Subgroups — #36525019

Order 22784.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030852	C₂	1	1	yes	maximal, characteristic
2	#26029221	C₂	1	1	yes	maximal, characteristic
3	#26029187	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019158	C₂	1	2	yes	maximal, complemented
5	#26019157	C₂	1	2	yes	maximal, complemented
6	#26019056	C₂	1	2	yes	maximal, complemented
7	#26019049	C₂	1	2	yes	maximal, complemented
8	#26019020	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018718	C₂	1	1	yes	maximal, characteristic
10	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1497	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152132	C₂²	1	1	yes	characteristic
13	#19152004	C₄	1	1	yes	characteristic
14	#19151990	C₄	1	1	yes	characteristic
15	#19151966	C₄	1	1	yes	characteristic
16	#19151960	C₄	1	1	yes	characteristic
17	#19151854	C₄	1	2	yes	—
18	#19151846	C₄	1	2	yes	—
19	#19151729	—	2	1	no	—
20	#19151729	C₂²	1	2	yes	—
21	#19151725	C₂²	1	1	yes	characteristic
22	Q₈×#10623494	—	2	1	no	—
23	Q₈×#10623494	C₂²	1	2	yes	—
24	#19151722	C₂²	1	1	yes	characteristic
25	C₄×#13083564	C₂²	1	2	yes	—
26	C₄×#13083561	C₂²	1	2	yes	—
27	#19151675	C₂²	1	1	yes	characteristic
28	#19151666	—	2	1	no	—
29	#19151663	C₂²	1	1	yes	characteristic
30	#19151661	—	2	1	no	—
31	#19151660	—	2	1	no	—
32	#19151625	—	2	1	no	—
33	#19151622	C₂²	1	1	yes	characteristic
34	#19151555	—	2	1	no	—
35	#19151554	—	2	1	no	—
36	C₄×#13083558	C₂²	1	1	yes	characteristic
37	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
38	#19151350	C₂²	1	2	yes	—
39	#19151348	C₂²	1	2	yes	—
40	#19151330	C₂²	1	2	yes	—
41	#19151327	C₂²	1	2	yes	—
42	#19151320	C₂²	1	2	yes	—
43	C₈×#10623494	C₂²	1	2	yes	—
44	#533×C₈₉	C₂²	1	1	yes	characteristic
45	#432×C₈₉	C₂²	1	1	yes	characteristic
46	#431×C₈₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
48	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	—
49	C₂×#13083564	C₂×C₄	1	2	yes	—
50	C₂×#13083561	C₂×C₄	1	2	yes	—
51	C₂×#13083558	—	2	1	no	—
52	C₂×#13083558	C₂×C₄	1	2	yes	—
53	C₂×#13083557	—	2	1	no	—
54	C₂²×#10623494	D₄	1	1	yes	characteristic
55	C₂²×#10623494	D₄	1	1	yes	characteristic
56	C₂×C₈×D₈₉	—	2	1	no	—
57	#15668006	—	2	1	no	—
58	#15668004	C₂×C₄	1	1	yes	characteristic
59	#15668000	C₂×C₄	1	1	yes	characteristic
60	#15667995	—	2	1	no	—
61	#15667991	C₂×C₄	1	1	yes	characteristic
62	#15667986	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
64	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
65	C₄×C₂²⋊D₈₉	—	2	1	no	—
66	#15667969	—	2	1	no	—
67	#15667945	C₂×C₄	1	2	yes	—
68	#15667943	C₂×C₄	1	2	yes	—
69	C₄⋊#10623494	—	2	2	no	—
70	C₄⋊#10623494	—	2	2	no	—
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#10623494	C₂³	1	2	yes	—
73	#15667941	—	2	1	no	—
74	#15667941	—	2	1	no	—
75	#15667936	C₂×C₄	1	2	yes	—
76	#15667936	C₂×C₄	1	2	yes	—
77	#15667935	C₂×C₄	1	2	yes	—
78	#15667932	C₂×C₄	1	2	yes	—
79	#15667924	—	2	1	no	—
80	#15667924	—	2	1	no	—
81	#15667923	—	2	2	no	—
82	#15667923	C₂×C₄	1	1	yes	characteristic
83	#15667923	C₂×C₄	1	1	yes	characteristic
84	#15667922	—	2	1	no	—
85	C₄×#10623494	—	2	2	no	—
86	C₄×#10623494	D₄	1	1	yes	characteristic
87	C₄×#10623494	D₄	1	1	yes	characteristic
88	C₄×#10623494	C₂³	1	2	yes	—
