Subgroups — #1581×D₇₃ #33055476

Order 18688.

838 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#436×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	#22608763	C₂	1	1	yes	maximal, characteristic, complemented
5	#22608762	C₂	1	1	yes	maximal, characteristic, complemented
6	#22608761	C₂	1	1	yes	maximal, characteristic, complemented
7	#22608760	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608759	C₂	1	1	yes	maximal, characteristic, complemented
9	#22608758	C₂	1	1	yes	maximal, characteristic, complemented
10	#22608757	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄⋊C₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄⋊C₈×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₇₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇₃×#1581	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×D₈×D₇₃	C₄	1	1	yes	characteristic
17	C₂×M₁₆×D₇₃	—	2	1	no	—
18	C₂²×C₈×D₇₃	—	2	1	no	—
19	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
20	C₄×D₄×D₇₃	C₂²	1	1	yes	characteristic
21	C₄×D₅₈₄	C₂²	1	1	yes	characteristic
22	D₈×Dic₇₃	C₄	1	1	yes	characteristic
23	#17988669	C₄	1	1	yes	characteristic
24	C₄×#11924013	C₂²	1	1	yes	characteristic
25	C₄×#11924013	C₂²	1	1	yes	characteristic
26	#17988667	C₄	1	1	yes	characteristic
27	#17988667	C₄	1	1	yes	characteristic
28	#17988666	C₂²	1	1	yes	characteristic, complemented
29	#17988665	C₂²	1	1	yes	characteristic, complemented
30	#17988664	C₂²	1	1	yes	characteristic, complemented
31	#17988663	—	2	1	no	—
32	#17988662	—	2	1	no	—
33	C₈×D₂₉₂	C₂²	1	1	yes	characteristic, complemented
34	D₄×#10596831	C₂²	1	1	yes	characteristic, complemented
35	#17988652	C₂²	1	1	yes	characteristic, complemented
36	C₈×C₂²⋊D₇₃	—	2	1	no	—
37	#17988650	—	2	1	no	—
38	#107×D₇₃	C₄	1	1	yes	characteristic
39	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₇₃	C₂²	1	1	yes	characteristic
41	#102×D₇₃	C₄	1	1	yes	characteristic
42	#102×D₇₃	C₄	1	1	yes	characteristic
43	C₂²⋊C₈×D₇₃	—	2	1	no	—
44	C₂²⋊C₈×D₇₃	—	2	1	no	—
45	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
48	#17988340	C₂²	1	1	yes	characteristic, complemented
49	#17988339	C₂²	1	1	yes	characteristic, complemented
50	#17988339	C₂²	1	1	yes	characteristic, complemented
51	#17988316	C₂²	1	1	yes	characteristic, complemented
52	#17988316	C₂²	1	1	yes	characteristic, complemented
53	D₄⋊#10596831	C₂²	1	1	yes	characteristic, complemented
54	D₄⋊#10596831	C₂²	1	1	yes	characteristic, complemented
55	#17988314	C₂²	1	1	yes	characteristic, complemented
56	#17988314	C₂²	1	1	yes	characteristic, complemented
57	#17988309	C₂²	1	1	yes	characteristic, complemented
58	#17988309	C₂²	1	1	yes	characteristic, complemented
59	#17988308	C₂²	1	1	yes	characteristic, complemented
60	C₄×D₈×C₇₃	C₂²	1	1	yes	characteristic
