Finite Group Databasebeta

← #26275140

Subgroups — #26275140

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689533C211yesmaximal, characteristic, complemented
2C2×#15689166C211yesmaximal, characteristic
3#20247090C211yesmaximal, characteristic
4#20244865C211yesmaximal, characteristic, complemented
5#20244859C211yesmaximal, characteristic, complemented
6#20244723C211yesmaximal, characteristic, complemented
7#20244721C211yesmaximal, characteristic, complemented
8#20244123C211yesmaximal, characteristic, complemented
9#20244118C211yesmaximal, characteristic, complemented
10#20243587C211yesmaximal, characteristic
11#20243580C211yesmaximal, characteristic
12#20243544C211yesmaximal, characteristic, complemented
13#20243419C211yesmaximal, characteristic
14#20243172C211yesmaximal, characteristic
15C47×#2441C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13094024C2211yescharacteristic
18C2×#13094001—21no—
19C22×C4⋊Dic47C2211yescharacteristic
20#15689533—24no—
21#15689166—24no—
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093955C2211yescharacteristic
27C2×#13093955C2211yescharacteristic
28C2×#13093955C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31C2×#13093955C2211yescharacteristic
32C2×C22⋊(C47⋊C8)C2211yescharacteristic
33C2×#13093935C2211yescharacteristic
34C2×C4×C47⋊C8C2211yescharacteristic
35#15689055—21no—
36#15689044—21no—
37#15689021C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15688998—21no—
40#15688993C2211yescharacteristic
41#15688983C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688878C2211yescharacteristic
49#15688878C2211yescharacteristic
50C2×#125×C47C2211yescharacteristic
51C2×#117×C47C2211yescharacteristic
52C47×#399—21no—
53C47×#396—21no—
54C47×#389—21no—
55C47×#389C2211yescharacteristic
56C47×#389C2211yescharacteristic
57C47×#387—21no—
58C47×#384C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C4×C22⋊C4×C47C2211yescharacteristic
61C22×Dic94—21no—
62C23×Dic47—21no—
63C2×#10625329—22no—
64C2×#10625329—22no—
65C2×#10625329Q814yescomplemented
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C22×C47⋊C8C2311yescharacteristic
70#13094024—22no—
71#13094024—41no—
72#13094001—44no—
73C2×C4⋊Dic47—22no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—41no—
79C2×C4⋊Dic47C2311yescharacteristic
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×Dic47⋊C4—21no—
84C2×Dic47⋊C4—21no—
85C2×C22⋊Dic47—21no—
86#13093957—22no—
87#13093957—22no—
88#13093957—22no—
89#13093957D414yes—
90#13093955—22no—
91#13093955—22no—
92#13093955—22no—
93#13093955—22no—
94#13093955—41no—
95#13093955—41no—
96C22⋊(C47⋊C8)Q814yescomplemented
97#13093935—22no—
98C4×C47⋊C8—22no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C23×C4×C47C2311yescharacteristic
103#125×C47—22no—
104#125×C47—41no—
105#117×C47—22no—
106#117×C47—41no—
107C2×C4⋊C4×C47—21no—
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×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47D411yescharacteristic
120C2×C22⋊C4×C47D411yescharacteristic
121C2×C42×C47—21no—
122C2×C42×C47C2311yescharacteristic
123C2×C42×C47C2311yescharacteristic
124#95×C47—21no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47D411yescharacteristic
128#95×C47D411yescharacteristic
129C24×C47C2×D411yescharacteristic
130C22×C4×C47—21no—
131C22×C4×C47—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×C47C2×D411yescharacteristic
139C22×C4×C47C2×D411yescharacteristic
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×Q812yes—
144C22×C4×C47C2×Q812yes—
145C22×C4×C47C2411yescharacteristic
146C22×Dic47—21no—
147C22×Dic47—21no—
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—42no—
151C22×Dic47—42no—
152C22×Dic47—81no—
153C2×Dic94—42no—
154C2×Dic94—42no—
155C2×Dic94—81no—
156C4⋊C4×C47—21no—
157C4⋊C4×C47—21no—
158C4⋊C4×C47—21no—
159C4⋊C4×C47—21no—
160C4⋊C4×C47—21no—
161C4⋊C4×C47—21no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—42no—
164C4⋊C4×C47—42no—
165C4⋊C4×C47—42no—
166C4⋊C4×C47—42no—
