Subgroups — #36612588

Order 22784.

658 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26025283	C₂	1	1	yes	maximal, characteristic
2	#26023209	C₂	1	1	yes	maximal, characteristic
3	#26021629	C₂	1	2	yes	maximal
4	#26021401	C₂	1	2	yes	maximal
5	#26021206	C₂	1	2	yes	maximal
6	#26021015	C₂	1	1	yes	maximal, characteristic
7	#26020970	C₂	1	1	yes	maximal, characteristic
8	#26020840	C₂	1	2	yes	maximal
9	#26020380	C₂	1	1	yes	maximal, characteristic
10	#26020257	C₂	1	1	yes	maximal, characteristic
11	C₄×#103×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668003	C₂²	1	2	yes	—
13	C₂×#15667943	C₂²	1	2	yes	—
14	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
15	C₂×#15667941	C₂²	1	2	yes	—
16	C₂×#15667936	C₂²	1	2	yes	—
17	#19151530	—	2	2	no	—
18	#19151505	C₂²	1	2	yes	—
19	#19151497	C₂²	1	2	yes	—
20	#19151496	—	2	1	no	—
21	#19151484	—	2	2	no	—
22	#19151468	—	2	1	no	—
23	#19151468	C₂²	1	1	yes	characteristic
24	#19151468	C₂²	1	1	yes	characteristic
25	#19151464	—	2	1	no	—
26	C₄⋊C₄×Dic₈₉	C₂²	1	2	yes	—
27	C₄×C₄⋊Dic₈₉	—	2	1	no	—
28	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
29	#19151361	C₂²	1	2	yes	—
30	#19151361	C₂²	1	2	yes	—
31	#19151360	C₂²	1	2	yes	—
32	#19151360	C₂²	1	2	yes	—
33	#19151352	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	#340×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×#10623494	C₂³	1	2	yes	—
42	#15668003	—	2	4	no	—
43	#15668003	—	4	2	no	—
44	C₂×C₄⋊Dic₈₉	—	2	2	no	—
45	C₂×C₄⋊Dic₈₉	—	2	2	no	—
46	C₂×C₄⋊Dic₈₉	—	2	1	no	—
47	C₂×C₄⋊Dic₈₉	—	2	1	no	—
48	C₂×C₄⋊Dic₈₉	—	2	1	no	—
49	C₂×C₄⋊Dic₈₉	—	2	1	no	—
50	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
53	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
54	C₂×#13083553	—	2	2	no	—
55	C₂×C₄×Dic₈₉	—	2	2	no	—
56	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
57	#15667943	—	2	4	no	—
58	C₄⋊#10623494	—	2	2	no	—
59	#15667941	—	4	2	no	—
60	#15667936	—	4	2	no	—
61	#15667919	—	2	2	no	—
62	#15667919	—	2	2	no	—
63	#15667919	—	2	2	no	—
64	#15667919	—	2	2	no	—
65	#15667919	D₄	1	2	yes	—
66	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₄×Q₈×C₈₉	—	2	2	no	—
70	C₄×Q₈×C₈₉	Q₈	1	4	yes	—
71	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	—	2	1	no	—
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	#103×C₈₉	—	2	2	no	—
79	#103×C₈₉	—	2	2	no	—
80	C₄×C₈×C₈₉	—	2	2	no	—
81	#95×C₈₉	—	2	1	no	—
82	C₂²×Dic₈₉	—	2	2	no	—
83	C₂²×Dic₈₉	—	2	2	no	—
84	C₂²×Dic₈₉	C₂×D₄	1	2	yes	—
85	C₂²×Dic₈₉	C₂×D₄	1	2	yes	—
86	C₂×#10623494	—	2	2	no	—
87	C₂×#10623494	—	2	2	no	—
88	C₂×#10623494	—	2	2	no	—
89	C₄⋊Dic₈₉	—	2	2	no	—
90	C₄⋊Dic₈₉	—	2	2	no	—
91	C₄⋊Dic₈₉	—	2	2	no	—
92	C₄⋊Dic₈₉	—	2	2	no	—
93	C₄⋊Dic₈₉	—	2	2	no	—
94	C₄⋊Dic₈₉	—	2	2	no	—
95	C₄⋊Dic₈₉	—	4	4	no	—
96	C₄⋊Dic₈₉	—	4	2	no	—
97	C₄⋊Dic₈₉	—	4	2	no	—
98	C₄⋊Dic₈₉	—	8	2	no	—
99	C₄⋊Dic₈₉	—	8	1	no	—