61	#436×C₇₃	C₂²	1	1	yes	characteristic, complemented
62	C₈×D₄×C₇₃	C₂²	1	1	yes	characteristic, complemented
63	#335×C₇₃	C₂²	1	1	yes	characteristic, complemented
64	D₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
65	D₄⋊C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
66	#322×C₇₃	C₂²	1	1	yes	characteristic, complemented
67	C₂×D₄×D₇₃	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₇₃	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₇₃	—	2	1	no	—
70	C₂²×C₄×D₇₃	—	2	1	no	—
71	C₂×D₅₈₄	C₂×C₄	1	1	yes	characteristic
72	C₂×#11924013	C₂×C₄	1	1	yes	characteristic
73	C₂×#11924013	C₂×C₄	1	1	yes	characteristic
74	D₈×D₇₃	—	2	4	no	—
75	C₂×#11924012	—	2	1	no	—
76	C₂×#11924011	—	2	1	no	—
77	C₂×#11924011	—	2	1	no	—
78	M₁₆×D₇₃	—	4	4	no	—
79	C₂²×#10596831	—	2	1	no	—
80	C₂×C₈×D₇₃	—	2	1	no	—
81	C₂×C₈×D₇₃	—	2	1	no	—
82	C₂×C₈×D₇₃	—	2	1	no	—
83	C₂×C₈×D₇₃	—	2	1	no	—
84	C₂×C₈×D₇₃	—	2	1	no	—
85	C₂×C₈×D₇₃	—	4	4	no	—
86	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
89	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
90	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
91	C₄×D₂₉₂	C₂³	1	1	yes	characteristic
92	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
93	D₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
94	#14556553	C₂×C₄	1	1	yes	characteristic
95	#14556553	C₂×C₄	1	1	yes	characteristic
96	C₄×C₂²⋊D₇₃	—	2	1	no	—
97	C₄×C₂²⋊D₇₃	—	2	1	no	—
98	#14556551	—	2	1	no	—
99	#14556551	—	2	1	no	—
100	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
101	C₄⋊C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
102	C₂²⋊C₄×D₇₃	—	2	1	no	—
103	C₂²⋊C₄×D₇₃	—	2	1	no	—
104	C₄²×D₇₃	C₂³	1	1	yes	characteristic
105	#14556525	C₂×C₄	1	1	yes	characteristic
106	#14556524	C₂×C₄	1	1	yes	characteristic
107	#14556524	C₂×C₄	1	1	yes	characteristic
108	C₄⋊#10596831	C₂³	1	1	yes	characteristic
109	C₄⋊#10596831	C₂³	1	1	yes	characteristic
110	#14556520	—	2	1	no	—
111	#14556520	—	2	1	no	—
112	#14556513	C₂×C₄	1	1	yes	characteristic
113	#14556513	C₂×C₄	1	1	yes	characteristic
114	#14556512	C₂×C₄	1	1	yes	characteristic
115	#14556512	C₂×C₄	1	1	yes	characteristic
116	#14556511	C₂×C₄	1	1	yes	characteristic
117	#14556511	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊#10596831	—	2	1	no	—
119	C₂²⋊#10596831	—	2	1	no	—
120	#14556503	—	2	1	no	—
121	#14556503	—	2	1	no	—
122	#14556503	—	2	1	no	—
123	#14556503	—	2	1	no	—
124	C₄×#10596831	C₂³	1	1	yes	characteristic
125	C₄×#10596831	C₂³	1	1	yes	characteristic
126	C₄×#10596831	C₂³	1	1	yes	characteristic
127	C₈×Dic₇₃	—	2	1	no	—
128	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₇₃	C₂×C₄	1	1	yes	characteristic
130	C₈×Dic₇₃	D₄	1	1	yes	characteristic
131	C₈×Dic₇₃	D₄	1	1	yes	characteristic
132	C₂×D₈×C₇₃	C₂×C₄	1	1	yes	characteristic
133	C₂×M₁₆×C₇₃	—	2	1	no	—
