Subgroups — #33088739

Order 18688.

1054 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22618492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#104×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22618446	C₂	1	1	yes	maximal, characteristic
4	#22618373	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#11924011	C₂	1	1	yes	maximal, characteristic, complemented
6	#22610645	C₂	1	1	yes	maximal, characteristic, complemented
7	#22610644	C₂	1	1	yes	maximal, characteristic, complemented
8	#22610641	C₂	1	1	yes	maximal, characteristic, complemented
9	#22610640	C₂	1	1	yes	maximal, characteristic, complemented
10	#22610636	C₂	1	1	yes	maximal, characteristic, complemented
11	#22610635	C₂	1	1	yes	maximal, characteristic, complemented
12	#22610632	C₂	1	1	yes	maximal, characteristic, complemented
13	#22609656	C₂	1	1	yes	maximal, characteristic, complemented
14	#339×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₇₃	C₂²	1	1	yes	characteristic
17	C₂²×#11924011	C₂²	1	1	yes	characteristic
18	C₂²×#11924011	C₂²	1	1	yes	characteristic
19	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
20	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
21	#117×D₇₃	C₂²	1	1	yes	characteristic
22	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
23	#17988615	C₂²	1	1	yes	characteristic, complemented
24	#17988614	C₂²	1	1	yes	characteristic, complemented
25	#17988613	C₂²	1	1	yes	characteristic, complemented
26	#17988612	—	2	2	no	—
27	#17988609	—	2	2	no	—
28	C₂×#14556519	C₂²	1	1	yes	characteristic
29	C₂×#14556518	C₂²	1	1	yes	characteristic
30	C₂×#14556517	C₂²	1	1	yes	characteristic
31	#104×D₇₃	—	2	4	no	—
32	#17988594	C₄	1	2	yes	complemented
33	#17988590	C₄	1	2	yes	complemented
34	#17988587	C₄	1	2	yes	complemented
35	#17988585	C₄	1	2	yes	complemented
36	#17988584	C₂²	1	1	yes	characteristic
37	#17988583	C₂²	1	1	yes	characteristic
38	#17988581	C₂²	1	1	yes	characteristic
39	#17988555	C₂²	1	1	yes	characteristic
40	#17988554	C₂²	1	1	yes	characteristic
41	#17988553	C₂²	1	1	yes	characteristic
42	#17988552	—	2	2	no	—
43	#17988549	—	2	2	no	—
44	C₄×#11924011	—	2	4	no	—
45	C₂×#14556501	C₂²	1	1	yes	characteristic, complemented
46	C₂×#14556501	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic, complemented
48	#17988352	C₂²	1	1	yes	characteristic, complemented
49	#17988351	C₂²	1	1	yes	characteristic, complemented
50	#17988351	C₂²	1	1	yes	characteristic, complemented
51	#17988348	C₂²	1	1	yes	characteristic, complemented
52	#17988347	C₂²	1	1	yes	characteristic, complemented
53	#17988346	C₂²	1	1	yes	characteristic, complemented
54	#424×C₇₃	C₂²	1	1	yes	characteristic, complemented
55	C₂×#104×C₇₃	C₂²	1	1	yes	characteristic
