Finite Group Databasebeta

← #26186362

Subgroups — #26186362

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253448C211yesmaximal, characteristic
2#20252499C211yesmaximal, characteristic, complemented
3#20252466C211yesmaximal, characteristic, complemented
4#20242263C211yesmaximal, characteristic, complemented
5#20242249C211yesmaximal, characteristic, complemented
6#20242228C211yesmaximal, characteristic, complemented
7#20242214C211yesmaximal, characteristic, complemented
8#20242209C211yesmaximal, characteristic, complemented
9#20242203C211yesmaximal, characteristic, complemented
10#20242185C211yesmaximal, characteristic, complemented
11#20242180C211yesmaximal, characteristic, complemented
12#20242174C211yesmaximal, characteristic, complemented
13#20241788C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#1488C211yesmaximal, characteristic, complemented
16#15689673C2211yescharacteristic
17#15689447C411yescharacteristic
18#15689447C411yescharacteristic
19#15689418C411yescharacteristic
20#15689413C411yescharacteristic
21#15689323C411yescharacteristic
22#15689318C411yescharacteristic
23#15689268C411yescharacteristic
24#15689268C411yescharacteristic
25Q8×C47⋊C8C2211yescharacteristic
26Q8×C47⋊C8C2211yescharacteristic
27C4×#10625336C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689200C2211yescharacteristic
32#15689200C2211yescharacteristic
33#15689196—21no—
34#15689196—21no—
35D4×C47⋊C8—21no—
36D4×C47⋊C8—21no—
37D4×C47⋊C8C2211yescharacteristic
38D4×C47⋊C8C2211yescharacteristic
39#15689188C2211yescharacteristic
40#15689188C2211yescharacteristic
41#15689176—21no—
42#15689176C2211yescharacteristic
43#15689176C2211yescharacteristic
44C2×C4⋊(C47⋊C8)—21no—
45C2×C4⋊(C47⋊C8)C2211yescharacteristic
46#15689088—21no—
47#15689088—21no—
48#15688875C2211yescharacteristic
49#15688875C2211yescharacteristic
50#15688873C2211yescharacteristic
51#15688873C2211yescharacteristic
52#15688852C2211yescharacteristic
53#15688852C2211yescharacteristic
54#15688852C2211yescharacteristic
55#15688852C2211yescharacteristic
56#15688845C2211yescharacteristic
57#15688845C2211yescharacteristic
58#15688844C2211yescharacteristic
59C8×C47⋊C8C2211yescharacteristic
60C4×#41×C47C2211yescharacteristic
61C47×#432C2211yescharacteristic
62C47×#431C2211yescharacteristic
63C47×Q8⋊C8C2211yescharacteristic
64C47×Q8⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625350—21no—
68C2×#10625336C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625334C2×C411yescharacteristic
72C2×#10625324—21no—
73C2×#10625324—21no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C22×C47⋊C8—21no—
77C2×C8×D47—21no—
78C2×C8×D47—21no—
79#13094024C2×C411yescharacteristic
80#13094021C2×C411yescharacteristic
81#13094012—21no—
82#13093998—21no—
83#13093998C2×C411yescharacteristic
84#13093998C2×C411yescharacteristic
85C4×D188—21no—
86C4×D188C2311yescharacteristic
87C4×D188C2311yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093957C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91#13093955C2×C411yescharacteristic
92C4⋊(C47⋊C8)—21no—
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)—21no—
95C4⋊(C47⋊C8)C2×C411yescharacteristic
96C4⋊(C47⋊C8)C2×C411yescharacteristic
97C4⋊(C47⋊C8)D411yescharacteristic
98C4⋊(C47⋊C8)D411yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100C4⋊(C47⋊C8)C2311yescharacteristic
101#13093948C2×C411yescharacteristic
102#13093948C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107#13093944C2×C411yescharacteristic
108#13093944C2×C411yescharacteristic
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112C22⋊(C47⋊C8)C2×C411yescharacteristic
113C22⋊(C47⋊C8)D411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115(C2×D47)⋊C8—21no—
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118(C2×D47)⋊C8—21no—
119C4×C47⋊C8—21no—
120C4×C47⋊C8—21no—
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C2×#41×C47C2×C411yescharacteristic
126C4×Q8×C47C2×C411yescharacteristic
127C4×Q8×C47C2311yescharacteristic
128C4×D4×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47C2×C411yescharacteristic
131C4×D4×C47C2311yescharacteristic
132#117×C47—21no—
133#117×C47C2×C411yescharacteristic
134C2×C42×C47—21no—
135C2×C42×C47C2311yescharacteristic
136C4⋊C8×C47—21no—
137C4⋊C8×C47C2311yescharacteristic
138C4⋊C8×C47C2311yescharacteristic
139C22⋊C8×C47—21no—
140C22⋊C8×C47—21no—
141#97×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—22no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×D4×C47—21no—
