Subgroups — #3170×D₇₃ #33955722

Order 18688.

2006 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×D₇₃	C₂	1	2	yes	maximal
2	#22620518	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620517	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620516	C₂	1	2	yes	maximal, complemented
5	#22620515	C₂	1	1	yes	maximal, characteristic, complemented
6	#22620514	C₂	1	4	yes	maximal, complemented
7	#22620513	C₂	1	2	yes	maximal, complemented
8	#22620512	C₂	1	4	yes	maximal, complemented
9	#500×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
10	#494×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
11	#487×D₇₃	C₂	1	2	yes	maximal, complemented
12	#467×D₇₃	C₂	1	4	yes	maximal
13	C₄×Q₁₆×D₇₃	C₂	1	4	yes	maximal, complemented
14	C₂×C₄×C₈×D₇₃	C₂	1	1	yes	maximal, characteristic
15	C₇₃×#3170	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₇₃	C₂²	1	4	yes	—
17	C₂²×C₈×D₇₃	C₂²	1	2	yes	—
18	#17989144	C₂²	1	2	yes	—
19	#17989143	—	2	2	no	—
20	#17989142	C₂²	1	2	yes	—
21	#17989142	C₂²	1	2	yes	—
22	#17989141	—	2	2	no	—
23	#17989141	C₂²	1	4	yes	—
24	#17989140	—	2	2	no	—
25	#17989139	—	2	2	no	—
26	#17989139	C₂²	1	4	yes	—
27	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
28	C₄⋊Q₈×D₇₃	C₂²	1	2	yes	—
29	#125×D₇₃	—	2	2	no	—
30	C₂²⋊Q₈×D₇₃	—	2	2	no	—
31	C₂²⋊Q₈×D₇₃	C₂²	1	4	yes	—
32	C₄×Q₈×D₇₃	—	2	2	no	—
33	C₄×Q₈×D₇₃	C₂²	1	4	yes	—
34	#117×D₇₃	—	2	2	no	—
35	C₂×C₄²×D₇₃	C₂²	1	1	yes	characteristic
36	#17988992	C₂²	1	1	yes	characteristic, complemented
37	#17988991	C₂²	1	4	yes	complemented
38	#17988990	C₂²	1	2	yes	complemented
39	#17988967	C₂²	1	1	yes	characteristic, complemented
40	#17988966	C₂²	1	2	yes	complemented
41	#17988965	C₂²	1	4	yes	complemented
42	#17988939	C₂²	1	2	yes	complemented
43	#17988938	C₂²	1	2	yes	complemented
44	#17988937	C₂²	1	2	yes	complemented
45	#17988936	C₂²	1	8	yes	complemented
46	#17988829	C₂²	1	4	yes	—
47	#17988828	C₂²	1	4	yes	—
48	#17988827	C₂²	1	8	yes	—
49	#17988826	C₂²	1	8	yes	—
50	#17988825	C₂²	1	4	yes	—
51	C₄×Dic₂₉₂	C₂²	1	4	yes	complemented
52	Q₁₆×Dic₇₃	C₂²	1	4	yes	complemented
53	#17988681	C₂²	1	4	yes	complemented
54	C₄×#11924018	C₂²	1	8	yes	complemented
55	#17988679	C₂²	1	8	yes	complemented
56	#107×D₇₃	C₂²	1	4	yes	—
57	#103×D₇₃	C₂²	1	8	yes	—
58	C₂×C₄×#10596831	C₂²	1	1	yes	characteristic
59	C₂×C₈×Dic₇₃	C₂²	1	2	yes	—
60	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
61	C₄×C₈×D₇₃	C₂²	1	2	yes	—
62	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
63	C₄×C₈×D₇₃	C₂²	1	2	yes	—
64	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
65	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
66	#533×C₇₃	C₂²	1	2	yes	—
67	#500×C₇₃	C₂²	1	1	yes	characteristic, complemented
68	#494×C₇₃	C₂²	1	1	yes	characteristic, complemented
69	#487×C₇₃	C₂²	1	2	yes	complemented
70	#467×C₇₃	C₂²	1	4	yes	—
