Subgroups — #36708819

Order 22784.

696 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033384	C₂	1	2	yes	maximal, complemented
2	#26030679	C₂	1	1	yes	maximal, characteristic, complemented
3	#443×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022334	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022333	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022325	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022320	C₂	1	2	yes	maximal, complemented
8	#26022319	C₂	1	2	yes	maximal, complemented
9	#364×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#26021998	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2213	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668031	—	2	1	no	—
13	C₂×#15668031	C₂²	1	2	yes	—
14	#135×D₈₉	C₂²	1	1	yes	characteristic
15	#131×D₈₉	—	2	1	no	—
16	#19152146	—	2	1	no	—
17	#19152041	C₂²	1	2	yes	—
18	#19152038	C₂²	1	2	yes	—
19	#19152037	—	2	2	no	—
20	#19152034	C₂²	1	2	yes	—
21	#19152032	—	2	2	no	—
22	#19152029	—	2	2	no	—
23	#19152027	—	2	2	no	—
24	M₃₂×D₈₉	C₂²	1	2	yes	—
25	#19151981	—	2	1	no	—
26	#19151981	C₂²	1	2	yes	complemented
27	#19151978	C₂²	1	1	yes	characteristic, complemented
28	#19151970	—	2	1	no	—
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	#19151413	C₂²	1	2	yes	complemented
41	#19151411	C₂²	1	2	yes	complemented
42	#509×C₈₉	C₂²	1	2	yes	—
43	#493×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	#361×C₈₉	C₂²	1	2	yes	complemented
47	C₂×#13083573	—	2	2	no	—
48	#41×D₈₉	—	2	1	no	—
49	#15668035	D₄	1	1	yes	characteristic, complemented
50	#15668034	C₂³	1	1	yes	characteristic
51	#15668033	—	2	1	no	—
52	#15668032	—	2	1	no	—
53	#15668031	—	2	2	no	—
54	#15668031	—	2	2	no	—
55	#15668031	—	2	2	no	—
56	#15668031	—	2	2	no	—
57	#15668031	—	4	1	no	—
58	#15668031	—	4	1	no	—
59	#15668031	—	4	1	no	—
60	#15668031	—	4	1	no	—
61	#15668031	D₄	1	1	yes	characteristic, complemented
62	C₂×Dic₃₅₆	—	2	1	no	—
63	C₂×Dic₃₅₆	C₂³	1	2	yes	—
64	Q₁₆×D₈₉	D₄	1	1	yes	characteristic, complemented
65	C₂×#13083562	—	2	2	no	—
66	C₂×#13083562	—	2	2	no	—
67	SD₁₆×D₈₉	—	2	1	no	—
68	D₈×D₈₉	D₄	1	1	yes	characteristic, complemented
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	#15667999	—	2	2	no	—
81	#15667983	—	4	2	no	—
82	D₄×Dic₈₉	—	4	2	no	—
83	C₄²×D₈₉	D₄	1	1	yes	characteristic
84	Dic₇₁₂	—	2	2	no	—
85	#15667958	—	2	2	no	—
86	#15667957	—	2	2	no	—
87	#15667956	—	2	2	no	—
88	#15667956	—	2	2	no	—
89	#15667953	—	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×D₈×C₈₉	—	2	1	no	—
103	C₂×D₈×C₈₉	C₂³	1	2	yes	—
104	#131×C₈₉	—	2	1	no	—
105	#127×C₈₉	—	2	1	no	—
106	SD₃₂×C₈₉	—	2	2	no	—
107	D₁₆×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	#13083573	—	4	2	no	—
