Finite Group Databasebeta

← #26185327

Subgroups — #26185327

Order 12032.

666 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252507C211yesmaximal, characteristic
2#20252502C211yesmaximal, characteristic
3C4×#13094032C211yesmaximal, characteristic
4#20242155C211yesmaximal, characteristic, complemented
5#20242154C211yesmaximal, characteristic, complemented
6#20242152C211yesmaximal, characteristic, complemented
7#20242149C211yesmaximal, characteristic, complemented
8#20242148C211yesmaximal, characteristic, complemented
9#20242146C211yesmaximal, characteristic, complemented
10#20242145C211yesmaximal, characteristic, complemented
11#20242139C211yesmaximal, characteristic, complemented
12#20242137C211yesmaximal, characteristic, complemented
13#20242133C211yesmaximal, characteristic, complemented
14#335×D47C211yesmaximal, characteristic, complemented
15C47×#1569C211yesmaximal, characteristic, complemented
16C2×#13094032C411yescharacteristic
17C2×#13094032C411yescharacteristic
18C4×#10625350C2211yescharacteristic
19#15689252—21no—
20#15689251—21no—
21#15689199—21no—
22#15689198—21no—
23#15689197—21no—
24#15689196—21no—
25#15689193—21no—
26#15689192—21no—
27#15689180C2211yescharacteristic
28#15689179C2211yescharacteristic
29#15689179C2211yescharacteristic
30#15689175C2211yescharacteristic
31#15689175C2211yescharacteristic
32#15689147C2211yescharacteristic
33#15689145C2211yescharacteristic
34#15689145C2211yescharacteristic
35C4⋊C8×D47C2211yescharacteristic
36C4⋊C8×D47C2211yescharacteristic
37#15689081C411yescharacteristic
38#15689081C411yescharacteristic
39#15689080C411yescharacteristic
40#15689080C411yescharacteristic
41#15689080C411yescharacteristic
42#15689080C411yescharacteristic
43C4×#10625324C2211yescharacteristic
44C4×#10625324C2211yescharacteristic
45C2×C4×C47⋊C8C2211yescharacteristic
46C4×C8×D47C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688875C2211yescharacteristic
52#15688875C2211yescharacteristic
53#15688875C2211yescharacteristic
54#15688875C2211yescharacteristic
55#15688875C2211yescharacteristic
56#15688874C2211yescharacteristic
57#15688874C2211yescharacteristic
58#15688873C2211yescharacteristic
59#15688873C2211yescharacteristic
60C47×#432C2211yescharacteristic
61C47×#423C2211yescharacteristic
62C4×M16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C2×#10625350C2×C411yescharacteristic
68#13094032—24no—
69#13094032—24no—
70C2×#10625329—21no—
71C2×#10625324—21no—
72C2×#10625324—21no—
73C2×#10625324C2×C411yescharacteristic
74C2×#10625324C2×C411yescharacteristic
75C2×#10625324C2×C411yescharacteristic
76C2×#10625324C2×C411yescharacteristic
77C22×C47⋊C8C2×C411yescharacteristic
78C22×C47⋊C8C2×C411yescharacteristic
79C2×C8×D47—21no—
80C2×C8×D47—21no—
81C2×C8×D47C2×C411yescharacteristic
82C2×C8×D47C2×C411yescharacteristic
83C2×C8×D47C2×C411yescharacteristic
84C2×C8×D47C2×C411yescharacteristic
85C4×Dic94D411yescharacteristic
86C4×Dic94Q811yescharacteristic
