Finite Group Databasebeta

← #26138032

Subgroups — #26138032

Order 12032.

1790 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×Dic94C211yesmaximal, characteristic
2C2×C4×Dic47⋊C4C211yesmaximal, characteristic
3C2×#15688969C211yesmaximal, characteristic
4#20241658C212yesmaximal
5#20241654C212yesmaximal
6#20241640C212yesmaximal
7#20241639C212yesmaximal
8C4×C47⋊#95C211yesmaximal, characteristic
9C4×C47⋊#95C211yesmaximal, characteristic
10C4×C47⋊#95C211yesmaximal, characteristic
11C4×#95×C47C211yesmaximal, characteristic
12C23×Dic94C2211yescharacteristic
13C2×C4×Dic94—24no—
14C2×C4×Dic94—24no—
15C2×C4×Dic94C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×Dic47⋊C4C2211yescharacteristic
19C22×Dic47⋊C4C2211yescharacteristic
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24C4×Dic47⋊C4—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⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C22×C42×C47C2211yescharacteristic
36C22×C42×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C2×#95×C47C2212yes—
39C2×#95×C47C2212yes—
40C22×Dic94—24no—
41C22×Dic94—22no—
42C22×Dic94—22no—
43C22×Dic94—24no—
44C22×Dic94C2×C414yes—
45C23×Dic47C2311yescharacteristic
46C23×Dic47C2312yes—
47C23×Dic47C2312yes—
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2311yescharacteristic
51C4×Dic94—232no—
52C2×C4⋊Dic47—22no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47C2×C414yes—
55C2×Dic47⋊C4—24no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—22no—
59C2×Dic47⋊C4—22no—
60C2×Dic47⋊C4—22no—
61C2×Dic47⋊C4—24no—
62C2×Dic47⋊C4C2×C414yes—
63C2×Dic47⋊C4C2×C414yes—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—22no—
66C2×C4×Dic47—22no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47C2×C414yes—
72C2×C4×Dic47C2×C414yes—
73C2×C4×Dic47D414yes—
74C2×C4×Dic47D414yes—
75C2×C4×Dic47Q814yescomplemented
76C47⋊#95—24no—
77C47⋊#95—24no—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2312yes—
87C23×C4×C47C2312yes—
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C2×C42×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47—22no—
93C2×C42×C47—22no—
94C2×C42×C47—22no—
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47C2×C414yes—
98C2×C42×C47Q814yescomplemented
99#95×C47—24no—
100#95×C47—24no—
101C24×C47C2411yescharacteristic
102C22×C4×C47—21no—
103C22×C4×C47—21no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—21no—
108C22×C4×C47—21no—
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×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—22no—
120C22×C4×C47—22no—
121C22×C4×C47C22×C412yes—
122C22×C4×C47C22×C412yes—
123C22×C4×C47C22×C412yes—
124C22×C4×C47C2×D412yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×Q814yes—
127C22×C4×C47C2×Q812yes—
128C22×C4×C47C2×Q812yes—
129C22×C4×C47#4114yes—
130C22×C4×C47#4114yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C412yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C22×C412yes—
160C22×Dic47C2×D412yes—
161C22×Dic47C2×D412yes—
162C22×Dic47C2×D412yes—
163C22×Dic47C2×D412yes—
164C22×Dic47C2×Q814yes—
165C22×Dic47#4114yes—
166C22×Dic47#4114yes—
167C2×Dic94—216no—
168C2×Dic94—216no—
169C2×Dic94—28no—
170C2×Dic94—28no—
171C2×Dic94—28no—
172C42×C47—28no—
173C42×C47—28no—
174C42×C47—44no—
175C4⋊Dic47—28no—
176Dic47⋊C4—216no—
177Dic47⋊C4—28no—
178Dic47⋊C4—28no—
179C4×Dic47—28no—
180C4×Dic47—28no—
181C4×Dic47—44no—
182C4×Dic47C22⋊C4116yes—
183C23×C47C23×C411yescharacteristic
184C23×C47C22×D411yescharacteristic
185C23×C47C22×D411yescharacteristic
186C23×C47C22×Q811yescharacteristic
187C23×C47C22×Q811yescharacteristic
188C23×C47C2×#4112yes—
189C23×C47C2×#4112yes—
190C23×C47C2×#4111yescharacteristic
191C23×C47C2×#4112yes—
192C23×C47C2×#4111yescharacteristic
193C23×C47C2×#4112yes—
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—24no—
197C2×C4×C47—24no—
