Subgroups — #36523453

Order 22784.

756 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028880	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151620	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019018	C₂	1	2	yes	maximal, complemented
5	#26019016	C₂	1	2	yes	maximal, complemented
6	#26019009	C₂	1	2	yes	maximal, complemented
7	#26019006	C₂	1	2	yes	maximal, complemented
8	#26019005	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#13083557	—	2	1	no	—
13	C₂×M₁₆×D₈₉	C₄	1	1	yes	characteristic
14	C₂×M₁₆×D₈₉	C₄	1	1	yes	characteristic
15	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
16	#19151654	C₂²	1	1	yes	characteristic
17	#19151654	C₂²	1	1	yes	characteristic
18	#19151652	—	2	1	no	—
19	#19151651	C₂²	1	1	yes	characteristic
20	#19151649	—	2	1	no	—
21	#19151620	—	2	1	no	—
22	#19151620	—	2	1	no	—
23	#19151620	C₂²	1	2	yes	—
24	#19151620	C₂²	1	2	yes	—
25	#19151620	C₂²	1	1	yes	characteristic
26	#19151620	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
28	C₂×#15667941	—	2	1	no	—
29	#19151560	—	2	1	no	—
30	C₄×#13083558	C₂²	1	1	yes	characteristic
31	#19151550	C₄	1	2	yes	—
32	M₁₆×Dic₈₉	C₄	1	1	yes	characteristic
33	M₁₆×Dic₈₉	C₄	1	1	yes	characteristic
34	C₄×#13083557	—	2	1	no	—
35	C₄×#13083557	C₂²	1	2	yes	—
36	#97×D₈₉	C₄	1	2	yes	—
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	#431×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×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	C₂×C₄	1	1	yes	characteristic
53	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
54	C₂×#13083557	—	2	2	no	—
55	C₂×#13083557	—	2	2	no	—
56	C₂×#13083557	—	2	1	no	—
57	C₂×#13083557	—	2	1	no	—
58	C₂×#13083557	—	4	4	no	—
59	C₂×#13083557	C₂×C₄	1	2	yes	—
60	C₂×#13083557	C₂×C₄	1	2	yes	—
61	M₁₆×D₈₉	—	2	4	no	—
62	M₁₆×D₈₉	—	2	4	no	—
63	C₂²×#10623494	—	2	1	no	—
64	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
65	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
68	C₂×C₄×Dic₈₉	Q₈	1	1	yes	characteristic
69	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₈₉	D₄	1	1	yes	characteristic
72	C₄²×D₈₉	D₄	1	1	yes	characteristic
73	C₄²×D₈₉	Q₈	1	1	yes	characteristic
74	C₄²×D₈₉	Q₈	1	1	yes	characteristic
75	C₄²×D₈₉	C₂³	1	1	yes	characteristic
76	C₄²×D₈₉	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	—	2	1	no	—
78	C₄⋊#10623494	C₂³	1	2	yes	—
79	C₄⋊#10623494	C₂³	1	1	yes	characteristic
80	C₄⋊#10623494	C₂³	1	1	yes	characteristic
81	#15667941	—	2	2	no	—
82	#15667941	—	2	2	no	—
83	#15667941	—	2	1	no	—
84	#15667941	—	2	1	no	—
85	C₂²⋊#10623494	—	2	1	no	—
86	#15667924	—	2	1	no	—
87	#15667924	—	2	1	no	—
88	#15667923	C₂×C₄	1	2	yes	—
89	#15667922	—	2	1	no	—
90	#15667922	—	2	1	no	—
91	#15667922	C₂×C₄	1	2	yes	—
92	#15667922	C₂×C₄	1	2	yes	—
93	C₄×#10623494	—	2	1	no	—
94	C₄×#10623494	C₂³	1	2	yes	—
95	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
96	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
97	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₂²×C₈×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	—	2	1	no	—
