Subgroups — #2170×D₈₉ #36707652

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#504×D₈₉	C₂	1	2	yes	maximal, complemented
2	#443×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022090	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022089	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022088	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022087	C₂	1	2	yes	maximal, complemented
7	#26022086	C₂	1	2	yes	maximal, complemented
8	#364×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#350×D₈₉	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2170	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	C₄	1	1	yes	characteristic
13	#131×D₈₉	C₂²	1	2	yes	—
14	#19152016	—	2	2	no	—
15	#19152016	C₂²	1	2	yes	complemented
16	#19152015	C₂²	1	2	yes	complemented
17	#19152014	—	2	2	no	—
18	#19152014	C₂²	1	2	yes	complemented
19	M₃₂×D₈₉	—	2	2	no	—
20	M₃₂×D₈₉	C₂²	1	2	yes	—
21	C₂×C₁₆×D₈₉	—	2	2	no	—
22	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
24	#19151716	C₂²	1	1	yes	characteristic
25	#19151715	C₄	1	1	yes	characteristic
26	#19151714	C₄	1	1	yes	characteristic
27	#19151713	C₂²	1	2	yes	—
28	#19151712	C₄	1	2	yes	—
29	#108×D₈₉	C₄	1	1	yes	characteristic
30	#104×D₈₉	C₄	1	2	yes	—
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151419	C₂²	1	1	yes	characteristic, complemented
33	#19151418	C₂²	1	2	yes	complemented
34	#19151383	C₂²	1	2	yes	complemented
35	#19151382	C₂²	1	2	yes	complemented
36	#19151381	C₂²	1	2	yes	complemented
37	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
40	#504×C₈₉	C₂²	1	2	yes	complemented
41	#443×C₈₉	C₂²	1	1	yes	characteristic
42	#364×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#350×C₈₉	C₂²	1	2	yes	complemented
44	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#41×D₈₉	C₂×C₄	1	2	yes	—
46	#15668035	C₈	1	1	yes	characteristic
47	#15668034	C₂×C₄	1	1	yes	characteristic
48	#15668033	C₈	1	2	yes	—
49	#15668032	C₂×C₄	1	2	yes	—
50	#15668031	C₈	1	1	yes	characteristic
51	Q₁₆×D₈₉	C₈	1	1	yes	characteristic
52	SD₁₆×D₈₉	C₈	1	2	yes	—
53	D₈×D₈₉	C₈	1	1	yes	characteristic
54	#15668020	—	2	2	no	—
55	#15668020	C₂×C₄	1	2	yes	—
56	#15668019	C₂×C₄	1	2	yes	—
57	#15668018	—	2	2	no	—
58	#15668018	C₂³	1	2	yes	—
59	M₁₆×D₈₉	—	2	2	no	—
60	M₁₆×D₈₉	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₈₉	—	2	2	no	—
62	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
64	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
65	#15667952	—	2	2	no	—
66	#15667952	C₂³	1	2	yes	—
67	#15667951	—	2	2	no	—
68	#15667951	—	2	2	no	—
69	#15667951	—	2	2	no	—
70	C₂×#13083549	—	2	2	no	—
71	C₂×#13083549	C₂³	1	1	yes	characteristic
72	C₂×#13083549	C₂³	1	1	yes	characteristic
73	C₁₆×D₈₉	—	2	2	no	—
74	C₁₆×D₈₉	—	2	1	no	—
75	C₁₆×D₈₉	—	2	1	no	—
76	C₁₆×D₈₉	—	2	2	no	—
77	C₁₆×D₈₉	—	2	2	no	—
78	C₁₆×D₈₉	D₄	1	1	yes	characteristic
79	C₁₆×D₈₉	D₄	1	1	yes	characteristic
