Subgroups — #3163×D₇₃ #33955601

Order 18688.

1854 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	#544×D₇₃	C₂	1	2	yes	maximal
2	#22620463	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620462	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620461	C₂	1	2	yes	maximal, complemented
5	#22620460	C₂	1	2	yes	maximal, complemented
6	#22620459	C₂	1	1	yes	maximal, characteristic, complemented
7	#22620458	C₂	1	4	yes	maximal, complemented
8	#22620457	C₂	1	2	yes	maximal, complemented
9	#22620456	C₂	1	2	yes	maximal, complemented
10	#501×D₇₃	C₂	1	4	yes	maximal, complemented
11	#499×D₇₃	C₂	1	2	yes	maximal, complemented
12	#498×D₇₃	C₂	1	2	yes	maximal, complemented
13	#428×D₇₃	C₂	1	2	yes	maximal
14	#427×D₇₃	C₂	1	1	yes	maximal, characteristic
15	C₂×#106×D₇₃	C₂	1	1	yes	maximal, characteristic
16	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
17	C₇₃×#3163	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
20	#17989218	C₂²	1	2	yes	—
21	#17989217	—	2	2	no	—
22	#17989217	C₂²	1	4	yes	—
23	#17989216	—	2	4	no	—
24	#17989215	C₂²	1	2	yes	—
25	#17989215	C₂²	1	2	yes	—
26	#17989214	—	2	2	no	—
27	#17989214	C₂²	1	4	yes	—
28	C₄⋊Q₈×D₇₃	—	2	2	no	—
29	C₄⋊Q₈×D₇₃	C₂²	1	4	yes	—
30	#125×D₇₃	—	2	2	no	—
31	#125×D₇₃	C₂²	1	4	yes	—
32	C₂²⋊Q₈×D₇₃	—	2	4	no	—
33	#117×D₇₃	C₂²	1	2	yes	—
34	#117×D₇₃	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×D₇₃	C₂²	1	2	yes	—
36	#17988997	C₂²	1	4	yes	complemented
37	#17988996	C₂²	1	4	yes	complemented
38	#17988995	C₂²	1	4	yes	complemented
39	#17988995	C₂²	1	4	yes	complemented
40	#17988994	C₂²	1	4	yes	complemented
41	#17988994	C₂²	1	4	yes	complemented
42	#17988993	C₂²	1	4	yes	complemented
43	#17988989	C₂²	1	2	yes	complemented
44	#17988988	C₂²	1	4	yes	complemented
45	#17988987	C₂²	1	2	yes	complemented
46	#17988987	C₂²	1	2	yes	complemented
47	#17988986	C₂²	1	4	yes	complemented
48	#17988985	C₂²	1	2	yes	complemented
49	#17988984	C₂²	1	2	yes	complemented
50	#17988984	C₂²	1	4	yes	complemented
51	#17988984	C₂²	1	2	yes	complemented
52	#17988983	C₂²	1	4	yes	complemented
53	#17988630	C₂²	1	2	yes	—
54	#17988629	C₂²	1	2	yes	—
55	#17988628	C₂²	1	4	yes	—
56	#17988627	C₂²	1	2	yes	—
57	#17988626	C₂²	1	4	yes	—
58	#17988625	C₂²	1	1	yes	characteristic
59	#17988624	C₂²	1	2	yes	—
60	#17988623	C₂²	1	2	yes	—
61	#17988622	C₂²	1	1	yes	characteristic
62	#17988622	C₂²	1	1	yes	characteristic
63	#107×D₇₃	C₂²	1	4	yes	—
64	#107×D₇₃	C₂²	1	2	yes	—
65	C₂×#14556523	C₂²	1	1	yes	characteristic
66	C₂×#14556522	C₂²	1	2	yes	—
67	#106×D₇₃	C₂²	1	1	yes	characteristic
68	#106×D₇₃	C₂²	1	2	yes	—
69	#106×D₇₃	C₂²	1	4	yes	—
70	#106×D₇₃	C₂²	1	1	yes	characteristic
71	#106×D₇₃	C₂²	1	2	yes	—
72	#106×D₇₃	C₂²	1	2	yes	—
73	#106×D₇₃	C₂²	1	2	yes	—
74	#17988545	C₂²	1	1	yes	characteristic
75	#17988544	C₂²	1	2	yes	—
76	#17988543	C₂²	1	1	yes	characteristic
