Subgroups — #2214×D₈₉ #36708810

Order 22784.

686 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#510×D₈₉	C₂	1	2	yes	maximal
2	#494×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26022334	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022333	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022332	C₂	1	2	yes	maximal, complemented
7	#26022331	C₂	1	2	yes	maximal, complemented
8	#26022330	C₂	1	1	yes	maximal, characteristic, complemented
9	#364×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#362×D₈₉	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2214	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	C₂²	1	1	yes	characteristic
13	C₂×Q₁₆×D₈₉	—	2	1	no	—
14	C₂×Q₁₆×D₈₉	C₂²	1	2	yes	—
15	#131×D₈₉	—	2	1	no	—
16	C₄⋊Q₈×D₈₉	—	2	1	no	—
17	#19152041	C₂²	1	2	yes	—
18	#19152040	—	2	2	no	—
19	#19152039	C₂²	1	2	yes	—
20	#19152038	C₂²	1	2	yes	—
21	#19152037	—	2	2	no	—
22	Q₃₂×D₈₉	—	2	2	no	—
23	SD₃₂×D₈₉	—	2	2	no	—
24	M₃₂×D₈₉	C₂²	1	2	yes	—
25	#19151978	C₂²	1	1	yes	characteristic, complemented
26	#19151977	—	2	1	no	—
27	#19151976	—	2	1	no	—
28	#19151976	C₂²	1	2	yes	complemented
29	#19151716	C₂²	1	1	yes	characteristic
30	#19151715	C₂²	1	1	yes	characteristic
31	#19151714	C₂²	1	1	yes	characteristic
32	#19151713	—	2	1	no	—
33	#19151712	—	2	1	no	—
34	#108×D₈₉	C₂²	1	1	yes	characteristic
35	#104×D₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151419	C₂²	1	1	yes	characteristic, complemented
38	#19151418	C₂²	1	2	yes	complemented
39	#19151415	C₂²	1	2	yes	complemented
40	#19151414	C₂²	1	2	yes	complemented
41	#19151413	C₂²	1	2	yes	complemented
42	#510×C₈₉	C₂²	1	2	yes	—
43	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#443×C₈₉	C₂²	1	1	yes	characteristic
45	#364×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	#362×C₈₉	C₂²	1	2	yes	complemented
47	#41×D₈₉	—	2	1	no	—
48	C₂×Q₈×D₈₉	—	2	2	no	—
49	#15668035	D₄	1	1	yes	characteristic
50	#15668034	C₂³	1	1	yes	characteristic
51	#15668033	—	2	1	no	—
52	#15668032	—	2	1	no	—
53	#15668031	D₄	1	1	yes	characteristic
54	C₂×Dic₃₅₆	—	2	1	no	—
55	C₂×Dic₃₅₆	C₂³	1	2	yes	—
56	C₂×#13083564	—	2	2	no	—
57	C₂×#13083564	—	2	2	no	—
58	Q₁₆×D₈₉	—	2	2	no	—
59	Q₁₆×D₈₉	—	2	2	no	—
60	Q₁₆×D₈₉	—	2	2	no	—
61	Q₁₆×D₈₉	—	2	2	no	—
62	Q₁₆×D₈₉	—	4	1	no	—
63	Q₁₆×D₈₉	—	4	1	no	—
64	Q₁₆×D₈₉	—	4	1	no	—
65	Q₁₆×D₈₉	—	4	1	no	—
66	Q₁₆×D₈₉	D₄	1	1	yes	characteristic
67	SD₁₆×D₈₉	—	2	1	no	—
68	D₈×D₈₉	D₄	1	1	yes	characteristic
69	#15668020	—	2	1	no	—
70	#15668020	—	4	1	no	—
71	#15668019	—	2	1	no	—
72	#15668018	—	2	1	no	—
73	#15668018	—	4	1	no	—
74	M₁₆×D₈₉	—	2	1	no	—
75	M₁₆×D₈₉	—	4	1	no	—
76	C₂×C₈×D₈₉	—	4	1	no	—
