Finite Group Databasebeta

← C2×#20253559 #27084426

Subgroups — C2×#20253559 #27084426

Order 12032.

2150 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689657C211yesmaximal, characteristic
2#20253559C2116yesmaximal, direct product factor
3C2×#15689458C211yesmaximal, characteristic, complemented
4C2×#15689441C211yesmaximal, characteristic
5C2×#15689430C212yesmaximal, complemented
6C2×#15689345C212yesmaximal, complemented
7C2×#15689279C211yesmaximal, characteristic, complemented
8C2×#15689262C211yesmaximal, characteristic
9C2×#15689228C212yesmaximal, complemented
10C2×#15689221C212yesmaximal, complemented
11C2×#15689180C211yesmaximal, characteristic, complemented
12C22×C4×Q8×C47C211yesmaximal, characteristic, complemented
13C22×#10625337C2212yes—
14C22×#10625336C2212yes—
15#15689657—24no—
16#15689657C2218yes—
17C2×#13094018—21no—
18C2×#13094016C2211yescharacteristic
19C2×#13094012C2211yescharacteristic
20C2×#13094007—21no—
21C2×#13094003C2211yescharacteristic
22C2×#13093998C2211yescharacteristic
23C2×C4×Dic94C2211yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×C4×C22⋊D47—21no—
26C2×#13093981—21no—
27#15689458C2218yescomplemented
28#15689441C2218yes—
29#15689430C22116yescomplemented
30#15689345C22116yescomplemented
31#15689279C2218yescomplemented
32#15689262C2218yes—
33#15689228C22116yescomplemented
34#15689221C22116yescomplemented
35#15689180C2218yescomplemented
36C2×#13093957C2212yes—
37C2×#13093955C2212yes—
38C2×C4⋊(C47⋊C8)C2212yes—
39C2×#13093948C2212yes—
40C2×#13093948C2212yes—
41C2×#13093947C2212yes—
42C2×#13093944C2212yes—
43C2×C22⋊(C47⋊C8)C2211yescharacteristic
44C2×C22⋊(C47⋊C8)C2211yescharacteristic
45C2×#13093935C2212yes—
46C23×Q8×C47C2211yescharacteristic
47C2×C4×Q8×C47—21no—
48C2×C4×Q8×C47—21no—
49C2×C4×Q8×C47—24no—
50C2×C4×Q8×C47C2212yes—
51C2×C4×Q8×C47C2212yes—
52C2×C4×Q8×C47C2218yescomplemented
53C22×C4⋊C4×C47—21no—
54C22×C4⋊C4×C47C2211yescharacteristic
55C22×C42×C47—21no—
56C22×C42×C47C2211yescharacteristic
57C22×Dic94C2311yescharacteristic
58C22×D188C2311yescharacteristic
59C22×C22⋊D47—21no—
60C22×C4×D47—21no—
61C2×#10625337—28no—
62C2×#10625337C2318yes—
63C2×#10625336—28no—
64C2×#10625336C2318yes—
65C22×C47⋊C8C2312yes—
66C22×C47⋊C8C2312yes—
67#13094018—28no—
68#13094016—22no—
69#13094016C2314yes—
70#13094012—22no—
71#13094012C2314yes—
72#13094007—28no—
73#13094003—22no—
74#13094003C2314yes—
75#13093998—22no—
76#13093998C2314yes—
77C4×Dic94—22no—
78C4×Dic94C2314yes—
79C4×D188—22no—
80C4×D188C2314yes—
81C4×C22⋊D47—28no—
82#13093981—28no—
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C2×C22⋊Dic47—21no—
90C2×(C2×D47)⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×C4×Dic47—21no—
