Subgroups — #32981661

Order 18688.

568 conjugacy classes of subgroups.

The subgroup lattice has 450 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	#22618278	C₂	1	1	yes	maximal, characteristic
3	#22609908	C₂	1	1	yes	maximal, characteristic
4	C₂×#17988336	C₂	1	1	yes	maximal, characteristic, complemented
5	#22607815	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#333×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14556567	C₄	1	2	yes	—
9	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
10	#17988643	—	2	2	no	—
11	#17988643	—	2	2	no	—
12	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
14	C₂×#14556503	—	2	1	no	—
15	C₂×#14556503	—	2	1	no	—
16	C₂×#14556501	—	2	1	no	—
17	#17988494	C₄	1	2	yes	—
18	#17988483	—	2	1	no	—
19	#17988483	—	2	1	no	—
20	#17988457	C₂²	1	1	yes	characteristic
21	#17988444	—	2	1	no	—
22	#17988444	—	2	1	no	—
23	#17988341	—	2	1	no	—
24	#17988336	—	2	2	no	—
25	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
28	#333×C₇₃	—	2	2	no	—
29	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
32	C₂²×#10596831	—	2	1	no	—
33	C₂²×#10596831	—	2	1	no	—
34	#14556567	—	4	4	no	—
35	C₂×C₄⋊Dic₇₃	—	2	1	no	—
36	C₂×C₄⋊Dic₇₃	—	2	1	no	—
37	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
38	C₂×#11924007	—	2	2	no	—
39	C₂×#11924005	—	2	2	no	—
40	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
42	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
43	C₄²×D₇₃	—	2	1	no	—
44	C₄²×D₇₃	—	2	1	no	—
45	C₄²×D₇₃	—	2	1	no	—
46	C₄²×D₇₃	—	2	1	no	—
47	C₄⋊#10596831	—	2	1	no	—
48	C₄⋊#10596831	—	2	1	no	—
49	C₄⋊#10596831	—	2	1	no	—
50	C₄⋊#10596831	D₄	1	2	yes	—
51	#14556503	—	2	4	no	—
52	#14556503	—	4	2	no	—
53	#14556501	—	2	4	no	—
54	#14556498	—	2	2	no	—
55	#14556498	—	2	2	no	—
56	C₂²×Q₈×C₇₃	C₂×C₄	1	2	yes	—
57	C₂²×C₈×C₇₃	—	2	1	no	—
58	C₂²×C₈×C₇₃	—	2	1	no	—
59	C₄⋊Q₈×C₇₃	—	2	1	no	—
60	C₄⋊Q₈×C₇₃	—	2	1	no	—
61	C₄⋊Q₈×C₇₃	—	2	1	no	—
62	C₄⋊Q₈×C₇₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
65	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₇₃	—	2	1	no	—
67	C₄⋊C₈×C₇₃	—	2	1	no	—
68	C₄⋊C₈×C₇₃	—	2	1	no	—
69	C₄⋊C₈×C₇₃	D₄	1	2	yes	—
70	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×Dic₇₃	—	2	2	no	—
72	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×D₇₃	—	2	2	no	—
76	C₂×C₄×D₇₃	—	2	1	no	—
77	C₂×C₄×D₇₃	—	2	1	no	—
78	C₂×C₄×D₇₃	—	2	1	no	—
79	C₂×C₄×D₇₃	—	2	1	no	—
80	C₂×C₄×D₇₃	—	2	1	no	—
81	C₂×C₄×D₇₃	—	2	1	no	—
82	C₂×C₄×D₇₃	—	2	1	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	—	4	1	no	—
