Subgroups — #2165×D₈₉ #36707546

Order 22784.

570 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×M₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#26022064	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022063	C₂	1	2	yes	maximal, complemented
4	#26022062	C₂	1	2	yes	maximal, complemented
5	#26022061	C₂	1	2	yes	maximal, complemented
6	#364×D₈₉	C₂	1	2	yes	maximal, complemented
7	#349×D₈₉	C₂	1	2	yes	maximal
8	#347×D₈₉	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×M₁₆×D₈₉	C₄	1	1	yes	characteristic
11	C₂×M₁₆×D₈₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×D₈₉	C₄	1	1	yes	characteristic
13	M₃₂×D₈₉	C₂²	1	4	yes	—
14	C₄×#13083558	C₄	1	1	yes	characteristic
15	#19151550	C₄	1	1	yes	characteristic
16	#19151550	C₂²	1	1	yes	characteristic
17	M₁₆×Dic₈₉	C₄	1	1	yes	characteristic
18	M₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
19	C₄×#13083557	C₄	1	1	yes	characteristic
20	C₄×#13083557	C₂²	1	1	yes	characteristic
21	#97×D₈₉	C₄	1	1	yes	characteristic
22	#97×D₈₉	C₂²	1	1	yes	characteristic
23	C₄×C₈×D₈₉	C₄	1	1	yes	characteristic
24	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
25	#19151419	C₂²	1	2	yes	complemented
26	#19151418	C₂²	1	4	yes	complemented
27	#19151380	C₂²	1	2	yes	—
28	#19151379	C₂²	1	4	yes	—
29	#19151376	C₂²	1	2	yes	complemented
30	#19151375	C₂²	1	4	yes	complemented
31	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
32	#364×C₈₉	C₂²	1	2	yes	complemented
33	#349×C₈₉	C₂²	1	2	yes	—
34	#347×C₈₉	C₂²	1	2	yes	complemented
35	C₂²×C₄×D₈₉	—	2	1	no	—
36	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
38	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
39	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
40	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
41	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
42	C₂×#13083557	C₂³	1	1	yes	characteristic
43	M₁₆×D₈₉	—	2	2	no	—
44	M₁₆×D₈₉	—	2	2	no	—
45	M₁₆×D₈₉	—	2	2	no	—
46	M₁₆×D₈₉	—	2	2	no	—
47	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
51	C₂×C₄×Dic₈₉	—	2	1	no	—
52	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₈₉	—	2	1	no	—
54	C₄²×D₈₉	—	2	1	no	—
55	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
56	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
57	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
59	#15667952	C₂³	1	4	yes	—
60	#15667951	—	2	4	no	—
61	C₁₆×D₈₉	—	2	4	no	—
62	#15667923	C₂×C₄	1	1	yes	characteristic
63	#15667923	C₂×C₄	1	1	yes	characteristic
64	#15667922	C₂×C₄	1	1	yes	characteristic
65	#15667922	C₂×C₄	1	1	yes	characteristic
66	#15667922	C₂×C₄	1	1	yes	characteristic
67	#15667922	C₂³	1	1	yes	characteristic
68	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
69	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
70	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
77	M₃₂×C₈₉	C₂³	1	4	yes	—
78	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
79	#97×C₈₉	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₂³×D₈₉	M₁₆	1	1	yes	characteristic
83	C₂²×Dic₈₉	—	2	1	no	—
84	C₂²×Dic₈₉	M₁₆	1	1	yes	characteristic
85	C₂×C₄×D₈₉	—	2	1	no	—
86	C₂×C₄×D₈₉	—	2	1	no	—
87	C₂×C₄×D₈₉	—	2	1	no	—
88	C₂×C₄×D₈₉	—	2	1	no	—
