Subgroups — #36526202

Order 22784.

586 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030835	C₂	1	1	yes	maximal, characteristic
2	#26029200	C₂	1	1	yes	maximal, characteristic
3	#26029194	C₂	1	1	yes	maximal, characteristic
4	#26019147	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019146	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019104	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019103	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019101	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13083564	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
11	#335×D₈₉	C₂	1	1	yes	maximal, characteristic
12	#26018653	C₂	1	1	yes	maximal, characteristic
13	#26018653	C₂	1	1	yes	maximal, characteristic
14	#26018531	C₂	1	1	yes	maximal, characteristic
15	C₈₉×#1584	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152152	C₂²	1	1	yes	characteristic
17	#19152152	C₂²	1	1	yes	characteristic
18	#19152002	C₄	1	1	yes	characteristic
19	#19151976	C₄	1	1	yes	characteristic
20	#19151947	C₄	1	1	yes	characteristic
21	#19151947	C₄	1	1	yes	characteristic
22	#19151840	C₄	1	1	yes	characteristic
23	#19151838	C₄	1	1	yes	characteristic
24	#19151838	C₄	1	1	yes	characteristic
25	#19151836	C₄	1	1	yes	characteristic
26	#19151729	C₂²	1	1	yes	characteristic
27	#19151728	—	2	1	no	—
28	#19151728	C₂²	1	1	yes	characteristic
29	#19151727	—	2	1	no	—
30	#19151726	—	2	1	no	—
31	#19151725	—	2	1	no	—
32	#19151725	C₂²	1	1	yes	characteristic
33	Q₈×#10623494	C₂²	1	1	yes	characteristic
34	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
35	#19151722	C₂²	1	1	yes	characteristic
36	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
37	C₄×#13083564	C₂²	1	1	yes	characteristic
38	C₄×#13083564	C₂²	1	1	yes	characteristic
39	#19151649	C₂²	1	1	yes	characteristic
40	#19151623	—	2	1	no	—
41	#19151623	—	2	1	no	—
42	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
44	#19151555	—	2	1	no	—
45	#19151552	—	2	1	no	—
46	C₄×#13083557	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	C₈×#10623494	C₂²	1	1	yes	characteristic
59	C₈×#10623494	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×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083564	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083557	D₄	1	1	yes	characteristic
71	C₂×#13083557	D₄	1	1	yes	characteristic
72	C₂×C₈×D₈₉	—	2	1	no	—
73	C₂×C₈×D₈₉	—	2	1	no	—
74	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
76	#15668011	C₂×C₄	1	1	yes	characteristic
77	#15668011	C₂×C₄	1	1	yes	characteristic
78	#15668010	C₂×C₄	1	1	yes	characteristic
79	#15668010	C₂×C₄	1	1	yes	characteristic
80	#15668002	—	2	1	no	—
81	#15668002	—	2	1	no	—
82	#15667992	C₂×C₄	1	1	yes	characteristic
83	#15667992	C₂×C₄	1	1	yes	characteristic
84	#15667990	—	2	1	no	—
85	#15667990	—	2	1	no	—
86	#15667988	C₂×C₄	1	1	yes	characteristic
87	#15667988	C₂×C₄	1	1	yes	characteristic
88	C₄×Dic₁₇₈	—	2	1	no	—
89	C₄×Dic₁₇₈	—	2	1	no	—
90	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
91	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
92	#15667969	—	2	1	no	—
93	#15667969	—	2	1	no	—