134	C₂²×C₈×C₇₃	—	2	1	no	—
135	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₇₃	C₂³	1	1	yes	characteristic
137	#107×C₇₃	C₂×C₄	1	1	yes	characteristic
138	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
139	C₄⋊C₈×C₇₃	C₂³	1	1	yes	characteristic
140	#102×C₇₃	C₂×C₄	1	1	yes	characteristic
141	#102×C₇₃	C₂×C₄	1	1	yes	characteristic
142	C₂²⋊C₈×C₇₃	—	2	1	no	—
143	C₂²⋊C₈×C₇₃	—	2	1	no	—
144	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
146	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
147	C₂³×D₇₃	—	2	1	no	—
148	C₂³×D₇₃	—	2	1	no	—
149	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₂₉₂	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₂²⋊D₇₃	—	2	1	no	—
152	C₂×C₂²⋊D₇₃	—	2	1	no	—
153	D₄×D₇₃	—	2	2	no	—
154	D₄×D₇₃	—	2	2	no	—
155	D₄×D₇₃	—	2	2	no	—
156	D₄×D₇₃	M₁₆	1	4	yes	complemented
157	C₂²×Dic₇₃	—	2	1	no	—
158	C₂²×Dic₇₃	—	2	1	no	—
159	C₂×C₄×D₇₃	—	2	1	no	—
160	C₂×C₄×D₇₃	—	2	1	no	—
161	C₂×C₄×D₇₃	—	2	1	no	—
162	C₂×C₄×D₇₃	—	2	1	no	—
163	C₂×C₄×D₇₃	—	2	1	no	—
164	C₂×C₄×D₇₃	—	2	1	no	—
165	C₂×C₄×D₇₃	—	4	2	no	—
166	C₂×C₄×D₇₃	—	4	2	no	—
167	C₂×C₄×D₇₃	—	4	2	no	—
168	C₂×C₄×D₇₃	—	4	2	no	—
169	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
171	C₂×C₄×D₇₃	#41	1	1	yes	characteristic
172	D₅₈₄	—	2	2	no	—
173	#11924013	—	2	2	no	—
174	#11924013	—	2	2	no	—
175	#11924012	—	4	2	no	—
176	#11924011	—	4	2	no	—
177	#11924011	—	4	2	no	—
178	C₂×#10596831	—	2	1	no	—
179	C₂×#10596831	—	2	1	no	—
180	C₂×#10596831	—	2	1	no	—
181	C₂×#10596831	—	4	2	no	—
182	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
183	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
184	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
185	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
186	C₈×D₇₃	—	2	2	no	—
187	C₈×D₇₃	—	2	2	no	—
188	C₈×D₇₃	—	2	2	no	—
189	C₈×D₇₃	—	4	2	no	—
190	C₈×D₇₃	—	4	2	no	—
191	C₈×D₇₃	—	4	2	no	—
192	C₈×D₇₃	—	4	2	no	—
193	C₈×D₇₃	—	4	2	no	—
194	C₈×D₇₃	D₈	1	4	yes	complemented
195	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊Dic₇₃	C₂²×C₄	1	1	yes	characteristic
197	#11924007	—	2	1	no	—
198	#11924007	—	2	1	no	—
199	C₂²⋊Dic₇₃	—	2	1	no	—
200	C₂²⋊Dic₇₃	—	2	1	no	—
201	#11924005	—	2	1	no	—
202	#11924005	—	2	1	no	—
203	#11924005	—	2	1	no	—
204	#11924005	—	2	1	no	—
205	C₄×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
206	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
207	C₄×Dic₇₃	#41	1	1	yes	characteristic
208	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
209	C₂×D₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
210	C₂²×C₄×C₇₃	—	2	1	no	—
211	C₂²×C₄×C₇₃	—	2	1	no	—
212	D₈×C₇₃	—	2	2	no	—
213	M₁₆×C₇₃	—	4	2	no	—
214	C₂×C₈×C₇₃	—	2	1	no	—
215	C₂×C₈×C₇₃	—	2	1	no	—
216	C₂×C₈×C₇₃	—	2	1	no	—
217	C₂×C₈×C₇₃	—	4	2	no	—
218	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
