Subgroups — C₄×SD₃₂×D₈₉ #36707691

Order 22784.

742 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₃₂×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26022107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#15667957	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₃₂×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×#15667955	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022103	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#15667956	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022101	C₂	1	1	yes	maximal, characteristic, complemented
11	#367×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#358×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#357×D₈₉	C₂	1	1	yes	maximal, characteristic
14	C₄×C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	C₂²	1	1	yes	characteristic
17	C₂×D₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₉	—	2	1	no	—
19	C₄×D₄×D₈₉	—	2	1	no	—
20	C₂×#15667957	C₂²	1	1	yes	characteristic
21	C₂×#15667956	C₂²	1	1	yes	characteristic
22	C₂×#15667955	C₂²	1	1	yes	characteristic
23	SD₃₂×D₈₉	C₄	1	8	yes	direct product factor
24	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
26	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic, complemented
27	Q₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
28	#19151692	C₂²	1	1	yes	characteristic, complemented
29	C₄×#13083564	—	2	1	no	—
30	#19151690	—	2	1	no	—
31	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
32	D₈×Dic₈₉	C₂²	1	1	yes	characteristic
33	#19151680	C₂²	1	1	yes	characteristic
34	C₄×#13083559	—	2	1	no	—
35	#19151678	—	2	1	no	—
36	#107×D₈₉	C₂²	1	1	yes	characteristic
37	#107×D₈₉	C₂²	1	1	yes	characteristic
38	#103×D₈₉	—	2	1	no	—
39	#102×D₈₉	—	2	1	no	—
40	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
41	#19151426	C₂²	1	1	yes	characteristic, complemented
42	#19151425	C₂²	1	1	yes	characteristic, complemented
43	#19151425	C₂²	1	1	yes	characteristic, complemented
44	#19151403	C₂²	1	1	yes	characteristic, complemented
45	#19151402	C₂²	1	1	yes	characteristic, complemented
46	#19151401	C₂²	1	1	yes	characteristic, complemented
47	#19151400	C₂²	1	1	yes	characteristic
48	#19151399	C₂²	1	1	yes	characteristic
49	#19151398	C₂²	1	1	yes	characteristic
50	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
51	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
52	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₃₂×C₈₉	C₂²	1	1	yes	characteristic
54	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
