Finite Group Databasebeta

← C59×#18443 #28430552

Subgroups — C59×#18443 #28430552

Order 15104.

832 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C59×#3563C211yesmaximal, characteristic
2C59×#3239C211yesmaximal, characteristic
3C59×#3230C211yesmaximal, characteristic, complemented
4C59×#2642C211yesmaximal, characteristic, complemented
5C59×#1617C214yesmaximal, complemented
6C59×#1615C214yesmaximal
7C59×#1506C211yesmaximal, characteristic, complemented
8C59×#1500C211yesmaximal, characteristic
9C59×#1470C211yesmaximal, characteristic, complemented
10C59×#564—21no—
11C59×#563—21no—
12C59×#557—21no—
13C59×#554—21no—
14C59×#552—21no—
15C59×#552—21no—
16C59×#552—22no—
17C59×#544—21no—
18C59×#544C2212yes—
19C59×#541—21no—
20C59×#541—22no—
21C59×#539C2212yes—
22C59×#533C2211yescharacteristic
23C2×C4⋊Q8×C59C2211yescharacteristic
24C59×#529C2211yescharacteristic
25C2×#125×C59C2211yescharacteristic
26C59×#501—21no—
27C59×#500—21no—
28C59×#489—21no—
29C59×#487—21no—
30C59×#484C2214yes—
31C59×#484C2212yes—
32C59×#481C2212yes—
33C59×#477—22no—
34C59×#475—21no—
35C59×#474—21no—
36C59×#432C2211yescharacteristic
37C59×#431C2211yescharacteristic
38C59×#400—22no—
39C59×#400C2214yes—
40C59×#391—21no—
41C59×#391—21no—
42C59×#376C2211yescharacteristic
43C59×#328C2212yes—
44C59×#328C2214yes—
45C59×#327C2212yes—
46C59×#324C2214yes—
47C22×Q8×C59—21no—
48C4⋊Q8×C59—21no—
49C4⋊Q8×C59—22no—
50C4⋊Q8×C59—22no—
51C4⋊Q8×C59—21no—
52C4⋊Q8×C59—21no—
53C4⋊Q8×C59—21no—
54C4⋊Q8×C59—21no—
55C4⋊Q8×C59D411yescharacteristic
56C4⋊Q8×C59D411yescharacteristic
57#126×C59—22no—
58#126×C59—22no—
59#126×C59—22no—
60#126×C59—22no—
61#126×C59—21no—
62#125×C59—22no—
63#125×C59—22no—
64#125×C59—22no—
65#125×C59—22no—
66#125×C59—21no—
67#125×C59—22no—
68#125×C59—22no—
69#125×C59—22no—
70#125×C59—22no—
71#125×C59—21no—
72#125×C59—21no—
73#125×C59—21no—
74#125×C59—21no—
75#125×C59—21no—
76#125×C59D411yescharacteristic
77#124×C59D411yescharacteristic
78#123×C59—22no—
79#123×C59—21no—
80#123×C59—22no—
81C22⋊Q8×C59—21no—
82C22⋊Q8×C59—21no—
83C22⋊Q8×C59—22no—
84C22⋊Q8×C59—22no—
85C22⋊Q8×C59—22no—
86C22⋊Q8×C59—21no—
87C22⋊Q8×C59—22no—
88C22⋊Q8×C59C2311yescharacteristic
89C22⋊Q8×C59C2312yes—
90#121×C59C2311yescharacteristic
91C4×Q8×C59—21no—
92C4×Q8×C59—22no—
93C4×Q8×C59—21no—
94C4×Q8×C59—21no—
95C4×Q8×C59D411yescharacteristic
96C4×Q8×C59D412yes—
97C4×D4×C59—21no—
98C4×D4×C59—22no—
99C4×D4×C59D411yescharacteristic
100#117×C59—22no—
101#117×C59—21no—
102#117×C59—21no—
103#117×C59—22no—
104#117×C59—21no—
105C2×C4⋊C4×C59—21no—
106C2×C4⋊C4×C59—21no—
107C2×C4⋊C4×C59D411yescharacteristic
108C2×C4⋊C4×C59D411yescharacteristic
109C2×C4⋊C4×C59D412yes—
110C2×C4⋊C4×C59C2312yes—
111C2×C4⋊C4×C59C2312yes—
112C2×C42×C59—21no—
113C2×C42×C59C2311yescharacteristic
114#107×C59—22no—
115#107×C59—24no—
116#106×C59—22no—
117C4⋊C8×C59—21no—
118C4⋊C8×C59—21no—
119#103×C59—22no—
120#103×C59—24no—
121#102×C59—22no—
122C22⋊C8×C59C2312yes—
123C22⋊C8×C59C2312yes—
124#97×C59—21no—