219	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
220	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
221	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
222	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
223	C₄⋊C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
224	C₂²⋊C₄×C₇₃	—	2	1	no	—
225	C₂²⋊C₄×C₇₃	—	2	1	no	—
226	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
227	C₂³×C₇₃	—	2	1	no	—
228	C₂³×C₇₃	—	2	1	no	—
229	C₂²×D₇₃	—	2	1	no	—
230	C₂²×D₇₃	—	2	4	no	—
231	C₂²×D₇₃	—	2	1	no	—
232	C₂²×D₇₃	—	4	2	no	—
233	C₂²×D₇₃	—	4	2	no	—
234	C₂²×D₇₃	—	4	2	no	—
235	C₂²×D₇₃	—	4	2	no	—
236	C₂²×D₇₃	—	4	2	no	—
237	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
238	D₄×C₇₃	—	2	1	no	—
239	D₄×C₇₃	—	2	1	no	—
240	D₄×C₇₃	—	2	1	no	—
241	D₄×C₇₃	C₂×M₁₆	1	2	yes	complemented
242	C₂×C₄×C₇₃	—	2	1	no	—
243	C₂×C₄×C₇₃	—	2	1	no	—
244	C₂×C₄×C₇₃	—	4	1	no	—
245	C₂×C₄×C₇₃	—	4	1	no	—
246	C₂×C₄×C₇₃	—	4	1	no	—
247	C₂×C₄×C₇₃	—	4	1	no	—
248	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
251	C₂²⋊D₇₃	—	2	4	no	—
252	C₂²⋊D₇₃	—	4	2	no	—
253	C₂×Dic₇₃	—	2	1	no	—
254	C₂×Dic₇₃	—	2	1	no	—
255	C₂×Dic₇₃	—	4	2	no	—
256	C₂×Dic₇₃	—	4	2	no	—
257	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
258	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
259	C₂×Dic₇₃	C₄×D₄	1	1	yes	characteristic
260	D₂₉₂	—	2	1	no	—
261	D₂₉₂	—	2	1	no	—
262	D₂₉₂	—	2	1	no	—
263	D₂₉₂	C₂×M₁₆	1	2	yes	complemented
264	C₄×D₇₃	—	2	2	no	—
265	C₄×D₇₃	—	4	2	no	—
266	C₄×D₇₃	—	4	2	no	—
267	C₄×D₇₃	—	4	1	no	—
268	C₄×D₇₃	—	4	1	no	—
269	C₄×D₇₃	—	4	1	no	—
270	C₄×D₇₃	—	4	1	no	—
271	C₄×D₇₃	—	4	2	no	—
272	C₄×D₇₃	—	4	2	no	—
273	C₄×D₇₃	C₂×M₁₆	1	2	yes	—
274	C₄×D₇₃	#131	1	2	yes	—
275	C₄×D₇₃	C₂×D₈	1	2	yes	—
276	C₄×D₇₃	#135	1	2	yes	—
277	C₈×C₇₃	—	2	1	no	—
278	C₈×C₇₃	—	2	1	no	—
279	C₈×C₇₃	—	2	1	no	—
280	C₈×C₇₃	—	4	1	no	—
281	C₈×C₇₃	—	4	1	no	—
282	C₈×C₇₃	—	4	1	no	—
283	C₈×C₇₃	C₂×D₈	1	2	yes	complemented
284	#10596831	—	2	1	no	—
285	#10596831	—	2	1	no	—
286	#10596831	—	2	1	no	—
287	#10596831	—	4	1	no	—
288	#10596831	—	4	1	no	—
289	#10596831	—	4	1	no	—
290	#10596831	C₂×D₈	1	2	yes	complemented
291	C₂²×C₇₃	—	2	2	no	—
292	C₂²×C₇₃	—	4	1	no	—
293	C₂²×C₇₃	—	4	1	no	—
294	C₂²×C₇₃	—	4	1	no	—
295	C₂²×C₇₃	—	4	1	no	—
296	C₂²×C₇₃	—	4	1	no	—
297	C₂²×C₇₃	C₂×C₄×D₄	1	1	yes	characteristic
298	C₂×D₇₃	—	2	2	no	—
299	C₂×D₇₃	—	4	1	no	—
300	C₂×D₇₃	—	4	1	no	—
301	C₂×D₇₃	—	4	8	no	—
302	C₂×D₇₃	—	4	1	no	—
303	C₂×D₇₃	—	4	1	no	—
304	C₂×D₇₃	—	4	1	no	—
305	C₂×D₇₃	—	8	4	no	—
306	C₂×D₇₃	#435	1	2	yes	—
307	C₂×D₇₃	C₄×D₈	1	2	yes	—
308	C₂×D₇₃	#444	1	2	yes	—
309	C₄×C₇₃	—	2	1	no	—
310	C₄×C₇₃	—	4	1	no	—
311	C₄×C₇₃	—	4	1	no	—
312	C₄×C₇₃	C₂²×M₁₆	1	1	yes	characteristic
313	C₄×C₇₃	C₂×#131	1	1	yes	characteristic
314	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