87C4×D188D411yescharacteristic
88C4×D188Q811yescharacteristic
89C4×C22⋊D47D411yescharacteristic
90C4×C22⋊D47D411yescharacteristic
91C4×C22⋊D47Q811yescharacteristic
92C4×C22⋊D47Q811yescharacteristic
93#13093983C2×C411yescharacteristic
94#13093981C2×C411yescharacteristic
95#13093981C2×C411yescharacteristic
96C42×D47C2311yescharacteristic
97C42×D47C2311yescharacteristic
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101C4⋊(C47⋊C8)C2311yescharacteristic
102C4⋊(C47⋊C8)C2311yescharacteristic
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8—21no—
107C22⋊(C47⋊C8)—21no—
108(C2×D47)⋊C8—21no—
109(C2×D47)⋊C8—21no—
110(C2×D47)⋊C8—21no—
111(C2×D47)⋊C8—21no—
112#13093935—21no—
113#13093934—21no—
114#13093934—21no—
115#13093934C2×C411yescharacteristic
116#13093934C2×C411yescharacteristic
117#13093934C2×C411yescharacteristic
118#13093934C2×C411yescharacteristic
119C4×C47⋊C8C2×C411yescharacteristic
120C4×C47⋊C8C2×C411yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C8×Dic47—21no—
124C8×Dic47—21no—
125C8×Dic47C2×C411yescharacteristic
126C8×Dic47C2×C411yescharacteristic
127C8×Dic47C2×C411yescharacteristic
128C8×Dic47C2×C411yescharacteristic
129C2×M16×C47—21no—
130C2×M16×C47C2×C411yescharacteristic
131C2×M16×C47C2×C411yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C4⋊C8×C47—21no—
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C4⋊C8×C47C2311yescharacteristic
138C22⋊C8×C47—21no—
139#97×C47—21no—
140#97×C47C2×C411yescharacteristic
141#97×C47C2×C411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C22×C4×C47C22×C411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×Q811yescharacteristic
147C2×C22⋊D47C4⋊C411yescharacteristic
148C2×C22⋊D47C4⋊C411yescharacteristic
149#10625350—22no—
150#10625350—22no—
151C2×D188C4⋊C411yescharacteristic
152C2×C4×D47C22×C411yescharacteristic
153C2×C4×D47C22×C411yescharacteristic
154C2×C4×D47C2×D411yescharacteristic
155C2×C4×D47C2×D411yescharacteristic
156C2×C4×D47C2×Q811yescharacteristic
157C2×C4×D47C2×Q811yescharacteristic
158C2×Dic94C4⋊C411yescharacteristic
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—81no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47C22×C411yescharacteristic
167C2×C8×C47C22×C411yescharacteristic
168C2×C8×C47C22×C411yescharacteristic
169C2×C8×C47C22×C411yescharacteristic
170C42×C47C22×C411yescharacteristic
171C42×C47C2×D411yescharacteristic
172C42×C47C2×Q811yescharacteristic
173C42×C47C2411yescharacteristic
174C22⋊Dic47C4⋊C411yescharacteristic
175C22⋊Dic47C4⋊C411yescharacteristic
176(C2×D47)⋊C4C4⋊C411yescharacteristic
177(C2×D47)⋊C4C4⋊C411yescharacteristic
178(C2×D47)⋊C4C4⋊C411yescharacteristic
179(C2×D47)⋊C4C4⋊C411yescharacteristic
180C4⋊Dic47C4⋊C411yescharacteristic
181C4⋊Dic47C4⋊C411yescharacteristic
182Dic47⋊C4C4⋊C411yescharacteristic
183Dic47⋊C4C4⋊C411yescharacteristic
184Dic47⋊C4C4⋊C411yescharacteristic
185Dic47⋊C4C4⋊C411yescharacteristic
186C4×Dic47C22×C411yescharacteristic
187C4×Dic47C22×C411yescharacteristic
