Finite Group Databasebeta

← C2×#21425281 #28616140

Subgroups — C2×#21425281 #28616140

Order 15104.

2006 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14273702C211yesmaximal, characteristic
2C22×#14273660C211yesmaximal, characteristic, complemented
3C22×#14273649C211yesmaximal, characteristic, complemented
4C22×#14273647C211yesmaximal, characteristic, complemented
5C22×(C2×D59)⋊C8C211yesmaximal, characteristic, complemented
6C2×#16837259C211yesmaximal, characteristic, complemented
7#21425281C218yesmaximal, direct product factor
8C2×C59×#340C211yesmaximal, characteristic, complemented
9C23×D236—21no—
10C23×D236C2211yescharacteristic
11C23×C4×D59C2211yescharacteristic
12C23×C59⋊C8C2211yescharacteristic
13C2×#14273702—24no—
14C2×#14273702—22no—
15C2×#14273702—24no—
16C2×#14273702C2214yes—
17C22×C4⋊Dic59C2211yescharacteristic
18C22×(C2×D59)⋊C4—21no—
19C22×(C2×D59)⋊C4—21no—
20C2×#14273660—24no—
21C2×#14273660C2214yescomplemented
22C2×#14273649—24no—
23C2×#14273649C2214yescomplemented
24C2×#14273647—24no—
25C2×#14273647C2214yescomplemented
26C2×(C2×D59)⋊C8—24no—
27C2×(C2×D59)⋊C8C2214yescomplemented
28#16837259—22no—
29#16837259C2214yescomplemented
30C2×C59⋊#95—21no—
31C23×C8×C59C2211yescharacteristic
32C22×C4⋊C4×C59C2211yescharacteristic
33C22×C4⋊C4×C59C2211yescharacteristic
34C59×#340C2214yescomplemented
35C24×D59—21no—
36C24×D59D411yescharacteristic
37C22×D236—22no—
38C22×D236—22no—
39C22×D236—22no—
40C22×D236—22no—
41C22×D236—28no—
42C22×D236—24no—
43C22×D236—22no—
44C22×D236—21no—
45C22×D236—44no—
46C22×D236—44no—
47C22×D236D414yes—
48C22×D236C2312yes—
49C23×Dic59—21no—
50C23×Dic59D411yescharacteristic
51C22×C4×D59—22no—
52C22×C4×D59—22no—
53C22×C4×D59—22no—
54C22×C4×D59—22no—
55C22×C4×D59—22no—
56C22×C4×D59—22no—
57C22×C4×D59D412yes—
58C22×C4×D59C2312yes—
59C22×C59⋊C8—22no—
60C22×C59⋊C8—22no—
61C22×C59⋊C8D414yescomplemented
62C22×C59⋊C8C2312yes—
63#14273702—216no—
64#14273702—28no—
65#14273702—28no—
66C2×C4⋊Dic59—22no—
67C2×C4⋊Dic59—22no—
68C2×C4⋊Dic59—21no—
69C2×C4⋊Dic59C2312yes—
70C2×(C2×D59)⋊C4—28no—
71C2×(C2×D59)⋊C4—24no—
72C2×(C2×D59)⋊C4—24no—
73C2×(C2×D59)⋊C4—44no—
74#14273660—28no—
75#14273649—28no—
76#14273647—28no—
77(C2×D59)⋊C8—28no—
78C59⋊#95—24no—
79C23×C4×C59—21no—
80C23×C4×C59—21no—
81C23×C4×C59C2311yescharacteristic
82C22×C8×C59—22no—
83C22×C8×C59—22no—
84C22×C8×C59—22no—
85C22×C8×C59C2312yes—
86C2×C4⋊C4×C59—21no—
87C2×C4⋊C4×C59—22no—
88C2×C4⋊C4×C59—22no—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—21no—
91C2×C4⋊C4×C59D414yes—
92C2×C4⋊C4×C59C2312yes—
93C2×C4⋊C4×C59C2312yes—
94C24×C59C2×D411yescharacteristic
95C23×D59—22no—
96C23×D59—22no—
97C23×D59—22no—
98C23×D59—22no—
99C23×D59—22no—
100C23×D59—22no—
101C23×D59—24no—
102C23×D59—22no—
103C23×D59—42no—
104C23×D59—42no—
105C23×D59—42no—
106C23×D59—42no—
107C23×D59—42no—
108C23×D59—42no—
109C23×D59D814yes—
110C23×D59C2×D412yes—
