Subgroups — #1584×D₈₉ #36523944

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#446×D₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019105	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019102	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019101	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019100	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019099	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₈₉	C₂	1	1	yes	maximal, characteristic
12	Q₈⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
13	Q₈⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
14	#322×D₈₉	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₈₉	C₄	1	1	yes	characteristic
17	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	#19151729	C₂²	1	1	yes	characteristic
20	#19151728	C₂²	1	1	yes	characteristic
21	#19151727	—	2	1	no	—
22	#19151726	—	2	1	no	—
23	#19151725	C₂²	1	1	yes	characteristic
24	Q₈×#10623494	C₂²	1	1	yes	characteristic
25	C₈×Dic₁₇₈	—	2	1	no	—
26	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
27	#19151722	—	2	1	no	—
28	#19151722	C₂²	1	1	yes	characteristic
29	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
30	Q₁₆×Dic₈₉	C₄	1	1	yes	characteristic
31	#19151692	C₄	1	1	yes	characteristic
32	C₄×#13083564	C₂²	1	1	yes	characteristic
33	C₄×#13083564	C₂²	1	1	yes	characteristic
34	#19151690	C₄	1	1	yes	characteristic
35	#19151690	C₄	1	1	yes	characteristic
36	#107×D₈₉	C₄	1	1	yes	characteristic
37	C₄⋊C₈×D₈₉	—	2	1	no	—
38	C₄⋊C₈×D₈₉	—	2	1	no	—
39	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
41	#103×D₈₉	C₄	1	1	yes	characteristic
42	#103×D₈₉	C₄	1	1	yes	characteristic
43	#97×D₈₉	—	2	1	no	—
44	C₄×C₈×D₈₉	—	2	1	no	—
45	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151351	C₂²	1	1	yes	characteristic
49	#19151350	C₂²	1	1	yes	characteristic
50	#19151350	C₂²	1	1	yes	characteristic
51	#19151330	C₂²	1	1	yes	characteristic
52	#19151330	C₂²	1	1	yes	characteristic
53	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
54	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
55	#19151328	C₂²	1	1	yes	characteristic
56	#19151328	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	#19151320	C₂²	1	1	yes	characteristic
59	#19151319	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
63	#335×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	#322×C₈₉	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
72	Q₁₆×D₈₉	—	2	4	no	—
73	C₂×C₈×D₈₉	—	2	1	no	—
74	C₂×C₈×D₈₉	—	2	1	no	—
75	C₂×C₈×D₈₉	—	2	1	no	—
76	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
79	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
80	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
81	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₄×Dic₁₇₈	—	2	1	no	—
83	C₄×Dic₁₇₈	—	2	1	no	—
84	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
85	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
86	#15667977	—	2	1	no	—
87	#15667977	—	2	1	no	—
88	#15667977	C₂×C₄	1	1	yes	characteristic
89	#15667977	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₄×D₈₉	—	2	1	no	—
91	C₄⋊C₄×D₈₉	—	2	1	no	—
92	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
94	C₄²×D₈₉	—	2	1	no	—
95	C₄²×D₈₉	—	2	1	no	—
96	C₄²×D₈₉	C₂³	1	1	yes	characteristic
97	#15667946	C₂×C₄	1	1	yes	characteristic
98	#15667945	C₂×C₄	1	1	yes	characteristic