77	#17988542	C₂²	1	1	yes	characteristic
78	#17988541	C₂²	1	2	yes	—
79	#97×D₇₃	C₂²	1	2	yes	—
80	C₄×C₈×D₇₃	C₂²	1	2	yes	—
81	#544×C₇₃	C₂²	1	2	yes	—
82	#501×C₇₃	C₂²	1	4	yes	complemented
83	#499×C₇₃	C₂²	1	2	yes	complemented
84	#498×C₇₃	C₂²	1	2	yes	complemented
85	#428×C₇₃	C₂²	1	2	yes	—
86	#427×C₇₃	C₂²	1	1	yes	characteristic
87	C₂×#106×C₇₃	C₂²	1	1	yes	characteristic
88	#405×C₇₃	C₂²	1	1	yes	characteristic
89	C₂×Q₈×D₇₃	—	2	4	no	—
90	C₂²×C₄×D₇₃	—	2	2	no	—
91	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
92	C₂×#11924012	C₂³	1	1	yes	characteristic
93	C₂×#11924011	C₂³	1	2	yes	—
94	M₁₆×D₇₃	Q₈	1	8	yes	complemented
95	C₂²×#10596831	C₂³	1	1	yes	characteristic
96	C₂×C₈×D₇₃	Q₈	1	8	yes	complemented
97	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₇₃	C₂³	1	2	yes	—
99	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
100	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
101	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
102	#14556591	—	2	2	no	—
103	#14556591	C₂³	1	4	yes	—
104	#14556590	—	2	2	no	—
105	#14556590	—	2	4	no	—
106	#14556590	—	2	4	no	—
107	#14556590	—	2	2	no	—
108	#14556590	C₂³	1	4	yes	—
109	#14556590	C₂³	1	4	yes	—
110	#14556589	—	2	4	no	—
111	#14556589	—	2	4	no	—
112	#14556583	—	2	2	no	—
113	#14556583	C₂³	1	4	yes	—
114	#14556582	—	2	2	no	—
115	#14556582	—	2	2	no	—
116	#14556582	C₂³	1	4	yes	—
117	#14556582	C₂³	1	4	yes	—
118	#14556581	—	2	4	no	—
119	#14556581	—	2	4	no	—
120	#14556581	—	2	4	no	—
121	#14556581	—	2	4	no	—
122	#14556571	—	2	4	no	—
123	#14556570	—	2	4	no	—
124	#14556569	—	2	4	no	—
125	#14556569	—	2	4	no	—
126	#14556568	—	2	4	no	—
127	#14556568	—	2	4	no	—
128	#14556567	—	2	4	no	—
129	#14556550	C₂³	1	2	yes	—
130	#14556550	C₂³	1	1	yes	characteristic
131	#14556549	D₄	1	2	yes	—
132	#14556549	C₂³	1	2	yes	—
133	#14556549	C₂³	1	2	yes	—
134	#14556548	—	2	2	no	—
135	#14556548	C₂³	1	2	yes	—
136	#14556547	—	2	2	no	—
137	#14556547	D₄	1	2	yes	—
138	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
139	C₂×#11924007	—	2	2	no	—
140	C₄⋊C₄×D₇₃	—	2	2	no	—
141	C₄⋊C₄×D₇₃	—	2	4	no	—
142	C₄⋊C₄×D₇₃	—	2	4	no	—
143	C₄⋊C₄×D₇₃	—	2	2	no	—
144	C₄⋊C₄×D₇₃	—	2	4	no	—
145	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
146	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
147	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
148	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
149	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
150	C₂²⋊C₄×D₇₃	—	2	2	no	—
151	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
152	C₄²×D₇₃	—	2	2	no	—
153	C₄²×D₇₃	C₂³	1	2	yes	—
154	#14556525	C₂³	1	2	yes	—
155	#14556525	C₂³	1	4	yes	—
156	#14556524	C₂³	1	2	yes	—
157	#14556524	C₂³	1	2	yes	—
158	#14556524	C₂³	1	4	yes	—
159	#14556524	C₂³	1	4	yes	—
160	#14556523	C₂³	1	2	yes	—
161	#14556523	C₂³	1	2	yes	—
