Finite Group Databasebeta

← C89×#3224 #26017698

Subgroups — C89×#3224 #26017698

Order 11392.

408 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#542×C89C211yesmaximal, characteristic, complemented
2#535×C89C211yesmaximal, characteristic, complemented
3#496×C89C211yesmaximal, characteristic, complemented
4#495×C89C211yesmaximal, characteristic, complemented
5#489×C89C211yesmaximal, characteristic, complemented
6#486×C89C211yesmaximal, characteristic, complemented
7#464×C89C211yesmaximal, characteristic, complemented
8#463×C89C211yesmaximal, characteristic, complemented
9#460×C89C211yesmaximal, characteristic, complemented
10#459×C89C211yesmaximal, characteristic, complemented
11#452×C89C211yesmaximal, characteristic, complemented
12#450×C89C211yesmaximal, characteristic, complemented
13#449×C89C211yesmaximal, characteristic, complemented
14#447×C89C211yesmaximal, characteristic, complemented
15#433×C89C211yesmaximal, characteristic, complemented
16C2×#41×C89C2211yescharacteristic
17C22×D4×C89C2211yescharacteristic
18C2×Q16×C89C2211yescharacteristic, complemented
19C2×SD16×C89C2211yescharacteristic
20C2×SD16×C89C2211yescharacteristic
21C2×SD16×C89C2211yescharacteristic, complemented
22C2×SD16×C89C2211yescharacteristic, complemented
23C2×D8×C89C2211yescharacteristic
24C2×D8×C89C2211yescharacteristic
25C2×D8×C89C2211yescharacteristic, complemented
26C4⋊Q8×C89C2211yescharacteristic, complemented
27#127×C89C2211yescharacteristic
28#127×C89C2211yescharacteristic
29#126×C89—21no—
30#124×C89—21no—
31#124×C89C2211yescharacteristic
32#124×C89C2211yescharacteristic
33#124×C89C2211yescharacteristic, complemented
34#123×C89—21no—
35C22⋊Q8×C89—21no—
36C22⋊Q8×C89C2211yescharacteristic
37#121×C89—21no—
38#121×C89—21no—
39#121×C89C2211yescharacteristic
40#120×C89—21no—
41#120×C89—21no—
42C4×Q8×C89C2211yescharacteristic, complemented
43C4×D4×C89C2211yescharacteristic, complemented
44#117×C89C2211yescharacteristic
45C4⋊C8×C89C2211yescharacteristic, complemented
46C4⋊C8×C89C2211yescharacteristic, complemented
47#103×C89C2211yescharacteristic, complemented
48#103×C89C2211yescharacteristic, complemented
49#102×C89C2211yescharacteristic
50#102×C89C2211yescharacteristic
51#102×C89C2211yescharacteristic
52#102×C89C2211yescharacteristic
53#102×C89C2211yescharacteristic, complemented
54#102×C89C2211yescharacteristic, complemented
55C22⋊C8×C89C2211yescharacteristic
56C22⋊C8×C89C2211yescharacteristic
57#97×C89C2211yescharacteristic, complemented
58C4×C8×C89C2211yescharacteristic, complemented
59C24×C89—21no—
60#41×C89—41no—
61#41×C89—41no—
62C2×Q8×C89—21no—
63C2×Q8×C89C2311yescharacteristic
64C2×Q8×C89C2311yescharacteristic
65C2×D4×C89—21no—
66C2×D4×C89—21no—
67C2×D4×C89—21no—
68C2×D4×C89—21no—
69C2×D4×C89—21no—
70C2×D4×C89—21no—
71C2×D4×C89—21no—
72C2×D4×C89—41no—
73C2×D4×C89—41no—
74C2×D4×C89C2311yescharacteristic
75C2×D4×C89C2311yescharacteristic
76C2×D4×C89C2311yescharacteristic
77C2×D4×C89C2311yescharacteristic
78C22×C4×C89—21no—
79C22×C4×C89—21no—
80C22×C4×C89C2311yescharacteristic
81Q16×C89—41no—
82SD16×C89—41no—
83SD16×C89—41no—
84SD16×C89—41no—
85SD16×C89—41no—
86D8×C89—41no—
87D8×C89—41no—
88D8×C89—41no—
89C2×C8×C89C2311yescharacteristic
90C2×C8×C89C2311yescharacteristic
91C2×C8×C89C2311yescharacteristic
92C2×C8×C89C2311yescharacteristic
93C4⋊C4×C89—21no—
94C4⋊C4×C89—21no—
95C4⋊C4×C89—21no—
96C4⋊C4×C89D411yescharacteristic
97C4⋊C4×C89D411yescharacteristic
