Subgroups — #34020324

Order 18688.

1002 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	D₇₃⋊#432	C₂	1	1	yes	maximal, characteristic
2	C₂×#17989523	C₂	1	1	yes	maximal, characteristic
3	#22625720	C₂	1	4	yes	maximal, complemented
4	#22625659	C₂	1	2	yes	maximal
5	C₂²⋊C₈×#64408	C₂	1	2	yes	maximal
6	#22625649	C₂	1	2	yes	maximal, complemented
7	#22625587	C₂	1	2	yes	maximal, complemented
8	#431×D₇₃	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄×#64408	C₂²	1	2	yes	—
10	#17989610	C₄	1	2	yes	complemented
11	#17989609	C₄	1	2	yes	complemented
12	#17989608	C₄	1	2	yes	complemented
13	#17989607	C₄	1	2	yes	complemented
14	#17989588	C₂²	1	2	yes	—
15	#17989555	C₂²	1	2	yes	—
16	#17989546	C₂²	1	2	yes	—
17	C₂×#14556645	C₂²	1	4	yes	—
18	C₂×C₈×#64408	C₂²	1	4	yes	—
19	#17989523	C₄	1	2	yes	—
20	#17989523	C₄	1	2	yes	—
21	#17989523	C₂²	1	1	yes	characteristic
22	#17989523	C₂²	1	1	yes	characteristic
23	#17989523	C₂²	1	2	yes	—
24	C₂×(C₂×#64408)⋊C₄	C₄	1	2	yes	—
25	C₂×(C₂×#64408)⋊C₄	C₄	1	2	yes	—
26	#17989452	C₂²	1	4	yes	—
27	#17989452	C₂²	1	4	yes	—
28	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
29	#17988640	C₄	1	1	yes	characteristic, complemented
30	#17988639	C₄	1	2	yes	complemented
31	#17988638	C₄	1	2	yes	complemented
32	#17988637	C₄	1	1	yes	characteristic, complemented
33	#17988637	C₄	1	1	yes	characteristic, complemented
34	C₄⋊C₈×D₇₃	C₂²	1	2	yes	—
35	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
36	C₂²⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₇₃	C₂²	1	2	yes	—
38	#431×C₇₃	C₄	1	1	yes	characteristic, complemented
39	C₂³×#64408	C₂×C₄	1	4	yes	—
40	C₂×#11924036	C₂³	1	4	yes	—
41	C₂×C₄×#64408	—	2	8	no	—
42	C₂×C₄×#64408	C₂×C₄	1	4	yes	—
43	C₂×C₄×#64408	C₂³	1	2	yes	—
44	C₂×C₄×#64408	C₂³	1	2	yes	—
45	#14556658	C₂×C₄	1	4	yes	complemented
46	C₄⋊#10596833	C₂×C₄	1	4	yes	complemented
47	#14556648	C₂×C₄	1	4	yes	—
48	C₂²⋊#10596833	C₂×C₄	1	4	yes	—
49	#14556646	C₂×C₄	1	4	yes	complemented
50	#14556646	C₂×C₄	1	4	yes	complemented
51	#14556645	—	2	8	no	—
52	C₈×#64408	—	2	8	no	—
53	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
54	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
55	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
56	(C₂×#64408)⋊C₄	C₂×C₄	1	4	yes	—
57	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
58	(C₂×#64408)⋊C₄	C₂×C₄	1	2	yes	—
59	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
62	C₂×C₈×D₇₃	C₂³	1	2	yes	—
63	C₂×C₈×D₇₃	C₂³	1	2	yes	—
64	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
72	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₄²×D₇₃	C₂³	1	1	yes	characteristic
74	C₄²×D₇₃	C₂³	1	1	yes	characteristic