80	C₁₆×D₈₉	D₄	1	1	yes	characteristic
81	C₁₆×D₈₉	D₄	1	1	yes	characteristic
82	#15667948	C₂×C₄	1	1	yes	characteristic
83	#15667947	C₂×C₄	1	2	yes	—
84	#15667940	C₂×C₄	1	2	yes	—
85	#15667939	C₂×C₄	1	2	yes	—
86	#15667938	C₂×C₄	1	2	yes	—
87	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
89	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
90	#135×C₈₉	C₂×C₄	1	1	yes	characteristic
91	#131×C₈₉	C₂³	1	2	yes	—
92	M₃₂×C₈₉	—	2	2	no	—
93	M₃₂×C₈₉	C₂³	1	2	yes	—
94	C₂×C₁₆×C₈₉	—	2	2	no	—
95	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
97	#108×C₈₉	C₂×C₄	1	1	yes	characteristic
98	#104×C₈₉	C₂×C₄	1	2	yes	—
99	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	#13083575	C₂×C₈	1	2	yes	—
101	#13083574	—	2	2	no	—
102	#13083574	C₂²×C₄	1	2	yes	—
103	#13083573	—	2	2	no	—
104	#13083573	C₂×C₈	1	2	yes	—
105	Q₈×D₈₉	C₂×C₈	1	2	yes	—
106	D₄×D₈₉	—	2	2	no	—
107	D₄×D₈₉	C₂×C₈	1	2	yes	—
108	C₂×C₄×D₈₉	—	2	1	no	—
109	C₂×C₄×D₈₉	—	2	2	no	—
110	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
111	Dic₃₅₆	C₂×C₈	1	1	yes	characteristic
112	#13083564	C₂×C₈	1	2	yes	—
113	#13083563	C₂×C₈	1	2	yes	—
114	#13083562	C₂×C₈	1	2	yes	—
115	#13083561	C₂×C₈	1	2	yes	—
116	D₇₁₂	C₂×C₈	1	1	yes	characteristic
117	#13083559	C₂×C₈	1	2	yes	—
118	#13083558	—	2	2	no	—
119	#13083558	C₂²×C₄	1	2	yes	—
120	#13083557	—	2	2	no	—
121	#13083557	—	2	2	no	—
122	#13083557	—	2	2	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
125	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
126	C₈×D₈₉	—	2	2	no	—
127	C₈×D₈₉	—	2	2	no	—
128	C₈×D₈₉	—	2	2	no	—
129	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
130	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
131	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
132	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
133	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
134	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
135	C₈×D₈₉	#41	1	1	yes	characteristic
136	C₈×D₈₉	#41	1	1	yes	characteristic
137	C₄×Dic₈₉	—	2	1	no	—
138	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
139	#13083549	—	2	2	no	—
140	#13083549	—	2	1	no	—
141	#13083549	C₂×D₄	1	1	yes	characteristic
142	#13083549	C₂×D₄	1	1	yes	characteristic
143	#41×C₈₉	C₂²×C₄	1	2	yes	—
144	Q₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
145	SD₁₆×C₈₉	C₂×C₈	1	2	yes	—
146	D₈×C₈₉	C₂×C₈	1	1	yes	characteristic
147	M₁₆×C₈₉	—	2	2	no	—
148	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₁₆×C₈₉	—	2	2	no	—
154	C₁₆×C₈₉	—	2	1	no	—
155	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×D₈₉	—	2	2	no	—
158	C₂²×D₈₉	#131	1	1	yes	characteristic
159	Q₈×C₈₉	C₂²×C₈	1	2	yes	—
160	D₄×C₈₉	—	2	2	no	—
161	D₄×C₈₉	C₂²×C₈	1	2	yes	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
165	C₂²⋊D₈₉	—	2	2	no	—
166	C₂²⋊D₈₉	—	2	2	no	—
