Subgroups — #36525080

Order 22784.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030854	C₂	1	1	yes	maximal, characteristic
2	#26029396	C₂	1	1	yes	maximal, characteristic
3	#26029348	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019159	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019154	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019150	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019070	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊#10623494	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019055	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019016	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018709	C₂	1	1	yes	maximal, characteristic
13	#26018705	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×#13083557	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152152	C₂²	1	1	yes	characteristic
17	#19152130	C₂²	1	1	yes	characteristic
18	#19152005	C₄	1	1	yes	characteristic
19	#19151989	C₄	1	1	yes	characteristic
20	#19151965	C₄	1	1	yes	characteristic
21	#19151956	C₄	1	1	yes	characteristic
22	#19151857	C₄	1	1	yes	characteristic
23	#19151855	C₄	1	1	yes	characteristic
24	#19151843	C₄	1	1	yes	characteristic
25	#19151841	C₄	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	#19151728	C₂²	1	1	yes	characteristic
28	#19151726	—	2	1	no	—
29	#19151725	—	2	1	no	—
30	Q₈×#10623494	C₂²	1	1	yes	characteristic
31	#19151722	C₂²	1	1	yes	characteristic
32	#19151722	C₂²	1	1	yes	characteristic
33	C₄×Dic₃₅₆	C₂²	1	1	yes	characteristic
34	C₄×#13083564	C₂²	1	1	yes	characteristic
35	C₄×#13083562	C₂²	1	1	yes	characteristic
36	#19151674	—	2	1	no	—
37	#19151666	—	2	1	no	—
38	D₄×#10623494	C₂²	1	1	yes	characteristic
39	#19151660	—	2	1	no	—
40	#19151658	—	2	1	no	—
41	#19151656	—	2	1	no	—
42	#19151654	C₂²	1	1	yes	characteristic
43	#19151649	C₂²	1	1	yes	characteristic
44	#19151626	—	2	1	no	—
45	#19151620	C₂²	1	1	yes	characteristic
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	#19151348	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	#19151328	C₂²	1	1	yes	characteristic
55	#19151328	C₂²	1	1	yes	characteristic
56	D₄⋊#10623494	C₂²	1	1	yes	characteristic
57	#19151320	C₂²	1	1	yes	characteristic
58	#19151319	C₂²	1	1	yes	characteristic
59	C₈×#10623494	C₂²	1	1	yes	characteristic
60	#446×C₈₉	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	#436×C₈₉	C₂²	1	1	yes	characteristic
63	#334×C₈₉	C₂²	1	1	yes	characteristic
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	C₈²×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×#13083562	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083557	—	2	1	no	—
71	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083557	C₂×C₄	1	1	yes	characteristic
73	C₂²×#10623494	—	2	1	no	—
74	C₂×C₈×D₈₉	—	2	1	no	—
75	#15668011	C₂×C₄	1	1	yes	characteristic
76	#15668010	C₂×C₄	1	1	yes	characteristic
77	#15668005	—	2	1	no	—
78	#15668003	C₂×C₄	1	1	yes	characteristic
79	#15668002	—	2	1	no	—
80	#15667999	C₂×C₄	1	1	yes	characteristic
81	#15667994	—	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	#15667988	C₂×C₄	1	1	yes	characteristic
86	#15667983	C₂×C₄	1	1	yes	characteristic
87	C₄×Dic₁₇₈	—	2	1	no	—
88	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
89	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
90	C₄×C₂²⋊D₈₉	—	2	1	no	—
