Finite Group Databasebeta

← #26221225

Subgroups — #26221225

Order 12032.

714 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252025C211yesmaximal, characteristic
2C2×#15689183C211yesmaximal, characteristic
3#20251805C211yesmaximal, characteristic
4#20244164C211yesmaximal, characteristic, complemented
5#20244163C211yesmaximal, characteristic, complemented
6#20244161C211yesmaximal, characteristic, complemented
7#20243594C211yesmaximal, characteristic
8#20243594C211yesmaximal, characteristic
9#20243591C211yesmaximal, characteristic
10#20243591C211yesmaximal, characteristic
11#20243296C211yesmaximal, characteristic, complemented
12#20243293C211yesmaximal, characteristic, complemented
13#108×Dic47C211yesmaximal, characteristic, complemented
14#20243289C211yesmaximal, characteristic, complemented
15C47×#1950C211yesmaximal, characteristic, complemented
16C2×M16×D47C2211yescharacteristic
17C2×M16×D47C2211yescharacteristic
18C2×#13093981C2211yescharacteristic
19#15689183—21no—
20#15689183—21no—
21#15689183—21no—
22#15689183—21no—
23#15689183C412yes—
24#15689183C412yes—
25#15689183C412yes—
26#15689183C412yes—
27C2×#13093960C2211yescharacteristic
28C2×#13093960C2211yescharacteristic
29C2×#13093959C2211yescharacteristic
30C2×#13093959C2211yescharacteristic
31C2×#13093959C2211yescharacteristic
32C2×#13093959C2211yescharacteristic
33#15689147C2211yescharacteristic
34C2×C4⋊(C47⋊C8)C2211yescharacteristic
35#15689086C2211yescharacteristic
36#15689086C2211yescharacteristic
37C2×(C2×D47)⋊C8C2211yescharacteristic
38C2×(C2×D47)⋊C8C2211yescharacteristic
39#15689080—21no—
40#15689080—21no—
41#15689077—21no—
42#15689077—21no—
43C4×#10625329C2211yescharacteristic
44M16×Dic47C2211yescharacteristic
45M16×Dic47C2211yescharacteristic
46M16×Dic47C2211yescharacteristic
47M16×Dic47C2211yescharacteristic
48C2×#13093934C2211yescharacteristic
49C2×C8×Dic47C2211yescharacteristic
50#15688888C2211yescharacteristic
51#15688888C2211yescharacteristic
52#15688887C2211yescharacteristic
53#15688887C2211yescharacteristic
54#15688887C2211yescharacteristic
55#15688887C2211yescharacteristic
56C2×#108×C47C2211yescharacteristic
57C2×#108×C47C2211yescharacteristic
58C47×#423C2211yescharacteristic
59C2×C4⋊C8×C47C2211yescharacteristic
60C4×M16×C47C2211yescharacteristic
61C47×#341C2211yescharacteristic
62C47×#341C2211yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C2×#10625329C2311yescharacteristic
65C2×#10625329C2311yescharacteristic
66C2×#10625329C2311yescharacteristic
67C2×#10625329C2311yescharacteristic
68C2×#10625324—21no—
69C2×#10625324—21no—
70M16×D47—22no—
71M16×D47—22no—
72M16×D47—22no—
73M16×D47—22no—
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78#13093981C2×C411yescharacteristic
79#13093981C2×C411yescharacteristic
80#13093981C2×C411yescharacteristic
81#13093981C2×C411yescharacteristic
82#13093981D411yescharacteristic
