Finite Group Databasebeta

← C2×#21425105 #28615486

Subgroups — C2×#21425105 #28615486

Order 15104.

2182 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#11745672C211yesmaximal, characteristic, complemented
2C22×#14273707C211yesmaximal, characteristic
3C22×#14273703C211yesmaximal, characteristic
4C22×#14273652C211yesmaximal, characteristic, complemented
5C22×(C2×D59)⋊C8C211yesmaximal, characteristic
6#21425105C218yesmaximal, direct product factor
7C2×#16837164C211yesmaximal, characteristic, complemented
8C22×#103×C59C211yesmaximal, characteristic, complemented
9C23×Dic118C2211yescharacteristic
10C23×C4×D59C2211yescharacteristic
11C22×#11745672—24no—
12C22×#11745672—24no—
13C22×#11745672—24no—
14C22×#11745672C2214yescomplemented
15C23×C59⋊C8C2211yescharacteristic
16C2×#14273707—24no—
17C2×#14273707—22no—
18C2×#14273707—24no—
19C2×#14273707C2214yes—
20C2×#14273703—22no—
21C2×#14273703—24no—
22C2×#14273703—24no—
23C2×#14273703C2214yes—
24C22×C4⋊Dic59—21no—
25C22×C4⋊Dic59C2211yescharacteristic
26C22×Dic59⋊C4—21no—
27C22×(C2×D59)⋊C4—21no—
28C22×(C2×D59)⋊C4—21no—
29C2×#14273652—24no—
30C2×#14273652C2214yescomplemented
31C2×(C2×D59)⋊C8—24no—
32C2×(C2×D59)⋊C8C2214yes—
33#16837164C2214yescomplemented
34C23×Q8×C59C2211yescharacteristic
35C23×C8×C59C2211yescharacteristic
36C22×C4⋊C4×C59C2211yescharacteristic
37C2×#103×C59—24no—
38C2×#103×C59C2214yescomplemented
39C24×D59D411yescharacteristic
40C22×Dic118—22no—
41C22×Dic118—22no—
42C22×Dic118—22no—
43C22×Dic118—22no—
44C22×Dic118—21no—
45C22×Dic118—22no—
46C22×Dic118D414yes—
47C22×Dic118C2312yes—
48C23×Dic59—21no—
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—
59C2×#11745672—232no—
60C2×#11745672—28no—
61C2×#11745672—28no—
62C2×#11745672—28no—
63C22×C59⋊C8—22no—
64C22×C59⋊C8—22no—
65C22×C59⋊C8D414yes—
66C22×C59⋊C8C2312yes—
67#14273707—216no—
68#14273707—28no—
69#14273707—28no—
70#14273703—216no—
71#14273703—28no—
72#14273703—28no—
73C2×C4⋊Dic59—28no—
74C2×C4⋊Dic59—22no—
75C2×C4⋊Dic59—21no—
76C2×C4⋊Dic59—24no—
77C2×C4⋊Dic59D414yes—
78C2×C4⋊Dic59C2312yes—
79C2×Dic59⋊C4—28no—
80C2×Dic59⋊C4—24no—
81C2×(C2×D59)⋊C4—28no—
82C2×(C2×D59)⋊C4—28no—
83C2×(C2×D59)⋊C4—24no—
84C2×(C2×D59)⋊C4—24no—
85#14273652—28no—
86(C2×D59)⋊C8—28no—
87C22×Q8×C59—22no—
88C22×Q8×C59—21no—
89C22×Q8×C59—22no—
90C22×Q8×C59—22no—
91C22×Q8×C59—22no—
92C22×Q8×C59—22no—
93C22×Q8×C59D414yes—
94C22×Q8×C59C2312yes—
95C23×C4×C59—21no—
96C23×C4×C59—21no—
97C23×C4×C59C2311yescharacteristic
98C22×C8×C59—22no—
99C22×C8×C59—22no—
100C22×C8×C59—22no—
101C22×C8×C59C2312yes—
102C2×C4⋊C4×C59—21no—
103C2×C4⋊C4×C59—22no—
104C2×C4⋊C4×C59D414yes—
105C2×C4⋊C4×C59C2312yes—
106#103×C59—28no—
107C24×C59C2×D411yescharacteristic
108C23×D59—22no—
109C23×D59—22no—
110C23×D59—22no—
111C23×D59—22no—
112C23×D59—22no—
113C23×D59—22no—
114C23×D59Q1614yescomplemented
115C23×D59C2×D412yes—
116C2×Q8×C59—24no—
