Subgroups — #36524964

Order 22784.

630 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030818	C₂	1	1	yes	maximal, characteristic
2	#26029230	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029226	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019147	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019144	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019135	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019056	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019051	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019044	C₂	1	1	yes	maximal, characteristic, complemented
11	#26019012	C₂	1	1	yes	maximal, characteristic, complemented
12	#26018711	C₂	1	1	yes	maximal, characteristic, complemented
13	#26018709	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈²×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1590	C₂	1	1	yes	maximal, characteristic, complemented
16	#19152135	C₂²	1	1	yes	characteristic
17	#19152130	C₂²	1	1	yes	characteristic
18	#19151998	C₄	1	1	yes	characteristic
19	#19151979	C₄	1	1	yes	characteristic
20	#19151954	C₄	1	1	yes	characteristic
21	#19151951	C₄	1	1	yes	characteristic
22	#19151838	C₄	1	1	yes	characteristic
23	#19151833	C₄	1	1	yes	characteristic
24	#19151828	C₄	1	1	yes	characteristic
25	#19151824	C₄	1	1	yes	characteristic
26	#19151728	C₂²	1	1	yes	characteristic
27	Q₈×#10623494	C₂²	1	1	yes	characteristic
28	#19151722	C₂²	1	1	yes	characteristic
29	C₄×#13083564	C₂²	1	1	yes	characteristic
30	C₄×#13083563	C₂²	1	1	yes	characteristic
31	C₄×#13083559	C₂²	1	1	yes	characteristic
32	#19151677	C₂²	1	1	yes	characteristic
33	#19151671	—	2	1	no	—
34	#19151667	—	2	1	no	—
35	D₄×#10623494	C₂²	1	1	yes	characteristic
36	#19151663	—	2	1	no	—
37	#19151663	C₂²	1	1	yes	characteristic
38	#19151661	—	2	1	no	—
39	#19151658	—	2	1	no	—
40	#19151656	—	2	1	no	—
41	#19151654	C₂²	1	1	yes	characteristic
42	#19151654	C₂²	1	1	yes	characteristic
43	#19151556	—	2	1	no	—
44	#19151555	—	2	1	no	—
45	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151350	C₂²	1	1	yes	characteristic
49	#19151350	C₂²	1	1	yes	characteristic
50	#19151349	C₂²	1	1	yes	characteristic
51	#19151330	C₂²	1	1	yes	characteristic
52	Q₈⋊#10623494	C₂²	1	1	yes	characteristic
53	#19151328	C₂²	1	1	yes	characteristic
54	#19151327	C₂²	1	1	yes	characteristic
55	D₄⋊#10623494	C₂²	1	1	yes	characteristic
56	#19151325	C₂²	1	1	yes	characteristic
57	C₈×#10623494	C₂²	1	1	yes	characteristic
58	C₈×#10623494	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×#13083564	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
69	C₂×#13083559	C₂×C₄	1	1	yes	characteristic
70	C₂×#13083557	—	2	1	no	—
71	C₂²×#10623494	—	2	1	no	—
72	C₂×C₈×D₈₉	—	2	1	no	—
73	C₂×C₈×D₈₉	—	2	1	no	—
74	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
77	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
78	#15668007	—	2	1	no	—
