Finite Group Databasebeta

← #26279150

Subgroups — #26279150

Order 12032.

860 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689420C211yesmaximal, characteristic, complemented
2C2×#15689163C211yesmaximal, characteristic, complemented
3#20246424C211yesmaximal, characteristic
4#20244912C211yesmaximal, characteristic, complemented
5#20244890C211yesmaximal, characteristic, complemented
6#20244759C211yesmaximal, characteristic, complemented
7#20244723C211yesmaximal, characteristic, complemented
8#20244154C211yesmaximal, characteristic, complemented
9#20243956C211yesmaximal, characteristic, complemented
10#20243824C211yesmaximal, characteristic
11#20243705C211yesmaximal, characteristic
12#20243634C211yesmaximal, characteristic, complemented
13#20243585C211yesmaximal, characteristic, complemented
14#20243573C211yesmaximal, characteristic, complemented
15C47×#2442C211yesmaximal, characteristic, complemented
16C22×#10625329C2211yescharacteristic
17C2×#13093998C2211yescharacteristic
18C2×C4×D188C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20#15689420—24no—
21#15689163—24no—
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×#13093955C2211yescharacteristic
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×#13093944C2211yescharacteristic
31C2×#13093944C2211yescharacteristic
32C2×#13093944C2211yescharacteristic
33C2×#13093944C2211yescharacteristic
34C2×C22⋊(C47⋊C8)C2211yescharacteristic
35#15689025C2211yescharacteristic
36#15689023—21no—
37#15689021C2211yescharacteristic
38#15689012—21no—
39#15688999—21no—
40C4×C4⋊Dic47C2211yescharacteristic
41#15688970—21no—
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×#125×C47C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C47×#400—21no—
53C47×#398—21no—
54C47×#389C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#385—21no—
57C47×#382C2211yescharacteristic
58C47×#380—21no—
59C47×#380C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C22×D188C2311yescharacteristic
62C22×C22⋊D47—21no—
63C22×C4×D47—21no—
64C2×#10625329—22no—
65C2×#10625329—22no—
66C2×#10625329—22no—
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71#13093998—22no—
72#13093998Q814yes—
73C4×D188—22no—
74C4×D188—41no—
75#13093983—22no—
76#13093983—41no—
77C2×C4⋊Dic47C2311yescharacteristic
78C2×C4⋊Dic47C2311yescharacteristic
79C2×C4⋊Dic47C2311yescharacteristic
80C2×Dic47⋊C4—21no—
81C2×C22⋊Dic47—21no—
82C2×(C2×D47)⋊C4—21no—
83C2×(C2×D47)⋊C4—21no—
84C2×(C2×D47)⋊C4—21no—
85C2×(C2×D47)⋊C4—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47—21no—
88#13093957—22no—
89#13093957—41no—
90#13093957D414yescomplemented
91#13093955—22no—
92#13093955—22no—
93#13093955—22no—
94C4⋊(C47⋊C8)—22no—
95C4⋊(C47⋊C8)—22no—
96#13093944—22no—
97#13093944—22no—
98#13093944—22no—
99#13093944—41no—
100C22⋊(C47⋊C8)—22no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C23×C4×C47—21no—
104C23×C4×C47C2311yescharacteristic
105#125×C47—22no—
106#125×C47—41no—
107C2×C4⋊C4×C47—22no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—21no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—41no—
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C22⋊C4×C47D411yescharacteristic
121C2×C42×C47C2311yescharacteristic
122C2×C42×C47C2311yescharacteristic
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47D411yescharacteristic
