Finite Group Databasebeta

← #26186161

Subgroups — #26186161

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253394C211yesmaximal, characteristic
2#20252319C211yesmaximal, characteristic, complemented
3C8×D4×D47C211yesmaximal, characteristic
4#20242226C211yesmaximal, characteristic, complemented
5#20242224C211yesmaximal, characteristic, complemented
6#20242222C211yesmaximal, characteristic, complemented
7#20242191C211yesmaximal, characteristic, complemented
8SD16×C47⋊C8C211yesmaximal, characteristic, complemented
9#20242187C211yesmaximal, characteristic, complemented
10#20242185C211yesmaximal, characteristic, complemented
11#20242157C211yesmaximal, characteristic, complemented
12#20241811C211yesmaximal, characteristic
13#20241789C211yesmaximal, characteristic, complemented
14#20241673C211yesmaximal, characteristic, complemented
15C47×#1582C211yesmaximal, characteristic, complemented
16C22×C8×D47—21no—
17#15689677C2211yescharacteristic
18C4×D4×D47C2211yescharacteristic
19#15689455C411yescharacteristic
20#15689452C411yescharacteristic
21#15689412C411yescharacteristic
22#15689411C411yescharacteristic
23#15689327C411yescharacteristic
24#15689326C411yescharacteristic
25#15689275C411yescharacteristic
26#15689272C411yescharacteristic
27#15689253C2211yescharacteristic, complemented
28#15689251—21no—
29Q8×C47⋊C8C2211yescharacteristic, complemented
30#15689247—21no—
31#15689247C2211yescharacteristic, complemented
32C4×#10625325C2211yescharacteristic
33C4×#10625336C2211yescharacteristic
34C4×#10625335C2211yescharacteristic
35C8×D188C2211yescharacteristic
36D4×C47⋊C8C2211yescharacteristic
37#15689188C2211yescharacteristic
38C8×C22⋊D47—21no—
39(C22⋊D47)⋊C8—21no—
40#15689174C2211yescharacteristic
41#15689174C2211yescharacteristic
42#15689148—21no—
43#15689145C2211yescharacteristic
44C4⋊C8×D47C2211yescharacteristic
45C22⋊C8×D47—21no—
46#15689080—21no—
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#15688844C2211yescharacteristic, 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—
73C22×C47⋊C8—21no—
74C2×C8×D47—21no—
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—44no—
78C2×C8×D47D411yescharacteristic
79C2×C8×D47D411yescharacteristic
80#13094023C2×C411yescharacteristic
81#13094022C2×C411yescharacteristic
82#13094014—21no—
83#13094004C2×C411yescharacteristic
84#13094002—21no—
85#13094000C2×C411yescharacteristic
86C4×Dic94—21no—
87C4×Dic94C2311yescharacteristic
88C4×D188C2311yescharacteristic
89D4×Dic47C2×C411yescharacteristic
90#13093986C2×C411yescharacteristic
91C4×C22⋊D47—21no—
92(C22⋊D47)⋊C4—21no—
93#13093981—21no—
94C4⋊C4×D47C2×C411yescharacteristic
95C22⋊C4×D47—21no—
96C42×D47C2311yescharacteristic
97#13093956C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100C4⋊(C47⋊C8)—21no—
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
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)⋊C8—21no—
120(C2×D47)⋊C8C2×C411yescharacteristic
121(C2×D47)⋊C8C2×C411yescharacteristic
122#13093934—21no—
123C4×C47⋊C8—21no—
124C4×C47⋊C8C2311yescharacteristic
125C4×C47⋊C8C2311yescharacteristic
126C4×C47⋊C8C2311yescharacteristic
127C8×Dic47—21no—
128C8×Dic47D411yescharacteristic
129C8×Dic47D411yescharacteristic
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—22no—
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—22no—
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—22no—
208#10625324—42no—
209C8×D47—22no—
210C8×D47—42no—
211C8×D47—42no—
212C8×D47—42no—
213C8×D47SD1614yescomplemented
214C23×C47—21no—
215C22×D47—24no—
216C22×D47—21no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47C4×D411yescharacteristic
220Q8×C47—21no—
221Q8×C47—21no—
222D4×C47—21no—
223D4×C47#13112yes—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47C23×C411yescharacteristic
230C2×C4×C47C22×D411yescharacteristic
231C2×C4×C47C2×#4111yescharacteristic
232C22⋊D47—24no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—42no—
