Finite Group Databasebeta

← C2×#21425301 #28616163

Subgroups — C2×#21425301 #28616163

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×#14273707C211yesmaximal, characteristic
2C22×#14273652C211yesmaximal, characteristic, complemented
3C22×#14273650C211yesmaximal, characteristic, complemented
4C22×(C2×D59)⋊C8C211yesmaximal, characteristic
5C2×#16837259C211yesmaximal, characteristic
6#21425301C218yesmaximal, direct product factor
7C2×#16837164C211yesmaximal, characteristic, complemented
8C22×#107×C59C211yesmaximal, characteristic, complemented
9C23×Dic118C2211yescharacteristic
10C23×C4×D59C2211yescharacteristic
11C23×C59⋊C8C2211yescharacteristic
12C2×#14273707—24no—
13C2×#14273707—22no—
14C2×#14273707—24no—
15C2×#14273707C2214yes—
16C22×C4⋊Dic59—21no—
17C22×C4⋊Dic59C2211yescharacteristic
18C22×(C2×D59)⋊C4—21no—
19C22×(C2×D59)⋊C4—21no—
20C2×#14273652—24no—
21C2×#14273652C2214yescomplemented
22C2×#14273650—24no—
23C2×#14273650C2214yescomplemented
24C2×(C2×D59)⋊C8—24no—
25C2×(C2×D59)⋊C8C2214yes—
26#16837259—22no—
27#16837259C2214yes—
28C2×C59⋊#95—21no—
29#16837164C2214yescomplemented
30C23×C8×C59C2211yescharacteristic
31C22×C4⋊C4×C59C2211yescharacteristic
32C22×C4⋊C4×C59C2211yescharacteristic
33C2×#107×C59—24no—
34C2×#107×C59C2214yescomplemented
35C24×D59D411yescharacteristic
36C22×Dic118—22no—
37C22×Dic118—22no—
38C22×Dic118—22no—
39C22×Dic118—22no—
40C22×Dic118—21no—
41C22×Dic118—22no—
42C22×Dic118D414yes—
43C22×Dic118C2312yes—
44C23×Dic59—21no—
45C23×Dic59—21no—
46C23×Dic59D411yescharacteristic
47C22×C4×D59—22no—
48C22×C4×D59—22no—
49C22×C4×D59—22no—
50C22×C4×D59—22no—
51C22×C4×D59—22no—
52C22×C4×D59—22no—
53C22×C4×D59D412yes—
54C22×C4×D59C2312yes—
55C22×C59⋊C8—22no—
56C22×C59⋊C8—22no—
57C22×C59⋊C8—22no—
58C22×C59⋊C8C2312yes—
59#14273707—216no—
60#14273707—28no—
61#14273707—28no—
62C2×C4⋊Dic59—28no—
63C2×C4⋊Dic59—24no—
64C2×C4⋊Dic59—22no—
65C2×C4⋊Dic59—22no—
66C2×C4⋊Dic59—21no—
67C2×C4⋊Dic59C2312yes—
68C2×(C2×D59)⋊C4—28no—
69C2×(C2×D59)⋊C4—24no—
70C2×(C2×D59)⋊C4—24no—
71C2×(C2×D59)⋊C4—44no—
72#14273652—28no—
73#14273650—28no—
74(C2×D59)⋊C8—28no—
75C59⋊#95—24no—
76C23×C4×C59—21no—
77C23×C4×C59—21no—
78C23×C4×C59C2311yescharacteristic
79C22×C8×C59—22no—
80C22×C8×C59—22no—
81C22×C8×C59D414yes—
82C22×C8×C59C2312yes—
83C2×C4⋊C4×C59—21no—
84C2×C4⋊C4×C59—22no—
85C2×C4⋊C4×C59—22no—
86C2×C4⋊C4×C59—22no—
87C2×C4⋊C4×C59—21no—
88C2×C4⋊C4×C59D414yes—
89C2×C4⋊C4×C59C2312yes—
90C2×C4⋊C4×C59C2312yes—
91#107×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—
101C22×C4×C59—24no—
102C22×C4×C59—22no—
103C22×C4×C59—22no—
104C22×C4×C59—42no—
105C22×C4×C59—42no—
106C22×C4×C59—42no—
107C22×C4×C59—42no—
108C22×C4×C59—42no—
109C22×C4×C59C2×D411yescharacteristic
110C22×C4×C59C2×D412yes—
111C22×C4×C59C2×D412yes—
112C22×C4×C59C2×D412yes—
113C22×C4×C59#4112yes—
114C22×C4×C59#4112yes—
115C22×C4×C59#4112yes—
116C22×C4×C59C2411yescharacteristic
117C22×Dic59—24no—
118C22×Dic59—22no—
119C22×Dic59—22no—
120C22×Dic59—22no—
121C22×Dic59—22no—
122C22×Dic59—22no—
123C22×Dic59—42no—
124C22×Dic59—42no—
125C22×Dic59—42no—
126C22×Dic59—42no—
127C22×Dic59—42no—
128C22×Dic59C2×D412yes—
129C2×C4×D59—24no—
130C2×C4×D59—24no—
131C2×C4×D59—24no—
132C2×C4×D59—22no—
133C2×C4×D59—22no—
134C2×C4×D59—22no—
135C2×C4×D59—22no—
136C2×C4×D59—22no—
137C2×C4×D59—22no—
138C2×C4×D59—44no—
139C2×C4×D59—44no—
140C2×C4×D59—44no—
141C2×C4×D59—44no—
