Subgroups — #36707899

Order 22784.

668 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#509×D₈₉	C₂	1	1	yes	maximal, characteristic
2	#26029166	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029101	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022153	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022152	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022151	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022150	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022149	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022148	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022147	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022023	C₂	1	1	yes	maximal, characteristic, complemented
12	#361×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#26021986	C₂	1	1	yes	maximal, characteristic, complemented
14	#26021855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×AGL(1,ℤ/16)	C₂	1	1	yes	maximal, characteristic, complemented
16	#135×D₈₉	C₂²	1	1	yes	characteristic
17	C₂×D₈×D₈₉	C₂²	1	1	yes	characteristic
18	#19152363	—	2	1	no	—
19	#19152070	—	2	1	no	—
20	#19152036	C₂²	1	1	yes	characteristic
21	#19152035	C₄	1	2	yes	complemented
22	#19152034	C₂²	1	1	yes	characteristic
23	#19152033	C₂²	1	1	yes	characteristic
24	#19152032	C₄	1	2	yes	complemented
25	SD₃₂×D₈₉	C₄	1	2	yes	complemented
26	D₁₆×D₈₉	C₄	1	2	yes	complemented
27	M₃₂×D₈₉	C₂²	1	1	yes	characteristic
28	M₃₂×D₈₉	C₂²	1	1	yes	characteristic
29	#19151721	C₂²	1	1	yes	characteristic, complemented
30	#19151720	C₂²	1	1	yes	characteristic, complemented
31	#19151719	C₂²	1	1	yes	characteristic, complemented
32	#19151713	—	2	1	no	—
33	#19151712	—	2	1	no	—
34	#19151711	C₂²	1	1	yes	characteristic, complemented
35	#19151710	C₂²	1	1	yes	characteristic, complemented
36	#19151709	C₂²	1	1	yes	characteristic, complemented
37	C₄×#13083559	—	2	1	no	—
38	#19151678	—	2	1	no	—
39	#108×D₈₉	C₂²	1	1	yes	characteristic
40	#19151633	C₂²	1	1	yes	characteristic
41	#19151613	—	2	1	no	—
42	#19151601	—	2	1	no	—
43	#19151555	C₂²	1	1	yes	characteristic
44	#19151422	C₂²	1	1	yes	characteristic, complemented
45	#19151421	C₂²	1	1	yes	characteristic, complemented
46	#19151420	C₂²	1	1	yes	characteristic, complemented
47	#19151412	C₂²	1	1	yes	characteristic, complemented
48	#19151411	C₂²	1	1	yes	characteristic, complemented
49	#19151410	C₂²	1	1	yes	characteristic, complemented
50	#19151409	C₂²	1	1	yes	characteristic, complemented
51	#19151408	C₂²	1	1	yes	characteristic, complemented