79	#15668005	—	2	1	no	—
80	#15668003	C₂×C₄	1	1	yes	characteristic
81	#15668003	C₂×C₄	1	1	yes	characteristic
82	#15668001	C₂×C₄	1	1	yes	characteristic
83	#15667999	C₂×C₄	1	1	yes	characteristic
84	#15667997	—	2	1	no	—
85	#15667994	—	2	1	no	—
86	#15667992	C₂×C₄	1	1	yes	characteristic
87	#15667988	C₂×C₄	1	1	yes	characteristic
88	#15667987	C₂×C₄	1	1	yes	characteristic
89	#15667983	C₂×C₄	1	1	yes	characteristic
90	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
91	C₄×D₃₅₆	—	2	1	no	—
92	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
93	C₄×C₂²⋊D₈₉	—	2	1	no	—
94	#15667971	—	2	1	no	—
95	#15667969	—	2	1	no	—
96	C₄²×D₈₉	C₂³	1	1	yes	characteristic
97	#15667945	C₂×C₄	1	1	yes	characteristic
98	#15667945	C₂×C₄	1	1	yes	characteristic
99	#15667944	C₂×C₄	1	1	yes	characteristic
100	C₄⋊#10623494	—	2	1	no	—
101	C₄⋊#10623494	C₂³	1	1	yes	characteristic
102	C₄⋊#10623494	C₂³	1	1	yes	characteristic
103	#15667941	—	2	1	no	—
104	#15667941	—	2	1	no	—
105	#15667937	C₂×C₄	1	1	yes	characteristic
106	#15667936	C₂×C₄	1	1	yes	characteristic
107	#15667935	C₂×C₄	1	1	yes	characteristic
108	#15667934	C₂×C₄	1	1	yes	characteristic
109	#15667933	C₂×C₄	1	1	yes	characteristic
110	#15667932	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊#10623494	—	2	1	no	—
112	#15667924	—	2	1	no	—
113	#15667924	—	2	1	no	—
114	#15667924	—	2	1	no	—
115	#15667924	—	2	1	no	—
116	#15667922	—	2	1	no	—
117	#15667922	—	2	1	no	—
118	#15667922	—	2	1	no	—
119	C₄×#10623494	—	2	1	no	—
120	C₄×#10623494	C₂³	1	1	yes	characteristic
121	C₄×#10623494	C₂³	1	1	yes	characteristic
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₈×Dic₈₉	—	2	1	no	—
124	C₈×Dic₈₉	—	2	1	no	—
125	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
127	C₈×Dic₈₉	D₄	1	1	yes	characteristic
128	C₈×Dic₈₉	D₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₃₅₆	—	2	1	no	—
146	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₂²⋊D₈₉	—	2	1	no	—
148	C₂×C₄×D₈₉	—	2	1	no	—
149	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
152	#13083564	—	2	2	no	—
153	#13083563	—	2	2	no	—
154	#13083559	—	2	2	no	—
155	#13083557	—	4	2	no	—
156	C₂×#10623494	—	2	1	no	—
157	C₂×#10623494	—	2	1	no	—
158	C₂×#10623494	—	2	1	no	—
159	C₂×#10623494	—	4	2	no	—
160	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
161	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
162	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
163	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
164	C₈×D₈₉	—	2	4	no	—
165	C₈×D₈₉	—	2	2	no	—
166	C₈×D₈₉	—	2	2	no	—
167	C₈×D₈₉	—	2	2	no	—
168	C₈×D₈₉	—	2	2	no	—
169	C₈×D₈₉	—	4	2	no	—
170	C₄⋊Dic₈₉	—	2	1	no	—
171	C₄⋊Dic₈₉	—	2	1	no	—
172	C₄⋊Dic₈₉	—	2	1	no	—
173	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
175	#13083553	—	2	1	no	—
176	#13083553	—	2	1	no	—
177	#13083553	—	2	1	no	—
178	#13083553	—	2	1	no	—
179	C₂²⋊Dic₈₉	—	2	1	no	—
180	C₂²⋊Dic₈₉	—	2	1	no	—