56	#416×C₇₃	C₂²	1	1	yes	characteristic
57	#408×C₇₃	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
59	#341×C₇₃	C₂²	1	1	yes	characteristic, complemented
60	#339×C₇₃	C₂²	1	1	yes	characteristic, complemented
61	C₂×#11924029	C₂×C₄	1	1	yes	characteristic
62	C₂×#11924028	—	2	1	no	—
63	C₂×#11924028	C₂³	1	1	yes	characteristic
64	C₂×#11924027	—	2	1	no	—
65	C₂×#11924027	C₂×C₄	1	1	yes	characteristic
66	#41×D₇₃	—	2	2	no	—
67	#41×D₇₃	—	2	2	no	—
68	#41×D₇₃	—	2	2	no	—
69	#41×D₇₃	—	2	2	no	—
70	C₂×Q₈×D₇₃	C₂×C₄	1	1	yes	characteristic
71	C₂×D₄×D₇₃	—	2	1	no	—
72	C₂×D₄×D₇₃	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₄×D₇₃	—	2	1	no	—
74	C₂²×C₄×D₇₃	—	2	1	no	—
75	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
76	C₂×#11924012	C₂³	1	1	yes	characteristic
77	C₂×#11924012	C₂³	1	1	yes	characteristic
78	C₂×#11924011	—	2	2	no	—
79	C₂×#11924011	—	2	2	no	—
80	C₂×#11924011	—	2	2	no	—
81	C₂×#11924011	—	2	2	no	—
82	C₂×#11924011	—	2	1	no	—
83	C₂×#11924011	—	2	1	no	—
84	C₂×#11924011	C₂×C₄	1	2	yes	—
85	C₂×#11924011	C₂×C₄	1	2	yes	—
86	C₂×#11924011	D₄	1	2	yes	—
87	C₂×#11924011	D₄	1	2	yes	—
88	M₁₆×D₇₃	—	2	2	no	—
89	M₁₆×D₇₃	—	2	2	no	—
90	M₁₆×D₇₃	—	2	2	no	—
91	M₁₆×D₇₃	—	2	2	no	—
92	C₂²×#10596831	C₂³	1	1	yes	characteristic
93	C₂²×#10596831	C₂³	1	1	yes	characteristic
94	C₂×C₈×D₇₃	—	2	1	no	—
95	C₂×C₈×D₇₃	—	2	1	no	—
96	#14556550	C₂³	1	1	yes	characteristic
97	#14556549	C₂×C₄	1	2	yes	—
98	#14556548	—	2	1	no	—
99	#14556547	—	2	1	no	—
100	C₄⋊C₄×D₇₃	C₂×C₄	1	2	yes	—
101	C₂²⋊C₄×D₇₃	—	2	1	no	—
102	C₂×C₄×Dic₇₃	—	2	1	no	—
103	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
104	C₄²×D₇₃	—	2	1	no	—
105	C₄²×D₇₃	—	2	2	no	—
106	C₄²×D₇₃	D₄	1	4	yes	—
107	C₄⋊#10596831	—	2	2	no	—
108	#14556520	—	2	2	no	—
109	#14556520	—	2	2	no	—
110	#14556519	—	2	2	no	—
111	#14556518	—	2	2	no	—
112	#14556517	—	2	2	no	—
113	#14556516	C₂×C₄	1	2	yes	complemented
114	#14556515	C₂×C₄	1	2	yes	complemented
115	#14556514	C₂×C₄	1	2	yes	complemented
116	#14556513	C₂×C₄	1	2	yes	complemented
117	#14556512	C₂×C₄	1	2	yes	complemented
118	#14556511	C₂×C₄	1	2	yes	complemented
119	C₂²⋊#10596831	—	2	2	no	—
120	#14556503	—	2	2	no	—
121	#14556503	—	2	2	no	—
122	#14556501	—	2	2	no	—
123	#14556501	—	2	2	no	—
124	C₄×#10596831	—	2	2	no	—
125	C₂×#41×C₇₃	C₂³	1	1	yes	characteristic
126	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
127	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
130	#117×C₇₃	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
132	C₄⋊C₈×C₇₃	—	2	2	no	—
133	#104×C₇₃	—	2	2	no	—
134	#103×C₇₃	C₂×C₄	1	2	yes	complemented
135	#102×C₇₃	C₂×C₄	1	2	yes	complemented
136	C₂²⋊C₈×C₇₃	—	2	2	no	—
137	C₄×C₈×C₇₃	—	2	2	no	—
138	C₂³×D₇₃	—	2	1	no	—
139	C₂³×D₇₃	#41	1	1	yes	characteristic
