Finite Group Databasebeta

← C2×#21425297 #28616159

Subgroups — C2×#21425297 #28616159

Order 15104.

1662 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273703C211yesmaximal, characteristic
2C22×#14273660C211yesmaximal, characteristic, complemented
3C22×#14273651C211yesmaximal, characteristic, complemented
4C22×(C2×D59)⋊C8C211yesmaximal, characteristic
5C2×#16837259C211yesmaximal, characteristic
6#21425297C218yesmaximal, direct product factor
7C2×#16837165C211yesmaximal, characteristic, complemented
8C22×#103×C59C211yesmaximal, characteristic, complemented
9C23×C4×D59C2211yescharacteristic
10C23×C59⋊C8C2211yescharacteristic
11C2×#14273703—22no—
12C2×#14273703—24no—
13C2×#14273703—24no—
14C2×#14273703C2214yes—
15C22×C4⋊Dic59C2211yescharacteristic
16C22×C4⋊Dic59C2211yescharacteristic
17C22×Dic59⋊C4—21no—
18C22×(C2×D59)⋊C4—21no—
19C22×(C2×D59)⋊C4—21no—
20C2×#14273660—24no—
21C2×#14273660C2214yescomplemented
22C2×#14273651—24no—
23C2×#14273651C2214yescomplemented
24C2×(C2×D59)⋊C8—24no—
25C2×(C2×D59)⋊C8C2214yes—
26#16837259—22no—
27#16837259C2214yes—
28C2×C59⋊#95—21no—
29#16837165C2214yescomplemented
30C23×Q8×C59C2211yescharacteristic
31C23×C8×C59C2211yescharacteristic
32C22×C4⋊C4×C59C2211yescharacteristic
33C2×#103×C59—24no—
34C2×#103×C59C2214yescomplemented
35C24×D59D411yescharacteristic
36C23×Dic59—21no—
37C23×Dic59—21no—
38C23×Dic59D411yescharacteristic
39C22×C4×D59—22no—
40C22×C4×D59—22no—
41C22×C4×D59—22no—
42C22×C4×D59—22no—
43C22×C4×D59—22no—
44C22×C4×D59—22no—
45C22×C4×D59D412yes—
46C22×C4×D59C2312yes—
47C22×C59⋊C8—22no—
48C22×C59⋊C8—22no—
49C22×C59⋊C8D414yes—
50C22×C59⋊C8C2312yes—
51#14273703—216no—
52#14273703—28no—
53#14273703—28no—
54C2×C4⋊Dic59—21no—
55C2×C4⋊Dic59—22no—
56C2×C4⋊Dic59—22no—
57C2×C4⋊Dic59—22no—
58C2×C4⋊Dic59—21no—
59C2×C4⋊Dic59D414yes—
60C2×C4⋊Dic59C2312yes—
61C2×C4⋊Dic59C2312yes—
62C2×Dic59⋊C4—28no—
63C2×Dic59⋊C4—24no—
64C2×(C2×D59)⋊C4—28no—
65C2×(C2×D59)⋊C4—24no—
66C2×(C2×D59)⋊C4—24no—
67C2×(C2×D59)⋊C4—44no—
68#14273660—28no—
69#14273651—28no—
70(C2×D59)⋊C8—28no—
71C59⋊#95—24no—
72C22×Q8×C59—22no—
73C22×Q8×C59—21no—
74C22×Q8×C59—22no—
75C22×Q8×C59—22no—
76C22×Q8×C59—22no—
77C22×Q8×C59—22no—
78C22×Q8×C59D414yes—
79C22×Q8×C59C2312yes—
80C23×C4×C59—21no—
81C23×C4×C59—21no—
82C23×C4×C59C2311yescharacteristic
83C22×C8×C59—22no—
84C22×C8×C59—22no—
85C22×C8×C59—22no—
86C22×C8×C59C2312yes—
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—21no—
90C2×C4⋊C4×C59C2312yes—
91#103×C59—28no—
92C24×C59C2×D411yescharacteristic
93C23×D59—22no—
94C23×D59—22no—
95C23×D59—22no—
96C23×D59—22no—
97C23×D59—22no—
98C23×D59—22no—
99C23×D59Q1614yes—
100C23×D59C2×D412yes—
