Subgroups — #36542270

Order 22784.

900 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031376	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031189	C₂	1	1	yes	maximal, characteristic, complemented
3	#26030810	C₂	1	1	yes	maximal, characteristic, complemented
4	#26030793	C₂	1	1	yes	maximal, characteristic, complemented
5	#26030703	C₂	1	1	yes	maximal, characteristic
6	#492×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019882	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019874	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019872	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019843	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019841	C₂	1	1	yes	maximal, characteristic, complemented
12	#26019840	C₂	1	1	yes	maximal, characteristic, complemented
13	#26019838	C₂	1	1	yes	maximal, characteristic, complemented
14	#26018531	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1715	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#15668036	—	2	2	no	—
17	C₂×SD₁₆×D₈₉	—	2	2	no	—
18	#19152153	C₂²	1	1	yes	characteristic
19	#19152146	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×D₈₉	C₂²	1	1	yes	characteristic
21	#127×D₈₉	C₂²	1	1	yes	characteristic
22	#19152005	—	2	2	no	—
23	#19152003	C₂²	1	1	yes	characteristic, complemented
24	#19152001	C₂²	1	1	yes	characteristic, complemented
25	#19151996	C₂²	1	1	yes	characteristic, complemented
26	#19151994	C₂²	1	1	yes	characteristic, complemented
27	#19151994	C₂²	1	1	yes	characteristic, complemented
28	#19151994	C₂²	1	1	yes	characteristic, complemented
29	#19151986	—	2	2	no	—
30	#19151974	C₂²	1	1	yes	characteristic
31	#19151972	C₂²	1	1	yes	characteristic
32	#19151972	C₂²	1	1	yes	characteristic
33	#19151971	C₂²	1	1	yes	characteristic
34	#19151971	C₂²	1	1	yes	characteristic
35	#19151970	C₂²	1	1	yes	characteristic
36	#19151970	C₂²	1	1	yes	characteristic
37	#19151970	C₂²	1	1	yes	characteristic, complemented
38	#19151969	—	2	2	no	—
39	#19151949	C₂²	1	1	yes	characteristic, complemented
40	#19151945	C₂²	1	1	yes	characteristic
41	#19151944	C₂²	1	1	yes	characteristic
42	#19151944	C₂²	1	1	yes	characteristic, complemented
43	#19151915	—	2	2	no	—
44	#19151886	—	2	2	no	—
45	#19151826	—	2	2	no	—
46	#19151796	—	2	2	no	—
47	#19151747	—	2	2	no	—
48	#19151689	—	2	2	no	—
49	#19151649	C₂²	1	1	yes	characteristic
50	#19151637	—	2	2	no	—
51	C₄×#13083557	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
53	#19151320	C₂²	1	1	yes	characteristic, complemented