71	C₄×Q₁₆×C₇₃	C₂²	1	4	yes	complemented
72	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
73	C₂×Q₈×D₇₃	—	2	2	no	—
74	C₂×Q₈×D₇₃	C₂³	1	4	yes	—
75	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
76	C₂²×C₄×D₇₃	D₄	1	1	yes	characteristic
77	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
78	C₂×Dic₂₉₂	C₂³	1	4	yes	—
79	C₂×#11924018	C₂³	1	8	yes	—
80	Q₁₆×D₇₃	—	2	16	no	—
81	C₂²×#10596831	C₂³	1	2	yes	—
82	C₂×C₈×D₇₃	—	2	8	no	—
83	C₂×C₈×D₇₃	C₂³	1	2	yes	—
84	C₂×C₈×D₇₃	C₂³	1	2	yes	—
85	C₂×C₈×D₇₃	C₂³	1	2	yes	—
86	C₂×C₈×D₇₃	C₂³	1	2	yes	—
87	#14556591	C₂³	1	2	yes	—
88	#14556591	C₂³	1	2	yes	—
89	#14556590	—	2	2	no	—
90	#14556590	—	2	2	no	—
91	#14556590	—	2	2	no	—
92	#14556590	C₂³	1	4	yes	—
93	#14556589	—	2	2	no	—
94	#14556589	C₂³	1	4	yes	—
95	#14556583	—	2	2	no	—
96	#14556582	—	2	2	no	—
97	#14556582	—	2	2	no	—
98	#14556581	—	2	4	no	—
99	#14556581	—	2	4	no	—
100	#14556571	—	2	2	no	—
101	#14556571	C₂³	1	4	yes	—
102	#14556570	—	2	2	no	—
103	#14556570	C₂³	1	4	yes	—
104	#14556569	—	2	4	no	—
105	#14556569	—	2	4	no	—
106	#14556568	—	2	4	no	—
107	#14556568	—	2	4	no	—
108	#14556567	—	2	2	no	—
109	#14556567	C₂³	1	4	yes	—
110	Q₈×Dic₇₃	—	2	2	no	—
111	Q₈×Dic₇₃	C₂³	1	4	yes	—
112	C₄×Dic₁₄₆	—	2	4	no	—
113	C₄×Dic₁₄₆	—	2	4	no	—
114	C₄×Dic₁₄₆	—	2	2	no	—
115	C₄×Dic₁₄₆	C₂³	1	4	yes	—
116	#14556556	—	2	2	no	—
117	#14556556	—	2	4	no	—
118	#14556556	—	2	4	no	—
119	#14556556	C₂³	1	4	yes	—
120	#14556550	—	2	2	no	—
121	#14556549	—	2	2	no	—
122	#14556549	—	2	2	no	—
123	#14556548	—	2	4	no	—
124	#14556547	—	2	4	no	—
125	C₄⋊C₄×D₇₃	—	2	2	no	—
126	C₄⋊C₄×D₇₃	—	2	2	no	—
127	C₄⋊C₄×D₇₃	—	2	2	no	—
128	C₄⋊C₄×D₇₃	—	2	4	no	—
129	C₄⋊C₄×D₇₃	—	2	4	no	—
130	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
131	C₂²⋊C₄×D₇₃	—	2	4	no	—
132	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
133	C₂×C₄×Dic₇₃	D₄	1	1	yes	characteristic
134	C₂×C₄×Dic₇₃	C₂³	1	1	yes	characteristic
135	C₄²×D₇₃	—	2	4	no	—
136	C₄²×D₇₃	D₄	1	1	yes	characteristic
137	C₄²×D₇₃	D₄	1	1	yes	characteristic
138	C₄²×D₇₃	D₄	1	1	yes	characteristic
139	C₄²×D₇₃	D₄	1	1	yes	characteristic
140	C₄²×D₇₃	C₂³	1	1	yes	characteristic
141	C₄²×D₇₃	C₂³	1	1	yes	characteristic
142	C₄²×D₇₃	C₂³	1	1	yes	characteristic
143	C₄²×D₇₃	C₂³	1	1	yes	characteristic
144	#14556525	C₂³	1	4	yes	—
145	#14556524	C₂³	1	8	yes	—
146	#14556516	C₂³	1	8	yes	—
147	#14556515	C₂³	1	8	yes	—
148	#14556514	C₂³	1	8	yes	—
149	C₄×#10596831	C₂³	1	2	yes	—
150	C₄×#10596831	C₂³	1	1	yes	characteristic
151	C₄×#10596831	C₂³	1	1	yes	characteristic
152	C₈×Dic₇₃	C₂³	1	2	yes	—
153	C₈×Dic₇₃	C₂³	1	2	yes	—
154	C₈×Dic₇₃	C₂³	1	2	yes	—
155	C₈×Dic₇₃	C₂³	1	2	yes	—
156	C₂×Q₁₆×C₇₃	C₂³	1	4	yes	—
157	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
158	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
159	C₄⋊Q₈×C₇₃	C₂³	1	2	yes	—
