Finite Group Databasebeta

← #26183264

Subgroups — #26183264

Order 12032.

1022 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257003C211yesmaximal, characteristic
2C4×#13094031C211yesmaximal, characteristic, complemented
3#20241846C212yesmaximal, complemented
4#20241842C211yesmaximal, characteristic, complemented
5#20241834C212yesmaximal, complemented
6#20241825C211yesmaximal, characteristic, complemented
7#20241808C211yesmaximal, characteristic, complemented
8#20241799C212yesmaximal, complemented
9#20241768C211yesmaximal, characteristic, complemented
10C2×#15688853C212yesmaximal, complemented
11C47×#2990C211yesmaximal, characteristic, complemented
12C2×#13094031—21no—
13#15689851C411yescharacteristic
14#15689846C411yescharacteristic
15#15689841—21no—
16#15689813C412yes—
17#15689806—22no—
18D4×Dic94C411yescharacteristic
19#15689782C412yes—
20#15689777C411yescharacteristic
21#15689772—21no—
22#15689680C2211yescharacteristic
23#15689677—21no—
24#15689657C2212yes—
25#15689653—22no—
26C4×#10625350C2211yescharacteristic
27C4×#10625352—21no—
28C2×C4×Dic94C2212yes—
29#15689079—22no—
30#15689079—21no—
31C4×#10625329C2212yes—
32C4×#10625329C2211yescharacteristic
33C2×C4×C47⋊C8C2212yes—
34C2×C4×C47⋊C8C2211yescharacteristic
35#15688853C2211yescharacteristic
36#15688853C2212yes—
37#15688853C2212yes—
38#15688853C2212yes—
39#15688853C2211yescharacteristic
40#15688853C2212yes—
41#15688853C2212yes—
42#15688850C2211yescharacteristic
43#15688850C2211yescharacteristic
44#15688850C2212yes—
45C4×#41×C47C2211yescharacteristic
46C47×#446—21no—
47C47×#435—22no—
48C8×D4×C47—21no—
49C47×#432C2212yes—
50C47×#431C2211yescharacteristic
51C47×#423C2211yescharacteristic
52C2×C4⋊C8×C47C2212yes—
53C2×#10625350C2×C411yescharacteristic
54C2×#10625352—21no—
55C22×Dic94C2×C412yes—
56#13094031—28no—
57C2×#10625329—22no—
58C2×#10625329—21no—
59C22×C47⋊C8—22no—
60C22×C47⋊C8—21no—
61#13094024C2×C411yescharacteristic
62#13094024C2×C411yescharacteristic
63#13094023—21no—
64#13094022—21no—
65#13094019—22no—
66#13094018—22no—
67#13094017—22no—
68#13094016—21no—
69#13094016C2×C412yes—
70#13094014—22no—
71#13094014—22no—
72#13094012C2×C412yes—
73#13094010—22no—
74#13094008—22no—
75#13094007—22no—
76#13094005—22no—
77#13094004—21no—
78#13094003—21no—
79#13094003C2×C412yes—
80#13094003C2×C412yes—
81#13094002—22no—
82#13094001—22no—
83#13094000—21no—
84#13093998C2×C412yes—
85#13093996—22no—
86C4×Dic94—22no—
87C4×Dic94—22no—
88C4×Dic94—21no—
89C4×Dic94C2×C412yes—
90C4×Dic94C2×C411yescharacteristic
91C4×Dic94C2×C412yes—
92C4×Dic94C2311yescharacteristic
93C4×Dic94C2312yes—
94#13093989—21no—
95C4×D188C2×C411yescharacteristic
96C4×D188C2311yescharacteristic
97D4×Dic47—21no—
98C4×C22⋊D47—21no—
99C4×C22⋊D47—22no—
100C4×C22⋊D47—21no—
101(C22⋊D47)⋊C4—22no—
102#13093983—21no—
103#13093983C2×C411yescharacteristic
