Finite Group Databasebeta

← #26182721

Subgroups — #26182721

Order 12032.

1214 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D47C211yesmaximal, characteristic
2#20252020C211yesmaximal, characteristic
3#20252016C211yesmaximal, characteristic
4#20241833C214yesmaximal, complemented
5#20241818C211yesmaximal, characteristic, complemented
6#20241817C211yesmaximal, characteristic, complemented
7#20241816C211yesmaximal, characteristic, complemented
8#20241781C214yesmaximal, complemented
9C47×#1487C211yesmaximal, characteristic, complemented
10C22×Q8×D47C411yescharacteristic
11C2×Q8×Dic47C411yescharacteristic
12C2×C4×Dic94—21no—
13C2×C4×Dic94C2211yescharacteristic
14C2×#13093989—21no—
15C2×#13093989C411yescharacteristic
16C4×Q8×D47—21no—
17C4×Q8×D47—21no—
18C4×Q8×D47—21no—
19C4×Q8×D47—21no—
20C4×Q8×D47C412yes—
21C4×Q8×D47C412yes—
22C4×Q8×D47C2212yes—
23C4×Q8×D47C2212yes—
24C2×C4⋊C4×D47—21no—
25C2×C4⋊C4×D47C411yescharacteristic
26C2×C42×D47—21no—
27C2×C42×D47C2211yescharacteristic
28#15689179—21no—
29#15689179—21no—
30#15689179C2212yes—
31#15689177—21no—
32#15689176C2211yescharacteristic
33#15689175—21no—
34#15689175C2212yes—
35#15689174C2212yes—
36#15689147C2211yescharacteristic
37#15689145—21no—
38#15689086—21no—
39#15689085—21no—
40M16×Dic47—21no—
41C4×#10625324C2212yes—
42#15688855C2214yescomplemented
43Q8⋊(C47⋊C8)C2214yescomplemented
44#15688853C2214yescomplemented
45C2×C4×Q8×C47C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#423C2211yescharacteristic
48C47×Q8⋊C8C2214yescomplemented
49C22×Dic94—21no—
50C22×Dic94C2×C411yescharacteristic
51C2×Q8×D47—28no—
52C2×Q8×D47—21no—
53C2×Q8×D47—21no—
54C2×Q8×D47C2×C412yes—
55C2×Q8×D47C2×C412yes—
56C22×C4×D47—21no—
57C22×C4×D47—21no—
58C22×C4×D47C2×C411yescharacteristic
59C22×C4×D47D411yescharacteristic
60C22×C4×D47D411yescharacteristic
61C2×#10625329—21no—
62C2×#10625324—22no—
63Q8×Dic47—21no—
64Q8×Dic47—21no—
65Q8×Dic47C2×C412yes—
66Q8×Dic47C2×C412yes—
67C4×Dic94—21no—
68C4×Dic94—21no—
69C4×Dic94—22no—
70C4×Dic94—22no—
71C4×Dic94—22no—
72C4×Dic94—22no—
73C4×Dic94C2×C412yes—
74C4×Dic94C2312yes—
75#13093989—21no—
76#13093989—21no—
77#13093989—22no—
78#13093989—22no—
79#13093989—22no—
80#13093989—22no—
81#13093989C2×C412yes—
82#13093989C2×C412yes—
83C2×C4⋊Dic47—21no—
84C2×C4⋊Dic47C2×C411yescharacteristic
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C4⋊C4×D47—22no—
89C4⋊C4×D47—22no—
90C4⋊C4×D47—21no—
91C4⋊C4×D47—21no—
92C4⋊C4×D47—22no—
93C4⋊C4×D47—22no—
94C4⋊C4×D47C2×C412yes—
95C4⋊C4×D47C2×C412yes—
96C2×C4×Dic47—21no—
97C2×C4×Dic47—21no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47C2×C411yescharacteristic
100C2×C4×Dic47D411yescharacteristic
101C2×C4×Dic47D411yescharacteristic
102C42×D47—22no—
103C42×D47—22no—
104C42×D47—22no—
105C42×D47—22no—
106C42×D47C2×C411yescharacteristic
107C42×D47C2×C411yescharacteristic
108C42×D47D411yescharacteristic
109C42×D47D411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47D411yescharacteristic
