Finite Group Databasebeta

← C2×#21425277 #28616136

Subgroups — C2×#21425277 #28616136

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×#14273698C211yesmaximal, characteristic
2C22×#14273661C211yesmaximal, characteristic, complemented
3C22×#14273648C211yesmaximal, characteristic, complemented
4C22×(C2×D59)⋊C8C211yesmaximal, characteristic, complemented
5C2×#16837259C211yesmaximal, characteristic, complemented
6#21425277C218yesmaximal, direct product factor
7C2×#16837164C211yesmaximal, characteristic, complemented
8C22×#102×C59C211yesmaximal, characteristic, complemented
9C23×C22⋊D59—21no—
10C23×C4×D59C2211yescharacteristic
11C23×C59⋊C8C2211yescharacteristic
12C2×#14273698—22no—
13C2×#14273698—24no—
14C2×#14273698—24no—
15C2×#14273698C2214yes—
16C22×C4⋊Dic59C2211yescharacteristic
17C22×C4⋊Dic59C2211yescharacteristic
18C22×C22⋊Dic59—21no—
19C22×(C2×D59)⋊C4—21no—
20C2×#14273661—24no—
21C2×#14273661C2214yescomplemented
22C2×#14273648—24no—
23C2×#14273648C2214yescomplemented
24C2×(C2×D59)⋊C8—24no—
25C2×(C2×D59)⋊C8C2214yescomplemented
26#16837259—22no—
27#16837259C2214yescomplemented
28C2×C59⋊#95—21no—
29#16837164C2214yescomplemented
30C23×D4×C59C2211yescharacteristic
31C23×C8×C59C2211yescharacteristic
32C22×C4⋊C4×C59C2211yescharacteristic
33C2×#102×C59—24no—
34C2×#102×C59C2214yescomplemented
35C24×D59D411yescharacteristic
36C22×C22⋊D59—28no—
37C22×C22⋊D59—24no—
38C22×C22⋊D59—44no—
39C22×C22⋊D59—44no—
40C23×Dic59—21no—
41C23×Dic59—21no—
42C23×Dic59D411yescharacteristic
43C22×C4×D59—22no—
44C22×C4×D59—22no—
45C22×C4×D59—22no—
46C22×C4×D59—22no—
47C22×C4×D59—22no—
48C22×C4×D59—22no—
49C22×C4×D59D412yes—
50C22×C4×D59C2312yes—
51C22×C59⋊C8—22no—
52C22×C59⋊C8—22no—
53C22×C59⋊C8—22no—
54C22×C59⋊C8C2312yes—
55#14273698—216no—
56#14273698—28no—
57#14273698—28no—
58C2×C4⋊Dic59—22no—
59C2×C4⋊Dic59—21no—
60C2×C4⋊Dic59—22no—
61C2×C4⋊Dic59—22no—
62C2×C4⋊Dic59—21no—
63C2×C4⋊Dic59D414yes—
64C2×C4⋊Dic59C2312yes—
65C2×C4⋊Dic59C2312yes—
66C2×C22⋊Dic59—28no—
67C2×C22⋊Dic59—24no—
68C2×(C2×D59)⋊C4—24no—
69C2×(C2×D59)⋊C4—44no—
70#14273661—28no—
71#14273648—28no—
72(C2×D59)⋊C8—28no—
73C59⋊#95—24no—
74C25×C59—21no—
75C22×D4×C59—22no—
76C22×D4×C59—21no—
77C22×D4×C59—22no—
78C22×D4×C59—22no—
79C22×D4×C59—22no—
80C22×D4×C59—22no—
81C22×D4×C59D414yes—
82C22×D4×C59C2312yes—
83C23×C4×C59—21no—
84C23×C4×C59C2311yescharacteristic
85C22×C8×C59—22no—
86C22×C8×C59—22no—
87C22×C8×C59D414yescomplemented
88C22×C8×C59C2312yes—
89C2×C4⋊C4×C59—22no—
90C2×C4⋊C4×C59—22no—
91C2×C4⋊C4×C59—21no—
92C2×C4⋊C4×C59C2312yes—
93#102×C59—28no—
94C24×C59—24no—
95C24×C59—22no—
96C24×C59—42no—
97C24×C59—42no—
98C24×C59—42no—
99C24×C59—42no—
100C24×C59—42no—
101C24×C59—42no—
102C24×C59C2×D411yescharacteristic
103C23×D59—22no—
104C23×D59—22no—
