Finite Group Databasebeta

← #26274445

Subgroups — #26274445

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#20246359C211yesmaximal, characteristic
2#20244773C211yesmaximal, characteristic
3#20244759C211yesmaximal, characteristic
4#20244531C211yesmaximal, characteristic
5#20244521C211yesmaximal, characteristic
6#20244346C211yesmaximal, characteristic, complemented
7#20244341C211yesmaximal, characteristic, complemented
8#20244156C211yesmaximal, characteristic, complemented
9#20244107C211yesmaximal, characteristic, complemented
10#20243977C211yesmaximal, characteristic, complemented
11#20243970C211yesmaximal, characteristic, complemented
12#20243518C211yesmaximal, characteristic, complemented
13#20243395C211yesmaximal, characteristic
14C4×#13093944C211yesmaximal, characteristic
15C47×#2550C211yesmaximal, characteristic, complemented
16C2×C4×D188C2211yescharacteristic
17C2×#13093957C2211yescharacteristic
18C2×#13093955C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×C4⋊(C47⋊C8)C2211yescharacteristic
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×#13093944C2211yescharacteristic
23C2×#13093944C2211yescharacteristic
24C2×#13093944C2211yescharacteristic
25C2×#13093944C2211yescharacteristic
26C2×C4×C47⋊C8C2211yescharacteristic
27#15689025C2211yescharacteristic
28#15689025C2211yescharacteristic
29#15689013—21no—
30#15689013—21no—
31#15688989C2211yescharacteristic
32#15688985—21no—
33C4×C4⋊Dic47C2211yescharacteristic
34C4×C4⋊Dic47C2211yescharacteristic
35#15688970—21no—
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4⋊Q8×C47C2211yescharacteristic
49C2×#125×C47C2211yescharacteristic
50C47×#398—21no—
51C47×#395—21no—
52C47×#391—21no—
53C47×#389—21no—
54C47×#389C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#382C2211yescharacteristic
57C4×C4⋊C4×C47C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C4×D47—21no—
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C4×D188—22no—
66C4×D188Q814yescomplemented
67C2×C4⋊Dic47C2311yescharacteristic
68C2×C4⋊Dic47C2311yescharacteristic
69C2×C4⋊Dic47C2311yescharacteristic
70C2×(C2×D47)⋊C4—21no—
71C2×(C2×D47)⋊C4—21no—
72C2×(C2×D47)⋊C4—21no—
73C2×(C2×D47)⋊C4—21no—
74C2×(C2×D47)⋊C4—21no—
75C2×C4×Dic47—21no—
76C2×C4×Dic47—21no—
77#13093957—22no—
78#13093955—22no—
79C4⋊(C47⋊C8)—22no—
80C4⋊(C47⋊C8)—41no—
81C4⋊(C47⋊C8)—41no—
82#13093944—22no—
83#13093944—22no—
84#13093944—41no—
85#13093944—41no—
86C4×C47⋊C8—22no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C22×Q8×C47—21no—
92C4⋊Q8×C47—22no—
93C4⋊Q8×C47—41no—
94#125×C47—22no—
95#125×C47—41no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47D411yescharacteristic
102C2×C4⋊C4×C47D411yescharacteristic
103C2×C4⋊C4×C47C2311yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C42×C47—21no—
108C2×C42×C47C2311yescharacteristic
109C2×C42×C47C2311yescharacteristic
110C2×C42×C47C2311yescharacteristic
111#95×C47—21no—
112#95×C47—21no—
113#95×C47—21no—
114#95×C47—21no—
115#95×C47—21no—
116#95×C47D411yescharacteristic
117#95×C47D411yescharacteristic