188C4×Dic47C2×D411yescharacteristic
189C4×Dic47C2×D411yescharacteristic
190C4×Dic47C2×Q811yescharacteristic
191C4×Dic47C2×Q811yescharacteristic
192#10625329—81no—
193C2×C47⋊C8—22no—
194C2×C47⋊C8—22no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8C22×C411yescharacteristic
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203#10625324—22no—
204#10625324—22no—
205#10625324—22no—
206#10625324—81no—
207#10625324—81no—
208#10625324M1614yescomplemented
209C8×D47—22no—
210C8×D47—22no—
211C8×D47—22no—
212C8×D47—81no—
213C8×D47—81no—
214C8×D47M1614yescomplemented
215C23×C47C2×C4⋊C411yescharacteristic
216C22×D47C2×C4⋊C411yescharacteristic
217C22×D47C2×C4⋊C411yescharacteristic
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—41no—
223C2×C4×C47C2×C4⋊C411yescharacteristic
224C2×C4×C47C2×C4⋊C411yescharacteristic
225C2×C4×C47C2×C4⋊C411yescharacteristic
226C2×C4×C47C23×C411yescharacteristic
227C2×C4×C47C22×D411yescharacteristic
228C2×C4×C47C22×Q811yescharacteristic
229C22⋊D47—22no—
230C22⋊D47—22no—
231C2×Dic47C2×C4⋊C411yescharacteristic
232C2×Dic47C2×C4⋊C411yescharacteristic
233C2×Dic47C2×C4⋊C411yescharacteristic
234C2×Dic47C2×C4⋊C411yescharacteristic
235C2×Dic47C2×C4⋊C411yescharacteristic
236C2×Dic47C2×C4⋊C411yescharacteristic
237D188—22no—
238C4×D47—21no—
239C4×D47—21no—
240C4×D47—21no—
241C4×D47—21no—
242C4×D47—21no—
243C4×D47—21no—
244C4×D47—41no—
245C4×D47—41no—
246C4×D47C2×M1612yes—
247C4×D47C2×M1612yes—
248Dic94—22no—
249C8×C47—21no—
250C8×C47—21no—
251C8×C47—41no—
252C8×C47—41no—
253C8×C47—41no—
254C8×C47—41no—
255C8×C47C2×M1612yes—
256C8×C47C2×M1612yes—
257C47⋊C8—21no—
258C47⋊C8—21no—
259C47⋊C8—41no—
260C47⋊C8—41no—
261C47⋊C8—41no—
262C47⋊C8—41no—
263C47⋊C8C2×M1612yes—
264C47⋊C8C2×M1612yes—
265#17799—471nomaximal, Sylow
266C22×C47—21no—
267C22×C47—21no—
268C22×C47—21no—
269C22×C47C22×C4⋊C411yescharacteristic
270C2×D47—21no—
271C2×D47—21no—
272C2×D47—21no—
273C2×D47—21no—
274C2×D47—21no—
275C2×D47#42312yes—
276C4×C47—21no—
277C4×C47—21no—
278C4×C47—21no—
279C4×C47—21no—
280C4×C47C22×M1611yescharacteristic
281C4×C47C22×M1611yescharacteristic
282C4×C47#57611yescharacteristic
283C4×C47#57811yescharacteristic
284Dic47—21no—
285Dic47—21no—
286Dic47—21no—
287Dic47—21no—
288Dic47—21no—
289Dic47#42312yes—
290#2989—471no—
291#2989—471no—
292C4×#131—471no—
293#1569—471no—
294#1569—471no—
295#1569—471no—
296#1569D4711yescharacteristic, complemented
297#1568—471no—
298#1568—471no—
299#1567—471no—
300#1567—471no—
301#1565—471no—
302#1565—471no—
303#1564—471no—
304C2×#335—471no—
305C2×C47—41no—
306C2×C47C2×#42311yescharacteristic
307C2×C47#291311yescharacteristic
308C2×C47#291611yescharacteristic
309D47—22no—
310D47—41no—
311C2×#131—471no—
312C2×#131—471no—
313C4×#41—471no—
314#446—941no—
315#446—941no—
316#436—941no—
317#436—941no—
318#435—941no—
319#435—941no—
320#435—941no—
321#435—941no—
322#432—471no—
323#432—471no—
324#432—471no—
325#432C2×D4711yescharacteristic
326#431—471no—
