Subgroups — #36526231

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	#26030812	C₂	1	1	yes	maximal, characteristic
2	#26028998	C₂	1	1	yes	maximal, characteristic
3	#26019152	C₂	1	2	yes	maximal, complemented
4	#26019130	C₂	1	2	yes	maximal, complemented
5	#26019107	C₂	1	2	yes	maximal, complemented
6	#26019062	C₂	1	2	yes	maximal, complemented
7	C₂×#19151350	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018655	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018650	C₂	1	1	yes	maximal, characteristic
10	#26018539	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2962	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151994	C₄	1	1	yes	characteristic
15	#19151972	C₄	1	1	yes	characteristic
16	#19151948	C₄	1	1	yes	characteristic
17	#19151946	C₄	1	1	yes	characteristic
18	#19151829	C₄	1	2	yes	—
19	#19151829	C₄	1	2	yes	—
20	C₄×#13083561	C₂²	1	2	yes	—
21	C₄×#13083561	C₂²	1	2	yes	—
22	#19151677	C₂²	1	2	yes	—
23	#19151671	—	2	2	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	#19151651	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
27	#19151566	—	2	1	no	—
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	#19151350	C₂²	1	1	yes	characteristic
30	#19151350	C₂²	1	1	yes	characteristic
31	#19151350	C₂²	1	1	yes	characteristic
32	#19151350	C₂²	1	1	yes	characteristic
33	Q₈⋊#10623494	C₂²	1	2	yes	—
34	Q₈⋊#10623494	C₂²	1	2	yes	—
35	#19151325	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151320	C₂²	1	2	yes	—
38	#19151320	C₂²	1	2	yes	—
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	#446×C₈₉	—	2	2	no	—
41	#446×C₈₉	C₂²	1	2	yes	—
42	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
43	#424×C₈₉	—	2	1	no	—
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#405×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083561	C₂×C₄	1	2	yes	—
49	C₂×#13083561	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	C₂×C₄	1	1	yes	characteristic
54	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₈₉	—	2	2	no	—
56	#15668012	C₂×C₄	1	1	yes	characteristic
57	#15668009	C₂×C₄	1	1	yes	characteristic
58	#15668000	—	2	1	no	—
59	#15667986	—	2	1	no	—
60	#15667986	C₂×C₄	1	2	yes	—
61	C₄×D₃₅₆	—	2	1	no	—
62	C₄×D₃₅₆	C₂³	1	2	yes	—
63	#15667943	C₂×C₄	1	2	yes	—
64	#15667943	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	#15667936	C₂×C₄	1	2	yes	—
70	#15667936	C₂×C₄	1	2	yes	—
71	#15667932	C₂×C₄	1	2	yes	—
72	#15667932	C₂×C₄	1	2	yes	—
73	C₂²⋊#10623494	—	2	1	no	—
74	#15667924	—	2	2	no	—
75	#15667924	—	2	2	no	—
76	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
77	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	2	yes	—
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₄×#10623494	C₂³	1	1	yes	characteristic
81	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
82	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
83	C₂²×C₈×C₈₉	—	2	1	no	—
84	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	#125×C₈₉	—	2	1	no	—
87	C₂²⋊Q₈×C₈₉	—	2	1	no	—
88	C₂²⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
89	C₄×Q₈×C₈₉	—	2	1	no	—
90	C₄×Q₈×C₈₉	C₂³	1	2	yes	—
91	#117×C₈₉	—	2	1	no	—
92	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₈₉	—	2	2	no	—
94	C₄⋊C₈×C₈₉	—	2	2	no	—
95	C₄⋊C₈×C₈₉	—	2	1	no	—
96	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#97×C₈₉	—	2	2	no	—
99	#97×C₈₉	D₄	1	2	yes	—
100	C₄×C₈×C₈₉	—	2	2	no	—
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×D₃₅₆	—	2	1	no	—
106	C₂×D₃₅₆	—	2	1	no	—
107	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
108	C₂×C₂²⋊D₈₉	—	2	2	no	—
109	C₂×C₄×D₈₉	—	2	2	no	—
110	#13083561	—	2	4	no	—
111	#13083561	—	4	2	no	—
112	#13083557	—	4	4	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	1	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	4	1	no	—
118	C₂×#10623494	—	4	2	no	—
119	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
120	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
123	C₈×D₈₉	—	4	4	no	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
126	#13083551	—	2	2	no	—
127	#13083551	—	2	2	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	—	2	2	no	—
134	M₁₆×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	4	2	no	—
138	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	2	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
146	C₂²⋊C₄×C₈₉	—	2	2	no	—
147	C₄²×C₈₉	—	2	2	no	—
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	Q₈×C₈₉	—	2	2	no	—
155	Q₈×C₈₉	—	2	2	no	—
156	Q₈×C₈₉	—	8	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	—	4	1	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	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₈₉	#137	1	2	yes	—
167	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
170	C₂²⋊D₈₉	—	4	4	no	—
171	C₂×Dic₈₉	—	2	2	no	—
172	D₃₅₆	—	2	2	no	—
173	D₃₅₆	—	2	2	no	—
174	D₃₅₆	—	4	2	no	—
175	D₃₅₆	—	8	1	no	—
176	C₄×D₈₉	—	4	2	no	—
177	C₄×D₈₉	—	4	2	no	—
178	Dic₁₇₈	—	4	2	no	—
179	C₈×C₈₉	—	2	2	no	—
180	C₈×C₈₉	—	2	2	no	—
181	C₈×C₈₉	—	4	1	no	—
182	C₈×C₈₉	—	4	1	no	—
183	#10623494	—	2	1	no	—
184	#10623494	—	2	1	no	—
185	#10623494	—	2	1	no	—
186	#10623494	—	4	2	no	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	1	no	—
189	#10623494	#131	1	2	yes	complemented
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	—	4	2	no	—
