Subgroups — #3164×D₇₃ #33955610

Order 18688.

1854 conjugacy classes of subgroups.

The subgroup lattice has 726 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	#22620471	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620470	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620469	C₂	1	2	yes	maximal, complemented
5	#22620468	C₂	1	2	yes	maximal, complemented
6	#22620467	C₂	1	1	yes	maximal, characteristic, complemented
7	#22620466	C₂	1	4	yes	maximal, complemented
8	#22620465	C₂	1	2	yes	maximal, complemented
9	#22620464	C₂	1	2	yes	maximal, complemented
10	#501×D₇₃	C₂	1	4	yes	maximal, complemented
11	#500×D₇₃	C₂	1	2	yes	maximal, complemented
12	#499×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×#107×D₇₃	C₂	1	1	yes	maximal, characteristic
16	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
17	C₇₃×#3164	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	#17988992	C₂²	1	2	yes	complemented
44	#17988991	C₂²	1	2	yes	complemented
45	#17988991	C₂²	1	4	yes	complemented
46	#17988991	C₂²	1	2	yes	complemented
47	#17988990	C₂²	1	4	yes	complemented
48	#17988989	C₂²	1	2	yes	complemented
49	#17988988	C₂²	1	2	yes	complemented
50	#17988988	C₂²	1	2	yes	complemented
51	#17988987	C₂²	1	4	yes	complemented
52	#17988986	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	1	yes	characteristic
60	#17988624	C₂²	1	1	yes	characteristic
61	#17988623	C₂²	1	2	yes	—
62	#17988622	C₂²	1	2	yes	—
63	C₂×#14556525	C₂²	1	1	yes	characteristic
64	C₂×#14556524	C₂²	1	2	yes	—
65	#107×D₇₃	C₂²	1	1	yes	characteristic
66	#107×D₇₃	C₂²	1	2	yes	—
67	#107×D₇₃	C₂²	1	1	yes	characteristic
68	#107×D₇₃	C₂²	1	4	yes	—
69	#107×D₇₃	C₂²	1	2	yes	—
70	#107×D₇₃	C₂²	1	2	yes	—
71	#107×D₇₃	C₂²	1	2	yes	—
72	#106×D₇₃	C₂²	1	4	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	#500×C₇₃	C₂²	1	2	yes	complemented
84	#499×C₇₃	C₂²	1	2	yes	complemented
85	#428×C₇₃	C₂²	1	2	yes	—
86	#427×C₇₃	C₂²	1	1	yes	characteristic
87	C₂×#107×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	2	yes	—
98	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
132	#14556549	D₄	1	1	yes	characteristic
133	#14556549	C₂³	1	2	yes	—
134	#14556549	C₂³	1	2	yes	—
135	#14556548	—	2	2	no	—
136	#14556548	C₂³	1	2	yes	—
137	#14556547	—	2	2	no	—
138	#14556547	D₄	1	2	yes	—
139	C₂×C₄⋊Dic₇₃	C₂³	1	2	yes	—
140	C₂×#11924007	—	2	2	no	—
141	C₄⋊C₄×D₇₃	—	2	2	no	—
142	C₄⋊C₄×D₇₃	—	2	4	no	—
143	C₄⋊C₄×D₇₃	—	2	4	no	—
144	C₄⋊C₄×D₇₃	—	2	2	no	—
145	C₄⋊C₄×D₇₃	—	2	4	no	—
146	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
147	C₄⋊C₄×D₇₃	D₄	1	1	yes	characteristic
148	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