181	C₂²⋊Dic₈₉	—	2	1	no	—
182	#13083551	—	2	1	no	—
183	#13083551	—	2	1	no	—
184	#13083551	—	2	1	no	—
185	#13083551	—	2	1	no	—
186	#13083551	—	2	1	no	—
187	#13083551	—	2	1	no	—
188	C₄×Dic₈₉	—	2	1	no	—
189	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
190	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₈₉	#41	1	1	yes	characteristic
192	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
193	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₈₉	—	2	1	no	—
195	SD₁₆×C₈₉	—	2	2	no	—
196	M₁₆×C₈₉	—	4	2	no	—
197	C₂×C₈×C₈₉	—	2	1	no	—
198	C₂×C₈×C₈₉	—	2	1	no	—
199	C₂×C₈×C₈₉	—	2	1	no	—
200	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
201	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
202	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₄⋊C₄×C₈₉	—	2	1	no	—
205	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
206	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
207	C₂²⋊C₄×C₈₉	—	2	1	no	—
208	C₄²×C₈₉	—	2	1	no	—
209	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
210	C₂³×C₈₉	—	2	1	no	—
211	C₂²×D₈₉	—	2	1	no	—
212	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₈₉	—	2	1	no	—
214	Q₈×C₈₉	—	2	1	no	—
215	D₄×C₈₉	—	2	1	no	—
216	D₄×C₈₉	—	2	1	no	—
217	C₂×C₄×C₈₉	—	2	1	no	—
218	C₂×C₄×C₈₉	—	2	1	no	—
219	C₂×C₄×C₈₉	—	2	1	no	—
220	C₂×C₄×C₈₉	—	4	1	no	—
221	C₂×C₄×C₈₉	—	4	1	no	—
222	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
225	C₂²⋊D₈₉	—	4	2	no	—
226	C₂×Dic₈₉	—	2	1	no	—
227	C₂×Dic₈₉	—	2	1	no	—
228	C₂×Dic₈₉	—	2	1	no	—
229	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
231	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
232	D₃₅₆	—	2	1	no	—
233	D₃₅₆	—	2	1	no	—
234	D₃₅₆	—	4	2	no	—
235	C₄×D₈₉	—	2	2	no	—
236	C₄×D₈₉	—	2	1	no	—
237	C₄×D₈₉	—	2	1	no	—
238	C₄×D₈₉	—	2	1	no	—
239	C₄×D₈₉	—	2	1	no	—
240	C₄×D₈₉	—	4	1	no	—
241	C₄×D₈₉	—	4	1	no	—
242	Dic₁₇₈	—	2	1	no	—
243	Dic₁₇₈	—	2	1	no	—
244	C₈×C₈₉	—	2	2	no	—
245	C₈×C₈₉	—	2	1	no	—
246	C₈×C₈₉	—	2	1	no	—
247	C₈×C₈₉	—	4	1	no	—
248	C₈×C₈₉	—	4	1	no	—
249	C₈×C₈₉	#131	1	2	yes	—
250	C₈×C₈₉	#135	1	2	yes	—
251	#10623494	—	2	2	no	—
252	#10623494	—	2	1	no	—
253	#10623494	—	2	1	no	—
254	#10623494	—	4	1	no	—
255	#10623494	—	4	1	no	—
256	#10623494	#131	1	2	yes	—
257	#10623494	#135	1	2	yes	—
258	C₂²×C₈₉	—	4	1	no	—
259	C₂²×C₈₉	—	4	1	no	—
260	C₂²×C₈₉	—	4	1	no	—
261	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂×D₈₉	—	2	1	no	—
263	C₂×D₈₉	—	2	1	no	—
264	C₂×D₈₉	—	4	1	no	—
265	C₂×D₈₉	—	4	1	no	—
266	C₂×D₈₉	—	4	1	no	—
267	C₂×D₈₉	#443	1	2	yes	—
268	C₄×C₈₉	—	2	1	no	—
269	C₄×C₈₉	—	4	1	no	—
270	C₄×C₈₉	—	4	1	no	—
271	C₄×C₈₉	—	4	1	no	—
272	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
273	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
274	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
275	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
276	Dic₈₉	—	2	1	no	—
277	Dic₈₉	—	2	1	no	—
278	Dic₈₉	—	2	1	no	—