89	C₂×C₄×D₈₉	—	2	1	no	—
90	C₂×C₄×D₈₉	—	2	1	no	—
91	C₂×C₄×D₈₉	—	2	1	no	—
92	C₂×C₄×D₈₉	—	2	1	no	—
93	C₂×C₄×D₈₉	—	4	4	no	—
94	C₂×C₄×D₈₉	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₈₉	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
98	#13083558	—	2	2	no	—
99	#13083558	—	2	2	no	—
100	#13083557	—	2	2	no	—
101	#13083557	—	2	2	no	—
102	#13083557	—	2	2	no	—
103	#13083557	—	2	2	no	—
104	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
105	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
106	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
107	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
108	C₈×D₈₉	—	2	1	no	—
109	C₈×D₈₉	—	2	1	no	—
110	C₈×D₈₉	—	2	1	no	—
111	C₈×D₈₉	—	2	1	no	—
112	C₈×D₈₉	M₁₆	1	2	yes	—
113	C₈×D₈₉	M₁₆	1	2	yes	—
114	C₈×D₈₉	#41	1	2	yes	—
115	C₈×D₈₉	#41	1	2	yes	—
116	C₄×Dic₈₉	—	2	1	no	—
117	C₄×Dic₈₉	—	2	1	no	—
118	C₄×Dic₈₉	—	2	1	no	—
119	C₄×Dic₈₉	—	2	1	no	—
120	C₄×Dic₈₉	—	2	1	no	—
121	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
123	#13083549	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	1	no	—
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	M₁₆×C₈₉	—	2	2	no	—
127	M₁₆×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
132	C₄²×C₈₉	—	2	1	no	—
133	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₁₆×C₈₉	—	2	4	no	—
136	C₂³×C₈₉	C₂×M₁₆	1	1	yes	characteristic
137	C₂²×D₈₉	—	2	1	no	—
138	C₂²×D₈₉	—	2	1	no	—
139	C₂²×D₈₉	—	4	2	no	—
140	C₂²×D₈₉	C₂×M₁₆	1	1	yes	characteristic
141	C₂²×D₈₉	C₂×M₁₆	1	1	yes	characteristic
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	2	1	no	—
145	C₂×C₄×C₈₉	—	2	1	no	—
146	C₂×C₄×C₈₉	—	4	2	no	—
147	C₂×C₄×C₈₉	C₂×M₁₆	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
149	C₂×Dic₈₉	—	2	1	no	—
150	C₂×Dic₈₉	—	2	1	no	—
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	4	2	no	—
154	C₂×Dic₈₉	C₂×M₁₆	1	1	yes	characteristic
155	C₂×Dic₈₉	C₂×M₁₆	1	1	yes	characteristic
156	C₄×D₈₉	—	2	4	no	—
157	C₄×D₈₉	—	2	1	no	—
158	C₄×D₈₉	—	2	1	no	—
159	C₄×D₈₉	—	2	1	no	—
160	C₄×D₈₉	—	2	1	no	—
161	C₄×D₈₉	—	2	1	no	—
162	C₄×D₈₉	—	2	1	no	—
163	C₄×D₈₉	—	4	2	no	—
164	C₄×D₈₉	—	4	2	no	—
165	C₄×D₈₉	—	4	2	no	—
166	C₄×D₈₉	#117	1	1	yes	characteristic
167	C₄×D₈₉	#117	1	1	yes	characteristic
168	C₄×D₈₉	C₂×M₁₆	1	1	yes	characteristic
169	C₄×D₈₉	C₂×M₁₆	1	1	yes	characteristic
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	C₈×C₈₉	C₂×M₁₆	1	2	yes	—
173	C₈×C₈₉	C₂×#41	1	2	yes	—
174	#10623494	—	2	1	no	—
175	#10623494	—	2	1	no	—
176	#10623494	#117	1	2	yes	—
177	#10623494	C₂×M₁₆	1	2	yes	—
178	C₂²×C₈₉	—	2	1	no	—
179	C₂²×C₈₉	—	4	1	no	—
180	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
181	C₂×D₈₉	—	2	2	no	—
182	C₂×D₈₉	—	2	1	no	—
183	C₂×D₈₉	—	4	2	no	—
184	C₂×D₈₉	—	4	2	no	—
185	C₂×D₈₉	—	4	1	no	—
186	C₂×D₈₉	#432	1	1	yes	characteristic
187	C₂×D₈₉	#432	1	1	yes	characteristic
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	4	1	no	—
191	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
192	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
193	Dic₈₉	—	2	2	no	—
194	Dic₈₉	—	2	1	no	—
195	Dic₈₉	—	4	1	no	—
196	Dic₈₉	#432	1	1	yes	characteristic
197	Dic₈₉	#432	1	1	yes	characteristic
198	C₂×#2165	—	89	1	no	maximal, Sylow
