Subgroups — #2103×D₇₃ #33115959

Order 18688.

662 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#430×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#424×D₇₃	C₂	1	1	yes	maximal, characteristic
3	#22611514	C₂	1	2	yes	maximal, complemented
4	#22611513	C₂	1	2	yes	maximal, complemented
5	#22611512	C₂	1	1	yes	maximal, characteristic, complemented
6	#22611511	C₂	1	1	yes	maximal, characteristic, complemented
7	#22611510	C₂	1	1	yes	maximal, characteristic, complemented
8	#344×D₇₃	C₂	1	2	yes	maximal
9	#341×D₇₃	C₂	1	2	yes	maximal
10	#338×D₇₃	C₂	1	1	yes	maximal, characteristic
11	C₇₃×#2103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
13	C₂×M₁₆×D₇₃	C₂²	1	2	yes	—
14	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
15	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
16	#117×D₇₃	C₂²	1	1	yes	characteristic
17	#17988636	C₂²	1	1	yes	characteristic
18	#17988635	C₂²	1	2	yes	—
19	#17988634	—	2	2	no	—
20	#108×D₇₃	—	2	2	no	—
21	#17988615	C₂²	1	1	yes	characteristic
22	#17988614	C₂²	1	1	yes	characteristic
23	#17988613	C₂²	1	1	yes	characteristic
24	#17988612	—	2	2	no	—
25	C₄⋊C₈×D₇₃	—	2	2	no	—
26	#17988359	C₂²	1	2	yes	—
27	#17988358	C₂²	1	2	yes	—
28	#17988357	C₂²	1	2	yes	—
29	#17988352	C₂²	1	2	yes	—
30	#17988351	C₂²	1	2	yes	—
31	#17988351	C₂²	1	2	yes	—
32	#17988345	C₂²	1	1	yes	characteristic
33	#17988345	C₂²	1	2	yes	—
34	#430×C₇₃	C₂²	1	1	yes	characteristic
35	#424×C₇₃	C₂²	1	1	yes	characteristic
36	#344×C₇₃	C₂²	1	2	yes	—
37	#341×C₇₃	C₂²	1	2	yes	—
38	#338×C₇₃	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
40	C₂×#11924012	C₂³	1	2	yes	—
41	C₂×#11924012	C₂³	1	2	yes	—
42	C₂×#11924012	C₂³	1	1	yes	characteristic
43	C₂×#11924011	—	2	2	no	—
44	C₂×#11924011	—	2	2	no	—
45	C₂×#11924011	D₄	1	2	yes	—
46	M₁₆×D₇₃	—	2	2	no	—
47	M₁₆×D₇₃	—	2	2	no	—
48	M₁₆×D₇₃	—	2	2	no	—
49	M₁₆×D₇₃	—	2	2	no	—
50	M₁₆×D₇₃	—	2	2	no	—
51	M₁₆×D₇₃	—	2	2	no	—
52	M₁₆×D₇₃	—	2	2	no	—
53	M₁₆×D₇₃	—	2	2	no	—
54	M₁₆×D₇₃	—	2	2	no	—
55	M₁₆×D₇₃	—	2	2	no	—
56	C₂²×#10596831	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₇₃	—	2	1	no	—
58	C₂×C₈×D₇₃	—	2	1	no	—
59	C₂×C₈×D₇₃	—	2	2	no	—
60	C₂×C₈×D₇₃	—	2	2	no	—
61	C₂×C₈×D₇₃	—	2	2	no	—
62	C₂×C₈×D₇₃	—	2	2	no	—
63	C₂×C₈×D₇₃	D₄	1	2	yes	—
64	#14556550	C₂³	1	1	yes	characteristic
65	#14556549	—	2	1	no	—
66	#14556548	—	2	1	no	—
67	#14556547	Q₈	1	2	yes	—
68	C₄⋊C₄×D₇₃	—	2	1	no	—
69	C₂²⋊C₄×D₇₃	Q₈	1	2	yes	—
70	C₄²×D₇₃	—	2	1	no	—
