Finite Group Databasebeta

← #26182923

Subgroups — #26182923

Order 12032.

988 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#20252020C211yesmaximal, characteristic
3C2×#15689174C211yesmaximal, characteristic
4#20241859C214yesmaximal, complemented
5#20241844C211yesmaximal, characteristic, complemented
6#20241843C211yesmaximal, characteristic, complemented
7#20241842C211yesmaximal, characteristic, complemented
8#20241781C214yesmaximal, complemented
9C47×#1493C211yesmaximal, characteristic, complemented
10#15689680C2211yescharacteristic
11#15689679—21no—
12#15689678C411yescharacteristic
13#15689678C411yescharacteristic
14#15689677—21no—
15#15689677C2212yes—
16#15689676—21no—
17#15689675—21no—
18#15689675C412yes—
19C4⋊Q8×D47C411yescharacteristic
20C4⋊Q8×D47C411yescharacteristic
21#125×D47—21no—
22C22⋊Q8×D47—21no—
23C22⋊Q8×D47C412yes—
24C4×Q8×D47—21no—
25C4×Q8×D47C2212yes—
26#117×D47—21no—
27C2×C42×D47C2211yescharacteristic
28#15689179—21no—
29#15689179C2212yes—
30#15689175—21no—
31#15689175C2212yes—
32#15689174—21no—
33#15689174—21no—
34#15689174C2212yes—
35#15689174C2212yes—
36#15689147C2211yescharacteristic
37C2×Dic47⋊C8—21no—
38#15689086—21no—
39C2×(C2×D47)⋊C8—21no—
40M16×Dic47—21no—
41C2×C4×C47⋊C8C2211yescharacteristic
42#15688855C2214yescomplemented
43Q8⋊(C47⋊C8)C2214yescomplemented
44#15688853C2214yescomplemented
45C47×#533C2211yescharacteristic
46C47×#423C2211yescharacteristic
47C2×C4×C8×C47C2211yescharacteristic
48C47×Q8⋊C8C2214yescomplemented
49C2×Q8×D47—21no—
50C2×Q8×D47C2×C412yes—
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47D411yescharacteristic
53C22×C4×D47D411yescharacteristic
54C2×#10625329—21no—
55C22×C47⋊C8—21no—
56#13094024C2×C411yescharacteristic
57#13094024C2×C411yescharacteristic
58#13094023—21no—
59#13094023—21no—
60#13094023—21no—
61#13094023C2×C412yes—
62#13094022—21no—
63#13094022C2×C412yes—
64#13094016—21no—
65#13094015—21no—
66#13094015—21no—
67#13094014—22no—
68#13094014—22no—
69#13094004—21no—
70#13094004C2×C412yes—
71#13094003—21no—
72#13094003C2×C412yes—
73#13094002—22no—
74#13094002—22no—
75#13094001—22no—
76#13094001—22no—
77#13094000—21no—
78#13094000C2×C412yes—
79Q8×Dic47—21no—
80Q8×Dic47C2×C412yes—
81C4×Dic94—21no—
82C4×Dic94—22no—
83C4×Dic94—22no—
84C4×Dic94C2312yes—
85#13093989—21no—
86#13093989—22no—
87#13093989—22no—
88#13093989C2×C412yes—
89#13093983—21no—
90#13093982—21no—
91#13093982—21no—
92#13093981—22no—
93#13093980—22no—
94C4⋊C4×D47—21no—
95C4⋊C4×D47—21no—
96C4⋊C4×D47—21no—
97C4⋊C4×D47—22no—
98C4⋊C4×D47—22no—
99C4⋊C4×D47C2×C412yes—
100C22⋊C4×D47—22no—
101C2×C4×Dic47C2×C411yescharacteristic
102C2×C4×Dic47D411yescharacteristic
103C2×C4×Dic47D411yescharacteristic
104C42×D47—22no—
105C42×D47C2×C411yescharacteristic