99	#15667945	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#10623494	—	2	1	no	—
101	C₄⋊#10623494	—	2	1	no	—
102	C₄⋊#10623494	C₂³	1	1	yes	characteristic
103	C₄⋊#10623494	C₂³	1	1	yes	characteristic
104	#15667941	—	2	1	no	—
105	#15667941	—	2	1	no	—
106	#15667941	—	2	1	no	—
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667941	—	2	1	no	—
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667937	C₂×C₄	1	1	yes	characteristic
112	#15667936	C₂×C₄	1	1	yes	characteristic
113	#15667936	C₂×C₄	1	1	yes	characteristic
114	#15667935	C₂×C₄	1	1	yes	characteristic
115	#15667935	C₂×C₄	1	1	yes	characteristic
116	#15667923	—	2	1	no	—
117	#15667922	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	C₄×#10623494	—	2	1	no	—
120	C₄×#10623494	C₂³	1	1	yes	characteristic
121	C₄×#10623494	C₂³	1	1	yes	characteristic
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₈×Dic₈₉	—	2	1	no	—
124	C₈×Dic₈₉	—	2	1	no	—
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₈₉	D₄	1	1	yes	characteristic
129	C₈×Dic₈₉	D₄	1	1	yes	characteristic
130	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
133	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
134	C₄⋊C₈×C₈₉	—	2	1	no	—
135	C₄⋊C₈×C₈₉	—	2	1	no	—
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#97×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	—	2	1	no	—
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₈₉	—	2	2	no	—
150	Q₈×D₈₉	—	2	2	no	—
151	Q₈×D₈₉	—	2	2	no	—
152	Q₈×D₈₉	M₁₆	1	4	yes	—
153	C₂×C₄×D₈₉	—	2	1	no	—
154	C₂×C₄×D₈₉	—	2	1	no	—
155	C₂×C₄×D₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	—	2	1	no	—
157	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
160	Dic₃₅₆	—	2	2	no	—
161	#13083564	—	2	2	no	—
162	#13083564	—	2	2	no	—
163	C₂×#10623494	—	2	1	no	—
164	C₂×#10623494	—	2	1	no	—
165	C₂×#10623494	—	2	1	no	—
166	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
167	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
168	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
169	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
170	C₈×D₈₉	—	2	2	no	—
171	C₈×D₈₉	—	2	2	no	—
172	C₈×D₈₉	—	2	2	no	—
173	C₈×D₈₉	—	4	2	no	—
174	C₈×D₈₉	—	4	2	no	—
175	C₈×D₈₉	—	4	2	no	—
176	C₈×D₈₉	Q₁₆	1	4	yes	complemented
177	C₄⋊Dic₈₉	—	2	1	no	—
178	C₄⋊Dic₈₉	—	2	1	no	—
179	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
180	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
181	#13083553	—	2	1	no	—
182	#13083553	—	2	1	no	—
183	#13083553	—	2	1	no	—
184	#13083553	—	2	1	no	—
185	#13083553	—	2	1	no	—
186	#13083553	—	2	1	no	—
187	C₄×Dic₈₉	—	2	1	no	—
188	C₄×Dic₈₉	—	2	1	no	—
189	C₄×Dic₈₉	—	2	1	no	—
190	C₄×Dic₈₉	—	2	1	no	—
191	C₄×Dic₈₉	—	2	1	no	—
192	C₄×Dic₈₉	—	2	1	no	—
193	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₈₉	#41	1	1	yes	characteristic
196	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	Q₁₆×C₈₉	—	2	2	no	—
199	C₂×C₈×C₈₉	—	2	1	no	—
200	C₂×C₈×C₈₉	—	2	1	no	—
201	C₂×C₈×C₈₉	—	2	1	no	—
202	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
204	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
205	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	—	2	1	no	—
207	C₄⋊C₄×C₈₉	—	2	1	no	—
208	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
210	C₄²×C₈₉	—	2	1	no	—
211	C₄²×C₈₉	—	2	1	no	—
212	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
213	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