118	#13083573	—	4	2	no	—
119	#13083573	—	4	2	no	—
120	#13083573	—	4	2	no	—
121	C₂×Dic₁₇₈	—	2	2	no	—
122	Q₈×D₈₉	—	2	1	no	—
123	C₂×C₂²⋊D₈₉	—	4	2	no	—
124	D₄×D₈₉	—	2	1	no	—
125	D₄×D₈₉	—	4	1	no	—
126	C₂²×Dic₈₉	—	4	2	no	—
127	C₂×C₄×D₈₉	—	2	1	no	—
128	C₂×C₄×D₈₉	—	4	1	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	#13083563	—	2	1	no	—
137	#13083562	—	2	1	no	—
138	#13083562	—	4	2	no	—
139	#13083562	—	4	2	no	—
140	#13083562	—	4	2	no	—
141	#13083562	—	4	2	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	C₂²⋊Dic₈₉	—	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×D₄×C₈₉	—	2	2	no	—
171	C₂×D₄×C₈₉	—	4	2	no	—
172	Q₁₆×C₈₉	C₂×D₄	1	1	yes	characteristic
173	SD₁₆×C₈₉	—	2	1	no	—
174	D₈×C₈₉	—	2	2	no	—
175	D₈×C₈₉	—	2	2	no	—
176	D₈×C₈₉	—	4	1	no	—
177	D₈×C₈₉	—	4	1	no	—
178	D₈×C₈₉	C₂×D₄	1	1	yes	characteristic
179	M₁₆×C₈₉	—	2	1	no	—
180	M₁₆×C₈₉	—	4	1	no	—
181	C₂×C₈×C₈₉	—	4	1	no	—
182	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
185	C₁₆×C₈₉	—	2	2	no	—
186	C₂³×C₈₉	—	4	2	no	—
187	C₂²×D₈₉	—	4	1	no	—
188	C₂²×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
189	Q₈×C₈₉	—	2	1	no	—
190	D₄×C₈₉	—	2	1	no	—
191	D₄×C₈₉	—	4	1	no	—
192	D₄×C₈₉	—	4	2	no	—
193	D₄×C₈₉	—	4	2	no	—
194	D₄×C₈₉	—	8	4	no	—
195	C₂×C₄×C₈₉	—	2	1	no	—
196	C₂×C₄×C₈₉	—	4	1	no	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂²⋊D₈₉	—	4	1	no	—
199	C₂²⋊D₈₉	—	4	1	no	—
200	C₂²⋊D₈₉	—	4	1	no	—
201	C₂²⋊D₈₉	—	8	2	no	—
202	C₂²⋊D₈₉	—	8	2	no	—
203	C₂×Dic₈₉	—	2	1	no	—
204	C₂×Dic₈₉	—	4	1	no	—
205	C₂×Dic₈₉	—	4	2	no	—
206	C₂×Dic₈₉	—	8	2	no	—
207	C₂×Dic₈₉	—	8	2	no	—
208	C₂×Dic₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
209	D₃₅₆	—	2	1	no	—
210	D₃₅₆	—	4	1	no	—
211	C₄×D₈₉	—	4	2	no	—
212	C₄×D₈₉	—	4	1	no	—
213	C₄×D₈₉	—	4	1	no	—
214	C₄×D₈₉	—	4	1	no	—
215	C₄×D₈₉	#121	1	1	yes	characteristic
216	C₄×D₈₉	#121	1	1	yes	characteristic
217	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
218	C₄×D₈₉	C₂×D₈	1	1	yes	characteristic
219	Dic₁₇₈	—	2	1	no	—
220	Dic₁₇₈	—	4	1	no	—
221	Dic₁₇₈	—	4	2	no	—
222	Dic₁₇₈	—	4	2	no	—
223	C₈×C₈₉	—	4	1	no	—
224	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
225	C₈×C₈₉	C₂×D₈	1	1	yes	characteristic
226	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
228	#10623494	—	4	1	no	—
229	#10623494	#121	1	1	yes	characteristic
230	#10623494	#121	1	1	yes	characteristic
231	#10623494	C₂×D₈	1	1	yes	characteristic
232	#10623494	C₂×D₈	1	1	yes	characteristic
233	C₂²×C₈₉	—	4	1	no	—
234	C₂²×C₈₉	—	8	4	no	—
235	C₂²×C₈₉	—	8	2	no	—
236	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂×D₈₉	—	4	1	no	—
238	C₂×D₈₉	—	4	1	no	—
239	C₂×D₈₉	—	8	2	no	—
240	C₂×D₈₉	#459	1	1	yes	characteristic
