Finite Group Databasebeta

← #26121739

Subgroups — #26121739

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#10625350C211yesmaximal, characteristic
2C2×#15689141C211yesmaximal, characteristic
3#20251908C211yesmaximal, characteristic
4C2×#15688895C211yesmaximal, characteristic, complemented
5#20243120C211yesmaximal, characteristic, complemented
6C2×#15688883C211yesmaximal, characteristic, complemented
7C2×C47×#339C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C4×#10625350—22no—
11C4×#10625350—22no—
12C4×#10625350—22no—
13C4×#10625350C414yescomplemented
14C2×C4×Dic94—21no—
15C2×C4×D188—21no—
16C2×C4×C22⋊D47—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19C2×#13093981—21no—
20C2×C42×D47—21no—
21#15689141—22no—
22#15689141C414yescomplemented
23C2×#13093952—22no—
24#15689133—21no—
25#15689129—21no—
26#15689125C414yescomplemented
27#15689120—22no—
28#15688895—22no—
29#15688889—22no—
30#15688883—21no—
31#15688883—21no—
32C22×M16×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C22×C42×C47C2211yescharacteristic
35C47×#339—22no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350C2×C412yes—
43C2×#10625350C2×C412yes—
44C2×#10625350C2×C412yes—
45C2×#10625350D412yes—
46C2×#10625350D412yes—
47C2×#10625350Q812yes—
48C22×Dic94D411yescharacteristic
49C22×D188D411yescharacteristic
50C22×C22⋊D47—21no—
51C22×C4×D47—21no—
52C22×C4×D47—22no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329C2×C412yescomplemented
59C22×C47⋊C8—21no—
60C4×Dic94—24no—
61C4×Dic94—24no—
62C4×D188—24no—
63C4×D188—24no—
64C4×C22⋊D47—28no—
65C4×C22⋊D47—28no—
66#13093983—21no—
67#13093983—21no—
68#13093983—21no—
69#13093983—21no—
70#13093983—21no—
71#13093983—21no—
72#13093983C2×C412yes—
73#13093983D412yes—
74#13093981—24no—
75#13093981—24no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47C2×C412yescomplemented
78C2×Dic47⋊C4—22no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47D412yes—
81C2×(C2×D47)⋊C4—22no—
82C2×C4×Dic47—22no—
83C2×C4×Dic47—21no—
84C2×C4×Dic47—21no—
85C42×D47—24no—
86C42×D47—24no—
87#13093952—28no—
88#13093949—24no—
89#13093946—24no—
90C23×C4×C47—21no—
91C23×C4×C47C2311yescharacteristic
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47—21no—
97C2×M16×C47C2×C412yescomplemented
98C22×C8×C47—21no—
99#117×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102#117×C47C2×C412yescomplemented
103C2×C4⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C42×C47—21no—
106C2×C42×C47—21no—
107C2×C42×C47—21no—
108C2×C42×C47—21no—
109C2×C42×C47C2×C412yes—
110C2×C42×C47D411yescharacteristic
111C2×C42×C47D411yescharacteristic
112C2×C42×C47D412yes—
113C24×C47C2×D411yescharacteristic
114C23×D47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—22no—
117C22×C4×C47—21no—
118C22×C4×C47—22no—
119C22×C4×C47—44no—
120C22×C4×C47—41no—
121C22×C4×C47C22×C411yescharacteristic
122C22×C4×C47C22×C411yescharacteristic
123C22×C4×C47C22×C411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×Q811yescharacteristic
131C22×C4×C47#4111yescharacteristic
132C22×C4×C47#4111yescharacteristic
133C22×C4×C47#4111yescharacteristic
