Finite Group Databasebeta

← #26279193

Subgroups — #26279193

Order 12032.

896 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689423C211yesmaximal, characteristic, complemented
2C2×#15689163C211yesmaximal, characteristic, complemented
3#20247101C211yesmaximal, characteristic, complemented
4#20244921C211yesmaximal, characteristic, complemented
5#20244890C211yesmaximal, characteristic, complemented
6#20244776C211yesmaximal, characteristic, complemented
7#20244726C211yesmaximal, characteristic, complemented
8#20244151C211yesmaximal, characteristic, complemented
9#20243959C211yesmaximal, characteristic, complemented
10#20243827C211yesmaximal, characteristic
11#20243711C211yesmaximal, characteristic
12#20243649C211yesmaximal, characteristic, complemented
13#20243581C211yesmaximal, characteristic, complemented
14#20243573C211yesmaximal, characteristic, complemented
15C47×#2361C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13094016C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19#15689423—24no—
20#15689163—24no—
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093955C2211yescharacteristic
24C2×#13093955C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×C4⋊(C47⋊C8)C2211yescharacteristic
28C2×C4⋊(C47⋊C8)C2211yescharacteristic
29C2×#13093945C2211yescharacteristic
30C2×#13093945C2211yescharacteristic
31C2×#13093945C2211yescharacteristic
32C2×#13093945C2211yescharacteristic
33C2×C22⋊(C47⋊C8)C2211yescharacteristic
34#15689059—21no—
35#15689046—21no—
36#15689021C2211yescharacteristic
37#15689021C2211yescharacteristic
38#15689020—21no—
39#15689006—21no—
40#15688993C2211yescharacteristic
41#15688983C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×#121×C47C2211yescharacteristic
51C2×C4×D4×C47—21no—
52C2×C4×D4×C47C2211yescharacteristic
53C22×C4⋊C4×C47C2211yescharacteristic
54C47×#390C2211yescharacteristic
55C47×#389C2211yescharacteristic
56C47×#388—21no—
57C47×#386—21no—
58C47×#385—21no—
59C4×C4⋊C4×C47C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C2×#10625329—22no—
62C2×#10625329—22no—
63C2×#10625329—22no—
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094016—22no—
69#13094016—41no—
70#13093983—22no—
71#13093983—41no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47C2311yescharacteristic
75C2×C4⋊Dic47C2311yescharacteristic
76C2×C4⋊Dic47C2311yescharacteristic
77C2×C4⋊Dic47C2311yescharacteristic
78C2×Dic47⋊C4—21no—
79C2×Dic47⋊C4—21no—
80C2×Dic47⋊C4—21no—
81C2×Dic47⋊C4—21no—
82C2×C22⋊Dic47—21no—
83C2×C22⋊Dic47—21no—
84C2×C4×Dic47—21no—
85#13093957—22no—
86#13093957D414yescomplemented
87#13093955—22no—
88#13093955—22no—
89#13093955—22no—
90#13093955—41no—
91C4⋊(C47⋊C8)—22no—
92C4⋊(C47⋊C8)—22no—
93#13093945—22no—
94#13093945—22no—
95#13093945—22no—
96#13093945—41no—
97C22⋊(C47⋊C8)—22no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C22×D4×C47—21no—
102C22×D4×C47C2311yescharacteristic
103C23×C4×C47—21no—
104C23×C4×C47—21no—
105C23×C4×C47C2311yescharacteristic
106#121×C47—22no—
107#121×C47Q814yes—
108C4×D4×C47—22no—
109C4×D4×C47—41no—
110C4×D4×C47—44no—
111C2×C4⋊C4×C47—22no—
112C2×C4⋊C4×C47—21no—
113C2×C4⋊C4×C47—21no—
114C2×C4⋊C4×C47—41no—
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C4⋊C4×C47C2311yescharacteristic
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47D411yescharacteristic
123C2×C22⋊C4×C47D411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126C2×C42×C47C2311yescharacteristic
127#95×C47—21no—
