Finite Group Databasebeta

← C59×#8991 #28421100

Subgroups — C59×#8991 #28421100

Order 15104.

578 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3100C211yesmaximal, characteristic
2D4×M16×C59C211yesmaximal, characteristic, complemented
3C59×#1980C211yesmaximal, characteristic, complemented
4C4×#102×C59C211yesmaximal, characteristic, complemented
5C59×#1492C211yesmaximal, characteristic, complemented
6C59×#1303C211yesmaximal, characteristic, complemented
7C59×#1278C211yesmaximal, characteristic, complemented
8C22×M16×C59—21no—
9C59×#532C2211yescharacteristic
10C2×C4×D4×C59C2211yescharacteristic
11C59×#480—21no—
12C59×#474C411yescharacteristic, complemented
13C59×#474C411yescharacteristic, complemented
14C59×#459C411yescharacteristic, complemented
15C59×#459C411yescharacteristic, complemented
16C59×#447—21no—
17C4×D8×C59—21no—
18C4×D8×C59—21no—
19C59×#436—21no—
20C59×#435—22no—
21C8×D4×C59—21no—
22C59×#431C2211yescharacteristic
23C59×#423C2211yescharacteristic
24C2×#104×C59—21no—
25C2×#104×C59—21no—
26C2×#102×C59—21no—
27C59×#407—21no—
28C4×M16×C59C2211yescharacteristic
29C2×C4×C8×C59C2211yescharacteristic
30C4×C4⋊C4×C59C2211yescharacteristic
31C59×#340—21no—
32C59×D4⋊C8—22no—
33C2×#41×C59—21no—
34C22×D4×C59D411yescharacteristic
35C23×C4×C59—21no—
36C2×D8×C59—21no—
37C2×D8×C59—21no—
38C2×M16×C59—22no—
39C2×M16×C59—21no—
40C2×M16×C59—42no—
41C2×M16×C59—42no—
42C2×M16×C59D411yescharacteristic
43C2×M16×C59D411yescharacteristic
44C22×C8×C59—22no—
45C22×C8×C59—21no—
46C4⋊Q8×C59C2×C411yescharacteristic
47#127×C59C2×C411yescharacteristic
48#124×C59—21no—
49#121×C59—21no—
50#121×C59—21no—
51C4×D4×C59—21no—
52C4×D4×C59—21no—
53C4×D4×C59—21no—
54C4×D4×C59—21no—
55C4×D4×C59C2×C411yescharacteristic
56C4×D4×C59C2×C411yescharacteristic
57C4×D4×C59D411yescharacteristic
58C4×D4×C59D411yescharacteristic
59C2×C4⋊C4×C59—21no—
60C2×C4⋊C4×C59D411yescharacteristic
61C2×C22⋊C4×C59—21no—
62C2×C42×C59—21no—
63C2×C42×C59C2311yescharacteristic
64#107×C59—21no—
65#107×C59—21no—
66C4⋊C8×C59—21no—
67C4⋊C8×C59C2×C411yescharacteristic
68C4⋊C8×C59C2×C411yescharacteristic
69C4⋊C8×C59D412yes—
70#104×C59—42no—
71#104×C59—42no—
72#102×C59—24no—
73#102×C59—21no—
74#102×C59—21no—
75#102×C59—21no—
76#102×C59—21no—
77C22⋊C8×C59—22no—
78C22⋊C8×C59—22no—
79C22⋊C8×C59—21no—
80#97×C59—21no—
81C4×C8×C59—21no—
82C4×C8×C59—21no—
83C4×C8×C59—21no—
84C4×C8×C59—21no—
85#95×C59—21no—
86C24×C59—21no—
87#41×C59—41no—
88#41×C59—41no—
89#41×C59—41no—
90#41×C59—41no—
91C2×Q8×C59—21no—
92C2×D4×C59—22no—
93C2×D4×C59—21no—
94C2×D4×C59—21no—
95C2×D4×C59—21no—
96C2×D4×C59—21no—
97C2×D4×C59—41no—
98C2×D4×C59—41no—
99C2×D4×C59C22⋊C411yescharacteristic
100C2×D4×C59C22⋊C411yescharacteristic
101C22×C4×C59—21no—
102C22×C4×C59—21no—
103C22×C4×C59—21no—
104C22×C4×C59—21no—
105C22×C4×C59—21no—
106C22×C4×C59—41no—
107C22×C4×C59—41no—
108C22×C4×C59—41no—
109C22×C4×C59—41no—
110C22×C4×C59—41no—
111C22×C4×C59—41no—
112C22×C4×C59C2×D411yescharacteristic
113C22×C4×C59C2×D411yescharacteristic