75	C₄⋊#10596831	C₂×C₄	1	2	yes	complemented
76	#14556520	C₂×C₄	1	2	yes	complemented
77	#14556520	C₂×C₄	1	2	yes	complemented
78	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊#10596831	C₂×C₄	1	1	yes	characteristic
80	#14556503	C₂×C₄	1	2	yes	—
81	#14556503	C₂×C₄	1	2	yes	—
82	C₄×#10596831	C₂×C₄	1	2	yes	complemented
83	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
84	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
85	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
86	C₄⋊C₈×C₇₃	C₂×C₄	1	2	yes	complemented
87	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
90	C₂²×#64408	—	2	8	no	—
91	C₂²×#64408	—	2	8	no	—
92	C₂²×#64408	—	4	4	no	—
93	C₂²×#64408	C₂²×C₄	1	4	yes	—
94	C₂²×#64408	C₂²×C₄	1	4	yes	—
95	#11924036	—	2	4	no	—
96	#11924036	—	2	4	no	—
97	C₂×#10596833	C₂²×C₄	1	8	yes	—
98	C₄×#64408	—	2	8	no	—
99	C₄×#64408	—	2	4	no	—
100	C₄×#64408	#41	1	8	yes	—
101	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
103	C₂²×Dic₇₃	C₄²	1	1	yes	characteristic
104	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₇₃	—	2	4	no	—
106	C₂×C₄×D₇₃	—	2	4	no	—
107	C₂×C₄×D₇₃	—	4	2	no	—
108	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
120	C₂×#10596831	C₂²×C₄	1	2	yes	—
121	C₂×#10596831	C₂²×C₄	1	2	yes	—
122	C₈×D₇₃	—	2	4	no	—
123	C₈×D₇₃	—	2	4	no	—
124	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
125	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
126	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
127	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
128	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
129	C₄×Dic₇₃	C₄²	1	1	yes	characteristic
130	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
137	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
138	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
140	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
141	C₄²×C₇₃	C₄²	1	1	yes	characteristic
142	C₄²×C₇₃	C₄²	1	1	yes	characteristic
143	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂³×C₇₃	C₂×C₄²	1	1	yes	characteristic
146	C₂²×D₇₃	—	2	2	no	—
147	C₂²×D₇₃	—	2	2	no	—
148	C₂²×D₇₃	C₂×C₄²	1	1	yes	characteristic
149	C₂²×D₇₃	#131	1	4	yes	—
150	C₂²×D₇₃	C₂³×C₄	1	1	yes	characteristic
151	C₂×#64408	—	2	4	no	—
152	C₂×#64408	—	2	4	no	—
153	C₂×#64408	—	2	4	no	—
154	C₂×#64408	—	2	4	no	—
155	C₂×#64408	—	2	4	no	—
156	C₂×#64408	—	4	16	no	—
157	C₂×#64408	#117	1	8	yes	—
158	C₂×C₄×C₇₃	—	2	2	no	—
159	C₂×C₄×C₇₃	—	2	2	no	—
160	C₂×C₄×C₇₃	—	4	1	no	—
161	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₇₃	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
167	C₂×Dic₇₃	—	2	2	no	—
168	C₂×Dic₇₃	—	2	2	no	—
