Finite Group Databasebeta

← #26139459

Subgroups — #26139459

Order 12032.

2038 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689025C211yesmaximal, characteristic
2C2×#15689024C211yesmaximal, characteristic
3C2×#15689024C211yesmaximal, characteristic
4C2×#15689012C214yesmaximal, complemented
5C2×#15688992C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic47C211yesmaximal, characteristic, complemented
7#20241632C214yesmaximal, complemented
8C4×C47⋊#95C211yesmaximal, characteristic, complemented
9C47×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D188C2211yescharacteristic
11C22×C4⋊Dic47C2211yescharacteristic
12C22×Dic47⋊C4C2214yes—
13C22×(C2×D47)⋊C4C2212yes—
14C22×(C2×D47)⋊C4C2214yes—
15C22×(C2×D47)⋊C4C2214yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×C4×Dic47C2212yes—
18C22×C4×Dic47C2211yescharacteristic
19C22×C4×Dic47C2211yescharacteristic
20#15689025—24no—
21#15689024—24no—
22#15689024C418yescomplemented
23#15689012—216no—
24#15688992—24no—
25C4⋊C4×Dic47—24no—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C22×C4⋊C4×C47C2211yescharacteristic
30C22×C4⋊C4×C47C2211yescharacteristic
31C22×C42×C47C2211yescharacteristic
32C2×#95×C47C2214yes—
33C24×D47C2312yes—
34C22×D188—22no—
35C22×D188—22no—
36C22×D188—22no—
37C22×D188—22no—
38C22×D188—22no—
39C22×D188—22no—
40C22×D188C2×C414yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C23×Dic47C2311yescharacteristic
45C2×C4⋊Dic47—22no—
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47D414yes—
48C2×Dic47⋊C4—28no—
49C2×Dic47⋊C4—28no—
50C2×Dic47⋊C4—44no—
51C2×(C2×D47)⋊C4—28no—
52C2×(C2×D47)⋊C4—28no—
53C2×(C2×D47)⋊C4—28no—
54C2×(C2×D47)⋊C4—28no—
55C2×(C2×D47)⋊C4—24no—
56C2×(C2×D47)⋊C4—24no—
57C2×(C2×D47)⋊C4—28no—
58C2×(C2×D47)⋊C4—44no—
59C2×(C2×D47)⋊C4—44no—
60C2×(C2×D47)⋊C4C2×C4116yes—
61C2×C4×Dic47—22no—
62C2×C4×Dic47—22no—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—28no—
67C2×C4×Dic47C2×C414yes—
68C2×C4×Dic47D414yes—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95D418yescomplemented
72C23×C4×C47C2312yes—
73C23×C4×C47C2312yes—
74C23×C4×C47C2312yes—
75C23×C4×C47C2311yescharacteristic
76C2×C4⋊C4×C47—22no—
77C2×C4⋊C4×C47—22no—
78C2×C4⋊C4×C47—22no—
79C2×C4⋊C4×C47—22no—
80C2×C4⋊C4×C47—22no—
81C2×C4⋊C4×C47C2×C414yes—
82C2×C42×C47—22no—
83C2×C42×C47—22no—
84C2×C42×C47—22no—
85#95×C47—28no—
86C24×C47C2411yescharacteristic
87C23×D47—24no—
88C23×D47—22no—
89C23×D47—22no—
90C23×D47—24no—
91C23×D47—22no—
92C23×D47—22no—
93C23×D47—22no—
94C23×D47—22no—
95C23×D47—24no—
96C23×D47—24no—
97C23×D47C22×C414yes—
98C22×C4×C47—22no—
99C22×C4×C47—22no—
100C22×C4×C47—24no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—22no—
104C22×C4×C47—22no—
105C22×C4×C47—24no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—22no—
110C22×C4×C47—24no—
111C22×C4×C47—22no—
112C22×C4×C47—24no—
113C22×C4×C47C22×C414yes—
114C22×C4×C47C22×C412yes—
115C22×C4×C47C2×D414yes—
116C22×C4×C47C2×D412yes—
117C22×C4×C47C2×D412yes—
118C22×C4×C47#4112yes—
119C22×C4×C47#4112yes—
120C22×C4×C47#4112yes—
121C22×C4×C47#4112yes—
122C22×Dic47—22no—
123C22×Dic47—22no—
124C22×Dic47—21no—
125C22×Dic47—21no—
126C22×Dic47—22no—
127C22×Dic47—22no—
128C22×Dic47—22no—
129C22×Dic47—22no—
130C22×Dic47—24no—
131C22×Dic47—22no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—22no—
