Finite Group Databasebeta

← #28490990

Subgroups — #28490990

Order 15104.

744 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837599C211yesmaximal, characteristic, complemented
2#21429018C211yesmaximal, characteristic, complemented
3#21424903C211yesmaximal, characteristic, complemented
4C2×#16837132C211yesmaximal, characteristic, complemented
5C2×D4⋊(C59⋊C8)C211yesmaximal, characteristic, complemented
6#21421980C211yesmaximal, characteristic, complemented
7C2×C59×#459C211yesmaximal, characteristic
8C22×#11745670—21no—
9C2×#14273706—21no—
10C2×C4×Dic118C2211yescharacteristic
11#16837599—22no—
12#16837599—22no—
13C2×C4⋊(C59⋊C8)C2211yescharacteristic
14C2×#14273648—21no—
15C2×#14273648—22no—
16C2×C4×C59⋊C8C2211yescharacteristic
17#16837325—22no—
18#16837305—21no—
19#16837298—21no—
20#16837272C2211yescharacteristic
21#16837262—21no—
22#16837132—22no—
23D4⋊(C59⋊C8)—22no—
24C22×D8×C59—21no—
25C2×#127×C59C2211yescharacteristic
26C2×C4×D4×C59C2211yescharacteristic
27C59×#459—22no—
28C59×#459—22no—
29C2×C4⋊C8×C59C2211yescharacteristic
30C2×#102×C59—21no—
31C22×Dic118D411yescharacteristic
32C2×#11745670—24no—
33C2×#11745670—42no—
34C2×#11745670—42no—
35C22×C59⋊C8—21no—
36C22×C59⋊C8—21no—
37#14273706—42no—
38#14273706—42no—
39C4×Dic118—21no—
40C4×Dic118—21no—
41C4×Dic118—21no—
42C4×Dic118—21no—
43C2×C4⋊Dic59—21no—
44C2×C4⋊Dic59—21no—
45C2×C4⋊Dic59D411yescharacteristic
46C2×C4⋊Dic59D412yes—
47C2×Dic59⋊C4—22no—
48C2×Dic59⋊C4—21no—
49C2×C22⋊Dic59—22no—
50C2×C22⋊Dic59—22no—
51C2×C4×Dic59—21no—
52C4⋊(C59⋊C8)—21no—
53C4⋊(C59⋊C8)D412yes—
54#14273648—24no—
55#14273648—44no—
56C4×C59⋊C8—21no—
57C4×C59⋊C8—21no—
58C59⋊#95—22no—
59C22×D4×C59—21no—
60C22×D4×C59—21no—
61C22×D4×C59—21no—
62C22×D4×C59D411yescharacteristic
63C23×C4×C59—21no—
64C2×D8×C59—24no—
65C2×D8×C59—42no—
66C2×D8×C59—42no—
67C22×C8×C59—21no—
68#127×C59—21no—
69#127×C59—21no—
70#127×C59—21no—
71#127×C59D412yes—
72C4×D4×C59—21no—
73C4×D4×C59—21no—
74C4×D4×C59—21no—
75C4×D4×C59—21no—
76C2×C4⋊C4×C59D411yescharacteristic
77C2×C22⋊C4×C59—21no—
78C2×C42×C59C2311yescharacteristic
79C4⋊C8×C59—21no—
80C4⋊C8×C59D412yes—
81#102×C59—24no—
82C24×C59—21no—
83C24×C59—41no—
84C2×D4×C59—21no—
85C2×D4×C59—22no—
86C2×D4×C59—22no—
87C2×D4×C59—21no—
88C2×D4×C59—22no—
89C2×D4×C59—21no—
90C2×D4×C59—21no—
91C2×D4×C59—21no—
92C2×D4×C59—42no—
93C2×D4×C59—42no—
94C2×D4×C59—41no—
95C2×D4×C59—41no—
96C2×D4×C59—41no—
97C2×D4×C59—41no—
98C2×D4×C59—41no—
99C2×D4×C59—41no—
100C2×D4×C59—41no—
101C2×D4×C59—41no—
102C2×D4×C59—41no—
103C2×D4×C59—41no—
104C2×D4×C59—41no—
105C2×D4×C59SD1612yescomplemented
106C22×C4×C59—21no—
107C22×C4×C59—41no—
108C22×C4×C59—41no—
109C22×C4×C59—41no—
110C22×C4×C59—41no—
111C22×C4×C59—41no—
112C22×C4×C59—41no—
113C22×C4×C59C2×D411yescharacteristic
114C22×C4×C59C2×D411yescharacteristic
115C22×C4×C59C2×D411yescharacteristic
116C22×Dic59—21no—
117C22×Dic59—21no—
118C22×Dic59—22no—
119C2×Dic118—21no—
120C2×Dic118—21no—
121C2×Dic118—21no—
122C2×Dic118—21no—
123C2×Dic118—21no—
124C2×Dic118D812yescomplemented
125D8×C59—48no—
126C2×C8×C59—22no—
