Subgroups — #1670×D₈₉ #36536758

Order 22784.

702 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#494×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#475×D₈₉	C₂	1	2	yes	maximal
3	C₈×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019623	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019622	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019621	C₂	1	2	yes	maximal, complemented
7	#26019620	C₂	1	2	yes	maximal, complemented
8	#26019619	C₂	1	1	yes	maximal, characteristic, complemented
9	#335×D₈₉	C₂	1	1	yes	maximal, characteristic
10	#332×D₈₉	C₂	1	2	yes	maximal
11	C₈₉×#1670	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×Q₁₆×D₈₉	—	2	1	no	—
13	C₂×Q₁₆×D₈₉	—	2	1	no	—
14	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
15	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
16	#19151978	C₂²	1	1	yes	characteristic
17	#19151977	C₂²	1	2	yes	—
18	#19151976	—	2	1	no	—
19	#19151976	—	2	1	no	—
20	#19151884	C₂²	1	2	yes	—
21	#19151883	C₂²	1	2	yes	—
22	#19151882	—	2	2	no	—
23	#19151881	—	2	2	no	—
24	#19151880	C₂²	1	2	yes	—
25	Q₈×#10623494	C₂²	1	1	yes	characteristic
26	C₈×Dic₁₇₈	—	2	1	no	—
27	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
28	#19151722	—	2	1	no	—
29	#19151722	C₂²	1	1	yes	characteristic
30	#106×D₈₉	—	2	2	no	—
31	C₄⋊C₈×D₈₉	—	2	1	no	—
32	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
34	#103×D₈₉	—	2	2	no	—
35	C₄×C₈×D₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151350	C₂²	1	2	yes	—
39	#19151345	C₂²	1	2	yes	—
40	#19151344	C₂²	1	2	yes	—
41	#19151343	C₂²	1	2	yes	—
42	#494×C₈₉	C₂²	1	1	yes	characteristic
43	#475×C₈₉	C₂²	1	2	yes	—
44	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#332×C₈₉	C₂²	1	2	yes	—
47	C₂×Q₈×D₈₉	—	2	2	no	—
48	C₂×Q₈×D₈₉	D₄	1	1	yes	characteristic
49	C₂×Dic₃₅₆	—	2	1	no	—
50	C₂×Dic₃₅₆	—	2	1	no	—
51	C₂×#13083564	—	2	2	no	—
52	C₂×#13083564	—	2	2	no	—
53	Q₁₆×D₈₉	—	4	4	no	—
54	Q₁₆×D₈₉	—	4	4	no	—
55	C₂×C₈×D₈₉	—	2	1	no	—
56	C₂×C₈×D₈₉	—	2	2	no	—
57	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
59	#15668012	C₂³	1	2	yes	—
60	#15668011	—	2	2	no	—
61	#15668011	—	2	2	no	—
62	#15668010	—	2	2	no	—
63	Q₈×Dic₈₉	D₄	1	1	yes	characteristic
64	C₄×Dic₁₇₈	—	2	1	no	—
65	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
66	#15667977	—	2	1	no	—
67	#15667977	D₄	1	1	yes	characteristic
68	C₄⋊C₄×D₈₉	—	2	1	no	—
69	C₄⋊C₄×D₈₉	—	2	2	no	—
70	C₄⋊C₄×D₈₉	—	2	2	no	—
71	C₄⋊C₄×D₈₉	D₄	1	1	yes	characteristic
72	C₄²×D₈₉	—	2	1	no	—
73	C₄²×D₈₉	C₂³	1	1	yes	characteristic
74	#15667944	—	2	2	no	—
75	#15667943	—	2	2	no	—
76	#15667943	—	2	2	no	—
