Subgroups — #36523454

Order 22784.

756 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028882	C₂	1	1	yes	maximal, characteristic
2	#423×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019020	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019019	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019017	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019009	C₂	1	2	yes	maximal, complemented
8	#26019006	C₂	1	2	yes	maximal, complemented
9	#26019003	C₂	1	2	yes	maximal, complemented
10	#26019001	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1569	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×M₁₆×D₈₉	—	2	1	no	—
13	C₂×M₁₆×D₈₉	C₄	1	2	yes	—
14	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
15	#19151655	C₂²	1	1	yes	characteristic
16	#19151653	—	2	1	no	—
17	#19151650	C₂²	1	1	yes	characteristic
18	#19151650	C₂²	1	1	yes	characteristic
19	#19151648	—	2	1	no	—
20	#19151622	C₂²	1	1	yes	characteristic
21	#19151621	—	2	1	no	—
22	#19151620	—	2	1	no	—
23	#19151620	C₂²	1	2	yes	—
24	#19151620	C₂²	1	1	yes	characteristic
25	#19151620	C₂²	1	1	yes	characteristic
26	C₄⋊C₈×D₈₉	—	2	1	no	—
27	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
28	#19151560	—	2	1	no	—
29	C₄×#13083558	C₂²	1	1	yes	characteristic
30	#19151550	—	2	1	no	—
31	#19151550	C₄	1	1	yes	characteristic
32	#19151550	C₄	1	1	yes	characteristic
33	M₁₆×Dic₈₉	C₄	1	2	yes	—
34	C₄×#13083557	C₂²	1	2	yes	—
35	#97×D₈₉	C₄	1	1	yes	characteristic
36	#97×D₈₉	C₄	1	1	yes	characteristic
37	C₄×C₈×D₈₉	C₂²	1	2	yes	—
38	#19151351	C₂²	1	2	yes	complemented
39	#19151350	C₂²	1	2	yes	complemented
40	#19151350	C₂²	1	2	yes	complemented
41	#19151349	C₂²	1	2	yes	complemented
42	#19151348	C₂²	1	2	yes	complemented
43	#19151348	C₂²	1	2	yes	complemented
44	#432×C₈₉	C₂²	1	1	yes	characteristic
45	#423×C₈₉	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	#335×C₈₉	C₂²	1	2	yes	complemented
48	#334×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
51	C₂²×C₄×D₈₉	Q₈	1	1	yes	characteristic
52	C₂×#13083558	—	2	1	no	—
53	C₂×#13083558	C₂×C₄	1	2	yes	—
54	C₂×#13083557	—	2	2	no	—
55	C₂×#13083557	—	2	1	no	—
56	C₂×#13083557	—	2	1	no	—
57	C₂×#13083557	C₂×C₄	1	2	yes	—
58	C₂×#13083557	C₂×C₄	1	2	yes	—
59	M₁₆×D₈₉	—	2	8	no	—
60	M₁₆×D₈₉	—	4	4	no	—
61	C₂×C₈×D₈₉	—	2	2	no	—
62	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
64	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
66	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
67	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₄²×D₈₉	D₄	1	1	yes	characteristic
70	C₄²×D₈₉	D₄	1	1	yes	characteristic
71	C₄²×D₈₉	Q₈	1	1	yes	characteristic
72	C₄²×D₈₉	Q₈	1	1	yes	characteristic
73	C₄²×D₈₉	C₂³	1	1	yes	characteristic
74	C₄²×D₈₉	C₂³	1	1	yes	characteristic
75	C₄⋊#10623494	—	2	1	no	—
76	C₄⋊#10623494	C₂³	1	2	yes	—
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	C₄⋊#10623494	C₂³	1	1	yes	characteristic
