Subgroups — C₈₉×#10267 #36388115

Order 22784.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#459×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1954	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#333×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#331×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₈×C₈₉	—	2	1	no	—
9	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
10	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
12	#486×C₈₉	—	2	2	no	—
13	#486×C₈₉	—	2	2	no	—
14	#476×C₈₉	—	2	2	no	—
15	#476×C₈₉	—	2	2	no	—
16	#459×C₈₉	—	2	2	no	—
17	#459×C₈₉	—	2	2	no	—
18	C₂×#106×C₈₉	—	2	1	no	—
19	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#102×C₈₉	—	2	1	no	—
23	C₂×#102×C₈₉	—	2	2	no	—
24	C₂×#102×C₈₉	—	2	1	no	—
25	C₂×C₂²⋊C₈×C₈₉	—	2	2	no	—
26	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
27	#333×C₈₉	—	2	2	no	—
28	#331×C₈₉	—	2	2	no	—
29	C₂²×Q₈×C₈₉	—	2	1	no	—
30	C₂²×D₄×C₈₉	—	2	1	no	—
31	C₂²×D₄×C₈₉	—	2	1	no	—
32	C₂²×D₄×C₈₉	—	2	1	no	—
33	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
34	C₂³×C₄×C₈₉	—	2	1	no	—
35	C₂×D₈×C₈₉	—	2	4	no	—
36	C₂×D₈×C₈₉	—	4	2	no	—
37	C₂×D₈×C₈₉	—	4	2	no	—
38	C₂²×C₈×C₈₉	—	2	1	no	—
39	C₂²×C₈×C₈₉	—	2	1	no	—
40	C₂²×C₈×C₈₉	—	2	1	no	—
41	C₂²×C₈×C₈₉	D₄	1	2	yes	—
42	C₄⋊Q₈×C₈₉	—	2	1	no	—
43	C₄⋊Q₈×C₈₉	—	2	1	no	—
44	C₄⋊Q₈×C₈₉	—	2	1	no	—
45	C₄⋊Q₈×C₈₉	D₄	1	2	yes	—
46	#127×C₈₉	—	2	1	no	—
47	#127×C₈₉	—	2	1	no	—
48	#127×C₈₉	—	2	1	no	—
49	#127×C₈₉	D₄	1	2	yes	—
50	C₄×D₄×C₈₉	—	2	1	no	—
51	C₄×D₄×C₈₉	—	2	1	no	—
52	C₄×D₄×C₈₉	—	2	1	no	—
53	C₄×D₄×C₈₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
56	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
58	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
59	#106×C₈₉	—	2	4	no	—
60	C₄⋊C₈×C₈₉	—	2	1	no	—
61	C₄⋊C₈×C₈₉	—	2	1	no	—
62	C₄⋊C₈×C₈₉	—	2	1	no	—
63	C₄⋊C₈×C₈₉	—	2	1	no	—
64	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
65	C₄⋊C₈×C₈₉	D₄	1	2	yes	—
66	#102×C₈₉	—	2	4	no	—
67	#102×C₈₉	—	2	4	no	—
68	#102×C₈₉	—	2	8	no	—
69	C₂²⋊C₈×C₈₉	—	4	4	no	—
70	C₄×C₈×C₈₉	—	2	1	no	—
71	C₄×C₈×C₈₉	—	2	1	no	—
72	C₂⁴×C₈₉	—	2	1	no	—
73	C₂⁴×C₈₉	—	4	1	no	—
74	C₂×Q₈×C₈₉	—	2	2	no	—
75	C₂×Q₈×C₈₉	—	4	1	no	—
76	C₂×Q₈×C₈₉	—	8	2	no	—
77	C₂×D₄×C₈₉	—	2	1	no	—
78	C₂×D₄×C₈₉	—	2	1	no	—
79	C₂×D₄×C₈₉	—	2	2	no	—
80	C₂×D₄×C₈₉	—	2	2	no	—
81	C₂×D₄×C₈₉	—	2	2	no	—
82	C₂×D₄×C₈₉	—	2	1	no	—
83	C₂×D₄×C₈₉	—	2	1	no	—
84	C₂×D₄×C₈₉	—	2	1	no	—
85	C₂×D₄×C₈₉	—	4	1	no	—
86	C₂×D₄×C₈₉	—	4	1	no	—
87	C₂×D₄×C₈₉	—	4	1	no	—
88	C₂×D₄×C₈₉	—	4	1	no	—
89	C₂×D₄×C₈₉	—	4	1	no	—
90	C₂×D₄×C₈₉	—	4	2	no	—
91	C₂×D₄×C₈₉	—	4	1	no	—
92	C₂×D₄×C₈₉	—	4	2	no	—
93	C₂×D₄×C₈₉	—	4	1	no	—
94	C₂×D₄×C₈₉	—	8	2	no	—
95	C₂×D₄×C₈₉	SD₁₆	1	2	yes	—
96	C₂²×C₄×C₈₉	—	2	1	no	—
97	C₂²×C₄×C₈₉	—	4	1	no	—
