Finite Group Databasebeta

← C2×#20254584 #27088419

Subgroups — C2×#20254584 #27088419

Order 12032.

2038 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic, complemented
2C2×#15689670C211yesmaximal, characteristic
3#20254584C2116yesmaximal, direct product factor
4C2×#15689530C212yesmaximal, complemented
5C2×#15689486C212yesmaximal, complemented
6C2×#15689449C212yesmaximal, complemented
7C2×#15689445C212yesmaximal, complemented
8C2×#15689410C211yesmaximal, characteristic, complemented
9C2×#15689404C211yesmaximal, characteristic, complemented
10C2×#15689403C211yesmaximal, characteristic, complemented
11C2×#15689179C211yesmaximal, characteristic, complemented
12C2×C47×#476C211yesmaximal, characteristic, complemented
13C22×#10625350—21no—
14#15689678—24no—
15#15689678C2218yescomplemented
16#15689670—24no—
17#15689670C2218yes—
18C2×#13094024C2211yescharacteristic
19C2×#13094023C2211yescharacteristic
20C2×#13094020C2211yescharacteristic
21C2×#13094015C2212yes—
22C2×#13094010—21no—
23C2×#13094004—21no—
24C2×#13094000—21no—
25C2×#13093999C2211yescharacteristic
26C2×#13093997—21no—
27C2×#13093995C2211yescharacteristic
28C2×Q8×Dic47—21no—
29C2×#13093989—21no—
30C2×C4×D188C2211yescharacteristic
31C2×C4×C22⋊D47—21no—
32C2×#13093982C2212yes—
33C2×C42×D47C2211yescharacteristic
34#15689530C22116yescomplemented
35#15689486C22116yescomplemented
36#15689449C22116yescomplemented
37#15689445C22116yescomplemented
38#15689410C2218yescomplemented
39#15689404C2218yescomplemented
40#15689403C2218yescomplemented
41#15689179C2218yescomplemented
42C2×#13093958C2212yes—
43C2×#13093957C2212yes—
44C2×#13093955C2212yes—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×#13093946C2212yes—
47C2×#13093945C2212yes—
48C2×#13093944C2212yes—
49C2×(C2×D47)⋊C8C2212yes—
50C2×#13093934C2212yes—
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C47×#476C2218yescomplemented
54C2×#106×C47C2212yes—
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×#102×C47C2212yes—
57C2×#10625350—28no—
58C2×#10625350—48no—
59C22×Dic94—21no—
60C22×Dic94—21no—
61C22×D188—21no—
62C22×D188C2311yescharacteristic
63C22×C22⋊D47—21no—
64C22×C22⋊D47—21no—
65C22×C22⋊D47—21no—
66C22×C4×D47—21no—
67C22×C4×D47D411yescharacteristic
68C22×C4×D47D411yescharacteristic
69C22×C4×D47C2311yescharacteristic
70C22×C47⋊C8C2312yes—
71#13094024—22no—
72#13094024C2314yes—
73#13094023—22no—
74#13094023C2314yes—
75#13094020—22no—
76#13094020C2314yes—
77#13094015—24no—
78#13094015C2318yes—
79#13094010—28no—
80#13094004—28no—
81#13094000—28no—
82#13093999—22no—
83#13093999C2314yes—
84#13093997—28no—
85#13093995—22no—
86#13093995C2314yes—
87Q8×Dic47—28no—
88#13093989—28no—
89C4×D188—22no—
90C4×D188C2314yes—
91C4×C22⋊D47—28no—
92#13093982—24no—
93#13093982C2318yes—
94C2×C4⋊Dic47—21no—