56	#367×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#358×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#357×C₈₉	C₂²	1	1	yes	characteristic
59	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	C₂×Q₈×D₈₉	—	2	1	no	—
61	C₂×D₄×D₈₉	—	2	1	no	—
62	C₂²×C₄×D₈₉	—	4	1	no	—
63	C₂×Dic₃₅₆	C₂³	1	1	yes	characteristic
64	C₂×#13083564	—	2	1	no	—
65	Q₁₆×D₈₉	—	2	2	no	—
66	Q₁₆×D₈₉	C₂×C₄	1	4	yes	complemented
67	C₂×D₇₁₂	C₂³	1	1	yes	characteristic
68	C₂×#13083559	—	2	1	no	—
69	D₈×D₈₉	—	2	2	no	—
70	D₈×D₈₉	C₂×C₄	1	4	yes	—
71	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
72	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
73	Q₈×Dic₈₉	—	2	1	no	—
74	C₄×Dic₁₇₈	—	2	1	no	—
75	C₄×Dic₁₇₈	—	4	1	no	—
76	#15667977	—	2	1	no	—
77	#15667977	—	4	1	no	—
78	C₄×D₃₅₆	—	2	1	no	—
79	D₄×Dic₈₉	—	2	1	no	—
80	#15667974	—	2	1	no	—
81	C₄×C₂²⋊D₈₉	—	4	1	no	—
82	#15667972	—	4	1	no	—
83	C₄⋊C₄×D₈₉	—	2	1	no	—
84	C₄⋊C₄×D₈₉	—	2	1	no	—
85	C₄⋊C₄×D₈₉	—	4	1	no	—
86	C₂²⋊C₄×D₈₉	—	4	1	no	—
87	C₄²×D₈₉	—	4	1	no	—
88	C₄²×D₈₉	D₄	1	1	yes	characteristic
89	#15667957	C₂×C₄	1	4	yes	complemented
90	#15667956	C₂×C₄	1	4	yes	complemented
91	#15667955	C₂×C₄	1	4	yes	complemented
92	C₂×#13083549	C₂³	1	1	yes	characteristic
93	C₂×#13083549	C₂³	1	1	yes	characteristic
94	C₁₆×D₈₉	—	2	2	no	—
95	C₁₆×D₈₉	C₂×C₄	1	4	yes	complemented
96	#15667946	C₂³	1	1	yes	characteristic
97	#15667946	C₂³	1	1	yes	characteristic
98	#15667945	—	2	1	no	—
99	#15667945	—	2	1	no	—
100	#15667937	—	2	1	no	—
101	#15667936	—	2	1	no	—
102	#15667935	—	2	1	no	—
103	#15667934	—	2	1	no	—
104	#15667933	—	2	1	no	—
105	#15667932	—	2	1	no	—
106	C₄×#10623494	D₄	1	1	yes	characteristic
107	C₈×Dic₈₉	D₄	1	1	yes	characteristic
108	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
109	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₈₉	—	2	1	no	—
112	C₄×D₄×C₈₉	—	2	1	no	—
113	SD₃₂×C₈₉	C₂×C₄	1	4	yes	complemented
114	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
116	#107×C₈₉	C₂³	1	1	yes	characteristic
117	#107×C₈₉	C₂³	1	1	yes	characteristic
118	#103×C₈₉	—	2	1	no	—
119	#102×C₈₉	—	2	1	no	—
120	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
121	C₂³×D₈₉	—	4	1	no	—
122	C₂×Dic₁₇₈	—	2	1	no	—
123	C₂×Dic₁₇₈	—	4	1	no	—
124	Q₈×D₈₉	—	2	4	no	—
125	Q₈×D₈₉	—	4	2	no	—
126	C₂×D₃₅₆	—	2	1	no	—
127	C₂×C₂²⋊D₈₉	—	4	1	no	—
128	D₄×D₈₉	—	2	4	no	—
129	D₄×D₈₉	—	4	2	no	—
130	C₂²×Dic₈₉	—	4	1	no	—
131	C₂×C₄×D₈₉	—	4	1	no	—
132	C₂×C₄×D₈₉	—	4	1	no	—
133	C₂×C₄×D₈₉	—	4	1	no	—
134	C₂×C₄×D₈₉	—	4	1	no	—
135	C₂×C₄×D₈₉	—	4	1	no	—
136	C₂×C₄×D₈₉	—	8	4	no	—
137	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
