Finite Group Databasebeta

← #26274449

Subgroups — #26274449

Order 12032.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20248403C211yesmaximal, characteristic, complemented
2#20246361C211yesmaximal, characteristic
3#20244772C211yesmaximal, characteristic
4#20244758C211yesmaximal, characteristic
5#20244532C211yesmaximal, characteristic
6#20244522C211yesmaximal, characteristic
7#20244344C211yesmaximal, characteristic, complemented
8#20244338C211yesmaximal, characteristic, complemented
9#20244156C211yesmaximal, characteristic, complemented
10#20244106C211yesmaximal, characteristic, complemented
11#20243983C211yesmaximal, characteristic, complemented
12#20243976C211yesmaximal, characteristic, complemented
13#20243519C211yesmaximal, characteristic, complemented
14#20243398C211yesmaximal, characteristic
15C4×#102×C47C211yesmaximal, characteristic
16C2×#13094023C2211yescharacteristic
17C2×#13094015C2211yescharacteristic
18C2×#13093957C2211yescharacteristic
19C2×#13093955C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25#15689055—21no—
26#15689044—21no—
27#15689029—21no—
28#15689026C2211yescharacteristic
29#15689026C2211yescharacteristic
30#15689022C2211yescharacteristic
31#15689022C2211yescharacteristic
32#15689021—21no—
33#15689016—21no—
34#15689016—21no—
35#15688989C2211yescharacteristic
36#15688989C2211yescharacteristic
37#15688986—21no—
38C4⋊C4×Dic47C2211yescharacteristic
39C4⋊C4×Dic47C2211yescharacteristic
40C4×C4⋊Dic47C2211yescharacteristic
41C4×C22⋊Dic47—21no—
42#15688886C2211yescharacteristic
43#15688886C2211yescharacteristic
44#15688886C2211yescharacteristic
45#15688886C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4×D4×C47C2211yescharacteristic
53C2×#102×C47C2211yescharacteristic
54C2×#102×C47C2211yescharacteristic
55C2×C4×C8×C47C2211yescharacteristic
56C4×C4⋊C4×C47C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C22×Dic94—21no—
60C22×C47⋊C8C2311yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62#13094023—22no—
63#13094023—41no—
64#13094015—22no—
65#13094015—41no—
66C2×C4⋊Dic47—21no—
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47D411yescharacteristic
70C2×C4⋊Dic47D411yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47C2311yescharacteristic
84C2×C4×Dic47C2311yescharacteristic
85#13093957—22no—
86#13093955—22no—
87C4⋊(C47⋊C8)—22no—
88Dic47⋊C8—41no—
89Dic47⋊C8—41no—
90#13093945—41no—
91#13093945—41no—
92C47⋊#95—21no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95D411yescharacteristic
101C47⋊#95D411yescharacteristic
102C22×D4×C47C2311yescharacteristic
103C23×C4×C47—21no—
104C22×C8×C47C2311yescharacteristic
105C22×C8×C47C2311yescharacteristic
106C4×D4×C47—22no—
107C4×D4×C47Q814yescomplemented
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C22⋊C4×C47—21no—
112C2×C42×C47—21no—
113C2×C42×C47C2311yescharacteristic
114#102×C47—22no—
115#102×C47—22no—
116C4×C8×C47—22no—
117#95×C47—21no—
118C24×C47—21no—
119C2×D4×C47—21no—
120C2×D4×C47—21no—
121C2×D4×C47—21no—
122C2×D4×C47—21no—
123C2×D4×C47—21no—
124C2×D4×C47C2×Q812yes—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—24no—
