Subgroups — #36577296

Order 22784.

820 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029973	C₂	1	1	yes	maximal, characteristic
2	#26029168	C₂	1	1	yes	maximal, characteristic, complemented
3	#26029163	C₂	1	2	yes	maximal, complemented
4	#26028860	C₂	1	1	yes	maximal, characteristic, complemented
5	#26021145	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021043	C₂	1	1	yes	maximal, characteristic, complemented
7	#26020921	C₂	1	2	yes	maximal, complemented
8	#26020615	C₂	1	2	yes	maximal, complemented
9	#26020473	C₂	1	2	yes	maximal, complemented
10	#26020096	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1778	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152398	C₂²	1	2	yes	—
13	C₂×#15668034	C₂²	1	1	yes	characteristic
14	#19152364	C₂²	1	2	yes	—
15	#19152364	C₂²	1	2	yes	—
16	C₂×#15668018	C₂²	1	1	yes	characteristic
17	#19151874	C₄	1	2	yes	complemented
18	#19151869	C₄	1	2	yes	complemented
19	#19151862	C₄	1	4	yes	complemented
20	#19151721	—	2	4	no	—
21	#19151719	—	2	2	no	—
22	#19151716	—	2	4	no	—
23	#19151714	—	2	2	no	—
24	#19151647	C₂²	1	2	yes	—
25	#19151646	C₂²	1	2	yes	—
26	#19151645	—	2	2	no	—
27	C₂×#15667948	C₂²	1	1	yes	characteristic
28	#108×D₈₉	—	2	2	no	—
29	#19151614	C₂²	1	2	yes	—
30	C₂×#15667940	C₂²	1	2	yes	—
31	C₂×#15667940	C₂²	1	1	yes	characteristic
32	#19151595	C₂²	1	1	yes	characteristic
33	#19151580	C₂²	1	2	yes	—
34	#19151564	C₂²	1	2	yes	—
35	#19151553	C₂²	1	1	yes	characteristic
36	#19151370	C₂²	1	2	yes	—
37	#19151363	C₂²	1	1	yes	characteristic
38	#19151358	C₂²	1	1	yes	characteristic
39	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
41	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
42	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
43	#341×C₈₉	C₂²	1	2	yes	—
44	C₂×#13083574	C₂³	1	2	yes	—
45	C₂×#13083574	C₂³	1	1	yes	characteristic
46	#15668045	—	2	2	no	—
47	#15668045	C₂×C₄	1	4	yes	—
48	#15668040	—	2	2	no	—
49	#15668040	C₂×C₄	1	4	yes	—
50	#15668034	—	2	4	no	—
51	#15668034	—	2	1	no	—
52	#15668034	—	2	1	no	—
53	#15668034	—	2	1	no	—
54	#15668034	—	2	1	no	—
55	C₂×Dic₃₅₆	C₂×C₄	1	1	yes	characteristic
56	C₂×#13083563	C₂×C₄	1	2	yes	—
57	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
58	#15668020	—	2	4	no	—
59	#15668020	—	4	2	no	—
60	#15668018	—	2	4	no	—
61	#15668018	—	2	4	no	—
62	#15668018	—	2	1	no	—
63	#15668018	—	2	1	no	—
64	#15668018	C₂×C₄	1	2	yes	—
65	#15668018	C₂×C₄	1	2	yes	—
66	C₂×#13083558	C₂³	1	2	yes	—
67	C₂×#13083558	C₂³	1	1	yes	characteristic
68	C₂×#13083558	C₂³	1	1	yes	characteristic
69	C₂×#13083557	—	2	1	no	—
70	M₁₆×D₈₉	—	2	4	no	—
71	M₁₆×D₈₉	—	4	2	no	—
72	C₂×C₈×D₈₉	—	2	1	no	—
73	#15667971	C₂³	1	1	yes	characteristic
74	#15667948	—	2	4	no	—
75	#15667948	—	2	1	no	—
76	#15667948	—	2	1	no	—
77	#15667947	—	2	4	no	—
