Finite Group Databasebeta

← #26279364

Subgroups — #26279364

Order 12032.

856 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689418C211yesmaximal, characteristic, complemented
2C2×C4×#10625336C211yesmaximal, characteristic
3#20247238C211yesmaximal, characteristic
4#20244912C211yesmaximal, characteristic
5#20244870C211yesmaximal, characteristic, complemented
6#20244773C211yesmaximal, characteristic
7#20244721C211yesmaximal, characteristic, complemented
8#20244118C211yesmaximal, characteristic, complemented
9#20243947C211yesmaximal, characteristic, complemented
10#20243743C211yesmaximal, characteristic
11#20243743C211yesmaximal, characteristic
12#20243656C211yesmaximal, characteristic, complemented
13#20243642C211yesmaximal, characteristic, complemented
14#20243634C211yesmaximal, characteristic
15C47×#2351C211yesmaximal, characteristic, complemented
16C22×#10625336C2211yescharacteristic
17C2×#13094024C2211yescharacteristic
18C2×#13094002—21no—
19C2×C4×D188C2211yescharacteristic
20#15689418—24no—
21C4×#10625336—24no—
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×C4⋊(C47⋊C8)C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35#15689045—21no—
36#15689036—21no—
37#15689025C2211yescharacteristic
38#15689025C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15689021C2211yescharacteristic
41#15688997—21no—
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×C4×Q8×C47C2211yescharacteristic
51C2×C4×Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C47×#389—21no—
54C47×#389—21no—
55C47×#389C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#382—21no—
58C47×#382C2211yescharacteristic
59C4×C4⋊C4×C47—21no—
60C4×C4⋊C4×C47C2211yescharacteristic
61C22×Dic94—21no—
62C22×D188C2311yescharacteristic
63C22×C4×D47—21no—
64C2×#10625336—22no—
65C2×#10625336—22no—
66C2×#10625336Q814yescomplemented
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71#13094024—22no—
72#13094024—41no—
73#13094002—44no—
74C4×D188—22no—
75C4×D188—41no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×(C2×D47)⋊C4—21no—
87#13093957—22no—
88#13093957—22no—
89#13093957—22no—
90#13093955—22no—
91#13093955—41no—
92C4⋊(C47⋊C8)—22no—
93#13093948—22no—
94#13093948—22no—
95#13093948D414yes—
96#13093944—22no—
97#13093944—22no—
98#13093944—41no—
99C4×C47⋊C8—22no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C22×Q8×C47C2311yescharacteristic
103C4×Q8×C47—22no—
104C4×Q8×C47—22no—
105C4×Q8×C47—22no—
106C4×Q8×C47—22no—
107C4×Q8×C47—41no—
108C4×Q8×C47—41no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47D411yescharacteristic
115C2×C4⋊C4×C47D411yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C4⋊C4×C47C2311yescharacteristic
119C2×C42×C47—21no—
120C2×C42×C47—21no—
121C2×C42×C47—21no—
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124C2×C42×C47C2311yescharacteristic
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47D411yescharacteristic
130#95×C47D411yescharacteristic
131C23×D47—21no—
132C2×Q8×C47—21no—
133C2×Q8×C47—21no—
134C2×Q8×C47—21no—
135C2×Q8×C47C2×D412yes—
136C2×Q8×C47C2×Q812yes—
137C2×Q8×C47#4112yes—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2411yescharacteristic