100	C₄⋊Dic₈₉	—	8	1	no	—
101	#13083553	—	4	4	no	—
102	C₄×Dic₈₉	—	2	2	no	—
103	C₄×Dic₈₉	—	2	2	no	—
104	C₄×Dic₈₉	—	8	2	no	—
105	C₂×Q₈×C₈₉	—	2	1	no	—
106	C₂×Q₈×C₈₉	—	2	1	no	—
107	C₂×Q₈×C₈₉	—	2	1	no	—
108	C₂×Q₈×C₈₉	—	2	1	no	—
109	C₂×Q₈×C₈₉	—	2	1	no	—
110	C₂×Q₈×C₈₉	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₈₉	—	2	1	no	—
112	C₂²×C₄×C₈₉	—	2	1	no	—
113	C₂²×C₄×C₈₉	—	2	1	no	—
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	—	2	1	no	—
123	C₂×C₈×C₈₉	—	2	1	no	—
124	C₄⋊C₄×C₈₉	—	2	4	no	—
125	C₄⋊C₄×C₈₉	—	2	1	no	—
126	C₄⋊C₄×C₈₉	—	2	1	no	—
127	C₄⋊C₄×C₈₉	—	2	1	no	—
128	C₄⋊C₄×C₈₉	C₂×Q₈	1	2	yes	—
129	C₄⋊C₄×C₈₉	#41	1	2	yes	—
130	C₄⋊C₄×C₈₉	#41	1	2	yes	—
131	C₄²×C₈₉	—	2	4	no	—
132	C₄²×C₈₉	—	4	2	no	—
133	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
134	C₄²×C₈₉	#41	1	2	yes	—
135	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₈₉	—	2	2	no	—
137	Q₈×C₈₉	—	2	2	no	—
138	Q₈×C₈₉	—	4	1	no	—
139	Q₈×C₈₉	—	4	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	—	4	1	no	—
148	C₂×C₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	1	no	—
151	C₂×C₄×C₈₉	—	4	1	no	—
152	C₂×C₄×C₈₉	—	4	1	no	—
153	C₂×C₄×C₈₉	—	4	1	no	—
154	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
156	C₂×C₄×C₈₉	#135	1	2	yes	—
157	C₂×C₄×C₈₉	#137	1	2	yes	—
158	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	—	2	2	no	—
167	C₂×Dic₈₉	—	2	2	no	—
168	C₂×Dic₈₉	—	2	2	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	4	2	no	—
171	C₂×Dic₈₉	—	4	2	no	—
172	C₂×Dic₈₉	—	4	2	no	—
173	C₂×Dic₈₉	—	4	2	no	—
174	C₂×Dic₈₉	—	4	2	no	—
175	C₂×Dic₈₉	—	4	2	no	—
176	C₈×C₈₉	—	4	1	no	—
177	C₈×C₈₉	—	4	1	no	—
178	#10623494	—	4	2	no	—
179	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
180	C₂²×C₈₉	#546	1	1	yes	characteristic
181	C₂²×C₈₉	#548	1	1	yes	characteristic
182	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
183	C₂²×C₈₉	C₂×#137	1	1	yes	characteristic
184	C₂²×C₈₉	#577	1	1	yes	characteristic
185	C₂²×C₈₉	#577	1	1	yes	characteristic
186	C₄×C₈₉	—	2	2	no	—
187	C₄×C₈₉	—	4	2	no	—
188	C₄×C₈₉	—	4	2	no	—
189	C₄×C₈₉	—	4	2	no	—
190	C₄×C₈₉	—	4	2	no	—
191	C₄×C₈₉	#479	1	4	yes	—
192	C₄×C₈₉	#533	1	1	yes	characteristic
193	C₄×C₈₉	#544	1	1	yes	characteristic
194	C₄×C₈₉	#555	1	1	yes	characteristic
195	C₄×C₈₉	#556	1	1	yes	characteristic
196	Dic₈₉	—	4	2	no	—
197	Dic₈₉	—	4	2	no	—
198	Dic₈₉	—	8	2	no	—
199	Dic₈₉	—	8	2	no	—
200	#26027	—	89	1	no	maximal, Sylow
201	C₂×C₈₉	#2439	1	1	yes	characteristic
202	C₂×C₈₉	C₂×#479	1	1	yes	characteristic
203	C₂×C₈₉	#3084	1	1	yes	characteristic
204	C₂×C₈₉	#3304	1	1	yes	characteristic
205	C₂×C₈₉	#3331	1	1	yes	characteristic
206	C₂×C₈₉	#3365	1	1	yes	characteristic
207	C₂×C₈₉	#3372	1	1	yes	characteristic
208	#2552	—	89	1	no	—
209	#2355	—	89	1	no	—
210	#2066	—	89	2	no	—
211	#2026	—	89	2	no	—
212	#1989	—	89	2	no	—
213	#1948	—	89	1	no	—