201	C₄×C₈₉	—	4	2	no	—
202	C₄×C₈₉	#440	1	2	yes	—
203	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
204	C₄×C₈₉	#568	1	1	yes	characteristic
205	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
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	D₈₉	1	1	yes	characteristic, complemented
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	—	89	1	no	—
225	C₈₉	#18071	1	1	yes	characteristic, complemented, Sylow
226	C₂×#131	—	178	1	no	—
227	#533	C₂×D₈₉	1	1	yes	characteristic
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	—	2	2	no	—
236	#446	C₂×D₈₉	1	2	yes	—
237	C₈×Q₈	C₂×D₈₉	1	2	yes	—
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	—	2	1	no	—
245	C₂×C₄⋊C₈	—	89	1	no	—
246	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
247	#408	—	178	1	no	—
248	#405	—	2	1	no	—
249	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
250	C₂×C₄×C₈	—	89	1	no	—
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	—	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	—	178	2	no	—
266	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
267	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	89	1	no	—
270	C₂²×C₈	—	89	1	no	—
271	C₂²×C₈	—	178	1	no	—
272	C₂²×C₈	—	178	2	no	—
273	C₄⋊Q₈	—	89	1	no	—
274	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
275	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
276	#127	—	89	1	no	—
277	#125	—	2	1	no	—
278	#124	—	178	1	no	—
279	C₂²⋊Q₈	—	2	1	no	—
280	C₂²⋊Q₈	C₄×D₈₉	1	2	yes	—
281	#121	—	89	2	no	—
282	#121	—	178	1	no	—
283	C₄×Q₈	—	2	1	no	—
284	C₄×Q₈	C₂²×D₈₉	1	2	yes	—
285	C₄×D₄	—	89	2	no	—
286	C₄×D₄	—	178	1	no	—
287	#117	—	2	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	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	89	1	no	—
295	C₄⋊C₈	—	89	1	no	—
296	C₄⋊C₈	—	178	1	no	—
297	C₄⋊C₈	—	178	1	no	—
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	1	no	—
305	C₂²⋊C₈	—	178	2	no	—
306	C₂²⋊C₈	—	178	2	no	—
307	#97	—	2	2	no	—
308	#97	C₂²⋊D₈₉	1	2	yes	—
309	C₄×C₈	—	2	2	no	—
310	C₄×C₈	—	89	1	no	—
311	C₄×C₈	—	89	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	89	2	no	—
315	C₄×C₈	C₂²×D₈₉	1	2	yes	—
316	#41	—	356	2	no	—
317	#41	—	356	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	178	1	no	—
320	C₂×Q₈	C₂×C₄×D₈₉	1	2	yes	—
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×C₂²⋊D₈₉	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	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	4	2	no	—
337	C₂×C₈	—	89	1	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	89	1	no	—
340	C₂×C₈	—	89	1	no	—
341	C₂×C₈	—	356	4	no	—
342	C₂×C₈	—	356	2	no	—
343	C₂×C₈	—	356	1	no	—
344	C₂×C₈	—	178	2	no	—
345	C₂×C₈	—	178	1	no	—
346	C₂×C₈	—	178	1	no	—
347	C₂×C₈	—	178	2	no	—
348	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
349	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	89	2	no	—
356	C₄⋊C₄	—	178	1	no	—
357	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	178	2	no	—
360	C₂²⋊C₄	—	178	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
363	C₄²	C₂×C₂²⋊D₈₉	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×C₂²⋊D₈₉	1	1	yes	characteristic
368	Q₈	—	2	2	no	—
369	Q₈	—	2	2	no	—
370	Q₈	—	8	1	no	—
371	Q₈	—	356	2	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	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	356	2	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	178	2	no	—
385	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
388	C₂×C₄	#15668037	1	2	yes	—
389	C₂×C₄	#15668043	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₂²⋊D₈₉	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	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	89	2	no	—
398	C₈	—	356	2	no	—
399	C₈	—	356	1	no	—
400	C₈	—	356	1	no	—
401	C₈	—	178	1	no	—
402	C₈	—	178	1	no	—
403	C₈	—	178	1	no	—
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	#19151696	1	2	yes	—
410	C₂²	C₂×C₄×C₂²⋊D₈₉	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	2	no	—
417	C₄	#19151696	1	2	yes	—
418	C₄	#131×D₈₉	1	1	yes	characteristic
419	C₄	#19152363	1	1	yes	characteristic
420	C₄	C₂×#15668037	1	1	yes	characteristic
421	C₄	C₂×#15668043	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	712	2	no	—
424	C₂	#26028994	1	1	yes	characteristic
425	C₂	C₂×#19151696	1	1	yes	characteristic
426	C₂	#26029167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2962	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#19152148	C₂²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2962	D₈₉
hypocenter	C₈₉	#18071
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2962

Complements

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

N	H ≅ G/N	type
3. #26019152	C₂	semidirect
4. #26019130	C₂	semidirect
5. #26019107	C₂	semidirect
6. #26019062	C₂	semidirect
7. C₂×#19151350	C₂	semidirect
8. #26018655	C₂	semidirect
10. #26018539	C₂	semidirect
11. C₈₉×#2962	C₂	semidirect
189. #10623494	#131	semidirect
215. #2962	D₈₉	semidirect
225. C₈₉	#18071	semidirect

Maximal subgroups

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

subgroup	index
#26030812	2
#26028998	2
#26019152	2
#26019130	2
#26019107	2
#26019062	2
C₂×#19151350	2
#26018655	2
#26018650	2
#26018539	2
C₈₉×#2962	2
#18071	89