89	C₄×#10623494	C₂³	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	1	yes	characteristic
91	C₈×Dic₈₉	—	2	1	no	—
92	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	#125×C₈₉	—	2	1	no	—
95	C₂²⋊Q₈×C₈₉	—	2	1	no	—
96	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
97	C₄×Q₈×C₈₉	—	2	1	no	—
98	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
99	#117×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₈₉	—	2	1	no	—
102	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²⋊C₈×C₈₉	—	2	1	no	—
105	C₂²⋊C₈×C₈₉	—	2	1	no	—
106	#97×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	C₂³	1	2	yes	—
108	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
109	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₂²⋊D₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	#13083564	—	2	4	no	—
113	#13083561	—	2	4	no	—
114	#13083558	—	2	4	no	—
115	#13083558	—	4	2	no	—
116	#13083557	—	4	2	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	2	2	no	—
119	C₂×#10623494	—	4	1	no	—
120	C₂×#10623494	C₂²×C₄	1	2	yes	—
121	C₂×#10623494	C₂²×C₄	1	2	yes	—
122	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
123	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
124	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
125	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
126	C₈×D₈₉	—	4	2	no	—
127	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	#13083553	—	2	1	no	—
130	#13083553	—	2	1	no	—
131	#13083553	—	2	1	no	—
132	#13083553	—	2	1	no	—
133	C₂²⋊Dic₈₉	—	2	1	no	—
134	#13083551	—	2	1	no	—
135	#13083551	—	2	1	no	—
136	#13083551	—	2	1	no	—
137	#13083551	—	2	1	no	—
138	C₄×Dic₈₉	—	2	1	no	—
139	C₂×Q₈×C₈₉	—	2	1	no	—
140	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
144	C₂×C₈×C₈₉	—	2	1	no	—
145	C₂×C₈×C₈₉	—	2	1	no	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	2	no	—
151	C₄⋊C₄×C₈₉	—	2	2	no	—
152	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₈₉	—	2	2	no	—
154	C₄²×C₈₉	—	2	2	no	—
155	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	#41	1	1	yes	characteristic
158	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂²×D₈₉	—	2	1	no	—
161	Q₈×C₈₉	—	2	2	no	—
162	Q₈×C₈₉	—	2	2	no	—
163	Q₈×C₈₉	—	4	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	2	no	—
169	C₂×C₄×C₈₉	—	4	1	no	—
170	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₈₉	—	4	2	no	—
177	C₂×Dic₈₉	—	2	1	no	—
178	C₂×Dic₈₉	—	2	1	no	—
179	C₂×Dic₈₉	—	2	1	no	—
180	D₃₅₆	—	2	2	no	—
181	C₄×D₈₉	—	4	1	no	—
182	C₄×D₈₉	—	4	1	no	—
183	Dic₁₇₈	—	2	2	no	—
184	C₈×C₈₉	—	4	2	no	—
185	C₈×C₈₉	—	4	1	no	—
186	C₈×C₈₉	—	4	1	no	—
187	#10623494	—	2	2	no	—
188	#10623494	—	2	1	no	—
189	#10623494	—	2	1	no	—
190	#10623494	—	2	1	no	—
191	#10623494	—	4	2	no	—
192	#10623494	#131	1	4	yes	—
193	#10623494	#137	1	2	yes	—
194	C₂²×C₈₉	—	2	1	no	—
195	C₂²×C₈₉	—	2	1	no	—
196	C₂²×C₈₉	—	2	1	no	—
197	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂×D₈₉	—	4	1	no	—
199	C₂×D₈₉	—	4	1	no	—
200	C₂×D₈₉	—	4	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	2	1	no	—
203	C₄×C₈₉	—	2	1	no	—
204	C₄×C₈₉	—	2	1	no	—
205	C₄×C₈₉	—	4	2	no	—
206	C₄×C₈₉	—	4	2	no	—
207	C₄×C₈₉	C₂×#131	1	2	yes	—
208	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
209	C₄×C₈₉	#575	1	1	yes	characteristic