138	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
139	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
140	Dic₃₅₆	—	2	1	no	—
141	Dic₃₅₆	C₂²×C₄	1	2	yes	complemented
142	#13083564	—	2	4	no	—
143	D₇₁₂	—	2	1	no	—
144	D₇₁₂	C₂²×C₄	1	2	yes	—
145	#13083559	—	2	4	no	—
146	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
147	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
148	C₈×D₈₉	—	2	2	no	—
149	C₈×D₈₉	C₂²×C₄	1	2	yes	—
150	C₈×D₈₉	#41	1	2	yes	—
151	C₄⋊Dic₈₉	—	2	1	no	—
152	C₄⋊Dic₈₉	—	2	1	no	—
153	C₄⋊Dic₈₉	—	4	1	no	—
154	#13083553	—	4	1	no	—
155	#13083553	—	4	1	no	—
156	#13083553	—	4	1	no	—
157	#13083553	—	4	1	no	—
158	C₂²⋊Dic₈₉	—	4	1	no	—
159	#13083551	—	4	1	no	—
160	#13083551	—	4	1	no	—
161	C₄×Dic₈₉	—	4	1	no	—
162	C₄×Dic₈₉	—	4	1	no	—
163	C₄×Dic₈₉	—	4	1	no	—
164	C₄×Dic₈₉	D₈	1	1	yes	characteristic
165	C₄×Dic₈₉	D₈	1	1	yes	characteristic
166	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
167	#13083549	—	2	1	no	—
168	#13083549	C₂²×C₄	1	2	yes	complemented
169	C₂×Q₈×C₈₉	—	2	1	no	—
170	C₂×D₄×C₈₉	—	2	1	no	—
171	C₂²×C₄×C₈₉	—	4	1	no	—
172	Q₁₆×C₈₉	—	2	1	no	—
173	Q₁₆×C₈₉	C₂²×C₄	1	2	yes	complemented
174	D₈×C₈₉	—	2	1	no	—
175	D₈×C₈₉	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₄⋊C₄×C₈₉	—	2	1	no	—
179	C₄⋊C₄×C₈₉	—	2	1	no	—
180	C₄⋊C₄×C₈₉	—	4	1	no	—
181	C₂²⋊C₄×C₈₉	—	4	1	no	—
182	C₄²×C₈₉	—	4	1	no	—
183	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₁₆×C₈₉	—	2	1	no	—
185	C₁₆×C₈₉	C₂²×C₄	1	2	yes	complemented
186	C₂³×C₈₉	—	4	1	no	—
187	C₂²×D₈₉	—	4	1	no	—
188	C₂²×D₈₉	—	4	4	no	—
189	C₂²×D₈₉	—	8	2	no	—
190	C₂²×D₈₉	—	8	2	no	—
191	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
192	Q₈×C₈₉	—	2	2	no	—
193	Q₈×C₈₉	—	4	1	no	—
194	D₄×C₈₉	—	2	2	no	—
195	D₄×C₈₉	—	4	1	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	8	2	no	—
200	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂²⋊D₈₉	—	4	4	no	—
204	C₂×Dic₈₉	—	4	1	no	—
205	C₂×Dic₈₉	—	4	1	no	—
206	C₂×Dic₈₉	—	4	1	no	—
207	C₂×Dic₈₉	—	8	2	no	—
208	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
209	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
210	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
211	D₃₅₆	—	2	2	no	—
212	D₃₅₆	—	4	1	no	—
213	C₄×D₈₉	—	2	2	no	—
214	C₄×D₈₉	—	4	4	no	—
215	C₄×D₈₉	—	8	2	no	—
216	C₄×D₈₉	—	8	2	no	—
217	C₄×D₈₉	—	8	2	no	—
218	C₄×D₈₉	—	8	2	no	—
219	C₄×D₈₉	SD₃₂	1	4	yes	direct product factor
220	C₄×D₈₉	C₄×D₄	1	2	yes	—
221	C₄×D₈₉	#135	1	2	yes	—
222	Dic₁₇₈	—	2	2	no	—
223	Dic₁₇₈	—	4	1	no	—
224	Dic₁₇₈	—	4	4	no	—
225	C₈×C₈₉	—	2	1	no	—
226	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