83#13093981D411yescharacteristic
84#13093981D411yescharacteristic
85#13093981D411yescharacteristic
86C2×Dic47⋊C4Q811yescharacteristic
87C2×Dic47⋊C4Q811yescharacteristic
88C2×(C2×D47)⋊C4Q811yescharacteristic
89C2×(C2×D47)⋊C4Q811yescharacteristic
90C2×C4×Dic47C2311yescharacteristic
91#13093960—22no—
92#13093960—22no—
93#13093959—22no—
94#13093959—22no—
95#13093959—22no—
96#13093959—22no—
97C4⋊(C47⋊C8)—21no—
98C4⋊(C47⋊C8)—21no—
99C4⋊(C47⋊C8)C2×C412yes—
100C4⋊(C47⋊C8)C2×C412yes—
101(C2×D47)⋊C8—21no—
102(C2×D47)⋊C8—21no—
103(C2×D47)⋊C8—21no—
104(C2×D47)⋊C8—21no—
105(C2×D47)⋊C8C2×C412yes—
106(C2×D47)⋊C8C2×C412yes—
107(C2×D47)⋊C8C2×C412yes—
108(C2×D47)⋊C8C2×C412yes—
109#13093935—21no—
110#13093934—21no—
111#13093934—21no—
112#13093934—21no—
113#13093934—21no—
114#13093934C2×C412yes—
115#13093934C2×C412yes—
116C4×C47⋊C8—21no—
117C8×Dic47—21no—
118C8×Dic47—21no—
119C8×Dic47—21no—
120C8×Dic47—21no—
121C8×Dic47C2×C412yes—
122C8×Dic47C2×C412yes—
123C2×M16×C47C2311yescharacteristic
124C2×M16×C47C2311yescharacteristic
125C2×M16×C47C2311yescharacteristic
126C2×M16×C47C2311yescharacteristic
127C22×C8×C47C2311yescharacteristic
128C22×C8×C47C2311yescharacteristic
129C2×C42×C47C2311yescharacteristic
130#108×C47—22no—
131#108×C47—22no—
132C4⋊C8×C47—21no—
133C4⋊C8×C47—21no—
134C4⋊C8×C47C2×C412yes—
135C4⋊C8×C47C2×C412yes—
136#97×C47—21no—
137C4×C8×C47—21no—
138C23×D47C2×Q811yescharacteristic
139C22×C4×C47C2×Q811yescharacteristic
140C22×C4×C47C2×Q811yescharacteristic
141C22×C4×C47C2411yescharacteristic
142C22×Dic47C2×Q811yescharacteristic
143C22×Dic47C2×Q811yescharacteristic
144C22×Dic47C2×Q811yescharacteristic
145C2×C4×D47—21no—
146C2×C4×D47—21no—
147C2×C4×D47—21no—
148C2×C4×D47—21no—
149C2×C4×D47C22×C411yescharacteristic
150C2×C4×D47C22×C411yescharacteristic
151C2×C4×D47C2×D411yescharacteristic
152C2×C4×D47C2×D411yescharacteristic
153M16×C47—21no—
154M16×C47—21no—
155M16×C47—21no—
156M16×C47—21no—
157M16×C47—21no—
158M16×C47—21no—
159M16×C47#4112yes—
160M16×C47#4112yes—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47C22×C412yes—
170C2×C8×C47C22×C412yes—
171C42×C47C22×C411yescharacteristic
172C42×C47C22×C411yescharacteristic
173C42×C47C2×D411yescharacteristic
174C42×C47C2×D411yescharacteristic
175(C2×D47)⋊C4C4⋊C411yescharacteristic
176(C2×D47)⋊C4C4⋊C411yescharacteristic
177(C2×D47)⋊C4C4⋊C411yescharacteristic
178(C2×D47)⋊C4C4⋊C411yescharacteristic
179(C2×D47)⋊C4C4⋊C411yescharacteristic
180(C2×D47)⋊C4C4⋊C411yescharacteristic
181(C2×D47)⋊C4C4⋊C411yescharacteristic
182(C2×D47)⋊C4C4⋊C411yescharacteristic
183Dic47⋊C4C4⋊C411yescharacteristic
184Dic47⋊C4C4⋊C411yescharacteristic
185Dic47⋊C4C4⋊C411yescharacteristic
186Dic47⋊C4C4⋊C411yescharacteristic
187Dic47⋊C4C4⋊C411yescharacteristic
188Dic47⋊C4C4⋊C411yescharacteristic
189Dic47⋊C4C4⋊C411yescharacteristic
190Dic47⋊C4C4⋊C411yescharacteristic
