Subgroups — #2220×D₈₉ #36708882

Order 22784.

734 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#467×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#466×D₈₉	C₂	1	1	yes	maximal, characteristic
5	#26022368	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022367	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022366	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022365	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022364	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022363	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022362	C₂	1	1	yes	maximal, characteristic, complemented
12	#366×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#358×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#357×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2220	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	C₂²	1	1	yes	characteristic
17	C₂×D₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
19	C₂²⋊Q₈×D₈₉	—	2	1	no	—
20	#121×D₈₉	—	2	1	no	—
21	C₂×#15667957	C₂²	1	1	yes	characteristic, complemented
22	C₂×#15667956	C₂²	1	1	yes	characteristic, complemented
23	C₂×#15667955	C₂²	1	1	yes	characteristic, complemented
24	SD₃₂×D₈₉	—	2	4	no	—
25	C₂×#15667952	C₂²	1	1	yes	characteristic, complemented
26	C₂×#15667951	C₂²	1	1	yes	characteristic, complemented
27	C₂×#15667951	C₂²	1	1	yes	characteristic, complemented
28	M₃₂×D₈₉	—	2	4	no	—
29	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
31	#19151840	C₂²	1	1	yes	characteristic, complemented
32	#19151839	C₂²	1	1	yes	characteristic, complemented
33	#19151838	—	2	1	no	—
34	#19151837	—	2	1	no	—
35	#19151836	C₂²	1	1	yes	characteristic, complemented
36	#19151835	C₂²	1	1	yes	characteristic
37	#19151834	C₂²	1	1	yes	characteristic
38	#19151833	—	2	1	no	—
39	#19151832	—	2	1	no	—
40	#19151831	C₂²	1	1	yes	characteristic
41	#107×D₈₉	C₂²	1	1	yes	characteristic
42	#107×D₈₉	C₂²	1	1	yes	characteristic
43	#103×D₈₉	—	2	1	no	—
44	#102×D₈₉	—	2	1	no	—
45	#19151424	C₂²	1	1	yes	characteristic, complemented
46	#19151423	C₂²	1	1	yes	characteristic, complemented
47	#19151423	C₂²	1	1	yes	characteristic, complemented
48	#19151403	C₂²	1	1	yes	characteristic, complemented
49	#19151402	C₂²	1	1	yes	characteristic, complemented
50	#19151401	C₂²	1	1	yes	characteristic, complemented
51	#19151400	C₂²	1	1	yes	characteristic, complemented
52	#19151399	C₂²	1	1	yes	characteristic, complemented
53	#19151398	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₃₂×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#467×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#466×C₈₉	C₂²	1	1	yes	characteristic