140	#11924029	—	2	2	no	—
141	#11924029	—	2	2	no	—
142	#11924028	—	2	1	no	—
143	#11924028	—	2	1	no	—
144	#11924028	—	2	1	no	—
145	#11924028	—	2	1	no	—
146	#11924028	—	4	2	no	—
147	#11924028	—	4	2	no	—
148	#11924027	—	2	2	no	—
149	#11924027	—	2	2	no	—
150	#11924027	—	4	2	no	—
151	#11924027	—	4	2	no	—
152	C₂×Dic₁₄₆	—	2	1	no	—
153	C₂×Dic₁₄₆	C₂²×C₄	1	1	yes	characteristic
154	Q₈×D₇₃	—	2	2	no	—
155	Q₈×D₇₃	—	2	2	no	—
156	C₂×D₂₉₂	—	2	1	no	—
157	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₂²⋊D₇₃	—	2	1	no	—
159	C₂×C₂²⋊D₇₃	—	2	1	no	—
160	C₂×C₂²⋊D₇₃	—	2	1	no	—
161	D₄×D₇₃	—	2	2	no	—
162	D₄×D₇₃	—	2	2	no	—
163	D₄×D₇₃	—	4	2	no	—
164	D₄×D₇₃	—	4	2	no	—
165	C₂²×Dic₇₃	—	2	1	no	—
166	C₂²×Dic₇₃	—	2	1	no	—
167	C₂²×Dic₇₃	#41	1	1	yes	characteristic
168	C₂×C₄×D₇₃	—	2	1	no	—
169	C₂×C₄×D₇₃	—	2	4	no	—
170	C₂×C₄×D₇₃	—	2	1	no	—
171	C₂×C₄×D₇₃	—	2	1	no	—
172	C₂×C₄×D₇₃	—	2	2	no	—
173	C₂×C₄×D₇₃	—	4	4	no	—
174	C₂×C₄×D₇₃	—	4	2	no	—
175	C₂×C₄×D₇₃	—	4	2	no	—
176	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
179	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
180	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
181	C₂×C₄×D₇₃	#41	1	2	yes	—
182	C₂×C₄×D₇₃	#41	1	2	yes	—
183	C₂×C₄×D₇₃	#41	1	2	yes	—
184	#11924012	—	2	1	no	—
185	#11924012	—	2	1	no	—
186	#11924012	—	2	1	no	—
187	#11924012	—	2	1	no	—
188	#11924011	—	2	4	no	—
189	#11924011	—	2	4	no	—
190	#11924011	—	2	4	no	—
191	#11924011	—	2	4	no	—
192	#11924011	—	4	2	no	—
193	#11924011	—	4	2	no	—
194	C₂×#10596831	—	2	1	no	—
195	C₂×#10596831	—	2	1	no	—
196	C₂×#10596831	—	2	1	no	—
197	C₂×#10596831	—	2	1	no	—
198	C₂×#10596831	—	2	1	no	—
199	C₂×#10596831	—	2	1	no	—
200	C₂×#10596831	C₂²×C₄	1	2	yes	—
201	C₂×#10596831	C₂×D₄	1	2	yes	—
202	C₈×D₇₃	—	4	2	no	—
203	C₈×D₇₃	—	4	2	no	—
204	C₄⋊Dic₇₃	C₂²×C₄	1	2	yes	—
205	#11924007	—	2	2	no	—
206	C₂²⋊Dic₇₃	—	2	1	no	—
207	#11924005	—	2	2	no	—
208	C₄×Dic₇₃	—	2	1	no	—
209	C₄×Dic₇₃	—	2	1	no	—
210	C₄×Dic₇₃	—	2	2	no	—
211	C₄×Dic₇₃	—	2	4	no	—
212	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
213	#41×C₇₃	—	2	1	no	—
214	#41×C₇₃	—	2	1	no	—
215	#41×C₇₃	—	2	1	no	—
216	#41×C₇₃	—	2	1	no	—
217	C₂×Q₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
218	C₂×D₄×C₇₃	—	2	1	no	—
219	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
220	C₂²×C₄×C₇₃	—	2	1	no	—
221	C₂²×C₄×C₇₃	—	2	1	no	—
222	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
223	M₁₆×C₇₃	—	2	1	no	—
224	M₁₆×C₇₃	—	2	1	no	—
225	M₁₆×C₇₃	—	2	1	no	—
226	M₁₆×C₇₃	—	2	1	no	—
227	C₂×C₈×C₇₃	—	2	1	no	—
228	C₂×C₈×C₇₃	—	2	1	no	—
229	C₂×C₈×C₇₃	—	2	1	no	—
230	C₂×C₈×C₇₃	—	2	1	no	—
231	C₂×C₈×C₇₃	—	2	1	no	—
232	C₂×C₈×C₇₃	—	2	1	no	—
233	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
234	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
