Finite Group Databasebeta

← D59×#2229 #28743320

Subgroups — D59×#2229 #28743320

Order 15104.

542 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#499×D59C211yesmaximal, characteristic
2C4×Q16×D59C211yesmaximal, characteristic
3#21426263C211yesmaximal, characteristic, complemented
4#21426262C211yesmaximal, characteristic, complemented
5#21426261C211yesmaximal, characteristic, complemented
6#21426260C211yesmaximal, characteristic, complemented
7#21426259C211yesmaximal, characteristic, complemented
8#21426258C211yesmaximal, characteristic, complemented
9#21426257C211yesmaximal, characteristic, complemented
10#367×D59C211yesmaximal, characteristic
11#366×D59C211yesmaximal, characteristic
12C4⋊C16×D59C211yesmaximal, characteristic
13#358×D59C211yesmaximal, characteristic
14#358×D59C211yesmaximal, characteristic
15C59×#2229C211yesmaximal, characteristic, complemented
16C2×Q16×D59C2211yescharacteristic
17#125×D59—21no—
18C4×Q8×D59—21no—
19C2×C16×D59C2211yescharacteristic
20C2×C16×D59C2211yescharacteristic
21#16837804C2211yescharacteristic
22#16837803C2211yescharacteristic
23#16837803C2211yescharacteristic
24#16837802—21no—
25#16837801—21no—
26C4×Dic236C2211yescharacteristic
27Q16×Dic59C2211yescharacteristic
28#16837496C2211yescharacteristic
29C4×#11745672—21no—
30#16837494—21no—
31#107×D59C2211yescharacteristic
32#107×D59C2211yescharacteristic
33#107×D59C2211yescharacteristic
34#106×D59—21no—
35#103×D59—21no—
36C4×C8×D59C2211yescharacteristic
37#16837230C2211yescharacteristic
38#16837229C2211yescharacteristic
39#16837229C2211yescharacteristic
40#16837228C2211yescharacteristic
41#16837227C2211yescharacteristic
42#16837227C2211yescharacteristic
43C4⋊(C59⋊C16)C2211yescharacteristic
44Dic59⋊C16C2211yescharacteristic
45Dic59⋊C16C2211yescharacteristic
46#16837207C2211yescharacteristic
47#16837207C2211yescharacteristic
48#16837206C2211yescharacteristic
49#16837206C2211yescharacteristic
50#16837205C2211yescharacteristic
51#16837205C2211yescharacteristic
52C59×#499C2211yescharacteristic
53C4×Q16×C59C2211yescharacteristic
54C59×#367C2211yescharacteristic
55C59×#366C2211yescharacteristic
56C59×C4⋊C16C2211yescharacteristic
57C59×#358C2211yescharacteristic
58C59×#358C2211yescharacteristic
59C2×Q8×D59—21no—
60C2×Dic236C2311yescharacteristic
61C2×#11745672—21no—
62Q16×D59—22no—
63Q16×D59Q814yes—
64C2×C8×D59D411yescharacteristic
65C2×C8×D59C2311yescharacteristic
66#14273719—21no—
67#14273718—21no—
68#14273718—21no—
69#14273717—41no—
70#14273717—41no—
71Q8×Dic59—21no—
72C4×Dic118—21no—
73C4×Dic118—41no—
74#14273692—21no—
75#14273692—41no—
76C4⋊C4×D59—21no—
77C4⋊C4×D59—21no—
78C4⋊C4×D59—21no—
79C4⋊C4×D59—41no—
80C4⋊C4×D59—41no—
81C4⋊C4×D59—41no—
82C42×D59—41no—
83C42×D59D411yescharacteristic
84C2×C59⋊C16C2311yescharacteristic
85C2×C59⋊C16C2311yescharacteristic