191C4×Dic47C22×C411yescharacteristic
192C4×Dic47C22×C411yescharacteristic
193C4×Dic47C2×D411yescharacteristic
194C4×Dic47C2×D411yescharacteristic
195#10625329—21no—
196#10625329—21no—
197#10625329—21no—
198#10625329—21no—
199#10625329—21no—
200#10625329—21no—
201#10625329#4112yes—
202#10625329#4112yes—
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⋊C8C22×C412yes—
212C2×C47⋊C8C22×C412yes—
213#10625324—24no—
214#10625324—24no—
215C8×D47—24no—
216C8×D47—24no—
217C23×C47C22×Q811yescharacteristic
218C22×D47—21no—
219C22×D47—21no—
220C22×D47—41no—
221C22×D47—41no—
222C22×D47C2×C4⋊C411yescharacteristic
223C22×D47C2×C4⋊C411yescharacteristic
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47C2×C4⋊C411yescharacteristic
227C2×C4×C47C2×C4⋊C411yescharacteristic
228C2×C4×C47C2×C4⋊C411yescharacteristic
229C2×C4×C47C2×C4⋊C411yescharacteristic
230C2×C4×C47C23×C411yescharacteristic
231C2×C4×C47C22×D411yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C2×Dic47—21no—
237C2×Dic47—21no—
238C2×Dic47—41no—
239C2×Dic47—41no—
240C2×Dic47C2×C4⋊C411yescharacteristic
241C2×Dic47C2×C4⋊C411yescharacteristic
242C2×Dic47C2×C4⋊C411yescharacteristic
243C2×Dic47C2×C4⋊C411yescharacteristic
244C2×Dic47C2×C4⋊C411yescharacteristic
245C2×Dic47C2×C4⋊C411yescharacteristic
246C4×D47—21no—
247C4×D47—21no—
248C4×D47—21no—
249C4×D47—21no—
250C4×D47—21no—
251C4×D47—21no—
252C4×D47—21no—
253C4×D47—21no—
254C8×C47—22no—
255C8×C47—22no—
256C8×C47—22no—
257C8×C47—22no—
258C8×C47—41no—
259C8×C47—41no—
260C47⋊C8—22no—
261C47⋊C8—22no—
262C47⋊C8—22no—
263C47⋊C8—22no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266#21372—471nomaximal, Sylow
267C22×C47—21no—
268C22×C47—21no—
269C22×C47C22×C4⋊C411yescharacteristic
270C22×C47#53311yescharacteristic
271C22×C47#53311yescharacteristic
272C2×D47—21no—
273C2×D47—21no—
274C2×D47—21no—
275C2×D47—21no—
276C2×D47—21no—
277C2×D47—21no—
278C2×D47—81no—
279C2×D47—81no—
280C4×C47—21no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—21no—
284C4×C47C4×#4111yescharacteristic
285C4×C47C4×#4111yescharacteristic
286C4×C47#52511yescharacteristic
287C4×C47#52511yescharacteristic
288Dic47—21no—
289Dic47—21no—
290Dic47—21no—
291Dic47—21no—
292Dic47—21no—
293Dic47—21no—
294#2921—471no—
295C2×#433—471no—
296#2873—471no—
297#1950—471no—
298#1950—471no—
299#1950—471no—
300#1950D4711yescharacteristic, complemented
301#1855—471no—
302#1855—471no—
303#1855—471no—
304#1855—471no—
305#1778—471no—
306#1778—471no—
307C4×#108—471no—
308C4×#108—471no—
309C2×C47—21no—
310C2×C47—21no—
311C2×C47#229611yescharacteristic
312C2×C47#291611yescharacteristic
313C2×C47#291611yescharacteristic
314D47—41no—
315D47—41no—
316C22×M16—471no—
317C22×M16—471no—
318C2×#117—471no—
319#433—472no—
320#433—472no—
321#433—472no—
322#433—472no—
323#433—941no—
324#433—941no—
325#433—941no—
326#433—941no—
327C2×#108—471no—
328C2×#108—471no—
