Finite Group Databasebeta

← C59×#33911 #28446020

Subgroups — C59×#33911 #28446020

Order 15104.

472 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
1C59×#3338C211yesmaximal, characteristic
2C59×#3336C211yesmaximal, characteristic
3C59×#2255C211yesmaximal, characteristic, complemented
4C59×#2237C211yesmaximal, characteristic, complemented
5C59×#2236C211yesmaximal, characteristic, complemented
6C59×#2235C211yesmaximal, characteristic, complemented
7C59×#2235C211yesmaximal, characteristic, complemented
8C59×#2229C211yesmaximal, characteristic, complemented
9C59×#2225C211yesmaximal, characteristic, complemented
10C59×#2219C211yesmaximal, characteristic, complemented
11C59×#2216C211yesmaximal, characteristic, complemented
12C59×#2176C211yesmaximal, characteristic, complemented
13C59×#2168C211yesmaximal, characteristic
14C59×#2159C211yesmaximal, characteristic, complemented
15C2×C59×#367C211yesmaximal, characteristic, complemented
16C59×#554—21no—
17C59×#552—21no—
18C2×Q32×C59C2211yescharacteristic
19C2×M32×C59C2211yescharacteristic
20C22×C16×C59C2211yescharacteristic
21C59×#500C2211yescharacteristic
22C59×#499C2211yescharacteristic
23C59×#485—21no—
24C59×#484—21no—
25C59×#484—21no—
26C59×#483—21no—
27C59×#479—21no—
28C59×#477—21no—
29C59×#467C2211yescharacteristic
30C59×#467C2211yescharacteristic
31C59×#467C2211yescharacteristic
32C59×#467C2211yescharacteristic
33C4×Q16×C59C2211yescharacteristic
34C4×Q16×C59C2211yescharacteristic
35C8×D4×C59C2211yescharacteristic
36C59×#427C2211yescharacteristic
37C2×#107×C59C2211yescharacteristic
38C2×#107×C59C2211yescharacteristic
39C2×#107×C59C2211yescharacteristic
40C59×#367C2211yescharacteristic
41C59×#367C2211yescharacteristic
42C59×#367C2211yescharacteristic
43C59×#367C2211yescharacteristic
44C59×#367C2211yescharacteristic
45C59×#367C2211yescharacteristic
46C59×#366C2211yescharacteristic
47C59×#366C2211yescharacteristic
48C59×#366C2211yescharacteristic
49C59×C4⋊C16C2211yescharacteristic
50C59×#358C2211yescharacteristic
51C59×#358C2211yescharacteristic
52C59×#358C2211yescharacteristic
53C59×#358C2211yescharacteristic
54C59×#358C2211yescharacteristic
55C59×#358C2211yescharacteristic
56C59×C22⋊C16C2211yescharacteristic
57C59×C22⋊C16C2211yescharacteristic
58C59×#346C2211yescharacteristic
59C2×Q16×C59C2311yescharacteristic
60C2×Q16×C59C2311yescharacteristic
61C22×C8×C59C2311yescharacteristic
62C22×C8×C59C2311yescharacteristic
63C4⋊Q8×C59—21no—
64#126×C59—41no—
65#125×C59—21no—
66#125×C59—41no—
67#125×C59—41no—
68#123×C59—41no—
69C22⋊Q8×C59—21no—
70C22⋊Q8×C59—21no—
71C22⋊Q8×C59—21no—
72C22⋊Q8×C59—21no—
73C22⋊Q8×C59—41no—
74C22⋊Q8×C59—41no—
75C4×Q8×C59—21no—
76C4×Q8×C59—21no—
77C4×D4×C59—41no—
78C4×D4×C59D411yescharacteristic
79#117×C59—21no—
80#117×C59—41no—
81C2×C4⋊C4×C59—21no—
82C2×C4⋊C4×C59—21no—
83C2×C4⋊C4×C59—21no—
84Q32×C59—22no—
85M32×C59—22no—
86C2×C16×C59—22no—
87C2×C16×C59C2311yescharacteristic
88C2×C16×C59C2311yescharacteristic
89C2×C16×C59C2311yescharacteristic
90C2×C16×C59C2311yescharacteristic
91#107×C59—21no—
92#107×C59—21no—
93#107×C59—21no—
94#107×C59—21no—
95#107×C59C2311yescharacteristic
96#107×C59C2311yescharacteristic
