Subgroups — #1720×D₈₉ #36542188

Order 22784.

850 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#498×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#494×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#487×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#486×D₈₉	C₂	1	1	yes	maximal, characteristic
5	#486×D₈₉	C₂	1	1	yes	maximal, characteristic
6	#486×D₈₉	C₂	1	1	yes	maximal, characteristic
7	#26019915	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019914	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019913	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019912	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019911	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019910	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019909	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1720	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	—	2	2	no	—
17	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
20	#127×D₈₉	C₂²	1	1	yes	characteristic
21	#19151996	C₂²	1	1	yes	characteristic, complemented
22	#19151995	—	2	2	no	—
23	#19151994	C₂²	1	1	yes	characteristic, complemented
24	#19151994	C₂²	1	1	yes	characteristic, complemented
25	#19151978	C₂²	1	1	yes	characteristic, complemented
26	#19151977	C₂²	1	1	yes	characteristic, complemented
27	#19151977	C₂²	1	1	yes	characteristic, complemented
28	#19151976	—	2	2	no	—
29	#19151950	C₂²	1	1	yes	characteristic, complemented
30	#19151949	C₂²	1	1	yes	characteristic, complemented
31	#19151948	C₂²	1	1	yes	characteristic, complemented
32	#19151947	—	2	2	no	—
33	#19151946	C₂²	1	1	yes	characteristic
34	#19151946	C₂²	1	1	yes	characteristic
35	#19151946	C₂²	1	1	yes	characteristic
36	#19151945	C₂²	1	1	yes	characteristic
37	#19151945	C₂²	1	1	yes	characteristic
38	#19151945	C₂²	1	1	yes	characteristic
39	#19151944	C₂²	1	1	yes	characteristic
40	#19151944	C₂²	1	1	yes	characteristic
41	#19151944	C₂²	1	1	yes	characteristic
42	#19151943	—	2	2	no	—
43	#19151943	—	2	2	no	—
44	#19151943	—	2	2	no	—
45	#106×D₈₉	—	2	2	no	—
46	#103×D₈₉	—	2	2	no	—
47	#102×D₈₉	—	2	2	no	—
48	#102×D₈₉	—	2	2	no	—
49	#102×D₈₉	—	2	2	no	—
50	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
51	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic, complemented
54	#19151320	C₂²	1	1	yes	characteristic, complemented
