Subgroups — #36526237

Order 22784.

646 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030811	C₂	1	1	yes	maximal, characteristic
2	#26029199	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028998	C₂	1	1	yes	maximal, characteristic
4	#26019156	C₂	1	2	yes	maximal, complemented
5	#26019132	C₂	1	2	yes	maximal, complemented
6	#26019111	C₂	1	2	yes	maximal, complemented
7	#26019066	C₂	1	2	yes	maximal, complemented
8	C₂×#19151351	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018656	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018652	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152155	C₂²	1	1	yes	characteristic
14	#19152148	C₂²	1	1	yes	characteristic
15	#19151996	C₄	1	1	yes	characteristic
16	#19151971	C₄	1	1	yes	characteristic
17	#19151949	C₄	1	1	yes	characteristic
18	#19151945	C₄	1	1	yes	characteristic
19	#19151827	C₄	1	2	yes	—
20	#19151827	C₄	1	2	yes	—
21	#19151728	C₂²	1	2	yes	—
22	#19151726	—	2	2	no	—
23	C₈×Dic₁₇₈	C₂²	1	2	yes	—
24	C₄×#13083563	C₂²	1	2	yes	—
25	C₄×#13083563	C₂²	1	2	yes	—
26	#19151677	C₂²	1	2	yes	—
27	#19151671	—	2	2	no	—
28	C₈×D₃₅₆	C₂²	1	2	yes	—
29	#19151626	—	2	1	no	—
30	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
32	#19151566	—	2	1	no	—
33	#19151556	—	2	1	no	—
34	#19151351	C₂²	1	1	yes	characteristic
35	#19151351	C₂²	1	1	yes	characteristic
36	#19151351	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151330	C₂²	1	2	yes	—
39	#19151330	C₂²	1	2	yes	—
40	#19151327	C₂²	1	2	yes	—
41	#19151327	C₂²	1	2	yes	—
42	#431×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#322×C₈₉	C₂²	1	2	yes	—
46	#322×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083563	C₂×C₄	1	2	yes	—
49	C₂×#13083563	C₂×C₄	1	2	yes	—
50	#15668020	—	4	4	no	—
51	C₂×#13083557	—	2	2	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂²×#10623494	—	2	1	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	#15668012	C₂×C₄	1	1	yes	characteristic
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668012	C₂×C₄	1	1	yes	characteristic
58	#15668009	C₂×C₄	1	1	yes	characteristic
59	#15668004	—	2	1	no	—
60	#15668000	—	2	1	no	—
61	#15667991	—	2	1	no	—
62	#15667991	C₂×C₄	1	2	yes	—
63	#15667986	—	2	1	no	—
64	#15667986	C₂×C₄	1	2	yes	—
65	C₄×Dic₁₇₈	—	2	1	no	—
66	C₄×Dic₁₇₈	C₂³	1	2	yes	—
67	C₄×D₃₅₆	—	2	1	no	—
68	C₄×D₃₅₆	C₂³	1	2	yes	—
69	#15667971	—	2	1	no	—
70	#15667944	C₂×C₄	1	2	yes	—
71	#15667944	C₂×C₄	1	2	yes	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	—	2	1	no	—
74	C₄⋊#10623494	C₂³	1	1	yes	characteristic
75	C₄⋊#10623494	C₂³	1	1	yes	characteristic
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	C₄⋊#10623494	C₂³	1	1	yes	characteristic
78	#15667941	—	2	2	no	—
79	#15667941	—	2	2	no	—
80	#15667937	C₂×C₄	1	2	yes	—
81	#15667937	C₂×C₄	1	2	yes	—
82	#15667934	C₂×C₄	1	2	yes	—
83	#15667934	C₂×C₄	1	2	yes	—
84	#15667924	—	2	2	no	—
85	#15667924	—	2	2	no	—
86	#15667922	—	2	2	no	—
87	C₈×Dic₈₉	—	2	2	no	—
88	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
89	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	—	2	1	no	—
94	C₂²⋊C₈×C₈₉	—	2	1	no	—
95	#97×C₈₉	D₄	1	2	yes	—
96	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