125C4×C8×C59—21no—
126#95×C59—21no—
127#95×C59—24no—
128#95×C59—24no—
129#95×C59C2312yes—
130C2×Q8×C59—22no—
131C2×Q8×C59—21no—
132C2×Q8×C59—44no—
133C2×Q8×C59—41no—
134C2×Q8×C59—41no—
135C2×Q8×C59C2×D412yes—
136C2×Q8×C59C2×D411yescharacteristic
137C2×D4×C59—21no—
138C2×D4×C59C2×D411yescharacteristic
139C22×C4×C59—22no—
140C22×C4×C59—21no—
141C22×C4×C59—22no—
142C22×C4×C59—22no—
143C22×C4×C59C2×D412yes—
144C22×C4×C59C2×D411yescharacteristic
145C22×C4×C59C2×D411yescharacteristic
146C22×C4×C59C2×D412yes—
147C22×C4×C59C2411yescharacteristic
148C2×C8×C59—22no—
149C2×C8×C59—22no—
150C4⋊C4×C59—22no—
151C4⋊C4×C59—22no—
152C4⋊C4×C59—22no—
153C4⋊C4×C59—22no—
154C4⋊C4×C59—22no—
155C4⋊C4×C59—22no—
156C4⋊C4×C59—22no—
157C4⋊C4×C59—22no—
158C4⋊C4×C59—21no—
159C4⋊C4×C59—21no—
160C4⋊C4×C59—21no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—21no—
163C4⋊C4×C59—22no—
164C4⋊C4×C59—21no—
165C4⋊C4×C59—21no—
166C4⋊C4×C59—21no—
167C4⋊C4×C59—21no—
168C4⋊C4×C59—21no—
169C4⋊C4×C59—21no—
170C4⋊C4×C59—22no—
171C4⋊C4×C59—22no—
172C4⋊C4×C59—22no—
173C4⋊C4×C59—21no—
174C4⋊C4×C59—22no—
175C4⋊C4×C59—22no—
176C4⋊C4×C59—22no—
177C4⋊C4×C59—41no—
178C4⋊C4×C59—41no—
179C4⋊C4×C59C2×D411yescharacteristic
180C4⋊C4×C59C2×D411yescharacteristic
181C4⋊C4×C59C2×D412yes—
182C22⋊C4×C59—22no—
183C22⋊C4×C59—22no—
184C22⋊C4×C59—22no—
185C22⋊C4×C59—22no—
186C22⋊C4×C59—21no—
187C22⋊C4×C59—21no—
188C22⋊C4×C59—21no—
189C22⋊C4×C59—21no—
190C22⋊C4×C59—21no—
191C42×C59—22no—
192C42×C59—22no—
193C42×C59—22no—
194C42×C59—22no—
195C42×C59—21no—
196C42×C59—42no—
197C42×C59C2×D411yescharacteristic
198C42×C59C2×D411yescharacteristic
199C42×C59C2×D411yescharacteristic
200C42×C59C2×D411yescharacteristic
201C23×C59—21no—
202C23×C59C22×D411yescharacteristic
203Q8×C59—41no—
204Q8×C59—42no—
205Q8×C59—42no—
206Q8×C59—82no—
207Q8×C59—82no—
208Q8×C59—82no—
209D4×C59—41no—
210D4×C59—42no—
211C2×C4×C59—22no—
212C2×C4×C59—22no—
213C2×C4×C59—22no—
214C2×C4×C59—21no—
215C2×C4×C59—21no—
216C2×C4×C59—22no—
217C2×C4×C59—21no—
218C2×C4×C59—22no—
219C2×C4×C59—22no—
220C2×C4×C59—24no—
221C2×C4×C59—41no—
222C2×C4×C59—42no—
223C2×C4×C59—42no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—44no—
227C2×C4×C59—42no—
228C2×C4×C59—42no—
229C2×C4×C59—82no—
230C2×C4×C59#12011yescharacteristic
231C2×C4×C59#12011yescharacteristic
232C2×C4×C59#12011yescharacteristic
233C2×C4×C59#12011yescharacteristic
234C2×C4×C59C22×D411yescharacteristic
235C2×C4×C59C22×D411yescharacteristic
236C8×C59—42no—
237C8×C59—42no—
238#18443C5911yesmaximal, characteristic, direct product factor, Sylow
239C22×C59—21no—
240C22×C59—21no—
241C22×C59—41no—
242C22×C59—41no—
243C22×C59—41no—
244C22×C59C2×#12011yescharacteristic
245C22×C59#57812yes—
246C4×C59—21no—
247C4×C59—21no—
248C4×C59—21no—
249C4×C59—21no—
250C4×C59—21no—
251C4×C59—42no—
252C4×C59—41no—
253C4×C59—41no—
254C4×C59—42no—
255C4×C59—42no—
256C4×C59—42no—
257C4×C59—41no—
258C4×C59—82no—
259C4×C59—82no—
260C4×C59#45412yes—
261#3563C2×C5911yescharacteristic