129C22×C4×C47—81no—
130C22×C4×C47—81no—
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2×D411yescharacteristic
133C22×C4×C47C2411yescharacteristic
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—21no—
137C22×Dic47—21no—
138C22×Dic47C2×D411yescharacteristic
139C22×Dic47C2×D411yescharacteristic
140C22×Dic47C2×D411yescharacteristic
141C22×Dic47C2×D411yescharacteristic
142C2×Dic94—42no—
143C2×Dic94—42no—
144C2×Dic94—81no—
145C2×C8×C47—21no—
146C2×C8×C47—21no—
147C2×C8×C47—21no—
148C2×C8×C47—21no—
149C2×C8×C47—21no—
150C2×C8×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—21no—
153C4⋊C4×C47—21no—
154C4⋊C4×C47C2×Q812yes—
155C4⋊C4×C47#4112yes—
156C4⋊C4×C47#4112yes—
157C22⋊C4×C47—24no—
158C42×C47—81no—
159C42×C47C2×Q812yes—
160C42×C47#4112yes—
161C22⋊Dic47—42no—
162C22⋊Dic47—42no—
163C22⋊Dic47—81no—
164C22⋊Dic47—81no—
165C4⋊Dic47—22no—
166C4⋊Dic47—21no—
167C4⋊Dic47—21no—
168C4⋊Dic47—21no—
169C4⋊Dic47—21no—
170C4⋊Dic47—21no—
171C4⋊Dic47—21no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—41no—
175C4⋊Dic47—42no—
176C4⋊Dic47—42no—
177C4⋊Dic47—81no—
178Dic47⋊C4—42no—
179Dic47⋊C4—42no—
180C4×Dic47—21no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—21no—
184C4×Dic47—81no—
185C4×Dic47—81no—
186C2×C47⋊C8—21no—
187C2×C47⋊C8—21no—
188C2×C47⋊C8—21no—
189C2×C47⋊C8—21no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C23×C47—22no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47—41no—
196C23×C47—41no—
197C23×C47—41no—
198C23×C47—41no—
199C23×C47C22×D411yescharacteristic
200D4×C47—22no—
201D4×C47—22no—
202D4×C47—41no—
203D4×C47—41no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—22no—
211C2×C4×C47—41no—
212C2×C4×C47—41no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47—41no—
216C2×C4×C47—41no—
217C2×C4×C47—84no—
218C2×C4×C47C22⋊Q812yes—
219C2×C4×C47C22⋊Q812yes—
220C2×C4×C47C22×Q811yescharacteristic
221C2×C4×C47C2×#4111yescharacteristic
222C2×C4×C47C2×#4111yescharacteristic
223C2×C4×C47C2×#4111yescharacteristic
224C2×C4×C47H(5,𝔽2)11yescharacteristic
225C2×C4×C472−1+411yescharacteristic
226C2×Dic47—21no—
227C2×Dic47—21no—
228C2×Dic47—21no—
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—21no—
232C2×Dic47—21no—
233C2×Dic47—21no—
234C2×Dic47—21no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—41no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246C2×Dic47—41no—
247C2×Dic47—41no—
248C2×Dic47—41no—
249C2×Dic47#13512yes—
250Dic94—84no—
251C8×C47—41no—
252C8×C47—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#26028—471nomaximal, Sylow
256C22×C47—42no—
257C22×C47—42no—
258C22×C47—42no—
259C22×C47—81no—
260C22×C47—81no—
261C22×C47—81no—
262C22×C47—81no—
263C22×C47C2×C22⋊Q811yescharacteristic
264C22×C47#54611yescharacteristic
265C22×C47#54811yescharacteristic
266C22×C47C2×#13511yescharacteristic
267C22×C47#57511yescharacteristic
268C22×C47#57611yescharacteristic
269C22×C47#57711yescharacteristic
270C4×C47—22no—
271C4×C47—22no—
272C4×C47—42no—
273C4×C47—42no—
274C4×C47—42no—
275C4×C47#53311yescharacteristic
276C4×C47#54411yescharacteristic