97	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
98	C₄×C₈×C₈₉	C₂³	1	2	yes	—
99	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	2	yes	—
102	#13083574	—	4	2	no	—
103	#13083574	—	4	2	no	—
104	C₂×Dic₁₇₈	—	2	1	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
107	C₂×D₃₅₆	—	2	1	no	—
108	C₂×D₃₅₆	—	2	1	no	—
109	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
110	C₂×C₂²⋊D₈₉	—	2	2	no	—
111	C₂×C₄×D₈₉	—	2	2	no	—
112	#13083563	—	2	4	no	—
113	#13083563	—	4	2	no	—
114	#13083557	—	4	4	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	4	2	no	—
120	C₂×#10623494	—	4	2	no	—
121	C₈×D₈₉	—	4	4	no	—
122	C₄⋊Dic₈₉	—	2	1	no	—
123	C₄⋊Dic₈₉	—	2	1	no	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
127	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
128	#13083553	—	2	2	no	—
129	#13083553	—	2	2	no	—
130	C₂²⋊Dic₈₉	—	2	2	no	—
131	#13083551	—	2	2	no	—
132	#13083551	—	2	2	no	—
133	C₄×Dic₈₉	—	2	2	no	—
134	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
137	M₁₆×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	—	2	2	no	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	4	1	no	—
142	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
148	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
149	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₈₉	#41	1	1	yes	characteristic
151	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
153	C₂²×D₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	4	1	no	—
157	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₈₉	#137	1	2	yes	—
162	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
165	C₂²⋊D₈₉	—	4	4	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	2	no	—
169	D₃₅₆	—	2	2	no	—
170	D₃₅₆	—	2	2	no	—
171	D₃₅₆	—	4	2	no	—
172	D₃₅₆	—	8	1	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	4	2	no	—
175	Dic₁₇₈	—	2	2	no	—
176	Dic₁₇₈	—	2	2	no	—
177	Dic₁₇₈	—	4	2	no	—
178	Dic₁₇₈	—	8	1	no	—
179	C₈×C₈₉	—	2	1	no	—
180	C₈×C₈₉	—	2	1	no	—
181	C₈×C₈₉	—	2	1	no	—
182	C₈×C₈₉	—	2	2	no	—
183	C₈×C₈₉	—	2	2	no	—
184	C₈×C₈₉	—	4	2	no	—
185	C₈×C₈₉	#131	1	2	yes	complemented
186	#10623494	—	4	1	no	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	1	no	—
189	#10623494	—	4	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	#440	1	2	yes	—
193	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₈₉	—	4	2	no	—
195	C₂×D₈₉	—	4	2	no	—
196	C₂×D₈₉	—	4	2	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	#440	1	2	yes	—
201	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
202	C₄×C₈₉	#568	1	1	yes	characteristic
203	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
205	Dic₈₉	—	4	2	no	—
206	Dic₈₉	—	4	2	no	—
207	Dic₈₉	—	4	2	no	—
208	#18071	—	89	1	no	maximal, Sylow
209	C₂×C₈₉	—	2	2	no	—
210	C₂×C₈₉	#2935	1	1	yes	characteristic
211	C₂×C₈₉	C₂×#440	1	1	yes	characteristic
212	C₂×C₈₉	#2957	1	1	yes	characteristic
213	D₈₉	—	8	2	no	—
214	#3167	—	89	1	no	—
215	#2962	—	89	1	no	—
216	#2935	—	89	1	no	—
217	#1592	—	89	2	no	—
218	#1588	—	89	2	no	—
219	#1585	—	89	2	no	—
220	SD₁₆⋊C₈	—	89	2	no	—
221	C₂×#335	—	89	1	no	—
222	#1481	—	89	1	no	—
223	#1480	—	89	1	no	—
