Finite Group Databasebeta

← C2×#20253517 #27084480

Subgroups — C2×#20253517 #27084480

Order 12032.

2118 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689678C211yesmaximal, characteristic
2C2×C4×Q8×D47C211yesmaximal, characteristic
3#20253517C2116yesmaximal, direct product factor
4C2×#15689452C212yesmaximal
5C2×#15689409C211yesmaximal, characteristic, complemented
6C2×#15689408C211yesmaximal, characteristic, complemented
7C2×#15689330C211yesmaximal, characteristic, complemented
8C2×#15689277C212yesmaximal
9C2×#15689230C212yesmaximal, complemented
10C2×#15689227C212yesmaximal, complemented
11C2×#15689179C211yesmaximal, characteristic
12C2×C47×#462C211yesmaximal, characteristic, complemented
13C22×Q8×D47C2211yescharacteristic
14C22×#10625337C2212yes—
15#15689678—24no—
16#15689678C2218yes—
17C2×#13094024C2211yescharacteristic
18C2×#13094015—21no—
19C2×#13094004—21no—
20C2×#13094000C2212yes—
21C2×Q8×Dic47C2212yes—
22C2×Q8×Dic47C2211yescharacteristic
23C2×C4×Dic94—21no—
24C2×C4×Dic94C2211yescharacteristic
25C2×#13093989—21no—
26C2×#13093989—21no—
27C2×#13093989C2211yescharacteristic
28C4×Q8×D47—24no—
29C4×Q8×D47C2218yes—
30C2×#13093982—21no—
31C2×C4⋊C4×D47—21no—
32C2×C4⋊C4×D47C2211yescharacteristic
33C2×C42×D47—21no—
34C2×C42×D47C2211yescharacteristic
35#15689452C22116yes—
36#15689409C2218yescomplemented
37#15689408C2218yescomplemented
38#15689330C2218yescomplemented
39#15689277C22116yes—
40#15689230C22116yescomplemented
41#15689227C22116yescomplemented
42#15689179C2218yes—
43C2×#13093956C2212yes—
44C2×#13093955C2212yes—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×#13093949C2212yes—
47C2×#13093948C2212yes—
48C2×#13093948C2212yes—
49C2×(C2×D47)⋊C8C2212yes—
50C2×#13093934C2212yes—
51C22×Q16×C47C2212yes—
52C2×C4⋊Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C47×#462C2218yescomplemented
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×#103×C47C2212yes—
57C22×Dic94—21no—
58C22×Dic94—21no—
59C22×Dic94C2311yescharacteristic
60C2×Q8×D47—24no—
61C2×Q8×D47—22no—
62C2×Q8×D47—24no—
63C2×Q8×D47C2314yes—
64C22×C4×D47—21no—
65C22×C4×D47—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—22no—
79Q8×Dic47—24no—
80Q8×Dic47C2318yes—
81Q8×Dic47C2314yes—
82C4×Dic94—22no—
83C4×Dic94—28no—
84C4×Dic94C2314yes—
85#13093989—22no—
86#13093989—28no—
87#13093989—28no—
88#13093989C2314yes—
89#13093982—28no—
90C2×C4⋊Dic47—21no—
91C2×C4⋊Dic47—21no—
92C2×C4⋊Dic47—22no—
93C2×C4⋊Dic47C2311yescharacteristic
94C2×C4⋊Dic47C2312yes—
95C2×Dic47⋊C4—21no—
96C2×Dic47⋊C4—21no—
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—22no—
99C4⋊C4×D47—28no—
100C4⋊C4×D47—22no—
101C4⋊C4×D47C2314yes—
102C2×(C2×D47)⋊C4—22no—
103C2×C4×Dic47—21no—
104C2×C4×Dic47—21no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—22no—
107C2×C4×Dic47D411yescharacteristic
108C2×C4×Dic47D411yescharacteristic
109C2×C4×Dic47C2311yescharacteristic
110C42×D47—28no—
111C42×D47D414yes—
112C42×D47C2314yes—
113#13093956C2318yes—
114#13093955C2318yes—
115C4⋊(C47⋊C8)C2314yes—
116#13093949C2318yes—
117#13093948C2318yes—
118#13093948C2318yes—
119(C2×D47)⋊C8C2318yes—
120#13093934C2318yes—
121C22×Q8×C47C2312yes—
122C22×Q8×C47C2311yescharacteristic
123C2×Q16×C47—28no—
124C2×Q16×C47C2318yes—