111C22×C4×C59—24no—
112C22×C4×C59—22no—
113C22×C4×C59—22no—
114C22×C4×C59—42no—
115C22×C4×C59—42no—
116C22×C4×C59—42no—
117C22×C4×C59—42no—
118C22×C4×C59—42no—
119C22×C4×C59C2×D411yescharacteristic
120C22×C4×C59C2×D412yes—
121C22×C4×C59C2×D412yes—
122C22×C4×C59C2×D412yes—
123C22×C4×C59#4112yes—
124C22×C4×C59#4112yes—
125C22×C4×C59#4112yes—
126C22×C4×C59C2411yescharacteristic
127C22×Dic59—22no—
128C22×Dic59—22no—
129C22×Dic59—22no—
130C22×Dic59—22no—
131C22×Dic59—42no—
132C22×Dic59—42no—
133C22×Dic59—42no—
134C22×Dic59C2×D412yes—
135C2×D236—28no—
136C2×D236—28no—
137C2×D236—22no—
138C2×D236—22no—
139C2×D236—22no—
140C2×D236—22no—
141C2×D236—216no—
142C2×D236—24no—
143C2×D236—22no—
144C2×D236—48no—
145C2×D236—432no—
146C2×D236—48no—
147C2×D236—44no—
148C2×D236—42no—
149C2×D236—42no—
150C2×D236—44no—
151C2×D236C2×D414yes—
152C2×C4×D59—24no—
153C2×C4×D59—24no—
154C2×C4×D59—24no—
155C2×C4×D59—22no—
156C2×C4×D59—22no—
157C2×C4×D59—22no—
158C2×C4×D59—22no—
159C2×C4×D59—22no—
160C2×C4×D59—22no—
161C2×C4×D59—44no—
162C2×C4×D59—44no—
163C2×C4×D59—44no—
164C2×C4×D59—44no—
165C2×C8×C59—22no—
166C2×C8×C59—22no—
167C2×C8×C59—22no—
168C2×C8×C59—44no—
169C4⋊C4×C59—24no—
170C4⋊C4×C59—22no—
171C4⋊C4×C59—22no—
172C4⋊C4×C59—22no—
173C4⋊C4×C59—42no—
174C4⋊C4×C59C2×D414yes—
175(C2×D59)⋊C4—216no—
176(C2×D59)⋊C4—48no—
177C4⋊Dic59—22no—
178C4⋊Dic59—22no—
179C4⋊Dic59—42no—
180C2×C59⋊C8—28no—
181C2×C59⋊C8—22no—
182C2×C59⋊C8—22no—
183C2×C59⋊C8C2×D414yescomplemented
184C23×C59#12012yes—
185C23×C59#12112yes—
186C23×C59#12312yes—
187C23×C59C2×D812yes—
188C23×C59#13512yes—
189C23×C59AGL(1,ℤ/8)12yes—
190C23×C59#13712yes—
191C23×C59C22×D411yescharacteristic
192C22×D59—22no—
193C22×D59—22no—
194C22×D59—22no—
195C22×D59—22no—
196C22×D59—22no—
197C22×D59—22no—
198C22×D59—28no—
199C22×D59—28no—
200C22×D59—28no—
201C22×D59—24no—
202C22×D59—44no—
203C22×D59—44no—
204C22×D59—44no—
205C22×D59—44no—
206C22×D59—42no—
207C22×D59—42no—
208C22×D59—42no—
209C22×D59—42no—
210C22×D59—42no—
211C22×D59—42no—
212C22×D59—48no—
213C22×D59—48no—
214C22×D59—48no—
215C22×D59—84no—
216C22×D59—84no—
217C22×D59—84no—
218C22×D59—84no—
219C22×D59C2×D814yes—
220C2×C4×C59—24no—
221C2×C4×C59—42no—
222C2×C4×C59—42no—
223C2×C4×C59—48no—
224C2×C4×C59—42no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—84no—
228C2×C4×C59#12012yes—
229C2×C4×C59#12114yes—
230C2×C4×C59#12112yes—
231C2×C4×C59#12114yes—
232C2×C4×C59#12314yes—
233C2×C4×C59#12312yes—
234C2×C4×C59#12414yes—
235C2×C4×C59C22×D411yescharacteristic
236C2×C4×C59C22×D411yescharacteristic
237C2×C4×C59C22×D411yescharacteristic
238C2×C4×C59C2×#4111yescharacteristic
239C2×C4×C59C2×#4111yescharacteristic
240C2×C4×C59C2×#4111yescharacteristic
241C2×Dic59—22no—
242C2×Dic59—22no—
243C2×Dic59—22no—
244C2×Dic59—44no—
245C2×Dic59—42no—
246C2×Dic59—42no—
247C2×Dic59—42no—
248C2×Dic59—84no—
249D236—24no—
250D236—24no—
251D236—432no—
