Finite Group Databasebeta

← #26182722

Subgroups — #26182722

Order 12032.

1214 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D47C211yesmaximal, characteristic
2#20252016C211yesmaximal, characteristic
3#20252016C211yesmaximal, characteristic
4#20241833C214yesmaximal, complemented
5#20241815C214yesmaximal, complemented
6#20241784C211yesmaximal, characteristic, complemented
7#20241783C211yesmaximal, characteristic, complemented
8#20241782C211yesmaximal, characteristic, complemented
9C47×#1479C211yesmaximal, 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#15689179C2212yes—
30#15689177—21no—
31#15689177—21no—
32#15689176C2211yescharacteristic
33#15689176C2211yescharacteristic
34#15689174—21no—
35#15689174C2212yes—
36#15689145—21no—
37#15689145C2212yes—
38#15689085—21no—
39#15689085—21no—
40C4×#10625324—21no—
41C4×#10625324C2212yes—
42#15688855C2214yescomplemented
43Q8⋊(C47⋊C8)C2214yescomplemented
44#15688853C2214yescomplemented
45C2×C4×Q8×C47C2211yescharacteristic
46C47×#431C2211yescharacteristic
47C47×#431C2211yescharacteristic
48C47×Q8⋊C8C2214yescomplemented
49C22×Dic94—21no—
50C22×Dic94C2×C411yescharacteristic
51C2×Q8×D47—24no—
52C2×Q8×D47—21no—
53C2×Q8×D47—21no—
54C2×Q8×D47—24no—
55C2×Q8×D47C2×C412yes—
56C2×Q8×D47C2×C412yes—
57C22×C4×D47—21no—
58C22×C4×D47—21no—
59C22×C4×D47C2×C411yescharacteristic
60C22×C4×D47D411yescharacteristic
61C22×C4×D47D411yescharacteristic
62C2×#10625324—22no—
63C2×#10625324—22no—
64Q8×Dic47—21no—
65Q8×Dic47—21no—
66Q8×Dic47C2×C412yes—
67Q8×Dic47C2×C412yes—
68C4×Dic94—21no—
69C4×Dic94—21no—
70C4×Dic94—22no—
71C4×Dic94—22no—
72C4×Dic94—22no—
73C4×Dic94—22no—
74C4×Dic94C2×C412yes—
75C4×Dic94C2312yes—
76#13093989—21no—
77#13093989—21no—
78#13093989—22no—
79#13093989—22no—
80#13093989—22no—
81#13093989—22no—
82#13093989C2×C412yes—
83#13093989C2×C412yes—
84C2×C4⋊Dic47—21no—
85C2×C4⋊Dic47C2×C411yescharacteristic
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C4⋊C4×D47—22no—
90C4⋊C4×D47—22no—
91C4⋊C4×D47—21no—
92C4⋊C4×D47—21no—
93C4⋊C4×D47—22no—
94C4⋊C4×D47—22no—
95C4⋊C4×D47C2×C412yes—
96C4⋊C4×D47C2×C412yes—
97C2×C4×Dic47—21no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47—21no—
100C2×C4×Dic47C2×C411yescharacteristic
101C2×C4×Dic47D411yescharacteristic
102C2×C4×Dic47D411yescharacteristic
103C42×D47—22no—
104C42×D47—22no—
105C42×D47—22no—
106C42×D47—22no—
107C42×D47C2×C411yescharacteristic
108C42×D47C2×C411yescharacteristic
109C42×D47D411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47D411yescharacteristic
112C42×D47D411yescharacteristic
113C42×D47C2311yescharacteristic
114C42×D47C2311yescharacteristic
115C4⋊(C47⋊C8)—21no—
116C4⋊(C47⋊C8)C2312yes—
117Dic47⋊C8—22no—
118Dic47⋊C8—22no—
119C22⋊(C47⋊C8)—21no—
120C22⋊(C47⋊C8)—21no—
121(C2×D47)⋊C8—22no—
122(C2×D47)⋊C8—22no—
123#13093934—22no—