101C2×Q8×C59—24no—
102C2×Q8×C59—22no—
103C2×Q8×C59—28no—
104C2×Q8×C59—28no—
105C2×Q8×C59—22no—
106C2×Q8×C59—22no—
107C2×Q8×C59—22no—
108C2×Q8×C59—22no—
109C2×Q8×C59—42no—
110C2×Q8×C59—44no—
111C2×Q8×C59—42no—
112C2×Q8×C59—44no—
113C2×Q8×C59C2×D414yes—
114C22×C4×C59—24no—
115C22×C4×C59—22no—
116C22×C4×C59—22no—
117C22×C4×C59—42no—
118C22×C4×C59—42no—
119C22×C4×C59—42no—
120C22×C4×C59—42no—
121C22×C4×C59—42no—
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×D412yes—
124C22×C4×C59C2×D412yes—
125C22×C4×C59C2×D412yes—
126C22×C4×C59#4112yes—
127C22×C4×C59#4112yes—
128C22×C4×C59#4112yes—
129C22×C4×C59C2411yescharacteristic
130C22×Dic59—24no—
131C22×Dic59—22no—
132C22×Dic59—22no—
133C22×Dic59—22no—
134C22×Dic59—22no—
135C22×Dic59—22no—
136C22×Dic59—42no—
137C22×Dic59—42no—
138C22×Dic59—42no—
139C22×Dic59—42no—
140C22×Dic59—42no—
141C22×Dic59C2×D412yes—
142C2×C4×D59—24no—
143C2×C4×D59—24no—
144C2×C4×D59—24no—
145C2×C4×D59—22no—
146C2×C4×D59—22no—
147C2×C4×D59—22no—
148C2×C4×D59—22no—
149C2×C4×D59—22no—
150C2×C4×D59—22no—
151C2×C4×D59—44no—
152C2×C4×D59—44no—
153C2×C4×D59—44no—
154C2×C4×D59—44no—
155C2×C8×C59—22no—
156C2×C8×C59—22no—
157C2×C8×C59—22no—
158C2×C8×C59—44no—
159C4⋊C4×C59—22no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—42no—
162(C2×D59)⋊C4—216no—
163(C2×D59)⋊C4—48no—
164C4⋊Dic59—24no—
165C4⋊Dic59—22no—
166C4⋊Dic59—22no—
167C4⋊Dic59—22no—
168C4⋊Dic59—42no—
169C4⋊Dic59C2×D414yes—
170Dic59⋊C4—216no—
171C2×C59⋊C8—28no—
172C2×C59⋊C8—22no—
173C2×C59⋊C8—22no—
174C2×C59⋊C8C2×D414yes—
175C23×C59#12012yes—
176C23×C59#12112yes—
177C23×C59#12312yes—
178C23×C59C2×Q1612yes—
179C23×C59#13512yes—
180C23×C59AGL(1,ℤ/8)12yes—
181C23×C59#13712yes—
182C23×C59C22×D411yescharacteristic
183C22×D59—22no—
184C22×D59—22no—
185C22×D59—22no—
186C22×D59—22no—
187C22×D59—22no—
188C22×D59—22no—
189C22×D59—28no—
190C22×D59—28no—
191C22×D59—28no—
192C22×D59—44no—
193C22×D59—44no—
194C22×D59—44no—
195C22×D59—44no—
196C22×D59C2×Q1614yes—
197Q8×C59—24no—
198Q8×C59—24no—
199Q8×C59—42no—
200Q8×C59—42no—
201Q8×C59—48no—
202C2×C4×C59—24no—
203C2×C4×C59—42no—
204C2×C4×C59—42no—
205C2×C4×C59—48no—
206C2×C4×C59—42no—
207C2×C4×C59—42no—
208C2×C4×C59—42no—
209C2×C4×C59—84no—
210C2×C4×C59#12012yes—
211C2×C4×C59#12114yes—
212C2×C4×C59#12114yes—
213C2×C4×C59#12112yes—
214C2×C4×C59#12312yes—
215C2×C4×C59#12314yes—
216C2×C4×C59#12414yes—
217C2×C4×C59C22×D411yescharacteristic
218C2×C4×C59C22×D411yescharacteristic
219C2×C4×C59C22×D411yescharacteristic
220C2×C4×C59C2×#4111yescharacteristic
221C2×C4×C59C2×#4111yescharacteristic
222C2×C4×C59C2×#4111yescharacteristic
223C2×Dic59—22no—
224C2×Dic59—24no—
225C2×Dic59—22no—