142C2×Dic118—28no—
143C2×Dic118—28no—
144C2×Dic118—22no—
145C2×Dic118—22no—
146C2×Dic118—22no—
147C2×Dic118—22no—
148C2×Dic118—24no—
149C2×Dic118—22no—
150C2×Dic118—44no—
151C2×Dic118—42no—
152C2×Dic118—42no—
153C2×Dic118—44no—
154C2×Dic118C2×D414yes—
155C2×C8×C59—28no—
156C2×C8×C59—22no—
157C2×C8×C59—22no—
158C2×C8×C59C2×D414yes—
159C4⋊C4×C59—24no—
160C4⋊C4×C59—22no—
161C4⋊C4×C59—22no—
162C4⋊C4×C59—22no—
163C4⋊C4×C59—42no—
164C4⋊C4×C59C2×D414yes—
165(C2×D59)⋊C4—216no—
166(C2×D59)⋊C4—48no—
167C4⋊Dic59—216no—
168C4⋊Dic59—22no—
169C4⋊Dic59—22no—
170C4⋊Dic59—42no—
171C2×C59⋊C8—22no—
172C2×C59⋊C8—22no—
173C2×C59⋊C8—22no—
174C2×C59⋊C8—44no—
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—
197C2×C4×C59—24no—
198C2×C4×C59—42no—
199C2×C4×C59—42no—
200C2×C4×C59—48no—
201C2×C4×C59—42no—
202C2×C4×C59—42no—
203C2×C4×C59—42no—
204C2×C4×C59—84no—
205C2×C4×C59#12012yes—
206C2×C4×C59#12114yes—
207C2×C4×C59#12114yes—
208C2×C4×C59#12112yes—
209C2×C4×C59#12314yes—
210C2×C4×C59#12312yes—
211C2×C4×C59#12414yes—
212C2×C4×C59C22×D411yescharacteristic
213C2×C4×C59C22×D411yescharacteristic
214C2×C4×C59C22×D411yescharacteristic
215C2×C4×C59C2×#4111yescharacteristic
216C2×C4×C59C2×#4111yescharacteristic
217C2×C4×C59C2×#4111yescharacteristic
218C2×Dic59—22no—
219C2×Dic59—24no—
220C2×Dic59—22no—
221C2×Dic59—22no—
222C2×Dic59—42no—
223C2×Dic59—42no—
224C2×Dic59—48no—
225C2×Dic59—44no—
226C2×Dic59—42no—
227C2×Dic59—42no—
228C2×Dic59—42no—
229C2×Dic59—84no—
230C4×D59—42no—
231C4×D59—42no—
232C4×D59—42no—
233C4×D59—42no—
234C4×D59—48no—
235Dic118—24no—
236Dic118—24no—
237Dic118—42no—
238Dic118—42no—
239Dic118—48no—
240C8×C59—24no—
241C59⋊C8—42no—
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—44no—
273Dic59—42no—
274Dic59—82no—
275C22×C22⋊Q8—591no—
276C22×#107D5911yescharacteristic, complemented
277C22×#103—591no—
278C22×#103—591no—
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×Q8—591no—
293C24×C4—591no—
294C23×C8—591no—
295C23×C8C2×D5911yescharacteristic
296C2×C22⋊Q8—594no—
297C2×C22⋊Q8—1182no—
298C2×C22⋊Q8—1184no—
299C2×C22⋊Q8—1184no—
300C22×C4⋊C4—591no—
301C22×C4⋊C4—1181no—
302C22×C4⋊C4C2×D5911yescharacteristic
303C22×C4⋊C4C2×D5911yescharacteristic
304C22×C22⋊C4—1181no—
305C22×C22⋊C4—1181no—
306C2×#107—24no—
307C2×#107C2×D5914yescomplemented
308C2×#103—594no—
309C2×#103—594no—
310C2×#103—1184no—
311C2×#103—1184no—
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—594no—
321C22×Q8—592no—
322C22×Q8—1181no—
323C22×Q8—1182no—
324C22×Q8—1182no—
325C22×Q8—1182no—
326C22×Q8—1182no—
327C22×Q8—1182no—
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—592no—
345C22×C8—1182no—
346C22×C8—1182no—
347C22×C8—1182no—
348C22×C8D23614yes—
349C22×C8C22×D5912yes—
350C22⋊Q8—1188no—
351C22⋊Q8—11816no—
352C22⋊Q8—1188no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—592no—
359C2×C4⋊C4—1184no—
360C2×C4⋊C4—1188no—
361C2×C4⋊C4—1182no—
362C2×C4⋊C4—1182no—
363C2×C4⋊C4—1181no—
364C2×C4⋊C4C22⋊D5914yes—
365C2×C4⋊C4C22×D5912yes—
366C2×C4⋊C4C22×D5912yes—
367C2×C22⋊C4—1184no—
368C2×C22⋊C4—1188no—
369C2×C22⋊C4—1184no—
370C2×C22⋊C4—2364no—
371#107—28no—
372#103—1188no—
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—594no—
386C2×Q8—1184no—
387C2×Q8—1182no—
388C2×Q8—1188no—
389C2×Q8—1188no—
390C2×Q8—1182no—
391C2×Q8—1182no—
392C2×Q8—1182no—
393C2×Q8—1182no—
394C2×Q8—2364no—
395C2×Q8—2362no—
396C2×Q8—2362no—
