Subgroups — #3176×D₇₃ #33955810

Order 18688.

2098 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#540×D₇₃	C₂	1	2	yes	maximal, complemented
2	#22620582	C₂	1	1	yes	maximal, characteristic, complemented
3	#22620581	C₂	1	1	yes	maximal, characteristic, complemented
4	#22620580	C₂	1	2	yes	maximal, complemented
5	#22620579	C₂	1	2	yes	maximal, complemented
6	#22620578	C₂	1	1	yes	maximal, characteristic, complemented
7	#22620577	C₂	1	2	yes	maximal, complemented
8	#22620576	C₂	1	2	yes	maximal, complemented
9	#22620575	C₂	1	2	yes	maximal, complemented
10	#22620574	C₂	1	2	yes	maximal, complemented
11	#499×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#493×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#490×D₇₃	C₂	1	2	yes	maximal, complemented
14	#469×D₇₃	C₂	1	2	yes	maximal, complemented
15	#466×D₇₃	C₂	1	2	yes	maximal, complemented
16	#442×D₇₃	C₂	1	2	yes	maximal, complemented
17	C₄×D₈×D₇₃	C₂	1	2	yes	maximal, complemented
18	#405×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇₃×#3176	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₈×D₇₃	C₂²	1	2	yes	—
21	C₂×D₈×D₇₃	C₂²	1	2	yes	—
22	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
24	#17989193	C₂²	1	2	yes	complemented
25	#17989192	C₂²	1	2	yes	complemented
26	#17989191	C₂²	1	2	yes	complemented
27	#17989190	C₂²	1	4	yes	complemented
28	#17989189	—	2	4	no	—
29	#17989188	C₂²	1	4	yes	complemented
30	#17989187	—	2	4	no	—
31	#127×D₇₃	C₂²	1	2	yes	—
32	#125×D₇₃	C₂²	1	2	yes	—
33	#123×D₇₃	—	2	4	no	—
34	#121×D₇₃	—	2	4	no	—
35	#121×D₇₃	C₂²	1	4	yes	—
36	C₄×D₄×D₇₃	C₂²	1	4	yes	—
37	#117×D₇₃	C₂²	1	1	yes	characteristic
38	#17988989	C₂²	1	1	yes	characteristic, complemented
39	#17988988	C₂²	1	2	yes	complemented
40	#17988987	C₂²	1	2	yes	complemented
41	#17988986	C₂²	1	2	yes	complemented
42	#17988964	C₂²	1	1	yes	characteristic, complemented
43	#17988963	C₂²	1	2	yes	complemented
44	#17988962	C₂²	1	2	yes	complemented
45	#17988962	C₂²	1	2	yes	complemented
46	#17988953	C₂²	1	2	yes	complemented
47	#17988952	C₂²	1	2	yes	complemented
48	#17988951	C₂²	1	2	yes	complemented
49	#17988950	C₂²	1	4	yes	complemented
50	#17988950	C₂²	1	4	yes	complemented
51	#17988841	C₂²	1	2	yes	complemented
52	#17988840	C₂²	1	2	yes	complemented
53	#17988839	C₂²	1	4	yes	complemented
54	#17988838	C₂²	1	4	yes	complemented
55	#17988837	C₂²	1	2	yes	complemented
56	#17988824	C₂²	1	2	yes	complemented
57	#17988823	C₂²	1	2	yes	complemented
58	#17988822	C₂²	1	4	yes	complemented
59	#17988821	C₂²	1	4	yes	complemented
60	#17988820	C₂²	1	2	yes	complemented
61	#17988700	C₂²	1	2	yes	complemented
62	#17988699	C₂²	1	2	yes	complemented
63	#17988698	C₂²	1	2	yes	complemented
64	#17988697	C₂²	1	4	yes	complemented
65	#17988696	C₂²	1	4	yes	complemented
66	C₄×D₅₈₄	C₂²	1	2	yes	complemented
67	D₈×Dic₇₃	C₂²	1	2	yes	complemented
68	#17988669	C₂²	1	2	yes	complemented
69	C₄×#11924013	C₂²	1	4	yes	complemented
70	#17988667	C₂²	1	4	yes	complemented
71	#107×D₇₃	C₂²	1	2	yes	—
72	#106×D₇₃	C₂²	1	2	yes	—
73	#102×D₇₃	C₂²	1	4	yes	—
74	#102×D₇₃	C₂²	1	4	yes	—
75	#17988545	C₂²	1	1	yes	characteristic, complemented
76	#17988544	C₂²	1	1	yes	characteristic, complemented
