Finite Group Databasebeta

← C59×#33685 #28445794

Subgroups — C59×#33685 #28445794

Order 15104.

546 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3175C211yesmaximal, characteristic, complemented
2C59×#2951C211yesmaximal, characteristic, complemented
3C59×#2235C211yesmaximal, characteristic, complemented
4C59×#2233C211yesmaximal, characteristic, complemented
5C59×#2226C211yesmaximal, characteristic, complemented
6C59×#2225C211yesmaximal, characteristic, complemented
7C59×#2211C211yesmaximal, characteristic, complemented
8C59×#2210C211yesmaximal, characteristic, complemented
9C59×#2189C211yesmaximal, characteristic, complemented
10C59×#2186C211yesmaximal, characteristic
11C59×#2177C211yesmaximal, characteristic, complemented
12C59×#2176C211yesmaximal, characteristic, complemented
13C4×SD32×C59C211yesmaximal, characteristic, complemented
14C4×SD32×C59C211yesmaximal, characteristic, complemented
15C59×#2164C211yesmaximal, characteristic, complemented
16C2×#135×C59C2211yescharacteristic
17C59×#542—21no—
18C59×#520—21no—
19C2×Q32×C59C2211yescharacteristic
20C2×SD32×C59C2211yescharacteristic
21C2×SD32×C59C2211yescharacteristic
22C2×D16×C59C2211yescharacteristic
23C59×#500C2211yescharacteristic
24C59×#495C2211yescharacteristic
25C59×#489—21no—
26C59×#468—21no—
27C59×#467C2211yescharacteristic
28C59×#466C2211yescharacteristic
29C59×#440—21no—
30C59×#440—21no—
31C59×#440—21no—
32C4×Q16×C59C2211yescharacteristic
33C4×Q16×C59C2211yescharacteristic
34C4×Q16×C59C2211yescharacteristic
35C4×D8×C59C2211yescharacteristic
36C4×D8×C59C2211yescharacteristic
37C4×D8×C59C2211yescharacteristic
38C2×#107×C59C2211yescharacteristic
39C59×#417—21no—
40C59×#405C2211yescharacteristic
41C59×#367C2211yescharacteristic
42C59×#367C2211yescharacteristic
43C59×#367C2211yescharacteristic
44C59×#367C2211yescharacteristic
45C59×C4⋊C16C2211yescharacteristic
46C59×C4⋊C16C2211yescharacteristic
47C59×#358C2211yescharacteristic
48C59×#358C2211yescharacteristic
49C59×#358C2211yescharacteristic
50C59×#358C2211yescharacteristic
51C59×#357C2211yescharacteristic
52C59×#357C2211yescharacteristic
53C59×#357C2211yescharacteristic
54C59×#357C2211yescharacteristic
55C59×C22⋊C16C2211yescharacteristic
56C59×C22⋊C16C2211yescharacteristic
57C59×#346C2211yescharacteristic
58C4×C16×C59C2211yescharacteristic
59C2×#41×C59—21no—
60#135×C59—22no—
61#135×C59—22no—
62C2×Q16×C59C2311yescharacteristic
63C2×Q16×C59C2311yescharacteristic
64C2×SD16×C59—21no—
65C2×SD16×C59—21no—
66C2×D8×C59C2311yescharacteristic
67C2×D8×C59C2311yescharacteristic
68C2×M16×C59D411yescharacteristic
69C22×C8×C59C2311yescharacteristic
70C4⋊Q8×C59—21no—
71#126×C59—41no—
72#124×C59—21no—
73#124×C59—41no—
74#123×C59—41no—
75C22⋊Q8×C59—21no—
76C22⋊Q8×C59—41no—
77#121×C59—21no—
78C4×Q8×C59—21no—
79C4×Q8×C59—21no—
80C4×Q8×C59—21no—
81C4×D4×C59—21no—
82C4×D4×C59—21no—
83C4×D4×C59—21no—
84C4×D4×C59—41no—
85C4×D4×C59—41no—
86#117×C59—41no—
87#117×C59D411yescharacteristic
88C2×C4⋊C4×C59—21no—
89C2×C4⋊C4×C59—41no—
90Q32×C59—22no—
91SD32×C59—22no—
92SD32×C59—22no—
93D16×C59—22no—
94C2×C16×C59C2311yescharacteristic
95C2×C16×C59C2311yescharacteristic
96C2×C16×C59C2311yescharacteristic
97C2×C16×C59C2311yescharacteristic
98#107×C59—21no—
99#107×C59—21no—
100#107×C59C2311yescharacteristic
101#107×C59C2311yescharacteristic
102#107×C59C2311yescharacteristic
103#107×C59C2311yescharacteristic
104#103×C59—21no—
105#103×C59—21no—
106#103×C59—21no—
107#103×C59—21no—
108#102×C59—21no—
109#102×C59—21no—
110#102×C59—21no—
111#102×C59—21no—
112#97×C59D411yescharacteristic
113#97×C59D411yescharacteristic
114C4×C8×C59C2311yescharacteristic
115C4×C8×C59C2311yescharacteristic
116#41×C59—24no—
117#41×C59—42no—
118C2×Q8×C59—21no—
119C2×Q8×C59—21no—
120C2×Q8×C59—41no—
121C2×D4×C59—21no—
122C2×D4×C59—21no—
123C2×D4×C59—41no—
124C2×D4×C59—41no—
125C22×C4×C59—41no—
126C22×C4×C59—41no—
127C22×C4×C59—41no—
128C22×C4×C59—41no—
129C22×C4×C59—41no—
130C22×C4×C59C2×D411yescharacteristic
131Q16×C59—21no—
132Q16×C59—21no—
133Q16×C59—21no—
134Q16×C59#4112yes—
135SD16×C59—24no—
136SD16×C59—42no—
137D8×C59—21no—