235	C₄⋊C₄×C₇₃	C₂²×C₄	1	2	yes	—
236	C₂²⋊C₄×C₇₃	—	2	1	no	—
237	C₄²×C₇₃	—	2	1	no	—
238	C₄²×C₇₃	—	2	1	no	—
239	C₄²×C₇₃	C₂×D₄	1	2	yes	—
240	C₂³×C₇₃	—	2	1	no	—
241	C₂³×C₇₃	C₂×#41	1	1	yes	characteristic
242	C₂²×D₇₃	—	2	1	no	—
243	C₂²×D₇₃	—	4	2	no	—
244	C₂²×D₇₃	—	4	2	no	—
245	C₂²×D₇₃	—	8	2	no	—
246	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
247	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
248	C₂²×D₇₃	#123	1	2	yes	—
249	C₂²×D₇₃	#126	1	2	yes	—
250	Q₈×C₇₃	—	2	1	no	—
251	Q₈×C₇₃	—	2	1	no	—
252	D₄×C₇₃	—	2	1	no	—
253	D₄×C₇₃	—	2	1	no	—
254	D₄×C₇₃	—	4	1	no	—
255	D₄×C₇₃	—	4	1	no	—
256	C₂×C₄×C₇₃	—	2	4	no	—
257	C₂×C₄×C₇₃	—	2	2	no	—
258	C₂×C₄×C₇₃	—	2	2	no	—
259	C₂×C₄×C₇₃	—	2	1	no	—
260	C₂×C₄×C₇₃	—	4	1	no	—
261	C₂×C₄×C₇₃	—	4	1	no	—
262	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
263	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
266	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
267	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
268	C₂²⋊D₇₃	—	4	1	no	—
269	C₂²⋊D₇₃	—	4	1	no	—
270	C₂²⋊D₇₃	—	4	2	no	—
271	C₂²⋊D₇₃	—	4	2	no	—
272	C₂×Dic₇₃	—	2	2	no	—
273	C₂×Dic₇₃	—	2	1	no	—
274	C₂×Dic₇₃	—	2	2	no	—
275	C₂×Dic₇₃	—	4	2	no	—
276	C₂×Dic₇₃	—	4	2	no	—
277	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
278	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
279	C₂×Dic₇₃	#123	1	2	yes	—
280	C₂×Dic₇₃	#126	1	2	yes	—
281	D₂₉₂	—	2	1	no	—
282	D₂₉₂	—	2	1	no	—
283	D₂₉₂	—	4	2	no	—
284	C₄×D₇₃	—	4	8	no	—
285	C₄×D₇₃	—	4	2	no	—
286	C₄×D₇₃	—	4	1	no	—
287	C₄×D₇₃	—	4	1	no	—
288	C₄×D₇₃	—	4	2	no	—
289	C₄×D₇₃	—	8	2	no	—
290	C₄×D₇₃	#117	1	2	yes	—
291	C₄×D₇₃	#117	1	2	yes	—
292	C₄×D₇₃	C₄×D₄	1	2	yes	—
293	C₄×D₇₃	C₄×D₄	1	2	yes	—
294	C₄×D₇₃	#121	1	2	yes	—
295	C₄×D₇₃	#121	1	2	yes	—
296	C₄×D₇₃	#124	1	2	yes	—
297	C₄×D₇₃	#124	1	2	yes	—
298	Dic₁₄₆	—	2	1	no	—
299	Dic₁₄₆	—	2	1	no	—
300	Dic₁₄₆	—	4	2	no	—
301	C₈×C₇₃	—	2	2	no	—
302	C₈×C₇₃	—	2	2	no	—
303	C₈×C₇₃	—	4	1	no	—
304	C₈×C₇₃	—	4	1	no	—
305	#10596831	—	2	2	no	—
306	#10596831	—	2	2	no	—
307	#10596831	—	4	1	no	—
308	#10596831	—	4	1	no	—
309	C₂²×C₇₃	—	2	2	no	—
310	C₂²×C₇₃	—	4	2	no	—
311	C₂²×C₇₃	—	4	1	no	—
312	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
313	C₂²×C₇₃	C₂×#123	1	1	yes	characteristic
314	C₂²×C₇₃	C₂×#126	1	1	yes	characteristic
315	C₂×D₇₃	—	2	2	no	—
316	C₂×D₇₃	—	2	2	no	—
317	C₂×D₇₃	—	4	2	no	—
318	C₂×D₇₃	—	4	2	no	—
319	C₂×D₇₃	—	4	2	no	—
320	C₂×D₇₃	—	4	1	no	—
321	C₂×D₇₃	—	8	4	no	—
322	C₂×D₇₃	#388	1	2	yes	—
323	C₂×D₇₃	#388	1	2	yes	—
324	C₄×C₇₃	—	2	4	no	—
325	C₄×C₇₃	—	4	2	no	—
326	C₄×C₇₃	—	4	1	no	—
327	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
328	C₄×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
329	C₄×C₇₃	C₂×#121	1	1	yes	characteristic
