Finite Group Databasebeta

← #26137478

Subgroups — #26137478

Order 12032.

2110 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13093989C211yesmaximal, characteristic
2C2×#15689027C212yesmaximal
3C2×#15688974C211yesmaximal, characteristic
4C2×C42×Dic47C211yesmaximal, characteristic
5#20241623C211yesmaximal, characteristic
6#20241621C211yesmaximal, characteristic
7#20241620C211yesmaximal, characteristic
8Dic47⋊#95C212yesmaximal
9#95×Dic47C212yesmaximal
10#95×Dic47C212yesmaximal
11C47×#1436C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×#13093989—24no—
14C2×#13093989—24no—
15C2×#13093989C418yescomplemented
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2212yes—
24C22×C4×Dic47C2212yes—
25C22×C4×Dic47C2211yescharacteristic
26#15689027C4116yescomplemented
27#15688974—24no—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2211yescharacteristic
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C42×Dic47—24no—
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2211yescharacteristic
40C2×#95×C47C2212yes—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—24no—
44C22×Dic94C2×C418yes—
45C22×Dic94C2×C414yes—
46C23×Dic47C2312yes—
47C23×Dic47C2311yescharacteristic
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2312yes—
50C23×Dic47C2311yescharacteristic
51C23×Dic47C2311yescharacteristic
52#13093989—232no—
53C2×Dic47⋊C4—22no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4C2×C418yes—
60C2×Dic47⋊C4C2×C414yes—
61C2×Dic47⋊C4C2×C414yes—
62C2×C4×Dic47—22no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—24no—
74C2×C4×Dic47—24no—
75C2×C4×Dic47C2×C418yes—
76C2×C4×Dic47C2×C414yes—
77C2×C4×Dic47C2×C414yes—
78C2×C4×Dic47C2×C414yes—
79C2×C4×Dic47D414yes—
80C2×C4×Dic47D414yes—
81C2×C4×Dic47Q818yescomplemented
82C47⋊#95—22no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—24no—
86C47⋊#95C2×C418yes—
87C47⋊#95C2×C418yes—
88C47⋊#95C2×C418yes—
89C23×C4×C47C2311yescharacteristic
90C23×C4×C47C2312yes—
91C23×C4×C47C2311yescharacteristic
92C23×C4×C47C2311yescharacteristic
93C23×C4×C47C2312yes—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—22no—
96C2×C4⋊C4×C47C2×C414yes—
97C2×C42×C47—22no—
98C2×C42×C47—24no—
99#95×C47—22no—
100#95×C47—24no—
101#95×C47C2×C418yes—
102C24×C47C2411yescharacteristic
103C22×C4×C47—22no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
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—21no—
113C22×C4×C47—21no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47—22no—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C22×C414yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C22×C414yes—
126C22×C4×C47C22×C412yes—
127C22×C4×C47C22×C414yes—
128C22×C4×C47C2×D412yes—
129C22×C4×C47C2×D412yes—
130C22×C4×C47C2×Q814yes—
131C22×C4×C47#4114yes—
132C22×Dic47—22no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—21no—
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×Dic47C22×C414yes—