98	C₂²×C₄×C₈₉	—	4	1	no	—
99	C₂²×C₄×C₈₉	—	4	1	no	—
100	C₂²×C₄×C₈₉	—	4	2	no	—
101	C₂²×C₄×C₈₉	—	4	2	no	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
105	D₈×C₈₉	—	4	8	no	—
106	C₂×C₈×C₈₉	—	2	2	no	—
107	C₂×C₈×C₈₉	—	2	2	no	—
108	C₂×C₈×C₈₉	—	2	2	no	—
109	C₂×C₈×C₈₉	—	2	2	no	—
110	C₂×C₈×C₈₉	—	2	2	no	—
111	C₂×C₈×C₈₉	—	4	1	no	—
112	C₂×C₈×C₈₉	—	4	1	no	—
113	C₂×C₈×C₈₉	—	4	1	no	—
114	C₂×C₈×C₈₉	—	4	1	no	—
115	C₂×C₈×C₈₉	—	4	1	no	—
116	C₂×C₈×C₈₉	—	4	2	no	—
117	C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₄⋊C₄×C₈₉	—	2	1	no	—
119	C₄⋊C₄×C₈₉	—	2	2	no	—
120	C₄⋊C₄×C₈₉	—	2	1	no	—
121	C₄⋊C₄×C₈₉	—	4	1	no	—
122	C₄⋊C₄×C₈₉	—	4	1	no	—
123	C₂²⋊C₄×C₈₉	—	4	1	no	—
124	C₂²⋊C₄×C₈₉	—	4	1	no	—
125	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂³×C₈₉	—	2	2	no	—
130	C₂³×C₈₉	—	4	1	no	—
131	C₂³×C₈₉	—	4	2	no	—
132	C₂³×C₈₉	—	4	1	no	—
133	C₂³×C₈₉	—	4	2	no	—
134	C₂³×C₈₉	—	4	2	no	—
135	C₂³×C₈₉	—	8	2	no	—
136	C₂³×C₈₉	—	8	1	no	—
137	C₂³×C₈₉	—	8	1	no	—
138	C₂³×C₈₉	—	8	2	no	—
139	C₂³×C₈₉	#121	1	1	yes	characteristic
140	Q₈×C₈₉	—	8	2	no	—
141	Q₈×C₈₉	—	8	2	no	—
142	D₄×C₈₉	—	2	2	no	—
143	D₄×C₈₉	—	2	2	no	—
144	D₄×C₈₉	—	4	1	no	—
145	D₄×C₈₉	—	4	4	no	—
146	D₄×C₈₉	—	4	2	no	—
147	D₄×C₈₉	—	4	1	no	—
148	D₄×C₈₉	—	4	2	no	—
149	D₄×C₈₉	—	8	2	no	—
150	D₄×C₈₉	—	8	2	no	—
151	D₄×C₈₉	—	8	1	no	—
152	D₄×C₈₉	—	8	1	no	—
153	D₄×C₈₉	—	8	1	no	—
154	D₄×C₈₉	—	8	1	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	—	4	2	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	8	2	no	—
160	C₂×C₄×C₈₉	—	8	2	no	—
161	C₂×C₄×C₈₉	—	8	1	no	—
162	C₂×C₄×C₈₉	—	8	1	no	—
163	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
164	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
165	C₂×C₄×C₈₉	#120	1	1	yes	characteristic
166	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
171	C₂×C₄×C₈₉	#135	1	2	yes	—
172	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
174	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
175	C₈×C₈₉	—	4	2	no	—
176	C₈×C₈₉	—	4	2	no	—
177	C₈×C₈₉	—	4	2	no	—
178	C₈×C₈₉	—	8	1	no	—
179	C₂²×C₈₉	—	4	4	no	—
180	C₂²×C₈₉	—	4	2	no	—
181	C₂²×C₈₉	—	8	2	no	—
182	C₂²×C₈₉	—	8	1	no	—
183	C₂²×C₈₉	—	8	1	no	—
184	C₂²×C₈₉	—	8	2	no	—
185	C₂²×C₈₉	—	8	2	no	—
186	C₂²×C₈₉	—	8	2	no	—
187	C₂²×C₈₉	—	16	2	no	—
188	C₂²×C₈₉	—	16	2	no	—
189	C₂²×C₈₉	#392	1	1	yes	characteristic
190	C₂²×C₈₉	#463	1	2	yes	—
191	C₂²×C₈₉	#465	1	1	yes	characteristic
192	C₂²×C₈₉	#468	1	1	yes	characteristic
193	C₂²×C₈₉	#472	1	2	yes	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	8	1	no	—
197	C₄×C₈₉	—	8	2	no	—
198	C₄×C₈₉	#448	1	1	yes	characteristic
199	C₄×C₈₉	#449	1	1	yes	characteristic
200	C₄×C₈₉	#449	1	2	yes	—
201	C₄×C₈₉	#450	1	1	yes	characteristic
202	C₄×C₈₉	#452	1	1	yes	characteristic
