Finite Group Databasebeta

← C59×#33916 #28446025

Subgroups — C59×#33916 #28446025

Order 15104.

464 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3342C211yesmaximal, characteristic
2C59×#3336C211yesmaximal, characteristic
3C59×#2255C211yesmaximal, characteristic, complemented
4C59×#2237C211yesmaximal, characteristic, complemented
5C59×#2237C211yesmaximal, characteristic, complemented
6C59×#2237C211yesmaximal, characteristic, complemented
7C59×#2236C211yesmaximal, characteristic, complemented
8C59×#2229C211yesmaximal, characteristic, complemented
9C59×#2227C211yesmaximal, characteristic, complemented
10C59×#2219C211yesmaximal, characteristic, complemented
11C59×#2216C211yesmaximal, characteristic, complemented
12C59×#2176C211yesmaximal, characteristic, complemented
13C59×#2168C211yesmaximal, characteristic
14C59×#2159C211yesmaximal, characteristic, complemented
15C59×#2158C211yesmaximal, characteristic, complemented
16C59×#556—21no—
17C59×#552—21no—
18C2×Q32×C59C2211yescharacteristic
19C2×M32×C59C2211yescharacteristic
20C22×C16×C59C2211yescharacteristic
21C59×#500C2211yescharacteristic
22C59×#499C2211yescharacteristic
23C59×#485—21no—
24C59×#485—21no—
25C59×#485—21no—
26C59×#483—21no—
27C59×#479—21no—
28C59×#475—21no—
29C59×#467C2211yescharacteristic
30C59×#467C2211yescharacteristic
31C59×#467C2211yescharacteristic
32C59×#467C2211yescharacteristic
33C4×Q16×C59C2211yescharacteristic
34C4×Q16×C59C2211yescharacteristic
35C8×D4×C59C2211yescharacteristic
36C59×#427C2211yescharacteristic
37C59×#427C2211yescharacteristic
38C59×#427C2211yescharacteristic
39C2×#107×C59C2211yescharacteristic
40C59×#367C2211yescharacteristic
41C59×#367C2211yescharacteristic
42C59×#367C2211yescharacteristic
43C59×#367C2211yescharacteristic
44C59×#366C2211yescharacteristic
45C59×#366C2211yescharacteristic
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#126×C59—41no—
66#126×C59—41no—
67#125×C59—21no—
68#125×C59—41no—
69#124×C59—41no—
70#123×C59—41no—
71C22⋊Q8×C59—21no—
72C22⋊Q8×C59—21no—
73C22⋊Q8×C59—21no—
74C22⋊Q8×C59—21no—
75C4×Q8×C59—21no—
76C4×Q8×C59—21no—
77C4×Q8×C59—41no—
78C4×D4×C59D411yescharacteristic
79#117×C59—21no—
80#117×C59—21no—
81#117×C59—21no—
82#117×C59—41no—
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×C59C2311yescharacteristic
94#107×C59C2311yescharacteristic
95#107×C59C2311yescharacteristic
96#107×C59C2311yescharacteristic
97#107×C59C2311yescharacteristic
98#107×C59C2311yescharacteristic
99#106×C59—21no—
100#106×C59—21no—
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×C59C2×D411yescharacteristic
119C22×C4×C59C2×D411yescharacteristic
120Q16×C59—21no—
121Q16×C59—21no—
122Q16×C59—21no—
123Q16×C59—21no—
124C2×C8×C59—21no—
125C2×C8×C59—21no—
126C2×C8×C59—21no—
127C2×C8×C59—21no—
128C2×C8×C59C2×D411yescharacteristic
129C2×C8×C59C2×D411yescharacteristic
130C2×C8×C59C2×D411yescharacteristic
131C2×C8×C59C2411yescharacteristic
132C4⋊C4×C59—21no—
133C4⋊C4×C59—21no—
134C4⋊C4×C59—21no—
135C4⋊C4×C59—21no—
136C4⋊C4×C59—21no—
137C4⋊C4×C59—21no—
138C4⋊C4×C59—41no—
139C4⋊C4×C59—41no—
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×C59D811yescharacteristic
149C22⋊C4×C59—41no—
150C22⋊C4×C59—41no—
151C22⋊C4×C59—41no—
152C22⋊C4×C59—41no—
153C22⋊C4×C59—41no—
154C22⋊C4×C59—41no—
155C22⋊C4×C59—41no—
156C22⋊C4×C59D811yescharacteristic
157C22⋊C4×C59D811yescharacteristic
158C42×C59—41no—
159C42×C59—41no—
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—82no—
175D4×C59—41no—