55	#19151319	C₂²	1	1	yes	characteristic, complemented
56	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#486×C₈₉	C₂²	1	1	yes	characteristic
60	#486×C₈₉	C₂²	1	1	yes	characteristic
61	#486×C₈₉	C₂²	1	1	yes	characteristic
62	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂×Q₈×D₈₉	—	2	1	no	—
64	C₂×Q₈×D₈₉	—	2	1	no	—
65	C₂×Q₈×D₈₉	—	2	1	no	—
66	C₂×D₄×D₈₉	—	2	1	no	—
67	C₂×D₄×D₈₉	—	2	1	no	—
68	C₂×D₄×D₈₉	—	2	1	no	—
69	C₂×Dic₃₅₆	—	2	2	no	—
70	C₂×#13083564	—	2	2	no	—
71	C₂×#13083564	—	2	2	no	—
72	Q₁₆×D₈₉	—	4	8	no	—
73	C₂×C₈×D₈₉	D₄	1	2	yes	—
74	C₂×C₈×D₈₉	D₄	1	2	yes	—
75	C₂×C₈×D₈₉	D₄	1	2	yes	—
76	#15668012	C₂³	1	1	yes	characteristic
77	#15668012	C₂³	1	1	yes	characteristic
78	#15668012	C₂³	1	1	yes	characteristic
79	#15668011	—	2	1	no	—
80	#15668011	—	2	1	no	—
81	#15668011	—	2	1	no	—
82	#15668011	—	2	1	no	—
83	#15668011	—	2	1	no	—
84	#15668011	—	2	1	no	—
85	#15668010	—	2	1	no	—
86	#15668010	—	2	1	no	—
87	#15668010	—	2	1	no	—
88	#15668009	C₂³	1	1	yes	characteristic
89	#15668008	—	2	1	no	—
90	#15668008	—	2	1	no	—
91	#15668008	—	2	1	no	—
92	C₄⋊C₄×D₈₉	—	2	1	no	—
93	C₄⋊C₄×D₈₉	—	2	1	no	—
94	C₄⋊C₄×D₈₉	—	2	1	no	—
95	C₄⋊C₄×D₈₉	—	2	1	no	—
96	C₄⋊C₄×D₈₉	—	2	1	no	—
97	C₄⋊C₄×D₈₉	—	2	1	no	—
98	C₄²×D₈₉	C₂³	1	1	yes	characteristic
99	#15667944	—	2	2	no	—
100	#15667943	—	2	2	no	—
101	#15667943	—	2	2	no	—
102	#15667937	—	2	2	no	—
103	#15667936	—	2	2	no	—
104	#15667935	—	2	2	no	—
105	#15667934	—	2	2	no	—
106	#15667934	—	2	2	no	—
107	#15667934	—	2	2	no	—
108	#15667933	—	2	2	no	—
109	#15667933	—	2	2	no	—
110	#15667933	—	2	2	no	—
111	#15667932	—	2	2	no	—
112	#15667932	—	2	2	no	—
113	#15667932	—	2	2	no	—
114	C₄×#10623494	C₂³	1	1	yes	characteristic
115	C₄×#10623494	C₂³	1	1	yes	characteristic
116	C₄×#10623494	C₂³	1	1	yes	characteristic
117	C₈×Dic₈₉	D₄	1	2	yes	—
118	C₈×Dic₈₉	D₄	1	2	yes	—
119	C₈×Dic₈₉	D₄	1	2	yes	—
120	C₂×Q₁₆×C₈₉	—	2	2	no	—
121	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
122	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
124	#127×C₈₉	C₂³	1	1	yes	characteristic
125	#106×C₈₉	—	2	2	no	—
126	#103×C₈₉	—	2	2	no	—
127	#102×C₈₉	—	2	2	no	—
128	#102×C₈₉	—	2	2	no	—
129	#102×C₈₉	—	2	2	no	—
130	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₂³×D₈₉	—	4	1	no	—
134	C₂×Dic₁₇₈	—	2	1	no	—
135	C₂×Dic₁₇₈	—	2	1	no	—
136	C₂×Dic₁₇₈	—	2	1	no	—
137	C₂×Dic₁₇₈	—	4	1	no	—
138	C₂×Dic₁₇₈	—	4	1	no	—
139	C₂×Dic₁₇₈	—	4	1	no	—
