Finite Group Databasebeta

← #26187176

Subgroups — #26187176

Order 12032.

680 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253394C211yesmaximal, characteristic
2#20252336C211yesmaximal, characteristic, complemented
3D4×#10625324C211yesmaximal, characteristic
4#20242278C211yesmaximal, characteristic, complemented
5#20242277C211yesmaximal, characteristic, complemented
6#20242233C211yesmaximal, characteristic, complemented
7#20242228C211yesmaximal, characteristic, complemented
8#20242221C211yesmaximal, characteristic, complemented
9SD16×C47⋊C8C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242157C211yesmaximal, characteristic, complemented
12#20241841C211yesmaximal, characteristic, complemented
13D4⋊C8×D47C211yesmaximal, characteristic
14#20241667C211yesmaximal, characteristic, complemented
15C47×#1582C211yesmaximal, characteristic, complemented
16C22×#10625324—21no—
17#15689677C2211yescharacteristic
18C4×D4×D47C2211yescharacteristic
19#15689455C411yescharacteristic
20#15689452C411yescharacteristic
21#15689412C411yescharacteristic
22#15689411C411yescharacteristic
23#15689327C411yescharacteristic
24#15689326C411yescharacteristic
25#15689275C411yescharacteristic
26#15689272C411yescharacteristic
27#15689251—21no—
28#15689250—21no—
29#15689250C2211yescharacteristic, complemented
30Q8×C47⋊C8C2211yescharacteristic, complemented
31C8×Dic94C2211yescharacteristic, complemented
32C4×#10625325C2211yescharacteristic
33C4×#10625336C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35#15689202C2211yescharacteristic
36#15689200C2211yescharacteristic
37#15689194—21no—
38#15689191—21no—
39D4×C47⋊C8C2211yescharacteristic
40#15689174C2211yescharacteristic
41#15689148—21no—
42#15689145C2211yescharacteristic
43C4⋊C8×D47C2211yescharacteristic
44#15689085—21no—
45#15689080—21no—
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688874C2211yescharacteristic, complemented
49#15688873C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688855C2211yescharacteristic, complemented
52Q8⋊(C47⋊C8)C2211yescharacteristic, complemented
53#15688853C2211yescharacteristic, complemented
54#15688852C2211yescharacteristic
55D4⋊(C47⋊C8)C2211yescharacteristic
56#15688850C2211yescharacteristic
57#15688845C2211yescharacteristic, complemented
58C8×C47⋊C8C2211yescharacteristic, complemented
59C8×C47⋊C8C2211yescharacteristic, complemented
60C47×#446C2211yescharacteristic, complemented
61C4×SD16×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#334C2211yescharacteristic, complemented
64C47×Q8⋊C8C2211yescharacteristic, complemented
65C47×D4⋊C8C2211yescharacteristic
66C47×#322C2211yescharacteristic, complemented
67C2×D4×D47C2×C411yescharacteristic
68C22×C4×D47—21no—
69C2×#10625325C2×C411yescharacteristic
70C2×#10625335C2×C411yescharacteristic
71C2×#10625336C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×#10625324—21no—
74C2×#10625324—21no—
75C2×#10625324—44no—
76C2×#10625324D411yescharacteristic
77C2×#10625324D411yescharacteristic
78C22×C47⋊C8—21no—
79C2×C8×D47—21no—
80C2×C8×D47—21no—
81#13094023C2×C411yescharacteristic
82#13094022C2×C411yescharacteristic
83#13094014—21no—
84#13094004C2×C411yescharacteristic
85#13094002—21no—
86#13094000C2×C411yescharacteristic
87C4×Dic94—21no—
88C4×Dic94C2311yescharacteristic
89C4×D188C2311yescharacteristic
90D4×Dic47C2×C411yescharacteristic
91#13093986C2×C411yescharacteristic
92C4×C22⋊D47—21no—
93(C22⋊D47)⋊C4—21no—
94#13093981—21no—
95C4⋊C4×D47C2×C411yescharacteristic
96C22⋊C4×D47—21no—
97C42×D47C2311yescharacteristic
98#13093956C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101C4⋊(C47⋊C8)—21no—
102C4⋊(C47⋊C8)C2311yescharacteristic
103C4⋊(C47⋊C8)C2311yescharacteristic
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107Dic47⋊C8—21no—
108Dic47⋊C8C2×C411yescharacteristic
109Dic47⋊C8C2×C411yescharacteristic
110#13093949C2×C411yescharacteristic
111#13093948C2×C411yescharacteristic
112#13093947C2×C411yescharacteristic
113#13093946C2×C411yescharacteristic
114#13093945C2×C411yescharacteristic
115#13093944C2×C411yescharacteristic
116C22⋊(C47⋊C8)—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119(C2×D47)⋊C8C2×C411yescharacteristic
120(C2×D47)⋊C8C2×C411yescharacteristic
121#13093934—21no—
122#13093934D411yescharacteristic
123#13093934D411yescharacteristic
124C4×C47⋊C8—21no—
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C4×C47⋊C8C2311yescharacteristic
128C8×Dic47—21no—
129C8×Dic47—21no—
130C2×SD16×C47C2×C411yescharacteristic
131C22×C8×C47—21no—