237C2×Dic47C4×D411yescharacteristic
238C2×Dic47C4×D411yescharacteristic
239C2×Dic47C4×D411yescharacteristic
240D188—21no—
241D188#13112yes—
242C4×D47—21no—
243C4×D47—21no—
244C4×D47—41no—
245C4×D47—42no—
246C4×D47—41no—
247C4×D47—41no—
248C4×D47—42no—
249C4×D47C2×SD1612yes—
250C4×D47#13512yes—
251Dic94—21no—
252Dic94—21no—
253Dic94—42no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—41no—
258C8×C47—41no—
259C8×C47—41no—
260C8×C47C2×SD1612yes—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8C2×SD1612yes—
268#17902—471nomaximal, Sylow
269C22×C47—22no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47C2×C4×D411yescharacteristic
273C2×D47—21no—
274C2×D47—21no—
275C2×D47—22no—
276C2×D47—48no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47C4×SD1612yes—
280C4×C47—21no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47C2×#13111yescharacteristic
285C4×C47C2×#13111yescharacteristic
286C4×C47C22×SD1611yescharacteristic
287C4×C47C2×#13511yescharacteristic
288Dic47—21no—
289Dic47—21no—
290Dic47—41no—
291Dic47—41no—
292Dic47—41no—
293Dic47C4×SD1612yes—
294#3101—471no—
295#2960—471no—
296C2×C8×D4—471no—
297#1582—471no—
298#1582—471no—
299#1582—471no—
300#1582D4711yescharacteristic, complemented
301C8×SD16—471no—
302C8×SD16—471no—
303C8×SD16—471no—
304C8×SD16—471no—
305#1570—471no—
306#1486—471no—
307#1481—471no—
308#1450—471no—
309C2×C47—42no—
310C2×C47#292911yescharacteristic
311C2×C47C2×C4×SD1611yescharacteristic
312C2×C47#295511yescharacteristic
313D47—22no—
314D47—42no—
315C23×C8—941no—
316#533—471no—
317C2×C4×D4—471no—
318#483—471no—
319#483—471no—
320#476—471no—
321#476—471no—
322#461—471no—
323#461—471no—
324#450—471no—
325#450—471no—
326#446—471no—
327#446—941no—
328#446C2×D4711yescharacteristic, complemented
329C8×Q8—471no—
330C8×Q8—471no—
331C8×Q8—941no—
332C4×SD16—471no—
333C4×SD16—471no—
334C4×SD16—471no—
335C4×SD16C2×D4711yescharacteristic
336C8×D4—471no—
337C8×D4—471no—
338C8×D4—471no—
339C8×D4—941no—
340C8×D4—941no—
341C8×D4C2×D4711yescharacteristic
342#431—471no—
343#431—471no—
344#424—941no—
345#423—471no—
346C2×C4⋊C8—471no—
347C2×C22⋊C8—941no—
348#405—941no—
349C2×C4×C8—471no—
350#334—471no—
351#334—471no—
352#334—471no—
353#334C2×D4711yescharacteristic, complemented
354Q8⋊C8—471no—
355Q8⋊C8—471no—
356Q8⋊C8—471no—
357Q8⋊C8C2×D4711yescharacteristic, complemented
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8C2×D4711yescharacteristic
362#322—471no—
363#322C2×D4711yescharacteristic, complemented
364C82—471no—
365C82—471no—
366C47#1790211yescharacteristic, complemented, Sylow
367C22×D4—471no—
368C23×C4—941no—
369C2×SD16—471no—
370C2×SD16—471no—
371C2×SD16—471no—
372C2×SD16C4×D4711yescharacteristic
373C2×M16—941no—
374C22×C8—21no—
375C22×C8—471no—
376C22×C8—471no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—1884no—
382C4⋊Q8—471no—
383C4⋊Q8—471no—
384#125—941no—
385C22⋊Q8—471no—
386C22⋊Q8—471no—
387C22⋊Q8—941no—
388C4×Q8—471no—
389C4×Q8—941no—
390C4×Q8C22×D4711yescharacteristic
391C4×D4—471no—
392C4×D4—471no—
393C4×D4—471no—
394C4×D4—941no—
395C4×D4—941no—
396C4×D4C22×D4711yescharacteristic
397#117—941no—
398C2×C4⋊C4—471no—
399C2×C22⋊C4—941no—
400C2×C42—471no—
401#106—471no—
402#106—471no—
403#106—471no—
404#106C4×D4711yescharacteristic
405C4⋊C8—21no—
406C4⋊C8—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8—941no—
415C4⋊C8—941no—
416C4⋊C8C22×D4711yescharacteristic
417C4⋊C8C22×D4711yescharacteristic
418#103—471no—
419#103—471no—
420#103—471no—
421#103C4×D4711yescharacteristic
422#102—471no—
423#102—471no—
424#102—471no—
425#102C4×D4711yescharacteristic
426C22⋊C8—21no—
427C22⋊C8—471no—
428C22⋊C8—471no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433#97—21no—
434#97—941no—
435C4×C8—471no—
436C4×C8—471no—
437C4×C8—471no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—941no—
441C4×C8—941no—
