Subgroups — #33083964

Order 18688.

1130 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17988612	C₂	1	1	yes	maximal, characteristic
2	C₂×#17988544	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988541	C₂	1	1	yes	maximal, characteristic
4	C₂×#17988539	C₂	1	1	yes	maximal, characteristic
5	#22612411	C₂	1	1	yes	maximal, characteristic
6	#22609808	C₂	1	1	yes	maximal, characteristic, complemented
7	#22609807	C₂	1	1	yes	maximal, characteristic, complemented
8	#22609807	C₂	1	1	yes	maximal, characteristic, complemented
9	#22609806	C₂	1	1	yes	maximal, characteristic, complemented
10	#22609797	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₄⋊Dic₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#22609792	C₂	1	1	yes	maximal, characteristic, complemented
13	#22609626	C₂	1	1	yes	maximal, characteristic
14	#336×D₇₃	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#1770	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#11924011	C₂²	1	1	yes	characteristic
17	C₂²×#11924011	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
20	C₂×#14556548	C₂²	1	1	yes	characteristic
21	C₂×#14556548	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
23	#17988612	C₄	1	8	yes	complemented
24	C₂×C₄⋊#10596831	C₂²	1	1	yes	characteristic
25	C₂×#14556520	C₂²	1	1	yes	characteristic
26	C₂×#14556520	C₂²	1	1	yes	characteristic
27	#17988544	—	2	4	no	—
28	#17988541	C₄	1	8	yes	complemented
29	#17988539	—	2	4	no	—
30	C₂×#14556502	C₂²	1	1	yes	characteristic
31	C₂×#14556502	C₂²	1	1	yes	characteristic
32	C₂×#14556501	C₂²	1	1	yes	characteristic
33	C₂×#14556501	C₂²	1	1	yes	characteristic
34	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₇₃	C₂²	1	1	yes	characteristic
39	#17988484	C₄	1	2	yes	—
40	#17988482	C₄	1	2	yes	—
41	#17988461	C₄	1	2	yes	—
42	#17988458	C₄	1	2	yes	—
43	C₄×#11924007	C₂²	1	1	yes	characteristic
44	C₄×#11924007	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊Dic₇₃	C₂²	1	1	yes	characteristic
46	#17988342	C₂²	1	1	yes	characteristic
47	#17988342	C₂²	1	1	yes	characteristic
48	#17988341	C₂²	1	1	yes	characteristic
49	#17988341	C₂²	1	1	yes	characteristic
50	#17988341	C₂²	1	1	yes	characteristic
51	#17988341	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic
53	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
54	C₂×#97×C₇₃	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₇₃	C₂²	1	1	yes	characteristic
57	#336×C₇₃	C₂²	1	1	yes	characteristic
58	#336×C₇₃	C₂²	1	1	yes	characteristic
59	C₂²×C₄×D₇₃	C₂×C₄	1	2	yes	—
60	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
61	C₂×#11924011	—	2	2	no	—
62	C₂×#11924011	—	2	2	no	—
63	C₂×#11924011	C₂×C₄	1	4	yes	—
64	C₂×#11924011	C₂×C₄	1	4	yes	—
65	C₂×#11924011	D₄	1	4	yes	—
66	C₂×#11924011	Q₈	1	4	yes	—
67	C₂²×#10596831	C₂³	1	1	yes	characteristic
68	C₂²×#10596831	C₂³	1	1	yes	characteristic
69	C₂²×#10596831	C₂³	1	1	yes	characteristic
70	C₂²×#10596831	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₇₃	—	2	2	no	—