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C2×D188—21no—
153C2×D188—21no—
154C2×D188—21no—
155C2×D188—21no—
156C2×D188—21no—
157C2×D188C2×Q812yes—
158C2×C4×D47—42no—
159C2×C4×D47—42no—
160C2×C4×D47—81no—
161C2×Dic94—42no—
162C2×Dic94—42no—
163C2×Dic94—81no—
164C4⋊C4×C47—24no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—22no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—42no—
173C4⋊C4×C47—42no—
174C4⋊C4×C47—42no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47#4112yes—
177C42×C47—24no—
178C42×C47—21no—
179C42×C47—21no—
180C42×C47—21no—
181C42×C47—21no—
182C42×C47—21no—
183C42×C47—21no—
184C42×C47—42no—
185C42×C47—42no—
186#10625336—28no—
187(C2×D47)⋊C4—42no—
188(C2×D47)⋊C4—42no—
189(C2×D47)⋊C4—42no—
190(C2×D47)⋊C4—42no—
191(C2×D47)⋊C4—81no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47—21no—
197C4⋊Dic47—42no—
198C4⋊Dic47C2×D412yes—
199Dic47⋊C4—42no—
200Dic47⋊C4—42no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8—21no—
208C2×C47⋊C8—21no—
209C2×C47⋊C8—21no—
210C2×C47⋊C8—21no—
211C2×C47⋊C8C2×D412yes—
212C2×C47⋊C8C2×Q812yes—
213C23×C47C22×D411yescharacteristic
214C22×D47—22no—
215C22×D47—41no—
216C22×D47—41no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47—41no—
220C22×D47—41no—
221Q8×C47—22no—
222Q8×C47—22no—
223Q8×C47—22no—
224Q8×C47C22⋊Q814yescomplemented
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—22no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—21no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47#13512yes—
254C2×C4×C47AGL(1,ℤ/8)12yes—
255C2×C4×C47C22×D411yescharacteristic
256C2×C4×C47C22×Q811yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×C4×C47C2×#4111yescharacteristic
259C2×C4×C47H(5,𝔽2)11yescharacteristic
260C2×C4×C472−1+411yescharacteristic
261C2×Dic47—22no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270D188—22no—
271D188—22no—
272D188—41no—
273D188—41no—
274C4×D47—84no—
275Dic94—84no—
276C47⋊C8—22no—
277C47⋊C8—22no—
278C47⋊C8—41no—
279C47⋊C8—41no—
280#26377—471nomaximal, Sylow
281C22×C47#52511yescharacteristic
282C22×C47D4211yescharacteristic
283C22×C47D4×Q811yescharacteristic
284C22×C47C2×#13511yescharacteristic
285C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
286C22×C47#57711yescharacteristic
287C22×C47#57811yescharacteristic
288C2×D47—42no—
289C2×D47—42no—
290C2×D47—42no—
291C2×D47—81no—
292C2×D47—81no—
293C2×D47—81no—
294C2×D47—81no—
295C4×C47—24no—
296C4×C47—22no—
297C4×C47—22no—
298C4×C47—41no—
299C4×C47—42no—
300C4×C47—41no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—81no—
304C4×C47—81no—
305C4×C47C2×C22⋊Q811yescharacteristic
306C4×C47#53911yescharacteristic
307C4×C47#54711yescharacteristic
308C4×C47#55411yescharacteristic
309Dic47—42no—
310Dic47—81no—
311Dic47—81no—
312C2×#477—471no—
313C2×C4×SD16—471no—
314#2452—471no—
315#2351D4711yescharacteristic, complemented
316#2092—471no—
317#2085—471no—
318#2067—471no—
319#2058—471no—
320#1942—471no—
321#1916—471no—
322#1880—471no—
323#1880—471no—
324#1865—471no—
325#1863—471no—
326#1862—471no—
327C2×C47#244911yescharacteristic
328C2×C47#310611yescharacteristic
329C2×C47#312111yescharacteristic