262#3239C2×C5911yescharacteristic
263#3230C2×C5911yescharacteristic, complemented
264#2642C2×C5911yescharacteristic, complemented
265#1617C2×C5914yescomplemented
266#1615C2×C5914yes—
267#1506C2×C5911yescharacteristic, complemented
268#1500C2×C5911yescharacteristic
269#1470C2×C5911yescharacteristic, complemented
270C2×C59—22no—
271C2×C59—81no—
272C2×C59#301111yescharacteristic
273C2×C59C2×#45411yescharacteristic
274C2×C59#302811yescharacteristic
275#564—21no—
276#563—21no—
277#557—21no—
278#554—21no—
279#552—21no—
280#552—21no—
281#552—22no—
282#544—21no—
283#544C22×C5912yes—
284#541—21no—
285#541—22no—
286#539C22×C5912yes—
287#533C22×C5911yescharacteristic
288C2×C4⋊Q8C22×C5911yescharacteristic
289#529C22×C5911yescharacteristic
290C2×#125C22×C5911yescharacteristic
291#501—21no—
292#500—21no—
293#489—21no—
294#487—21no—
295#484C22×C5914yes—
296#484C22×C5912yes—
297#481C22×C5912yes—
298#477—22no—
299#475—21no—
300#474—21no—
301#432C22×C5911yescharacteristic
302#431C22×C5911yescharacteristic
303#400—22no—
304#400C22×C5914yes—
305#391—21no—
306#391—21no—
307#376C22×C5911yescharacteristic
308#328C22×C5914yes—
309#328C22×C5912yes—
310#327C22×C5912yes—
311#324C22×C5914yes—
312C59#1844311yescharacteristic, direct product factor, Sylow
313C22×Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—22no—
316C4⋊Q8—22no—
317C4⋊Q8—21no—
318C4⋊Q8—21no—
319C4⋊Q8—21no—
320C4⋊Q8—21no—
321C4⋊Q8D4×C5911yescharacteristic
322C4⋊Q8D4×C5911yescharacteristic
323#126—22no—
324#126—22no—
325#126—22no—
326#126—22no—
327#126—21no—
328#125—22no—
329#125—22no—
330#125—22no—
331#125—22no—
332#125—21no—
333#125—22no—
334#125—22no—
335#125—22no—
336#125—22no—
337#125—21no—
338#125—21no—
339#125—21no—
340#125—21no—
341#125—21no—
342#125D4×C5911yescharacteristic
343#124D4×C5911yescharacteristic
344#123—22no—
345#123—21no—
346#123—22no—
347C22⋊Q8—21no—
348C22⋊Q8—21no—
349C22⋊Q8—22no—
350C22⋊Q8—22no—
351C22⋊Q8—22no—
352C22⋊Q8—21no—
353C22⋊Q8—22no—
354C22⋊Q8C23×C5911yescharacteristic
355C22⋊Q8C23×C5912yes—
356#121C23×C5911yescharacteristic
357C4×Q8—21no—
358C4×Q8—22no—
359C4×Q8—21no—
360C4×Q8—21no—
361C4×Q8D4×C5911yescharacteristic
362C4×Q8D4×C5912yes—
363C4×D4—21no—
364C4×D4—22no—
365C4×D4D4×C5911yescharacteristic
366#117—22no—
367#117—21no—
368#117—21no—
369#117—22no—
370#117—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4D4×C5911yescharacteristic
374C2×C4⋊C4D4×C5912yes—
375C2×C4⋊C4D4×C5911yescharacteristic
376C2×C4⋊C4C23×C5912yes—
377C2×C4⋊C4C23×C5912yes—
378C2×C42—21no—
379C2×C42C23×C5911yescharacteristic
380#107—22no—
381#107—24no—
382#106—22no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385#103—22no—
386#103—24no—
387#102—22no—
388C22⋊C8C23×C5912yes—
389C22⋊C8C23×C5912yes—
390#97—21no—
391C4×C8—21no—
392#95—21no—
393#95—24no—
394#95—24no—
395#95C23×C5912yes—
396C2×Q8—22no—
397C2×Q8—21no—
398C2×Q8—44no—
399C2×Q8—41no—
400C2×Q8—41no—
401C2×Q8C2×D4×C5912yes—
402C2×Q8C2×D4×C5911yescharacteristic
403C2×D4—21no—