149	C₄⋊C₄×D₇₃	C₂³	1	2	yes	—
150	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
151	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
152	C₂²⋊C₄×D₇₃	—	2	2	no	—
153	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
154	C₄²×D₇₃	—	2	2	no	—
155	C₄²×D₇₃	C₂³	1	2	yes	—
156	#14556525	C₂³	1	2	yes	—
157	#14556525	C₂³	1	2	yes	—
158	#14556525	C₂³	1	1	yes	characteristic
159	#14556525	C₂³	1	1	yes	characteristic
160	#14556525	C₂³	1	4	yes	—
161	#14556524	C₂³	1	4	yes	—
162	#14556524	C₂³	1	4	yes	—
163	#14556524	C₂³	1	2	yes	—
164	#14556524	C₂³	1	2	yes	—
165	#14556524	C₂³	1	4	yes	—
166	#14556524	C₂³	1	4	yes	—
167	#14556523	C₂³	1	2	yes	—
168	#14556523	C₂³	1	4	yes	—
169	#14556522	C₂³	1	2	yes	—
170	#14556522	C₂³	1	2	yes	—
171	#14556522	C₂³	1	4	yes	—
172	#14556522	C₂³	1	4	yes	—
173	#14556502	C₂³	1	2	yes	—
174	#14556501	C₂³	1	2	yes	—
175	#14556501	C₂³	1	2	yes	—
176	C₄×#10596831	C₂³	1	2	yes	—
177	C₈×Dic₇₃	C₂³	1	2	yes	—
178	C₈×Dic₇₃	C₂³	1	2	yes	—
179	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₇₃	—	2	2	no	—
182	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	—
183	#125×C₇₃	—	2	2	no	—
184	#125×C₇₃	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₇₃	—	2	4	no	—
186	#117×C₇₃	C₂³	1	2	yes	—
187	#117×C₇₃	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₇₃	C₂³	1	2	yes	—
189	#107×C₇₃	C₂³	1	2	yes	—
190	#107×C₇₃	C₂³	1	2	yes	—
191	#107×C₇₃	C₂³	1	1	yes	characteristic
192	#107×C₇₃	C₂³	1	1	yes	characteristic
193	#107×C₇₃	C₂³	1	4	yes	—
194	#106×C₇₃	C₂³	1	2	yes	—
195	#106×C₇₃	C₂³	1	4	yes	—
196	#97×C₇₃	C₂³	1	2	yes	—
197	C₄×C₈×C₇₃	C₂³	1	2	yes	—
198	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
199	C₂×Dic₁₄₆	—	2	4	no	—
200	C₂×Dic₁₄₆	—	2	4	no	—
201	C₂×Dic₁₄₆	—	2	4	no	—
202	Q₈×D₇₃	—	8	8	no	—
203	C₂²×Dic₇₃	—	2	2	no	—
204	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
205	C₂×C₄×D₇₃	—	2	2	no	—
206	C₂×C₄×D₇₃	—	2	2	no	—
207	C₂×C₄×D₇₃	—	2	4	no	—
208	C₂×C₄×D₇₃	—	2	4	no	—
209	C₂×C₄×D₇₃	—	8	4	no	—
210	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
211	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
212	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
213	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
215	C₂×C₄×D₇₃	C₂×Q₈	1	4	yes	—
216	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
218	#11924012	C₂×Q₈	1	4	yes	complemented
219	#11924011	C₂×Q₈	1	8	yes	complemented
220	C₂×#10596831	C₂×Q₈	1	4	yes	complemented
221	C₂×#10596831	C₂⁴	1	1	yes	characteristic
222	C₂×#10596831	C₂⁴	1	2	yes	—
223	C₂×#10596831	C₂⁴	1	1	yes	characteristic
224	C₈×D₇₃	C₂×Q₈	1	4	yes	—
225	C₈×D₇₃	C₂×Q₈	1	4	yes	—