138D8×C59—21no—
139D8×C59—21no—
140D8×C59#4112yes—
141M16×C59—41no—
142C2×C8×C59—21no—
143C2×C8×C59—21no—
144C2×C8×C59C2×D411yescharacteristic
145C2×C8×C59C2×D411yescharacteristic
146C2×C8×C59C2×D411yescharacteristic
147C2×C8×C59C2411yescharacteristic
148C4⋊C4×C59—21no—
149C4⋊C4×C59—21no—
150C4⋊C4×C59—21no—
151C4⋊C4×C59—21no—
152C4⋊C4×C59—41no—
153C4⋊C4×C59—41no—
154C4⋊C4×C59—41no—
155C4⋊C4×C59—41no—
156C4⋊C4×C59—41no—
157C4⋊C4×C59—41no—
158C4⋊C4×C59D811yescharacteristic
159C4⋊C4×C59D811yescharacteristic
160C22⋊C4×C59—41no—
161C22⋊C4×C59—41no—
162C22⋊C4×C59—41no—
163C22⋊C4×C59—41no—
164C22⋊C4×C59—41no—
165C22⋊C4×C59—41no—
166C22⋊C4×C59—41no—
167C22⋊C4×C59D811yescharacteristic
168C22⋊C4×C59D811yescharacteristic
169C42×C59—41no—
170C42×C59—41no—
171C42×C59—41no—
172C42×C59C2×D411yescharacteristic
173C42×C59C2×D411yescharacteristic
174C16×C59—21no—
175C16×C59—21no—
176C16×C59—21no—
177C16×C59—21no—
178C23×C59—41no—
179C23×C59—41no—
180C23×C59C2×D811yescharacteristic
181Q8×C59—22no—
182Q8×C59—41no—
183Q8×C59—41no—
184Q8×C59—41no—
185Q8×C59—161no—
186D4×C59—22no—
187D4×C59—44no—
188D4×C59—41no—
189D4×C59—41no—
190D4×C59—41no—
191D4×C59—161no—
192C2×C4×C59—21no—
193C2×C4×C59—21no—
194C2×C4×C59—44no—
195C2×C4×C59—41no—
196C2×C4×C59—41no—
197C2×C4×C59—41no—
198C2×C4×C59—41no—
199C2×C4×C59—41no—
200C2×C4×C59—41no—
201C2×C4×C59—161no—
202C2×C4×C59—161no—
203C2×C4×C59—161no—
204C2×C4×C59—161no—
205C2×C4×C59C2×D811yescharacteristic
206C2×C4×C59C2×D811yescharacteristic
207C2×C4×C59C2×D811yescharacteristic
208C2×C4×C59C2×D811yescharacteristic
209C2×C4×C59C2×D811yescharacteristic
210C2×C4×C59C22×D411yescharacteristic
211C8×C59—21no—
212C8×C59—21no—
213C8×C59—21no—
214C8×C59C2×#4111yescharacteristic
215C8×C59C2×#4111yescharacteristic
216#33685C5911yesmaximal, characteristic, direct product factor, Sylow
217C22×C59—21no—
218C22×C59—21no—
219C22×C59—21no—
220C22×C59—42no—
221C22×C59—81no—
222C22×C59—81no—
223C22×C59—81no—
224C22×C59—81no—
225C22×C59—81no—
226C22×C59C22×D811yescharacteristic
227C4×C59—21no—
228C4×C59—21no—
229C4×C59—21no—
230C4×C59—21no—
231C4×C59—21no—
232C4×C59—42no—
233C4×C59—81no—
234C4×C59—81no—
235C4×C59—81no—
236C4×C59—81no—
237C4×C59—81no—
238C4×C59#52511yescharacteristic
239C4×C59#57511yescharacteristic
240#3175C2×C5911yescharacteristic, complemented
241#2951C2×C5911yescharacteristic, complemented
242#2235C2×C5911yescharacteristic, complemented
243#2233C2×C5911yescharacteristic, complemented
244#2226C2×C5911yescharacteristic, complemented
245#2225C2×C5911yescharacteristic, complemented
246#2211C2×C5911yescharacteristic, complemented
247#2210C2×C5911yescharacteristic, complemented
248#2189C2×C5911yescharacteristic, complemented
249#2186C2×C5911yescharacteristic
250#2177C2×C5911yescharacteristic, complemented
251#2176C2×C5911yescharacteristic, complemented
252C4×SD32C2×C5911yescharacteristic, complemented
253C4×SD32C2×C5911yescharacteristic, complemented
254#2164C2×C5911yescharacteristic, complemented
255C2×C59—41no—
256C2×C59—82no—
257C2×C59—161no—
258C2×C59#310011yescharacteristic
259C2×C59#341611yescharacteristic
260C2×C59#341611yescharacteristic
261C2×#135C22×C5911yescharacteristic
262#542—21no—
263#520—21no—
264C2×Q32C22×C5911yescharacteristic
265C2×SD32C22×C5911yescharacteristic
266C2×SD32C22×C5911yescharacteristic
267C2×D16C22×C5911yescharacteristic
268#500C22×C5911yescharacteristic
269#495C22×C5911yescharacteristic
270#489—21no—
271#468—21no—
272#467C22×C5911yescharacteristic
273#466C22×C5911yescharacteristic
274#440—21no—
275#440—21no—
276#440—21no—
277C4×Q16C22×C5911yescharacteristic
278C4×Q16C22×C5911yescharacteristic
279C4×Q16C22×C5911yescharacteristic
280C4×D8C22×C5911yescharacteristic
281C4×D8C22×C5911yescharacteristic
282C4×D8C22×C5911yescharacteristic
283C2×#107C22×C5911yescharacteristic
284#417—21no—
285#405C22×C5911yescharacteristic
286#367C22×C5911yescharacteristic
287#367C22×C5911yescharacteristic
288#367C22×C5911yescharacteristic
289#367C22×C5911yescharacteristic
290C4⋊C16C22×C5911yescharacteristic
291C4⋊C16C22×C5911yescharacteristic
292#358C22×C5911yescharacteristic