91	#15667971	—	2	1	no	—
92	#15667969	—	2	1	no	—
93	C₄²×D₈₉	C₂³	1	1	yes	characteristic
94	#15667946	C₂×C₄	1	1	yes	characteristic
95	#15667945	C₂×C₄	1	1	yes	characteristic
96	#15667943	C₂×C₄	1	1	yes	characteristic
97	C₄⋊#10623494	—	2	1	no	—
98	C₄⋊#10623494	C₂³	1	1	yes	characteristic
99	C₄⋊#10623494	C₂³	1	1	yes	characteristic
100	#15667941	—	2	1	no	—
101	#15667941	—	2	1	no	—
102	#15667941	—	2	1	no	—
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667941	D₄	1	1	yes	characteristic
106	#15667941	D₄	1	1	yes	characteristic
107	#15667937	C₂×C₄	1	1	yes	characteristic
108	#15667937	C₂×C₄	1	1	yes	characteristic
109	#15667936	C₂×C₄	1	1	yes	characteristic
110	#15667935	C₂×C₄	1	1	yes	characteristic
111	#15667935	C₂×C₄	1	1	yes	characteristic
112	#15667933	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊#10623494	—	2	1	no	—
114	#15667924	—	2	1	no	—
115	#15667924	D₄	1	1	yes	characteristic
116	#15667924	D₄	1	1	yes	characteristic
117	#15667922	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	#15667922	—	2	1	no	—
120	#15667922	C₂×C₄	1	1	yes	characteristic
121	#15667922	C₂×C₄	1	1	yes	characteristic
122	C₄×#10623494	—	2	1	no	—
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₄×#10623494	C₂³	1	1	yes	characteristic
125	C₄×#10623494	C₂³	1	1	yes	characteristic
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	—	2	1	no	—
128	C₈×Dic₈₉	—	2	1	no	—
129	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
130	C₂×M₁₆×C₈₉	—	2	1	no	—
131	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
133	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
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	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
139	C₂²⋊C₈×C₈₉	—	2	1	no	—
140	#97×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	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₈₉	—	2	1	no	—
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	—	2	2	no	—
152	#13083564	—	2	2	no	—
153	#13083562	—	2	2	no	—
154	#13083557	—	2	2	no	—
155	#13083557	—	2	2	no	—
156	#13083557	—	8	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	2	1	no	—
160	C₂×#10623494	—	8	1	no	—
161	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
162	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
163	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
164	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
165	C₈×D₈₉	—	4	2	no	—
166	C₄⋊Dic₈₉	—	2	1	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	C₂²⋊Dic₈₉	—	2	1	no	—
179	C₂²⋊Dic₈₉	—	2	1	no	—
180	C₂²⋊Dic₈₉	—	2	1	no	—
181	#13083551	—	2	1	no	—
182	#13083551	—	2	1	no	—
183	#13083551	—	2	1	no	—
184	C₄×Dic₈₉	—	2	1	no	—
185	C₄×Dic₈₉	—	2	1	no	—
186	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
187	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
188	C₄×Dic₈₉	#41	1	1	yes	characteristic
189	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	—	2	1	no	—
192	SD₁₆×C₈₉	—	2	2	no	—
193	M₁₆×C₈₉	—	8	1	no	—
194	C₂×C₈×C₈₉	—	2	1	no	—
195	C₂×C₈×C₈₉	—	2	1	no	—
196	C₂×C₈×C₈₉	—	2	1	no	—
197	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
198	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
199	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₈₉	—	2	1	no	—
205	C₄²×C₈₉	—	2	1	no	—
206	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
207	C₂³×C₈₉	—	2	1	no	—