106C42×D47C2×C411yescharacteristic
107C42×D47D411yescharacteristic
108C42×D47D411yescharacteristic
109C42×D47D411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47C2311yescharacteristic
112C42×D47C2311yescharacteristic
113C4⋊(C47⋊C8)—21no—
114C4⋊(C47⋊C8)C2312yes—
115Dic47⋊C8—22no—
116Dic47⋊C8—22no—
117(C2×D47)⋊C8—22no—
118(C2×D47)⋊C8—22no—
119(C2×D47)⋊C8—22no—
120(C2×D47)⋊C8—22no—
121#13093934—22no—
122C4×C47⋊C8—21no—
123C4×C47⋊C8C2312yes—
124C8×Dic47—22no—
125C2×M16×C47—21no—
126C22×C8×C47—21no—
127C4⋊Q8×C47C2×C411yescharacteristic
128C4⋊Q8×C47C2×C411yescharacteristic
129#125×C47—21no—
130C22⋊Q8×C47—21no—
131C22⋊Q8×C47C2×C412yes—
132C4×Q8×C47—21no—
133C4×Q8×C47C2312yes—
134#117×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2312yes—
138C4×C8×C47—21no—
139C4×C8×C47C2312yes—
140C23×D47C22⋊C411yescharacteristic
141C2×Q8×C47—21no—
142C2×Q8×C47C22×C412yes—
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×Dic47C22⋊C411yescharacteristic
147C22×Dic47C22⋊C411yescharacteristic
148C22×Dic47C22⋊C411yescharacteristic
149Q8×D47—28no—
150Q8×D47—44no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×C4×D47—24no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—42no—
157C2×C4×D47C22⋊C411yescharacteristic
158C2×C4×D47C22⋊C411yescharacteristic
159C2×C4×D47C22⋊C411yescharacteristic
160C2×C4×D47C22⋊C411yescharacteristic
161C2×C4×D47C22⋊C411yescharacteristic
162C2×C4×D47C22⋊C411yescharacteristic
163C2×C4×D47C22×C411yescharacteristic
164C2×C4×D47C22×C411yescharacteristic
165C2×C4×D47C2×D411yescharacteristic
166C2×C4×D47C2×D411yescharacteristic
167C2×C4×D47C2×D411yescharacteristic
168C2×C4×D47C2×D411yescharacteristic
169C2×Dic94—21no—
170C2×Dic94—22no—
171C2×Dic94—22no—
172C2×Dic94C22×C412yes—
173M16×C47—42no—
174C2×C8×C47—22no—
175C2×C8×C47—22no—
176C2×C8×C47—42no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—22no—
181C4⋊C4×C47—22no—
182C4⋊C4×C47C22×C412yes—
183C22⋊C4×C47—22no—
184C42×C47—22no—
185C42×C47C22×C411yescharacteristic
186C42×C47C2×D411yescharacteristic
187C42×C47C2×D411yescharacteristic
188C42×C47C2411yescharacteristic
189C22⋊Dic47—22no—
190(C2×D47)⋊C4—22no—
191(C2×D47)⋊C4—22no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—22no—
196C4⋊Dic47—22no—
197C4⋊Dic47C22×C412yes—
198Dic47⋊C4—22no—
199Dic47⋊C4—22no—
200Dic47⋊C4—22no—
201Dic47⋊C4—22no—
202Dic47⋊C4—22no—
203Dic47⋊C4—22no—
204Dic47⋊C4—22no—
205Dic47⋊C4—22no—
206C4×Dic47—22no—
207C4×Dic47—22no—
208C4×Dic47—22no—
209C4×Dic47C22⋊C411yescharacteristic
210C4×Dic47C22⋊C411yescharacteristic
211C4×Dic47C22⋊C411yescharacteristic
212C4×Dic47C22⋊C411yescharacteristic
213C4×Dic47C22⋊C411yescharacteristic
214C4×Dic47C22⋊C411yescharacteristic
215C4×Dic47C22×C411yescharacteristic
216C4×Dic47C22×C411yescharacteristic
