Subgroups — #36562765

Order 22784.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#15668003	C₂	1	1	yes	maximal, characteristic
2	#26020970	C₂	1	1	yes	maximal, characteristic
3	#26020817	C₂	1	2	yes	maximal
4	#26020813	C₂	1	2	yes	maximal
5	#26020368	C₂	1	1	yes	maximal, characteristic
6	#26020123	C₂	1	2	yes	maximal
7	#26020122	C₂	1	1	yes	maximal, characteristic
8	#26020122	C₂	1	2	yes	maximal
9	C₄⋊C₄×#10623494	C₂	1	1	yes	maximal, characteristic
10	C₄×#15667922	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1939	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668003	C₄	1	1	yes	characteristic
13	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
14	C₂×#15667941	C₂²	1	2	yes	—
15	C₂×#15667922	C₂²	1	2	yes	—
16	C₂×#15667922	C₂²	1	1	yes	characteristic
17	C₂×#15667922	C₂²	1	1	yes	characteristic
18	C₂×#15667922	C₂²	1	1	yes	characteristic
19	C₂×#15667922	C₂²	1	1	yes	characteristic
20	C₂×C₄×#10623494	C₂²	1	2	yes	—
21	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
22	#19151497	C₄	1	1	yes	characteristic
23	#19151494	C₄	1	1	yes	characteristic
24	#19151485	C₄	1	2	yes	—
25	#19151481	C₄	1	2	yes	—
26	#19151463	C₄	1	1	yes	characteristic
27	C₄×#13083553	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
30	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151353	C₂²	1	2	yes	—
32	#19151352	C₂²	1	2	yes	—
33	#19151352	C₂²	1	2	yes	—
34	#19151352	C₂²	1	2	yes	—
35	#19151352	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	2	yes	—
41	C₂²×#10623494	C₂³	1	2	yes	—
42	C₂²×#10623494	C₂³	1	1	yes	characteristic
43	C₂²×#10623494	C₂³	1	1	yes	characteristic
44	#15668003	—	2	4	no	—
45	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₈₉	C₂×C₄	1	2	yes	—
49	C₂×#13083553	C₂×C₄	1	2	yes	—
50	C₂×#13083553	C₂×C₄	1	2	yes	—
51	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	C₂³	1	2	yes	—
56	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
58	C₄⋊#10623494	—	2	2	no	—
59	#15667941	—	2	4	no	—
60	#15667922	—	2	2	no	—
61	#15667922	—	2	2	no	—
62	#15667922	—	2	4	no	—
63	#15667922	—	2	2	no	—
64	#15667922	—	2	2	no	—
65	C₄×#10623494	—	2	4	no	—
66	C₄×#10623494	Q₈	1	4	yes	—
67	#15667919	C₂×C₄	1	2	yes	—
68	#15667919	C₂×C₄	1	2	yes	—
69	#15667919	C₂×C₄	1	2	yes	—
70	#15667919	C₂×C₄	1	2	yes	—
71	#15667919	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₈₉	—	2	4	no	—
80	C₄⋊C₈×C₈₉	—	2	2	no	—
81	C₄×C₈×C₈₉	—	2	2	no	—
82	#95×C₈₉	C₂×C₄	1	2	yes	—
83	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
84	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
85	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×Dic₈₉	C₂²×C₄	1	2	yes	—
89	C₂×#10623494	—	2	1	no	—
90	C₂×#10623494	—	2	1	no	—
91	C₂×#10623494	—	2	2	no	—
92	C₂×#10623494	—	2	2	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	C₂×Q₈	1	2	yes	—
95	C₂×#10623494	C₂×Q₈	1	2	yes	—
96	C₂×#10623494	#41	1	2	yes	—
97	C₂×#10623494	#41	1	2	yes	—
