Subgroups — #1580×D₈₉ #36523823

Order 22784.

894 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈×D₄×D₈₉	C₂	1	2	yes	maximal, complemented
3	#26019077	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019076	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019075	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019074	C₂	1	2	yes	maximal, complemented
7	#26019073	C₂	1	2	yes	maximal, complemented
8	#334×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄⋊C₈×D₈₉	C₂	1	2	yes	maximal, complemented
10	#322×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₈₉	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₈₉	—	2	2	no	—
14	C₄×D₄×D₈₉	C₂²	1	2	yes	—
15	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
16	D₈×Dic₈₉	C₄	1	1	yes	characteristic
17	#19151680	C₄	1	1	yes	characteristic
18	C₄×#13083559	C₂²	1	2	yes	—
19	#19151678	C₄	1	2	yes	—
20	C₈×D₃₅₆	C₂²	1	2	yes	complemented
21	D₄×#10623494	C₂²	1	2	yes	complemented
22	#19151663	C₂²	1	2	yes	complemented
23	C₈×C₂²⋊D₈₉	—	2	2	no	—
24	#19151661	—	2	2	no	—
25	#107×D₈₉	C₄	1	1	yes	characteristic
26	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
27	#102×D₈₉	C₄	1	2	yes	—
28	C₂²⋊C₈×D₈₉	—	2	2	no	—
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151349	C₂²	1	1	yes	characteristic, complemented
33	#19151348	C₂²	1	2	yes	complemented
34	#19151327	C₂²	1	2	yes	complemented
35	D₄⋊#10623494	C₂²	1	2	yes	complemented
36	#19151325	C₂²	1	2	yes	complemented
37	#19151320	C₂²	1	1	yes	characteristic, complemented
38	#19151320	C₂²	1	1	yes	characteristic, complemented
39	#19151319	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
42	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
44	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₈₉	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₈₉	—	2	2	no	—
47	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083559	C₂×C₄	1	2	yes	—
49	D₈×D₈₉	C₈	1	8	yes	complemented
50	C₂²×#10623494	—	2	2	no	—
51	C₂×C₈×D₈₉	—	2	2	no	—
52	C₂×C₈×D₈₉	—	2	1	no	—
53	C₂×C₈×D₈₉	—	2	2	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₂×C₈×D₈₉	—	4	8	no	—
56	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₈₉	D₄	1	2	yes	—
59	C₄×D₃₅₆	C₂³	1	2	yes	—
60	D₄×Dic₈₉	C₂×C₄	1	2	yes	—
61	#15667974	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₈₉	—	2	2	no	—
63	#15667972	—	2	2	no	—
64	C₄⋊C₄×D₈₉	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₈₉	—	2	2	no	—
66	C₄²×D₈₉	C₂³	1	1	yes	characteristic
67	#15667946	C₂×C₄	1	1	yes	characteristic
68	#15667945	C₂×C₄	1	2	yes	—
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	#15667941	—	2	2	no	—
71	#15667934	C₂×C₄	1	2	yes	—
72	#15667933	C₂×C₄	1	2	yes	—
73	#15667932	C₂×C₄	1	2	yes	—
