Finite Group Databasebeta

← C2×#21424326 #28589548

Subgroups — C2×#21424326 #28589548

Order 15104.

1478 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16837882C211yesmaximal, characteristic
2C22×#14273653C211yesmaximal, characteristic
3C2×#16837401C211yesmaximal, characteristic
4C2×#16837267C211yesmaximal, characteristic, complemented
5#21424326C218yesmaximal, direct product factor
6C2×#16837170C211yesmaximal, characteristic, complemented
7C2×#16837161C211yesmaximal, characteristic, complemented
8C2×C59×#428C211yesmaximal, characteristic, complemented
9C22×#11745685C2211yescharacteristic
10C22×#11745664C2211yescharacteristic
11#16837882—22no—
12#16837882—22no—
13#16837882—22no—
14#16837882C2214yes—
15C2×C4×Dic118—21no—
16C2×C4×D236—21no—
17C2×(C22⋊D59)⋊C4—22no—
18C2×#14273685—21no—
19C22×C4⋊Dic59C2211yescharacteristic
20C2×C4⋊C4×D59—21no—
21C22×C4×Dic59C2211yescharacteristic
22C2×#14273653C418yescomplemented
23C2×#14273653C2214yes—
24#16837401—22no—
25#16837401C2214yes—
26C2×#14273650—21no—
27C2×#14273647—21no—
28#16837267—22no—
29#16837267C2214yescomplemented
30C2×C59⋊#95—22no—
31#16837170C2214yescomplemented
32#16837161C2214yescomplemented
33C22×M16×C59C2211yescharacteristic
34C2×#117×C59C2211yescharacteristic
35C22×C4⋊C4×C59C2211yescharacteristic
36C59×#428—22no—
37C59×#428C2214yescomplemented
38C2×#107×C59—21no—
39C2×#106×C59—21no—
40C2×#11745685—21no—
41C2×#11745685—21no—
42C2×#11745685—22no—
43C2×#11745685—22no—
44C2×#11745685C2×C414yes—
45C2×#11745685D412yes—
46C2×#11745685Q814yes—
47C2×#11745685C2312yes—
48C22×Dic118D411yescharacteristic
49C22×D236D411yescharacteristic
50C22×C22⋊D59—21no—
51C23×Dic59—21no—
52C23×Dic59D412yes—
53C22×C4×D59—21no—
54C22×C4×D59—22no—
55C2×#11745664—21no—
56C2×#11745664—22no—
57C2×#11745664—22no—
58C2×#11745664C2312yes—
59C22×C59⋊C8—21no—
60C4×Dic118—24no—
61C4×Dic118—24no—
62C4×D236—24no—
63C4×D236—24no—
64(C22⋊D59)⋊C4—28no—
65(C22⋊D59)⋊C4—28no—
66#14273685—24no—
67#14273685—24no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59—21no—
70C2×C4⋊Dic59—21no—
71C2×C4⋊Dic59—21no—
72C2×C4⋊Dic59D412yes—
73C2×C4⋊Dic59C2312yes—
74C2×Dic59⋊C4—22no—
75C4⋊C4×D59—24no—
76C4⋊C4×D59—24no—
77C2×(C2×D59)⋊C4—22no—
78C2×C4×Dic59—22no—
79C2×C4×Dic59—21no—
80C2×C4×Dic59—22no—
81C2×C4×Dic59C2×C414yescomplemented
82C2×C4×Dic59C2312yes—
83#14273653C2×C4116yescomplemented
84#14273650—24no—
85#14273647—24no—
86C59⋊#95—28no—
87C23×C4×C59—21no—
88C23×C4×C59C2311yescharacteristic
89C2×M16×C59—21no—
90C2×M16×C59—22no—
91C2×M16×C59C2×C414yescomplemented
92C2×M16×C59C2312yes—
93C22×C8×C59—21no—
94#117×C59—21no—
95#117×C59—21no—
96#117×C59D412yes—
97#117×C59C2312yes—
98C2×C4⋊C4×C59—21no—
99C2×C4⋊C4×C59—21no—
100C2×C4⋊C4×C59—21no—
101C2×C4⋊C4×C59—21no—
102C2×C4⋊C4×C59—21no—
103C2×C4⋊C4×C59D411yescharacteristic