404C2×D4C2×D4×C5911yescharacteristic
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4C2×D4×C5912yes—
410C22×C4C2×D4×C5911yescharacteristic
411C22×C4C2×D4×C5911yescharacteristic
412C22×C4C2×D4×C5912yes—
413C22×C4C24×C5911yescharacteristic
414C2×C8—22no—
415C2×C8—22no—
416C4⋊C4—22no—
417C4⋊C4—22no—
418C4⋊C4—22no—
419C4⋊C4—22no—
420C4⋊C4—22no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—21no—
425C4⋊C4—21no—
426C4⋊C4—21no—
427C4⋊C4—22no—
428C4⋊C4—21no—
429C4⋊C4—22no—
430C4⋊C4—21no—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—22no—
438C4⋊C4—22no—
439C4⋊C4—21no—
440C4⋊C4—22no—
441C4⋊C4—22no—
442C4⋊C4—22no—
443C4⋊C4—41no—
444C4⋊C4—41no—
445C4⋊C4C2×D4×C5911yescharacteristic
446C4⋊C4C2×D4×C5911yescharacteristic
447C4⋊C4C2×D4×C5912yes—
448C22⋊C4—22no—
449C22⋊C4—22no—
450C22⋊C4—22no—
451C22⋊C4—22no—
452C22⋊C4—21no—
453C22⋊C4—21no—
454C22⋊C4—21no—
455C22⋊C4—21no—
456C22⋊C4—21no—
457C42—22no—
458C42—22no—
459C42—22no—
460C42—22no—
461C42—21no—
462C42—42no—
463C42C2×D4×C5911yescharacteristic
464C42C2×D4×C5911yescharacteristic
465C42C2×D4×C5911yescharacteristic
466C42C2×D4×C5911yescharacteristic
467C23—21no—
468C23C22×D4×C5911yescharacteristic
469Q8—41no—
470Q8—42no—
471Q8—42no—
472Q8—82no—
473Q8—82no—
474Q8—82no—
475D4—41no—
476D4—42no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—22no—
483C2×C4—21no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—41no—
488C2×C4—42no—
489C2×C4—42no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—82no—
496C2×C4#120×C5911yescharacteristic
497C2×C4#120×C5911yescharacteristic
498C2×C4#120×C5911yescharacteristic
499C2×C4#120×C5911yescharacteristic
500C2×C4C22×D4×C5911yescharacteristic
501C2×C4C22×D4×C5911yescharacteristic
502C8—42no—
503C8—42no—
504C22—21no—
505C22—21no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22C2×#120×C5911yescharacteristic
510C22C59×#57812yes—
511C4—21no—
512C4—21no—
513C4—21no—
514C4—21no—
515C4—21no—
516C4—42no—
517C4—41no—
518C4—41no—
519C4—42no—
520C4—42no—
521C4—42no—
522C4—41no—
523C4—82no—
524C4—82no—
525C4C59×#45412yes—
526C2—22no—
527C2—81no—
528C2C59×#301111yescharacteristic
529C2C2×C59×#45411yescharacteristic
530C2C59×#302811yescharacteristic
subgroupG/H
center, socleC22×C59C2×#120
commutator, Frattini, cosocleC22×C4C24×C59
prime radical#121×C59C23
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C59 ◁ C2×C42×C59 ◁ G

Complements

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

NH ≅ G/Ntype
3. C59×#3230C2semidirect
4. C59×#2642C2semidirect
5. C59×#1617C2semidirect
7. C59×#1506C2semidirect
9. C59×#1470C2semidirect
238. #18443C59direct (N × H)
263. #3230C2×C59semidirect
264. #2642C2×C59semidirect
265. #1617C2×C59semidirect
267. #1506C2×C59semidirect
269. #1470C2×C59semidirect
312. C59#18443direct (N × H)

Maximal subgroups

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

subgroupindex
C59×#35632
C59×#32392
C59×#32302
C59×#26422
C59×#16172
C59×#16152
C59×#15062
C59×#15002
C59×#14702
#1844359