Subgroups — #36447867

Order 22784.

514 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26022657	C₂	1	1	yes	maximal, characteristic
2	#26020229	C₂	1	1	yes	maximal, characteristic
3	#26020229	C₂	1	1	yes	maximal, characteristic
4	#26018136	C₂	1	1	yes	maximal, characteristic, complemented
5	#26018136	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018135	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15667970	C₄	1	2	yes	—
9	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
12	C₂×#15667924	—	2	1	no	—
13	C₂×#15667924	—	2	1	no	—
14	#19151468	C₂²	1	1	yes	characteristic
15	#19151463	C₄	1	2	yes	—
16	#19151455	—	2	1	no	—
17	#19151455	—	2	1	no	—
18	C₄⋊C₄×Dic₈₉	—	2	1	no	—
19	C₄⋊C₄×Dic₈₉	—	2	1	no	—
20	#19151352	—	2	1	no	—
21	#19151352	—	2	1	no	—
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
24	#384×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
28	C₂²×#10623494	—	2	1	no	—
29	C₂²×#10623494	—	2	1	no	—
30	#15667970	—	4	4	no	—
31	C₂×C₄⋊Dic₈₉	—	2	1	no	—
32	C₂×C₄⋊Dic₈₉	—	2	1	no	—
33	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
34	C₂×#13083551	—	2	2	no	—
35	C₂×C₄×Dic₈₉	—	2	2	no	—
36	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
38	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
39	C₄²×D₈₉	—	2	1	no	—
40	C₄²×D₈₉	—	2	1	no	—
41	C₄²×D₈₉	—	2	1	no	—
42	C₄²×D₈₉	—	2	1	no	—
43	C₄⋊#10623494	—	2	1	no	—
44	C₄⋊#10623494	—	2	1	no	—
45	C₄⋊#10623494	—	2	1	no	—
46	C₄⋊#10623494	—	2	1	no	—
47	#15667924	—	4	2	no	—
48	#15667924	—	4	2	no	—
49	#15667919	—	2	2	no	—
50	#15667919	—	2	2	no	—
51	C₂²×C₈×C₈₉	—	2	1	no	—
52	C₂²×C₈×C₈₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
57	C₄⋊C₈×C₈₉	—	2	1	no	—
58	C₄⋊C₈×C₈₉	—	2	1	no	—
59	C₄⋊C₈×C₈₉	—	2	1	no	—
60	C₄⋊C₈×C₈₉	—	2	1	no	—
61	C₂³×D₈₉	C₂²⋊C₄	1	1	yes	characteristic
62	C₂²×Dic₈₉	—	2	2	no	—
63	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₄×D₈₉	—	2	2	no	—
67	C₂×C₄×D₈₉	—	2	1	no	—
68	C₂×C₄×D₈₉	—	2	1	no	—
69	C₂×C₄×D₈₉	—	2	2	no	—
70	C₂×C₄×D₈₉	—	2	1	no	—
71	C₂×C₄×D₈₉	—	2	1	no	—
72	C₂×C₄×D₈₉	—	2	1	no	—
73	C₂×C₄×D₈₉	—	2	1	no	—
74	C₂×C₄×D₈₉	—	2	1	no	—
75	C₂×C₄×D₈₉	—	2	1	no	—
76	C₂×C₄×D₈₉	—	2	1	no	—
77	C₂×C₄×D₈₉	—	2	1	no	—
78	C₂×C₄×D₈₉	—	2	1	no	—
79	C₂×C₄×D₈₉	—	2	1	no	—
80	C₂×C₄×D₈₉	—	2	1	no	—
81	C₂×C₄×D₈₉	—	2	1	no	—
82	C₂×#10623494	—	4	1	no	—
83	C₂×#10623494	—	4	1	no	—
84	C₂×#10623494	—	4	1	no	—
85	C₂×#10623494	—	4	1	no	—
86	C₂×#10623494	—	4	1	no	—
87	C₂×#10623494	—	4	1	no	—
88	C₄⋊Dic₈₉	—	4	1	no	—