217C4×Dic47C2×D411yescharacteristic
218C4×Dic47C2×D411yescharacteristic
219C4×Dic47C2×D411yescharacteristic
220C4×Dic47C2×D411yescharacteristic
221#10625329—42no—
222C2×C47⋊C8—22no—
223C2×C47⋊C8—22no—
224C2×C47⋊C8—42no—
225C23×C47C2×C22⋊C411yescharacteristic
226C22×D47—22no—
227C22×D47—22no—
228C22×D47—41no—
229C22×D47C2×C22⋊C411yescharacteristic
230C22×D47C2×C22⋊C411yescharacteristic
231Q8×C47—24no—
232Q8×C47—42no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47C2×C22⋊C411yescharacteristic
238C2×C4×C47C2×C22⋊C411yescharacteristic
239C2×C4×C47C2×C22⋊C411yescharacteristic
240C2×C4×C47#13712yes—
241C2×C4×C47#13712yes—
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C22×D411yescharacteristic
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—41no—
250C2×Dic47C2×C22⋊C411yescharacteristic
251C2×Dic47C2×C22⋊C411yescharacteristic
252C2×Dic47C2×C22⋊C411yescharacteristic
253C2×Dic47C2×C22⋊C411yescharacteristic
254C2×Dic47C2×C22⋊C411yescharacteristic
255C2×Dic47C2×C22⋊C411yescharacteristic
256C4×D47—22no—
257C4×D47—22no—
258C4×D47—21no—
259C4×D47—21no—
260C4×D47—21no—
261C4×D47—21no—
262C4×D47—22no—
263C4×D47—22no—
264C4×D47—22no—
265C4×D47—22no—
266C4×D47—22no—
267C4×D47—41no—
268C4×D47—41no—
269C4×D47—44no—
270C4×D47—44no—
271C4×D47#13114yes—
272Dic94—24no—
273Dic94—44no—
274Dic94—42no—
275Dic94—44no—
276C8×C47—42no—
277C8×C47—42no—
278C47⋊C8—42no—
279C47⋊C8—42no—
280#17479—471nomaximal, Sylow
281C22×C47—21no—
282C22×C47—21no—
283C22×C47#41912yes—
284C22×C47C22×C22⋊C411yescharacteristic
285C2×D47—21no—
286C2×D47—21no—
287C2×D47—21no—
288C2×D47—21no—
289C2×D47—21no—
290C2×D47—44no—
291C2×D47#40812yes—
292C4×C47—21no—
293C4×C47—21no—
294C4×C47—42no—
295C4×C47—42no—
296C4×C47#41912yes—
297C4×C47#42112yes—
298C4×C47C2×#13112yes—
299C4×C47C2×#13711yescharacteristic
300C4×C47C2×#13711yescharacteristic
301Dic47—21no—
302Dic47—21no—
303Dic47—21no—
304Dic47—21no—
305Dic47—21no—
306Dic47—42no—
307Dic47—42no—
308Dic47#40812yes—
309C2×#533—471no—
310#2920—471no—
311C2×#431—471no—
312#1497—474no—
313#1493—471no—
314#1493—471no—
315#1493—471no—
316#1493D4711yescharacteristic, complemented
317#1479—474no—
318C2×C47—22no—
319C2×C47C2×#40811yescharacteristic
320C2×C47C2×#41911yescharacteristic
321C2×C47C2×#42111yescharacteristic
322D47—22no—
323D47—41no—
324#533—471no—
325#533—471no—
326#533—472no—
327#533—472no—
328#533—471no—
329#533—941no—
330#533—941no—
331#533—941no—
332#533—941no—
333#533C2×D4711yescharacteristic
334C2×C4⋊Q8—471no—
335C2×C4⋊Q8—471no—
336C2×#125—941no—
337C2×C22⋊Q8—472no—
338C2×C22⋊Q8—941no—
339C2×C4×Q8—472no—
340C2×C4×Q8—941no—
341C2×#117—941no—
342C22×C42—471no—
343#432—472no—
344#432—941no—
345#431—472no—
346#431—472no—
347#431—472no—
348#431—941no—
349#431—941no—
350#431—941no—