226C2×Dic59—22no—
227C2×Dic59—42no—
228C2×Dic59—42no—
229C2×Dic59—44no—
230C2×Dic59—48no—
231C2×Dic59—42no—
232C2×Dic59—42no—
233C2×Dic59—42no—
234C2×Dic59—84no—
235C4×D59—42no—
236C4×D59—42no—
237C4×D59—42no—
238C4×D59—42no—
239C4×D59—48no—
240C8×C59—42no—
241C59⋊C8—24no—
242C2×#2036—591nomaximal, Sylow
243C22×C59#39414yes—
244C22×C59#44914yes—
245C22×C59#45114yes—
246C22×C59#46714yes—
247C22×C59#46814yes—
248C22×C59#48414yes—
249C22×C59#48514yes—
250C22×C59C2×#12011yescharacteristic
251C22×C59C2×#12111yescharacteristic
252C22×C59C2×#12311yescharacteristic
253C22×C59C22×Q1611yescharacteristic
254C22×C59C2×#13511yescharacteristic
255C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C59C2×#13711yescharacteristic
257C2×D59—24no—
258C2×D59—24no—
259C2×D59—24no—
260C2×D59—42no—
261C2×D59—42no—
262C2×D59—42no—
263C2×D59—42no—
264C2×D59—416no—
265C4×C59—44no—
266C4×C59—82no—
267C4×C59#39414yes—
268C4×C59C2×#12111yescharacteristic
269C4×C59C2×#12111yescharacteristic
270C4×C59C2×#12311yescharacteristic
271C4×C59C2×#12411yescharacteristic
272Dic59—42no—
273Dic59—44no—
274Dic59—82no—
275C22×C22⋊Q8—591no—
276C22×#107—591no—
277C22×#103—591no—
278C22×#103D5911yescharacteristic, complemented
279C22×C22⋊C8—591no—
280C2×#380—591no—
281#2036—598no—
282C2×#340—591no—
283C2×C59#203618yescomplemented
284C2×C59C2×#39411yescharacteristic
285C2×C59C2×#45111yescharacteristic
286C2×C59C2×#44911yescharacteristic
287C2×C59C2×#46711yescharacteristic
288C2×C59C2×#46811yescharacteristic
289C2×C59C2×#48511yescharacteristic
290C2×C59C2×#48411yescharacteristic
291D59—44no—
292C23×Q8C2×D5911yescharacteristic
293C24×C4—591no—
294C23×C8—591no—
295C23×C8C2×D5911yescharacteristic
296C2×C22⋊Q8—594no—
297C2×C22⋊Q8—1184no—
298C2×C22⋊Q8—1182no—
299C2×C22⋊Q8—1184no—
300C22×C4⋊C4—591no—
301C22×C4⋊C4—591no—
302C22×C4⋊C4—1181no—
303C22×C4⋊C4C2×D5911yescharacteristic
304C22×C22⋊C4—1181no—
305C22×C22⋊C4—1181no—
306C2×#107—594no—
307C2×#107—1184no—
308C2×#103—24no—
309C2×#103—594no—
310C2×#103—1184no—
311C2×#103C2×D5914yescomplemented
312C2×C22⋊C8—594no—
313C2×C22⋊C8—1184no—
314#380—594no—
315#380—1182no—
316C2×#95—1181no—
317#340—594no—
318C59C2×#203611yescharacteristic, complemented, Sylow
319C25—591no—
320C22×Q8—22no—
321C22×Q8—21no—
322C22×Q8—22no—
323C22×Q8—22no—
324C22×Q8—22no—
325C22×Q8—22no—
326C22×Q8C22⋊D5914yes—
327C22×Q8C22×D5912yes—
328C23×C4—21no—
329C23×C4—21no—
330C23×C4—591no—
331C23×C4—592no—
332C23×C4—592no—
333C23×C4—1181no—
334C23×C4—1182no—
335C23×C4—1182no—
336C23×C4—1182no—
337C23×C4—1182no—
338C23×C4—1182no—
339C23×C4—1182no—
340C23×C4—1181no—
341C23×C4C22×D5911yescharacteristic
342C22×C8—22no—