117C2×Q8×C59—22no—
118C2×Q8×C59—28no—
119C2×Q8×C59—28no—
120C2×Q8×C59—22no—
121C2×Q8×C59—22no—
122C2×Q8×C59—22no—
123C2×Q8×C59—22no—
124C2×Q8×C59—42no—
125C2×Q8×C59—42no—
126C2×Q8×C59—44no—
127C2×Q8×C59—44no—
128C2×Q8×C59C2×D414yes—
129C22×C4×C59—24no—
130C22×C4×C59—24no—
131C22×C4×C59—22no—
132C22×C4×C59—22no—
133C22×C4×C59—42no—
134C22×C4×C59—42no—
135C22×C4×C59—42no—
136C22×C4×C59—42no—
137C22×C4×C59C2×D411yescharacteristic
138C22×C4×C59C2×D412yes—
139C22×C4×C59C2×D412yes—
140C22×C4×C59C2×D412yes—
141C22×C4×C59C2×D412yes—
142C22×C4×C59C2×D412yes—
143C22×C4×C59#4112yes—
144C22×C4×C59C2411yescharacteristic
145C22×Dic59—24no—
146C22×Dic59—24no—
147C22×Dic59—22no—
148C22×Dic59—22no—
149C22×Dic59—22no—
150C22×Dic59—22no—
151C22×Dic59—22no—
152C22×Dic59—42no—
153C22×Dic59—42no—
154C22×Dic59—42no—
155C22×Dic59—42no—
156C22×Dic59C2×D412yes—
157C2×C4×D59—24no—
158C2×C4×D59—24no—
159C2×C4×D59—24no—
160C2×C4×D59—22no—
161C2×C4×D59—22no—
162C2×C4×D59—22no—
163C2×C4×D59—22no—
164C2×C4×D59—22no—
165C2×C4×D59—22no—
166C2×C4×D59—44no—
167C2×C4×D59—44no—
168C2×C4×D59—44no—
169C2×C4×D59—44no—
170C2×Dic118—28no—
171C2×Dic118—28no—
172C2×Dic118—22no—
173C2×Dic118—22no—
174C2×Dic118—22no—
175C2×Dic118—22no—
176C2×Dic118—24no—
177C2×Dic118—22no—
178C2×Dic118—42no—
179C2×Dic118—44no—
180C2×Dic118—42no—
181C2×Dic118—44no—
182C2×Dic118C2×D414yes—
183C2×C8×C59—22no—
184C2×C8×C59—22no—
185C2×C8×C59—22no—
186C2×C8×C59—44no—
187C4⋊C4×C59—24no—
188C4⋊C4×C59—22no—
189C4⋊C4×C59C2×D414yes—
190#11745672—232no—
191(C2×D59)⋊C4—216no—
192(C2×D59)⋊C4—216no—
193C4⋊Dic59—216no—
194C4⋊Dic59—24no—
195C4⋊Dic59—22no—
196C4⋊Dic59C2×D414yes—
197Dic59⋊C4—216no—
198C2×C59⋊C8—28no—
199C2×C59⋊C8—22no—
200C2×C59⋊C8—22no—
201C2×C59⋊C8C2×D414yes—
202C23×C59#12012yes—
203C23×C59#12012yes—
204C23×C59#12112yes—
205C23×C59C2×Q1612yes—
206C23×C59#13512yes—
207C23×C59#13712yes—
208C23×C59#13712yes—
209C23×C59C22×D411yescharacteristic
210C22×D59—22no—
211C22×D59—22no—
212C22×D59—22no—
213C22×D59—22no—
214C22×D59—22no—
215C22×D59—22no—
216C22×D59—28no—
217C22×D59—28no—
218C22×D59—28no—
219C22×D59—44no—
220C22×D59—44no—
221C22×D59—44no—
222C22×D59—44no—
223C22×D59C2×Q1614yescomplemented
224Q8×C59—24no—
225Q8×C59—24no—
226Q8×C59—42no—
227Q8×C59—42no—
228Q8×C59—48no—
229C2×C4×C59—24no—
230C2×C4×C59—24no—
231C2×C4×C59—42no—
232C2×C4×C59—42no—
233C2×C4×C59—42no—
234C2×C4×C59—42no—
235C2×C4×C59—48no—
236C2×C4×C59—48no—
237C2×C4×C59#12012yes—
238C2×C4×C59#12014yes—
239C2×C4×C59#12012yes—
240C2×C4×C59#12114yes—
241C2×C4×C59#12112yes—
242C2×C4×C59#12114yes—
243C2×C4×C59#12714yes—
244C2×C4×C59C22×D411yescharacteristic
245C2×C4×C59C22×D411yescharacteristic
246C2×C4×C59C22×D411yescharacteristic
247C2×C4×C59C22×D411yescharacteristic
248C2×C4×C59C22×D411yescharacteristic
249C2×C4×C59C2×#4111yescharacteristic
250C2×Dic59—22no—
251C2×Dic59—24no—
252C2×Dic59—22no—
253C2×Dic59—24no—