112C42×D47C2311yescharacteristic
113C42×D47C2311yescharacteristic
114C4⋊(C47⋊C8)—21no—
115C4⋊(C47⋊C8)—21no—
116C4⋊(C47⋊C8)C2312yes—
117Dic47⋊C8—22no—
118C22⋊(C47⋊C8)—21no—
119(C2×D47)⋊C8—22no—
120(C2×D47)⋊C8—22no—
121(C2×D47)⋊C8—22no—
122#13093934—22no—
123#13093934—22no—
124C4×C47⋊C8C2312yes—
125C8×Dic47—22no—
126C22×Q8×C47C2×C411yescharacteristic
127C2×M16×C47—21no—
128C4×Q8×C47—21no—
129C4×Q8×C47—21no—
130C4×Q8×C47C2×C412yes—
131C4×Q8×C47C2312yes—
132C2×C4⋊C4×C47—21no—
133C2×C4⋊C4×C47C2×C411yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47—21no—
138C4⋊C8×C47C2312yes—
139C22⋊C8×C47—21no—
140C4×C8×C47C2312yes—
141C23×D47C22⋊C411yescharacteristic
142C2×Q8×C47—24no—
143C2×Q8×C47—21no—
144C2×Q8×C47C22×C412yes—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47C22×C411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×Dic47—21no—
151C22×Dic47—21no—
152C22×Dic47C22⋊C411yescharacteristic
153C22×Dic47C22⋊C411yescharacteristic
154C22×Dic47C22⋊C411yescharacteristic
155Q8×D47—28no—
156Q8×D47—28no—
157Q8×D47—24no—
158Q8×D47—24no—
159Q8×D47—24no—
160Q8×D47M1618yescomplemented
161C2×C4×D47—28no—
162C2×C4×D47—22no—
163C2×C4×D47—22no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—24no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—42no—
170C2×C4×D47—44no—
171C2×C4×D47C22⋊C411yescharacteristic
172C2×C4×D47C22⋊C411yescharacteristic
173C2×C4×D47C22⋊C411yescharacteristic
174C2×C4×D47C22⋊C411yescharacteristic
175C2×C4×D47C22⋊C411yescharacteristic
176C2×C4×D47C22⋊C411yescharacteristic
177C2×C4×D47C22×C411yescharacteristic
178C2×C4×D47C22×C411yescharacteristic
179C2×C4×D47C2×D411yescharacteristic
180C2×C4×D47C2×D411yescharacteristic
181C2×C4×D47C2×D411yescharacteristic
182C2×C4×D47C2×D411yescharacteristic
183C2×Dic94—28no—
184C2×Dic94—21no—
185C2×Dic94—22no—
186C2×Dic94—22no—
187C2×Dic94—24no—
188C2×Dic94C22×C412yes—
189M16×C47—42no—
190C2×C8×C47—22no—
191C2×C8×C47—22no—
192C4⋊C4×C47—22no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47C22×C412yes—
196C42×C47—22no—
197C42×C47—22no—
198C42×C47C22×C411yescharacteristic
199C42×C47C2×D411yescharacteristic
200C42×C47C2×D411yescharacteristic
201C42×C47C2411yescharacteristic
202C4⋊Dic47—21no—
203C4⋊Dic47—22no—
204C4⋊Dic47—22no—
205C4⋊Dic47C22×C412yes—
206Dic47⋊C4—22no—
207Dic47⋊C4—22no—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210Dic47⋊C4—22no—
211Dic47⋊C4—22no—
212C4×Dic47—22no—
213C4×Dic47—22no—
214C4×Dic47—22no—
215C4×Dic47—22no—
216C4×Dic47—22no—
217C4×Dic47—22no—
218C4×Dic47C22⋊C411yescharacteristic
219C4×Dic47C22⋊C411yescharacteristic
220C4×Dic47C22⋊C411yescharacteristic
221C4×Dic47C22⋊C411yescharacteristic
222C4×Dic47C22⋊C411yescharacteristic
223C4×Dic47C22⋊C411yescharacteristic
224C4×Dic47C22×C411yescharacteristic
225C4×Dic47C22×C411yescharacteristic
226C4×Dic47C2×D411yescharacteristic
227C4×Dic47C2×D411yescharacteristic
228C4×Dic47C2×D411yescharacteristic
229C4×Dic47C2×D411yescharacteristic
230#10625329—42no—