74	C₂²⋊#10623494	—	2	2	no	—
75	#15667924	—	2	2	no	—
76	#15667924	—	2	2	no	—
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₈×Dic₈₉	—	2	1	no	—
81	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₈₉	D₄	1	2	yes	—
84	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₈₉	—	2	2	no	—
86	C₄×D₄×C₈₉	C₂³	1	2	yes	—
87	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
89	#102×C₈₉	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₈₉	—	2	2	no	—
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₂³×D₈₉	—	2	2	no	—
95	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
96	C₂×C₂²⋊D₈₉	—	2	2	no	—
97	D₄×D₈₉	—	2	4	no	—
98	D₄×D₈₉	C₂×C₈	1	8	yes	complemented
99	C₂²×Dic₈₉	—	2	2	no	—
100	C₂×C₄×D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	—	2	2	no	—
102	C₂×C₄×D₈₉	—	2	2	no	—
103	C₂×C₄×D₈₉	—	4	4	no	—
104	C₂×C₄×D₈₉	—	4	4	no	—
105	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
108	D₇₁₂	C₂×C₈	1	4	yes	complemented
109	#13083559	C₂×C₈	1	8	yes	complemented
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	2	1	no	—
112	C₂×#10623494	—	4	4	no	—
113	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
114	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
115	C₂×#10623494	C₂×D₄	1	2	yes	—
116	C₈×D₈₉	—	2	2	no	—
117	C₈×D₈₉	—	2	4	no	—
118	C₈×D₈₉	—	4	4	no	—
119	C₈×D₈₉	—	4	4	no	—
120	C₈×D₈₉	—	4	2	no	—
121	C₈×D₈₉	—	4	4	no	—
122	C₈×D₈₉	C₂×C₈	1	4	yes	complemented
123	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
124	#13083553	—	2	2	no	—
125	C₂²⋊Dic₈₉	—	2	2	no	—
126	#13083551	—	2	2	no	—
127	#13083551	—	2	2	no	—
128	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
130	C₄×Dic₈₉	#41	1	1	yes	characteristic
131	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₈₉	—	2	2	no	—
133	D₈×C₈₉	C₂×C₈	1	4	yes	complemented
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	4	4	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
141	C₂²⋊C₄×C₈₉	—	2	2	no	—
142	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₂³×C₈₉	—	2	2	no	—
144	C₂²×D₈₉	—	2	2	no	—
145	C₂²×D₈₉	—	2	8	no	—
146	C₂²×D₈₉	—	4	4	no	—
147	C₂²×D₈₉	—	4	4	no	—
148	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
149	D₄×C₈₉	—	2	2	no	—
150	D₄×C₈₉	C₂²×C₈	1	4	yes	complemented
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
157	C₂²⋊D₈₉	—	2	8	no	—
158	C₂×Dic₈₉	—	2	2	no	—
159	C₂×Dic₈₉	—	4	4	no	—
160	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
163	D₃₅₆	—	2	2	no	—
164	D₃₅₆	C₂²×C₈	1	4	yes	complemented
165	C₄×D₈₉	—	2	2	no	—
166	C₄×D₈₉	—	4	4	no	—
167	C₄×D₈₉	—	4	2	no	—
168	C₄×D₈₉	—	4	2	no	—
169	C₄×D₈₉	—	4	4	no	—
170	C₄×D₈₉	C₂²×C₈	1	2	yes	—
171	C₄×D₈₉	#131	1	2	yes	—
172	C₄×D₈₉	AGL(1,ℤ/8)	1	4	yes	—
173	C₈×C₈₉	—	2	1	no	—
174	C₈×C₈₉	—	2	2	no	—