162	#14556523	C₂³	1	1	yes	characteristic
163	#14556523	C₂³	1	1	yes	characteristic
164	#14556523	C₂³	1	4	yes	—
165	#14556522	C₂³	1	4	yes	—
166	#14556522	C₂³	1	4	yes	—
167	#14556522	C₂³	1	2	yes	—
168	#14556522	C₂³	1	2	yes	—
169	#14556522	C₂³	1	4	yes	—
170	#14556522	C₂³	1	4	yes	—
171	#14556502	C₂³	1	2	yes	—
172	#14556501	C₂³	1	2	yes	—
173	#14556501	C₂³	1	2	yes	—
174	C₄×#10596831	C₂³	1	2	yes	—
175	C₈×Dic₇₃	C₂³	1	2	yes	—
176	C₈×Dic₇₃	C₂³	1	2	yes	—
177	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₇₃	—	2	2	no	—
180	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
181	#125×C₇₃	—	2	2	no	—
182	#125×C₇₃	C₂³	1	4	yes	—
183	C₂²⋊Q₈×C₇₃	—	2	4	no	—
184	#117×C₇₃	C₂³	1	2	yes	—
185	#117×C₇₃	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
187	#107×C₇₃	C₂³	1	2	yes	—
188	#107×C₇₃	C₂³	1	4	yes	—
189	#106×C₇₃	C₂³	1	2	yes	—
190	#106×C₇₃	C₂³	1	2	yes	—
191	#106×C₇₃	C₂³	1	1	yes	characteristic
192	#106×C₇₃	C₂³	1	1	yes	characteristic
193	#106×C₇₃	C₂³	1	4	yes	—
194	#97×C₇₃	C₂³	1	2	yes	—
195	C₄×C₈×C₇₃	C₂³	1	2	yes	—
196	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
197	C₂×Dic₁₄₆	—	2	4	no	—
198	C₂×Dic₁₄₆	—	2	4	no	—
199	C₂×Dic₁₄₆	—	2	4	no	—
200	Q₈×D₇₃	—	8	8	no	—
201	C₂²×Dic₇₃	—	2	2	no	—
202	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
203	C₂×C₄×D₇₃	—	2	2	no	—
204	C₂×C₄×D₇₃	—	2	2	no	—
205	C₂×C₄×D₇₃	—	2	4	no	—
206	C₂×C₄×D₇₃	—	2	4	no	—
207	C₂×C₄×D₇₃	—	8	4	no	—
208	C₂×C₄×D₇₃	C₂×D₄	1	4	yes	—
209	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
211	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
212	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
213	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
215	#11924012	C₂×Q₈	1	4	yes	complemented
216	#11924011	C₂×Q₈	1	8	yes	complemented
217	C₂×#10596831	C₂×Q₈	1	4	yes	complemented
218	C₂×#10596831	C₂⁴	1	1	yes	characteristic
219	C₂×#10596831	C₂⁴	1	2	yes	—
220	C₂×#10596831	C₂⁴	1	1	yes	characteristic
221	C₈×D₇₃	C₂×Q₈	1	4	yes	—
222	C₈×D₇₃	C₂×Q₈	1	4	yes	—
223	C₈×D₇₃	C₂×Q₈	1	8	yes	—
224	C₈×D₇₃	C₂×Q₈	1	4	yes	complemented
225	C₈×D₇₃	C₂×Q₈	1	4	yes	complemented
226	C₄⋊Dic₇₃	—	2	2	no	—
227	C₄⋊Dic₇₃	—	2	4	no	—
228	C₄⋊Dic₇₃	—	2	4	no	—
229	C₄⋊Dic₇₃	—	2	4	no	—
230	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
231	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
232	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
233	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
234	#11924007	—	2	4	no	—
235	#11924007	—	2	4	no	—
236	#11924007	—	2	4	no	—
237	#11924007	—	2	4	no	—
238	#11924007	—	2	4	no	—
239	#11924007	—	2	4	no	—
240	#11924007	—	2	4	no	—
241	#11924007	—	2	4	no	—
242	#11924007	—	2	2	no	—
243	#11924007	—	2	2	no	—
244	#11924007	C₂×D₄	1	4	yes	—
245	C₂²⋊Dic₇₃	—	2	2	no	—
246	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
247	#11924005	—	2	2	no	—
248	#11924005	—	2	2	no	—
