Finite Group Databasebeta

← #26184869

Subgroups — #26184869

Order 12032.

1178 conjugacy classes of subgroups.

The subgroup lattice has 592 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#20252016C211yesmaximal, characteristic
4#20242103C214yesmaximal, complemented
5#20242071C214yesmaximal, complemented
6#20242061C211yesmaximal, characteristic, complemented
7#20242060C211yesmaximal, characteristic, complemented
8#20242059C211yesmaximal, characteristic, complemented
9C47×#1546C211yesmaximal, characteristic, complemented
10C22×Q8×D47—21no—
11C2×#13094024C2211yescharacteristic
12C2×#13094023—21no—
13C2×#13094023C412yes—
14C2×#13094022—21no—
15C4⋊Q8×D47—21no—
16C4⋊Q8×D47—21no—
17C4⋊Q8×D47—21no—
18C4⋊Q8×D47—21no—
19C4⋊Q8×D47C412yes—
20C4⋊Q8×D47C412yes—
21C4⋊Q8×D47C2212yes—
22C4⋊Q8×D47C2212yes—
23C2×C4⋊C4×D47—21no—
24C2×C4⋊C4×D47C412yes—
25C2×C42×D47C2211yescharacteristic
26#15689179—21no—
27#15689179C2212yes—
28#15689179C2212yes—
29#15689177—21no—
30#15689176C2211yescharacteristic
31#15689175—21no—
32#15689175C2212yes—
33#15689174—21no—
34#15689147C2211yescharacteristic
35#15689145C2212yes—
36#15689086—21no—
37#15689085—21no—
38M16×Dic47—21no—
39C4×#10625324—21no—
40#15688870C2214yescomplemented
41#15688869C2214yescomplemented
42#15688868C2214yescomplemented
43C2×C4⋊Q8×C47C2211yescharacteristic
44C47×#431C2211yescharacteristic
45C47×#423C2211yescharacteristic
46C47×#332C2214yescomplemented
47C22×Dic94—21no—
48C22×Dic94—22no—
49C2×Q8×D47—22no—
50C2×Q8×D47—22no—
51C2×Q8×D47—22no—
52C2×Q8×D47—22no—
53C2×Q8×D47—44no—
54C2×Q8×D47—44no—
55C22×C4×D47—22no—
56C22×C4×D47C2×C411yescharacteristic
57C22×C4×D47D411yescharacteristic
58C22×C4×D47D411yescharacteristic
59C2×#10625329—21no—
60C2×#10625324—22no—
61#13094024—21no—
62#13094024—21no—
63#13094024C2×C412yes—
64#13094024C2312yes—
65#13094023—22no—
66#13094023—22no—
67#13094023—22no—
68#13094023—22no—
69#13094023—22no—
70#13094023—22no—
71#13094023C2×C414yes—
72#13094023C2×C414yes—
73#13094022—22no—
74#13094022—22no—
75#13094022—22no—
76#13094022—22no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47C2×C412yes—
79C2×Dic47⋊C4—22no—
80C2×Dic47⋊C4—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×D47C2×C414yes—
88C4⋊C4×D47C2×C414yes—
89C2×C4×Dic47C2×C411yescharacteristic
90C2×C4×Dic47D411yescharacteristic
91C2×C4×Dic47D411yescharacteristic
92C42×D47C2×C411yescharacteristic
93C42×D47C2×C411yescharacteristic
94C42×D47D411yescharacteristic
95C42×D47D411yescharacteristic
96C42×D47D411yescharacteristic
97C42×D47D411yescharacteristic
98C42×D47C2311yescharacteristic
99C42×D47C2311yescharacteristic
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)C2312yes—