134C22×C4×C47#4111yescharacteristic
135C2×C22⋊D47—22no—
136C2×C22⋊D47—22no—
137C2×C22⋊D47—22no—
138C2×C22⋊D47—22no—
139C2×C22⋊D47—22no—
140C2×C22⋊D47—22no—
141C22×Dic47—21no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144#10625350—22no—
145#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149#10625350—22no—
150#10625350—22no—
151#10625350—22no—
152#10625350—22no—
153#10625350—22no—
154#10625350—22no—
155#10625350—22no—
156#10625350C4214yes—
157#10625350C22⋊C414yes—
158#10625350C4⋊C414yes—
159#10625350C4⋊C414yes—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188—21no—
163C2×D188C22⋊C412yes—
164C2×D188C22⋊C412yes—
165C2×D188C4⋊C412yes—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—22no—
170C2×C4×D47—22no—
171C2×C4×D47—22no—
172C2×C4×D47—28no—
173C2×C4×D47—48no—
174C2×Dic94—21no—
175C2×Dic94—21no—
176C2×Dic94—21no—
177C2×Dic94C22⋊C412yes—
178C2×Dic94C22⋊C412yes—
179C2×Dic94C4⋊C412yes—
180M16×C47—22no—
181M16×C47—22no—
182M16×C47—41no—
183M16×C47—41no—
184C2×C8×C47—22no—
185C2×C8×C47—41no—
186C2×C8×C47—41no—
187C4⋊C4×C47—22no—
188C4⋊C4×C47—41no—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—41no—
191C42×C47—22no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—22no—
195C42×C47—22no—
196C42×C47—41no—
197C42×C47C22⋊C412yes—
198C42×C47C22⋊C412yes—
199C22⋊Dic47—22no—
200C22⋊Dic47—41no—
201C22⋊Dic47—41no—
202C22⋊Dic47C22⋊C414yes—
203(C2×D47)⋊C4—28no—
204C4⋊Dic47—22no—
205C4⋊Dic47—22no—
206C4⋊Dic47—22no—
207C4⋊Dic47—22no—
208Dic47⋊C4—28no—
209C4×Dic47—28no—
210C4×Dic47—22no—
211C4×Dic47—22no—
212C4×Dic47—41no—
213C4×Dic47—41no—
214#10625329—22no—
215#10625329—22no—
216#10625329—41no—
217#10625329—41no—
218C2×C47⋊C8—22no—
219C2×C47⋊C8—41no—
220C2×C47⋊C8—41no—
221C23×C47—42no—
222C23×C47C2×C22⋊C411yescharacteristic
223C23×C47C4×D411yescharacteristic
224C23×C47C4×D411yescharacteristic
225C23×C47#12011yescharacteristic
226C23×C47#12011yescharacteristic
227C23×C47#12111yescharacteristic
228C23×C47C22⋊Q811yescharacteristic
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—22no—
232C22×D47—44no—
233C2×C4×C47—24no—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—44no—
237C2×C4×C47—44no—
238C2×C4×C47—42no—
239C2×C4×C47—42no—
240C2×C4×C47—82no—
241C2×C4×C47C2×C4211yescharacteristic
242C2×C4×C47C2×C22⋊C411yescharacteristic
243C2×C4×C47C2×C22⋊C411yescharacteristic
244C2×C4×C47C2×C22⋊C411yescharacteristic
245C2×C4×C47C2×C22⋊C411yescharacteristic
246C2×C4×C47C2×C4⋊C411yescharacteristic
247C2×C4×C47C2×C4⋊C411yescharacteristic
248C2×C4×C47C2×C4⋊C411yescharacteristic
249C2×C4×C47#11711yescharacteristic
250C2×C4×C47#11711yescharacteristic
251C2×C4×C47C4×D411yescharacteristic
252C2×C4×C47C4×D411yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C4×D411yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C4×D411yescharacteristic
257C2×C4×C47#12011yescharacteristic
258C2×C4×C47#12011yescharacteristic
259C2×C4×C47#12111yescharacteristic
260C2×C4×C47#12111yescharacteristic
261C2×C4×C47#12111yescharacteristic
262C2×C4×C47C22⋊Q811yescharacteristic
263C2×C4×C47C22⋊Q811yescharacteristic
