Subgroups — C₄×D₁₆×D₈₉ #36707685

Order 22784.

806 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₄×D₈×D₈₉	C₂	1	2	yes	maximal, complemented
3	C₄×D₁₄₂₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022098	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#15667953	C₂	1	2	yes	maximal, complemented
7	#26022096	C₂	1	2	yes	maximal, complemented
8	#366×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#357×D₈₉	C₂	1	2	yes	maximal, complemented
10	C₄×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×D₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₈₉	C₂²	1	2	yes	—
13	C₄×D₄×D₈₉	—	2	2	no	—
14	C₂×D₁₄₂₄	C₂²	1	1	yes	characteristic
15	C₂×#15667953	C₂²	1	2	yes	—
16	D₁₆×D₈₉	C₄	1	8	yes	direct product factor
17	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
19	C₄×D₇₁₂	C₂²	1	2	yes	complemented
20	D₈×Dic₈₉	C₂²	1	2	yes	complemented
21	#19151680	C₂²	1	2	yes	complemented
22	C₄×#13083559	—	2	2	no	—
23	#19151678	—	2	2	no	—
24	#107×D₈₉	C₂²	1	2	yes	—
25	#102×D₈₉	—	2	2	no	—
26	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
27	#19151424	C₂²	1	1	yes	characteristic, complemented
28	#19151423	C₂²	1	2	yes	complemented
29	#19151400	C₂²	1	2	yes	complemented
30	#19151399	C₂²	1	2	yes	complemented
31	#19151398	C₂²	1	2	yes	complemented
32	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
33	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×D₁₆×C₈₉	C₂²	1	1	yes	characteristic
36	C₄×D₈×C₈₉	C₂²	1	2	yes	complemented
37	#366×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	#357×C₈₉	C₂²	1	2	yes	complemented
39	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₈₉	—	2	2	no	—
41	C₂²×C₄×D₈₉	—	4	2	no	—
42	C₂×D₇₁₂	C₂³	1	2	yes	—
43	C₂×#13083559	—	2	2	no	—
44	D₈×D₈₉	—	2	4	no	—
45	D₈×D₈₉	C₂×C₄	1	8	yes	complemented
46	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
47	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
48	C₄×D₃₅₆	—	2	2	no	—
49	D₄×Dic₈₉	—	2	2	no	—
50	#15667974	—	2	2	no	—
51	C₄×C₂²⋊D₈₉	—	4	2	no	—
52	#15667972	—	4	2	no	—
53	C₄⋊C₄×D₈₉	—	2	2	no	—
54	C₂²⋊C₄×D₈₉	—	4	2	no	—
55	C₄²×D₈₉	D₄	1	1	yes	characteristic
56	D₁₄₂₄	C₂×C₄	1	4	yes	complemented
57	#15667953	C₂×C₄	1	8	yes	complemented
58	C₂×#13083549	C₂³	1	1	yes	characteristic
59	C₂×#13083549	C₂³	1	1	yes	characteristic
60	C₁₆×D₈₉	—	2	2	no	—
61	C₁₆×D₈₉	C₂×C₄	1	4	yes	complemented
62	#15667946	C₂³	1	2	yes	—
63	#15667945	—	2	2	no	—
64	#15667934	—	2	2	no	—
65	#15667933	—	2	2	no	—
66	#15667932	—	2	2	no	—
67	C₄×#10623494	D₄	1	1	yes	characteristic
68	C₈×Dic₈₉	D₄	1	1	yes	characteristic
69	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
70	C₂×D₈×C₈₉	C₂³	1	2	yes	—
