Finite Group Databasebeta

← C59×#33681 #28445790

Subgroups — C59×#33681 #28445790

Order 15104.

532 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3175C211yesmaximal, characteristic
2C59×#2950C211yesmaximal, characteristic, complemented
3C59×#2237C211yesmaximal, characteristic, complemented
4C59×#2234C211yesmaximal, characteristic
5C59×#2227C211yesmaximal, characteristic, complemented
6C59×#2225C211yesmaximal, characteristic, complemented
7C59×#2211C211yesmaximal, characteristic, complemented
8C59×#2211C211yesmaximal, characteristic, complemented
9C59×#2188C211yesmaximal, characteristic, complemented
10C59×#2185C211yesmaximal, characteristic
11C59×#2176C211yesmaximal, characteristic, complemented
12C59×#2175C211yesmaximal, characteristic, complemented
13C4×Q32×C59C211yesmaximal, characteristic, complemented
14C4×SD32×C59C211yesmaximal, characteristic, complemented
15C59×#2164C211yesmaximal, characteristic, complemented
16C22×Q16×C59C2211yescharacteristic
17C59×#542—21no—
18C59×#519—21no—
19C2×Q32×C59C2211yescharacteristic
20C2×Q32×C59C2211yescharacteristic
21C2×SD32×C59C2211yescharacteristic
22C2×SD32×C59C2211yescharacteristic
23C59×#500C2211yescharacteristic
24C59×#495C2211yescharacteristic
25C59×#489—21no—
26C59×#468—21no—
27C59×#467C2211yescharacteristic
28C59×#466C2211yescharacteristic
29C59×#441—21no—
30C59×#441—21no—
31C59×#440—21no—
32C4×Q16×C59C2211yescharacteristic
33C4×Q16×C59C2211yescharacteristic
34C4×Q16×C59C2211yescharacteristic
35C4×Q16×C59C2211yescharacteristic
36C4×Q16×C59C2211yescharacteristic
37C4×D8×C59C2211yescharacteristic
38C59×#427C2211yescharacteristic
39C59×#419—21no—
40C59×#405C2211yescharacteristic
41C59×#367C2211yescharacteristic
42C59×#367C2211yescharacteristic
43C59×#366C2211yescharacteristic
44C59×#366C2211yescharacteristic
45C59×C4⋊C16C2211yescharacteristic
46C59×C4⋊C16C2211yescharacteristic
47C59×#358C2211yescharacteristic
48C59×#358C2211yescharacteristic
49C59×#358C2211yescharacteristic
50C59×#358C2211yescharacteristic
51C59×#358C2211yescharacteristic
52C59×#358C2211yescharacteristic
53C59×#357C2211yescharacteristic
54C59×#357C2211yescharacteristic
55C59×C22⋊C16C2211yescharacteristic
56C59×C22⋊C16C2211yescharacteristic
57C59×#346C2211yescharacteristic
58C4×C16×C59C2211yescharacteristic
59C22×Q8×C59—21no—
60C2×Q16×C59—22no—
61C2×Q16×C59—22no—
62C2×Q16×C59—21no—
63C2×Q16×C59C2311yescharacteristic
64C2×Q16×C59C2311yescharacteristic
65C2×Q16×C59C2311yescharacteristic
66C2×SD16×C59—21no—
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×Q8×C59—21no—
82C4×Q8×C59—21no—
83C4×Q8×C59—41no—
84C4×Q8×C59—41no—
85C4×D4×C59—21no—
86#117×C59—21no—
87#117×C59—41no—
88#117×C59—41no—
89#117×C59D411yescharacteristic
90Q32×C59—22no—
91Q32×C59—22no—
92SD32×C59—22no—
93SD32×C59—22no—
94C2×C16×C59C2311yescharacteristic
95C2×C16×C59C2311yescharacteristic
96C2×C16×C59C2311yescharacteristic
97C2×C16×C59C2311yescharacteristic
98#107×C59—21no—
99#107×C59C2311yescharacteristic
100#107×C59C2311yescharacteristic
101#107×C59C2311yescharacteristic
102#107×C59C2311yescharacteristic
103#106×C59—21no—
104#103×C59—21no—
105#103×C59—21no—