94	C₄²×D₈₉	C₂³	1	1	yes	characteristic
95	#15667946	C₂×C₄	1	1	yes	characteristic
96	#15667945	C₂×C₄	1	1	yes	characteristic
97	#15667945	C₂×C₄	1	1	yes	characteristic
98	C₄⋊#10623494	—	2	1	no	—
99	C₄⋊#10623494	—	2	1	no	—
100	C₄⋊#10623494	C₂³	1	1	yes	characteristic
101	C₄⋊#10623494	C₂³	1	1	yes	characteristic
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
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	#15667937	C₂×C₄	1	1	yes	characteristic
110	#15667937	C₂×C₄	1	1	yes	characteristic
111	#15667936	C₂×C₄	1	1	yes	characteristic
112	#15667936	C₂×C₄	1	1	yes	characteristic
113	#15667935	C₂×C₄	1	1	yes	characteristic
114	#15667935	C₂×C₄	1	1	yes	characteristic
115	#15667924	—	2	1	no	—
116	#15667923	—	2	1	no	—
117	#15667922	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	D₄	1	1	yes	characteristic
120	#15667922	D₄	1	1	yes	characteristic
121	C₄×#10623494	—	2	1	no	—
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
129	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
133	C₄⋊C₈×C₈₉	—	2	1	no	—
134	C₄⋊C₈×C₈₉	—	2	1	no	—
135	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
137	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
138	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
139	#97×C₈₉	—	2	1	no	—
140	C₄×C₈×C₈₉	—	2	1	no	—
141	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×Dic₁₇₈	—	2	1	no	—
145	C₂×Dic₁₇₈	—	2	1	no	—
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
151	Dic₃₅₆	—	4	1	no	—
152	#13083564	—	2	2	no	—
153	#13083564	—	2	2	no	—
154	#13083557	—	2	2	no	—
155	#13083557	Q₁₆	1	4	yes	complemented
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
160	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
161	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
162	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
163	C₈×D₈₉	—	2	2	no	—
164	C₈×D₈₉	—	4	1	no	—
165	C₈×D₈₉	—	4	2	no	—
166	C₈×D₈₉	—	4	2	no	—
167	C₄⋊Dic₈₉	—	2	1	no	—
168	C₄⋊Dic₈₉	—	2	1	no	—
169	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
171	#13083553	—	2	1	no	—
172	#13083553	—	2	1	no	—
173	#13083553	—	2	1	no	—
174	#13083553	—	2	1	no	—
175	#13083553	—	2	1	no	—
176	#13083553	—	2	1	no	—
177	#13083553	—	2	1	no	—
178	#13083553	—	2	1	no	—
179	#13083553	—	2	1	no	—
180	#13083553	—	2	1	no	—
181	#13083551	—	2	1	no	—
182	#13083551	—	2	1	no	—
183	#13083551	—	2	1	no	—
184	#13083551	—	2	1	no	—
185	C₄×Dic₈₉	—	2	1	no	—
186	C₄×Dic₈₉	—	2	1	no	—
187	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
189	C₄×Dic₈₉	#41	1	1	yes	characteristic
190	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
192	Q₁₆×C₈₉	—	4	1	no	—
193	C₂×C₈×C₈₉	—	2	1	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
197	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₄⋊C₄×C₈₉	—	2	1	no	—
201	C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
204	C₄²×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
207	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
208	Q₈×C₈₉	—	2	1	no	—
209	Q₈×C₈₉	—	2	1	no	—
210	Q₈×C₈₉	—	2	1	no	—
211	Q₈×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	1	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	1	no	—
