃	—	2	1	no	—
60	C₂×C₈×D₇₃	—	2	1	no	—
61	#14556591	C₂³	1	2	yes	—
62	#14556588	C₂³	1	2	yes	—
63	#14556579	—	2	2	no	—
64	#14556565	—	2	2	no	—
65	#14556565	—	2	2	no	—
66	C₄×Dic₁₄₆	D₄	1	1	yes	characteristic
67	C₄×Dic₁₄₆	C₂³	1	1	yes	characteristic
68	C₄×D₂₉₂	—	2	2	no	—
69	C₄×D₂₉₂	—	2	2	no	—
70	C₄×D₂₉₂	D₄	1	1	yes	characteristic
71	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
72	C₄×C₂²⋊D₇₃	—	2	1	no	—
73	C₄×C₂²⋊D₇₃	—	2	1	no	—
74	#14556550	D₄	1	1	yes	characteristic
75	#14556548	—	2	1	no	—
76	C₄²×D₇₃	—	2	1	no	—
77	#14556525	—	2	2	no	—
78	#14556523	—	2	2	no	—
79	C₄⋊#10596831	C₂³	1	1	yes	characteristic
80	C₄⋊#10596831	C₂³	1	1	yes	characteristic
81	#14556520	—	2	1	no	—
82	#14556520	—	2	1	no	—
83	#14556516	—	2	2	no	—
84	#14556513	—	2	2	no	—
85	#14556513	—	2	2	no	—
86	#14556513	—	2	2	no	—
87	C₂²⋊#10596831	—	2	1	no	—
88	#14556503	—	2	1	no	—
89	#14556503	—	2	1	no	—
90	C₄×#10596831	—	2	1	no	—
91	C₈×Dic₇₃	—	2	1	no	—
92	C₈×Dic₇₃	—	2	1	no	—
93	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
97	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
98	C₂²⋊C₈×C₇₃	—	2	2	no	—
99	#97×C₇₃	—	2	2	no	—
100	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
101	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
102	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
104	#11924028	—	2	2	no	—
105	#11924028	—	2	2	no	—
106	#11924028	—	4	4	no	—
107	#11924028	—	4	4	no	—
108	C₂×Dic₁₄₆	—	2	2	no	—
109	C₂×Dic₁₄₆	C₂×D₄	1	1	yes	characteristic
110	C₂×D₂₉₂	—	2	2	no	—
111	C₂×D₂₉₂	—	2	2	no	—
112	C₂×D₂₉₂	—	2	2	no	—
113	C₂×D₂₉₂	C₂×D₄	1	1	yes	characteristic
114	C₂×C₂²⋊D₇₃	—	2	1	no	—
115	C₂×C₂²⋊D₇₃	—	4	2	no	—
116	C₂×C₄×D₇₃	—	2	1	no	—
117	C₂×C₄×D₇₃	—	2	1	no	—
118	C₂×C₄×D₇₃	—	2	1	no	—
119	C₂×C₄×D₇₃	—	4	2	no	—
120	Dic₂₉₂	—	4	2	no	—
121	Dic₂₉₂	—	4	2	no	—
122	#11924017	—	4	4	no	—
123	#11924017	—	4	4	no	—
124	#11924017	—	4	4	no	—
125	D₅₈₄	—	4	2	no	—
126	D₅₈₄	—	4	4	no	—
127	D₅₈₄	—	4	2	no	—
128	C₂×#10596831	—	2	1	no	—
129	C₂×#10596831	—	2	1	no	—
130	C₈×D₇₃	—	4	2	no	—
131	C₈×D₇₃	—	4	2	no	—
132	C₄⋊Dic₇₃	—	2	2	no	—
133	C₄⋊Dic₇₃	—	2	2	no	—
134	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
135	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
136	#11924007	—	2	1	no	—
137	#11924007	—	2	1	no	—
138	C₂²⋊Dic₇₃	—	2	1	no	—
139	#11924005	—	2	1	no	—
140	#11924005	—	2	1	no	—
141	#11924005	—	4	2	no	—
142	#11924005	—	4	2	no	—
143	C₄×Dic₇₃	—	2	1	no	—
144	C₄×Dic₇₃	—	2	1	no	—
145	C₄×Dic₇₃	—	2	1	no	—
146	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
149	C₂×C₈×C₇₃	—	2	2	no	—
150	C₂×C₈×C₇₃	—	2	2	no	—
151	C₂×C₈×C₇₃	—	2	2	no	—
152	C₂×C₈×C₇₃	—	2	2	no	—
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	C₂×D₄	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	#121	1	1	yes	characteristic
162	C₂²×D₇₃	—	2	1	no	—
163	C₂²×D₇₃	—	4	2	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	1	no	—
168	C₂×C₄×C₇₃	—	4	1	no	—
169	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
