Subgroups — #36525613

Order 22784.

600 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030317	C₂	1	1	yes	maximal, characteristic
2	#26029378	C₂	1	1	yes	maximal, characteristic
3	#26029354	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019146	C₂	1	2	yes	maximal, complemented
5	#26019120	C₂	1	2	yes	maximal, complemented
6	#26019112	C₂	1	2	yes	maximal, complemented
7	#26019049	C₂	1	2	yes	maximal, complemented
8	#26019043	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018635	C₂	1	1	yes	maximal, characteristic
10	#26018535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1493	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#13083574	C₂²	1	1	yes	characteristic
13	#19151936	C₄	1	2	yes	—
14	#19151880	C₄	1	1	yes	characteristic
15	#19151875	C₄	1	1	yes	characteristic
16	#19151805	C₄	1	1	yes	characteristic
17	#19151800	C₄	1	1	yes	characteristic
18	#19151758	C₄	1	2	yes	—
19	#19151729	—	2	1	no	—
20	#19151729	C₂²	1	2	yes	—
21	#19151725	C₂²	1	2	yes	—
22	Q₈×#10623494	—	2	1	no	—
23	Q₈×#10623494	C₂²	1	2	yes	—
24	C₄×#13083564	C₂²	1	2	yes	—
25	C₄×#13083561	C₂²	1	2	yes	—
26	#19151667	—	2	2	no	—
27	#19151663	C₂²	1	2	yes	—
28	#19151659	—	2	2	no	—
29	#19151654	—	2	1	no	—
30	#19151651	C₂²	1	1	yes	characteristic
31	#19151651	C₂²	1	1	yes	characteristic
32	#19151651	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₈₉	—	2	1	no	—
34	#19151350	C₂²	1	2	yes	—
35	#19151348	C₂²	1	2	yes	—
36	#19151330	C₂²	1	1	yes	characteristic
37	#19151330	C₂²	1	1	yes	characteristic
38	#19151327	C₂²	1	1	yes	characteristic
39	#19151327	C₂²	1	1	yes	characteristic
40	#19151319	C₂²	1	2	yes	—
41	C₈×#10623494	C₂²	1	2	yes	—
42	#533×C₈₉	C₂²	1	1	yes	characteristic
43	#423×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
46	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083564	C₂×C₄	1	2	yes	—
49	C₂×#13083561	C₂×C₄	1	2	yes	—
50	C₂×C₈×D₈₉	—	2	2	no	—
51	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
52	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
53	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
54	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₈₉	—	2	1	no	—
56	C₄×C₂²⋊D₈₉	—	2	1	no	—
57	#15667971	C₂×C₄	1	1	yes	characteristic
58	#15667969	—	2	1	no	—
59	C₄²×D₈₉	—	2	1	no	—
60	#15667945	C₂×C₄	1	2	yes	—
61	#15667943	C₂×C₄	1	2	yes	—
62	C₄⋊#10623494	—	2	2	no	—
63	C₄⋊#10623494	—	2	2	no	—
64	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
65	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
66	C₄⋊#10623494	D₄	1	1	yes	characteristic
67	C₄⋊#10623494	D₄	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	1	yes	characteristic
70	#15667941	—	2	2	no	—
71	#15667936	C₂×C₄	1	2	yes	—
72	#15667936	C₂×C₄	1	2	yes	—
73	#15667935	C₂×C₄	1	2	yes	—
74	#15667932	C₂×C₄	1	2	yes	—
75	C₂²⋊#10623494	—	2	1	no	—
76	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
77	C₂²⋊#10623494	D₄	1	2	yes	—
78	#15667924	—	2	2	no	—
79	#15667923	—	2	2	no	—
80	#15667922	—	2	2	no	—
81	C₄×#10623494	—	2	2	no	—
82	C₄×#10623494	—	2	1	no	—
83	C₄×#10623494	C₂³	1	2	yes	—
84	C₄×#10623494	C₂³	1	2	yes	—