249	#11924005	C₂×D₄	1	4	yes	—
250	C₄×Dic₇₃	—	2	2	no	—
251	C₄×Dic₇₃	—	2	2	no	—
252	C₄×Dic₇₃	—	2	2	no	—
253	C₄×Dic₇₃	C₂×D₄	1	4	yes	—
254	C₄×Dic₇₃	C₂⁴	1	2	yes	—
255	C₂×Q₈×C₇₃	—	2	4	no	—
256	C₂²×C₄×C₇₃	—	2	2	no	—
257	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
258	M₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
259	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	complemented
260	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
261	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
263	C₄⋊C₄×C₇₃	—	2	2	no	—
264	C₄⋊C₄×C₇₃	—	2	4	no	—
265	C₄⋊C₄×C₇₃	—	2	4	no	—
266	C₄⋊C₄×C₇₃	—	2	4	no	—
267	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
268	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
270	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
271	C₂²⋊C₄×C₇₃	—	2	2	no	—
272	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
273	C₄²×C₇₃	—	2	2	no	—
274	C₄²×C₇₃	C₂⁴	1	2	yes	—
275	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
276	C₂²×D₇₃	—	2	4	no	—
277	C₂²×D₇₃	C₄⋊Q₈	1	4	yes	—
278	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
279	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₇₃	—	8	4	no	—
281	C₂×C₄×C₇₃	—	2	2	no	—
282	C₂×C₄×C₇₃	—	2	2	no	—
283	C₂×C₄×C₇₃	—	2	4	no	—
284	C₂×C₄×C₇₃	—	8	2	no	—
285	C₂×C₄×C₇₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
288	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
289	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
290	C₂×Dic₇₃	—	2	2	no	—
291	C₂×Dic₇₃	—	2	2	no	—
292	C₂×Dic₇₃	—	2	4	no	—
293	C₂×Dic₇₃	—	8	2	no	—
294	C₂×Dic₇₃	C₄⋊Q₈	1	4	yes	—
295	C₂×Dic₇₃	C₂²×D₄	1	4	yes	—
296	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
298	C₄×D₇₃	—	2	8	no	—
299	C₄×D₇₃	—	4	4	no	—
300	C₄×D₇₃	—	4	8	no	—
301	C₄×D₇₃	—	4	4	no	—
302	C₄×D₇₃	—	8	4	no	—
303	C₄×D₇₃	C₄⋊Q₈	1	4	yes	—
304	C₄×D₇₃	C₄⋊Q₈	1	4	yes	—
305	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
306	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
307	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
308	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
309	Dic₁₄₆	—	8	4	no	—
310	Dic₁₄₆	—	8	4	no	—
311	Dic₁₄₆	—	8	4	no	—
312	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
313	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
314	C₈×C₇₃	C₂²×Q₈	1	4	yes	—
315	#10596831	C₂²×Q₈	1	2	yes	—
316	#10596831	C₂²×Q₈	1	2	yes	—
317	#10596831	C₂²×Q₈	1	4	yes	—
318	C₂²×C₇₃	—	2	2	no	—
319	C₂²×C₇₃	C₂×C₄⋊Q₈	1	2	yes	—
320	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
321	C₂×D₇₃	—	2	2	no	—
322	C₂×D₇₃	—	2	8	no	—
323	C₂×D₇₃	C₂×C₄⋊Q₈	1	2	yes	—
324	C₂×D₇₃	C₂×C₄⋊Q₈	1	2	yes	—
325	C₂×D₇₃	#577	1	4	yes	—
326	C₄×C₇₃	—	2	4	no	—
327	C₄×C₇₃	—	4	2	no	—
328	C₄×C₇₃	—	4	4	no	—
329	C₄×C₇₃	—	4	2	no	—
330	C₄×C₇₃	C₂×C₄⋊Q₈	1	2	yes	—
331	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