140	Q₈×D₈₉	—	4	4	no	—
141	Q₈×D₈₉	—	4	4	no	—
142	Q₈×D₈₉	—	4	4	no	—
143	C₂×D₃₅₆	—	2	1	no	—
144	C₂×D₃₅₆	—	2	1	no	—
145	C₂×D₃₅₆	—	2	1	no	—
146	C₂×C₂²⋊D₈₉	—	4	1	no	—
147	C₂×C₂²⋊D₈₉	—	4	1	no	—
148	C₂×C₂²⋊D₈₉	—	4	1	no	—
149	D₄×D₈₉	—	4	4	no	—
150	D₄×D₈₉	—	4	4	no	—
151	D₄×D₈₉	—	4	4	no	—
152	C₂×C₄×D₈₉	—	4	1	no	—
153	C₂×C₄×D₈₉	—	4	1	no	—
154	C₂×C₄×D₈₉	—	4	1	no	—
155	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
158	Dic₃₅₆	—	4	4	no	—
159	#13083564	—	4	4	no	—
160	#13083564	—	4	4	no	—
161	C₂×#10623494	C₂×D₄	1	2	yes	—
162	C₂×#10623494	C₂×D₄	1	2	yes	—
163	C₂×#10623494	C₂×D₄	1	2	yes	—
164	C₈×D₈₉	—	2	4	no	—
165	C₈×D₈₉	—	2	4	no	—
166	C₈×D₈₉	—	2	4	no	—
167	C₄⋊Dic₈₉	—	2	1	no	—
168	C₄⋊Dic₈₉	—	2	1	no	—
169	C₄⋊Dic₈₉	—	2	1	no	—
170	C₄⋊Dic₈₉	—	2	1	no	—
171	C₄⋊Dic₈₉	—	2	1	no	—
172	C₄⋊Dic₈₉	—	2	1	no	—
173	#13083553	—	4	1	no	—
174	#13083553	—	4	1	no	—
175	#13083553	—	4	1	no	—
176	#13083553	—	4	1	no	—
177	#13083553	—	4	1	no	—
178	#13083553	—	4	1	no	—
179	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
180	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
181	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂×Q₈×C₈₉	—	2	1	no	—
183	C₂×Q₈×C₈₉	—	2	1	no	—
184	C₂×Q₈×C₈₉	—	2	1	no	—
185	C₂×D₄×C₈₉	—	2	1	no	—
186	C₂×D₄×C₈₉	—	2	1	no	—
187	C₂×D₄×C₈₉	—	2	1	no	—
188	Q₁₆×C₈₉	—	4	4	no	—
189	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₄⋊C₄×C₈₉	—	2	1	no	—
198	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
199	C₂³×C₈₉	—	4	1	no	—
200	C₂²×D₈₉	—	4	1	no	—
201	C₂²×D₈₉	—	8	2	no	—
202	C₂²×D₈₉	—	8	2	no	—
203	C₂²×D₈₉	—	8	2	no	—
204	C₂²×D₈₉	#127	1	1	yes	characteristic
205	Q₈×C₈₉	—	4	2	no	—
206	Q₈×C₈₉	—	4	2	no	—
207	Q₈×C₈₉	—	4	2	no	—
208	D₄×C₈₉	—	4	2	no	—
209	D₄×C₈₉	—	4	2	no	—
210	D₄×C₈₉	—	4	2	no	—
211	C₂×C₄×C₈₉	—	4	1	no	—
212	C₂×C₄×C₈₉	—	4	1	no	—
213	C₂×C₄×C₈₉	—	4	1	no	—
214	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
217	C₂²⋊D₈₉	—	8	2	no	—
218	C₂²⋊D₈₉	—	8	2	no	—
219	C₂²⋊D₈₉	—	8	2	no	—
220	C₂×Dic₈₉	—	4	1	no	—
221	C₂×Dic₈₉	—	4	1	no	—
222	C₂×Dic₈₉	—	4	1	no	—
223	C₂×Dic₈₉	#127	1	1	yes	characteristic
224	C₂×Dic₈₉	#127	1	1	yes	characteristic
225	C₂×Dic₈₉	#127	1	1	yes	characteristic
226	D₃₅₆	—	4	2	no	—
227	D₃₅₆	—	4	2	no	—
228	D₃₅₆	—	4	2	no	—
229	C₄×D₈₉	—	8	2	no	—
230	C₄×D₈₉	—	8	2	no	—
231	C₄×D₈₉	—	8	2	no	—
232	C₄×D₈₉	#135	1	4	yes	—
233	C₄×D₈₉	AGL(1,ℤ/8)	1	4	yes	—
234	C₄×D₈₉	#137	1	4	yes	—