71	C₄×D₄×C₈₉	—	2	2	no	—
72	D₁₆×C₈₉	C₂×C₄	1	4	yes	complemented
73	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
75	#107×C₈₉	C₂³	1	2	yes	—
76	#102×C₈₉	—	2	2	no	—
77	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×D₈₉	—	4	2	no	—
79	C₂×D₃₅₆	—	2	2	no	—
80	C₂×C₂²⋊D₈₉	—	4	2	no	—
81	D₄×D₈₉	—	2	8	no	—
82	D₄×D₈₉	—	4	4	no	—
83	C₂²×Dic₈₉	—	4	2	no	—
84	C₂×C₄×D₈₉	—	4	2	no	—
85	C₂×C₄×D₈₉	—	4	2	no	—
86	C₂×C₄×D₈₉	—	4	2	no	—
87	C₂×C₄×D₈₉	—	8	8	no	—
88	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
89	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
90	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
91	D₇₁₂	—	2	2	no	—
92	D₇₁₂	C₂²×C₄	1	4	yes	complemented
93	#13083559	—	2	8	no	—
94	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
95	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
96	C₈×D₈₉	—	2	2	no	—
97	C₈×D₈₉	C₂²×C₄	1	2	yes	—
98	C₈×D₈₉	#41	1	2	yes	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	#13083553	—	4	2	no	—
101	C₂²⋊Dic₈₉	—	4	2	no	—
102	#13083551	—	4	2	no	—
103	#13083551	—	4	2	no	—
104	C₄×Dic₈₉	D₈	1	1	yes	characteristic
105	C₄×Dic₈₉	D₈	1	1	yes	characteristic
106	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
107	#13083549	—	2	1	no	—
108	#13083549	C₂²×C₄	1	2	yes	complemented
109	C₂×D₄×C₈₉	—	2	2	no	—
110	C₂²×C₄×C₈₉	—	4	2	no	—
111	D₈×C₈₉	—	2	2	no	—
112	D₈×C₈₉	C₂²×C₄	1	4	yes	complemented
113	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₈₉	—	2	2	no	—
116	C₂²⋊C₄×C₈₉	—	4	2	no	—
117	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
118	C₁₆×C₈₉	—	2	1	no	—
119	C₁₆×C₈₉	C₂²×C₄	1	2	yes	complemented
120	C₂³×C₈₉	—	4	2	no	—
121	C₂²×D₈₉	—	4	2	no	—
122	C₂²×D₈₉	—	4	8	no	—
123	C₂²×D₈₉	—	8	4	no	—
124	C₂²×D₈₉	—	8	4	no	—
125	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
126	D₄×C₈₉	—	2	4	no	—
127	D₄×C₈₉	—	4	2	no	—
128	C₂×C₄×C₈₉	—	4	2	no	—
129	C₂×C₄×C₈₉	—	8	4	no	—
130	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
131	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
132	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
133	C₂²⋊D₈₉	—	4	8	no	—
134	C₂×Dic₈₉	—	4	2	no	—
135	C₂×Dic₈₉	—	8	4	no	—
136	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
137	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
138	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
139	D₃₅₆	—	2	4	no	—
140	D₃₅₆	—	4	2	no	—
141	C₄×D₈₉	—	2	2	no	—
142	C₄×D₈₉	—	8	4	no	—
143	C₄×D₈₉	—	8	4	no	—
144	C₄×D₈₉	—	8	4	no	—
145	C₄×D₈₉	D₁₆	1	4	yes	direct product factor
146	C₄×D₈₉	C₄×D₄	1	2	yes	—
147	C₄×D₈₉	#135	1	2	yes	—
148	C₈×C₈₉	—	2	1	no	—
149	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