114C22×C4×C59#4111yescharacteristic
115D8×C59—42no—
116D8×C59—42no—
117M16×C59—21no—
118M16×C59—21no—
119M16×C59—21no—
120M16×C59—44no—
121M16×C59—41no—
122M16×C59—41no—
123M16×C59D812yescomplemented
124C2×C8×C59—21no—
125C2×C8×C59—22no—
126C2×C8×C59—21no—
127C2×C8×C59—21no—
128C2×C8×C59—21no—
129C2×C8×C59—22no—
130C2×C8×C59—44no—
131C2×C8×C59—41no—
132C2×C8×C59—41no—
133C4⋊C4×C59—21no—
134C4⋊C4×C59—22no—
135C4⋊C4×C59—21no—
136C4⋊C4×C59—21no—
137C4⋊C4×C59—41no—
138C4⋊C4×C59C22⋊C411yescharacteristic
139C4⋊C4×C59C22⋊C411yescharacteristic
140C22⋊C4×C59—21no—
141C22⋊C4×C59—21no—
142C22⋊C4×C59—21no—
143C22⋊C4×C59—21no—
144C22⋊C4×C59—41no—
145C22⋊C4×C59—41no—
146C42×C59—41no—
147C42×C59—41no—
148C42×C59C22×C411yescharacteristic
149C42×C59C2×D411yescharacteristic
150C42×C59C2×D411yescharacteristic
151C42×C59#4111yescharacteristic
152C23×C59—21no—
153C23×C59—21no—
154C23×C59—42no—
155C23×C59—41no—
156C23×C59—41no—
157C23×C59—41no—
158C23×C59—81no—
159C23×C59#12111yescharacteristic
160Q8×C59—41no—
161Q8×C59—41no—
162D4×C59—21no—
163D4×C59—21no—
164D4×C59—21no—
165D4×C59—42no—
166D4×C59—42no—
167D4×C59—41no—
168D4×C59—41no—
169D4×C59—41no—
170D4×C59—41no—
171D4×C59—81no—
172D4×C59—81no—
173D4×C59#10412yescomplemented
174C2×C4×C59—21no—
175C2×C4×C59—21no—
176C2×C4×C59—21no—
177C2×C4×C59—21no—
178C2×C4×C59—41no—
179C2×C4×C59—41no—
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—41no—
189C2×C4×C59—42no—
190C2×C4×C59—41no—
191C2×C4×C59—81no—
192C2×C4×C59—81no—
193C2×C4×C59—81no—
194C2×C4×C59—81no—
195C2×C4×C59C2×C22⋊C411yescharacteristic
196C2×C4×C59C4×D411yescharacteristic
197C2×C4×C59C4×D411yescharacteristic
198C2×C4×C59#12011yescharacteristic
199C2×C4×C59#12111yescharacteristic
200C2×C4×C59#12311yescharacteristic
201C2×C4×C59C2×D811yescharacteristic
202C2×C4×C59#13511yescharacteristic
203C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
204C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
205C8×C59—22no—
206C8×C59—42no—
207C8×C59—41no—
208C8×C59—41no—
209C8×C59—42no—
210C8×C59—41no—
211#8991C5911yesmaximal, characteristic, direct product factor, Sylow
212C22×C59—21no—
213C22×C59—21no—
214C22×C59—22no—
215C22×C59—41no—
216C22×C59—41no—
217C22×C59—41no—
218C22×C59—41no—
219C22×C59—41no—
220C22×C59—82no—
221C22×C59—82no—
222C22×C59—81no—
223C22×C59—81no—
224C22×C59—81no—
225C22×C59#38611yescharacteristic
226C22×C59#45911yescharacteristic
227C22×C59#46311yescharacteristic
228C4×C59—21no—
229C4×C59—21no—
230C4×C59—21no—
231C4×C59—41no—
232C4×C59—41no—
233C4×C59—82no—
234C4×C59—81no—
235C4×C59C2×#10411yescharacteristic
236C4×C59#42111yescharacteristic
237C4×C59C4×D811yescharacteristic
238C4×C59#44211yescharacteristic
239C4×C59#44711yescharacteristic
240C4×C59#44911yescharacteristic
241#3100C2×C5911yescharacteristic
242D4×M16C2×C5911yescharacteristic, complemented
243#1980C2×C5911yescharacteristic, complemented
244C4×#102C2×C5911yescharacteristic, complemented
245#1492C2×C5911yescharacteristic, complemented