102	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
103	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²⋊C₈×C₈₉	—	2	1	no	—
106	#97×C₈₉	C₂×C₄	1	2	yes	—
107	C₄×C₈×C₈₉	—	2	1	no	—
108	C₄×C₈×C₈₉	C₂³	1	2	yes	—
109	C₂³×D₈₉	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	C₂²×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
113	C₂×C₄×D₈₉	—	2	2	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	C₂×C₄×D₈₉	—	2	2	no	—
116	C₂×C₄×D₈₉	—	2	2	no	—
117	C₂×C₄×D₈₉	—	4	2	no	—
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	C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄×D₈₉	C₄⋊C₄	1	1	yes	characteristic
124	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
129	C₂×C₄×D₈₉	C₂×Q₈	1	1	yes	characteristic
130	#13083558	—	2	2	no	—
131	#13083558	M₁₆	1	4	yes	complemented
132	#13083557	—	2	4	no	—
133	#13083557	—	2	4	no	—
134	#13083557	—	4	4	no	—
135	#13083557	—	4	2	no	—
136	#13083557	—	4	4	no	—
137	#13083557	—	4	2	no	—
138	C₂×#10623494	—	2	2	no	—
139	C₂×#10623494	—	2	1	no	—
140	C₂×#10623494	—	2	1	no	—
141	C₂×#10623494	—	4	2	no	—
142	C₂×#10623494	C₂²×C₄	1	2	yes	—
143	C₂×#10623494	C₂²×C₄	1	2	yes	—
144	C₈×D₈₉	—	2	4	no	—
145	C₈×D₈₉	—	2	4	no	—
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	C₄⋊C₄	1	1	yes	characteristic
150	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
151	C₄×Dic₈₉	C₄⋊C₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
154	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
155	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
157	C₄×Dic₈₉	C₂×Q₈	1	1	yes	characteristic
158	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
161	M₁₆×C₈₉	—	2	2	no	—
162	M₁₆×C₈₉	M₁₆	1	4	yes	complemented
163	C₂×C₈×C₈₉	—	2	2	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	—	2	1	no	—
166	C₂×C₈×C₈₉	—	4	2	no	—
167	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
169	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₄²×C₈₉	C₂×Q₈	1	1	yes	characteristic
172	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂²×D₈₉	—	2	2	no	—
175	C₂²×D₈₉	—	2	2	no	—
176	C₂²×D₈₉	—	4	1	no	—
177	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₂²×D₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	—	4	1	no	—
182	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
186	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
190	C₂×Dic₈₉	—	2	2	no	—
191	C₂×Dic₈₉	—	2	2	no	—
192	C₂×Dic₈₉	—	2	2	no	—
193	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
194	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
197	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₂×Dic₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₄×D₈₉	—	2	2	no	—
200	C₄×D₈₉	—	2	1	no	—
201	C₄×D₈₉	—	2	1	no	—
202	C₄×D₈₉	—	2	1	no	—
203	C₄×D₈₉	—	2	1	no	—
204	C₄×D₈₉	—	2	1	no	—
205	C₄×D₈₉	—	2	1	no	—
206	C₄×D₈₉	—	2	2	no	—
207	C₄×D₈₉	—	2	2	no	—
208	C₄×D₈₉	—	2	2	no	—
209	C₄×D₈₉	—	2	2	no	—
210	C₄×D₈₉	—	2	2	no	—
211	C₄×D₈₉	—	4	1	no	—
212	C₄×D₈₉	—	4	1	no	—
