Finite Group Databasebeta

← #26153034

Subgroups — #26153034

Order 12032.

1410 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689054C211yesmaximal, characteristic
2C2×#15689018C212yesmaximal
3C2×#15689018C211yesmaximal, characteristic
4C2×C4⋊C4×Dic47C211yesmaximal, characteristic
5#20241647C212yesmaximal
6#20241646C212yesmaximal
7#20241642C211yesmaximal, characteristic
8#20241641C211yesmaximal, characteristic
9Dic47⋊#95C211yesmaximal, characteristic
10Dic47⋊#95C212yesmaximal
11C2×C47×#398C211yesmaximal, characteristic
12C22×C4⋊Dic47C2211yescharacteristic
13C22×Dic47⋊C4C2211yescharacteristic
14C22×Dic47⋊C4C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×Dic47⋊C4C2211yescharacteristic
17C22×Dic47⋊C4C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2211yescharacteristic
20#15689054—24no—
21#15689018—28no—
22#15689018—24no—
23C4⋊C4×Dic47—24no—
24C2×C47⋊#95C2212yes—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2211yescharacteristic
27C2×C47⋊#95C2211yescharacteristic
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C22×C4⋊C4×C47C2211yescharacteristic
35C22×C4⋊C4×C47C2212yes—
36C22×C4⋊C4×C47C2211yescharacteristic
37C47×#398—24no—
38C2×#95×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C23×Dic47C2311yescharacteristic
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C23×Dic47C2311yescharacteristic
46C2×C4⋊Dic47—22no—
47C2×C4⋊Dic47—24no—
48C2×Dic47⋊C4—22no—
49C2×Dic47⋊C4—24no—
50C2×Dic47⋊C4—22no—
51C2×Dic47⋊C4—24no—
52C2×Dic47⋊C4—22no—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—22no—
55C2×Dic47⋊C4—22no—
56C2×Dic47⋊C4—24no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—42no—
60C2×Dic47⋊C4D414yes—
61C2×Dic47⋊C4Q818yes—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—24no—
64C2×C4×Dic47—24no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47D414yes—
67C47⋊#95—24no—
68C47⋊#95—22no—
69C47⋊#95—24no—
70C47⋊#95—24no—
71C47⋊#95—24no—
72C47⋊#95—22no—
73C47⋊#95—22no—
74C47⋊#95—24no—
75C47⋊#95—24no—
76C47⋊#95—42no—
77C23×C4×C47C2311yescharacteristic
78C23×C4×C47C2311yescharacteristic
79C23×C4×C47C2312yes—
80C23×C4×C47C2312yes—
81C23×C4×C47C2311yescharacteristic
82C2×C4⋊C4×C47—22no—
83C2×C4⋊C4×C47—22no—
84C2×C4⋊C4×C47—24no—
85C2×C4⋊C4×C47—22no—
86C2×C4⋊C4×C47—24no—
87C2×C4⋊C4×C47—22no—
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—42no—
90C2×C4⋊C4×C47D414yes—
91#95×C47—22no—
92#95×C47—24no—
93C24×C47C2411yescharacteristic
94C22×C4×C47—22no—
95C22×C4×C47—22no—
96C22×C4×C47—21no—
97C22×C4×C47—22no—
98C22×C4×C47—21no—
99C22×C4×C47—22no—
100C22×C4×C47—22no—
101C22×C4×C47—22no—
102C22×C4×C47—22no—
103C22×C4×C47—21no—
104C22×C4×C47—22no—
105C22×C4×C47—22no—
106C22×C4×C47—21no—
107C22×C4×C47—22no—
108C22×C4×C47—21no—
109C22×C4×C47—22no—
110C22×C4×C47—22no—
111C22×C4×C47—21no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47C2×D412yes—
120C22×C4×C47C2×D414yes—
121C22×C4×C47C2×D412yes—
122C22×C4×C47C2×D412yes—
123C22×C4×C47C2×Q814yes—
124C22×C4×C47#4112yes—
125C22×Dic47—22no—
126C22×Dic47—22no—
127C22×Dic47—22no—
128C22×Dic47—21no—