104#13093982—21no—
105#13093981—21no—
106#13093981—22no—
107#13093980—22no—
108C2×C4⋊Dic47C2×C412yes—
109C2×Dic47⋊C4—22no—
110C2×C4×Dic47—22no—
111C42×D47—21no—
112#13093935—21no—
113#13093935—22no—
114C4×C47⋊C8—21no—
115C4×C47⋊C8—22no—
116C4×C47⋊C8C2311yescharacteristic
117C4×C47⋊C8C2312yes—
118C4×C47⋊C8C2311yescharacteristic
119C2×#41×C47D411yescharacteristic
120C2×M16×C47—21no—
121C22×C8×C47—22no—
122C4×Q8×C47C2×C411yescharacteristic
123C4×Q8×C47D411yescharacteristic
124C4×D4×C47C2×C411yescharacteristic
125C4×D4×C47C2×C412yes—
126C4×D4×C47D411yescharacteristic
127C4×D4×C47D412yes—
128#117×C47D412yes—
129#117×C47D411yescharacteristic
130C2×C42×C47C2312yes—
131C2×C42×C47C2311yescharacteristic
132C4⋊C8×C47—22no—
133C4⋊C8×C47—21no—
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2312yes—
136C4⋊C8×C47C2311yescharacteristic
137C22⋊C8×C47—21no—
138C22⋊C8×C47—22no—
139#97×C47—22no—
140C4×C8×C47—21no—
141#41×C47—24no—
142C2×Q8×C47C22⋊C411yescharacteristic
143C2×D4×C47C22⋊C412yes—
144C2×D4×C47C22⋊C411yescharacteristic
145C22×C4×C47C22×C412yes—
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C2×D412yes—
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D412yes—
150C22×C4×C47C2×D411yescharacteristic
151C2×C22⋊D47—22no—
152C2×C22⋊D47—21no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155#10625352—44no—
156#10625350—22no—
157#10625350—41no—
158C2×D188C22×C411yescharacteristic
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×Dic94—24no—
163C2×Dic94—21no—
164C2×Dic94—22no—
165C2×Dic94—42no—
166C2×Dic94C22×C412yes—
167C2×Dic94C22×C411yescharacteristic
168M16×C47—81no—
169C2×C8×C47—21no—
170C2×C8×C47—22no—
171C2×C8×C47—21no—
172C2×C8×C47—82no—
173C4⋊C4×C47C22⋊C412yes—
174C4⋊C4×C47C22⋊C411yescharacteristic
175C4⋊C4×C47C22⋊C411yescharacteristic
176C4⋊C4×C47C22⋊C412yes—
177C22⋊C4×C47C22⋊C412yes—
178C22⋊C4×C47C22⋊C412yes—
179C22⋊C4×C47C22⋊C412yes—
180C42×C47C22×C411yescharacteristic
181C42×C47C22×C412yes—
182C42×C47C2×D411yescharacteristic
183C42×C47C2×D412yes—
184C42×C47C2×D411yescharacteristic
185C42×C47C2×D412yes—
186C42×C47C2411yescharacteristic
187C22⋊Dic47—22no—
188C22⋊Dic47—22no—
189C22⋊Dic47—21no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—22no—
192(C2×D47)⋊C4—22no—
193(C2×D47)⋊C4—22no—
194(C2×D47)⋊C4—21no—
195C4⋊Dic47—22no—
196C4⋊Dic47—21no—
197C4⋊Dic47—21no—
198C4⋊Dic47—21no—
199C4⋊Dic47C22×C411yescharacteristic
200C4⋊Dic47C22×C412yes—
201C4⋊Dic47C22×C411yescharacteristic
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206Dic47⋊C4—21no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—21no—
210Dic47⋊C4—22no—
211C4×Dic47—21no—
212C4×Dic47—21no—
213C4×Dic47—22no—
214C4×Dic47—22no—
215C4×Dic47—21no—
216C4×Dic47—22no—
217#10625329—28no—
218#10625329—24no—
219C2×C47⋊C8—28no—
220C2×C47⋊C8—24no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—22no—