279	Dic₈₉	—	4	1	no	—
280	Dic₈₉	—	4	1	no	—
281	Dic₈₉	—	4	1	no	—
282	#17959	—	89	1	no	maximal, Sylow
283	C₂×C₈₉	—	8	1	no	—
284	C₂×C₈₉	#2931	1	1	yes	characteristic
285	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
286	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
287	D₈₉	—	2	2	no	—
288	D₈₉	—	8	1	no	—
289	#3168	—	89	1	no	—
290	#2966	—	89	1	no	—
291	#2966	—	89	1	no	—
292	#1591	—	89	1	no	—
293	#1590	—	89	1	no	—
294	#1590	D₈₉	1	1	yes	characteristic, complemented
295	#1589	—	89	1	no	—
296	C₈×Q₁₆	—	89	1	no	—
297	C₈×SD₁₆	—	89	1	no	—
298	C₈×SD₁₆	—	89	1	no	—
299	C₈×D₈	—	89	1	no	—
300	#1568	—	89	1	no	—
301	#1494	—	89	1	no	—
302	#1494	—	89	1	no	—
303	C₂×C₈²	—	89	1	no	—
304	C₈₉	#17959	1	1	yes	characteristic, complemented, Sylow
305	#529	—	89	1	no	—
306	#529	—	89	1	no	—
307	#499	—	89	1	no	—
308	#495	—	89	1	no	—
309	#488	—	89	1	no	—
310	#488	—	89	1	no	—
311	#467	—	89	1	no	—
312	#466	—	89	1	no	—
313	#465	—	89	1	no	—
314	#465	—	89	1	no	—
315	#446	—	89	1	no	—
316	#446	C₂×D₈₉	1	1	yes	characteristic
317	C₈×Q₈	—	89	1	no	—
318	C₈×Q₈	—	89	1	no	—
319	C₄×Q₁₆	—	89	1	no	—
320	C₄×SD₁₆	—	89	1	no	—
321	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
322	C₄×D₈	—	89	1	no	—
323	#436	—	89	1	no	—
324	#436	C₂×D₈₉	1	1	yes	characteristic
325	#435	—	178	1	no	—
326	#435	—	178	1	no	—
327	C₈×D₄	—	89	1	no	—
328	C₈×D₄	—	89	1	no	—
329	C₈×D₄	—	178	1	no	—
330	C₈×D₄	—	178	1	no	—
331	#433	—	178	1	no	—
332	#433	—	178	1	no	—
333	#432	—	89	1	no	—
334	#432	—	89	1	no	—
335	#405	—	178	1	no	—
336	#405	—	178	1	no	—
337	C₂×C₄×C₈	—	89	1	no	—
338	C₂×C₄×C₈	—	89	1	no	—
339	C₂×C₄×C₈	—	89	1	no	—
340	#335	—	89	1	no	—
341	#335	—	89	1	no	—
342	#334	—	89	1	no	—
343	#334	C₂×D₈₉	1	1	yes	characteristic
344	Q₈⋊C₈	—	89	1	no	—
345	Q₈⋊C₈	—	89	1	no	—
346	Q₈⋊C₈	—	89	1	no	—
347	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic
348	D₄⋊C₈	—	89	1	no	—
349	D₄⋊C₈	—	89	1	no	—
350	D₄⋊C₈	—	89	1	no	—
351	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
352	C₈²	—	89	1	no	—
353	C₈²	—	89	1	no	—
354	C₈²	—	89	1	no	—
355	C₈²	C₂×D₈₉	1	1	yes	characteristic
356	C₂×Q₁₆	—	89	1	no	—
357	C₂×SD₁₆	—	89	1	no	—
358	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
359	C₂×D₈	—	89	1	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	178	1	no	—
362	C₂²×C₈	—	89	1	no	—
363	C₂²×C₈	—	89	1	no	—
364	C₂²×C₈	—	89	1	no	—
365	C₂²×C₈	—	89	1	no	—
366	C₂²×C₈	—	178	1	no	—
367	C₂²×C₈	—	178	1	no	—
368	C₂²×C₈	—	178	1	no	—
369	#126	—	178	1	no	—
370	#126	—	178	1	no	—
371	#125	—	89	1	no	—
372	#125	—	89	1	no	—
373	#124	—	89	1	no	—
374	#124	—	89	1	no	—
375	#123	—	178	1	no	—
376	#123	—	178	1	no	—
377	C₂²⋊Q₈	—	89	1	no	—
378	C₂²⋊Q₈	—	89	1	no	—
379	#121	—	89	1	no	—
380	#121	—	89	1	no	—
381	C₄×Q₈	—	89	1	no	—
382	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
383	C₄×D₄	—	89	1	no	—
384	C₄×D₄	—	178	1	no	—
385	C₄×D₄	—	178	1	no	—
386	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