77	#17988544	C₂²	1	1	yes	characteristic, complemented
78	#17988543	C₂²	1	1	yes	characteristic, complemented
79	#17988542	C₂²	1	1	yes	characteristic, complemented
80	#17988541	C₂²	1	1	yes	characteristic, complemented
81	#17988541	C₂²	1	1	yes	characteristic, complemented
82	#97×D₇₃	C₂²	1	1	yes	characteristic
83	#97×D₇₃	C₂²	1	1	yes	characteristic
84	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
85	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
86	#540×C₇₃	C₂²	1	2	yes	complemented
87	#499×C₇₃	C₂²	1	1	yes	characteristic, complemented
88	#493×C₇₃	C₂²	1	1	yes	characteristic, complemented
89	#490×C₇₃	C₂²	1	2	yes	complemented
90	#469×C₇₃	C₂²	1	2	yes	complemented
91	#466×C₇₃	C₂²	1	2	yes	complemented
92	#442×C₇₃	C₂²	1	2	yes	complemented
93	C₄×D₈×C₇₃	C₂²	1	2	yes	complemented
94	#405×C₇₃	C₂²	1	1	yes	characteristic, complemented
95	C₂×D₄×D₇₃	—	2	4	no	—
96	C₂×D₄×D₇₃	—	2	4	no	—
97	C₂×D₄×D₇₃	C₂³	1	4	yes	—
98	C₂²×C₄×D₇₃	—	2	4	no	—
99	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
100	C₂×D₅₈₄	C₂³	1	2	yes	—
101	C₂×D₅₈₄	C₂³	1	2	yes	—
102	C₂×#11924013	C₂³	1	4	yes	—
103	C₂×#11924013	C₂³	1	4	yes	—
104	D₈×D₇₃	—	2	8	no	—
105	D₈×D₇₃	—	2	8	no	—
106	C₂×#11924012	C₂³	1	1	yes	characteristic
107	C₂×#11924011	C₂³	1	1	yes	characteristic
108	C₂×#11924011	C₂³	1	1	yes	characteristic
109	M₁₆×D₇₃	—	2	4	no	—
110	C₂²×#10596831	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₇₃	—	2	4	no	—
112	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
113	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
115	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
116	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
117	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
118	#14556588	C₂³	1	2	yes	—
119	#14556587	—	2	4	no	—
120	#14556587	C₂³	1	4	yes	—
121	#14556583	C₂³	1	2	yes	—
122	#14556582	C₂³	1	4	yes	—
123	#14556581	—	2	4	no	—
124	#14556576	—	2	4	no	—
125	#14556576	—	2	4	no	—
126	#14556575	—	2	4	no	—
127	#14556574	—	2	4	no	—
128	#14556573	—	2	4	no	—
129	#14556573	—	2	4	no	—
130	#14556572	—	2	4	no	—
131	#14556566	—	2	4	no	—
132	#14556566	C₂³	1	4	yes	—
133	#14556565	—	2	4	no	—
134	#14556565	C₂³	1	4	yes	—
135	#14556564	—	2	4	no	—
136	#14556564	—	2	4	no	—
137	#14556564	—	2	4	no	—
138	#14556563	—	2	4	no	—
139	#14556563	—	2	4	no	—
140	#14556563	—	2	4	no	—
141	#14556562	—	2	4	no	—
142	#14556562	C₂³	1	4	yes	—
143	C₄×D₂₉₂	C₂³	1	4	yes	—
144	D₄×Dic₇₃	C₂³	1	4	yes	—
145	#14556553	C₂³	1	4	yes	—
146	C₄×C₂²⋊D₇₃	—	2	4	no	—
147	#14556551	—	2	4	no	—
148	#14556550	C₂³	1	1	yes	characteristic
149	#14556549	D₄	1	2	yes	—
150	#14556548	C₂³	1	1	yes	characteristic
151	#14556548	C₂³	1	1	yes	characteristic
152	#14556547	D₄	1	2	yes	—
153	C₄⋊C₄×D₇₃	—	2	4	no	—
154	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
155	C₄⋊C₄×D₇₃	C₂³	1	4	yes	—
156	C₂²⋊C₄×D₇₃	—	2	4	no	—
157	C₂²⋊C₄×D₇₃	—	2	4	no	—
158	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
159	C₄²×D₇₃	C₂³	1	1	yes	characteristic
160	C₄²×D₇₃	C₂³	1	1	yes	characteristic
161	#14556525	C₂³	1	2	yes	—
162	#14556524	C₂³	1	4	yes	—
163	#14556523	C₂³	1	2	yes	—
164	#14556522	C₂³	1	4	yes	—
165	#14556513	C₂³	1	4	yes	—
166	#14556513	C₂³	1	4	yes	—