224C23×C47C2×C22⋊C411yescharacteristic
225C23×C47C2×C22⋊C412yes—
226C22×D47—21no—
227Q8×C47—22no—
228D4×C47—24no—
229D4×C47#10414yes—
230C2×C4×C47—24no—
231C2×C4×C47—22no—
232C2×C4×C47—21no—
233C2×C4×C47—22no—
234C2×C4×C47—21no—
235C2×C4×C47—22no—
236C2×C4×C47—21no—
237C2×C4×C47—22no—
238C2×C4×C47—21no—
239C2×C4×C47—22no—
240C2×C4×C47C2×C22⋊C412yes—
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47C2×C22⋊C412yes—
243C2×C4×C47C2×C22⋊C411yescharacteristic
244C2×C4×C47C2×C22⋊C412yes—
245C2×C4×C47C2×C22⋊C411yescharacteristic
246C2×C4×C47C23×C411yescharacteristic
247C2×C4×C47C22×D411yescharacteristic
248C2×C4×C47C22×D411yescharacteristic
249C22⋊D47—42no—
250C22⋊D47—44no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—22no—
255C2×Dic47—22no—
256C2×Dic47—44no—
257C2×Dic47—44no—
258D188—21no—
259D188—21no—
260C4×D47—42no—
261C4×D47—41no—
262C4×D47—41no—
263C4×D47—42no—
264Dic94—21no—
265Dic94—22no—
266Dic94—22no—
267Dic94—44no—
268Dic94—42no—
269Dic94#13112yescomplemented
270C8×C47—41no—
271C8×C47—42no—
272C8×C47—41no—
273C47⋊C8—22no—
274C47⋊C8—24no—
275C47⋊C8—22no—
276#17519—471nomaximal, Sylow
277C22×C47—22no—
278C22×C47—22no—
279C22×C47—21no—
280C22×C47—21no—
281C22×C47—21no—
282C22×C47C2×#10414yes—
283C22×C47C22×C22⋊C411yescharacteristic
284C2×D47—41no—
285C2×D47—41no—
286C2×D47—41no—
287C4×C47—22no—
288C4×C47—21no—
289C4×C47—22no—
290C4×C47—21no—
291C4×C47—21no—
292C4×C47—22no—
293C4×C47C2×#10412yes—
294C4×C47C2×#13111yescharacteristic
295C4×C47#56811yescharacteristic
296C4×C47#57711yescharacteristic
297C4×C47#57811yescharacteristic
298Dic47—22no—
299Dic47—42no—
300Dic47—41no—
301Dic47—42no—
302Dic47—41no—
303#3482—471no—
304#2990D4711yescharacteristic, complemented
305C4×#131—471no—
306#1494—472no—
307#1493—471no—
308#1491—472no—
309#1489—471no—
310#1485—471no—
311#1483—472no—
312#1476—471no—
313C2×Q8⋊C8—472no—
314C2×C47—24no—
315C2×C47—41no—
316C2×C47#288011yescharacteristic
317C2×C47#289811yescharacteristic
318C2×C47C22×#10411yescharacteristic
319D47—81no—
320C2×#131—941no—
321#557—471no—
322#556—471no—
323#556—941no—
324#552—472no—
325#552—942no—
326D4×Q8—471no—
327#548—472no—
328#547—471no—
329#547—941no—
330#533—471no—
331#533—941no—
332#529—472no—
333#529—942no—
334C4×#41—471no—
335C4×#41—941no—
336C4×#41C2×D4711yescharacteristic
337C2×C4×Q8—472no—
338#446—21no—
339#435—22no—
340C8×D4—21no—
341#432C2×D4712yes—
342#431C2×D4711yescharacteristic
343#423C2×D4711yescharacteristic
344C2×C4⋊C8C2×D4712yes—
345#405—942no—
346#405—941no—
347C4×M16—472no—
348C4×M16—471no—
349C2×C4×C8—472no—
350C2×C4×C8—471no—
351Q8⋊C8—471no—
352Q8⋊C8—472no—
353Q8⋊C8—472no—
354Q8⋊C8—472no—
355Q8⋊C8—471no—
356Q8⋊C8—472no—
357Q8⋊C8—472no—
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—472no—
361C47#1751911yescharacteristic, complemented, Sylow