215	C₂×C₄×C₈₉	—	2	1	no	—
216	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
219	C₂×Dic₈₉	—	2	1	no	—
220	C₂×Dic₈₉	—	2	1	no	—
221	C₂×Dic₈₉	—	2	1	no	—
222	C₂×Dic₈₉	—	2	1	no	—
223	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
224	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
226	C₄×D₈₉	—	2	1	no	—
227	C₄×D₈₉	—	2	1	no	—
228	C₄×D₈₉	—	4	1	no	—
229	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
230	C₄×D₈₉	#135	1	2	yes	—
231	Dic₁₇₈	—	2	1	no	—
232	Dic₁₇₈	—	2	1	no	—
233	Dic₁₇₈	—	2	1	no	—
234	Dic₁₇₈	—	2	1	no	—
235	Dic₁₇₈	—	8	1	no	—
236	Dic₁₇₈	—	8	1	no	—
237	C₈×C₈₉	—	2	1	no	—
238	C₈×C₈₉	—	2	1	no	—
239	C₈×C₈₉	—	2	1	no	—
240	C₈×C₈₉	—	4	1	no	—
241	C₈×C₈₉	—	4	1	no	—
242	C₈×C₈₉	—	4	1	no	—
243	C₈×C₈₉	C₂×Q₁₆	1	2	yes	—
244	#10623494	—	2	1	no	—
245	#10623494	—	2	1	no	—
246	#10623494	—	4	1	no	—
247	#10623494	—	4	1	no	—
248	#10623494	—	4	1	no	—
249	#10623494	#131	1	2	yes	—
250	#10623494	C₂×Q₁₆	1	2	yes	—
251	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂×D₈₉	—	2	1	no	—
253	C₂×D₈₉	—	2	1	no	—
254	C₂×D₈₉	C₄×Q₁₆	1	2	yes	—
255	C₄×C₈₉	—	2	1	no	—
256	C₄×C₈₉	—	4	1	no	—
257	C₄×C₈₉	—	4	1	no	—
258	C₄×C₈₉	—	4	1	no	—
259	C₄×C₈₉	—	4	1	no	—
260	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
261	C₄×C₈₉	#568	1	1	yes	characteristic
262	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
263	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
264	Dic₈₉	—	2	1	no	—
265	Dic₈₉	—	2	1	no	—
266	Dic₈₉	—	4	1	no	—
267	Dic₈₉	—	4	1	no	—
268	Dic₈₉	—	4	1	no	—
269	Dic₈₉	—	4	1	no	—
270	Dic₈₉	C₄×Q₁₆	1	2	yes	—
271	#18068	—	89	1	no	maximal, Sylow
272	C₂×C₈₉	#2935	1	1	yes	characteristic
273	C₂×C₈₉	C₂×C₄×Q₁₆	1	1	yes	characteristic
274	C₂×C₈₉	#2957	1	1	yes	characteristic
275	D₈₉	—	2	2	no	—
276	#3170	—	89	1	no	—
277	#2962	—	89	1	no	—
278	#2962	—	89	1	no	—
279	#1591	—	89	1	no	—
280	#1591	—	89	1	no	—
281	#1584	—	89	1	no	—
282	#1584	—	89	1	no	—
283	#1584	—	89	1	no	—
284	#1584	D₈₉	1	1	yes	characteristic, complemented
285	C₈×Q₁₆	—	89	1	no	—
286	C₈×Q₁₆	—	89	1	no	—
287	C₂×#335	—	89	1	no	—
288	#1481	—	89	1	no	—
289	#1481	—	89	1	no	—
290	C₈×M₁₆	—	89	1	no	—
291	C₈₉	#18068	1	1	yes	characteristic, complemented, Sylow
292	#533	—	89	1	no	—
293	#533	—	89	1	no	—
294	#500	—	89	1	no	—
295	#494	—	89	1	no	—
296	#487	—	89	1	no	—
297	#487	—	89	1	no	—
298	#467	—	89	1	no	—
299	#467	—	89	1	no	—
300	#467	—	89	1	no	—
301	#467	—	89	1	no	—
302	#446	—	89	1	no	—
303	#446	—	89	1	no	—
304	#446	—	89	1	no	—
305	#446	—	178	1	no	—
306	#446	—	178	1	no	—
307	#446	—	178	1	no	—
308	#446	—	178	1	no	—
309	#446	C₂×D₈₉	1	1	yes	characteristic
310	C₈×Q₈	—	89	1	no	—
311	C₈×Q₈	—	89	1	no	—
312	C₈×Q₈	—	89	1	no	—
313	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
314	C₄×Q₁₆	—	89	1	no	—
315	C₄×Q₁₆	—	89	1	no	—
316	C₄×Q₁₆	—	89	1	no	—
317	C₄×Q₁₆	C₂×D₈₉	1	1	yes	characteristic
318	#431	—	89	1	no	—
319	#424	—	178	1	no	—
320	#424	—	178	1	no	—
321	C₂×C₄⋊C₈	—	89	1	no	—
322	C₂×C₄⋊C₈	—	89	1	no	—
323	#405	—	178	1	no	—
324	#405	—	178	1	no	—
325	C₄×M₁₆	—	89	1	no	—
326	C₂×C₄×C₈	—	89	1	no	—
327	#335	—	89	1	no	—
328	#335	—	89	1	no	—
329	#335	—	89	1	no	—