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×C59C2×D811yescharacteristic
190C2×C4×C59C2×D811yescharacteristic
191C2×C4×C59C2×D811yescharacteristic
192C2×C4×C59C2×D811yescharacteristic
193C2×C4×C59C22×D411yescharacteristic
194C8×C59—21no—
195C8×C59—21no—
196C8×C59—21no—
197C8×C59C2×#4111yescharacteristic
198C8×C592−1+411yescharacteristic
199#33916C5911yesmaximal, characteristic, direct product factor, Sylow
200C22×C59—21no—
201C22×C59—21no—
202C22×C59—21no—
203C22×C59—21no—
204C22×C59—21no—
205C22×C59—21no—
206C22×C59C22×D811yescharacteristic
207C4×C59—21no—
208C4×C59—21no—
209C4×C59—21no—
210C4×C59—21no—
211C4×C59—81no—
212C4×C59—81no—
213C4×C59—81no—
214C4×C59—81no—
215C4×C59—81no—
216C4×C59—81no—
217C4×C59—81no—
218C4×C59—81no—
219C4×C59#54711yescharacteristic
220C4×C59#57811yescharacteristic
221#3342C2×C5911yescharacteristic
222#3336C2×C5911yescharacteristic
223#2255C2×C5911yescharacteristic, complemented
224#2237C2×C5911yescharacteristic, complemented
225#2237C2×C5911yescharacteristic, complemented
226#2237C2×C5911yescharacteristic, complemented
227#2236C2×C5911yescharacteristic, complemented
228#2229C2×C5911yescharacteristic, complemented
229#2227C2×C5911yescharacteristic, complemented
230#2219C2×C5911yescharacteristic, complemented
231#2216C2×C5911yescharacteristic, complemented
232#2176C2×C5911yescharacteristic, complemented
233#2168C2×C5911yescharacteristic
234#2159C2×C5911yescharacteristic, complemented
235#2158C2×C5911yescharacteristic, complemented
236C2×C59—41no—
237C2×C59—41no—
238C2×C59#333411yescharacteristic
239C2×C59#341411yescharacteristic
240C2×C59#341711yescharacteristic
241#556—21no—
242#552—21no—
243C2×Q32C22×C5911yescharacteristic
244C2×M32C22×C5911yescharacteristic
245C22×C16C22×C5911yescharacteristic
246#500C22×C5911yescharacteristic
247#499C22×C5911yescharacteristic
248#485—21no—
249#485—21no—
250#485—21no—
251#483—21no—
252#479—21no—
253#475—21no—
254#467C22×C5911yescharacteristic
255#467C22×C5911yescharacteristic
256#467C22×C5911yescharacteristic
257#467C22×C5911yescharacteristic
258C4×Q16C22×C5911yescharacteristic
259C4×Q16C22×C5911yescharacteristic
260C8×D4C22×C5911yescharacteristic
261#427C22×C5911yescharacteristic
262#427C22×C5911yescharacteristic
263#427C22×C5911yescharacteristic
264C2×#107C22×C5911yescharacteristic
265#367C22×C5911yescharacteristic
266#367C22×C5911yescharacteristic
267#367C22×C5911yescharacteristic
268#367C22×C5911yescharacteristic
269#366C22×C5911yescharacteristic
270#366C22×C5911yescharacteristic
271#366C22×C5911yescharacteristic
272#366C22×C5911yescharacteristic
273#366C22×C5911yescharacteristic
274C4⋊C16C22×C5911yescharacteristic
275#358C22×C5911yescharacteristic
276#358C22×C5911yescharacteristic
277#358C22×C5911yescharacteristic
278#358C22×C5911yescharacteristic
279#358C22×C5911yescharacteristic
280#358C22×C5911yescharacteristic
281C22⋊C16C22×C5911yescharacteristic
282C22⋊C16C22×C5911yescharacteristic
283#346C22×C5911yescharacteristic
284C59#3391611yescharacteristic, direct product factor, Sylow
285C2×Q16C23×C5911yescharacteristic
286C2×Q16C23×C5911yescharacteristic
287C22×C8C23×C5911yescharacteristic
288C22×C8C23×C5911yescharacteristic
289C4⋊Q8—21no—
290#126—41no—
291#126—41no—
292#126—41no—
293#125—21no—
294#125—41no—
295#124—41no—
296#123—41no—
297C22⋊Q8—21no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C4×Q8—21no—
302C4×Q8—21no—
303C4×Q8—41no—
304C4×D4D4×C5911yescharacteristic
305#117—21no—
306#117—21no—
307#117—21no—
308#117—41no—