105C23×D59—22no—
106C23×D59—22no—
107C23×D59—22no—
108C23×D59—22no—
109C23×D59D814yes—
110C23×D59C2×D412yes—
111C2×D4×C59—24no—
112C2×D4×C59—28no—
113C2×D4×C59—28no—
114C2×D4×C59—22no—
115C2×D4×C59—22no—
116C2×D4×C59—22no—
117C2×D4×C59—22no—
118C2×D4×C59—22no—
119C2×D4×C59—42no—
120C2×D4×C59—44no—
121C2×D4×C59—42no—
122C2×D4×C59—44no—
123C2×D4×C59C2×D414yes—
124C22×C4×C59—22no—
125C22×C4×C59—42no—
126C22×C4×C59—42no—
127C22×C4×C59—42no—
128C22×C4×C59C2×D411yescharacteristic
129C22×C4×C59C2×D412yes—
130C22×C4×C59C2×D412yes—
131C22×C4×C59C2×D412yes—
132C22×C4×C59#4112yes—
133C22×C4×C59#4112yes—
134C22×C4×C59#4112yes—
135C22×C4×C59C2411yescharacteristic
136C2×C22⋊D59—216no—
137C2×C22⋊D59—48no—
138C2×C22⋊D59—432no—
139C2×C22⋊D59—48no—
140C22×Dic59—22no—
141C22×Dic59—24no—
142C22×Dic59—22no—
143C22×Dic59—22no—
144C22×Dic59—22no—
145C22×Dic59—22no—
146C22×Dic59—42no—
147C22×Dic59—42no—
148C22×Dic59—42no—
149C22×Dic59—42no—
150C22×Dic59—42no—
151C22×Dic59C2×D412yes—
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—28no—
166C2×C8×C59—22no—
167C2×C8×C59—22no—
168C2×C8×C59C2×D414yescomplemented
169C4⋊C4×C59—22no—
170C4⋊C4×C59—22no—
171C4⋊C4×C59—42no—
172C22⋊Dic59—216no—
173(C2×D59)⋊C4—48no—
174C4⋊Dic59—24no—
175C4⋊Dic59—22no—
176C4⋊Dic59—22no—
177C4⋊Dic59—22no—
178C4⋊Dic59—42no—
179C4⋊Dic59C2×D414yes—
180C2×C59⋊C8—22no—
181C2×C59⋊C8—22no—
182C2×C59⋊C8—22no—
183C2×C59⋊C8—44no—
184C23×C59—24no—
185C23×C59—42no—
186C23×C59—42no—
187C23×C59—42no—
188C23×C59—42no—
189C23×C59—42no—
190C23×C59—42no—
191C23×C59—48no—
192C23×C59—48no—
193C23×C59—48no—
194C23×C59—84no—
195C23×C59—84no—
196C23×C59—84no—
197C23×C59—84no—
198C23×C59#12012yes—
199C23×C59#12112yes—
200C23×C59#12312yes—
201C23×C59C2×D812yes—
202C23×C59#13512yes—
203C23×C59AGL(1,ℤ/8)12yes—
204C23×C59#13712yes—
205C23×C59C22×D411yescharacteristic
206C22×D59—22no—
207C22×D59—22no—
208C22×D59—22no—
209C22×D59—22no—
210C22×D59—22no—
211C22×D59—22no—
212C22×D59—28no—
213C22×D59—28no—
214C22×D59—28no—
215C22×D59—44no—
216C22×D59—44no—
217C22×D59—44no—
218C22×D59—44no—
219C22×D59C2×D814yes—
220D4×C59—24no—
221D4×C59—24no—
222D4×C59—42no—
223D4×C59—42no—
224D4×C59—48no—
225C2×C4×C59—42no—
226C2×C4×C59—42no—
227C2×C4×C59—42no—
228C2×C4×C59—84no—
229C2×C4×C59#12012yes—
230C2×C4×C59#12112yes—
231C2×C4×C59#12114yes—
232C2×C4×C59#12114yes—
233C2×C4×C59#12312yes—
234C2×C4×C59#12314yes—
235C2×C4×C59#12414yes—
236C2×C4×C59C22×D411yescharacteristic
237C2×C4×C59C22×D411yescharacteristic
238C2×C4×C59C22×D411yescharacteristic
239C2×C4×C59C2×#4111yescharacteristic
240C2×C4×C59C2×#4111yescharacteristic
241C2×C4×C59C2×#4111yescharacteristic
242C22⋊D59—432no—
243C2×Dic59—24no—
244C2×Dic59—22no—
245C2×Dic59—22no—
246C2×Dic59—22no—
247C2×Dic59—42no—
248C2×Dic59—42no—