129#95×C47D411yescharacteristic
130C24×C47C2×D411yescharacteristic
131C23×D47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—42no—
141C22×C4×C47—42no—
142C22×C4×C47—81no—
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×Q812yes—
149C22×C4×C47#4112yes—
150C22×C4×C47C2411yescharacteristic
151C2×C22⋊D47—24no—
152C2×C22⋊D47—81no—
153C2×C22⋊D47—81no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C2×D188—21no—
158C2×D188—21no—
159C2×D188—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188C2×Q812yes—
163C2×C4×D47—42no—
164C2×C4×D47—42no—
165C2×C4×D47—81no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—42no—
174C4⋊C4×C47—42no—
175C4⋊C4×C47—42no—
176C4⋊C4×C47—81no—
177C4⋊C4×C47—81no—
178C4⋊C4×C47C2×D412yes—
179C22⋊C4×C47—41no—
180C22⋊C4×C47—41no—
181C22⋊C4×C47—42no—
182C42×C47—21no—
183C42×C47—21no—
184C42×C47—21no—
185C42×C47—21no—
186C22⋊Dic47—42no—
187(C2×D47)⋊C4—24no—
188(C2×D47)⋊C4—42no—
189(C2×D47)⋊C4—42no—
190(C2×D47)⋊C4—81no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47C2×D412yes—
196C4⋊Dic47C2×Q812yes—
197Dic47⋊C4—81no—
198C4×Dic47—42no—
199C4×Dic47—81no—
200#10625329—28no—
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⋊C8#4112yes—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47C22⋊Q812yes—
220C23×C47C22×D411yescharacteristic
221C22×D47—22no—
222C22×D47—41no—
223C22×D47—41no—
224C22×D47—41no—
225C22×D47—41no—
226C22×D47—41no—
227C22×D47—41no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—22no—
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—21no—
246C2×C4×C47—21no—
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—41no—
254C2×C4×C47—41no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—84no—
259C2×C4×C47C22⋊Q812yes—
260C2×C4×C47C22×D411yescharacteristic
261C2×C4×C47C22×Q811yescharacteristic
262C2×C4×C47C2×#4111yescharacteristic
263C2×C4×C47C2×#4111yescharacteristic
264C2×C4×C47H(5,𝔽2)11yescharacteristic
265C2×C4×C472−1+411yescharacteristic
266C22⋊D47—84no—
267C2×Dic47—22no—
268C2×Dic47—22no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276D188—22no—
277D188—22no—
278D188—41no—
279D188—41no—
280C4×D47—84no—
281C47⋊C8—22no—
282C47⋊C8—22no—
283C47⋊C8—41no—
284C47⋊C8—41no—
285#26363—471nomaximal, Sylow
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47—41no—
290C22×C47—41no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47C2×C22⋊Q811yescharacteristic
294C22×C47D4211yescharacteristic
295C22×C47#54711yescharacteristic
296C22×C47#57511yescharacteristic
297C22×C47#57511yescharacteristic
298C22×C47#57611yescharacteristic
299C22×C47#57711yescharacteristic
300C2×D47—42no—
301C2×D47—42no—
302C2×D47—42no—
303C2×D47—81no—
304C2×D47—81no—
305C2×D47—81no—
306C2×D47—81no—
307C4×C47—22no—
308C4×C47—41no—
309C4×C47—41no—
310C4×C47—41no—
311C4×C47—41no—
312C4×C47—42no—
313C4×C47—81no—
314C4×C47—81no—
315C4×C47—81no—
316C4×C47#52511yescharacteristic
317C4×C47#53911yescharacteristic
318C4×C47D4×Q811yescharacteristic
319C4×C47#55411yescharacteristic
320Dic47—42no—
321Dic47—42no—
322Dic47—81no—
323C2×#478—471no—
324C2×#428—471no—
325#2442D4711yescharacteristic, complemented
326#2363—471no—
327#2092—471no—
328#2088—471no—
329#2065—471no—
330#2059—471no—
331#1949—471no—
332#1918—471no—
333#1895—471no—
334#1874—471no—
335#1862—471no—