132C4×Q8×C47C2311yescharacteristic
133C4×D4×C47C2311yescharacteristic
134#106×C47C2×C411yescharacteristic
135C4⋊C8×C47—21no—
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138#103×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47—21no—
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C4×C8×C47C2311yescharacteristic
145C23×D47—21no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×D4×C47C22×C411yescharacteristic
148C22×C4×C47—21no—
149C2×C22⋊D47—21no—
150C22×Dic47—21no—
151D4×D47—22no—
152D4×D47—41no—
153C2×D188C22×C411yescharacteristic
154C2×C4×D47—21no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—42no—
158C2×C4×D47—42no—
159C2×C4×D47C22×C411yescharacteristic
160C2×C4×D47C2×D411yescharacteristic
161C2×C4×D47#4111yescharacteristic
162C2×Dic94—21no—
163C2×Dic94C22×C411yescharacteristic
164SD16×C47—22no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—42no—
169C2×C8×C47C22×C411yescharacteristic
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C4⋊C4×C47—21no—
174C4⋊C4×C47C22×C411yescharacteristic
175C4⋊C4×C47C22×C411yescharacteristic
176C22⋊C4×C47—21no—
177C42×C47—21no—
178C42×C47C2411yescharacteristic
179C22⋊Dic47—21no—
180#10625336—41no—
181#10625335—22no—
182(C2×D47)⋊C4—21no—
183(C2×D47)⋊C4—21no—
184(C2×D47)⋊C4—21no—
185(C2×D47)⋊C4—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47C22×C411yescharacteristic
188C4⋊Dic47C22×C411yescharacteristic
189Dic47⋊C4—21no—
190Dic47⋊C4—21no—
191Dic47⋊C4—21no—
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195C4×Dic47—21no—
196C4×Dic47C22×C411yescharacteristic
197C4×Dic47C2×D411yescharacteristic
198C4×Dic47#4111yescharacteristic
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—42no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207#10625325—41no—
208#10625324—22no—
209#10625324—42no—
210#10625324—42no—
211#10625324—42no—
212#10625324SD1614yescomplemented
213C8×D47—42no—
214C8×D47—42no—
215C23×C47—21no—
216C22×D47—21no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—81no—
220C22×D47C4×D411yescharacteristic
221Q8×C47—21no—
222Q8×C47—21no—
223D4×C47—21no—
224D4×C47#13112yes—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47C23×C411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C22⋊D47—42no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—42no—
238C2×Dic47C4×D411yescharacteristic
239C2×Dic47C4×D411yescharacteristic
240C2×Dic47C4×D411yescharacteristic
241D188—21no—
242D188—21no—
243C4×D47—21no—
244C4×D47—21no—
245C4×D47—41no—
246C4×D47—42no—
247C4×D47—41no—
248C4×D47—41no—
249C4×D47—42no—
250C4×D47C2×SD1612yes—
251C4×D47#13512yes—
252Dic94—21no—
253Dic94—21no—
254Dic94—81no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47—41no—
261C8×C47C2×SD1612yes—
262C47⋊C8—22no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268C47⋊C8C2×SD1612yes—
269#17995—471nomaximal, Sylow
270C22×C47—22no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47C2×C4×D411yescharacteristic
274C2×D47—21no—
275C2×D47—21no—
276C2×D47—41no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—84no—
280C2×D47C4×SD1612yes—
281C4×C47—21no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—41no—
285C4×C47C2×#13111yescharacteristic
286C4×C47#56811yescharacteristic
287C4×C47C22×SD1611yescharacteristic
288C4×C47C2×#13511yescharacteristic
289Dic47—21no—
290Dic47—21no—
291Dic47—41no—
292Dic47—41no—
293Dic47—41no—
294Dic47C4×SD1612yes—
295#3101—471no—
296#2962—471no—
297D4×M16—471no—
298#1590—471no—
299#1590—471no—
300#1583—471no—
301#1583—471no—
302#1582—471no—
303#1582D4711yescharacteristic, complemented
304C8×SD16—471no—
305C8×SD16—471no—
306#1570—471no—
307#1493—471no—
308C2×D4⋊C8—471no—
309C8×M16—471no—
310C2×C47—42no—
311C2×C47#293311yescharacteristic
312C2×C47C2×C4×SD1611yescharacteristic
313C2×C47#295611yescharacteristic
314D47—22no—
315D47—81no—
316C22×M16—941no—
317#533—471no—
318C2×C4×D4—471no—
319#483—471no—
320#483—471no—
321#476—471no—
322#476—471no—
323#461—471no—
324#461—471no—
325#450—471no—
326#450—471no—
327#446—471no—
328#446—941no—
329#446—941no—
330#446C2×D4711yescharacteristic, complemented
331C8×Q8—471no—
332C8×Q8—471no—
333C4×SD16—471no—
334C4×SD16—471no—
335C4×SD16—471no—
336C4×SD16C2×D4711yescharacteristic
337#436—471no—
338#436—471no—
339#435—941no—
340#435—941no—
341C8×D4—471no—
342C8×D4C2×D4711yescharacteristic
343#431—471no—
344#424—941no—
345#423—471no—
346C2×C4⋊C8—471no—
347#407—941no—
348#405—941no—
349C4×M16—471no—
350C2×C4×C8—471no—
351#334—471no—
352#334—471no—
353#334—471no—