150C22×Dic47C22×C412yes—
151C22×Dic47C22×C414yes—
152C22×Dic47C22×C412yes—
153C22×Dic47C22×C414yes—
154C22×Dic47C22×C412yes—
155C22×Dic47C22×C414yes—
156C22×Dic47C22×C412yes—
157C22×Dic47C2×D412yes—
158C22×Dic47C2×D412yes—
159C22×Dic47C2×D412yes—
160C22×Dic47C2×D412yes—
161C22×Dic47C2×Q814yes—
162C22×Dic47C2×Q814yes—
163C22×Dic47#4114yes—
164C22×Dic47#4114yes—
165C22×Dic47#4114yes—
166C2×Dic94—28no—
167C2×Dic94—28no—
168C2×Dic94—216no—
169C2×Dic94—216no—
170C2×Dic94C42116yescomplemented
171C4⋊C4×C47—28no—
172C42×C47—28no—
173Dic47⋊C4—28no—
174Dic47⋊C4—28no—
175Dic47⋊C4—216no—
176C4×Dic47—28no—
177C4×Dic47—28no—
178C4×Dic47—28no—
179C4×Dic47—216no—
180C4×Dic47—216no—
181C4×Dic47—48no—
182C4×Dic47C22⋊C4116yes—
183C23×C47C23×C411yescharacteristic
184C23×C47C23×C412yes—
185C23×C47C22×D411yescharacteristic
186C23×C47C22×D411yescharacteristic
187C23×C47C22×Q812yes—
188C23×C47C2×#4112yes—
189C23×C47C2×#4112yes—
190C23×C47C2×#4112yes—
191C23×C47C2×#4112yes—
192C2×C4×C47—22no—
193C2×C4×C47—22no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—24no—
197C2×C4×C47—24no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—22no—
201C2×C4×C47—22no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—22no—
207C2×C4×C47—24no—
208C2×C4×C47—24no—
209C2×C4×C47—24no—
210C2×C4×C47—24no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47—42no—
218C2×C4×C47C2×C4214yes—
219C2×C4×C47C2×C22⋊C414yes—
220C2×C4×C47C4×Q818yescomplemented
221C2×Dic47—22no—
222C2×Dic47—22no—
223C2×Dic47—24no—
224C2×Dic47—24no—
225C2×Dic47—24no—
226C2×Dic47—24no—
227C2×Dic47—24no—
228C2×Dic47—24no—
229C2×Dic47—24no—
230C2×Dic47—24no—
231C2×Dic47—22no—
232C2×Dic47—24no—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—41no—
237C2×Dic47—41no—
238C2×Dic47—42no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47C2×C4214yes—
244C2×Dic47C2×C4214yes—
245C2×Dic47C2×C22⋊C414yes—
246C2×Dic47C2×C22⋊C414yes—
247C2×Dic47#11714yes—
248C2×Dic47C4×D418yes—
249C2×Dic47C4×D418yes—
250C2×Dic47C4×Q818yes—
251C2×Dic47C4×Q818yescomplemented
252C2×Dic47C22⋊Q818yes—
253C2×Dic47#12414yes—
254C2×Dic47C4⋊Q814yes—
255Dic94—232no—
256C4×#391—471nomaximal, Sylow
257C22×C47C22×C4211yescharacteristic
258C22×C47C22×C22⋊C411yescharacteristic
259C22×C47C2×#11711yescharacteristic
260C22×C47C2×C4×D412yes—
261C22×C47C2×C4×D412yes—
262C22×C47C2×C4×Q812yes—
263C22×C47C2×C4×Q812yes—
264C22×C47C2×C4×Q812yes—
265C22×C47C4×#4112yes—
266C22×C47C4×#4112yes—
267C22×C47C4×#4112yes—
268C22×C47C2×C22⋊Q812yes—
269C22×C47#52511yescharacteristic
270C22×C47#52511yescharacteristic
271C22×C47C2×#12411yescharacteristic
272C22×C47#52912yes—
273C22×C47#52912yes—
274C22×C47C2×C4⋊Q811yescharacteristic
275C22×C47#53212yes—
276C22×C47#53312yes—
277C22×C47#53312yes—
278C4×C47—24no—
279C4×C47—24no—
280C4×C47—28no—
281C4×C47—42no—
282C4×C47—44no—
283Dic47—24no—
284Dic47—28no—
285Dic47—42no—
286Dic47—44no—
287Dic47C4×C22⋊C418yes—
288Dic47#39118yescomplemented