58	#366×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#358×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#357×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₂×Q₈×D₈₉	—	2	1	no	—
62	C₂×D₄×D₈₉	—	2	1	no	—
63	C₂×D₄×D₈₉	—	4	1	no	—
64	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
65	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
66	C₂×#13083564	—	2	1	no	—
67	Q₁₆×D₈₉	—	2	2	no	—
68	Q₁₆×D₈₉	—	2	2	no	—
69	C₂×D₇₁₂	C₂³	1	1	yes	characteristic
70	C₂×#13083559	—	2	1	no	—
71	D₈×D₈₉	—	2	2	no	—
72	D₈×D₈₉	—	2	2	no	—
73	C₂²×#10623494	D₄	1	1	yes	characteristic
74	C₂×C₈×D₈₉	—	2	2	no	—
75	C₂×C₈×D₈₉	—	2	2	no	—
76	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
77	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
78	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
80	#15667992	—	2	1	no	—
81	#15667991	—	2	1	no	—
82	#15667990	—	4	1	no	—
83	#15667989	—	4	1	no	—
84	#15667988	—	2	1	no	—
85	#15667987	—	2	1	no	—
86	#15667986	—	2	1	no	—
87	#15667985	—	4	1	no	—
88	#15667984	—	4	1	no	—
89	#15667983	—	2	1	no	—
90	C₄⋊C₄×D₈₉	—	2	1	no	—
91	C₄⋊C₄×D₈₉	—	2	1	no	—
92	C₄⋊C₄×D₈₉	—	4	1	no	—
93	C₂²⋊C₄×D₈₉	—	4	1	no	—
94	C₂²⋊C₄×D₈₉	—	4	1	no	—
95	#15667957	—	2	2	no	—
96	#15667956	—	2	2	no	—
97	#15667955	—	2	2	no	—
98	#15667952	—	2	2	no	—
99	#15667951	—	2	2	no	—
100	#15667951	—	2	2	no	—
101	C₂×#13083549	C₂³	1	1	yes	characteristic
102	C₂×#13083549	C₂³	1	1	yes	characteristic
103	C₁₆×D₈₉	—	2	2	no	—
104	C₁₆×D₈₉	D₄	1	4	yes	complemented
105	#15667946	C₂³	1	1	yes	characteristic
106	#15667946	C₂³	1	1	yes	characteristic
107	#15667945	—	2	1	no	—
108	#15667945	—	2	1	no	—
109	#15667937	—	2	1	no	—
110	#15667936	—	2	1	no	—
111	#15667935	—	2	1	no	—
112	#15667934	—	2	1	no	—
113	#15667933	—	2	1	no	—
114	#15667932	—	2	1	no	—
115	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²⋊Q₈×C₈₉	—	2	1	no	—
119	#121×C₈₉	—	2	1	no	—
120	SD₃₂×C₈₉	—	2	2	no	—
121	M₃₂×C₈₉	—	2	2	no	—
122	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
124	#107×C₈₉	C₂³	1	1	yes	characteristic
125	#107×C₈₉	C₂³	1	1	yes	characteristic
126	#103×C₈₉	—	2	1	no	—
127	#102×C₈₉	—	2	1	no	—
128	C₂³×D₈₉	—	4	1	no	—
129	C₂³×D₈₉	D₈	1	1	yes	characteristic
130	C₂×Dic₁₇₈	—	2	1	no	—
131	C₂×Dic₁₇₈	—	4	1	no	—
132	Q₈×D₈₉	—	4	2	no	—
133	Q₈×D₈₉	—	4	2	no	—
134	C₂×D₃₅₆	—	2	1	no	—
135	C₂×D₃₅₆	—	4	1	no	—
136	C₂×C₂²⋊D₈₉	—	4	1	no	—
137	C₂×C₂²⋊D₈₉	—	4	1	no	—
138	C₂×C₂²⋊D₈₉	—	4	1	no	—
139	D₄×D₈₉	—	4	2	no	—
140	D₄×D₈₉	—	4	2	no	—
141	D₄×D₈₉	—	8	4	no	—
142	C₂²×Dic₈₉	D₈	1	1	yes	characteristic
143	C₂×C₄×D₈₉	—	2	2	no	—
144	C₂×C₄×D₈₉	—	2	2	no	—
145	C₂×C₄×D₈₉	—	4	1	no	—
