Subgroups — #36526232

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	#26029195	C₂	1	1	yes	maximal, characteristic, complemented
3	#26028995	C₂	1	1	yes	maximal, characteristic
4	#26019153	C₂	1	2	yes	maximal, complemented
5	#26019129	C₂	1	2	yes	maximal, complemented
6	#26019108	C₂	1	2	yes	maximal, complemented
7	#26019063	C₂	1	2	yes	maximal, complemented
8	#26018654	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018650	C₂	1	1	yes	maximal, characteristic
10	#26018541	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#335×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	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	#19151727	—	2	2	no	—
22	#19151725	C₂²	1	2	yes	—
23	#19151722	C₂²	1	2	yes	—
24	C₄×#13083563	C₂²	1	2	yes	—
25	C₄×#13083563	C₂²	1	2	yes	—
26	#19151675	C₂²	1	2	yes	—
27	#19151668	—	2	2	no	—
28	#19151663	C₂²	1	2	yes	—
29	#19151651	C₂²	1	1	yes	characteristic
30	#19151624	—	2	1	no	—
31	#19151564	—	2	1	no	—
32	#19151553	—	2	1	no	—
33	C₄×#13083558	C₂²	1	1	yes	characteristic
34	#19151328	C₂²	1	2	yes	—
35	#19151328	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151325	C₂²	1	2	yes	—
38	#19151320	C₂²	1	2	yes	—
39	#19151319	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
43	#335×C₈₉	C₂²	1	1	yes	characteristic
44	#335×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#335×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083563	C₂×C₄	1	2	yes	—
49	C₂×#13083563	C₂×C₄	1	2	yes	—
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	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	#15667941	—	2	2	no	—
74	#15667941	—	2	2	no	—
75	#15667937	C₂×C₄	1	2	yes	—
76	#15667937	C₂×C₄	1	2	yes	—
77	#15667934	C₂×C₄	1	2	yes	—
78	#15667934	C₂×C₄	1	2	yes	—
79	C₂²⋊#10623494	—	2	1	no	—
80	#15667924	—	2	2	no	—
81	#15667924	—	2	2	no	—
82	#15667923	D₄	1	2	yes	—
83	#15667922	—	2	2	no	—
84	C₄×#10623494	C₂³	1	2	yes	—
85	C₄×#10623494	C₂³	1	2	yes	—
86	C₈×Dic₈₉	—	2	2	no	—
87	C₂²×C₈×C₈₉	—	2	1	no	—
88	C₂²×C₈×C₈₉	—	2	1	no	—
89	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₈₉	—	2	1	no	—
93	C₄⋊C₈×C₈₉	—	2	1	no	—
94	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
99	C₄×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
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	#13083558	—	2	2	no	—
115	#13083558	—	2	2	no	—
116	#13083557	—	4	4	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	C₂×D₄	1	2	yes	—
119	C₂×#10623494	C₂×D₄	1	2	yes	—
120	C₈×D₈₉	—	4	4	no	—
121	C₄⋊Dic₈₉	—	2	1	no	—
122	C₄⋊Dic₈₉	—	2	1	no	—
123	C₄⋊Dic₈₉	—	2	1	no	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
126	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
127	#13083553	—	2	2	no	—
128	#13083553	—	2	2	no	—
129	C₂²⋊Dic₈₉	—	2	2	no	—
130	#13083551	—	2	2	no	—
131	#13083551	—	2	2	no	—
132	C₄×Dic₈₉	—	2	2	no	—
133	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	2	1	no	—
139	C₂×C₈×C₈₉	—	2	1	no	—
140	C₂×C₈×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	4	1	no	—
142	C₂×C₈×C₈₉	—	4	2	no	—
143	C₂×C₈×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
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	—	4	1	no	—
183	C₈×C₈₉	—	4	1	no	—
184	C₈×C₈₉	—	4	1	no	—
185	C₈×C₈₉	—	4	1	no	—
186	C₈×C₈₉	#131	1	2	yes	complemented
187	#10623494	—	2	2	no	—
188	#10623494	—	2	2	no	—
189	#10623494	—	4	2	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	D₈₉	1	1	yes	characteristic, complemented
222	#1481	—	89	1	no	—
223	#1480	—	89	1	no	—
224	#1451	—	89	1	no	—
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	—	89	1	no	—
244	#424	—	178	1	no	—
245	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