227	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
228	#10623494	—	2	1	no	—
229	#10623494	C₄×D₄	1	2	yes	—
230	C₂²×C₈₉	—	4	2	no	—
231	C₂²×C₈₉	—	8	1	no	—
232	C₂²×C₈₉	—	8	1	no	—
233	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
234	C₂×D₈₉	—	4	2	no	—
235	C₂×D₈₉	—	8	1	no	—
236	C₂×D₈₉	—	8	1	no	—
237	C₂×D₈₉	—	8	8	no	—
238	C₂×D₈₉	C₄×D₈	1	2	yes	—
239	C₂×D₈₉	C₂×SD₃₂	1	2	yes	—
240	C₂×D₈₉	#508	1	2	yes	—
241	C₄×C₈₉	—	2	1	no	—
242	C₄×C₈₉	—	4	2	no	—
243	C₄×C₈₉	—	8	1	no	—
244	C₄×C₈₉	—	8	1	no	—
245	C₄×C₈₉	C₂×SD₃₂	1	2	yes	complemented
246	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
248	Dic₈₉	—	2	1	no	—
249	Dic₈₉	—	4	2	no	—
250	Dic₈₉	—	8	1	no	—
251	Dic₈₉	—	8	1	no	—
252	Dic₈₉	C₄×D₈	1	2	yes	—
253	Dic₈₉	C₂×SD₃₂	1	2	yes	complemented
254	C₂×C₄×SD₃₂	—	89	1	no	maximal, Sylow
255	C₂×C₈₉	—	8	2	no	—
256	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
257	C₂×C₈₉	C₂²×SD₃₂	1	1	yes	characteristic
258	C₂×C₈₉	C₂×#508	1	1	yes	characteristic
259	D₈₉	—	8	2	no	—
260	D₈₉	C₄×SD₃₂	1	4	yes	direct product factor
261	C₂²×SD₃₂	—	89	1	no	—
262	C₂×C₄×Q₁₆	—	89	1	no	—
263	C₂×C₄×D₈	—	89	1	no	—
264	C₄×SD₃₂	—	89	1	no	—
265	C₄×SD₃₂	—	89	1	no	—
266	C₄×SD₃₂	—	89	1	no	—
267	C₄×SD₃₂	—	89	1	no	—
268	C₄×SD₃₂	—	89	1	no	—
269	C₄×SD₃₂	—	89	1	no	—
270	C₄×SD₃₂	—	89	1	no	—
271	C₄×SD₃₂	D₈₉	1	1	yes	characteristic, direct product factor
272	C₂×#367	—	89	1	no	—
273	C₂×#358	—	89	1	no	—
274	C₂×#357	—	89	1	no	—
275	C₂×C₄×C₁₆	—	89	1	no	—
276	C₈₉	C₂×C₄×SD₃₂	1	1	yes	characteristic, complemented, Sylow
277	C₂²×Q₁₆	—	89	1	no	—
278	C₂²×D₈	—	89	1	no	—
279	C₂×C₄×Q₈	—	178	1	no	—
280	C₂×C₄×D₄	—	178	1	no	—
281	C₂×SD₃₂	—	89	1	no	—
282	C₂×SD₃₂	—	89	1	no	—
283	C₂×SD₃₂	—	89	8	no	—
284	C₂×SD₃₂	—	89	1	no	—
285	C₂×SD₃₂	C₂×D₈₉	1	1	yes	characteristic
286	C₂²×C₁₆	—	89	1	no	—
287	C₂²×C₁₆	—	89	1	no	—
288	C₄×Q₁₆	—	89	1	no	—
289	C₄×Q₁₆	—	89	1	no	—
290	C₄×Q₁₆	—	89	1	no	—
291	C₄×Q₁₆	—	178	1	no	—
292	C₄×Q₁₆	—	178	1	no	—
293	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
294	C₄×D₈	—	89	1	no	—
295	C₄×D₈	—	89	1	no	—
296	C₄×D₈	—	89	1	no	—
297	C₄×D₈	—	178	1	no	—
298	C₄×D₈	—	178	1	no	—
299	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
300	C₂×#107	—	89	1	no	—
301	C₂×#107	—	89	1	no	—
302	C₂×#103	—	178	1	no	—
303	C₂×#102	—	178	1	no	—
304	C₂×C₄×C₈	—	89	1	no	—
305	#367	—	89	1	no	—
306	#367	—	89	1	no	—
307	#367	—	89	1	no	—
308	#367	C₂×D₈₉	1	1	yes	characteristic, complemented
309	#358	—	89	1	no	—
310	#358	—	89	1	no	—
311	#358	—	89	1	no	—
312	#358	C₂×D₈₉	1	1	yes	characteristic, complemented
313	#357	—	89	1	no	—