252D236—42no—
253D236—42no—
254D236—48no—
255C4×D59—42no—
256C4×D59—42no—
257C4×D59—42no—
258C4×D59—42no—
259C4×D59—48no—
260C8×C59—42no—
261C59⋊C8—24no—
262C2×#2033—591nomaximal, Sylow
263C22×C59#39414yes—
264C22×C59#44714yes—
265C22×C59#45214yes—
266C22×C59#46614yes—
267C22×C59#46814yes—
268C22×C59#48014yes—
269C22×C59#48214yes—
270C22×C59C2×#12011yescharacteristic
271C22×C59C2×#12111yescharacteristic
272C22×C59C2×#12311yescharacteristic
273C22×C59C22×D811yescharacteristic
274C22×C59C2×#13511yescharacteristic
275C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C59C2×#13711yescharacteristic
277C2×D59—24no—
278C2×D59—24no—
279C2×D59—24no—
280C2×D59—42no—
281C2×D59—42no—
282C2×D59—42no—
283C2×D59—42no—
284C2×D59—416no—
285C2×D59—44no—
286C2×D59—44no—
287C2×D59—44no—
288C2×D59—82no—
289C2×D59—82no—
290C2×D59—82no—
291C2×D59—82no—
292C2×D59—816no—
293C4×C59—44no—
294C4×C59—82no—
295C4×C59#39414yes—
296C4×C59C2×#12111yescharacteristic
297C4×C59C2×#12111yescharacteristic
298C4×C59C2×#12311yescharacteristic
299C4×C59C2×#12411yescharacteristic
300Dic59—42no—
301Dic59—82no—
302C22×#121—591no—
303C22×#107—591no—
304C22×#102—591no—
305C22×#102—591no—
306C22×C22⋊C8—591no—
307C2×#380—591no—
308#2033—598no—
309C2×#340D5911yescharacteristic, complemented
310C2×C59#203318yescomplemented
311C2×C59C2×#39411yescharacteristic
312C2×C59C2×#44711yescharacteristic
313C2×C59C2×#45211yescharacteristic
314C2×C59C2×#46611yescharacteristic
315C2×C59C2×#46811yescharacteristic
316C2×C59C2×#48011yescharacteristic
317C2×C59C2×#48211yescharacteristic
318D59—44no—
319D59—84no—
320C23×D4—591no—
321C23×D4—1181no—
322C24×C4—591no—
323C23×C8—591no—
324C23×C8C2×D5911yescharacteristic
325C2×#121—594no—
326C2×#121—1182no—
327C2×#121—1184no—
328C2×#121—1184no—
329C22×C4⋊C4—591no—
330C22×C4⋊C4C2×D5911yescharacteristic
331C22×C4⋊C4C2×D5911yescharacteristic
332C22×C22⋊C4—1181no—
333C22×C22⋊C4—1181no—
334C2×#107—594no—
335C2×#107—1184no—
336C2×#102—594no—
337C2×#102—594no—
338C2×#102—1184no—
339C2×#102—1184no—
340C2×C22⋊C8—594no—
341C2×C22⋊C8—1184no—
342#380—594no—
343#380—1182no—
344C2×#95—1181no—
345#340C2×D5914yescomplemented
346C59C2×#203311yescharacteristic, complemented, Sylow
347C25—591no—
348C25—1181no—
349C22×D4—594no—
350C22×D4—592no—
351C22×D4—1184no—
352C22×D4—1188no—
353C22×D4—1182no—
354C22×D4—1182no—
355C22×D4—1182no—
356C22×D4—1182no—
357C22×D4—1181no—
358C22×D4—1182no—
359C22×D4—2364no—
360C22×D4—2364no—
361C23×C4—21no—
362C23×C4—21no—
363C23×C4—591no—
364C23×C4—592no—
365C23×C4—592no—
366C23×C4—1182no—
367C23×C4—1182no—
368C23×C4—1182no—
369C23×C4—1182no—
370C23×C4—1182no—
371C23×C4—1182no—
372C23×C4—1181no—
373C23×C4C22×D5911yescharacteristic
374C22×C8—22no—
375C22×C8—22no—
376C22×C8—22no—
377C22×C8—594no—
378C22×C8—592no—
379C22×C8—1182no—
380C22×C8—1182no—
381C22×C8C22×D5912yes—
382#121—1188no—
383#121—11816no—