150	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
151	#10623494	—	2	1	no	—
152	#10623494	C₄×D₄	1	2	yes	—
153	C₂²×C₈₉	—	4	4	no	—
154	C₂²×C₈₉	—	8	2	no	—
155	C₂²×C₈₉	—	8	2	no	—
156	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
157	C₂×D₈₉	—	4	4	no	—
158	C₂×D₈₉	—	8	2	no	—
159	C₂×D₈₉	—	8	2	no	—
160	C₂×D₈₉	—	8	16	no	—
161	C₂×D₈₉	C₄×D₈	1	2	yes	—
162	C₂×D₈₉	C₂×D₁₆	1	2	yes	—
163	C₂×D₈₉	#508	1	2	yes	—
164	C₄×C₈₉	—	2	1	no	—
165	C₄×C₈₉	—	8	2	no	—
166	C₄×C₈₉	C₂×D₁₆	1	2	yes	complemented
167	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
168	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
169	Dic₈₉	—	2	1	no	—
170	Dic₈₉	—	8	2	no	—
171	Dic₈₉	C₄×D₈	1	2	yes	—
172	Dic₈₉	C₂×D₁₆	1	2	yes	complemented
173	C₂×C₄×D₁₆	—	89	1	no	maximal, Sylow
174	C₂×C₈₉	—	8	4	no	—
175	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
176	C₂×C₈₉	C₂²×D₁₆	1	1	yes	characteristic
177	C₂×C₈₉	C₂×#508	1	1	yes	characteristic
178	D₈₉	—	8	4	no	—
179	D₈₉	C₄×D₁₆	1	4	yes	direct product factor
180	C₂²×D₁₆	—	89	1	no	—
181	C₂×C₄×D₈	—	89	2	no	—
182	C₄×D₁₆	—	89	1	no	—
183	C₄×D₁₆	—	89	2	no	—
184	C₄×D₁₆	—	89	1	no	—
185	C₄×D₁₆	—	89	2	no	—
186	C₄×D₁₆	—	89	1	no	—
187	C₄×D₁₆	D₈₉	1	1	yes	characteristic, direct product factor
188	C₂×#366	—	89	1	no	—
189	C₂×#357	—	89	2	no	—
190	C₂×C₄×C₁₆	—	89	1	no	—
191	C₈₉	C₂×C₄×D₁₆	1	1	yes	characteristic, complemented, Sylow
192	C₂²×D₈	—	89	2	no	—
193	C₂×C₄×D₄	—	178	2	no	—
194	C₂×D₁₆	—	89	2	no	—
195	C₂×D₁₆	—	89	8	no	—
196	C₂×D₁₆	—	89	1	no	—
197	C₂×D₁₆	C₂×D₈₉	1	1	yes	characteristic
198	C₂²×C₁₆	—	89	1	no	—
199	C₂²×C₁₆	—	89	1	no	—
200	C₄×D₈	—	89	2	no	—
201	C₄×D₈	—	89	2	no	—
202	C₄×D₈	—	89	2	no	—
203	C₄×D₈	—	178	2	no	—
204	C₄×D₈	—	178	2	no	—
205	C₄×D₈	C₂×D₈₉	1	2	yes	complemented
206	C₂×#107	—	89	2	no	—
207	C₂×#102	—	178	2	no	—
208	C₂×C₄×C₈	—	89	1	no	—
209	#366	—	89	1	no	—
210	#366	—	89	2	no	—
211	#366	C₂×D₈₉	1	1	yes	characteristic, complemented
212	#357	—	89	2	no	—
213	#357	—	89	2	no	—
214	#357	—	89	2	no	—
215	#357	C₂×D₈₉	1	2	yes	complemented
216	C₄×C₁₆	—	89	1	no	—
217	C₄×C₁₆	—	89	1	no	—
218	C₄×C₁₆	—	89	1	no	—
219	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
220	C₂²×D₄	—	178	2	no	—
221	C₂³×C₄	—	356	2	no	—
222	C₂×D₈	—	89	8	no	—
223	C₂×D₈	—	89	2	no	—
224	C₂×D₈	—	178	4	no	—
225	C₂×D₈	—	178	2	no	—
226	C₂×D₈	C₂²×D₈₉	1	2	yes	—
227	C₂²×C₈	—	89	1	no	—
228	C₂²×C₈	—	89	1	no	—
229	C₄×D₄	—	2	2	no	—
230	C₄×D₄	—	356	2	no	—
231	C₄×D₄	—	356	2	no	—
232	C₄×D₄	—	178	2	no	—
233	C₄×D₄	—	178	2	no	—
234	C₄×D₄	—	178	2	no	—
235	C₂×C₄⋊C₄	—	178	2	no	—
236	C₂×C₂²⋊C₄	—	356	2	no	—
237	C₂×C₄²	—	89	1	no	—
238	D₁₆	—	89	8	no	—
239	D₁₆	—	89	4	no	—
240	D₁₆	C₄×D₈₉	1	4	yes	direct product factor