351#423—471no—
352#423C2×D4711yescharacteristic
353C2×C4⋊C8—941no—
354#407—941no—
355C2×C22⋊C8—941no—
356C4×M16—941no—
357C2×C4×C8—471no—
358C2×C4×C8C2×D4711yescharacteristic
359Q8⋊C8—474no—
360Q8⋊C8—474no—
361Q8⋊C8—474no—
362Q8⋊C8C2×D4714yescomplemented
363C47#1747911yescharacteristic, complemented, Sylow
364C22×Q8—472no—
365C22×Q8—941no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—471no—
369C2×M16—21no—
370C2×M16—941no—
371C22×C8—21no—
372C22×C8—941no—
373C4⋊Q8—472no—
374C4⋊Q8—472no—
375C4⋊Q8—471no—
376C4⋊Q8—471no—
377C4⋊Q8—941no—
378C4⋊Q8—941no—
379C4⋊Q8—941no—
380C4⋊Q8—941no—
381C4⋊Q8C4×D4711yescharacteristic
382C4⋊Q8C4×D4711yescharacteristic
383#125—21no—
384#125—942no—
385#125—942no—
386#125—941no—
387#125—941no—
388#125—941no—
389C22⋊Q8—21no—
390C22⋊Q8—472no—
391C22⋊Q8—472no—
392C22⋊Q8—472no—
393C22⋊Q8—942no—
394C22⋊Q8—942no—
395C22⋊Q8—942no—
396C22⋊Q8—942no—
397C22⋊Q8—941no—
398C22⋊Q8—941no—
399C22⋊Q8—941no—
400C22⋊Q8C4×D4712yes—
401C4×Q8—21no—
402C4×Q8—472no—
403C4×Q8—472no—
404C4×Q8—472no—
405C4×Q8—942no—
406C4×Q8—942no—
407C4×Q8—942no—
408C4×Q8—941no—
409C4×Q8—942no—
410C4×Q8—941no—
411C4×Q8—941no—
412C4×Q8C22×D4712yes—
413#117—21no—
414#117—942no—
415#117—942no—
416#117—941no—
417#117—941no—
418#117—941no—
419C2×C4⋊C4—472no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4—941no—
422C2×C4⋊C4—942no—
423C2×C4⋊C4—942no—
424C2×C4⋊C4—941no—
425C2×C22⋊C4—942no—
426C2×C42—471no—
427C2×C42—471no—
428C2×C42—471no—
429C2×C42—471no—
430C2×C42—471no—
431C2×C42—471no—
432C2×C42—471no—
433C2×C42—471no—
434C2×C42—471no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—942no—
438C2×C42C22×D4711yescharacteristic
439C4⋊C8—21no—
440C4⋊C8—472no—
441C4⋊C8—942no—
442C4⋊C8—942no—
443C4⋊C8—941no—
444C4⋊C8C22×D4712yes—
445C22⋊C8—942no—
446C22⋊C8—942no—
447C22⋊C8—942no—
448C22⋊C8—942no—
449#97—942no—
450C4×C8—21no—
451C4×C8—472no—
452C4×C8—942no—
453C4×C8—941no—
454C4×C8C22×D4712yes—
455C24—471no—
456C2×Q8—21no—
457C2×Q8—472no—
458C2×Q8—942no—
459C2×Q8—942no—
460C2×Q8—948no—
461C2×Q8—941no—
462C2×Q8—1884no—
463C2×Q8C2×C4×D4712yes—
464C22×C4—471no—
465C22×C4—471no—
466C22×C4—471no—
467C22×C4—471no—
468C22×C4—471no—
469C22×C4—471no—
470C22×C4—471no—
471C22×C4—471no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—471no—
475C22×C4—471no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—471no—
479C22×C4—944no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—1882no—
485C22×C4C2×C4×D4711yescharacteristic
486C22×C4D4×D4711yescharacteristic
487C22×C4D4×D4711yescharacteristic
488M16—42no—
489M16—1882no—
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—42no—
493C2×C8—942no—
494C2×C8—942no—
495C2×C8—1882no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—472no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—942no—