214	Q₈×C₈₉	—	2	1	no	—
215	Q₈×C₈₉	—	2	1	no	—
216	Q₈×C₈₉	—	2	1	no	—
217	Q₈×C₈₉	C₂×M₁₆	1	2	yes	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	2	1	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
225	C₂×Dic₈₉	—	2	1	no	—
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
231	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
232	C₄×D₈₉	—	2	4	no	—
233	C₄×D₈₉	—	2	2	no	—
234	C₄×D₈₉	—	4	2	no	—
235	C₄×D₈₉	—	4	2	no	—
236	C₄×D₈₉	—	4	2	no	—
237	C₄×D₈₉	C₂×M₁₆	1	2	yes	—
238	C₄×D₈₉	#131	1	2	yes	—
239	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
240	C₄×D₈₉	#135	1	2	yes	—
241	Dic₁₇₈	—	2	1	no	—
242	Dic₁₇₈	—	2	4	no	—
243	Dic₁₇₈	—	2	1	no	—
244	Dic₁₇₈	—	2	1	no	—
245	Dic₁₇₈	—	4	2	no	—
246	Dic₁₇₈	C₂×M₁₆	1	2	yes	—
247	C₈×C₈₉	—	2	1	no	—
248	C₈×C₈₉	—	2	1	no	—
249	C₈×C₈₉	—	2	1	no	—
250	C₈×C₈₉	—	4	1	no	—
251	C₈×C₈₉	—	4	1	no	—
252	C₈×C₈₉	—	4	1	no	—
253	C₈×C₈₉	C₂×Q₁₆	1	2	yes	complemented
254	#10623494	—	2	1	no	—
255	#10623494	—	2	1	no	—
256	#10623494	—	2	1	no	—
257	#10623494	—	4	1	no	—
258	#10623494	—	4	1	no	—
259	#10623494	—	4	1	no	—
260	#10623494	C₂×Q₁₆	1	2	yes	complemented
261	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂×D₈₉	#435	1	2	yes	—
263	C₂×D₈₉	C₄×Q₁₆	1	2	yes	—
264	C₂×D₈₉	#444	1	2	yes	—
265	C₄×C₈₉	—	2	2	no	—
266	C₄×C₈₉	—	2	1	no	—
267	C₄×C₈₉	—	4	1	no	—
268	C₄×C₈₉	—	4	1	no	—
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
271	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
272	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
273	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
274	Dic₈₉	—	2	2	no	—
275	Dic₈₉	—	2	1	no	—
276	Dic₈₉	—	4	1	no	—
277	Dic₈₉	—	4	1	no	—
278	Dic₈₉	—	4	1	no	—
279	Dic₈₉	#435	1	2	yes	—
280	Dic₈₉	C₄×Q₁₆	1	2	yes	—
281	C₂×#1584	—	89	1	no	maximal, Sylow
282	C₂×C₈₉	C₂×#435	1	1	yes	characteristic
283	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
284	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
285	D₈₉	#1584	1	4	yes	direct product factor
286	C₂×#446	—	89	1	no	—
287	C₂×C₈×Q₈	—	89	1	no	—
288	C₂×C₄×Q₁₆	—	89	1	no	—
289	#1584	—	89	1	no	—
290	#1584	—	89	1	no	—
291	#1584	—	89	1	no	—
292	#1584	—	89	1	no	—
293	#1584	—	89	1	no	—
294	#1584	—	89	1	no	—
295	#1584	—	89	1	no	—
296	#1584	D₈₉	1	1	yes	characteristic, direct product factor
297	C₂×#335	—	89	1	no	—
298	C₂×Q₈⋊C₈	—	89	1	no	—
299	C₂×Q₈⋊C₈	—	89	1	no	—
300	C₂×#322	—	89	1	no	—
301	C₈₉	C₂×#1584	1	1	yes	characteristic, complemented, Sylow
302	C₂²×Q₁₆	—	89	1	no	—
303	C₂×C₄×Q₈	—	89	1	no	—
304	C₂×C₄×Q₈	—	89	1	no	—
305	#446	—	89	1	no	—
306	#446	—	89	1	no	—
307	#446	—	89	1	no	—
308	#446	—	178	1	no	—
309	#446	—	178	1	no	—
310	#446	C₂×D₈₉	1	1	yes	characteristic
311	C₈×Q₈	—	89	1	no	—
312	C₈×Q₈	—	89	1	no	—
313	C₈×Q₈	—	89	1	no	—
314	C₈×Q₈	—	178	1	no	—
315	C₈×Q₈	—	178	1	no	—
316	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
317	C₄×Q₁₆	—	89	1	no	—
318	C₄×Q₁₆	—	89	1	no	—
319	C₄×Q₁₆	—	89	1	no	—
320	C₄×Q₁₆	—	89	1	no	—
321	C₄×Q₁₆	—	89	1	no	—
322	C₄×Q₁₆	—	89	1	no	—
323	C₄×Q₁₆	—	89	1	no	—
324	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
325	C₂×#107	—	89	1	no	—
326	C₂×C₄⋊C₈	—	89	1	no	—
327	C₂×C₄⋊C₈	—	89	1	no	—
328	C₂×C₄⋊C₈	—	178	1	no	—
329	C₂×C₄⋊C₈	—	178	1	no	—
330	C₂×#103	—	89	1	no	—
331	C₂×#103	—	89	1	no	—
332	C₂×#97	—	178	1	no	—
333	C₂×C₄×C₈	—	89	1	no	—
334	C₂×C₄×C₈	—	89	1	no	—
335	C₂×C₄×C₈	—	89	1	no	—
336	C₂×C₄×C₈	—	178	1	no	—