54	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
55	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
56	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#493×C₈₉	C₂²	1	1	yes	characteristic
58	#492×C₈₉	C₂²	1	1	yes	characteristic
59	#492×C₈₉	C₂²	1	1	yes	characteristic
60	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
62	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₂×#13083573	—	2	1	no	—
64	C₂×Q₈×D₈₉	—	2	1	no	—
65	C₂×D₄×D₈₉	—	2	1	no	—
66	C₂×D₄×D₈₉	—	2	1	no	—
67	C₂×D₄×D₈₉	—	2	1	no	—
68	#15668036	—	4	8	no	—
69	C₂×#13083563	—	2	2	no	—
70	C₂×#13083563	—	2	2	no	—
71	C₂×#13083562	—	2	2	no	—
72	C₂×#13083562	—	2	2	no	—
73	C₂×#13083562	—	2	2	no	—
74	C₂×#13083561	—	2	2	no	—
75	C₂×#13083561	—	2	2	no	—
76	SD₁₆×D₈₉	—	4	8	no	—
77	C₂×#13083559	—	2	2	no	—
78	C₂×#13083557	D₄	1	2	yes	—
79	C₂×C₈×D₈₉	D₄	1	2	yes	—
80	#15668012	C₂³	1	1	yes	characteristic
81	#15668012	C₂³	1	1	yes	characteristic
82	#15668012	C₂³	1	1	yes	characteristic
83	#15668011	—	2	1	no	—
84	#15668011	—	2	1	no	—
85	#15668010	—	2	1	no	—
86	#15668009	C₂³	1	1	yes	characteristic
87	#15668008	—	2	1	no	—
88	#15668008	—	2	1	no	—
89	#15668008	—	2	1	no	—
90	#15668003	—	2	1	no	—
91	#15667999	—	2	1	no	—
92	#15667992	—	2	1	no	—
93	#15667988	—	2	1	no	—
94	#15667983	—	2	1	no	—
95	#15667983	—	2	1	no	—
96	Q₈×Dic₈₉	—	2	1	no	—
97	#15667977	—	2	1	no	—
98	D₄×Dic₈₉	—	2	1	no	—
99	D₄×Dic₈₉	—	2	1	no	—
100	#15667970	—	2	1	no	—
101	C₄⋊C₄×D₈₉	—	2	1	no	—
102	C₄⋊C₄×D₈₉	—	2	1	no	—
103	C₄²×D₈₉	C₂³	1	1	yes	characteristic
104	#15667946	—	2	2	no	—
105	#15667945	—	2	2	no	—
106	#15667944	—	2	2	no	—
107	#15667943	—	2	2	no	—
108	#15667943	—	2	2	no	—
109	#15667943	—	2	2	no	—
110	#15667941	D₄	1	2	yes	—
111	#15667937	—	2	2	no	—
112	#15667934	—	2	2	no	—
113	#15667933	—	2	2	no	—
114	#15667933	—	2	2	no	—
115	#15667924	D₄	1	2	yes	—
116	#15667922	D₄	1	2	yes	—
117	C₄×#10623494	C₂³	1	1	yes	characteristic
118	C₄×#10623494	C₂³	1	1	yes	characteristic
119	C₄×#10623494	C₂³	1	1	yes	characteristic
120	C₈×Dic₈₉	D₄	1	2	yes	—
121	C₂×SD₁₆×C₈₉	—	2	2	no	—
122	C₂×SD₁₆×C₈₉	—	2	2	no	—
123	C₂×D₈×C₈₉	—	2	2	no	—
124	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
126	#127×C₈₉	C₂³	1	1	yes	characteristic
127	#127×C₈₉	C₂³	1	1	yes	characteristic
128	#106×C₈₉	—	2	2	no	—
129	#102×C₈₉	—	2	2	no	—
130	#102×C₈₉	—	2	2	no	—
131	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
133	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₂³×D₈₉	—	4	1	no	—
135	#13083573	—	4	4	no	—
