Subgroups — #33096609

Order 18688.

724 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618563	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988638	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22610705	C₂	1	4	yes	maximal, complemented
5	#22610137	C₂	1	4	yes	maximal
6	#22610103	C₂	1	1	yes	maximal, characteristic, complemented
7	#22610102	C₂	1	1	yes	maximal, characteristic, complemented
8	#22610068	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#1837	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
11	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
12	#17988643	—	2	1	no	—
13	#17988643	—	2	1	no	—
14	#17988639	—	2	1	no	—
15	#17988639	—	2	1	no	—
16	#17988638	C₄	1	2	yes	—
17	#17988638	C₄	1	2	yes	—
18	#17988638	C₄	1	2	yes	—
19	#17988638	C₄	1	2	yes	—
20	C₂×#14556527	C₂²	1	4	yes	—
21	C₂×#14556526	C₂²	1	4	yes	—
22	#17988611	C₂²	1	1	yes	characteristic
23	#17988611	C₂²	1	1	yes	characteristic
24	#17988610	C₂²	1	2	yes	—
25	#17988609	—	2	1	no	—
26	#17988609	—	2	1	no	—
27	C₂×#14556520	C₂²	1	2	yes	—
28	C₄⋊C₈×D₇₃	—	2	1	no	—
29	C₄⋊C₈×D₇₃	—	2	1	no	—
30	#17988550	C₂²	1	2	yes	—
31	C₂×#14556503	C₂²	1	2	yes	—
32	M₁₆×Dic₇₃	C₂²	1	2	yes	—
33	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
34	#17988351	C₂²	1	4	yes	—
35	#423×C₇₃	C₂²	1	1	yes	characteristic
36	#423×C₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
38	#341×C₇₃	C₂²	1	4	yes	—
39	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
40	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
41	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
42	C₂×#11924012	C₂³	1	2	yes	—
43	C₂×#11924012	C₂³	1	2	yes	—
44	C₂×#11924011	—	2	2	no	—
45	M₁₆×D₇₃	—	4	4	no	—
46	C₂²×#10596831	C₂³	1	2	yes	—
47	C₂×C₈×D₇₃	—	2	2	no	—
48	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
49	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
50	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
51	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
54	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
55	C₄²×D₇₃	D₄	1	1	yes	characteristic
56	C₄²×D₇₃	D₄	1	1	yes	characteristic
57	C₄²×D₇₃	D₄	1	1	yes	characteristic
58	C₄²×D₇₃	D₄	1	1	yes	characteristic
59	#14556527	—	4	4	no	—
60	#14556526	—	4	4	no	—
61	C₄⋊#10596831	—	2	1	no	—
62	C₄⋊#10596831	—	2	1	no	—
63	C₄⋊#10596831	—	2	1	no	—
64	C₄⋊#10596831	—	2	1	no	—
65	#14556520	—	2	2	no	—
66	#14556520	—	2	2	no	—
67	#14556520	C₂×C₄	1	4	yes	—
68	#14556520	C₂×C₄	1	4	yes	—
69	#14556503	—	2	2	no	—
70	#14556503	—	2	2	no	—
71	#14556503	C₂×C₄	1	4	yes	—
72	#14556503	C₂×C₄	1	4	yes	—
73	#14556501	—	2	2	no	—
74	C₄×#10596831	C₂×C₄	1	2	yes	—
75	C₄×#10596831	C₂×C₄	1	2	yes	—
76	C₈×Dic₇₃	—	2	2	no	—
77	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
79	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
80	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₇₃	—	2	1	no	—
82	C₄⋊C₈×C₇₃	—	2	1	no	—
83	C₄⋊C₈×C₇₃	—	2	1	no	—
84	C₄⋊C₈×C₇₃	—	2	1	no	—
85	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