98	C₄⋊Dic₈₉	—	2	4	no	—
99	C₄⋊Dic₈₉	—	2	2	no	—
100	C₄⋊Dic₈₉	—	2	2	no	—
101	C₄⋊Dic₈₉	—	4	2	no	—
102	#13083553	—	2	4	no	—
103	#13083553	—	4	2	no	—
104	C₄×Dic₈₉	—	2	2	no	—
105	C₄×Dic₈₉	—	2	2	no	—
106	C₄×Dic₈₉	—	2	1	no	—
107	C₄×Dic₈₉	—	2	2	no	—
108	C₄×Dic₈₉	—	2	1	no	—
109	C₄×Dic₈₉	—	2	1	no	—
110	C₄×Dic₈₉	—	2	1	no	—
111	C₄×Dic₈₉	—	2	2	no	—
112	C₄×Dic₈₉	—	4	1	no	—
113	C₄×Dic₈₉	—	4	1	no	—
114	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
124	C₂×C₈×C₈₉	—	2	2	no	—
125	C₂×C₈×C₈₉	—	2	2	no	—
126	C₂×C₈×C₈₉	#41	1	2	yes	—
127	C₂×C₈×C₈₉	#41	1	2	yes	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	M₁₆	1	4	yes	—
130	C₄²×C₈₉	—	2	2	no	—
131	C₄²×C₈₉	—	2	2	no	—
132	C₄²×C₈₉	C₂×Q₈	1	2	yes	—
133	C₄²×C₈₉	#41	1	2	yes	—
134	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	1	no	—
137	C₂×C₄×C₈₉	—	2	1	no	—
138	C₂×C₄×C₈₉	—	2	2	no	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
145	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
146	C₂×C₄×C₈₉	#131	1	2	yes	—
147	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₂×Dic₈₉	—	2	1	no	—
154	C₂×Dic₈₉	—	2	1	no	—
155	C₂×Dic₈₉	—	2	1	no	—
156	C₂×Dic₈₉	—	2	2	no	—
157	C₂×Dic₈₉	—	2	1	no	—
158	C₂×Dic₈₉	—	2	2	no	—
159	C₂×Dic₈₉	—	2	1	no	—
160	C₂×Dic₈₉	—	2	1	no	—
161	C₂×Dic₈₉	—	2	2	no	—
162	C₂×Dic₈₉	—	2	1	no	—
163	C₂×Dic₈₉	—	2	1	no	—
164	C₂×Dic₈₉	—	2	2	no	—
165	C₂×Dic₈₉	—	2	1	no	—
166	C₂×Dic₈₉	—	2	1	no	—
167	C₂×Dic₈₉	—	2	1	no	—
168	C₂×Dic₈₉	—	2	1	no	—
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₈×C₈₉	—	2	2	no	—
172	C₈×C₈₉	—	2	2	no	—
173	C₈×C₈₉	—	4	2	no	—
174	#10623494	—	2	2	no	—
175	#10623494	—	4	2	no	—
176	#10623494	#125	1	4	yes	complemented
177	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
178	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
179	C₂²×C₈₉	C₄×#41	1	1	yes	characteristic
180	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
181	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
182	C₂²×C₈₉	#568	1	1	yes	characteristic
183	C₂²×C₈₉	#568	1	1	yes	characteristic
184	C₄×C₈₉	—	2	2	no	—
185	C₄×C₈₉	—	2	4	no	—
186	C₄×C₈₉	—	4	2	no	—
187	C₄×C₈₉	#446	1	4	yes	—
188	C₄×C₈₉	C₂×#125	1	1	yes	characteristic
189	C₄×C₈₉	#529	1	1	yes	characteristic
190	C₄×C₈₉	#529	1	1	yes	characteristic
191	C₄×C₈₉	#533	1	1	yes	characteristic
192	Dic₈₉	—	4	1	no	—
193	Dic₈₉	—	4	2	no	—
194	Dic₈₉	—	4	1	no	—
195	Dic₈₉	—	4	1	no	—
196	Dic₈₉	—	4	1	no	—
197	Dic₈₉	—	4	2	no	—
198	#21675	—	89	1	no	maximal, Sylow
199	C₂×C₈₉	C₄×#125	1	1	yes	characteristic
200	C₂×C₈₉	C₂×#446	1	1	yes	characteristic
201	C₂×C₈₉	#2961	1	1	yes	characteristic
202	C₂×C₈₉	#2969	1	1	yes	characteristic
203	C₂×C₈₉	#2969	1	1	yes	characteristic
204	C₂×C₈₉	#2970	1	1	yes	characteristic
205	C₂×C₈₉	#2971	1	1	yes	characteristic
206	C₄×#125	—	89	1	no	—
207	#1939	—	89	1	no	—
208	#1939	D₈₉	1	1	yes	characteristic
209	#1917	—	89	2	no	—
210	#1917	—	89	2	no	—
211	#1831	—	89	1	no	—
212	#1771	—	89	2	no	—
213	#1770	—	89	2	no	—
