Subgroups — #32981673

Order 18688.

568 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988643	C₂	1	1	yes	maximal, characteristic
2	#22618284	C₂	1	1	yes	maximal, characteristic
3	#22609908	C₂	1	1	yes	maximal, characteristic
4	C₂×#17988334	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#17988332	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607814	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14556591	C₂²	1	1	yes	characteristic
9	C₂×#14556571	—	2	1	no	—
10	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#17988643	—	2	2	no	—
12	#17988643	—	2	2	no	—
13	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
15	C₂×#14556503	—	2	1	no	—
16	C₂×#14556503	—	2	1	no	—
17	C₂×#14556501	—	2	1	no	—
18	#17988492	—	2	1	no	—
19	#17988486	—	2	1	no	—
20	#17988486	C₄	1	2	yes	—
21	#17988444	—	2	1	no	—
22	#17988444	C₄	1	2	yes	—
23	#17988341	—	2	1	no	—
24	#17988334	—	2	2	no	—
25	#17988332	—	2	2	no	—
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	#384×C₇₃	C₂²	1	1	yes	characteristic
29	C₂²×Dic₁₄₆	—	2	1	no	—
30	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
32	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
33	C₂²×#10596831	—	2	1	no	—
34	C₂²×#10596831	—	2	1	no	—
35	#14556591	—	2	1	no	—
36	#14556591	—	2	1	no	—
37	#14556591	—	2	1	no	—
38	#14556591	—	2	1	no	—
39	#14556571	—	4	2	no	—
40	#14556571	—	4	2	no	—
41	C₂×C₄⋊Dic₇₃	—	2	2	no	—
42	C₂×C₄⋊Dic₇₃	—	2	1	no	—
43	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
44	C₂×#11924005	—	2	2	no	—
45	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
48	C₄²×D₇₃	—	2	1	no	—
49	C₄²×D₇₃	—	2	1	no	—
50	C₄²×D₇₃	—	2	1	no	—
51	C₄²×D₇₃	—	2	1	no	—
52	C₄⋊#10596831	—	2	1	no	—
53	C₄⋊#10596831	—	2	1	no	—
54	C₄⋊#10596831	—	2	1	no	—
55	C₄⋊#10596831	D₄	1	2	yes	—
56	#14556503	—	2	4	no	—
57	#14556503	—	4	2	no	—
58	#14556501	—	2	4	no	—
59	#14556498	—	2	2	no	—
60	#14556498	—	2	2	no	—
61	C₂²×C₈×C₇₃	—	2	1	no	—
62	C₂²×C₈×C₇₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
67	C₄⋊C₈×C₇₃	—	2	1	no	—
68	C₄⋊C₈×C₇₃	—	2	1	no	—
69	C₄⋊C₈×C₇₃	—	2	1	no	—
70	C₄⋊C₈×C₇₃	D₄	1	2	yes	—
71	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂×Dic₁₄₆	—	4	1	no	—
73	C₂×Dic₁₄₆	—	4	1	no	—
74	C₂×Dic₁₄₆	—	4	1	no	—
75	C₂×Dic₁₄₆	—	4	1	no	—
76	C₂×Dic₁₄₆	—	4	1	no	—
77	C₂×Dic₁₄₆	—	4	1	no	—
78	C₂²×Dic₇₃	—	2	2	no	—
79	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₇₃	—	2	2	no	—
83	C₂×C₄×D₇₃	—	2	1	no	—
84	C₂×C₄×D₇₃	—	2	1	no	—
85	C₂×C₄×D₇₃	—	2	1	no	—
86	C₂×C₄×D₇₃	—	2	1	no	—
87	C₂×C₄×D₇₃	—	2	1	no	—
88	C₂×C₄×D₇₃	—	2	1	no	—
89	C₂×C₄×D₇₃	—	2	1	no	—