314	#357	—	89	1	no	—
315	#357	—	89	1	no	—
316	#357	C₂×D₈₉	1	1	yes	characteristic
317	C₄×C₁₆	—	89	1	no	—
318	C₄×C₁₆	—	89	1	no	—
319	C₄×C₁₆	—	89	1	no	—
320	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
321	C₂²×Q₈	—	178	1	no	—
322	C₂²×D₄	—	178	1	no	—
323	C₂³×C₄	—	356	1	no	—
324	C₂×Q₁₆	—	89	4	no	—
325	C₂×Q₁₆	—	89	1	no	—
326	C₂×Q₁₆	—	178	2	no	—
327	C₂×Q₁₆	—	178	1	no	—
328	C₂×Q₁₆	C₂²×D₈₉	1	1	yes	characteristic
329	C₂×D₈	—	89	4	no	—
330	C₂×D₈	—	89	1	no	—
331	C₂×D₈	—	178	2	no	—
332	C₂×D₈	—	178	1	no	—
333	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₂²×C₈	—	89	1	no	—
335	C₂²×C₈	—	89	1	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	—	356	1	no	—
338	C₄×Q₈	—	356	1	no	—
339	C₄×Q₈	—	178	1	no	—
340	C₄×Q₈	—	178	1	no	—
341	C₄×Q₈	—	178	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	356	1	no	—
344	C₄×D₄	—	356	1	no	—
345	C₄×D₄	—	178	1	no	—
346	C₄×D₄	—	178	1	no	—
347	C₄×D₄	—	178	1	no	—
348	C₂×C₄⋊C₄	—	356	1	no	—
349	C₂×C₄⋊C₄	—	178	1	no	—
350	C₂×C₄⋊C₄	—	178	1	no	—
351	C₂×C₂²⋊C₄	—	356	1	no	—
352	C₂×C₄²	—	89	1	no	—
353	C₂×C₄²	—	356	1	no	—
354	SD₃₂	—	89	4	no	—
355	SD₃₂	—	89	4	no	—
356	SD₃₂	—	89	4	no	—
357	SD₃₂	C₄×D₈₉	1	4	yes	direct product factor
358	C₂×C₁₆	—	89	1	no	—
359	C₂×C₁₆	—	89	4	no	—
360	C₂×C₁₆	—	89	1	no	—
361	C₂×C₁₆	—	178	2	no	—
362	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
363	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
364	#107	—	89	1	no	—
365	#107	—	89	1	no	—
366	#107	—	178	1	no	—
367	#107	—	178	1	no	—
368	#107	C₂²×D₈₉	1	1	yes	characteristic
369	#107	C₂²×D₈₉	1	1	yes	characteristic
370	#103	—	2	1	no	—
371	#103	—	178	1	no	—
372	#103	—	178	1	no	—
373	#103	—	178	1	no	—
374	#102	—	2	1	no	—
375	#102	—	178	1	no	—
376	#102	—	178	1	no	—
377	#102	—	178	1	no	—
378	C₄×C₈	—	89	1	no	—
379	C₄×C₈	—	89	1	no	—
380	C₄×C₈	—	89	1	no	—
381	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
382	C₂⁴	—	356	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	356	1	no	—
385	C₂×Q₈	—	356	2	no	—
386	C₂×Q₈	—	178	4	no	—
387	C₂×Q₈	—	178	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	356	2	no	—
390	C₂×D₄	—	356	1	no	—
391	C₂×D₄	—	178	4	no	—
392	C₂×D₄	—	178	1	no	—
393	C₂²×C₄	—	4	1	no	—
394	C₂²×C₄	—	89	1	no	—
395	C₂²×C₄	—	89	1	no	—
396	C₂²×C₄	—	89	1	no	—
397	C₂²×C₄	—	356	1	no	—
398	C₂²×C₄	—	356	1	no	—
399	C₂²×C₄	—	356	1	no	—
400	C₂²×C₄	—	356	1	no	—
401	C₂²×C₄	—	356	1	no	—
402	C₂²×C₄	—	356	1	no	—
403	C₂²×C₄	—	712	4	no	—
404	Q₁₆	—	2	1	no	—
405	Q₁₆	—	89	2	no	—
406	Q₁₆	—	178	4	no	—
407	Q₁₆	—	178	1	no	—
408	Q₁₆	C₂×C₄×D₈₉	1	2	yes	complemented