329C2×#108—471no—
330C2×#108—471no—
331C2×#108—471no—
332C2×#108—471no—
333C2×#108C2×D4711yescharacteristic
334C2×#108C2×D4711yescharacteristic
335#423—471no—
336#423C2×D4711yescharacteristic
337C2×C4⋊C8—471no—
338C2×C4⋊C8C2×D4711yescharacteristic
339#407—471no—
340#407—471no—
341C2×C22⋊C8—471no—
342C2×C22⋊C8—471no—
343#405—941no—
344#405—941no—
345#405—941no—
346#405—941no—
347C4×M16—471no—
348C4×M16—471no—
349C4×M16—471no—
350C4×M16—471no—
351C4×M16—471no—
352C4×M16C2×D4711yescharacteristic
353C2×#97—471no—
354C2×C4×C8—471no—
355#341—471no—
356#341—471no—
357#341—471no—
358#341—471no—
359#341—471no—
360#341—471no—
361#341C2×D4711yescharacteristic
362#341C2×D4711yescharacteristic
363C47#2137211yescharacteristic, complemented, Sylow
364C23×C4—471no—
365C2×M16—471no—
366C2×M16—471no—
367C2×M16—471no—
368C2×M16—471no—
369C2×M16—941no—
370C2×M16—941no—
371C2×M16—942no—
372C2×M16—942no—
373C2×M16—942no—
374C2×M16—942no—
375C2×M16C22×D4711yescharacteristic
376C2×M16C22×D4711yescharacteristic
377C2×M16C22×D4711yescharacteristic
378C2×M16C22×D4711yescharacteristic
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—941no—
382C22×C8—941no—
383C22×C8C22×D4711yescharacteristic
384C22×C8C22×D4711yescharacteristic
385#117—471no—
386#117—471no—
387#117—471no—
388#117—471no—
389#117—471no—
390#117—471no—
391#117—471no—
392#117—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C22⋊C4—471no—
396C2×C22⋊C4—471no—
397C2×C42—471no—
398C2×C42C22×D4711yescharacteristic
399#108—22no—
400#108—22no—
401#108—942no—
402#108—942no—
403#108—942no—
404#108—942no—
405#108—942no—
406#108—942no—
407C4⋊C8—21no—
408C4⋊C8—21no—
409C4⋊C8—472no—
410C4⋊C8—472no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8C4×D4712yes—
414C4⋊C8C4×D4712yes—
415C22⋊C8—472no—
416C22⋊C8—472no—
417C22⋊C8—472no—
418C22⋊C8—472no—
419C22⋊C8—941no—
420C22⋊C8—941no—
421C22⋊C8—941no—
422C22⋊C8—941no—
423#97—21no—
424#97—472no—
425#97—472no—
426#97—941no—
427#97—941no—
428#97—941no—
429#97—941no—
430#97—941no—
431C4×C8—21no—
432C4×C8—472no—
433C4×C8—472no—
434C4×C8—941no—
435C4×C8—941no—
436C4×C8—941no—
437C4×C8—941no—
438C4×C8—941no—
439C24—471no—
440C22×C4—471no—
441C22×C4—471no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—471no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4Q8×D4711yescharacteristic
452C22×C4Q8×D4711yescharacteristic
453C22×C4C23×D4711yescharacteristic
454M16—21no—
455M16—21no—
456M16—21no—
457M16—21no—
458M16—21no—
459M16—21no—
460M16—472no—
461M16—472no—
462M16—944no—
463M16—944no—
464M16—941no—
465M16—941no—
466M16—941no—
467M16—941no—
468M16—941no—
469M16—941no—
470M16#1062535212yes—
471M16#1062535412yes—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—472no—
481C2×C8—472no—
482C2×C8—944no—
483C2×C8—944no—
484C2×C8—941no—
485C2×C8—941no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8C2×C4×D4712yes—
