Finite Group Databasebeta

← C59×#33914 #28446023

Subgroups — C59×#33914 #28446023

Order 15104.

488 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3341C211yesmaximal, characteristic, complemented
2C59×#3339C211yesmaximal, characteristic, complemented
3C59×#2255C211yesmaximal, characteristic, complemented
4C59×#2234C211yesmaximal, characteristic, complemented
5C59×#2234C211yesmaximal, characteristic, complemented
6C59×#2234C211yesmaximal, characteristic, complemented
7C59×#2232C211yesmaximal, characteristic, complemented
8C59×#2228C211yesmaximal, characteristic, complemented
9C59×#2224C211yesmaximal, characteristic, complemented
10C59×#2218C211yesmaximal, characteristic, complemented
11C59×#2215C211yesmaximal, characteristic, complemented
12C59×#2177C211yesmaximal, characteristic, complemented
13C59×#2168C211yesmaximal, characteristic, complemented
14C59×#2159C211yesmaximal, characteristic, complemented
15C59×#2158C211yesmaximal, characteristic, complemented
16C59×#555—21no—
17C59×#553—21no—
18C2×D16×C59C2211yescharacteristic
19C2×M32×C59C2211yescharacteristic
20C22×C16×C59C2211yescharacteristic
21C59×#500C2211yescharacteristic
22C59×#499C2211yescharacteristic
23C59×#482—21no—
24C59×#482—21no—
25C59×#482—21no—
26C59×#481—21no—
27C59×#478—21no—
28C59×#476—21no—
29C59×#466C2211yescharacteristic
30C59×#466C2211yescharacteristic
31C59×#466C2211yescharacteristic
32C59×#466C2211yescharacteristic
33C4×D8×C59C2211yescharacteristic
34C4×D8×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×#357C2211yescharacteristic
51C59×#357C2211yescharacteristic
52C59×#357C2211yescharacteristic
53C59×#357C2211yescharacteristic
54C59×#357C2211yescharacteristic
55C59×#357C2211yescharacteristic
56C59×C22⋊C16C2211yescharacteristic
57C59×C22⋊C16C2211yescharacteristic
58C59×#346C2211yescharacteristic
59C2×D8×C59C2311yescharacteristic
60C2×D8×C59C2311yescharacteristic
61C22×C8×C59C2311yescharacteristic
62C22×C8×C59C2311yescharacteristic
63C4⋊Q8×C59—21no—
64#126×C59—41no—
65#125×C59—21no—
66#124×C59—41no—
67#124×C59—41no—
68#123×C59—41no—
69#121×C59—21no—
70#121×C59—21no—
71#121×C59—21no—
72#121×C59—21no—
73#121×C59—41no—
74#121×C59—41no—
75C4×D4×C59—21no—
76C4×D4×C59—21no—
77C4×D4×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—
84D16×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#102×C59—21no—
105#102×C59—21no—
106#102×C59—21no—
107#102×C59—21no—
108#102×C59—21no—
109#102×C59—21no—
110C22⋊C8×C59D411yescharacteristic
111C22⋊C8×C59D411yescharacteristic
112C4×C8×C59C2311yescharacteristic
113C2×Q8×C59—41no—
114C2×D4×C59—21no—
115C2×D4×C59—21no—
116C2×D4×C59—41no—
117C2×D4×C59—41no—
118C2×D4×C59—41no—
119C2×D4×C59—41no—
120C2×D4×C59D811yescharacteristic
121C22×C4×C59—41no—
122C22×C4×C59—41no—
123C22×C4×C59—41no—
124C22×C4×C59C2×D411yescharacteristic
125C22×C4×C59C2×D411yescharacteristic
126D8×C59—21no—
127D8×C59—21no—
128D8×C59—21no—
129D8×C59—21no—
130C2×C8×C59—21no—
131C2×C8×C59—21no—
132C2×C8×C59—21no—
133C2×C8×C59—21no—
134C2×C8×C59C2×D411yescharacteristic
135C2×C8×C59C2×D411yescharacteristic
136C2×C8×C59C2×D411yescharacteristic
137C2×C8×C59C2411yescharacteristic
138C4⋊C4×C59—21no—
139C4⋊C4×C59—21no—
140C4⋊C4×C59—21no—
141C4⋊C4×C59—21no—
142C4⋊C4×C59—21no—
143C4⋊C4×C59—21no—
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×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×C59—41no—
169C23×C59—41no—
170C23×C59C2×D811yescharacteristic
171C23×C59C2×D811yescharacteristic
172Q8×C59—161no—
173D4×C59—41no—
174D4×C59—41no—
175D4×C59—41no—
176D4×C59—41no—
177D4×C59—41no—
178D4×C59—82no—
179D4×C59—161no—
180D4×C59—161no—
181D4×C59—161no—
182C2×C4×C59—21no—
183C2×C4×C59—21no—
184C2×C4×C59—21no—
185C2×C4×C59—21no—
186C2×C4×C59—41no—
187C2×C4×C59—41no—
188C2×C4×C59—41no—
189C2×C4×C59—41no—
190C2×C4×C59—41no—
191C2×C4×C59—41no—