104C2×C4⋊C4×C59D411yescharacteristic
105C2×C4⋊C4×C59C2312yes—
106C2×C22⋊C4×C59—21no—
107C2×C42×C59—21no—
108#107×C59—24no—
109#106×C59—24no—
110C24×C59C2×D411yescharacteristic
111C23×D59—21no—
112C22×C4×C59—21no—
113C22×C4×C59—21no—
114C22×C4×C59—22no—
115C22×C4×C59—44no—
116C22×C4×C59—41no—
117C22×C4×C59—41no—
118C22×C4×C59C22×C412yes—
119C22×C4×C59C2×D411yescharacteristic
120C22×C4×C59C2×D411yescharacteristic
121C22×C4×C59C2×D411yescharacteristic
122C22×C4×C59C2×D411yescharacteristic
123C22×C4×C59C2×D411yescharacteristic
124C22×C4×C59C2×Q812yes—
125C22×C4×C59#4112yes—
126C22×C4×C59#4112yes—
127C22×C4×C59C2411yescharacteristic
128C2×C22⋊D59—24no—
129C2×C22⋊D59—22no—
130C2×C22⋊D59—24no—
131C2×C22⋊D59—22no—
132C22×Dic59—21no—
133C22×Dic59—24no—
134C22×Dic59—22no—
135C22×Dic59—22no—
136C22×Dic59—22no—
137C22×Dic59—42no—
138C22×Dic59—42no—
139C22×Dic59—44no—
140C22×Dic59C2×D414yes—
141#11745685—24no—
142#11745685—24no—
143#11745685—24no—
144#11745685—24no—
145#11745685—24no—
146#11745685—22no—
147#11745685—22no—
148#11745685C4⋊C418yes—
149#11745685C22×C414yes—
150#11745685C2×Q814yes—
151C2×D236—21no—
152C2×D236—22no—
153C2×D236C4⋊C414yes—
154C2×D236C2×D412yes—
155C2×C4×D59—24no—
156C2×C4×D59—22no—
157C2×C4×D59—24no—
158C2×C4×D59—22no—
159C2×C4×D59—28no—
160C2×C4×D59—84no—
161C2×Dic118—21no—
162C2×Dic118—22no—
163C2×Dic118C4⋊C414yes—
164C2×Dic118C2×D412yes—
165M16×C59—24no—
166M16×C59—22no—
167M16×C59C22×C414yescomplemented
168C2×C8×C59—24no—
169C2×C8×C59—22no—
170C4⋊C4×C59—21no—
171C4⋊C4×C59—21no—
172C4⋊C4×C59—22no—
173C4⋊C4×C59—22no—
174C4⋊C4×C59—41no—
175C4⋊C4×C59—41no—
176C4⋊C4×C59C2×D412yes—
177C4⋊C4×C59C2×D412yes—
178C22⋊C4×C59—22no—
179C22⋊C4×C59—22no—
180C42×C59—22no—
181C42×C59—22no—
182(C2×D59)⋊C4—28no—
183C4⋊Dic59—22no—
184C4⋊Dic59—22no—
185C4⋊Dic59—22no—
186C4⋊Dic59—22no—
187Dic59⋊C4—28no—
188C4×Dic59—28no—
189C4×Dic59—24no—
190C4×Dic59—22no—
191C4×Dic59C22×C414yescomplemented
192#11745664—22no—
193#11745664—22no—
194#11745664—42no—
195C2×C59⋊C8—22no—
196C2×C59⋊C8—42no—
197C23×C59—22no—
198C23×C59—22no—
199C23×C59C4×D412yes—
200C23×C59#12011yescharacteristic
201C23×C59#12011yescharacteristic
202C23×C59C22⋊Q812yes—
203C23×C59C22×D411yescharacteristic
204C22×D59—22no—
205C22×D59—24no—
206C22×D59—42no—
207C22×D59—42no—
208C2×C4×C59—22no—
209C2×C4×C59—22no—
210C2×C4×C59—42no—
211C2×C4×C59—42no—
212C2×C4×C59—44no—
213C2×C4×C59—42no—
214C2×C4×C59—82no—
215C2×C4×C59—82no—
216C2×C4×C59C2×C4⋊C412yes—
217C2×C4×C59C2×C4⋊C412yes—
218C2×C4×C59C4×D412yes—
219C2×C4×C59C4×D412yes—
220C2×C4×C59C4×D412yes—
221C2×C4×C59#12011yescharacteristic
222C2×C4×C59#12011yescharacteristic
223C2×C4×C59C22⋊Q812yes—
224C2×C4×C59C22⋊Q812yes—
225C2×C4×C59C22⋊Q812yes—
226C2×C4×C59#12312yes—
227C2×C4×C59#12312yes—