249C2×Dic59—44no—
250C2×Dic59—48no—
251C2×Dic59—42no—
252C2×Dic59—42no—
253C2×Dic59—42no—
254C2×Dic59—84no—
255C4×D59—42no—
256C4×D59—42no—
257C4×D59—42no—
258C4×D59—42no—
259C4×D59—48no—
260C8×C59—24no—
261C59⋊C8—42no—
262C2×#2033—591nomaximal, Sylow
263C22×C59—44no—
264C22×C59—44no—
265C22×C59—44no—
266C22×C59—82no—
267C22×C59—82no—
268C22×C59—82no—
269C22×C59—82no—
270C22×C59—816no—
271C22×C59#39414yes—
272C22×C59#44714yes—
273C22×C59#45214yes—
274C22×C59#46614yes—
275C22×C59#46814yes—
276C22×C59#48014yes—
277C22×C59#48214yes—
278C22×C59C2×#12011yescharacteristic
279C22×C59C2×#12111yescharacteristic
280C22×C59C2×#12311yescharacteristic
281C22×C59C22×D811yescharacteristic
282C22×C59C2×#13511yescharacteristic
283C22×C59C2×AGL(1,ℤ/8)11yescharacteristic
284C22×C59C2×#13711yescharacteristic
285C2×D59—24no—
286C2×D59—24no—
287C2×D59—24no—
288C2×D59—42no—
289C2×D59—42no—
290C2×D59—42no—
291C2×D59—42no—
292C2×D59—416no—
293C4×C59—82no—
294C4×C59#39414yes—
295C4×C59C2×#12111yescharacteristic
296C4×C59C2×#12111yescharacteristic
297C4×C59C2×#12311yescharacteristic
298C4×C59C2×#12411yescharacteristic
299Dic59—42no—
300Dic59—44no—
301Dic59—82no—
302C22×#121—591no—
303C22×#107—591no—
304C22×#102—591no—
305C22×#102D5911yescharacteristic, complemented
306C22×C22⋊C8—591no—
307C2×#380—591no—
308#2033—598no—
309C2×#340—591no—
310C2×C59—84no—
311C2×C59#203318yescomplemented
312C2×C59C2×#39411yescharacteristic
313C2×C59C2×#44711yescharacteristic
314C2×C59C2×#45211yescharacteristic
315C2×C59C2×#46611yescharacteristic
316C2×C59C2×#46811yescharacteristic
317C2×C59C2×#48011yescharacteristic
318C2×C59C2×#48211yescharacteristic
319D59—44no—
320C23×D4—1181no—
321C23×D4C2×D5911yescharacteristic
322C24×C4—591no—
323C23×C8—591no—
324C23×C8C2×D5911yescharacteristic
325C2×#121—594no—
326C2×#121—1184no—
327C2×#121—1182no—
328C2×#121—1184no—
329C22×C4⋊C4—591no—
330C22×C4⋊C4—591no—
331C22×C4⋊C4C2×D5911yescharacteristic
332C22×C22⋊C4—1181no—
333C22×C22⋊C4—1181no—
334C2×#107—594no—
335C2×#107—1184no—
336C2×#102—24no—
337C2×#102—594no—
338C2×#102—1184no—
339C2×#102C2×D5914yescomplemented
340C2×C22⋊C8—594no—
341C2×C22⋊C8—1184no—
342#380—594no—
343#380—1182no—
344C2×#95—1181no—
345#340—594no—
346C59C2×#203311yescharacteristic, complemented, Sylow
347C25—21no—
348C25—591no—
349C22×D4—22no—
350C22×D4—21no—
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—22no—
354C22×D4—22no—
355C22×D4—1184no—
356C22×D4—1188no—
357C22×D4—2364no—
358C22×D4—2364no—
359C22×D4D23614yes—
360C22×D4C22×D5912yes—
361C23×C4—21no—
362C23×C4—591no—
363C23×C4—592no—
364C23×C4—592no—
365C23×C4—1181no—
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—592no—
377C22×C8—1182no—
378C22×C8—1182no—
379C22×C8—1182no—
380C22×C8C22⋊D5914yescomplemented