254C2×Dic59—22no—
255C2×Dic59—42no—
256C2×Dic59—42no—
257C2×Dic59—42no—
258C2×Dic59—42no—
259C2×Dic59—48no—
260C2×Dic59—44no—
261C2×Dic59—48no—
262C4×D59—42no—
263C4×D59—42no—
264C4×D59—42no—
265C4×D59—42no—
266C4×D59—48no—
267Dic118—24no—
268Dic118—24no—
269Dic118—42no—
270Dic118—42no—
271Dic118—48no—
272C8×C59—42no—
273C59⋊C8—24no—
274C2×#2001—591nomaximal, Sylow
275C22×C59#39214yes—
276C22×C59#45114yes—
277C22×C59#45114yes—
278C22×C59#45214yes—
279C22×C59#45214yes—
280C22×C59#46714yes—
281C22×C59#47014yes—
282C22×C59C2×#12011yescharacteristic
283C22×C59C2×#12011yescharacteristic
284C22×C59C2×#12111yescharacteristic
285C22×C59C22×Q1611yescharacteristic
286C22×C59C2×#13511yescharacteristic
287C22×C59C2×#13711yescharacteristic
288C22×C59C2×#13711yescharacteristic
289C2×D59—24no—
290C2×D59—24no—
291C2×D59—24no—
292C2×D59—42no—
293C2×D59—42no—
294C2×D59—42no—
295C2×D59—416no—
296C2×D59—42no—
297C4×C59—44no—
298C4×C59—44no—
299C4×C59#39214yes—
300C4×C59C2×#12011yescharacteristic
301C4×C59C2×#12111yescharacteristic
302C4×C59C2×#12111yescharacteristic
303C4×C59C2×#12711yescharacteristic
304Dic59—44no—
305Dic59—42no—
306Dic59—44no—
307C23×Q16—591no—
308C22×C22⋊Q8—591no—
309C22×C22⋊Q8—591no—
310C22×#103—591no—
311C22×#103D5911yescharacteristic, complemented
312C22×C22⋊C8—591no—
313#2001—598no—
314C2×#340—591no—
315C2×C59#200118yescomplemented
316C2×C59C2×#39211yescharacteristic
317C2×C59C2×#45111yescharacteristic
318C2×C59C2×#45111yescharacteristic
319C2×C59C2×#45211yescharacteristic
320C2×C59C2×#45211yescharacteristic
321C2×C59C2×#46711yescharacteristic
322C2×C59C2×#47011yescharacteristic
323D59—44no—
324C23×Q8—591no—
325C23×Q8C2×D5911yescharacteristic
326C24×C4—591no—
327C22×Q16—594no—
328C22×Q16—1184no—
329C22×Q16—1184no—
330C22×Q16—1184no—
331C23×C8—591no—
332C23×C8C2×D5911yescharacteristic
333C2×C22⋊Q8—594no—
334C2×C22⋊Q8—594no—
335C2×C22⋊Q8—1182no—
336C2×C22⋊Q8—1184no—
337C2×C22⋊Q8—1184no—
338C2×C22⋊Q8—1182no—
339C2×C22⋊Q8—1184no—
340C2×C22⋊Q8—1184no—
341C22×C4⋊C4—591no—
342C22×C4⋊C4—1181no—
343C22×C4⋊C4—1181no—
344C22×C4⋊C4C2×D5911yescharacteristic
345C22×C22⋊C4—1181no—
346C22×C22⋊C4—1181no—
347C2×#103—24no—
348C2×#103—594no—
349C2×#103—1184no—
350C2×#103C2×D5914yescomplemented
351C2×C22⋊C8—594no—
352C2×C22⋊C8—1184no—
353#340—594no—
354C59C2×#200111yescharacteristic, complemented, Sylow
355C25—591no—
356C22×Q8—22no—
357C22×Q8—21no—
358C22×Q8—22no—
359C22×Q8—22no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—594no—
363C22×Q8—592no—
364C22×Q8—1181no—
365C22×Q8—1182no—
366C22×Q8—1182no—
367C22×Q8—1182no—
368C22×Q8—1182no—
369C22×Q8—1182no—
370C22×Q8D23614yes—
371C22×Q8C22×D5912yes—
372C23×C4—21no—
373C23×C4—21no—
374C23×C4—591no—
375C23×C4—592no—
376C23×C4—592no—
377C23×C4—1181no—
378C23×C4—1181no—
379C23×C4—1182no—
380C23×C4—1182no—
381C23×C4—1182no—
382C23×C4—1182no—
383C23×C4—1182no—