330C2×C47#326511yescharacteristic
331C2×C47#328511yescharacteristic
332C2×C47#338111yescharacteristic
333C2×C47#338611yescharacteristic
334D47—82no—
335C22×SD16—471no—
336C2×C4⋊Q8—471no—
337C2×C22⋊Q8—941no—
338C2×C4×Q8C2×D4711yescharacteristic
339C2×C4×Q8C2×D4711yescharacteristic
340C2×C4×Q8C2×D4711yescharacteristic
341C2×C4×D4—471no—
342#477—944no—
343C4×SD16—944no—
344C2×#107—471no—
345C2×#107—471no—
346C2×#107—471no—
347C2×#106—471no—
348C2×#106—471no—
349C2×C4⋊C8—471no—
350C2×#103—471no—
351C2×#103—471no—
352C2×#103—471no—
353C2×#102—471no—
354C2×#102—471no—
355C2×#102—471no—
356C2×C4×C8—471no—
357#396—941no—
358#393—941no—
359#390—471no—
360#390—471no—
361#389—21no—
362#389—21no—
363#389—471no—
364#389—471no—
365#389C2×D4711yescharacteristic
366#389C2×D4711yescharacteristic
367#385—941no—
368#382—21no—
369#382C2×D4711yescharacteristic
370C4×C4⋊C4—21no—
371C4×C4⋊C4C2×D4711yescharacteristic
372#340—471no—
373#340—471no—
374#340—471no—
375#340—471no—
376#336—471no—
377#336—471no—
378#336—471no—
379#336—471no—
380C47#2637711yescharacteristic, complemented, Sylow
381C22×Q8—941no—
382C22×Q8C22×D4711yescharacteristic
383C22×D4—471no—
384C23×C4—941no—
385C2×SD16—474no—
386C2×SD16—942no—
387C2×SD16—942no—
388C22×C8—471no—
389C22×C8—471no—
390C22×C8—471no—
391C22×C8—471no—
392C4⋊Q8—942no—
393C4⋊Q8—1881no—
394C22⋊Q8—1884no—
395C4×Q8—22no—
396C4×Q8—22no—
397C4×Q8—22no—
398C4×Q8—22no—
399C4×Q8—41no—
400C4×Q8—41no—
401C4×D4—942no—
402C4×D4—1881no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—471no—
410C2×C4⋊C4—471no—
411C2×C4⋊C4—941no—
412C2×C4⋊C4—941no—
413C2×C4⋊C4—941no—
414C2×C4⋊C4C22⋊D4711yescharacteristic
415C2×C4⋊C4C22⋊D4711yescharacteristic
416C2×C4⋊C4C22×D4711yescharacteristic
417C2×C4⋊C4C22×D4711yescharacteristic
418C2×C4⋊C4C22×D4711yescharacteristic
419C2×C22⋊C4—941no—
420C2×C22⋊C4—941no—
421C2×C22⋊C4—941no—
422C2×C22⋊C4—941no—
423C2×C22⋊C4—941no—
424C2×C42—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C22×D4711yescharacteristic
428C2×C42C22×D4711yescharacteristic
429C2×C42C22×D4711yescharacteristic
430#107—942no—
431#107—942no—
432#107—942no—
433#106—942no—
434#106—1881no—
435C4⋊C8—942no—
436#103—474no—
437#103—942no—
438#103—942no—
439#102—942no—
440#102—942no—
441#102—1881no—
442C4×C8—942no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—941no—
448#95—941no—
449#95C22⋊D4711yescharacteristic
450#95C22⋊D4711yescharacteristic
451C24—941no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—3761no—
456C2×Q8—1882no—
457C2×Q8—1882no—
458C2×Q8#1062535012yes—
459C2×Q8D4×D4712yes—
460C2×Q8Q8×D4712yes—
461C2×D4—472no—
462C2×D4—941no—
463C2×D4—941no—
464C2×D4—941no—
465C2×D4—941no—
466C2×D4—941no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—941no—
472C22×C4—941no—
473C22×C4—941no—
474C22×C4—3761no—
475C22×C4—1882no—
476C22×C4—1882no—
477C22×C4C2×C22⋊D4711yescharacteristic
478C22×C4C2×C22⋊D4711yescharacteristic
479C22×C4C2×C22⋊D4711yescharacteristic
480C22×C4C2×C22⋊D4711yescharacteristic
481C22×C4C2×C22⋊D4711yescharacteristic
482C22×C4C2×C22⋊D4711yescharacteristic
483C22×C4C23×D4711yescharacteristic
484SD16—948no—
485C2×C8—472no—
486C2×C8—472no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—941no—