95#13093957C2318yes—
96#13093955C2318yes—
97C4⋊(C47⋊C8)C2318yes—
98#13093948C2318yes—
99#13093948C2318yes—
100#13093947C2318yes—
101#13093944C2318yes—
102C22⋊(C47⋊C8)C2314yes—
103C22⋊(C47⋊C8)C2314yes—
104#13093935C2318yes—
105C22×Q8×C47—28no—
106C22×Q8×C47—21no—
107C22×Q8×C47—22no—
108C22×Q8×C47C2314yes—
109C22×Q8×C47C2312yes—
110C23×C4×C47—21no—
111C23×C4×C47—21no—
112C23×C4×C47D411yescharacteristic
113C23×C4×C47D411yescharacteristic
114C23×C4×C47C2311yescharacteristic
115C4×Q8×C47—24no—
116C4×Q8×C47—24no—
117C4×Q8×C47—28no—
118C4×Q8×C47—28no—
119C4×Q8×C47C2318yes—
120C4×Q8×C47C2318yes—
121C2×C4⋊C4×C47—22no—
122C2×C4⋊C4×C47—22no—
123C2×C4⋊C4×C47—28no—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—22no—
126C2×C4⋊C4×C47C2312yes—
127C2×C4⋊C4×C47C2314yes—
128C2×C42×C47—22no—
129C2×C42×C47—22no—
130C2×C42×C47—28no—
131C2×C42×C47D411yescharacteristic
132C2×C42×C47D411yescharacteristic
133C2×C42×C47D414yes—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136C2×C42×C47C2314yes—
137C24×C47C2×D411yescharacteristic
138C23×D47—21no—
139C2×Q8×C47—216no—
140C2×Q8×C47—28no—
141C2×Q8×C47—216no—
142C2×Q8×C47—24no—
143C2×Q8×C47—22no—
144C2×Q8×C47—24no—
145C2×Q8×C47#4118yes—
146C2×Q8×C47C2414yes—
147C22×C4×C47—28no—
148C22×C4×C47—24no—
149C22×C4×C47—24no—
150C22×C4×C47—22no—
151C22×C4×C47—24no—
152C22×C4×C47—24no—
153C22×C4×C47—22no—
154C22×C4×C47—42no—
155C22×C4×C47—44no—
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D414yes—
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×D412yes—
161C22×C4×C47C2×D411yescharacteristic
162C22×C4×C47C2×D411yescharacteristic
163C22×C4×C47C2×D414yes—
164C22×C4×C47C2412yes—
165C22×C4×C47C2411yescharacteristic
166C2×C22⋊D47—24no—
167C2×C22⋊D47—44no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C2×D188—24no—
172C2×D188—21no—
173C2×D188C2412yes—
174C2×C4×D47—24no—
175C2×C4×D47—44no—
176C2×Dic94—24no—
177C2×Dic94—21no—
178C2×Dic94C2412yes—
179C4⋊C4×C47—28no—
180C4⋊C4×C47—28no—
181C4⋊C4×C47—24no—
182C4⋊C4×C47—22no—
183C4⋊C4×C47C2414yes—
184C42×C47—28no—
185C42×C47—28no—
186C42×C47C2×D414yes—
187C42×C47C2×D412yes—
188C42×C47C2×D412yes—
189C42×C47C2×D414yes—
190C42×C47C2412yes—
191C42×C47C2412yes—
192C22⋊Dic47—24no—
193#10625337—216no—
194#10625336—216no—
195(C2×D47)⋊C4—24no—
196(C2×D47)⋊C4—24no—
197(C2×D47)⋊C4—24no—
198(C2×D47)⋊C4—24no—
199C4⋊Dic47—21no—
200C4⋊Dic47—21no—
201C4⋊Dic47C2412yes—
202C4⋊Dic47C2412yes—
203Dic47⋊C4—24no—
204Dic47⋊C4—24no—
205Dic47⋊C4—24no—
206Dic47⋊C4—24no—
207C4×Dic47—24no—
208C2×C47⋊C8—24no—
209C2×C47⋊C8—24no—
210C2×C47⋊C8C2414yes—
211C2×C47⋊C8C2414yes—
212C23×C47—22no—
213C23×C47—22no—
214C23×C47#13714yes—
215C23×C47C22×D412yes—