175	C₈×C₈₉	—	4	1	no	—
176	C₈×C₈₉	—	4	2	no	—
177	C₈×C₈₉	C₂²×C₈	1	2	yes	complemented
178	#10623494	—	2	1	no	—
179	#10623494	—	2	2	no	—
180	#10623494	—	4	1	no	—
181	#10623494	—	4	2	no	—
182	#10623494	C₂²×C₈	1	2	yes	complemented
183	C₂²×C₈₉	—	2	4	no	—
184	C₂²×C₈₉	—	4	2	no	—
185	C₂²×C₈₉	—	4	2	no	—
186	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂×D₈₉	—	2	4	no	—
188	C₂×D₈₉	—	4	2	no	—
189	C₂×D₈₉	—	4	2	no	—
190	C₂×D₈₉	—	4	16	no	—
191	C₂×D₈₉	C₈×D₄	1	2	yes	—
192	C₂×D₈₉	#442	1	2	yes	—
193	C₂×D₈₉	#444	1	2	yes	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	4	2	no	—
196	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
197	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
198	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
199	Dic₈₉	—	2	1	no	—
200	Dic₈₉	—	4	2	no	—
201	Dic₈₉	C₈×D₄	1	2	yes	—
202	Dic₈₉	#442	1	2	yes	—
203	C₂×#1580	—	89	1	no	maximal, Sylow
204	C₂×C₈₉	—	4	4	no	—
205	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
206	C₂×C₈₉	C₂×#442	1	1	yes	characteristic
207	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
208	D₈₉	—	4	4	no	—
209	D₈₉	#1580	1	4	yes	direct product factor
210	C₂×C₄×D₈	—	89	1	no	—
211	C₂×C₈×D₄	—	89	2	no	—
212	#1580	—	89	1	no	—
213	#1580	—	89	2	no	—
214	#1580	—	89	1	no	—
215	#1580	—	89	2	no	—
216	#1580	—	89	1	no	—
217	#1580	D₈₉	1	1	yes	characteristic, direct product factor
218	C₂×#334	—	89	1	no	—
219	C₂×D₄⋊C₈	—	89	2	no	—
220	C₂×#322	—	89	1	no	—
221	C₈₉	C₂×#1580	1	1	yes	characteristic, complemented, Sylow
222	C₂²×D₈	—	89	1	no	—
223	C₂³×C₈	—	178	2	no	—
224	C₂×C₄×D₄	—	89	2	no	—
225	C₄×D₈	—	89	1	no	—
226	C₄×D₈	—	89	2	no	—
227	C₄×D₈	—	89	1	no	—
228	C₄×D₈	—	89	2	no	—
229	C₄×D₈	—	89	1	no	—
230	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
231	C₈×D₄	—	89	2	no	—
232	C₈×D₄	—	89	2	no	—
233	C₈×D₄	—	89	2	no	—
234	C₈×D₄	—	178	2	no	—
235	C₈×D₄	—	178	2	no	—
236	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
237	C₂×#107	—	89	1	no	—
238	C₂×C₄⋊C₈	—	89	2	no	—
239	C₂×#102	—	89	2	no	—
240	C₂×C₂²⋊C₈	—	178	2	no	—
241	C₂×C₄×C₈	—	89	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	C₂×C₄×C₈	—	89	1	no	—
244	#334	—	89	2	no	—
245	#334	—	89	1	no	—
246	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
247	D₄⋊C₈	—	89	2	no	—
248	D₄⋊C₈	—	89	2	no	—
249	D₄⋊C₈	—	89	2	no	—
250	D₄⋊C₈	C₂×D₈₉	1	2	yes	complemented
251	#322	—	89	1	no	—
252	#322	—	89	1	no	—
253	#322	—	89	1	no	—
254	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
255	C₂²×D₄	—	89	2	no	—
256	C₂³×C₄	—	178	2	no	—
257	C₂×D₈	—	89	2	no	—
258	C₂×D₈	—	89	8	no	—
259	C₂×D₈	—	89	1	no	—
260	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	89	1	no	—
263	C₂²×C₈	—	89	1	no	—
264	C₂²×C₈	—	89	2	no	—
265	C₂²×C₈	—	356	8	no	—
