Subgroups — #32976222

Order 18688.

634 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#431×D₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988609	C₂	1	1	yes	maximal, characteristic
3	#423×D₇₃	C₂	1	1	yes	maximal, characteristic
4	#22607828	C₂	1	1	yes	maximal, characteristic, complemented
5	#22607827	C₂	1	1	yes	maximal, characteristic, complemented
6	#22607826	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇₃×#1301	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#11924011	—	2	1	no	—
9	C₂×M₁₆×D₇₃	—	2	1	no	—
10	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
11	#17988640	C₂²	1	1	yes	characteristic
12	#17988639	—	2	1	no	—
13	#17988638	—	2	1	no	—
14	#17988637	C₄	1	2	yes	—
15	#17988611	C₂²	1	1	yes	characteristic
16	#17988610	—	2	1	no	—
17	#17988609	—	2	1	no	—
18	#17988609	—	2	1	no	—
19	#17988609	—	2	1	no	—
20	#17988609	C₄	1	2	yes	—
21	#17988609	C₄	1	2	yes	—
22	#17988609	C₄	1	2	yes	—
23	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
24	C₂×#14556520	—	2	1	no	—
25	C₄⋊C₈×D₇₃	—	2	1	no	—
26	C₄⋊C₈×D₇₃	—	2	1	no	—
27	C₄⋊C₈×D₇₃	C₄	1	2	yes	—
28	C₂²⋊C₈×D₇₃	C₄	1	2	yes	—
29	C₄×C₈×D₇₃	—	2	1	no	—
30	#431×C₇₃	C₂²	1	1	yes	characteristic
31	#423×C₇₃	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₇₃	Q₈	1	1	yes	characteristic
36	C₂×#11924012	—	2	1	no	—
37	C₂×#11924011	—	2	2	no	—
38	C₂×#11924011	—	2	2	no	—
39	C₂×#11924011	—	2	2	no	—
40	C₂×#11924011	—	4	2	no	—
41	C₂×#11924011	—	4	2	no	—
42	M₁₆×D₇₃	—	4	2	no	—
43	M₁₆×D₇₃	—	4	2	no	—
44	C₂²×#10596831	—	2	1	no	—
45	C₂×C₈×D₇₃	—	2	2	no	—
46	C₂×C₈×D₇₃	—	2	2	no	—
47	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₇₃	Q₈	1	1	yes	characteristic
50	C₄²×D₇₃	C₂×C₄	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	D₄	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	C₄⋊#10596831	—	2	1	no	—
59	C₄⋊#10596831	—	2	1	no	—
60	C₄⋊#10596831	—	2	1	no	—
61	C₄⋊#10596831	C₂×C₄	1	2	yes	—
62	C₄⋊#10596831	C₂×C₄	1	2	yes	—
63	#14556520	—	2	2	no	—
64	#14556520	—	2	2	no	—
65	#14556520	—	2	2	no	—
66	#14556520	—	2	2	no	—
67	#14556520	—	2	2	no	—
68	C₂²⋊#10596831	C₂×C₄	1	2	yes	—
69	#14556503	—	2	2	no	—
70	C₄×#10596831	—	2	1	no	—
71	C₈×Dic₇₃	—	2	2	no	—
72	C₂×M₁₆×C₇₃	—	2	1	no	—
73	C₂²×C₈×C₇₃	—	2	1	no	—
74	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₇₃	—	2	1	no	—
76	C₄⋊C₈×C₇₃	—	2	1	no	—
77	C₄⋊C₈×C₇₃	—	2	1	no	—
78	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
79	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
80	C₂²⋊C₈×C₇₃	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₇₃	—	2	1	no	—
82	C₂³×D₇₃	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₇₃	—	4	2	no	—
87	C₂×C₄×D₇₃	—	4	2	no	—
88	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₂²⋊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	D₈	1	2	yes	—
101	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
102	C₂×C₄×D₇₃	SD₁₆	1	2	yes	—
103	C₂×C₄×D₇₃	Q₁₆	1	2	yes	—
104	#11924012	—	4	1	no	—
105	#11924012	—	4	1	no	—
106	#11924011	—	4	4	no	—
107	#11924011	—	4	4	no	—
108	#11924011	—	4	4	no	—
109	C₂×#10596831	—	2	2	no	—
110	C₂×#10596831	—	2	2	no	—
111	C₂×#10596831	—	2	2	no	—