210	Dic₈₉	—	4	1	no	—
211	Dic₈₉	—	4	1	no	—
212	Dic₈₉	—	4	1	no	—
213	#17965	—	89	1	no	maximal, Sylow
214	C₂×C₈₉	—	4	1	no	—
215	C₂×C₈₉	#2931	1	1	yes	characteristic
216	C₂×C₈₉	C₄×#137	1	1	yes	characteristic
217	C₂×C₈₉	#2955	1	1	yes	characteristic
218	D₈₉	—	8	1	no	—
219	#3172	—	89	1	no	—
220	#2966	—	89	1	no	—
221	#2960	—	89	1	no	—
222	#1593	—	89	2	no	—
223	#1592	—	89	2	no	—
224	C₈×Q₁₆	—	89	2	no	—
225	C₈×SD₁₆	—	89	2	no	—
226	#1569	—	89	1	no	—
227	#1497	D₈₉	1	1	yes	characteristic, complemented
228	#1495	—	89	1	no	—
229	C₈×M₁₆	—	89	1	no	—
230	C₈₉	#17965	1	1	yes	characteristic, complemented, Sylow
231	#533	C₂×D₈₉	1	1	yes	characteristic
232	#529	—	89	1	no	—
233	#501	—	89	1	no	—
234	#497	—	89	1	no	—
235	#491	—	89	1	no	—
236	#489	—	89	1	no	—
237	#470	—	89	2	no	—
238	#468	—	89	2	no	—
239	#446	—	89	2	no	—
240	#446	—	89	1	no	—
241	#446	—	178	1	no	—
242	C₈×Q₈	—	89	2	no	—
243	C₈×Q₈	—	89	1	no	—
244	C₈×Q₈	—	178	1	no	—
245	C₄×Q₁₆	—	89	2	no	—
246	C₄×SD₁₆	—	89	2	no	—
247	#436	—	89	1	no	—
248	#435	—	178	1	no	—
249	C₈×D₄	—	89	1	no	—
250	C₈×D₄	—	178	1	no	—
251	#433	—	178	1	no	—
252	#432	C₂×D₈₉	1	1	yes	characteristic
253	#431	C₂×D₈₉	1	1	yes	characteristic
254	#424	—	178	1	no	—
255	#423	—	89	1	no	—
256	#405	—	178	1	no	—
257	#405	—	178	1	no	—
258	C₄×M₁₆	—	89	1	no	—
259	C₂×C₄×C₈	—	89	1	no	—
260	#335	—	89	2	no	—
261	#334	—	89	2	no	—
262	Q₈⋊C₈	—	89	2	no	—
263	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
264	Q₈⋊C₈	C₂×D₈₉	1	2	yes	—
265	D₄⋊C₈	—	89	2	no	—
266	#322	—	89	2	no	—
267	C₈²	—	89	2	no	—
268	C₂×Q₁₆	—	89	2	no	—
269	C₂×SD₁₆	—	89	2	no	—
270	C₂×M₁₆	—	89	2	no	—
271	C₂×M₁₆	—	178	1	no	—
272	C₂×M₁₆	—	178	1	no	—
273	C₂²×C₈	—	89	1	no	—
274	C₂²×C₈	—	89	1	no	—
275	C₂²×C₈	—	178	1	no	—
276	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
277	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
278	#126	—	178	1	no	—
279	#125	—	2	1	no	—
280	#125	—	89	1	no	—
281	#124	—	89	1	no	—
282	#123	—	178	1	no	—
283	C₂²⋊Q₈	—	2	1	no	—
284	C₂²⋊Q₈	—	89	1	no	—
285	C₂²⋊Q₈	C₄×D₈₉	1	2	yes	—
286	#121	—	89	1	no	—
287	C₄×Q₈	—	2	1	no	—
288	C₄×Q₈	—	89	1	no	—
289	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
290	C₄×D₄	—	89	1	no	—
291	C₄×D₄	—	178	1	no	—
292	#117	—	2	1	no	—
293	#117	—	178	1	no	—
294	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
295	#107	—	89	2	no	—
296	#106	—	89	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	—	178	2	no	—
300	C₄⋊C₈	—	178	2	no	—
301	C₄⋊C₈	—	178	1	no	—
302	C₄⋊C₈	—	178	1	no	—
303	C₄⋊C₈	—	178	1	no	—
304	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
306	#103	—	89	2	no	—
307	#103	—	89	2	no	—
308	#103	—	89	2	no	—
309	#102	—	89	2	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	178	1	no	—
313	C₂²⋊C₈	—	178	1	no	—
314	#97	—	2	1	no	—
315	#97	—	89	1	no	—
316	#97	—	89	1	no	—
317	#97	—	178	2	no	—
318	#97	—	178	1	no	—
319	C₄×C₈	—	89	1	no	—
320	C₄×C₈	—	89	1	no	—
321	C₄×C₈	—	89	1	no	—
322	C₄×C₈	—	89	2	no	—
323	C₄×C₈	—	89	1	no	—
324	C₄×C₈	—	178	2	no	—
325	C₄×C₈	—	178	1	no	—
326	C₄×C₈	C₂²×D₈₉	1	2	yes	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	89	1	no	—
329	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
330	C₂×D₄	—	89	1	no	—
331	C₂×D₄	—	178	1	no	—
332	C₂²×C₄	—	178	1	no	—