98C4⋊C4×C89C2311yescharacteristic
99C4⋊C4×C89C2311yescharacteristic
100C22⋊C4×C89—21no—
101C22⋊C4×C89—21no—
102C22⋊C4×C89—21no—
103C22⋊C4×C89—21no—
104C22⋊C4×C89—21no—
105C22⋊C4×C89—21no—
106C22⋊C4×C89—21no—
107C22⋊C4×C89—21no—
108C22⋊C4×C89—21no—
109C22⋊C4×C89D411yescharacteristic
110C22⋊C4×C89D411yescharacteristic
111C42×C89—21no—
112C42×C89C2311yescharacteristic
113C42×C89C2311yescharacteristic
114C23×C89—21no—
115C23×C89—21no—
116C23×C89—21no—
117C23×C89—21no—
118C23×C89—42no—
119C23×C89—81no—
120C23×C89—81no—
121C23×C89C2×D411yescharacteristic
122Q8×C89—21no—
123Q8×C89—21no—
124Q8×C89—21no—
125Q8×C89—21no—
126Q8×C89—81no—
127D4×C89—21no—
128D4×C89—21no—
129D4×C89—21no—
130D4×C89—21no—
131D4×C89—21no—
132D4×C89—21no—
133D4×C89—21no—
134D4×C89—21no—
135D4×C89—42no—
136D4×C89—42no—
137D4×C89—81no—
138D4×C89—81no—
139D4×C89—81no—
140D4×C89—81no—
141D4×C89—81no—
142C2×C4×C89—21no—
143C2×C4×C89—21no—
144C2×C4×C89—21no—
145C2×C4×C89—21no—
146C2×C4×C89—21no—
147C2×C4×C89—21no—
148C2×C4×C89—42no—
149C2×C4×C89—81no—
150C2×C4×C89C2×D411yescharacteristic
151C2×C4×C89C2×D411yescharacteristic
152C2×C4×C89C2×D411yescharacteristic
153C2×C4×C89C2×D411yescharacteristic
154C2×C4×C89C2×D411yescharacteristic
155C2×C4×C89C2411yescharacteristic
156C8×C89—21no—
157C8×C89—21no—
158C8×C89—21no—
159C8×C89—21no—
160C22×C89—21no—
161C22×C89—21no—
162C22×C89—21no—
163C22×C89—41no—
164C22×C89—41no—
165C22×C89—41no—
166C22×C89—41no—
167C22×C89—41no—
168C22×C89—41no—
169C22×C89—41no—
170C22×C89—41no—
171C22×C89—41no—
172C22×C89—41no—
173C22×C89—41no—
174C22×C89—41no—
175C22×C89—84no—
176C22×C89C22×D411yescharacteristic
177C4×C89—21no—
178C4×C89—21no—
179C4×C89—21no—
180C4×C89—21no—
181C4×C89—21no—
182C4×C89—41no—
183C4×C89—41no—
184C4×C89—41no—
185C4×C89—41no—
186C4×C89H(5,𝔽2)11yescharacteristic
187C4×C89H(5,𝔽2)11yescharacteristic
188C2×C89—41no—
189C2×C89—81no—
190C2×C89—81no—
191C2×C89—81no—
192C2×C89—81no—
193C2×C89#53511yescharacteristic
194C2×C89#57611yescharacteristic
195C2×C89#57711yescharacteristic
196#3224C8911yesmaximal, characteristic, direct product factor, Sylow
197C89#322411yescharacteristic, direct product factor, Sylow
198#542C2×C8911yescharacteristic, complemented
199#535C2×C8911yescharacteristic, complemented
200#496C2×C8911yescharacteristic, complemented
201#495C2×C8911yescharacteristic, complemented
202#489C2×C8911yescharacteristic, complemented
203#486C2×C8911yescharacteristic, complemented
204#464C2×C8911yescharacteristic, complemented
205#463C2×C8911yescharacteristic, complemented
206#460C2×C8911yescharacteristic, complemented
207#459C2×C8911yescharacteristic, complemented
208#452C2×C8911yescharacteristic, complemented
209#450C2×C8911yescharacteristic, complemented
210#449C2×C8911yescharacteristic, complemented
211#447C2×C8911yescharacteristic, complemented
212#433C2×C8911yescharacteristic, complemented
213C2×#41C22×C8911yescharacteristic
214C22×D4C22×C8911yescharacteristic
215C2×Q16C22×C8911yescharacteristic, complemented
216C2×SD16C22×C8911yescharacteristic
217C2×SD16C22×C8911yescharacteristic
218C2×SD16C22×C8911yescharacteristic, complemented
219C2×SD16C22×C8911yescharacteristic, complemented
220C2×D8C22×C8911yescharacteristic
221C2×D8C22×C8911yescharacteristic
222C2×D8C22×C8911yescharacteristic, complemented
223C4⋊Q8C22×C8911yescharacteristic, complemented
224#127C22×C8911yescharacteristic
225#127C22×C8911yescharacteristic
226#126—21no—