213	C₄×D₈₉	AGL(1,ℤ/8)	1	2	yes	—
214	C₄×D₈₉	#137	1	2	yes	—
215	C₈×C₈₉	—	2	2	no	—
216	C₈×C₈₉	—	4	2	no	—
217	C₈×C₈₉	—	4	1	no	—
218	C₈×C₈₉	—	4	1	no	—
219	C₈×C₈₉	C₂×M₁₆	1	4	yes	complemented
220	#10623494	—	2	2	no	—
221	#10623494	—	4	2	no	—
222	#10623494	—	4	1	no	—
223	#10623494	—	4	1	no	—
224	#10623494	C₂×M₁₆	1	4	yes	complemented
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	#423	1	2	yes	—
228	C₂²×C₈₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
229	C₂×D₈₉	—	2	1	no	—
230	C₂×D₈₉	—	2	1	no	—
231	C₂×D₈₉	—	2	1	no	—
232	C₂×D₈₉	—	2	1	no	—
233	C₂×D₈₉	—	2	1	no	—
234	C₂×D₈₉	—	4	4	no	—
235	C₂×D₈₉	#428	1	2	yes	—
236	C₄×C₈₉	—	2	1	no	—
237	C₄×C₈₉	—	2	1	no	—
238	C₄×C₈₉	—	2	1	no	—
239	C₄×C₈₉	#423	1	2	yes	—
240	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
241	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
242	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
243	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
244	Dic₈₉	—	2	1	no	—
245	Dic₈₉	—	2	1	no	—
246	Dic₈₉	—	2	1	no	—
247	Dic₈₉	—	2	1	no	—
248	Dic₈₉	#428	1	2	yes	—
249	Dic₈₉	#430	1	2	yes	—
250	#17796	—	89	1	no	maximal, Sylow
251	C₂×C₈₉	—	2	2	no	—
252	C₂×C₈₉	C₂×#423	1	1	yes	characteristic
253	C₂×C₈₉	C₂×#428	1	1	yes	characteristic
254	C₂×C₈₉	C₂×#430	1	1	yes	characteristic
255	D₈₉	—	2	2	no	—
256	D₈₉	—	4	1	no	—
257	#2920	—	89	1	no	—
258	C₂×#423	—	89	1	no	—
259	C₂×C₄×M₁₆	—	89	1	no	—
260	#1569	—	89	2	no	—
261	#1569	—	89	2	no	—
262	#1567	—	89	2	no	—
263	#1566	—	89	2	no	—
264	#1565	—	89	1	no	—
265	#1565	—	89	1	no	—
266	#1565	—	89	1	no	—
267	#1565	D₈₉	1	1	yes	characteristic, complemented
268	C₈₉	#17796	1	1	yes	characteristic, complemented, Sylow
269	C₂²×M₁₆	—	89	1	no	—
270	C₂²×M₁₆	—	89	1	no	—
271	C₂²×M₁₆	—	178	1	no	—
272	C₂²×C₄²	—	89	1	no	—
273	#432	—	89	1	no	—
274	#432	—	89	1	no	—
275	#432	—	178	1	no	—
276	#431	—	89	1	no	—
277	#431	—	178	1	no	—
278	#431	C₂×D₈₉	1	1	yes	characteristic
279	#423	—	89	1	no	—
280	#423	—	89	2	no	—
281	#423	—	89	1	no	—
282	#423	—	89	2	no	—
283	#423	—	178	1	no	—
284	#423	—	178	1	no	—
285	C₂×C₄⋊C₈	—	89	1	no	—
286	C₂×C₄⋊C₈	—	178	1	no	—
287	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
288	#407	—	178	1	no	—
289	C₄×M₁₆	—	89	1	no	—
290	C₄×M₁₆	—	89	1	no	—
291	C₄×M₁₆	—	89	1	no	—
292	C₄×M₁₆	—	89	2	no	—
293	C₄×M₁₆	—	89	2	no	—
294	C₄×M₁₆	—	178	1	no	—
295	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
296	C₂×#97	—	89	2	no	—
297	C₂×C₄×C₈	—	89	2	no	—
298	#335	—	89	2	no	—
299	#335	—	89	2	no	—
300	#335	—	89	2	no	—
301	#335	C₂×D₈₉	1	2	yes	complemented
302	#334	—	89	2	no	—
303	#334	—	89	2	no	—
304	#334	—	89	2	no	—
305	#334	C₂×D₈₉	1	2	yes	complemented
306	C₂³×C₄	—	89	1	no	—
307	C₂³×C₄	—	89	1	no	—
308	C₂³×C₄	—	89	1	no	—
309	C₂×M₁₆	—	89	1	no	—
310	C₂×M₁₆	—	89	1	no	—
311	C₂×M₁₆	—	89	2	no	—
312	C₂×M₁₆	—	89	2	no	—
313	C₂×M₁₆	—	356	4	no	—
314	C₂×M₁₆	—	178	2	no	—
315	C₂×M₁₆	—	178	2	no	—
316	C₂×M₁₆	—	178	1	no	—
317	C₂×M₁₆	—	178	1	no	—
318	C₂×M₁₆	—	178	4	no	—
319	C₂×M₁₆	—	178	4	no	—
320	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