52	#19151407	C₂²	1	1	yes	characteristic, complemented
53	#19151376	C₂²	1	1	yes	characteristic, complemented
54	#19151375	C₂²	1	1	yes	characteristic, complemented
55	#19151375	C₂²	1	1	yes	characteristic, complemented
56	#509×C₈₉	C₂²	1	1	yes	characteristic
57	#444×C₈₉	C₂²	1	1	yes	characteristic, complemented
58	#442×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#365×C₈₉	C₂²	1	1	yes	characteristic, complemented
60	#361×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#360×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#347×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	#41×D₈₉	—	2	1	no	—
64	C₂×D₄×D₈₉	—	2	1	no	—
65	#15668035	C₂×C₄	1	1	yes	characteristic, complemented
66	#15668034	C₂³	1	1	yes	characteristic
67	#15668033	—	2	1	no	—
68	#15668032	—	2	1	no	—
69	#15668031	C₂×C₄	1	1	yes	characteristic, complemented
70	Q₁₆×D₈₉	C₂×C₄	1	1	yes	characteristic, complemented
71	SD₁₆×D₈₉	—	2	1	no	—
72	C₂×D₇₁₂	C₂³	1	1	yes	characteristic
73	C₂×#13083559	—	2	1	no	—
74	D₈×D₈₉	—	2	1	no	—
75	D₈×D₈₉	—	2	1	no	—
76	D₈×D₈₉	C₂×C₄	1	2	yes	—
77	D₈×D₈₉	C₂×C₄	1	2	yes	—
78	D₈×D₈₉	C₂×C₄	1	1	yes	characteristic, complemented
79	#15668020	—	2	1	no	—
80	#15668020	—	4	1	no	—
81	#15668019	—	2	1	no	—
82	#15668018	—	2	1	no	—
83	#15668018	—	4	1	no	—
84	C₂×#13083557	—	4	1	no	—
85	C₂×#13083557	D₄	1	1	yes	characteristic
86	M₁₆×D₈₉	—	2	1	no	—
87	M₁₆×D₈₉	—	4	1	no	—
88	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
89	C₄×D₃₅₆	—	2	1	no	—
90	D₄×Dic₈₉	—	2	1	no	—
91	#15667974	—	2	1	no	—
92	C₄×C₂²⋊D₈₉	—	4	1	no	—
93	#15667972	—	4	1	no	—
94	#15667970	—	2	1	no	—
95	#15667969	D₄	1	1	yes	characteristic
96	C₂×#13083551	—	4	1	no	—
97	C₂²⋊C₄×D₈₉	—	4	1	no	—
98	#15667957	C₂×C₄	1	2	yes	complemented
99	#15667956	C₂×C₄	1	2	yes	complemented
100	#15667955	C₂×C₄	1	2	yes	complemented
101	D₁₄₂₄	C₂×C₄	1	2	yes	complemented
102	#15667953	C₂×C₄	1	2	yes	complemented
103	#15667953	C₂×C₄	1	2	yes	complemented
104	#15667952	C₂³	1	1	yes	characteristic
105	#15667952	C₂³	1	1	yes	characteristic
106	#15667951	—	2	1	no	—
107	#15667951	C₂×C₄	1	2	yes	complemented
108	C₁₆×D₈₉	—	2	1	no	—
109	C₁₆×D₈₉	C₂×C₄	1	2	yes	complemented
110	#15667948	C₂³	1	1	yes	characteristic
111	#15667947	—	2	1	no	—
112	#15667945	—	2	1	no	—
113	#15667944	C₂³	1	1	yes	characteristic
114	#15667940	—	2	1	no	—
115	#15667939	—	2	1	no	—
116	#15667938	—	2	1	no	—
117	#15667934	—	2	1	no	—
118	#15667933	—	2	1	no	—
119	#15667932	—	2	1	no	—
120	#15667922	C₂³	1	1	yes	characteristic
121	C₄×#10623494	D₄	1	1	yes	characteristic
122	C₈×Dic₈₉	D₄	1	1	yes	characteristic