337	#335	—	89	1	no	—
338	#335	—	89	1	no	—
339	#335	—	89	1	no	—
340	#335	C₂×D₈₉	1	1	yes	characteristic
341	Q₈⋊C₈	—	89	1	no	—
342	Q₈⋊C₈	—	89	1	no	—
343	Q₈⋊C₈	—	89	1	no	—
344	Q₈⋊C₈	—	89	1	no	—
345	Q₈⋊C₈	—	89	1	no	—
346	Q₈⋊C₈	—	89	1	no	—
347	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
348	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
349	#322	—	89	1	no	—
350	#322	—	89	1	no	—
351	#322	—	89	1	no	—
352	#322	C₂×D₈₉	1	1	yes	characteristic
353	C₂²×Q₈	—	89	1	no	—
354	C₂²×Q₈	—	89	1	no	—
355	C₂×Q₁₆	—	89	1	no	—
356	C₂×Q₁₆	—	89	1	no	—
357	C₂×Q₁₆	—	89	1	no	—
358	C₂×Q₁₆	—	178	4	no	—
359	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
360	C₂²×C₈	—	89	1	no	—
361	C₂²×C₈	—	89	1	no	—
362	C₂²×C₈	—	89	1	no	—
363	C₂²×C₈	—	89	1	no	—
364	C₂²×C₈	—	178	1	no	—
365	C₂²×C₈	—	178	1	no	—
366	C₂²×C₈	—	178	1	no	—
367	C₄×Q₈	—	89	1	no	—
368	C₄×Q₈	—	89	1	no	—
369	C₄×Q₈	—	89	1	no	—
370	C₄×Q₈	—	89	1	no	—
371	C₄×Q₈	—	89	1	no	—
372	C₄×Q₈	—	89	1	no	—
373	C₄×Q₈	—	178	1	no	—
374	C₄×Q₈	—	178	1	no	—
375	C₄×Q₈	—	178	1	no	—
376	C₄×Q₈	—	178	1	no	—
377	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
378	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	89	1	no	—
380	C₂×C₄⋊C₄	—	89	1	no	—
381	C₂×C₄⋊C₄	—	178	1	no	—
382	C₂×C₄⋊C₄	—	178	1	no	—
383	C₂×C₄²	—	89	1	no	—
384	C₂×C₄²	—	178	1	no	—
385	C₂×C₄²	—	178	1	no	—
386	#107	—	89	1	no	—
387	#107	—	89	1	no	—
388	#107	—	89	1	no	—
389	#107	C₄×D₈₉	1	1	yes	characteristic
390	C₄⋊C₈	—	2	1	no	—
391	C₄⋊C₈	—	2	1	no	—
392	C₄⋊C₈	—	89	1	no	—
393	C₄⋊C₈	—	89	1	no	—
394	C₄⋊C₈	—	178	1	no	—
395	C₄⋊C₈	—	178	1	no	—
396	C₄⋊C₈	—	178	1	no	—
397	C₄⋊C₈	—	178	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	—	178	1	no	—
401	C₄⋊C₈	—	178	1	no	—
402	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
403	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
404	#103	—	89	1	no	—
405	#103	—	89	1	no	—
406	#103	—	89	1	no	—
407	#103	—	89	1	no	—
408	#103	—	89	1	no	—
409	#103	—	89	1	no	—
410	#103	C₄×D₈₉	1	1	yes	characteristic
411	#103	C₄×D₈₉	1	1	yes	characteristic
412	#97	—	2	1	no	—
413	#97	—	178	1	no	—
414	#97	—	178	1	no	—
415	#97	—	178	1	no	—
416	C₄×C₈	—	2	1	no	—
417	C₄×C₈	—	89	1	no	—
418	C₄×C₈	—	89	1	no	—
419	C₄×C₈	—	89	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	89	1	no	—
424	C₄×C₈	—	178	1	no	—
425	C₄×C₈	—	178	1	no	—
426	C₄×C₈	—	178	1	no	—
427	C₄×C₈	—	178	1	no	—
428	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
429	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
430	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
431	C₂×Q₈	—	89	4	no	—
432	C₂×Q₈	—	89	1	no	—
433	C₂×Q₈	—	89	1	no	—
434	C₂×Q₈	—	178	1	no	—
435	C₂×Q₈	—	178	1	no	—
436	C₂×Q₈	—	178	2	no	—
437	C₂×Q₈	—	178	2	no	—
438	C₂×Q₈	—	178	2	no	—
439	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
440	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
441	C₂²×C₄	—	89	1	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	89	1	no	—
444	C₂²×C₄	—	178	1	no	—
445	C₂²×C₄	—	178	1	no	—
446	C₂²×C₄	—	178	1	no	—
447	C₂²×C₄	—	178	1	no	—
448	Q₁₆	—	2	2	no	—
449	Q₁₆	—	178	2	no	—
450	Q₁₆	—	178	2	no	—
451	Q₁₆	—	178	2	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	89	1	no	—
456	C₂×C₈	—	89	4	no	—
457	C₂×C₈	—	89	1	no	—
458	C₂×C₈	—	89	1	no	—
459	C₂×C₈	—	89	1	no	—
460	C₂×C₈	—	356	2	no	—
461	C₂×C₈	—	356	2	no	—
462	C₂×C₈	—	356	2	no	—
463	C₂×C₈	—	178	2	no	—
464	C₂×C₈	—	178	2	no	—