228C2×C4×C59C23×C411yescharacteristic
229C2×C4×C59C22×D411yescharacteristic
230C2×C4×C59C22×D411yescharacteristic
231C2×C4×C59C22×Q811yescharacteristic
232C2×C4×C59C2×#4111yescharacteristic
233C2×C4×C59C2×#4111yescharacteristic
234C22⋊D59—24no—
235C22⋊D59—24no—
236C22⋊D59—28no—
237C2×Dic59—22no—
238C2×Dic59—24no—
239C2×Dic59—24no—
240C2×Dic59—24no—
241C2×Dic59—48no—
242C2×Dic59—42no—
243C2×Dic59—42no—
244C2×Dic59—44no—
245C2×Dic59—44no—
246C2×Dic59—82no—
247D236—22no—
248D236—24no—
249D236C2×C4⋊C414yes—
250C4×D59—24no—
251C4×D59—24no—
252C4×D59—28no—
253C4×D59—88no—
254Dic118—22no—
255Dic118—24no—
256Dic118C2×C4⋊C414yes—
257C8×C59—24no—
258C59⋊C8—42no—
259C2×#1860—591nomaximal, Sylow
260C22×C59—24no—
261C22×C59—24no—
262C22×C59—21no—
263C22×C59—21no—
264C22×C59—21no—
265C22×C59—21no—
266C22×C59#38512yes—
267C22×C59#38512yes—
268C22×C59#45412yes—
269C22×C59#45512yes—
270C22×C59C2×C4×D411yescharacteristic
271C22×C59C2×#12011yescharacteristic
272C22×C59C2×C22⋊Q811yescharacteristic
273C2×D59—24no—
274C2×D59—48no—
275C2×D59—42no—
276C2×D59—42no—
277C4×C59—42no—
278C4×C59—42no—
279C4×C59—82no—
280C4×C59#38512yes—
281C4×C59#38512yes—
282C4×C59C22×C4⋊C411yescharacteristic
283C4×C59C2×C4×D411yescharacteristic
284C4×C59C2×C22⋊Q811yescharacteristic
285C4×C59C2×#12311yescharacteristic
286Dic59—24no—
287Dic59—44no—
288Dic59—44no—
289C2×#520—591no—
290C2×#428D5911yescharacteristic, complemented
291C22×#104—591no—
292C2×#417—591no—
293C2×#382—591no—
294#1860—598no—
295C2×#343—591no—
296C2×#339—591no—
297C2×C59—21no—
298C2×C59—21no—
299C2×C59—22no—
300C2×C59#186014yescomplemented
301C2×C59C2×#38511yescharacteristic
302C2×C59C2×#45511yescharacteristic
303C2×C59C2×#45411yescharacteristic
304D59—44no—
305C22×#41—591no—
306C22×M16—591no—
307C22×M16C2×D5911yescharacteristic
308#520—594no—
309#520—1182no—
310#520—1182no—
311#520—1182no—
312C2×C4×Q8—1181no—
313C2×C4×D4—1181no—
314C2×C4×D4—1182no—
315C2×#117—1181no—
316C2×#117C2×D5911yescharacteristic
317C22×C4⋊C4—591no—
318C22×C4⋊C4—1181no—
319C22×C4⋊C4C2×D5911yescharacteristic
320C22×C42—591no—
321#428—22no—
322#428C2×D5914yescomplemented
323C2×#107—21no—
324C2×#106—21no—
325C2×#104—598no—
326C2×#104—594no—
327#417—594no—
328#417—1182no—
329C2×#103—1181no—
330C2×#102—1181no—
331#382—594no—
332#382—1182no—
333C2×#95—1182no—
334#343—594no—
335#339—594no—
336C59C2×#186011yescharacteristic, complemented, Sylow
337C2×#41—594no—
338C2×#41—592no—
339C2×#41—594no—
340C2×#41—592no—
341C2×#41—1182no—
342C2×#41—1181no—
343C2×#41—1182no—
344C2×#41—1181no—
345C22×Q8—591no—
346C22×D4—591no—
347C22×D4—1181no—
348C23×C4—21no—
349C23×C4—592no—
350C23×C4—1182no—
351C23×C4—1181no—
352C23×C4—1181no—
353C23×C4C22×D5911yescharacteristic
354C2×M16—22no—
355C2×M16—21no—
356C2×M16—592no—
357C2×M16—1181no—
358C2×M16—1182no—