160	#125×C₇₃	—	2	2	no	—
161	C₂²⋊Q₈×C₇₃	—	2	2	no	—
162	C₂²⋊Q₈×C₇₃	C₂³	1	4	yes	—
163	C₄×Q₈×C₇₃	—	2	2	no	—
164	C₄×Q₈×C₇₃	C₂³	1	4	yes	—
165	#117×C₇₃	—	2	2	no	—
166	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
167	#107×C₇₃	C₂³	1	4	yes	—
168	#103×C₇₃	C₂³	1	8	yes	—
169	C₄×C₈×C₇₃	C₂³	1	2	yes	—
170	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
171	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
172	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
173	C₂×Dic₁₄₆	—	2	2	no	—
174	C₂×Dic₁₄₆	—	2	4	no	—
175	C₂×Dic₁₄₆	—	2	4	no	—
176	C₂×Dic₁₄₆	C₂⁴	1	4	yes	—
177	Q₈×D₇₃	—	2	16	no	—
178	Q₈×D₇₃	—	4	8	no	—
179	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
182	C₂×C₄×D₇₃	—	2	4	no	—
183	C₂×C₄×D₇₃	—	2	4	no	—
184	C₂×C₄×D₇₃	—	2	4	no	—
185	C₂×C₄×D₇₃	—	2	4	no	—
186	C₂×C₄×D₇₃	Q₁₆	1	8	yes	complemented
187	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
188	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
190	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
191	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
192	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
193	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
194	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
195	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
197	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
198	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
199	Dic₂₉₂	—	2	8	no	—
200	#11924018	—	2	16	no	—
201	C₂×#10596831	—	2	4	no	—
202	C₂×#10596831	C₂⁴	1	2	yes	—
203	C₂×#10596831	C₂⁴	1	2	yes	—
204	C₈×D₇₃	—	2	4	no	—
205	C₈×D₇₃	—	2	4	no	—
206	C₈×D₇₃	—	2	4	no	—
207	C₈×D₇₃	#41	1	8	yes	—
208	C₄⋊Dic₇₃	—	2	2	no	—
209	C₄⋊Dic₇₃	—	2	2	no	—
210	C₄⋊Dic₇₃	—	2	2	no	—
211	C₄⋊Dic₇₃	—	2	4	no	—
212	C₄⋊Dic₇₃	—	2	4	no	—
213	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
214	#11924007	—	2	4	no	—
215	#11924007	—	2	4	no	—
216	#11924007	—	2	4	no	—
217	#11924007	—	2	4	no	—
218	#11924007	—	2	4	no	—
219	#11924007	—	2	4	no	—
220	#11924007	—	2	4	no	—
221	#11924007	—	2	4	no	—
222	C₂²⋊Dic₇₃	—	2	4	no	—
223	#11924005	—	2	4	no	—
224	#11924005	—	2	4	no	—
225	C₄×Dic₇₃	—	2	4	no	—
226	C₄×Dic₇₃	—	2	4	no	—
227	C₄×Dic₇₃	—	2	4	no	—
228	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
229	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
230	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
231	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
232	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
233	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
234	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
235	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
236	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
237	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