293#358C22×C5911yescharacteristic
294#358C22×C5911yescharacteristic
295#358C22×C5911yescharacteristic
296#357C22×C5911yescharacteristic
297#357C22×C5911yescharacteristic
298#357C22×C5911yescharacteristic
299#357C22×C5911yescharacteristic
300C22⋊C16C22×C5911yescharacteristic
301C22⋊C16C22×C5911yescharacteristic
302#346C22×C5911yescharacteristic
303C4×C16C22×C5911yescharacteristic
304C59#3368511yescharacteristic, direct product factor, Sylow
305C2×#41—21no—
306#135—22no—
307#135—22no—
308C2×Q16C23×C5911yescharacteristic
309C2×Q16C23×C5911yescharacteristic
310C2×SD16—21no—
311C2×SD16—21no—
312C2×D8C23×C5911yescharacteristic
313C2×D8C23×C5911yescharacteristic
314C2×M16D4×C5911yescharacteristic
315C22×C8C23×C5911yescharacteristic
316C4⋊Q8—21no—
317#126—41no—
318#124—21no—
319#124—41no—
320#123—41no—
321C22⋊Q8—21no—
322C22⋊Q8—41no—
323#121—21no—
324C4×Q8—21no—
325C4×Q8—21no—
326C4×Q8—21no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—41no—
331C4×D4—41no—
332#117—41no—
333#117D4×C5911yescharacteristic
334C2×C4⋊C4—21no—
335C2×C4⋊C4—41no—
336Q32—22no—
337SD32—22no—
338SD32—22no—
339D16—22no—
340C2×C16C23×C5911yescharacteristic
341C2×C16C23×C5911yescharacteristic
342C2×C16C23×C5911yescharacteristic
343C2×C16C23×C5911yescharacteristic
344#107—21no—
345#107—21no—
346#107C23×C5911yescharacteristic
347#107C23×C5911yescharacteristic
348#107C23×C5911yescharacteristic
349#107C23×C5911yescharacteristic
350#103—21no—
351#103—21no—
352#103—21no—
353#103—21no—
354#102—21no—
355#102—21no—
356#102—21no—
357#102—21no—
358#97D4×C5911yescharacteristic
359#97D4×C5911yescharacteristic
360C4×C8C23×C5911yescharacteristic
361C4×C8C23×C5911yescharacteristic
362#41—24no—
363#41—42no—
364C2×Q8—21no—
365C2×Q8—21no—
366C2×Q8—41no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—41no—
370C2×D4—41no—
371C22×C4—41no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4C2×D4×C5911yescharacteristic
377Q16—21no—
378Q16—21no—
379Q16—21no—
380Q16#41×C5912yes—
381SD16—24no—
382SD16—42no—
383D8—21no—
384D8—21no—
385D8—21no—
386D8#41×C5912yes—
387M16—41no—
388C2×C8—21no—
389C2×C8—21no—
390C2×C8C2×D4×C5911yescharacteristic
391C2×C8C2×D4×C5911yescharacteristic
392C2×C8C2×D4×C5911yescharacteristic
393C2×C8C24×C5911yescharacteristic
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—41no—
402C4⋊C4—41no—
403C4⋊C4—41no—
404C4⋊C4D8×C5911yescharacteristic
405C4⋊C4D8×C5911yescharacteristic
406C22⋊C4—41no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—41no—
413C22⋊C4D8×C5911yescharacteristic
414C22⋊C4D8×C5911yescharacteristic
415C42—41no—
416C42—41no—
417C42—41no—
418C42C2×D4×C5911yescharacteristic
419C42C2×D4×C5911yescharacteristic
420C16—21no—
421C16—21no—
422C16—21no—
423C16—21no—
424C23—41no—
425C23—41no—
426C23C2×D8×C5911yescharacteristic
427Q8—22no—
428Q8—41no—
429Q8—41no—
430Q8—41no—
431Q8—161no—
432D4—22no—
433D4—44no—
434D4—41no—
435D4—41no—
436D4—41no—
437D4—161no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—44no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—161no—
448C2×C4—161no—
449C2×C4—161no—
450C2×C4—161no—
451C2×C4C2×D8×C5911yescharacteristic
452C2×C4C2×D8×C5911yescharacteristic
453C2×C4C2×D8×C5911yescharacteristic
454C2×C4C2×D8×C5911yescharacteristic
455C2×C4C2×D8×C5911yescharacteristic
456C2×C4C22×D4×C5911yescharacteristic
457C8—21no—
458C8—21no—
459C8—21no—
460C8C2×#41×C5911yescharacteristic
461C8C2×#41×C5911yescharacteristic
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—81no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22C22×D8×C5911yescharacteristic
472C4—21no—
473C4—21no—
474C4—21no—
475C4—21no—
476C4—21no—
477C4—42no—
478C4—81no—
479C4—81no—
480C4—81no—
481C4—81no—
482C4—81no—
483C4C59×#52511yescharacteristic
484C4C59×#57511yescharacteristic
485C2—41no—
486C2—82no—
487C2—161no—
488C2C59×#310011yescharacteristic
489C2C59×#341611yescharacteristic
490C2C59×#341611yescharacteristic
subgroupG/H
center, socleC22×C59C22×D8
commutator, Frattini, cosocleC2×C8C24×C59
prime radicalC59×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C59 ◁ #117×C59 ◁ C59×#405 ◁ G