362C2×#41—471no—
363C2×#41—941no—
364C2×#41D18811yescharacteristic
365C22×Q8—472no—
366#131—948no—
367C2×M16—21no—
368C2×M16—942no—
369C2×M16—941no—
370C22×C8—22no—
371C22×C8—942no—
372C22×C8—941no—
373C4⋊Q8—471no—
374C4⋊Q8—471no—
375C4⋊Q8—941no—
376C4⋊Q8—941no—
377#126—942no—
378#126—942no—
379#126—942no—
380#125—472no—
381#125—942no—
382#125—942no—
383#125—941no—
384#124—472no—
385#124—942no—
386#123—942no—
387#123—942no—
388#123—942no—
389C22⋊Q8—472no—
390C22⋊Q8—472no—
391C22⋊Q8—941no—
392C22⋊Q8—941no—
393C22⋊Q8—941no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396#121—472no—
397#121—942no—
398C4×Q8—472no—
399C4×Q8—472no—
400C4×Q8—471no—
401C4×Q8—471no—
402C4×Q8—472no—
403C4×Q8—941no—
404C4×Q8—942no—
405C4×Q8—942no—
406C4×Q8—941no—
407C4×Q8C4×D4711yescharacteristic
408C4×Q8C22⋊D4711yescharacteristic
409C4×D4—471no—
410C4×D4—471no—
411C4×D4—941no—
412C4×D4—941no—
413C4×D4—941no—
414C4×D4—942no—
415C4×D4—942no—
416C4×D4C4×D4711yescharacteristic
417C4×D4C4×D4712yes—
418C4×D4C22⋊D4711yescharacteristic
419C4×D4C22⋊D4712yes—
420#117—471no—
421#117—941no—
422#117—941no—
423#117—942no—
424#117—941no—
425#117—942no—
426#117D18812yes—
427#117D18811yescharacteristic
428C2×C4⋊C4—472no—
429C2×C4⋊C4—942no—
430C2×C42—942no—
431C2×C42—941no—
432C2×C42C22×D4712yes—
433C2×C42C22×D4711yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—21no—
436C4⋊C8C22×D4711yescharacteristic
437C4⋊C8C22×D4712yes—
438C4⋊C8C22×D4711yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—22no—
441#97—22no—
442#97—941no—
443#97—942no—
444C4×C8—21no—
445C4×C8—471no—
446C4×C8—471no—
447C4×C8—472no—
448C4×C8—941no—
449C4×C8—942no—
450#41—24no—
451#41—942no—
452#41—1881no—
453#41—1884no—
454C2×Q8—471no—
455C2×Q8—472no—
456C2×Q8—944no—
457C2×Q8—942no—
458C2×Q8—941no—
459C2×Q8—1882no—
460C2×Q8(C2×D47)⋊C411yescharacteristic
461C2×D4—471no—
462C2×D4—942no—
463C2×D4—941no—
464C2×D4(C2×D47)⋊C412yes—
465C2×D4(C2×D47)⋊C411yescharacteristic
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—941no—
469C22×C4—941no—
470C22×C4—941no—
471C22×C4C2×C4×D4712yes—
472C22×C4C2×C4×D4711yescharacteristic
473C22×C4C2×D18812yes—
474C22×C4C2×D18811yescharacteristic
475C22×C4C2×C22⋊D4712yes—
476C22×C4C2×C22⋊D4711yescharacteristic
477M16—81no—
478M16—948no—
479M16—944no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—22no—
483C2×C8—82no—
484C2×C8—948no—
485C2×C8—944no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—942no—
489C4⋊C4—471no—
490C4⋊C4—472no—
491C4⋊C4—471no—
492C4⋊C4—942no—
493C4⋊C4—942no—
494C4⋊C4—941no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—942no—
498C4⋊C4—942no—
499C4⋊C4—942no—
500C4⋊C4—941no—
501C4⋊C4—941no—
502C4⋊C4—941no—
503C4⋊C4—941no—
504C4⋊C4—942no—
505C4⋊C4(C2×D47)⋊C411yescharacteristic
506C4⋊C4(C2×D47)⋊C412yes—
507C4⋊C4(C2×D47)⋊C411yescharacteristic
508C4⋊C4(C2×D47)⋊C412yes—