123	#135×C₈₉	C₂³	1	1	yes	characteristic
124	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
125	#131×C₈₉	—	2	1	no	—
126	C₄×D₄×C₈₉	—	2	1	no	—
127	SD₃₂×C₈₉	C₂×C₄	1	2	yes	complemented
128	D₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
129	M₃₂×C₈₉	C₂³	1	1	yes	characteristic
130	M₃₂×C₈₉	C₂³	1	1	yes	characteristic
131	#108×C₈₉	C₂³	1	1	yes	characteristic
132	#106×C₈₉	C₂³	1	1	yes	characteristic
133	#104×C₈₉	—	2	1	no	—
134	#102×C₈₉	—	2	1	no	—
135	#97×C₈₉	C₂³	1	1	yes	characteristic
136	C₂³×D₈₉	—	4	1	no	—
137	#13083575	—	2	1	no	—
138	#13083574	—	2	1	no	—
139	#13083574	—	4	1	no	—
140	#13083573	—	2	1	no	—
141	#13083573	—	4	1	no	—
142	Q₈×D₈₉	—	2	1	no	—
143	C₂×D₃₅₆	—	2	1	no	—
144	C₂×C₂²⋊D₈₉	—	4	1	no	—
145	D₄×D₈₉	—	2	2	no	—
146	D₄×D₈₉	—	2	2	no	—
147	D₄×D₈₉	—	2	1	no	—
148	D₄×D₈₉	—	4	1	no	—
149	D₄×D₈₉	—	4	1	no	—
150	D₄×D₈₉	—	4	1	no	—
151	C₂²×Dic₈₉	—	4	1	no	—
152	C₂×C₄×D₈₉	—	4	1	no	—
153	C₂×C₄×D₈₉	—	4	1	no	—
154	C₂×C₄×D₈₉	—	4	1	no	—
155	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
156	Dic₃₅₆	C₂²×C₄	1	1	yes	characteristic
157	#13083564	—	2	1	no	—
158	#13083563	—	2	1	no	—
159	#13083562	—	2	1	no	—
160	#13083561	—	2	1	no	—
161	D₇₁₂	—	2	1	no	—
162	D₇₁₂	C₂²×C₄	1	2	yes	—
163	D₇₁₂	C₂²×C₄	1	1	yes	characteristic
164	#13083559	—	2	2	no	—
165	#13083559	—	2	2	no	—
166	#13083559	—	2	1	no	—
167	#13083558	—	2	1	no	—
168	#13083558	—	4	1	no	—
169	#13083557	—	2	1	no	—
170	#13083557	—	2	1	no	—
171	#13083557	—	4	1	no	—
172	#13083557	—	4	1	no	—
173	#13083557	—	4	1	no	—
174	C₂×#10623494	—	4	1	no	—
175	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
176	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
177	C₈×D₈₉	—	4	1	no	—
178	C₈×D₈₉	—	4	1	no	—
179	C₈×D₈₉	—	4	1	no	—
180	C₈×D₈₉	C₂²×C₄	1	1	yes	characteristic
181	C₈×D₈₉	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₈₉	#41	1	1	yes	characteristic
183	C₈×D₈₉	#41	1	1	yes	characteristic
184	C₄⋊Dic₈₉	—	2	1	no	—
185	#13083553	—	2	1	no	—
186	C₂²⋊Dic₈₉	—	4	1	no	—
187	#13083551	—	2	1	no	—
188	#13083551	—	4	1	no	—
189	#13083551	—	4	1	no	—
190	#13083551	—	4	1	no	—
191	C₄×Dic₈₉	—	4	1	no	—
192	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
193	#13083549	—	2	1	no	—
194	#13083549	C₂²×C₄	1	2	yes	—
195	#41×C₈₉	—	2	1	no	—
196	C₂×D₄×C₈₉	—	2	1	no	—
197	C₂²×C₄×C₈₉	—	4	1	no	—
198	Q₁₆×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	SD₁₆×C₈₉	—	2	1	no	—
200	D₈×C₈₉	—	2	1	no	—
201	D₈×C₈₉	C₂²×C₄	1	2	yes	—
202	D₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	M₁₆×C₈₉	—	2	1	no	—
204	M₁₆×C₈₉	—	4	1	no	—