264C2×C4×C47C22⋊Q811yescharacteristic
265C2×C4×C47#12311yescharacteristic
266C2×C4×C47#12311yescharacteristic
267C2×C4×C47#12311yescharacteristic
268C2×C4×C47#12311yescharacteristic
269C22⋊D47—24no—
270C22⋊D47—24no—
271C22⋊D47—24no—
272C22⋊D47—24no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—24no—
277C2×Dic47—44no—
278C2×Dic47—42no—
279C2×Dic47—82no—
280D188—22no—
281D188—22no—
282D188—22no—
283D188#9514yes—
284C4×D47—24no—
285C4×D47—24no—
286C4×D47—24no—
287C4×D47—24no—
288C4×D47—416no—
289Dic94—22no—
290Dic94—22no—
291Dic94—22no—
292Dic94#9514yes—
293C8×C47—42no—
294C47⋊C8—42no—
295#10772—471nomaximal, Sylow
296C22×C47—22no—
297C22×C47—22no—
298C22×C47—22no—
299C22×C47—41no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—41no—
303C22×C47C4×C22⋊C411yescharacteristic
304C22×C47#37911yescharacteristic
305C22×C47#38011yescharacteristic
306C22×C47#38511yescharacteristic
307C22×C47#38511yescharacteristic
308C22×C47#38611yescharacteristic
309C22×C47#38611yescharacteristic
310C2×D47—24no—
311C2×D47—44no—
312C2×D47—44no—
313C2×D47—44no—
314C4×C47—24no—
315C4×C47—42no—
316C4×C47—82no—
317C4×C47C2×#9511yescharacteristic
318C4×C47C4×C22⋊C411yescharacteristic
319C4×C47#38011yescharacteristic
320C4×C47#38111yescharacteristic
321C4×C47#38511yescharacteristic
322C4×C47#38511yescharacteristic
323C4×C47#38611yescharacteristic
324C4×C47#38611yescharacteristic
325Dic47—24no—
326Dic47—44no—
327Dic47—82no—
328C2×C4×#41—471no—
329C2×#421—471no—
330#2896—471no—
331C2×#344—471no—
332#1740—471no—
333C2×#339—471no—
334C2×#339D4711yescharacteristic, complemented
335C2×C47—21no—
336C2×C47—21no—
337C2×C47—21no—
338C2×C47—21no—
339C2×C47—21no—
340C2×C47—21no—
341C2×C47C22⋊#9511yescharacteristic
342C2×C47#190612yes—
343D47—44no—
344C22×#41—471no—
345C22×M16—471no—
346C22×M16C2×D4711yescharacteristic
347C4×#41—474no—
348C4×#41—942no—
349C4×#41—942no—
350C4×#41—942no—
351C2×C4×Q8—941no—
352C2×C4×D4—941no—
353C2×C4×D4—942no—
354C2×#117—471no—
355C2×#117—471no—
356C2×#117—941no—
357C2×#117C2×D4711yescharacteristic
358C22×C42—941no—
359C22×C42C2×D4711yescharacteristic
360#421—474no—
361#421—942no—
362C2×#104—942no—
363#419—941no—
364#418—941no—
365#417—474no—
366#416—942no—
367#344—942no—
368#342—942no—
369#339—22no—
370#339—941no—
371#339—941no—
372C47#1077211yescharacteristic, complemented, Sylow
373C2×#41—472no—
374C2×#41—472no—
375C2×#41—472no—
376C2×#41—472no—
377C2×#41—472no—
378C2×#41—472no—
379C2×#41—941no—
380C2×#41—941no—
381C2×#41—941no—
382C2×#41—941no—
383C2×#41—941no—
384C2×#41—941no—
385C22×Q8—471no—
386C22×D4—471no—
387C22×D4—941no—
388C23×C4—21no—
389C23×C4—942no—
390C23×C4—941no—
391C23×C4C22×D4711yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C2×M16—21no—
396C2×M16—21no—
397C2×M16—472no—
398C2×M16—941no—
399C2×M16—941no—
400C2×M16—941no—
401C2×M16—941no—
402C2×M16—941no—
403C2×M16C4×D4712yescomplemented
404C22×C8—21no—
405C22×C8—941no—
406C4×Q8—944no—
407C4×Q8—944no—
408C4×D4—944no—
409C4×D4—944no—
410C4×D4—948no—
411C4×D4—948no—
412#117—21no—
413#117—21no—
414#117—21no—
415#117—472no—