125C22×C8×C47C2312yes—
126C4⋊Q8×C47—22no—
127C4⋊Q8×C47C2314yes—
128C4×Q8×C47—22no—
129C4×Q8×C47C2314yes—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47—21no—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47C2311yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47C2314yes—
137#103×C47C2318yes—
138C23×D47C2×D411yescharacteristic
139C2×Q8×C47—21no—
140C2×Q8×C47—22no—
141C2×Q8×C47—22no—
142C2×Q8×C47—24no—
143C2×Q8×C47—24no—
144C2×Q8×C47#4114yes—
145C2×Q8×C47C2414yes—
146C2×Q8×C47C2412yes—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2411yescharacteristic
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—22no—
156C22×Dic47C2×D411yescharacteristic
157C22×Dic47C2×D411yescharacteristic
158C22×Dic47C2×D411yescharacteristic
159Q8×D47—216no—
160Q8×D47—28no—
161Q8×D47—28no—
162C2×C4×D47—28no—
163C2×C4×D47—24no—
164C2×C4×D47—24no—
165C2×C4×D47—24no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—24no—
169C2×C4×D47—44no—
170C2×C4×D47C2×D414yes—
171C2×C4×D47C2×D412yes—
172C2×C4×D47C2×D414yes—
173C2×C4×D47C2412yes—
174C2×Dic94—28no—
175C2×Dic94—21no—
176C2×Dic94—22no—
177C2×Dic94—24no—
178C2×Dic94—24no—
179C2×Dic94—44no—
180C2×Dic94#4114yes—
181C2×Dic94C2412yes—
182Q16×C47—216no—
183C2×C8×C47—24no—
184C2×C8×C47C2414yes—
185C4⋊C4×C47—24no—
186C4⋊C4×C47—24no—
187C4⋊C4×C47—24no—
188C4⋊C4×C47—21no—
189C4⋊C4×C47C2412yes—
190C42×C47—24no—
191C42×C47C2×D412yes—
192C42×C47C2412yes—
193#10625337—216no—
194(C2×D47)⋊C4—28no—
195C4⋊Dic47—21no—
196C4⋊Dic47—24no—
197C4⋊Dic47—22no—
198C4⋊Dic47—24no—
199C4⋊Dic47—28no—
200C4⋊Dic47C2412yes—
201C4⋊Dic47C2414yes—
202Dic47⋊C4—24no—
203Dic47⋊C4—24no—
204Dic47⋊C4—24no—
205Dic47⋊C4—28no—
206C4×Dic47—24no—
207C4×Dic47—24no—
208C4×Dic47—24no—
209C4×Dic47—28no—
210C4×Dic47C2×D412yes—
211C4×Dic47C2×D414yes—
212C4×Dic47C2×D414yes—
213C4×Dic47C2412yes—
214C2×C47⋊C8—24no—
215C2×C47⋊C8C2414yes—
216C23×C47C22×D411yescharacteristic
217C22×D47—22no—
218C22×D47—22no—
219C22×D47#13714yes—
220C22×D47C22×D412yes—
221Q8×C47—24no—
222Q8×C47—22no—
223Q8×C47—24no—
224Q8×C47—24no—
225Q8×C47—44no—
226Q8×C47C2×#4114yes—
227C2×C4×C47—24no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—24no—
232C2×C4×C47—44no—
233C2×C4×C47—42no—
234C2×C4×C47#13714yes—
235C2×C4×C47C22×D412yes—
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C22×D412yes—
238C2×C4×C47C2×#4112yes—
239C2×C4×C47C2×#4112yes—
240C2×C4×C47C2511yescharacteristic
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—24no—
248C2×Dic47—44no—
249C2×Dic47—42no—
250C2×Dic47C22×D412yes—
251C2×Dic47C22×D412yes—
252C2×Dic47C22×D412yes—
253C4×D47—216no—
254C4×D47—28no—
255C4×D47—24no—
256C4×D47—28no—
257C4×D47—22no—
258C4×D47—22no—
259C4×D47—48no—
260Dic94—216no—
261Dic94—24no—
262Dic94—22no—
263Dic94—48no—
264Dic94C2×#4114yes—
265C8×C47—24no—
266C47⋊C8—24no—
267C2×#3113—471nomaximal, Sylow
268C22×C47#52512yes—
269C22×C47C2×#13712yes—
270C22×C47C2×#13712yes—
271C22×C47C23×D411yescharacteristic
272C2×D47—28no—
273C2×D47—22no—
274C2×D47—22no—
275C2×D47C2×#13714yes—
276C4×C47—24no—
277C4×C47—22no—
278C4×C47—44no—
279C4×C47—42no—
280C4×C47#52512yes—
281C4×C47C2×#13714yes—
282C4×C47C22×#4111yescharacteristic
283C4×C47C22×#4111yescharacteristic
284Dic47—22no—
285Dic47—24no—