515C4⋊C4C2×C4×D4712yes—
516C22⋊C4—22no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C42—22no—
521C42—471no—
522C42—471no—
523C42—471no—
524C42—471no—
525C42—471no—
526C42—471no—
527C42—471no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42—471no—
532C42—471no—
533C42—942no—
534C42—942no—
535C42—942no—
536C42C2×C4×D4711yescharacteristic
537C42D4×D4711yescharacteristic
538C42D4×D4711yescharacteristic
539C42C23×D4711yescharacteristic
540C23—471no—
541C23—471no—
542C23—942no—
543C23—942no—
544C23—1881no—
545C23C22⋊C4×D4711yescharacteristic
546Q8—24no—
547Q8—42no—
548Q8—944no—
549Q8—1884no—
550Q8—1884no—
551Q8—1882no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—471no—
557C2×C4—474no—
558C2×C4—471no—
559C2×C4—471no—
560C2×C4—471no—
561C2×C4—471no—
562C2×C4—471no—
563C2×C4—942no—
564C2×C4—942no—
565C2×C4—942no—
566C2×C4—942no—
567C2×C4—942no—
568C2×C4—942no—
569C2×C4—942no—
570C2×C4—942no—
571C2×C4—942no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—1881no—
579C2×C4—1881no—
580C2×C4—1884no—
581C2×C4—1884no—
582C2×C4—1881no—
583C2×C4C22⋊C4×D4711yescharacteristic
584C2×C4C22⋊C4×D4711yescharacteristic
585C2×C4C22⋊C4×D4711yescharacteristic
586C2×C4#1309405312yes—
587C2×C4#1309405612yes—
588C2×C4C22×C4×D4711yescharacteristic
589C2×C4C2×D4×D4711yescharacteristic
590C2×C4C2×D4×D4711yescharacteristic
591C8—42no—
592C8—42no—
593C8—1882no—
594C8—1882no—
595C22—21no—
596C22—21no—
597C22—472no—
598C22—941no—
599C22—941no—
600C22—941no—
601C22—941no—
602C22—941no—
603C22—1884no—
604C22#1568913012yes—
605C22C2×C22⋊C4×D4711yescharacteristic
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—472no—
611C4—941no—
612C4—941no—
613C4—941no—
614C4—941no—
615C4—941no—
616C4—1882no—
617C4—1882no—
618C4#1568913012yes—
619C4#1568913812yes—
620C4#131×D4712yes—
621C4C2×#1309405311yescharacteristic
622C4C2×#1309405611yescharacteristic
623C2—22no—
624C2—942no—
625C2—1881no—
626C2#408×D4711yescharacteristic
627C2C2×#1568913011yescharacteristic
628C2C2×#1568913811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1493C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1493D47
hypocenterC47#17479
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
4. #20241859C2semidirect
5. #20241844C2semidirect
6. #20241843C2semidirect
7. #20241842C2semidirect
8. #20241781C2semidirect
9. C47×#1493C2semidirect
42. #15688855C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
44. #15688853C22semidirect
48. C47×Q8⋊C8C22semidirect
316. #1493D47semidirect
362. Q8⋊C8C2×D47semidirect
363. C47#17479semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#202520202
C2×#156891742
#202418592
#202418442
#202418432
#202418422
#202417812
C47×#14932
#1747947