208	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₈₉	—	2	1	no	—
210	Q₈×C₈₉	—	2	1	no	—
211	D₄×C₈₉	—	2	1	no	—
212	D₄×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	—	4	1	no	—
217	C₂×C₄×C₈₉	—	4	1	no	—
218	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
221	C₂²⋊D₈₉	—	8	1	no	—
222	C₂×Dic₈₉	—	2	1	no	—
223	C₂×Dic₈₉	—	2	1	no	—
224	C₂×Dic₈₉	—	2	1	no	—
225	C₂×Dic₈₉	—	2	1	no	—
226	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
227	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
228	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
229	C₄×D₈₉	—	2	1	no	—
230	C₄×D₈₉	—	2	1	no	—
231	C₄×D₈₉	—	2	1	no	—
232	C₄×D₈₉	—	2	1	no	—
233	C₄×D₈₉	—	4	1	no	—
234	Dic₁₇₈	—	2	1	no	—
235	Dic₁₇₈	—	2	1	no	—
236	Dic₁₇₈	—	2	1	no	—
237	Dic₁₇₈	—	2	1	no	—
238	Dic₁₇₈	—	8	1	no	—
239	C₈×C₈₉	—	2	2	no	—
240	C₈×C₈₉	—	2	1	no	—
241	C₈×C₈₉	—	2	1	no	—
242	C₈×C₈₉	—	2	1	no	—
243	C₈×C₈₉	—	4	1	no	—
244	C₈×C₈₉	—	4	1	no	—
245	C₈×C₈₉	#131	1	2	yes	—
246	#10623494	—	2	1	no	—
247	#10623494	—	2	1	no	—
248	#10623494	—	2	1	no	—
249	#10623494	—	4	1	no	—
250	#10623494	—	4	1	no	—
251	#10623494	—	4	1	no	—
252	#10623494	#131	1	2	yes	—
253	C₂²×C₈₉	—	4	1	no	—
254	C₂²×C₈₉	—	4	1	no	—
255	C₂²×C₈₉	—	4	1	no	—
256	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
257	C₂×D₈₉	—	2	1	no	—
258	C₂×D₈₉	—	2	1	no	—
259	C₂×D₈₉	—	2	1	no	—
260	C₄×C₈₉	—	2	1	no	—
261	C₄×C₈₉	—	4	1	no	—
262	C₄×C₈₉	—	4	1	no	—
263	C₄×C₈₉	—	4	1	no	—
264	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
265	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
266	C₄×C₈₉	#577	1	1	yes	characteristic
267	C₄×C₈₉	#578	1	1	yes	characteristic
268	Dic₈₉	—	2	1	no	—
269	Dic₈₉	—	2	1	no	—
270	Dic₈₉	—	2	1	no	—
271	Dic₈₉	—	4	1	no	—
272	Dic₈₉	—	4	1	no	—
273	Dic₈₉	—	4	1	no	—
274	Dic₈₉	—	4	1	no	—
275	#17969	—	89	1	no	maximal, Sylow
276	C₂×C₈₉	—	8	1	no	—
277	C₂×C₈₉	#2931	1	1	yes	characteristic
278	C₂×C₈₉	#2947	1	1	yes	characteristic
279	C₂×C₈₉	#2956	1	1	yes	characteristic
280	D₈₉	—	4	1	no	—
281	#3172	—	89	1	no	—
282	#2993	—	89	1	no	—
283	#2985	—	89	1	no	—
284	#1593	—	89	1	no	—
285	#1592	—	89	1	no	—
286	#1591	—	89	1	no	—
287	#1590	D₈₉	1	1	yes	characteristic, complemented
288	#1579	—	89	1	no	—
289	SD₁₆⋊C₈	—	89	1	no	—
290	C₈×Q₁₆	—	89	1	no	—
291	C₈×SD₁₆	—	89	1	no	—
292	#1569	—	89	1	no	—
293	#1494	—	89	1	no	—
294	#1493	—	89	1	no	—
295	C₈×M₁₆	—	89	1	no	—
296	C₈₉	#17969	1	1	yes	characteristic, complemented, Sylow
297	#533	—	89	1	no	—
298	#529	—	89	1	no	—
299	#501	—	89	1	no	—
300	#497	—	89	1	no	—
301	#491	—	89	1	no	—
302	#489	—	89	1	no	—
303	#470	—	89	1	no	—
304	#470	—	89	1	no	—
305	#468	—	89	1	no	—
306	#468	—	89	1	no	—
307	#446	—	89	1	no	—
308	#446	—	89	1	no	—
309	#446	—	178	1	no	—
310	#446	—	178	1	no	—
311	#446	C₂×D₈₉	1	1	yes	characteristic
312	C₈×Q₈	—	89	1	no	—
313	C₈×Q₈	—	89	1	no	—
314	C₈×Q₈	—	89	1	no	—
315	C₄×Q₁₆	—	89	1	no	—
316	C₄×Q₁₆	—	89	1	no	—
317	C₄×SD₁₆	—	89	1	no	—
318	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
319	#436	—	178	1	no	—
320	#436	C₂×D₈₉	1	1	yes	characteristic
321	#435	—	178	1	no	—
322	C₈×D₄	—	89	1	no	—
323	#433	—	178	1	no	—
324	#433	—	178	1	no	—
325	#433	—	178	1	no	—
326	#432	—	89	1	no	—
327	#431	—	89	1	no	—
328	#424	—	178	1	no	—
329	#423	—	89	1	no	—
330	C₄×M₁₆	—	89	1	no	—
331	C₂×C₄×C₈	—	89	1	no	—
332	#335	—	89	1	no	—
333	#335	—	89	1	no	—
334	#334	—	89	1	no	—