112	C₂×#10596831	—	4	1	no	—
113	C₂×#10596831	—	4	1	no	—
114	C₈×D₇₃	—	4	4	no	—
115	C₈×D₇₃	—	4	4	no	—
116	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
117	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
118	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
128	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
131	M₁₆×C₇₃	—	4	1	no	—
132	M₁₆×C₇₃	—	4	1	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	—	4	1	no	—
137	C₂×C₈×C₇₃	—	4	1	no	—
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	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₇₃	—	4	1	no	—
144	C₂²×D₇₃	—	4	1	no	—
145	C₂²×D₇₃	#95	1	1	yes	characteristic
146	C₂²×D₇₃	#95	1	1	yes	characteristic
147	C₂²×D₇₃	#106	1	2	yes	—
148	C₂²×D₇₃	#107	1	2	yes	—
149	C₂×C₄×C₇₃	—	2	2	no	—
150	C₂×C₄×C₇₃	—	4	1	no	—
151	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
152	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₇₃	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₇₃	C₂×Q₁₆	1	1	yes	characteristic
161	C₂×Dic₇₃	—	2	2	no	—
162	C₂×Dic₇₃	—	4	1	no	—
163	C₂×Dic₇₃	#95	1	1	yes	characteristic
164	C₂×Dic₇₃	#95	1	1	yes	characteristic
165	C₂×Dic₇₃	#95	1	1	yes	characteristic
166	C₂×Dic₇₃	#95	1	1	yes	characteristic
167	C₂×Dic₇₃	#95	1	1	yes	characteristic
168	C₂×Dic₇₃	#95	1	1	yes	characteristic
169	C₂×Dic₇₃	#106	1	2	yes	—
170	C₂×Dic₇₃	#107	1	2	yes	—
171	C₄×D₇₃	—	2	2	no	—
172	C₄×D₇₃	—	2	2	no	—
173	C₄×D₇₃	—	2	2	no	—
174	C₄×D₇₃	—	2	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	#102	1	2	yes	—
180	C₄×D₇₃	#102	1	2	yes	—
181	C₄×D₇₃	#102	1	2	yes	—
182	C₄×D₇₃	#102	1	2	yes	—
183	C₄×D₇₃	#103	1	2	yes	—
184	C₄×D₇₃	#103	1	2	yes	—
185	C₄×D₇₃	#103	1	2	yes	—
186	C₄×D₇₃	#103	1	2	yes	—
187	C₈×C₇₃	—	4	2	no	—
188	C₈×C₇₃	—	4	2	no	—
189	C₈×C₇₃	—	4	2	no	—
190	#10596831	—	4	2	no	—
191	#10596831	—	4	2	no	—
192	#10596831	—	4	2	no	—
193	C₂²×C₇₃	—	2	1	no	—
194	C₂²×C₇₃	—	2	1	no	—
195	C₂²×C₇₃	C₂×#95	1	1	yes	characteristic
196	C₂²×C₇₃	C₂×#106	1	1	yes	characteristic
197	C₂²×C₇₃	C₂×#107	1	1	yes	characteristic
198	C₂×D₇₃	—	2	1	no	—
199	C₂×D₇₃	—	2	1	no	—
200	C₂×D₇₃	—	2	1	no	—
201	C₂×D₇₃	—	2	1	no	—
202	C₂×D₇₃	—	4	2	no	—
203	C₂×D₇₃	—	4	2	no	—
204	C₂×D₇₃	#340	1	2	yes	—
205	C₂×D₇₃	#340	1	2	yes	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	—	2	1	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	C₂×#102	1	1	yes	characteristic
210	C₄×C₇₃	C₂×#102	1	1	yes	characteristic
211	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
212	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
213	C₄×C₇₃	#430	1	2	yes	—
214	Dic₇₃	—	2	1	no	—
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	—	2	1	no	—
217	Dic₇₃	#340	1	2	yes	—
218	Dic₇₃	#340	1	2	yes	—
219	Dic₇₃	#344	1	2	yes	—
220	#8079	—	73	1	no	maximal, Sylow
221	C₂×C₇₃	—	2	1	no	—
222	C₂×C₇₃	—	2	1	no	—
223	C₂×C₇₃	C₂×#340	1	1	yes	characteristic
224	C₂×C₇₃	#1738	1	1	yes	characteristic
225	C₂×C₇₃	C₂×#344	1	1	yes	characteristic
226	D₇₃	—	2	2	no	—
227	D₇₃	—	2	2	no	—
228	C₂×#431	—	73	1	no	—
229	C₂×#423	—	73	1	no	—
230	C₂×#423	—	73	1	no	—
231	#1301	—	73	1	no	—
232	#1301	—	73	1	no	—
233	#1301	—	73	1	no	—
234	#1301	D₇₃	1	1	yes	characteristic, complemented