286Dic47—22no—
287Dic47—22no—
288Dic47—44no—
289Dic47—42no—
290C2×#533—471no—
291C22×C4×Q8—471no—
292#3113—4716no—
293C2×#483—472no—
294C2×#475—471no—
295C2×#475—471no—
296C2×#462—471no—
297C2×#462D4711yescharacteristic, complemented
298C2×#451—472no—
299C2×#441—472no—
300C2×#441—472no—
301C2×#432—471no—
302C2×C47#311314yescomplemented
303C2×C47C2×#52511yescharacteristic
304C2×C47C22×#13711yescharacteristic
305C2×C47C22×#13711yescharacteristic
306D47—24no—
307C23×Q8—471no—
308C22×Q16—472no—
309C22×Q16C2×D4712yes—
310#533—478no—
311#533—944no—
312C2×C4⋊Q8—471no—
313C2×C4⋊Q8C2×D4711yescharacteristic
314C2×#125—941no—
315C2×C22⋊Q8—472no—
316C2×C22⋊Q8—941no—
317C2×C4×Q8—471no—
318C2×C4×Q8—472no—
319C2×C4×Q8—478no—
320C2×C4×Q8—471no—
321C2×C4×Q8—471no—
322C2×C4×Q8—941no—
323C2×C4×Q8—941no—
324C2×C4×Q8—941no—
325C2×C4×Q8—944no—
326C2×C4×Q8C2×D4711yescharacteristic
327C2×#117—941no—
328C22×C4⋊C4—471no—
329C22×C4⋊C4—941no—
330C22×C42—471no—
331C22×C42—941no—
332#483—4716no—
333#475—478no—
334#475—478no—
335#462—478no—
336#462C2×D4718yescomplemented
337#451—4716no—
338#441—4716no—
339#441—4716no—
340#432—478no—
341C2×#106—472no—
342C2×#106—472no—
343C2×C4⋊C8—471no—
344C2×C4⋊C8C2×D4711yescharacteristic
345C2×#103—472no—
346C2×#103—472no—
347C2×#103—472no—
348C2×#103C2×D4712yes—
349C2×C22⋊C8—472no—
350C2×#97—472no—
351C47C2×#311311yescharacteristic, complemented, Sylow
352C22×Q8—474no—
353C22×Q8—471no—
354C22×Q8—941no—
355C22×Q8—942no—
356C22×Q8—944no—
357C22×Q8—944no—
358C22×Q8—941no—
359C22×Q8C22×D4712yes—
360C22×Q8C22×D4711yescharacteristic
361C23×C4—471no—
362C23×C4—471no—
363C23×C4—471no—
364C23×C4—941no—
365C23×C4—941no—
366C2×Q16—28no—
367C2×Q16—478no—
368C2×Q16—948no—
369C2×Q16C22×D4718yes—
370C22×C8—472no—
371C22×C8C22×D4712yes—
372C4⋊Q8—22no—
373C4⋊Q8—474no—
374C4⋊Q8—942no—
375C4⋊Q8C22×D4714yes—
376#125—948no—
377C22⋊Q8—478no—
378C22⋊Q8—948no—
379C22⋊Q8—944no—
380C4×Q8—22no—
381C4×Q8—474no—
382C4×Q8—478no—
383C4×Q8—474no—
384C4×Q8—474no—
385C4×Q8—948no—
386C4×Q8—942no—
387C4×Q8—948no—
388C4×Q8—948no—
389C4×Q8—942no—
390C4×Q8—944no—
391C4×Q8—942no—
392C4×Q8C22×D4714yes—
393#117—948no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—472no—
399C2×C4⋊C4—474no—
400C2×C4⋊C4—942no—
401C2×C4⋊C4—948no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—942no—
406C2×C4⋊C4—942no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4—941no—
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C22⋊C4—942no—
411C2×C42—21no—
412C2×C42—471no—
413C2×C42—471no—
414C2×C42—471no—
415C2×C42—474no—
416C2×C42—474no—
417C2×C42—948no—
418C2×C42—942no—
419C2×C42—941no—
420C2×C42—941no—
421C2×C42—941no—
422C2×C42C22×D4711yescharacteristic
423#106—478no—
424#106—478no—
425C4⋊C8—474no—
426C4⋊C8C22×D4714yes—
427#103—478no—
428#103—478no—
429#103—478no—
430#103C22×D4718yes—
431C22⋊C8—478no—
432#97—478no—
433C24—471no—
434C2×Q8—21no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—24no—
438C2×Q8—24no—
439C2×Q8—474no—
440C2×Q8—472no—
441C2×Q8—944no—
442C2×Q8—948no—
443C2×Q8—948no—
444C2×Q8—9416no—
445C2×Q8—948no—
446C2×Q8—941no—
447C2×Q8—944no—
448C2×Q8—942no—
449C2×Q8—1884no—
450C2×Q8#1062535214yes—
451C2×Q8C23×D4714yes—
452C2×Q8C23×D4712yes—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—474no—