205	C₂×C₈×C₈₉	—	4	1	no	—
206	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
207	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₈₉	—	2	1	no	—
209	C₂²⋊C₄×C₈₉	—	4	1	no	—
210	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
211	C₁₆×C₈₉	—	2	1	no	—
212	C₁₆×C₈₉	C₂²×C₄	1	2	yes	—
213	C₂³×C₈₉	—	4	1	no	—
214	C₂²×D₈₉	—	4	1	no	—
215	C₂²×D₈₉	—	4	1	no	—
216	C₂²×D₈₉	—	4	2	no	—
217	C₂²×D₈₉	—	4	2	no	—
218	C₂²×D₈₉	—	16	1	no	—
219	C₂²×D₈₉	—	16	1	no	—
220	C₂²×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
221	Q₈×C₈₉	—	2	1	no	—
222	D₄×C₈₉	—	2	2	no	—
223	D₄×C₈₉	—	2	1	no	—
224	D₄×C₈₉	—	4	1	no	—
225	D₄×C₈₉	—	4	1	no	—
226	C₂×C₄×C₈₉	—	2	1	no	—
227	C₂×C₄×C₈₉	—	4	1	no	—
228	C₂×C₄×C₈₉	—	4	1	no	—
229	C₂×C₄×C₈₉	—	16	1	no	—
230	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
231	C₂²⋊D₈₉	—	4	1	no	—
232	C₂²⋊D₈₉	—	4	1	no	—
233	C₂²⋊D₈₉	—	4	2	no	—
234	C₂²⋊D₈₉	—	4	2	no	—
235	C₂²⋊D₈₉	—	4	1	no	—
236	C₂×Dic₈₉	—	2	1	no	—
237	C₂×Dic₈₉	—	4	1	no	—
238	C₂×Dic₈₉	—	4	1	no	—
239	C₂×Dic₈₉	—	16	1	no	—
240	C₂×Dic₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
241	D₃₅₆	—	2	2	no	—
242	D₃₅₆	—	2	1	no	—
243	D₃₅₆	—	4	1	no	—
244	D₃₅₆	—	4	1	no	—
245	C₄×D₈₉	—	4	1	no	—
246	C₄×D₈₉	—	4	1	no	—
247	C₄×D₈₉	—	4	1	no	—
248	C₄×D₈₉	—	16	1	no	—
249	C₄×D₈₉	—	16	1	no	—
250	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
251	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
252	C₄×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₄×D₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
254	Dic₁₇₈	—	2	1	no	—
255	Dic₁₇₈	—	4	1	no	—
256	C₈×C₈₉	—	2	1	no	—
257	C₈×C₈₉	—	4	1	no	—
258	C₈×C₈₉	C₂³×C₄	1	1	yes	characteristic
259	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
260	#10623494	—	2	1	no	—
261	#10623494	—	4	1	no	—
262	#10623494	C₄×D₄	1	1	yes	characteristic
263	#10623494	C₄×D₄	1	1	yes	characteristic
264	C₂²×C₈₉	—	4	1	no	—
265	C₂²×C₈₉	—	4	2	no	—
266	C₂²×C₈₉	—	8	1	no	—
267	C₂²×C₈₉	—	8	1	no	—
268	C₂²×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₂×D₈₉	—	4	1	no	—
270	C₂×D₈₉	—	4	1	no	—
271	C₂×D₈₉	—	4	2	no	—
272	C₂×D₈₉	—	8	1	no	—
273	C₂×D₈₉	—	8	1	no	—
274	C₂×D₈₉	—	16	1	no	—
275	C₂×D₈₉	—	16	2	no	—
276	C₂×D₈₉	—	16	2	no	—
277	C₂×D₈₉	#442	1	1	yes	characteristic
278	C₂×D₈₉	#442	1	1	yes	characteristic
279	C₄×C₈₉	—	4	1	no	—
280	C₄×C₈₉	—	4	1	no	—
281	C₄×C₈₉	—	8	1	no	—
282	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
284	Dic₈₉	—	4	1	no	—
285	Dic₈₉	—	4	1	no	—
286	Dic₈₉	—	8	1	no	—
287	Dic₈₉	#442	1	1	yes	characteristic
288	Dic₈₉	#442	1	1	yes	characteristic
289	#33471	—	89	1	no	maximal, Sylow
