Finite Group Databasebeta

← #28491029

Subgroups — #28491029

Order 15104.

712 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837689C211yesmaximal, characteristic, complemented
2#21429009C211yesmaximal, characteristic
3#21424899C211yesmaximal, characteristic, complemented
4C2×D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
5C2×#16837129C211yesmaximal, characteristic, complemented
6#21421980C211yesmaximal, characteristic, complemented
7C2×C59×#476C211yesmaximal, characteristic, complemented
8C2×#14273701—21no—
9C2×#14273698—21no—
10C2×C4×D236C2211yescharacteristic
11#16837689—22no—
12#16837689—22no—
13C2×#14273658—21no—
14C2×C4⋊(C59⋊C8)C2211yescharacteristic
15C2×#14273651—22no—
16C2×#14273647—21no—
17C2×C4×C59⋊C8C2211yescharacteristic
18#16837318—22no—
19#16837272C2211yescharacteristic
20#16837262—21no—
21#16837259—21no—
22D4⋊(C59⋊C8)—22no—
23#16837129—22no—
24C2×C4⋊Q8×C59C2211yescharacteristic
25C2×C4×D4×C59C2211yescharacteristic
26C59×#476—22no—
27C59×#476—22no—
28C2×#106×C59—21no—
29C2×C4⋊C8×C59C2211yescharacteristic
30C2×#102×C59—21no—
31C22×D236D411yescharacteristic
32C22×C22⋊D59—22no—
33C22×C4×D59—21no—
34C22×C59⋊C8—21no—
35C22×C59⋊C8—21no—
36#14273701—42no—
37#14273701—42no—
38#14273698—42no—
39#14273698—42no—
40C4×D236—21no—
41C4×D236—21no—
42C4×D236—21no—
43C4×D236—21no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59—21no—
46C2×C4⋊Dic59D411yescharacteristic
47C2×C4⋊Dic59D412yes—
48C2×C22⋊Dic59—22no—
49C2×(C2×D59)⋊C4—22no—
50C2×(C2×D59)⋊C4—21no—
51#14273658—24no—
52C4⋊(C59⋊C8)—21no—
53C4⋊(C59⋊C8)D412yescomplemented
54#14273651—44no—
55#14273647—24no—
56C4×C59⋊C8—21no—
57C4×C59⋊C8—21no—
58C59⋊#95—22no—
59C22×Q8×C59—21no—
60C22×D4×C59D411yescharacteristic
61C23×C4×C59—21no—
62C22×C8×C59—21no—
63C4⋊Q8×C59—21no—
64C4⋊Q8×C59—21no—
65C4⋊Q8×C59—21no—
66C4⋊Q8×C59D412yescomplemented
67C4×D4×C59—21no—
68C4×D4×C59—21no—
69C4×D4×C59—21no—
70C4×D4×C59—21no—
71C2×C4⋊C4×C59—21no—
72C2×C4⋊C4×C59—21no—
73C2×C4⋊C4×C59D411yescharacteristic
74C2×C22⋊C4×C59—21no—
75C2×C42×C59C2311yescharacteristic
76#106×C59—24no—
77C4⋊C8×C59—21no—
78C4⋊C8×C59D412yescomplemented
79#102×C59—24no—
80C24×C59—21no—
81C23×D59—21no—
82C2×Q8×C59—22no—
83C2×Q8×C59—42no—
84C2×Q8×C59—42no—
85C2×Q8×C59—41no—
86C2×D4×C59—21no—
87C2×D4×C59—21no—
88C2×D4×C59—21no—
89C2×D4×C59—21no—
90C2×D4×C59—21no—
91C2×D4×C59SD1612yes—
92C22×C4×C59—21no—
93C22×C4×C59—41no—
94C22×C4×C59—41no—
95C22×C4×C59—41no—
96C22×C4×C59—41no—
97C22×C4×C59—41no—
98C22×C4×C59—41no—
99C22×C4×C59—41no—
100C22×C4×C59C2×D411yescharacteristic
101C22×C4×C59C2×D411yescharacteristic
102C22×C4×C59C2×D411yescharacteristic
103C2×C22⋊D59—44no—
104C2×C22⋊D59—44no—
105C2×C22⋊D59—82no—
106C22×Dic59—21no—
107C22×Dic59—22no—
108C2×D236—21no—
109C2×D236—21no—
110C2×D236—21no—
111C2×D236—21no—
112C2×D236—21no—
113C2×D236SD1612yes—
114C2×C4×D59—41no—
115C2×C4×D59—41no—
116C2×C4×D59—41no—
117C2×C4×D59—41no—
118C2×C4×D59—41no—
119C2×C4×D59—41no—
120C2×C8×C59—22no—
121C2×C8×C59—41no—
122C2×C8×C59—41no—
123C4⋊C4×C59—22no—
124C4⋊C4×C59—21no—
125C4⋊C4×C59—22no—