465	C₂×C₈	—	178	2	no	—
466	C₂×C₈	—	178	1	no	—
467	C₂×C₈	—	178	1	no	—
468	C₂×C₈	—	178	1	no	—
469	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
472	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	89	1	no	—
476	C₄⋊C₄	—	89	1	no	—
477	C₄⋊C₄	—	178	1	no	—
478	C₄⋊C₄	—	178	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	—	178	1	no	—
482	C₄⋊C₄	—	178	1	no	—
483	C₄⋊C₄	—	178	1	no	—
484	C₄⋊C₄	—	178	1	no	—
485	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
486	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	89	1	no	—
490	C₄²	—	89	1	no	—
491	C₄²	—	89	1	no	—
492	C₄²	—	178	1	no	—
493	C₄²	—	178	1	no	—
494	C₄²	—	178	1	no	—
495	C₄²	—	178	1	no	—
496	C₄²	—	178	1	no	—
497	C₄²	—	178	1	no	—
498	C₄²	C₂³×D₈₉	1	1	yes	characteristic
499	C₂³	—	89	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	89	2	no	—
504	Q₈	—	356	2	no	—
505	Q₈	—	178	4	no	—
506	Q₈	—	178	1	no	—
507	Q₈	—	178	1	no	—
508	Q₈	—	178	1	no	—
509	Q₈	M₁₆×D₈₉	1	2	yes	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	89	1	no	—
515	C₂×C₄	—	89	1	no	—
516	C₂×C₄	—	89	2	no	—
517	C₂×C₄	—	89	2	no	—
518	C₂×C₄	—	89	2	no	—
519	C₂×C₄	—	89	2	no	—
520	C₂×C₄	—	89	1	no	—
521	C₂×C₄	—	356	2	no	—
522	C₂×C₄	—	356	2	no	—
523	C₂×C₄	—	356	2	no	—
524	C₂×C₄	—	178	2	no	—
525	C₂×C₄	—	178	4	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
532	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	4	1	no	—
539	C₈	—	89	2	no	—
540	C₈	—	356	1	no	—
541	C₈	—	356	1	no	—
542	C₈	—	356	1	no	—
543	C₈	—	178	1	no	—
544	C₈	—	178	1	no	—
545	C₈	—	178	1	no	—
546	C₈	Q₁₆×D₈₉	1	2	yes	complemented
547	C₂²	—	89	2	no	—
548	C₂²	—	89	2	no	—
549	C₂²	—	89	2	no	—
550	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
551	C₄	—	2	1	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	1	no	—
556	C₄	—	89	2	no	—
557	C₄	—	89	2	no	—
558	C₄	—	356	1	no	—
559	C₄	—	356	1	no	—
560	C₄	—	356	1	no	—
561	C₄	—	178	1	no	—
562	C₄	—	178	2	no	—
563	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
564	C₄	#131×D₈₉	1	1	yes	characteristic
565	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
566	C₄	#135×D₈₉	1	1	yes	characteristic
567	C₂	—	89	4	no	—
568	C₂	#435×D₈₉	1	1	yes	characteristic
569	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
570	C₂	#444×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1584	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂²×D₈₉	C₄×D₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1584	D₈₉
hypocenter	C₈₉	C₂×#1584
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1584

Complements

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

N	H ≅ G/N	type
4. #26019105	C₂	semidirect
5. #26019104	C₂	semidirect
6. #26019103	C₂	semidirect
7. #26019102	C₂	semidirect
8. #26019101	C₂	semidirect
9. #26019100	C₂	semidirect
10. #26019099	C₂	semidirect
15. C₈₉×#1584	C₂	semidirect
176. C₈×D₈₉	Q₁₆	semidirect
253. C₈×C₈₉	C₂×Q₁₆	semidirect
260. #10623494	C₂×Q₁₆	semidirect
285. D₈₉	#1584	direct (N × H)
296. #1584	D₈₉	direct (N × H)
301. C₈₉	C₂×#1584	semidirect
546. C₈	Q₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#446×D₈₉	2
C₈×Q₈×D₈₉	2
C₄×Q₁₆×D₈₉	2
#26019105	2
#26019104	2
#26019103	2
#26019102	2
#26019101	2
#26019100	2
#26019099	2
#335×D₈₉	2
Q₈⋊C₈×D₈₉	2
#322×D₈₉	2
C₈₉×#1584	2
C₂×#1584	89

Subgroups — #1584×D89 #36523944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1584×D₈₉ #36523944