118C23×D47—21no—
119C2×Q8×C47—42no—
120C2×Q8×C47—42no—
121C2×Q8×C47—81no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47C2×D411yescharacteristic
127C22×C4×C47C2×D411yescharacteristic
128C22×C4×C47C2×D411yescharacteristic
129C22×C4×C47C2×D411yescharacteristic
130C22×C4×C47C2×D411yescharacteristic
131C22×C4×C47C2×D411yescharacteristic
132C22×C4×C47C2411yescharacteristic
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C2×D188—21no—
137C2×D188—21no—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188C2×Q812yes—
142C2×C4×D47—24no—
143C2×C4×D47—81no—
144C2×C4×D47—81no—
145C4⋊C4×C47—22no—
146C4⋊C4×C47—21no—
147C4⋊C4×C47—21no—
148C4⋊C4×C47—21no—
149C4⋊C4×C47—21no—
150C4⋊C4×C47—21no—
151C4⋊C4×C47—21no—
152C4⋊C4×C47—41no—
153C4⋊C4×C47—42no—
154C4⋊C4×C47—42no—
155C4⋊C4×C47—42no—
156C4⋊C4×C47—42no—
157C4⋊C4×C47—81no—
158C4⋊C4×C47#4112yes—
159C4⋊C4×C47#4112yes—
160C42×C47—21no—
161C42×C47—21no—
162C42×C47—21no—
163C42×C47—21no—
164C42×C47—81no—
165C42×C47C2×Q812yes—
166C42×C47#4112yes—
167(C2×D47)⋊C4—24no—
168(C2×D47)⋊C4—42no—
169(C2×D47)⋊C4—42no—
170(C2×D47)⋊C4—81no—
171(C2×D47)⋊C4—81no—
172C4⋊Dic47—21no—
173C4⋊Dic47—21no—
174C4⋊Dic47—21no—
175C4⋊Dic47—21no—
176C4⋊Dic47—21no—
177C4⋊Dic47C2×Q812yes—
178C4×Dic47—81no—
179C4×Dic47—81no—
180C2×C47⋊C8—21no—
181C2×C47⋊C8—21no—
182C2×C47⋊C8—21no—
183C2×C47⋊C8—21no—
184C2×C47⋊C8—21no—
185C2×C47⋊C8—21no—
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×C47C22×D411yescharacteristic
193C22×D47—22no—
194C22×D47—41no—
195C22×D47—41no—
196C22×D47—41no—
197C22×D47—41no—
198C22×D47—41no—
199C22×D47—41no—
200Q8×C47—84no—
201C2×C4×C47—21no—
202C2×C4×C47—21no—
203C2×C4×C47—21no—
204C2×C4×C47—21no—
205C2×C4×C47—21no—
206C2×C4×C47—21no—
207C2×C4×C47—21no—
208C2×C4×C47—21no—
209C2×C4×C47—21no—
210C2×C4×C47—22no—
211C2×C4×C47—22no—
212C2×C4×C47—21no—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—41no—
219C2×C4×C47—41no—
220C2×C4×C47—41no—
221C2×C4×C47—41no—
222C2×C4×C47—41no—
223C2×C4×C47—41no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47C22⋊Q812yes—
229C2×C4×C47C22⋊Q812yes—
230C2×C4×C47#13512yes—
231C2×C4×C47C22×Q811yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47H(5,𝔽2)11yescharacteristic
236C2×C4×C472−1+411yescharacteristic
237C2×Dic47—22no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47—41no—
243C2×Dic47—41no—
244C2×Dic47—41no—
245C2×Dic47—41no—
246D188—22no—
247D188—22no—
248D188—41no—
249D188—41no—
250C4×D47—84no—
251C47⋊C8—41no—
252C47⋊C8—41no—
253C47⋊C8—41no—
254C47⋊C8—41no—
255#26028—471nomaximal, Sylow
256C22×C47C2×C22⋊Q811yescharacteristic
257C22×C47#54611yescharacteristic
258C22×C47#54811yescharacteristic
259C22×C47C2×#13511yescharacteristic
260C22×C47#57511yescharacteristic
261C22×C47#57611yescharacteristic
262C22×C47#57711yescharacteristic
263C2×D47—42no—
264C2×D47—42no—
265C2×D47—42no—
266C2×D47—81no—
267C2×D47—81no—
268C2×D47—81no—
269C2×D47—81no—
270C4×C47—22no—
271C4×C47—22no—
272C4×C47—22no—
273C4×C47—42no—
274C4×C47—41no—
275C4×C47—42no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47—81no—