199	C₂×C₈₉	—	2	1	no	—
200	C₂×C₈₉	—	4	1	no	—
201	C₂×C₈₉	C₂×#432	1	1	yes	characteristic
202	D₈₉	—	2	1	no	—
203	D₈₉	—	4	1	no	—
204	D₈₉	#2165	1	2	yes	direct product factor
205	C₂×C₄×M₁₆	—	89	1	no	—
206	#2165	—	89	1	no	—
207	#2165	—	89	2	no	—
208	#2165	—	89	2	no	—
209	#2165	—	89	2	no	—
210	#2165	D₈₉	1	1	yes	characteristic, direct product factor
211	C₂×#364	—	89	2	no	—
212	C₂×#349	—	89	2	no	—
213	C₂×#347	—	89	2	no	—
214	C₈₉	C₂×#2165	1	1	yes	characteristic, complemented, Sylow
215	C₂²×M₁₆	—	89	1	no	—
216	C₂²×M₁₆	—	89	1	no	—
217	C₂²×C₄²	—	89	1	no	—
218	C₂×M₃₂	—	89	4	no	—
219	C₄×M₁₆	—	89	1	no	—
220	C₄×M₁₆	—	89	1	no	—
221	C₄×M₁₆	—	89	1	no	—
222	C₄×M₁₆	—	89	1	no	—
223	C₄×M₁₆	—	89	1	no	—
224	C₄×M₁₆	—	89	1	no	—
225	C₄×M₁₆	—	89	1	no	—
226	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
227	C₂×#97	—	89	1	no	—
228	C₂×#97	—	89	1	no	—
229	C₂×C₄×C₈	—	89	1	no	—
230	C₂×C₄×C₈	—	89	1	no	—
231	#364	—	89	4	no	—
232	#364	—	89	2	no	—
233	#364	C₂×D₈₉	1	2	yes	complemented
234	#349	—	89	2	no	—
235	#349	—	89	4	no	—
236	#349	C₂×D₈₉	1	2	yes	—
237	#347	—	89	4	no	—
238	#347	—	89	2	no	—
239	#347	C₂×D₈₉	1	2	yes	complemented
240	C₂³×C₄	—	89	1	no	—
241	C₂³×C₄	—	178	1	no	—
242	C₂×M₁₆	—	89	1	no	—
243	C₂×M₁₆	—	89	1	no	—
244	C₂×M₁₆	—	89	1	no	—
245	C₂×M₁₆	—	89	1	no	—
246	C₂×M₁₆	—	89	1	no	—
247	C₂×M₁₆	—	89	1	no	—
248	C₂×M₁₆	—	178	2	no	—
249	C₂×M₁₆	—	178	2	no	—
250	C₂×M₁₆	—	178	2	no	—
251	C₂×M₁₆	—	178	2	no	—
252	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
253	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
254	C₂²×C₈	—	89	1	no	—
255	C₂²×C₈	—	89	1	no	—
256	C₂²×C₈	—	89	1	no	—
257	C₂²×C₈	—	89	1	no	—
258	C₂×C₄²	—	89	1	no	—
259	C₂×C₄²	—	89	1	no	—
260	C₂×C₄²	—	89	1	no	—
261	C₂×C₄²	—	89	1	no	—
262	C₂×C₄²	—	89	1	no	—
263	C₂×C₄²	—	178	1	no	—
264	C₂×C₄²	—	178	1	no	—
265	C₂×C₄²	—	178	1	no	—
266	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
267	M₃₂	—	89	4	no	—
268	M₃₂	—	178	4	no	—
269	M₃₂	C₂²×D₈₉	1	4	yes	—
270	C₂×C₁₆	—	178	4	no	—
271	#97	—	89	1	no	—
272	#97	—	89	1	no	—
273	#97	—	89	1	no	—
274	#97	—	89	1	no	—
275	#97	—	89	1	no	—
276	#97	—	89	1	no	—
277	#97	C₄×D₈₉	1	1	yes	characteristic
278	#97	C₂²×D₈₉	1	1	yes	characteristic
279	C₄×C₈	—	89	1	no	—
280	C₄×C₈	—	89	1	no	—
281	C₄×C₈	—	89	1	no	—
282	C₄×C₈	—	89	1	no	—
283	C₄×C₈	—	89	1	no	—
284	C₄×C₈	—	89	1	no	—
285	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
286	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
287	C₂⁴	—	89	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	89	1	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	89	1	no	—
292	C₂²×C₄	—	89	1	no	—
293	C₂²×C₄	—	89	1	no	—
294	C₂²×C₄	—	356	4	no	—
295	C₂²×C₄	—	178	1	no	—
296	C₂²×C₄	—	178	1	no	—
297	C₂²×C₄	—	178	1	no	—
298	C₂²×C₄	—	178	1	no	—
299	C₂²×C₄	—	178	1	no	—
300	C₂²×C₄	—	178	1	no	—
301	C₂²×C₄	—	178	1	no	—
302	C₂²×C₄	—	178	1	no	—
303	C₂²×C₄	—	178	1	no	—
304	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	178	2	no	—
308	M₁₆	—	178	2	no	—
309	M₁₆	—	178	2	no	—
310	M₁₆	—	178	2	no	—
311	M₁₆	—	178	2	no	—
312	M₁₆	—	178	2	no	—
313	C₂×C₈	—	89	1	no	—
314	C₂×C₈	—	89	1	no	—
315	C₂×C₈	—	89	2	no	—
316	C₂×C₈	—	89	2	no	—
317	C₂×C₈	—	89	2	no	—