266	C₂²×C₈	—	178	2	no	—
267	C₂²×C₈	—	178	2	no	—
268	C₂²×C₈	—	178	1	no	—
269	C₂²×C₈	—	178	2	no	—
270	C₂²×C₈	—	178	2	no	—
271	C₄×D₄	—	89	2	no	—
272	C₄×D₄	—	89	2	no	—
273	C₄×D₄	—	89	2	no	—
274	C₄×D₄	—	178	2	no	—
275	C₄×D₄	—	178	2	no	—
276	C₄×D₄	C₂²×D₈₉	1	2	yes	—
277	C₂×C₄⋊C₄	—	89	2	no	—
278	C₂×C₂²⋊C₄	—	178	2	no	—
279	C₂×C₄²	—	89	1	no	—
280	#107	—	89	1	no	—
281	#107	—	89	2	no	—
282	#107	C₄×D₈₉	1	1	yes	characteristic
283	C₄⋊C₈	—	89	2	no	—
284	C₄⋊C₈	—	178	2	no	—
285	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
286	#102	—	89	2	no	—
287	#102	—	89	2	no	—
288	#102	—	89	2	no	—
289	#102	C₄×D₈₉	1	2	yes	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	178	2	no	—
292	C₂²⋊C₈	—	178	2	no	—
293	C₂²⋊C₈	—	178	2	no	—
294	C₄×C₈	—	89	1	no	—
295	C₄×C₈	—	89	1	no	—
296	C₄×C₈	—	89	2	no	—
297	C₄×C₈	—	89	1	no	—
298	C₄×C₈	—	89	1	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	178	1	no	—
301	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₂⁴	—	178	2	no	—
305	C₂×D₄	—	89	8	no	—
306	C₂×D₄	—	89	2	no	—
307	C₂×D₄	—	178	4	no	—
308	C₂×D₄	—	178	2	no	—
309	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	89	1	no	—
312	C₂²×C₄	—	89	1	no	—
313	C₂²×C₄	—	89	1	no	—
314	C₂²×C₄	—	356	4	no	—
315	C₂²×C₄	—	356	4	no	—
316	C₂²×C₄	—	178	2	no	—
317	C₂²×C₄	—	178	2	no	—
318	C₂²×C₄	—	178	2	no	—
319	C₂²×C₄	—	178	2	no	—
320	D₈	—	89	8	no	—
321	D₈	—	89	4	no	—
322	D₈	C₈×D₈₉	1	4	yes	complemented
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	—	89	1	no	—
327	C₂×C₈	—	89	4	no	—
328	C₂×C₈	—	89	1	no	—
329	C₂×C₈	—	89	2	no	—
330	C₂×C₈	—	356	4	no	—
331	C₂×C₈	—	356	4	no	—
332	C₂×C₈	—	356	2	no	—
333	C₂×C₈	—	356	4	no	—
334	C₂×C₈	—	356	4	no	—
335	C₂×C₈	—	178	4	no	—
336	C₂×C₈	—	178	2	no	—
337	C₂×C₈	—	178	2	no	—
338	C₂×C₈	—	178	1	no	—
339	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₂×C₈	D₄×D₈₉	1	2	yes	—
342	C₄⋊C₄	—	89	2	no	—
343	C₄⋊C₄	—	178	2	no	—
344	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	178	2	no	—
347	C₂²⋊C₄	—	178	2	no	—
348	C₂²⋊C₄	—	178	2	no	—
349	C₄²	—	89	1	no	—
350	C₄²	—	89	1	no	—
351	C₄²	—	89	1	no	—
352	C₄²	C₂³×D₈₉	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	89	1	no	—
355	C₂³	—	356	4	no	—
356	C₂³	—	356	4	no	—
357	C₂³	—	178	8	no	—
358	C₂³	—	178	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	89	4	no	—
361	D₄	—	178	8	no	—
362	D₄	—	178	2	no	—
363	D₄	C₂×C₈×D₈₉	1	4	yes	complemented
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	89	1	no	—
368	C₂×C₄	—	89	1	no	—
369	C₂×C₄	—	89	2	no	—
370	C₂×C₄	—	89	2	no	—
371	C₂×C₄	—	89	4	no	—
372	C₂×C₄	—	89	1	no	—
373	C₂×C₄	—	356	4	no	—
374	C₂×C₄	—	356	4	no	—
375	C₂×C₄	—	356	4	no	—
376	C₂×C₄	—	356	2	no	—
377	C₂×C₄	—	356	2	no	—
378	C₂×C₄	—	178	2	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