246#1303C2×C5911yescharacteristic, complemented
247#1278C2×C5911yescharacteristic, complemented
248C2×C59—21no—
249C2×C59—21no—
250C2×C59—42no—
251C2×C59—81no—
252C2×C59—161no—
253C2×C59#187111yescharacteristic
254C2×C59#187911yescharacteristic
255C2×C59#188111yescharacteristic
256C22×M16—21no—
257#532C22×C5911yescharacteristic
258C2×C4×D4C22×C5911yescharacteristic
259#480—21no—
260#474C4×C5911yescharacteristic, complemented
261#474C4×C5911yescharacteristic, complemented
262#459C4×C5911yescharacteristic, complemented
263#459C4×C5911yescharacteristic, complemented
264#447—21no—
265C4×D8—21no—
266C4×D8—21no—
267#436—21no—
268#435—22no—
269C8×D4—21no—
270#431C22×C5911yescharacteristic
271#423C22×C5911yescharacteristic
272C2×#104—21no—
273C2×#104—21no—
274C2×#102—21no—
275#407—21no—
276C4×M16C22×C5911yescharacteristic
277C2×C4×C8C22×C5911yescharacteristic
278C4×C4⋊C4C22×C5911yescharacteristic
279#340—21no—
280D4⋊C8—22no—
281C59#899111yescharacteristic, direct product factor, Sylow
282C2×#41—21no—
283C22×D4D4×C5911yescharacteristic
284C23×C4—21no—
285C2×D8—21no—
286C2×D8—21no—
287C2×M16—22no—
288C2×M16—21no—
289C2×M16—42no—
290C2×M16—42no—
291C2×M16D4×C5911yescharacteristic
292C2×M16D4×C5911yescharacteristic
293C22×C8—22no—
294C22×C8—21no—
295C4⋊Q8C2×C4×C5911yescharacteristic
296#127C2×C4×C5911yescharacteristic
297#124—21no—
298#121—21no—
299#121—21no—
300C4×D4—21no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—21no—
304C4×D4C2×C4×C5911yescharacteristic
305C4×D4C2×C4×C5911yescharacteristic
306C4×D4D4×C5911yescharacteristic
307C4×D4D4×C5911yescharacteristic
308C2×C4⋊C4—21no—
309C2×C4⋊C4D4×C5911yescharacteristic
310C2×C22⋊C4—21no—
311C2×C42—21no—
312C2×C42C23×C5911yescharacteristic
313#107—21no—
314#107—21no—
315C4⋊C8—21no—
316C4⋊C8C2×C4×C5911yescharacteristic
317C4⋊C8C2×C4×C5911yescharacteristic
318C4⋊C8D4×C5912yes—
319#104—42no—
320#104—42no—
321#102—24no—
322#102—21no—
323#102—21no—
324#102—21no—
325#102—21no—
326C22⋊C8—22no—
327C22⋊C8—22no—
328C22⋊C8—21no—
329#97—21no—
330C4×C8—21no—
331C4×C8—21no—
332C4×C8—21no—
333C4×C8—21no—
334#95—21no—
335C24—21no—
336#41—41no—
337#41—41no—
338#41—41no—
339#41—41no—
340C2×Q8—21no—
341C2×D4—22no—
342C2×D4—21no—
343C2×D4—21no—
344C2×D4—21no—
345C2×D4—21no—
346C2×D4—41no—
347C2×D4—41no—
348C2×D4C22⋊C4×C5911yescharacteristic
349C2×D4C22⋊C4×C5911yescharacteristic
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—41no—
356C22×C4—41no—
357C22×C4—41no—
358C22×C4—41no—
359C22×C4—41no—
360C22×C4—41no—
361C22×C4C2×D4×C5911yescharacteristic
362C22×C4C2×D4×C5911yescharacteristic
363C22×C4#41×C5911yescharacteristic
364D8—42no—
365D8—42no—
366M16—21no—
367M16—21no—
368M16—21no—
369M16—44no—
370M16—41no—
371M16—41no—
372M16D8×C5912yescomplemented
373C2×C8—21no—
374C2×C8—22no—
375C2×C8—21no—
376C2×C8—21no—
377C2×C8—21no—
378C2×C8—22no—
379C2×C8—44no—
380C2×C8—41no—
381C2×C8—41no—
382C4⋊C4—21no—
383C4⋊C4—22no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—41no—