97#107×C59C2311yescharacteristic
98#107×C59C2311yescharacteristic
99#107×C59C2311yescharacteristic
100#107×C59C2311yescharacteristic
101#106×C59—21no—
102#106×C59—21no—
103C4⋊C8×C59D411yescharacteristic
104#103×C59—21no—
105#103×C59—21no—
106#103×C59—21no—
107#103×C59—21no—
108#103×C59—21no—
109#103×C59—21no—
110C22⋊C8×C59D411yescharacteristic
111C22⋊C8×C59D411yescharacteristic
112C4×C8×C59C2311yescharacteristic
113C2×Q8×C59—21no—
114C2×Q8×C59—21no—
115C2×Q8×C59—41no—
116C2×D4×C59D811yescharacteristic
117C22×C4×C59—41no—
118C22×C4×C59—41no—
119C22×C4×C59—41no—
120C22×C4×C59C2×D411yescharacteristic
121C22×C4×C59C2×D411yescharacteristic
122Q16×C59—21no—
123Q16×C59—21no—
124Q16×C59—21no—
125Q16×C59—21no—
126C2×C8×C59—21no—
127C2×C8×C59—21no—
128C2×C8×C59—21no—
129C2×C8×C59—21no—
130C2×C8×C59C2×D411yescharacteristic
131C2×C8×C59C2×D411yescharacteristic
132C2×C8×C59C2×D411yescharacteristic
133C2×C8×C59C2411yescharacteristic
134C4⋊C4×C59—21no—
135C4⋊C4×C59—21no—
136C4⋊C4×C59—21no—
137C4⋊C4×C59—21no—
138C4⋊C4×C59—21no—
139C4⋊C4×C59—21no—
140C4⋊C4×C59—41no—
141C4⋊C4×C59—41no—
142C4⋊C4×C59—41no—
143C4⋊C4×C59—41no—
144C4⋊C4×C59—41no—
145C4⋊C4×C59—41no—
146C4⋊C4×C59—41no—
147C4⋊C4×C59—41no—
148C4⋊C4×C59—41no—
149C4⋊C4×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59—41no—
152C4⋊C4×C59D811yescharacteristic
153C22⋊C4×C59—41no—
154C22⋊C4×C59—41no—
155C22⋊C4×C59—41no—
156C22⋊C4×C59—41no—
157C22⋊C4×C59—41no—
158C22⋊C4×C59D811yescharacteristic
159C22⋊C4×C59D811yescharacteristic
160C42×C59—41no—
161C42×C59—41no—
162C42×C59—41no—
163C42×C59C2×D411yescharacteristic
164C16×C59—21no—
165C16×C59—21no—
166C16×C59—21no—
167C16×C59#4112yes—
168C23×C59C2×D811yescharacteristic
169C23×C59C2×D811yescharacteristic
170Q8×C59—41no—
171Q8×C59—41no—
172Q8×C59—41no—
173Q8×C59—41no—
174Q8×C59—161no—
175D4×C59—22no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—21no—
179C2×C4×C59—21no—
180C2×C4×C59—41no—
181C2×C4×C59—41no—
182C2×C4×C59—41no—
183C2×C4×C59—41no—
184C2×C4×C59—41no—
185C2×C4×C59—41no—
186C2×C4×C59—41no—
187C2×C4×C59—41no—
188C2×C4×C59—82no—
189C2×C4×C59—161no—
190C2×C4×C59—161no—
191C2×C4×C59C2×D811yescharacteristic
192C2×C4×C59C2×D811yescharacteristic
193C2×C4×C59C2×D811yescharacteristic
194C2×C4×C59C2×D811yescharacteristic
195C2×C4×C59C22×D411yescharacteristic
196C8×C59—21no—
197C8×C59—21no—
198C8×C59—21no—
199C8×C59C2×#4111yescharacteristic
200C8×C592−1+411yescharacteristic
201#33911C5911yesmaximal, characteristic, direct product factor, Sylow
202C22×C59—21no—
203C22×C59—21no—
204C22×C59—21no—
205C22×C59—21no—
206C22×C59—21no—
207C22×C59#51012yes—
208C22×C59C22×D811yescharacteristic
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—21no—
212C4×C59—21no—
213C4×C59—81no—
214C4×C59—81no—
215C4×C59—81no—
216C4×C59—81no—
217C4×C59—81no—
218C4×C59—81no—
219C4×C59—81no—
220C4×C59—81no—
221C4×C59#54711yescharacteristic
222C4×C59#57811yescharacteristic
223#3338C2×C5911yescharacteristic
224#3336C2×C5911yescharacteristic
225#2255C2×C5911yescharacteristic, complemented
226#2237C2×C5911yescharacteristic, complemented
227#2236C2×C5911yescharacteristic, complemented