192C2×C4×C59—82no—
193C2×C4×C59—161no—
194C2×C4×C59—161no—
195C2×C4×C59C2×D811yescharacteristic
196C2×C4×C59C2×D811yescharacteristic
197C2×C4×C59C2×D811yescharacteristic
198C2×C4×C59C2×D811yescharacteristic
199C2×C4×C59C22×D411yescharacteristic
200C8×C59—21no—
201C8×C59—21no—
202C8×C59—21no—
203C8×C59C2×#4111yescharacteristic
204C8×C592−1+411yescharacteristic
205#33914C5911yesmaximal, characteristic, direct product factor, Sylow
206C22×C59—21no—
207C22×C59—21no—
208C22×C59—21no—
209C22×C59—21no—
210C22×C59—21no—
211C22×C59—21no—
212C22×C59—81no—
213C22×C59—81no—
214C22×C59—81no—
215C22×C59—81no—
216C22×C59—81no—
217C22×C59—81no—
218C22×C59C22×D811yescharacteristic
219C4×C59—21no—
220C4×C59—21no—
221C4×C59—21no—
222C4×C59—21no—
223C4×C59—81no—
224C4×C59—81no—
225C4×C59—81no—
226C4×C59—81no—
227C4×C59—81no—
228C4×C59—81no—
229C4×C59#54711yescharacteristic
230C4×C59#57811yescharacteristic
231#3341C2×C5911yescharacteristic, complemented
232#3339C2×C5911yescharacteristic, complemented
233#2255C2×C5911yescharacteristic, complemented
234#2234C2×C5911yescharacteristic, complemented
235#2234C2×C5911yescharacteristic, complemented
236#2234C2×C5911yescharacteristic, complemented
237#2232C2×C5911yescharacteristic, complemented
238#2228C2×C5911yescharacteristic, complemented
239#2224C2×C5911yescharacteristic, complemented
240#2218C2×C5911yescharacteristic, complemented
241#2215C2×C5911yescharacteristic, complemented
242#2177C2×C5911yescharacteristic, complemented
243#2168C2×C5911yescharacteristic, complemented
244#2159C2×C5911yescharacteristic, complemented
245#2158C2×C5911yescharacteristic, complemented
246C2×C59—41no—
247C2×C59—41no—
248C2×C59—161no—
249C2×C59—161no—
250C2×C59#333411yescharacteristic
251C2×C59#341411yescharacteristic
252C2×C59#341511yescharacteristic
253#555—21no—
254#553—21no—
255C2×D16C22×C5911yescharacteristic
256C2×M32C22×C5911yescharacteristic
257C22×C16C22×C5911yescharacteristic
258#500C22×C5911yescharacteristic
259#499C22×C5911yescharacteristic
260#482—21no—
261#482—21no—
262#482—21no—
263#481—21no—
264#478—21no—
265#476—21no—
266#466C22×C5911yescharacteristic
267#466C22×C5911yescharacteristic
268#466C22×C5911yescharacteristic
269#466C22×C5911yescharacteristic
270C4×D8C22×C5911yescharacteristic
271C4×D8C22×C5911yescharacteristic
272C8×D4C22×C5911yescharacteristic
273#427C22×C5911yescharacteristic
274#427C22×C5911yescharacteristic
275#427C22×C5911yescharacteristic
276C2×#107C22×C5911yescharacteristic
277#367C22×C5911yescharacteristic
278#367C22×C5911yescharacteristic
279#367C22×C5911yescharacteristic
280#367C22×C5911yescharacteristic
281#366C22×C5911yescharacteristic
282#366C22×C5911yescharacteristic
283#366C22×C5911yescharacteristic
284#366C22×C5911yescharacteristic
285#366C22×C5911yescharacteristic
286C4⋊C16C22×C5911yescharacteristic
287#357C22×C5911yescharacteristic
288#357C22×C5911yescharacteristic
289#357C22×C5911yescharacteristic
290#357C22×C5911yescharacteristic
291#357C22×C5911yescharacteristic
292#357C22×C5911yescharacteristic
293C22⋊C16C22×C5911yescharacteristic
294C22⋊C16C22×C5911yescharacteristic
295#346C22×C5911yescharacteristic
296C59#3391411yescharacteristic, direct product factor, Sylow
297C2×D8C23×C5911yescharacteristic
298C2×D8C23×C5911yescharacteristic
299C22×C8C23×C5911yescharacteristic
300C22×C8C23×C5911yescharacteristic
301C4⋊Q8—21no—
302#126—41no—
303#125—21no—
304#124—41no—
305#124—41no—
306#123—41no—
307#121—21no—
308#121—21no—
309#121—21no—
310#121—21no—
311#121—41no—
312#121—41no—
313C4×D4—21no—
314C4×D4—21no—
315C4×D4—41no—
316C4×D4D4×C5911yescharacteristic
317#117—21no—
318#117—21no—
319#117—21no—
320#117—41no—
321C2×C4⋊C4—21no—
322D16—22no—
323M32—22no—
324C2×C16—22no—
325C2×C16C23×C5911yescharacteristic
326C2×C16C23×C5911yescharacteristic
327C2×C16C23×C5911yescharacteristic