214	#1770	—	89	1	no	—
215	C₈×C₄⋊C₄	—	89	1	no	—
216	C₄×#97	—	89	1	no	—
217	C₈₉	#21675	1	1	yes	characteristic, complemented, Sylow
218	C₂×#125	—	89	1	no	—
219	C₂×C₄⋊C₈	—	89	2	no	—
220	C₂×C₄⋊C₈	—	89	1	no	—
221	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
222	C₂×C₄⋊C₈	C₂×D₈₉	1	2	yes	—
223	C₂×#97	—	89	1	no	—
224	C₂×#97	—	89	1	no	—
225	C₂×#97	—	89	1	no	—
226	C₂×#97	—	89	1	no	—
227	C₂×#97	—	89	2	no	—
228	C₂×C₄×C₈	—	89	1	no	—
229	C₂×C₄×C₈	—	89	2	no	—
230	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
231	#389	—	89	1	no	—
232	#389	—	89	1	no	—
233	#387	—	89	2	no	—
234	#387	—	89	2	no	—
235	#382	—	89	1	no	—
236	C₄×C₄⋊C₄	—	89	2	no	—
237	C₄×C₄⋊C₄	—	89	1	no	—
238	C₄×C₄⋊C₄	—	89	2	no	—
239	C₄×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
240	C₄³	—	89	1	no	—
241	#336	—	89	2	no	—
242	#336	—	89	2	no	—
243	#336	—	89	2	no	—
244	#336	—	89	2	no	—
245	#336	—	89	2	no	—
246	#336	C₂×D₈₉	1	2	yes	—
247	C₂²×C₈	—	89	1	no	—
248	C₂²×C₈	—	89	1	no	—
249	C₂²×C₈	—	89	2	no	—
250	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
251	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
253	#125	—	178	4	no	—
254	C₂×C₄⋊C₄	—	89	2	no	—
255	C₂×C₄⋊C₄	—	89	2	no	—
256	C₂×C₄⋊C₄	—	89	2	no	—
257	C₂×C₄⋊C₄	—	89	2	no	—
258	C₂×C₄⋊C₄	—	89	1	no	—
259	C₂×C₄⋊C₄	—	89	1	no	—
260	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₄×D₈₉	1	1	yes	characteristic
262	C₂×C₄²	—	89	1	no	—
263	C₂×C₄²	—	89	1	no	—
264	C₂×C₄²	—	89	1	no	—
265	C₂×C₄²	—	89	1	no	—
266	C₂×C₄²	—	89	1	no	—
267	C₂×C₄²	—	89	1	no	—
268	C₂×C₄²	—	89	2	no	—
269	C₂×C₄²	C₂²×D₈₉	1	2	yes	—
270	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
271	C₄⋊C₈	—	2	4	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	178	4	no	—
274	C₄⋊C₈	—	178	2	no	—
275	#97	—	178	2	no	—
276	#97	—	178	2	no	—
277	#97	—	178	4	no	—
278	#97	—	178	2	no	—
279	#97	—	178	2	no	—
280	C₄×C₈	—	2	2	no	—
281	C₄×C₈	—	89	4	no	—
282	C₄×C₈	—	178	4	no	—
283	#95	—	89	2	no	—
284	#95	—	89	2	no	—
285	#95	—	89	2	no	—
286	#95	—	89	2	no	—
287	#95	—	89	2	no	—
288	#95	C₄×D₈₉	1	2	yes	—
289	C₂²×C₄	—	89	2	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	89	1	no	—
292	C₂²×C₄	—	89	1	no	—
293	C₂²×C₄	—	89	1	no	—
294	C₂²×C₄	—	89	2	no	—
295	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
296	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
298	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
299	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	89	2	no	—
308	C₂×C₈	—	89	2	no	—
309	C₂×C₈	—	89	2	no	—
310	C₂×C₈	—	89	2	no	—
311	C₂×C₈	—	178	2	no	—
312	C₂×C₈	—	178	2	no	—
313	C₂×C₈	—	178	2	no	—
314	C₂×C₈	—	178	1	no	—
315	C₂×C₈	—	178	1	no	—
316	C₂×C₈	#13083573	1	2	yes	—
317	C₂×C₈	#13083575	1	2	yes	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	356	2	no	—
320	C₄⋊C₄	—	356	2	no	—
321	C₄⋊C₄	—	178	4	no	—
322	C₄⋊C₄	—	178	4	no	—
323	C₄⋊C₄	—	178	2	no	—
324	C₄⋊C₄	—	178	2	no	—