226	C₈×D₇₃	C₂×Q₈	1	8	yes	—
227	C₈×D₇₃	C₂×Q₈	1	4	yes	complemented
228	C₈×D₇₃	C₂×Q₈	1	4	yes	complemented
229	C₄⋊Dic₇₃	—	2	2	no	—
230	C₄⋊Dic₇₃	—	2	4	no	—
231	C₄⋊Dic₇₃	—	2	4	no	—
232	C₄⋊Dic₇₃	—	2	4	no	—
233	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
234	C₄⋊Dic₇₃	C₂×D₄	1	1	yes	characteristic
235	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
236	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
237	C₄⋊Dic₇₃	C₂⁴	1	2	yes	—
238	#11924007	—	2	4	no	—
239	#11924007	—	2	4	no	—
240	#11924007	—	2	4	no	—
241	#11924007	—	2	4	no	—
242	#11924007	—	2	4	no	—
243	#11924007	—	2	4	no	—
244	#11924007	—	2	4	no	—
245	#11924007	—	2	4	no	—
246	#11924007	—	2	2	no	—
247	#11924007	—	2	2	no	—
248	#11924007	C₂×D₄	1	2	yes	—
249	#11924007	C₂×D₄	1	2	yes	—
250	C₂²⋊Dic₇₃	—	2	2	no	—
251	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
252	#11924005	—	2	2	no	—
253	#11924005	—	2	2	no	—
254	#11924005	C₂×D₄	1	2	yes	—
255	#11924005	C₂×D₄	1	2	yes	—
256	C₄×Dic₇₃	—	2	2	no	—
257	C₄×Dic₇₃	—	2	2	no	—
258	C₄×Dic₇₃	—	2	2	no	—
259	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
260	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
261	C₄×Dic₇₃	C₂⁴	1	2	yes	—
262	C₂×Q₈×C₇₃	—	2	4	no	—
263	C₂²×C₄×C₇₃	—	2	2	no	—
264	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
265	M₁₆×C₇₃	C₂×Q₈	1	4	yes	complemented
266	C₂×C₈×C₇₃	C₂×Q₈	1	4	yes	complemented
267	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
268	C₂×C₈×C₇₃	C₂⁴	1	2	yes	—
269	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
270	C₄⋊C₄×C₇₃	—	2	2	no	—
271	C₄⋊C₄×C₇₃	—	2	4	no	—
272	C₄⋊C₄×C₇₃	—	2	4	no	—
273	C₄⋊C₄×C₇₃	—	2	4	no	—
274	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
275	C₄⋊C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
276	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
278	C₄⋊C₄×C₇₃	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₇₃	—	2	2	no	—
280	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
281	C₄²×C₇₃	—	2	2	no	—
282	C₄²×C₇₃	C₂⁴	1	2	yes	—
283	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
284	C₂²×D₇₃	—	2	2	no	—
285	C₂²×D₇₃	—	2	2	no	—
286	C₂²×D₇₃	C₄⋊Q₈	1	4	yes	—
287	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
288	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₇₃	—	8	4	no	—
290	C₂×C₄×C₇₃	—	2	2	no	—
291	C₂×C₄×C₇₃	—	2	2	no	—
292	C₂×C₄×C₇₃	—	2	4	no	—
293	C₂×C₄×C₇₃	—	8	2	no	—
294	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
298	C₂×C₄×C₇₃	C₂²×Q₈	1	2	yes	—
299	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
300	C₂×Dic₇₃	—	2	2	no	—
301	C₂×Dic₇₃	—	2	2	no	—
302	C₂×Dic₇₃	—	2	4	no	—