91	C₂×#10596831	—	2	2	no	—
92	C₂×#10596831	—	4	1	no	—
93	C₂×#10596831	—	4	1	no	—
94	C₂×#10596831	—	4	1	no	—
95	C₂×#10596831	—	4	1	no	—
96	C₂×#10596831	—	4	1	no	—
97	C₄⋊Dic₇₃	—	4	1	no	—
98	C₄⋊Dic₇₃	—	4	1	no	—
99	C₄⋊Dic₇₃	—	4	1	no	—
100	C₄⋊Dic₇₃	—	4	1	no	—
101	C₄⋊Dic₇₃	—	4	2	no	—
102	#11924007	—	4	4	no	—
103	#11924005	—	4	4	no	—
104	C₄×Dic₇₃	—	2	1	no	—
105	C₄×Dic₇₃	—	2	1	no	—
106	C₄×Dic₇₃	—	2	1	no	—
107	C₄×Dic₇₃	—	2	1	no	—
108	C₄×Dic₇₃	—	2	1	no	—
109	C₄×Dic₇₃	—	2	1	no	—
110	C₂×Q₈×C₇₃	—	2	2	no	—
111	C₂×Q₈×C₇₃	—	2	2	no	—
112	C₂×Q₈×C₇₃	—	4	2	no	—
113	C₂×Q₈×C₇₃	—	4	2	no	—
114	C₂²×C₄×C₇₃	—	2	2	no	—
115	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₇₃	—	2	2	no	—
119	C₂×C₈×C₇₃	—	4	1	no	—
120	C₂×C₈×C₇₃	—	4	1	no	—
121	C₂×C₈×C₇₃	—	4	1	no	—
122	C₂×C₈×C₇₃	—	4	1	no	—
123	C₂×C₈×C₇₃	—	4	1	no	—
124	C₄⋊C₄×C₇₃	—	4	1	no	—
125	C₄⋊C₄×C₇₃	—	4	1	no	—
126	C₄⋊C₄×C₇₃	—	4	1	no	—
127	C₄⋊C₄×C₇₃	—	4	1	no	—
128	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₇₃	#41	1	1	yes	characteristic
131	C₄²×C₇₃	#41	1	1	yes	characteristic
132	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×D₇₃	—	2	1	no	—
134	C₂²×D₇₃	—	2	1	no	—
135	C₂²×D₇₃	—	2	1	no	—
136	C₂²×D₇₃	—	2	1	no	—
137	C₂²×D₇₃	—	2	1	no	—
138	C₂²×D₇₃	—	2	1	no	—
139	C₂²×D₇₃	#100	1	2	yes	—
140	Q₈×C₇₃	—	8	2	no	—
141	Q₈×C₇₃	—	8	2	no	—
142	C₂×C₄×C₇₃	—	2	1	no	—
143	C₂×C₄×C₇₃	—	2	1	no	—
144	C₂×C₄×C₇₃	—	4	2	no	—
145	C₂×C₄×C₇₃	—	4	2	no	—
146	C₂×C₄×C₇₃	—	4	2	no	—
147	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₇₃	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₇₃	#120	1	1	yes	characteristic
150	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
151	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
152	C₂×C₄×C₇₃	#123	1	1	yes	characteristic
153	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
154	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
155	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	1	yes	characteristic
156	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
157	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
158	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
159	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
160	C₂×C₄×C₇₃	#137	1	1	yes	characteristic
161	C₂×Dic₇₃	—	2	1	no	—
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	—	4	2	no	—
171	C₂×Dic₇₃	—	4	2	no	—
172	C₂×Dic₇₃	—	4	2	no	—
173	C₄×D₇₃	—	4	2	no	—
174	C₄×D₇₃	—	4	2	no	—
175	C₄×D₇₃	—	4	1	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	C₈×C₇₃	—	4	2	no	—
184	C₈×C₇₃	—	8	1	no	—