279C4×C47—81no—
280C4×C47#53311yescharacteristic
281C4×C47#54411yescharacteristic
282C4×C47#55511yescharacteristic
283C4×C47#55611yescharacteristic
284Dic47—42no—
285Dic47—81no—
286Dic47—81no—
287#2550D4711yescharacteristic, complemented
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×#102—471no—
302C2×C47#243911yescharacteristic
303C2×C47#307611yescharacteristic
304C2×C47#308111yescharacteristic
305C2×C47#329711yescharacteristic
306C2×C47#332611yescharacteristic
307C2×C47#336511yescharacteristic
308C2×C47#337011yescharacteristic
309D47—82no—
310C2×C4⋊Q8C2×D4711yescharacteristic
311C2×#125C2×D4711yescharacteristic
312C2×C4×D4—471no—
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×#102—471no—
321C2×#102—471no—
322C2×C4×C8—471no—
323#398—21no—
324#395—21no—
325#391—21no—
326#390—471no—
327#390—471no—
328#389—21no—
329#389C2×D4711yescharacteristic
330#389C2×D4711yescharacteristic
331#388—941no—
332#388—941no—
333#382—471no—
334#382C2×D4711yescharacteristic
335#381—941no—
336C4×C4⋊C4—471no—
337C4×C4⋊C4—471no—
338C4×C4⋊C4C2×D4711yescharacteristic
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#340—471no—
350#340—471no—
351#336—471no—
352#336—471no—
353C47#2602811yescharacteristic, complemented, Sylow
354C22×Q8—21no—
355C22×D4—471no—
356C23×C4—941no—
357C22×C8—471no—
358C22×C8—471no—
359C22×C8—471no—
360C22×C8—471no—
361C4⋊Q8—22no—
362C4⋊Q8—41no—
363#125—22no—
364#125—41no—
365C4×D4—474no—
366C4×D4—942no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—471no—
373C2×C4⋊C4—471no—
374C2×C4⋊C4—471no—
375C2×C4⋊C4C22⋊D4711yescharacteristic
376C2×C4⋊C4C22⋊D4711yescharacteristic
377C2×C4⋊C4C22×D4711yescharacteristic
378C2×C4⋊C4C22×D4711yescharacteristic
379C2×C4⋊C4C22×D4711yescharacteristic
380C2×C4⋊C4C22×D4711yescharacteristic
381C2×C22⋊C4—941no—
382C2×C22⋊C4—941no—
383C2×C22⋊C4—941no—
384C2×C22⋊C4—941no—
385C2×C22⋊C4—941no—
386C2×C42—21no—
387C2×C42—941no—
388C2×C42—941no—
389C2×C42C22×D4711yescharacteristic
390C2×C42C22×D4711yescharacteristic
391C2×C42C22×D4711yescharacteristic
392#107—942no—
393#106—942no—
394C4⋊C8—942no—
395C4⋊C8—1881no—
396C4⋊C8—1881no—
397#102—942no—
398#102—942no—
399#102—1881no—
400#102—1881no—
401C4×C8—942no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—941no—
408#95—941no—
409#95—941no—
410#95—941no—
411#95C22⋊D4711yescharacteristic
412#95C22⋊D4711yescharacteristic
413C24—941no—
414C2×Q8—42no—
415C2×Q8—42no—
416C2×Q8—81no—
417C2×D4—472no—
418C2×D4—941no—
419C2×D4—941no—
420C2×D4—941no—
421C2×D4—941no—
422C2×D4—941no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—941no—
428C22×C4—944no—
429C22×C4—941no—
430C22×C4—941no—
431C22×C4—3761no—
432C22×C4—3761no—
433C22×C4C2×C22⋊D4711yescharacteristic
434C22×C4C2×C22⋊D4711yescharacteristic
435C22×C4C2×C22⋊D4711yescharacteristic
436C22×C4C2×C22⋊D4711yescharacteristic
437C22×C4C2×C22⋊D4711yescharacteristic
438C22×C4C2×C22⋊D4711yescharacteristic
439C22×C4C23×D4711yescharacteristic
440C2×C8—941no—
441C2×C8—941no—
442C2×C8—941no—
443C2×C8—941no—
444C2×C8—941no—