79	#15667941	—	2	2	no	—
80	#15667941	—	2	2	no	—
81	#15667941	—	2	1	no	—
82	#15667941	—	2	1	no	—
83	C₂²⋊#10623494	—	2	1	no	—
84	#15667924	—	2	1	no	—
85	#15667924	—	2	1	no	—
86	#15667923	—	2	1	no	—
87	#15667923	C₂×C₄	1	1	yes	characteristic
88	#15667923	C₂×C₄	1	1	yes	characteristic
89	#15667922	C₂×C₄	1	2	yes	—
90	#15667922	C₂×C₄	1	2	yes	—
91	C₄×#10623494	C₂³	1	2	yes	—
92	C₈×Dic₈₉	—	2	1	no	—
93	C₈×Dic₈₉	—	2	1	no	—
94	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
95	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
96	C₂×M₁₆×C₈₉	—	2	1	no	—
97	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
98	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	—	2	1	no	—
100	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
101	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²⋊C₈×C₈₉	—	2	1	no	—
104	#97×C₈₉	—	2	1	no	—
105	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
106	#97×C₈₉	C₂×C₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	C₂³×D₈₉	C₄⋊C₄	1	1	yes	characteristic
109	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
110	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
111	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
112	C₂×C₄×D₈₉	—	2	4	no	—
113	C₂×C₄×D₈₉	—	2	2	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	C₂×C₄×D₈₉	—	4	2	no	—
116	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
119	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
122	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
127	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
128	#13083558	—	2	4	no	—
129	#13083558	—	4	2	no	—
130	#13083557	—	2	4	no	—
131	#13083557	—	4	4	no	—
132	#13083557	—	4	2	no	—
133	#13083557	—	4	2	no	—
134	#13083557	M₁₆	1	8	yes	complemented
135	C₂×#10623494	—	2	2	no	—
136	C₂×#10623494	—	2	1	no	—
137	C₂×#10623494	—	2	1	no	—
138	C₂×#10623494	C₂²×C₄	1	2	yes	—
139	C₂×#10623494	C₂²×C₄	1	2	yes	—
140	C₈×D₈₉	—	2	4	no	—
141	C₈×D₈₉	—	2	4	no	—
142	C₈×D₈₉	—	4	4	no	—
143	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
144	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
145	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
146	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
147	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
148	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
149	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
154	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
158	M₁₆×C₈₉	—	2	4	no	—
159	M₁₆×C₈₉	—	4	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
165	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
168	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×D₈₉	—	2	2	no	—
171	C₂²×D₈₉	—	2	2	no	—
172	C₂²×D₈₉	—	4	1	no	—
173	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
185	C₂×Dic₈₉	—	2	2	no	—
186	C₂×Dic₈₉	—	2	2	no	—
187	C₂×Dic₈₉	—	2	2	no	—