185	#10596831	—	4	2	no	—
186	#10596831	—	8	1	no	—
187	C₂²×C₇₃	#386	1	1	yes	characteristic
188	C₂²×C₇₃	C₂×#100	1	1	yes	characteristic
189	C₂²×C₇₃	#413	1	1	yes	characteristic
190	C₂²×C₇₃	#416	1	1	yes	characteristic
191	C₂²×C₇₃	#417	1	1	yes	characteristic
192	C₂²×C₇₃	#419	1	1	yes	characteristic
193	C₂²×C₇₃	#419	1	1	yes	characteristic
194	C₂×D₇₃	—	2	2	no	—
195	C₂×D₇₃	—	2	2	no	—
196	C₂×D₇₃	—	2	2	no	—
197	C₂×D₇₃	—	4	1	no	—
198	C₂×D₇₃	—	4	1	no	—
199	C₂×D₇₃	—	4	1	no	—
200	C₂×D₇₃	—	4	1	no	—
201	C₄×C₇₃	—	2	1	no	—
202	C₄×C₇₃	—	2	1	no	—
203	C₄×C₇₃	—	8	2	no	—
204	C₄×C₇₃	#452	1	1	yes	characteristic
205	C₄×C₇₃	#452	1	1	yes	characteristic
206	C₄×C₇₃	#468	1	1	yes	characteristic
207	C₄×C₇₃	#468	1	1	yes	characteristic
208	C₄×C₇₃	#470	1	1	yes	characteristic
209	C₄×C₇₃	#470	1	1	yes	characteristic
210	C₄×C₇₃	#485	1	1	yes	characteristic
211	C₄×C₇₃	#485	1	1	yes	characteristic
212	Dic₇₃	—	4	1	no	—
213	Dic₇₃	—	4	1	no	—
214	Dic₇₃	—	4	1	no	—
215	Dic₇₃	—	8	2	no	—
216	#9136	—	73	1	no	maximal, Sylow
217	C₂×C₇₃	#1551	1	1	yes	characteristic
218	C₂×C₇₃	#1554	1	1	yes	characteristic
219	C₂×C₇₃	#1558	1	1	yes	characteristic
220	C₂×C₇₃	#1559	1	1	yes	characteristic
221	C₂×C₇₃	#1873	1	1	yes	characteristic
222	C₂×C₇₃	#1894	1	1	yes	characteristic
223	C₂×C₇₃	#1900	1	1	yes	characteristic
224	D₇₃	—	4	2	no	—
225	C₂×#432	—	73	1	no	—
226	#2857	—	73	1	no	—
227	#1797	—	73	1	no	—
228	C₂×#333	—	73	1	no	—
229	C₂×#333	D₇₃	1	1	yes	characteristic, complemented
230	#1296	—	73	1	no	—
231	#1296	—	73	1	no	—
232	C₇₃	#9136	1	1	yes	characteristic, complemented, Sylow
233	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
234	C₂×C₂²⋊Q₈	—	73	2	no	—
235	C₂²×C₄²	—	73	1	no	—
236	#432	—	146	2	no	—
237	#432	—	146	2	no	—
238	C₂×C₄⋊C₈	—	73	1	no	—
239	C₂×C₄⋊C₈	—	73	1	no	—
240	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	—	146	1	no	—
243	C₂×C₂²⋊C₈	—	146	1	no	—
244	C₂×#97	—	146	1	no	—
245	#391	—	73	2	no	—
246	#389	—	146	1	no	—
247	#389	—	146	1	no	—
248	#384	—	73	1	no	—
249	#380	—	146	1	no	—
250	#380	—	146	1	no	—
251	#336	—	146	1	no	—
252	#333	—	2	2	no	—
253	#333	—	146	2	no	—
254	C₂²×Q₈	C₄×D₇₃	1	2	yes	—
255	C₂³×C₄	—	73	1	no	—
256	C₂³×C₄	—	73	1	no	—
257	C₂³×C₄	—	73	1	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	146	1	no	—
261	C₂²×C₈	—	146	1	no	—
262	C₄⋊Q₈	—	2	1	no	—
263	C₄⋊Q₈	—	2	1	no	—
264	C₄⋊Q₈	—	2	1	no	—
265	C₄⋊Q₈	—	2	1	no	—
266	C₂²⋊Q₈	—	292	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	73	2	no	—
270	C₂×C₄⋊C₄	—	146	2	no	—
271	C₂×C₄⋊C₄	—	146	1	no	—
272	C₂×C₄⋊C₄	—	146	1	no	—