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	C₄⋊#10623494	C₂³	1	1	yes	characteristic
80	#15667941	—	2	1	no	—
81	#15667941	—	2	2	no	—
82	#15667941	—	2	1	no	—
83	#15667941	—	2	1	no	—
84	#15667937	—	2	2	no	—
85	#15667936	—	2	2	no	—
86	#15667935	—	2	2	no	—
87	C₄×#10623494	—	2	1	no	—
88	C₄×#10623494	C₂³	1	1	yes	characteristic
89	C₈×Dic₈₉	—	2	1	no	—
90	C₈×Dic₈₉	—	2	1	no	—
91	C₈×Dic₈₉	D₄	1	1	yes	characteristic
92	C₈×Dic₈₉	D₄	1	1	yes	characteristic
93	C₂×Q₁₆×C₈₉	—	2	1	no	—
94	C₂×Q₁₆×C₈₉	—	2	1	no	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	#106×C₈₉	—	2	2	no	—
98	C₄⋊C₈×C₈₉	—	2	1	no	—
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
101	#103×C₈₉	—	2	2	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×Dic₁₇₈	—	2	1	no	—
105	C₂×Dic₁₇₈	—	2	2	no	—
106	C₂×Dic₁₇₈	—	4	2	no	—
107	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
108	Q₈×D₈₉	—	2	2	no	—
109	Q₈×D₈₉	—	4	4	no	—
110	Q₈×D₈₉	—	4	4	no	—
111	Q₈×D₈₉	Q₁₆	1	4	yes	complemented
112	C₂×C₄×D₈₉	—	2	1	no	—
113	C₂×C₄×D₈₉	—	2	1	no	—
114	C₂×C₄×D₈₉	—	4	2	no	—
115	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
118	Dic₃₅₆	—	4	2	no	—
119	Dic₃₅₆	—	4	2	no	—
120	#13083564	—	4	4	no	—
121	#13083564	—	4	4	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
126	C₈×D₈₉	—	2	2	no	—
127	C₈×D₈₉	—	4	4	no	—
128	C₈×D₈₉	—	4	2	no	—
129	C₈×D₈₉	SD₁₆	1	4	yes	—
130	C₄⋊Dic₈₉	—	2	1	no	—
131	C₄⋊Dic₈₉	—	2	2	no	—
132	C₄⋊Dic₈₉	—	2	2	no	—
133	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
134	#13083553	—	2	1	no	—
135	#13083553	—	2	1	no	—
136	#13083553	—	2	1	no	—
137	#13083553	—	4	2	no	—
138	#13083553	—	4	2	no	—
139	C₄×Dic₈₉	—	2	1	no	—
140	C₄×Dic₈₉	—	2	1	no	—
141	C₄×Dic₈₉	—	2	1	no	—
142	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
143	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
144	C₄×Dic₈₉	#41	1	1	yes	characteristic
145	C₂×Q₈×C₈₉	—	2	2	no	—
146	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
147	Q₁₆×C₈₉	—	4	2	no	—
148	Q₁₆×C₈₉	—	4	2	no	—
149	C₂×C₈×C₈₉	—	2	1	no	—
150	C₂×C₈×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	—	2	2	no	—
156	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	—	2	1	no	—
158	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂²×D₈₉	#121	1	1	yes	characteristic
160	Q₈×C₈₉	—	2	1	no	—
161	Q₈×C₈₉	—	4	2	no	—
162	Q₈×C₈₉	—	4	2	no	—
163	Q₈×C₈₉	C₂×Q₁₆	1	2	yes	complemented
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂×Dic₈₉	—	2	1	no	—
171	C₂×Dic₈₉	—	2	1	no	—
172	C₂×Dic₈₉	—	4	2	no	—
173	C₂×Dic₈₉	#121	1	1	yes	characteristic
174	C₂×Dic₈₉	#121	1	1	yes	characteristic
175	C₂×Dic₈₉	#121	1	1	yes	characteristic
176	C₄×D₈₉	—	2	4	no	—
177	C₄×D₈₉	—	2	2	no	—