384C23×C4—1182no—
385C23×C4C22×D5911yescharacteristic
386C2×Q16—1188no—
387C2×Q16—1188no—
388C2×Q16—11832no—
389C2×Q16—1188no—
390C22×C8—22no—
391C22×C8—22no—
392C22×C8—22no—
393C22×C8—594no—
394C22×C8—592no—
395C22×C8—1182no—
396C22×C8—1182no—
397C22×C8C22×D5912yes—
398C22⋊Q8—1188no—
399C22⋊Q8—11816no—
400C22⋊Q8—1188no—
401C22⋊Q8—11816no—
402C22⋊Q8—1188no—
403C22⋊Q8—1188no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—594no—
407C2×C4⋊C4—592no—
408C2×C4⋊C4—1184no—
409C2×C4⋊C4—1184no—
410C2×C4⋊C4—1188no—
411C2×C4⋊C4—1188no—
412C2×C4⋊C4—1182no—
413C2×C4⋊C4—1181no—
414C2×C4⋊C4C22⋊D5914yes—
415C2×C4⋊C4C22×D5912yes—
416C2×C22⋊C4—1184no—
417C2×C22⋊C4—1184no—
418C2×C22⋊C4—1188no—
419C2×C22⋊C4—1188no—
420#103—28no—
421#103—1188no—
422C22⋊C8—1188no—
423C24—594no—
424C24—592no—
425C24—1182no—
426C24—1182no—
427C24—1182no—
428C24—1182no—
429C24—1182no—
430C24—1182no—
431C24D4×D5911yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—28no—
435C2×Q8—28no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8—22no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8—44no—
443C2×Q8—44no—
444C2×Q8—594no—
445C2×Q8—1184no—
446C2×Q8—1182no—
447C2×Q8—1188no—
448C2×Q8—1188no—
449C2×Q8—1182no—
450C2×Q8—1182no—
451C2×Q8—1182no—
452C2×Q8—1182no—
453C2×Q8—2362no—
454C2×Q8—2362no—
455C2×Q8—2364no—
456C2×Q8—2364no—
457C2×Q8C2×D23614yes—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—42no—
463C22×C4—42no—
464C22×C4—42no—
465C22×C4—42no—
466C22×C4—592no—
467C22×C4—1184no—
468C22×C4—1182no—
469C22×C4—1184no—
470C22×C4—1182no—
471C22×C4—1182no—
472C22×C4—1182no—
473C22×C4—1182no—
474C22×C4—1184no—
475C22×C4—1184no—
476C22×C4—1184no—
477C22×C4—1182no—
478C22×C4—1182no—
479C22×C4—1182no—
480C22×C4—1182no—
481C22×C4—1182no—
482C22×C4—1182no—
483C22×C4—2362no—
484C22×C4—2362no—
485C22×C4—2362no—
486C22×C4—2362no—
487C22×C4—2364no—
488C22×C4—2364no—
489C22×C4—2364no—
490C22×C4—2364no—
491C22×C4C2×D23612yes—
492C22×C4#1174568512yes—
493C22×C4D4×D5911yescharacteristic
494C22×C4D4×D5912yes—
495C22×C4D4×D5912yes—
496C22×C4D4×D5912yes—
497C22×C4C2×C22⋊D5912yes—
498C22×C4C23×D5911yescharacteristic
499Q16—11832no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—44no—
504C2×C8—594no—
505C2×C8—1188no—
506C2×C8—1182no—
507C2×C8—1182no—
508C4⋊C4—24no—
509C4⋊C4—22no—
510C4⋊C4—594no—
511C4⋊C4—11816no—
512C4⋊C4—11816no—
513C4⋊C4—1184no—
514C4⋊C4—1182no—
515C4⋊C4C2×C22⋊D5914yes—
516C22⋊C4—11816no—
517C22⋊C4—11816no—
518C23—594no—
519C23—1182no—
520C23—1182no—
521C23—1188no—
522C23—1182no—
523C23—1182no—
524C23—1182no—
525C23—1188no—
526C23—1188no—
527C23—1182no—
528C23—2364no—
529C23—2364no—
530C23—2364no—
531C23—2364no—
532C23#1427369512yes—
533C23#1427369712yes—
534C23#1427370012yes—
535C23Q16×D5912yes—
536C23#1427374812yes—
537C23#1427375612yes—
538C23#1427375912yes—
539C23C2×D4×D5911yescharacteristic
540Q8—24no—
541Q8—24no—