129C22×Dic47—22no—
130C22×Dic47—21no—
131C22×Dic47—22no—
132C22×Dic47—22no—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—22no—
136C22×Dic47—21no—
137C22×Dic47—22no—
138C22×Dic47—21no—
139C22×Dic47—22no—
140C22×Dic47—21no—
141C22×Dic47—22no—
142C22×Dic47—21no—
143C22×Dic47—21no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—22no—
150C22×Dic47—21no—
151C22×Dic47—22no—
152C22×Dic47C2×D412yes—
153C22×Dic47C2×D412yes—
154C22×Dic47C2×D412yes—
155C22×Dic47C2×D412yes—
156C22×Dic47C2×Q814yes—
157C22×Dic47C2×Q814yes—
158C22×Dic47#4114yes—
159C22×Dic47#4112yes—
160C22×Dic47#4114yes—
161C4⋊C4×C47—28no—
162C4⋊C4×C47—48no—
163C4⋊C4×C47—44no—
164C4⋊Dic47—28no—
165Dic47⋊C4—28no—
166Dic47⋊C4—216no—
167Dic47⋊C4—48no—
168Dic47⋊C4—44no—
169Dic47⋊C4—44no—
170C4×Dic47—28no—
171C4×Dic47—48no—
172C23×C47C22×D411yescharacteristic
173C23×C47C22×D411yescharacteristic
174C23×C47C22×D411yescharacteristic
175C23×C47C22×Q812yes—
176C23×C47C2×#4111yescharacteristic
177C23×C47C2×#4112yes—
178C23×C47C2×#4112yes—
179C23×C47C2×#4111yescharacteristic
180C23×C47H(5,𝔽2)11yescharacteristic
181C23×C472−1+411yescharacteristic
182C23×C472−1+412yes—
183C2×C4×C47—22no—
184C2×C4×C47—22no—
185C2×C4×C47—24no—
186C2×C4×C47—24no—
187C2×C4×C47—22no—
188C2×C4×C47—24no—
189C2×C4×C47—24no—
190C2×C4×C47—24no—
191C2×C4×C47—22no—
192C2×C4×C47—24no—
193C2×C4×C47—22no—
194C2×C4×C47—24no—
195C2×C4×C47—24no—
196C2×C4×C47—42no—
197C2×C4×C47—41no—
198C2×C4×C47—42no—
199C2×C4×C47—42no—
200C2×C4×C47—41no—
201C2×C4×C47—42no—
202C2×C4×C47—42no—
203C2×C4×C47—41no—
204C2×C4×C47—42no—
205C2×C4×C47—42no—
206C2×C4×C47—42no—
207C2×C4×C47—41no—
208C2×C4×C47—41no—
209C2×C4×C47—41no—
210C2×C4×C47—41no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47#12114yes—
214C2×Dic47—22no—
215C2×Dic47—24no—
216C2×Dic47—22no—
217C2×Dic47—24no—
218C2×Dic47—22no—
219C2×Dic47—22no—
220C2×Dic47—22no—
221C2×Dic47—22no—
222C2×Dic47—24no—
223C2×Dic47—24no—
224C2×Dic47—24no—
225C2×Dic47—24no—
226C2×Dic47—42no—
227C2×Dic47—41no—
228C2×Dic47—42no—
229C2×Dic47—42no—
230C2×Dic47—41no—
231C2×Dic47—42no—
232C2×Dic47—42no—
233C2×Dic47—42no—
234C2×Dic47—42no—
235C2×Dic47—41no—
236C2×Dic47—42no—
237C2×Dic47—42no—
238C2×Dic47—42no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47#12114yes—
246C2×Dic47C22⋊Q818yes—
247C2×Dic47#12314yes—
248C2×Dic47#12518yes—
249C2×Dic47C4⋊Q814yes—
250#15149—471nomaximal, Sylow
251C22×C47C2×#12111yescharacteristic
252C22×C47C2×#12111yescharacteristic
253C22×C47C2×C22⋊Q812yes—
254C22×C47C2×#12311yescharacteristic
255C22×C47#52511yescharacteristic
256C22×C47C2×#12512yes—
257C22×C47#52912yes—
258C22×C47C2×C4⋊Q811yescharacteristic
259C22×C47#53212yes—
260C22×C47#53611yescharacteristic
261C22×C47#53711yescharacteristic
262C22×C47#54112yes—
263C22×C47#54212yes—
264C22×C47D4211yescharacteristic
265C22×C47#54711yescharacteristic
266C22×C47#54711yescharacteristic
267C22×C47#54812yes—
268C22×C47D4×Q812yes—
269C22×C47#55212yes—
270C22×C47#55412yes—
271C22×C47#55511yescharacteristic
272C22×C47#55712yes—
273C22×C47#55712yes—