330	C₄×C₇₃	C₂×#124	1	1	yes	characteristic
331	Dic₇₃	—	4	2	no	—
332	Dic₇₃	—	4	2	no	—
333	Dic₇₃	—	4	1	no	—
334	Dic₇₃	#388	1	2	yes	—
335	Dic₇₃	#388	1	2	yes	—
336	#21099	—	73	1	no	maximal, Sylow
337	C₂×C₇₃	—	2	1	no	—
338	C₂×C₇₃	—	2	1	no	—
339	C₂×C₇₃	—	8	1	no	—
340	C₂×C₇₃	C₂×#388	1	1	yes	characteristic
341	C₂×C₇₃	#2956	1	2	yes	—
342	D₇₃	—	2	2	no	—
343	D₇₃	—	2	2	no	—
344	D₇₃	—	8	1	no	—
345	#2905	—	73	1	no	—
346	C₂²×#104	—	73	1	no	—
347	#2896	—	73	1	no	—
348	#2879	—	73	1	no	—
349	C₂×C₄×M₁₆	—	73	1	no	—
350	#1938	—	73	1	no	—
351	#1938	—	73	1	no	—
352	#1938	—	73	1	no	—
353	#1938	—	73	1	no	—
354	#1937	—	73	1	no	—
355	#1937	—	73	1	no	—
356	#1937	—	73	1	no	—
357	#1937	D₇₃	1	1	yes	characteristic, complemented
358	#1738	—	73	1	no	—
359	C₂×#339	—	73	1	no	—
360	C₇₃	#21099	1	1	yes	characteristic, complemented, Sylow
361	C₂²×#41	—	73	1	no	—
362	C₂²×M₁₆	—	73	1	no	—
363	C₂²×M₁₆	—	73	1	no	—
364	C₂²×M₁₆	—	73	1	no	—
365	C₂²×M₁₆	—	73	1	no	—
366	C₂×#117	—	73	1	no	—
367	C₂²×C₄²	—	73	1	no	—
368	#424	—	73	1	no	—
369	#424	—	73	1	no	—
370	#424	—	73	1	no	—
371	#424	—	146	2	no	—
372	#424	C₂×D₇₃	1	1	yes	characteristic, complemented
373	#423	—	146	2	no	—
374	C₂×#104	—	73	1	no	—
375	C₂×#104	—	73	1	no	—
376	C₂×#104	—	73	1	no	—
377	C₂×#104	—	146	4	no	—
378	C₂×#104	C₂×D₇₃	1	1	yes	characteristic
379	#419	—	73	2	no	—
380	#418	—	73	2	no	—
381	#417	—	73	2	no	—
382	#417	—	73	2	no	—
383	#416	—	73	1	no	—
384	#416	—	73	1	no	—
385	#416	—	73	1	no	—
386	#416	C₂×D₇₃	1	1	yes	characteristic
387	#408	—	73	1	no	—
388	#408	—	73	1	no	—
389	#408	—	73	1	no	—
390	#408	—	146	2	no	—
391	#408	C₂×D₇₃	1	1	yes	characteristic
392	#407	—	146	2	no	—
393	C₄×M₁₆	—	146	4	no	—
394	C₂×#97	—	73	1	no	—
395	C₂×#97	—	73	1	no	—
396	C₂×C₄×C₈	—	73	1	no	—
397	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
398	#341	—	73	1	no	—
399	#341	—	73	1	no	—
400	#341	—	73	1	no	—
401	#341	C₂×D₇₃	1	1	yes	characteristic, complemented
402	#339	—	73	1	no	—
403	#339	—	73	1	no	—
404	#339	—	73	1	no	—
405	#339	C₂×D₇₃	1	1	yes	characteristic, complemented
406	C₂×#41	—	73	1	no	—
407	C₂×#41	—	73	1	no	—
408	C₂×#41	—	73	1	no	—
409	C₂×#41	—	146	1	no	—
410	C₂×#41	—	146	2	no	—
411	C₂×#41	—	146	2	no	—
412	C₂×#41	—	146	2	no	—
413	C₂×#41	—	146	2	no	—
414	C₂×#41	—	146	1	no	—
415	C₂×#41	C₂²×D₇₃	1	1	yes	characteristic
416	C₂²×Q₈	—	73	1	no	—
417	C₂²×D₄	—	73	1	no	—
418	C₂²×D₄	—	146	1	no	—
419	C₂³×C₄	—	73	1	no	—
420	C₂³×C₄	—	146	1	no	—
421	C₂³×C₄	—	146	1	no	—
422	C₂×M₁₆	—	73	2	no	—
423	C₂×M₁₆	—	73	2	no	—
424	C₂×M₁₆	—	73	2	no	—
425	C₂×M₁₆	—	73	2	no	—
426	C₂×M₁₆	—	73	1	no	—
427	C₂×M₁₆	—	73	1	no	—
428	C₂×M₁₆	—	146	1	no	—
429	C₂×M₁₆	—	146	1	no	—
430	C₂×M₁₆	—	146	2	no	—
431	C₂×M₁₆	—	146	2	no	—
432	C₂×M₁₆	—	146	2	no	—