102C4⋊(C47⋊C8)C2312yes—
103Dic47⋊C8—22no—
104C22⋊(C47⋊C8)—21no—
105(C2×D47)⋊C8—22no—
106(C2×D47)⋊C8—22no—
107(C2×D47)⋊C8—22no—
108#13093934—22no—
109#13093934—22no—
110C4×C47⋊C8—21no—
111C8×Dic47—22no—
112C22×Q8×C47—21no—
113C2×M16×C47—21no—
114C4⋊Q8×C47—21no—
115C4⋊Q8×C47—21no—
116C4⋊Q8×C47C2×C412yes—
117C4⋊Q8×C47C2312yes—
118C2×C4⋊C4×C47—21no—
119C2×C4⋊C4×C47C2×C412yes—
120C2×C42×C47C2311yescharacteristic
121C4⋊C8×C47—21no—
122C4⋊C8×C47C2312yes—
123C4⋊C8×C47C2312yes—
124C22⋊C8×C47—21no—
125C4×C8×C47—21no—
126C23×D47C22⋊C411yescharacteristic
127C2×Q8×C47—22no—
128C2×Q8×C47—22no—
129C2×Q8×C47—42no—
130C2×Q8×C47—42no—
131C22×C4×C47—22no—
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C2×D411yescharacteristic
134C22×C4×C47C2×D411yescharacteristic
135C22×Dic47—22no—
136C22×Dic47C22⋊C411yescharacteristic
137C22×Dic47C22⋊C411yescharacteristic
138C22×Dic47C22⋊C411yescharacteristic
139Q8×D47—44no—
140Q8×D47—44no—
141Q8×D47—44no—
142Q8×D47—44no—
143Q8×D47—48no—
144Q8×D47—48no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—24no—
148C2×C4×D47—24no—
149C2×C4×D47—24no—
150C2×C4×D47—24no—
151C2×C4×D47—48no—
152C2×C4×D47C22⋊C411yescharacteristic
153C2×C4×D47C22⋊C411yescharacteristic
154C2×C4×D47C22⋊C411yescharacteristic
155C2×C4×D47C22⋊C411yescharacteristic
156C2×C4×D47C22⋊C411yescharacteristic
157C2×C4×D47C22⋊C411yescharacteristic
158C2×C4×D47C22×C411yescharacteristic
159C2×C4×D47C22×C411yescharacteristic
160C2×C4×D47C2×D411yescharacteristic
161C2×C4×D47C2×D411yescharacteristic
162C2×C4×D47C2×D411yescharacteristic
163C2×C4×D47C2×D411yescharacteristic
164C2×Dic94—22no—
165C2×Dic94—22no—
166C2×Dic94—24no—
167C2×Dic94—24no—
168C2×Dic94—48no—
169C2×Dic94—42no—
170C2×Dic94—42no—
171M16×C47—42no—
172C2×C8×C47—22no—
173C2×C8×C47—22no—
174C4⋊C4×C47—22no—
175C4⋊C4×C47—22no—
176C4⋊C4×C47—22no—
177C4⋊C4×C47C22×C414yes—
178C42×C47C22×C411yescharacteristic
179C42×C47C2×D411yescharacteristic
180C42×C47C2×D411yescharacteristic
181C42×C47C2411yescharacteristic
182C4⋊Dic47—22no—
183C4⋊Dic47—22no—
184C4⋊Dic47—22no—
185C4⋊Dic47C22×C414yes—
186Dic47⋊C4—24no—
187Dic47⋊C4—24no—
188Dic47⋊C4—24no—
189Dic47⋊C4—24no—
190C4×Dic47C22⋊C411yescharacteristic
191C4×Dic47C22⋊C411yescharacteristic
192C4×Dic47C22⋊C411yescharacteristic
193C4×Dic47C22⋊C411yescharacteristic
194C4×Dic47C22⋊C411yescharacteristic
195C4×Dic47C22⋊C411yescharacteristic
196C4×Dic47C22×C411yescharacteristic
197C4×Dic47C22×C411yescharacteristic
198C4×Dic47C2×D411yescharacteristic
199C4×Dic47C2×D411yescharacteristic
200C4×Dic47C2×D411yescharacteristic
201C4×Dic47C2×D411yescharacteristic
202#10625329—42no—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205#10625324—44no—