327#431—471no—
328#423—471no—
329#423—471no—
330#423—471no—
331#423C2×D4711yescharacteristic
332C2×C4⋊C8—471no—
333C2×C4⋊C8—471no—
334#405—471no—
335#405—471no—
336#405—471no—
337#405—471no—
338#405—471no—
339#405—471no—
340C4×M16—471no—
341C4×M16—471no—
342C4×M16C2×D4711yescharacteristic
343C2×C4×C8—471no—
344C2×C4×C8—471no—
345C2×C4×C8—471no—
346#335—471no—
347#335—471no—
348#335—471no—
349#335—471no—
350#335—471no—
351#335—471no—
352#335—471no—
353#335—471no—
354#335C2×D4711yescharacteristic
355#335C2×D4711yescharacteristic
356#334—471no—
357#334—471no—
358#334—471no—
359#334—471no—
360#334C2×D4711yescharacteristic
361#334C2×D4711yescharacteristic
362C47#1779911yescharacteristic, complemented, Sylow
363C2×#41—471no—
364#131—944no—
365#131—944no—
366C2×M16—21no—
367C2×M16—471no—
368C2×M16—471no—
369C2×M16—471no—
370C2×M16—471no—
371C2×M16—941no—
372C2×M16—941no—
373C2×M16—941no—
374C2×M16C4×D4711yescharacteristic
375C2×M16C4×D4711yescharacteristic
376C22×C8—471no—
377C22×C8—471no—
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382C22×C8—941no—
383C22×C8—941no—
384C4×Q8—471no—
385C4×Q8—471no—
386C4×D4—471no—
387C4×D4—471no—
388C4×D4—471no—
389C4×D4—471no—
390C4×D4—471no—
391C4×D4—471no—
392#117—471no—
393#117—471no—
394#117—471no—
395C2×C42—471no—
396C2×C42—471no—
397C2×C42C22×D4711yescharacteristic
398C4⋊C8—21no—
399C4⋊C8—471no—
400C4⋊C8—471no—
401C4⋊C8—471no—
402C4⋊C8—471no—
403C4⋊C8—941no—
404C4⋊C8—941no—
405C4⋊C8—941no—
406C4⋊C8—941no—
407C4⋊C8—941no—
408C4⋊C8C22×D4711yescharacteristic
409C4⋊C8C22×D4711yescharacteristic
410C4⋊C8C22×D4711yescharacteristic
411C4⋊C8C22×D4711yescharacteristic
412C22⋊C8—21no—
413C22⋊C8—941no—
414C22⋊C8—941no—
415C22⋊C8—941no—
416C22⋊C8—941no—
417C22⋊C8—941no—
418#97—21no—
419#97—471no—
420#97—471no—
421#97—471no—
422#97—471no—
423#97—941no—
424#97—941no—
425#97—941no—
426#97C4×D4711yescharacteristic
427#97C4×D4711yescharacteristic
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—471no—
431C4×C8—471no—
432C4×C8—471no—
433C4×C8—471no—
434C4×C8—471no—
435C4×C8—471no—
436C4×C8—941no—
437C4×C8—941no—
438C4×C8C22×D4711yescharacteristic
439C4×C8C22×D4711yescharacteristic
440#41—942no—
441#41—942no—
442C2×Q8—471no—
443C2×D4—471no—
444C2×D4—471no—
445C2×D4—471no—
446C22×C4—471no—
447C22×C4—471no—
448C22×C4—471no—
449C22×C4—471no—
450C22×C4—471no—
451C22×C4—471no—
452C22×C4C2×C4×D4711yescharacteristic
453C22×C4D4×D4711yescharacteristic
454C22×C4Q8×D4711yescharacteristic
455M16—22no—
456M16—22no—
457M16—81no—
458M16—474no—
459M16—942no—
460M16—942no—
461M16—942no—
462M16—3761no—
463M16—3761no—
464M16—3761no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—471no—
470C2×C8—471no—
471C2×C8—474no—
472C2×C8—471no—
473C2×C8—471no—
474C2×C8—942no—
475C2×C8—942no—
476C2×C8—942no—
477C2×C8—942no—
478C2×C8—942no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—3761no—
484C2×C8—3761no—
485C2×C8C2×C4×D4711yescharacteristic
486C2×C8C2×C4×D4711yescharacteristic