381C22×C8C22×D5912yes—
382#121—1188no—
383#121—11816no—
384#121—1188no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—594no—
389C2×C4⋊C4—592no—
390C2×C4⋊C4—592no—
391C2×C4⋊C4—1182no—
392C2×C4⋊C4—1181no—
393C2×C4⋊C4—1182no—
394C2×C4⋊C4—1182no—
395C2×C4⋊C4—1181no—
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—28no—
403#102—1188no—
404C22⋊C8—1188no—
405#95—1184no—
406C24—24no—
407C24—22no—
408C24—42no—
409C24—42no—
410C24—42no—
411C24—42no—
412C24—42no—
413C24—42no—
414C24—594no—
415C24—592no—
416C24—1182no—
417C24—1182no—
418C24—1182no—
419C24—1182no—
420C24—1182no—
421C24—1182no—
422C24D4×D5911yescharacteristic
423C2×D4—24no—
424C2×D4—28no—
425C2×D4—28no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—42no—
432C2×D4—44no—
433C2×D4—42no—
434C2×D4—44no—
435C2×D4—11816no—
436C2×D4—2368no—
437C2×D4—2368no—
438C2×D4—23632no—
439C2×D4C2×D23614yes—
440C22×C4—22no—
441C22×C4—42no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—592no—
445C22×C4—1182no—
446C22×C4—1184no—
447C22×C4—1182no—
448C22×C4—1182no—
449C22×C4—1182no—
450C22×C4—1184no—
451C22×C4—1184no—
452C22×C4—1184no—
453C22×C4—1182no—
454C22×C4—1182no—
455C22×C4—1182no—
456C22×C4—1182no—
457C22×C4—1182no—
458C22×C4—1182no—
459C22×C4—1182no—
460C22×C4—2362no—
461C22×C4—2362no—
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×C4D4×D5911yescharacteristic
472C22×C4D4×D5912yes—
473C22×C4#1174568712yes—
474C22×C4#1174568712yes—
475C22×C4C2×C22⋊D5912yes—
476C22×C4C23×D5911yescharacteristic
477C2×C8—28no—
478C2×C8—22no—
479C2×C8—22no—
480C2×C8—1182no—
481C2×C8—1182no—
482C2×C8—1182no—
483C2×C8—2364no—
484C2×C8C2×C22⋊D5914yescomplemented
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—42no—
488C4⋊C4—594no—
489C4⋊C4—1184no—
490C4⋊C4—1182no—
491C4⋊C4—1182no—
492C4⋊C4—1182no—
493C4⋊C4—2362no—
494C22⋊C4—11816no—
495C22⋊C4—2368no—
496C23—24no—
497C23—42no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—42no—
502C23—42no—
503C23—48no—
504C23—48no—
505C23—48no—
506C23—84no—
507C23—84no—
508C23—84no—
509C23—84no—
510C23—594no—
511C23—1182no—
512C23—1188no—
513C23—1182no—
514C23—1182no—
515C23—1182no—
516C23—1182no—
517C23—1182no—
518C23—1188no—
519C23—1188no—
520C23—2364no—
521C23—2364no—
522C23—2364no—
523C23—2364no—
524C23#1427369712yes—
525C23#1427369812yes—
526C23#1427370912yes—
527C23D8×D5912yes—
528C23#1427374612yes—
529C23#1427375412yes—
530C23#1427375612yes—
531C23C2×D4×D5911yescharacteristic
532D4—24no—
533D4—24no—
534D4—42no—
535D4—42no—
536D4—48no—
537D4—23632no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—84no—
542C2×C4—1182no—
543C2×C4—1184no—
544C2×C4—1182no—
545C2×C4—1182no—
546C2×C4—4724no—
547C2×C4—2362no—
548C2×C4—2362no—
549C2×C4—2362no—
550C2×C4—2362no—
551C2×C4—2362no—
552C2×C4—2368no—
553C2×C4—2364no—