167	#14556512	C₂³	1	4	yes	—
168	#14556512	C₂³	1	4	yes	—
169	#14556511	C₂³	1	4	yes	—
170	#14556511	C₂³	1	4	yes	—
171	#14556502	C₂³	1	1	yes	characteristic
172	#14556502	C₂³	1	1	yes	characteristic
173	#14556501	C₂³	1	1	yes	characteristic
174	#14556501	C₂³	1	1	yes	characteristic
175	#14556501	C₂³	1	1	yes	characteristic
176	#14556501	C₂³	1	1	yes	characteristic
177	C₄×#10596831	C₂³	1	1	yes	characteristic
178	C₄×#10596831	C₂³	1	1	yes	characteristic
179	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
180	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
181	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
182	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
183	C₂×D₈×C₇₃	C₂³	1	2	yes	—
184	C₂×D₈×C₇₃	C₂³	1	2	yes	—
185	C₂×M₁₆×C₇₃	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
187	#127×C₇₃	C₂³	1	2	yes	—
188	#125×C₇₃	C₂³	1	2	yes	—
189	#123×C₇₃	—	2	4	no	—
190	#121×C₇₃	—	2	4	no	—
191	#121×C₇₃	C₂³	1	4	yes	—
192	C₄×D₄×C₇₃	C₂³	1	4	yes	—
193	#117×C₇₃	C₂³	1	1	yes	characteristic
194	#107×C₇₃	C₂³	1	2	yes	—
195	#106×C₇₃	C₂³	1	2	yes	—
196	#102×C₇₃	C₂³	1	4	yes	—
197	#102×C₇₃	C₂³	1	4	yes	—
198	#97×C₇₃	C₂³	1	1	yes	characteristic
199	#97×C₇₃	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
202	C₂³×D₇₃	—	2	4	no	—
203	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
204	C₂×D₂₉₂	—	2	4	no	—
205	C₂×D₂₉₂	—	2	4	no	—
206	C₂×D₂₉₂	C₂⁴	1	4	yes	—
207	C₂×C₂²⋊D₇₃	—	2	4	no	—
208	C₂×C₂²⋊D₇₃	—	2	4	no	—
209	C₂×C₂²⋊D₇₃	—	2	4	no	—
210	C₂×C₂²⋊D₇₃	—	2	4	no	—
211	C₂×C₂²⋊D₇₃	—	2	4	no	—
212	D₄×D₇₃	—	2	8	no	—
213	D₄×D₇₃	—	2	8	no	—
214	D₄×D₇₃	—	8	8	no	—
215	D₄×D₇₃	—	8	8	no	—
216	C₂²×Dic₇₃	—	2	4	no	—
217	C₂²×Dic₇₃	C₂×D₄	1	1	yes	characteristic
218	C₂×C₄×D₇₃	—	2	2	no	—
219	C₂×C₄×D₇₃	—	2	2	no	—
220	C₂×C₄×D₇₃	—	2	4	no	—
221	C₂×C₄×D₇₃	—	2	4	no	—
222	C₂×C₄×D₇₃	—	2	4	no	—
223	C₂×C₄×D₇₃	—	8	8	no	—
224	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
225	C₂×C₄×D₇₃	C₂×D₄	1	2	yes	—
226	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
227	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
228	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
230	D₅₈₄	—	2	4	no	—
231	D₅₈₄	—	2	4	no	—
232	#11924013	—	2	8	no	—
233	#11924013	—	2	8	no	—
234	#11924012	—	2	2	no	—
235	#11924011	—	2	2	no	—
236	#11924011	—	2	2	no	—
237	C₂×#10596831	—	2	2	no	—
238	C₂×#10596831	C₂⁴	1	1	yes	characteristic
239	C₂×#10596831	C₂⁴	1	1	yes	characteristic
240	C₂×#10596831	C₂⁴	1	1	yes	characteristic
241	C₂×#10596831	C₂⁴	1	1	yes	characteristic
242	C₈×D₇₃	—	2	2	no	—
243	C₈×D₇₃	—	2	2	no	—
244	C₈×D₇₃	—	2	2	no	—
245	C₈×D₇₃	—	2	2	no	—
246	C₈×D₇₃	#41	1	4	yes	—
247	C₈×D₇₃	#41	1	4	yes	—
248	C₄⋊Dic₇₃	—	2	4	no	—
249	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
250	C₄⋊Dic₇₃	C₂⁴	1	4	yes	—
251	#11924007	—	2	4	no	—
252	#11924007	—	2	4	no	—
253	#11924007	—	2	4	no	—
254	#11924007	C₂×D₄	1	2	yes	—
255	#11924007	C₂×D₄	1	2	yes	—
256	C₂²⋊Dic₇₃	—	2	4	no	—
257	C₂²⋊Dic₇₃	—	2	4	no	—
258	C₂²⋊Dic₇₃	C₂×D₄	1	2	yes	—
259	#11924005	—	2	4	no	—
260	#11924005	—	2	4	no	—
261	#11924005	—	2	4	no	—
262	#11924005	—	2	4	no	—
263	#11924005	C₂×D₄	1	2	yes	—
264	#11924005	C₂×D₄	1	2	yes	—
265	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