238	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
239	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
240	C₂×Q₈×C₇₃	—	2	2	no	—
241	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
242	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
243	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
245	Q₁₆×C₇₃	—	2	8	no	—
246	C₂×C₈×C₇₃	—	2	4	no	—
247	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₇₃	—	2	2	no	—
250	C₄⋊C₄×C₇₃	—	2	2	no	—
251	C₄⋊C₄×C₇₃	—	2	2	no	—
252	C₄⋊C₄×C₇₃	—	2	4	no	—
253	C₄⋊C₄×C₇₃	—	2	4	no	—
254	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
255	C₂²⋊C₄×C₇₃	—	2	4	no	—
256	C₄²×C₇₃	—	2	4	no	—
257	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
258	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
259	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
260	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
262	C₂²×D₇₃	—	2	2	no	—
263	C₂²×D₇₃	—	2	2	no	—
264	C₂²×D₇₃	C₂×Q₁₆	1	4	yes	—
265	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
266	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₇₃	—	2	8	no	—
268	Q₈×C₇₃	—	4	4	no	—
269	C₂×C₄×C₇₃	—	2	2	no	—
270	C₂×C₄×C₇₃	—	2	2	no	—
271	C₂×C₄×C₇₃	—	2	4	no	—
272	C₂×C₄×C₇₃	—	2	4	no	—
273	C₂×C₄×C₇₃	C₂×Q₁₆	1	4	yes	complemented
274	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
280	C₂×Dic₇₃	—	2	2	no	—
281	C₂×Dic₇₃	—	2	2	no	—
282	C₂×Dic₇₃	—	2	4	no	—
283	C₂×Dic₇₃	—	2	4	no	—
284	C₂×Dic₇₃	C₂×Q₁₆	1	4	yes	complemented
285	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
288	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
291	C₄×D₇₃	—	2	2	no	—
292	C₄×D₇₃	—	2	2	no	—
293	C₄×D₇₃	—	2	2	no	—
294	C₄×D₇₃	—	2	2	no	—
295	C₄×D₇₃	—	2	2	no	—
296	C₄×D₇₃	—	2	2	no	—
297	C₄×D₇₃	—	4	8	no	—
298	C₄×D₇₃	—	4	8	no	—
299	C₄×D₇₃	C₂×Q₁₆	1	4	yes	—
300	C₄×D₇₃	C₂×Q₁₆	1	4	yes	—
301	C₄×D₇₃	C₂×Q₁₆	1	4	yes	complemented
302	C₄×D₇₃	C₂×Q₁₆	1	4	yes	complemented
303	C₄×D₇₃	#135	1	4	yes	—
304	C₄×D₇₃	C₂×#41	1	4	yes	—
305	Dic₁₄₆	—	2	8	no	—
306	Dic₁₄₆	—	4	4	no	—
307	Dic₁₄₆	—	4	8	no	—
308	Dic₁₄₆	—	4	8	no	—
309	C₈×C₇₃	—	2	2	no	—
310	C₈×C₇₃	C₂×#41	1	4	yes	—
311	#10596831	—	2	2	no	—
312	#10596831	C₂×#41	1	4	yes	—
313	C₂²×C₇₃	—	2	1	no	—
314	C₂²×C₇₃	—	2	1	no	—
315	C₂²×C₇₃	C₂²×Q₁₆	1	2	yes	—
316	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
317	C₂×D₇₃	—	2	1	no	—
318	C₂×D₇₃	—	2	1	no	—
319	C₂×D₇₃	—	2	8	no	—
320	C₂×D₇₃	#532	1	2	yes	—
321	C₂×D₇₃	C₂²×Q₁₆	1	2	yes	—
322	C₂×D₇₃	C₂²×Q₁₆	1	2	yes	—
323	C₂×D₇₃	C₂×#135	1	2	yes	—
324	C₄×C₇₃	—	2	1	no	—
325	C₄×C₇₃	—	2	1	no	—
326	C₄×C₇₃	—	4	4	no	—
327	C₄×C₇₃	—	4	4	no	—
328	C₄×C₇₃	C₂²×Q₁₆	1	2	yes	—
329	C₄×C₇₃	C₂²×Q₁₆	1	2	yes	—
330	C₄×C₇₃	C₂×#135	1	2	yes	—
331	C₄×C₇₃	C₂²×#41	1	2	yes	—
332	Dic₇₃	—	2	1	no	—
333	Dic₇₃	—	2	1	no	—
334	Dic₇₃	—	4	4	no	—
335	Dic₇₃	—	4	4	no	—
336	Dic₇₃	#532	1	2	yes	—