227#124—21no—
228#124C22×C8911yescharacteristic
229#124C22×C8911yescharacteristic
230#124C22×C8911yescharacteristic, complemented
231#123—21no—
232C22⋊Q8—21no—
233C22⋊Q8C22×C8911yescharacteristic
234#121—21no—
235#121—21no—
236#121C22×C8911yescharacteristic
237#120—21no—
238#120—21no—
239C4×Q8C22×C8911yescharacteristic, complemented
240C4×D4C22×C8911yescharacteristic, complemented
241#117C22×C8911yescharacteristic
242C4⋊C8C22×C8911yescharacteristic, complemented
243C4⋊C8C22×C8911yescharacteristic, complemented
244#103C22×C8911yescharacteristic, complemented
245#103C22×C8911yescharacteristic, complemented
246#102C22×C8911yescharacteristic
247#102C22×C8911yescharacteristic
248#102C22×C8911yescharacteristic
249#102C22×C8911yescharacteristic
250#102C22×C8911yescharacteristic, complemented
251#102C22×C8911yescharacteristic, complemented
252C22⋊C8C22×C8911yescharacteristic
253C22⋊C8C22×C8911yescharacteristic
254#97C22×C8911yescharacteristic, complemented
255C4×C8C22×C8911yescharacteristic, complemented
256C24—21no—
257#41—41no—
258#41—41no—
259C2×Q8—21no—
260C2×Q8C23×C8911yescharacteristic
261C2×Q8C23×C8911yescharacteristic
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—41no—
270C2×D4—41no—
271C2×D4C23×C8911yescharacteristic
272C2×D4C23×C8911yescharacteristic
273C2×D4C23×C8911yescharacteristic
274C2×D4C23×C8911yescharacteristic
275C22×C4—21no—
276C22×C4—21no—
277C22×C4C23×C8911yescharacteristic
278Q16—41no—
279SD16—41no—
280SD16—41no—
281SD16—41no—
282SD16—41no—
283D8—41no—
284D8—41no—
285D8—41no—
286C2×C8C23×C8911yescharacteristic
287C2×C8C23×C8911yescharacteristic
288C2×C8C23×C8911yescharacteristic
289C2×C8C23×C8911yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4D4×C8911yescharacteristic
294C4⋊C4D4×C8911yescharacteristic
295C4⋊C4C23×C8911yescharacteristic
296C4⋊C4C23×C8911yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—21no—
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—21no—
305C22⋊C4—21no—
306C22⋊C4D4×C8911yescharacteristic
307C22⋊C4D4×C8911yescharacteristic
308C42—21no—
309C42C23×C8911yescharacteristic
310C42C23×C8911yescharacteristic
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—42no—
316C23—81no—
317C23—81no—
318C23C2×D4×C8911yescharacteristic
319Q8—21no—
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8—81no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—21no—
330D4—21no—
331D4—21no—
332D4—42no—
333D4—42no—
334D4—81no—
335D4—81no—
336D4—81no—
337D4—81no—
338D4—81no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—42no—
346C2×C4—81no—
347C2×C4C2×D4×C8911yescharacteristic
348C2×C4C2×D4×C8911yescharacteristic
349C2×C4C2×D4×C8911yescharacteristic
350C2×C4C2×D4×C8911yescharacteristic
351C2×C4C2×D4×C8911yescharacteristic
352C2×C4C24×C8911yescharacteristic
353C8—21no—
354C8—21no—
355C8—21no—
356C8—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—41no—
371C22—41no—
372C22—84no—
373C22C22×D4×C8911yescharacteristic
374C4—21no—
375C4—21no—
376C4—21no—
377C4—21no—
378C4—21no—
379C4—41no—
380C4—41no—
381C4—41no—
382C4—41no—
383C4H(5,𝔽2)×C8911yescharacteristic
384C4H(5,𝔽2)×C8911yescharacteristic
385C2—41no—
386C2—81no—
387C2—81no—
388C2—81no—
389C2—81no—
390C2#535×C8911yescharacteristic
391C2#576×C8911yescharacteristic
392C2#577×C8911yescharacteristic
subgroupG/H
center, socleC22×C89C22×D4
commutator, Frattini, cosocleC2×C4C24×C89
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C89 ◁ #117×C89 ◁ G