266	C₄×Dic₇₃	C₂×D₄	1	2	yes	—
267	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
268	C₄×Dic₇₃	C₂⁴	1	1	yes	characteristic
269	C₂×D₄×C₇₃	—	2	4	no	—
270	C₂×D₄×C₇₃	—	2	4	no	—
271	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
272	C₂²×C₄×C₇₃	—	2	4	no	—
273	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
274	D₈×C₇₃	—	2	4	no	—
275	D₈×C₇₃	—	2	4	no	—
276	M₁₆×C₇₃	—	2	2	no	—
277	C₂×C₈×C₇₃	—	2	2	no	—
278	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
279	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
280	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
281	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
282	C₄⋊C₄×C₇₃	—	2	4	no	—
283	C₄⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
284	C₄⋊C₄×C₇₃	C₂⁴	1	4	yes	—
285	C₂²⋊C₄×C₇₃	—	2	4	no	—
286	C₂²⋊C₄×C₇₃	—	2	4	no	—
287	C₂²⋊C₄×C₇₃	C₂×D₄	1	2	yes	—
288	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
289	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
290	C₂³×C₇₃	—	2	4	no	—
291	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
292	C₂²×D₇₃	—	2	2	no	—
293	C₂²×D₇₃	—	2	4	no	—
294	C₂²×D₇₃	—	2	4	no	—
295	C₂²×D₇₃	—	4	8	no	—
296	C₂²×D₇₃	—	4	8	no	—
297	C₂²×D₇₃	—	4	8	no	—
298	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
299	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
300	D₄×C₇₃	—	2	4	no	—
301	D₄×C₇₃	—	2	4	no	—
302	D₄×C₇₃	—	8	4	no	—
303	D₄×C₇₃	—	8	4	no	—
304	C₂×C₄×C₇₃	—	2	1	no	—
305	C₂×C₄×C₇₃	—	2	1	no	—
306	C₂×C₄×C₇₃	—	2	4	no	—
307	C₂×C₄×C₇₃	—	8	4	no	—
308	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
312	C₂²⋊D₇₃	—	4	8	no	—
313	C₂²⋊D₇₃	—	8	4	no	—
314	C₂²⋊D₇₃	—	8	4	no	—
315	C₂²⋊D₇₃	—	8	4	no	—
316	C₂²⋊D₇₃	—	8	4	no	—
317	C₂×Dic₇₃	—	2	2	no	—
318	C₂×Dic₇₃	—	2	4	no	—
319	C₂×Dic₇₃	—	8	4	no	—
320	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
321	C₂×Dic₇₃	C₂²×D₄	1	2	yes	—
322	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
323	C₂×Dic₇₃	C₂²×D₄	1	1	yes	characteristic
324	D₂₉₂	—	2	4	no	—
325	D₂₉₂	—	2	4	no	—
326	D₂₉₂	—	8	4	no	—
327	D₂₉₂	—	8	4	no	—
328	C₄×D₇₃	—	2	2	no	—
329	C₄×D₇₃	—	2	4	no	—
330	C₄×D₇₃	—	2	4	no	—
331	C₄×D₇₃	—	2	1	no	—
332	C₄×D₇₃	—	2	1	no	—
333	C₄×D₇₃	—	2	2	no	—
334	C₄×D₇₃	—	4	8	no	—
335	C₄×D₇₃	—	8	4	no	—
336	C₄×D₇₃	—	8	4	no	—
337	C₄×D₇₃	C₂×#41	1	2	yes	—
338	C₄×D₇₃	C₂×#41	1	2	yes	—
339	C₈×C₇₃	—	2	1	no	—
340	C₈×C₇₃	—	2	1	no	—
341	C₈×C₇₃	C₂×#41	1	2	yes	—
342	C₈×C₇₃	C₂×#41	1	2	yes	—
343	#10596831	—	2	1	no	—
344	#10596831	—	2	1	no	—
345	#10596831	C₂×#41	1	2	yes	—
346	#10596831	C₂×#41	1	2	yes	—
347	C₂²×C₇₃	—	2	1	no	—
348	C₂²×C₇₃	—	2	2	no	—
349	C₂²×C₇₃	—	4	4	no	—
350	C₂²×C₇₃	—	4	4	no	—
351	C₂²×C₇₃	—	4	4	no	—
352	C₂²×C₇₃	C₂³×D₄	1	1	yes	characteristic
353	C₂×D₇₃	—	2	1	no	—
354	C₂×D₇₃	—	2	2	no	—
355	C₂×D₇₃	—	4	4	no	—
356	C₂×D₇₃	—	4	4	no	—
357	C₂×D₇₃	—	4	4	no	—
358	C₂×D₇₃	—	4	4	no	—
359	C₂×D₇₃	—	8	16	no	—
360	C₂×D₇₃	#532	1	2	yes	—
361	C₂×D₇₃	#576	1	4	yes	—
362	C₄×C₇₃	—	2	1	no	—
363	C₄×C₇₃	—	2	2	no	—
364	C₄×C₇₃	—	2	2	no	—
365	C₄×C₇₃	—	4	4	no	—
366	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
367	C₄×C₇₃	C₂²×#41	1	1	yes	characteristic
368	Dic₇₃	—	2	1	no	—
369	Dic₇₃	—	2	2	no	—
370	Dic₇₃	—	2	2	no	—