335	#334	C₂×D₈₉	1	1	yes	characteristic
336	Q₈⋊C₈	—	89	1	no	—
337	Q₈⋊C₈	—	89	1	no	—
338	Q₈⋊C₈	—	89	1	no	—
339	Q₈⋊C₈	—	89	1	no	—
340	Q₈⋊C₈	—	89	1	no	—
341	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
342	D₄⋊C₈	—	89	1	no	—
343	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
344	#322	—	89	1	no	—
345	#322	—	89	1	no	—
346	C₈²	—	89	1	no	—
347	C₈²	C₂×D₈₉	1	1	yes	characteristic
348	C₂×Q₁₆	—	89	1	no	—
349	C₂×Q₁₆	—	89	1	no	—
350	C₂×SD₁₆	—	89	1	no	—
351	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	89	1	no	—
354	C₂×M₁₆	—	89	1	no	—
355	C₂×M₁₆	—	178	1	no	—
356	C₂²×C₈	—	178	1	no	—
357	C₂²×C₈	—	178	1	no	—
358	C₄⋊Q₈	—	89	1	no	—
359	C₄⋊Q₈	—	89	1	no	—
360	#126	—	178	1	no	—
361	#125	—	89	1	no	—
362	#125	—	178	1	no	—
363	#124	—	89	1	no	—
364	#123	—	178	1	no	—
365	C₂²⋊Q₈	—	89	1	no	—
366	C₂²⋊Q₈	—	89	1	no	—
367	C₂²⋊Q₈	—	89	1	no	—
368	C₂²⋊Q₈	—	178	1	no	—
369	#121	—	89	1	no	—
370	C₄×Q₈	—	89	1	no	—
371	C₄×Q₈	—	89	1	no	—
372	C₄×Q₈	—	178	1	no	—
373	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
374	C₄×D₄	—	178	1	no	—
375	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
376	#117	—	178	1	no	—
377	#117	—	178	1	no	—
378	C₂×C₄²	—	89	1	no	—
379	#107	—	89	1	no	—
380	#107	—	89	1	no	—
381	#106	—	89	1	no	—
382	#106	C₄×D₈₉	1	1	yes	characteristic
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	89	1	no	—
385	C₄⋊C₈	—	89	1	no	—
386	C₄⋊C₈	—	89	1	no	—
387	C₄⋊C₈	—	89	1	no	—
388	C₄⋊C₈	—	178	1	no	—
389	C₄⋊C₈	—	178	1	no	—
390	C₄⋊C₈	—	178	1	no	—
391	C₄⋊C₈	—	178	1	no	—
392	C₄⋊C₈	—	178	1	no	—
393	C₄⋊C₈	—	178	1	no	—
394	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
396	#103	—	89	1	no	—
397	#103	—	89	1	no	—
398	#103	—	89	1	no	—
399	#103	—	89	1	no	—
400	#103	—	89	1	no	—
401	#103	C₄×D₈₉	1	1	yes	characteristic
402	#102	—	89	1	no	—
403	#102	C₄×D₈₉	1	1	yes	characteristic
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	89	1	no	—
406	C₂²⋊C₈	—	89	1	no	—
407	C₂²⋊C₈	—	178	1	no	—
408	C₂²⋊C₈	—	178	1	no	—
409	#97	—	2	1	no	—
410	#97	—	89	1	no	—
411	#97	—	89	1	no	—
412	#97	—	178	1	no	—
413	#97	—	178	1	no	—
414	#97	—	178	1	no	—
415	C₄×C₈	—	89	1	no	—
416	C₄×C₈	—	89	1	no	—
417	C₄×C₈	—	89	1	no	—
418	C₄×C₈	—	178	1	no	—
419	C₄×C₈	—	178	1	no	—
420	C₄×C₈	—	178	1	no	—
421	C₄×C₈	—	178	1	no	—
422	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
423	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
425	C₂×Q₈	—	89	1	no	—
426	C₂×Q₈	—	89	1	no	—
427	C₂×Q₈	—	178	1	no	—
428	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
429	C₂×D₄	—	178	1	no	—
430	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	89	1	no	—
433	C₂²×C₄	—	89	1	no	—
434	C₂²×C₄	—	89	1	no	—
435	Q₁₆	—	178	2	no	—
436	Q₁₆	—	178	2	no	—
437	SD₁₆	—	2	2	no	—
438	SD₁₆	—	178	2	no	—
439	M₁₆	—	8	1	no	—
440	M₁₆	—	178	2	no	—
441	M₁₆	—	178	2	no	—
442	M₁₆	—	712	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	89	1	no	—
447	C₂×C₈	—	89	1	no	—
448	C₂×C₈	—	89	1	no	—
449	C₂×C₈	—	89	1	no	—
450	C₂×C₈	—	356	2	no	—
451	C₂×C₈	—	178	1	no	—
452	C₂×C₈	—	178	1	no	—
453	C₂×C₈	—	178	1	no	—
454	C₂×C₈	—	712	1	no	—
455	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
456	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
457	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
458	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	89	1	no	—