86C16×D59—22no—
87C16×D59—22no—
88#14273661C2311yescharacteristic
89#14273661C2311yescharacteristic
90#14273661C2311yescharacteristic
91#14273660—21no—
92#14273660—21no—
93#14273660—21no—
94#14273659—21no—
95#14273658—21no—
96#14273658—21no—
97#14273652—21no—
98#14273651—21no—
99#14273650—21no—
100C4×C59⋊C8D411yescharacteristic
101C8×Dic59D411yescharacteristic
102C8×Dic59C2311yescharacteristic
103C2×Q16×C59C2311yescharacteristic
104#125×C59—21no—
105C4×Q8×C59—21no—
106C2×C16×C59C2311yescharacteristic
107C2×C16×C59C2311yescharacteristic
108#107×C59C2311yescharacteristic
109#107×C59C2311yescharacteristic
110#107×C59C2311yescharacteristic
111#106×C59—21no—
112#103×C59—21no—
113C4×C8×C59C2311yescharacteristic
114C2×Q8×C59—21no—
115Q8×D59—24no—
116Q8×D59—42no—
117C2×C4×D59—41no—
118C2×C4×D59—41no—
119C2×C4×D59—41no—
120C2×C4×D59—41no—
121C2×C4×D59D811yescharacteristic
122C2×C4×D59D811yescharacteristic
123C2×C4×D59C2×D411yescharacteristic
124C2×Dic118—21no—
125C2×Dic118—41no—
126Q16×C59—21no—
127Q16×C59C2×Q812yes—
128C2×C8×C59C2×D411yescharacteristic
129C2×C8×C59C2411yescharacteristic
130C4⋊C4×C59—21no—
131C4⋊C4×C59—21no—
132C4⋊C4×C59—21no—
133C4⋊C4×C59—41no—
134C4⋊C4×C59—41no—
135C4⋊C4×C59—41no—
136C42×C59—41no—
137C42×C59C2×D411yescharacteristic
138#11745672—24no—
139C4⋊Dic59—21no—
140C4⋊Dic59—21no—
141C4⋊Dic59—21no—
142C4⋊Dic59—41no—
143C4⋊Dic59—41no—
144C4⋊Dic59—41no—
145Dic59⋊C4—41no—
146Dic59⋊C4—41no—
147Dic59⋊C4—41no—
148Dic59⋊C4—41no—
149Dic59⋊C4—41no—
150Dic59⋊C4—41no—
151Dic59⋊C4—41no—
152Dic59⋊C4—41no—
153Dic59⋊C4—41no—
154C4×Dic59—41no—
155C4×Dic59—41no—
156C4×Dic59—41no—
157C4×Dic59D811yescharacteristic
158C4×Dic59D811yescharacteristic
159C4×Dic59C2×D411yescharacteristic
160C2×C59⋊C8C2×D411yescharacteristic
161C2×C59⋊C8C2×D411yescharacteristic
162Dic236—21no—
163Dic236C2×Q812yes—
164C8×D59—22no—
165C8×D59C2×Q812yes—
166C8×D59#4112yes—
167C16×C59—21no—
168C16×C59—21no—
169C59⋊C16—21no—
170C59⋊C16—21no—
171C22×D59C2×D811yescharacteristic
172Q8×C59—22no—
173Q8×C59—41no—
174C2×C4×C59—41no—
175C2×C4×C59—41no—
176C2×C4×C59—41no—
177C2×C4×C59—41no—
178C2×C4×C59C2×D811yescharacteristic
179C2×C4×C59C2×D811yescharacteristic
180C2×C4×C59C22×D411yescharacteristic
181C2×Dic59—41no—
182C2×Dic59—41no—
183C2×Dic59—41no—
184C2×Dic59—41no—
185C2×Dic59C2×D811yescharacteristic
186C2×Dic59C2×D811yescharacteristic
187C2×Dic59C2×D811yescharacteristic
188C4×D59—22no—
189C4×D59—22no—
190C4×D59—44no—
191C4×D59—82no—
192C4×D59—82no—
193C4×D59—82no—
194C4×D59C22⋊Q812yes—
195C4×D59#13712yes—
196Dic118—22no—
197Dic118—41no—
198Dic118—44no—
199C8×C59—21no—
200C8×C59C22×Q811yescharacteristic
201C8×C59C2×#4111yescharacteristic
202C59⋊C8—21no—
203C59⋊C8C22⋊Q812yes—
204C2×#2229—591nomaximal, Sylow
205C22×C59C22×D811yescharacteristic
206C2×D59#47412yes—