332	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
333	Dic₇₃	—	2	4	no	—
334	Dic₇₃	—	4	2	no	—
335	Dic₇₃	—	4	4	no	—
336	Dic₇₃	—	4	2	no	—
337	Dic₇₃	C₂×C₄⋊Q₈	1	2	yes	—
338	Dic₇₃	C₂×C₄⋊Q₈	1	2	yes	—
339	C₂×#3163	—	73	1	no	maximal, Sylow
340	C₂×C₇₃	—	2	2	no	—
341	C₂×C₇₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
342	C₂×C₇₃	C₂×#577	1	2	yes	—
343	D₇₃	—	2	2	no	—
344	D₇₃	#3163	1	4	yes	direct product factor
345	C₂×#544	—	73	2	no	—
346	#3163	—	73	4	no	—
347	#3163	—	73	2	no	—
348	#3163	—	73	2	no	—
349	#3163	—	73	2	no	—
350	#3163	—	73	1	no	—
351	#3163	—	73	1	no	—
352	#3163	—	73	1	no	—
353	#3163	—	73	2	no	—
354	#3163	D₇₃	1	1	yes	characteristic, direct product factor
355	C₂×#501	—	73	4	no	—
356	C₂×#499	—	73	2	no	—
357	C₂×#498	—	73	2	no	—
358	C₂×#428	—	73	2	no	—
359	C₂×#427	—	73	1	no	—
360	C₂²×#106	—	73	1	no	—
361	C₂×#405	—	73	1	no	—
362	C₇₃	C₂×#3163	1	1	yes	characteristic, complemented, Sylow
363	C₂²×M₁₆	—	73	1	no	—
364	C₂³×C₈	—	73	1	no	—
365	#544	—	73	4	no	—
366	#544	—	73	4	no	—
367	#544	—	73	2	no	—
368	#544	—	73	2	no	—
369	#544	—	73	2	no	—
370	#544	—	146	4	no	—
371	#544	—	146	2	no	—
372	#544	—	146	2	no	—
373	#544	C₂×D₇₃	1	2	yes	—
374	C₂×C₄⋊Q₈	—	73	4	no	—
375	C₂×C₄⋊Q₈	—	146	2	no	—
376	C₂×#125	—	73	4	no	—
377	C₂×#125	—	146	2	no	—
378	C₂×C₂²⋊Q₈	—	146	4	no	—
379	C₂×#117	—	73	1	no	—
380	C₂×#117	—	73	2	no	—
381	C₂²×C₄⋊C₄	—	73	2	no	—
382	#501	—	73	4	no	—
383	#501	—	73	4	no	—
384	#501	—	73	4	no	—
385	#501	—	73	4	no	—
386	#501	—	73	4	no	—
387	#501	—	73	4	no	—
388	#501	—	73	4	no	—
389	#501	C₂×D₇₃	1	4	yes	complemented
390	#499	—	73	4	no	—
391	#499	—	73	4	no	—
392	#499	—	73	2	no	—
393	#499	—	73	2	no	—
394	#499	—	73	2	no	—
395	#499	C₂×D₇₃	1	2	yes	complemented
396	#498	—	73	4	no	—
397	#498	—	73	2	no	—
398	#498	—	73	2	no	—
399	#498	—	73	4	no	—
400	#498	—	73	2	no	—
401	#498	C₂×D₇₃	1	2	yes	complemented
402	#428	—	73	2	no	—
403	#428	—	73	2	no	—
404	#428	—	73	2	no	—
405	#428	—	73	4	no	—
406	#428	—	73	4	no	—
407	#428	C₂×D₇₃	1	2	yes	—
408	#427	—	73	1	no	—
409	#427	—	73	2	no	—
410	#427	—	73	2	no	—
411	#427	—	73	1	no	—
412	#427	—	73	1	no	—
413	#427	C₂×D₇₃	1	1	yes	characteristic
414	C₂×#107	—	73	4	no	—
415	C₂×#107	—	73	2	no	—
416	C₂×#106	—	73	1	no	—
417	C₂×#106	—	73	2	no	—
418	C₂×#106	—	73	1	no	—
419	C₂×#106	—	73	2	no	—
420	C₂×#106	—	73	4	no	—
421	C₂×#106	—	73	1	no	—
422	C₂×#106	—	73	2	no	—
423	C₂×#106	—	73	2	no	—
424	C₂×#106	—	73	2	no	—
425	C₂×#106	C₂×D₇₃	1	1	yes	characteristic
426	#405	—	73	1	no	—
427	#405	—	73	1	no	—
428	#405	—	73	1	no	—
429	#405	—	73	2	no	—
430	#405	—	73	2	no	—
431	#405	C₂×D₇₃	1	1	yes	characteristic
432	C₂×#97	—	73	2	no	—
433	C₂×C₄×C₈	—	73	2	no	—
434	C₂²×Q₈	—	146	4	no	—
435	C₂³×C₄	—	73	1	no	—
436	C₂³×C₄	—	146	2	no	—
437	C₂×M₁₆	—	73	1	no	—
438	C₂×M₁₆	—	73	8	no	—
439	C₂×M₁₆	—	73	2	no	—
