Finite Group Databasebeta

← D59×#1386 #28503602

Subgroups — D59×#1386 #28503602

Order 15104.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D59C211yesmaximal, characteristic
2#427×D59C211yesmaximal, characteristic
3C2×#106×D59C211yesmaximal, characteristic
4#21422203C211yesmaximal, characteristic, complemented
5#21422202C211yesmaximal, characteristic, complemented
6#21422201C211yesmaximal, characteristic, complemented
7C59×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D59C2211yescharacteristic
9#117×D59—21no—
10C2×C4⋊C4×D59—21no—
11C2×#14273667C2211yescharacteristic
12C2×#14273666—21no—
13M32×D59—22no—
14M32×D59C414yescomplemented
15C2×C16×D59—21no—
16#16837440C2211yescharacteristic
17#16837439C412yescomplemented
18#16837438—21no—
19#16837437—21no—
20#107×D59C412yescomplemented
21C2×#14273659C2211yescharacteristic
22C2×#14273658—21no—
23#106×D59—22no—
24#106×D59—21no—
25#106×D59C414yescomplemented
26C2×M32×C59C2211yescharacteristic
27C59×#427C2211yescharacteristic
28C2×#106×C59C2211yescharacteristic
29C22×C4×D59—41no—
30C22×C4×D59D411yescharacteristic
31C22×C59⋊C8D411yescharacteristic
32C2×C8×D59C2×C412yes—
33C2×C8×D59C2×C412yes—
34C2×C8×D59C2×C411yescharacteristic
35C2×C8×D59C2×C411yescharacteristic
36C2×C8×D59D411yescharacteristic
37C2×C8×D59D412yes—
38C2×C8×D59D411yescharacteristic
39C2×C8×D59Q812yes—
40#14273686—21no—
41#14273685—22no—
42#14273684—41no—
43#14273683—41no—
44C2×C4⋊Dic59—21no—
45C2×Dic59⋊C4—41no—
46C4⋊C4×D59—24no—
47C4⋊C4×D59—22no—
48C4⋊C4×D59—42no—
49C22⋊C4×D59—41no—
50C42×D59—41no—
51#14273667—21no—
52#14273667C2×C412yescomplemented
53#14273666—24no—
54C2×C59⋊C16—21no—
55C16×D59—24no—
56#14273661C2×C412yescomplemented
57#14273660—22no—
58#14273659—21no—
59#14273659—21no—
60#14273659C2×C412yescomplemented
61#14273658—24no—
62#14273658—22no—
63C22×C8×C59C2311yescharacteristic
64#117×C59—21no—
65C2×C4⋊C4×C59—21no—
66M32×C59—21no—
67M32×C59C2×C412yescomplemented
68C2×C16×C59—21no—
69#107×C59C2×C412yescomplemented
70#106×C59—21no—
71#106×C59—21no—
72#106×C59C2×C412yescomplemented
73C23×D59D811yescharacteristic
74C22×C4×C59—41no—
75C22×C4×C59C2×D411yescharacteristic
76C22×Dic59—41no—
77C22×Dic59D811yescharacteristic
78C2×C4×D59—42no—
79C2×C4×D59—44no—
80C2×C4×D59—84no—
81C2×C4×D59C22⋊C412yes—
82C2×C4×D59C22⋊C411yescharacteristic
83C2×C4×D59C22⋊C411yescharacteristic
84C2×C4×D59C4⋊C412yes—
85C2×C4×D59SD1611yescharacteristic
86C2×C4×D59SD1612yes—
87C2×C4×D59SD1611yescharacteristic
88C2×C4×D59Q1612yes—
89C2×C8×C59C22×C411yescharacteristic
90C2×C8×C59C22×C411yescharacteristic
91C2×C8×C59C22×C411yescharacteristic
92C2×C8×C59C2×D411yescharacteristic
93C2×C8×C59C2×D411yescharacteristic
94C2×C8×C59C2×Q811yescharacteristic
95C4⋊C4×C59—22no—
96C4⋊C4×C59—22no—
97C4⋊C4×C59—41no—
98C22⋊C4×C59—41no—
99C42×C59—41no—
100C22⋊Dic59—41no—
101(C2×D59)⋊C4—42no—
102C4⋊Dic59—22no—
103C4⋊Dic59—22no—
104C4⋊Dic59—41no—
105Dic59⋊C4—44no—
106Dic59⋊C4—42no—
107C4×Dic59—41no—
108C4×Dic59—42no—
109C2×C59⋊C8C22⋊C412yes—
110C2×C59⋊C8C22⋊C411yescharacteristic
111C2×C59⋊C8C22⋊C411yescharacteristic
112C2×C59⋊C8C4⋊C412yes—
113C8×D59C4212yes—
114C8×D59C4212yes—
115C8×D59C22⋊C412yes—
116C8×D59C22⋊C412yes—
117C8×D59C4⋊C412yes—
118C8×D59C4⋊C412yes—