86	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	—
87	C₂³×D₇₃	C₂×Q₈	1	1	yes	characteristic
88	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
89	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
90	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
91	C₂×C₄×D₇₃	—	2	2	no	—
92	C₂×C₄×D₇₃	—	2	2	no	—
93	C₂×C₄×D₇₃	—	2	4	no	—
94	C₂×C₄×D₇₃	—	4	2	no	—
95	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
107	#11924012	—	2	4	no	—
108	#11924012	—	2	4	no	—
109	#11924011	—	4	4	no	—
110	C₂×#10596831	—	2	2	no	—
111	C₂×#10596831	—	2	2	no	—
112	C₂×#10596831	—	2	2	no	—
113	C₂×#10596831	—	2	2	no	—
114	C₂×#10596831	C₂²×C₄	1	4	yes	—
115	C₈×D₇₃	—	4	4	no	—
116	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₇₃	—	2	4	no	—
132	M₁₆×C₇₃	—	2	4	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	—	2	2	no	—
137	C₂×C₈×C₇₃	C₂²×C₄	1	4	yes	—
138	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₂³×C₇₃	C₂²×Q₈	1	1	yes	characteristic
143	C₂²×D₇₃	—	2	2	no	—
144	C₂²×D₇₃	—	2	2	no	—
145	C₂²×D₇₃	—	4	1	no	—
146	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₇₃	—	2	2	no	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₇₃	H(5,𝔽₂)	1	2	yes	—
157	C₂×C₄×C₇₃	2₋¹⁺⁴	1	2	yes	—
158	C₂×Dic₇₃	—	2	2	no	—
159	C₂×Dic₇₃	—	2	2	no	—
160	C₂×Dic₇₃	—	4	1	no	—
161	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
167	C₄×D₇₃	—	2	2	no	—
168	C₄×D₇₃	—	2	2	no	—
169	C₄×D₇₃	—	2	2	no	—
170	C₄×D₇₃	—	2	1	no	—
171	C₄×D₇₃	—	2	1	no	—
172	C₄×D₇₃	—	2	1	no	—
173	C₄×D₇₃	—	2	1	no	—
174	C₄×D₇₃	—	2	2	no	—
175	C₄×D₇₃	—	2	2	no	—
176	C₄×D₇₃	—	2	2	no	—
177	C₄×D₇₃	—	2	2	no	—
178	C₄×D₇₃	—	4	1	no	—
179	C₄×D₇₃	—	4	1	no	—
180	C₄×D₇₃	#108	1	4	yes	complemented
181	C₈×C₇₃	—	2	4	no	—
182	C₈×C₇₃	—	4	2	no	—
183	C₈×C₇₃	—	4	2	no	—
184	#10596831	—	2	4	no	—
185	#10596831	—	4	2	no	—
186	#10596831	—	4	2	no	—
187	C₂²×C₇₃	—	2	1	no	—
188	C₂²×C₇₃	—	2	1	no	—
189	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₇₃	#544	1	2	yes	—
191	C₂×D₇₃	—	2	1	no	—
192	C₂×D₇₃	—	2	1	no	—
193	C₂×D₇₃	—	2	1	no	—
194	C₂×D₇₃	—	2	1	no	—
195	C₂×D₇₃	—	2	1	no	—
196	C₂×D₇₃	—	4	4	no	—
197	C₂×D₇₃	C₂×#108	1	2	yes	—
198	C₄×C₇₃	—	2	1	no	—
199	C₄×C₇₃	—	2	1	no	—
200	C₄×C₇₃	C₂×#108	1	2	yes	—
201	C₄×C₇₃	#430	1	2	yes	—
202	C₄×C₇₃	#520	1	2	yes	—
203	C₄×C₇₃	#535	1	1	yes	characteristic
204	C₄×C₇₃	#536	1	1	yes	characteristic
205	Dic₇₃	—	2	1	no	—
206	Dic₇₃	—	2	1	no	—
207	Dic₇₃	—	2	1	no	—
208	Dic₇₃	—	2	1	no	—
209	Dic₇₃	—	2	1	no	—
210	Dic₇₃	C₂×#108	1	2	yes	—
211	#21993	—	73	1	no	maximal, Sylow
212	C₂×C₇₃	—	2	2	no	—
213	C₂×C₇₃	#2317	1	1	yes	characteristic
214	C₂×C₇₃	C₂²×#108	1	1	yes	characteristic
215	C₂×C₇₃	C₂×#430	1	1	yes	characteristic
216	D₇₃	—	2	2	no	—
217	D₇₃	—	4	1	no	—
218	#2920	—	73	1	no	—
219	C₂×#431	—	73	1	no	—
220	C₂×#423	—	73	1	no	—
221	#1950	—	73	4	no	—
222	#1855	—	73	4	no	—
223	#1848	—	73	1	no	—
224	#1848	—	73	1	no	—
225	#1837	—	73	1	no	—
226	#1837	D₇₃	1	1	yes	characteristic, complemented
227	C₇₃	#21993	1	1	yes	characteristic, complemented, Sylow
228	C₂²×M₁₆	—	73	2	no	—