89	C₄⋊Dic₈₉	—	4	1	no	—
90	C₄⋊Dic₈₉	—	4	1	no	—
91	C₄⋊Dic₈₉	—	4	1	no	—
92	C₄⋊Dic₈₉	—	4	2	no	—
93	#13083551	—	4	4	no	—
94	C₄×Dic₈₉	—	2	1	no	—
95	C₄×Dic₈₉	—	2	1	no	—
96	C₄×Dic₈₉	—	2	1	no	—
97	C₄×Dic₈₉	—	2	1	no	—
98	C₄×Dic₈₉	—	2	1	no	—
99	C₄×Dic₈₉	—	2	1	no	—
100	C₄×Dic₈₉	—	4	4	no	—
101	C₂²×C₄×C₈₉	—	2	2	no	—
102	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
105	C₂×C₈×C₈₉	—	4	1	no	—
106	C₂×C₈×C₈₉	—	4	1	no	—
107	C₂×C₈×C₈₉	—	4	1	no	—
108	C₂×C₈×C₈₉	—	4	1	no	—
109	C₂×C₈×C₈₉	—	4	1	no	—
110	C₂×C₈×C₈₉	—	4	1	no	—
111	C₄⋊C₄×C₈₉	—	4	2	no	—
112	C₄⋊C₄×C₈₉	—	4	1	no	—
113	C₄⋊C₄×C₈₉	—	4	1	no	—
114	C₄⋊C₄×C₈₉	—	4	1	no	—
115	C₄⋊C₄×C₈₉	—	4	1	no	—
116	C₄²×C₈₉	#41	1	1	yes	characteristic
117	C₄²×C₈₉	#41	1	1	yes	characteristic
118	C₄²×C₈₉	#41	1	1	yes	characteristic
119	C₄²×C₈₉	#41	1	1	yes	characteristic
120	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂²×D₈₉	—	2	1	no	—
122	C₂²×D₈₉	—	2	1	no	—
123	C₂²×D₈₉	—	2	1	no	—
124	C₂²×D₈₉	—	2	1	no	—
125	C₂²×D₈₉	—	2	1	no	—
126	C₂²×D₈₉	—	2	1	no	—
127	C₂²×D₈₉	#100	1	2	yes	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	4	2	no	—
131	C₂×C₄×C₈₉	—	4	2	no	—
132	C₂×C₄×C₈₉	—	4	2	no	—
133	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
134	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
135	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
136	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
137	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
138	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
139	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
140	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
141	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
142	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
143	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
144	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
146	C₂×C₄×C₈₉	#137	1	1	yes	characteristic
147	C₂×Dic₈₉	—	2	1	no	—
148	C₂×Dic₈₉	—	2	1	no	—
149	C₂×Dic₈₉	—	2	1	no	—
150	C₂×Dic₈₉	—	2	1	no	—
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	2	1	no	—
155	C₂×Dic₈₉	—	4	2	no	—
156	C₂×Dic₈₉	—	4	2	no	—
157	C₂×Dic₈₉	—	4	2	no	—
158	C₂×Dic₈₉	#101	1	2	yes	—
159	C₄×D₈₉	—	2	4	no	—
160	C₄×D₈₉	—	2	4	no	—
161	C₄×D₈₉	—	4	1	no	—
162	C₄×D₈₉	—	4	1	no	—
163	C₄×D₈₉	—	4	1	no	—
164	C₄×D₈₉	—	4	1	no	—
165	C₄×D₈₉	—	4	1	no	—
166	C₄×D₈₉	—	4	1	no	—
167	C₄×D₈₉	—	4	1	no	—
168	C₄×D₈₉	—	4	1	no	—
169	C₈×C₈₉	—	8	1	no	—
170	C₈×C₈₉	—	8	1	no	—