231C2×C47⋊C8—22no—
232C2×C47⋊C8—22no—
233#10625324—44no—
234C23×C47C2×C22⋊C411yescharacteristic
235C22×D47—22no—
236C22×D47—22no—
237C22×D47—22no—
238C22×D47C2×C22⋊C411yescharacteristic
239C22×D47C2×C22⋊C411yescharacteristic
240Q8×C47—24no—
241Q8×C47—22no—
242Q8×C47C2×M1614yes—
243C2×C4×C47—24no—
244C2×C4×C47—22no—
245C2×C4×C47—22no—
246C2×C4×C47—22no—
247C2×C4×C47—41no—
248C2×C4×C47—42no—
249C2×C4×C47C2×C22⋊C411yescharacteristic
250C2×C4×C47C2×C22⋊C411yescharacteristic
251C2×C4×C47C2×C22⋊C411yescharacteristic
252C2×C4×C47#13712yes—
253C2×C4×C47#13712yes—
254C2×C4×C47C23×C411yescharacteristic
255C2×C4×C47C22×D411yescharacteristic
256C2×C4×C47C22×D411yescharacteristic
257C2×Dic47—24no—
258C2×Dic47—22no—
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—22no—
262C2×Dic47—41no—
263C2×Dic47—42no—
264C2×Dic47C2×C22⋊C411yescharacteristic
265C2×Dic47C2×C22⋊C411yescharacteristic
266C2×Dic47C2×C22⋊C411yescharacteristic
267C2×Dic47C2×C22⋊C411yescharacteristic
268C2×Dic47C2×C22⋊C411yescharacteristic
269C2×Dic47C2×C22⋊C411yescharacteristic
270C4×D47—28no—
271C4×D47—28no—
272C4×D47—22no—
273C4×D47—22no—
274C4×D47—22no—
275C4×D47—22no—
276C4×D47—21no—
277C4×D47—21no—
278C4×D47—21no—
279C4×D47—21no—
280C4×D47—22no—
281C4×D47—22no—
282C4×D47—22no—
283C4×D47—41no—
284C4×D47—41no—
285C4×D47—44no—
286C4×D47—44no—
287C4×D47C2×M1614yes—
288Dic94—28no—
289Dic94—24no—
290Dic94—22no—
291Dic94—28no—
292Dic94C2×M1614yes—
293C8×C47—42no—
294C8×C47—42no—
295C47⋊C8—42no—
296C47⋊C8—42no—
297#17449—471nomaximal, Sylow
298C22×C47—21no—
299C22×C47—21no—
300C22×C47#41912yes—
301C22×C47C22×C22⋊C411yescharacteristic
302C2×D47—28no—
303C2×D47—21no—
304C2×D47—21no—
305C2×D47—21no—
306C2×D47—21no—
307C2×D47#40712yes—
308C2×D47#42112yes—
309C4×C47—24no—
310C4×C47—21no—
311C4×C47—21no—
312C4×C47—21no—
313C4×C47—42no—
314C4×C47#41912yes—
315C4×C47C22×M1612yes—
316C4×C47C2×#13711yescharacteristic
317C4×C47C2×#13711yescharacteristic
318Dic47—21no—
319Dic47—24no—
320Dic47—21no—
321Dic47—21no—
322Dic47—21no—
323Dic47—21no—
324Dic47—42no—
325Dic47#40712yes—
326C22×C4×Q8—471no—
327#2920—471no—
328#2920—471no—
329#1491—474no—
330#1487—471no—
331#1487—471no—
332#1487—471no—
333#1487D4711yescharacteristic, complemented
334#1479—474no—
335C2×C47—22no—
336C2×C47C2×#40711yescharacteristic
337C2×C47C2×#41911yescharacteristic
338C2×C47C2×#42111yescharacteristic
339D47—22no—
340D47—22no—
341C23×Q8—471no—
342C2×C4×Q8—471no—
343C2×C4×Q8—472no—
344C2×C4×Q8—472no—
345C2×C4×Q8—472no—
346C2×C4×Q8—472no—
347C2×C4×Q8—471no—
348C2×C4×Q8—471no—
349C2×C4×Q8—941no—
350C2×C4×Q8—941no—
351C2×C4×Q8—941no—
352C2×C4×Q8—941no—
353C2×C4×Q8—941no—
354C2×C4×Q8—941no—
355C2×C4×Q8C2×D4711yescharacteristic
356C22×C4⋊C4—471no—
357C22×C4⋊C4—941no—
358C22×C42—471no—
359C22×C42—941no—
360#432—472no—
361#432—941no—
362#432—941no—
363#432—941no—
364#431—471no—
365#431—472no—
366#431—472no—
367#431—941no—
368#431C2×D4711yescharacteristic
369#423—471no—
370#423—941no—