235	C₇₃	#8079	1	1	yes	characteristic, complemented, Sylow
236	C₂²×M₁₆	—	146	1	no	—
237	C₂²×M₁₆	—	146	1	no	—
238	C₂²×C₄²	—	73	1	no	—
239	#431	—	73	1	no	—
240	#431	—	73	2	no	—
241	#431	—	146	1	no	—
242	#431	—	146	1	no	—
243	#431	C₂×D₇₃	1	1	yes	characteristic
244	#423	—	73	1	no	—
245	#423	—	73	2	no	—
246	#423	—	73	2	no	—
247	#423	—	73	2	no	—
248	#423	—	146	1	no	—
249	#423	—	146	1	no	—
250	#423	—	146	1	no	—
251	#423	—	146	1	no	—
252	#423	C₂×D₇₃	1	1	yes	characteristic
253	C₂×C₄⋊C₈	—	73	1	no	—
254	C₂×C₄⋊C₈	—	73	2	no	—
255	C₂×C₄⋊C₈	—	146	1	no	—
256	C₂×C₄⋊C₈	—	146	1	no	—
257	C₂×C₄⋊C₈	—	146	1	no	—
258	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
259	C₂×C₂²⋊C₈	—	73	2	no	—
260	C₂×C₄×C₈	—	146	1	no	—
261	C₂³×C₄	—	73	1	no	—
262	C₂³×C₄	—	73	1	no	—
263	C₂³×C₄	—	73	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	292	2	no	—
266	C₂×M₁₆	—	292	2	no	—
267	C₂×M₁₆	—	292	2	no	—
268	C₂×M₁₆	—	292	2	no	—
269	C₂×M₁₆	—	146	2	no	—
270	C₂×M₁₆	—	146	2	no	—
271	C₂×M₁₆	—	146	2	no	—
272	C₂×M₁₆	—	146	1	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	146	2	no	—
275	C₂²×C₈	—	146	2	no	—
276	C₂²×C₈	—	146	1	no	—
277	C₂×C₄²	—	73	1	no	—
278	C₂×C₄²	—	73	1	no	—
279	C₂×C₄²	—	73	1	no	—
280	C₂×C₄²	—	73	1	no	—
281	C₂×C₄²	—	73	1	no	—
282	C₂×C₄²	—	73	1	no	—
283	C₂×C₄²	—	73	1	no	—
284	C₂×C₄²	—	73	1	no	—
285	C₂×C₄²	—	73	1	no	—
286	C₂×C₄²	—	73	1	no	—
287	C₂×C₄²	—	73	1	no	—
288	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
289	C₄⋊C₈	—	2	1	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	73	2	no	—
293	C₄⋊C₈	—	73	2	no	—
294	C₄⋊C₈	—	146	2	no	—
295	C₄⋊C₈	—	146	2	no	—
296	C₄⋊C₈	—	146	2	no	—
297	C₄⋊C₈	—	146	2	no	—
298	C₄⋊C₈	—	146	2	no	—
299	C₄⋊C₈	—	146	1	no	—
300	C₄⋊C₈	—	146	1	no	—
301	C₄⋊C₈	—	146	1	no	—
302	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
303	C₄⋊C₈	C₄×D₇₃	1	2	yes	—
304	C₂²⋊C₈	—	73	2	no	—
305	C₂²⋊C₈	—	146	2	no	—
306	C₂²⋊C₈	C₄×D₇₃	1	2	yes	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	146	2	no	—
309	C₄×C₈	—	146	1	no	—
310	C₂⁴	—	73	1	no	—
311	C₂²×C₄	—	292	2	no	—
312	C₂²×C₄	—	292	2	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	—	73	1	no	—
323	C₂²×C₄	—	73	2	no	—
324	C₂²×C₄	—	73	2	no	—
325	C₂²×C₄	—	73	2	no	—
326	C₂²×C₄	—	73	2	no	—
327	C₂²×C₄	—	73	1	no	—
328	C₂²×C₄	—	73	1	no	—
329	C₂²×C₄	—	73	1	no	—
330	C₂²×C₄	—	73	1	no	—
331	C₂²×C₄	—	73	1	no	—
332	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
333	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
334	C₂²×C₄	Q₈×D₇₃	1	1	yes	characteristic
335	M₁₆	—	4	1	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	292	4	no	—
338	M₁₆	—	292	4	no	—
339	M₁₆	—	292	4	no	—
340	M₁₆	—	292	1	no	—
341	M₁₆	—	292	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	1	no	—
347	C₂×C₈	—	292	4	no	—
348	C₂×C₈	—	292	4	no	—
349	C₂×C₈	—	292	1	no	—
350	C₂×C₈	—	292	1	no	—
351	C₂×C₈	—	146	2	no	—
352	C₂×C₈	—	146	2	no	—
353	C₂×C₈	—	146	2	no	—
354	C₄²	—	73	1	no	—
355	C₄²	—	73	1	no	—
356	C₄²	—	73	1	no	—
357	C₄²	—	73	1	no	—
358	C₄²	—	73	1	no	—
359	C₄²	—	73	1	no	—
360	C₄²	—	73	1	no	—
361	C₄²	—	73	1	no	—
362	C₄²	—	73	1	no	—
363	C₄²	—	73	1	no	—
364	C₄²	—	73	1	no	—