126C4⋊C4×C59—21no—
127C4⋊C4×C59—41no—
128C4⋊C4×C59—41no—
129C22⋊C4×C59—41no—
130C22⋊C4×C59—41no—
131C42×C59C2×D411yescharacteristic
132C42×C59C2×D411yescharacteristic
133C42×C59C2×D411yescharacteristic
134C42×C59#4111yescharacteristic
135C22⋊Dic59—44no—
136(C2×D59)⋊C4—44no—
137(C2×D59)⋊C4—41no—
138(C2×D59)⋊C4—41no—
139C4⋊Dic59—21no—
140C4⋊Dic59—21no—
141C4⋊Dic59—41no—
142C4⋊Dic59—41no—
143C4⋊Dic59—41no—
144C4⋊Dic59—41no—
145C4⋊Dic59—42no—
146C2×C59⋊C8—22no—
147C2×C59⋊C8—22no—
148C2×C59⋊C8—41no—
149C2×C59⋊C8—41no—
150C2×C59⋊C8—41no—
151C2×C59⋊C8—41no—
152C23×C59—22no—
153C23×C59—41no—
154C23×C59—41no—
155C23×C59—41no—
156C23×C59—41no—
157C23×C59—41no—
158C23×C59—41no—
159C23×C59#12011yescharacteristic
160C22×D59—22no—
161C22×D59—41no—
162C22×D59—41no—
163C22×D59—41no—
164C22×D59—41no—
165C22×D59—41no—
166C22×D59—41no—
167Q8×C59—44no—
168Q8×C59—82no—
169D4×C59—22no—
170D4×C59—22no—
171D4×C59—41no—
172D4×C59—41no—
173C2×C4×C59—21no—
174C2×C4×C59—21no—
175C2×C4×C59—41no—
176C2×C4×C59—42no—
177C2×C4×C59—41no—
178C2×C4×C59—41no—
179C2×C4×C59—81no—
180C2×C4×C59—81no—
181C2×C4×C59—81no—
182C2×C4×C59—81no—
183C2×C4×C59—81no—
184C2×C4×C59—81no—
185C2×C4×C59#12011yescharacteristic
186C2×C4×C59#12011yescharacteristic
187C2×C4×C59#12111yescharacteristic
188C2×C4×C59#12111yescharacteristic
189C2×C4×C59#12111yescharacteristic
190C2×C4×C59#12711yescharacteristic
191C2×C4×C59C2×SD1611yescharacteristic
192C2×C4×C59C2×SD1611yescharacteristic
193C2×C4×C59#13511yescharacteristic
194C2×C4×C59#13511yescharacteristic
195C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
196C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
197C2×C4×C59#13711yescharacteristic
198C2×C4×C59#13711yescharacteristic
199C22⋊D59—88no—
200C2×Dic59—41no—
201C2×Dic59—42no—
202C2×Dic59—42no—
203C2×Dic59—41no—
204C2×Dic59—41no—
205C2×Dic59—42no—
206D236—22no—
207D236—22no—
208D236—41no—
209D236—41no—
210C4×D59—81no—
211C4×D59—81no—
212C4×D59—81no—
213C4×D59—81no—
214C8×C59—42no—
215C59⋊C8—42no—
216C59⋊C8—42no—
217#10235—591nomaximal, Sylow
218C22×C59—42no—
219C22×C59—42no—
220C22×C59—42no—
221C22×C59—81no—
222C22×C59—81no—
223C22×C59—81no—
224C22×C59—81no—
225C22×C59#39211yescharacteristic
226C22×C59#45011yescharacteristic
227C22×C59#45011yescharacteristic
228C22×C59#45211yescharacteristic
229C22×C59#45211yescharacteristic
230C22×C59#45311yescharacteristic
231C22×C59#45411yescharacteristic
232C2×D59—42no—
233C2×D59—42no—
234C2×D59—42no—
235C2×D59—81no—
236C2×D59—81no—
237C2×D59—81no—
238C2×D59—81no—
239C4×C59—21no—
240C4×C59—21no—
241C4×C59—81no—
242C4×C59—82no—
243C4×C59#44811yescharacteristic
244C4×C59#44811yescharacteristic
245C4×C59#44911yescharacteristic
246C4×C59#44911yescharacteristic
247C4×C59#46511yescharacteristic
248C4×C59#46511yescharacteristic
249C4×C59#46811yescharacteristic
250C4×C59#46811yescharacteristic
251Dic59—82no—
252Dic59—81no—
253C2×#476—591no—
254C2×#476D5911yescharacteristic, complemented
255#2537—591no—
256#1956—591no—
257C2×D4⋊C8—591no—
258C2×D4⋊C8—591no—
259#1296—591no—
260C2×C59—82no—