354#334C2×D4711yescharacteristic, complemented
355Q8⋊C8—471no—
356Q8⋊C8—471no—
357Q8⋊C8—471no—
358Q8⋊C8C2×D4711yescharacteristic, complemented
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8C2×D4711yescharacteristic
363#322—471no—
364#322C2×D4711yescharacteristic, complemented
365C82—471no—
366C82—471no—
367C47#1799511yescharacteristic, complemented, Sylow
368C22×D4—471no—
369C23×C4—941no—
370C2×SD16—471no—
371C2×SD16—471no—
372C2×SD16—471no—
373C2×SD16C4×D4711yescharacteristic
374C2×M16—471no—
375C2×M16—471no—
376C2×M16—941no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—1884no—
380C22×C8—21no—
381C22×C8—941no—
382C22×C8—941no—
383C22×C8—941no—
384C4⋊Q8—471no—
385C4⋊Q8—471no—
386#125—941no—
387C22⋊Q8—471no—
388C22⋊Q8—471no—
389C22⋊Q8—941no—
390C4×Q8—471no—
391C4×Q8—941no—
392C4×Q8C22×D4711yescharacteristic
393C4×D4—471no—
394C4×D4—471no—
395C4×D4—471no—
396C4×D4—941no—
397C4×D4—941no—
398C4×D4C22×D4711yescharacteristic
399#117—941no—
400C2×C4⋊C4—471no—
401C2×C22⋊C4—941no—
402C2×C42—471no—
403#106—471no—
404#106—471no—
405#106—471no—
406#106C4×D4711yescharacteristic
407C4⋊C8—21no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—471no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8—941no—
415C4⋊C8—941no—
416C4⋊C8—941no—
417C4⋊C8C22×D4711yescharacteristic
418C4⋊C8C22×D4711yescharacteristic
419#103—471no—
420#103—471no—
421#103—471no—
422#103C4×D4711yescharacteristic
423#102—471no—
424#102—471no—
425#102—471no—
426#102C4×D4711yescharacteristic
427C22⋊C8—21no—
428C22⋊C8—471no—
429C22⋊C8—471no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433#97—21no—
434#97—471no—
435#97—471no—
436#97—941no—
437C4×C8—471no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—941no—
441C4×C8—941no—
442C4×C8—941no—
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445C4×C8C22×D4711yescharacteristic
446C24—941no—
447C2×Q8—471no—
448C2×Q8—941no—
449C2×Q8C2×C4×D4711yescharacteristic
450C2×D4—471no—
451C2×D4—941no—
452C2×D4—942no—
453C2×D4—1881no—
454C2×D4C2×C4×D4711yescharacteristic
455C22×C4—21no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—941no—
463C22×C4—1882no—
464C22×C4—1882no—
465SD16—22no—
466SD16—942no—
467SD16—1881no—
468SD16—1881no—
469M16—474no—
470M16—942no—
471M16—1882no—
472M16—1882no—
473M16—1882no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—42no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—471no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—1882no—
486C2×C8—1882no—
487C2×C8—1882no—
488C2×C8C2×C4×D4711yescharacteristic
489C2×C8C2×C4×D4711yescharacteristic
490C2×C8D4×D4711yescharacteristic
491C2×C8D4×D4711yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—471no—
494C4⋊C4—471no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4C2×C4×D4711yescharacteristic
503C4⋊C4C2×C4×D4711yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C22⋊C4—941no—
510C42—21no—
511C42—471no—
512C42—471no—
513C42—471no—
514C42—941no—
515C42C23×D4711yescharacteristic
516C23—21no—
517C23—471no—
518C23—941no—
519C23—3761no—
520C23—1882no—
521C23—1882no—
522Q8—21no—
523Q8—21no—
524Q8—941no—
525Q8—941no—
526Q8—3761no—
527D4—21no—
528D4—941no—
529D4—941no—
530D4—1882no—
531D4#1309403212yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—471no—
538C2×C4—472no—
539C2×C4—472no—
540C2×C4—471no—
541C2×C4—471no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—941no—
547C2×C4—1881no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4C22×C4×D4711yescharacteristic
554C2×C4C2×D4×D4711yescharacteristic
555C2×C4#41×D4711yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—472no—
563C8—942no—
564C8—941no—
565C8—941no—
566C8—941no—
567C8—1881no—
568C8—1881no—
569C8SD16×D4712yes—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—472no—
574C22—941no—
575C22—941no—
576C22—3764no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22C4×D4×D4711yescharacteristic
581C4—21no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—472no—
586C4—941no—
587C4—941no—
588C4—1881no—
589C4—1881no—
590C4—1881no—
591C4C2×#1309403211yescharacteristic
592C4#1568988811yescharacteristic
593C4C2×SD16×D4711yescharacteristic
594C4#135×D4711yescharacteristic
595C2—42no—
596C2—942no—
597C2—3761no—
598C2#2025211411yescharacteristic
599C2C4×SD16×D4711yescharacteristic
600C2#2025229611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1582C2
socleC22×C47C2×C4×D4
prime radicalC2×D4×D47C2×C4
cosocleC42×C47C24
hypercenter#1582D47
hypocenterC47#17995
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1582