72	C₂×C₈×D₇₃	—	2	2	no	—
73	C₂×C₈×D₇₃	—	2	2	no	—
74	C₂×C₈×D₇₃	—	2	2	no	—
75	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
76	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
77	#14556548	—	2	2	no	—
78	#14556548	—	2	2	no	—
79	#14556548	C₂×C₄	1	4	yes	—
80	#14556548	C₂×C₄	1	4	yes	—
81	C₂×C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
82	C₂×#11924007	C₂×C₄	1	2	yes	—
83	C₂×#11924007	C₂×C₄	1	2	yes	—
84	C₂×#11924007	C₂×C₄	1	2	yes	—
85	C₂×#11924007	C₂×C₄	1	1	yes	characteristic
86	C₂×#11924007	C₂×C₄	1	1	yes	characteristic
87	C₂×#11924005	C₂×C₄	1	2	yes	—
88	C₂×#11924005	C₂×C₄	1	1	yes	characteristic
89	C₂×#11924005	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄×Dic₇₃	C₂×C₄	1	2	yes	—
91	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
94	C₄²×D₇₃	—	2	2	no	—
95	C₄²×D₇₃	—	2	2	no	—
96	C₄⋊#10596831	C₂×C₄	1	4	yes	complemented
97	#14556520	C₂×C₄	1	4	yes	complemented
98	#14556520	C₂×C₄	1	4	yes	complemented
99	#14556502	—	2	2	no	—
100	#14556502	C₂×C₄	1	4	yes	complemented
101	#14556501	—	2	2	no	—
102	#14556501	C₂×C₄	1	4	yes	complemented
103	C₄×#10596831	—	2	2	no	—
104	C₈×Dic₇₃	—	2	2	no	—
105	C₈×Dic₇₃	—	2	2	no	—
106	C₈×Dic₇₃	—	2	2	no	—
107	C₈×Dic₇₃	C₂×C₄	1	4	yes	complemented
108	#14556498	C₂×C₄	1	2	yes	—
109	#14556498	C₂×C₄	1	2	yes	—
110	#14556498	C₂×C₄	1	2	yes	—
111	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
116	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
119	C₄⋊C₈×C₇₃	C₂×C₄	1	4	yes	complemented
120	#97×C₇₃	—	2	2	no	—
121	#97×C₇₃	—	2	2	no	—
122	C₄×C₈×C₇₃	C₂×C₄	1	4	yes	complemented
123	#95×C₇₃	C₂×C₄	1	2	yes	—
124	C₂³×D₇₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
126	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₇₃	C₂²×C₄	1	2	yes	—
129	C₂²×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₄×D₇₃	—	2	4	no	—
131	C₂×C₄×D₇₃	—	2	4	no	—
132	C₂×C₄×D₇₃	—	4	2	no	—
133	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
134	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
135	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
136	C₂×C₄×D₇₃	C₂×Q₈	1	2	yes	—
137	C₂×C₄×D₇₃	#41	1	2	yes	—
138	C₂×C₄×D₇₃	#41	1	2	yes	—
139	#11924011	—	2	8	no	—
140	#11924011	C₄⋊C₄	1	16	yes	complemented
141	C₂×#10596831	—	2	1	no	—
142	C₂×#10596831	—	2	1	no	—
143	C₂×#10596831	—	2	1	no	—
144	C₂×#10596831	—	2	1	no	—
145	C₂×#10596831	—	2	1	no	—
146	C₂×#10596831	—	2	1	no	—
147	C₂×#10596831	C₂²×C₄	1	2	yes	—
148	C₂×#10596831	C₂²×C₄	1	2	yes	—
149	C₂×#10596831	C₂²×C₄	1	2	yes	—
150	C₂×#10596831	C₂²×C₄	1	2	yes	—
151	C₂×#10596831	C₂×D₄	1	2	yes	—
152	C₂×#10596831	C₂×Q₈	1	2	yes	—
153	C₈×D₇₃	—	2	8	no	—
154	C₈×D₇₃	—	2	8	no	—
155	C₄⋊Dic₇₃	—	2	4	no	—
156	#11924007	—	2	4	no	—
157	#11924007	—	2	4	no	—
158	#11924007	—	4	2	no	—
159	#11924007	C₄²	1	4	yes	—
160	#11924007	C₄²	1	4	yes	—
161	#11924005	—	2	4	no	—
162	#11924005	C₄²	1	4	yes	—
163	#11924005	C₄²	1	4	yes	—
164	C₄×Dic₇₃	—	2	1	no	—
165	C₄×Dic₇₃	—	2	1	no	—
166	C₄×Dic₇₃	—	2	1	no	—