229	C₂²×C₄²	—	73	1	no	—
230	#432	—	146	1	no	—
231	#432	—	146	1	no	—
232	#431	—	73	2	no	—
233	#431	—	73	2	no	—
234	#431	—	73	2	no	—
235	#431	—	73	2	no	—
236	#431	—	146	1	no	—
237	#431	—	146	1	no	—
238	C₂×#108	—	73	4	no	—
239	C₂×#108	—	73	4	no	—
240	#423	—	73	2	no	—
241	#423	—	73	1	no	—
242	#423	—	73	1	no	—
243	#423	—	146	1	no	—
244	#423	—	146	1	no	—
245	#423	C₂×D₇₃	1	1	yes	characteristic
246	#423	C₂×D₇₃	1	1	yes	characteristic
247	C₂×C₄⋊C₈	—	73	2	no	—
248	C₂×C₄⋊C₈	—	146	1	no	—
249	C₂×C₄⋊C₈	—	146	1	no	—
250	#407	—	73	2	no	—
251	C₂×C₂²⋊C₈	—	73	2	no	—
252	C₄×M₁₆	—	73	2	no	—
253	C₂×C₄×C₈	—	73	1	no	—
254	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
255	#341	—	73	4	no	—
256	#341	C₂×D₇₃	1	4	yes	—
257	C₂³×C₄	—	73	1	no	—
258	C₂³×C₄	—	73	1	no	—
259	C₂³×C₄	—	73	1	no	—
260	C₂×M₁₆	—	292	4	no	—
261	C₂×M₁₆	—	73	2	no	—
262	C₂×M₁₆	—	73	2	no	—
263	C₂×M₁₆	—	146	2	no	—
264	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
265	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
266	C₂²×C₈	—	73	2	no	—
267	C₂²×C₈	—	146	2	no	—
268	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
269	C₂×C₄²	—	73	1	no	—
270	C₂×C₄²	—	73	1	no	—
271	C₂×C₄²	—	73	1	no	—
272	C₂×C₄²	—	73	1	no	—
273	C₂×C₄²	—	73	1	no	—
274	C₂×C₄²	—	73	1	no	—
275	C₂×C₄²	—	73	1	no	—
276	C₂×C₄²	—	73	1	no	—
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	—	73	1	no	—
279	C₂×C₄²	—	73	1	no	—
280	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
281	#108	—	292	4	no	—
282	#108	—	292	4	no	—
283	C₄⋊C₈	—	2	1	no	—
284	C₄⋊C₈	—	2	1	no	—
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	73	4	no	—
288	C₄⋊C₈	—	73	4	no	—
289	C₄⋊C₈	—	146	2	no	—
290	C₄⋊C₈	—	146	2	no	—
291	C₄⋊C₈	—	146	1	no	—
292	C₄⋊C₈	—	146	1	no	—
293	C₄⋊C₈	—	146	1	no	—
294	C₄⋊C₈	—	146	1	no	—
295	C₂²⋊C₈	—	73	4	no	—
296	C₂²⋊C₈	—	73	4	no	—
297	C₂²⋊C₈	—	146	2	no	—
298	C₂²⋊C₈	—	146	2	no	—
299	#97	—	146	2	no	—
300	C₄×C₈	—	73	2	no	—
301	C₄×C₈	—	73	2	no	—
302	C₄×C₈	—	146	2	no	—
303	C₄×C₈	C₄×D₇₃	1	2	yes	—
304	C₄×C₈	C₄×D₇₃	1	2	yes	—
305	C₂⁴	—	73	1	no	—
306	C₂²×C₄	—	292	2	no	—
307	C₂²×C₄	—	73	1	no	—
308	C₂²×C₄	—	73	1	no	—
309	C₂²×C₄	—	73	1	no	—
310	C₂²×C₄	—	73	1	no	—
311	C₂²×C₄	—	73	1	no	—
312	C₂²×C₄	—	73	1	no	—
313	C₂²×C₄	—	73	1	no	—
314	C₂²×C₄	—	73	1	no	—
315	C₂²×C₄	—	73	1	no	—
316	C₂²×C₄	—	73	1	no	—
317	C₂²×C₄	—	73	1	no	—
318	C₂²×C₄	—	73	1	no	—
319	C₂²×C₄	—	73	1	no	—
320	C₂²×C₄	—	73	1	no	—
321	C₂²×C₄	—	73	1	no	—
322	C₂²×C₄	—	146	4	no	—
323	C₂²×C₄	—	146	2	no	—
324	C₂²×C₄	—	146	2	no	—
325	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
326	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
327	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
328	M₁₆	—	2	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	292	4	no	—
331	M₁₆	—	146	4	no	—
332	M₁₆	—	146	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	292	4	no	—
338	C₂×C₈	—	73	4	no	—
339	C₂×C₈	—	146	2	no	—
340	C₂×C₈	—	146	2	no	—
341	C₂×C₈	—	146	2	no	—
342	C₂×C₈	—	146	2	no	—
343	C₂×C₈	C₂×C₄×D₇₃	1	4	yes	—
344	C₄²	—	73	1	no	—