124#13093934—22no—
125C4×C47⋊C8—21no—
126C4×C47⋊C8C2312yes—
127C22×Q8×C47C2×C411yescharacteristic
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×C47C2312yes—
138C22⋊C8×C47—21no—
139C22⋊C8×C47—21no—
140C4×C8×C47—21no—
141C4×C8×C47C2312yes—
142C23×D47C22⋊C411yescharacteristic
143C2×Q8×C47—21no—
144C2×Q8×C47—22no—
145C2×Q8×C47M1614yescomplemented
146C2×Q8×C47C22×C412yes—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47C22⋊C411yescharacteristic
155C22×Dic47C22⋊C411yescharacteristic
156C22×Dic47C22⋊C411yescharacteristic
157Q8×D47—28no—
158Q8×D47—28no—
159Q8×D47—24no—
160Q8×D47—24no—
161Q8×D47—24no—
162Q8×D47—24no—
163C2×C4×D47—28no—
164C2×C4×D47—22no—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—24no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—42no—
172C2×C4×D47—44no—
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×D47C22×C411yescharacteristic
180C2×C4×D47C22×C411yescharacteristic
181C2×C4×D47C2×D411yescharacteristic
182C2×C4×D47C2×D411yescharacteristic
183C2×C4×D47C2×D411yescharacteristic
184C2×C4×D47C2×D411yescharacteristic
185C2×Dic94—28no—
186C2×Dic94—21no—
187C2×Dic94—22no—
188C2×Dic94—22no—
189C2×Dic94—22no—
190C2×Dic94M1614yescomplemented
191C2×Dic94C22×C412yes—
192C2×C8×C47—22no—
193C2×C8×C47—22no—
194C4⋊C4×C47—22no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—22no—
197C4⋊C4×C47C22×C412yes—
198C42×C47—22no—
199C42×C47—22no—
200C42×C47C22×C411yescharacteristic
201C42×C47C2×D411yescharacteristic
202C42×C47C2×D411yescharacteristic
203C42×C47C2411yescharacteristic
204C4⋊Dic47—21no—
205C4⋊Dic47—22no—
206C4⋊Dic47—22no—
207C4⋊Dic47C22×C412yes—
208Dic47⋊C4—22no—
209Dic47⋊C4—22no—
210Dic47⋊C4—22no—
211Dic47⋊C4—22no—
212Dic47⋊C4—22no—
213Dic47⋊C4—22no—
214C4×Dic47—22no—
215C4×Dic47—22no—
216C4×Dic47—22no—
217C4×Dic47—22no—
218C4×Dic47—22no—
219C4×Dic47—22no—
220C4×Dic47C22⋊C411yescharacteristic
221C4×Dic47C22⋊C411yescharacteristic
222C4×Dic47C22⋊C411yescharacteristic
223C4×Dic47C22⋊C411yescharacteristic
224C4×Dic47C22⋊C411yescharacteristic
225C4×Dic47C22⋊C411yescharacteristic
226C4×Dic47C22×C411yescharacteristic
227C4×Dic47C22×C411yescharacteristic
228C4×Dic47C2×D411yescharacteristic
229C4×Dic47C2×D411yescharacteristic
230C4×Dic47C2×D411yescharacteristic
231C4×Dic47C2×D411yescharacteristic
232C2×C47⋊C8—22no—
233C2×C47⋊C8—22no—
234#10625324—44no—
235#10625324—44no—
236C23×C47C2×C22⋊C411yescharacteristic
237C22×D47—22no—
238C22×D47—22no—
239C22×D47—22no—
240C22×D47C2×C22⋊C411yescharacteristic
241C22×D47C2×C22⋊C411yescharacteristic
242Q8×C47—22no—
243Q8×C47—24no—
244Q8×C47C2×M1614yes—
245C2×C4×C47—22no—
246C2×C4×C47—24no—
247C2×C4×C47—22no—
248C2×C4×C47—22no—
249C2×C4×C47—41no—
250C2×C4×C47—42no—
251C2×C4×C47C2×C22⋊C411yescharacteristic
252C2×C4×C47C2×C22⋊C411yescharacteristic