146	C₂×C₄×D₈₉	—	4	1	no	—
147	C₂×C₄×D₈₉	—	4	1	no	—
148	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
149	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
152	Dic₃₅₆	—	2	1	no	—
153	Dic₃₅₆	—	2	1	no	—
154	#13083564	—	4	2	no	—
155	D₇₁₂	—	2	1	no	—
156	D₇₁₂	—	2	1	no	—
157	#13083559	—	4	2	no	—
158	C₂×#10623494	—	2	2	no	—
159	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
160	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
161	C₈×D₈₉	—	2	2	no	—
162	C₈×D₈₉	—	2	1	no	—
163	C₈×D₈₉	—	2	1	no	—
164	C₈×D₈₉	—	2	2	no	—
165	C₈×D₈₉	C₂×D₄	1	2	yes	—
166	C₈×D₈₉	#41	1	2	yes	—
167	C₄⋊Dic₈₉	—	2	1	no	—
168	C₄⋊Dic₈₉	—	2	1	no	—
169	C₄⋊Dic₈₉	—	4	1	no	—
170	#13083553	—	4	1	no	—
171	#13083553	—	4	1	no	—
172	#13083553	—	4	1	no	—
173	#13083553	—	4	1	no	—
174	C₂²⋊Dic₈₉	—	4	1	no	—
175	C₂²⋊Dic₈₉	—	4	1	no	—
176	#13083551	—	4	1	no	—
177	#13083551	—	4	1	no	—
178	#13083551	—	4	1	no	—
179	#13083551	—	4	1	no	—
180	#13083549	—	2	1	no	—
181	#13083549	C₂×D₄	1	2	yes	complemented
182	C₂×Q₈×C₈₉	—	2	1	no	—
183	C₂×D₄×C₈₉	—	2	1	no	—
184	C₂×D₄×C₈₉	—	4	1	no	—
185	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
186	Q₁₆×C₈₉	—	2	1	no	—
187	Q₁₆×C₈₉	—	2	1	no	—
188	D₈×C₈₉	—	2	1	no	—
189	D₈×C₈₉	—	2	1	no	—
190	C₂×C₈×C₈₉	—	2	1	no	—
191	C₂×C₈×C₈₉	—	2	1	no	—
192	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
193	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	4	1	no	—
197	C₂²⋊C₄×C₈₉	—	4	1	no	—
198	C₂²⋊C₄×C₈₉	—	4	1	no	—
199	C₁₆×C₈₉	—	2	1	no	—
200	C₁₆×C₈₉	C₂×D₄	1	2	yes	complemented
201	C₂³×C₈₉	—	4	1	no	—
202	C₂³×C₈₉	C₂×D₈	1	1	yes	characteristic
203	C₂²×D₈₉	—	2	2	no	—
204	C₂²×D₈₉	—	2	2	no	—
205	C₂²×D₈₉	—	2	2	no	—
206	C₂²×D₈₉	—	4	1	no	—
207	C₂²×D₈₉	—	8	2	no	—
208	C₂²×D₈₉	—	8	2	no	—
209	C₂²×D₈₉	—	8	2	no	—
210	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
211	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
212	Q₈×C₈₉	—	4	1	no	—
213	Q₈×C₈₉	—	4	1	no	—
214	D₄×C₈₉	—	4	1	no	—
215	D₄×C₈₉	—	4	1	no	—
216	D₄×C₈₉	—	8	2	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	4	1	no	—
220	C₂×C₄×C₈₉	—	4	1	no	—
221	C₂×C₄×C₈₉	—	4	1	no	—
222	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
224	C₂²⋊D₈₉	—	8	2	no	—
225	C₂²⋊D₈₉	—	8	2	no	—
226	C₂²⋊D₈₉	—	8	2	no	—
227	C₂×Dic₈₉	—	2	2	no	—
228	C₂×Dic₈₉	—	4	1	no	—
229	C₂×Dic₈₉	—	4	1	no	—
230	C₂×Dic₈₉	—	4	1	no	—
231	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
232	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
233	D₃₅₆	—	4	1	no	—
234	D₃₅₆	—	4	1	no	—
235	D₃₅₆	—	8	2	no	—
236	C₄×D₈₉	—	2	2	no	—
237	C₄×D₈₉	—	2	1	no	—
238	C₄×D₈₉	—	2	1	no	—
239	C₄×D₈₉	—	2	2	no	—
240	C₄×D₈₉	—	8	2	no	—