325	C₄⋊C₄	#13083557	1	4	yes	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	356	1	no	—
329	C₄²	—	356	1	no	—
330	C₄²	—	178	2	no	—
331	C₄²	—	178	2	no	—
332	C₄²	—	178	1	no	—
333	C₄²	—	178	1	no	—
334	C₄²	—	178	2	no	—
335	C₄²	—	178	1	no	—
336	C₄²	—	178	1	no	—
337	C₄²	—	178	2	no	—
338	C₄²	Q₈×D₈₉	1	2	yes	—
339	C₄²	#13083573	1	2	yes	—
340	C₂³	C₂²×C₄×D₈₉	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	178	1	no	—
349	C₂×C₄	—	178	1	no	—
350	C₂×C₄	—	178	1	no	—
351	C₂×C₄	—	178	2	no	—
352	C₂×C₄	—	178	1	no	—
353	C₂×C₄	—	178	2	no	—
354	C₂×C₄	—	178	1	no	—
355	C₂×C₄	—	178	1	no	—
356	C₂×C₄	—	178	2	no	—
357	C₂×C₄	—	178	1	no	—
358	C₂×C₄	—	178	1	no	—
359	C₂×C₄	—	178	2	no	—
360	C₂×C₄	—	178	1	no	—
361	C₂×C₄	—	178	1	no	—
362	C₂×C₄	—	178	1	no	—
363	C₂×C₄	—	178	1	no	—
364	C₂×C₄	—	178	2	no	—
365	C₂×C₄	—	178	2	no	—
366	C₂×C₄	#15667977	1	2	yes	—
367	C₂×C₄	#15667977	1	2	yes	—
368	C₂×C₄	C₂×#13083557	1	4	yes	—
369	C₂×C₄	C₂×#13083557	1	2	yes	—
370	C₂×C₄	#15668020	1	2	yes	—
371	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
372	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
373	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
375	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
376	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
377	C₈	—	2	2	no	—
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	89	4	no	—
381	C₈	—	356	2	no	—
382	C₈	—	178	2	no	—
383	C₂²	C₂×#15667977	1	1	yes	characteristic
384	C₂²	C₄×#13083573	1	1	yes	characteristic
385	C₂²	C₄×#13083575	1	1	yes	characteristic
386	C₂²	C₂²×#13083557	1	1	yes	characteristic
387	C₂²	C₂×#15668020	1	1	yes	characteristic
388	C₂²	#19152363	1	1	yes	characteristic
389	C₂²	#19152363	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	4	no	—
392	C₄	—	4	2	no	—
393	C₄	—	356	1	no	—
394	C₄	—	356	2	no	—
395	C₄	—	356	1	no	—
396	C₄	—	356	1	no	—
397	C₄	—	356	1	no	—
398	C₄	—	356	2	no	—
399	C₄	#19151725	1	4	yes	—
400	C₄	#125×D₈₉	1	1	yes	characteristic
401	C₄	#19152129	1	1	yes	characteristic
402	C₄	#19152134	1	1	yes	characteristic
403	C₄	#19152153	1	1	yes	characteristic
404	C₂	#26022811	1	1	yes	characteristic
405	C₂	C₂×#19151725	1	1	yes	characteristic
406	C₂	#26029191	1	1	yes	characteristic
407	C₂	#26029258	1	1	yes	characteristic
408	C₂	#26029259	1	1	yes	characteristic
409	C₂	#26029260	1	1	yes	characteristic
410	C₂	#26029271	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₈₉
commutator, socle, prime radical	C₂³×C₈₉	C₂³×C₄
Fitting	C₈₉×#1939	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1939	D₈₉
hypocenter	C₈₉	#21675
LCS	G ▷ C₂³×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
176. #10623494	#125	semidirect
217. C₈₉	#21675	semidirect

Maximal subgroups

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

subgroup	index
C₄×#15668003	2
#26020970	2
#26020817	2
#26020813	2
#26020368	2
#26020123	2
#26020122	2
C₄⋊C₄×#10623494	2
C₄×#15667922	2
C₈₉×#1939	2
#21675	89