235	Dic₁₇₈	—	4	2	no	—
236	Dic₁₇₈	—	4	2	no	—
237	Dic₁₇₈	—	4	2	no	—
238	Dic₁₇₈	—	8	2	no	—
239	Dic₁₇₈	—	8	2	no	—
240	Dic₁₇₈	—	8	2	no	—
241	C₈×C₈₉	—	2	2	no	—
242	C₈×C₈₉	—	2	2	no	—
243	C₈×C₈₉	—	2	2	no	—
244	#10623494	—	2	2	no	—
245	#10623494	—	2	2	no	—
246	#10623494	—	2	2	no	—
247	C₂²×C₈₉	—	8	1	no	—
248	C₂²×C₈₉	—	8	1	no	—
249	C₂²×C₈₉	—	8	1	no	—
250	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
251	C₂×D₈₉	—	8	1	no	—
252	C₂×D₈₉	—	8	1	no	—
253	C₂×D₈₉	—	8	1	no	—
254	C₂×D₈₉	—	16	4	no	—
255	C₂×D₈₉	#495	1	2	yes	—
256	C₂×D₈₉	#496	1	2	yes	—
257	C₂×D₈₉	#497	1	2	yes	—
258	C₄×C₈₉	—	8	1	no	—
259	C₄×C₈₉	—	8	1	no	—
260	C₄×C₈₉	—	8	1	no	—
261	C₄×C₈₉	C₂×#135	1	2	yes	—
262	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
263	C₄×C₈₉	C₂×#137	1	2	yes	—
264	Dic₈₉	—	8	1	no	—
265	Dic₈₉	—	8	1	no	—
266	Dic₈₉	—	8	1	no	—
267	Dic₈₉	#495	1	2	yes	—
268	Dic₈₉	#496	1	2	yes	—
269	Dic₈₉	#497	1	2	yes	—
270	C₂×#1720	—	89	1	no	maximal, Sylow
271	C₂×C₈₉	—	16	1	no	—
272	C₂×C₈₉	C₂×#495	1	1	yes	characteristic
273	C₂×C₈₉	C₂×#496	1	1	yes	characteristic
274	C₂×C₈₉	C₂×#497	1	1	yes	characteristic
275	D₈₉	—	16	1	no	—
276	D₈₉	#1720	1	4	yes	direct product factor
277	C₂×#498	—	89	1	no	—
278	C₂×#494	—	89	1	no	—
279	C₂×#487	—	89	1	no	—
280	C₂×#486	—	89	1	no	—
281	C₂×#486	—	89	1	no	—
282	C₂×#486	—	89	1	no	—
283	#1720	—	89	1	no	—
284	#1720	—	89	1	no	—
285	#1720	—	89	1	no	—
286	#1720	—	89	1	no	—
287	#1720	—	89	1	no	—
288	#1720	—	89	1	no	—
289	#1720	—	89	1	no	—
290	#1720	D₈₉	1	1	yes	characteristic, direct product factor
291	C₂×#322	—	89	1	no	—
292	C₈₉	C₂×#1720	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₁₆	—	178	2	no	—
294	C₂×C₄⋊Q₈	—	89	1	no	—
295	C₂×C₄⋊Q₈	—	89	1	no	—
296	C₂×C₄⋊Q₈	—	89	1	no	—
297	C₂×#127	—	89	1	no	—
298	#498	—	89	1	no	—
299	#498	—	89	1	no	—
300	#498	—	89	1	no	—
301	#498	—	178	2	no	—
302	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
303	#494	—	89	1	no	—
304	#494	—	89	1	no	—
305	#494	—	89	1	no	—
306	#494	—	178	2	no	—
307	#494	C₂×D₈₉	1	1	yes	characteristic, complemented
308	#487	—	89	1	no	—
309	#487	—	89	1	no	—
310	#487	—	89	1	no	—
311	#487	—	178	2	no	—
312	#487	C₂×D₈₉	1	1	yes	characteristic, complemented
313	#486	—	89	1	no	—
314	#486	—	89	1	no	—
315	#486	—	89	1	no	—
316	#486	—	89	1	no	—
317	#486	—	89	1	no	—
318	#486	—	89	1	no	—
319	#486	—	89	1	no	—
320	#486	—	89	1	no	—
