Finite Group Databasebeta

← #26182978

Subgroups — #26182978

Order 12032.

1026 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D47C211yesmaximal, characteristic
2#431×D47C211yesmaximal, characteristic
3C2×#15689145C211yesmaximal, characteristic
4#20241841C214yesmaximal, complemented
5#20241815C214yesmaximal, complemented
6#20241792C211yesmaximal, characteristic, complemented
7#20241791C211yesmaximal, characteristic, complemented
8#20241790C211yesmaximal, characteristic, complemented
9C47×#1481C211yesmaximal, characteristic, complemented
10C22×#10625324—21no—
11#15689680C2211yescharacteristic
12#15689679—21no—
13#15689678C411yescharacteristic
14#15689678C411yescharacteristic
15#15689677—21no—
16#15689677C2212yes—
17#15689676—21no—
18#15689675—21no—
19#15689675C412yes—
20C4⋊Q8×D47C411yescharacteristic
21C4⋊Q8×D47C411yescharacteristic
22#125×D47—21no—
23C22⋊Q8×D47—21no—
24C22⋊Q8×D47C412yes—
25C4×Q8×D47—21no—
26C4×Q8×D47C2212yes—
27#117×D47—21no—
28C2×C42×D47C2211yescharacteristic
29#15689176C2211yescharacteristic
30#15689175—21no—
31#15689174C2212yes—
32#15689173—21no—
33#15689145—21no—
34#15689145—21no—
35#15689145C2212yes—
36#15689145C2212yes—
37C2×C4⋊(C47⋊C8)C2211yescharacteristic
38C2×Dic47⋊C8—21no—
39C4⋊C8×D47—21no—
40C22⋊C8×D47—21no—
41C4×C8×D47C2212yes—
42#15688855C2214yescomplemented
43Q8⋊(C47⋊C8)C2214yescomplemented
44#15688853C2214yescomplemented
45C47×#533C2211yescharacteristic
46C47×#431C2211yescharacteristic
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×#10625324—22no—
55C2×#10625324—22no—
56C2×#10625324—44no—
57C22×C47⋊C8—21no—
58C2×C8×D47—22no—
59#13094024C2×C411yescharacteristic
60#13094024C2×C411yescharacteristic
61#13094023—21no—
62#13094023—21no—
63#13094023—21no—
64#13094023C2×C412yes—
65#13094022—21no—
66#13094022C2×C412yes—
67#13094016—21no—
68#13094015—21no—
69#13094015—21no—
70#13094014—22no—
71#13094014—22no—
72#13094004—21no—
73#13094004C2×C412yes—
74#13094003—21no—
75#13094003C2×C412yes—
76#13094002—22no—
77#13094002—22no—
78#13094001—22no—
79#13094001—22no—
80#13094000—21no—
81#13094000C2×C412yes—
82Q8×Dic47—21no—
83Q8×Dic47C2×C412yes—
84C4×Dic94—21no—
85C4×Dic94—22no—
86C4×Dic94—22no—
87C4×Dic94C2312yes—
88#13093989—21no—
89#13093989—22no—
90#13093989—22no—
91#13093989C2×C412yes—
92#13093983—21no—
93#13093982—21no—
94#13093982—21no—
95#13093981—22no—
96#13093980—22no—
97C4⋊C4×D47—21no—
98C4⋊C4×D47—21no—
99C4⋊C4×D47—21no—
100C4⋊C4×D47—22no—
101C4⋊C4×D47—22no—
102C4⋊C4×D47C2×C412yes—
103C22⋊C4×D47—22no—
104C2×C4×Dic47C2×C411yescharacteristic
105C2×C4×Dic47D411yescharacteristic
106C2×C4×Dic47D411yescharacteristic
107C42×D47—22no—
108C42×D47C2×C411yescharacteristic
109C42×D47C2×C411yescharacteristic
110C42×D47D411yescharacteristic
111C42×D47D411yescharacteristic
112C42×D47D411yescharacteristic
113C42×D47D411yescharacteristic
114C42×D47C2311yescharacteristic
115C42×D47C2311yescharacteristic
116C4⋊(C47⋊C8)—21no—
117C4⋊(C47⋊C8)—21no—
118C4⋊(C47⋊C8)C2312yes—
119Dic47⋊C8—22no—
120Dic47⋊C8—22no—
121Dic47⋊C8—22no—
122C22⋊(C47⋊C8)—21no—
123(C2×D47)⋊C8—22no—
124C4×C47⋊C8C2312yes—
125C8×Dic47—22no—
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×C47—21no—
138C4⋊C8×C47C2312yes—