371#423C2×D4711yescharacteristic
372#407—941no—
373#407—941no—
374C4×M16—472no—
375C4×M16—941no—
376Q8⋊C8—474no—
377Q8⋊C8—474no—
378Q8⋊C8—474no—
379Q8⋊C8C2×D4714yescomplemented
380C47#1744911yescharacteristic, complemented, Sylow
381C22×Q8—472no—
382C22×Q8—472no—
383C22×Q8—471no—
384C22×Q8—941no—
385C22×Q8—941no—
386C22×Q8—941no—
387C22×Q8—948no—
388C22×Q8C4×D4711yescharacteristic
389C23×C4—471no—
390C23×C4—471no—
391C23×C4—471no—
392C23×C4—941no—
393C23×C4—941no—
394C2×M16—21no—
395C2×M16—942no—
396C2×M16—941no—
397C4×Q8—21no—
398C4×Q8—21no—
399C4×Q8—472no—
400C4×Q8—472no—
401C4×Q8—472no—
402C4×Q8—472no—
403C4×Q8—472no—
404C4×Q8—472no—
405C4×Q8—942no—
406C4×Q8—942no—
407C4×Q8—942no—
408C4×Q8—942no—
409C4×Q8—942no—
410C4×Q8—942no—
411C4×Q8—941no—
412C4×Q8—941no—
413C4×Q8—942no—
414C4×Q8—942no—
415C4×Q8—941no—
416C4×Q8—941no—
417C4×Q8—941no—
418C4×Q8—941no—
419C4×Q8C4×D4712yes—
420C4×Q8C22×D4712yes—
421C2×C4⋊C4—21no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—472no—
424C2×C4⋊C4—472no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4—942no—
428C2×C4⋊C4—942no—
429C2×C4⋊C4—942no—
430C2×C4⋊C4—942no—
431C2×C4⋊C4—941no—
432C2×C4⋊C4—941no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4C4×D4711yescharacteristic
436C2×C42—21no—
437C2×C42—471no—
438C2×C42—471no—
439C2×C42—471no—
440C2×C42—471no—
441C2×C42—471no—
442C2×C42—471no—
443C2×C42—471no—
444C2×C42—471no—
445C2×C42—471no—
446C2×C42—471no—
447C2×C42—471no—
448C2×C42—942no—
449C2×C42—942no—
450C2×C42—942no—
451C2×C42—942no—
452C2×C42—941no—
453C2×C42—941no—
454C2×C42—941no—
455C2×C42C22×D4711yescharacteristic
456C4⋊C8—21no—
457C4⋊C8—21no—
458C4⋊C8—472no—
459C4⋊C8—942no—
460C4⋊C8—941no—
461C4⋊C8—941no—
462C4⋊C8C22×D4712yes—
463C22⋊C8—21no—
464C22⋊C8—942no—
465C22⋊C8—942no—
466C22⋊C8—942no—
467C22⋊C8—941no—
468#97—942no—
469#97—942no—
470C4×C8—472no—
471C4×C8—942no—
472C4×C8C22×D4712yes—
473C24—471no—
474C2×Q8—24no—
475C2×Q8—21no—
476C2×Q8—478no—
477C2×Q8—472no—
478C2×Q8—942no—
479C2×Q8—942no—
480C2×Q8—944no—
481C2×Q8—948no—
482C2×Q8—944no—
483C2×Q8—944no—
484C2×Q8—948no—
485C2×Q8—948no—
486C2×Q8—944no—
487C2×Q8—941no—
488C2×Q8C2×C4×D4712yes—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—471no—
492C22×C4—471no—
493C22×C4—471no—
494C22×C4—471no—
495C22×C4—471no—
496C22×C4—471no—
497C22×C4—471no—
498C22×C4—471no—
499C22×C4—471no—
500C22×C4—471no—
501C22×C4—471no—
502C22×C4—471no—
503C22×C4—471no—
504C22×C4—471no—
505C22×C4—471no—
506C22×C4—944no—
507C22×C4—942no—
508C22×C4—942no—
509C22×C4—948no—
510C22×C4—942no—
511C22×C4—942no—
512C22×C4—941no—
513C22×C4—942no—
514C22×C4—942no—
515C22×C4—941no—
516C22×C4—1882no—
517C22×C4—1884no—
518C22×C4C2×C4×D4711yescharacteristic
519C22×C4D4×D4711yescharacteristic
520C22×C4D4×D4711yescharacteristic
521M16—42no—
522M16—1884no—
523M16—1882no—
524C2×C8—22no—
525C2×C8—22no—
526C2×C8—942no—
527C2×C8—942no—
528C4⋊C4—22no—
529C4⋊C4—21no—
530C4⋊C4—22no—
531C4⋊C4—472no—
532C4⋊C4—942no—
533C4⋊C4—942no—
534C4⋊C4—942no—