95C2×C4⋊Dic47—22no—
96C2×C4⋊Dic47C2312yes—
97C2×C4⋊Dic47C2311yescharacteristic
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—22no—
100C2×C22⋊Dic47—21no—
101C2×(C2×D47)⋊C4—22no—
102C2×(C2×D47)⋊C4—21no—
103C2×(C2×D47)⋊C4—21no—
104C2×C4×Dic47—22no—
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D411yescharacteristic
107C2×C4×Dic47C2311yescharacteristic
108C42×D47D414yes—
109C42×D47C2314yes—
110#13093958C2318yes—
111#13093957C2318yes—
112#13093955C2318yes—
113C4⋊(C47⋊C8)C2314yes—
114#13093946C2318yes—
115#13093945C2318yes—
116#13093944C2318yes—
117(C2×D47)⋊C8C2318yes—
118#13093934C2318yes—
119C22×Q8×C47—21no—
120C22×D4×C47C2311yescharacteristic
121C23×C4×C47—21no—
122C22×C8×C47C2312yes—
123C4⋊Q8×C47—22no—
124C4⋊Q8×C47C2314yes—
125C4×D4×C47—22no—
126C4×D4×C47C2314yes—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2312yes—
130C2×C22⋊C4×C47—21no—
131C2×C42×C47C2311yescharacteristic
132#106×C47C2318yes—
133C4⋊C8×C47C2314yes—
134#102×C47C2318yes—
135C24×C47—21no—
136C23×D47—21no—
137C23×D47C2×D411yescharacteristic
138C2×Q8×C47—24no—
139C2×Q8×C47—44no—
140C2×D4×C47—21no—
141C2×D4×C47—22no—
142C2×D4×C47—22no—
143C2×D4×C47C2412yes—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—24no—
147C22×C4×C47—44no—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2411yescharacteristic
151C2×C22⋊D47—24no—
152C2×C22⋊D47—24no—
153C2×C22⋊D47—24no—
154C2×C22⋊D47—44no—
155C2×C22⋊D47—44no—
156C2×C22⋊D47—44no—
157C22×Dic47—22no—
158C22×Dic47—21no—
159C22×Dic47C2×D411yescharacteristic
160C22×Dic47C2×D411yescharacteristic
161C22×Dic47C2×D411yescharacteristic
162#10625350—432no—
163C2×D188—22no—
164C2×D188—22no—
165C2×D188—24no—
166C2×D188—21no—
167C2×D188—44no—
168C2×D188C2412yes—
169C2×C4×D47—24no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—24no—
173C2×C4×D47—42no—
174C2×C4×D47—44no—
175C2×C4×D47C2×D412yes—
176C2×C4×D47C2×D414yes—
177C2×C4×D47C2×D414yes—
178C2×C4×D47C2412yes—
179C2×Dic94—24no—
180C2×Dic94—24no—
181C2×Dic94—44no—
182C2×Dic94—44no—
183C2×C8×C47—24no—
184C2×C8×C47C2414yes—
185C4⋊C4×C47—24no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—22no—
188C4⋊C4×C47C2412yes—
189C4⋊C4×C47C2414yes—
190C22⋊C4×C47—24no—
191C42×C47C2×D412yes—
192C42×C47C2412yes—
193C22⋊Dic47—24no—
194(C2×D47)⋊C4—28no—
195(C2×D47)⋊C4—24no—
196(C2×D47)⋊C4—24no—
197C4⋊Dic47—24no—
198C4⋊Dic47—22no—
199C4⋊Dic47—21no—
200C4⋊Dic47—28no—
201C4⋊Dic47C2414yes—
202C4⋊Dic47C2412yes—
203Dic47⋊C4—24no—
204Dic47⋊C4—28no—
205C4×Dic47—28no—
206C4×Dic47C2×D412yes—
207C4×Dic47C2×D414yes—
208C4×Dic47C2×D414yes—
209C4×Dic47C2412yes—
210C2×C47⋊C8—24no—
211C2×C47⋊C8C2414yes—
212C23×C47—22no—
213C23×C47—42no—
214C23×C47—42no—
215C23×C47—42no—
216C23×C47C22×D411yescharacteristic
217C22×D47—22no—
218C22×D47—22no—
219C22×D47—22no—
220C22×D47—22no—