321	#486	—	89	1	no	—
322	#486	—	178	2	no	—
323	#486	—	178	2	no	—
324	#486	—	178	2	no	—
325	#486	C₂×D₈₉	1	1	yes	characteristic
326	#486	C₂×D₈₉	1	1	yes	characteristic
327	#486	C₂×D₈₉	1	1	yes	characteristic
328	C₂×#106	—	178	2	no	—
329	C₂×#103	—	178	2	no	—
330	C₂×#102	—	178	2	no	—
331	C₂×#102	—	178	2	no	—
332	C₂×#102	—	178	2	no	—
333	C₂×C₄×C₈	—	89	1	no	—
334	C₂×C₄×C₈	—	89	1	no	—
335	C₂×C₄×C₈	—	89	1	no	—
336	#322	—	89	1	no	—
337	#322	—	89	1	no	—
338	#322	—	89	1	no	—
339	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
340	C₂²×Q₈	—	178	1	no	—
341	C₂²×Q₈	—	178	1	no	—
342	C₂²×Q₈	—	178	1	no	—
343	C₂²×D₄	—	178	1	no	—
344	C₂²×D₄	—	178	1	no	—
345	C₂²×D₄	—	178	1	no	—
346	C₂×Q₁₆	—	2	2	no	—
347	C₂×Q₁₆	—	356	8	no	—
348	C₂×Q₁₆	—	178	2	no	—
349	C₂×Q₁₆	—	178	2	no	—
350	C₂×Q₁₆	—	178	2	no	—
351	C₂²×C₈	—	89	2	no	—
352	C₂²×C₈	—	89	2	no	—
353	C₂²×C₈	—	89	2	no	—
354	C₄⋊Q₈	—	89	1	no	—
355	C₄⋊Q₈	—	89	1	no	—
356	C₄⋊Q₈	—	89	1	no	—
357	C₄⋊Q₈	—	178	1	no	—
358	C₄⋊Q₈	—	178	1	no	—
359	C₄⋊Q₈	—	178	1	no	—
360	C₄⋊Q₈	—	178	1	no	—
361	C₄⋊Q₈	—	178	1	no	—
362	C₄⋊Q₈	—	178	1	no	—
363	C₄⋊Q₈	—	178	1	no	—
364	C₄⋊Q₈	—	178	1	no	—
365	C₄⋊Q₈	—	178	1	no	—
366	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
367	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
368	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
369	#127	—	89	1	no	—
370	#127	—	178	1	no	—
371	#127	—	178	1	no	—
372	#127	—	178	1	no	—
373	#127	C₂²×D₈₉	1	1	yes	characteristic
374	C₂×C₄⋊C₄	—	178	1	no	—
375	C₂×C₄⋊C₄	—	178	1	no	—
376	C₂×C₄⋊C₄	—	178	1	no	—
377	C₂×C₄⋊C₄	—	178	1	no	—
378	C₂×C₄⋊C₄	—	178	1	no	—
379	C₂×C₄⋊C₄	—	178	1	no	—
380	C₂×C₄²	—	89	1	no	—
381	#106	—	2	2	no	—
382	#106	—	178	2	no	—
383	#106	—	178	2	no	—
384	#106	—	178	2	no	—
385	#103	—	2	2	no	—
386	#103	—	178	2	no	—
387	#103	—	178	2	no	—
388	#103	—	178	2	no	—
389	#102	—	2	2	no	—
390	#102	—	2	2	no	—
391	#102	—	2	2	no	—
392	#102	—	178	2	no	—
393	#102	—	178	2	no	—
394	#102	—	178	2	no	—
395	#102	—	178	2	no	—
396	#102	—	178	2	no	—
397	#102	—	178	2	no	—
398	#102	—	178	2	no	—
399	#102	—	178	2	no	—
400	#102	—	178	2	no	—
401	C₄×C₈	—	89	2	no	—
402	C₄×C₈	—	89	2	no	—
403	C₄×C₈	—	89	2	no	—
404	C₄×C₈	—	89	1	no	—
405	C₄×C₈	—	89	1	no	—
406	C₄×C₈	—	89	1	no	—
407	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
408	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
409	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