214	#1939	—	89	1	no	—
215	#1920	—	89	2	no	—
216	#1834	—	89	1	no	—
217	#1803	—	89	1	no	—
218	C₄×#103	D₈₉	1	1	yes	characteristic
219	C₈₉	#26027	1	1	yes	characteristic, complemented, Sylow
220	C₂×#125	—	89	2	no	—
221	C₂×C₄×Q₈	C₂×D₈₉	1	1	yes	characteristic
222	C₂×#106	—	89	2	no	—
223	C₂×C₄⋊C₈	—	89	2	no	—
224	C₂×C₄⋊C₈	—	89	1	no	—
225	C₂×#103	—	89	2	no	—
226	C₂×#103	C₂×D₈₉	1	1	yes	characteristic
227	C₂×#103	C₂×D₈₉	1	1	yes	characteristic
228	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
229	#398	—	178	2	no	—
230	#391	—	89	2	no	—
231	#389	—	89	2	no	—
232	#389	—	178	1	no	—
233	#387	—	178	2	no	—
234	#384	—	89	1	no	—
235	#384	—	89	1	no	—
236	#384	—	178	1	no	—
237	#382	—	178	1	no	—
238	C₄×C₄⋊C₄	—	89	1	no	—
239	C₄×C₄⋊C₄	—	89	2	no	—
240	C₄×C₄⋊C₄	—	178	1	no	—
241	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
242	#340	—	89	2	no	—
243	#340	—	89	2	no	—
244	#340	—	89	2	no	—
245	#340	—	89	2	no	—
246	#340	C₂×D₈₉	1	1	yes	characteristic
247	#340	C₂×D₈₉	1	1	yes	characteristic
248	#336	—	89	2	no	—
249	C₂²×Q₈	C₂²×D₈₉	1	1	yes	characteristic
250	C₂²×C₈	—	89	2	no	—
251	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
253	#125	—	356	2	no	—
254	#125	—	178	4	no	—
255	C₄×Q₈	—	2	2	no	—
256	C₄×Q₈	Dic₁₇₈	1	4	yes	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	89	1	no	—
259	C₂×C₄⋊C₄	—	89	1	no	—
260	C₂×C₄⋊C₄	—	89	2	no	—
261	C₂×C₄⋊C₄	—	89	2	no	—
262	C₂×C₄⋊C₄	—	178	2	no	—
263	C₂×C₄⋊C₄	—	178	2	no	—
264	C₂×C₄⋊C₄	—	178	1	no	—
265	C₂×C₄⋊C₄	—	178	1	no	—
266	C₂×C₄⋊C₄	—	178	2	no	—
267	C₂×C₄⋊C₄	—	178	1	no	—
268	C₂×C₄⋊C₄	—	178	1	no	—
269	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²×D₈₉	1	1	yes	characteristic
272	C₂×C₄²	—	2	1	no	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	89	2	no	—
275	C₂×C₄²	—	178	2	no	—
276	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
277	#106	—	178	4	no	—
278	C₄⋊C₈	—	356	2	no	—
279	C₄⋊C₈	—	178	2	no	—
280	#103	—	2	2	no	—
281	#103	—	2	2	no	—
282	#103	—	356	2	no	—
283	C₄×C₈	—	2	2	no	—
284	#95	—	2	1	no	—
285	#95	—	89	2	no	—
286	#95	—	178	2	no	—
287	#95	—	178	2	no	—
288	#95	—	178	2	no	—
289	#95	—	178	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×Q₈	C₂×Dic₁₇₈	1	2	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	89	2	no	—
301	C₂²×C₄	—	89	2	no	—
302	C₂²×C₄	—	178	2	no	—
303	C₂²×C₄	—	178	2	no	—
304	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	178	2	no	—
314	C₂×C₈	—	178	2	no	—
315	C₂×C₈	—	178	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	1	no	—
318	C₄⋊C₄	—	2	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	356	4	no	—
321	C₄⋊C₄	—	356	4	no	—
322	C₄⋊C₄	—	356	2	no	—
323	C₄⋊C₄	—	356	2	no	—
324	C₄⋊C₄	—	178	2	no	—
325	C₄⋊C₄	—	178	2	no	—
326	C₄⋊C₄	—	178	2	no	—
327	C₄⋊C₄	—	178	2	no	—
328	C₄⋊C₄	—	178	2	no	—
329	C₄⋊C₄	—	178	2	no	—
330	C₄⋊C₄	—	712	1	no	—