277C4×C47#55511yescharacteristic
278C4×C47#55611yescharacteristic
279Dic47—22no—
280Dic47—41no—
281Dic47—41no—
282Dic47—41no—
283Dic47—81no—
284Dic47—81no—
285Dic47—81no—
286Dic47—81no—
287#2550—471no—
288#2357—471no—
289#2067—471no—
290#2065—471no—
291#2025—471no—
292#2023—471no—
293#1989—471no—
294#1988—471no—
295#1949—471no—
296#1939—471no—
297#1921—471no—
298#1920—471no—
299#1835—471no—
300#1804—471no—
301C4×#102D4711yescharacteristic
302C2×C47—82no—
303C2×C47#243911yescharacteristic
304C2×C47#307611yescharacteristic
305C2×C47#308111yescharacteristic
306C2×C47#329711yescharacteristic
307C2×C47#332611yescharacteristic
308C2×C47#336511yescharacteristic
309C2×C47#337011yescharacteristic
310C2×C4⋊Q8—471no—
311C2×#125—471no—
312C2×C4×D4C2×D4711yescharacteristic
313C2×#107—471no—
314C2×#106—471no—
315C2×C4⋊C8—471no—
316C2×C4⋊C8—471no—
317C2×C4⋊C8—471no—
318C2×#102—471no—
319C2×#102—471no—
320C2×#102C2×D4711yescharacteristic
321C2×#102C2×D4711yescharacteristic
322C2×C4×C8C2×D4711yescharacteristic
323#398—941no—
324#395—941no—
325#391—941no—
326#390—471no—
327#390—471no—
328#389—471no—
329#389—471no—
330#389—941no—
331#388—941no—
332#388—941no—
333#382—471no—
334#382—471no—
335#381—941no—
336C4×C4⋊C4—471no—
337C4×C4⋊C4—471no—
338C4×C4⋊C4—471no—
339C4×C4⋊C4C2×D4711yescharacteristic
340C4×C22⋊C4—941no—
341#340—471no—
342#340—471no—
343#340—471no—
344#340—471no—
345#340—471no—
346#340—471no—
347#340—471no—
348#340—471no—
349#340C2×D4711yescharacteristic
350#340C2×D4711yescharacteristic
351#336—471no—
352#336—471no—
353C47#2602811yescharacteristic, complemented, Sylow
354C22×Q8—941no—
355C22×D4C22×D4711yescharacteristic
356C23×C4—21no—
357C22×C8—471no—
358C22×C8—471no—
359C22×C8C22×D4711yescharacteristic
360C22×C8C22×D4711yescharacteristic
361C4⋊Q8—942no—
362C4⋊Q8—1881no—
363#125—942no—
364#125—1881no—
365C4×D4—22no—
366C4×D4Dic9414yescomplemented
367C2×C4⋊C4—471no—
368C2×C4⋊C4—471no—
369C2×C4⋊C4—471no—
370C2×C4⋊C4—471no—
371C2×C4⋊C4—471no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—941no—
374C2×C4⋊C4—941no—
375C2×C4⋊C4—941no—
376C2×C4⋊C4—941no—
377C2×C4⋊C4—941no—
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C22⋊C4—21no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C22⋊C4—941no—
386C2×C42—21no—
387C2×C42—471no—
388C2×C42—471no—
389C2×C42—941no—
390C2×C42—941no—
391C2×C42C22×D4711yescharacteristic
392#107—942no—
393#106—942no—
394C4⋊C8—942no—
395C4⋊C8—1881no—
396C4⋊C8—1881no—
397#102—22no—
398#102—22no—
399#102—1881no—
400#102—1881no—
401C4×C8—22no—
402#95—21no—
403#95—471no—
404#95—471no—
405#95—941no—
406#95—941no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95—941no—
412#95—941no—
413C24—21no—
414C2×Q8—3761no—
415C2×Q8—1882no—
416C2×Q8—1882no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4C2×Dic9412yes—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—24no—
427C22×C4—81no—
428C22×C4—81no—
429C22×C4—471no—
430C22×C4—471no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4D4×D4711yescharacteristic
438C22×C4D4×D4711yescharacteristic
