Finite Group Databasebeta

← D59×#1992 #28593252

Subgroups — D59×#1992 #28593252

Order 15104.

1294 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D59C211yesmaximal, characteristic
2C2×#97×D59C211yesmaximal, characteristic
3#384×D59C211yesmaximal, characteristic
4#21425066C211yesmaximal, characteristic, complemented
5#21425065C211yesmaximal, characteristic, complemented
6#21425064C211yesmaximal, characteristic, complemented
7#21425063C214yesmaximal, complemented
8#340×D59C214yesmaximal
9C59×#1992C211yesmaximal, characteristic, complemented
10C22×C8×D59C2212yes—
11C2×#14273719C2211yescharacteristic
12C2×#14273718C2212yes—
13C2×#14273717—22no—
14#125×D59—24no—
15#125×D59C418yescomplemented
16C2×C4⋊C4×D59—22no—
17C2×C4⋊C4×D59—22no—
18C2×C4⋊C4×D59C2212yes—
19C2×C4⋊C4×D59C2212yes—
20C2×C42×D59C2211yescharacteristic
21C2×#14273638C2211yescharacteristic
22C2×#14273637C2212yes—
23#97×D59—24no—
24#16837272C2211yescharacteristic
25#16837271—22no—
26#16837271C2212yes—
27#16837165C2214yes—
28#16837164C2214yes—
29#16837164C2214yes—
30C2×#125×C59C2211yescharacteristic
31C2×#97×C59C2211yescharacteristic
32C59×#384C2211yescharacteristic
33C59×#340C2214yes—
34C22×C4×D59—22no—
35C22×C4×D59—22no—
36C22×C4×D59D412yes—
37C22×C4×D59C2311yescharacteristic
38C22×C59⋊C8C2312yes—
39C2×C8×D59—24no—
40C2×C8×D59—24no—
41C2×C8×D59Q818yes—
42#14273719—22no—
43#14273719C2×C414yescomplemented
44#14273718—24no—
45#14273718C2×C418yescomplemented
46#14273717—216no—
47C2×C4⋊Dic59—22no—
48C2×C4⋊Dic59—22no—
49C2×C4⋊Dic59C2312yes—
50C2×C4⋊Dic59C2312yes—
51C2×Dic59⋊C4—22no—
52C2×Dic59⋊C4—22no—
53C2×Dic59⋊C4—22no—
54C2×Dic59⋊C4—22no—
55C2×Dic59⋊C4—24no—
56C4⋊C4×D59—216no—
57C4⋊C4×D59—24no—
58C4⋊C4×D59—28no—
59C4⋊C4×D59—48no—
60C4⋊C4×D59C2×C418yes—
61C2×C4×Dic59D412yes—
62C2×C4×Dic59C2311yescharacteristic
63C42×D59C2×C414yes—
64C42×D59D414yes—
65#14273638—22no—
66#14273637—24no—
67C22×C8×C59C2312yes—
68#125×C59—22no—
69#125×C59C2×C414yescomplemented
70C2×C4⋊C4×C59—22no—
71C2×C4⋊C4×C59—22no—
72C2×C4⋊C4×C59C2312yes—
73C2×C4⋊C4×C59C2312yes—
74C2×C42×C59C2311yescharacteristic
75#97×C59—22no—
76C23×D59C2×D411yescharacteristic
77C22×C4×C59—22no—
78C22×C4×C59—22no—
79C22×C4×C59C2×D412yes—
80C22×C4×C59C2411yescharacteristic
81C22×Dic59—22no—
82C22×Dic59—22no—
83C22×Dic59C2×D412yes—
84C22×Dic59C2×D411yescharacteristic
85C2×C4×D59—24no—
86C2×C4×D59—24no—
87C2×C4×D59—28no—
88C2×C4×D59—44no—
89C2×C4×D59—44no—
90C2×C4×D59—44no—
91C2×C4×D59—48no—
92C2×C4×D59C22⋊C418yes—
93C2×C4×D59C22×C412yes—
94C2×C4×D59C2×D412yes—
95C2×C4×D59C2×Q814yes—
96C2×C4×D59#4114yes—
97C2×C8×C59—22no—
98C2×C8×C59—22no—
99C2×C8×C59C2×Q814yes—
100C4⋊C4×C59—28no—
101C4⋊C4×C59—22no—
102C4⋊C4×C59—24no—
103C4⋊C4×C59—44no—
104C4⋊C4×C59C22×C414yes—
105C42×C59C22×C412yes—
106C42×C59C2×D412yes—
107C4⋊Dic59—22no—
108C4⋊Dic59—28no—
109C4⋊Dic59—24no—
110C4⋊Dic59—44no—
111C4⋊Dic59C22×C414yes—
112Dic59⋊C4—28no—
113Dic59⋊C4—28no—
114Dic59⋊C4—28no—
115Dic59⋊C4—48no—
116Dic59⋊C4—44no—
