Finite Group Databasebeta

← #26138024

Subgroups — #26138024

Order 12032.

1598 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×Dic47⋊C4C211yesmaximal, characteristic
2C2×C4×Dic47⋊C4C211yesmaximal, characteristic
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic
4C2×C4×C4⋊Dic47C211yesmaximal, characteristic
5C2×#15688969C211yesmaximal, characteristic
6#20241652C212yesmaximal
7#20241646C212yesmaximal
8#20241642C212yesmaximal
9#20241639C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C4×#95×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2212yes—
13C22×Dic47⋊C4C2212yes—
14C22×Dic47⋊C4C2212yes—
15C22×Dic47⋊C4C2211yescharacteristic
16C22×Dic47⋊C4C2211yescharacteristic
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C4×Dic47⋊C4—24no—
22C4×Dic47⋊C4—24no—
23C4×Dic47⋊C4C418yescomplemented
24C4×C4⋊Dic47—24no—
25#15688969—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2311yescharacteristic
46C2×C4⋊Dic47—24no—
47C2×C4⋊Dic47—24no—
48C2×C4⋊Dic47—24no—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4—24no—
51C2×Dic47⋊C4—24no—
52C2×Dic47⋊C4—24no—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—24no—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4C2×C414yes—
58C2×Dic47⋊C4C2×C414yes—
59C2×C4×Dic47—22no—
60C2×C4×Dic47—22no—
61C2×C4×Dic47—22no—
62C2×C4×Dic47—22no—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47C2×C414yes—
67C2×C4×Dic47C2×C414yes—
68C2×C4×Dic47D414yes—
69C2×C4×Dic47D414yes—
70C2×C4×Dic47Q814yes—
71C47⋊#95—24no—
72C47⋊#95—24no—
73C47⋊#95—24no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95C2×C414yes—
79C47⋊#95C2×C414yes—
80C23×C4×C47C2311yescharacteristic
81C23×C4×C47C2312yes—
82C23×C4×C47C2312yes—
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2311yescharacteristic
85C2×C42×C47—22no—
86C2×C42×C47—22no—
87C2×C42×C47—22no—
88C2×C42×C47—22no—
89C2×C42×C47—22no—
90C2×C42×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47C2×C414yes—
93C2×C42×C47Q814yes—
94#95×C47—24no—
95#95×C47—24no—
96C24×C47C2411yescharacteristic
97C22×C4×C47—21no—
98C22×C4×C47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—21no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47C22×C412yes—
117C22×C4×C47C22×C412yes—
118C22×C4×C47C22×C412yes—
119C22×C4×C47C2×D412yes—
120C22×C4×C47C2×D412yes—
121C22×C4×C47C2×Q814yes—
122C22×C4×C47C2×Q812yes—
123C22×C4×C47C2×Q812yes—
124C22×C4×C47#4114yes—
125C22×C4×C47#4114yes—
126C22×C4×C47#4112yes—
127C22×C4×C47#4112yes—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—22no—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—22no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47C22×C412yes—
152C22×Dic47C22×C412yes—
153C22×Dic47C22×C412yes—
154C22×Dic47C22×C412yes—
155C22×Dic47C2×D414yes—
156C22×Dic47C2×D412yes—
157C22×Dic47C2×D412yes—
158C22×Dic47C2×Q812yes—
159C22×Dic47C2×Q812yes—
160C22×Dic47#4114yes—
161C22×Dic47#4114yes—
162C42×C47—28no—
163C42×C47—28no—
164C42×C47—44no—
165C4⋊Dic47—216no—
166Dic47⋊C4—216no—
167Dic47⋊C4—216no—
168Dic47⋊C4—28no—
169Dic47⋊C4—28no—
170C4×Dic47—28no—
171C4×Dic47—28no—
172C4×Dic47—44no—
173C4×Dic47C4⋊C4116yescomplemented
174C23×C47C23×C411yescharacteristic
175C23×C47C22×D411yescharacteristic
176C23×C47C22×D411yescharacteristic
177C23×C47C22×Q811yescharacteristic
178C23×C47C22×Q811yescharacteristic
179C23×C47C2×#4112yes—
180C23×C47C2×#4112yes—
181C23×C47C2×#4111yescharacteristic
182C23×C47C2×#4112yes—
183C23×C47C2×#4111yescharacteristic
184C23×C47C2×#4112yes—
185C2×C4×C47—22no—
186C2×C4×C47—22no—
187C2×C4×C47—24no—
188C2×C4×C47—24no—
189C2×C4×C47—22no—
190C2×C4×C47—22no—
191C2×C4×C47—22no—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—24no—