85	C₂×M₁₆×C₈₉	—	2	1	no	—
86	C₂²×C₈×C₈₉	—	2	1	no	—
87	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
88	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#125×C₈₉	—	2	1	no	—
90	C₂²⋊Q₈×C₈₉	—	2	1	no	—
91	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
94	#117×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	2	yes	—
98	C₄×C₈×C₈₉	—	2	1	no	—
99	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
101	#13083574	—	2	2	no	—
102	#13083574	—	4	1	no	—
103	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
104	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₂²⋊D₈₉	—	2	1	no	—
106	C₂×C₄×D₈₉	—	2	1	no	—
107	C₂×C₄×D₈₉	—	2	1	no	—
108	C₂×C₄×D₈₉	—	2	1	no	—
109	#13083564	—	4	2	no	—
110	#13083561	—	2	4	no	—
111	C₂×#10623494	—	2	1	no	—
112	C₂×#10623494	—	2	1	no	—
113	C₂×#10623494	C₂²×C₄	1	2	yes	—
114	C₂×#10623494	C₂²×C₄	1	2	yes	—
115	C₂×#10623494	C₂×D₄	1	2	yes	—
116	C₂×#10623494	C₂×D₄	1	2	yes	—
117	C₈×D₈₉	—	8	2	no	—
118	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
120	#13083553	—	2	1	no	—
121	#13083553	—	2	1	no	—
122	C₂²⋊Dic₈₉	—	2	1	no	—
123	#13083551	—	2	1	no	—
124	#13083551	—	2	1	no	—
125	C₄×Dic₈₉	—	2	1	no	—
126	C₄×Dic₈₉	—	2	1	no	—
127	C₄×Dic₈₉	—	2	1	no	—
128	C₂×Q₈×C₈₉	—	2	1	no	—
129	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	M₁₆×C₈₉	—	8	1	no	—
134	C₂×C₈×C₈₉	—	2	4	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	2	2	no	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	1	no	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	—	2	2	no	—
143	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₈₉	—	2	2	no	—
145	C₄²×C₈₉	—	2	2	no	—
146	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₈₉	#41	1	1	yes	characteristic
149	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
150	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₈₉	—	2	1	no	—
152	Q₈×C₈₉	—	2	2	no	—
153	Q₈×C₈₉	—	2	2	no	—
154	Q₈×C₈₉	—	4	2	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₈₉	—	4	2	no	—
169	C₂×Dic₈₉	—	2	1	no	—
170	C₂×Dic₈₉	—	2	1	no	—
171	C₂×Dic₈₉	—	2	1	no	—
172	D₃₅₆	—	2	1	no	—
173	D₃₅₆	#131	1	2	yes	—
174	C₄×D₈₉	—	4	2	no	—
175	C₄×D₈₉	—	4	1	no	—
176	C₄×D₈₉	—	4	1	no	—
177	C₄×D₈₉	—	4	2	no	—
178	Dic₁₇₈	—	2	1	no	—
179	Dic₁₇₈	—	2	1	no	—
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	2	2	no	—
182	C₈×C₈₉	—	4	2	no	—
183	#10623494	—	2	2	no	—
184	#10623494	—	2	2	no	—
185	#10623494	—	2	2	no	—
186	#10623494	—	2	2	no	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	1	no	—
189	C₂²×C₈₉	—	2	1	no	—
190	C₂²×C₈₉	—	2	1	no	—
191	C₂²×C₈₉	—	2	1	no	—
192	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂×D₈₉	—	2	2	no	—
194	C₂×D₈₉	—	4	1	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	—	4	2	no	—
201	C₄×C₈₉	#443	1	2	yes	—
202	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
203	C₄×C₈₉	#568	1	1	yes	characteristic
204	C₄×C₈₉	#577	1	1	yes	characteristic
205	C₄×C₈₉	#578	1	1	yes	characteristic
206	Dic₈₉	—	4	1	no	—
207	Dic₈₉	—	4	1	no	—
208	Dic₈₉	—	4	1	no	—
209	#18016	—	89	1	no	maximal, Sylow
210	C₂×C₈₉	—	4	1	no	—
211	C₂×C₈₉	#2933	1	1	yes	characteristic