290	C₂×C₈₉	—	2	1	no	—
291	C₂×C₈₉	—	8	2	no	—
292	C₂×C₈₉	—	8	1	no	—
293	C₂×C₈₉	C₂×#442	1	1	yes	characteristic
294	D₈₉	—	2	1	no	—
295	D₈₉	—	2	1	no	—
296	D₈₉	—	8	2	no	—
297	D₈₉	—	8	1	no	—
298	C₂×#509	—	89	1	no	—
299	#2957	—	89	1	no	—
300	#2948	—	89	1	no	—
301	AGL(1,ℤ/16)	—	89	1	no	—
302	AGL(1,ℤ/16)	—	89	1	no	—
303	AGL(1,ℤ/16)	—	89	1	no	—
304	AGL(1,ℤ/16)	—	89	1	no	—
305	AGL(1,ℤ/16)	—	89	1	no	—
306	AGL(1,ℤ/16)	—	89	1	no	—
307	AGL(1,ℤ/16)	—	89	1	no	—
308	AGL(1,ℤ/16)	D₈₉	1	1	yes	characteristic, complemented
309	#2155	—	89	1	no	—
310	C₂×#361	—	89	1	no	—
311	#2145	—	89	1	no	—
312	#2110	—	89	1	no	—
313	C₈₉	#33471	1	1	yes	characteristic, complemented, Sylow
314	C₂×#135	—	89	1	no	—
315	C₂²×D₈	—	89	1	no	—
316	#568	—	178	1	no	—
317	#518	—	178	1	no	—
318	#509	—	89	1	no	—
319	#509	—	89	1	no	—
320	#509	—	89	2	no	—
321	#509	—	89	2	no	—
322	#509	—	89	1	no	—
323	#509	C₂×D₈₉	1	1	yes	characteristic
324	C₂×SD₃₂	—	89	2	no	—
325	C₂×D₁₆	—	89	2	no	—
326	C₂×M₃₂	—	89	1	no	—
327	C₂×M₃₂	—	89	1	no	—
328	#444	—	89	1	no	—
329	#444	—	89	1	no	—
330	#444	—	89	1	no	—
331	#444	C₂×D₈₉	1	1	yes	characteristic, complemented
332	#443	—	178	1	no	—
333	#443	—	178	1	no	—
334	#442	—	89	1	no	—
335	#442	—	89	1	no	—
336	#442	—	89	1	no	—
337	#442	C₂×D₈₉	1	1	yes	characteristic, complemented
338	C₄×D₈	—	178	1	no	—
339	C₄×D₈	—	178	1	no	—
340	C₂×#108	—	89	1	no	—
341	#427	—	89	1	no	—
342	#421	—	178	1	no	—
343	#418	—	178	1	no	—
344	#405	—	89	1	no	—
345	#365	—	89	1	no	—
346	#365	—	89	1	no	—
347	#365	—	89	1	no	—
348	#365	C₂×D₈₉	1	1	yes	characteristic, complemented
349	#361	—	89	1	no	—
350	#361	—	89	1	no	—
351	#361	—	89	1	no	—
352	#361	C₂×D₈₉	1	1	yes	characteristic, complemented
353	#360	—	89	1	no	—
354	#360	—	89	1	no	—
355	#360	—	89	1	no	—
356	#360	C₂×D₈₉	1	1	yes	characteristic, complemented
357	#347	—	89	1	no	—
358	#347	—	89	1	no	—
359	#347	—	89	1	no	—
360	#347	C₂×D₈₉	1	1	yes	characteristic, complemented
361	C₂×#41	—	178	1	no	—
362	C₂²×D₄	—	178	1	no	—
363	#135	—	89	1	no	—
364	#135	—	89	1	no	—
365	#135	—	89	1	no	—
366	#135	—	178	1	no	—
367	#135	—	178	1	no	—
368	#135	C₂²×D₈₉	1	1	yes	characteristic
369	C₂×Q₁₆	—	89	1	no	—
370	C₂×SD₁₆	—	178	1	no	—
371	C₂×D₈	—	89	2	no	—
372	C₂×D₈	—	89	2	no	—
373	C₂×D₈	—	89	1	no	—
374	C₂×D₈	—	89	1	no	—
375	C₂×D₈	—	178	1	no	—
376	C₂×D₈	—	178	1	no	—
377	C₂×D₈	—	178	1	no	—
378	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
379	#131	—	2	1	no	—
380	#131	—	356	1	no	—
381	#131	—	356	1	no	—
382	#131	—	178	1	no	—
383	#131	—	178	1	no	—
384	#131	—	178	1	no	—