261C2×C59#162911yescharacteristic
262C2×C59#163411yescharacteristic
263C2×C59#163511yescharacteristic
264C2×C59#163511yescharacteristic
265C2×C59#200011yescharacteristic
266C2×C59#200011yescharacteristic
267C2×C59#200611yescharacteristic
268D59—82no—
269C2×C4⋊Q8C2×D5911yescharacteristic
270C2×#121—1181no—
271C2×#121—1181no—
272C2×C4×D4—591no—
273C2×C4×D4C2×D5911yescharacteristic
274#476—22no—
275#476—22no—
276#476—1182no—
277#476—1182no—
278C2×#106—21no—
279C2×#106—1181no—
280C2×C4⋊C8—591no—
281C2×C4⋊C8C2×D5911yescharacteristic
282C2×#103—1182no—
283C2×#102—21no—
284C2×#102—1181no—
285C2×C4×C8—591no—
286#394—1182no—
287#384—591no—
288#380—1181no—
289#380—1181no—
290D4⋊C8—1182no—
291D4⋊C8—1182no—
292C59#1023511yescharacteristic, complemented, Sylow
293C22×Q8—21no—
294C22×D4—591no—
295C22×D4—1182no—
296C22×D4C22⋊D5911yescharacteristic
297C23×C4—21no—
298C23×C4—1181no—
299C22×C8—21no—
300C22×C8—1181no—
301C22×C8—1181no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8C22⋊D5912yescomplemented
306#121—2362no—
307#121—2362no—
308#121—2362no—
309#121—2362no—
310C4×D4—21no—
311C4×D4—21no—
312C4×D4—21no—
313C4×D4—21no—
314C4×D4—1181no—
315C4×D4—1181no—
316C4×D4—1181no—
317C4×D4—1181no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—591no—
321C2×C4⋊C4—592no—
322C2×C4⋊C4—1181no—
323C2×C4⋊C4—1181no—
324C2×C4⋊C4C22⋊D5911yescharacteristic
325C2×C22⋊C4—21no—
326C2×C22⋊C4—1182no—
327C2×C22⋊C4—1182no—
328C2×C22⋊C4—1181no—
329C2×C42C22×D5911yescharacteristic
330#106—24no—
331#106—1184no—
332C4⋊C8—21no—
333C4⋊C8—592no—
334C4⋊C8—1181no—
335C4⋊C8C22⋊D5912yescomplemented
336#103—2364no—
337#102—24no—
338#102—1184no—
339C4×C8—1181no—
340C4×C8—1181no—
341#95—1182no—
342C24—21no—
343C24—1181no—
344C2×Q8—22no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—41no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—21no—
351C2×D4—21no—
352C2×D4—21no—
353C2×D4—592no—
354C2×D4—1181no—
355C2×D4—1181no—
356C2×D4—1181no—
357C2×D4—1181no—
358C2×D4—1181no—
359C2×D4—4722no—
360C2×D4—2364no—
361C2×D4—2364no—
362C2×D4#1174567112yes—
363C22×C4—21no—
364C22×C4—41no—
365C22×C4—41no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—41no—
369C22×C4—41no—
370C22×C4—41no—
371C22×C4—1181no—
372C22×C4—1182no—
373C22×C4—2361no—
374C22×C4—2361no—
375C22×C4—2361no—
376C22×C4—2361no—
377C22×C4—2361no—
378C22×C4—2361no—
379C22×C4D4×D5911yescharacteristic
380C22×C4D4×D5911yescharacteristic
381C22×C4C2×C22⋊D5911yescharacteristic
382C2×C8—22no—
383C2×C8—41no—
384C2×C8—41no—
385C2×C8—1182no—
386C2×C8—1182no—
387C2×C8—2361no—
388C2×C8—2361no—
389C2×C8—2361no—
390C2×C8—2361no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—21no—
394C4⋊C4—21no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—1181no—
398C4⋊C4—1181no—
399C4⋊C4—2362no—
400C4⋊C4—2361no—
401C4⋊C4—2361no—
402C4⋊C4—2361no—
403C4⋊C4—2361no—
404C22⋊C4—41no—
405C22⋊C4—41no—
406C22⋊C4—2364no—
407C22⋊C4—2364no—
408C22⋊C4—2361no—
409C22⋊C4—2361no—
410C42D4×D5911yescharacteristic
411C42#1174568711yescharacteristic
412C42C2×C22⋊D5911yescharacteristic
413C42C2×C22⋊D5911yescharacteristic
