Finite Group Databasebeta

← C2×#20253547 #27084413

Subgroups — C2×#20253547 #27084413

Order 12032.

2150 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic, complemented
2C2×C4×#10625352C211yesmaximal, characteristic
3#20253547C2116yesmaximal, direct product factor
4C2×#15689463C212yesmaximal, complemented
5C2×#15689419C211yesmaximal, characteristic, complemented
6C2×#15689413C211yesmaximal, characteristic, complemented
7C2×#15689330C211yesmaximal, characteristic, complemented
8C2×#15689282C212yesmaximal
9C2×#15689227C212yesmaximal, complemented
10C2×#15689224C212yesmaximal, complemented
11C2×#15689179C211yesmaximal, characteristic, complemented
12C2×C47×#461C211yesmaximal, characteristic, complemented
13C22×#10625352C2211yescharacteristic
14C22×#10625337C2212yes—
15#15689678—24no—
16#15689678C2218yescomplemented
17C2×#13094024C2211yescharacteristic
18C2×#13094015—21no—
19C2×#13094004—21no—
20C2×#13094000C2212yes—
21C4×#10625352—24no—
22C4×#10625352C2218yes—
23C2×Q8×Dic47C2212yes—
24C2×C4×Dic94C2211yescharacteristic
25C2×#13093989—21no—
26C2×#13093989C2211yescharacteristic
27C2×D4×Dic47C2211yescharacteristic
28C2×C4×C22⋊D47—21no—
29C2×(C22⋊D47)⋊C4—21no—
30C2×#13093982—21no—
31C2×#13093982C2211yescharacteristic
32C2×#13093980—21no—
33C22×C4×Dic47—21no—
34C2×C42×D47C2211yescharacteristic
35#15689463C22116yescomplemented
36#15689419C2218yescomplemented
37#15689413C2218yescomplemented
38#15689330C2218yescomplemented
39#15689282C22116yes—
40#15689227C22116yescomplemented
41#15689224C22116yescomplemented
42#15689179C2218yescomplemented
43C2×#13093958C2212yes—
44C2×#13093955C2212yes—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×#13093949C2212yes—
47C2×#13093948C2212yes—
48C2×#13093945C2212yes—
49C2×(C2×D47)⋊C8C2212yes—
50C2×#13093934C2212yes—
51C22×SD16×C47C2212yes—
52C2×C4⋊Q8×C47C2211yescharacteristic
53C2×C4×D4×C47C2211yescharacteristic
54C47×#461C2218yescomplemented
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×#103×C47C2212yes—
57C2×#10625352—24no—
58C2×#10625352—22no—
59C2×#10625352—24no—
60C2×#10625352C2314yes—
61C22×Dic94—21no—
62C22×Dic94C2311yescharacteristic
63C22×C22⋊D47—21no—
64C23×Dic47—21no—
65C23×Dic47—21no—
66C22×C4×D47D411yescharacteristic
67C22×C4×D47D411yescharacteristic
68C22×C4×D47C2311yescharacteristic
69C2×#10625337—28no—
70C2×#10625337C2318yes—
71C22×C47⋊C8C2312yes—
72#13094024—22no—
73#13094024C2314yes—
74#13094015—28no—
75#13094004—28no—
76#13094000—24no—
77#13094000C2318yes—
78Q8×Dic47—24no—
79Q8×Dic47C2318yes—
80C4×Dic94—22no—
81C4×Dic94C2314yes—
82#13093989—28no—
83#13093989—22no—
84#13093989C2314yes—
85D4×Dic47—22no—
86D4×Dic47C2314yes—
87C4×C22⋊D47—28no—
88(C22⋊D47)⋊C4—28no—
89#13093982—28no—
90#13093982—22no—
91#13093982C2314yes—
92#13093980—28no—