188	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₄×D₈₉	—	2	2	no	—
195	C₄×D₈₉	—	2	2	no	—
196	C₄×D₈₉	—	2	2	no	—
197	C₄×D₈₉	—	2	1	no	—
198	C₄×D₈₉	—	2	1	no	—
199	C₄×D₈₉	—	2	2	no	—
200	C₄×D₈₉	—	2	2	no	—
201	C₄×D₈₉	—	2	2	no	—
202	C₄×D₈₉	—	2	2	no	—
203	C₄×D₈₉	—	4	1	no	—
204	C₄×D₈₉	—	4	1	no	—
205	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
206	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
207	C₄×D₈₉	#137	1	2	yes	—
208	C₈×C₈₉	—	2	2	no	—
209	C₈×C₈₉	—	4	2	no	—
210	C₈×C₈₉	—	4	1	no	—
211	C₈×C₈₉	—	4	1	no	—
212	C₈×C₈₉	C₂×M₁₆	1	4	yes	complemented
213	#10623494	—	2	2	no	—
214	#10623494	—	4	2	no	—
215	#10623494	—	4	1	no	—
216	#10623494	—	4	1	no	—
217	#10623494	C₂×M₁₆	1	4	yes	complemented
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
222	C₂×D₈₉	—	2	1	no	—
223	C₂×D₈₉	—	2	1	no	—
224	C₂×D₈₉	—	2	1	no	—
225	C₂×D₈₉	—	2	1	no	—
226	C₂×D₈₉	—	4	4	no	—
227	C₂×D₈₉	#423	1	2	yes	—
228	C₂×D₈₉	#428	1	2	yes	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
234	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
236	Dic₈₉	—	2	1	no	—
237	Dic₈₉	—	2	1	no	—
238	Dic₈₉	—	2	1	no	—
239	Dic₈₉	#423	1	2	yes	—
240	Dic₈₉	#428	1	2	yes	—
241	Dic₈₉	#430	1	2	yes	—
242	#17796	—	89	1	no	maximal, Sylow
243	C₂×C₈₉	—	4	1	no	—
244	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
245	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
246	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
247	D₈₉	—	2	2	no	—
248	D₈₉	—	2	2	no	—
249	#2920	—	89	1	no	—
250	C₂×#423	—	89	1	no	—
251	C₂×C₄×M₁₆	—	89	1	no	—
252	#1569	—	89	1	no	—
253	#1569	—	89	1	no	—
254	#1569	—	89	1	no	—
255	#1569	D₈₉	1	1	yes	characteristic, complemented
256	#1567	—	89	2	no	—
257	#1566	—	89	2	no	—
258	#1565	—	89	2	no	—
259	#1565	—	89	2	no	—
260	C₈₉	#17796	1	1	yes	characteristic, complemented, Sylow
261	C₂²×M₁₆	—	89	2	no	—
262	C₂²×M₁₆	—	178	1	no	—
263	C₂²×C₄²	—	89	1	no	—
264	#432	—	89	1	no	—
265	#432	—	178	1	no	—
266	#432	C₂×D₈₉	1	1	yes	characteristic
267	#431	—	89	1	no	—
268	#431	—	89	1	no	—
269	#431	—	178	1	no	—
270	#423	—	89	1	no	—
271	#423	—	89	1	no	—
272	#423	—	89	2	no	—
273	#423	—	89	1	no	—
274	#423	—	178	1	no	—
275	#423	—	178	1	no	—
276	#423	C₂×D₈₉	1	1	yes	characteristic
277	C₂×C₄⋊C₈	—	89	2	no	—
278	C₂×C₄⋊C₈	—	178	1	no	—
279	#407	—	178	1	no	—
280	C₄×M₁₆	—	89	2	no	—
281	C₄×M₁₆	—	89	1	no	—
282	C₄×M₁₆	—	89	1	no	—
283	C₄×M₁₆	—	89	1	no	—
284	C₄×M₁₆	—	89	2	no	—
285	C₄×M₁₆	—	178	1	no	—
286	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
287	C₂×#97	—	89	1	no	—
288	C₂×#97	—	89	1	no	—
289	C₂×C₄×C₈	—	89	2	no	—
290	#335	—	89	2	no	—
291	#335	—	89	2	no	—
292	#335	—	89	2	no	—
293	#335	C₂×D₈₉	1	2	yes	complemented
294	#334	—	89	2	no	—
295	#334	—	89	2	no	—
296	#334	—	89	2	no	—
297	#334	C₂×D₈₉	1	2	yes	complemented
298	C₂³×C₄	—	89	1	no	—
299	C₂³×C₄	—	89	1	no	—
300	C₂³×C₄	—	89	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	89	2	no	—