303	C₂×Dic₇₃	—	8	2	no	—
304	C₂×Dic₇₃	C₄⋊Q₈	1	4	yes	—
305	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
306	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
307	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
308	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
309	C₄×D₇₃	—	2	4	no	—
310	C₄×D₇₃	—	2	4	no	—
311	C₄×D₇₃	—	4	8	no	—
312	C₄×D₇₃	—	4	4	no	—
313	C₄×D₇₃	—	4	4	no	—
314	C₄×D₇₃	—	8	4	no	—
315	C₄×D₇₃	C₄⋊Q₈	1	4	yes	—
316	C₄×D₇₃	C₄⋊Q₈	1	4	yes	—
317	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
318	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
319	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
320	C₄×D₇₃	C₂²×Q₈	1	2	yes	—
321	Dic₁₄₆	—	8	4	no	—
322	Dic₁₄₆	—	8	4	no	—
323	Dic₁₄₆	—	8	4	no	—
324	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
325	C₈×C₇₃	C₂²×Q₈	1	2	yes	—
326	C₈×C₇₃	C₂²×Q₈	1	4	yes	—
327	#10596831	C₂²×Q₈	1	2	yes	—
328	#10596831	C₂²×Q₈	1	2	yes	—
329	#10596831	C₂²×Q₈	1	4	yes	—
330	C₂²×C₇₃	—	2	1	no	—
331	C₂²×C₇₃	—	2	1	no	—
332	C₂²×C₇₃	C₂×C₄⋊Q₈	1	2	yes	—
333	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
334	C₂×D₇₃	—	2	1	no	—
335	C₂×D₇₃	—	2	1	no	—
336	C₂×D₇₃	—	2	8	no	—
337	C₂×D₇₃	C₂×C₄⋊Q₈	1	2	yes	—
338	C₂×D₇₃	C₂×C₄⋊Q₈	1	2	yes	—
339	C₂×D₇₃	#576	1	2	yes	—
340	C₂×D₇₃	#578	1	2	yes	—
341	C₄×C₇₃	—	2	2	no	—
342	C₄×C₇₃	—	2	2	no	—
343	C₄×C₇₃	—	4	2	no	—
344	C₄×C₇₃	—	4	4	no	—
345	C₄×C₇₃	—	4	2	no	—
346	C₄×C₇₃	C₂×C₄⋊Q₈	1	2	yes	—
347	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
348	C₄×C₇₃	C₂³×Q₈	1	1	yes	characteristic
349	Dic₇₃	—	2	2	no	—
350	Dic₇₃	—	2	2	no	—
351	Dic₇₃	—	4	2	no	—
352	Dic₇₃	—	4	4	no	—
353	Dic₇₃	—	4	2	no	—
354	Dic₇₃	C₂×C₄⋊Q₈	1	2	yes	—
355	Dic₇₃	C₂×C₄⋊Q₈	1	2	yes	—
356	C₂×#3164	—	73	1	no	maximal, Sylow
357	C₂×C₇₃	—	2	2	no	—
358	C₂×C₇₃	C₂²×C₄⋊Q₈	1	1	yes	characteristic
359	C₂×C₇₃	C₂×#576	1	1	yes	characteristic
360	C₂×C₇₃	C₂×#578	1	1	yes	characteristic
361	D₇₃	—	2	2	no	—
362	D₇₃	#3164	1	4	yes	direct product factor
363	C₂×#544	—	73	2	no	—
364	#3164	—	73	4	no	—
365	#3164	—	73	2	no	—
366	#3164	—	73	2	no	—
367	#3164	—	73	2	no	—
368	#3164	—	73	1	no	—
369	#3164	—	73	1	no	—
370	#3164	—	73	1	no	—
371	#3164	—	73	2	no	—
372	#3164	D₇₃	1	1	yes	characteristic, direct product factor
373	C₂×#501	—	73	4	no	—
374	C₂×#500	—	73	2	no	—
375	C₂×#499	—	73	2	no	—
376	C₂×#428	—	73	2	no	—
377	C₂×#427	—	73	1	no	—
378	C₂²×#107	—	73	1	no	—
379	C₂×#405	—	73	1	no	—
380	C₇₃	C₂×#3164	1	1	yes	characteristic, complemented, Sylow
381	C₂²×M₁₆	—	73	1	no	—
382	C₂³×C₈	—	73	1	no	—
383	#544	—	73	4	no	—
384	#544	—	73	4	no	—
385	#544	—	73	2	no	—
386	#544	—	73	2	no	—
387	#544	—	73	2	no	—