460C22×C4—474no—
461C22×C4—472no—
462C22×C4—472no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—948no—
466C22×C4—944no—
467C22×C4—941no—
468C22×C4—944no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—941no—
472C22×C4—942no—
473C22×C4—1884no—
474C22×C4D4×D4711yescharacteristic
475C22×C4D4×D4711yescharacteristic
476C22×C4C23×D4711yescharacteristic
477Q16—216no—
478Q16—9416no—
479C2×C8—24no—
480C2×C8—474no—
481C2×C8—944no—
482C2×C8C23×D4714yes—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—24no—
486C4⋊C4—21no—
487C4⋊C4—472no—
488C4⋊C4—474no—
489C4⋊C4—944no—
490C4⋊C4—944no—
491C4⋊C4—948no—
492C4⋊C4—944no—
493C4⋊C4—948no—
494C4⋊C4—944no—
495C4⋊C4—941no—
496C4⋊C4—942no—
497C4⋊C4—944no—
498C4⋊C4C23×D4712yes—
499C22⋊C4—948no—
500C42—24no—
501C42—472no—
502C42—474no—
503C42—474no—
504C42—472no—
505C42—944no—
506C42—944no—
507C42—948no—
508C42—944no—
509C42D4×D4712yes—
510C42C23×D4712yes—
511C23—474no—
512C23—472no—
513C23—942no—
514C23—942no—
515C23C2×D4×D4711yescharacteristic
516Q8—24no—
517Q8—22no—
518Q8—24no—
519Q8—24no—
520Q8—44no—
521Q8—474no—
522Q8—9416no—
523Q8—944no—
524Q8—942no—
525Q8—1888no—
526Q8C2×#1062535214yes—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—472no—
535C2×C4—472no—
536C2×C4—472no—
537C2×C4—948no—
538C2×C4—9416no—
539C2×C4—942no—
540C2×C4—944no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—944no—
545C2×C4—948no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—944no—
550C2×C4—1888no—
551C2×C4—1882no—
552C2×C4—1884no—
553C2×C4#1309405614yes—
554C2×C4C2×D4×D4712yes—
555C2×C4C2×D4×D4711yescharacteristic
556C2×C4C2×D4×D4712yes—
557C2×C4#41×D4712yes—
558C2×C4C2×#1062535212yes—
559C2×C4C24×D4711yescharacteristic
560C8—24no—
561C8—944no—
562C22—474no—
563C22—948no—
564C22—942no—
565C22—942no—
566C22#1568963312yes—
567C22#137×D4712yes—
568C22C2×#1309405612yes—
569C22C22×D4×D4711yescharacteristic
570C4—22no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—942no—
575C4—942no—
576C4—942no—
577C4—944no—
578C4—1882no—
579C4—1884no—
580C4#1568963312yes—
581C4C2×#1309405614yes—
582C4C2×#41×D4711yescharacteristic
583C4C22×#1062535211yescharacteristic
584C2—944no—
585C2#2025351714yesdirect product factor
586C2C2×#1568963311yescharacteristic
587C2C2×#137×D4711yescharacteristic
588C2C22×#1309405611yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#462C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#462D47
hypocenterC47C2×#3113
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
3. #20253517C2direct (N × H)
5. C2×#15689409C2semidirect
6. C2×#15689408C2semidirect
7. C2×#15689330C2semidirect
9. C2×#15689230C2semidirect
10. C2×#15689227C2semidirect
12. C2×C47×#462C2semidirect
36. #15689409C22semidirect
37. #15689408C22semidirect
38. #15689330C22semidirect
40. #15689230C22semidirect
41. #15689227C22semidirect
54. C47×#462C22semidirect
297. C2×#462D47semidirect
302. C2×C47#3113semidirect
336. #462C2×D47semidirect
351. C47C2×#3113semidirect
585. C2#20253517direct (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×Q8×D472
#202535172
C2×#156894522
C2×#156894092
C2×#156894082
C2×#156893302
C2×#156892772
C2×#156892302
C2×#156892272
C2×#156891792
C2×C47×#4622
C2×#311347