461	C₄⋊C₄	—	89	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	—	178	1	no	—
470	C₄⋊C₄	—	178	1	no	—
471	C₄⋊C₄	—	178	1	no	—
472	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
473	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	178	1	no	—
476	C₂²⋊C₄	—	178	1	no	—
477	C₂²⋊C₄	—	178	1	no	—
478	C₂²⋊C₄	—	178	1	no	—
479	C₂²⋊C₄	—	178	1	no	—
480	C₂²⋊C₄	—	178	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	89	1	no	—
483	C₄²	—	89	1	no	—
484	C₄²	—	89	1	no	—
485	C₄²	—	178	1	no	—
486	C₄²	—	178	1	no	—
487	C₄²	C₂³×D₈₉	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	—	89	1	no	—
490	Q₈	—	2	1	no	—
491	Q₈	—	2	1	no	—
492	Q₈	—	178	1	no	—
493	Q₈	—	178	1	no	—
494	Q₈	—	178	1	no	—
495	Q₈	—	178	1	no	—
496	Q₈	—	712	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	2	1	no	—
499	D₄	—	712	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	89	1	no	—
506	C₂×C₄	—	89	1	no	—
507	C₂×C₄	—	89	1	no	—
508	C₂×C₄	—	356	1	no	—
509	C₂×C₄	—	178	1	no	—
510	C₂×C₄	—	178	1	no	—
511	C₂×C₄	—	178	1	no	—
512	C₂×C₄	—	178	1	no	—
513	C₂×C₄	—	178	1	no	—
514	C₂×C₄	—	178	1	no	—
515	C₂×C₄	—	178	1	no	—
516	C₂×C₄	—	178	1	no	—
517	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
518	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
519	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
520	C₈	—	2	2	no	—
521	C₈	—	2	1	no	—
522	C₈	—	2	1	no	—
523	C₈	—	2	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	89	2	no	—
527	C₈	—	356	1	no	—
528	C₈	—	356	1	no	—
529	C₈	—	356	1	no	—
530	C₈	—	178	1	no	—
531	C₈	—	178	1	no	—
532	C₈	—	178	1	no	—
533	C₈	#15668020	1	2	yes	—
534	C₂²	—	4	1	no	—
535	C₂²	—	4	1	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	178	1	no	—
538	C₂²	—	178	1	no	—
539	C₂²	—	178	1	no	—
540	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
541	C₄	—	2	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	356	1	no	—
546	C₄	—	356	1	no	—
547	C₄	—	356	1	no	—
548	C₄	—	356	1	no	—
549	C₄	—	178	1	no	—
550	C₄	—	178	1	no	—
551	C₄	—	178	1	no	—
552	C₄	#131×D₈₉	1	1	yes	characteristic
553	C₄	C₂×#15668020	1	1	yes	characteristic
554	C₄	#19152404	1	1	yes	characteristic
555	C₄	#19152412	1	1	yes	characteristic
556	C₂	—	8	1	no	—
557	C₂	—	356	1	no	—
558	C₂	#26028961	1	1	yes	characteristic
559	C₂	#26029088	1	1	yes	characteristic
560	C₂	#26029157	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×#1590	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667983	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1590	D₈₉
hypocenter	C₈₉	#17969
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1590

Complements

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

N	H ≅ G/N	type
3. #26029348	C₂	semidirect
4. #26019159	C₂	semidirect
5. #26019154	C₂	semidirect
6. #26019150	C₂	semidirect
7. #26019070	C₂	semidirect
8. SD₁₆⋊#10623494	C₂	semidirect
9. #26019056	C₂	semidirect
10. #26019055	C₂	semidirect
11. #26019016	C₂	semidirect
13. #26018705	C₂	semidirect
14. C₈×#13083557	C₂	semidirect
15. C₈₉×#1590	C₂	semidirect
287. #1590	D₈₉	semidirect
296. C₈₉	#17969	semidirect

Maximal subgroups

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

subgroup	index
#26030854	2
#26029396	2
#26029348	2
#26019159	2
#26019154	2
#26019150	2
#26019070	2
SD₁₆⋊#10623494	2
#26019056	2
#26019055	2
#26019016	2
#26018709	2
#26018705	2
C₈×#13083557	2
C₈₉×#1590	2
#17969	89