388	#544	—	146	4	no	—
389	#544	—	146	2	no	—
390	#544	—	146	2	no	—
391	#544	C₂×D₇₃	1	2	yes	—
392	C₂×C₄⋊Q₈	—	73	4	no	—
393	C₂×C₄⋊Q₈	—	146	2	no	—
394	C₂×#125	—	73	4	no	—
395	C₂×#125	—	146	2	no	—
396	C₂×C₂²⋊Q₈	—	146	4	no	—
397	C₂×#117	—	73	1	no	—
398	C₂×#117	—	73	2	no	—
399	C₂²×C₄⋊C₄	—	73	2	no	—
400	#501	—	73	4	no	—
401	#501	—	73	4	no	—
402	#501	—	73	4	no	—
403	#501	—	73	4	no	—
404	#501	—	73	4	no	—
405	#501	—	73	4	no	—
406	#501	—	73	4	no	—
407	#501	C₂×D₇₃	1	4	yes	complemented
408	#500	—	73	4	no	—
409	#500	—	73	2	no	—
410	#500	—	73	2	no	—
411	#500	—	73	4	no	—
412	#500	—	73	2	no	—
413	#500	C₂×D₇₃	1	2	yes	complemented
414	#499	—	73	4	no	—
415	#499	—	73	2	no	—
416	#499	—	73	2	no	—
417	#499	—	73	4	no	—
418	#499	—	73	2	no	—
419	#499	C₂×D₇₃	1	2	yes	complemented
420	#428	—	73	2	no	—
421	#428	—	73	2	no	—
422	#428	—	73	2	no	—
423	#428	—	73	4	no	—
424	#428	—	73	4	no	—
425	#428	C₂×D₇₃	1	2	yes	—
426	#427	—	73	1	no	—
427	#427	—	73	2	no	—
428	#427	—	73	1	no	—
429	#427	—	73	1	no	—
430	#427	—	73	2	no	—
431	#427	C₂×D₇₃	1	1	yes	characteristic
432	C₂×#107	—	73	1	no	—
433	C₂×#107	—	73	2	no	—
434	C₂×#107	—	73	1	no	—
435	C₂×#107	—	73	2	no	—
436	C₂×#107	—	73	1	no	—
437	C₂×#107	—	73	4	no	—
438	C₂×#107	—	73	2	no	—
439	C₂×#107	—	73	2	no	—
440	C₂×#107	—	73	2	no	—
441	C₂×#107	C₂×D₇₃	1	1	yes	characteristic
442	C₂×#106	—	73	4	no	—
443	C₂×#106	—	73	2	no	—
444	#405	—	73	1	no	—
445	#405	—	73	1	no	—
446	#405	—	73	1	no	—
447	#405	—	73	2	no	—
448	#405	—	73	2	no	—
449	#405	C₂×D₇₃	1	1	yes	characteristic
450	C₂×#97	—	73	2	no	—
451	C₂×C₄×C₈	—	73	2	no	—
452	C₂²×Q₈	—	146	4	no	—
453	C₂³×C₄	—	73	1	no	—
454	C₂³×C₄	—	146	2	no	—
455	C₂×M₁₆	—	73	1	no	—
456	C₂×M₁₆	—	73	8	no	—
457	C₂×M₁₆	—	73	2	no	—
458	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
459	C₂²×C₈	—	73	1	no	—
460	C₂²×C₈	—	73	8	no	—
461	C₂²×C₈	—	73	1	no	—
462	C₂²×C₈	—	73	1	no	—
463	C₂²×C₈	—	73	1	no	—
464	C₂²×C₈	—	73	1	no	—
465	C₂²×C₈	—	73	2	no	—
466	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	—	73	4	no	—
469	C₄⋊Q₈	—	73	4	no	—
470	C₄⋊Q₈	—	73	4	no	—
471	C₄⋊Q₈	—	146	2	no	—
472	C₄⋊Q₈	—	146	4	no	—
473	C₄⋊Q₈	—	146	4	no	—
474	C₄⋊Q₈	—	146	4	no	—
475	C₄⋊Q₈	—	146	2	no	—
476	C₄⋊Q₈	—	146	4	no	—
477	C₄⋊Q₈	—	146	2	no	—
478	C₄⋊Q₈	C₂²×D₇₃	1	4	yes	—
479	#125	—	2	2	no	—
480	#125	—	73	4	no	—
481	#125	—	73	4	no	—
482	#125	—	73	4	no	—
483	#125	—	146	2	no	—
484	#125	—	146	4	no	—
485	#125	—	146	4	no	—
486	#125	—	146	4	no	—
487	#125	—	146	4	no	—
488	#125	—	146	2	no	—
489	#125	—	146	2	no	—
490	#125	C₂²×D₇₃	1	4	yes	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	146	4	no	—
493	C₂²⋊Q₈	—	146	4	no	—