119C8×D59C4⋊C412yes—
120C8×D59C4⋊C412yes—
121C16×C59—22no—
122C59⋊C16—22no—
123C23×C59C2×D811yescharacteristic
124C22×D59—24no—
125C22×D59#10211yescharacteristic
126C22×D59#10212yes—
127C22×D59#10211yescharacteristic
128C22×D59#10712yes—
129C2×C4×C59—42no—
130C2×C4×C59—42no—
131C2×C4×C59—82no—
132C2×C4×C59C2×C22⋊C411yescharacteristic
133C2×C4×C59C2×C22⋊C411yescharacteristic
134C2×C4×C59C2×C4⋊C411yescharacteristic
135C2×C4×C59C2×SD1611yescharacteristic
136C2×C4×C59C2×SD1611yescharacteristic
137C2×C4×C59C2×Q1611yescharacteristic
138C2×Dic59—42no—
139C2×Dic59—42no—
140C2×Dic59—82no—
141C2×Dic59#10211yescharacteristic
142C2×Dic59#10212yes—
143C2×Dic59#10211yescharacteristic
144C2×Dic59#10712yes—
145C4×D59—88no—
146C4×D59—84no—
147C4×D59#9512yes—
148C4×D59#9512yes—
149C4×D59#10312yes—
150C4×D59#10312yes—
151C4×D59#10312yes—
152C4×D59#10312yes—
153C4×D59#10612yes—
154C4×D59#10612yes—
155C8×C59C2×C4211yescharacteristic
156C8×C59C2×C22⋊C411yescharacteristic
157C8×C59C2×C4⋊C411yescharacteristic
158C8×C59C2×C4⋊C411yescharacteristic
159C59⋊C8#9512yes—
160C59⋊C8#9512yes—
161C2×#1386—591nomaximal, Sylow
162C22×C59—22no—
163C22×C59C2×#10211yescharacteristic
164C22×C59C2×#10211yescharacteristic
165C22×C59C2×#10711yescharacteristic
166C2×D59—22no—
167C2×D59—24no—
168C2×D59—24no—
169C2×D59#34012yes—
170C2×D59#34012yes—
171C2×D59#36014yes—
172C4×C59—82no—
173C4×C59—82no—
174C4×C59C2×#9511yescharacteristic
175C4×C59C2×#10311yescharacteristic
176C4×C59C2×#10311yescharacteristic
177C4×C59C2×#10611yescharacteristic
178Dic59—82no—
179Dic59—82no—
180Dic59#34012yes—
181Dic59#34012yes—
182C22×M32—591no—
183C2×#427—591no—
184C22×#106—591no—
185#1386—591no—
186#1386—591no—
187#1386—591no—
188#1386D5911yescharacteristic, direct product factor
189C2×C59—21no—
190C2×C59—21no—
191C2×C59C2×#34011yescharacteristic
192C2×C59C2×#36012yes—
193D59—22no—
194D59#138614yesdirect product factor
195C23×C8—591no—
196C2×#117—1181no—
197C22×C4⋊C4—1181no—
198C2×M32—591no—
199C2×M32—594no—
200C2×M32—1181no—
201C2×M32—1182no—
202C2×M32C2×D5911yescharacteristic
203C22×C16—1181no—
204#427—591no—
205#427—592no—
206#427—1181no—
207#427—1181no—
208#427C2×D5911yescharacteristic
209C2×#107—592no—
210C2×#106—591no—
211C2×#106—594no—
212C2×#106—1182no—
213C2×#106—1181no—
214C2×#106—1181no—
215C2×#106C2×D5911yescharacteristic
216C59C2×#138611yescharacteristic, complemented, Sylow
217C23×C4—591no—
218C23×C4—2361no—
219C22×C8—591no—
220C22×C8—592no—
221C22×C8—591no—
222C22×C8—591no—
223C22×C8—592no—
224C22×C8—591no—
225C22×C8—592no—
226C22×C8—591no—
227C22×C8—592no—
228C22×C8C22×D5911yescharacteristic
229#117—21no—
230#117—1182no—
231#117—1181no—
232#117—2361no—
233#117—2361no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—1184no—
236C2×C4⋊C4—1182no—
237C2×C4⋊C4—1181no—
238C2×C4⋊C4—2362no—
239C2×C4⋊C4—2361no—
240C2×C22⋊C4—2361no—
241C2×C42—2361no—
242M32—21no—
243M32—592no—
244M32—1184no—
245M32—1181no—
246M32C4×D5912yescomplemented
247C2×C16—21no—
248C2×C16—1184no—
249C2×C16—1181no—
250#107—592no—
251#107—1182no—
252#107C4×D5912yescomplemented
253#106—21no—
254#106—21no—
255#106—592no—
256#106—1184no—
257#106—1182no—
258#106—1181no—
259#106—1181no—
260#106C4×D5912yescomplemented