445C2×C8—941no—
446C2×C8—941no—
447C2×C8—941no—
448C2×C8—941no—
449C2×C8—941no—
450C2×C8—941no—
451C2×C8—941no—
452C4⋊C4—22no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—42no—
461C4⋊C4—42no—
462C4⋊C4—42no—
463C4⋊C4—42no—
464C4⋊C4—81no—
465C4⋊C4—472no—
466C4⋊C4—941no—
467C4⋊C4—941no—
468C4⋊C4—941no—
469C4⋊C4—941no—
470C4⋊C4—941no—
471C4⋊C4#1062535212yes—
472C4⋊C4#1062535412yes—
473C22⋊C4—944no—
474C22⋊C4—3761no—
475C22⋊C4—3761no—
476C22⋊C4—1882no—
477C22⋊C4—1882no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—81no—
483C42—3761no—
484C42—3761no—
485C42Q8×D4712yes—
486C42#1062535412yes—
487C23—942no—
488C23—1881no—
489C23—1881no—
490C23—1881no—
491C23—1881no—
492C23—1881no—
493C23—1881no—
494C23C22×C22⋊D4711yescharacteristic
495Q8—84no—
496D4—942no—
497D4—942no—
498D4—1881no—
499D4—1881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—942no—
528C2×C4—3764no—
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#1309400012yes—
538C2×C4#1309400012yes—
539C2×C4#1309404412yes—
540C2×C4C2×Q8×D4711yescharacteristic
541C2×C4C2×#1062535211yescharacteristic
542C2×C4C2×#1062535411yescharacteristic
543C2×C4C2×#1062535411yescharacteristic
544C2×C4#1309406911yescharacteristic
545C2×C4#1309407211yescharacteristic
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C22—3761no—
551C22—3761no—
552C22—3761no—
553C22—3761no—
554C22—1882no—
555C22—1882no—
556C22—1882no—
557C22C2×#1309400011yescharacteristic
558C22#1568976711yescharacteristic
559C22#1568978411yescharacteristic
560C22C2×#1309404411yescharacteristic
561C22#1568992111yescharacteristic
562C22#1568992611yescharacteristic
563C22#1568993111yescharacteristic
564C4—22no—
565C4—22no—
566C4—22no—
567C4—41no—
568C4—42no—
569C4—42no—
570C4—41no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—3761no—
575C4—3761no—
576C4—1882no—
577C4#1568967811yescharacteristic
578C4#1568975011yescharacteristic
579C4#1568983911yescharacteristic
580C4#1568984711yescharacteristic
581C2—3762no—
582C2#2024707511yescharacteristic
583C2#2025317011yescharacteristic
584C2#2025321311yescharacteristic
585C2#2025523811yescharacteristic
586C2#2025564111yescharacteristic
587C2#2025608411yescharacteristic
588C2#2025614111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2550C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2550D47
hypocenterC47#26028
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2550

Complements

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

NH ≅ G/Ntype
6. #20244346C2semidirect
7. #20244341C2semidirect
8. #20244156C2semidirect
9. #20244107C2semidirect
10. #20243977C2semidirect
11. #20243970C2semidirect
12. #20243518C2semidirect
15. C47×#2550C2semidirect
66. C4×D188Q8semidirect
287. #2550D47semidirect
353. C47#26028semidirect

Maximal subgroups

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

subgroupindex
#202463592
#202447732
#202447592
#202445312
#202445212
#202443462
#202443412
#202441562
#202441072
#202439772
#202439702
#202435182
#202433952
C4×#130939442
C47×#25502
#2602847