77	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
78	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
79	#15668012	—	2	1	no	—
80	#15668011	—	4	2	no	—
81	#15668010	—	2	2	no	—
82	C₄⋊C₄×D₈₉	—	4	2	no	—
83	C₄²×D₈₉	D₄	1	1	yes	characteristic
84	Dic₇₁₂	—	2	2	no	—
85	#15667958	—	2	2	no	—
86	#15667958	—	2	2	no	—
87	#15667957	—	2	2	no	—
88	#15667956	—	2	2	no	—
89	#15667955	—	2	2	no	—
90	#15667952	C₂³	1	2	yes	—
91	#15667951	—	2	2	no	—
92	C₁₆×D₈₉	—	2	2	no	—
93	#15667948	C₂³	1	1	yes	characteristic
94	#15667947	—	2	1	no	—
95	#15667940	—	2	1	no	—
96	#15667939	—	2	1	no	—
97	#15667938	—	2	1	no	—
98	C₄×#10623494	D₄	1	1	yes	characteristic
99	C₈×Dic₈₉	D₄	1	1	yes	characteristic
100	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
101	#135×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×Q₁₆×C₈₉	—	2	1	no	—
103	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
104	#131×C₈₉	—	2	1	no	—
105	C₄⋊Q₈×C₈₉	—	2	1	no	—
106	Q₃₂×C₈₉	—	2	2	no	—
107	SD₃₂×C₈₉	—	2	2	no	—
108	M₃₂×C₈₉	C₂³	1	2	yes	—
109	#108×C₈₉	C₂³	1	1	yes	characteristic
110	#104×C₈₉	—	2	1	no	—
111	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
112	#13083575	—	2	1	no	—
113	#13083574	—	2	1	no	—
114	#13083574	—	4	1	no	—
115	#13083573	—	2	1	no	—
116	#13083573	—	4	1	no	—
117	C₂×Dic₁₇₈	—	2	2	no	—
118	C₂×Dic₁₇₈	—	4	2	no	—
119	Q₈×D₈₉	—	2	1	no	—
120	Q₈×D₈₉	—	4	2	no	—
121	Q₈×D₈₉	—	4	2	no	—
122	Q₈×D₈₉	—	4	2	no	—
123	Q₈×D₈₉	—	4	2	no	—
124	D₄×D₈₉	—	2	1	no	—
125	D₄×D₈₉	—	4	1	no	—
126	C₂×C₄×D₈₉	—	2	1	no	—
127	C₂×C₄×D₈₉	—	4	1	no	—
128	C₂×C₄×D₈₉	—	4	2	no	—
129	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
130	Dic₃₅₆	—	2	2	no	—
131	Dic₃₅₆	—	2	2	no	—
132	Dic₃₅₆	—	4	1	no	—
133	Dic₃₅₆	—	4	1	no	—
134	Dic₃₅₆	C₂×D₄	1	1	yes	characteristic
135	#13083564	—	2	1	no	—
136	#13083564	—	4	2	no	—
137	#13083564	—	4	2	no	—
138	#13083564	—	4	2	no	—
139	#13083564	—	4	2	no	—
140	#13083563	—	2	1	no	—
141	#13083562	—	2	1	no	—
142	#13083561	—	2	1	no	—
143	D₇₁₂	C₂×D₄	1	1	yes	characteristic
144	#13083559	—	2	1	no	—
145	#13083558	—	2	1	no	—
146	#13083558	—	4	1	no	—
147	#13083557	—	4	1	no	—
148	#13083557	—	4	1	no	—
149	#13083557	—	4	1	no	—
150	C₂×#10623494	—	4	1	no	—
151	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
152	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
153	C₈×D₈₉	—	4	1	no	—
154	C₈×D₈₉	—	4	1	no	—
155	C₈×D₈₉	—	4	1	no	—
156	C₈×D₈₉	D₈	1	1	yes	characteristic
157	C₈×D₈₉	D₈	1	1	yes	characteristic
158	C₈×D₈₉	D₈	1	1	yes	characteristic
159	C₈×D₈₉	D₈	1	1	yes	characteristic
160	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
161	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