167	C₄×Dic₇₃	—	2	1	no	—
168	C₄×Dic₇₃	—	2	4	no	—
169	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
170	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
172	C₂²×C₄×C₇₃	C₂²×C₄	1	2	yes	—
173	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₈×C₇₃	—	2	1	no	—
177	C₂×C₈×C₇₃	—	2	1	no	—
178	C₂×C₈×C₇₃	—	2	1	no	—
179	C₂×C₈×C₇₃	—	2	1	no	—
180	C₂×C₈×C₇₃	—	2	1	no	—
181	C₂×C₈×C₇₃	—	2	1	no	—
182	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
183	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
184	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
185	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
186	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
187	C₂×C₈×C₇₃	C₂×Q₈	1	2	yes	—
188	C₄⋊C₄×C₇₃	—	4	2	no	—
189	C₄²×C₇₃	—	2	1	no	—
190	C₄²×C₇₃	—	2	1	no	—
191	C₄²×C₇₃	—	2	1	no	—
192	C₄²×C₇₃	—	2	1	no	—
193	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
194	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
195	C₂³×C₇₃	C₂³×C₄	1	1	yes	characteristic
196	C₂²×D₇₃	—	2	2	no	—
197	C₂²×D₇₃	—	2	2	no	—
198	C₂²×D₇₃	C₂×C₄²	1	2	yes	—
199	C₂²×D₇₃	C₄×D₄	1	2	yes	—
200	C₂²×D₇₃	C₄×Q₈	1	2	yes	—
201	C₂×C₄×C₇₃	—	2	2	no	—
202	C₂×C₄×C₇₃	—	2	2	no	—
203	C₂×C₄×C₇₃	—	2	2	no	—
204	C₂×C₄×C₇₃	—	2	2	no	—
205	C₂×C₄×C₇₃	—	2	2	no	—
206	C₂×C₄×C₇₃	—	2	2	no	—
207	C₂×C₄×C₇₃	—	2	2	no	—
208	C₂×C₄×C₇₃	—	2	2	no	—
209	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
210	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
211	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
212	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₇₃	C₂²×Q₈	1	1	yes	characteristic
215	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
217	C₂×Dic₇₃	—	2	2	no	—
218	C₂×Dic₇₃	—	2	2	no	—
219	C₂×Dic₇₃	—	2	2	no	—
220	C₂×Dic₇₃	—	2	2	no	—
221	C₂×Dic₇₃	—	2	2	no	—
222	C₂×Dic₇₃	—	2	2	no	—
223	C₂×Dic₇₃	—	2	2	no	—
224	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
225	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
226	C₂×Dic₇₃	C₂×C₄²	1	2	yes	—
227	C₂×Dic₇₃	C₄×D₄	1	2	yes	—
228	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
229	C₂×Dic₇₃	#131	1	4	yes	—
230	C₄×D₇₃	—	4	8	no	—
231	C₄×D₇₃	C₂×C₄⋊C₄	1	4	yes	—
232	C₄×D₇₃	#117	1	4	yes	—
233	C₄×D₇₃	C₄×D₄	1	4	yes	—
234	C₄×D₇₃	C₄×Q₈	1	4	yes	—
235	C₈×C₇₃	—	2	2	no	—
236	C₈×C₇₃	—	2	2	no	—
237	C₈×C₇₃	—	2	2	no	—
238	C₈×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
239	#10596831	—	2	2	no	—
240	#10596831	—	2	2	no	—
241	#10596831	—	2	2	no	—
242	#10596831	C₂×C₄⋊C₄	1	4	yes	—
243	C₂²×C₇₃	C₂²×C₄²	1	1	yes	characteristic
244	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
246	C₂²×C₇₃	C₂×#131	1	2	yes	—
247	C₂²×C₇₃	#568	1	2	yes	—
248	C₂×D₇₃	—	2	2	no	—
249	C₂×D₇₃	—	2	2	no	—
250	C₂×D₇₃	—	2	4	no	—
251	C₂×D₇₃	—	2	4	no	—
252	C₂×D₇₃	C₄×C₄⋊C₄	1	4	yes	—
253	C₄×C₇₃	—	2	2	no	—
254	C₄×C₇₃	—	2	2	no	—
255	C₄×C₇₃	—	4	2	no	—
256	C₄×C₇₃	—	4	2	no	—
257	C₄×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