253C2×C4×C47C2×C22⋊C411yescharacteristic
254C2×C4×C47C2×M1612yes—
255C2×C4×C47C2×M1612yes—
256C2×C4×C47C23×C411yescharacteristic
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C22×D411yescharacteristic
259C2×Dic47—22no—
260C2×Dic47—22no—
261C2×Dic47—24no—
262C2×Dic47—22no—
263C2×Dic47—22no—
264C2×Dic47—41no—
265C2×Dic47—42no—
266C2×Dic47C2×C22⋊C411yescharacteristic
267C2×Dic47C2×C22⋊C411yescharacteristic
268C2×Dic47C2×C22⋊C411yescharacteristic
269C2×Dic47C2×C22⋊C411yescharacteristic
270C2×Dic47C2×C22⋊C411yescharacteristic
271C2×Dic47C2×C22⋊C411yescharacteristic
272C4×D47—28no—
273C4×D47—28no—
274C4×D47—22no—
275C4×D47—22no—
276C4×D47—22no—
277C4×D47—21no—
278C4×D47—21no—
279C4×D47—21no—
280C4×D47—21no—
281C4×D47—22no—
282C4×D47—22no—
283C4×D47—22no—
284C4×D47—22no—
285C4×D47—41no—
286C4×D47—41no—
287C4×D47—44no—
288C4×D47—44no—
289C4×D47#13714yes—
290Dic94—28no—
291Dic94—28no—
292Dic94—22no—
293Dic94—24no—
294Dic94C2×M1614yes—
295C8×C47—42no—
296C8×C47—42no—
297C47⋊C8—42no—
298C47⋊C8—42no—
299#17449—471nomaximal, Sylow
300C22×C47—21no—
301C22×C47—21no—
302C22×C47#40712yes—
303C22×C47C22×C22⋊C411yescharacteristic
304C2×D47—28no—
305C2×D47—21no—
306C2×D47—21no—
307C2×D47—21no—
308C2×D47—21no—
309C2×D47#41912yes—
310C2×D47#42112yes—
311C4×C47—24no—
312C4×C47—21no—
313C4×C47—21no—
314C4×C47—21no—
315C4×C47—42no—
316C4×C47#40712yes—
317C4×C47C22×M1611yescharacteristic
318C4×C47C22×M1611yescharacteristic
319C4×C47C2×#13712yes—
320Dic47—21no—
321Dic47—21no—
322Dic47—24no—
323Dic47—21no—
324Dic47—21no—
325Dic47—21no—
326Dic47—42no—
327Dic47#41912yes—
328C22×C4×Q8—471no—
329#2920—471no—
330#2920—471no—
331#1491—474no—
332#1487—474no—
333#1479—471no—
334#1479—471no—
335#1479—471no—
336#1479D4711yescharacteristic, complemented
337C2×C47—22no—
338C2×C47C2×#40711yescharacteristic
339C2×C47C2×#41911yescharacteristic
340C2×C47C2×#42111yescharacteristic
341D47—22no—
342D47—22no—
343C23×Q8—471no—
344C2×C4×Q8—471no—
345C2×C4×Q8—472no—
346C2×C4×Q8—472no—
347C2×C4×Q8—472no—
348C2×C4×Q8—472no—
349C2×C4×Q8—471no—
350C2×C4×Q8—471no—
351C2×C4×Q8—941no—
352C2×C4×Q8—941no—
353C2×C4×Q8—941no—
354C2×C4×Q8—941no—
355C2×C4×Q8—941no—
356C2×C4×Q8—941no—
357C2×C4×Q8C2×D4711yescharacteristic
358C22×C4⋊C4—471no—
359C22×C4⋊C4—941no—
360C22×C42—471no—
361C22×C42—941no—
362#432—472no—
363#432—941no—
364#432—941no—
365#432—941no—
366#431—471no—
367#431—472no—
368#431—471no—
369#431—941no—
370#431C2×D4711yescharacteristic
371#431C2×D4711yescharacteristic
372#423—472no—
373#423—941no—
374#407—941no—
375#407—941no—
376C4×M16—472no—
377C4×M16—941no—
378Q8⋊C8—474no—
379Q8⋊C8—474no—
380Q8⋊C8—474no—
381Q8⋊C8C2×D4714yescomplemented
382C47#1744911yescharacteristic, complemented, Sylow
383C22×Q8—472no—
384C22×Q8—472no—
385C22×Q8—471no—
386C22×Q8—941no—
387C22×Q8—941no—
388C22×Q8—941no—