494	C₂²⋊Q₈	—	146	4	no	—
495	C₂²⋊Q₈	—	146	4	no	—
496	C₂²⋊Q₈	—	146	4	no	—
497	C₂²⋊Q₈	—	146	4	no	—
498	C₂²⋊Q₈	—	146	4	no	—
499	#117	—	73	1	no	—
500	#117	—	73	1	no	—
501	#117	—	73	1	no	—
502	#117	—	73	2	no	—
503	#117	—	73	2	no	—
504	#117	—	73	2	no	—
505	#117	—	73	2	no	—
506	#117	—	73	2	no	—
507	#117	—	146	2	no	—
508	#117	—	146	2	no	—
509	#117	C₂²×D₇₃	1	2	yes	—
510	#117	C₂²×D₇₃	1	1	yes	characteristic
511	C₂×C₄⋊C₄	—	73	1	no	—
512	C₂×C₄⋊C₄	—	73	1	no	—
513	C₂×C₄⋊C₄	—	73	2	no	—
514	C₂×C₄⋊C₄	—	73	4	no	—
515	C₂×C₄⋊C₄	—	73	4	no	—
516	C₂×C₄⋊C₄	—	73	2	no	—
517	C₂×C₄⋊C₄	—	73	2	no	—
518	C₂×C₄⋊C₄	—	146	2	no	—
519	C₂×C₄⋊C₄	—	146	2	no	—
520	C₂×C₄⋊C₄	—	146	4	no	—
521	C₂×C₄⋊C₄	—	146	4	no	—
522	C₂×C₄⋊C₄	—	146	4	no	—
523	C₂×C₄⋊C₄	—	146	2	no	—
524	C₂×C₄⋊C₄	C₂²×D₇₃	1	2	yes	—
525	C₂×C₂²⋊C₄	—	73	2	no	—
526	C₂×C₂²⋊C₄	—	146	2	no	—
527	C₂×C₄²	—	73	2	no	—
528	C₂×C₄²	—	146	2	no	—
529	#107	—	73	2	no	—
530	#107	—	73	2	no	—
531	#107	—	73	1	no	—
532	#107	—	73	1	no	—
533	#107	—	73	4	no	—
534	#107	—	73	4	no	—
535	#107	—	73	4	no	—
536	#107	—	73	2	no	—
537	#107	—	73	2	no	—
538	#107	—	73	4	no	—
539	#107	—	73	4	no	—
540	#107	C₂²×D₇₃	1	2	yes	—
541	#107	C₂²×D₇₃	1	2	yes	—
542	#107	C₂²×D₇₃	1	1	yes	characteristic
543	#107	C₂²×D₇₃	1	1	yes	characteristic
544	#107	C₂²×D₇₃	1	4	yes	—
545	#106	—	73	2	no	—
546	#106	—	73	4	no	—
547	#106	—	73	2	no	—
548	#106	—	73	2	no	—
549	#106	—	73	4	no	—
550	#106	—	73	4	no	—
551	#106	C₂²×D₇₃	1	2	yes	—
552	#106	C₂²×D₇₃	1	4	yes	—
553	#97	—	73	2	no	—
554	#97	—	73	2	no	—
555	#97	—	73	2	no	—
556	#97	C₂²×D₇₃	1	2	yes	—
557	C₄×C₈	—	73	2	no	—
558	C₄×C₈	—	73	2	no	—
559	C₄×C₈	—	73	2	no	—
560	C₄×C₈	C₂²×D₇₃	1	2	yes	—
561	C₂⁴	—	73	1	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	584	8	no	—
564	C₂×Q₈	—	146	4	no	—
565	C₂×Q₈	—	146	4	no	—
566	C₂×Q₈	—	146	4	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	584	4	no	—
569	C₂²×C₄	—	73	1	no	—
570	C₂²×C₄	—	73	1	no	—
571	C₂²×C₄	—	73	1	no	—
572	C₂²×C₄	—	73	4	no	—
573	C₂²×C₄	—	73	4	no	—
574	C₂²×C₄	—	73	1	no	—
575	C₂²×C₄	—	73	1	no	—
576	C₂²×C₄	—	73	2	no	—
577	C₂²×C₄	—	73	2	no	—
578	C₂²×C₄	—	146	2	no	—
579	C₂²×C₄	—	146	2	no	—
580	C₂²×C₄	—	146	4	no	—
581	C₂²×C₄	—	146	4	no	—
582	C₂²×C₄	—	146	2	no	—
583	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
584	M₁₆	—	73	4	no	—
585	M₁₆	—	73	8	no	—
586	M₁₆	Q₈×D₇₃	1	4	yes	complemented
587	C₂×C₈	—	73	4	no	—
588	C₂×C₈	—	73	1	no	—
589	C₂×C₈	—	73	2	no	—
590	C₂×C₈	—	73	1	no	—
591	C₂×C₈	—	73	4	no	—
592	C₂×C₈	—	73	4	no	—
593	C₂×C₈	—	73	8	no	—
594	C₂×C₈	—	73	4	no	—
595	C₂×C₈	—	73	4	no	—
596	C₂×C₈	Q₈×D₇₃	1	4	yes	complemented
597	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