197C2×C4×C47—24no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—42no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—42no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47C2×C4⋊C414yes—
209C2×C4×C47#11714yes—
210C2×C4×C47C4×D414yes—
211C2×C4×C47C4×Q814yes—
212C2×C4×C47#12114yes—
213C2×C4×C47C22⋊Q814yes—
214C2×C4×C47#12514yes—
215C2×C4×C47C4⋊Q814yes—
216C2×Dic47—22no—
217C2×Dic47—22no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—22no—
221C2×Dic47—22no—
222C2×Dic47—24no—
223C2×Dic47—24no—
224C2×Dic47—24no—
225C2×Dic47—24no—
226C2×Dic47—24no—
227C2×Dic47—24no—
228C2×Dic47—22no—
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47C2×C4⋊C414yes—
248C2×Dic47C2×C4⋊C414yes—
249C2×Dic47#11714yes—
250#13848—471nomaximal, Sylow
251C22×C47C22×C4⋊C411yescharacteristic
252C22×C47C2×#11711yescharacteristic
253C22×C47C2×#11711yescharacteristic
254C22×C47C2×C4×D411yescharacteristic
255C22×C47C2×C4×Q811yescharacteristic
256C22×C47C4×#4111yescharacteristic
257C22×C47C4×#4111yescharacteristic
258C22×C47C2×#12111yescharacteristic
259C22×C47C2×C22⋊Q811yescharacteristic
260C22×C47#52512yes—
261C22×C47#52512yes—
262C22×C47#52512yes—
263C22×C47C2×#12511yescharacteristic
264C22×C47#52912yes—
265C22×C47#52912yes—
266C22×C47#52912yes—
267C22×C47#52912yes—
268C22×C47C2×C4⋊Q811yescharacteristic
269C22×C47#53212yes—
270C22×C47#53312yes—
271C22×C47#53312yes—
272C22×C47#53312yes—
273C22×C47#53312yes—
274C4×C47—24no—
275C4×C47—44no—
276C4×C47—44no—
277C4×C47—42no—
278C4×C47#38918yes—
279Dic47—24no—
280Dic47—24no—
281Dic47—24no—
282Dic47—44no—
283Dic47—44no—
284Dic47—42no—
285C2×C4×C4⋊C4—471no—
286C2×C4×C4⋊C4—471no—
287C2×C4×C4⋊C4—471no—
288C2×C4×C4⋊C4—471no—
289C2×#376—471no—
290#1444—472no—
291#1442—472no—
292#1441—472no—
293#1441—472no—
294C4×#95—471no—
295C4×#95D4711yescharacteristic
296C2×C47#228511yescharacteristic
297C2×C47#229011yescharacteristic
298C2×C47#229011yescharacteristic
299C2×C47C2×#38911yescharacteristic
300C2×C47#229511yescharacteristic
301C2×C47#229511yescharacteristic
302C2×C47#229611yescharacteristic
303C2×C47#239212yes—
304C2×C47#239612yes—
305C2×C47#239912yes—
306C2×C47#240212yes—
307C22×C4⋊C4—471no—
308C22×C4⋊C4—471no—
309C22×C4⋊C4—472no—
310C22×C4⋊C4—472no—
311C22×C4⋊C4—472no—
312C22×C42—471no—
313C22×C42—471no—
314C22×C42—471no—
315C22×C42—471no—
316C22×C42C2×D4711yescharacteristic
317C22×C42C2×D4711yescharacteristic
318C22×C42C2×D4711yescharacteristic
319C4×C4⋊C4—478no—
320C4×C4⋊C4—944no—
321C4×C4⋊C4—944no—
322C4×C4⋊C4—944no—
323#376—944no—
324C2×#95—471no—
325C2×#95—471no—
326C2×#95—472no—
327C2×#95—472no—
328C2×#95—472no—
329C2×#95—472no—
330C2×#95—472no—
331C2×#95—472no—
332C2×#95—472no—
333C2×#95C2×D4712yes—
334C2×#95C2×D4712yes—
335C47#1384811yescharacteristic, complemented, Sylow
336C23×C4—471no—
337C23×C4—471no—
338C23×C4—471no—
339C23×C4—472no—
340C23×C4—472no—
341C23×C4—471no—
342C23×C4C22×D4712yes—
343C23×C4C22×D4711yescharacteristic
344C23×C4C22×D4712yes—
345C23×C4C22×D4711yescharacteristic
346C23×C4C22×D4711yescharacteristic
347C2×C4⋊C4—474no—
348C2×C4⋊C4—474no—
349C2×C4⋊C4—944no—
350C2×C4⋊C4—944no—
351C2×C4⋊C4—944no—
352C2×C4⋊C4—944no—
353C2×C4⋊C4—944no—
354C2×C4⋊C4—944no—
355C2×C4⋊C4—944no—
356C2×C4⋊C4—944no—
357C2×C4⋊C4—944no—
358C2×C4⋊C4—944no—
359C2×C4⋊C4—944no—
360C2×C42—22no—
361C2×C42—22no—
362C2×C42—22no—
363C2×C42—22no—
364C2×C42—22no—
365C2×C42—22no—
366C2×C42—22no—
367C2×C42—474no—
368C2×C42—474no—
369C2×C42—474no—
370C2×C42—474no—
371C2×C42—474no—
372C2×C42—942no—
373C2×C42—942no—
374C2×C42—942no—
375C2×C42—942no—
376C2×C42—942no—
377C2×C42—942no—
378C2×C42—942no—
379C2×C42Dic9414yes—
380C2×C42C4×D4714yes—
381#95—24no—
382#95—24no—
383#95—474no—
384#95—474no—
385#95—944no—
386#95—944no—
387#95—944no—
388#95—944no—
389#95—944no—
390#95—944no—
391#95—944no—
392C24C23×D4711yescharacteristic