385	C₂×M₁₆	—	89	1	no	—
386	C₂×M₁₆	—	356	1	no	—
387	C₂×M₁₆	—	356	1	no	—
388	C₂×M₁₆	—	178	1	no	—
389	C₂²×C₈	—	89	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	356	1	no	—
392	C₄×D₄	—	356	1	no	—
393	C₄×D₄	—	178	1	no	—
394	C₄×D₄	—	178	1	no	—
395	C₄×D₄	—	178	1	no	—
396	#117	—	89	1	no	—
397	#117	—	178	1	no	—
398	C₂×C₂²⋊C₄	—	356	1	no	—
399	C₂×C₂²⋊C₄	—	356	1	no	—
400	SD₃₂	—	89	2	no	—
401	SD₃₂	—	89	2	no	—
402	SD₃₂	—	89	2	no	—
403	SD₃₂	C₄×D₈₉	1	2	yes	complemented
404	D₁₆	—	89	2	no	—
405	D₁₆	—	89	2	no	—
406	D₁₆	—	89	2	no	—
407	D₁₆	C₄×D₈₉	1	2	yes	complemented
408	M₃₂	—	89	1	no	—
409	M₃₂	—	89	2	no	—
410	M₃₂	—	89	1	no	—
411	M₃₂	—	178	1	no	—
412	M₃₂	C₂²×D₈₉	1	1	yes	characteristic
413	M₃₂	C₂²×D₈₉	1	1	yes	characteristic
414	C₂×C₁₆	—	89	2	no	—
415	C₂×C₁₆	—	178	1	no	—
416	#108	—	89	1	no	—
417	#108	—	178	1	no	—
418	#108	C₂²×D₈₉	1	1	yes	characteristic
419	#107	—	178	1	no	—
420	#106	—	89	1	no	—
421	#106	C₂²×D₈₉	1	1	yes	characteristic
422	#104	—	2	1	no	—
423	#104	—	178	1	no	—
424	#104	—	178	1	no	—
425	#104	—	178	1	no	—
426	#102	—	2	1	no	—
427	#102	—	178	1	no	—
428	#102	—	178	1	no	—
429	#102	—	178	1	no	—
430	#97	—	89	1	no	—
431	#97	C₂²×D₈₉	1	1	yes	characteristic
432	C₄×C₈	—	89	1	no	—
433	C₄×C₈	—	89	1	no	—
434	C₂⁴	—	356	1	no	—
435	#41	—	2	1	no	—
436	#41	—	356	1	no	—
437	#41	—	356	1	no	—
438	#41	—	178	1	no	—
439	#41	—	178	1	no	—
440	#41	—	178	1	no	—
441	C₂×Q₈	—	178	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	356	1	no	—
444	C₂×D₄	—	356	1	no	—
445	C₂×D₄	—	356	1	no	—
446	C₂×D₄	—	356	1	no	—
447	C₂×D₄	—	178	2	no	—
448	C₂×D₄	—	178	2	no	—
449	C₂×D₄	—	178	1	no	—
450	C₂×D₄	—	178	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	89	1	no	—
453	C₂²×C₄	—	356	1	no	—
454	C₂²×C₄	—	356	1	no	—
455	C₂²×C₄	—	356	1	no	—
456	C₂²×C₄	—	356	1	no	—
457	Q₁₆	—	89	1	no	—
458	Q₁₆	—	178	1	no	—
459	Q₁₆	C₂×C₄×D₈₉	1	1	yes	characteristic
460	SD₁₆	—	2	1	no	—
461	SD₁₆	—	178	1	no	—
462	SD₁₆	—	178	1	no	—
463	SD₁₆	—	178	1	no	—
464	D₈	—	2	1	no	—
465	D₈	—	89	1	no	—
466	D₈	—	89	2	no	—
467	D₈	—	178	2	no	—
468	D₈	—	178	2	no	—
469	D₈	—	178	1	no	—
470	D₈	—	178	1	no	—
471	D₈	C₂×C₄×D₈₉	1	1	yes	characteristic
472	D₈	C₂×C₄×D₈₉	1	2	yes	—
473	M₁₆	—	2	1	no	—
474	M₁₆	—	4	1	no	—
475	M₁₆	—	356	1	no	—
476	M₁₆	—	356	1	no	—
477	M₁₆	—	356	1	no	—
478	M₁₆	—	356	1	no	—
479	M₁₆	—	178	1	no	—
480	M₁₆	—	178	1	no	—
481	M₁₆	—	178	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	89	1	no	—
484	C₂×C₈	—	89	1	no	—
485	C₂×C₈	—	89	1	no	—
486	C₂×C₈	—	89	1	no	—
487	C₂×C₈	—	89	1	no	—
488	C₂×C₈	—	89	1	no	—
489	C₂×C₈	—	356	1	no	—
