Finite Group Databasebeta

← C2×#20253520 #27084483

Subgroups — C2×#20253520 #27084483

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#20253520C2116yesmaximal, direct product factor
4C2×#15689455C212yesmaximal
5C2×#15689405C211yesmaximal, characteristic, complemented
6C2×#15689334C211yesmaximal, characteristic, complemented
7C2×#15689333C211yesmaximal, characteristic, complemented
8C2×#15689280C212yesmaximal
9C2×#15689229C212yesmaximal, complemented
10C2×#15689227C212yesmaximal, complemented
11C2×#15689179C211yesmaximal, characteristic
12C2×C47×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D47C2211yescharacteristic
14C22×Dic188C2212yes—
15C22×#10625337C2212yes—
16#15689678—24no—
17#15689678C2218yes—
18C2×#13094024C2211yescharacteristic
19C2×#13094015—21no—
20C2×#13094004C2212yes—
21C2×#13094000—21no—
22C2×Q8×Dic47—21no—
23C2×Q8×Dic47C2211yescharacteristic
24C2×C4×Dic94—21no—
25C2×C4×Dic94C2211yescharacteristic
26C2×#13093989—21no—
27C2×#13093989C2212yes—
28C2×#13093989C2211yescharacteristic
29C4×Q8×D47—24no—
30C4×Q8×D47C2218yes—
31C2×#13093982—21no—
32C2×C4⋊C4×D47—21no—
33C2×C4⋊C4×D47C2211yescharacteristic
34C2×C42×D47—21no—
35C2×C42×D47C2211yescharacteristic
36#15689455C22116yes—
37#15689405C2218yescomplemented
38#15689334C2218yescomplemented
39#15689333C2218yescomplemented
40#15689280C22116yes—
41#15689229C22116yescomplemented
42#15689227C22116yescomplemented
43#15689179C2218yes—
44C2×#13093955C2212yes—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46C2×#13093949C2212yes—
47C2×#13093947C2212yes—
48C2×#13093947C2212yes—
49C2×(C2×D47)⋊C8C2212yes—
50C2×#13093934C2212yes—
51C2×C4⋊Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C47×#475C2218yescomplemented
54C2×#106×C47C2212yes—
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×#103×C47C2212yes—
57C22×Dic94—21no—
58C22×Dic94C2312yes—
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×Dic188—28no—
70C2×Dic188C2318yes—
71C2×#10625337—28no—
72C2×#10625337C2318yes—
73C22×C47⋊C8C2312yes—
74#13094024—22no—
75#13094024C2314yes—
76#13094015—28no—
77#13094004—24no—
78#13094004C2318yes—
79#13094000—28no—
80Q8×Dic47—22no—
81Q8×Dic47—28no—
82Q8×Dic47C2314yes—
83C4×Dic94—22no—
84C4×Dic94—28no—
85C4×Dic94C2314yes—
86#13093989—22no—
87#13093989—28no—
88#13093989—24no—
89#13093989C2318yes—
90#13093989C2314yes—
91#13093982—28no—
92C2×C4⋊Dic47—21no—
93C2×C4⋊Dic47—21no—
94C2×C4⋊Dic47—21no—
95C2×C4⋊Dic47—22no—
96C2×C4⋊Dic47C2311yescharacteristic
97C2×Dic47⋊C4—21no—
98C2×Dic47⋊C4—21no—
99C2×Dic47⋊C4—21no—
100C2×Dic47⋊C4—22no—
101C4⋊C4×D47—28no—
102C4⋊C4×D47—22no—
103C4⋊C4×D47C2314yes—
104C2×(C2×D47)⋊C4—22no—
105C2×C4×Dic47—21no—
106C2×C4×Dic47—21no—
107C2×C4×Dic47—21no—
108C2×C4×Dic47—22no—
109C2×C4×Dic47D411yescharacteristic
110C2×C4×Dic47D411yescharacteristic
111C2×C4×Dic47C2311yescharacteristic
112C42×D47—28no—
113C42×D47D414yes—
114C42×D47C2314yes—
115#13093955C2318yes—
116C4⋊(C47⋊C8)C2314yes—
117#13093949C2318yes—
118#13093947C2318yes—
119#13093947C2318yes—
120(C2×D47)⋊C8C2318yes—
121#13093934C2318yes—
122C22×Q8×C47—21no—
123C22×Q8×C47C2311yescharacteristic
124C22×C8×C47C2312yes—
125C4⋊Q8×C47—22no—
126C4⋊Q8×C47C2314yes—
127C4×Q8×C47—22no—
128C4×Q8×C47C2314yes—
129C2×C4⋊C4×C47—21no—
130C2×C4⋊C4×C47—21no—
131C2×C4⋊C4×C47C2311yescharacteristic
132C2×C4⋊C4×C47C2312yes—
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135#106×C47C2318yes—
136C4⋊C8×C47C2314yes—
137#103×C47C2318yes—
138C23×D47C2×D411yescharacteristic