598	C₂×C₈	C₂³×D₇₃	1	2	yes	—
599	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	73	2	no	—
605	C₄⋊C₄	—	73	2	no	—
606	C₄⋊C₄	—	73	1	no	—
607	C₄⋊C₄	—	73	1	no	—
608	C₄⋊C₄	—	73	2	no	—
609	C₄⋊C₄	—	73	4	no	—
610	C₄⋊C₄	—	73	2	no	—
611	C₄⋊C₄	—	146	4	no	—
612	C₄⋊C₄	—	146	4	no	—
613	C₄⋊C₄	—	146	2	no	—
614	C₄⋊C₄	—	146	2	no	—
615	C₄⋊C₄	—	146	4	no	—
616	C₄⋊C₄	—	146	4	no	—
617	C₄⋊C₄	—	146	4	no	—
618	C₄⋊C₄	—	146	4	no	—
619	C₄⋊C₄	—	146	4	no	—
620	C₄⋊C₄	—	146	4	no	—
621	C₄⋊C₄	—	146	4	no	—
622	C₄⋊C₄	—	146	4	no	—
623	C₄⋊C₄	—	146	2	no	—
624	C₄⋊C₄	—	146	4	no	—
625	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
626	C₄⋊C₄	D₄×D₇₃	1	1	yes	characteristic
627	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
628	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
629	C₄⋊C₄	C₂³×D₇₃	1	2	yes	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	73	2	no	—
632	C₂²⋊C₄	—	73	2	no	—
633	C₂²⋊C₄	—	73	2	no	—
634	C₂²⋊C₄	—	146	2	no	—
635	C₂²⋊C₄	—	146	2	no	—
636	C₂²⋊C₄	—	146	2	no	—
637	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
638	C₄²	—	2	2	no	—
639	C₄²	—	73	2	no	—
640	C₄²	—	73	2	no	—
641	C₄²	—	73	2	no	—
642	C₄²	—	146	2	no	—
643	C₄²	—	146	2	no	—
644	C₄²	—	146	2	no	—
645	C₄²	C₂³×D₇₃	1	2	yes	—
646	C₂³	—	73	1	no	—
647	C₂³	—	73	4	no	—
648	C₂³	—	73	1	no	—
649	C₂³	—	146	2	no	—
650	C₂³	—	146	2	no	—
651	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
652	Q₈	—	8	4	no	—
653	Q₈	—	584	4	no	—
654	Q₈	—	584	4	no	—
655	Q₈	—	584	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	8	2	no	—
660	C₂×C₄	—	292	8	no	—
661	C₂×C₄	—	292	4	no	—
662	C₂×C₄	—	292	4	no	—
663	C₂×C₄	—	584	4	no	—
664	C₂×C₄	—	584	2	no	—
665	C₂×C₄	—	73	4	no	—
666	C₂×C₄	—	73	1	no	—
667	C₂×C₄	—	73	1	no	—
668	C₂×C₄	—	73	4	no	—
669	C₂×C₄	—	73	4	no	—
670	C₂×C₄	—	73	2	no	—
671	C₂×C₄	—	73	2	no	—
672	C₂×C₄	—	73	2	no	—
673	C₂×C₄	—	73	2	no	—
674	C₂×C₄	—	73	2	no	—
675	C₂×C₄	—	73	2	no	—
676	C₂×C₄	—	146	4	no	—
677	C₂×C₄	—	146	4	no	—
678	C₂×C₄	—	146	2	no	—
679	C₂×C₄	—	146	2	no	—
680	C₂×C₄	—	146	4	no	—
681	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
682	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
683	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
684	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
685	C₂×C₄	C₂×Q₈×D₇₃	1	2	yes	—
686	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
687	C₈	—	73	2	no	—
688	C₈	—	73	2	no	—
689	C₈	—	73	4	no	—
690	C₈	C₂×Q₈×D₇₃	1	2	yes	—
691	C₈	C₂×Q₈×D₇₃	1	2	yes	—
692	C₈	C₂×Q₈×D₇₃	1	4	yes	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	73	2	no	—
696	C₂²	—	73	2	no	—
697	C₂²	—	73	2	no	—
698	C₂²	—	73	2	no	—