128#95×C47—21no—
129#95×C47D411yescharacteristic
130#95×C47D411yescharacteristic
131C24×C47—21no—
132C24×C47C2×D411yescharacteristic
133C2×D4×C47—24no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—21no—
137C2×D4×C47—21no—
138C2×D4×C47—21no—
139C2×D4×C47—42no—
140C2×D4×C47—42no—
141C2×D4×C47C2×Q812yes—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—42no—
150C22×C4×C47—42no—
151C22×C4×C47—42no—
152C22×C4×C47—42no—
153C22×C4×C47—81no—
154C22×C4×C47—81no—
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47C2×D411yescharacteristic
160C22×C4×C47C2×Q812yes—
161C22×C4×C47#4112yes—
162C22×C4×C47C2411yescharacteristic
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—21no—
166C22×Dic47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—42no—
172C4⋊C4×C47—42no—
173C4⋊C4×C47C2×D412yes—
174C4⋊C4×C47C2×Q812yes—
175C22⋊C4×C47—24no—
176C22⋊C4×C47—22no—
177C22⋊C4×C47—41no—
178C22⋊C4×C47—42no—
179C22⋊C4×C47—42no—
180C22⋊C4×C47—81no—
181C42×C47—21no—
182C42×C47—21no—
183C42×C47—21no—
184C42×C47—21no—
185C42×C47—42no—
186C22⋊Dic47—42no—
187C22⋊Dic47—81no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—42no—
196C4⋊Dic47—81no—
197C4⋊Dic47C2×D412yes—
198Dic47⋊C4—42no—
199Dic47⋊C4—42no—
200Dic47⋊C4—42no—
201Dic47⋊C4—81no—
202C4×Dic47—42no—
203#10625329—28no—
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⋊C8—21no—
212C2×C47⋊C8—21no—
213C2×C47⋊C8—21no—
214C2×C47⋊C8C2×D412yes—
215C2×C47⋊C8#4112yes—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—21no—
222C23×C47—22no—
223C23×C47—41no—
224C23×C47—41no—
225C23×C47—41no—
226C23×C47—41no—
227C23×C47—41no—
228C23×C47—41no—
229C23×C47C22⋊Q812yes—
230C23×C47C22×D411yescharacteristic
231D4×C47—22no—
232D4×C47—22no—
233D4×C47—48no—
234D4×C47—41no—
235D4×C47—41no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—22no—
241C2×C4×C47—22no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—21no—
246C2×C4×C47—21no—
247C2×C4×C47—22no—
248C2×C4×C47—21no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—41no—
256C2×C4×C47—41no—
257C2×C4×C47—41no—
258C2×C4×C47—41no—
259C2×C4×C47—41no—
260C2×C4×C47—41no—
261C2×C4×C47—41no—
262C2×C4×C47—84no—
263C2×C4×C47—84no—
264C2×C4×C47C22⋊Q812yes—
265C2×C4×C47AGL(1,ℤ/8)12yes—
266C2×C4×C47C22×D411yescharacteristic
267C2×C4×C47C22×Q811yescharacteristic
268C2×C4×C47C2×#4111yescharacteristic
269C2×C4×C47C2×#4111yescharacteristic
270C2×C4×C47H(5,𝔽2)11yescharacteristic
271C2×C4×C472−1+411yescharacteristic
272C2×Dic47—22no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—41no—
277C2×Dic47—41no—
278C2×Dic47—41no—
279C2×Dic47—41no—
280C2×Dic47—41no—
281C2×Dic47—41no—
282C2×Dic47—41no—
283C2×Dic47—41no—
284C47⋊C8—22no—
285C47⋊C8—22no—
286C47⋊C8—41no—
287C47⋊C8—41no—
288#26366—471nomaximal, Sylow
289C22×C47—22no—
290C22×C47—22no—
291C22×C47—22no—
292C22×C47—41no—
293C22×C47—41no—
294C22×C47—41no—
295C22×C47—41no—
296C22×C47—42no—
297C22×C47—42no—
298C22×C47—42no—
299C22×C47—81no—
300C22×C47—81no—
301C22×C47—81no—
302C22×C47—81no—
303C22×C47C2×C22⋊Q811yescharacteristic
304C22×C47D4211yescharacteristic
305C22×C47#54711yescharacteristic
306C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
307C22×C47#57511yescharacteristic
308C22×C47#57711yescharacteristic
309C22×C47#57711yescharacteristic
310C4×C47—22no—
311C4×C47—22no—
312C4×C47—42no—
313C4×C47—41no—
314C4×C47—41no—
315C4×C47—41no—
316C4×C47—42no—
317C4×C47—81no—
318C4×C47#52511yescharacteristic
319C4×C47#53911yescharacteristic
