Subgroups — C₈₉×#18723 #36396571

Order 22784.

932 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3548	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3206	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3141	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1643	C₂	1	4	yes	maximal, complemented
6	C₈₉×#1642	C₂	1	4	yes	maximal, complemented
7	C₈₉×#1543	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1484	C₂	1	1	yes	maximal, characteristic, complemented
10	#562×C₈₉	—	2	2	no	—
11	#554×C₈₉	—	2	1	no	—
12	#554×C₈₉	C₂²	1	2	yes	—
13	#550×C₈₉	—	2	1	no	—
14	#550×C₈₉	C₂²	1	2	yes	—
15	#547×C₈₉	—	2	1	no	—
16	#547×C₈₉	—	2	1	no	—
17	#540×C₈₉	—	2	2	no	—
18	#537×C₈₉	—	2	2	no	—
19	#537×C₈₉	—	2	2	no	—
20	#533×C₈₉	C₂²	1	1	yes	characteristic
21	#532×C₈₉	C₂²	1	1	yes	characteristic
22	#532×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	#498×C₈₉	—	2	1	no	—
25	#492×C₈₉	—	2	1	no	—
26	#489×C₈₉	—	2	2	no	—
27	#487×C₈₉	—	2	1	no	—
28	#487×C₈₉	—	2	1	no	—
29	#487×C₈₉	C₂²	1	2	yes	—
30	#486×C₈₉	C₂²	1	2	yes	—
31	#483×C₈₉	—	2	2	no	—
32	#475×C₈₉	C₂²	1	4	yes	—
33	#461×C₈₉	C₂²	1	4	yes	—
34	#448×C₈₉	—	2	2	no	—
35	#431×C₈₉	C₂²	1	1	yes	characteristic
36	#431×C₈₉	C₂²	1	1	yes	characteristic
37	#417×C₈₉	—	2	2	no	—
38	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
39	#333×C₈₉	C₂²	1	2	yes	—
40	#331×C₈₉	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₈₉	C₂²	1	4	yes	—
42	D₄⋊C₈×C₈₉	C₂²	1	4	yes	—
43	C₂×#41×C₈₉	—	2	2	no	—
44	C₂×#41×C₈₉	—	2	2	no	—
45	C₂×#41×C₈₉	—	2	1	no	—
46	C₂×#41×C₈₉	D₄	1	2	yes	—
47	C₂²×Q₈×C₈₉	—	2	1	no	—
48	C₂×SD₁₆×C₈₉	—	2	4	no	—
49	C₂×M₁₆×C₈₉	—	2	1	no	—
50	C₄⋊Q₈×C₈₉	—	2	1	no	—
51	C₄⋊Q₈×C₈₉	—	2	1	no	—
52	C₄⋊Q₈×C₈₉	—	2	1	no	—
53	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
55	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
58	#127×C₈₉	—	2	2	no	—
59	#127×C₈₉	D₄	1	1	yes	characteristic
60	#127×C₈₉	C₂³	1	1	yes	characteristic
61	#125×C₈₉	—	2	2	no	—
62	#125×C₈₉	—	2	1	no	—
63	#124×C₈₉	—	2	1	no	—
64	#124×C₈₉	D₄	1	2	yes	—
65	#123×C₈₉	—	2	4	no	—
66	#123×C₈₉	—	2	4	no	—
67	C₂²⋊Q₈×C₈₉	—	2	2	no	—
68	C₂²⋊Q₈×C₈₉	—	2	4	no	—
69	C₂²⋊Q₈×C₈₉	—	2	2	no	—
70	C₂²⋊Q₈×C₈₉	—	2	4	no	—
71	C₂²⋊Q₈×C₈₉	—	2	1	no	—
72	C₂²⋊Q₈×C₈₉	D₄	1	2	yes	—
73	#121×C₈₉	—	2	4	no	—
74	#121×C₈₉	—	2	4	no	—
75	#121×C₈₉	—	2	2	no	—
76	#121×C₈₉	—	2	4	no	—
77	#121×C₈₉	—	2	4	no	—
78	#121×C₈₉	—	2	1	no	—
79	#121×C₈₉	—	2	1	no	—
80	#121×C₈₉	—	2	1	no	—
81	#121×C₈₉	—	2	2	no	—
82	#121×C₈₉	D₄	1	2	yes	—
83	C₄×Q₈×C₈₉	—	2	1	no	—
84	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
85	C₄×D₄×C₈₉	—	2	2	no	—
86	C₄×D₄×C₈₉	—	2	2	no	—
87	C₄×D₄×C₈₉	—	2	1	no	—
88	C₄×D₄×C₈₉	—	2	1	no	—
89	C₄×D₄×C₈₉	—	2	1	no	—
90	C₄×D₄×C₈₉	C₂³	1	2	yes	—
91	#117×C₈₉	—	2	1	no	—
92	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
93	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	#106×C₈₉	—	2	4	no	—
98	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
99	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
100	#103×C₈₉	—	2	4	no	—
101	#103×C₈₉	—	2	4	no	—
102	#103×C₈₉	—	2	4	no	—
103	#102×C₈₉	—	2	4	no	—
104	C₂²⋊C₈×C₈₉	—	2	1	no	—
