Subgroups — #33053276

Order 18688.

1272 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618564	C₂	1	1	yes	maximal, characteristic, complemented
2	#22612329	C₂	1	1	yes	maximal, characteristic, complemented
3	#22608478	C₂	1	4	yes	maximal, complemented
4	#22608460	C₂	1	4	yes	maximal, complemented
5	#22608426	C₂	1	4	yes	maximal, complemented
6	C₂×#532×C₇₃	C₂	1	1	yes	maximal, characteristic
7	#17988644	—	2	1	no	—
8	#17988644	C₂²	1	2	yes	complemented
9	#17988640	—	2	1	no	—
10	#17988640	C₂²	1	2	yes	complemented
11	#17988611	—	2	1	no	—
12	#17988551	C₂²	1	2	yes	—
13	C₄×#11924012	—	2	1	no	—
14	#17988455	C₂²	1	2	yes	complemented
15	#17988453	—	2	1	no	—
16	#17988450	C₂²	1	2	yes	—
17	#17988447	—	2	1	no	—
18	C₄×C₄⋊Dic₇₃	C₂²	1	2	yes	complemented
19	C₄×C₂²⋊Dic₇₃	—	2	1	no	—
20	#17988433	—	2	1	no	—
21	#17988321	C₂²	1	16	yes	complemented
22	C₂²×#41×C₇₃	—	2	1	no	—
23	#532×C₇₃	—	2	1	no	—
24	#532×C₇₃	—	2	1	no	—
25	#532×C₇₃	—	2	1	no	—
26	#532×C₇₃	—	2	1	no	—
27	#532×C₇₃	C₄	1	2	yes	complemented
28	#532×C₇₃	C₄	1	2	yes	complemented
29	#532×C₇₃	C₂²	1	2	yes	—
30	#532×C₇₃	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic, complemented
32	C₂×#127×C₇₃	C₄	1	1	yes	characteristic, complemented
33	C₂×#124×C₇₃	—	2	1	no	—
34	C₂×#121×C₇₃	—	2	1	no	—
35	C₂×#121×C₇₃	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₇₃	—	2	1	no	—
37	C₂×C₄×D₄×C₇₃	C₄	1	2	yes	complemented
38	C₂²×C₄²×C₇₃	C₂²	1	1	yes	characteristic
39	C₂×#11924012	—	2	2	no	—
40	C₂×C₄⋊Dic₇₃	—	2	2	no	—
41	C₂×C₂²⋊Dic₇₃	—	2	2	no	—
42	C₂×C₄×Dic₇₃	—	2	2	no	—
43	C₄⋊#10596831	—	2	2	no	—
44	C₄⋊#10596831	—	2	2	no	—
45	C₂²⋊#10596831	—	2	2	no	—
46	C₂²⋊#10596831	C₂³	1	4	yes	—
47	#14556502	—	2	2	no	—
48	C₄×#10596831	—	2	2	no	—
49	#14556498	—	2	2	no	—
50	#14556498	—	2	2	no	—
51	#14556498	—	2	2	no	—
52	#14556498	C₂³	1	4	yes	—
53	C₂×#41×C₇₃	—	2	2	no	—
54	C₂×#41×C₇₃	—	2	2	no	—
55	C₂×#41×C₇₃	—	2	2	no	—
56	C₂×#41×C₇₃	—	2	2	no	—
57	C₂×#41×C₇₃	—	4	8	no	—
58	C₂²×Q₈×C₇₃	—	2	1	no	—
59	C₂²×D₄×C₇₃	—	2	2	no	—
60	C₂²×D₄×C₇₃	—	2	1	no	—
61	C₂²×D₄×C₇₃	—	2	1	no	—
62	C₂²×D₄×C₇₃	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₇₃	—	2	2	no	—
64	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₇₃	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₇₃	—	2	1	no	—
68	C₄⋊Q₈×C₇₃	—	2	1	no	—
69	C₄⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
70	C₄⋊Q₈×C₇₃	C₂×C₄	1	2	yes	—
71	#127×C₇₃	—	2	1	no	—
72	#127×C₇₃	—	2	1	no	—
73	#127×C₇₃	C₂×C₄	1	2	yes	—
74	#127×C₇₃	C₂×C₄	1	2	yes	—
75	#124×C₇₃	—	2	2	no	—
76	#124×C₇₃	—	2	2	no	—
77	#124×C₇₃	—	2	2	no	—
78	#124×C₇₃	—	2	2	no	—
79	#121×C₇₃	—	2	2	no	—
80	#121×C₇₃	—	2	2	no	—
81	#121×C₇₃	—	2	2	no	—
82	#121×C₇₃	—	2	2	no	—
83	#121×C₇₃	—	2	2	no	—
84	#121×C₇₃	—	2	2	no	—
85	#121×C₇₃	C₂×C₄	1	4	yes	—
86	#121×C₇₃	C₂³	1	4	yes	—
87	C₄×D₄×C₇₃	—	2	2	no	—
88	C₄×D₄×C₇₃	—	2	2	no	—
89	C₄×D₄×C₇₃	—	2	2	no	—
90	C₄×D₄×C₇₃	—	2	2	no	—
91	C₄×D₄×C₇₃	—	2	2	no	—
92	C₄×D₄×C₇₃	—	2	2	no	—
93	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
94	C₄×D₄×C₇₃	C₂×C₄	1	4	yes	—
95	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₇₃	—	2	2	no	—
99	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