167	C₂²⋊D₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	#131	1	1	yes	characteristic
171	D₃₅₆	—	2	2	no	—
172	D₃₅₆	C₂²×C₈	1	2	yes	—
173	C₄×D₈₉	—	2	4	no	—
174	C₄×D₈₉	—	2	2	no	—
175	C₄×D₈₉	—	2	2	no	—
176	C₄×D₈₉	—	2	2	no	—
177	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
178	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
179	C₄×D₈₉	C₂²×C₈	1	1	yes	characteristic
180	C₄×D₈₉	C₂²×C₈	1	1	yes	characteristic
181	Dic₁₇₈	—	2	2	no	—
182	Dic₁₇₈	C₂²×C₈	1	2	yes	—
183	C₈×C₈₉	—	2	2	no	—
184	C₈×C₈₉	C₂²×C₈	1	1	yes	characteristic
185	C₈×C₈₉	C₂²×C₈	1	1	yes	characteristic
186	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
188	#10623494	—	2	2	no	—
189	#10623494	C₄×D₄	1	1	yes	characteristic
190	#10623494	C₄×D₄	1	1	yes	characteristic
191	#10623494	C₂²×C₈	1	1	yes	characteristic
192	#10623494	C₂²×C₈	1	1	yes	characteristic
193	C₂²×C₈₉	—	2	2	no	—
194	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
195	C₂×D₈₉	—	2	2	no	—
196	C₂×D₈₉	—	2	2	no	—
197	C₂×D₈₉	—	4	4	no	—
198	C₂×D₈₉	C₈×D₄	1	1	yes	characteristic
199	C₂×D₈₉	C₈×D₄	1	1	yes	characteristic
200	C₄×C₈₉	—	2	2	no	—
201	C₄×C₈₉	—	2	2	no	—
202	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
203	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
204	Dic₈₉	—	2	2	no	—
205	Dic₈₉	—	2	2	no	—
206	Dic₈₉	C₈×D₄	1	1	yes	characteristic
207	Dic₈₉	C₈×D₄	1	1	yes	characteristic
208	C₂×#2170	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	—	2	1	no	—
210	C₂×C₈₉	—	4	2	no	—
211	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
212	D₈₉	—	2	1	no	—
213	D₈₉	—	4	2	no	—
214	D₈₉	#2170	1	2	yes	direct product factor
215	C₂×#504	—	89	2	no	—
216	C₂×#443	—	89	1	no	—
217	#2170	—	89	2	no	—
218	#2170	—	89	1	no	—
219	#2170	—	89	1	no	—
220	#2170	—	89	2	no	—
221	#2170	—	89	1	no	—
222	#2170	D₈₉	1	1	yes	characteristic, direct product factor
223	C₂×#364	—	89	1	no	—
224	C₂×#350	—	89	2	no	—
225	C₂×C₄×C₁₆	—	89	1	no	—
226	C₈₉	C₂×#2170	1	1	yes	characteristic, complemented, Sylow
227	C₂×#135	—	89	1	no	—
228	C₂×#131	—	89	2	no	—
229	#504	—	89	2	no	—
230	#504	—	89	2	no	—
231	#504	—	89	2	no	—
232	#504	—	178	2	no	—
233	#504	—	178	2	no	—
234	#504	C₂×D₈₉	1	2	yes	complemented
235	C₂×M₃₂	—	89	2	no	—
236	C₂×M₃₂	—	178	2	no	—
237	C₂²×C₁₆	—	89	1	no	—
238	C₂²×C₁₆	—	89	1	no	—
239	C₂²×C₁₆	—	178	2	no	—
240	#443	—	89	1	no	—
241	#443	—	89	2	no	—
242	#443	—	89	1	no	—
243	#443	—	89	2	no	—
244	#443	—	89	1	no	—
245	#443	C₂×D₈₉	1	1	yes	characteristic
246	C₂×#108	—	89	1	no	—
247	C₂×#104	—	89	2	no	—
248	C₂×C₄×C₈	—	89	1	no	—
249	#364	—	89	2	no	—
250	#364	—	89	1	no	—
251	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
252	#350	—	89	2	no	—
253	#350	—	89	2	no	—
254	#350	—	89	2	no	—
255	#350	C₂×D₈₉	1	2	yes	complemented
256	C₄×C₁₆	—	89	1	no	—
257	C₄×C₁₆	—	89	1	no	—
258	C₄×C₁₆	—	89	1	no	—
259	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
260	C₂×#41	—	89	2	no	—
261	#135	—	89	2	no	—