203	C₄×C₈₉	#495	1	1	yes	characteristic
204	C₄×C₈₉	#496	1	1	yes	characteristic
205	#10267	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
206	C₂×C₈₉	—	8	2	no	—
207	C₂×C₈₉	—	16	2	no	—
208	C₂×C₈₉	#1677	1	2	yes	—
209	C₂×C₈₉	#1697	1	2	yes	—
210	C₂×C₈₉	#2000	1	1	yes	characteristic
211	C₂×C₈₉	#2012	1	1	yes	characteristic
212	C₂×C₈₉	#2018	1	1	yes	characteristic
213	C₂×#486	C₂×C₈₉	1	1	yes	characteristic, complemented
214	C₂×#476	C₂×C₈₉	1	1	yes	characteristic, complemented
215	C₂×#459	C₂×C₈₉	1	1	yes	characteristic
216	#1954	C₂×C₈₉	1	1	yes	characteristic, complemented
217	C₂×#333	C₂×C₈₉	1	1	yes	characteristic, complemented
218	C₂×#331	C₂×C₈₉	1	1	yes	characteristic, complemented
219	#1277	C₂×C₈₉	1	1	yes	characteristic, complemented
220	C₈₉	#10267	1	1	yes	characteristic, direct product factor, Sylow
221	C₂²×D₈	—	2	1	no	—
222	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
223	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
225	#486	—	2	2	no	—
226	#486	—	2	2	no	—
227	#476	—	2	2	no	—
228	#476	—	2	2	no	—
229	#459	—	2	2	no	—
230	#459	—	2	2	no	—
231	C₂×#106	—	2	1	no	—
232	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
235	C₂×#102	—	2	1	no	—
236	C₂×#102	—	2	2	no	—
237	C₂×#102	—	2	1	no	—
238	C₂×C₂²⋊C₈	—	2	2	no	—
239	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
240	#333	—	2	2	no	—
241	#331	—	2	2	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
247	C₂³×C₄	—	2	1	no	—
248	C₂×D₈	—	2	4	no	—
249	C₂×D₈	—	4	2	no	—
250	C₂×D₈	—	4	2	no	—
251	C₂²×C₈	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	D₄×C₈₉	1	2	yes	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	2	1	no	—
258	C₄⋊Q₈	D₄×C₈₉	1	2	yes	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	—	2	1	no	—
262	#127	D₄×C₈₉	1	2	yes	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	—	2	1	no	—
271	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
272	#106	—	2	4	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
278	C₄⋊C₈	D₄×C₈₉	1	2	yes	—
279	#102	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	—	2	8	no	—
282	C₂²⋊C₈	—	4	4	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	—	2	1	no	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	—	4	1	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	4	1	no	—
289	C₂×Q₈	—	8	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	8	2	no	—
308	C₂×D₄	SD₁₆×C₈₉	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	2	no	—
315	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
317	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
318	D₈	—	4	8	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
339	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