111	C₂²×Dic₇₃	—	2	4	no	—
112	#11924012	—	4	4	no	—
113	C₂×#10596831	—	2	4	no	—
114	C₄⋊Dic₇₃	—	4	4	no	—
115	C₂²⋊Dic₇₃	—	4	4	no	—
116	C₄×Dic₇₃	—	4	4	no	—
117	C₂⁴×C₇₃	—	2	2	no	—
118	C₂⁴×C₇₃	C₂×D₄	1	1	yes	characteristic
119	#41×C₇₃	—	4	8	no	—
120	#41×C₇₃	—	4	8	no	—
121	#41×C₇₃	—	4	8	no	—
122	#41×C₇₃	—	4	8	no	—
123	C₂×Q₈×C₇₃	—	2	2	no	—
124	C₂×Q₈×C₇₃	—	2	2	no	—
125	C₂×Q₈×C₇₃	—	4	4	no	—
126	C₂×D₄×C₇₃	—	2	4	no	—
127	C₂×D₄×C₇₃	—	2	4	no	—
128	C₂×D₄×C₇₃	—	2	2	no	—
129	C₂×D₄×C₇₃	—	2	2	no	—
130	C₂×D₄×C₇₃	—	2	2	no	—
131	C₂×D₄×C₇₃	—	2	2	no	—
132	C₂×D₄×C₇₃	—	2	2	no	—
133	C₂×D₄×C₇₃	—	4	4	no	—
134	C₂×D₄×C₇₃	—	4	4	no	—
135	C₂×D₄×C₇₃	—	4	4	no	—
136	C₂×D₄×C₇₃	—	4	8	no	—
137	C₂×D₄×C₇₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₇₃	—	2	4	no	—
139	C₂²×C₄×C₇₃	—	2	2	no	—
140	C₂²×C₄×C₇₃	—	2	4	no	—
141	C₂²×C₄×C₇₃	—	2	4	no	—
142	C₂²×C₄×C₇₃	—	4	2	no	—
143	C₂²×C₄×C₇₃	—	4	2	no	—
144	C₂²×C₄×C₇₃	—	4	8	no	—
145	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
163	C₄⋊C₄×C₇₃	—	2	2	no	—
164	C₄⋊C₄×C₇₃	—	2	2	no	—
165	C₄⋊C₄×C₇₃	—	2	2	no	—
166	C₄⋊C₄×C₇₃	C₂²×C₄	1	4	yes	—
167	C₂²⋊C₄×C₇₃	—	2	4	no	—
168	C₂²⋊C₄×C₇₃	—	2	4	no	—
169	C₂²⋊C₄×C₇₃	—	2	4	no	—
170	C₂²⋊C₄×C₇₃	—	2	4	no	—
171	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
177	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
178	C₄²×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
179	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
180	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
181	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
183	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
186	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
187	C₂³×C₇₃	—	2	2	no	—
188	C₂³×C₇₃	—	2	2	no	—
189	C₂³×C₇₃	—	2	4	no	—
190	C₂³×C₇₃	—	4	1	no	—
191	C₂³×C₇₃	—	4	4	no	—
192	C₂³×C₇₃	—	4	4	no	—
193	C₂³×C₇₃	—	4	4	no	—
194	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂³×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₇₃	—	4	4	no	—
198	Q₈×C₇₃	—	4	4	no	—
199	D₄×C₇₃	—	4	4	no	—
200	D₄×C₇₃	—	4	4	no	—
201	D₄×C₇₃	—	4	4	no	—
202	D₄×C₇₃	—	4	4	no	—
203	D₄×C₇₃	—	4	8	no	—
204	D₄×C₇₃	—	4	8	no	—
205	D₄×C₇₃	—	4	4	no	—
206	D₄×C₇₃	—	4	4	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	—	2	2	no	—
210	C₂×C₄×C₇₃	—	2	2	no	—
211	C₂×C₄×C₇₃	—	2	2	no	—
212	C₂×C₄×C₇₃	—	2	2	no	—
213	C₂×C₄×C₇₃	—	2	2	no	—
214	C₂×C₄×C₇₃	—	2	2	no	—
215	C₂×C₄×C₇₃	—	2	2	no	—
216	C₂×C₄×C₇₃	—	2	2	no	—
217	C₂×C₄×C₇₃	—	2	4	no	—
218	C₂×C₄×C₇₃	—	4	1	no	—
219	C₂×C₄×C₇₃	—	4	1	no	—
220	C₂×C₄×C₇₃	—	4	1	no	—
221	C₂×C₄×C₇₃	—	4	1	no	—
222	C₂×C₄×C₇₃	—	4	1	no	—
223	C₂×C₄×C₇₃	—	4	1	no	—
224	C₂×C₄×C₇₃	—	4	1	no	—
225	C₂×C₄×C₇₃	—	4	8	no	—
226	C₂×C₄×C₇₃	—	4	4	no	—
227	C₂×C₄×C₇₃	—	4	8	no	—
228	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
230	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
231	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	4	yes	—
239	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
240	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
241	C₂×Dic₇₃	—	4	4	no	—
242	C₂×Dic₇₃	—	4	4	no	—
243	C₂×Dic₇₃	—	4	4	no	—
244	#10596831	—	4	4	no	—