337	Dic₇₃	C₂²×Q₁₆	1	2	yes	—
338	Dic₇₃	C₂²×Q₁₆	1	2	yes	—
339	Dic₇₃	C₂×#135	1	2	yes	—
340	C₂×#3170	—	73	1	no	maximal, Sylow
341	C₂×C₇₃	—	2	2	no	—
342	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
343	C₂×C₇₃	C₂³×Q₁₆	1	1	yes	characteristic
344	C₂×C₇₃	C₂²×#135	1	1	yes	characteristic
345	D₇₃	—	2	2	no	—
346	D₇₃	#3170	1	4	yes	direct product factor
347	C₂×#533	—	73	2	no	—
348	#3170	—	73	1	no	—
349	#3170	—	73	1	no	—
350	#3170	—	73	2	no	—
351	#3170	—	73	4	no	—
352	#3170	—	73	4	no	—
353	#3170	—	73	1	no	—
354	#3170	—	73	2	no	—
355	#3170	D₇₃	1	1	yes	characteristic, direct product factor
356	C₂×#500	—	73	1	no	—
357	C₂×#494	—	73	1	no	—
358	C₂×#487	—	73	2	no	—
359	C₂×#467	—	73	4	no	—
360	C₂×C₄×Q₁₆	—	73	4	no	—
361	C₂²×C₄×C₈	—	73	1	no	—
362	C₇₃	C₂×#3170	1	1	yes	characteristic, complemented, Sylow
363	C₂²×Q₁₆	—	73	4	no	—
364	C₂³×C₈	—	73	2	no	—
365	#533	—	73	2	no	—
366	#533	—	73	2	no	—
367	#533	—	73	4	no	—
368	#533	—	73	4	no	—
369	#533	—	73	2	no	—
370	#533	—	146	2	no	—
371	#533	—	146	2	no	—
372	#533	—	146	2	no	—
373	#533	—	146	2	no	—
374	#533	C₂×D₇₃	1	2	yes	—
375	C₂×C₄⋊Q₈	—	73	2	no	—
376	C₂×C₄⋊Q₈	—	73	2	no	—
377	C₂×#125	—	146	2	no	—
378	C₂×C₂²⋊Q₈	—	73	4	no	—
379	C₂×C₂²⋊Q₈	—	146	2	no	—
380	C₂×C₄×Q₈	—	73	4	no	—
381	C₂×C₄×Q₈	—	146	2	no	—
382	C₂×#117	—	146	2	no	—
383	C₂²×C₄²	—	73	1	no	—
384	#500	—	73	2	no	—
385	#500	—	73	4	no	—
386	#500	—	73	1	no	—
387	#500	C₂×D₇₃	1	1	yes	characteristic, complemented
388	#494	—	73	4	no	—
389	#494	—	73	2	no	—
390	#494	—	73	1	no	—
391	#494	C₂×D₇₃	1	1	yes	characteristic, complemented
392	#487	—	73	2	no	—
393	#487	—	73	2	no	—
394	#487	—	73	8	no	—
395	#487	—	73	2	no	—
396	#487	C₂×D₇₃	1	2	yes	complemented
397	#467	—	73	4	no	—
398	#467	—	73	4	no	—
399	#467	—	73	8	no	—
400	#467	—	73	4	no	—
401	#467	—	73	8	no	—
402	#467	C₂×D₇₃	1	4	yes	—
403	C₄×Q₁₆	—	73	4	no	—
404	C₄×Q₁₆	—	73	8	no	—
405	C₄×Q₁₆	—	73	4	no	—
406	C₄×Q₁₆	—	73	8	no	—
407	C₄×Q₁₆	—	73	4	no	—
408	C₄×Q₁₆	C₂×D₇₃	1	4	yes	complemented
409	C₂×#107	—	73	4	no	—
410	C₂×#103	—	73	8	no	—
411	C₂×C₄×C₈	—	73	2	no	—
412	C₂×C₄×C₈	—	73	1	no	—
413	C₂×C₄×C₈	—	73	1	no	—
414	C₂×C₄×C₈	—	73	1	no	—
415	C₂×C₄×C₈	—	73	1	no	—
416	C₂×C₄×C₈	—	73	1	no	—
417	C₂×C₄×C₈	—	73	2	no	—
418	C₂×C₄×C₈	—	73	2	no	—
419	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
420	C₂²×Q₈	—	73	4	no	—
421	C₂²×Q₈	—	146	2	no	—
422	C₂³×C₄	—	73	1	no	—
423	C₂³×C₄	—	73	1	no	—
424	C₂³×C₄	—	73	1	no	—
425	C₂×Q₁₆	—	73	8	no	—
426	C₂×Q₁₆	—	73	4	no	—
427	C₂×Q₁₆	—	146	16	no	—
428	C₂×Q₁₆	C₂²×D₇₃	1	4	yes	—
429	C₂²×C₈	—	73	2	no	—
430	C₂²×C₈	—	73	2	no	—
431	C₂²×C₈	—	73	2	no	—
432	C₂²×C₈	—	73	2	no	—
433	C₂²×C₈	—	73	2	no	—
434	C₂²×C₈	—	146	8	no	—
435	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
436	C₄⋊Q₈	—	73	4	no	—
437	C₄⋊Q₈	—	73	4	no	—
438	C₄⋊Q₈	—	73	2	no	—
439	C₄⋊Q₈	—	73	2	no	—