341	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	2	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	2	no	—
352	C₂³	#121×C₈₉	1	1	yes	characteristic
353	Q₈	—	8	2	no	—
354	Q₈	—	8	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	4	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	D₄	—	8	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	8	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	8	1	no	—
375	C₂×C₄	—	8	1	no	—
376	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
377	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
378	C₂×C₄	#120×C₈₉	1	1	yes	characteristic
379	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
380	C₂×C₄	#121×C₈₉	1	1	yes	characteristic
381	C₂×C₄	#127×C₈₉	1	1	yes	characteristic
382	C₂×C₄	C₂×SD₁₆×C₈₉	1	1	yes	characteristic
383	C₂×C₄	#135×C₈₉	1	1	yes	characteristic
384	C₂×C₄	#135×C₈₉	1	2	yes	—
385	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
386	C₂×C₄	AGL(1,ℤ/8)×C₈₉	1	2	yes	—
387	C₂×C₄	#137×C₈₉	1	1	yes	characteristic
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	8	1	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	16	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	#392×C₈₉	1	1	yes	characteristic
403	C₂²	#463×C₈₉	1	2	yes	—
404	C₂²	#465×C₈₉	1	1	yes	characteristic
405	C₂²	#468×C₈₉	1	1	yes	characteristic
406	C₂²	#472×C₈₉	1	2	yes	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	#448×C₈₉	1	1	yes	characteristic
412	C₄	#449×C₈₉	1	1	yes	characteristic
413	C₄	#449×C₈₉	1	2	yes	—
414	C₄	#450×C₈₉	1	1	yes	characteristic
415	C₄	#452×C₈₉	1	1	yes	characteristic
416	C₄	#495×C₈₉	1	1	yes	characteristic
417	C₄	#496×C₈₉	1	1	yes	characteristic
418	C₂	—	8	2	no	—
419	C₂	—	16	2	no	—
420	C₂	C₈₉×#1677	1	2	yes	—
421	C₂	C₈₉×#1697	1	2	yes	—
422	C₂	C₈₉×#2000	1	1	yes	characteristic
423	C₂	C₈₉×#2012	1	1	yes	characteristic
424	C₂	C₈₉×#2018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	#121
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₉
prime radical	C₂×#459×C₈₉	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#486×C₈₉	C₂	semidirect
2. C₂×#476×C₈₉	C₂	semidirect
4. C₈₉×#1954	C₂	semidirect
5. C₂×#333×C₈₉	C₂	semidirect
6. C₂×#331×C₈₉	C₂	semidirect
7. C₈₉×#1277	C₂	semidirect
205. #10267	C₈₉	direct (N × H)
213. C₂×#486	C₂×C₈₉	semidirect
214. C₂×#476	C₂×C₈₉	semidirect
216. #1954	C₂×C₈₉	semidirect
217. C₂×#333	C₂×C₈₉	semidirect
218. C₂×#331	C₂×C₈₉	semidirect
219. #1277	C₂×C₈₉	semidirect
220. C₈₉	#10267	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×#486×C₈₉	2
C₂×#476×C₈₉	2
C₂×#459×C₈₉	2
C₈₉×#1954	2
C₂×#333×C₈₉	2
C₂×#331×C₈₉	2
C₈₉×#1277	2
#10267	89

Subgroups — C89×#10267 #36388115

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#10267 #36388115