258	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
259	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
260	C₄×C₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
261	Dic₇₃	—	2	2	no	—
262	Dic₇₃	—	2	2	no	—
263	Dic₇₃	—	2	4	no	—
264	Dic₇₃	—	4	2	no	—
265	Dic₇₃	C₄×C₄⋊C₄	1	4	yes	—
266	#20439	—	73	1	no	maximal, Sylow
267	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
268	C₂×C₇₃	C₄×#131	1	1	yes	characteristic
269	C₂×C₇₃	#2875	1	1	yes	characteristic
270	C₂×C₇₃	#2933	1	2	yes	—
271	C₂×C₇₃	#2962	1	2	yes	—
272	D₇₃	—	2	4	no	—
273	C₂×#424	—	73	1	no	—
274	C₂×#405	—	73	1	no	—
275	C₂×#405	—	73	1	no	—
276	C₂×C₄×M₁₆	—	73	1	no	—
277	#2296	—	73	1	no	—
278	#1771	—	73	1	no	—
279	#1771	—	73	1	no	—
280	#1771	—	73	1	no	—
281	#1771	—	73	1	no	—
282	#1770	—	73	1	no	—
283	#1770	D₇₃	1	1	yes	characteristic, complemented
284	C₈×C₄⋊C₄	—	73	1	no	—
285	C₈×C₄⋊C₄	—	73	1	no	—
286	#1729	—	73	1	no	—
287	C₂×#336	—	73	1	no	—
288	C₇₃	#20439	1	1	yes	characteristic, complemented, Sylow
289	C₂²×M₁₆	—	73	1	no	—
290	C₂²×M₁₆	—	73	1	no	—
291	C₂³×C₈	—	73	1	no	—
292	C₂³×C₈	—	73	1	no	—
293	C₂×#117	—	73	1	no	—
294	C₂×#117	—	73	1	no	—
295	C₂²×C₄²	—	73	1	no	—
296	#424	—	73	8	no	—
297	C₂×C₄⋊C₈	—	73	1	no	—
298	C₂×C₄⋊C₈	—	73	1	no	—
299	C₂×C₄⋊C₈	—	73	1	no	—
300	C₂×C₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic
301	#405	—	73	8	no	—
302	#405	—	146	4	no	—
303	C₄×M₁₆	—	146	4	no	—
304	C₂×#97	—	73	1	no	—
305	C₂×#97	—	73	1	no	—
306	C₂×#97	—	73	1	no	—
307	C₂×#97	—	73	1	no	—
308	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
309	C₂×#97	C₂×D₇₃	1	1	yes	characteristic
310	C₂×C₄×C₈	—	73	1	no	—
311	C₂×C₄×C₈	—	73	1	no	—
312	C₂×C₄×C₈	—	73	1	no	—
313	C₂×C₄×C₈	—	73	1	no	—
314	C₂×C₄×C₈	—	73	1	no	—
315	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
316	#389	—	73	2	no	—
317	#389	—	73	2	no	—
318	#385	—	73	2	no	—
319	#385	—	73	2	no	—
320	C₄×C₄⋊C₄	—	73	1	no	—
321	C₄×C₄⋊C₄	—	73	1	no	—
322	C₄×C₄⋊C₄	—	73	1	no	—
323	C₄×C₄⋊C₄	C₂×D₇₃	1	1	yes	characteristic
324	#336	—	73	1	no	—
325	#336	—	73	1	no	—
326	#336	—	73	1	no	—
327	#336	—	73	1	no	—
328	#336	—	73	1	no	—
329	#336	—	73	1	no	—
330	#336	C₂×D₇₃	1	1	yes	characteristic
331	#336	C₂×D₇₃	1	1	yes	characteristic
332	C₂³×C₄	—	73	2	no	—
333	C₂³×C₄	—	73	1	no	—
334	C₂×M₁₆	—	73	4	no	—
335	C₂×M₁₆	—	73	4	no	—
336	C₂×M₁₆	—	73	4	no	—
337	C₂×M₁₆	—	73	4	no	—
338	C₂×M₁₆	—	146	2	no	—
339	C₂×M₁₆	—	146	2	no	—
340	C₂²×C₈	—	73	1	no	—
341	C₂²×C₈	—	73	1	no	—
342	C₂²×C₈	—	73	1	no	—
343	C₂²×C₈	—	73	1	no	—
344	C₂²×C₈	—	73	4	no	—
345	C₂²×C₈	—	73	4	no	—
346	C₂²×C₈	—	146	2	no	—
347	C₂²×C₈	—	146	2	no	—
348	C₂²×C₈	—	146	2	no	—
349	C₂²×C₈	—	146	2	no	—
350	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
351	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
352	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
353	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
354	#117	—	73	4	no	—
355	#117	—	73	4	no	—
356	#117	—	146	2	no	—
357	#117	—	146	2	no	—
358	C₂×C₄⋊C₄	—	73	2	no	—