78	#15667940	—	2	2	no	—
79	#15667940	—	2	2	no	—
80	#15667940	D₄	1	4	yes	—
81	#15667938	—	2	4	no	—
82	#15667937	—	2	1	no	—
83	#15667934	—	2	1	no	—
84	#15667930	C₂×C₄	1	4	yes	—
85	#15667928	C₂×C₄	1	4	yes	—
86	#15667924	—	4	2	no	—
87	#15667922	—	2	1	no	—
88	C₈×Dic₈₉	—	2	1	no	—
89	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
90	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
91	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
94	#108×C₈₉	C₂×C₄	1	2	yes	—
95	#108×C₈₉	C₂×C₄	1	2	yes	—
96	#108×C₈₉	D₄	1	2	yes	—
97	#108×C₈₉	D₄	1	2	yes	—
98	#97×C₈₉	—	2	1	no	—
99	#97×C₈₉	—	2	1	no	—
100	#97×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	—	2	2	no	—
102	#13083574	—	2	1	no	—
103	#13083574	—	2	1	no	—
104	#13083574	—	2	2	no	—
105	#13083574	—	2	2	no	—
106	#13083574	—	2	2	no	—
107	#13083574	—	2	2	no	—
108	#13083574	C₂²×C₄	1	2	yes	—
109	#13083574	C₂×D₄	1	2	yes	—
110	C₂×Dic₁₇₈	C₂²×C₄	1	2	yes	—
111	C₂×Dic₁₇₈	#41	1	1	yes	characteristic
112	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
113	C₂×D₃₅₆	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₈₉	—	2	1	no	—
115	C₂×C₂²⋊D₈₉	—	2	2	no	—
116	C₂×C₄×D₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	2	no	—
118	Dic₃₅₆	—	2	4	no	—
119	Dic₃₅₆	—	2	1	no	—
120	Dic₃₅₆	—	2	1	no	—
121	#13083563	—	2	4	no	—
122	#13083563	—	2	4	no	—
123	#13083563	—	2	2	no	—
124	#13083563	—	2	2	no	—
125	D₇₁₂	—	2	4	no	—
126	D₇₁₂	—	2	1	no	—
127	D₇₁₂	—	2	1	no	—
128	#13083558	—	2	1	no	—
129	#13083558	—	2	1	no	—
130	#13083558	—	2	2	no	—
131	#13083558	—	2	2	no	—
132	#13083558	C₂²×C₄	1	2	yes	—
133	#13083558	C₂×D₄	1	2	yes	—
134	#13083557	—	2	2	no	—
135	#13083557	—	2	2	no	—
136	#13083557	—	4	4	no	—
137	#13083557	—	4	4	no	—
138	C₂×#10623494	—	2	1	no	—
139	C₂×#10623494	—	2	1	no	—
140	C₂×#10623494	—	2	2	no	—
141	C₈×D₈₉	—	2	2	no	—
142	C₈×D₈₉	—	2	2	no	—
143	C₈×D₈₉	—	4	4	no	—
144	C₈×D₈₉	—	4	4	no	—
145	C₄⋊Dic₈₉	—	2	1	no	—
146	C₂²⋊Dic₈₉	—	2	1	no	—
147	C₄×Dic₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₈₉	—	2	2	no	—
151	M₁₆×C₈₉	—	2	2	no	—
152	M₁₆×C₈₉	C₂²×C₄	1	4	yes	—
153	M₁₆×C₈₉	C₂×D₄	1	4	yes	—
154	C₂×C₈×C₈₉	—	2	2	no	—
155	C₂×C₈×C₈₉	—	2	2	no	—
156	C₂×C₈×C₈₉	—	2	1	no	—
157	C₂×C₈×C₈₉	—	2	1	no	—
158	C₂×C₈×C₈₉	—	2	1	no	—
159	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
164	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
165	C₄²×C₈₉	—	2	1	no	—
166	C₄²×C₈₉	C₂×D₄	1	2	yes	—
167	C₂³×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
168	C₂²×D₈₉	—	2	1	no	—
169	C₂²×D₈₉	—	2	2	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	8	1	no	—
172	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂²×D₄	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	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂²⋊D₈₉	—	2	2	no	—
