Subgroups — #36537975

Order 22784.

662 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031559	C₂	1	1	yes	maximal, characteristic
2	#26031382	C₂	1	1	yes	maximal, characteristic, complemented
3	#26030645	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028995	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019826	C₂	1	2	yes	maximal, complemented
6	#26019784	C₂	1	2	yes	maximal, complemented
7	#26019702	C₂	1	2	yes	maximal, complemented
8	#26019660	C₂	1	2	yes	maximal, complemented
9	#26019005	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151346	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1540	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	C₂×#15668012	C₂²	1	1	yes	characteristic
15	#19151996	—	2	1	no	—
16	#19151957	—	2	2	no	—
17	#19151948	C₂²	1	2	yes	—
18	#19151945	—	2	1	no	—
19	#19151944	C₂²	1	2	yes	—
20	#19151917	—	2	2	no	—
21	#19151889	C₂²	1	2	yes	—
22	#19151889	C₂²	1	2	yes	—
23	#19151878	—	2	1	no	—
24	#19151875	C₂²	1	2	yes	—
25	#19151832	—	2	2	no	—
26	#19151793	—	2	1	no	—
27	#19151790	C₂²	1	2	yes	—
28	#19151675	C₂²	1	2	yes	—
29	#19151668	—	2	2	no	—
30	#19151663	C₂²	1	2	yes	—
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151599	—	2	1	no	—
33	#19151599	—	2	1	no	—
34	#19151564	—	2	1	no	—
35	C₄×#13083558	C₂²	1	1	yes	characteristic
36	#19151350	C₂²	1	2	yes	—
37	#19151348	C₂²	1	2	yes	—
38	#19151346	C₂²	1	2	yes	—
39	#19151346	C₂²	1	2	yes	—
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	#431×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#332×C₈₉	C₂²	1	1	yes	characteristic
44	#332×C₈₉	C₂²	1	1	yes	characteristic
45	#331×C₈₉	C₂²	1	1	yes	characteristic
46	#331×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂²×Dic₁₇₈	—	2	1	no	—
49	C₂×#13083559	—	2	2	no	—
50	#15668018	—	4	4	no	—
51	C₂×#13083558	D₄	1	1	yes	characteristic
52	C₂×#13083558	D₄	1	1	yes	characteristic
53	C₂×#13083557	—	2	2	no	—
54	C₂²×#10623494	—	2	1	no	—
55	C₂×C₈×D₈₉	—	2	2	no	—
56	#15668012	—	2	1	no	—
57	#15668012	—	2	1	no	—
58	#15668012	—	2	1	no	—
59	#15668012	D₄	1	1	yes	characteristic
60	#15668012	C₂³	1	2	yes	—
61	#15668009	D₄	1	1	yes	characteristic
62	#15668000	—	2	1	no	—
63	#15667986	—	2	1	no	—
64	#15667986	D₄	1	2	yes	—
65	C₄×D₃₅₆	—	2	1	no	—
66	C₄×D₃₅₆	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	C₂×C₄⋊Dic₈₉	—	2	1	no	—
69	#15667945	—	2	2	no	—
70	#15667944	—	2	2	no	—
71	#15667944	—	2	2	no	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	#15667936	—	2	2	no	—
75	#15667936	—	2	2	no	—
76	#15667934	—	2	2	no	—
77	#15667934	—	2	2	no	—
78	#15667933	—	2	2	no	—
79	#15667933	—	2	2	no	—
80	#15667933	—	2	2	no	—
81	#15667932	—	2	2	no	—
82	#15667924	—	2	2	no	—
83	#15667924	—	2	2	no	—
84	#15667923	D₄	1	2	yes	—
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₂×#41×C₈₉	—	2	1	no	—
87	C₂²×C₈×C₈₉	—	2	1	no	—
88	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
89	#127×C₈₉	C₂³	1	1	yes	characteristic
90	#124×C₈₉	—	2	1	no	—
91	#121×C₈₉	—	2	1	no	—
92	#121×C₈₉	—	2	1	no	—
93	C₄×D₄×C₈₉	—	2	1	no	—
94	C₄×D₄×C₈₉	—	2	1	no	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂²⋊C₈×C₈₉	—	2	1	no	—
102	C₄×C₈×C₈₉	—	2	1	no	—
103	#13083574	—	4	2	no	—