365	C₄²	—	73	1	no	—
366	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
367	C₄²	C₂×C₄×D₇₃	1	1	yes	characteristic
368	C₄²	D₄×D₇₃	1	1	yes	characteristic
369	C₄²	D₄×D₇₃	1	1	yes	characteristic
370	C₂³	—	292	1	no	—
371	C₂³	—	292	1	no	—
372	C₂³	—	73	2	no	—
373	C₂³	—	73	2	no	—
374	C₂³	—	73	1	no	—
375	C₂³	—	73	1	no	—
376	C₂³	C₄⋊C₄×D₇₃	1	1	yes	characteristic
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	292	1	no	—
380	C₂×C₄	—	292	1	no	—
381	C₂×C₄	—	292	1	no	—
382	C₂×C₄	—	292	1	no	—
383	C₂×C₄	—	292	1	no	—
384	C₂×C₄	—	73	2	no	—
385	C₂×C₄	—	73	2	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	2	no	—
390	C₂×C₄	—	73	2	no	—
391	C₂×C₄	—	73	2	no	—
392	C₂×C₄	—	73	2	no	—
393	C₂×C₄	—	73	2	no	—
394	C₂×C₄	—	73	2	no	—
395	C₂×C₄	—	73	2	no	—
396	C₂×C₄	—	73	2	no	—
397	C₂×C₄	—	73	1	no	—
398	C₂×C₄	—	73	1	no	—
399	C₂×C₄	—	73	1	no	—
400	C₂×C₄	—	146	2	no	—
401	C₂×C₄	—	146	2	no	—
402	C₂×C₄	—	146	2	no	—
403	C₂×C₄	—	146	2	no	—
404	C₂×C₄	—	146	2	no	—
405	C₂×C₄	C₄²×D₇₃	1	1	yes	characteristic
406	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
407	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
408	C₂×C₄	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
409	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
410	C₂×C₄	C₄⋊C₄×D₇₃	1	1	yes	characteristic
411	C₂×C₄	D₈×D₇₃	1	1	yes	characteristic
412	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
413	C₂×C₄	SD₁₆×D₇₃	1	1	yes	characteristic
414	C₂×C₄	Q₁₆×D₇₃	1	1	yes	characteristic
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	—	292	2	no	—
419	C₈	—	292	2	no	—
420	C₈	—	292	2	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	292	2	no	—
424	C₂²	—	292	2	no	—
425	C₂²	—	73	2	no	—
426	C₂²	—	73	2	no	—
427	C₂²	—	146	1	no	—
428	C₂²	—	146	1	no	—
429	C₂²	—	146	1	no	—
430	C₂²	—	146	1	no	—
431	C₂²	#95×D₇₃	1	1	yes	characteristic
432	C₂²	#106×D₇₃	1	1	yes	characteristic
433	C₂²	#107×D₇₃	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	73	2	no	—
438	C₄	—	73	2	no	—
439	C₄	—	73	2	no	—
440	C₄	—	146	1	no	—
441	C₄	—	146	1	no	—
442	C₄	—	146	1	no	—
443	C₄	#102×D₇₃	1	1	yes	characteristic
444	C₄	#102×D₇₃	1	1	yes	characteristic
445	C₄	#103×D₇₃	1	1	yes	characteristic
446	C₄	#103×D₇₃	1	1	yes	characteristic
447	C₄	#17988634	1	2	yes	—
448	C₂	—	2	1	no	—
449	C₂	—	2	1	no	—
450	C₂	—	146	2	no	—
451	C₂	—	146	2	no	—
452	C₂	#340×D₇₃	1	1	yes	characteristic
453	C₂	#22609656	1	1	yes	characteristic
454	C₂	#344×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₇₃
Fitting	C₇₃×#1301	C₂
socle	C₂²×C₇₃	C₂×#95
prime radical	C₂³×D₇₃	C₄⋊C₄
cosocle	C₂×C₄²×C₇₃	C₂³
hypercenter	#1301	D₇₃
hypocenter	C₇₃	#8079
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1301

Complements

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

N	H ≅ G/N	type
4. #22607828	C₂	semidirect
5. #22607827	C₂	semidirect
6. #22607826	C₂	semidirect
7. C₇₃×#1301	C₂	semidirect
234. #1301	D₇₃	semidirect
235. C₇₃	#8079	semidirect

Maximal subgroups

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

subgroup	index
#431×D₇₃	2
C₂×#17988609	2
#423×D₇₃	2
#22607828	2
#22607827	2
#22607826	2
C₇₃×#1301	2
#8079	73