490	C₂×C₈	—	356	1	no	—
491	C₂×C₈	—	356	1	no	—
492	C₂×C₈	—	356	1	no	—
493	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
494	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	178	1	no	—
497	C₄⋊C₄	—	178	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	356	1	no	—
500	C₂²⋊C₄	—	356	1	no	—
501	C₂²⋊C₄	—	356	1	no	—
502	C₂²⋊C₄	—	356	1	no	—
503	C₂²⋊C₄	—	178	1	no	—
504	C₄²	—	89	1	no	—
505	C₄²	—	356	1	no	—
506	C₄²	D₄×D₈₉	1	1	yes	characteristic
507	C₁₆	—	2	1	no	—
508	C₁₆	—	89	2	no	—
509	C₁₆	—	178	1	no	—
510	C₁₆	C₂×C₄×D₈₉	1	2	yes	—
511	C₂³	—	4	1	no	—
512	C₂³	—	89	1	no	—
513	C₂³	—	356	1	no	—
514	C₂³	—	356	2	no	—
515	C₂³	—	356	2	no	—
516	C₂³	—	356	1	no	—
517	C₂³	—	1424	1	no	—
518	C₂³	—	1424	1	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	356	1	no	—
521	Q₈	—	178	1	no	—
522	D₄	—	2	2	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	1	no	—
525	D₄	—	4	1	no	—
526	D₄	—	356	1	no	—
527	D₄	—	356	2	no	—
528	D₄	—	356	2	no	—
529	D₄	—	356	1	no	—
530	D₄	—	356	1	no	—
531	D₄	—	356	1	no	—
532	D₄	—	356	1	no	—
533	D₄	—	178	2	no	—
534	D₄	—	178	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	16	1	no	—
539	C₂×C₄	—	89	1	no	—
540	C₂×C₄	—	89	1	no	—
541	C₂×C₄	—	89	1	no	—
542	C₂×C₄	—	89	1	no	—
543	C₂×C₄	—	89	1	no	—
544	C₂×C₄	—	356	1	no	—
545	C₂×C₄	—	356	1	no	—
546	C₂×C₄	—	356	1	no	—
547	C₂×C₄	—	356	1	no	—
548	C₂×C₄	—	356	1	no	—
549	C₂×C₄	—	1424	1	no	—
550	C₂×C₄	—	1424	1	no	—
551	C₂×C₄	—	1424	1	no	—
552	C₂×C₄	—	178	1	no	—
553	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
554	C₈	—	2	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	89	1	no	—
557	C₈	—	89	1	no	—
558	C₈	—	356	1	no	—
559	C₈	—	178	1	no	—
560	C₈	C₂²×C₄×D₈₉	1	1	yes	characteristic
561	C₈	#41×D₈₉	1	1	yes	characteristic
562	C₂²	—	4	1	no	—
563	C₂²	—	4	2	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	89	1	no	—
567	C₂²	—	89	1	no	—
568	C₂²	—	356	1	no	—
569	C₂²	—	356	1	no	—
570	C₂²	—	356	2	no	—
571	C₂²	—	1424	2	no	—
572	C₂²	—	1424	2	no	—
573	C₂²	—	1424	1	no	—
574	C₂²	—	712	1	no	—
575	C₂²	—	712	1	no	—
576	C₂²	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	89	1	no	—
581	C₄	—	89	1	no	—
582	C₄	—	356	1	no	—
583	C₄	—	356	1	no	—
584	C₄	—	712	1	no	—
585	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
586	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
587	C₂	—	2	1	no	—
588	C₂	—	8	2	no	—
589	C₂	—	8	1	no	—
590	C₂	—	178	1	no	—
591	C₂	—	178	1	no	—
592	C₂	—	712	1	no	—
593	C₂	—	712	2	no	—
594	C₂	#442×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#442×D₈₉