384#121—1188no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—22no—
388C2×C4⋊C4—22no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—592no—
391C2×C4⋊C4—1182no—
392C2×C4⋊C4—1182no—
393C2×C4⋊C4—1181no—
394C2×C4⋊C4D23614yes—
395C2×C4⋊C4C22×D5912yes—
396C2×C4⋊C4C22×D5912yes—
397C2×C22⋊C4—1184no—
398C2×C22⋊C4—1188no—
399C2×C22⋊C4—1184no—
400C2×C22⋊C4—2364no—
401#107—1188no—
402#102—1188no—
403#102—1188no—
404C22⋊C8—1188no—
405#95—1184no—
406C24—594no—
407C24—592no—
408C24—1182no—
409C24—1182no—
410C24—1182no—
411C24—1182no—
412C24—1182no—
413C24—1182no—
414C24—1184no—
415C24—1182no—
416C24—2362no—
417C24—2362no—
418C24—2362no—
419C24—2362no—
420C24—2362no—
421C24—2362no—
422C24D4×D5911yescharacteristic
423C2×D4—594no—
424C2×D4—11816no—
425C2×D4—1184no—
426C2×D4—1188no—
427C2×D4—1188no—
428C2×D4—1182no—
429C2×D4—1182no—
430C2×D4—1182no—
431C2×D4—1182no—
432C2×D4—1182no—
433C2×D4—2368no—
434C2×D4—2368no—
435C2×D4—23632no—
436C2×D4—2362no—
437C2×D4—2364no—
438C2×D4—2362no—
439C2×D4—2364no—
440C22×C4—24no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—42no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—592no—
449C22×C4—1182no—
450C22×C4—1182no—
451C22×C4—1182no—
452C22×C4—1184no—
453C22×C4—1184no—
454C22×C4—1184no—
455C22×C4—1182no—
456C22×C4—1182no—
457C22×C4—1182no—
458C22×C4—1182no—
459C22×C4—1182no—
460C22×C4—1182no—
461C22×C4—1182no—
462C22×C4—2362no—
463C22×C4—2362no—
464C22×C4—2362no—
465C22×C4—2364no—
466C22×C4—2364no—
467C22×C4—2364no—
468C22×C4—2364no—
469C22×C4C2×D23612yes—
470C22×C4#1174568512yes—
471C22×C4#1174568512yes—
472C22×C4D4×D5911yescharacteristic
473C22×C4D4×D5912yes—
474C22×C4D4×D5912yes—
475C22×C4#1174568912yes—
476C22×C4C23×D5911yescharacteristic
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—44no—
481C2×C8—594no—
482C2×C8—1188no—
483C2×C8—1182no—
484C2×C8—1182no—
485C4⋊C4—24no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—42no—
490C4⋊C4—1182no—
491C4⋊C4—1182no—
492C4⋊C4—2362no—
493C4⋊C4C2×D23614yes—
494C22⋊C4—11816no—
495C22⋊C4—2368no—
496C23—594no—
497C23—1182no—
498C23—1188no—
499C23—1182no—
500C23—1182no—
501C23—1182no—
502C23—1182no—
503C23—1182no—
504C23—1188no—
505C23—1188no—
506C23—1184no—
507C23—4724no—
508C23—4724no—
509C23—4724no—
510C23—4724no—
511C23—2362no—
512C23—2362no—
513C23—2362no—
514C23—2362no—
515C23—2362no—
516C23—2362no—
517C23—2368no—
518C23—2368no—
519C23—2368no—
520C23—2364no—
521C23—2364no—
522C23—2364no—
523C23—2364no—
524C23#1427369712yes—
525C23#1427370012yes—
526C23#1427371212yes—
527C23D8×D5912yes—
528C23#1427374812yes—
529C23#1427375412yes—
530C23#1427375912yes—
531C23C2×D4×D5911yescharacteristic
532D4—1184no—
533D4—1184no—
534D4—23632no—
535D4—2362no—
536D4—2362no—
537D4—2368no—
538C2×C4—24no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—48no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—84no—
546C2×C4—1182no—
547C2×C4—1182no—
548C2×C4—1182no—