440	C₄⋊Q₈	—	146	2	no	—
441	C₄⋊Q₈	—	146	2	no	—
442	C₄⋊Q₈	—	146	2	no	—
443	C₄⋊Q₈	—	146	2	no	—
444	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
445	C₄⋊Q₈	C₂²×D₇₃	1	2	yes	—
446	#125	—	2	2	no	—
447	#125	—	146	4	no	—
448	#125	—	146	4	no	—
449	#125	—	146	2	no	—
450	#125	—	146	2	no	—
451	#125	—	146	2	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	73	4	no	—
454	C₂²⋊Q₈	—	73	4	no	—
455	C₂²⋊Q₈	—	73	4	no	—
456	C₂²⋊Q₈	—	146	4	no	—
457	C₂²⋊Q₈	—	146	4	no	—
458	C₂²⋊Q₈	—	146	4	no	—
459	C₂²⋊Q₈	—	146	4	no	—
460	C₂²⋊Q₈	—	146	2	no	—
461	C₂²⋊Q₈	—	146	2	no	—
462	C₂²⋊Q₈	—	146	2	no	—
463	C₂²⋊Q₈	C₂²×D₇₃	1	4	yes	—
464	C₄×Q₈	—	2	2	no	—
465	C₄×Q₈	—	73	4	no	—
466	C₄×Q₈	—	73	4	no	—
467	C₄×Q₈	—	73	4	no	—
468	C₄×Q₈	—	146	4	no	—
469	C₄×Q₈	—	146	4	no	—
470	C₄×Q₈	—	146	4	no	—
471	C₄×Q₈	—	146	2	no	—
472	C₄×Q₈	—	146	4	no	—
473	C₄×Q₈	—	146	2	no	—
474	C₄×Q₈	—	146	2	no	—
475	C₄×Q₈	C₂²×D₇₃	1	4	yes	—
476	#117	—	2	2	no	—
477	#117	—	146	4	no	—
478	#117	—	146	4	no	—
479	#117	—	146	2	no	—
480	#117	—	146	2	no	—
481	#117	—	146	2	no	—
482	C₂×C₄⋊C₄	—	73	4	no	—
483	C₂×C₄⋊C₄	—	146	2	no	—
484	C₂×C₄⋊C₄	—	146	2	no	—
485	C₂×C₄⋊C₄	—	146	4	no	—
486	C₂×C₄⋊C₄	—	146	4	no	—
487	C₂×C₄⋊C₄	—	146	2	no	—
488	C₂×C₂²⋊C₄	—	146	4	no	—
489	C₂×C₄²	—	73	1	no	—
490	C₂×C₄²	—	73	1	no	—
491	C₂×C₄²	—	73	1	no	—
492	C₂×C₄²	—	73	1	no	—
493	C₂×C₄²	—	73	1	no	—
494	C₂×C₄²	—	73	1	no	—
495	C₂×C₄²	—	73	1	no	—
496	C₂×C₄²	—	73	1	no	—
497	C₂×C₄²	—	73	1	no	—
498	C₂×C₄²	—	73	1	no	—
499	C₂×C₄²	—	73	1	no	—
500	C₂×C₄²	—	146	4	no	—
501	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
502	#107	—	73	4	no	—
503	#107	—	73	8	no	—
504	#107	C₂²×D₇₃	1	4	yes	—
505	#103	—	73	8	no	—
506	#103	—	73	8	no	—
507	#103	—	73	8	no	—
508	#103	C₂²×D₇₃	1	8	yes	—
509	C₄×C₈	—	73	2	no	—
510	C₄×C₈	—	73	2	no	—
511	C₄×C₈	—	73	2	no	—
512	C₄×C₈	—	73	2	no	—
513	C₄×C₈	—	73	2	no	—
514	C₄×C₈	—	73	1	no	—
515	C₄×C₈	—	73	1	no	—
516	C₄×C₈	C₂²×D₇₃	1	2	yes	—
517	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
518	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
519	C₂⁴	—	73	1	no	—
520	C₂×Q₈	—	2	2	no	—
521	C₂×Q₈	—	292	8	no	—
522	C₂×Q₈	—	73	4	no	—
523	C₂×Q₈	—	146	4	no	—
524	C₂×Q₈	—	146	4	no	—
525	C₂×Q₈	—	146	16	no	—
526	C₂×Q₈	—	146	2	no	—
527	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
528	C₂²×C₄	—	73	1	no	—
529	C₂²×C₄	—	73	8	no	—
530	C₂²×C₄	—	73	1	no	—
531	C₂²×C₄	—	73	1	no	—
532	C₂²×C₄	—	73	1	no	—
533	C₂²×C₄	—	73	1	no	—
534	C₂²×C₄	—	73	1	no	—
535	C₂²×C₄	—	73	1	no	—
536	C₂²×C₄	—	73	1	no	—
537	C₂²×C₄	—	73	1	no	—
538	C₂²×C₄	—	73	1	no	—
539	C₂²×C₄	—	73	1	no	—
540	C₂²×C₄	—	73	1	no	—
541	C₂²×C₄	—	73	1	no	—
542	C₂²×C₄	—	73	1	no	—
543	C₂²×C₄	—	73	1	no	—
544	C₂²×C₄	—	146	4	no	—
545	C₂²×C₄	—	146	4	no	—
546	C₂²×C₄	—	146	4	no	—
547	C₂²×C₄	—	146	4	no	—
548	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