330	#335	C₂×D₈₉	1	1	yes	characteristic
331	Q₈⋊C₈	—	89	1	no	—
332	Q₈⋊C₈	—	89	1	no	—
333	Q₈⋊C₈	—	89	1	no	—
334	Q₈⋊C₈	—	89	1	no	—
335	Q₈⋊C₈	—	89	1	no	—
336	Q₈⋊C₈	—	89	1	no	—
337	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
338	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
339	#322	—	89	1	no	—
340	#322	C₂×D₈₉	1	1	yes	characteristic
341	C₈²	—	89	1	no	—
342	C₈²	—	89	1	no	—
343	C₂×Q₁₆	—	89	1	no	—
344	C₂×Q₁₆	—	89	1	no	—
345	C₂×Q₁₆	—	89	1	no	—
346	C₂×Q₁₆	C₄×D₈₉	1	1	yes	characteristic
347	C₂×M₁₆	—	89	1	no	—
348	C₂×M₁₆	—	89	1	no	—
349	C₂²×C₈	—	89	1	no	—
350	C₂²×C₈	—	89	1	no	—
351	C₂²×C₈	—	178	1	no	—
352	C₂²×C₈	—	178	1	no	—
353	C₄⋊Q₈	—	89	1	no	—
354	C₄⋊Q₈	—	89	1	no	—
355	C₄⋊Q₈	—	89	1	no	—
356	C₄⋊Q₈	—	89	1	no	—
357	#125	—	178	1	no	—
358	#125	—	178	1	no	—
359	C₂²⋊Q₈	—	89	1	no	—
360	C₂²⋊Q₈	—	89	1	no	—
361	C₂²⋊Q₈	—	89	1	no	—
362	C₂²⋊Q₈	—	89	1	no	—
363	C₂²⋊Q₈	—	178	1	no	—
364	C₂²⋊Q₈	—	178	1	no	—
365	C₄×Q₈	—	89	1	no	—
366	C₄×Q₈	—	89	1	no	—
367	C₄×Q₈	—	178	1	no	—
368	C₄×Q₈	—	178	1	no	—
369	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
370	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
371	#117	—	178	1	no	—
372	#117	—	178	1	no	—
373	C₂×C₄²	—	89	1	no	—
374	#107	—	89	1	no	—
375	#107	—	89	1	no	—
376	#107	—	89	1	no	—
377	#107	C₄×D₈₉	1	1	yes	characteristic
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	2	1	no	—
380	C₄⋊C₈	—	89	1	no	—
381	C₄⋊C₈	—	89	1	no	—
382	C₄⋊C₈	—	178	1	no	—
383	C₄⋊C₈	—	178	1	no	—
384	C₄⋊C₈	—	178	1	no	—
385	C₄⋊C₈	—	178	1	no	—
386	C₄⋊C₈	—	178	1	no	—
387	C₄⋊C₈	—	178	1	no	—
388	C₄⋊C₈	—	178	1	no	—
389	C₄⋊C₈	—	178	1	no	—
390	C₄⋊C₈	—	178	1	no	—
391	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
392	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
393	#103	—	89	1	no	—
394	#103	—	89	1	no	—
395	#103	—	89	1	no	—
396	#103	—	89	1	no	—
397	#103	—	89	1	no	—
398	#103	—	89	1	no	—
399	#103	C₄×D₈₉	1	1	yes	characteristic
400	#103	C₄×D₈₉	1	1	yes	characteristic
401	C₂²⋊C₈	—	178	1	no	—
402	#97	—	2	1	no	—
403	#97	—	89	1	no	—
404	#97	—	89	1	no	—
405	#97	—	178	1	no	—
406	#97	—	178	1	no	—
407	#97	—	178	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	89	1	no	—
410	C₄×C₈	—	89	1	no	—
411	C₄×C₈	—	89	1	no	—
412	C₄×C₈	—	89	1	no	—
413	C₄×C₈	—	89	1	no	—
414	C₄×C₈	—	178	1	no	—
415	C₄×C₈	—	178	1	no	—
416	C₄×C₈	—	178	1	no	—
417	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
418	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
420	C₂×Q₈	—	89	1	no	—
421	C₂×Q₈	—	89	1	no	—
422	C₂×Q₈	—	178	1	no	—
423	C₂×Q₈	—	178	1	no	—
424	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
425	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
426	C₂²×C₄	—	89	1	no	—
427	C₂²×C₄	—	89	1	no	—
428	C₂²×C₄	—	89	1	no	—
429	Q₁₆	—	4	1	no	—
430	Q₁₆	—	356	1	no	—
431	Q₁₆	—	178	2	no	—
432	Q₁₆	—	178	2	no	—
433	M₁₆	—	89	4	no	—
434	M₁₆	—	178	2	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	89	1	no	—
439	C₂×C₈	—	89	1	no	—
440	C₂×C₈	—	89	1	no	—
441	C₂×C₈	—	89	1	no	—
442	C₂×C₈	—	356	1	no	—
443	C₂×C₈	—	356	2	no	—
444	C₂×C₈	—	356	2	no	—
445	C₂×C₈	—	178	2	no	—
446	C₂×C₈	—	178	1	no	—
447	C₂×C₈	—	178	1	no	—