93C2×C4⋊Dic47—21no—
94C2×C4⋊Dic47—22no—
95C2×C4⋊Dic47C2311yescharacteristic
96C2×C4⋊Dic47C2312yes—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—22no—
100C2×C22⋊Dic47—21no—
101C2×(C2×D47)⋊C4—22no—
102C2×(C2×D47)⋊C4—21no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47—28no—
108C2×C4×Dic47D411yescharacteristic
109C2×C4×Dic47D411yescharacteristic
110C2×C4×Dic47C2311yescharacteristic
111C42×D47D414yes—
112C42×D47C2314yes—
113#13093958C2318yes—
114#13093955C2318yes—
115C4⋊(C47⋊C8)C2314yes—
116#13093949C2318yes—
117#13093948C2318yes—
118#13093945C2318yes—
119(C2×D47)⋊C8C2318yes—
120#13093934C2318yes—
121C22×Q8×C47C2312yes—
122C22×D4×C47C2311yescharacteristic
123C23×C4×C47—21no—
124C2×SD16×C47—28no—
125C2×SD16×C47C2318yes—
126C22×C8×C47C2312yes—
127C4⋊Q8×C47—22no—
128C4⋊Q8×C47C2314yes—
129C4×D4×C47—22no—
130C4×D4×C47C2314yes—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C22⋊C4×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47C2314yes—
137#103×C47C2318yes—
138C24×C47—21no—
139C23×D47C2×D411yescharacteristic
140C2×Q8×C47—22no—
141C2×Q8×C47—24no—
142C2×Q8×C47—24no—
143C2×Q8×C47C2414yes—
144C2×D4×C47—21no—
145C2×D4×C47—22no—
146C2×D4×C47#4114yes—
147C2×D4×C47C2412yes—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—24no—
151C22×C4×C47—44no—
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2411yescharacteristic
155C2×C22⋊D47—28no—
156C2×C22⋊D47—24no—
157C22×Dic47—28no—
158C22×Dic47—21no—
159C22×Dic47—24no—
160C22×Dic47—21no—
161C22×Dic47—22no—
162C22×Dic47—24no—
163C22×Dic47—44no—
164C22×Dic47C2×D411yescharacteristic
165C22×Dic47C2×D411yescharacteristic
166C22×Dic47C2×D411yescharacteristic
167#10625352—216no—
168#10625352—28no—
169#10625352—28no—
170C2×C4×D47—24no—
171C2×C4×D47—22no—
172C2×C4×D47—22no—
173C2×C4×D47—42no—
174C2×C4×D47C2×D412yes—
175C2×C4×D47C2×D414yes—
176C2×C4×D47C2×D414yes—
177C2×C4×D47C2412yes—
178C2×Dic94—21no—
179C2×Dic94—22no—
180C2×Dic94—24no—
181C2×Dic94—44no—
182C2×Dic94#4114yes—
183C2×Dic94C2412yes—
184SD16×C47—216no—
185C2×C8×C47—24no—
186C2×C8×C47C2414yes—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—24no—
189C4⋊C4×C47—21no—
190C4⋊C4×C47C2412yes—
191C22⋊C4×C47—24no—
192C42×C47C2×D412yes—
193C42×C47C2412yes—
194C22⋊Dic47—24no—
195#10625337—216no—
196(C2×D47)⋊C4—28no—
197(C2×D47)⋊C4—24no—
198C4⋊Dic47—24no—
199C4⋊Dic47—21no—
200C4⋊Dic47—22no—
201C4⋊Dic47—28no—
202C4⋊Dic47C2414yes—
203C4⋊Dic47C2412yes—
204Dic47⋊C4—24no—
205Dic47⋊C4—24no—
206Dic47⋊C4—28no—
207C4×Dic47—24no—
208C4×Dic47—24no—
209C4×Dic47—24no—
210C4×Dic47—28no—
211C4×Dic47C2×D412yes—
212C4×Dic47C2×D414yes—
213C4×Dic47C2×D414yes—
214C4×Dic47C2412yes—
215C2×C47⋊C8—24no—
216C2×C47⋊C8C2414yes—
217C23×C47—24no—
218C23×C47—22no—
219C23×C47—42no—
220C23×C47—42no—