328C2×C16C23×C5911yescharacteristic
329#107—21no—
330#107—21no—
331#107C23×C5911yescharacteristic
332#107C23×C5911yescharacteristic
333#107C23×C5911yescharacteristic
334#107C23×C5911yescharacteristic
335#107C23×C5911yescharacteristic
336#107C23×C5911yescharacteristic
337#106—21no—
338#106—21no—
339#106—21no—
340#106—21no—
341C4⋊C8D4×C5911yescharacteristic
342#102—21no—
343#102—21no—
344#102—21no—
345#102—21no—
346#102—21no—
347#102—21no—
348C22⋊C8D4×C5911yescharacteristic
349C22⋊C8D4×C5911yescharacteristic
350C4×C8C23×C5911yescharacteristic
351C2×Q8—41no—
352C2×D4—21no—
353C2×D4—21no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4D8×C5911yescharacteristic
359C22×C4—41no—
360C22×C4—41no—
361C22×C4—41no—
362C22×C4C2×D4×C5911yescharacteristic
363C22×C4C2×D4×C5911yescharacteristic
364D8—21no—
365D8—21no—
366D8—21no—
367D8—21no—
368C2×C8—21no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8C2×D4×C5911yescharacteristic
373C2×C8C2×D4×C5911yescharacteristic
374C2×C8C2×D4×C5911yescharacteristic
375C2×C8C24×C5911yescharacteristic
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—41no—
385C4⋊C4—41no—
386C4⋊C4D8×C5911yescharacteristic
387C22⋊C4—41no—
388C22⋊C4—41no—
389C22⋊C4—41no—
390C22⋊C4—41no—
391C22⋊C4—41no—
392C22⋊C4—41no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C22⋊C4—41no—
396C22⋊C4D8×C5911yescharacteristic
397C22⋊C4D8×C5911yescharacteristic
398C42—41no—
399C42—41no—
400C42—41no—
401C42C2×D4×C5911yescharacteristic
402C16—21no—
403C16—21no—
404C16—21no—
405C16#41×C5912yes—
406C23—41no—
407C23—41no—
408C23C2×D8×C5911yescharacteristic
409C23C2×D8×C5911yescharacteristic
410Q8—161no—
411D4—41no—
412D4—41no—
413D4—41no—
414D4—41no—
415D4—41no—
416D4—82no—
417D4—161no—
418D4—161no—
419D4—161no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—82no—
431C2×C4—161no—
432C2×C4—161no—
433C2×C4C2×D8×C5911yescharacteristic
434C2×C4C2×D8×C5911yescharacteristic
435C2×C4C2×D8×C5911yescharacteristic
436C2×C4C2×D8×C5911yescharacteristic
437C2×C4C22×D4×C5911yescharacteristic
438C8—21no—
439C8—21no—
440C8—21no—
441C8C2×#41×C5911yescharacteristic
442C82−1+4×C5911yescharacteristic
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—81no—
450C22—81no—
451C22—81no—
452C22—81no—
453C22—81no—
454C22—81no—
455C22C22×D8×C5911yescharacteristic
456C4—21no—
457C4—21no—
458C4—21no—
459C4—21no—
460C4—81no—
461C4—81no—
462C4—81no—
463C4—81no—
464C4—81no—
465C4—81no—
466C4C59×#54711yescharacteristic
467C4C59×#57811yescharacteristic
468C2—41no—
469C2—41no—
470C2—161no—
471C2—161no—
472C2C59×#333411yescharacteristic
473C2C59×#341411yescharacteristic
474C2C59×#341511yescharacteristic
subgroupG/H
center, socleC22×C59C22×D8
commutator, Frattini, cosocleC2×C8C24×C59
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
1. C59×#3341C2semidirect
2. C59×#3339C2semidirect
3. C59×#2255C2semidirect
4. C59×#2234C2semidirect
5. C59×#2234C2semidirect
6. C59×#2234C2semidirect
7. C59×#2232C2semidirect
8. C59×#2228C2semidirect
9. C59×#2224C2semidirect
10. C59×#2218C2semidirect
11. C59×#2215C2semidirect
12. C59×#2177C2semidirect
13. C59×#2168C2semidirect
14. C59×#2159C2semidirect
15. C59×#2158C2semidirect
205. #33914C59direct (N × H)
231. #3341C2×C59semidirect
232. #3339C2×C59semidirect
233. #2255C2×C59semidirect
234. #2234C2×C59semidirect
235. #2234C2×C59semidirect
236. #2234C2×C59semidirect
237. #2232C2×C59semidirect
238. #2228C2×C59semidirect
239. #2224C2×C59semidirect
240. #2218C2×C59semidirect
241. #2215C2×C59semidirect
242. #2177C2×C59semidirect
243. #2168C2×C59semidirect
244. #2159C2×C59semidirect
245. #2158C2×C59semidirect
296. C59#33914direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#33412
C59×#33392
C59×#22552
C59×#22342
C59×#22322
C59×#22282
C59×#22242
C59×#22182
C59×#22152
C59×#21772
C59×#21682
C59×#21592
C59×#21582
#3391459