409	D₈	—	2	1	no	—
410	D₈	—	89	2	no	—
411	D₈	—	178	4	no	—
412	D₈	—	178	1	no	—
413	D₈	C₂×C₄×D₈₉	1	2	yes	—
414	C₂×C₈	—	89	1	no	—
415	C₂×C₈	—	89	2	no	—
416	C₂×C₈	—	89	2	no	—
417	C₂×C₈	—	89	1	no	—
418	C₂×C₈	—	178	2	no	—
419	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
420	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	356	1	no	—
425	C₄⋊C₄	—	356	1	no	—
426	C₄⋊C₄	—	356	1	no	—
427	C₄⋊C₄	—	356	1	no	—
428	C₄⋊C₄	—	356	1	no	—
429	C₄⋊C₄	—	178	1	no	—
430	C₄⋊C₄	—	178	1	no	—
431	C₂²⋊C₄	—	4	1	no	—
432	C₂²⋊C₄	—	356	1	no	—
433	C₂²⋊C₄	—	356	1	no	—
434	C₂²⋊C₄	—	356	1	no	—
435	C₄²	—	4	1	no	—
436	C₄²	—	89	1	no	—
437	C₄²	—	89	1	no	—
438	C₄²	—	89	1	no	—
439	C₄²	—	356	1	no	—
440	C₄²	—	356	1	no	—
441	C₄²	—	356	1	no	—
442	C₄²	D₄×D₈₉	1	1	yes	characteristic
443	C₁₆	—	2	1	no	—
444	C₁₆	—	89	2	no	—
445	C₁₆	—	178	1	no	—
446	C₁₆	C₂×C₄×D₈₉	1	2	yes	complemented
447	C₂³	—	4	1	no	—
448	C₂³	—	89	1	no	—
449	C₂³	—	356	4	no	—
450	C₂³	—	356	1	no	—
451	C₂³	—	712	2	no	—
452	C₂³	—	712	2	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	4	1	no	—
455	Q₈	—	356	4	no	—
456	Q₈	—	356	1	no	—
457	Q₈	—	178	2	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	1	no	—
460	D₄	—	356	4	no	—
461	D₄	—	356	1	no	—
462	D₄	—	178	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	8	2	no	—
467	C₂×C₄	—	89	1	no	—
468	C₂×C₄	—	89	1	no	—
469	C₂×C₄	—	89	4	no	—
470	C₂×C₄	—	89	2	no	—
471	C₂×C₄	—	89	2	no	—
472	C₂×C₄	—	89	1	no	—
473	C₂×C₄	—	356	4	no	—
474	C₂×C₄	—	356	1	no	—
475	C₂×C₄	—	356	1	no	—
476	C₂×C₄	—	356	1	no	—
477	C₂×C₄	—	178	2	no	—
478	C₂×C₄	—	712	2	no	—
479	C₂×C₄	—	712	2	no	—
480	C₂×C₄	—	712	2	no	—
481	C₂×C₄	—	712	2	no	—
482	C₂×C₄	—	712	2	no	—
483	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
484	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
485	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
486	C₈	—	2	1	no	—
487	C₈	—	89	2	no	—
488	C₈	—	178	1	no	—
489	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
490	C₈	#41×D₈₉	1	1	yes	characteristic
491	C₂²	—	4	2	no	—
492	C₂²	—	8	1	no	—
493	C₂²	—	8	1	no	—
494	C₂²	—	89	2	no	—
495	C₂²	—	89	2	no	—
496	C₂²	—	89	2	no	—
497	C₂²	—	356	2	no	—
498	C₂²	—	712	8	no	—
499	C₂²	—	712	1	no	—
500	C₂²	—	712	1	no	—
501	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
502	C₄	—	2	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	8	1	no	—
505	C₄	—	8	1	no	—
506	C₄	—	89	2	no	—
507	C₄	—	89	2	no	—
508	C₄	—	356	2	no	—
509	C₄	—	178	1	no	—
510	C₄	—	712	1	no	—
511	C₄	—	712	1	no	—
512	C₄	SD₃₂×D₈₉	1	2	yes	direct product factor
513	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