487C2×C8C2×C4×D4711yescharacteristic
488C2×C8C2×C4×D4711yescharacteristic
489C4⋊C4—471no—
490C4⋊C4—471no—
491C4⋊C4—471no—
492C4⋊C4—471no—
493C4⋊C4—471no—
494C4⋊C4—471no—
495C22⋊C4—471no—
496C22⋊C4—471no—
497C22⋊C4—471no—
498C22⋊C4—471no—
499C22⋊C4—471no—
500C22⋊C4—471no—
501C42—471no—
502C42—471no—
503C42—471no—
504C42—471no—
505C42—471no—
506C42—471no—
507C42C2×C4×D4711yescharacteristic
508C42D4×D4711yescharacteristic
509C42Q8×D4711yescharacteristic
510C42C23×D4711yescharacteristic
511C23—471no—
512C23—471no—
513C23C4⋊C4×D4711yescharacteristic
514Q8—942no—
515D4—942no—
516D4—942no—
517D4—942no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—471no—
524C2×C4—472no—
525C2×C4—472no—
526C2×C4—471no—
527C2×C4—471no—
528C2×C4—471no—
529C2×C4—471no—
530C2×C4—471no—
531C2×C4—941no—
532C2×C4—941no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—941no—
536C2×C4—941no—
537C2×C4—1881no—
538C2×C4—1881no—
539C2×C4C4⋊C4×D4711yescharacteristic
540C2×C4C4⋊C4×D4711yescharacteristic
541C2×C4C4⋊C4×D4711yescharacteristic
542C2×C4C22×C4×D4711yescharacteristic
543C2×C4C2×D4×D4711yescharacteristic
544C2×C4C2×Q8×D4711yescharacteristic
545C8—21no—
546C8—21no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8—41no—
551C8—472no—
552C8—472no—
553C8—941no—
554C8—941no—
555C8—1881no—
556C8—1881no—
557C8—1881no—
558C8—1881no—
559C8M16×D4712yes—
560C8M16×D4712yes—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—472no—
565C22—941no—
566C22—941no—
567C22—941no—
568C22—941no—
569C22—941no—
570C22C2×C4⋊C4×D4711yescharacteristic
571C4—21no—
572C4—21no—
573C4—21no—
574C4—21no—
575C4—472no—
576C4—941no—
577C4—941no—
578C4—941no—
579C4—941no—
580C4—941no—
581C4C2×M16×D4711yescharacteristic
582C4C2×M16×D4711yescharacteristic
583C4#1568992711yescharacteristic
584C4#1568993911yescharacteristic
585C2—41no—
586C2—942no—
587C2—1881no—
588C2#423×D4711yescharacteristic
589C2#2025198711yescharacteristic
590C2#2025199811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1569C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#10625350C2×C4
cosocleC42×C47C24
hypercenter#1569D47
hypocenterC47#17799
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1569

Complements

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

NH ≅ G/Ntype
4. #20242155C2semidirect
5. #20242154C2semidirect
6. #20242152C2semidirect
7. #20242149C2semidirect
8. #20242148C2semidirect
9. #20242146C2semidirect
10. #20242145C2semidirect
11. #20242139C2semidirect
12. #20242137C2semidirect
13. #20242133C2semidirect
14. #335×D47C2semidirect
15. C47×#1569C2semidirect
208. #10625324M16semidirect
214. C8×D47M16semidirect
296. #1569D47semidirect
362. C47#17799semidirect

Maximal subgroups

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

subgroupindex
#202525072
#202525022
C4×#130940322
#202421552
#202421542
#202421522
#202421492
#202421482
#202421462
#202421452
#202421392
#202421372
#202421332
#335×D472
C47×#15692
#1779947