371	Dic₇₃	—	4	4	no	—
372	Dic₇₃	#532	1	2	yes	—
373	C₂×#3176	—	73	1	no	maximal, Sylow
374	C₂×C₇₃	—	4	1	no	—
375	C₂×C₇₃	—	8	4	no	—
376	C₂×C₇₃	C₂×#532	1	1	yes	characteristic
377	C₂×C₇₃	C₂×#576	1	2	yes	—
378	D₇₃	—	4	1	no	—
379	D₇₃	—	8	4	no	—
380	D₇₃	#3176	1	4	yes	direct product factor
381	C₂×#540	—	73	2	no	—
382	#3176	—	73	1	no	—
383	#3176	—	73	1	no	—
384	#3176	—	73	2	no	—
385	#3176	—	73	2	no	—
386	#3176	—	73	2	no	—
387	#3176	—	73	2	no	—
388	#3176	—	73	2	no	—
389	#3176	—	73	1	no	—
390	#3176	—	73	2	no	—
391	#3176	D₇₃	1	1	yes	characteristic, direct product factor
392	C₂×#499	—	73	1	no	—
393	C₂×#493	—	73	1	no	—
394	C₂×#490	—	73	2	no	—
395	C₂×#469	—	73	2	no	—
396	C₂×#466	—	73	2	no	—
397	C₂×#442	—	73	2	no	—
398	C₂×C₄×D₈	—	73	2	no	—
399	C₂×#405	—	73	1	no	—
400	C₇₃	C₂×#3176	1	1	yes	characteristic, complemented, Sylow
401	C₂²×D₈	—	73	2	no	—
402	C₂²×D₈	—	73	2	no	—
403	C₂²×M₁₆	—	73	1	no	—
404	C₂³×C₈	—	73	1	no	—
405	#540	—	73	2	no	—
406	#540	—	73	2	no	—
407	#540	—	73	4	no	—
408	#540	—	73	4	no	—
409	#540	—	73	2	no	—
410	#540	—	146	4	no	—
411	#540	—	146	4	no	—
412	#540	C₂×D₇₃	1	2	yes	complemented
413	C₂×#127	—	73	2	no	—
414	C₂×#125	—	73	2	no	—
415	C₂×#123	—	146	4	no	—
416	C₂×#121	—	73	4	no	—
417	C₂×#121	—	146	4	no	—
418	C₂×C₄×D₄	—	73	4	no	—
419	C₂×#117	—	73	1	no	—
420	#499	—	73	2	no	—
421	#499	—	73	2	no	—
422	#499	—	73	2	no	—
423	#499	—	73	1	no	—
424	#499	C₂×D₇₃	1	1	yes	characteristic, complemented
425	#493	—	73	2	no	—
426	#493	—	73	2	no	—
427	#493	—	73	2	no	—
428	#493	—	73	1	no	—
429	#493	C₂×D₇₃	1	1	yes	characteristic, complemented
430	#490	—	73	2	no	—
431	#490	—	73	2	no	—
432	#490	—	73	4	no	—
433	#490	—	73	4	no	—
434	#490	—	73	2	no	—
435	#490	C₂×D₇₃	1	2	yes	complemented
436	#469	—	73	2	no	—
437	#469	—	73	2	no	—
438	#469	—	73	4	no	—
439	#469	—	73	2	no	—
440	#469	—	73	4	no	—
441	#469	C₂×D₇₃	1	2	yes	complemented
442	#466	—	73	2	no	—
443	#466	—	73	2	no	—
444	#466	—	73	4	no	—
445	#466	—	73	2	no	—
446	#466	—	73	4	no	—
447	#466	C₂×D₇₃	1	2	yes	complemented
448	#442	—	73	2	no	—
449	#442	—	73	4	no	—
450	#442	—	73	2	no	—
451	#442	—	73	4	no	—
452	#442	—	73	2	no	—
453	#442	C₂×D₇₃	1	2	yes	complemented
454	C₄×D₈	—	73	2	no	—
455	C₄×D₈	—	73	4	no	—
456	C₄×D₈	—	73	2	no	—
457	C₄×D₈	—	73	4	no	—
458	C₄×D₈	—	73	2	no	—
459	C₄×D₈	C₂×D₇₃	1	2	yes	complemented
460	C₂×#107	—	73	2	no	—
461	C₂×#106	—	73	2	no	—
462	C₂×#102	—	73	4	no	—
463	C₂×#102	—	73	4	no	—
464	#405	—	73	1	no	—
465	#405	—	73	1	no	—
466	#405	—	73	1	no	—
467	#405	—	73	1	no	—
468	#405	—	73	1	no	—
469	#405	—	73	1	no	—
470	#405	—	73	1	no	—
471	#405	C₂×D₇₃	1	1	yes	characteristic, complemented
472	C₂×#97	—	73	1	no	—
473	C₂×#97	—	73	1	no	—
474	C₂×C₄×C₈	—	73	1	no	—
475	C₂×C₄×C₈	—	73	1	no	—
476	C₂²×D₄	—	73	4	no	—
477	C₂²×D₄	—	146	4	no	—
478	C₂²×D₄	—	146	4	no	—
479	C₂³×C₄	—	73	1	no	—
480	C₂³×C₄	—	146	4	no	—
481	C₂×D₈	—	73	4	no	—
482	C₂×D₈	—	73	4	no	—
483	C₂×D₈	—	73	2	no	—
484	C₂×D₈	—	73	2	no	—
485	C₂×D₈	—	146	8	no	—
486	C₂×D₈	—	146	8	no	—
487	C₂×D₈	C₂²×D₇₃	1	2	yes	—
488	C₂×D₈	C₂²×D₇₃	1	2	yes	—
489	C₂×M₁₆	—	73	1	no	—
490	C₂×M₁₆	—	73	1	no	—
491	C₂×M₁₆	—	73	1	no	—
492	C₂×M₁₆	—	146	4	no	—
493	C₂×M₁₆	C₂²×D₇₃	1	1	yes	characteristic
494	C₂²×C₈	—	73	1	no	—