221C22×D47—42no—
222C22×D47—42no—
223C22×D47—42no—
224C22×D47C22×D412yes—
225Q8×C47—48no—
226D4×C47—22no—
227D4×C47—22no—
228D4×C47—42no—
229C2×C4×C47—22no—
230C2×C4×C47—24no—
231C2×C4×C47—22no—
232C2×C4×C47—42no—
233C2×C4×C47—44no—
234C2×C4×C47—48no—
235C2×C4×C47AGL(1,ℤ/8)14yes—
236C2×C4×C47C22×D412yes—
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C22×D412yes—
239C2×C4×C472−1+412yes—
240C2×C4×C472−1+412yes—
241C2×C4×C47C2511yescharacteristic
242C22⋊D47—48no—
243C22⋊D47—48no—
244C22⋊D47—48no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—24no—
249C2×Dic47—22no—
250C2×Dic47—42no—
251C2×Dic47—44no—
252C2×Dic47C22×D412yes—
253C2×Dic47C22×D412yes—
254C2×Dic47C22×D412yes—
255D188—22no—
256D188—22no—
257D188—48no—
258D188—42no—
259C4×D47—24no—
260C4×D47—28no—
261C4×D47—22no—
262C4×D47—22no—
263C4×D47—44no—
264C4×D47—48no—
265Dic94—48no—
266Dic94—48no—
267C8×C47—24no—
268C47⋊C8—24no—
269C2×#3235—471nomaximal, Sylow
270C22×C47—42no—
271C22×C47—42no—
272C22×C47—42no—
273C22×C47—84no—
274C22×C47#53612yes—
275C22×C47C2×AGL(1,ℤ/8)12yes—
276C22×C47#57512yes—
277C22×C47C23×D411yescharacteristic
278C2×D47—22no—
279C2×D47—22no—
280C2×D47—22no—
281C2×D47—44no—
282C2×D47—42no—
283C2×D47—42no—
284C2×D47—42no—
285C2×D47—84no—
286C4×C47—22no—
287C4×C47—42no—
288C4×C47—44no—
289C4×C47#53612yes—
290C4×C47C2×AGL(1,ℤ/8)14yes—
291C4×C47C2×2−1+411yescharacteristic
292C4×C47C2×2−1+411yescharacteristic
293Dic47—22no—
294Dic47—22no—
295Dic47—22no—
296Dic47—42no—
297Dic47—44no—
298C2×#533—471no—
299C2×#532—471no—
300#3235—4716no—
301C2×#501—472no—
302C2×#490—472no—
303C2×#482—472no—
304C2×#482—472no—
305C2×#476—471no—
306C2×#476D4711yescharacteristic, complemented
307C2×#474—471no—
308C2×#474—471no—
309C2×#432—471no—
310C2×C47—82no—
311C2×C47#323514yescomplemented
312C2×C47C2×#53611yescharacteristic
313C2×C47C22×AGL(1,ℤ/8)11yescharacteristic
314C2×C47C2×#57511yescharacteristic
315D47—42no—
316D47—82no—
317C22×#41—941no—
318#533—478no—
319#533—944no—
320#532—478no—
321#532—944no—
322C2×C4⋊Q8—471no—
323C2×C4⋊Q8—471no—
324C2×C4⋊Q8C2×D4711yescharacteristic
325C2×#127—471no—
326C2×#125—472no—
327C2×#124—941no—
328C2×C22⋊Q8—941no—
329C2×C22⋊Q8—941no—
330C2×#121—471no—
331C2×#121—471no—
332C2×#121—941no—
333C2×C4×Q8—941no—
334C2×C4×Q8—941no—
335C2×C4×D4—471no—
336C2×C4×D4—941no—
337C2×C4×D4C2×D4711yescharacteristic
338C2×#117—472no—
339C22×C42—471no—
340#501—4716no—
341#490—4716no—
342#482—4716no—
343#482—4716no—
344#476—478no—
345#476C2×D4718yescomplemented
346#474—478no—
347#474—478no—
348#432—478no—
349C2×#107—472no—
350C2×#107—472no—
351C2×#106—472no—
352C2×#106C2×D4712yes—
353C2×C4⋊C8—471no—
354C2×C4⋊C8C2×D4711yescharacteristic
355C2×#102—472no—
356C2×#102—472no—
357C2×#102—472no—
358C2×#102C2×D4712yes—
359C2×C22⋊C8—472no—