410	C₂⁴	—	356	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	356	1	no	—
415	C₂×Q₈	—	356	1	no	—
416	C₂×Q₈	—	356	1	no	—
417	C₂×Q₈	—	356	4	no	—
418	C₂×Q₈	—	356	4	no	—
419	C₂×Q₈	—	356	4	no	—
420	C₂×Q₈	—	178	1	no	—
421	C₂×Q₈	—	178	1	no	—
422	C₂×Q₈	—	178	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	356	4	no	—
427	C₂×D₄	—	356	4	no	—
428	C₂×D₄	—	356	4	no	—
429	C₂×D₄	—	356	1	no	—
430	C₂×D₄	—	356	1	no	—
431	C₂×D₄	—	356	1	no	—
432	C₂×D₄	—	178	1	no	—
433	C₂×D₄	—	178	1	no	—
434	C₂×D₄	—	178	1	no	—
435	C₂²×C₄	—	89	1	no	—
436	C₂²×C₄	—	89	1	no	—
437	C₂²×C₄	—	89	1	no	—
438	C₂²×C₄	—	356	1	no	—
439	C₂²×C₄	—	356	1	no	—
440	C₂²×C₄	—	356	1	no	—
441	Q₁₆	—	4	4	no	—
442	Q₁₆	—	356	4	no	—
443	Q₁₆	—	356	4	no	—
444	Q₁₆	—	356	4	no	—
445	C₂×C₈	—	89	2	no	—
446	C₂×C₈	—	89	2	no	—
447	C₂×C₈	—	89	2	no	—
448	C₂×C₈	—	178	4	no	—
449	C₂×C₈	—	178	4	no	—
450	C₂×C₈	—	178	4	no	—
451	C₂×C₈	D₄×D₈₉	1	2	yes	—
452	C₂×C₈	D₄×D₈₉	1	2	yes	—
453	C₂×C₈	D₄×D₈₉	1	2	yes	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	356	1	no	—
461	C₄⋊C₄	—	356	1	no	—
462	C₄⋊C₄	—	356	1	no	—
463	C₄⋊C₄	—	356	1	no	—
464	C₄⋊C₄	—	356	1	no	—
465	C₄⋊C₄	—	356	1	no	—
466	C₄⋊C₄	—	178	1	no	—
467	C₄⋊C₄	—	178	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	—	178	1	no	—
470	C₄⋊C₄	—	178	1	no	—
471	C₄⋊C₄	—	178	1	no	—
472	C₄²	—	89	1	no	—
473	C₄²	—	89	1	no	—
474	C₄²	—	89	1	no	—
475	C₄²	C₂³×D₈₉	1	1	yes	characteristic
476	C₂³	—	4	1	no	—
477	C₂³	—	89	1	no	—
478	C₂³	—	356	1	no	—
479	C₂³	—	712	2	no	—
480	C₂³	—	712	2	no	—
481	C₂³	—	712	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	Q₈	—	356	2	no	—
486	Q₈	—	356	2	no	—
487	Q₈	—	356	2	no	—
488	Q₈	—	712	2	no	—
489	Q₈	—	712	2	no	—
490	Q₈	—	712	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	4	2	no	—
494	D₄	—	356	2	no	—
495	D₄	—	356	2	no	—
496	D₄	—	356	2	no	—
497	D₄	—	712	2	no	—
498	D₄	—	712	2	no	—
499	D₄	—	712	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	89	1	no	—
504	C₂×C₄	—	89	1	no	—
505	C₂×C₄	—	89	1	no	—
506	C₂×C₄	—	89	4	no	—
507	C₂×C₄	—	89	4	no	—
508	C₂×C₄	—	89	4	no	—
509	C₂×C₄	—	356	1	no	—
510	C₂×C₄	—	356	1	no	—
511	C₂×C₄	—	356	1	no	—
512	C₂×C₄	—	712	2	no	—
513	C₂×C₄	—	712	2	no	—
514	C₂×C₄	—	712	2	no	—
515	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
516	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
518	C₈	—	2	2	no	—
519	C₈	—	2	2	no	—