171	#10623494	—	8	1	no	—
172	#10623494	—	8	1	no	—
173	C₂²×C₈₉	#381	1	1	yes	characteristic
174	C₂²×C₈₉	C₂×#100	1	1	yes	characteristic
175	C₂²×C₈₉	C₂×#101	1	1	yes	characteristic
176	C₂²×C₈₉	#416	1	1	yes	characteristic
177	C₂²×C₈₉	#416	1	1	yes	characteristic
178	C₂²×C₈₉	#417	1	1	yes	characteristic
179	C₂²×C₈₉	#417	1	1	yes	characteristic
180	C₂×D₈₉	—	2	2	no	—
181	C₂×D₈₉	—	2	2	no	—
182	C₂×D₈₉	—	2	2	no	—
183	C₂×D₈₉	—	4	1	no	—
184	C₂×D₈₉	—	4	1	no	—
185	C₂×D₈₉	—	4	1	no	—
186	C₂×D₈₉	—	4	1	no	—
187	C₄×C₈₉	—	2	1	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	8	2	no	—
190	C₄×C₈₉	#482	1	1	yes	characteristic
191	C₄×C₈₉	#482	1	1	yes	characteristic
192	C₄×C₈₉	#482	1	1	yes	characteristic
193	C₄×C₈₉	#482	1	1	yes	characteristic
194	C₄×C₈₉	#485	1	1	yes	characteristic
195	C₄×C₈₉	#485	1	1	yes	characteristic
196	C₄×C₈₉	#485	1	1	yes	characteristic
197	C₄×C₈₉	#485	1	1	yes	characteristic
198	Dic₈₉	—	2	2	no	—
199	Dic₈₉	—	4	1	no	—
200	Dic₈₉	—	4	1	no	—
201	Dic₈₉	—	8	2	no	—
202	#8729	—	89	1	no	maximal, Sylow
203	C₂×C₈₉	#1544	1	1	yes	characteristic
204	C₂×C₈₉	#1551	1	1	yes	characteristic
205	C₂×C₈₉	#1551	1	1	yes	characteristic
206	C₂×C₈₉	#1561	1	1	yes	characteristic
207	C₂×C₈₉	#1821	1	1	yes	characteristic
208	C₂×C₈₉	#1825	1	1	yes	characteristic
209	C₂×C₈₉	#1825	1	1	yes	characteristic
210	D₈₉	—	4	2	no	—
211	#2285	—	89	1	no	—
212	#1797	—	89	1	no	—
213	#1797	—	89	1	no	—
214	#1296	—	89	1	no	—
215	#1296	—	89	1	no	—
216	#1296	—	89	1	no	—
217	#1296	D₈₉	1	1	yes	characteristic, complemented
218	C₈₉	#8729	1	1	yes	characteristic, complemented, Sylow
219	C₂×#117	—	89	2	no	—
220	C₂²×C₄²	—	89	1	no	—
221	C₂×C₄⋊C₈	—	89	1	no	—
222	C₂×C₄⋊C₈	—	89	1	no	—
223	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	—	178	1	no	—
226	C₂×C₂²⋊C₈	—	178	1	no	—
227	#384	—	89	1	no	—
228	#384	C₂×D₈₉	1	1	yes	characteristic
229	#382	—	89	2	no	—
230	#380	—	178	1	no	—
231	#380	—	178	1	no	—
232	C₄×C₄⋊C₄	—	178	1	no	—
233	C₄×C₄⋊C₄	—	178	1	no	—
234	#336	—	178	1	no	—
235	#336	—	178	1	no	—
236	C₂³×C₄	—	89	1	no	—
237	C₂³×C₄	—	89	1	no	—
238	C₂³×C₄	—	89	1	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	178	1	no	—
242	C₂²×C₈	—	178	1	no	—
243	#117	—	356	4	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	89	2	no	—
247	C₂×C₄⋊C₄	—	178	1	no	—
248	C₂×C₄⋊C₄	—	178	1	no	—
249	C₂×C₄⋊C₄	C₄×D₈₉	1	2	yes	—
250	C₂×C₂²⋊C₄	—	178	2	no	—
251	C₂×C₄²	—	89	1	no	—
252	C₂×C₄²	—	89	1	no	—
253	C₂×C₄²	—	89	1	no	—
254	C₂×C₄²	—	178	2	no	—