303	C₂×M₁₆	—	89	2	no	—
304	C₂×M₁₆	—	89	2	no	—
305	C₂×M₁₆	—	356	4	no	—
306	C₂×M₁₆	—	178	2	no	—
307	C₂×M₁₆	—	178	1	no	—
308	C₂×M₁₆	—	178	1	no	—
309	C₂×M₁₆	—	178	8	no	—
310	C₂×M₁₆	—	178	1	no	—
311	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
312	C₂²×C₈	—	89	2	no	—
313	C₂²×C₈	—	89	2	no	—
314	C₂²×C₈	—	178	2	no	—
315	C₂×C₄²	—	89	1	no	—
316	C₂×C₄²	—	89	1	no	—
317	C₂×C₄²	—	89	1	no	—
318	C₂×C₄²	—	89	1	no	—
319	C₂×C₄²	—	89	1	no	—
320	C₂×C₄²	—	89	1	no	—
321	C₂×C₄²	—	89	1	no	—
322	C₂×C₄²	—	89	1	no	—
323	C₂×C₄²	—	89	1	no	—
324	C₂×C₄²	—	89	1	no	—
325	C₂×C₄²	—	89	1	no	—
326	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	—	89	1	no	—
329	C₄⋊C₈	—	89	2	no	—
330	C₄⋊C₈	—	89	1	no	—
331	C₄⋊C₈	—	178	2	no	—
332	C₄⋊C₈	—	178	2	no	—
333	C₄⋊C₈	—	178	1	no	—
334	C₄⋊C₈	—	178	1	no	—
335	C₄⋊C₈	—	178	1	no	—
336	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
337	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
338	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
339	C₂²⋊C₈	—	2	1	no	—
340	C₂²⋊C₈	—	178	1	no	—
341	C₂²⋊C₈	—	178	1	no	—
342	C₂²⋊C₈	—	178	1	no	—
343	#97	—	2	1	no	—
344	#97	—	89	2	no	—
345	#97	—	89	2	no	—
346	#97	—	89	1	no	—
347	#97	—	89	1	no	—
348	#97	—	178	1	no	—
349	#97	C₄×D₈₉	1	1	yes	characteristic
350	#97	C₄×D₈₉	1	1	yes	characteristic
351	C₄×C₈	—	89	2	no	—
352	C₄×C₈	—	89	2	no	—
353	C₄×C₈	—	89	2	no	—
354	C₄×C₈	—	178	1	no	—
355	C₄×C₈	—	178	1	no	—
356	C₄×C₈	C₂²×D₈₉	1	2	yes	—
357	C₂⁴	—	89	1	no	—
358	C₂²×C₄	—	89	1	no	—
359	C₂²×C₄	—	89	1	no	—
360	C₂²×C₄	—	89	1	no	—
361	C₂²×C₄	—	89	1	no	—
362	C₂²×C₄	—	89	1	no	—
363	C₂²×C₄	—	89	1	no	—
364	C₂²×C₄	—	89	1	no	—
365	C₂²×C₄	—	89	1	no	—
366	C₂²×C₄	—	89	1	no	—
367	C₂²×C₄	—	89	1	no	—
368	C₂²×C₄	—	89	1	no	—
369	C₂²×C₄	—	89	1	no	—
370	C₂²×C₄	—	89	1	no	—
371	C₂²×C₄	—	89	1	no	—
372	C₂²×C₄	—	89	1	no	—
373	C₂²×C₄	—	356	2	no	—
374	C₂²×C₄	—	178	2	no	—
375	C₂²×C₄	—	178	4	no	—
376	C₂²×C₄	—	178	2	no	—
377	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
378	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
379	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
380	M₁₆	—	2	4	no	—
381	M₁₆	—	4	2	no	—
382	M₁₆	—	89	8	no	—
383	M₁₆	—	356	4	no	—
384	M₁₆	—	356	2	no	—
385	M₁₆	—	356	2	no	—
386	M₁₆	—	356	2	no	—
387	M₁₆	—	178	4	no	—
388	M₁₆	—	178	4	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	89	2	no	—
393	C₂×C₈	—	89	2	no	—
394	C₂×C₈	—	356	4	no	—
395	C₂×C₈	—	178	4	no	—
396	C₂×C₈	—	178	1	no	—
397	C₂×C₈	—	178	1	no	—
398	C₂×C₈	—	178	2	no	—
399	C₂×C₈	—	178	4	no	—
400	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
401	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
402	C₄²	—	89	1	no	—
403	C₄²	—	89	1	no	—
404	C₄²	—	89	1	no	—
405	C₄²	—	89	1	no	—
406	C₄²	—	89	1	no	—
407	C₄²	—	89	1	no	—
408	C₄²	—	89	1	no	—
409	C₄²	—	89	1	no	—
410	C₄²	—	89	1	no	—
411	C₄²	—	89	1	no	—
412	C₄²	—	89	1	no	—
413	C₄²	—	89	1	no	—