228#2235C2×C5911yescharacteristic, complemented
229#2235C2×C5911yescharacteristic, complemented
230#2229C2×C5911yescharacteristic, complemented
231#2225C2×C5911yescharacteristic, complemented
232#2219C2×C5911yescharacteristic, complemented
233#2216C2×C5911yescharacteristic, complemented
234#2176C2×C5911yescharacteristic, complemented
235#2168C2×C5911yescharacteristic
236#2159C2×C5911yescharacteristic, complemented
237C2×#367C2×C5911yescharacteristic, complemented
238C2×C59—22no—
239C2×C59—41no—
240C2×C59#333411yescharacteristic
241C2×C59C2×#51011yescharacteristic
242C2×C59#341611yescharacteristic
243#554—21no—
244#552—21no—
245C2×Q32C22×C5911yescharacteristic
246C2×M32C22×C5911yescharacteristic
247C22×C16C22×C5911yescharacteristic
248#500C22×C5911yescharacteristic
249#499C22×C5911yescharacteristic
250#485—21no—
251#484—21no—
252#484—21no—
253#483—21no—
254#479—21no—
255#477—21no—
256#467C22×C5911yescharacteristic
257#467C22×C5911yescharacteristic
258#467C22×C5911yescharacteristic
259#467C22×C5911yescharacteristic
260C4×Q16C22×C5911yescharacteristic
261C4×Q16C22×C5911yescharacteristic
262C8×D4C22×C5911yescharacteristic
263#427C22×C5911yescharacteristic
264C2×#107C22×C5911yescharacteristic
265C2×#107C22×C5911yescharacteristic
266C2×#107C22×C5911yescharacteristic
267#367C22×C5911yescharacteristic
268#367C22×C5911yescharacteristic
269#367C22×C5911yescharacteristic
270#367C22×C5911yescharacteristic
271#367C22×C5911yescharacteristic
272#367C22×C5911yescharacteristic
273#366C22×C5911yescharacteristic
274#366C22×C5911yescharacteristic
275#366C22×C5911yescharacteristic
276C4⋊C16C22×C5911yescharacteristic
277#358C22×C5911yescharacteristic
278#358C22×C5911yescharacteristic
279#358C22×C5911yescharacteristic
280#358C22×C5911yescharacteristic
281#358C22×C5911yescharacteristic
282#358C22×C5911yescharacteristic
283C22⋊C16C22×C5911yescharacteristic
284C22⋊C16C22×C5911yescharacteristic
285#346C22×C5911yescharacteristic
286C59#3391111yescharacteristic, direct product factor, Sylow
287C2×Q16C23×C5911yescharacteristic
288C2×Q16C23×C5911yescharacteristic
289C22×C8C23×C5911yescharacteristic
290C22×C8C23×C5911yescharacteristic
291C4⋊Q8—21no—
292#126—41no—
293#125—21no—
294#125—41no—
295#125—41no—
296#123—41no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—41no—
302C22⋊Q8—41no—
303C4×Q8—21no—
304C4×Q8—21no—
305C4×D4—41no—
306C4×D4D4×C5911yescharacteristic
307#117—21no—
308#117—41no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—21no—
312Q32—22no—
313M32—22no—
314C2×C16—22no—
315C2×C16C23×C5911yescharacteristic
316C2×C16C23×C5911yescharacteristic
317C2×C16C23×C5911yescharacteristic
318C2×C16C23×C5911yescharacteristic
319#107—21no—
320#107—21no—
321#107—21no—
322#107—21no—
323#107C23×C5911yescharacteristic
324#107C23×C5911yescharacteristic
325#107C23×C5911yescharacteristic
326#107C23×C5911yescharacteristic
327#107C23×C5911yescharacteristic
328#107C23×C5911yescharacteristic
329#106—21no—
330#106—21no—
331C4⋊C8D4×C5911yescharacteristic
332#103—21no—
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—21no—
338C22⋊C8D4×C5911yescharacteristic
339C22⋊C8D4×C5911yescharacteristic
340C4×C8C23×C5911yescharacteristic