117C4×Dic59C22⋊C418yes—
118C4×Dic59C22×C412yes—
119C4×Dic59C2×D412yes—
120C2×C59⋊C8—22no—
121C2×C59⋊C8—22no—
122C2×C59⋊C8C2×Q814yes—
123C8×D59—216no—
124C23×C59C22×D411yescharacteristic
125C22×D59C2×C22⋊C412yes—
126C22×D59#12412yes—
127C22×D59C4⋊Q812yes—
128C22×D59AGL(1,ℤ/8)14yes—
129C22×D59#13714yes—
130C2×C4×C59—22no—
131C2×C4×C59—22no—
132C2×C4×C59—24no—
133C2×C4×C59—42no—
134C2×C4×C59—42no—
135C2×C4×C59—42no—
136C2×C4×C59—44no—
137C2×C4×C59C2×C22⋊C414yes—
138C2×C4×C59C23×C411yescharacteristic
139C2×C4×C59C22×D411yescharacteristic
140C2×C4×C59C22×Q812yes—
141C2×C4×C59C2×#4112yes—
142C2×Dic59—22no—
143C2×Dic59—22no—
144C2×Dic59—24no—
145C2×Dic59—42no—
146C2×Dic59—42no—
147C2×Dic59—42no—
148C2×Dic59—44no—
149C2×Dic59C2×C22⋊C414yes—
150C2×Dic59C2×C22⋊C412yes—
151C2×Dic59#12412yes—
152C2×Dic59C4⋊Q812yes—
153C4×D59—216no—
154C4×D59—416no—
155C4×D59—88no—
156C4×D59C4×Q818yes—
157C4×D59C22⋊Q818yes—
158C8×C59—24no—
159C59⋊C8—24no—
160C2×#1992—591nomaximal, Sylow
161C22×C59C22×C22⋊C411yescharacteristic
162C22×C59C2×#12411yescharacteristic
163C22×C59C2×C4⋊Q811yescharacteristic
164C22×C59C2×AGL(1,ℤ/8)12yes—
165C22×C59C2×#13712yes—
166C2×D59#39114yes—
167C2×D59#41718yes—
168C2×D59#49014yes—
169C2×D59#49114yes—
170C2×D59#50118yes—
171C4×C59—24no—
172C4×C59—44no—
173C4×C59—82no—
174C4×C59C2×C4×Q812yes—
175C4×C59C2×C22⋊Q812yes—
176Dic59—24no—
177Dic59—44no—
178Dic59—82no—
179Dic59#39114yes—
180C22×#125—591no—
181C22×#97—591no—
182C2×#384—591no—
183#1992—591no—
184#1992—591no—
185#1992—594no—
186#1992—591no—
187#1992D5911yescharacteristic, direct product factor
188C2×#340—594no—
189C2×C59C2×#39111yescharacteristic
190C2×C59C2×#41712yes—
191C2×C59C2×#49011yescharacteristic
192C2×C59C2×#49111yescharacteristic
193C2×C59C2×#50112yes—
194D59#199218yesdirect product factor
195C23×C8—592no—
196C2×#125—598no—
197C2×#125—592no—
198C2×#125—591no—
199C2×#125—1182no—
200C2×#125—1184no—
201C2×#125C2×D5911yescharacteristic
202C22×C4⋊C4—592no—
203C22×C4⋊C4—592no—
204C22×C4⋊C4—1182no—
205C22×C4⋊C4—1182no—
206C22×C42—591no—
207C2×#97—592no—
208C2×#97—591no—
209C2×#97—1184no—
210C2×#97C2×D5911yescharacteristic
211#384—592no—
212#384—591no—
213#384—1182no—
214#384C2×D5911yescharacteristic
215#340—594no—
216#340—594no—
217#340—594no—
218#340C2×D5914yes—
219C59C2×#199211yescharacteristic, complemented, Sylow
220C23×C4—591no—
221C23×C4—592no—
222C23×C4—1182no—
223C23×C4—1182no—
224C22×C8—592no—
225C22×C8—598no—
226C22×C8—1184no—
227C22×C8—1184no—
228C22×C8C22×D5912yes—
229#125—22no—
230#125—598no—
231#125—594no—
232#125—11816no—
233#125—1184no—
234#125—1182no—
235#125C4×D5914yescomplemented
236C2×C4⋊C4—22no—
237C2×C4⋊C4—22no—
238C2×C4⋊C4—592no—
239C2×C4⋊C4—598no—
240C2×C4⋊C4—592no—
241C2×C4⋊C4—1184no—
242C2×C4⋊C4—11816no—
243C2×C4⋊C4—1188no—
244C2×C4⋊C4—1182no—
245C2×C4⋊C4—1182no—
246C2×C4⋊C4—1182no—
247C2×C4⋊C4—1182no—
248C2×C4⋊C4—1182no—
249C2×C4⋊C4—1184no—
250C2×C4⋊C4—1182no—
251C2×C4⋊C4—2368no—
252C2×C4⋊C4C22×D5912yes—