139C22⋊C8×C47—21no—
140C4×C8×C47C2312yes—
141C23×D47C22⋊C411yescharacteristic
142C2×Q8×C47—21no—
143C2×Q8×C47C22×C412yes—
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×Dic47C22⋊C411yescharacteristic
148C22×Dic47C22⋊C411yescharacteristic
149C22×Dic47C22⋊C411yescharacteristic
150Q8×D47—44no—
151Q8×D47—44no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—42no—
155C2×C4×D47—42no—
156C2×C4×D47C22⋊C411yescharacteristic
157C2×C4×D47C22⋊C411yescharacteristic
158C2×C4×D47C22⋊C411yescharacteristic
159C2×C4×D47C22⋊C411yescharacteristic
160C2×C4×D47C22⋊C411yescharacteristic
161C2×C4×D47C22⋊C411yescharacteristic
162C2×C4×D47SD1614yes—
163C2×C4×D47Q1614yes—
164C2×C4×D47C22×C411yescharacteristic
165C2×C4×D47C22×C411yescharacteristic
166C2×C4×D47C2×D411yescharacteristic
167C2×C4×D47C2×D411yescharacteristic
168C2×C4×D47C2×D411yescharacteristic
169C2×C4×D47C2×D411yescharacteristic
170C2×Dic94—21no—
171C2×Dic94—22no—
172C2×Dic94—22no—
173C2×Dic94C22×C412yes—
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
221C2×C47⋊C8—22no—
222C2×C47⋊C8—22no—
223C2×C47⋊C8—42no—
224#10625324—44no—
225#10625324—44no—
226C8×D47—44no—
227C23×C47C2×C22⋊C411yescharacteristic
228C22×D47—41no—
229C22×D47—41no—
230C22×D47#10314yes—
231C22×D47C2×C22⋊C411yescharacteristic
232C22×D47C2×C22⋊C411yescharacteristic
233Q8×C47—24no—
234Q8×C47—42no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—41no—
239C2×C4×C47C2×C22⋊C411yescharacteristic
240C2×C4×C47C2×C22⋊C411yescharacteristic
241C2×C4×C47C2×C22⋊C411yescharacteristic
242C2×C4×C47C2×SD1612yes—
243C2×C4×C47C2×Q1612yes—
244C2×C4×C47C23×C411yescharacteristic
245C2×C4×C47C22×D411yescharacteristic
246C2×C4×C47C22×D411yescharacteristic
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—41no—
251C2×Dic47#10314yes—
252C2×Dic47C2×C22⋊C411yescharacteristic
253C2×Dic47C2×C22⋊C411yescharacteristic
254C2×Dic47C2×C22⋊C411yescharacteristic
255C2×Dic47C2×C22⋊C411yescharacteristic
256C2×Dic47C2×C22⋊C411yescharacteristic
257C2×Dic47C2×C22⋊C411yescharacteristic
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—41no—
263C4×D47—41no—
264C4×D47—41no—
265C4×D47—41no—
266C4×D47—44no—
267C4×D47—44no—
268C4×D47#10314yes—
269C4×D47#10314yes—
270C4×D47C2×SD1612yes—
271C4×D47C2×SD1612yes—
272C4×D47C2×Q1612yes—
273C4×D47C2×Q1612yes—
274Dic94—24no—
275Dic94—44no—
276Dic94—42no—
277Dic94—44no—
278C8×C47—42no—
279C8×C47—42no—
280C47⋊C8—42no—
281C47⋊C8—42no—
282#17486—471nomaximal, Sylow
283C22×C47—21no—
284C22×C47—21no—
285C22×C47C2×#10312yes—
286C22×C47C22×C22⋊C411yescharacteristic
287C2×D47—21no—
288C2×D47—21no—
289C2×D47—21no—
290C2×D47—21no—
291C2×D47—44no—
292C2×D47C2×#10312yes—
293C2×D47C2×#10312yes—
294C4×C47—21no—
295C4×C47—21no—
296C4×C47—21no—
297C4×C47—42no—
298C4×C47—42no—
299C4×C47C2×#10312yes—
300C4×C47#56812yes—
301C4×C47C22×SD1611yescharacteristic
302C4×C47C22×Q1611yescharacteristic
303Dic47—21no—
304Dic47—21no—
305Dic47—21no—
306Dic47—42no—
307Dic47—42no—
308Dic47C2×#10312yes—
309Dic47C2×#10312yes—
310Dic47#42112yes—
311C2×#533—471no—
312C2×#431—471no—
313C2×#423—471no—
314#1493—474no—
315#1487—474no—
316#1481—471no—
317#1481—471no—
318#1481—471no—
319#1481D4711yescharacteristic, complemented