433	C₂×M₁₆	—	146	2	no	—
434	C₂×M₁₆	—	146	2	no	—
435	C₂×M₁₆	—	146	2	no	—
436	C₂×M₁₆	—	146	2	no	—
437	C₂×M₁₆	—	146	2	no	—
438	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
439	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
440	C₂²×C₈	—	73	1	no	—
441	C₂²×C₈	—	73	1	no	—
442	C₂²×C₈	—	146	1	no	—
443	C₂²×C₈	—	146	1	no	—
444	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
445	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
446	#117	—	73	1	no	—
447	#117	—	73	2	no	—
448	#117	—	146	1	no	—
449	#117	—	146	1	no	—
450	#117	C₂²×D₇₃	1	1	yes	characteristic
451	C₂×C₄⋊C₄	—	73	2	no	—
452	C₂×C₂²⋊C₄	—	146	1	no	—
453	C₂×C₄²	—	73	1	no	—
454	C₂×C₄²	—	73	4	no	—
455	C₂×C₄²	—	146	1	no	—
456	C₂×C₄²	—	146	2	no	—
457	C₂×C₄²	—	146	1	no	—
458	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
459	C₄⋊C₈	—	2	2	no	—
460	C₄⋊C₈	—	146	2	no	—
461	C₄⋊C₈	—	146	2	no	—
462	C₄⋊C₈	—	146	2	no	—
463	#104	—	2	2	no	—
464	#104	—	146	2	no	—
465	#104	—	146	2	no	—
466	#104	—	146	2	no	—
467	#103	—	73	2	no	—
468	#103	—	73	2	no	—
469	#103	—	73	2	no	—
470	#103	C₄×D₇₃	1	2	yes	complemented
471	#102	—	73	2	no	—
472	#102	—	73	2	no	—
473	#102	—	73	2	no	—
474	#102	C₄×D₇₃	1	2	yes	complemented
475	C₂²⋊C₈	—	2	2	no	—
476	C₂²⋊C₈	—	146	2	no	—
477	C₂²⋊C₈	—	146	2	no	—
478	C₂²⋊C₈	—	146	2	no	—
479	#97	—	146	2	no	—
480	#97	—	146	2	no	—
481	C₄×C₈	—	2	2	no	—
482	C₄×C₈	—	146	2	no	—
483	C₂⁴	—	73	1	no	—
484	C₂⁴	—	146	1	no	—
485	#41	—	2	1	no	—
486	#41	—	2	1	no	—
487	#41	—	2	1	no	—
488	#41	—	2	1	no	—
489	#41	—	292	2	no	—
490	#41	—	292	2	no	—
491	#41	—	292	2	no	—
492	#41	—	292	2	no	—
493	#41	—	146	2	no	—
494	#41	—	146	2	no	—
495	#41	—	146	2	no	—
496	#41	—	146	2	no	—
497	#41	—	146	1	no	—
498	#41	—	146	1	no	—
499	#41	—	146	1	no	—
500	#41	—	146	1	no	—
501	C₂×Q₈	—	73	1	no	—
502	C₂×Q₈	—	146	1	no	—
503	C₂×Q₈	—	146	2	no	—
504	C₂×Q₈	—	146	2	no	—
505	C₂×Q₈	C₂×C₄×D₇₃	1	1	yes	characteristic
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	292	2	no	—
508	C₂×D₄	—	292	2	no	—
509	C₂×D₄	—	73	1	no	—
510	C₂×D₄	—	146	1	no	—
511	C₂×D₄	—	146	2	no	—
512	C₂×D₄	—	146	2	no	—
513	C₂×D₄	—	146	1	no	—
514	C₂×D₄	—	146	1	no	—
515	C₂×D₄	—	146	1	no	—
516	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	292	4	no	—
520	C₂²×C₄	—	292	2	no	—
521	C₂²×C₄	—	292	2	no	—
522	C₂²×C₄	—	73	1	no	—
523	C₂²×C₄	—	73	1	no	—
524	C₂²×C₄	—	73	1	no	—
525	C₂²×C₄	—	73	2	no	—
526	C₂²×C₄	—	73	1	no	—
527	C₂²×C₄	—	73	1	no	—
528	C₂²×C₄	—	73	2	no	—
529	C₂²×C₄	—	73	2	no	—
530	C₂²×C₄	—	73	2	no	—
531	C₂²×C₄	—	146	1	no	—
532	C₂²×C₄	—	146	4	no	—
533	C₂²×C₄	—	146	1	no	—
534	C₂²×C₄	—	146	2	no	—
535	C₂²×C₄	—	146	1	no	—
536	C₂²×C₄	—	146	1	no	—
537	C₂²×C₄	—	146	1	no	—
538	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