90	C₂×C₄×D₇₃	—	2	1	no	—
91	C₂×C₄×D₇₃	—	2	1	no	—
92	C₂×C₄×D₇₃	—	2	1	no	—
93	C₂×C₄×D₇₃	—	2	1	no	—
94	C₂×C₄×D₇₃	—	2	1	no	—
95	C₂×C₄×D₇₃	—	2	1	no	—
96	C₂×C₄×D₇₃	—	2	1	no	—
97	C₂×C₄×D₇₃	—	4	1	no	—
98	C₂×#10596831	—	2	2	no	—
99	C₂×#10596831	—	4	1	no	—
100	C₂×#10596831	—	4	1	no	—
101	C₂×#10596831	—	4	1	no	—
102	C₂×#10596831	—	4	1	no	—
103	C₂×#10596831	—	4	1	no	—
104	C₄⋊Dic₇₃	—	2	2	no	—
105	C₄⋊Dic₇₃	—	2	2	no	—
106	C₄⋊Dic₇₃	—	4	4	no	—
107	C₄⋊Dic₇₃	—	4	1	no	—
108	C₄⋊Dic₇₃	—	4	1	no	—
109	#11924005	—	4	4	no	—
110	C₄×Dic₇₃	—	2	1	no	—
111	C₄×Dic₇₃	—	2	1	no	—
112	C₄×Dic₇₃	—	2	1	no	—
113	C₄×Dic₇₃	—	2	1	no	—
114	C₄×Dic₇₃	—	2	1	no	—
115	C₄×Dic₇₃	—	2	1	no	—
116	C₂²×C₄×C₇₃	—	2	2	no	—
117	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₇₃	—	2	2	no	—
121	C₂×C₈×C₇₃	—	4	1	no	—
122	C₂×C₈×C₇₃	—	4	1	no	—
123	C₂×C₈×C₇₃	—	4	1	no	—
124	C₂×C₈×C₇₃	—	4	1	no	—
125	C₂×C₈×C₇₃	—	4	1	no	—
126	C₄⋊C₄×C₇₃	—	4	2	no	—
127	C₄⋊C₄×C₇₃	—	4	1	no	—
128	C₄⋊C₄×C₇₃	—	4	1	no	—
129	C₄⋊C₄×C₇₃	—	4	1	no	—
130	C₄⋊C₄×C₇₃	—	4	1	no	—
131	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₇₃	#41	1	1	yes	characteristic
134	C₄²×C₇₃	#41	1	1	yes	characteristic
135	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
136	C₂²×D₇₃	—	2	1	no	—
137	C₂²×D₇₃	—	2	1	no	—
138	C₂²×D₇₃	—	2	1	no	—
139	C₂²×D₇₃	—	2	1	no	—
140	C₂²×D₇₃	—	2	1	no	—
141	C₂²×D₇₃	—	2	1	no	—
142	C₂²×D₇₃	#101	1	2	yes	—
143	C₂×C₄×C₇₃	—	2	1	no	—
144	C₂×C₄×C₇₃	—	2	1	no	—
145	C₂×C₄×C₇₃	—	4	2	no	—
146	C₂×C₄×C₇₃	—	4	2	no	—
147	C₂×C₄×C₇₃	—	4	2	no	—
148	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
151	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
154	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
155	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
156	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
160	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
161	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
162	C₂×Dic₇₃	—	2	1	no	—
163	C₂×Dic₇₃	—	2	1	no	—
164	C₂×Dic₇₃	—	2	1	no	—
165	C₂×Dic₇₃	—	2	1	no	—
166	C₂×Dic₇₃	—	2	1	no	—
167	C₂×Dic₇₃	—	2	1	no	—
168	C₂×Dic₇₃	—	2	1	no	—
169	C₂×Dic₇₃	—	2	1	no	—
170	C₂×Dic₇₃	—	2	1	no	—
171	C₂×Dic₇₃	—	4	2	no	—
172	C₂×Dic₇₃	—	4	2	no	—
173	C₂×Dic₇₃	—	4	2	no	—
174	C₄×D₇₃	—	4	2	no	—
175	C₄×D₇₃	—	4	2	no	—
176	C₄×D₇₃	—	4	1	no	—
177	C₄×D₇₃	—	4	1	no	—
178	C₄×D₇₃	—	4	1	no	—
179	C₄×D₇₃	—	4	1	no	—
180	C₄×D₇₃	—	4	1	no	—
181	C₄×D₇₃	—	4	1	no	—
182	C₄×D₇₃	—	4	1	no	—
183	C₄×D₇₃	—	4	1	no	—
184	Dic₁₄₆	—	8	1	no	—
185	Dic₁₄₆	—	8	1	no	—
186	Dic₁₄₆	—	8	1	no	—
187	Dic₁₄₆	—	8	1	no	—
188	C₈×C₇₃	—	4	2	no	—
189	C₈×C₇₃	—	8	1	no	—
190	#10596831	—	4	2	no	—