273	C₂×C₂²⋊C₄	—	146	2	no	—
274	C₂×C₄²	—	73	1	no	—
275	C₂×C₄²	—	73	1	no	—
276	C₂×C₄²	—	73	1	no	—
277	C₂×C₄²	—	146	1	no	—
278	C₂×C₄²	—	146	1	no	—
279	C₂×C₄²	—	146	1	no	—
280	C₂×C₄²	—	146	1	no	—
281	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
282	C₄⋊C₈	—	2	1	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	73	2	no	—
286	C₄⋊C₈	—	146	1	no	—
287	C₄⋊C₈	—	146	1	no	—
288	C₄⋊C₈	—	146	1	no	—
289	C₄⋊C₈	C₂²⋊D₇₃	1	2	yes	—
290	C₂²⋊C₈	—	292	2	no	—
291	C₂²⋊C₈	—	146	4	no	—
292	#97	—	146	4	no	—
293	#95	—	146	2	no	—
294	#95	—	146	2	no	—
295	C₂⁴	—	73	1	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	292	1	no	—
302	C₂²×C₄	—	73	1	no	—
303	C₂²×C₄	—	73	1	no	—
304	C₂²×C₄	—	73	1	no	—
305	C₂²×C₄	—	146	2	no	—
306	C₂²×C₄	—	146	2	no	—
307	C₂²×C₄	—	146	1	no	—
308	C₂²×C₄	—	146	1	no	—
309	C₂²×C₄	—	146	1	no	—
310	C₂²×C₄	—	146	1	no	—
311	C₂²×C₄	—	146	1	no	—
312	C₂²×C₄	—	146	1	no	—
313	C₂²×C₄	—	146	1	no	—
314	C₂²×C₄	—	146	1	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	C₂×C₄×D₇₃	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	292	1	no	—
331	C₂×C₈	—	292	1	no	—
332	C₂×C₈	—	292	1	no	—
333	C₂×C₈	—	292	1	no	—
334	C₂×C₈	—	292	1	no	—
335	C₂×C₈	—	146	2	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	292	2	no	—
341	C₄⋊C₄	—	292	4	no	—
342	C₄⋊C₄	—	292	1	no	—
343	C₄⋊C₄	—	292	1	no	—
344	C₄⋊C₄	—	292	1	no	—
345	C₄⋊C₄	—	292	1	no	—
346	C₂²⋊C₄	—	292	4	no	—
347	C₄²	—	146	1	no	—
348	C₄²	—	146	1	no	—
349	C₄²	—	146	1	no	—
350	C₄²	—	146	1	no	—
351	C₄²	—	146	1	no	—
352	C₄²	—	146	1	no	—
353	C₄²	D₄×D₇₃	1	1	yes	characteristic
354	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
355	C₄²	#11924027	1	1	yes	characteristic
356	C₄²	#11924028	1	1	yes	characteristic
357	C₂³	—	73	2	no	—
358	C₂³	—	146	1	no	—
359	C₂³	—	146	1	no	—
360	C₂³	—	146	1	no	—
361	C₂³	—	146	1	no	—
362	C₂³	—	146	1	no	—
363	C₂³	—	146	1	no	—
364	C₂³	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
365	Q₈	—	8	2	no	—
366	Q₈	—	8	2	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	292	2	no	—
373	C₂×C₄	—	292	2	no	—
374	C₂×C₄	—	292	1	no	—
375	C₂×C₄	—	292	1	no	—
376	C₂×C₄	—	292	1	no	—
377	C₂×C₄	—	292	1	no	—
378	C₂×C₄	—	292	1	no	—
379	C₂×C₄	—	292	1	no	—
380	C₂×C₄	—	292	1	no	—
381	C₂×C₄	—	292	1	no	—
382	C₂×C₄	—	292	2	no	—
383	C₂×C₄	—	292	2	no	—
384	C₂×C₄	—	292	2	no	—
385	C₂×C₄	—	146	1	no	—
386	C₂×C₄	—	146	1	no	—
387	C₂×C₄	—	146	1	no	—
388	C₂×C₄	—	146	1	no	—
389	C₂×C₄	—	146	1	no	—
390	C₂×C₄	—	146	1	no	—
391	C₂×C₄	—	146	1	no	—
392	C₂×C₄	—	146	1	no	—
393	C₂×C₄	—	146	1	no	—