127C2×C8×C59—41no—
128C2×C8×C59—41no—
129C4⋊C4×C59—21no—
130C4⋊C4×C59—21no—
131C22⋊C4×C59—41no—
132C22⋊C4×C59—41no—
133C42×C59C2×D411yescharacteristic
134C42×C59C2×D411yescharacteristic
135C42×C59C2×D411yescharacteristic
136C42×C59#4111yescharacteristic
137C22⋊Dic59—44no—
138C22⋊Dic59—82no—
139#11745670—48no—
140C4⋊Dic59—21no—
141C4⋊Dic59—21no—
142C4⋊Dic59—41no—
143C4⋊Dic59—41no—
144C4⋊Dic59—41no—
145C4⋊Dic59—41no—
146C4⋊Dic59—42no—
147Dic59⋊C4—44no—
148Dic59⋊C4—41no—
149Dic59⋊C4—41no—
150C4×Dic59—41no—
151C4×Dic59—41no—
152C2×C59⋊C8—22no—
153C2×C59⋊C8—22no—
154C2×C59⋊C8—41no—
155C2×C59⋊C8—41no—
156C2×C59⋊C8—41no—
157C2×C59⋊C8—41no—
158C23×C59—22no—
159C23×C59—41no—
160C23×C59—41no—
161C23×C59—41no—
162C23×C59—41no—
163C23×C59—41no—
164C23×C59—41no—
165C23×C59—42no—
166C23×C59—81no—
167C23×C59—81no—
168C23×C59—81no—
169C23×C59—81no—
170C23×C59—81no—
171C23×C59—81no—
172C23×C59#12011yescharacteristic
173D4×C59—22no—
174D4×C59—22no—
175D4×C59—44no—
176D4×C59—42no—
177D4×C59—42no—
178D4×C59—42no—
179D4×C59—41no—
180D4×C59—42no—
181D4×C59—41no—
182D4×C59—82no—
183D4×C59—81no—
184D4×C59—81no—
185D4×C59—81no—
186D4×C59—81no—
187C2×C4×C59—21no—
188C2×C4×C59—21no—
189C2×C4×C59—41no—
190C2×C4×C59—41no—
191C2×C4×C59—41no—
192C2×C4×C59—81no—
193C2×C4×C59—81no—
194C2×C4×C59—81no—
195C2×C4×C59—81no—
196C2×C4×C59#12011yescharacteristic
197C2×C4×C59#12011yescharacteristic
198C2×C4×C59#12111yescharacteristic
199C2×C4×C59#12111yescharacteristic
200C2×C4×C59#12111yescharacteristic
201C2×C4×C59#12711yescharacteristic
202C2×C4×C59C2×D811yescharacteristic
203C2×C4×C59C2×SD1611yescharacteristic
204C2×C4×C59#13511yescharacteristic
205C2×C4×C59#13511yescharacteristic
206C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
208C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
209C2×C4×C59#13711yescharacteristic
210C2×Dic59—22no—
211C2×Dic59—41no—
212C2×Dic59—41no—
213C2×Dic59—41no—
214C2×Dic59—42no—
215C2×Dic59—42no—
216C2×Dic59—42no—
217C2×Dic59—41no—
218C2×Dic59—41no—
219Dic118—22no—
220Dic118—22no—
221Dic118—41no—
222Dic118—41no—
223C8×C59—42no—
224C59⋊C8—42no—
225C59⋊C8—42no—
226#10229—591nomaximal, Sylow
227C22×C59—42no—
228C22×C59—42no—
229C22×C59—42no—
230C22×C59—81no—
231C22×C59—81no—
232C22×C59—81no—
233C22×C59—81no—
234C22×C59—82no—
235C22×C59—82no—
236C22×C59—82no—
237C22×C59—161no—
238C22×C59—161no—
239C22×C59—161no—
240C22×C59—161no—
241C22×C59#39211yescharacteristic
242C22×C59#44711yescharacteristic
243C22×C59#44811yescharacteristic
244C22×C59#44911yescharacteristic
245C22×C59#44911yescharacteristic
246C22×C59#45311yescharacteristic
247C22×C59#45411yescharacteristic
248C4×C59—21no—
249C4×C59—21no—
250C4×C59—81no—
251C4×C59#44711yescharacteristic
252C4×C59#44911yescharacteristic
253C4×C59#45011yescharacteristic
254C4×C59#45211yescharacteristic
255C4×C59#46511yescharacteristic
256C4×C59#46611yescharacteristic
257C4×C59#46811yescharacteristic
258C4×C59#46911yescharacteristic
259Dic59—42no—
260Dic59—82no—
261Dic59—81no—
262C2×#460—591no—
263C2×#459D5911yescharacteristic
264#2538—591no—