221C23×C47C22×D411yescharacteristic
222C22×D47—22no—
223C22×D47—22no—
224C22×D47—22no—
225C22×D47C22×D412yes—
226Q8×C47—24no—
227Q8×C47—24no—
228Q8×C47—44no—
229D4×C47—24no—
230D4×C47—22no—
231D4×C47C2×#4114yes—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—24no—
235C2×C4×C47—44no—
236C2×C4×C47—42no—
237C2×C4×C47—48no—
238C2×C4×C47#13714yes—
239C2×C4×C47C22×D412yes—
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C22×D412yes—
242C2×C4×C47C2×#4112yes—
243C2×C4×C47C2×#4112yes—
244C2×C4×C47C2511yescharacteristic
245C22⋊D47—216no—
246C2×Dic47—216no—
247C2×Dic47—24no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
253C2×Dic47—24no—
254C2×Dic47—48no—
255C2×Dic47—44no—
256C2×Dic47—42no—
257C2×Dic47C22×D412yes—
258C2×Dic47C22×D412yes—
259C2×Dic47C22×D412yes—
260C4×D47—24no—
261C4×D47—28no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—44no—
265Dic94—24no—
266Dic94—22no—
267Dic94—48no—
268Dic94C2×#4114yes—
269C8×C47—24no—
270C47⋊C8—24no—
271C2×#3116—471nomaximal, Sylow
272C22×C47—24no—
273C22×C47—48no—
274C22×C47—42no—
275C22×C47—42no—
276C22×C47#52512yes—
277C22×C47C2×#13712yes—
278C22×C47#57512yes—
279C22×C47C23×D411yescharacteristic
280C2×D47—22no—
281C2×D47—22no—
282C2×D47—22no—
283C2×D47—44no—
284C4×C47—22no—
285C4×C47—44no—
286C4×C47—42no—
287C4×C47#52512yes—
288C4×C47C2×#13714yes—
289C4×C47C22×#4111yescharacteristic
290C4×C47C22×#4111yescharacteristic
291Dic47—24no—
292Dic47—22no—
293Dic47—22no—
294Dic47—22no—
295Dic47—44no—
296Dic47—42no—
297C2×#533—471no—
298C2×C4×#41—471no—
299#3116—4716no—
300C2×#485—472no—
301C2×#477—471no—
302C2×#476—471no—
303C2×#462—471no—
304C2×#461D4711yescharacteristic, complemented
305C2×#452—472no—
306C2×#441—472no—
307C2×#440—472no—
308C2×#432—471no—
309C2×C47—44no—
310C2×C47#311614yescomplemented
311C2×C47C2×#52511yescharacteristic
312C2×C47C22×#13711yescharacteristic
313C2×C47C2×#57511yescharacteristic
314D47—42no—
315C22×#41—471no—
316C22×Q16—472no—
317C22×SD16C2×D4712yes—
318#533—478no—
319#533—944no—
320C2×C4⋊Q8—471no—
321C2×C4⋊Q8C2×D4711yescharacteristic
322C2×#125—941no—
323C2×C22⋊Q8—472no—
324C2×C22⋊Q8—941no—
325C4×#41—478no—
326C4×#41—944no—
327C2×C4×Q8—472no—
328C2×C4×Q8—471no—
329C2×C4×Q8—471no—
330C2×C4×Q8—941no—
331C2×C4×D4—471no—
332C2×C4×D4—941no—
333C2×C4×D4—941no—
334C2×C4×D4C2×D4711yescharacteristic
335C2×#117—471no—
336C2×#117—941no—
337C2×#117—941no—
338C22×C42—471no—
339C22×C42—941no—
340#485—4716no—
341#477—478no—
342#476—478no—
343#462—478no—
344#461C2×D4718yescomplemented
345#452—4716no—
346#441—4716no—
347#440—4716no—
348#432—478no—
349C2×#107—472no—
350C2×#106—472no—
351C2×C4⋊C8—471no—
352C2×C4⋊C8C2×D4711yescharacteristic
353C2×#103—472no—
354C2×#103—472no—
355C2×#103C2×D4712yes—
356C2×#102—472no—
357C2×C22⋊C8—472no—
358C2×#97—472no—