191	#10596831	—	8	1	no	—
192	C₂²×C₇₃	#386	1	1	yes	characteristic
193	C₂²×C₇₃	C₂×#101	1	1	yes	characteristic
194	C₂²×C₇₃	#413	1	1	yes	characteristic
195	C₂²×C₇₃	#416	1	1	yes	characteristic
196	C₂²×C₇₃	#417	1	1	yes	characteristic
197	C₂²×C₇₃	#418	1	1	yes	characteristic
198	C₂²×C₇₃	#419	1	1	yes	characteristic
199	C₂×D₇₃	—	2	2	no	—
200	C₂×D₇₃	—	2	2	no	—
201	C₂×D₇₃	—	2	2	no	—
202	C₂×D₇₃	—	4	1	no	—
203	C₂×D₇₃	—	4	1	no	—
204	C₂×D₇₃	—	4	1	no	—
205	C₂×D₇₃	—	4	1	no	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	—	2	1	no	—
208	C₄×C₇₃	—	8	2	no	—
209	C₄×C₇₃	#452	1	1	yes	characteristic
210	C₄×C₇₃	#452	1	1	yes	characteristic
211	C₄×C₇₃	#468	1	1	yes	characteristic
212	C₄×C₇₃	#468	1	1	yes	characteristic
213	C₄×C₇₃	#469	1	1	yes	characteristic
214	C₄×C₇₃	#469	1	1	yes	characteristic
215	C₄×C₇₃	#485	1	1	yes	characteristic
216	C₄×C₇₃	#485	1	1	yes	characteristic
217	Dic₇₃	—	4	1	no	—
218	Dic₇₃	—	4	1	no	—
219	Dic₇₃	—	4	1	no	—
220	Dic₇₃	—	8	2	no	—
221	#9138	—	73	1	no	maximal, Sylow
222	C₂×C₇₃	#1552	1	1	yes	characteristic
223	C₂×C₇₃	#1553	1	1	yes	characteristic
224	C₂×C₇₃	#1556	1	1	yes	characteristic
225	C₂×C₇₃	#1559	1	1	yes	characteristic
226	C₂×C₇₃	#1873	1	1	yes	characteristic
227	C₂×C₇₃	#1895	1	1	yes	characteristic
228	C₂×C₇₃	#1901	1	1	yes	characteristic
229	D₇₃	—	4	2	no	—
230	C₂×#432	—	73	1	no	—
231	#2857	—	73	1	no	—
232	#1797	—	73	1	no	—
233	C₂×#332	—	73	1	no	—
234	C₂×#332	—	73	1	no	—
235	#1296	—	73	1	no	—
236	#1296	D₇₃	1	1	yes	characteristic, complemented
237	C₇₃	#9138	1	1	yes	characteristic, complemented, Sylow
238	C₂×C₄⋊Q₈	—	73	1	no	—
239	C₂×C₂²⋊Q₈	—	146	1	no	—
240	C₂²×C₄²	—	73	1	no	—
241	#432	—	146	2	no	—
242	#432	—	146	2	no	—
243	C₂×C₄⋊C₈	—	73	1	no	—
244	C₂×C₄⋊C₈	—	73	1	no	—
245	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
247	C₂×C₂²⋊C₈	—	146	1	no	—
248	C₂×C₂²⋊C₈	—	146	1	no	—
249	C₂×#97	—	146	1	no	—
250	#391	—	146	1	no	—
251	#389	—	73	2	no	—
252	#389	—	146	1	no	—
253	#384	C₂×D₇₃	1	1	yes	characteristic
254	#380	—	73	2	no	—
255	#380	—	146	1	no	—
256	#336	—	146	1	no	—
257	#332	—	146	2	no	—
258	#332	—	146	2	no	—
259	C₂²×Q₈	—	146	1	no	—
260	C₂³×C₄	—	73	1	no	—
261	C₂³×C₄	—	73	1	no	—
262	C₂³×C₄	—	73	1	no	—
263	C₂²×C₈	—	2	1	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	146	1	no	—
266	C₂²×C₈	—	146	1	no	—
267	C₄⋊Q₈	—	146	1	no	—
268	C₄⋊Q₈	—	146	1	no	—
269	C₄⋊Q₈	—	146	1	no	—
270	C₄⋊Q₈	—	146	1	no	—
271	C₂²⋊Q₈	—	292	2	no	—
272	C₂²⋊Q₈	—	292	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	73	2	no	—
276	C₂×C₄⋊C₄	—	146	2	no	—
277	C₂×C₄⋊C₄	—	146	1	no	—