495	C₂²×C₈	—	73	1	no	—
496	C₂²×C₈	—	73	1	no	—
497	C₂²×C₈	—	73	1	no	—
498	C₂²×C₈	—	73	1	no	—
499	C₂²×C₈	—	73	1	no	—
500	C₂²×C₈	—	73	1	no	—
501	C₂²×C₈	—	146	4	no	—
502	C₂²×C₈	C₂²×D₇₃	1	1	yes	characteristic
503	#127	—	73	4	no	—
504	#127	—	73	2	no	—
505	#127	—	146	4	no	—
506	#127	C₂²×D₇₃	1	2	yes	—
507	#125	—	73	4	no	—
508	#125	—	73	2	no	—
509	#125	—	146	4	no	—
510	#125	C₂²×D₇₃	1	2	yes	—
511	#123	—	2	4	no	—
512	#123	—	146	4	no	—
513	#123	—	146	4	no	—
514	#123	—	146	4	no	—
515	#123	—	146	4	no	—
516	#123	—	146	4	no	—
517	#123	—	146	4	no	—
518	#123	—	146	4	no	—
519	#121	—	2	4	no	—
520	#121	—	73	4	no	—
521	#121	—	73	4	no	—
522	#121	—	73	4	no	—
523	#121	—	146	4	no	—
524	#121	—	146	4	no	—
525	#121	—	146	4	no	—
526	#121	—	146	4	no	—
527	#121	—	146	4	no	—
528	#121	—	146	4	no	—
529	#121	—	146	4	no	—
530	#121	—	146	4	no	—
531	#121	—	146	4	no	—
532	#121	C₂²×D₇₃	1	4	yes	—
533	C₄×D₄	—	73	4	no	—
534	C₄×D₄	—	73	4	no	—
535	C₄×D₄	—	73	4	no	—
536	C₄×D₄	—	146	4	no	—
537	C₄×D₄	—	146	4	no	—
538	C₄×D₄	C₂²×D₇₃	1	4	yes	—
539	#117	—	73	1	no	—
540	#117	—	73	2	no	—
541	#117	—	73	2	no	—
542	#117	—	73	1	no	—
543	#117	—	73	1	no	—
544	#117	C₂²×D₇₃	1	1	yes	characteristic
545	C₂×C₄⋊C₄	—	73	2	no	—
546	C₂×C₄⋊C₄	—	73	4	no	—
547	C₂×C₄⋊C₄	—	146	4	no	—
548	C₂×C₂²⋊C₄	—	73	2	no	—
549	C₂×C₂²⋊C₄	—	146	4	no	—
550	C₂×C₂²⋊C₄	—	146	4	no	—
551	C₂×C₄²	—	73	1	no	—
552	C₂×C₄²	—	73	1	no	—
553	#107	—	73	2	no	—
554	#107	—	73	4	no	—
555	#107	C₂²×D₇₃	1	2	yes	—
556	#106	—	73	2	no	—
557	#106	—	73	4	no	—
558	#106	C₂²×D₇₃	1	2	yes	—
559	#102	—	73	4	no	—
560	#102	—	73	4	no	—
561	#102	—	73	4	no	—
562	#102	—	73	4	no	—
563	#102	—	73	4	no	—
564	#102	—	73	4	no	—
565	#102	C₂²×D₇₃	1	4	yes	—
566	#102	C₂²×D₇₃	1	4	yes	—
567	#97	—	73	1	no	—
568	#97	—	73	1	no	—
569	#97	—	73	1	no	—
570	#97	—	73	1	no	—
571	#97	—	73	1	no	—
572	#97	—	73	1	no	—
573	#97	C₂²×D₇₃	1	1	yes	characteristic
574	#97	C₂²×D₇₃	1	1	yes	characteristic
575	C₄×C₈	—	73	1	no	—
576	C₄×C₈	—	73	1	no	—
577	C₄×C₈	—	73	1	no	—
578	C₄×C₈	—	73	1	no	—
579	C₄×C₈	—	73	1	no	—
580	C₄×C₈	—	73	1	no	—
581	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
582	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
583	C₂⁴	—	73	1	no	—
584	C₂⁴	—	146	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	584	8	no	—
588	C₂×D₄	—	584	8	no	—
589	C₂×D₄	—	73	4	no	—
590	C₂×D₄	—	146	4	no	—
591	C₂×D₄	—	146	8	no	—
592	C₂×D₄	—	146	8	no	—
593	C₂×D₄	—	146	4	no	—
594	C₂×D₄	—	146	4	no	—
595	C₂×D₄	—	146	4	no	—
596	C₂×D₄	—	146	4	no	—
597	C₂×D₄	—	146	4	no	—
598	C₂×D₄	—	146	4	no	—
599	C₂×D₄	C₂³×D₇₃	1	4	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	584	8	no	—
602	C₂²×C₄	—	73	1	no	—
603	C₂²×C₄	—	73	1	no	—
604	C₂²×C₄	—	73	2	no	—
605	C₂²×C₄	—	73	2	no	—
606	C₂²×C₄	—	73	1	no	—
607	C₂²×C₄	—	73	1	no	—
608	C₂²×C₄	—	73	1	no	—
609	C₂²×C₄	—	146	4	no	—
610	C₂²×C₄	—	146	4	no	—
611	C₂²×C₄	—	146	2	no	—
612	C₂²×C₄	—	146	2	no	—
613	C₂²×C₄	—	146	4	no	—
614	C₂²×C₄	—	146	4	no	—
615	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
616	D₈	—	2	4	no	—
617	D₈	—	2	4	no	—
618	D₈	—	146	8	no	—
619	D₈	—	146	8	no	—
620	D₈	—	146	4	no	—
621	D₈	—	146	4	no	—
622	M₁₆	—	2	2	no	—
623	M₁₆	—	146	2	no	—
624	M₁₆	—	146	2	no	—