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—22no—
201C2×C4×C47—24no—
202C2×C4×C47—24no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—24no—
206C2×C4×C47—24no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47—42no—
215C2×C4×C47—42no—
216C2×C4×C47—42no—
217C2×C4×C47C2×C22⋊C414yes—
218C2×C4×C47#11714yes—
219C2×C4×C47C4×Q814yes—
220C2×C4×C47C4×Q814yes—
221C2×C4×C47C22⋊Q814yes—
222C2×C4×C47C22⋊Q814yes—
223C2×C4×C47#12414yes—
224C2×C4×C47C4⋊Q814yes—
225C2×Dic47—22no—
226C2×Dic47—22no—
227C2×Dic47—22no—
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—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—24no—
241C2×Dic47—24no—
242C2×Dic47—24no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—42no—
254C2×Dic47—42no—
255C2×Dic47—42no—
256C2×Dic47C2×C22⋊C414yes—
257C2×Dic47C2×C22⋊C414yes—
258C2×Dic47#11714yes—
259Dic94—232no—
260#13850—471nomaximal, Sylow
261C22×C47C22×C22⋊C411yescharacteristic
262C22×C47C2×#11711yescharacteristic
263C22×C47C2×#11711yescharacteristic
264C22×C47C2×C4×Q811yescharacteristic
265C22×C47C2×C4×Q811yescharacteristic
266C22×C47C4×#4111yescharacteristic
267C22×C47C4×#4111yescharacteristic
268C22×C47C2×C22⋊Q811yescharacteristic
269C22×C47C2×C22⋊Q811yescharacteristic
270C22×C47#52512yes—
271C22×C47#52512yes—
272C22×C47#52512yes—
273C22×C47C2×#12411yescharacteristic
274C22×C47#52912yes—
275C22×C47#52912yes—
276C22×C47#52912yes—
277C22×C47#52912yes—
278C22×C47C2×C4⋊Q811yescharacteristic
279C22×C47#53212yes—
280C22×C47#53312yes—
281C22×C47#53312yes—
282C22×C47#53312yes—
283C22×C47#53312yes—
284C4×C47—24no—
285C4×C47—44no—
286C4×C47—44no—
287C4×C47—42no—
288C4×C47#39118yes—
289Dic47—24no—
290Dic47—24no—
291Dic47—24no—
292Dic47—44no—
293Dic47—44no—
294Dic47—42no—
295C22×C4×Q8—471no—
296C2×C4×C4⋊C4—471no—
297C2×#376—471no—
298#1446—472no—
299#1445—472no—
300#1441—472no—
301#1441—472no—
302C4×#95—471no—
303C4×#95—471no—
304C4×#95—471no—
305C4×#95D4711yescharacteristic
306C2×C47#228011yescharacteristic
307C2×C47C2×#39111yescharacteristic
308C2×C47#229511yescharacteristic
309C2×C47#229511yescharacteristic
310C2×C47#229511yescharacteristic
311C2×C47#229511yescharacteristic
312C2×C47#229711yescharacteristic
313C2×C47#239612yes—
314C2×C47#239612yes—
315C2×C47#239812yes—
316C2×C47#239912yes—
317C23×Q8—471no—
318C2×C4×Q8—478no—
319C2×C4×Q8—944no—
320C2×C4×Q8—944no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—471no—
324C22×C4⋊C4—472no—
325C22×C42—471no—
326C22×C42—471no—
327C22×C42—471no—
328C22×C42—471no—
329C22×C42C2×D4711yescharacteristic
330C22×C42C2×D4711yescharacteristic
331C22×C42C2×D4711yescharacteristic
332C4×C4⋊C4—944no—
333#376—944no—
334C2×#95—472no—
335C2×#95—472no—
336C2×#95—472no—
337C2×#95—472no—
338C2×#95—472no—
339C2×#95—472no—
340C2×#95—472no—
341C2×#95—472no—
342C2×#95—472no—
343C2×#95C2×D4712yes—
344C2×#95C2×D4712yes—
345C47#1385011yescharacteristic, complemented, Sylow
346C22×Q8—474no—
347C22×Q8—942no—
348C22×Q8—942no—
349C22×Q8—944no—
350C22×Q8—944no—
351C23×C4—471no—
352C23×C4—471no—
353C23×C4—471no—
354C23×C4—471no—
355C23×C4—472no—
356C23×C4—472no—
357C23×C4C22×D4712yes—
358C23×C4C22×D4711yescharacteristic
359C23×C4C22×D4712yes—
360C23×C4C22×D4711yescharacteristic
361C23×C4C22×D4711yescharacteristic
362C4×Q8—9432no—
363C2×C4⋊C4—474no—
364C2×C4⋊C4—474no—
365C2×C4⋊C4—474no—
366C2×C4⋊C4—942no—
367C2×C4⋊C4—942no—
368C2×C4⋊C4—942no—
369C2×C4⋊C4—942no—
370C2×C4⋊C4—942no—
371C2×C4⋊C4—942no—
372C2×C4⋊C4—944no—
373C2×C4⋊C4—944no—
374C2×C4⋊C4—944no—
375C2×C42—22no—
376C2×C42—22no—
377C2×C42—22no—
378C2×C42—22no—
379C2×C42—22no—
380C2×C42—22no—
381C2×C42—22no—
382C2×C42—474no—
383C2×C42—474no—
384C2×C42—474no—
385C2×C42—474no—
386C2×C42—474no—
387C2×C42—942no—
388C2×C42—942no—
389C2×C42—942no—
390C2×C42—942no—
391C2×C42—942no—
392C2×C42—942no—
393C2×C42—942no—
394C2×C42Dic9414yescomplemented