416#117—472no—
417#117—944no—
418#117—941no—
419#117—941no—
420#117—944no—
421#117—941no—
422#117—941no—
423#117—941no—
424#117—941no—
425#117C4×D4712yescomplemented
426C2×C4⋊C4—21no—
427C2×C4⋊C4—472no—
428C2×C4⋊C4—942no—
429C2×C4⋊C4—941no—
430C2×C22⋊C4—21no—
431C2×C22⋊C4—472no—
432C2×C22⋊C4—942no—
433C2×C22⋊C4—941no—
434C2×C42—21no—
435C2×C42—21no—
436C2×C42—21no—
437C2×C42—21no—
438C2×C42—944no—
439C2×C42—942no—
440C2×C42—941no—
441C2×C42—944no—
442C2×C42—941no—
443C2×C42C4×D4712yes—
444C2×C42D18811yescharacteristic
445C2×C42D18811yescharacteristic
446C2×C42C22⋊D4712yes—
447#104—948no—
448#103—944no—
449#102—944no—
450C24—941no—
451C24D4×D4711yescharacteristic
452#41—474no—
453#41—474no—
454#41—474no—
455#41—474no—
456#41—942no—
457#41—942no—
458#41—942no—
459#41—942no—
460#41—942no—
461#41—942no—
462#41—942no—
463#41—942no—
464#41—942no—
465#41—942no—
466#41—942no—
467#41—942no—
468C2×Q8—472no—
469C2×Q8—472no—
470C2×Q8—472no—
471C2×Q8—941no—
472C2×Q8—941no—
473C2×Q8—941no—
474C2×D4—472no—
475C2×D4—472no—
476C2×D4—472no—
477C2×D4—942no—
478C2×D4—942no—
479C2×D4—942no—
480C2×D4—942no—
481C2×D4—942no—
482C2×D4—942no—
483C2×D4—941no—
484C2×D4—941no—
485C2×D4—941no—
486C22×C4—21no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—21no—
490C22×C4—44no—
491C22×C4—41no—
492C22×C4—948no—
493C22×C4—941no—
494C22×C4—942no—
495C22×C4—942no—
496C22×C4—942no—
497C22×C4—942no—
498C22×C4—942no—
499C22×C4—942no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—1888no—
503C22×C4C2×C4×D4711yescharacteristic
504C22×C4C2×C4×D4711yescharacteristic
505C22×C4C2×C4×D4711yescharacteristic
506C22×C4C2×D18811yescharacteristic
507C22×C4#1062535011yescharacteristic
508C22×C4#1062535011yescharacteristic
509C22×C4D4×D4711yescharacteristic
510C22×C4D4×D4711yescharacteristic
511C22×C4D4×D4711yescharacteristic
512C22×C4D4×D4711yescharacteristic
513C22×C4#1062535211yescharacteristic
514C22×C4Q8×D4711yescharacteristic
515C22×C4#1062535411yescharacteristic
516C22×C4C2×C22⋊D4711yescharacteristic
517M16—22no—
518M16—22no—
519M16—41no—
520M16—41no—
521M16—942no—
522M16—942no—
523M16—1881no—
524M16—1881no—
525C2×C8—22no—
526C2×C8—41no—
527C2×C8—41no—
528C2×C8—942no—
529C2×C8—1881no—
530C2×C8—1881no—
531C4⋊C4—22no—
532C4⋊C4—41no—
533C4⋊C4—948no—
534C4⋊C4—942no—
535C4⋊C4—942no—
536C4⋊C4—942no—
537C4⋊C4—942no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—474no—
541C22⋊C4—948no—
542C22⋊C4—942no—
543C22⋊C4—1881no—
544C22⋊C4—1881no—
545C42—22no—
546C42—22no—
547C42—21no—
548C42—21no—
549C42—22no—
550C42—41no—
551C42—948no—
552C42—942no—
553C42—942no—
554C42—1881no—
555C42—1881no—
556C42(C2×D47)⋊C412yes—
557C42(C2×D47)⋊C412yes—
558C23—42no—
559C23—942no—
560C23—942no—
561C23—942no—
562C23—1884no—
563C23C22⋊C4×D4711yescharacteristic
564C23(C22⋊D47)⋊C411yescharacteristic
565C23#1309398611yescharacteristic
566C23#1309399211yescharacteristic
567C23#1309399411yescharacteristic
568C23#1309399711yescharacteristic
569C23#1309400211yescharacteristic
570Q8—474no—
571Q8—942no—
572Q8—942no—
573Q8—942no—
574D4—474no—
575D4—944no—
576D4—944no—