448	C₂×C₈	—	178	1	no	—
449	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
450	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
451	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
452	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	89	1	no	—
456	C₄⋊C₄	—	89	1	no	—
457	C₄⋊C₄	—	178	1	no	—
458	C₄⋊C₄	—	178	1	no	—
459	C₄⋊C₄	—	178	1	no	—
460	C₄⋊C₄	—	178	1	no	—
461	C₄⋊C₄	—	178	1	no	—
462	C₄⋊C₄	—	178	1	no	—
463	C₄⋊C₄	—	178	1	no	—
464	C₄⋊C₄	—	178	1	no	—
465	C₄⋊C₄	—	178	1	no	—
466	C₄⋊C₄	—	178	1	no	—
467	C₄⋊C₄	—	178	1	no	—
468	C₄⋊C₄	—	178	1	no	—
469	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
470	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
471	C₂²⋊C₄	—	178	1	no	—
472	C₂²⋊C₄	—	178	1	no	—
473	C₂²⋊C₄	—	178	1	no	—
474	C₂²⋊C₄	—	178	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	89	1	no	—
478	C₄²	—	89	1	no	—
479	C₄²	—	89	1	no	—
480	C₄²	—	178	1	no	—
481	C₄²	—	178	1	no	—
482	C₄²	C₂³×D₈₉	1	1	yes	characteristic
483	C₂³	—	89	1	no	—
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	178	1	no	—
489	Q₈	—	178	1	no	—
490	Q₈	—	178	1	no	—
491	Q₈	—	178	1	no	—
492	Q₈	—	712	1	no	—
493	Q₈	—	712	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	89	1	no	—
499	C₂×C₄	—	89	2	no	—
500	C₂×C₄	—	89	2	no	—
501	C₂×C₄	—	89	1	no	—
502	C₂×C₄	—	89	1	no	—
503	C₂×C₄	—	356	1	no	—
504	C₂×C₄	—	178	1	no	—
505	C₂×C₄	—	178	1	no	—
506	C₂×C₄	—	178	1	no	—
507	C₂×C₄	—	178	1	no	—
508	C₂×C₄	—	178	1	no	—
509	C₂×C₄	—	178	1	no	—
510	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
511	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
512	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	89	2	no	—
520	C₈	—	89	2	no	—
521	C₈	—	356	1	no	—
522	C₈	—	356	1	no	—
523	C₈	—	356	1	no	—
524	C₈	—	178	1	no	—
525	C₈	—	178	1	no	—
526	C₈	Q₁₆×D₈₉	1	2	yes	—
527	C₂²	—	89	2	no	—
528	C₂²	—	178	1	no	—
529	C₂²	—	178	1	no	—
530	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	4	1	no	—
535	C₄	—	4	1	no	—
536	C₄	—	89	2	no	—
537	C₄	—	356	1	no	—
538	C₄	—	356	1	no	—
539	C₄	—	356	1	no	—
540	C₄	—	356	1	no	—
541	C₄	—	178	1	no	—
542	C₄	—	178	1	no	—
543	C₄	#131×D₈₉	1	1	yes	characteristic
544	C₄	#19152364	1	1	yes	characteristic
545	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
546	C₄	#135×D₈₉	1	1	yes	characteristic
547	C₂	—	178	2	no	—
548	C₂	#26028993	1	1	yes	characteristic
549	C₂	C₄×Q₁₆×D₈₉	1	1	yes	characteristic
550	C₂	#26029166	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	#18068
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. #26019147	C₂	semidirect
5. #26019146	C₂	semidirect
6. #26019104	C₂	semidirect
7. #26019103	C₂	semidirect
8. #26019101	C₂	semidirect
9. C₈×#13083564	C₂	semidirect
10. #26019056	C₂	semidirect
15. C₈₉×#1584	C₂	semidirect
155. #13083557	Q₁₆	semidirect
284. #1584	D₈₉	semidirect
291. C₈₉	#18068	semidirect

Maximal subgroups

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

subgroup	index
#26030835	2
#26029200	2
#26029194	2
#26019147	2
#26019146	2
#26019104	2
#26019103	2
#26019101	2
C₈×#13083564	2
#26019056	2
#335×D₈₉	2
#26018653	2
#26018531	2
C₈₉×#1584	2
#18068	89