359	C₂×C₄⋊C₄	—	73	1	no	—
360	C₂×C₄⋊C₄	—	73	1	no	—
361	C₂×C₄⋊C₄	—	73	2	no	—
362	C₂×C₄⋊C₄	—	73	2	no	—
363	C₂×C₄⋊C₄	—	73	2	no	—
364	C₂×C₄⋊C₄	C₄×D₇₃	1	2	yes	—
365	C₂×C₂²⋊C₄	—	73	1	no	—
366	C₂×C₂²⋊C₄	—	73	1	no	—
367	C₂×C₂²⋊C₄	—	73	2	no	—
368	C₂×C₄²	—	73	1	no	—
369	C₂×C₄²	—	73	2	no	—
370	C₂×C₄²	—	73	1	no	—
371	C₂×C₄²	—	73	1	no	—
372	C₂×C₄²	—	146	2	no	—
373	C₂×C₄²	—	146	2	no	—
374	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
375	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
376	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
377	C₄⋊C₈	—	73	4	no	—
378	C₄⋊C₈	—	73	4	no	—
379	C₄⋊C₈	—	73	4	no	—
380	C₄⋊C₈	C₄×D₇₃	1	4	yes	complemented
381	#97	—	2	2	no	—
382	#97	—	2	2	no	—
383	#97	—	73	4	no	—
384	#97	—	73	4	no	—
385	#97	—	146	2	no	—
386	#97	—	146	2	no	—
387	C₄×C₈	—	73	4	no	—
388	C₄×C₈	—	146	2	no	—
389	C₄×C₈	—	146	2	no	—
390	C₄×C₈	—	146	2	no	—
391	C₄×C₈	—	146	2	no	—
392	C₄×C₈	C₄×D₇₃	1	4	yes	complemented
393	#95	—	73	2	no	—
394	#95	—	73	2	no	—
395	#95	—	73	2	no	—
396	#95	C₄×D₇₃	1	2	yes	—
397	C₂⁴	—	73	1	no	—
398	C₂²×C₄	—	292	2	no	—
399	C₂²×C₄	—	73	1	no	—
400	C₂²×C₄	—	73	2	no	—
401	C₂²×C₄	—	73	2	no	—
402	C₂²×C₄	—	73	2	no	—
403	C₂²×C₄	—	73	2	no	—
404	C₂²×C₄	—	73	2	no	—
405	C₂²×C₄	—	73	2	no	—
406	C₂²×C₄	—	73	2	no	—
407	C₂²×C₄	—	73	1	no	—
408	C₂²×C₄	—	73	1	no	—
409	C₂²×C₄	—	73	2	no	—
410	C₂²×C₄	—	146	4	no	—
411	C₂²×C₄	—	146	4	no	—
412	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
413	C₂²×C₄	C₂×C₄×D₇₃	1	2	yes	—
414	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
416	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
417	M₁₆	—	73	16	no	—
418	M₁₆	—	146	8	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	73	2	no	—
426	C₂×C₈	—	73	2	no	—
427	C₂×C₈	—	73	2	no	—
428	C₂×C₈	—	73	2	no	—
429	C₂×C₈	—	73	2	no	—
430	C₂×C₈	—	73	2	no	—
431	C₂×C₈	—	146	8	no	—
432	C₂×C₈	—	146	8	no	—
433	C₂×C₈	—	146	1	no	—
434	C₂×C₈	—	146	1	no	—
435	C₂×C₈	—	146	1	no	—
436	C₂×C₈	—	146	1	no	—
437	C₂×C₈	—	146	1	no	—
438	C₂×C₈	—	146	1	no	—
439	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
440	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
441	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
442	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
443	C₂×C₈	D₄×D₇₃	1	2	yes	—
444	C₂×C₈	Q₈×D₇₃	1	2	yes	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	292	2	no	—
447	C₄⋊C₄	—	73	4	no	—
448	C₄⋊C₄	—	73	4	no	—
449	C₄⋊C₄	—	146	4	no	—
450	C₄⋊C₄	—	146	4	no	—
451	C₄⋊C₄	—	146	4	no	—
452	C₂²⋊C₄	—	73	4	no	—
453	C₂²⋊C₄	—	73	4	no	—
454	C₂²⋊C₄	—	146	4	no	—
455	C₄²	—	2	1	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	73	2	no	—
460	C₄²	—	73	2	no	—
461	C₄²	—	146	4	no	—
462	C₄²	—	146	1	no	—
463	C₄²	—	146	1	no	—
464	C₄²	—	146	1	no	—
465	C₄²	—	146	1	no	—
466	C₄²	C₂×C₄×D₇₃	1	2	yes	—
467	C₄²	C₂×C₄×D₇₃	1	2	yes	—
468	C₂³	—	73	2	no	—
469	C₂³	—	73	2	no	—
470	C₂³	—	73	2	no	—
471	C₂³	—	146	2	no	—
472	C₂³	—	146	2	no	—
473	C₂³	C₂²×C₄×D₇₃	1	1	yes	characteristic