359C47C2×#311611yescharacteristic, complemented, Sylow
360C2×#41—474no—
361C2×#41—942no—
362C2×#41—944no—
363C2×#41—944no—
364C22×Q8—471no—
365C22×Q8—941no—
366C22×Q8C22×D4712yes—
367C22×D4—941no—
368C22×D4C22×D4711yescharacteristic
369C23×C4—21no—
370C23×C4—471no—
371C23×C4—471no—
372C23×C4—471no—
373C23×C4—941no—
374C23×C4—941no—
375C2×Q16—478no—
376C2×Q16—948no—
377C2×SD16—28no—
378C2×SD16C22×D4718yes—
379C22×C8—472no—
380C22×C8C22×D4712yes—
381C4⋊Q8—22no—
382C4⋊Q8—474no—
383C4⋊Q8—942no—
384C4⋊Q8C22×D4714yes—
385#125—948no—
386C22⋊Q8—478no—
387C22⋊Q8—948no—
388C22⋊Q8—944no—
389C4×Q8—478no—
390C4×Q8—474no—
391C4×Q8—474no—
392C4×Q8—942no—
393C4×Q8—948no—
394C4×Q8—944no—
395C4×Q8—942no—
396C4×D4—22no—
397C4×D4—474no—
398C4×D4—942no—
399C4×D4—948no—
400C4×D4—948no—
401C4×D4C22×D4714yes—
402#117—474no—
403#117—948no—
404#117—942no—
405#117—948no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—472no—
410C2×C4⋊C4—941no—
411C2×C4⋊C4—942no—
412C2×C4⋊C4—942no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4—941no—
415C2×C4⋊C4C22×D4711yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—941no—
418C2×C22⋊C4—942no—
419C2×C22⋊C4—941no—
420C2×C42—471no—
421C2×C42—471no—
422C2×C42—471no—
423C2×C42—474no—
424C2×C42—474no—
425C2×C42—948no—
426C2×C42—941no—
427C2×C42—942no—
428C2×C42—941no—
429C2×C42—941no—
430C2×C42C22×D4711yescharacteristic
431#107—478no—
432#106—478no—
433C4⋊C8—474no—
434C4⋊C8C22×D4714yes—
435#103—478no—
436#103—478no—
437#103C22×D4718yes—
438#102—478no—
439C22⋊C8—478no—
440#97—478no—
441C24—21no—
442C24—471no—
443#41—948no—
444#41—9416no—
445#41—948no—
446C2×Q8—22no—
447C2×Q8—24no—
448C2×Q8—24no—
449C2×Q8—474no—
450C2×Q8—472no—
451C2×Q8—941no—
452C2×Q8—944no—
453C2×Q8—942no—
454C2×Q8—1884no—
455C2×Q8C23×D4714yes—
456C2×D4—21no—
457C2×D4—22no—
458C2×D4—944no—
459C2×D4—948no—
460C2×D4#1062535214yes—
461C2×D4C23×D4712yes—
462C22×C4—21no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—44no—
466C22×C4—471no—
467C22×C4—471no—
468C22×C4—471no—
469C22×C4—474no—
470C22×C4—472no—
471C22×C4—472no—
472C22×C4—474no—
473C22×C4—944no—
474C22×C4—944no—
475C22×C4—948no—
476C22×C4—941no—
477C22×C4—944no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—941no—
481C22×C4—942no—
482C22×C4—1882no—
483C22×C4—1884no—
484C22×C4D4×D4711yescharacteristic
485C22×C4D4×D4711yescharacteristic
486C22×C4C23×D4711yescharacteristic
487Q16—9416no—
488SD16—216no—
489C2×C8—24no—
490C2×C8—474no—
491C2×C8—944no—
492C2×C8C23×D4714yes—
493C4⋊C4—24no—
494C4⋊C4—24no—
495C4⋊C4—21no—
496C4⋊C4—474no—
497C4⋊C4—472no—
498C4⋊C4—944no—
499C4⋊C4—948no—
500C4⋊C4—948no—
501C4⋊C4—944no—
502C4⋊C4—941no—
503C4⋊C4—942no—
504C4⋊C4—944no—
505C4⋊C4C23×D4712yes—
506C22⋊C4—24no—
507C22⋊C4—944no—
508C22⋊C4—948no—
509C22⋊C4—944no—