106#103×C59—21no—
107#103×C59—21no—
108#103×C59—21no—
109#103×C59—21no—
110#102×C59—21no—
111#102×C59—21no—
112#97×C59D411yescharacteristic
113#97×C59D411yescharacteristic
114C4×C8×C59C2311yescharacteristic
115C4×C8×C59C2311yescharacteristic
116C2×Q8×C59—24no—
117C2×Q8×C59—21no—
118C2×Q8×C59—21no—
119C2×Q8×C59—21no—
120C2×Q8×C59—42no—
121C2×Q8×C59—41no—
122C2×Q8×C59—41no—
123C2×D4×C59—21no—
124C2×D4×C59—41no—
125C22×C4×C59—41no—
126C22×C4×C59—41no—
127C22×C4×C59C2×D411yescharacteristic
128Q16×C59—24no—
129Q16×C59—21no—
130Q16×C59—21no—
131Q16×C59—21no—
132Q16×C59—21no—
133Q16×C59#4112yes—
134Q16×C59#4112yes—
135SD16×C59—42no—
136D8×C59—21no—
137D8×C59—21no—
138M16×C59—41no—
139C2×C8×C59—21no—
140C2×C8×C59—21no—
141C2×C8×C59C2×D411yescharacteristic
142C2×C8×C59C2×D411yescharacteristic
143C2×C8×C59C2×D411yescharacteristic
144C2×C8×C59C2411yescharacteristic
145C4⋊C4×C59—21no—
146C4⋊C4×C59—21no—
147C4⋊C4×C59—21no—
148C4⋊C4×C59—21no—
149C4⋊C4×C59—41no—
150C4⋊C4×C59—41no—
151C4⋊C4×C59—41no—
152C4⋊C4×C59—41no—
153C4⋊C4×C59—41no—
154C4⋊C4×C59—41no—
155C4⋊C4×C59—41no—
156C4⋊C4×C59D811yescharacteristic
157C4⋊C4×C59D811yescharacteristic
158C22⋊C4×C59—41no—
159C22⋊C4×C59—41no—
160C22⋊C4×C59—41no—
161C22⋊C4×C59—41no—
162C22⋊C4×C59—41no—
163C22⋊C4×C59—41no—
164C22⋊C4×C59D811yescharacteristic
165C22⋊C4×C59D811yescharacteristic
166C42×C59—41no—
167C42×C59—41no—
168C42×C59—41no—
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×C59C2×D811yescharacteristic
180Q8×C59—22no—
181Q8×C59—22no—
182Q8×C59—44no—
183Q8×C59—41no—
184Q8×C59—41no—
185Q8×C59—41no—
186Q8×C59—41no—
187Q8×C59—161no—
188D4×C59—41no—
189D4×C59—41no—
190D4×C59—161no—
191C2×C4×C59—21no—
192C2×C4×C59—21no—
193C2×C4×C59—44no—
194C2×C4×C59—41no—
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×C59C2×D811yescharacteristic
203C2×C4×C59C2×D811yescharacteristic
204C2×C4×C59C2×D811yescharacteristic
205C2×C4×C59C2×D811yescharacteristic
206C2×C4×C59C2×D811yescharacteristic
207C2×C4×C59C22×D411yescharacteristic
208C8×C59—21no—
209C8×C59—21no—
210C8×C59—21no—
211C8×C59C2×#4111yescharacteristic
212C8×C59C2×#4111yescharacteristic
213#33681C5911yesmaximal, characteristic, direct product factor, Sylow
214C22×C59—21no—
215C22×C59—21no—
216C22×C59—21no—
217C22×C59—81no—
218C22×C59—81no—
219C22×C59—81no—
220C22×C59C22×D811yescharacteristic
221C4×C59—21no—
222C4×C59—21no—
223C4×C59—21no—
224C4×C59—21no—
225C4×C59—21no—
226C4×C59—42no—
227C4×C59—42no—
228C4×C59—81no—
229C4×C59—81no—
230C4×C59—81no—
231C4×C59—81no—
232C4×C59—81no—
233C4×C59#52511yescharacteristic
234C4×C59#57511yescharacteristic
235#3175C2×C5911yescharacteristic
236#2950C2×C5911yescharacteristic, complemented
237#2237C2×C5911yescharacteristic, complemented
238#2234C2×C5911yescharacteristic
239#2227C2×C5911yescharacteristic, complemented
240#2225C2×C5911yescharacteristic, complemented
241#2211C2×C5911yescharacteristic, complemented
242#2211C2×C5911yescharacteristic, complemented
243#2188C2×C5911yescharacteristic, complemented
244#2185C2×C5911yescharacteristic
245#2176C2×C5911yescharacteristic, complemented
246#2175C2×C5911yescharacteristic, complemented
