Finite Group Databasebeta

← #26225736

Subgroups — #26225736

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D47C211yesmaximal, characteristic
2#20252020C211yesmaximal, characteristic
3#20252019C211yesmaximal, characteristic
4#20244378C211yesmaximal, characteristic, complemented
5#20244377C211yesmaximal, characteristic, complemented
6#20244376C211yesmaximal, characteristic, complemented
7#20244375C214yesmaximal, complemented
8#20243467C214yesmaximal
9C47×#1997C211yesmaximal, characteristic, complemented
10C22×Q8×D47C412yes—
11C2×#13094024C2211yescharacteristic
12C2×#13094023C412yes—
13C2×#13094023C2212yes—
14C2×#13094022C412yes—
15C4⋊Q8×D47—21no—
16C4⋊Q8×D47—21no—
17C4⋊Q8×D47—21no—
18C4⋊Q8×D47—21no—
19C4⋊Q8×D47—21no—
20C4⋊Q8×D47—21no—
21C4⋊Q8×D47—21no—
22C4⋊Q8×D47—21no—
23C2×C4⋊C4×D47C412yes—
24C2×C4⋊C4×D47C2212yes—
25C2×C42×D47C2211yescharacteristic
26#15689179—21no—
27#15689179—21no—
28#15689178—21no—
29#15689178—21no—
30#15689175—21no—
31#15689175—21no—
32#15689174—21no—
33#15689174—21no—
34#15689147C2211yescharacteristic
35#15689146C2212yes—
36#15689086C2212yes—
37#15689086C2212yes—
38C4×#10625329C2211yescharacteristic
39M16×Dic47C2212yes—
40#15688892C2214yes—
41#15688891C2214yes—
42#15688891C2214yes—
43C2×C4⋊Q8×C47C2211yescharacteristic
44C47×#423C2211yescharacteristic
45C4×M16×C47C2211yescharacteristic
46C47×#343C2214yes—
47C22×Dic94C2×C412yes—
48C22×Dic94C2×C414yes—
49C2×Q8×D47—22no—
50C2×Q8×D47—22no—
51C2×Q8×D47—22no—
52C2×Q8×D47—22no—
53C2×Q8×D47—48no—
54C22×C4×D47C2×C411yescharacteristic
55C22×C4×D47C2×C411yescharacteristic
56C22×C4×D47C2×C414yes—
57C22×C4×D47C2311yescharacteristic
58C2×#10625329C2312yes—
59C2×#10625329C2312yes—
60#13094024—21no—
61#13094024—21no—
62#13094024—21no—
63#13094024—21no—
64#13094023—22no—
65#13094023—22no—
66#13094023—22no—
67#13094023—22no—
68#13094023—22no—
69#13094023—22no—
70#13094023—22no—
71#13094023—22no—
72#13094022—22no—
73#13094022—22no—
74#13094022—22no—
75#13094022—22no—
76C2×C4⋊Dic47C2×C412yes—
77C2×C4⋊Dic47C2312yes—
78C2×Dic47⋊C4C2×C414yes—
79C2×Dic47⋊C4C2×C414yes—
80C4⋊C4×D47—22no—
81C4⋊C4×D47—22no—
82C4⋊C4×D47—22no—
83C4⋊C4×D47—22no—
84C4⋊C4×D47—22no—
85C4⋊C4×D47—22no—
86C4⋊C4×D47—22no—
87C4⋊C4×D47—22no—
88C2×C4×Dic47C2×C411yescharacteristic
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91C42×D47D411yescharacteristic
92C42×D47D411yescharacteristic
93C42×D47D411yescharacteristic
94C42×D47D411yescharacteristic
95C42×D47D411yescharacteristic
96C42×D47D411yescharacteristic
97C42×D47D411yescharacteristic
98C42×D47D411yescharacteristic
99C4⋊(C47⋊C8)—21no—
100C4⋊(C47⋊C8)—21no—
101Dic47⋊C8—22no—
102Dic47⋊C8—22no—
103(C2×D47)⋊C8—22no—
104(C2×D47)⋊C8—22no—
105(C2×D47)⋊C8—22no—
106(C2×D47)⋊C8—22no—
107#13093935—21no—
108#13093934—22no—
109C4×C47⋊C8—21no—
110C8×Dic47—22no—
111C22×Q8×C47C2×C412yes—
112C2×M16×C47C2312yes—
113C2×M16×C47C2312yes—
114C4⋊Q8×C47—21no—
115C4⋊Q8×C47—21no—
116C4⋊Q8×C47—21no—
117C4⋊Q8×C47—21no—
118C2×C4⋊C4×C47C2×C412yes—
119C2×C4⋊C4×C47C2312yes—
120C2×C42×C47C2311yescharacteristic
121C4⋊C8×C47—21no—
122C4⋊C8×C47—21no—
123#97×C47—21no—
124C4×C8×C47—21no—
125C23×D47C22×C411yescharacteristic
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×Q8×C47—44no—
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C22×C414yes—