493C2×C8C2×C4×D4712yes—
494C4⋊C4—471no—
495C4⋊C4—471no—
496C4⋊C4—471no—
497C4⋊C4—471no—
498C4⋊C4—471no—
499C4⋊C4—471no—
500C4⋊C4—471no—
501C4⋊C4—471no—
502C22⋊C4—471no—
503C22⋊C4—471no—
504C22⋊C4—471no—
505C22⋊C4—471no—
506C22⋊C4—471no—
507C22⋊C4—471no—
508C22⋊C4—471no—
509C22⋊C4—471no—
510C42—471no—
511C42—471no—
512C42—471no—
513C42—471no—
514C42C2×C4×D4711yescharacteristic
515C42C2×C4×D4711yescharacteristic
516C42D4×D4711yescharacteristic
517C42D4×D4711yescharacteristic
518C23—471no—
519C23—471no—
520C23—941no—
521C23—941no—
522C23—1881no—
523C23—1881no—
524C23C2×Q8×D4711yescharacteristic
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—471no—
528C2×C4—471no—
529C2×C4—471no—
530C2×C4—471no—
531C2×C4—471no—
532C2×C4—471no—
533C2×C4—941no—
534C2×C4—941no—
535C2×C4—941no—
536C2×C4—941no—
537C2×C4—941no—
538C2×C4—941no—
539C2×C4—941no—
540C2×C4—941no—
541C2×C4—941no—
542C2×C4—941no—
543C2×C4—1881no—
544C2×C4—1881no—
545C2×C4C4⋊C4×D4711yescharacteristic
546C2×C4C4⋊C4×D4711yescharacteristic
547C2×C4C4⋊C4×D4711yescharacteristic
548C2×C4C4⋊C4×D4711yescharacteristic
549C2×C4C22×C4×D4711yescharacteristic
550C2×C4C2×D4×D4711yescharacteristic
551C2×C4#41×D4711yescharacteristic
552C2×C4#41×D4711yescharacteristic
553C2×C4C2×#1062535211yescharacteristic
554C2×C4C2×#1062535411yescharacteristic
555C8—22no—
556C8—22no—
557C8—22no—
558C8—22no—
559C8—41no—
560C8—41no—
561C8—942no—
562C8—942no—
563C8—942no—
564C8—942no—
565C8—1881no—
566C8—1881no—
567C22—21no—
568C22—21no—
569C22—941no—
570C22—941no—
571C22—941no—
572C22—941no—
573C22—941no—
574C22—941no—
575C22—3761no—
576C22—3761no—
577C22C2×C4⋊C4×D4711yescharacteristic
578C22#1568967811yescharacteristic
579C22#1568967911yescharacteristic
580C4—21no—
581C4—21no—
582C4—21no—
583C4—21no—
584C4—941no—
585C4—941no—
586C4—941no—
587C4—941no—
588C4—941no—
589C4—941no—
590C4C4×#1062535211yescharacteristic
591C4C4×#1062535411yescharacteristic
592C4#1568963311yescharacteristic
593C4#1568963611yescharacteristic
594C2—21no—
595C2—21no—
596C2—1881no—
597C2—1881no—
598C2#2024586911yescharacteristic
599C2#2025199611yescharacteristic
600C2#2025199811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1950C2
socleC22×C47C22×C4⋊C4
prime radicalC23×D47C2×Q8
cosocleC22×C4×C47C24
hypercenter#1950D47
hypocenterC47#21372
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
4. #20244164C2semidirect
5. #20244163C2semidirect
6. #20244161C2semidirect
11. #20243296C2semidirect
12. #20243293C2semidirect
13. #108×Dic47C2semidirect
14. #20243289C2semidirect
15. C47×#1950C2semidirect
300. #1950D47semidirect
363. C47#21372semidirect

Maximal subgroups

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

subgroupindex
#202520252
C2×#156891832
#202518052
#202441642
#202441632
#202441612
#202435942
#202435912
#202432962
#202432932
#108×Dic472
#202432892
C47×#19502
#2137247