104	#13083574	—	4	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×Dic₁₇₈	—	2	2	no	—
107	C₂×Dic₁₇₈	—	4	1	no	—
108	C₂×Dic₁₇₈	—	8	2	no	—
109	C₂×D₃₅₆	—	2	1	no	—
110	C₂×D₃₅₆	—	2	1	no	—
111	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
112	C₂×C₂²⋊D₈₉	—	2	2	no	—
113	C₂²×Dic₈₉	—	4	1	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	#13083559	—	8	2	no	—
116	#13083558	—	2	2	no	—
117	#13083558	—	2	2	no	—
118	#13083557	—	4	4	no	—
119	C₂×#10623494	—	2	2	no	—
120	C₂×#10623494	—	8	1	no	—
121	C₂×#10623494	C₂×D₄	1	2	yes	—
122	C₂×#10623494	C₂×D₄	1	2	yes	—
123	C₈×D₈₉	—	4	4	no	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	—	2	2	no	—
126	C₄⋊Dic₈₉	—	2	2	no	—
127	C₄⋊Dic₈₉	—	4	1	no	—
128	C₄⋊Dic₈₉	—	4	1	no	—
129	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
130	#13083551	—	2	2	no	—
131	#13083551	—	2	2	no	—
132	#41×C₈₉	—	4	2	no	—
133	#41×C₈₉	—	4	2	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	2	1	no	—
136	C₂×D₄×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	2	1	no	—
138	C₂×D₄×C₈₉	—	4	1	no	—
139	C₂²×C₄×C₈₉	—	4	1	no	—
140	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	4	2	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₂²⋊C₄×C₈₉	—	4	1	no	—
151	C₂²⋊C₄×C₈₉	—	4	1	no	—
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	#41	1	1	yes	characteristic
155	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂³×C₈₉	—	4	1	no	—
157	C₂³×C₈₉	#121	1	1	yes	characteristic
158	C₂²×D₈₉	—	2	2	no	—
159	Q₈×C₈₉	—	4	1	no	—
160	Q₈×C₈₉	—	4	1	no	—
161	D₄×C₈₉	—	4	1	no	—
162	D₄×C₈₉	—	4	1	no	—
163	D₄×C₈₉	—	4	1	no	—
164	D₄×C₈₉	—	4	1	no	—
165	D₄×C₈₉	—	8	1	no	—
166	D₄×C₈₉	—	8	2	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	—	4	1	no	—
171	C₂×C₄×C₈₉	—	8	2	no	—
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₈₉	#135	1	2	yes	—
176	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₈₉	—	4	4	no	—
181	C₂×Dic₈₉	—	2	2	no	—
182	C₂×Dic₈₉	—	4	2	no	—
183	C₂×Dic₈₉	—	8	2	no	—
184	D₃₅₆	—	2	2	no	—
185	D₃₅₆	—	2	2	no	—
186	D₃₅₆	—	4	2	no	—
187	D₃₅₆	—	8	1	no	—
188	C₄×D₈₉	—	4	2	no	—
189	C₄×D₈₉	—	4	2	no	—
190	Dic₁₇₈	—	4	2	no	—
191	Dic₁₇₈	—	8	2	no	—
192	Dic₁₇₈	—	8	2	no	—
193	C₈×C₈₉	—	4	1	no	—
194	C₈×C₈₉	—	4	1	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	—	4	1	no	—
197	#10623494	—	2	2	no	—
198	#10623494	—	2	2	no	—
199	#10623494	—	4	2	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	8	1	no	—
203	C₂²×C₈₉	—	8	1	no	—
204	C₂²×C₈₉	—	8	1	no	—
205	C₂²×C₈₉	#463	1	2	yes	—
206	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
207	C₂×D₈₉	—	4	2	no	—
208	C₂×D₈₉	—	4	2	no	—
209	C₂×D₈₉	—	4	2	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	—	8	1	no	—
214	C₄×C₈₉	#463	1	2	yes	—
215	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
216	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₄×C₈₉	#577	1	1	yes	characteristic
218	C₄×C₈₉	#578	1	1	yes	characteristic
219	Dic₈₉	—	4	2	no	—
220	Dic₈₉	—	8	2	no	—
221	#19236	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	2	2	no	—
223	C₂×C₈₉	—	16	1	no	—
224	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
225	C₂×C₈₉	#3063	1	1	yes	characteristic
226	C₂×C₈₉	#3068	1	1	yes	characteristic
227	D₈₉	—	8	2	no	—
228	#3245	—	89	1	no	—
229	#3227	—	89	1	no	—
230	#3141	—	89	1	no	—