224	#1451	D₈₉	1	1	yes	characteristic, complemented
225	C₈₉	#18071	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	178	1	no	—
227	#533	—	89	1	no	—
228	#532	—	89	1	no	—
229	#498	—	89	1	no	—
230	#492	—	89	1	no	—
231	#487	—	89	1	no	—
232	#486	—	89	1	no	—
233	#465	—	89	2	no	—
234	#465	—	89	2	no	—
235	#446	—	89	2	no	—
236	#446	—	178	2	no	—
237	C₈×Q₈	—	89	2	no	—
238	C₄×SD₁₆	—	89	2	no	—
239	C₄×SD₁₆	—	89	2	no	—
240	#436	—	89	2	no	—
241	#435	—	178	2	no	—
242	C₈×D₄	—	89	2	no	—
243	#431	C₂×D₈₉	1	1	yes	characteristic
244	#424	—	178	1	no	—
245	C₂×C₄⋊C₈	—	89	1	no	—
246	C₂×C₄⋊C₈	—	89	1	no	—
247	#408	—	178	1	no	—
248	#405	—	178	1	no	—
249	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
250	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
251	#335	—	89	1	no	—
252	#335	—	89	1	no	—
253	#335	—	89	1	no	—
254	#335	—	89	1	no	—
255	Q₈⋊C₈	—	89	2	no	—
256	Q₈⋊C₈	—	89	2	no	—
257	D₄⋊C₈	—	89	2	no	—
258	D₄⋊C₈	—	89	2	no	—
259	#322	C₂×D₈₉	1	2	yes	—
260	#322	C₂×D₈₉	1	2	yes	—
261	C₂×#41	—	178	1	no	—
262	C₂×SD₁₆	—	89	2	no	—
263	C₂×SD₁₆	—	89	2	no	—
264	#131	—	356	4	no	—
265	C₂×M₁₆	—	178	2	no	—
266	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
267	C₂×M₁₆	D₃₅₆	1	1	yes	characteristic
268	C₂²×C₈	—	178	1	no	—
269	C₂²×C₈	—	178	1	no	—
270	C₂²×C₈	—	178	2	no	—
271	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
272	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
273	C₄⋊Q₈	—	89	1	no	—
274	C₄⋊Q₈	—	89	1	no	—
275	C₄⋊Q₈	—	89	1	no	—
276	#127	—	89	1	no	—
277	#125	—	178	1	no	—
278	#124	—	178	1	no	—
279	C₂²⋊Q₈	—	89	2	no	—
280	C₂²⋊Q₈	—	178	1	no	—
281	#121	—	89	2	no	—
282	#121	—	178	1	no	—
283	C₄×Q₈	—	89	2	no	—
284	C₄×Q₈	—	178	1	no	—
285	C₄×D₄	—	89	2	no	—
286	C₄×D₄	—	178	1	no	—
287	#117	—	178	1	no	—
288	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
289	#106	—	89	2	no	—
290	#106	—	89	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	89	1	no	—
293	C₄⋊C₈	—	89	1	no	—
294	C₄⋊C₈	—	89	1	no	—
295	C₄⋊C₈	—	89	1	no	—
296	C₄⋊C₈	—	178	2	no	—
297	C₄⋊C₈	—	178	2	no	—
298	C₄⋊C₈	—	178	1	no	—
299	C₄⋊C₈	—	178	1	no	—
300	#103	—	89	2	no	—
301	#103	—	89	2	no	—
302	#102	—	89	2	no	—
303	#102	—	89	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	178	2	no	—
306	C₂²⋊C₈	—	178	2	no	—
307	#97	—	178	2	no	—
308	#97	D₃₅₆	1	2	yes	—
309	C₄×C₈	—	178	2	no	—
310	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
311	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₈₉	1	2	yes	—
313	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₈₉	1	2	yes	—
316	#41	—	356	2	no	—
317	#41	—	356	2	no	—
318	C₂×Q₈	—	89	2	no	—
319	C₂×Q₈	—	178	1	no	—
320	C₂×Q₈	—	178	1	no	—
321	C₂×D₄	—	89	2	no	—
322	C₂×D₄	—	178	2	no	—
323	C₂×D₄	—	178	1	no	—
324	C₂×D₄	—	178	1	no	—
325	C₂²×C₄	—	178	2	no	—
326	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
328	C₂²×C₄	#13083574	1	1	yes	characteristic
329	SD₁₆	—	356	2	no	—
330	SD₁₆	—	178	4	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	356	4	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	356	4	no	—
338	C₂×C₈	—	356	2	no	—
339	C₂×C₈	—	356	2	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	—	178	1	no	—
342	C₂×C₈	—	178	1	no	—
343	C₂×C₈	—	178	1	no	—