241	C₂×C₁₆	—	89	1	no	—
242	C₂×C₁₆	—	89	4	no	—
243	C₂×C₁₆	—	89	1	no	—
244	C₂×C₁₆	—	178	2	no	—
245	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
246	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
247	#107	—	89	2	no	—
248	#107	—	178	2	no	—
249	#107	C₂²×D₈₉	1	2	yes	—
250	#102	—	2	2	no	—
251	#102	—	178	2	no	—
252	#102	—	178	2	no	—
253	#102	—	178	2	no	—
254	C₄×C₈	—	89	1	no	—
255	C₄×C₈	—	89	1	no	—
256	C₄×C₈	—	89	1	no	—
257	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
258	C₂⁴	—	356	2	no	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	—	356	4	no	—
261	C₂×D₄	—	356	2	no	—
262	C₂×D₄	—	178	8	no	—
263	C₂×D₄	—	178	2	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	—	89	1	no	—
266	C₂²×C₄	—	89	1	no	—
267	C₂²×C₄	—	89	1	no	—
268	C₂²×C₄	—	356	2	no	—
269	C₂²×C₄	—	356	2	no	—
270	C₂²×C₄	—	356	2	no	—
271	C₂²×C₄	—	356	2	no	—
272	C₂²×C₄	—	712	8	no	—
273	D₈	—	2	2	no	—
274	D₈	—	89	4	no	—
275	D₈	—	178	8	no	—
276	D₈	—	178	2	no	—
277	D₈	C₂×C₄×D₈₉	1	4	yes	complemented
278	C₂×C₈	—	89	1	no	—
279	C₂×C₈	—	89	2	no	—
280	C₂×C₈	—	89	2	no	—
281	C₂×C₈	—	89	1	no	—
282	C₂×C₈	—	178	2	no	—
283	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
284	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	356	2	no	—
287	C₄⋊C₄	—	178	2	no	—
288	C₂²⋊C₄	—	4	2	no	—
289	C₂²⋊C₄	—	356	2	no	—
290	C₂²⋊C₄	—	356	2	no	—
291	C₂²⋊C₄	—	356	2	no	—
292	C₄²	—	89	1	no	—
293	C₄²	—	89	1	no	—
294	C₄²	—	89	1	no	—
295	C₄²	D₄×D₈₉	1	1	yes	characteristic
296	C₁₆	—	2	1	no	—
297	C₁₆	—	89	2	no	—
298	C₁₆	—	178	1	no	—
299	C₁₆	C₂×C₄×D₈₉	1	2	yes	complemented
300	C₂³	—	4	2	no	—
301	C₂³	—	89	1	no	—
302	C₂³	—	356	8	no	—
303	C₂³	—	356	2	no	—
304	C₂³	—	712	4	no	—
305	C₂³	—	712	4	no	—
306	D₄	—	2	4	no	—
307	D₄	—	4	2	no	—
308	D₄	—	356	8	no	—
309	D₄	—	356	2	no	—
310	D₄	—	178	4	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	8	4	no	—
313	C₂×C₄	—	89	1	no	—
314	C₂×C₄	—	89	1	no	—
315	C₂×C₄	—	89	4	no	—
316	C₂×C₄	—	89	2	no	—
317	C₂×C₄	—	89	2	no	—
318	C₂×C₄	—	89	1	no	—
319	C₂×C₄	—	356	2	no	—
320	C₂×C₄	—	178	2	no	—
321	C₂×C₄	—	712	4	no	—
322	C₂×C₄	—	712	4	no	—
323	C₂×C₄	—	712	4	no	—
324	C₂×C₄	—	712	4	no	—
325	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
326	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
327	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
328	C₈	—	2	1	no	—
329	C₈	—	89	2	no	—
330	C₈	—	178	1	no	—
331	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
332	C₈	#41×D₈₉	1	1	yes	characteristic
333	C₂²	—	4	4	no	—
334	C₂²	—	8	2	no	—
335	C₂²	—	8	2	no	—
336	C₂²	—	89	2	no	—
337	C₂²	—	89	2	no	—
338	C₂²	—	89	2	no	—
339	C₂²	—	356	4	no	—
340	C₂²	—	712	16	no	—