Complements

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

NH ≅ G/Ntype
2. #20252336C2semidirect
4. #20242278C2semidirect
5. #20242277C2semidirect
6. #20242233C2semidirect
7. #20242228C2semidirect
8. #20242221C2semidirect
9. SD16×C47⋊C8C2semidirect
10. C8×#10625335C2semidirect
11. #20242157C2semidirect
12. #20241841C2semidirect
14. #20241667C2semidirect
15. C47×#1582C2semidirect
29. #15689250C22semidirect
30. Q8×C47⋊C8C22semidirect
31. C8×Dic94C22semidirect
48. #15688874C22semidirect
49. #15688873C22semidirect
50. #15688873C22semidirect
51. #15688855C22semidirect
52. Q8⋊(C47⋊C8)C22semidirect
53. #15688853C22semidirect
57. #15688845C22semidirect
58. C8×C47⋊C8C22semidirect
59. C8×C47⋊C8C22semidirect
60. C47×#446C22semidirect
63. C47×#334C22semidirect
64. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
212. #10625324SD16semidirect
303. #1582D47semidirect
330. #446C2×D47semidirect
354. #334C2×D47semidirect
358. Q8⋊C8C2×D47semidirect
364. #322C2×D47semidirect
367. C47#17995semidirect

Maximal subgroups

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

subgroupindex
#202533942
#202523362
D4×#106253242
#202422782
#202422772
#202422332
#202422282
#202422212
SD16×C47⋊C82
C8×#106253352
#202421572
#202418412
D4⋊C8×D472
#202416672
C47×#15822
#1799547