136	C₂×Dic₁₇₈	—	2	1	no	—
137	C₂×Dic₁₇₈	—	2	1	no	—
138	C₂×Dic₁₇₈	—	2	1	no	—
139	C₂×Dic₁₇₈	—	4	1	no	—
140	Q₈×D₈₉	—	4	4	no	—
141	C₂×D₃₅₆	—	2	1	no	—
142	C₂×D₃₅₆	—	2	1	no	—
143	C₂×D₃₅₆	—	2	1	no	—
144	C₂×C₂²⋊D₈₉	—	4	1	no	—
145	C₂×C₂²⋊D₈₉	—	4	1	no	—
146	C₂×C₂²⋊D₈₉	—	4	1	no	—
147	C₂×C₂²⋊D₈₉	—	4	1	no	—
148	D₄×D₈₉	—	4	4	no	—
149	D₄×D₈₉	—	4	4	no	—
150	D₄×D₈₉	—	8	2	no	—
151	C₂²×Dic₈₉	—	4	1	no	—
152	C₂×C₄×D₈₉	—	4	1	no	—
153	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
156	#13083563	—	4	4	no	—
157	#13083563	—	4	4	no	—
158	#13083562	—	4	4	no	—
159	#13083562	—	4	4	no	—
160	#13083562	—	4	4	no	—
161	#13083561	—	4	4	no	—
162	#13083561	—	8	2	no	—
163	#13083559	—	4	4	no	—
164	#13083557	SD₁₆	1	8	yes	complemented
165	C₂×#10623494	C₂×D₄	1	2	yes	—
166	C₂×#10623494	C₂×D₄	1	2	yes	—
167	C₂×#10623494	C₂×D₄	1	2	yes	—
168	C₈×D₈₉	—	2	4	no	—
169	C₄⋊Dic₈₉	—	2	1	no	—
170	C₄⋊Dic₈₉	—	2	1	no	—
171	C₄⋊Dic₈₉	—	2	1	no	—
172	C₄⋊Dic₈₉	—	2	1	no	—
173	C₄⋊Dic₈₉	—	2	1	no	—
174	C₄⋊Dic₈₉	—	2	1	no	—
175	C₄⋊Dic₈₉	—	4	1	no	—
176	#13083553	—	4	1	no	—
177	#13083553	—	4	1	no	—
178	#13083553	—	4	1	no	—
179	C₂²⋊Dic₈₉	—	4	1	no	—
180	C₂²⋊Dic₈₉	—	4	1	no	—
181	#13083551	—	4	1	no	—
182	C₄×Dic₈₉	—	4	1	no	—
183	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
184	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
185	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₈₉	—	2	1	no	—
187	C₂×Q₈×C₈₉	—	2	1	no	—
188	C₂×D₄×C₈₉	—	2	1	no	—
189	C₂×D₄×C₈₉	—	2	1	no	—
190	C₂×D₄×C₈₉	—	2	1	no	—
191	C₂×D₄×C₈₉	—	2	1	no	—
192	C₂×D₄×C₈₉	—	2	1	no	—
193	C₂×D₄×C₈₉	—	2	1	no	—
194	SD₁₆×C₈₉	—	4	4	no	—
195	SD₁₆×C₈₉	—	8	2	no	—
196	D₈×C₈₉	—	4	4	no	—
197	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
198	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
199	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
200	C₄⋊C₄×C₈₉	—	2	1	no	—
201	C₄⋊C₄×C₈₉	—	2	1	no	—
202	C₄⋊C₄×C₈₉	—	2	1	no	—
203	C₄⋊C₄×C₈₉	—	2	1	no	—
204	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
205	C₂³×C₈₉	—	4	1	no	—
206	C₂³×C₈₉	—	4	1	no	—
207	C₂²×D₈₉	—	4	1	no	—
208	C₂²×D₈₉	—	8	2	no	—
209	C₂²×D₈₉	—	8	2	no	—
210	C₂²×D₈₉	—	8	2	no	—
211	C₂²×D₈₉	#127	1	1	yes	characteristic
212	Q₈×C₈₉	—	4	2	no	—
213	Q₈×C₈₉	—	4	2	no	—
214	D₄×C₈₉	—	4	2	no	—
215	D₄×C₈₉	—	4	2	no	—
216	D₄×C₈₉	—	4	2	no	—
217	D₄×C₈₉	—	4	2	no	—
218	D₄×C₈₉	—	4	2	no	—
219	D₄×C₈₉	—	4	2	no	—
220	C₂×C₄×C₈₉	—	4	1	no	—
221	C₂×C₄×C₈₉	—	4	1	no	—
222	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
225	C₂²⋊D₈₉	—	8	2	no	—
226	C₂²⋊D₈₉	—	8	2	no	—