320C2×C47—22no—
321C2×C47#287911yescharacteristic
322C2×C47C22×#10311yescharacteristic
323C2×C47C2×#42111yescharacteristic
324D47—22no—
325D47—22no—
326C22×M16—941no—
327#533—471no—
328#533—471no—
329#533—472no—
330#533—472no—
331#533—471no—
332#533—941no—
333#533—941no—
334#533—941no—
335#533—941no—
336#533C2×D4711yescharacteristic
337C2×C4⋊Q8—471no—
338C2×C4⋊Q8—471no—
339C2×#125—941no—
340C2×C22⋊Q8—472no—
341C2×C22⋊Q8—941no—
342C2×C4×Q8—472no—
343C2×C4×Q8—941no—
344C2×#117—941no—
345C22×C42—471no—
346#431—471no—
347#431—472no—
348#431—941no—
349#431—941no—
350#431C2×D4711yescharacteristic
351#423—472no—
352#423—472no—
353#423—941no—
354#423—941no—
355C2×C4⋊C8—471no—
356C2×C4⋊C8—941no—
357C2×C4⋊C8—941no—
358C2×C4⋊C8C2×D4711yescharacteristic
359C2×C22⋊C8—941no—
360C2×C4×C8—472no—
361Q8⋊C8—474no—
362Q8⋊C8—474no—
363Q8⋊C8—474no—
364Q8⋊C8C2×D4714yescomplemented
365C47#1748611yescharacteristic, complemented, Sylow
366C22×Q8—472no—
367C22×Q8—941no—
368C23×C4—471no—
369C23×C4—471no—
370C23×C4—471no—
371C2×M16—942no—
372C2×M16—942no—
373C2×M16—1884no—
374C22×C8—21no—
375C22×C8—942no—
376C22×C8—941no—
377C4⋊Q8—472no—
378C4⋊Q8—472no—
379C4⋊Q8—471no—
380C4⋊Q8—471no—
381C4⋊Q8—941no—
382C4⋊Q8—941no—
383C4⋊Q8—941no—
384C4⋊Q8—941no—
385C4⋊Q8C4×D4711yescharacteristic
386C4⋊Q8C4×D4711yescharacteristic
387#125—21no—
388#125—942no—
389#125—942no—
390#125—941no—
391#125—941no—
392#125—941no—
393C22⋊Q8—21no—
394C22⋊Q8—472no—
395C22⋊Q8—472no—
396C22⋊Q8—472no—
397C22⋊Q8—942no—
398C22⋊Q8—942no—
399C22⋊Q8—942no—
400C22⋊Q8—942no—
401C22⋊Q8—941no—
402C22⋊Q8—941no—
403C22⋊Q8—941no—
404C22⋊Q8C4×D4712yes—
405C4×Q8—21no—
406C4×Q8—472no—
407C4×Q8—472no—
408C4×Q8—472no—
409C4×Q8—942no—
410C4×Q8—942no—
411C4×Q8—942no—
412C4×Q8—941no—
413C4×Q8—942no—
414C4×Q8—941no—
415C4×Q8—941no—
416C4×Q8C22×D4712yes—
417#117—21no—
418#117—942no—
419#117—942no—
420#117—941no—
421#117—941no—
422#117—941no—
423C2×C4⋊C4—472no—
424C2×C4⋊C4—941no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—942no—
427C2×C4⋊C4—942no—
428C2×C4⋊C4—941no—
429C2×C22⋊C4—942no—
430C2×C42—471no—
431C2×C42—471no—
432C2×C42—471no—
433C2×C42—471no—
434C2×C42—471no—
435C2×C42—471no—
436C2×C42—471no—
437C2×C42—471no—
438C2×C42—471no—
439C2×C42—471no—
440C2×C42—471no—
441C2×C42—942no—
442C2×C42C22×D4711yescharacteristic
443C4⋊C8—21no—
444C4⋊C8—21no—
445C4⋊C8—472no—
446C4⋊C8—942no—
447C4⋊C8—942no—
448C4⋊C8—942no—
449C4⋊C8—941no—
450C4⋊C8—941no—
451C4⋊C8C22×D4712yes—
452C22⋊C8—21no—
453C22⋊C8—942no—
454C22⋊C8—941no—
455C4×C8—472no—
456C4×C8—942no—
457C4×C8C22×D4712yes—
458C24—471no—
459C2×Q8—21no—
460C2×Q8—472no—
461C2×Q8—942no—
462C2×Q8—942no—
463C2×Q8—941no—
464C2×Q8—1884no—
465C2×Q8—1884no—
466C2×Q8C2×C4×D4712yes—
467C22×C4—471no—
468C22×C4—471no—
469C22×C4—471no—
470C22×C4—474no—
471C22×C4—474no—
472C22×C4—471no—
473C22×C4—471no—
474C22×C4—471no—
475C22×C4—471no—
476C22×C4—471no—
477C22×C4—471no—
478C22×C4—471no—
479C22×C4—471no—
480C22×C4—471no—
481C22×C4—471no—
482C22×C4—471no—
483C22×C4—471no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—1882no—
487C22×C4—1882no—
488C22×C4C2×C4×D4711yescharacteristic
489C22×C4D4×D4711yescharacteristic
490C22×C4D4×D4711yescharacteristic