132C22×C4×C47C2411yescharacteristic
133C22×Dic47C22×C411yescharacteristic
134C22×Dic47C22×C411yescharacteristic
135C22×Dic47C22×C411yescharacteristic
136C22×Dic47C22×C414yes—
137Q8×D47—48no—
138Q8×D47—48no—
139Q8×D47—48no—
140Q8×D47—48no—
141C2×C4×D47—22no—
142C2×C4×D47—22no—
143C2×C4×D47—24no—
144C2×C4×D47—24no—
145C2×C4×D47—24no—
146C2×C4×D47—24no—
147C2×C4×D47—48no—
148C2×C4×D47C22⋊C411yescharacteristic
149C2×C4×D47C22⋊C411yescharacteristic
150C2×C4×D47C22⋊C411yescharacteristic
151C2×C4×D47C22⋊C411yescharacteristic
152C2×C4×D47C22⋊C411yescharacteristic
153C2×C4×D47C22⋊C411yescharacteristic
154C2×C4×D47C22⋊C411yescharacteristic
155C2×C4×D47C22⋊C411yescharacteristic
156C2×C4×D47C2×D411yescharacteristic
157C2×C4×D47C2×D411yescharacteristic
158C2×C4×D47C2×D411yescharacteristic
159C2×C4×D47C2×D411yescharacteristic
160C2×Dic94—22no—
161C2×Dic94—22no—
162C2×Dic94—24no—
163C2×Dic94—24no—
164C2×Dic94—48no—
165C2×Dic94—44no—
166M16×C47—24no—
167M16×C47—22no—
168M16×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C4⋊C4×C47—22no—
172C4⋊C4×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C42×C47C2×D411yescharacteristic
176C42×C47C2×D411yescharacteristic
177C42×C47C2×D411yescharacteristic
178C42×C47C2×D411yescharacteristic
179C4⋊Dic47—22no—
180C4⋊Dic47—22no—
181C4⋊Dic47—22no—
182C4⋊Dic47—22no—
183Dic47⋊C4—24no—
184Dic47⋊C4—24no—
185Dic47⋊C4—24no—
186Dic47⋊C4—24no—
187C4×Dic47C22⋊C411yescharacteristic
188C4×Dic47C22⋊C411yescharacteristic
189C4×Dic47C22⋊C411yescharacteristic
190C4×Dic47C22⋊C411yescharacteristic
191C4×Dic47C22⋊C411yescharacteristic
192C4×Dic47C22⋊C411yescharacteristic
193C4×Dic47C22⋊C411yescharacteristic
194C4×Dic47C22⋊C411yescharacteristic
195C4×Dic47C2×D411yescharacteristic
196C4×Dic47C2×D411yescharacteristic
197C4×Dic47C2×D411yescharacteristic
198C4×Dic47C2×D411yescharacteristic
199#10625329—22no—
200#10625329—24no—
201#10625329—22no—
202C2×C47⋊C8—22no—
203C2×C47⋊C8—22no—
204C23×C47C23×C411yescharacteristic
205C22×D47—22no—
206C22×D47—22no—
207C22×D47—22no—
208C22×D47C2×C22⋊C411yescharacteristic
209C22×D47C2×C22⋊C411yescharacteristic
210Q8×C47—44no—
211Q8×C47—44no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—24no—
215C2×C4×C47—44no—
216C2×C4×C47C2×C22⋊C411yescharacteristic
217C2×C4×C47C2×C22⋊C411yescharacteristic
218C2×C4×C47C2×C22⋊C411yescharacteristic
219C2×C4×C47C2×C22⋊C411yescharacteristic
220C2×C4×C47C22×D411yescharacteristic
221C2×C4×C47C22×D411yescharacteristic
222C2×C4×C472−1+412yes—
223C2×C4×C472−1+412yes—
224C2×Dic47—22no—
225C2×Dic47—22no—
226C2×Dic47—22no—
227C2×Dic47—24no—
228C2×Dic47—44no—
229C2×Dic47C2×C22⋊C411yescharacteristic
230C2×Dic47C2×C22⋊C411yescharacteristic
231C2×Dic47C2×C22⋊C411yescharacteristic
232C2×Dic47C2×C22⋊C411yescharacteristic
233C2×Dic47C2×C22⋊C411yescharacteristic
234C2×Dic47C2×C22⋊C411yescharacteristic
235C4×D47—22no—
236C4×D47—22no—
237C4×D47—21no—
238C4×D47—21no—
239C4×D47—22no—
240C4×D47—22no—
241C4×D47—21no—
242C4×D47—21no—
243C4×D47—22no—
244C4×D47—22no—
245C4×D47—22no—
246C4×D47—22no—
247C4×D47—48no—
248C4×D47—48no—
249C4×D47#10014yes—
250C4×D47#10114yes—
251Dic94—48no—
252Dic94—44no—
253Dic94—44no—
254Dic94—48no—
255C8×C47—42no—
256C8×C47—42no—
257C47⋊C8—42no—
258C47⋊C8—42no—
259#21829—471nomaximal, Sylow
260C22×C47—21no—