227	C₂²⋊D₈₉	—	8	2	no	—
228	C₂²⋊D₈₉	—	8	2	no	—
229	C₂×Dic₈₉	—	4	1	no	—
230	C₂×Dic₈₉	—	4	1	no	—
231	C₂×Dic₈₉	—	4	1	no	—
232	C₂×Dic₈₉	—	8	2	no	—
233	C₂×Dic₈₉	#127	1	1	yes	characteristic
234	C₂×Dic₈₉	#127	1	1	yes	characteristic
235	C₂×Dic₈₉	#127	1	1	yes	characteristic
236	D₃₅₆	—	4	2	no	—
237	D₃₅₆	—	4	2	no	—
238	D₃₅₆	—	4	2	no	—
239	C₄×D₈₉	—	2	2	no	—
240	C₄×D₈₉	—	2	2	no	—
241	C₄×D₈₉	—	8	2	no	—
242	C₄×D₈₉	C₂×SD₁₆	1	4	yes	—
243	Dic₁₇₈	—	4	2	no	—
244	Dic₁₇₈	—	4	2	no	—
245	Dic₁₇₈	—	4	2	no	—
246	Dic₁₇₈	—	8	2	no	—
247	C₈×C₈₉	—	2	2	no	—
248	C₈×C₈₉	—	2	2	no	—
249	C₈×C₈₉	C₂×SD₁₆	1	4	yes	complemented
250	#10623494	—	2	2	no	—
251	#10623494	C₂×SD₁₆	1	4	yes	complemented
252	#10623494	AGL(1,ℤ/8)	1	4	yes	complemented
253	C₂²×C₈₉	—	8	1	no	—
254	C₂²×C₈₉	—	8	1	no	—
255	C₂²×C₈₉	—	8	1	no	—
256	C₂²×C₈₉	—	8	1	no	—
257	C₂²×C₈₉	—	8	1	no	—
258	C₂²×C₈₉	—	8	1	no	—
259	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
260	C₂×D₈₉	—	2	1	no	—
261	C₂×D₈₉	—	2	1	no	—
262	C₂×D₈₉	—	8	1	no	—
263	C₂×D₈₉	—	8	1	no	—
264	C₂×D₈₉	—	8	1	no	—
265	C₂×D₈₉	—	16	4	no	—
266	C₂×D₈₉	#492	1	2	yes	—
267	C₄×C₈₉	—	8	1	no	—
268	C₄×C₈₉	—	8	1	no	—
269	C₄×C₈₉	C₂²×SD₁₆	1	2	yes	—
270	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
271	C₄×C₈₉	#577	1	2	yes	—
272	Dic₈₉	—	2	1	no	—
273	Dic₈₉	—	2	1	no	—
274	Dic₈₉	—	8	1	no	—
275	Dic₈₉	—	8	1	no	—
276	Dic₈₉	—	8	1	no	—
277	Dic₈₉	#492	1	2	yes	—
278	#19621	—	89	1	no	maximal, Sylow
279	C₂×C₈₉	—	16	1	no	—
280	C₂×C₈₉	—	16	1	no	—
281	C₂×C₈₉	C₂×#492	1	1	yes	characteristic
282	C₂×C₈₉	#3151	1	1	yes	characteristic
283	C₂×C₈₉	#3154	1	1	yes	characteristic
284	D₈₉	—	2	2	no	—
285	D₈₉	—	16	1	no	—
286	#3227	—	89	1	no	—
287	#3208	—	89	1	no	—
288	#3167	—	89	1	no	—
289	#3165	—	89	1	no	—
290	#3151	—	89	1	no	—
291	C₂×#492	—	89	1	no	—
292	#1715	—	89	1	no	—
293	#1715	D₈₉	1	1	yes	characteristic, complemented
294	#1714	—	89	1	no	—
295	#1714	—	89	1	no	—
296	#1706	—	89	1	no	—
297	#1706	—	89	1	no	—
298	#1705	—	89	1	no	—
299	#1705	—	89	1	no	—
300	C₈×M₁₆	—	89	1	no	—
301	C₈₉	#19621	1	1	yes	characteristic, complemented, Sylow
302	C₂×AGL(1,ℤ/8)	—	178	2	no	—
303	C₂²×SD₁₆	—	178	2	no	—
304	#533	—	89	1	no	—
305	#532	—	89	1	no	—
306	C₂×C₄⋊Q₈	—	89	1	no	—
307	C₂×#127	—	89	1	no	—
308	#501	—	178	2	no	—
309	#500	—	89	1	no	—
310	#500	—	89	1	no	—
311	#498	—	89	1	no	—
312	#498	—	89	1	no	—
313	#498	—	89	1	no	—
314	#498	—	89	1	no	—
315	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
316	#496	—	178	2	no	—
317	#493	—	89	1	no	—
318	#493	C₂×D₈₉	1	1	yes	characteristic