231	#2935	—	89	1	no	—
232	#1703	—	89	2	no	—
233	#1697	—	89	2	no	—
234	#1683	—	89	2	no	—
235	#1677	—	89	2	no	—
236	#1565	—	89	1	no	—
237	C₂×#333	—	89	1	no	—
238	#1540	D₈₉	1	1	yes	characteristic, complemented
239	C₈₉	#19236	1	1	yes	characteristic, complemented, Sylow
240	C₂×#131	—	178	1	no	—
241	#532	—	89	1	no	—
242	#532	C₂×D₈₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	—	89	1	no	—
244	#498	—	178	1	no	—
245	#489	—	178	2	no	—
246	#487	—	89	2	no	—
247	#486	—	89	2	no	—
248	#486	—	178	1	no	—
249	#481	—	178	2	no	—
250	#476	—	89	2	no	—
251	#476	—	89	2	no	—
252	#474	—	89	2	no	—
253	#474	—	178	1	no	—
254	#466	—	178	2	no	—
255	#459	—	89	2	no	—
256	#459	—	178	1	no	—
257	#436	—	89	2	no	—
258	#435	—	178	2	no	—
259	C₈×D₄	—	89	2	no	—
260	#431	C₂×D₈₉	1	1	yes	characteristic
261	C₂×C₄⋊C₈	—	89	1	no	—
262	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
263	#417	—	178	1	no	—
264	#417	—	178	1	no	—
265	#408	—	178	1	no	—
266	C₄×M₁₆	—	89	1	no	—
267	#335	—	89	2	no	—
268	#334	—	89	2	no	—
269	#333	—	89	2	no	—
270	#333	—	89	2	no	—
271	#332	C₂×D₈₉	1	1	yes	characteristic
272	#332	C₂×D₈₉	1	1	yes	characteristic
273	#331	C₂×D₈₉	1	1	yes	characteristic
274	#331	C₂×D₈₉	1	1	yes	characteristic
275	C₂×#41	—	2	1	no	—
276	C₂×#41	—	178	1	no	—
277	C₂²×Q₈	—	178	1	no	—
278	C₂×D₈	—	178	2	no	—
279	#131	—	356	4	no	—
280	C₂×M₁₆	—	89	1	no	—
281	C₂×M₁₆	—	89	1	no	—
282	C₂×M₁₆	—	178	2	no	—
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	178	2	no	—
285	C₂²×C₈	—	178	1	no	—
286	C₄⋊Q₈	—	89	1	no	—
287	C₄⋊Q₈	—	89	2	no	—
288	C₄⋊Q₈	—	178	1	no	—
289	C₄⋊Q₈	—	178	1	no	—
290	C₄⋊Q₈	—	178	1	no	—
291	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
292	#127	—	89	1	no	—
293	#127	C₂²×D₈₉	1	1	yes	characteristic
294	#124	—	2	1	no	—
295	#124	—	178	1	no	—
296	#121	—	2	1	no	—
297	#121	—	2	1	no	—
298	#121	—	89	2	no	—
299	#121	—	178	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	89	2	no	—
303	C₄×D₄	—	178	1	no	—
304	C₂×C₄⋊C₄	—	178	1	no	—
305	C₂×C₄⋊C₄	—	178	1	no	—
306	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
307	#107	—	178	2	no	—
308	#106	—	178	2	no	—
309	#106	—	178	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	89	2	no	—
312	C₄⋊C₈	—	178	1	no	—
313	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
315	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
317	#103	—	178	2	no	—
318	#103	—	178	2	no	—
319	#102	—	178	2	no	—
320	#102	—	178	2	no	—
321	#102	—	178	2	no	—
322	#102	—	178	2	no	—
323	#102	—	178	2	no	—
324	#102	—	178	2	no	—
325	C₂²⋊C₈	—	2	1	no	—
326	C₂²⋊C₈	—	178	2	no	—
327	C₂²⋊C₈	—	178	2	no	—
328	#97	—	89	2	no	—
329	C₄×C₈	—	2	1	no	—
330	C₄×C₈	—	89	2	no	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	356	2	no	—
334	#41	—	356	2	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	356	1	no	—
337	C₂×Q₈	—	178	2	no	—
338	C₂×Q₈	—	178	1	no	—
339	C₂×Q₈	—	712	2	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	89	2	no	—
345	C₂×D₄	—	178	2	no	—
346	C₂×D₄	—	178	1	no	—
347	C₂×D₄	—	178	1	no	—
348	C₂²×C₄	—	4	1	no	—
349	C₂²×C₄	—	356	1	no	—
350	C₂²×C₄	—	178	2	no	—
351	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
353	C₂²×C₄	#13083574	1	1	yes	characteristic
354	D₈	—	712	2	no	—
355	M₁₆	—	356	4	no	—
356	M₁₆	—	178	2	no	—