331	C₄⋊C₄	—	712	1	no	—
332	C₄⋊C₄	—	712	2	no	—
333	C₄⋊C₄	C₂×Dic₁₇₈	1	2	yes	—
334	C₄⋊C₄	#13083574	1	2	yes	—
335	C₄⋊C₄	#13083574	1	2	yes	—
336	C₄²	—	2	4	no	—
337	C₄²	—	4	2	no	—
338	C₄²	—	178	2	no	—
339	C₄²	—	178	2	no	—
340	C₄²	—	712	2	no	—
341	C₄²	C₂×Dic₁₇₈	1	2	yes	—
342	C₄²	#13083573	1	2	yes	—
343	C₂³	C₂×D₄×D₈₉	1	1	yes	characteristic
344	Q₈	—	2	2	no	—
345	Q₈	—	2	2	no	—
346	Q₈	—	4	1	no	—
347	Q₈	—	4	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	4	1	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	356	2	no	—
363	C₂×C₄	—	356	2	no	—
364	C₂×C₄	—	356	2	no	—
365	C₂×C₄	—	356	2	no	—
366	C₂×C₄	—	356	2	no	—
367	C₂×C₄	—	356	2	no	—
368	C₂×C₄	—	178	2	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	—	178	2	no	—
372	C₂×C₄	—	178	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	#15667989	1	2	yes	—
375	C₂×C₄	#15667989	1	2	yes	—
376	C₂×C₄	#15668035	1	2	yes	—
377	C₂×C₄	#15668041	1	2	yes	—
378	C₂×C₄	C₂²×Dic₁₇₈	1	1	yes	characteristic
379	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
380	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
381	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
382	C₂×C₄	#15668058	1	1	yes	characteristic
383	C₂×C₄	#15668059	1	1	yes	characteristic
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	—	356	2	no	—
387	C₂²	C₂×#15667989	1	1	yes	characteristic
388	C₂²	#19152244	1	1	yes	characteristic
389	C₂²	#19152257	1	1	yes	characteristic
390	C₂²	C₂×#15668035	1	1	yes	characteristic
391	C₂²	C₂×#15668041	1	1	yes	characteristic
392	C₂²	#19152405	1	1	yes	characteristic
393	C₂²	#19152405	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	2	no	—
399	C₄	—	356	2	no	—
400	C₄	—	356	2	no	—
401	C₄	—	712	2	no	—
402	C₄	—	712	2	no	—
403	C₄	#19151907	1	4	yes	—
404	C₄	#19152155	1	1	yes	characteristic
405	C₄	#19152226	1	1	yes	characteristic
406	C₄	#19152313	1	1	yes	characteristic
407	C₄	#19152318	1	1	yes	characteristic
408	C₂	#26023943	1	1	yes	characteristic
409	C₂	C₂×#19151907	1	1	yes	characteristic
410	C₂	#26030112	1	1	yes	characteristic
411	C₂	#26032193	1	1	yes	characteristic
412	C₂	#26032570	1	1	yes	characteristic
413	C₂	#26032946	1	1	yes	characteristic
414	C₂	#26033031	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₈₉
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₄×#103×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	C₂²×D₄
hypercenter	C₄×#103	D₈₉
hypocenter	C₈₉	#26027
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₄×#103

Complements

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

N	H ≅ G/N	type
219. C₈₉	#26027	semidirect

Maximal subgroups

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

subgroup	index
#26025283	2
#26023209	2
#26021629	2
#26021401	2
#26021206	2
#26021015	2
#26020970	2
#26020840	2
#26020380	2
#26020257	2
C₄×#103×C₈₉	2
#26027	89