212	C₂×C₈₉	#2947	1	1	yes	characteristic
213	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
214	D₈₉	—	4	2	no	—
215	#3107	—	89	1	no	—
216	#2990	—	89	1	no	—
217	#2986	—	89	1	no	—
218	#1591	—	89	2	no	—
219	#1587	—	89	2	no	—
220	#1585	—	89	2	no	—
221	C₈×SD₁₆	—	89	2	no	—
222	#1574	—	89	1	no	—
223	#1493	D₈₉	1	1	yes	characteristic, complemented
224	#1476	—	89	1	no	—
225	#1450	—	89	1	no	—
226	C₈₉	#18016	1	1	yes	characteristic, complemented, Sylow
227	#533	C₂×D₈₉	1	1	yes	characteristic
228	C₄×#41	—	89	1	no	—
229	#485	—	89	2	no	—
230	#475	—	89	1	no	—
231	#474	—	89	1	no	—
232	#462	—	89	1	no	—
233	#461	—	89	1	no	—
234	#452	—	89	2	no	—
235	#446	—	89	2	no	—
236	#446	—	89	2	no	—
237	#446	—	178	1	no	—
238	C₈×Q₈	—	89	2	no	—
239	C₈×Q₈	—	178	1	no	—
240	C₄×Q₁₆	—	89	2	no	—
241	C₄×SD₁₆	—	89	2	no	—
242	#435	—	178	2	no	—
243	C₈×D₄	—	89	2	no	—
244	#433	—	178	2	no	—
245	#432	—	178	1	no	—
246	#431	—	89	1	no	—
247	#431	—	89	1	no	—
248	#431	—	89	1	no	—
249	#423	C₂×D₈₉	1	1	yes	characteristic
250	C₂×C₄⋊C₈	—	178	1	no	—
251	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
252	#335	—	89	2	no	—
253	#334	—	89	2	no	—
254	Q₈⋊C₈	—	89	1	no	—
255	Q₈⋊C₈	—	89	1	no	—
256	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
257	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
258	D₄⋊C₈	—	89	1	no	—
259	D₄⋊C₈	—	89	1	no	—
260	#322	—	89	2	no	—
261	C₈²	—	89	2	no	—
262	C₂×#41	—	89	1	no	—
263	C₂×Q₁₆	—	89	2	no	—
264	C₂×SD₁₆	—	89	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	178	2	no	—
268	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
269	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₄×D₈₉	1	2	yes	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	89	1	no	—
275	C₄×Q₈	—	89	1	no	—
276	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
277	C₄×D₄	—	89	1	no	—
278	C₄×D₄	—	89	1	no	—
279	C₄×D₄	—	178	1	no	—
280	C₄×D₄	—	178	1	no	—
281	#117	—	2	1	no	—
282	#117	—	89	1	no	—
283	#117	—	178	1	no	—
284	C₂×C₄²	—	178	1	no	—
285	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
286	#107	—	89	2	no	—
287	#106	—	89	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	89	1	no	—
290	C₄⋊C₈	—	89	1	no	—
291	C₄⋊C₈	—	89	1	no	—
292	C₄⋊C₈	—	89	1	no	—
293	C₄⋊C₈	—	89	1	no	—
294	C₄⋊C₈	—	89	1	no	—
295	C₄⋊C₈	—	178	2	no	—
296	C₄⋊C₈	—	178	2	no	—
297	C₄⋊C₈	—	178	2	no	—
298	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
299	#103	—	89	2	no	—
300	#103	—	89	2	no	—
301	#103	—	89	2	no	—
302	#102	—	89	2	no	—
303	C₂²⋊C₈	—	89	2	no	—
304	C₂²⋊C₈	—	89	2	no	—
305	C₂²⋊C₈	—	178	2	no	—
306	C₂²⋊C₈	—	178	1	no	—
307	#97	—	178	2	no	—
308	#97	—	178	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	89	2	no	—
311	C₄×C₈	—	89	2	no	—
312	C₄×C₈	—	178	2	no	—
313	C₄×C₈	—	178	1	no	—
314	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
316	#41	—	356	1	no	—
317	#41	—	178	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	89	1	no	—
320	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
321	C₂×D₄	—	89	1	no	—
322	C₂×D₄	—	178	1	no	—
323	C₂²×C₄	—	178	1	no	—
324	C₂²×C₄	—	178	1	no	—
325	C₂²×C₄	—	178	1	no	—