245	C₂²×C₇₃	—	2	1	no	—
246	C₂²×C₇₃	—	2	1	no	—
247	C₂²×C₇₃	—	2	1	no	—
248	C₂²×C₇₃	—	2	1	no	—
249	C₂²×C₇₃	—	2	1	no	—
250	C₂²×C₇₃	—	2	1	no	—
251	C₂²×C₇₃	—	2	1	no	—
252	C₂²×C₇₃	—	4	4	no	—
253	C₂²×C₇₃	—	4	4	no	—
254	C₂²×C₇₃	—	4	4	no	—
255	C₂²×C₇₃	—	4	4	no	—
256	C₂²×C₇₃	—	8	8	no	—
257	C₂²×C₇₃	#410	1	2	yes	—
258	C₂²×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
259	C₂²×C₇₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
260	C₄×C₇₃	—	2	1	no	—
261	C₄×C₇₃	—	2	1	no	—
262	C₄×C₇₃	—	2	1	no	—
263	C₄×C₇₃	—	2	1	no	—
264	C₄×C₇₃	—	2	1	no	—
265	C₄×C₇₃	—	2	1	no	—
266	C₄×C₇₃	—	2	1	no	—
267	C₄×C₇₃	—	2	1	no	—
268	C₄×C₇₃	—	2	1	no	—
269	C₄×C₇₃	—	4	4	no	—
270	C₄×C₇₃	#418	1	2	yes	—
271	C₄×C₇₃	#418	1	2	yes	—
272	C₄×C₇₃	#421	1	2	yes	—
273	Dic₇₃	—	8	4	no	—
274	#17561	—	73	1	no	maximal, Sylow
275	C₂×C₇₃	—	2	2	no	—
276	C₂×C₇₃	—	2	2	no	—
277	C₂×C₇₃	—	4	1	no	—
278	C₂×C₇₃	—	8	4	no	—
279	C₂×C₇₃	C₂×#410	1	1	yes	characteristic
280	C₂×C₇₃	C₂×#418	1	1	yes	characteristic
281	C₂×C₇₃	C₂×#421	1	1	yes	characteristic
282	C₂×#532	D₇₃	1	1	yes	characteristic
283	#2920	—	73	1	no	—
284	#2283	—	73	1	no	—
285	#1514	—	73	4	no	—
286	#1510	—	73	4	no	—
287	#1502	—	73	4	no	—
288	C₇₃	#17561	1	1	yes	characteristic, complemented, Sylow
289	C₂²×#41	—	2	1	no	—
290	#532	—	2	1	no	—
291	#532	—	2	1	no	—
292	#532	—	2	1	no	—
293	#532	—	2	1	no	—
294	#532	Dic₇₃	1	2	yes	complemented
295	#532	Dic₇₃	1	2	yes	complemented
296	#532	C₂×D₇₃	1	2	yes	—
297	#532	C₂×D₇₃	1	2	yes	—
298	C₂×C₄⋊Q₈	Dic₇₃	1	1	yes	characteristic, complemented
299	C₂×#127	Dic₇₃	1	1	yes	characteristic, complemented
300	C₂×#124	—	2	1	no	—
301	C₂×#121	—	2	1	no	—
302	C₂×#121	C₂×D₇₃	1	2	yes	—
303	C₂×C₄×D₄	—	2	1	no	—
304	C₂×C₄×D₄	Dic₇₃	1	2	yes	complemented
305	C₂²×C₄²	C₂×D₇₃	1	1	yes	characteristic
306	#432	—	73	2	no	—
307	#432	—	146	1	no	—
308	#431	—	73	2	no	—
309	#431	—	146	1	no	—
310	#423	—	146	1	no	—
311	#407	—	73	2	no	—
312	C₄×M₁₆	—	146	1	no	—
313	#383	—	73	2	no	—
314	#382	—	146	1	no	—
315	#381	—	73	2	no	—
316	#380	—	146	1	no	—
317	C₄×C₄⋊C₄	—	73	2	no	—
318	C₄×C₂²⋊C₄	—	146	1	no	—
319	#376	—	146	1	no	—
320	#327	—	73	16	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	4	8	no	—
326	C₂²×Q₈	—	2	1	no	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂×Dic₇₃	1	2	yes	—
331	C₂³×C₄	—	2	2	no	—
332	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
333	C₂³×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
334	C₂³×C₄	C₂²×D₇₃	1	1	yes	characteristic
335	C₂×M₁₆	—	146	2	no	—
336	C₄⋊Q₈	—	2	1	no	—
337	C₄⋊Q₈	—	2	1	no	—
338	C₄⋊Q₈	C₂×Dic₇₃	1	2	yes	—
339	C₄⋊Q₈	C₂×Dic₇₃	1	2	yes	—
340	#127	—	2	1	no	—
341	#127	—	2	1	no	—
342	#127	C₂×Dic₇₃	1	2	yes	—
343	#127	C₂×Dic₇₃	1	2	yes	—
344	#124	—	2	2	no	—
345	#124	—	2	2	no	—
346	#124	—	2	2	no	—
347	#124	—	2	2	no	—
348	#121	—	2	2	no	—
349	#121	—	2	2	no	—
350	#121	—	2	2	no	—
351	#121	—	2	2	no	—
352	#121	—	2	2	no	—
353	#121	—	2	2	no	—
354	#121	C₂×Dic₇₃	1	4	yes	—
355	#121	C₂²×D₇₃	1	4	yes	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	C₂×Dic₇₃	1	4	yes	—
363	C₄×D₄	C₂×Dic₇₃	1	4	yes	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	146	2	no	—