309C2×C4⋊C4—21no—
310Q32—22no—
311M32—22no—
312C2×C16—22no—
313C2×C16C23×C5911yescharacteristic
314C2×C16C23×C5911yescharacteristic
315C2×C16C23×C5911yescharacteristic
316C2×C16C23×C5911yescharacteristic
317#107—21no—
318#107—21no—
319#107C23×C5911yescharacteristic
320#107C23×C5911yescharacteristic
321#107C23×C5911yescharacteristic
322#107C23×C5911yescharacteristic
323#107C23×C5911yescharacteristic
324#107C23×C5911yescharacteristic
325#106—21no—
326#106—21no—
327#106—21no—
328#106—21no—
329C4⋊C8D4×C5911yescharacteristic
330#103—21no—
331#103—21no—
332#103—21no—
333#103—21no—
334#103—21no—
335#103—21no—
336C22⋊C8D4×C5911yescharacteristic
337C22⋊C8D4×C5911yescharacteristic
338C4×C8C23×C5911yescharacteristic
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—41no—
342C2×D4D8×C5911yescharacteristic
343C22×C4—41no—
344C22×C4C2×D4×C5911yescharacteristic
345C22×C4C2×D4×C5911yescharacteristic
346Q16—21no—
347Q16—21no—
348Q16—21no—
349Q16—21no—
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—21no—
354C2×C8C2×D4×C5911yescharacteristic
355C2×C8C2×D4×C5911yescharacteristic
356C2×C8C2×D4×C5911yescharacteristic
357C2×C8C24×C5911yescharacteristic
358C4⋊C4—21no—
359C4⋊C4—21no—
360C4⋊C4—21no—
361C4⋊C4—21no—
362C4⋊C4—21no—
363C4⋊C4—21no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—41no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4D8×C5911yescharacteristic
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4D8×C5911yescharacteristic
383C22⋊C4D8×C5911yescharacteristic
384C42—41no—
385C42—41no—
386C42—41no—
387C42—41no—
388C42—41no—
389C42C2×D4×C5911yescharacteristic
390C16—21no—
391C16—21no—
392C16—21no—
393C16#41×C5912yes—
394C23C2×D8×C5911yescharacteristic
395C23C2×D8×C5911yescharacteristic
396Q8—41no—
397Q8—41no—
398Q8—41no—
399Q8—41no—
400Q8—82no—
401D4—41no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—82no—
415C2×C4C2×D8×C5911yescharacteristic
416C2×C4C2×D8×C5911yescharacteristic
417C2×C4C2×D8×C5911yescharacteristic
418C2×C4C2×D8×C5911yescharacteristic
419C2×C4C22×D4×C5911yescharacteristic
420C8—21no—
421C8—21no—
422C8—21no—
423C8C2×#41×C5911yescharacteristic
424C82−1+4×C5911yescharacteristic
425C22—21no—
426C22—21no—
427C22—21no—
428C22—21no—
429C22—21no—
430C22—21no—
431C22C22×D8×C5911yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—81no—
437C4—81no—
438C4—81no—
439C4—81no—
440C4—81no—
441C4—81no—
442C4—81no—
443C4—81no—
444C4C59×#54711yescharacteristic
445C4C59×#57811yescharacteristic
446C2—41no—
447C2—41no—
448C2C59×#333411yescharacteristic
449C2C59×#341411yescharacteristic
450C2C59×#341711yescharacteristic
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×#2237C2semidirect
6. C59×#2237C2semidirect
7. C59×#2236C2semidirect
8. C59×#2229C2semidirect
9. C59×#2227C2semidirect
10. C59×#2219C2semidirect
11. C59×#2216C2semidirect
12. C59×#2176C2semidirect
14. C59×#2159C2semidirect
15. C59×#2158C2semidirect
199. #33916C59direct (N × H)
223. #2255C2×C59semidirect
224. #2237C2×C59semidirect
225. #2237C2×C59semidirect
226. #2237C2×C59semidirect
227. #2236C2×C59semidirect
228. #2229C2×C59semidirect
229. #2227C2×C59semidirect
230. #2219C2×C59semidirect
231. #2216C2×C59semidirect
232. #2176C2×C59semidirect
234. #2159C2×C59semidirect
235. #2158C2×C59semidirect
284. C59#33916direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#33422
C59×#33362
C59×#22552
C59×#22372
C59×#22362
C59×#22292
C59×#22272
C59×#22192
C59×#22162
C59×#21762
C59×#21682
C59×#21592
C59×#21582
#3391659