206C23×C47C2×C22⋊C411yescharacteristic
207C22×D47—22no—
208C22×D47—22no—
209C22×D47—22no—
210C22×D47C2×C22⋊C411yescharacteristic
211C22×D47C2×C22⋊C411yescharacteristic
212Q8×C47—42no—
213Q8×C47—42no—
214Q8×C47—44no—
215C2×C4×C47—22no—
216C2×C4×C47—22no—
217C2×C4×C47—24no—
218C2×C4×C47—44no—
219C2×C4×C47C2×C22⋊C411yescharacteristic
220C2×C4×C47C2×C22⋊C411yescharacteristic
221C2×C4×C47C2×C22⋊C411yescharacteristic
222C2×C4×C47AGL(1,ℤ/8)12yes—
223C2×C4×C47AGL(1,ℤ/8)12yes—
224C2×C4×C47C23×C411yescharacteristic
225C2×C4×C47C22×D411yescharacteristic
226C2×C4×C47C22×D411yescharacteristic
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—22no—
230C2×Dic47—24no—
231C2×Dic47—44no—
232C2×Dic47C2×C22⋊C411yescharacteristic
233C2×Dic47C2×C22⋊C411yescharacteristic
234C2×Dic47C2×C22⋊C411yescharacteristic
235C2×Dic47C2×C22⋊C411yescharacteristic
236C2×Dic47C2×C22⋊C411yescharacteristic
237C2×Dic47C2×C22⋊C411yescharacteristic
238C4×D47—22no—
239C4×D47—22no—
240C4×D47—21no—
241C4×D47—21no—
242C4×D47—21no—
243C4×D47—21no—
244C4×D47—22no—
245C4×D47—22no—
246C4×D47—22no—
247C4×D47—22no—
248C4×D47—22no—
249C4×D47—22no—
250C4×D47—48no—
251C4×D47—48no—
252C4×D47#10114yes—
253C4×D47#13714yes—
254Dic94—48no—
255Dic94—48no—
256Dic94—42no—
257Dic94—42no—
258Dic94—44no—
259C8×C47—42no—
260C8×C47—42no—
261C47⋊C8—42no—
262C47⋊C8—42no—
263#17742—471nomaximal, Sylow
264C22×C47—21no—
265C22×C47—21no—
266C22×C47#41812yes—
267C22×C47C22×C22⋊C411yescharacteristic
268C2×D47—28no—
269C2×D47—21no—
270C2×D47—21no—
271C2×D47—21no—
272C2×D47—21no—
273C2×D47C2×#10112yes—
274C2×D47#41912yes—
275C4×C47—21no—
276C4×C47—21no—
277C4×C47—44no—
278C4×C47C2×#10112yes—
279C4×C47#41812yes—
280C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C4×C47C2×#13712yes—
283Dic47—21no—
284Dic47—21no—
285Dic47—21no—
286Dic47—21no—
287Dic47—44no—
288Dic47C2×#10112yes—
289Dic47#41912yes—
290C22×C4⋊Q8—471no—
291#2920—471no—
292#2920—471no—
293#1556—474no—
294#1549—474no—
295#1546—471no—
296#1546—471no—
297#1546—471no—
298#1546D4711yescharacteristic, complemented
299C2×C47—22no—
300C2×C47C22×#10111yescharacteristic
301C2×C47C2×#41811yescharacteristic
302C2×C47C2×#41911yescharacteristic
303D47—22no—
304D47—22no—
305C23×Q8—941no—
306C2×C4⋊Q8—472no—
307C2×C4⋊Q8—472no—
308C2×C4⋊Q8—472no—
309C2×C4⋊Q8—472no—
310C2×C4⋊Q8—472no—
311C2×C4⋊Q8—471no—
312C2×C4⋊Q8—941no—
313C2×C4⋊Q8—941no—
314C2×C4⋊Q8—941no—
315C2×C4⋊Q8—941no—
316C2×C4⋊Q8—941no—
317C2×C4⋊Q8—941no—
318C2×C4⋊Q8C2×D4711yescharacteristic
319C22×C4⋊C4—472no—
320C22×C4⋊C4—941no—
321C22×C42—471no—
322#432—472no—
323#432—472no—
324#432—941no—
325#432—941no—
326#431—471no—