241	C₄×D₈₉	—	8	2	no	—
242	C₄×D₈₉	—	8	2	no	—
243	C₄×D₈₉	#121	1	2	yes	—
244	C₄×D₈₉	#135	1	2	yes	—
245	Dic₁₇₈	—	4	1	no	—
246	Dic₁₇₈	—	4	1	no	—
247	Dic₁₇₈	—	8	2	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
250	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
251	#10623494	—	2	1	no	—
252	#10623494	#121	1	2	yes	—
253	C₂²×C₈₉	—	2	1	no	—
254	C₂²×C₈₉	—	2	1	no	—
255	C₂²×C₈₉	—	2	1	no	—
256	C₂²×C₈₉	—	8	1	no	—
257	C₂²×C₈₉	—	8	1	no	—
258	C₂²×C₈₉	—	8	1	no	—
259	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
260	C₂×D₈₉	—	2	1	no	—
261	C₂×D₈₉	—	2	1	no	—
262	C₂×D₈₉	—	2	1	no	—
263	C₂×D₈₉	—	4	4	no	—
264	C₂×D₈₉	—	8	1	no	—
265	C₂×D₈₉	—	8	1	no	—
266	C₂×D₈₉	—	8	1	no	—
267	C₂×D₈₉	—	16	4	no	—
268	C₂×D₈₉	#466	1	2	yes	—
269	C₂×D₈₉	#509	1	2	yes	—
270	C₂×D₈₉	#510	1	2	yes	—
271	C₄×C₈₉	—	2	1	no	—
272	C₄×C₈₉	—	8	1	no	—
273	C₄×C₈₉	—	8	1	no	—
274	C₄×C₈₉	—	8	1	no	—
275	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
276	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
277	Dic₈₉	—	2	1	no	—
278	Dic₈₉	—	8	1	no	—
279	Dic₈₉	—	8	1	no	—
280	Dic₈₉	—	8	1	no	—
281	Dic₈₉	#466	1	2	yes	—
282	C₂×#2220	—	89	1	no	maximal, Sylow
283	C₂×C₈₉	—	4	1	no	—
284	C₂×C₈₉	—	16	1	no	—
285	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
286	C₂×C₈₉	C₂×#509	1	1	yes	characteristic
287	C₂×C₈₉	C₂×#510	1	1	yes	characteristic
288	D₈₉	—	4	1	no	—
289	D₈₉	—	16	1	no	—
290	D₈₉	#2220	1	4	yes	direct product factor
291	C₂²×SD₃₂	—	89	1	no	—
292	C₂²×M₃₂	—	89	1	no	—
293	C₂×#467	—	89	1	no	—
294	C₂×#466	—	89	1	no	—
295	#2220	—	89	1	no	—
296	#2220	—	89	1	no	—
297	#2220	—	89	1	no	—
298	#2220	—	89	1	no	—
299	#2220	—	89	1	no	—
300	#2220	—	89	1	no	—
301	#2220	—	89	1	no	—
302	#2220	D₈₉	1	1	yes	characteristic, direct product factor
303	C₂×#366	—	89	1	no	—
304	C₂×#358	—	89	1	no	—
305	C₂×#357	—	89	1	no	—
306	C₈₉	C₂×#2220	1	1	yes	characteristic, complemented, Sylow
307	C₂²×Q₁₆	—	89	1	no	—
308	C₂²×D₈	—	89	1	no	—
309	C₂³×C₈	—	89	1	no	—
310	C₂×C₂²⋊Q₈	—	178	1	no	—
311	C₂×#121	—	178	1	no	—
312	C₂×SD₃₂	—	89	1	no	—
313	C₂×SD₃₂	—	89	1	no	—
314	C₂×SD₃₂	—	89	1	no	—
315	C₂×SD₃₂	—	178	4	no	—
316	C₂×SD₃₂	C₂×D₈₉	1	1	yes	characteristic, complemented
317	C₂×M₃₂	—	89	1	no	—
318	C₂×M₃₂	—	89	1	no	—
319	C₂×M₃₂	—	89	1	no	—
320	C₂×M₃₂	—	178	4	no	—
321	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic, complemented
322	C₂²×C₁₆	—	89	1	no	—
323	C₂²×C₁₆	—	89	1	no	—
324	#467	—	89	1	no	—
325	#467	—	89	1	no	—
326	#467	—	89	1	no	—
327	#467	—	178	1	no	—
328	#467	—	178	1	no	—
329	#467	C₂×D₈₉	1	1	yes	characteristic, complemented
330	#466	—	89	1	no	—
331	#466	—	89	1	no	—
332	#466	—	89	1	no	—