491M16—1884no—
492M16—1884no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—42no—
496C2×C8—942no—
497C2×C8—942no—
498C2×C8—1884no—
499C2×C8—1882no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—472no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—942no—
512C4⋊C4—942no—
513C4⋊C4—942no—
514C4⋊C4—942no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4—941no—
518C4⋊C4—942no—
519C4⋊C4C2×C4×D4712yes—
520C22⋊C4—22no—
521C22⋊C4—942no—
522C22⋊C4—942no—
523C22⋊C4—942no—
524C42—22no—
525C42—471no—
526C42—471no—
527C42—471no—
528C42—471no—
529C42—471no—
530C42—471no—
531C42—471no—
532C42—471no—
533C42—471no—
534C42—471no—
535C42—471no—
536C42—471no—
537C42—942no—
538C42—942no—
539C42—942no—
540C42C2×C4×D4711yescharacteristic
541C42D4×D4711yescharacteristic
542C42D4×D4711yescharacteristic
543C42C23×D4711yescharacteristic
544C23—471no—
545C23—471no—
546C23—474no—
547C23—1881no—
548C23—1881no—
549C23C22⋊C4×D4711yescharacteristic
550Q8—24no—
551Q8—42no—
552Q8—944no—
553Q8—1882no—
554Q8—1884no—
555Q8—1884no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—41no—
560C2×C4—471no—
561C2×C4—471no—
562C2×C4—471no—
563C2×C4—474no—
564C2×C4—474no—
565C2×C4—474no—
566C2×C4—472no—
567C2×C4—472no—
568C2×C4—472no—
569C2×C4—472no—
570C2×C4—471no—
571C2×C4—471no—
572C2×C4—471no—
573C2×C4—942no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4—1884no—
585C2×C4—1884no—
586C2×C4—1881no—
587C2×C4C22⋊C4×D4711yescharacteristic
588C2×C4C22⋊C4×D4711yescharacteristic
589C2×C4C22⋊C4×D4711yescharacteristic
590C2×C4SD16×D4712yes—
591C2×C4Q16×D4712yes—
592C2×C4C22×C4×D4711yescharacteristic
593C2×C4C2×D4×D4711yescharacteristic
594C2×C4C2×D4×D4711yescharacteristic
595C8—42no—
596C8—42no—
597C8—1882no—
598C8—1882no—
599C22—21no—
600C22—21no—
601C22—472no—
602C22—472no—
603C22—941no—
604C22—941no—
605C22—941no—
606C22—941no—
607C22—1884no—
608C22#103×D4712yes—
609C22C2×C22⋊C4×D4711yescharacteristic
610C4—21no—
611C4—21no—
612C4—21no—
613C4—42no—
614C4—42no—
615C4—472no—
616C4—472no—
617C4—472no—
618C4—941no—
619C4—941no—
620C4—941no—
621C4—1882no—
622C4—1882no—
623C4#103×D4712yes—
624C4#1568988812yes—
625C4C2×SD16×D4711yescharacteristic
626C4C2×Q16×D4711yescharacteristic
627C2—22no—
628C2—942no—
629C2—942no—
630C2#2025183011yescharacteristic
631C2C2×#103×D4711yescharacteristic
632C2#421×D4711yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1481C2
socleC22×C47C22×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC42×C47C24
hypercenter#1481D47
hypocenterC47#17486
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1481

Complements

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

NH ≅ G/Ntype
4. #20241841C2semidirect
5. #20241815C2semidirect
6. #20241792C2semidirect
7. #20241791C2semidirect
8. #20241790C2semidirect
9. C47×#1481C2semidirect
42. #15688855C22semidirect
43. Q8⋊(C47⋊C8)C22semidirect
44. #15688853C22semidirect
48. C47×Q8⋊C8C22semidirect
319. #1481D47semidirect
364. Q8⋊C8C2×D47semidirect
365. C47#17486semidirect

Maximal subgroups

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

subgroupindex
#533×D472
#431×D472
C2×#156891452
#202418412
#202418152
#202417922
#202417912
#202417902
C47×#14812
#1748647