318	C₂×C₈	—	89	2	no	—
319	C₂×C₈	—	89	1	no	—
320	C₂×C₈	—	89	1	no	—
321	C₂×C₈	—	178	1	no	—
322	C₂×C₈	—	178	1	no	—
323	C₂×C₈	—	178	1	no	—
324	C₂×C₈	—	178	1	no	—
325	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
326	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
329	C₄²	—	2	1	no	—
330	C₄²	—	89	1	no	—
331	C₄²	—	89	1	no	—
332	C₄²	—	178	1	no	—
333	C₄²	—	178	1	no	—
334	C₄²	—	178	1	no	—
335	C₄²	—	178	1	no	—
336	C₄²	—	178	1	no	—
337	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
339	C₁₆	—	2	4	no	—
340	C₁₆	—	178	4	no	—
341	C₂³	—	89	1	no	—
342	C₂³	—	89	1	no	—
343	C₂³	—	356	2	no	—
344	C₂³	—	178	1	no	—
345	C₂³	—	178	1	no	—
346	C₂³	M₁₆×D₈₉	1	1	yes	characteristic
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	89	1	no	—
353	C₂×C₄	—	89	1	no	—
354	C₂×C₄	—	89	1	no	—
355	C₂×C₄	—	89	1	no	—
356	C₂×C₄	—	89	1	no	—
357	C₂×C₄	—	89	1	no	—
358	C₂×C₄	—	356	2	no	—
359	C₂×C₄	—	356	2	no	—
360	C₂×C₄	—	356	2	no	—
361	C₂×C₄	—	356	2	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	1	no	—
365	C₂×C₄	—	178	1	no	—
366	C₂×C₄	—	178	4	no	—
367	C₂×C₄	—	178	1	no	—
368	C₂×C₄	—	178	1	no	—
369	C₂×C₄	—	178	1	no	—
370	C₂×C₄	—	178	1	no	—
371	C₂×C₄	—	178	1	no	—
372	C₂×C₄	—	178	1	no	—
373	C₂×C₄	M₁₆×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	89	2	no	—
378	C₈	—	89	2	no	—
379	C₈	—	178	1	no	—
380	C₈	—	178	1	no	—
381	C₈	M₁₆×D₈₉	1	2	yes	—
382	C₈	#41×D₈₉	1	2	yes	—
383	C₂²	—	2	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	89	1	no	—
386	C₂²	—	89	1	no	—
387	C₂²	—	356	1	no	—
388	C₂²	—	356	2	no	—
389	C₂²	—	356	2	no	—
390	C₂²	—	178	2	no	—
391	C₂²	—	178	1	no	—
392	C₂²	C₂×M₁₆×D₈₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	1	no	—
396	C₄	—	89	1	no	—
397	C₄	—	89	1	no	—
398	C₄	—	356	1	no	—
399	C₄	—	178	2	no	—
400	C₄	—	178	1	no	—
401	C₄	#117×D₈₉	1	1	yes	characteristic
402	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
403	C₂	—	2	1	no	—
404	C₂	—	4	1	no	—
405	C₂	—	89	2	no	—
406	C₂	—	356	1	no	—
407	C₂	—	178	1	no	—
408	C₂	#432×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#117×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2165	C₂
socle	C₂×C₈₉	C₂×#432
prime radical	C₂³×D₈₉	M₁₆
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2165	D₈₉
hypocenter	C₈₉	C₂×#2165
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ #97 ◁ #2165

Complements

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

N	H ≅ G/N	type
2. #26022064	C₂	semidirect
3. #26022063	C₂	semidirect
4. #26022062	C₂	semidirect
5. #26022061	C₂	semidirect
6. #364×D₈₉	C₂	semidirect
8. #347×D₈₉	C₂	semidirect
9. C₈₉×#2165	C₂	semidirect
25. #19151419	C₂²	semidirect
26. #19151418	C₂²	semidirect
29. #19151376	C₂²	semidirect
30. #19151375	C₂²	semidirect
32. #364×C₈₉	C₂²	semidirect
34. #347×C₈₉	C₂²	semidirect
204. D₈₉	#2165	direct (N × H)
210. #2165	D₈₉	direct (N × H)
214. C₈₉	C₂×#2165	semidirect
233. #364	C₂×D₈₉	semidirect
239. #347	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×M₁₆×D₈₉	2
#26022064	2
#26022063	2
#26022062	2
#26022061	2
#364×D₈₉	2
#349×D₈₉	2
#347×D₈₉	2
C₈₉×#2165	2
C₂×#2165	89

Subgroups — #2165×D89 #36707546

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2165×D₈₉ #36707546