542Q8—42no—
543Q8—42no—
544Q8—48no—
545Q8—1184no—
546Q8—1184no—
547Q8—2362no—
548Q8—2362no—
549Q8—2368no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—48no—
556C2×C4—48no—
557C2×C4—42no—
558C2×C4—1184no—
559C2×C4—1182no—
560C2×C4—1182no—
561C2×C4—1184no—
562C2×C4—1182no—
563C2×C4—2362no—
564C2×C4—2362no—
565C2×C4—2362no—
566C2×C4—2362no—
567C2×C4—2364no—
568C2×C4—2368no—
569C2×C4—2368no—
570C2×C4—2362no—
571C2×C4—2362no—
572C2×C4—2362no—
573C2×C4—2362no—
574C2×C4—2368no—
575C2×C4#1427369512yes—
576C2×C4#1427369714yes—
577C2×C4#1427369712yes—
578C2×C4#1427370014yes—
579C2×C4#1427370012yes—
580C2×C4#1427370114yes—
581C2×C4#1427372314yes—
582C2×C4C2×D4×D5911yescharacteristic
583C2×C4C2×D4×D5911yescharacteristic
584C2×C4C2×D4×D5911yescharacteristic
585C2×C4C22×C22⋊D5911yescharacteristic
586C2×C4C22×D23611yescharacteristic
587C2×C4C2×#1174568511yescharacteristic
588C8—42no—
589C8—1184no—
590C22—1184no—
591C22—1184no—
592C22—1184no—
593C22—2362no—
594C22—2362no—
595C22—23616no—
596C22—2362no—
597C22—2362no—
598C22#1683731114yes—
599C22#1683755614yes—
600C22#1683755914yes—
601C22#1683756114yes—
602C22#1683756714yes—
603C22#1683764214yes—
604C22#1683765914yes—
605C22C2×#1427369511yescharacteristic
606C22C2×#1427369711yescharacteristic
607C22C2×#1427370011yescharacteristic
608C22C2×Q16×D5911yescharacteristic
609C22C2×#1427374811yescharacteristic
610C22C2×#1427375611yescharacteristic
611C22C2×#1427375911yescharacteristic
612C4—44no—
613C4—44no—
614C4—2362no—
615C4—2364no—
616C4—2364no—
617C4#1683731114yes—
618C4C2×#1427369711yescharacteristic
619C4C2×#1427370011yescharacteristic
620C4C2×#1427370111yescharacteristic
621C4C2×#1427372311yescharacteristic
622C2—2364no—
623C2#2142510518yesdirect product factor
624C2C2×#1683731111yescharacteristic
625C2C2×#1683755611yescharacteristic
626C2C2×#1683755911yescharacteristic
627C2C2×#1683756111yescharacteristic
628C2C2×#1683756711yescharacteristic
629C2C2×#1683764211yescharacteristic
630C2C2×#1683765911yescharacteristic
subgroupG/H
centerC24D4×D59
commutator, cosocleC22×C4×C59C24
FrattiniC22×C4C23×D59
FittingC22×#103×C59C2
socleC24×C59C2×D4
prime radicalC24×D59D4
hypercenterC22×#103D59
hypocenterC59C2×#2001
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
1. C23×#11745672C2semidirect
4. C22×#14273652C2semidirect
6. #21425105C2direct (N × H)
7. C2×#16837164C2semidirect
8. C22×#103×C59C2semidirect
14. C22×#11745672C22semidirect
30. C2×#14273652C22semidirect
33. #16837164C22semidirect
38. C2×#103×C59C22semidirect
114. C23×D59Q16semidirect
223. C22×D59C2×Q16semidirect
311. C22×#103D59semidirect
315. C2×C59#2001semidirect
350. C2×#103C2×D59semidirect
354. C59C2×#2001semidirect
623. C2#21425105direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#117456722
C22×#142737072
C22×#142737032
C22×#142736522
C22×(C2×D59)⋊C82
#214251052
C2×#168371642
C22×#103×C592
C2×#200159