514	C₄	#135×D₈₉	1	1	yes	characteristic
515	C₂	—	8	2	no	—
516	C₂	—	89	4	no	—
517	C₂	—	712	2	no	—
518	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic
519	C₂	C₂×SD₃₂×D₈₉	1	1	yes	characteristic
520	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×SD₃₂×C₈₉	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂×D₈×D₈₉	C₂²
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₄×SD₃₂	D₈₉
hypocenter	C₈₉	C₂×C₄×SD₃₂
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×SD₃₂

Complements

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

N	H ≅ G/N	type
2. C₄×Q₁₆×D₈₉	C₂	semidirect
4. #26022107	C₂	semidirect
5. C₄×#15667957	C₂	semidirect
6. SD₃₂×Dic₈₉	C₂	semidirect
7. C₄×#15667955	C₂	semidirect
8. #26022103	C₂	semidirect
9. C₄×#15667956	C₂	semidirect
10. #26022101	C₂	semidirect
11. #367×D₈₉	C₂	semidirect
12. #358×D₈₉	C₂	semidirect
14. C₄×C₁₆×D₈₉	C₂	semidirect
15. C₄×SD₃₂×C₈₉	C₂	semidirect
23. SD₃₂×D₈₉	C₄	direct (N × H)
26. C₄×Dic₃₅₆	C₂²	semidirect
27. Q₁₆×Dic₈₉	C₂²	semidirect
28. #19151692	C₂²	semidirect
41. #19151426	C₂²	semidirect
42. #19151425	C₂²	semidirect
43. #19151425	C₂²	semidirect
44. #19151403	C₂²	semidirect
45. #19151402	C₂²	semidirect
46. #19151401	C₂²	semidirect
50. C₄×#13083549	C₂²	semidirect
51. C₁₆×Dic₈₉	C₂²	semidirect
52. C₁₆×Dic₈₉	C₂²	semidirect
54. C₄×Q₁₆×C₈₉	C₂²	semidirect
56. #367×C₈₉	C₂²	semidirect
57. #358×C₈₉	C₂²	semidirect
59. C₄×C₁₆×C₈₉	C₂²	semidirect
66. Q₁₆×D₈₉	C₂×C₄	semidirect
89. #15667957	C₂×C₄	semidirect
90. #15667956	C₂×C₄	semidirect
91. #15667955	C₂×C₄	semidirect
95. C₁₆×D₈₉	C₂×C₄	semidirect
113. SD₃₂×C₈₉	C₂×C₄	semidirect
141. Dic₃₅₆	C₂²×C₄	semidirect
168. #13083549	C₂²×C₄	semidirect
173. Q₁₆×C₈₉	C₂²×C₄	semidirect
185. C₁₆×C₈₉	C₂²×C₄	semidirect
219. C₄×D₈₉	SD₃₂	direct (N × H)
245. C₄×C₈₉	C₂×SD₃₂	semidirect
253. Dic₈₉	C₂×SD₃₂	semidirect
260. D₈₉	C₄×SD₃₂	direct (N × H)
271. C₄×SD₃₂	D₈₉	direct (N × H)
276. C₈₉	C₂×C₄×SD₃₂	semidirect
293. C₄×Q₁₆	C₂×D₈₉	semidirect
308. #367	C₂×D₈₉	semidirect
312. #358	C₂×D₈₉	semidirect
320. C₄×C₁₆	C₂×D₈₉	semidirect
357. SD₃₂	C₄×D₈₉	direct (N × H)
408. Q₁₆	C₂×C₄×D₈₉	semidirect
446. C₁₆	C₂×C₄×D₈₉	semidirect
512. C₄	SD₃₂×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×SD₃₂×D₈₉	2
C₄×Q₁₆×D₈₉	2
C₄×D₈×D₈₉	2
#26022107	2
C₄×#15667957	2
SD₃₂×Dic₈₉	2
C₄×#15667955	2
#26022103	2
C₄×#15667956	2
#26022101	2
#367×D₈₉	2
#358×D₈₉	2
#357×D₈₉	2
C₄×C₁₆×D₈₉	2
C₄×SD₃₂×C₈₉	2
C₂×C₄×SD₃₂	89

Subgroups — C4×SD32×D89 #36707691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×SD₃₂×D₈₉ #36707691