315	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
316	Dic₇₃	—	2	1	no	—
317	Dic₇₃	—	4	1	no	—
318	Dic₇₃	—	4	1	no	—
319	Dic₇₃	#435	1	2	yes	—
320	Dic₇₃	C₄×D₈	1	2	yes	—
321	C₂×#1581	—	73	1	no	maximal, Sylow
322	C₂×C₇₃	—	4	2	no	—
323	C₂×C₇₃	—	8	1	no	—
324	C₂×C₇₃	C₂×#435	1	1	yes	characteristic
325	C₂×C₇₃	C₂×C₄×D₈	1	1	yes	characteristic
326	C₂×C₇₃	C₂×#444	1	1	yes	characteristic
327	D₇₃	—	4	2	no	—
328	D₇₃	—	8	1	no	—
329	D₇₃	#1581	1	4	yes	direct product factor
330	C₂×C₄×D₈	—	73	1	no	—
331	C₂×#436	—	73	1	no	—
332	C₂×C₈×D₄	—	73	1	no	—
333	#1581	—	73	1	no	—
334	#1581	—	73	1	no	—
335	#1581	—	73	1	no	—
336	#1581	—	73	1	no	—
337	#1581	—	73	1	no	—
338	#1581	—	73	1	no	—
339	#1581	—	73	1	no	—
340	#1581	D₇₃	1	1	yes	characteristic, direct product factor
341	C₂×#335	—	73	1	no	—
342	C₂×D₄⋊C₈	—	73	1	no	—
343	C₂×D₄⋊C₈	—	73	1	no	—
344	C₂×#322	—	73	1	no	—
345	C₇₃	C₂×#1581	1	1	yes	characteristic, complemented, Sylow
346	C₂²×D₈	—	73	1	no	—
347	C₂²×M₁₆	—	146	1	no	—
348	C₂³×C₈	—	146	1	no	—
349	C₂×C₄×D₄	—	73	1	no	—
350	C₂×C₄×D₄	—	73	1	no	—
351	C₄×D₈	—	73	1	no	—
352	C₄×D₈	—	73	1	no	—
353	C₄×D₈	—	73	1	no	—
354	C₄×D₈	—	73	1	no	—
355	C₄×D₈	—	73	1	no	—
356	C₄×D₈	—	73	1	no	—
357	C₄×D₈	—	73	1	no	—
358	C₄×D₈	C₂×D₇₃	1	1	yes	characteristic
359	#436	—	73	1	no	—
360	#436	—	73	1	no	—
361	#436	—	73	1	no	—
362	#436	—	146	1	no	—
363	#436	—	146	1	no	—
364	#436	C₂×D₇₃	1	1	yes	characteristic, complemented
365	C₈×D₄	—	73	1	no	—
366	C₈×D₄	—	73	1	no	—
367	C₈×D₄	—	73	1	no	—
368	C₈×D₄	—	146	1	no	—
369	C₈×D₄	—	146	1	no	—
370	C₈×D₄	C₂×D₇₃	1	1	yes	characteristic, complemented
371	C₂×#107	—	73	1	no	—
372	C₂×C₄⋊C₈	—	73	1	no	—
373	C₂×C₄⋊C₈	—	73	1	no	—
374	C₂×#102	—	73	1	no	—
375	C₂×#102	—	73	1	no	—
376	C₂×C₂²⋊C₈	—	146	1	no	—
377	C₂×C₂²⋊C₈	—	146	1	no	—
378	C₂×C₄×C₈	—	73	1	no	—
379	C₂×C₄×C₈	—	73	1	no	—
380	C₂×C₄×C₈	—	73	1	no	—
381	#335	—	73	1	no	—
382	#335	—	73	1	no	—
383	#335	—	73	1	no	—
384	#335	C₂×D₇₃	1	1	yes	characteristic, complemented
385	D₄⋊C₈	—	73	1	no	—
386	D₄⋊C₈	—	73	1	no	—
387	D₄⋊C₈	—	73	1	no	—
388	D₄⋊C₈	—	73	1	no	—
389	D₄⋊C₈	—	73	1	no	—
390	D₄⋊C₈	—	73	1	no	—
391	D₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
392	D₄⋊C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
393	#322	—	73	1	no	—
394	#322	—	73	1	no	—
395	#322	—	73	1	no	—
396	#322	C₂×D₇₃	1	1	yes	characteristic, complemented
397	C₂²×D₄	—	73	1	no	—
398	C₂²×D₄	—	73	1	no	—
399	C₂³×C₄	—	146	1	no	—
400	C₂³×C₄	—	146	1	no	—
401	C₂×D₈	—	73	1	no	—
402	C₂×D₈	—	73	1	no	—
403	C₂×D₈	—	73	1	no	—
404	C₂×D₈	—	146	4	no	—
405	C₂×D₈	C₄×D₇₃	1	1	yes	characteristic
406	C₂×M₁₆	—	2	1	no	—
407	C₂×M₁₆	—	292	4	no	—
408	C₂×M₁₆	—	146	1	no	—
409	C₂×M₁₆	—	146	1	no	—
410	C₂×M₁₆	—	146	1	no	—
411	C₂²×C₈	—	2	1	no	—
412	C₂²×C₈	—	292	4	no	—
413	C₂²×C₈	—	73	1	no	—
414	C₂²×C₈	—	73	1	no	—
