Finite Group Databasebeta

← #26275155

Subgroups — #26275155

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689533C211yesmaximal, characteristic, complemented
2C2×#15689163C211yesmaximal, characteristic
3#20247079C211yesmaximal, characteristic
4#20244870C211yesmaximal, characteristic, complemented
5#20244869C211yesmaximal, characteristic, complemented
6#20244723C211yesmaximal, characteristic, complemented
7#20244716C211yesmaximal, characteristic, complemented
8#20244123C211yesmaximal, characteristic, complemented
9#20244118C211yesmaximal, characteristic, complemented
10#20243585C211yesmaximal, characteristic
11#20243576C211yesmaximal, characteristic
12#20243550C211yesmaximal, characteristic, complemented
13#20243419C211yesmaximal, characteristic
14#20243172C211yesmaximal, characteristic
15C47×#2442C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13094024C2211yescharacteristic
18C2×#13093983C2211yescharacteristic
19#15689533—24no—
20#15689163—24no—
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×#13093957C2211yescharacteristic
24C2×#13093957C2211yescharacteristic
25C2×#13093957C2211yescharacteristic
26C2×#13093957C2211yescharacteristic
27C2×#13093955C2211yescharacteristic
28C2×#13093955C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31C2×C22⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093935C2211yescharacteristic
33C2×C4×C47⋊C8C2211yescharacteristic
34#15689046—21no—
35#15689035—21no—
36#15689027—21no—
37#15689021C2211yescharacteristic
38#15689021C2211yescharacteristic
39#15689010—21no—
40#15688989C2211yescharacteristic
41#15688983C2211yescharacteristic
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×Dic94—21no—
62C2×#10625329—22no—
63C2×#10625329—22no—
64C2×#10625329Q814yescomplemented
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69#13094024—22no—
70#13094024—41no—
71#13093983—22no—
72#13093983—41no—
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×C22⋊Dic47—21no—
81C2×C22⋊Dic47—21no—
82C2×C4×Dic47—21no—
83#13093957—22no—
84#13093957—22no—
85#13093957—22no—
86#13093957—41no—
87#13093957—41no—
88#13093957D414yes—
89#13093955—22no—
90#13093955—22no—
91#13093955—22no—
92#13093955—22no—
93C22⋊(C47⋊C8)Q814yescomplemented
94#13093935—22no—
95C4×C47⋊C8—22no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C23×C4×C47—21no—
102C23×C4×C47C2311yescharacteristic
103#125×C47—22no—
104#125×C47—41no—
105C2×C4⋊C4×C47—22no—
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C4⋊C4×C47—21no—
109C2×C4⋊C4×C47—21no—
110C2×C4⋊C4×C47—21no—
111C2×C4⋊C4×C47—41no—
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C4⋊C4×C47C2311yescharacteristic
114C2×C4⋊C4×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121#95×C47—21no—
122#95×C47—21no—
123#95×C47—21no—
124#95×C47—21no—
125#95×C47—21no—
126#95×C47D411yescharacteristic
127#95×C47D411yescharacteristic
128C24×C47C2×D411yescharacteristic
129C22×C4×C47—21no—
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—42no—
138C22×C4×C47—42no—
139C22×C4×C47—81no—
140C22×C4×C47C2×D411yescharacteristic
141C22×C4×C47C2×D411yescharacteristic
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×Q812yes—
146C22×C4×C47C2×Q812yes—
147C22×C4×C47C2411yescharacteristic
148C22×Dic47—21no—
149C22×Dic47—21no—
150C22×Dic47—21no—
151C22×Dic47—21no—
152C2×Dic94—42no—
153C2×Dic94—42no—
154C2×Dic94—81no—
155C4⋊C4×C47—21no—
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—42no—
163C4⋊C4×C47—42no—
164C4⋊C4×C47—42no—
165C4⋊C4×C47—81no—
166C4⋊C4×C47—81no—
167C4⋊C4×C47C2×D412yes—
168C22⋊C4×C47—41no—
169C22⋊C4×C47—41no—
170C22⋊C4×C47—42no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C22⋊Dic47—42no—
176C22⋊Dic47—81no—
177C4⋊Dic47—21no—
178C4⋊Dic47—21no—
179C4⋊Dic47—21no—
180C4⋊Dic47—21no—
181C4⋊Dic47—21no—
182C4⋊Dic47—21no—
183C4⋊Dic47—21no—
184C4⋊Dic47—42no—
185C4⋊Dic47C2×D412yes—
186Dic47⋊C4—42no—