216C23×C47C22×D411yescharacteristic
217C22×D47—22no—
218C22×D47—42no—
219C22×D47—42no—
220C22×D47—42no—
221Q8×C47—216no—
222Q8×C47—28no—
223Q8×C47—24no—
224Q8×C47C2×#4118yes—
225C2×C4×C47—216no—
226C2×C4×C47—28no—
227C2×C4×C47—22no—
228C2×C4×C47—28no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—24no—
234C2×C4×C47—24no—
235C2×C4×C47—24no—
236C2×C4×C47—24no—
237C2×C4×C47—44no—
238C2×C4×C47—48no—
239C2×C4×C47—44no—
240C2×C4×C47C22×D412yes—
241C2×C4×C47C22×D412yes—
242C2×C4×C47C22×D412yes—
243C2×C4×C47C22×D412yes—
244C2×C4×C47C22×D412yes—
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C2×#4114yes—
247C2×C4×C47C2511yescharacteristic
248C22⋊D47—48no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255D188—24no—
256D188—42no—
257C4×D47—48no—
258Dic94—24no—
259Dic94—42no—
260C47⋊C8—24no—
261C47⋊C8—24no—
262C2×#3117—471nomaximal, Sylow
263C22×C47—28no—
264C22×C47—22no—
265C22×C47—22no—
266C22×C47#52512yes—
267C22×C47C2×#13714yes—
268C22×C47C2×#13712yes—
269C22×C47#57512yes—
270C22×C47C23×D411yescharacteristic
271C2×D47—42no—
272C2×D47—42no—
273C2×D47—42no—
274C2×D47—84no—
275C4×C47—28no—
276C4×C47—22no—
277C4×C47—22no—
278C4×C47—22no—
279C4×C47—22no—
280C4×C47—22no—
281C4×C47—44no—
282C4×C47#52512yes—
283C4×C47C22×#4112yes—
284Dic47—42no—
285Dic47—42no—
286Dic47—42no—
287C2×#529—471no—
288C22×C4×Q8D4711yescharacteristic, complemented
289#3117—4716no—
290C2×#484—471no—
291C2×#481—471no—
292C2×#479—472no—
293C2×#464—472no—
294C2×#451—471no—
295C2×#448—471no—
296C2×#441—472no—
297C2×#440—472no—
298C2×#432—471no—
299C2×C47—24no—
300C2×C47#311714yescomplemented
301C2×C47C2×#52511yescharacteristic
302C2×C47C22×#13711yescharacteristic
303C2×C47C2×#57511yescharacteristic
304D47—82no—
305C23×Q8C2×D4711yescharacteristic
306C22×Q16—472no—
307C22×SD16—472no—
308#529—478no—
309#529—944no—
310C2×#126—941no—
311C2×#125—471no—
312C2×#124—471no—
313C2×#123—941no—
314C2×C22⋊Q8—471no—
315C2×#121—471no—
316C2×C4×Q8—21no—
317C2×C4×Q8—21no—
318C2×C4×Q8—24no—
319C2×C4×Q8—471no—
320C2×C4×Q8C2×D4712yes—
321C2×C4×Q8C2×D4712yes—
322C2×C4×Q8C2×D4718yescomplemented
323C2×C4×D4—471no—
324C2×C4×D4—941no—
325C2×#117—941no—
326C22×C4⋊C4—21no—
327C22×C4⋊C4C2×D4711yescharacteristic
328C22×C42—21no—
329C22×C42C2×D4711yescharacteristic
330#484—478no—
331#481—478no—
332#479—4716no—
333#464—4716no—
334#451—478no—
335#448—478no—
336#441—4716no—
337#440—4716no—
338#432—478no—
339C2×#107—472no—
340C2×#106—472no—
341C2×C4⋊C8—472no—
342C2×#103—472no—
343C2×#103—472no—
344C2×#103—472no—
345C2×#102—472no—
346C2×C22⋊C8—471no—
347C2×C22⋊C8—471no—
348C2×#97—472no—
349C47C2×#311711yescharacteristic, complemented, Sylow
350C22×Q8—28no—
351C22×Q8—22no—