415	C₂²×C₈	—	73	1	no	—
416	C₂²×C₈	—	73	1	no	—
417	C₂²×C₈	—	146	1	no	—
418	C₂²×C₈	—	146	1	no	—
419	C₂²×C₈	—	146	1	no	—
420	C₂²×C₈	—	146	1	no	—
421	C₂²×C₈	—	146	1	no	—
422	C₂²×C₈	—	146	1	no	—
423	C₄×D₄	—	73	1	no	—
424	C₄×D₄	—	73	1	no	—
425	C₄×D₄	—	73	1	no	—
426	C₄×D₄	—	73	1	no	—
427	C₄×D₄	—	73	1	no	—
428	C₄×D₄	—	73	1	no	—
429	C₄×D₄	—	146	1	no	—
430	C₄×D₄	—	146	1	no	—
431	C₄×D₄	—	146	1	no	—
432	C₄×D₄	—	146	1	no	—
433	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
434	C₄×D₄	C₂²×D₇₃	1	1	yes	characteristic
435	C₂×C₄⋊C₄	—	73	1	no	—
436	C₂×C₄⋊C₄	—	73	1	no	—
437	C₂×C₂²⋊C₄	—	146	1	no	—
438	C₂×C₂²⋊C₄	—	146	1	no	—
439	C₂×C₄²	—	73	1	no	—
440	#107	—	73	1	no	—
441	#107	—	73	1	no	—
442	#107	—	73	1	no	—
443	#107	C₄×D₇₃	1	1	yes	characteristic
444	C₄⋊C₈	—	73	1	no	—
445	C₄⋊C₈	—	73	1	no	—
446	C₄⋊C₈	—	146	1	no	—
447	C₄⋊C₈	—	146	1	no	—
448	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
449	C₄⋊C₈	C₂²×D₇₃	1	1	yes	characteristic
450	#102	—	73	1	no	—
451	#102	—	73	1	no	—
452	#102	—	73	1	no	—
453	#102	—	73	1	no	—
454	#102	—	73	1	no	—
455	#102	—	73	1	no	—
456	#102	C₄×D₇₃	1	1	yes	characteristic
457	#102	C₄×D₇₃	1	1	yes	characteristic
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	146	1	no	—
461	C₂²⋊C₈	—	146	1	no	—
462	C₂²⋊C₈	—	146	1	no	—
463	C₂²⋊C₈	—	146	1	no	—
464	C₂²⋊C₈	—	146	1	no	—
465	C₂²⋊C₈	—	146	1	no	—
466	C₄×C₈	—	73	1	no	—
467	C₄×C₈	—	73	1	no	—
468	C₄×C₈	—	73	1	no	—
469	C₄×C₈	—	73	1	no	—
470	C₄×C₈	—	73	1	no	—
471	C₄×C₈	—	73	1	no	—
472	C₄×C₈	—	73	1	no	—
473	C₄×C₈	—	146	1	no	—
474	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
475	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
476	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
477	C₂⁴	—	146	1	no	—
478	C₂⁴	—	146	1	no	—
479	C₂×D₄	—	73	4	no	—
480	C₂×D₄	—	73	1	no	—
481	C₂×D₄	—	73	1	no	—
482	C₂×D₄	—	146	2	no	—
483	C₂×D₄	—	146	2	no	—
484	C₂×D₄	—	146	2	no	—
485	C₂×D₄	—	146	1	no	—
486	C₂×D₄	—	146	1	no	—
487	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
488	C₂×D₄	C₂×C₄×D₇₃	1	1	yes	characteristic
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	292	2	no	—
492	C₂²×C₄	—	292	2	no	—
493	C₂²×C₄	—	292	2	no	—
494	C₂²×C₄	—	292	2	no	—
495	C₂²×C₄	—	73	1	no	—
496	C₂²×C₄	—	73	1	no	—
497	C₂²×C₄	—	73	1	no	—
498	C₂²×C₄	—	146	1	no	—
499	C₂²×C₄	—	146	1	no	—
500	C₂²×C₄	—	146	1	no	—
501	C₂²×C₄	—	146	1	no	—
502	C₂²×C₄	—	146	1	no	—
503	C₂²×C₄	—	146	1	no	—
504	C₂²×C₄	—	146	1	no	—
505	C₂²×C₄	—	146	1	no	—
506	D₈	—	2	2	no	—
507	D₈	—	146	2	no	—
508	D₈	—	146	2	no	—
509	D₈	—	146	2	no	—
510	M₁₆	—	4	2	no	—
511	M₁₆	—	292	2	no	—
512	M₁₆	—	292	2	no	—
513	M₁₆	—	292	2	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	4	2	no	—
518	C₂×C₈	—	292	2	no	—
519	C₂×C₈	—	292	2	no	—
520	C₂×C₈	—	292	2	no	—
521	C₂×C₈	—	292	2	no	—
522	C₂×C₈	—	292	2	no	—