336#1854—471no—
337#1851—471no—
338C2×C47—42no—
339C2×C47#244911yescharacteristic
340C2×C47#308011yescharacteristic
341C2×C47#308111yescharacteristic
342C2×C47#327111yescharacteristic
343C2×C47#327311yescharacteristic
344C2×C47#334811yescharacteristic
345C2×C47#335511yescharacteristic
346D47—82no—
347C22×M16—471no—
348C2×#125C2×D4711yescharacteristic
349C2×#121—471no—
350C2×C4×D4—471no—
351C2×#117—471no—
352C22×C4⋊C4C2×D4711yescharacteristic
353#478—944no—
354#428—944no—
355C2×#107—471no—
356C2×#107—471no—
357C2×#107—471no—
358C2×#106—471no—
359C2×#106—471no—
360C2×#106—471no—
361C2×C4⋊C8—471no—
362C2×C4⋊C8—471no—
363C2×#102—471no—
364C2×#102—471no—
365C2×#102—471no—
366C2×#102—471no—
367C2×C22⋊C8—471no—
368#400—21no—
369#398—21no—
370#390—471no—
371#390—941no—
372#389—471no—
373#389C2×D4711yescharacteristic
374#389C2×D4711yescharacteristic
375#388—941no—
376#386—941no—
377#385—21no—
378#382C2×D4711yescharacteristic
379#380—21no—
380#380C2×D4711yescharacteristic
381C4×C4⋊C4—471no—
382C4×C22⋊C4—941no—
383C4×C22⋊C4C2×D4711yescharacteristic
384#340—471no—
385#340—471no—
386#340—471no—
387#340—471no—
388#340—471no—
389#340—471no—
390#336—471no—
391#336—471no—
392C47#2636311yescharacteristic, complemented, Sylow
393C22×D4—471no—
394C22×D4—941no—
395C23×C4—21no—
396C23×C4—941no—
397C23×C4C22×D4711yescharacteristic
398C2×M16—942no—
399C2×M16—942no—
400C2×M16—942no—
401C22×C8—471no—
402C22×C8—471no—
403C22×C8—471no—
404C22×C8—471no—
405#125—22no—
406#125—41no—
407#121—474no—
408#121—942no—
409C4×D4—942no—
410C4×D4—1881no—
411#117—942no—
412#117—1881no—
413C2×C4⋊C4—22no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—41no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—471no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—941no—
424C2×C4⋊C4C22×D4711yescharacteristic
425C2×C4⋊C4C22×D4711yescharacteristic
426C2×C4⋊C4C22×D4711yescharacteristic
427C2×C4⋊C4C22×D4711yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—941no—
430C2×C22⋊C4—941no—
431C2×C22⋊C4—941no—
432C2×C22⋊C4—941no—
433C2×C22⋊C4—941no—
434C2×C22⋊C4C22⋊D4711yescharacteristic
435C2×C22⋊C4C22⋊D4711yescharacteristic
436C2×C42—941no—
437C2×C42—941no—
438C2×C42C22×D4711yescharacteristic
439C2×C42C22×D4711yescharacteristic
440#107—474no—
441#107—942no—
442#107—1881no—
443#106—942no—
444#106—942no—
445#106—942no—
446C4⋊C8—942no—
447C4⋊C8—942no—
448#102—942no—
449#102—942no—
450#102—942no—
451#102—1881no—
452C22⋊C8—942no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—21no—
457#95—21no—
458#95—941no—
459#95—941no—
460#95C22⋊D4711yescharacteristic
461#95C22⋊D4711yescharacteristic
462C24—941no—
463C24C2×C22⋊D4711yescharacteristic
464C2×D4—472no—
465C2×D4—944no—
466C2×D4—941no—
467C2×D4—941no—
468C2×D4—941no—
469C2×D4—941no—
470C2×D4—941no—
471C2×D4—3761no—
472C2×D4—3761no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—42no—
482C22×C4—42no—
483C22×C4—81no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4—3761no—
488C22×C4—1882no—
489C22×C4—1882no—
490C22×C4Q8×D4712yes—
491C22×C4#1062535412yes—
492C22×C4C2×C22⋊D4711yescharacteristic
493C22×C4C2×C22⋊D4711yescharacteristic
494C22×C4C2×C22⋊D4711yescharacteristic
495C22×C4C2×C22⋊D4711yescharacteristic
496C22×C4C2×C22⋊D4711yescharacteristic
497C22×C4C23×D4711yescharacteristic
498M16—948no—
499C2×C8—472no—