509C22⋊C4—941no—
510C22⋊C4—942no—
511C22⋊C4—942no—
512C22⋊C4—941no—
513C22⋊C4—942no—
514C22⋊C4—942no—
515C22⋊C4—942no—
516C22⋊C4—941no—
517C22⋊C4(C2×D47)⋊C412yes—
518C22⋊C4(C2×D47)⋊C412yes—
519C22⋊C4(C2×D47)⋊C412yes—
520C42—941no—
521C42—942no—
522C42—941no—
523C42—942no—
524C42—941no—
525C42—942no—
526C42C2×C4×D4711yescharacteristic
527C42C2×C4×D4712yes—
528C42C2×D18811yescharacteristic
529C42C2×D18812yes—
530C42C2×C22⋊D4711yescharacteristic
531C42C2×C22⋊D4712yes—
532C42C23×D4711yescharacteristic
533C23—941no—
534C23C2×(C2×D47)⋊C411yescharacteristic
535C23C2×(C2×D47)⋊C412yes—
536Q8—22no—
537Q8—472no—
538Q8—941no—
539Q8—942no—
540Q8—942no—
541Q8—1884no—
542Q8—1882no—
543D4—24no—
544D4—941no—
545D4—941no—
546D4—1882no—
547D4—1884no—
548D4#1309395014yes—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—21no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—941no—
562C2×C4—942no—
563C2×C4—942no—
564C2×C4—1882no—
565C2×C4—1884no—
566C2×C4—1884no—
567C2×C4—1882no—
568C2×C4—1881no—
569C2×C4—1881no—
570C2×C4C2×(C2×D47)⋊C412yes—
571C2×C4C2×(C2×D47)⋊C411yescharacteristic
572C2×C4C2×(C2×D47)⋊C411yescharacteristic
573C2×C4C2×(C2×D47)⋊C412yes—
574C2×C4C2×(C2×D47)⋊C412yes—
575C2×C4C2×(C2×D47)⋊C411yescharacteristic
576C2×C4C22×C4×D4711yescharacteristic
577C2×C4C22×C22⋊D4711yescharacteristic
578C2×C4C22×D18811yescharacteristic
579C8—41no—
580C8—42no—
581C8—41no—
582C8—942no—
583C8—944no—
584C8—942no—
585C22—22no—
586C22—22no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—1881no—
591C22—1881no—
592C22—1881no—
593C22C2×#1309395014yes—
594C22C22×(C2×D47)⋊C411yescharacteristic
595C4—22no—
596C4—21no—
597C4—21no—
598C4—22no—
599C4—21no—
600C4—22no—
601C4—942no—
602C4—1881no—
603C4—1881no—
604C4—1882no—
605C4—1882no—
606C4C2×#1309395012yes—
607C4#131×D4711yescharacteristic
608C4#1568988811yescharacteristic
609C4#1568993411yescharacteristic
610C4#1568993811yescharacteristic
611C2—24no—
612C2—41no—
613C2—3761no—
614C2#2025183511yescharacteristic
615C2#2025191811yescharacteristic
616C2C22×#1309395011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2990C2
socleC22×C47C22×C22⋊C4
prime radical#20257003C2
cosocleC42×C47C24
hypercenter#2990D47
hypocenterC47#17519
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. C4×#13094031C2semidirect
3. #20241846C2semidirect
4. #20241842C2semidirect
5. #20241834C2semidirect
6. #20241825C2semidirect
7. #20241808C2semidirect
8. #20241799C2semidirect
9. #20241768C2semidirect
10. C2×#15688853C2semidirect
11. C47×#2990C2semidirect
269. Dic94#131semidirect
304. #2990D47semidirect
361. C47#17519semidirect

Maximal subgroups

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

subgroupindex
#202570032
C4×#130940312
#202418462
#202418422
#202418342
#202418252
#202418082
#202417992
#202417682
C2×#156888532
C47×#29902
#1751947