387	#117	—	178	1	no	—
388	#117	—	178	1	no	—
389	C₂×C₄²	—	89	1	no	—
390	#107	—	89	1	no	—
391	#107	—	89	1	no	—
392	#106	—	89	1	no	—
393	#106	C₄×D₈₉	1	1	yes	characteristic
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	89	1	no	—
396	C₄⋊C₈	—	89	1	no	—
397	C₄⋊C₈	—	178	1	no	—
398	C₄⋊C₈	—	178	1	no	—
399	C₄⋊C₈	—	178	1	no	—
400	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
401	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
402	#103	—	89	1	no	—
403	#103	—	89	1	no	—
404	#103	—	89	1	no	—
405	#103	C₄×D₈₉	1	1	yes	characteristic
406	#102	—	89	1	no	—
407	#102	—	89	1	no	—
408	#102	—	89	1	no	—
409	#102	C₄×D₈₉	1	1	yes	characteristic
410	C₂²⋊C₈	—	2	1	no	—
411	C₂²⋊C₈	—	178	1	no	—
412	C₂²⋊C₈	—	178	1	no	—
413	C₂²⋊C₈	—	178	1	no	—
414	C₂²⋊C₈	—	178	1	no	—
415	C₂²⋊C₈	—	178	1	no	—
416	#97	—	2	1	no	—
417	#97	—	178	1	no	—
418	#97	—	178	1	no	—
419	#97	—	178	1	no	—
420	C₄×C₈	—	89	1	no	—
421	C₄×C₈	—	89	1	no	—
422	C₄×C₈	—	89	1	no	—
423	C₄×C₈	—	89	1	no	—
424	C₄×C₈	—	89	1	no	—
425	C₄×C₈	—	89	1	no	—
426	C₄×C₈	—	89	1	no	—
427	C₄×C₈	—	178	1	no	—
428	C₄×C₈	—	178	1	no	—
429	C₄×C₈	—	178	1	no	—
430	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
431	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
432	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
433	C₂×Q₈	—	89	1	no	—
434	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
435	C₂×D₄	—	89	1	no	—
436	C₂×D₄	—	178	1	no	—
437	C₂×D₄	—	178	1	no	—
438	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	89	1	no	—
441	C₂²×C₄	—	89	1	no	—
442	C₂²×C₄	—	89	1	no	—
443	C₂²×C₄	—	178	1	no	—
444	Q₁₆	—	178	2	no	—
445	SD₁₆	—	2	2	no	—
446	SD₁₆	—	178	2	no	—
447	D₈	—	178	2	no	—
448	M₁₆	—	4	2	no	—
449	M₁₆	—	356	2	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	89	1	no	—
454	C₂×C₈	—	89	1	no	—
455	C₂×C₈	—	89	1	no	—
456	C₂×C₈	—	89	1	no	—
457	C₂×C₈	—	356	2	no	—
458	C₂×C₈	—	356	2	no	—
459	C₂×C₈	—	178	2	no	—
460	C₂×C₈	—	178	2	no	—
461	C₂×C₈	—	178	4	no	—
462	C₂×C₈	—	178	1	no	—
463	C₂×C₈	—	178	1	no	—
464	C₂×C₈	—	178	1	no	—
465	C₂×C₈	—	178	2	no	—
466	C₂×C₈	—	178	2	no	—
467	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
468	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
469	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
470	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	89	1	no	—
473	C₄⋊C₄	—	89	1	no	—
474	C₄⋊C₄	—	178	1	no	—
475	C₄⋊C₄	—	178	1	no	—
476	C₄⋊C₄	—	178	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	C₂×C₄×D₈₉	1	1	yes	characteristic
482	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	178	1	no	—
485	C₂²⋊C₄	—	178	1	no	—
486	C₂²⋊C₄	—	178	1	no	—
487	C₂²⋊C₄	—	178	1	no	—
488	C₂²⋊C₄	—	178	1	no	—
489	C₂²⋊C₄	—	178	1	no	—
490	C₂²⋊C₄	—	178	1	no	—
491	C₂²⋊C₄	—	178	1	no	—
492	C₂²⋊C₄	—	178	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	89	1	no	—
495	C₄²	—	89	1	no	—
496	C₄²	—	89	1	no	—
497	C₄²	—	178	1	no	—