440	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
441	C₂²×C₈	—	73	1	no	—
442	C₂²×C₈	—	73	8	no	—
443	C₂²×C₈	—	73	1	no	—
444	C₂²×C₈	—	73	1	no	—
445	C₂²×C₈	—	73	1	no	—
446	C₂²×C₈	—	73	1	no	—
447	C₂²×C₈	—	73	2	no	—
448	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
449	C₄⋊Q₈	—	2	2	no	—
450	C₄⋊Q₈	—	73	4	no	—
451	C₄⋊Q₈	—	73	4	no	—
452	C₄⋊Q₈	—	73	4	no	—
453	C₄⋊Q₈	—	146	2	no	—
454	C₄⋊Q₈	—	146	4	no	—
455	C₄⋊Q₈	—	146	4	no	—
456	C₄⋊Q₈	—	146	4	no	—
457	C₄⋊Q₈	—	146	2	no	—
458	C₄⋊Q₈	—	146	4	no	—
459	C₄⋊Q₈	—	146	2	no	—
460	C₄⋊Q₈	C₂²×D₇₃	1	4	yes	—
461	#125	—	2	2	no	—
462	#125	—	73	4	no	—
463	#125	—	73	4	no	—
464	#125	—	73	4	no	—
465	#125	—	146	2	no	—
466	#125	—	146	4	no	—
467	#125	—	146	4	no	—
468	#125	—	146	4	no	—
469	#125	—	146	4	no	—
470	#125	—	146	2	no	—
471	#125	—	146	2	no	—
472	#125	C₂²×D₇₃	1	4	yes	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	—	146	4	no	—
475	C₂²⋊Q₈	—	146	4	no	—
476	C₂²⋊Q₈	—	146	4	no	—
477	C₂²⋊Q₈	—	146	4	no	—
478	C₂²⋊Q₈	—	146	4	no	—
479	C₂²⋊Q₈	—	146	4	no	—
480	C₂²⋊Q₈	—	146	4	no	—
481	#117	—	73	1	no	—
482	#117	—	73	2	no	—
483	#117	—	73	2	no	—
484	#117	—	73	2	no	—
485	#117	—	73	2	no	—
486	#117	—	73	2	no	—
487	#117	—	73	2	no	—
488	#117	—	146	2	no	—
489	#117	—	146	2	no	—
490	#117	C₂²×D₇₃	1	2	yes	—
491	#117	C₂²×D₇₃	1	1	yes	characteristic
492	C₂×C₄⋊C₄	—	73	2	no	—
493	C₂×C₄⋊C₄	—	73	2	no	—
494	C₂×C₄⋊C₄	—	73	4	no	—
495	C₂×C₄⋊C₄	—	73	4	no	—
496	C₂×C₄⋊C₄	—	73	2	no	—
497	C₂×C₄⋊C₄	—	73	2	no	—
498	C₂×C₄⋊C₄	—	146	2	no	—
499	C₂×C₄⋊C₄	—	146	2	no	—
500	C₂×C₄⋊C₄	—	146	4	no	—
501	C₂×C₄⋊C₄	—	146	4	no	—
502	C₂×C₄⋊C₄	—	146	4	no	—
503	C₂×C₄⋊C₄	—	146	2	no	—
504	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
505	C₂×C₂²⋊C₄	—	73	2	no	—
506	C₂×C₂²⋊C₄	—	146	2	no	—
507	C₂×C₄²	—	73	2	no	—
508	C₂×C₄²	—	146	2	no	—
509	#107	—	73	2	no	—
510	#107	—	73	4	no	—
511	#107	—	73	2	no	—
512	#107	—	73	2	no	—
513	#107	—	73	4	no	—
514	#107	—	73	4	no	—
515	#107	C₂²×D₇₃	1	2	yes	—
516	#107	C₂²×D₇₃	1	4	yes	—
517	#106	—	73	2	no	—
518	#106	—	73	2	no	—
519	#106	—	73	1	no	—
520	#106	—	73	1	no	—
521	#106	—	73	4	no	—
522	#106	—	73	4	no	—
523	#106	—	73	4	no	—
524	#106	—	73	2	no	—
525	#106	—	73	2	no	—
526	#106	—	73	4	no	—
527	#106	—	73	4	no	—
528	#106	C₂²×D₇₃	1	2	yes	—
529	#106	C₂²×D₇₃	1	2	yes	—
530	#106	C₂²×D₇₃	1	1	yes	characteristic
531	#106	C₂²×D₇₃	1	1	yes	characteristic
532	#106	C₂²×D₇₃	1	4	yes	—
533	#97	—	73	2	no	—
534	#97	—	73	2	no	—
535	#97	—	73	2	no	—
536	#97	C₂²×D₇₃	1	2	yes	—
537	C₄×C₈	—	73	2	no	—
538	C₄×C₈	—	73	2	no	—
539	C₄×C₈	—	73	2	no	—
540	C₄×C₈	C₂²×D₇₃	1	2	yes	—
541	C₂⁴	—	73	1	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	584	8	no	—
544	C₂×Q₈	—	146	4	no	—
545	C₂×Q₈	—	146	4	no	—
546	C₂×Q₈	—	146	4	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	584	4	no	—
549	C₂²×C₄	—	73	1	no	—
550	C₂²×C₄	—	73	1	no	—
551	C₂²×C₄	—	73	1	no	—