535C4⋊C4—942no—
536C4⋊C4—942no—
537C4⋊C4—942no—
538C4⋊C4—942no—
539C4⋊C4—941no—
540C4⋊C4—942no—
541C4⋊C4C2×C4×D4712yes—
542C42—22no—
543C42—22no—
544C42—471no—
545C42—471no—
546C42—471no—
547C42—471no—
548C42—471no—
549C42—471no—
550C42—471no—
551C42—471no—
552C42—471no—
553C42—471no—
554C42—471no—
555C42—471no—
556C42—942no—
557C42—942no—
558C42—942no—
559C42—942no—
560C42—942no—
561C42—942no—
562C42C2×C4×D4711yescharacteristic
563C42D4×D4711yescharacteristic
564C42D4×D4711yescharacteristic
565C42C23×D4711yescharacteristic
566C23—471no—
567C23—471no—
568C23—942no—
569C23—942no—
570C23—942no—
571C23C22⋊C4×D4711yescharacteristic
572Q8—24no—
573Q8—22no—
574Q8—474no—
575Q8—948no—
576Q8—948no—
577Q8—944no—
578Q8—942no—
579Q8M16×D4714yes—
580C2×C4—24no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—42no—
586C2×C4—471no—
587C2×C4—474no—
588C2×C4—471no—
589C2×C4—471no—
590C2×C4—471no—
591C2×C4—471no—
592C2×C4—471no—
593C2×C4—942no—
594C2×C4—942no—
595C2×C4—942no—
596C2×C4—942no—
597C2×C4—948no—
598C2×C4—948no—
599C2×C4—942no—
600C2×C4—944no—
601C2×C4—942no—
602C2×C4—942no—
603C2×C4—942no—
604C2×C4—942no—
605C2×C4—942no—
606C2×C4—941no—
607C2×C4—941no—
608C2×C4—941no—
609C2×C4—941no—
610C2×C4—942no—
611C2×C4—1881no—
612C2×C4—1881no—
613C2×C4—1884no—
614C2×C4—1884no—
615C2×C4—1881no—
616C2×C4—1882no—
617C2×C4C22⋊C4×D4711yescharacteristic
618C2×C4C22⋊C4×D4711yescharacteristic
619C2×C4C22⋊C4×D4711yescharacteristic
620C2×C4#1309405312yes—
621C2×C4#1309405612yes—
622C2×C4C22×C4×D4711yescharacteristic
623C2×C4C2×D4×D4711yescharacteristic
624C2×C4C2×D4×D4711yescharacteristic
625C8—42no—
626C8—42no—
627C8—1882no—
628C8—1882no—
629C22—21no—
630C22—21no—
631C22—472no—
632C22—472no—
633C22—948no—
634C22—941no—
635C22—941no—
636C22—941no—
637C22—941no—
638C22#1568913012yes—
639C22C2×C22⋊C4×D4711yescharacteristic
640C4—21no—
641C4—21no—
642C4—24no—
643C4—21no—
644C4—42no—
645C4—472no—
646C4—941no—
647C4—941no—
648C4—941no—
649C4—944no—
650C4—941no—
651C4—941no—
652C4—1882no—
653C4#1568913012yes—
654C4C2×M16×D4712yes—
655C4C2×#1309405311yescharacteristic
656C4C2×#1309405611yescharacteristic
657C2—22no—
658C2—942no—
659C2—942no—
660C2#407×D4711yescharacteristic
661C2C2×#1568913011yescharacteristic
662C2#421×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1487C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1487D47
hypocenterC47#17449
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
4. #20241833C2semidirect
5. #20241818C2semidirect
6. #20241817C2semidirect
7. #20241816C2semidirect
8. #20241781C2semidirect
9. C47×#1487C2semidirect
42. #15688855C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
44. #15688853C22semidirect
48. C47×Q8⋊C8C22semidirect
160. Q8×D47M16semidirect
333. #1487D47semidirect
379. Q8⋊C8C2×D47semidirect
380. C47#17449semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D472
#202520202
#202520162
#202418332
#202418182
#202418172
#202418162
#202417812
C47×#14872
#1744947