333	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
334	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	#13083573	1	1	yes	characteristic
336	Q₁₆	—	178	4	no	—
337	SD₁₆	—	178	4	no	—
338	M₁₆	—	356	2	no	—
339	M₁₆	—	356	2	no	—
340	M₁₆	—	178	4	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	89	2	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	89	2	no	—
347	C₂×C₈	—	89	1	no	—
348	C₂×C₈	—	89	1	no	—
349	C₂×C₈	—	89	1	no	—
350	C₂×C₈	—	356	2	no	—
351	C₂×C₈	—	356	1	no	—
352	C₂×C₈	—	178	2	no	—
353	C₂×C₈	—	178	2	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	89	1	no	—
360	C₄⋊C₄	—	89	1	no	—
361	C₄⋊C₄	—	178	1	no	—
362	C₄⋊C₄	—	178	1	no	—
363	C₄⋊C₄	—	178	1	no	—
364	C₄⋊C₄	—	178	1	no	—
365	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	178	1	no	—
368	C₂²⋊C₄	—	178	1	no	—
369	C₂²⋊C₄	—	178	1	no	—
370	C₂²⋊C₄	—	178	1	no	—
371	C₂²⋊C₄	—	178	1	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	178	1	no	—
374	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
375	C₄²	D₄×D₈₉	1	1	yes	characteristic
376	C₄²	#13083573	1	1	yes	characteristic
377	C₄²	C₂³×D₈₉	1	1	yes	characteristic
378	C₂³	—	178	1	no	—
379	C₂³	#15667972	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	178	2	no	—
384	D₄	—	356	2	no	—
385	D₄	—	178	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	356	1	no	—
393	C₂×C₄	—	356	1	no	—
394	C₂×C₄	—	178	1	no	—
395	C₂×C₄	—	178	1	no	—
396	C₂×C₄	—	178	1	no	—
397	C₂×C₄	#15667972	1	1	yes	characteristic
398	C₂×C₄	#15667972	1	1	yes	characteristic
399	C₂×C₄	#15667972	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
402	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
403	C₈	—	4	2	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	89	2	no	—
407	C₈	—	89	4	no	—
408	C₈	—	356	2	no	—
409	C₈	—	178	1	no	—
410	C₈	—	178	1	no	—
411	C₈	—	178	1	no	—
412	C₈	—	178	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	356	1	no	—
417	C₂²	—	356	1	no	—
418	C₂²	—	356	1	no	—
419	C₂²	C₂×#15667972	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	356	1	no	—
427	C₄	—	356	1	no	—
428	C₄	—	356	1	no	—
429	C₄	#131×D₈₉	1	2	yes	—
430	C₄	#137×D₈₉	1	1	yes	characteristic
431	C₄	#19152397	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	712	1	no	—
434	C₂	#26028960	1	1	yes	characteristic
435	C₂	#26029067	1	1	yes	characteristic
436	C₂	#26029151	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×#1497	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#15667986	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1497	D₈₉
hypocenter	C₈₉	#17965
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1497

Complements

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

N	H ≅ G/N	type
3. #26029187	C₂	semidirect
4. #26019158	C₂	semidirect
5. #26019157	C₂	semidirect
6. #26019056	C₂	semidirect
7. #26019049	C₂	semidirect
8. #26019020	C₂	semidirect
10. #26018533	C₂	semidirect
11. C₈₉×#1497	C₂	semidirect
227. #1497	D₈₉	semidirect
230. C₈₉	#17965	semidirect

Maximal subgroups

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

subgroup	index
#26030852	2
#26029221	2
#26029187	2
#26019158	2
#26019157	2
#26019056	2
#26019049	2
#26019020	2
#26018718	2
#26018533	2
C₈₉×#1497	2
#17965	89