255	C₂×C₄²	—	178	1	no	—
256	C₂×C₄²	—	178	1	no	—
257	C₂×C₄²	—	178	1	no	—
258	C₂×C₄²	—	178	1	no	—
259	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	178	1	no	—
265	C₄⋊C₈	—	178	1	no	—
266	C₄⋊C₈	—	178	1	no	—
267	C₄⋊C₈	—	178	1	no	—
268	C₂²⋊C₈	—	356	2	no	—
269	C₂²⋊C₈	—	356	2	no	—
270	#95	—	178	2	no	—
271	#95	—	178	2	no	—
272	C₂⁴	—	89	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	89	1	no	—
275	C₂²×C₄	—	89	1	no	—
276	C₂²×C₄	—	89	1	no	—
277	C₂²×C₄	—	178	2	no	—
278	C₂²×C₄	—	178	2	no	—
279	C₂²×C₄	—	178	2	no	—
280	C₂²×C₄	—	178	1	no	—
281	C₂²×C₄	—	178	1	no	—
282	C₂²×C₄	—	178	1	no	—
283	C₂²×C₄	—	178	1	no	—
284	C₂²×C₄	—	178	1	no	—
285	C₂²×C₄	—	178	1	no	—
286	C₂²×C₄	—	178	1	no	—
287	C₂²×C₄	—	178	1	no	—
288	C₂²×C₄	—	178	1	no	—
289	C₂²×C₄	—	178	1	no	—
290	C₂²×C₄	—	178	1	no	—
291	C₂²×C₄	—	178	1	no	—
292	C₂²×C₄	—	178	1	no	—
293	C₂²×C₄	—	178	1	no	—
294	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
295	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
296	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	356	1	no	—
304	C₂×C₈	—	356	1	no	—
305	C₂×C₈	—	356	1	no	—
306	C₂×C₈	—	356	1	no	—
307	C₂×C₈	—	356	1	no	—
308	C₂×C₈	—	356	1	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	356	2	no	—
315	C₄⋊C₄	—	356	1	no	—
316	C₄⋊C₄	—	356	1	no	—
317	C₄⋊C₄	—	356	1	no	—
318	C₄⋊C₄	—	356	1	no	—
319	C₂²⋊C₄	—	356	4	no	—
320	C₄²	—	356	4	no	—
321	C₄²	—	178	1	no	—
322	C₄²	—	178	1	no	—
323	C₄²	—	178	1	no	—
324	C₄²	—	178	1	no	—
325	C₄²	—	178	1	no	—
326	C₄²	—	178	1	no	—
327	C₄²	#13083573	1	1	yes	characteristic
328	C₄²	#13083574	1	1	yes	characteristic
329	C₄²	#13083574	1	1	yes	characteristic
330	C₄²	#13083575	1	1	yes	characteristic
331	C₂³	—	89	2	no	—
332	C₂³	—	178	1	no	—
333	C₂³	—	178	1	no	—
334	C₂³	—	178	1	no	—
335	C₂³	—	178	1	no	—
336	C₂³	—	178	1	no	—
337	C₂³	—	178	1	no	—
338	C₂³	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	89	2	no	—
345	C₂×C₄	—	356	1	no	—
346	C₂×C₄	—	356	1	no	—
347	C₂×C₄	—	356	1	no	—
348	C₂×C₄	—	356	1	no	—
349	C₂×C₄	—	356	1	no	—
350	C₂×C₄	—	356	1	no	—
351	C₂×C₄	—	356	1	no	—
352	C₂×C₄	—	356	1	no	—
353	C₂×C₄	—	356	2	no	—
354	C₂×C₄	—	356	2	no	—
355	C₂×C₄	—	356	2	no	—
356	C₂×C₄	—	178	4	no	—
357	C₂×C₄	—	178	4	no	—
358	C₂×C₄	—	178	1	no	—
359	C₂×C₄	—	178	1	no	—
360	C₂×C₄	—	178	1	no	—
361	C₂×C₄	—	178	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	1	no	—
365	C₂×C₄	—	178	1	no	—
366	C₂×C₄	#15667969	1	1	yes	characteristic
367	C₂×C₄	#15667970	1	1	yes	characteristic