357	M₁₆	—	178	2	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	4	2	no	—
363	C₂×C₈	—	89	2	no	—
364	C₂×C₈	—	89	2	no	—
365	C₂×C₈	—	356	4	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	712	1	no	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	89	2	no	—
371	C₄⋊C₄	—	356	1	no	—
372	C₄⋊C₄	—	356	1	no	—
373	C₄⋊C₄	—	178	2	no	—
374	C₄⋊C₄	—	178	2	no	—
375	C₄⋊C₄	—	178	1	no	—
376	C₂²⋊C₄	—	4	1	no	—
377	C₂²⋊C₄	—	4	1	no	—
378	C₂²⋊C₄	—	178	2	no	—
379	C₂²⋊C₄	—	178	2	no	—
380	C₄²	D₄×D₈₉	1	1	yes	characteristic
381	C₄²	D₄×D₈₉	1	1	yes	characteristic
382	C₄²	#13083574	1	1	yes	characteristic
383	C₄²	C₂³×D₈₉	1	1	yes	characteristic
384	C₂³	—	4	1	no	—
385	C₂³	—	178	2	no	—
386	C₂³	#15667985	1	1	yes	characteristic
387	Q₈	—	4	1	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	356	2	no	—
390	Q₈	—	712	2	no	—
391	Q₈	—	712	2	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	4	1	no	—
396	D₄	—	8	1	no	—
397	D₄	—	8	2	no	—
398	D₄	—	356	4	no	—
399	D₄	—	356	2	no	—
400	D₄	—	178	2	no	—
401	D₄	—	178	2	no	—
402	D₄	—	712	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	8	2	no	—
408	C₂×C₄	—	356	2	no	—
409	C₂×C₄	—	356	2	no	—
410	C₂×C₄	—	356	2	no	—
411	C₂×C₄	—	178	2	no	—
412	C₂×C₄	—	712	2	no	—
413	C₂×C₄	#15667985	1	1	yes	characteristic
414	C₂×C₄	#15667985	1	1	yes	characteristic
415	C₂×C₄	#15667985	1	1	yes	characteristic
416	C₂×C₄	#15668033	1	2	yes	—
417	C₂×C₄	#15668036	1	2	yes	—
418	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
420	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
421	C₈	—	4	1	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	356	2	no	—
426	C₈	—	178	2	no	—
427	C₈	—	178	2	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	356	2	no	—
434	C₂²	—	356	2	no	—
435	C₂²	—	356	2	no	—
436	C₂²	#19151812	1	2	yes	—
437	C₂²	C₂×#15667985	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	356	2	no	—
443	C₄	—	712	2	no	—
444	C₄	#19151812	1	2	yes	—
445	C₄	C₂×#15668033	1	1	yes	characteristic
446	C₄	C₂×#15668036	1	1	yes	characteristic
447	C₄	#19152405	1	1	yes	characteristic
448	C₄	#19152412	1	1	yes	characteristic
449	C₂	—	2	2	no	—
450	C₂	—	16	1	no	—
451	C₂	—	712	2	no	—
452	C₂	C₂×#19151812	1	1	yes	characteristic
453	C₂	#26029946	1	1	yes	characteristic
454	C₂	#26029983	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667985
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1540	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26031559	C₂
hypercenter	#1540	D₈₉
hypocenter	C₈₉	#19236
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1540

Complements

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

N	H ≅ G/N	type
2. #26031382	C₂	semidirect
3. #26030645	C₂	semidirect
4. #26028995	C₂	semidirect
5. #26019826	C₂	semidirect
6. #26019784	C₂	semidirect
7. #26019702	C₂	semidirect
8. #26019660	C₂	semidirect
9. #26019005	C₂	semidirect
10. C₂×#19151346	C₂	semidirect
11. C₈₉×#1540	C₂	semidirect
238. #1540	D₈₉	semidirect
239. C₈₉	#19236	semidirect

Maximal subgroups

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

subgroup	index
#26031559	2
#26031382	2
#26030645	2
#26028995	2
#26019826	2
#26019784	2
#26019702	2
#26019660	2
#26019005	2
C₂×#19151346	2
C₈₉×#1540	2
#19236	89