539	M₁₆	—	2	1	no	—
540	M₁₆	—	2	1	no	—
541	M₁₆	—	2	1	no	—
542	M₁₆	—	2	1	no	—
543	M₁₆	—	292	2	no	—
544	M₁₆	—	292	2	no	—
545	M₁₆	—	146	4	no	—
546	M₁₆	—	146	4	no	—
547	M₁₆	—	146	4	no	—
548	M₁₆	—	146	4	no	—
549	M₁₆	—	146	1	no	—
550	M₁₆	—	146	1	no	—
551	M₁₆	—	146	1	no	—
552	M₁₆	—	146	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	292	2	no	—
560	C₂×C₈	—	292	2	no	—
561	C₂×C₈	—	73	2	no	—
562	C₂×C₈	—	73	2	no	—
563	C₂×C₈	—	146	1	no	—
564	C₂×C₈	—	146	1	no	—
565	C₂×C₈	—	146	1	no	—
566	C₂×C₈	—	146	1	no	—
567	C₂×C₈	—	146	1	no	—
568	C₂×C₈	—	146	1	no	—
569	C₂×C₈	C₂×C₄×D₇₃	1	2	yes	—
570	C₂×C₈	D₄×D₇₃	1	2	yes	—
571	C₄⋊C₄	—	73	2	no	—
572	C₄⋊C₄	—	146	2	no	—
573	C₄⋊C₄	C₂×C₄×D₇₃	1	2	yes	—
574	C₂²⋊C₄	—	2	1	no	—
575	C₂²⋊C₄	—	146	2	no	—
576	C₂²⋊C₄	—	146	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	73	2	no	—
580	C₄²	—	146	4	no	—
581	C₄²	—	146	2	no	—
582	C₄²	—	146	1	no	—
583	C₄²	—	146	1	no	—
584	C₄²	D₄×D₇₃	1	2	yes	—
585	C₂³	—	2	1	no	—
586	C₂³	—	292	2	no	—
587	C₂³	—	292	2	no	—
588	C₂³	—	584	2	no	—
589	C₂³	—	73	2	no	—
590	C₂³	—	73	2	no	—
591	C₂³	—	73	1	no	—
592	C₂³	—	73	1	no	—
593	C₂³	—	146	1	no	—
594	C₂³	#41×D₇₃	1	1	yes	characteristic
595	Q₈	—	2	1	no	—
596	Q₈	—	2	1	no	—
597	Q₈	—	292	2	no	—
598	Q₈	—	146	1	no	—
599	Q₈	—	146	1	no	—
600	D₄	—	2	1	no	—
601	D₄	—	2	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	292	2	no	—
605	D₄	—	292	2	no	—
606	D₄	—	292	1	no	—
607	D₄	—	292	1	no	—
608	D₄	—	292	2	no	—
609	D₄	—	146	1	no	—
610	D₄	—	146	1	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	292	8	no	—
618	C₂×C₄	—	292	2	no	—
619	C₂×C₄	—	292	2	no	—
620	C₂×C₄	—	292	2	no	—
621	C₂×C₄	—	292	2	no	—
622	C₂×C₄	—	292	1	no	—
623	C₂×C₄	—	292	1	no	—
624	C₂×C₄	—	584	2	no	—
625	C₂×C₄	—	73	1	no	—
626	C₂×C₄	—	73	1	no	—
627	C₂×C₄	—	73	2	no	—
628	C₂×C₄	—	73	2	no	—
629	C₂×C₄	—	73	2	no	—
630	C₂×C₄	—	73	2	no	—
631	C₂×C₄	—	73	2	no	—
632	C₂×C₄	—	73	2	no	—
633	C₂×C₄	—	73	2	no	—
634	C₂×C₄	—	73	2	no	—
635	C₂×C₄	—	73	2	no	—
636	C₂×C₄	—	73	2	no	—
637	C₂×C₄	—	146	2	no	—
638	C₂×C₄	—	146	1	no	—
639	C₂×C₄	—	146	2	no	—
640	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
641	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
642	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
643	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
644	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
645	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
646	C₈	—	2	2	no	—
647	C₈	—	2	2	no	—
648	C₈	—	4	1	no	—
649	C₈	—	4	1	no	—
650	C₈	—	292	1	no	—
651	C₈	—	292	1	no	—
652	C₈	—	146	2	no	—
653	C₈	—	146	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	2	no	—
657	C₂²	—	292	2	no	—
658	C₂²	—	292	2	no	—
659	C₂²	—	292	1	no	—
660	C₂²	—	292	2	no	—
661	C₂²	—	584	4	no	—