382	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	89	2	no	—
388	C₈	—	356	1	no	—
389	C₈	—	356	2	no	—
390	C₈	—	178	1	no	—
391	C₈	—	178	2	no	—
392	C₈	C₂×C₈×D₈₉	1	2	yes	complemented
393	C₂²	—	2	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	89	2	no	—
397	C₂²	—	89	2	no	—
398	C₂²	—	89	2	no	—
399	C₂²	—	356	16	no	—
400	C₂²	—	356	2	no	—
401	C₂²	—	356	2	no	—
402	C₂²	—	178	4	no	—
403	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	89	2	no	—
407	C₄	—	89	2	no	—
408	C₄	—	356	2	no	—
409	C₄	—	178	1	no	—
410	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
411	C₄	#131×D₈₉	1	1	yes	characteristic
412	C₄	AGL(1,ℤ/8)×D₈₉	1	2	yes	—
413	C₂	—	4	4	no	—
414	C₂	—	89	4	no	—
415	C₂	—	356	4	no	—
416	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
417	C₂	#442×D₈₉	1	1	yes	characteristic
418	C₂	#444×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1580	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×D₈×D₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1580	D₈₉
hypocenter	C₈₉	C₂×#1580
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
2. C₈×D₄×D₈₉	C₂	semidirect
3. #26019077	C₂	semidirect
4. #26019076	C₂	semidirect
5. #26019075	C₂	semidirect
6. #26019074	C₂	semidirect
7. #26019073	C₂	semidirect
8. #334×D₈₉	C₂	semidirect
9. D₄⋊C₈×D₈₉	C₂	semidirect
10. #322×D₈₉	C₂	semidirect
11. C₈₉×#1580	C₂	semidirect
20. C₈×D₃₅₆	C₂²	semidirect
21. D₄×#10623494	C₂²	semidirect
22. #19151663	C₂²	semidirect
32. #19151349	C₂²	semidirect
33. #19151348	C₂²	semidirect
34. #19151327	C₂²	semidirect
35. D₄⋊#10623494	C₂²	semidirect
36. #19151325	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. #19151320	C₂²	semidirect
39. #19151319	C₂²	semidirect
41. C₈×D₄×C₈₉	C₂²	semidirect
42. #334×C₈₉	C₂²	semidirect
43. D₄⋊C₈×C₈₉	C₂²	semidirect
44. #322×C₈₉	C₂²	semidirect
49. D₈×D₈₉	C₈	semidirect
98. D₄×D₈₉	C₂×C₈	semidirect
108. D₇₁₂	C₂×C₈	semidirect
109. #13083559	C₂×C₈	semidirect
122. C₈×D₈₉	C₂×C₈	semidirect
133. D₈×C₈₉	C₂×C₈	semidirect
150. D₄×C₈₉	C₂²×C₈	semidirect
164. D₃₅₆	C₂²×C₈	semidirect
177. C₈×C₈₉	C₂²×C₈	semidirect
182. #10623494	C₂²×C₈	semidirect
209. D₈₉	#1580	direct (N × H)
217. #1580	D₈₉	direct (N × H)
221. C₈₉	C₂×#1580	semidirect
236. C₈×D₄	C₂×D₈₉	semidirect
246. #334	C₂×D₈₉	semidirect
250. D₄⋊C₈	C₂×D₈₉	semidirect
254. #322	C₂×D₈₉	semidirect
322. D₈	C₈×D₈₉	semidirect
363. D₄	C₂×C₈×D₈₉	semidirect
392. C₈	C₂×C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₈₉	2
C₈×D₄×D₈₉	2
#26019077	2
#26019076	2
#26019075	2
#26019074	2
#26019073	2
#334×D₈₉	2
D₄⋊C₈×D₈₉	2
#322×D₈₉	2
C₈₉×#1580	2
C₂×#1580	89

Subgroups — #1580×D89 #36523823

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1580×D₈₉ #36523823