289C22×C4×Q8—471no—
290C2×#391—472no—
291C2×C4×C4⋊C4—471no—
292C2×C43—471no—
293#1436—471no—
294#1436—471no—
295#1436—471no—
296#1436D4711yescharacteristic
297C4⋊#95—472no—
298C4×#95—472no—
299C4×#95—472no—
300C2×C47C2×C4×C22⋊C411yescharacteristic
301C2×C47C42×Q812yes—
302C2×C47C2×#39111yescharacteristic
303C2×C47#229512yes—
304C2×C47#229711yescharacteristic
305C2×C47C4×C22⋊Q812yes—
306C2×C47C4×C22⋊Q812yes—
307C2×C47C4×#12412yes—
308C2×C47C4×C4⋊Q812yes—
309C23×Q8—471no—
310C2×C4×Q8—478no—
311C2×C4×Q8—944no—
312C2×C4×Q8—944no—
313C22×C4⋊C4—471no—
314C22×C4⋊C4—471no—
315C22×C4⋊C4—472no—
316C22×C4⋊C4C2×D4711yescharacteristic
317C22×C42—471no—
318C22×C42—471no—
319C22×C42—471no—
320C22×C42—472no—
321C22×C42—472no—
322C22×C42—472no—
323C22×C42—471no—
324C22×C42C2×D4711yescharacteristic
325#391—4716no—
326C4×C4⋊C4—944no—
327C2×#95—472no—
328C2×#95—472no—
329C2×#95—472no—
330C2×#95—472no—
331C2×#95—472no—
332C2×#95—472no—
333C2×#95—471no—
334C2×#95C2×D4712yes—
335C2×#95C2×D4711yescharacteristic
336C2×#95C2×D4712yes—
337C43—944no—
338C47C4×#39111yescharacteristic, complemented, Sylow
339C22×Q8—474no—
340C22×Q8—478no—
341C22×Q8—942no—
342C22×Q8—942no—
343C22×Q8—944no—
344C23×C4—471no—
345C23×C4—471no—
346C23×C4—471no—
347C23×C4—472no—
348C23×C4—471no—
349C23×C4—472no—
350C23×C4C22×D4711yescharacteristic
351C23×C4C22×D4712yes—
352C23×C4C22×D4711yescharacteristic
353C23×C4C22×D4711yescharacteristic
354C23×C4C22×D4712yes—
355C4×Q8—9432no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—474no—
359C2×C4⋊C4—474no—
360C2×C4⋊C4—478no—
361C2×C4⋊C4—942no—
362C2×C4⋊C4—942no—
363C2×C4⋊C4—944no—
364C2×C4⋊C4—944no—
365C2×C4⋊C4—942no—
366C2×C4⋊C4—942no—
367C2×C4⋊C4C4×D4714yes—
368C2×C42—22no—
369C2×C42—24no—
370C2×C42—474no—
371C2×C42—474no—
372C2×C42—474no—
373C2×C42—474no—
374C2×C42—474no—
375C2×C42—478no—
376C2×C42—478no—
377C2×C42—942no—
378C2×C42—942no—
379C2×C42—942no—
380C2×C42—942no—
381C2×C42—944no—
382C2×C42—944no—
383C2×C42—944no—
384C2×C42—944no—
385C2×C42—944no—
386C2×C42—942no—
387C2×C42—944no—
388C2×C42—944no—
389C2×C42—944no—
390#95—22no—
391#95—24no—
392#95—478no—
393#95—478no—
394#95—478no—
395#95—944no—
396#95—944no—
397#95—942no—
398#95—944no—
399#95C4×D4718yes—
400C24C23×D4711yescharacteristic
401C2×Q8—4716no—
402C2×Q8—948no—
403C2×Q8—948no—
404C2×Q8—9416no—
405C2×Q8—9416no—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—472no—
426C22×C4—472no—
427C22×C4—474no—
428C22×C4—472no—
429C22×C4—472no—
430C22×C4—472no—
431C22×C4—472no—
432C22×C4—474no—
433C22×C4—474no—
434C22×C4—474no—
435C22×C4—474no—
436C22×C4—474no—
437C22×C4—472no—
438C22×C4—474no—
439C22×C4—474no—
440C22×C4—474no—
441C22×C4—472no—
442C22×C4—942no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—942no—
459C22×C4C2×C4×D4714yes—
460C22×C4C2×C4×D4712yes—
461C22×C4C2×C4×D4714yes—
462C22×C4C2×C4×D4712yes—
463C22×C4C2×C4×D4712yes—
464C22×C4C2×C4×D4714yes—
465C22×C4D4×D4712yes—