105	C₂²⋊C₈×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	#41×C₈₉	—	4	4	no	—
111	#41×C₈₉	—	8	2	no	—
112	#41×C₈₉	—	8	4	no	—
113	#41×C₈₉	—	8	4	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×Q₈×C₈₉	—	2	1	no	—
116	C₂×Q₈×C₈₉	—	2	2	no	—
117	C₂×Q₈×C₈₉	—	4	1	no	—
118	C₂×Q₈×C₈₉	—	8	2	no	—
119	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
121	C₂×D₄×C₈₉	—	2	4	no	—
122	C₂×D₄×C₈₉	—	2	4	no	—
123	C₂×D₄×C₈₉	—	2	2	no	—
124	C₂×D₄×C₈₉	—	2	2	no	—
125	C₂×D₄×C₈₉	—	2	1	no	—
126	C₂×D₄×C₈₉	—	2	1	no	—
127	C₂×D₄×C₈₉	—	2	1	no	—
128	C₂×D₄×C₈₉	—	2	1	no	—
129	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	—	2	4	no	—
133	C₂²×C₄×C₈₉	—	2	2	no	—
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	—	4	1	no	—
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	SD₁₆×C₈₉	—	8	4	no	—
140	M₁₆×C₈₉	—	4	2	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	—	2	4	no	—
145	C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₄⋊C₄×C₈₉	—	2	2	no	—
155	C₄⋊C₄×C₈₉	—	2	2	no	—
156	C₄⋊C₄×C₈₉	—	4	1	no	—
157	C₄⋊C₄×C₈₉	—	4	1	no	—
158	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
159	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₈₉	—	2	4	no	—
161	C₂²⋊C₄×C₈₉	—	2	4	no	—
162	C₂²⋊C₄×C₈₉	—	2	2	no	—
163	C₂²⋊C₄×C₈₉	—	2	2	no	—
164	C₂²⋊C₄×C₈₉	—	2	2	no	—
165	C₂²⋊C₄×C₈₉	—	2	2	no	—
166	C₂²⋊C₄×C₈₉	—	2	2	no	—
167	C₄²×C₈₉	—	2	2	no	—
168	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₈₉	—	2	2	no	—
173	C₂³×C₈₉	—	2	2	no	—
174	C₂³×C₈₉	#120	1	1	yes	characteristic
175	Q₈×C₈₉	—	2	4	no	—
176	Q₈×C₈₉	—	4	2	no	—
177	Q₈×C₈₉	—	4	2	no	—
178	Q₈×C₈₉	—	4	4	no	—
179	Q₈×C₈₉	—	8	1	no	—
180	Q₈×C₈₉	—	8	2	no	—
181	D₄×C₈₉	—	2	4	no	—
182	D₄×C₈₉	—	4	2	no	—
183	D₄×C₈₉	—	4	2	no	—
184	D₄×C₈₉	—	4	2	no	—
185	D₄×C₈₉	—	4	2	no	—
186	D₄×C₈₉	—	8	1	no	—
187	D₄×C₈₉	—	8	2	no	—
188	D₄×C₈₉	—	8	2	no	—
189	D₄×C₈₉	—	8	4	no	—
190	D₄×C₈₉	—	8	4	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	2	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	2	no	—
197	C₂×C₄×C₈₉	—	2	2	no	—
198	C₂×C₄×C₈₉	—	4	4	no	—
199	C₂×C₄×C₈₉	—	4	4	no	—
200	C₂×C₄×C₈₉	—	4	2	no	—
201	C₂×C₄×C₈₉	—	8	4	no	—
202	C₂×C₄×C₈₉	—	8	4	no	—
203	C₂×C₄×C₈₉	—	8	2	no	—
204	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
205	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
206	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
207	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
210	C₈×C₈₉	—	4	2	no	—
211	C₈×C₈₉	—	4	2	no	—
212	C₈×C₈₉	—	4	2	no	—
213	C₂²×C₈₉	—	2	1	no	—
214	C₂²×C₈₉	—	2	1	no	—
215	C₂²×C₈₉	—	2	1	no	—
216	C₂²×C₈₉	—	4	2	no	—
217	C₂²×C₈₉	—	4	2	no	—
218	C₂²×C₈₉	—	4	2	no	—
219	C₂²×C₈₉	—	4	2	no	—
220	C₂²×C₈₉	—	4	2	no	—
221	C₂²×C₈₉	—	4	2	no	—
222	C₂²×C₈₉	C₂×#120	1	1	yes	characteristic
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	2	1	no	—
225	C₄×C₈₉	—	2	1	no	—
226	C₄×C₈₉	—	4	2	no	—
227	C₄×C₈₉	—	4	2	no	—
228	C₄×C₈₉	—	4	2	no	—
229	C₄×C₈₉	—	4	2	no	—
230	C₄×C₈₉	—	8	2	no	—
231	C₄×C₈₉	#455	1	2	yes	—
232	C₄×C₈₉	#577	1	2	yes	—
233	C₄×C₈₉	#577	1	2	yes	—
234	#18723	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂×C₈₉	—	4	1	no	—
236	C₂×C₈₉	—	8	2	no	—
237	C₂×C₈₉	—	8	2	no	—