549C2×C4—4724no—
550C2×C4—2362no—
551C2×C4—2362no—
552C2×C4—2362no—
553C2×C4—2364no—
554C2×C4—2362no—
555C2×C4—2362no—
556C2×C4—2362no—
557C2×C4—2362no—
558C2×C4—2368no—
559C2×C4#1427369712yes—
560C2×C4#1427370014yes—
561C2×C4#1427370012yes—
562C2×C4#1427370214yes—
563C2×C4#1427371214yes—
564C2×C4#1427371212yes—
565C2×C4#1427371514yes—
566C2×C4C2×D4×D5911yescharacteristic
567C2×C4C2×D4×D5911yescharacteristic
568C2×C4C22×D23611yescharacteristic
569C2×C4C2×#1174568511yescharacteristic
570C2×C4C2×#1174568511yescharacteristic
571C2×C4C2×#1174568911yescharacteristic
572C8—42no—
573C8—1184no—
574C22—1184no—
575C22—1184no—
576C22—1184no—
577C22—4722no—
578C22—4722no—
579C22—4722no—
580C22—4722no—
581C22—47216no—
582C22—2364no—
583C22—2364no—
584C22—2364no—
585C22—2362no—
586C22—2362no—
587C22—2362no—
588C22—23616no—
589C22—2362no—
590C22#1683732014yes—
591C22#1683753714yes—
592C22#1683756714yes—
593C22#1683763714yes—
594C22#1683765114yes—
595C22#1683771714yes—
596C22#1683772814yes—
597C22C2×#1427369711yescharacteristic
598C22C2×#1427370011yescharacteristic
599C22C2×#1427371211yescharacteristic
600C22C2×D8×D5911yescharacteristic
601C22C2×#1427374811yescharacteristic
602C22C2×#1427375411yescharacteristic
603C22C2×#1427375911yescharacteristic
604C4—44no—
605C4—82no—
606C4—4722no—
607C4—2362no—
608C4#1683732014yes—
609C4C2×#1427370011yescharacteristic
610C4C2×#1427370211yescharacteristic
611C4C2×#1427371211yescharacteristic
612C4C2×#1427371511yescharacteristic
613C2—4724no—
614C2—2364no—
615C2#2142528118yesdirect product factor
616C2C2×#1683732011yescharacteristic
617C2C2×#1683753711yescharacteristic
618C2C2×#1683756711yescharacteristic
619C2C2×#1683763711yescharacteristic
620C2C2×#1683765111yescharacteristic
621C2C2×#1683771711yescharacteristic
622C2C2×#1683772811yescharacteristic
subgroupG/H
centerC24D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC2×C59×#340C2
socleC24×C59C2×D4
prime radicalC22×#14273702C2
hypercenterC2×#340D59
hypocenterC59C2×#2033
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C2×#340

Complements

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

NH ≅ G/Ntype
2. C22×#14273660C2semidirect
3. C22×#14273649C2semidirect
4. C22×#14273647C2semidirect
5. C22×(C2×D59)⋊C8C2semidirect
6. C2×#16837259C2semidirect
7. #21425281C2direct (N × H)
8. C2×C59×#340C2semidirect
21. C2×#14273660C22semidirect
23. C2×#14273649C22semidirect
25. C2×#14273647C22semidirect
27. C2×(C2×D59)⋊C8C22semidirect
29. #16837259C22semidirect
34. C59×#340C22semidirect
61. C22×C59⋊C8D4semidirect
183. C2×C59⋊C8C2×D4semidirect
309. C2×#340D59semidirect
310. C2×C59#2033semidirect
345. #340C2×D59semidirect
346. C59C2×#2033semidirect
615. C2#21425281direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142737022
C22×#142736602
C22×#142736492
C22×#142736472
C22×(C2×D59)⋊C82
C2×#168372592
#214252812
C2×C59×#3402
C2×#203359