207C2×D59#50812yes—
208C2×D59#51012yes—
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—42no—
212C4×C59—81no—
213C4×C59—81no—
214C4×C59—81no—
215C4×C59C2×C22⋊Q811yescharacteristic
216C4×C59C2×#13711yescharacteristic
217Dic59—21no—
218Dic59—21no—
219Dic59—42no—
220Dic59—81no—
221Dic59—81no—
222Dic59—81no—
223Dic59#47412yes—
224C2×#499—591no—
225C2×C4×Q16—591no—
226#2229—591no—
227#2229—591no—
228#2229—591no—
229#2229—591no—
230#2229—591no—
231#2229—591no—
232#2229—591no—
233#2229D5911yescharacteristic, direct product factor
234C2×#367—591no—
235C2×#366—591no—
236C2×C4⋊C16—591no—
237C2×#358—591no—
238C2×#358—591no—
239C2×C59C2×#47411yescharacteristic
240C2×C59C2×#50811yescharacteristic
241C2×C59C2×#51011yescharacteristic
242D59#222914yesdirect product factor
243C22×Q16—591no—
244C2×#125—1181no—
245C2×C4×Q8—1181no—
246C22×C16—591no—
247C22×C16—591no—
248#499—591no—
249#499—591no—
250#499—591no—
251#499—1181no—
252#499—1181no—
253#499C2×D5911yescharacteristic
254C4×Q16—591no—
255C4×Q16—591no—
256C4×Q16—591no—
257C4×Q16—1181no—
258C4×Q16—1181no—
259C4×Q16C2×D5911yescharacteristic
260C2×#107—591no—
261C2×#107—591no—
262C2×#107—591no—
263C2×#106—1181no—
264C2×#103—1181no—
265C2×C4×C8—591no—
266#367—591no—
267#367—591no—
268#367—591no—
269#367C2×D5911yescharacteristic
270#366—591no—
271#366—591no—
272#366—591no—
273#366C2×D5911yescharacteristic
274C4⋊C16—591no—
275C4⋊C16—591no—
276C4⋊C16—591no—
277C4⋊C16C2×D5911yescharacteristic
278#358—591no—
279#358—591no—
280#358—591no—
281#358—591no—
282#358—591no—
283#358—591no—
284#358C2×D5911yescharacteristic
285#358C2×D5911yescharacteristic
286C59C2×#222911yescharacteristic, complemented, Sylow
287C22×Q8—1181no—
288C2×Q16—594no—
289C2×Q16—591no—
290C2×Q16—1182no—
291C2×Q16—1181no—
292C2×Q16C22×D5911yescharacteristic
293C22×C8—591no—
294C22×C8—591no—
295#125—21no—
296#125—1181no—
297#125—1181no—
298#125—1181no—
299#125—2361no—
300#125—2361no—
301C4×Q8—21no—
302C4×Q8—1181no—
303C4×Q8—1181no—
304C4×Q8—1181no—
305C4×Q8—2361no—
306C4×Q8—2361no—
307C2×C4⋊C4—1181no—
308C2×C4⋊C4—1181no—
309C2×C4⋊C4—1181no—
310C2×C4⋊C4—2361no—
311C2×C4⋊C4—2361no—
312C2×C4⋊C4—2361no—
313C2×C42—591no—
314C2×C42—2361no—
315C2×C16—591no—
316C2×C16—591no—
317C2×C16—1182no—
318C2×C16—1182no—
319C2×C16C22×D5911yescharacteristic
320C2×C16C22×D5911yescharacteristic
321#107—591no—
322#107—591no—
323#107—591no—
324#107—1181no—
325#107—1181no—
326#107—1181no—
327#107C22×D5911yescharacteristic
328#107C22×D5911yescharacteristic
329#107C22×D5911yescharacteristic
330#106—21no—
331#106—1181no—
332#106—1181no—
333#106—1181no—
334#103—21no—
335#103—1181no—
336#103—1181no—
337#103—1181no—
338C4×C8—591no—
339C4×C8—591no—
340C4×C8—591no—
341C4×C8C22×D5911yescharacteristic
342C2×Q8—21no—
343C2×Q8—1184no—
344C2×Q8—1181no—
345C2×Q8—2361no—
346C2×Q8—2362no—