135C22×Dic47—22no—
136C22×Dic47—24no—
137C22×Dic47C22×C414yes—
138C22×Dic47C2×D412yes—
139C22×Dic47C2×D414yes—
140C22×Dic47C2×D414yes—
141C22×Dic47C2×D414yes—
142C22×Dic47C2×D412yes—
143C22×Dic47#4114yes—
144C2×D188—28no—
145C2×D188—28no—
146C2×D188—28no—
147C2×D188—44no—
148C2×D188—44no—
149C2×D188—44no—
150C2×D188—44no—
151C4⋊C4×C47—28no—
152C4⋊C4×C47—44no—
153C42×C47—44no—
154(C2×D47)⋊C4—232no—
155(C2×D47)⋊C4—416no—
156(C2×D47)⋊C4—48no—
157(C2×D47)⋊C4—48no—
158C4⋊Dic47—28no—
159Dic47⋊C4—416no—
160C4×Dic47—28no—
161C4×Dic47—28no—
162C4×Dic47—48no—
163C23×C47C23×C411yescharacteristic
164C23×C47C22×D411yescharacteristic
165C23×C47C22×D411yescharacteristic
166C23×C47C22×D412yes—
167C23×C47C2×#4112yes—
168C23×C47C2×#4111yescharacteristic
169C23×C47C2×#4111yescharacteristic
170C23×C47C2×#4111yescharacteristic
171C23×C47C2×#4111yescharacteristic
172C23×C47H(5,𝔽2)12yes—
173C23×C472−1+412yes—
174C22×D47—24no—
175C22×D47—28no—
176C22×D47—24no—
177C22×D47—24no—
178C22×D47—28no—
179C22×D47—42no—
180C22×D47—42no—
181C22×D47—42no—
182C22×D47—42no—
183C22×D47—42no—
184C22×D47—44no—
185C22×D47—42no—
186C22×D47—42no—
187C22×D47—42no—
188C22×D47—44no—
189C22×D47—44no—
190C22×D47—44no—
191C22×D47—44no—
192C22×D47—44no—
193C22×D47—44no—
194C22×D47—44no—
195C22×D47—44no—
196C22×D47—44no—
197C2×C4×C47—28no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—42no—
203C2×C4×C47—42no—
204C2×C4×C47—44no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—42no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—44no—
213C2×C4×C47—44no—
214C2×C4×C47#11714yes—
215C2×C4×C47C4×D414yes—
216C2×C4×C47C4×D414yes—
217C2×C4×C47#12114yes—
218C2×C4×C47#12314yes—
219C2×C4×C47#12414yes—
220C2×C4×C47#12614yes—
221C2×Dic47—24no—
222C2×Dic47—24no—
223C2×Dic47—22no—
224C2×Dic47—22no—
225C2×Dic47—24no—
226C2×Dic47—24no—
227C2×Dic47—24no—
228C2×Dic47—24no—
229C2×Dic47—24no—
230C2×Dic47—24no—
231C2×Dic47—24no—
232C2×Dic47—22no—
233C2×Dic47—22no—
234C2×Dic47—22no—
235C2×Dic47—28no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—44no—
239C2×Dic47—42no—
240C2×Dic47—42no—
241C2×Dic47C4×D418yes—
242C2×Dic47#12714yes—
243D188—416no—
244#14001—471nomaximal, Sylow
245C22×C47C2×#11711yescharacteristic
246C22×C47C2×C4×D412yes—
247C22×C47C2×C4×D411yescharacteristic
248C22×C47C2×C4×D411yescharacteristic
249C22×C47#52012yes—
250C22×C47C2×#12111yescharacteristic
251C22×C47C2×#12311yescharacteristic
252C22×C47C2×#12411yescharacteristic
253C22×C47C2×#12611yescharacteristic
254C22×C47C2×#12711yescharacteristic
255C22×C47#53212yes—
256C22×C47#53211yescharacteristic
257C22×C47#53511yescharacteristic
258C22×C47#53611yescharacteristic
259C22×C47#54212yes—
260C22×C47D4212yes—
261C22×C47#54712yes—
262C22×C47#54712yes—
263C22×C47#54812yes—
264C22×C47#55012yes—
265C22×C47#55312yes—
266C22×C47#55512yes—
267C22×C47#55612yes—
268C2×D47—44no—
269C2×D47—44no—
270C2×D47—48no—
271C2×D47—48no—
272C2×D47—44no—
273C2×D47—84no—
274C2×D47—82no—
275C2×D47—82no—
276C2×D47—84no—
277C2×D47—82no—
278C2×D47—82no—
279C4×C47—44no—
280C4×C47—44no—
281C4×C47—82no—
282C4×C47#38818yescomplemented
283Dic47—28no—
284Dic47—24no—
285Dic47—42no—
286Dic47—44no—
287C2×#390—471no—
288C2×#390—471no—
289C2×#390—471no—
290C2×#388—474no—
291C2×#384—471no—
292C2×C4×C4⋊C4—471no—
293#1439—474no—