320C4×C47D4×Q811yescharacteristic
321C4×C47#55411yescharacteristic
322Dic47—42no—
323Dic47—81no—
324Dic47—81no—
325Dic47—81no—
326C2×#478—471no—
327C2×#428—471no—
328#2441—471no—
329#2361D4711yescharacteristic
330#2094—471no—
331#2088—471no—
332#2067—471no—
333#2059—471no—
334#1948—471no—
335#1918—471no—
336#1895—471no—
337#1875—471no—
338#1864—471no—
339#1853—471no—
340#1851—471no—
341C2×C47—42no—
342C2×C47—82no—
343C2×C47#244911yescharacteristic
344C2×C47#307711yescharacteristic
345C2×C47#308411yescharacteristic
346C2×C47#327111yescharacteristic
347C2×C47#327211yescharacteristic
348C2×C47#334511yescharacteristic
349C2×C47#335111yescharacteristic
350C22×M16—471no—
351C2×#125—471no—
352C2×#121C2×D4711yescharacteristic
353C2×C4×D4—21no—
354C2×C4×D4C2×D4711yescharacteristic
355C2×#117—471no—
356C22×C4⋊C4C2×D4711yescharacteristic
357#478—944no—
358#428—944no—
359C2×#107—471no—
360C2×#107—471no—
361C2×#106—471no—
362C2×#106—471no—
363C2×#106—471no—
364C2×#106—471no—
365C2×C4⋊C8—471no—
366C2×C4⋊C8—471no—
367C2×#102—471no—
368C2×#102—471no—
369C2×#102—471no—
370C2×#102—471no—
371C2×C22⋊C8—471no—
372#399—941no—
373#396—941no—
374#390C2×D4711yescharacteristic
375#389—471no—
376#389—471no—
377#389—941no—
378#389C2×D4711yescharacteristic
379#388—21no—
380#387—941no—
381#386—21no—
382#385—21no—
383#384—471no—
384#380—471no—
385C4×C4⋊C4C2×D4711yescharacteristic
386C4×C22⋊C4C2×D4711yescharacteristic
387#340—471no—
388#340—471no—
389#340—471no—
390#340—471no—
391#340—471no—
392#340—471no—
393#336—471no—
394#336—471no—
395C47#2636611yescharacteristic, complemented, Sylow
396C22×D4—21no—
397C22×D4C22×D4711yescharacteristic
398C23×C4—21no—
399C23×C4—21no—
400C23×C4C22×D4711yescharacteristic
401C2×M16—942no—
402C2×M16—942no—
403C2×M16—942no—
404C22×C8—471no—
405C22×C8—471no—
406C22×C8—471no—
407C22×C8—471no—
408#125—942no—
409#125—1881no—
410#121—22no—
411#121Dic9414yes—
412C4×D4—22no—
413C4×D4—41no—
414C4×D4—44no—
415#117—942no—
416#117—1881no—
417C2×C4⋊C4—22no—
418C2×C4⋊C4—21no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—41no—
421C2×C4⋊C4—471no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—471no—
424C2×C4⋊C4—471no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4—941no—
430C2×C4⋊C4—941no—
431C2×C4⋊C4C22×D4711yescharacteristic
432C2×C4⋊C4C22×D4711yescharacteristic
433C2×C4⋊C4C22×D4711yescharacteristic
434C2×C22⋊C4—21no—
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—941no—
439C2×C22⋊C4—941no—
440C2×C22⋊C4C22⋊D4711yescharacteristic
441C2×C22⋊C4C22⋊D4711yescharacteristic
442C2×C42—21no—
443C2×C42—941no—
444C2×C42C22×D4711yescharacteristic
445C2×C42C22×D4711yescharacteristic
446#107—474no—
447#107—942no—
448#106—942no—
449#106—942no—
450#106—942no—
451#106—1881no—
452C4⋊C8—942no—
453C4⋊C8—942no—
454#102—942no—
455#102—942no—
456#102—942no—
457#102—1881no—
458C22⋊C8—942no—
459#95—21no—
460#95—21no—
461#95—941no—
462#95—941no—
463#95—941no—
464#95C22⋊D4711yescharacteristic
465#95C22⋊D4711yescharacteristic
466C24—21no—
467C24C2×C22⋊D4711yescharacteristic
468C2×D4—24no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4C2×Dic9412yes—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4—42no—
488C22×C4—81no—
489C22×C4—81no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4C2×Dic9412yes—
495C22×C4#1062535012yes—
496C22×C4C2×C22⋊D4711yescharacteristic
497C22×C4C2×C22⋊D4711yescharacteristic
498C22×C4C2×C22⋊D4711yescharacteristic
499C22×C4C2×C22⋊D4711yescharacteristic