179	C₂²⋊D₈₉	—	2	2	no	—
180	C₂²⋊D₈₉	—	4	2	no	—
181	C₂²⋊D₈₉	—	4	2	no	—
182	C₂×Dic₈₉	—	2	1	no	—
183	C₂×Dic₈₉	—	2	2	no	—
184	C₂×Dic₈₉	—	4	1	no	—
185	D₃₅₆	—	2	2	no	—
186	D₃₅₆	—	2	2	no	—
187	D₃₅₆	—	2	1	no	—
188	D₃₅₆	C₄×D₄	1	2	yes	—
189	C₄×D₈₉	—	2	2	no	—
190	C₄×D₈₉	—	2	2	no	—
191	C₄×D₈₉	—	4	2	no	—
192	C₄×D₈₉	—	4	2	no	—
193	Dic₁₇₈	—	2	1	no	—
194	Dic₁₇₈	—	2	2	no	—
195	Dic₁₇₈	—	2	2	no	—
196	Dic₁₇₈	C₄×D₄	1	2	yes	—
197	C₈×C₈₉	—	2	4	no	—
198	C₈×C₈₉	—	2	4	no	—
199	C₈×C₈₉	—	4	1	no	—
200	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
201	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
202	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
203	C₈×C₈₉	C₄×D₄	1	1	yes	characteristic
204	#10623494	—	2	2	no	—
205	#10623494	—	2	2	no	—
206	#10623494	—	4	2	no	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	#520	1	1	yes	characteristic
209	C₂²×C₈₉	#547	1	1	yes	characteristic
210	C₂²×C₈₉	#548	1	1	yes	characteristic
211	C₂×D₈₉	—	2	2	no	—
212	C₂×D₈₉	—	4	2	no	—
213	C₂×D₈₉	—	8	1	no	—
214	C₂×D₈₉	—	8	2	no	—
215	C₄×C₈₉	—	4	2	no	—
216	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
217	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
218	C₄×C₈₉	D₄²	1	1	yes	characteristic
219	C₄×C₈₉	#553	1	1	yes	characteristic
220	Dic₈₉	—	2	2	no	—
221	Dic₈₉	—	4	2	no	—
222	Dic₈₉	—	8	1	no	—
223	#23043	—	89	1	no	maximal, Sylow
224	C₂×C₈₉	—	2	1	no	—
225	C₂×C₈₉	—	2	1	no	—
226	C₂×C₈₉	—	2	1	no	—
227	C₂×C₈₉	#2361	1	1	yes	characteristic
228	D₈₉	—	4	2	no	—
229	D₈₉	—	8	2	no	—
230	#3067	—	89	1	no	—
231	#2957	—	89	1	no	—
232	#2956	—	89	2	no	—
233	#2916	—	89	1	no	—
234	#1975	—	89	1	no	—
235	#1953	—	89	1	no	—
236	#1932	—	89	2	no	—
237	#1881	—	89	2	no	—
238	#1858	—	89	2	no	—
239	#1778	D₈₉	1	1	yes	characteristic, complemented
240	#1765	—	89	1	no	—
241	C₈₉	#23043	1	1	yes	characteristic, complemented, Sylow
242	#575	—	89	2	no	—
243	C₂×#135	—	89	1	no	—
244	#568	—	89	2	no	—
245	#568	—	89	2	no	—
246	C₂×#131	—	89	1	no	—
247	#473	—	89	2	no	—
248	#472	—	89	2	no	—
249	#471	—	89	4	no	—
250	#444	—	178	4	no	—
251	#444	—	178	2	no	—
252	#443	—	178	4	no	—
253	#443	—	178	2	no	—
254	#430	—	89	2	no	—
255	#430	—	89	2	no	—
256	#430	—	178	2	no	—
257	C₂×#108	—	89	1	no	—
258	C₂×#108	—	178	2	no	—
259	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
260	C₂×#108	C₂×D₈₉	1	1	yes	characteristic
261	#421	—	89	2	no	—
262	C₂×#104	—	89	1	no	—
263	C₂×#104	—	89	2	no	—
264	#416	—	89	1	no	—
265	#413	—	89	2	no	—
266	#408	—	89	2	no	—
267	#405	—	89	1	no	—
268	C₄×M₁₆	C₂×D₈₉	1	2	yes	—
269	C₂×#97	C₂×D₈₉	1	1	yes	characteristic
270	#344	—	89	2	no	—
271	#341	—	89	1	no	—
272	#341	C₂×D₈₉	1	2	yes	—
273	#339	—	89	1	no	—
274	C₂×#41	—	89	1	no	—
275	C₂×#41	—	89	2	no	—
276	#137	—	89	4	no	—
277	#137	—	178	2	no	—
278	AGL(1,ℤ/8)	—	89	4	no	—