commutator	C₈×C₈₉	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×AGL(1,ℤ/16)	C₂
socle	C₂×C₈₉	C₂×#442
prime radical	#509×D₈₉	C₂
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	AGL(1,ℤ/16)	D₈₉
hypocenter	C₈₉	#33471
LCS	G ▷ C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #97 ◁ AGL(1,ℤ/16)

Complements

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

N	H ≅ G/N	type
2. #26029166	C₂	semidirect
3. #26029101	C₂	semidirect
4. #26022153	C₂	semidirect
5. #26022152	C₂	semidirect
6. #26022151	C₂	semidirect
7. #26022150	C₂	semidirect
8. #26022149	C₂	semidirect
9. #26022148	C₂	semidirect
10. #26022147	C₂	semidirect
11. #26022023	C₂	semidirect
12. #361×D₈₉	C₂	semidirect
13. #26021986	C₂	semidirect
14. #26021855	C₂	semidirect
15. C₈₉×AGL(1,ℤ/16)	C₂	semidirect
21. #19152035	C₄	semidirect
24. #19152032	C₄	semidirect
25. SD₃₂×D₈₉	C₄	semidirect
26. D₁₆×D₈₉	C₄	semidirect
29. #19151721	C₂²	semidirect
30. #19151720	C₂²	semidirect
31. #19151719	C₂²	semidirect
34. #19151711	C₂²	semidirect
35. #19151710	C₂²	semidirect
36. #19151709	C₂²	semidirect
44. #19151422	C₂²	semidirect
45. #19151421	C₂²	semidirect
46. #19151420	C₂²	semidirect
47. #19151412	C₂²	semidirect
48. #19151411	C₂²	semidirect
49. #19151410	C₂²	semidirect
50. #19151409	C₂²	semidirect
51. #19151408	C₂²	semidirect
52. #19151407	C₂²	semidirect
53. #19151376	C₂²	semidirect
54. #19151375	C₂²	semidirect
55. #19151375	C₂²	semidirect
57. #444×C₈₉	C₂²	semidirect
58. #442×C₈₉	C₂²	semidirect
59. #365×C₈₉	C₂²	semidirect
60. #361×C₈₉	C₂²	semidirect
61. #360×C₈₉	C₂²	semidirect
62. #347×C₈₉	C₂²	semidirect
65. #15668035	C₂×C₄	semidirect
69. #15668031	C₂×C₄	semidirect
70. Q₁₆×D₈₉	C₂×C₄	semidirect
78. D₈×D₈₉	C₂×C₄	semidirect
98. #15667957	C₂×C₄	semidirect
99. #15667956	C₂×C₄	semidirect
100. #15667955	C₂×C₄	semidirect
101. D₁₄₂₄	C₂×C₄	semidirect
102. #15667953	C₂×C₄	semidirect
103. #15667953	C₂×C₄	semidirect
107. #15667951	C₂×C₄	semidirect
109. C₁₆×D₈₉	C₂×C₄	semidirect
127. SD₃₂×C₈₉	C₂×C₄	semidirect
128. D₁₆×C₈₉	C₂×C₄	semidirect
308. AGL(1,ℤ/16)	D₈₉	semidirect
313. C₈₉	#33471	semidirect
331. #444	C₂×D₈₉	semidirect
337. #442	C₂×D₈₉	semidirect
348. #365	C₂×D₈₉	semidirect
352. #361	C₂×D₈₉	semidirect
356. #360	C₂×D₈₉	semidirect
360. #347	C₂×D₈₉	semidirect
403. SD₃₂	C₄×D₈₉	semidirect
407. D₁₆	C₄×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#509×D₈₉	2
#26029166	2
#26029101	2
#26022153	2
#26022152	2
#26022151	2
#26022150	2
#26022149	2
#26022148	2
#26022147	2
#26022023	2
#361×D₈₉	2
#26021986	2
#26021855	2
C₈₉×AGL(1,ℤ/16)	2
#33471	89