169	C₂×Dic₇₃	—	4	1	no	—
170	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
171	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
172	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₇₃	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₇₃	C₂³×C₄	1	1	yes	characteristic
176	C₄×D₇₃	—	2	2	no	—
177	C₄×D₇₃	—	2	2	no	—
178	C₄×D₇₃	—	2	2	no	—
179	C₄×D₇₃	—	2	2	no	—
180	C₄×D₇₃	—	2	2	no	—
181	C₄×D₇₃	—	2	2	no	—
182	C₄×D₇₃	—	2	2	no	—
183	C₄×D₇₃	—	2	2	no	—
184	C₄×D₇₃	—	2	2	no	—
185	C₄×D₇₃	—	4	1	no	—
186	C₄×D₇₃	—	4	1	no	—
187	C₄×D₇₃	C₂×#41	1	4	yes	—
188	#10596833	—	2	8	no	—
189	C₈×C₇₃	—	2	2	no	—
190	C₈×C₇₃	—	2	2	no	—
191	#10596831	—	2	2	no	—
192	#10596831	—	2	2	no	—
193	C₂²×C₇₃	—	2	1	no	—
194	C₂²×C₇₃	—	2	1	no	—
195	C₂²×C₇₃	#405	1	2	yes	—
196	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
197	C₂×D₇₃	—	2	1	no	—
198	C₂×D₇₃	—	2	1	no	—
199	C₂×D₇₃	—	2	8	no	—
200	C₂×D₇₃	#405	1	2	yes	—
201	C₂×D₇₃	C₂×#117	1	2	yes	—
202	C₂×D₇₃	C₂×#131	1	2	yes	—
203	C₂×D₇₃	#568	1	2	yes	—
204	#64408	—	2	8	no	—
205	#64408	—	4	4	no	—
206	C₄×C₇₃	—	2	1	no	—
207	C₄×C₇₃	—	2	1	no	—
208	C₄×C₇₃	—	2	1	no	—
209	C₄×C₇₃	—	2	1	no	—
210	C₄×C₇₃	—	2	1	no	—
211	C₄×C₇₃	C₄×#41	1	2	yes	—
212	Dic₇₃	—	2	1	no	—
213	Dic₇₃	—	2	1	no	—
214	Dic₇₃	—	2	1	no	—
215	Dic₇₃	—	2	1	no	—
216	Dic₇₃	—	2	1	no	—
217	Dic₇₃	C₄×#41	1	2	yes	—
218	#20469	—	73	1	no	maximal, Sylow
219	C₂×C₇₃	—	2	2	no	—
220	C₂×C₇₃	C₄×#117	1	1	yes	characteristic
221	C₂×C₇₃	C₂×#405	1	1	yes	characteristic
222	C₂×C₇₃	#2873	1	1	yes	characteristic
223	D₇₃	—	2	2	no	—
224	D₇₃	#2924	1	4	yes	—
225	C₂×#432	—	73	1	no	—
226	C₂×#431	—	73	1	no	—
227	C₂×#376	—	73	1	no	—
228	#1768	—	73	4	no	—
229	#1749	—	73	2	no	—
230	C₄×C₂²⋊C₈	—	73	2	no	—
231	#1746	—	73	2	no	—
232	#1726	—	73	2	no	—
233	C₇₃	#20469	1	1	yes	characteristic, complemented, Sylow
234	C₂²×C₄²	—	73	1	no	—
235	C₂²×C₄²	—	73	2	no	—
236	#432	—	73	2	no	—
237	#432	—	73	2	no	—
238	#432	—	73	2	no	—
239	#432	—	73	2	no	—
240	#431	—	73	1	no	—
241	#431	—	73	2	no	—
242	#431	—	73	1	no	—
243	#431	—	73	1	no	—
244	#431	—	73	2	no	—
245	#431	#64408	1	1	yes	characteristic, complemented
246	C₂×C₄⋊C₈	—	73	2	no	—
247	C₂×C₄⋊C₈	—	73	2	no	—
248	C₂×C₂²⋊C₈	—	73	2	no	—
249	C₂×C₂²⋊C₈	—	73	1	no	—
250	C₂×C₂²⋊C₈	—	73	1	no	—
251	C₂×#97	—	73	2	no	—
252	C₂×#97	—	73	4	no	—
253	C₂×C₄×C₈	—	73	2	no	—
254	C₂×C₄×C₈	—	73	4	no	—
255	#376	—	73	2	no	—
256	#376	—	73	2	no	—
257	#376	—	73	1	no	—
258	#376	—	73	1	no	—
259	#376	—	73	2	no	—
260	C₂×#95	—	73	2	no	—
261	C₂×#95	—	73	2	no	—
262	#336	—	73	4	no	—
263	#336	—	73	4	no	—
264	C₂³×C₄	—	73	1	no	—
265	C₂³×C₄	—	73	4	no	—
266	C₂³×C₄	—	73	1	no	—
267	C₂³×C₄	—	73	1	no	—
268	C₂²×C₈	—	73	4	no	—
269	C₂²×C₈	—	73	2	no	—