360C2×#97—472no—
361C47C2×#323511yescharacteristic, complemented, Sylow
362C2×#41—948no—
363C2×#41—1888no—
364C22×Q8—21no—
365C22×Q8—941no—
366C22×Q8—941no—
367C22×D4—471no—
368C22×D4—941no—
369C22×D4—941no—
370C22×D4—941no—
371C22×D4—941no—
372C22×D4C22×D4711yescharacteristic
373C23×C4—21no—
374C23×C4—471no—
375C23×C4—471no—
376C23×C4—471no—
377C23×C4—941no—
378C22×C8—472no—
379C22×C8C22×D4712yes—
380C4⋊Q8—22no—
381C4⋊Q8—474no—
382C4⋊Q8—474no—
383C4⋊Q8—942no—
384C4⋊Q8—942no—
385C4⋊Q8C22×D4714yes—
386#127—474no—
387#127—942no—
388#125—478no—
389#125—944no—
390#124—948no—
391C22⋊Q8—948no—
392C22⋊Q8—948no—
393#121—474no—
394#121—474no—
395#121—948no—
396#121—942no—
397#121—942no—
398C4×Q8—948no—
399C4×Q8—948no—
400C4×D4—22no—
401C4×D4—474no—
402C4×D4—948no—
403C4×D4—942no—
404C4×D4C22×D4714yes—
405#117—478no—
406#117—944no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—472no—
409C2×C4⋊C4—471no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4C22×D4712yes—
415C2×C4⋊C4C22×D4711yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—942no—
419C2×C22⋊C4—941no—
420C2×C22⋊C4—941no—
421C2×C42—471no—
422C2×C42—471no—
423C2×C42—471no—
424C2×C42—474no—
425C2×C42—474no—
426C2×C42—942no—
427C2×C42C22×D4711yescharacteristic
428#107—478no—
429#107—478no—
430#106—478no—
431#106C22×D4718yes—
432C4⋊C8—474no—
433C4⋊C8C22×D4714yes—
434#102—478no—
435#102—478no—
436#102—478no—
437#102C22×D4718yes—
438C22⋊C8—478no—
439#97—478no—
440C24—21no—
441C24—471no—
442C24—941no—
443#41—18832no—
444C2×Q8—24no—
445C2×Q8—44no—
446C2×Q8—944no—
447C2×Q8—944no—
448C2×Q8—1884no—
449C2×Q8—1884no—
450C2×D4—21no—
451C2×D4—22no—
452C2×D4—22no—
453C2×D4—472no—
454C2×D4—944no—
455C2×D4—944no—
456C2×D4—944no—
457C2×D4—944no—
458C2×D4—941no—
459C2×D4—942no—
460C2×D4—942no—
461C2×D4—1884no—
462C2×D4—1884no—
463C2×D4—1884no—
464C2×D4—1884no—
465C2×D4C23×D4712yes—
466C22×C4—22no—
467C22×C4—21no—
468C22×C4—24no—
469C22×C4—44no—
470C22×C4—471no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—472no—
474C22×C4—474no—
475C22×C4—472no—
476C22×C4—474no—
477C22×C4—944no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—941no—
482C22×C4—944no—
483C22×C4—1882no—
484C22×C4—1884no—
485C22×C4D4×D4711yescharacteristic
486C22×C4D4×D4711yescharacteristic
487C22×C4C23×D4711yescharacteristic
488C2×C8—24no—
489C2×C8—474no—
490C2×C8—944no—
491C2×C8C23×D4714yes—
492C4⋊C4—24no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—474no—
496C4⋊C4—472no—
497C4⋊C4—944no—
498C4⋊C4—948no—
499C4⋊C4—948no—
500C4⋊C4—942no—
501C4⋊C4—941no—
502C4⋊C4—944no—
503C4⋊C4C23×D4714yes—
504C4⋊C4C23×D4712yes—
505C22⋊C4—24no—
506C22⋊C4—944no—
507C22⋊C4—948no—
508C22⋊C4—944no—
509C22⋊C4—944no—
510C42—474no—
511C42—474no—
512C42—472no—
513C42—472no—
514C42—948no—
515C42D4×D4712yes—
516C42C23×D4712yes—