319	#492	—	89	1	no	—
320	#492	—	89	1	no	—
321	#492	—	89	1	no	—
322	#492	—	89	1	no	—
323	#492	—	89	1	no	—
324	#492	—	89	1	no	—
325	#492	—	89	1	no	—
326	#492	—	178	2	no	—
327	#492	C₂×D₈₉	1	1	yes	characteristic
328	#492	C₂×D₈₉	1	1	yes	characteristic
329	#487	—	89	1	no	—
330	#486	—	89	1	no	—
331	#486	—	89	1	no	—
332	#486	—	89	1	no	—
333	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
334	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
335	#481	—	178	2	no	—
336	#476	—	178	2	no	—
337	#465	—	178	2	no	—
338	#460	—	178	2	no	—
339	#450	—	178	2	no	—
340	C₄×SD₁₆	—	178	2	no	—
341	#431	—	89	1	no	—
342	#428	—	178	2	no	—
343	C₄×M₁₆	—	89	1	no	—
344	C₂×C₄×C₈	—	89	1	no	—
345	#322	—	89	1	no	—
346	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
347	C₈²	—	89	1	no	—
348	C₈²	—	89	1	no	—
349	C₂×#41	—	178	1	no	—
350	C₂²×Q₈	—	178	1	no	—
351	C₂²×D₄	—	178	1	no	—
352	C₂²×D₄	—	178	1	no	—
353	C₂²×D₄	—	178	1	no	—
354	AGL(1,ℤ/8)	—	356	8	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×SD₁₆	—	356	8	no	—
358	C₂×SD₁₆	—	178	2	no	—
359	C₂×SD₁₆	—	178	2	no	—
360	C₂×SD₁₆	—	178	2	no	—
361	C₂×SD₁₆	—	178	2	no	—
362	C₂×SD₁₆	—	178	2	no	—
363	C₂×SD₁₆	—	178	2	no	—
364	C₂×SD₁₆	—	178	2	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	—	178	2	no	—
367	C₂×M₁₆	—	89	2	no	—
368	C₂²×C₈	—	89	2	no	—
369	C₄⋊Q₈	—	89	1	no	—
370	C₄⋊Q₈	—	89	1	no	—
371	C₄⋊Q₈	—	89	1	no	—
372	C₄⋊Q₈	—	178	1	no	—
373	C₄⋊Q₈	—	178	1	no	—
374	C₄⋊Q₈	—	178	1	no	—
375	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
376	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
377	#127	—	89	1	no	—
378	#127	—	178	1	no	—
379	#127	—	178	1	no	—
380	#127	—	178	1	no	—
381	#127	C₂²×D₈₉	1	1	yes	characteristic
382	#127	C₂²×D₈₉	1	1	yes	characteristic
383	#125	—	178	1	no	—
384	#124	—	178	1	no	—
385	C₂²⋊Q₈	—	178	1	no	—
386	C₂²⋊Q₈	—	178	1	no	—
387	#121	—	178	1	no	—
388	#121	—	178	1	no	—
389	C₄×Q₈	—	178	1	no	—
390	C₄×Q₈	—	178	1	no	—
391	C₄×D₄	—	178	1	no	—
392	C₄×D₄	—	178	1	no	—
393	#117	—	178	1	no	—
394	C₂×C₄⋊C₄	—	178	1	no	—
395	C₂×C₄⋊C₄	—	178	1	no	—
396	C₂×C₄²	—	89	1	no	—
397	#107	—	178	2	no	—
398	#107	—	178	2	no	—
399	#106	—	2	2	no	—
400	#106	—	178	2	no	—
401	#106	—	178	2	no	—
402	#106	—	178	2	no	—
403	#106	—	178	2	no	—
404	C₄⋊C₈	—	89	2	no	—
405	#103	—	178	2	no	—
406	#102	—	2	2	no	—
407	#102	—	2	2	no	—
408	#102	—	178	2	no	—
409	#102	—	178	2	no	—
410	#102	—	178	2	no	—
411	C₂²⋊C₈	—	89	2	no	—
412	#97	—	89	2	no	—
413	C₄×C₈	—	89	2	no	—
414	C₄×C₈	—	89	1	no	—