552	C₂²×C₄	—	73	4	no	—
553	C₂²×C₄	—	73	4	no	—
554	C₂²×C₄	—	73	1	no	—
555	C₂²×C₄	—	73	1	no	—
556	C₂²×C₄	—	73	4	no	—
557	C₂²×C₄	—	146	2	no	—
558	C₂²×C₄	—	146	2	no	—
559	C₂²×C₄	—	146	4	no	—
560	C₂²×C₄	—	146	4	no	—
561	C₂²×C₄	—	146	2	no	—
562	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
563	M₁₆	—	73	4	no	—
564	M₁₆	—	73	8	no	—
565	M₁₆	Q₈×D₇₃	1	4	yes	complemented
566	C₂×C₈	—	73	4	no	—
567	C₂×C₈	—	73	1	no	—
568	C₂×C₈	—	73	2	no	—
569	C₂×C₈	—	73	1	no	—
570	C₂×C₈	—	73	4	no	—
571	C₂×C₈	—	73	4	no	—
572	C₂×C₈	—	73	8	no	—
573	C₂×C₈	—	73	4	no	—
574	C₂×C₈	—	73	4	no	—
575	C₂×C₈	Q₈×D₇₃	1	4	yes	complemented
576	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
577	C₂×C₈	C₂³×D₇₃	1	2	yes	—
578	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	73	4	no	—
584	C₄⋊C₄	—	73	2	no	—
585	C₄⋊C₄	—	73	4	no	—
586	C₄⋊C₄	—	73	2	no	—
587	C₄⋊C₄	—	73	2	no	—
588	C₄⋊C₄	—	146	4	no	—
589	C₄⋊C₄	—	146	4	no	—
590	C₄⋊C₄	—	146	2	no	—
591	C₄⋊C₄	—	146	2	no	—
592	C₄⋊C₄	—	146	4	no	—
593	C₄⋊C₄	—	146	4	no	—
594	C₄⋊C₄	—	146	4	no	—
595	C₄⋊C₄	—	146	4	no	—
596	C₄⋊C₄	—	146	4	no	—
597	C₄⋊C₄	—	146	4	no	—
598	C₄⋊C₄	—	146	4	no	—
599	C₄⋊C₄	—	146	4	no	—
600	C₄⋊C₄	—	146	2	no	—
601	C₄⋊C₄	—	146	4	no	—
602	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
603	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
604	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
605	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	73	2	no	—
608	C₂²⋊C₄	—	73	4	no	—
609	C₂²⋊C₄	—	146	2	no	—
610	C₂²⋊C₄	—	146	2	no	—
611	C₂²⋊C₄	—	146	2	no	—
612	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
613	C₄²	—	2	2	no	—
614	C₄²	—	73	4	no	—
615	C₄²	—	73	2	no	—
616	C₄²	—	146	2	no	—
617	C₄²	—	146	2	no	—
618	C₄²	—	146	2	no	—
619	C₄²	C₂³×D₇₃	1	2	yes	—
620	C₂³	—	73	1	no	—
621	C₂³	—	73	4	no	—
622	C₂³	—	73	1	no	—
623	C₂³	—	146	4	no	—
624	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
625	Q₈	—	8	4	no	—
626	Q₈	—	584	4	no	—
627	Q₈	—	584	4	no	—
628	Q₈	—	584	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	8	2	no	—
633	C₂×C₄	—	292	8	no	—
634	C₂×C₄	—	292	4	no	—
635	C₂×C₄	—	292	4	no	—
636	C₂×C₄	—	584	4	no	—
637	C₂×C₄	—	584	2	no	—
638	C₂×C₄	—	73	4	no	—
639	C₂×C₄	—	73	1	no	—
640	C₂×C₄	—	73	1	no	—
641	C₂×C₄	—	73	4	no	—
642	C₂×C₄	—	73	4	no	—
643	C₂×C₄	—	73	2	no	—
644	C₂×C₄	—	73	2	no	—
645	C₂×C₄	—	73	2	no	—
646	C₂×C₄	—	73	2	no	—
647	C₂×C₄	—	73	4	no	—
648	C₂×C₄	—	146	8	no	—
649	C₂×C₄	—	146	2	no	—
650	C₂×C₄	—	146	2	no	—
651	C₂×C₄	—	146	4	no	—
652	C₂×C₄	C₂×D₄×D₇₃	1	4	yes	—
653	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
654	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
655	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
656	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
657	C₈	—	73	2	no	—
658	C₈	—	73	2	no	—
659	C₈	—	73	4	no	—
660	C₈	C₂×Q₈×D₇₃	1	2	yes	—