345	C₄²	—	73	1	no	—
346	C₄²	—	73	1	no	—
347	C₄²	—	73	1	no	—
348	C₄²	—	73	1	no	—
349	C₄²	—	73	1	no	—
350	C₄²	—	73	1	no	—
351	C₄²	—	73	1	no	—
352	C₄²	—	73	1	no	—
353	C₄²	—	73	1	no	—
354	C₄²	—	73	1	no	—
355	C₄²	—	73	1	no	—
356	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
358	C₄²	D₄×D₇₃	1	1	yes	characteristic
359	C₄²	D₄×D₇₃	1	1	yes	characteristic
360	C₂³	—	292	1	no	—
361	C₂³	—	73	1	no	—
362	C₂³	—	73	1	no	—
363	C₂³	—	146	2	no	—
364	C₂³	—	146	2	no	—
365	C₂³	C₂×Q₈×D₇₃	1	1	yes	characteristic
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	292	1	no	—
369	C₂×C₄	—	292	1	no	—
370	C₂×C₄	—	292	1	no	—
371	C₂×C₄	—	73	1	no	—
372	C₂×C₄	—	73	4	no	—
373	C₂×C₄	—	73	1	no	—
374	C₂×C₄	—	73	1	no	—
375	C₂×C₄	—	73	1	no	—
376	C₂×C₄	—	73	1	no	—
377	C₂×C₄	—	73	1	no	—
378	C₂×C₄	—	146	2	no	—
379	C₂×C₄	—	146	2	no	—
380	C₂×C₄	—	146	2	no	—
381	C₂×C₄	—	146	2	no	—
382	C₂×C₄	—	146	2	no	—
383	C₂×C₄	—	146	2	no	—
384	C₂×C₄	—	146	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	2	no	—
390	C₂×C₄	—	146	2	no	—
391	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
392	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
393	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
394	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
397	C₂×C₄	#14556637	1	2	yes	—
398	C₂×C₄	#14556638	1	2	yes	—
399	C₈	—	2	4	no	—
400	C₈	—	4	2	no	—
401	C₈	—	4	2	no	—
402	C₈	—	292	2	no	—
403	C₈	—	292	2	no	—
404	C₈	—	146	4	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	292	4	no	—
408	C₂²	—	73	2	no	—
409	C₂²	—	146	1	no	—
410	C₂²	—	146	1	no	—
411	C₂²	—	146	1	no	—
412	C₂²	—	146	1	no	—
413	C₂²	—	146	1	no	—
414	C₂²	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
415	C₂²	#17989217	1	2	yes	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	73	2	no	—
419	C₄	—	146	1	no	—
420	C₄	—	146	1	no	—
421	C₄	—	146	1	no	—
422	C₄	—	146	1	no	—
423	C₄	—	146	1	no	—
424	C₄	#108×D₇₃	1	2	yes	—
425	C₄	#17988634	1	2	yes	—
426	C₄	#17989067	1	2	yes	—
427	C₄	#17989155	1	1	yes	characteristic
428	C₄	#17989157	1	1	yes	characteristic
429	C₂	—	2	2	no	—
430	C₂	—	292	1	no	—
431	C₂	—	146	2	no	—
432	C₂	#22612556	1	1	yes	characteristic
433	C₂	C₂×#108×D₇₃	1	1	yes	characteristic
434	C₂	C₂×#17988634	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1837	C₂
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×Q₈
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1837	D₇₃
hypocenter	C₇₃	#21993
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1837

Complements

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

N	H ≅ G/N	type
4. #22610705	C₂	semidirect
6. #22610103	C₂	semidirect
7. #22610102	C₂	semidirect
8. #22610068	C₂	semidirect
9. C₇₃×#1837	C₂	semidirect
180. C₄×D₇₃	#108	semidirect
226. #1837	D₇₃	semidirect
227. C₇₃	#21993	semidirect

Maximal subgroups

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

subgroup	index
#22618563	2
C₂×#17988638	2
#423×D₇₃	2
#22610705	2
#22610137	2
#22610103	2
#22610102	2
#22610068	2
C₇₃×#1837	2
#21993	73