162	C₈×D₈₉	#41	1	1	yes	characteristic
163	C₈×D₈₉	#41	1	1	yes	characteristic
164	C₄⋊Dic₈₉	—	4	2	no	—
165	#13083553	—	4	4	no	—
166	C₄×Dic₈₉	—	2	1	no	—
167	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
168	#13083549	—	2	2	no	—
169	#41×C₈₉	—	2	1	no	—
170	C₂×Q₈×C₈₉	—	2	2	no	—
171	Q₁₆×C₈₉	—	2	2	no	—
172	Q₁₆×C₈₉	—	2	2	no	—
173	Q₁₆×C₈₉	—	4	1	no	—
174	Q₁₆×C₈₉	—	4	1	no	—
175	Q₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
176	SD₁₆×C₈₉	—	2	1	no	—
177	D₈×C₈₉	C₂×D₄	1	1	yes	characteristic
178	M₁₆×C₈₉	—	2	1	no	—
179	M₁₆×C₈₉	—	4	1	no	—
180	C₂×C₈×C₈₉	—	4	1	no	—
181	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₄⋊C₄×C₈₉	—	4	2	no	—
184	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₁₆×C₈₉	—	2	2	no	—
186	C₂²×D₈₉	—	4	1	no	—
187	C₂²×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
188	Q₈×C₈₉	—	2	1	no	—
189	Q₈×C₈₉	—	4	2	no	—
190	Q₈×C₈₉	—	4	2	no	—
191	D₄×C₈₉	—	2	1	no	—
192	D₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
197	C₂²⋊D₈₉	—	4	1	no	—
198	C₂²⋊D₈₉	—	4	1	no	—
199	C₂²⋊D₈₉	—	4	1	no	—
200	C₂×Dic₈₉	—	2	1	no	—
201	C₂×Dic₈₉	—	4	1	no	—
202	C₂×Dic₈₉	—	4	2	no	—
203	C₂×Dic₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
204	D₃₅₆	—	2	1	no	—
205	D₃₅₆	—	4	1	no	—
206	C₄×D₈₉	—	2	4	no	—
207	C₄×D₈₉	—	4	1	no	—
208	C₄×D₈₉	—	4	1	no	—
209	C₄×D₈₉	—	4	1	no	—
210	C₄×D₈₉	—	8	2	no	—
211	C₄×D₈₉	—	8	2	no	—
212	C₄×D₈₉	#121	1	1	yes	characteristic
213	C₄×D₈₉	#121	1	1	yes	characteristic
214	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
215	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
216	Dic₁₇₈	—	2	1	no	—
217	Dic₁₇₈	—	4	1	no	—
218	Dic₁₇₈	—	4	2	no	—
219	Dic₁₇₈	—	4	2	no	—
220	Dic₁₇₈	—	8	2	no	—
221	Dic₁₇₈	—	8	2	no	—
222	C₈×C₈₉	—	4	1	no	—
223	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
224	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
225	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
226	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
227	#10623494	—	4	1	no	—
228	#10623494	#121	1	1	yes	characteristic
229	#10623494	#121	1	1	yes	characteristic
230	#10623494	C₂×D₈	1	1	yes	characteristic
231	#10623494	C₂×D₈	1	1	yes	characteristic
232	C₂²×C₈₉	—	4	1	no	—
233	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
234	C₂×D₈₉	—	2	2	no	—
235	C₂×D₈₉	—	4	1	no	—
236	C₂×D₈₉	—	8	2	no	—
237	C₂×D₈₉	#459	1	1	yes	characteristic
238	C₂×D₈₉	#459	1	1	yes	characteristic
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	4	1	no	—
241	C₄×C₈₉	—	8	2	no	—
242	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
243	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
244	Dic₈₉	—	2	2	no	—
245	Dic₈₉	—	4	1	no	—
246	Dic₈₉	—	8	2	no	—