352C22×Q8—21no—
353C22×Q8—471no—
354C22×Q8C22×D4714yes—
355C22×Q8C22×D4712yes—
356C22×D4—471no—
357C22×D4—941no—
358C23×C4—21no—
359C23×C4—21no—
360C23×C4—941no—
361C23×C4C22⋊D4711yescharacteristic
362C23×C4C22⋊D4711yescharacteristic
363C23×C4C22×D4711yescharacteristic
364C2×Q16—478no—
365C2×Q16—948no—
366C2×SD16—478no—
367C2×SD16—948no—
368C22×C8—472no—
369C22×C8—472no—
370#126—948no—
371#125—474no—
372#125—942no—
373#124—474no—
374#124—942no—
375#123—948no—
376C22⋊Q8—474no—
377C22⋊Q8—942no—
378#121—474no—
379#121—942no—
380C4×Q8—24no—
381C4×Q8—24no—
382C4×Q8—28no—
383C4×Q8—28no—
384C4×Q8—474no—
385C4×Q8—942no—
386C4×Q8C22×D4718yes—
387C4×Q8C22×D4718yes—
388C4×D4—474no—
389C4×D4—948no—
390C4×D4—942no—
391#117—948no—
392C2×C4⋊C4—22no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—28no—
395C2×C4⋊C4—22no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4C22×D4712yes—
404C2×C4⋊C4C22×D4714yes—
405C2×C22⋊C4—941no—
406C2×C22⋊C4—941no—
407C2×C22⋊C4—941no—
408C2×C22⋊C4—941no—
409C2×C22⋊C4—941no—
410C2×C42—22no—
411C2×C42—22no—
412C2×C42—28no—
413C2×C42—941no—
414C2×C42C22⋊D4711yescharacteristic
415C2×C42C22⋊D4711yescharacteristic
416C2×C42C22⋊D4714yes—
417C2×C42C22×D4711yescharacteristic
418C2×C42C22×D4711yescharacteristic
419C2×C42C22×D4714yes—
420#107—478no—
421#106—478no—
422C4⋊C8—478no—
423#103—478no—
424#103—478no—
425#103—478no—
426#102—478no—
427C22⋊C8—474no—
428C22⋊C8—474no—
429#97—478no—
430C24—941no—
431C24C2×C22⋊D4711yescharacteristic
432C2×Q8—216no—
433C2×Q8—28no—
434C2×Q8—216no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—24no—
438C2×Q8—472no—
439C2×Q8—941no—
440C2×Q8—944no—
441C2×Q8#1062535018yes—
442C2×Q8C23×D4714yes—
443C2×D4—472no—
444C2×D4—944no—
445C2×D4—941no—
446C2×D4—944no—
447C2×D4—1884no—
448C22×C4—28no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—22no—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—22no—
455C22×C4—42no—
456C22×C4—44no—
457C22×C4—941no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—944no—
461C22×C4—1884no—
462C22×C4C2×C22⋊D4714yes—
463C22×C4C2×C22⋊D4712yes—
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C2×C22⋊D4711yescharacteristic
468C22×C4C2×C22⋊D4711yescharacteristic
469C22×C4C2×C22⋊D4714yes—
470C22×C4C23×D4712yes—
471C22×C4C23×D4711yescharacteristic
472Q16—9416no—
473SD16—9416no—
474C2×C8—474no—
475C2×C8—474no—
476C2×C8—944no—
477C2×C8—944no—
478C4⋊C4—28no—
479C4⋊C4—28no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—472no—
483C4⋊C4—472no—
484C4⋊C4—944no—
485C4⋊C4—944no—
486C4⋊C4—944no—
487C4⋊C4—944no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4C23×D4714yes—
491C22⋊C4—944no—
492C22⋊C4—944no—
493C22⋊C4—944no—