414C23—22no—
415C23—41no—
416C23—41no—
417C23—41no—
418C23—41no—
419C23—41no—
420C23—41no—
421C23—1182no—
422C23—2361no—
423C23—2361no—
424C23—2361no—
425C23—2361no—
426C23—2361no—
427C23—2361no—
428C23#1427369511yescharacteristic
429Q8—44no—
430Q8—82no—
431D4—22no—
432D4—22no—
433D4—41no—
434D4—41no—
435D4—1182no—
436D4—1182no—
437D4—4728no—
438D4—2361no—
439D4—2361no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—42no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4—81no—
449C2×C4—81no—
450C2×C4—81no—
451C2×C4—81no—
452C2×C4—4721no—
453C2×C4—4721no—
454C2×C4—4721no—
455C2×C4—4721no—
456C2×C4—2362no—
457C2×C4—2361no—
458C2×C4—2362no—
459C2×C4—2361no—
460C2×C4—2361no—
461C2×C4—2362no—
462C2×C4#1427369511yescharacteristic
463C2×C4#1427369611yescharacteristic
464C2×C4#1427369811yescharacteristic
465C2×C4#1427369911yescharacteristic
466C2×C4#1427369911yescharacteristic
467C2×C4#1427372311yescharacteristic
468C2×C4SD16×D5911yescharacteristic
469C2×C4C2×#1174567111yescharacteristic
470C2×C4#1427374711yescharacteristic
471C2×C4#1427374811yescharacteristic
472C2×C4#1427375211yescharacteristic
473C2×C4#1427375411yescharacteristic
474C2×C4#1427375611yescharacteristic
475C2×C4#1427375811yescharacteristic
476C8—42no—
477C8—2362no—
478C8—2362no—
479C22—42no—
480C22—42no—
481C22—42no—
482C22—81no—
483C22—81no—
484C22—81no—
485C22—81no—
486C22—4721no—
487C22—4721no—
488C22—4721no—
489C22—4721no—
490C22—2362no—
491C22—2362no—
492C22—2362no—
493C22#1683731011yescharacteristic
494C22#1683755111yescharacteristic
495C22#1683755211yescharacteristic
496C22#1683756111yescharacteristic
497C22#1683756211yescharacteristic
498C22#1683756811yescharacteristic
499C22#1683757311yescharacteristic
500C4—21no—
501C4—21no—
502C4—81no—
503C4—82no—
504C4—4722no—
505C4—4721no—
506C4#1683753911yescharacteristic
507C4#1683754111yescharacteristic
508C4#1683754611yescharacteristic
509C4#1683754711yescharacteristic
510C4#1683762811yescharacteristic
511C4#1683763311yescharacteristic
512C4#1683764511yescharacteristic
513C4#1683765011yescharacteristic
514C2—82no—
515C2—4722no—
516C2#2142321111yescharacteristic
517C2#2142324011yescharacteristic
518C2#2142324511yescharacteristic
519C2#2142324611yescharacteristic
520C2#2142509611yescharacteristic
521C2#2142509711yescharacteristic
522C2#2142513611yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC2×C59×#476C2
socleC23×C59#120
prime radical#21429009C2
hypercenterC2×#476D59
hypocenterC59#10235
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#16837689C2semidirect
3. #21424899C2semidirect
4. C2×D4⋊(C59⋊C8)C2semidirect
5. C2×#16837129C2semidirect
6. #21421980C2semidirect
7. C2×C59×#476C2semidirect
53. C4⋊(C59⋊C8)D4semidirect
66. C4⋊Q8×C59D4semidirect
78. C4⋊C8×C59D4semidirect
254. C2×#476D59semidirect
292. C59#10235semidirect
305. C4⋊Q8C22⋊D59semidirect
335. C4⋊C8C22⋊D59semidirect

Maximal subgroups

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

subgroupindex
C2×#168376892
#214290092
#214248992
C2×D4⋊(C59⋊C8)2
C2×#168371292
#214219802
C2×C59×#4762
#1023559