274C4×C47—24no—
275C4×C47—44no—
276C4×C47—42no—
277C4×C47—44no—
278C4×C47—81no—
279Dic47—42no—
280Dic47—44no—
281Dic47—44no—
282Dic47—42no—
283Dic47—81no—
284Dic47#39818yescomplemented
285C2×#398—471no—
286C2×#398D4711yescharacteristic
287C2×#389—472no—
288C2×#389—471no—
289C2×C4×C4⋊C4—471no—
290#1442—472no—
291#1442—472no—
292#1441—471no—
293#1441—471no—
294C4⋊#95—471no—
295C4⋊#95—472no—
296C2×C47C2×#39811yescharacteristic
297C2×C47#245212yes—
298C2×C47#245312yes—
299C2×C47#250612yes—
300C2×C47#250812yes—
301C2×C47#253611yescharacteristic
302C2×C47#253711yescharacteristic
303C2×C47#254611yescharacteristic
304C2×C47#258411yescharacteristic
305C2×C47#262511yescharacteristic
306C2×C47#285411yescharacteristic
307C22×C4⋊C4—472no—
308C22×C4⋊C4—471no—
309C22×C4⋊C4—471no—
310C22×C4⋊C4—471no—
311C22×C4⋊C4—471no—
312C22×C4⋊C4—472no—
313C22×C4⋊C4C2×D4711yescharacteristic
314C22×C4⋊C4C2×D4712yes—
315C22×C4⋊C4C2×D4711yescharacteristic
316C22×C42—471no—
317C22×C42—472no—
318#398—24no—
319#398—944no—
320#389—944no—
321#389—948no—
322C4×C4⋊C4—944no—
323C2×#95—471no—
324C2×#95—472no—
325C2×#95—472no—
326C2×#95—472no—
327C2×#95—472no—
328C2×#95—472no—
329C2×#95—472no—
330C2×#95—471no—
331C2×#95—471no—
332C2×#95—472no—
333C2×#95C2×D4711yescharacteristic
334C2×#95C2×D4712yes—
335C47#1514911yescharacteristic, complemented, Sylow
336C23×C4—471no—
337C23×C4—471no—
338C23×C4—472no—
339C23×C4—472no—
340C23×C4—471no—
341C23×C4—471no—
342C23×C4C22×D4711yescharacteristic
343C23×C4C22×D4711yescharacteristic
344C23×C4C22×D4712yes—
345C23×C4C22×D4712yes—
346C23×C4C22×D4711yescharacteristic
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—24no—
350C2×C4⋊C4—22no—
351C2×C4⋊C4—22no—
352C2×C4⋊C4—24no—
353C2×C4⋊C4—22no—
354C2×C4⋊C4—42no—
355C2×C4⋊C4—474no—
356C2×C4⋊C4—478no—
357C2×C4⋊C4—942no—
358C2×C4⋊C4—944no—
359C2×C4⋊C4—942no—
360C2×C4⋊C4—944no—
361C2×C4⋊C4—944no—
362C2×C4⋊C4—942no—
363C2×C4⋊C4—944no—
364C2×C4⋊C4—944no—
365C2×C4⋊C4—942no—
366C2×C4⋊C4—942no—
367C2×C4⋊C4—942no—
368C2×C4⋊C4—944no—
369C2×C4⋊C4—942no—
370C2×C4⋊C4—1882no—
371C2×C4⋊C4C22⋊D4714yes—
372C2×C42—474no—
373C2×C42—944no—
374C2×C42—944no—
375C2×C42—944no—
376C2×C42—944no—
377#95—22no—
378#95—24no—
379#95—944no—
380#95—944no—
381#95—944no—
382#95—942no—
383#95—944no—
384#95—942no—
385#95—944no—
386#95—942no—
387#95—944no—
388#95—1882no—
389C24C23×D4711yescharacteristic
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—22no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—21no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—22no—
414C22×C4—21no—
415C22×C4—472no—
416C22×C4—472no—
417C22×C4—474no—
418C22×C4—472no—
419C22×C4—474no—
420C22×C4—472no—
421C22×C4—472no—
422C22×C4—474no—
423C22×C4—474no—
424C22×C4—942no—
425C22×C4—942no—
426C22×C4—941no—
427C22×C4—942no—
428C22×C4—942no—
429C22×C4—941no—
430C22×C4—942no—
431C22×C4—942no—
432C22×C4—942no—
433C22×C4—941no—
434C22×C4—942no—
435C22×C4—942no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—942no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—942no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—941no—