71	#14556527	—	2	2	no	—
72	#14556526	—	2	4	no	—
73	C₄⋊#10596831	—	2	2	no	—
74	#14556520	—	2	2	no	—
75	#14556520	—	2	2	no	—
76	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
77	C₂×M₁₆×C₇₃	C₂³	1	2	yes	—
78	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
80	#117×C₇₃	C₂³	1	1	yes	characteristic
81	#108×C₇₃	—	2	2	no	—
82	C₄⋊C₈×C₇₃	—	2	2	no	—
83	C₂³×D₇₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
85	C₂×C₄×D₇₃	—	2	2	no	—
86	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
88	C₂×C₄×D₇₃	#41	1	2	yes	—
89	C₂×C₄×D₇₃	#41	1	2	yes	—
90	C₂×C₄×D₇₃	#41	1	2	yes	—
91	C₂×C₄×D₇₃	#41	1	2	yes	—
92	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
93	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
94	#11924012	—	2	2	no	—
95	#11924012	—	2	2	no	—
96	#11924012	—	2	2	no	—
97	#11924012	—	2	2	no	—
98	#11924012	—	2	2	no	—
99	#11924011	—	2	4	no	—
100	#11924011	—	4	2	no	—
101	#11924011	—	4	2	no	—
102	#11924011	—	4	2	no	—
103	#11924011	—	4	2	no	—
104	C₂×#10596831	—	2	1	no	—
105	C₂×#10596831	—	2	2	no	—
106	C₂×#10596831	—	2	2	no	—
107	C₂×#10596831	—	2	2	no	—
108	C₂×#10596831	C₂×D₄	1	2	yes	—
109	C₈×D₇₃	—	2	2	no	—
110	C₈×D₇₃	—	2	2	no	—
111	C₈×D₇₃	—	4	1	no	—
112	C₈×D₇₃	—	4	1	no	—
113	C₈×D₇₃	—	4	2	no	—
114	C₈×D₇₃	—	4	2	no	—
115	C₈×D₇₃	—	4	2	no	—
116	C₈×D₇₃	—	4	2	no	—
117	C₈×D₇₃	—	4	2	no	—
118	C₄⋊Dic₇₃	—	2	1	no	—
119	#11924007	—	2	2	no	—
120	C₂²⋊Dic₇₃	C₂×Q₈	1	2	yes	—
121	#11924005	—	2	2	no	—
122	C₄×Dic₇₃	—	2	1	no	—
123	C₄×Dic₇₃	—	2	2	no	—
124	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
125	M₁₆×C₇₃	—	2	2	no	—
126	M₁₆×C₇₃	—	2	2	no	—
127	M₁₆×C₇₃	—	2	2	no	—
128	M₁₆×C₇₃	—	2	2	no	—
129	M₁₆×C₇₃	—	2	2	no	—
130	C₂×C₈×C₇₃	—	2	1	no	—
131	C₂×C₈×C₇₃	—	2	2	no	—
132	C₂×C₈×C₇₃	—	2	2	no	—
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₇₃	—	2	1	no	—
136	C₂²⋊C₄×C₇₃	C₂×Q₈	1	2	yes	—
137	C₄²×C₇₃	—	2	1	no	—
138	C₂³×C₇₃	C₂²×Q₈	1	1	yes	characteristic
139	C₂²×D₇₃	—	4	2	no	—
140	C₂²×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂²×D₇₃	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂²×D₇₃	#125	1	2	yes	—
143	C₂²×D₇₃	#125	1	2	yes	—
144	C₂×C₄×C₇₃	—	2	2	no	—
145	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
147	C₂×C₄×C₇₃	C₂×#41	1	2	yes	—
148	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
149	C₂×Dic₇₃	—	2	2	no	—
150	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
152	C₂×Dic₇₃	#125	1	2	yes	—