247C4×Q32C2×C5911yescharacteristic, complemented
248C4×SD32C2×C5911yescharacteristic, complemented
249#2164C2×C5911yescharacteristic, complemented
250C2×C59—41no—
251C2×C59—161no—
252C2×C59#310011yescharacteristic
253C2×C59#341611yescharacteristic
254C2×C59#341711yescharacteristic
255C22×Q16C22×C5911yescharacteristic
256#542—21no—
257#519—21no—
258C2×Q32C22×C5911yescharacteristic
259C2×Q32C22×C5911yescharacteristic
260C2×SD32C22×C5911yescharacteristic
261C2×SD32C22×C5911yescharacteristic
262#500C22×C5911yescharacteristic
263#495C22×C5911yescharacteristic
264#489—21no—
265#468—21no—
266#467C22×C5911yescharacteristic
267#466C22×C5911yescharacteristic
268#441—21no—
269#441—21no—
270#440—21no—
271C4×Q16C22×C5911yescharacteristic
272C4×Q16C22×C5911yescharacteristic
273C4×Q16C22×C5911yescharacteristic
274C4×Q16C22×C5911yescharacteristic
275C4×Q16C22×C5911yescharacteristic
276C4×D8C22×C5911yescharacteristic
277#427C22×C5911yescharacteristic
278#419—21no—
279#405C22×C5911yescharacteristic
280#367C22×C5911yescharacteristic
281#367C22×C5911yescharacteristic
282#366C22×C5911yescharacteristic
283#366C22×C5911yescharacteristic
284C4⋊C16C22×C5911yescharacteristic
285C4⋊C16C22×C5911yescharacteristic
286#358C22×C5911yescharacteristic
287#358C22×C5911yescharacteristic
288#358C22×C5911yescharacteristic
289#358C22×C5911yescharacteristic
290#358C22×C5911yescharacteristic
291#358C22×C5911yescharacteristic
292#357C22×C5911yescharacteristic
293#357C22×C5911yescharacteristic
294C22⋊C16C22×C5911yescharacteristic
295C22⋊C16C22×C5911yescharacteristic
296#346C22×C5911yescharacteristic
297C4×C16C22×C5911yescharacteristic
298C59#3368111yescharacteristic, direct product factor, Sylow
299C22×Q8—21no—
300C2×Q16—22no—
301C2×Q16—22no—
302C2×Q16—21no—
303C2×Q16C23×C5911yescharacteristic
304C2×Q16C23×C5911yescharacteristic
305C2×Q16C23×C5911yescharacteristic
306C2×SD16—21no—
307C2×D8C23×C5911yescharacteristic
308C2×M16D4×C5911yescharacteristic
309C22×C8C23×C5911yescharacteristic
310C4⋊Q8—21no—
311#126—41no—
312#124—21no—
313#124—41no—
314#123—41no—
315C22⋊Q8—21no—
316C22⋊Q8—41no—
317#121—21no—
318C4×Q8—21no—
319C4×Q8—21no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—41no—
324C4×Q8—41no—
325C4×D4—21no—
326#117—21no—
327#117—41no—
328#117—41no—
329#117D4×C5911yescharacteristic
330Q32—22no—
331Q32—22no—
332SD32—22no—
333SD32—22no—
334C2×C16C23×C5911yescharacteristic
335C2×C16C23×C5911yescharacteristic
336C2×C16C23×C5911yescharacteristic
337C2×C16C23×C5911yescharacteristic
338#107—21no—
339#107C23×C5911yescharacteristic
340#107C23×C5911yescharacteristic
341#107C23×C5911yescharacteristic
342#107C23×C5911yescharacteristic
343#106—21no—
344#103—21no—
345#103—21no—
346#103—21no—
347#103—21no—
348#103—21no—
349#103—21no—
350#102—21no—
351#102—21no—
352#97D4×C5911yescharacteristic
353#97D4×C5911yescharacteristic
354C4×C8C23×C5911yescharacteristic
355C4×C8C23×C5911yescharacteristic
356C2×Q8—24no—
357C2×Q8—21no—
358C2×Q8—21no—
359C2×Q8—21no—
360C2×Q8—42no—
361C2×Q8—41no—
362C2×Q8—41no—
363C2×D4—21no—
364C2×D4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4C2×D4×C5911yescharacteristic