549	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
550	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
551	Q₁₆	—	2	8	no	—
552	Q₁₆	—	146	16	no	—
553	Q₁₆	—	146	8	no	—
554	C₂×C₈	—	2	4	no	—
555	C₂×C₈	—	73	2	no	—
556	C₂×C₈	—	73	8	no	—
557	C₂×C₈	—	73	2	no	—
558	C₂×C₈	—	146	4	no	—
559	C₂×C₈	—	146	4	no	—
560	C₂×C₈	—	146	4	no	—
561	C₂×C₈	—	146	4	no	—
562	C₂×C₈	C₂³×D₇₃	1	2	yes	—
563	C₂×C₈	C₂³×D₇₃	1	2	yes	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	4	no	—
568	C₄⋊C₄	—	2	4	no	—
569	C₄⋊C₄	—	73	4	no	—
570	C₄⋊C₄	—	146	4	no	—
571	C₄⋊C₄	—	146	4	no	—
572	C₄⋊C₄	—	146	4	no	—
573	C₄⋊C₄	—	146	4	no	—
574	C₄⋊C₄	—	146	4	no	—
575	C₄⋊C₄	—	146	4	no	—
576	C₄⋊C₄	—	146	4	no	—
577	C₄⋊C₄	—	146	4	no	—
578	C₄⋊C₄	—	146	4	no	—
579	C₄⋊C₄	—	146	4	no	—
580	C₄⋊C₄	—	146	2	no	—
581	C₄⋊C₄	—	146	2	no	—
582	C₄⋊C₄	—	146	2	no	—
583	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
584	C₂²⋊C₄	—	2	4	no	—
585	C₂²⋊C₄	—	146	4	no	—
586	C₂²⋊C₄	—	146	4	no	—
587	C₂²⋊C₄	—	146	4	no	—
588	C₄²	—	2	4	no	—
589	C₄²	—	73	1	no	—
590	C₄²	—	73	1	no	—
591	C₄²	—	73	1	no	—
592	C₄²	—	73	1	no	—
593	C₄²	—	73	1	no	—
594	C₄²	—	73	1	no	—
595	C₄²	—	73	1	no	—
596	C₄²	—	73	1	no	—
597	C₄²	—	73	1	no	—
598	C₄²	—	73	1	no	—
599	C₄²	—	73	1	no	—
600	C₄²	—	73	1	no	—
601	C₄²	—	146	4	no	—
602	C₄²	—	146	4	no	—
603	C₄²	—	146	4	no	—
604	C₄²	D₄×D₇₃	1	1	yes	characteristic
605	C₄²	D₄×D₇₃	1	1	yes	characteristic
606	C₄²	C₂³×D₇₃	1	1	yes	characteristic
607	C₄²	C₂³×D₇₃	1	1	yes	characteristic
608	C₂³	—	73	1	no	—
609	C₂³	—	73	1	no	—
610	C₂³	—	73	4	no	—
611	C₂³	—	146	2	no	—
612	C₂³	—	146	2	no	—
613	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
614	Q₈	—	2	8	no	—
615	Q₈	—	4	4	no	—
616	Q₈	—	292	8	no	—
617	Q₈	—	292	8	no	—
618	Q₈	—	292	4	no	—
619	Q₈	—	146	8	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	4	no	—
623	C₂×C₄	—	2	4	no	—
624	C₂×C₄	—	292	8	no	—
625	C₂×C₄	—	292	8	no	—
626	C₂×C₄	—	73	1	no	—
627	C₂×C₄	—	73	1	no	—
628	C₂×C₄	—	73	1	no	—
629	C₂×C₄	—	73	1	no	—
630	C₂×C₄	—	73	4	no	—
631	C₂×C₄	—	73	4	no	—
632	C₂×C₄	—	73	4	no	—
633	C₂×C₄	—	73	4	no	—
634	C₂×C₄	—	73	4	no	—
635	C₂×C₄	—	73	4	no	—
636	C₂×C₄	—	73	4	no	—
637	C₂×C₄	—	73	1	no	—
638	C₂×C₄	—	73	1	no	—
639	C₂×C₄	—	146	2	no	—
640	C₂×C₄	—	146	2	no	—
641	C₂×C₄	—	146	2	no	—
642	C₂×C₄	—	146	2	no	—
643	C₂×C₄	—	146	4	no	—
644	C₂×C₄	—	146	4	no	—
645	C₂×C₄	—	146	2	no	—
646	C₂×C₄	—	146	2	no	—
647	C₂×C₄	—	146	2	no	—
648	C₂×C₄	—	146	2	no	—
649	C₂×C₄	Q₁₆×D₇₃	1	4	yes	complemented
650	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
651	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
652	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
653	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
654	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
655	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	73	4	no	—