414	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
415	C₄²	D₄×D₈₉	1	1	yes	characteristic
416	C₄²	Q₈×D₈₉	1	1	yes	characteristic
417	C₄²	C₂³×D₈₉	1	1	yes	characteristic
418	C₂³	—	89	1	no	—
419	C₂³	—	89	1	no	—
420	C₂³	—	356	1	no	—
421	C₂³	—	178	2	no	—
422	C₂³	—	178	2	no	—
423	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	89	1	no	—
429	C₂×C₄	—	89	1	no	—
430	C₂×C₄	—	89	1	no	—
431	C₂×C₄	—	89	2	no	—
432	C₂×C₄	—	89	4	no	—
433	C₂×C₄	—	89	2	no	—
434	C₂×C₄	—	89	1	no	—
435	C₂×C₄	—	89	1	no	—
436	C₂×C₄	—	89	1	no	—
437	C₂×C₄	—	356	1	no	—
438	C₂×C₄	—	356	1	no	—
439	C₂×C₄	—	178	2	no	—
440	C₂×C₄	—	178	2	no	—
441	C₂×C₄	—	178	2	no	—
442	C₂×C₄	—	178	2	no	—
443	C₂×C₄	—	178	2	no	—
444	C₂×C₄	—	178	2	no	—
445	C₂×C₄	—	178	2	no	—
446	C₂×C₄	—	178	2	no	—
447	C₂×C₄	—	178	2	no	—
448	C₂×C₄	—	178	1	no	—
449	C₂×C₄	—	178	2	no	—
450	C₂×C₄	—	178	1	no	—
451	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₈	—	4	1	no	—
461	C₈	—	89	4	no	—
462	C₈	—	356	1	no	—
463	C₈	—	356	2	no	—
464	C₈	—	356	1	no	—
465	C₈	—	178	2	no	—
466	C₈	M₁₆×D₈₉	1	4	yes	complemented
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	89	2	no	—
471	C₂²	—	89	2	no	—
472	C₂²	—	356	4	no	—
473	C₂²	—	178	1	no	—
474	C₂²	—	178	1	no	—
475	C₂²	—	178	1	no	—
476	C₂²	—	178	1	no	—
477	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	89	2	no	—
483	C₄	—	89	2	no	—
484	C₄	—	89	2	no	—
485	C₄	—	178	1	no	—
486	C₄	—	178	1	no	—
487	C₄	—	178	1	no	—
488	C₄	C₂×M₁₆×D₈₉	1	2	yes	—
489	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
490	C₄	#137×D₈₉	1	1	yes	characteristic
491	C₂	—	4	1	no	—
492	C₂	—	178	2	no	—
493	C₂	—	178	2	no	—
494	C₂	#423×D₈₉	1	1	yes	characteristic
495	C₂	#428×D₈₉	1	1	yes	characteristic
496	C₂	#430×D₈₉	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×#1569	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1569	D₈₉
hypocenter	C₈₉	#17796
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1569

Complements

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

N	H ≅ G/N	type
4. #26019020	C₂	semidirect
5. #26019019	C₂	semidirect
6. #26019017	C₂	semidirect
7. #26019009	C₂	semidirect
8. #26019006	C₂	semidirect
9. #26019003	C₂	semidirect
10. #26019001	C₂	semidirect
11. C₈₉×#1569	C₂	semidirect
38. #19151351	C₂²	semidirect
39. #19151350	C₂²	semidirect
40. #19151350	C₂²	semidirect
41. #19151349	C₂²	semidirect
42. #19151348	C₂²	semidirect
43. #19151348	C₂²	semidirect
47. #335×C₈₉	C₂²	semidirect
48. #334×C₈₉	C₂²	semidirect
134. #13083557	M₁₆	semidirect
212. C₈×C₈₉	C₂×M₁₆	semidirect
217. #10623494	C₂×M₁₆	semidirect
255. #1569	D₈₉	semidirect
260. C₈₉	#17796	semidirect
293. #335	C₂×D₈₉	semidirect
297. #334	C₂×D₈₉	semidirect
466. C₈	M₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028882	2
#423×D₈₉	2
C₄×M₁₆×D₈₉	2
#26019020	2
#26019019	2
#26019017	2
#26019009	2
#26019006	2
#26019003	2
#26019001	2
C₈₉×#1569	2
#17796	89