366	C₂×C₄⋊C₄	C₂×Dic₇₃	1	2	yes	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₂²⋊C₄	—	2	2	no	—
369	C₂×C₂²⋊C₄	—	146	2	no	—
370	C₂×C₄²	—	146	2	no	—
371	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
372	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
373	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
374	C₂×C₄²	C₂×Dic₇₃	1	1	yes	characteristic
375	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
376	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
377	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
378	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
379	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
380	C₂×C₄²	C₂²⋊D₇₃	1	1	yes	characteristic
381	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
382	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
383	C₄⋊C₈	—	146	2	no	—
384	C₄⋊C₈	—	146	2	no	—
385	C₂²⋊C₈	—	73	4	no	—
386	C₂²⋊C₈	—	146	2	no	—
387	#97	—	146	2	no	—
388	C₄×C₈	—	146	2	no	—
389	#95	—	73	4	no	—
390	#95	—	146	2	no	—
391	#95	—	146	2	no	—
392	#95	—	146	2	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
395	#41	—	4	8	no	—
396	#41	—	4	8	no	—
397	#41	—	4	8	no	—
398	#41	—	4	8	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	—	4	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	4	no	—
412	C₂×D₄	—	4	8	no	—
413	C₂×D₄	C₂²×Dic₇₃	1	4	yes	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	2	no	—
420	C₂²×C₄	—	4	8	no	—
421	C₂²×C₄	—	146	4	no	—
422	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
424	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
425	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
426	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
427	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
428	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
429	C₂²×C₄	C₂²⋊Dic₇₃	1	1	yes	characteristic
430	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
431	C₂²×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
439	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
440	M₁₆	—	292	4	no	—
441	C₂×C₈	—	146	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	292	4	no	—
446	C₄⋊C₄	C₂²×Dic₇₃	1	4	yes	—
447	C₂²⋊C₄	—	2	4	no	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	292	4	no	—
452	C₄²	—	292	4	no	—
453	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
454	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
455	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
456	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
457	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
458	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
459	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
460	C₄²	C₂²⋊Dic₇₃	1	1	yes	characteristic
461	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
462	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
463	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
464	C₄²	C₂²×Dic₇₃	1	1	yes	characteristic
465	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
466	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
467	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