699	C₂²	—	146	8	no	—
700	C₂²	—	146	1	no	—
701	C₂²	—	146	1	no	—
702	C₂²	C₄⋊Q₈×D₇₃	1	2	yes	—
703	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	4	4	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	292	4	no	—
710	C₄	—	292	2	no	—
711	C₄	—	292	2	no	—
712	C₄	—	73	2	no	—
713	C₄	—	73	2	no	—
714	C₄	—	146	2	no	—
715	C₄	—	146	2	no	—
716	C₄	C₄⋊Q₈×D₇₃	1	2	yes	—
717	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
718	C₄	C₂²×Q₈×D₇₃	1	1	yes	characteristic
719	C₂	—	2	2	no	—
720	C₂	—	73	4	no	—
721	C₂	—	146	2	no	—
722	C₂	C₂×C₄⋊Q₈×D₇₃	1	1	yes	characteristic
723	C₂	#576×D₇₃	1	1	yes	characteristic
724	C₂	#578×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₇₃
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₇₃×#3164	C₂
socle	C₂²×C₇₃	C₂³×D₄
prime radical	C₂³×D₇₃	C₂×D₄
hypercenter	#3164	D₇₃
hypocenter	C₇₃	C₂×#3164
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3164

Complements

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

N	H ≅ G/N	type
2. #22620471	C₂	semidirect
3. #22620470	C₂	semidirect
4. #22620469	C₂	semidirect
5. #22620468	C₂	semidirect
6. #22620467	C₂	semidirect
7. #22620466	C₂	semidirect
8. #22620465	C₂	semidirect
9. #22620464	C₂	semidirect
10. #501×D₇₃	C₂	semidirect
11. #500×D₇₃	C₂	semidirect
12. #499×D₇₃	C₂	semidirect
17. C₇₃×#3164	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. #17988992	C₂²	semidirect
44. #17988991	C₂²	semidirect
45. #17988991	C₂²	semidirect
46. #17988991	C₂²	semidirect
47. #17988990	C₂²	semidirect
48. #17988989	C₂²	semidirect
49. #17988988	C₂²	semidirect
50. #17988988	C₂²	semidirect
51. #17988987	C₂²	semidirect
52. #17988986	C₂²	semidirect
82. #501×C₇₃	C₂²	semidirect
83. #500×C₇₃	C₂²	semidirect
84. #499×C₇₃	C₂²	semidirect
94. M₁₆×D₇₃	Q₈	semidirect
96. C₂×C₈×D₇₃	Q₈	semidirect
218. #11924012	C₂×Q₈	semidirect
219. #11924011	C₂×Q₈	semidirect
220. C₂×#10596831	C₂×Q₈	semidirect
227. C₈×D₇₃	C₂×Q₈	semidirect
228. C₈×D₇₃	C₂×Q₈	semidirect
265. M₁₆×C₇₃	C₂×Q₈	semidirect
266. C₂×C₈×C₇₃	C₂×Q₈	semidirect
362. D₇₃	#3164	direct (N × H)
372. #3164	D₇₃	direct (N × H)
380. C₇₃	C₂×#3164	semidirect
407. #501	C₂×D₇₃	semidirect
413. #500	C₂×D₇₃	semidirect
419. #499	C₂×D₇₃	semidirect
586. M₁₆	Q₈×D₇₃	semidirect
596. 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
#22620471	2
#22620470	2
#22620469	2
#22620468	2
#22620467	2
#22620466	2
#22620465	2
#22620464	2
#501×D₇₃	2
#500×D₇₃	2
#499×D₇₃	2
#428×D₇₃	2
#427×D₇₃	2
C₂×#107×D₇₃	2
#405×D₇₃	2
C₇₃×#3164	2
C₂×#3164	73

Subgroups — #3164×D73 #33955610

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3164×D₇₃ #33955610