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—21no—
396C22×C4—21no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—472no—
413C22×C4—472no—
414C22×C4—472no—
415C22×C4—472no—
416C22×C4—472no—
417C22×C4—472no—
418C22×C4—472no—
419C22×C4—474no—
420C22×C4—472no—
421C22×C4—474no—
422C22×C4—474no—
423C22×C4—941no—
424C22×C4—942no—
425C22×C4—942no—
426C22×C4—941no—
427C22×C4—942no—
428C22×C4—942no—
429C22×C4—942no—
430C22×C4—941no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—942no—
437C22×C4—942no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4C2×Dic9414yes—
447C22×C4C2×Dic9412yes—
448C22×C4C2×C4×D4712yes—
449C22×C4C2×C4×D4712yes—
450C22×C4C2×C4×D4712yes—
451C22×C4#1062535014yes—
452C22×C4#1062535014yes—
453C22×C4#1062535012yes—
454C22×C4D4×D4712yes—
455C22×C4D4×D4712yes—
456C22×C4#1062535212yes—
457C22×C4Q8×D4712yes—
458C4⋊C4—948no—
459C4⋊C4—9416no—
460C4⋊C4—9416no—
461C4⋊C4—9416no—
462C4⋊C4—948no—
463C42—28no—
464C42—28no—
465C42—44no—
466C42—4716no—
467C42—948no—
468C42—948no—
469C42—1884no—
470C23C22×C4×D4711yescharacteristic
471C23C2×D4×D4711yescharacteristic
472C23C2×D4×D4711yescharacteristic
473C23C2×Q8×D4711yescharacteristic
474C23C22×Dic9411yescharacteristic
475C23#41×D4712yes—
476C23#41×D4712yes—
477C23C2×#1062535211yescharacteristic
478C23C2×#1062535012yes—
479C23C2×#1062535011yescharacteristic
480C23C2×#1062535012yes—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—24no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—22no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—474no—
505C2×C4—474no—
506C2×C4—474no—
507C2×C4—942no—
508C2×C4—942no—
509C2×C4—942no—
510C2×C4—942no—
511C2×C4—942no—
512C2×C4—942no—
513C2×C4—944no—
514C2×C4—944no—
515C2×C4—944no—
516C2×C4—944no—
517C2×C4—944no—
518C2×C4—944no—
519C2×C4—942no—
520C2×C4—942no—
521C2×C4—942no—
522C2×C4—944no—
523C2×C4—944no—
524C2×C4—944no—
525C2×C4—944no—
526C2×C4—944no—
527C2×C4—944no—
528C2×C4—1882no—
529C2×C4—1882no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4—1882no—
537C2×C4—1882no—
538C2×C4C4⋊C4×D4714yes—
539C2×C4#1309398114yes—
540C2×C4(C22⋊D47)⋊C414yes—
541C2×C4C4×Dic9414yes—
542C2×C4#1309399714yes—
543C2×C4#1309400114yes—
544C2×C4#1309401414yes—
545C2×C4#1309402314yes—
546C22C2×C4⋊C4×D4711yescharacteristic
547C22#117×D4711yescharacteristic
548C22C2×#1309398111yescharacteristic
549C22C2×(C22⋊D47)⋊C411yescharacteristic
550C22C2×C4×Dic9411yescharacteristic
551C22#1568959111yescharacteristic
552C22C4×#1062535011yescharacteristic
553C22C2×#1309399711yescharacteristic
554C22C2×#1309400111yescharacteristic
555C22#1568963212yes—
556C22#1568963212yes—
557C22#1568963212yes—
558C22C2×#1309401411yescharacteristic
559C22#1568965112yes—
560C22#1568965312yes—
561C22#1568965512yes—
562C22#1568965712yes—
563C22C2×#1309402311yescharacteristic
564C22#1568967012yes—
565C22#1568967612yes—
566C22#1568967712yes—
567C22#1568967712yes—
568C22#1568968012yes—
569C4—24no—
570C4—42no—
571C4—44no—
572C4—44no—
573C4—944no—
574C4—944no—
575C4—944no—
576C4—1882no—
577C4—1884no—
578C4—1884no—
579C4#1568902018yes—
580C2#2024579211yescharacteristic
581C2#2024582711yescharacteristic
582C2#2024583411yescharacteristic
583C2C2×#1568902011yescharacteristic
584C2#2024586011yescharacteristic
585C2#2024586511yescharacteristic
586C2#2024586811yescharacteristic
587C2#2024663212yes—
588C2#2024666212yes—
589C2#2024668212yes—
590C2#2024669512yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4×#95D47
hypocenterC47#13848
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
23. C4×Dic47⋊C4C4semidirect
173. C4×Dic47C4⋊C4semidirect
335. C47#13848semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic47⋊C42
C2×C4×C4⋊Dic472
C2×#156889692
#202416522
#202416462
#202416422
#202416392
C4×C47⋊#952
C4×#95×C472
#1384847