498	C₄²	C₂³×D₈₉	1	1	yes	characteristic
499	C₂³	—	2	1	no	—
500	C₂³	—	89	1	no	—
501	C₂³	—	178	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	2	1	no	—
504	Q₈	—	178	1	no	—
505	Q₈	—	178	1	no	—
506	D₄	—	2	1	no	—
507	D₄	—	2	1	no	—
508	D₄	—	356	2	no	—
509	D₄	—	356	2	no	—
510	D₄	—	178	1	no	—
511	D₄	—	178	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	89	1	no	—
518	C₂×C₄	—	89	1	no	—
519	C₂×C₄	—	89	1	no	—
520	C₂×C₄	—	356	1	no	—
521	C₂×C₄	—	356	1	no	—
522	C₂×C₄	—	178	2	no	—
523	C₂×C₄	—	178	1	no	—
524	C₂×C₄	—	178	1	no	—
525	C₂×C₄	—	178	1	no	—
526	C₂×C₄	—	178	1	no	—
527	C₂×C₄	—	178	1	no	—
528	C₂×C₄	—	178	1	no	—
529	C₂×C₄	—	178	1	no	—
530	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
531	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
532	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
533	C₈	—	2	2	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	—	4	1	no	—
537	C₈	—	4	1	no	—
538	C₈	—	89	2	no	—
539	C₈	—	89	2	no	—
540	C₈	—	356	1	no	—
541	C₈	—	356	1	no	—
542	C₈	—	178	2	no	—
543	C₈	—	178	1	no	—
544	C₈	—	178	1	no	—
545	C₈	#15668020	1	2	yes	—
546	C₈	#15668033	1	2	yes	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	89	2	no	—
551	C₂²	—	356	1	no	—
552	C₂²	—	356	1	no	—
553	C₂²	—	356	1	no	—
554	C₂²	—	178	1	no	—
555	C₂²	—	178	1	no	—
556	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
557	C₄	—	2	1	no	—
558	C₄	—	4	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	356	1	no	—
562	C₄	—	356	1	no	—
563	C₄	—	356	1	no	—
564	C₄	—	178	1	no	—
565	C₄	—	178	1	no	—
566	C₄	—	178	1	no	—
567	C₄	#131×D₈₉	1	1	yes	characteristic
568	C₄	C₂×#15668020	1	1	yes	characteristic
569	C₄	#135×D₈₉	1	1	yes	characteristic
570	C₄	C₂×#15668033	1	1	yes	characteristic
571	C₂	—	8	1	no	—
572	C₂	—	178	2	no	—
573	C₂	—	712	1	no	—
574	C₂	#26028961	1	1	yes	characteristic
575	C₂	C₄×#15668033	1	1	yes	characteristic
576	C₂	#443×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×#1590	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19151833	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1590	D₈₉
hypocenter	C₈₉	#17959
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
2. #26029230	C₂	semidirect
3. #26029226	C₂	semidirect
4. #26019147	C₂	semidirect
5. #26019144	C₂	semidirect
6. #26019135	C₂	semidirect
7. #26019056	C₂	semidirect
8. SD₁₆×#10623494	C₂	semidirect
9. #26019051	C₂	semidirect
10. #26019044	C₂	semidirect
11. #26019012	C₂	semidirect
12. #26018711	C₂	semidirect
13. #26018709	C₂	semidirect
14. C₈²×D₈₉	C₂	semidirect
15. C₈₉×#1590	C₂	semidirect
294. #1590	D₈₉	semidirect
304. C₈₉	#17959	semidirect

Maximal subgroups

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

subgroup	index
#26030818	2
#26029230	2
#26029226	2
#26019147	2
#26019144	2
#26019135	2
#26019056	2
SD₁₆×#10623494	2
#26019051	2
#26019044	2
#26019012	2
#26018711	2
#26018709	2
C₈²×D₈₉	2
C₈₉×#1590	2
#17959	89