359C2×M16—1182no—
360C2×M16C4×D5914yescomplemented
361C2×M16C22×D5912yes—
362C22×C8—21no—
363C22×C8—1181no—
364C4×Q8—1184no—
365C4×Q8—1184no—
366C4×D4—1184no—
367C4×D4—1184no—
368C4×D4—1188no—
369C4×D4—1188no—
370#117—21no—
371#117—21no—
372#117—1184no—
373#117—1184no—
374#117C22⋊D5912yes—
375#117C22×D5912yes—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—592no—
382C2×C4⋊C4—592no—
383C2×C4⋊C4—1184no—
384C2×C4⋊C4—1182no—
385C2×C4⋊C4—1181no—
386C2×C4⋊C4—1181no—
387C2×C4⋊C4—1181no—
388C2×C4⋊C4—1181no—
389C2×C4⋊C4—1184no—
390C2×C4⋊C4C22⋊D5911yescharacteristic
391C2×C4⋊C4C22⋊D5911yescharacteristic
392C2×C4⋊C4C22×D5912yes—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—1182no—
395C2×C42—21no—
396C2×C42—594no—
397C2×C42—592no—
398C2×C42—1182no—
399C2×C42—1181no—
400C2×C42—1182no—
401#107—24no—
402#106—24no—
403#104—5916no—
404#103—1184no—
405#102—1184no—
406#95—1188no—
407C24—1181no—
408C24D4×D5911yescharacteristic
409#41—598no—
410#41—594no—
411#41—594no—
412#41—1184no—
413#41—1184no—
414#41—1184no—
415#41—1184no—
416#41—1184no—
417#41—1182no—
418#41—1182no—
419C2×Q8—594no—
420C2×Q8—592no—
421C2×Q8—1181no—
422C2×Q8—1182no—
423C2×D4—594no—
424C2×D4—592no—
425C2×D4—1184no—
426C2×D4—1182no—
427C2×D4—1184no—
428C2×D4—1182no—
429C2×D4—1181no—
430C2×D4—1182no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—594no—
438C22×C4—1188no—
439C22×C4—1181no—
440C22×C4—1184no—
441C22×C4—1182no—
442C22×C4—1184no—
443C22×C4—1182no—
444C22×C4—1182no—
445C22×C4—1184no—
446C22×C4—1182no—
447C22×C4—1182no—
448C22×C4—4724no—
449C22×C4—2364no—
450C22×C4—2362no—
451C22×C4—2362no—
452C22×C4C2×C4×D5912yes—
453C22×C4#1174568512yes—
454C22×C4D4×D5911yescharacteristic
455C22×C4D4×D5911yescharacteristic
456C22×C4D4×D5911yescharacteristic
457C22×C4Q8×D5912yes—
458C22×C4#1174568912yes—
459C22×C4C2×C22⋊D5911yescharacteristic
460C22×C4C2×C22⋊D5911yescharacteristic
461C22×C4C23×D5911yescharacteristic
462M16—24no—
463M16—22no—
464M16—1182no—
465M16—1182no—
466M16—2362no—
467M16C2×C4×D5914yescomplemented
468C2×C8—24no—
469C2×C8—22no—
470C2×C8—1182no—
471C2×C8—2362no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—1188no—
479C4⋊C4—1182no—
480C4⋊C4—1182no—
481C4⋊C4—1182no—
482C4⋊C4—1182no—
483C4⋊C4C2×C22⋊D5912yes—
484C4⋊C4C2×C22⋊D5912yes—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—1188no—
488C42—22no—
489C42—22no—
490C42—594no—
491C42—1188no—
492C42—1184no—
493C42—1182no—
494C23—22no—
495C23—22no—
496C23—1184no—
497C23—1182no—
498C23—2362no—
499C23—2362no—
500C23#1427368912yes—
501C23#1427369511yescharacteristic
502C23#1427369511yescharacteristic
503C23#1427370512yes—
504C23C2×D4×D5911yescharacteristic
505Q8—594no—
506Q8—1182no—
507Q8—1184no—
508D4—594no—
509D4—1184no—
510D4—1188no—
511D4—1184no—
512D4—1182no—