238	C₂×C₈₉	#3009	1	1	yes	characteristic
239	C₂×C₈₉	#3010	1	1	yes	characteristic
240	C₂×C₈₉	C₂×#455	1	1	yes	characteristic
241	#3548	C₂×C₈₉	1	1	yes	characteristic
242	#3229	C₂×C₈₉	1	1	yes	characteristic, complemented
243	#3206	C₂×C₈₉	1	1	yes	characteristic, complemented
244	#3141	C₂×C₈₉	1	1	yes	characteristic, complemented
245	#1643	C₂×C₈₉	1	4	yes	complemented
246	#1642	C₂×C₈₉	1	4	yes	complemented
247	#1543	C₂×C₈₉	1	1	yes	characteristic, complemented
248	#1485	C₂×C₈₉	1	1	yes	characteristic, complemented
249	#1484	C₂×C₈₉	1	1	yes	characteristic, complemented
250	C₈₉	#18723	1	1	yes	characteristic, direct product factor, Sylow
251	#562	—	2	2	no	—
252	#554	—	2	1	no	—
253	#554	C₂²×C₈₉	1	2	yes	—
254	#550	—	2	1	no	—
255	#550	C₂²×C₈₉	1	2	yes	—
256	#547	—	2	1	no	—
257	#547	—	2	1	no	—
258	#540	—	2	2	no	—
259	#537	—	2	2	no	—
260	#537	—	2	2	no	—
261	#533	C₂²×C₈₉	1	1	yes	characteristic
262	#532	C₂²×C₈₉	1	1	yes	characteristic
263	#532	C₂²×C₈₉	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
265	#498	—	2	1	no	—
266	#492	—	2	1	no	—
267	#489	—	2	2	no	—
268	#487	—	2	1	no	—
269	#487	—	2	1	no	—
270	#487	C₂²×C₈₉	1	2	yes	—
271	#486	C₂²×C₈₉	1	2	yes	—
272	#483	—	2	2	no	—
273	#475	C₂²×C₈₉	1	4	yes	—
274	#461	C₂²×C₈₉	1	4	yes	—
275	#448	—	2	2	no	—
276	#431	C₂²×C₈₉	1	1	yes	characteristic
277	#431	C₂²×C₈₉	1	1	yes	characteristic
278	#417	—	2	2	no	—
279	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
280	#333	C₂²×C₈₉	1	2	yes	—
281	#331	C₂²×C₈₉	1	2	yes	—
282	Q₈⋊C₈	C₂²×C₈₉	1	4	yes	—
283	D₄⋊C₈	C₂²×C₈₉	1	4	yes	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	2	1	no	—
287	C₂×#41	D₄×C₈₉	1	2	yes	—
288	C₂²×Q₈	—	2	1	no	—
289	C₂×SD₁₆	—	2	4	no	—
290	C₂×M₁₆	—	2	1	no	—
291	C₄⋊Q₈	—	2	1	no	—
292	C₄⋊Q₈	—	2	1	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
295	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
296	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
297	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
298	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
299	#127	—	2	2	no	—
300	#127	D₄×C₈₉	1	1	yes	characteristic
301	#127	C₂³×C₈₉	1	1	yes	characteristic
302	#125	—	2	2	no	—
303	#125	—	2	1	no	—
304	#124	—	2	1	no	—
305	#124	D₄×C₈₉	1	2	yes	—
306	#123	—	2	4	no	—
307	#123	—	2	4	no	—
308	C₂²⋊Q₈	—	2	2	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	4	no	—
312	C₂²⋊Q₈	—	2	1	no	—
313	C₂²⋊Q₈	D₄×C₈₉	1	2	yes	—
314	#121	—	2	4	no	—
315	#121	—	2	4	no	—
316	#121	—	2	2	no	—
317	#121	—	2	4	no	—
318	#121	—	2	4	no	—
319	#121	—	2	1	no	—
320	#121	—	2	1	no	—
321	#121	—	2	1	no	—
322	#121	—	2	2	no	—
323	#121	D₄×C₈₉	1	2	yes	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	C₂³×C₈₉	1	2	yes	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₄×D₄	—	2	1	no	—
329	C₄×D₄	—	2	1	no	—
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	C₂³×C₈₉	1	2	yes	—
332	#117	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
338	#106	—	2	4	no	—
339	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
340	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
341	#103	—	2	4	no	—
342	#103	—	2	4	no	—
343	#103	—	2	4	no	—
344	#102	—	2	4	no	—