167C4⋊C4×C47—81no—
168C4⋊C4×C47—81no—
169C4⋊C4×C47C2×D412yes—
170C22⋊C4×C47—22no—
171C22⋊C4×C47—22no—
172C22⋊C4×C47—42no—
173C22⋊C4×C47—81no—
174C42×C47—21no—
175C42×C47—21no—
176C42×C47—21no—
177C42×C47—21no—
178C42×C47—42no—
179C22⋊Dic47—42no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—42no—
188C4⋊Dic47—42no—
189C4⋊Dic47—42no—
190C4⋊Dic47—81no—
191C4⋊Dic47C2×D412yes—
192Dic47⋊C4—42no—
193Dic47⋊C4—42no—
194#10625329—28no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8C2×D412yes—
202C2×C47⋊C8C2×Q812yes—
203C2×C47⋊C8C2×Q812yes—
204C2×C47⋊C8C2×Q812yes—
205C2×C47⋊C8C2×Q812yes—
206C2×C47⋊C8#4112yes—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47C4⋊Q812yes—
214C23×C47C22×D411yescharacteristic
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
223C2×C4×C47—22no—
224C2×C4×C47—22no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—22no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47C4⋊Q812yes—
244C2×C4×C47AGL(1,ℤ/8)12yes—
245C2×C4×C47#13712yes—
246C2×C4×C47C22×D411yescharacteristic
247C2×C4×C47C22×Q811yescharacteristic
248C2×C4×C47C22×Q811yescharacteristic
249C2×C4×C47C2×#4111yescharacteristic
250C2×C4×C47H(5,𝔽2)11yescharacteristic
251C2×C4×C472−1+411yescharacteristic
252C2×Dic47—22no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C2×Dic47—84no—
265Dic94—84no—
266C47⋊C8—22no—
267C47⋊C8—22no—
268C47⋊C8—22no—
269C47⋊C8C22⋊Q814yescomplemented
270#26078—471nomaximal, Sylow
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47C2×C4⋊Q811yescharacteristic
279C22×C47D4211yescharacteristic
280C22×C47#54711yescharacteristic
281C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C47C2×#13711yescharacteristic
283C22×C47#57711yescharacteristic
284C22×C47#57711yescharacteristic
285C4×C47—22no—
286C4×C47—22no—
287C4×C47—22no—
288C4×C47—41no—
289C4×C47—42no—
290C4×C47—41no—
291C4×C47—81no—
292C4×C47—81no—
293C4×C47—81no—
294C4×C47C2×C22⋊Q811yescharacteristic
295C4×C47#54411yescharacteristic
296C4×C47D4×Q811yescharacteristic
297C4×C47#55411yescharacteristic
298Dic47—42no—
299Dic47—81no—
300Dic47—81no—
301Dic47—81no—
302C2×#501—471no—
303C2×#428—471no—
304#2441D4711yescharacteristic
305#2440—471no—
306#2084—471no—
307#2083—471no—
308#2059—471no—
309#2058—471no—
310#1943—471no—
311#1942—471no—
312#1854—471no—
313#1853—471no—
314#1844—471no—
315#1809—471no—
316#1753—471no—
317C2×C47—42no—
318C2×C47#244011yescharacteristic
319C2×C47#316311yescharacteristic
320C2×C47#316511yescharacteristic
321C2×C47#327211yescharacteristic
322C2×C47#327811yescharacteristic
323C2×C47#334411yescharacteristic
324C2×C47#334511yescharacteristic
325C22×M16—471no—
326C2×C4⋊Q8—471no—
327C2×#125C2×D4711yescharacteristic
328C2×C22⋊Q8—941no—
329C2×#117C2×D4711yescharacteristic
330C22×C4⋊C4—471no—
331#501—944no—
332#428—944no—
333C2×#107—471no—
334C2×#107—471no—
335C2×#107—471no—
336C2×#107—471no—
337C2×#106—471no—
338C2×#106—471no—
339C2×#106—471no—
340C2×#106—471no—
341C2×#106—471no—
342C2×#106—471no—
343C2×C22⋊C8—471no—
344C2×#97—471no—
345C2×C4×C8—471no—
346#399—21no—
347#398—941no—
348#396—21no—
349#395—941no—
350#389—21no—
351#389—471no—
352#389—471no—
353#389C2×D4711yescharacteristic
354#389C2×D4711yescharacteristic
355#387—21no—
356#385—941no—
357#384—471no—
358#384C2×D4711yescharacteristic
359#380—471no—
360#380C2×D4711yescharacteristic
361C4×C22⋊C4C2×D4711yescharacteristic
362#340—471no—
363#340—471no—
364#340—471no—
365#340—471no—
366#340—471no—
367#340—471no—
368#336—471no—
369#336—471no—
370C47#2607811yescharacteristic, complemented, Sylow
371C22×Q8—941no—
372C23×C4—941no—
373C23×C4C22×D4711yescharacteristic
374C2×M16—474no—
375C2×M16—942no—
376C2×M16—942no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C4⋊Q8—942no—
382C4⋊Q8—1881no—
383#125—22no—
384#125—41no—
385C22⋊Q8—1884no—
386#117—22no—
387#117—41no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—942no—
399C2×C4⋊C4—941no—
400C2×C4⋊C4—941no—
401C2×C4⋊C4—941no—
402C2×C4⋊C4—941no—