347C22×C4—591no—
348C22×C4—591no—
349C22×C4—591no—
350C22×C4—2361no—
351C22×C4—2361no—
352C22×C4—2361no—
353C22×C4—2361no—
354Q16—21no—
355Q16—592no—
356Q16—1184no—
357Q16—1181no—
358Q16Q8×D5912yes—
359C2×C8—591no—
360C2×C8—592no—
361C2×C8—592no—
362C2×C8—591no—
363C2×C8—1182no—
364C2×C8D4×D5911yescharacteristic
365C2×C8C23×D5911yescharacteristic
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—21no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—1181no—
373C4⋊C4—1181no—
374C4⋊C4—1181no—
375C4⋊C4—2361no—
376C4⋊C4—2361no—
377C4⋊C4—2361no—
378C4⋊C4—2361no—
379C4⋊C4—2361no—
380C4⋊C4—2361no—
381C4⋊C4—2361no—
382C4⋊C4—2361no—
383C4⋊C4—2361no—
384C4⋊C4—2361no—
385C4⋊C4—2361no—
386C4⋊C4—2361no—
387C42—41no—
388C42—591no—
389C42—591no—
390C42—591no—
391C42—2361no—
392C42—2361no—
393C42—2361no—
394C42D4×D5911yescharacteristic
395C16—21no—
396C16—21no—
397C16—1181no—
398C16—1181no—
399C23—591no—
400Q8—22no—
401Q8—41no—
402Q8—1182no—
403Q8—2364no—
404Q8—2361no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—591no—
410C2×C4—592no—
411C2×C4—592no—
412C2×C4—591no—
413C2×C4—591no—
414C2×C4—1182no—
415C2×C4—1182no—
416C2×C4—4722no—
417C2×C4—4722no—
418C2×C4—4722no—
419C2×C4—2364no—
420C2×C4—2361no—
421C2×C4—2361no—
422C2×C4—2361no—
423C2×C4—2361no—
424C2×C4D8×D5911yescharacteristic
425C2×C4D8×D5911yescharacteristic
426C2×C4C2×D4×D5911yescharacteristic
427C8—21no—
428C8—592no—
429C8—1181no—
430C8C2×Q8×D5911yescharacteristic
431C8#41×D5911yescharacteristic
432C22—592no—
433C22—592no—
434C22—592no—
435C22C2×D8×D5911yescharacteristic
436C4—21no—
437C4—21no—
438C4—42no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—592no—
443C4—1181no—
444C4—1181no—
445C4—4721no—
446C4—4721no—
447C4—4721no—
448C4—2362no—
449C4C22⋊Q8×D5911yescharacteristic
450C4#137×D5911yescharacteristic
451C2—594no—
452C2#474×D5911yescharacteristic
453C2#508×D5911yescharacteristic
454C2#510×D5911yescharacteristic
subgroupG/H
centerC22C2×D8×D59
commutator, cosocleC2×C8×C59C24
FrattiniC2×C8C23×D59
FittingC59×#2229C2
socleC22×C59C22×D8
prime radicalC22×D59C2×D8
hypercenter#2229D59
hypocenterC59C2×#2229
LCSG ▷ C2×C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2229

Complements

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

NH ≅ G/Ntype
3. #21426263C2semidirect
4. #21426262C2semidirect
5. #21426261C2semidirect
6. #21426260C2semidirect
7. #21426259C2semidirect
8. #21426258C2semidirect
9. #21426257C2semidirect
15. C59×#2229C2semidirect
233. #2229D59direct (N × H)
242. D59#2229direct (N × H)
286. C59C2×#2229semidirect

Maximal subgroups

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

subgroupindex
#499×D592
C4×Q16×D592
#214262632
#214262622
#214262612
#214262602
#214262592
#214262582
#214262572
#367×D592
#366×D592
C4⋊C16×D592
#358×D592
C59×#22292
C2×#222959