333	#466	—	178	1	no	—
334	#466	—	178	1	no	—
335	#466	C₂×D₈₉	1	1	yes	characteristic
336	C₂×#107	—	89	1	no	—
337	C₂×#107	—	89	1	no	—
338	C₂×#103	—	178	1	no	—
339	C₂×#102	—	178	1	no	—
340	#366	—	89	1	no	—
341	#366	—	89	1	no	—
342	#366	—	89	1	no	—
343	#366	C₂×D₈₉	1	1	yes	characteristic, complemented
344	#358	—	89	1	no	—
345	#358	—	89	1	no	—
346	#358	—	89	1	no	—
347	#358	C₂×D₈₉	1	1	yes	characteristic, complemented
348	#357	—	89	1	no	—
349	#357	—	89	1	no	—
350	#357	—	89	1	no	—
351	#357	C₂×D₈₉	1	1	yes	characteristic, complemented
352	C₂²×Q₈	—	178	1	no	—
353	C₂²×D₄	—	356	1	no	—
354	C₂²×D₄	—	178	1	no	—
355	C₂³×C₄	—	89	1	no	—
356	C₂×Q₁₆	—	89	1	no	—
357	C₂×Q₁₆	—	178	2	no	—
358	C₂×Q₁₆	—	178	2	no	—
359	C₂×Q₁₆	—	178	1	no	—
360	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
361	C₂×D₈	—	89	1	no	—
362	C₂×D₈	—	178	2	no	—
363	C₂×D₈	—	178	2	no	—
364	C₂×D₈	—	178	1	no	—
365	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
366	C₂²×C₈	—	89	1	no	—
367	C₂²×C₈	—	89	1	no	—
368	C₂²×C₈	—	89	1	no	—
369	C₂²×C₈	—	89	1	no	—
370	C₂²×C₈	—	89	1	no	—
371	C₂²×C₈	—	178	2	no	—
372	C₂²×C₈	—	178	2	no	—
373	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	356	1	no	—
376	C₂²⋊Q₈	—	356	1	no	—
377	C₂²⋊Q₈	—	178	1	no	—
378	C₂²⋊Q₈	—	178	1	no	—
379	C₂²⋊Q₈	—	178	1	no	—
380	#121	—	2	1	no	—
381	#121	—	356	1	no	—
382	#121	—	356	1	no	—
383	#121	—	178	1	no	—
384	#121	—	178	1	no	—
385	#121	—	178	1	no	—
386	C₂×C₄⋊C₄	—	356	1	no	—
387	C₂×C₄⋊C₄	—	178	1	no	—
388	C₂×C₄⋊C₄	—	178	1	no	—
389	C₂×C₂²⋊C₄	—	356	1	no	—
390	C₂×C₂²⋊C₄	—	356	1	no	—
391	SD₃₂	—	2	2	no	—
392	SD₃₂	—	178	2	no	—
393	SD₃₂	—	178	2	no	—
394	SD₃₂	—	178	2	no	—
395	M₃₂	—	2	2	no	—
396	M₃₂	—	178	2	no	—
397	M₃₂	—	178	2	no	—
398	M₃₂	—	178	2	no	—
399	C₂×C₁₆	—	89	1	no	—
400	C₂×C₁₆	—	89	4	no	—
401	C₂×C₁₆	—	89	1	no	—
402	C₂×C₁₆	—	178	2	no	—
403	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
404	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
405	#107	—	89	1	no	—
406	#107	—	89	1	no	—
407	#107	—	178	1	no	—
408	#107	—	178	1	no	—
409	#107	C₂²×D₈₉	1	1	yes	characteristic
410	#107	C₂²×D₈₉	1	1	yes	characteristic
411	#103	—	2	1	no	—
412	#103	—	178	1	no	—
413	#103	—	178	1	no	—
414	#103	—	178	1	no	—
415	#102	—	2	1	no	—
416	#102	—	178	1	no	—
417	#102	—	178	1	no	—
418	#102	—	178	1	no	—
419	C₂⁴	—	89	1	no	—
420	C₂⁴	—	356	1	no	—
421	C₂×Q₈	—	2	1	no	—
422	C₂×Q₈	—	356	1	no	—
423	C₂×Q₈	—	356	2	no	—
424	C₂×Q₈	—	356	2	no	—
425	C₂×Q₈	—	178	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	356	1	no	—
429	C₂×D₄	—	356	2	no	—
430	C₂×D₄	—	356	2	no	—
431	C₂×D₄	—	356	1	no	—
432	C₂×D₄	—	356	1	no	—
433	C₂×D₄	—	356	1	no	—