170	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
171	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
172	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₇₃	—	2	4	no	—
176	C₂²⋊D₇₃	—	8	4	no	—
177	C₂×Dic₇₃	—	2	1	no	—
178	C₂×Dic₇₃	—	2	1	no	—
179	C₂×Dic₇₃	—	2	1	no	—
180	C₂×Dic₇₃	—	4	2	no	—
181	D₂₉₂	—	2	1	no	—
182	D₂₉₂	—	4	2	no	—
183	D₂₉₂	—	4	2	no	—
184	D₂₉₂	—	4	2	no	—
185	D₂₉₂	—	4	2	no	—
186	D₂₉₂	—	8	2	no	—
187	D₂₉₂	#135	1	2	yes	complemented
188	C₄×D₇₃	—	2	4	no	—
189	C₄×D₇₃	—	4	2	no	—
190	C₄×D₇₃	—	4	1	no	—
191	C₄×D₇₃	—	4	1	no	—
192	C₄×D₇₃	—	8	4	no	—
193	Dic₁₄₆	—	2	1	no	—
194	Dic₁₄₆	—	4	2	no	—
195	Dic₁₄₆	—	4	2	no	—
196	Dic₁₄₆	#135	1	2	yes	complemented
197	C₈×C₇₃	—	2	1	no	—
198	C₈×C₇₃	—	2	1	no	—
199	C₈×C₇₃	—	4	2	no	—
200	C₈×C₇₃	—	4	2	no	—
201	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
202	C₈×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
203	#10596831	—	4	1	no	—
204	#10596831	—	4	1	no	—
205	C₂²×C₇₃	—	2	1	no	—
206	C₂²×C₇₃	—	2	1	no	—
207	C₂²×C₇₃	—	2	1	no	—
208	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
209	C₂×D₇₃	—	2	2	no	—
210	C₂×D₇₃	—	4	1	no	—
211	C₂×D₇₃	—	4	1	no	—
212	C₂×D₇₃	—	8	2	no	—
213	C₂×D₇₃	—	8	2	no	—
214	C₂×D₇₃	—	8	2	no	—
215	C₄×C₇₃	—	2	1	no	—
216	C₄×C₇₃	—	2	1	no	—
217	C₄×C₇₃	—	2	1	no	—
218	C₄×C₇₃	—	2	1	no	—
219	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
220	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
221	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
223	Dic₇₃	—	2	2	no	—
224	Dic₇₃	—	4	1	no	—
225	Dic₇₃	—	4	1	no	—
226	Dic₇₃	—	8	2	no	—
227	#19269	—	73	1	no	maximal, Sylow
228	C₂×C₇₃	—	4	1	no	—
229	C₂×C₇₃	#3038	1	1	yes	characteristic
230	C₂×C₇₃	#3050	1	1	yes	characteristic
231	C₂×C₇₃	#3067	1	1	yes	characteristic
232	D₇₃	—	4	2	no	—
233	D₇₃	—	16	2	no	—
234	#3147	—	73	1	no	—
235	#3115	—	73	2	no	—
236	C₈×#41	—	73	1	no	—
237	#1670	—	73	1	no	—
238	#1669	—	73	1	no	—
239	#1668	—	73	1	no	—
240	#1667	—	73	1	no	—
241	#1666	—	73	2	no	—
242	#1665	—	73	2	no	—
243	#1568	D₇₃	1	1	yes	characteristic, complemented
244	#1553	—	73	2	no	—
245	C₇₃	#19269	1	1	yes	characteristic, complemented, Sylow
246	C₂×#135	—	146	1	no	—
247	C₂×#135	—	146	1	no	—
248	#532	—	73	2	no	—
249	C₄×#41	—	73	1	no	—
250	#495	—	146	1	no	—
251	#495	—	146	1	no	—
252	#494	—	73	1	no	—
253	#493	—	73	1	no	—
254	#492	—	73	2	no	—
255	#482	—	146	2	no	—
256	#475	—	73	2	no	—
257	#474	—	73	2	no	—
258	#460	—	73	2	no	—
259	#459	—	73	2	no	—
260	#449	—	146	2	no	—
261	C₈×Q₈	—	73	1	no	—
262	C₈×Q₈	—	73	1	no	—
263	#442	—	146	2	no	—
264	#440	—	146	2	no	—
265	C₈×D₄	—	73	1	no	—
266	C₈×D₄	—	73	1	no	—
267	C₈×D₄	—	146	1	no	—
268	C₈×D₄	—	146	1	no	—
269	#432	C₂×D₇₃	1	2	yes	—
270	#431	—	73	1	no	—
271	#431	—	146	1	no	—
272	C₂×C₄×C₈	—	146	1	no	—
273	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
274	#335	C₂×D₇₃	1	1	yes	characteristic
275	#335	C₂×D₇₃	1	1	yes	characteristic
276	#334	C₂×D₇₃	1	2	yes	—