241	C₂×D₈₉	#459	1	1	yes	characteristic
242	C₄×C₈₉	—	2	2	no	—
243	C₄×C₈₉	—	4	1	no	—
244	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
245	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
246	Dic₈₉	—	4	1	no	—
247	Dic₈₉	—	4	1	no	—
248	Dic₈₉	—	8	2	no	—
249	Dic₈₉	#459	1	1	yes	characteristic
250	Dic₈₉	#459	1	1	yes	characteristic
251	#33594	—	89	1	no	maximal, Sylow
252	C₂×C₈₉	—	2	1	no	—
253	C₂×C₈₉	—	8	1	no	—
254	C₂×C₈₉	—	16	2	no	—
255	C₂×C₈₉	C₂×#459	1	1	yes	characteristic
256	D₈₉	—	2	1	no	—
257	D₈₉	—	2	1	no	—
258	D₈₉	—	8	1	no	—
259	#3414	—	89	2	no	—
260	#3147	—	89	1	no	—
261	C₂×#443	—	89	1	no	—
262	#2214	—	89	1	no	—
263	#2214	—	89	1	no	—
264	#2213	—	89	1	no	—
265	#2213	D₈₉	1	1	yes	characteristic, complemented
266	#2212	—	89	2	no	—
267	#2212	—	89	2	no	—
268	C₂×#364	—	89	1	no	—
269	#2148	—	89	2	no	—
270	C₈₉	#33594	1	1	yes	characteristic, complemented, Sylow
271	C₂×#135	—	89	1	no	—
272	C₂×#135	—	89	2	no	—
273	C₂×#135	—	178	1	no	—
274	C₂×#131	—	178	1	no	—
275	#532	—	178	1	no	—
276	#510	—	89	2	no	—
277	#510	—	89	2	no	—
278	#510	—	178	2	no	—
279	#509	—	89	2	no	—
280	#509	—	178	2	no	—
281	#509	C₂×D₈₉	1	2	yes	—
282	#508	—	178	2	no	—
283	#508	—	178	2	no	—
284	C₂×M₃₂	—	89	2	no	—
285	#495	—	89	2	no	—
286	#495	—	178	1	no	—
287	#494	—	89	1	no	—
288	#493	C₂×D₈₉	1	1	yes	characteristic, complemented
289	#492	—	178	1	no	—
290	#443	—	89	1	no	—
291	#443	—	89	1	no	—
292	#443	—	89	1	no	—
293	#443	—	178	1	no	—
294	#443	—	178	1	no	—
295	#443	C₂×D₈₉	1	1	yes	characteristic
296	C₂×#108	—	89	1	no	—
297	C₂×#104	—	178	1	no	—
298	C₂×C₄×C₈	—	89	1	no	—
299	#364	—	89	2	no	—
300	#364	—	89	1	no	—
301	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
302	#362	—	89	2	no	—
303	#362	—	89	2	no	—
304	#361	—	89	2	no	—
305	#361	C₂×D₈₉	1	2	yes	complemented
306	C₂×#41	—	178	2	no	—
307	C₂×#41	—	178	1	no	—
308	#135	—	89	1	no	—
309	#135	—	89	1	no	—
310	#135	—	89	1	no	—
311	#135	—	356	1	no	—
312	#135	—	356	1	no	—
313	#135	—	356	1	no	—
314	#135	—	356	1	no	—
315	#135	—	178	2	no	—
316	#135	—	178	2	no	—
317	#135	—	178	2	no	—
318	#135	—	178	2	no	—
319	#135	—	178	1	no	—
320	#135	—	178	1	no	—
321	#135	C₂²×D₈₉	1	1	yes	characteristic
322	C₂×Q₁₆	—	89	1	no	—
323	C₂×Q₁₆	—	89	2	no	—
324	C₂×Q₁₆	—	178	1	no	—
325	C₂×SD₁₆	—	178	1	no	—
326	C₂×SD₁₆	—	178	2	no	—
327	C₂×SD₁₆	—	178	2	no	—
328	C₂×D₈	—	2	1	no	—
329	C₂×D₈	—	89	1	no	—
330	C₂×D₈	C₂²×D₈₉	1	2	yes	—
331	#131	—	2	1	no	—
332	#131	—	356	1	no	—
333	#131	—	356	1	no	—
334	#131	—	178	1	no	—
335	#131	—	178	1	no	—
336	#131	—	178	1	no	—
337	C₂×M₁₆	—	356	1	no	—
338	C₂×M₁₆	—	178	1	no	—
339	C₂²×C₈	—	89	1	no	—
340	C₂²×C₈	—	89	1	no	—
341	C₂²×C₈	—	356	1	no	—