368Q16—24no—
369Q16—21no—
370Q16—21no—
371Q16—21no—
372Q16—21no—
373Q16#41×C5912yes—
374Q16#41×C5912yes—
375SD16—42no—
376D8—21no—
377D8—21no—
378M16—41no—
379C2×C8—21no—
380C2×C8—21no—
381C2×C8C2×D4×C5911yescharacteristic
382C2×C8C2×D4×C5911yescharacteristic
383C2×C8C2×D4×C5911yescharacteristic
384C2×C8C24×C5911yescharacteristic
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—41no—
390C4⋊C4—41no—
391C4⋊C4—41no—
392C4⋊C4—41no—
393C4⋊C4—41no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4D8×C5911yescharacteristic
397C4⋊C4D8×C5911yescharacteristic
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—41no—
404C22⋊C4D8×C5911yescharacteristic
405C22⋊C4D8×C5911yescharacteristic
406C42—41no—
407C42—41no—
408C42—41no—
409C42—41no—
410C42—41no—
411C42—41no—
412C42C2×D4×C5911yescharacteristic
413C42C2×D4×C5911yescharacteristic
414C16—21no—
415C16—21no—
416C16—21no—
417C16—21no—
418C23—41no—
419C23C2×D8×C5911yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—44no—
423Q8—41no—
424Q8—41no—
425Q8—41no—
426Q8—41no—
427Q8—161no—
428D4—41no—
429D4—41no—
430D4—161no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—44no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—41no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—161no—
442C2×C4C2×D8×C5911yescharacteristic
443C2×C4C2×D8×C5911yescharacteristic
444C2×C4C2×D8×C5911yescharacteristic
445C2×C4C2×D8×C5911yescharacteristic
446C2×C4C2×D8×C5911yescharacteristic
447C2×C4C22×D4×C5911yescharacteristic
448C8—21no—
449C8—21no—
450C8—21no—
451C8C2×#41×C5911yescharacteristic
452C8C2×#41×C5911yescharacteristic
453C22—21no—
454C22—21no—
455C22—21no—
456C22—81no—
457C22—81no—
458C22—81no—
459C22C22×D8×C5911yescharacteristic
460C4—21no—
461C4—21no—
462C4—21no—
463C4—21no—
464C4—21no—
465C4—42no—
466C4—42no—
467C4—81no—
468C4—81no—
469C4—81no—
470C4—81no—
471C4—81no—
472C4C59×#52511yescharacteristic
473C4C59×#57511yescharacteristic
474C2—41no—
475C2—161no—
476C2C59×#310011yescharacteristic
477C2C59×#341611yescharacteristic
478C2C59×#341711yescharacteristic
subgroupG/H
center, socleC22×C59C22×D8
commutator, Frattini, cosocleC2×C8C24×C59
prime radicalC59×#466C22
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
2. C59×#2950C2semidirect
3. C59×#2237C2semidirect
5. C59×#2227C2semidirect
6. C59×#2225C2semidirect
7. C59×#2211C2semidirect
8. C59×#2211C2semidirect
9. C59×#2188C2semidirect
11. C59×#2176C2semidirect
12. C59×#2175C2semidirect
13. C4×Q32×C59C2semidirect
14. C4×SD32×C59C2semidirect
15. C59×#2164C2semidirect
213. #33681C59direct (N × H)
236. #2950C2×C59semidirect
237. #2237C2×C59semidirect
239. #2227C2×C59semidirect
240. #2225C2×C59semidirect
241. #2211C2×C59semidirect
242. #2211C2×C59semidirect
243. #2188C2×C59semidirect
245. #2176C2×C59semidirect
246. #2175C2×C59semidirect
247. C4×Q32C2×C59semidirect
248. C4×SD32C2×C59semidirect
249. #2164C2×C59semidirect
298. C59#33681direct (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×#29502
C59×#22372
C59×#22342
C59×#22272
C59×#22252
C59×#22112
C59×#21882
C59×#21852
C59×#21762
C59×#21752
C4×Q32×C592
C4×SD32×C592
C59×#21642
#3368159