497C4⋊C4—24no—
498C4⋊C4—22no—
499C4⋊C4—22no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—42no—
506C4⋊C4—42no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—472no—
510C4⋊C4—941no—
511C4⋊C4—941no—
512C4⋊C4—941no—
513C4⋊C4—941no—
514C4⋊C4—941no—
515C4⋊C4—1882no—
516C4⋊C4—1882no—
517C4⋊C4—1882no—
518C4⋊C4#1062535012yes—
519C22⋊C4—3761no—
520C22⋊C4—1882no—
521C22⋊C4—1882no—
522C22⋊C4—1882no—
523C22⋊C4—1882no—
524C42—24no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—42no—
532C42—42no—
533C23—942no—
534C23—1881no—
535C23—1881no—
536C23—1881no—
537C23—1881no—
538C23—1881no—
539C23—1881no—
540C23C22×C22⋊D4711yescharacteristic
541Q8—22no—
542Q8—22no—
543Q8—22no—
544Q8—3764no—
545Q8#1309400214yescomplemented
546D4—942no—
547D4—942no—
548D4—1881no—
549D4—1881no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—942no—
579C2×C4—3764no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4—1881no—
583C2×C4—1881no—
584C2×C4—1881no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4#1309404412yes—
589C2×C4#1309404912yes—
590C2×C4C2×D4×D4711yescharacteristic
591C2×C4C2×Q8×D4711yescharacteristic
592C2×C4C2×#1062535011yescharacteristic
593C2×C4C2×#1062535011yescharacteristic
594C2×C4#1309406911yescharacteristic
595C2×C4#1309407211yescharacteristic
596C8—942no—
597C8—942no—
598C8—1881no—
599C8—1881no—
600C22—3761no—
601C22—3761no—
602C22—3761no—
603C22—3761no—
604C22—1882no—
605C22—1882no—
606C22—1882no—
607C22#1568963411yescharacteristic
608C22D4×C22⋊D4711yescharacteristic
609C22Q8×C22⋊D4711yescharacteristic
610C22C2×#1309404411yescharacteristic
611C22C2×#1309404911yescharacteristic
612C22#1568993111yescharacteristic
613C22#1568993811yescharacteristic
614C4—22no—
615C4—24no—
616C4—22no—
617C4—41no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—81no—
623C4—81no—
624C4—3761no—
625C4—3761no—
626C4—1882no—
627C4C2×#1309400211yescharacteristic
628C4#1568972011yescharacteristic
629C4#1568977411yescharacteristic
630C4#1568982811yescharacteristic
631C2—3762no—
632C2#2024719711yescharacteristic
633C2#2025344811yescharacteristic
634C2#2025361711yescharacteristic
635C2#2025488411yescharacteristic
636C2#2025512511yescharacteristic
637C2#2025625911yescharacteristic
638C2#2025630511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2351C2
socleC23×C47C22×D4
prime radicalC22×D188C23
hypercenter#2351D47
hypocenterC47#26377
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2351

Complements

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

NH ≅ G/Ntype
1. C2×#15689418C2semidirect
5. #20244870C2semidirect
7. #20244721C2semidirect
8. #20244118C2semidirect
9. #20243947C2semidirect
12. #20243656C2semidirect
13. #20243642C2semidirect
15. C47×#2351C2semidirect
66. C2×#10625336Q8semidirect
224. Q8×C47C22⋊Q8semidirect
315. #2351D47semidirect
380. C47#26377semidirect
545. Q8#13094002semidirect

Maximal subgroups

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

subgroupindex
C2×#156894182
C2×C4×#106253362
#202472382
#202449122
#202448702
#202447732
#202447212
#202441182
#202439472
#202437432
#202436562
#202436422
#202436342
C47×#23512
#2637747