262	#135	—	89	1	no	—
263	#135	—	89	2	no	—
264	#135	—	89	1	no	—
265	#135	—	89	1	no	—
266	#135	C₄×D₈₉	1	1	yes	characteristic
267	C₂×Q₁₆	—	89	1	no	—
268	C₂×SD₁₆	—	89	2	no	—
269	C₂×D₈	—	89	1	no	—
270	#131	—	89	2	no	—
271	#131	—	89	2	no	—
272	#131	—	89	2	no	—
273	#131	—	178	2	no	—
274	#131	—	178	2	no	—
275	#131	C₂²×D₈₉	1	2	yes	—
276	C₂×M₁₆	—	89	2	no	—
277	C₂×M₁₆	—	178	2	no	—
278	C₂²×C₈	—	89	1	no	—
279	C₂²×C₈	—	89	1	no	—
280	C₂²×C₈	—	178	2	no	—
281	C₂×C₄²	—	89	1	no	—
282	M₃₂	—	2	2	no	—
283	M₃₂	—	89	2	no	—
284	M₃₂	—	178	2	no	—
285	M₃₂	—	178	2	no	—
286	M₃₂	—	178	2	no	—
287	M₃₂	—	178	2	no	—
288	M₃₂	C₂²×D₈₉	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	89	1	no	—
291	C₂×C₁₆	—	89	1	no	—
292	C₂×C₁₆	—	89	1	no	—
293	C₂×C₁₆	—	89	1	no	—
294	C₂×C₁₆	—	89	1	no	—
295	C₂×C₁₆	—	89	1	no	—
296	C₂×C₁₆	—	178	2	no	—
297	C₂×C₁₆	—	178	1	no	—
298	C₂×C₁₆	—	178	1	no	—
299	C₂×C₁₆	—	178	2	no	—
300	C₂×C₁₆	—	178	2	no	—
301	C₂×C₁₆	—	178	2	no	—
302	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
303	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
304	#108	—	89	2	no	—
305	#108	—	89	1	no	—
306	#108	C₄×D₈₉	1	1	yes	characteristic
307	#104	—	89	2	no	—
308	#104	—	89	2	no	—
309	#104	—	89	2	no	—
310	#104	C₄×D₈₉	1	2	yes	—
311	C₄×C₈	—	89	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
315	#41	—	89	2	no	—
316	#41	—	89	2	no	—
317	#41	—	89	2	no	—
318	#41	—	178	2	no	—
319	#41	—	178	2	no	—
320	#41	C₂×C₄×D₈₉	1	2	yes	—
321	C₂×Q₈	—	89	2	no	—
322	C₂×D₄	—	89	2	no	—
323	C₂×D₄	—	178	2	no	—
324	C₂²×C₄	—	89	1	no	—
325	C₂²×C₄	—	178	2	no	—
326	C₂²×C₄	—	178	1	no	—
327	Q₁₆	—	89	2	no	—
328	Q₁₆	—	89	1	no	—
329	Q₁₆	C₈×D₈₉	1	1	yes	characteristic
330	SD₁₆	—	89	2	no	—
331	SD₁₆	—	89	2	no	—
332	SD₁₆	—	89	2	no	—
333	SD₁₆	C₈×D₈₉	1	2	yes	—
334	D₈	—	89	2	no	—
335	D₈	—	89	1	no	—
336	D₈	C₈×D₈₉	1	1	yes	characteristic
337	M₁₆	—	2	2	no	—
338	M₁₆	—	89	2	no	—
339	M₁₆	—	178	2	no	—
340	M₁₆	—	178	2	no	—
341	M₁₆	—	178	2	no	—
342	M₁₆	—	178	2	no	—
343	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	89	1	no	—
347	C₂×C₈	—	89	1	no	—
348	C₂×C₈	—	89	1	no	—
349	C₂×C₈	—	89	1	no	—
350	C₂×C₈	—	89	1	no	—
351	C₂×C₈	—	89	1	no	—
352	C₂×C₈	—	89	1	no	—
353	C₂×C₈	—	89	1	no	—
354	C₂×C₈	—	89	1	no	—
355	C₂×C₈	—	178	2	no	—
356	C₂×C₈	—	178	2	no	—
357	C₂×C₈	—	178	2	no	—
358	C₂×C₈	—	178	2	no	—
359	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
360	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
361	C₄²	—	89	1	no	—
362	C₄²	—	178	1	no	—
363	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
364	C₁₆	—	2	2	no	—
365	C₁₆	—	2	1	no	—
366	C₁₆	—	89	1	no	—
367	C₁₆	—	89	1	no	—
368	C₁₆	—	178	2	no	—
369	C₁₆	—	178	1	no	—
370	C₁₆	D₄×D₈₉	1	1	yes	characteristic
371	C₁₆	D₄×D₈₉	1	1	yes	characteristic
372	C₂³	—	89	1	no	—
373	C₂³	—	178	2	no	—
374	Q₈	—	89	2	no	—
375	Q₈	—	178	2	no	—
376	Q₈	C₂×C₈×D₈₉	1	2	yes	—
377	D₄	—	2	2	no	—
378	D₄	—	89	2	no	—