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C2×C22⋊D47—21no—
156C2×C22⋊D47—21no—
157#10625350—81no—
158#10625350—81no—
159C2×D188—21no—
160C2×D188—21no—
161C2×D188C22×C411yescharacteristic
162C2×D188C22×C411yescharacteristic
163C2×C4×D47—21no—
164C2×C4×D47—21no—
165C2×Dic94—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47—21no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47—21no—
172C4⋊C4×C47C22×C411yescharacteristic
173C4⋊C4×C47C22×C411yescharacteristic
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C42×C47—21no—
178C42×C47—21no—
179C42×C47—21no—
180C42×C47C22×C411yescharacteristic
181C42×C47C2×D411yescharacteristic
182C42×C47#4111yescharacteristic
183C42×C47C2411yescharacteristic
184#10625336—22no—
185#10625336—22no—
186#10625334—22no—
187#10625334—22no—
188(C2×D47)⋊C4—21no—
189(C2×D47)⋊C4—21no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47C22×C411yescharacteristic
194C4⋊Dic47C22×C411yescharacteristic
195C2×C47⋊C8—21no—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—81no—
198C2×C47⋊C8—81no—
199C2×C47⋊C8—81no—
200C2×C47⋊C8C22×C411yescharacteristic
201C2×C47⋊C8C22×C411yescharacteristic
202C2×C47⋊C8C22×C411yescharacteristic
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C2×D411yescharacteristic
205C2×C47⋊C8C2×D411yescharacteristic
206C2×C47⋊C8C2×D411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208#10625324—81no—
209#10625324—81no—
210C8×D47—81no—
211C8×D47—81no—
212C23×C47—21no—
213C23×C47C4×D411yescharacteristic
214C22×D47—21no—
215C22×D47—21no—
216Q8×C47—21no—
217Q8×C47#13112yes—
218D4×C47—24no—
219D4×C47—21no—
220D4×C47#13112yes—
221C2×C4×C47—24no—
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—81no—
233C2×C4×C47C4×D411yescharacteristic
234C2×C4×C47C4×D411yescharacteristic
235C2×C4×C47C4×D411yescharacteristic
236C2×C4×C47C23×C411yescharacteristic
237C2×C4×C47C22×D411yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C22⋊D47—81no—
240C22⋊D47—81no—
241C2×Dic47—21no—
242C2×Dic47—21no—
243D188—21no—
244D188—21no—
245D188—21no—
246D188—21no—
247D188—81no—
248D188—81no—
249C4×D47—41no—
250C4×D47—41no—
251C4×D47—41no—
252C4×D47—41no—
253Dic94—81no—
254C8×C47—41no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C47⋊C8—21no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#17920—471nomaximal, Sylow
269C22×C47—21no—
270C22×C47—22no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47C2×C4×D411yescharacteristic
276C2×D47—41no—
277C2×D47—41no—
278C2×D47—41no—
279C2×D47—41no—
280C2×D47—41no—
281C2×D47—41no—
282C4×C47—21no—
283C4×C47—22no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47C2×#13111yescharacteristic
290C4×C47C2×#13111yescharacteristic
291C4×C47#57611yescharacteristic
292C4×C47#57711yescharacteristic
293Dic47—41no—
294Dic47—41no—
295#3106—471no—
296#2988—471no—
297#2981—471no—
298#1588—471no—
299#1586—471no—
300#1583—471no—
301#1581—471no—
302#1580—471no—
303SD16⋊C8—471no—
304C8×SD16—471no—
305C8×D8—471no—
306#1573—471no—
307#1488D4711yescharacteristic, complemented
308#1480—471no—
309#1454—471no—
310C2×C47—41no—
311C2×C47—42no—
312C2×C47#292911yescharacteristic
313C2×C47#294611yescharacteristic
314C2×C47#295711yescharacteristic
315D47—81no—
316D47—81no—
317#532—471no—
318C4×#41C2×D4711yescharacteristic
319#482—471no—
320#482—471no—
321#477—471no—
322#476—471no—
323#460—471no—
324#459—471no—
325#449—471no—
326#449—471no—
327C8×Q8—471no—
328C8×Q8—471no—
329C4×SD16—471no—
330C4×SD16—471no—
331C4×D8—471no—
332C4×D8—471no—
333#436—471no—
334#436—471no—
335#435—941no—
336#435—941no—
337C8×D4—471no—
338C8×D4—471no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—941no—
342C8×D4—941no—
343#432C2×D4711yescharacteristic
344#431—471no—
345#431—471no—
346#431—941no—
347#431C2×D4711yescharacteristic
348C2×C4⋊C8—471no—
349C2×C4⋊C8—941no—
350#408—941no—
351#408—941no—
352#335—471no—
353#335—471no—
354#334—471no—
355#334—471no—
356Q8⋊C8C2×D4711yescharacteristic
357Q8⋊C8C2×D4711yescharacteristic
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8C2×D4711yescharacteristic
363D4⋊C8C2×D4711yescharacteristic
364#322—471no—
365#322—471no—
366#322—471no—
367C82—471no—
368C47#1792011yescharacteristic, complemented, Sylow
369C2×#41—941no—
370C2×#41C4×D4711yescharacteristic
371C2×SD16—471no—
372C2×SD16—471no—
373C2×D8—471no—
374C2×D8—471no—
375C2×M16—941no—
376C2×M16—941no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C4⋊Q8—471no—
383#127—471no—
384#124—941no—
385#121—471no—
386#121—471no—