513D4—1184no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—44no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—1184no—
523C2×C4—1182no—
524C2×C4—1184no—
525C2×C4—1188no—
526C2×C4—1184no—
527C2×C4—1184no—
528C2×C4—1184no—
529C2×C4—4728no—
530C2×C4—4722no—
531C2×C4—2362no—
532C2×C4—2362no—
533C2×C4—2368no—
534C2×C4—2364no—
535C2×C4—2364no—
536C2×C4C4⋊C4×D5912yes—
537C2×C4C4⋊C4×D5912yes—
538C2×C4C4×C22⋊D5912yes—
539C2×C4C4×C22⋊D5912yes—
540C2×C4#1427368912yes—
541C2×C4#1427369511yescharacteristic
542C2×C4#1427369511yescharacteristic
543C2×C4#1427370312yes—
544C2×C4#1427370312yes—
545C2×C4#1427370512yes—
546C2×C4#1427371212yes—
547C2×C4#1427371212yes—
548C2×C4C22×C4×D5911yescharacteristic
549C2×C4C2×D4×D5911yescharacteristic
550C2×C4C22×C22⋊D5911yescharacteristic
551C2×C4C2×Q8×D5911yescharacteristic
552C2×C4C2×#1174568511yescharacteristic
553C2×C4C2×#1174568911yescharacteristic
554C8—24no—
555C8—2362no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—21no—
560C22—24no—
561C22—24no—
562C22—1184no—
563C22—2362no—
564C22—2362no—
565C22—2368no—
566C22#1683727312yes—
567C22#1683727312yes—
568C22#1683757312yes—
569C22#1683757812yes—
570C22C2×#1427368911yescharacteristic
571C22C2×#1427369511yescharacteristic
572C22C2×#1427370511yescharacteristic
573C4—42no—
574C4—42no—
575C4—82no—
576C4—1184no—
577C4—2364no—
578C4—2364no—
579C4#1683727312yes—
580C4#1683727312yes—
581C4C2×C4⋊C4×D5911yescharacteristic
582C4C2×C4×C22⋊D5911yescharacteristic
583C4C2×#1427370311yescharacteristic
584C4C2×#1427371211yescharacteristic
585C2—21no—
586C2—21no—
587C2—22no—
588C2—2364no—
589C2#2142432614yesdirect product factor
590C2C2×#1683727311yescharacteristic
591C2C2×#1683757811yescharacteristic
592C2C2×#1683757311yescharacteristic
subgroupG/H
centerC23#14273695
commutatorC2×C4×C59C23×C4
FrattiniC22×C4C23×D59
FittingC2×C59×#428C2
socleC23×C59#120
prime radicalC22×#11745685C22
cosocleC22×C4×C59C24
hypercenterC2×#428D59
hypocenterC59C2×#1860
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
4. C2×#16837267C2semidirect
5. #21424326C2direct (N × H)
6. C2×#16837170C2semidirect
7. C2×#16837161C2semidirect
8. C2×C59×#428C2semidirect
22. C2×#14273653C4semidirect
29. #16837267C22semidirect
31. #16837170C22semidirect
32. #16837161C22semidirect
37. C59×#428C22semidirect
81. C2×C4×Dic59C2×C4semidirect
83. #14273653C2×C4semidirect
91. C2×M16×C59C2×C4semidirect
167. M16×C59C22×C4semidirect
191. C4×Dic59C22×C4semidirect
290. C2×#428D59semidirect
300. C2×C59#1860semidirect
322. #428C2×D59semidirect
336. C59C2×#1860semidirect
360. C2×M16C4×D59semidirect
467. M16C2×C4×D59semidirect
589. C2#21424326direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168378822
C22×#142736532
C2×#168374012
C2×#168372672
#214243262
C2×#168371702
C2×#168371612
C2×C59×#4282
C2×#186059