153	C₂×Dic₇₃	#125	1	2	yes	—
154	C₄×D₇₃	—	4	4	no	—
155	C₄×D₇₃	#123	1	1	yes	characteristic
156	C₄×D₇₃	#123	1	1	yes	characteristic
157	C₄×D₇₃	#123	1	2	yes	—
158	C₄×D₇₃	#124	1	1	yes	characteristic
159	C₄×D₇₃	#124	1	2	yes	—
160	C₄×D₇₃	#124	1	1	yes	characteristic
161	C₄×D₇₃	#126	1	2	yes	—
162	C₄×D₇₃	#126	1	2	yes	—
163	C₄×D₇₃	#126	1	2	yes	—
164	C₄×D₇₃	#126	1	2	yes	—
165	C₈×C₇₃	—	2	2	no	—
166	C₈×C₇₃	—	4	1	no	—
167	C₈×C₇₃	—	4	2	no	—
168	C₈×C₇₃	—	4	2	no	—
169	#10596831	—	2	2	no	—
170	#10596831	—	4	1	no	—
171	#10596831	—	4	2	no	—
172	#10596831	—	4	2	no	—
173	C₂²×C₇₃	—	4	1	no	—
174	C₂²×C₇₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
175	C₂²×C₇₃	C₂×#125	1	2	yes	—
176	C₂×D₇₃	—	2	2	no	—
177	C₂×D₇₃	—	2	4	no	—
178	C₂×D₇₃	—	4	1	no	—
179	C₂×D₇₃	—	4	2	no	—
180	C₂×D₇₃	#400	1	1	yes	characteristic
181	C₂×D₇₃	#400	1	2	yes	—
182	C₂×D₇₃	#400	1	1	yes	characteristic
183	C₄×C₇₃	—	4	2	no	—
184	C₄×C₇₃	C₂×#123	1	1	yes	characteristic
185	C₄×C₇₃	C₂×#124	1	1	yes	characteristic
186	C₄×C₇₃	C₂×#126	1	2	yes	—
187	Dic₇₃	—	4	2	no	—
188	Dic₇₃	#400	1	1	yes	characteristic
189	Dic₇₃	#400	1	1	yes	characteristic
190	Dic₇₃	#400	1	2	yes	—
191	C₂×#2103	—	73	1	no	maximal, Sylow
192	C₂×C₇₃	—	2	1	no	—
193	C₂×C₇₃	—	2	2	no	—
194	C₂×C₇₃	C₂×#400	1	1	yes	characteristic
195	D₇₃	—	2	1	no	—
196	D₇₃	—	2	2	no	—
197	D₇₃	#2103	1	2	yes	direct product factor
198	C₂×#430	—	73	1	no	—
199	C₂×#424	—	73	1	no	—
200	#2103	—	73	1	no	—
201	#2103	—	73	1	no	—
202	#2103	—	73	2	no	—
203	#2103	—	73	2	no	—
204	#2103	—	73	1	no	—
205	#2103	D₇₃	1	1	yes	characteristic, direct product factor
206	C₂×#344	—	73	2	no	—
207	C₂×#341	—	73	2	no	—
208	C₂×#338	—	73	1	no	—
209	C₇₃	C₂×#2103	1	1	yes	characteristic, complemented, Sylow
210	C₂²×M₁₆	—	73	1	no	—
211	C₂²×M₁₆	—	73	2	no	—
212	C₂²×M₁₆	—	73	2	no	—
213	C₂³×C₈	—	73	1	no	—
214	C₂×#117	—	73	1	no	—
215	#430	—	73	2	no	—
216	#430	—	73	1	no	—
217	#430	—	146	2	no	—
218	#430	C₂×D₇₃	1	1	yes	characteristic
219	C₂×#108	—	146	2	no	—
220	#424	—	73	1	no	—
221	#424	—	73	1	no	—
222	#424	—	73	1	no	—
223	#424	—	146	2	no	—
224	#424	C₂×D₇₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	—	146	2	no	—
226	#344	—	73	2	no	—
227	#344	—	73	2	no	—
228	#344	—	73	2	no	—
229	#344	C₂×D₇₃	1	2	yes	—
230	#341	—	73	2	no	—
231	#341	—	73	2	no	—
232	#341	—	73	2	no	—
233	#341	C₂×D₇₃	1	2	yes	—
234	#338	—	73	2	no	—
235	#338	—	73	1	no	—
236	#338	C₂×D₇₃	1	1	yes	characteristic
237	C₂³×C₄	—	73	1	no	—