341	C₂²	—	712	2	no	—
342	C₂²	—	712	2	no	—
343	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	8	2	no	—
346	C₄	—	89	2	no	—
347	C₄	—	89	2	no	—
348	C₄	—	178	1	no	—
349	C₄	—	712	2	no	—
350	C₄	D₁₆×D₈₉	1	2	yes	direct product factor
351	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
352	C₄	#135×D₈₉	1	1	yes	characteristic
353	C₂	—	8	4	no	—
354	C₂	—	89	4	no	—
355	C₂	—	712	4	no	—
356	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic
357	C₂	C₂×D₁₆×D₈₉	1	1	yes	characteristic
358	C₂	#508×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈×D₈₉
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₄×D₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂×D₁₆×D₈₉	C₂
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₄×D₁₆	D₈₉
hypocenter	C₈₉	C₂×C₄×D₁₆
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×D₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×D₈×D₈₉	C₂	semidirect
3. C₄×D₁₄₂₄	C₂	semidirect
4. D₁₆×Dic₈₉	C₂	semidirect
5. #26022098	C₂	semidirect
6. C₄×#15667953	C₂	semidirect
7. #26022096	C₂	semidirect
8. #366×D₈₉	C₂	semidirect
9. #357×D₈₉	C₂	semidirect
10. C₄×C₁₆×D₈₉	C₂	semidirect
11. C₄×D₁₆×C₈₉	C₂	semidirect
16. D₁₆×D₈₉	C₄	direct (N × H)
19. C₄×D₇₁₂	C₂²	semidirect
20. D₈×Dic₈₉	C₂²	semidirect
21. #19151680	C₂²	semidirect
27. #19151424	C₂²	semidirect
28. #19151423	C₂²	semidirect
29. #19151400	C₂²	semidirect
30. #19151399	C₂²	semidirect
31. #19151398	C₂²	semidirect
32. C₄×#13083549	C₂²	semidirect
33. C₁₆×Dic₈₉	C₂²	semidirect
34. C₁₆×Dic₈₉	C₂²	semidirect
36. C₄×D₈×C₈₉	C₂²	semidirect
37. #366×C₈₉	C₂²	semidirect
38. #357×C₈₉	C₂²	semidirect
39. C₄×C₁₆×C₈₉	C₂²	semidirect
45. D₈×D₈₉	C₂×C₄	semidirect
56. D₁₄₂₄	C₂×C₄	semidirect
57. #15667953	C₂×C₄	semidirect
61. C₁₆×D₈₉	C₂×C₄	semidirect
72. D₁₆×C₈₉	C₂×C₄	semidirect
92. D₇₁₂	C₂²×C₄	semidirect
108. #13083549	C₂²×C₄	semidirect
112. D₈×C₈₉	C₂²×C₄	semidirect
119. C₁₆×C₈₉	C₂²×C₄	semidirect
145. C₄×D₈₉	D₁₆	direct (N × H)
166. C₄×C₈₉	C₂×D₁₆	semidirect
172. Dic₈₉	C₂×D₁₆	semidirect
179. D₈₉	C₄×D₁₆	direct (N × H)
187. C₄×D₁₆	D₈₉	direct (N × H)
191. C₈₉	C₂×C₄×D₁₆	semidirect
205. C₄×D₈	C₂×D₈₉	semidirect
211. #366	C₂×D₈₉	semidirect
215. #357	C₂×D₈₉	semidirect
219. C₄×C₁₆	C₂×D₈₉	semidirect
240. D₁₆	C₄×D₈₉	direct (N × H)
277. D₈	C₂×C₄×D₈₉	semidirect
299. C₁₆	C₂×C₄×D₈₉	semidirect
350. C₄	D₁₆×D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×D₁₆×D₈₉	2
C₄×D₈×D₈₉	2
C₄×D₁₄₂₄	2
D₁₆×Dic₈₉	2
#26022098	2
C₄×#15667953	2
#26022096	2
#366×D₈₉	2
#357×D₈₉	2
C₄×C₁₆×D₈₉	2
C₄×D₁₆×C₈₉	2
C₂×C₄×D₁₆	89

Subgroups — C4×D16×D89 #36707685

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₁₆×D₈₉ #36707685