379	D₄	—	178	2	no	—
380	D₄	—	178	2	no	—
381	D₄	—	178	2	no	—
382	D₄	—	178	2	no	—
383	D₄	C₂×C₈×D₈₉	1	2	yes	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	89	1	no	—
387	C₂×C₄	—	89	1	no	—
388	C₂×C₄	—	89	1	no	—
389	C₂×C₄	—	89	1	no	—
390	C₂×C₄	—	89	1	no	—
391	C₂×C₄	—	178	2	no	—
392	C₂×C₄	—	178	2	no	—
393	C₂×C₄	—	178	4	no	—
394	C₂×C₄	—	178	2	no	—
395	C₂×C₄	—	178	1	no	—
396	C₂×C₄	—	178	2	no	—
397	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
398	C₈	—	2	2	no	—
399	C₈	—	89	1	no	—
400	C₈	—	89	1	no	—
401	C₈	—	89	1	no	—
402	C₈	—	89	1	no	—
403	C₈	—	178	2	no	—
404	C₈	C₂×C₈×D₈₉	1	1	yes	characteristic
405	C₈	C₂×C₈×D₈₉	1	1	yes	characteristic
406	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
407	C₈	#41×D₈₉	1	1	yes	characteristic
408	C₂²	—	2	2	no	—
409	C₂²	—	89	1	no	—
410	C₂²	—	89	1	no	—
411	C₂²	—	356	4	no	—
412	C₂²	—	178	2	no	—
413	C₂²	—	178	2	no	—
414	C₂²	#131×D₈₉	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	89	1	no	—
418	C₄	—	89	1	no	—
419	C₄	—	178	2	no	—
420	C₄	—	178	2	no	—
421	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
422	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	4	2	no	—
425	C₂	—	89	2	no	—
426	C₂	—	356	2	no	—
427	C₂	—	178	1	no	—
428	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₁₆	D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2170	C₂
socle	C₂×C₈₉	C₂×C₈×D₄
prime radical	#135×D₈₉	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2170	D₈₉
hypocenter	C₈₉	C₂×#2170
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₁₆ ◁ C₂×C₁₆ ◁ #2170

Complements

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

N	H ≅ G/N	type
1. #504×D₈₉	C₂	semidirect
3. #26022090	C₂	semidirect
4. #26022089	C₂	semidirect
5. #26022088	C₂	semidirect
6. #26022087	C₂	semidirect
7. #26022086	C₂	semidirect
8. #364×D₈₉	C₂	semidirect
9. #350×D₈₉	C₂	semidirect
10. C₄×C₁₆×D₈₉	C₂	semidirect
11. C₈₉×#2170	C₂	semidirect
15. #19152016	C₂²	semidirect
16. #19152015	C₂²	semidirect
18. #19152014	C₂²	semidirect
32. #19151419	C₂²	semidirect
33. #19151418	C₂²	semidirect
34. #19151383	C₂²	semidirect
35. #19151382	C₂²	semidirect
36. #19151381	C₂²	semidirect
37. C₄×#13083549	C₂²	semidirect
38. C₁₆×Dic₈₉	C₂²	semidirect
39. C₁₆×Dic₈₉	C₂²	semidirect
40. #504×C₈₉	C₂²	semidirect
42. #364×C₈₉	C₂²	semidirect
43. #350×C₈₉	C₂²	semidirect
44. C₄×C₁₆×C₈₉	C₂²	semidirect
214. D₈₉	#2170	direct (N × H)
222. #2170	D₈₉	direct (N × H)
226. C₈₉	C₂×#2170	semidirect
234. #504	C₂×D₈₉	semidirect
251. #364	C₂×D₈₉	semidirect
255. #350	C₂×D₈₉	semidirect
259. C₄×C₁₆	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#504×D₈₉	2
#443×D₈₉	2
#26022090	2
#26022089	2
#26022088	2
#26022087	2
#26022086	2
#364×D₈₉	2
#350×D₈₉	2
C₄×C₁₆×D₈₉	2
C₈₉×#2170	2
C₂×#2170	89

Subgroups — #2170×D89 #36707652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2170×D₈₉ #36707652