238	C₂×M₁₆	—	73	1	no	—
239	C₂×M₁₆	—	73	2	no	—
240	C₂×M₁₆	—	73	2	no	—
241	C₂×M₁₆	—	73	2	no	—
242	C₂×M₁₆	—	146	2	no	—
243	C₂×M₁₆	—	146	2	no	—
244	C₂×M₁₆	—	146	2	no	—
245	C₂×M₁₆	—	146	2	no	—
246	C₂×M₁₆	—	146	2	no	—
247	C₂×M₁₆	—	146	2	no	—
248	C₂×M₁₆	—	146	2	no	—
249	C₂×M₁₆	—	146	2	no	—
250	C₂×M₁₆	—	146	2	no	—
251	C₂×M₁₆	—	146	2	no	—
252	C₂×M₁₆	—	146	2	no	—
253	C₂×M₁₆	—	146	2	no	—
254	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
255	C₂×M₁₆	C₂²×D₇₃	1	2	yes	—
256	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
257	C₂²×C₈	—	73	2	no	—
258	C₂²×C₈	—	73	1	no	—
259	C₂²×C₈	—	146	1	no	—
260	C₂²×C₈	—	146	1	no	—
261	C₂²×C₈	—	146	2	no	—
262	C₂²×C₈	—	146	2	no	—
263	C₂²×C₈	—	146	2	no	—
264	C₂²×C₈	—	146	2	no	—
265	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
266	#117	—	73	1	no	—
267	#117	—	73	2	no	—
268	#117	—	146	1	no	—
269	#117	—	146	1	no	—
270	#117	C₂²×D₇₃	1	1	yes	characteristic
271	C₂×C₄⋊C₄	—	146	1	no	—
272	C₂×C₂²⋊C₄	—	73	2	no	—
273	C₂×C₄²	—	146	1	no	—
274	#108	—	2	2	no	—
275	#108	—	146	4	no	—
276	#108	—	146	2	no	—
277	C₄⋊C₈	—	2	2	no	—
278	C₄⋊C₈	—	146	2	no	—
279	C₄⋊C₈	—	146	2	no	—
280	C₄⋊C₈	—	146	2	no	—
281	C₂⁴	—	73	1	no	—
282	C₂²×C₄	—	73	1	no	—
283	C₂²×C₄	—	73	1	no	—
284	C₂²×C₄	—	73	1	no	—
285	C₂²×C₄	—	73	1	no	—
286	C₂²×C₄	—	73	1	no	—
287	C₂²×C₄	—	73	2	no	—
288	C₂²×C₄	—	73	2	no	—
289	C₂²×C₄	—	73	2	no	—
290	C₂²×C₄	—	73	2	no	—
291	C₂²×C₄	—	146	2	no	—
292	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
293	M₁₆	—	2	2	no	—
294	M₁₆	—	2	2	no	—
295	M₁₆	—	2	2	no	—
296	M₁₆	—	2	2	no	—
297	M₁₆	—	2	2	no	—
298	M₁₆	—	292	2	no	—
299	M₁₆	—	292	2	no	—
300	M₁₆	—	292	2	no	—
301	M₁₆	—	292	2	no	—
302	M₁₆	—	146	4	no	—
303	M₁₆	—	146	2	no	—
304	M₁₆	—	146	2	no	—
305	M₁₆	—	146	2	no	—
306	M₁₆	—	146	2	no	—
307	M₁₆	—	146	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	292	1	no	—
313	C₂×C₈	—	292	1	no	—
314	C₂×C₈	—	292	2	no	—
315	C₂×C₈	—	292	2	no	—
316	C₂×C₈	—	292	2	no	—
317	C₂×C₈	—	292	2	no	—
318	C₂×C₈	—	292	2	no	—
319	C₂×C₈	—	73	2	no	—
320	C₂×C₈	—	146	2	no	—
321	C₂×C₈	—	146	2	no	—
322	C₂×C₈	—	146	1	no	—
323	C₂×C₈	—	146	2	no	—
324	C₂×C₈	—	146	2	no	—
325	C₂×C₈	—	146	2	no	—
326	C₂×C₈	D₄×D₇₃	1	2	yes	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	146	2	no	—
329	C₄⋊C₄	—	146	1	no	—
330	C₂²⋊C₄	—	73	2	no	—
331	C₂²⋊C₄	—	146	2	no	—
332	C₂²⋊C₄	Q₈×D₇₃	1	2	yes	—
333	C₄²	—	2	1	no	—
334	C₄²	—	146	2	no	—
335	C₄²	—	146	1	no	—