294C4⋊#95D4711yescharacteristic, complemented
295C4×#95—471no—
296C2×C47C2×#38811yescharacteristic
297C2×C47C4×#12711yescharacteristic
298C2×C47#232611yescharacteristic
299C2×C47#235412yes—
300C2×C47#236112yes—
301C2×C47#249112yes—
302C2×C47#250011yescharacteristic
303C2×C47#250111yescharacteristic
304C2×C47#251212yes—
305C2×C47#254111yescharacteristic
306C2×C47#254511yescharacteristic
307D47—84no—
308C23×D4—471no—
309C22×C4⋊C4—471no—
310C22×C4⋊C4—474no—
311C22×C4⋊C4C2×D4711yescharacteristic
312C22×C4⋊C4C2×D4711yescharacteristic
313C22×C22⋊C4—474no—
314C22×C22⋊C4—472no—
315C22×C22⋊C4—474no—
316C22×C22⋊C4—472no—
317C22×C42—471no—
318C22×C42—471no—
319C22×C42—472no—
320C22×C42C2×D4711yescharacteristic
321#390—478no—
322#390—944no—
323#390—944no—
324#388—9416no—
325#384—944no—
326C4×C4⋊C4—944no—
327C2×#95—472no—
328C2×#95—472no—
329C2×#95—472no—
330C2×#95C2×D4714yes—
331C47#1400111yescharacteristic, complemented, Sylow
332C25—472no—
333C22×D4—474no—
334C22×D4—942no—
335C22×D4—942no—
336C22×D4—942no—
337C22×D4—942no—
338C22×D4—942no—
339C22×D4—942no—
340C23×C4—472no—
341C23×C4—471no—
342C23×C4—472no—
343C23×C4—471no—
344C23×C4C22×D4712yes—
345C23×C4C22×D4712yes—
346C23×C4C22×D4712yes—
347C23×C4C22×D4711yescharacteristic
348C2×C4⋊C4—22no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—22no—
353C2×C4⋊C4—474no—
354C2×C4⋊C4—942no—
355C2×C4⋊C4—942no—
356C2×C4⋊C4—948no—
357C2×C4⋊C4—948no—
358C2×C4⋊C4—1884no—
359C2×C4⋊C4C4×D4714yes—
360C2×C22⋊C4—4716no—
361C2×C22⋊C4—948no—
362C2×C22⋊C4—948no—
363C2×C22⋊C4—948no—
364C2×C22⋊C4—948no—
365C2×C22⋊C4—944no—
366C2×C22⋊C4—944no—
367C2×C22⋊C4—948no—
368C2×C22⋊C4—1884no—
369C2×C22⋊C4—1884no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—474no—
374C2×C42—474no—
375C2×C42—942no—
376C2×C42—942no—
377C2×C42—942no—
378C2×C42—942no—
379C2×C42—944no—
380C2×C42—948no—
381#95—28no—
382#95—478no—
383#95—944no—
384#95—944no—
385C24—474no—
386C24—944no—
387C24—942no—
388C24—942no—
389C24—944no—
390C24—942no—
391C24—942no—
392C24—942no—
393C24—942no—
394C24—944no—
395C24—944no—
396C24C23×D4711yescharacteristic
397C2×D4—948no—
398C2×D4—948no—
399C2×D4—948no—
400C2×D4—1884no—
401C2×D4—1884no—
402C2×D4—1884no—
403C2×D4—1884no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—24no—
409C22×C4—22no—
410C22×C4—22no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—474no—
420C22×C4—474no—
421C22×C4—474no—
422C22×C4—472no—
423C22×C4—474no—
424C22×C4—472no—
425C22×C4—474no—
426C22×C4—942no—
427C22×C4—941no—
428C22×C4—941no—
429C22×C4—942no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—942no—
434C22×C4—944no—
435C22×C4—942no—
436C22×C4—941no—
437C22×C4—942no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—944no—
441C22×C4C2×C4×D4714yes—
442C22×C4C2×C4×D4712yes—
443C22×C4#1062535012yes—
444C22×C4#1062535012yes—
445C22×C4D4×D4714yes—
446C22×C4D4×D4712yes—
447C22×C4D4×D4712yes—
448C22×C4#1062535212yes—
449C22×C4#1062535412yes—
450C4⋊C4—28no—
451C4⋊C4—44no—
452C4⋊C4—948no—
453C4⋊C4—18816no—
454C22⋊C4—9432no—
455C22⋊C4—18816no—
456C22⋊C4—1888no—
457C22⋊C4—1888no—
458C42—44no—
459C42—948no—
460C42—948no—
461C42—1888no—
462C23—944no—
463C23—948no—
464C23—944no—
465C23—944no—
466C23—948no—
467C23—1884no—
468C23—1884no—
469C23—1884no—
470C23—1884no—
471C23—1884no—