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—594no—
346C22×C8—592no—
347C22×C8—1182no—
348C22×C8—1182no—
349C22×C8C22×D5912yes—
350C22⋊Q8—1188no—
351C22⋊Q8—11816no—
352C22⋊Q8—1188no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—594no—
357C2×C4⋊C4—592no—
358C2×C4⋊C4—592no—
359C2×C4⋊C4—1184no—
360C2×C4⋊C4—1188no—
361C2×C4⋊C4—1181no—
362C2×C4⋊C4—1182no—
363C2×C4⋊C4—1182no—
364C2×C4⋊C4—1182no—
365C2×C4⋊C4—1181no—
366C2×C4⋊C4C22×D5912yes—
367C2×C22⋊C4—1184no—
368C2×C22⋊C4—1188no—
369C2×C22⋊C4—1184no—
370C2×C22⋊C4—2364no—
371#107—1188no—
372#103—28no—
373#103—1188no—
374C22⋊C8—1188no—
375#95—1184no—
376C24—594no—
377C24—592no—
378C24—1182no—
379C24—1182no—
380C24—1182no—
381C24—1182no—
382C24—1182no—
383C24—1182no—
384C24D4×D5911yescharacteristic
385C2×Q8—24no—
386C2×Q8—22no—
387C2×Q8—28no—
388C2×Q8—28no—
389C2×Q8—22no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—22no—
393C2×Q8—42no—
394C2×Q8—44no—
395C2×Q8—42no—
396C2×Q8—44no—
397C2×Q8C2×C22⋊D5914yes—
398C22×C4—24no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—42no—
402C22×C4—42no—
403C22×C4—42no—
404C22×C4—42no—
405C22×C4—42no—
406C22×C4—592no—
407C22×C4—1184no—
408C22×C4—1182no—
409C22×C4—1182no—
410C22×C4—1182no—
411C22×C4—1182no—
412C22×C4—1184no—
413C22×C4—1184no—
414C22×C4—1184no—
415C22×C4—1182no—
416C22×C4—1182no—
417C22×C4—1182no—
418C22×C4—1182no—
419C22×C4—1182no—
420C22×C4—1182no—
421C22×C4—1182no—
422C22×C4—2362no—
423C22×C4—2362no—
424C22×C4—2362no—
425C22×C4—2362no—
426C22×C4—2362no—
427C22×C4—2364no—
428C22×C4—2364no—
429C22×C4—2364no—
430C22×C4—2364no—
431C22×C4#1174568512yes—
432C22×C4#1174568512yes—
433C22×C4D4×D5911yescharacteristic
434C22×C4D4×D5912yes—
435C22×C4D4×D5912yes—
436C22×C4#1174568712yes—
437C22×C4C2×C22⋊D5912yes—
438C22×C4C23×D5911yescharacteristic
439C2×C8—22no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—44no—
443C2×C8—594no—
444C2×C8—1188no—
445C2×C8—1182no—
446C2×C8—1182no—
447C4⋊C4—22no—
448C4⋊C4—22no—
449C4⋊C4—42no—
450C4⋊C4—594no—
451C4⋊C4—11816no—
452C4⋊C4—1184no—
453C4⋊C4—1182no—
454C4⋊C4—1182no—
455C4⋊C4—1182no—
456C4⋊C4—2362no—
457C22⋊C4—11816no—
458C22⋊C4—2368no—
459C23—594no—
460C23—1182no—
461C23—1188no—
462C23—1182no—
463C23—1182no—
464C23—1182no—
465C23—1182no—
466C23—1188no—
467C23—1188no—
468C23—1182no—
469C23—2364no—
470C23—2364no—
471C23—2364no—
472C23—2364no—
473C23#1427369512yes—
474C23#1427370012yes—
475C23#1427370912yes—
476C23Q16×D5912yes—
477C23#1427374812yes—
478C23#1427375412yes—
479C23#1427375912yes—
480C23C2×D4×D5911yescharacteristic
481Q8—24no—
482Q8—24no—
483Q8—42no—
484Q8—42no—
485Q8—48no—
486C2×C4—24no—
487C2×C4—42no—
488C2×C4—42no—