Complements

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

NH ≅ G/Ntype
1. #542×C89C2semidirect
2. #535×C89C2semidirect
3. #496×C89C2semidirect
4. #495×C89C2semidirect
5. #489×C89C2semidirect
6. #486×C89C2semidirect
7. #464×C89C2semidirect
8. #463×C89C2semidirect
9. #460×C89C2semidirect
10. #459×C89C2semidirect
11. #452×C89C2semidirect
12. #450×C89C2semidirect
13. #449×C89C2semidirect
14. #447×C89C2semidirect
15. #433×C89C2semidirect
18. C2×Q16×C89C22semidirect
21. C2×SD16×C89C22semidirect
22. C2×SD16×C89C22semidirect
25. C2×D8×C89C22semidirect
26. C4⋊Q8×C89C22semidirect
33. #124×C89C22semidirect
42. C4×Q8×C89C22semidirect
43. C4×D4×C89C22semidirect
45. C4⋊C8×C89C22semidirect
46. C4⋊C8×C89C22semidirect
47. #103×C89C22semidirect
48. #103×C89C22semidirect
53. #102×C89C22semidirect
54. #102×C89C22semidirect
57. #97×C89C22semidirect
58. C4×C8×C89C22semidirect
196. #3224C89direct (N × H)
197. C89#3224direct (N × H)
198. #542C2×C89semidirect
199. #535C2×C89semidirect
200. #496C2×C89semidirect
201. #495C2×C89semidirect
202. #489C2×C89semidirect
203. #486C2×C89semidirect
204. #464C2×C89semidirect
205. #463C2×C89semidirect
206. #460C2×C89semidirect
207. #459C2×C89semidirect
208. #452C2×C89semidirect
209. #450C2×C89semidirect
210. #449C2×C89semidirect
211. #447C2×C89semidirect
212. #433C2×C89semidirect
215. C2×Q16C22×C89semidirect
218. C2×SD16C22×C89semidirect
219. C2×SD16C22×C89semidirect
222. C2×D8C22×C89semidirect
223. C4⋊Q8C22×C89semidirect
230. #124C22×C89semidirect
239. C4×Q8C22×C89semidirect
240. C4×D4C22×C89semidirect
242. C4⋊C8C22×C89semidirect
243. C4⋊C8C22×C89semidirect
244. #103C22×C89semidirect
245. #103C22×C89semidirect
250. #102C22×C89semidirect
251. #102C22×C89semidirect
254. #97C22×C89semidirect
255. C4×C8C22×C89semidirect

Maximal subgroups

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

subgroupindex
#542×C892
#535×C892
#496×C892
#495×C892
#489×C892
#486×C892
#464×C892
#463×C892
#460×C892
#459×C892
#452×C892
#450×C892
#449×C892
#447×C892
#433×C892
#322489