389C22×Q8—944no—
390C22×Q8—944no—
391C22×Q8C4×D4711yescharacteristic
392C23×C4—471no—
393C23×C4—471no—
394C23×C4—471no—
395C23×C4—941no—
396C23×C4—941no—
397C2×M16—942no—
398C2×M16—942no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8—472no—
402C4×Q8—472no—
403C4×Q8—472no—
404C4×Q8—472no—
405C4×Q8—472no—
406C4×Q8—472no—
407C4×Q8—942no—
408C4×Q8—942no—
409C4×Q8—942no—
410C4×Q8—942no—
411C4×Q8—942no—
412C4×Q8—942no—
413C4×Q8—941no—
414C4×Q8—941no—
415C4×Q8—942no—
416C4×Q8—942no—
417C4×Q8—941no—
418C4×Q8—941no—
419C4×Q8—941no—
420C4×Q8—941no—
421C4×Q8C4×D4712yes—
422C4×Q8C22×D4712yes—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—471no—
425C2×C4⋊C4—472no—
426C2×C4⋊C4—472no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4—942no—
430C2×C4⋊C4—942no—
431C2×C4⋊C4—942no—
432C2×C4⋊C4—942no—
433C2×C4⋊C4—941no—
434C2×C4⋊C4—941no—
435C2×C4⋊C4—941no—
436C2×C4⋊C4—941no—
437C2×C4⋊C4C4×D4711yescharacteristic
438C2×C42—21no—
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—471no—
449C2×C42—471no—
450C2×C42—942no—
451C2×C42—942no—
452C2×C42—942no—
453C2×C42—942no—
454C2×C42—941no—
455C2×C42—941no—
456C2×C42—941no—
457C2×C42C22×D4711yescharacteristic
458C4⋊C8—21no—
459C4⋊C8—472no—
460C4⋊C8—942no—
461C4⋊C8—942no—
462C4⋊C8—941no—
463C4⋊C8C22×D4712yes—
464C22⋊C8—21no—
465C22⋊C8—21no—
466C22⋊C8—942no—
467C22⋊C8—942no—
468C22⋊C8—941no—
469C22⋊C8—941no—
470#97—942no—
471#97—942no—
472C4×C8—21no—
473C4×C8—472no—
474C4×C8—941no—
475C4×C8C22×D4712yes—
476C24—471no—
477C2×Q8—21no—
478C2×Q8—22no—
479C2×Q8—474no—
480C2×Q8—472no—
481C2×Q8—942no—
482C2×Q8—942no—
483C2×Q8—948no—
484C2×Q8—944no—
485C2×Q8—944no—
486C2×Q8—948no—
487C2×Q8—948no—
488C2×Q8—944no—
489C2×Q8—944no—
490C2×Q8—941no—
491C2×Q8—942no—
492C2×Q8#1062532414yescomplemented
493C2×Q8C2×C4×D4712yes—
494C22×C4—21no—
495C22×C4—21no—
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—471no—
507C22×C4—471no—
508C22×C4—471no—
509C22×C4—471no—
510C22×C4—471no—
511C22×C4—944no—
512C22×C4—942no—
513C22×C4—942no—
514C22×C4—948no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—941no—
518C22×C4—942no—
519C22×C4—942no—
520C22×C4—941no—
521C22×C4—1882no—
522C22×C4—1884no—
523C22×C4C2×C4×D4711yescharacteristic
524C22×C4D4×D4711yescharacteristic
525C22×C4D4×D4711yescharacteristic
526M16—1884no—
527M16—1884no—
528C2×C8—22no—
529C2×C8—22no—
530C2×C8—942no—
531C2×C8—942no—
532C4⋊C4—22no—
533C4⋊C4—21no—
534C4⋊C4—22no—
535C4⋊C4—472no—
536C4⋊C4—942no—
537C4⋊C4—942no—
538C4⋊C4—942no—
539C4⋊C4—942no—
540C4⋊C4—942no—
541C4⋊C4—942no—
542C4⋊C4—942no—
543C4⋊C4—941no—
544C4⋊C4—942no—
545C4⋊C4C2×C4×D4712yes—
546C42—22no—
547C42—22no—
548C42—471no—
549C42—471no—
550C42—471no—
551C42—471no—
552C42—471no—
553C42—471no—
554C42—471no—
555C42—471no—
556C42—471no—
557C42—471no—
558C42—471no—
559C42—471no—