321	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	89	2	no	—
324	C₂²×C₈	—	89	2	no	—
325	C₂²×C₈	—	178	1	no	—
326	C₂×C₄²	—	89	1	no	—
327	C₂×C₄²	—	89	1	no	—
328	C₂×C₄²	—	89	1	no	—
329	C₂×C₄²	—	89	1	no	—
330	C₂×C₄²	—	89	1	no	—
331	C₂×C₄²	—	89	1	no	—
332	C₂×C₄²	—	89	1	no	—
333	C₂×C₄²	—	89	1	no	—
334	C₂×C₄²	—	89	1	no	—
335	C₂×C₄²	—	89	1	no	—
336	C₂×C₄²	—	89	1	no	—
337	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	89	1	no	—
340	C₄⋊C₈	—	89	2	no	—
341	C₄⋊C₈	—	89	1	no	—
342	C₄⋊C₈	—	178	2	no	—
343	C₄⋊C₈	—	178	2	no	—
344	C₄⋊C₈	—	178	1	no	—
345	C₄⋊C₈	—	178	1	no	—
346	C₄⋊C₈	—	178	1	no	—
347	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
348	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
349	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
350	C₂²⋊C₈	—	2	1	no	—
351	C₂²⋊C₈	—	178	1	no	—
352	C₂²⋊C₈	—	178	1	no	—
353	C₂²⋊C₈	—	178	1	no	—
354	#97	—	89	2	no	—
355	#97	—	89	2	no	—
356	#97	—	89	2	no	—
357	#97	—	178	1	no	—
358	#97	—	178	1	no	—
359	#97	C₄×D₈₉	1	2	yes	—
360	C₄×C₈	—	2	1	no	—
361	C₄×C₈	—	89	2	no	—
362	C₄×C₈	—	89	2	no	—
363	C₄×C₈	—	89	2	no	—
364	C₄×C₈	—	178	1	no	—
365	C₄×C₈	C₂²×D₈₉	1	2	yes	—
366	C₂⁴	—	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	—	89	1	no	—
374	C₂²×C₄	—	89	1	no	—
375	C₂²×C₄	—	89	1	no	—
376	C₂²×C₄	—	89	1	no	—
377	C₂²×C₄	—	89	1	no	—
378	C₂²×C₄	—	89	1	no	—
379	C₂²×C₄	—	89	1	no	—
380	C₂²×C₄	—	89	1	no	—
381	C₂²×C₄	—	89	1	no	—
382	C₂²×C₄	—	356	2	no	—
383	C₂²×C₄	—	178	2	no	—
384	C₂²×C₄	—	178	2	no	—
385	C₂²×C₄	—	178	2	no	—
386	C₂²×C₄	—	178	2	no	—
387	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
388	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
389	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
390	M₁₆	—	2	2	no	—
391	M₁₆	—	89	4	no	—
392	M₁₆	—	356	4	no	—
393	M₁₆	—	356	2	no	—
394	M₁₆	—	356	2	no	—
395	M₁₆	—	356	4	no	—
396	M₁₆	—	178	4	no	—
397	M₁₆	—	178	2	no	—
398	M₁₆	—	178	4	no	—
399	M₁₆	#13083557	1	4	yes	complemented
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	4	2	no	—
404	C₂×C₈	—	89	2	no	—
405	C₂×C₈	—	89	2	no	—
406	C₂×C₈	—	356	2	no	—
407	C₂×C₈	—	178	4	no	—
408	C₂×C₈	—	178	1	no	—
409	C₂×C₈	—	178	1	no	—
410	C₂×C₈	—	178	2	no	—
411	C₂×C₈	—	178	4	no	—
412	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
413	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
414	C₄²	—	89	1	no	—
415	C₄²	—	89	1	no	—
416	C₄²	—	89	1	no	—
417	C₄²	—	89	1	no	—
418	C₄²	—	89	1	no	—
419	C₄²	—	89	1	no	—
420	C₄²	—	89	1	no	—
421	C₄²	—	89	1	no	—
422	C₄²	—	89	1	no	—
423	C₄²	—	89	1	no	—
424	C₄²	—	89	1	no	—
425	C₄²	—	89	1	no	—
426	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
427	C₄²	D₄×D₈₉	1	1	yes	characteristic
428	C₄²	Q₈×D₈₉	1	1	yes	characteristic
429	C₄²	C₂³×D₈₉	1	1	yes	characteristic
430	C₂³	—	89	1	no	—
431	C₂³	—	89	1	no	—
432	C₂³	—	356	1	no	—
433	C₂³	—	178	2	no	—
434	C₂³	—	178	2	no	—
435	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	89	1	no	—
440	C₂×C₄	—	89	1	no	—
441	C₂×C₄	—	89	2	no	—
442	C₂×C₄	—	89	2	no	—