277	#332	—	73	2	no	—
278	#332	—	73	2	no	—
279	#331	—	73	2	no	—
280	#331	—	73	2	no	—
281	C₂×#41	—	73	1	no	—
282	C₂×#41	—	146	2	no	—
283	#135	—	292	4	no	—
284	#135	—	292	4	no	—
285	C₂×Q₁₆	—	146	1	no	—
286	C₂×Q₁₆	—	146	1	no	—
287	C₂×SD₁₆	—	146	2	no	—
288	C₂×SD₁₆	—	146	2	no	—
289	C₂×SD₁₆	—	146	2	no	—
290	C₂×D₈	—	146	2	no	—
291	C₂×D₈	—	146	1	no	—
292	C₂×D₈	—	146	1	no	—
293	C₂²×C₈	—	146	1	no	—
294	C₂²×C₈	—	146	1	no	—
295	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
296	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
297	C₄⋊Q₈	—	73	2	no	—
298	#127	—	73	2	no	—
299	#124	—	146	2	no	—
300	#121	—	146	2	no	—
301	#121	—	146	2	no	—
302	C₄×Q₈	—	73	1	no	—
303	C₄×Q₈	—	73	1	no	—
304	C₄×D₄	—	73	1	no	—
305	C₄×D₄	—	73	1	no	—
306	C₄×D₄	—	146	1	no	—
307	C₄×D₄	—	146	1	no	—
308	C₄×D₄	—	146	2	no	—
309	C₄×D₄	—	146	2	no	—
310	#117	—	73	1	no	—
311	#117	—	146	1	no	—
312	C₂×C₄²	—	146	1	no	—
313	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
314	#107	—	146	2	no	—
315	#106	—	146	2	no	—
316	C₄⋊C₈	—	73	1	no	—
317	C₄⋊C₈	—	73	1	no	—
318	C₄⋊C₈	—	146	1	no	—
319	C₄⋊C₈	—	146	1	no	—
320	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
321	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
322	#103	—	146	2	no	—
323	#102	—	146	2	no	—
324	#102	—	146	2	no	—
325	#102	—	146	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	146	1	no	—
328	C₂²⋊C₈	—	146	1	no	—
329	C₂²⋊C₈	—	146	1	no	—
330	#97	—	2	2	no	—
331	C₄×C₈	—	146	1	no	—
332	C₄×C₈	—	146	1	no	—
333	C₄×C₈	—	146	1	no	—
334	C₄×C₈	D₂₉₂	1	1	yes	characteristic
335	C₄×C₈	D₂₉₂	1	1	yes	characteristic
336	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
337	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
338	#41	—	292	4	no	—
339	#41	—	292	4	no	—
340	#41	—	146	2	no	—
341	#41	—	146	2	no	—
342	C₂×Q₈	—	73	1	no	—
343	C₂×Q₈	—	146	2	no	—
344	C₂×D₄	—	292	2	no	—
345	C₂×D₄	—	73	1	no	—
346	C₂×D₄	—	146	1	no	—
347	C₂×D₄	—	146	2	no	—
348	C₂×D₄	—	146	2	no	—
349	C₂×D₄	—	146	2	no	—
350	C₂²×C₄	—	292	2	no	—
351	C₂²×C₄	—	146	1	no	—
352	C₂²×C₄	—	146	1	no	—
353	C₂²×C₄	—	146	1	no	—
354	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
356	C₂²×C₄	#11924029	1	1	yes	characteristic
357	Q₁₆	—	292	2	no	—
358	Q₁₆	—	292	2	no	—
359	SD₁₆	—	292	4	no	—
360	SD₁₆	—	292	4	no	—
361	SD₁₆	—	292	4	no	—
362	D₈	—	292	2	no	—
363	D₈	—	292	4	no	—
364	D₈	—	292	2	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	292	2	no	—
370	C₂×C₈	—	292	2	no	—
371	C₂×C₈	—	146	1	no	—
372	C₂×C₈	—	146	1	no	—
373	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
374	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
375	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
376	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
377	C₄⋊C₄	—	73	1	no	—
378	C₄⋊C₄	—	73	1	no	—
379	C₄⋊C₄	—	146	2	no	—
380	C₄⋊C₄	—	146	2	no	—
381	C₄⋊C₄	—	146	1	no	—
382	C₄⋊C₄	—	146	1	no	—
383	C₂²⋊C₄	—	292	2	no	—
384	C₂²⋊C₄	—	292	2	no	—
385	C₂²⋊C₄	—	146	1	no	—