403C2×C4⋊C4—941no—
404C2×C4⋊C4—941no—
405C2×C4⋊C4—1881no—
406C2×C4⋊C4C22×D4711yescharacteristic
407C2×C4⋊C4C22×D4711yescharacteristic
408C2×C4⋊C4C22×D4711yescharacteristic
409C2×C4⋊C4C22×D4711yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—941no—
413C2×C22⋊C4C22⋊D4711yescharacteristic
414C2×C22⋊C4C22⋊D4711yescharacteristic
415C2×C42—21no—
416C2×C42C22×D4711yescharacteristic
417C2×C42C22×D4711yescharacteristic
418#107—474no—
419#107—942no—
420#107—942no—
421#107—942no—
422#106—942no—
423#106—942no—
424#106—942no—
425#106—942no—
426#106—1881no—
427#106—1881no—
428C22⋊C8—474no—
429#97—942no—
430C4×C8—942no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—941no—
435#95—941no—
436#95—941no—
437#95C22⋊D4711yescharacteristic
438#95C22⋊D4711yescharacteristic
439C24C2×C22⋊D4711yescharacteristic
440C2×Q8—3761no—
441C2×Q8—1882no—
442C2×Q8—1882no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—3761no—
456C22×C4—1882no—
457C22×C4—1882no—
458C22×C4Q8×D4712yes—
459C22×C4Q8×D4712yes—
460C22×C4C2×C22⋊D4711yescharacteristic
461C22×C4C2×C22⋊D4711yescharacteristic
462C22×C4C2×C22⋊D4711yescharacteristic
463C22×C4C2×C22⋊D4711yescharacteristic
464C22×C4C2×C22⋊D4711yescharacteristic
465C22×C4C23×D4711yescharacteristic
466M16—948no—
467C2×C8—472no—
468C2×C8—472no—
469C2×C8—472no—
470C2×C8—472no—
471C2×C8—472no—
472C2×C8—472no—
473C2×C8—941no—
474C2×C8—941no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4—42no—
490C4⋊C4—81no—
491C4⋊C4—81no—
492C4⋊C4—472no—
493C4⋊C4—941no—
494C4⋊C4—941no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4—3761no—
501C4⋊C4—1882no—
502C4⋊C4—1882no—
503C4⋊C4—1882no—
504C4⋊C4—1882no—
505C4⋊C4—1882no—
506C4⋊C4D4×D4712yes—
507C22⋊C4—22no—
508C22⋊C4—22no—
509C22⋊C4—42no—
510C22⋊C4—81no—
511C22⋊C4—1882no—
512C42—21no—
513C42—21no—
514C42—21no—
515C42—21no—
516C42—42no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—21no—
521C23—21no—
522C23—21no—
523C23#1309402212yes—
524C23C22×C22⋊D4711yescharacteristic
525Q8—3764no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—942no—
555C2×C4—3764no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4#1309402212yes—
568C2×C4#1309404912yes—
569C2×C4#1309405412yes—
570C2×C4C2×D4×D4711yescharacteristic
571C2×C4C2×Q8×D4711yescharacteristic
572C2×C4C2×Q8×D4711yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309407111yescharacteristic
576C8—474no—
577C8—942no—
578C8—942no—
579C8—942no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#1309402211yescharacteristic
588C22D4×C22⋊D4711yescharacteristic
589C22#1568977211yescharacteristic
590C22C2×#1309404911yescharacteristic
591C22C2×#1309405411yescharacteristic
592C22#1568993111yescharacteristic
593C22#1568993411yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4—81no—
603C4—3761no—
604C4—3761no—
605C4—3761no—
606C4—1882no—
607C4C22⋊Q8×D4711yescharacteristic
608C4#1568975211yescharacteristic
609C4#1568978611yescharacteristic
610C4#1568982711yescharacteristic
611C2—42no—
612C2#2024708711yescharacteristic
613C2#2025391411yescharacteristic
614C2#2025393511yescharacteristic
615C2#2025498811yescharacteristic
616C2#2025505411yescharacteristic
617C2#2025584311yescharacteristic
618C2#2025585211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2441C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2441D47
hypocenterC47#26078
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
1. C2×#15689533C2semidirect
4. #20244865C2semidirect
5. #20244859C2semidirect
6. #20244723C2semidirect
7. #20244721C2semidirect
8. #20244123C2semidirect
9. #20244118C2semidirect
12. #20243544C2semidirect
65. C2×#10625329Q8semidirect
96. C22⋊(C47⋊C8)Q8semidirect
269. C47⋊C8C22⋊Q8semidirect
370. C47#26078semidirect

Maximal subgroups

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

subgroupindex
C2×#156895332
C2×#156891662
#202470902
#202448652
#202448592
#202447232
#202447212
#202441232
#202441182
#202435872
#202435802
#202435442
#202434192
#202431722
C47×#24412
#2607847