466C22×C4D4×D4712yes—
467C22×C4#1062535214yes—
468C22×C4Q8×D4714yes—
469C4⋊C4—28no—
470C4⋊C4—9416no—
471C4⋊C4—948no—
472C4⋊C4—948no—
473C42—28no—
474C42—4716no—
475C42—9416no—
476C42—9416no—
477C42—948no—
478C42—948no—
479C42—948no—
480C42—1888no—
481C23C22×C4×D4711yescharacteristic
482C23C22×C4×D4712yes—
483C23C2×D4×D4711yescharacteristic
484C23C2×D4×D4711yescharacteristic
485C23C2×Q8×D4712yes—
486C23#41×D4712yes—
487C23#41×D4712yes—
488C23#41×D4712yes—
489C23C2×#1062535212yes—
490Q8—9432no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—24no—
494C2×C4—24no—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—474no—
518C2×C4—474no—
519C2×C4—474no—
520C2×C4—474no—
521C2×C4—478no—
522C2×C4—478no—
523C2×C4—478no—
524C2×C4—478no—
525C2×C4—474no—
526C2×C4—474no—
527C2×C4—474no—
528C2×C4—478no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—944no—
532C2×C4—944no—
533C2×C4—944no—
534C2×C4—944no—
535C2×C4—944no—
536C2×C4—944no—
537C2×C4—944no—
538C2×C4—944no—
539C2×C4—942no—
540C2×C4—944no—
541C2×C4—944no—
542C2×C4—944no—
543C2×C4—944no—
544C2×C4—1881no—
545C2×C4—1881no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4C42×D4714yes—
552C2×C4C22⋊C4×D4714yes—
553C2×C4#1309398918yescomplemented
554C22C2×C42×D4711yescharacteristic
555C22C2×C22⋊C4×D4711yescharacteristic
556C22#117×D4711yescharacteristic
557C22C4×D4×D4712yes—
558C22C4×D4×D4712yes—
559C22C4×Q8×D4712yes—
560C22C4×Q8×D4712yes—
561C22C2×#1309398912yes—
562C22C4×#1062535212yes—
563C22C4×#1062535212yes—
564C22#1568959112yes—
565C22C22⋊Q8×D4712yes—
566C22#1568962911yescharacteristic
567C22#1568963111yescharacteristic
568C22#124×D4711yescharacteristic
569C22#1568965012yes—
570C22#1568965612yes—
571C22C4⋊Q8×D4711yescharacteristic
572C22#1568966812yes—
573C22#1568967512yes—
574C22#1568967912yes—
575C4—24no—
576C4—28no—
577C4—24no—
578C4—42no—
579C4—44no—
580C4—478no—
581C4—478no—
582C4—948no—
583C4—944no—
584C4—1882no—
585C4—1884no—
586C2C4×C22⋊C4×D4711yescharacteristic
587C2C4×#1309398912yes—
588C2#391×D4711yescharacteristic
589C2#2024586112yes—
590C2#2024587311yescharacteristic
591C2#2024592012yes—
592C2#2024592212yes—
593C2#2024592912yes—
594C2#2024595912yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC47×#1436C2
socle, prime radical, cosocleC24×C47C24
hypercenter#1436D47
hypocenterC47C4×#391
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ #1436

Complements

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

NH ≅ G/Ntype
15. C2×#13093989C4semidirect
26. #15689027C4semidirect
81. C2×C4×Dic47Q8semidirect
170. C2×Dic94C42semidirect
220. C2×C4×C47C4×Q8semidirect
251. C2×Dic47C4×Q8semidirect
288. Dic47#391semidirect
338. C47C4×#391semidirect
553. C2×C4#13093989semidirect

Maximal subgroups

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

subgroupindex
C22×#130939892
C2×#156890272
C2×#156889742
C2×C42×Dic472
#202416232
#202416212
#202416202
Dic47⋊#952
#95×Dic472
C47×#14362
C4×#39147