326	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
328	C₂²×C₄	#13083573	1	1	yes	characteristic
329	Q₁₆	—	356	2	no	—
330	SD₁₆	—	178	4	no	—
331	M₁₆	—	8	1	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	89	2	no	—
337	C₂×C₈	—	89	2	no	—
338	C₂×C₈	—	89	2	no	—
339	C₂×C₈	—	89	2	no	—
340	C₂×C₈	—	178	1	no	—
341	C₂×C₈	—	178	1	no	—
342	C₂×C₈	—	712	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	89	1	no	—
349	C₄⋊C₄	—	89	1	no	—
350	C₄⋊C₄	—	178	1	no	—
351	C₄⋊C₄	—	178	1	no	—
352	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	178	1	no	—
355	C₂²⋊C₄	—	178	1	no	—
356	C₂²⋊C₄	—	178	1	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	178	1	no	—
359	C₄²	—	178	1	no	—
360	C₄²	—	178	1	no	—
361	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
362	C₄²	D₄×D₈₉	1	1	yes	characteristic
363	C₄²	#13083573	1	1	yes	characteristic
364	C₄²	C₂³×D₈₉	1	1	yes	characteristic
365	C₂³	—	178	1	no	—
366	C₂³	#15667972	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	178	1	no	—
371	Q₈	—	178	1	no	—
372	D₄	—	89	2	no	—
373	D₄	—	356	2	no	—
374	D₄	—	178	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	356	2	no	—
383	C₂×C₄	—	356	1	no	—
384	C₂×C₄	—	356	1	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	178	1	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	—	178	1	no	—
389	C₂×C₄	#15667972	1	1	yes	characteristic
390	C₂×C₄	#15667972	1	1	yes	characteristic
391	C₂×C₄	#15667972	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
394	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	356	1	no	—
399	C₈	—	356	1	no	—
400	C₈	—	178	2	no	—
401	C₈	—	178	2	no	—
402	C₈	—	178	2	no	—
403	C₈	—	178	2	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	356	1	no	—
408	C₂²	—	356	1	no	—
409	C₂²	—	178	2	no	—
410	C₂²	C₂×#15667972	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	356	1	no	—
417	C₄	—	356	1	no	—
418	C₄	—	356	1	no	—
419	C₄	#19151712	1	2	yes	—
420	C₄	#131×D₈₉	1	1	yes	characteristic
421	C₄	#19152363	1	1	yes	characteristic
422	C₄	#19152404	1	1	yes	characteristic
423	C₄	#19152411	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	356	2	no	—
426	C₂	#26028982	1	1	yes	characteristic
427	C₂	#26029089	1	1	yes	characteristic
428	C₂	C₂×#19151712	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×#1493	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#13083574	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1493	D₈₉
hypocenter	C₈₉	#18016
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1493

Complements

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

N	H ≅ G/N	type
3. #26029354	C₂	semidirect
4. #26019146	C₂	semidirect
5. #26019120	C₂	semidirect
6. #26019112	C₂	semidirect
7. #26019049	C₂	semidirect
8. #26019043	C₂	semidirect
10. #26018535	C₂	semidirect
11. C₈₉×#1493	C₂	semidirect
223. #1493	D₈₉	semidirect
226. C₈₉	#18016	semidirect

Maximal subgroups

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

subgroup	index
#26030317	2
#26029378	2
#26029354	2
#26019146	2
#26019120	2
#26019112	2
#26019049	2
#26019043	2
#26018635	2
#26018535	2
C₈₉×#1493	2
#18016	89