265#1957—591no—
266C2×Q8⋊C8—591no—
267C2×D4⋊C8—591no—
268#1296—591no—
269C2×C59—82no—
270C2×C59—162no—
271C2×C59#162111yescharacteristic
272C2×C59#162211yescharacteristic
273C2×C59#162711yescharacteristic
274C2×C59#162811yescharacteristic
275C2×C59#199911yescharacteristic
276C2×C59#200011yescharacteristic
277C2×C59#200611yescharacteristic
278C22×SD16—1181no—
279C22×D8—21no—
280C2×#127C2×D5911yescharacteristic
281C2×C22⋊Q8—1181no—
282C2×C4×Q8—591no—
283C2×C4×D4C2×D5911yescharacteristic
284#460—1182no—
285#460—1182no—
286#459—22no—
287#459—22no—
288C2×C4⋊C8—591no—
289C2×C4⋊C8C2×D5911yescharacteristic
290C2×#102—21no—
291C2×#102—1181no—
292C2×#102—1182no—
293C2×C4×C8—591no—
294#396—1182no—
295#390—1181no—
296#389—1181no—
297#384—591no—
298#380—1181no—
299Q8⋊C8—1182no—
300D4⋊C8—1182no—
301C59#1022911yescharacteristic, complemented, Sylow
302C22×Q8—591no—
303C22×D4—21no—
304C22×D4—21no—
305C22×D4—21no—
306C22×D4C22⋊D5911yescharacteristic
307C23×C4—21no—
308C2×SD16—1184no—
309C2×SD16—2362no—
310C2×SD16—2362no—
311C2×D8—24no—
312C2×D8—42no—
313C2×D8—42no—
314C22×C8—21no—
315C22×C8—1181no—
316C22×C8—1181no—
317#127—21no—
318#127—21no—
319#127—21no—
320#127C22⋊D5912yes—
321C22⋊Q8—2362no—
322C22⋊Q8—2362no—
323C4×Q8—1181no—
324C4×Q8—1181no—
325C4×Q8—1181no—
326C4×Q8—1181no—
327C4×D4—21no—
328C4×D4—21no—
329C4×D4—21no—
330C4×D4—21no—
331C2×C4⋊C4—591no—
332C2×C4⋊C4—592no—
333C2×C4⋊C4—1182no—
334C2×C4⋊C4—1181no—
335C2×C4⋊C4—1181no—
336C2×C4⋊C4—1181no—
337C2×C4⋊C4C22⋊D5911yescharacteristic
338C2×C22⋊C4—21no—
339C2×C22⋊C4—1182no—
340C2×C22⋊C4—1182no—
341C2×C42—1181no—
342C2×C42C22×D5911yescharacteristic
343C4⋊C8—21no—
344C4⋊C8—592no—
345C4⋊C8—1181no—
346C4⋊C8C22⋊D5912yes—
347#102—24no—
348#102—1184no—
349#102—2364no—
350C4×C8—1181no—
351C4×C8—1181no—
352#95—1182no—
353C24—21no—
354C24—41no—
355C2×Q8—592no—
356C2×Q8—1181no—
357C2×Q8—1181no—
358C2×Q8—1181no—
359C2×Q8—1181no—
360C2×Q8—1181no—
361C2×D4—22no—
362C2×D4—21no—
363C2×D4—22no—
364C2×D4—21no—
365C2×D4—22no—
366C2×D4—21no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4—42no—
370C2×D4—42no—
371C2×D4—41no—
372C2×D4—41no—
373C2×D4—41no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—41no—
378C2×D4—41no—
379C2×D4—41no—
380C2×D4—41no—
381C2×D4—41no—
382C2×D4#1174567012yescomplemented
383C22×C4—21no—
384C22×C4—41no—
385C22×C4—41no—
386C22×C4—41no—
387C22×C4—41no—
388C22×C4—41no—
389C22×C4—41no—
390C22×C4—1181no—
391C22×C4—1181no—
392C22×C4—1182no—
393C22×C4D4×D5911yescharacteristic
394C22×C4D4×D5911yescharacteristic
395C22×C4C2×C22⋊D5911yescharacteristic
396SD16—2368no—
397D8—48no—
398C2×C8—22no—
399C2×C8—41no—
400C2×C8—41no—
401C2×C8—1182no—
402C2×C8—1182no—
403C2×C8—2361no—
404C2×C8—2361no—
405C2×C8—2361no—
406C2×C8—2361no—
407C4⋊C4—21no—
408C4⋊C4—21no—
409C4⋊C4—1181no—
410C4⋊C4—1181no—
411C4⋊C4—2362no—
412C4⋊C4—2364no—
413C4⋊C4—2361no—
414C4⋊C4—2361no—
415C4⋊C4—2361no—
416C4⋊C4—2361no—
417C4⋊C4—2361no—
418C4⋊C4—2361no—
419C22⋊C4—41no—
420C22⋊C4—41no—
421C22⋊C4—4722no—
422C22⋊C4—2364no—
423C42—2361no—
424C42—2361no—