520	C₈	—	2	2	no	—
521	C₈	—	178	2	no	—
522	C₈	—	178	2	no	—
523	C₈	—	178	2	no	—
524	C₂²	—	8	1	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	89	2	no	—
528	C₂²	—	89	2	no	—
529	C₂²	—	89	2	no	—
530	C₂²	—	1424	4	no	—
531	C₂²	—	712	1	no	—
532	C₂²	—	712	1	no	—
533	C₂²	—	712	1	no	—
534	C₂²	#127×D₈₉	1	1	yes	characteristic
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	—	89	2	no	—
539	C₄	—	89	2	no	—
540	C₄	—	89	2	no	—
541	C₄	—	712	1	no	—
542	C₄	—	712	1	no	—
543	C₄	—	712	1	no	—
544	C₄	#135×D₈₉	1	2	yes	—
545	C₄	AGL(1,ℤ/8)×D₈₉	1	2	yes	—
546	C₄	#137×D₈₉	1	2	yes	—
547	C₂	—	16	1	no	—
548	C₂	—	89	4	no	—
549	C₂	—	1424	1	no	—
550	C₂	#495×D₈₉	1	1	yes	characteristic
551	C₂	#496×D₈₉	1	1	yes	characteristic
552	C₂	#497×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1720	C₂
socle	C₂²×C₈₉	C₂×#127
prime radical	#127×D₈₉	C₂²
hypercenter	#1720	D₈₉
hypocenter	C₈₉	C₂×#1720
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1720

Complements

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

N	H ≅ G/N	type
1. #498×D₈₉	C₂	semidirect
2. #494×D₈₉	C₂	semidirect
3. #487×D₈₉	C₂	semidirect
7. #26019915	C₂	semidirect
8. #26019914	C₂	semidirect
9. #26019913	C₂	semidirect
10. #26019912	C₂	semidirect
11. #26019911	C₂	semidirect
12. #26019910	C₂	semidirect
13. #26019909	C₂	semidirect
14. #322×D₈₉	C₂	semidirect
15. C₈₉×#1720	C₂	semidirect
21. #19151996	C₂²	semidirect
23. #19151994	C₂²	semidirect
24. #19151994	C₂²	semidirect
25. #19151978	C₂²	semidirect
26. #19151977	C₂²	semidirect
27. #19151977	C₂²	semidirect
29. #19151950	C₂²	semidirect
30. #19151949	C₂²	semidirect
31. #19151948	C₂²	semidirect
53. #19151320	C₂²	semidirect
54. #19151320	C₂²	semidirect
55. #19151319	C₂²	semidirect
56. #498×C₈₉	C₂²	semidirect
57. #494×C₈₉	C₂²	semidirect
58. #487×C₈₉	C₂²	semidirect
62. #322×C₈₉	C₂²	semidirect
276. D₈₉	#1720	direct (N × H)
290. #1720	D₈₉	direct (N × H)
292. C₈₉	C₂×#1720	semidirect
302. #498	C₂×D₈₉	semidirect
307. #494	C₂×D₈₉	semidirect
312. #487	C₂×D₈₉	semidirect
339. #322	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#498×D₈₉	2
#494×D₈₉	2
#487×D₈₉	2
#486×D₈₉	2
#26019915	2
#26019914	2
#26019913	2
#26019912	2
#26019911	2
#26019910	2
#26019909	2
#322×D₈₉	2
C₈₉×#1720	2
C₂×#1720	89

Subgroups — #1720×D89 #36542188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1720×D₈₉ #36542188