489C2×C4—48no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—84no—
494C2×C4—1182no—
495C2×C4—1182no—
496C2×C4—1184no—
497C2×C4—1182no—
498C2×C4—4724no—
499C2×C4—2362no—
500C2×C4—2362no—
501C2×C4—2362no—
502C2×C4—2362no—
503C2×C4—2362no—
504C2×C4—2368no—
505C2×C4—2364no—
506C2×C4—2362no—
507C2×C4—2362no—
508C2×C4—2362no—
509C2×C4—2362no—
510C2×C4—2368no—
511C2×C4#1427369512yes—
512C2×C4#1427369914yes—
513C2×C4#1427370014yes—
514C2×C4#1427370012yes—
515C2×C4#1427370912yes—
516C2×C4#1427371014yes—
517C2×C4#1427371314yes—
518C2×C4C2×D4×D5911yescharacteristic
519C2×C4C2×D4×D5911yescharacteristic
520C2×C4C22×C22⋊D5911yescharacteristic
521C2×C4C2×#1174568711yescharacteristic
522C2×C4C2×#1174568511yescharacteristic
523C2×C4C2×#1174568511yescharacteristic
524C8—42no—
525C8—1184no—
526C22—1184no—
527C22—1184no—
528C22—1184no—
529C22—2362no—
530C22—2362no—
531C22—2362no—
532C22—23616no—
533C22—2362no—
534C22#1683731714yes—
535C22#1683754614yes—
536C22#1683755614yes—
537C22#1683764214yes—
538C22#1683765114yes—
539C22#1683773614yes—
540C22#1683774114yes—
541C22C2×#1427369511yescharacteristic
542C22C2×#1427370011yescharacteristic
543C22C2×#1427370911yescharacteristic
544C22C2×Q16×D5911yescharacteristic
545C22C2×#1427374811yescharacteristic
546C22C2×#1427375411yescharacteristic
547C22C2×#1427375911yescharacteristic
548C4—44no—
549C4—82no—
550C4—4722no—
551C4—2362no—
552C4—2364no—
553C4#1683731714yes—
554C4C2×#1427369911yescharacteristic
555C4C2×#1427370011yescharacteristic
556C4C2×#1427371011yescharacteristic
557C4C2×#1427371311yescharacteristic
558C2—2364no—
559C2#2142529718yesdirect product factor
560C2C2×#1683731711yescharacteristic
561C2C2×#1683755611yescharacteristic
562C2C2×#1683754611yescharacteristic
563C2C2×#1683764211yescharacteristic
564C2C2×#1683765111yescharacteristic
565C2C2×#1683774111yescharacteristic
566C2C2×#1683773611yescharacteristic
subgroupG/H
centerC24D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#103×C59C2
socleC24×C59C2×D4
prime radicalC24×D59D4
hypercenterC22×#103D59
hypocenterC59C2×#2036
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#14273660C2semidirect
3. C22×#14273651C2semidirect
6. #21425297C2direct (N × H)
7. C2×#16837165C2semidirect
8. C22×#103×C59C2semidirect
21. C2×#14273660C22semidirect
23. C2×#14273651C22semidirect
29. #16837165C22semidirect
34. C2×#103×C59C22semidirect
278. C22×#103D59semidirect
283. C2×C59#2036semidirect
311. C2×#103C2×D59semidirect
318. C59C2×#2036semidirect
559. C2#21425297direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737032
C22×#142736602
C22×#142736512
C22×(C2×D59)⋊C82
C2×#168372592
#214252972
C2×#168371652
C22×#103×C592
C2×#203659