247	Dic₈₉	#459	1	1	yes	characteristic
248	Dic₈₉	#459	1	1	yes	characteristic
249	C₂×#2214	—	89	1	no	maximal, Sylow
250	C₂×C₈₉	—	2	1	no	—
251	C₂×C₈₉	—	8	1	no	—
252	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
253	D₈₉	—	2	1	no	—
254	D₈₉	—	8	1	no	—
255	D₈₉	#2214	1	2	yes	direct product factor
256	C₂×#510	—	89	2	no	—
257	C₂×#494	—	89	1	no	—
258	C₂×#443	—	89	1	no	—
259	#2214	—	89	2	no	—
260	#2214	—	89	1	no	—
261	#2214	—	89	1	no	—
262	#2214	—	89	1	no	—
263	#2214	—	89	2	no	—
264	#2214	D₈₉	1	1	yes	characteristic, direct product factor
265	C₂×#364	—	89	1	no	—
266	C₂×#362	—	89	2	no	—
267	C₈₉	C₂×#2214	1	1	yes	characteristic, complemented, Sylow
268	C₂×#135	—	89	1	no	—
269	C₂²×Q₁₆	—	89	2	no	—
270	C₂²×Q₁₆	—	178	1	no	—
271	C₂×#131	—	178	1	no	—
272	C₂×C₄⋊Q₈	—	178	1	no	—
273	#510	—	89	2	no	—
274	#510	—	89	2	no	—
275	#510	—	89	2	no	—
276	#510	—	178	2	no	—
277	#510	—	178	2	no	—
278	#510	C₂×D₈₉	1	2	yes	—
279	C₂×Q₃₂	—	178	2	no	—
280	C₂×SD₃₂	—	178	2	no	—
281	C₂×M₃₂	—	89	2	no	—
282	#494	—	89	2	no	—
283	#494	—	89	1	no	—
284	#494	—	178	1	no	—
285	#494	—	178	1	no	—
286	#494	C₂×D₈₉	1	1	yes	characteristic, complemented
287	#443	—	89	1	no	—
288	#443	—	89	1	no	—
289	#443	—	89	1	no	—
290	#443	—	178	1	no	—
291	#443	—	178	1	no	—
292	#443	C₂×D₈₉	1	1	yes	characteristic
293	C₂×#108	—	89	1	no	—
294	C₂×#104	—	178	1	no	—
295	C₂×C₄×C₈	—	89	1	no	—
296	#364	—	89	2	no	—
297	#364	—	89	1	no	—
298	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
299	#362	—	89	2	no	—
300	#362	—	89	2	no	—
301	#362	—	89	2	no	—
302	#362	C₂×D₈₉	1	2	yes	complemented
303	C₂×#41	—	178	1	no	—
304	C₂²×Q₈	—	178	2	no	—
305	#135	—	89	1	no	—
306	#135	—	89	1	no	—
307	#135	—	89	1	no	—
308	#135	—	178	1	no	—
309	#135	—	178	1	no	—
310	#135	C₂²×D₈₉	1	1	yes	characteristic
311	C₂×Q₁₆	—	2	1	no	—
312	C₂×Q₁₆	—	89	1	no	—
313	C₂×Q₁₆	—	89	2	no	—
314	C₂×Q₁₆	—	356	1	no	—
315	C₂×Q₁₆	—	356	1	no	—
316	C₂×Q₁₆	—	356	1	no	—
317	C₂×Q₁₆	—	356	1	no	—
318	C₂×Q₁₆	—	178	2	no	—
319	C₂×Q₁₆	—	178	2	no	—
320	C₂×Q₁₆	—	178	2	no	—
321	C₂×Q₁₆	—	178	2	no	—
322	C₂×Q₁₆	—	178	2	no	—
323	C₂×Q₁₆	—	178	2	no	—
324	C₂×Q₁₆	—	178	1	no	—
325	C₂×Q₁₆	C₂²×D₈₉	1	2	yes	—
326	C₂×SD₁₆	—	178	1	no	—
327	C₂×D₈	—	89	1	no	—
328	#131	—	2	1	no	—
329	#131	—	356	1	no	—
330	#131	—	356	1	no	—
331	#131	—	178	1	no	—
332	#131	—	178	1	no	—
333	#131	—	178	1	no	—
334	C₂×M₁₆	—	356	1	no	—
335	C₂×M₁₆	—	178	1	no	—
336	C₂²×C₈	—	89	1	no	—
337	C₂²×C₈	—	89	1	no	—
338	C₂²×C₈	—	356	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	—	356	2	no	—
341	C₄⋊Q₈	—	178	2	no	—
342	C₄⋊Q₈	—	178	1	no	—
343	C₂×C₄⋊C₄	—	356	2	no	—
344	C₂×C₄²	—	89	1	no	—
345	Q₃₂	—	2	2	no	—