434	C₂×D₄	—	178	1	no	—
435	C₂×D₄	—	712	4	no	—
436	C₂²×C₄	—	89	1	no	—
437	C₂²×C₄	—	89	1	no	—
438	C₂²×C₄	—	89	1	no	—
439	C₂²×C₄	—	89	1	no	—
440	C₂²×C₄	—	89	1	no	—
441	C₂²×C₄	—	356	1	no	—
442	C₂²×C₄	—	356	1	no	—
443	C₂²×C₄	—	356	1	no	—
444	C₂²×C₄	—	178	2	no	—
445	C₂²×C₄	—	178	2	no	—
446	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
447	Q₁₆	—	2	1	no	—
448	Q₁₆	—	2	1	no	—
449	Q₁₆	—	356	2	no	—
450	Q₁₆	—	178	1	no	—
451	Q₁₆	—	178	1	no	—
452	D₈	—	2	1	no	—
453	D₈	—	2	1	no	—
454	D₈	—	356	2	no	—
455	D₈	—	178	1	no	—
456	D₈	—	178	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	89	2	no	—
461	C₂×C₈	—	89	2	no	—
462	C₂×C₈	—	89	1	no	—
463	C₂×C₈	—	178	2	no	—
464	C₂×C₈	—	178	2	no	—
465	C₂×C₈	—	178	2	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
469	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	—	356	1	no	—
474	C₄⋊C₄	—	356	1	no	—
475	C₄⋊C₄	—	356	1	no	—
476	C₄⋊C₄	—	356	1	no	—
477	C₄⋊C₄	—	356	1	no	—
478	C₄⋊C₄	—	178	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	356	1	no	—
483	C₂²⋊C₄	—	356	1	no	—
484	C₂²⋊C₄	—	356	1	no	—
485	C₂²⋊C₄	—	356	1	no	—
486	C₂²⋊C₄	—	356	1	no	—
487	C₂²⋊C₄	—	356	1	no	—
488	C₁₆	—	2	1	no	—
489	C₁₆	—	89	2	no	—
490	C₁₆	—	178	1	no	—
491	C₁₆	D₄×D₈₉	1	2	yes	complemented
492	C₂³	—	4	1	no	—
493	C₂³	—	89	1	no	—
494	C₂³	—	89	1	no	—
495	C₂³	—	356	1	no	—
496	C₂³	—	178	2	no	—
497	C₂³	—	178	2	no	—
498	C₂³	—	178	2	no	—
499	C₂³	—	712	2	no	—
500	C₂³	—	712	2	no	—
501	C₂³	—	712	2	no	—
502	C₂³	D₈×D₈₉	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	356	1	no	—
506	Q₈	—	356	1	no	—
507	Q₈	—	712	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	8	2	no	—
511	D₄	—	356	1	no	—
512	D₄	—	356	1	no	—
513	D₄	—	712	2	no	—
514	D₄	—	712	2	no	—
515	D₄	—	712	2	no	—
516	D₄	—	712	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	89	1	no	—
523	C₂×C₄	—	89	2	no	—
524	C₂×C₄	—	89	2	no	—
525	C₂×C₄	—	89	1	no	—
526	C₂×C₄	—	356	1	no	—
527	C₂×C₄	—	356	1	no	—
528	C₂×C₄	—	356	1	no	—
529	C₂×C₄	—	178	2	no	—
530	C₂×C₄	—	178	2	no	—
531	C₂×C₄	—	178	2	no	—
532	C₂×C₄	—	178	1	no	—
533	C₂×C₄	—	178	1	no	—
534	C₂×C₄	—	712	2	no	—
535	C₂×C₄	—	712	2	no	—
536	C₂×C₄	—	712	2	no	—
537	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
539	C₈	—	2	1	no	—
540	C₈	—	89	2	no	—
541	C₈	—	178	1	no	—
542	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
543	C₈	#41×D₈₉	1	1	yes	characteristic
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	89	2	no	—
551	C₂²	—	89	2	no	—
552	C₂²	—	89	2	no	—
553	C₂²	—	356	4	no	—
554	C₂²	—	1424	4	no	—
555	C₂²	—	178	1	no	—
556	C₂²	—	178	1	no	—
557	C₂²	—	178	1	no	—
558	C₂²	—	712	1	no	—
559	C₂²	—	712	1	no	—