253C2×C4⋊C4C22×D5912yes—
254C2×C42—592no—
255C2×C42—591no—
256C2×C42—594no—
257C2×C42—594no—
258C2×C42C22×D5911yescharacteristic
259#97—22no—
260#97—1184no—
261#97—1182no—
262C24—591no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—591no—
266C22×C4—592no—
267C22×C4—592no—
268C22×C4—594no—
269C22×C4—594no—
270C22×C4—592no—
271C22×C4—598no—
272C22×C4—1184no—
273C22×C4—1184no—
274C22×C4—1188no—
275C22×C4—1182no—
276C22×C4—1182no—
277C22×C4—2364no—
278C22×C4—2368no—
279C22×C4—2364no—
280C22×C4—2364no—
281C22×C4D4×D5912yes—
282C22×C4C23×D5911yescharacteristic
283C2×C8—22no—
284C2×C8—22no—
285C2×C8—594no—
286C2×C8—11816no—
287C2×C8—1182no—
288C2×C8—1182no—
289C2×C8Q8×D5914yes—
290C4⋊C4—28no—
291C4⋊C4—22no—
292C4⋊C4—24no—
293C4⋊C4—44no—
294C4⋊C4—594no—
295C4⋊C4—1188no—
296C4⋊C4—1188no—
297C4⋊C4—1188no—
298C4⋊C4—1188no—
299C4⋊C4—1182no—
300C4⋊C4—1184no—
301C4⋊C4—2364no—
302C4⋊C4—2364no—
303C4⋊C4—2368no—
304C4⋊C4C2×C4×D5914yes—
305C42—598no—
306C42—592no—
307C42—592no—
308C42C2×C4×D5912yes—
309C42D4×D5912yes—
310C23—592no—
311C23—594no—
312C23—594no—
313C23—592no—
314C23—592no—
315C23C2×D4×D5911yescharacteristic
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—24no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—44no—
323C2×C4—592no—
324C2×C4—592no—
325C2×C4—592no—
326C2×C4—598no—
327C2×C4—598no—
328C2×C4—594no—
329C2×C4—11816no—
330C2×C4—1182no—
331C2×C4—1182no—
332C2×C4—1184no—
333C2×C4—4728no—
334C2×C4—23616no—
335C2×C4—2362no—
336C2×C4—2364no—
337C2×C4—2362no—
338C2×C4—2362no—
339C2×C4C22⋊C4×D5914yes—
340C2×C4C22×C4×D5911yescharacteristic
341C2×C4C2×D4×D5911yescharacteristic
342C2×C4C2×Q8×D5912yes—
343C2×C4#41×D5912yes—
344C8—24no—
345C8—1184no—
346C22—598no—
347C22—594no—
348C22—594no—
349C22—594no—
350C22—598no—
351C22C2×C22⋊C4×D5911yescharacteristic
352C22#124×D5911yescharacteristic
353C22C4⋊Q8×D5911yescharacteristic
354C22AGL(1,ℤ/8)×D5912yes—
355C22#137×D5912yes—
356C4—24no—
357C4—44no—
358C4—82no—
359C4—594no—
360C4—1184no—
361C4—4722no—
362C4—2364no—
363C4C4×Q8×D5912yes—
364C4C22⋊Q8×D5912yes—
365C2—598no—
366C2#391×D5911yescharacteristic
367C2#417×D5912yes—
368C2#490×D5911yescharacteristic
369C2#491×D5911yescharacteristic
370C2#501×D5912yes—
subgroupG/H
centerC23C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC59×#1992C2
socleC23×C59C22×D4
prime radicalC23×D59C2×D4
cosocleC22×C4×C59C24
hypercenter#1992D59
hypocenterC59C2×#1992
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
4. #21425066C2semidirect
5. #21425065C2semidirect
6. #21425064C2semidirect
7. #21425063C2semidirect
9. C59×#1992C2semidirect
15. #125×D59C4semidirect
43. #14273719C2×C4semidirect
45. #14273718C2×C4semidirect
69. #125×C59C2×C4semidirect
187. #1992D59direct (N × H)
194. D59#1992direct (N × H)
219. C59C2×#1992semidirect
235. #125C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D592
C2×#97×D592
#384×D592
#214250662
#214250652
#214250642
#214250632
#340×D592
C59×#19922
C2×#199259