625	M₁₆	—	146	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	73	1	no	—
628	C₂×C₈	—	73	1	no	—
629	C₂×C₈	—	73	4	no	—
630	C₂×C₈	—	73	4	no	—
631	C₂×C₈	—	73	1	no	—
632	C₂×C₈	—	73	1	no	—
633	C₂×C₈	—	146	2	no	—
634	C₂×C₈	—	146	2	no	—
635	C₂×C₈	—	146	2	no	—
636	C₂×C₈	—	146	2	no	—
637	C₂×C₈	—	146	2	no	—
638	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
639	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
640	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
641	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	73	2	no	—
644	C₄⋊C₄	—	73	2	no	—
645	C₄⋊C₄	—	73	2	no	—
646	C₄⋊C₄	—	73	4	no	—
647	C₄⋊C₄	—	146	4	no	—
648	C₄⋊C₄	—	146	4	no	—
649	C₄⋊C₄	—	146	4	no	—
650	C₄⋊C₄	—	146	4	no	—
651	C₄⋊C₄	D₄×D₇₃	1	2	yes	—
652	C₄⋊C₄	C₂³×D₇₃	1	4	yes	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	73	2	no	—
656	C₂²⋊C₄	—	73	2	no	—
657	C₂²⋊C₄	—	73	2	no	—
658	C₂²⋊C₄	—	146	4	no	—
659	C₂²⋊C₄	—	146	4	no	—
660	C₂²⋊C₄	—	146	4	no	—
661	C₂²⋊C₄	—	146	4	no	—
662	C₂²⋊C₄	—	146	4	no	—
663	C₂²⋊C₄	—	146	4	no	—
664	C₂²⋊C₄	D₄×D₇₃	1	2	yes	—
665	C₄²	—	73	2	no	—
666	C₄²	—	73	2	no	—
667	C₄²	—	73	1	no	—
668	C₄²	—	73	1	no	—
669	C₄²	C₂³×D₇₃	1	1	yes	characteristic
670	C₄²	C₂³×D₇₃	1	1	yes	characteristic
671	C₂³	—	2	4	no	—
672	C₂³	—	292	8	no	—
673	C₂³	—	292	8	no	—
674	C₂³	—	292	8	no	—
675	C₂³	—	73	1	no	—
676	C₂³	—	73	1	no	—
677	C₂³	—	146	2	no	—
678	C₂³	—	146	4	no	—
679	C₂³	—	146	4	no	—
680	C₂³	C₂×D₄×D₇₃	1	1	yes	characteristic
681	D₄	—	2	4	no	—
682	D₄	—	2	4	no	—
683	D₄	—	8	4	no	—
684	D₄	—	8	4	no	—
685	D₄	—	292	8	no	—
686	D₄	—	584	4	no	—
687	D₄	—	584	4	no	—
688	D₄	—	584	4	no	—
689	D₄	—	584	4	no	—
690	D₄	—	584	4	no	—
691	D₄	—	584	4	no	—
692	D₄	—	146	4	no	—
693	D₄	—	146	4	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	8	4	no	—
698	C₂×C₄	—	292	8	no	—
699	C₂×C₄	—	584	4	no	—
700	C₂×C₄	—	584	4	no	—
701	C₂×C₄	—	584	4	no	—
702	C₂×C₄	—	73	1	no	—
703	C₂×C₄	—	73	2	no	—
704	C₂×C₄	—	73	2	no	—
705	C₂×C₄	—	73	2	no	—
706	C₂×C₄	—	73	2	no	—
707	C₂×C₄	—	73	1	no	—
708	C₂×C₄	—	146	2	no	—
709	C₂×C₄	—	146	4	no	—
710	C₂×C₄	—	146	2	no	—
711	C₂×C₄	—	146	4	no	—
712	C₂×C₄	—	146	4	no	—
713	C₂×C₄	—	146	2	no	—
714	C₂×C₄	—	146	1	no	—
715	C₂×C₄	—	146	1	no	—
716	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
717	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
718	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
719	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
720	C₈	—	2	1	no	—
721	C₈	—	2	1	no	—
722	C₈	—	73	2	no	—
723	C₈	—	73	2	no	—
724	C₈	—	146	1	no	—
725	C₈	—	146	1	no	—
726	C₈	#41×D₇₃	1	2	yes	—
727	C₈	#41×D₇₃	1	2	yes	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	292	4	no	—
734	C₂²	—	292	4	no	—
735	C₂²	—	292	4	no	—
736	C₂²	—	292	4	no	—
737	C₂²	—	584	16	no	—
738	C₂²	—	73	4	no	—
739	C₂²	—	73	2	no	—
740	C₂²	—	146	2	no	—
741	C₂²	—	146	1	no	—
742	C₂²	C₂²×D₄×D₇₃	1	1	yes	characteristic
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	1	no	—
746	C₄	—	4	4	no	—
747	C₄	—	292	4	no	—
748	C₄	—	73	2	no	—
749	C₄	—	146	2	no	—
750	C₄	—	146	2	no	—
751	C₄	—	146	1	no	—
752	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
753	C₄	C₂×#41×D₇₃	1	1	yes	characteristic
754	C₂	—	4	1	no	—