270	C₂²×C₈	—	73	2	no	—
271	C₂×C₄²	—	73	2	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	—	73	1	no	—
281	C₂×C₄²	—	73	1	no	—
282	C₂×C₄²	—	73	1	no	—
283	C₂×C₄²	—	73	2	no	—
284	C₂×C₄²	—	73	4	no	—
285	C₂×C₄²	—	146	8	no	—
286	C₂×C₄²	C₂×#64408	1	1	yes	characteristic
287	C₄⋊C₈	—	73	4	no	—
288	C₄⋊C₈	—	73	4	no	—
289	C₄⋊C₈	—	73	2	no	—
290	C₄⋊C₈	—	73	2	no	—
291	C₄⋊C₈	—	73	2	no	—
292	C₄⋊C₈	C₂×#64408	1	2	yes	complemented
293	C₂²⋊C₈	—	73	4	no	—
294	C₂²⋊C₈	—	73	4	no	—
295	C₂²⋊C₈	—	73	1	no	—
296	C₂²⋊C₈	—	73	1	no	—
297	C₂²⋊C₈	—	73	2	no	—
298	C₂²⋊C₈	—	73	2	no	—
299	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
300	C₂²⋊C₈	C₂×#64408	1	1	yes	characteristic
301	#97	—	73	4	no	—
302	#97	—	73	4	no	—
303	#97	—	146	8	no	—
304	C₄×C₈	—	73	2	no	—
305	C₄×C₈	—	73	2	no	—
306	C₄×C₈	—	73	2	no	—
307	C₄×C₈	—	146	8	no	—
308	C₄×C₈	C₂×#64408	1	2	yes	complemented
309	#95	—	73	2	no	—
310	#95	—	73	2	no	—
311	#95	—	73	4	no	—
312	#95	—	73	4	no	—
313	#95	—	73	2	no	—
314	#95	—	73	2	no	—
315	C₂⁴	—	73	1	no	—
316	C₂²×C₄	—	292	2	no	—
317	C₂²×C₄	—	292	4	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	4	no	—
323	C₂²×C₄	—	73	1	no	—
324	C₂²×C₄	—	73	1	no	—
325	C₂²×C₄	—	73	1	no	—
326	C₂²×C₄	—	73	1	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	—	73	1	no	—
333	C₂²×C₄	—	73	1	no	—
334	C₂²×C₄	—	73	4	no	—
335	C₂²×C₄	—	146	4	no	—
336	C₂²×C₄	—	146	4	no	—
337	C₂²×C₄	—	146	8	no	—
338	C₂²×C₄	—	146	8	no	—
339	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
340	C₂²×C₄	C₄×#64408	1	1	yes	characteristic
341	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
342	C₂×C₈	—	73	8	no	—
343	C₂×C₈	—	73	2	no	—
344	C₂×C₈	—	73	2	no	—
345	C₂×C₈	—	146	4	no	—
346	C₂×C₈	—	146	4	no	—
347	C₂×C₈	—	146	4	no	—
348	C₂×C₈	—	146	4	no	—
349	C₂×C₈	C₂²×#64408	1	2	yes	—
350	C₂×C₈	C₂²×#64408	1	2	yes	—
351	C₄²	—	73	8	no	—
352	C₄²	—	73	1	no	—
353	C₄²	—	73	1	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	—	146	4	no	—
365	C₄²	—	146	8	no	—
366	C₄²	C₄×#64408	1	1	yes	characteristic
367	C₄²	C₄×#64408	1	1	yes	characteristic
368	C₄²	C₂²×#64408	1	1	yes	characteristic
369	C₄²	C₂²×#64408	1	1	yes	characteristic
370	C₂³	—	73	1	no	—
371	C₂³	—	73	1	no	—
372	C₂³	—	73	4	no	—
373	C₂³	—	146	2	no	—
374	C₂³	—	146	2	no	—
375	C₂³	C₂×C₄×#64408	1	1	yes	characteristic
376	C₂×C₄	—	2	2	no	—
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	16	no	—
382	C₂×C₄	—	292	1	no	—
383	C₂×C₄	—	73	1	no	—
384	C₂×C₄	—	73	4	no	—
385	C₂×C₄	—	73	8	no	—
386	C₂×C₄	—	73	1	no	—
387	C₂×C₄	—	73	1	no	—
388	C₂×C₄	—	73	1	no	—
389	C₂×C₄	—	73	1	no	—
390	C₂×C₄	—	73	1	no	—
391	C₂×C₄	—	146	2	no	—
392	C₂×C₄	—	146	2	no	—
393	C₂×C₄	—	146	2	no	—