346	Q₃₂	—	178	2	no	—
347	Q₃₂	—	178	2	no	—
348	Q₃₂	—	178	2	no	—
349	SD₃₂	—	2	2	no	—
350	SD₃₂	—	178	2	no	—
351	SD₃₂	—	178	2	no	—
352	SD₃₂	—	178	2	no	—
353	M₃₂	—	89	2	no	—
354	M₃₂	—	178	2	no	—
355	M₃₂	C₂²×D₈₉	1	2	yes	—
356	C₂×C₁₆	—	178	2	no	—
357	#108	—	89	1	no	—
358	#108	—	178	1	no	—
359	#108	C₂²×D₈₉	1	1	yes	characteristic
360	#104	—	2	1	no	—
361	#104	—	178	1	no	—
362	#104	—	178	1	no	—
363	#104	—	178	1	no	—
364	C₄×C₈	—	89	1	no	—
365	C₄×C₈	—	89	1	no	—
366	C₄×C₈	—	89	1	no	—
367	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
368	#41	—	2	1	no	—
369	#41	—	356	1	no	—
370	#41	—	356	1	no	—
371	#41	—	178	1	no	—
372	#41	—	178	1	no	—
373	#41	—	178	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	356	2	no	—
376	C₂×Q₈	—	356	2	no	—
377	C₂×Q₈	—	356	2	no	—
378	C₂×Q₈	—	356	2	no	—
379	C₂×Q₈	—	356	2	no	—
380	C₂×Q₈	—	178	1	no	—
381	C₂×Q₈	—	178	2	no	—
382	C₂×D₄	—	356	1	no	—
383	C₂×D₄	—	178	1	no	—
384	C₂²×C₄	—	89	1	no	—
385	C₂²×C₄	—	356	1	no	—
386	C₂²×C₄	—	356	2	no	—
387	C₂²×C₄	—	178	1	no	—
388	Q₁₆	—	2	2	no	—
389	Q₁₆	—	2	2	no	—
390	Q₁₆	—	4	1	no	—
391	Q₁₆	—	4	1	no	—
392	Q₁₆	—	89	1	no	—
393	Q₁₆	—	356	2	no	—
394	Q₁₆	—	356	2	no	—
395	Q₁₆	—	356	2	no	—
396	Q₁₆	—	356	2	no	—
397	Q₁₆	—	356	1	no	—
398	Q₁₆	—	356	1	no	—
399	Q₁₆	—	178	1	no	—
400	Q₁₆	—	178	2	no	—
401	Q₁₆	—	178	2	no	—
402	Q₁₆	D₄×D₈₉	1	1	yes	characteristic
403	SD₁₆	—	2	1	no	—
404	SD₁₆	—	178	1	no	—
405	SD₁₆	—	178	1	no	—
406	SD₁₆	—	178	1	no	—
407	D₈	—	89	1	no	—
408	D₈	—	178	1	no	—
409	D₈	D₄×D₈₉	1	1	yes	characteristic
410	M₁₆	—	2	1	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	356	1	no	—
413	M₁₆	—	356	1	no	—
414	M₁₆	—	356	1	no	—
415	M₁₆	—	356	1	no	—
416	M₁₆	—	178	1	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	—	89	1	no	—
419	C₂×C₈	—	89	1	no	—
420	C₂×C₈	—	89	1	no	—
421	C₂×C₈	—	89	1	no	—
422	C₂×C₈	—	89	1	no	—
423	C₂×C₈	—	89	1	no	—
424	C₂×C₈	—	89	1	no	—
425	C₂×C₈	—	89	1	no	—
426	C₂×C₈	—	89	1	no	—
427	C₂×C₈	—	89	1	no	—
428	C₂×C₈	—	356	1	no	—
429	C₂×C₈	—	356	1	no	—
430	C₂×C₈	—	356	1	no	—
431	C₂×C₈	—	356	1	no	—
432	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
433	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	—	356	2	no	—
436	C₄⋊C₄	—	356	4	no	—
437	C₄²	—	89	1	no	—
438	C₄²	—	178	1	no	—
439	C₄²	D₄×D₈₉	1	1	yes	characteristic
440	C₁₆	—	2	2	no	—
441	C₁₆	—	178	2	no	—
442	C₂³	—	89	1	no	—
443	C₂³	—	356	1	no	—
444	Q₈	—	2	1	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	356	1	no	—
448	Q₈	—	356	2	no	—
449	Q₈	—	356	2	no	—
450	Q₈	—	178	1	no	—
451	Q₈	—	712	2	no	—
452	Q₈	—	712	2	no	—
453	D₄	—	2	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	356	1	no	—
456	D₄	—	356	1	no	—