139C2×Q8×C47—21no—
140C2×Q8×C47—24no—
141C2×Q8×C47—22no—
142C2×Q8×C47—44no—
143C2×Q8×C47#4114yes—
144C2×Q8×C47C2412yes—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—22no—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2411yescharacteristic
151C22×Dic47—21no—
152C22×Dic47—21no—
153C22×Dic47—22no—
154C22×Dic47C2×D411yescharacteristic
155C22×Dic47C2×D411yescharacteristic
156C22×Dic47C2×D411yescharacteristic
157Q8×D47—216no—
158Q8×D47—28no—
159Q8×D47—28no—
160C2×C4×D47—28no—
161C2×C4×D47—24no—
162C2×C4×D47—24no—
163C2×C4×D47—24no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—24no—
167C2×C4×D47—44no—
168C2×C4×D47C2×D414yes—
169C2×C4×D47C2×D412yes—
170C2×C4×D47C2×D414yes—
171C2×C4×D47C2412yes—
172C2×Dic94—28no—
173C2×Dic94—21no—
174C2×Dic94—22no—
175C2×Dic94—24no—
176C2×Dic94—24no—
177C2×Dic94—24no—
178C2×Dic94—22no—
179C2×Dic94#4114yes—
180C2×Dic94C2414yes—
181C2×Dic94C2412yes—
182C2×C8×C47—24no—
183C2×C8×C47C2414yes—
184C4⋊C4×C47—24no—
185C4⋊C4×C47—24no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—22no—
188C4⋊C4×C47C2414yes—
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—24no—
198C4⋊Dic47—24no—
199C4⋊Dic47—28no—
200C4⋊Dic47C2412yes—
201Dic47⋊C4—24no—
202Dic47⋊C4—24no—
203Dic47⋊C4—24no—
204Dic47⋊C4—28no—
205C4×Dic47—24no—
206C4×Dic47—24no—
207C4×Dic47—24no—
208C4×Dic47—28no—
209C4×Dic47C2×D412yes—
210C4×Dic47C2×D414yes—
211C4×Dic47C2×D414yes—
212C4×Dic47C2412yes—
213C2×C47⋊C8—24no—
214C2×C47⋊C8C2414yes—
215Dic188—216no—
216C23×C47C22×D411yescharacteristic
217C22×D47—22no—
218C22×D47—22no—
219C22×D47#13714yes—
220C22×D47C22×D412yes—
221Q8×C47—24no—
222Q8×C47—22no—
223Q8×C47—48no—
224Q8×C47C2×#4114yes—
225C2×C4×C47—24no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—22no—
229C2×C4×C47—24no—
230C2×C4×C47—42no—
231C2×C4×C47—44no—
232C2×C4×C47#13714yes—
233C2×C4×C47C22×D412yes—
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C22×D412yes—
236C2×C4×C47C2×#4112yes—
237C2×C4×C47C2×#4112yes—
238C2×C4×C47C2511yescharacteristic
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—24no—
246C2×Dic47—44no—
247C2×Dic47—42no—
248C2×Dic47C22×D412yes—
249C2×Dic47C22×D412yes—
250C2×Dic47C22×D412yes—
251C4×D47—216no—
252C4×D47—28no—
253C4×D47—24no—
254C4×D47—28no—
255C4×D47—22no—
256C4×D47—22no—
257C4×D47—48no—
258Dic94—216no—
259Dic94—24no—
260Dic94—22no—
261Dic94—24no—
262Dic94—24no—
263Dic94—44no—
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—42no—
279C4×C47—44no—
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×#475D4711yescharacteristic, complemented
296C2×#462—471no—
297C2×#462—471no—
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×Q16—472no—
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—478no—
319C2×C4×Q8—471no—
320C2×C4×Q8—472no—
321C2×C4×Q8—471no—
322C2×C4×Q8—941no—
323C2×C4×Q8—941no—
324C2×C4×Q8—944no—
325C2×C4×Q8—941no—
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#475C2×D4718yescomplemented
335#462—478no—
336#462—478no—
337#451—4716no—
338#441—4716no—
339#441—4716no—
340#432—478no—
341C2×#106—472no—
342C2×#106C2×D4712yes—
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—21no—
353C22×Q8—474no—
354C22×Q8—471no—
355C22×Q8—472no—
356C22×Q8—941no—
357C22×Q8—942no—
358C22×Q8—944no—
359C22×Q8—944no—
360C22×Q8C22×D4711yescharacteristic
361C23×C4—471no—
362C23×C4—471no—
363C23×C4—471no—
364C23×C4—941no—
365C23×C4—941no—
366C2×Q16—478no—
367C2×Q16—478no—
368C2×Q16—948no—
369C2×Q16—948no—