247	#408	—	178	1	no	—
248	#405	—	178	1	no	—
249	C₄×M₁₆	—	89	1	no	—
250	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
251	#335	C₂×D₈₉	1	1	yes	characteristic
252	#335	C₂×D₈₉	1	1	yes	characteristic
253	#335	C₂×D₈₉	1	1	yes	characteristic
254	#335	C₂×D₈₉	1	1	yes	characteristic
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	—	89	2	no	—
260	#322	—	89	2	no	—
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	—	89	1	no	—
266	C₂×M₁₆	—	89	1	no	—
267	C₂×M₁₆	—	178	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	2	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	—	2	1	no	—
293	C₄⋊C₈	—	178	2	no	—
294	C₄⋊C₈	—	178	2	no	—
295	C₄⋊C₈	—	178	1	no	—
296	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
300	#103	—	89	2	no	—
301	#103	—	89	2	no	—
302	#102	—	89	2	no	—
303	#102	—	89	2	no	—
304	C₂²⋊C₈	—	178	2	no	—
305	C₂²⋊C₈	—	178	2	no	—
306	C₂²⋊C₈	—	178	1	no	—
307	#97	—	89	2	no	—
308	#97	—	178	2	no	—
309	C₄×C₈	—	89	2	no	—
310	C₄×C₈	—	89	2	no	—
311	C₄×C₈	—	178	2	no	—
312	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
313	C₄×C₈	C₄×D₈₉	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
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	D₄×D₈₉	1	1	yes	characteristic
328	C₂²×C₄	#13083575	1	1	yes	characteristic
329	SD₁₆	—	356	2	no	—
330	SD₁₆	—	178	4	no	—
331	M₁₆	—	356	4	no	—
332	M₁₆	—	178	2	no	—
333	M₁₆	—	178	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	4	1	no	—
340	C₂×C₈	—	4	2	no	—
341	C₂×C₈	—	4	2	no	—
342	C₂×C₈	—	89	2	no	—
343	C₂×C₈	—	89	2	no	—
344	C₂×C₈	—	356	4	no	—
345	C₂×C₈	—	178	2	no	—
346	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
348	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
349	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
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	D₄×D₈₉	1	1	yes	characteristic
364	C₄²	#13083575	1	1	yes	characteristic
365	C₄²	C₂³×D₈₉	1	1	yes	characteristic
366	C₂³	—	178	2	no	—
367	C₂³	#15667974	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	#15667974	1	1	yes	characteristic
386	C₂×C₄	#15667974	1	1	yes	characteristic
387	C₂×C₄	#15667974	1	1	yes	characteristic
388	C₂×C₄	#15668036	1	2	yes	—
389	C₂×C₄	#15668044	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	356	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₈	#15668018	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	#19151697	1	2	yes	—
410	C₂²	C₂×#15667974	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	#19151697	1	2	yes	—
418	C₄	C₂×#15668018	1	1	yes	characteristic
419	C₄	#19152364	1	1	yes	characteristic
420	C₄	C₂×#15668036	1	1	yes	characteristic
421	C₄	C₂×#15668044	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	712	2	no	—
424	C₂	#26028995	1	1	yes	characteristic
425	C₂	C₂×#19151697	1	1	yes	characteristic
426	C₂	#26029168	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#335×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19152148	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₂×#335	D₈₉
hypocenter	C₈₉	#18071
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
2. #26029195	C₂	semidirect
4. #26019153	C₂	semidirect
5. #26019129	C₂	semidirect
6. #26019108	C₂	semidirect
7. #26019063	C₂	semidirect
8. #26018654	C₂	semidirect
10. #26018541	C₂	semidirect
11. C₂×#335×C₈₉	C₂	semidirect
186. C₈×C₈₉	#131	semidirect
221. C₂×#335	D₈₉	semidirect
225. C₈₉	#18071	semidirect
403. C₈	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26030811	2
#26029195	2
#26028995	2
#26019153	2
#26019129	2
#26019108	2
#26019063	2
#26018654	2
#26018650	2
#26018541	2
C₂×#335×C₈₉	2
#18071	89