560C42—942no—
561C42—942no—
562C42—942no—
563C42—942no—
564C42—942no—
565C42—942no—
566C42C2×C4×D4711yescharacteristic
567C42D4×D4711yescharacteristic
568C42D4×D4711yescharacteristic
569C42C23×D4711yescharacteristic
570C23—471no—
571C23—471no—
572C23—942no—
573C23—942no—
574C23—942no—
575C23C22⋊C4×D4711yescharacteristic
576Q8—24no—
577Q8—22no—
578Q8—474no—
579Q8—948no—
580Q8—948no—
581Q8—944no—
582Q8—942no—
583Q8C2×#1062532414yes—
584C2×C4—22no—
585C2×C4—24no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—41no—
589C2×C4—42no—
590C2×C4—471no—
591C2×C4—474no—
592C2×C4—471no—
593C2×C4—471no—
594C2×C4—471no—
595C2×C4—471no—
596C2×C4—471no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—948no—
602C2×C4—948no—
603C2×C4—942no—
604C2×C4—942no—
605C2×C4—942no—
606C2×C4—944no—
607C2×C4—942no—
608C2×C4—942no—
609C2×C4—941no—
610C2×C4—941no—
611C2×C4—941no—
612C2×C4—941no—
613C2×C4—942no—
614C2×C4—942no—
615C2×C4—1881no—
616C2×C4—1881no—
617C2×C4—1884no—
618C2×C4—1884no—
619C2×C4—1881no—
620C2×C4—1882no—
621C2×C4C22⋊C4×D4711yescharacteristic
622C2×C4C22⋊C4×D4711yescharacteristic
623C2×C4C22⋊C4×D4711yescharacteristic
624C2×C4M16×D4712yes—
625C2×C4C2×#1062532412yes—
626C2×C4C22×C4×D4711yescharacteristic
627C2×C4C2×D4×D4711yescharacteristic
628C2×C4C2×D4×D4711yescharacteristic
629C8—42no—
630C8—42no—
631C8—1882no—
632C8—1882no—
633C22—21no—
634C22—21no—
635C22—472no—
636C22—472no—
637C22—948no—
638C22—941no—
639C22—941no—
640C22—941no—
641C22—941no—
642C22#1568908512yes—
643C22C2×C22⋊C4×D4711yescharacteristic
644C4—21no—
645C4—21no—
646C4—24no—
647C4—21no—
648C4—42no—
649C4—472no—
650C4—941no—
651C4—941no—
652C4—941no—
653C4—941no—
654C4—944no—
655C4—941no—
656C4—1882no—
657C4#1568908512yes—
658C4C2×M16×D4711yescharacteristic
659C4C22×#1062532411yescharacteristic
660C4#137×D4712yes—
661C2—22no—
662C2—942no—
663C2—942no—
664C2C2×#1568908511yescharacteristic
665C2#419×D4711yescharacteristic
666C2#421×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1479C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1479D47
hypocenterC47#17449
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1479

Complements

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

NH ≅ G/Ntype
4. #20241833C2semidirect
5. #20241815C2semidirect
6. #20241784C2semidirect
7. #20241783C2semidirect
8. #20241782C2semidirect
9. C47×#1479C2semidirect
42. #15688855C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
44. #15688853C22semidirect
48. C47×Q8⋊C8C22semidirect
145. C2×Q8×C47M16semidirect
190. C2×Dic94M16semidirect
336. #1479D47semidirect
381. Q8⋊C8C2×D47semidirect
382. C47#17449semidirect
492. C2×Q8#10625324semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D472
#202520162
#202418332
#202418152
#202417842
#202417832
#202417822
C47×#14792
#1744947