457	D₄	—	356	1	no	—
458	D₄	—	356	1	no	—
459	D₄	—	178	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	89	1	no	—
464	C₂×C₄	—	89	1	no	—
465	C₂×C₄	—	89	1	no	—
466	C₂×C₄	—	89	1	no	—
467	C₂×C₄	—	89	1	no	—
468	C₂×C₄	—	356	1	no	—
469	C₂×C₄	—	356	1	no	—
470	C₂×C₄	—	356	1	no	—
471	C₂×C₄	—	356	1	no	—
472	C₂×C₄	—	356	2	no	—
473	C₂×C₄	—	178	4	no	—
474	C₂×C₄	—	178	1	no	—
475	C₂×C₄	—	712	2	no	—
476	C₂×C₄	—	712	2	no	—
477	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
478	C₈	—	4	1	no	—
479	C₈	—	89	1	no	—
480	C₈	—	89	1	no	—
481	C₈	—	89	1	no	—
482	C₈	—	89	1	no	—
483	C₈	—	356	1	no	—
484	C₈	D₈×D₈₉	1	1	yes	characteristic
485	C₈	D₈×D₈₉	1	1	yes	characteristic
486	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
487	C₈	#41×D₈₉	1	1	yes	characteristic
488	C₂²	—	4	1	no	—
489	C₂²	—	89	1	no	—
490	C₂²	—	89	1	no	—
491	C₂²	—	356	1	no	—
492	C₂²	—	178	2	no	—
493	C₂²	—	712	2	no	—
494	C₂²	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	2	no	—
498	C₄	—	89	1	no	—
499	C₄	—	89	1	no	—
500	C₄	—	356	1	no	—
501	C₄	—	178	2	no	—
502	C₄	—	712	2	no	—
503	C₄	#121×D₈₉	1	1	yes	characteristic
504	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
505	C₂	—	2	1	no	—
506	C₂	—	8	1	no	—
507	C₂	—	89	2	no	—
508	C₂	—	178	1	no	—
509	C₂	—	712	1	no	—
510	C₂	#459×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#459×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2214	C₂
socle	C₂×C₈₉	C₂×#459
prime radical	#135×D₈₉	C₂²
hypercenter	#2214	D₈₉
hypocenter	C₈₉	C₂×#2214
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2214

Complements

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

N	H ≅ G/N	type
2. #494×D₈₉	C₂	semidirect
4. #26022334	C₂	semidirect
5. #26022333	C₂	semidirect
6. #26022332	C₂	semidirect
7. #26022331	C₂	semidirect
8. #26022330	C₂	semidirect
9. #364×D₈₉	C₂	semidirect
10. #362×D₈₉	C₂	semidirect
11. C₈₉×#2214	C₂	semidirect
25. #19151978	C₂²	semidirect
28. #19151976	C₂²	semidirect
37. #19151419	C₂²	semidirect
38. #19151418	C₂²	semidirect
39. #19151415	C₂²	semidirect
40. #19151414	C₂²	semidirect
41. #19151413	C₂²	semidirect
43. #494×C₈₉	C₂²	semidirect
45. #364×C₈₉	C₂²	semidirect
46. #362×C₈₉	C₂²	semidirect
255. D₈₉	#2214	direct (N × H)
264. #2214	D₈₉	direct (N × H)
267. C₈₉	C₂×#2214	semidirect
286. #494	C₂×D₈₉	semidirect
298. #364	C₂×D₈₉	semidirect
302. #362	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#510×D₈₉	2
#494×D₈₉	2
#443×D₈₉	2
#26022334	2
#26022333	2
#26022332	2
#26022331	2
#26022330	2
#364×D₈₉	2
#362×D₈₉	2
C₈₉×#2214	2
C₂×#2214	89

Subgroups — #2214×D89 #36708810

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2214×D₈₉ #36708810