345	C₂²⋊C₈	—	2	1	no	—
346	C₂²⋊C₈	—	2	1	no	—
347	#97	—	2	1	no	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	C₂³×C₈₉	1	2	yes	—
351	#41	—	4	4	no	—
352	#41	—	8	2	no	—
353	#41	—	8	4	no	—
354	#41	—	8	4	no	—
355	C₂×Q₈	—	2	1	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	4	1	no	—
359	C₂×Q₈	—	8	2	no	—
360	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
361	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
371	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
380	SD₁₆	—	8	4	no	—
381	M₁₆	—	4	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	4	1	no	—
398	C₄⋊C₄	—	4	1	no	—
399	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
400	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	2	4	no	—
403	C₂²⋊C₄	—	2	2	no	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	2	2	no	—
407	C₂²⋊C₄	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
410	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
411	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
412	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	#120×C₈₉	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	4	no	—
420	Q₈	—	8	1	no	—
421	Q₈	—	8	2	no	—
422	D₄	—	2	4	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	4	2	no	—
426	D₄	—	4	2	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	2	no	—
429	D₄	—	8	2	no	—
430	D₄	—	8	4	no	—
431	D₄	—	8	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	4	no	—
443	C₂×C₄	—	8	4	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
446	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
447	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
448	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
451	C₈	—	4	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	4	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₂×#120×C₈₉	1	1	yes	characteristic
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	1	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	#455×C₈₉	1	2	yes	—
473	C₄	#577×C₈₉	1	2	yes	—
474	C₄	#577×C₈₉	1	2	yes	—
475	C₂	—	4	1	no	—
476	C₂	—	8	2	no	—
477	C₂	—	8	2	no	—
478	C₂	C₈₉×#3009	1	1	yes	characteristic
479	C₂	C₈₉×#3010	1	1	yes	characteristic
480	C₂	C₂×#455×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₈₉
prime radical	C₈₉×#3548	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈₉×#3229	C₂	semidirect
3. C₈₉×#3206	C₂	semidirect
4. C₈₉×#3141	C₂	semidirect
5. C₈₉×#1643	C₂	semidirect
6. C₈₉×#1642	C₂	semidirect
7. C₈₉×#1543	C₂	semidirect
8. C₈₉×#1485	C₂	semidirect
9. C₈₉×#1484	C₂	semidirect
234. #18723	C₈₉	direct (N × H)
242. #3229	C₂×C₈₉	semidirect
243. #3206	C₂×C₈₉	semidirect
244. #3141	C₂×C₈₉	semidirect
245. #1643	C₂×C₈₉	semidirect
246. #1642	C₂×C₈₉	semidirect
247. #1543	C₂×C₈₉	semidirect
248. #1485	C₂×C₈₉	semidirect
249. #1484	C₂×C₈₉	semidirect
250. C₈₉	#18723	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3548	2
C₈₉×#3229	2
C₈₉×#3206	2
C₈₉×#3141	2
C₈₉×#1643	2
C₈₉×#1642	2
C₈₉×#1543	2
C₈₉×#1485	2
C₈₉×#1484	2
#18723	89

Subgroups — C89×#18723 #36396571

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#18723 #36396571