415	C₄×C₈	—	89	1	no	—
416	C₄×C₈	—	89	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	C₂⁴	—	356	1	no	—
421	#41	—	356	4	no	—
422	C₂×Q₈	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	356	1	no	—
425	C₂×Q₈	—	356	4	no	—
426	C₂×Q₈	—	178	1	no	—
427	C₂×Q₈	—	178	1	no	—
428	C₂×Q₈	—	178	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	356	4	no	—
436	C₂×D₄	—	356	1	no	—
437	C₂×D₄	—	356	1	no	—
438	C₂×D₄	—	356	1	no	—
439	C₂×D₄	—	356	1	no	—
440	C₂×D₄	—	356	4	no	—
441	C₂×D₄	—	178	1	no	—
442	C₂×D₄	—	178	1	no	—
443	C₂×D₄	—	178	1	no	—
444	C₂×D₄	—	712	2	no	—
445	C₂²×C₄	—	89	1	no	—
446	C₂²×C₄	—	89	1	no	—
447	C₂²×C₄	—	89	1	no	—
448	C₂²×C₄	—	356	1	no	—
449	C₂²×C₄	—	356	1	no	—
450	SD₁₆	—	4	4	no	—
451	SD₁₆	—	8	2	no	—
452	SD₁₆	—	356	4	no	—
453	SD₁₆	—	356	4	no	—
454	SD₁₆	—	356	4	no	—
455	SD₁₆	—	356	4	no	—
456	SD₁₆	—	356	4	no	—
457	SD₁₆	—	356	4	no	—
458	SD₁₆	—	712	2	no	—
459	D₈	—	4	4	no	—
460	D₈	—	356	4	no	—
461	M₁₆	—	89	8	no	—
462	C₂×C₈	—	89	2	no	—
463	C₂×C₈	—	89	2	no	—
464	C₂×C₈	—	89	2	no	—
465	C₂×C₈	—	178	4	no	—
466	C₂×C₈	D₄×D₈₉	1	2	yes	—
467	C₂×C₈	D₄×D₈₉	1	2	yes	—
468	C₂×C₈	D₄×D₈₉	1	2	yes	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	356	1	no	—
474	C₄⋊C₄	—	356	1	no	—
475	C₄⋊C₄	—	356	1	no	—
476	C₄⋊C₄	—	356	1	no	—
477	C₄⋊C₄	—	178	1	no	—
478	C₄⋊C₄	—	178	1	no	—
479	C₄⋊C₄	—	178	1	no	—
480	C₄⋊C₄	—	178	1	no	—
481	C₄⋊C₄	—	178	1	no	—
482	C₄⋊C₄	—	178	1	no	—
483	C₂²⋊C₄	—	356	1	no	—
484	C₂²⋊C₄	—	356	1	no	—
485	C₂²⋊C₄	—	356	1	no	—
486	C₄²	—	89	1	no	—
487	C₄²	—	89	1	no	—
488	C₄²	—	89	1	no	—
489	C₄²	—	356	1	no	—
490	C₄²	C₂³×D₈₉	1	1	yes	characteristic
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	89	1	no	—
494	C₂³	—	356	1	no	—
495	C₂³	—	712	2	no	—
496	C₂³	—	712	2	no	—
497	C₂³	—	712	2	no	—
498	Q₈	—	4	2	no	—
499	Q₈	—	4	2	no	—
500	Q₈	—	356	2	no	—
501	Q₈	—	356	2	no	—
502	Q₈	—	356	2	no	—
503	Q₈	—	712	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	356	2	no	—
511	D₄	—	356	2	no	—
512	D₄	—	356	2	no	—
513	D₄	—	712	2	no	—
514	D₄	—	712	2	no	—
515	D₄	—	712	2	no	—
516	D₄	—	712	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	89	1	no	—
520	C₂×C₄	—	89	4	no	—
521	C₂×C₄	—	89	1	no	—
522	C₂×C₄	—	89	1	no	—
523	C₂×C₄	—	356	1	no	—
524	C₂×C₄	—	356	1	no	—
525	C₂×C₄	—	356	1	no	—
526	C₂×C₄	—	178	2	no	—
527	C₂×C₄	—	178	2	no	—
528	C₂×C₄	—	712	2	no	—
529	C₂×C₄	—	712	2	no	—
530	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
532	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
533	C₈	—	2	2	no	—
534	C₈	—	2	2	no	—
535	C₈	—	89	4	no	—