279	AGL(1,ℤ/8)	—	178	2	no	—
280	#135	—	178	4	no	—
281	#135	—	178	1	no	—
282	#135	—	178	1	no	—
283	#135	—	178	1	no	—
284	#135	—	178	1	no	—
285	C₂×Q₁₆	—	89	1	no	—
286	C₂×SD₁₆	—	89	2	no	—
287	C₂×D₈	—	89	1	no	—
288	#131	—	89	2	no	—
289	#131	—	89	2	no	—
290	#131	—	356	2	no	—
291	#131	—	178	4	no	—
292	#131	—	178	4	no	—
293	#131	—	178	4	no	—
294	#131	—	178	1	no	—
295	#131	—	178	1	no	—
296	C₂×M₁₆	—	89	1	no	—
297	C₂×M₁₆	—	89	1	no	—
298	C₂×M₁₆	—	89	2	no	—
299	C₂×M₁₆	—	356	2	no	—
300	C₂×M₁₆	—	178	4	no	—
301	C₂×M₁₆	—	178	1	no	—
302	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
303	C₂×M₁₆	C₂²×D₈₉	1	2	yes	—
304	C₂²×C₈	—	178	1	no	—
305	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	#117	—	89	1	no	—
308	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
309	#108	—	178	4	no	—
310	#108	—	178	4	no	—
311	#108	—	178	1	no	—
312	#108	—	178	1	no	—
313	#108	C₄×D₈₉	1	2	yes	—
314	#108	C₄×D₈₉	1	2	yes	—
315	#108	D₃₅₆	1	2	yes	—
316	#108	D₃₅₆	1	2	yes	—
317	#104	—	89	4	no	—
318	#104	—	178	4	no	—
319	#104	—	178	2	no	—
320	#104	—	178	2	no	—
321	#103	—	178	1	no	—
322	#102	—	178	1	no	—
323	#101	—	89	4	no	—
324	#100	—	89	4	no	—
325	C₂²⋊C₈	—	356	2	no	—
326	#97	—	2	1	no	—
327	#97	—	2	1	no	—
328	#97	—	2	2	no	—
329	#97	—	178	1	no	—
330	C₄×C₈	—	2	2	no	—
331	C₄×C₈	—	178	1	no	—
332	#41	—	89	2	no	—
333	#41	—	89	2	no	—
334	#41	—	178	2	no	—
335	#41	—	178	2	no	—
336	#41	—	178	2	no	—
337	#41	—	178	2	no	—
338	#41	—	178	1	no	—
339	#41	—	178	1	no	—
340	C₂×Q₈	—	89	2	no	—
341	C₂×Q₈	—	89	1	no	—
342	C₂×D₄	—	89	2	no	—
343	C₂×D₄	—	89	1	no	—
344	C₂×D₄	—	178	2	no	—
345	C₂×D₄	—	178	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	178	2	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
350	Q₁₆	—	178	4	no	—
351	Q₁₆	—	178	1	no	—
352	Q₁₆	—	178	1	no	—
353	SD₁₆	—	178	4	no	—
354	SD₁₆	—	178	4	no	—
355	SD₁₆	—	178	2	no	—
356	SD₁₆	—	178	2	no	—
357	D₈	—	178	4	no	—
358	D₈	—	178	1	no	—
359	D₈	—	178	1	no	—
360	M₁₆	—	2	2	no	—
361	M₁₆	—	2	2	no	—
362	M₁₆	—	89	2	no	—
363	M₁₆	—	89	2	no	—
364	M₁₆	—	356	4	no	—
365	M₁₆	—	356	4	no	—
366	M₁₆	—	178	2	no	—
367	M₁₆	—	178	2	no	—
368	M₁₆	—	178	1	no	—
369	M₁₆	—	178	1	no	—
370	M₁₆	—	178	2	no	—
371	M₁₆	—	178	2	no	—
372	M₁₆	C₂×C₄×D₈₉	1	4	yes	—
373	M₁₆	C₂×D₃₅₆	1	4	yes	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	1	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	356	4	no	—
380	C₂×C₈	—	356	4	no	—
381	C₂×C₈	—	178	2	no	—
382	C₂×C₈	—	178	1	no	—
383	C₂×C₈	—	178	1	no	—
384	C₂×C₈	—	178	2	no	—
385	C₂×C₈	—	178	2	no	—
386	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
387	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
388	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
389	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