560	C₂²	—	712	1	no	—
561	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	89	2	no	—
567	C₄	—	178	1	no	—
568	C₄	—	712	1	no	—
569	C₄	—	712	1	no	—
570	C₄	—	712	1	no	—
571	C₄	#121×D₈₉	1	1	yes	characteristic
572	C₄	#135×D₈₉	1	1	yes	characteristic
573	C₂	—	4	1	no	—
574	C₂	—	16	1	no	—
575	C₂	—	89	4	no	—
576	C₂	—	356	1	no	—
577	C₂	—	1424	1	no	—
578	C₂	#466×D₈₉	1	1	yes	characteristic
579	C₂	#509×D₈₉	1	1	yes	characteristic
580	C₂	#510×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2220	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	#466×D₈₉	C₂
hypercenter	#2220	D₈₉
hypocenter	C₈₉	C₂×#2220
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #2220

Complements

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

N	H ≅ G/N	type
1. C₂×SD₃₂×D₈₉	C₂	semidirect
2. C₂×M₃₂×D₈₉	C₂	semidirect
3. #467×D₈₉	C₂	semidirect
5. #26022368	C₂	semidirect
6. #26022367	C₂	semidirect
7. #26022366	C₂	semidirect
8. #26022365	C₂	semidirect
9. #26022364	C₂	semidirect
10. #26022363	C₂	semidirect
11. #26022362	C₂	semidirect
12. #366×D₈₉	C₂	semidirect
13. #358×D₈₉	C₂	semidirect
14. #357×D₈₉	C₂	semidirect
15. C₈₉×#2220	C₂	semidirect
21. C₂×#15667957	C₂²	semidirect
22. C₂×#15667956	C₂²	semidirect
23. C₂×#15667955	C₂²	semidirect
25. C₂×#15667952	C₂²	semidirect
26. C₂×#15667951	C₂²	semidirect
27. C₂×#15667951	C₂²	semidirect
31. #19151840	C₂²	semidirect
32. #19151839	C₂²	semidirect
35. #19151836	C₂²	semidirect
45. #19151424	C₂²	semidirect
46. #19151423	C₂²	semidirect
47. #19151423	C₂²	semidirect
48. #19151403	C₂²	semidirect
49. #19151402	C₂²	semidirect
50. #19151401	C₂²	semidirect
51. #19151400	C₂²	semidirect
52. #19151399	C₂²	semidirect
53. #19151398	C₂²	semidirect
54. C₂×SD₃₂×C₈₉	C₂²	semidirect
55. C₂×M₃₂×C₈₉	C₂²	semidirect
56. #467×C₈₉	C₂²	semidirect
58. #366×C₈₉	C₂²	semidirect
59. #358×C₈₉	C₂²	semidirect
60. #357×C₈₉	C₂²	semidirect
104. C₁₆×D₈₉	D₄	semidirect
181. #13083549	C₂×D₄	semidirect
200. C₁₆×C₈₉	C₂×D₄	semidirect
290. D₈₉	#2220	direct (N × H)
302. #2220	D₈₉	direct (N × H)
306. C₈₉	C₂×#2220	semidirect
316. C₂×SD₃₂	C₂×D₈₉	semidirect
321. C₂×M₃₂	C₂×D₈₉	semidirect
329. #467	C₂×D₈₉	semidirect
343. #366	C₂×D₈₉	semidirect
347. #358	C₂×D₈₉	semidirect
351. #357	C₂×D₈₉	semidirect
491. C₁₆	D₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₃₂×D₈₉	2
C₂×M₃₂×D₈₉	2
#467×D₈₉	2
#466×D₈₉	2
#26022368	2
#26022367	2
#26022366	2
#26022365	2
#26022364	2
#26022363	2
#26022362	2
#366×D₈₉	2
#358×D₈₉	2
#357×D₈₉	2
C₈₉×#2220	2
C₂×#2220	89

Subgroups — #2220×D89 #36708882

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2220×D₈₉ #36708882