178	C₄×D₈₉	—	4	2	no	—
179	C₄×D₈₉	—	8	4	no	—
180	C₄×D₈₉	C₂×SD₁₆	1	2	yes	—
181	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
182	C₄×D₈₉	#135	1	2	yes	—
183	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
184	Dic₁₇₈	—	2	1	no	—
185	Dic₁₇₈	—	2	4	no	—
186	Dic₁₇₈	—	4	2	no	—
187	Dic₁₇₈	—	4	2	no	—
188	Dic₁₇₈	—	8	4	no	—
189	Dic₁₇₈	C₂×Q₁₆	1	2	yes	complemented
190	C₈×C₈₉	—	2	1	no	—
191	C₈×C₈₉	—	4	2	no	—
192	C₈×C₈₉	—	4	1	no	—
193	C₈×C₈₉	C₂×SD₁₆	1	2	yes	—
194	#10623494	—	2	1	no	—
195	#10623494	—	4	2	no	—
196	#10623494	—	4	1	no	—
197	#10623494	C₂×SD₁₆	1	2	yes	—
198	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
199	C₂×D₈₉	#460	1	2	yes	—
200	C₂×D₈₉	#467	1	2	yes	—
201	C₂×D₈₉	#473	1	2	yes	—
202	C₄×C₈₉	—	2	2	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	4	1	no	—
205	C₄×C₈₉	—	8	2	no	—
206	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
207	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
208	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
209	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	Dic₈₉	—	2	2	no	—
211	Dic₈₉	—	2	1	no	—
212	Dic₈₉	—	4	1	no	—
213	Dic₈₉	—	8	2	no	—
214	Dic₈₉	#460	1	2	yes	—
215	Dic₈₉	#467	1	2	yes	—
216	C₂×#1670	—	89	1	no	maximal, Sylow
217	C₂×C₈₉	C₂×#460	1	1	yes	characteristic
218	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
219	C₂×C₈₉	C₂×#473	1	1	yes	characteristic
220	D₈₉	#1670	1	4	yes	direct product factor
221	C₂×#494	—	89	1	no	—
222	C₂×#475	—	89	2	no	—
223	C₂×C₈×Q₈	—	89	1	no	—
224	#1670	—	89	1	no	—
225	#1670	—	89	2	no	—
226	#1670	—	89	1	no	—
227	#1670	—	89	1	no	—
228	#1670	—	89	2	no	—
229	#1670	D₈₉	1	1	yes	characteristic, direct product factor
230	C₂×#335	—	89	1	no	—
231	C₂×#332	—	89	2	no	—
232	C₈₉	C₂×#1670	1	1	yes	characteristic, complemented, Sylow
233	C₂²×Q₁₆	—	178	1	no	—
234	C₂²×Q₁₆	—	178	1	no	—
235	C₂×C₄⋊Q₈	—	89	2	no	—
236	C₂×C₄×Q₈	—	89	1	no	—
237	#494	—	89	2	no	—
238	#494	—	89	1	no	—
239	#494	—	178	1	no	—
240	#494	—	178	1	no	—
241	#494	C₂×D₈₉	1	1	yes	characteristic
242	#475	—	89	2	no	—
243	#475	—	89	2	no	—
244	#475	—	89	2	no	—
245	#475	—	178	2	no	—
246	#475	—	178	2	no	—
247	#475	C₂×D₈₉	1	2	yes	—
248	C₈×Q₈	—	89	1	no	—
249	C₈×Q₈	—	89	1	no	—
250	C₈×Q₈	—	89	1	no	—
251	C₈×Q₈	—	178	1	no	—
252	C₈×Q₈	—	178	1	no	—
253	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
254	C₂×#106	—	178	2	no	—
255	C₂×C₄⋊C₈	—	89	2	no	—
256	C₂×C₄⋊C₈	—	89	1	no	—
257	C₂×C₄⋊C₈	—	178	1	no	—
258	C₂×#103	—	178	2	no	—
259	C₂×C₄×C₈	—	89	1	no	—
260	C₂×C₄×C₈	—	178	1	no	—
261	#335	—	89	2	no	—
262	#335	—	89	1	no	—
263	#335	C₂×D₈₉	1	1	yes	characteristic
264	#332	—	89	2	no	—
265	#332	—	89	2	no	—