387#121—941no—
388C4×Q8C4×D4711yescharacteristic
389C4×Q8C22×D4711yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—471no—
393C4×D4—471no—
394C4×D4—941no—
395C4×D4C4×D4711yescharacteristic
396C4×D4C22×D4711yescharacteristic
397#117—21no—
398#117C4×D4711yescharacteristic
399C2×C42—21no—
400C2×C42C22×D4711yescharacteristic
401#107—471no—
402#107—471no—
403#106—471no—
404#106—471no—
405C4⋊C8—21no—
406C4⋊C8—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—471no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8—941no—
415C4⋊C8C22×D4711yescharacteristic
416C4⋊C8C22×D4711yescharacteristic
417#103—471no—
418#103—471no—
419#102—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C22⋊C8—471no—
428C22⋊C8—471no—
429C22⋊C8—471no—
430C22⋊C8—471no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437#97—21no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—941no—
443C4×C8—941no—
444C4×C8C22×D4711yescharacteristic
445C4×C8C22×D4711yescharacteristic
446#41—22no—
447#41—22no—
448#41—3761no—
449#41—3761no—
450C2×Q8—941no—
451C2×Q8C2×C4×D4711yescharacteristic
452C2×D4—21no—
453C2×D4—471no—
454C2×D4—471no—
455C2×D4—941no—
456C2×D4—941no—
457C2×D4—941no—
458C2×D4—941no—
459C2×D4C2×C4×D4711yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—941no—
464C22×C4—941no—
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4#1062535211yescharacteristic
468SD16—942no—
469SD16—942no—
470D8—942no—
471D8—942no—
472M16—3761no—
473M16—3761no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—471no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—471no—
482C2×C8—471no—
483C2×C8—471no—
484C2×C8—471no—
485C2×C8—471no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—3761no—
489C2×C8—3761no—
490C2×C8—3761no—
491C2×C8—3761no—
492C2×C8—3761no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—471no—
496C4⋊C4—471no—
497C4⋊C4—941no—
498C4⋊C4C2×C4×D4711yescharacteristic
499C4⋊C4C2×C4×D4711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—941no—
504C22⋊C4—941no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42C2×C4×D4711yescharacteristic
511C42D4×D4711yescharacteristic
512C42#1062535211yescharacteristic
513C42C23×D4711yescharacteristic
514C23—21no—
515C23—941no—
516C23—941no—
517C23(C22⋊D47)⋊C411yescharacteristic
518Q8—21no—
519Q8—3761no—
520Q8#1309403212yes—
521D4—24no—
522D4—21no—
523D4—941no—
524D4—941no—
525D4—941no—
526D4—941no—
527D4—3761no—
528D4—3761no—
529D4—3761no—
530D4—3761no—
531D4#1309403212yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—1881no—
547C2×C4—1881no—
548C2×C4—1881no—
549C2×C4—1881no—
550C2×C4(C22⋊D47)⋊C411yescharacteristic
551C2×C4(C22⋊D47)⋊C411yescharacteristic
552C2×C4(C22⋊D47)⋊C411yescharacteristic
553C2×C4C22×C4×D4711yescharacteristic
554C2×C4C2×D4×D4711yescharacteristic
555C2×C4C2×#1062535211yescharacteristic
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—941no—
561C8—941no—
562C8—941no—
563C8—941no—
564C8—941no—
565C8—941no—
566C8—941no—
567C8—941no—
568C8—1881no—
569C8—1881no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—1881no—
577C22—1881no—
578C22—1881no—
579C22—1881no—
580C22—1881no—
581C22—1881no—
582C22C2×(C22⋊D47)⋊C411yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—1881no—
591C4—1881no—
592C4C2×#1309403211yescharacteristic
593C4C2×#1309403211yescharacteristic
594C4#1568992511yescharacteristic
595C4#1568993011yescharacteristic
596C2—41no—
597C2—42no—
598C2—3761no—
599C2—3761no—
600C2#2025207811yescharacteristic
601C2#2025222311yescharacteristic
602C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1488C2
socleC22×C47C2×C4×D4
prime radical#20253448C2
cosocleC42×C47C24
hypercenter#1488D47
hypocenterC47#17920
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1488

Complements

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

NH ≅ G/Ntype
2. #20252499C2semidirect
3. #20252466C2semidirect
4. #20242263C2semidirect
5. #20242249C2semidirect
6. #20242228C2semidirect
7. #20242214C2semidirect
8. #20242209C2semidirect
9. #20242203C2semidirect
10. #20242185C2semidirect
11. #20242180C2semidirect
12. #20242174C2semidirect
13. #20241788C2semidirect
14. #20241688C2semidirect
15. C47×#1488C2semidirect
307. #1488D47semidirect
368. C47#17920semidirect

Maximal subgroups

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

subgroupindex
#202534482
#202524992
#202524662
#202422632
#202422492
#202422282
#202422142
#202422092
#202422032
#202421852
#202421802
#202421742
#202417882
#202416882
C47×#14882
#1792047