387C4⋊C4C22⋊C4×C5911yescharacteristic
388C4⋊C4C22⋊C4×C5911yescharacteristic
389C22⋊C4—21no—
390C22⋊C4—21no—
391C22⋊C4—21no—
392C22⋊C4—21no—
393C22⋊C4—41no—
394C22⋊C4—41no—
395C42—41no—
396C42—41no—
397C42C22×C4×C5911yescharacteristic
398C42C2×D4×C5911yescharacteristic
399C42C2×D4×C5911yescharacteristic
400C42#41×C5911yescharacteristic
401C23—21no—
402C23—21no—
403C23—42no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23—81no—
408C23#121×C5911yescharacteristic
409Q8—41no—
410Q8—41no—
411D4—21no—
412D4—21no—
413D4—21no—
414D4—42no—
415D4—42no—
416D4—41no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—81no—
421D4—81no—
422D4#104×C5912yescomplemented
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—81no—
441C2×C4—81no—
442C2×C4—81no—
443C2×C4—81no—
444C2×C4C2×C22⋊C4×C5911yescharacteristic
445C2×C4C4×D4×C5911yescharacteristic
446C2×C4C4×D4×C5911yescharacteristic
447C2×C4#120×C5911yescharacteristic
448C2×C4#121×C5911yescharacteristic
449C2×C4#123×C5911yescharacteristic
450C2×C4C2×D8×C5911yescharacteristic
451C2×C4#135×C5911yescharacteristic
452C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
453C2×C4AGL(1,ℤ/8)×C5911yescharacteristic
454C8—22no—
455C8—42no—
456C8—41no—
457C8—41no—
458C8—42no—
459C8—41no—
460C22—21no—
461C22—21no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—82no—
469C22—82no—
470C22—81no—
471C22—81no—
472C22—81no—
473C22C59×#38611yescharacteristic
474C22C59×#45911yescharacteristic
475C22C59×#46311yescharacteristic
476C4—21no—
477C4—21no—
478C4—21no—
479C4—41no—
480C4—41no—
481C4—82no—
482C4—81no—
483C4C2×#104×C5911yescharacteristic
484C4C59×#42111yescharacteristic
485C4C4×D8×C5911yescharacteristic
486C4C59×#44211yescharacteristic
487C4C59×#44711yescharacteristic
488C4C59×#44911yescharacteristic
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—161no—
494C2C59×#187111yescharacteristic
495C2C59×#187911yescharacteristic
496C2C59×#188111yescharacteristic
subgroupG/H
centerC2×C4×C59#120
commutatorC42C22×C4×C59
Frattini, cosocleC2×C42C23×C59
socleC22×C59#386
prime radicalC59×#3100C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
2. D4×M16×C59C2semidirect
3. C59×#1980C2semidirect
4. C4×#102×C59C2semidirect
5. C59×#1492C2semidirect
6. C59×#1303C2semidirect
7. C59×#1278C2semidirect
12. C59×#474C4semidirect
13. C59×#474C4semidirect
14. C59×#459C4semidirect
15. C59×#459C4semidirect
123. M16×C59D8semidirect
173. D4×C59#104semidirect
211. #8991C59direct (N × H)
242. D4×M16C2×C59semidirect
243. #1980C2×C59semidirect
244. C4×#102C2×C59semidirect
245. #1492C2×C59semidirect
246. #1303C2×C59semidirect
247. #1278C2×C59semidirect
260. #474C4×C59semidirect
261. #474C4×C59semidirect
262. #459C4×C59semidirect
263. #459C4×C59semidirect
281. C59#8991direct (N × H)
372. M16D8×C59semidirect
422. D4#104×C59semidirect

Maximal subgroups

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

subgroupindex
C59×#31002
D4×M16×C592
C59×#19802
C4×#102×C592
C59×#14922
C59×#13032
C59×#12782
#899159