342	C₄⋊Q₈	—	178	1	no	—
343	#127	—	2	1	no	—
344	#124	—	178	2	no	—
345	#121	—	356	2	no	—
346	C₄×D₄	—	356	2	no	—
347	C₂×C₄²	—	89	1	no	—
348	Q₃₂	—	178	2	no	—
349	Q₃₂	—	178	2	no	—
350	SD₃₂	—	2	2	no	—
351	SD₃₂	—	178	2	no	—
352	SD₃₂	—	178	2	no	—
353	SD₃₂	—	178	2	no	—
354	D₁₆	—	2	2	no	—
355	D₁₆	—	178	2	no	—
356	M₃₂	—	89	2	no	—
357	M₃₂	—	178	2	no	—
358	M₃₂	C₂²×D₈₉	1	2	yes	—
359	C₂×C₁₆	—	178	2	no	—
360	#108	—	89	1	no	—
361	#108	—	178	1	no	—
362	#108	C₂²×D₈₉	1	1	yes	characteristic
363	#104	—	2	1	no	—
364	#104	—	178	1	no	—
365	#104	—	178	1	no	—
366	#104	—	178	1	no	—
367	C₄×C₈	—	89	1	no	—
368	C₄×C₈	—	89	1	no	—
369	C₄×C₈	—	89	1	no	—
370	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
371	#41	—	2	1	no	—
372	#41	—	356	1	no	—
373	#41	—	356	1	no	—
374	#41	—	356	2	no	—
375	#41	—	356	2	no	—
376	#41	—	356	2	no	—
377	#41	—	356	2	no	—
378	#41	—	178	1	no	—
379	#41	—	178	1	no	—
380	#41	—	178	1	no	—
381	C₂×Q₈	—	178	1	no	—
382	C₂×Q₈	—	178	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	356	1	no	—
386	C₂×D₄	—	356	2	no	—
387	C₂×D₄	—	178	1	no	—
388	C₂²×C₄	—	89	1	no	—
389	C₂²×C₄	—	356	1	no	—
390	C₂²×C₄	—	356	2	no	—
391	C₂²×C₄	—	178	1	no	—
392	Q₁₆	—	89	1	no	—
393	Q₁₆	—	356	1	no	—
394	Q₁₆	—	356	1	no	—
395	Q₁₆	—	178	1	no	—
396	Q₁₆	—	178	2	no	—
397	Q₁₆	—	178	2	no	—
398	Q₁₆	D₄×D₈₉	1	1	yes	characteristic
399	SD₁₆	—	2	1	no	—
400	SD₁₆	—	356	2	no	—
401	SD₁₆	—	356	2	no	—
402	SD₁₆	—	356	2	no	—
403	SD₁₆	—	356	2	no	—
404	SD₁₆	—	178	1	no	—
405	SD₁₆	—	178	1	no	—
406	SD₁₆	—	178	1	no	—
407	D₈	—	2	2	no	—
408	D₈	—	2	2	no	—
409	D₈	—	4	1	no	—
410	D₈	—	4	1	no	—
411	D₈	—	89	1	no	—
412	D₈	—	178	1	no	—
413	D₈	D₄×D₈₉	1	1	yes	characteristic
414	M₁₆	—	2	1	no	—
415	M₁₆	—	4	1	no	—
416	M₁₆	—	356	1	no	—
417	M₁₆	—	356	1	no	—
418	M₁₆	—	356	1	no	—
419	M₁₆	—	356	1	no	—
420	M₁₆	—	178	1	no	—
421	C₂×C₈	—	4	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	—	89	1	no	—
429	C₂×C₈	—	89	1	no	—
430	C₂×C₈	—	89	1	no	—
431	C₂×C₈	—	89	1	no	—
432	C₂×C₈	—	356	1	no	—
433	C₂×C₈	—	356	1	no	—
434	C₂×C₈	—	356	1	no	—
435	C₂×C₈	—	356	1	no	—
436	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
437	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
438	C₄⋊C₄	—	356	2	no	—
439	C₂²⋊C₄	—	356	4	no	—
440	C₄²	—	89	1	no	—
441	C₄²	—	178	1	no	—
442	C₄²	D₄×D₈₉	1	1	yes	characteristic
443	C₁₆	—	2	2	no	—
444	C₁₆	—	178	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	89	1	no	—
447	C₂³	—	356	1	no	—
448	Q₈	—	2	1	no	—
449	Q₈	—	356	1	no	—
450	Q₈	—	356	2	no	—
451	Q₈	—	356	2	no	—
452	Q₈	—	178	1	no	—
453	D₄	—	2	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	8	4	no	—
458	D₄	—	356	1	no	—
459	D₄	—	356	1	no	—
460	D₄	—	356	1	no	—
461	D₄	—	356	1	no	—