442C4×C8C22×D4711yescharacteristic
443C4×C8C22×D4711yescharacteristic
444C4×C8C22×D4711yescharacteristic
445C24—941no—
446C2×Q8—471no—
447C2×Q8—941no—
448C2×Q8C2×C4×D4711yescharacteristic
449C2×D4—471no—
450C2×D4—941no—
451C2×D4—942no—
452C2×D4—942no—
453C2×D4C2×C4×D4711yescharacteristic
454C22×C4—21no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—941no—
459C22×C4—941no—
460C22×C4—941no—
461C22×C4—941no—
462C22×C4—1882no—
463C22×C4—1882no—
464SD16—22no—
465SD16—942no—
466SD16—942no—
467SD16—942no—
468M16—1882no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—42no—
473C2×C8—471no—
474C2×C8—474no—
475C2×C8—471no—
476C2×C8—471no—
477C2×C8—471no—
478C2×C8—942no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—1882no—
483C2×C8—1882no—
484C2×C8—1882no—
485C2×C8—1882no—
486C2×C8C2×C4×D4711yescharacteristic
487C2×C8C2×C4×D4711yescharacteristic
488C2×C8D4×D4711yescharacteristic
489C2×C8D4×D4711yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—471no—
492C4⋊C4—471no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4C2×C4×D4711yescharacteristic
501C4⋊C4C2×C4×D4711yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C42—21no—
509C42—471no—
510C42—471no—
511C42—471no—
512C42—941no—
513C42C23×D4711yescharacteristic
514C23—21no—
515C23—471no—
516C23—944no—
517C23—941no—
518C23—1882no—
519C23—1882no—
520Q8—21no—
521Q8—21no—
522Q8—941no—
523Q8—941no—
524Q8—1882no—
525D4—21no—
526D4—472no—
527D4—944no—
528D4—941no—
529D4#1309403212yes—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—471no—
536C2×C4—472no—
537C2×C4—472no—
538C2×C4—471no—
539C2×C4—471no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—941no—
544C2×C4—941no—
545C2×C4—1881no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4C22×C4×D4711yescharacteristic
552C2×C4C2×D4×D4711yescharacteristic
553C2×C4#41×D4711yescharacteristic
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—472no—
561C8—941no—
562C8—941no—
563C8—941no—
564C8—1881no—
565C8—1881no—
566C8—1881no—
567C8SD16×D4712yes—
568C22—22no—
569C22—41no—
570C22—41no—
571C22—472no—
572C22—941no—
573C22—941no—
574C22—942no—
575C22—1888no—
576C22—1881no—
577C22—1881no—
578C22C4×D4×D4711yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—472no—
584C4—941no—
585C4—941no—
586C4—1881no—
587C4—1881no—
588C4—1881no—
589C4#131×D4711yescharacteristic
590C4C2×#1309403211yescharacteristic
591C4C2×SD16×D4711yescharacteristic
592C4#135×D4711yescharacteristic
593C2—42no—
594C2—942no—
595C2—1882no—
596C2#2025207911yescharacteristic
597C2C4×SD16×D4711yescharacteristic
598C2#2025228811yescharacteristic
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#17902
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. #20252319C2semidirect
4. #20242226C2semidirect
5. #20242224C2semidirect
6. #20242222C2semidirect
7. #20242191C2semidirect
8. SD16×C47⋊C8C2semidirect
9. #20242187C2semidirect
10. #20242185C2semidirect
11. #20242157C2semidirect
13. #20241789C2semidirect
14. #20241673C2semidirect
15. C47×#1582C2semidirect
27. #15689253C22semidirect
29. Q8×C47⋊C8C22semidirect
31. #15689247C22semidirect
48. #15688874C22semidirect
49. #15688873C22semidirect
50. #15688873C22semidirect
51. #15688855C22semidirect
52. Q8⋊(C47⋊C8)C22semidirect
53. #15688853C22semidirect
57. #15688844C22semidirect
58. C8×C47⋊C8C22semidirect
59. C8×C47⋊C8C22semidirect
60. C47×#446C22semidirect
63. C47×#334C22semidirect
64. C47×Q8⋊C8C22semidirect
66. C47×#322C22semidirect
213. C8×D47SD16semidirect
300. #1582D47semidirect
328. #446C2×D47semidirect
353. #334C2×D47semidirect
357. Q8⋊C8C2×D47semidirect
363. #322C2×D47semidirect
366. C47#17902semidirect

Maximal subgroups

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

subgroupindex
#202533942
#202523192
C8×D4×D472
#202422262
#202422242
#202422222
#202421912
SD16×C47⋊C82
#202421872
#202421852
#202421572
#202418112
#202417892
#202416732
C47×#15822
#1790247