261C22×C47—21no—
262C22×C47C22×C22⋊C411yescharacteristic
263C22×C47#51912yes—
264C2×D47—28no—
265C2×D47—21no—
266C2×D47—21no—
267C2×D47—21no—
268C2×D47—21no—
269C2×D47C2×#10012yes—
270C2×D47C2×#10112yes—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—44no—
274C4×C47C2×#10012yes—
275C4×C47C2×#10112yes—
276C4×C47#53611yescharacteristic
277C4×C47#53612yes—
278C4×C47#53611yescharacteristic
279Dic47—21no—
280Dic47—21no—
281Dic47—21no—
282Dic47—21no—
283Dic47—44no—
284Dic47C2×#10012yes—
285Dic47C2×#10112yes—
286C22×C4⋊Q8—471no—
287#2920—471no—
288#2920—471no—
289#1997—471no—
290#1997—471no—
291#1997—474no—
292#1997—471no—
293#1997D4711yescharacteristic, complemented
294#1821—474no—
295C2×C47—22no—
296C2×C47#231011yescharacteristic
297C2×C47C22×#10011yescharacteristic
298C2×C47C22×#10111yescharacteristic
299D47—22no—
300D47—22no—
301C23×Q8—472no—
302C2×C4⋊Q8—472no—
303C2×C4⋊Q8—472no—
304C2×C4⋊Q8—472no—
305C2×C4⋊Q8—471no—
306C2×C4⋊Q8—941no—
307C2×C4⋊Q8—941no—
308C2×C4⋊Q8—941no—
309C2×C4⋊Q8—941no—
310C2×C4⋊Q8—941no—
311C2×C4⋊Q8—941no—
312C2×C4⋊Q8—941no—
313C2×C4⋊Q8—941no—
314C2×C4⋊Q8C2×D4711yescharacteristic
315C22×C4⋊C4—472no—
316C22×C4⋊C4—472no—
317C22×C42—471no—
318#432—941no—
319#432—941no—
320#432—941no—
321#432—941no—
322#431—941no—
323#431—941no—
324#431—941no—
325#431—941no—
326#423—472no—
327#423—471no—
328#423C2×D4711yescharacteristic
329#407—472no—
330#407—472no—
331C4×M16—472no—
332C4×M16—471no—
333C4×M16C2×D4711yescharacteristic
334#343—474no—
335#343—474no—
336#343—474no—
337#343C2×D4714yes—
338C47#2182911yescharacteristic, complemented, Sylow
339C22×Q8—474no—
340C22×Q8—472no—
341C22×Q8—942no—
342C22×Q8—942no—
343C22×Q8—942no—
344C22×Q8—942no—
345C22×Q8—1888no—
346C22×Q8C4×D4712yes—
347C23×C4—471no—
348C23×C4—471no—
349C23×C4—471no—
350C23×C4—474no—
351C2×M16—472no—
352C2×M16—472no—
353C2×M16C22×D4712yes—
354C2×M16C22×D4712yes—
355C4⋊Q8—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8—942no—
360C4⋊Q8—942no—
361C4⋊Q8—942no—
362C4⋊Q8—942no—
363C4⋊Q8—942no—
364C4⋊Q8—942no—
365C4⋊Q8—942no—
366C4⋊Q8—942no—
367C4⋊Q8—942no—
368C4⋊Q8—942no—
369C4⋊Q8—942no—
370C4⋊Q8—942no—
371C4⋊Q8—941no—
372C4⋊Q8—941no—
373C4⋊Q8—941no—
374C4⋊Q8—941no—
375C2×C4⋊C4—474no—
376C2×C4⋊C4—474no—
377C2×C4⋊C4—472no—
378C2×C4⋊C4—472no—
379C2×C4⋊C4—942no—
380C2×C4⋊C4—942no—
381C2×C4⋊C4—942no—
382C2×C4⋊C4—942no—
383C2×C4⋊C4—942no—
384C2×C4⋊C4—942no—
385C2×C4⋊C4—942no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4C4×D4712yes—
388C2×C4⋊C4C22×D4712yes—
389C2×C42—471no—
390C2×C42—471no—
391C2×C42—471no—
392C2×C42—471no—
393C2×C42—471no—
394C2×C42—471no—
395C2×C42—471no—
396C2×C42—471no—
397C2×C42—471no—
398C2×C42—471no—
399C2×C42—471no—
400C2×C42C22×D4711yescharacteristic
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8—942no—
404C4⋊C8—942no—
405C4⋊C8—941no—
406C4⋊C8—941no—
407C22⋊C8—942no—
408C22⋊C8—942no—
409C22⋊C8—942no—
410C22⋊C8—942no—
411#97—21no—
412#97—942no—
413#97—941no—
414C4×C8—21no—
415C4×C8—942no—
416C4×C8—941no—
417C24—471no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—44no—
421C2×Q8—944no—
422C2×Q8—944no—
423C2×Q8—942no—
424C2×Q8—942no—
425C2×Q8—1884no—
426C2×Q8—1888no—
427C2×Q8—1888no—
428C2×Q8—1888no—
429C2×Q8—1888no—
430C2×Q8—1888no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—471no—