658	C₈	—	146	2	no	—
659	C₈	#41×D₇₃	1	4	yes	—
660	C₂²	—	2	1	no	—
661	C₂²	—	2	1	no	—
662	C₂²	—	73	2	no	—
663	C₂²	—	73	2	no	—
664	C₂²	—	73	2	no	—
665	C₂²	—	73	2	no	—
666	C₂²	—	146	8	no	—
667	C₂²	—	146	1	no	—
668	C₂²	—	146	1	no	—
669	C₂²	C₂×Q₁₆×D₇₃	1	2	yes	—
670	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
671	C₄	—	2	1	no	—
672	C₄	—	2	1	no	—
673	C₄	—	4	4	no	—
674	C₄	—	4	4	no	—
675	C₄	—	292	4	no	—
676	C₄	—	292	4	no	—
677	C₄	—	73	2	no	—
678	C₄	—	73	2	no	—
679	C₄	—	73	2	no	—
680	C₄	—	73	2	no	—
681	C₄	—	146	1	no	—
682	C₄	—	146	1	no	—
683	C₄	C₂×Q₁₆×D₇₃	1	2	yes	—
684	C₄	C₂×Q₁₆×D₇₃	1	2	yes	—
685	C₄	#135×D₇₃	1	2	yes	—
686	C₄	C₂×#41×D₇₃	1	2	yes	—
687	C₂	—	2	2	no	—
688	C₂	—	73	4	no	—
689	C₂	—	146	2	no	—
690	C₂	#532×D₇₃	1	1	yes	characteristic
691	C₂	C₂²×Q₁₆×D₇₃	1	1	yes	characteristic
692	C₂	C₂×#135×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3170	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂³×D₇₃	C₂×D₄
hypercenter	#3170	D₇₃
hypocenter	C₇₃	C₂×#3170
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3170

Complements

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

N	H ≅ G/N	type
2. #22620518	C₂	semidirect
3. #22620517	C₂	semidirect
4. #22620516	C₂	semidirect
5. #22620515	C₂	semidirect
6. #22620514	C₂	semidirect
7. #22620513	C₂	semidirect
8. #22620512	C₂	semidirect
9. #500×D₇₃	C₂	semidirect
10. #494×D₇₃	C₂	semidirect
11. #487×D₇₃	C₂	semidirect
13. C₄×Q₁₆×D₇₃	C₂	semidirect
15. C₇₃×#3170	C₂	semidirect
36. #17988992	C₂²	semidirect
37. #17988991	C₂²	semidirect
38. #17988990	C₂²	semidirect
39. #17988967	C₂²	semidirect
40. #17988966	C₂²	semidirect
41. #17988965	C₂²	semidirect
42. #17988939	C₂²	semidirect
43. #17988938	C₂²	semidirect
44. #17988937	C₂²	semidirect
45. #17988936	C₂²	semidirect
51. C₄×Dic₂₉₂	C₂²	semidirect
52. Q₁₆×Dic₇₃	C₂²	semidirect
53. #17988681	C₂²	semidirect
54. C₄×#11924018	C₂²	semidirect
55. #17988679	C₂²	semidirect
67. #500×C₇₃	C₂²	semidirect
68. #494×C₇₃	C₂²	semidirect
69. #487×C₇₃	C₂²	semidirect
71. C₄×Q₁₆×C₇₃	C₂²	semidirect
186. C₂×C₄×D₇₃	Q₁₆	semidirect
273. C₂×C₄×C₇₃	C₂×Q₁₆	semidirect
284. C₂×Dic₇₃	C₂×Q₁₆	semidirect
301. C₄×D₇₃	C₂×Q₁₆	semidirect
302. C₄×D₇₃	C₂×Q₁₆	semidirect
346. D₇₃	#3170	direct (N × H)
355. #3170	D₇₃	direct (N × H)
362. C₇₃	C₂×#3170	semidirect
387. #500	C₂×D₇₃	semidirect
391. #494	C₂×D₇₃	semidirect
396. #487	C₂×D₇₃	semidirect
408. C₄×Q₁₆	C₂×D₇₃	semidirect
649. C₂×C₄	Q₁₆×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#533×D₇₃	2
#22620518	2
#22620517	2
#22620516	2
#22620515	2
#22620514	2
#22620513	2
#22620512	2
#500×D₇₃	2
#494×D₇₃	2
#487×D₇₃	2
#467×D₇₃	2
C₄×Q₁₆×D₇₃	2
C₂×C₄×C₈×D₇₃	2
C₇₃×#3170	2
C₂×#3170	73

Subgroups — #3170×D73 #33955722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3170×D₇₃ #33955722