451C22×C4D4×D4712yes—
452C22×C4D4×D4712yes—
453C22×C4#1062535212yes—
454C22×C4Q8×D4714yes—
455C22×C4C2×C22⋊D4714yes—
456C22×C4C2×C22⋊D4712yes—
457C4⋊C4—28no—
458C4⋊C4—48no—
459C4⋊C4—44no—
460C4⋊C4—948no—
461C4⋊C4—9416no—
462C4⋊C4—948no—
463C4⋊C4—1888no—
464C4⋊C4—1884no—
465C4⋊C4—1884no—
466C42—948no—
467C42—1888no—
468C23C2×D4×D4711yescharacteristic
469C23C2×D4×D4711yescharacteristic
470C23C22×C22⋊D4711yescharacteristic
471C23C2×Q8×D4712yes—
472C23#41×D4712yes—
473C23#41×D4711yescharacteristic
474C23#41×D4712yes—
475C23C2×#1062535211yescharacteristic
476C23#1309406911yescharacteristic
477C23#1309407111yescharacteristic
478C23#1309407212yes—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—22no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—41no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—474no—
510C2×C4—478no—
511C2×C4—474no—
512C2×C4—478no—
513C2×C4—474no—
514C2×C4—942no—
515C2×C4—942no—
516C2×C4—944no—
517C2×C4—944no—
518C2×C4—944no—
519C2×C4—944no—
520C2×C4—942no—
521C2×C4—944no—
522C2×C4—942no—
523C2×C4—944no—
524C2×C4—942no—
525C2×C4—942no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1882no—
530C2×C4—1882no—
531C2×C4—1882no—
532C2×C4—1882no—
533C2×C4—1882no—
534C2×C4—1882no—
535C2×C4—1881no—
536C2×C4—1882no—
537C2×C4—1882no—
538C2×C4—1882no—
539C2×C4—1881no—
540C2×C4—1882no—
541C2×C4—1881no—
542C2×C4—1882no—
543C2×C4—1882no—
544C2×C4—1881no—
545C2×C4#1309399614yes—
546C22#121×D4711yescharacteristic
547C22C2×#1309399611yescharacteristic
548C22C22⋊Q8×D4712yes—
549C22#123×D4711yescharacteristic
550C22#1568963111yescharacteristic
551C22#125×D4712yes—
552C22#1568965012yes—
553C22C4⋊Q8×D4711yescharacteristic
554C22#1568966912yes—
555C22#1568969811yescharacteristic
556C22#1568970211yescharacteristic
557C22#1568973212yes—
558C22#1568974312yes—
559C22D4×C22⋊D4711yescharacteristic
560C22#1568977211yescharacteristic
561C22#1568977311yescharacteristic
562C22#1568978312yes—
563C22Q8×C22⋊D4712yes—
564C22#1568980512yes—
565C22#1568982712yes—
566C22#1568983711yescharacteristic
567C22#1568984812yes—
568C22#1568985012yes—
569C4—24no—
570C4—44no—
571C4—42no—
572C4—44no—
573C4—81no—
574C4—478no—
575C4—3761no—
576C4—1882no—
577C4—1884no—
578C4—1884no—
579C4—1882no—
580C2#398×D4711yescharacteristic
581C2#2024723712yes—
582C2#2024724412yes—
583C2#2024790312yes—
584C2#2024792112yes—
585C2#2024829411yescharacteristic
586C2#2024830211yescharacteristic
587C2#2024837411yescharacteristic
588C2#2024877211yescharacteristic
589C2#2024919111yescharacteristic
590C2#2025171711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, prime radical, cosocleC24×C47C24
FittingC2×C47×#398C2
hypercenterC2×#398D47
hypocenterC47#15149
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
284. Dic47#398semidirect
335. C47#15149semidirect

Maximal subgroups

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

subgroupindex
C2×#156890542
C2×#156890182
C2×C4⋊C4×Dic472
#202416472
#202416462
#202416422
#202416412
Dic47⋊#952
C2×C47×#3982
#1514947