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	292	8	no	—
483	C₂×C₄	—	73	2	no	—
484	C₂×C₄	—	73	2	no	—
485	C₂×C₄	—	73	2	no	—
486	C₂×C₄	—	73	4	no	—
487	C₂×C₄	—	73	4	no	—
488	C₂×C₄	—	73	4	no	—
489	C₂×C₄	—	73	4	no	—
490	C₂×C₄	—	73	2	no	—
491	C₂×C₄	—	73	2	no	—
492	C₂×C₄	—	73	4	no	—
493	C₂×C₄	—	146	2	no	—
494	C₂×C₄	—	146	2	no	—
495	C₂×C₄	—	146	2	no	—
496	C₂×C₄	—	146	2	no	—
497	C₂×C₄	—	146	2	no	—
498	C₂×C₄	—	146	2	no	—
499	C₂×C₄	—	146	2	no	—
500	C₂×C₄	C₄²×D₇₃	1	2	yes	—
501	C₂×C₄	C₄²×D₇₃	1	2	yes	—
502	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
504	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
505	C₂×C₄	C₂×Q₈×D₇₃	1	1	yes	characteristic
506	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
507	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	2	2	no	—
510	C₈	—	2	2	no	—
511	C₈	—	73	4	no	—
512	C₈	—	146	2	no	—
513	C₈	—	146	2	no	—
514	C₈	—	146	2	no	—
515	C₈	C₄⋊C₄×D₇₃	1	4	yes	—
516	C₂²	—	73	4	no	—
517	C₂²	—	146	4	no	—
518	C₂²	—	146	2	no	—
519	C₂²	—	146	2	no	—
520	C₂²	—	146	4	no	—
521	C₂²	C₂×C₄²×D₇₃	1	1	yes	characteristic
522	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
523	C₂²	C₄×Q₈×D₇₃	1	1	yes	characteristic
524	C₂²	#131×D₇₃	1	2	yes	—
525	C₂²	#17989353	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	292	2	no	—
531	C₄	—	73	4	no	—
532	C₄	—	146	4	no	—
533	C₄	—	146	2	no	—
534	C₄	—	146	2	no	—
535	C₄	C₂×C₄⋊C₄×D₇₃	1	1	yes	characteristic
536	C₄	#117×D₇₃	1	1	yes	characteristic
537	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
538	C₄	C₄×Q₈×D₇₃	1	1	yes	characteristic
539	C₂	—	146	4	no	—
540	C₂	C₄×C₄⋊C₄×D₇₃	1	1	yes	characteristic
541	C₂	#22618353	1	1	yes	characteristic
542	C₂	#22618356	1	1	yes	characteristic
543	C₂	#22618660	1	2	yes	—
544	C₂	#22618876	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₇₃
commutator	C₂²×C₇₃	C₂²×C₄²
Fitting	C₇₃×#1770	C₂
socle	C₂³×C₇₃	C₂³×C₄
prime radical	C₂³×D₇₃	C₂²×C₄
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1770	D₇₃
hypocenter	C₇₃	#20439
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
6. #22609808	C₂	semidirect
7. #22609807	C₂	semidirect
8. #22609807	C₂	semidirect
9. #22609806	C₂	semidirect
10. #22609797	C₂	semidirect
11. C₈×C₄⋊Dic₇₃	C₂	semidirect
12. #22609792	C₂	semidirect
15. C₇₃×#1770	C₂	semidirect
23. #17988612	C₄	semidirect
28. #17988541	C₄	semidirect
96. C₄⋊#10596831	C₂×C₄	semidirect
97. #14556520	C₂×C₄	semidirect
98. #14556520	C₂×C₄	semidirect
100. #14556502	C₂×C₄	semidirect
102. #14556501	C₂×C₄	semidirect
107. C₈×Dic₇₃	C₂×C₄	semidirect
119. C₄⋊C₈×C₇₃	C₂×C₄	semidirect
122. C₄×C₈×C₇₃	C₂×C₄	semidirect
140. #11924011	C₄⋊C₄	semidirect
283. #1770	D₇₃	semidirect
288. C₇₃	#20439	semidirect
380. C₄⋊C₈	C₄×D₇₃	semidirect
392. C₄×C₈	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17988612	2
C₂×#17988544	2
C₂×#17988541	2
C₂×#17988539	2
#22612411	2
#22609808	2
#22609807	2
#22609806	2
#22609797	2
C₈×C₄⋊Dic₇₃	2
#22609792	2
#22609626	2
#336×D₇₃	2
C₇₃×#1770	2
#20439	73