278	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
279	C₂×C₂²⋊C₄	—	146	2	no	—
280	C₂×C₄²	—	73	1	no	—
281	C₂×C₄²	—	73	1	no	—
282	C₂×C₄²	—	73	1	no	—
283	C₂×C₄²	—	146	1	no	—
284	C₂×C₄²	—	146	1	no	—
285	C₂×C₄²	—	146	1	no	—
286	C₂×C₄²	—	146	1	no	—
287	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	73	2	no	—
292	C₄⋊C₈	—	146	1	no	—
293	C₄⋊C₈	—	146	1	no	—
294	C₄⋊C₈	—	146	1	no	—
295	C₄⋊C₈	D₂₉₂	1	2	yes	—
296	C₂²⋊C₈	—	292	2	no	—
297	C₂²⋊C₈	—	146	4	no	—
298	#97	—	146	4	no	—
299	#95	—	146	2	no	—
300	#95	—	146	2	no	—
301	C₂⁴	—	73	1	no	—
302	C₂×Q₈	—	292	1	no	—
303	C₂×Q₈	—	292	1	no	—
304	C₂×Q₈	—	292	1	no	—
305	C₂×Q₈	—	292	1	no	—
306	C₂×Q₈	—	292	1	no	—
307	C₂×Q₈	—	292	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	292	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	146	2	no	—
314	C₂²×C₄	—	146	2	no	—
315	C₂²×C₄	—	146	1	no	—
316	C₂²×C₄	—	146	1	no	—
317	C₂²×C₄	—	146	1	no	—
318	C₂²×C₄	—	146	1	no	—
319	C₂²×C₄	—	146	1	no	—
320	C₂²×C₄	—	146	1	no	—
321	C₂²×C₄	—	146	1	no	—
322	C₂²×C₄	—	146	1	no	—
323	C₂²×C₄	—	146	1	no	—
324	C₂²×C₄	—	146	1	no	—
325	C₂²×C₄	—	146	1	no	—
326	C₂²×C₄	—	146	1	no	—
327	C₂²×C₄	—	146	1	no	—
328	C₂²×C₄	—	146	1	no	—
329	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	1	no	—
338	C₂×C₈	—	292	1	no	—
339	C₂×C₈	—	292	1	no	—
340	C₂×C₈	—	292	1	no	—
341	C₂×C₈	—	292	1	no	—
342	C₂×C₈	—	292	1	no	—
343	C₂×C₈	—	146	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	292	4	no	—
350	C₄⋊C₄	—	292	1	no	—
351	C₄⋊C₄	—	292	1	no	—
352	C₄⋊C₄	—	146	2	no	—
353	C₄⋊C₄	—	146	2	no	—
354	C₂²⋊C₄	—	292	4	no	—
355	C₄²	—	146	1	no	—
356	C₄²	—	146	1	no	—
357	C₄²	—	146	1	no	—
358	C₄²	—	146	1	no	—
359	C₄²	—	146	1	no	—
360	C₄²	—	146	1	no	—
361	C₄²	D₄×D₇₃	1	1	yes	characteristic
362	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
363	C₄²	#11924028	1	1	yes	characteristic
364	C₄²	#11924029	1	1	yes	characteristic
365	C₂³	—	73	2	no	—
366	C₂³	—	146	1	no	—
367	C₂³	—	146	1	no	—
368	C₂³	—	146	1	no	—
369	C₂³	—	146	1	no	—
370	C₂³	—	146	1	no	—
371	C₂³	—	146	1	no	—
372	C₂³	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
373	Q₈	—	584	1	no	—
374	Q₈	—	584	1	no	—
375	Q₈	—	584	1	no	—
376	Q₈	—	584	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	292	2	no	—
383	C₂×C₄	—	292	2	no	—
384	C₂×C₄	—	292	1	no	—
385	C₂×C₄	—	292	1	no	—
386	C₂×C₄	—	292	1	no	—
387	C₂×C₄	—	292	1	no	—
388	C₂×C₄	—	292	1	no	—
389	C₂×C₄	—	292	1	no	—
390	C₂×C₄	—	292	1	no	—
391	C₂×C₄	—	292	1	no	—
392	C₂×C₄	—	292	2	no	—
393	C₂×C₄	—	292	2	no	—
394	C₂×C₄	—	292	2	no	—
395	C₂×C₄	—	146	1	no	—
396	C₂×C₄	—	146	1	no	—
397	C₂×C₄	—	146	1	no	—