523	C₂×C₈	—	292	2	no	—
524	C₂×C₈	—	73	1	no	—
525	C₂×C₈	—	73	4	no	—
526	C₂×C₈	—	73	1	no	—
527	C₂×C₈	—	73	1	no	—
528	C₂×C₈	—	73	1	no	—
529	C₂×C₈	—	146	2	no	—
530	C₂×C₈	—	146	2	no	—
531	C₂×C₈	—	146	2	no	—
532	C₂×C₈	—	146	1	no	—
533	C₂×C₈	—	146	1	no	—
534	C₂×C₈	—	146	1	no	—
535	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
536	C₂×C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
537	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
538	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
539	C₄⋊C₄	—	73	1	no	—
540	C₄⋊C₄	—	73	1	no	—
541	C₄⋊C₄	—	146	1	no	—
542	C₄⋊C₄	—	146	1	no	—
543	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
544	C₄⋊C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	146	1	no	—
548	C₂²⋊C₄	—	146	1	no	—
549	C₂²⋊C₄	—	146	1	no	—
550	C₂²⋊C₄	—	146	1	no	—
551	C₂²⋊C₄	—	146	1	no	—
552	C₂²⋊C₄	—	146	1	no	—
553	C₄²	—	73	1	no	—
554	C₄²	—	73	1	no	—
555	C₄²	—	73	1	no	—
556	C₄²	C₂³×D₇₃	1	1	yes	characteristic
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	292	2	no	—
560	C₂³	—	292	2	no	—
561	C₂³	—	292	2	no	—
562	C₂³	—	292	2	no	—
563	C₂³	—	292	2	no	—
564	C₂³	—	73	1	no	—
565	C₂³	—	146	4	no	—
566	C₂³	—	146	1	no	—
567	C₂³	—	146	1	no	—
568	D₄	—	2	1	no	—
569	D₄	—	2	1	no	—
570	D₄	—	2	1	no	—
571	D₄	—	292	2	no	—
572	D₄	—	73	2	no	—
573	D₄	—	146	4	no	—
574	D₄	—	146	1	no	—
575	D₄	—	146	1	no	—
576	D₄	—	146	1	no	—
577	D₄	M₁₆×D₇₃	1	2	yes	complemented
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	292	2	no	—
585	C₂×C₄	—	292	2	no	—
586	C₂×C₄	—	292	2	no	—
587	C₂×C₄	—	292	2	no	—
588	C₂×C₄	—	292	2	no	—
589	C₂×C₄	—	292	2	no	—
590	C₂×C₄	—	292	1	no	—
591	C₂×C₄	—	292	1	no	—
592	C₂×C₄	—	292	1	no	—
593	C₂×C₄	—	292	1	no	—
594	C₂×C₄	—	73	1	no	—
595	C₂×C₄	—	73	1	no	—
596	C₂×C₄	—	73	2	no	—
597	C₂×C₄	—	73	2	no	—
598	C₂×C₄	—	73	2	no	—
599	C₂×C₄	—	73	2	no	—
600	C₂×C₄	—	73	1	no	—
601	C₂×C₄	—	146	2	no	—
602	C₂×C₄	—	146	1	no	—
603	C₂×C₄	—	146	1	no	—
604	C₂×C₄	C₂²×C₄×D₇₃	1	1	yes	characteristic
605	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
606	C₂×C₄	#41×D₇₃	1	1	yes	characteristic
607	C₈	—	2	1	no	—
608	C₈	—	2	1	no	—
609	C₈	—	2	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	1	no	—
613	C₈	—	292	1	no	—
614	C₈	—	292	1	no	—
615	C₈	—	292	1	no	—
616	C₈	—	73	2	no	—
617	C₈	—	146	1	no	—
618	C₈	—	146	1	no	—
619	C₈	—	146	1	no	—
620	C₈	D₈×D₇₃	1	2	yes	complemented
621	C₂²	—	2	2	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	1	no	—
625	C₂²	—	4	1	no	—
626	C₂²	—	4	1	no	—
627	C₂²	—	292	8	no	—
628	C₂²	—	292	1	no	—
629	C₂²	—	292	1	no	—
630	C₂²	—	292	1	no	—
631	C₂²	—	292	1	no	—
632	C₂²	—	292	1	no	—
633	C₂²	—	584	4	no	—
634	C₂²	—	73	2	no	—
635	C₂²	—	73	2	no	—
636	C₂²	—	73	2	no	—
637	C₂²	—	146	2	no	—
638	C₂²	C₄×D₄×D₇₃	1	1	yes	characteristic