187Dic47⋊C4—81no—
188C4×Dic47—42no—
189#10625329—28no—
190C2×C47⋊C8—21no—
191C2×C47⋊C8—21no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C2×D412yes—
197C2×C47⋊C8C2×Q812yes—
198C2×C47⋊C8C2×Q812yes—
199C2×C47⋊C8C2×Q812yes—
200C2×C47⋊C8C2×Q812yes—
201C2×C47⋊C8#4112yes—
202C23×C47—21no—
203C23×C47—21no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—21no—
207C23×C47—21no—
208C23×C47C4⋊Q812yes—
209C23×C47C22×D411yescharacteristic
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—22no—
213C2×C4×C47—22no—
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—22no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—41no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
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—84no—
241C2×C4×C47C4⋊Q812yes—
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C22×Q811yescharacteristic
244C2×C4×C47C22×Q811yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C2×C4×C47H(5,𝔽2)11yescharacteristic
247C2×C4×C472−1+411yescharacteristic
248C2×Dic47—22no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260Dic94—84no—
261C47⋊C8—22no—
262C47⋊C8—22no—
263C47⋊C8—22no—
264C47⋊C8C22⋊Q814yes—
265#26079—471nomaximal, Sylow
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—22no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—41no—
273C22×C47C2×C4⋊Q811yescharacteristic
274C22×C47D4211yescharacteristic
275C22×C47#54711yescharacteristic
276C22×C47#57511yescharacteristic
277C22×C47#57511yescharacteristic
278C22×C47#57611yescharacteristic
279C22×C47#57811yescharacteristic
280C4×C47—22no—
281C4×C47—41no—
282C4×C47—41no—
283C4×C47—41no—
284C4×C47—42no—
285C4×C47—41no—
286C4×C47—81no—
287C4×C47—81no—
288C4×C47—81no—
289C4×C47C2×C22⋊Q811yescharacteristic
290C4×C47#54411yescharacteristic
291C4×C47D4×Q811yescharacteristic
292C4×C47#55411yescharacteristic
293Dic47—42no—
294Dic47—81no—
295Dic47—81no—
296Dic47—81no—
297C2×#501—471no—
298C2×#428—471no—
299#2442D4711yescharacteristic
300#2439—471no—
301#2085—471no—
302#2085—471no—
303#2059—471no—
304#2057—471no—
305#1943—471no—
306#1942—471no—
307#1854—471no—
308#1852—471no—
309#1846—471no—
310#1809—471no—
311#1753—471no—
312C2×C47—42no—
313C2×C47#244011yescharacteristic
314C2×C47#316411yescharacteristic
315C2×C47#316611yescharacteristic
316C2×C47#327311yescharacteristic
317C2×C47#327711yescharacteristic
318C2×C47#334711yescharacteristic
319C2×C47#334911yescharacteristic
320C22×M16—471no—
321C2×C4⋊Q8—471no—
322C2×#125C2×D4711yescharacteristic
323C2×#117—471no—
324C22×C4⋊C4C2×D4711yescharacteristic
325#501—944no—
326#428—944no—
327C2×#107—471no—
328C2×#107—471no—
329C2×#107—471no—
330C2×#107—471no—
331C2×#107—471no—
332C2×#107—471no—
333C2×#106—471no—
334C2×#106—471no—
335C2×#106—471no—
336C2×#106—471no—
337C2×C22⋊C8—471no—
338C2×#97—471no—
339C2×C4×C8—471no—
340#400—21no—
341#398—21no—
342#396—941no—
343#393—941no—
344#391—941no—
345#389—471no—
346#389—471no—
347#389C2×D4711yescharacteristic
348#389C2×D4711yescharacteristic
349#387—941no—
350#385—21no—
351#382—471no—
352#382C2×D4711yescharacteristic
353#380—21no—
354#380—471no—
355#380C2×D4711yescharacteristic
356C4×C22⋊C4C2×D4711yescharacteristic
357#340—471no—
358#340—471no—
359#340—471no—
360#340—471no—
361#340—471no—
362#340—471no—
363#336—471no—
364#336—471no—
365C47#2607911yescharacteristic, complemented, Sylow
366C22×Q8—941no—
367C23×C4—21no—
368C23×C4C22×D4711yescharacteristic
369C2×M16—474no—
370C2×M16—942no—
371C2×M16—942no—
372C22×C8—471no—
373C22×C8—471no—
374C22×C8—471no—
375C22×C8—471no—
376C4⋊Q8—942no—
377C4⋊Q8—1881no—
378#125—22no—
379#125—41no—
380#117—942no—
381#117—1881no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—41no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—941no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4C22×D4711yescharacteristic
397C2×C4⋊C4C22×D4711yescharacteristic