261C24—591no—
262C22×C4—41no—
263C22×C4—591no—
264C22×C4—592no—
265C22×C4—591no—
266C22×C4—591no—
267C22×C4—592no—
268C22×C4—591no—
269C22×C4—592no—
270C22×C4—591no—
271C22×C4—592no—
272C22×C4—4724no—
273C22×C4—2362no—
274C22×C4—2364no—
275C22×C4—2361no—
276C22×C4D4×D5911yescharacteristic
277C2×C8—592no—
278C2×C8—591no—
279C2×C8—591no—
280C2×C8—592no—
281C2×C8—592no—
282C2×C8—592no—
283C2×C8—592no—
284C2×C8—592no—
285C2×C8—592no—
286C2×C8—592no—
287C2×C8—592no—
288C2×C8—592no—
289C2×C8C2×C4×D5911yescharacteristic
290C2×C8C2×C4×D5911yescharacteristic
291C2×C8C2×C4×D5911yescharacteristic
292C2×C8D4×D5911yescharacteristic
293C2×C8D4×D5911yescharacteristic
294C2×C8Q8×D5911yescharacteristic
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—1182no—
299C4⋊C4—1182no—
300C4⋊C4—2364no—
301C4⋊C4—2362no—
302C4⋊C4—2361no—
303C22⋊C4—41no—
304C22⋊C4—2362no—
305C22⋊C4—2361no—
306C42—41no—
307C42—2362no—
308C42—2361no—
309C16—22no—
310C16—1182no—
311C23—591no—
312C23—592no—
313C23—591no—
314C23—592no—
315C23—1184no—
316C23D8×D5911yescharacteristic
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—592no—
321C2×C4—591no—
322C2×C4—591no—
323C2×C4—592no—
324C2×C4—592no—
325C2×C4—592no—
326C2×C4—592no—
327C2×C4—592no—
328C2×C4—592no—
329C2×C4—592no—
330C2×C4—592no—
331C2×C4—592no—
332C2×C4—4724no—
333C2×C4—4728no—
334C2×C4—4722no—
335C2×C4—2362no—
336C2×C4—2362no—
337C2×C4C22⋊C4×D5911yescharacteristic
338C2×C4C22⋊C4×D5911yescharacteristic
339C2×C4C4⋊C4×D5911yescharacteristic
340C2×C4SD16×D5911yescharacteristic
341C2×C4SD16×D5911yescharacteristic
342C2×C4Q16×D5911yescharacteristic
343C8—592no—
344C8—592no—
345C8C42×D5911yescharacteristic
346C8C22⋊C4×D5911yescharacteristic
347C8C4⋊C4×D5911yescharacteristic
348C8C4⋊C4×D5911yescharacteristic
349C22—22no—
350C22—594no—
351C22—592no—
352C22—592no—
353C22—1184no—
354C22—1184no—
355C22—1182no—
356C22#102×D5911yescharacteristic
357C22#102×D5911yescharacteristic
358C22#107×D5911yescharacteristic
359C4—82no—
360C4—82no—
361C4—592no—
362C4—592no—
363C4—4722no—
364C4—4722no—
365C4#95×D5911yescharacteristic
366C4#103×D5911yescharacteristic
367C4#103×D5911yescharacteristic
368C4#106×D5911yescharacteristic
369C2—21no—
370C2—21no—
371C2—594no—
372C2—1182no—
373C2#340×D5911yescharacteristic
374C2#360×D5912yes—
subgroupG/H
centerC22#102×D59
commutatorC8×C59C2×C42
FrattiniC22×C8C22×D59
FittingC59×#1386C2
socleC22×C59C2×#102
prime radicalC23×D59D8
cosocleC22×C8×C59C23
hypercenter#1386D59
hypocenterC59C2×#1386
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #21422203C2semidirect
5. #21422202C2semidirect
6. #21422201C2semidirect
7. C59×#1386C2semidirect
14. M32×D59C4semidirect
17. #16837439C4semidirect
20. #107×D59C4semidirect
25. #106×D59C4semidirect
52. #14273667C2×C4semidirect
56. #14273661C2×C4semidirect
60. #14273659C2×C4semidirect
67. M32×C59C2×C4semidirect
69. #107×C59C2×C4semidirect
72. #106×C59C2×C4semidirect
188. #1386D59direct (N × H)
194. D59#1386direct (N × H)
216. C59C2×#1386semidirect
246. M32C4×D59semidirect
252. #107C4×D59semidirect
260. #106C4×D59semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D592
#427×D592
C2×#106×D592
#214222032
#214222022
#214222012
C59×#13862
C2×#138659