398	C₂×C₄	—	146	1	no	—
399	C₂×C₄	—	146	1	no	—
400	C₂×C₄	—	146	1	no	—
401	C₂×C₄	—	146	1	no	—
402	C₂×C₄	—	146	1	no	—
403	C₂×C₄	—	146	1	no	—
404	C₂×C₄	#14556553	1	1	yes	characteristic
405	C₂×C₄	C₄×D₂₉₂	1	1	yes	characteristic
406	C₂×C₄	#14556561	1	1	yes	characteristic
407	C₂×C₄	#14556564	1	1	yes	characteristic
408	C₂×C₄	#14556566	1	1	yes	characteristic
409	C₂×C₄	#14556576	1	1	yes	characteristic
410	C₂×C₄	#14556610	1	1	yes	characteristic
411	C₂×C₄	#14556612	1	1	yes	characteristic
412	C₂×C₄	#14556615	1	1	yes	characteristic
413	C₂×C₄	#14556618	1	1	yes	characteristic
414	C₂×C₄	#14556618	1	1	yes	characteristic
415	C₂×C₄	#14556620	1	1	yes	characteristic
416	C₂×C₄	#14556623	1	1	yes	characteristic
417	C₂×C₄	#14556623	1	1	yes	characteristic
418	C₈	—	4	2	no	—
419	C₈	—	8	1	no	—
420	C₈	—	292	2	no	—
421	C₈	—	584	1	no	—
422	C₂²	—	292	1	no	—
423	C₂²	—	292	1	no	—
424	C₂²	—	292	1	no	—
425	C₂²	—	292	1	no	—
426	C₂²	—	146	2	no	—
427	C₂²	—	146	2	no	—
428	C₂²	—	146	2	no	—
429	C₂²	#17988465	1	1	yes	characteristic
430	C₂²	#101×D₇₃	1	1	yes	characteristic
431	C₂²	#17988568	1	1	yes	characteristic
432	C₂²	#17988580	1	1	yes	characteristic
433	C₂²	#17988587	1	1	yes	characteristic
434	C₂²	#17988590	1	1	yes	characteristic
435	C₂²	#17988594	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	8	2	no	—
439	C₄	—	292	1	no	—
440	C₄	—	292	1	no	—
441	C₄	—	292	1	no	—
442	C₄	—	584	2	no	—
443	C₄	#17988750	1	1	yes	characteristic
444	C₄	#17988752	1	1	yes	characteristic
445	C₄	#17988834	1	1	yes	characteristic
446	C₄	#17988836	1	1	yes	characteristic
447	C₄	#17988839	1	1	yes	characteristic
448	C₄	#17988841	1	1	yes	characteristic
449	C₄	#17988930	1	1	yes	characteristic
450	C₄	#17988931	1	1	yes	characteristic
451	C₂	—	292	2	no	—
452	C₂	#22608628	1	1	yes	characteristic
453	C₂	#22608633	1	1	yes	characteristic
454	C₂	#22608646	1	1	yes	characteristic
455	C₂	#22608658	1	1	yes	characteristic
456	C₂	#22610242	1	1	yes	characteristic
457	C₂	#22610368	1	1	yes	characteristic
458	C₂	#22610398	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₇₃
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1296	C₂
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1296	D₇₃
hypocenter	C₇₃	#9138
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. C₂×#17988334	C₂	semidirect
5. C₂×#17988332	C₂	semidirect
6. #22607814	C₂	semidirect
7. C₇₃×#1296	C₂	semidirect
236. #1296	D₇₃	semidirect
237. C₇₃	#9138	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988643	2
#22618284	2
#22609908	2
C₂×#17988334	2
C₂×#17988332	2
#22607814	2
C₇₃×#1296	2
#9138	73