536	C₈	—	89	4	no	—
537	C₈	—	178	2	no	—
538	C₈	SD₁₆×D₈₉	1	4	yes	complemented
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	89	2	no	—
546	C₂²	—	1424	4	no	—
547	C₂²	—	178	1	no	—
548	C₂²	—	178	1	no	—
549	C₂²	—	712	1	no	—
550	C₂²	—	712	1	no	—
551	C₂²	—	712	1	no	—
552	C₂²	#127×D₈₉	1	1	yes	characteristic
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	—	89	2	no	—
556	C₄	—	178	1	no	—
557	C₄	—	178	1	no	—
558	C₄	—	712	1	no	—
559	C₄	—	712	1	no	—
560	C₄	—	712	1	no	—
561	C₄	C₂×SD₁₆×D₈₉	1	2	yes	—
562	C₄	AGL(1,ℤ/8)×D₈₉	1	2	yes	—
563	C₄	#19152408	1	2	yes	—
564	C₂	—	16	1	no	—
565	C₂	—	16	1	no	—
566	C₂	—	1424	1	no	—
567	C₂	—	178	2	no	—
568	C₂	#492×D₈₉	1	1	yes	characteristic
569	C₂	#26030701	1	1	yes	characteristic
570	C₂	#26030725	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1715	C₂
socle	C₂²×C₈₉	C₂×#127
prime radical	#26030703	C₂
hypercenter	#1715	D₈₉
hypocenter	C₈₉	#19621
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1715

Complements

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

N	H ≅ G/N	type
1. #26031376	C₂	semidirect
2. #26031189	C₂	semidirect
3. #26030810	C₂	semidirect
4. #26030793	C₂	semidirect
6. #492×D₈₉	C₂	semidirect
7. #26019882	C₂	semidirect
8. #26019874	C₂	semidirect
9. #26019872	C₂	semidirect
10. #26019843	C₂	semidirect
11. #26019841	C₂	semidirect
12. #26019840	C₂	semidirect
13. #26019838	C₂	semidirect
14. #26018531	C₂	semidirect
15. C₈₉×#1715	C₂	semidirect
23. #19152003	C₂²	semidirect
24. #19152001	C₂²	semidirect
25. #19151996	C₂²	semidirect
26. #19151994	C₂²	semidirect
27. #19151994	C₂²	semidirect
28. #19151994	C₂²	semidirect
37. #19151970	C₂²	semidirect
39. #19151949	C₂²	semidirect
42. #19151944	C₂²	semidirect
53. #19151320	C₂²	semidirect
54. C₈×#10623494	C₂²	semidirect
55. C₈×#10623494	C₂²	semidirect
56. #498×C₈₉	C₂²	semidirect
60. #486×C₈₉	C₂²	semidirect
61. #486×C₈₉	C₂²	semidirect
62. #322×C₈₉	C₂²	semidirect
164. #13083557	SD₁₆	semidirect
249. C₈×C₈₉	C₂×SD₁₆	semidirect
251. #10623494	C₂×SD₁₆	semidirect
252. #10623494	AGL(1,ℤ/8)	semidirect
293. #1715	D₈₉	semidirect
301. C₈₉	#19621	semidirect
315. #498	C₂×D₈₉	semidirect
333. #486	C₂×D₈₉	semidirect
334. #486	C₂×D₈₉	semidirect
346. #322	C₂×D₈₉	semidirect
538. C₈	SD₁₆×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26031376	2
#26031189	2
#26030810	2
#26030793	2
#26030703	2
#492×D₈₉	2
#26019882	2
#26019874	2
#26019872	2
#26019843	2
#26019841	2
#26019840	2
#26019838	2
#26018531	2
C₈₉×#1715	2
#19621	89