327#431—472no—
328#431—941no—
329#431—941no—
330#431C2×D4711yescharacteristic
331#423—471no—
332#423—472no—
333#423C2×D4711yescharacteristic
334#407—941no—
335#407—941no—
336C4×M16—941no—
337C4×M16—941no—
338#332—474no—
339#332—474no—
340#332—474no—
341#332C2×D4714yescomplemented
342C47#1774211yescharacteristic, complemented, Sylow
343C22×Q8—21no—
344C22×Q8—942no—
345C22×Q8—942no—
346C22×Q8—942no—
347C22×Q8—942no—
348C22×Q8—942no—
349C22×Q8—941no—
350C22×Q8—1884no—
351C22×Q8—1884no—
352C23×C4—471no—
353C23×C4—471no—
354C23×C4—471no—
355C23×C4—942no—
356C2×M16—21no—
357C2×M16—942no—
358C2×M16—941no—
359C4⋊Q8—21no—
360C4⋊Q8—21no—
361C4⋊Q8—474no—
362C4⋊Q8—474no—
363C4⋊Q8—472no—
364C4⋊Q8—472no—
365C4⋊Q8—942no—
366C4⋊Q8—942no—
367C4⋊Q8—942no—
368C4⋊Q8—942no—
369C4⋊Q8—942no—
370C4⋊Q8—942no—
371C4⋊Q8—942no—
372C4⋊Q8—942no—
373C4⋊Q8—942no—
374C4⋊Q8—942no—
375C4⋊Q8—941no—
376C4⋊Q8—941no—
377C4⋊Q8C4×D4712yes—
378C4⋊Q8C22×D4712yes—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—472no—
381C2×C4⋊C4—474no—
382C2×C4⋊C4—474no—
383C2×C4⋊C4—942no—
384C2×C4⋊C4—942no—
385C2×C4⋊C4—942no—
386C2×C4⋊C4—942no—
387C2×C4⋊C4—942no—
388C2×C4⋊C4—942no—
389C2×C4⋊C4—942no—
390C2×C4⋊C4—942no—
391C2×C4⋊C4—941no—
392C2×C4⋊C4C4×D4712yes—
393C2×C42—471no—
394C2×C42—471no—
395C2×C42—471no—
396C2×C42—471no—
397C2×C42—471no—
398C2×C42—471no—
399C2×C42—471no—
400C2×C42—471no—
401C2×C42—471no—
402C2×C42—471no—
403C2×C42—471no—
404C2×C42C22×D4711yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—472no—
407C4⋊C8—472no—
408C4⋊C8—942no—
409C4⋊C8—941no—
410C4⋊C8C22×D4712yes—
411C4⋊C8C22×D4712yes—
412C22⋊C8—21no—
413C22⋊C8—942no—
414C22⋊C8—942no—
415C22⋊C8—942no—
416C22⋊C8—941no—
417#97—942no—
418#97—942no—
419C4×C8—21no—
420C4×C8—942no—
421C4×C8—941no—
422C24—471no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—42no—
426C2×Q8—42no—
427C2×Q8—944no—
428C2×Q8—944no—
429C2×Q8—942no—
430C2×Q8—942no—
431C2×Q8—1888no—
432C2×Q8—1888no—
433C2×Q8—1888no—
434C2×Q8—1884no—
435C2×Q8—1884no—
436C2×Q8—1884no—
437C2×Q8—1884no—
438C2×Q8—1882no—
439C2×Q8—1882no—
440C22×C4—22no—
441C22×C4—471no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—471no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—471no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—471no—
456C22×C4—944no—
457C22×C4—944no—
458C22×C4—944no—
459C22×C4—944no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—1888no—
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467M16—42no—
468M16—1884no—
469M16—1882no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—942no—
473C2×C8—942no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—474no—
478C4⋊C4—944no—