443	C₂×C₄	—	89	1	no	—
444	C₂×C₄	—	89	1	no	—
445	C₂×C₄	—	89	1	no	—
446	C₂×C₄	—	89	1	no	—
447	C₂×C₄	—	356	1	no	—
448	C₂×C₄	—	356	1	no	—
449	C₂×C₄	—	178	2	no	—
450	C₂×C₄	—	178	2	no	—
451	C₂×C₄	—	178	2	no	—
452	C₂×C₄	—	178	2	no	—
453	C₂×C₄	—	178	2	no	—
454	C₂×C₄	—	178	2	no	—
455	C₂×C₄	—	178	2	no	—
456	C₂×C₄	—	178	2	no	—
457	C₂×C₄	—	178	2	no	—
458	C₂×C₄	—	178	1	no	—
459	C₂×C₄	—	178	1	no	—
460	C₂×C₄	—	178	1	no	—
461	C₂×C₄	—	178	1	no	—
462	C₂×C₄	—	178	1	no	—
463	C₂×C₄	—	178	1	no	—
464	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
465	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
466	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
467	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
468	C₂×C₄	C₂×#13083557	1	2	yes	—
469	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
471	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
472	C₈	—	2	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	2	no	—
475	C₈	—	4	1	no	—
476	C₈	—	89	4	no	—
477	C₈	—	356	1	no	—
478	C₈	—	356	2	no	—
479	C₈	—	356	1	no	—
480	C₈	—	178	2	no	—
481	C₈	C₂×#13083557	1	4	yes	complemented
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	89	2	no	—
485	C₂²	—	356	4	no	—
486	C₂²	—	178	1	no	—
487	C₂²	—	178	1	no	—
488	C₂²	—	178	1	no	—
489	C₂²	—	178	1	no	—
490	C₂²	—	178	1	no	—
491	C₂²	#19151620	1	2	yes	—
492	C₂²	C₂×C₄⋊C₄×D₈₉	1	1	yes	characteristic
493	C₄	—	2	1	no	—
494	C₄	—	2	1	no	—
495	C₄	—	2	1	no	—
496	C₄	—	89	2	no	—
497	C₄	—	89	2	no	—
498	C₄	—	178	1	no	—
499	C₄	—	178	1	no	—
500	C₄	—	178	1	no	—
501	C₄	—	178	1	no	—
502	C₄	#19151620	1	2	yes	—
503	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
504	C₄	C₂²×#13083557	1	1	yes	characteristic
505	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
506	C₄	#137×D₈₉	1	1	yes	characteristic
507	C₂	—	2	2	no	—
508	C₂	—	356	1	no	—
509	C₂	—	178	2	no	—
510	C₂	C₂×#19151620	1	1	yes	characteristic
511	C₂	#428×D₈₉	1	1	yes	characteristic
512	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×#1565	C₂
socle	C₂²×C₈₉	C₂²×C₄⋊C₄
prime radical	C₂³×D₈₉	C₄⋊C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1565	D₈₉
hypocenter	C₈₉	#17796
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #26019018	C₂	semidirect
5. #26019016	C₂	semidirect
6. #26019009	C₂	semidirect
7. #26019006	C₂	semidirect
8. #26019005	C₂	semidirect
9. #26019004	C₂	semidirect
10. #26019002	C₂	semidirect
11. C₈₉×#1565	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
131. #13083558	M₁₆	semidirect
162. M₁₆×C₈₉	M₁₆	semidirect
219. C₈×C₈₉	C₂×M₁₆	semidirect
224. #10623494	C₂×M₁₆	semidirect
267. #1565	D₈₉	semidirect
268. C₈₉	#17796	semidirect
301. #335	C₂×D₈₉	semidirect
305. #334	C₂×D₈₉	semidirect
399. M₁₆	#13083557	semidirect
481. C₈	C₂×#13083557	semidirect

Maximal subgroups

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

subgroup	index
#26028880	2
C₂×#19151620	2
C₄×M₁₆×D₈₉	2
#26019018	2
#26019016	2
#26019009	2
#26019006	2
#26019005	2
#26019004	2
#26019002	2
C₈₉×#1565	2
#17796	89