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—41no—
344C2×D4D8×C5911yescharacteristic
345C22×C4—41no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4C2×D4×C5911yescharacteristic
349C22×C4C2×D4×C5911yescharacteristic
350Q16—21no—
351Q16—21no—
352Q16—21no—
353Q16—21no—
354C2×C8—21no—
355C2×C8—21no—
356C2×C8—21no—
357C2×C8—21no—
358C2×C8C2×D4×C5911yescharacteristic
359C2×C8C2×D4×C5911yescharacteristic
360C2×C8C2×D4×C5911yescharacteristic
361C2×C8C24×C5911yescharacteristic
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—21no—
367C4⋊C4—21no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C4⋊C4—41no—
378C4⋊C4—41no—
379C4⋊C4—41no—
380C4⋊C4D8×C5911yescharacteristic
381C22⋊C4—41no—
382C22⋊C4—41no—
383C22⋊C4—41no—
384C22⋊C4—41no—
385C22⋊C4—41no—
386C22⋊C4D8×C5911yescharacteristic
387C22⋊C4D8×C5911yescharacteristic
388C42—41no—
389C42—41no—
390C42—41no—
391C42C2×D4×C5911yescharacteristic
392C16—21no—
393C16—21no—
394C16—21no—
395C16#41×C5912yes—
396C23C2×D8×C5911yescharacteristic
397C23C2×D8×C5911yescharacteristic
398Q8—41no—
399Q8—41no—
400Q8—41no—
401Q8—41no—
402Q8—161no—
403D4—22no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—21no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—82no—
417C2×C4—161no—
418C2×C4—161no—
419C2×C4C2×D8×C5911yescharacteristic
420C2×C4C2×D8×C5911yescharacteristic
421C2×C4C2×D8×C5911yescharacteristic
422C2×C4C2×D8×C5911yescharacteristic
423C2×C4C22×D4×C5911yescharacteristic
424C8—21no—
425C8—21no—
426C8—21no—
427C8C2×#41×C5911yescharacteristic
428C82−1+4×C5911yescharacteristic
429C22—21no—
430C22—21no—
431C22—21no—
432C22—21no—
433C22—21no—
434C22C59×#51012yes—
435C22C22×D8×C5911yescharacteristic
436C4—21no—
437C4—21no—
438C4—21no—
439C4—21no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4—81no—
445C4—81no—
446C4—81no—
447C4—81no—
448C4C59×#54711yescharacteristic
449C4C59×#57811yescharacteristic
450C2—22no—
451C2—41no—
452C2C59×#333411yescharacteristic
453C2C2×C59×#51011yescharacteristic
454C2C59×#341611yescharacteristic
subgroupG/H
center, socleC22×C59C22×D8
commutator, Frattini, cosocleC2×C8C24×C59
prime radicalC2×D4×C59D8
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ C4×D4×C59 ◁ C8×D4×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#2255C2semidirect
4. C59×#2237C2semidirect
5. C59×#2236C2semidirect
6. C59×#2235C2semidirect
7. C59×#2235C2semidirect
8. C59×#2229C2semidirect
9. C59×#2225C2semidirect
10. C59×#2219C2semidirect
11. C59×#2216C2semidirect
12. C59×#2176C2semidirect
14. C59×#2159C2semidirect
15. C2×C59×#367C2semidirect
201. #33911C59direct (N × H)
225. #2255C2×C59semidirect
226. #2237C2×C59semidirect
227. #2236C2×C59semidirect
228. #2235C2×C59semidirect
229. #2235C2×C59semidirect
230. #2229C2×C59semidirect
231. #2225C2×C59semidirect
232. #2219C2×C59semidirect
233. #2216C2×C59semidirect
234. #2176C2×C59semidirect
236. #2159C2×C59semidirect
237. C2×#367C2×C59semidirect
286. C59#33911direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#33382
C59×#33362
C59×#22552
C59×#22372
C59×#22362
C59×#22352
C59×#22292
C59×#22252
C59×#22192
C59×#22162
C59×#21762
C59×#21682
C59×#21592
C2×C59×#3672
#3391159