395C2×C42C4×D4714yes—
396#95—24no—
397#95—24no—
398#95—944no—
399#95—944no—
400#95—944no—
401#95—944no—
402#95—944no—
403#95—944no—
404#95—944no—
405#95—944no—
406#95—944no—
407C24C23×D4711yescharacteristic
408C2×Q8—948no—
409C2×Q8—948no—
410C2×Q8—9416no—
411C2×Q8—9416no—
412C2×Q8—948no—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—472no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—472no—
438C22×C4—472no—
439C22×C4—474no—
440C22×C4—472no—
441C22×C4—474no—
442C22×C4—474no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—942no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—942no—
459C22×C4—942no—
460C22×C4—942no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4C2×Dic9414yes—
467C22×C4C2×Dic9412yes—
468C22×C4C2×C4×D4712yes—
469C22×C4C2×C4×D4712yes—
470C22×C4C2×C4×D4712yes—
471C22×C4#1062535014yes—
472C22×C4#1062535014yes—
473C22×C4#1062535012yes—
474C22×C4D4×D4712yes—
475C22×C4D4×D4712yes—
476C22×C4#1062535212yes—
477C22×C4Q8×D4712yes—
478C4⋊C4—948no—
479C4⋊C4—948no—
480C4⋊C4—948no—
481C4⋊C4—9416no—
482C42—28no—
483C42—28no—
484C42—44no—
485C42—4716no—
486C42—948no—
487C42—948no—
488C42—1884no—
489C23C22×C4×D4711yescharacteristic
490C23C2×D4×D4711yescharacteristic
491C23C2×D4×D4711yescharacteristic
492C23C2×Q8×D4711yescharacteristic
493C23C22×Dic9411yescharacteristic
494C23#41×D4712yes—
495C23#41×D4712yes—
496C23C2×#1062535211yescharacteristic
497C23C2×#1062535012yes—
498C23C2×#1062535011yescharacteristic
499C23C2×#1062535012yes—
500Q8—9432no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—474no—
525C2×C4—474no—
526C2×C4—474no—
527C2×C4—942no—
528C2×C4—942no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—942no—
533C2×C4—944no—
534C2×C4—944no—
535C2×C4—944no—
536C2×C4—944no—
537C2×C4—944no—
538C2×C4—944no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—944no—
543C2×C4—944no—
544C2×C4—944no—
545C2×C4—944no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4—1882no—
555C2×C4—1882no—
556C2×C4—1882no—
557C2×C4—1882no—
558C2×C4C22⋊C4×D4714yes—
559C2×C4#1309398114yes—
560C2×C4#1309398914yes—
561C2×C4C4×Dic9414yes—
562C2×C4#1309400114yes—
563C2×C4#1309400214yes—
564C2×C4#1309401014yes—
565C2×C4#1309402314yes—
566C22C2×C22⋊C4×D4711yescharacteristic
567C22#117×D4711yescharacteristic
568C22C2×#1309398111yescharacteristic
569C22C2×#1309398911yescharacteristic
570C22C2×C4×Dic9411yescharacteristic
571C22#1568959111yescharacteristic
572C22C4×#1062535011yescharacteristic
573C22C2×#1309400111yescharacteristic
574C22C2×#1309400211yescharacteristic
575C22#1568963212yes—
576C22#1568963212yes—
577C22#1568963212yes—
578C22C2×#1309401011yescharacteristic
579C22#1568965112yes—
580C22#1568965312yes—
581C22#1568965512yes—
582C22#1568965712yes—
583C22C2×#1309402311yescharacteristic
584C22#1568967012yes—
585C22#1568967612yes—
586C22#1568967712yes—
587C22#1568967712yes—
588C22#1568968012yes—
589C4—24no—
590C4—42no—
591C4—44no—
592C4—44no—
593C4—944no—
594C4—944no—
595C4—944no—
596C4—1882no—
597C4—1884no—
598C4—1884no—
599C4#1568902718yes—
600C2#2024576911yescharacteristic
601C2C2×#1568902711yescharacteristic
602C2#2024586011yescharacteristic
603C2#2024586211yescharacteristic
604C2#2024586411yescharacteristic
605C2#2024586511yescharacteristic
606C2#2024587411yescharacteristic
607C2#2024666212yes—
608C2#2024666412yes—
609C2#2024667512yes—
610C2#2024668212yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4×#95D47
hypocenterC47#13850
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
15. C2×C4×Dic94C4semidirect
75. C2×C4×Dic47Q8semidirect
98. C2×C42×C47Q8semidirect
345. C47#13850semidirect
394. C2×C42Dic94semidirect

Maximal subgroups

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

subgroupindex
C22×C4×Dic942
C2×C4×Dic47⋊C42
C2×#156889692
#202416582
#202416542
#202416402
#202416392
C4×C47⋊#952
C4×#95×C472
#1385047