662	C₂²	—	73	2	no	—
663	C₂²	—	73	2	no	—
664	C₂²	—	146	2	no	—
665	C₂²	—	146	2	no	—
666	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
667	C₂²	#123×D₇₃	1	1	yes	characteristic
668	C₂²	#126×D₇₃	1	1	yes	characteristic
669	C₄	—	2	4	no	—
670	C₄	—	4	1	no	—
671	C₄	—	4	2	no	—
672	C₄	—	292	2	no	—
673	C₄	—	292	1	no	—
674	C₄	—	292	2	no	—
675	C₄	—	73	2	no	—
676	C₄	—	73	2	no	—
677	C₄	#117×D₇₃	1	1	yes	characteristic
678	C₄	C₄×D₄×D₇₃	1	1	yes	characteristic
679	C₄	#121×D₇₃	1	1	yes	characteristic
680	C₄	#124×D₇₃	1	1	yes	characteristic
681	C₂	—	2	1	no	—
682	C₂	—	2	1	no	—
683	C₂	—	8	1	no	—
684	C₂	—	584	1	no	—
685	C₂	—	146	2	no	—
686	C₂	—	146	2	no	—
687	C₂	#388×D₇₃	1	1	yes	characteristic
688	C₂	#22618836	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#1937	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×#41×D₇₃	C₂²
cosocle	C₂²×C₄×C₇₃	C₂⁴
hypercenter	#1937	D₇₃
hypocenter	C₇₃	#21099
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1937

Complements

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

N	H ≅ G/N	type
1. #22618492	C₂	semidirect
5. C₂×C₄×#11924011	C₂	semidirect
6. #22610645	C₂	semidirect
7. #22610644	C₂	semidirect
8. #22610641	C₂	semidirect
9. #22610640	C₂	semidirect
10. #22610636	C₂	semidirect
11. #22610635	C₂	semidirect
12. #22610632	C₂	semidirect
13. #22609656	C₂	semidirect
14. #339×D₇₃	C₂	semidirect
15. C₇₃×#1937	C₂	semidirect
23. #17988615	C₂²	semidirect
24. #17988614	C₂²	semidirect
25. #17988613	C₂²	semidirect
32. #17988594	C₄	semidirect
33. #17988590	C₄	semidirect
34. #17988587	C₄	semidirect
35. #17988585	C₄	semidirect
45. C₂×#14556501	C₂²	semidirect
46. C₂×#14556501	C₂²	semidirect
47. C₂×C₄×#10596831	C₂²	semidirect
48. #17988352	C₂²	semidirect
49. #17988351	C₂²	semidirect
50. #17988351	C₂²	semidirect
51. #17988348	C₂²	semidirect
52. #17988347	C₂²	semidirect
53. #17988346	C₂²	semidirect
54. #424×C₇₃	C₂²	semidirect
58. C₂×C₄×C₈×C₇₃	C₂²	semidirect
59. #341×C₇₃	C₂²	semidirect
60. #339×C₇₃	C₂²	semidirect
113. #14556516	C₂×C₄	semidirect
114. #14556515	C₂×C₄	semidirect
115. #14556514	C₂×C₄	semidirect
116. #14556513	C₂×C₄	semidirect
117. #14556512	C₂×C₄	semidirect
118. #14556511	C₂×C₄	semidirect
134. #103×C₇₃	C₂×C₄	semidirect
135. #102×C₇₃	C₂×C₄	semidirect
357. #1937	D₇₃	semidirect
360. C₇₃	#21099	semidirect
372. #424	C₂×D₇₃	semidirect
397. C₂×C₄×C₈	C₂×D₇₃	semidirect
401. #341	C₂×D₇₃	semidirect
405. #339	C₂×D₇₃	semidirect
470. #103	C₄×D₇₃	semidirect
474. #102	C₄×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#22618492	2
C₂×#104×D₇₃	2
#22618446	2
#22618373	2
C₂×C₄×#11924011	2
#22610645	2
#22610644	2
#22610641	2
#22610640	2
#22610636	2
#22610635	2
#22610632	2
#22609656	2
#339×D₇₃	2
C₇₃×#1937	2
#21099	73