390	C₂×C₈	#13083574	1	1	yes	characteristic
391	C₂×C₈	#13083574	1	1	yes	characteristic
392	C₄⋊C₄	—	178	1	no	—
393	C₂²⋊C₄	—	178	1	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	178	1	no	—
396	C₄²	D₄×D₈₉	1	2	yes	—
397	C₂³	—	178	2	no	—
398	C₂³	—	178	1	no	—
399	C₂³	#15668060	1	1	yes	characteristic
400	Q₈	—	89	2	no	—
401	Q₈	—	178	2	no	—
402	Q₈	—	178	2	no	—
403	Q₈	—	178	1	no	—
404	D₄	—	89	2	no	—
405	D₄	—	356	2	no	—
406	D₄	—	356	2	no	—
407	D₄	—	178	2	no	—
408	D₄	—	178	2	no	—
409	D₄	—	178	1	no	—
410	D₄	—	178	2	no	—
411	D₄	—	178	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	8	1	no	—
414	C₂×C₄	—	356	2	no	—
415	C₂×C₄	—	356	2	no	—
416	C₂×C₄	—	356	1	no	—
417	C₂×C₄	—	178	2	no	—
418	C₂×C₄	—	178	1	no	—
419	C₂×C₄	—	178	2	no	—
420	C₂×C₄	—	178	2	no	—
421	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
424	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
426	C₂×C₄	#15668058	1	1	yes	characteristic
427	C₈	—	2	4	no	—
428	C₈	—	2	4	no	—
429	C₈	—	4	1	no	—
430	C₈	—	356	2	no	—
431	C₈	—	178	2	no	—
432	C₈	—	178	2	no	—
433	C₈	C₄×D₃₅₆	1	1	yes	characteristic
434	C₈	C₄×D₃₅₆	1	1	yes	characteristic
435	C₈	C₄×D₃₅₆	1	1	yes	characteristic
436	C₈	C₄×D₃₅₆	1	1	yes	characteristic
437	C₂²	—	4	1	no	—
438	C₂²	—	356	2	no	—
439	C₂²	—	178	2	no	—
440	C₂²	—	712	1	no	—
441	C₂²	—	712	2	no	—
442	C₂²	#19152080	1	1	yes	characteristic
443	C₂²	#19152249	1	1	yes	characteristic
444	C₂²	#19152260	1	1	yes	characteristic
445	C₄	—	4	2	no	—
446	C₄	—	356	2	no	—
447	C₄	—	178	2	no	—
448	C₄	—	712	1	no	—
449	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
450	C₄	C₂×C₄×D₃₅₆	1	1	yes	characteristic
451	C₄	D₄×D₃₅₆	1	1	yes	characteristic
452	C₄	#19152292	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	356	2	no	—
457	C₂	—	712	2	no	—
458	C₂	#26023270	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1778	C₂
socle	C₂×C₈₉	#2361
prime radical	#26029973	C₂
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1778	D₈₉
hypocenter	C₈₉	#23043
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1778

Complements

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

N	H ≅ G/N	type
2. #26029168	C₂	semidirect
3. #26029163	C₂	semidirect
4. #26028860	C₂	semidirect
5. #26021145	C₂	semidirect
6. #26021043	C₂	semidirect
7. #26020921	C₂	semidirect
8. #26020615	C₂	semidirect
9. #26020473	C₂	semidirect
10. #26020096	C₂	semidirect
11. C₈₉×#1778	C₂	semidirect
17. #19151874	C₄	semidirect
18. #19151869	C₄	semidirect
19. #19151862	C₄	semidirect
239. #1778	D₈₉	semidirect
241. C₈₉	#23043	semidirect

Maximal subgroups

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

subgroup	index
#26029973	2
#26029168	2
#26029163	2
#26028860	2
#26021145	2
#26021043	2
#26020921	2
#26020615	2
#26020473	2
#26020096	2
C₈₉×#1778	2
#23043	89