639	C₄	—	2	1	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	292	1	no	—
643	C₄	—	292	1	no	—
644	C₄	—	73	2	no	—
645	C₄	—	73	2	no	—
646	C₄	—	146	1	no	—
647	C₄	C₂×M₁₆×D₇₃	1	1	yes	characteristic
648	C₄	#131×D₇₃	1	1	yes	characteristic
649	C₄	C₂×D₈×D₇₃	1	1	yes	characteristic
650	C₄	#135×D₇₃	1	1	yes	characteristic
651	C₂	—	4	2	no	—
652	C₂	—	8	1	no	—
653	C₂	—	292	2	no	—
654	C₂	—	584	1	no	—
655	C₂	—	73	4	no	—
656	C₂	#435×D₇₃	1	1	yes	characteristic
657	C₂	C₄×D₈×D₇₃	1	1	yes	characteristic
658	C₂	#444×D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂³×C₄
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1581	C₂
socle	C₂²×C₇₃	C₂×C₄×D₄
prime radical	C₂×D₈×D₇₃	C₄
cosocle	C₄²×C₇₃	C₂⁴
hypercenter	#1581	D₇₃
hypocenter	C₇₃	C₂×#1581
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1581

Complements

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

N	H ≅ G/N	type
2. #436×D₇₃	C₂	semidirect
3. C₈×D₄×D₇₃	C₂	semidirect
4. #22608763	C₂	semidirect
5. #22608762	C₂	semidirect
6. #22608761	C₂	semidirect
7. #22608760	C₂	semidirect
8. #22608759	C₂	semidirect
9. #22608758	C₂	semidirect
10. #22608757	C₂	semidirect
11. #335×D₇₃	C₂	semidirect
12. D₄⋊C₈×D₇₃	C₂	semidirect
13. D₄⋊C₈×D₇₃	C₂	semidirect
14. #322×D₇₃	C₂	semidirect
15. C₇₃×#1581	C₂	semidirect
28. #17988666	C₂²	semidirect
29. #17988665	C₂²	semidirect
30. #17988664	C₂²	semidirect
33. C₈×D₂₉₂	C₂²	semidirect
34. D₄×#10596831	C₂²	semidirect
35. #17988652	C₂²	semidirect
48. #17988340	C₂²	semidirect
49. #17988339	C₂²	semidirect
50. #17988339	C₂²	semidirect
51. #17988316	C₂²	semidirect
52. #17988316	C₂²	semidirect
53. D₄⋊#10596831	C₂²	semidirect
54. D₄⋊#10596831	C₂²	semidirect
55. #17988314	C₂²	semidirect
56. #17988314	C₂²	semidirect
57. #17988309	C₂²	semidirect
58. #17988309	C₂²	semidirect
59. #17988308	C₂²	semidirect
61. #436×C₇₃	C₂²	semidirect
62. C₈×D₄×C₇₃	C₂²	semidirect
63. #335×C₇₃	C₂²	semidirect
64. D₄⋊C₈×C₇₃	C₂²	semidirect
65. D₄⋊C₈×C₇₃	C₂²	semidirect
66. #322×C₇₃	C₂²	semidirect
156. D₄×D₇₃	M₁₆	semidirect
194. C₈×D₇₃	D₈	semidirect
241. D₄×C₇₃	C₂×M₁₆	semidirect
263. D₂₉₂	C₂×M₁₆	semidirect
283. C₈×C₇₃	C₂×D₈	semidirect
290. #10596831	C₂×D₈	semidirect
329. D₇₃	#1581	direct (N × H)
340. #1581	D₇₃	direct (N × H)
345. C₇₃	C₂×#1581	semidirect
364. #436	C₂×D₇₃	semidirect
370. C₈×D₄	C₂×D₇₃	semidirect
384. #335	C₂×D₇₃	semidirect
391. D₄⋊C₈	C₂×D₇₃	semidirect
392. D₄⋊C₈	C₂×D₇₃	semidirect
396. #322	C₂×D₇₃	semidirect
577. D₄	M₁₆×D₇₃	semidirect
620. C₈	D₈×D₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₇₃	2
#436×D₇₃	2
C₈×D₄×D₇₃	2
#22608763	2
#22608762	2
#22608761	2
#22608760	2
#22608759	2
#22608758	2
#22608757	2
#335×D₇₃	2
D₄⋊C₈×D₇₃	2
#322×D₇₃	2
C₇₃×#1581	2
C₂×#1581	73

Subgroups — #1581×D73 #33055476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1581×D₇₃ #33055476