554C2×C4—2362no—
555C2×C4—2362no—
556C2×C4—2362no—
557C2×C4—2362no—
558C2×C4—2368no—
559C2×C4#1427369712yes—
560C2×C4#1427369812yes—
561C2×C4#1427369914yes—
562C2×C4#1427370114yes—
563C2×C4#1427370912yes—
564C2×C4#1427371114yes—
565C2×C4#1427371314yes—
566C2×C4C2×D4×D5911yescharacteristic
567C2×C4C22×C22⋊D5911yescharacteristic
568C2×C4C22×D23611yescharacteristic
569C2×C4C2×#1174568711yescharacteristic
570C2×C4C2×#1174568711yescharacteristic
571C2×C4C2×#1174568511yescharacteristic
572C8—24no—
573C8—2362no—
574C22—44no—
575C22—44no—
576C22—44no—
577C22—82no—
578C22—82no—
579C22—82no—
580C22—82no—
581C22—816no—
582C22—1184no—
583C22—1184no—
584C22—1184no—
585C22—2362no—
586C22—2362no—
587C22—2362no—
588C22—23616no—
589C22—2362no—
590C22#1683731814yes—
591C22#1683753714yes—
592C22#1683756514yes—
593C22#1683763514yes—
594C22#1683764514yes—
595C22#1683771414yes—
596C22#1683772414yes—
597C22C2×#1427369711yescharacteristic
598C22C2×#1427369811yescharacteristic
599C22C2×#1427370911yescharacteristic
600C22C2×D8×D5911yescharacteristic
601C22C2×#1427374611yescharacteristic
602C22C2×#1427375411yescharacteristic
603C22C2×#1427375611yescharacteristic
604C4—82no—
605C4—4722no—
606C4—2362no—
607C4—2364no—
608C4#1683731814yes—
609C4C2×#1427369911yescharacteristic
610C4C2×#1427370111yescharacteristic
611C4C2×#1427371111yescharacteristic
612C4C2×#1427371311yescharacteristic
613C2—84no—
614C2—2364no—
615C2#2142527718yesdirect product factor
616C2C2×#1683731811yescharacteristic
617C2C2×#1683753711yescharacteristic
618C2C2×#1683756511yescharacteristic
619C2C2×#1683763511yescharacteristic
620C2C2×#1683764511yescharacteristic
621C2C2×#1683771411yescharacteristic
622C2C2×#1683772411yescharacteristic
subgroupG/H
centerC24D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#102×C59C2
socleC24×C59C2×D4
prime radicalC22×#14273698C2
hypercenterC22×#102D59
hypocenterC59C2×#2033
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
2. C22×#14273661C2semidirect
3. C22×#14273648C2semidirect
4. C22×(C2×D59)⋊C8C2semidirect
5. C2×#16837259C2semidirect
6. #21425277C2direct (N × H)
7. C2×#16837164C2semidirect
8. C22×#102×C59C2semidirect
21. C2×#14273661C22semidirect
23. C2×#14273648C22semidirect
25. C2×(C2×D59)⋊C8C22semidirect
27. #16837259C22semidirect
29. #16837164C22semidirect
34. C2×#102×C59C22semidirect
87. C22×C8×C59D4semidirect
168. C2×C8×C59C2×D4semidirect
305. C22×#102D59semidirect
311. C2×C59#2033semidirect
339. C2×#102C2×D59semidirect
346. C59C2×#2033semidirect
380. C22×C8C22⋊D59semidirect
484. C2×C8C2×C22⋊D59semidirect
615. C2#21425277direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#142736982
C22×#142736612
C22×#142736482
C22×(C2×D59)⋊C82
C2×#168372592
#214252772
C2×#168371642
C22×#102×C592
C2×#203359