500C22×C4C2×C22⋊D4711yescharacteristic
501C22×C4C23×D4711yescharacteristic
502M16—948no—
503C2×C8—472no—
504C2×C8—472no—
505C2×C8—941no—
506C2×C8—941no—
507C2×C8—941no—
508C2×C8—941no—
509C2×C8—941no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8—941no—
513C2×C8—941no—
514C2×C8—941no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—42no—
520C4⋊C4—42no—
521C4⋊C4—472no—
522C4⋊C4—941no—
523C4⋊C4—941no—
524C4⋊C4—941no—
525C4⋊C4—941no—
526C4⋊C4—941no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4—3761no—
530C4⋊C4—3761no—
531C4⋊C4—1882no—
532C4⋊C4—1882no—
533C4⋊C4—1882no—
534C4⋊C4—1882no—
535C4⋊C4C2×Dic9412yes—
536C4⋊C4D4×D4712yes—
537C22⋊C4—24no—
538C22⋊C4—22no—
539C22⋊C4—41no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—3761no—
544C22⋊C4—1882no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—21no—
549C42—42no—
550C42—1882no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—22no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23#1309400312yes—
565C23C22×C22⋊D4711yescharacteristic
566D4—22no—
567D4—22no—
568D4—48no—
569D4—41no—
570D4—41no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4—84no—
599C2×C4—942no—
600C2×C4—1881no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4—1881no—
606C2×C4—1881no—
607C2×C4—1881no—
608C2×C4—1881no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4#1309400312yes—
612C2×C4#1309405012yes—
613C2×C4C2×D4×D4711yescharacteristic
614C2×C4C22×Dic9411yescharacteristic
615C2×C4#41×D4711yescharacteristic
616C2×C4C2×#1062535011yescharacteristic
617C2×C4#1309406911yescharacteristic
618C2×C4#1309407111yescharacteristic
619C8—942no—
620C8—942no—
621C8—1881no—
622C8—1881no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—81no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22C2×#1309400311yescharacteristic
638C22D4×C22⋊D4711yescharacteristic
639C22#1568977211yescharacteristic
640C22C2×#1309405011yescharacteristic
641C22#1568992111yescharacteristic
642C22#1568993111yescharacteristic
643C22#1568993411yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—41no—
651C4—81no—
652C4—3761no—
653C4—3761no—
654C4—3761no—
655C4—1882no—
656C4#1568963211yescharacteristic
657C4#1568971511yescharacteristic
658C4D4×Dic9411yescharacteristic
659C4#1568983211yescharacteristic
660C2—42no—
661C2—82no—
662C2#2024719111yescharacteristic
663C2#2025318511yescharacteristic
664C2#2025325011yescharacteristic
665C2#2025497411yescharacteristic
666C2#2025498411yescharacteristic
667C2#2025585811yescharacteristic
668C2#2025594211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2361C2
socleC23×C47C22×D4
prime radicalC2×#121×C47C22
hypercenter#2361D47
hypocenterC47#26366
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2361

Complements

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

NH ≅ G/Ntype
1. C2×#15689423C2semidirect
2. C2×#15689163C2semidirect
3. #20247101C2semidirect
4. #20244921C2semidirect
5. #20244890C2semidirect
6. #20244776C2semidirect
7. #20244726C2semidirect
8. #20244151C2semidirect
9. #20243959C2semidirect
12. #20243649C2semidirect
13. #20243581C2semidirect
14. #20243573C2semidirect
86. #13093957D4semidirect
395. C47#26366semidirect

Maximal subgroups

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

subgroupindex
C2×#156894232
C2×#156891632
#202471012
#202449212
#202448902
#202447762
#202447262
#202441512
#202439592
#202438272
#202437112
#202436492
#202435812
#202435732
C47×#23612
#2636647