266	#332	—	89	2	no	—
267	#332	C₂×D₈₉	1	2	yes	—
268	C₂²×Q₈	—	89	1	no	—
269	C₂²×Q₈	—	178	2	no	—
270	C₂×Q₁₆	—	2	1	no	—
271	C₂×Q₁₆	—	2	1	no	—
272	C₂×Q₁₆	—	356	4	no	—
273	C₂×Q₁₆	—	356	4	no	—
274	C₂×Q₁₆	—	178	2	no	—
275	C₂×Q₁₆	—	178	2	no	—
276	C₂×Q₁₆	—	178	1	no	—
277	C₂×Q₁₆	—	178	1	no	—
278	C₂²×C₈	—	89	1	no	—
279	C₂²×C₈	—	89	1	no	—
280	C₂²×C₈	—	178	1	no	—
281	C₂²×C₈	—	178	2	no	—
282	C₄⋊Q₈	—	89	2	no	—
283	C₄⋊Q₈	—	178	2	no	—
284	C₄⋊Q₈	—	178	2	no	—
285	C₄⋊Q₈	—	178	2	no	—
286	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
287	C₄×Q₈	—	89	1	no	—
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	—	89	1	no	—
290	C₄×Q₈	—	178	1	no	—
291	C₄×Q₈	—	178	1	no	—
292	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
293	C₂×C₄⋊C₄	—	89	1	no	—
294	C₂×C₄⋊C₄	—	178	2	no	—
295	C₂×C₄⋊C₄	—	178	2	no	—
296	C₂×C₄⋊C₄	—	178	1	no	—
297	C₂×C₄²	—	89	1	no	—
298	C₂×C₄²	—	178	1	no	—
299	#106	—	2	2	no	—
300	#106	—	178	2	no	—
301	#106	—	178	2	no	—
302	#106	—	178	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	—	89	1	no	—
305	C₄⋊C₈	—	89	2	no	—
306	C₄⋊C₈	—	178	1	no	—
307	C₄⋊C₈	—	178	1	no	—
308	C₄⋊C₈	—	178	2	no	—
309	C₄⋊C₈	—	178	1	no	—
310	C₄⋊C₈	—	178	1	no	—
311	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
313	#103	—	2	2	no	—
314	#103	—	178	2	no	—
315	#103	—	178	2	no	—
316	#103	—	178	2	no	—
317	C₄×C₈	—	2	1	no	—
318	C₄×C₈	—	89	1	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	—	89	1	no	—
321	C₄×C₈	—	178	1	no	—
322	C₄×C₈	—	178	1	no	—
323	C₄×C₈	—	178	1	no	—
324	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	89	4	no	—
327	C₂×Q₈	—	89	1	no	—
328	C₂×Q₈	—	356	2	no	—
329	C₂×Q₈	—	356	4	no	—
330	C₂×Q₈	—	356	4	no	—
331	C₂×Q₈	—	178	1	no	—
332	C₂×Q₈	—	178	2	no	—
333	C₂×Q₈	—	178	2	no	—
334	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	—	89	1	no	—
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	356	2	no	—
339	C₂²×C₄	—	178	1	no	—
340	C₂²×C₄	—	178	1	no	—
341	Q₁₆	—	4	2	no	—
342	Q₁₆	—	4	2	no	—
343	Q₁₆	—	356	2	no	—
344	Q₁₆	—	356	4	no	—
345	Q₁₆	—	356	4	no	—
346	Q₁₆	—	356	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	89	1	no	—
350	C₂×C₈	—	89	4	no	—
351	C₂×C₈	—	89	1	no	—
352	C₂×C₈	—	356	4	no	—
353	C₂×C₈	—	356	2	no	—
354	C₂×C₈	—	178	2	no	—
355	C₂×C₈	—	178	1	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
358	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	89	1	no	—
363	C₄⋊C₄	—	356	2	no	—
364	C₄⋊C₄	—	356	2	no	—
365	C₄⋊C₄	—	178	1	no	—
366	C₄⋊C₄	—	178	1	no	—
367	C₄⋊C₄	—	178	1	no	—
368	C₄⋊C₄	—	178	2	no	—
369	C₄⋊C₄	—	178	2	no	—
370	C₄⋊C₄	—	178	1	no	—
371	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