494C22⋊C4—944no—
495C22⋊C4—944no—
496C42—28no—
497C42—28no—
498C42—944no—
499C42C2×C22⋊D4714yes—
500C42C2×C22⋊D4712yes—
501C42C2×C22⋊D4712yes—
502C42C2×C22⋊D4714yes—
503C42C23×D4712yes—
504C42C23×D4712yes—
505C23—22no—
506C23—22no—
507C23—942no—
508C23—1882no—
509C23—1882no—
510C23—1882no—
511C23#1309405514yes—
512C23C22×C22⋊D4712yes—
513C23C22×C22⋊D4711yescharacteristic
514Q8—216no—
515Q8—28no—
516Q8—24no—
517Q8—944no—
518Q8—1882no—
519Q8C2×#1062535018yes—
520D4—944no—
521D4—1888no—
522D4—1882no—
523C2×C4—216no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—28no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—24no—
535C2×C4—44no—
536C2×C4—48no—
537C2×C4—44no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—1888no—
542C2×C4—1882no—
543C2×C4—1882no—
544C2×C4—1882no—
545C2×C4C22×C22⋊D4712yes—
546C2×C4C22×C22⋊D4712yes—
547C2×C4C22×C22⋊D4712yes—
548C2×C4C22×C22⋊D4712yes—
549C2×C4C22×C22⋊D4712yes—
550C2×C4C22×C22⋊D4711yescharacteristic
551C2×C4C2×#1062535014yes—
552C2×C4C24×D4711yescharacteristic
553C8—944no—
554C8—944no—
555C22—22no—
556C22—22no—
557C22—28no—
558C22—3764no—
559C22—1882no—
560C22—1882no—
561C22—1882no—
562C22#1568963412yes—
563C22C2×#1309405514yes—
564C22C2×#1309405512yes—
565C22#1568992112yes—
566C22C23×C22⋊D4711yescharacteristic
567C4—22no—
568C4—22no—
569C4—22no—
570C4—22no—
571C4—28no—
572C4—22no—
573C4—44no—
574C4—1882no—
575C4—1882no—
576C4—1882no—
577C4#1568963412yes—
578C4C22×#1062535012yes—
579C2—24no—
580C2—3762no—
581C2#2025355914yesdirect product factor
582C2C2×#1568963411yescharacteristic
583C2C22×#1309405511yescharacteristic
584C2C2×#1568992111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC22×C4×Q8×C47C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenterC22×C4×Q8D47
hypocenterC47C2×#3117
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #20253559C2direct (N × H)
3. C2×#15689458C2semidirect
5. C2×#15689430C2semidirect
6. C2×#15689345C2semidirect
7. C2×#15689279C2semidirect
9. C2×#15689228C2semidirect
10. C2×#15689221C2semidirect
11. C2×#15689180C2semidirect
12. C22×C4×Q8×C47C2semidirect
27. #15689458C22semidirect
29. #15689430C22semidirect
30. #15689345C22semidirect
31. #15689279C22semidirect
33. #15689228C22semidirect
34. #15689221C22semidirect
35. #15689180C22semidirect
52. C2×C4×Q8×C47C22semidirect
288. C22×C4×Q8D47semidirect
300. C2×C47#3117semidirect
322. C2×C4×Q8C2×D47semidirect
349. C47C2×#3117semidirect
581. C2#20253559direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896572
#202535592
C2×#156894582
C2×#156894412
C2×#156894302
C2×#156893452
C2×#156892792
C2×#156892622
C2×#156892282
C2×#156892212
C2×#156891802
C22×C4×Q8×C472
C2×#311747