Complements

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

NH ≅ G/Ntype
1. C59×#3175C2semidirect
2. C59×#2951C2semidirect
3. C59×#2235C2semidirect
4. C59×#2233C2semidirect
5. C59×#2226C2semidirect
6. C59×#2225C2semidirect
7. C59×#2211C2semidirect
8. C59×#2210C2semidirect
9. C59×#2189C2semidirect
11. C59×#2177C2semidirect
12. C59×#2176C2semidirect
13. C4×SD32×C59C2semidirect
14. C4×SD32×C59C2semidirect
15. C59×#2164C2semidirect
216. #33685C59direct (N × H)
240. #3175C2×C59semidirect
241. #2951C2×C59semidirect
242. #2235C2×C59semidirect
243. #2233C2×C59semidirect
244. #2226C2×C59semidirect
245. #2225C2×C59semidirect
246. #2211C2×C59semidirect
247. #2210C2×C59semidirect
248. #2189C2×C59semidirect
250. #2177C2×C59semidirect
251. #2176C2×C59semidirect
252. C4×SD32C2×C59semidirect
253. C4×SD32C2×C59semidirect
254. #2164C2×C59semidirect
304. C59#33685direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#31752
C59×#29512
C59×#22352
C59×#22332
C59×#22262
C59×#22252
C59×#22112
C59×#22102
C59×#21892
C59×#21862
C59×#21772
C59×#21762
C4×SD32×C592
C59×#21642
#3368559