661	C₈	C₂×Q₈×D₇₃	1	2	yes	—
662	C₈	C₂×Q₈×D₇₃	1	4	yes	—
663	C₂²	—	2	2	no	—
664	C₂²	—	73	4	no	—
665	C₂²	—	73	2	no	—
666	C₂²	—	73	2	no	—
667	C₂²	—	146	8	no	—
668	C₂²	—	146	2	no	—
669	C₂²	C₄⋊Q₈×D₇₃	1	2	yes	—
670	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
671	C₄	—	2	4	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	292	4	no	—
676	C₄	—	292	2	no	—
677	C₄	—	292	2	no	—
678	C₄	—	73	2	no	—
679	C₄	—	73	2	no	—
680	C₄	—	146	4	no	—
681	C₄	C₄⋊Q₈×D₇₃	1	2	yes	—
682	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
683	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
684	C₂	—	2	2	no	—
685	C₂	—	73	4	no	—
686	C₂	—	146	2	no	—
687	C₂	C₂×C₄⋊Q₈×D₇₃	1	1	yes	characteristic
688	C₂	#577×D₇₃	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3163	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂³×D₇₃	C₂×D₄
hypercenter	#3163	D₇₃
hypocenter	C₇₃	C₂×#3163
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3163

Complements

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

N	H ≅ G/N	type
2. #22620463	C₂	semidirect
3. #22620462	C₂	semidirect
4. #22620461	C₂	semidirect
5. #22620460	C₂	semidirect
6. #22620459	C₂	semidirect
7. #22620458	C₂	semidirect
8. #22620457	C₂	semidirect
9. #22620456	C₂	semidirect
10. #501×D₇₃	C₂	semidirect
11. #499×D₇₃	C₂	semidirect
12. #498×D₇₃	C₂	semidirect
17. C₇₃×#3163	C₂	semidirect
36. #17988997	C₂²	semidirect
37. #17988996	C₂²	semidirect
38. #17988995	C₂²	semidirect
39. #17988995	C₂²	semidirect
40. #17988994	C₂²	semidirect
41. #17988994	C₂²	semidirect
42. #17988993	C₂²	semidirect
43. #17988989	C₂²	semidirect
44. #17988988	C₂²	semidirect
45. #17988987	C₂²	semidirect
46. #17988987	C₂²	semidirect
47. #17988986	C₂²	semidirect
48. #17988985	C₂²	semidirect
49. #17988984	C₂²	semidirect
50. #17988984	C₂²	semidirect
51. #17988984	C₂²	semidirect
52. #17988983	C₂²	semidirect
82. #501×C₇₃	C₂²	semidirect
83. #499×C₇₃	C₂²	semidirect
84. #498×C₇₃	C₂²	semidirect
94. M₁₆×D₇₃	Q₈	semidirect
96. C₂×C₈×D₇₃	Q₈	semidirect
215. #11924012	C₂×Q₈	semidirect
216. #11924011	C₂×Q₈	semidirect
217. C₂×#10596831	C₂×Q₈	semidirect
224. C₈×D₇₃	C₂×Q₈	semidirect
225. C₈×D₇₃	C₂×Q₈	semidirect
258. M₁₆×C₇₃	C₂×Q₈	semidirect
259. C₂×C₈×C₇₃	C₂×Q₈	semidirect
344. D₇₃	#3163	direct (N × H)
354. #3163	D₇₃	direct (N × H)
362. C₇₃	C₂×#3163	semidirect
389. #501	C₂×D₇₃	semidirect
395. #499	C₂×D₇₃	semidirect
401. #498	C₂×D₇₃	semidirect
565. M₁₆	Q₈×D₇₃	semidirect
575. C₂×C₈	Q₈×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#544×D₇₃	2
#22620463	2
#22620462	2
#22620461	2
#22620460	2
#22620459	2
#22620458	2
#22620457	2
#22620456	2
#501×D₇₃	2
#499×D₇₃	2
#498×D₇₃	2
#428×D₇₃	2
#427×D₇₃	2
C₂×#106×D₇₃	2
#405×D₇₃	2
C₇₃×#3163	2
C₂×#3163	73

Subgroups — #3163×D73 #33955601

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3163×D₇₃ #33955601