398C2×C4⋊C4C22×D4711yescharacteristic
399C2×C4⋊C4C22×D4711yescharacteristic
400C2×C22⋊C4—21no—
401C2×C22⋊C4—941no—
402C2×C22⋊C4—941no—
403C2×C22⋊C4C22⋊D4711yescharacteristic
404C2×C22⋊C4C22⋊D4711yescharacteristic
405C2×C42—941no—
406C2×C42C22×D4711yescharacteristic
407C2×C42C22×D4711yescharacteristic
408#107—474no—
409#107—942no—
410#107—942no—
411#107—942no—
412#107—1881no—
413#107—1881no—
414#106—942no—
415#106—942no—
416#106—942no—
417#106—942no—
418C22⋊C8—474no—
419#97—942no—
420C4×C8—942no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426#95—941no—
427#95—941no—
428#95—941no—
429#95—941no—
430#95—941no—
431#95C22⋊D4711yescharacteristic
432#95C22⋊D4711yescharacteristic
433C24C2×C22⋊D4711yescharacteristic
434C2×Q8—3761no—
435C2×Q8—1882no—
436C2×Q8—1882no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4Q8×D4712yes—
453C22×C4Q8×D4712yes—
454C22×C4C2×C22⋊D4711yescharacteristic
455C22×C4C2×C22⋊D4711yescharacteristic
456C22×C4C2×C22⋊D4711yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460M16—948no—
461C2×C8—472no—
462C2×C8—472no—
463C2×C8—472no—
464C2×C8—472no—
465C2×C8—472no—
466C2×C8—472no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—941no—
472C2×C8—941no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—81no—
484C4⋊C4—81no—
485C4⋊C4—472no—
486C4⋊C4—941no—
487C4⋊C4—941no—
488C4⋊C4—941no—
489C4⋊C4—941no—
490C4⋊C4—941no—
491C4⋊C4—941no—
492C4⋊C4—941no—
493C4⋊C4—3761no—
494C4⋊C4—1882no—
495C4⋊C4—1882no—
496C4⋊C4D4×D4712yes—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—42no—
500C22⋊C4—3761no—
501C22⋊C4—1882no—
502C42—21no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—1882no—
507C23—21no—
508C23—21no—
509C23—21no—
510C23—21no—
511C23—21no—
512C23—21no—
513C23#1309402212yes—
514C23C22×C22⋊D4711yescharacteristic
515Q8—3764no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—22no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—84no—
547C2×C4—942no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4#1309402212yes—
560C2×C4C2×D4×D4711yescharacteristic
561C2×C4C2×Q8×D4711yescharacteristic
562C2×C4C2×Q8×D4711yescharacteristic
563C2×C4#41×D4711yescharacteristic
564C2×C4#1309406911yescharacteristic
565C2×C4#1309407111yescharacteristic
566C8—474no—
567C8—942no—
568C8—942no—
569C8—942no—
570C22—22no—
571C22—22no—
572C22—22no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22C2×#1309402211yescharacteristic
578C22D4×C22⋊D4711yescharacteristic
579C22#1568977211yescharacteristic
580C22#1568992111yescharacteristic
581C22#1568992111yescharacteristic
582C22#1568992611yescharacteristic
583C22#1568993811yescharacteristic
584C4—22no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4—3761no—
594C4—3761no—
595C4—3761no—
596C4—1882no—
597C4C22⋊Q8×D4711yescharacteristic
598C4#1568975211yescharacteristic
599C4#1568978611yescharacteristic
600C4#1568982711yescharacteristic
601C2—42no—
602C2#2024708711yescharacteristic
603C2#2025392211yescharacteristic
604C2#2025393711yescharacteristic
605C2#2025499511yescharacteristic
606C2#2025504111yescharacteristic
607C2#2025588211yescharacteristic
608C2#2025591811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC47×#2442C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
hypercenter#2442D47
hypocenterC47#26079
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×#15689533C2semidirect
4. #20244870C2semidirect
5. #20244869C2semidirect
6. #20244723C2semidirect
7. #20244716C2semidirect
8. #20244123C2semidirect
9. #20244118C2semidirect
12. #20243550C2semidirect
64. C2×#10625329Q8semidirect
93. C22⋊(C47⋊C8)Q8semidirect
365. C47#26079semidirect

Maximal subgroups

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

subgroupindex
C2×#156895332
C2×#156891632
#202470792
#202448702
#202448692
#202447232
#202447162
#202441232
#202441182
#202435852
#202435762
#202435502
#202434192
#202431722
C47×#24422
#2607947