510C42—474no—
511C42—474no—
512C42—472no—
513C42—472no—
514C42—944no—
515C42—944no—
516C42—948no—
517C42—944no—
518C42D4×D4712yes—
519C42C23×D4712yes—
520C23—24no—
521C23—22no—
522C23—42no—
523C23—42no—
524C23—472no—
525C23—942no—
526C23—942no—
527C23—942no—
528C23C2×D4×D4711yescharacteristic
529Q8—24no—
530Q8—24no—
531Q8—44no—
532Q8—474no—
533Q8—944no—
534Q8—942no—
535Q8—1888no—
536D4—24no—
537D4—22no—
538D4—9416no—
539D4C2×#1062535214yes—
540C2×C4—22no—
541C2×C4—22no—
542C2×C4—24no—
543C2×C4—44no—
544C2×C4—42no—
545C2×C4—48no—
546C2×C4—472no—
547C2×C4—472no—
548C2×C4—472no—
549C2×C4—9416no—
550C2×C4—942no—
551C2×C4—944no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—944no—
556C2×C4—948no—
557C2×C4—942no—
558C2×C4—942no—
559C2×C4—942no—
560C2×C4—944no—
561C2×C4—1884no—
562C2×C4—1888no—
563C2×C4—1882no—
564C2×C4—1884no—
565C2×C4#1309405314yes—
566C2×C4C2×D4×D4712yes—
567C2×C4C2×D4×D4711yescharacteristic
568C2×C4C2×D4×D4712yes—
569C2×C4#41×D4712yes—
570C2×C4C2×#1062535212yes—
571C2×C4C24×D4711yescharacteristic
572C8—24no—
573C8—944no—
574C22—24no—
575C22—42no—
576C22—42no—
577C22—48no—
578C22—942no—
579C22—942no—
580C22—942no—
581C22—1884no—
582C22#1568963312yes—
583C22C2×#1309405312yes—
584C22#1568992212yes—
585C22C22×D4×D4711yescharacteristic
586C4—22no—
587C4—42no—
588C4—44no—
589C4—942no—
590C4—942no—
591C4—942no—
592C4—944no—
593C4—1882no—
594C4—1884no—
595C4#1568963312yes—
596C4C2×#1309405314yes—
597C4C2×#41×D4711yescharacteristic
598C4C22×#1062535211yescharacteristic
599C2—44no—
600C2—1882no—
601C2#2025354714yesdirect product factor
602C2C2×#1568963311yescharacteristic
603C2C22×#1309405311yescharacteristic
604C2C2×#1568992211yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#461C2
socleC23×C47C22×D4
prime radicalC22×#10625352C22
hypercenterC2×#461D47
hypocenterC47C2×#3116
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#15689678C2semidirect
3. #20253547C2direct (N × H)
4. C2×#15689463C2semidirect
5. C2×#15689419C2semidirect
6. C2×#15689413C2semidirect
7. C2×#15689330C2semidirect
9. C2×#15689227C2semidirect
10. C2×#15689224C2semidirect
11. C2×#15689179C2semidirect
12. C2×C47×#461C2semidirect
16. #15689678C22semidirect
35. #15689463C22semidirect
36. #15689419C22semidirect
37. #15689413C22semidirect
38. #15689330C22semidirect
40. #15689227C22semidirect
41. #15689224C22semidirect
42. #15689179C22semidirect
54. C47×#461C22semidirect
304. C2×#461D47semidirect
310. C2×C47#3116semidirect
344. #461C2×D47semidirect
359. C47C2×#3116semidirect
601. C2#20253547direct (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×C4×#106253522
#202535472
C2×#156894632
C2×#156894192
C2×#156894132
C2×#156893302
C2×#156892822
C2×#156892272
C2×#156892242
C2×#156891792
C2×C47×#4612
C2×#311647