755	C₂	—	8	4	no	—
756	C₂	—	292	1	no	—
757	C₂	—	584	4	no	—
758	C₂	—	73	4	no	—
759	C₂	#532×D₇₃	1	1	yes	characteristic
760	C₂	#576×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×#3176	C₂
socle	C₂²×C₇₃	C₂³×D₄
hypercenter	#3176	D₇₃
hypocenter	C₇₃	C₂×#3176
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #540×D₇₃	C₂	semidirect
2. #22620582	C₂	semidirect
3. #22620581	C₂	semidirect
4. #22620580	C₂	semidirect
5. #22620579	C₂	semidirect
6. #22620578	C₂	semidirect
7. #22620577	C₂	semidirect
8. #22620576	C₂	semidirect
9. #22620575	C₂	semidirect
10. #22620574	C₂	semidirect
11. #499×D₇₃	C₂	semidirect
12. #493×D₇₃	C₂	semidirect
13. #490×D₇₃	C₂	semidirect
14. #469×D₇₃	C₂	semidirect
15. #466×D₇₃	C₂	semidirect
16. #442×D₇₃	C₂	semidirect
17. C₄×D₈×D₇₃	C₂	semidirect
18. #405×D₇₃	C₂	semidirect
19. C₇₃×#3176	C₂	semidirect
24. #17989193	C₂²	semidirect
25. #17989192	C₂²	semidirect
26. #17989191	C₂²	semidirect
27. #17989190	C₂²	semidirect
29. #17989188	C₂²	semidirect
38. #17988989	C₂²	semidirect
39. #17988988	C₂²	semidirect
40. #17988987	C₂²	semidirect
41. #17988986	C₂²	semidirect
42. #17988964	C₂²	semidirect
43. #17988963	C₂²	semidirect
44. #17988962	C₂²	semidirect
45. #17988962	C₂²	semidirect
46. #17988953	C₂²	semidirect
47. #17988952	C₂²	semidirect
48. #17988951	C₂²	semidirect
49. #17988950	C₂²	semidirect
50. #17988950	C₂²	semidirect
51. #17988841	C₂²	semidirect
52. #17988840	C₂²	semidirect
53. #17988839	C₂²	semidirect
54. #17988838	C₂²	semidirect
55. #17988837	C₂²	semidirect
56. #17988824	C₂²	semidirect
57. #17988823	C₂²	semidirect
58. #17988822	C₂²	semidirect
59. #17988821	C₂²	semidirect
60. #17988820	C₂²	semidirect
61. #17988700	C₂²	semidirect
62. #17988699	C₂²	semidirect
63. #17988698	C₂²	semidirect
64. #17988697	C₂²	semidirect
65. #17988696	C₂²	semidirect
66. C₄×D₅₈₄	C₂²	semidirect
67. D₈×Dic₇₃	C₂²	semidirect
68. #17988669	C₂²	semidirect
69. C₄×#11924013	C₂²	semidirect
70. #17988667	C₂²	semidirect
75. #17988545	C₂²	semidirect
76. #17988544	C₂²	semidirect
77. #17988544	C₂²	semidirect
78. #17988543	C₂²	semidirect
79. #17988542	C₂²	semidirect
80. #17988541	C₂²	semidirect
81. #17988541	C₂²	semidirect
86. #540×C₇₃	C₂²	semidirect
87. #499×C₇₃	C₂²	semidirect
88. #493×C₇₃	C₂²	semidirect
89. #490×C₇₃	C₂²	semidirect
90. #469×C₇₃	C₂²	semidirect
91. #466×C₇₃	C₂²	semidirect
92. #442×C₇₃	C₂²	semidirect
93. C₄×D₈×C₇₃	C₂²	semidirect
94. #405×C₇₃	C₂²	semidirect
380. D₇₃	#3176	direct (N × H)
391. #3176	D₇₃	direct (N × H)
400. C₇₃	C₂×#3176	semidirect
412. #540	C₂×D₇₃	semidirect
424. #499	C₂×D₇₃	semidirect
429. #493	C₂×D₇₃	semidirect
435. #490	C₂×D₇₃	semidirect
441. #469	C₂×D₇₃	semidirect
447. #466	C₂×D₇₃	semidirect
453. #442	C₂×D₇₃	semidirect
459. C₄×D₈	C₂×D₇₃	semidirect
471. #405	C₂×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
#540×D₇₃	2
#22620582	2
#22620581	2
#22620580	2
#22620579	2
#22620578	2
#22620577	2
#22620576	2
#22620575	2
#22620574	2
#499×D₇₃	2
#493×D₇₃	2
#490×D₇₃	2
#469×D₇₃	2
#466×D₇₃	2
#442×D₇₃	2
C₄×D₈×D₇₃	2
#405×D₇₃	2
C₇₃×#3176	2
C₂×#3176	73

Subgroups — #3176×D73 #33955810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #3176×D₇₃ #33955810