336	C₂³	—	292	2	no	—
337	C₂³	—	73	1	no	—
338	C₂³	—	73	2	no	—
339	C₂³	—	73	1	no	—
340	C₂³	—	73	2	no	—
341	C₂³	C₂×Q₈×D₇₃	1	1	yes	characteristic
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	292	4	no	—
344	C₂×C₄	—	73	1	no	—
345	C₂×C₄	—	73	1	no	—
346	C₂×C₄	—	73	2	no	—
347	C₂×C₄	—	73	2	no	—
348	C₂×C₄	—	73	1	no	—
349	C₂×C₄	—	73	1	no	—
350	C₂×C₄	—	73	2	no	—
351	C₂×C₄	—	73	1	no	—
352	C₂×C₄	—	73	2	no	—
353	C₂×C₄	—	73	1	no	—
354	C₂×C₄	—	73	2	no	—
355	C₂×C₄	—	73	2	no	—
356	C₂×C₄	—	73	2	no	—
357	C₂×C₄	—	73	2	no	—
358	C₂×C₄	—	146	2	no	—
359	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
360	C₂×C₄	#41×D₇₃	1	2	yes	—
361	C₂×C₄	#41×D₇₃	1	2	yes	—
362	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₈	—	4	2	no	—
367	C₈	—	292	1	no	—
368	C₈	—	292	2	no	—
369	C₈	—	292	2	no	—
370	C₈	—	146	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	292	1	no	—
373	C₂²	—	292	2	no	—
374	C₂²	—	73	1	no	—
375	C₂²	—	73	1	no	—
376	C₂²	—	73	2	no	—
377	C₂²	—	146	2	no	—
378	C₂²	—	146	4	no	—
379	C₂²	C₂²⋊Q₈×D₇₃	1	1	yes	characteristic
380	C₂²	#125×D₇₃	1	2	yes	—
381	C₄	—	4	2	no	—
382	C₄	—	292	2	no	—
383	C₄	—	73	1	no	—
384	C₄	—	73	1	no	—
385	C₄	—	73	2	no	—
386	C₄	#123×D₇₃	1	1	yes	characteristic
387	C₄	#124×D₇₃	1	1	yes	characteristic
388	C₄	#126×D₇₃	1	2	yes	—
389	C₂	—	2	1	no	—
390	C₂	—	2	2	no	—
391	C₂	—	73	2	no	—
392	C₂	—	146	1	no	—
393	C₂	—	146	2	no	—
394	C₂	#400×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#124×D₇₃
commutator, cosocle	C₂²×C₄×C₇₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₃
Fitting	C₇₃×#2103	C₂
socle	C₂×C₇₃	C₂×#400
prime radical	C₂³×D₇₃	C₂×Q₈
hypercenter	#2103	D₇₃
hypocenter	C₇₃	C₂×#2103
LCS	G ▷ C₂²×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2103

Complements

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

N	H ≅ G/N	type
3. #22611514	C₂	semidirect
4. #22611513	C₂	semidirect
5. #22611512	C₂	semidirect
6. #22611511	C₂	semidirect
7. #22611510	C₂	semidirect
11. C₇₃×#2103	C₂	semidirect
197. D₇₃	#2103	direct (N × H)
205. #2103	D₇₃	direct (N × H)
209. C₇₃	C₂×#2103	semidirect

Maximal subgroups

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

subgroup	index
#430×D₇₃	2
#424×D₇₃	2
#22611514	2
#22611513	2
#22611512	2
#22611511	2
#22611510	2
#344×D₇₃	2
#341×D₇₃	2
#338×D₇₃	2
C₇₃×#2103	2
C₂×#2103	73

Subgroups — #2103×D73 #33115959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2103×D₇₃ #33115959