394	C₂×C₄	—	146	2	no	—
395	C₂×C₄	—	146	2	no	—
396	C₂×C₄	—	146	2	no	—
397	C₂×C₄	—	146	2	no	—
398	C₂×C₄	—	146	2	no	—
399	C₂×C₄	—	146	4	no	—
400	C₂×C₄	—	146	4	no	—
401	C₂×C₄	—	146	4	no	—
402	C₂×C₄	—	146	2	no	—
403	C₂×C₄	—	146	4	no	—
404	C₂×C₄	—	146	4	no	—
405	C₂×C₄	—	146	2	no	—
406	C₂×C₄	—	146	2	no	—
407	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
408	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
409	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄×#64408	1	1	yes	characteristic
412	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
413	C₈	—	2	2	no	—
414	C₈	—	2	2	no	—
415	C₈	—	146	8	no	—
416	C₈	—	146	2	no	—
417	C₈	—	146	2	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	73	2	no	—
421	C₂²	—	73	2	no	—
422	C₂²	—	73	2	no	—
423	C₂²	—	73	2	no	—
424	C₂²	—	146	8	no	—
425	C₂²	—	146	1	no	—
426	C₂²	—	146	1	no	—
427	C₂²	#17989550	1	2	yes	—
428	C₂²	C₂²×C₄×#64408	1	1	yes	characteristic
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	292	4	no	—
435	C₄	—	73	2	no	—
436	C₄	—	146	8	no	—
437	C₄	—	146	1	no	—
438	C₄	—	146	1	no	—
439	C₄	—	146	1	no	—
440	C₄	—	146	1	no	—
441	C₄	—	146	1	no	—
442	C₄	#41×#64408	1	2	yes	—
443	C₂	—	2	2	no	—
444	C₂	—	73	4	no	—
445	C₂	—	146	2	no	—
446	C₂	#117×#64408	1	1	yes	characteristic
447	C₂	C₂×#17989550	1	1	yes	characteristic
448	C₂	#22626494	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₄²
Fitting	#431×C₇₃	C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#431	#64408
hypocenter	C₇₃	#20469
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
3. #22625720	C₂	semidirect
6. #22625649	C₂	semidirect
7. #22625587	C₂	semidirect
10. #17989610	C₄	semidirect
11. #17989609	C₄	semidirect
12. #17989608	C₄	semidirect
13. #17989607	C₄	semidirect
29. #17988640	C₄	semidirect
30. #17988639	C₄	semidirect
31. #17988638	C₄	semidirect
32. #17988637	C₄	semidirect
33. #17988637	C₄	semidirect
38. #431×C₇₃	C₄	semidirect
45. #14556658	C₂×C₄	semidirect
46. C₄⋊#10596833	C₂×C₄	semidirect
49. #14556646	C₂×C₄	semidirect
50. #14556646	C₂×C₄	semidirect
75. C₄⋊#10596831	C₂×C₄	semidirect
76. #14556520	C₂×C₄	semidirect
77. #14556520	C₂×C₄	semidirect
82. C₄×#10596831	C₂×C₄	semidirect
83. C₈×Dic₇₃	C₂×C₄	semidirect
84. C₈×Dic₇₃	C₂×C₄	semidirect
86. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
89. C₄×C₈×C₇₃	C₂×C₄	semidirect
233. C₇₃	#20469	semidirect
245. #431	#64408	semidirect
292. C₄⋊C₈	C₂×#64408	semidirect
308. C₄×C₈	C₂×#64408	semidirect

Maximal subgroups

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

subgroup	index
D₇₃⋊#432	2
C₂×#17989523	2
#22625720	2
#22625659	2
C₂²⋊C₈×#64408	2
#22625649	2
#22625587	2
#431×D₇₃	2
#20469	73