434C22×C4—471no—
435C22×C4—471no—
436C22×C4—471no—
437C22×C4—471no—
438C22×C4—471no—
439C22×C4—471no—
440C22×C4—471no—
441C22×C4—471no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—474no—
447C22×C4—944no—
448C22×C4—944no—
449C22×C4—944no—
450C22×C4—944no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—1888no—
454C22×C4C2×C4×D4711yescharacteristic
455C22×C4C2×C4×D4711yescharacteristic
456C22×C4C2×C4×D4714yes—
457C22×C4C23×D4711yescharacteristic
458M16—24no—
459M16—22no—
460M16—22no—
461M16—942no—
462M16—942no—
463M16—944no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—942no—
467C2×C8—942no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—944no—
473C4⋊C4—944no—
474C4⋊C4—944no—
475C4⋊C4—944no—
476C4⋊C4—942no—
477C4⋊C4—942no—
478C4⋊C4—942no—
479C4⋊C4—942no—
480C42—471no—
481C42—471no—
482C42—471no—
483C42—471no—
484C42—471no—
485C42—471no—
486C42—471no—
487C42—471no—
488C42—471no—
489C42—471no—
490C42—471no—
491C42—471no—
492C42D4×D4711yescharacteristic
493C42D4×D4711yescharacteristic
494C42D4×D4711yescharacteristic
495C42D4×D4711yescharacteristic
496C23—471no—
497C23—471no—
498C23—942no—
499C23—942no—
500C23—942no—
501C23C22×C4×D4711yescharacteristic
502Q8—44no—
503Q8—44no—
504Q8—1884no—
505Q8—1888no—
506Q8—1888no—
507Q8—1884no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—44no—
512C2×C4—471no—
513C2×C4—471no—
514C2×C4—474no—
515C2×C4—474no—
516C2×C4—471no—
517C2×C4—471no—
518C2×C4—471no—
519C2×C4—471no—
520C2×C4—942no—
521C2×C4—942no—
522C2×C4—942no—
523C2×C4—942no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—942no—
527C2×C4—942no—
528C2×C4—942no—
529C2×C4—941no—
530C2×C4—941no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—944no—
536C2×C4—1888no—
537C2×C4—1888no—
538C2×C4—1884no—
539C2×C4C22⋊C4×D4711yescharacteristic
540C2×C4C22⋊C4×D4711yescharacteristic
541C2×C4C22⋊C4×D4711yescharacteristic
542C2×C4C22⋊C4×D4711yescharacteristic
543C2×C4C2×D4×D4711yescharacteristic
544C2×C4C2×D4×D4711yescharacteristic
545C2×C4#1309407112yes—
546C2×C4#1309407212yes—
547C8—42no—
548C8—42no—
549C8—1882no—
550C8—1882no—
551C22—21no—
552C22—21no—
553C22—472no—
554C22—472no—
555C22—948no—
556C22—941no—
557C22—941no—
558C22—941no—
559C22—941no—
560C22C2×C22⋊C4×D4711yescharacteristic
561C22#1568959912yes—
562C4—21no—
563C4—21no—
564C4—44no—
565C4—472no—
566C4—472no—
567C4—941no—
568C4—941no—
569C4—941no—
570C4—941no—
571C4—1884no—
572C4#100×D4712yes—
573C4#101×D4712yes—
574C4#1568969311yescharacteristic
575C4#1568969612yes—
576C4#1568969811yescharacteristic
577C2—22no—
578C2—942no—
579C2—942no—
580C2#2024597111yescharacteristic
581C2C2×#100×D4711yescharacteristic
582C2C2×#101×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1997C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1997D47
hypocenterC47#21829
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1997

Complements

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

NH ≅ G/Ntype
4. #20244378C2semidirect
5. #20244377C2semidirect
6. #20244376C2semidirect
7. #20244375C2semidirect
9. C47×#1997C2semidirect
293. #1997D47semidirect
338. C47#21829semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D472
#202520202
#202520192
#202443782
#202443772
#202443762
#202443752
#202434672
C47×#19972
#2182947