368	C₂×C₄	#15667994	1	1	yes	characteristic
369	C₂×C₄	#15667994	1	1	yes	characteristic
370	C₂×C₄	#15667997	1	1	yes	characteristic
371	C₂×C₄	#15667997	1	1	yes	characteristic
372	C₂×C₄	#15668031	1	1	yes	characteristic
373	C₂×C₄	#15668033	1	1	yes	characteristic
374	C₂×C₄	#15668033	1	1	yes	characteristic
375	C₂×C₄	#15668035	1	1	yes	characteristic
376	C₂×C₄	#15668036	1	1	yes	characteristic
377	C₂×C₄	#15668039	1	1	yes	characteristic
378	C₂×C₄	#15668041	1	1	yes	characteristic
379	C₂×C₄	#15668044	1	1	yes	characteristic
380	C₈	—	8	1	no	—
381	C₈	—	8	1	no	—
382	C₈	—	712	1	no	—
383	C₈	—	712	1	no	—
384	C₂²	—	356	1	no	—
385	C₂²	—	356	1	no	—
386	C₂²	—	356	1	no	—
387	C₂²	—	356	1	no	—
388	C₂²	—	178	2	no	—
389	C₂²	—	178	2	no	—
390	C₂²	—	178	2	no	—
391	C₂²	#19151460	1	1	yes	characteristic
392	C₂²	#100×D₈₉	1	1	yes	characteristic
393	C₂²	#101×D₈₉	1	1	yes	characteristic
394	C₂²	#19151591	1	1	yes	characteristic
395	C₂²	#19151593	1	1	yes	characteristic
396	C₂²	#19151596	1	1	yes	characteristic
397	C₂²	#19151598	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	356	1	no	—
402	C₄	—	356	1	no	—
403	C₄	—	178	2	no	—
404	C₄	—	712	2	no	—
405	C₄	#19151920	1	1	yes	characteristic
406	C₄	#19151921	1	1	yes	characteristic
407	C₄	#19151924	1	1	yes	characteristic
408	C₄	#19151925	1	1	yes	characteristic
409	C₄	#19151937	1	1	yes	characteristic
410	C₄	#19151938	1	1	yes	characteristic
411	C₄	#19151941	1	1	yes	characteristic
412	C₄	#19151942	1	1	yes	characteristic
413	C₂	—	356	2	no	—
414	C₂	#26018915	1	1	yes	characteristic
415	C₂	#26018944	1	1	yes	characteristic
416	C₂	#26018946	1	1	yes	characteristic
417	C₂	#26018988	1	1	yes	characteristic
418	C₂	#26020331	1	1	yes	characteristic
419	C₂	#26020345	1	1	yes	characteristic
420	C₂	#26020346	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₈₉
commutator	C₂²×C₄×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₈₉×#1296	C₂
socle	C₂³×C₈₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₈₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	#1296	D₈₉
hypocenter	C₈₉	#8729
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #26018136	C₂	semidirect
5. #26018136	C₂	semidirect
6. #26018135	C₂	semidirect
7. C₈₉×#1296	C₂	semidirect
217. #1296	D₈₉	semidirect
218. C₈₉	#8729	semidirect

Maximal subgroups

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

subgroup	index
#26022657	2
#26020229	2
#26018136	2
#26018135	2
C₈₉×#1296	2
#8729	89