394	C₂×C₄	#14556551	1	1	yes	characteristic
395	C₂×C₄	C₄×C₂²⋊D₇₃	1	1	yes	characteristic
396	C₂×C₄	#14556559	1	1	yes	characteristic
397	C₂×C₄	#14556562	1	1	yes	characteristic
398	C₂×C₄	#14556564	1	1	yes	characteristic
399	C₂×C₄	#14556573	1	1	yes	characteristic
400	C₂×C₄	#14556612	1	1	yes	characteristic
401	C₂×C₄	#14556614	1	1	yes	characteristic
402	C₂×C₄	#14556618	1	1	yes	characteristic
403	C₂×C₄	#14556620	1	1	yes	characteristic
404	C₂×C₄	#14556620	1	1	yes	characteristic
405	C₂×C₄	#14556623	1	1	yes	characteristic
406	C₂×C₄	#14556623	1	1	yes	characteristic
407	C₂×C₄	#14556623	1	1	yes	characteristic
408	C₈	—	4	2	no	—
409	C₈	—	8	1	no	—
410	C₈	—	292	2	no	—
411	C₈	—	584	1	no	—
412	C₂²	—	292	1	no	—
413	C₂²	—	292	1	no	—
414	C₂²	—	292	1	no	—
415	C₂²	—	292	1	no	—
416	C₂²	—	146	2	no	—
417	C₂²	—	146	2	no	—
418	C₂²	—	146	2	no	—
419	C₂²	#17988463	1	1	yes	characteristic
420	C₂²	#100×D₇₃	1	1	yes	characteristic
421	C₂²	#17988568	1	1	yes	characteristic
422	C₂²	#17988582	1	1	yes	characteristic
423	C₂²	#17988587	1	1	yes	characteristic
424	C₂²	#17988594	1	1	yes	characteristic
425	C₂²	#17988594	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	292	1	no	—
430	C₄	—	292	1	no	—
431	C₄	—	292	1	no	—
432	C₄	—	584	2	no	—
433	C₄	#17988746	1	1	yes	characteristic
434	C₄	#17988748	1	1	yes	characteristic
435	C₄	#17988830	1	1	yes	characteristic
436	C₄	#17988836	1	1	yes	characteristic
437	C₄	#17988842	1	1	yes	characteristic
438	C₄	#17988844	1	1	yes	characteristic
439	C₄	#17988926	1	1	yes	characteristic
440	C₄	#17988927	1	1	yes	characteristic
441	C₂	—	292	2	no	—
442	C₂	#22608625	1	1	yes	characteristic
443	C₂	#22608640	1	1	yes	characteristic
444	C₂	#22608655	1	1	yes	characteristic
445	C₂	#22608658	1	1	yes	characteristic
446	C₂	#22610240	1	1	yes	characteristic
447	C₂	#22610361	1	1	yes	characteristic
448	C₂	#22610391	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₇₃
commutator	C₂²×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₂×#333×C₇₃	C₂
socle	C₂³×C₇₃	C₂×C₂²⋊C₄
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	C₂×#333	D₇₃
hypocenter	C₇₃	#9136
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#333

Complements

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

N	H ≅ G/N	type
4. C₂×#17988336	C₂	semidirect
5. #22607815	C₂	semidirect
6. #22607815	C₂	semidirect
7. C₂×#333×C₇₃	C₂	semidirect
229. C₂×#333	D₇₃	semidirect
232. C₇₃	#9136	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
#22618278	2
#22609908	2
C₂×#17988336	2
#22607815	2
C₂×#333×C₇₃	2
#9136	73