397C2×Q8—2364no—
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×C4C2×D23612yes—
432C22×C4#1174568512yes—
433C22×C4D4×D5911yescharacteristic
434C22×C4D4×D5912yes—
435C22×C4#1174568912yes—
436C22×C4#1174568912yes—
437C22×C4C2×C22⋊D5912yes—
438C22×C4C23×D5911yescharacteristic
439C2×C8—28no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—1182no—
443C2×C8—1182no—
444C2×C8—1182no—
445C2×C8—2364no—
446C2×C8C2×D23614yes—
447C4⋊C4—24no—
448C4⋊C4—22no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—11816no—
453C4⋊C4—1182no—
454C4⋊C4—1182no—
455C4⋊C4—2362no—
456C4⋊C4C2×C22⋊D5914yes—
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#1427370212yes—
475C23#1427371212yes—
476C23Q16×D5912yes—
477C23#1427374612yes—
478C23#1427375112yes—
479C23#1427375912yes—
480C23C2×D4×D5911yescharacteristic
481Q8—1184no—
482Q8—1184no—
483Q8—2362no—
484Q8—2362no—
485Q8—2368no—
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—2364no—
505C2×C4—2368no—
506C2×C4—2362no—
507C2×C4—2362no—
508C2×C4—2362no—
509C2×C4—2362no—
510C2×C4—2368no—
511C2×C4#1427369512yes—
512C2×C4#1427370114yes—
513C2×C4#1427370214yes—
514C2×C4#1427370212yes—
515C2×C4#1427371214yes—
516C2×C4#1427371212yes—
517C2×C4#1427371614yes—
518C2×C4C2×D4×D5911yescharacteristic
519C2×C4C22×C22⋊D5911yescharacteristic
520C2×C4C22×D23611yescharacteristic
521C2×C4C2×#1174568511yescharacteristic
522C2×C4C2×#1174568911yescharacteristic
523C2×C4C2×#1174568911yescharacteristic
524C8—24no—
525C8—2362no—
526C22—1184no—
527C22—1184no—
528C22—1184no—
529C22—2362no—
530C22—2362no—
531C22—2362no—
532C22—23616no—
533C22—2362no—
534C22#1683731914yes—
535C22#1683754414yes—
536C22#1683755614yes—
537C22#1683764414yes—
538C22#1683764914yes—
539C22#1683773914yes—
540C22#1683774514yes—
541C22C2×#1427369511yescharacteristic
542C22C2×#1427370211yescharacteristic
543C22C2×#1427371211yescharacteristic
544C22C2×Q16×D5911yescharacteristic
545C22C2×#1427374611yescharacteristic
546C22C2×#1427375111yescharacteristic
547C22C2×#1427375911yescharacteristic
548C4—44no—
549C4—82no—
550C4—4722no—
551C4—2362no—
552C4—2364no—
553C4#1683731914yes—
554C4C2×#1427370111yescharacteristic
555C4C2×#1427370211yescharacteristic
556C4C2×#1427371211yescharacteristic
557C4C2×#1427371611yescharacteristic
558C2—2364no—
559C2#2142530118yesdirect product factor
560C2C2×#1683731911yescharacteristic
561C2C2×#1683755611yescharacteristic
562C2C2×#1683754411yescharacteristic
563C2C2×#1683764411yescharacteristic
564C2C2×#1683764911yescharacteristic
565C2C2×#1683774511yescharacteristic
566C2C2×#1683773911yescharacteristic
subgroupG/H
centerC24D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#107×C59C2
socleC24×C59C2×D4
prime radicalC24×D59D4
hypercenterC22×#107D59
hypocenterC59C2×#2036
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
2. C22×#14273652C2semidirect
3. C22×#14273650C2semidirect
6. #21425301C2direct (N × H)
7. C2×#16837164C2semidirect
8. C22×#107×C59C2semidirect
21. C2×#14273652C22semidirect
23. C2×#14273650C22semidirect
29. #16837164C22semidirect
34. C2×#107×C59C22semidirect
276. C22×#107D59semidirect
283. C2×C59#2036semidirect
307. C2×#107C2×D59semidirect
318. C59C2×#2036semidirect
559. C2#21425301direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737072
C22×#142736522
C22×#142736502
C22×(C2×D59)⋊C82
C2×#168372592
#214253012
C2×#168371642
C22×#107×C592
C2×#203659