439C22×C4C23×D4711yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—942no—
456C4⋊C4—941no—
457C4⋊C4—941no—
458C4⋊C4—941no—
459C4⋊C4—941no—
460C4⋊C4—941no—
461C4⋊C4—941no—
462C4⋊C4—941no—
463C4⋊C4—941no—
464C4⋊C4—3761no—
465C4⋊C4—1881no—
466C4⋊C4—1882no—
467C4⋊C4—1882no—
468C4⋊C4—1882no—
469C4⋊C4—1882no—
470C4⋊C4C2×Dic9412yes—
471C4⋊C4#1062535012yes—
472C4⋊C4#1062535012yes—
473C22⋊C4—24no—
474C22⋊C4—3761no—
475C22⋊C4—3761no—
476C22⋊C4—1882no—
477C22⋊C4—1882no—
478C42—81no—
479C42—941no—
480C42—941no—
481C42—941no—
482C42—941no—
483C42—3761no—
484C42—3761no—
485C42C2×Dic9412yes—
486C42#1062535212yes—
487C23—22no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23C2×D4×D4711yescharacteristic
495Q8—3764no—
496D4—22no—
497D4—22no—
498D4—41no—
499D4—41no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—84no—
514C2×C4—472no—
515C2×C4—941no—
516C2×C4—941no—
517C2×C4—941no—
518C2×C4—941no—
519C2×C4—941no—
520C2×C4—941no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—1881no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4—1881no—
532C2×C4—1881no—
533C2×C4—1881no—
534C2×C4—1881no—
535C2×C4—1881no—
536C2×C4—1881no—
537C2×C4—1881no—
538C2×C4#1309400112yes—
539C2×C4#1309400112yes—
540C2×C4C22×Dic9411yescharacteristic
541C2×C4C2×#1062535211yescharacteristic
542C2×C4C2×#1062535011yescharacteristic
543C2×C4C2×#1062535011yescharacteristic
544C2×C4#1309407011yescharacteristic
545C2×C4#1309407111yescharacteristic
546C8—41no—
547C8—41no—
548C8—1881no—
549C8—1881no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#1309400111yescharacteristic
558C22#1568976911yescharacteristic
559C22#1568978211yescharacteristic
560C22#135×D4711yescharacteristic
561C22#1568992011yescharacteristic
562C22#1568992411yescharacteristic
563C22#1568992911yescharacteristic
564C4—22no—
565C4—22no—
566C4—42no—
567C4—42no—
568C4—42no—
569C4—942no—
570C4—3761no—
571C4—3761no—
572C4—3761no—
573C4—3761no—
574C4—1881no—
575C4—1881no—
576C4—1881no—
577C4#1568968011yescharacteristic
578C4#1568975111yescharacteristic
579C4#1568983811yescharacteristic
580C4#1568984311yescharacteristic
581C2—82no—
582C2#2024707911yescharacteristic
583C2#2025317211yescharacteristic
584C2#2025321511yescharacteristic
585C2#2025524311yescharacteristic
586C2#2025564611yescharacteristic
587C2#2025608511yescharacteristic
588C2#2025613711yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC4×#102×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×C47C23
hypercenterC4×#102D47
hypocenterC47#26028
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
1. #20248403C2semidirect
7. #20244344C2semidirect
8. #20244338C2semidirect
9. #20244156C2semidirect
10. #20244106C2semidirect
11. #20243983C2semidirect
12. #20243976C2semidirect
13. #20243519C2semidirect
107. C4×D4×C47Q8semidirect
353. C47#26028semidirect
366. C4×D4Dic94semidirect

Maximal subgroups

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

subgroupindex
#202484032
#202463612
#202447722
#202447582
#202445322
#202445222
#202443442
#202443382
#202441562
#202441062
#202439832
#202439762
#202435192
#202433982
C4×#102×C472
#2602847