344	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
348	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
349	C₂×C₈	C₂×D₃₅₆	1	2	yes	—
350	C₄⋊C₄	—	89	2	no	—
351	C₄⋊C₄	—	89	2	no	—
352	C₄⋊C₄	—	178	1	no	—
353	C₄⋊C₄	—	178	1	no	—
354	C₄⋊C₄	—	178	1	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	—	178	1	no	—
357	C₄⋊C₄	—	178	2	no	—
358	C₂²⋊C₄	—	178	2	no	—
359	C₂²⋊C₄	—	178	2	no	—
360	C₂²⋊C₄	—	178	2	no	—
361	C₄²	—	178	2	no	—
362	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
363	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
364	C₄²	#13083574	1	1	yes	characteristic
365	C₄²	C₂³×D₈₉	1	1	yes	characteristic
366	C₂³	—	178	2	no	—
367	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
368	Q₈	—	356	2	no	—
369	Q₈	—	178	2	no	—
370	Q₈	—	178	2	no	—
371	Q₈	—	712	1	no	—
372	D₄	—	356	4	no	—
373	D₄	—	356	2	no	—
374	D₄	—	178	2	no	—
375	D₄	—	178	2	no	—
376	D₄	—	712	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	356	2	no	—
381	C₂×C₄	—	356	2	no	—
382	C₂×C₄	—	178	2	no	—
383	C₂×C₄	—	178	2	no	—
384	C₂×C₄	—	178	2	no	—
385	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
386	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
387	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
388	C₂×C₄	#15668040	1	2	yes	—
389	C₂×C₄	#15668045	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
392	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
393	C₈	—	2	2	no	—
394	C₈	—	2	2	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	4	2	no	—
399	C₈	—	356	1	no	—
400	C₈	—	356	1	no	—
401	C₈	—	356	1	no	—
402	C₈	—	356	1	no	—
403	C₈	#15668020	1	2	yes	complemented
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	356	2	no	—
407	C₂²	—	356	2	no	—
408	C₂²	—	356	2	no	—
409	C₂²	#19151700	1	2	yes	—
410	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	356	2	no	—
415	C₄	—	356	2	no	—
416	C₄	—	356	2	no	—
417	C₄	#19151700	1	2	yes	—
418	C₄	C₂×#15668020	1	1	yes	characteristic
419	C₄	#19152364	1	1	yes	characteristic
420	C₄	C₂×#15668040	1	1	yes	characteristic
421	C₄	C₂×#15668045	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	712	2	no	—
424	C₂	#26028998	1	1	yes	characteristic
425	C₂	C₂×#19151700	1	1	yes	characteristic
426	C₂	#26029170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1451	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19152148	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1451	D₈₉
hypocenter	C₈₉	#18071
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #1451

Complements

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

N	H ≅ G/N	type
2. #26029199	C₂	semidirect
4. #26019156	C₂	semidirect
5. #26019132	C₂	semidirect
6. #26019111	C₂	semidirect
7. #26019066	C₂	semidirect
8. C₂×#19151351	C₂	semidirect
9. #26018656	C₂	semidirect
11. C₈₉×#1451	C₂	semidirect
185. C₈×C₈₉	#131	semidirect
224. #1451	D₈₉	semidirect
225. C₈₉	#18071	semidirect
403. C₈	#15668020	semidirect

Maximal subgroups

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

subgroup	index
#26030811	2
#26029199	2
#26028998	2
#26019156	2
#26019132	2
#26019111	2
#26019066	2
C₂×#19151351	2
#26018656	2
#26018652	2
C₈₉×#1451	2
#18071	89