517C23—22no—
518C23—42no—
519C23—42no—
520C23—42no—
521C23—472no—
522C23—942no—
523C23—942no—
524C23—942no—
525C23—942no—
526C23—1882no—
527C23—1882no—
528C23—1882no—
529C23C2×D4×D4711yescharacteristic
530Q8—48no—
531Q8—1888no—
532Q8—1888no—
533D4—22no—
534D4—22no—
535D4—42no—
536D4—942no—
537D4—942no—
538D4—1888no—
539D4—1888no—
540D4—1888no—
541D4—1888no—
542D4—1882no—
543C2×C4—22no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—42no—
547C2×C4—44no—
548C2×C4—48no—
549C2×C4—472no—
550C2×C4—472no—
551C2×C4—472no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—948no—
556C2×C4—944no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—944no—
560C2×C4—942no—
561C2×C4—1884no—
562C2×C4—1882no—
563C2×C4—1884no—
564C2×C4—1888no—
565C2×C4#1309405114yes—
566C2×C4C2×D4×D4712yes—
567C2×C4C2×D4×D4712yes—
568C2×C4C2×D4×D4711yescharacteristic
569C2×C4#1309407112yes—
570C2×C4#1309407212yes—
571C2×C4C24×D4711yescharacteristic
572C8—24no—
573C8—944no—
574C22—42no—
575C22—42no—
576C22—42no—
577C22—84no—
578C22—942no—
579C22—942no—
580C22—942no—
581C22—3764no—
582C22—1882no—
583C22—1882no—
584C22—1882no—
585C22—1884no—
586C22#1568969612yes—
587C22C2×#1309405112yes—
588C22#1568991912yes—
589C22C22×D4×D4711yescharacteristic
590C4—22no—
591C4—42no—
592C4—44no—
593C4—942no—
594C4—942no—
595C4—942no—
596C4—1882no—
597C4—1884no—
598C4#1568969612yes—
599C4C2×#1309405114yes—
600C4C2×#1309407111yescharacteristic
601C4C2×#1309407211yescharacteristic
602C2—82no—
603C2—3762no—
604C2—1882no—
605C2#2025458414yesdirect product factor
606C2C2×#1568969611yescharacteristic
607C2C22×#1309405111yescharacteristic
608C2C2×#1568991911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#476C2
socleC23×C47C22×D4
prime radicalC2×#15689670C2
hypercenterC2×#476D47
hypocenterC47C2×#3235
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#15689678C2semidirect
3. #20254584C2direct (N × H)
4. C2×#15689530C2semidirect
5. C2×#15689486C2semidirect
6. C2×#15689449C2semidirect
7. C2×#15689445C2semidirect
8. C2×#15689410C2semidirect
9. C2×#15689404C2semidirect
10. C2×#15689403C2semidirect
11. C2×#15689179C2semidirect
12. C2×C47×#476C2semidirect
15. #15689678C22semidirect
34. #15689530C22semidirect
35. #15689486C22semidirect
36. #15689449C22semidirect
37. #15689445C22semidirect
38. #15689410C22semidirect
39. #15689404C22semidirect
40. #15689403C22semidirect
41. #15689179C22semidirect
53. C47×#476C22semidirect
306. C2×#476D47semidirect
311. C2×C47#3235semidirect
345. #476C2×D47semidirect
361. C47C2×#3235semidirect
605. C2#20254584direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896782
C2×#156896702
#202545842
C2×#156895302
C2×#156894862
C2×#156894492
C2×#156894452
C2×#156894102
C2×#156894042
C2×#156894032
C2×#156891792
C2×C47×#4762
C2×#323547