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—944no—
379C22⋊Q8—948no—
380C4×Q8—22no—
381C4×Q8—474no—
382C4×Q8—474no—
383C4×Q8—478no—
384C4×Q8—474no—
385C4×Q8—948no—
386C4×Q8—942no—
387C4×Q8—948no—
388C4×Q8—944no—
389C4×Q8—942no—
390C4×Q8—948no—
391C4×Q8—942no—
392C4×Q8C22×D4714yes—
393#117—948no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—474no—
398C2×C4⋊C4—942no—
399C2×C4⋊C4—948no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—942no—
404C2×C4⋊C4—942no—
405C2×C4⋊C4—941no—
406C2×C4⋊C4—941no—
407C2×C4⋊C4—941no—
408C2×C4⋊C4C22×D4711yescharacteristic
409C2×C4⋊C4C22×D4712yes—
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#106C22×D4718yes—
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—24no—
436C2×Q8—22no—
437C2×Q8—44no—
438C2×Q8—474no—
439C2×Q8—472no—
440C2×Q8—474no—
441C2×Q8—944no—
442C2×Q8—948no—
443C2×Q8—948no—
444C2×Q8—9416no—
445C2×Q8—948no—
446C2×Q8—941no—
447C2×Q8—942no—
448C2×Q8—942no—
449C2×Q8—944no—
450C2×Q8—944no—
451C2×Q8#1062535414yes—
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—9416no—
478Q16—9416no—
479C2×C8—24no—
480C2×C8—474no—
481C2×C8—944no—
482C2×C8C23×D4714yes—
483C4⋊C4—24no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—22no—
487C4⋊C4—472no—
488C4⋊C4—944no—
489C4⋊C4—944no—
490C4⋊C4—948no—
491C4⋊C4—944no—
492C4⋊C4—948no—
493C4⋊C4—944no—
494C4⋊C4—941no—
495C4⋊C4—944no—
496C4⋊C4—944no—
497C4⋊C4C23×D4712yes—
498C4⋊C4C23×D4714yes—
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—48no—
519Q8—474no—
520Q8—9416no—
521Q8—944no—
522Q8—942no—
523Q8—944no—
524Q8—944no—
525Q8—1884no—
526Q8C2×#1062535414yes—
527C2×C4—24no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—42no—
533C2×C4—44no—
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—1884no—
552C2×C4—1882no—
553C2×C4#1309405314yes—
554C2×C4C2×D4×D4712yes—
555C2×C4C2×D4×D4711yescharacteristic
556C2×C4C2×D4×D4712yes—
557C2×C4#41×D4712yes—
558C2×C4C2×#1062535412yes—
559C2×C4C24×D4711yescharacteristic
560C8—24no—
561C8—944no—
562C22—474no—
563C22—942no—
564C22—948no—
565C22—942no—
566C22#1568963612yes—
567C22#137×D4712yes—
568C22C2×#1309405312yes—
569C22C22×D4×D4711yescharacteristic
570C4—22no—
571C4—24no—
572C4—42no—
573C4—44no—
574C4—942no—
575C4—942no—
576C4—942no—
577C4—944no—
578C4—1882no—
579C4—1884no—
580C4#1568963612yes—
581C4C2×#1309405314yes—
582C4C2×#41×D4711yescharacteristic
583C4C22×#1062535411yescharacteristic
584C2—944no—
585C2#2025352014yesdirect product factor
586C2C2×#1568963611yescharacteristic
587C2C2×#137×D4711yescharacteristic
588C2C22×#1309405311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#475C2
socleC23×C47C22×D4
prime radicalC23×D47C2×D4
hypercenterC2×#475D47
hypocenterC47C2×#3113
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. #20253520C2direct (N × H)
5. C2×#15689405C2semidirect
6. C2×#15689334C2semidirect
7. C2×#15689333C2semidirect
9. C2×#15689229C2semidirect
10. C2×#15689227C2semidirect
12. C2×C47×#475C2semidirect
37. #15689405C22semidirect
38. #15689334C22semidirect
39. #15689333C22semidirect
41. #15689229C22semidirect
42. #15689227C22semidirect
53. C47×#475C22semidirect
295. C2×#475D47semidirect
302. C2×C47#3113semidirect
334. #475C2×D47semidirect
351. C47C2×#3113semidirect
585. C2#20253520direct (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
#202535202
C2×#156894552
C2×#156894052
C2×#156893342
C2×#156893332
C2×#156892802
C2×#156892292
C2×#156892272
C2×#156891792
C2×C47×#4752
C2×#311347