479C4⋊C4—944no—
480C4⋊C4—944no—
481C4⋊C4—944no—
482C4⋊C4—942no—
483C4⋊C4—942no—
484C4⋊C4—942no—
485C4⋊C4C2×C4×D4714yes—
486C42—471no—
487C42—471no—
488C42—471no—
489C42—471no—
490C42—471no—
491C42—471no—
492C42—471no—
493C42—471no—
494C42—471no—
495C42—471no—
496C42—471no—
497C42—471no—
498C42C2×C4×D4711yescharacteristic
499C42D4×D4711yescharacteristic
500C42D4×D4711yescharacteristic
501C42C23×D4711yescharacteristic
502C23—471no—
503C23—471no—
504C23—942no—
505C23—942no—
506C23—942no—
507C23C22⋊C4×D4711yescharacteristic
508Q8—44no—
509Q8—42no—
510Q8—42no—
511Q8—1888no—
512Q8—1888no—
513Q8—1884no—
514Q8—1882no—
515Q8—1882no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—471no—
521C2×C4—471no—
522C2×C4—474no—
523C2×C4—474no—
524C2×C4—471no—
525C2×C4—471no—
526C2×C4—471no—
527C2×C4—471no—
528C2×C4—942no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—942no—
534C2×C4—942no—
535C2×C4—942no—
536C2×C4—942no—
537C2×C4—942no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—942no—
543C2×C4—944no—
544C2×C4—1888no—
545C2×C4—1888no—
546C2×C4—1884no—
547C2×C4C22⋊C4×D4711yescharacteristic
548C2×C4C22⋊C4×D4711yescharacteristic
549C2×C4C22⋊C4×D4711yescharacteristic
550C2×C4#1309404812yes—
551C2×C4#1309405112yes—
552C2×C4C22×C4×D4711yescharacteristic
553C2×C4C2×D4×D4711yescharacteristic
554C2×C4C2×D4×D4711yescharacteristic
555C8—42no—
556C8—42no—
557C8—1882no—
558C8—1882no—
559C22—21no—
560C22—21no—
561C22—472no—
562C22—472no—
563C22—948no—
564C22—941no—
565C22—941no—
566C22—941no—
567C22—941no—
568C22#1568912612yes—
569C22C2×C22⋊C4×D4711yescharacteristic
570C4—21no—
571C4—21no—
572C4—44no—
573C4—472no—
574C4—472no—
575C4—941no—
576C4—941no—
577C4—941no—
578C4—941no—
579C4—1884no—
580C4#101×D4712yes—
581C4#1568912612yes—
582C4C2×#1309404811yescharacteristic
583C4C2×#1309405111yescharacteristic
584C4#137×D4712yes—
585C2—22no—
586C2—942no—
587C2—942no—
588C2C2×#101×D4711yescharacteristic
589C2C2×#1568912611yescharacteristic
590C2#419×D4711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1546C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1546D47
hypocenterC47#17742
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
4. #20242103C2semidirect
5. #20242071C2semidirect
6. #20242061C2semidirect
7. #20242060C2semidirect
8. #20242059C2semidirect
9. C47×#1546C2semidirect
40. #15688870C22semidirect
41. #15688869C22semidirect
42. #15688868C22semidirect
46. C47×#332C22semidirect
298. #1546D47semidirect
341. #332C2×D47semidirect
342. C47#17742semidirect

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
#202520162
#202421032
#202420712
#202420612
#202420602
#202420592
C47×#15462
#1774247