372	C₄²	—	2	1	no	—
373	C₄²	—	89	1	no	—
374	C₄²	—	89	1	no	—
375	C₄²	—	89	1	no	—
376	C₄²	—	178	1	no	—
377	C₄²	—	178	1	no	—
378	C₄²	—	178	1	no	—
379	C₄²	C₂³×D₈₉	1	1	yes	characteristic
380	C₂³	—	89	1	no	—
381	Q₈	—	2	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	Q₈	—	89	2	no	—
385	Q₈	—	356	2	no	—
386	Q₈	—	356	2	no	—
387	Q₈	—	178	4	no	—
388	Q₈	—	178	1	no	—
389	Q₈	—	712	4	no	—
390	Q₈	Q₁₆×D₈₉	1	2	yes	complemented
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	89	2	no	—
397	C₂×C₄	—	89	2	no	—
398	C₂×C₄	—	89	2	no	—
399	C₂×C₄	—	89	2	no	—
400	C₂×C₄	—	89	1	no	—
401	C₂×C₄	—	356	2	no	—
402	C₂×C₄	—	356	2	no	—
403	C₂×C₄	—	178	2	no	—
404	C₂×C₄	—	178	4	no	—
405	C₂×C₄	—	178	1	no	—
406	C₂×C₄	—	178	1	no	—
407	C₂×C₄	—	712	4	no	—
408	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
410	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	4	2	no	—
413	C₈	—	4	1	no	—
414	C₈	—	89	2	no	—
415	C₈	—	356	2	no	—
416	C₈	—	356	1	no	—
417	C₈	—	178	1	no	—
418	C₈	SD₁₆×D₈₉	1	2	yes	—
419	C₂²	—	89	2	no	—
420	C₂²	—	89	2	no	—
421	C₂²	—	89	2	no	—
422	C₂²	#121×D₈₉	1	1	yes	characteristic
423	C₄	—	2	1	no	—
424	C₄	—	2	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	8	2	no	—
427	C₄	—	89	2	no	—
428	C₄	—	89	2	no	—
429	C₄	—	356	1	no	—
430	C₄	—	178	1	no	—
431	C₄	—	178	2	no	—
432	C₄	—	712	2	no	—
433	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
434	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
435	C₄	#135×D₈₉	1	1	yes	characteristic
436	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
437	C₂	—	89	4	no	—
438	C₂	#460×D₈₉	1	1	yes	characteristic
439	C₂	#467×D₈₉	1	1	yes	characteristic
440	C₂	#473×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1670	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂²×D₈₉	#121
hypercenter	#1670	D₈₉
hypocenter	C₈₉	C₂×#1670
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1670

Complements

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

N	H ≅ G/N	type
4. #26019623	C₂	semidirect
5. #26019622	C₂	semidirect
6. #26019621	C₂	semidirect
7. #26019620	C₂	semidirect
8. #26019619	C₂	semidirect
11. C₈₉×#1670	C₂	semidirect
111. Q₈×D₈₉	Q₁₆	semidirect
163. Q₈×C₈₉	C₂×Q₁₆	semidirect
189. Dic₁₇₈	C₂×Q₁₆	semidirect
220. D₈₉	#1670	direct (N × H)
229. #1670	D₈₉	direct (N × H)
232. C₈₉	C₂×#1670	semidirect
390. Q₈	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#494×D₈₉	2
#475×D₈₉	2
C₈×Q₈×D₈₉	2
#26019623	2
#26019622	2
#26019621	2
#26019620	2
#26019619	2
#335×D₈₉	2
#332×D₈₉	2
C₈₉×#1670	2
C₂×#1670	89

Subgroups — #1670×D89 #36536758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1670×D₈₉ #36536758