386	C₂²⋊C₄	—	146	1	no	—
387	C₂²⋊C₄	—	146	1	no	—
388	C₄²	—	146	1	no	—
389	C₄²	—	146	1	no	—
390	C₄²	—	146	1	no	—
391	C₄²	D₄×D₇₃	1	1	yes	characteristic
392	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
393	C₄²	#11924029	1	1	yes	characteristic
394	C₄²	C₂³×D₇₃	1	1	yes	characteristic
395	C₂³	—	292	2	no	—
396	C₂³	—	146	1	no	—
397	C₂³	#14556566	1	1	yes	characteristic
398	Q₈	—	292	2	no	—
399	Q₈	—	292	2	no	—
400	Q₈	—	73	2	no	—
401	Q₈	—	146	1	no	—
402	D₄	—	292	2	no	—
403	D₄	—	292	2	no	—
404	D₄	—	292	2	no	—
405	D₄	—	292	2	no	—
406	D₄	—	584	2	no	—
407	D₄	—	584	4	no	—
408	D₄	—	73	2	no	—
409	D₄	—	146	4	no	—
410	D₄	—	146	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	292	2	no	—
417	C₂×C₄	—	292	1	no	—
418	C₂×C₄	—	292	1	no	—
419	C₂×C₄	—	292	2	no	—
420	C₂×C₄	—	584	4	no	—
421	C₂×C₄	—	146	4	no	—
422	C₂×C₄	—	146	1	no	—
423	C₂×C₄	—	146	1	no	—
424	C₂×C₄	—	146	1	no	—
425	C₂×C₄	#14556566	1	1	yes	characteristic
426	C₂×C₄	#14556566	1	1	yes	characteristic
427	C₂×C₄	#14556566	1	1	yes	characteristic
428	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
430	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	2	1	no	—
433	C₈	—	4	2	no	—
434	C₈	—	4	2	no	—
435	C₈	—	292	1	no	—
436	C₈	—	292	1	no	—
437	C₈	#14556619	1	2	yes	—
438	C₈	#14556619	1	2	yes	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	292	1	no	—
443	C₂²	—	292	1	no	—
444	C₂²	—	584	2	no	—
445	C₂²	—	584	2	no	—
446	C₂²	—	584	2	no	—
447	C₂²	—	146	2	no	—
448	C₂²	C₂×#14556566	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	292	1	no	—
454	C₄	—	292	1	no	—
455	C₄	—	584	2	no	—
456	C₄	—	146	2	no	—
457	C₄	#135×D₇₃	1	1	yes	characteristic
458	C₄	#135×D₇₃	1	1	yes	characteristic
459	C₄	C₂×#14556619	1	1	yes	characteristic
460	C₄	C₂×#14556619	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	292	2	no	—
463	C₂	—	1168	2	no	—
464	C₂	#22619412	1	1	yes	characteristic
465	C₂	#22619513	1	1	yes	characteristic
466	C₂	#22619652	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14556566
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1568	C₂
socle	C₂²×C₇₃	C₂×#121
hypercenter	#1568	D₇₃
hypocenter	C₇₃	#19269
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1568

Complements

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

N	H ≅ G/N	type
1. #22620359	C₂	semidirect
2. #22620083	C₂	semidirect
3. C₈×#11924028	C₂	semidirect
4. #22609302	C₂	semidirect
5. #22609297	C₂	semidirect
6. #22609292	C₂	semidirect
7. #22609287	C₂	semidirect
8. #22609280	C₂	semidirect
9. #22609273	C₂	semidirect
10. #22608637	C₂	semidirect
11. C₇₃×#1568	C₂	semidirect
187. D₂₉₂	#135	semidirect
196. Dic₁₄₆	#135	semidirect
243. #1568	D₇₃	semidirect
245. C₇₃	#19269	semidirect

Maximal subgroups

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

subgroup	index
#22620359	2
#22620083	2
C₈×#11924028	2
#22609302	2
#22609297	2
#22609292	2
#22609287	2
#22609280	2
#22609273	2
#22608637	2
C₇₃×#1568	2
#19269	73