425C42D4×D5911yescharacteristic
426C42#1174568711yescharacteristic
427C42C2×C22⋊D5911yescharacteristic
428C42C2×C22⋊D5911yescharacteristic
429C23—22no—
430C23—41no—
431C23—41no—
432C23—41no—
433C23—41no—
434C23—41no—
435C23—41no—
436C23—42no—
437C23—81no—
438C23—81no—
439C23—81no—
440C23—81no—
441C23—81no—
442C23—81no—
443C23#1427369511yescharacteristic
444Q8—1182no—
445Q8—1182no—
446Q8—2361no—
447Q8—2361no—
448D4—22no—
449D4—22no—
450D4—44no—
451D4—41no—
452D4—42no—
453D4—42no—
454D4—42no—
455D4—41no—
456D4—42no—
457D4—82no—
458D4—81no—
459D4—81no—
460D4—81no—
461D4—81no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—81no—
471C2×C4—1182no—
472C2×C4—2362no—
473C2×C4—2362no—
474C2×C4—2361no—
475C2×C4—2361no—
476C2×C4—2362no—
477C2×C4—2361no—
478C2×C4—2361no—
479C2×C4—2361no—
480C2×C4#1427369511yescharacteristic
481C2×C4#1427369611yescharacteristic
482C2×C4#1427369811yescharacteristic
483C2×C4#1427369911yescharacteristic
484C2×C4#1427369911yescharacteristic
485C2×C4#1427372311yescharacteristic
486C2×C4D8×D5911yescharacteristic
487C2×C4C2×#1174567011yescharacteristic
488C2×C4#1427374611yescharacteristic
489C2×C4#1427374711yescharacteristic
490C2×C4#1427375111yescharacteristic
491C2×C4#1427375111yescharacteristic
492C2×C4#1427375311yescharacteristic
493C2×C4#1427375711yescharacteristic
494C8—42no—
495C8—2362no—
496C8—2362no—
497C22—42no—
498C22—42no—
499C22—42no—
500C22—81no—
501C22—81no—
502C22—81no—
503C22—81no—
504C22—82no—
505C22—82no—
506C22—82no—
507C22—161no—
508C22—161no—
509C22—161no—
510C22—161no—
511C22#1683731011yescharacteristic
512C22#1683753411yescharacteristic
513C22#1683754011yescharacteristic
514C22#1683754411yescharacteristic
515C22#1683754511yescharacteristic
516C22#1683756811yescharacteristic
517C22#1683757311yescharacteristic
518C4—21no—
519C4—21no—
520C4—81no—
521C4—4722no—
522C4—4721no—
523C4—2362no—
524C4#1683753411yescharacteristic
525C4#1683754411yescharacteristic
526C4#1683755311yescharacteristic
527C4#1683756411yescharacteristic
528C4#1683762911yescharacteristic
529C4#1683763511yescharacteristic
530C4#1683764611yescharacteristic
531C4#1683765211yescharacteristic
532C2—82no—
533C2—162no—
534C2#2142316011yescharacteristic
535C2#2142316611yescharacteristic
536C2#2142319811yescharacteristic
537C2#2142320411yescharacteristic
538C2#2142509111yescharacteristic
539C2#2142509911yescharacteristic
540C2#2142513611yescharacteristic
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
Fitting, prime radicalC2×C59×#459C2
socleC23×C59#120
hypercenterC2×#459D59
hypocenterC59#10229
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#16837599C2semidirect
2. #21429018C2semidirect
3. #21424903C2semidirect
4. C2×#16837132C2semidirect
5. C2×D4⋊(C59⋊C8)C2semidirect
6. #21421980C2semidirect
105. C2×D4×C59SD16semidirect
124. C2×Dic118D8semidirect
301. C59#10229semidirect
382. C2×D4#11745670semidirect

Maximal subgroups

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

subgroupindex
C2×#168375992
#214290182
#214249032
C2×#168371322
C2×D4⋊(C59⋊C8)2
#214219802
C2×C59×#4592
#1022959