472C23—1884no—
473C23—1884no—
474C23—1884no—
475C23—1884no—
476C23—1882no—
477C23—1882no—
478C23—1882no—
479C23—1882no—
480C23—1882no—
481C23—1884no—
482C23—1882no—
483C23—1882no—
484C23—1882no—
485C23C22×C4×D4711yescharacteristic
486C23C2×D4×D4711yescharacteristic
487C23C2×D4×D4712yes—
488C23C2×D4×D4711yescharacteristic
489C23#41×D4712yes—
490C23C2×#1062535211yescharacteristic
491C23C2×#1062535011yescharacteristic
492C23C2×#1062535011yescharacteristic
493C23C2×#1062535411yescharacteristic
494C23#1309407012yes—
495C23#1309407212yes—
496D4—18816no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—28no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—44no—
508C2×C4—42no—
509C2×C4—44no—
510C2×C4—44no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—478no—
515C2×C4—474no—
516C2×C4—944no—
517C2×C4—944no—
518C2×C4—944no—
519C2×C4—944no—
520C2×C4—944no—
521C2×C4—944no—
522C2×C4—944no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—948no—
527C2×C4—944no—
528C2×C4—942no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—1884no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1882no—
536C2×C4#1309398114yes—
537C2×C4(C22⋊D47)⋊C414yes—
538C2×C4#1309398614yes—
539C2×C4#1309399714yes—
540C2×C4#1309400914yes—
541C2×C4#1309401014yes—
542C2×C4#1309401914yes—
543C22—3762no—
544C22—3762no—
545C22—3762no—
546C22—3762no—
547C22—3764no—
548C22—3764no—
549C22—1884no—
550C22—1888no—
551C22—1884no—
552C22—1888no—
553C22—1884no—
554C22C2×#1309398111yescharacteristic
555C22C4×D4×D4712yes—
556C22C2×(C22⋊D47)⋊C411yescharacteristic
557C22C2×#1309398611yescharacteristic
558C22#1568960512yes—
559C22C2×#1309399711yescharacteristic
560C22C2×#1309400911yescharacteristic
561C22C2×#1309401011yescharacteristic
562C22C2×#1309401911yescharacteristic
563C22#127×D4711yescharacteristic
564C22#1568966812yes—
565C22#1568967211yescharacteristic
566C22#1568969111yescharacteristic
567C22#1568969811yescharacteristic
568C22#1568974612yes—
569C22#1568975712yes—
570C22#1568977412yes—
571C22#1568977612yes—
572C22#1568978312yes—
573C22#1568979412yes—
574C22#1568982612yes—
575C22#1568983612yes—
576C22#1568984512yes—
577C4—44no—
578C4—44no—
579C4—82no—
580C4—944no—
581C4—948no—
582C4—1884no—
583C4—1882no—
584C4#1568901218yescomplemented
585C2—3764no—
586C2C2×#1568901211yescharacteristic
587C2#2024595211yescharacteristic
588C2#2024610211yescharacteristic
589C2#2024633312yes—
590C2#2024640312yes—
591C2#2024774712yes—
592C2#2024785311yescharacteristic
593C2#2024785611yescharacteristic
594C2#2024797712yes—
595C2#2024833311yescharacteristic
596C2#2024837111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C4⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC4⋊#95D47
hypocenterC47#14001
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#15689012C2semidirect
5. C2×#15688992C2semidirect
6. C2×C4⋊C4×Dic47C2semidirect
7. #20241632C2semidirect
8. C4×C47⋊#95C2semidirect
9. C47×C4⋊#95C2semidirect
22. #15689024C4semidirect
71. C47⋊#95D4semidirect
282. C4×C47#388semidirect
294. C4⋊#95D47semidirect
331. C47#14001semidirect
584. C4#15689012semidirect

Maximal subgroups

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

subgroupindex
C2×#156890252
C2×#156890242
C2×#156890122
C2×#156889922
C2×C4⋊C4×Dic472
#202416322
C4×C47⋊#952
C47×C4⋊#952
#1400147