468	C₄²	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
469	C₂³	—	2	2	no	—
470	C₂³	—	2	2	no	—
471	C₂³	—	2	4	no	—
472	C₂³	—	4	1	no	—
473	C₂³	—	4	4	no	—
474	C₂³	—	4	4	no	—
475	C₂³	—	4	4	no	—
476	C₂³	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
477	C₂³	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
478	C₂³	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
479	Q₈	—	4	4	no	—
480	Q₈	—	4	4	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	8	no	—
487	D₄	—	4	4	no	—
488	D₄	—	4	4	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	8	no	—
508	C₂×C₄	—	4	4	no	—
509	C₂×C₄	—	4	8	no	—
510	C₂×C₄	—	292	4	no	—
511	C₂×C₄	—	292	4	no	—
512	C₂×C₄	—	292	4	no	—
513	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
514	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
515	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
516	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
517	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
518	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
519	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
520	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
521	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
522	C₂×C₄	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
523	C₂×C₄	#14556617	1	4	yes	—
524	C₂×C₄	C₂³×Dic₇₃	1	1	yes	characteristic
525	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
526	C₈	—	292	4	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	4	4	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	4	4	no	—
537	C₂²	—	4	4	no	—
538	C₂²	—	8	8	no	—
539	C₂²	#17988561	1	2	yes	—
540	C₂²	C₂²×C₂²⋊Dic₇₃	1	1	yes	characteristic
541	C₂²	C₂×#14556617	1	2	yes	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	4	no	—
552	C₄	—	584	4	no	—
553	C₄	#17988592	1	2	yes	—
554	C₄	#17988592	1	2	yes	—
555	C₄	#17988604	1	2	yes	—
556	C₂	—	2	2	no	—
557	C₂	—	2	2	no	—
558	C₂	—	4	1	no	—
559	C₂	—	8	4	no	—
560	C₂	C₂×#17988561	1	1	yes	characteristic
561	C₂	C₂×#17988592	1	1	yes	characteristic
562	C₂	C₂×#17988604	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊Dic₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting, prime radical	C₂×#532×C₇₃	C₂
socle	C₂²×C₇₃	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	C₂×#532	D₇₃
hypocenter	C₇₃	#17561
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #22618564	C₂	semidirect
2. #22612329	C₂	semidirect
3. #22608478	C₂	semidirect
4. #22608460	C₂	semidirect
5. #22608426	C₂	semidirect
8. #17988644	C₂²	semidirect
10. #17988640	C₂²	semidirect
14. #17988455	C₂²	semidirect
18. C₄×C₄⋊Dic₇₃	C₂²	semidirect
21. #17988321	C₂²	semidirect
27. #532×C₇₃	C₄	semidirect
28. #532×C₇₃	C₄	semidirect
31. C₂×C₄⋊Q₈×C₇₃	C₄	semidirect
32. C₂×#127×C₇₃	C₄	semidirect
37. C₂×C₄×D₄×C₇₃	C₄	semidirect
288. C₇₃	#17561	semidirect
294. #532	Dic₇₃	semidirect
295. #532	Dic₇₃	semidirect
298. C₂×C₄⋊Q₈	Dic₇₃	semidirect
299. C₂×#127	Dic₇₃	semidirect
304. C₂×C₄×D₄	Dic₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22618564	2
#22612329	2
#22608478	2
#22608460	2
#22608426	2
C₂×#532×C₇₃	2
#17561	73