462	D₄	—	178	1	no	—
463	D₄	—	712	2	no	—
464	D₄	—	712	2	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	89	1	no	—
468	C₂×C₄	—	89	1	no	—
469	C₂×C₄	—	89	1	no	—
470	C₂×C₄	—	89	1	no	—
471	C₂×C₄	—	89	1	no	—
472	C₂×C₄	—	356	2	no	—
473	C₂×C₄	—	356	1	no	—
474	C₂×C₄	—	356	1	no	—
475	C₂×C₄	—	356	1	no	—
476	C₂×C₄	—	356	1	no	—
477	C₂×C₄	—	356	2	no	—
478	C₂×C₄	—	178	1	no	—
479	C₂×C₄	—	712	2	no	—
480	C₂×C₄	—	712	2	no	—
481	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
482	C₈	—	4	1	no	—
483	C₈	—	89	1	no	—
484	C₈	—	89	1	no	—
485	C₈	—	89	1	no	—
486	C₈	—	89	1	no	—
487	C₈	—	356	1	no	—
488	C₈	D₈×D₈₉	1	1	yes	characteristic
489	C₈	D₈×D₈₉	1	1	yes	characteristic
490	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
491	C₈	#41×D₈₉	1	1	yes	characteristic
492	C₂²	—	4	1	no	—
493	C₂²	—	8	4	no	—
494	C₂²	—	8	2	no	—
495	C₂²	—	89	1	no	—
496	C₂²	—	89	1	no	—
497	C₂²	—	356	1	no	—
498	C₂²	—	356	1	no	—
499	C₂²	—	712	2	no	—
500	C₂²	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
501	C₄	—	2	2	no	—
502	C₄	—	4	1	no	—
503	C₄	—	89	1	no	—
504	C₄	—	89	1	no	—
505	C₄	—	356	1	no	—
506	C₄	—	356	1	no	—
507	C₄	—	712	2	no	—
508	C₄	#121×D₈₉	1	1	yes	characteristic
509	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
510	C₂	—	2	1	no	—
511	C₂	—	8	1	no	—
512	C₂	—	16	2	no	—
513	C₂	—	178	1	no	—
514	C₂	—	178	1	no	—
515	C₂	—	712	1	no	—
516	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×#2213	C₂
socle	C₂×C₈₉	C₂×#459
hypercenter	#2213	D₈₉
hypocenter	C₈₉	#33594
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #2213

Complements

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

N	H ≅ G/N	type
1. #26033384	C₂	semidirect
2. #26030679	C₂	semidirect
3. #443×D₈₉	C₂	semidirect
4. #26022334	C₂	semidirect
5. #26022333	C₂	semidirect
6. #26022325	C₂	semidirect
7. #26022320	C₂	semidirect
8. #26022319	C₂	semidirect
9. #364×D₈₉	C₂	semidirect
10. #26021998	C₂	semidirect
11. C₈₉×#2213	C₂	semidirect
26. #19151981	C₂²	semidirect
27. #19151978	C₂²	semidirect
37. #19151419	C₂²	semidirect
38. #19151418	C₂²	semidirect
39. #19151415	C₂²	semidirect
40. #19151413	C₂²	semidirect
41. #19151411	C₂²	semidirect
43. #493×C₈₉	C₂²	semidirect
45. #364×C₈₉	C₂²	semidirect
46. #361×C₈₉	C₂²	semidirect
49. #15668035	D₄	semidirect
61. #15668031	D₄	semidirect
64. Q₁₆×D₈₉	D₄	semidirect
68. D₈×D₈₉	D₄	semidirect
265. #2213	D₈₉	semidirect
270. C₈₉	#33594	semidirect
288. #493	C₂×D₈₉	semidirect
301. #364	C₂×D₈₉	semidirect
305. #361	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26033384	2
#26030679	2
#443×D₈₉	2
#26022334	2
#26022333	2
#26022325	2
#26022320	2
#26022319	2
#364×D₈₉	2
#26021998	2
C₈₉×#2213	2
#33594	89