577D4—944no—
578D4—944no—
579D4—942no—
580D4—942no—
581D4—942no—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—44no—
586C2×C4—44no—
587C2×C4—42no—
588C2×C4—42no—
589C2×C4—82no—
590C2×C4—942no—
591C2×C4—942no—
592C2×C4—942no—
593C2×C4—944no—
594C2×C4—944no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—3762no—
599C2×C4—18816no—
600C2×C4—1882no—
601C2×C4—1884no—
602C2×C4C42×D4711yescharacteristic
603C2×C4C22⋊C4×D4711yescharacteristic
604C2×C4C22⋊C4×D4711yescharacteristic
605C2×C4C22⋊C4×D4711yescharacteristic
606C2×C4C2×(C2×D47)⋊C411yescharacteristic
607C2×C4C4⋊C4×D4711yescharacteristic
608C2×C4C4⋊C4×D4711yescharacteristic
609C2×C4C4⋊C4×D4711yescharacteristic
610C2×C4#1309398111yescharacteristic
611C2×C4#1309398211yescharacteristic
612C2×C4(C22⋊D47)⋊C411yescharacteristic
613C2×C4C4×C22⋊D4711yescharacteristic
614C2×C4C4×C22⋊D4711yescharacteristic
615C2×C4#1309398611yescharacteristic
616C2×C4C4×D18811yescharacteristic
617C2×C4C4×D18811yescharacteristic
618C2×C4#1309399211yescharacteristic
619C2×C4#1309399411yescharacteristic
620C2×C4#1309399511yescharacteristic
621C2×C4#1309399711yescharacteristic
622C2×C4#1309399911yescharacteristic
623C2×C4#1309400011yescharacteristic
624C2×C4#1309400211yescharacteristic
625C2×C4#1309400411yescharacteristic
626C2×C4#1309400611yescharacteristic
627C2×C4#1309400611yescharacteristic
628C2×C4#1309400911yescharacteristic
629C2×C4#1309400911yescharacteristic
630C8—42no—
631C8—1882no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—944no—
640C22—1884no—
641C22—1884no—
642C22—1884no—
643C22#1568897011yescharacteristic
644C22#1568897811yescharacteristic
645C22#1568898211yescharacteristic
646C22#1568899411yescharacteristic
647C22#1568899711yescharacteristic
648C22#1568899911yescharacteristic
649C22#1568900111yescharacteristic
650C4—24no—
651C4—42no—
652C4—82no—
653C4—944no—
654C4—3762no—
655C4—1884no—
656C4#95×D4711yescharacteristic
657C4C4×(C2×D47)⋊C411yescharacteristic
658C4#1568898011yescharacteristic
659C4#1568898511yescharacteristic
660C4#1568899411yescharacteristic
661C4#1568899711yescharacteristic
662C4#1568899911yescharacteristic
663C4#1568900111yescharacteristic
664C2—21no—
665C2—21no—
666C2—21no—
667C2—21no—
668C2—21no—
669C2—21no—
670C2—1884no—
671C2(C2×D47)⋊#9511yescharacteristic
672C2#2024388812yes—
subgroupG/H
centerC2×C4#13093999
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#339C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#339D47
hypocenterC47#10772
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
4. C2×#15688895C2semidirect
5. #20243120C2semidirect
6. C2×#15688883C2semidirect
7. C2×C47×#339C2semidirect
13. C4×#10625350C4semidirect
22. #15689141C4semidirect
26. #15689125C4semidirect
58. C2×#10625329C2×C4semidirect
77. C2×C4⋊Dic47C2×C4semidirect
97. C2×M16×C47C2×C4semidirect
102. #117×C47C2×C4semidirect
334. C2×#339D47semidirect
372. C47#10772semidirect
403. C2×M16C4×D47semidirect
425. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#106253502
C2×#156891412
#202519082
C2×#156888952
#202431202
C2×#156888832
C2×C47×#3392
#1077247