500C2×C8—472no—
501C2×C8—941no—
502C2×C8—941no—
503C2×C8—941no—
504C2×C8—941no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8—941no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—81no—
522C4⋊C4—81no—
523C4⋊C4—472no—
524C4⋊C4—472no—
525C4⋊C4—941no—
526C4⋊C4—941no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4—3761no—
530C4⋊C4D4×D4712yes—
531C22⋊C4—41no—
532C22⋊C4—41no—
533C22⋊C4—42no—
534C22⋊C4—944no—
535C22⋊C4—3761no—
536C22⋊C4—1882no—
537C22⋊C4—1882no—
538C22⋊C4—1882no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—3761no—
544C42—1882no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—942no—
552C23—1881no—
553C23—1881no—
554C23—1881no—
555C23—1881no—
556C23—1881no—
557C23—1881no—
558C23#1309400012yes—
559C23C22×C22⋊D4711yescharacteristic
560D4—942no—
561D4—942no—
562D4—3764no—
563D4—1881no—
564D4—1881no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—22no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—84no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—3764no—
599C2×C4—1881no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4—1881no—
606C2×C4#1309400012yes—
607C2×C4C2×D4×D4711yescharacteristic
608C2×C4C2×Q8×D4711yescharacteristic
609C2×C4#41×D4711yescharacteristic
610C2×C4C2×#1062535411yescharacteristic
611C2×C4#1309406911yescharacteristic
612C2×C4#1309407111yescharacteristic
613C8—942no—
614C8—942no—
615C8—1881no—
616C8—1881no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—3761no—
625C22—3761no—
626C22—3761no—
627C22—3761no—
628C22—1882no—
629C22—1882no—
630C22—1882no—
631C22C2×#1309400011yescharacteristic
632C22D4×C22⋊D4711yescharacteristic
633C22#1568977211yescharacteristic
634C22#1568992111yescharacteristic
635C22#1568992111yescharacteristic
636C22#1568992611yescharacteristic
637C22#1568993111yescharacteristic
638C4—22no—
639C4—41no—
640C4—42no—
641C4—41no—
642C4—41no—
643C4—41no—
644C4—81no—
645C4—81no—
646C4—81no—
647C4—3761no—
648C4—1882no—
649C4—1882no—
650C4#1568963611yescharacteristic
651C4#1568972211yescharacteristic
652C4#1568978611yescharacteristic
653C4#1568982711yescharacteristic
654C2—42no—
655C2—3762no—
656C2#2024719311yescharacteristic
657C2#2025320611yescharacteristic
658C2#2025321311yescharacteristic
659C2#2025497411yescharacteristic
660C2#2025499511yescharacteristic
661C2#2025589711yescharacteristic
662C2#2025598811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2442C2
socleC23×C47C22×D4
prime radicalC2×#13093998C22
hypercenter#2442D47
hypocenterC47#26363
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2442

Complements

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

NH ≅ G/Ntype
1. C2×#15689420C2semidirect
2. C2×#15689163C2semidirect
4. #20244912C2semidirect
5. #20244890C2semidirect
6. #20244759C2semidirect
7. #20244723C2semidirect
8. #20244154C2semidirect
9. #20243956C2semidirect
12. #20243634C2semidirect
13. #20243585C2semidirect
14. #20243573C2semidirect
15. C47×#2442C2semidirect
90. #13093957D4semidirect
325. #2442D47semidirect
392. C47#26363semidirect

Maximal subgroups

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

subgroupindex
C2×#156894202
C2×#156891632
#202464242
#202449122
#202448902
#202447592
#202447232
#202441542
#202439562
#202438242
#202437052
#202436342
#202435852
#202435732
C47×#24422
#2636347